Properties

Label 195.2.i.a.61.1
Level $195$
Weight $2$
Character 195.61
Analytic conductor $1.557$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [195,2,Mod(16,195)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(195, 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("195.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.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: \(1.55708283941\)
Analytic rank: \(1\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 61.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 195.61
Dual form 195.2.i.a.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(-2.50000 - 4.33013i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(-2.50000 - 4.33013i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(-1.00000 + 1.73205i) q^{11} +2.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} +10.0000 q^{14} +(0.500000 - 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +2.00000 q^{18} +(1.00000 + 1.73205i) q^{20} +5.00000 q^{21} +(-2.00000 - 3.46410i) q^{22} +(-3.00000 + 5.19615i) q^{23} +1.00000 q^{25} +(-2.00000 - 6.92820i) q^{26} +1.00000 q^{27} +(-5.00000 + 8.66025i) q^{28} +(2.00000 - 3.46410i) q^{29} +(1.00000 + 1.73205i) q^{30} -7.00000 q^{31} +(4.00000 + 6.92820i) q^{32} +(-1.00000 - 1.73205i) q^{33} +4.00000 q^{34} +(2.50000 + 4.33013i) q^{35} +(-1.00000 + 1.73205i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-1.00000 - 3.46410i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +4.00000 q^{44} +(0.500000 + 0.866025i) q^{45} +(-6.00000 - 10.3923i) q^{46} -8.00000 q^{47} +(2.00000 + 3.46410i) q^{48} +(-9.00000 + 15.5885i) q^{49} +(-1.00000 + 1.73205i) q^{50} +2.00000 q^{51} +(7.00000 + 1.73205i) q^{52} -4.00000 q^{53} +(-1.00000 + 1.73205i) q^{54} +(1.00000 - 1.73205i) q^{55} +(4.00000 + 6.92820i) q^{58} +(-6.00000 - 10.3923i) q^{59} -2.00000 q^{60} +(6.50000 + 11.2583i) q^{61} +(7.00000 - 12.1244i) q^{62} +(-2.50000 + 4.33013i) q^{63} -8.00000 q^{64} +(2.50000 - 2.59808i) q^{65} +4.00000 q^{66} +(3.50000 - 6.06218i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-3.00000 - 5.19615i) q^{69} -10.0000 q^{70} +(-6.00000 - 10.3923i) q^{71} +15.0000 q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +10.0000 q^{77} +(7.00000 + 1.73205i) q^{78} +3.00000 q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} +8.00000 q^{83} +(-5.00000 - 8.66025i) q^{84} +(1.00000 + 1.73205i) q^{85} +2.00000 q^{86} +(2.00000 + 3.46410i) q^{87} +(-7.00000 + 12.1244i) q^{89} -2.00000 q^{90} +(17.5000 + 4.33013i) q^{91} +12.0000 q^{92} +(3.50000 - 6.06218i) q^{93} +(8.00000 - 13.8564i) q^{94} -8.00000 q^{96} +(2.50000 + 4.33013i) q^{97} +(-18.0000 - 31.1769i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 5 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 5 q^{13} + 20 q^{14} + q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} + 10 q^{21} - 4 q^{22} - 6 q^{23} + 2 q^{25} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{30} - 14 q^{31} + 8 q^{32} - 2 q^{33} + 8 q^{34} + 5 q^{35} - 2 q^{36} + 2 q^{37} - 2 q^{39} - 6 q^{41} - 10 q^{42} - q^{43} + 8 q^{44} + q^{45} - 12 q^{46} - 16 q^{47} + 4 q^{48} - 18 q^{49} - 2 q^{50} + 4 q^{51} + 14 q^{52} - 8 q^{53} - 2 q^{54} + 2 q^{55} + 8 q^{58} - 12 q^{59} - 4 q^{60} + 13 q^{61} + 14 q^{62} - 5 q^{63} - 16 q^{64} + 5 q^{65} + 8 q^{66} + 7 q^{67} - 4 q^{68} - 6 q^{69} - 20 q^{70} - 12 q^{71} + 30 q^{73} + 4 q^{74} - q^{75} + 20 q^{77} + 14 q^{78} + 6 q^{79} - 4 q^{80} - q^{81} - 12 q^{82} + 16 q^{83} - 10 q^{84} + 2 q^{85} + 4 q^{86} + 4 q^{87} - 14 q^{89} - 4 q^{90} + 35 q^{91} + 24 q^{92} + 7 q^{93} + 16 q^{94} - 16 q^{96} + 5 q^{97} - 36 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).

\(n\) \(106\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) −1.00000 −0.447214
\(6\) −1.00000 1.73205i −0.408248 0.707107i
\(7\) −2.50000 4.33013i −0.944911 1.63663i −0.755929 0.654654i \(-0.772814\pi\)
−0.188982 0.981981i \(-0.560519\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 2.00000 0.577350
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 10.0000 2.67261
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 2.00000 0.471405
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 1.00000 + 1.73205i 0.223607 + 0.387298i
\(21\) 5.00000 1.09109
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.00000 6.92820i −0.392232 1.35873i
\(27\) 1.00000 0.192450
\(28\) −5.00000 + 8.66025i −0.944911 + 1.63663i
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) 1.00000 + 1.73205i 0.182574 + 0.316228i
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 4.00000 + 6.92820i 0.707107 + 1.22474i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) 4.00000 0.685994
\(35\) 2.50000 + 4.33013i 0.422577 + 0.731925i
\(36\) −1.00000 + 1.73205i −0.166667 + 0.288675i
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) −1.00000 3.46410i −0.160128 0.554700i
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) −5.00000 + 8.66025i −0.771517 + 1.33631i
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 4.00000 0.603023
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) −6.00000 10.3923i −0.884652 1.53226i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 2.00000 + 3.46410i 0.288675 + 0.500000i
\(49\) −9.00000 + 15.5885i −1.28571 + 2.22692i
\(50\) −1.00000 + 1.73205i −0.141421 + 0.244949i
\(51\) 2.00000 0.280056
\(52\) 7.00000 + 1.73205i 0.970725 + 0.240192i
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) −1.00000 + 1.73205i −0.136083 + 0.235702i
\(55\) 1.00000 1.73205i 0.134840 0.233550i
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 + 6.92820i 0.525226 + 0.909718i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) −2.00000 −0.258199
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 7.00000 12.1244i 0.889001 1.53979i
\(63\) −2.50000 + 4.33013i −0.314970 + 0.545545i
\(64\) −8.00000 −1.00000
\(65\) 2.50000 2.59808i 0.310087 0.322252i
\(66\) 4.00000 0.492366
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) −3.00000 5.19615i −0.361158 0.625543i
\(70\) −10.0000 −1.19523
\(71\) −6.00000 10.3923i −0.712069 1.23334i −0.964079 0.265615i \(-0.914425\pi\)
