Properties

Label 525.2.i.a.226.1
Level $525$
Weight $2$
Character 525.226
Analytic conductor $4.192$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(151,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, 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("525.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 525.226
Dual form 525.2.i.a.151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +3.00000 q^{13} +(-5.00000 - 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} -12.0000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} -8.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-3.00000 + 5.19615i) q^{33} +8.00000 q^{34} +2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +(-1.00000 - 5.19615i) q^{42} -1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +4.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(2.00000 + 3.46410i) q^{53} +(1.00000 - 1.73205i) q^{54} -1.00000 q^{57} +(8.00000 - 13.8564i) q^{58} +(4.00000 + 6.92820i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +(-2.50000 - 0.866025i) q^{63} -8.00000 q^{64} +(-6.00000 - 10.3923i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-4.00000 + 6.92820i) q^{68} -4.00000 q^{69} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} -2.00000 q^{83} +(5.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(6.00000 - 10.3923i) q^{89} +(1.50000 + 7.79423i) q^{91} +8.00000 q^{92} +(0.500000 - 0.866025i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-4.00000 + 6.92820i) q^{96} +6.00000 q^{97} +(2.00000 - 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{6} + q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{6} + q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 6 q^{13} - 10 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{18} - q^{19} - 4 q^{21} - 24 q^{22} - 4 q^{23} - 6 q^{26} - 2 q^{27} + 8 q^{28} - 16 q^{29} - q^{31} + 8 q^{32} - 6 q^{33} + 16 q^{34} + 4 q^{36} + 7 q^{37} - 2 q^{38} + 3 q^{39} - 12 q^{41} - 2 q^{42} - 2 q^{43} + 12 q^{44} - 8 q^{46} + 2 q^{47} + 8 q^{48} - 13 q^{49} + 4 q^{51} - 6 q^{52} + 4 q^{53} + 2 q^{54} - 2 q^{57} + 16 q^{58} + 8 q^{59} + 14 q^{61} + 4 q^{62} - 5 q^{63} - 16 q^{64} - 12 q^{66} + 7 q^{67} - 8 q^{68} - 8 q^{69} + 12 q^{71} + q^{73} + 14 q^{74} + 4 q^{76} - 24 q^{77} - 12 q^{78} + q^{79} - q^{81} + 12 q^{82} - 4 q^{83} + 10 q^{84} + 2 q^{86} - 8 q^{87} + 12 q^{89} + 3 q^{91} + 16 q^{92} + q^{93} + 4 q^{94} - 8 q^{96} + 12 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 0 0
\(6\) −2.00000 −0.816497
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) 1.00000 1.73205i 0.288675 0.500000i
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) −5.00000 1.73205i −1.33631 0.462910i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) −12.0000 −2.55841
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) −1.00000 −0.192450
\(28\) 4.00000 3.46410i 0.755929 0.654654i
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 4.00000 + 6.92820i 0.707107 + 1.22474i
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −1.00000 5.19615i −0.154303 0.801784i
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 6.00000 10.3923i 0.904534 1.56670i
\(45\) 0 0
\(46\) −4.00000 6.92820i −0.589768 1.02151i
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 4.00000 0.577350
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 2.00000 3.46410i 0.280056 0.485071i
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 1.00000 1.73205i 0.136083 0.235702i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 8.00000 13.8564i 1.05045 1.81944i
\(59\) 4.00000 + 6.92820i 0.520756 + 0.901975i 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) 0 0
\(61\) 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i \(-0.479608\pi\)
0.832240 0.554416i \(-0.187058\pi\)
\(62\) 2.00000 0.254000
\(63\) −2.50000 0.866025i −0.314970 0.109109i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) −6.00000 10.3923i −0.738549 1.27920i
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) −4.00000 + 6.92820i −0.485071 + 0.840168i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) 7.00000 + 12.1244i 0.813733 + 1.40943i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −12.0000 + 10.3923i −1.36753 + 1.18431i
\(78\) −6.00000 −0.679366
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.00000 10.3923i 0.662589 1.14764i
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 5.00000 + 1.73205i 0.545545 + 0.188982i
\(85\) 0 0
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) 0 0
\(89\) 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i \(-0.613922\pi\)
0.986303 0.164946i \(-0.0527450\pi\)
\(90\) 0 0
\(91\) 1.50000 + 7.79423i 0.157243 + 0.817057i
\(92\) 8.00000 0.834058
\(93\) 0.500000 0.866025i 0.0518476 0.0898027i
\(94\) 2.00000 + 3.46410i 0.206284 + 0.357295i
\(95\) 0 0
\(96\) −4.00000 + 6.92820i −0.408248 + 0.707107i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 2.00000 13.8564i 0.202031 1.39971i
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) 4.00000 + 6.92820i 0.396059 + 0.685994i
\(103\) −9.50000 + 16.4545i −0.936063 + 1.62131i −0.163335 + 0.986571i \(0.552225\pi\)
−0.772728 + 0.634738i \(0.781108\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −8.00000 −0.777029
