Properties

Label 920.2.bv.a.433.18
Level $920$
Weight $2$
Character 920.433
Analytic conductor $7.346$
Analytic rank $0$
Dimension $720$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(17,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bv (of order \(44\), degree \(20\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(720\)
Relative dimension: \(36\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 433.18
Character \(\chi\) \(=\) 920.433
Dual form 920.2.bv.a.17.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0410298 - 0.0224040i) q^{3} +(-0.288669 - 2.21736i) q^{5} +(1.73059 - 2.31180i) q^{7} +(-1.62074 - 2.52192i) q^{9} +(0.565611 + 0.258306i) q^{11} +(-0.890094 + 0.666316i) q^{13} +(-0.0378336 + 0.0974451i) q^{15} +(-0.149145 + 2.08532i) q^{17} +(1.43969 - 1.66149i) q^{19} +(-0.122799 + 0.0560805i) q^{21} +(-4.23404 - 2.25231i) q^{23} +(-4.83334 + 1.28017i) q^{25} +(0.0200025 + 0.279672i) q^{27} +(-1.86944 + 1.61988i) q^{29} +(-8.11526 - 2.38286i) q^{31} +(-0.0174198 - 0.0232702i) q^{33} +(-5.62564 - 3.16999i) q^{35} +(-0.876858 - 0.190749i) q^{37} +(0.0514485 - 0.00739718i) q^{39} +(6.19326 + 3.98017i) q^{41} +(2.73894 - 5.01600i) q^{43} +(-5.12414 + 4.32176i) q^{45} +(1.83333 - 1.83333i) q^{47} +(-0.377336 - 1.28509i) q^{49} +(0.0528390 - 0.0822190i) q^{51} +(2.56327 + 1.91884i) q^{53} +(0.409482 - 1.32873i) q^{55} +(-0.0962940 + 0.0359158i) q^{57} +(-6.13247 - 0.881716i) q^{59} +(3.88373 - 13.2268i) q^{61} +(-8.63501 - 0.617588i) q^{63} +(1.73440 + 1.78131i) q^{65} +(4.76778 - 12.7829i) q^{67} +(0.123261 + 0.187271i) q^{69} +(-0.404054 - 0.884756i) q^{71} +(3.80740 - 0.272310i) q^{73} +(0.226992 + 0.0557611i) q^{75} +(1.57599 - 0.860556i) q^{77} +(0.310067 - 2.15657i) q^{79} +(-3.73057 + 8.16880i) q^{81} +(2.23428 - 10.2708i) q^{83} +(4.66696 - 0.271261i) q^{85} +(0.112994 - 0.0245804i) q^{87} +(-9.66802 + 2.83879i) q^{89} +3.21083i q^{91} +(0.279582 + 0.279582i) q^{93} +(-4.09970 - 2.71268i) q^{95} +(2.33842 + 10.7495i) q^{97} +(-0.265282 - 1.84507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(e\left(\frac{15}{22}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) −0.0410298 0.0224040i −0.0236886 0.0129349i 0.467361 0.884067i \(-0.345205\pi\)
−0.491050 + 0.871132i \(0.663387\pi\)
\(4\) 0 0
\(5\) −0.288669 2.21736i −0.129097 0.991632i
\(6\) 0 0
\(7\) 1.73059 2.31180i 0.654101 0.873777i −0.343766 0.939055i \(-0.611703\pi\)
0.997867 + 0.0652785i \(0.0207936\pi\)
\(8\) 0 0
\(9\) −1.62074 2.52192i −0.540247 0.840641i
\(10\) 0 0
\(11\) 0.565611 + 0.258306i 0.170538 + 0.0778822i 0.498855 0.866686i \(-0.333754\pi\)
−0.328317 + 0.944568i \(0.606481\pi\)
\(12\) 0 0
\(13\) −0.890094 + 0.666316i −0.246868 + 0.184803i −0.715545 0.698567i \(-0.753822\pi\)
0.468677 + 0.883369i \(0.344731\pi\)
\(14\) 0 0
\(15\) −0.0378336 + 0.0974451i −0.00976858 + 0.0251602i
\(16\) 0 0
\(17\) −0.149145 + 2.08532i −0.0361730 + 0.505765i 0.946777 + 0.321891i \(0.104318\pi\)
−0.982950 + 0.183874i \(0.941136\pi\)
\(18\) 0 0
\(19\) 1.43969 1.66149i 0.330287 0.381171i −0.566180 0.824281i \(-0.691579\pi\)
0.896467 + 0.443110i \(0.146125\pi\)
\(20\) 0 0
\(21\) −0.122799 + 0.0560805i −0.0267970 + 0.0122378i
\(22\) 0 0
\(23\) −4.23404 2.25231i −0.882859 0.469639i
\(24\) 0 0
\(25\) −4.83334 + 1.28017i −0.966668 + 0.256033i
\(26\) 0 0
\(27\) 0.0200025 + 0.279672i 0.00384949 + 0.0538229i
\(28\) 0 0
\(29\) −1.86944 + 1.61988i −0.347145 + 0.300803i −0.810928 0.585146i \(-0.801037\pi\)
0.463783 + 0.885949i \(0.346492\pi\)
\(30\) 0 0
\(31\) −8.11526 2.38286i −1.45754 0.427974i −0.545516 0.838101i \(-0.683666\pi\)
−0.912028 + 0.410127i \(0.865484\pi\)
\(32\) 0 0
\(33\) −0.0174198 0.0232702i −0.00303241 0.00405082i
\(34\) 0 0
\(35\) −5.62564 3.16999i −0.950907 0.535826i
\(36\) 0 0
\(37\) −0.876858 0.190749i −0.144155 0.0313589i 0.139909 0.990164i \(-0.455319\pi\)
−0.284064 + 0.958805i \(0.591683\pi\)
\(38\) 0 0
\(39\) 0.0514485 0.00739718i 0.00823836 0.00118450i
\(40\) 0 0
\(41\) 6.19326 + 3.98017i 0.967225 + 0.621597i 0.925988 0.377552i \(-0.123234\pi\)
0.0412362 + 0.999149i \(0.486870\pi\)
\(42\) 0 0
\(43\) 2.73894 5.01600i 0.417685 0.764933i −0.581119 0.813818i \(-0.697385\pi\)
0.998804 + 0.0488854i \(0.0155669\pi\)
\(44\) 0 0
\(45\) −5.12414 + 4.32176i −0.763862 + 0.644250i
\(46\) 0 0
\(47\) 1.83333 1.83333i 0.267418 0.267418i −0.560641 0.828059i \(-0.689445\pi\)
0.828059 + 0.560641i \(0.189445\pi\)
\(48\) 0 0
\(49\) −0.377336 1.28509i −0.0539051 0.183584i
\(50\) 0 0
\(51\) 0.0528390 0.0822190i 0.00739893 0.0115130i
\(52\) 0 0
\(53\) 2.56327 + 1.91884i 0.352092 + 0.263573i 0.760654 0.649158i \(-0.224879\pi\)
−0.408561 + 0.912731i \(0.633969\pi\)
\(54\) 0 0
\(55\) 0.409482 1.32873i 0.0552145 0.179165i
\(56\) 0 0
\(57\) −0.0962940 + 0.0359158i −0.0127545 + 0.00475717i
\(58\) 0 0
\(59\) −6.13247 0.881716i −0.798379 0.114790i −0.268962 0.963151i \(-0.586680\pi\)
−0.529418 + 0.848361i \(0.677590\pi\)
\(60\) 0 0
\(61\) 3.88373 13.2268i 0.497260 1.69351i −0.202624 0.979257i \(-0.564947\pi\)
0.699884 0.714256i \(-0.253235\pi\)
\(62\) 0 0
\(63\) −8.63501 0.617588i −1.08791 0.0778088i
\(64\) 0 0
\(65\) 1.73440 + 1.78131i 0.215126 + 0.220944i
\(66\) 0 0
\(67\) 4.76778 12.7829i 0.582477 1.56168i −0.226605 0.973987i \(-0.572763\pi\)
0.809082 0.587695i \(-0.199965\pi\)
\(68\) 0 0
\(69\) 0.123261 + 0.187271i 0.0148389 + 0.0225448i
\(70\) 0 0
\(71\) −0.404054 0.884756i −0.0479524 0.105001i 0.884139 0.467223i \(-0.154746\pi\)
−0.932092 + 0.362222i \(0.882018\pi\)
\(72\) 0 0
\(73\) 3.80740 0.272310i 0.445622 0.0318715i 0.153275 0.988184i \(-0.451018\pi\)
0.292348 + 0.956312i \(0.405564\pi\)
\(74\) 0 0
