Properties

Label 546.2.i.g.79.1
Level $546$
Weight $2$
Character 546.79
Analytic conductor $4.360$
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] = [546,2,Mod(79,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.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: \(4.35983195036\)
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 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.79
Dual form 546.2.i.g.235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} -2.00000 q^{20} +(2.00000 - 1.73205i) q^{21} -3.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} +3.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -1.00000 q^{34} +(-5.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.00000 + 1.73205i) q^{40} +2.00000 q^{41} +(-0.500000 - 2.59808i) q^{42} +6.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.00000 + 1.73205i) q^{45} +(4.50000 - 7.79423i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(0.500000 - 0.866025i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -6.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +3.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-5.50000 + 9.52628i) q^{61} +4.00000 q^{62} +(2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(-4.00000 + 3.46410i) q^{70} +15.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -3.00000 q^{76} +(-6.00000 + 5.19615i) q^{77} -1.00000 q^{78} +(-1.00000 + 1.73205i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-2.50000 - 0.866025i) q^{84} -2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(1.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-5.00000 + 8.66025i) q^{89} +2.00000 q^{90} +(0.500000 + 2.59808i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} + q^{12} - 2 q^{13} - 5 q^{14} + 4 q^{15} - q^{16} - q^{17} + q^{18} + 3 q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} - q^{24} + q^{25} - q^{26} - 2 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 4 q^{31} + q^{32} + 3 q^{33} - 2 q^{34} - 10 q^{35} + 2 q^{36} + 2 q^{37} - 3 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - q^{42} + 12 q^{43} - 3 q^{44} + 2 q^{45} + 9 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} + q^{51} + q^{52} - q^{53} - q^{54} - 12 q^{55} + q^{56} + 6 q^{57} + 3 q^{58} - 11 q^{59} - 2 q^{60} - 11 q^{61} + 8 q^{62} + 5 q^{63} + 2 q^{64} - 2 q^{65} - 3 q^{66} + 7 q^{67} - q^{68} - 8 q^{70} + 30 q^{71} + q^{72} + 12 q^{73} - 2 q^{74} - q^{75} - 6 q^{76} - 12 q^{77} - 2 q^{78} - 2 q^{79} + 2 q^{80} - q^{81} + 2 q^{82} - 5 q^{84} - 4 q^{85} + 6 q^{86} + 3 q^{87} + 3 q^{88} - 10 q^{89} + 4 q^{90} + q^{91} - 4 q^{93} - 9 q^{94} - 6 q^{95} - q^{96} - 24 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −1.00000 −0.277350
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 2.00000 0.516398
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.500000 0.866025i −0.121268 0.210042i 0.799000 0.601331i \(-0.205363\pi\)
−0.920268 + 0.391289i \(0.872029\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) −2.00000 −0.447214
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) −3.00000 −0.639602
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) −1.00000 −0.192450
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 1.00000 1.73205i 0.182574 0.316228i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) −1.00000 −0.171499
\(35\) −5.00000 1.73205i −0.845154 0.292770i
\(36\) 1.00000 0.166667
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) −1.50000 2.59808i −0.243332 0.421464i
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) −1.00000 + 1.73205i −0.158114 + 0.273861i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −0.500000 2.59808i −0.0771517 0.400892i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 0 0
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 1.00000 0.141421
\(51\) 0.500000 0.866025i 0.0700140 0.121268i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i \(-0.188546\pi\)
−0.898321 + 0.439340i \(0.855212\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −6.00000 −0.809040
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 3.00000 0.397360
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) −5.50000 9.52628i −0.716039 1.24022i −0.962557 0.271078i \(-0.912620\pi\)
0.246518 0.969138i \(-0.420713\pi\)
\(60\) −1.00000 1.73205i −0.129099 0.223607i
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 4.00000 0.508001
\(63\) 2.50000 + 0.866025i 0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) −0.500000 + 0.866025i −0.0606339 + 0.105021i
\(69\) 0 0
\(70\) −4.00000 + 3.46410i −0.478091 + 0.414039i
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 6.00000 + 10.3923i 0.702247 + 1.21633i 0.967676 + 0.252197i \(0.0811531\pi\)
−0.265429 + 0.964130i \(0.585514\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) −3.00000 −0.344124
\(77\) −6.00000 + 5.19615i −0.683763 + 0.592157i
\(78\) −1.00000 −0.113228
\(79\) −1.00000 + 1.73205i −0.112509 + 0.194871i −0.916781 0.399390i \(-0.869222\pi\)
0.804272 + 0.594261i \(0.202555\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −2.50000 0.866025i −0.272772 0.0944911i
\(85\) −2.00000 −0.216930
\(86\) 3.00000 5.19615i 0.323498 0.560316i
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) 2.00000 0.210819
\(91\) 0.500000 + 2.59808i 0.0524142 + 0.272352i
\(92\) 0 0
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −12.0000 −1.21842 −0.609208 0.793011i \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 3.00000 0.301511
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) −0.500000 0.866025i −0.0495074 0.0857493i
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) 1.00000 0.0980581
\(105\) −1.00000 5.19615i −0.0975900 0.507093i
\(106\) −1.00000 −0.0971286
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 4.00000 + 6.92820i 0.383131 + 0.663602i 0.991508 0.130046i \(-0.0415126\pi\)