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 1.00000 + 1.73205i 0.0962250 + 0.166667i
\(109\) 7.50000 + 12.9904i 0.718370 + 1.24425i 0.961645 + 0.274296i \(0.0884447\pi\)
−0.243276 + 0.969957i \(0.578222\pi\)
\(110\) 0 0
\(111\) 7.00000 0.664411
\(112\) 10.0000 + 3.46410i 0.944911 + 0.327327i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) 8.00000 + 13.8564i 0.742781 + 1.28654i
\(117\) −1.50000 + 2.59808i −0.138675 + 0.240192i
\(118\) −16.0000 −1.47292
\(119\) 8.00000 6.92820i 0.733359 0.635107i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 14.0000 + 24.2487i 1.26750 + 2.19538i
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 0 0
\(126\) 4.00000 3.46410i 0.356348 0.308607i
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) −0.500000 0.866025i −0.0440225 0.0762493i
\(130\) 0 0
\(131\) −1.00000 + 1.73205i −0.0873704 + 0.151330i −0.906399 0.422423i \(-0.861180\pi\)
0.819028 + 0.573753i \(0.194513\pi\)
\(132\) 12.0000 1.04447
\(133\) −2.50000 0.866025i −0.216777 0.0750939i
\(134\) −14.0000 −1.20942
\(135\) 0 0
\(136\) 0 0
\(137\) 4.00000 + 6.92820i 0.341743 + 0.591916i 0.984757 0.173939i \(-0.0556494\pi\)
−0.643013 + 0.765855i \(0.722316\pi\)
\(138\) 4.00000 6.92820i 0.340503 0.589768i
\(139\) 21.0000 1.78120 0.890598 0.454791i \(-0.150286\pi\)
0.890598 + 0.454791i \(0.150286\pi\)
\(140\) 0 0
\(141\) 2.00000 0.168430
\(142\) −6.00000 + 10.3923i −0.503509 + 0.872103i
\(143\) 9.00000 + 15.5885i 0.752618 + 1.30357i
\(144\) 2.00000 + 3.46410i 0.166667 + 0.288675i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) −14.0000 −1.15079
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) −6.00000 31.1769i −0.483494 2.51231i
\(155\) 0 0
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i \(-0.0360089\pi\)
−0.594565 + 0.804048i \(0.702676\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) −2.00000 + 3.46410i −0.158610 + 0.274721i
\(160\) 0 0
\(161\) −10.0000 3.46410i −0.788110 0.273009i
\(162\) 2.00000 0.157135
\(163\) −6.00000 + 10.3923i −0.469956 + 0.813988i −0.999410 0.0343508i \(-0.989064\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(164\) 6.00000 + 10.3923i 0.468521 + 0.811503i
\(165\) 0 0
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) 10.0000 0.773823 0.386912 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) 12.0000 20.7846i 0.912343 1.58022i 0.101598 0.994826i \(-0.467605\pi\)
0.810745 0.585399i \(-0.199062\pi\)
\(174\) 16.0000 1.21296
\(175\) 0 0
\(176\) 24.0000 1.80907
\(177\) −4.00000 + 6.92820i −0.300658 + 0.520756i
\(178\) 12.0000 + 20.7846i 0.899438 + 1.55787i
\(179\) −9.00000 15.5885i −0.672692 1.16514i −0.977138 0.212607i \(-0.931805\pi\)
0.304446 0.952529i \(-0.401529\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) −15.0000 5.19615i −1.11187 0.385164i
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) 0 0
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) 12.0000 20.7846i 0.877527 1.51992i
\(188\) −4.00000 −0.291730
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) −4.00000 6.92820i −0.288675 0.500000i
\(193\) −4.50000 7.79423i −0.323917 0.561041i 0.657376 0.753563i \(-0.271667\pi\)
−0.981293 + 0.192522i \(0.938333\pi\)
\(194\) −6.00000 + 10.3923i −0.430775 + 0.746124i
\(195\) 0 0
\(196\) 11.0000 + 8.66025i 0.785714 + 0.618590i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 6.00000 10.3923i 0.426401 0.738549i
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 0 0
\(201\) −3.50000 + 6.06218i −0.246871 + 0.427593i
\(202\) −20.0000 −1.40720
\(203\) −4.00000 20.7846i −0.280745 1.45879i
\(204\) −8.00000 −0.560112
\(205\) 0 0
\(206\) −19.0000 32.9090i −1.32379 2.29288i
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) 6.00000 10.3923i 0.416025 0.720577i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 4.00000 6.92820i 0.274721 0.475831i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) 12.0000 + 20.7846i 0.820303 + 1.42081i
\(215\) 0 0
\(216\) 0 0
\(217\) 2.00000 1.73205i 0.135769 0.117579i
\(218\) −30.0000 −2.03186
\(219\) −0.500000 + 0.866025i −0.0337869 + 0.0585206i
\(220\) 0 0
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) −7.00000 + 12.1244i −0.469809 + 0.813733i
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) −16.0000 + 13.8564i −1.06904 + 0.925820i
\(225\) 0 0
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) −5.00000 8.66025i −0.331862 0.574801i 0.651015 0.759065i \(-0.274343\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) −6.50000 + 11.2583i −0.429532 + 0.743971i −0.996832 0.0795401i \(-0.974655\pi\)
0.567300 + 0.823511i \(0.307988\pi\)
\(230\) 0 0
\(231\) −15.0000 5.19615i −0.986928 0.341882i
\(232\) 0 0
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) 0 0
\(236\) 8.00000 13.8564i 0.520756 0.901975i
\(237\) 1.00000 0.0649570
\(238\) 4.00000 + 20.7846i 0.259281 + 1.34727i
\(239\) 14.0000 0.905585 0.452792 0.891616i \(-0.350428\pi\)
0.452792 + 0.891616i \(0.350428\pi\)
\(240\) 0 0
\(241\) 9.00000 + 15.5885i 0.579741 + 1.00414i 0.995509 + 0.0946700i \(0.0301796\pi\)
−0.415768 + 0.909471i \(0.636487\pi\)
\(242\) −25.0000 43.3013i −1.60706 2.78351i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −28.0000 −1.79252
