Properties

Label 1014.2.i.c.361.2
Level $1014$
Weight $2$
Character 1014.361
Analytic conductor $8.097$
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] = [1014,2,Mod(361,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.i (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: \(8.09683076496\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.361
Dual form 1014.2.i.c.823.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} -1.00000 q^{12} +2.00000 q^{14} +(1.73205 - 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +1.00000i q^{18} +(5.19615 + 3.00000i) q^{19} +(1.73205 + 1.00000i) q^{20} -2.00000i q^{21} +(-2.00000 - 3.46410i) q^{23} +(-0.866025 + 0.500000i) q^{24} +1.00000 q^{25} +1.00000 q^{27} +(1.73205 - 1.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} +(1.00000 - 1.73205i) q^{30} +10.0000i q^{31} +(-0.866025 - 0.500000i) q^{32} -2.00000i q^{34} +(-2.00000 + 3.46410i) q^{35} +(0.500000 + 0.866025i) q^{36} +(6.92820 - 4.00000i) q^{37} +6.00000 q^{38} +2.00000 q^{40} +(8.66025 - 5.00000i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(-1.73205 - 1.00000i) q^{45} +(-3.46410 - 2.00000i) q^{46} -12.0000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} -2.00000 q^{51} -6.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.00000 - 1.73205i) q^{56} -6.00000i q^{57} +(8.66025 + 5.00000i) q^{58} +(-3.46410 - 2.00000i) q^{59} -2.00000i q^{60} +(-1.00000 + 1.73205i) q^{61} +(5.00000 + 8.66025i) q^{62} +(-1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +(-1.73205 + 1.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-2.00000 + 3.46410i) q^{69} +4.00000i q^{70} +(0.866025 + 0.500000i) q^{72} -4.00000i q^{73} +(4.00000 - 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(5.19615 - 3.00000i) q^{76} +(1.73205 - 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} -4.00000i q^{83} +(-1.73205 - 1.00000i) q^{84} +(3.46410 + 2.00000i) q^{85} +4.00000i q^{86} +(5.00000 - 8.66025i) q^{87} +(-5.19615 + 3.00000i) q^{89} -2.00000 q^{90} -4.00000 q^{92} +(8.66025 - 5.00000i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} +1.00000i q^{96} +(10.3923 + 6.00000i) q^{97} +(-2.59808 - 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} + 8 q^{14} - 2 q^{16} + 4 q^{17} - 8 q^{23} + 4 q^{25} + 4 q^{27} + 20 q^{29} + 4 q^{30} - 8 q^{35} + 2 q^{36} + 24 q^{38} + 8 q^{40} - 4 q^{42} - 8 q^{43} - 2 q^{48} - 6 q^{49} - 8 q^{51} - 24 q^{53} + 4 q^{56} - 4 q^{61} + 20 q^{62} - 4 q^{64} - 4 q^{68} - 8 q^{69} + 16 q^{74} - 2 q^{75} - 2 q^{81} + 20 q^{82} + 20 q^{87} - 8 q^{90} - 16 q^{92} - 24 q^{94} - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.00000i 0.894427i 0.894427 + 0.447214i \(0.147584\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 1.73205 + 1.00000i 0.654654 + 0.377964i 0.790237 0.612801i \(-0.209957\pi\)
−0.135583 + 0.990766i \(0.543291\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 2.00000 0.534522
\(15\) 1.73205 1.00000i 0.447214 0.258199i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.19615 + 3.00000i 1.19208 + 0.688247i 0.958778 0.284157i \(-0.0917138\pi\)
0.233301 + 0.972404i \(0.425047\pi\)
\(20\) 1.73205 + 1.00000i 0.387298 + 0.223607i
\(21\) 2.00000i 0.436436i
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.73205 1.00000i 0.327327 0.188982i
\(29\) 5.00000 + 8.66025i 0.928477 + 1.60817i 0.785872 + 0.618389i \(0.212214\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) 1.00000 1.73205i 0.182574 0.316228i
\(31\) 10.0000i 1.79605i 0.439941 + 0.898027i \(0.354999\pi\)
−0.439941 + 0.898027i \(0.645001\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 2.00000i 0.342997i
\(35\) −2.00000 + 3.46410i −0.338062 + 0.585540i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 6.92820 4.00000i 1.13899 0.657596i 0.192809 0.981236i \(-0.438240\pi\)
0.946180 + 0.323640i \(0.104907\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) 8.66025 5.00000i 1.35250 0.780869i 0.363905 0.931436i \(-0.381443\pi\)
0.988600 + 0.150567i \(0.0481100\pi\)
\(42\) −1.00000 1.73205i −0.154303 0.267261i
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 0 0
\(45\) −1.73205 1.00000i −0.258199 0.149071i
\(46\) −3.46410 2.00000i −0.510754 0.294884i
\(47\) 12.0000i 1.75038i −0.483779 0.875190i \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) −2.00000 −0.280056
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 6.00000i 0.794719i
\(58\) 8.66025 + 5.00000i 1.13715 + 0.656532i
\(59\) −3.46410 2.00000i −0.450988 0.260378i 0.257260 0.966342i \(-0.417180\pi\)
−0.708247 + 0.705965i \(0.750514\pi\)
\(60\) 2.00000i 0.258199i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 5.00000 + 8.66025i 0.635001 + 1.09985i
\(63\) −1.73205 + 1.00000i −0.218218 + 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.73205 + 1.00000i −0.211604 + 0.122169i −0.602056 0.798454i \(-0.705652\pi\)
0.390453 + 0.920623i \(0.372318\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) 4.00000i 0.478091i
\(71\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 4.00000 6.92820i 0.464991 0.805387i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 5.19615 3.00000i 0.596040 0.344124i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.73205 1.00000i 0.193649 0.111803i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.00000 8.66025i 0.552158 0.956365i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) −1.73205 1.00000i −0.188982 0.109109i
\(85\) 3.46410 + 2.00000i 0.375735 + 0.216930i
\(86\) 4.00000i 0.431331i
\(87\) 5.00000 8.66025i 0.536056 0.928477i
\(88\) 0 0
\(89\) −5.19615 + 3.00000i −0.550791 + 0.317999i −0.749441 0.662071i \(-0.769678\pi\)
0.198650 + 0.980071i \(0.436344\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 8.66025 5.00000i 0.898027 0.518476i
