Properties

Label 1134.2.h.o.109.1
Level $1134$
Weight $2$
Character 1134.109
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(109,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (of order \(3\), 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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.109
Dual form 1134.2.h.o.541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} -5.00000 q^{11} +(-3.00000 + 5.19615i) q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(2.00000 + 3.46410i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(-2.50000 + 4.33013i) q^{22} +4.00000 q^{23} -1.00000 q^{25} +(3.00000 + 5.19615i) q^{26} +(2.00000 + 1.73205i) q^{28} +(3.50000 + 6.06218i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} +(-5.00000 + 1.73205i) q^{35} +(-4.00000 - 6.92820i) q^{37} +4.00000 q^{38} -2.00000 q^{40} +(-3.00000 + 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +6.00000 q^{52} +(-3.00000 + 5.19615i) q^{53} -10.0000 q^{55} +(2.50000 - 0.866025i) q^{56} +7.00000 q^{58} +(3.50000 + 6.06218i) q^{59} -3.00000 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-5.00000 - 8.66025i) q^{67} +4.00000 q^{68} +(-1.00000 + 5.19615i) q^{70} +4.00000 q^{71} +(-6.50000 + 11.2583i) q^{73} -8.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(12.5000 - 4.33013i) q^{77} +(1.50000 - 2.59808i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(3.00000 + 5.19615i) q^{82} +(-3.50000 - 6.06218i) q^{83} +(-4.00000 + 6.92820i) q^{85} -8.00000 q^{86} +5.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(3.00000 - 15.5885i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(4.00000 + 6.92820i) q^{95} +(2.50000 + 4.33013i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 4 q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 4 q^{5} - 5 q^{7} - 2 q^{8} + 2 q^{10} - 10 q^{11} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} + 4 q^{19} - 2 q^{20} - 5 q^{22} + 8 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 7 q^{29} - 3 q^{31} + q^{32} + 4 q^{34} - 10 q^{35} - 8 q^{37} + 8 q^{38} - 4 q^{40} - 6 q^{41} - 8 q^{43} + 5 q^{44} + 4 q^{46} + 6 q^{47} + 11 q^{49} - q^{50} + 12 q^{52} - 6 q^{53} - 20 q^{55} + 5 q^{56} + 14 q^{58} + 7 q^{59} - 6 q^{62} + 2 q^{64} - 12 q^{65} - 10 q^{67} + 8 q^{68} - 2 q^{70} + 8 q^{71} - 13 q^{73} - 16 q^{74} + 4 q^{76} + 25 q^{77} + 3 q^{79} - 2 q^{80} + 6 q^{82} - 7 q^{83} - 8 q^{85} - 16 q^{86} + 10 q^{88} + 6 q^{89} + 6 q^{91} - 4 q^{92} - 6 q^{94} + 8 q^{95} + 5 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i \(0.479500\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) −0.500000 + 2.59808i −0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −1.00000 1.73205i −0.223607 0.387298i
\(21\) 0 0
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.00000 + 5.19615i 0.588348 + 1.01905i
\(27\) 0 0
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) 3.50000 + 6.06218i 0.649934 + 1.12572i 0.983138 + 0.182864i \(0.0585367\pi\)
−0.333205 + 0.942855i \(0.608130\pi\)
\(30\) 0 0
\(31\) −1.50000 2.59808i −0.269408 0.466628i 0.699301 0.714827i \(-0.253495\pi\)
−0.968709 + 0.248199i \(0.920161\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) −5.00000 + 1.73205i −0.845154 + 0.292770i
\(36\) 0 0
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) −2.00000 −0.316228
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) 0 0
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 6.00000 0.832050
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) −10.0000 −1.34840
\(56\) 2.50000 0.866025i 0.334077 0.115728i
\(57\) 0 0
\(58\) 7.00000 0.919145
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) −3.00000 −0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) −1.00000 + 5.19615i −0.119523 + 0.621059i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) −6.50000 + 11.2583i −0.760767 + 1.31769i 0.181688 + 0.983356i \(0.441844\pi\)
−0.942455 + 0.334332i \(0.891489\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 12.5000 4.33013i 1.42451 0.493464i
\(78\) 0 0
\(79\) 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i \(-0.779356\pi\)
0.937985 + 0.346675i \(0.112689\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) 0 0
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) −3.50000 6.06218i −0.384175 0.665410i 0.607479 0.794335i \(-0.292181\pi\)
−0.991654 + 0.128925i \(0.958847\pi\)
\(84\) 0 0
\(85\) −4.00000 + 6.92820i −0.433861 + 0.751469i
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 5.00000 0.533002
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 3.00000 15.5885i 0.314485 1.63411i
\(92\) −2.00000 3.46410i −0.208514 0.361158i
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) 2.50000 + 4.33013i 0.253837 + 0.439658i 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 5.00000 0.497519 0.248759 0.968565i \(-0.419977\pi\)
0.248759 + 0.968565i \(0.419977\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 3.00000 5.19615i 0.294174 0.509525i