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) 0 0
\(249\) −1.00000 1.73205i −0.0633724 0.109764i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 1.00000 + 5.19615i 0.0629941 + 0.327327i
\(253\) −24.0000 −1.50887
\(254\) 5.00000 8.66025i 0.313728 0.543393i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 2.00000 0.124515
\(259\) 17.5000 + 6.06218i 1.08740 + 0.376685i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) −2.00000 3.46410i −0.123560 0.214013i
\(263\) 2.00000 + 3.46410i 0.123325 + 0.213606i 0.921077 0.389380i \(-0.127311\pi\)
−0.797752 + 0.602986i \(0.793977\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) 12.0000 0.734388
\(268\) 7.00000 12.1244i 0.427593 0.740613i
\(269\) 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i \(-0.0680585\pi\)
−0.672374 + 0.740212i \(0.734725\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) −16.0000 −0.970143
\(273\) −6.00000 + 5.19615i −0.363137 + 0.314485i
\(274\) −16.0000 −0.966595
\(275\) 0 0
\(276\) 4.00000 + 6.92820i 0.240772 + 0.417029i
\(277\) −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i \(-0.234109\pi\)
−0.951807 + 0.306699i \(0.900776\pi\)
\(278\) −21.0000 + 36.3731i −1.25950 + 2.18151i
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −2.00000 + 3.46410i −0.119098 + 0.206284i
\(283\) −3.50000 6.06218i −0.208053 0.360359i 0.743048 0.669238i \(-0.233379\pi\)
−0.951101 + 0.308879i \(0.900046\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) 0 0
\(286\) −36.0000 −2.12872
\(287\) −3.00000 15.5885i −0.177084 0.920158i
\(288\) −8.00000 −0.471405
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 16.0000 0.934730 0.467365 0.884064i \(-0.345203\pi\)
0.467365 + 0.884064i \(0.345203\pi\)
\(294\) 13.0000 5.19615i 0.758175 0.303046i
\(295\) 0 0
\(296\) 0 0
\(297\) −3.00000 5.19615i −0.174078 0.301511i
\(298\) 4.00000 + 6.92820i 0.231714 + 0.401340i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 0 0
\(301\) −0.500000 2.59808i −0.0288195 0.149751i
\(302\) 16.0000 0.920697
\(303\) −5.00000 + 8.66025i −0.287242 + 0.497519i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 0 0
\(306\) −4.00000 + 6.92820i −0.228665 + 0.396059i
\(307\) −3.00000 −0.171219 −0.0856095 0.996329i \(-0.527284\pi\)
−0.0856095 + 0.996329i \(0.527284\pi\)
\(308\) 30.0000 + 10.3923i 1.70941 + 0.592157i
\(309\) −19.0000 −1.08087
\(310\) 0 0
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) 0 0
\(313\) 5.50000 9.52628i 0.310878 0.538457i −0.667674 0.744453i \(-0.732710\pi\)
0.978553 + 0.205996i \(0.0660435\pi\)
\(314\) −20.0000 −1.12867
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) 10.0000 17.3205i 0.561656 0.972817i −0.435696 0.900094i \(-0.643498\pi\)
0.997352 0.0727229i \(-0.0231689\pi\)
\(318\) −4.00000 6.92820i −0.224309 0.388514i
\(319\) −24.0000 41.5692i −1.34374 2.32743i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 16.0000 13.8564i 0.891645 0.772187i
\(323\) 4.00000 0.222566
\(324\) −1.00000 + 1.73205i −0.0555556 + 0.0962250i
\(325\) 0 0
\(326\) −12.0000 20.7846i −0.664619 1.15115i
\(327\) −7.50000 + 12.9904i −0.414751 + 0.718370i
\(328\) 0 0
\(329\) 5.00000 + 1.73205i 0.275659 + 0.0954911i
\(330\) 0 0
\(331\) 4.50000 7.79423i 0.247342 0.428410i −0.715445 0.698669i \(-0.753776\pi\)
0.962788 + 0.270259i \(0.0871094\pi\)
\(332\) 2.00000 + 3.46410i 0.109764 + 0.190117i
\(333\) 3.50000 + 6.06218i 0.191799 + 0.332205i
\(334\) −10.0000 + 17.3205i −0.547176 + 0.947736i
\(335\) 0 0
\(336\) 2.00000 + 10.3923i 0.109109 + 0.566947i
\(337\) −25.0000 −1.36184 −0.680918 0.732359i \(-0.738419\pi\)
−0.680918 + 0.732359i \(0.738419\pi\)
\(338\) 4.00000 6.92820i 0.217571 0.376845i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 2.00000 0.108148
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 24.0000 + 41.5692i 1.29025 + 2.23478i
\(347\) 8.00000 + 13.8564i 0.429463 + 0.743851i 0.996826 0.0796169i \(-0.0253697\pi\)
−0.567363 + 0.823468i \(0.692036\pi\)
\(348\) −8.00000 + 13.8564i −0.428845 + 0.742781i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) −3.00000 −0.160128
\(352\) −24.0000 + 41.5692i −1.27920 + 2.21565i
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) −8.00000 13.8564i −0.425195 0.736460i
\(355\) 0 0
\(356\) −24.0000 −1.27200
\(357\) 10.0000 + 3.46410i 0.529256 + 0.183340i
\(358\) 36.0000 1.90266
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −13.0000 + 22.5167i −0.683265 + 1.18345i
\(363\) −25.0000 −1.31216
\(364\) 12.0000 10.3923i 0.628971 0.544705i
\(365\) 0 0
\(366\) −14.0000 + 24.2487i −0.731792 + 1.26750i
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 8.00000 + 13.8564i 0.417029 + 0.722315i
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) −8.00000 + 6.92820i −0.415339 + 0.359694i
\(372\) −2.00000 −0.103695
\(373\) 5.50000 9.52628i 0.284779 0.493252i −0.687776 0.725923i \(-0.741413\pi\)
0.972556 + 0.232671i \(0.0747464\pi\)
\(374\) 24.0000 + 41.5692i 1.24101 + 2.14949i
\(375\) 0 0
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 5.00000 + 1.73205i 0.257172 + 0.0890871i
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 0 0
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) −10.0000 17.3205i −0.511645 0.886194i
