Properties

Label 1014.2.e.c.991.1
Level $1014$
Weight $2$
Character 1014.991
Analytic conductor $8.097$
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] = [1014,2,Mod(529,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.09683076496\)
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: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1014.991
Dual form 1014.2.e.c.529.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-2.00000 - 3.46410i) q^{11} -1.00000 q^{12} -4.00000 q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +1.00000 q^{18} +(-4.00000 + 6.92820i) q^{19} +(1.00000 - 1.73205i) q^{20} +4.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} -1.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.00000 + 1.73205i) q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} +(-4.00000 + 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} +8.00000 q^{38} -2.00000 q^{40} +(-5.00000 - 8.66025i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(-2.00000 + 3.46410i) q^{43} +4.00000 q^{44} +(1.00000 - 1.73205i) q^{45} -8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} -2.00000 q^{51} -10.0000 q^{53} +(0.500000 + 0.866025i) q^{54} +(4.00000 + 6.92820i) q^{55} +(2.00000 - 3.46410i) q^{56} -8.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(2.00000 - 3.46410i) q^{59} +2.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} -4.00000 q^{66} +(-8.00000 - 13.8564i) q^{67} +(-1.00000 - 1.73205i) q^{68} +8.00000 q^{70} +(-4.00000 + 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} -2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-4.00000 - 6.92820i) q^{76} -16.0000 q^{77} +8.00000 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} -12.0000 q^{83} +(-2.00000 + 3.46410i) q^{84} +(2.00000 - 3.46410i) q^{85} +4.00000 q^{86} +(3.00000 - 5.19615i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(7.00000 + 12.1244i) q^{89} -2.00000 q^{90} +(2.00000 + 3.46410i) q^{93} +(4.00000 + 6.92820i) q^{94} +(8.00000 - 13.8564i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-4.50000 + 7.79423i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - 4 q^{5} + q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} - 4 q^{5} + q^{6} + 4 q^{7} + 2 q^{8} - q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 8 q^{14} - 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{20} + 8 q^{21} - 4 q^{22} + q^{24} - 2 q^{25} - 2 q^{27} + 4 q^{28} - 6 q^{29} - 2 q^{30} + 8 q^{31} - q^{32} + 4 q^{33} + 4 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 16 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{42} - 4 q^{43} + 8 q^{44} + 2 q^{45} - 16 q^{47} + q^{48} - 9 q^{49} + q^{50} - 4 q^{51} - 20 q^{53} + q^{54} + 8 q^{55} + 4 q^{56} - 16 q^{57} - 6 q^{58} + 4 q^{59} + 4 q^{60} + 2 q^{61} - 4 q^{62} + 4 q^{63} + 2 q^{64} - 8 q^{66} - 16 q^{67} - 2 q^{68} + 16 q^{70} - 8 q^{71} - q^{72} - 4 q^{73} - 2 q^{74} - q^{75} - 8 q^{76} - 32 q^{77} + 16 q^{79} + 2 q^{80} - q^{81} - 10 q^{82} - 24 q^{83} - 4 q^{84} + 4 q^{85} + 8 q^{86} + 6 q^{87} - 4 q^{88} + 14 q^{89} - 4 q^{90} + 4 q^{93} + 8 q^{94} + 16 q^{95} - 2 q^{96} + 10 q^{97} - 9 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 2.00000 3.46410i 0.755929 1.30931i −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −4.00000 −1.06904
\(15\) −1.00000 1.73205i −0.258199 0.447214i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.00000 + 6.92820i −0.917663 + 1.58944i −0.114708 + 0.993399i \(0.536593\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 4.00000 0.872872
\(22\) −2.00000 + 3.46410i −0.426401 + 0.738549i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 2.00000 + 3.46410i 0.377964 + 0.654654i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) 2.00000 0.342997
\(35\) −4.00000 + 6.92820i −0.676123 + 1.17108i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 8.00000 1.29777
\(39\) 0 0
\(40\) −2.00000 −0.316228
\(41\) −5.00000 8.66025i −0.780869 1.35250i −0.931436 0.363905i \(-0.881443\pi\)
0.150567 0.988600i \(-0.451890\pi\)
\(42\) −2.00000 3.46410i −0.308607 0.534522i
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 4.00000 0.603023
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −2.00000 −0.280056
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 4.00000 + 6.92820i 0.539360 + 0.934199i
\(56\) 2.00000 3.46410i 0.267261 0.462910i
\(57\) −8.00000 −1.05963
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 2.00000 0.258199
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) 2.00000 + 3.46410i 0.251976 + 0.436436i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) −8.00000 13.8564i −0.977356 1.69283i −0.671932 0.740613i \(-0.734535\pi\)
−0.305424 0.952217i \(-0.598798\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) 0 0
\(70\) 8.00000 0.956183
\(71\) −4.00000 + 6.92820i −0.474713 + 0.822226i −0.999581 0.0289572i \(-0.990781\pi\)
0.524868 + 0.851184i \(0.324115\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −4.00000 6.92820i −0.458831 0.794719i
\(77\) −16.0000 −1.82337
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.00000 + 8.66025i −0.552158 + 0.956365i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −2.00000 + 3.46410i −0.218218 + 0.377964i
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) 4.00000 0.431331
\(87\) 3.00000 5.19615i 0.321634 0.557086i