0.252010 0.967725i \(-0.418908\pi\)
\(72\) 0 0
\(73\) 15.0000 1.75562 0.877809 0.479012i \(-0.159005\pi\)
0.877809 + 0.479012i \(0.159005\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 10.0000 1.13961
\(78\) 7.00000 + 1.73205i 0.792594 + 0.196116i
\(79\) 3.00000 0.337526 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) −2.00000 + 3.46410i −0.223607 + 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.00000 10.3923i −0.662589 1.14764i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) −5.00000 8.66025i −0.545545 0.944911i
\(85\) 1.00000 + 1.73205i 0.108465 + 0.187867i
\(86\) 2.00000 0.215666
\(87\) 2.00000 + 3.46410i 0.214423 + 0.371391i
\(88\) 0 0
\(89\) −7.00000 + 12.1244i −0.741999 + 1.28518i 0.209585 + 0.977790i \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) −2.00000 −0.210819
\(91\) 17.5000 + 4.33013i 1.83450 + 0.453921i
\(92\) 12.0000 1.25109
\(93\) 3.50000 6.06218i 0.362933 0.628619i
\(94\) 8.00000 13.8564i 0.825137 1.42918i
\(95\) 0 0
\(96\) −8.00000 −0.816497
\(97\) 2.50000 + 4.33013i 0.253837 + 0.439658i 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −18.0000 31.1769i −1.81827 3.14934i
\(99\) 2.00000 0.201008
\(100\) −1.00000 1.73205i −0.100000 0.173205i
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) −5.00000 −0.487950
\(106\) 4.00000 6.92820i 0.388514 0.672927i
\(107\) −2.00000 + 3.46410i −0.193347 + 0.334887i −0.946357 0.323122i \(-0.895268\pi\)
0.753010 + 0.658009i \(0.228601\pi\)
\(108\) −1.00000 1.73205i −0.0962250 0.166667i
\(109\) −11.0000 −1.05361 −0.526804 0.849987i \(-0.676610\pi\)
−0.526804 + 0.849987i \(0.676610\pi\)
\(110\) 2.00000 + 3.46410i 0.190693 + 0.330289i
\(111\) 1.00000 + 1.73205i 0.0949158 + 0.164399i
\(112\) −20.0000 −1.88982
\(113\) 1.00000 + 1.73205i 0.0940721 + 0.162938i 0.909221 0.416314i \(-0.136678\pi\)
−0.815149 + 0.579252i \(0.803345\pi\)
\(114\) 0 0
\(115\) 3.00000 5.19615i 0.279751 0.484544i
\(116\) −8.00000 −0.742781
\(117\) 3.50000 + 0.866025i 0.323575 + 0.0800641i
\(118\) 24.0000 2.20938
\(119\) −5.00000 + 8.66025i −0.458349 + 0.793884i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −26.0000 −2.35393
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) 7.00000 + 12.1244i 0.628619 + 1.08880i
\(125\) −1.00000 −0.0894427
\(126\) −5.00000 8.66025i −0.445435 0.771517i
\(127\) 5.50000 9.52628i 0.488046 0.845321i −0.511859 0.859069i \(-0.671043\pi\)
0.999905 + 0.0137486i \(0.00437646\pi\)
\(128\) 0 0
\(129\) 1.00000 0.0880451
\(130\) 2.00000 + 6.92820i 0.175412 + 0.607644i
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) −2.00000 + 3.46410i −0.174078 + 0.301511i
\(133\) 0 0
\(134\) 7.00000 + 12.1244i 0.604708 + 1.04738i
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 12.0000 1.02151
\(139\) 1.50000 + 2.59808i 0.127228 + 0.220366i 0.922602 0.385754i \(-0.126059\pi\)
−0.795373 + 0.606120i \(0.792725\pi\)
\(140\) 5.00000 8.66025i 0.422577 0.731925i
\(141\) 4.00000 6.92820i 0.336861 0.583460i
\(142\) 24.0000 2.01404
\(143\) −2.00000 6.92820i −0.167248 0.579365i
\(144\) −4.00000 −0.333333
\(145\) −2.00000 + 3.46410i −0.166091 + 0.287678i
\(146\) −15.0000 + 25.9808i −1.24141 + 2.15018i
\(147\) −9.00000 15.5885i −0.742307 1.28571i
\(148\) −4.00000 −0.328798
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) −1.00000 1.73205i −0.0816497 0.141421i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) −1.00000 + 1.73205i −0.0808452 + 0.140028i
\(154\) −10.0000 + 17.3205i −0.805823 + 1.39573i
\(155\) 7.00000 0.562254
\(156\) −5.00000 + 5.19615i −0.400320 + 0.416025i
\(157\) −15.0000 −1.19713 −0.598565 0.801074i \(-0.704262\pi\)
−0.598565 + 0.801074i \(0.704262\pi\)
\(158\) −3.00000 + 5.19615i −0.238667 + 0.413384i
\(159\) 2.00000 3.46410i 0.158610 0.274721i
\(160\) −4.00000 6.92820i −0.316228 0.547723i
\(161\) 30.0000 2.36433
\(162\) −1.00000 1.73205i −0.0785674 0.136083i
\(163\) 7.50000 + 12.9904i 0.587445 + 1.01749i 0.994566 + 0.104111i \(0.0331996\pi\)
−0.407120 + 0.913375i \(0.633467\pi\)
\(164\) 12.0000 0.937043
\(165\) 1.00000 + 1.73205i 0.0778499 + 0.134840i
\(166\) −8.00000 + 13.8564i −0.620920 + 1.07547i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) −8.00000 −0.606478
\(175\) −2.50000 4.33013i −0.188982 0.327327i
\(176\) 4.00000 + 6.92820i 0.301511 + 0.522233i
\(177\) 12.0000 0.901975
\(178\) −14.0000 24.2487i −1.04934 1.81752i
\(179\) 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 1.00000 1.73205i 0.0745356 0.129099i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −25.0000 + 25.9808i −1.85312 + 1.92582i
\(183\) −13.0000 −0.960988
\(184\) 0 0
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) 7.00000 + 12.1244i 0.513265 + 0.889001i
\(187\) 4.00000 0.292509
\(188\) 8.00000 + 13.8564i 0.583460 + 1.01058i
\(189\) −2.50000 4.33013i −0.181848 0.314970i
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 4.00000 6.92820i 0.288675 0.500000i
\(193\) 5.50000 9.52628i 0.395899 0.685717i −0.597317 0.802005i \(-0.703766\pi\)
0.993215 + 0.116289i \(0.0370998\pi\)
\(194\) −10.0000 −0.717958
\(195\) 1.00000 + 3.46410i 0.0716115 + 0.248069i
\(196\) 36.0000 2.57143
\(197\) 6.00000 10.3923i 0.427482 0.740421i −0.569166 0.822222i \(-0.692734\pi\)
0.996649 + 0.0818013i \(0.0260673\pi\)
\(198\) −2.00000 + 3.46410i −0.142134 + 0.246183i
\(199\) −8.50000 14.7224i −0.602549 1.04365i −0.992434 0.122782i \(-0.960818\pi\)
0.389885 0.920864i \(-0.372515\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 18.0000 + 31.1769i 1.26648 + 2.19360i
\(203\) −20.0000 −1.40372
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 6.00000 0.417029
\(208\) 4.00000 + 13.8564i 0.277350 + 0.960769i
\(209\) 0 0
\(210\) 5.00000 8.66025i 0.345033 0.597614i
\(211\) −7.50000 + 12.9904i −0.516321 + 0.894295i 0.483499 + 0.875345i \(0.339366\pi\)
−0.999820 + 0.0189499i \(0.993968\pi\)
\(212\) 4.00000 + 6.92820i 0.274721 + 0.475831i
\(213\) 12.0000 0.822226
\(214\) −4.00000 6.92820i −0.273434 0.473602i
\(215\) 0.500000 + 0.866025i 0.0340997 + 0.0590624i
\(216\) 0 0
\(217\) 17.5000 + 30.3109i 1.18798 + 2.05764i
\(218\) 11.0000 19.0526i 0.745014 1.29040i
\(219\) −7.50000 + 12.9904i −0.506803 + 0.877809i