\(383\) 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i \(-0.579593\pi\)
0.962818 0.270151i \(-0.0870736\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.0000 0.916176
\(387\) 0.500000 0.866025i 0.0254164 0.0440225i
\(388\) −6.00000 10.3923i −0.304604 0.527589i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) −2.00000 −0.100887
\(394\) 12.0000 20.7846i 0.604551 1.04711i
\(395\) 0 0
\(396\) 6.00000 + 10.3923i 0.301511 + 0.522233i
\(397\) −18.5000 + 32.0429i −0.928488 + 1.60819i −0.142636 + 0.989775i \(0.545558\pi\)
−0.785853 + 0.618414i \(0.787776\pi\)
\(398\) 16.0000 0.802008
\(399\) −0.500000 2.59808i −0.0250313 0.130066i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) −7.00000 12.1244i −0.349128 0.604708i
\(403\) −1.50000 2.59808i −0.0747203 0.129419i
\(404\) 10.0000 17.3205i 0.497519 0.861727i
\(405\) 0 0
\(406\) 40.0000 + 13.8564i 1.98517 + 0.687682i
\(407\) 42.0000 2.08186
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 0 0
\(411\) −4.00000 + 6.92820i −0.197305 + 0.341743i
\(412\) 38.0000 1.87213
\(413\) −16.0000 + 13.8564i −0.787309 + 0.681829i
\(414\) 8.00000 0.393179
\(415\) 0 0
\(416\) 12.0000 + 20.7846i 0.588348 + 1.01905i
\(417\) 10.5000 + 18.1865i 0.514187 + 0.890598i
\(418\) 6.00000 10.3923i 0.293470 0.508304i
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 0 0
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) 20.0000 34.6410i 0.973585 1.68630i
\(423\) 1.00000 + 1.73205i 0.0486217 + 0.0842152i
\(424\) 0 0
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 35.0000 + 12.1244i 1.69377 + 0.586739i
\(428\) −24.0000 −1.16008
\(429\) −9.00000 + 15.5885i −0.434524 + 0.752618i
\(430\) 0 0
\(431\) 1.00000 + 1.73205i 0.0481683 + 0.0834300i 0.889104 0.457705i \(-0.151328\pi\)
−0.840936 + 0.541135i \(0.817995\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 1.00000 + 5.19615i 0.0480015 + 0.249423i
\(435\) 0 0
\(436\) 15.0000 25.9808i 0.718370 1.24425i
\(437\) −2.00000 3.46410i −0.0956730 0.165710i
\(438\) −1.00000 1.73205i −0.0477818 0.0827606i
\(439\) −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i \(-0.958036\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 24.0000 1.14156
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) −7.00000 12.1244i −0.332205 0.575396i
\(445\) 0 0
\(446\) −24.0000 + 41.5692i −1.13643 + 1.96836i
\(447\) 4.00000 0.189194
\(448\) −4.00000 20.7846i −0.188982 0.981981i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) −18.0000 31.1769i −0.847587 1.46806i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i \(-0.947436\pi\)
0.635561 + 0.772051i \(0.280769\pi\)
\(458\) −13.0000 22.5167i −0.607450 1.05213i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0 0
\(461\) −8.00000 −0.372597 −0.186299 0.982493i \(-0.559649\pi\)
−0.186299 + 0.982493i \(0.559649\pi\)
\(462\) 24.0000 20.7846i 1.11658 0.966988i
\(463\) −3.00000 −0.139422 −0.0697109 0.997567i \(-0.522208\pi\)
−0.0697109 + 0.997567i \(0.522208\pi\)
\(464\) −16.0000 + 27.7128i −0.742781 + 1.28654i
\(465\) 0 0
\(466\) 6.00000 + 10.3923i 0.277945 + 0.481414i
\(467\) 11.0000 19.0526i 0.509019 0.881647i −0.490926 0.871201i \(-0.663342\pi\)
0.999945 0.0104461i \(-0.00332515\pi\)
\(468\) 6.00000 0.277350
\(469\) −14.0000 + 12.1244i −0.646460 + 0.559851i
\(470\) 0 0
\(471\) −5.00000 + 8.66025i −0.230388 + 0.399043i
\(472\) 0 0
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) −1.00000 + 1.73205i −0.0459315 + 0.0795557i
\(475\) 0 0
\(476\) −20.0000 6.92820i −0.916698 0.317554i
\(477\) −4.00000 −0.183147
\(478\) −14.0000 + 24.2487i −0.640345 + 1.10911i
\(479\) 2.00000 + 3.46410i 0.0913823 + 0.158279i 0.908093 0.418769i \(-0.137538\pi\)
−0.816711 + 0.577047i \(0.804205\pi\)
\(480\) 0 0
\(481\) 10.5000 18.1865i 0.478759 0.829235i
\(482\) −36.0000 −1.63976
\(483\) −2.00000 10.3923i −0.0910032 0.472866i
\(484\) 50.0000 2.27273
\(485\) 0 0
\(486\) 1.00000 + 1.73205i 0.0453609 + 0.0785674i
\(487\) −6.50000 11.2583i −0.294543 0.510164i 0.680335 0.732901i \(-0.261834\pi\)
−0.974879 + 0.222737i \(0.928501\pi\)
\(488\) 0 0
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) 16.0000 + 27.7128i 0.720604 + 1.24812i
\(494\) −3.00000 5.19615i −0.134976 0.233786i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 3.00000 + 15.5885i 0.134568 + 0.699238i
\(498\) 4.00000 0.179244
\(499\) −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i \(0.391525\pi\)
−0.983336 + 0.181797i \(0.941809\pi\)
\(500\) 0 0
\(501\) 5.00000 + 8.66025i 0.223384 + 0.386912i
\(502\) −12.0000 + 20.7846i −0.535586 + 0.927663i
\(503\) 2.00000 0.0891756 0.0445878 0.999005i \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 24.0000 41.5692i 1.06693 1.84798i
\(507\) −2.00000 3.46410i −0.0888231 0.153846i
\(508\) 5.00000 + 8.66025i 0.221839 + 0.384237i
\(509\) −5.00000 + 8.66025i −0.221621 + 0.383859i −0.955300 0.295637i \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(510\) 0 0
\(511\) −2.00000 + 1.73205i −0.0884748 + 0.0766214i
\(512\) 32.0000 1.41421
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) −18.0000 31.1769i −0.793946 1.37515i
\(515\) 0 0
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 12.0000 0.527759
\(518\) −28.0000 + 24.2487i −1.23025 + 1.06543i
