Properties

Label 630.2.j.d.421.1
Level $630$
Weight $2$
Character 630.421
Analytic conductor $5.031$
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] = [630,2,Mod(211,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.j (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: \(5.03057532734\)
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 421.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 630.421
Dual form 630.2.j.d.211.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +(1.50000 - 0.866025i) q^{12} +(3.50000 + 6.06218i) q^{13} +(0.500000 + 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} +2.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} -1.73205i q^{24} +(-0.500000 + 0.866025i) q^{25} +7.00000 q^{26} -5.19615i q^{27} +1.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} -1.73205i q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.50000 - 2.59808i) q^{33} +(-1.50000 + 2.59808i) q^{34} +1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} +2.00000 q^{37} +(1.00000 - 1.73205i) q^{38} +(-10.5000 + 6.06218i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-1.50000 + 0.866025i) q^{42} +(-1.00000 + 1.73205i) q^{43} +3.00000 q^{44} +(1.50000 + 2.59808i) q^{45} +6.00000 q^{46} +(4.50000 - 7.79423i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} -5.19615i q^{51} +(3.50000 - 6.06218i) q^{52} -12.0000 q^{53} +(-4.50000 - 2.59808i) q^{54} +3.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +3.46410i q^{57} +(3.00000 + 5.19615i) q^{58} +(-1.50000 - 0.866025i) q^{60} +(-7.00000 + 12.1244i) q^{61} -2.00000 q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(3.50000 - 6.06218i) q^{65} +(-4.50000 + 2.59808i) q^{66} +(5.00000 + 8.66025i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-9.00000 + 5.19615i) q^{69} +(0.500000 - 0.866025i) q^{70} +3.00000 q^{71} +3.00000 q^{72} +11.0000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.50000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-1.50000 - 2.59808i) q^{77} +12.1244i q^{78} +(6.50000 - 11.2583i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(7.50000 - 12.9904i) q^{83} +1.73205i q^{84} +(1.50000 + 2.59808i) q^{85} +(1.00000 + 1.73205i) q^{86} +(-9.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} -18.0000 q^{89} +3.00000 q^{90} -7.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(3.00000 - 1.73205i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(-1.50000 + 0.866025i) q^{96} +(3.50000 - 6.06218i) q^{97} -1.00000 q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9} - 2 q^{10} - 3 q^{11} + 3 q^{12} + 7 q^{13} + q^{14} + 3 q^{15} - q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} + 6 q^{23} - q^{25} + 14 q^{26} + 2 q^{28} - 6 q^{29} - 2 q^{31} + q^{32} - 9 q^{33} - 3 q^{34} + 2 q^{35} + 3 q^{36} + 4 q^{37} + 2 q^{38} - 21 q^{39} + q^{40} - 3 q^{42} - 2 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} + 9 q^{47} - 3 q^{48} - q^{49} + q^{50} + 7 q^{52} - 24 q^{53} - 9 q^{54} + 6 q^{55} + q^{56} + 6 q^{58} - 3 q^{60} - 14 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} + 7 q^{65} - 9 q^{66} + 10 q^{67} + 3 q^{68} - 18 q^{69} + q^{70} + 6 q^{71} + 6 q^{72} + 22 q^{73} + 2 q^{74} - 3 q^{75} - 2 q^{76} - 3 q^{77} + 13 q^{79} + 2 q^{80} + 18 q^{81} + 15 q^{83} + 3 q^{85} + 2 q^{86} - 18 q^{87} + 3 q^{88} - 36 q^{89} + 6 q^{90} - 14 q^{91} + 6 q^{92} + 6 q^{93} - 9 q^{94} - 2 q^{95} - 3 q^{96} + 7 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.73205i 1.00000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) −1.00000 −0.316228
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) 3.50000 + 6.06218i 0.970725 + 1.68135i 0.693375 + 0.720577i \(0.256123\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) −1.50000 0.866025i −0.327327 0.188982i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 7.00000 1.37281
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 0.188982
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 1.73205i 0.316228i
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −4.50000 2.59808i −0.783349 0.452267i
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) 1.00000 0.169031
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) −10.5000 + 6.06218i −1.68135 + 0.970725i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) −1.50000 + 0.866025i −0.231455 + 0.133631i
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) 3.00000 0.452267
\(45\) 1.50000 + 2.59808i 0.223607 + 0.387298i
\(46\) 6.00000 0.884652
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) −1.50000 0.866025i −0.216506 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 5.19615i 0.727607i
\(52\) 3.50000 6.06218i 0.485363 0.840673i
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 3.00000 0.404520
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 3.46410i 0.458831i
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) −1.50000 0.866025i −0.193649 0.111803i
\(61\) −7.00000 + 12.1244i −0.896258 + 1.55236i −0.0640184 + 0.997949i \(0.520392\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −2.00000 −0.254000
\(63\) 1.50000 2.59808i 0.188982 0.327327i
\(64\) 1.00000 0.125000
\(65\) 3.50000 6.06218i 0.434122 0.751921i
\(66\) −4.50000 + 2.59808i −0.553912 + 0.319801i
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) −9.00000 + 5.19615i −1.08347 + 0.625543i
\(70\) 0.500000 0.866025i 0.0597614 0.103510i
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 3.00000 0.353553
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −1.50000 0.866025i −0.173205 0.100000i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −1.50000 2.59808i −0.170941 0.296078i
\(78\) 12.1244i 1.37281i
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 1.00000 0.111803
