Properties

Label 304.5.r.d.145.2
Level $304$
Weight $5$
Character 304.145
Analytic conductor $31.424$
Analytic rank $0$
Dimension $40$
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] = [304,5,Mod(65,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.65");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.r (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: \(31.4244687775\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.2
Character \(\chi\) \(=\) 304.145
Dual form 304.5.r.d.65.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-13.5253 + 7.80881i) q^{3} +(14.4872 + 25.0925i) q^{5} +26.1842 q^{7} +(81.4552 - 141.085i) q^{9} +O(q^{10})\) \(q+(-13.5253 + 7.80881i) q^{3} +(14.4872 + 25.0925i) q^{5} +26.1842 q^{7} +(81.4552 - 141.085i) q^{9} -151.830 q^{11} +(25.6769 + 14.8246i) q^{13} +(-391.885 - 226.255i) q^{15} +(14.4596 + 25.0447i) q^{17} +(-348.126 - 95.5488i) q^{19} +(-354.148 + 204.468i) q^{21} +(-116.619 + 201.990i) q^{23} +(-107.255 + 185.771i) q^{25} +1279.25i q^{27} +(-1408.94 - 813.453i) q^{29} -382.463i q^{31} +(2053.54 - 1185.61i) q^{33} +(379.335 + 657.027i) q^{35} +1725.42i q^{37} -463.050 q^{39} +(2538.96 - 1465.87i) q^{41} +(264.444 + 458.031i) q^{43} +4720.21 q^{45} +(1897.52 - 3286.61i) q^{47} -1715.39 q^{49} +(-391.139 - 225.824i) q^{51} +(-2502.11 - 1444.59i) q^{53} +(-2199.58 - 3809.78i) q^{55} +(5454.61 - 1426.13i) q^{57} +(384.650 - 222.078i) q^{59} +(2706.99 - 4688.64i) q^{61} +(2132.84 - 3694.19i) q^{63} +859.064i q^{65} +(2699.23 + 1558.40i) q^{67} -3642.63i q^{69} +(380.479 - 219.670i) q^{71} +(1622.43 + 2810.13i) q^{73} -3350.14i q^{75} -3975.54 q^{77} +(2331.93 - 1346.34i) q^{79} +(-3391.52 - 5874.29i) q^{81} +9939.75 q^{83} +(-418.956 + 725.653i) q^{85} +25408.4 q^{87} +(-3521.51 - 2033.14i) q^{89} +(672.331 + 388.170i) q^{91} +(2986.59 + 5172.92i) q^{93} +(-2645.79 - 10119.6i) q^{95} +(-13922.1 + 8037.95i) q^{97} +(-12367.3 + 21420.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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
\(3\) −13.5253 + 7.80881i −1.50281 + 0.867646i −0.502812 + 0.864396i \(0.667701\pi\)
−0.999995 + 0.00325055i \(0.998965\pi\)
\(4\) 0 0
\(5\) 14.4872 + 25.0925i 0.579486 + 1.00370i 0.995538 + 0.0943585i \(0.0300800\pi\)
−0.416052 + 0.909341i \(0.636587\pi\)
\(6\) 0 0
\(7\) 26.1842 0.534372 0.267186 0.963645i \(-0.413906\pi\)
0.267186 + 0.963645i \(0.413906\pi\)
\(8\) 0 0
\(9\) 81.4552 141.085i 1.00562 1.74178i
\(10\) 0 0
\(11\) −151.830 −1.25479 −0.627395 0.778701i \(-0.715879\pi\)
−0.627395 + 0.778701i \(0.715879\pi\)
\(12\) 0 0