−0.608377 + 0.793648i \(0.708179\pi\)
\(110\) −3.00000 + 5.19615i −0.286039 + 0.495434i
\(111\) 2.00000 0.189832
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) 3.00000 0.282216 0.141108 0.989994i \(-0.454933\pi\)
0.141108 + 0.989994i \(0.454933\pi\)
\(114\) 1.50000 2.59808i 0.140488 0.243332i
\(115\) 0 0
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) −11.0000 −1.01263
\(119\) −2.00000 + 1.73205i −0.183340 + 0.158777i
\(120\) −2.00000 −0.182574
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 5.50000 + 9.52628i 0.497947 + 0.862469i
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 12.0000 1.07331
\(126\) 2.00000 1.73205i 0.178174 0.154303i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 3.00000 + 5.19615i 0.264135 + 0.457496i
\(130\) 1.00000 + 1.73205i 0.0877058 + 0.151911i
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) −3.00000 −0.261116
\(133\) −7.50000 2.59808i −0.650332 0.225282i
\(134\) 7.00000 0.604708
\(135\) −1.00000 + 1.73205i −0.0860663 + 0.149071i
\(136\) 0.500000 + 0.866025i 0.0428746 + 0.0742611i
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 1.00000 + 5.19615i 0.0845154 + 0.439155i
\(141\) 9.00000 0.757937
\(142\) 7.50000 12.9904i 0.629386 1.09013i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 3.00000 5.19615i 0.249136 0.431517i
\(146\) 12.0000 0.993127
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) −2.00000 −0.164399
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i \(0.0764802\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) −1.50000 + 2.59808i −0.121666 + 0.210732i
\(153\) 1.00000 0.0808452
\(154\) 1.50000 + 7.79423i 0.120873 + 0.628077i
\(155\) 8.00000 0.642575
\(156\) −0.500000 + 0.866025i −0.0400320 + 0.0693375i
\(157\) 5.50000 + 9.52628i 0.438948 + 0.760280i 0.997609 0.0691164i \(-0.0220180\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 12.5000 21.6506i 0.979076 1.69581i 0.313304 0.949653i \(-0.398564\pi\)
0.665771 0.746156i \(-0.268103\pi\)
\(164\) −1.00000 1.73205i −0.0780869 0.135250i
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 0 0
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) −2.00000 + 1.73205i −0.154303 + 0.133631i
\(169\) 1.00000 0.0769231
\(170\) −1.00000 + 1.73205i −0.0766965 + 0.132842i
\(171\) 1.50000 + 2.59808i 0.114708 + 0.198680i
\(172\) −3.00000 5.19615i −0.228748 0.396203i
\(173\) −3.50000 + 6.06218i −0.266100 + 0.460899i −0.967851 0.251523i \(-0.919068\pi\)
0.701751 + 0.712422i \(0.252402\pi\)
\(174\) 3.00000 0.227429
\(175\) 2.00000 1.73205i 0.151186 0.130931i
\(176\) 3.00000 0.226134
\(177\) 5.50000 9.52628i 0.413405 0.716039i
\(178\) 5.00000 + 8.66025i 0.374766 + 0.649113i
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 1.00000 1.73205i 0.0745356 0.129099i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 2.50000 + 0.866025i 0.185312 + 0.0641941i
\(183\) −11.0000 −0.813143
\(184\) 0 0
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) −9.00000 −0.656392
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) −6.00000 −0.435286
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) −6.00000 + 10.3923i −0.430775 + 0.746124i
\(195\) −2.00000 −0.143223
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) −6.00000 10.3923i −0.425329 0.736691i 0.571122 0.820865i \(-0.306508\pi\)
−0.996451 + 0.0841740i \(0.973175\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −3.50000 + 6.06218i −0.246871 + 0.427593i
\(202\) 14.0000 0.985037
\(203\) −1.50000 7.79423i −0.105279 0.547048i
\(204\) −1.00000 −0.0700140
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) −9.00000 −0.622543
\(210\) −5.00000 1.73205i −0.345033 0.119523i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) 7.50000 + 12.9904i 0.513892 + 0.890086i
\(214\) −2.00000 3.46410i −0.136717 0.236801i
\(215\) 6.00000 10.3923i 0.409197 0.708749i
\(216\) 1.00000 0.0680414
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 8.00000 0.541828
\(219\) −6.00000 + 10.3923i −0.405442 + 0.702247i
\(220\) 3.00000 + 5.19615i 0.202260 + 0.350325i
\(221\) 0.500000 + 0.866025i 0.0336336 + 0.0582552i
\(222\) 1.00000 1.73205i 0.0671156 0.116248i
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) −1.00000 −0.0666667
\(226\) 1.50000 2.59808i 0.0997785 0.172821i
\(227\) −4.00000 6.92820i −0.265489 0.459841i 0.702202 0.711977i \(-0.252200\pi\)
−0.967692 + 0.252136i \(0.918867\pi\)
\(228\) −1.50000 2.59808i −0.0993399 0.172062i
\(229\) 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i \(-0.812283\pi\)
0.897173 + 0.441679i \(0.145617\pi\)
\(230\) 0 0
\(231\) −7.50000 2.59808i −0.493464 0.170941i
\(232\) −3.00000 −0.196960
\(233\) −3.50000 + 6.06218i −0.229293 + 0.397146i −0.957599 0.288106i \(-0.906975\pi\)
0.728306 + 0.685252i \(0.240308\pi\)
\(234\) −0.500000 0.866025i −0.0326860 0.0566139i
\(235\) −9.00000 15.5885i −0.587095 1.01688i
\(236\) −5.50000 + 9.52628i −0.358020 + 0.620108i
\(237\) −2.00000 −0.129914
\(238\) 0.500000 + 2.59808i 0.0324102 + 0.168408i
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) −1.00000 + 1.73205i −0.0645497 + 0.111803i
\(241\) −6.00000 10.3923i −0.386494 0.669427i 0.605481 0.795860i \(-0.292981\pi\)
−0.991975 + 0.126432i \(0.959647\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 11.0000 0.704203
\(245\) −2.00000 + 13.8564i −0.127775 + 0.885253i
\(246\) 2.00000 0.127515
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) 0 0
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −10.0000 −0.631194 −0.315597 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) −0.500000 2.59808i −0.0314970 0.163663i
\(253\) 0 0
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) −1.00000 1.73205i −0.0626224 0.108465i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.0000 22.5167i 0.810918 1.40455i −0.101305 0.994855i \(-0.532302\pi\)
