Properties

Label 2052.3.be.a.125.11
Level $2052$
Weight $3$
Character 2052.125
Analytic conductor $55.913$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2052,3,Mod(125,2052)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2052, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2052.125");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2052.be (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(55.9129502467\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 684)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 125.11
Character \(\chi\) \(=\) 2052.125
Dual form 2052.3.be.a.197.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.92443 + 2.84312i) q^{5} +(-1.27053 - 2.20061i) q^{7} +O(q^{10})\) \(q+(-4.92443 + 2.84312i) q^{5} +(-1.27053 - 2.20061i) q^{7} +(16.6159 - 9.59321i) q^{11} +15.3309 q^{13} +(-23.5119 - 13.5746i) q^{17} +(-3.43177 + 18.6875i) q^{19} +14.0875i q^{23} +(3.66670 - 6.35091i) q^{25} +(-3.83381 - 2.21345i) q^{29} +(0.818629 - 1.41791i) q^{31} +(12.5132 + 7.22452i) q^{35} -10.2519 q^{37} +(41.3655 - 23.8824i) q^{41} +27.6865 q^{43} +(-63.5252 - 36.6763i) q^{47} +(21.2715 - 36.8434i) q^{49} +(-25.9371 + 14.9748i) q^{53} +(-54.5494 + 94.4823i) q^{55} +(-94.3617 + 54.4798i) q^{59} +(-27.4453 + 47.5366i) q^{61} +(-75.4962 + 43.5878i) q^{65} +38.5522 q^{67} +(-101.956 - 58.8645i) q^{71} +(43.2124 - 74.8461i) q^{73} +(-42.2219 - 24.3768i) q^{77} +126.252 q^{79} +(35.1083 - 20.2698i) q^{83} +154.377 q^{85} +(99.4601 - 57.4233i) q^{89} +(-19.4783 - 33.7375i) q^{91} +(-36.2314 - 101.782i) q^{95} +48.6430 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + q^{7} - 18 q^{11} + 10 q^{13} - 9 q^{17} + 20 q^{19} + 200 q^{25} + 27 q^{29} - 8 q^{31} + 22 q^{37} + 54 q^{41} + 88 q^{43} - 198 q^{47} - 267 q^{49} - 36 q^{53} - 171 q^{59} + 7 q^{61} + 144 q^{65} + 154 q^{67} - 135 q^{71} + 43 q^{73} - 216 q^{77} + 34 q^{79} + 171 q^{83} + 216 q^{89} + 122 q^{91} + 216 q^{95} + 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2052\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1027\) \(1217\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −4.92443 + 2.84312i −0.984887 + 0.568625i −0.903742 0.428078i \(-0.859191\pi\)
−0.0811448 + 0.996702i \(0.525858\pi\)
\(6\) 0 0
\(7\) −1.27053 2.20061i −0.181504 0.314373i 0.760889 0.648882i \(-0.224763\pi\)
−0.942393 + 0.334508i \(0.891430\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 16.6159 9.59321i 1.51054 0.872110i 0.510614 0.859810i \(-0.329418\pi\)
0.999924 0.0123002i \(-0.00391537\pi\)
\(12\) 0 0
\(13\) 15.3309 1.17930 0.589652 0.807658i \(-0.299265\pi\)
0.589652 + 0.807658i \(0.299265\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −23.5119 13.5746i −1.38305 0.798506i −0.390533 0.920589i \(-0.627709\pi\)
−0.992520 + 0.122083i \(0.961043\pi\)
\(18\) 0 0
\(19\) −3.43177 + 18.6875i −0.180619 + 0.983553i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 14.0875i 0.612500i 0.951951 + 0.306250i \(0.0990744\pi\)
−0.951951 + 0.306250i \(0.900926\pi\)
\(24\) 0 0
\(25\) 3.66670 6.35091i 0.146668 0.254036i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.83381 2.21345i −0.132200 0.0763260i 0.432441 0.901662i \(-0.357652\pi\)
−0.564642 + 0.825336i \(0.690986\pi\)
\(30\) 0 0
\(31\) 0.818629 1.41791i 0.0264074 0.0457389i −0.852520 0.522695i \(-0.824927\pi\)
0.878927 + 0.476956i \(0.158260\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 12.5132 + 7.22452i 0.357521 + 0.206415i
\(36\) 0 0
\(37\) −10.2519 −0.277079 −0.138540 0.990357i \(-0.544241\pi\)
−0.138540 + 0.990357i \(0.544241\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 41.3655 23.8824i 1.00892 0.582498i 0.0980416 0.995182i \(-0.468742\pi\)
0.910874 + 0.412685i \(0.135409\pi\)
\(42\) 0 0
\(43\) 27.6865 0.643873 0.321936 0.946761i \(-0.395666\pi\)
0.321936 + 0.946761i \(0.395666\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −63.5252 36.6763i −1.35160 0.780347i −0.363127 0.931740i \(-0.618291\pi\)
−0.988474 + 0.151393i \(0.951624\pi\)
\(48\) 0 0
\(49\) 21.2715 36.8434i 0.434113 0.751906i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −25.9371 + 14.9748i −0.489379 + 0.282543i −0.724317 0.689467i \(-0.757845\pi\)
0.234938 + 0.972010i \(0.424511\pi\)
\(54\) 0 0
\(55\) −54.5494 + 94.4823i −0.991806 + 1.71786i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −94.3617 + 54.4798i −1.59935 + 0.923386i −0.607739 + 0.794137i \(0.707923\pi\)
−0.991612 + 0.129249i \(0.958743\pi\)
\(60\) 0 0
\(61\) −27.4453 + 47.5366i −0.449923 + 0.779289i −0.998381 0.0568892i \(-0.981882\pi\)
0.548458 + 0.836178i \(0.315215\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −75.4962 + 43.5878i −1.16148 + 0.670581i
\(66\) 0 0
