Properties

Label 570.2.i.e.121.1
Level $570$
Weight $2$
Character 570.121
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
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(121,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(6))
 
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("570.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.e.391.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -5.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -5.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +1.00000 q^{11} -1.00000 q^{12} +(-3.00000 + 5.19615i) q^{13} +(-2.50000 - 4.33013i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} -1.00000 q^{18} +(-0.500000 - 4.33013i) q^{19} +1.00000 q^{20} +(-2.50000 - 4.33013i) q^{21} +(0.500000 + 0.866025i) q^{22} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{27} +(2.50000 - 4.33013i) q^{28} +(-3.00000 + 5.19615i) q^{29} +1.00000 q^{30} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(2.00000 - 3.46410i) q^{34} +(2.50000 + 4.33013i) q^{35} +(-0.500000 - 0.866025i) q^{36} +7.00000 q^{37} +(3.50000 - 2.59808i) q^{38} -6.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(2.50000 + 4.33013i) q^{41} +(2.50000 - 4.33013i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(-0.500000 + 0.866025i) q^{44} +1.00000 q^{45} -7.00000 q^{46} +(4.00000 - 6.92820i) q^{47} +(0.500000 - 0.866025i) q^{48} +18.0000 q^{49} -1.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(-5.50000 + 9.52628i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +5.00000 q^{56} +(3.50000 - 2.59808i) q^{57} -6.00000 q^{58} +(4.00000 + 6.92820i) q^{59} +(0.500000 + 0.866025i) q^{60} +(2.00000 - 3.46410i) q^{61} +(2.50000 - 4.33013i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(-0.500000 + 0.866025i) q^{66} +(-6.00000 + 10.3923i) q^{67} +4.00000 q^{68} -7.00000 q^{69} +(-2.50000 + 4.33013i) q^{70} +(-1.00000 - 1.73205i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 + 1.73205i) q^{73} +(3.50000 + 6.06218i) q^{74} -1.00000 q^{75} +(4.00000 + 1.73205i) q^{76} -5.00000 q^{77} +(-3.00000 - 5.19615i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50000 + 4.33013i) q^{82} -10.0000 q^{83} +5.00000 q^{84} +(-2.00000 + 3.46410i) q^{85} +(3.00000 - 5.19615i) q^{86} -6.00000 q^{87} -1.00000 q^{88} +(-6.50000 + 11.2583i) q^{89} +(0.500000 + 0.866025i) q^{90} +(15.0000 - 25.9808i) q^{91} +(-3.50000 - 6.06218i) q^{92} +8.00000 q^{94} +(-3.50000 + 2.59808i) q^{95} +1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(9.00000 + 15.5885i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 10 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 10 q^{7} - 2 q^{8} - q^{9} + q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} - 5 q^{14} + q^{15} - q^{16} - 4 q^{17} - 2 q^{18} - q^{19} + 2 q^{20} - 5 q^{21} + q^{22} - 7 q^{23} - q^{24} - q^{25} - 12 q^{26} - 2 q^{27} + 5 q^{28} - 6 q^{29} + 2 q^{30} + q^{32} + q^{33} + 4 q^{34} + 5 q^{35} - q^{36} + 14 q^{37} + 7 q^{38} - 12 q^{39} + q^{40} + 5 q^{41} + 5 q^{42} - 6 q^{43} - q^{44} + 2 q^{45} - 14 q^{46} + 8 q^{47} + q^{48} + 36 q^{49} - 2 q^{50} + 4 q^{51} - 6 q^{52} - 11 q^{53} - q^{54} - q^{55} + 10 q^{56} + 7 q^{57} - 12 q^{58} + 8 q^{59} + q^{60} + 4 q^{61} + 5 q^{63} + 2 q^{64} + 12 q^{65} - q^{66} - 12 q^{67} + 8 q^{68} - 14 q^{69} - 5 q^{70} - 2 q^{71} + q^{72} + 2 q^{73} + 7 q^{74} - 2 q^{75} + 8 q^{76} - 10 q^{77} - 6 q^{78} - 10 q^{79} - q^{80} - q^{81} - 5 q^{82} - 20 q^{83} + 10 q^{84} - 4 q^{85} + 6 q^{86} - 12 q^{87} - 2 q^{88} - 13 q^{89} + q^{90} + 30 q^{91} - 7 q^{92} + 16 q^{94} - 7 q^{95} + 2 q^{96} - 2 q^{97} + 18 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) −1.00000 −0.288675
\(13\) −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i \(0.479500\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) −2.50000 4.33013i −0.668153 1.15728i
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) −1.00000 −0.235702
\(19\) −0.500000 4.33013i −0.114708 0.993399i
\(20\) 1.00000 0.223607
\(21\) −2.50000 4.33013i −0.545545 0.944911i
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i \(0.427054\pi\)
−0.956967 + 0.290196i \(0.906280\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −6.00000 −1.17670
\(27\) −1.00000 −0.192450
\(28\) 2.50000 4.33013i 0.472456 0.818317i
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 1.00000 0.182574
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) 2.00000 3.46410i 0.342997 0.594089i
\(35\) 2.50000 + 4.33013i 0.422577 + 0.731925i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 3.50000 2.59808i 0.567775 0.421464i
\(39\) −6.00000 −0.960769
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 2.50000 4.33013i 0.385758 0.668153i
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 1.00000 0.149071
\(46\) −7.00000 −1.03209
\(47\) 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i \(-0.635032\pi\)
0.995066 0.0992202i \(-0.0316348\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 18.0000 2.57143
\(50\) −1.00000 −0.141421
\(51\) 2.00000 3.46410i 0.280056 0.485071i
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) −5.50000 + 9.52628i −0.755483 + 1.30854i 0.189651 + 0.981852i \(0.439264\pi\)
−0.945134 + 0.326683i \(0.894069\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −0.500000 0.866025i −0.0674200 0.116775i
\(56\) 5.00000 0.668153
\(57\) 3.50000 2.59808i 0.463586 0.344124i
\(58\) −6.00000 −0.787839
\(59\) 4.00000 + 6.92820i 0.520756 + 0.901975i 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 0 0
\(63\) 2.50000 4.33013i 0.314970 0.545545i
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) 4.00000 0.485071
\(69\) −7.00000 −0.842701
\(70\) −2.50000 + 4.33013i −0.298807 + 0.517549i
\(71\) −1.00000 1.73205i −0.118678 0.205557i 0.800566 0.599245i \(-0.204532\pi\)
−0.919244 + 0.393688i \(0.871199\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) −1.00000 −0.115470
\(76\) 4.00000 + 1.73205i 0.458831 + 0.198680i
\(77\) −5.00000 −0.569803
\(78\) −3.00000 5.19615i −0.339683 0.588348i
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) −10.0000 −1.09764 −0.548821 0.835940i \(-0.684923\pi\)
