Properties

Label 201.3.o.a.170.1
Level $201$
Weight $3$
Character 201.170
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 170.1
Root \(0.580057 + 0.814576i\) of defining polynomial
Character \(\chi\) \(=\) 201.170
Dual form 201.3.o.a.188.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.96458 + 2.26725i) q^{3} +(0.943036 + 3.88725i) q^{4} +(1.84264 - 0.737681i) q^{7} +(-1.28083 + 8.90839i) q^{9} +O(q^{10})\) \(q+(1.96458 + 2.26725i) q^{3} +(0.943036 + 3.88725i) q^{4} +(1.84264 - 0.737681i) q^{7} +(-1.28083 + 8.90839i) q^{9} +(-6.96068 + 9.77491i) q^{12} +(15.2050 + 1.45190i) q^{13} +(-14.2214 + 7.33162i) q^{16} +(-35.2504 - 14.1121i) q^{19} +(5.29252 + 2.72848i) q^{21} +(10.3854 + 22.7408i) q^{25} +(-22.7138 + 14.5973i) q^{27} +(4.60522 + 6.46713i) q^{28} +(43.5130 - 4.15499i) q^{31} +(-35.8370 + 3.42202i) q^{36} +(26.1102 - 45.2242i) q^{37} +(26.5797 + 37.3260i) q^{39} +(77.2237 - 22.6749i) q^{43} +(-44.5617 - 17.8398i) q^{48} +(-32.6118 + 31.0953i) q^{49} +(8.69497 + 60.4749i) q^{52} +(-37.2566 - 107.646i) q^{57} +(-5.51299 - 115.732i) q^{61} +(4.21144 + 17.3598i) q^{63} +(-41.9111 - 48.3680i) q^{64} +(12.8093 - 65.7641i) q^{67} +(4.96661 + 104.262i) q^{73} +(-31.1561 + 68.2224i) q^{75} +(21.6150 - 150.335i) q^{76} +(78.1750 - 109.781i) q^{79} +(-77.7189 - 22.8203i) q^{81} +(-5.61525 + 23.1464i) q^{84} +(29.0884 - 8.54113i) q^{91} +(94.9052 + 90.4919i) q^{93} +(17.3745 - 30.0935i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{3} + 4 q^{4} + 2 q^{7} - 18 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{33}\right)\)

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 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(3\) 1.96458 + 2.26725i 0.654861 + 0.755750i
\(4\) 0.943036 + 3.88725i 0.235759 + 0.971812i
\(5\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(6\) 0 0
\(7\) 1.84264 0.737681i 0.263234 0.105383i −0.236291 0.971682i \(-0.575932\pi\)
0.499525 + 0.866299i \(0.333508\pi\)
\(8\) 0 0
\(9\) −1.28083 + 8.90839i −0.142315 + 0.989821i
\(10\) 0 0
\(11\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(12\) −6.96068 + 9.77491i −0.580057 + 0.814576i
\(13\) 15.2050 + 1.45190i 1.16962 + 0.111685i 0.661732 0.749740i \(-0.269821\pi\)
0.507885 + 0.861425i \(0.330428\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −14.2214 + 7.33162i −0.888835 + 0.458227i
\(17\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(18\) 0 0
\(19\) −35.2504 14.1121i −1.85529 0.742744i −0.942328 0.334691i \(-0.891368\pi\)
−0.912958 0.408054i \(-0.866208\pi\)
\(20\) 0 0
\(21\) 5.29252 + 2.72848i 0.252025 + 0.129928i
\(22\) 0 0
\(23\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(24\) 0 0
\(25\) 10.3854 + 22.7408i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) −22.7138 + 14.5973i −0.841254 + 0.540641i
\(28\) 4.60522 + 6.46713i 0.164472 + 0.230969i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 43.5130 4.15499i 1.40364 0.134032i 0.634409 0.772997i \(-0.281243\pi\)
0.769235 + 0.638966i \(0.220637\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −35.8370 + 3.42202i −0.995472 + 0.0950560i
\(37\) 26.1102 45.2242i 0.705681 1.22227i −0.260765 0.965402i \(-0.583975\pi\)
0.966445 0.256872i \(-0.0826920\pi\)
\(38\) 0 0
\(39\) 26.5797 + 37.3260i 0.681531 + 0.957076i
\(40\) 0 0
\(41\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(42\) 0 0
\(43\) 77.2237 22.6749i 1.79590 0.527324i 0.798674 0.601764i \(-0.205535\pi\)
0.997225 + 0.0744407i \(0.0237172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(48\) −44.5617 17.8398i −0.928368 0.371662i
\(49\) −32.6118 + 31.0953i −0.665547 + 0.634598i
\(50\) 0 0
\(51\) 0 0
\(52\) 8.69497 + 60.4749i 0.167211 + 1.16298i
