Properties

Label 770.2.i.e.221.1
Level $770$
Weight $2$
Character 770.221
Analytic conductor $6.148$
Analytic rank $1$
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] = [770,2,Mod(221,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.221");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.14848095564\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 221.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 770.221
Dual form 770.2.i.e.331.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -3.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(-3.00000 - 5.19615i) q^{19} +1.00000 q^{20} +(2.00000 - 1.73205i) q^{21} -1.00000 q^{22} +(-1.00000 - 1.73205i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.50000 - 2.59808i) q^{26} -5.00000 q^{27} +(2.00000 - 1.73205i) q^{28} -7.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +(0.500000 + 2.59808i) q^{35} -2.00000 q^{36} +(3.00000 - 5.19615i) q^{38} +(1.50000 - 2.59808i) q^{39} +(0.500000 + 0.866025i) q^{40} -4.00000 q^{41} +(2.50000 + 0.866025i) q^{42} -6.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.00000 - 1.73205i) q^{46} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -1.00000 q^{50} +(1.50000 - 2.59808i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-2.50000 - 4.33013i) q^{54} +1.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +6.00000 q^{57} +(-3.50000 - 6.06218i) q^{58} +(0.500000 - 0.866025i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +8.00000 q^{62} +(-1.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(0.500000 - 0.866025i) q^{66} +(2.50000 - 4.33013i) q^{67} +2.00000 q^{69} +(-2.00000 + 1.73205i) q^{70} +8.00000 q^{71} +(-1.00000 - 1.73205i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-0.500000 - 0.866025i) q^{75} +6.00000 q^{76} +(2.00000 - 1.73205i) q^{77} +3.00000 q^{78} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} -6.00000 q^{83} +(0.500000 + 2.59808i) q^{84} +(-3.00000 - 5.19615i) q^{86} +(3.50000 - 6.06218i) q^{87} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +2.00000 q^{90} +(7.50000 + 2.59808i) q^{91} +2.00000 q^{92} +(4.00000 + 6.92820i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} -7.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} - q^{11} - q^{12} - 6 q^{13} - q^{14} + 2 q^{15} - q^{16} - 2 q^{18} - 6 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} + q^{24} - q^{25} - 3 q^{26} - 10 q^{27} + 4 q^{28} - 14 q^{29} + q^{30} + 8 q^{31} + q^{32} - q^{33} + q^{35} - 4 q^{36} + 6 q^{38} + 3 q^{39} + q^{40} - 8 q^{41} + 5 q^{42} - 12 q^{43} - q^{44} + 2 q^{45} + 2 q^{46} + 2 q^{48} + 11 q^{49} - 2 q^{50} + 3 q^{52} - 6 q^{53} - 5 q^{54} + 2 q^{55} + 5 q^{56} + 12 q^{57} - 7 q^{58} + q^{59} - q^{60} + q^{61} + 16 q^{62} - 2 q^{63} + 2 q^{64} + 3 q^{65} + q^{66} + 5 q^{67} + 4 q^{69} - 4 q^{70} + 16 q^{71} - 2 q^{72} - 14 q^{73} - q^{75} + 12 q^{76} + 4 q^{77} + 6 q^{78} + 13 q^{79} - q^{80} - q^{81} - 4 q^{82} - 12 q^{83} + q^{84} - 6 q^{86} + 7 q^{87} + q^{88} + 6 q^{89} + 4 q^{90} + 15 q^{91} + 4 q^{92} + 8 q^{93} - 6 q^{95} + q^{96} - 14 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −1.00000 −0.408248
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 1.00000 0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −1.00000 + 1.73205i −0.235702 + 0.408248i
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) −1.00000 −0.213201
\(23\) −1.00000 1.73205i −0.208514 0.361158i 0.742732 0.669588i \(-0.233529\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.50000 2.59808i −0.294174 0.509525i
\(27\) −5.00000 −0.962250
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.500000 0.866025i −0.0870388 0.150756i
\(34\) 0 0
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) −2.00000 −0.333333
\(37\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(38\) 3.00000 5.19615i 0.486664 0.842927i
\(39\) 1.50000 2.59808i 0.240192 0.416025i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 2.50000 + 0.866025i 0.385758 + 0.133631i
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 1.00000 1.73205i 0.147442 0.255377i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.50000 2.59808i 0.208013 0.360288i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) −2.50000 4.33013i −0.340207 0.589256i
\(55\) 1.00000 0.134840
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 6.00000 0.794719
\(58\) −3.50000 6.06218i −0.459573 0.796003i
\(59\) 0.500000 0.866025i 0.0650945 0.112747i −0.831641 0.555313i \(-0.812598\pi\)
0.896736 + 0.442566i \(0.145932\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 8.00000 1.01600
\(63\) −1.00000 5.19615i −0.125988 0.654654i
\(64\) 1.00000 0.125000
\(65\) 1.50000 + 2.59808i 0.186052 + 0.322252i
\(66\) 0.500000 0.866025i 0.0615457 0.106600i
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 0 0
\(69\) 2.00000 0.240772
\(70\) −2.00000 + 1.73205i −0.239046 + 0.207020i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 1.73205i −0.117851 0.204124i
\(73\) −7.00000 + 12.1244i −0.819288 + 1.41905i 0.0869195 + 0.996215i \(0.472298\pi\)
−0.906208 + 0.422833i \(0.861036\pi\)
\(74\) 0 0
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 6.00000 0.688247
\(77\) 2.00000 1.73205i 0.227921 0.197386i
\(78\) 3.00000 0.339683
\(79\) 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i \(0.0944227\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) 0 0
\(86\) −3.00000 5.19615i −0.323498 0.560316i
\(87\) 3.50000 6.06218i 0.375239 0.649934i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 2.00000 0.210819
\(91\) 7.50000 + 2.59808i 0.786214 + 0.272352i
\(92\) 2.00000 0.208514
\(93\) 4.00000 + 6.92820i 0.414781 + 0.718421i
\(94\) 0 0
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) −2.00000 −0.201008
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) 3.00000 0.294174
