Properties

Label 1950.2.i.o.601.1
Level $1950$
Weight $2$
Character 1950.601
Analytic conductor $15.571$
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] = [1950,2,Mod(451,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.451");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 601.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1950.601
Dual form 1950.2.i.o.451.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} -3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +3.00000 q^{21} +(0.500000 - 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(-1.50000 - 2.59808i) q^{28} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(-0.500000 - 0.866025i) q^{37} +5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-1.00000 + 1.73205i) q^{43} +1.00000 q^{44} +(2.00000 - 3.46410i) q^{46} +9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(3.50000 - 0.866025i) q^{52} +13.0000 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{56} -5.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(5.00000 + 8.66025i) q^{62} +(-1.50000 - 2.59808i) q^{63} +1.00000 q^{64} -1.00000 q^{66} +(-6.00000 - 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{69} +(1.00000 - 1.73205i) q^{71} +(0.500000 - 0.866025i) q^{72} +16.0000 q^{73} +(0.500000 - 0.866025i) q^{74} +(2.50000 + 4.33013i) q^{76} +3.00000 q^{77} +(-3.50000 + 0.866025i) q^{78} -10.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -12.0000 q^{83} +(-1.50000 + 2.59808i) q^{84} -2.00000 q^{86} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +(10.5000 - 2.59808i) q^{91} +4.00000 q^{92} +(-5.00000 - 8.66025i) q^{93} +(4.50000 + 7.79423i) q^{94} -1.00000 q^{96} +(6.00000 - 10.3923i) q^{97} +(1.00000 - 1.73205i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 3 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 3 q^{7} - 2 q^{8} - q^{9} - q^{11} + 2 q^{12} - 5 q^{13} - 6 q^{14} - q^{16} - 2 q^{18} + 5 q^{19} + 6 q^{21} + q^{22} - 4 q^{23} + q^{24} + 2 q^{26} + 2 q^{27} - 3 q^{28} + 20 q^{31} + q^{32} - q^{33} - q^{36} - q^{37} + 10 q^{38} - 2 q^{39} - 6 q^{41} + 3 q^{42} - 2 q^{43} + 2 q^{44} + 4 q^{46} + 18 q^{47} - q^{48} - 2 q^{49} + 7 q^{52} + 26 q^{53} + q^{54} + 3 q^{56} - 10 q^{57} - 4 q^{59} + 2 q^{61} + 10 q^{62} - 3 q^{63} + 2 q^{64} - 2 q^{66} - 12 q^{67} - 4 q^{69} + 2 q^{71} + q^{72} + 32 q^{73} + q^{74} + 5 q^{76} + 6 q^{77} - 7 q^{78} - 20 q^{79} - q^{81} + 6 q^{82} - 24 q^{83} - 3 q^{84} - 4 q^{86} + q^{88} - q^{89} + 21 q^{91} + 8 q^{92} - 10 q^{93} + 9 q^{94} - 2 q^{96} + 12 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) −3.00000 −0.801784
\(15\) 0 0
\(16\) −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 −0.235702
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0.500000 0.866025i 0.106600 0.184637i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 1.00000 0.192450
\(28\) −1.50000 2.59808i −0.283473 0.490990i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −0.500000 0.866025i −0.0821995 0.142374i 0.821995 0.569495i \(-0.192861\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 5.00000 0.811107
\(39\) −1.00000 + 3.46410i −0.160128 + 0.554700i
\(40\) 0 0
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) 1.50000 + 2.59808i 0.231455 + 0.400892i
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) 3.50000 0.866025i 0.485363 0.120096i
\(53\) 13.0000 1.78569 0.892844 0.450367i \(-0.148707\pi\)
0.892844 + 0.450367i \(0.148707\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) −5.00000 −0.662266
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 5.00000 + 8.66025i 0.635001 + 1.09985i
\(63\) −1.50000 2.59808i −0.188982 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 0 0
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) 0 0
\(71\) 1.00000 1.73205i 0.118678 0.205557i −0.800566 0.599245i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 16.0000 1.87266 0.936329 0.351123i \(-0.114200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 0 0
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) 3.00000 0.341882
\(78\) −3.50000 + 0.866025i −0.396297 + 0.0980581i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −1.50000 + 2.59808i −0.163663 + 0.283473i
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −0.500000 0.866025i −0.0529999 0.0917985i 0.838308 0.545197i \(-0.183545\pi\)
−0.891308 + 0.453398i \(0.850212\pi\)
\(90\) 0 0
\(91\) 10.5000 2.59808i 1.10070 0.272352i
\(92\) 4.00000 0.417029
\(93\) −5.00000 8.66025i −0.518476 0.898027i
\(94\) 4.50000 + 7.79423i 0.464140 + 0.803913i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 6.00000 10.3923i 0.609208 1.05518i −0.382164 0.924095i \(-0.624821\pi\)
0.991371 0.131084i \(-0.0418458\pi\)
\(98\) 1.00000 1.73205i 0.101015 0.174964i
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) −2.00000 3.46410i −0.199007 0.344691i 0.749199 0.662344i \(-0.230438\pi\)
−0.948207 + 0.317653i \(0.897105\pi\)
\(102\) 0 0
\(103\) 9.00000 0.886796 0.443398 0.896325i \(-0.353773\pi\)
0.443398 + 0.896325i \(0.353773\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) 0 0
