Properties

Label 405.4.e.l.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,4,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.136");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.l.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-3.00000 - 5.19615i) q^{7} +20.0000 q^{10} +(-16.0000 - 27.7128i) q^{11} +(19.0000 - 32.9090i) q^{13} +(12.0000 - 20.7846i) q^{14} +(32.0000 + 55.4256i) q^{16} +26.0000 q^{17} +100.000 q^{19} +(20.0000 + 34.6410i) q^{20} +(64.0000 - 110.851i) q^{22} +(39.0000 - 67.5500i) q^{23} +(-12.5000 - 21.6506i) q^{25} +152.000 q^{26} +48.0000 q^{28} +(25.0000 + 43.3013i) q^{29} +(54.0000 - 93.5307i) q^{31} +(-128.000 + 221.703i) q^{32} +(52.0000 + 90.0666i) q^{34} -30.0000 q^{35} +266.000 q^{37} +(200.000 + 346.410i) q^{38} +(-11.0000 + 19.0526i) q^{41} +(-221.000 - 382.783i) q^{43} +256.000 q^{44} +312.000 q^{46} +(257.000 + 445.137i) q^{47} +(153.500 - 265.870i) q^{49} +(50.0000 - 86.6025i) q^{50} +(152.000 + 263.272i) q^{52} +2.00000 q^{53} -160.000 q^{55} +(-100.000 + 173.205i) q^{58} +(-250.000 + 433.013i) q^{59} +(259.000 + 448.601i) q^{61} +432.000 q^{62} -512.000 q^{64} +(-95.0000 - 164.545i) q^{65} +(-63.0000 + 109.119i) q^{67} +(-104.000 + 180.133i) q^{68} +(-60.0000 - 103.923i) q^{70} +412.000 q^{71} -878.000 q^{73} +(532.000 + 921.451i) q^{74} +(-400.000 + 692.820i) q^{76} +(-96.0000 + 166.277i) q^{77} +(-300.000 - 519.615i) q^{79} +320.000 q^{80} -88.0000 q^{82} +(-141.000 - 244.219i) q^{83} +(65.0000 - 112.583i) q^{85} +(884.000 - 1531.13i) q^{86} -150.000 q^{89} -228.000 q^{91} +(312.000 + 540.400i) q^{92} +(-1028.00 + 1780.55i) q^{94} +(250.000 - 433.013i) q^{95} +(-193.000 - 334.286i) q^{97} +1228.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 6 q^{7} + 40 q^{10} - 32 q^{11} + 38 q^{13} + 24 q^{14} + 64 q^{16} + 52 q^{17} + 200 q^{19} + 40 q^{20} + 128 q^{22} + 78 q^{23} - 25 q^{25} + 304 q^{26} + 96 q^{28}+ \cdots + 2456 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 3.46410i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) 0 0
\(4\) −4.00000 + 6.92820i −0.500000 + 0.866025i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 0 0
\(7\) −3.00000 5.19615i −0.161985 0.280566i 0.773596 0.633680i \(-0.218456\pi\)
−0.935580 + 0.353114i \(0.885123\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 20.0000 0.632456
\(11\) −16.0000 27.7128i −0.438562 0.759612i 0.559017 0.829156i \(-0.311179\pi\)
−0.997579 + 0.0695447i \(0.977845\pi\)
\(12\) 0 0
\(13\) 19.0000 32.9090i 0.405358 0.702100i −0.589005 0.808129i \(-0.700480\pi\)
0.994363 + 0.106029i \(0.0338136\pi\)
\(14\) 12.0000 20.7846i 0.229081 0.396780i
\(15\) 0 0
\(16\) 32.0000 + 55.4256i 0.500000 + 0.866025i
\(17\) 26.0000 0.370937 0.185468 0.982650i \(-0.440620\pi\)
0.185468 + 0.982650i \(0.440620\pi\)
\(18\) 0 0
\(19\) 100.000 1.20745 0.603726 0.797192i \(-0.293682\pi\)
0.603726 + 0.797192i \(0.293682\pi\)
\(20\) 20.0000 + 34.6410i 0.223607 + 0.387298i
\(21\) 0 0
\(22\) 64.0000 110.851i 0.620220 1.07425i
\(23\) 39.0000 67.5500i 0.353568 0.612398i −0.633304 0.773903i \(-0.718302\pi\)
0.986872 + 0.161506i \(0.0516350\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 152.000 1.14653
\(27\) 0 0
\(28\) 48.0000 0.323970
\(29\) 25.0000 + 43.3013i 0.160082 + 0.277270i 0.934898 0.354917i \(-0.115491\pi\)
−0.774816 + 0.632187i \(0.782157\pi\)
\(30\) 0 0
\(31\) 54.0000 93.5307i 0.312861 0.541891i −0.666120 0.745845i \(-0.732046\pi\)
0.978980 + 0.203954i \(0.0653793\pi\)
\(32\) −128.000 + 221.703i −0.707107 + 1.22474i
\(33\) 0 0
\(34\) 52.0000 + 90.0666i 0.262292 + 0.454303i
\(35\) −30.0000 −0.144884
\(36\) 0 0
\(37\) 266.000 1.18190 0.590948 0.806710i \(-0.298754\pi\)
0.590948 + 0.806710i \(0.298754\pi\)
\(38\) 200.000 + 346.410i 0.853797 + 1.47882i
\(39\) 0 0
\(40\) 0 0
\(41\) −11.0000 + 19.0526i −0.0419003 + 0.0725734i −0.886215 0.463274i \(-0.846675\pi\)
0.844315 + 0.535848i \(0.180008\pi\)
\(42\) 0 0
\(43\) −221.000 382.783i −0.783772 1.35753i −0.929730 0.368242i \(-0.879960\pi\)
0.145958 0.989291i \(-0.453373\pi\)
\(44\) 256.000 0.877124
\(45\) 0 0
\(46\) 312.000 1.00004
\(47\) 257.000 + 445.137i 0.797602 + 1.38149i 0.921174 + 0.389152i \(0.127232\pi\)
−0.123571 + 0.992336i \(0.539435\pi\)
\(48\) 0 0
\(49\) 153.500 265.870i 0.447522 0.775131i
\(50\) 50.0000 86.6025i 0.141421 0.244949i
\(51\) 0 0
\(52\) 152.000 + 263.272i 0.405358 + 0.702100i
\(53\) 2.00000 0.00518342 0.00259171 0.999997i \(-0.499175\pi\)
0.00259171 + 0.999997i \(0.499175\pi\)
\(54\) 0 0
\(55\) −160.000 −0.392262
\(56\) 0 0
\(57\) 0 0
\(58\) −100.000 + 173.205i −0.226390 + 0.392120i
\(59\) −250.000 + 433.013i −0.551648 + 0.955482i 0.446508 + 0.894780i \(0.352667\pi\)
−0.998156 + 0.0607026i \(0.980666\pi\)
\(60\) 0 0
\(61\) 259.000 + 448.601i 0.543632 + 0.941598i 0.998692 + 0.0511373i \(0.0162846\pi\)
−0.455060 + 0.890461i \(0.650382\pi\)
\(62\) 432.000 0.884904
\(63\) 0 0
\(64\) −512.000 −1.00000
\(65\) −95.0000 164.545i −0.181282 0.313989i
\(66\) 0 0
\(67\) −63.0000 + 109.119i −0.114876 + 0.198971i −0.917730 0.397205i \(-0.869980\pi\)
0.802854 + 0.596175i \(0.203314\pi\)
\(68\) −104.000 + 180.133i −0.185468 + 0.321241i
\(69\) 0 0
\(70\) −60.0000 103.923i −0.102448 0.177445i
\(71\) 412.000 0.688668 0.344334 0.938847i \(-0.388105\pi\)
0.344334 + 0.938847i \(0.388105\pi\)
\(72\) 0 0
\(73\) −878.000 −1.40770 −0.703850 0.710348i \(-0.748537\pi\)
−0.703850 + 0.710348i \(0.748537\pi\)
\(74\) 532.000 + 921.451i 0.835726 + 1.44752i
\(75\) 0 0
\(76\) −400.000 + 692.820i −0.603726 + 1.04568i
\(77\) −96.0000 + 166.277i −0.142081 + 0.246091i
\(78\) 0 0
\(79\) −300.000 519.615i −0.427249 0.740016i 0.569379 0.822075i \(-0.307184\pi\)
−0.996627 + 0.0820590i \(0.973850\pi\)
\(80\) 320.000 0.447214
\(81\) 0 0
\(82\) −88.0000 −0.118512