\(105\) −2.50000 0.866025i −0.243975 0.0845154i
\(106\) −6.00000 −0.582772
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 2.50000 4.33013i 0.240563 0.416667i
\(109\) −9.00000 + 15.5885i −0.862044 + 1.49310i 0.00790932 + 0.999969i \(0.497482\pi\)
−0.869953 + 0.493135i \(0.835851\pi\)
\(110\) 0.500000 + 0.866025i 0.0476731 + 0.0825723i
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) −13.0000 −1.22294 −0.611469 0.791269i \(-0.709421\pi\)
−0.611469 + 0.791269i \(0.709421\pi\)
\(114\) 3.00000 + 5.19615i 0.280976 + 0.486664i
\(115\) −1.00000 + 1.73205i −0.0932505 + 0.161515i
\(116\) 3.50000 6.06218i 0.324967 0.562859i
\(117\) −3.00000 5.19615i −0.277350 0.480384i
\(118\) 1.00000 0.0920575
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) 2.00000 3.46410i 0.180334 0.312348i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 4.00000 3.46410i 0.356348 0.308607i
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 3.00000 5.19615i 0.264135 0.457496i
\(130\) −1.50000 + 2.59808i −0.131559 + 0.227866i
\(131\) 7.00000 + 12.1244i 0.611593 + 1.05931i 0.990972 + 0.134069i \(0.0428042\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(132\) 1.00000 0.0870388
\(133\) 3.00000 + 15.5885i 0.260133 + 1.35169i
\(134\) 5.00000 0.431934
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 1.00000 + 1.73205i 0.0851257 + 0.147442i
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −2.50000 0.866025i −0.211289 0.0731925i
\(141\) 0 0
\(142\) 4.00000 + 6.92820i 0.335673 + 0.581402i
\(143\) 1.50000 2.59808i 0.125436 0.217262i
\(144\) 1.00000 1.73205i 0.0833333 0.144338i
\(145\) 3.50000 + 6.06218i 0.290659 + 0.503436i
\(146\) −14.0000 −1.15865
\(147\) −6.50000 + 2.59808i −0.536111 + 0.214286i
\(148\) 0 0
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 8.50000 14.7224i 0.691720 1.19809i −0.279554 0.960130i \(-0.590186\pi\)
0.971274 0.237964i \(-0.0764802\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) 0 0
\(154\) 2.50000 + 0.866025i 0.201456 + 0.0697863i
\(155\) −8.00000 −0.642575
\(156\) 1.50000 + 2.59808i 0.120096 + 0.208013i
\(157\) −3.00000 + 5.19615i −0.239426 + 0.414698i −0.960550 0.278108i \(-0.910293\pi\)
0.721124 + 0.692806i \(0.243626\pi\)
\(158\) −6.50000 + 11.2583i −0.517112 + 0.895665i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) −1.00000 −0.0790569
\(161\) 1.00000 + 5.19615i 0.0788110 + 0.409514i
\(162\) −1.00000 −0.0785674
\(163\) 5.50000 + 9.52628i 0.430793 + 0.746156i 0.996942 0.0781474i \(-0.0249005\pi\)
−0.566149 + 0.824303i \(0.691567\pi\)
\(164\) 2.00000 3.46410i 0.156174 0.270501i
\(165\) −0.500000 + 0.866025i −0.0389249 + 0.0674200i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 19.0000 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(168\) −2.00000 + 1.73205i −0.154303 + 0.133631i
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 6.00000 10.3923i 0.458831 0.794719i
\(172\) 3.00000 5.19615i 0.228748 0.396203i
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 7.00000 0.530669
\(175\) 2.00000 1.73205i 0.151186 0.130931i
\(176\) 1.00000 0.0753778
\(177\) 0.500000 + 0.866025i 0.0375823 + 0.0650945i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −7.50000 + 12.9904i −0.560576 + 0.970947i 0.436870 + 0.899525i \(0.356087\pi\)
−0.997446 + 0.0714220i \(0.977246\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 1.50000 + 7.79423i 0.111187 + 0.577747i
\(183\) −1.00000 −0.0739221
\(184\) 1.00000 + 1.73205i 0.0737210 + 0.127688i
\(185\) 0 0
\(186\) −4.00000 + 6.92820i −0.293294 + 0.508001i
\(187\) 0 0
\(188\) 0 0
\(189\) 12.5000 + 4.33013i 0.909241 + 0.314970i
\(190\) −6.00000 −0.435286
\(191\) −2.00000 3.46410i −0.144715 0.250654i 0.784552 0.620063i \(-0.212893\pi\)
−0.929267 + 0.369410i \(0.879560\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) −3.00000 −0.214834
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 11.0000 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(198\) −1.00000 1.73205i −0.0710669 0.123091i
\(199\) 3.00000 5.19615i 0.212664 0.368345i −0.739883 0.672735i \(-0.765119\pi\)
0.952548 + 0.304390i \(0.0984526\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 2.50000 + 4.33013i 0.176336 + 0.305424i
\(202\) 15.0000 1.05540
\(203\) 17.5000 + 6.06218i 1.22826 + 0.425481i
\(204\) 0 0
\(205\) 2.00000 + 3.46410i 0.139686 + 0.241943i
\(206\) 2.00000 3.46410i 0.139347 0.241355i
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) 1.50000 + 2.59808i 0.104006 + 0.180144i
\(209\) 6.00000 0.415029
\(210\) −0.500000 2.59808i −0.0345033 0.179284i
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) −4.00000 + 6.92820i −0.274075 + 0.474713i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 3.00000 + 5.19615i 0.204598 + 0.354375i
\(216\) 5.00000 0.340207
\(217\) −16.0000 + 13.8564i −1.08615 + 0.940634i
\(218\) −18.0000 −1.21911
\(219\) −7.00000 12.1244i −0.473016 0.819288i
\(220\) −0.500000 + 0.866025i −0.0337100 + 0.0583874i
\(221\) 0 0
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) −2.00000 −0.133333
\(226\) −6.50000 11.2583i −0.432374 0.748893i
\(227\) 4.00000 6.92820i 0.265489 0.459841i −0.702202 0.711977i \(-0.747800\pi\)
0.967692 + 0.252136i \(0.0811332\pi\)
\(228\) −3.00000 + 5.19615i −0.198680 + 0.344124i
\(229\) −13.0000 22.5167i −0.859064 1.48794i −0.872823 0.488037i \(-0.837713\pi\)
0.0137585 0.999905i \(-0.495620\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0.500000 + 2.59808i 0.0328976 + 0.170941i
\(232\) 7.00000 0.459573
\(233\) 6.00000 + 10.3923i 0.393073 + 0.680823i 0.992853 0.119342i \(-0.0380786\pi\)
−0.599780 + 0.800165i \(0.704745\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) 0 0
\(236\) 0.500000 + 0.866025i 0.0325472 + 0.0563735i
\(237\) −13.0000 −0.844441