\(105\) 0 0
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 0 0
\(109\) −8.00000 + 13.8564i −0.766261 + 1.32720i 0.173316 + 0.984866i \(0.444552\pi\)
−0.939577 + 0.342337i \(0.888782\pi\)
\(110\) −5.00000 + 8.66025i −0.476731 + 0.825723i
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) 2.00000 3.46410i 0.188144 0.325875i −0.756487 0.654008i \(-0.773086\pi\)
0.944632 + 0.328133i \(0.106419\pi\)
\(114\) 0 0
\(115\) 8.00000 0.746004
\(116\) 3.50000 6.06218i 0.324967 0.562859i
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) 2.00000 10.3923i 0.183340 0.952661i
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 0 0
\(124\) −1.50000 + 2.59808i −0.134704 + 0.233314i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) −13.0000 −1.13582 −0.567908 0.823092i \(-0.692247\pi\)
−0.567908 + 0.823092i \(0.692247\pi\)
\(132\) 0 0
\(133\) −8.00000 6.92820i −0.693688 0.600751i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) 8.00000 0.683486 0.341743 0.939793i \(-0.388983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) 0 0
\(139\) 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i \(-0.723151\pi\)
0.984297 + 0.176522i \(0.0564848\pi\)
\(140\) 4.00000 + 3.46410i 0.338062 + 0.292770i
\(141\) 0 0
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) 15.0000 25.9808i 1.25436 2.17262i
\(144\) 0 0
\(145\) 7.00000 + 12.1244i 0.581318 + 1.00687i
\(146\) 6.50000 + 11.2583i 0.537944 + 0.931746i
\(147\) 0 0
\(148\) −4.00000 + 6.92820i −0.328798 + 0.569495i
\(149\) −9.00000 −0.737309 −0.368654 0.929567i \(-0.620181\pi\)
−0.368654 + 0.929567i \(0.620181\pi\)
\(150\) 0 0
\(151\) −17.0000 −1.38344 −0.691720 0.722166i \(-0.743147\pi\)
−0.691720 + 0.722166i \(0.743147\pi\)
\(152\) −2.00000 3.46410i −0.162221 0.280976i
\(153\) 0 0
\(154\) 2.50000 12.9904i 0.201456 1.04679i
\(155\) −3.00000 5.19615i −0.240966 0.417365i
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) −1.50000 2.59808i −0.119334 0.206692i
\(159\) 0 0
\(160\) 1.00000 + 1.73205i 0.0790569 + 0.136931i
\(161\) −10.0000 + 3.46410i −0.788110 + 0.273009i
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −7.00000 −0.543305
\(167\) −7.00000 + 12.1244i −0.541676 + 0.938211i 0.457132 + 0.889399i \(0.348877\pi\)
−0.998808 + 0.0488118i \(0.984457\pi\)
\(168\) 0 0
\(169\) −11.5000 19.9186i −0.884615 1.53220i
\(170\) 4.00000 + 6.92820i 0.306786 + 0.531369i
\(171\) 0 0
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) 0.500000 0.866025i 0.0380143 0.0658427i −0.846392 0.532560i \(-0.821230\pi\)
0.884407 + 0.466717i \(0.154563\pi\)
\(174\) 0 0
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) 2.50000 4.33013i 0.188445 0.326396i
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) −7.50000 + 12.9904i −0.560576 + 0.970947i 0.436870 + 0.899525i \(0.356087\pi\)
−0.997446 + 0.0714220i \(0.977246\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −12.0000 10.3923i −0.889499 0.770329i
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) −8.00000 13.8564i −0.588172 1.01874i
\(186\) 0 0
\(187\) 10.0000 17.3205i 0.731272 1.26660i
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) 5.00000 0.358979
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 25.0000 1.78118 0.890588 0.454811i \(-0.150293\pi\)
0.890588 + 0.454811i \(0.150293\pi\)
\(198\) 0 0
\(199\) 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) 2.50000 4.33013i 0.175899 0.304667i
\(203\) −14.0000 12.1244i −0.982607 0.850963i
\(204\) 0 0
\(205\) −6.00000 + 10.3923i −0.419058 + 0.725830i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 0 0
\(208\) −3.00000 5.19615i −0.208013 0.360288i
\(209\) −10.0000 17.3205i −0.691714 1.19808i
\(210\) 0 0
\(211\) −13.0000 + 22.5167i −0.894957 + 1.55011i −0.0610990 + 0.998132i \(0.519461\pi\)
−0.833858 + 0.551979i \(0.813873\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) 0 0
\(217\) 6.00000 + 5.19615i 0.407307 + 0.352738i
\(218\) 8.00000 + 13.8564i 0.541828 + 0.938474i
\(219\) 0 0
\(220\) 5.00000 + 8.66025i 0.337100 + 0.583874i
\(221\) −12.0000 20.7846i −0.807207 1.39812i
\(222\) 0 0
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) −2.00000 1.73205i −0.133631 0.115728i
\(225\) 0 0
\(226\) −2.00000 3.46410i −0.133038 0.230429i
\(227\) 27.0000 1.79205 0.896026 0.444001i \(-0.146441\pi\)
0.896026 + 0.444001i \(0.146441\pi\)
\(228\) 0 0
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 4.00000 6.92820i 0.263752 0.456832i
\(231\) 0 0
\(232\) −3.50000 6.06218i −0.229786 0.398001i
\(233\) −11.0000 19.0526i −0.720634 1.24817i −0.960746 0.277429i \(-0.910518\pi\)
0.240112 0.970745i \(-0.422816\pi\)
\(234\) 0 0
\(235\) 6.00000 10.3923i 0.391397 0.677919i
\(236\) 3.50000 6.06218i 0.227831 0.394614i
\(237\) 0 0
\(238\) −8.00000 6.92820i −0.518563 0.449089i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157 −0.0322078 0.999481i \(-0.510254\pi\)
−0.0322078 + 0.999481i \(0.510254\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) 0 0