\(94\) −6.00000 10.3923i −0.618853 1.07188i
\(95\) −6.00000 + 10.3923i −0.615587 + 1.06623i
\(96\) 1.00000i 0.102062i
\(97\) 10.3923 + 6.00000i 1.05518 + 0.609208i 0.924095 0.382164i \(-0.124821\pi\)
0.131084 + 0.991371i \(0.458154\pi\)
\(98\) −2.59808 1.50000i −0.262445 0.151523i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) −1.73205 + 1.00000i −0.171499 + 0.0990148i
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 4.00000 0.390360
\(106\) −5.19615 + 3.00000i −0.504695 + 0.291386i
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.00000i 0.383131i 0.981480 + 0.191565i \(0.0613564\pi\)
−0.981480 + 0.191565i \(0.938644\pi\)
\(110\) 0 0
\(111\) −6.92820 4.00000i −0.657596 0.379663i
\(112\) 2.00000i 0.188982i
\(113\) −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i \(0.395477\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(114\) −3.00000 5.19615i −0.280976 0.486664i
\(115\) 6.92820 4.00000i 0.646058 0.373002i
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 3.46410 2.00000i 0.317554 0.183340i
\(120\) −1.00000 1.73205i −0.0912871 0.158114i
\(121\) −5.50000 + 9.52628i −0.500000 + 0.866025i
\(122\) 2.00000i 0.181071i
\(123\) −8.66025 5.00000i −0.780869 0.450835i
\(124\) 8.66025 + 5.00000i 0.777714 + 0.449013i
\(125\) 12.0000i 1.07331i
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −4.00000 6.92820i −0.354943 0.614779i 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 6.00000 + 10.3923i 0.520266 + 0.901127i
\(134\) −1.00000 + 1.73205i −0.0863868 + 0.149626i
\(135\) 2.00000i 0.172133i
\(136\) −1.73205 1.00000i −0.148522 0.0857493i
\(137\) 1.73205 + 1.00000i 0.147979 + 0.0854358i 0.572161 0.820141i \(-0.306105\pi\)
−0.424182 + 0.905577i \(0.639438\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) 2.00000 + 3.46410i 0.169031 + 0.292770i
\(141\) −10.3923 + 6.00000i −0.875190 + 0.505291i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −17.3205 + 10.0000i −1.43839 + 0.830455i
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) −1.50000 + 2.59808i −0.123718 + 0.214286i
\(148\) 8.00000i 0.657596i
\(149\) −12.1244 7.00000i −0.993266 0.573462i −0.0870170 0.996207i \(-0.527733\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) −0.866025 0.500000i −0.0707107 0.0408248i
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) 1.00000 + 1.73205i 0.0808452 + 0.140028i
\(154\) 0 0
\(155\) −20.0000 −1.60644
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) 1.00000 1.73205i 0.0790569 0.136931i
\(161\) 8.00000i 0.630488i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 12.1244 + 7.00000i 0.949653 + 0.548282i 0.892973 0.450110i \(-0.148615\pi\)
0.0566798 + 0.998392i \(0.481949\pi\)
\(164\) 10.0000i 0.780869i
\(165\) 0 0
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) −10.3923 + 6.00000i −0.804181 + 0.464294i −0.844931 0.534875i \(-0.820359\pi\)
0.0407502 + 0.999169i \(0.487025\pi\)
\(168\) −2.00000 −0.154303
\(169\) 0 0
\(170\) 4.00000 0.306786
\(171\) −5.19615 + 3.00000i −0.397360 + 0.229416i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 10.0000i 0.758098i
\(175\) 1.73205 + 1.00000i 0.130931 + 0.0755929i
\(176\) 0 0
\(177\) 4.00000i 0.300658i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) −1.73205 + 1.00000i −0.129099 + 0.0745356i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) −3.46410 + 2.00000i −0.255377 + 0.147442i
\(185\) 8.00000 + 13.8564i 0.588172 + 1.01874i
\(186\) 5.00000 8.66025i 0.366618 0.635001i
\(187\) 0 0
\(188\) −10.3923 6.00000i −0.757937 0.437595i
\(189\) 1.73205 + 1.00000i 0.125988 + 0.0727393i
\(190\) 12.0000i 0.870572i
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 13.8564 8.00000i 0.997406 0.575853i 0.0899262 0.995948i \(-0.471337\pi\)
0.907480 + 0.420096i \(0.138004\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −19.0526 + 11.0000i −1.35744 + 0.783718i −0.989278 0.146045i \(-0.953346\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 1.73205 + 1.00000i 0.122169 + 0.0705346i
\(202\) −1.73205 1.00000i −0.121867 0.0703598i
\(203\) 20.0000i 1.40372i
\(204\) −1.00000 + 1.73205i −0.0700140 + 0.121268i
\(205\) 10.0000 + 17.3205i 0.698430 + 1.20972i
\(206\) −13.8564 + 8.00000i −0.965422 + 0.557386i
\(207\) 4.00000 0.278019
\(208\) 0 0
\(209\) 0 0
\(210\) 3.46410 2.00000i 0.239046 0.138013i
\(211\) −6.00000 10.3923i −0.413057 0.715436i 0.582165 0.813070i \(-0.302206\pi\)
−0.995222 + 0.0976347i \(0.968872\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) −6.92820 4.00000i −0.473602 0.273434i
\(215\) −6.92820 4.00000i −0.472500 0.272798i
\(216\) 1.00000i 0.0680414i
\(217\) −10.0000 + 17.3205i −0.678844 + 1.17579i
\(218\) 2.00000 + 3.46410i 0.135457 + 0.234619i
\(219\) −3.46410 + 2.00000i −0.234082 + 0.135147i
\(220\) 0 0
\(221\) 0 0
\(222\) −8.00000 −0.536925
\(223\) −12.1244 + 7.00000i −0.811907 + 0.468755i −0.847618 0.530607i \(-0.821964\pi\)
0.0357107 + 0.999362i \(0.488630\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 14.0000i 0.931266i
\(227\) −6.92820 4.00000i −0.459841 0.265489i 0.252136 0.967692i \(-0.418867\pi\)
−0.711977 + 0.702202i \(0.752200\pi\)
\(228\) −5.19615 3.00000i −0.344124 0.198680i
\(229\) 4.00000i 0.264327i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 4.00000 6.92820i 0.263752 0.456832i
\(231\) 0 0
\(232\) 8.66025 5.00000i 0.568574 0.328266i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 24.0000 1.56559
\(236\) −3.46410 + 2.00000i −0.225494 + 0.130189i
\(237\) 0 0
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) 16.0000i 1.03495i −0.855697 0.517477i \(-0.826871\pi\)
0.855697 0.517477i \(-0.173129\pi\)
\(240\) −1.73205 1.00000i −0.111803 0.0645497i
\(241\) −17.3205 10.0000i −1.11571 0.644157i −0.175409 0.984496i \(-0.556125\pi\)