\(67\) 38.5522 0.575406 0.287703 0.957720i \(-0.407108\pi\)
0.287703 + 0.957720i \(0.407108\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −101.956 58.8645i −1.43600 0.829077i −0.438435 0.898763i \(-0.644467\pi\)
−0.997569 + 0.0696859i \(0.977800\pi\)
\(72\) 0 0
\(73\) 43.2124 74.8461i 0.591951 1.02529i −0.402019 0.915631i \(-0.631691\pi\)
0.993969 0.109657i \(-0.0349753\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −42.2219 24.3768i −0.548337 0.316582i
\(78\) 0 0
\(79\) 126.252 1.59813 0.799064 0.601246i \(-0.205329\pi\)
0.799064 + 0.601246i \(0.205329\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 35.1083 20.2698i 0.422992 0.244214i −0.273365 0.961910i \(-0.588137\pi\)
0.696357 + 0.717696i \(0.254803\pi\)
\(84\) 0 0
\(85\) 154.377 1.81620
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 99.4601 57.4233i 1.11753 0.645206i 0.176760 0.984254i \(-0.443438\pi\)
0.940769 + 0.339048i \(0.110105\pi\)
\(90\) 0 0
\(91\) −19.4783 33.7375i −0.214048 0.370742i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −36.2314 101.782i −0.381383 1.07139i
\(96\) 0 0
\(97\) 48.6430 0.501474 0.250737 0.968055i \(-0.419327\pi\)
0.250737 + 0.968055i \(0.419327\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 19.6614 + 11.3515i 0.194667 + 0.112391i 0.594165 0.804343i \(-0.297482\pi\)
−0.399499 + 0.916734i \(0.630816\pi\)
\(102\) 0 0
\(103\) 25.6106 44.3589i 0.248647 0.430668i −0.714504 0.699631i \(-0.753348\pi\)
0.963151 + 0.268963i \(0.0866809\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 67.3620i 0.629552i −0.949166 0.314776i \(-0.898071\pi\)
0.949166 0.314776i \(-0.101929\pi\)
\(108\) 0 0
\(109\) 24.1043 41.7498i 0.221140 0.383026i −0.734014 0.679134i \(-0.762356\pi\)
0.955154 + 0.296108i \(0.0956889\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 15.2621 + 8.81158i 0.135063 + 0.0779785i 0.566009 0.824399i \(-0.308487\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(114\) 0 0
\(115\) −40.0525 69.3730i −0.348283 0.603243i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 68.9875i 0.579727i
\(120\) 0 0
\(121\) 123.559 214.011i 1.02115 1.76869i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 100.457i 0.803653i
\(126\) 0 0
\(127\) −75.5505 130.857i −0.594885 1.03037i −0.993563 0.113281i \(-0.963864\pi\)
0.398678 0.917091i \(-0.369469\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 171.741 99.1549i 1.31100 0.756907i 0.328740 0.944421i \(-0.393376\pi\)
0.982262 + 0.187513i \(0.0600427\pi\)
\(132\) 0 0
\(133\) 45.4841 16.1910i 0.341986 0.121737i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.8433 + 6.26037i 0.0791480 + 0.0456961i 0.539052 0.842273i \(-0.318783\pi\)
−0.459904 + 0.887969i \(0.652116\pi\)
\(138\) 0 0
\(139\) 91.1354 0.655650 0.327825 0.944738i \(-0.393684\pi\)
0.327825 + 0.944738i \(0.393684\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 254.738 147.073i 1.78138 1.02848i
\(144\) 0 0
\(145\) 25.1725 0.173603
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 157.715 91.0570i 1.05849 0.611121i 0.133478 0.991052i \(-0.457386\pi\)
0.925015 + 0.379931i \(0.124052\pi\)
\(150\) 0 0
\(151\) −123.511 213.927i −0.817951 1.41673i −0.907189 0.420722i \(-0.861777\pi\)
0.0892386 0.996010i \(-0.471557\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.30985i 0.0600635i
\(156\) 0 0
\(157\) 104.590 + 181.155i 0.666178 + 1.15385i 0.978965 + 0.204030i \(0.0654040\pi\)
−0.312787 + 0.949823i \(0.601263\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 31.0012 17.8985i 0.192554 0.111171i
\(162\) 0 0
\(163\) −18.8681 −0.115755 −0.0578776 0.998324i \(-0.518433\pi\)
−0.0578776 + 0.998324i \(0.518433\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 224.543i 1.34457i −0.740293 0.672284i \(-0.765313\pi\)
0.740293 0.672284i \(-0.234687\pi\)
\(168\) 0 0
\(169\) 66.0377 0.390756
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 73.9870i 0.427670i 0.976870 + 0.213835i \(0.0685955\pi\)
−0.976870 + 0.213835i \(0.931404\pi\)
\(174\) 0 0
\(175\) −18.6345 −0.106483
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 196.345i 1.09690i 0.836184 + 0.548449i \(0.184782\pi\)
−0.836184 + 0.548449i \(0.815218\pi\)
\(180\) 0 0
\(181\) −20.4913 35.4920i −0.113212 0.196088i 0.803852 0.594830i \(-0.202780\pi\)
−0.917063 + 0.398741i \(0.869447\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 50.4850 29.1475i 0.272892 0.157554i
\(186\) 0 0
\(187\) −520.896 −2.78554
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −71.5656 + 41.3184i −0.374689 + 0.216327i −0.675505 0.737355i \(-0.736074\pi\)
0.300816 + 0.953682i \(0.402741\pi\)
\(192\) 0 0
\(193\) −163.937 283.947i −0.849412 1.47123i −0.881733 0.471748i \(-0.843623\pi\)