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −2.00000 3.46410i −0.0876216 0.151765i 0.818884 0.573959i \(-0.194593\pi\)
−0.906505 + 0.422194i \(0.861260\pi\)
\(522\) 8.00000 + 13.8564i 0.350150 + 0.606478i
\(523\) 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i \(-0.756023\pi\)
0.960856 + 0.277047i \(0.0893559\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) −2.00000 + 3.46410i −0.0871214 + 0.150899i
\(528\) 12.0000 + 20.7846i 0.522233 + 0.904534i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −8.00000 −0.347170
\(532\) 1.00000 + 5.19615i 0.0433555 + 0.225282i
\(533\) −18.0000 −0.779667
\(534\) −12.0000 + 20.7846i −0.519291 + 0.899438i
\(535\) 0 0
\(536\) 0 0
\(537\) 9.00000 15.5885i 0.388379 0.672692i
\(538\) −20.0000 −0.862261
\(539\) −33.0000 25.9808i −1.42141 1.11907i
\(540\) 0 0
\(541\) 1.50000 2.59808i 0.0644900 0.111700i −0.831978 0.554809i \(-0.812791\pi\)
0.896468 + 0.443109i \(0.146125\pi\)
\(542\) 24.0000 + 41.5692i 1.03089 + 1.78555i
\(543\) 6.50000 + 11.2583i 0.278942 + 0.483141i
\(544\) 16.0000 27.7128i 0.685994 1.18818i
\(545\) 0 0
\(546\) −3.00000 15.5885i −0.128388 0.667124i
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 8.00000 13.8564i 0.341743 0.591916i
\(549\) 7.00000 + 12.1244i 0.298753 + 0.517455i
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) 2.50000 + 0.866025i 0.106311 + 0.0368271i
\(554\) 14.0000 0.594803
\(555\) 0 0
\(556\) −21.0000 36.3731i −0.890598 1.54256i
\(557\) −5.00000 8.66025i −0.211857 0.366947i 0.740439 0.672124i \(-0.234618\pi\)
−0.952296 + 0.305177i \(0.901284\pi\)
\(558\) −1.00000 + 1.73205i −0.0423334 + 0.0733236i
\(559\) −3.00000 −0.126886
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 12.0000 20.7846i 0.506189 0.876746i
\(563\) −13.0000 22.5167i −0.547885 0.948964i −0.998419 0.0562051i \(-0.982100\pi\)
0.450535 0.892759i \(-0.351233\pi\)
\(564\) −2.00000 3.46410i −0.0842152 0.145865i
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 2.00000 1.73205i 0.0839921 0.0727393i
\(568\) 0 0
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 0 0
\(571\) 1.50000 + 2.59808i 0.0627730 + 0.108726i 0.895704 0.444651i \(-0.146672\pi\)
−0.832931 + 0.553377i \(0.813339\pi\)
\(572\) 18.0000 31.1769i 0.752618 1.30357i
\(573\) −10.0000 −0.417756
\(574\) 30.0000 + 10.3923i 1.25218 + 0.433766i
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) −14.5000 25.1147i −0.603643 1.04554i −0.992264 0.124143i \(-0.960382\pi\)
0.388621 0.921397i \(-0.372951\pi\)
\(578\) 1.00000 + 1.73205i 0.0415945 + 0.0720438i
\(579\) 4.50000 7.79423i 0.187014 0.323917i
\(580\) 0 0
\(581\) −1.00000 5.19615i −0.0414870 0.215573i
\(582\) −12.0000 −0.497416
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) −16.0000 + 27.7128i −0.660954 + 1.14481i
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −2.00000 + 13.8564i −0.0824786 + 0.571429i
\(589\) 1.00000 0.0412043
\(590\) 0 0
\(591\) −6.00000 10.3923i −0.246807 0.427482i
\(592\) −14.0000 24.2487i −0.575396 0.996616i
\(593\) −9.00000 + 15.5885i −0.369586 + 0.640141i −0.989501 0.144528i \(-0.953834\pi\)
0.619915 + 0.784669i \(0.287167\pi\)
\(594\) 12.0000 0.492366
\(595\) 0 0
\(596\) −8.00000 −0.327693
\(597\) 4.00000 6.92820i 0.163709 0.283552i
\(598\) −12.0000 20.7846i −0.490716 0.849946i
\(599\) 2.00000 + 3.46410i 0.0817178 + 0.141539i 0.903988 0.427558i \(-0.140626\pi\)
−0.822270 + 0.569097i \(0.807293\pi\)
\(600\) 0 0
\(601\) −33.0000 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(602\) 5.00000 + 1.73205i 0.203785 + 0.0705931i
\(603\) −7.00000 −0.285062
\(604\) −8.00000 + 13.8564i −0.325515 + 0.563809i
\(605\) 0 0
\(606\) −10.0000 17.3205i −0.406222 0.703598i
\(607\) 17.5000 30.3109i 0.710303 1.23028i −0.254440 0.967088i \(-0.581891\pi\)
0.964743 0.263193i \(-0.0847754\pi\)
\(608\) −8.00000 −0.324443
\(609\) 16.0000 13.8564i 0.648353 0.561490i
\(610\) 0 0
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) −4.00000 6.92820i −0.161690 0.280056i
\(613\) −15.0000 25.9808i −0.605844 1.04935i −0.991917 0.126885i \(-0.959502\pi\)
0.386073 0.922468i \(-0.373831\pi\)
\(614\) 3.00000 5.19615i 0.121070 0.209700i
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 19.0000 32.9090i 0.764292 1.32379i
\(619\) −1.50000 2.59808i −0.0602901 0.104425i 0.834305 0.551303i \(-0.185869\pi\)
−0.894595 + 0.446878i \(0.852536\pi\)
\(620\) 0 0
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) 12.0000 0.481156
\(623\) 30.0000 + 10.3923i 1.20192 + 0.416359i
\(624\) 12.0000 0.480384
\(625\) 0 0
\(626\) 11.0000 + 19.0526i 0.439648 + 0.761493i
\(627\) −3.00000 5.19615i −0.119808 0.207514i
\(628\) 10.0000 17.3205i 0.399043 0.691164i
\(629\) −28.0000 −1.11643
\(630\) 0 0
\(631\) 24.0000 0.955425 0.477712 0.878516i \(-0.341466\pi\)
0.477712 + 0.878516i \(0.341466\pi\)
\(632\) 0 0
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 20.0000 + 34.6410i 0.794301 + 1.37577i
\(635\) 0 0
\(636\) 8.00000 0.317221
\(637\) −19.5000 + 7.79423i −0.772618 + 0.308819i
\(638\) 96.0000 3.80068
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i \(-0.242826\pi\)
−0.959848 + 0.280521i \(0.909493\pi\)
\(642\) −12.0000 + 20.7846i −0.473602 + 0.820303i
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 4.00000 + 20.7846i 0.157622 + 0.819028i