\(244\) 0 0
\(245\) 11.0000 8.66025i 0.702764 0.553283i
\(246\) 0 0
\(247\) −24.0000 −1.52708
\(248\) 1.50000 + 2.59808i 0.0952501 + 0.164978i
\(249\) 0 0
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 16.0000 + 13.8564i 0.994192 + 0.860995i
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −6.50000 + 11.2583i −0.401571 + 0.695542i
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) −6.00000 + 10.3923i −0.368577 + 0.638394i
\(266\) −10.0000 + 3.46410i −0.613139 + 0.212398i
\(267\) 0 0
\(268\) −5.00000 + 8.66025i −0.305424 + 0.529009i
\(269\) 15.5000 26.8468i 0.945052 1.63688i 0.189404 0.981899i \(-0.439344\pi\)
0.755648 0.654978i \(-0.227322\pi\)
\(270\) 0 0
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) 0 0
\(274\) 4.00000 6.92820i 0.241649 0.418548i
\(275\) 5.00000 0.301511
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −4.00000 6.92820i −0.239904 0.415526i
\(279\) 0 0
\(280\) 5.00000 1.73205i 0.298807 0.103510i
\(281\) 1.00000 + 1.73205i 0.0596550 + 0.103325i 0.894311 0.447447i \(-0.147667\pi\)
−0.834656 + 0.550772i \(0.814333\pi\)
\(282\) 0 0
\(283\) −8.00000 13.8564i −0.475551 0.823678i 0.524057 0.851683i \(-0.324418\pi\)
−0.999608 + 0.0280052i \(0.991084\pi\)
\(284\) −2.00000 3.46410i −0.118678 0.205557i
\(285\) 0 0
\(286\) −15.0000 25.9808i −0.886969 1.53627i
\(287\) 3.00000 15.5885i 0.177084 0.920158i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 14.0000 0.822108
\(291\) 0 0
\(292\) 13.0000 0.760767
\(293\) 13.5000 23.3827i 0.788678 1.36603i −0.138098 0.990419i \(-0.544099\pi\)
0.926777 0.375613i \(-0.122568\pi\)
\(294\) 0 0
\(295\) 7.00000 + 12.1244i 0.407556 + 0.705907i
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) 0 0
\(298\) −4.50000 + 7.79423i −0.260678 + 0.451508i
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) 16.0000 + 13.8564i 0.922225 + 0.798670i
\(302\) −8.50000 + 14.7224i −0.489120 + 0.847181i
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 0 0
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) −10.0000 8.66025i −0.569803 0.493464i
\(309\) 0 0
\(310\) −6.00000 −0.340777
\(311\) 11.0000 + 19.0526i 0.623753 + 1.08037i 0.988781 + 0.149375i \(0.0477261\pi\)
−0.365028 + 0.930997i \(0.618941\pi\)
\(312\) 0 0
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −3.00000 −0.168763
\(317\) −16.5000 + 28.5788i −0.926732 + 1.60515i −0.137981 + 0.990435i \(0.544061\pi\)
−0.788751 + 0.614713i \(0.789272\pi\)
\(318\) 0 0
\(319\) −17.5000 30.3109i −0.979812 1.69708i
\(320\) 2.00000 0.111803
\(321\) 0 0
\(322\) −2.00000 + 10.3923i −0.111456 + 0.579141i
\(323\) −16.0000 −0.890264
\(324\) 0 0
\(325\) 3.00000 5.19615i 0.166410 0.288231i
\(326\) −2.00000 −0.110770
\(327\) 0 0
\(328\) 3.00000 5.19615i 0.165647 0.286910i
\(329\) −3.00000 + 15.5885i −0.165395 + 0.859419i
\(330\) 0 0
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) −3.50000 + 6.06218i −0.192087 + 0.332705i
\(333\) 0 0
\(334\) 7.00000 + 12.1244i 0.383023 + 0.663415i
\(335\) −10.0000 17.3205i −0.546358 0.946320i
\(336\) 0 0
\(337\) 13.5000 23.3827i 0.735392 1.27374i −0.219159 0.975689i \(-0.570331\pi\)
0.954551 0.298047i \(-0.0963352\pi\)
\(338\) −23.0000 −1.25104
\(339\) 0 0
\(340\) 8.00000 0.433861
\(341\) 7.50000 + 12.9904i 0.406148 + 0.703469i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 4.00000 + 6.92820i 0.215666 + 0.373544i
\(345\) 0 0
\(346\) −0.500000 0.866025i −0.0268802 0.0465578i
\(347\) −13.5000 23.3827i −0.724718 1.25525i −0.959090 0.283101i \(-0.908637\pi\)
0.234372 0.972147i \(-0.424697\pi\)
\(348\) 0 0
\(349\) 10.0000 + 17.3205i 0.535288 + 0.927146i 0.999149 + 0.0412379i \(0.0131301\pi\)
−0.463862 + 0.885908i \(0.653537\pi\)
\(350\) 0.500000 2.59808i 0.0267261 0.138873i
\(351\) 0 0
\(352\) −2.50000 4.33013i −0.133250 0.230797i
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 0 0
\(358\) 7.50000 + 12.9904i 0.396387 + 0.686563i
\(359\) 8.00000 + 13.8564i 0.422224 + 0.731313i 0.996157 0.0875892i \(-0.0279163\pi\)
−0.573933 + 0.818902i \(0.694583\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) −15.0000 + 5.19615i −0.786214 + 0.272352i
\(365\) −13.0000 + 22.5167i −0.680451 + 1.17858i
\(366\) 0 0
\(367\) −4.00000 −0.208798 −0.104399 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 0 0
\(370\) −16.0000 −0.831800
\(371\) 3.00000 15.5885i 0.155752 0.809312i
\(372\) 0 0
\(373\) −20.0000 −1.03556 −0.517780 0.855514i \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) −10.0000 17.3205i −0.517088 0.895622i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −42.0000 −2.16311
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 4.00000 6.92820i 0.205196 0.355409i
\(381\) 0 0
\(382\) 9.00000 + 15.5885i 0.460480 + 0.797575i
\(383\) 4.00000 0.204390 0.102195 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) 0 0
\(385\) 25.0000 8.66025i 1.27412 0.441367i
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) 2.50000 4.33013i 0.126918 0.219829i
