Properties

Label 525.2.r.d.499.2
Level $525$
Weight $2$
Character 525.499
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(424,525)]
 
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, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.424");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) 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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 499.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.499
Dual form 525.2.r.d.424.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 + 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.73205 + 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(-1.73205 - 1.00000i) q^{12} +3.00000i q^{13} +(5.00000 + 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(1.73205 - 1.00000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} +12.0000i q^{22} +(-3.46410 - 2.00000i) q^{23} +(-3.00000 + 5.19615i) q^{26} +1.00000i q^{27} +(3.46410 + 4.00000i) q^{28} +8.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(6.92820 - 4.00000i) q^{32} +(-5.19615 - 3.00000i) q^{33} -8.00000 q^{34} +2.00000 q^{36} +(-6.06218 - 3.50000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(-1.50000 - 2.59808i) q^{39} -6.00000 q^{41} +(-5.19615 + 1.00000i) q^{42} -1.00000i q^{43} +(-6.00000 + 10.3923i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(-1.73205 - 1.00000i) q^{47} +4.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(-5.19615 + 3.00000i) q^{52} +(-3.46410 + 2.00000i) q^{53} +(-1.00000 + 1.73205i) q^{54} +1.00000i q^{57} +(13.8564 + 8.00000i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(7.00000 - 12.1244i) q^{61} -2.00000i q^{62} +(0.866025 - 2.50000i) q^{63} +8.00000 q^{64} +(-6.00000 - 10.3923i) q^{66} +(6.06218 - 3.50000i) q^{67} +(-6.92820 - 4.00000i) q^{68} +4.00000 q^{69} +6.00000 q^{71} +(-0.866025 + 0.500000i) q^{73} +(-7.00000 - 12.1244i) q^{74} +2.00000 q^{76} +(10.3923 + 12.0000i) q^{77} -6.00000i q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-10.3923 - 6.00000i) q^{82} -2.00000i q^{83} +(-5.00000 - 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-6.92820 + 4.00000i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(1.50000 + 7.79423i) q^{91} -8.00000i q^{92} +(0.866025 + 0.500000i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(-4.00000 + 6.92820i) q^{96} -6.00000i q^{97} +(13.8564 + 2.00000i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} - 8 q^{6} + 2 q^{9} + 12 q^{11} + 20 q^{14} + 8 q^{16} + 2 q^{19} - 8 q^{21} - 12 q^{26} + 32 q^{29} - 2 q^{31} - 32 q^{34} + 8 q^{36} - 6 q^{39} - 24 q^{41} - 24 q^{44} - 16 q^{46} + 26 q^{49} + 8 q^{51} - 4 q^{54} - 16 q^{59} + 28 q^{61} + 32 q^{64} - 24 q^{66} + 16 q^{69} + 24 q^{71} - 28 q^{74} + 8 q^{76} - 2 q^{79} - 2 q^{81} - 20 q^{84} + 4 q^{86} - 24 q^{89} + 6 q^{91} - 8 q^{94} - 16 q^{96} + 24 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 + 1.00000i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 0 0
\(6\) −2.00000 −0.816497
\(7\) 2.59808 0.500000i 0.981981 0.188982i
\(8\) 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 \(0.473552\pi\)
\(12\) −1.73205 1.00000i −0.500000 0.288675i
\(13\) 3.00000i 0.832050i 0.909353 + 0.416025i \(0.136577\pi\)
−0.909353 + 0.416025i \(0.863423\pi\)
\(14\) 5.00000 + 1.73205i 1.33631 + 0.462910i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −3.46410 + 2.00000i −0.840168 + 0.485071i −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) 1.73205 1.00000i 0.408248 0.235702i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 12.0000i 2.55841i
\(23\) −3.46410 2.00000i −0.722315 0.417029i 0.0932891 0.995639i \(-0.470262\pi\)
−0.815604 + 0.578610i \(0.803595\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) 1.00000i 0.192450i
\(28\) 3.46410 + 4.00000i 0.654654 + 0.755929i
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 6.92820 4.00000i 1.22474 0.707107i
\(33\) −5.19615 3.00000i −0.904534 0.522233i
\(34\) −8.00000 −1.37199
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −6.06218 3.50000i −0.996616 0.575396i −0.0893706 0.995998i \(-0.528486\pi\)
−0.907245 + 0.420602i \(0.861819\pi\)
\(38\) 1.73205 1.00000i 0.280976 0.162221i
\(39\) −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 \(0.655213\pi\)
\(42\) −5.19615 + 1.00000i −0.801784 + 0.154303i
\(43\) 1.00000i 0.152499i −0.997089 0.0762493i \(-0.975706\pi\)
0.997089 0.0762493i \(-0.0242945\pi\)
\(44\) −6.00000 + 10.3923i −0.904534 + 1.56670i
\(45\) 0 0
\(46\) −4.00000 6.92820i −0.589768 1.02151i
\(47\) −1.73205 1.00000i −0.252646 0.145865i 0.368329 0.929695i \(-0.379930\pi\)
−0.620975 + 0.783830i \(0.713263\pi\)
\(48\) 4.00000i 0.577350i
\(49\) 6.50000 2.59808i 0.928571 0.371154i
\(50\) 0 0
\(51\) 2.00000 3.46410i 0.280056 0.485071i
\(52\) −5.19615 + 3.00000i −0.720577 + 0.416025i
\(53\) −3.46410 + 2.00000i −0.475831 + 0.274721i −0.718677 0.695344i \(-0.755252\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(54\) −1.00000 + 1.73205i −0.136083 + 0.235702i
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 13.8564 + 8.00000i 1.81944 + 1.05045i
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i \(-0.479608\pi\)
0.832240 0.554416i \(-0.187058\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0.866025 2.50000i 0.109109 0.314970i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) −6.00000 10.3923i −0.738549 1.27920i
\(67\) 6.06218 3.50000i 0.740613 0.427593i −0.0816792 0.996659i \(-0.526028\pi\)
0.822292 + 0.569066i \(0.192695\pi\)
\(68\) −6.92820 4.00000i −0.840168 0.485071i