\(106\) 6.50000 + 11.2583i 0.631336 + 1.09351i
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −0.500000 + 0.866025i −0.0474579 + 0.0821995i
\(112\) 3.00000 0.283473
\(113\) 8.00000 13.8564i 0.752577 1.30350i −0.193993 0.981003i \(-0.562144\pi\)
0.946570 0.322498i \(-0.104523\pi\)
\(114\) −2.50000 4.33013i −0.234146 0.405554i
\(115\) 0 0
\(116\) 0 0
\(117\) 3.50000 0.866025i 0.323575 0.0800641i
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 2.00000 0.181071
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) −5.00000 + 8.66025i −0.449013 + 0.777714i
\(125\) 0 0
\(126\) 1.50000 2.59808i 0.133631 0.231455i
\(127\) 2.50000 + 4.33013i 0.221839 + 0.384237i 0.955366 0.295423i \(-0.0954607\pi\)
−0.733527 + 0.679660i \(0.762127\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) −0.500000 0.866025i −0.0435194 0.0753778i
\(133\) 7.50000 + 12.9904i 0.650332 + 1.12641i
\(134\) 6.00000 10.3923i 0.518321 0.897758i
\(135\) 0 0
\(136\) 0 0
\(137\) 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i \(-0.593796\pi\)
0.973910 0.226935i \(-0.0728704\pi\)
\(138\) −4.00000 −0.340503
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 0 0
\(141\) −4.50000 7.79423i −0.378968 0.656392i
\(142\) 2.00000 0.167836
\(143\) −1.00000 + 3.46410i −0.0836242 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 8.00000 + 13.8564i 0.662085 + 1.14676i
\(147\) −1.00000 + 1.73205i −0.0824786 + 0.142857i
\(148\) 1.00000 0.0821995
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) 0 0
\(154\) 1.50000 + 2.59808i 0.120873 + 0.209359i
\(155\) 0 0
\(156\) −2.50000 2.59808i −0.200160 0.208013i
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) −5.00000 8.66025i −0.397779 0.688973i
\(159\) −6.50000 11.2583i −0.515484 0.892844i
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) −6.50000 11.2583i −0.502985 0.871196i −0.999994 0.00345033i \(-0.998902\pi\)
0.497009 0.867745i \(-0.334432\pi\)
\(168\) −3.00000 −0.231455
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 2.50000 + 4.33013i 0.191180 + 0.331133i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.500000 + 0.866025i −0.0376889 + 0.0652791i
\(177\) 4.00000 0.300658
\(178\) 0.500000 0.866025i 0.0374766 0.0649113i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 7.50000 + 7.79423i 0.555937 + 0.577747i
\(183\) −2.00000 −0.147844
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 0 0
\(186\) 5.00000 8.66025i 0.366618 0.635001i
\(187\) 0 0
\(188\) −4.50000 + 7.79423i −0.328196 + 0.568453i
\(189\) −1.50000 + 2.59808i −0.109109 + 0.188982i
\(190\) 0 0
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −7.50000 12.9904i −0.534353 0.925526i −0.999194 0.0401324i \(-0.987222\pi\)
0.464841 0.885394i \(-0.346111\pi\)
\(198\) 0.500000 + 0.866025i 0.0355335 + 0.0615457i
\(199\) 1.00000 1.73205i 0.0708881 0.122782i −0.828403 0.560133i \(-0.810750\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(200\) 0 0
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 2.00000 3.46410i 0.140720 0.243733i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 4.50000 + 7.79423i 0.313530 + 0.543050i
\(207\) 4.00000 0.278019
\(208\) −1.00000 + 3.46410i −0.0693375 + 0.240192i
\(209\) −5.00000 −0.345857
\(210\) 0 0
\(211\) 7.50000 + 12.9904i 0.516321 + 0.894295i 0.999820 + 0.0189499i \(0.00603229\pi\)
−0.483499 + 0.875345i \(0.660634\pi\)
\(212\) −6.50000 + 11.2583i −0.446422 + 0.773225i
\(213\) −2.00000 −0.137038
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −15.0000 + 25.9808i −1.01827 + 1.76369i
\(218\) −5.00000 8.66025i −0.338643 0.586546i
\(219\) −8.00000 13.8564i −0.540590 0.936329i
\(220\) 0 0
\(221\) 0 0
\(222\) −1.00000 −0.0671156
\(223\) 5.50000 + 9.52628i 0.368307 + 0.637927i 0.989301 0.145889i \(-0.0466041\pi\)
−0.620994 + 0.783815i \(0.713271\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 2.50000 4.33013i 0.165567 0.286770i
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) −1.50000 2.59808i −0.0986928 0.170941i
\(232\) 0 0
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 2.50000 + 2.59808i 0.163430 + 0.169842i
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 5.00000 + 8.66025i 0.324785 + 0.562544i
\(238\) 0 0
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) 0 0
\(241\) −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) 10.0000 0.642824
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) −17.5000 + 4.33013i −1.11350 + 0.275519i
\(248\) −10.0000 −0.635001
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) −5.50000 + 9.52628i −0.347157 + 0.601293i −0.985743 0.168257i \(-0.946186\pi\)
0.638586 + 0.769550i \(0.279520\pi\)
\(252\) 3.00000 0.188982
\(253\) −2.00000 + 3.46410i −0.125739 + 0.217786i
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.0000 20.7846i −0.748539 1.29651i −0.948523 0.316709i \(-0.897422\pi\)
0.199983 0.979799i \(-0.435911\pi\)
\(258\) 1.00000 + 1.73205i 0.0622573 + 0.107833i
\(259\) 3.00000 0.186411
\(260\) 0 0
\(261\) 0 0
\(262\) −7.50000 12.9904i −0.463352 0.802548i
\(263\) 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 0 0