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i \(0.0994552\pi\)
−0.209585 + 0.977790i \(0.567211\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) 0 0
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 4.00000 + 6.92820i 0.412568 + 0.714590i
\(95\) 8.00000 13.8564i 0.820783 1.42164i
\(96\) −1.00000 −0.102062
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −4.50000 + 7.79423i −0.454569 + 0.787336i
\(99\) 4.00000 0.402015
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 1.00000 + 1.73205i 0.0990148 + 0.171499i
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 5.00000 + 8.66025i 0.485643 + 0.841158i
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 4.00000 6.92820i 0.381385 0.660578i
\(111\) 1.00000 1.73205i 0.0949158 0.164399i
\(112\) −4.00000 −0.377964
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 4.00000 + 6.92820i 0.374634 + 0.648886i
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 4.00000 + 6.92820i 0.366679 + 0.635107i
\(120\) −1.00000 1.73205i −0.0912871 0.158114i
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) −2.00000 −0.181071
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 12.0000 1.07331
\(126\) 2.00000 3.46410i 0.178174 0.308607i
\(127\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 2.00000 + 3.46410i 0.174078 + 0.301511i
\(133\) 16.0000 + 27.7128i 1.38738 + 2.40301i
\(134\) −8.00000 + 13.8564i −0.691095 + 1.19701i
\(135\) 2.00000 0.172133
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) −4.00000 6.92820i −0.338062 0.585540i
\(141\) −4.00000 6.92820i −0.336861 0.583460i
\(142\) 8.00000 0.671345
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 6.00000 + 10.3923i 0.498273 + 0.863034i
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 4.50000 7.79423i 0.371154 0.642857i
\(148\) 2.00000 0.164399
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) −4.00000 + 6.92820i −0.324443 + 0.561951i
\(153\) −1.00000 1.73205i −0.0808452 0.140028i
\(154\) 8.00000 + 13.8564i 0.644658 + 1.11658i
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) −5.00000 8.66025i −0.396526 0.686803i
\(160\) 1.00000 1.73205i 0.0790569 0.136931i
\(161\) 0 0
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i \(0.382224\pi\)
−0.988227 + 0.152992i \(0.951109\pi\)
\(164\) 10.0000 0.780869
\(165\) −4.00000 + 6.92820i −0.311400 + 0.539360i
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 4.00000 0.308607
\(169\) 0 0
\(170\) −4.00000 −0.306786
\(171\) −4.00000 6.92820i −0.305888 0.529813i
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 5.00000 8.66025i 0.380143 0.658427i −0.610939 0.791677i \(-0.709208\pi\)
0.991082 + 0.133250i \(0.0425415\pi\)
\(174\) −6.00000 −0.454859
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) −2.00000 + 3.46410i −0.150756 + 0.261116i
\(177\) 4.00000 0.300658
\(178\) 7.00000 12.1244i 0.524672 0.908759i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) 8.00000 0.585018
\(188\) 4.00000 6.92820i 0.291730 0.505291i
\(189\) −2.00000 + 3.46410i −0.145479 + 0.251976i
\(190\) −16.0000 −1.16076
\(191\) 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 9.00000 + 15.5885i 0.641223 + 1.11063i 0.985160 + 0.171639i \(0.0549062\pi\)
−0.343937 + 0.938993i \(0.611761\pi\)
\(198\) −2.00000 3.46410i −0.142134 0.246183i
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.00000 13.8564i 0.564276 0.977356i
\(202\) 1.00000 1.73205i 0.0703598 0.121867i
\(203\) −24.0000 −1.68447
\(204\) 1.00000 1.73205i 0.0700140 0.121268i
\(205\) 10.0000 + 17.3205i 0.698430 + 1.20972i
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) 0 0
\(208\) 0 0
\(209\) 32.0000 2.21349
\(210\) 4.00000 + 6.92820i 0.276026 + 0.478091i
\(211\) −6.00000 10.3923i −0.413057 0.715436i 0.582165 0.813070i \(-0.302206\pi\)
−0.995222 + 0.0976347i \(0.968872\pi\)
\(212\) 5.00000 8.66025i 0.343401 0.594789i
\(213\) −8.00000 −0.548151
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 4.00000 6.92820i 0.272798 0.472500i
\(216\) −1.00000 −0.0680414
\(217\) 8.00000 13.8564i 0.543075 0.940634i
\(218\) −1.00000 1.73205i −0.0677285 0.117309i
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) −8.00000 −0.539360
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 2.00000 + 3.46410i 0.133631 + 0.231455i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −6.00000 −0.399114
\(227\) 10.0000 17.3205i 0.663723 1.14960i −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) 4.00000 6.92820i 0.264906 0.458831i
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) −8.00000 13.8564i −0.526361 0.911685i
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 4.00000 + 6.92820i 0.259828 + 0.450035i
\(238\) 4.00000 6.92820i 0.259281 0.449089i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 + 1.73205i −0.0645497 + 0.111803i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 5.00000 0.321412
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) −10.0000 −0.637577
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) −2.00000 + 3.46410i −0.126239 + 0.218652i −0.922217 0.386674i \(-0.873624\pi\)
0.795978 + 0.605326i \(0.206957\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) 0 0
\(255\) 4.00000 0.250490
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 2.00000 + 3.46410i 0.124515 + 0.215666i
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) −2.00000 3.46410i −0.123560 0.214013i