\(13\) 25.6769 + 14.8246i 0.151935 + 0.0877195i 0.574040 0.818827i \(-0.305375\pi\)
−0.422105 + 0.906547i \(0.638709\pi\)
\(14\) 0 0
\(15\) −391.885 226.255i −1.74171 1.00558i
\(16\) 0 0
\(17\) 14.4596 + 25.0447i 0.0500331 + 0.0866599i 0.889957 0.456044i \(-0.150734\pi\)
−0.839924 + 0.542704i \(0.817401\pi\)
\(18\) 0 0
\(19\) −348.126 95.5488i −0.964337 0.264678i
\(20\) 0 0
\(21\) −354.148 + 204.468i −0.803058 + 0.463646i
\(22\) 0 0
\(23\) −116.619 + 201.990i −0.220452 + 0.381835i −0.954945 0.296782i \(-0.904087\pi\)
0.734493 + 0.678616i \(0.237420\pi\)
\(24\) 0 0
\(25\) −107.255 + 185.771i −0.171608 + 0.297234i
\(26\) 0 0
\(27\) 1279.25i 1.75480i
\(28\) 0 0
\(29\) −1408.94 813.453i −1.67532 0.967245i −0.964581 0.263788i \(-0.915028\pi\)
−0.710737 0.703457i \(-0.751639\pi\)
\(30\) 0 0
\(31\) 382.463i 0.397985i −0.980001 0.198992i \(-0.936233\pi\)
0.980001 0.198992i \(-0.0637669\pi\)
\(32\) 0 0
\(33\) 2053.54 1185.61i 1.88571 1.08871i
\(34\) 0 0
\(35\) 379.335 + 657.027i 0.309661 + 0.536349i
\(36\) 0 0
\(37\) 1725.42i 1.26035i 0.776453 + 0.630176i \(0.217017\pi\)
−0.776453 + 0.630176i \(0.782983\pi\)
\(38\) 0 0
\(39\) −463.050 −0.304438
\(40\) 0 0
\(41\) 2538.96 1465.87i 1.51039 0.872024i 0.510463 0.859900i \(-0.329474\pi\)
0.999927 0.0121237i \(-0.00385920\pi\)
\(42\) 0 0
\(43\) 264.444 + 458.031i 0.143020 + 0.247718i 0.928633 0.371001i \(-0.120985\pi\)
−0.785612 + 0.618719i \(0.787652\pi\)
\(44\) 0 0
\(45\) 4720.21 2.33097
\(46\) 0 0
\(47\) 1897.52 3286.61i 0.858996 1.48783i −0.0138908 0.999904i \(-0.504422\pi\)
0.872887 0.487922i \(-0.162245\pi\)
\(48\) 0 0
\(49\) −1715.39 −0.714447
\(50\) 0 0
\(51\) −391.139 225.824i −0.150380 0.0868221i
\(52\) 0 0
\(53\) −2502.11 1444.59i −0.890746 0.514273i −0.0165599 0.999863i \(-0.505271\pi\)
−0.874187 + 0.485590i \(0.838605\pi\)
\(54\) 0 0
\(55\) −2199.58 3809.78i −0.727134 1.25943i
\(56\) 0 0
\(57\) 5454.61 1426.13i 1.67886 0.438943i
\(58\) 0 0
\(59\) 384.650 222.078i 0.110500 0.0637971i −0.443732 0.896160i \(-0.646346\pi\)
0.554231 + 0.832363i \(0.313012\pi\)
\(60\) 0 0
\(61\) 2706.99 4688.64i 0.727489 1.26005i −0.230453 0.973084i \(-0.574021\pi\)
0.957941 0.286964i \(-0.0926460\pi\)
\(62\) 0 0
\(63\) 2132.84 3694.19i 0.537375 0.930760i
\(64\) 0 0
\(65\) 859.064i 0.203329i
\(66\) 0 0
\(67\) 2699.23 + 1558.40i 0.601299 + 0.347160i 0.769552 0.638584i \(-0.220479\pi\)
−0.168254 + 0.985744i \(0.553813\pi\)
\(68\) 0 0
\(69\) 3642.63i 0.765098i
\(70\) 0 0
\(71\) 380.479 219.670i 0.0754769 0.0435766i −0.461787 0.886991i \(-0.652791\pi\)
0.537263 + 0.843414i \(0.319458\pi\)