\(69\) 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
\(73\) −0.866025 + 0.500000i −0.101361 + 0.0585206i −0.549823 0.835281i \(-0.685305\pi\)
0.448463 + 0.893801i \(0.351972\pi\)
\(74\) −7.00000 12.1244i −0.813733 1.40943i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 10.3923 + 12.0000i 1.18431 + 1.36753i
\(78\) 6.00000i 0.679366i
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −10.3923 6.00000i −1.14764 0.662589i
\(83\) 2.00000i 0.219529i −0.993958 0.109764i \(-0.964990\pi\)
0.993958 0.109764i \(-0.0350096\pi\)
\(84\) −5.00000 1.73205i −0.545545 0.188982i
\(85\) 0 0
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −6.92820 + 4.00000i −0.742781 + 0.428845i
\(88\) 0 0
\(89\) −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i \(0.386078\pi\)
−0.986303 + 0.164946i \(0.947255\pi\)
\(90\) 0 0
\(91\) 1.50000 + 7.79423i 0.157243 + 0.817057i
\(92\) 8.00000i 0.834058i
\(93\) 0.866025 + 0.500000i 0.0898027 + 0.0518476i
\(94\) −2.00000 3.46410i −0.206284 0.357295i
\(95\) 0 0
\(96\) −4.00000 + 6.92820i −0.408248 + 0.707107i
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 13.8564 + 2.00000i 1.39971 + 0.202031i
\(99\) 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 \(0.667578\pi\)
\(102\) 6.92820 4.00000i 0.685994 0.396059i
\(103\) −16.4545 9.50000i −1.62131 0.936063i −0.986571 0.163335i \(-0.947775\pi\)
−0.634738 0.772728i \(-0.718892\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −8.00000 −0.777029
\(107\) −10.3923 6.00000i −1.00466 0.580042i −0.0950377 0.995474i \(-0.530297\pi\)
−0.909624 + 0.415432i \(0.863630\pi\)
\(108\) −1.73205 + 1.00000i −0.166667 + 0.0962250i
\(109\) −7.50000 12.9904i −0.718370 1.24425i −0.961645 0.274296i \(-0.911555\pi\)
0.243276 0.969957i \(-0.421778\pi\)
\(110\) 0 0
\(111\) 7.00000 0.664411
\(112\) 3.46410 10.0000i 0.327327 0.944911i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) 0 0
\(116\) 8.00000 + 13.8564i 0.742781 + 1.28654i
\(117\) 2.59808 + 1.50000i 0.240192 + 0.138675i
\(118\) 16.0000i 1.47292i
\(119\) −8.00000 + 6.92820i −0.733359 + 0.635107i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 24.2487 14.0000i 2.19538 1.26750i
\(123\) 5.19615 3.00000i 0.468521 0.270501i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 0 0
\(126\) 4.00000 3.46410i 0.356348 0.308607i
\(127\) 5.00000i 0.443678i 0.975083 + 0.221839i \(0.0712060\pi\)
−0.975083 + 0.221839i \(0.928794\pi\)
\(128\) 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 \(0.194513\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 0.866025 2.50000i 0.0750939 0.216777i
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) 0 0
\(137\) 6.92820 4.00000i 0.591916 0.341743i −0.173939 0.984757i \(-0.555649\pi\)
0.765855 + 0.643013i \(0.222316\pi\)
\(138\) 6.92820 + 4.00000i 0.589768 + 0.340503i
\(139\) −21.0000 −1.78120 −0.890598 0.454791i \(-0.849714\pi\)
−0.890598 + 0.454791i \(0.849714\pi\)
\(140\) 0 0
\(141\) 2.00000 0.168430
\(142\) 10.3923 + 6.00000i 0.872103 + 0.503509i
\(143\) −15.5885 + 9.00000i −1.30357 + 0.752618i
\(144\) −2.00000 3.46410i −0.166667 0.288675i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −4.33013 + 5.50000i −0.357143 + 0.453632i
\(148\) 14.0000i 1.15079i
\(149\) −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i \(-0.885723\pi\)
0.772399 + 0.635138i \(0.219057\pi\)
\(150\) 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
\(153\) 4.00000i 0.323381i
\(154\) 6.00000 + 31.1769i 0.483494 + 2.51231i
\(155\) 0 0
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) 8.66025 5.00000i 0.691164 0.399043i −0.112884 0.993608i \(-0.536009\pi\)
0.804048 + 0.594565i \(0.202676\pi\)
\(158\) −1.73205 + 1.00000i −0.137795 + 0.0795557i
\(159\) 2.00000 3.46410i 0.158610 0.274721i
\(160\) 0 0
\(161\) −10.0000 3.46410i −0.788110 0.273009i
\(162\) 2.00000i 0.157135i
\(163\) −10.3923 6.00000i −0.813988 0.469956i 0.0343508 0.999410i \(-0.489064\pi\)
−0.848339 + 0.529454i \(0.822397\pi\)
\(164\) −6.00000 10.3923i −0.468521 0.811503i
\(165\) 0 0
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) 10.0000i 0.773823i −0.922117 0.386912i \(-0.873542\pi\)
0.922117 0.386912i \(-0.126458\pi\)
\(168\) 0 0
\(169\) 4.00000 0.307692
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 1.73205 1.00000i 0.132068 0.0762493i
\(173\) 20.7846 + 12.0000i 1.58022 + 0.912343i 0.994826 + 0.101598i \(0.0323955\pi\)
0.585399 + 0.810745i \(0.300938\pi\)
\(174\) −16.0000 −1.21296
\(175\) 0 0
\(176\) 24.0000 1.80907
\(177\) 6.92820 + 4.00000i 0.520756 + 0.300658i
\(178\) −20.7846 + 12.0000i −1.55787 + 0.899438i
\(179\) 9.00000 + 15.5885i 0.672692 + 1.16514i 0.977138 + 0.212607i \(0.0681952\pi\)
−0.304446 + 0.952529i \(0.598471\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) −5.19615 + 15.0000i −0.385164 + 1.11187i
\(183\) 14.0000i 1.03491i
\(184\) 0 0
\(185\) 0 0
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) −20.7846 12.0000i −1.51992 0.877527i
\(188\) 4.00000i 0.291730i
\(189\) 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 \(0.284500\pi\)
\(192\) −6.92820 + 4.00000i −0.500000 + 0.288675i
\(193\) 7.79423 4.50000i 0.561041 0.323917i −0.192522 0.981293i \(-0.561667\pi\)
0.753563 + 0.657376i \(0.228333\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) 0 0
\(196\) 11.0000 + 8.66025i 0.785714 + 0.618590i
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 10.3923 + 6.00000i 0.738549 + 0.426401i
\(199\) 4.00000 + 6.92820i 0.283552 + 0.491127i 0.972257 0.233915i \(-0.0751537\pi\)
−0.688705 + 0.725042i \(0.741820\pi\)
\(200\) 0 0
\(201\) −3.50000 + 6.06218i −0.246871 + 0.427593i
\(202\) 20.0000i 1.40720i