−0.940303 + 0.340339i \(0.889458\pi\)
\(242\) 11.0000i 0.707107i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) 5.19615 3.00000i 0.331970 0.191663i
\(246\) −10.0000 −0.637577
\(247\) 0 0
\(248\) 10.0000 0.635001
\(249\) −3.46410 + 2.00000i −0.219529 + 0.126745i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 14.0000 24.2487i 0.883672 1.53057i 0.0364441 0.999336i \(-0.488397\pi\)
0.847228 0.531229i \(-0.178270\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 0 0
\(254\) −6.92820 4.00000i −0.434714 0.250982i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 3.46410 2.00000i 0.215666 0.124515i
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) −10.0000 −0.618984
\(262\) −6.92820 + 4.00000i −0.428026 + 0.247121i
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 12.0000i 0.737154i
\(266\) 10.3923 + 6.00000i 0.637193 + 0.367884i
\(267\) 5.19615 + 3.00000i 0.317999 + 0.183597i
\(268\) 2.00000i 0.122169i
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 1.00000 + 1.73205i 0.0608581 + 0.105409i
\(271\) −8.66025 + 5.00000i −0.526073 + 0.303728i −0.739416 0.673249i \(-0.764898\pi\)
0.213343 + 0.976977i \(0.431565\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 20.0000i 1.19952i
\(279\) −8.66025 5.00000i −0.518476 0.299342i
\(280\) 3.46410 + 2.00000i 0.207020 + 0.119523i
\(281\) 10.0000i 0.596550i −0.954480 0.298275i \(-0.903589\pi\)
0.954480 0.298275i \(-0.0964112\pi\)
\(282\) −6.00000 + 10.3923i −0.357295 + 0.618853i
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 0 0
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) 20.0000 1.18056
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −10.0000 + 17.3205i −0.587220 + 1.01710i
\(291\) 12.0000i 0.703452i
\(292\) −3.46410 2.00000i −0.202721 0.117041i
\(293\) 12.1244 + 7.00000i 0.708312 + 0.408944i 0.810436 0.585827i \(-0.199230\pi\)
−0.102123 + 0.994772i \(0.532564\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 4.00000 6.92820i 0.232889 0.403376i
\(296\) −4.00000 6.92820i −0.232495 0.402694i
\(297\) 0 0
\(298\) −14.0000 −0.810998
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) −6.92820 + 4.00000i −0.399335 + 0.230556i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 6.00000i 0.344124i
\(305\) −3.46410 2.00000i −0.198354 0.114520i
\(306\) 1.73205 + 1.00000i 0.0990148 + 0.0571662i
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) 0 0
\(309\) 8.00000 + 13.8564i 0.455104 + 0.788263i
\(310\) −17.3205 + 10.0000i −0.983739 + 0.567962i
\(311\) −28.0000 −1.58773 −0.793867 0.608091i \(-0.791935\pi\)
−0.793867 + 0.608091i \(0.791935\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) −1.73205 + 1.00000i −0.0977453 + 0.0564333i
\(315\) −2.00000 3.46410i −0.112687 0.195180i
\(316\) 0 0
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) 0 0
\(320\) 2.00000i 0.111803i
\(321\) −4.00000 + 6.92820i −0.223258 + 0.386695i
\(322\) −4.00000 6.92820i −0.222911 0.386094i
\(323\) 10.3923 6.00000i 0.578243 0.333849i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 14.0000 0.775388
\(327\) 3.46410 2.00000i 0.191565 0.110600i
\(328\) −5.00000 8.66025i −0.276079 0.478183i
\(329\) 12.0000 20.7846i 0.661581 1.14589i
\(330\) 0 0
\(331\) 8.66025 + 5.00000i 0.476011 + 0.274825i 0.718752 0.695266i \(-0.244713\pi\)
−0.242742 + 0.970091i \(0.578047\pi\)
\(332\) −3.46410 2.00000i −0.190117 0.109764i
\(333\) 8.00000i 0.438397i
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) −1.73205 + 1.00000i −0.0944911 + 0.0545545i
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 0 0
\(339\) 14.0000 0.760376
\(340\) 3.46410 2.00000i 0.187867 0.108465i
\(341\) 0 0
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 20.0000i 1.07990i
\(344\) 3.46410 + 2.00000i 0.186772 + 0.107833i
\(345\) −6.92820 4.00000i −0.373002 0.215353i
\(346\) 6.00000i 0.322562i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) −5.00000 8.66025i −0.268028 0.464238i
\(349\) −13.8564 + 8.00000i −0.741716 + 0.428230i −0.822693 0.568486i \(-0.807529\pi\)
0.0809766 + 0.996716i \(0.474196\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 0 0
\(353\) 22.5167 13.0000i 1.19844 0.691920i 0.238233 0.971208i \(-0.423432\pi\)
0.960207 + 0.279288i \(0.0900983\pi\)
\(354\) 2.00000 + 3.46410i 0.106299 + 0.184115i
\(355\) 0 0
\(356\) 6.00000i 0.317999i
\(357\) −3.46410 2.00000i −0.183340 0.105851i
\(358\) 0 0
\(359\) 4.00000i 0.211112i 0.994413 + 0.105556i \(0.0336622\pi\)
−0.994413 + 0.105556i \(0.966338\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) 8.50000 + 14.7224i 0.447368 + 0.774865i
\(362\) 19.0526 11.0000i 1.00138 0.578147i
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) 1.73205 1.00000i 0.0905357 0.0522708i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 10.0000i 0.520579i
\(370\) 13.8564 + 8.00000i 0.720360 + 0.415900i
\(371\) −10.3923 6.00000i −0.539542 0.311504i
\(372\) 10.0000i 0.518476i
\(373\) 3.00000 5.19615i 0.155334 0.269047i −0.777847 0.628454i \(-0.783688\pi\)
0.933181 + 0.359408i \(0.117021\pi\)
\(374\) 0 0
\(375\) 10.3923 6.00000i 0.536656 0.309839i
\(376\) −12.0000 −0.618853
\(377\) 0 0
\(378\) 2.00000 0.102869
\(379\) 29.4449 17.0000i 1.51248 0.873231i 0.512588 0.858635i \(-0.328687\pi\)
0.999893 0.0145964i \(-0.00464634\pi\)
\(380\) 6.00000 + 10.3923i 0.307794 + 0.533114i
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 12.0000i 0.613973i
\(383\) 3.46410 + 2.00000i 0.177007 + 0.102195i 0.585886 0.810394i \(-0.300747\pi\)
−0.408879 + 0.912589i \(0.634080\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 8.00000 13.8564i 0.407189 0.705273i
\(387\) −2.00000 3.46410i −0.101666 0.176090i
\(388\) 10.3923 6.00000i 0.527589 0.304604i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) −2.59808 + 1.50000i −0.131223 + 0.0757614i