\(645\) 0 0
\(646\) −4.00000 + 6.92820i −0.157378 + 0.272587i
\(647\) 15.0000 + 25.9808i 0.589711 + 1.02141i 0.994270 + 0.106897i \(0.0340916\pi\)
−0.404559 + 0.914512i \(0.632575\pi\)
\(648\) 0 0
\(649\) −24.0000 + 41.5692i −0.942082 + 1.63173i
\(650\) 0 0
\(651\) 2.50000 + 0.866025i 0.0979827 + 0.0339422i
\(652\) 24.0000 0.939913
\(653\) 7.00000 12.1244i 0.273931 0.474463i −0.695934 0.718106i \(-0.745009\pi\)
0.969865 + 0.243643i \(0.0783426\pi\)
\(654\) −15.0000 25.9808i −0.586546 1.01593i
\(655\) 0 0
\(656\) −12.0000 + 20.7846i −0.468521 + 0.811503i
\(657\) −1.00000 −0.0390137
\(658\) −8.00000 + 6.92820i −0.311872 + 0.270089i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) 9.00000 + 15.5885i 0.349795 + 0.605863i
\(663\) 6.00000 10.3923i 0.233021 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) −14.0000 −0.542489
\(667\) 16.0000 27.7128i 0.619522 1.07304i
\(668\) −10.0000 17.3205i −0.386912 0.670151i
\(669\) 12.0000 + 20.7846i 0.463947 + 0.803579i
\(670\) 0 0
\(671\) 84.0000 3.24278
\(672\) −20.0000 6.92820i −0.771517 0.267261i
\(673\) 37.0000 1.42625 0.713123 0.701039i \(-0.247280\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(674\) 25.0000 43.3013i 0.962964 1.66790i
\(675\) 0 0
\(676\) 4.00000 + 6.92820i 0.153846 + 0.266469i
\(677\) 8.00000 13.8564i 0.307465 0.532545i −0.670342 0.742052i \(-0.733853\pi\)
0.977807 + 0.209507i \(0.0671860\pi\)
\(678\) −12.0000 −0.460857
\(679\) 3.00000 + 15.5885i 0.115129 + 0.598230i
\(680\) 0 0
\(681\) 5.00000 8.66025i 0.191600 0.331862i
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) −24.0000 41.5692i −0.918334 1.59060i −0.801945 0.597398i \(-0.796201\pi\)
−0.116390 0.993204i \(-0.537132\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) 37.0000 1.73205i 1.41267 0.0661300i
\(687\) −13.0000 −0.495981
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −13.5000 + 23.3827i −0.513564 + 0.889519i 0.486312 + 0.873785i \(0.338342\pi\)
−0.999876 + 0.0157341i \(0.994991\pi\)
\(692\) −48.0000 −1.82469
\(693\) −3.00000 15.5885i −0.113961 0.592157i
\(694\) −32.0000 −1.21470
\(695\) 0 0
\(696\) 0 0
\(697\) 12.0000 + 20.7846i 0.454532 + 0.787273i
\(698\) −2.00000 + 3.46410i −0.0757011 + 0.131118i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) 3.00000 5.19615i 0.113228 0.196116i
\(703\) 3.50000 + 6.06218i 0.132005 + 0.228639i
\(704\) −24.0000 41.5692i −0.904534 1.56670i
\(705\) 0 0
\(706\) 36.0000 1.35488
\(707\) −20.0000 + 17.3205i −0.752177 + 0.651405i
\(708\) 16.0000 0.601317
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) −16.0000 + 13.8564i −0.598785 + 0.518563i
\(715\) 0 0
\(716\) −18.0000 + 31.1769i −0.672692 + 1.16514i
\(717\) 7.00000 + 12.1244i 0.261420 + 0.452792i
\(718\) 24.0000 + 41.5692i 0.895672 + 1.55135i
\(719\) 17.0000 29.4449i 0.633993 1.09811i −0.352735 0.935723i \(-0.614748\pi\)
0.986728 0.162385i \(-0.0519185\pi\)
\(720\) 0 0
\(721\) −47.5000 16.4545i −1.76899 0.612797i
\(722\) −36.0000 −1.33978
\(723\) −9.00000 + 15.5885i −0.334714 + 0.579741i
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) 0 0
\(726\) 25.0000 43.3013i 0.927837 1.60706i
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.00000 + 3.46410i 0.0739727 + 0.128124i
\(732\) −14.0000 24.2487i −0.517455 0.896258i
\(733\) −21.5000 + 37.2391i −0.794121 + 1.37546i 0.129275 + 0.991609i \(0.458735\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) −38.0000 −1.40261
\(735\) 0 0
\(736\) −32.0000 −1.17954
\(737\) −21.0000 + 36.3731i −0.773545 + 1.33982i
\(738\) 6.00000 + 10.3923i 0.220863 + 0.382546i
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) −4.00000 20.7846i −0.146845 0.763027i
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 11.0000 + 19.0526i 0.402739 + 0.697564i
\(747\) 1.00000 1.73205i 0.0365881 0.0633724i
\(748\) −48.0000 −1.75505
\(749\) 30.0000 + 10.3923i 1.09618 + 0.379727i
\(750\) 0 0
\(751\) −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i \(0.344142\pi\)
−0.999424 + 0.0339490i \(0.989192\pi\)
\(752\) −4.00000 6.92820i −0.145865 0.252646i
\(753\) 6.00000 + 10.3923i 0.218652 + 0.378717i
\(754\) 24.0000 41.5692i 0.874028 1.51386i
\(755\) 0 0
\(756\) −4.00000 + 3.46410i −0.145479 + 0.125988i
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −11.0000 + 19.0526i −0.399538 + 0.692020i
\(759\) −12.0000 20.7846i −0.435572 0.754434i
\(760\) 0 0
\(761\) 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) 10.0000 0.362262
\(763\) −30.0000 + 25.9808i −1.08607 + 0.940567i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 28.0000 + 48.4974i 1.01168 + 1.75228i
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 8.00000 13.8564i 0.288675 0.500000i
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) −9.00000 + 15.5885i −0.323917 + 0.561041i
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 0 0
\(776\) 0 0
\(777\) 3.50000 + 18.1865i 0.125562 + 0.652438i
\(778\) 12.0000 0.430221
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) 0 0
\(781\) 18.0000 + 31.1769i 0.644091 + 1.11560i
\(782\) −16.0000 + 27.7128i −0.572159 + 0.991008i
\(783\) 8.00000 0.285897
\(784\) −4.00000 + 27.7128i −0.142857 + 0.989743i
\(785\) 0 0