\(83\) −141.000 244.219i −0.186467 0.322970i 0.757603 0.652716i \(-0.226370\pi\)
−0.944070 + 0.329745i \(0.893037\pi\)
\(84\) 0 0
\(85\) 65.0000 112.583i 0.0829440 0.143663i
\(86\) 884.000 1531.13i 1.10842 1.91984i
\(87\) 0 0
\(88\) 0 0
\(89\) −150.000 −0.178651 −0.0893257 0.996002i \(-0.528471\pi\)
−0.0893257 + 0.996002i \(0.528471\pi\)
\(90\) 0 0
\(91\) −228.000 −0.262647
\(92\) 312.000 + 540.400i 0.353568 + 0.612398i
\(93\) 0 0
\(94\) −1028.00 + 1780.55i −1.12798 + 1.95372i
\(95\) 250.000 433.013i 0.269994 0.467644i
\(96\) 0 0
\(97\) −193.000 334.286i −0.202022 0.349913i 0.747157 0.664647i \(-0.231418\pi\)
−0.949180 + 0.314734i \(0.898085\pi\)
\(98\) 1228.00 1.26578
\(99\) 0 0
\(100\) 200.000 0.200000
\(101\) −351.000 607.950i −0.345800 0.598943i 0.639699 0.768626i \(-0.279059\pi\)
−0.985499 + 0.169682i \(0.945726\pi\)
\(102\) 0 0
\(103\) 299.000 517.883i 0.286032 0.495423i −0.686827 0.726821i \(-0.740997\pi\)
0.972859 + 0.231399i \(0.0743301\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.00000 + 6.92820i 0.00366523 + 0.00634836i
\(107\) −1194.00 −1.07877 −0.539385 0.842059i \(-0.681343\pi\)
−0.539385 + 0.842059i \(0.681343\pi\)
\(108\) 0 0
\(109\) −550.000 −0.483307 −0.241653 0.970363i \(-0.577690\pi\)
−0.241653 + 0.970363i \(0.577690\pi\)
\(110\) −320.000 554.256i −0.277371 0.480421i
\(111\) 0 0
\(112\) 192.000 332.554i 0.161985 0.280566i
\(113\) −781.000 + 1352.73i −0.650180 + 1.12614i 0.332899 + 0.942962i \(0.391973\pi\)
−0.983079 + 0.183182i \(0.941360\pi\)
\(114\) 0 0
\(115\) −195.000 337.750i −0.158120 0.273873i
\(116\) −400.000 −0.320164
\(117\) 0 0
\(118\) −2000.00 −1.56030
\(119\) −78.0000 135.100i −0.0600861 0.104072i
\(120\) 0 0
\(121\) 153.500 265.870i 0.115327 0.199752i
\(122\) −1036.00 + 1794.40i −0.768812 + 1.33162i
\(123\) 0 0
\(124\) 432.000 + 748.246i 0.312861 + 0.541891i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1846.00 1.28981 0.644906 0.764262i \(-0.276897\pi\)
0.644906 + 0.764262i \(0.276897\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 380.000 658.179i 0.256371 0.444047i
\(131\) 1104.00 1912.18i 0.736312 1.27533i −0.217833 0.975986i \(-0.569899\pi\)
0.954145 0.299344i \(-0.0967680\pi\)
\(132\) 0 0
\(133\) −300.000 519.615i −0.195589 0.338770i
\(134\) −504.000 −0.324918
\(135\) 0 0
\(136\) 0 0
\(137\) 1167.00 + 2021.30i 0.727763 + 1.26052i 0.957827 + 0.287347i \(0.0927733\pi\)
−0.230064 + 0.973176i \(0.573893\pi\)
\(138\) 0 0
\(139\) 350.000 606.218i 0.213573 0.369919i −0.739257 0.673423i \(-0.764823\pi\)
0.952830 + 0.303504i \(0.0981566\pi\)
\(140\) 120.000 207.846i 0.0724418 0.125473i
\(141\) 0 0
\(142\) 824.000 + 1427.21i 0.486962 + 0.843442i
\(143\) −1216.00 −0.711098
\(144\) 0 0
\(145\) 250.000 0.143182
\(146\) −1756.00 3041.48i −0.995394 1.72407i
\(147\) 0 0
\(148\) −1064.00 + 1842.90i −0.590948 + 1.02355i
\(149\) −1025.00 + 1775.35i −0.563566 + 0.976124i 0.433616 + 0.901098i \(0.357237\pi\)
−0.997182 + 0.0750264i \(0.976096\pi\)
\(150\) 0 0
\(151\) −926.000 1603.88i −0.499052 0.864383i 0.500948 0.865478i \(-0.332985\pi\)
−0.999999 + 0.00109462i \(0.999652\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −768.000 −0.401865
\(155\) −270.000 467.654i −0.139916 0.242341i
\(156\) 0 0
\(157\) 1247.00 2159.87i 0.633894 1.09794i −0.352854 0.935678i \(-0.614789\pi\)
0.986748 0.162259i \(-0.0518780\pi\)
\(158\) 1200.00 2078.46i 0.604221 1.04654i
\(159\) 0 0
\(160\) 640.000 + 1108.51i 0.316228 + 0.547723i
\(161\) −468.000 −0.229090
\(162\) 0 0
\(163\) 2762.00 1.32722 0.663609 0.748080i \(-0.269024\pi\)
0.663609 + 0.748080i \(0.269024\pi\)
\(164\) −88.0000 152.420i −0.0419003 0.0725734i
\(165\) 0 0
\(166\) 564.000 976.877i 0.263704 0.456749i
\(167\) −1563.00 + 2707.20i −0.724243 + 1.25443i 0.235042 + 0.971985i \(0.424477\pi\)
−0.959285 + 0.282440i \(0.908856\pi\)
\(168\) 0 0
\(169\) 376.500 + 652.117i 0.171370 + 0.296822i
\(170\) 520.000 0.234601
\(171\) 0 0
\(172\) 3536.00 1.56754
\(173\) 39.0000 + 67.5500i 0.0171394 + 0.0296863i 0.874468 0.485083i \(-0.161211\pi\)
−0.857328 + 0.514770i \(0.827877\pi\)
\(174\) 0 0
\(175\) −75.0000 + 129.904i −0.0323970 + 0.0561132i
\(176\) 1024.00 1773.62i 0.438562 0.759612i
\(177\) 0 0
\(178\) −300.000 519.615i −0.126326 0.218802i
\(179\) −1300.00 −0.542830 −0.271415 0.962462i \(-0.587492\pi\)
−0.271415 + 0.962462i \(0.587492\pi\)
\(180\) 0 0
\(181\) 1742.00 0.715369 0.357685 0.933842i \(-0.383566\pi\)
0.357685 + 0.933842i \(0.383566\pi\)
\(182\) −456.000 789.815i −0.185720 0.321676i
\(183\) 0 0
\(184\) 0 0
\(185\) 665.000 1151.81i 0.264280 0.457746i
\(186\) 0 0
\(187\) −416.000 720.533i −0.162679 0.281768i
\(188\) −4112.00 −1.59520
\(189\) 0 0
\(190\) 2000.00 0.763659
\(191\) −1886.00 3266.65i −0.714483 1.23752i −0.963159 0.268933i \(-0.913329\pi\)
0.248676 0.968587i \(-0.420004\pi\)
\(192\) 0 0
\(193\) 179.000 310.037i 0.0667601 0.115632i −0.830713 0.556700i \(-0.812067\pi\)
0.897473 + 0.441069i \(0.145400\pi\)
\(194\) 772.000 1337.14i 0.285703 0.494852i
\(195\) 0 0
\(196\) 1228.00 + 2126.96i 0.447522 + 0.775131i
\(197\) −2214.00 −0.800716 −0.400358 0.916359i \(-0.631114\pi\)
−0.400358 + 0.916359i \(0.631114\pi\)
\(198\) 0 0
\(199\) −2600.00 −0.926176 −0.463088 0.886312i \(-0.653259\pi\)
−0.463088 + 0.886312i \(0.653259\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1404.00 2431.80i 0.489035 0.847034i
\(203\) 150.000 259.808i 0.0518618 0.0898272i
\(204\) 0 0
\(205\) 55.0000 + 95.2628i 0.0187384 + 0.0324558i
\(206\) 2392.00 0.809022
\(207\) 0 0
\(208\) 2432.00 0.810716
\(209\) −1600.00 2771.28i −0.529542 0.917194i
\(210\) 0 0
\(211\) 584.000 1011.52i 0.190541 0.330027i −0.754888 0.655853i \(-0.772309\pi\)
0.945430 + 0.325826i \(0.105642\pi\)
\(212\) −8.00000 + 13.8564i −0.00259171 + 0.00448897i
\(213\) 0 0
\(214\) −2388.00 4136.14i −0.762805 1.32122i
\(215\) −2210.00 −0.701027