\(389\) −1.00000 −0.0507020 −0.0253510 0.999679i \(-0.508070\pi\)
−0.0253510 + 0.999679i \(0.508070\pi\)
\(390\) 0 0
\(391\) −8.00000 + 13.8564i −0.404577 + 0.700749i
\(392\) −5.50000 + 4.33013i −0.277792 + 0.218704i
\(393\) 0 0
\(394\) 12.5000 21.6506i 0.629741 1.09074i
\(395\) 3.00000 5.19615i 0.150946 0.261447i
\(396\) 0 0
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) −9.50000 16.4545i −0.476192 0.824789i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 18.0000 0.896644
\(404\) −2.50000 4.33013i −0.124380 0.215432i
\(405\) 0 0
\(406\) −17.5000 + 6.06218i −0.868510 + 0.300861i
\(407\) 20.0000 + 34.6410i 0.991363 + 1.71709i
\(408\) 0 0
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 6.00000 + 10.3923i 0.296319 + 0.513239i
\(411\) 0 0
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) −14.0000 12.1244i −0.688895 0.596601i
\(414\) 0 0
\(415\) −7.00000 12.1244i −0.343616 0.595161i
\(416\) −6.00000 −0.294174
\(417\) 0 0
\(418\) −20.0000 −0.978232
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) 9.00000 + 15.5885i 0.438633 + 0.759735i 0.997584 0.0694656i \(-0.0221294\pi\)
−0.558951 + 0.829201i \(0.688796\pi\)
\(422\) 13.0000 + 22.5167i 0.632830 + 1.09609i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) 0 0
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 0 0
\(430\) −16.0000 −0.771589
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 0 0
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 7.50000 2.59808i 0.360012 0.124712i
\(435\) 0 0
\(436\) 16.0000 0.766261
\(437\) 8.00000 + 13.8564i 0.382692 + 0.662842i
\(438\) 0 0
\(439\) −1.50000 + 2.59808i −0.0715911 + 0.123999i −0.899599 0.436717i \(-0.856141\pi\)
0.828008 + 0.560717i \(0.189474\pi\)
\(440\) 10.0000 0.476731
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) 5.50000 9.52628i 0.261313 0.452607i −0.705278 0.708931i \(-0.749178\pi\)
0.966591 + 0.256323i \(0.0825112\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) 1.00000 0.0473514
\(447\) 0 0
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 15.0000 25.9808i 0.706322 1.22339i
\(452\) −4.00000 −0.188144
\(453\) 0 0
\(454\) 13.5000 23.3827i 0.633586 1.09740i
\(455\) 6.00000 31.1769i 0.281284 1.46160i
\(456\) 0 0
\(457\) 13.0000 22.5167i 0.608114 1.05328i −0.383437 0.923567i \(-0.625260\pi\)
0.991551 0.129718i \(-0.0414071\pi\)
\(458\) 2.00000 3.46410i 0.0934539 0.161867i
\(459\) 0 0
\(460\) −4.00000 6.92820i −0.186501 0.323029i
\(461\) −11.5000 19.9186i −0.535608 0.927701i −0.999134 0.0416172i \(-0.986749\pi\)
0.463525 0.886084i \(-0.346584\pi\)
\(462\) 0 0
\(463\) 14.5000 25.1147i 0.673872 1.16718i −0.302925 0.953014i \(-0.597963\pi\)
0.976797 0.214166i \(-0.0687035\pi\)
\(464\) −7.00000 −0.324967
\(465\) 0 0
\(466\) −22.0000 −1.01913
\(467\) 3.50000 + 6.06218i 0.161961 + 0.280524i 0.935572 0.353137i \(-0.114885\pi\)
−0.773611 + 0.633661i \(0.781552\pi\)
\(468\) 0 0
\(469\) 20.0000 + 17.3205i 0.923514 + 0.799787i
\(470\) −6.00000 10.3923i −0.276759 0.479361i
\(471\) 0 0
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 20.0000 + 34.6410i 0.919601 + 1.59280i
\(474\) 0 0
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) −10.0000 + 3.46410i −0.458349 + 0.158777i
\(477\) 0 0
\(478\) 0 0
\(479\) −26.0000 −1.18797 −0.593985 0.804476i \(-0.702446\pi\)
−0.593985 + 0.804476i \(0.702446\pi\)
\(480\) 0 0
\(481\) 48.0000 2.18861
\(482\) −0.500000 + 0.866025i −0.0227744 + 0.0394464i
\(483\) 0 0
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) 0 0
\(487\) 6.50000 11.2583i 0.294543 0.510164i −0.680335 0.732901i \(-0.738166\pi\)
0.974879 + 0.222737i \(0.0714992\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −2.00000 13.8564i −0.0903508 0.625969i
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 0 0
\(493\) −28.0000 −1.26106
\(494\) −12.0000 + 20.7846i −0.539906 + 0.935144i
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) −10.0000 + 3.46410i −0.448561 + 0.155386i
\(498\) 0 0
\(499\) −8.00000 −0.358129 −0.179065 0.983837i \(-0.557307\pi\)
−0.179065 + 0.983837i \(0.557307\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) 0 0
\(502\) 10.5000 18.1865i 0.468638 0.811705i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −10.0000 + 17.3205i −0.444554 + 0.769991i
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 −0.132973 −0.0664863 0.997787i \(-0.521179\pi\)
−0.0664863 + 0.997787i \(0.521179\pi\)
\(510\) 0 0
\(511\) 6.50000 33.7750i 0.287543 1.49412i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) −15.0000 + 25.9808i −0.659699 + 1.14263i
\(518\) 20.0000 6.92820i 0.878750 0.304408i
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) 0 0
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) 6.50000 + 11.2583i 0.283954 + 0.491822i
\(525\) 0 0
\(526\) −6.00000 + 10.3923i −0.261612 + 0.453126i
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 6.00000 + 10.3923i 0.260623 + 0.451413i
\(531\) 0 0