\(266\) −7.50000 + 12.9904i −0.459855 + 0.796491i
\(267\) −0.500000 + 0.866025i −0.0305995 + 0.0529999i
\(268\) 12.0000 0.733017
\(269\) 10.0000 17.3205i 0.609711 1.05605i −0.381577 0.924337i \(-0.624619\pi\)
0.991288 0.131713i \(-0.0420477\pi\)
\(270\) 0 0
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) 0 0
\(273\) −7.50000 7.79423i −0.453921 0.471728i
\(274\) 16.0000 0.966595
\(275\) 0 0
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) 11.5000 19.9186i 0.690968 1.19679i −0.280553 0.959839i \(-0.590518\pi\)
0.971521 0.236953i \(-0.0761488\pi\)
\(278\) 9.00000 0.539784
\(279\) −5.00000 + 8.66025i −0.299342 + 0.518476i
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 4.50000 7.79423i 0.267971 0.464140i
\(283\) 1.00000 + 1.73205i 0.0594438 + 0.102960i 0.894216 0.447636i \(-0.147734\pi\)
−0.834772 + 0.550596i \(0.814401\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −3.50000 + 0.866025i −0.206959 + 0.0512092i
\(287\) 18.0000 1.06251
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) −8.00000 + 13.8564i −0.468165 + 0.810885i
\(293\) 6.50000 11.2583i 0.379734 0.657719i −0.611289 0.791407i \(-0.709349\pi\)
0.991023 + 0.133689i \(0.0426822\pi\)
\(294\) −2.00000 −0.116642
\(295\) 0 0
\(296\) 0.500000 + 0.866025i 0.0290619 + 0.0503367i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 6.00000 0.347571
\(299\) −4.00000 + 13.8564i −0.231326 + 0.801337i
\(300\) 0 0
\(301\) −3.00000 5.19615i −0.172917 0.299501i
\(302\) −3.00000 5.19615i −0.172631 0.299005i
\(303\) −2.00000 + 3.46410i −0.114897 + 0.199007i
\(304\) −5.00000 −0.286770
\(305\) 0 0
\(306\) 0 0
\(307\) −18.0000 −1.02731 −0.513657 0.857996i \(-0.671710\pi\)
−0.513657 + 0.857996i \(0.671710\pi\)
\(308\) −1.50000 + 2.59808i −0.0854704 + 0.148039i
\(309\) −4.50000 7.79423i −0.255996 0.443398i
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 1.00000 3.46410i 0.0566139 0.196116i
\(313\) 34.0000 1.92179 0.960897 0.276907i \(-0.0893093\pi\)
0.960897 + 0.276907i \(0.0893093\pi\)
\(314\) −0.500000 0.866025i −0.0282166 0.0488726i
\(315\) 0 0
\(316\) 5.00000 8.66025i 0.281272 0.487177i
\(317\) −19.0000 −1.06715 −0.533573 0.845754i \(-0.679151\pi\)
−0.533573 + 0.845754i \(0.679151\pi\)
\(318\) 6.50000 11.2583i 0.364502 0.631336i
\(319\) 0 0
\(320\) 0 0
\(321\) −3.00000 + 5.19615i −0.167444 + 0.290021i
\(322\) 6.00000 + 10.3923i 0.334367 + 0.579141i
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) 5.00000 + 8.66025i 0.276501 + 0.478913i
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) −13.5000 + 23.3827i −0.744279 + 1.28913i
\(330\) 0 0
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) 1.00000 0.0547997
\(334\) 6.50000 11.2583i 0.355664 0.616028i
\(335\) 0 0
\(336\) −1.50000 2.59808i −0.0818317 0.141737i
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −11.5000 + 6.06218i −0.625518 + 0.329739i
\(339\) −16.0000 −0.869001
\(340\) 0 0
\(341\) −5.00000 8.66025i −0.270765 0.468979i
\(342\) −2.50000 + 4.33013i −0.135185 + 0.234146i
\(343\) −15.0000 −0.809924
\(344\) 1.00000 1.73205i 0.0539164 0.0933859i
\(345\) 0 0
\(346\) −9.00000 −0.483843
\(347\) −14.0000 + 24.2487i −0.751559 + 1.30174i 0.195507 + 0.980702i \(0.437365\pi\)
−0.947067 + 0.321037i \(0.895969\pi\)
\(348\) 0 0
\(349\) −18.0000 31.1769i −0.963518 1.66886i −0.713545 0.700609i \(-0.752912\pi\)
−0.249973 0.968253i \(-0.580422\pi\)
\(350\) 0 0
\(351\) −2.50000 2.59808i −0.133440 0.138675i
\(352\) −1.00000 −0.0533002
\(353\) −18.0000 31.1769i −0.958043 1.65938i −0.727245 0.686378i \(-0.759200\pi\)
−0.230799 0.973002i \(-0.574134\pi\)
\(354\) 2.00000 + 3.46410i 0.106299 + 0.184115i
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 34.0000 1.79445 0.897226 0.441572i \(-0.145579\pi\)
0.897226 + 0.441572i \(0.145579\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 3.00000 + 5.19615i 0.157676 + 0.273104i
\(363\) −10.0000 −0.524864
\(364\) −3.00000 + 10.3923i −0.157243 + 0.544705i
\(365\) 0 0
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) −19.5000 + 33.7750i −1.01239 + 1.75351i
\(372\) 10.0000 0.518476
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) 0 0
\(378\) −3.00000 −0.154303
\(379\) 0.500000 + 0.866025i 0.0256833 + 0.0444847i 0.878581 0.477593i \(-0.158491\pi\)
−0.852898 + 0.522077i \(0.825157\pi\)
\(380\) 0 0
\(381\) 2.50000 4.33013i 0.128079 0.221839i
\(382\) 18.0000 0.920960
\(383\) −14.0000 + 24.2487i −0.715367 + 1.23905i 0.247451 + 0.968900i \(0.420407\pi\)
−0.962818 + 0.270151i \(0.912926\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) −8.00000 + 13.8564i −0.407189 + 0.705273i
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) 6.00000 + 10.3923i 0.304604 + 0.527589i
\(389\) −16.0000 −0.811232 −0.405616 0.914044i \(-0.632943\pi\)
−0.405616 + 0.914044i \(0.632943\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 + 1.73205i 0.0505076 + 0.0874818i
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 7.50000 12.9904i 0.377845 0.654446i
\(395\) 0 0
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) −16.5000 + 28.5788i −0.828111 + 1.43433i 0.0714068 + 0.997447i \(0.477251\pi\)