−0.548821 + 0.835940i \(0.684923\pi\)
\(84\) 5.00000 0.545545
\(85\) −2.00000 + 3.46410i −0.216930 + 0.375735i
\(86\) 3.00000 5.19615i 0.323498 0.560316i
\(87\) −6.00000 −0.643268
\(88\) −1.00000 −0.106600
\(89\) −6.50000 + 11.2583i −0.688999 + 1.19338i 0.283164 + 0.959072i \(0.408616\pi\)
−0.972162 + 0.234309i \(0.924717\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) 15.0000 25.9808i 1.57243 2.72352i
\(92\) −3.50000 6.06218i −0.364900 0.632026i
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −3.50000 + 2.59808i −0.359092 + 0.266557i
\(96\) 1.00000 0.102062
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 9.00000 + 15.5885i 0.909137 + 1.57467i
\(99\) −0.500000 + 0.866025i −0.0502519 + 0.0870388i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 4.00000 0.396059
\(103\) 15.0000 1.47799 0.738997 0.673709i \(-0.235300\pi\)
0.738997 + 0.673709i \(0.235300\pi\)
\(104\) 3.00000 5.19615i 0.294174 0.509525i
\(105\) −2.50000 + 4.33013i −0.243975 + 0.422577i
\(106\) −11.0000 −1.06841
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) 3.50000 + 6.06218i 0.332205 + 0.575396i
\(112\) 2.50000 + 4.33013i 0.236228 + 0.409159i
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 4.00000 + 1.73205i 0.374634 + 0.162221i
\(115\) 7.00000 0.652753
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) −3.00000 5.19615i −0.277350 0.480384i
\(118\) −4.00000 + 6.92820i −0.368230 + 0.637793i
\(119\) 10.0000 + 17.3205i 0.916698 + 1.58777i
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) −10.0000 −0.909091
\(122\) 4.00000 0.362143
\(123\) −2.50000 + 4.33013i −0.225417 + 0.390434i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 5.00000 0.445435
\(127\) 2.50000 4.33013i 0.221839 0.384237i −0.733527 0.679660i \(-0.762127\pi\)
0.955366 + 0.295423i \(0.0954607\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 3.00000 5.19615i 0.264135 0.457496i
\(130\) 3.00000 + 5.19615i 0.263117 + 0.455733i
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 2.50000 + 21.6506i 0.216777 + 1.87735i
\(134\) −12.0000 −1.03664
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) −3.50000 6.06218i −0.297940 0.516047i
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) −5.00000 −0.422577
\(141\) 8.00000 0.673722
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 9.00000 + 15.5885i 0.742307 + 1.28571i
\(148\) −3.50000 + 6.06218i −0.287698 + 0.498308i
\(149\) 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i \(-0.114277\pi\)
−0.772399 + 0.635138i \(0.780943\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0.500000 + 4.33013i 0.0405554 + 0.351220i
\(153\) 4.00000 0.323381
\(154\) −2.50000 4.33013i −0.201456 0.348932i
\(155\) 0 0
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) −4.50000 7.79423i −0.359139 0.622047i 0.628678 0.777666i \(-0.283596\pi\)
−0.987817 + 0.155618i \(0.950263\pi\)
\(158\) 5.00000 8.66025i 0.397779 0.688973i
\(159\) −11.0000 −0.872357
\(160\) −1.00000 −0.0790569
\(161\) 17.5000 30.3109i 1.37919 2.38883i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0.500000 0.866025i 0.0389249 0.0674200i
\(166\) −5.00000 8.66025i −0.388075 0.672166i
\(167\) −10.5000 + 18.1865i −0.812514 + 1.40732i 0.0985846 + 0.995129i \(0.468568\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(168\) 2.50000 + 4.33013i 0.192879 + 0.334077i
\(169\) −11.5000 19.9186i −0.884615 1.53220i
\(170\) −4.00000 −0.306786
\(171\) 4.00000 + 1.73205i 0.305888 + 0.132453i
\(172\) 6.00000 0.457496
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) −3.00000 5.19615i −0.227429 0.393919i
\(175\) 2.50000 4.33013i 0.188982 0.327327i
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) −4.00000 + 6.92820i −0.300658 + 0.520756i
\(178\) −13.0000 −0.974391
\(179\) 7.00000 0.523205 0.261602 0.965176i \(-0.415749\pi\)
0.261602 + 0.965176i \(0.415749\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) −9.00000 + 15.5885i −0.668965 + 1.15868i 0.309229 + 0.950988i \(0.399929\pi\)
−0.978194 + 0.207693i \(0.933404\pi\)
\(182\) 30.0000 2.22375
\(183\) 4.00000 0.295689
\(184\) 3.50000 6.06218i 0.258023 0.446910i
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) 4.00000 + 6.92820i 0.291730 + 0.505291i
\(189\) 5.00000 0.363696
\(190\) −4.00000 1.73205i −0.290191 0.125656i
\(191\) −14.0000 −1.01300 −0.506502 0.862239i \(-0.669062\pi\)
−0.506502 + 0.862239i \(0.669062\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 3.00000 + 5.19615i 0.214834 + 0.372104i
\(196\) −9.00000 + 15.5885i −0.642857 + 1.11346i
\(197\) 1.00000 0.0712470 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −12.0000 −0.846415
\(202\) −2.00000 −0.140720
\(203\) 15.0000 25.9808i 1.05279 1.82349i
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 2.50000 4.33013i 0.174608 0.302429i
\(206\) 7.50000 + 12.9904i 0.522550 + 0.905083i
\(207\) −3.50000 6.06218i −0.243267 0.421350i
\(208\) 6.00000 0.416025
\(209\) −0.500000 4.33013i −0.0345857 0.299521i
\(210\) −5.00000 −0.345033
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) −5.50000 9.52628i −0.377742 0.654268i
\(213\) 1.00000 1.73205i 0.0685189 0.118678i
\(214\) −2.00000 3.46410i −0.136717 0.236801i
\(215\) −3.00000 + 5.19615i −0.204598 + 0.354375i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −8.00000 + 13.8564i −0.541828 + 0.938474i
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) 1.00000 0.0674200
\(221\) 24.0000 1.61441
\(222\) −3.50000 + 6.06218i −0.234905 + 0.406867i
\(223\) 10.5000 + 18.1865i 0.703132 + 1.21786i 0.967361 + 0.253401i \(0.0815490\pi\)
−0.264229 + 0.964460i \(0.585118\pi\)
\(224\) −2.50000 + 4.33013i −0.167038 + 0.289319i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) 2.00000 + 3.46410i 0.133038 + 0.230429i
\(227\) 2.00000 0.132745 0.0663723 0.997795i \(-0.478857\pi\)
0.0663723 + 0.997795i \(0.478857\pi\)
\(228\) 0.500000 + 4.33013i 0.0331133 + 0.286770i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 3.50000 + 6.06218i 0.230783 + 0.399728i
\(231\) −2.50000 4.33013i −0.164488 0.284901i
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 9.00000 + 15.5885i 0.589610 + 1.02123i 0.994283 + 0.106773i \(0.0340517\pi\)