0.912222 0.409695i \(-0.134365\pi\)
\(258\) 6.00000 0.373544
\(259\) −5.00000 1.73205i −0.310685 0.107624i
\(260\) 2.00000 0.124035
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) −5.00000 8.66025i −0.308313 0.534014i 0.669680 0.742650i \(-0.266431\pi\)
−0.977993 + 0.208635i \(0.933098\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) −2.00000 −0.122859
\(266\) −6.00000 + 5.19615i −0.367884 + 0.318597i
\(267\) −10.0000 −0.611990
\(268\) 3.50000 6.06218i 0.213797 0.370306i
\(269\) 10.5000 + 18.1865i 0.640196 + 1.10885i 0.985389 + 0.170321i \(0.0544803\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(270\) 1.00000 + 1.73205i 0.0608581 + 0.105409i
\(271\) −7.50000 + 12.9904i −0.455593 + 0.789109i −0.998722 0.0505395i \(-0.983906\pi\)
0.543130 + 0.839649i \(0.317239\pi\)
\(272\) 1.00000 0.0606339
\(273\) −2.00000 + 1.73205i −0.121046 + 0.104828i
\(274\) −18.0000 −1.08742
\(275\) 1.50000 2.59808i 0.0904534 0.156670i
\(276\) 0 0
\(277\) −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i \(-0.214662\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) −7.00000 + 12.1244i −0.419832 + 0.727171i
\(279\) −4.00000 −0.239474
\(280\) 5.00000 + 1.73205i 0.298807 + 0.103510i
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 4.50000 7.79423i 0.267971 0.464140i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −7.50000 12.9904i −0.445043 0.770837i
\(285\) 3.00000 5.19615i 0.177705 0.307794i
\(286\) 3.00000 0.177394
\(287\) −1.00000 5.19615i −0.0590281 0.306719i
\(288\) −1.00000 −0.0589256
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) −6.00000 10.3923i −0.351726 0.609208i
\(292\) 6.00000 10.3923i 0.351123 0.608164i
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) −6.50000 + 2.59808i −0.379088 + 0.151523i
\(295\) −22.0000 −1.28089
\(296\) −1.00000 + 1.73205i −0.0581238 + 0.100673i
\(297\) 1.50000 + 2.59808i 0.0870388 + 0.150756i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) −3.00000 15.5885i −0.172917 0.898504i
\(302\) 17.0000 0.978240
\(303\) −7.00000 + 12.1244i −0.402139 + 0.696526i
\(304\) 1.50000 + 2.59808i 0.0860309 + 0.149010i
\(305\) 11.0000 + 19.0526i 0.629858 + 1.09095i
\(306\) 0.500000 0.866025i 0.0285831 0.0495074i
\(307\) −15.0000 −0.856095 −0.428048 0.903756i \(-0.640798\pi\)
−0.428048 + 0.903756i \(0.640798\pi\)
\(308\) 7.50000 + 2.59808i 0.427352 + 0.148039i
\(309\) −14.0000 −0.796432
\(310\) 4.00000 6.92820i 0.227185 0.393496i
\(311\) −7.00000 12.1244i −0.396934 0.687509i 0.596412 0.802678i \(-0.296592\pi\)
−0.993346 + 0.115169i \(0.963259\pi\)
\(312\) 0.500000 + 0.866025i 0.0283069 + 0.0490290i
\(313\) 7.00000 12.1244i 0.395663 0.685309i −0.597522 0.801852i \(-0.703848\pi\)
0.993186 + 0.116543i \(0.0371814\pi\)
\(314\) 11.0000 0.620766
\(315\) 4.00000 3.46410i 0.225374 0.195180i
\(316\) 2.00000 0.112509
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) −0.500000 0.866025i −0.0280386 0.0485643i
\(319\) −4.50000 7.79423i −0.251952 0.436393i
\(320\) 1.00000 1.73205i 0.0559017 0.0968246i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) −12.5000 21.6506i −0.692311 1.19912i
\(327\) −4.00000 + 6.92820i −0.221201 + 0.383131i
\(328\) −2.00000 −0.110432
\(329\) −22.5000 7.79423i −1.24047 0.429710i
\(330\) −6.00000 −0.330289
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 0 0
\(333\) 1.00000 + 1.73205i 0.0547997 + 0.0949158i
\(334\) −9.50000 + 16.4545i −0.519817 + 0.900349i
\(335\) 14.0000 0.764902
\(336\) 0.500000 + 2.59808i 0.0272772 + 0.141737i
\(337\) 7.00000 0.381314 0.190657 0.981657i \(-0.438938\pi\)
0.190657 + 0.981657i \(0.438938\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) 1.50000 + 2.59808i 0.0814688 + 0.141108i
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 3.00000 0.162221
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) 3.50000 + 6.06218i 0.188161 + 0.325905i
\(347\) −1.00000 1.73205i −0.0536828 0.0929814i 0.837935 0.545770i \(-0.183763\pi\)
−0.891618 + 0.452788i \(0.850429\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) −0.500000 2.59808i −0.0267261 0.138873i
\(351\) 1.00000 0.0533761
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) −5.50000 9.52628i −0.292322 0.506316i
\(355\) 15.0000 25.9808i 0.796117 1.37892i
\(356\) 10.0000 0.529999
\(357\) −2.50000 0.866025i −0.132314 0.0458349i
\(358\) 6.00000 0.317110
\(359\) −8.00000 + 13.8564i −0.422224 + 0.731313i −0.996157 0.0875892i \(-0.972084\pi\)
0.573933 + 0.818902i \(0.305417\pi\)
\(360\) −1.00000 1.73205i −0.0527046 0.0912871i
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) −2.50000 + 4.33013i −0.131397 + 0.227586i
\(363\) 2.00000 0.104973
\(364\) 2.00000 1.73205i 0.104828 0.0907841i
\(365\) 24.0000 1.25622
\(366\) −5.50000 + 9.52628i −0.287490 + 0.497947i
\(367\) −9.00000 15.5885i −0.469796 0.813711i 0.529607 0.848243i \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) −4.00000 −0.207950
\(371\) −2.00000 + 1.73205i −0.103835 + 0.0899236i
\(372\) 4.00000 0.207390
\(373\) 5.50000 9.52628i 0.284779 0.493252i −0.687776 0.725923i \(-0.741413\pi\)
0.972556 + 0.232671i \(0.0747464\pi\)
\(374\) 1.50000 + 2.59808i 0.0775632 + 0.134343i
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) −4.50000 + 7.79423i −0.232070 + 0.401957i
\(377\) −3.00000 −0.154508
\(378\) 2.50000 + 0.866025i 0.128586 + 0.0445435i
\(379\) 36.0000 1.84920 0.924598 0.380945i \(-0.124401\pi\)
0.924598 + 0.380945i \(0.124401\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) 16.0000 27.7128i 0.817562 1.41606i −0.0899119 0.995950i \(-0.528659\pi\)
0.907474 0.420109i \(-0.138008\pi\)
\(384\) 1.00000 0.0510310
\(385\) 3.00000 + 15.5885i 0.152894 + 0.794461i
\(386\) 14.0000 0.712581
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) 6.00000 + 10.3923i 0.304604 + 0.527589i