\(72\) 0 0
\(73\) 1622.43 + 2810.13i 0.304453 + 0.527327i 0.977139 0.212600i \(-0.0681932\pi\)
−0.672687 + 0.739927i \(0.734860\pi\)
\(74\) 0 0
\(75\) 3350.14i 0.595580i
\(76\) 0 0
\(77\) −3975.54 −0.670525
\(78\) 0 0
\(79\) 2331.93 1346.34i 0.373646 0.215725i −0.301404 0.953497i \(-0.597455\pi\)
0.675050 + 0.737772i \(0.264122\pi\)
\(80\) 0 0
\(81\) −3391.52 5874.29i −0.516922 0.895335i
\(82\) 0 0
\(83\) 9939.75 1.44284 0.721422 0.692496i \(-0.243489\pi\)
0.721422 + 0.692496i \(0.243489\pi\)
\(84\) 0 0
\(85\) −418.956 + 725.653i −0.0579870 + 0.100436i
\(86\) 0 0
\(87\) 25408.4 3.35691
\(88\) 0 0
\(89\) −3521.51 2033.14i −0.444578 0.256677i 0.260959 0.965350i \(-0.415961\pi\)
−0.705538 + 0.708672i \(0.749294\pi\)
\(90\) 0 0
\(91\) 672.331 + 388.170i 0.0811896 + 0.0468748i
\(92\) 0 0
\(93\) 2986.59 + 5172.92i 0.345310 + 0.598094i
\(94\) 0 0
\(95\) −2645.79 10119.6i −0.293162 1.12128i
\(96\) 0 0
\(97\) −13922.1 + 8037.95i −1.47966 + 0.854283i −0.999735 0.0230249i \(-0.992670\pi\)
−0.479927 + 0.877308i \(0.659337\pi\)
\(98\) 0 0
\(99\) −12367.3 + 21420.8i −1.26184 + 2.18557i
\(100\) 0 0
\(101\) −2300.27 + 3984.19i −0.225495 + 0.390568i −0.956468 0.291838i \(-0.905733\pi\)
0.730973 + 0.682406i \(0.239067\pi\)
\(102\) 0 0
\(103\) 7603.38i 0.716691i 0.933589 + 0.358346i \(0.116659\pi\)
−0.933589 + 0.358346i \(0.883341\pi\)
\(104\) 0 0
\(105\) −10261.2 5924.31i −0.930722 0.537352i
\(106\) 0 0
\(107\) 22180.9i 1.93736i −0.248307 0.968681i \(-0.579874\pi\)
0.248307 0.968681i \(-0.420126\pi\)
\(108\) 0 0
\(109\) −2667.96 + 1540.35i −0.224557 + 0.129648i −0.608059 0.793892i \(-0.708051\pi\)
0.383501 + 0.923540i \(0.374718\pi\)
\(110\) 0 0
\(111\) −13473.5 23336.8i −1.09354 1.89406i
\(112\) 0 0
\(113\) 14436.4i 1.13058i 0.824891 + 0.565292i \(0.191237\pi\)
−0.824891 + 0.565292i \(0.808763\pi\)
\(114\) 0 0
\(115\) −6757.92 −0.510996
\(116\) 0 0
\(117\) 4183.04 2415.08i 0.305577 0.176425i
\(118\) 0 0
\(119\) 378.613 + 655.777i 0.0267363 + 0.0463086i
\(120\) 0 0
\(121\) 8411.25 0.574500
\(122\) 0 0
\(123\) −22893.4 + 39652.6i −1.51322 + 2.62097i
\(124\) 0 0
\(125\) 11893.7 0.761194
\(126\) 0 0
\(127\) −8245.29 4760.42i −0.511209 0.295147i 0.222122 0.975019i \(-0.428702\pi\)
−0.733330 + 0.679872i \(0.762035\pi\)
\(128\) 0 0
\(129\) −7153.36 4129.99i −0.429863 0.248182i
\(130\) 0 0
\(131\) 12953.1 + 22435.4i 0.754797 + 1.30735i 0.945475 + 0.325693i \(0.105598\pi\)
−0.190679 + 0.981652i \(0.561069\pi\)
\(132\) 0 0
\(133\) −9115.40 2501.87i −0.515314 0.141437i
\(134\) 0 0
\(135\) −32099.4 + 18532.6i −1.76129 + 1.01688i
\(136\) 0 0