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −1.00000 −0.0640184
\(245\) 1.00000 6.92820i 0.0638877 0.442627i
\(246\) 4.00000 0.255031
\(247\) 9.00000 + 15.5885i 0.572656 + 0.991870i
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 5.00000 + 1.73205i 0.314970 + 0.109109i
\(253\) 2.00000 0.125739
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.50000 11.2583i −0.405459 0.702275i 0.588916 0.808194i \(-0.299555\pi\)
−0.994375 + 0.105919i \(0.966222\pi\)
\(258\) 6.00000 0.373544
\(259\) 0 0
\(260\) −3.00000 −0.186052
\(261\) −7.00000 12.1244i −0.433289 0.750479i
\(262\) −7.00000 + 12.1244i −0.432461 + 0.749045i
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0.500000 + 0.866025i 0.0307729 + 0.0533002i
\(265\) 6.00000 0.368577
\(266\) −12.0000 + 10.3923i −0.735767 + 0.637193i
\(267\) −6.00000 −0.367194
\(268\) 2.50000 + 4.33013i 0.152712 + 0.264505i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) −2.50000 + 4.33013i −0.152145 + 0.263523i
\(271\) 0.500000 + 0.866025i 0.0303728 + 0.0526073i 0.880812 0.473466i \(-0.156997\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0 0
\(273\) −6.00000 + 5.19615i −0.363137 + 0.314485i
\(274\) 3.00000 0.181237
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) −1.00000 + 1.73205i −0.0601929 + 0.104257i
\(277\) 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i \(-0.662714\pi\)
0.999923 0.0124177i \(-0.00395278\pi\)
\(278\) −8.00000 13.8564i −0.479808 0.831052i
\(279\) 16.0000 0.957895
\(280\) −0.500000 2.59808i −0.0298807 0.155265i
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 0 0
\(283\) −5.00000 + 8.66025i −0.297219 + 0.514799i −0.975499 0.220005i \(-0.929393\pi\)
0.678280 + 0.734804i \(0.262726\pi\)
\(284\) −4.00000 + 6.92820i −0.237356 + 0.411113i
\(285\) −3.00000 5.19615i −0.177705 0.307794i
\(286\) 3.00000 0.177394
\(287\) 10.0000 + 3.46410i 0.590281 + 0.204479i
\(288\) 2.00000 0.117851
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −3.50000 + 6.06218i −0.205527 + 0.355983i
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) −5.50000 4.33013i −0.320767 0.252538i
\(295\) −1.00000 −0.0582223
\(296\) 0 0
\(297\) 2.50000 4.33013i 0.145065 0.251259i
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 1.00000 0.0577350
\(301\) 15.0000 + 5.19615i 0.864586 + 0.299501i
\(302\) 17.0000 0.978240
\(303\) 7.50000 + 12.9904i 0.430864 + 0.746278i
\(304\) −3.00000 + 5.19615i −0.172062 + 0.298020i
\(305\) 0.500000 0.866025i 0.0286299 0.0495885i
\(306\) 0 0
\(307\) −26.0000 −1.48390 −0.741949 0.670456i \(-0.766098\pi\)
−0.741949 + 0.670456i \(0.766098\pi\)
\(308\) 0.500000 + 2.59808i 0.0284901 + 0.148039i
\(309\) 4.00000 0.227552
\(310\) −4.00000 6.92820i −0.227185 0.393496i
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) −1.50000 + 2.59808i −0.0849208 + 0.147087i
\(313\) 6.50000 + 11.2583i 0.367402 + 0.636358i 0.989158 0.146852i \(-0.0469141\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −6.00000 −0.338600
\(315\) −4.00000 + 3.46410i −0.225374 + 0.195180i
\(316\) −13.0000 −0.731307
\(317\) 10.0000 + 17.3205i 0.561656 + 0.972817i 0.997352 + 0.0727229i \(0.0231689\pi\)
−0.435696 + 0.900094i \(0.643498\pi\)
\(318\) 3.00000 5.19615i 0.168232 0.291386i
\(319\) 3.50000 6.06218i 0.195962 0.339417i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 6.00000 0.334887
\(322\) −4.00000 + 3.46410i −0.222911 + 0.193047i
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) −5.50000 + 9.52628i −0.304617 + 0.527612i
\(327\) −9.00000 15.5885i −0.497701 0.862044i
\(328\) 4.00000 0.220863
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 0 0
\(334\) 9.50000 + 16.4545i 0.519817 + 0.900349i
\(335\) −5.00000 −0.273179
\(336\) −2.50000 0.866025i −0.136386 0.0472456i
\(337\) −4.00000 −0.217894 −0.108947 0.994048i \(-0.534748\pi\)
−0.108947 + 0.994048i \(0.534748\pi\)
\(338\) −2.00000 3.46410i −0.108786 0.188422i
\(339\) 6.50000 11.2583i 0.353032 0.611469i
\(340\) 0 0
\(341\) 4.00000 + 6.92820i 0.216612 + 0.375183i
\(342\) 12.0000 0.648886
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 6.00000 0.323498
\(345\) −1.00000 1.73205i −0.0538382 0.0932505i
\(346\) 4.50000 7.79423i 0.241921 0.419020i
\(347\) 13.0000 22.5167i 0.697877 1.20876i −0.271325 0.962488i \(-0.587462\pi\)
0.969201 0.246270i \(-0.0792049\pi\)
\(348\) 3.50000 + 6.06218i 0.187620 + 0.324967i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 2.50000 + 0.866025i 0.133631 + 0.0462910i
\(351\) 15.0000 0.800641
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) −0.500000 + 0.866025i −0.0265747 + 0.0460287i
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) −15.5000 26.8468i −0.818059 1.41692i −0.907111 0.420892i \(-0.861717\pi\)
0.0890519 0.996027i \(-0.471616\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 6.00000 + 10.3923i 0.315353 + 0.546207i
\(363\) 1.00000 0.0524864
\(364\) −6.00000 + 5.19615i −0.314485 + 0.272352i
\(365\) 14.0000 0.732793
\(366\) −0.500000 0.866025i −0.0261354 0.0452679i
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) −1.00000 + 1.73205i −0.0521286 + 0.0902894i
\(369\) −4.00000 6.92820i −0.208232 0.360668i
\(370\) 0 0
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) −8.00000 −0.414781
\(373\) 0.500000 + 0.866025i 0.0258890 + 0.0448411i 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 21.0000 1.08156
\(378\) 2.50000 + 12.9904i 0.128586 + 0.668153i
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 9.50000 16.4545i 0.486700 0.842989i
\(382\) 2.00000 3.46410i 0.102329 0.177239i
\(383\) −8.00000 13.8564i −0.408781 0.708029i 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −2.50000 0.866025i −0.127412 0.0441367i
\(386\) −8.00000 −0.407189
\(387\) −6.00000 10.3923i −0.304997 0.528271i
\(388\) 3.50000 6.06218i 0.177686 0.307760i