\(203\) 20.7846 4.00000i 1.45879 0.280745i
\(204\) 8.00000 0.560112
\(205\) 0 0
\(206\) −19.0000 32.9090i −1.32379 2.29288i
\(207\) −3.46410 + 2.00000i −0.240772 + 0.139010i
\(208\) 10.3923 + 6.00000i 0.720577 + 0.416025i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −6.92820 4.00000i −0.475831 0.274721i
\(213\) −5.19615 + 3.00000i −0.356034 + 0.205557i
\(214\) −12.0000 20.7846i −0.820303 1.42081i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.73205 2.00000i −0.117579 0.135769i
\(218\) 30.0000i 2.03186i
\(219\) 0.500000 0.866025i 0.0337869 0.0585206i
\(220\) 0 0
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 12.1244 + 7.00000i 0.813733 + 0.469809i
\(223\) 24.0000i 1.60716i 0.595198 + 0.803579i \(0.297074\pi\)
−0.595198 + 0.803579i \(0.702926\pi\)
\(224\) 16.0000 13.8564i 1.06904 0.925820i
\(225\) 0 0
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) −8.66025 + 5.00000i −0.574801 + 0.331862i −0.759065 0.651015i \(-0.774343\pi\)
0.184263 + 0.982877i \(0.441010\pi\)
\(228\) −1.73205 + 1.00000i −0.114708 + 0.0662266i
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) 0 0
\(231\) −15.0000 5.19615i −0.986928 0.341882i
\(232\) 0 0
\(233\) 5.19615 + 3.00000i 0.340411 + 0.196537i 0.660454 0.750867i \(-0.270364\pi\)
−0.320043 + 0.947403i \(0.603697\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) 8.00000 13.8564i 0.520756 0.901975i
\(237\) 1.00000i 0.0649570i
\(238\) −20.7846 + 4.00000i −1.34727 + 0.259281i
\(239\) −14.0000 −0.905585 −0.452792 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(240\) 0 0
\(241\) 9.00000 + 15.5885i 0.579741 + 1.00414i 0.995509 + 0.0946700i \(0.0301796\pi\)
−0.415768 + 0.909471i \(0.636487\pi\)
\(242\) −43.3013 + 25.0000i −2.78351 + 1.60706i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 28.0000 1.79252
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 2.59808 + 1.50000i 0.165312 + 0.0954427i
\(248\) 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 \(0.376365\pi\)
\(252\) 5.19615 1.00000i 0.327327 0.0629941i
\(253\) 24.0000i 1.50887i
\(254\) −5.00000 + 8.66025i −0.313728 + 0.543393i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) 2.00000i 0.124515i
\(259\) −17.5000 6.06218i −1.08740 0.376685i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) −3.46410 + 2.00000i −0.214013 + 0.123560i
\(263\) −3.46410 + 2.00000i −0.213606 + 0.123325i −0.602986 0.797752i \(-0.706023\pi\)
0.389380 + 0.921077i \(0.372689\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) 12.0000i 0.734388i
\(268\) 12.1244 + 7.00000i 0.740613 + 0.427593i
\(269\) −5.00000 8.66025i −0.304855 0.528025i 0.672374 0.740212i \(-0.265275\pi\)
−0.977229 + 0.212187i \(0.931941\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 16.0000i 0.970143i
\(273\) −5.19615 6.00000i −0.314485 0.363137i
\(274\) 16.0000 0.966595
\(275\) 0 0
\(276\) 4.00000 + 6.92820i 0.240772 + 0.417029i
\(277\) −6.06218 + 3.50000i −0.364241 + 0.210295i −0.670940 0.741512i \(-0.734109\pi\)
0.306699 + 0.951807i \(0.400776\pi\)
\(278\) −36.3731 21.0000i −2.18151 1.25950i
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 3.46410 + 2.00000i 0.206284 + 0.119098i
\(283\) 6.06218 3.50000i 0.360359 0.208053i −0.308879 0.951101i \(-0.599954\pi\)
0.669238 + 0.743048i \(0.266621\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) −36.0000 −2.12872
\(287\) −15.5885 + 3.00000i −0.920158 + 0.177084i
\(288\) 8.00000i 0.471405i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) −1.73205 1.00000i −0.101361 0.0585206i
\(293\) 16.0000i 0.934730i 0.884064 + 0.467365i \(0.154797\pi\)
−0.884064 + 0.467365i \(0.845203\pi\)
\(294\) −13.0000 + 5.19615i −0.758175 + 0.303046i
\(295\) 0 0
\(296\) 0 0
\(297\) −5.19615 + 3.00000i −0.301511 + 0.174078i
\(298\) −6.92820 + 4.00000i −0.401340 + 0.231714i
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) −0.500000 2.59808i −0.0288195 0.149751i
\(302\) 16.0000i 0.920697i
\(303\) −8.66025 5.00000i −0.497519 0.287242i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) 0 0
\(306\) −4.00000 + 6.92820i −0.228665 + 0.396059i
\(307\) 3.00000i 0.171219i 0.996329 + 0.0856095i \(0.0272838\pi\)
−0.996329 + 0.0856095i \(0.972716\pi\)
\(308\) −10.3923 + 30.0000i −0.592157 + 1.70941i
\(309\) 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
\(313\) 9.52628 + 5.50000i 0.538457 + 0.310878i 0.744453 0.667674i \(-0.232710\pi\)
−0.205996 + 0.978553i \(0.566043\pi\)
\(314\) 20.0000 1.12867
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) −17.3205 10.0000i −0.972817 0.561656i −0.0727229 0.997352i \(-0.523169\pi\)
−0.900094 + 0.435696i \(0.856502\pi\)
\(318\) 6.92820 4.00000i 0.388514 0.224309i
\(319\) 24.0000 + 41.5692i 1.34374 + 2.32743i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) −13.8564 16.0000i −0.772187 0.891645i
\(323\) 4.00000i 0.222566i
\(324\) 1.00000 1.73205i 0.0555556 0.0962250i
\(325\) 0 0
\(326\) −12.0000 20.7846i −0.664619 1.15115i
\(327\) 12.9904 + 7.50000i 0.718370 + 0.414751i
\(328\) 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 \(0.0871094\pi\)
\(332\) 3.46410 2.00000i 0.190117 0.109764i
\(333\) −6.06218 + 3.50000i −0.332205 + 0.191799i
\(334\) 10.0000 17.3205i 0.547176 0.947736i
\(335\) 0 0
\(336\) 2.00000 + 10.3923i 0.109109 + 0.566947i
\(337\) 25.0000i 1.36184i 0.732359 + 0.680918i \(0.238419\pi\)
−0.732359 + 0.680918i \(0.761581\pi\)
\(338\) 6.92820 + 4.00000i 0.376845 + 0.217571i
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 2.00000i 0.108148i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 24.0000 + 41.5692i 1.29025 + 2.23478i