\(532\) −2.00000 + 10.3923i −0.0867110 + 0.450564i
\(533\) −18.0000 31.1769i −0.779667 1.35042i
\(534\) 0 0
\(535\) 12.0000 + 20.7846i 0.518805 + 0.898597i
\(536\) 5.00000 + 8.66025i 0.215967 + 0.374066i
\(537\) 0 0
\(538\) −15.5000 26.8468i −0.668252 1.15745i
\(539\) −27.5000 + 21.6506i −1.18451 + 0.932559i
\(540\) 0 0
\(541\) 15.0000 + 25.9808i 0.644900 + 1.11700i 0.984325 + 0.176367i \(0.0564345\pi\)
−0.339424 + 0.940633i \(0.610232\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) −16.0000 + 27.7128i −0.685365 + 1.18709i
\(546\) 0 0
\(547\) 9.00000 + 15.5885i 0.384812 + 0.666514i 0.991743 0.128240i \(-0.0409329\pi\)
−0.606931 + 0.794755i \(0.707600\pi\)
\(548\) −4.00000 6.92820i −0.170872 0.295958i
\(549\) 0 0
\(550\) 2.50000 4.33013i 0.106600 0.184637i
\(551\) −14.0000 + 24.2487i −0.596420 + 1.03303i
\(552\) 0 0
\(553\) −1.50000 + 7.79423i −0.0637865 + 0.331444i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) −5.50000 + 9.52628i −0.233042 + 0.403641i −0.958702 0.284413i \(-0.908201\pi\)
0.725660 + 0.688054i \(0.241535\pi\)
\(558\) 0 0
\(559\) 48.0000 2.03018
\(560\) 1.00000 5.19615i 0.0422577 0.219578i
\(561\) 0 0
\(562\) 2.00000 0.0843649
\(563\) 10.0000 + 17.3205i 0.421450 + 0.729972i 0.996082 0.0884397i \(-0.0281881\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(564\) 0 0
\(565\) 4.00000 6.92820i 0.168281 0.291472i
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) −6.00000 + 10.3923i −0.251533 + 0.435668i −0.963948 0.266090i \(-0.914268\pi\)
0.712415 + 0.701758i \(0.247601\pi\)
\(570\) 0 0
\(571\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(572\) −30.0000 −1.25436
\(573\) 0 0
\(574\) −12.0000 10.3923i −0.500870 0.433766i
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −21.5000 + 37.2391i −0.895057 + 1.55028i −0.0613223 + 0.998118i \(0.519532\pi\)
−0.833734 + 0.552166i \(0.813802\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) 7.00000 12.1244i 0.290659 0.503436i
\(581\) 14.0000 + 12.1244i 0.580818 + 0.503003i
\(582\) 0 0
\(583\) 15.0000 25.9808i 0.621237 1.07601i
\(584\) 6.50000 11.2583i 0.268972 0.465873i
\(585\) 0 0
\(586\) −13.5000 23.3827i −0.557680 0.965930i
\(587\) 10.0000 + 17.3205i 0.412744 + 0.714894i 0.995189 0.0979766i \(-0.0312370\pi\)
−0.582445 + 0.812870i \(0.697904\pi\)
\(588\) 0 0
\(589\) 6.00000 10.3923i 0.247226 0.428207i
\(590\) 14.0000 0.576371
\(591\) 0 0
\(592\) 8.00000 0.328798
\(593\) 18.0000 + 31.1769i 0.739171 + 1.28028i 0.952869 + 0.303383i \(0.0981160\pi\)
−0.213697 + 0.976900i \(0.568551\pi\)
\(594\) 0 0
\(595\) 4.00000 20.7846i 0.163984 0.852086i
\(596\) 4.50000 + 7.79423i 0.184327 + 0.319264i
\(597\) 0 0
\(598\) 12.0000 + 20.7846i 0.490716 + 0.849946i
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 0 0
\(601\) 5.00000 + 8.66025i 0.203954 + 0.353259i 0.949799 0.312861i \(-0.101287\pi\)
−0.745845 + 0.666120i \(0.767954\pi\)
\(602\) 20.0000 6.92820i 0.815139 0.282372i
\(603\) 0 0
\(604\) 8.50000 + 14.7224i 0.345860 + 0.599047i
\(605\) 28.0000 1.13836
\(606\) 0 0
\(607\) −9.00000 −0.365299 −0.182649 0.983178i \(-0.558467\pi\)
−0.182649 + 0.983178i \(0.558467\pi\)
\(608\) −2.00000 + 3.46410i −0.0811107 + 0.140488i
\(609\) 0 0
\(610\) 0 0
\(611\) 18.0000 + 31.1769i 0.728202 + 1.26128i
\(612\) 0 0
\(613\) 3.00000 5.19615i 0.121169 0.209871i −0.799060 0.601251i \(-0.794669\pi\)
0.920229 + 0.391381i \(0.128002\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) −12.5000 + 4.33013i −0.503639 + 0.174466i
\(617\) 1.00000 1.73205i 0.0402585 0.0697297i −0.845194 0.534460i \(-0.820515\pi\)
0.885453 + 0.464730i \(0.153849\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) −3.00000 + 5.19615i −0.120483 + 0.208683i
\(621\) 0 0
\(622\) 22.0000 0.882120
\(623\) −12.0000 10.3923i −0.480770 0.416359i
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 0 0
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 32.0000 1.27592
\(630\) 0 0
\(631\) 5.00000 0.199047 0.0995234 0.995035i \(-0.468268\pi\)
0.0995234 + 0.995035i \(0.468268\pi\)
\(632\) −1.50000 + 2.59808i −0.0596668 + 0.103346i
\(633\) 0 0
\(634\) 16.5000 + 28.5788i 0.655299 + 1.13501i
\(635\) 0 0
\(636\) 0 0
\(637\) 6.00000 + 41.5692i 0.237729 + 1.64703i
\(638\) −35.0000 −1.38566
\(639\) 0 0
\(640\) 1.00000 1.73205i 0.0395285 0.0684653i
\(641\) −14.0000 −0.552967 −0.276483 0.961019i \(-0.589169\pi\)
−0.276483 + 0.961019i \(0.589169\pi\)
\(642\) 0 0
\(643\) −7.00000 + 12.1244i −0.276053 + 0.478138i −0.970400 0.241502i \(-0.922360\pi\)
0.694347 + 0.719640i \(0.255693\pi\)
\(644\) 8.00000 + 6.92820i 0.315244 + 0.273009i
\(645\) 0 0
\(646\) −8.00000 + 13.8564i −0.314756 + 0.545173i
\(647\) −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i \(-0.948453\pi\)
0.633090 + 0.774078i \(0.281786\pi\)
\(648\) 0 0
\(649\) −17.5000 30.3109i −0.686935 1.18981i
\(650\) −3.00000 5.19615i −0.117670 0.203810i
\(651\) 0 0
\(652\) −1.00000 + 1.73205i −0.0391630 + 0.0678323i