\(263\) −4.00000 6.92820i −0.246651 0.427211i 0.715944 0.698158i \(-0.245997\pi\)
−0.962594 + 0.270947i \(0.912663\pi\)
\(264\) 2.00000 3.46410i 0.123091 0.213201i
\(265\) 20.0000 1.22859
\(266\) 16.0000 27.7128i 0.981023 1.69918i
\(267\) −7.00000 + 12.1244i −0.428393 + 0.741999i
\(268\) 16.0000 0.977356
\(269\) 13.0000 22.5167i 0.792624 1.37287i −0.131713 0.991288i \(-0.542048\pi\)
0.924337 0.381577i \(-0.124619\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −2.00000 3.46410i −0.121491 0.210429i 0.798865 0.601511i \(-0.205434\pi\)
−0.920356 + 0.391082i \(0.872101\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 0 0
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) 12.0000 0.719712
\(279\) −2.00000 + 3.46410i −0.119737 + 0.207390i
\(280\) −4.00000 + 6.92820i −0.239046 + 0.414039i
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) −4.00000 + 6.92820i −0.238197 + 0.412568i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) 16.0000 0.947758
\(286\) 0 0
\(287\) −40.0000 −2.36113
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 6.00000 10.3923i 0.352332 0.610257i
\(291\) 10.0000 0.586210
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 13.0000 22.5167i 0.759468 1.31544i −0.183654 0.982991i \(-0.558793\pi\)
0.943122 0.332446i \(-0.107874\pi\)
\(294\) −9.00000 −0.524891
\(295\) −4.00000 + 6.92820i −0.232889 + 0.403376i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 8.00000 + 13.8564i 0.461112 + 0.798670i
\(302\) 6.00000 + 10.3923i 0.345261 + 0.598010i
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 8.00000 0.458831
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) −1.00000 + 1.73205i −0.0571662 + 0.0990148i
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 8.00000 13.8564i 0.455842 0.789542i
\(309\) 8.00000 + 13.8564i 0.455104 + 0.788263i
\(310\) 4.00000 + 6.92820i 0.227185 + 0.393496i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −7.00000 12.1244i −0.395033 0.684217i
\(315\) −4.00000 6.92820i −0.225374 0.390360i
\(316\) −4.00000 + 6.92820i −0.225018 + 0.389742i
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) −5.00000 + 8.66025i −0.280386 + 0.485643i
\(319\) −12.0000 + 20.7846i −0.671871 + 1.16371i
\(320\) −2.00000 −0.111803
\(321\) 6.00000 10.3923i 0.334887 0.580042i
\(322\) 0 0
\(323\) −8.00000 13.8564i −0.445132 0.770991i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 16.0000 0.886158
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) −5.00000 8.66025i −0.276079 0.478183i
\(329\) −16.0000 + 27.7128i −0.882109 + 1.52786i
\(330\) 8.00000 0.440386
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) 2.00000 0.109599
\(334\) 0 0
\(335\) 16.0000 + 27.7128i 0.874173 + 1.51411i
\(336\) −2.00000 3.46410i −0.109109 0.188982i
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) −8.00000 13.8564i −0.433224 0.750366i
\(342\) −4.00000 + 6.92820i −0.216295 + 0.374634i
\(343\) −8.00000 −0.431959
\(344\) −2.00000 + 3.46410i −0.107833 + 0.186772i
\(345\) 0 0
\(346\) −10.0000 −0.537603
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) 3.00000 + 5.19615i 0.160586 + 0.278144i 0.935079 0.354439i \(-0.115328\pi\)
−0.774493 + 0.632583i \(0.781995\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 4.00000 0.213201
\(353\) 7.00000 + 12.1244i 0.372572 + 0.645314i 0.989960 0.141344i \(-0.0451425\pi\)
−0.617388 + 0.786659i \(0.711809\pi\)
\(354\) −2.00000 3.46410i −0.106299 0.184115i
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) −14.0000 −0.741999
\(357\) −4.00000 + 6.92820i −0.211702 + 0.366679i
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 1.00000 1.73205i 0.0527046 0.0912871i
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) 2.00000 3.46410i 0.103975 0.180090i
\(371\) −20.0000 + 34.6410i −1.03835 + 1.79847i
\(372\) −4.00000 −0.207390
\(373\) −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) −4.00000 6.92820i −0.206835 0.358249i
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) −8.00000 −0.412568
\(377\) 0 0
\(378\) 4.00000 0.205738
\(379\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(380\) 8.00000 + 13.8564i 0.410391 + 0.710819i
\(381\) 0 0
\(382\) −8.00000 −0.409316
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 32.0000 1.63087
\(386\) −7.00000 + 12.1244i −0.356291 + 0.617113i
\(387\) −2.00000 3.46410i −0.101666 0.176090i
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.50000 7.79423i −0.227284 0.393668i
\(393\) 2.00000 + 3.46410i 0.100887 + 0.174741i
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) −16.0000 −0.805047
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) 3.00000 5.19615i 0.150566 0.260787i −0.780870 0.624694i \(-0.785224\pi\)
0.931436 + 0.363906i \(0.118557\pi\)
\(398\) −8.00000 −0.401004
\(399\) −16.0000 + 27.7128i −0.801002 + 1.38738i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) −16.0000 −0.798007
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) 1.00000 + 1.73205i 0.0496904 + 0.0860663i
\(406\) 12.0000 + 20.7846i 0.595550 + 1.03152i
\(407\) −4.00000 + 6.92820i −0.198273 + 0.343418i
\(408\) −2.00000 −0.0990148
\(409\) 1.00000 1.73205i 0.0494468 0.0856444i −0.840243 0.542211i \(-0.817588\pi\)
0.889689 + 0.456566i \(0.150921\pi\)
\(410\) 10.0000 17.3205i 0.493865 0.855399i
\(411\) −10.0000 −0.493264
\(412\) −8.00000 + 13.8564i −0.394132 + 0.682656i
\(413\) −8.00000 13.8564i −0.393654 0.681829i