\(220\) −4.00000 −0.269680
\(221\) 7.00000 + 1.73205i 0.470871 + 0.116510i
\(222\) −4.00000 −0.268462
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) 20.0000 34.6410i 1.33631 2.31455i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −4.00000 −0.266076
\(227\) −5.00000 8.66025i −0.331862 0.574801i 0.651015 0.759065i \(-0.274343\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 6.00000 + 10.3923i 0.395628 + 0.685248i
\(231\) −5.00000 + 8.66025i −0.328976 + 0.569803i
\(232\) 0 0
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −5.00000 + 5.19615i −0.326860 + 0.339683i
\(235\) 8.00000 0.521862
\(236\) −12.0000 + 20.7846i −0.781133 + 1.35296i
\(237\) −1.50000 + 2.59808i −0.0974355 + 0.168763i
\(238\) −10.0000 17.3205i −0.648204 1.12272i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −2.00000 3.46410i −0.129099 0.223607i
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) −14.0000 −0.899954
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 13.0000 22.5167i 0.832240 1.44148i
\(245\) 9.00000 15.5885i 0.574989 0.995910i
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) 0 0
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) 1.00000 1.73205i 0.0632456 0.109545i
\(251\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) 10.0000 0.629941
\(253\) −6.00000 10.3923i −0.377217 0.653359i
\(254\) 11.0000 + 19.0526i 0.690201 + 1.19546i
\(255\) −2.00000 −0.125245
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 11.0000 19.0526i 0.686161 1.18847i −0.286909 0.957958i \(-0.592628\pi\)
0.973070 0.230508i \(-0.0740389\pi\)
\(258\) −1.00000 + 1.73205i −0.0622573 + 0.107833i
\(259\) −10.0000 −0.621370
\(260\) −7.00000 1.73205i −0.434122 0.107417i
\(261\) −4.00000 −0.247594
\(262\) 4.00000 6.92820i 0.247121 0.428026i
\(263\) 5.00000 8.66025i 0.308313 0.534014i −0.669680 0.742650i \(-0.733569\pi\)
0.977993 + 0.208635i \(0.0669022\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) −7.00000 12.1244i −0.428393 0.741999i
\(268\) −14.0000 −0.855186
\(269\) 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) 1.00000 1.73205i 0.0608581 0.105409i
\(271\) −14.5000 + 25.1147i −0.880812 + 1.52561i −0.0303728 + 0.999539i \(0.509669\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −8.00000 −0.485071
\(273\) −12.5000 + 12.9904i −0.756534 + 0.786214i
\(274\) −4.00000 −0.241649
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) −6.00000 −0.359856
\(279\) 3.50000 + 6.06218i 0.209540 + 0.362933i
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 8.00000 + 13.8564i 0.476393 + 0.825137i
\(283\) −2.50000 + 4.33013i −0.148610 + 0.257399i −0.930714 0.365748i \(-0.880813\pi\)
0.782104 + 0.623148i \(0.214146\pi\)
\(284\) −12.0000 + 20.7846i −0.712069 + 1.23334i
\(285\) 0 0
\(286\) 14.0000 + 3.46410i 0.827837 + 0.204837i
\(287\) 30.0000 1.77084
\(288\) 4.00000 6.92820i 0.235702 0.408248i
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −4.00000 6.92820i −0.234888 0.406838i
\(291\) −5.00000 −0.293105
\(292\) −15.0000 25.9808i −0.877809 1.52041i
\(293\) −8.00000 13.8564i −0.467365 0.809500i 0.531940 0.846782i \(-0.321463\pi\)
−0.999305 + 0.0372823i \(0.988130\pi\)
\(294\) 36.0000 2.09956
\(295\) 6.00000 + 10.3923i 0.349334 + 0.605063i
\(296\) 0 0
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) −24.0000 −1.39028
\(299\) −6.00000 20.7846i −0.346989 1.20201i
\(300\) 2.00000 0.115470
\(301\) −2.50000 + 4.33013i −0.144098 + 0.249584i
\(302\) 8.00000 13.8564i 0.460348 0.797347i
\(303\) 9.00000 + 15.5885i 0.517036 + 0.895533i
\(304\) 0 0
\(305\) −6.50000 11.2583i −0.372189 0.644650i
\(306\) −2.00000 3.46410i −0.114332 0.198030i
\(307\) −31.0000 −1.76926 −0.884632 0.466290i \(-0.845590\pi\)
−0.884632 + 0.466290i \(0.845590\pi\)
\(308\) −10.0000 17.3205i −0.569803 0.986928i
\(309\) 3.50000 6.06218i 0.199108 0.344865i
\(310\) −7.00000 + 12.1244i −0.397573 + 0.688617i
\(311\) −22.0000 −1.24751 −0.623753 0.781622i \(-0.714393\pi\)
−0.623753 + 0.781622i \(0.714393\pi\)
\(312\) 0 0
\(313\) −31.0000 −1.75222 −0.876112 0.482108i \(-0.839871\pi\)
−0.876112 + 0.482108i \(0.839871\pi\)
\(314\) 15.0000 25.9808i 0.846499 1.46618i
\(315\) 2.50000 4.33013i 0.140859 0.243975i
\(316\) −3.00000 5.19615i −0.168763 0.292306i
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 4.00000 + 6.92820i 0.224309 + 0.388514i
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 8.00000 0.447214
\(321\) −2.00000 3.46410i −0.111629 0.193347i
\(322\) −30.0000 + 51.9615i −1.67183 + 2.89570i
\(323\) 0 0
\(324\) 2.00000 0.111111
\(325\) −2.50000 + 2.59808i −0.138675 + 0.144115i
\(326\) −30.0000 −1.66155
\(327\) 5.50000 9.52628i 0.304151 0.526804i
\(328\) 0 0
\(329\) 20.0000 + 34.6410i 1.10264 + 1.90982i
\(330\) −4.00000 −0.220193
\(331\) −4.50000 7.79423i −0.247342 0.428410i 0.715445 0.698669i \(-0.246224\pi\)
−0.962788 + 0.270259i \(0.912891\pi\)
\(332\) −8.00000 13.8564i −0.439057 0.760469i
\(333\) −2.00000 −0.109599
\(334\) −12.0000 20.7846i −0.656611 1.13728i
\(335\) −3.50000 + 6.06218i −0.191225 + 0.331212i
\(336\) 10.0000 17.3205i 0.545545 0.944911i
\(337\) −1.00000 −0.0544735 −0.0272367 0.999629i \(-0.508671\pi\)
−0.0272367 + 0.999629i \(0.508671\pi\)
\(338\) 23.0000 + 12.1244i 1.25104 + 0.659478i
\(339\) −2.00000 −0.108625
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) 7.00000 12.1244i 0.379071 0.656571i
\(342\) 0 0
\(343\) 55.0000 2.96972
\(344\) 0 0
\(345\) 3.00000 + 5.19615i 0.161515 + 0.279751i
\(346\) 0 0
\(347\) 8.00000 + 13.8564i 0.429463 + 0.743851i 0.996826 0.0796169i \(-0.0253697\pi\)
−0.567363 + 0.823468i \(0.692036\pi\)
\(348\) 4.00000 6.92820i 0.214423 0.371391i
\(349\) −1.50000 + 2.59808i −0.0802932 + 0.139072i −0.903376 0.428850i \(-0.858919\pi\)
0.823083 + 0.567922i \(0.192252\pi\)
\(350\) 10.0000 0.534522
\(351\) −2.50000 + 2.59808i −0.133440 + 0.138675i
\(352\) −16.0000 −0.852803
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) −12.0000 + 20.7846i −0.637793 + 1.10469i
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 28.0000 1.48400
\(357\) −5.00000 8.66025i −0.264628 0.458349i
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 2.00000 0.105556 0.0527780 0.998606i \(-0.483192\pi\)