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −37.2566 107.646i −0.653625 1.88853i
\(58\) 0 0
\(59\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(60\) 0 0
\(61\) −5.51299 115.732i −0.0903770 1.89725i −0.357999 0.933722i \(-0.616541\pi\)
0.267622 0.963524i \(-0.413762\pi\)
\(62\) 0 0
\(63\) 4.21144 + 17.3598i 0.0668483 + 0.275552i
\(64\) −41.9111 48.3680i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0 0
\(67\) 12.8093 65.7641i 0.191183 0.981554i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(72\) 0 0
\(73\) 4.96661 + 104.262i 0.0680357 + 1.42825i 0.732419 + 0.680854i \(0.238391\pi\)
−0.664384 + 0.747392i \(0.731306\pi\)
\(74\) 0 0
\(75\) −31.1561 + 68.2224i −0.415415 + 0.909632i
\(76\) 21.6150 150.335i 0.284407 1.97810i
\(77\) 0 0
\(78\) 0 0
\(79\) 78.1750 109.781i 0.989558 1.38964i 0.0696203 0.997574i \(-0.477821\pi\)
0.919937 0.392066i \(-0.128239\pi\)
\(80\) 0 0
\(81\) −77.7189 22.8203i −0.959493 0.281733i
\(82\) 0 0
\(83\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(84\) −5.61525 + 23.1464i −0.0668483 + 0.275552i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(90\) 0 0
\(91\) 29.0884 8.54113i 0.319653 0.0938585i
\(92\) 0 0
\(93\) 94.9052 + 90.4919i 1.02049 + 0.973032i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 17.3745 30.0935i 0.179118 0.310242i −0.762461 0.647035i \(-0.776009\pi\)
0.941579 + 0.336793i \(0.109342\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −78.6053 + 61.8159i −0.786053 + 0.618159i
\(101\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(102\) 0 0
\(103\) −40.7823 + 3.89423i −0.395944 + 0.0378081i −0.291129 0.956684i \(-0.594031\pi\)
−0.104815 + 0.994492i \(0.533425\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(108\) −78.1633 74.5285i −0.723734 0.690079i
\(109\) 71.1035 + 155.695i 0.652326 + 1.42839i 0.889503 + 0.456928i \(0.151050\pi\)
−0.237177 + 0.971466i \(0.576222\pi\)
\(110\) 0 0
\(111\) 153.830 29.6483i 1.38586 0.267102i
\(112\) −20.7964 + 24.0004i −0.185682 + 0.214289i
\(113\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −32.4092 + 133.593i −0.277002 + 1.14182i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −120.452 11.5018i −0.995472 0.0950560i
\(122\) 0 0
\(123\) 0 0
\(124\) 57.1857 + 165.227i 0.461175 + 1.33248i
\(125\) 0 0
\(126\) 0 0
\(127\) −78.5568 + 31.4494i −0.618557 + 0.247633i −0.659710 0.751520i \(-0.729321\pi\)
0.0411533 + 0.999153i \(0.486897\pi\)
\(128\) 0 0
\(129\) 203.122 + 130.539i 1.57459 + 1.01193i
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 0 0
\(133\) −75.3641 −0.566647
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(138\) 0 0
\(139\) 25.9480 + 16.6757i 0.186676 + 0.119969i 0.630641 0.776075i \(-0.282792\pi\)
−0.443965 + 0.896044i \(0.646428\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −47.0978 136.080i −0.327068 0.945001i
\(145\) 0 0
\(146\) 0 0
\(147\) −134.569 12.8498i −0.915438 0.0874138i
\(148\) 200.420 + 58.8487i 1.35419 + 0.397626i
\(149\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(150\) 0 0
\(151\) −26.0498 + 107.379i −0.172515 + 0.711118i 0.818173 + 0.574971i \(0.194987\pi\)
−0.990689 + 0.136146i \(0.956528\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −120.030 + 138.522i −0.769420 + 0.887959i
\(157\) −266.328 + 51.3305i −1.69636 + 0.326946i −0.943534 0.331276i \(-0.892521\pi\)
−0.752824 + 0.658222i \(0.771309\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −63.3763 109.771i −0.388812 0.673441i 0.603478 0.797379i \(-0.293781\pi\)
−0.992290 + 0.123938i \(0.960448\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(168\) 0 0
\(169\) 63.1388 + 12.1690i 0.373603 + 0.0720060i
\(170\) 0 0
\(171\) 170.866 295.949i 0.999219 1.73070i
\(172\) 160.968 + 278.804i 0.935858 + 1.62095i