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 12.0000 + 20.7846i 0.427482 + 0.740421i
\(789\) −2.00000 + 3.46410i −0.0712019 + 0.123325i
\(790\) 0 0
\(791\) 3.00000 + 15.5885i 0.106668 + 0.554262i
\(792\) 0 0
\(793\) 21.0000 36.3731i 0.745732 1.29165i
\(794\) −37.0000 64.0859i −1.31308 2.27432i
\(795\) 0 0
\(796\) −8.00000 + 13.8564i −0.283552 + 0.491127i
\(797\) 36.0000 1.27519 0.637593 0.770374i \(-0.279930\pi\)
0.637593 + 0.770374i \(0.279930\pi\)
\(798\) 5.00000 + 1.73205i 0.176998 + 0.0613139i
\(799\) −8.00000 −0.283020
\(800\) 0 0
\(801\) 6.00000 + 10.3923i 0.212000 + 0.367194i
\(802\) 12.0000 + 20.7846i 0.423735 + 0.733930i
\(803\) −3.00000 + 5.19615i −0.105868 + 0.183368i
\(804\) 14.0000 0.493742
\(805\) 0 0
\(806\) 6.00000 0.211341
\(807\) −5.00000 + 8.66025i −0.176008 + 0.304855i
\(808\) 0 0
\(809\) 21.0000 + 36.3731i 0.738321 + 1.27881i 0.953251 + 0.302180i \(0.0977142\pi\)
−0.214930 + 0.976629i \(0.568952\pi\)
\(810\) 0 0
\(811\) −48.0000 −1.68551 −0.842754 0.538299i \(-0.819067\pi\)
−0.842754 + 0.538299i \(0.819067\pi\)
\(812\) −32.0000 + 27.7128i −1.12298 + 0.972529i
\(813\) 24.0000 0.841717
\(814\) −42.0000 + 72.7461i −1.47210 + 2.54975i
\(815\) 0 0
\(816\) −8.00000 13.8564i −0.280056 0.485071i
\(817\) 0.500000 0.866025i 0.0174928 0.0302984i
\(818\) 10.0000 0.349642
\(819\) −7.50000 2.59808i −0.262071 0.0907841i
\(820\) 0 0
\(821\) −27.0000 + 46.7654i −0.942306 + 1.63212i −0.181250 + 0.983437i \(0.558014\pi\)
−0.761056 + 0.648686i \(0.775319\pi\)
\(822\) −8.00000 13.8564i −0.279032 0.483298i
\(823\) 4.00000 + 6.92820i 0.139431 + 0.241502i 0.927281 0.374365i \(-0.122139\pi\)
−0.787850 + 0.615867i \(0.788806\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −8.00000 41.5692i −0.278356 1.44638i
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) −4.00000 + 6.92820i −0.139010 + 0.240772i
\(829\) −28.5000 49.3634i −0.989846 1.71446i −0.618024 0.786159i \(-0.712066\pi\)
−0.371822 0.928304i \(-0.621267\pi\)
\(830\) 0 0
\(831\) 3.50000 6.06218i 0.121414 0.210295i
\(832\) −24.0000 −0.832050
\(833\) 22.0000 + 17.3205i 0.762255 + 0.600120i
\(834\) −42.0000 −1.45434
\(835\) 0 0
\(836\) 6.00000 + 10.3923i 0.207514 + 0.359425i
\(837\) 0.500000 + 0.866025i 0.0172825 + 0.0299342i
\(838\) −6.00000 + 10.3923i −0.207267 + 0.358996i
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) −1.00000 + 1.73205i −0.0344623 + 0.0596904i
\(843\) −6.00000 10.3923i −0.206651 0.357930i
\(844\) 20.0000 + 34.6410i 0.688428 + 1.19239i
\(845\) 0 0
\(846\) −4.00000 −0.137523
\(847\) −62.5000 21.6506i −2.14753 0.743925i
\(848\) 16.0000 0.549442
\(849\) 3.50000 6.06218i 0.120120 0.208053i
\(850\) 0 0
\(851\) 14.0000 + 24.2487i 0.479914 + 0.831235i
\(852\) 6.00000 10.3923i 0.205557 0.356034i
\(853\) 9.00000 0.308154 0.154077 0.988059i \(-0.450760\pi\)
0.154077 + 0.988059i \(0.450760\pi\)
\(854\) −56.0000 + 48.4974i −1.91628 + 1.65955i
\(855\) 0 0
\(856\) 0 0
\(857\) −6.00000 10.3923i −0.204956 0.354994i 0.745163 0.666883i \(-0.232372\pi\)
−0.950119 + 0.311888i \(0.899038\pi\)
\(858\) −18.0000 31.1769i −0.614510 1.06436i
\(859\) 20.0000 34.6410i 0.682391 1.18194i −0.291858 0.956462i \(-0.594273\pi\)
0.974249 0.225475i \(-0.0723932\pi\)
\(860\) 0 0
\(861\) 12.0000 10.3923i 0.408959 0.354169i
\(862\) −4.00000 −0.136241
\(863\) −3.00000 + 5.19615i −0.102121 + 0.176879i −0.912558 0.408946i \(-0.865896\pi\)
0.810437 + 0.585826i \(0.199230\pi\)
\(864\) −4.00000 6.92820i −0.136083 0.235702i
\(865\) 0 0
\(866\) −5.00000 + 8.66025i −0.169907 + 0.294287i
\(867\) 1.00000 0.0339618
\(868\) −5.00000 1.73205i −0.169711 0.0587896i
\(869\) 6.00000 0.203536
\(870\) 0 0
\(871\) 10.5000 + 18.1865i 0.355779 + 0.616227i
\(872\) 0 0
\(873\) −3.00000 + 5.19615i −0.101535 + 0.175863i
\(874\) 8.00000 0.270604
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −11.0000 + 19.0526i −0.371444 + 0.643359i −0.989788 0.142548i \(-0.954470\pi\)
0.618344 + 0.785907i \(0.287804\pi\)
\(878\) −16.0000 27.7128i −0.539974 0.935262i
\(879\) 8.00000 + 13.8564i 0.269833 + 0.467365i
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 11.0000 + 8.66025i 0.370389 + 0.291606i
\(883\) −7.00000 −0.235569 −0.117784 0.993039i \(-0.537579\pi\)
−0.117784 + 0.993039i \(0.537579\pi\)
\(884\) −12.0000 + 20.7846i −0.403604 + 0.699062i
\(885\) 0 0
\(886\) −36.0000 62.3538i −1.20944 2.09482i
\(887\) 5.00000 8.66025i 0.167884 0.290783i −0.769792 0.638295i \(-0.779640\pi\)
0.937676 + 0.347512i \(0.112973\pi\)
\(888\) 0 0
\(889\) −2.50000 12.9904i −0.0838473 0.435683i
\(890\) 0 0
\(891\) 3.00000 5.19615i 0.100504 0.174078i
\(892\) −24.0000 41.5692i −0.803579 1.39184i
\(893\) 1.00000 + 1.73205i 0.0334637 + 0.0579609i
\(894\) −4.00000 + 6.92820i −0.133780 + 0.231714i
\(895\) 0 0
\(896\) 0 0
\(897\) −12.0000 −0.400668
\(898\) −30.0000 + 51.9615i −1.00111 + 1.73398i
\(899\) 4.00000 + 6.92820i 0.133407 + 0.231069i
\(900\) 0 0
\(901\) 8.00000 13.8564i 0.266519 0.461624i
\(902\) 72.0000 2.39734
\(903\) 2.00000 1.73205i 0.0665558 0.0576390i
\(904\) 0 0
\(905\) 0 0
\(906\) 8.00000 + 13.8564i 0.265782 + 0.460348i
\(907\) 15.5000 + 26.8468i 0.514669 + 0.891433i 0.999855 + 0.0170220i \(0.00541854\pi\)
−0.485186 + 0.874411i \(0.661248\pi\)
\(908\) −10.0000 + 17.3205i −0.331862 + 0.574801i