\(347\) 13.8564 8.00000i 0.743851 0.429463i −0.0796169 0.996826i \(-0.525370\pi\)
0.823468 + 0.567363i \(0.192036\pi\)
\(348\) −13.8564 8.00000i −0.742781 0.428845i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −3.00000 −0.160128
\(352\) 41.5692 + 24.0000i 2.21565 + 1.27920i
\(353\) 15.5885 9.00000i 0.829690 0.479022i −0.0240566 0.999711i \(-0.507658\pi\)
0.853746 + 0.520689i \(0.174325\pi\)
\(354\) 8.00000 + 13.8564i 0.425195 + 0.736460i
\(355\) 0 0
\(356\) −24.0000 −1.27200
\(357\) 3.46410 10.0000i 0.183340 0.529256i
\(358\) 36.0000i 1.90266i
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 22.5167 + 13.0000i 1.18345 + 0.683265i
\(363\) 25.0000i 1.31216i
\(364\) −12.0000 + 10.3923i −0.628971 + 0.544705i
\(365\) 0 0
\(366\) −14.0000 + 24.2487i −0.731792 + 1.26750i
\(367\) 16.4545 9.50000i 0.858917 0.495896i −0.00473247 0.999989i \(-0.501506\pi\)
0.863649 + 0.504093i \(0.168173\pi\)
\(368\) −13.8564 + 8.00000i −0.722315 + 0.417029i
\(369\) −3.00000 + 5.19615i −0.156174 + 0.270501i
\(370\) 0 0
\(371\) −8.00000 + 6.92820i −0.415339 + 0.359694i
\(372\) 2.00000i 0.103695i
\(373\) 9.52628 + 5.50000i 0.493252 + 0.284779i 0.725923 0.687776i \(-0.241413\pi\)
−0.232671 + 0.972556i \(0.574746\pi\)
\(374\) −24.0000 41.5692i −1.24101 2.14949i
\(375\) 0 0
\(376\) 0 0
\(377\) 24.0000i 1.23606i
\(378\) −1.73205 + 5.00000i −0.0890871 + 0.257172i
\(379\) −11.0000 −0.565032 −0.282516 0.959263i \(-0.591169\pi\)
−0.282516 + 0.959263i \(0.591169\pi\)
\(380\) 0 0
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) −17.3205 + 10.0000i −0.886194 + 0.511645i
\(383\) 24.2487 + 14.0000i 1.23905 + 0.715367i 0.968900 0.247451i \(-0.0795931\pi\)
0.270151 + 0.962818i \(0.412926\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.0000 0.916176
\(387\) −0.866025 0.500000i −0.0440225 0.0254164i
\(388\) 10.3923 6.00000i 0.527589 0.304604i
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 2.00000i 0.100887i
\(394\) −12.0000 + 20.7846i −0.604551 + 1.04711i
\(395\) 0 0
\(396\) 6.00000 + 10.3923i 0.301511 + 0.522233i
\(397\) 32.0429 + 18.5000i 1.60819 + 0.928488i 0.989775 + 0.142636i \(0.0455577\pi\)
0.618414 + 0.785853i \(0.287776\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 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 \(0.0698049\pi\)
\(402\) −12.1244 + 7.00000i −0.604708 + 0.349128i
\(403\) 2.59808 1.50000i 0.129419 0.0747203i
\(404\) −10.0000 + 17.3205i −0.497519 + 0.861727i
\(405\) 0 0
\(406\) 40.0000 + 13.8564i 1.98517 + 0.687682i
\(407\) 42.0000i 2.08186i
\(408\) 0 0
\(409\) 2.50000 + 4.33013i 0.123617 + 0.214111i 0.921192 0.389109i \(-0.127217\pi\)
−0.797574 + 0.603220i \(0.793884\pi\)
\(410\) 0 0
\(411\) −4.00000 + 6.92820i −0.197305 + 0.341743i
\(412\) 38.0000i 1.87213i
\(413\) −13.8564 16.0000i −0.681829 0.787309i
\(414\) −8.00000 −0.393179
\(415\) 0 0
\(416\) 12.0000 + 20.7846i 0.588348 + 1.01905i
\(417\) 18.1865 10.5000i 0.890598 0.514187i
\(418\) 10.3923 + 6.00000i 0.508304 + 0.293470i
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 0 0
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) −34.6410 20.0000i −1.68630 0.973585i
\(423\) −1.73205 + 1.00000i −0.0842152 + 0.0486217i
\(424\) 0 0
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 12.1244 35.0000i 0.586739 1.69377i
\(428\) 24.0000i 1.16008i
\(429\) 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 \(0.817995\pi\)
\(432\) 3.46410 + 2.00000i 0.166667 + 0.0962250i
\(433\) 5.00000i 0.240285i 0.992757 + 0.120142i \(0.0383351\pi\)
−0.992757 + 0.120142i \(0.961665\pi\)
\(434\) −1.00000 5.19615i −0.0480015 0.249423i
\(435\) 0 0
\(436\) 15.0000 25.9808i 0.718370 1.24425i
\(437\) −3.46410 + 2.00000i −0.165710 + 0.0956730i
\(438\) 1.73205 1.00000i 0.0827606 0.0477818i
\(439\) 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 24.0000i 1.14156i
\(443\) −31.1769 18.0000i −1.48126 0.855206i −0.481486 0.876454i \(-0.659903\pi\)
−0.999774 + 0.0212481i \(0.993236\pi\)
\(444\) 7.00000 + 12.1244i 0.332205 + 0.575396i
\(445\) 0 0
\(446\) −24.0000 + 41.5692i −1.13643 + 1.96836i
\(447\) 4.00000i 0.189194i
\(448\) 20.7846 4.00000i 0.981981 0.188982i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −18.0000 31.1769i −0.847587 1.46806i
\(452\) −10.3923 + 6.00000i −0.488813 + 0.282216i
\(453\) 6.92820 + 4.00000i 0.325515 + 0.187936i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) 12.9904 + 7.50000i 0.607664 + 0.350835i 0.772051 0.635561i \(-0.219231\pi\)
−0.164386 + 0.986396i \(0.552564\pi\)
\(458\) 22.5167 13.0000i 1.05213 0.607450i
\(459\) −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 \(0.559649\pi\)
\(462\) −20.7846 24.0000i −0.966988 1.11658i
\(463\) 3.00000i 0.139422i −0.997567 0.0697109i \(-0.977792\pi\)
0.997567 0.0697109i \(-0.0222077\pi\)
\(464\) 16.0000 27.7128i 0.742781 1.28654i
\(465\) 0 0
\(466\) 6.00000 + 10.3923i 0.277945 + 0.481414i
\(467\) −19.0526 11.0000i −0.881647 0.509019i −0.0104461 0.999945i \(-0.503325\pi\)
−0.871201 + 0.490926i \(0.836658\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 14.0000 12.1244i 0.646460 0.559851i
\(470\) 0 0
\(471\) −5.00000 + 8.66025i −0.230388 + 0.399043i
\(472\) 0 0
\(473\) 5.19615 3.00000i 0.238919 0.137940i
\(474\) 1.00000 1.73205i 0.0459315 0.0795557i
\(475\) 0 0
\(476\) −20.0000 6.92820i −0.916698 0.317554i
\(477\) 4.00000i 0.183147i
\(478\) −24.2487 14.0000i −1.10911 0.640345i
\(479\) −2.00000 3.46410i −0.0913823 0.158279i 0.816711 0.577047i \(-0.195795\pi\)
−0.908093 + 0.418769i \(0.862462\pi\)
\(480\) 0 0
\(481\) 10.5000 18.1865i 0.478759 0.829235i
\(482\) 36.0000i 1.63976i