\(173\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(174\) 0 0
\(175\) 35.9120 + 34.2420i 0.205211 + 0.195668i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0 0
\(181\) −111.993 + 323.583i −0.618748 + 1.78775i −0.00276243 + 0.999996i \(0.500879\pi\)
−0.615985 + 0.787758i \(0.711242\pi\)
\(182\) 0 0
\(183\) 251.563 239.864i 1.37466 1.31073i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −31.0853 + 43.6531i −0.164472 + 0.230969i
\(190\) 0 0
\(191\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(192\) 27.3244 190.046i 0.142315 0.989821i
\(193\) 138.971 304.303i 0.720054 1.57670i −0.0937737 0.995594i \(-0.529893\pi\)
0.813828 0.581106i \(-0.197380\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −151.629 97.4462i −0.773619 0.497175i
\(197\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(198\) 0 0
\(199\) −272.207 214.066i −1.36787 1.07571i −0.988623 0.150412i \(-0.951940\pi\)
−0.379249 0.925295i \(-0.623818\pi\)
\(200\) 0 0
\(201\) 174.269 100.157i 0.867008 0.498295i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −226.881 + 90.8295i −1.09077 + 0.436680i
\(209\) 0 0
\(210\) 0 0
\(211\) 9.88915 + 28.5728i 0.0468680 + 0.135416i 0.966006 0.258519i \(-0.0832346\pi\)
−0.919138 + 0.393935i \(0.871113\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 77.1136 39.7548i 0.355362 0.183202i
\(218\) 0 0
\(219\) −226.630 + 216.092i −1.03484 + 0.986720i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −181.280 + 209.209i −0.812916 + 0.938155i −0.999015 0.0443757i \(-0.985870\pi\)
0.186099 + 0.982531i \(0.440416\pi\)
\(224\) 0 0
\(225\) −215.886 + 63.3898i −0.959493 + 0.281733i
\(226\) 0 0
\(227\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(228\) 383.312 246.340i 1.68119 1.08044i
\(229\) 10.1993 + 14.3228i 0.0445382 + 0.0625452i 0.836245 0.548357i \(-0.184746\pi\)
−0.791706 + 0.610902i \(0.790807\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 402.483 38.4325i 1.69824 0.162162i
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 208.484 133.984i 0.865078 0.555952i −0.0311655 0.999514i \(-0.509922\pi\)
0.896244 + 0.443562i \(0.146286\pi\)
\(242\) 0 0
\(243\) −100.946 221.041i −0.415415 0.909632i
\(244\) 444.680 130.570i 1.82246 0.535122i
\(245\) 0 0
\(246\) 0 0
\(247\) −515.494 265.756i −2.08702 1.07593i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(252\) −63.5103 + 32.7418i −0.252025 + 0.129928i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 148.495 208.531i 0.580057 0.814576i
\(257\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(258\) 0 0
\(259\) 14.7506 102.593i 0.0569522 0.396111i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 267.721 12.2251i 0.998959 0.0456161i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −71.7507 82.8047i −0.264763 0.305552i 0.607765 0.794117i \(-0.292066\pi\)
−0.872528 + 0.488564i \(0.837521\pi\)
\(272\) 0 0
\(273\) 76.5114 + 49.1709i 0.280262 + 0.180113i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −78.8324 + 548.291i −0.284593 + 1.97939i −0.126497 + 0.991967i \(0.540373\pi\)
−0.158096 + 0.987424i \(0.550536\pi\)
\(278\) 0 0
\(279\) −18.7186 + 392.953i −0.0670919 + 1.40843i
\(280\) 0 0
\(281\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(282\) 0 0
\(283\) −80.4202 559.334i −0.284170 1.97645i −0.198306 0.980140i \(-0.563544\pi\)
−0.0858637 0.996307i \(-0.527365\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −256.873 132.427i −0.888835 0.458227i
\(290\) 0 0
\(291\) 102.363 19.7288i 0.351763 0.0677967i
\(292\) −400.608 + 117.629i −1.37195 + 0.402840i
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −294.579 56.7754i −0.981929 0.189251i
\(301\) 125.568 98.7481i 0.417171 0.328067i
\(302\) 0 0
\(303\) 0 0
\(304\) 604.774 57.7489i 1.98939 0.189964i