\(389\) 16.0000 27.7128i 0.811232 1.40510i −0.100770 0.994910i \(-0.532131\pi\)
0.912002 0.410186i \(-0.134536\pi\)
\(390\) −1.50000 2.59808i −0.0759555 0.131559i
\(391\) 0 0
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) −14.0000 −0.706207
\(394\) 5.50000 + 9.52628i 0.277086 + 0.479927i
\(395\) 6.50000 11.2583i 0.327050 0.566468i
\(396\) 1.00000 1.73205i 0.0502519 0.0870388i
\(397\) −13.0000 22.5167i −0.652451 1.13008i −0.982526 0.186124i \(-0.940407\pi\)
0.330075 0.943955i \(-0.392926\pi\)
\(398\) 6.00000 0.300753
\(399\) −15.0000 5.19615i −0.750939 0.260133i
\(400\) 1.00000 0.0500000
\(401\) 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i \(0.141579\pi\)
−0.0787327 + 0.996896i \(0.525087\pi\)
\(402\) −2.50000 + 4.33013i −0.124689 + 0.215967i
\(403\) −12.0000 + 20.7846i −0.597763 + 1.03536i
\(404\) 7.50000 + 12.9904i 0.373139 + 0.646296i
\(405\) 1.00000 0.0496904
\(406\) 3.50000 + 18.1865i 0.173702 + 0.902583i
\(407\) 0 0
\(408\) 0 0
\(409\) 4.00000 6.92820i 0.197787 0.342578i −0.750023 0.661411i \(-0.769958\pi\)
0.947811 + 0.318834i \(0.103291\pi\)
\(410\) −2.00000 + 3.46410i −0.0987730 + 0.171080i
\(411\) 1.50000 + 2.59808i 0.0739895 + 0.128154i
\(412\) 4.00000 0.197066
\(413\) −2.00000 + 1.73205i −0.0984136 + 0.0852286i
\(414\) 4.00000 0.196589
\(415\) 3.00000 + 5.19615i 0.147264 + 0.255069i
\(416\) −1.50000 + 2.59808i −0.0735436 + 0.127381i
\(417\) 8.00000 13.8564i 0.391762 0.678551i
\(418\) 3.00000 + 5.19615i 0.146735 + 0.254152i
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 2.00000 1.73205i 0.0975900 0.0845154i
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) −6.00000 10.3923i −0.292075 0.505889i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 0 0
\(426\) −8.00000 −0.387601
\(427\) −0.500000 2.59808i −0.0241967 0.125730i
\(428\) 6.00000 0.290021
\(429\) 1.50000 + 2.59808i 0.0724207 + 0.125436i
\(430\) −3.00000 + 5.19615i −0.144673 + 0.250581i
\(431\) 18.5000 32.0429i 0.891114 1.54345i 0.0525716 0.998617i \(-0.483258\pi\)
0.838542 0.544837i \(-0.183408\pi\)
\(432\) 2.50000 + 4.33013i 0.120281 + 0.208333i
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −20.0000 6.92820i −0.960031 0.332564i
\(435\) −7.00000 −0.335624
\(436\) −9.00000 15.5885i −0.431022 0.746552i
\(437\) −6.00000 + 10.3923i −0.287019 + 0.497131i
\(438\) 7.00000 12.1244i 0.334473 0.579324i
\(439\) −12.5000 21.6506i −0.596592 1.03333i −0.993320 0.115392i \(-0.963188\pi\)
0.396728 0.917936i \(-0.370146\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −2.00000 + 13.8564i −0.0952381 + 0.659829i
\(442\) 0 0
\(443\) −20.0000 34.6410i −0.950229 1.64584i −0.744927 0.667146i \(-0.767516\pi\)
−0.205301 0.978699i \(-0.565817\pi\)
\(444\) 0 0
\(445\) 3.00000 5.19615i 0.142214 0.246321i
\(446\) −6.00000 10.3923i −0.284108 0.492090i
\(447\) −18.0000 −0.851371
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) −1.00000 1.73205i −0.0471405 0.0816497i
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) 6.50000 11.2583i 0.305734 0.529547i
\(453\) 8.50000 + 14.7224i 0.399365 + 0.691720i
\(454\) 8.00000 0.375459
\(455\) −1.50000 7.79423i −0.0703211 0.365399i
\(456\) −6.00000 −0.280976
\(457\) 20.0000 + 34.6410i 0.935561 + 1.62044i 0.773631 + 0.633636i \(0.218438\pi\)
0.161929 + 0.986802i \(0.448228\pi\)
\(458\) 13.0000 22.5167i 0.607450 1.05213i
\(459\) 0 0
\(460\) −1.00000 1.73205i −0.0466252 0.0807573i
\(461\) −23.0000 −1.07122 −0.535608 0.844466i \(-0.679918\pi\)
−0.535608 + 0.844466i \(0.679918\pi\)
\(462\) −2.00000 + 1.73205i −0.0930484 + 0.0805823i
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 3.50000 + 6.06218i 0.162483 + 0.281430i
\(465\) 4.00000 6.92820i 0.185496 0.321288i
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) 18.0000 + 31.1769i 0.832941 + 1.44270i 0.895696 + 0.444667i \(0.146678\pi\)
−0.0627555 + 0.998029i \(0.519989\pi\)
\(468\) 6.00000 0.277350
\(469\) −10.0000 + 8.66025i −0.461757 + 0.399893i
\(470\) 0 0
\(471\) −3.00000 5.19615i −0.138233 0.239426i
\(472\) −0.500000 + 0.866025i −0.0230144 + 0.0398621i
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) −6.50000 11.2583i −0.298555 0.517112i
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 4.50000 + 7.79423i 0.205825 + 0.356500i
\(479\) −20.5000 + 35.5070i −0.936669 + 1.62236i −0.165038 + 0.986287i \(0.552775\pi\)
−0.771631 + 0.636071i \(0.780559\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 0 0
\(482\) 10.0000 0.455488
\(483\) −5.00000 1.73205i −0.227508 0.0788110i
\(484\) 1.00000 0.0454545
\(485\) 3.50000 + 6.06218i 0.158927 + 0.275269i
\(486\) 8.00000 13.8564i 0.362887 0.628539i
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) −11.0000 −0.497437
\(490\) 6.50000 2.59808i 0.293640 0.117369i
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 2.00000 + 3.46410i 0.0901670 + 0.156174i
\(493\) 0 0
\(494\) −9.00000 + 15.5885i −0.404929 + 0.701358i
\(495\) 1.00000 + 1.73205i 0.0449467 + 0.0778499i
\(496\) −8.00000 −0.359211
\(497\) −20.0000 6.92820i −0.897123 0.310772i
\(498\) 6.00000 0.268866
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −9.50000 + 16.4545i −0.424429 + 0.735132i
\(502\) 2.00000 + 3.46410i 0.0892644 + 0.154610i
\(503\) 3.00000 0.133763 0.0668817 0.997761i \(-0.478695\pi\)
0.0668817 + 0.997761i \(0.478695\pi\)
\(504\) 1.00000 + 5.19615i 0.0445435 + 0.231455i
\(505\) −15.0000 −0.667491
\(506\) 1.00000 + 1.73205i 0.0444554 + 0.0769991i
\(507\) 2.00000 3.46410i 0.0888231 0.153846i
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 28.0000 24.2487i 1.23865 1.07270i
\(512\) −1.00000 −0.0441942
\(513\) 15.0000 + 25.9808i 0.662266 + 1.14708i
\(514\) 6.50000 11.2583i 0.286703 0.496584i
\(515\) −2.00000 + 3.46410i −0.0881305 + 0.152647i
\(516\) 3.00000 + 5.19615i 0.132068 + 0.228748i
\(517\) 0 0