−0.899518 + 0.436884i \(0.856082\pi\)
\(398\) 2.00000 0.100251
\(399\) 7.50000 12.9904i 0.375470 0.650332i
\(400\) 0 0
\(401\) −12.5000 21.6506i −0.624220 1.08118i −0.988691 0.149966i \(-0.952083\pi\)
0.364471 0.931215i \(-0.381250\pi\)
\(402\) −12.0000 −0.598506
\(403\) −25.0000 25.9808i −1.24534 1.29419i
\(404\) 4.00000 0.199007
\(405\) 0 0
\(406\) 0 0
\(407\) −0.500000 + 0.866025i −0.0247841 + 0.0429273i
\(408\) 0 0
\(409\) −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 0 0
\(411\) −16.0000 −0.789222
\(412\) −4.50000 + 7.79423i −0.221699 + 0.383994i
\(413\) −6.00000 10.3923i −0.295241 0.511372i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) 0 0
\(416\) −3.50000 + 0.866025i −0.171602 + 0.0424604i
\(417\) −9.00000 −0.440732
\(418\) −2.50000 4.33013i −0.122279 0.211793i
\(419\) 14.0000 + 24.2487i 0.683945 + 1.18463i 0.973767 + 0.227547i \(0.0730704\pi\)
−0.289822 + 0.957080i \(0.593596\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) −7.50000 + 12.9904i −0.365094 + 0.632362i
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) −13.0000 −0.631336
\(425\) 0 0
\(426\) −1.00000 1.73205i −0.0484502 0.0839181i
\(427\) 3.00000 + 5.19615i 0.145180 + 0.251459i
\(428\) 6.00000 0.290021
\(429\) 3.50000 0.866025i 0.168982 0.0418121i
\(430\) 0 0
\(431\) −18.0000 31.1769i −0.867029 1.50174i −0.865018 0.501741i \(-0.832693\pi\)
−0.00201168 0.999998i \(-0.500640\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 8.00000 13.8564i 0.384455 0.665896i −0.607238 0.794520i \(-0.707723\pi\)
0.991693 + 0.128624i \(0.0410559\pi\)
\(434\) −30.0000 −1.44005
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) −20.0000 −0.956730
\(438\) 8.00000 13.8564i 0.382255 0.662085i
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 18.0000 0.855206 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) −0.500000 0.866025i −0.0237289 0.0410997i
\(445\) 0 0
\(446\) −5.50000 + 9.52628i −0.260433 + 0.451082i
\(447\) −6.00000 −0.283790
\(448\) −1.50000 + 2.59808i −0.0708683 + 0.122748i
\(449\) 7.50000 12.9904i 0.353947 0.613054i −0.632990 0.774160i \(-0.718173\pi\)
0.986937 + 0.161106i \(0.0515060\pi\)
\(450\) 0 0
\(451\) −3.00000 + 5.19615i −0.141264 + 0.244677i
\(452\) 8.00000 + 13.8564i 0.376288 + 0.651751i
\(453\) 3.00000 + 5.19615i 0.140952 + 0.244137i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) 5.00000 0.234146
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) −5.00000 8.66025i −0.233635 0.404667i
\(459\) 0 0
\(460\) 0 0
\(461\) 6.00000 10.3923i 0.279448 0.484018i −0.691800 0.722089i \(-0.743182\pi\)
0.971248 + 0.238071i \(0.0765153\pi\)
\(462\) 1.50000 2.59808i 0.0697863 0.120873i
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −5.00000 8.66025i −0.231621 0.401179i
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) −1.00000 + 3.46410i −0.0462250 + 0.160128i
\(469\) 36.0000 1.66233
\(470\) 0 0
\(471\) 0.500000 + 0.866025i 0.0230388 + 0.0399043i
\(472\) 2.00000 3.46410i 0.0920575 0.159448i
\(473\) 2.00000 0.0919601
\(474\) −5.00000 + 8.66025i −0.229658 + 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) −6.50000 + 11.2583i −0.297615 + 0.515484i
\(478\) −1.00000 1.73205i −0.0457389 0.0792222i
\(479\) 4.00000 + 6.92820i 0.182765 + 0.316558i 0.942821 0.333300i \(-0.108162\pi\)
−0.760056 + 0.649857i \(0.774829\pi\)
\(480\) 0 0
\(481\) −1.00000 + 3.46410i −0.0455961 + 0.157949i
\(482\) −15.0000 −0.683231
\(483\) −6.00000 10.3923i −0.273009 0.472866i
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 17.5000 30.3109i 0.793001 1.37352i −0.131100 0.991369i \(-0.541851\pi\)
0.924101 0.382148i \(-0.124816\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) −12.5000 21.6506i −0.564117 0.977079i −0.997131 0.0756923i \(-0.975883\pi\)
0.433014 0.901387i \(-0.357450\pi\)
\(492\) −3.00000 5.19615i −0.135250 0.234261i
\(493\) 0 0
\(494\) −12.5000 12.9904i −0.562402 0.584465i
\(495\) 0 0
\(496\) −5.00000 8.66025i −0.224507 0.388857i
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) −6.00000 + 10.3923i −0.268866 + 0.465690i
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) −6.50000 + 11.2583i −0.290399 + 0.502985i
\(502\) −11.0000 −0.490954
\(503\) −0.500000 + 0.866025i −0.0222939 + 0.0386142i −0.876957 0.480569i \(-0.840430\pi\)
0.854663 + 0.519183i \(0.173764\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 0 0
\(506\) −4.00000 −0.177822
\(507\) 11.5000 6.06218i 0.510733 0.269231i
\(508\) −5.00000 −0.221839
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) −24.0000 + 41.5692i −1.06170 + 1.83891i
\(512\) −1.00000 −0.0441942
\(513\) 2.50000 4.33013i 0.110378 0.191180i
\(514\) 12.0000 20.7846i 0.529297 0.916770i
\(515\) 0 0
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) −4.50000 7.79423i −0.197910 0.342790i
\(518\) 1.50000 + 2.59808i 0.0659062 + 0.114153i
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) 0 0
\(523\) 3.00000 + 5.19615i 0.131181 + 0.227212i 0.924132 0.382073i \(-0.124790\pi\)
−0.792951 + 0.609285i \(0.791456\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 0 0