\(216\) 0 0
\(217\) −648.000 −0.202715
\(218\) −1100.00 1905.26i −0.341750 0.591928i
\(219\) 0 0
\(220\) 640.000 1108.51i 0.196131 0.339709i
\(221\) 494.000 855.633i 0.150362 0.260435i
\(222\) 0 0
\(223\) 3239.00 + 5610.11i 0.972643 + 1.68467i 0.687502 + 0.726182i \(0.258707\pi\)
0.285141 + 0.958486i \(0.407959\pi\)
\(224\) 1536.00 0.458162
\(225\) 0 0
\(226\) −6248.00 −1.83899
\(227\) −323.000 559.452i −0.0944417 0.163578i 0.814934 0.579554i \(-0.196773\pi\)
−0.909375 + 0.415976i \(0.863440\pi\)
\(228\) 0 0
\(229\) −1875.00 + 3247.60i −0.541063 + 0.937149i 0.457780 + 0.889065i \(0.348645\pi\)
−0.998843 + 0.0480836i \(0.984689\pi\)
\(230\) 780.000 1351.00i 0.223616 0.387314i
\(231\) 0 0
\(232\) 0 0
\(233\) 1482.00 0.416691 0.208346 0.978055i \(-0.433192\pi\)
0.208346 + 0.978055i \(0.433192\pi\)
\(234\) 0 0
\(235\) 2570.00 0.713397
\(236\) −2000.00 3464.10i −0.551648 0.955482i
\(237\) 0 0
\(238\) 312.000 540.400i 0.0849746 0.147180i
\(239\) −700.000 + 1212.44i −0.189453 + 0.328142i −0.945068 0.326874i \(-0.894005\pi\)
0.755615 + 0.655016i \(0.227338\pi\)
\(240\) 0 0
\(241\) −1511.00 2617.13i −0.403867 0.699519i 0.590321 0.807168i \(-0.299001\pi\)
−0.994189 + 0.107649i \(0.965668\pi\)
\(242\) 1228.00 0.326194
\(243\) 0 0
\(244\) −4144.00 −1.08726
\(245\) −767.500 1329.35i −0.200138 0.346649i
\(246\) 0 0
\(247\) 1900.00 3290.90i 0.489450 0.847752i
\(248\) 0 0
\(249\) 0 0
\(250\) −250.000 433.013i −0.0632456 0.109545i
\(251\) −1248.00 −0.313837 −0.156918 0.987612i \(-0.550156\pi\)
−0.156918 + 0.987612i \(0.550156\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) 3692.00 + 6394.73i 0.912034 + 1.57969i
\(255\) 0 0
\(256\) −2048.00 + 3547.24i −0.500000 + 0.866025i
\(257\) −1053.00 + 1823.85i −0.255581 + 0.442679i −0.965053 0.262054i \(-0.915600\pi\)
0.709472 + 0.704734i \(0.248933\pi\)
\(258\) 0 0
\(259\) −798.000 1382.18i −0.191449 0.331600i
\(260\) 1520.00 0.362563
\(261\) 0 0
\(262\) 8832.00 2.08261
\(263\) 1819.00 + 3150.60i 0.426480 + 0.738686i 0.996557 0.0829055i \(-0.0264200\pi\)
−0.570077 + 0.821591i \(0.693087\pi\)
\(264\) 0 0
\(265\) 5.00000 8.66025i 0.00115905 0.00200753i
\(266\) 1200.00 2078.46i 0.276604 0.479093i
\(267\) 0 0
\(268\) −504.000 872.954i −0.114876 0.198971i
\(269\) −6550.00 −1.48461 −0.742306 0.670061i \(-0.766268\pi\)
−0.742306 + 0.670061i \(0.766268\pi\)
\(270\) 0 0
\(271\) −4388.00 −0.983587 −0.491793 0.870712i \(-0.663658\pi\)
−0.491793 + 0.870712i \(0.663658\pi\)
\(272\) 832.000 + 1441.07i 0.185468 + 0.321241i
\(273\) 0 0
\(274\) −4668.00 + 8085.21i −1.02921 + 1.78265i
\(275\) −400.000 + 692.820i −0.0877124 + 0.151922i
\(276\) 0 0
\(277\) −273.000 472.850i −0.0592165 0.102566i 0.834897 0.550406i \(-0.185527\pi\)
−0.894114 + 0.447840i \(0.852194\pi\)
\(278\) 2800.00 0.604075
\(279\) 0 0
\(280\) 0 0
\(281\) 3429.00 + 5939.20i 0.727961 + 1.26087i 0.957744 + 0.287623i \(0.0928651\pi\)
−0.229783 + 0.973242i \(0.573802\pi\)
\(282\) 0 0
\(283\) −4641.00 + 8038.45i −0.974837 + 1.68847i −0.294364 + 0.955693i \(0.595108\pi\)
−0.680473 + 0.732774i \(0.738225\pi\)
\(284\) −1648.00 + 2854.42i −0.344334 + 0.596404i
\(285\) 0 0
\(286\) −2432.00 4212.35i −0.502822 0.870914i
\(287\) 132.000 0.0271488
\(288\) 0 0
\(289\) −4237.00 −0.862406
\(290\) 500.000 + 866.025i 0.101245 + 0.175361i
\(291\) 0 0
\(292\) 3512.00 6082.96i 0.703850 1.21910i
\(293\) −2421.00 + 4193.30i −0.482718 + 0.836092i −0.999803 0.0198420i \(-0.993684\pi\)
0.517085 + 0.855934i \(0.327017\pi\)
\(294\) 0 0
\(295\) 1250.00 + 2165.06i 0.246704 + 0.427305i
\(296\) 0 0
\(297\) 0 0
\(298\) −8200.00 −1.59400
\(299\) −1482.00 2566.90i −0.286643 0.496480i
\(300\) 0 0
\(301\) −1326.00 + 2296.70i −0.253918 + 0.439799i
\(302\) 3704.00 6415.52i 0.705766 1.22242i
\(303\) 0 0
\(304\) 3200.00 + 5542.56i 0.603726 + 1.04568i
\(305\) 2590.00 0.486239
\(306\) 0 0
\(307\) −2594.00 −0.482239 −0.241120 0.970495i \(-0.577515\pi\)
−0.241120 + 0.970495i \(0.577515\pi\)
\(308\) −768.000 1330.22i −0.142081 0.246091i
\(309\) 0 0
\(310\) 1080.00 1870.61i 0.197871 0.342722i
\(311\) −3666.00 + 6349.70i −0.668424 + 1.15774i 0.309921 + 0.950762i \(0.399697\pi\)
−0.978345 + 0.206982i \(0.933636\pi\)
\(312\) 0 0
\(313\) −781.000 1352.73i −0.141037 0.244284i 0.786850 0.617144i \(-0.211710\pi\)
−0.927888 + 0.372860i \(0.878377\pi\)
\(314\) 9976.00 1.79292
\(315\) 0 0
\(316\) 4800.00 0.854497
\(317\) −713.000 1234.95i −0.126328 0.218807i 0.795923 0.605398i \(-0.206986\pi\)
−0.922251 + 0.386591i \(0.873653\pi\)
\(318\) 0 0
\(319\) 800.000 1385.64i 0.140412 0.243201i
\(320\) −1280.00 + 2217.03i −0.223607 + 0.387298i
\(321\) 0 0
\(322\) −936.000 1621.20i −0.161991 0.280577i
\(323\) 2600.00 0.447888
\(324\) 0 0
\(325\) −950.000 −0.162143
\(326\) 5524.00 + 9567.85i 0.938485 + 1.62550i
\(327\) 0 0
\(328\) 0 0
\(329\) 1542.00 2670.82i 0.258399 0.447560i
\(330\) 0 0
\(331\) 2004.00 + 3471.03i 0.332779 + 0.576390i 0.983056 0.183308i \(-0.0586804\pi\)
−0.650277 + 0.759697i \(0.725347\pi\)
\(332\) 2256.00 0.372934
\(333\) 0 0
\(334\) −12504.0 −2.04847
\(335\) 315.000 + 545.596i 0.0513740 + 0.0889824i
\(336\) 0 0
\(337\) −4433.00 + 7678.18i −0.716561 + 1.24112i 0.245794 + 0.969322i \(0.420951\pi\)
−0.962355 + 0.271797i \(0.912382\pi\)
\(338\) −1506.00 + 2608.47i −0.242354 + 0.419769i
\(339\) 0 0
\(340\) 520.000 + 900.666i 0.0829440 + 0.143663i
\(341\) −3456.00 −0.548835
\(342\) 0 0
\(343\) −3900.00 −0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) −156.000 + 270.200i −0.0242388 + 0.0419828i
\(347\) 857.000 1484.37i 0.132583 0.229640i −0.792089 0.610406i \(-0.791006\pi\)
0.924671 + 0.380766i \(0.124340\pi\)
\(348\) 0 0
\(349\) −575.000 995.929i −0.0881921 0.152753i 0.818555 0.574428i \(-0.194776\pi\)
−0.906747 + 0.421675i \(0.861442\pi\)
\(350\) −600.000 −0.0916324
\(351\) 0 0
\(352\) 8192.00 1.24044