\(137\) 14553.6 25207.6i 0.775408 1.34305i −0.159158 0.987253i \(-0.550878\pi\)
0.934565 0.355792i \(-0.115789\pi\)
\(138\) 0 0
\(139\) 7423.68 12858.2i 0.384229 0.665504i −0.607433 0.794371i \(-0.707801\pi\)
0.991662 + 0.128867i \(0.0411341\pi\)
\(140\) 0 0
\(141\) 59269.6i 2.98122i
\(142\) 0 0
\(143\) −3898.52 2250.81i −0.190646 0.110070i
\(144\) 0 0
\(145\) 47138.5i 2.24202i
\(146\) 0 0
\(147\) 23201.1 13395.1i 1.07368 0.619887i
\(148\) 0 0
\(149\) 5125.65 + 8877.89i 0.230875 + 0.399887i 0.958066 0.286548i \(-0.0925079\pi\)
−0.727191 + 0.686435i \(0.759175\pi\)
\(150\) 0 0
\(151\) 16460.0i 0.721896i −0.932586 0.360948i \(-0.882453\pi\)
0.932586 0.360948i \(-0.117547\pi\)
\(152\) 0 0
\(153\) 4711.23 0.201257
\(154\) 0 0
\(155\) 9596.96 5540.80i 0.399457 0.230627i
\(156\) 0 0
\(157\) −10562.8 18295.2i −0.428527 0.742231i 0.568215 0.822880i \(-0.307634\pi\)
−0.996743 + 0.0806490i \(0.974301\pi\)
\(158\) 0 0
\(159\) 45122.2 1.78483
\(160\) 0 0
\(161\) −3053.58 + 5288.96i −0.117803 + 0.204042i
\(162\) 0 0
\(163\) −2366.79 −0.0890811 −0.0445405 0.999008i \(-0.514182\pi\)
−0.0445405 + 0.999008i \(0.514182\pi\)
\(164\) 0 0
\(165\) 59499.8 + 34352.2i 2.18548 + 1.26179i
\(166\) 0 0
\(167\) −37914.9 21890.2i −1.35949 0.784904i −0.369938 0.929056i \(-0.620621\pi\)
−0.989556 + 0.144152i \(0.953954\pi\)
\(168\) 0 0
\(169\) −13841.0 23973.3i −0.484611 0.839370i
\(170\) 0 0
\(171\) −41837.1 + 41332.2i −1.43077 + 1.41350i
\(172\) 0 0
\(173\) 13009.4 7510.96i 0.434674 0.250959i −0.266662 0.963790i \(-0.585921\pi\)
0.701336 + 0.712831i \(0.252587\pi\)
\(174\) 0 0
\(175\) −2808.39 + 4864.27i −0.0917025 + 0.158833i
\(176\) 0 0
\(177\) −3468.33 + 6007.32i −0.110707 + 0.191750i
\(178\) 0 0
\(179\) 27426.6i 0.855984i −0.903783 0.427992i \(-0.859221\pi\)
0.903783 0.427992i \(-0.140779\pi\)
\(180\) 0 0
\(181\) −46522.7 26859.9i −1.42006 0.819874i −0.423760 0.905774i \(-0.639290\pi\)
−0.996304 + 0.0859000i \(0.972623\pi\)
\(182\) 0 0
\(183\) 84553.4i 2.52481i
\(184\) 0 0
\(185\) −43295.1 + 24996.4i −1.26501 + 0.730356i
\(186\) 0 0
\(187\) −2195.39 3802.53i −0.0627811 0.108740i
\(188\) 0 0
\(189\) 33496.1i 0.937713i
\(190\) 0 0
\(191\) 57805.6 1.58454 0.792271 0.610170i \(-0.208899\pi\)
0.792271 + 0.610170i \(0.208899\pi\)
\(192\) 0 0
\(193\) 26896.3 15528.6i 0.722068 0.416886i −0.0934455 0.995624i \(-0.529788\pi\)
0.815513 + 0.578738i \(0.196455\pi\)
\(194\) 0 0
\(195\) −6708.27 11619.1i −0.176417 0.305564i
\(196\) 0 0
\(197\) 19725.7 0.508277 0.254139 0.967168i \(-0.418208\pi\)
0.254139 + 0.967168i \(0.418208\pi\)
\(198\) 0 0