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 0 0
\(655\) −26.0000 −1.01590
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) 0 0
\(658\) 12.0000 + 10.3923i 0.467809 + 0.405134i
\(659\) 20.5000 + 35.5070i 0.798567 + 1.38316i 0.920550 + 0.390626i \(0.127741\pi\)
−0.121983 + 0.992532i \(0.538925\pi\)
\(660\) 0 0
\(661\) 19.0000 + 32.9090i 0.739014 + 1.28001i 0.952940 + 0.303160i \(0.0980418\pi\)
−0.213925 + 0.976850i \(0.568625\pi\)
\(662\) 16.0000 + 27.7128i 0.621858 + 1.07709i
\(663\) 0 0
\(664\) 3.50000 + 6.06218i 0.135826 + 0.235258i
\(665\) −16.0000 13.8564i −0.620453 0.537328i
\(666\) 0 0
\(667\) 14.0000 + 24.2487i 0.542082 + 0.938914i
\(668\) 14.0000 0.541676
\(669\) 0 0
\(670\) −20.0000 −0.772667
\(671\) 0 0
\(672\) 0 0
\(673\) −1.00000 1.73205i −0.0385472 0.0667657i 0.846108 0.533011i \(-0.178940\pi\)
−0.884655 + 0.466246i \(0.845606\pi\)
\(674\) −13.5000 23.3827i −0.520001 0.900667i
\(675\) 0 0
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) 4.50000 7.79423i 0.172949 0.299557i −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 0 0
\(679\) −10.0000 8.66025i −0.383765 0.332350i
\(680\) 4.00000 6.92820i 0.153393 0.265684i
\(681\) 0 0
\(682\) 15.0000 0.574380
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) 16.0000 0.611329
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 0 0
\(688\) 8.00000 0.304997
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −1.00000 −0.0380143
\(693\) 0 0
\(694\) −27.0000 −1.02491
\(695\) 8.00000 13.8564i 0.303457 0.525603i
\(696\) 0 0
\(697\) −12.0000 20.7846i −0.454532 0.787273i
\(698\) 20.0000 0.757011
\(699\) 0 0
\(700\) −2.00000 1.73205i −0.0755929 0.0654654i
\(701\) 14.0000 0.528773 0.264386 0.964417i \(-0.414831\pi\)
0.264386 + 0.964417i \(0.414831\pi\)
\(702\) 0 0
\(703\) 16.0000 27.7128i 0.603451 1.04521i
\(704\) −5.00000 −0.188445
\(705\) 0 0
\(706\) 15.0000 25.9808i 0.564532 0.977799i
\(707\) −12.5000 + 4.33013i −0.470111 + 0.162851i
\(708\) 0 0
\(709\) −4.00000 + 6.92820i −0.150223 + 0.260194i −0.931309 0.364229i \(-0.881333\pi\)
0.781086 + 0.624423i \(0.214666\pi\)
\(710\) 4.00000 6.92820i 0.150117 0.260011i
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −6.00000 10.3923i −0.224702 0.389195i
\(714\) 0 0
\(715\) 30.0000 51.9615i 1.12194 1.94325i
\(716\) 15.0000 0.560576
\(717\) 0 0
\(718\) 16.0000 0.597115
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 0 0
\(721\) −20.0000 + 6.92820i −0.744839 + 0.258020i
\(722\) −1.50000 2.59808i −0.0558242 0.0966904i
\(723\) 0 0
\(724\) 0 0
\(725\) −3.50000 6.06218i −0.129987 0.225144i
\(726\) 0 0
\(727\) 16.0000 + 27.7128i 0.593407 + 1.02781i 0.993770 + 0.111454i \(0.0355509\pi\)
−0.400362 + 0.916357i \(0.631116\pi\)
\(728\) −3.00000 + 15.5885i −0.111187 + 0.577747i
\(729\) 0 0
\(730\) 13.0000 + 22.5167i 0.481152 + 0.833379i
\(731\) 32.0000 1.18356
\(732\) 0 0
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) −2.00000 + 3.46410i −0.0738213 + 0.127862i
\(735\) 0 0
\(736\) 2.00000 + 3.46410i 0.0737210 + 0.127688i
\(737\) 25.0000 + 43.3013i 0.920887 + 1.59502i
\(738\) 0 0
\(739\) 3.00000 5.19615i 0.110357 0.191144i −0.805557 0.592518i \(-0.798134\pi\)
0.915914 + 0.401374i \(0.131467\pi\)
\(740\) −8.00000 + 13.8564i −0.294086 + 0.509372i
\(741\) 0 0
\(742\) −12.0000 10.3923i −0.440534 0.381514i
\(743\) −3.00000 + 5.19615i −0.110059 + 0.190628i −0.915794 0.401648i \(-0.868437\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) −10.0000 + 17.3205i −0.366126 + 0.634149i
\(747\) 0 0
\(748\) −20.0000 −0.731272
\(749\) −24.0000 20.7846i −0.876941 0.759453i
\(750\) 0 0
\(751\) 12.0000 0.437886 0.218943 0.975738i \(-0.429739\pi\)
0.218943 + 0.975738i \(0.429739\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −21.0000 + 36.3731i −0.764775 + 1.32463i
\(755\) −34.0000 −1.23739
\(756\) 0 0
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) 5.00000 8.66025i 0.181608 0.314555i
\(759\) 0 0
\(760\) −4.00000 6.92820i −0.145095 0.251312i
\(761\) −8.00000 −0.290000 −0.145000 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(762\) 0 0
\(763\) 8.00000 41.5692i 0.289619 1.50491i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 2.00000 3.46410i 0.0722629 0.125163i
\(767\) −42.0000 −1.51653
\(768\) 0 0
\(769\) −0.500000 + 0.866025i −0.0180305 + 0.0312297i −0.874900 0.484304i \(-0.839073\pi\)
0.856869 + 0.515534i \(0.172406\pi\)
\(770\) 5.00000 25.9808i 0.180187 0.936282i
\(771\) 0 0
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) −19.0000 + 32.9090i −0.683383 + 1.18365i 0.290560 + 0.956857i \(0.406159\pi\)
−0.973942 + 0.226796i \(0.927175\pi\)
\(774\) 0 0
\(775\) 1.50000 + 2.59808i 0.0538816 + 0.0933257i
\(776\) −2.50000 4.33013i −0.0897448 0.155443i
\(777\) 0 0
\(778\) −0.500000 + 0.866025i −0.0179259 + 0.0310485i
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) −20.0000 −0.715656
\(782\) 8.00000 + 13.8564i 0.286079 + 0.495504i
\(783\) 0 0
\(784\) 1.00000 + 6.92820i 0.0357143 + 0.247436i