0.0323211 0.999478i \(-0.489710\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 247.337i 1.25552i −0.778407 0.627760i \(-0.783972\pi\)
0.778407 0.627760i \(-0.216028\pi\)
\(198\) 0 0
\(199\) 70.5278 + 122.158i 0.354411 + 0.613858i 0.987017 0.160616i \(-0.0513481\pi\)
−0.632606 + 0.774474i \(0.718015\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 11.2490i 0.0554138i
\(204\) 0 0
\(205\) −135.801 + 235.215i −0.662445 + 1.14739i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 122.251 + 343.432i 0.584934 + 1.64321i
\(210\) 0 0
\(211\) 96.9990 + 168.007i 0.459711 + 0.796243i 0.998945 0.0459131i \(-0.0146197\pi\)
−0.539235 + 0.842156i \(0.681286\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −136.340 + 78.7162i −0.634142 + 0.366122i
\(216\) 0 0
\(217\) −4.16035 −0.0191721
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −360.459 208.111i −1.63104 0.941680i
\(222\) 0 0
\(223\) 330.514 1.48212 0.741062 0.671436i \(-0.234322\pi\)
0.741062 + 0.671436i \(0.234322\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −80.2262 + 46.3186i −0.353419 + 0.204047i −0.666190 0.745782i \(-0.732076\pi\)
0.312771 + 0.949829i \(0.398743\pi\)
\(228\) 0 0
\(229\) −27.5909 + 47.7889i −0.120484 + 0.208685i −0.919959 0.392015i \(-0.871778\pi\)
0.799474 + 0.600700i \(0.205111\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −24.3726 14.0715i −0.104603 0.0603927i 0.446786 0.894641i \(-0.352569\pi\)
−0.551389 + 0.834248i \(0.685902\pi\)
\(234\) 0 0
\(235\) 417.101 1.77490
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −25.2620 14.5850i −0.105699 0.0610251i 0.446219 0.894924i \(-0.352770\pi\)
−0.551917 + 0.833899i \(0.686104\pi\)
\(240\) 0 0
\(241\) −3.98576 + 6.90354i −0.0165384 + 0.0286454i −0.874176 0.485609i \(-0.838598\pi\)
0.857638 + 0.514254i \(0.171931\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 241.910i 0.987389i
\(246\) 0 0
\(247\) −52.6122 + 286.497i −0.213005 + 1.15991i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 254.626 147.009i 1.01445 0.585692i 0.101957 0.994789i \(-0.467490\pi\)
0.912491 + 0.409097i \(0.134156\pi\)
\(252\) 0 0
\(253\) 135.144 + 234.077i 0.534167 + 0.925205i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 53.6039i 0.208575i 0.994547 + 0.104288i \(0.0332563\pi\)
−0.994547 + 0.104288i \(0.966744\pi\)
\(258\) 0 0
\(259\) 13.0253 + 22.5606i 0.0502909 + 0.0871064i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 499.348i 1.89866i −0.314278 0.949331i \(-0.601762\pi\)
0.314278 0.949331i \(-0.398238\pi\)
\(264\) 0 0
\(265\) 85.1504 147.485i 0.321322 0.556546i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −215.111 124.195i −0.799670 0.461690i 0.0436856 0.999045i \(-0.486090\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(270\) 0 0
\(271\) 103.664 179.551i 0.382524 0.662552i −0.608898 0.793248i \(-0.708388\pi\)
0.991422 + 0.130697i \(0.0417215\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 140.702i 0.511642i
\(276\) 0 0
\(277\) −214.427 371.398i −0.774104 1.34079i −0.935297 0.353864i \(-0.884868\pi\)
0.161193 0.986923i \(-0.448466\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −423.424 244.464i −1.50685 0.869978i −0.999968 0.00795961i \(-0.997466\pi\)
−0.506877 0.862018i \(-0.669200\pi\)
\(282\) 0 0
\(283\) −174.925 302.980i −0.618111 1.07060i −0.989830 0.142254i \(-0.954565\pi\)
0.371719 0.928345i \(-0.378768\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −105.112 60.6864i −0.366244 0.211451i
\(288\) 0 0
\(289\) 224.039 + 388.048i 0.775223 + 1.34273i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.7663 + 14.2988i 0.0845266 + 0.0488015i 0.541668 0.840593i \(-0.317793\pi\)
−0.457141 + 0.889394i \(0.651127\pi\)
\(294\) 0 0
\(295\) 309.785 536.564i 1.05012 1.81886i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 215.975i 0.722323i
\(300\) 0 0
\(301\) −35.1764 60.9274i −0.116865 0.202417i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 312.121i 1.02335i
\(306\) 0 0
\(307\) −98.3532 + 170.353i −0.320369 + 0.554895i −0.980564 0.196199i \(-0.937140\pi\)
0.660195 + 0.751094i \(0.270473\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 184.438 + 106.485i 0.593047 + 0.342396i 0.766301 0.642481i \(-0.222095\pi\)
−0.173254 + 0.984877i \(0.555428\pi\)
\(312\) 0 0
\(313\) −202.221 + 350.256i −0.646072 + 1.11903i 0.337980 + 0.941153i \(0.390256\pi\)
−0.984053 + 0.177877i \(0.943077\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 184.527 + 106.537i 0.582104 + 0.336078i 0.761969 0.647613i \(-0.224233\pi\)
−0.179865 + 0.983691i \(0.557566\pi\)
\(318\) 0 0
\(319\) −84.9365 −0.266259
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 334.363 392.794i 1.03518 1.21608i
\(324\) 0 0
\(325\) 56.2139 97.3654i 0.172966 0.299586i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 186.393i 0.566543i