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 7.50000 12.9904i 0.823232 1.42588i −0.0800311 0.996792i \(-0.525502\pi\)
0.903263 0.429087i \(-0.141165\pi\)
\(84\) 1.73205i 0.188982i
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) −9.00000 5.19615i −0.964901 0.557086i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 3.00000 0.316228
\(91\) −7.00000 −0.733799
\(92\) 3.00000 5.19615i 0.312772 0.541736i
\(93\) 3.00000 1.73205i 0.311086 0.179605i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) −1.50000 + 0.866025i −0.153093 + 0.0883883i
\(97\) 3.50000 6.06218i 0.355371 0.615521i −0.631810 0.775123i \(-0.717688\pi\)
0.987181 + 0.159602i \(0.0510211\pi\)
\(98\) −1.00000 −0.101015
\(99\) 4.50000 7.79423i 0.452267 0.783349i
\(100\) 1.00000 0.100000
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) −3.50000 6.06218i −0.343203 0.594445i
\(105\) 1.73205i 0.169031i
\(106\) −6.00000 + 10.3923i −0.582772 + 1.00939i
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) 3.46410i 0.328798i
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 3.00000 + 1.73205i 0.280976 + 0.162221i
\(115\) 3.00000 5.19615i 0.279751 0.484544i
\(116\) 6.00000 0.557086
\(117\) −10.5000 18.1865i −0.970725 1.68135i
\(118\) 0 0
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) −1.50000 + 0.866025i −0.136931 + 0.0790569i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 7.00000 + 12.1244i 0.633750 + 1.09769i
\(123\) 0 0
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 1.00000 0.0894427
\(126\) −1.50000 2.59808i −0.133631 0.231455i
\(127\) 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 1.73205i −0.264135 0.152499i
\(130\) −3.50000 6.06218i −0.306970 0.531688i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 5.19615i 0.452267i
\(133\) −1.00000 + 1.73205i −0.0867110 + 0.150188i
\(134\) 10.0000 0.863868
\(135\) −4.50000 + 2.59808i −0.387298 + 0.223607i
\(136\) 3.00000 0.257248
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 10.3923i 0.884652i
\(139\) 11.0000 + 19.0526i 0.933008 + 1.61602i 0.778148 + 0.628080i \(0.216159\pi\)
0.154859 + 0.987937i \(0.450508\pi\)
\(140\) −0.500000 0.866025i −0.0422577 0.0731925i
\(141\) 13.5000 + 7.79423i 1.13691 + 0.656392i
\(142\) 1.50000 2.59808i 0.125877 0.218026i
\(143\) −21.0000 −1.75611
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 6.00000 0.498273
\(146\) 5.50000 9.52628i 0.455183 0.788400i
\(147\) 1.50000 0.866025i 0.123718 0.0714286i
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 7.50000 + 12.9904i 0.614424 + 1.06421i 0.990485 + 0.137619i \(0.0439449\pi\)
−0.376061 + 0.926595i \(0.622722\pi\)
\(150\) −1.50000 + 0.866025i −0.122474 + 0.0707107i
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) −2.00000 −0.162221
\(153\) 9.00000 0.727607
\(154\) −3.00000 −0.241747
\(155\) −1.00000 + 1.73205i −0.0803219 + 0.139122i
\(156\) 10.5000 + 6.06218i 0.840673 + 0.485363i
\(157\) −2.50000 4.33013i −0.199522 0.345582i 0.748852 0.662738i \(-0.230606\pi\)
−0.948373 + 0.317156i \(0.897272\pi\)
\(158\) −6.50000 11.2583i −0.517112 0.895665i
\(159\) 20.7846i 1.64833i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −6.00000 −0.472866
\(162\) 4.50000 7.79423i 0.353553 0.612372i
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 0 0
\(165\) 5.19615i 0.404520i
\(166\) −7.50000 12.9904i −0.582113 1.00825i
\(167\) −4.50000 7.79423i −0.348220 0.603136i 0.637713 0.770274i \(-0.279881\pi\)
−0.985933 + 0.167139i \(0.946547\pi\)
\(168\) 1.50000 + 0.866025i 0.115728 + 0.0668153i
\(169\) −18.0000 + 31.1769i −1.38462 + 2.39822i
\(170\) 3.00000 0.230089
\(171\) −6.00000 −0.458831
\(172\) 2.00000 0.152499
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −9.00000 + 5.19615i −0.682288 + 0.393919i
\(175\) −0.500000 0.866025i −0.0377964 0.0654654i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) −9.00000 + 15.5885i −0.674579 + 1.16840i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −3.50000 + 6.06218i −0.259437 + 0.449359i
\(183\) −21.0000 12.1244i −1.55236 0.896258i
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 3.46410i 0.254000i
\(187\) 4.50000 7.79423i 0.329073 0.569970i
\(188\) −9.00000 −0.656392
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) −2.00000 −0.145095
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 1.73205i 0.125000i
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) 10.5000 + 6.06218i 0.751921 + 0.434122i
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −4.50000 7.79423i −0.319801 0.553912i
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −15.0000 + 8.66025i −1.05802 + 0.610847i
\(202\) −9.00000 15.5885i −0.633238 1.09680i
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) −4.50000 + 2.59808i −0.315063 + 0.181902i
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) −9.00000 15.5885i −0.625543 1.08347i
\(208\) −7.00000 −0.485363
\(209\) −3.00000 + 5.19615i −0.207514 + 0.359425i
\(210\) 1.50000 + 0.866025i 0.103510 + 0.0597614i
\(211\) −8.50000 14.7224i −0.585164 1.01353i −0.994855 0.101310i \(-0.967697\pi\)
0.409691 0.912224i \(-0.365637\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 5.19615i 0.356034i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 2.00000 0.136399
\(216\) 5.19615i 0.353553i
\(217\) 2.00000 0.135769
\(218\) −0.500000 + 0.866025i −0.0338643 + 0.0586546i
\(219\) 19.0526i 1.28745i
\(220\) −1.50000 2.59808i −0.101130 0.175162i
\(221\) −10.5000 18.1865i −0.706306 1.22336i
\(222\) 3.00000 + 1.73205i 0.201347 + 0.116248i
\(223\) 9.50000 16.4545i 0.636167 1.10187i −0.350100 0.936713i \(-0.613852\pi\)
0.986267 0.165161i \(-0.0528144\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.50000 2.59808i 0.100000 0.173205i
\(226\) −6.00000 −0.399114
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 3.00000 1.73205i 0.198680 0.114708i