\(483\) 10.3923 2.00000i 0.472866 0.0910032i
\(484\) −50.0000 −2.27273
\(485\) 0 0
\(486\) 1.00000 + 1.73205i 0.0453609 + 0.0785674i
\(487\) −11.2583 + 6.50000i −0.510164 + 0.294543i −0.732901 0.680335i \(-0.761834\pi\)
0.222737 + 0.974879i \(0.428501\pi\)
\(488\) 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 \(0.587280\pi\)
\(492\) 10.3923 + 6.00000i 0.468521 + 0.270501i
\(493\) −27.7128 + 16.0000i −1.24812 + 0.720604i
\(494\) 3.00000 + 5.19615i 0.134976 + 0.233786i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 15.5885 3.00000i 0.699238 0.134568i
\(498\) 4.00000i 0.179244i
\(499\) 14.5000 25.1147i 0.649109 1.12429i −0.334227 0.942493i \(-0.608475\pi\)
0.983336 0.181797i \(-0.0581915\pi\)
\(500\) 0 0
\(501\) 5.00000 + 8.66025i 0.223384 + 0.386912i
\(502\) 20.7846 + 12.0000i 0.927663 + 0.535586i
\(503\) 2.00000i 0.0891756i 0.999005 + 0.0445878i \(0.0141974\pi\)
−0.999005 + 0.0445878i \(0.985803\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 24.0000 41.5692i 1.06693 1.84798i
\(507\) −3.46410 + 2.00000i −0.153846 + 0.0888231i
\(508\) −8.66025 + 5.00000i −0.384237 + 0.221839i
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 0 0
\(511\) −2.00000 + 1.73205i −0.0884748 + 0.0766214i
\(512\) 32.0000i 1.41421i
\(513\) 0.866025 + 0.500000i 0.0382360 + 0.0220755i
\(514\) 18.0000 + 31.1769i 0.793946 + 1.37515i
\(515\) 0 0
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 12.0000i 0.527759i
\(518\) −24.2487 28.0000i −1.06543 1.23025i
\(519\) −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 \(0.861260\pi\)
\(522\) 13.8564 8.00000i 0.606478 0.350150i
\(523\) 9.52628 + 5.50000i 0.416555 + 0.240498i 0.693602 0.720358i \(-0.256023\pi\)
−0.277047 + 0.960856i \(0.589356\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) 3.46410 + 2.00000i 0.150899 + 0.0871214i
\(528\) −20.7846 + 12.0000i −0.904534 + 0.522233i
\(529\) −3.50000 6.06218i −0.152174 0.263573i
\(530\) 0 0
\(531\) −8.00000 −0.347170
\(532\) 5.19615 1.00000i 0.225282 0.0433555i
\(533\) 18.0000i 0.779667i
\(534\) 12.0000 20.7846i 0.519291 0.899438i
\(535\) 0 0
\(536\) 0 0
\(537\) −15.5885 9.00000i −0.672692 0.388379i
\(538\) 20.0000i 0.862261i
\(539\) 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 \(0.146125\pi\)
\(542\) 41.5692 24.0000i 1.78555 1.03089i
\(543\) −11.2583 + 6.50000i −0.483141 + 0.278942i
\(544\) −16.0000 + 27.7128i −0.685994 + 1.18818i
\(545\) 0 0
\(546\) −3.00000 15.5885i −0.128388 0.667124i
\(547\) 36.0000i 1.53925i 0.638497 + 0.769624i \(0.279557\pi\)
−0.638497 + 0.769624i \(0.720443\pi\)
\(548\) 13.8564 + 8.00000i 0.591916 + 0.341743i
\(549\) −7.00000 12.1244i −0.298753 0.517455i
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) −0.866025 + 2.50000i −0.0368271 + 0.106311i
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) −21.0000 36.3731i −0.890598 1.54256i
\(557\) −8.66025 + 5.00000i −0.366947 + 0.211857i −0.672124 0.740439i \(-0.734618\pi\)
0.305177 + 0.952296i \(0.401284\pi\)
\(558\) −1.73205 1.00000i −0.0733236 0.0423334i
\(559\) 3.00000 0.126886
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) −20.7846 12.0000i −0.876746 0.506189i
\(563\) 22.5167 13.0000i 0.948964 0.547885i 0.0562051 0.998419i \(-0.482100\pi\)
0.892759 + 0.450535i \(0.148767\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) −1.73205 2.00000i −0.0727393 0.0839921i
\(568\) 0 0
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 0 0
\(571\) 1.50000 + 2.59808i 0.0627730 + 0.108726i 0.895704 0.444651i \(-0.146672\pi\)
−0.832931 + 0.553377i \(0.813339\pi\)
\(572\) −31.1769 18.0000i −1.30357 0.752618i
\(573\) 10.0000i 0.417756i
\(574\) −30.0000 10.3923i −1.25218 0.433766i
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) −25.1147 + 14.5000i −1.04554 + 0.603643i −0.921397 0.388621i \(-0.872951\pi\)
−0.124143 + 0.992264i \(0.539618\pi\)
\(578\) −1.73205 + 1.00000i −0.0720438 + 0.0415945i
\(579\) −4.50000 + 7.79423i −0.187014 + 0.323917i
\(580\) 0 0
\(581\) −1.00000 5.19615i −0.0414870 0.215573i
\(582\) 12.0000i 0.497416i
\(583\) −20.7846 12.0000i −0.860811 0.496989i
\(584\) 0 0
\(585\) 0 0
\(586\) −16.0000 + 27.7128i −0.660954 + 1.14481i
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) −13.8564 2.00000i −0.571429 0.0824786i
\(589\) −1.00000 −0.0412043
\(590\) 0 0
\(591\) −6.00000 10.3923i −0.246807 0.427482i
\(592\) −24.2487 + 14.0000i −0.996616 + 0.575396i
\(593\) −15.5885 9.00000i −0.640141 0.369586i 0.144528 0.989501i \(-0.453834\pi\)
−0.784669 + 0.619915i \(0.787167\pi\)
\(594\) −12.0000 −0.492366
\(595\) 0 0
\(596\) −8.00000 −0.327693
\(597\) −6.92820 4.00000i −0.283552 0.163709i
\(598\) 20.7846 12.0000i 0.849946 0.490716i
\(599\) −2.00000 3.46410i −0.0817178 0.141539i 0.822270 0.569097i \(-0.192707\pi\)
−0.903988 + 0.427558i \(0.859374\pi\)
\(600\) 0 0
\(601\) −33.0000 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(602\) 1.73205 5.00000i 0.0705931 0.203785i
\(603\) 7.00000i 0.285062i
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) 0 0
\(606\) −10.0000 17.3205i −0.406222 0.703598i
\(607\) −30.3109 17.5000i −1.23028 0.710303i −0.263193 0.964743i \(-0.584775\pi\)
−0.967088 + 0.254440i \(0.918109\pi\)
\(608\) 8.00000i 0.324443i
\(609\) −16.0000 + 13.8564i −0.648353 + 0.561490i
\(610\) 0 0
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) −6.92820 + 4.00000i −0.280056 + 0.161690i
\(613\) 25.9808 15.0000i 1.04935 0.605844i 0.126885 0.991917i \(-0.459502\pi\)
0.922468 + 0.386073i \(0.126169\pi\)
\(614\) −3.00000 + 5.19615i −0.121070 + 0.209700i
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 32.9090 + 19.0000i 1.32379 + 0.764292i