\(353\) 2199.00 + 3808.78i 0.331561 + 0.574280i 0.982818 0.184577i \(-0.0590915\pi\)
−0.651257 + 0.758857i \(0.725758\pi\)
\(354\) 0 0
\(355\) 1030.00 1784.01i 0.153991 0.266720i
\(356\) 600.000 1039.23i 0.0893257 0.154717i
\(357\) 0 0
\(358\) −2600.00 4503.33i −0.383839 0.664828i
\(359\) 1800.00 0.264625 0.132312 0.991208i \(-0.457760\pi\)
0.132312 + 0.991208i \(0.457760\pi\)
\(360\) 0 0
\(361\) 3141.00 0.457938
\(362\) 3484.00 + 6034.47i 0.505842 + 0.876145i
\(363\) 0 0
\(364\) 912.000 1579.63i 0.131324 0.227459i
\(365\) −2195.00 + 3801.85i −0.314771 + 0.545200i
\(366\) 0 0
\(367\) 2937.00 + 5087.03i 0.417739 + 0.723545i 0.995712 0.0925111i \(-0.0294894\pi\)
−0.577973 + 0.816056i \(0.696156\pi\)
\(368\) 4992.00 0.707136
\(369\) 0 0
\(370\) 5320.00 0.747496
\(371\) −6.00000 10.3923i −0.000839635 0.00145429i
\(372\) 0 0
\(373\) 1039.00 1799.60i 0.144229 0.249812i −0.784856 0.619678i \(-0.787263\pi\)
0.929085 + 0.369866i \(0.120597\pi\)
\(374\) 1664.00 2882.13i 0.230063 0.398480i
\(375\) 0 0
\(376\) 0 0
\(377\) 1900.00 0.259562
\(378\) 0 0
\(379\) 7900.00 1.07070 0.535351 0.844630i \(-0.320179\pi\)
0.535351 + 0.844630i \(0.320179\pi\)
\(380\) 2000.00 + 3464.10i 0.269994 + 0.467644i
\(381\) 0 0
\(382\) 7544.00 13066.6i 1.01043 1.75012i
\(383\) 3759.00 6510.78i 0.501504 0.868630i −0.498495 0.866893i \(-0.666114\pi\)
0.999998 0.00173723i \(-0.000552976\pi\)
\(384\) 0 0
\(385\) 480.000 + 831.384i 0.0635404 + 0.110055i
\(386\) 1432.00 0.188826
\(387\) 0 0
\(388\) 3088.00 0.404045
\(389\) 975.000 + 1688.75i 0.127081 + 0.220111i 0.922544 0.385891i \(-0.126106\pi\)
−0.795464 + 0.606001i \(0.792773\pi\)
\(390\) 0 0
\(391\) 1014.00 1756.30i 0.131151 0.227161i
\(392\) 0 0
\(393\) 0 0
\(394\) −4428.00 7669.52i −0.566191 0.980672i
\(395\) −3000.00 −0.382143
\(396\) 0 0
\(397\) 13786.0 1.74282 0.871410 0.490555i \(-0.163206\pi\)
0.871410 + 0.490555i \(0.163206\pi\)
\(398\) −5200.00 9006.66i −0.654906 1.13433i
\(399\) 0 0
\(400\) 800.000 1385.64i 0.100000 0.173205i
\(401\) −3201.00 + 5544.29i −0.398629 + 0.690446i −0.993557 0.113333i \(-0.963847\pi\)
0.594928 + 0.803779i \(0.297181\pi\)
\(402\) 0 0
\(403\) −2052.00 3554.17i −0.253641 0.439319i
\(404\) 5616.00 0.691600
\(405\) 0 0
\(406\) 1200.00 0.146687
\(407\) −4256.00 7371.61i −0.518334 0.897781i
\(408\) 0 0
\(409\) −5575.00 + 9656.18i −0.674000 + 1.16740i 0.302760 + 0.953067i \(0.402092\pi\)
−0.976760 + 0.214335i \(0.931241\pi\)
\(410\) −220.000 + 381.051i −0.0265001 + 0.0458995i
\(411\) 0 0
\(412\) 2392.00 + 4143.07i 0.286032 + 0.495423i
\(413\) 3000.00 0.357434
\(414\) 0 0
\(415\) −1410.00 −0.166781
\(416\) 4864.00 + 8424.70i 0.573263 + 0.992920i
\(417\) 0 0
\(418\) 6400.00 11085.1i 0.748886 1.29711i
\(419\) 6850.00 11864.5i 0.798674 1.38334i −0.121806 0.992554i \(-0.538869\pi\)
0.920480 0.390790i \(-0.127798\pi\)
\(420\) 0 0
\(421\) 2719.00 + 4709.45i 0.314765 + 0.545189i 0.979387 0.201991i \(-0.0647410\pi\)
−0.664623 + 0.747179i \(0.731408\pi\)
\(422\) 4672.00 0.538932
\(423\) 0 0
\(424\) 0 0
\(425\) −325.000 562.917i −0.0370937 0.0642481i
\(426\) 0 0
\(427\) 1554.00 2691.61i 0.176120 0.305049i
\(428\) 4776.00 8272.27i 0.539385 0.934242i
\(429\) 0 0
\(430\) −4420.00 7655.66i −0.495701 0.858579i
\(431\) 7692.00 0.859653 0.429827 0.902911i \(-0.358575\pi\)
0.429827 + 0.902911i \(0.358575\pi\)
\(432\) 0 0
\(433\) −1118.00 −0.124082 −0.0620412 0.998074i \(-0.519761\pi\)
−0.0620412 + 0.998074i \(0.519761\pi\)
\(434\) −1296.00 2244.74i −0.143341 0.248274i
\(435\) 0 0
\(436\) 2200.00 3810.51i 0.241653 0.418556i
\(437\) 3900.00 6755.00i 0.426916 0.739440i
\(438\) 0 0
\(439\) 1300.00 + 2251.67i 0.141334 + 0.244798i 0.927999 0.372582i \(-0.121528\pi\)
−0.786665 + 0.617380i \(0.788194\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3952.00 0.425288
\(443\) 5979.00 + 10355.9i 0.641243 + 1.11067i 0.985155 + 0.171664i \(0.0549145\pi\)
−0.343912 + 0.939002i \(0.611752\pi\)
\(444\) 0 0
\(445\) −375.000 + 649.519i −0.0399477 + 0.0691914i
\(446\) −12956.0 + 22440.5i −1.37553 + 2.38248i
\(447\) 0 0
\(448\) 1536.00 + 2660.43i 0.161985 + 0.280566i
\(449\) −17050.0 −1.79207 −0.896035 0.443984i \(-0.853565\pi\)
−0.896035 + 0.443984i \(0.853565\pi\)
\(450\) 0 0
\(451\) 704.000 0.0735035
\(452\) −6248.00 10821.9i −0.650180 1.12614i
\(453\) 0 0
\(454\) 1292.00 2237.81i 0.133561 0.231334i
\(455\) −570.000 + 987.269i −0.0587297 + 0.101723i
\(456\) 0 0
\(457\) 4747.00 + 8222.05i 0.485898 + 0.841600i 0.999869 0.0162080i \(-0.00515939\pi\)
−0.513971 + 0.857808i \(0.671826\pi\)
\(458\) −15000.0 −1.53036
\(459\) 0 0
\(460\) 3120.00 0.316241
\(461\) 5709.00 + 9888.28i 0.576778 + 0.999009i 0.995846 + 0.0910539i \(0.0290235\pi\)
−0.419068 + 0.907955i \(0.637643\pi\)
\(462\) 0 0
\(463\) −3981.00 + 6895.29i −0.399596 + 0.692120i −0.993676 0.112286i \(-0.964183\pi\)
0.594080 + 0.804406i \(0.297516\pi\)
\(464\) −1600.00 + 2771.28i −0.160082 + 0.277270i
\(465\) 0 0
\(466\) 2964.00 + 5133.80i 0.294645 + 0.510340i
\(467\) 6526.00 0.646654 0.323327 0.946287i \(-0.395199\pi\)
0.323327 + 0.946287i \(0.395199\pi\)
\(468\) 0 0
\(469\) 756.000 0.0744325
\(470\) 5140.00 + 8902.74i 0.504448 + 0.873729i
\(471\) 0 0
\(472\) 0 0
\(473\) −7072.00 + 12249.1i −0.687465 + 1.19072i
\(474\) 0 0
\(475\) −1250.00 2165.06i −0.120745 0.209137i
\(476\) 1248.00 0.120172
\(477\) 0 0
\(478\) −5600.00 −0.535854
\(479\) −8700.00 15068.8i −0.829881 1.43740i −0.898131 0.439728i \(-0.855075\pi\)
0.0682495 0.997668i \(-0.478259\pi\)
\(480\) 0 0
\(481\) 5054.00 8753.78i 0.479091 0.829809i
\(482\) 6044.00 10468.5i 0.571155 0.989269i
\(483\) 0 0
\(484\) 1228.00 + 2126.96i 0.115327 + 0.199752i
\(485\) −1930.00 −0.180694
\(486\) 0 0
\(487\) 1166.00 0.108494 0.0542469 0.998528i \(-0.482724\pi\)
0.0542469 + 0.998528i \(0.482724\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 3070.00 5317.40i 0.283038 0.490236i