0.0527780 + 0.998606i \(0.483192\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 22.0000 38.1051i 1.15629 2.00276i
\(363\) −7.00000 −0.367405
\(364\) −10.0000 34.6410i −0.524142 1.81568i
\(365\) −15.0000 −0.785136
\(366\) 13.0000 22.5167i 0.679521 1.17696i
\(367\) −3.50000 + 6.06218i −0.182699 + 0.316443i −0.942799 0.333363i \(-0.891817\pi\)
0.760100 + 0.649806i \(0.225150\pi\)
\(368\) 12.0000 + 20.7846i 0.625543 + 1.08347i
\(369\) 6.00000 0.312348
\(370\) −2.00000 3.46410i −0.103975 0.180090i
\(371\) 10.0000 + 17.3205i 0.519174 + 0.899236i
\(372\) −14.0000 −0.725866
\(373\) −6.50000 11.2583i −0.336557 0.582934i 0.647225 0.762299i \(-0.275929\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) 4.00000 + 13.8564i 0.206010 + 0.713641i
\(378\) 10.0000 0.514344
\(379\) 2.50000 4.33013i 0.128416 0.222424i −0.794647 0.607072i \(-0.792344\pi\)
0.923063 + 0.384648i \(0.125677\pi\)
\(380\) 0 0
\(381\) 5.50000 + 9.52628i 0.281774 + 0.488046i
\(382\) 24.0000 1.22795
\(383\) 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i \(-0.0145596\pi\)
−0.539076 + 0.842257i \(0.681226\pi\)
\(384\) 0 0
\(385\) −10.0000 −0.509647
\(386\) 11.0000 + 19.0526i 0.559885 + 0.969750i
\(387\) −0.500000 + 0.866025i −0.0254164 + 0.0440225i
\(388\) 5.00000 8.66025i 0.253837 0.439658i
\(389\) 8.00000 0.405616 0.202808 0.979219i \(-0.434993\pi\)
0.202808 + 0.979219i \(0.434993\pi\)
\(390\) −7.00000 1.73205i −0.354459 0.0877058i
\(391\) 12.0000 0.606866
\(392\) 0 0
\(393\) 2.00000 3.46410i 0.100887 0.174741i
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) −3.00000 −0.150946
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) 7.50000 + 12.9904i 0.376414 + 0.651969i 0.990538 0.137241i \(-0.0438236\pi\)
−0.614123 + 0.789210i \(0.710490\pi\)
\(398\) 34.0000 1.70427
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) −8.00000 + 13.8564i −0.399501 + 0.691956i −0.993664 0.112388i \(-0.964150\pi\)
0.594163 + 0.804344i \(0.297483\pi\)
\(402\) −14.0000 −0.698257
\(403\) 17.5000 18.1865i 0.871737 0.905936i
\(404\) −36.0000 −1.79107
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 20.0000 34.6410i 0.992583 1.71920i
\(407\) 2.00000 + 3.46410i 0.0991363 + 0.171709i
\(408\) 0 0
\(409\) 7.50000 + 12.9904i 0.370851 + 0.642333i 0.989697 0.143180i \(-0.0457327\pi\)
−0.618846 + 0.785513i \(0.712399\pi\)
\(410\) 6.00000 + 10.3923i 0.296319 + 0.513239i
\(411\) −2.00000 −0.0986527
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) −30.0000 + 51.9615i −1.47620 + 2.55686i
\(414\) −6.00000 + 10.3923i −0.294884 + 0.510754i
\(415\) −8.00000 −0.392705
\(416\) −28.0000 6.92820i −1.37281 0.339683i
\(417\) −3.00000 −0.146911
\(418\) 0 0
\(419\) −19.0000 + 32.9090i −0.928211 + 1.60771i −0.141896 + 0.989882i \(0.545320\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(420\) 5.00000 + 8.66025i 0.243975 + 0.422577i
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) −15.0000 25.9808i −0.730189 1.26472i
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 0 0
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) −12.0000 + 20.7846i −0.581402 + 1.00702i
\(427\) 32.5000 56.2917i 1.57279 2.72414i
\(428\) 8.00000 0.386695
\(429\) 7.00000 + 1.73205i 0.337963 + 0.0836242i
\(430\) −2.00000 −0.0964486
\(431\) 14.0000 24.2487i 0.674356 1.16802i −0.302300 0.953213i \(-0.597755\pi\)
0.976657 0.214807i \(-0.0689121\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) −0.500000 0.866025i −0.0240285 0.0416185i 0.853761 0.520665i \(-0.174316\pi\)
−0.877790 + 0.479046i \(0.840983\pi\)
\(434\) −70.0000 −3.36011
\(435\) −2.00000 3.46410i −0.0958927 0.166091i
\(436\) 11.0000 + 19.0526i 0.526804 + 0.912452i
\(437\) 0 0
\(438\) −15.0000 25.9808i −0.716728 1.24141i
\(439\) −7.50000 + 12.9904i −0.357955 + 0.619997i −0.987619 0.156871i \(-0.949859\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) −10.0000 + 10.3923i −0.475651 + 0.494312i
\(443\) 26.0000 1.23530 0.617649 0.786454i \(-0.288085\pi\)
0.617649 + 0.786454i \(0.288085\pi\)
\(444\) 2.00000 3.46410i 0.0949158 0.164399i
\(445\) 7.00000 12.1244i 0.331832 0.574750i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) −12.0000 −0.567581
\(448\) 20.0000 + 34.6410i 0.944911 + 1.63663i
\(449\) −9.00000 15.5885i −0.424736 0.735665i 0.571660 0.820491i \(-0.306300\pi\)
−0.996396 + 0.0848262i \(0.972967\pi\)
\(450\) 2.00000 0.0942809
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 2.00000 3.46410i 0.0940721 0.162938i
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 20.0000 0.938647
\(455\) −17.5000 4.33013i −0.820413 0.202999i
\(456\) 0 0
\(457\) −17.5000 + 30.3109i −0.818615 + 1.41788i 0.0880870 + 0.996113i \(0.471925\pi\)
−0.906702 + 0.421771i \(0.861409\pi\)
\(458\) −14.0000 + 24.2487i −0.654177 + 1.13307i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) −12.0000 −0.559503
\(461\) 1.00000 + 1.73205i 0.0465746 + 0.0806696i 0.888373 0.459123i \(-0.151836\pi\)
−0.841798 + 0.539792i \(0.818503\pi\)
\(462\) −10.0000 17.3205i −0.465242 0.805823i
\(463\) 3.00000 0.139422 0.0697109 0.997567i \(-0.477792\pi\)
0.0697109 + 0.997567i \(0.477792\pi\)
\(464\) −8.00000 13.8564i −0.371391 0.643268i
\(465\) −3.50000 + 6.06218i −0.162309 + 0.281127i
\(466\) 14.0000 24.2487i 0.648537 1.12330i
\(467\) −4.00000 −0.185098 −0.0925490 0.995708i \(-0.529501\pi\)
−0.0925490 + 0.995708i \(0.529501\pi\)
\(468\) −2.00000 6.92820i −0.0924500 0.320256i
\(469\) −35.0000 −1.61615
\(470\) −8.00000 + 13.8564i −0.369012 + 0.639148i
\(471\) 7.50000 12.9904i 0.345582 0.598565i
\(472\) 0 0
\(473\) 2.00000 0.0919601
\(474\) −3.00000 5.19615i −0.137795 0.238667i
\(475\) 0 0
\(476\) 20.0000 0.916698
\(477\) 2.00000 + 3.46410i 0.0915737 + 0.158610i
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −21.0000 + 36.3731i −0.959514 + 1.66193i −0.235833 + 0.971794i \(0.575782\pi\)
−0.723681 + 0.690134i \(0.757551\pi\)
\(480\) 8.00000 0.365148
\(481\) 2.00000 + 6.92820i 0.0911922 + 0.315899i
\(482\) 20.0000 0.910975
\(483\) −15.0000 + 25.9808i −0.682524 + 1.18217i
\(484\) 7.00000 12.1244i 0.318182 0.551107i
\(485\) −2.50000 4.33013i −0.113519 0.196621i
\(486\) 2.00000 0.0907218
