Properties

Label 201.3.o.a.167.1
Level $201$
Weight $3$
Character 201.167
Analytic conductor $5.477$
Analytic rank $0$
Dimension $20$
CM discriminant -3
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,3,Mod(17,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 64]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.o (of order \(66\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label 167.1
Root \(0.928368 + 0.371662i\) of defining polynomial
Character \(\chi\) \(=\) 201.167
Dual form 201.3.o.a.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.87848 - 0.845198i) q^{3} +(-3.98189 + 0.380224i) q^{4} +(-11.9416 - 6.15630i) q^{7} +(7.57128 - 4.86577i) q^{9} +O(q^{10})\) \(q+(2.87848 - 0.845198i) q^{3} +(-3.98189 + 0.380224i) q^{4} +(-11.9416 - 6.15630i) q^{7} +(7.57128 - 4.86577i) q^{9} +(-11.1404 + 4.45995i) q^{12} +(-20.3617 - 16.0126i) q^{13} +(15.7109 - 3.02802i) q^{16} +(15.2339 - 7.85364i) q^{19} +(-39.5768 - 7.62781i) q^{21} +(-3.55787 + 24.7455i) q^{25} +(17.6812 - 20.4052i) q^{27} +(49.8907 + 19.9732i) q^{28} +(-42.7047 + 33.5834i) q^{31} +(-28.2979 + 22.2537i) q^{36} +(36.1385 - 62.5937i) q^{37} +(-72.1446 - 28.8824i) q^{39} +(-21.3206 - 46.6855i) q^{43} +(42.6641 - 21.9949i) q^{48} +(76.2780 + 107.117i) q^{49} +(87.1665 + 56.0185i) q^{52} +(37.2127 - 35.4822i) q^{57} +(4.37545 + 12.6420i) q^{61} +(-120.368 + 11.4938i) q^{63} +(-61.4076 + 18.0309i) q^{64} +(46.3306 - 48.3991i) q^{67} +(23.3501 + 67.4656i) q^{73} +(10.6736 + 74.2366i) q^{75} +(-57.6737 + 37.0646i) q^{76} +(63.8645 - 25.5675i) q^{79} +(33.6486 - 73.6802i) q^{81} +(160.491 + 15.3250i) q^{84} +(144.572 + 316.569i) q^{91} +(-94.5401 + 132.763i) q^{93} +(94.0250 - 162.856i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{3} + 4 q^{4} + 2 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{3} + 4 q^{4} + 2 q^{7} - 18 q^{9} - 12 q^{12} + 23 q^{13} + 16 q^{16} + 26 q^{19} - 6 q^{21} - 50 q^{25} + 54 q^{27} + 8 q^{28} - 13 q^{31} + 36 q^{36} + 26 q^{37} - 69 q^{39} + 122 q^{43} - 48 q^{48} - 45 q^{49} + 828 q^{52} - 441 q^{57} + 47 q^{61} - 1269 q^{63} - 128 q^{64} + 109 q^{67} - 924 q^{73} + 150 q^{75} - 208 q^{76} + 252 q^{79} - 162 q^{81} + 1692 q^{84} - 92 q^{91} + 39 q^{93} + 167 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{16}{33}\right)\)

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 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(3\) 2.87848 0.845198i 0.959493 0.281733i
\(4\) −3.98189 + 0.380224i −0.995472 + 0.0950560i
\(5\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(6\) 0 0
\(7\) −11.9416 6.15630i −1.70594 0.879472i −0.981825 0.189789i \(-0.939220\pi\)
−0.724112 0.689682i \(-0.757750\pi\)
\(8\) 0 0
\(9\) 7.57128 4.86577i 0.841254 0.540641i
\(10\) 0 0
\(11\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(12\) −11.1404 + 4.45995i −0.928368 + 0.371662i
\(13\) −20.3617 16.0126i −1.56629 1.23174i −0.836283 0.548298i \(-0.815276\pi\)
−0.730003 0.683443i \(-0.760482\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 15.7109 3.02802i 0.981929 0.189251i
\(17\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(18\) 0 0
\(19\) 15.2339 7.85364i 0.801786 0.413350i −0.00807751 0.999967i \(-0.502571\pi\)
0.809864 + 0.586618i \(0.199541\pi\)
\(20\) 0 0
\(21\) −39.5768 7.62781i −1.88461 0.363229i
\(22\) 0 0
\(23\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(24\) 0 0
\(25\) −3.55787 + 24.7455i −0.142315 + 0.989821i
\(26\) 0 0
\(27\) 17.6812 20.4052i 0.654861 0.755750i
\(28\) 49.8907 + 19.9732i 1.78181 + 0.713330i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) −42.7047 + 33.5834i −1.37757 + 1.08334i −0.390933 + 0.920419i \(0.627847\pi\)
−0.986640 + 0.162916i \(0.947910\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −28.2979 + 22.2537i −0.786053 + 0.618159i