\(75\) 0.226992 + 0.0557611i 0.0262108 + 0.00643873i
\(76\) 0 0
\(77\) 1.57599 0.860556i 0.179601 0.0980695i
\(78\) 0 0
\(79\) 0.310067 2.15657i 0.0348853 0.242633i −0.964916 0.262558i \(-0.915434\pi\)
0.999801 + 0.0199256i \(0.00634293\pi\)
\(80\) 0 0
\(81\) −3.73057 + 8.16880i −0.414507 + 0.907645i
\(82\) 0 0
\(83\) 2.23428 10.2708i 0.245244 1.12737i −0.675548 0.737316i \(-0.736093\pi\)
0.920792 0.390053i \(-0.127543\pi\)
\(84\) 0 0
\(85\) 4.66696 0.271261i 0.506203 0.0294224i
\(86\) 0 0
\(87\) 0.112994 0.0245804i 0.0121143 0.00263530i
\(88\) 0 0
\(89\) −9.66802 + 2.83879i −1.02481 + 0.300911i −0.750598 0.660759i \(-0.770235\pi\)
−0.274210 + 0.961670i \(0.588416\pi\)
\(90\) 0 0
\(91\) 3.21083i 0.336587i
\(92\) 0 0
\(93\) 0.279582 + 0.279582i 0.0289913 + 0.0289913i
\(94\) 0 0
\(95\) −4.09970 2.71268i −0.420621 0.278315i
\(96\) 0 0
\(97\) 2.33842 + 10.7495i 0.237430 + 1.09145i 0.929271 + 0.369399i \(0.120436\pi\)
−0.691841 + 0.722050i \(0.743200\pi\)
\(98\) 0 0
\(99\) −0.265282 1.84507i −0.0266618 0.185437i
\(100\) 0 0
\(101\) 3.59659 2.31139i 0.357874 0.229991i −0.349332 0.936999i \(-0.613592\pi\)
0.707206 + 0.707007i \(0.249955\pi\)
\(102\) 0 0
\(103\) 1.31849 + 3.53500i 0.129915 + 0.348314i 0.985579 0.169217i \(-0.0541239\pi\)
−0.855664 + 0.517531i \(0.826851\pi\)
\(104\) 0 0
\(105\) 0.159799 + 0.256101i 0.0155948 + 0.0249929i
\(106\) 0 0
\(107\) 3.94846 + 7.23107i 0.381712 + 0.699054i 0.995935 0.0900793i \(-0.0287121\pi\)
−0.614222 + 0.789133i \(0.710530\pi\)
\(108\) 0 0
\(109\) −9.46629 10.9247i −0.906706 1.04639i −0.998717 0.0506366i \(-0.983875\pi\)
0.0920111 0.995758i \(-0.470670\pi\)
\(110\) 0 0
\(111\) 0.0317038 + 0.0274715i 0.00300919 + 0.00260748i
\(112\) 0 0
\(113\) 12.4213 + 4.63290i 1.16850 + 0.435826i 0.857449 0.514569i \(-0.172048\pi\)
0.311046 + 0.950395i \(0.399321\pi\)
\(114\) 0 0
\(115\) −3.77193 + 10.0386i −0.351735 + 0.936100i
\(116\) 0 0
\(117\) 3.12301 + 1.16482i 0.288722 + 0.107688i
\(118\) 0 0
\(119\) 4.56273 + 3.95363i 0.418265 + 0.362429i
\(120\) 0 0
\(121\) −6.95027 8.02104i −0.631843 0.729186i
\(122\) 0 0
\(123\) −0.164937 0.302059i −0.0148719 0.0272358i
\(124\) 0 0
\(125\) 4.23382 + 10.3477i 0.378685 + 0.925526i
\(126\) 0 0
\(127\) 2.33011 + 6.24728i 0.206764 + 0.554356i 0.998394 0.0566443i \(-0.0180401\pi\)
−0.791630 + 0.611000i \(0.790767\pi\)
\(128\) 0 0
\(129\) −0.224757 + 0.144442i −0.0197887 + 0.0127174i
\(130\) 0 0
\(131\) −1.65287 11.4959i −0.144412 1.00440i −0.925165 0.379565i \(-0.876074\pi\)
0.780753 0.624839i \(-0.214836\pi\)
\(132\) 0 0
\(133\) −1.34951 6.20361i −0.117018 0.537921i
\(134\) 0 0
\(135\) 0.614359 0.125086i 0.0528756 0.0107657i
\(136\) 0 0
\(137\) 13.8908 + 13.8908i 1.18677 + 1.18677i 0.977954 + 0.208819i \(0.0669621\pi\)
0.208819 + 0.977954i \(0.433038\pi\)
\(138\) 0 0
\(139\) 12.3148i 1.04453i 0.852784 + 0.522264i \(0.174912\pi\)
−0.852784 + 0.522264i \(0.825088\pi\)
\(140\) 0 0
\(141\) −0.116295 + 0.0341473i −0.00979380 + 0.00287572i
\(142\) 0 0
\(143\) −0.675560 + 0.146959i −0.0564932 + 0.0122893i
\(144\) 0 0
\(145\) 4.13149 + 3.67760i 0.343102 + 0.305408i
\(146\) 0 0
\(147\) −0.0133091 + 0.0611807i −0.00109771 + 0.00504610i
\(148\) 0 0
\(149\) −3.32109 + 7.27217i −0.272074 + 0.595759i −0.995513 0.0946298i \(-0.969833\pi\)
0.723439 + 0.690389i \(0.242561\pi\)
\(150\) 0 0
\(151\) 3.34577 23.2704i 0.272275 1.89372i −0.152318 0.988332i \(-0.548674\pi\)
0.424593 0.905384i \(-0.360417\pi\)
\(152\) 0 0
\(153\) 5.50075 3.00364i 0.444709 0.242830i
\(154\) 0 0
\(155\) −2.94101 + 18.6823i −0.236228 + 1.50060i
\(156\) 0 0
\(157\) 6.07076 0.434190i 0.484500 0.0346521i 0.173047 0.984914i \(-0.444639\pi\)
0.311453 + 0.950262i \(0.399184\pi\)
\(158\) 0 0
\(159\) −0.0621809 0.136157i −0.00493127 0.0107980i
\(160\) 0 0
\(161\) −12.5343 + 5.89042i −0.987838 + 0.464230i
\(162\) 0 0
\(163\) 2.82382 7.57095i 0.221179 0.593003i −0.778209 0.628006i \(-0.783871\pi\)
0.999387 + 0.0350031i \(0.0111441\pi\)
\(164\) 0 0
\(165\) −0.0465697 + 0.0453434i −0.00362545 + 0.00352998i
\(166\) 0 0
\(167\) 8.28055 + 0.592237i 0.640768 + 0.0458287i 0.387943 0.921683i \(-0.373186\pi\)
0.252825 + 0.967512i \(0.418640\pi\)
\(168\) 0 0
\(169\) −3.31423 + 11.2872i −0.254941 + 0.868249i
\(170\) 0 0
\(171\) −6.52350 0.937938i −0.498864 0.0717259i
\(172\) 0 0
\(173\) −2.43148 + 0.906895i −0.184862 + 0.0689499i −0.440190 0.897904i \(-0.645089\pi\)
0.255329 + 0.966854i \(0.417816\pi\)
\(174\) 0 0
\(175\) −5.40504 + 13.3891i −0.408583 + 1.01212i
\(176\) 0 0
\(177\) 0.231860 + 0.173568i 0.0174277 + 0.0130462i
\(178\) 0 0
\(179\) −0.0260598 + 0.0405498i −0.00194780 + 0.00303084i −0.842226 0.539125i \(-0.818755\pi\)
0.840278 + 0.542155i \(0.182392\pi\)
\(180\) 0 0
\(181\) −1.62901 5.54788i −0.121083 0.412371i 0.876536 0.481336i \(-0.159848\pi\)
−0.997619 + 0.0689653i \(0.978030\pi\)
\(182\) 0 0
\(183\) −0.455681 + 0.455681i −0.0336849 + 0.0336849i
\(184\) 0 0
\(185\) −0.169836 + 1.99937i −0.0124866 + 0.146997i
\(186\) 0 0
\(187\) −0.623010 + 1.14096i −0.0455590 + 0.0834350i
\(188\) 0 0
\(189\) 0.681161 + 0.437756i 0.0495472 + 0.0318420i
\(190\) 0 0
\(191\) 8.15000 1.17179i 0.589713 0.0847880i 0.159003 0.987278i \(-0.449172\pi\)
0.430710 + 0.902490i \(0.358263\pi\)
\(192\) 0 0
\(193\) 15.1665 + 3.29926i 1.09171 + 0.237486i 0.722160 0.691726i \(-0.243149\pi\)
0.369546 + 0.929212i \(0.379513\pi\)
\(194\) 0 0
\(195\) −0.0312538 0.111944i −0.00223813 0.00801651i
\(196\) 0 0
\(197\) 1.65720 + 2.21376i 0.118070 + 0.157724i 0.855683 0.517501i \(-0.173138\pi\)
−0.737612 + 0.675225i \(0.764047\pi\)
\(198\) 0 0
\(199\) 18.4366 + 5.41346i 1.30693 + 0.383750i 0.859760 0.510698i \(-0.170613\pi\)