\(305\) 0 0
\(306\) 0 0
\(307\) −349.965 491.458i −1.13995 1.60084i −0.721180 0.692748i \(-0.756400\pi\)
−0.418772 0.908091i \(-0.637539\pi\)
\(308\) 0 0
\(309\) −88.9493 84.8130i −0.287862 0.274476i
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) −408.427 + 471.350i −1.30488 + 1.50591i −0.587503 + 0.809222i \(0.699889\pi\)
−0.717375 + 0.696687i \(0.754657\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 500.470 + 200.358i 1.58376 + 0.634044i
\(317\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 15.4165 323.633i 0.0475819 0.998867i
\(325\) 124.892 + 360.853i 0.384284 + 1.11032i
\(326\) 0 0
\(327\) −213.311 + 467.085i −0.652326 + 1.42839i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 95.5705 + 393.947i 0.288733 + 1.19017i 0.912670 + 0.408698i \(0.134017\pi\)
−0.623937 + 0.781475i \(0.714468\pi\)
\(332\) 0 0
\(333\) 369.432 + 290.524i 1.10940 + 0.872446i
\(334\) 0 0
\(335\) 0 0
\(336\) −95.2711 −0.283545
\(337\) −521.427 410.055i −1.54726 1.21678i −0.883093 0.469198i \(-0.844543\pi\)
−0.664169 0.747583i \(-0.731214\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −77.5550 + 169.822i −0.226108 + 0.495107i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(348\) 0 0
\(349\) 274.217 + 80.5175i 0.785723 + 0.230709i 0.649896 0.760023i \(-0.274813\pi\)
0.135827 + 0.990733i \(0.456631\pi\)
\(350\) 0 0
\(351\) −366.558 + 188.974i −1.04433 + 0.538388i
\(352\) 0 0
\(353\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0 0
\(361\) 782.172 + 745.800i 2.16668 + 2.06593i
\(362\) 0 0
\(363\) −210.561 295.691i −0.580057 0.814576i
\(364\) 60.6329 + 105.019i 0.166574 + 0.288514i
\(365\) 0 0
\(366\) 0 0
\(367\) −674.020 129.907i −1.83657 0.353969i −0.851258 0.524748i \(-0.824160\pi\)
−0.985309 + 0.170778i \(0.945372\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −262.265 + 454.257i −0.705015 + 1.22112i
\(373\) 192.961 + 334.218i 0.517321 + 0.896026i 0.999798 + 0.0201171i \(0.00640391\pi\)
−0.482477 + 0.875909i \(0.660263\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 720.697 138.903i 1.90158 0.366499i 0.903505 0.428578i \(-0.140985\pi\)
0.998071 + 0.0620789i \(0.0197730\pi\)
\(380\) 0 0
\(381\) −225.635 116.323i −0.592217 0.305309i
\(382\) 0 0
\(383\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 103.086 + 716.982i 0.266373 + 1.85267i
\(388\) 133.365 + 39.1596i 0.343725 + 0.100927i
\(389\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 630.649 + 405.294i 1.58854 + 1.02089i 0.972420 + 0.233237i \(0.0749319\pi\)
0.616118 + 0.787654i \(0.288704\pi\)
\(398\) 0 0
\(399\) −148.059 170.869i −0.371075 0.428243i
\(400\) −314.421 247.264i −0.786053 0.618159i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 667.649 1.65670
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 224.622 89.9252i 0.549198 0.219866i −0.0804328 0.996760i \(-0.525630\pi\)
0.629631 + 0.776894i \(0.283206\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −53.5970 154.858i −0.130090 0.375870i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 13.1689 + 91.5914i 0.0315800 + 0.219644i
\(418\) 0 0
\(419\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(420\) 0 0
\(421\) −769.107 307.904i −1.82686 0.731363i −0.979836 0.199805i \(-0.935969\pi\)
−0.847022 0.531558i \(-0.821607\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −95.5318 209.185i −0.223728 0.489896i
\(428\) 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
\(433\) 281.183 26.8498i 0.649384 0.0620087i 0.234835 0.972035i \(-0.424545\pi\)
0.414550 + 0.910027i \(0.363939\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −538.172 + 423.223i −1.23434 + 0.970695i
\(437\) 0 0
\(438\) 0 0
\(439\) 435.254 753.882i 0.991467 1.71727i 0.382838 0.923815i \(-0.374947\pi\)