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) −3.00000 5.19615i −0.197814 0.342624i
\(231\) 4.50000 2.59808i 0.296078 0.170941i
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) −21.0000 −1.37281
\(235\) −9.00000 −0.587095
\(236\) 0 0
\(237\) 19.5000 + 11.2583i 1.26666 + 0.731307i
\(238\) −1.50000 2.59808i −0.0972306 0.168408i
\(239\) 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 1.73205i 0.111803i
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) 2.00000 0.128565
\(243\) 15.5885i 1.00000i
\(244\) 14.0000 0.896258
\(245\) −0.500000 + 0.866025i −0.0319438 + 0.0553283i
\(246\) 0 0
\(247\) 7.00000 + 12.1244i 0.445399 + 0.771454i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 22.5000 + 12.9904i 1.42588 + 0.823232i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) −3.00000 −0.188982
\(253\) −18.0000 −1.13165
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) −4.50000 + 2.59808i −0.281801 + 0.162698i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.5000 + 23.3827i 0.842107 + 1.45857i 0.888110 + 0.459631i \(0.152018\pi\)
−0.0460033 + 0.998941i \(0.514648\pi\)
\(258\) −3.00000 + 1.73205i −0.186772 + 0.107833i
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) −7.00000 −0.434122
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 0 0
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 4.50000 + 2.59808i 0.276956 + 0.159901i
\(265\) 6.00000 + 10.3923i 0.368577 + 0.638394i
\(266\) 1.00000 + 1.73205i 0.0613139 + 0.106199i
\(267\) 31.1769i 1.90800i
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 5.19615i 0.316228i
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 1.50000 2.59808i 0.0909509 0.157532i
\(273\) 12.1244i 0.733799i
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 9.00000 + 5.19615i 0.541736 + 0.312772i
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 22.0000 1.31947
\(279\) 3.00000 + 5.19615i 0.179605 + 0.311086i
\(280\) −1.00000 −0.0597614
\(281\) 4.50000 7.79423i 0.268447 0.464965i −0.700014 0.714130i \(-0.746823\pi\)
0.968461 + 0.249165i \(0.0801561\pi\)
\(282\) 13.5000 7.79423i 0.803913 0.464140i
\(283\) 0.500000 + 0.866025i 0.0297219 + 0.0514799i 0.880504 0.474039i \(-0.157204\pi\)
−0.850782 + 0.525519i \(0.823871\pi\)
\(284\) −1.50000 2.59808i −0.0890086 0.154167i
\(285\) 3.00000 1.73205i 0.177705 0.102598i
\(286\) −10.5000 + 18.1865i −0.620878 + 1.07539i
\(287\) 0 0
\(288\) −1.50000 2.59808i −0.0883883 0.153093i
\(289\) −8.00000 −0.470588
\(290\) 3.00000 5.19615i 0.176166 0.305129i
\(291\) 10.5000 + 6.06218i 0.615521 + 0.355371i
\(292\) −5.50000 9.52628i −0.321863 0.557483i
\(293\) −3.00000 5.19615i −0.175262 0.303562i 0.764990 0.644042i \(-0.222744\pi\)
−0.940252 + 0.340480i \(0.889411\pi\)
\(294\) 1.73205i 0.101015i
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 13.5000 + 7.79423i 0.783349 + 0.452267i
\(298\) 15.0000 0.868927
\(299\) −21.0000 + 36.3731i −1.21446 + 2.10351i
\(300\) 1.73205i 0.100000i
\(301\) −1.00000 1.73205i −0.0576390 0.0998337i
\(302\) 2.50000 + 4.33013i 0.143859 + 0.249171i
\(303\) 27.0000 + 15.5885i 1.55111 + 0.895533i
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 14.0000 0.801638
\(306\) 4.50000 7.79423i 0.257248 0.445566i
\(307\) 29.0000 1.65512 0.827559 0.561379i \(-0.189729\pi\)
0.827559 + 0.561379i \(0.189729\pi\)
\(308\) −1.50000 + 2.59808i −0.0854704 + 0.148039i
\(309\) 12.0000 6.92820i 0.682656 0.394132i
\(310\) 1.00000 + 1.73205i 0.0567962 + 0.0983739i
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 10.5000 6.06218i 0.594445 0.343203i
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) −5.00000 −0.282166
\(315\) −3.00000 −0.169031
\(316\) −13.0000 −0.731307
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) −18.0000 10.3923i −1.00939 0.582772i
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 10.3923i 0.580042i
\(322\) −3.00000 + 5.19615i −0.167183 + 0.289570i
\(323\) −6.00000 −0.333849
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −7.00000 −0.388290
\(326\) 1.00000 1.73205i 0.0553849 0.0959294i
\(327\) 1.73205i 0.0957826i
\(328\) 0 0
\(329\) 4.50000 + 7.79423i 0.248093 + 0.429710i
\(330\) 4.50000 + 2.59808i 0.247717 + 0.143019i
\(331\) −8.50000 + 14.7224i −0.467202 + 0.809218i −0.999298 0.0374662i \(-0.988071\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(332\) −15.0000 −0.823232
\(333\) −6.00000 −0.328798
\(334\) −9.00000 −0.492458
\(335\) 5.00000 8.66025i 0.273179 0.473160i
\(336\) 1.50000 0.866025i 0.0818317 0.0472456i
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 18.0000 + 31.1769i 0.979071 + 1.69580i
\(339\) 9.00000 5.19615i 0.488813 0.282216i
\(340\) 1.50000 2.59808i 0.0813489 0.140900i
\(341\) 6.00000 0.324918
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 1.00000 0.0539949
\(344\) 1.00000 1.73205i 0.0539164 0.0933859i
\(345\) 9.00000 + 5.19615i 0.484544 + 0.279751i
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 10.3923i 0.557086i
\(349\) 14.0000 24.2487i 0.749403 1.29800i −0.198706 0.980059i \(-0.563674\pi\)
0.948109 0.317945i \(-0.102993\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 31.5000 18.1865i 1.68135 0.970725i
\(352\) −3.00000 −0.159901
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) −1.50000 2.59808i −0.0796117 0.137892i
\(356\) 9.00000 + 15.5885i 0.476999 + 0.826187i
\(357\) 4.50000 + 2.59808i 0.238165 + 0.137505i
\(358\) −4.50000 + 7.79423i −0.237832 + 0.411938i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −1.50000 2.59808i −0.0790569 0.136931i
\(361\) −15.0000 −0.789474
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) −3.00000 + 1.73205i −0.157459 + 0.0909091i
\(364\) 3.50000 + 6.06218i 0.183450 + 0.317744i
\(365\) −5.50000 9.52628i −0.287883 0.498628i
\(366\) −21.0000 + 12.1244i −1.09769 + 0.633750i