\(37\) 36.1385 62.5937i 0.976717 1.69172i 0.302567 0.953128i \(-0.402157\pi\)
0.674150 0.738595i \(-0.264510\pi\)
\(38\) 0 0
\(39\) −72.1446 28.8824i −1.84986 0.740573i
\(40\) 0 0
\(41\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(42\) 0 0
\(43\) −21.3206 46.6855i −0.495827 1.08571i −0.977803 0.209526i \(-0.932808\pi\)
0.481976 0.876184i \(-0.339919\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(48\) 42.6641 21.9949i 0.888835 0.458227i
\(49\) 76.2780 + 107.117i 1.55669 + 2.18607i
\(50\) 0 0
\(51\) 0 0
\(52\) 87.1665 + 56.0185i 1.67628 + 1.07728i
\(53\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 37.2127 35.4822i 0.652854 0.622495i
\(58\) 0 0
\(59\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(60\) 0 0
\(61\) 4.37545 + 12.6420i 0.0717286 + 0.207246i 0.975167 0.221473i \(-0.0710863\pi\)
−0.903438 + 0.428719i \(0.858965\pi\)
\(62\) 0 0
\(63\) −120.368 + 11.4938i −1.91060 + 0.182441i
\(64\) −61.4076 + 18.0309i −0.959493 + 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) 46.3306 48.3991i 0.691502 0.722375i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(72\) 0 0
\(73\) 23.3501 + 67.4656i 0.319864 + 0.924187i 0.984248 + 0.176795i \(0.0565729\pi\)
−0.664384 + 0.747392i \(0.731306\pi\)
\(74\) 0 0
\(75\) 10.6736 + 74.2366i 0.142315 + 0.989821i
\(76\) −57.6737 + 37.0646i −0.758865 + 0.487693i
\(77\) 0 0
\(78\) 0 0
\(79\) 63.8645 25.5675i 0.808411 0.323639i 0.0696203 0.997574i \(-0.477821\pi\)
0.738791 + 0.673934i \(0.235397\pi\)
\(80\) 0 0
\(81\) 33.6486 73.6802i 0.415415 0.909632i
\(82\) 0 0
\(83\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(84\) 160.491 + 15.3250i 1.91060 + 0.182441i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(90\) 0 0
\(91\) 144.572 + 316.569i 1.58870 + 3.47878i
\(92\) 0 0
\(93\) −94.5401 + 132.763i −1.01656 + 1.42756i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 94.0250 162.856i 0.969329 1.67893i 0.271826 0.962346i \(-0.412373\pi\)
0.697504 0.716581i \(-0.254294\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.75819 99.8867i 0.0475819 0.998867i
\(101\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(102\) 0 0
\(103\) −98.8434 + 77.7313i −0.959645 + 0.754673i −0.969453 0.245279i \(-0.921120\pi\)
0.00980773 + 0.999952i \(0.496878\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) −62.6461 + 87.9742i −0.580057 + 0.814576i
\(109\) 28.7854 200.207i 0.264086 1.83676i −0.237177 0.971466i \(-0.576222\pi\)
0.501264 0.865295i \(-0.332869\pi\)
\(110\) 0 0
\(111\) 51.1199 210.719i 0.460539 1.89837i
\(112\) −206.254 60.5615i −1.84155 0.540728i
\(113\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −232.078 22.1608i −1.98357 0.189408i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −95.1124 74.7972i −0.786053 0.618159i
\(122\) 0 0
\(123\) 0 0
\(124\) 157.276 149.963i 1.26836 1.20938i
\(125\) 0 0
\(126\) 0 0
\(127\) −51.8130 26.7115i −0.407976 0.210326i 0.242008 0.970274i \(-0.422194\pi\)
−0.649984 + 0.759948i \(0.725224\pi\)
\(128\) 0 0
\(129\) −100.829 116.363i −0.781622 0.902040i
\(130\) 0 0
\(131\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(132\) 0 0
\(133\) −230.266 −1.73133
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(138\) 0 0
\(139\) −172.968 199.616i −1.24437 1.43609i −0.857925 0.513775i \(-0.828247\pi\)
−0.386450 0.922310i \(-0.626299\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 104.218 99.3714i 0.723734 0.690079i
\(145\) 0 0
\(146\) 0 0
\(147\) 310.100 + 243.865i 2.10952 + 1.65895i
\(148\) −120.100 + 262.982i −0.811485 + 1.77691i
\(149\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(150\) 0 0
\(151\) −184.363 17.6045i −1.22095 0.116586i −0.535390 0.844605i \(-0.679835\pi\)
−0.685557 + 0.728019i \(0.740441\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 298.254 + 87.5752i 1.91188 + 0.561379i
\(157\) 13.6859 56.4139i 0.0871710 0.359324i −0.911474 0.411357i \(-0.865055\pi\)