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) −1.50000 2.59808i −0.0657794 0.113933i
\(521\) 5.00000 8.66025i 0.219054 0.379413i −0.735465 0.677563i \(-0.763036\pi\)
0.954519 + 0.298150i \(0.0963696\pi\)
\(522\) 7.00000 12.1244i 0.306382 0.530669i
\(523\) −17.0000 29.4449i −0.743358 1.28753i −0.950958 0.309320i \(-0.899899\pi\)
0.207600 0.978214i \(-0.433435\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0.500000 + 2.59808i 0.0218218 + 0.113389i
\(526\) 9.00000 0.392419
\(527\) 0 0
\(528\) −0.500000 + 0.866025i −0.0217597 + 0.0376889i
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 3.00000 + 5.19615i 0.130312 + 0.225706i
\(531\) 2.00000 0.0867926
\(532\) −15.0000 5.19615i −0.650332 0.225282i
\(533\) 12.0000 0.519778
\(534\) −3.00000 5.19615i −0.129823 0.224860i
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) −2.50000 + 4.33013i −0.107984 + 0.187033i
\(537\) −7.50000 12.9904i −0.323649 0.560576i
\(538\) 14.0000 0.603583
\(539\) −6.50000 + 2.59808i −0.279975 + 0.111907i
\(540\) −5.00000 −0.215166
\(541\) 6.50000 + 11.2583i 0.279457 + 0.484033i 0.971250 0.238062i \(-0.0765123\pi\)
−0.691793 + 0.722096i \(0.743179\pi\)
\(542\) −0.500000 + 0.866025i −0.0214768 + 0.0371990i
\(543\) −6.00000 + 10.3923i −0.257485 + 0.445976i
\(544\) 0 0
\(545\) 18.0000 0.771035
\(546\) −7.50000 2.59808i −0.320970 0.111187i
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 1.50000 + 2.59808i 0.0640768 + 0.110984i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0.500000 0.866025i 0.0213201 0.0369274i
\(551\) 21.0000 + 36.3731i 0.894630 + 1.54954i
\(552\) −2.00000 −0.0851257
\(553\) −6.50000 33.7750i −0.276408 1.43626i
\(554\) 17.0000 0.722261
\(555\) 0 0
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 8.00000 + 13.8564i 0.338667 + 0.586588i
\(559\) 18.0000 0.761319
\(560\) 2.00000 1.73205i 0.0845154 0.0731925i
\(561\) 0 0
\(562\) −4.00000 6.92820i −0.168730 0.292249i
\(563\) −19.0000 + 32.9090i −0.800755 + 1.38695i 0.118366 + 0.992970i \(0.462235\pi\)
−0.919120 + 0.393977i \(0.871099\pi\)
\(564\) 0 0
\(565\) 6.50000 + 11.2583i 0.273457 + 0.473642i
\(566\) −10.0000 −0.420331
\(567\) 2.00000 1.73205i 0.0839921 0.0727393i
\(568\) −8.00000 −0.335673
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 3.00000 5.19615i 0.125656 0.217643i
\(571\) 14.0000 24.2487i 0.585882 1.01478i −0.408883 0.912587i \(-0.634082\pi\)
0.994765 0.102190i \(-0.0325850\pi\)
\(572\) 1.50000 + 2.59808i 0.0627182 + 0.108631i
\(573\) 4.00000 0.167102
\(574\) 2.00000 + 10.3923i 0.0834784 + 0.433766i
\(575\) 2.00000 0.0834058
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −15.5000 + 26.8468i −0.645273 + 1.11765i 0.338965 + 0.940799i \(0.389923\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(578\) −8.50000 + 14.7224i −0.353553 + 0.612372i
\(579\) −4.00000 6.92820i −0.166234 0.287926i
\(580\) −7.00000 −0.290659
\(581\) 15.0000 + 5.19615i 0.622305 + 0.215573i
\(582\) 7.00000 0.290159
\(583\) −3.00000 5.19615i −0.124247 0.215203i
\(584\) 7.00000 12.1244i 0.289662 0.501709i
\(585\) −3.00000 + 5.19615i −0.124035 + 0.214834i
\(586\) 13.0000 + 22.5167i 0.537025 + 0.930155i
\(587\) 17.0000 0.701665 0.350833 0.936438i \(-0.385899\pi\)
0.350833 + 0.936438i \(0.385899\pi\)
\(588\) 1.00000 6.92820i 0.0412393 0.285714i
\(589\) −48.0000 −1.97781
\(590\) −0.500000 0.866025i −0.0205847 0.0356537i
\(591\) −5.50000 + 9.52628i −0.226240 + 0.391859i
\(592\) 0 0
\(593\) −15.0000 25.9808i −0.615976 1.06690i −0.990212 0.139569i \(-0.955428\pi\)
0.374236 0.927333i \(-0.377905\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 3.00000 + 5.19615i 0.122782 + 0.212664i
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) −16.0000 + 27.7128i −0.653742 + 1.13231i 0.328465 + 0.944516i \(0.393469\pi\)
−0.982208 + 0.187799i \(0.939865\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) 4.00000 0.163163 0.0815817 0.996667i \(-0.474003\pi\)
0.0815817 + 0.996667i \(0.474003\pi\)
\(602\) 3.00000 + 15.5885i 0.122271 + 0.635338i
\(603\) 10.0000 0.407231
\(604\) 8.50000 + 14.7224i 0.345860 + 0.599047i
\(605\) −0.500000 + 0.866025i −0.0203279 + 0.0352089i
\(606\) −7.50000 + 12.9904i −0.304667 + 0.527698i
\(607\) 12.0000 + 20.7846i 0.487065 + 0.843621i 0.999889 0.0148722i \(-0.00473415\pi\)
−0.512824 + 0.858494i \(0.671401\pi\)
\(608\) −6.00000 −0.243332
\(609\) −14.0000 + 12.1244i −0.567309 + 0.491304i
\(610\) 1.00000 0.0404888
\(611\) 0 0
\(612\) 0 0
\(613\) −3.00000 + 5.19615i −0.121169 + 0.209871i −0.920229 0.391381i \(-0.871998\pi\)
0.799060 + 0.601251i \(0.205331\pi\)
\(614\) −13.0000 22.5167i −0.524637 0.908698i
\(615\) −4.00000 −0.161296
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) 27.0000 1.08698 0.543490 0.839416i \(-0.317103\pi\)
0.543490 + 0.839416i \(0.317103\pi\)
\(618\) 2.00000 + 3.46410i 0.0804518 + 0.139347i
\(619\) −16.0000 + 27.7128i −0.643094 + 1.11387i 0.341644 + 0.939829i \(0.389016\pi\)
−0.984738 + 0.174042i \(0.944317\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 5.00000 + 8.66025i 0.200643 + 0.347524i
\(622\) −12.0000 −0.481156
\(623\) −3.00000 15.5885i −0.120192 0.624538i
\(624\) −3.00000 −0.120096
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −6.50000 + 11.2583i −0.259792 + 0.449973i
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) −3.00000 5.19615i −0.119713 0.207349i
\(629\) 0 0
\(630\) −5.00000 1.73205i −0.199205 0.0690066i
\(631\) −14.0000 −0.557331 −0.278666 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) −6.50000 11.2583i −0.258556 0.447832i
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) −10.0000 + 17.3205i −0.397151 + 0.687885i
\(635\) 9.50000 + 16.4545i 0.376996 + 0.652976i
\(636\) 6.00000 0.237915
\(637\) −16.5000 12.9904i −0.653754 0.514698i
\(638\) 7.00000 0.277133