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) −3.00000 1.73205i −0.155543 0.0898027i
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) −4.50000 7.79423i −0.232689 0.403030i
\(375\) 1.73205i 0.0894427i
\(376\) −4.50000 + 7.79423i −0.232070 + 0.401957i
\(377\) −42.0000 −2.16311
\(378\) 4.50000 2.59808i 0.231455 0.133631i
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) −1.00000 + 1.73205i −0.0512989 + 0.0888523i
\(381\) 13.8564i 0.709885i
\(382\) 0 0
\(383\) 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i \(0.0756427\pi\)
−0.282079 + 0.959391i \(0.591024\pi\)
\(384\) 1.50000 + 0.866025i 0.0765466 + 0.0441942i
\(385\) −1.50000 + 2.59808i −0.0764471 + 0.132410i
\(386\) 10.0000 0.508987
\(387\) 3.00000 5.19615i 0.152499 0.264135i
\(388\) −7.00000 −0.355371
\(389\) −7.50000 + 12.9904i −0.380265 + 0.658638i −0.991100 0.133120i \(-0.957501\pi\)
0.610835 + 0.791758i \(0.290834\pi\)
\(390\) 10.5000 6.06218i 0.531688 0.306970i
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) −13.0000 −0.654101
\(396\) −9.00000 −0.452267
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) −2.00000 + 3.46410i −0.100251 + 0.173640i
\(399\) −3.00000 1.73205i −0.150188 0.0867110i
\(400\) −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 \(0.785466\pi\)
\(402\) 17.3205i 0.863868i
\(403\) 7.00000 12.1244i 0.348695 0.603957i
\(404\) −18.0000 −0.895533
\(405\) −4.50000 7.79423i −0.223607 0.387298i
\(406\) −6.00000 −0.297775
\(407\) −3.00000 + 5.19615i −0.148704 + 0.257564i
\(408\) 5.19615i 0.257248i
\(409\) −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i \(-0.876150\pi\)
0.134107 0.990967i \(-0.457183\pi\)
\(410\) 0 0
\(411\) −9.00000 5.19615i −0.443937 0.256307i
\(412\) −4.00000 + 6.92820i −0.197066 + 0.341328i
\(413\) 0 0
\(414\) −18.0000 −0.884652
\(415\) −15.0000 −0.736321
\(416\) −3.50000 + 6.06218i −0.171602 + 0.297223i
\(417\) −33.0000 + 19.0526i −1.61602 + 0.933008i
\(418\) 3.00000 + 5.19615i 0.146735 + 0.254152i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 1.50000 0.866025i 0.0731925 0.0422577i
\(421\) 18.5000 32.0429i 0.901635 1.56168i 0.0762630 0.997088i \(-0.475701\pi\)
0.825372 0.564590i \(-0.190966\pi\)
\(422\) −17.0000 −0.827547
\(423\) −13.5000 + 23.3827i −0.656392 + 1.13691i
\(424\) 12.0000 0.582772
\(425\) 1.50000 2.59808i 0.0727607 0.126025i
\(426\) 4.50000 + 2.59808i 0.218026 + 0.125877i
\(427\) −7.00000 12.1244i −0.338754 0.586739i
\(428\) −3.00000 5.19615i −0.145010 0.251166i
\(429\) 36.3731i 1.75611i
\(430\) 1.00000 1.73205i 0.0482243 0.0835269i
\(431\) −33.0000 −1.58955 −0.794777 0.606902i \(-0.792412\pi\)
−0.794777 + 0.606902i \(0.792412\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 1.00000 1.73205i 0.0480015 0.0831411i
\(435\) 10.3923i 0.498273i
\(436\) 0.500000 + 0.866025i 0.0239457 + 0.0414751i
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) 16.5000 + 9.52628i 0.788400 + 0.455183i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) −3.00000 −0.143019
\(441\) 1.50000 + 2.59808i 0.0714286 + 0.123718i
\(442\) −21.0000 −0.998868
\(443\) −9.00000 + 15.5885i −0.427603 + 0.740630i −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) 3.00000 1.73205i 0.142374 0.0821995i
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −9.50000 16.4545i −0.449838 0.779142i
\(447\) −22.5000 + 12.9904i −1.06421 + 0.614424i
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −1.50000 2.59808i −0.0707107 0.122474i
\(451\) 0 0
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) −7.50000 4.33013i −0.352381 0.203447i
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 3.50000 + 6.06218i 0.164083 + 0.284199i
\(456\) 3.46410i 0.162221i
\(457\) −19.0000 + 32.9090i −0.888783 + 1.53942i −0.0474665 + 0.998873i \(0.515115\pi\)
−0.841316 + 0.540544i \(0.818219\pi\)
\(458\) 10.0000 0.467269
\(459\) 15.5885i 0.727607i
\(460\) −6.00000 −0.279751
\(461\) 21.0000 36.3731i 0.978068 1.69406i 0.308651 0.951175i \(-0.400123\pi\)
0.669417 0.742887i \(-0.266544\pi\)
\(462\) 5.19615i 0.241747i
\(463\) −16.0000 27.7128i −0.743583 1.28792i −0.950854 0.309640i \(-0.899791\pi\)
0.207271 0.978284i \(-0.433542\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) −3.00000 1.73205i −0.139122 0.0803219i
\(466\) 0 0
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) −10.5000 + 18.1865i −0.485363 + 0.840673i
\(469\) −10.0000 −0.461757
\(470\) −4.50000 + 7.79423i −0.207570 + 0.359521i
\(471\) 7.50000 4.33013i 0.345582 0.199522i
\(472\) 0 0
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 19.5000 11.2583i 0.895665 0.517112i
\(475\) −1.00000 + 1.73205i −0.0458831 + 0.0794719i
\(476\) −3.00000 −0.137505
\(477\) 36.0000 1.64833
\(478\) 24.0000 1.09773
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 1.50000 + 0.866025i 0.0684653 + 0.0395285i
\(481\) 7.00000 + 12.1244i 0.319173 + 0.552823i
\(482\) 4.00000 + 6.92820i 0.182195 + 0.315571i
\(483\) 10.3923i 0.472866i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −7.00000 −0.317854
\(486\) 13.5000 + 7.79423i 0.612372 + 0.353553i
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 7.00000 12.1244i 0.316875 0.548844i
\(489\) 3.46410i 0.156652i
\(490\) 0.500000 + 0.866025i 0.0225877 + 0.0391230i
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 14.0000 0.629890
\(495\) −9.00000 −0.404520
\(496\) 2.00000 0.0898027
\(497\) −1.50000 + 2.59808i −0.0672842 + 0.116540i
\(498\) 22.5000 12.9904i 1.00825 0.582113i
\(499\) −2.50000 4.33013i −0.111915 0.193843i 0.804627 0.593780i \(-0.202365\pi\)
−0.916542 + 0.399937i \(0.869032\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 13.5000 7.79423i 0.603136 0.348220i
\(502\) −3.00000 + 5.19615i −0.133897 + 0.231916i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) −18.0000 −0.800989