\(393\) 4.00000 + 6.92820i 0.201773 + 0.349482i
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) 0 0
\(396\) 0 0
\(397\) −6.92820 4.00000i −0.347717 0.200754i 0.315963 0.948772i \(-0.397673\pi\)
−0.663679 + 0.748017i \(0.731006\pi\)
\(398\) 0 0
\(399\) 6.00000 10.3923i 0.300376 0.520266i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −25.9808 + 15.0000i −1.29742 + 0.749064i −0.979957 0.199207i \(-0.936163\pi\)
−0.317460 + 0.948272i \(0.602830\pi\)
\(402\) 2.00000 0.0997509
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) 1.73205 1.00000i 0.0860663 0.0496904i
\(406\) 10.0000 + 17.3205i 0.496292 + 0.859602i
\(407\) 0 0
\(408\) 2.00000i 0.0990148i
\(409\) −3.46410 2.00000i −0.171289 0.0988936i 0.411905 0.911227i \(-0.364864\pi\)
−0.583193 + 0.812333i \(0.698197\pi\)
\(410\) 17.3205 + 10.0000i 0.855399 + 0.493865i
\(411\) 2.00000i 0.0986527i
\(412\) −8.00000 + 13.8564i −0.394132 + 0.682656i
\(413\) −4.00000 6.92820i −0.196827 0.340915i
\(414\) 3.46410 2.00000i 0.170251 0.0982946i
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) −20.0000 −0.979404
\(418\) 0 0
\(419\) −20.0000 34.6410i −0.977064 1.69232i −0.672949 0.739689i \(-0.734973\pi\)
−0.304115 0.952635i \(-0.598361\pi\)
\(420\) 2.00000 3.46410i 0.0975900 0.169031i
\(421\) 20.0000i 0.974740i 0.873195 + 0.487370i \(0.162044\pi\)
−0.873195 + 0.487370i \(0.837956\pi\)
\(422\) −10.3923 6.00000i −0.505889 0.292075i
\(423\) 10.3923 + 6.00000i 0.505291 + 0.291730i
\(424\) 6.00000i 0.291386i
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) −3.46410 + 2.00000i −0.167640 + 0.0967868i
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) −17.3205 + 10.0000i −0.834300 + 0.481683i −0.855323 0.518096i \(-0.826641\pi\)
0.0210230 + 0.999779i \(0.493308\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 13.0000 22.5167i 0.624740 1.08208i −0.363851 0.931457i \(-0.618538\pi\)
0.988591 0.150624i \(-0.0481284\pi\)
\(434\) 20.0000i 0.960031i
\(435\) 17.3205 + 10.0000i 0.830455 + 0.479463i
\(436\) 3.46410 + 2.00000i 0.165900 + 0.0957826i
\(437\) 24.0000i 1.14808i
\(438\) −2.00000 + 3.46410i −0.0955637 + 0.165521i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) −16.0000 −0.760183 −0.380091 0.924949i \(-0.624107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(444\) −6.92820 + 4.00000i −0.328798 + 0.189832i
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) −7.00000 + 12.1244i −0.331460 + 0.574105i
\(447\) 14.0000i 0.662177i
\(448\) −1.73205 1.00000i −0.0818317 0.0472456i
\(449\) 5.19615 + 3.00000i 0.245222 + 0.141579i 0.617574 0.786513i \(-0.288115\pi\)
−0.372353 + 0.928091i \(0.621449\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 0 0
\(452\) 7.00000 + 12.1244i 0.329252 + 0.570282i
\(453\) 8.66025 5.00000i 0.406894 0.234920i
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 24.2487 14.0000i 1.13431 0.654892i 0.189292 0.981921i \(-0.439381\pi\)
0.945015 + 0.327028i \(0.106047\pi\)
\(458\) 2.00000 + 3.46410i 0.0934539 + 0.161867i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 8.00000i 0.373002i
\(461\) 25.9808 + 15.0000i 1.21004 + 0.698620i 0.962769 0.270326i \(-0.0871313\pi\)
0.247276 + 0.968945i \(0.420465\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) 5.00000 8.66025i 0.232119 0.402042i
\(465\) 10.0000 + 17.3205i 0.463739 + 0.803219i
\(466\) −5.19615 + 3.00000i −0.240707 + 0.138972i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 20.7846 12.0000i 0.958723 0.553519i
\(471\) 1.00000 + 1.73205i 0.0460776 + 0.0798087i
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) 0 0
\(474\) 0 0
\(475\) 5.19615 + 3.00000i 0.238416 + 0.137649i
\(476\) 4.00000i 0.183340i
\(477\) 3.00000 5.19615i 0.137361 0.237915i
\(478\) −8.00000 13.8564i −0.365911 0.633777i
\(479\) 20.7846 12.0000i 0.949673 0.548294i 0.0566937 0.998392i \(-0.481944\pi\)
0.892979 + 0.450098i \(0.148611\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 0 0
\(482\) −20.0000 −0.910975
\(483\) −6.92820 + 4.00000i −0.315244 + 0.182006i
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) 1.00000i 0.0453609i
\(487\) −15.5885 9.00000i −0.706380 0.407829i 0.103339 0.994646i \(-0.467047\pi\)
−0.809719 + 0.586817i \(0.800381\pi\)
\(488\) 1.73205 + 1.00000i 0.0784063 + 0.0452679i
\(489\) 14.0000i 0.633102i
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) 14.0000 + 24.2487i 0.631811 + 1.09433i 0.987181 + 0.159603i \(0.0510215\pi\)
−0.355370 + 0.934726i \(0.615645\pi\)
\(492\) −8.66025 + 5.00000i −0.390434 + 0.225417i
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) 0 0
\(496\) 8.66025 5.00000i 0.388857 0.224507i
\(497\) 0 0
\(498\) −2.00000 + 3.46410i −0.0896221 + 0.155230i
\(499\) 14.0000i 0.626726i 0.949633 + 0.313363i \(0.101456\pi\)
−0.949633 + 0.313363i \(0.898544\pi\)
\(500\) 10.3923 + 6.00000i 0.464758 + 0.268328i
\(501\) 10.3923 + 6.00000i 0.464294 + 0.268060i
\(502\) 28.0000i 1.24970i
\(503\) −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i \(0.346375\pi\)
−0.999161 + 0.0409609i \(0.986958\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) 3.46410 2.00000i 0.154150 0.0889988i
\(506\) 0 0
\(507\) 0 0
\(508\) −8.00000 −0.354943
\(509\) −5.19615 + 3.00000i −0.230315 + 0.132973i −0.610718 0.791849i \(-0.709119\pi\)
0.380402 + 0.924821i \(0.375786\pi\)
\(510\) −2.00000 3.46410i −0.0885615 0.153393i
\(511\) 4.00000 6.92820i 0.176950 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) 5.19615 + 3.00000i 0.229416 + 0.132453i
\(514\) −15.5885 9.00000i −0.687577 0.396973i
\(515\) 32.0000i 1.41009i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 0 0
\(518\) 13.8564 8.00000i 0.608816 0.351500i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −8.66025 + 5.00000i −0.379049 + 0.218844i