\(330\) 0 0
\(331\) 23.2252 + 40.2273i 0.0701669 + 0.121533i 0.898974 0.438001i \(-0.144313\pi\)
−0.828807 + 0.559534i \(0.810980\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −189.848 + 109.609i −0.566710 + 0.327190i
\(336\) 0 0
\(337\) −283.898 491.725i −0.842427 1.45913i −0.887837 0.460158i \(-0.847793\pi\)
0.0454104 0.998968i \(-0.485540\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 31.4131i 0.0921205i
\(342\) 0 0
\(343\) −232.616 −0.678179
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 197.965 114.295i 0.570504 0.329381i −0.186847 0.982389i \(-0.559827\pi\)
0.757351 + 0.653009i \(0.226493\pi\)
\(348\) 0 0
\(349\) −125.287 217.003i −0.358988 0.621786i 0.628804 0.777564i \(-0.283545\pi\)
−0.987792 + 0.155778i \(0.950212\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 135.138 78.0218i 0.382826 0.221025i −0.296221 0.955119i \(-0.595726\pi\)
0.679047 + 0.734095i \(0.262393\pi\)
\(354\) 0 0
\(355\) 669.436 1.88573
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 262.509 + 151.560i 0.731222 + 0.422171i 0.818869 0.573980i \(-0.194601\pi\)
−0.0876469 + 0.996152i \(0.527935\pi\)
\(360\) 0 0
\(361\) −337.446 128.262i −0.934753 0.355297i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 491.433i 1.34639i
\(366\) 0 0
\(367\) −11.1332 + 19.2833i −0.0303358 + 0.0525432i −0.880795 0.473498i \(-0.842991\pi\)
0.850459 + 0.526041i \(0.176324\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 65.9075 + 38.0517i 0.177648 + 0.102565i
\(372\) 0 0
\(373\) −242.162 + 419.437i −0.649229 + 1.12450i 0.334079 + 0.942545i \(0.391575\pi\)
−0.983307 + 0.181952i \(0.941759\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −58.7760 33.9343i −0.155904 0.0900114i
\(378\) 0 0
\(379\) −515.865 −1.36112 −0.680561 0.732692i \(-0.738264\pi\)
−0.680561 + 0.732692i \(0.738264\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 172.390 99.5296i 0.450105 0.259868i −0.257769 0.966206i \(-0.582987\pi\)
0.707875 + 0.706338i \(0.249654\pi\)
\(384\) 0 0
\(385\) 277.225 0.720066
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −156.994 90.6403i −0.403583 0.233008i 0.284446 0.958692i \(-0.408190\pi\)
−0.688029 + 0.725684i \(0.741524\pi\)
\(390\) 0 0
\(391\) 191.232 331.224i 0.489085 0.847120i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −621.720 + 358.950i −1.57398 + 0.908735i
\(396\) 0 0
\(397\) −224.772 + 389.316i −0.566176 + 0.980645i 0.430763 + 0.902465i \(0.358244\pi\)
−0.996939 + 0.0781804i \(0.975089\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −96.1997 + 55.5409i −0.239900 + 0.138506i −0.615131 0.788425i \(-0.710897\pi\)
0.375231 + 0.926931i \(0.377563\pi\)
\(402\) 0 0
\(403\) 12.5503 21.7378i 0.0311423 0.0539400i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −170.345 + 98.3490i −0.418539 + 0.241644i
\(408\) 0 0
\(409\) 502.935 1.22967 0.614835 0.788655i \(-0.289222\pi\)
0.614835 + 0.788655i \(0.289222\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 239.778 + 138.436i 0.580576 + 0.335196i
\(414\) 0 0
\(415\) −115.259 + 199.635i −0.277733 + 0.481047i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 411.162 + 237.385i 0.981295 + 0.566551i 0.902661 0.430353i \(-0.141611\pi\)
0.0786339 + 0.996904i \(0.474944\pi\)
\(420\) 0 0
\(421\) 703.876 1.67191 0.835957 0.548795i \(-0.184913\pi\)
0.835957 + 0.548795i \(0.184913\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −172.422 + 99.5479i −0.405699 + 0.234230i
\(426\) 0 0
\(427\) 139.480 0.326650
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −704.096 + 406.510i −1.63363 + 0.943178i −0.650672 + 0.759359i \(0.725513\pi\)
−0.982960 + 0.183820i \(0.941154\pi\)
\(432\) 0 0
\(433\) 124.092 + 214.934i 0.286588 + 0.496384i 0.972993 0.230835i \(-0.0741457\pi\)
−0.686405 + 0.727219i \(0.740812\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −263.260 48.3450i −0.602426 0.110629i
\(438\) 0 0
\(439\) −68.9527 −0.157068 −0.0785339 0.996911i \(-0.525024\pi\)
−0.0785339 + 0.996911i \(0.525024\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −182.038 105.100i −0.410922 0.237246i 0.280264 0.959923i \(-0.409578\pi\)
−0.691186 + 0.722677i \(0.742911\pi\)
\(444\) 0 0
\(445\) −326.523 + 565.554i −0.733760 + 1.27091i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 478.696i 1.06614i −0.846072 0.533069i \(-0.821039\pi\)
0.846072 0.533069i \(-0.178961\pi\)
\(450\) 0 0
\(451\) 458.218 793.657i 1.01600 1.75977i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 191.840 + 110.759i 0.421626 + 0.243426i
\(456\) 0 0
\(457\) 221.421 + 383.512i 0.484510 + 0.839195i 0.999842 0.0177952i \(-0.00566470\pi\)
−0.515332 + 0.856991i \(0.672331\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 717.965i 1.55741i 0.627392 + 0.778704i \(0.284122\pi\)