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) −16.0000 27.7128i −0.782586 1.35548i
\(419\) −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i \(-0.197817\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(420\) 4.00000 6.92820i 0.195180 0.338062i
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) −6.00000 + 10.3923i −0.292075 + 0.505889i
\(423\) 4.00000 6.92820i 0.194487 0.336861i
\(424\) −10.0000 −0.485643
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 4.00000 + 6.92820i 0.193801 + 0.335673i
\(427\) −4.00000 6.92820i −0.193574 0.335279i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) −4.00000 6.92820i −0.192673 0.333720i 0.753462 0.657491i \(-0.228382\pi\)
−0.946135 + 0.323772i \(0.895049\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 15.0000 25.9808i 0.720854 1.24856i −0.239804 0.970821i \(-0.577083\pi\)
0.960658 0.277734i \(-0.0895835\pi\)
\(434\) −16.0000 −0.768025
\(435\) −6.00000 + 10.3923i −0.287678 + 0.498273i
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) −1.00000 + 1.73205i −0.0477818 + 0.0827606i
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 4.00000 + 6.92820i 0.190693 + 0.330289i
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 1.00000 + 1.73205i 0.0474579 + 0.0821995i
\(445\) −14.0000 24.2487i −0.663664 1.14950i
\(446\) −2.00000 + 3.46410i −0.0947027 + 0.164030i
\(447\) −6.00000 −0.283790
\(448\) 2.00000 3.46410i 0.0944911 0.163663i
\(449\) 3.00000 5.19615i 0.141579 0.245222i −0.786513 0.617574i \(-0.788115\pi\)
0.928091 + 0.372353i \(0.121449\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −20.0000 + 34.6410i −0.941763 + 1.63118i
\(452\) 3.00000 + 5.19615i 0.141108 + 0.244406i
\(453\) −6.00000 10.3923i −0.281905 0.488273i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) −15.0000 25.9808i −0.701670 1.21533i −0.967880 0.251414i \(-0.919105\pi\)
0.266209 0.963915i \(-0.414229\pi\)
\(458\) 11.0000 + 19.0526i 0.513996 + 0.890268i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 0 0
\(461\) −3.00000 + 5.19615i −0.139724 + 0.242009i −0.927392 0.374091i \(-0.877955\pi\)
0.787668 + 0.616100i \(0.211288\pi\)
\(462\) −8.00000 + 13.8564i −0.372194 + 0.644658i
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) −4.00000 6.92820i −0.185496 0.321288i
\(466\) −9.00000 15.5885i −0.416917 0.722121i
\(467\) −4.00000 −0.185098 −0.0925490 0.995708i \(-0.529501\pi\)
−0.0925490 + 0.995708i \(0.529501\pi\)
\(468\) 0 0
\(469\) −64.0000 −2.95525
\(470\) −8.00000 13.8564i −0.369012 0.639148i
\(471\) 7.00000 + 12.1244i 0.322543 + 0.558661i
\(472\) 2.00000 3.46410i 0.0920575 0.159448i
\(473\) 16.0000 0.735681
\(474\) 4.00000 6.92820i 0.183726 0.318223i
\(475\) 4.00000 6.92820i 0.183533 0.317888i
\(476\) −8.00000 −0.366679
\(477\) 5.00000 8.66025i 0.228934 0.396526i
\(478\) 0 0
\(479\) −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) 2.00000 0.0912871
\(481\) 0 0
\(482\) −10.0000 −0.455488
\(483\) 0 0
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) −10.0000 + 17.3205i −0.454077 + 0.786484i
\(486\) −1.00000 −0.0453609
\(487\) 2.00000 3.46410i 0.0906287 0.156973i −0.817147 0.576429i \(-0.804446\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) −16.0000 −0.723545
\(490\) 9.00000 15.5885i 0.406579 0.704215i
\(491\) −18.0000 31.1769i −0.812329 1.40699i −0.911230 0.411897i \(-0.864866\pi\)
0.0989017 0.995097i \(-0.468467\pi\)
\(492\) 5.00000 + 8.66025i 0.225417 + 0.390434i
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) −8.00000 −0.359573
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) 16.0000 + 27.7128i 0.717698 + 1.24309i
\(498\) −6.00000 + 10.3923i −0.268866 + 0.465690i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 4.00000 0.178529
\(503\) −20.0000 + 34.6410i −0.891756 + 1.54457i −0.0539870 + 0.998542i \(0.517193\pi\)
−0.837769 + 0.546025i \(0.816140\pi\)
\(504\) 2.00000 + 3.46410i 0.0890871 + 0.154303i
\(505\) −2.00000 3.46410i −0.0889988 0.154150i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 21.0000 + 36.3731i 0.930809 + 1.61221i 0.781943 + 0.623350i \(0.214229\pi\)
0.148866 + 0.988857i \(0.452438\pi\)
\(510\) −2.00000 3.46410i −0.0885615 0.153393i
\(511\) −4.00000 + 6.92820i −0.176950 + 0.306486i
\(512\) 1.00000 0.0441942
\(513\) 4.00000 6.92820i 0.176604 0.305888i
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) −32.0000 −1.41009
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 16.0000 + 27.7128i 0.703679 + 1.21881i
\(518\) 4.00000 + 6.92820i 0.175750 + 0.304408i
\(519\) 10.0000 0.438951
\(520\) 0 0
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) −2.00000 + 3.46410i −0.0873704 + 0.151330i
\(525\) −4.00000 −0.174574
\(526\) −4.00000 + 6.92820i −0.174408 + 0.302084i
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) −4.00000 −0.174078
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −10.0000 17.3205i −0.434372 0.752355i
\(531\) 2.00000 + 3.46410i 0.0867926 + 0.150329i
\(532\) −32.0000 −1.38738
\(533\) 0 0
\(534\) 14.0000 0.605839
\(535\) 12.0000 + 20.7846i 0.518805 + 0.898597i
\(536\) −8.00000 13.8564i −0.345547 0.598506i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) −26.0000 −1.12094
\(539\) −18.0000 + 31.1769i −0.775315 + 1.34288i
\(540\) −1.00000 + 1.73205i −0.0430331 + 0.0745356i
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) −2.00000 + 3.46410i −0.0859074 + 0.148796i