\(491\) −3536.00 + 6124.53i −0.325005 + 0.562925i −0.981513 0.191394i \(-0.938699\pi\)
0.656508 + 0.754319i \(0.272033\pi\)
\(492\) 0 0
\(493\) 650.000 + 1125.83i 0.0593804 + 0.102850i
\(494\) 15200.0 1.38437
\(495\) 0 0
\(496\) 6912.00 0.625722
\(497\) −1236.00 2140.81i −0.111554 0.193217i
\(498\) 0 0
\(499\) −50.0000 + 86.6025i −0.00448559 + 0.00776926i −0.868259 0.496110i \(-0.834761\pi\)
0.863774 + 0.503880i \(0.168094\pi\)
\(500\) 500.000 866.025i 0.0447214 0.0774597i
\(501\) 0 0
\(502\) −2496.00 4323.20i −0.221916 0.384370i
\(503\) 2602.00 0.230651 0.115325 0.993328i \(-0.463209\pi\)
0.115325 + 0.993328i \(0.463209\pi\)
\(504\) 0 0
\(505\) −3510.00 −0.309293
\(506\) −4992.00 8646.40i −0.438580 0.759643i
\(507\) 0 0
\(508\) −7384.00 + 12789.5i −0.644906 + 1.11701i
\(509\) −5575.00 + 9656.18i −0.485476 + 0.840870i −0.999861 0.0166899i \(-0.994687\pi\)
0.514384 + 0.857560i \(0.328021\pi\)
\(510\) 0 0
\(511\) 2634.00 + 4562.22i 0.228026 + 0.394953i
\(512\) −16384.0 −1.41421
\(513\) 0 0
\(514\) −8424.00 −0.722892
\(515\) −1495.00 2589.42i −0.127918 0.221560i
\(516\) 0 0
\(517\) 8224.00 14244.4i 0.699596 1.21174i
\(518\) 3192.00 5528.71i 0.270750 0.468953i
\(519\) 0 0
\(520\) 0 0
\(521\) −3638.00 −0.305919 −0.152959 0.988232i \(-0.548880\pi\)
−0.152959 + 0.988232i \(0.548880\pi\)
\(522\) 0 0
\(523\) −2078.00 −0.173737 −0.0868686 0.996220i \(-0.527686\pi\)
−0.0868686 + 0.996220i \(0.527686\pi\)
\(524\) 8832.00 + 15297.5i 0.736312 + 1.27533i
\(525\) 0 0
\(526\) −7276.00 + 12602.4i −0.603134 + 1.04466i
\(527\) 1404.00 2431.80i 0.116052 0.201007i
\(528\) 0 0
\(529\) 3041.50 + 5268.03i 0.249979 + 0.432977i
\(530\) 40.0000 0.00327828
\(531\) 0 0
\(532\) 4800.00 0.391177
\(533\) 418.000 + 723.997i 0.0339692 + 0.0588364i
\(534\) 0 0
\(535\) −2985.00 + 5170.17i −0.241220 + 0.417806i
\(536\) 0 0
\(537\) 0 0
\(538\) −13100.0 22689.9i −1.04978 1.81827i
\(539\) −9824.00 −0.785064
\(540\) 0 0
\(541\) 5622.00 0.446781 0.223391 0.974729i \(-0.428287\pi\)
0.223391 + 0.974729i \(0.428287\pi\)
\(542\) −8776.00 15200.5i −0.695501 1.20464i
\(543\) 0 0
\(544\) −3328.00 + 5764.27i −0.262292 + 0.454303i
\(545\) −1375.00 + 2381.57i −0.108071 + 0.187184i
\(546\) 0 0
\(547\) −8243.00 14277.3i −0.644324 1.11600i −0.984457 0.175625i \(-0.943805\pi\)
0.340133 0.940377i \(-0.389528\pi\)
\(548\) −18672.0 −1.45553
\(549\) 0 0
\(550\) −3200.00 −0.248088
\(551\) 2500.00 + 4330.13i 0.193291 + 0.334791i
\(552\) 0 0
\(553\) −1800.00 + 3117.69i −0.138416 + 0.239743i
\(554\) 1092.00 1891.40i 0.0837448 0.145050i
\(555\) 0 0
\(556\) 2800.00 + 4849.74i 0.213573 + 0.369919i
\(557\) 11706.0 0.890483 0.445242 0.895410i \(-0.353118\pi\)
0.445242 + 0.895410i \(0.353118\pi\)
\(558\) 0 0
\(559\) −16796.0 −1.27083
\(560\) −960.000 1662.77i −0.0724418 0.125473i
\(561\) 0 0
\(562\) −13716.0 + 23756.8i −1.02949 + 1.78313i
\(563\) 12519.0 21683.5i 0.937146 1.62318i 0.166383 0.986061i \(-0.446791\pi\)
0.770763 0.637123i \(-0.219875\pi\)
\(564\) 0 0
\(565\) 3905.00 + 6763.66i 0.290769 + 0.503627i
\(566\) −37128.0 −2.75725
\(567\) 0 0
\(568\) 0 0
\(569\) −8775.00 15198.7i −0.646515 1.11980i −0.983949 0.178448i \(-0.942892\pi\)
0.337434 0.941349i \(-0.390441\pi\)
\(570\) 0 0
\(571\) −5356.00 + 9276.86i −0.392542 + 0.679903i −0.992784 0.119915i \(-0.961738\pi\)
0.600242 + 0.799819i \(0.295071\pi\)
\(572\) 4864.00 8424.70i 0.355549 0.615829i
\(573\) 0 0
\(574\) 264.000 + 457.261i 0.0191971 + 0.0332504i
\(575\) −1950.00 −0.141427
\(576\) 0 0
\(577\) −13654.0 −0.985136 −0.492568 0.870274i \(-0.663942\pi\)
−0.492568 + 0.870274i \(0.663942\pi\)
\(578\) −8474.00 14677.4i −0.609813 1.05623i
\(579\) 0 0
\(580\) −1000.00 + 1732.05i −0.0715909 + 0.123999i
\(581\) −846.000 + 1465.31i −0.0604096 + 0.104633i
\(582\) 0 0
\(583\) −32.0000 55.4256i −0.00227325 0.00393738i
\(584\) 0 0
\(585\) 0 0
\(586\) −19368.0 −1.36533
\(587\) −7083.00 12268.1i −0.498035 0.862622i 0.501962 0.864890i \(-0.332612\pi\)
−0.999997 + 0.00226720i \(0.999278\pi\)
\(588\) 0 0
\(589\) 5400.00 9353.07i 0.377764 0.654307i
\(590\) −5000.00 + 8660.25i −0.348893 + 0.604300i
\(591\) 0 0
\(592\) 8512.00 + 14743.2i 0.590948 + 1.02355i
\(593\) 17842.0 1.23555 0.617777 0.786354i \(-0.288034\pi\)
0.617777 + 0.786354i \(0.288034\pi\)
\(594\) 0 0
\(595\) −780.000 −0.0537427
\(596\) −8200.00 14202.8i −0.563566 0.976124i
\(597\) 0 0
\(598\) 5928.00 10267.6i 0.405374 0.702129i
\(599\) 8800.00 15242.0i 0.600264 1.03969i −0.392517 0.919745i \(-0.628395\pi\)
0.992781 0.119943i \(-0.0382712\pi\)
\(600\) 0 0
\(601\) −13651.0 23644.2i −0.926516 1.60477i −0.789105 0.614258i \(-0.789455\pi\)
−0.137410 0.990514i \(-0.543878\pi\)
\(602\) −10608.0 −0.718189
\(603\) 0 0
\(604\) 14816.0 0.998103
\(605\) −767.500 1329.35i −0.0515757 0.0893318i
\(606\) 0 0
\(607\) 1897.00 3285.70i 0.126848 0.219708i −0.795606 0.605815i \(-0.792847\pi\)
0.922454 + 0.386107i \(0.126181\pi\)
\(608\) −12800.0 + 22170.3i −0.853797 + 1.47882i
\(609\) 0 0
\(610\) 5180.00 + 8972.02i 0.343823 + 0.595519i
\(611\) 19532.0 1.29326
\(612\) 0 0
\(613\) −13238.0 −0.872231 −0.436116 0.899891i \(-0.643646\pi\)
−0.436116 + 0.899891i \(0.643646\pi\)
\(614\) −5188.00 8985.88i −0.340995 0.590620i
\(615\) 0 0
\(616\) 0 0
\(617\) 5787.00 10023.4i 0.377595 0.654013i −0.613117 0.789992i \(-0.710085\pi\)
0.990712 + 0.135979i \(0.0434180\pi\)
\(618\) 0 0
\(619\) −4150.00 7188.01i −0.269471 0.466738i 0.699254 0.714873i \(-0.253516\pi\)
−0.968725 + 0.248135i \(0.920182\pi\)
\(620\) 4320.00 0.279831
\(621\) 0 0
\(622\) −29328.0 −1.89059
\(623\) 450.000 + 779.423i 0.0289388 + 0.0501235i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 3124.00 5410.93i 0.199457 0.345470i
\(627\) 0 0
\(628\) 9976.00 + 17278.9i 0.633894 + 1.09794i
\(629\) 6916.00 0.438409