−0.627392 + 0.778704i \(0.715878\pi\)
\(462\) 0 0
\(463\) −409.863 + 709.903i −0.885232 + 1.53327i −0.0397854 + 0.999208i \(0.512667\pi\)
−0.845447 + 0.534059i \(0.820666\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 928.612i 1.98846i −0.107255 0.994232i \(-0.534206\pi\)
0.107255 0.994232i \(-0.465794\pi\)
\(468\) 0 0
\(469\) −48.9815 84.8385i −0.104438 0.180892i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 460.037 265.603i 0.972595 0.561528i
\(474\) 0 0
\(475\) 106.099 + 90.3163i 0.223367 + 0.190140i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −395.774 228.500i −0.826251 0.477036i 0.0263164 0.999654i \(-0.491622\pi\)
−0.852567 + 0.522617i \(0.824956\pi\)
\(480\) 0 0
\(481\) −157.172 −0.326761
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −239.539 + 138.298i −0.493895 + 0.285151i
\(486\) 0 0
\(487\) 540.475 1.10980 0.554902 0.831916i \(-0.312756\pi\)
0.554902 + 0.831916i \(0.312756\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 768.591 443.746i 1.56536 0.903760i 0.568660 0.822573i \(-0.307462\pi\)
0.996699 0.0811879i \(-0.0258714\pi\)
\(492\) 0 0
\(493\) 60.0935 + 104.085i 0.121893 + 0.211126i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 299.155i 0.601922i
\(498\) 0 0
\(499\) 65.2082 + 112.944i 0.130678 + 0.226340i 0.923938 0.382542i \(-0.124951\pi\)
−0.793260 + 0.608883i \(0.791618\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −246.777 + 142.477i −0.490609 + 0.283254i −0.724827 0.688931i \(-0.758080\pi\)
0.234218 + 0.972184i \(0.424747\pi\)
\(504\) 0 0
\(505\) −129.095 −0.255633
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 352.715i 0.692957i 0.938058 + 0.346479i \(0.112623\pi\)
−0.938058 + 0.346479i \(0.887377\pi\)
\(510\) 0 0
\(511\) −219.610 −0.429765
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 291.256i 0.565546i
\(516\) 0 0
\(517\) −1407.37 −2.72219
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 479.212i 0.919793i 0.887973 + 0.459897i \(0.152114\pi\)
−0.887973 + 0.459897i \(0.847886\pi\)
\(522\) 0 0
\(523\) −372.327 644.890i −0.711907 1.23306i −0.964140 0.265392i \(-0.914498\pi\)
0.252234 0.967666i \(-0.418835\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −38.4950 + 22.2251i −0.0730456 + 0.0421729i
\(528\) 0 0
\(529\) 330.542 0.624844
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 634.173 366.140i 1.18982 0.686941i
\(534\) 0 0
\(535\) 191.519 + 331.720i 0.357979 + 0.620037i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 816.249i 1.51438i
\(540\) 0 0
\(541\) −49.4363 85.6262i −0.0913795 0.158274i 0.816712 0.577045i \(-0.195794\pi\)
−0.908092 + 0.418771i \(0.862461\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 274.125i 0.502983i
\(546\) 0 0
\(547\) 189.203 327.710i 0.345893 0.599104i −0.639623 0.768689i \(-0.720909\pi\)
0.985516 + 0.169585i \(0.0542427\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 54.5207 64.0484i 0.0989486 0.116240i
\(552\) 0 0
\(553\) −160.407 277.832i −0.290066 0.502409i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −314.531 + 181.594i −0.564687 + 0.326022i −0.755025 0.655696i \(-0.772375\pi\)
0.190337 + 0.981719i \(0.439042\pi\)
\(558\) 0 0
\(559\) 424.460 0.759321
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 451.834 + 260.866i 0.802546 + 0.463350i 0.844361 0.535775i \(-0.179980\pi\)
−0.0418144 + 0.999125i \(0.513314\pi\)
\(564\) 0 0
\(565\) −100.210 −0.177362
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −274.251 + 158.339i −0.481988 + 0.278276i −0.721244 0.692681i \(-0.756430\pi\)
0.239257 + 0.970956i \(0.423096\pi\)
\(570\) 0 0
\(571\) 425.013 736.145i 0.744331 1.28922i −0.206175 0.978515i \(-0.566102\pi\)
0.950506 0.310705i \(-0.100565\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 89.4684 + 51.6546i 0.155597 + 0.0898341i
\(576\) 0 0
\(577\) 939.590 1.62841 0.814203 0.580581i \(-0.197174\pi\)
0.814203 + 0.580581i \(0.197174\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −89.2120 51.5066i −0.153549 0.0886516i
\(582\) 0 0
\(583\) −287.313 + 497.640i −0.492818 + 0.853585i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 205.221i 0.349610i −0.984603 0.174805i \(-0.944070\pi\)
0.984603 0.174805i \(-0.0559295\pi\)
\(588\) 0 0
\(589\) 23.6878 + 20.1641i 0.0402170 + 0.0342344i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −710.973 + 410.481i −1.19894 + 0.692210i −0.960320 0.278902i \(-0.910030\pi\)
−0.238623 + 0.971112i \(0.576696\pi\)
\(594\) 0 0
\(595\) −196.140 339.724i −0.329647 0.570965i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 380.778i 0.635689i −0.948143 0.317845i \(-0.897041\pi\)
0.948143 0.317845i \(-0.102959\pi\)
\(600\) 0 0