\(619\) 1.50000 + 2.59808i 0.0602901 + 0.104425i 0.894595 0.446878i \(-0.147464\pi\)
−0.834305 + 0.551303i \(0.814131\pi\)
\(620\) 0 0
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) 12.0000i 0.481156i
\(623\) −10.3923 + 30.0000i −0.416359 + 1.20192i
\(624\) −12.0000 −0.480384
\(625\) 0 0
\(626\) 11.0000 + 19.0526i 0.439648 + 0.761493i
\(627\) −5.19615 + 3.00000i −0.207514 + 0.119808i
\(628\) 17.3205 + 10.0000i 0.691164 + 0.399043i
\(629\) 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
\(633\) 17.3205 10.0000i 0.688428 0.397464i
\(634\) −20.0000 34.6410i −0.794301 1.37577i
\(635\) 0 0
\(636\) 8.00000 0.317221
\(637\) 7.79423 + 19.5000i 0.308819 + 0.772618i
\(638\) 96.0000i 3.80068i
\(639\) 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 \(0.909493\pi\)
\(642\) 20.7846 + 12.0000i 0.820303 + 0.473602i
\(643\) 1.00000i 0.0394362i −0.999806 0.0197181i \(-0.993723\pi\)
0.999806 0.0197181i \(-0.00627687\pi\)
\(644\) −4.00000 20.7846i −0.157622 0.819028i
\(645\) 0 0
\(646\) −4.00000 + 6.92820i −0.157378 + 0.272587i
\(647\) 25.9808 15.0000i 1.02141 0.589711i 0.106897 0.994270i \(-0.465908\pi\)
0.914512 + 0.404559i \(0.132575\pi\)
\(648\) 0 0
\(649\) 24.0000 41.5692i 0.942082 1.63173i
\(650\) 0 0
\(651\) 2.50000 + 0.866025i 0.0979827 + 0.0339422i
\(652\) 24.0000i 0.939913i
\(653\) 12.1244 + 7.00000i 0.474463 + 0.273931i 0.718106 0.695934i \(-0.245009\pi\)
−0.243643 + 0.969865i \(0.578343\pi\)
\(654\) 15.0000 + 25.9808i 0.586546 + 1.01593i
\(655\) 0 0
\(656\) −12.0000 + 20.7846i −0.468521 + 0.811503i
\(657\) 1.00000i 0.0390137i
\(658\) −6.92820 8.00000i −0.270089 0.311872i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) 15.5885 9.00000i 0.605863 0.349795i
\(663\) 10.3923 + 6.00000i 0.403604 + 0.233021i
\(664\) 0 0
\(665\) 0 0
\(666\) −14.0000 −0.542489
\(667\) −27.7128 16.0000i −1.07304 0.619522i
\(668\) 17.3205 10.0000i 0.670151 0.386912i
\(669\) −12.0000 20.7846i −0.463947 0.803579i
\(670\) 0 0
\(671\) 84.0000 3.24278
\(672\) −6.92820 + 20.0000i −0.267261 + 0.771517i
\(673\) 37.0000i 1.42625i 0.701039 + 0.713123i \(0.252720\pi\)
−0.701039 + 0.713123i \(0.747280\pi\)
\(674\) −25.0000 + 43.3013i −0.962964 + 1.66790i
\(675\) 0 0
\(676\) 4.00000 + 6.92820i 0.153846 + 0.266469i
\(677\) −13.8564 8.00000i −0.532545 0.307465i 0.209507 0.977807i \(-0.432814\pi\)
−0.742052 + 0.670342i \(0.766147\pi\)
\(678\) 12.0000i 0.460857i
\(679\) −3.00000 15.5885i −0.115129 0.598230i
\(680\) 0 0
\(681\) 5.00000 8.66025i 0.191600 0.331862i
\(682\) 10.3923 6.00000i 0.397942 0.229752i
\(683\) 41.5692 24.0000i 1.59060 0.918334i 0.597398 0.801945i \(-0.296201\pi\)
0.993204 0.116390i \(-0.0371322\pi\)
\(684\) 1.00000 1.73205i 0.0382360 0.0662266i
\(685\) 0 0
\(686\) 37.0000 1.73205i 1.41267 0.0661300i
\(687\) 13.0000i 0.495981i
\(688\) −3.46410 2.00000i −0.132068 0.0762493i
\(689\) −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 \(0.994991\pi\)
\(692\) 48.0000i 1.82469i
\(693\) 15.5885 3.00000i 0.592157 0.113961i
\(694\) 32.0000 1.21470
\(695\) 0 0
\(696\) 0 0
\(697\) 20.7846 12.0000i 0.787273 0.454532i
\(698\) −3.46410 2.00000i −0.131118 0.0757011i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) −5.19615 3.00000i −0.196116 0.113228i
\(703\) −6.06218 + 3.50000i −0.228639 + 0.132005i
\(704\) 24.0000 + 41.5692i 0.904534 + 1.56670i
\(705\) 0 0
\(706\) 36.0000 1.35488
\(707\) 17.3205 + 20.0000i 0.651405 + 0.752177i
\(708\) 16.0000i 0.601317i
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) 4.00000i 0.149801i
\(714\) 16.0000 13.8564i 0.598785 0.518563i
\(715\) 0 0
\(716\) −18.0000 + 31.1769i −0.672692 + 1.16514i
\(717\) 12.1244 7.00000i 0.452792 0.261420i
\(718\) −41.5692 + 24.0000i −1.55135 + 0.895672i
\(719\) −17.0000 + 29.4449i −0.633993 + 1.09811i 0.352735 + 0.935723i \(0.385252\pi\)
−0.986728 + 0.162385i \(0.948081\pi\)
\(720\) 0 0
\(721\) −47.5000 16.4545i −1.76899 0.612797i
\(722\) 36.0000i 1.33978i
\(723\) −15.5885 9.00000i −0.579741 0.334714i
\(724\) 13.0000 + 22.5167i 0.483141 + 0.836825i
\(725\) 0 0
\(726\) 25.0000 43.3013i 0.927837 1.60706i
\(727\) 7.00000i 0.259616i 0.991539 + 0.129808i \(0.0414360\pi\)
−0.991539 + 0.129808i \(0.958564\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 2.00000 + 3.46410i 0.0739727 + 0.128124i
\(732\) −24.2487 + 14.0000i −0.896258 + 0.517455i
\(733\) −37.2391 21.5000i −1.37546 0.794121i −0.383849 0.923396i \(-0.625402\pi\)
−0.991609 + 0.129275i \(0.958735\pi\)
\(734\) 38.0000 1.40261
\(735\) 0 0
\(736\) −32.0000 −1.17954
\(737\) 36.3731 + 21.0000i 1.33982 + 0.773545i
\(738\) −10.3923 + 6.00000i −0.382546 + 0.220863i
\(739\) 20.5000 + 35.5070i 0.754105 + 1.30615i 0.945818 + 0.324697i \(0.105262\pi\)
−0.191714 + 0.981451i \(0.561404\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) −20.7846 + 4.00000i −0.763027 + 0.146845i
\(743\) 6.00000i 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 11.0000 + 19.0526i 0.402739 + 0.697564i
\(747\) −1.73205 1.00000i −0.0633724 0.0365881i
\(748\) 48.0000i 1.75505i
\(749\) −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 \(0.989192\pi\)
\(752\) −6.92820 + 4.00000i −0.252646 + 0.145865i
\(753\) −10.3923 + 6.00000i −0.378717 + 0.218652i
\(754\) −24.0000 + 41.5692i −0.874028 + 1.51386i
\(755\) 0 0
\(756\) −4.00000 + 3.46410i −0.145479 + 0.125988i
\(757\) 22.0000i 0.799604i −0.916602 0.399802i \(-0.869079\pi\)
0.916602 0.399802i \(-0.130921\pi\)
\(758\) −19.0526 11.0000i −0.692020 0.399538i
\(759\) 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 \(0.0968765\pi\)
\(762\) 10.0000i 0.362262i
\(763\) −25.9808 30.0000i −0.940567 1.08607i