\(630\) 0 0
\(631\) −7508.00 −0.473675 −0.236837 0.971549i \(-0.576111\pi\)
−0.236837 + 0.971549i \(0.576111\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2852.00 4939.81i 0.178655 0.309440i
\(635\) 4615.00 7993.41i 0.288411 0.499542i
\(636\) 0 0
\(637\) −5833.00 10103.1i −0.362813 0.628411i
\(638\) 6400.00 0.397145
\(639\) 0 0
\(640\) 0 0
\(641\) 13689.0 + 23710.0i 0.843499 + 1.46098i 0.886918 + 0.461927i \(0.152842\pi\)
−0.0434190 + 0.999057i \(0.513825\pi\)
\(642\) 0 0
\(643\) −921.000 + 1595.22i −0.0564863 + 0.0978372i −0.892886 0.450283i \(-0.851323\pi\)
0.836400 + 0.548120i \(0.184656\pi\)
\(644\) 1872.00 3242.40i 0.114545 0.198398i
\(645\) 0 0
\(646\) 5200.00 + 9006.66i 0.316705 + 0.548549i
\(647\) −10114.0 −0.614563 −0.307282 0.951619i \(-0.599419\pi\)
−0.307282 + 0.951619i \(0.599419\pi\)
\(648\) 0 0
\(649\) 16000.0 0.967727
\(650\) −1900.00 3290.90i −0.114653 0.198584i
\(651\) 0 0
\(652\) −11048.0 + 19135.7i −0.663609 + 1.14940i
\(653\) −5201.00 + 9008.40i −0.311686 + 0.539856i −0.978727 0.205165i \(-0.934227\pi\)
0.667042 + 0.745020i \(0.267560\pi\)
\(654\) 0 0
\(655\) −5520.00 9560.92i −0.329289 0.570345i
\(656\) −1408.00 −0.0838006
\(657\) 0 0
\(658\) 12336.0 0.730862
\(659\) −3550.00 6148.78i −0.209846 0.363464i 0.741820 0.670599i \(-0.233963\pi\)
−0.951666 + 0.307135i \(0.900630\pi\)
\(660\) 0 0
\(661\) 3559.00 6164.37i 0.209424 0.362732i −0.742109 0.670279i \(-0.766175\pi\)
0.951533 + 0.307546i \(0.0995079\pi\)
\(662\) −8016.00 + 13884.1i −0.470620 + 0.815138i
\(663\) 0 0
\(664\) 0 0
\(665\) −3000.00 −0.174940
\(666\) 0 0
\(667\) 3900.00 0.226400
\(668\) −12504.0 21657.6i −0.724243 1.25443i
\(669\) 0 0
\(670\) −1260.00 + 2182.38i −0.0726538 + 0.125840i
\(671\) 8288.00 14355.2i 0.476833 0.825898i
\(672\) 0 0
\(673\) 15639.0 + 27087.5i 0.895749 + 1.55148i 0.832875 + 0.553462i \(0.186693\pi\)
0.0628744 + 0.998021i \(0.479973\pi\)
\(674\) −35464.0 −2.02674
\(675\) 0 0
\(676\) −6024.00 −0.342740
\(677\) 15027.0 + 26027.5i 0.853079 + 1.47758i 0.878416 + 0.477897i \(0.158601\pi\)
−0.0253367 + 0.999679i \(0.508066\pi\)
\(678\) 0 0
\(679\) −1158.00 + 2005.71i −0.0654491 + 0.113361i
\(680\) 0 0
\(681\) 0 0
\(682\) −6912.00 11971.9i −0.388085 0.672183i
\(683\) −4518.00 −0.253113 −0.126557 0.991959i \(-0.540393\pi\)
−0.126557 + 0.991959i \(0.540393\pi\)
\(684\) 0 0
\(685\) 11670.0 0.650931
\(686\) −7800.00 13510.0i −0.434119 0.751916i
\(687\) 0 0
\(688\) 14144.0 24498.1i 0.783772 1.35753i
\(689\) 38.0000 65.8179i 0.00210114 0.00363928i
\(690\) 0 0
\(691\) −14636.0 25350.3i −0.805759 1.39562i −0.915777 0.401686i \(-0.868424\pi\)
0.110018 0.993930i \(-0.464909\pi\)
\(692\) −624.000 −0.0342788
\(693\) 0 0
\(694\) 6856.00 0.375000
\(695\) −1750.00 3031.09i −0.0955126 0.165433i
\(696\) 0 0
\(697\) −286.000 + 495.367i −0.0155424 + 0.0269202i
\(698\) 2300.00 3983.72i 0.124722 0.216026i
\(699\) 0 0
\(700\) −600.000 1039.23i −0.0323970 0.0561132i
\(701\) −5798.00 −0.312393 −0.156196 0.987726i \(-0.549923\pi\)
−0.156196 + 0.987726i \(0.549923\pi\)
\(702\) 0 0
\(703\) 26600.0 1.42708
\(704\) 8192.00 + 14189.0i 0.438562 + 0.759612i
\(705\) 0 0
\(706\) −8796.00 + 15235.1i −0.468898 + 0.812155i
\(707\) −2106.00 + 3647.70i −0.112029 + 0.194039i
\(708\) 0 0
\(709\) −4475.00 7750.93i −0.237041 0.410567i 0.722823 0.691033i \(-0.242844\pi\)
−0.959864 + 0.280466i \(0.909511\pi\)
\(710\) 8240.00 0.435552
\(711\) 0 0
\(712\) 0 0
\(713\) −4212.00 7295.40i −0.221235 0.383190i
\(714\) 0 0
\(715\) −3040.00 + 5265.43i −0.159006 + 0.275407i
\(716\) 5200.00 9006.66i 0.271415 0.470105i
\(717\) 0 0
\(718\) 3600.00 + 6235.38i 0.187118 + 0.324098i
\(719\) 7800.00 0.404577 0.202289 0.979326i \(-0.435162\pi\)
0.202289 + 0.979326i \(0.435162\pi\)
\(720\) 0 0
\(721\) −3588.00 −0.185332
\(722\) 6282.00 + 10880.7i 0.323811 + 0.560858i
\(723\) 0 0
\(724\) −6968.00 + 12068.9i −0.357685 + 0.619528i
\(725\) 625.000 1082.53i 0.0320164 0.0554541i
\(726\) 0 0
\(727\) 4277.00 + 7407.98i 0.218191 + 0.377919i 0.954255 0.298994i \(-0.0966510\pi\)
−0.736064 + 0.676912i \(0.763318\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −17560.0 −0.890308
\(731\) −5746.00 9952.36i −0.290730 0.503559i
\(732\) 0 0
\(733\) −1441.00 + 2495.89i −0.0726119 + 0.125768i −0.900045 0.435796i \(-0.856467\pi\)
0.827433 + 0.561564i \(0.189800\pi\)
\(734\) −11748.0 + 20348.1i −0.590772 + 1.02325i
\(735\) 0 0
\(736\) 9984.00 + 17292.8i 0.500021 + 0.866061i
\(737\) 4032.00 0.201521
\(738\) 0 0
\(739\) 18700.0 0.930840 0.465420 0.885090i \(-0.345903\pi\)
0.465420 + 0.885090i \(0.345903\pi\)
\(740\) 5320.00 + 9214.51i 0.264280 + 0.457746i
\(741\) 0 0
\(742\) 24.0000 41.5692i 0.00118742 0.00205668i
\(743\) −6121.00 + 10601.9i −0.302231 + 0.523480i −0.976641 0.214878i \(-0.931065\pi\)
0.674410 + 0.738357i \(0.264398\pi\)
\(744\) 0 0
\(745\) 5125.00 + 8876.76i 0.252034 + 0.436536i
\(746\) 8312.00 0.407941
\(747\) 0 0
\(748\) 6656.00 0.325358
\(749\) 3582.00 + 6204.21i 0.174744 + 0.302666i
\(750\) 0 0
\(751\) 15574.0 26975.0i 0.756729 1.31069i −0.187781 0.982211i \(-0.560130\pi\)
0.944510 0.328482i \(-0.106537\pi\)
\(752\) −16448.0 + 28488.8i −0.797602 + 1.38149i
\(753\) 0 0
\(754\) 3800.00 + 6581.79i 0.183538 + 0.317898i
\(755\) −9260.00 −0.446365
\(756\) 0 0
\(757\) −7694.00 −0.369410 −0.184705 0.982794i \(-0.559133\pi\)
−0.184705 + 0.982794i \(0.559133\pi\)
\(758\) 15800.0 + 27366.4i 0.757100 + 1.31134i
\(759\) 0 0
\(760\) 0 0
\(761\) 2259.00 3912.70i 0.107607 0.186380i −0.807194 0.590287i \(-0.799015\pi\)
0.914800 + 0.403907i \(0.132348\pi\)
\(762\) 0 0
\(763\) 1650.00 + 2857.88i 0.0782883 + 0.135599i
\(764\) 30176.0 1.42897
\(765\) 0 0
\(766\) 30072.0 1.41847
\(767\) 9500.00 + 16454.5i 0.447230 + 0.774624i
\(768\) 0 0
\(769\) 19775.0 34251.3i 0.927314 1.60616i 0.139518 0.990220i \(-0.455445\pi\)