\(389\) −6.50000 11.2583i −0.329563 0.570820i 0.652862 0.757477i \(-0.273568\pi\)
−0.982425 + 0.186657i \(0.940235\pi\)
\(390\) −1.00000 + 1.73205i −0.0506370 + 0.0877058i
\(391\) 0 0
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 12.0000 0.605320
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 2.00000 + 3.46410i 0.100631 + 0.174298i
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) 10.0000 17.3205i 0.501886 0.869291i −0.498112 0.867113i \(-0.665973\pi\)
0.999998 0.00217869i \(-0.000693499\pi\)
\(398\) −12.0000 −0.601506
\(399\) −1.50000 7.79423i −0.0750939 0.390199i
\(400\) −1.00000 −0.0500000
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 3.50000 + 6.06218i 0.174564 + 0.302354i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 7.00000 12.1244i 0.348263 0.603209i
\(405\) −2.00000 −0.0993808
\(406\) −7.50000 2.59808i −0.372219 0.128940i
\(407\) −6.00000 −0.297409
\(408\) −0.500000 + 0.866025i −0.0247537 + 0.0428746i
\(409\) 19.0000 + 32.9090i 0.939490 + 1.62724i 0.766426 + 0.642333i \(0.222033\pi\)
0.173064 + 0.984911i \(0.444633\pi\)
\(410\) −2.00000 3.46410i −0.0987730 0.171080i
\(411\) 9.00000 15.5885i 0.443937 0.768922i
\(412\) 14.0000 0.689730
\(413\) −22.0000 + 19.0526i −1.08255 + 0.937515i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) −7.00000 12.1244i −0.342791 0.593732i
\(418\) −4.50000 + 7.79423i −0.220102 + 0.381228i
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) −4.00000 + 3.46410i −0.195180 + 0.169031i
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 4.50000 + 7.79423i 0.218797 + 0.378968i
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) 0.500000 0.866025i 0.0242536 0.0420084i
\(426\) 15.0000 0.726752
\(427\) 27.5000 + 9.52628i 1.33082 + 0.461009i
\(428\) −4.00000 −0.193347
\(429\) −1.50000 + 2.59808i −0.0724207 + 0.125436i
\(430\) −6.00000 10.3923i −0.289346 0.501161i
\(431\) 20.0000 + 34.6410i 0.963366 + 1.66860i 0.713942 + 0.700205i \(0.246908\pi\)
0.249424 + 0.968394i \(0.419759\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) −2.00000 10.3923i −0.0960031 0.498847i
\(435\) 6.00000 0.287678
\(436\) 4.00000 6.92820i 0.191565 0.331801i
\(437\) 0 0
\(438\) 6.00000 + 10.3923i 0.286691 + 0.496564i
\(439\) −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i \(-0.958036\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(440\) 6.00000 0.286039
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 1.00000 0.0475651
\(443\) −3.00000 + 5.19615i −0.142534 + 0.246877i −0.928450 0.371457i \(-0.878858\pi\)
0.785916 + 0.618333i \(0.212192\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) 10.0000 + 17.3205i 0.474045 + 0.821071i
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) −40.0000 −1.88772 −0.943858 0.330350i \(-0.892833\pi\)
−0.943858 + 0.330350i \(0.892833\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) −1.50000 2.59808i −0.0705541 0.122203i
\(453\) −8.50000 + 14.7224i −0.399365 + 0.691720i
\(454\) −8.00000 −0.375459
\(455\) 5.00000 + 1.73205i 0.234404 + 0.0811998i
\(456\) −3.00000 −0.140488
\(457\) 16.0000 27.7128i 0.748448 1.29635i −0.200118 0.979772i \(-0.564132\pi\)
0.948566 0.316579i \(-0.102534\pi\)
\(458\) −1.00000 1.73205i −0.0467269 0.0809334i
\(459\) 0.500000 + 0.866025i 0.0233380 + 0.0404226i
\(460\) 0 0
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) −6.00000 + 5.19615i −0.279145 + 0.241747i
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) 3.50000 + 6.06218i 0.162134 + 0.280825i
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 14.0000 12.1244i 0.646460 0.559851i
\(470\) −18.0000 −0.830278
\(471\) −5.50000 + 9.52628i −0.253427 + 0.438948i
\(472\) 5.50000 + 9.52628i 0.253158 + 0.438483i
\(473\) −9.00000 15.5885i −0.413820 0.716758i
\(474\) −1.00000 + 1.73205i −0.0459315 + 0.0795557i
\(475\) 3.00000 0.137649
\(476\) 2.50000 + 0.866025i 0.114587 + 0.0396942i
\(477\) 1.00000 0.0457869
\(478\) −5.50000 + 9.52628i −0.251564 + 0.435722i
\(479\) −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(480\) 1.00000 + 1.73205i 0.0456435 + 0.0790569i
\(481\) −1.00000 + 1.73205i −0.0455961 + 0.0789747i
\(482\) −12.0000 −0.546585
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 16.5000 + 28.5788i 0.747686 + 1.29503i 0.948929 + 0.315489i \(0.102169\pi\)
−0.201243 + 0.979541i \(0.564498\pi\)
\(488\) 5.50000 9.52628i 0.248973 0.431234i
\(489\) 25.0000 1.13054
\(490\) 11.0000 + 8.66025i 0.496929 + 0.391230i
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 1.00000 1.73205i 0.0450835 0.0780869i
\(493\) −1.50000 2.59808i −0.0675566 0.117011i
\(494\) 1.50000 + 2.59808i 0.0674882 + 0.116893i
\(495\) 3.00000 5.19615i 0.134840 0.233550i
\(496\) −4.00000 −0.179605
\(497\) −7.50000 38.9711i −0.336421 1.74809i
\(498\) 0 0
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) −9.50000 16.4545i −0.424429 0.735132i
\(502\) −5.00000 + 8.66025i −0.223161 + 0.386526i
\(503\) −20.0000 −0.891756 −0.445878 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) −2.50000 0.866025i −0.111359 0.0385758i
\(505\) 28.0000 1.24598
\(506\) 0 0
\(507\) 0.500000 + 0.866025i 0.0222058 + 0.0384615i
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) −6.00000 + 10.3923i −0.265945 + 0.460631i −0.967811 0.251679i \(-0.919017\pi\)
0.701866 + 0.712309i \(0.252351\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 24.0000 20.7846i 1.06170 0.919457i
\(512\) −1.00000 −0.0441942
\(513\) −1.50000 + 2.59808i −0.0662266 + 0.114708i
\(514\) −13.0000 22.5167i −0.573405 0.993167i
\(515\) 14.0000 + 24.2487i 0.616914 + 1.06853i
\(516\) 3.00000 5.19615i 0.132068 0.228748i
\(517\) −27.0000 −1.18746
\(518\) −4.00000 + 3.46410i −0.175750 + 0.152204i
\(519\) −7.00000 −0.307266
\(520\) 1.00000 1.73205i 0.0438529 0.0759555i
\(521\) 19.0000 + 32.9090i 0.832405 + 1.44177i 0.896126 + 0.443800i \(0.146370\pi\)