0.998645 + 0.0520330i \(0.0165701\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −139.627 241.841i −0.856606 1.48369i −0.875147 0.483857i \(-0.839236\pi\)
0.0185412 0.999828i \(-0.494098\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(168\) 0 0
\(169\) 118.352 + 487.854i 0.700308 + 2.88671i
\(170\) 0 0
\(171\) 77.1265 133.587i 0.451032 0.781210i
\(172\) 102.647 + 177.790i 0.596785 + 1.03366i
\(173\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(174\) 0 0
\(175\) 194.827 273.597i 1.11330 1.56341i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(180\) 0 0
\(181\) 180.271 + 171.888i 0.995970 + 0.949655i 0.998732 0.0503410i \(-0.0160308\pi\)
−0.00276243 + 0.999996i \(0.500879\pi\)
\(182\) 0 0
\(183\) 23.2796 + 32.6917i 0.127211 + 0.178643i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −336.762 + 134.819i −1.78181 + 0.713330i
\(190\) 0 0
\(191\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(192\) −161.521 + 103.803i −0.841254 + 0.540641i
\(193\) 10.4657 + 72.7906i 0.0542265 + 0.377153i 0.998805 + 0.0488685i \(0.0155615\pi\)
−0.944579 + 0.328285i \(0.893529\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −344.459 397.527i −1.75744 2.02820i
\(197\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(198\) 0 0
\(199\) 6.89425 + 144.728i 0.0346445 + 0.727277i 0.947646 + 0.319322i \(0.103455\pi\)
−0.913002 + 0.407955i \(0.866242\pi\)
\(200\) 0 0
\(201\) 92.4549 178.474i 0.459975 0.887932i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −368.387 189.917i −1.77109 0.913061i
\(209\) 0 0
\(210\) 0 0
\(211\) −64.8282 + 61.8135i −0.307243 + 0.292955i −0.827975 0.560765i \(-0.810507\pi\)
0.520733 + 0.853720i \(0.325659\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 716.711 138.135i 3.30281 0.636565i
\(218\) 0 0
\(219\) 124.235 + 174.463i 0.567281 + 0.796635i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 194.869 + 57.2186i 0.873851 + 0.256586i 0.687753 0.725945i \(-0.258597\pi\)
0.186099 + 0.982531i \(0.440416\pi\)
\(224\) 0 0
\(225\) 93.4684 + 204.667i 0.415415 + 0.909632i
\(226\) 0 0
\(227\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(228\) −134.686 + 155.435i −0.590726 + 0.681734i
\(229\) 243.439 + 97.4584i 1.06305 + 0.425583i 0.836245 0.548357i \(-0.184746\pi\)
0.226809 + 0.973939i \(0.427171\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 162.223 127.574i 0.684485 0.538285i
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 9.83716 11.3527i 0.0408181 0.0471066i −0.734973 0.678096i \(-0.762805\pi\)
0.775792 + 0.630989i \(0.217351\pi\)
\(242\) 0 0
\(243\) 34.5825 240.527i 0.142315 0.989821i
\(244\) −22.2293 48.6755i −0.0911038 0.199490i
\(245\) 0 0
\(246\) 0 0
\(247\) −435.947 84.0219i −1.76497 0.340170i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(252\) 474.922 91.5337i 1.88461 0.363229i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 237.662 95.1456i 0.928368 0.371662i
\(257\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(258\) 0 0
\(259\) −816.896 + 524.987i −3.15404 + 2.02698i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −166.081 + 210.336i −0.619705 + 0.784835i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 453.754 133.234i 1.67437 0.491639i 0.699540 0.714594i \(-0.253388\pi\)
0.974829 + 0.222955i \(0.0715702\pi\)
\(272\) 0 0
\(273\) 683.711 + 789.044i 2.50444 + 2.89027i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −58.9545 + 37.8877i −0.212832 + 0.136779i −0.642714 0.766106i \(-0.722192\pi\)
0.429882 + 0.902885i \(0.358555\pi\)
\(278\) 0 0
\(279\) −159.921 + 462.061i −0.573193 + 1.65613i
\(280\) 0 0
\(281\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(282\) 0 0
\(283\) −463.744 298.030i −1.63867 1.05311i −0.941942 0.335776i \(-0.891001\pi\)