0.447173 + 0.894448i \(0.352431\pi\)
\(200\) 0 0
\(201\) −0.482010 + 0.417664i −0.0339983 + 0.0294597i
\(202\) 0 0
\(203\) 0.509597 + 7.12509i 0.0357667 + 0.500083i
\(204\) 0 0
\(205\) 7.03764 14.8816i 0.491530 1.03938i
\(206\) 0 0
\(207\) 1.18214 + 14.3283i 0.0821641 + 0.995888i
\(208\) 0 0
\(209\) 1.24347 0.567876i 0.0860129 0.0392808i
\(210\) 0 0
\(211\) 1.83738 2.12045i 0.126490 0.145978i −0.688972 0.724788i \(-0.741938\pi\)
0.815462 + 0.578811i \(0.196483\pi\)
\(212\) 0 0
\(213\) −0.00324377 + 0.0453538i −0.000222259 + 0.00310759i
\(214\) 0 0
\(215\) −11.9129 4.62525i −0.812454 0.315439i
\(216\) 0 0
\(217\) −19.5529 + 14.6371i −1.32733 + 0.993630i
\(218\) 0 0
\(219\) −0.162318 0.0741280i −0.0109684 0.00500911i
\(220\) 0 0
\(221\) −1.25673 1.95551i −0.0845369 0.131542i
\(222\) 0 0
\(223\) 9.49522 12.6841i 0.635847 0.849392i −0.360678 0.932691i \(-0.617455\pi\)
0.996525 + 0.0832984i \(0.0265455\pi\)
\(224\) 0 0
\(225\) 11.0621 + 10.1145i 0.737471 + 0.674299i
\(226\) 0 0
\(227\) 11.4244 + 6.23822i 0.758267 + 0.414045i 0.811362 0.584544i \(-0.198727\pi\)
−0.0530949 + 0.998589i \(0.516909\pi\)
\(228\) 0 0
\(229\) 1.27982 0.0845730 0.0422865 0.999106i \(-0.486536\pi\)
0.0422865 + 0.999106i \(0.486536\pi\)
\(230\) 0 0
\(231\) −0.0839425 −0.00552301
\(232\) 0 0
\(233\) −13.8859 7.58228i −0.909696 0.496731i −0.0449770 0.998988i \(-0.514321\pi\)
−0.864719 + 0.502257i \(0.832503\pi\)
\(234\) 0 0
\(235\) −4.59436 3.53591i −0.299703 0.230658i
\(236\) 0 0
\(237\) −0.0610377 + 0.0815368i −0.00396482 + 0.00529638i
\(238\) 0 0
\(239\) −4.50993 7.01758i −0.291723 0.453930i 0.664197 0.747558i \(-0.268774\pi\)
−0.955920 + 0.293628i \(0.905137\pi\)
\(240\) 0 0
\(241\) −13.2858 6.06744i −0.855816 0.390838i −0.0613278 0.998118i \(-0.519534\pi\)
−0.794488 + 0.607280i \(0.792261\pi\)
\(242\) 0 0
\(243\) 1.00946 0.755673i 0.0647570 0.0484765i
\(244\) 0 0
\(245\) −2.74057 + 1.20765i −0.175089 + 0.0771541i
\(246\) 0 0
\(247\) −0.174381 + 2.43817i −0.0110956 + 0.155137i
\(248\) 0 0
\(249\) −0.321779 + 0.371353i −0.0203919 + 0.0235335i
\(250\) 0 0
\(251\) 7.92879 3.62096i 0.500461 0.228553i −0.149157 0.988813i \(-0.547656\pi\)
0.649618 + 0.760261i \(0.274929\pi\)
\(252\) 0 0
\(253\) −1.81304 2.36761i −0.113985 0.148850i
\(254\) 0 0
\(255\) −0.197562 0.0934287i −0.0123718 0.00585073i
\(256\) 0 0
\(257\) 1.47010 + 20.5547i 0.0917025 + 1.28217i 0.809999 + 0.586431i \(0.199467\pi\)
−0.718297 + 0.695737i \(0.755078\pi\)
\(258\) 0 0
\(259\) −1.95845 + 1.69701i −0.121692 + 0.105447i
\(260\) 0 0
\(261\) 7.11507 + 2.08917i 0.440412 + 0.129317i
\(262\) 0 0
\(263\) 3.43557 + 4.58938i 0.211846 + 0.282993i 0.893860 0.448346i \(-0.147987\pi\)
−0.682014 + 0.731339i \(0.738896\pi\)
\(264\) 0 0
\(265\) 3.51482 6.23760i 0.215913 0.383172i
\(266\) 0 0
\(267\) 0.460277 + 0.100127i 0.0281685 + 0.00612769i
\(268\) 0 0
\(269\) 5.04128 0.724827i 0.307373 0.0441935i 0.0130973 0.999914i \(-0.495831\pi\)
0.294275 + 0.955721i \(0.404922\pi\)
\(270\) 0 0
\(271\) 17.3028 + 11.1198i 1.05107 + 0.675481i 0.947700 0.319162i \(-0.103401\pi\)
0.103369 + 0.994643i \(0.467038\pi\)
\(272\) 0 0
\(273\) 0.0719355 0.131740i 0.00435373 0.00797327i
\(274\) 0 0
\(275\) −3.06447 0.524404i −0.184794 0.0316228i
\(276\) 0 0
\(277\) 19.5001 19.5001i 1.17165 1.17165i 0.189831 0.981817i \(-0.439206\pi\)
0.981817 0.189831i \(-0.0607940\pi\)
\(278\) 0 0
\(279\) 7.14336 + 24.3280i 0.427662 + 1.45648i
\(280\) 0 0
\(281\) −15.2584 + 23.7425i −0.910239 + 1.41636i −0.00103862 + 0.999999i \(0.500331\pi\)
−0.909200 + 0.416360i \(0.863306\pi\)
\(282\) 0 0
\(283\) −10.5953 7.93155i −0.629826 0.471482i 0.236050 0.971741i \(-0.424147\pi\)
−0.865876 + 0.500259i \(0.833238\pi\)
\(284\) 0 0
\(285\) 0.107435 + 0.203150i 0.00636392 + 0.0120336i
\(286\) 0 0
\(287\) 19.9193 7.42952i 1.17580 0.438551i
\(288\) 0 0
\(289\) 12.5006 + 1.79732i 0.735331 + 0.105725i
\(290\) 0 0
\(291\) 0.144887 0.493441i 0.00849345 0.0289260i
\(292\) 0 0
\(293\) 15.8495 + 1.13358i 0.925940 + 0.0662245i 0.526159 0.850386i \(-0.323632\pi\)
0.399781 + 0.916611i \(0.369086\pi\)
\(294\) 0 0
\(295\) −0.184822 + 13.8524i −0.0107608 + 0.806517i
\(296\) 0 0
\(297\) −0.0609273 + 0.163352i −0.00353536 + 0.00947867i
\(298\) 0 0
\(299\) 5.26944 0.816442i 0.304740 0.0472161i
\(300\) 0 0
\(301\) −6.85599 15.0125i −0.395172 0.865307i
\(302\) 0 0
\(303\) −0.199352 + 0.0142579i −0.0114524 + 0.000819095i
\(304\) 0 0
\(305\) −30.4496 4.79345i −1.74354 0.274472i
\(306\) 0 0
\(307\) −10.0122 + 5.46708i −0.571427 + 0.312023i −0.738858 0.673861i \(-0.764635\pi\)
0.167431 + 0.985884i \(0.446453\pi\)
\(308\) 0 0
\(309\) 0.0251008 0.174580i 0.00142794 0.00993151i
\(310\) 0 0
\(311\) 4.59387 10.0592i 0.260494 0.570403i −0.733518 0.679670i \(-0.762123\pi\)
0.994012 + 0.109267i \(0.0348503\pi\)
\(312\) 0 0
\(313\) 3.26733 15.0197i 0.184681 0.848963i −0.787791 0.615942i \(-0.788775\pi\)
0.972472 0.233021i \(-0.0748610\pi\)
\(314\) 0 0
\(315\) 1.12325 + 19.3252i 0.0632880 + 1.08885i
\(316\) 0 0
\(317\) 23.1232 5.03014i 1.29873 0.282521i 0.490526 0.871426i \(-0.336805\pi\)
0.808202 + 0.588905i \(0.200441\pi\)
\(318\) 0 0
\(319\) −1.47580 + 0.433333i −0.0826288 + 0.0242620i
\(320\) 0 0
\(321\) 0.385151i 0.0214970i
\(322\) 0 0
\(323\) 3.25002 + 3.25002i 0.180836 + 0.180836i
\(324\) 0 0
\(325\) 3.44913 4.36000i 0.191323 0.241849i
\(326\) 0 0
\(327\) 0.143644 + 0.660320i 0.00794353 + 0.0365158i
\(328\) 0 0
\(329\) −1.06554 7.41101i −0.0587453 0.408582i
\(330\) 0 0
\(331\) 0.748852 0.481258i 0.0411606 0.0264523i −0.519899 0.854228i \(-0.674030\pi\)
0.561059 + 0.827776i \(0.310394\pi\)
\(332\) 0 0