\(601\) −205.436 355.826i −0.341824 0.592057i 0.642947 0.765910i \(-0.277711\pi\)
−0.984771 + 0.173854i \(0.944378\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1405.18i 2.32261i
\(606\) 0 0
\(607\) −176.593 + 305.869i −0.290928 + 0.503902i −0.974029 0.226421i \(-0.927297\pi\)
0.683101 + 0.730324i \(0.260631\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −973.902 562.282i −1.59395 0.920266i
\(612\) 0 0
\(613\) 84.7338 146.763i 0.138228 0.239418i −0.788598 0.614909i \(-0.789193\pi\)
0.926826 + 0.375491i \(0.122526\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 128.808i 0.208766i 0.994537 + 0.104383i \(0.0332867\pi\)
−0.994537 + 0.104383i \(0.966713\pi\)
\(618\) 0 0
\(619\) 185.687 + 321.619i 0.299978 + 0.519578i 0.976131 0.217184i \(-0.0696872\pi\)
−0.676152 + 0.736762i \(0.736354\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −252.733 145.916i −0.405671 0.234214i
\(624\) 0 0
\(625\) 377.278 + 653.465i 0.603645 + 1.04554i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 241.042 + 139.166i 0.383215 + 0.221250i
\(630\) 0 0
\(631\) −120.458 208.640i −0.190900 0.330649i 0.754649 0.656129i \(-0.227807\pi\)
−0.945549 + 0.325480i \(0.894474\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 744.086 + 429.599i 1.17179 + 0.676533i
\(636\) 0 0
\(637\) 326.113 564.844i 0.511951 0.886725i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 510.534i 0.796465i 0.917285 + 0.398232i \(0.130376\pi\)
−0.917285 + 0.398232i \(0.869624\pi\)
\(642\) 0 0
\(643\) 24.9822 + 43.2704i 0.0388525 + 0.0672946i 0.884798 0.465975i \(-0.154296\pi\)
−0.845945 + 0.533270i \(0.820963\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1066.24i 1.64798i 0.566602 + 0.823991i \(0.308258\pi\)
−0.566602 + 0.823991i \(0.691742\pi\)
\(648\) 0 0
\(649\) −1045.27 + 1810.46i −1.61059 + 2.78962i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 689.970 + 398.354i 1.05661 + 0.610037i 0.924494 0.381197i \(-0.124488\pi\)
0.132121 + 0.991234i \(0.457821\pi\)
\(654\) 0 0
\(655\) −563.819 + 976.563i −0.860792 + 1.49094i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 944.767 + 545.461i 1.43364 + 0.827711i 0.997396 0.0721190i \(-0.0229761\pi\)
0.436241 + 0.899830i \(0.356309\pi\)
\(660\) 0 0
\(661\) −39.9813 −0.0604861 −0.0302431 0.999543i \(-0.509628\pi\)
−0.0302431 + 0.999543i \(0.509628\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −177.951 + 209.048i −0.267595 + 0.314358i
\(666\) 0 0
\(667\) 31.1820 54.0088i 0.0467497 0.0809728i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1053.15i 1.56953i
\(672\) 0 0
\(673\) −529.340 916.844i −0.786538 1.36232i −0.928076 0.372391i \(-0.878538\pi\)
0.141538 0.989933i \(-0.454795\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 844.755 487.719i 1.24779 0.720413i 0.277123 0.960834i \(-0.410619\pi\)
0.970669 + 0.240422i \(0.0772858\pi\)
\(678\) 0 0
\(679\) −61.8022 107.044i −0.0910194 0.157650i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 991.533i 1.45173i −0.687836 0.725866i \(-0.741439\pi\)
0.687836 0.725866i \(-0.258561\pi\)
\(684\) 0 0
\(685\) −71.1960 −0.103936
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −397.640 + 229.578i −0.577127 + 0.333204i
\(690\) 0 0
\(691\) −482.918 836.438i −0.698868 1.21047i −0.968859 0.247612i \(-0.920354\pi\)
0.269991 0.962863i \(-0.412979\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −448.790 + 259.109i −0.645741 + 0.372819i
\(696\) 0 0
\(697\) −1296.78 −1.86051
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 271.500 + 156.751i 0.387304 + 0.223610i 0.680991 0.732292i \(-0.261549\pi\)
−0.293688 + 0.955901i \(0.594883\pi\)
\(702\) 0 0
\(703\) 35.1823 191.583i 0.0500459 0.272522i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 57.6894i 0.0815975i
\(708\) 0 0
\(709\) −498.245 + 862.985i −0.702743 + 1.21719i 0.264757 + 0.964315i \(0.414708\pi\)
−0.967500 + 0.252871i \(0.918625\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19.9748 + 11.5324i 0.0280151 + 0.0161745i
\(714\) 0 0
\(715\) −836.293 + 1448.50i −1.16964 + 2.02588i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −864.450 499.090i −1.20229 0.694145i −0.241230 0.970468i \(-0.577551\pi\)
−0.961065 + 0.276323i \(0.910884\pi\)
\(720\) 0 0
\(721\) −130.156 −0.180521
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −28.1149 + 16.2321i −0.0387791 + 0.0223891i
\(726\) 0 0
\(727\) 738.667 1.01605 0.508024 0.861343i \(-0.330376\pi\)
0.508024 + 0.861343i \(0.330376\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −650.963 375.833i −0.890510 0.514136i
\(732\) 0 0
\(733\) −428.638 + 742.423i −0.584773 + 1.01286i 0.410131 + 0.912027i \(0.365483\pi\)
−0.994904 + 0.100829i \(0.967850\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 640.581 369.839i 0.869173 0.501817i