\(526\) −1.50000 + 2.59808i −0.0654031 + 0.113282i
\(527\) 0 0
\(528\) 1.00000 0.0435194
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −2.00000 3.46410i −0.0867926 0.150329i
\(532\) −15.0000 −0.650332
\(533\) −6.00000 + 20.7846i −0.259889 + 0.900281i
\(534\) −1.00000 −0.0432742
\(535\) 0 0
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) 20.0000 0.862261
\(539\) −1.00000 + 1.73205i −0.0430730 + 0.0746047i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −12.0000 + 20.7846i −0.515444 + 0.892775i
\(543\) −3.00000 5.19615i −0.128742 0.222988i
\(544\) 0 0
\(545\) 0 0
\(546\) 3.00000 10.3923i 0.128388 0.444750i
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 8.00000 + 13.8564i 0.341743 + 0.591916i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 0 0
\(552\) 2.00000 3.46410i 0.0851257 0.147442i
\(553\) 15.0000 25.9808i 0.637865 1.10481i
\(554\) 23.0000 0.977176
\(555\) 0 0
\(556\) 4.50000 + 7.79423i 0.190843 + 0.330549i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) −10.0000 −0.423334
\(559\) 7.00000 1.73205i 0.296068 0.0732579i
\(560\) 0 0
\(561\) 0 0
\(562\) 5.00000 + 8.66025i 0.210912 + 0.365311i
\(563\) 12.0000 20.7846i 0.505740 0.875967i −0.494238 0.869326i \(-0.664553\pi\)
0.999978 0.00664037i \(-0.00211371\pi\)
\(564\) 9.00000 0.378968
\(565\) 0 0
\(566\) −1.00000 + 1.73205i −0.0420331 + 0.0728035i
\(567\) 3.00000 0.125988
\(568\) −1.00000 + 1.73205i −0.0419591 + 0.0726752i
\(569\) 5.50000 + 9.52628i 0.230572 + 0.399362i 0.957977 0.286846i \(-0.0926069\pi\)
−0.727405 + 0.686209i \(0.759274\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) −2.50000 2.59808i −0.104530 0.108631i
\(573\) −18.0000 −0.751961
\(574\) 9.00000 + 15.5885i 0.375653 + 0.650650i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −8.50000 + 14.7224i −0.353553 + 0.612372i
\(579\) 8.00000 13.8564i 0.332469 0.575853i
\(580\) 0 0
\(581\) 18.0000 31.1769i 0.746766 1.29344i
\(582\) −6.00000 10.3923i −0.248708 0.430775i
\(583\) −6.50000 11.2583i −0.269202 0.466272i
\(584\) −16.0000 −0.662085
\(585\) 0 0
\(586\) 13.0000 0.537025
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) −1.00000 1.73205i −0.0412393 0.0714286i
\(589\) 25.0000 43.3013i 1.03011 1.78420i
\(590\) 0 0
\(591\) −7.50000 + 12.9904i −0.308509 + 0.534353i
\(592\) −0.500000 + 0.866025i −0.0205499 + 0.0355934i
\(593\) −28.0000 −1.14982 −0.574911 0.818216i \(-0.694963\pi\)
−0.574911 + 0.818216i \(0.694963\pi\)
\(594\) 0.500000 0.866025i 0.0205152 0.0355335i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) −2.00000 −0.0818546
\(598\) −14.0000 + 3.46410i −0.572503 + 0.141658i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) 13.5000 + 23.3827i 0.550676 + 0.953800i 0.998226 + 0.0595404i \(0.0189635\pi\)
−0.447549 + 0.894259i \(0.647703\pi\)
\(602\) 3.00000 5.19615i 0.122271 0.211779i
\(603\) 12.0000 0.488678
\(604\) 3.00000 5.19615i 0.122068 0.211428i
\(605\) 0 0
\(606\) −4.00000 −0.162489
\(607\) 18.5000 32.0429i 0.750892 1.30058i −0.196499 0.980504i \(-0.562957\pi\)
0.947391 0.320079i \(-0.103709\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) 0 0
\(611\) −22.5000 23.3827i −0.910253 0.945962i
\(612\) 0 0
\(613\) 11.5000 + 19.9186i 0.464481 + 0.804504i 0.999178 0.0405396i \(-0.0129077\pi\)
−0.534697 + 0.845044i \(0.679574\pi\)
\(614\) −9.00000 15.5885i −0.363210 0.629099i
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) −3.00000 + 5.19615i −0.120775 + 0.209189i −0.920074 0.391745i \(-0.871871\pi\)
0.799298 + 0.600935i \(0.205205\pi\)
\(618\) 4.50000 7.79423i 0.181017 0.313530i
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) −6.00000 10.3923i −0.240578 0.416693i
\(623\) 3.00000 0.120192
\(624\) 3.50000 0.866025i 0.140112 0.0346688i
\(625\) 0 0
\(626\) 17.0000 + 29.4449i 0.679457 + 1.17685i
\(627\) 2.50000 + 4.33013i 0.0998404 + 0.172929i
\(628\) 0.500000 0.866025i 0.0199522 0.0345582i
\(629\) 0 0
\(630\) 0 0
\(631\) 2.00000 3.46410i 0.0796187 0.137904i −0.823467 0.567365i \(-0.807963\pi\)
0.903085 + 0.429461i \(0.141296\pi\)
\(632\) 10.0000 0.397779
\(633\) 7.50000 12.9904i 0.298098 0.516321i
\(634\) −9.50000 16.4545i −0.377293 0.653491i
\(635\) 0 0
\(636\) 13.0000 0.515484
\(637\) −2.00000 + 6.92820i −0.0792429 + 0.274505i
\(638\) 0 0
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i \(-0.776455\pi\)
0.941106 + 0.338112i \(0.109788\pi\)
\(642\) −6.00000 −0.236801
\(643\) −22.0000 + 38.1051i −0.867595 + 1.50272i −0.00314839 + 0.999995i \(0.501002\pi\)
−0.864447 + 0.502724i \(0.832331\pi\)
\(644\) −6.00000 + 10.3923i −0.236433 + 0.409514i
\(645\) 0 0
\(646\) 0 0
\(647\) 4.50000 + 7.79423i 0.176913 + 0.306423i 0.940822 0.338902i \(-0.110055\pi\)
−0.763908 + 0.645325i \(0.776722\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 30.0000 1.17579
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 20.5000 + 35.5070i 0.802227 + 1.38950i 0.918147 + 0.396239i \(0.129685\pi\)
−0.115920 + 0.993259i \(0.536982\pi\)
\(654\) −5.00000 + 8.66025i −0.195515 + 0.338643i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) −8.00000 + 13.8564i −0.312110 + 0.540590i
\(658\) −27.0000 −1.05257