\(333\) 0.940106 + 2.52052i 0.0515175 + 0.138124i
\(334\) 0 0
\(335\) −29.7206 6.88183i −1.62381 0.375995i
\(336\) 0 0
\(337\) 5.29012 + 9.68813i 0.288171 + 0.527746i 0.981159 0.193203i \(-0.0618877\pi\)
−0.692987 + 0.720950i \(0.743706\pi\)
\(338\) 0 0
\(339\) −0.405847 0.468373i −0.0220426 0.0254385i
\(340\) 0 0
\(341\) −3.97458 3.44399i −0.215235 0.186503i
\(342\) 0 0
\(343\) 15.3161 + 5.71262i 0.826994 + 0.308453i
\(344\) 0 0
\(345\) 0.379665 0.327374i 0.0204405 0.0176252i
\(346\) 0 0
\(347\) 7.53487 + 2.81036i 0.404493 + 0.150868i 0.543472 0.839427i \(-0.317109\pi\)
−0.138979 + 0.990295i \(0.544382\pi\)
\(348\) 0 0
\(349\) −19.0865 16.5386i −1.02168 0.885289i −0.0282326 0.999601i \(-0.508988\pi\)
−0.993445 + 0.114313i \(0.963533\pi\)
\(350\) 0 0
\(351\) −0.204154 0.235606i −0.0108969 0.0125757i
\(352\) 0 0
\(353\) −13.3304 24.4128i −0.709507 1.29936i −0.944866 0.327456i \(-0.893809\pi\)
0.235360 0.971908i \(-0.424373\pi\)
\(354\) 0 0
\(355\) −1.84518 + 1.15133i −0.0979320 + 0.0611065i
\(356\) 0 0
\(357\) −0.0986311 0.264440i −0.00522011 0.0139957i
\(358\) 0 0
\(359\) −15.5908 + 10.0196i −0.822853 + 0.528816i −0.883000 0.469374i \(-0.844480\pi\)
0.0601462 + 0.998190i \(0.480843\pi\)
\(360\) 0 0
\(361\) 2.01614 + 14.0226i 0.106113 + 0.738030i
\(362\) 0 0
\(363\) 0.105465 + 0.484816i 0.00553549 + 0.0254462i
\(364\) 0 0
\(365\) −1.70289 8.36375i −0.0891333 0.437779i
\(366\) 0 0
\(367\) −14.6761 14.6761i −0.766085 0.766085i 0.211330 0.977415i \(-0.432221\pi\)
−0.977415 + 0.211330i \(0.932221\pi\)
\(368\) 0 0
\(369\) 22.0697i 1.14890i
\(370\) 0 0
\(371\) 8.87194 2.60504i 0.460608 0.135247i
\(372\) 0 0
\(373\) 9.80702 2.13339i 0.507788 0.110463i 0.0486298 0.998817i \(-0.484515\pi\)
0.459159 + 0.888354i \(0.348151\pi\)
\(374\) 0 0
\(375\) 0.0581165 0.519419i 0.00300112 0.0268227i
\(376\) 0 0
\(377\) 0.584625 2.68748i 0.0301097 0.138412i
\(378\) 0 0
\(379\) −9.57218 + 20.9601i −0.491690 + 1.07665i 0.487392 + 0.873183i \(0.337948\pi\)
−0.979082 + 0.203467i \(0.934779\pi\)
\(380\) 0 0
\(381\) 0.0443597 0.308529i 0.00227262 0.0158064i
\(382\) 0 0
\(383\) −21.5957 + 11.7921i −1.10349 + 0.602549i −0.924454 0.381294i \(-0.875479\pi\)
−0.179032 + 0.983843i \(0.557297\pi\)
\(384\) 0 0
\(385\) −2.36310 3.24612i −0.120435 0.165437i
\(386\) 0 0
\(387\) −17.0891 + 1.22224i −0.868687 + 0.0621297i
\(388\) 0 0
\(389\) −5.42505 11.8792i −0.275061 0.602300i 0.720805 0.693138i \(-0.243773\pi\)
−0.995866 + 0.0908387i \(0.971045\pi\)
\(390\) 0 0
\(391\) 5.32828 8.49342i 0.269463 0.429531i
\(392\) 0 0
\(393\) −0.189738 + 0.508707i −0.00957101 + 0.0256609i
\(394\) 0 0
\(395\) −4.87138 0.0649952i −0.245106 0.00327026i
\(396\) 0 0
\(397\) −7.22169 0.516506i −0.362446 0.0259227i −0.111071 0.993812i \(-0.535428\pi\)
−0.251375 + 0.967890i \(0.580883\pi\)
\(398\) 0 0
\(399\) −0.0836153 + 0.284768i −0.00418600 + 0.0142562i
\(400\) 0 0
\(401\) −37.5899 5.40462i −1.87715 0.269894i −0.893377 0.449307i \(-0.851671\pi\)
−0.983774 + 0.179413i \(0.942580\pi\)
\(402\) 0 0
\(403\) 8.81108 3.28636i 0.438911 0.163705i
\(404\) 0 0
\(405\) 19.1900 + 5.91391i 0.953561 + 0.293865i
\(406\) 0 0
\(407\) −0.446689 0.334387i −0.0221416 0.0165750i
\(408\) 0 0
\(409\) 8.61194 13.4004i 0.425833 0.662609i −0.560352 0.828254i \(-0.689334\pi\)
0.986185 + 0.165645i \(0.0529707\pi\)
\(410\) 0 0
\(411\) −0.258728 0.881148i −0.0127621 0.0434638i
\(412\) 0 0
\(413\) −12.6511 + 12.6511i −0.622521 + 0.622521i
\(414\) 0 0
\(415\) −23.4190 1.98932i −1.14959 0.0976520i
\(416\) 0 0
\(417\) 0.275901 0.505274i 0.0135109 0.0247434i
\(418\) 0 0
\(419\) 10.2159 + 6.56534i 0.499078 + 0.320738i 0.765847 0.643023i \(-0.222320\pi\)
−0.266770 + 0.963760i \(0.585956\pi\)
\(420\) 0 0
\(421\) 24.3000 3.49382i 1.18431 0.170278i 0.478117 0.878296i \(-0.341320\pi\)
0.706194 + 0.708018i \(0.250410\pi\)
\(422\) 0 0
\(423\) −7.59485 1.65216i −0.369274 0.0803307i
\(424\) 0 0
\(425\) −1.94869 10.2700i −0.0945254 0.498169i
\(426\) 0 0
\(427\) −23.8564 31.8685i −1.15449 1.54222i
\(428\) 0 0
\(429\) 0.0310106 + 0.00910553i 0.00149721 + 0.000439619i
\(430\) 0 0
\(431\) −4.43914 + 3.84653i −0.213826 + 0.185281i −0.755188 0.655509i \(-0.772454\pi\)
0.541362 + 0.840790i \(0.317909\pi\)
\(432\) 0 0
\(433\) −1.16911 16.3463i −0.0561840 0.785555i −0.944954 0.327202i \(-0.893894\pi\)
0.888770 0.458353i \(-0.151560\pi\)
\(434\) 0 0
\(435\) −0.0871215 0.243453i −0.00417716 0.0116727i
\(436\) 0 0
\(437\) −9.83787 + 3.79218i −0.470609 + 0.181405i
\(438\) 0 0
\(439\) 8.36448 3.81993i 0.399215 0.182315i −0.205682 0.978619i \(-0.565941\pi\)
0.604897 + 0.796303i \(0.293214\pi\)
\(440\) 0 0
\(441\) −2.62933 + 3.03440i −0.125206 + 0.144495i
\(442\) 0 0
\(443\) −1.94384 + 27.1784i −0.0923546 + 1.29129i 0.714122 + 0.700021i \(0.246826\pi\)
−0.806477 + 0.591265i \(0.798629\pi\)
\(444\) 0 0
\(445\) 9.08547 + 20.6180i 0.430692 + 0.977386i
\(446\) 0 0
\(447\) 0.299189 0.223970i 0.0141512 0.0105934i
\(448\) 0 0
\(449\) −9.78375 4.46809i −0.461724 0.210862i 0.170951 0.985279i \(-0.445316\pi\)
−0.632675 + 0.774417i \(0.718043\pi\)
\(450\) 0 0
\(451\) 2.47488 + 3.85098i 0.116537 + 0.181336i
\(452\) 0 0
\(453\) −0.658626 + 0.879821i −0.0309449 + 0.0413376i
\(454\) 0 0
\(455\) 7.11957 0.926870i 0.333770 0.0434523i
\(456\) 0 0
\(457\) −19.2356 10.5034i −0.899804 0.491330i −0.0384067 0.999262i \(-0.512228\pi\)
−0.861397 + 0.507932i \(0.830410\pi\)
\(458\) 0 0
\(459\) −0.586190 −0.0273610
\(460\) 0 0
\(461\) 5.44735 0.253709 0.126854 0.991921i \(-0.459512\pi\)
0.126854 + 0.991921i \(0.459512\pi\)
\(462\) 0 0
\(463\) −14.0218 7.65647i −0.651647 0.355826i 0.119178 0.992873i \(-0.461974\pi\)
−0.770825 + 0.637046i \(0.780156\pi\)