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 28.0000 + 48.4974i 1.01168 + 1.75228i
\(767\) 20.7846 12.0000i 0.750489 0.433295i
\(768\) 13.8564 + 8.00000i 0.500000 + 0.288675i
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 15.5885 + 9.00000i 0.561041 + 0.323917i
\(773\) −15.5885 + 9.00000i −0.560678 + 0.323708i −0.753418 0.657542i \(-0.771596\pi\)
0.192740 + 0.981250i \(0.438263\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 0 0
\(776\) 0 0
\(777\) 18.1865 3.50000i 0.652438 0.125562i
\(778\) 12.0000i 0.430221i
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) 18.0000 + 31.1769i 0.644091 + 1.11560i
\(782\) 27.7128 + 16.0000i 0.991008 + 0.572159i
\(783\) 8.00000i 0.285897i
\(784\) 4.00000 27.7128i 0.142857 0.989743i
\(785\) 0 0
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) −27.7128 + 16.0000i −0.987855 + 0.570338i −0.904632 0.426193i \(-0.859855\pi\)
−0.0832226 + 0.996531i \(0.526521\pi\)
\(788\) −20.7846 + 12.0000i −0.740421 + 0.427482i
\(789\) 2.00000 3.46410i 0.0712019 0.123325i
\(790\) 0 0
\(791\) 3.00000 + 15.5885i 0.106668 + 0.554262i
\(792\) 0 0
\(793\) 36.3731 + 21.0000i 1.29165 + 0.745732i
\(794\) 37.0000 + 64.0859i 1.31308 + 2.27432i
\(795\) 0 0
\(796\) −8.00000 + 13.8564i −0.283552 + 0.491127i
\(797\) 36.0000i 1.27519i −0.770374 0.637593i \(-0.779930\pi\)
0.770374 0.637593i \(-0.220070\pi\)
\(798\) −1.73205 + 5.00000i −0.0613139 + 0.176998i
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 6.00000 + 10.3923i 0.212000 + 0.367194i
\(802\) 20.7846 12.0000i 0.733930 0.423735i
\(803\) −5.19615 3.00000i −0.183368 0.105868i
\(804\) −14.0000 −0.493742
\(805\) 0 0
\(806\) 6.00000 0.211341
\(807\) 8.66025 + 5.00000i 0.304855 + 0.176008i
\(808\) 0 0
\(809\) −21.0000 36.3731i −0.738321 1.27881i −0.953251 0.302180i \(-0.902286\pi\)
0.214930 0.976629i \(-0.431048\pi\)
\(810\) 0 0
\(811\) −48.0000 −1.68551 −0.842754 0.538299i \(-0.819067\pi\)
−0.842754 + 0.538299i \(0.819067\pi\)
\(812\) 27.7128 + 32.0000i 0.972529 + 1.12298i
\(813\) 24.0000i 0.841717i
\(814\) 42.0000 72.7461i 1.47210 2.54975i
\(815\) 0 0
\(816\) −8.00000 13.8564i −0.280056 0.485071i
\(817\) −0.866025 0.500000i −0.0302984 0.0174928i
\(818\) 10.0000i 0.349642i
\(819\) 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 \(0.775319\pi\)
\(822\) −13.8564 + 8.00000i −0.483298 + 0.279032i
\(823\) −6.92820 + 4.00000i −0.241502 + 0.139431i −0.615867 0.787850i \(-0.711194\pi\)
0.374365 + 0.927281i \(0.377861\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −8.00000 41.5692i −0.278356 1.44638i
\(827\) 30.0000i 1.04320i −0.853189 0.521601i \(-0.825335\pi\)
0.853189 0.521601i \(-0.174665\pi\)
\(828\) −6.92820 4.00000i −0.240772 0.139010i
\(829\) 28.5000 + 49.3634i 0.989846 + 1.71446i 0.618024 + 0.786159i \(0.287934\pi\)
0.371822 + 0.928304i \(0.378733\pi\)
\(830\) 0 0
\(831\) 3.50000 6.06218i 0.121414 0.210295i
\(832\) 24.0000i 0.832050i
\(833\) −17.3205 + 22.0000i −0.600120 + 0.762255i
\(834\) 42.0000 1.45434
\(835\) 0 0
\(836\) 6.00000 + 10.3923i 0.207514 + 0.359425i
\(837\) 0.866025 0.500000i 0.0299342 0.0172825i
\(838\) −10.3923 6.00000i −0.358996 0.207267i
\(839\) −24.0000 −0.828572 −0.414286 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 1.73205 + 1.00000i 0.0596904 + 0.0344623i
\(843\) 10.3923 6.00000i 0.357930 0.206651i
\(844\) −20.0000 34.6410i −0.688428 1.19239i
\(845\) 0 0
\(846\) −4.00000 −0.137523
\(847\) −21.6506 + 62.5000i −0.743925 + 2.14753i
\(848\) 16.0000i 0.549442i
\(849\) −3.50000 + 6.06218i −0.120120 + 0.208053i
\(850\) 0 0
\(851\) 14.0000 + 24.2487i 0.479914 + 0.831235i
\(852\) −10.3923 6.00000i −0.356034 0.205557i
\(853\) 9.00000i 0.308154i 0.988059 + 0.154077i \(0.0492404\pi\)
−0.988059 + 0.154077i \(0.950760\pi\)
\(854\) 56.0000 48.4974i 1.91628 1.65955i
\(855\) 0 0
\(856\) 0 0
\(857\) −10.3923 + 6.00000i −0.354994 + 0.204956i −0.666883 0.745163i \(-0.732372\pi\)
0.311888 + 0.950119i \(0.399038\pi\)
\(858\) 31.1769 18.0000i 1.06436 0.614510i
\(859\) −20.0000 + 34.6410i −0.682391 + 1.18194i 0.291858 + 0.956462i \(0.405727\pi\)
−0.974249 + 0.225475i \(0.927607\pi\)
\(860\) 0 0
\(861\) 12.0000 10.3923i 0.408959 0.354169i
\(862\) 4.00000i 0.136241i
\(863\) −5.19615 3.00000i −0.176879 0.102121i 0.408946 0.912558i \(-0.365896\pi\)
−0.585826 + 0.810437i \(0.699230\pi\)
\(864\) 4.00000 + 6.92820i 0.136083 + 0.235702i
\(865\) 0 0
\(866\) −5.00000 + 8.66025i −0.169907 + 0.294287i
\(867\) 1.00000i 0.0339618i
\(868\) 1.73205 5.00000i 0.0587896 0.169711i
\(869\) −6.00000 −0.203536
\(870\) 0 0
\(871\) 10.5000 + 18.1865i 0.355779 + 0.616227i
\(872\) 0 0
\(873\) −5.19615 3.00000i −0.175863 0.101535i
\(874\) −8.00000 −0.270604
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 19.0526 + 11.0000i 0.643359 + 0.371444i 0.785907 0.618344i \(-0.212196\pi\)
−0.142548 + 0.989788i \(0.545530\pi\)
\(878\) 27.7128 16.0000i 0.935262 0.539974i
\(879\) −8.00000 13.8564i −0.269833 0.467365i
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 8.66025 11.0000i 0.291606 0.370389i
\(883\) 7.00000i 0.235569i −0.993039 0.117784i \(-0.962421\pi\)
0.993039 0.117784i \(-0.0375792\pi\)
\(884\) 12.0000 20.7846i 0.403604 0.699062i
\(885\) 0 0
\(886\) −36.0000 62.3538i −1.20944 2.09482i
\(887\) −8.66025 5.00000i −0.290783 0.167884i 0.347512 0.937676i \(-0.387027\pi\)
−0.638295 + 0.769792i \(0.720360\pi\)
\(888\) 0 0
\(889\) 2.50000 + 12.9904i 0.0838473 + 0.435683i
\(890\) 0 0
\(891\) 3.00000 5.19615i 0.100504 0.174078i
\(892\) −41.5692 + 24.0000i −1.39184 + 0.803579i
\(893\) −1.73205 + 1.00000i −0.0579609 + 0.0334637i