\(639\) 8.00000 + 13.8564i 0.316475 + 0.548151i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −0.500000 + 0.866025i −0.0197488 + 0.0342059i −0.875731 0.482800i \(-0.839620\pi\)
0.855982 + 0.517005i \(0.172953\pi\)
\(642\) 3.00000 + 5.19615i 0.118401 + 0.205076i
\(643\) 37.0000 1.45914 0.729569 0.683907i \(-0.239721\pi\)
0.729569 + 0.683907i \(0.239721\pi\)
\(644\) −5.00000 1.73205i −0.197028 0.0682524i
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 3.00000 5.19615i 0.117942 0.204282i −0.801010 0.598651i \(-0.795704\pi\)
0.918952 + 0.394369i \(0.129037\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 0.500000 + 0.866025i 0.0196267 + 0.0339945i
\(650\) 3.00000 0.117670
\(651\) −4.00000 20.7846i −0.156772 0.814613i
\(652\) −11.0000 −0.430793
\(653\) −11.0000 19.0526i −0.430463 0.745584i 0.566450 0.824096i \(-0.308316\pi\)
−0.996913 + 0.0785119i \(0.974983\pi\)
\(654\) 9.00000 15.5885i 0.351928 0.609557i
\(655\) 7.00000 12.1244i 0.273513 0.473738i
\(656\) 2.00000 + 3.46410i 0.0780869 + 0.135250i
\(657\) −28.0000 −1.09238
\(658\) 0 0
\(659\) −14.0000 −0.545363 −0.272681 0.962104i \(-0.587910\pi\)
−0.272681 + 0.962104i \(0.587910\pi\)
\(660\) −0.500000 0.866025i −0.0194625 0.0337100i
\(661\) −17.0000 + 29.4449i −0.661223 + 1.14527i 0.319071 + 0.947731i \(0.396629\pi\)
−0.980294 + 0.197542i \(0.936704\pi\)
\(662\) 6.50000 11.2583i 0.252630 0.437567i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 12.0000 10.3923i 0.465340 0.402996i
\(666\) 0 0
\(667\) 7.00000 + 12.1244i 0.271041 + 0.469457i
\(668\) −9.50000 + 16.4545i −0.367566 + 0.636643i
\(669\) 6.00000 10.3923i 0.231973 0.401790i
\(670\) −2.50000 4.33013i −0.0965834 0.167287i
\(671\) −1.00000 −0.0386046
\(672\) −0.500000 2.59808i −0.0192879 0.100223i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −2.00000 3.46410i −0.0770371 0.133432i
\(675\) 2.50000 4.33013i 0.0962250 0.166667i
\(676\) 2.00000 3.46410i 0.0769231 0.133235i
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 13.0000 0.499262
\(679\) 17.5000 + 6.06218i 0.671588 + 0.232645i
\(680\) 0 0
\(681\) 4.00000 + 6.92820i 0.153280 + 0.265489i
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) 0.500000 0.866025i 0.0191320 0.0331375i −0.856301 0.516477i \(-0.827243\pi\)
0.875433 + 0.483340i \(0.160576\pi\)
\(684\) 6.00000 + 10.3923i 0.229416 + 0.397360i
\(685\) −3.00000 −0.114624
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 26.0000 0.991962
\(688\) 3.00000 + 5.19615i 0.114374 + 0.198101i
\(689\) 9.00000 15.5885i 0.342873 0.593873i
\(690\) 1.00000 1.73205i 0.0380693 0.0659380i
\(691\) 13.5000 + 23.3827i 0.513564 + 0.889519i 0.999876 + 0.0157341i \(0.00500851\pi\)
−0.486312 + 0.873785i \(0.661658\pi\)
\(692\) 9.00000 0.342129
\(693\) 5.00000 + 1.73205i 0.189934 + 0.0657952i
\(694\) 26.0000 0.986947
\(695\) 8.00000 + 13.8564i 0.303457 + 0.525603i
\(696\) −3.50000 + 6.06218i −0.132667 + 0.229786i
\(697\) 0 0
\(698\) −13.0000 22.5167i −0.492057 0.852268i
\(699\) −12.0000 −0.453882
\(700\) 0.500000 + 2.59808i 0.0188982 + 0.0981981i
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 7.50000 + 12.9904i 0.283069 + 0.490290i
\(703\) 0 0
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) −30.0000 + 25.9808i −1.12827 + 0.977107i
\(708\) −1.00000 −0.0375823
\(709\) 9.00000 + 15.5885i 0.338002 + 0.585437i 0.984057 0.177854i \(-0.0569156\pi\)
−0.646055 + 0.763291i \(0.723582\pi\)
\(710\) 4.00000 6.92820i 0.150117 0.260011i
\(711\) −13.0000 + 22.5167i −0.487538 + 0.844441i
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) −7.50000 12.9904i −0.280288 0.485473i
\(717\) −4.50000 + 7.79423i −0.168056 + 0.291081i
\(718\) 15.5000 26.8468i 0.578455 1.00191i
\(719\) 2.00000 + 3.46410i 0.0745874 + 0.129189i 0.900907 0.434013i \(-0.142903\pi\)
−0.826319 + 0.563202i \(0.809569\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 2.00000 + 10.3923i 0.0744839 + 0.387030i
\(722\) −17.0000 −0.632674
\(723\) 5.00000 + 8.66025i 0.185952 + 0.322078i
\(724\) −6.00000 + 10.3923i −0.222988 + 0.386227i
\(725\) 3.50000 6.06218i 0.129987 0.225144i
\(726\) 0.500000 + 0.866025i 0.0185567 + 0.0321412i
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) −7.50000 2.59808i −0.277968 0.0962911i
\(729\) 13.0000 0.481481
\(730\) 7.00000 + 12.1244i 0.259082 + 0.448743i
\(731\) 0 0
\(732\) 0.500000 0.866025i 0.0184805 0.0320092i
\(733\) 23.5000 + 40.7032i 0.867992 + 1.50341i 0.864045 + 0.503415i \(0.167923\pi\)
0.00394730 + 0.999992i \(0.498744\pi\)
\(734\) −8.00000 −0.295285
\(735\) 5.50000 + 4.33013i 0.202871 + 0.159719i
\(736\) −2.00000 −0.0737210
\(737\) 2.50000 + 4.33013i 0.0920887 + 0.159502i
\(738\) 4.00000 6.92820i 0.147242 0.255031i
\(739\) 6.00000 10.3923i 0.220714 0.382287i −0.734311 0.678813i \(-0.762495\pi\)
0.955025 + 0.296526i \(0.0958281\pi\)
\(740\) 0 0
\(741\) −18.0000 −0.661247
\(742\) 15.0000 + 5.19615i 0.550667 + 0.190757i
\(743\) 40.0000 1.46746 0.733729 0.679442i \(-0.237778\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(744\) −4.00000 6.92820i −0.146647 0.254000i
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) −0.500000 + 0.866025i −0.0183063 + 0.0317074i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 0 0
\(749\) 3.00000 + 15.5885i 0.109618 + 0.569590i
\(750\) −1.00000 −0.0365148
\(751\) 25.0000 + 43.3013i 0.912263 + 1.58009i 0.810860 + 0.585240i \(0.199000\pi\)
0.101403 + 0.994845i \(0.467667\pi\)
\(752\) 0 0
\(753\) −2.00000 + 3.46410i −0.0728841 + 0.126239i
\(754\) 10.5000 + 18.1865i 0.382387 + 0.662314i
\(755\) −17.0000 −0.618693
\(756\) −10.0000 + 8.66025i −0.363696 + 0.314970i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −3.50000 6.06218i −0.127126 0.220188i
\(759\) −1.00000 + 1.73205i −0.0362977 + 0.0628695i
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) 19.0000 0.688297
\(763\) 36.0000 31.1769i 1.30329 1.12868i
\(764\) 4.00000 0.144715