0.787796 0.615936i \(-0.211222\pi\)
\(770\) −1920.00 + 3325.54i −0.0898597 + 0.155642i
\(771\) 0 0
\(772\) 1432.00 + 2480.30i 0.0667601 + 0.115632i
\(773\) 22122.0 1.02933 0.514666 0.857391i \(-0.327916\pi\)
0.514666 + 0.857391i \(0.327916\pi\)
\(774\) 0 0
\(775\) −2700.00 −0.125144
\(776\) 0 0
\(777\) 0 0
\(778\) −3900.00 + 6755.00i −0.179720 + 0.311283i
\(779\) −1100.00 + 1905.26i −0.0505925 + 0.0876289i
\(780\) 0 0
\(781\) −6592.00 11417.7i −0.302023 0.523120i
\(782\) 8112.00 0.370952
\(783\) 0 0
\(784\) 19648.0 0.895044
\(785\) −6235.00 10799.3i −0.283486 0.491013i
\(786\) 0 0
\(787\) 8317.00 14405.5i 0.376708 0.652477i −0.613873 0.789405i \(-0.710389\pi\)
0.990581 + 0.136928i \(0.0437228\pi\)
\(788\) 8856.00 15339.0i 0.400358 0.693440i
\(789\) 0 0
\(790\) −6000.00 10392.3i −0.270216 0.468027i
\(791\) 9372.00 0.421277
\(792\) 0 0
\(793\) 19684.0 0.881462
\(794\) 27572.0 + 47756.1i 1.23236 + 2.13451i
\(795\) 0 0
\(796\) 10400.0 18013.3i 0.463088 0.802092i
\(797\) −13793.0 + 23890.2i −0.613015 + 1.06177i 0.377714 + 0.925922i \(0.376710\pi\)
−0.990729 + 0.135851i \(0.956623\pi\)
\(798\) 0 0
\(799\) 6682.00 + 11573.6i 0.295860 + 0.512445i
\(800\) 6400.00 0.282843
\(801\) 0 0
\(802\) −25608.0 −1.12749
\(803\) 14048.0 + 24331.8i 0.617364 + 1.06931i
\(804\) 0 0
\(805\) −1170.00 + 2026.50i −0.0512262 + 0.0887264i
\(806\) 8208.00 14216.7i 0.358703 0.621292i
\(807\) 0 0
\(808\) 0 0
\(809\) 3850.00 0.167316 0.0836581 0.996495i \(-0.473340\pi\)
0.0836581 + 0.996495i \(0.473340\pi\)
\(810\) 0 0
\(811\) 10032.0 0.434366 0.217183 0.976131i \(-0.430313\pi\)
0.217183 + 0.976131i \(0.430313\pi\)
\(812\) 1200.00 + 2078.46i 0.0518618 + 0.0898272i
\(813\) 0 0
\(814\) 17024.0 29486.4i 0.733035 1.26965i
\(815\) 6905.00 11959.8i 0.296775 0.514029i
\(816\) 0 0
\(817\) −22100.0 38278.3i −0.946366 1.63915i
\(818\) −44600.0 −1.90636
\(819\) 0 0
\(820\) −880.000 −0.0374767
\(821\) −10281.0 17807.2i −0.437039 0.756975i 0.560420 0.828208i \(-0.310640\pi\)
−0.997460 + 0.0712339i \(0.977306\pi\)
\(822\) 0 0
\(823\) −5161.00 + 8939.11i −0.218592 + 0.378612i −0.954378 0.298602i \(-0.903480\pi\)
0.735786 + 0.677214i \(0.236813\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 6000.00 + 10392.3i 0.252744 + 0.437766i
\(827\) 8846.00 0.371954 0.185977 0.982554i \(-0.440455\pi\)
0.185977 + 0.982554i \(0.440455\pi\)
\(828\) 0 0
\(829\) −25350.0 −1.06205 −0.531026 0.847355i \(-0.678194\pi\)
−0.531026 + 0.847355i \(0.678194\pi\)
\(830\) −2820.00 4884.38i −0.117932 0.204264i
\(831\) 0 0
\(832\) −9728.00 + 16849.4i −0.405358 + 0.702100i
\(833\) 3991.00 6912.61i 0.166002 0.287524i
\(834\) 0 0
\(835\) 7815.00 + 13536.0i 0.323891 + 0.560996i
\(836\) 25600.0 1.05908
\(837\) 0 0
\(838\) 54800.0 2.25899
\(839\) −23000.0 39837.2i −0.946422 1.63925i −0.752878 0.658160i \(-0.771335\pi\)
−0.193544 0.981092i \(-0.561998\pi\)
\(840\) 0 0
\(841\) 10944.5 18956.4i 0.448747 0.777253i
\(842\) −10876.0 + 18837.8i −0.445145 + 0.771013i
\(843\) 0 0
\(844\) 4672.00 + 8092.14i 0.190541 + 0.330027i
\(845\) 3765.00 0.153278
\(846\) 0 0
\(847\) −1842.00 −0.0747248
\(848\) 64.0000 + 110.851i 0.00259171 + 0.00448897i
\(849\) 0 0
\(850\) 1300.00 2251.67i 0.0524584 0.0908606i
\(851\) 10374.0 17968.3i 0.417880 0.723790i
\(852\) 0 0
\(853\) 8499.00 + 14720.7i 0.341149 + 0.590888i 0.984646 0.174561i \(-0.0558505\pi\)
−0.643497 + 0.765448i \(0.722517\pi\)
\(854\) 12432.0 0.498143
\(855\) 0 0
\(856\) 0 0
\(857\) 13247.0 + 22944.5i 0.528015 + 0.914549i 0.999467 + 0.0326569i \(0.0103969\pi\)
−0.471452 + 0.881892i \(0.656270\pi\)
\(858\) 0 0
\(859\) 10750.0 18619.5i 0.426991 0.739570i −0.569613 0.821913i \(-0.692907\pi\)
0.996604 + 0.0823429i \(0.0262403\pi\)
\(860\) 8840.00 15311.3i 0.350513 0.607107i
\(861\) 0 0
\(862\) 15384.0 + 26645.9i 0.607867 + 1.05286i
\(863\) 25762.0 1.01616 0.508082 0.861309i \(-0.330355\pi\)
0.508082 + 0.861309i \(0.330355\pi\)
\(864\) 0 0
\(865\) 390.000 0.0153299
\(866\) −2236.00 3872.87i −0.0877395 0.151969i
\(867\) 0 0
\(868\) 2592.00 4489.48i 0.101357 0.175556i
\(869\) −9600.00 + 16627.7i −0.374750 + 0.649086i
\(870\) 0 0
\(871\) 2394.00 + 4146.53i 0.0931316 + 0.161309i
\(872\) 0 0
\(873\) 0 0
\(874\) 31200.0 1.20750
\(875\) 375.000 + 649.519i 0.0144884 + 0.0250946i
\(876\) 0 0
\(877\) −15273.0 + 26453.6i −0.588064 + 1.01856i 0.406421 + 0.913686i \(0.366777\pi\)
−0.994486 + 0.104872i \(0.966557\pi\)
\(878\) −5200.00 + 9006.66i −0.199876 + 0.346196i
\(879\) 0 0
\(880\) −5120.00 8868.10i −0.196131 0.339709i
\(881\) 32942.0 1.25976 0.629878 0.776694i \(-0.283105\pi\)
0.629878 + 0.776694i \(0.283105\pi\)
\(882\) 0 0
\(883\) −27118.0 −1.03351 −0.516757 0.856132i \(-0.672861\pi\)
−0.516757 + 0.856132i \(0.672861\pi\)
\(884\) 3952.00 + 6845.06i 0.150362 + 0.260435i
\(885\) 0 0
\(886\) −23916.0 + 41423.7i −0.906855 + 1.57072i
\(887\) 19317.0 33458.0i 0.731230 1.26653i −0.225127 0.974329i \(-0.572280\pi\)
0.956358 0.292199i \(-0.0943869\pi\)
\(888\) 0 0
\(889\) −5538.00 9592.10i −0.208930 0.361877i
\(890\) −3000.00 −0.112989
\(891\) 0 0
\(892\) −51824.0 −1.94529
\(893\) 25700.0 + 44513.7i 0.963066 + 1.66808i
\(894\) 0 0
\(895\) −3250.00 + 5629.17i −0.121380 + 0.210237i
\(896\) 0 0
\(897\) 0 0
\(898\) −34100.0 59062.9i −1.26718 2.19483i
\(899\) 5400.00 0.200334
\(900\) 0 0
\(901\) 52.0000 0.00192272
\(902\) 1408.00 + 2438.73i 0.0519748 + 0.0900230i
\(903\) 0 0
\(904\) 0 0
\(905\) 4355.00 7543.08i 0.159961 0.277061i
\(906\) 0 0
\(907\) 897.000 + 1553.65i 0.0328384 + 0.0568777i 0.881978 0.471291i \(-0.156212\pi\)
−0.849139 + 0.528169i \(0.822879\pi\)
\(908\) 5168.00 0.188883
\(909\) 0 0
\(910\) −4560.00 −0.166113
\(911\) −20866.0 36141.0i −0.758860 1.31438i −0.943432 0.331565i \(-0.892423\pi\)
0.184572 0.982819i \(-0.440910\pi\)
\(912\) 0 0
\(913\) −4512.00 + 7815.01i −0.163555 + 0.283285i