−0.404674 + 0.914461i \(0.632615\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) −8.00000 −0.521862
\(236\) −8.00000 −0.520756
\(237\) 5.00000 8.66025i 0.324785 0.562544i
\(238\) −10.0000 + 17.3205i −0.648204 + 1.12272i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i \(-0.517406\pi\)
0.892058 0.451920i \(-0.149261\pi\)
\(242\) −5.00000 8.66025i −0.321412 0.556702i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 2.00000 + 3.46410i 0.128037 + 0.221766i
\(245\) −9.00000 15.5885i −0.574989 0.995910i
\(246\) −5.00000 −0.318788
\(247\) 24.0000 + 10.3923i 1.52708 + 0.661247i
\(248\) 0 0
\(249\) −5.00000 8.66025i −0.316862 0.548821i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 2.50000 + 4.33013i 0.157485 + 0.272772i
\(253\) −3.50000 + 6.06218i −0.220043 + 0.381126i
\(254\) 5.00000 0.313728
\(255\) −4.00000 −0.250490
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 6.00000 0.373544
\(259\) −35.0000 −2.17479
\(260\) −3.00000 + 5.19615i −0.186052 + 0.322252i
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) −1.50000 + 2.59808i −0.0926703 + 0.160510i
\(263\) −10.5000 18.1865i −0.647458 1.12143i −0.983728 0.179664i \(-0.942499\pi\)
0.336270 0.941766i \(-0.390834\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 11.0000 0.675725
\(266\) −17.5000 + 12.9904i −1.07299 + 0.796491i
\(267\) −13.0000 −0.795587
\(268\) −6.00000 10.3923i −0.366508 0.634811i
\(269\) −16.0000 27.7128i −0.975537 1.68968i −0.678151 0.734923i \(-0.737218\pi\)
−0.297386 0.954757i \(-0.596115\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) −2.00000 + 3.46410i −0.121268 + 0.210042i
\(273\) 30.0000 1.81568
\(274\) 12.0000 0.724947
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 3.50000 6.06218i 0.210675 0.364900i
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 16.0000 0.959616
\(279\) 0 0
\(280\) −2.50000 4.33013i −0.149404 0.258775i
\(281\) 5.50000 9.52628i 0.328102 0.568290i −0.654033 0.756466i \(-0.726924\pi\)
0.982135 + 0.188176i \(0.0602575\pi\)
\(282\) 4.00000 + 6.92820i 0.238197 + 0.412568i
\(283\) −11.0000 19.0526i −0.653882 1.13256i −0.982173 0.187980i \(-0.939806\pi\)
0.328291 0.944577i \(-0.393527\pi\)
\(284\) 2.00000 0.118678
\(285\) −4.00000 1.73205i −0.236940 0.102598i
\(286\) −6.00000 −0.354787
\(287\) −12.5000 21.6506i −0.737852 1.27800i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 3.00000 + 5.19615i 0.176166 + 0.305129i
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) −2.00000 −0.117041
\(293\) 5.00000 0.292103 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(294\) −9.00000 + 15.5885i −0.524891 + 0.909137i
\(295\) 4.00000 6.92820i 0.232889 0.403376i
\(296\) −7.00000 −0.406867
\(297\) −1.00000 −0.0580259
\(298\) −2.00000 + 3.46410i −0.115857 + 0.200670i
\(299\) −21.0000 36.3731i −1.21446 2.10351i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) 15.0000 + 25.9808i 0.864586 + 1.49751i
\(302\) −10.0000 17.3205i −0.575435 0.996683i
\(303\) −2.00000 −0.114897
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) −4.00000 −0.229039
\(306\) 2.00000 + 3.46410i 0.114332 + 0.198030i
\(307\) −9.00000 15.5885i −0.513657 0.889680i −0.999875 0.0158424i \(-0.994957\pi\)
0.486217 0.873838i \(-0.338376\pi\)
\(308\) 2.50000 4.33013i 0.142451 0.246732i
\(309\) 7.50000 + 12.9904i 0.426660 + 0.738997i
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 6.00000 0.339683
\(313\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(314\) 4.50000 7.79423i 0.253950 0.439854i
\(315\) −5.00000 −0.281718
\(316\) 10.0000 0.562544
\(317\) −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i \(-0.860182\pi\)
0.820822 + 0.571184i \(0.193516\pi\)
\(318\) −5.50000 9.52628i −0.308425 0.534207i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −2.00000 3.46410i −0.111629 0.193347i
\(322\) 35.0000 1.95047
\(323\) −14.0000 + 10.3923i −0.778981 + 0.578243i
\(324\) 1.00000 0.0555556
\(325\) −3.00000 5.19615i −0.166410 0.288231i
\(326\) −5.00000 8.66025i −0.276924 0.479647i
\(327\) −8.00000 + 13.8564i −0.442401 + 0.766261i
\(328\) −2.50000 4.33013i −0.138039 0.239091i
\(329\) −20.0000 + 34.6410i −1.10264 + 1.90982i
\(330\) 1.00000 0.0550482
\(331\) 15.0000 0.824475 0.412237 0.911077i \(-0.364747\pi\)
0.412237 + 0.911077i \(0.364747\pi\)
\(332\) 5.00000 8.66025i 0.274411 0.475293i
\(333\) −3.50000 + 6.06218i −0.191799 + 0.332205i
\(334\) −21.0000 −1.14907
\(335\) 12.0000 0.655630
\(336\) −2.50000 + 4.33013i −0.136386 + 0.236228i
\(337\) −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 2.00000 + 3.46410i 0.108625 + 0.188144i
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) 0 0
\(342\) 0.500000 + 4.33013i 0.0270369 + 0.234146i
\(343\) −55.0000 −2.96972
\(344\) 3.00000 + 5.19615i 0.161749 + 0.280158i
\(345\) 3.50000 + 6.06218i 0.188434 + 0.326377i
\(346\) −4.50000 + 7.79423i −0.241921 + 0.419020i
\(347\) 1.00000 + 1.73205i 0.0536828 + 0.0929814i 0.891618 0.452788i \(-0.149571\pi\)
−0.837935 + 0.545770i \(0.816237\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 5.00000 0.267261
\(351\) 3.00000 5.19615i 0.160128 0.277350i
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 36.0000 1.91609 0.958043 0.286623i \(-0.0925328\pi\)
0.958043 + 0.286623i \(0.0925328\pi\)
\(354\) −8.00000 −0.425195
\(355\) −1.00000 + 1.73205i −0.0530745 + 0.0919277i
\(356\) −6.50000 11.2583i −0.344499 0.596690i
\(357\) −10.0000 + 17.3205i −0.529256 + 0.916698i
\(358\) 3.50000 + 6.06218i 0.184981 + 0.320396i
\(359\) 9.00000 + 15.5885i 0.475002 + 0.822727i 0.999590 0.0286287i \(-0.00911406\pi\)
−0.524588 + 0.851356i \(0.675781\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) −18.0000 −0.946059
\(363\) −5.00000 8.66025i −0.262432 0.454545i
\(364\) 15.0000 + 25.9808i 0.786214 + 1.36176i
\(365\) 1.00000 1.73205i 0.0523424 0.0906597i
\(366\) 2.00000 + 3.46410i 0.104542 + 0.181071i
\(367\) 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) 7.00000 0.364900
\(369\) −5.00000 −0.260290
\(370\) 3.50000 6.06218i 0.181956 0.315158i
\(371\) 27.5000 47.6314i 1.42773 2.47290i
\(372\) 0 0
\(373\) 5.00000 0.258890 0.129445 0.991587i \(-0.458680\pi\)