\(487\) 14.0000 + 24.2487i 0.634401 + 1.09881i 0.986642 + 0.162905i \(0.0520863\pi\)
−0.352241 + 0.935909i \(0.614580\pi\)
\(488\) 0 0
\(489\) −15.0000 −0.678323
\(490\) 18.0000 + 31.1769i 0.813157 + 1.40843i
\(491\) 12.0000 20.7846i 0.541552 0.937996i −0.457263 0.889332i \(-0.651170\pi\)
0.998815 0.0486647i \(-0.0154966\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) −14.0000 + 24.2487i −0.628619 + 1.08880i
\(497\) −30.0000 + 51.9615i −1.34568 + 2.33079i
\(498\) −8.00000 13.8564i −0.358489 0.620920i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 1.00000 + 1.73205i 0.0447214 + 0.0774597i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 3.00000 + 5.19615i 0.133763 + 0.231685i 0.925124 0.379664i \(-0.123960\pi\)
−0.791361 + 0.611349i \(0.790627\pi\)
\(504\) 0 0
\(505\) −9.00000 + 15.5885i −0.400495 + 0.693677i
\(506\) 24.0000 1.06693
\(507\) 11.5000 + 6.06218i 0.510733 + 0.269231i
\(508\) −22.0000 −0.976092
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) −37.5000 64.9519i −1.65890 2.87330i
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) 22.0000 + 38.1051i 0.970378 + 1.68074i
\(515\) 7.00000 0.308457
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 8.00000 13.8564i 0.351840 0.609404i
\(518\) 10.0000 17.3205i 0.439375 0.761019i
\(519\) 0 0
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 4.00000 6.92820i 0.175075 0.303239i
\(523\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(524\) 4.00000 + 6.92820i 0.174741 + 0.302660i
\(525\) 5.00000 0.218218
\(526\) 10.0000 + 17.3205i 0.436021 + 0.755210i
\(527\) 7.00000 + 12.1244i 0.304925 + 0.528145i
\(528\) −8.00000 −0.348155
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −4.00000 + 6.92820i −0.173749 + 0.300942i
\(531\) −6.00000 + 10.3923i −0.260378 + 0.450988i
\(532\) 0 0
\(533\) −6.00000 20.7846i −0.259889 0.900281i
\(534\) 28.0000 1.21168
\(535\) 2.00000 3.46410i 0.0864675 0.149766i
\(536\) 0 0
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) −12.0000 −0.517357
\(539\) −18.0000 31.1769i −0.775315 1.34288i
\(540\) 1.00000 + 1.73205i 0.0430331 + 0.0745356i
\(541\) 29.0000 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) −29.0000 50.2295i −1.24566 2.15754i
\(543\) 11.0000 19.0526i 0.472055 0.817624i
\(544\) 8.00000 13.8564i 0.342997 0.594089i
\(545\) 11.0000 0.471188
\(546\) −10.0000 34.6410i −0.427960 1.48250i
\(547\) −9.00000 −0.384812 −0.192406 0.981315i \(-0.561629\pi\)
−0.192406 + 0.981315i \(0.561629\pi\)
\(548\) 2.00000 3.46410i 0.0854358 0.147979i
\(549\) 6.50000 11.2583i 0.277413 0.480494i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) 0 0
\(552\) 0 0
\(553\) −7.50000 12.9904i −0.318932 0.552407i
\(554\) 20.0000 0.849719
\(555\) −1.00000 1.73205i −0.0424476 0.0735215i
\(556\) 3.00000 5.19615i 0.127228 0.220366i
\(557\) 10.0000 17.3205i 0.423714 0.733893i −0.572586 0.819845i \(-0.694060\pi\)
0.996299 + 0.0859514i \(0.0273930\pi\)
\(558\) −14.0000 −0.592667
\(559\) 3.50000 + 0.866025i 0.148034 + 0.0366290i
\(560\) 20.0000 0.845154
\(561\) −2.00000 + 3.46410i −0.0844401 + 0.146254i
\(562\) 12.0000 20.7846i 0.506189 0.876746i
\(563\) −13.0000 22.5167i −0.547885 0.948964i −0.998419 0.0562051i \(-0.982100\pi\)
0.450535 0.892759i \(-0.351233\pi\)
\(564\) −16.0000 −0.673722
\(565\) −1.00000 1.73205i −0.0420703 0.0728679i
\(566\) −5.00000 8.66025i −0.210166 0.364018i
\(567\) 5.00000 0.209980
\(568\) 0 0
\(569\) 10.0000 17.3205i 0.419222 0.726113i −0.576640 0.816999i \(-0.695636\pi\)
0.995861 + 0.0908852i \(0.0289696\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) −10.0000 + 10.3923i −0.418121 + 0.434524i
\(573\) 12.0000 0.501307
\(574\) −30.0000 + 51.9615i −1.25218 + 2.16883i
\(575\) −3.00000 + 5.19615i −0.125109 + 0.216695i
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 13.0000 + 22.5167i 0.540729 + 0.936570i
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 8.00000 0.332182
\(581\) −20.0000 34.6410i −0.829740 1.43715i
\(582\) 5.00000 8.66025i 0.207257 0.358979i
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) 0 0
\(585\) −3.50000 0.866025i −0.144707 0.0358057i
\(586\) 32.0000 1.32191
\(587\) −14.0000 + 24.2487i −0.577842 + 1.00085i 0.417885 + 0.908500i \(0.362772\pi\)
−0.995726 + 0.0923513i \(0.970562\pi\)
\(588\) −18.0000 + 31.1769i −0.742307 + 1.28571i
\(589\) 0 0
\(590\) −24.0000 −0.988064
\(591\) 6.00000 + 10.3923i 0.246807 + 0.427482i
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) −10.0000 −0.410651 −0.205325 0.978694i \(-0.565825\pi\)
−0.205325 + 0.978694i \(0.565825\pi\)
\(594\) −2.00000 3.46410i −0.0820610 0.142134i
\(595\) 5.00000 8.66025i 0.204980 0.355036i
\(596\) 12.0000 20.7846i 0.491539 0.851371i
\(597\) 17.0000 0.695764
\(598\) 42.0000 + 10.3923i 1.71751 + 0.424973i
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 0 0
\(601\) −11.0000 + 19.0526i −0.448699 + 0.777170i −0.998302 0.0582563i \(-0.981446\pi\)
0.549602 + 0.835426i \(0.314779\pi\)
\(602\) −5.00000 8.66025i −0.203785 0.352966i
\(603\) −7.00000 −0.285062
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) −36.0000 −1.46240
\(607\) −8.00000 13.8564i −0.324710 0.562414i 0.656744 0.754114i \(-0.271933\pi\)
−0.981454 + 0.191700i \(0.938600\pi\)
\(608\) 0 0
\(609\) 10.0000 17.3205i 0.405220 0.701862i
\(610\) 26.0000 1.05271
\(611\) 20.0000 20.7846i 0.809113 0.840855i
\(612\) 4.00000 0.161690
\(613\) 7.50000 12.9904i 0.302922 0.524677i −0.673874 0.738846i \(-0.735371\pi\)
0.976797 + 0.214169i \(0.0687045\pi\)
\(614\) 31.0000 53.6936i 1.25106 2.16690i
\(615\) 3.00000 + 5.19615i 0.120972 + 0.209529i
\(616\) 0 0
\(617\) −3.00000 5.19615i −0.120775 0.209189i 0.799298 0.600935i \(-0.205205\pi\)
−0.920074 + 0.391745i \(0.871871\pi\)
\(618\) 7.00000 + 12.1244i 0.281581 + 0.487713i
\(619\) 37.0000 1.48716 0.743578 0.668649i \(-0.233127\pi\)
0.743578 + 0.668649i \(0.233127\pi\)
\(620\) −7.00000 12.1244i −0.281127 0.486926i
\(621\) −3.00000 + 5.19615i −0.120386 + 0.208514i
\(622\) 22.0000 38.1051i 0.882120 1.52788i
\(623\) 70.0000 2.80449
\(624\) −14.0000 3.46410i −0.560449 0.138675i
\(625\) 1.00000 0.0400000
\(626\) 31.0000 53.6936i 1.23901 2.14603i
\(627\) 0 0
\(628\) 15.0000 + 25.9808i 0.598565 + 1.03675i