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −5.00000 8.66025i −0.213589 0.369948i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 2.00000 3.46410i 0.0852803 0.147710i
\(551\) 48.0000 2.04487
\(552\) 0 0
\(553\) 16.0000 27.7128i 0.680389 1.17847i
\(554\) 22.0000 0.934690
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) −6.00000 10.3923i −0.254457 0.440732i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 8.00000 0.338062
\(561\) 4.00000 + 6.92820i 0.168880 + 0.292509i
\(562\) −13.0000 22.5167i −0.548372 0.949808i
\(563\) −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) 8.00000 0.336861
\(565\) −6.00000 + 10.3923i −0.252422 + 0.437208i
\(566\) 2.00000 3.46410i 0.0840663 0.145607i
\(567\) −4.00000 −0.167984
\(568\) −4.00000 + 6.92820i −0.167836 + 0.290701i
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) −8.00000 13.8564i −0.335083 0.580381i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 20.0000 + 34.6410i 0.834784 + 1.44589i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) 7.00000 12.1244i 0.290910 0.503871i
\(580\) −12.0000 −0.498273
\(581\) −24.0000 + 41.5692i −0.995688 + 1.72458i
\(582\) −5.00000 8.66025i −0.207257 0.358979i
\(583\) 20.0000 + 34.6410i 0.828315 + 1.43468i
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −26.0000 −1.07405
\(587\) 2.00000 + 3.46410i 0.0825488 + 0.142979i 0.904344 0.426804i \(-0.140361\pi\)
−0.821795 + 0.569783i \(0.807027\pi\)
\(588\) 4.50000 + 7.79423i 0.185577 + 0.321429i
\(589\) −16.0000 + 27.7128i −0.659269 + 1.14189i
\(590\) 8.00000 0.329355
\(591\) −9.00000 + 15.5885i −0.370211 + 0.641223i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) 2.00000 3.46410i 0.0820610 0.142134i
\(595\) −8.00000 13.8564i −0.327968 0.568057i
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) −13.0000 22.5167i −0.530281 0.918474i −0.999376 0.0353259i \(-0.988753\pi\)
0.469095 0.883148i \(-0.344580\pi\)
\(602\) 8.00000 13.8564i 0.326056 0.564745i
\(603\) 16.0000 0.651570
\(604\) 6.00000 10.3923i 0.244137 0.422857i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 2.00000 0.0812444
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −4.00000 6.92820i −0.162221 0.280976i
\(609\) −12.0000 20.7846i −0.486265 0.842235i
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) 2.00000 0.0808452
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) −10.0000 + 17.3205i −0.403239 + 0.698430i
\(616\) −16.0000 −0.644658
\(617\) 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i \(-0.794795\pi\)
0.920074 + 0.391745i \(0.128129\pi\)
\(618\) 8.00000 13.8564i 0.321807 0.557386i
\(619\) −32.0000 −1.28619 −0.643094 0.765787i \(-0.722350\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 0 0
\(622\) 0 0
\(623\) 56.0000 2.24359
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 16.0000 + 27.7128i 0.638978 + 1.10674i
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 4.00000 0.159490
\(630\) −4.00000 + 6.92820i −0.159364 + 0.276026i
\(631\) −18.0000 + 31.1769i −0.716569 + 1.24113i 0.245783 + 0.969325i \(0.420955\pi\)
−0.962351 + 0.271808i \(0.912378\pi\)
\(632\) 8.00000 0.318223
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 0 0
\(636\) 10.0000 0.396526
\(637\) 0 0
\(638\) 24.0000 0.950169
\(639\) −4.00000 6.92820i −0.158238 0.274075i
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) −12.0000 −0.473602
\(643\) −8.00000 + 13.8564i −0.315489 + 0.546443i −0.979541 0.201243i \(-0.935502\pi\)
0.664052 + 0.747686i \(0.268835\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) −8.00000 + 13.8564i −0.314756 + 0.545173i
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −16.0000 −0.628055
\(650\) 0 0
\(651\) 16.0000 0.627089
\(652\) −8.00000 13.8564i −0.313304 0.542659i
\(653\) 5.00000 + 8.66025i 0.195665 + 0.338902i 0.947118 0.320884i \(-0.103980\pi\)
−0.751453 + 0.659786i \(0.770647\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) −8.00000 −0.312586
\(656\) −5.00000 + 8.66025i −0.195217 + 0.338126i
\(657\) 1.00000 1.73205i 0.0390137 0.0675737i
\(658\) 32.0000 1.24749
\(659\) 18.0000 31.1769i 0.701180 1.21448i −0.266872 0.963732i \(-0.585990\pi\)
0.968052 0.250748i \(-0.0806766\pi\)
\(660\) −4.00000 6.92820i −0.155700 0.269680i
\(661\) −1.00000 1.73205i −0.0388955 0.0673690i 0.845922 0.533306i \(-0.179051\pi\)
−0.884818 + 0.465937i \(0.845717\pi\)
\(662\) −8.00000 −0.310929
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) −32.0000 55.4256i −1.24091 2.14931i
\(666\) −1.00000 1.73205i −0.0387492 0.0671156i
\(667\) 0 0
\(668\) 0 0
\(669\) 2.00000 3.46410i 0.0773245 0.133930i
\(670\) 16.0000 27.7128i 0.618134 1.07064i
\(671\) −8.00000 −0.308837
\(672\) −2.00000 + 3.46410i −0.0771517 + 0.133631i
\(673\) 7.00000 + 12.1244i 0.269830 + 0.467360i 0.968818 0.247774i \(-0.0796991\pi\)
−0.698988 + 0.715134i \(0.746366\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 38.0000 1.46046 0.730229 0.683202i \(-0.239413\pi\)
0.730229 + 0.683202i \(0.239413\pi\)
\(678\) −3.00000 5.19615i −0.115214 0.199557i
\(679\) −20.0000 34.6410i −0.767530 1.32940i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 20.0000 0.766402
\(682\) −8.00000 + 13.8564i −0.306336 + 0.530589i
\(683\) 22.0000 38.1051i 0.841807 1.45805i −0.0465592 0.998916i \(-0.514826\pi\)
0.888366 0.459136i \(-0.151841\pi\)
\(684\) 8.00000 0.305888
\(685\) 10.0000 17.3205i 0.382080 0.661783i