0.129445 + 0.991587i \(0.458680\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −4.00000 + 6.92820i −0.206284 + 0.357295i
\(377\) −18.0000 31.1769i −0.927047 1.60569i
\(378\) 2.50000 + 4.33013i 0.128586 + 0.222718i
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) −0.500000 4.33013i −0.0256495 0.222131i
\(381\) 5.00000 0.256158
\(382\) −7.00000 12.1244i −0.358151 0.620336i
\(383\) −16.0000 27.7128i −0.817562 1.41606i −0.907474 0.420109i \(-0.861992\pi\)
0.0899119 0.995950i \(-0.471341\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 2.50000 + 4.33013i 0.127412 + 0.220684i
\(386\) −2.00000 + 3.46410i −0.101797 + 0.176318i
\(387\) 6.00000 0.304997
\(388\) 2.00000 0.101535
\(389\) 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i \(-0.751748\pi\)
0.964490 + 0.264120i \(0.0850816\pi\)
\(390\) −3.00000 + 5.19615i −0.151911 + 0.263117i
\(391\) 28.0000 1.41602
\(392\) −18.0000 −0.909137
\(393\) −1.50000 + 2.59808i −0.0756650 + 0.131056i
\(394\) 0.500000 + 0.866025i 0.0251896 + 0.0436297i
\(395\) −5.00000 + 8.66025i −0.251577 + 0.435745i
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) 16.5000 + 28.5788i 0.828111 + 1.43433i 0.899518 + 0.436884i \(0.143918\pi\)
−0.0714068 + 0.997447i \(0.522749\pi\)
\(398\) 4.00000 0.200502
\(399\) −17.5000 + 12.9904i −0.876096 + 0.650332i
\(400\) 1.00000 0.0500000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) −6.00000 10.3923i −0.299253 0.518321i
\(403\) 0 0
\(404\) −1.00000 1.73205i −0.0497519 0.0861727i
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) 30.0000 1.48888
\(407\) 7.00000 0.346977
\(408\) −2.00000 + 3.46410i −0.0990148 + 0.171499i
\(409\) 1.50000 2.59808i 0.0741702 0.128467i −0.826555 0.562856i \(-0.809703\pi\)
0.900725 + 0.434389i \(0.143036\pi\)
\(410\) 5.00000 0.246932
\(411\) 12.0000 0.591916
\(412\) −7.50000 + 12.9904i −0.369498 + 0.639990i
\(413\) −20.0000 34.6410i −0.984136 1.70457i
\(414\) 3.50000 6.06218i 0.172016 0.297940i
\(415\) 5.00000 + 8.66025i 0.245440 + 0.425115i
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) 16.0000 0.783523
\(418\) 3.50000 2.59808i 0.171191 0.127076i
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) −2.50000 4.33013i −0.121988 0.211289i
\(421\) 4.00000 + 6.92820i 0.194948 + 0.337660i 0.946883 0.321577i \(-0.104213\pi\)
−0.751935 + 0.659237i \(0.770879\pi\)
\(422\) 6.50000 11.2583i 0.316415 0.548047i
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 5.50000 9.52628i 0.267104 0.462637i
\(425\) 4.00000 0.194029
\(426\) 2.00000 0.0969003
\(427\) −10.0000 + 17.3205i −0.483934 + 0.838198i
\(428\) 2.00000 3.46410i 0.0966736 0.167444i
\(429\) −6.00000 −0.289683
\(430\) −6.00000 −0.289346
\(431\) 2.00000 3.46410i 0.0963366 0.166860i −0.813829 0.581104i \(-0.802621\pi\)
0.910166 + 0.414244i \(0.135954\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −3.00000 + 5.19615i −0.144171 + 0.249711i −0.929063 0.369921i \(-0.879385\pi\)
0.784892 + 0.619632i \(0.212718\pi\)
\(434\) 0 0
\(435\) 3.00000 + 5.19615i 0.143839 + 0.249136i
\(436\) −16.0000 −0.766261
\(437\) 28.0000 + 12.1244i 1.33942 + 0.579987i
\(438\) −2.00000 −0.0955637
\(439\) 16.0000 + 27.7128i 0.763638 + 1.32266i 0.940963 + 0.338508i \(0.109922\pi\)
−0.177325 + 0.984152i \(0.556744\pi\)
\(440\) 0.500000 + 0.866025i 0.0238366 + 0.0412861i
\(441\) −9.00000 + 15.5885i −0.428571 + 0.742307i
\(442\) 12.0000 + 20.7846i 0.570782 + 0.988623i
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) −7.00000 −0.332205
\(445\) 13.0000 0.616259
\(446\) −10.5000 + 18.1865i −0.497189 + 0.861157i
\(447\) −2.00000 + 3.46410i −0.0945968 + 0.163846i
\(448\) −5.00000 −0.236228
\(449\) −39.0000 −1.84052 −0.920262 0.391303i \(-0.872024\pi\)
−0.920262 + 0.391303i \(0.872024\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) 2.50000 + 4.33013i 0.117720 + 0.203898i
\(452\) −2.00000 + 3.46410i −0.0940721 + 0.162938i
\(453\) −10.0000 17.3205i −0.469841 0.813788i
\(454\) 1.00000 + 1.73205i 0.0469323 + 0.0812892i
\(455\) −30.0000 −1.40642
\(456\) −3.50000 + 2.59808i −0.163903 + 0.121666i
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) −3.50000 + 6.06218i −0.163188 + 0.282650i
\(461\) 3.00000 + 5.19615i 0.139724 + 0.242009i 0.927392 0.374091i \(-0.122045\pi\)
−0.787668 + 0.616100i \(0.788712\pi\)
\(462\) 2.50000 4.33013i 0.116311 0.201456i
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) 38.0000 1.75843 0.879215 0.476425i \(-0.158068\pi\)
0.879215 + 0.476425i \(0.158068\pi\)
\(468\) 6.00000 0.277350
\(469\) 30.0000 51.9615i 1.38527 2.39936i
\(470\) −4.00000 6.92820i −0.184506 0.319574i
\(471\) 4.50000 7.79423i 0.207349 0.359139i
\(472\) −4.00000 6.92820i −0.184115 0.318896i
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 10.0000 0.459315
\(475\) 4.00000 + 1.73205i 0.183533 + 0.0794719i
\(476\) −20.0000 −0.916698
\(477\) −5.50000 9.52628i −0.251828 0.436178i
\(478\) 0 0
\(479\) −21.0000 + 36.3731i −0.959514 + 1.66193i −0.235833 + 0.971794i \(0.575782\pi\)
−0.723681 + 0.690134i \(0.757551\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −21.0000 + 36.3731i −0.957518 + 1.65847i
\(482\) 26.0000 1.18427
\(483\) 35.0000 1.59256
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 1.00000 0.0453609
\(487\) −13.0000 −0.589086 −0.294543 0.955638i \(-0.595167\pi\)
−0.294543 + 0.955638i \(0.595167\pi\)
\(488\) −2.00000 + 3.46410i −0.0905357 + 0.156813i
\(489\) −5.00000 8.66025i −0.226108 0.391630i
\(490\) 9.00000 15.5885i 0.406579 0.704215i
\(491\) 16.5000 + 28.5788i 0.744635 + 1.28974i 0.950365 + 0.311136i \(0.100710\pi\)
−0.205731 + 0.978609i \(0.565957\pi\)
\(492\) −2.50000 4.33013i −0.112709 0.195217i
\(493\) 24.0000 1.08091
\(494\) 3.00000 + 25.9808i 0.134976 + 1.16893i
\(495\) 1.00000 0.0449467
\(496\) 0 0
\(497\) 5.00000 + 8.66025i 0.224281 + 0.388465i
\(498\) 5.00000 8.66025i 0.224055 0.388075i
\(499\) 3.50000 + 6.06218i 0.156682 + 0.271380i 0.933670 0.358134i \(-0.116587\pi\)
−0.776989 + 0.629515i \(0.783254\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −21.0000 −0.938211
\(502\) −12.0000 −0.535586
\(503\) −0.500000 + 0.866025i −0.0222939 + 0.0386142i −0.876957 0.480569i \(-0.840430\pi\)