\(914\) −18988.0 + 32888.2i −0.687163 + 1.19020i
\(915\) 0 0
\(916\) −15000.0 25980.8i −0.541063 0.937149i
\(917\) −13248.0 −0.477086
\(918\) 0 0
\(919\) 29200.0 1.04812 0.524058 0.851682i \(-0.324417\pi\)
0.524058 + 0.851682i \(0.324417\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −22836.0 + 39553.1i −0.815687 + 1.41281i
\(923\) 7828.00 13558.5i 0.279157 0.483514i
\(924\) 0 0
\(925\) −3325.00 5759.07i −0.118190 0.204710i
\(926\) −31848.0 −1.13023
\(927\) 0 0
\(928\) −12800.0 −0.452781
\(929\) 24325.0 + 42132.1i 0.859071 + 1.48796i 0.872816 + 0.488050i \(0.162292\pi\)
−0.0137443 + 0.999906i \(0.504375\pi\)
\(930\) 0 0
\(931\) 15350.0 26587.0i 0.540361 0.935932i
\(932\) −5928.00 + 10267.6i −0.208346 + 0.360865i
\(933\) 0 0
\(934\) 13052.0 + 22606.7i 0.457253 + 0.791986i
\(935\) −4160.00 −0.145504
\(936\) 0 0
\(937\) −11334.0 −0.395161 −0.197580 0.980287i \(-0.563308\pi\)
−0.197580 + 0.980287i \(0.563308\pi\)
\(938\) 1512.00 + 2618.86i 0.0526317 + 0.0911608i
\(939\) 0 0
\(940\) −10280.0 + 17805.5i −0.356699 + 0.617820i
\(941\) 15589.0 27000.9i 0.540050 0.935394i −0.458851 0.888513i \(-0.651739\pi\)
0.998901 0.0468803i \(-0.0149279\pi\)
\(942\) 0 0
\(943\) 858.000 + 1486.10i 0.0296292 + 0.0513193i
\(944\) −32000.0 −1.10330
\(945\) 0 0
\(946\) −56576.0 −1.94444
\(947\) −2343.00 4058.20i −0.0803984 0.139254i 0.823023 0.568008i \(-0.192286\pi\)
−0.903421 + 0.428754i \(0.858953\pi\)
\(948\) 0 0
\(949\) −16682.0 + 28894.1i −0.570622 + 0.988347i
\(950\) 5000.00 8660.25i 0.170759 0.295764i
\(951\) 0 0
\(952\) 0 0
\(953\) −598.000 −0.0203265 −0.0101632 0.999948i \(-0.503235\pi\)
−0.0101632 + 0.999948i \(0.503235\pi\)
\(954\) 0 0
\(955\) −18860.0 −0.639053
\(956\) −5600.00 9699.48i −0.189453 0.328142i
\(957\) 0 0
\(958\) 34800.0 60275.4i 1.17363 2.03279i
\(959\) 7002.00 12127.8i 0.235773 0.408371i
\(960\) 0 0
\(961\) 9063.50 + 15698.4i 0.304236 + 0.526953i
\(962\) 40432.0 1.35507
\(963\) 0 0
\(964\) 24176.0 0.807735
\(965\) −895.000 1550.19i −0.0298560 0.0517122i
\(966\) 0 0
\(967\) −20863.0 + 36135.8i −0.693804 + 1.20170i 0.276778 + 0.960934i \(0.410733\pi\)
−0.970582 + 0.240770i \(0.922600\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −3860.00 6685.72i −0.127770 0.221305i
\(971\) 24312.0 0.803511 0.401756 0.915747i \(-0.368400\pi\)
0.401756 + 0.915747i \(0.368400\pi\)
\(972\) 0 0
\(973\) −4200.00 −0.138382
\(974\) 2332.00 + 4039.14i 0.0767167 + 0.132877i
\(975\) 0 0
\(976\) −16576.0 + 28710.5i −0.543632 + 0.941598i
\(977\) −20473.0 + 35460.3i −0.670409 + 1.16118i 0.307380 + 0.951587i \(0.400548\pi\)
−0.977788 + 0.209595i \(0.932785\pi\)
\(978\) 0 0
\(979\) 2400.00 + 4156.92i 0.0783497 + 0.135706i
\(980\) 12280.0 0.400276
\(981\) 0 0
\(982\) −28288.0 −0.919253
\(983\) −21141.0 36617.3i −0.685954 1.18811i −0.973136 0.230232i \(-0.926052\pi\)
0.287181 0.957876i \(-0.407282\pi\)
\(984\) 0 0
\(985\) −5535.00 + 9586.90i −0.179045 + 0.310116i
\(986\) −2600.00 + 4503.33i −0.0839765 + 0.145452i
\(987\) 0 0
\(988\) 15200.0 + 26327.2i 0.489450 + 0.847752i
\(989\) −34476.0 −1.10847
\(990\) 0 0
\(991\) 1172.00 0.0375679 0.0187840 0.999824i \(-0.494021\pi\)
0.0187840 + 0.999824i \(0.494021\pi\)
\(992\) 13824.0 + 23943.9i 0.442452 + 0.766349i
\(993\) 0 0
\(994\) 4944.00 8563.26i 0.157761 0.273250i
\(995\) −6500.00 + 11258.3i −0.207099 + 0.358707i
\(996\) 0 0
\(997\) 15807.0 + 27378.5i 0.502119 + 0.869696i 0.999997 + 0.00244862i \(0.000779421\pi\)
−0.497878 + 0.867247i \(0.665887\pi\)
\(998\) −400.000 −0.0126872
\(999\) 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 405.4.e.l.271.1 2
3.2 odd 2 405.4.e.c.271.1 2
9.2 odd 6 405.4.e.c.136.1 2
9.4 even 3 5.4.a.a.1.1 1
9.5 odd 6 45.4.a.d.1.1 1
9.7 even 3 inner 405.4.e.l.136.1 2
36.23 even 6 720.4.a.u.1.1 1
36.31 odd 6 80.4.a.d.1.1 1
45.4 even 6 25.4.a.c.1.1 1
45.13 odd 12 25.4.b.a.24.2 2
45.14 odd 6 225.4.a.b.1.1 1
45.22 odd 12 25.4.b.a.24.1 2
45.23 even 12 225.4.b.c.199.1 2
45.32 even 12 225.4.b.c.199.2 2
63.4 even 3 245.4.e.f.226.1 2
63.13 odd 6 245.4.a.a.1.1 1
63.31 odd 6 245.4.e.g.226.1 2
63.40 odd 6 245.4.e.g.116.1 2
63.41 even 6 2205.4.a.q.1.1 1
63.58 even 3 245.4.e.f.116.1 2
72.13 even 6 320.4.a.g.1.1 1
72.67 odd 6 320.4.a.h.1.1 1
99.76 odd 6 605.4.a.d.1.1 1
117.103 even 6 845.4.a.b.1.1 1
144.13 even 12 1280.4.d.e.641.2 2
144.67 odd 12 1280.4.d.l.641.1 2
144.85 even 12 1280.4.d.e.641.1 2
144.139 odd 12 1280.4.d.l.641.2 2
153.67 even 6 1445.4.a.a.1.1 1
171.94 odd 6 1805.4.a.h.1.1 1
180.67 even 12 400.4.c.k.49.2 2
180.103 even 12 400.4.c.k.49.1 2
180.139 odd 6 400.4.a.m.1.1 1
315.139 odd 6 1225.4.a.k.1.1 1
360.139 odd 6 1600.4.a.s.1.1 1
360.229 even 6 1600.4.a.bi.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.4.a.a.1.1 1 9.4 even 3
25.4.a.c.1.1 1 45.4 even 6
25.4.b.a.24.1 2 45.22 odd 12
25.4.b.a.24.2 2 45.13 odd 12
45.4.a.d.1.1 1 9.5 odd 6
80.4.a.d.1.1 1 36.31 odd 6
225.4.a.b.1.1 1 45.14 odd 6
225.4.b.c.199.1 2 45.23 even 12
225.4.b.c.199.2 2 45.32 even 12
245.4.a.a.1.1 1 63.13 odd 6
245.4.e.f.116.1 2 63.58 even 3
245.4.e.f.226.1 2 63.4 even 3
245.4.e.g.116.1 2 63.40 odd 6
245.4.e.g.226.1 2 63.31 odd 6
320.4.a.g.1.1 1 72.13 even 6
320.4.a.h.1.1 1 72.67 odd 6
400.4.a.m.1.1 1 180.139 odd 6
400.4.c.k.49.1 2 180.103 even 12
400.4.c.k.49.2 2 180.67 even 12
405.4.e.c.136.1 2 9.2 odd 6
405.4.e.c.271.1 2 3.2 odd 2
405.4.e.l.136.1 2 9.7 even 3 inner
405.4.e.l.271.1 2 1.1 even 1 trivial
605.4.a.d.1.1 1 99.76 odd 6
720.4.a.u.1.1 1 36.23 even 6
845.4.a.b.1.1 1 117.103 even 6
1225.4.a.k.1.1 1 315.139 odd 6
1280.4.d.e.641.1 2 144.85 even 12
1280.4.d.e.641.2 2 144.13 even 12
1280.4.d.l.641.1 2 144.67 odd 12
1280.4.d.l.641.2 2 144.139 odd 12
1445.4.a.a.1.1 1 153.67 even 6
1600.4.a.s.1.1 1 360.139 odd 6
1600.4.a.bi.1.1 1 360.229 even 6
1805.4.a.h.1.1 1 171.94 odd 6
2205.4.a.q.1.1 1 63.41 even 6