0.608629 0.793455i \(-0.291720\pi\)
\(440\) 0 0
\(441\) −235.239 330.347i −0.533422 0.749086i
\(442\) 0 0
\(443\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(444\) 260.317 + 570.016i 0.586301 + 1.28382i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −112.907 58.2077i −0.252025 0.129928i
\(449\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −294.631 + 151.893i −0.650400 + 0.335305i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −527.961 + 741.418i −1.15528 + 1.62236i −0.503326 + 0.864096i \(0.667891\pi\)
−0.651950 + 0.758262i \(0.726049\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) −32.3313 678.718i −0.0698301 1.46591i −0.713524 0.700631i \(-0.752902\pi\)
0.643694 0.765283i \(-0.277401\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(468\) −549.871 −1.17494
\(469\) −24.9101 130.629i −0.0531132 0.278526i
\(470\) 0 0
\(471\) −639.603 502.989i −1.35797 1.06792i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −45.1675 948.183i −0.0950895 1.99617i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(480\) 0 0
\(481\) 462.667 649.725i 0.961886 1.35078i
\(482\) 0 0
\(483\) 0 0
\(484\) −68.8804 479.074i −0.142315 0.989821i
\(485\) 0 0
\(486\) 0 0
\(487\) 56.9406 54.2927i 0.116921 0.111484i −0.629363 0.777111i \(-0.716684\pi\)
0.746285 + 0.665627i \(0.231836\pi\)
\(488\) 0 0
\(489\) 124.370 359.344i 0.254336 0.734855i
\(490\) 0 0
\(491\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −588.351 + 378.110i −1.18619 + 0.762319i
\(497\) 0 0
\(498\) 0 0
\(499\) 448.352 776.568i 0.898501 1.55625i 0.0690896 0.997610i \(-0.477991\pi\)
0.829411 0.558639i \(-0.188676\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 96.4513 + 167.058i 0.190239 + 0.329504i
\(508\) −196.333 275.712i −0.386483 0.542739i
\(509\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(510\) 0 0
\(511\) 86.0637 + 188.453i 0.168422 + 0.368793i
\(512\) 0 0
\(513\) 1006.67 194.020i 1.96232 0.378207i
\(514\) 0 0
\(515\) 0 0
\(516\) −315.884 + 912.687i −0.612179 + 1.76877i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(522\) 0 0
\(523\) 215.865 + 20.6126i 0.412743 + 0.0394122i 0.299362 0.954139i \(-0.403226\pi\)
0.113380 + 0.993552i \(0.463832\pi\)
\(524\) 0 0
\(525\) −7.08310 + 148.693i −0.0134916 + 0.283224i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 491.107 196.609i 0.928368 0.371662i
\(530\) 0 0
\(531\) 0 0
\(532\) −71.0710 292.959i −0.133592 0.550674i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 465.624 + 299.238i 0.860673 + 0.553121i 0.894887 0.446294i \(-0.147256\pi\)
−0.0342135 + 0.999415i \(0.510893\pi\)
\(542\) 0 0
\(543\) −953.664 + 381.790i −1.75629 + 0.703112i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −39.1748 + 822.381i −0.0716176 + 1.50344i 0.621956 + 0.783052i \(0.286338\pi\)
−0.693574 + 0.720386i \(0.743965\pi\)
\(548\) 0 0
\(549\) 1038.05 + 99.1215i 1.89080 + 0.180549i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 63.0646 259.956i 0.114041 0.470083i
\(554\) 0 0
\(555\) 0 0
\(556\) −40.3529 + 116.592i −0.0725771 + 0.209698i
\(557\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(558\) 0 0
\(559\) 1207.11 232.651i 2.15941 0.416192i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −160.042 + 15.2822i −0.282261 + 0.0269527i
\(568\) 0 0
\(569\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(570\) 0 0
\(571\) −384.054 74.0204i −0.672599 0.129633i −0.158494 0.987360i \(-0.550664\pi\)
−0.514105 + 0.857727i \(0.671876\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 484.562 311.409i 0.841254 0.540641i
\(577\) −830.218 791.611i −1.43885 1.37194i −0.794608 0.607123i \(-0.792324\pi\)
−0.644244 0.764820i \(-0.722828\pi\)
\(578\) 0 0