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) −54.0000 31.1769i −2.39822 1.38462i
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 5.19615i 0.230089i
\(511\) −5.50000 + 9.52628i −0.243306 + 0.421418i
\(512\) −1.00000 −0.0441942
\(513\) 10.3923i 0.458831i
\(514\) 27.0000 1.19092
\(515\) −4.00000 + 6.92820i −0.176261 + 0.305293i
\(516\) 3.46410i 0.152499i
\(517\) 13.5000 + 23.3827i 0.593729 + 1.02837i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) 9.00000 + 5.19615i 0.395056 + 0.228086i
\(520\) −3.50000 + 6.06218i −0.153485 + 0.265844i
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) −13.0000 −0.568450 −0.284225 0.958758i \(-0.591736\pi\)
−0.284225 + 0.958758i \(0.591736\pi\)
\(524\) 0 0
\(525\) 1.50000 0.866025i 0.0654654 0.0377964i
\(526\) −6.00000 10.3923i −0.261612 0.453126i
\(527\) 3.00000 + 5.19615i 0.130682 + 0.226348i
\(528\) 4.50000 2.59808i 0.195837 0.113067i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 2.00000 0.0867110
\(533\) 0 0
\(534\) −27.0000 15.5885i −1.16840 0.674579i
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) 15.5885i 0.672692i
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) 3.00000 0.129219
\(540\) 4.50000 + 2.59808i 0.193649 + 0.111803i
\(541\) −43.0000 −1.84871 −0.924357 0.381528i \(-0.875398\pi\)
−0.924357 + 0.381528i \(0.875398\pi\)
\(542\) −14.0000 + 24.2487i −0.601351 + 1.04157i
\(543\) 3.46410i 0.148659i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0.500000 + 0.866025i 0.0214176 + 0.0370965i
\(546\) −10.5000 6.06218i −0.449359 0.259437i
\(547\) 11.0000 19.0526i 0.470326 0.814629i −0.529098 0.848561i \(-0.677470\pi\)
0.999424 + 0.0339321i \(0.0108030\pi\)
\(548\) 6.00000 0.256307
\(549\) 21.0000 36.3731i 0.896258 1.55236i
\(550\) −3.00000 −0.127920
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 9.00000 5.19615i 0.383065 0.221163i
\(553\) 6.50000 + 11.2583i 0.276408 + 0.478753i
\(554\) 1.00000 + 1.73205i 0.0424859 + 0.0735878i
\(555\) 3.00000 1.73205i 0.127343 0.0735215i
\(556\) 11.0000 19.0526i 0.466504 0.808008i
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 6.00000 0.254000
\(559\) −14.0000 −0.592137
\(560\) −0.500000 + 0.866025i −0.0211289 + 0.0365963i
\(561\) 13.5000 + 7.79423i 0.569970 + 0.329073i
\(562\) −4.50000 7.79423i −0.189821 0.328780i
\(563\) 7.50000 + 12.9904i 0.316087 + 0.547479i 0.979668 0.200625i \(-0.0642974\pi\)
−0.663581 + 0.748105i \(0.730964\pi\)
\(564\) 15.5885i 0.656392i
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) 1.00000 0.0420331
\(567\) −4.50000 + 7.79423i −0.188982 + 0.327327i
\(568\) −3.00000 −0.125877
\(569\) −4.50000 + 7.79423i −0.188650 + 0.326751i −0.944800 0.327647i \(-0.893744\pi\)
0.756151 + 0.654398i \(0.227078\pi\)
\(570\) 3.46410i 0.145095i
\(571\) −2.50000 4.33013i −0.104622 0.181210i 0.808962 0.587861i \(-0.200030\pi\)
−0.913584 + 0.406651i \(0.866697\pi\)
\(572\) 10.5000 + 18.1865i 0.439027 + 0.760417i
\(573\) 0 0
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) −3.00000 −0.125000
\(577\) 23.0000 0.957503 0.478751 0.877951i \(-0.341090\pi\)
0.478751 + 0.877951i \(0.341090\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) −15.0000 + 8.66025i −0.623379 + 0.359908i
\(580\) −3.00000 5.19615i −0.124568 0.215758i
\(581\) 7.50000 + 12.9904i 0.311152 + 0.538932i
\(582\) 10.5000 6.06218i 0.435239 0.251285i
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) −11.0000 −0.455183
\(585\) −10.5000 + 18.1865i −0.434122 + 0.751921i
\(586\) −6.00000 −0.247858
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) −1.50000 0.866025i −0.0618590 0.0357143i
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) 31.1769i 1.28245i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 13.5000 7.79423i 0.553912 0.319801i
\(595\) −3.00000 −0.122988
\(596\) 7.50000 12.9904i 0.307212 0.532107i
\(597\) 6.92820i 0.283552i
\(598\) 21.0000 + 36.3731i 0.858754 + 1.48741i
\(599\) −19.5000 33.7750i −0.796748 1.38001i −0.921723 0.387849i \(-0.873218\pi\)
0.124975 0.992160i \(-0.460115\pi\)
\(600\) 1.50000 + 0.866025i 0.0612372 + 0.0353553i
\(601\) 2.00000 3.46410i 0.0815817 0.141304i −0.822348 0.568985i \(-0.807336\pi\)
0.903929 + 0.427682i \(0.140670\pi\)
\(602\) −2.00000 −0.0815139
\(603\) −15.0000 25.9808i −0.610847 1.05802i
\(604\) 5.00000 0.203447
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 27.0000 15.5885i 1.09680 0.633238i
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) 9.00000 5.19615i 0.364698 0.210559i
\(610\) 7.00000 12.1244i 0.283422 0.490901i
\(611\) 63.0000 2.54871
\(612\) −4.50000 7.79423i −0.181902 0.315063i
\(613\) −46.0000 −1.85792 −0.928961 0.370177i \(-0.879297\pi\)
−0.928961 + 0.370177i \(0.879297\pi\)
\(614\) 14.5000 25.1147i 0.585172 1.01355i
\(615\) 0 0
\(616\) 1.50000 + 2.59808i 0.0604367 + 0.104679i
\(617\) 6.00000 + 10.3923i 0.241551 + 0.418378i 0.961156 0.276005i \(-0.0890106\pi\)
−0.719605 + 0.694383i \(0.755677\pi\)
\(618\) 13.8564i 0.557386i
\(619\) 17.0000 29.4449i 0.683288 1.18349i −0.290684 0.956819i \(-0.593883\pi\)
0.973972 0.226670i \(-0.0727838\pi\)
\(620\) 2.00000 0.0803219
\(621\) 27.0000 15.5885i 1.08347 0.625543i
\(622\) 24.0000 0.962312
\(623\) 9.00000 15.5885i 0.360577 0.624538i
\(624\) 12.1244i 0.485363i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) −9.00000 5.19615i −0.359425 0.207514i
\(628\) −2.50000 + 4.33013i −0.0997609 + 0.172791i
\(629\) −6.00000 −0.239236
\(630\) −1.50000 + 2.59808i −0.0597614 + 0.103510i
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −6.50000 + 11.2583i −0.258556 + 0.447832i
\(633\) 25.5000 14.7224i 1.01353 0.585164i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) −18.0000 + 10.3923i −0.713746 + 0.412082i
\(637\) 3.50000 6.06218i 0.138675 0.240192i
\(638\) −18.0000 −0.712627
\(639\) −9.00000 −0.356034
\(640\) −1.00000 −0.0395285