0.854663 + 0.519183i \(0.173764\pi\)
\(504\) −2.50000 + 4.33013i −0.111359 + 0.192879i
\(505\) 2.00000 0.0889988
\(506\) −7.00000 −0.311188
\(507\) 11.5000 19.9186i 0.510733 0.884615i
\(508\) 2.50000 + 4.33013i 0.110920 + 0.192118i
\(509\) −1.00000 + 1.73205i −0.0443242 + 0.0767718i −0.887336 0.461123i \(-0.847447\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(510\) −2.00000 3.46410i −0.0885615 0.153393i
\(511\) −5.00000 8.66025i −0.221187 0.383107i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 + 4.33013i 0.0220755 + 0.191180i
\(514\) −18.0000 −0.793946
\(515\) −7.50000 12.9904i −0.330489 0.572425i
\(516\) 3.00000 + 5.19615i 0.132068 + 0.228748i
\(517\) 4.00000 6.92820i 0.175920 0.304702i
\(518\) −17.5000 30.3109i −0.768906 1.33178i
\(519\) −4.50000 + 7.79423i −0.197528 + 0.342129i
\(520\) −6.00000 −0.263117
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 7.00000 12.1244i 0.306089 0.530161i −0.671414 0.741082i \(-0.734313\pi\)
0.977503 + 0.210921i \(0.0676463\pi\)
\(524\) −3.00000 −0.131056
\(525\) 5.00000 0.218218
\(526\) 10.5000 18.1865i 0.457822 0.792971i
\(527\) 0 0
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) 5.50000 + 9.52628i 0.238905 + 0.413795i
\(531\) −8.00000 −0.347170
\(532\) −20.0000 8.66025i −0.867110 0.375470i
\(533\) −30.0000 −1.29944
\(534\) −6.50000 11.2583i −0.281283 0.487196i
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 3.50000 + 6.06218i 0.151036 + 0.261602i
\(538\) 16.0000 27.7128i 0.689809 1.19478i
\(539\) 18.0000 0.775315
\(540\) −1.00000 −0.0430331
\(541\) −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 1.00000 1.73205i 0.0429537 0.0743980i
\(543\) −18.0000 −0.772454
\(544\) −4.00000 −0.171499
\(545\) 8.00000 13.8564i 0.342682 0.593543i
\(546\) 15.0000 + 25.9808i 0.641941 + 1.11187i
\(547\) −7.00000 + 12.1244i −0.299298 + 0.518400i −0.975976 0.217880i \(-0.930086\pi\)
0.676677 + 0.736280i \(0.263419\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 2.00000 + 3.46410i 0.0853579 + 0.147844i
\(550\) −1.00000 −0.0426401
\(551\) 24.0000 + 10.3923i 1.02243 + 0.442727i
\(552\) 7.00000 0.297940
\(553\) 25.0000 + 43.3013i 1.06311 + 1.84136i
\(554\) −7.00000 12.1244i −0.297402 0.515115i
\(555\) 3.50000 6.06218i 0.148567 0.257325i
\(556\) 8.00000 + 13.8564i 0.339276 + 0.587643i
\(557\) −0.500000 + 0.866025i −0.0211857 + 0.0366947i −0.876424 0.481540i \(-0.840077\pi\)
0.855238 + 0.518235i \(0.173411\pi\)
\(558\) 0 0
\(559\) 36.0000 1.52264
\(560\) 2.50000 4.33013i 0.105644 0.182981i
\(561\) 2.00000 3.46410i 0.0844401 0.146254i
\(562\) 11.0000 0.464007
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −4.00000 + 6.92820i −0.168430 + 0.291730i
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) 11.0000 19.0526i 0.462364 0.800839i
\(567\) 2.50000 + 4.33013i 0.104990 + 0.181848i
\(568\) 1.00000 + 1.73205i 0.0419591 + 0.0726752i
\(569\) 33.0000 1.38343 0.691716 0.722170i \(-0.256855\pi\)
0.691716 + 0.722170i \(0.256855\pi\)
\(570\) −0.500000 4.33013i −0.0209427 0.181369i
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) −3.00000 5.19615i −0.125436 0.217262i
\(573\) −7.00000 12.1244i −0.292429 0.506502i
\(574\) 12.5000 21.6506i 0.521740 0.903680i
\(575\) −3.50000 6.06218i −0.145960 0.252810i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −32.0000 −1.33218 −0.666089 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) 1.00000 0.0415945
\(579\) −2.00000 + 3.46410i −0.0831172 + 0.143963i
\(580\) −3.00000 + 5.19615i −0.124568 + 0.215758i
\(581\) 50.0000 2.07435
\(582\) 2.00000 0.0829027
\(583\) −5.50000 + 9.52628i −0.227787 + 0.394538i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) −3.00000 + 5.19615i −0.124035 + 0.214834i
\(586\) 2.50000 + 4.33013i 0.103274 + 0.178876i
\(587\) 10.0000 + 17.3205i 0.412744 + 0.714894i 0.995189 0.0979766i \(-0.0312370\pi\)
−0.582445 + 0.812870i \(0.697904\pi\)
\(588\) −18.0000 −0.742307
\(589\) 0 0
\(590\) 8.00000 0.329355
\(591\) 0.500000 + 0.866025i 0.0205673 + 0.0356235i
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) −11.0000 + 19.0526i −0.451716 + 0.782395i −0.998493 0.0548835i \(-0.982521\pi\)
0.546777 + 0.837278i \(0.315855\pi\)
\(594\) −0.500000 0.866025i −0.0205152 0.0355335i
\(595\) 10.0000 17.3205i 0.409960 0.710072i
\(596\) −4.00000 −0.163846
\(597\) 4.00000 0.163709
\(598\) 21.0000 36.3731i 0.858754 1.48741i
\(599\) −4.00000 + 6.92820i −0.163436 + 0.283079i −0.936099 0.351738i \(-0.885591\pi\)
0.772663 + 0.634816i \(0.218924\pi\)
\(600\) 1.00000 0.0408248
\(601\) −3.00000 −0.122373 −0.0611863 0.998126i \(-0.519488\pi\)
−0.0611863 + 0.998126i \(0.519488\pi\)
\(602\) −15.0000 + 25.9808i −0.611354 + 1.05890i
\(603\) −6.00000 10.3923i −0.244339 0.423207i
\(604\) 10.0000 17.3205i 0.406894 0.704761i
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) −1.00000 1.73205i −0.0406222 0.0703598i
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) −4.00000 1.73205i −0.162221 0.0702439i
\(609\) 30.0000 1.21566
\(610\) −2.00000 3.46410i −0.0809776 0.140257i
\(611\) 24.0000 + 41.5692i 0.970936 + 1.68171i
\(612\) −2.00000 + 3.46410i −0.0808452 + 0.140028i
\(613\) −17.5000 30.3109i −0.706818 1.22425i −0.966031 0.258425i \(-0.916796\pi\)
0.259213 0.965820i \(-0.416537\pi\)
\(614\) 9.00000 15.5885i 0.363210 0.629099i
\(615\) 5.00000 0.201619
\(616\) 5.00000 0.201456
\(617\) −24.0000 + 41.5692i −0.966204 + 1.67351i −0.259858 + 0.965647i \(0.583676\pi\)
−0.706346 + 0.707867i \(0.749658\pi\)
\(618\) −7.50000 + 12.9904i −0.301694 + 0.522550i
\(619\) 43.0000 1.72832 0.864158 0.503221i \(-0.167852\pi\)
0.864158 + 0.503221i \(0.167852\pi\)
\(620\) 0 0
\(621\) 3.50000 6.06218i 0.140450 0.243267i
\(622\) −10.0000 17.3205i −0.400963 0.694489i
\(623\) 32.5000 56.2917i 1.30209 2.25528i
\(624\) 3.00000 + 5.19615i 0.120096 + 0.208013i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 3.50000 2.59808i 0.139777 0.103757i
\(628\) 9.00000 0.359139
\(629\) −14.0000 24.2487i −0.558217 0.966859i
\(630\) −2.50000 4.33013i −0.0996024 0.172516i
\(631\) −19.0000 + 32.9090i −0.756378 + 1.31009i 0.188308 + 0.982110i \(0.439700\pi\)
−0.944686 + 0.327975i \(0.893634\pi\)