\(738\) 0 0
\(739\) 320.378 554.910i 0.433529 0.750894i −0.563646 0.826017i \(-0.690602\pi\)
0.997174 + 0.0751231i \(0.0239350\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1085.64 626.793i 1.46115 0.843598i 0.462090 0.886833i \(-0.347100\pi\)
0.999065 + 0.0432348i \(0.0137663\pi\)
\(744\) 0 0
\(745\) −517.773 + 896.809i −0.694997 + 1.20377i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −148.238 + 85.5852i −0.197914 + 0.114266i
\(750\) 0 0
\(751\) −250.171 −0.333117 −0.166558 0.986032i \(-0.553265\pi\)
−0.166558 + 0.986032i \(0.553265\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1216.44 + 702.312i 1.61118 + 0.930214i
\(756\) 0 0
\(757\) 64.0809 110.991i 0.0846512 0.146620i −0.820591 0.571515i \(-0.806356\pi\)
0.905243 + 0.424895i \(0.139689\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 157.748 + 91.0757i 0.207290 + 0.119679i 0.600051 0.799962i \(-0.295147\pi\)
−0.392761 + 0.919640i \(0.628480\pi\)
\(762\) 0 0
\(763\) −122.500 −0.160551
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1446.65 + 835.226i −1.88612 + 1.08895i
\(768\) 0 0
\(769\) 1084.06 1.40970 0.704849 0.709357i \(-0.251015\pi\)
0.704849 + 0.709357i \(0.251015\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −524.842 + 303.018i −0.678968 + 0.392002i −0.799466 0.600711i \(-0.794884\pi\)
0.120498 + 0.992714i \(0.461551\pi\)
\(774\) 0 0
\(775\) −6.00333 10.3981i −0.00774623 0.0134169i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 304.346 + 854.978i 0.390688 + 1.09753i
\(780\) 0 0
\(781\) −2258.80 −2.89219
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1030.09 594.724i −1.31222 0.757610i
\(786\) 0 0
\(787\) 431.411 747.227i 0.548172 0.949462i −0.450228 0.892914i \(-0.648657\pi\)
0.998400 0.0565482i \(-0.0180095\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 44.7813i 0.0566136i
\(792\) 0 0
\(793\) −420.762 + 728.781i −0.530595 + 0.919018i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −28.8187 16.6385i −0.0361590 0.0208764i 0.481812 0.876275i \(-0.339979\pi\)
−0.517971 + 0.855398i \(0.673312\pi\)
\(798\) 0 0
\(799\) 995.732 + 1724.66i 1.24622 + 2.15852i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1658.18i 2.06498i
\(804\) 0 0
\(805\) −101.775 + 176.280i −0.126429 + 0.218982i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 797.081i 0.985267i −0.870237 0.492633i \(-0.836034\pi\)
0.870237 0.492633i \(-0.163966\pi\)
\(810\) 0 0
\(811\) −233.636 404.670i −0.288084 0.498977i 0.685268 0.728291i \(-0.259685\pi\)
−0.973352 + 0.229314i \(0.926352\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 92.9147 53.6443i 0.114006 0.0658213i
\(816\) 0 0
\(817\) −95.0137 + 517.392i −0.116296 + 0.633283i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 611.361 + 352.970i 0.744655 + 0.429927i 0.823759 0.566940i \(-0.191873\pi\)
−0.0791046 + 0.996866i \(0.525206\pi\)
\(822\) 0 0
\(823\) −43.3500 −0.0526732 −0.0263366 0.999653i \(-0.508384\pi\)
−0.0263366 + 0.999653i \(0.508384\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −272.721 + 157.455i −0.329771 + 0.190393i −0.655739 0.754987i \(-0.727643\pi\)
0.325968 + 0.945381i \(0.394310\pi\)
\(828\) 0 0
\(829\) −175.140 −0.211266 −0.105633 0.994405i \(-0.533687\pi\)
−0.105633 + 0.994405i \(0.533687\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1000.27 + 577.505i −1.20080 + 0.693283i
\(834\) 0 0
\(835\) 638.403 + 1105.75i 0.764554 + 1.32425i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 223.819i 0.266769i 0.991064 + 0.133385i \(0.0425846\pi\)
−0.991064 + 0.133385i \(0.957415\pi\)
\(840\) 0 0
\(841\) −410.701 711.355i −0.488349 0.845845i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −325.198 + 187.753i −0.384850 + 0.222193i
\(846\) 0 0
\(847\) −627.941 −0.741371
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 144.424i 0.169711i
\(852\) 0 0
\(853\) −1180.41 −1.38383 −0.691916 0.721978i \(-0.743233\pi\)
−0.691916 + 0.721978i \(0.743233\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 565.357i 0.659693i 0.944035 + 0.329847i \(0.106997\pi\)
−0.944035 + 0.329847i \(0.893003\pi\)
\(858\) 0 0
\(859\) −704.601 −0.820258 −0.410129 0.912028i \(-0.634516\pi\)
−0.410129 + 0.912028i \(0.634516\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 585.783i 0.678775i 0.940647 + 0.339388i \(0.110220\pi\)
−0.940647 + 0.339388i \(0.889780\pi\)
\(864\) 0 0
\(865\) −210.354 364.344i −0.243184 0.421207i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2097.80 1211.16i 2.41404 1.39374i
\(870\) 0 0
\(871\) 591.042 0.678578
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −221.066 + 127.633i −0.252647 + 0.145866i
\(876\) 0 0
\(877\) −675.042 1169.21i −0.769717 1.33319i −0.937716 0.347401i \(-0.887064\pi\)