−0.696730 0.717334i \(-0.745362\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 283.777 + 54.6936i 0.981929 + 0.189251i
\(290\) 0 0
\(291\) 133.003 548.247i 0.457056 1.88401i
\(292\) −118.629 259.762i −0.406265 0.889597i
\(293\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −70.7277 291.543i −0.235759 0.971812i
\(301\) −32.8094 + 688.754i −0.109001 + 2.28822i
\(302\) 0 0
\(303\) 0 0
\(304\) 215.557 169.516i 0.709070 0.557619i
\(305\) 0 0
\(306\) 0 0
\(307\) 184.444 + 73.8401i 0.600793 + 0.240521i 0.652065 0.758163i \(-0.273903\pi\)
−0.0512713 + 0.998685i \(0.516327\pi\)
\(308\) 0 0
\(309\) −218.820 + 307.290i −0.708157 + 0.994467i
\(310\) 0 0
\(311\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(312\) 0 0
\(313\) 430.886 + 126.520i 1.37663 + 0.404216i 0.884596 0.466358i \(-0.154434\pi\)
0.492037 + 0.870574i \(0.336252\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −244.580 + 126.090i −0.773987 + 0.399018i
\(317\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −105.970 + 306.180i −0.327068 + 0.945001i
\(325\) 468.686 446.891i 1.44211 1.37505i
\(326\) 0 0
\(327\) −86.3562 600.621i −0.264086 1.83676i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −641.554 + 61.2610i −1.93823 + 0.185079i −0.990844 0.135014i \(-0.956892\pi\)
−0.947386 + 0.320093i \(0.896286\pi\)
\(332\) 0 0
\(333\) −30.9517 649.756i −0.0929481 1.95122i
\(334\) 0 0
\(335\) 0 0
\(336\) −644.883 −1.91929
\(337\) 29.6231 + 621.865i 0.0879023 + 1.84530i 0.426647 + 0.904418i \(0.359695\pi\)
−0.338745 + 0.940878i \(0.610002\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −157.742 1097.12i −0.459890 3.19861i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(348\) 0 0
\(349\) 277.673 608.019i 0.795625 1.74218i 0.135827 0.990733i \(-0.456631\pi\)
0.659798 0.751443i \(-0.270642\pi\)
\(350\) 0 0
\(351\) −686.762 + 132.363i −1.95659 + 0.377101i
\(352\) 0 0
\(353\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(360\) 0 0
\(361\) −39.0073 + 54.7780i −0.108053 + 0.151740i
\(362\) 0 0
\(363\) −336.998 134.913i −0.928368 0.371662i
\(364\) −696.037 1205.57i −1.91219 3.31201i
\(365\) 0 0
\(366\) 0 0
\(367\) 138.009 + 568.881i 0.376046 + 1.55008i 0.774306 + 0.632811i \(0.218099\pi\)
−0.398260 + 0.917273i \(0.630386\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 325.968 564.594i 0.876259 1.51773i
\(373\) 114.881 + 198.979i 0.307991 + 0.533456i 0.977923 0.208967i \(-0.0670100\pi\)
−0.669932 + 0.742423i \(0.733677\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −79.5728 + 328.003i −0.209955 + 0.865444i 0.765177 + 0.643819i \(0.222651\pi\)
−0.975132 + 0.221625i \(0.928864\pi\)
\(380\) 0 0
\(381\) −171.719 33.0961i −0.450706 0.0868665i
\(382\) 0 0
\(383\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −388.585 249.728i −1.00410 0.645293i
\(388\) −312.475 + 684.225i −0.805348 + 1.76347i
\(389\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 239.457 + 276.348i 0.603167 + 0.696092i 0.972420 0.233237i \(-0.0749319\pi\)
−0.369253 + 0.929329i \(0.620386\pi\)
\(398\) 0 0
\(399\) −662.817 + 194.621i −1.66120 + 0.487771i
\(400\) 19.0328 + 399.547i 0.0475819 + 0.998867i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 1407.30 3.49206
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 10.6730 + 5.50231i 0.0260953 + 0.0134531i 0.471225 0.882013i \(-0.343812\pi\)
−0.445129 + 0.895466i \(0.646842\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 364.028 347.100i 0.883563 0.842476i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −666.600 428.398i −1.59856 1.02733i
\(418\) 0 0
\(419\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(420\) 0 0
\(421\) 547.168 282.085i 1.29969 0.670034i 0.337217 0.941427i \(-0.390514\pi\)
0.962469 + 0.271393i \(0.0874842\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 25.5784 177.902i 0.0599027 0.416632i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 216.000 374.123i 0.500000 0.866025i