\(523\) −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) −4.00000 + 6.92820i −0.174741 + 0.302660i
\(525\) 2.00000i 0.0872872i
\(526\) −20.7846 12.0000i −0.906252 0.523225i
\(527\) 17.3205 + 10.0000i 0.754493 + 0.435607i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) 3.46410 2.00000i 0.150329 0.0867926i
\(532\) 12.0000 0.520266
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) 13.8564 8.00000i 0.599065 0.345870i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) 0 0
\(540\) 1.73205 + 1.00000i 0.0745356 + 0.0430331i
\(541\) 20.0000i 0.859867i −0.902861 0.429934i \(-0.858537\pi\)
0.902861 0.429934i \(-0.141463\pi\)
\(542\) −5.00000 + 8.66025i −0.214768 + 0.371990i
\(543\) −11.0000 19.0526i −0.472055 0.817624i
\(544\) −1.73205 + 1.00000i −0.0742611 + 0.0428746i
\(545\) −8.00000 −0.342682
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 1.73205 1.00000i 0.0739895 0.0427179i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) 60.0000i 2.55609i
\(552\) 3.46410 + 2.00000i 0.147442 + 0.0851257i
\(553\) 0 0
\(554\) 2.00000i 0.0849719i
\(555\) 8.00000 13.8564i 0.339581 0.588172i
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) 15.5885 9.00000i 0.660504 0.381342i −0.131965 0.991254i \(-0.542129\pi\)
0.792469 + 0.609912i \(0.208795\pi\)
\(558\) −10.0000 −0.423334
\(559\) 0 0
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) −5.00000 8.66025i −0.210912 0.365311i
\(563\) 8.00000 13.8564i 0.337160 0.583978i −0.646737 0.762713i \(-0.723867\pi\)
0.983897 + 0.178735i \(0.0572004\pi\)
\(564\) 12.0000i 0.505291i
\(565\) −24.2487 14.0000i −1.02015 0.588984i
\(566\) −3.46410 2.00000i −0.145607 0.0840663i
\(567\) 2.00000i 0.0839921i
\(568\) 0 0
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 10.3923 6.00000i 0.435286 0.251312i
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 17.3205 10.0000i 0.722944 0.417392i
\(575\) −2.00000 3.46410i −0.0834058 0.144463i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 8.00000i 0.333044i 0.986038 + 0.166522i \(0.0532537\pi\)
−0.986038 + 0.166522i \(0.946746\pi\)
\(578\) 11.2583 + 6.50000i 0.468285 + 0.270364i
\(579\) −13.8564 8.00000i −0.575853 0.332469i
\(580\) 20.0000i 0.830455i
\(581\) 4.00000 6.92820i 0.165948 0.287430i
\(582\) −6.00000 10.3923i −0.248708 0.430775i
\(583\) 0 0
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) 24.2487 14.0000i 1.00085 0.577842i 0.0923513 0.995726i \(-0.470562\pi\)
0.908500 + 0.417885i \(0.137228\pi\)
\(588\) 1.50000 + 2.59808i 0.0618590 + 0.107143i
\(589\) −30.0000 + 51.9615i −1.23613 + 2.14104i
\(590\) 8.00000i 0.329355i
\(591\) 19.0526 + 11.0000i 0.783718 + 0.452480i
\(592\) −6.92820 4.00000i −0.284747 0.164399i
\(593\) 26.0000i 1.06769i 0.845582 + 0.533846i \(0.179254\pi\)
−0.845582 + 0.533846i \(0.820746\pi\)
\(594\) 0 0
\(595\) 4.00000 + 6.92820i 0.163984 + 0.284029i
\(596\) −12.1244 + 7.00000i −0.496633 + 0.286731i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −0.866025 + 0.500000i −0.0353553 + 0.0204124i
\(601\) −11.0000 19.0526i −0.448699 0.777170i 0.549602 0.835426i \(-0.314779\pi\)
−0.998302 + 0.0582563i \(0.981446\pi\)
\(602\) −4.00000 + 6.92820i −0.163028 + 0.282372i
\(603\) 2.00000i 0.0814463i
\(604\) 8.66025 + 5.00000i 0.352381 + 0.203447i
\(605\) −19.0526 11.0000i −0.774597 0.447214i
\(606\) 2.00000i 0.0812444i
\(607\) 16.0000 27.7128i 0.649420 1.12483i −0.333842 0.942629i \(-0.608345\pi\)
0.983262 0.182199i \(-0.0583216\pi\)
\(608\) −3.00000 5.19615i −0.121666 0.210732i
\(609\) 17.3205 10.0000i 0.701862 0.405220i
\(610\) −4.00000 −0.161955
\(611\) 0 0
\(612\) 2.00000 0.0808452
\(613\) 13.8564 8.00000i 0.559655 0.323117i −0.193352 0.981129i \(-0.561936\pi\)
0.753007 + 0.658012i \(0.228603\pi\)
\(614\) −1.00000 1.73205i −0.0403567 0.0698999i
\(615\) 10.0000 17.3205i 0.403239 0.698430i
\(616\) 0 0
\(617\) 19.0526 + 11.0000i 0.767027 + 0.442843i 0.831813 0.555056i \(-0.187303\pi\)
−0.0647859 + 0.997899i \(0.520636\pi\)
\(618\) 13.8564 + 8.00000i 0.557386 + 0.321807i
\(619\) 26.0000i 1.04503i −0.852631 0.522514i \(-0.824994\pi\)
0.852631 0.522514i \(-0.175006\pi\)
\(620\) −10.0000 + 17.3205i −0.401610 + 0.695608i
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) −24.2487 + 14.0000i −0.972285 + 0.561349i
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −22.5167 + 13.0000i −0.899947 + 0.519584i
\(627\) 0 0
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) 16.0000i 0.637962i
\(630\) −3.46410 2.00000i −0.138013 0.0796819i
\(631\) −8.66025 5.00000i −0.344759 0.199047i 0.317615 0.948220i \(-0.397118\pi\)
−0.662375 + 0.749173i \(0.730451\pi\)
\(632\) 0 0
\(633\) −6.00000 + 10.3923i −0.238479 + 0.413057i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 13.8564 8.00000i 0.549875 0.317470i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 8.00000i 0.315735i
\(643\) −5.19615 3.00000i −0.204916 0.118308i 0.394030 0.919097i \(-0.371080\pi\)
−0.598947 + 0.800789i \(0.704414\pi\)
\(644\) −6.92820 4.00000i −0.273009 0.157622i
\(645\) 8.00000i 0.315000i
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 16.0000 + 27.7128i 0.629025 + 1.08950i 0.987748 + 0.156059i \(0.0498790\pi\)
−0.358723 + 0.933444i \(0.616788\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 0 0
\(650\) 0 0
\(651\) 20.0000 0.783862
\(652\) 12.1244 7.00000i 0.474826 0.274141i
\(653\) 13.0000 + 22.5167i 0.508729 + 0.881145i 0.999949 + 0.0101092i \(0.00321793\pi\)
−0.491220 + 0.871036i \(0.663449\pi\)
\(654\) 2.00000 3.46410i 0.0782062 0.135457i
\(655\) 16.0000i 0.625172i
\(656\) −8.66025 5.00000i −0.338126 0.195217i
\(657\) 3.46410 + 2.00000i 0.135147 + 0.0780274i
\(658\) 24.0000i 0.935617i
\(659\) −10.0000 + 17.3205i −0.389545 + 0.674711i −0.992388 0.123148i \(-0.960701\pi\)