\(629\) −4.00000 −0.159490
\(630\) 5.00000 + 8.66025i 0.199205 + 0.345033i
\(631\) −3.50000 6.06218i −0.139333 0.241331i 0.787911 0.615789i \(-0.211162\pi\)
−0.927244 + 0.374457i \(0.877829\pi\)
\(632\) 0 0
\(633\) −7.50000 12.9904i −0.298098 0.516321i
\(634\) −12.0000 + 20.7846i −0.476581 + 0.825462i
\(635\) −5.50000 + 9.52628i −0.218261 + 0.378039i
\(636\) −8.00000 −0.317221
\(637\) −18.0000 62.3538i −0.713186 2.47055i
\(638\) −16.0000 −0.633446
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) 0 0
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 8.00000 0.315735
\(643\) 9.50000 + 16.4545i 0.374643 + 0.648901i 0.990274 0.139134i \(-0.0444318\pi\)
−0.615630 + 0.788035i \(0.711098\pi\)
\(644\) −30.0000 51.9615i −1.18217 2.04757i
\(645\) −1.00000 −0.0393750
\(646\) 0 0
\(647\) −19.0000 + 32.9090i −0.746967 + 1.29378i 0.202303 + 0.979323i \(0.435157\pi\)
−0.949270 + 0.314462i \(0.898176\pi\)
\(648\) 0 0
\(649\) 24.0000 0.942082
\(650\) −2.00000 6.92820i −0.0784465 0.271746i
\(651\) −35.0000 −1.37176
\(652\) 15.0000 25.9808i 0.587445 1.01749i
\(653\) −21.0000 + 36.3731i −0.821794 + 1.42339i 0.0825519 + 0.996587i \(0.473693\pi\)
−0.904345 + 0.426801i \(0.859640\pi\)
\(654\) 11.0000 + 19.0526i 0.430134 + 0.745014i
\(655\) 4.00000 0.156293
\(656\) 12.0000 + 20.7846i 0.468521 + 0.811503i
\(657\) −7.50000 12.9904i −0.292603 0.506803i
\(658\) −80.0000 −3.11872
\(659\) 12.0000 + 20.7846i 0.467454 + 0.809653i 0.999309 0.0371821i \(-0.0118382\pi\)
−0.531855 + 0.846836i \(0.678505\pi\)
\(660\) 2.00000 3.46410i 0.0778499 0.134840i
\(661\) −17.5000 + 30.3109i −0.680671 + 1.17896i 0.294105 + 0.955773i \(0.404978\pi\)
−0.974776 + 0.223184i \(0.928355\pi\)
\(662\) 18.0000 0.699590
\(663\) −5.00000 + 5.19615i −0.194184 + 0.201802i
\(664\) 0 0
\(665\) 0 0
\(666\) 2.00000 3.46410i 0.0774984 0.134231i
\(667\) 12.0000 + 20.7846i 0.464642 + 0.804783i
\(668\) 24.0000 0.928588
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) −7.00000 12.1244i −0.270434 0.468405i
\(671\) −26.0000 −1.00372
\(672\) 20.0000 + 34.6410i 0.771517 + 1.33631i
\(673\) −16.5000 + 28.5788i −0.636028 + 1.10163i 0.350268 + 0.936650i \(0.386091\pi\)
−0.986296 + 0.164984i \(0.947243\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 1.00000 0.0384900
\(676\) −22.0000 + 13.8564i −0.846154 + 0.532939i
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 2.00000 3.46410i 0.0768095 0.133038i
\(679\) 12.5000 21.6506i 0.479706 0.830875i
\(680\) 0 0
\(681\) 10.0000 0.383201
\(682\) 14.0000 + 24.2487i 0.536088 + 0.928531i
\(683\) 10.0000 + 17.3205i 0.382639 + 0.662751i 0.991439 0.130573i \(-0.0416818\pi\)
−0.608799 + 0.793324i \(0.708349\pi\)
\(684\) 0 0
\(685\) −1.00000 1.73205i −0.0382080 0.0661783i
\(686\) −55.0000 + 95.2628i −2.09991 + 3.63715i
\(687\) −7.00000 + 12.1244i −0.267067 + 0.462573i
\(688\) −4.00000 −0.152499
\(689\) 10.0000 10.3923i 0.380970 0.395915i
\(690\) −12.0000 −0.456832
\(691\) −18.5000 + 32.0429i −0.703773 + 1.21897i 0.263359 + 0.964698i \(0.415170\pi\)
−0.967132 + 0.254273i \(0.918164\pi\)
\(692\) 0 0
\(693\) −5.00000 8.66025i −0.189934 0.328976i
\(694\) −32.0000 −1.21470
\(695\) −1.50000 2.59808i −0.0568982 0.0985506i
\(696\) 0 0
\(697\) 12.0000 0.454532
\(698\) −3.00000 5.19615i −0.113552 0.196677i
\(699\) 7.00000 12.1244i 0.264764 0.458585i
\(700\) −5.00000 + 8.66025i −0.188982 + 0.327327i
\(701\) 40.0000 1.51078 0.755390 0.655276i \(-0.227448\pi\)
0.755390 + 0.655276i \(0.227448\pi\)
\(702\) −2.00000 6.92820i −0.0754851 0.261488i
\(703\) 0 0
\(704\) 8.00000 13.8564i 0.301511 0.522233i
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) −6.00000 10.3923i −0.225813 0.391120i
\(707\) −90.0000 −3.38480
\(708\) −12.0000 20.7846i −0.450988 0.781133i
\(709\) 11.5000 + 19.9186i 0.431892 + 0.748058i 0.997036 0.0769337i \(-0.0245130\pi\)
−0.565145 + 0.824992i \(0.691180\pi\)
\(710\) −24.0000 −0.900704
\(711\) −1.50000 2.59808i −0.0562544 0.0974355i
\(712\) 0 0
\(713\) 21.0000 36.3731i 0.786456 1.36218i
\(714\) 20.0000 0.748481
\(715\) 2.00000 + 6.92820i 0.0747958 + 0.259100i
\(716\) −12.0000 −0.448461
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) −2.00000 + 3.46410i −0.0746393 + 0.129279i
\(719\) −20.0000 34.6410i −0.745874 1.29189i −0.949785 0.312903i \(-0.898699\pi\)
0.203911 0.978989i \(-0.434635\pi\)
\(720\) 4.00000 0.149071
\(721\) 17.5000 + 30.3109i 0.651734 + 1.12884i
\(722\) 19.0000 + 32.9090i 0.707107 + 1.22474i
\(723\) 10.0000 0.371904
\(724\) 22.0000 + 38.1051i 0.817624 + 1.41617i
\(725\) 2.00000 3.46410i 0.0742781 0.128654i
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) 9.00000 0.333792 0.166896 0.985975i \(-0.446626\pi\)
0.166896 + 0.985975i \(0.446626\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 15.0000 25.9808i 0.555175 0.961591i
\(731\) −1.00000 + 1.73205i −0.0369863 + 0.0640622i
\(732\) 13.0000 + 22.5167i 0.480494 + 0.832240i
\(733\) 7.00000 0.258551 0.129275 0.991609i \(-0.458735\pi\)
0.129275 + 0.991609i \(0.458735\pi\)
\(734\) −7.00000 12.1244i −0.258375 0.447518i
\(735\) 9.00000 + 15.5885i 0.331970 + 0.574989i
\(736\) −48.0000 −1.76930
\(737\) 7.00000 + 12.1244i 0.257848 + 0.446606i
\(738\) −6.00000 + 10.3923i −0.220863 + 0.382546i
\(739\) 18.0000 31.1769i 0.662141 1.14686i −0.317911 0.948120i \(-0.602981\pi\)
0.980052 0.198741i \(-0.0636852\pi\)
\(740\) 4.00000 0.147043
\(741\) 0 0
\(742\) −40.0000 −1.46845
\(743\) −12.0000 + 20.7846i −0.440237 + 0.762513i −0.997707 0.0676840i \(-0.978439\pi\)
0.557470 + 0.830197i \(0.311772\pi\)
\(744\) 0 0
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 26.0000 0.951928
\(747\) −4.00000 6.92820i −0.146352 0.253490i
\(748\) −4.00000 6.92820i −0.146254 0.253320i
\(749\) 20.0000 0.730784
\(750\) 1.00000 + 1.73205i 0.0365148 + 0.0632456i
\(751\) 14.0000 24.2487i 0.510867 0.884848i −0.489053 0.872254i \(-0.662658\pi\)
0.999921 0.0125942i \(-0.00400897\pi\)
\(752\) −16.0000 + 27.7128i −0.583460 + 1.01058i
\(753\) 0 0
\(754\) −28.0000 6.92820i −1.01970 0.252310i
\(755\) 8.00000 0.291150
\(756\) −5.00000 + 8.66025i −0.181848 + 0.314970i
\(757\) −1.00000 + 1.73205i −0.0363456 + 0.0629525i −0.883626 0.468193i \(-0.844905\pi\)