\(894\) 4.00000 6.92820i 0.133780 0.231714i
\(895\) 0 0
\(896\) 0 0
\(897\) 12.0000i 0.400668i
\(898\) −51.9615 30.0000i −1.73398 1.00111i
\(899\) −4.00000 6.92820i −0.133407 0.231069i
\(900\) 0 0
\(901\) 8.00000 13.8564i 0.266519 0.461624i
\(902\) 72.0000i 2.39734i
\(903\) 1.73205 + 2.00000i 0.0576390 + 0.0665558i
\(904\) 0 0
\(905\) 0 0
\(906\) 8.00000 + 13.8564i 0.265782 + 0.460348i
\(907\) 26.8468 15.5000i 0.891433 0.514669i 0.0170220 0.999855i \(-0.494581\pi\)
0.874411 + 0.485186i \(0.161248\pi\)
\(908\) −17.3205 10.0000i −0.574801 0.331862i
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 3.46410 + 2.00000i 0.114708 + 0.0662266i
\(913\) 10.3923 6.00000i 0.343935 0.198571i
\(914\) 15.0000 + 25.9808i 0.496156 + 0.859367i
\(915\) 0 0
\(916\) 26.0000 0.859064
\(917\) −1.73205 + 5.00000i −0.0571974 + 0.165115i
\(918\) 8.00000i 0.264039i
\(919\) −4.50000 + 7.79423i −0.148441 + 0.257108i −0.930652 0.365907i \(-0.880759\pi\)
0.782210 + 0.623015i \(0.214092\pi\)
\(920\) 0 0
\(921\) −1.50000 2.59808i −0.0494267 0.0856095i
\(922\) −13.8564 8.00000i −0.456336 0.263466i
\(923\) 18.0000i 0.592477i
\(924\) −6.00000 31.1769i −0.197386 1.02565i
\(925\) 0 0
\(926\) 3.00000 5.19615i 0.0985861 0.170756i
\(927\) −16.4545 + 9.50000i −0.540436 + 0.312021i
\(928\) 55.4256 32.0000i 1.81944 1.05045i
\(929\) −7.00000 + 12.1244i −0.229663 + 0.397787i −0.957708 0.287742i \(-0.907096\pi\)
0.728046 + 0.685529i \(0.240429\pi\)
\(930\) 0 0
\(931\) 1.00000 6.92820i 0.0327737 0.227063i
\(932\) 12.0000i 0.393073i
\(933\) 5.19615 + 3.00000i 0.170114 + 0.0982156i
\(934\) −22.0000 38.1051i −0.719862 1.24684i
\(935\) 0 0
\(936\) 0 0
\(937\) 29.0000i 0.947389i −0.880689 0.473694i \(-0.842920\pi\)
0.880689 0.473694i \(-0.157080\pi\)
\(938\) 36.3731 7.00000i 1.18762 0.228558i
\(939\) −11.0000 −0.358971
\(940\) 0 0
\(941\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(942\) −17.3205 + 10.0000i −0.564333 + 0.325818i
\(943\) 20.7846 + 12.0000i 0.676840 + 0.390774i
\(944\) −32.0000 −1.04151
\(945\) 0 0
\(946\) 12.0000 0.390154
\(947\) −22.5167 13.0000i −0.731693 0.422443i 0.0873481 0.996178i \(-0.472161\pi\)
−0.819041 + 0.573735i \(0.805494\pi\)
\(948\) 1.73205 1.00000i 0.0562544 0.0324785i
\(949\) −1.50000 2.59808i −0.0486921 0.0843371i
\(950\) 0 0
\(951\) 20.0000 0.648544
\(952\) 0 0
\(953\) 4.00000i 0.129573i −0.997899 0.0647864i \(-0.979363\pi\)
0.997899 0.0647864i \(-0.0206366\pi\)
\(954\) −4.00000 + 6.92820i −0.129505 + 0.224309i
\(955\) 0 0
\(956\) −14.0000 24.2487i −0.452792 0.784259i
\(957\) −41.5692 24.0000i −1.34374 0.775810i
\(958\) 8.00000i 0.258468i
\(959\) 16.0000 13.8564i 0.516667 0.447447i
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) 36.3731 21.0000i 1.17271 0.677067i
\(963\) −10.3923 + 6.00000i −0.334887 + 0.193347i
\(964\) −18.0000 + 31.1769i −0.579741 + 1.00414i
\(965\) 0 0
\(966\) 20.0000 + 6.92820i 0.643489 + 0.222911i
\(967\) 55.0000i 1.76868i 0.466843 + 0.884340i \(0.345391\pi\)
−0.466843 + 0.884340i \(0.654609\pi\)
\(968\) 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 \(-0.147507\pi\)
\(972\) 2.00000i 0.0641500i
\(973\) −54.5596 + 10.5000i −1.74910 + 0.336615i
\(974\) −26.0000 −0.833094
\(975\) 0 0
\(976\) −28.0000 48.4974i −0.896258 1.55236i
\(977\) −19.0526 + 11.0000i −0.609545 + 0.351921i −0.772787 0.634665i \(-0.781138\pi\)
0.163242 + 0.986586i \(0.447805\pi\)
\(978\) 20.7846 + 12.0000i 0.664619 + 0.383718i
\(979\) −72.0000 −2.30113
\(980\) 0 0
\(981\) −15.0000 −0.478913
\(982\) −20.7846 12.0000i −0.663264 0.382935i
\(983\) −27.7128 + 16.0000i −0.883901 + 0.510321i −0.871943 0.489608i \(-0.837140\pi\)
−0.0119587 + 0.999928i \(0.503807\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −64.0000 −2.03818
\(987\) 5.19615 1.00000i 0.165395 0.0318304i
\(988\) 6.00000i 0.190885i
\(989\) −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 \(0.756761\pi\)
\(992\) −6.92820 4.00000i −0.219971 0.127000i
\(993\) 9.00000i 0.285606i
\(994\) 30.0000 + 10.3923i 0.951542 + 0.329624i
\(995\) 0 0
\(996\) −2.00000 + 3.46410i −0.0633724 + 0.109764i
\(997\) −21.6506 + 12.5000i −0.685682 + 0.395879i −0.801993 0.597334i \(-0.796227\pi\)
0.116310 + 0.993213i \(0.462893\pi\)
\(998\) 50.2295 29.0000i 1.58999 0.917979i
\(999\) 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.r.d.499.2 4
5.2 odd 4 525.2.i.a.226.1 2
5.3 odd 4 105.2.i.b.16.1 2
5.4 even 2 inner 525.2.r.d.499.1 4
7.4 even 3 inner 525.2.r.d.424.1 4
15.8 even 4 315.2.j.a.226.1 2
20.3 even 4 1680.2.bg.l.961.1 2
35.2 odd 12 3675.2.a.o.1.1 1
35.3 even 12 735.2.i.f.361.1 2
35.4 even 6 inner 525.2.r.d.424.2 4
35.12 even 12 3675.2.a.p.1.1 1
35.13 even 4 735.2.i.f.226.1 2
35.18 odd 12 105.2.i.b.46.1 yes 2
35.23 odd 12 735.2.a.b.1.1 1
35.32 odd 12 525.2.i.a.151.1 2
35.33 even 12 735.2.a.a.1.1 1
105.23 even 12 2205.2.a.k.1.1 1
105.53 even 12 315.2.j.a.46.1 2
105.68 odd 12 2205.2.a.m.1.1 1
140.123 even 12 1680.2.bg.l.1201.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.i.b.16.1 2 5.3 odd 4
105.2.i.b.46.1 yes 2 35.18 odd 12
315.2.j.a.46.1 2 105.53 even 12
315.2.j.a.226.1 2 15.8 even 4
525.2.i.a.151.1 2 35.32 odd 12
525.2.i.a.226.1 2 5.2 odd 4
525.2.r.d.424.1 4 7.4 even 3 inner
525.2.r.d.424.2 4 35.4 even 6 inner
525.2.r.d.499.1 4 5.4 even 2 inner
525.2.r.d.499.2 4 1.1 even 1 trivial
735.2.a.a.1.1 1 35.33 even 12
735.2.a.b.1.1 1 35.23 odd 12
735.2.i.f.226.1 2 35.13 even 4
735.2.i.f.361.1 2 35.3 even 12
1680.2.bg.l.961.1 2 20.3 even 4
1680.2.bg.l.1201.1 2 140.123 even 12
2205.2.a.k.1.1 1 105.23 even 12
2205.2.a.m.1.1 1 105.68 odd 12
3675.2.a.o.1.1 1 35.2 odd 12
3675.2.a.p.1.1 1 35.12 even 12