\(632\) 5.00000 + 8.66025i 0.198889 + 0.344486i
\(633\) 6.50000 11.2583i 0.258352 0.447478i
\(634\) −3.00000 −0.119145
\(635\) −5.00000 −0.198419
\(636\) 5.50000 9.52628i 0.218089 0.377742i
\(637\) −54.0000 + 93.5307i −2.13956 + 3.70582i
\(638\) −6.00000 −0.237542
\(639\) 2.00000 0.0791188
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 13.0000 + 22.5167i 0.513469 + 0.889355i 0.999878 + 0.0156233i \(0.00497325\pi\)
−0.486409 + 0.873731i \(0.661693\pi\)
\(642\) 2.00000 3.46410i 0.0789337 0.136717i
\(643\) 22.0000 + 38.1051i 0.867595 + 1.50272i 0.864447 + 0.502724i \(0.167669\pi\)
0.00314839 + 0.999995i \(0.498998\pi\)
\(644\) 17.5000 + 30.3109i 0.689597 + 1.19442i
\(645\) −6.00000 −0.236250
\(646\) −16.0000 6.92820i −0.629512 0.272587i
\(647\) 3.00000 0.117942 0.0589711 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 4.00000 + 6.92820i 0.157014 + 0.271956i
\(650\) 3.00000 5.19615i 0.117670 0.203810i
\(651\) 0 0
\(652\) 5.00000 8.66025i 0.195815 0.339162i
\(653\) 9.00000 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) −16.0000 −0.625650
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) 2.50000 4.33013i 0.0976086 0.169063i
\(657\) −2.00000 −0.0780274
\(658\) −40.0000 −1.55936
\(659\) 5.50000 9.52628i 0.214250 0.371091i −0.738791 0.673935i \(-0.764603\pi\)
0.953040 + 0.302844i \(0.0979361\pi\)
\(660\) 0.500000 + 0.866025i 0.0194625 + 0.0337100i
\(661\) 10.0000 17.3205i 0.388955 0.673690i −0.603354 0.797473i \(-0.706170\pi\)
0.992309 + 0.123784i \(0.0395028\pi\)
\(662\) 7.50000 + 12.9904i 0.291496 + 0.504885i
\(663\) 12.0000 + 20.7846i 0.466041 + 0.807207i
\(664\) 10.0000 0.388075
\(665\) 17.5000 12.9904i 0.678621 0.503745i
\(666\) −7.00000 −0.271244
\(667\) −21.0000 36.3731i −0.813123 1.40837i
\(668\) −10.5000 18.1865i −0.406257 0.703658i
\(669\) −10.5000 + 18.1865i −0.405953 + 0.703132i
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) 2.00000 3.46410i 0.0772091 0.133730i
\(672\) −5.00000 −0.192879
\(673\) −40.0000 −1.54189 −0.770943 0.636904i \(-0.780215\pi\)
−0.770943 + 0.636904i \(0.780215\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 23.0000 0.884615
\(677\) 21.0000 0.807096 0.403548 0.914959i \(-0.367777\pi\)
0.403548 + 0.914959i \(0.367777\pi\)
\(678\) −2.00000 + 3.46410i −0.0768095 + 0.133038i
\(679\) 5.00000 + 8.66025i 0.191882 + 0.332350i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 1.00000 + 1.73205i 0.0383201 + 0.0663723i
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −3.50000 + 2.59808i −0.133826 + 0.0993399i
\(685\) −12.0000 −0.458496
\(686\) −27.5000 47.6314i −1.04995 1.81858i
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) −3.00000 + 5.19615i −0.114374 + 0.198101i
\(689\) −33.0000 57.1577i −1.25720 2.17753i
\(690\) −3.50000 + 6.06218i −0.133243 + 0.230783i
\(691\) 1.00000 0.0380418 0.0190209 0.999819i \(-0.493945\pi\)
0.0190209 + 0.999819i \(0.493945\pi\)
\(692\) −9.00000 −0.342129
\(693\) 2.50000 4.33013i 0.0949671 0.164488i
\(694\) −1.00000 + 1.73205i −0.0379595 + 0.0657477i
\(695\) −16.0000 −0.606915
\(696\) 6.00000 0.227429
\(697\) 10.0000 17.3205i 0.378777 0.656061i
\(698\) 8.00000 + 13.8564i 0.302804 + 0.524473i
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) 2.50000 + 4.33013i 0.0944911 + 0.163663i
\(701\) −17.0000 29.4449i −0.642081 1.11212i −0.984967 0.172740i \(-0.944738\pi\)
0.342886 0.939377i \(-0.388595\pi\)
\(702\) 6.00000 0.226455
\(703\) −3.50000 30.3109i −0.132005 1.14320i
\(704\) 1.00000 0.0376889
\(705\) −4.00000 6.92820i −0.150649 0.260931i
\(706\) 18.0000 + 31.1769i 0.677439 + 1.17336i
\(707\) 5.00000 8.66025i 0.188044 0.325702i
\(708\) −4.00000 6.92820i −0.150329 0.260378i
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) −2.00000 −0.0750587
\(711\) 10.0000 0.375029
\(712\) 6.50000 11.2583i 0.243598 0.421924i
\(713\) 0 0
\(714\) −20.0000 −0.748481
\(715\) 6.00000 0.224387
\(716\) −3.50000 + 6.06218i −0.130801 + 0.226554i
\(717\) 0 0
\(718\) −9.00000 + 15.5885i −0.335877 + 0.581756i
\(719\) 22.0000 + 38.1051i 0.820462 + 1.42108i 0.905339 + 0.424690i \(0.139617\pi\)
−0.0848774 + 0.996391i \(0.527050\pi\)
\(720\) −0.500000 0.866025i −0.0186339 0.0322749i
\(721\) −75.0000 −2.79315
\(722\) −13.0000 13.8564i −0.483810 0.515682i
\(723\) 26.0000 0.966950
\(724\) −9.00000 15.5885i −0.334482 0.579340i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 5.00000 8.66025i 0.185567 0.321412i
\(727\) −16.0000 27.7128i −0.593407 1.02781i −0.993770 0.111454i \(-0.964449\pi\)
0.400362 0.916357i \(-0.368884\pi\)
\(728\) −15.0000 + 25.9808i −0.555937 + 0.962911i
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) −2.00000 + 3.46410i −0.0739221 + 0.128037i
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 4.00000 0.147643
\(735\) 9.00000 15.5885i 0.331970 0.574989i
\(736\) 3.50000 + 6.06218i 0.129012 + 0.223455i
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) −2.50000 4.33013i −0.0920263 0.159394i
\(739\) 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i \(0.165674\pi\)
−0.00311943 + 0.999995i \(0.500993\pi\)
\(740\) 7.00000 0.257325
\(741\) 3.00000 + 25.9808i 0.110208 + 0.954427i
\(742\) 55.0000 2.01911
\(743\) −7.50000 12.9904i −0.275148 0.476571i 0.695024 0.718986i \(-0.255394\pi\)
−0.970173 + 0.242415i \(0.922060\pi\)
\(744\) 0 0
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) 2.50000 + 4.33013i 0.0915315 + 0.158537i
\(747\) 5.00000 8.66025i 0.182940 0.316862i
\(748\) 4.00000 0.146254
\(749\) 20.0000 0.730784
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −20.0000 + 34.6410i −0.729810 + 1.26407i 0.227153 + 0.973859i \(0.427058\pi\)
−0.956963 + 0.290209i \(0.906275\pi\)
\(752\) −8.00000 −0.291730
\(753\) −12.0000 −0.437304
\(754\) 18.0000 31.1769i 0.655521 1.13540i
\(755\) 10.0000 + 17.3205i 0.363937 + 0.630358i
\(756\) −2.50000 + 4.33013i −0.0909241 + 0.157485i
\(757\) 6.50000 + 11.2583i 0.236247 + 0.409191i 0.959634 0.281251i \(-0.0907494\pi\)
−0.723388 + 0.690442i \(0.757416\pi\)
\(758\) −2.00000 3.46410i −0.0726433 0.125822i
\(759\) −7.00000 −0.254084
\(760\) 3.50000 2.59808i 0.126958 0.0942421i
\(761\) −31.0000 −1.12375 −0.561875 0.827222i \(-0.689920\pi\)