\(464\) 0 0
\(465\) 0.539227 0.700641i 0.0250060 0.0324914i
\(466\) 0 0
\(467\) 20.4468 27.3138i 0.946166 1.26393i −0.0183300 0.999832i \(-0.505835\pi\)
0.964496 0.264098i \(-0.0850741\pi\)
\(468\) 0 0
\(469\) −21.3004 33.1441i −0.983562 1.53045i
\(470\) 0 0
\(471\) −0.258810 0.118195i −0.0119253 0.00544612i
\(472\) 0 0
\(473\) 2.84484 2.12962i 0.130806 0.0979200i
\(474\) 0 0
\(475\) −4.83152 + 9.87357i −0.221685 + 0.453030i
\(476\) 0 0
\(477\) 0.684768 9.57431i 0.0313534 0.438378i
\(478\) 0 0
\(479\) −7.08995 + 8.18224i −0.323948 + 0.373856i −0.894241 0.447585i \(-0.852284\pi\)
0.570293 + 0.821441i \(0.306830\pi\)
\(480\) 0 0
\(481\) 0.907585 0.414480i 0.0413823 0.0188987i
\(482\) 0 0
\(483\) 0.646248 + 0.0391346i 0.0294053 + 0.00178068i
\(484\) 0 0
\(485\) 23.1605 8.28816i 1.05166 0.376346i
\(486\) 0 0
\(487\) 1.24307 + 17.3804i 0.0563289 + 0.787581i 0.944592 + 0.328246i \(0.106458\pi\)
−0.888263 + 0.459335i \(0.848088\pi\)
\(488\) 0 0
\(489\) −0.285480 + 0.247370i −0.0129099 + 0.0111865i
\(490\) 0 0
\(491\) 8.92733 + 2.62130i 0.402885 + 0.118298i 0.476896 0.878960i \(-0.341762\pi\)
−0.0740112 + 0.997257i \(0.523580\pi\)
\(492\) 0 0
\(493\) −3.09915 4.13997i −0.139579 0.186455i
\(494\) 0 0
\(495\) −4.01461 + 1.12084i −0.180443 + 0.0503780i
\(496\) 0 0
\(497\) −2.74463 0.597057i −0.123113 0.0267817i
\(498\) 0 0
\(499\) −8.96005 + 1.28826i −0.401107 + 0.0576705i −0.339916 0.940456i \(-0.610399\pi\)
−0.0611905 + 0.998126i \(0.519490\pi\)
\(500\) 0 0
\(501\) −0.326481 0.209817i −0.0145861 0.00937392i
\(502\) 0 0
\(503\) 2.60394 4.76877i 0.116104 0.212629i −0.813164 0.582034i \(-0.802257\pi\)
0.929268 + 0.369406i \(0.120439\pi\)
\(504\) 0 0
\(505\) −6.16339 7.30769i −0.274267 0.325188i
\(506\) 0 0
\(507\) 0.388862 0.388862i 0.0172699 0.0172699i
\(508\) 0 0
\(509\) −7.09233 24.1543i −0.314362 1.07062i −0.953466 0.301499i \(-0.902513\pi\)
0.639104 0.769120i \(-0.279305\pi\)
\(510\) 0 0
\(511\) 5.95951 9.27318i 0.263633 0.410222i
\(512\) 0 0
\(513\) 0.493469 + 0.369406i 0.0217872 + 0.0163097i
\(514\) 0 0
\(515\) 7.45776 3.94401i 0.328628 0.173794i
\(516\) 0 0
\(517\) 1.51051 0.563391i 0.0664321 0.0247779i
\(518\) 0 0
\(519\) 0.120081 + 0.0172651i 0.00527098 + 0.000757853i
\(520\) 0 0
\(521\) −10.1091 + 34.4283i −0.442886 + 1.50833i 0.371735 + 0.928339i \(0.378763\pi\)
−0.814621 + 0.579994i \(0.803055\pi\)
\(522\) 0 0
\(523\) 40.2388 + 2.87793i 1.75952 + 0.125843i 0.913377 0.407115i \(-0.133465\pi\)
0.846142 + 0.532958i \(0.178920\pi\)
\(524\) 0 0
\(525\) 0.521738 0.428260i 0.0227705 0.0186908i
\(526\) 0 0
\(527\) 6.17938 16.5676i 0.269178 0.721694i
\(528\) 0 0
\(529\) 12.8542 + 19.0727i 0.558879 + 0.829250i
\(530\) 0 0
\(531\) 7.71552 + 16.8946i 0.334825 + 0.733165i
\(532\) 0 0
\(533\) −8.16463 + 0.583946i −0.353649 + 0.0252935i
\(534\) 0 0
\(535\) 14.8941 10.8425i 0.643926 0.468764i
\(536\) 0 0
\(537\) 0.00197771 0.00107991i 8.53444e−5 4.66015e-5i
\(538\) 0 0
\(539\) 0.118520 0.824327i 0.00510503 0.0355063i
\(540\) 0 0
\(541\) 9.00737 19.7234i 0.387257 0.847975i −0.611148 0.791516i \(-0.709292\pi\)
0.998405 0.0564583i \(-0.0179808\pi\)
\(542\) 0 0
\(543\) −0.0574569 + 0.264125i −0.00246571 + 0.0113347i
\(544\) 0 0
\(545\) −21.4913 + 24.1438i −0.920585 + 1.03420i
\(546\) 0 0
\(547\) 10.6625 2.31948i 0.455895 0.0991738i 0.0212467 0.999774i \(-0.493236\pi\)
0.434648 + 0.900600i \(0.356873\pi\)
\(548\) 0 0
\(549\) −39.6514 + 11.6427i −1.69228 + 0.496898i
\(550\) 0 0
\(551\) 5.43816i 0.231673i
\(552\) 0 0
\(553\) −4.44894 4.44894i −0.189188 0.189188i
\(554\) 0 0
\(555\) 0.0517622 0.0782288i 0.00219718 0.00332063i
\(556\) 0 0
\(557\) 2.20022 + 10.1142i 0.0932263 + 0.428554i 0.999976 + 0.00688568i \(0.00219180\pi\)
−0.906750 + 0.421669i \(0.861445\pi\)
\(558\) 0 0
\(559\) 0.904324 + 6.28971i 0.0382488 + 0.266027i
\(560\) 0 0
\(561\) 0.0511240 0.0328554i 0.00215846 0.00138716i
\(562\) 0 0
\(563\) −5.77770 15.4906i −0.243501 0.652851i 0.756498 0.653996i \(-0.226908\pi\)
−0.999999 + 0.00114429i \(0.999636\pi\)
\(564\) 0 0
\(565\) 6.68714 28.8798i 0.281330 1.21498i
\(566\) 0 0
\(567\) 12.4285 + 22.7611i 0.521949 + 0.955878i
\(568\) 0 0
\(569\) −3.37859 3.89910i −0.141638 0.163459i 0.680498 0.732750i \(-0.261763\pi\)
−0.822136 + 0.569291i \(0.807218\pi\)
\(570\) 0 0
\(571\) −13.9138 12.0564i −0.582275 0.504544i 0.313182 0.949693i \(-0.398605\pi\)
−0.895456 + 0.445149i \(0.853151\pi\)
\(572\) 0 0
\(573\) −0.360646 0.134514i −0.0150662 0.00561940i
\(574\) 0 0
\(575\) 23.3479 + 5.46590i 0.973674 + 0.227944i
\(576\) 0 0
\(577\) 29.6682 + 11.0657i 1.23510 + 0.460670i 0.880365 0.474296i \(-0.157297\pi\)
0.354738 + 0.934966i \(0.384570\pi\)
\(578\) 0 0
\(579\) −0.548361 0.475158i −0.0227891 0.0197469i
\(580\) 0 0
\(581\) −19.8774 22.9398i −0.824654 0.951702i
\(582\) 0 0
\(583\) 0.954166 + 1.74743i 0.0395175 + 0.0723710i
\(584\) 0 0
\(585\) 1.68131 7.26107i 0.0695135 0.300208i
\(586\) 0 0
\(587\) −6.12545 16.4230i −0.252824 0.677848i −0.999914 0.0131249i \(-0.995822\pi\)
0.747089 0.664723i \(-0.231451\pi\)
\(588\) 0 0
\(589\) −15.6425 + 10.0528i −0.644539 + 0.414220i
\(590\) 0 0
\(591\) −0.0183976 0.127958i −0.000756775 0.00526349i
\(592\) 0 0
\(593\) −0.0135628 0.0623474i −0.000556959 0.00256030i 0.976868 0.213845i \(-0.0685988\pi\)
−0.977425 + 0.211285i \(0.932235\pi\)
\(594\) 0 0
\(595\) 7.44949 11.2585i 0.305399 0.461553i
\(596\) 0 0
\(597\) −0.635166 0.635166i −0.0259956 0.0259956i
\(598\) 0 0
\(599\) 22.7964i 0.931437i −0.884933 0.465719i \(-0.845796\pi\)
0.884933 0.465719i \(-0.154204\pi\)
\(600\) 0 0
\(601\) 35.2693 10.3560i 1.43867 0.422430i 0.532888 0.846186i \(-0.321107\pi\)