\(433\) −161.115 + 126.703i −0.372091 + 0.292616i −0.786641 0.617411i \(-0.788182\pi\)
0.414550 + 0.910027i \(0.363939\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −38.4968 + 808.146i −0.0882953 + 1.85355i
\(437\) 0 0
\(438\) 0 0
\(439\) −5.29742 + 9.17540i −0.0120670 + 0.0209007i −0.871996 0.489513i \(-0.837174\pi\)
0.859929 + 0.510414i \(0.170508\pi\)
\(440\) 0 0
\(441\) 1098.73 + 439.865i 2.49145 + 0.997427i
\(442\) 0 0
\(443\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(444\) −123.433 + 858.496i −0.278003 + 1.93355i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 844.305 + 162.727i 1.88461 + 0.363229i
\(449\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −545.564 + 105.149i −1.20434 + 0.232117i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 494.849 198.108i 1.08282 0.433496i 0.239494 0.970898i \(-0.423018\pi\)
0.843326 + 0.537402i \(0.180594\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(462\) 0 0
\(463\) 9.96763 + 28.7996i 0.0215284 + 0.0622021i 0.955253 0.295790i \(-0.0955828\pi\)
−0.933725 + 0.357992i \(0.883462\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(468\) 932.535 1.99260
\(469\) −851.219 + 292.735i −1.81497 + 0.624169i
\(470\) 0 0
\(471\) −8.28642 173.953i −0.0175932 0.369328i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 140.142 + 404.914i 0.295036 + 0.852451i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(480\) 0 0
\(481\) −1738.13 + 695.844i −3.61358 + 1.44666i
\(482\) 0 0
\(483\) 0 0
\(484\) 407.167 + 261.670i 0.841254 + 0.540641i
\(485\) 0 0
\(486\) 0 0
\(487\) −563.892 791.876i −1.15789 1.62603i −0.629363 0.777111i \(-0.716684\pi\)
−0.528526 0.848917i \(-0.677255\pi\)
\(488\) 0 0
\(489\) −606.316 578.121i −1.23991 1.18225i
\(490\) 0 0
\(491\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −569.237 + 656.935i −1.14766 + 1.32447i
\(497\) 0 0
\(498\) 0 0
\(499\) 495.603 858.410i 0.993193 1.72026i 0.395722 0.918370i \(-0.370494\pi\)
0.597471 0.801891i \(-0.296172\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 753.007 + 1304.25i 1.48522 + 2.57248i
\(508\) 216.470 + 86.6615i 0.426122 + 0.170593i
\(509\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 136.502 949.395i 0.267128 1.85792i
\(512\) 0 0
\(513\) 109.100 449.714i 0.212670 0.876636i
\(514\) 0 0
\(515\) 0 0
\(516\) 445.735 + 425.007i 0.863828 + 0.823658i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(522\) 0 0
\(523\) 496.264 + 390.266i 0.948879 + 0.746207i 0.967303 0.253624i \(-0.0816224\pi\)
−0.0184240 + 0.999830i \(0.505865\pi\)
\(524\) 0 0
\(525\) 329.563 952.211i 0.627740 1.81373i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −470.194 242.402i −0.888835 0.458227i
\(530\) 0 0
\(531\) 0 0
\(532\) 916.895 87.5529i 1.72349 0.164573i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 654.221 + 755.012i 1.20928 + 1.39559i 0.894887 + 0.446294i \(0.147256\pi\)
0.314395 + 0.949292i \(0.398198\pi\)
\(542\) 0 0
\(543\) 664.184 + 342.411i 1.22317 + 0.630590i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 194.902 563.134i 0.356312 1.02950i −0.614347 0.789036i \(-0.710581\pi\)
0.970659 0.240459i \(-0.0772981\pi\)
\(548\) 0 0
\(549\) 94.6409 + 74.4264i 0.172388 + 0.135567i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −920.043 87.8534i −1.66373 0.158867i
\(554\) 0 0
\(555\) 0 0
\(556\) 764.638 + 729.081i 1.37525 + 1.31130i
\(557\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(558\) 0 0
\(559\) −313.435 + 1292.00i −0.560706 + 2.31126i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −855.414 + 672.705i −1.50867 + 1.18643i
\(568\) 0 0
\(569\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(570\) 0 0
\(571\) −268.401 1106.36i −0.470053 1.93759i −0.311560 0.950227i \(-0.600851\pi\)