−0.0637207 + 0.997968i \(0.520297\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) −3.00000 + 5.19615i −0.131181 + 0.227212i −0.924132 0.382073i \(-0.875210\pi\)
0.792951 + 0.609285i \(0.208544\pi\)
\(524\) −12.0000 −0.524222
\(525\) 2.50000 + 0.866025i 0.109109 + 0.0377964i
\(526\) −10.0000 −0.436021
\(527\) 2.00000 3.46410i 0.0871214 0.150899i
\(528\) 1.50000 + 2.59808i 0.0652791 + 0.113067i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −1.00000 + 1.73205i −0.0434372 + 0.0752355i
\(531\) 11.0000 0.477359
\(532\) 1.50000 + 7.79423i 0.0650332 + 0.337923i
\(533\) −2.00000 −0.0866296
\(534\) −5.00000 + 8.66025i −0.216371 + 0.374766i
\(535\) −4.00000 6.92820i −0.172935 0.299532i
\(536\) −3.50000 6.06218i −0.151177 0.261846i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) 21.0000 0.905374
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 2.00000 0.0860663
\(541\) −11.0000 + 19.0526i −0.472927 + 0.819133i −0.999520 0.0309841i \(-0.990136\pi\)
0.526593 + 0.850118i \(0.323469\pi\)
\(542\) 7.50000 + 12.9904i 0.322153 + 0.557985i
\(543\) −2.50000 4.33013i −0.107285 0.185824i
\(544\) 0.500000 0.866025i 0.0214373 0.0371305i
\(545\) 16.0000 0.685365
\(546\) 0.500000 + 2.59808i 0.0213980 + 0.111187i
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) −5.50000 9.52628i −0.234734 0.406572i
\(550\) −1.50000 2.59808i −0.0639602 0.110782i
\(551\) 4.50000 7.79423i 0.191706 0.332045i
\(552\) 0 0
\(553\) 5.00000 + 1.73205i 0.212622 + 0.0736543i
\(554\) −5.00000 −0.212430
\(555\) 2.00000 3.46410i 0.0848953 0.147043i
\(556\) 7.00000 + 12.1244i 0.296866 + 0.514187i
\(557\) 11.0000 + 19.0526i 0.466085 + 0.807283i 0.999250 0.0387286i \(-0.0123308\pi\)
−0.533165 + 0.846011i \(0.678997\pi\)
\(558\) −2.00000 + 3.46410i −0.0846668 + 0.146647i
\(559\) −6.00000 −0.253773
\(560\) 4.00000 3.46410i 0.169031 0.146385i
\(561\) −3.00000 −0.126660
\(562\) −12.0000 + 20.7846i −0.506189 + 0.876746i
\(563\) −12.0000 20.7846i −0.505740 0.875967i −0.999978 0.00664037i \(-0.997886\pi\)
0.494238 0.869326i \(-0.335447\pi\)
\(564\) −4.50000 7.79423i −0.189484 0.328196i
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 4.00000 0.168133
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) −15.0000 −0.629386
\(569\) −19.5000 + 33.7750i −0.817483 + 1.41592i 0.0900490 + 0.995937i \(0.471298\pi\)
−0.907532 + 0.419984i \(0.862036\pi\)
\(570\) −3.00000 5.19615i −0.125656 0.217643i
\(571\) −22.0000 38.1051i −0.920671 1.59465i −0.798379 0.602155i \(-0.794309\pi\)
−0.122292 0.992494i \(-0.539025\pi\)
\(572\) 1.50000 2.59808i 0.0627182 0.108631i
\(573\) 12.0000 0.501307
\(574\) −5.00000 1.73205i −0.208696 0.0722944i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 9.00000 + 15.5885i 0.374675 + 0.648956i 0.990278 0.139100i \(-0.0444210\pi\)
−0.615603 + 0.788056i \(0.711088\pi\)
\(578\) −8.00000 13.8564i −0.332756 0.576351i
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) −6.00000 −0.249136
\(581\) 0 0
\(582\) −12.0000 −0.497416
\(583\) −1.50000 + 2.59808i −0.0621237 + 0.107601i
\(584\) −6.00000 10.3923i −0.248282 0.430037i
\(585\) −1.00000 1.73205i −0.0413449 0.0716115i
\(586\) −6.00000 + 10.3923i −0.247858 + 0.429302i
\(587\) 39.0000 1.60970 0.804851 0.593477i \(-0.202245\pi\)
0.804851 + 0.593477i \(0.202245\pi\)
\(588\) −1.00000 + 6.92820i −0.0412393 + 0.285714i
\(589\) 12.0000 0.494451
\(590\) −11.0000 + 19.0526i −0.452863 + 0.784381i
\(591\) 4.00000 + 6.92820i 0.164538 + 0.284988i
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) 17.0000 29.4449i 0.698106 1.20916i −0.271016 0.962575i \(-0.587360\pi\)
0.969122 0.246581i \(-0.0793071\pi\)
\(594\) 3.00000 0.123091
\(595\) 1.00000 + 5.19615i 0.0409960 + 0.213021i
\(596\) 0 0
\(597\) 6.00000 10.3923i 0.245564 0.425329i
\(598\) 0 0
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) −35.0000 −1.42768 −0.713840 0.700309i \(-0.753046\pi\)
−0.713840 + 0.700309i \(0.753046\pi\)
\(602\) −15.0000 5.19615i −0.611354 0.211779i
\(603\) −7.00000 −0.285062
\(604\) 8.50000 14.7224i 0.345860 0.599047i
\(605\) −2.00000 3.46410i −0.0813116 0.140836i
\(606\) 7.00000 + 12.1244i 0.284356 + 0.492518i
\(607\) −14.0000 + 24.2487i −0.568242 + 0.984225i 0.428497 + 0.903543i \(0.359043\pi\)
−0.996740 + 0.0806818i \(0.974290\pi\)
\(608\) 3.00000 0.121666
\(609\) 6.00000 5.19615i 0.243132 0.210559i
\(610\) 22.0000 0.890754
\(611\) −4.50000 + 7.79423i −0.182051 + 0.315321i
\(612\) −0.500000 0.866025i −0.0202113 0.0350070i
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −7.50000 + 12.9904i −0.302675 + 0.524249i
\(615\) 4.00000 0.161296
\(616\) 6.00000 5.19615i 0.241747 0.209359i
\(617\) −14.0000 −0.563619 −0.281809 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) −7.00000 + 12.1244i −0.281581 + 0.487713i
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) −4.00000 6.92820i −0.160644 0.278243i
\(621\) 0 0
\(622\) −14.0000 −0.561349
\(623\) 25.0000 + 8.66025i 1.00160 + 0.346966i
\(624\) 1.00000 0.0400320
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) −7.00000 12.1244i −0.279776 0.484587i
\(627\) −4.50000 7.79423i −0.179713 0.311272i
\(628\) 5.50000 9.52628i 0.219474 0.380140i
\(629\) −2.00000 −0.0797452
\(630\) −1.00000 5.19615i −0.0398410 0.207020i
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 1.00000 1.73205i 0.0397779 0.0688973i
\(633\) −8.00000 13.8564i −0.317971 0.550743i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 8.00000 13.8564i 0.317470 0.549875i
\(636\) −1.00000 −0.0396526
\(637\) 6.50000 2.59808i 0.257539 0.102940i
\(638\) −9.00000 −0.356313
\(639\) −7.50000 + 12.9904i −0.296695 + 0.513892i
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i \(-0.0509845\pi\)
−0.631721 + 0.775196i \(0.717651\pi\)
\(642\) 2.00000 3.46410i 0.0789337 0.136717i
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) −1.50000 + 2.59808i −0.0590167 + 0.102220i