0.905777 + 0.423755i \(0.139288\pi\)
\(602\) 0 0
\(603\) −39.9649 + 8.69382i −1.62749 + 0.354040i
\(604\) 0 0
\(605\) −15.7792 + 17.7267i −0.641515 + 0.720691i
\(606\) 0 0
\(607\) 6.27596 28.8501i 0.254733 1.17099i −0.654945 0.755676i \(-0.727308\pi\)
0.909678 0.415313i \(-0.136328\pi\)
\(608\) 0 0
\(609\) 0.138722 0.303758i 0.00562129 0.0123089i
\(610\) 0 0
\(611\) −0.410258 + 2.85341i −0.0165973 + 0.115437i
\(612\) 0 0
\(613\) −22.4381 + 12.2521i −0.906267 + 0.494859i −0.863570 0.504229i \(-0.831777\pi\)
−0.0426970 + 0.999088i \(0.513595\pi\)
\(614\) 0 0
\(615\) −0.622161 + 0.452919i −0.0250879 + 0.0182635i
\(616\) 0 0
\(617\) −30.0344 + 2.14810i −1.20914 + 0.0864793i −0.661311 0.750112i \(-0.730000\pi\)
−0.547828 + 0.836591i \(0.684545\pi\)
\(618\) 0 0
\(619\) −14.7832 32.3707i −0.594188 1.30109i −0.932878 0.360192i \(-0.882711\pi\)
0.338691 0.940898i \(-0.390016\pi\)
\(620\) 0 0
\(621\) 0.545216 1.22920i 0.0218788 0.0493259i
\(622\) 0 0
\(623\) −10.1687 + 27.2633i −0.407399 + 1.09228i
\(624\) 0 0
\(625\) 21.7223 12.3750i 0.868894 0.494998i
\(626\) 0 0
\(627\) −0.0637422 0.00455893i −0.00254562 0.000182066i
\(628\) 0 0
\(629\) 0.528552 1.80008i 0.0210748 0.0717740i
\(630\) 0 0
\(631\) −44.0286 6.33036i −1.75275 0.252008i −0.810220 0.586125i \(-0.800653\pi\)
−0.942531 + 0.334118i \(0.891562\pi\)
\(632\) 0 0
\(633\) −0.122894 + 0.0458371i −0.00488459 + 0.00182186i
\(634\) 0 0
\(635\) 13.1798 6.97009i 0.523025 0.276600i
\(636\) 0 0
\(637\) 1.19214 + 0.892423i 0.0472342 + 0.0353591i
\(638\) 0 0
\(639\) −1.57642 + 2.45295i −0.0623621 + 0.0970373i
\(640\) 0 0
\(641\) 3.57248 + 12.1667i 0.141104 + 0.480557i 0.999472 0.0324770i \(-0.0103396\pi\)
−0.858368 + 0.513034i \(0.828521\pi\)
\(642\) 0 0
\(643\) 25.5764 25.5764i 1.00863 1.00863i 0.00867061 0.999962i \(-0.497240\pi\)
0.999962 0.00867061i \(-0.00275998\pi\)
\(644\) 0 0
\(645\) 0.385161 + 0.456670i 0.0151657 + 0.0179814i
\(646\) 0 0
\(647\) 4.19382 7.68042i 0.164876 0.301948i −0.782158 0.623080i \(-0.785881\pi\)
0.947035 + 0.321131i \(0.104063\pi\)
\(648\) 0 0
\(649\) −3.24084 2.08276i −0.127214 0.0817555i
\(650\) 0 0
\(651\) 1.13018 0.162495i 0.0442952 0.00636869i
\(652\) 0 0
\(653\) 17.1798 + 3.73723i 0.672296 + 0.146249i 0.535740 0.844383i \(-0.320033\pi\)
0.136556 + 0.990632i \(0.456397\pi\)
\(654\) 0 0
\(655\) −25.0135 + 6.98352i −0.977357 + 0.272869i
\(656\) 0 0
\(657\) −6.85755 9.16062i −0.267539 0.357390i
\(658\) 0 0
\(659\) 45.1308 + 13.2516i 1.75805 + 0.516210i 0.991963 0.126529i \(-0.0403838\pi\)
0.766085 + 0.642739i \(0.222202\pi\)
\(660\) 0 0
\(661\) −5.93565 + 5.14327i −0.230870 + 0.200050i −0.762612 0.646857i \(-0.776083\pi\)
0.531742 + 0.846907i \(0.321538\pi\)
\(662\) 0 0
\(663\) 0.00775221 + 0.108390i 0.000301071 + 0.00420952i
\(664\) 0 0
\(665\) −13.3661 + 4.78315i −0.518314 + 0.185482i
\(666\) 0 0
\(667\) 11.5637 2.64807i 0.447749 0.102534i
\(668\) 0 0
\(669\) −0.673762 + 0.307697i −0.0260492 + 0.0118963i
\(670\) 0 0
\(671\) 5.61323 6.47801i 0.216696 0.250081i
\(672\) 0 0
\(673\) −1.86113 + 26.0220i −0.0717412 + 1.00307i 0.826319 + 0.563202i \(0.190431\pi\)
−0.898061 + 0.439872i \(0.855024\pi\)
\(674\) 0 0
\(675\) −0.454706 1.32614i −0.0175016 0.0510433i
\(676\) 0 0
\(677\) −38.9391 + 29.1494i −1.49655 + 1.12030i −0.535289 + 0.844669i \(0.679797\pi\)
−0.961262 + 0.275635i \(0.911112\pi\)
\(678\) 0 0
\(679\) 28.8976 + 13.1971i 1.10899 + 0.506457i
\(680\) 0 0
\(681\) −0.328982 0.511906i −0.0126066 0.0196163i
\(682\) 0 0
\(683\) −25.4505 + 33.9979i −0.973837 + 1.30089i −0.0202434 + 0.999795i \(0.506444\pi\)
−0.953593 + 0.301098i \(0.902647\pi\)
\(684\) 0 0
\(685\) 26.7911 34.8108i 1.02363 1.33005i
\(686\) 0 0
\(687\) −0.0525109 0.0286731i −0.00200341 0.00109395i
\(688\) 0 0
\(689\) −3.56011 −0.135629
\(690\) 0 0
\(691\) 18.2417 0.693947 0.346974 0.937875i \(-0.387209\pi\)
0.346974 + 0.937875i \(0.387209\pi\)
\(692\) 0 0
\(693\) −4.72453 2.57979i −0.179470 0.0979980i
\(694\) 0 0
\(695\) 27.3063 3.55491i 1.03579 0.134845i
\(696\) 0 0
\(697\) −9.22363 + 12.3213i −0.349370 + 0.466703i
\(698\) 0 0
\(699\) 0.399863 + 0.622199i 0.0151242 + 0.0235337i
\(700\) 0 0
\(701\) −5.66689 2.58798i −0.214036 0.0977468i 0.305512 0.952188i \(-0.401172\pi\)
−0.519548 + 0.854441i \(0.673900\pi\)
\(702\) 0 0
\(703\) −1.57933 + 1.18227i −0.0595655 + 0.0445902i
\(704\) 0 0
\(705\) 0.109287 + 0.248010i 0.00411600 + 0.00934060i
\(706\) 0 0
\(707\) 0.880760 12.3146i 0.0331244 0.463139i
\(708\) 0 0
\(709\) 21.3230 24.6080i 0.800801 0.924174i −0.197624 0.980278i \(-0.563322\pi\)
0.998425 + 0.0561043i \(0.0178679\pi\)
\(710\) 0 0
\(711\) −5.94123 + 2.71327i −0.222814 + 0.101756i
\(712\) 0 0
\(713\) 28.9934 + 28.3672i 1.08581 + 1.06236i
\(714\) 0 0
\(715\) 0.520874 + 1.45554i 0.0194796 + 0.0544339i
\(716\) 0 0
\(717\) 0.0278197 + 0.388971i 0.00103895 + 0.0145264i
\(718\) 0 0
\(719\) −30.4326 + 26.3700i −1.13494 + 0.983435i −0.999973 0.00741457i \(-0.997640\pi\)
−0.134972 + 0.990849i \(0.543094\pi\)
\(720\) 0 0
\(721\) 10.4540 + 3.06956i 0.389326 + 0.114316i
\(722\) 0 0
\(723\) 0.409181 + 0.546602i 0.0152176 + 0.0203283i
\(724\) 0 0
\(725\) 6.96191 10.2226i 0.258559 0.379658i
\(726\) 0 0
\(727\) −47.3516 10.3007i −1.75617 0.382032i −0.784830 0.619711i \(-0.787250\pi\)
−0.971344 + 0.237679i \(0.923613\pi\)
\(728\) 0 0
\(729\) 26.6084 3.82572i 0.985498 0.141693i
\(730\) 0 0
\(731\) 10.0515 + 6.45970i 0.371768 + 0.238920i
\(732\) 0 0
\(733\) 10.9886 20.1241i 0.405873 0.743301i −0.592171 0.805812i \(-0.701729\pi\)
0.998044 + 0.0625110i \(0.0199108\pi\)
\(734\) 0 0
\(735\) 0.139501 + 0.0118499i 0.00514559 + 0.000437090i
\(736\) 0 0
\(737\) 5.99861 5.99861i 0.220962 0.220962i