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) −11.0000 19.0526i −0.419676 0.726900i
\(688\) 4.00000 0.152499
\(689\) 0 0
\(690\) 0 0
\(691\) −16.0000 27.7128i −0.608669 1.05425i −0.991460 0.130410i \(-0.958371\pi\)
0.382791 0.923835i \(-0.374963\pi\)
\(692\) 5.00000 + 8.66025i 0.190071 + 0.329213i
\(693\) 8.00000 13.8564i 0.303895 0.526361i
\(694\) −12.0000 −0.455514
\(695\) 12.0000 20.7846i 0.455186 0.788405i
\(696\) 3.00000 5.19615i 0.113715 0.196960i
\(697\) 20.0000 0.757554
\(698\) 3.00000 5.19615i 0.113552 0.196677i
\(699\) 9.00000 + 15.5885i 0.340411 + 0.589610i
\(700\) −2.00000 3.46410i −0.0755929 0.130931i
\(701\) −50.0000 −1.88847 −0.944237 0.329267i \(-0.893198\pi\)
−0.944237 + 0.329267i \(0.893198\pi\)
\(702\) 0 0
\(703\) 16.0000 0.603451
\(704\) −2.00000 3.46410i −0.0753778 0.130558i
\(705\) 8.00000 + 13.8564i 0.301297 + 0.521862i
\(706\) 7.00000 12.1244i 0.263448 0.456306i
\(707\) 8.00000 0.300871
\(708\) −2.00000 + 3.46410i −0.0751646 + 0.130189i
\(709\) 3.00000 5.19615i 0.112667 0.195146i −0.804178 0.594389i \(-0.797394\pi\)
0.916845 + 0.399244i \(0.130727\pi\)
\(710\) −16.0000 −0.600469
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) 7.00000 + 12.1244i 0.262336 + 0.454379i
\(713\) 0 0
\(714\) 8.00000 0.299392
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) 0 0
\(719\) 12.0000 20.7846i 0.447524 0.775135i −0.550700 0.834703i \(-0.685639\pi\)
0.998224 + 0.0595683i \(0.0189724\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 32.0000 55.4256i 1.19174 2.06416i
\(722\) −22.5000 + 38.9711i −0.837363 + 1.45036i
\(723\) 10.0000 0.371904
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 2.50000 + 4.33013i 0.0927837 + 0.160706i
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.00000 3.46410i −0.0740233 0.128212i
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) −8.00000 + 13.8564i −0.295285 + 0.511449i
\(735\) −9.00000 + 15.5885i −0.331970 + 0.574989i
\(736\) 0 0
\(737\) −32.0000 + 55.4256i −1.17874 + 2.04163i
\(738\) −5.00000 8.66025i −0.184053 0.318788i
\(739\) 20.0000 + 34.6410i 0.735712 + 1.27429i 0.954410 + 0.298498i \(0.0964856\pi\)
−0.218698 + 0.975793i \(0.570181\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) 40.0000 1.46845
\(743\) −12.0000 20.7846i −0.440237 0.762513i 0.557470 0.830197i \(-0.311772\pi\)
−0.997707 + 0.0676840i \(0.978439\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) 6.00000 0.219676
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) −4.00000 + 6.92820i −0.146254 + 0.253320i
\(749\) −48.0000 −1.75388
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 4.00000 + 6.92820i 0.145865 + 0.252646i
\(753\) −4.00000 −0.145768
\(754\) 0 0
\(755\) 24.0000 0.873449
\(756\) −2.00000 3.46410i −0.0727393 0.125988i
\(757\) −27.0000 46.7654i −0.981332 1.69972i −0.657222 0.753697i \(-0.728269\pi\)
−0.324109 0.946020i \(-0.605065\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 8.00000 13.8564i 0.290191 0.502625i
\(761\) −13.0000 + 22.5167i −0.471250 + 0.816228i −0.999459 0.0328858i \(-0.989530\pi\)
0.528209 + 0.849114i \(0.322864\pi\)
\(762\) 0 0
\(763\) 4.00000 6.92820i 0.144810 0.250818i
\(764\) 4.00000 + 6.92820i 0.144715 + 0.250654i
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 24.0000 0.867155
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 1.00000 + 1.73205i 0.0360609 + 0.0624593i 0.883493 0.468445i \(-0.155186\pi\)
−0.847432 + 0.530904i \(0.821852\pi\)
\(770\) −16.0000 27.7128i −0.576600 0.998700i
\(771\) −3.00000 + 5.19615i −0.108042 + 0.187135i
\(772\) 14.0000 0.503871
\(773\) −27.0000 + 46.7654i −0.971123 + 1.68203i −0.278944 + 0.960307i \(0.589984\pi\)
−0.692179 + 0.721726i \(0.743349\pi\)
\(774\) −2.00000 + 3.46410i −0.0718885 + 0.124515i
\(775\) −4.00000 −0.143684
\(776\) 5.00000 8.66025i 0.179490 0.310885i
\(777\) −4.00000 6.92820i −0.143499 0.248548i
\(778\) 13.0000 + 22.5167i 0.466073 + 0.807261i
\(779\) 80.0000 2.86630
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) 0 0
\(783\) 3.00000 + 5.19615i 0.107211 + 0.185695i
\(784\) −4.50000 + 7.79423i −0.160714 + 0.278365i
\(785\) −28.0000 −0.999363
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) 20.0000 34.6410i 0.712923 1.23482i −0.250832 0.968031i \(-0.580704\pi\)
0.963755 0.266788i \(-0.0859624\pi\)
\(788\) −18.0000 −0.641223
\(789\) 4.00000 6.92820i 0.142404 0.246651i
\(790\) 8.00000 + 13.8564i 0.284627 + 0.492989i
\(791\) −12.0000 20.7846i −0.426671 0.739016i
\(792\) 4.00000 0.142134
\(793\) 0 0
\(794\) −6.00000 −0.212932
\(795\) 10.0000 + 17.3205i 0.354663 + 0.614295i
\(796\) 4.00000 + 6.92820i 0.141776 + 0.245564i
\(797\) 1.00000 1.73205i 0.0354218 0.0613524i −0.847771 0.530362i \(-0.822056\pi\)
0.883193 + 0.469010i \(0.155389\pi\)
\(798\) 32.0000 1.13279
\(799\) 8.00000 13.8564i 0.283020 0.490204i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) −14.0000 −0.494666
\(802\) 3.00000 5.19615i 0.105934 0.183483i
\(803\) 4.00000 + 6.92820i 0.141157 + 0.244491i
\(804\) 8.00000 + 13.8564i 0.282138 + 0.488678i
\(805\) 0 0
\(806\) 0 0
\(807\) 26.0000 0.915243
\(808\) 1.00000 + 1.73205i 0.0351799 + 0.0609333i
\(809\) −1.00000 1.73205i −0.0351581 0.0608957i 0.847911 0.530139i \(-0.177860\pi\)
−0.883069 + 0.469243i \(0.844527\pi\)
\(810\) 1.00000 1.73205i 0.0351364 0.0608581i
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 12.0000 20.7846i 0.421117 0.729397i