−0.561875 + 0.827222i \(0.689920\pi\)
\(762\) 2.50000 + 4.33013i 0.0905654 + 0.156864i
\(763\) −40.0000 69.2820i −1.44810 2.50818i
\(764\) 7.00000 12.1244i 0.253251 0.438644i
\(765\) −2.00000 3.46410i −0.0723102 0.125245i
\(766\) 16.0000 27.7128i 0.578103 1.00130i
\(767\) −48.0000 −1.73318
\(768\) −1.00000 −0.0360844
\(769\) −3.00000 + 5.19615i −0.108183 + 0.187378i −0.915034 0.403376i \(-0.867837\pi\)
0.806851 + 0.590755i \(0.201170\pi\)
\(770\) −2.50000 + 4.33013i −0.0900937 + 0.156047i
\(771\) −18.0000 −0.648254
\(772\) −4.00000 −0.143963
\(773\) 10.5000 18.1865i 0.377659 0.654124i −0.613062 0.790034i \(-0.710063\pi\)
0.990721 + 0.135910i \(0.0433959\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) 0 0
\(776\) 1.00000 + 1.73205i 0.0358979 + 0.0621770i
\(777\) −17.5000 30.3109i −0.627809 1.08740i
\(778\) 10.0000 0.358517
\(779\) 17.5000 12.9904i 0.627003 0.465429i
\(780\) −6.00000 −0.214834
\(781\) −1.00000 1.73205i −0.0357828 0.0619777i
\(782\) 14.0000 + 24.2487i 0.500639 + 0.867132i
\(783\) 3.00000 5.19615i 0.107211 0.185695i
\(784\) −9.00000 15.5885i −0.321429 0.556731i
\(785\) −4.50000 + 7.79423i −0.160612 + 0.278188i
\(786\) −3.00000 −0.107006
\(787\) −26.0000 −0.926800 −0.463400 0.886149i \(-0.653371\pi\)
−0.463400 + 0.886149i \(0.653371\pi\)
\(788\) −0.500000 + 0.866025i −0.0178118 + 0.0308509i
\(789\) 10.5000 18.1865i 0.373810 0.647458i
\(790\) −10.0000 −0.355784
\(791\) −20.0000 −0.711118
\(792\) 0.500000 0.866025i 0.0177667 0.0307729i
\(793\) 12.0000 + 20.7846i 0.426132 + 0.738083i
\(794\) −16.5000 + 28.5788i −0.585563 + 1.01423i
\(795\) 5.50000 + 9.52628i 0.195065 + 0.337862i
\(796\) 2.00000 + 3.46410i 0.0708881 + 0.122782i
\(797\) 47.0000 1.66483 0.832413 0.554156i \(-0.186959\pi\)
0.832413 + 0.554156i \(0.186959\pi\)
\(798\) −20.0000 8.66025i −0.707992 0.306570i
\(799\) −32.0000 −1.13208
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) −6.50000 11.2583i −0.229666 0.397794i
\(802\) −9.00000 + 15.5885i −0.317801 + 0.550448i
\(803\) 1.00000 + 1.73205i 0.0352892 + 0.0611227i
\(804\) 6.00000 10.3923i 0.211604 0.366508i
\(805\) −35.0000 −1.23359
\(806\) 0 0
\(807\) 16.0000 27.7128i 0.563227 0.975537i
\(808\) 1.00000 1.73205i 0.0351799 0.0609333i
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −21.5000 + 37.2391i −0.754967 + 1.30764i 0.190424 + 0.981702i \(0.439014\pi\)
−0.945391 + 0.325939i \(0.894319\pi\)
\(812\) 15.0000 + 25.9808i 0.526397 + 0.911746i
\(813\) 1.00000 1.73205i 0.0350715 0.0607457i
\(814\) 3.50000 + 6.06218i 0.122675 + 0.212479i
\(815\) 5.00000 + 8.66025i 0.175142 + 0.303355i
\(816\) −4.00000 −0.140028
\(817\) −21.0000 + 15.5885i −0.734697 + 0.545371i
\(818\) 3.00000 0.104893
\(819\) 15.0000 + 25.9808i 0.524142 + 0.907841i
\(820\) 2.50000 + 4.33013i 0.0873038 + 0.151215i
\(821\) −21.0000 + 36.3731i −0.732905 + 1.26943i 0.222731 + 0.974880i \(0.428503\pi\)
−0.955636 + 0.294549i \(0.904831\pi\)
\(822\) 6.00000 + 10.3923i 0.209274 + 0.362473i
\(823\) 11.5000 19.9186i 0.400865 0.694318i −0.592966 0.805228i \(-0.702043\pi\)
0.993831 + 0.110910i \(0.0353764\pi\)
\(824\) −15.0000 −0.522550
\(825\) −1.00000 −0.0348155
\(826\) 20.0000 34.6410i 0.695889 1.20532i
\(827\) 15.0000 25.9808i 0.521601 0.903440i −0.478083 0.878315i \(-0.658668\pi\)
0.999684 0.0251251i \(-0.00799840\pi\)
\(828\) 7.00000 0.243267
\(829\) −28.0000 −0.972480 −0.486240 0.873825i \(-0.661632\pi\)
−0.486240 + 0.873825i \(0.661632\pi\)
\(830\) −5.00000 + 8.66025i −0.173553 + 0.300602i
\(831\) −7.00000 12.1244i −0.242827 0.420589i
\(832\) −3.00000 + 5.19615i −0.104006 + 0.180144i
\(833\) −36.0000 62.3538i −1.24733 2.16043i
\(834\) 8.00000 + 13.8564i 0.277017 + 0.479808i
\(835\) 21.0000 0.726735
\(836\) 4.00000 + 1.73205i 0.138343 + 0.0599042i
\(837\) 0 0
\(838\) −1.50000 2.59808i −0.0518166 0.0897491i
\(839\) 9.00000 + 15.5885i 0.310715 + 0.538173i 0.978517 0.206165i \(-0.0660984\pi\)
−0.667803 + 0.744338i \(0.732765\pi\)
\(840\) 2.50000 4.33013i 0.0862582 0.149404i
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) −4.00000 + 6.92820i −0.137849 + 0.238762i
\(843\) 11.0000 0.378860
\(844\) 13.0000 0.447478
\(845\) −11.5000 + 19.9186i −0.395612 + 0.685220i
\(846\) −4.00000 + 6.92820i −0.137523 + 0.238197i
\(847\) 50.0000 1.71802
\(848\) 11.0000 0.377742
\(849\) 11.0000 19.0526i 0.377519 0.653882i
\(850\) 2.00000 + 3.46410i 0.0685994 + 0.118818i
\(851\) −24.5000 + 42.4352i −0.839849 + 1.45466i
\(852\) 1.00000 + 1.73205i 0.0342594 + 0.0593391i
\(853\) −9.00000 15.5885i −0.308154 0.533739i 0.669804 0.742538i \(-0.266378\pi\)
−0.977959 + 0.208799i \(0.933045\pi\)
\(854\) −20.0000 −0.684386
\(855\) −0.500000 4.33013i −0.0170996 0.148087i
\(856\) 4.00000 0.136717
\(857\) 18.0000 + 31.1769i 0.614868 + 1.06498i 0.990408 + 0.138177i \(0.0441242\pi\)
−0.375539 + 0.926806i \(0.622542\pi\)
\(858\) −3.00000 5.19615i −0.102418 0.177394i
\(859\) 8.50000 14.7224i 0.290016 0.502323i −0.683797 0.729672i \(-0.739673\pi\)
0.973813 + 0.227349i \(0.0730059\pi\)
\(860\) −3.00000 5.19615i −0.102299 0.177187i
\(861\) 12.5000 21.6506i 0.425999 0.737852i
\(862\) 4.00000 0.136241
\(863\) −1.00000 −0.0340404 −0.0170202 0.999855i \(-0.505418\pi\)
−0.0170202 + 0.999855i \(0.505418\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) 4.50000 7.79423i 0.153005 0.265012i
\(866\) −6.00000 −0.203888
\(867\) 1.00000 0.0339618
\(868\) 0 0
\(869\) −5.00000 8.66025i −0.169613 0.293779i
\(870\) −3.00000 + 5.19615i −0.101710 + 0.176166i
\(871\) −36.0000 62.3538i −1.21981 2.11278i
\(872\) −8.00000 13.8564i −0.270914 0.469237i
\(873\) 2.00000 0.0676897
\(874\) 3.50000 + 30.3109i 0.118389 + 1.02528i
\(875\) −5.00000 −0.169031
\(876\) −1.00000 1.73205i −0.0337869 0.0585206i
\(877\) 3.50000 + 6.06218i 0.118187 + 0.204705i 0.919049 0.394143i \(-0.128959\pi\)
−0.800862 + 0.598848i \(0.795625\pi\)
\(878\) −16.0000 + 27.7128i −0.539974 + 0.935262i
\(879\) 2.50000 + 4.33013i 0.0843229 + 0.146052i
\(880\) −0.500000 + 0.866025i −0.0168550 + 0.0291937i
\(881\) 33.0000 1.11180 0.555899 0.831250i \(-0.312374\pi\)
0.555899 + 0.831250i \(0.312374\pi\)
\(882\) −18.0000 −0.606092