\(199\) −35403.2 + 61320.2i −0.893998 + 1.54845i −0.0589584 + 0.998260i \(0.518778\pi\)
−0.835040 + 0.550190i \(0.814555\pi\)
\(200\) 0 0
\(201\) −48677.1 −1.20485
\(202\) 0 0
\(203\) −36892.1 21299.6i −0.895243 0.516869i
\(204\) 0 0
\(205\) 73564.7 + 42472.6i 1.75050 + 1.01065i
\(206\) 0 0
\(207\) 18998.5 + 32906.3i 0.443382 + 0.767961i
\(208\) 0 0
\(209\) 52855.8 + 14507.1i 1.21004 + 0.332116i
\(210\) 0 0
\(211\) −1039.66 + 600.246i −0.0233521 + 0.0134823i −0.511631 0.859206i \(-0.670958\pi\)
0.488279 + 0.872688i \(0.337625\pi\)
\(212\) 0 0
\(213\) −3430.72 + 5942.18i −0.0756181 + 0.130974i
\(214\) 0 0
\(215\) −7662.09 + 13271.1i −0.165756 + 0.287098i
\(216\) 0 0
\(217\) 10014.5i 0.212672i
\(218\) 0 0
\(219\) −43887.5 25338.5i −0.915067 0.528314i
\(220\) 0 0
\(221\) 857.429i 0.0175555i
\(222\) 0 0
\(223\) −59249.9 + 34207.9i −1.19146 + 0.687887i −0.958637 0.284633i \(-0.908128\pi\)
−0.232819 + 0.972520i \(0.574795\pi\)
\(224\) 0 0
\(225\) 17473.0 + 30264.1i 0.345145 + 0.597809i
\(226\) 0 0
\(227\) 90560.9i 1.75747i −0.477306 0.878737i \(-0.658387\pi\)
0.477306 0.878737i \(-0.341613\pi\)
\(228\) 0 0
\(229\) −39212.6 −0.747747 −0.373874 0.927480i \(-0.621971\pi\)
−0.373874 + 0.927480i \(0.621971\pi\)
\(230\) 0 0
\(231\) 53770.3 31044.3i 1.00767 0.581778i
\(232\) 0 0
\(233\) −20451.0 35422.2i −0.376707 0.652475i 0.613874 0.789404i \(-0.289610\pi\)
−0.990581 + 0.136929i \(0.956277\pi\)
\(234\) 0 0
\(235\) 109959. 1.99111
\(236\) 0 0
\(237\) −21026.6 + 36419.2i −0.374345 + 0.648385i
\(238\) 0 0
\(239\) −87676.6 −1.53493 −0.767464 0.641092i \(-0.778482\pi\)
−0.767464 + 0.641092i \(0.778482\pi\)
\(240\) 0 0
\(241\) 35152.4 + 20295.3i 0.605231 + 0.349430i 0.771097 0.636718i \(-0.219709\pi\)
−0.165866 + 0.986148i \(0.553042\pi\)
\(242\) 0 0
\(243\) 2005.90 + 1158.11i 0.0339701 + 0.0196127i
\(244\) 0 0
\(245\) −24851.1 43043.3i −0.414012 0.717090i
\(246\) 0 0
\(247\) −7522.33 7614.22i −0.123299 0.124805i
\(248\) 0 0
\(249\) −134438. + 77617.7i −2.16832 + 1.25188i
\(250\) 0 0
\(251\) −13850.9 + 23990.4i −0.219851 + 0.380794i −0.954762 0.297370i \(-0.903891\pi\)
0.734911 + 0.678164i \(0.237224\pi\)
\(252\) 0 0
\(253\) 17706.3 30668.1i 0.276621 0.479122i
\(254\) 0 0
\(255\) 13086.2i 0.201249i
\(256\) 0 0
\(257\) −74472.0 42996.4i −1.12753 0.650978i −0.184215 0.982886i \(-0.558974\pi\)
−0.943312 + 0.331908i \(0.892308\pi\)
\(258\) 0 0
\(259\) 45178.8i 0.673496i
\(260\) 0 0
\(261\) −229531. + 132520.i −3.36947 + 1.94536i
\(262\) 0 0
\(263\) 12692.5 + 21984.1i 0.183500 + 0.317831i 0.943070 0.332594i \(-0.107924\pi\)