\(813\) 2.00000 3.46410i 0.0701431 0.121491i
\(814\) 8.00000 0.280400
\(815\) 16.0000 27.7128i 0.560456 0.970737i
\(816\) 1.00000 + 1.73205i 0.0350070 + 0.0606339i
\(817\) −16.0000 27.7128i −0.559769 0.969549i
\(818\) −2.00000 −0.0699284
\(819\) 0 0
\(820\) −20.0000 −0.698430
\(821\) 21.0000 + 36.3731i 0.732905 + 1.26943i 0.955636 + 0.294549i \(0.0951694\pi\)
−0.222731 + 0.974880i \(0.571497\pi\)
\(822\) 5.00000 + 8.66025i 0.174395 + 0.302061i
\(823\) 8.00000 13.8564i 0.278862 0.483004i −0.692240 0.721668i \(-0.743376\pi\)
0.971102 + 0.238664i \(0.0767093\pi\)
\(824\) 16.0000 0.557386
\(825\) −2.00000 + 3.46410i −0.0696311 + 0.120605i
\(826\) −8.00000 + 13.8564i −0.278356 + 0.482126i
\(827\) −28.0000 −0.973655 −0.486828 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) 0 0
\(829\) 1.00000 + 1.73205i 0.0347314 + 0.0601566i 0.882869 0.469620i \(-0.155609\pi\)
−0.848137 + 0.529777i \(0.822276\pi\)
\(830\) −12.0000 20.7846i −0.416526 0.721444i
\(831\) −22.0000 −0.763172
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) 6.00000 + 10.3923i 0.207763 + 0.359856i
\(835\) 0 0
\(836\) −16.0000 + 27.7128i −0.553372 + 0.958468i
\(837\) −4.00000 −0.138260
\(838\) −2.00000 + 3.46410i −0.0690889 + 0.119665i
\(839\) −20.0000 + 34.6410i −0.690477 + 1.19594i 0.281205 + 0.959648i \(0.409266\pi\)
−0.971682 + 0.236293i \(0.924067\pi\)
\(840\) −8.00000 −0.276026
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 11.0000 + 19.0526i 0.379085 + 0.656595i
\(843\) 13.0000 + 22.5167i 0.447744 + 0.775515i
\(844\) 12.0000 0.413057
\(845\) 0 0
\(846\) −8.00000 −0.275046
\(847\) 10.0000 + 17.3205i 0.343604 + 0.595140i
\(848\) 5.00000 + 8.66025i 0.171701 + 0.297394i
\(849\) −2.00000 + 3.46410i −0.0686398 + 0.118888i
\(850\) −2.00000 −0.0685994
\(851\) 0 0
\(852\) 4.00000 6.92820i 0.137038 0.237356i
\(853\) 2.00000 0.0684787 0.0342393 0.999414i \(-0.489099\pi\)
0.0342393 + 0.999414i \(0.489099\pi\)
\(854\) −4.00000 + 6.92820i −0.136877 + 0.237078i
\(855\) 8.00000 + 13.8564i 0.273594 + 0.473879i
\(856\) −6.00000 10.3923i −0.205076 0.355202i
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −44.0000 −1.50126 −0.750630 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) 4.00000 + 6.92820i 0.136399 + 0.236250i
\(861\) −20.0000 34.6410i −0.681598 1.18056i
\(862\) −4.00000 + 6.92820i −0.136241 + 0.235976i
\(863\) −40.0000 −1.36162 −0.680808 0.732462i \(-0.738371\pi\)
−0.680808 + 0.732462i \(0.738371\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) −10.0000 + 17.3205i −0.340010 + 0.588915i
\(866\) −30.0000 −1.01944
\(867\) −6.50000 + 11.2583i −0.220752 + 0.382353i
\(868\) 8.00000 + 13.8564i 0.271538 + 0.470317i
\(869\) −16.0000 27.7128i −0.542763 0.940093i
\(870\) 12.0000 0.406838
\(871\) 0 0
\(872\) 2.00000 0.0677285
\(873\) 5.00000 + 8.66025i 0.169224 + 0.293105i
\(874\) 0 0
\(875\) 24.0000 41.5692i 0.811348 1.40530i
\(876\) 2.00000 0.0675737
\(877\) 11.0000 19.0526i 0.371444 0.643359i −0.618344 0.785907i \(-0.712196\pi\)
0.989788 + 0.142548i \(0.0455296\pi\)
\(878\) −8.00000 + 13.8564i −0.269987 + 0.467631i
\(879\) 26.0000 0.876958
\(880\) 4.00000 6.92820i 0.134840 0.233550i
\(881\) −13.0000 22.5167i −0.437981 0.758606i 0.559553 0.828795i \(-0.310973\pi\)
−0.997534 + 0.0701893i \(0.977640\pi\)
\(882\) −4.50000 7.79423i −0.151523 0.262445i
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 0 0
\(885\) −8.00000 −0.268917
\(886\) 2.00000 + 3.46410i 0.0671913 + 0.116379i
\(887\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 1.00000 1.73205i 0.0335578 0.0581238i
\(889\) 0 0
\(890\) −14.0000 + 24.2487i −0.469281 + 0.812819i
\(891\) −2.00000 + 3.46410i −0.0670025 + 0.116052i
\(892\) 4.00000 0.133930
\(893\) 32.0000 55.4256i 1.07084 1.85475i
\(894\) 3.00000 + 5.19615i 0.100335 + 0.173785i
\(895\) −12.0000 20.7846i −0.401116 0.694753i
\(896\) −4.00000 −0.133631
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) −12.0000 20.7846i −0.400222 0.693206i
\(900\) 0.500000 + 0.866025i 0.0166667 + 0.0288675i
\(901\) 10.0000 17.3205i 0.333148 0.577030i
\(902\) 40.0000 1.33185
\(903\) −8.00000 + 13.8564i −0.266223 + 0.461112i
\(904\) 3.00000 5.19615i 0.0997785 0.172821i
\(905\) 20.0000 0.664822
\(906\) −6.00000 + 10.3923i −0.199337 + 0.345261i
\(907\) −14.0000 24.2487i −0.464862 0.805165i 0.534333 0.845274i \(-0.320563\pi\)
−0.999195 + 0.0401089i \(0.987230\pi\)
\(908\) 10.0000 + 17.3205i 0.331862 + 0.574801i
\(909\) −2.00000 −0.0663358
\(910\) 0 0
\(911\) 40.0000 1.32526 0.662630 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) 4.00000 + 6.92820i 0.132453 + 0.229416i
\(913\) 24.0000 + 41.5692i 0.794284 + 1.37574i
\(914\) −15.0000 + 25.9808i −0.496156 + 0.859367i
\(915\) −4.00000 −0.132236
\(916\) 11.0000 19.0526i 0.363450 0.629514i
\(917\) 8.00000 13.8564i 0.264183 0.457579i
\(918\) −2.00000 −0.0660098
\(919\) 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i \(-0.748326\pi\)
0.967274 + 0.253735i \(0.0816592\pi\)
\(920\) 0 0
\(921\) 4.00000 + 6.92820i 0.131804 + 0.228292i
\(922\) 6.00000 0.197599
\(923\) 0 0
\(924\) 16.0000 0.526361
\(925\) 1.00000 + 1.73205i 0.0328798 + 0.0569495i
\(926\) −10.0000 17.3205i −0.328620 0.569187i
\(927\) −8.00000 + 13.8564i −0.262754 + 0.455104i
\(928\) 6.00000 0.196960
\(929\) 23.0000 39.8372i 0.754606 1.30702i −0.190965 0.981597i \(-0.561162\pi\)
0.945570 0.325418i \(-0.105505\pi\)
\(930\) −4.00000 + 6.92820i −0.131165 + 0.227185i