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −16.5000 + 28.5788i −0.647682 + 1.12182i
\(650\) −1.00000 −0.0392232
\(651\) 10.0000 + 3.46410i 0.391931 + 0.135769i
\(652\) −25.0000 −0.979076
\(653\) 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i \(-0.633644\pi\)
0.994623 0.103558i \(-0.0330227\pi\)
\(654\) 4.00000 + 6.92820i 0.156412 + 0.270914i
\(655\) −12.0000 20.7846i −0.468879 0.812122i
\(656\) −1.00000 + 1.73205i −0.0390434 + 0.0676252i
\(657\) −12.0000 −0.468165
\(658\) −18.0000 + 15.5885i −0.701713 + 0.607701i
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) −19.0000 32.9090i −0.739014 1.28001i −0.952940 0.303160i \(-0.901958\pi\)
0.213925 0.976850i \(-0.431375\pi\)
\(662\) −14.0000 24.2487i −0.544125 0.942453i
\(663\) −0.500000 + 0.866025i −0.0194184 + 0.0336336i
\(664\) 0 0
\(665\) −12.0000 + 10.3923i −0.465340 + 0.402996i
\(666\) 2.00000 0.0774984
\(667\) 0 0
\(668\) 9.50000 + 16.4545i 0.367566 + 0.636643i
\(669\) −0.500000 0.866025i −0.0193311 0.0334825i
\(670\) 7.00000 12.1244i 0.270434 0.468405i
\(671\) 33.0000 1.27395
\(672\) 2.50000 + 0.866025i 0.0964396 + 0.0334077i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 3.50000 6.06218i 0.134815 0.233506i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) −0.500000 + 0.866025i −0.0192166 + 0.0332841i −0.875474 0.483266i \(-0.839451\pi\)
0.856257 + 0.516550i \(0.172784\pi\)
\(678\) 3.00000 0.115214
\(679\) 6.00000 + 31.1769i 0.230259 + 1.19646i
\(680\) 2.00000 0.0766965
\(681\) 4.00000 6.92820i 0.153280 0.265489i
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) 22.0000 + 38.1051i 0.841807 + 1.45805i 0.888366 + 0.459136i \(0.151841\pi\)
−0.0465592 + 0.998916i \(0.514826\pi\)
\(684\) 1.50000 2.59808i 0.0573539 0.0993399i
\(685\) −36.0000 −1.37549
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 2.00000 0.0763048
\(688\) −3.00000 + 5.19615i −0.114374 + 0.198101i
\(689\) 0.500000 + 0.866025i 0.0190485 + 0.0329929i
\(690\) 0 0
\(691\) −17.5000 + 30.3109i −0.665731 + 1.15308i 0.313355 + 0.949636i \(0.398547\pi\)
−0.979086 + 0.203445i \(0.934786\pi\)
\(692\) 7.00000 0.266100
\(693\) −1.50000 7.79423i −0.0569803 0.296078i
\(694\) −2.00000 −0.0759190
\(695\) −14.0000 + 24.2487i −0.531050 + 0.919806i
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) −1.00000 1.73205i −0.0378777 0.0656061i
\(698\) 10.0000 17.3205i 0.378506 0.655591i
\(699\) −7.00000 −0.264764
\(700\) −2.50000 0.866025i −0.0944911 0.0327327i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0.500000 0.866025i 0.0188713 0.0326860i
\(703\) −3.00000 5.19615i −0.113147 0.195977i
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 9.00000 15.5885i 0.338960 0.587095i
\(706\) 18.0000 0.677439
\(707\) 28.0000 24.2487i 1.05305 0.911967i
\(708\) −11.0000 −0.413405
\(709\) 10.0000 17.3205i 0.375558 0.650485i −0.614852 0.788642i \(-0.710784\pi\)
0.990410 + 0.138157i \(0.0441178\pi\)
\(710\) −15.0000 25.9808i −0.562940 0.975041i
\(711\) −1.00000 1.73205i −0.0375029 0.0649570i
\(712\) 5.00000 8.66025i 0.187383 0.324557i
\(713\) 0 0
\(714\) −2.00000 + 1.73205i −0.0748481 + 0.0648204i
\(715\) 6.00000 0.224387
\(716\) 3.00000 5.19615i 0.112115 0.194189i
\(717\) −5.50000 9.52628i −0.205401 0.355765i
\(718\) 8.00000 + 13.8564i 0.298557 + 0.517116i
\(719\) −19.0000 + 32.9090i −0.708580 + 1.22730i 0.256803 + 0.966464i \(0.417331\pi\)
−0.965384 + 0.260834i \(0.916003\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 35.0000 + 12.1244i 1.30347 + 0.451535i
\(722\) 10.0000 0.372161
\(723\) 6.00000 10.3923i 0.223142 0.386494i
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) 1.50000 + 2.59808i 0.0557086 + 0.0964901i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) −12.0000 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) −0.500000 2.59808i −0.0185312 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) 12.0000 20.7846i 0.444140 0.769273i
\(731\) −3.00000 5.19615i −0.110959 0.192187i
\(732\) 5.50000 + 9.52628i 0.203286 + 0.352101i
\(733\) 4.00000 6.92820i 0.147743 0.255899i −0.782650 0.622462i \(-0.786132\pi\)
0.930393 + 0.366563i \(0.119466\pi\)
\(734\) −18.0000 −0.664392
\(735\) −13.0000 + 5.19615i −0.479512 + 0.191663i
\(736\) 0 0
\(737\) 10.5000 18.1865i 0.386772 0.669910i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) −3.00000 −0.110208
\(742\) 0.500000 + 2.59808i 0.0183556 + 0.0953784i
\(743\) −35.0000 −1.28403 −0.642013 0.766694i \(-0.721900\pi\)
−0.642013 + 0.766694i \(0.721900\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) 0 0
\(746\) −5.50000 9.52628i −0.201369 0.348782i
\(747\) 0 0
\(748\) 3.00000 0.109691
\(749\) −10.0000 3.46410i −0.365392 0.126576i
\(750\) 12.0000 0.438178
\(751\) −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i \(0.337342\pi\)
−0.999921 + 0.0125942i \(0.995991\pi\)
\(752\) 4.50000 + 7.79423i 0.164098 + 0.284226i
\(753\) −5.00000 8.66025i −0.182210 0.315597i
\(754\) −1.50000 + 2.59808i −0.0546268 + 0.0946164i
\(755\) 34.0000 1.23739
\(756\) 2.00000 1.73205i 0.0727393 0.0629941i
\(757\) 19.0000 0.690567 0.345283 0.938498i \(-0.387783\pi\)
0.345283 + 0.938498i \(0.387783\pi\)
\(758\) 18.0000 31.1769i 0.653789 1.13240i
\(759\) 0 0
\(760\) 3.00000 + 5.19615i 0.108821 + 0.188484i
\(761\) −14.0000 + 24.2487i −0.507500 + 0.879015i 0.492463 + 0.870334i \(0.336097\pi\)
−0.999962 + 0.00868155i \(0.997237\pi\)
\(762\) 8.00000 0.289809
\(763\) 16.0000 13.8564i 0.579239 0.501636i
\(764\) −12.0000 −0.434145
\(765\) 1.00000 1.73205i 0.0361551 0.0626224i
\(766\) −16.0000 27.7128i −0.578103 1.00130i
\(767\) 5.50000 + 9.52628i 0.198593 + 0.343974i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −4.00000 −0.144244 −0.0721218 0.997396i \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 15.0000 + 5.19615i 0.540562 + 0.187256i
\(771\) 26.0000 0.936367
\(772\) 7.00000 12.1244i 0.251936 0.436365i