\(579\) 962.949 282.747i 1.66313 0.488338i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(588\) −76.9534 535.222i −0.130873 0.910242i
\(589\) −1592.49 467.596i −2.70371 0.793882i
\(590\) 0 0
\(591\) 0 0
\(592\) −39.7559 + 834.579i −0.0671553 + 1.40976i
\(593\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −49.4322 1037.71i −0.0828010 1.73821i
\(598\) 0 0
\(599\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(600\) 0 0
\(601\) 868.277 + 682.821i 1.44472 + 1.13614i 0.966115 + 0.258111i \(0.0830999\pi\)
0.478605 + 0.878030i \(0.341143\pi\)
\(602\) 0 0
\(603\) 569.446 + 198.343i 0.944355 + 0.328927i
\(604\) −441.974 −0.731744
\(605\) 0 0
\(606\) 0 0
\(607\) 282.110 + 1162.87i 0.464761 + 1.91577i 0.396316 + 0.918114i \(0.370289\pi\)
0.0684450 + 0.997655i \(0.478196\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 375.996 + 1086.37i 0.613370 + 1.77222i 0.635074 + 0.772451i \(0.280970\pi\)
−0.0217041 + 0.999764i \(0.506909\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) 0 0
\(619\) −1073.54 + 553.446i −1.73431 + 0.894097i −0.766559 + 0.642174i \(0.778033\pi\)
−0.967747 + 0.251923i \(0.918937\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −651.660 335.954i −1.04433 0.538388i
\(625\) −409.288 + 472.343i −0.654861 + 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) −450.691 986.876i −0.717661 1.57146i
\(629\) 0 0
\(630\) 0 0
\(631\) 211.701 + 297.292i 0.335501 + 0.471145i 0.947519 0.319699i \(-0.103582\pi\)
−0.612019 + 0.790843i \(0.709642\pi\)
\(632\) 0 0
\(633\) −45.3536 + 78.5548i −0.0716487 + 0.124099i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −541.011 + 425.456i −0.849311 + 0.667905i
\(638\) 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
\(643\) 42.1142 27.0652i 0.0654965 0.0420920i −0.507483 0.861662i \(-0.669424\pi\)
0.572979 + 0.819570i \(0.305788\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 241.630 + 96.7341i 0.371168 + 0.148593i
\(652\) 366.941 349.877i 0.562792 0.536621i
\(653\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −935.168 89.2977i −1.42339 0.135917i
\(658\) 0 0
\(659\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(660\) 0 0
\(661\) 177.963 1237.76i 0.269233 1.87256i −0.186517 0.982452i \(-0.559720\pi\)
0.455750 0.890108i \(-0.349371\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −830.468 −1.24136
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 417.229 + 481.508i 0.619954 + 0.715465i 0.975698 0.219119i \(-0.0703181\pi\)
−0.355745 + 0.934583i \(0.615773\pi\)
\(674\) 0 0
\(675\) −567.846 364.933i −0.841254 0.540641i
\(676\) 12.2382 + 256.912i 0.0181039 + 0.380047i
\(677\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(678\) 0 0
\(679\) 9.81548 68.2682i 0.0144558 0.100542i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(684\) 1311.56 + 385.109i 1.91749 + 0.563025i
\(685\) 0 0
\(686\) 0 0
\(687\) −12.4362 + 51.2626i −0.0181022 + 0.0746181i
\(688\) −931.982 + 888.643i −1.35463 + 1.29163i
\(689\) 0 0
\(690\) 0 0
\(691\) 822.745 + 424.155i 1.19066 + 0.613827i 0.935587 0.353095i \(-0.114871\pi\)
0.255071 + 0.966922i \(0.417901\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −99.2407 + 171.890i −0.141772 + 0.245557i
\(701\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(702\) 0 0
\(703\) −1558.61 + 1225.70i −2.21708 + 1.74353i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 822.510 + 1155.05i 1.16010 + 1.62913i 0.584169 + 0.811632i \(0.301421\pi\)
0.575930 + 0.817499i \(0.304640\pi\)
\(710\) 0 0
\(711\) 877.847 + 837.026i 1.23467 + 1.17725i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(720\) 0 0
\(721\) −72.2743 + 37.2600i −0.100242 + 0.0516782i
\(722\) 0 0
\(723\) 713.360 + 209.461i 0.986666 + 0.289711i
\(724\) −1363.46 130.195i −1.88324 0.179827i