\(909\) −10.0000 −0.331679
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −2.00000 + 3.46410i −0.0662266 + 0.114708i
\(913\) −6.00000 10.3923i −0.198571 0.343935i
\(914\) −15.0000 25.9808i −0.496156 0.859367i
\(915\) 0 0
\(916\) 26.0000 0.859064
\(917\) −5.00000 1.73205i −0.165115 0.0571974i
\(918\) −8.00000 −0.264039
\(919\) 4.50000 7.79423i 0.148441 0.257108i −0.782210 0.623015i \(-0.785908\pi\)
0.930652 + 0.365907i \(0.119241\pi\)
\(920\) 0 0
\(921\) −1.50000 2.59808i −0.0494267 0.0856095i
\(922\) 8.00000 13.8564i 0.263466 0.456336i
\(923\) 18.0000 0.592477
\(924\) 6.00000 + 31.1769i 0.197386 + 1.02565i
\(925\) 0 0
\(926\) 3.00000 5.19615i 0.0985861 0.170756i
\(927\) −9.50000 16.4545i −0.312021 0.540436i
\(928\) −32.0000 55.4256i −1.05045 1.81944i
\(929\) 7.00000 12.1244i 0.229663 0.397787i −0.728046 0.685529i \(-0.759571\pi\)
0.957708 + 0.287742i \(0.0929044\pi\)
\(930\) 0 0
\(931\) 1.00000 6.92820i 0.0327737 0.227063i
\(932\) −12.0000 −0.393073
\(933\) 3.00000 5.19615i 0.0982156 0.170114i
\(934\) 22.0000 + 38.1051i 0.719862 + 1.24684i
\(935\) 0 0
\(936\) 0 0
\(937\) 29.0000 0.947389 0.473694 0.880689i \(-0.342920\pi\)
0.473694 + 0.880689i \(0.342920\pi\)
\(938\) −7.00000 36.3731i −0.228558 1.18762i
\(939\) 11.0000 0.358971
\(940\) 0 0
\(941\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(942\) −10.0000 17.3205i −0.325818 0.564333i
\(943\) 12.0000 20.7846i 0.390774 0.676840i
\(944\) 32.0000 1.04151
\(945\) 0 0
\(946\) 12.0000 0.390154
\(947\) 13.0000 22.5167i 0.422443 0.731693i −0.573735 0.819041i \(-0.694506\pi\)
0.996178 + 0.0873481i \(0.0278392\pi\)
\(948\) −1.00000 1.73205i −0.0324785 0.0562544i
\(949\) 1.50000 + 2.59808i 0.0486921 + 0.0843371i
\(950\) 0 0
\(951\) 20.0000 0.648544
\(952\) 0 0
\(953\) −4.00000 −0.129573 −0.0647864 0.997899i \(-0.520637\pi\)
−0.0647864 + 0.997899i \(0.520637\pi\)
\(954\) 4.00000 6.92820i 0.129505 0.224309i
\(955\) 0 0
\(956\) −14.0000 24.2487i −0.452792 0.784259i
\(957\) 24.0000 41.5692i 0.775810 1.34374i
\(958\) −8.00000 −0.258468
\(959\) −16.0000 + 13.8564i −0.516667 + 0.447447i
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) 21.0000 + 36.3731i 0.677067 + 1.17271i
\(963\) 6.00000 + 10.3923i 0.193347 + 0.334887i
\(964\) 18.0000 31.1769i 0.579741 1.00414i
\(965\) 0 0
\(966\) 20.0000 + 6.92820i 0.643489 + 0.222911i
\(967\) −55.0000 −1.76868 −0.884340 0.466843i \(-0.845391\pi\)
−0.884340 + 0.466843i \(0.845391\pi\)
\(968\) 0 0
\(969\) 2.00000 + 3.46410i 0.0642493 + 0.111283i
\(970\) 0 0
\(971\) 26.0000 45.0333i 0.834380 1.44519i −0.0601548 0.998189i \(-0.519159\pi\)
0.894534 0.446999i \(-0.147507\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 10.5000 + 54.5596i 0.336615 + 1.74910i
\(974\) 26.0000 0.833094
\(975\) 0 0
\(976\) −28.0000 48.4974i −0.896258 1.55236i
\(977\) −11.0000 19.0526i −0.351921 0.609545i 0.634665 0.772787i \(-0.281138\pi\)
−0.986586 + 0.163242i \(0.947805\pi\)
\(978\) 12.0000 20.7846i 0.383718 0.664619i
\(979\) 72.0000 2.30113
\(980\) 0 0
\(981\) −15.0000 −0.478913
\(982\) 12.0000 20.7846i 0.382935 0.663264i
\(983\) 16.0000 + 27.7128i 0.510321 + 0.883901i 0.999928 + 0.0119587i \(0.00380665\pi\)
−0.489608 + 0.871943i \(0.662860\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −64.0000 −2.03818
\(987\) 1.00000 + 5.19615i 0.0318304 + 0.165395i
\(988\) 6.00000 0.190885
\(989\) 2.00000 3.46410i 0.0635963 0.110152i
\(990\) 0 0
\(991\) 7.50000 + 12.9904i 0.238245 + 0.412653i 0.960211 0.279276i \(-0.0900944\pi\)
−0.721966 + 0.691929i \(0.756761\pi\)
\(992\) 4.00000 6.92820i 0.127000 0.219971i
\(993\) 9.00000 0.285606
\(994\) −30.0000 10.3923i −0.951542 0.329624i
\(995\) 0 0
\(996\) −2.00000 + 3.46410i −0.0633724 + 0.109764i
\(997\) −12.5000 21.6506i −0.395879 0.685682i 0.597334 0.801993i \(-0.296227\pi\)
−0.993213 + 0.116310i \(0.962893\pi\)
\(998\) −29.0000 50.2295i −0.917979 1.58999i
\(999\) −3.50000 + 6.06218i −0.110735 + 0.191799i
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 525.2.i.a.226.1 2
5.2 odd 4 525.2.r.d.499.1 4
5.3 odd 4 525.2.r.d.499.2 4
5.4 even 2 105.2.i.b.16.1 2
7.2 even 3 3675.2.a.o.1.1 1
7.4 even 3 inner 525.2.i.a.151.1 2
7.5 odd 6 3675.2.a.p.1.1 1
15.14 odd 2 315.2.j.a.226.1 2
20.19 odd 2 1680.2.bg.l.961.1 2
35.4 even 6 105.2.i.b.46.1 yes 2
35.9 even 6 735.2.a.b.1.1 1
35.18 odd 12 525.2.r.d.424.1 4
35.19 odd 6 735.2.a.a.1.1 1
35.24 odd 6 735.2.i.f.361.1 2
35.32 odd 12 525.2.r.d.424.2 4
35.34 odd 2 735.2.i.f.226.1 2
105.44 odd 6 2205.2.a.k.1.1 1
105.74 odd 6 315.2.j.a.46.1 2
105.89 even 6 2205.2.a.m.1.1 1
140.39 odd 6 1680.2.bg.l.1201.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.i.b.16.1 2 5.4 even 2
105.2.i.b.46.1 yes 2 35.4 even 6
315.2.j.a.46.1 2 105.74 odd 6
315.2.j.a.226.1 2 15.14 odd 2
525.2.i.a.151.1 2 7.4 even 3 inner
525.2.i.a.226.1 2 1.1 even 1 trivial
525.2.r.d.424.1 4 35.18 odd 12
525.2.r.d.424.2 4 35.32 odd 12
525.2.r.d.499.1 4 5.2 odd 4
525.2.r.d.499.2 4 5.3 odd 4
735.2.a.a.1.1 1 35.19 odd 6
735.2.a.b.1.1 1 35.9 even 6
735.2.i.f.226.1 2 35.34 odd 2
735.2.i.f.361.1 2 35.24 odd 6
1680.2.bg.l.961.1 2 20.19 odd 2
1680.2.bg.l.1201.1 2 140.39 odd 6
2205.2.a.k.1.1 1 105.44 odd 6
2205.2.a.m.1.1 1 105.89 even 6
3675.2.a.o.1.1 1 7.2 even 3
3675.2.a.p.1.1 1 7.5 odd 6