−0.158494 0.987360i \(-0.550664\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −377.200 + 435.312i −0.654861 + 0.755750i
\(577\) 617.902 867.721i 1.07089 1.50385i 0.222166 0.975009i \(-0.428687\pi\)
0.848721 0.528841i \(-0.177373\pi\)
\(578\) 0 0
\(579\) 91.6478 + 200.681i 0.158286 + 0.346599i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(588\) −1327.51 853.137i −2.25766 1.45091i
\(589\) −386.810 + 846.995i −0.656723 + 1.43802i
\(590\) 0 0
\(591\) 0 0
\(592\) 378.232 1092.83i 0.638905 1.84600i
\(593\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 142.169 + 410.770i 0.238139 + 0.688057i
\(598\) 0 0
\(599\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(600\) 0 0
\(601\) 56.7840 + 1192.04i 0.0944825 + 1.98343i 0.166553 + 0.986032i \(0.446736\pi\)
−0.0720706 + 0.997400i \(0.522961\pi\)
\(602\) 0 0
\(603\) 115.284 591.877i 0.191183 0.981554i
\(604\) 740.807 1.22650
\(605\) 0 0
\(606\) 0 0
\(607\) 934.129 89.1985i 1.53893 0.146950i 0.709155 0.705052i \(-0.249076\pi\)
0.829772 + 0.558103i \(0.188470\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −186.793 + 178.106i −0.304719 + 0.290549i −0.826974 0.562241i \(-0.809939\pi\)
0.522255 + 0.852789i \(0.325091\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(618\) 0 0
\(619\) −1062.75 + 204.828i −1.71688 + 0.330901i −0.950321 0.311272i \(-0.899245\pi\)
−0.766559 + 0.642174i \(0.778033\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −1220.91 235.311i −1.95659 0.377101i
\(625\) −599.683 176.083i −0.959493 0.281733i
\(626\) 0 0
\(627\) 0 0
\(628\) −33.0456 + 229.837i −0.0526204 + 0.365983i
\(629\) 0 0
\(630\) 0 0
\(631\) −879.435 352.072i −1.39372 0.557960i −0.451291 0.892377i \(-0.649036\pi\)
−0.942425 + 0.334418i \(0.891460\pi\)
\(632\) 0 0
\(633\) −134.362 + 232.722i −0.212262 + 0.367649i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 162.081 3402.51i 0.254445 5.34146i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 0 0
\(643\) −828.282 + 955.888i −1.28815 + 1.48661i −0.507483 + 0.861662i \(0.669424\pi\)
−0.780669 + 0.624945i \(0.785122\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1946.29 1003.38i 2.98969 1.54129i
\(652\) 647.932 + 909.893i 0.993760 + 1.39554i
\(653\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 505.062 + 397.185i 0.768740 + 0.604544i
\(658\) 0 0
\(659\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(660\) 0 0
\(661\) −207.432 + 133.309i −0.313816 + 0.201677i −0.688062 0.725652i \(-0.741538\pi\)
0.374245 + 0.927330i \(0.377902\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 609.287 0.910743
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −266.048 + 78.1186i −0.395316 + 0.116075i −0.473348 0.880876i \(-0.656955\pi\)
0.0780319 + 0.996951i \(0.475136\pi\)
\(674\) 0 0
\(675\) 442.031 + 510.131i 0.654861 + 0.755750i
\(676\) −656.758 1897.58i −0.971536 2.80707i
\(677\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(678\) 0 0
\(679\) −2125.40 + 1365.91i −3.13018 + 2.01165i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(684\) −256.316 + 561.254i −0.374731 + 0.820546i
\(685\) 0 0
\(686\) 0 0
\(687\) 783.107 + 74.7776i 1.13989 + 0.108847i
\(688\) −476.329 668.911i −0.692339 0.972254i
\(689\) 0 0
\(690\) 0 0
\(691\) −219.844 42.3715i −0.318154 0.0613191i 0.0276745 0.999617i \(-0.491190\pi\)
−0.345828 + 0.938298i \(0.612402\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −671.753 + 1163.51i −0.959647 + 1.66216i
\(701\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(702\) 0 0
\(703\) 58.9431 1237.37i 0.0838451 1.76013i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 552.912 + 221.352i 0.779847 + 0.312204i 0.727215 0.686410i \(-0.240815\pi\)
0.0526326 + 0.998614i \(0.483239\pi\)
\(710\) 0 0
\(711\) 359.131 504.328i 0.505106 0.709323i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(720\) 0 0