\(883\) 18.0000 31.1769i 0.605748 1.04919i −0.386185 0.922422i \(-0.626207\pi\)
0.991933 0.126765i \(-0.0404595\pi\)
\(884\) −12.0000 + 20.7846i −0.403604 + 0.699062i
\(885\) 8.00000 0.268917
\(886\) −24.0000 −0.806296
\(887\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(888\) −3.50000 6.06218i −0.117452 0.203433i
\(889\) −12.5000 + 21.6506i −0.419237 + 0.726139i
\(890\) 6.50000 + 11.2583i 0.217880 + 0.377380i
\(891\) −0.500000 0.866025i −0.0167506 0.0290129i
\(892\) −21.0000 −0.703132
\(893\) −32.0000 13.8564i −1.07084 0.463687i
\(894\) −4.00000 −0.133780
\(895\) −3.50000 6.06218i −0.116992 0.202636i
\(896\) −2.50000 4.33013i −0.0835191 0.144659i
\(897\) 21.0000 36.3731i 0.701170 1.21446i
\(898\) −19.5000 33.7750i −0.650723 1.12709i
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 44.0000 1.46585
\(902\) −2.50000 + 4.33013i −0.0832409 + 0.144177i
\(903\) −15.0000 + 25.9808i −0.499169 + 0.864586i
\(904\) −4.00000 −0.133038
\(905\) 18.0000 0.598340
\(906\) 10.0000 17.3205i 0.332228 0.575435i
\(907\) −11.0000 19.0526i −0.365249 0.632630i 0.623567 0.781770i \(-0.285683\pi\)
−0.988816 + 0.149140i \(0.952349\pi\)
\(908\) −1.00000 + 1.73205i −0.0331862 + 0.0574801i
\(909\) −1.00000 1.73205i −0.0331679 0.0574485i
\(910\) −15.0000 25.9808i −0.497245 0.861254i
\(911\) −18.0000 −0.596367 −0.298183 0.954509i \(-0.596381\pi\)
−0.298183 + 0.954509i \(0.596381\pi\)
\(912\) −4.00000 1.73205i −0.132453 0.0573539i
\(913\) −10.0000 −0.330952
\(914\) 4.00000 + 6.92820i 0.132308 + 0.229165i
\(915\) −2.00000 3.46410i −0.0661180 0.114520i
\(916\) −5.00000 + 8.66025i −0.165205 + 0.286143i
\(917\) −7.50000 12.9904i −0.247672 0.428980i
\(918\) −2.00000 + 3.46410i −0.0660098 + 0.114332i
\(919\) −26.0000 −0.857661 −0.428830 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(920\) −7.00000 −0.230783
\(921\) 9.00000 15.5885i 0.296560 0.513657i
\(922\) −3.00000 + 5.19615i −0.0987997 + 0.171126i
\(923\) 12.0000 0.394985
\(924\) 5.00000 0.164488
\(925\) −3.50000 + 6.06218i −0.115079 + 0.199323i
\(926\) −4.50000 7.79423i −0.147879 0.256134i
\(927\) −7.50000 + 12.9904i −0.246332 + 0.426660i
\(928\) 3.00000 + 5.19615i 0.0984798 + 0.170572i
\(929\) 7.50000 + 12.9904i 0.246067 + 0.426201i 0.962431 0.271526i \(-0.0875283\pi\)
−0.716364 + 0.697727i \(0.754195\pi\)
\(930\) 0 0
\(931\) −9.00000 77.9423i −0.294963 2.55446i
\(932\) −18.0000 −0.589610
\(933\) −10.0000 17.3205i −0.327385 0.567048i
\(934\) 19.0000 + 32.9090i 0.621699 + 1.07681i
\(935\) −2.00000 + 3.46410i −0.0654070 + 0.113288i
\(936\) 3.00000 + 5.19615i 0.0980581 + 0.169842i
\(937\) 11.0000 19.0526i 0.359354 0.622420i −0.628499 0.777811i \(-0.716330\pi\)
0.987853 + 0.155391i \(0.0496636\pi\)
\(938\) 60.0000 1.95907
\(939\) 0 0
\(940\) 4.00000 6.92820i 0.130466 0.225973i
\(941\) −23.0000 + 39.8372i −0.749779 + 1.29865i 0.198150 + 0.980172i \(0.436507\pi\)
−0.947929 + 0.318483i \(0.896827\pi\)
\(942\) 9.00000 0.293236
\(943\) −35.0000 −1.13976
\(944\) 4.00000 6.92820i 0.130189 0.225494i
\(945\) −2.50000 4.33013i −0.0813250 0.140859i
\(946\) 3.00000 5.19615i 0.0975384 0.168941i
\(947\) 16.0000 + 27.7128i 0.519930 + 0.900545i 0.999732 + 0.0231683i \(0.00737536\pi\)
−0.479801 + 0.877377i \(0.659291\pi\)
\(948\) 5.00000 + 8.66025i 0.162392 + 0.281272i
\(949\) −12.0000 −0.389536
\(950\) 0.500000 + 4.33013i 0.0162221 + 0.140488i
\(951\) −3.00000 −0.0972817
\(952\) −10.0000 17.3205i −0.324102 0.561361i
\(953\) 18.0000 + 31.1769i 0.583077 + 1.00992i 0.995112 + 0.0987513i \(0.0314848\pi\)
−0.412035 + 0.911168i \(0.635182\pi\)
\(954\) 5.50000 9.52628i 0.178069 0.308425i
\(955\) 7.00000 + 12.1244i 0.226515 + 0.392335i
\(956\) 0 0
\(957\) −6.00000 −0.193952
\(958\) −42.0000 −1.35696
\(959\) −30.0000 + 51.9615i −0.968751 + 1.67793i
\(960\) 0.500000 0.866025i 0.0161374 0.0279508i
\(961\) −31.0000 −1.00000
\(962\) −42.0000 −1.35413
\(963\) 2.00000 3.46410i 0.0644491 0.111629i
\(964\) 13.0000 + 22.5167i 0.418702 + 0.725213i
\(965\) 2.00000 3.46410i 0.0643823 0.111513i
\(966\) 17.5000 + 30.3109i 0.563053 + 0.975237i
\(967\) −12.0000 20.7846i −0.385894 0.668388i 0.605999 0.795466i \(-0.292774\pi\)
−0.991893 + 0.127078i \(0.959440\pi\)
\(968\) 10.0000 0.321412
\(969\) −16.0000 6.92820i −0.513994 0.222566i
\(970\) −2.00000 −0.0642161
\(971\) −6.00000 10.3923i −0.192549 0.333505i 0.753545 0.657396i \(-0.228342\pi\)
−0.946094 + 0.323891i \(0.895009\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) −40.0000 + 69.2820i −1.28234 + 2.22108i
\(974\) −6.50000 11.2583i −0.208273 0.360740i
\(975\) 3.00000 5.19615i 0.0960769 0.166410i
\(976\) −4.00000 −0.128037
\(977\) −6.00000 −0.191957 −0.0959785 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 5.00000 8.66025i 0.159882 0.276924i
\(979\) −6.50000 + 11.2583i −0.207741 + 0.359818i
\(980\) 18.0000 0.574989
\(981\) −16.0000 −0.510841
\(982\) −16.5000 + 28.5788i −0.526536 + 0.911987i
\(983\) −1.50000 2.59808i −0.0478426 0.0828658i 0.841112 0.540860i \(-0.181901\pi\)
−0.888955 + 0.457995i \(0.848568\pi\)
\(984\) 2.50000 4.33013i 0.0796971 0.138039i
\(985\) −0.500000 0.866025i −0.0159313 0.0275939i
\(986\) 12.0000 + 20.7846i 0.382158 + 0.661917i
\(987\) −40.0000 −1.27321
\(988\) −21.0000 + 15.5885i −0.668099 + 0.495935i
\(989\) 42.0000 1.33552
\(990\) 0.500000 + 0.866025i 0.0158910 + 0.0275241i
\(991\) −5.00000 8.66025i −0.158830 0.275102i 0.775617 0.631204i \(-0.217439\pi\)
−0.934447 + 0.356102i \(0.884106\pi\)
\(992\) 0 0
\(993\) 7.50000 + 12.9904i 0.238005 + 0.412237i
\(994\) −5.00000 + 8.66025i −0.158590 + 0.274687i
\(995\) −4.00000 −0.126809
\(996\) 10.0000 0.316862
\(997\) 15.5000 26.8468i 0.490890 0.850246i −0.509055 0.860734i \(-0.670005\pi\)
0.999945 + 0.0104877i \(0.00333839\pi\)
\(998\) −3.50000 + 6.06218i −0.110791 + 0.191895i
\(999\) −7.00000 −0.221470
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.i.e.121.1 2
3.2 odd 2 1710.2.l.c.1261.1 2
19.11 even 3 inner 570.2.i.e.391.1 yes 2
57.11 odd 6 1710.2.l.c.1531.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.i.e.121.1 2 1.1 even 1 trivial
570.2.i.e.391.1 yes 2 19.11 even 3 inner
1710.2.l.c.1261.1 2 3.2 odd 2
1710.2.l.c.1531.1 2 57.11 odd 6