\(765\) 0 0
\(766\) 8.00000 13.8564i 0.289052 0.500652i
\(767\) −1.50000 + 2.59808i −0.0541619 + 0.0938111i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −0.500000 2.59808i −0.0180187 0.0936282i
\(771\) 13.0000 0.468184
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 6.00000 10.3923i 0.215666 0.373544i
\(775\) 4.00000 + 6.92820i 0.143684 + 0.248868i
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) 32.0000 1.14726
\(779\) 12.0000 + 20.7846i 0.429945 + 0.744686i
\(780\) 1.50000 2.59808i 0.0537086 0.0930261i
\(781\) −4.00000 + 6.92820i −0.143131 + 0.247911i
\(782\) 0 0
\(783\) 35.0000 1.25080
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 6.00000 0.214149
\(786\) −7.00000 12.1244i −0.249682 0.432461i
\(787\) −9.00000 + 15.5885i −0.320815 + 0.555668i −0.980656 0.195737i \(-0.937290\pi\)
0.659841 + 0.751405i \(0.270624\pi\)
\(788\) −5.50000 + 9.52628i −0.195929 + 0.339360i
\(789\) 4.50000 + 7.79423i 0.160204 + 0.277482i
\(790\) 13.0000 0.462519
\(791\) 32.5000 + 11.2583i 1.15557 + 0.400300i
\(792\) 2.00000 0.0710669
\(793\) −1.50000 2.59808i −0.0532666 0.0922604i
\(794\) 13.0000 22.5167i 0.461353 0.799086i
\(795\) −3.00000 + 5.19615i −0.106399 + 0.184289i
\(796\) 3.00000 + 5.19615i 0.106332 + 0.184173i
\(797\) −24.0000 −0.850124 −0.425062 0.905164i \(-0.639748\pi\)
−0.425062 + 0.905164i \(0.639748\pi\)
\(798\) −3.00000 15.5885i −0.106199 0.551825i
\(799\) 0 0
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) −6.00000 + 10.3923i −0.212000 + 0.367194i
\(802\) −16.5000 + 28.5788i −0.582635 + 1.00915i
\(803\) −7.00000 12.1244i −0.247025 0.427859i
\(804\) −5.00000 −0.176336
\(805\) 4.00000 3.46410i 0.140981 0.122094i
\(806\) −24.0000 −0.845364
\(807\) 7.00000 + 12.1244i 0.246412 + 0.426798i
\(808\) −7.50000 + 12.9904i −0.263849 + 0.457000i
\(809\) 24.0000 41.5692i 0.843795 1.46150i −0.0428684 0.999081i \(-0.513650\pi\)
0.886664 0.462415i \(-0.153017\pi\)
\(810\) 0.500000 + 0.866025i 0.0175682 + 0.0304290i
\(811\) −32.0000 −1.12367 −0.561836 0.827249i \(-0.689905\pi\)
−0.561836 + 0.827249i \(0.689905\pi\)
\(812\) −14.0000 + 12.1244i −0.491304 + 0.425481i
\(813\) −1.00000 −0.0350715
\(814\) 0 0
\(815\) 5.50000 9.52628i 0.192657 0.333691i
\(816\) 0 0
\(817\) 18.0000 + 31.1769i 0.629740 + 1.09074i
\(818\) 8.00000 0.279713
\(819\) 3.00000 + 15.5885i 0.104828 + 0.544705i
\(820\) −4.00000 −0.139686
\(821\) −26.5000 45.8993i −0.924856 1.60190i −0.791792 0.610791i \(-0.790852\pi\)
−0.133064 0.991107i \(-0.542482\pi\)
\(822\) −1.50000 + 2.59808i −0.0523185 + 0.0906183i
\(823\) 2.00000 3.46410i 0.0697156 0.120751i −0.829060 0.559159i \(-0.811124\pi\)
0.898776 + 0.438408i \(0.144457\pi\)
\(824\) 2.00000 + 3.46410i 0.0696733 + 0.120678i
\(825\) 1.00000 0.0348155
\(826\) −2.50000 0.866025i −0.0869861 0.0301329i
\(827\) 42.0000 1.46048 0.730242 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) 2.00000 + 3.46410i 0.0695048 + 0.120386i
\(829\) 2.00000 3.46410i 0.0694629 0.120313i −0.829202 0.558949i \(-0.811205\pi\)
0.898665 + 0.438636i \(0.144538\pi\)
\(830\) −3.00000 + 5.19615i −0.104132 + 0.180361i
\(831\) 8.50000 + 14.7224i 0.294862 + 0.510716i
\(832\) −3.00000 −0.104006
\(833\) 0 0
\(834\) 16.0000 0.554035
\(835\) −9.50000 16.4545i −0.328761 0.569431i
\(836\) −3.00000 + 5.19615i −0.103757 + 0.179713i
\(837\) −20.0000 + 34.6410i −0.691301 + 1.19737i
\(838\) −4.00000 6.92820i −0.138178 0.239331i
\(839\) 2.00000 0.0690477 0.0345238 0.999404i \(-0.489009\pi\)
0.0345238 + 0.999404i \(0.489009\pi\)
\(840\) 2.50000 + 0.866025i 0.0862582 + 0.0298807i
\(841\) 20.0000 0.689655
\(842\) −6.00000 10.3923i −0.206774 0.358142i
\(843\) 4.00000 6.92820i 0.137767 0.238620i
\(844\) 6.00000 10.3923i 0.206529 0.357718i
\(845\) 2.00000 + 3.46410i 0.0688021 + 0.119169i
\(846\) 0 0
\(847\) 0.500000 + 2.59808i 0.0171802 + 0.0892710i
\(848\) 6.00000 0.206041
\(849\) −5.00000 8.66025i −0.171600 0.297219i
\(850\) 0 0
\(851\) 0 0
\(852\) −4.00000 6.92820i −0.137038 0.237356i
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 2.00000 1.73205i 0.0684386 0.0592696i
\(855\) −12.0000 −0.410391
\(856\) 3.00000 + 5.19615i 0.102538 + 0.177601i
\(857\) −15.0000 + 25.9808i −0.512390 + 0.887486i 0.487507 + 0.873119i \(0.337907\pi\)
−0.999897 + 0.0143666i \(0.995427\pi\)
\(858\) −1.50000 + 2.59808i −0.0512092 + 0.0886969i
\(859\) 15.5000 + 26.8468i 0.528853 + 0.916001i 0.999434 + 0.0336436i \(0.0107111\pi\)
−0.470581 + 0.882357i \(0.655956\pi\)
\(860\) −6.00000 −0.204598
\(861\) −8.00000 + 6.92820i −0.272639 + 0.236113i
\(862\) 37.0000 1.26023
\(863\) −8.00000 13.8564i −0.272323 0.471678i 0.697133 0.716942i \(-0.254459\pi\)
−0.969456 + 0.245264i \(0.921125\pi\)
\(864\) −2.50000 + 4.33013i −0.0850517 + 0.147314i
\(865\) −4.50000 + 7.79423i −0.153005 + 0.265012i
\(866\) 13.0000 + 22.5167i 0.441758 + 0.765147i
\(867\) −17.0000 −0.577350
\(868\) −4.00000 20.7846i −0.135769 0.705476i
\(869\) −13.0000 −0.440995
\(870\) −3.50000 6.06218i −0.118661 0.205527i
\(871\) −7.50000 + 12.9904i −0.254128 + 0.440162i
\(872\) 9.00000 15.5885i 0.304778 0.527892i
\(873\) −7.00000 12.1244i −0.236914 0.410347i
\(874\) −12.0000 −0.405906
\(875\) −2.50000 0.866025i −0.0845154 0.0292770i
\(876\) 14.0000 0.473016
\(877\) 14.5000 + 25.1147i 0.489630 + 0.848064i 0.999929 0.0119329i \(-0.00379845\pi\)
−0.510299 + 0.859997i \(0.670465\pi\)
\(878\) 12.5000 21.6506i 0.421855 0.730674i
\(879\) −13.0000 + 22.5167i −0.438479 + 0.759468i
\(880\) −0.500000 0.866025i −0.0168550 0.0291937i
\(881\) −35.0000 −1.17918 −0.589590 0.807703i \(-0.700711\pi\)
−0.589590 + 0.807703i \(0.700711\pi\)
\(882\) −13.0000 + 5.19615i −0.437733 + 0.174964i
\(883\) 37.0000 1.24515 0.622575 0.782560i \(-0.286087\pi\)
0.622575 + 0.782560i \(0.286087\pi\)
\(884\) 0 0
\(885\) 0.500000 0.866025i 0.0168073 0.0291111i