\(725\) 0 0
\(726\) 0 0
\(727\) −423.710 1224.23i −0.582820 1.68395i −0.720487 0.693468i \(-0.756082\pi\)
0.137668 0.990478i \(-0.456039\pi\)
\(728\) 0 0
\(729\) 302.838 663.122i 0.415415 0.909632i
\(730\) 0 0
\(731\) 0 0
\(732\) 1169.64 + 751.685i 1.59787 + 1.02689i
\(733\) 207.821 + 856.651i 0.283522 + 1.16869i 0.918264 + 0.395968i \(0.129591\pi\)
−0.634743 + 0.772724i \(0.718894\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1146.16 + 901.352i 1.55096 + 1.21969i 0.876519 + 0.481368i \(0.159860\pi\)
0.674446 + 0.738324i \(0.264383\pi\)
\(740\) 0 0
\(741\) −410.196 1690.85i −0.553571 2.28185i
\(742\) 0 0
\(743\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 863.125 + 253.436i 1.14930 + 0.337465i 0.800266 0.599645i \(-0.204691\pi\)
0.349034 + 0.937110i \(0.386510\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −199.005 79.6696i −0.263234 0.105383i
\(757\) −398.902 + 1152.55i −0.526951 + 1.52253i 0.296439 + 0.955052i \(0.404201\pi\)
−0.823391 + 0.567475i \(0.807920\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) 0 0
\(763\) 245.871 + 234.438i 0.322243 + 0.307258i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 764.522 73.0030i 0.995472 0.0950560i
\(769\) −785.062 151.308i −1.02089 0.196760i −0.348773 0.937207i \(-0.613402\pi\)
−0.672114 + 0.740447i \(0.734614\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1313.95 + 253.244i 1.70201 + 0.328036i
\(773\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(774\) 0 0
\(775\) 546.386 + 946.369i 0.705015 + 1.22112i
\(776\) 0 0
\(777\) 261.582 168.109i 0.336657 0.216356i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 235.806 681.316i 0.300772 0.869025i
\(785\) 0 0
\(786\) 0 0
\(787\) 194.581 802.073i 0.247244 1.01915i −0.703875 0.710324i \(-0.748548\pi\)
0.951118 0.308828i \(-0.0999366\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 84.2065 1767.71i 0.106187 2.22915i
\(794\) 0 0
\(795\) 0 0
\(796\) 575.425 1260.01i 0.722896 1.58292i
\(797\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 553.677 + 582.973i 0.688653 + 0.725091i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(810\) 0 0
\(811\) −1450.54 + 580.709i −1.78858 + 0.716041i −0.794521 + 0.607237i \(0.792278\pi\)
−0.994063 + 0.108804i \(0.965298\pi\)
\(812\) 0 0
\(813\) 46.7787 325.353i 0.0575384 0.400189i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −3042.16 290.491i −3.72357 0.355558i
\(818\) 0 0
\(819\) 38.8303 + 270.071i 0.0474119 + 0.329757i
\(820\) 0 0
\(821\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(822\) 0 0
\(823\) −48.4488 19.3960i −0.0588686 0.0235674i 0.342041 0.939685i \(-0.388882\pi\)
−0.400910 + 0.916117i \(0.631306\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(828\) 0 0
\(829\) −598.443 1310.41i −0.721886 1.58071i −0.811243 0.584710i \(-0.801208\pi\)
0.0893571 0.996000i \(-0.471519\pi\)
\(830\) 0 0
\(831\) −1397.99 + 898.431i −1.68229 + 1.08114i
\(832\) −567.034 796.287i −0.681531 0.957076i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −927.695 + 729.548i −1.10836 + 0.871622i
\(838\) 0 0
\(839\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(840\) 0 0
\(841\) −420.500 + 728.327i −0.500000 + 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) −101.744 + 65.3867i −0.120549 + 0.0774724i
\(845\) 0 0
\(846\) 0 0
\(847\) −230.434 + 67.6616i −0.272059 + 0.0798839i
\(848\) 0 0
\(849\) 1110.16 1281.19i 1.30761 1.50906i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 459.143 437.792i 0.538269 0.513238i −0.371456 0.928451i \(-0.621141\pi\)
0.909724 + 0.415213i \(0.136293\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(858\) 0 0
\(859\) 935.410 1313.60i 1.08895 1.52922i 0.263574 0.964639i \(-0.415099\pi\)