\(785\) −14.0000 24.2487i −0.499681 0.865474i
\(786\) 0 0
\(787\) −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i \(-0.270624\pi\)
−0.980656 + 0.195737i \(0.937290\pi\)
\(788\) −12.5000 21.6506i −0.445294 0.771272i
\(789\) 0 0
\(790\) −3.00000 5.19615i −0.106735 0.184871i
\(791\) −2.00000 + 10.3923i −0.0711118 + 0.369508i
\(792\) 0 0
\(793\) 0 0
\(794\) 18.0000 0.638796
\(795\) 0 0
\(796\) −19.0000 −0.673437
\(797\) 16.5000 28.5788i 0.584460 1.01231i −0.410483 0.911868i \(-0.634640\pi\)
0.994943 0.100446i \(-0.0320269\pi\)
\(798\) 0 0
\(799\) 12.0000 + 20.7846i 0.424529 + 0.735307i
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) 0 0
\(802\) 9.00000 15.5885i 0.317801 0.550448i
\(803\) 32.5000 56.2917i 1.14690 1.98649i
\(804\) 0 0
\(805\) −20.0000 + 6.92820i −0.704907 + 0.244187i
\(806\) 9.00000 15.5885i 0.317011 0.549080i
\(807\) 0 0
\(808\) −5.00000 −0.175899
\(809\) 17.0000 29.4449i 0.597688 1.03523i −0.395473 0.918477i \(-0.629419\pi\)
0.993161 0.116749i \(-0.0372472\pi\)
\(810\) 0 0
\(811\) −50.0000 −1.75574 −0.877869 0.478901i \(-0.841035\pi\)
−0.877869 + 0.478901i \(0.841035\pi\)
\(812\) −3.50000 + 18.1865i −0.122826 + 0.638222i
\(813\) 0 0
\(814\) 40.0000 1.40200
\(815\) −2.00000 3.46410i −0.0700569 0.121342i
\(816\) 0 0
\(817\) 16.0000 27.7128i 0.559769 0.969549i
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) 12.0000 0.419058
\(821\) −24.5000 + 42.4352i −0.855056 + 1.48100i 0.0215373 + 0.999768i \(0.493144\pi\)
−0.876593 + 0.481232i \(0.840189\pi\)
\(822\) 0 0
\(823\) −6.50000 11.2583i −0.226576 0.392441i 0.730215 0.683217i \(-0.239420\pi\)
−0.956791 + 0.290776i \(0.906086\pi\)
\(824\) −8.00000 −0.278693
\(825\) 0 0
\(826\) −17.5000 + 6.06218i −0.608903 + 0.210930i
\(827\) −51.0000 −1.77344 −0.886722 0.462303i \(-0.847023\pi\)
−0.886722 + 0.462303i \(0.847023\pi\)
\(828\) 0 0
\(829\) −11.0000 + 19.0526i −0.382046 + 0.661723i −0.991355 0.131210i \(-0.958114\pi\)
0.609309 + 0.792933i \(0.291447\pi\)
\(830\) −14.0000 −0.485947
\(831\) 0 0
\(832\) −3.00000 + 5.19615i −0.104006 + 0.180144i
\(833\) 4.00000 + 27.7128i 0.138592 + 0.960192i
\(834\) 0 0
\(835\) −14.0000 + 24.2487i −0.484490 + 0.839161i
\(836\) −10.0000 + 17.3205i −0.345857 + 0.599042i
\(837\) 0 0
\(838\) −6.00000 10.3923i −0.207267 0.358996i
\(839\) −2.00000 3.46410i −0.0690477 0.119594i 0.829435 0.558604i \(-0.188663\pi\)
−0.898482 + 0.439010i \(0.855329\pi\)
\(840\) 0 0
\(841\) −10.0000 + 17.3205i −0.344828 + 0.597259i
\(842\) 18.0000 0.620321
\(843\) 0 0
\(844\) 26.0000 0.894957
\(845\) −23.0000 39.8372i −0.791224 1.37044i
\(846\) 0 0
\(847\) −35.0000 + 12.1244i −1.20261 + 0.416598i
\(848\) −3.00000 5.19615i −0.103020 0.178437i
\(849\) 0 0
\(850\) −2.00000 3.46410i −0.0685994 0.118818i
\(851\) −16.0000 27.7128i −0.548473 0.949983i
\(852\) 0 0
\(853\) 23.0000 + 39.8372i 0.787505 + 1.36400i 0.927491 + 0.373845i \(0.121961\pi\)
−0.139986 + 0.990153i \(0.544706\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −6.00000 10.3923i −0.205076 0.355202i
\(857\) −30.0000 −1.02478 −0.512390 0.858753i \(-0.671240\pi\)
−0.512390 + 0.858753i \(0.671240\pi\)
\(858\) 0 0
\(859\) −16.0000 −0.545913 −0.272956 0.962026i \(-0.588002\pi\)
−0.272956 + 0.962026i \(0.588002\pi\)
\(860\) −8.00000 + 13.8564i −0.272798 + 0.472500i
\(861\) 0 0
\(862\) 9.00000 + 15.5885i 0.306541 + 0.530945i
\(863\) −19.0000 32.9090i −0.646768 1.12023i −0.983890 0.178774i \(-0.942787\pi\)
0.337123 0.941461i \(-0.390546\pi\)
\(864\) 0 0
\(865\) 1.00000 1.73205i 0.0340010 0.0588915i
\(866\) −3.50000 + 6.06218i −0.118935 + 0.206001i
\(867\) 0 0
\(868\) 1.50000 7.79423i 0.0509133 0.264553i
\(869\) −7.50000 + 12.9904i −0.254420 + 0.440668i
\(870\) 0 0
\(871\) 60.0000 2.03302
\(872\) 8.00000 13.8564i 0.270914 0.469237i
\(873\) 0 0
\(874\) 16.0000 0.541208
\(875\) 30.0000 10.3923i 1.01419 0.351324i
\(876\) 0 0
\(877\) 34.0000 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) 1.50000 + 2.59808i 0.0506225 + 0.0876808i
\(879\) 0 0
\(880\) 5.00000 8.66025i 0.168550 0.291937i
\(881\) 54.0000 1.81931 0.909653 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 0 0
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) −12.0000 + 20.7846i −0.403604 + 0.699062i
\(885\) 0 0
\(886\) −5.50000 9.52628i −0.184776 0.320042i
\(887\) 42.0000 1.41022 0.705111 0.709097i \(-0.250897\pi\)
0.705111 + 0.709097i \(0.250897\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 12.0000 0.402241
\(891\) 0 0
\(892\) 0.500000 0.866025i 0.0167412 0.0289967i
\(893\) 24.0000 0.803129
\(894\) 0 0
\(895\) −15.0000 + 25.9808i −0.501395 + 0.868441i
\(896\) −0.500000 + 2.59808i −0.0167038 + 0.0867956i
\(897\) 0 0
\(898\) 7.00000 12.1244i 0.233593 0.404595i
\(899\) 10.5000 18.1865i 0.350195 0.606555i
\(900\) 0 0
\(901\) −12.0000 20.7846i −0.399778 0.692436i
\(902\) −15.0000 25.9808i −0.499445 0.865065i
\(903\) 0 0
\(904\) −2.00000 + 3.46410i −0.0665190 + 0.115214i
\(905\) 0 0
\(906\) 0 0