\(886\) 20.0000 34.6410i 0.671913 1.16379i
\(887\) −23.5000 40.7032i −0.789053 1.36668i −0.926548 0.376177i \(-0.877238\pi\)
0.137495 0.990502i \(-0.456095\pi\)
\(888\) 0 0
\(889\) 47.5000 + 16.4545i 1.59310 + 0.551866i
\(890\) 6.00000 0.201120
\(891\) −0.500000 0.866025i −0.0167506 0.0290129i
\(892\) 6.00000 10.3923i 0.200895 0.347960i
\(893\) 0 0
\(894\) −9.00000 15.5885i −0.301005 0.521356i
\(895\) 15.0000 0.501395
\(896\) −0.500000 2.59808i −0.0167038 0.0867956i
\(897\) −6.00000 −0.200334
\(898\) 13.0000 + 22.5167i 0.433816 + 0.751391i
\(899\) −28.0000 + 48.4974i −0.933852 + 1.61748i
\(900\) 1.00000 1.73205i 0.0333333 0.0577350i
\(901\) 0 0
\(902\) 4.00000 0.133185
\(903\) −12.0000 + 10.3923i −0.399335 + 0.345834i
\(904\) 13.0000 0.432374
\(905\) −6.00000 10.3923i −0.199447 0.345452i
\(906\) −8.50000 + 14.7224i −0.282394 + 0.489120i
\(907\) −6.00000 + 10.3923i −0.199227 + 0.345071i −0.948278 0.317441i \(-0.897176\pi\)
0.749051 + 0.662512i \(0.230510\pi\)
\(908\) 4.00000 + 6.92820i 0.132745 + 0.229920i
\(909\) 30.0000 0.995037
\(910\) 6.00000 5.19615i 0.198898 0.172251i
\(911\) 4.00000 0.132526 0.0662630 0.997802i \(-0.478892\pi\)
0.0662630 + 0.997802i \(0.478892\pi\)
\(912\) −3.00000 5.19615i −0.0993399 0.172062i
\(913\) 3.00000 5.19615i 0.0992855 0.171968i
\(914\) −20.0000 + 34.6410i −0.661541 + 1.14582i
\(915\) 0.500000 + 0.866025i 0.0165295 + 0.0286299i
\(916\) 26.0000 0.859064
\(917\) −7.00000 36.3731i −0.231160 1.20114i
\(918\) 0 0
\(919\) −8.00000 13.8564i −0.263896 0.457081i 0.703378 0.710816i \(-0.251674\pi\)
−0.967274 + 0.253735i \(0.918341\pi\)
\(920\) 1.00000 1.73205i 0.0329690 0.0571040i
\(921\) 13.0000 22.5167i 0.428365 0.741949i
\(922\) −11.5000 19.9186i −0.378732 0.655984i
\(923\) −24.0000 −0.789970
\(924\) −2.50000 0.866025i −0.0822440 0.0284901i
\(925\) 0 0
\(926\) 2.00000 + 3.46410i 0.0657241 + 0.113837i
\(927\) 4.00000 6.92820i 0.131377 0.227552i
\(928\) −3.50000 + 6.06218i −0.114893 + 0.199001i
\(929\) 10.5000 + 18.1865i 0.344494 + 0.596681i 0.985262 0.171054i \(-0.0547172\pi\)
−0.640768 + 0.767735i \(0.721384\pi\)
\(930\) 8.00000 0.262330
\(931\) 6.00000 41.5692i 0.196642 1.36238i
\(932\) −12.0000 −0.393073
\(933\) −6.00000 10.3923i −0.196431 0.340229i
\(934\) −18.0000 + 31.1769i −0.588978 + 1.02014i
\(935\) 0 0
\(936\) 3.00000 + 5.19615i 0.0980581 + 0.169842i
\(937\) −36.0000 −1.17607 −0.588034 0.808836i \(-0.700098\pi\)
−0.588034 + 0.808836i \(0.700098\pi\)
\(938\) −12.5000 4.33013i −0.408139 0.141384i
\(939\) −13.0000 −0.424239
\(940\) 0 0
\(941\) −1.50000 + 2.59808i −0.0488986 + 0.0846949i −0.889439 0.457054i \(-0.848904\pi\)
0.840540 + 0.541749i \(0.182238\pi\)
\(942\) 3.00000 5.19615i 0.0977453 0.169300i
\(943\) 4.00000 + 6.92820i 0.130258 + 0.225613i
\(944\) −1.00000 −0.0325472
\(945\) −2.50000 12.9904i −0.0813250 0.422577i
\(946\) 6.00000 0.195077
\(947\) −24.0000 41.5692i −0.779895 1.35082i −0.932002 0.362454i \(-0.881939\pi\)
0.152106 0.988364i \(-0.451394\pi\)
\(948\) 6.50000 11.2583i 0.211110 0.365654i
\(949\) 21.0000 36.3731i 0.681689 1.18072i
\(950\) 3.00000 + 5.19615i 0.0973329 + 0.168585i
\(951\) −20.0000 −0.648544
\(952\) 0 0
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) −6.00000 10.3923i −0.194257 0.336463i
\(955\) −2.00000 + 3.46410i −0.0647185 + 0.112096i
\(956\) −4.50000 + 7.79423i −0.145540 + 0.252083i
\(957\) 3.50000 + 6.06218i 0.113139 + 0.195962i
\(958\) −41.0000 −1.32465
\(959\) −6.00000 + 5.19615i −0.193750 + 0.167793i
\(960\) 1.00000 0.0322749
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) 0 0
\(963\) 6.00000 10.3923i 0.193347 0.334887i
\(964\) 5.00000 + 8.66025i 0.161039 + 0.278928i
\(965\) 8.00000 0.257529
\(966\) −1.00000 5.19615i −0.0321745 0.167183i
\(967\) 24.0000 0.771788 0.385894 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(968\) 0.500000 + 0.866025i 0.0160706 + 0.0278351i
\(969\) 0 0
\(970\) −3.50000 + 6.06218i −0.112378 + 0.194645i
\(971\) 21.5000 + 37.2391i 0.689968 + 1.19506i 0.971848 + 0.235610i \(0.0757087\pi\)
−0.281880 + 0.959450i \(0.590958\pi\)
\(972\) 16.0000 0.513200
\(973\) 40.0000 + 13.8564i 1.28234 + 0.444216i
\(974\) −2.00000 −0.0640841
\(975\) 1.50000 + 2.59808i 0.0480384 + 0.0832050i
\(976\) 0.500000 0.866025i 0.0160046 0.0277208i
\(977\) −15.0000 + 25.9808i −0.479893 + 0.831198i −0.999734 0.0230645i \(-0.992658\pi\)
0.519841 + 0.854263i \(0.325991\pi\)
\(978\) −5.50000 9.52628i −0.175871 0.304617i
\(979\) −6.00000 −0.191761
\(980\) 5.50000 + 4.33013i 0.175691 + 0.138321i
\(981\) −36.0000 −1.14939
\(982\) −18.0000 31.1769i −0.574403 0.994895i
\(983\) −7.00000 + 12.1244i −0.223265 + 0.386707i −0.955798 0.294025i \(-0.905005\pi\)
0.732532 + 0.680732i \(0.238338\pi\)
\(984\) −2.00000 + 3.46410i −0.0637577 + 0.110432i
\(985\) −5.50000 9.52628i −0.175245 0.303533i
\(986\) 0 0
\(987\) 0 0
\(988\) −18.0000 −0.572656
\(989\) 6.00000 + 10.3923i 0.190789 + 0.330456i
\(990\) −1.00000 + 1.73205i −0.0317821 + 0.0550482i
\(991\) −28.0000 + 48.4974i −0.889449 + 1.54057i −0.0489218 + 0.998803i \(0.515578\pi\)
−0.840528 + 0.541769i \(0.817755\pi\)
\(992\) −4.00000 6.92820i −0.127000 0.219971i
\(993\) 13.0000 0.412543
\(994\) −4.00000 20.7846i −0.126872 0.659248i
\(995\) −6.00000 −0.190213
\(996\) 3.00000 + 5.19615i 0.0950586 + 0.164646i
\(997\) 3.00000 5.19615i 0.0950110 0.164564i −0.814602 0.580020i \(-0.803045\pi\)
0.909613 + 0.415456i \(0.136378\pi\)
\(998\) −2.00000 + 3.46410i −0.0633089 + 0.109654i
\(999\) 0 0
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 770.2.i.e.221.1 2
7.2 even 3 inner 770.2.i.e.331.1 yes 2
7.3 odd 6 5390.2.a.f.1.1 1
7.4 even 3 5390.2.a.o.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.i.e.221.1 2 1.1 even 1 trivial
770.2.i.e.331.1 yes 2 7.2 even 3 inner
5390.2.a.f.1.1 1 7.3 odd 6
5390.2.a.o.1.1 1 7.4 even 3