0.847280 + 0.531146i \(0.178238\pi\)
\(758\) 5.00000 + 8.66025i 0.181608 + 0.314555i
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) 18.0000 + 31.1769i 0.652499 + 1.13016i 0.982514 + 0.186187i \(0.0596129\pi\)
−0.330015 + 0.943976i \(0.607054\pi\)
\(762\) −22.0000 −0.796976
\(763\) 27.5000 + 47.6314i 0.995567 + 1.72437i
\(764\) −12.0000 + 20.7846i −0.434145 + 0.751961i
\(765\) 1.00000 1.73205i 0.0361551 0.0626224i
\(766\) −36.0000 −1.30073
\(767\) 42.0000 + 10.3923i 1.51653 + 0.375244i
\(768\) 16.0000 0.577350
\(769\) 17.0000 29.4449i 0.613036 1.06181i −0.377690 0.925932i \(-0.623282\pi\)
0.990726 0.135877i \(-0.0433852\pi\)
\(770\) 10.0000 17.3205i 0.360375 0.624188i
\(771\) 11.0000 + 19.0526i 0.396155 + 0.686161i
\(772\) −22.0000 −0.791797
\(773\) −23.0000 39.8372i −0.827253 1.43284i −0.900186 0.435507i \(-0.856569\pi\)
0.0729331 0.997337i \(-0.476764\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) −7.00000 −0.251447
\(776\) 0 0
\(777\) 5.00000 8.66025i 0.179374 0.310685i
\(778\) −8.00000 + 13.8564i −0.286814 + 0.496776i
\(779\) 0 0
\(780\) 5.00000 5.19615i 0.179029 0.186052i
\(781\) 24.0000 0.858788
\(782\) −12.0000 + 20.7846i −0.429119 + 0.743256i
\(783\) 2.00000 3.46410i 0.0714742 0.123797i
\(784\) 36.0000 + 62.3538i 1.28571 + 2.22692i
\(785\) 15.0000 0.535373
\(786\) 4.00000 + 6.92820i 0.142675 + 0.247121i
\(787\) −8.50000 14.7224i −0.302992 0.524798i 0.673820 0.738896i \(-0.264652\pi\)
−0.976812 + 0.214097i \(0.931319\pi\)
\(788\) −24.0000 −0.854965
\(789\) 5.00000 + 8.66025i 0.178005 + 0.308313i
\(790\) 3.00000 5.19615i 0.106735 0.184871i
\(791\) 5.00000 8.66025i 0.177780 0.307923i
\(792\) 0 0
\(793\) −45.5000 11.2583i −1.61575 0.399795i
\(794\) −30.0000 −1.06466
\(795\) −2.00000 + 3.46410i −0.0709327 + 0.122859i
\(796\) −17.0000 + 29.4449i −0.602549 + 1.04365i
\(797\) −15.0000 25.9808i −0.531327 0.920286i −0.999331 0.0365596i \(-0.988360\pi\)
0.468004 0.883726i \(-0.344973\pi\)
\(798\) 0 0
\(799\) 8.00000 + 13.8564i 0.283020 + 0.490204i
\(800\) 4.00000 + 6.92820i 0.141421 + 0.244949i
\(801\) 14.0000 0.494666
\(802\) −16.0000 27.7128i −0.564980 0.978573i
\(803\) −15.0000 + 25.9808i −0.529339 + 0.916841i
\(804\) 7.00000 12.1244i 0.246871 0.427593i
\(805\) −30.0000 −1.05736
\(806\) 14.0000 + 48.4974i 0.493129 + 1.70825i
\(807\) −6.00000 −0.211210
\(808\) 0 0
\(809\) −2.00000 + 3.46410i −0.0703163 + 0.121791i −0.899040 0.437867i \(-0.855734\pi\)
0.828724 + 0.559658i \(0.189068\pi\)
\(810\) 1.00000 + 1.73205i 0.0351364 + 0.0608581i
\(811\) 45.0000 1.58016 0.790082 0.613001i \(-0.210038\pi\)
0.790082 + 0.613001i \(0.210038\pi\)
\(812\) 20.0000 + 34.6410i 0.701862 + 1.21566i
\(813\) −14.5000 25.1147i −0.508537 0.880812i
\(814\) −8.00000 −0.280400
\(815\) −7.50000 12.9904i −0.262714 0.455033i
\(816\) 4.00000 6.92820i 0.140028 0.242536i
\(817\) 0 0
\(818\) −30.0000 −1.04893
\(819\) −5.00000 17.3205i −0.174714 0.605228i
\(820\) −12.0000 −0.419058
\(821\) 11.0000 19.0526i 0.383903 0.664939i −0.607714 0.794156i \(-0.707913\pi\)
0.991616 + 0.129217i \(0.0412465\pi\)
\(822\) 2.00000 3.46410i 0.0697580 0.120824i
\(823\) −10.0000 17.3205i −0.348578 0.603755i 0.637419 0.770517i \(-0.280002\pi\)
−0.985997 + 0.166762i \(0.946669\pi\)
\(824\) 0 0
\(825\) −1.00000 1.73205i −0.0348155 0.0603023i
\(826\) −60.0000 103.923i −2.08767 3.61595i
\(827\) 46.0000 1.59958 0.799788 0.600282i \(-0.204945\pi\)
0.799788 + 0.600282i \(0.204945\pi\)
\(828\) −6.00000 10.3923i −0.208514 0.361158i
\(829\) 5.50000 9.52628i 0.191023 0.330861i −0.754567 0.656223i \(-0.772153\pi\)
0.945589 + 0.325362i \(0.105486\pi\)
\(830\) 8.00000 13.8564i 0.277684 0.480963i
\(831\) 10.0000 0.346896
\(832\) 20.0000 20.7846i 0.693375 0.720577i
\(833\) 36.0000 1.24733
\(834\) 3.00000 5.19615i 0.103882 0.179928i
\(835\) 6.00000 10.3923i 0.207639 0.359641i
\(836\) 0 0
\(837\) −7.00000 −0.241955
\(838\) −38.0000 65.8179i −1.31269 2.27364i
\(839\) 17.0000 + 29.4449i 0.586905 + 1.01655i 0.994635 + 0.103447i \(0.0329872\pi\)
−0.407730 + 0.913103i \(0.633679\pi\)
\(840\) 0 0
\(841\) 6.50000 + 11.2583i 0.224138 + 0.388218i
\(842\) 23.0000 39.8372i 0.792632 1.37288i
\(843\) 6.00000 10.3923i 0.206651 0.357930i
\(844\) 30.0000 1.03264
\(845\) 0.500000 + 12.9904i 0.0172005 + 0.446883i
\(846\) −16.0000 −0.550091
\(847\) 17.5000 30.3109i 0.601307 1.04149i
\(848\) −8.00000 + 13.8564i −0.274721 + 0.475831i
\(849\) −2.50000 4.33013i −0.0857998 0.148610i
\(850\) 4.00000 0.137199
\(851\) 6.00000 + 10.3923i 0.205677 + 0.356244i
\(852\) −12.0000 20.7846i −0.411113 0.712069i
\(853\) 9.00000 0.308154 0.154077 0.988059i \(-0.450760\pi\)
0.154077 + 0.988059i \(0.450760\pi\)
\(854\) 65.0000 + 112.583i 2.22425 + 3.85252i
\(855\) 0 0
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) −10.0000 + 10.3923i −0.341394 + 0.354787i
\(859\) 43.0000 1.46714 0.733571 0.679613i \(-0.237852\pi\)
0.733571 + 0.679613i \(0.237852\pi\)
\(860\) 1.00000 1.73205i 0.0340997 0.0590624i
\(861\) −15.0000 + 25.9808i −0.511199 + 0.885422i
\(862\) 28.0000 + 48.4974i 0.953684 + 1.65183i
\(863\) 6.00000 0.204242 0.102121 0.994772i \(-0.467437\pi\)
0.102121 + 0.994772i \(0.467437\pi\)
\(864\) 4.00000 + 6.92820i 0.136083 + 0.235702i
\(865\) 0 0
\(866\) 2.00000 0.0679628
\(867\) 6.50000 + 11.2583i 0.220752 + 0.382353i
\(868\) 35.0000 60.6218i 1.18798 2.05764i
\(869\) −3.00000 + 5.19615i −0.101768 + 0.176267i
\(870\) 8.00000 0.271225
\(871\) 7.00000 + 24.2487i 0.237186 + 0.821636i
\(872\) 0 0
\(873\) 2.50000 4.33013i 0.0846122 0.146553i
\(874\) 0 0
\(875\) 2.50000 + 4.33013i 0.0845154 + 0.146385i
\(876\) 30.0000 1.01361
\(877\) −3.00000 5.19615i −0.101303 0.175462i 0.810919 0.585159i \(-0.198968\pi\)
−0.912222 + 0.409697i \(0.865634\pi\)
\(878\) −15.0000 25.9808i −0.506225 0.876808i
\(879\) 16.0000 0.539667
\(880\) −4.00000 6.92820i −0.134840 0.233550i
\(881\) −10.0000 + 17.3205i −0.336909 + 0.583543i −0.983850 0.178997i \(-0.942715\pi\)
0.646941 + 0.762540i \(0.276048\pi\)
\(882\) −18.0000 + 31.1769i −0.606092 + 1.04978i
\(883\) −25.0000 −0.841317 −0.420658 0.907219i \(-0.638201\pi\)
−0.420658 + 0.907219i \(0.638201\pi\)
\(884\) −4.00000 13.8564i −0.134535 0.466041i