\(907\) −42.0000 −1.39459 −0.697294 0.716786i \(-0.745613\pi\)
−0.697294 + 0.716786i \(0.745613\pi\)
\(908\) −13.5000 23.3827i −0.448013 0.775982i
\(909\) 0 0
\(910\) −24.0000 20.7846i −0.795592 0.689003i
\(911\) 18.0000 + 31.1769i 0.596367 + 1.03294i 0.993352 + 0.115113i \(0.0367229\pi\)
−0.396986 + 0.917825i \(0.629944\pi\)
\(912\) 0 0
\(913\) 17.5000 + 30.3109i 0.579165 + 1.00314i
\(914\) −13.0000 22.5167i −0.430002 0.744785i
\(915\) 0 0
\(916\) −2.00000 3.46410i −0.0660819 0.114457i
\(917\) 32.5000 11.2583i 1.07324 0.371783i
\(918\) 0 0
\(919\) −6.50000 11.2583i −0.214415 0.371378i 0.738676 0.674060i \(-0.235451\pi\)
−0.953092 + 0.302682i \(0.902118\pi\)
\(920\) −8.00000 −0.263752
\(921\) 0 0
\(922\) −23.0000 −0.757465
\(923\) −12.0000 + 20.7846i −0.394985 + 0.684134i
\(924\) 0 0
\(925\) 4.00000 + 6.92820i 0.131519 + 0.227798i
\(926\) −14.5000 25.1147i −0.476500 0.825321i
\(927\) 0 0
\(928\) −3.50000 + 6.06218i −0.114893 + 0.199001i
\(929\) 18.0000 31.1769i 0.590561 1.02288i −0.403596 0.914937i \(-0.632240\pi\)
0.994157 0.107944i \(-0.0344268\pi\)
\(930\) 0 0
\(931\) 26.0000 + 10.3923i 0.852116 + 0.340594i
\(932\) −11.0000 + 19.0526i −0.360317 + 0.624087i
\(933\) 0 0
\(934\) 7.00000 0.229047
\(935\) 20.0000 34.6410i 0.654070 1.13288i
\(936\) 0 0
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 25.0000 8.66025i 0.816279 0.282767i
\(939\) 0 0
\(940\) −12.0000 −0.391397
\(941\) 6.50000 + 11.2583i 0.211894 + 0.367011i 0.952307 0.305141i \(-0.0987035\pi\)
−0.740413 + 0.672152i \(0.765370\pi\)
\(942\) 0 0
\(943\) −12.0000 + 20.7846i −0.390774 + 0.676840i
\(944\) −7.00000 −0.227831
\(945\) 0 0
\(946\) 40.0000 1.30051
\(947\) 12.5000 21.6506i 0.406195 0.703551i −0.588264 0.808669i \(-0.700189\pi\)
0.994460 + 0.105118i \(0.0335219\pi\)
\(948\) 0 0
\(949\) −39.0000 67.5500i −1.26599 2.19277i
\(950\) −4.00000 −0.129777
\(951\) 0 0
\(952\) −2.00000 + 10.3923i −0.0648204 + 0.336817i
\(953\) −2.00000 −0.0647864 −0.0323932 0.999475i \(-0.510313\pi\)
−0.0323932 + 0.999475i \(0.510313\pi\)
\(954\) 0 0
\(955\) −18.0000 + 31.1769i −0.582466 + 1.00886i
\(956\) 0 0
\(957\) 0 0
\(958\) −13.0000 + 22.5167i −0.420011 + 0.727480i
\(959\) −20.0000 + 6.92820i −0.645834 + 0.223723i
\(960\) 0 0
\(961\) 11.0000 19.0526i 0.354839 0.614599i
\(962\) 24.0000 41.5692i 0.773791 1.34025i
\(963\) 0 0
\(964\) 0.500000 + 0.866025i 0.0161039 + 0.0278928i
\(965\) 19.0000 + 32.9090i 0.611632 + 1.05938i
\(966\) 0 0
\(967\) −4.00000 + 6.92820i −0.128631 + 0.222796i −0.923147 0.384448i \(-0.874392\pi\)
0.794515 + 0.607244i \(0.207725\pi\)
\(968\) −14.0000 −0.449977
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) 6.00000 + 10.3923i 0.192549 + 0.333505i 0.946094 0.323891i \(-0.104991\pi\)
−0.753545 + 0.657396i \(0.771658\pi\)
\(972\) 0 0
\(973\) −4.00000 + 20.7846i −0.128234 + 0.666324i
\(974\) −6.50000 11.2583i −0.208273 0.360740i
\(975\) 0 0
\(976\) 0 0
\(977\) −9.00000 15.5885i −0.287936 0.498719i 0.685381 0.728184i \(-0.259636\pi\)
−0.973317 + 0.229465i \(0.926302\pi\)
\(978\) 0 0
\(979\) −15.0000 25.9808i −0.479402 0.830349i
\(980\) −13.0000 5.19615i −0.415270 0.165985i
\(981\) 0 0
\(982\) −6.00000 10.3923i −0.191468 0.331632i
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) 50.0000 1.59313
\(986\) −14.0000 + 24.2487i −0.445851 + 0.772236i
\(987\) 0 0
\(988\) 12.0000 + 20.7846i 0.381771 + 0.661247i
\(989\) −16.0000 27.7128i −0.508770 0.881216i
\(990\) 0 0
\(991\) −4.00000 + 6.92820i −0.127064 + 0.220082i −0.922538 0.385906i \(-0.873889\pi\)
0.795474 + 0.605988i \(0.207222\pi\)
\(992\) 1.50000 2.59808i 0.0476250 0.0824890i
\(993\) 0 0
\(994\) −2.00000 + 10.3923i −0.0634361 + 0.329624i
\(995\) 19.0000 32.9090i 0.602340 1.04328i
\(996\) 0 0
\(997\) −58.0000 −1.83688 −0.918439 0.395562i \(-0.870550\pi\)
−0.918439 + 0.395562i \(0.870550\pi\)
\(998\) −4.00000 + 6.92820i −0.126618 + 0.219308i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1134.2.h.o.109.1 2
3.2 odd 2 1134.2.h.b.109.1 2
7.2 even 3 1134.2.e.b.919.1 2
9.2 odd 6 1134.2.e.o.865.1 2
9.4 even 3 378.2.g.d.109.1 yes 2
9.5 odd 6 378.2.g.c.109.1 2
9.7 even 3 1134.2.e.b.865.1 2
21.2 odd 6 1134.2.e.o.919.1 2
63.2 odd 6 1134.2.h.b.541.1 2
63.4 even 3 2646.2.a.k.1.1 1
63.16 even 3 inner 1134.2.h.o.541.1 2
63.23 odd 6 378.2.g.c.163.1 yes 2
63.31 odd 6 2646.2.a.c.1.1 1
63.32 odd 6 2646.2.a.t.1.1 1
63.58 even 3 378.2.g.d.163.1 yes 2
63.59 even 6 2646.2.a.bb.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.g.c.109.1 2 9.5 odd 6
378.2.g.c.163.1 yes 2 63.23 odd 6
378.2.g.d.109.1 yes 2 9.4 even 3
378.2.g.d.163.1 yes 2 63.58 even 3
1134.2.e.b.865.1 2 9.7 even 3
1134.2.e.b.919.1 2 7.2 even 3
1134.2.e.o.865.1 2 9.2 odd 6
1134.2.e.o.919.1 2 21.2 odd 6
1134.2.h.b.109.1 2 3.2 odd 2
1134.2.h.b.541.1 2 63.2 odd 6
1134.2.h.o.109.1 2 1.1 even 1 trivial
1134.2.h.o.541.1 2 63.16 even 3 inner
2646.2.a.c.1.1 1 63.31 odd 6
2646.2.a.k.1.1 1 63.4 even 3
2646.2.a.t.1.1 1 63.32 odd 6
2646.2.a.bb.1.1 1 63.59 even 6