\(721\) 1658.88 319.723i 2.30081 0.443444i
\(722\) 0 0
\(723\) 18.7208 40.9928i 0.0258932 0.0566982i
\(724\) −783.173 615.894i −1.08173 0.850682i
\(725\) 0 0
\(726\) 0 0
\(727\) −606.370 + 578.172i −0.834071 + 0.795285i −0.981030 0.193857i \(-0.937900\pi\)
0.146959 + 0.989143i \(0.453052\pi\)
\(728\) 0 0
\(729\) −103.748 721.580i −0.142315 0.989821i
\(730\) 0 0
\(731\) 0 0
\(732\) −105.127 121.323i −0.143616 0.165742i
\(733\) −306.611 + 29.2778i −0.418296 + 0.0399424i −0.302082 0.953282i \(-0.597682\pi\)
−0.116214 + 0.993224i \(0.537076\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.50377 31.5680i −0.00203487 0.0427172i 0.997622 0.0689296i \(-0.0219584\pi\)
−0.999656 + 0.0262124i \(0.991655\pi\)
\(740\) 0 0
\(741\) −1325.88 + 126.606i −1.78931 + 0.170858i
\(742\) 0 0
\(743\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 547.768 1199.44i 0.729385 1.59713i −0.0708817 0.997485i \(-0.522581\pi\)
0.800266 0.599645i \(-0.204691\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1289.69 664.881i 1.70594 0.879472i
\(757\) −664.026 633.147i −0.877181 0.836390i 0.110338 0.993894i \(-0.464807\pi\)
−0.987518 + 0.157504i \(0.949655\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(762\) 0 0
\(763\) −1576.28 + 2213.57i −2.06589 + 2.90114i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 603.689 474.746i 0.786053 0.618159i
\(769\) −326.035 1343.93i −0.423973 1.74764i −0.637259 0.770650i \(-0.719932\pi\)
0.213286 0.976990i \(-0.431583\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −69.3500 285.865i −0.0898317 0.370291i
\(773\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(774\) 0 0
\(775\) −679.101 1176.24i −0.876259 1.51773i
\(776\) 0 0
\(777\) −1907.70 + 2201.60i −2.45521 + 2.83347i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1522.75 + 1451.94i 1.94228 + 1.85196i
\(785\) 0 0
\(786\) 0 0
\(787\) 30.1435 + 2.87836i 0.0383018 + 0.00365738i 0.114189 0.993459i \(-0.463573\pi\)
−0.0758876 + 0.997116i \(0.524179\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 113.340 327.476i 0.142926 0.412958i
\(794\) 0 0
\(795\) 0 0
\(796\) −82.4813 573.670i −0.103620 0.720691i
\(797\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −300.285 + 745.818i −0.373489 + 0.927635i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(810\) 0 0
\(811\) 1377.55 + 710.175i 1.69858 + 0.875678i 0.984450 + 0.175663i \(0.0562070\pi\)
0.714128 + 0.700015i \(0.246823\pi\)
\(812\) 0 0
\(813\) 1193.51 767.023i 1.46803 0.943448i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −691.448 543.761i −0.846325 0.665558i
\(818\) 0 0
\(819\) 2634.95 + 1693.38i 3.21727 + 2.06762i
\(820\) 0 0
\(821\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(822\) 0 0
\(823\) 1074.75 554.071i 1.30589 0.673233i 0.342041 0.939685i \(-0.388882\pi\)
0.963848 + 0.266452i \(0.0858514\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(828\) 0 0
\(829\) 86.4416 601.214i 0.104272 0.725228i −0.868873 0.495035i \(-0.835155\pi\)
0.973145 0.230193i \(-0.0739358\pi\)
\(830\) 0 0
\(831\) −137.677 + 158.887i −0.165676 + 0.191200i
\(832\) 1539.09 + 616.157i 1.84986 + 0.740573i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −69.7959 + 1465.20i −0.0833882 + 1.75053i
\(838\) 0 0
\(839\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(840\) 0 0
\(841\) −420.500 + 728.327i −0.500000 + 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) 234.636 270.784i 0.278004 0.320834i
\(845\) 0 0
\(846\) 0 0
\(847\) 675.316 + 1478.74i 0.797304 + 1.74585i
\(848\) 0 0
\(849\) −1586.77 465.918i −1.86899 0.548785i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 806.213 + 1132.17i 0.945151 + 1.32728i 0.944928 + 0.327278i \(0.106131\pi\)
0.000222537 1.00000i \(0.499929\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(858\) 0 0
\(859\) 1556.80 623.248i 1.81234 0.725551i 0.825378 0.564580i \(-0.190962\pi\)