\(773\) −21.0000 36.3731i −0.755318 1.30825i −0.945216 0.326445i \(-0.894149\pi\)
0.189899 0.981804i \(-0.439184\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) 12.0000 0.430775
\(777\) −1.00000 5.19615i −0.0358748 0.186411i
\(778\) −13.0000 −0.466073
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) 1.00000 + 1.73205i 0.0358057 + 0.0620174i
\(781\) −22.5000 38.9711i −0.805113 1.39450i
\(782\) 0 0
\(783\) −3.00000 −0.107211
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 22.0000 0.785214
\(786\) 6.00000 10.3923i 0.214013 0.370681i
\(787\) −3.50000 6.06218i −0.124762 0.216093i 0.796878 0.604140i \(-0.206483\pi\)
−0.921640 + 0.388047i \(0.873150\pi\)
\(788\) −4.00000 6.92820i −0.142494 0.246807i
\(789\) 5.00000 8.66025i 0.178005 0.308313i
\(790\) 4.00000 0.142314
\(791\) −1.50000 7.79423i −0.0533339 0.277131i
\(792\) −3.00000 −0.106600
\(793\) 5.50000 9.52628i 0.195311 0.338288i
\(794\) −10.0000 17.3205i −0.354887 0.614682i
\(795\) −1.00000 1.73205i −0.0354663 0.0614295i
\(796\) −6.00000 + 10.3923i −0.212664 + 0.368345i
\(797\) 34.0000 1.20434 0.602171 0.798367i \(-0.294303\pi\)
0.602171 + 0.798367i \(0.294303\pi\)
\(798\) −7.50000 2.59808i −0.265497 0.0919709i
\(799\) −9.00000 −0.318397
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) −5.00000 8.66025i −0.176666 0.305995i
\(802\) 6.00000 + 10.3923i 0.211867 + 0.366965i
\(803\) 18.0000 31.1769i 0.635206 1.10021i
\(804\) 7.00000 0.246871
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −10.5000 + 18.1865i −0.369618 + 0.640196i
\(808\) −7.00000 12.1244i −0.246259 0.426533i
\(809\) −3.50000 6.06218i −0.123053 0.213135i 0.797917 0.602767i \(-0.205935\pi\)
−0.920970 + 0.389633i \(0.872602\pi\)
\(810\) −1.00000 + 1.73205i −0.0351364 + 0.0608581i
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) −6.00000 + 5.19615i −0.210559 + 0.182349i
\(813\) −15.0000 −0.526073
\(814\) −3.00000 + 5.19615i −0.105150 + 0.182125i
\(815\) −25.0000 43.3013i −0.875712 1.51678i
\(816\) 0.500000 + 0.866025i 0.0175035 + 0.0303170i
\(817\) 9.00000 15.5885i 0.314870 0.545371i
\(818\) 38.0000 1.32864
\(819\) −2.50000 0.866025i −0.0873571 0.0302614i
\(820\) −4.00000 −0.139686
\(821\) 3.00000 5.19615i 0.104701 0.181347i −0.808915 0.587925i \(-0.799945\pi\)
0.913616 + 0.406578i \(0.133278\pi\)
\(822\) −9.00000 15.5885i −0.313911 0.543710i
\(823\) −13.0000 22.5167i −0.453152 0.784881i 0.545428 0.838157i \(-0.316367\pi\)
−0.998580 + 0.0532760i \(0.983034\pi\)
\(824\) 7.00000 12.1244i 0.243857 0.422372i
\(825\) 3.00000 0.104447
\(826\) 5.50000 + 28.5788i 0.191369 + 0.994385i
\(827\) −3.00000 −0.104320 −0.0521601 0.998639i \(-0.516611\pi\)
−0.0521601 + 0.998639i \(0.516611\pi\)
\(828\) 0 0
\(829\) −26.5000 45.8993i −0.920383 1.59415i −0.798823 0.601566i \(-0.794544\pi\)
−0.121560 0.992584i \(-0.538790\pi\)
\(830\) 0 0
\(831\) 2.50000 4.33013i 0.0867240 0.150210i
\(832\) −1.00000 −0.0346688
\(833\) 5.50000 + 4.33013i 0.190564 + 0.150030i
\(834\) −14.0000 −0.484780
\(835\) −19.0000 + 32.9090i −0.657522 + 1.13886i
\(836\) 4.50000 + 7.79423i 0.155636 + 0.269569i
\(837\) −2.00000 3.46410i −0.0691301 0.119737i
\(838\) −3.00000 + 5.19615i −0.103633 + 0.179498i
\(839\) 23.0000 0.794048 0.397024 0.917808i \(-0.370043\pi\)
0.397024 + 0.917808i \(0.370043\pi\)
\(840\) 1.00000 + 5.19615i 0.0345033 + 0.179284i
\(841\) −20.0000 −0.689655
\(842\) 0 0
\(843\) −12.0000 20.7846i −0.413302 0.715860i
\(844\) 8.00000 + 13.8564i 0.275371 + 0.476957i
\(845\) 1.00000 1.73205i 0.0344010 0.0595844i
\(846\) 9.00000 0.309426
\(847\) −5.00000 1.73205i −0.171802 0.0595140i
\(848\) 1.00000 0.0343401
\(849\) −2.00000 + 3.46410i −0.0686398 + 0.118888i
\(850\) −0.500000 0.866025i −0.0171499 0.0297044i
\(851\) 0 0
\(852\) 7.50000 12.9904i 0.256946 0.445043i
\(853\) −32.0000 −1.09566 −0.547830 0.836590i \(-0.684546\pi\)
−0.547830 + 0.836590i \(0.684546\pi\)
\(854\) 22.0000 19.0526i 0.752825 0.651965i
\(855\) 6.00000 0.205196
\(856\) −2.00000 + 3.46410i −0.0683586 + 0.118401i
\(857\) −3.50000 6.06218i −0.119558 0.207080i 0.800035 0.599954i \(-0.204814\pi\)
−0.919592 + 0.392874i \(0.871481\pi\)
\(858\) 1.50000 + 2.59808i 0.0512092 + 0.0886969i
\(859\) −20.0000 + 34.6410i −0.682391 + 1.18194i 0.291858 + 0.956462i \(0.405727\pi\)
−0.974249 + 0.225475i \(0.927607\pi\)
\(860\) −12.0000 −0.409197
\(861\) 4.00000 3.46410i 0.136320 0.118056i
\(862\) 40.0000 1.36241
\(863\) −2.00000 + 3.46410i −0.0680808 + 0.117919i −0.898056 0.439880i \(-0.855021\pi\)
0.829976 + 0.557800i \(0.188354\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) 7.00000 + 12.1244i 0.238007 + 0.412240i
\(866\) −5.50000 + 9.52628i −0.186898 + 0.323716i
\(867\) 16.0000 0.543388
\(868\) −10.0000 3.46410i −0.339422 0.117579i
\(869\) 6.00000 0.203536
\(870\) 3.00000 5.19615i 0.101710 0.176166i
\(871\) −3.50000 6.06218i −0.118593 0.205409i
\(872\) −4.00000 6.92820i −0.135457 0.234619i
\(873\) 6.00000 10.3923i 0.203069 0.351726i
\(874\) 0 0
\(875\) −6.00000 31.1769i −0.202837 1.05397i
\(876\) 12.0000 0.405442
\(877\) 21.0000 36.3731i 0.709120 1.22823i −0.256064 0.966660i \(-0.582426\pi\)
0.965184 0.261571i \(-0.0842407\pi\)
\(878\) 8.00000 + 13.8564i 0.269987 + 0.467631i
\(879\) −6.00000 10.3923i −0.202375 0.350524i
\(880\) 3.00000 5.19615i 0.101130 0.175162i
\(881\) −10.0000 −0.336909 −0.168454 0.985709i \(-0.553878\pi\)
−0.168454 + 0.985709i \(0.553878\pi\)
\(882\) −5.50000 4.33013i −0.185195 0.145803i
\(883\) −14.0000 −0.471138 −0.235569 0.971858i \(-0.575695\pi\)
−0.235569 + 0.971858i \(0.575695\pi\)
\(884\) 0.500000 0.866025i 0.0168168 0.0291276i
\(885\) −11.0000 19.0526i −0.369761 0.640445i
\(886\) 3.00000 + 5.19615i 0.100787 + 0.174568i
\(887\) 3.00000 5.19615i 0.100730 0.174470i −0.811256 0.584692i \(-0.801215\pi\)
0.911986 + 0.410222i \(0.134549\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −4.00000 20.7846i −0.134156 0.697093i