0.602844 + 0.797859i \(0.294034\pi\)
\(660\) 0 0
\(661\) −34.6410 + 20.0000i −1.34738 + 0.777910i −0.987878 0.155235i \(-0.950387\pi\)
−0.359502 + 0.933144i \(0.617053\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) −20.7846 + 12.0000i −0.805993 + 0.465340i
\(666\) 4.00000 + 6.92820i 0.154997 + 0.268462i
\(667\) 20.0000 34.6410i 0.774403 1.34131i
\(668\) 12.0000i 0.464294i
\(669\) 12.1244 + 7.00000i 0.468755 + 0.270636i
\(670\) −3.46410 2.00000i −0.133830 0.0772667i
\(671\) 0 0
\(672\) −1.00000 + 1.73205i −0.0385758 + 0.0668153i
\(673\) 3.00000 + 5.19615i 0.115642 + 0.200297i 0.918036 0.396497i \(-0.129774\pi\)
−0.802395 + 0.596794i \(0.796441\pi\)
\(674\) −1.73205 + 1.00000i −0.0667161 + 0.0385186i
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 12.1244 7.00000i 0.465633 0.268833i
\(679\) 12.0000 + 20.7846i 0.460518 + 0.797640i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 8.00000i 0.306561i
\(682\) 0 0
\(683\) 20.7846 + 12.0000i 0.795301 + 0.459167i 0.841825 0.539750i \(-0.181481\pi\)
−0.0465244 + 0.998917i \(0.514815\pi\)
\(684\) 6.00000i 0.229416i
\(685\) −2.00000 + 3.46410i −0.0764161 + 0.132357i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 3.46410 2.00000i 0.132164 0.0763048i
\(688\) 4.00000 0.152499
\(689\) 0 0
\(690\) −8.00000 −0.304555
\(691\) −8.66025 + 5.00000i −0.329452 + 0.190209i −0.655598 0.755110i \(-0.727583\pi\)
0.326146 + 0.945319i \(0.394250\pi\)
\(692\) −3.00000 5.19615i −0.114043 0.197528i
\(693\) 0 0
\(694\) 12.0000i 0.455514i
\(695\) 34.6410 + 20.0000i 1.31401 + 0.758643i
\(696\) −8.66025 5.00000i −0.328266 0.189525i
\(697\) 20.0000i 0.757554i
\(698\) −8.00000 + 13.8564i −0.302804 + 0.524473i
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) 1.73205 1.00000i 0.0654654 0.0377964i
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 48.0000 1.81035
\(704\) 0 0
\(705\) −12.0000 20.7846i −0.451946 0.782794i
\(706\) 13.0000 22.5167i 0.489261 0.847426i
\(707\) 4.00000i 0.150435i
\(708\) 3.46410 + 2.00000i 0.130189 + 0.0751646i
\(709\) 31.1769 + 18.0000i 1.17087 + 0.676004i 0.953886 0.300170i \(-0.0970434\pi\)
0.216988 + 0.976174i \(0.430377\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 34.6410 20.0000i 1.29732 0.749006i
\(714\) −4.00000 −0.149696
\(715\) 0 0
\(716\) 0 0
\(717\) −13.8564 + 8.00000i −0.517477 + 0.298765i
\(718\) 2.00000 + 3.46410i 0.0746393 + 0.129279i
\(719\) −10.0000 + 17.3205i −0.372937 + 0.645946i −0.990016 0.140955i \(-0.954983\pi\)
0.617079 + 0.786901i \(0.288316\pi\)
\(720\) 2.00000i 0.0745356i
\(721\) −27.7128 16.0000i −1.03208 0.595871i
\(722\) 14.7224 + 8.50000i 0.547912 + 0.316337i
\(723\) 20.0000i 0.743808i
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) 5.00000 + 8.66025i 0.185695 + 0.321634i
\(726\) 9.52628 5.50000i 0.353553 0.204124i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.92820 4.00000i 0.256424 0.148047i
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 1.00000 1.73205i 0.0369611 0.0640184i
\(733\) 44.0000i 1.62518i −0.582838 0.812589i \(-0.698058\pi\)
0.582838 0.812589i \(-0.301942\pi\)
\(734\) −6.92820 4.00000i −0.255725 0.147643i
\(735\) −5.19615 3.00000i −0.191663 0.110657i
\(736\) 4.00000i 0.147442i
\(737\) 0 0
\(738\) 5.00000 + 8.66025i 0.184053 + 0.318788i
\(739\) −22.5167 + 13.0000i −0.828289 + 0.478213i −0.853266 0.521475i \(-0.825382\pi\)
0.0249776 + 0.999688i \(0.492049\pi\)
\(740\) 16.0000 0.588172
\(741\) 0 0
\(742\) −12.0000 −0.440534
\(743\) 13.8564 8.00000i 0.508342 0.293492i −0.223810 0.974633i \(-0.571849\pi\)
0.732152 + 0.681141i \(0.238516\pi\)
\(744\) −5.00000 8.66025i −0.183309 0.317500i
\(745\) 14.0000 24.2487i 0.512920 0.888404i
\(746\) 6.00000i 0.219676i
\(747\) 3.46410 + 2.00000i 0.126745 + 0.0731762i
\(748\) 0 0
\(749\) 16.0000i 0.584627i
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) −10.3923 + 6.00000i −0.378968 + 0.218797i
\(753\) −28.0000 −1.02038
\(754\) 0 0
\(755\) −20.0000 −0.727875
\(756\) 1.73205 1.00000i 0.0629941 0.0363696i
\(757\) 11.0000 + 19.0526i 0.399802 + 0.692477i 0.993701 0.112062i \(-0.0357456\pi\)
−0.593899 + 0.804539i \(0.702412\pi\)
\(758\) 17.0000 29.4449i 0.617468 1.06949i
\(759\) 0 0
\(760\) 10.3923 + 6.00000i 0.376969 + 0.217643i
\(761\) −25.9808 15.0000i −0.941802 0.543750i −0.0512772 0.998684i \(-0.516329\pi\)
−0.890525 + 0.454935i \(0.849663\pi\)
\(762\) 8.00000i 0.289809i
\(763\) −4.00000 + 6.92820i −0.144810 + 0.250818i
\(764\) 6.00000 + 10.3923i 0.217072 + 0.375980i
\(765\) −3.46410 + 2.00000i −0.125245 + 0.0723102i
\(766\) 4.00000 0.144526
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 20.7846 12.0000i 0.749512 0.432731i −0.0760054 0.997107i \(-0.524217\pi\)
0.825518 + 0.564376i \(0.190883\pi\)
\(770\) 0 0
\(771\) −9.00000 + 15.5885i −0.324127 + 0.561405i
\(772\) 16.0000i 0.575853i
\(773\) −5.19615 3.00000i −0.186893 0.107903i 0.403634 0.914920i \(-0.367747\pi\)
−0.590527 + 0.807018i \(0.701080\pi\)
\(774\) −3.46410 2.00000i −0.124515 0.0718885i
\(775\) 10.0000i 0.359211i
\(776\) 6.00000 10.3923i 0.215387 0.373062i
\(777\) −8.00000 13.8564i −0.286998 0.497096i
\(778\) 25.9808 15.0000i 0.931455 0.537776i
\(779\) 60.0000 2.14972
\(780\) 0 0
\(781\) 0 0
\(782\) −6.92820 + 4.00000i −0.247752 + 0.143040i
\(783\) 5.00000 + 8.66025i 0.178685 + 0.309492i
\(784\) −1.50000 + 2.59808i −0.0535714 + 0.0927884i
\(785\) 4.00000i 0.142766i
\(786\) 6.92820 + 4.00000i 0.247121 + 0.142675i
\(787\) −32.9090 19.0000i −1.17308 0.677277i −0.218675 0.975798i \(-0.570173\pi\)
−0.954403 + 0.298521i \(0.903507\pi\)
\(788\) 22.0000i 0.783718i
\(789\) −12.0000 + 20.7846i −0.427211 + 0.739952i
\(790\) 0 0
\(791\) −24.2487 + 14.0000i −0.862185 + 0.497783i
\(792\) 0 0
\(793\) 0 0
\(794\) −8.00000 −0.283909
\(795\) −10.3923 + 6.00000i −0.368577 + 0.212798i