\(738\) 0 0
\(739\) 12.6529 + 43.0918i 0.465444 + 1.58516i 0.773504 + 0.633791i \(0.218502\pi\)
−0.308060 + 0.951367i \(0.599680\pi\)
\(740\) 0 0
\(741\) 0.0617794 0.0961307i 0.00226952 0.00353145i
\(742\) 0 0
\(743\) −8.95832 6.70612i −0.328649 0.246024i 0.422192 0.906506i \(-0.361261\pi\)
−0.750841 + 0.660483i \(0.770352\pi\)
\(744\) 0 0
\(745\) 17.0837 + 5.26478i 0.625898 + 0.192887i
\(746\) 0 0
\(747\) −29.5234 + 11.0117i −1.08020 + 0.402895i
\(748\) 0 0
\(749\) 23.5499 + 3.38597i 0.860495 + 0.123721i
\(750\) 0 0
\(751\) −11.4649 + 39.0458i −0.418359 + 1.42480i 0.433559 + 0.901125i \(0.357258\pi\)
−0.851918 + 0.523675i \(0.824561\pi\)
\(752\) 0 0
\(753\) −0.406441 0.0290692i −0.0148115 0.00105934i
\(754\) 0 0
\(755\) −52.5645 0.701329i −1.91302 0.0255240i
\(756\) 0 0
\(757\) −2.14697 + 5.75625i −0.0780330 + 0.209215i −0.970108 0.242672i \(-0.921976\pi\)
0.892075 + 0.451887i \(0.149249\pi\)
\(758\) 0 0
\(759\) 0.0213447 + 0.137762i 0.000774763 + 0.00500044i
\(760\) 0 0
\(761\) 4.22538 + 9.25230i 0.153170 + 0.335396i 0.970625 0.240597i \(-0.0773431\pi\)
−0.817455 + 0.575992i \(0.804616\pi\)
\(762\) 0 0
\(763\) −41.6379 + 2.97800i −1.50739 + 0.107811i
\(764\) 0 0
\(765\) −8.24803 11.3301i −0.298208 0.409639i
\(766\) 0 0
\(767\) 6.04597 3.30135i 0.218307 0.119205i
\(768\) 0 0
\(769\) −2.92270 + 20.3278i −0.105395 + 0.733039i 0.866764 + 0.498718i \(0.166196\pi\)
−0.972159 + 0.234321i \(0.924713\pi\)
\(770\) 0 0
\(771\) 0.400189 0.876293i 0.0144125 0.0315589i
\(772\) 0 0
\(773\) −4.28263 + 19.6869i −0.154036 + 0.708090i 0.833734 + 0.552167i \(0.186199\pi\)
−0.987769 + 0.155923i \(0.950165\pi\)
\(774\) 0 0
\(775\) 42.2743 + 1.12827i 1.51854 + 0.0405286i
\(776\) 0 0
\(777\) 0.118375 0.0257509i 0.00424667 0.000923807i
\(778\) 0 0
\(779\) 15.5293 4.55983i 0.556397 0.163373i
\(780\) 0 0
\(781\) 0.604797i 0.0216413i
\(782\) 0 0
\(783\) −0.490427 0.490427i −0.0175264 0.0175264i
\(784\) 0 0
\(785\) −2.71520 13.3357i −0.0969095 0.475972i
\(786\) 0 0
\(787\) 9.13827 + 42.0079i 0.325744 + 1.49742i 0.790764 + 0.612121i \(0.209683\pi\)
−0.465020 + 0.885300i \(0.653953\pi\)
\(788\) 0 0
\(789\) −0.0381403 0.265272i −0.00135783 0.00944393i
\(790\) 0 0
\(791\) 32.2064 20.6978i 1.14513 0.735930i
\(792\) 0 0
\(793\) 5.35632 + 14.3608i 0.190208 + 0.509969i
\(794\) 0 0
\(795\) −0.283959 + 0.177182i −0.0100710 + 0.00628399i
\(796\) 0 0
\(797\) 24.1007 + 44.1371i 0.853690 + 1.56342i 0.825910 + 0.563802i \(0.190662\pi\)
0.0277795 + 0.999614i \(0.491156\pi\)
\(798\) 0 0
\(799\) 3.54965 + 4.09651i 0.125577 + 0.144924i
\(800\) 0 0
\(801\) 22.8286 + 19.7811i 0.806607 + 0.698929i
\(802\) 0 0
\(803\) 2.22385 + 0.829452i 0.0784778 + 0.0292707i
\(804\) 0 0
\(805\) 16.6794 + 26.0925i 0.587872 + 0.919642i
\(806\) 0 0
\(807\) −0.223082 0.0832053i −0.00785286 0.00292897i
\(808\) 0 0
\(809\) 34.4294 + 29.8333i 1.21047 + 1.04888i 0.997416 + 0.0718416i \(0.0228876\pi\)
0.213057 + 0.977040i \(0.431658\pi\)
\(810\) 0 0
\(811\) −34.8890 40.2641i −1.22512 1.41386i −0.879776 0.475388i \(-0.842308\pi\)
−0.345344 0.938476i \(-0.612238\pi\)
\(812\) 0 0
\(813\) −0.460802 0.843896i −0.0161610 0.0295967i
\(814\) 0 0
\(815\) −17.6026 4.07591i −0.616594 0.142773i
\(816\) 0 0
\(817\) −4.39080 11.7722i −0.153615 0.411857i
\(818\) 0 0
\(819\) 8.09747 5.20393i 0.282949 0.181840i
\(820\) 0 0
\(821\) 0.848233 + 5.89959i 0.0296035 + 0.205897i 0.999255 0.0385944i \(-0.0122880\pi\)
−0.969651 + 0.244492i \(0.921379\pi\)
\(822\) 0 0
\(823\) −0.239309 1.10009i −0.00834179 0.0383466i 0.972788 0.231698i \(-0.0744280\pi\)
−0.981130 + 0.193351i \(0.938064\pi\)
\(824\) 0 0
\(825\) 0.113986 + 0.0901724i 0.00396847 + 0.00313940i
\(826\) 0 0
\(827\) 2.56413 + 2.56413i 0.0891635 + 0.0891635i 0.750282 0.661118i \(-0.229918\pi\)
−0.661118 + 0.750282i \(0.729918\pi\)
\(828\) 0 0
\(829\) 6.22752i 0.216291i 0.994135 + 0.108145i \(0.0344912\pi\)
−0.994135 + 0.108145i \(0.965509\pi\)
\(830\) 0 0
\(831\) −1.23697 + 0.363206i −0.0429099 + 0.0125995i
\(832\) 0 0
\(833\) 2.73610 0.595202i 0.0948002 0.0206225i
\(834\) 0 0
\(835\) −1.07714 18.5319i −0.0372760 0.641323i
\(836\) 0 0
\(837\) 0.504092 2.31728i 0.0174240 0.0800968i
\(838\) 0 0
\(839\) 15.7581 34.5054i 0.544030 1.19126i −0.415484 0.909600i \(-0.636388\pi\)
0.959514 0.281659i \(-0.0908848\pi\)
\(840\) 0 0
\(841\) −3.25634 + 22.6483i −0.112287 + 0.780976i
\(842\) 0 0
\(843\) 1.15798 0.632302i 0.0398828 0.0217777i
\(844\) 0 0
\(845\) 25.9846 + 4.09055i 0.893896 + 0.140719i
\(846\) 0 0
\(847\) −30.5711 + 2.18649i −1.05043 + 0.0751286i
\(848\) 0 0
\(849\) 0.257026 + 0.562808i 0.00882110 + 0.0193155i
\(850\) 0 0
\(851\) 3.28303 + 2.78259i 0.112541 + 0.0953861i
\(852\) 0 0
\(853\) −9.59827 + 25.7340i −0.328638 + 0.881114i 0.662593 + 0.748979i \(0.269456\pi\)
−0.991232 + 0.132134i \(0.957817\pi\)
\(854\) 0 0
\(855\) −0.196607 + 14.7357i −0.00672382 + 0.503950i
\(856\) 0 0
\(857\) 12.2424 + 0.875592i 0.418192 + 0.0299097i 0.278850 0.960335i \(-0.410047\pi\)
0.139342 + 0.990244i \(0.455501\pi\)
\(858\) 0 0
\(859\) −5.72595 + 19.5008i −0.195367 + 0.665359i 0.802289 + 0.596935i \(0.203615\pi\)
−0.997656 + 0.0684234i \(0.978203\pi\)
\(860\) 0 0
\(861\) −0.983737 0.141440i −0.0335257 0.00482026i
\(862\) 0 0
\(863\) 18.0898 6.74716i 0.615785 0.229676i −0.0221643 0.999754i \(-0.507056\pi\)
0.637949 + 0.770078i \(0.279783\pi\)
\(864\) 0 0
\(865\) 2.71280 + 5.12966i 0.0922381 + 0.174414i
\(866\) 0 0
\(867\) −0.472632 0.353808i −0.0160514 0.0120159i
\(868\) 0 0
\(869\) 0.732431 1.13969i 0.0248460 0.0386612i
\(870\) 0 0
\(871\) 4.27369 + 14.5548i 0.144808 + 0.493172i
\(872\) 0 0
\(873\) 23.3195 23.3195i 0.789246 0.789246i