0.825378 0.564580i \(-0.190962\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −204.403 842.561i −0.235759 0.971812i
\(868\) 227.258 + 262.269i 0.261818 + 0.302154i
\(869\) 0 0
\(870\) 0 0
\(871\) 290.249 981.348i 0.333236 1.12669i
\(872\) 0 0
\(873\) 245.831 + 193.323i 0.281593 + 0.221447i
\(874\) 0 0
\(875\) 0 0
\(876\) −1053.72 677.186i −1.20288 0.773043i
\(877\) −55.5758 1166.68i −0.0633704 1.33031i −0.776874 0.629656i \(-0.783196\pi\)
0.713504 0.700652i \(-0.247107\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(882\) 0 0
\(883\) 439.988 617.877i 0.498288 0.699747i −0.486466 0.873699i \(-0.661714\pi\)
0.984754 + 0.173952i \(0.0556537\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(888\) 0 0
\(889\) −121.552 + 115.900i −0.136729 + 0.130371i
\(890\) 0 0
\(891\) 0 0
\(892\) −984.199 507.390i −1.10336 0.568823i
\(893\) 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
\(903\) 470.576 + 90.6961i 0.521125 + 0.100439i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1148.68 109.685i 1.26646 0.120932i 0.559884 0.828571i \(-0.310846\pi\)
0.706574 + 0.707639i \(0.250240\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(912\) 1319.06 + 1257.72i 1.44634 + 1.37908i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −46.0582 + 53.1540i −0.0502818 + 0.0580283i
\(917\) 0 0
\(918\) 0 0
\(919\) −137.362 54.9916i −0.149469 0.0598385i 0.295722 0.955274i \(-0.404440\pi\)
−0.445191 + 0.895436i \(0.646864\pi\)
\(920\) 0 0
\(921\) 426.721 1758.97i 0.463323 1.90985i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1299.60 + 124.097i 1.40497 + 0.134158i
\(926\) 0 0
\(927\) 17.5439 368.292i 0.0189255 0.397295i
\(928\) 0 0
\(929\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(930\) 0 0
\(931\) 1588.40 635.900i 1.70613 0.683029i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1861.48 −1.98664 −0.993321 0.115386i \(-0.963189\pi\)
−0.993321 + 0.115386i \(0.963189\pi\)
\(938\) 0 0
\(939\) −1871.05 −1.99260
\(940\) 0 0
\(941\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(948\) 528.953 + 1528.31i 0.557967 + 1.61214i
\(949\) −75.8609 + 1592.52i −0.0799377 + 1.67810i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 932.482 179.721i 0.970324 0.187015i
\(962\) 0 0
\(963\) 0 0
\(964\) 717.438 + 684.076i 0.744230 + 0.709622i
\(965\) 0 0
\(966\) 0 0
\(967\) 641.690 + 1111.44i 0.663588 + 1.14937i 0.979666 + 0.200635i \(0.0643006\pi\)
−0.316078 + 0.948733i \(0.602366\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(972\) 764.044 600.851i 0.786053 0.618159i
\(973\) 60.1141 + 11.5860i 0.0617822 + 0.0119075i
\(974\) 0 0
\(975\) −572.782 + 992.088i −0.587469 + 1.01753i
\(976\) 926.906 + 1605.45i 0.949699 + 1.64493i
\(977\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1478.06 + 433.999i −1.50669 + 0.442405i
\(982\) 0 0
\(983\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 546.929 2254.47i 0.553571 2.28185i
\(989\) 0 0
\(990\) 0 0
\(991\) −990.738 290.907i −0.999735 0.293549i −0.259388 0.965773i \(-0.583521\pi\)
−0.740347 + 0.672224i \(0.765339\pi\)
\(992\) 0 0
\(993\) −705.420 + 990.624i −0.710393 + 0.997607i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 319.482 699.568i 0.320443 0.701673i −0.679030 0.734110i \(-0.737600\pi\)
0.999474 + 0.0324369i \(0.0103268\pi\)
\(998\) 0 0
\(999\) 67.0881 + 1408.35i 0.0671553 + 1.40976i
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.170.1 20
3.2 odd 2 CM 201.3.o.a.170.1 20
67.54 even 33 inner 201.3.o.a.188.1 yes 20
201.188 odd 66 inner 201.3.o.a.188.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.o.a.170.1 20 1.1 even 1 trivial
201.3.o.a.170.1 20 3.2 odd 2 CM
201.3.o.a.188.1 yes 20 67.54 even 33 inner
201.3.o.a.188.1 yes 20 201.188 odd 66 inner