\(796\) 0 0
\(797\) 1.00000 1.73205i 0.0354218 0.0613524i −0.847771 0.530362i \(-0.822056\pi\)
0.883193 + 0.469010i \(0.155389\pi\)
\(798\) 12.0000i 0.424795i
\(799\) −20.7846 12.0000i −0.735307 0.424529i
\(800\) −0.866025 0.500000i −0.0306186 0.0176777i
\(801\) 6.00000i 0.212000i
\(802\) −15.0000 + 25.9808i −0.529668 + 0.917413i
\(803\) 0 0
\(804\) 1.73205 1.00000i 0.0610847 0.0352673i
\(805\) 16.0000 0.563926
\(806\) 0 0
\(807\) −10.0000 −0.352017
\(808\) −1.73205 + 1.00000i −0.0609333 + 0.0351799i
\(809\) 25.0000 + 43.3013i 0.878953 + 1.52239i 0.852491 + 0.522742i \(0.175091\pi\)
0.0264621 + 0.999650i \(0.491576\pi\)
\(810\) 1.00000 1.73205i 0.0351364 0.0608581i
\(811\) 10.0000i 0.351147i 0.984466 + 0.175574i \(0.0561780\pi\)
−0.984466 + 0.175574i \(0.943822\pi\)
\(812\) 17.3205 + 10.0000i 0.607831 + 0.350931i
\(813\) 8.66025 + 5.00000i 0.303728 + 0.175358i
\(814\) 0 0
\(815\) −14.0000 + 24.2487i −0.490399 + 0.849395i
\(816\) 1.00000 + 1.73205i 0.0350070 + 0.0606339i
\(817\) −20.7846 + 12.0000i −0.727161 + 0.419827i
\(818\) −4.00000 −0.139857
\(819\) 0 0
\(820\) 20.0000 0.698430
\(821\) 25.9808 15.0000i 0.906735 0.523504i 0.0273557 0.999626i \(-0.491291\pi\)
0.879379 + 0.476122i \(0.157958\pi\)
\(822\) −1.00000 1.73205i −0.0348790 0.0604122i
\(823\) −12.0000 + 20.7846i −0.418294 + 0.724506i −0.995768 0.0919029i \(-0.970705\pi\)
0.577474 + 0.816409i \(0.304038\pi\)
\(824\) 16.0000i 0.557386i
\(825\) 0 0
\(826\) −6.92820 4.00000i −0.241063 0.139178i
\(827\) 48.0000i 1.66912i 0.550914 + 0.834562i \(0.314279\pi\)
−0.550914 + 0.834562i \(0.685721\pi\)
\(828\) 2.00000 3.46410i 0.0695048 0.120386i
\(829\) 15.0000 + 25.9808i 0.520972 + 0.902349i 0.999703 + 0.0243876i \(0.00776357\pi\)
−0.478731 + 0.877962i \(0.658903\pi\)
\(830\) 6.92820 4.00000i 0.240481 0.138842i
\(831\) −2.00000 −0.0693792
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) −17.3205 + 10.0000i −0.599760 + 0.346272i
\(835\) −12.0000 20.7846i −0.415277 0.719281i
\(836\) 0 0
\(837\) 10.0000i 0.345651i
\(838\) −34.6410 20.0000i −1.19665 0.690889i
\(839\) 13.8564 + 8.00000i 0.478376 + 0.276191i 0.719740 0.694244i \(-0.244261\pi\)
−0.241363 + 0.970435i \(0.577595\pi\)
\(840\) 4.00000i 0.138013i
\(841\) −35.5000 + 61.4878i −1.22414 + 2.12027i
\(842\) 10.0000 + 17.3205i 0.344623 + 0.596904i
\(843\) −8.66025 + 5.00000i −0.298275 + 0.172209i
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) 12.0000 0.412568
\(847\) −19.0526 + 11.0000i −0.654654 + 0.377964i
\(848\) 3.00000 + 5.19615i 0.103020 + 0.178437i
\(849\) −2.00000 + 3.46410i −0.0686398 + 0.118888i
\(850\) 2.00000i 0.0685994i
\(851\) −27.7128 16.0000i −0.949983 0.548473i
\(852\) 0 0
\(853\) 56.0000i 1.91740i 0.284413 + 0.958702i \(0.408201\pi\)
−0.284413 + 0.958702i \(0.591799\pi\)
\(854\) −2.00000 + 3.46410i −0.0684386 + 0.118539i
\(855\) −6.00000 10.3923i −0.205196 0.355409i
\(856\) −6.92820 + 4.00000i −0.236801 + 0.136717i
\(857\) −22.0000 −0.751506 −0.375753 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) −6.92820 + 4.00000i −0.236250 + 0.136399i
\(861\) −10.0000 17.3205i −0.340799 0.590281i
\(862\) −10.0000 + 17.3205i −0.340601 + 0.589939i
\(863\) 44.0000i 1.49778i −0.662696 0.748889i \(-0.730588\pi\)
0.662696 0.748889i \(-0.269412\pi\)
\(864\) −0.866025 0.500000i −0.0294628 0.0170103i
\(865\) 10.3923 + 6.00000i 0.353349 + 0.204006i
\(866\) 26.0000i 0.883516i
\(867\) 6.50000 11.2583i 0.220752 0.382353i
\(868\) 10.0000 + 17.3205i 0.339422 + 0.587896i
\(869\) 0 0
\(870\) 20.0000 0.678064
\(871\) 0 0
\(872\) 4.00000 0.135457
\(873\) −10.3923 + 6.00000i −0.351726 + 0.203069i
\(874\) −12.0000 20.7846i −0.405906 0.703050i
\(875\) −12.0000 + 20.7846i −0.405674 + 0.702648i
\(876\) 4.00000i 0.135147i
\(877\) −6.92820 4.00000i −0.233949 0.135070i 0.378444 0.925624i \(-0.376459\pi\)
−0.612392 + 0.790554i \(0.709793\pi\)
\(878\) 0 0
\(879\) 14.0000i 0.472208i
\(880\) 0 0
\(881\) −21.0000 36.3731i −0.707508 1.22544i −0.965779 0.259367i \(-0.916486\pi\)
0.258271 0.966073i \(-0.416847\pi\)
\(882\) 2.59808 1.50000i 0.0874818 0.0505076i
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 0 0
\(885\) −8.00000 −0.268917
\(886\) −13.8564 + 8.00000i −0.465515 + 0.268765i
\(887\) 6.00000 + 10.3923i 0.201460 + 0.348939i 0.948999 0.315279i \(-0.102098\pi\)
−0.747539 + 0.664218i \(0.768765\pi\)
\(888\) −4.00000 + 6.92820i −0.134231 + 0.232495i
\(889\) 16.0000i 0.536623i
\(890\) −10.3923 6.00000i −0.348351 0.201120i
\(891\) 0 0
\(892\) 14.0000i 0.468755i
\(893\) 36.0000 62.3538i 1.20469 2.08659i
\(894\) 7.00000 + 12.1244i 0.234115 + 0.405499i
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) 6.00000 0.200223
\(899\) −86.6025 + 50.0000i −2.88836 + 1.66759i
\(900\) 0.500000 + 0.866025i 0.0166667 + 0.0288675i
\(901\) −6.00000 + 10.3923i −0.199889 + 0.346218i
\(902\) 0 0
\(903\) 6.92820 + 4.00000i 0.230556 + 0.133112i
\(904\) 12.1244 + 7.00000i 0.403250 + 0.232817i
\(905\) 44.0000i 1.46261i
\(906\) 5.00000 8.66025i 0.166114 0.287718i
\(907\) −14.0000 24.2487i −0.464862 0.805165i 0.534333 0.845274i \(-0.320563\pi\)
−0.999195 + 0.0401089i \(0.987230\pi\)
\(908\) −6.92820 + 4.00000i −0.229920 + 0.132745i
\(909\) 2.00000 0.0663358
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −5.19615 + 3.00000i −0.172062 + 0.0993399i
\(913\) 0 0
\(914\) 14.0000 24.2487i 0.463079 0.802076i
\(915\) 4.00000i 0.132236i
\(916\) 3.46410 + 2.00000i 0.114457 + 0.0660819i
\(917\) −13.8564 8.00000i −0.457579 0.264183i
\(918\) 2.00000i 0.0660098i
\(919\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(920\) −4.00000 6.92820i −0.131876 0.228416i
\(921\) −1.73205 + 1.00000i −0.0570730 + 0.0329511i
\(922\) 30.0000 0.987997
\(923\) 0 0
\(924\) 0 0
\(925\) 6.92820 4.00000i 0.227798 0.131519i