−0.759570 + 0.650425i \(0.774591\pi\)
\(264\) 0 0
\(265\) 83712.1i 1.19206i
\(266\) 0 0
\(267\) 63505.7 0.890821
\(268\) 0 0
\(269\) −34445.2 + 19887.0i −0.476019 + 0.274830i −0.718756 0.695262i \(-0.755288\pi\)
0.242737 + 0.970092i \(0.421955\pi\)
\(270\) 0 0
\(271\) 5496.61 + 9520.41i 0.0748439 + 0.129633i 0.901018 0.433781i \(-0.142821\pi\)
−0.826174 + 0.563414i \(0.809487\pi\)
\(272\) 0 0
\(273\) −12124.6 −0.162683
\(274\) 0 0
\(275\) 16284.5 28205.6i 0.215332 0.372966i
\(276\) 0 0
\(277\) 75853.3 0.988587 0.494294 0.869295i \(-0.335427\pi\)
0.494294 + 0.869295i \(0.335427\pi\)
\(278\) 0 0
\(279\) −53959.7 31153.6i −0.693204 0.400221i
\(280\) 0 0
\(281\) −94497.4 54558.1i −1.19676 0.690950i −0.236929 0.971527i \(-0.576141\pi\)
−0.959831 + 0.280577i \(0.909474\pi\)
\(282\) 0 0
\(283\) 16943.2 + 29346.5i 0.211555 + 0.366423i 0.952201 0.305471i \(-0.0988141\pi\)
−0.740647 + 0.671895i \(0.765481\pi\)
\(284\) 0 0
\(285\) 114807. + 116209.i 1.41344 + 1.43071i
\(286\) 0 0
\(287\) 66480.8 38382.7i 0.807109 0.465985i
\(288\) 0 0
\(289\) 41342.3 71607.0i 0.494993 0.857354i
\(290\) 0 0
\(291\) 125534. 217431.i 1.48243 2.56765i
\(292\) 0 0
\(293\) 109192.i 1.27191i −0.771725 0.635956i \(-0.780606\pi\)
0.771725 0.635956i \(-0.219394\pi\)
\(294\) 0 0
\(295\) 11145.0 + 6434.55i 0.128066 + 0.0739391i
\(296\) 0 0
\(297\) 194227.i 2.20190i
\(298\) 0 0
\(299\) −5988.85 + 3457.67i −0.0669886 + 0.0386759i
\(300\) 0 0
\(301\) 6924.27 + 11993.2i 0.0764259 + 0.132374i
\(302\) 0 0
\(303\) 71849.6i 0.782599i
\(304\) 0 0
\(305\) 156866. 1.68628
\(306\) 0 0
\(307\) −130929. + 75591.9i −1.38918 + 0.802044i −0.993223 0.116224i \(-0.962921\pi\)
−0.395958 + 0.918268i \(0.629588\pi\)
\(308\) 0 0
\(309\) −59373.4 102838.i −0.621835 1.07705i
\(310\) 0 0
\(311\) 63635.6 0.657929 0.328965 0.944342i \(-0.393300\pi\)
0.328965 + 0.944342i \(0.393300\pi\)
\(312\) 0 0
\(313\) 62756.5 108697.i 0.640575 1.10951i −0.344730 0.938702i \(-0.612029\pi\)
0.985305 0.170806i \(-0.0546372\pi\)
\(314\) 0 0
\(315\) 123595. 1.24560
\(316\) 0 0
\(317\) 68452.4 + 39521.0i 0.681193 + 0.393287i 0.800305 0.599594i \(-0.204671\pi\)
−0.119111 + 0.992881i \(0.538004\pi\)
\(318\) 0 0
\(319\) 213919. + 123506.i 2.10217 + 1.21369i
\(320\) 0 0
\(321\) 173206. + 300002.i 1.68095 + 2.91148i
\(322\) 0 0
\(323\) −2640.75 10100.3i −0.0253118 0.0968121i
\(324\) 0 0
\(325\) −5507.96 + 3180.02i −0.0521464 + 0.0301067i
\(326\) 0 0
\(327\) 24056.6 41667.3i 0.224977 0.389672i
\(328\) 0 0
\(329\) 49685.2 86057.2i 0.459024 0.795052i
\(330\) 0 0
\(331\) 51095.1i 0.466363i 0.972433 + 0.233181i \(0.0749135\pi\)