\(659\) −2.00000 + 3.46410i −0.0779089 + 0.134942i −0.902348 0.431009i \(-0.858158\pi\)
0.824439 + 0.565951i \(0.191491\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 0.500000 + 0.866025i 0.0193746 + 0.0335578i
\(667\) 0 0
\(668\) 13.0000 0.502985
\(669\) 5.50000 9.52628i 0.212642 0.368307i
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) 1.50000 2.59808i 0.0578638 0.100223i
\(673\) −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) −1.00000 1.73205i −0.0385186 0.0667161i
\(675\) 0 0
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 26.0000 0.999261 0.499631 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) −8.00000 13.8564i −0.307238 0.532152i
\(679\) 18.0000 + 31.1769i 0.690777 + 1.19646i
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) 5.00000 8.66025i 0.191460 0.331618i
\(683\) −13.0000 + 22.5167i −0.497431 + 0.861576i −0.999996 0.00296369i \(-0.999057\pi\)
0.502564 + 0.864540i \(0.332390\pi\)
\(684\) −5.00000 −0.191180
\(685\) 0 0
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) 2.00000 0.0762493
\(689\) −32.5000 33.7750i −1.23815 1.28672i
\(690\) 0 0
\(691\) −16.5000 28.5788i −0.627690 1.08719i −0.988014 0.154363i \(-0.950667\pi\)
0.360325 0.932827i \(-0.382666\pi\)
\(692\) −4.50000 7.79423i −0.171064 0.296292i
\(693\) −1.50000 + 2.59808i −0.0569803 + 0.0986928i
\(694\) −28.0000 −1.06287
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 18.0000 31.1769i 0.681310 1.18006i
\(699\) 5.00000 + 8.66025i 0.189117 + 0.327561i
\(700\) 0 0
\(701\) 4.00000 0.151078 0.0755390 0.997143i \(-0.475932\pi\)
0.0755390 + 0.997143i \(0.475932\pi\)
\(702\) 1.00000 3.46410i 0.0377426 0.130744i
\(703\) −5.00000 −0.188579
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 18.0000 31.1769i 0.677439 1.17336i
\(707\) 12.0000 0.451306
\(708\) −2.00000 + 3.46410i −0.0751646 + 0.130189i
\(709\) −2.00000 + 3.46410i −0.0751116 + 0.130097i −0.901135 0.433539i \(-0.857265\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(710\) 0 0
\(711\) 5.00000 8.66025i 0.187515 0.324785i
\(712\) 0.500000 + 0.866025i 0.0187383 + 0.0324557i
\(713\) −20.0000 34.6410i −0.749006 1.29732i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 1.00000 + 1.73205i 0.0373457 + 0.0646846i
\(718\) 17.0000 + 29.4449i 0.634434 + 1.09887i
\(719\) −18.0000 + 31.1769i −0.671287 + 1.16270i 0.306253 + 0.951950i \(0.400925\pi\)
−0.977539 + 0.210752i \(0.932409\pi\)
\(720\) 0 0
\(721\) −13.5000 + 23.3827i −0.502766 + 0.870817i
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) 15.0000 0.557856
\(724\) −3.00000 + 5.19615i −0.111494 + 0.193113i
\(725\) 0 0
\(726\) −5.00000 8.66025i −0.185567 0.321412i
\(727\) 37.0000 1.37225 0.686127 0.727482i \(-0.259309\pi\)
0.686127 + 0.727482i \(0.259309\pi\)
\(728\) −10.5000 + 2.59808i −0.389156 + 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 1.00000 1.73205i 0.0369611 0.0640184i
\(733\) 5.00000 0.184679 0.0923396 0.995728i \(-0.470565\pi\)
0.0923396 + 0.995728i \(0.470565\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) −17.5000 30.3109i −0.643748 1.11500i −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) 0 0
\(741\) 12.5000 + 12.9904i 0.459199 + 0.477214i
\(742\) −39.0000 −1.43174
\(743\) 12.0000 + 20.7846i 0.440237 + 0.762513i 0.997707 0.0676840i \(-0.0215610\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(744\) 5.00000 + 8.66025i 0.183309 + 0.317500i
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 0 0
\(749\) 18.0000 0.657706
\(750\) 0 0
\(751\) −22.0000 38.1051i −0.802791 1.39048i −0.917772 0.397108i \(-0.870014\pi\)
0.114981 0.993368i \(-0.463319\pi\)
\(752\) −4.50000 7.79423i −0.164098 0.284226i
\(753\) 11.0000 0.400862
\(754\) 0 0
\(755\) 0 0
\(756\) −1.50000 2.59808i −0.0545545 0.0944911i
\(757\) 19.5000 + 33.7750i 0.708740 + 1.22757i 0.965325 + 0.261051i \(0.0840692\pi\)
−0.256585 + 0.966522i \(0.582597\pi\)
\(758\) −0.500000 + 0.866025i −0.0181608 + 0.0314555i
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) −22.5000 + 38.9711i −0.815624 + 1.41270i 0.0932544 + 0.995642i \(0.470273\pi\)
−0.908879 + 0.417061i \(0.863060\pi\)
\(762\) 5.00000 0.181131
\(763\) 15.0000 25.9808i 0.543036 0.940567i
\(764\) 9.00000 + 15.5885i 0.325609 + 0.563971i
\(765\) 0 0
\(766\) −28.0000 −1.01168
\(767\) 14.0000 3.46410i 0.505511 0.125081i
\(768\) 1.00000 0.0360844
\(769\) 13.0000 + 22.5167i 0.468792 + 0.811972i 0.999364 0.0356685i \(-0.0113561\pi\)
−0.530572 + 0.847640i \(0.678023\pi\)
\(770\) 0 0
\(771\) −12.0000 + 20.7846i −0.432169 + 0.748539i
\(772\) −16.0000 −0.575853
\(773\) −18.5000 + 32.0429i −0.665399 + 1.15250i 0.313778 + 0.949496i \(0.398405\pi\)
−0.979177 + 0.203008i \(0.934928\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) 0 0
\(776\) −6.00000 + 10.3923i −0.215387 + 0.373062i
\(777\) −1.50000 2.59808i −0.0538122 0.0932055i
\(778\) −8.00000 13.8564i −0.286814 0.496776i
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) 0 0
\(783\) 0 0
\(784\) −1.00000 + 1.73205i −0.0357143 + 0.0618590i
\(785\) 0 0
\(786\) −7.50000 + 12.9904i −0.267516 + 0.463352i