\(874\) 0 0
\(875\) 31.2488 + 8.11987i 1.05640 + 0.274502i
\(876\) 0 0
\(877\) 5.16978 9.46774i 0.174571 0.319703i −0.775714 0.631085i \(-0.782610\pi\)
0.950285 + 0.311382i \(0.100792\pi\)
\(878\) 0 0
\(879\) −0.624907 0.401604i −0.0210776 0.0135458i
\(880\) 0 0
\(881\) −0.0444367 + 0.00638903i −0.00149711 + 0.000215252i −0.143063 0.989714i \(-0.545695\pi\)
0.141566 + 0.989929i \(0.454786\pi\)
\(882\) 0 0
\(883\) −26.3106 5.72351i −0.885421 0.192612i −0.253213 0.967411i \(-0.581487\pi\)
−0.632208 + 0.774799i \(0.717851\pi\)
\(884\) 0 0
\(885\) 0.317932 0.564221i 0.0106872 0.0189661i
\(886\) 0 0
\(887\) −25.3893 33.9162i −0.852490 1.13879i −0.988965 0.148150i \(-0.952668\pi\)
0.136475 0.990644i \(-0.456423\pi\)
\(888\) 0 0
\(889\) 18.4749 + 5.42472i 0.619628 + 0.181939i
\(890\) 0 0
\(891\) −4.22010 + 3.65674i −0.141379 + 0.122505i
\(892\) 0 0
\(893\) −0.406632 5.68546i −0.0136074 0.190257i
\(894\) 0 0
\(895\) 0.0974361 + 0.0460784i 0.00325693 + 0.00154023i
\(896\) 0 0
\(897\) −0.234496 0.0845580i −0.00782959 0.00282331i
\(898\) 0 0
\(899\) 19.0309 8.69111i 0.634716 0.289865i
\(900\) 0 0
\(901\) −4.38370 + 5.05906i −0.146042 + 0.168542i
\(902\) 0 0
\(903\) −0.0550402 + 0.769562i −0.00183162 + 0.0256094i
\(904\) 0 0
\(905\) −11.8314 + 5.21359i −0.393289 + 0.173306i
\(906\) 0 0
\(907\) 8.90444 6.66578i 0.295667 0.221334i −0.441137 0.897440i \(-0.645425\pi\)
0.736804 + 0.676106i \(0.236334\pi\)
\(908\) 0 0
\(909\) −11.6583 5.32415i −0.386680 0.176591i
\(910\) 0 0
\(911\) 12.2990 + 19.1376i 0.407485 + 0.634059i 0.982973 0.183752i \(-0.0588242\pi\)
−0.575488 + 0.817810i \(0.695188\pi\)
\(912\) 0 0
\(913\) 3.91675 5.23216i 0.129625 0.173159i
\(914\) 0 0
\(915\) 1.14195 + 0.878866i 0.0377516 + 0.0290544i
\(916\) 0 0
\(917\) −29.4367 16.0736i −0.972085 0.530799i
\(918\) 0 0
\(919\) 17.6471 0.582125 0.291063 0.956704i \(-0.405991\pi\)
0.291063 + 0.956704i \(0.405991\pi\)
\(920\) 0 0
\(921\) 0.533283 0.0175723
\(922\) 0 0
\(923\) 0.949173 + 0.518288i 0.0312424 + 0.0170596i
\(924\) 0 0
\(925\) 4.48234 0.200570i 0.147379 0.00659471i
\(926\) 0 0
\(927\) 6.77808 9.05445i 0.222621 0.297387i
\(928\) 0 0
\(929\) 4.94656 + 7.69700i 0.162292 + 0.252531i 0.912870 0.408251i \(-0.133861\pi\)
−0.750578 + 0.660782i \(0.770225\pi\)
\(930\) 0 0
\(931\) −2.67840 1.22318i −0.0877810 0.0400882i
\(932\) 0 0
\(933\) −0.413851 + 0.309805i −0.0135489 + 0.0101426i
\(934\) 0 0
\(935\) 2.70975 + 1.05208i 0.0886184 + 0.0344065i
\(936\) 0 0
\(937\) 0.587675 8.21678i 0.0191985 0.268430i −0.978782 0.204906i \(-0.934311\pi\)
0.997980 0.0635248i \(-0.0202342\pi\)
\(938\) 0 0
\(939\) −0.470559 + 0.543054i −0.0153561 + 0.0177219i
\(940\) 0 0
\(941\) −28.3568 + 12.9501i −0.924405 + 0.422162i −0.819994 0.572373i \(-0.806023\pi\)
−0.104411 + 0.994534i \(0.533296\pi\)
\(942\) 0 0
\(943\) −17.2579 30.8013i −0.561996 1.00303i
\(944\) 0 0
\(945\) 0.774030 1.63674i 0.0251792 0.0532433i
\(946\) 0 0
\(947\) 2.30311 + 32.2017i 0.0748411 + 1.04641i 0.886635 + 0.462470i \(0.153037\pi\)
−0.811794 + 0.583944i \(0.801509\pi\)
\(948\) 0 0
\(949\) −3.20750 + 2.77931i −0.104120 + 0.0902203i
\(950\) 0 0
\(951\) −1.06144 0.311666i −0.0344194 0.0101065i
\(952\) 0 0
\(953\) 23.2659 + 31.0797i 0.753658 + 1.00677i 0.999300 + 0.0374085i \(0.0119103\pi\)
−0.245642 + 0.969361i \(0.578999\pi\)
\(954\) 0 0
\(955\) −4.95094 17.7332i −0.160209 0.573833i
\(956\) 0 0
\(957\) 0.0702601 + 0.0152841i 0.00227119 + 0.000494066i
\(958\) 0 0
\(959\) 56.1521 8.07345i 1.81325 0.260705i
\(960\) 0 0
\(961\) 34.1006 + 21.9151i 1.10002 + 0.706940i
\(962\) 0 0
\(963\) 11.8368 21.6774i 0.381434 0.698544i
\(964\) 0 0
\(965\) 2.93755 34.5819i 0.0945630 1.11323i
\(966\) 0 0
\(967\) 10.2193 10.2193i 0.328630 0.328630i −0.523435 0.852065i \(-0.675350\pi\)
0.852065 + 0.523435i \(0.175350\pi\)
\(968\) 0 0
\(969\) −0.0605343 0.206161i −0.00194464 0.00662284i
\(970\) 0 0
\(971\) −4.46633 + 6.94974i −0.143331 + 0.223028i −0.905495 0.424356i \(-0.860501\pi\)
0.762164 + 0.647384i \(0.224137\pi\)
\(972\) 0 0
\(973\) 28.4693 + 21.3119i 0.912684 + 0.683227i
\(974\) 0 0
\(975\) −0.239199 + 0.101616i −0.00766049 + 0.00325431i
\(976\) 0 0
\(977\) −14.7228 + 5.49131i −0.471024 + 0.175683i −0.573756 0.819026i \(-0.694514\pi\)
0.102732 + 0.994709i \(0.467241\pi\)
\(978\) 0 0
\(979\) −6.20162 0.891658i −0.198205 0.0284975i
\(980\) 0 0
\(981\) −12.2088 + 41.5793i −0.389797 + 1.32753i
\(982\) 0 0
\(983\) 1.22934 + 0.0879238i 0.0392097 + 0.00280433i 0.0909303 0.995857i \(-0.471016\pi\)
−0.0517205 + 0.998662i \(0.516471\pi\)
\(984\) 0 0
\(985\) 4.43031 4.31364i 0.141161 0.137444i
\(986\) 0 0
\(987\) −0.122317 + 0.327945i −0.00389340 + 0.0104386i
\(988\) 0 0
\(989\) −22.8944 + 15.0690i −0.727999 + 0.479166i
\(990\) 0 0
\(991\) 23.7777 + 52.0659i 0.755323 + 1.65393i 0.756557 + 0.653927i \(0.226880\pi\)
−0.00123431 + 0.999999i \(0.500393\pi\)
\(992\) 0 0
\(993\) −0.0415074 + 0.00296867i −0.00131720 + 9.42078e-5i
\(994\) 0 0
\(995\) 6.68150 42.4431i 0.211818 1.34554i
\(996\) 0 0
\(997\) −48.8369 + 26.6669i −1.54668 + 0.844551i −0.546705 + 0.837325i \(0.684118\pi\)
−0.999974 + 0.00722554i \(0.997700\pi\)
\(998\) 0 0
\(999\) 0.0358077 0.249048i 0.00113291 0.00787954i
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 920.2.bv.a.433.18 yes 720
5.2 odd 4 inner 920.2.bv.a.617.18 yes 720
23.17 odd 22 inner 920.2.bv.a.753.18 yes 720
115.17 even 44 inner 920.2.bv.a.17.18 720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bv.a.17.18 720 115.17 even 44 inner
920.2.bv.a.433.18 yes 720 1.1 even 1 trivial
920.2.bv.a.617.18 yes 720 5.2 odd 4 inner
920.2.bv.a.753.18 yes 720 23.17 odd 22 inner