\(885\) −12.0000 −0.403376
\(886\) −26.0000 + 45.0333i −0.873487 + 1.51292i
\(887\) 22.0000 38.1051i 0.738688 1.27944i −0.214399 0.976746i \(-0.568779\pi\)
0.953086 0.302698i \(-0.0978875\pi\)
\(888\) 0 0
\(889\) −55.0000 −1.84464
\(890\) 14.0000 + 24.2487i 0.469281 + 0.812819i
\(891\) −1.00000 1.73205i −0.0335013 0.0580259i
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) 12.0000 20.7846i 0.401340 0.695141i
\(895\) −3.00000 + 5.19615i −0.100279 + 0.173688i
\(896\) 0 0
\(897\) 21.0000 + 5.19615i 0.701170 + 0.173494i
\(898\) 36.0000 1.20134
\(899\) −14.0000 + 24.2487i −0.466926 + 0.808740i
\(900\) −1.00000 + 1.73205i −0.0333333 + 0.0577350i
\(901\) 4.00000 + 6.92820i 0.133259 + 0.230812i
\(902\) 24.0000 0.799113
\(903\) −2.50000 4.33013i −0.0831948 0.144098i
\(904\) 0 0
\(905\) 22.0000 0.731305
\(906\) 8.00000 + 13.8564i 0.265782 + 0.460348i
\(907\) −10.0000 + 17.3205i −0.332045 + 0.575118i −0.982913 0.184073i \(-0.941072\pi\)
0.650868 + 0.759191i \(0.274405\pi\)
\(908\) −10.0000 + 17.3205i −0.331862 + 0.574801i
\(909\) −18.0000 −0.597022
\(910\) 25.0000 25.9808i 0.828742 0.861254i
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −8.00000 + 13.8564i −0.264761 + 0.458580i
\(914\) −35.0000 60.6218i −1.15770 2.00519i
\(915\) 13.0000 0.429767
\(916\) −14.0000 24.2487i −0.462573 0.801200i
\(917\) 10.0000 + 17.3205i 0.330229 + 0.571974i
\(918\) 4.00000 0.132020
\(919\) −4.00000 6.92820i −0.131948 0.228540i 0.792480 0.609898i \(-0.208790\pi\)
−0.924427 + 0.381358i \(0.875456\pi\)
\(920\) 0 0
\(921\) 15.5000 26.8468i 0.510742 0.884632i
\(922\) −4.00000 −0.131733
\(923\) 42.0000 + 10.3923i 1.38245 + 0.342067i
\(924\) 20.0000 0.657952
\(925\) 1.00000 1.73205i 0.0328798 0.0569495i
\(926\) −3.00000 + 5.19615i −0.0985861 + 0.170756i
\(927\) 3.50000 + 6.06218i 0.114955 + 0.199108i
\(928\) 32.0000 1.05045
\(929\) −26.0000 45.0333i −0.853032 1.47750i −0.878459 0.477819i \(-0.841428\pi\)
0.0254262 0.999677i \(-0.491906\pi\)
\(930\) −7.00000 12.1244i −0.229539 0.397573i
\(931\) 0 0
\(932\) 14.0000 + 24.2487i 0.458585 + 0.794293i
\(933\) 11.0000 19.0526i 0.360124 0.623753i
\(934\) 4.00000 6.92820i 0.130884 0.226698i
\(935\) −4.00000 −0.130814
\(936\) 0 0
\(937\) −30.0000 −0.980057 −0.490029 0.871706i \(-0.663014\pi\)
−0.490029 + 0.871706i \(0.663014\pi\)
\(938\) 35.0000 60.6218i 1.14279 1.97937i
\(939\) 15.5000 26.8468i 0.505823 0.876112i
\(940\) −8.00000 13.8564i −0.260931 0.451946i
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 15.0000 + 25.9808i 0.488726 + 0.846499i
\(943\) −18.0000 31.1769i −0.586161 1.01526i
\(944\) −48.0000 −1.56227
\(945\) 2.50000 + 4.33013i 0.0813250 + 0.140859i
\(946\) −2.00000 + 3.46410i −0.0650256 + 0.112628i
\(947\) −9.00000 + 15.5885i −0.292461 + 0.506557i −0.974391 0.224860i \(-0.927807\pi\)
0.681930 + 0.731417i \(0.261141\pi\)
\(948\) 6.00000 0.194871
\(949\) −37.5000 + 38.9711i −1.21730 + 1.26506i
\(950\) 0 0
\(951\) −6.00000 + 10.3923i −0.194563 + 0.336994i
\(952\) 0 0
\(953\) −3.00000 5.19615i −0.0971795 0.168320i 0.813337 0.581793i \(-0.197649\pi\)
−0.910516 + 0.413473i \(0.864315\pi\)
\(954\) −8.00000 −0.259010
\(955\) 6.00000 + 10.3923i 0.194155 + 0.336287i
\(956\) −12.0000 20.7846i −0.388108 0.672222i
\(957\) −8.00000 −0.258603
\(958\) −42.0000 72.7461i −1.35696 2.35032i
\(959\) 5.00000 8.66025i 0.161458 0.279654i
\(960\) −4.00000 + 6.92820i −0.129099 + 0.223607i
\(961\) 18.0000 0.580645
\(962\) −14.0000 3.46410i −0.451378 0.111687i
\(963\) 4.00000 0.128898
\(964\) −10.0000 + 17.3205i −0.322078 + 0.557856i
\(965\) −5.50000 + 9.52628i −0.177051 + 0.306662i
\(966\) −30.0000 51.9615i −0.965234 1.67183i
\(967\) −56.0000 −1.80084 −0.900419 0.435023i \(-0.856740\pi\)
−0.900419 + 0.435023i \(0.856740\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) −10.0000 17.3205i −0.320915 0.555842i 0.659762 0.751475i \(-0.270657\pi\)
−0.980677 + 0.195633i \(0.937324\pi\)
\(972\) −1.00000 + 1.73205i −0.0320750 + 0.0555556i
\(973\) 7.50000 12.9904i 0.240439 0.416452i
\(974\) −56.0000 −1.79436
\(975\) −1.00000 3.46410i −0.0320256 0.110940i
\(976\) 52.0000 1.66448
\(977\) −30.0000 + 51.9615i −0.959785 + 1.66240i −0.236768 + 0.971566i \(0.576088\pi\)
−0.723017 + 0.690830i \(0.757245\pi\)
\(978\) 15.0000 25.9808i 0.479647 0.830773i
\(979\) −14.0000 24.2487i −0.447442 0.774992i
\(980\) −36.0000 −1.14998
\(981\) 5.50000 + 9.52628i 0.175601 + 0.304151i
\(982\) 24.0000 + 41.5692i 0.765871 + 1.32653i
\(983\) 38.0000 1.21201 0.606006 0.795460i \(-0.292771\pi\)
0.606006 + 0.795460i \(0.292771\pi\)
\(984\) 0 0
\(985\) −6.00000 + 10.3923i −0.191176 + 0.331126i
\(986\) 8.00000 13.8564i 0.254772 0.441278i
\(987\) −40.0000 −1.27321
\(988\) 0 0
\(989\) 6.00000 0.190789
\(990\) 2.00000 3.46410i 0.0635642 0.110096i
\(991\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(992\) −28.0000 48.4974i −0.889001 1.53979i
\(993\) 9.00000 0.285606
\(994\) −60.0000 103.923i −1.90308 3.29624i
\(995\) 8.50000 + 14.7224i 0.269468 + 0.466732i
\(996\) 16.0000 0.506979
\(997\) −14.5000 25.1147i −0.459220 0.795392i 0.539700 0.841857i \(-0.318538\pi\)
−0.998920 + 0.0464655i \(0.985204\pi\)
\(998\) −4.00000 + 6.92820i −0.126618 + 0.219308i
\(999\) 1.00000 1.73205i 0.0316386 0.0547997i
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 195.2.i.a.61.1 yes 2
3.2 odd 2 585.2.j.b.451.1 2
5.2 odd 4 975.2.bb.f.724.1 4
5.3 odd 4 975.2.bb.f.724.2 4
5.4 even 2 975.2.i.i.451.1 2
13.3 even 3 inner 195.2.i.a.16.1 2
13.4 even 6 2535.2.a.c.1.1 1
13.9 even 3 2535.2.a.m.1.1 1
39.17 odd 6 7605.2.a.s.1.1 1
39.29 odd 6 585.2.j.b.406.1 2
39.35 odd 6 7605.2.a.a.1.1 1
65.3 odd 12 975.2.bb.f.874.1 4
65.29 even 6 975.2.i.i.601.1 2
65.42 odd 12 975.2.bb.f.874.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.i.a.16.1 2 13.3 even 3 inner
195.2.i.a.61.1 yes 2 1.1 even 1 trivial
585.2.j.b.406.1 2 39.29 odd 6
585.2.j.b.451.1 2 3.2 odd 2
975.2.i.i.451.1 2 5.4 even 2
975.2.i.i.601.1 2 65.29 even 6
975.2.bb.f.724.1 4 5.2 odd 4
975.2.bb.f.724.2 4 5.3 odd 4
975.2.bb.f.874.1 4 65.3 odd 12
975.2.bb.f.874.2 4 65.42 odd 12
2535.2.a.c.1.1 1 13.4 even 6
2535.2.a.m.1.1 1 13.9 even 3
7605.2.a.a.1.1 1 39.35 odd 6
7605.2.a.s.1.1 1 39.17 odd 6