\(787\) 8.00000 13.8564i 0.285169 0.493928i −0.687481 0.726202i \(-0.741284\pi\)
0.972650 + 0.232275i \(0.0746169\pi\)
\(788\) 15.0000 0.534353
\(789\) 1.50000 2.59808i 0.0534014 0.0924940i
\(790\) 0 0
\(791\) 24.0000 + 41.5692i 0.853342 + 1.47803i
\(792\) −1.00000 −0.0355335
\(793\) −7.00000 + 1.73205i −0.248577 + 0.0615069i
\(794\) −33.0000 −1.17113
\(795\) 0 0
\(796\) 1.00000 + 1.73205i 0.0354441 + 0.0613909i
\(797\) −7.00000 + 12.1244i −0.247953 + 0.429467i −0.962958 0.269653i \(-0.913091\pi\)
0.715005 + 0.699119i \(0.246424\pi\)
\(798\) 15.0000 0.530994
\(799\) 0 0
\(800\) 0 0
\(801\) 1.00000 0.0353333
\(802\) 12.5000 21.6506i 0.441390 0.764511i
\(803\) −8.00000 13.8564i −0.282314 0.488982i
\(804\) −6.00000 10.3923i −0.211604 0.366508i
\(805\) 0 0
\(806\) 10.0000 34.6410i 0.352235 1.22018i
\(807\) −20.0000 −0.704033
\(808\) 2.00000 + 3.46410i 0.0703598 + 0.121867i
\(809\) 9.00000 + 15.5885i 0.316423 + 0.548061i 0.979739 0.200279i \(-0.0641847\pi\)
−0.663316 + 0.748340i \(0.730851\pi\)
\(810\) 0 0
\(811\) 33.0000 1.15879 0.579393 0.815048i \(-0.303290\pi\)
0.579393 + 0.815048i \(0.303290\pi\)
\(812\) 0 0
\(813\) 12.0000 20.7846i 0.420858 0.728948i
\(814\) −1.00000 −0.0350500
\(815\) 0 0
\(816\) 0 0
\(817\) 5.00000 + 8.66025i 0.174928 + 0.302984i
\(818\) −17.0000 −0.594391
\(819\) −3.00000 + 10.3923i −0.104828 + 0.363137i
\(820\) 0 0
\(821\) −9.00000 15.5885i −0.314102 0.544041i 0.665144 0.746715i \(-0.268370\pi\)
−0.979246 + 0.202674i \(0.935037\pi\)
\(822\) −8.00000 13.8564i −0.279032 0.483298i
\(823\) −2.50000 + 4.33013i −0.0871445 + 0.150939i −0.906303 0.422628i \(-0.861108\pi\)
0.819159 + 0.573567i \(0.194441\pi\)
\(824\) −9.00000 −0.313530
\(825\) 0 0
\(826\) 6.00000 10.3923i 0.208767 0.361595i
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) −2.00000 + 3.46410i −0.0695048 + 0.120386i
\(829\) 22.0000 + 38.1051i 0.764092 + 1.32345i 0.940726 + 0.339169i \(0.110146\pi\)
−0.176634 + 0.984277i \(0.556521\pi\)
\(830\) 0 0
\(831\) −23.0000 −0.797861
\(832\) −2.50000 2.59808i −0.0866719 0.0900721i
\(833\) 0 0
\(834\) −4.50000 7.79423i −0.155822 0.269892i
\(835\) 0 0
\(836\) 2.50000 4.33013i 0.0864643 0.149761i
\(837\) 10.0000 0.345651
\(838\) −14.0000 + 24.2487i −0.483622 + 0.837658i
\(839\) 27.0000 46.7654i 0.932144 1.61452i 0.152493 0.988304i \(-0.451270\pi\)
0.779650 0.626215i \(-0.215397\pi\)
\(840\) 0 0
\(841\) 14.5000 25.1147i 0.500000 0.866025i
\(842\) 10.0000 + 17.3205i 0.344623 + 0.596904i
\(843\) −5.00000 8.66025i −0.172209 0.298275i
\(844\) −15.0000 −0.516321
\(845\) 0 0
\(846\) −9.00000 −0.309426
\(847\) 15.0000 + 25.9808i 0.515406 + 0.892710i
\(848\) −6.50000 11.2583i −0.223211 0.386613i
\(849\) 1.00000 1.73205i 0.0343199 0.0594438i
\(850\) 0 0
\(851\) −2.00000 + 3.46410i −0.0685591 + 0.118748i
\(852\) 1.00000 1.73205i 0.0342594 0.0593391i
\(853\) 14.0000 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) −3.00000 + 5.19615i −0.102658 + 0.177809i
\(855\) 0 0
\(856\) 3.00000 + 5.19615i 0.102538 + 0.177601i
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 2.50000 + 2.59808i 0.0853486 + 0.0886969i
\(859\) 19.0000 0.648272 0.324136 0.946011i \(-0.394927\pi\)
0.324136 + 0.946011i \(0.394927\pi\)
\(860\) 0 0
\(861\) −9.00000 15.5885i −0.306719 0.531253i
\(862\) 18.0000 31.1769i 0.613082 1.06189i
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 0 0
\(866\) 16.0000 0.543702
\(867\) 8.50000 14.7224i 0.288675 0.500000i
\(868\) −15.0000 25.9808i −0.509133 0.881845i
\(869\) 5.00000 + 8.66025i 0.169613 + 0.293779i
\(870\) 0 0
\(871\) −12.0000 + 41.5692i −0.406604 + 1.40852i
\(872\) 10.0000 0.338643
\(873\) 6.00000 + 10.3923i 0.203069 + 0.351726i
\(874\) −10.0000 17.3205i −0.338255 0.585875i
\(875\) 0 0
\(876\) 16.0000 0.540590
\(877\) 19.0000 32.9090i 0.641584 1.11126i −0.343495 0.939155i \(-0.611611\pi\)
0.985079 0.172102i \(-0.0550559\pi\)
\(878\) −5.00000 + 8.66025i −0.168742 + 0.292269i
\(879\) −13.0000 −0.438479
\(880\) 0 0
\(881\) −2.50000 4.33013i −0.0842271 0.145886i 0.820834 0.571166i \(-0.193509\pi\)
−0.905062 + 0.425280i \(0.860175\pi\)
\(882\) 1.00000 + 1.73205i 0.0336718 + 0.0583212i
\(883\) −42.0000 −1.41341 −0.706706 0.707507i \(-0.749820\pi\)
−0.706706 + 0.707507i \(0.749820\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 9.00000 + 15.5885i 0.302361 + 0.523704i
\(887\) −6.50000 11.2583i −0.218249 0.378018i 0.736024 0.676955i \(-0.236701\pi\)
−0.954273 + 0.298938i \(0.903368\pi\)
\(888\) 0.500000 0.866025i 0.0167789 0.0290619i
\(889\) −15.0000 −0.503084
\(890\) 0 0
\(891\) −0.500000 + 0.866025i −0.0167506 + 0.0290129i
\(892\) −11.0000 −0.368307
\(893\) 22.5000 38.9711i 0.752934 1.30412i
\(894\) −3.00000 5.19615i −0.100335 0.173785i
\(895\) 0 0
\(896\) −3.00000 −0.100223
\(897\) 14.0000 3.46410i 0.467446 0.115663i
\(898\) 15.0000 0.500556
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) −6.00000 −0.199778
\(903\) −3.00000 + 5.19615i −0.0998337 + 0.172917i
\(904\) −8.00000 + 13.8564i −0.266076 + 0.460857i
\(905\) 0 0
\(906\) −3.00000 + 5.19615i −0.0996683 + 0.172631i
\(907\) 21.0000 + 36.3731i 0.697294 + 1.20775i 0.969401 + 0.245481i \(0.0789459\pi\)