\(931\) 72.0000 2.35970
\(932\) −9.00000 + 15.5885i −0.294805 + 0.510617i
\(933\) 0 0
\(934\) 2.00000 + 3.46410i 0.0654420 + 0.113349i
\(935\) −16.0000 −0.523256
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 32.0000 + 55.4256i 1.04484 + 1.80971i
\(939\) −3.00000 5.19615i −0.0979013 0.169570i
\(940\) −8.00000 + 13.8564i −0.260931 + 0.451946i
\(941\) 46.0000 1.49956 0.749779 0.661689i \(-0.230160\pi\)
0.749779 + 0.661689i \(0.230160\pi\)
\(942\) 7.00000 12.1244i 0.228072 0.395033i
\(943\) 0 0
\(944\) −4.00000 −0.130189
\(945\) 4.00000 6.92820i 0.130120 0.225374i
\(946\) −8.00000 13.8564i −0.260102 0.450511i
\(947\) −2.00000 3.46410i −0.0649913 0.112568i 0.831699 0.555227i \(-0.187369\pi\)
−0.896690 + 0.442659i \(0.854035\pi\)
\(948\) −8.00000 −0.259828
\(949\) 0 0
\(950\) −8.00000 −0.259554
\(951\) 3.00000 + 5.19615i 0.0972817 + 0.168497i
\(952\) 4.00000 + 6.92820i 0.129641 + 0.224544i
\(953\) 15.0000 25.9808i 0.485898 0.841599i −0.513971 0.857808i \(-0.671826\pi\)
0.999869 + 0.0162081i \(0.00515944\pi\)
\(954\) −10.0000 −0.323762
\(955\) −8.00000 + 13.8564i −0.258874 + 0.448383i
\(956\) 0 0
\(957\) −24.0000 −0.775810
\(958\) −8.00000 + 13.8564i −0.258468 + 0.447680i
\(959\) 20.0000 + 34.6410i 0.645834 + 1.11862i
\(960\) −1.00000 1.73205i −0.0322749 0.0559017i
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 12.0000 0.386695
\(964\) 5.00000 + 8.66025i 0.161039 + 0.278928i
\(965\) 14.0000 + 24.2487i 0.450676 + 0.780594i
\(966\) 0 0
\(967\) −4.00000 −0.128631 −0.0643157 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) −2.50000 + 4.33013i −0.0803530 + 0.139176i
\(969\) 8.00000 13.8564i 0.256997 0.445132i
\(970\) 20.0000 0.642161
\(971\) 14.0000 24.2487i 0.449281 0.778178i −0.549058 0.835784i \(-0.685013\pi\)
0.998339 + 0.0576061i \(0.0183467\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) 24.0000 + 41.5692i 0.769405 + 1.33265i
\(974\) −4.00000 −0.128168
\(975\) 0 0
\(976\) −2.00000 −0.0640184
\(977\) 3.00000 + 5.19615i 0.0959785 + 0.166240i 0.910017 0.414572i \(-0.136069\pi\)
−0.814038 + 0.580812i \(0.802735\pi\)
\(978\) 8.00000 + 13.8564i 0.255812 + 0.443079i
\(979\) 28.0000 48.4974i 0.894884 1.54998i
\(980\) −18.0000 −0.574989
\(981\) −1.00000 + 1.73205i −0.0319275 + 0.0553001i
\(982\) −18.0000 + 31.1769i −0.574403 + 0.994895i
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 5.00000 8.66025i 0.159394 0.276079i
\(985\) −18.0000 31.1769i −0.573528 0.993379i
\(986\) −6.00000 10.3923i −0.191079 0.330958i
\(987\) −32.0000 −1.01857
\(988\) 0 0
\(989\) 0 0
\(990\) 4.00000 + 6.92820i 0.127128 + 0.220193i
\(991\) 24.0000 + 41.5692i 0.762385 + 1.32049i 0.941618 + 0.336683i \(0.109305\pi\)
−0.179233 + 0.983807i \(0.557362\pi\)
\(992\) −2.00000 + 3.46410i −0.0635001 + 0.109985i
\(993\) 8.00000 0.253872
\(994\) 16.0000 27.7128i 0.507489 0.878997i
\(995\) −8.00000 + 13.8564i −0.253617 + 0.439278i
\(996\) 12.0000 0.380235
\(997\) 13.0000 22.5167i 0.411714 0.713110i −0.583363 0.812211i \(-0.698264\pi\)
0.995077 + 0.0991016i \(0.0315969\pi\)
\(998\) 0 0
\(999\) 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 1014.2.e.c.991.1 2
13.2 odd 12 1014.2.b.b.337.1 2
13.3 even 3 1014.2.a.d.1.1 1
13.4 even 6 1014.2.e.f.529.1 2
13.5 odd 4 1014.2.i.d.361.1 4
13.6 odd 12 1014.2.i.d.823.2 4
13.7 odd 12 1014.2.i.d.823.1 4
13.8 odd 4 1014.2.i.d.361.2 4
13.9 even 3 inner 1014.2.e.c.529.1 2
13.10 even 6 78.2.a.a.1.1 1
13.11 odd 12 1014.2.b.b.337.2 2
13.12 even 2 1014.2.e.f.991.1 2
39.2 even 12 3042.2.b.g.1351.2 2
39.11 even 12 3042.2.b.g.1351.1 2
39.23 odd 6 234.2.a.c.1.1 1
39.29 odd 6 3042.2.a.f.1.1 1
52.3 odd 6 8112.2.a.v.1.1 1
52.23 odd 6 624.2.a.h.1.1 1
65.23 odd 12 1950.2.e.i.1249.2 2
65.49 even 6 1950.2.a.w.1.1 1
65.62 odd 12 1950.2.e.i.1249.1 2
91.62 odd 6 3822.2.a.j.1.1 1
104.75 odd 6 2496.2.a.b.1.1 1
104.101 even 6 2496.2.a.t.1.1 1
117.23 odd 6 2106.2.e.j.703.1 2
117.49 even 6 2106.2.e.q.703.1 2
117.88 even 6 2106.2.e.q.1405.1 2
117.101 odd 6 2106.2.e.j.1405.1 2
143.10 odd 6 9438.2.a.t.1.1 1
156.23 even 6 1872.2.a.c.1.1 1
195.23 even 12 5850.2.e.bb.5149.1 2
195.62 even 12 5850.2.e.bb.5149.2 2
195.179 odd 6 5850.2.a.d.1.1 1
312.101 odd 6 7488.2.a.bz.1.1 1
312.179 even 6 7488.2.a.bk.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.a.a.1.1 1 13.10 even 6
234.2.a.c.1.1 1 39.23 odd 6
624.2.a.h.1.1 1 52.23 odd 6
1014.2.a.d.1.1 1 13.3 even 3
1014.2.b.b.337.1 2 13.2 odd 12
1014.2.b.b.337.2 2 13.11 odd 12
1014.2.e.c.529.1 2 13.9 even 3 inner
1014.2.e.c.991.1 2 1.1 even 1 trivial
1014.2.e.f.529.1 2 13.4 even 6
1014.2.e.f.991.1 2 13.12 even 2
1014.2.i.d.361.1 4 13.5 odd 4
1014.2.i.d.361.2 4 13.8 odd 4
1014.2.i.d.823.1 4 13.7 odd 12
1014.2.i.d.823.2 4 13.6 odd 12
1872.2.a.c.1.1 1 156.23 even 6
1950.2.a.w.1.1 1 65.49 even 6
1950.2.e.i.1249.1 2 65.62 odd 12
1950.2.e.i.1249.2 2 65.23 odd 12
2106.2.e.j.703.1 2 117.23 odd 6
2106.2.e.j.1405.1 2 117.101 odd 6
2106.2.e.q.703.1 2 117.49 even 6
2106.2.e.q.1405.1 2 117.88 even 6
2496.2.a.b.1.1 1 104.75 odd 6
2496.2.a.t.1.1 1 104.101 even 6
3042.2.a.f.1.1 1 39.29 odd 6
3042.2.b.g.1351.1 2 39.11 even 12
3042.2.b.g.1351.2 2 39.2 even 12
3822.2.a.j.1.1 1 91.62 odd 6
5850.2.a.d.1.1 1 195.179 odd 6
5850.2.e.bb.5149.1 2 195.23 even 12
5850.2.e.bb.5149.2 2 195.62 even 12
7488.2.a.bk.1.1 1 312.179 even 6
7488.2.a.bz.1.1 1 312.101 odd 6
8112.2.a.v.1.1 1 52.3 odd 6
9438.2.a.t.1.1 1 143.10 odd 6