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 9.00000 + 5.19615i 0.355202 + 0.205076i
\(643\) 15.5000 + 26.8468i 0.611260 + 1.05873i 0.991028 + 0.133652i \(0.0426705\pi\)
−0.379768 + 0.925082i \(0.623996\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) 3.46410i 0.136399i
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) 36.0000 1.41531 0.707653 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(648\) −9.00000 −0.353553
\(649\) 0 0
\(650\) −3.50000 + 6.06218i −0.137281 + 0.237778i
\(651\) 3.46410i 0.135769i
\(652\) −1.00000 1.73205i −0.0391630 0.0678323i
\(653\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) −1.50000 0.866025i −0.0586546 0.0338643i
\(655\) 0 0
\(656\) 0 0
\(657\) −33.0000 −1.28745
\(658\) 9.00000 0.350857
\(659\) 1.50000 2.59808i 0.0584317 0.101207i −0.835330 0.549749i \(-0.814723\pi\)
0.893762 + 0.448542i \(0.148057\pi\)
\(660\) 4.50000 2.59808i 0.175162 0.101130i
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 8.50000 + 14.7224i 0.330362 + 0.572204i
\(663\) 31.5000 18.1865i 1.22336 0.706306i
\(664\) −7.50000 + 12.9904i −0.291056 + 0.504125i
\(665\) 2.00000 0.0775567
\(666\) −3.00000 + 5.19615i −0.116248 + 0.201347i
\(667\) −36.0000 −1.39393
\(668\) −4.50000 + 7.79423i −0.174110 + 0.301568i
\(669\) 28.5000 + 16.4545i 1.10187 + 0.636167i
\(670\) −5.00000 8.66025i −0.193167 0.334575i
\(671\) −21.0000 36.3731i −0.810696 1.40417i
\(672\) 1.73205i 0.0668153i
\(673\) −4.00000 + 6.92820i −0.154189 + 0.267063i −0.932763 0.360489i \(-0.882610\pi\)
0.778575 + 0.627552i \(0.215943\pi\)
\(674\) 22.0000 0.847408
\(675\) 4.50000 + 2.59808i 0.173205 + 0.100000i
\(676\) 36.0000 1.38462
\(677\) −16.5000 + 28.5788i −0.634147 + 1.09837i 0.352549 + 0.935793i \(0.385315\pi\)
−0.986695 + 0.162581i \(0.948018\pi\)
\(678\) 10.3923i 0.399114i
\(679\) 3.50000 + 6.06218i 0.134318 + 0.232645i
\(680\) −1.50000 2.59808i −0.0575224 0.0996317i
\(681\) −4.50000 2.59808i −0.172440 0.0995585i
\(682\) 3.00000 5.19615i 0.114876 0.198971i
\(683\) 48.0000 1.83667 0.918334 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) 3.00000 + 5.19615i 0.114708 + 0.198680i
\(685\) 6.00000 0.229248
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) −15.0000 + 8.66025i −0.572286 + 0.330409i
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) −42.0000 72.7461i −1.60007 2.77141i
\(690\) 9.00000 5.19615i 0.342624 0.197814i
\(691\) −1.00000 + 1.73205i −0.0380418 + 0.0658903i −0.884419 0.466693i \(-0.845445\pi\)
0.846378 + 0.532583i \(0.178779\pi\)
\(692\) −6.00000 −0.228086
\(693\) 4.50000 + 7.79423i 0.170941 + 0.296078i
\(694\) −12.0000 −0.455514
\(695\) 11.0000 19.0526i 0.417254 0.722705i
\(696\) 9.00000 + 5.19615i 0.341144 + 0.196960i
\(697\) 0 0
\(698\) −14.0000 24.2487i −0.529908 0.917827i
\(699\) 0 0
\(700\) −0.500000 + 0.866025i −0.0188982 + 0.0327327i
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 36.3731i 1.37281i
\(703\) 4.00000 0.150863
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 15.5885i 0.587095i
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) 9.00000 + 15.5885i 0.338480 + 0.586264i
\(708\) 0 0
\(709\) 17.0000 29.4449i 0.638448 1.10583i −0.347325 0.937745i \(-0.612910\pi\)
0.985773 0.168080i \(-0.0537568\pi\)
\(710\) −3.00000 −0.112588
\(711\) −19.5000 + 33.7750i −0.731307 + 1.26666i
\(712\) 18.0000 0.674579
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 4.50000 2.59808i 0.168408 0.0972306i
\(715\) 10.5000 + 18.1865i 0.392678 + 0.680138i
\(716\) 4.50000 + 7.79423i 0.168173 + 0.291284i
\(717\) −36.0000 + 20.7846i −1.34444 + 0.776215i
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) 18.0000 0.671287 0.335643 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) −3.00000 −0.111803
\(721\) 8.00000 0.297936
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) −12.0000 6.92820i −0.446285 0.257663i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 3.46410i 0.128565i
\(727\) 9.50000 16.4545i 0.352335 0.610263i −0.634323 0.773068i \(-0.718721\pi\)
0.986658 + 0.162805i \(0.0520543\pi\)
\(728\) 7.00000 0.259437
\(729\) −27.0000 −1.00000
\(730\) −11.0000 −0.407128
\(731\) 3.00000 5.19615i 0.110959 0.192187i
\(732\) 24.2487i 0.896258i
\(733\) 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) −9.50000 16.4545i −0.350651 0.607346i
\(735\) −1.50000 0.866025i −0.0553283 0.0319438i
\(736\) −3.00000 + 5.19615i −0.110581 + 0.191533i
\(737\) −30.0000 −1.10506
\(738\) 0 0
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) −1.00000 + 1.73205i −0.0367607 + 0.0636715i
\(741\) −21.0000 + 12.1244i −0.771454 + 0.445399i
\(742\) −6.00000 10.3923i −0.220267 0.381514i
\(743\) 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.320166 + 0.947361i \(0.603739\pi\)
\(744\) −3.00000 + 1.73205i −0.109985 + 0.0635001i
\(745\) 7.50000 12.9904i 0.274779 0.475931i
\(746\) 4.00000 0.146450
\(747\) −22.5000 + 38.9711i −0.823232 + 1.42588i
\(748\) −9.00000 −0.329073
\(749\) −3.00000 + 5.19615i −0.109618 + 0.189863i
\(750\) 1.50000 + 0.866025i 0.0547723 + 0.0316228i
\(751\) 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) 4.50000 + 7.79423i 0.164098 + 0.284226i
\(753\) 10.3923i 0.378717i
\(754\) −21.0000 + 36.3731i −0.764775 + 1.32463i
\(755\) 5.00000 0.181969
\(756\) 5.19615i 0.188982i
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) 14.5000 25.1147i 0.526664 0.912208i
\(759\) 31.1769i 1.13165i
\(760\) 1.00000 + 1.73205i 0.0362738 + 0.0628281i
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 12.0000 + 6.92820i 0.434714 + 0.250982i
\(763\) 0.500000 0.866025i 0.0181012 0.0313522i
\(764\) 0 0
\(765\) −4.50000 7.79423i −0.162698 0.281801i
\(766\) 27.0000 0.975550
\(767\) 0 0
\(768\) 1.50000 0.866025i 0.0541266 0.0312500i
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) 1.50000 + 2.59808i 0.0540562 + 0.0936282i