\(926\) 3.00000 + 5.19615i 0.0985861 + 0.170756i
\(927\) 8.00000 13.8564i 0.262754 0.455104i
\(928\) 10.0000i 0.328266i
\(929\) 5.19615 + 3.00000i 0.170480 + 0.0984268i 0.582812 0.812607i \(-0.301952\pi\)
−0.412332 + 0.911034i \(0.635286\pi\)
\(930\) 17.3205 + 10.0000i 0.567962 + 0.327913i
\(931\) 18.0000i 0.589926i
\(932\) −3.00000 + 5.19615i −0.0982683 + 0.170206i
\(933\) 14.0000 + 24.2487i 0.458339 + 0.793867i
\(934\) −10.3923 + 6.00000i −0.340047 + 0.196326i
\(935\) 0 0
\(936\) 0 0
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) −3.46410 + 2.00000i −0.113107 + 0.0653023i
\(939\) 13.0000 + 22.5167i 0.424239 + 0.734803i
\(940\) 12.0000 20.7846i 0.391397 0.677919i
\(941\) 10.0000i 0.325991i −0.986627 0.162995i \(-0.947884\pi\)
0.986627 0.162995i \(-0.0521156\pi\)
\(942\) 1.73205 + 1.00000i 0.0564333 + 0.0325818i
\(943\) −34.6410 20.0000i −1.12807 0.651290i
\(944\) 4.00000i 0.130189i
\(945\) −2.00000 + 3.46410i −0.0650600 + 0.112687i
\(946\) 0 0
\(947\) −45.0333 + 26.0000i −1.46339 + 0.844886i −0.999166 0.0408333i \(-0.986999\pi\)
−0.464220 + 0.885720i \(0.653665\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 6.00000 0.194666
\(951\) 15.5885 9.00000i 0.505490 0.291845i
\(952\) −2.00000 3.46410i −0.0648204 0.112272i
\(953\) 3.00000 5.19615i 0.0971795 0.168320i −0.813337 0.581793i \(-0.802351\pi\)
0.910516 + 0.413473i \(0.135685\pi\)
\(954\) 6.00000i 0.194257i
\(955\) −20.7846 12.0000i −0.672574 0.388311i
\(956\) −13.8564 8.00000i −0.448148 0.258738i
\(957\) 0 0
\(958\) 12.0000 20.7846i 0.387702 0.671520i
\(959\) 2.00000 + 3.46410i 0.0645834 + 0.111862i
\(960\) −1.73205 + 1.00000i −0.0559017 + 0.0322749i
\(961\) −69.0000 −2.22581
\(962\) 0 0
\(963\) 8.00000 0.257796
\(964\) −17.3205 + 10.0000i −0.557856 + 0.322078i
\(965\) 16.0000 + 27.7128i 0.515058 + 0.892107i
\(966\) −4.00000 + 6.92820i −0.128698 + 0.222911i
\(967\) 22.0000i 0.707472i −0.935345 0.353736i \(-0.884911\pi\)
0.935345 0.353736i \(-0.115089\pi\)
\(968\) 9.52628 + 5.50000i 0.306186 + 0.176777i
\(969\) −10.3923 6.00000i −0.333849 0.192748i
\(970\) 24.0000i 0.770594i
\(971\) −6.00000 + 10.3923i −0.192549 + 0.333505i −0.946094 0.323891i \(-0.895009\pi\)
0.753545 + 0.657396i \(0.228342\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) 34.6410 20.0000i 1.11054 0.641171i
\(974\) −18.0000 −0.576757
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) −36.3731 + 21.0000i −1.16368 + 0.671850i −0.952183 0.305530i \(-0.901167\pi\)
−0.211495 + 0.977379i \(0.567833\pi\)
\(978\) −7.00000 12.1244i −0.223835 0.387694i
\(979\) 0 0
\(980\) 6.00000i 0.191663i
\(981\) −3.46410 2.00000i −0.110600 0.0638551i
\(982\) 24.2487 + 14.0000i 0.773807 + 0.446758i
\(983\) 24.0000i 0.765481i −0.923856 0.382741i \(-0.874980\pi\)
0.923856 0.382741i \(-0.125020\pi\)
\(984\) −5.00000 + 8.66025i −0.159394 + 0.276079i
\(985\) −22.0000 38.1051i −0.700978 1.21413i
\(986\) 17.3205 10.0000i 0.551597 0.318465i
\(987\) −24.0000 −0.763928
\(988\) 0 0
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) 4.00000 + 6.92820i 0.127064 + 0.220082i 0.922538 0.385906i \(-0.126111\pi\)
−0.795474 + 0.605988i \(0.792778\pi\)
\(992\) 5.00000 8.66025i 0.158750 0.274963i
\(993\) 10.0000i 0.317340i
\(994\) 0 0
\(995\) 0 0
\(996\) 4.00000i 0.126745i
\(997\) 21.0000 36.3731i 0.665077 1.15195i −0.314188 0.949361i \(-0.601732\pi\)
0.979265 0.202586i \(-0.0649345\pi\)
\(998\) 7.00000 + 12.1244i 0.221581 + 0.383790i
\(999\) 6.92820 4.00000i 0.219199 0.126554i
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 1014.2.i.c.361.2 4
13.2 odd 12 1014.2.a.g.1.1 1
13.3 even 3 78.2.b.a.25.2 yes 2
13.4 even 6 inner 1014.2.i.c.823.2 4
13.5 odd 4 1014.2.e.b.991.1 2
13.6 odd 12 1014.2.e.b.529.1 2
13.7 odd 12 1014.2.e.e.529.1 2
13.8 odd 4 1014.2.e.e.991.1 2
13.9 even 3 inner 1014.2.i.c.823.1 4
13.10 even 6 78.2.b.a.25.1 2
13.11 odd 12 1014.2.a.b.1.1 1
13.12 even 2 inner 1014.2.i.c.361.1 4
39.2 even 12 3042.2.a.c.1.1 1
39.11 even 12 3042.2.a.n.1.1 1
39.23 odd 6 234.2.b.a.181.2 2
39.29 odd 6 234.2.b.a.181.1 2
52.3 odd 6 624.2.c.a.337.2 2
52.11 even 12 8112.2.a.g.1.1 1
52.15 even 12 8112.2.a.j.1.1 1
52.23 odd 6 624.2.c.a.337.1 2
65.3 odd 12 1950.2.f.g.649.2 2
65.23 odd 12 1950.2.f.d.649.2 2
65.29 even 6 1950.2.b.c.1351.1 2
65.42 odd 12 1950.2.f.d.649.1 2
65.49 even 6 1950.2.b.c.1351.2 2
65.62 odd 12 1950.2.f.g.649.1 2
91.55 odd 6 3822.2.c.d.883.2 2
91.62 odd 6 3822.2.c.d.883.1 2
104.3 odd 6 2496.2.c.m.961.1 2
104.29 even 6 2496.2.c.f.961.1 2
104.75 odd 6 2496.2.c.m.961.2 2
104.101 even 6 2496.2.c.f.961.2 2
156.23 even 6 1872.2.c.b.1585.2 2
156.107 even 6 1872.2.c.b.1585.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.b.a.25.1 2 13.10 even 6
78.2.b.a.25.2 yes 2 13.3 even 3
234.2.b.a.181.1 2 39.29 odd 6
234.2.b.a.181.2 2 39.23 odd 6
624.2.c.a.337.1 2 52.23 odd 6
624.2.c.a.337.2 2 52.3 odd 6
1014.2.a.b.1.1 1 13.11 odd 12
1014.2.a.g.1.1 1 13.2 odd 12
1014.2.e.b.529.1 2 13.6 odd 12
1014.2.e.b.991.1 2 13.5 odd 4
1014.2.e.e.529.1 2 13.7 odd 12
1014.2.e.e.991.1 2 13.8 odd 4
1014.2.i.c.361.1 4 13.12 even 2 inner
1014.2.i.c.361.2 4 1.1 even 1 trivial
1014.2.i.c.823.1 4 13.9 even 3 inner
1014.2.i.c.823.2 4 13.4 even 6 inner
1872.2.c.b.1585.1 2 156.107 even 6
1872.2.c.b.1585.2 2 156.23 even 6
1950.2.b.c.1351.1 2 65.29 even 6
1950.2.b.c.1351.2 2 65.49 even 6
1950.2.f.d.649.1 2 65.42 odd 12
1950.2.f.d.649.2 2 65.23 odd 12
1950.2.f.g.649.1 2 65.62 odd 12
1950.2.f.g.649.2 2 65.3 odd 12
2496.2.c.f.961.1 2 104.29 even 6
2496.2.c.f.961.2 2 104.101 even 6
2496.2.c.m.961.1 2 104.3 odd 6
2496.2.c.m.961.2 2 104.75 odd 6
3042.2.a.c.1.1 1 39.2 even 12
3042.2.a.n.1.1 1 39.11 even 12
3822.2.c.d.883.1 2 91.62 odd 6
3822.2.c.d.883.2 2 91.55 odd 6
8112.2.a.g.1.1 1 52.11 even 12
8112.2.a.j.1.1 1 52.15 even 12