0.168000 0.985787i \(-0.446269\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1018.07i 1.15558i 0.816185 + 0.577790i \(0.196085\pi\)
−0.816185 + 0.577790i \(0.803915\pi\)
\(882\) 0 0
\(883\) −792.523 1372.69i −0.897535 1.55458i −0.830636 0.556816i \(-0.812023\pi\)
−0.0668992 0.997760i \(-0.521311\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1174.84i 1.32451i 0.749277 + 0.662256i \(0.230401\pi\)
−0.749277 + 0.662256i \(0.769599\pi\)
\(888\) 0 0
\(889\) −191.978 + 332.515i −0.215948 + 0.374032i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 903.393 1061.26i 1.01164 1.18843i
\(894\) 0 0
\(895\) −558.232 966.887i −0.623723 1.08032i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6.27694 + 3.62399i −0.00698213 + 0.00403114i
\(900\) 0 0
\(901\) 813.107 0.902450
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 201.816 + 116.519i 0.223001 + 0.128750i
\(906\) 0 0
\(907\) 953.908 1.05172 0.525859 0.850572i \(-0.323744\pi\)
0.525859 + 0.850572i \(0.323744\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −28.1810 + 16.2703i −0.0309342 + 0.0178599i −0.515387 0.856957i \(-0.672352\pi\)
0.484453 + 0.874817i \(0.339019\pi\)
\(912\) 0 0
\(913\) 388.905 673.603i 0.425964 0.737791i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −436.403 251.958i −0.475903 0.274763i
\(918\) 0 0
\(919\) −1215.43 −1.32256 −0.661280 0.750139i \(-0.729986\pi\)
−0.661280 + 0.750139i \(0.729986\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1563.09 902.448i −1.69348 0.977733i
\(924\) 0 0
\(925\) −37.5908 + 65.1091i −0.0406387 + 0.0703883i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1180.08i 1.27027i 0.772402 + 0.635134i \(0.219055\pi\)
−0.772402 + 0.635134i \(0.780945\pi\)
\(930\) 0 0
\(931\) 615.512 + 523.950i 0.661130 + 0.562782i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2565.12 1480.97i 2.74344 1.58393i
\(936\) 0 0
\(937\) 339.618 + 588.236i 0.362453 + 0.627786i 0.988364 0.152108i \(-0.0486062\pi\)
−0.625911 + 0.779894i \(0.715273\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 529.877i 0.563100i 0.959547 + 0.281550i \(0.0908485\pi\)
−0.959547 + 0.281550i \(0.909152\pi\)
\(942\) 0 0
\(943\) 336.443 + 582.737i 0.356780 + 0.617961i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 114.564i 0.120976i −0.998169 0.0604880i \(-0.980734\pi\)
0.998169 0.0604880i \(-0.0192657\pi\)
\(948\) 0 0
\(949\) 662.487 1147.46i 0.698089 1.20913i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −178.049 102.797i −0.186830 0.107867i 0.403668 0.914906i \(-0.367735\pi\)
−0.590498 + 0.807039i \(0.701069\pi\)
\(954\) 0 0
\(955\) 234.947 406.939i 0.246017 0.426115i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 31.8158i 0.0331760i
\(960\) 0 0
\(961\) 479.160 + 829.929i 0.498605 + 0.863610i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1614.59 + 932.184i 1.67315 + 0.965994i
\(966\) 0 0
\(967\) −603.557 1045.39i −0.624154 1.08107i −0.988704 0.149882i \(-0.952110\pi\)
0.364550 0.931184i \(-0.381223\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 247.794 + 143.064i 0.255194 + 0.147337i 0.622140 0.782906i \(-0.286263\pi\)
−0.366946 + 0.930242i \(0.619597\pi\)
\(972\) 0 0
\(973\) −115.790 200.554i −0.119003 0.206119i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 239.324 + 138.174i 0.244958 + 0.141427i 0.617453 0.786607i \(-0.288164\pi\)
−0.372495 + 0.928034i \(0.621498\pi\)
\(978\) 0 0
\(979\) 1101.75 1908.28i 1.12538 1.94922i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1014.26i 1.03180i 0.856650 + 0.515899i \(0.172542\pi\)
−0.856650 + 0.515899i \(0.827458\pi\)
\(984\) 0 0
\(985\) 703.211 + 1218.00i 0.713920 + 1.23655i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 390.034i 0.394372i
\(990\) 0 0
\(991\) −668.318 + 1157.56i −0.674388 + 1.16807i 0.302260 + 0.953226i \(0.402259\pi\)
−0.976647 + 0.214848i \(0.931074\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −694.619 401.038i −0.698109 0.403054i
\(996\) 0 0
\(997\) 30.0956 52.1270i 0.0301861 0.0522839i −0.850538 0.525914i \(-0.823723\pi\)
0.880724 + 0.473630i \(0.157057\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2052.3.be.a.125.11 80
3.2 odd 2 684.3.be.a.581.3 yes 80
9.2 odd 6 2052.3.m.a.1493.30 80
9.7 even 3 684.3.m.a.353.31 80
19.7 even 3 2052.3.m.a.881.11 80
57.26 odd 6 684.3.m.a.653.31 yes 80
171.7 even 3 684.3.be.a.425.3 yes 80
171.83 odd 6 inner 2052.3.be.a.197.11 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.3.m.a.353.31 80 9.7 even 3
684.3.m.a.653.31 yes 80 57.26 odd 6
684.3.be.a.425.3 yes 80 171.7 even 3
684.3.be.a.581.3 yes 80 3.2 odd 2
2052.3.m.a.881.11 80 19.7 even 3
2052.3.m.a.1493.30 80 9.2 odd 6
2052.3.be.a.125.11 80 1.1 even 1 trivial
2052.3.be.a.197.11 80 171.83 odd 6 inner