0.986959 0.160971i \(-0.0514624\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 863.074 82.4136i 0.995472 0.0950560i
\(868\) −2801.34 + 822.547i −3.22735 + 0.947635i
\(869\) 0 0
\(870\) 0 0
\(871\) −1718.37 + 243.613i −1.97287 + 0.279694i
\(872\) 0 0
\(873\) −80.5300 1690.53i −0.0922451 1.93646i
\(874\) 0 0
\(875\) 0 0
\(876\) −561.023 647.455i −0.640437 0.739104i
\(877\) 73.2802 + 211.729i 0.0835578 + 0.241424i 0.979038 0.203676i \(-0.0652891\pi\)
−0.895480 + 0.445101i \(0.853168\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(882\) 0 0
\(883\) 1639.30 656.276i 1.85651 0.743235i 0.922473 0.386061i \(-0.126164\pi\)
0.934038 0.357174i \(-0.116260\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(888\) 0 0
\(889\) 454.284 + 637.953i 0.511006 + 0.717607i
\(890\) 0 0
\(891\) 0 0
\(892\) −797.702 153.744i −0.894284 0.172359i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −450.000 779.423i −0.500000 0.866025i
\(901\) 0 0
\(902\) 0 0
\(903\) 487.692 + 2010.29i 0.540080 + 2.22624i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1180.26 + 928.164i −1.30127 + 1.02333i −0.303769 + 0.952746i \(0.598245\pi\)
−0.997506 + 0.0705881i \(0.977512\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(912\) 477.203 670.137i 0.523248 0.734800i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1006.40 295.507i −1.09869 0.322606i
\(917\) 0 0
\(918\) 0 0
\(919\) −584.953 + 301.564i −0.636510 + 0.328144i −0.746101 0.665833i \(-0.768076\pi\)
0.109591 + 0.993977i \(0.465046\pi\)
\(920\) 0 0
\(921\) 593.326 + 56.6558i 0.644220 + 0.0615155i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1420.34 + 1116.97i 1.53550 + 1.20753i
\(926\) 0 0
\(927\) −370.149 + 1069.47i −0.399298 + 1.15369i
\(928\) 0 0
\(929\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(930\) 0 0
\(931\) 2003.28 + 1032.76i 2.15175 + 1.10930i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 478.950 0.511152 0.255576 0.966789i \(-0.417735\pi\)
0.255576 + 0.966789i \(0.417735\pi\)
\(938\) 0 0
\(939\) 1347.23 1.43475
\(940\) 0 0
\(941\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(948\) −597.447 + 569.665i −0.630219 + 0.600912i
\(949\) 604.855 1747.61i 0.637360 1.84153i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 469.287 1934.43i 0.488332 2.01293i
\(962\) 0 0
\(963\) 0 0
\(964\) −34.8539 + 48.9454i −0.0361555 + 0.0507733i
\(965\) 0 0
\(966\) 0 0
\(967\) −391.470 678.046i −0.404829 0.701185i 0.589472 0.807789i \(-0.299336\pi\)
−0.994302 + 0.106604i \(0.966002\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(972\) −46.2496 + 970.899i −0.0475819 + 0.998867i
\(973\) 836.614 + 3448.57i 0.859829 + 3.54426i
\(974\) 0 0
\(975\) 971.391 1682.50i 0.996298 1.72564i
\(976\) 107.022 + 185.368i 0.109654 + 0.189926i
\(977\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −756.218 1655.89i −0.770864 1.68796i
\(982\) 0 0
\(983\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1767.84 + 168.808i 1.78931 + 0.170858i
\(989\) 0 0
\(990\) 0 0
\(991\) −609.567 + 1334.77i −0.615103 + 1.34689i 0.303925 + 0.952696i \(0.401703\pi\)
−0.919028 + 0.394192i \(0.871025\pi\)
\(992\) 0 0
\(993\) −1794.92 + 718.579i −1.80758 + 0.723644i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −283.626 1972.67i −0.284480 1.97860i −0.174347 0.984684i \(-0.555781\pi\)
−0.110133 0.993917i \(-0.535128\pi\)
\(998\) 0 0
\(999\) −638.266 1844.15i −0.638905 1.84600i
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 201.3.o.a.167.1 yes 20
3.2 odd 2 CM 201.3.o.a.167.1 yes 20
67.65 even 33 inner 201.3.o.a.65.1 20
201.65 odd 66 inner 201.3.o.a.65.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.o.a.65.1 20 67.65 even 33 inner
201.3.o.a.65.1 20 201.65 odd 66 inner
201.3.o.a.167.1 yes 20 1.1 even 1 trivial
201.3.o.a.167.1 yes 20 3.2 odd 2 CM