\(771\) −40.5000 + 23.3827i −1.45857 + 0.842107i
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) 21.0000 0.755318 0.377659 0.925945i \(-0.376729\pi\)
0.377659 + 0.925945i \(0.376729\pi\)
\(774\) −3.00000 5.19615i −0.107833 0.186772i
\(775\) 2.00000 0.0718421
\(776\) −3.50000 + 6.06218i −0.125643 + 0.217620i
\(777\) −3.00000 1.73205i −0.107624 0.0621370i
\(778\) 7.50000 + 12.9904i 0.268888 + 0.465728i
\(779\) 0 0
\(780\) 12.1244i 0.434122i
\(781\) −4.50000 + 7.79423i −0.161023 + 0.278899i
\(782\) −18.0000 −0.643679
\(783\) 27.0000 + 15.5885i 0.964901 + 0.557086i
\(784\) 1.00000 0.0357143
\(785\) −2.50000 + 4.33013i −0.0892288 + 0.154549i
\(786\) 0 0
\(787\) 12.5000 + 21.6506i 0.445577 + 0.771762i 0.998092 0.0617409i \(-0.0196653\pi\)
−0.552515 + 0.833503i \(0.686332\pi\)
\(788\) −9.00000 15.5885i −0.320612 0.555316i
\(789\) 18.0000 + 10.3923i 0.640817 + 0.369976i
\(790\) −6.50000 + 11.2583i −0.231260 + 0.400553i
\(791\) 6.00000 0.213335
\(792\) −4.50000 + 7.79423i −0.159901 + 0.276956i
\(793\) −98.0000 −3.48008
\(794\) 13.0000 22.5167i 0.461353 0.799086i
\(795\) −18.0000 + 10.3923i −0.638394 + 0.368577i
\(796\) 2.00000 + 3.46410i 0.0708881 + 0.122782i
\(797\) −19.5000 33.7750i −0.690725 1.19637i −0.971601 0.236627i \(-0.923958\pi\)
0.280875 0.959744i \(-0.409375\pi\)
\(798\) −3.00000 + 1.73205i −0.106199 + 0.0613139i
\(799\) −13.5000 + 23.3827i −0.477596 + 0.827220i
\(800\) −1.00000 −0.0353553
\(801\) 54.0000 1.90800
\(802\) 6.00000 0.211867
\(803\) −16.5000 + 28.5788i −0.582272 + 1.00853i
\(804\) 15.0000 + 8.66025i 0.529009 + 0.305424i
\(805\) 3.00000 + 5.19615i 0.105736 + 0.183140i
\(806\) −7.00000 12.1244i −0.246564 0.427062i
\(807\) 31.1769i 1.09748i
\(808\) −9.00000 + 15.5885i −0.316619 + 0.548400i
\(809\) 33.0000 1.16022 0.580109 0.814539i \(-0.303010\pi\)
0.580109 + 0.814539i \(0.303010\pi\)
\(810\) −9.00000 −0.316228
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −3.00000 + 5.19615i −0.105279 + 0.182349i
\(813\) 48.4974i 1.70088i
\(814\) 3.00000 + 5.19615i 0.105150 + 0.182125i
\(815\) −1.00000 1.73205i −0.0350285 0.0606711i
\(816\) 4.50000 + 2.59808i 0.157532 + 0.0909509i
\(817\) −2.00000 + 3.46410i −0.0699711 + 0.121194i
\(818\) −32.0000 −1.11885
\(819\) 21.0000 0.733799
\(820\) 0 0
\(821\) 16.5000 28.5788i 0.575854 0.997408i −0.420094 0.907480i \(-0.638003\pi\)
0.995948 0.0899279i \(-0.0286637\pi\)
\(822\) −9.00000 + 5.19615i −0.313911 + 0.181237i
\(823\) −22.0000 38.1051i −0.766872 1.32826i −0.939251 0.343230i \(-0.888479\pi\)
0.172379 0.985031i \(-0.444854\pi\)
\(824\) 4.00000 + 6.92820i 0.139347 + 0.241355i
\(825\) 4.50000 2.59808i 0.156670 0.0904534i
\(826\) 0 0
\(827\) 18.0000 0.625921 0.312961 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(828\) −9.00000 + 15.5885i −0.312772 + 0.541736i
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) −7.50000 + 12.9904i −0.260329 + 0.450903i
\(831\) −3.00000 1.73205i −0.104069 0.0600842i
\(832\) 3.50000 + 6.06218i 0.121341 + 0.210168i
\(833\) 1.50000 + 2.59808i 0.0519719 + 0.0900180i
\(834\) 38.1051i 1.31947i
\(835\) −4.50000 + 7.79423i −0.155729 + 0.269730i
\(836\) 6.00000 0.207514
\(837\) −9.00000 + 5.19615i −0.311086 + 0.179605i
\(838\) 12.0000 0.414533
\(839\) −18.0000 + 31.1769i −0.621429 + 1.07635i 0.367791 + 0.929909i \(0.380114\pi\)
−0.989220 + 0.146438i \(0.953219\pi\)
\(840\) 1.73205i 0.0597614i
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) −18.5000 32.0429i −0.637552 1.10427i
\(843\) 13.5000 + 7.79423i 0.464965 + 0.268447i
\(844\) −8.50000 + 14.7224i −0.292582 + 0.506767i
\(845\) 36.0000 1.23844
\(846\) 13.5000 + 23.3827i 0.464140 + 0.803913i
\(847\) −2.00000 −0.0687208
\(848\) 6.00000 10.3923i 0.206041 0.356873i
\(849\) −1.50000 + 0.866025i −0.0514799 + 0.0297219i
\(850\) −1.50000 2.59808i −0.0514496 0.0891133i
\(851\) 6.00000 + 10.3923i 0.205677 + 0.356244i
\(852\) 4.50000 2.59808i 0.154167 0.0890086i
\(853\) 23.0000 39.8372i 0.787505 1.36400i −0.139986 0.990153i \(-0.544706\pi\)
0.927491 0.373845i \(-0.121961\pi\)
\(854\) −14.0000 −0.479070
\(855\) 3.00000 + 5.19615i 0.102598 + 0.177705i
\(856\) −6.00000 −0.205076
\(857\) 22.5000 38.9711i 0.768585 1.33123i −0.169745 0.985488i \(-0.554294\pi\)
0.938330 0.345741i \(-0.112372\pi\)
\(858\) −31.5000 18.1865i −1.07539 0.620878i
\(859\) −25.0000 43.3013i −0.852989 1.47742i −0.878498 0.477746i \(-0.841454\pi\)
0.0255092 0.999675i \(-0.491879\pi\)
\(860\) −1.00000 1.73205i −0.0340997 0.0590624i
\(861\) 0 0
\(862\) −16.5000 + 28.5788i −0.561992 + 0.973399i
\(863\) 18.0000 0.612727 0.306364 0.951915i \(-0.400888\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(864\) 4.50000 2.59808i 0.153093 0.0883883i
\(865\) −6.00000 −0.204006
\(866\) 7.00000 12.1244i 0.237870 0.412002i
\(867\) 13.8564i 0.470588i
\(868\) −1.00000 1.73205i −0.0339422 0.0587896i
\(869\) 19.5000 + 33.7750i 0.661492 + 1.14574i
\(870\) 9.00000 + 5.19615i 0.305129 + 0.176166i
\(871\) −35.0000 + 60.6218i −1.18593 + 2.05409i
\(872\) 1.00000 0.0338643
\(873\) −10.5000 + 18.1865i −0.355371 + 0.615521i
\(874\) 12.0000 0.405906
\(875\) −0.500000 + 0.866025i −0.0169031 + 0.0292770i
\(876\) 16.5000 9.52628i 0.557483 0.321863i
\(877\) 11.0000 + 19.0526i 0.371444 + 0.643359i 0.989788 0.142548i \(-0.0455296\pi\)
−0.618344 + 0.785907i \(0.712196\pi\)
\(878\) 4.00000 + 6.92820i 0.134993 + 0.233816i
\(879\) 9.00000 5.19615i 0.303562 0.175262i
\(880\) −1.50000 + 2.59808i −0.0505650 + 0.0875811i
\(881\) −36.0000 −1.21287 −0.606435 0.795133i \(-0.707401\pi\)
−0.606435 + 0.795133i \(0.707401\pi\)
\(882\) 3.00000 0.101015
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) −10.5000 + 18.1865i −0.353153 + 0.611679i
\(885\) 0 0
\(886\) 9.00000 + 15.5885i 0.302361 + 0.523704i
\(887\) −12.0000 20.7846i −0.402921 0.697879i 0.591156 0.806557i \(-0.298672\pi\)