−0.272108 + 0.962267i \(0.587721\pi\)
\(908\) −10.0000 17.3205i −0.331862 0.574801i
\(909\) 4.00000 0.132672
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 2.50000 + 4.33013i 0.0827833 + 0.143385i
\(913\) 6.00000 + 10.3923i 0.198571 + 0.343935i
\(914\) −11.0000 + 19.0526i −0.363848 + 0.630203i
\(915\) 0 0
\(916\) 5.00000 8.66025i 0.165205 0.286143i
\(917\) 22.5000 38.9711i 0.743015 1.28694i
\(918\) 0 0
\(919\) −17.0000 + 29.4449i −0.560778 + 0.971296i 0.436650 + 0.899631i \(0.356165\pi\)
−0.997429 + 0.0716652i \(0.977169\pi\)
\(920\) 0 0
\(921\) 9.00000 + 15.5885i 0.296560 + 0.513657i
\(922\) 12.0000 0.395199
\(923\) −7.00000 + 1.73205i −0.230408 + 0.0570111i
\(924\) 3.00000 0.0986928
\(925\) 0 0
\(926\) 8.00000 + 13.8564i 0.262896 + 0.455350i
\(927\) −4.50000 + 7.79423i −0.147799 + 0.255996i
\(928\) 0 0
\(929\) −17.0000 + 29.4449i −0.557752 + 0.966055i 0.439932 + 0.898031i \(0.355003\pi\)
−0.997684 + 0.0680235i \(0.978331\pi\)
\(930\) 0 0
\(931\) −10.0000 −0.327737
\(932\) 5.00000 8.66025i 0.163780 0.283676i
\(933\) 6.00000 + 10.3923i 0.196431 + 0.340229i
\(934\) 18.0000 + 31.1769i 0.588978 + 1.02014i
\(935\) 0 0
\(936\) −3.50000 + 0.866025i −0.114401 + 0.0283069i
\(937\) 10.0000 0.326686 0.163343 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) 18.0000 + 31.1769i 0.587721 + 1.01796i
\(939\) −17.0000 29.4449i −0.554774 0.960897i
\(940\) 0 0
\(941\) 24.0000 0.782378 0.391189 0.920310i \(-0.372064\pi\)
0.391189 + 0.920310i \(0.372064\pi\)
\(942\) −0.500000 + 0.866025i −0.0162909 + 0.0282166i
\(943\) −12.0000 + 20.7846i −0.390774 + 0.676840i
\(944\) 4.00000 0.130189
\(945\) 0 0
\(946\) 1.00000 + 1.73205i 0.0325128 + 0.0563138i
\(947\) −19.0000 32.9090i −0.617417 1.06940i −0.989955 0.141381i \(-0.954846\pi\)
0.372538 0.928017i \(-0.378488\pi\)
\(948\) −10.0000 −0.324785
\(949\) −40.0000 41.5692i −1.29845 1.34939i
\(950\) 0 0
\(951\) 9.50000 + 16.4545i 0.308059 + 0.533573i
\(952\) 0 0
\(953\) 11.0000 19.0526i 0.356325 0.617173i −0.631019 0.775768i \(-0.717363\pi\)
0.987344 + 0.158595i \(0.0506963\pi\)
\(954\) −13.0000 −0.420891
\(955\) 0 0
\(956\) 1.00000 1.73205i 0.0323423 0.0560185i
\(957\) 0 0
\(958\) −4.00000 + 6.92820i −0.129234 + 0.223840i
\(959\) 24.0000 + 41.5692i 0.775000 + 1.34234i
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) −3.50000 + 0.866025i −0.112845 + 0.0279218i
\(963\) 6.00000 0.193347
\(964\) −7.50000 12.9904i −0.241559 0.418392i
\(965\) 0 0
\(966\) 6.00000 10.3923i 0.193047 0.334367i
\(967\) −7.00000 −0.225105 −0.112552 0.993646i \(-0.535903\pi\)
−0.112552 + 0.993646i \(0.535903\pi\)
\(968\) −5.00000 + 8.66025i −0.160706 + 0.278351i
\(969\) 0 0
\(970\) 0 0
\(971\) −13.5000 + 23.3827i −0.433236 + 0.750386i −0.997150 0.0754473i \(-0.975962\pi\)
0.563914 + 0.825833i \(0.309295\pi\)
\(972\) −0.500000 0.866025i −0.0160375 0.0277778i
\(973\) 13.5000 + 23.3827i 0.432790 + 0.749614i
\(974\) 35.0000 1.12147
\(975\) 0 0
\(976\) −2.00000 −0.0640184
\(977\) 24.0000 + 41.5692i 0.767828 + 1.32992i 0.938738 + 0.344631i \(0.111996\pi\)
−0.170910 + 0.985287i \(0.554671\pi\)
\(978\) 10.0000 + 17.3205i 0.319765 + 0.553849i
\(979\) −0.500000 + 0.866025i −0.0159801 + 0.0276783i
\(980\) 0 0
\(981\) 5.00000 8.66025i 0.159638 0.276501i
\(982\) 12.5000 21.6506i 0.398891 0.690900i
\(983\) −53.0000 −1.69044 −0.845219 0.534421i \(-0.820530\pi\)
−0.845219 + 0.534421i \(0.820530\pi\)
\(984\) 3.00000 5.19615i 0.0956365 0.165647i
\(985\) 0 0
\(986\) 0 0
\(987\) 27.0000 0.859419
\(988\) 5.00000 17.3205i 0.159071 0.551039i
\(989\) 8.00000 0.254385
\(990\) 0 0
\(991\) −19.0000 32.9090i −0.603555 1.04539i −0.992278 0.124033i \(-0.960417\pi\)
0.388723 0.921355i \(-0.372916\pi\)
\(992\) 5.00000 8.66025i 0.158750 0.274963i
\(993\) 28.0000 0.888553
\(994\) −3.00000 + 5.19615i −0.0951542 + 0.164812i
\(995\) 0 0
\(996\) −12.0000 −0.380235
\(997\) −3.50000 + 6.06218i −0.110846 + 0.191991i −0.916112 0.400923i \(-0.868689\pi\)
0.805266 + 0.592914i \(0.202023\pi\)
\(998\) 10.0000 + 17.3205i 0.316544 + 0.548271i
\(999\) −0.500000 0.866025i −0.0158193 0.0273998i
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 1950.2.i.o.601.1 2
5.2 odd 4 1950.2.z.i.1849.1 4
5.3 odd 4 1950.2.z.i.1849.2 4
5.4 even 2 390.2.i.b.211.1 yes 2
13.9 even 3 inner 1950.2.i.o.451.1 2
15.14 odd 2 1170.2.i.j.991.1 2
65.9 even 6 390.2.i.b.61.1 2
65.22 odd 12 1950.2.z.i.1699.2 4
65.24 odd 12 5070.2.b.a.1351.2 2
65.29 even 6 5070.2.a.q.1.1 1
65.48 odd 12 1950.2.z.i.1699.1 4
65.49 even 6 5070.2.a.c.1.1 1
65.54 odd 12 5070.2.b.a.1351.1 2
195.74 odd 6 1170.2.i.j.451.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.i.b.61.1 2 65.9 even 6
390.2.i.b.211.1 yes 2 5.4 even 2
1170.2.i.j.451.1 2 195.74 odd 6
1170.2.i.j.991.1 2 15.14 odd 2
1950.2.i.o.451.1 2 13.9 even 3 inner
1950.2.i.o.601.1 2 1.1 even 1 trivial
1950.2.z.i.1699.1 4 65.48 odd 12
1950.2.z.i.1699.2 4 65.22 odd 12
1950.2.z.i.1849.1 4 5.2 odd 4
1950.2.z.i.1849.2 4 5.3 odd 4
5070.2.a.c.1.1 1 65.49 even 6
5070.2.a.q.1.1 1 65.29 even 6
5070.2.b.a.1351.1 2 65.54 odd 12
5070.2.b.a.1351.2 2 65.24 odd 12