\(890\) 20.0000 0.670402
\(891\) −1.50000 + 2.59808i −0.0502519 + 0.0870388i
\(892\) 0.500000 + 0.866025i 0.0167412 + 0.0289967i
\(893\) −13.5000 23.3827i −0.451760 0.782472i
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) −2.50000 0.866025i −0.0835191 0.0289319i
\(897\) 0 0
\(898\) −20.0000 + 34.6410i −0.667409 + 1.15599i
\(899\) 6.00000 + 10.3923i 0.200111 + 0.346603i
\(900\) 0.500000 + 0.866025i 0.0166667 + 0.0288675i
\(901\) −0.500000 + 0.866025i −0.0166574 + 0.0288515i
\(902\) −6.00000 −0.199778
\(903\) 12.0000 10.3923i 0.399335 0.345834i
\(904\) −3.00000 −0.0997785
\(905\) −5.00000 + 8.66025i −0.166206 + 0.287877i
\(906\) 8.50000 + 14.7224i 0.282394 + 0.489120i
\(907\) 22.0000 + 38.1051i 0.730498 + 1.26526i 0.956671 + 0.291172i \(0.0940453\pi\)
−0.226173 + 0.974087i \(0.572621\pi\)
\(908\) −4.00000 + 6.92820i −0.132745 + 0.229920i
\(909\) −14.0000 −0.464351
\(910\) 4.00000 3.46410i 0.132599 0.114834i
\(911\) −14.0000 −0.463841 −0.231920 0.972735i \(-0.574501\pi\)
−0.231920 + 0.972735i \(0.574501\pi\)
\(912\) −1.50000 + 2.59808i −0.0496700 + 0.0860309i
\(913\) 0 0
\(914\) −16.0000 27.7128i −0.529233 0.916658i
\(915\) −11.0000 + 19.0526i −0.363649 + 0.629858i
\(916\) −2.00000 −0.0660819
\(917\) −30.0000 10.3923i −0.990687 0.343184i
\(918\) 1.00000 0.0330049
\(919\) −23.0000 + 39.8372i −0.758700 + 1.31411i 0.184814 + 0.982774i \(0.440832\pi\)
−0.943514 + 0.331333i \(0.892502\pi\)
\(920\) 0 0
\(921\) −7.50000 12.9904i −0.247133 0.428048i
\(922\) −10.0000 + 17.3205i −0.329332 + 0.570421i
\(923\) −15.0000 −0.493731
\(924\) 1.50000 + 7.79423i 0.0493464 + 0.256411i
\(925\) 2.00000 0.0657596
\(926\) −16.0000 + 27.7128i −0.525793 + 0.910700i
\(927\) −7.00000 12.1244i −0.229910 0.398216i
\(928\) 1.50000 + 2.59808i 0.0492399 + 0.0852860i
\(929\) −17.0000 + 29.4449i −0.557752 + 0.966055i 0.439932 + 0.898031i \(0.355003\pi\)
−0.997684 + 0.0680235i \(0.978331\pi\)
\(930\) 8.00000 0.262330
\(931\) −3.00000 + 20.7846i −0.0983210 + 0.681188i
\(932\) 7.00000 0.229293
\(933\) 7.00000 12.1244i 0.229170 0.396934i
\(934\) 0 0
\(935\) 3.00000 + 5.19615i 0.0981105 + 0.169932i
\(936\) −0.500000 + 0.866025i −0.0163430 + 0.0283069i
\(937\) −13.0000 −0.424691 −0.212346 0.977195i \(-0.568110\pi\)
−0.212346 + 0.977195i \(0.568110\pi\)
\(938\) −3.50000 18.1865i −0.114279 0.593811i
\(939\) 14.0000 0.456873
\(940\) −9.00000 + 15.5885i −0.293548 + 0.508439i
\(941\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(942\) 5.50000 + 9.52628i 0.179200 + 0.310383i
\(943\) 0 0
\(944\) 11.0000 0.358020
\(945\) 5.00000 + 1.73205i 0.162650 + 0.0563436i
\(946\) −18.0000 −0.585230
\(947\) 16.5000 28.5788i 0.536178 0.928687i −0.462927 0.886396i \(-0.653201\pi\)
0.999105 0.0422912i \(-0.0134657\pi\)
\(948\) 1.00000 + 1.73205i 0.0324785 + 0.0562544i
\(949\) −6.00000 10.3923i −0.194768 0.337348i
\(950\) 1.50000 2.59808i 0.0486664 0.0842927i
\(951\) −18.0000 −0.583690
\(952\) 2.00000 1.73205i 0.0648204 0.0561361i
\(953\) −33.0000 −1.06897 −0.534487 0.845176i \(-0.679495\pi\)
−0.534487 + 0.845176i \(0.679495\pi\)
\(954\) 0.500000 0.866025i 0.0161881 0.0280386i
\(955\) −12.0000 20.7846i −0.388311 0.672574i
\(956\) 5.50000 + 9.52628i 0.177883 + 0.308102i
\(957\) 4.50000 7.79423i 0.145464 0.251952i
\(958\) −15.0000 −0.484628
\(959\) −36.0000 + 31.1769i −1.16250 + 1.00676i
\(960\) 2.00000 0.0645497
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) 1.00000 + 1.73205i 0.0322413 + 0.0558436i
\(963\) 2.00000 + 3.46410i 0.0644491 + 0.111629i
\(964\) −6.00000 + 10.3923i −0.193247 + 0.334714i
\(965\) 28.0000 0.901352
\(966\) 0 0
\(967\) 21.0000 0.675314 0.337657 0.941269i \(-0.390366\pi\)
0.337657 + 0.941269i \(0.390366\pi\)
\(968\) −1.00000 + 1.73205i −0.0321412 + 0.0556702i
\(969\) −1.50000 2.59808i −0.0481869 0.0834622i
\(970\) 12.0000 + 20.7846i 0.385297 + 0.667354i
\(971\) −5.00000 + 8.66025i −0.160458 + 0.277921i −0.935033 0.354561i \(-0.884630\pi\)
0.774575 + 0.632482i \(0.217964\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 7.00000 + 36.3731i 0.224410 + 1.16607i
\(974\) 33.0000 1.05739
\(975\) 0.500000 0.866025i 0.0160128 0.0277350i
\(976\) −5.50000 9.52628i −0.176051 0.304929i
\(977\) −19.0000 32.9090i −0.607864 1.05285i −0.991592 0.129405i \(-0.958693\pi\)
0.383728 0.923446i \(-0.374640\pi\)
\(978\) 12.5000 21.6506i 0.399706 0.692311i
\(979\) 30.0000 0.958804
\(980\) 13.0000 5.19615i 0.415270 0.165985i
\(981\) −8.00000 −0.255420
\(982\) 11.0000 19.0526i 0.351024 0.607992i
\(983\) −10.5000 18.1865i −0.334898 0.580060i 0.648567 0.761157i \(-0.275369\pi\)
−0.983465 + 0.181097i \(0.942035\pi\)
\(984\) −1.00000 1.73205i −0.0318788 0.0552158i
\(985\) 8.00000 13.8564i 0.254901 0.441502i
\(986\) −3.00000 −0.0955395
\(987\) −4.50000 23.3827i −0.143237 0.744279i
\(988\) 3.00000 0.0954427
\(989\) 0 0
\(990\) −3.00000 5.19615i −0.0953463 0.165145i
\(991\) 12.0000 + 20.7846i 0.381193 + 0.660245i 0.991233 0.132125i \(-0.0421802\pi\)
−0.610040 + 0.792370i \(0.708847\pi\)
\(992\) −2.00000 + 3.46410i −0.0635001 + 0.109985i
\(993\) 28.0000 0.888553
\(994\) −37.5000 12.9904i −1.18943 0.412030i
\(995\) −24.0000 −0.760851
\(996\) 0 0
\(997\) −5.50000 9.52628i −0.174187 0.301700i 0.765693 0.643206i \(-0.222396\pi\)
−0.939880 + 0.341506i \(0.889063\pi\)
\(998\) 14.0000 + 24.2487i 0.443162 + 0.767580i
\(999\) −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 546.2.i.g.79.1 2
3.2 odd 2 1638.2.j.b.1171.1 2
7.2 even 3 3822.2.a.c.1.1 1
7.4 even 3 inner 546.2.i.g.235.1 yes 2
7.5 odd 6 3822.2.a.q.1.1 1
21.11 odd 6 1638.2.j.b.235.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.i.g.79.1 2 1.1 even 1 trivial
546.2.i.g.235.1 yes 2 7.4 even 3 inner
1638.2.j.b.235.1 2 21.11 odd 6
1638.2.j.b.1171.1 2 3.2 odd 2
3822.2.a.c.1.1 1 7.2 even 3
3822.2.a.q.1.1 1 7.5 odd 6