−0.994077 + 0.108678i \(0.965338\pi\)
\(888\) 3.46410i 0.116248i
\(889\) −4.00000 + 6.92820i −0.134156 + 0.232364i
\(890\) 18.0000 0.603361
\(891\) −13.5000 + 23.3827i −0.452267 + 0.783349i
\(892\) −19.0000 −0.636167
\(893\) 9.00000 15.5885i 0.301174 0.521648i
\(894\) 25.9808i 0.868927i
\(895\) 4.50000 + 7.79423i 0.150418 + 0.260532i
\(896\) 0.500000 + 0.866025i 0.0167038 + 0.0289319i
\(897\) −63.0000 36.3731i −2.10351 1.21446i
\(898\) −15.0000 + 25.9808i −0.500556 + 0.866989i
\(899\) 12.0000 0.400222
\(900\) −3.00000 −0.100000
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 3.00000 1.73205i 0.0998337 0.0576390i
\(904\) 3.00000 + 5.19615i 0.0997785 + 0.172821i
\(905\) −1.00000 1.73205i −0.0332411 0.0575753i
\(906\) −7.50000 + 4.33013i −0.249171 + 0.143859i
\(907\) −7.00000 + 12.1244i −0.232431 + 0.402583i −0.958523 0.285015i \(-0.908001\pi\)
0.726092 + 0.687598i \(0.241335\pi\)
\(908\) 3.00000 0.0995585
\(909\) −27.0000 + 46.7654i −0.895533 + 1.55111i
\(910\) 7.00000 0.232048
\(911\) 1.50000 2.59808i 0.0496972 0.0860781i −0.840107 0.542421i \(-0.817508\pi\)
0.889804 + 0.456343i \(0.150841\pi\)
\(912\) −3.00000 1.73205i −0.0993399 0.0573539i
\(913\) 22.5000 + 38.9711i 0.744641 + 1.28976i
\(914\) 19.0000 + 32.9090i 0.628464 + 1.08853i
\(915\) 24.2487i 0.801638i
\(916\) 5.00000 8.66025i 0.165205 0.286143i
\(917\) 0 0
\(918\) 13.5000 + 7.79423i 0.445566 + 0.257248i
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) −3.00000 + 5.19615i −0.0989071 + 0.171312i
\(921\) 50.2295i 1.65512i
\(922\) −21.0000 36.3731i −0.691598 1.19788i
\(923\) 10.5000 + 18.1865i 0.345612 + 0.598617i
\(924\) −4.50000 2.59808i −0.148039 0.0854704i
\(925\) −1.00000 + 1.73205i −0.0328798 + 0.0569495i
\(926\) −32.0000 −1.05159
\(927\) 12.0000 + 20.7846i 0.394132 + 0.682656i
\(928\) −6.00000 −0.196960
\(929\) 9.00000 15.5885i 0.295280 0.511441i −0.679770 0.733426i \(-0.737920\pi\)
0.975050 + 0.221985i \(0.0712536\pi\)
\(930\) −3.00000 + 1.73205i −0.0983739 + 0.0567962i
\(931\) −1.00000 1.73205i −0.0327737 0.0567657i
\(932\) 0 0
\(933\) −36.0000 + 20.7846i −1.17859 + 0.680458i
\(934\) 1.50000 2.59808i 0.0490815 0.0850117i
\(935\) −9.00000 −0.294331
\(936\) 10.5000 + 18.1865i 0.343203 + 0.594445i
\(937\) −43.0000 −1.40475 −0.702374 0.711808i \(-0.747877\pi\)
−0.702374 + 0.711808i \(0.747877\pi\)
\(938\) −5.00000 + 8.66025i −0.163256 + 0.282767i
\(939\) 15.0000 + 8.66025i 0.489506 + 0.282617i
\(940\) 4.50000 + 7.79423i 0.146774 + 0.254220i
\(941\) −6.00000 10.3923i −0.195594 0.338779i 0.751501 0.659732i \(-0.229330\pi\)
−0.947095 + 0.320953i \(0.895997\pi\)
\(942\) 8.66025i 0.282166i
\(943\) 0 0
\(944\) 0 0
\(945\) 5.19615i 0.169031i
\(946\) −6.00000 −0.195077
\(947\) −6.00000 + 10.3923i −0.194974 + 0.337705i −0.946892 0.321552i \(-0.895796\pi\)
0.751918 + 0.659256i \(0.229129\pi\)
\(948\) 22.5167i 0.731307i
\(949\) 38.5000 + 66.6840i 1.24976 + 2.16465i
\(950\) 1.00000 + 1.73205i 0.0324443 + 0.0561951i
\(951\) −27.0000 15.5885i −0.875535 0.505490i
\(952\) −1.50000 + 2.59808i −0.0486153 + 0.0842041i
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 18.0000 31.1769i 0.582772 1.00939i
\(955\) 0 0
\(956\) 12.0000 20.7846i 0.388108 0.672222i
\(957\) 27.0000 15.5885i 0.872786 0.503903i
\(958\) −3.00000 5.19615i −0.0969256 0.167880i
\(959\) −3.00000 5.19615i −0.0968751 0.167793i
\(960\) 1.50000 0.866025i 0.0484123 0.0279508i
\(961\) 13.5000 23.3827i 0.435484 0.754280i
\(962\) 14.0000 0.451378
\(963\) −18.0000 −0.580042
\(964\) 8.00000 0.257663
\(965\) 5.00000 8.66025i 0.160956 0.278783i
\(966\) −9.00000 5.19615i −0.289570 0.167183i
\(967\) 23.0000 + 39.8372i 0.739630 + 1.28108i 0.952662 + 0.304032i \(0.0983329\pi\)
−0.213032 + 0.977045i \(0.568334\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 10.3923i 0.333849i
\(970\) −3.50000 + 6.06218i −0.112378 + 0.194645i
\(971\) 30.0000 0.962746 0.481373 0.876516i \(-0.340138\pi\)
0.481373 + 0.876516i \(0.340138\pi\)
\(972\) 13.5000 7.79423i 0.433013 0.250000i
\(973\) −22.0000 −0.705288
\(974\) 1.00000 1.73205i 0.0320421 0.0554985i
\(975\) 12.1244i 0.388290i
\(976\) −7.00000 12.1244i −0.224065 0.388091i
\(977\) −12.0000 20.7846i −0.383914 0.664959i 0.607704 0.794164i \(-0.292091\pi\)
−0.991618 + 0.129205i \(0.958757\pi\)
\(978\) 3.00000 + 1.73205i 0.0959294 + 0.0553849i
\(979\) 27.0000 46.7654i 0.862924 1.49463i
\(980\) 1.00000 0.0319438
\(981\) 3.00000 0.0957826
\(982\) 9.00000 0.287202
\(983\) 13.5000 23.3827i 0.430583 0.745792i −0.566340 0.824171i \(-0.691641\pi\)
0.996924 + 0.0783795i \(0.0249746\pi\)
\(984\) 0 0
\(985\) −9.00000 15.5885i −0.286764 0.496690i
\(986\) −9.00000 15.5885i −0.286618 0.496438i
\(987\) −13.5000 + 7.79423i −0.429710 + 0.248093i
\(988\) 7.00000 12.1244i 0.222700 0.385727i
\(989\) −12.0000 −0.381578
\(990\) −4.50000 + 7.79423i −0.143019 + 0.247717i
\(991\) 41.0000 1.30241 0.651204 0.758903i \(-0.274264\pi\)
0.651204 + 0.758903i \(0.274264\pi\)
\(992\) 1.00000 1.73205i 0.0317500 0.0549927i
\(993\) −25.5000 14.7224i −0.809218 0.467202i
\(994\) 1.50000 + 2.59808i 0.0475771 + 0.0824060i
\(995\) 2.00000 + 3.46410i 0.0634043 + 0.109819i
\(996\) 25.9808i 0.823232i
\(997\) −13.0000 + 22.5167i −0.411714 + 0.713110i −0.995077 0.0991016i \(-0.968403\pi\)
0.583363 + 0.812211i \(0.301736\pi\)
\(998\) −5.00000 −0.158272
\(999\) 10.3923i 0.328798i
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 630.2.j.d.421.1 yes 2
3.2 odd 2 1890.2.j.d.1261.1 2
9.2 odd 6 5670.2.a.j.1.1 1
9.4 even 3 inner 630.2.j.d.211.1 2
9.5 odd 6 1890.2.j.d.631.1 2
9.7 even 3 5670.2.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.j.d.211.1 2 9.4 even 3 inner
630.2.j.d.421.1 yes 2 1.1 even 1 trivial
1890.2.j.d.631.1 2 9.5 odd 6
1890.2.j.d.1261.1 2 3.2 odd 2
5670.2.a.i.1.1 1 9.7 even 3
5670.2.a.j.1.1 1 9.2 odd 6