−0.972433 + 0.233181i \(0.925086\pi\)
\(332\) 0 0
\(333\) 243430. + 140544.i 2.19526 + 1.26743i
\(334\) 0 0
\(335\) 90307.2i 0.804698i
\(336\) 0 0
\(337\) 50433.4 29117.8i 0.444078 0.256388i −0.261248 0.965272i \(-0.584134\pi\)
0.705326 + 0.708883i \(0.250801\pi\)
\(338\) 0 0
\(339\) −112731. 195257.i −0.980947 1.69905i
\(340\) 0 0
\(341\) 58069.3i 0.499388i
\(342\) 0 0
\(343\) −107784. −0.916152
\(344\) 0 0
\(345\) 91402.7 52771.4i 0.767928 0.443364i
\(346\) 0 0
\(347\) −53216.5 92173.7i −0.441965 0.765505i 0.555871 0.831269i \(-0.312385\pi\)
−0.997835 + 0.0657637i \(0.979052\pi\)
\(348\) 0 0
\(349\) 86665.4 0.711533 0.355767 0.934575i \(-0.384220\pi\)
0.355767 + 0.934575i \(0.384220\pi\)
\(350\) 0 0
\(351\) −18964.3 + 32847.1i −0.153930 + 0.266614i
\(352\) 0 0
\(353\) −93586.9 −0.751045 −0.375522 0.926813i \(-0.622537\pi\)
−0.375522 + 0.926813i \(0.622537\pi\)
\(354\) 0 0
\(355\) 11024.1 + 6364.78i 0.0874756 + 0.0505041i
\(356\) 0 0
\(357\) −10241.7 5913.03i −0.0803590 0.0463953i
\(358\) 0 0
\(359\) −45001.8 77945.4i −0.349173 0.604786i 0.636929 0.770922i \(-0.280204\pi\)
−0.986103 + 0.166136i \(0.946871\pi\)
\(360\) 0 0
\(361\) 112062. + 66526.0i 0.859891 + 0.510478i
\(362\) 0 0
\(363\) −113764. + 65681.9i −0.863362 + 0.498463i
\(364\) 0 0
\(365\) −47008.7 + 81421.5i −0.352852 + 0.611158i
\(366\) 0 0
\(367\) 16656.8 28850.4i 0.123668 0.214200i −0.797543 0.603262i \(-0.793867\pi\)
0.921212 + 0.389062i \(0.127201\pi\)
\(368\) 0 0
\(369\) 477611.i 3.50770i
\(370\) 0 0
\(371\) −65515.7 37825.5i −0.475990 0.274813i
\(372\) 0 0
\(373\) 89569.8i 0.643789i 0.946775 + 0.321895i \(0.104320\pi\)
−0.946775 + 0.321895i \(0.895680\pi\)
\(374\) 0 0
\(375\) −160865. + 92875.4i −1.14393 + 0.660447i
\(376\) 0 0
\(377\) −24118.2 41774.0i −0.169693 0.293916i
\(378\) 0 0
\(379\) 33228.0i 0.231327i 0.993288 + 0.115663i \(0.0368994\pi\)
−0.993288 + 0.115663i \(0.963101\pi\)
\(380\) 0 0
\(381\) 148693. 1.02433
\(382\) 0 0
\(383\) 122413. 70675.3i 0.834508 0.481804i −0.0208855 0.999782i \(-0.506649\pi\)
0.855394 + 0.517978i \(0.173315\pi\)
\(384\) 0 0
\(385\) −57594.3 99756.2i −0.388560 0.673005i
\(386\) 0 0
\(387\) 86161.4 0.575295
\(388\) 0 0
\(389\) 45995.4 79666.4i 0.303959 0.526473i −0.673070 0.739579i \(-0.735025\pi\)
0.977029 + 0.213106i \(0.0683580\pi\)
\(390\) 0 0
\(391\) −6745.06 −0.0441197
\(392\) 0 0
\(393\) −350387. 202296.i −2.26863 1.30979i
\(394\) 0 0
\(395\) 67565.9 + 39009.2i 0.433045 + 0.250019i
\(396\) 0 0
\(397\) −57126.4 98945.8i −0.362456 0.627793i 0.625908 0.779897i \(-0.284728\pi\)
−0.988364 + 0.152104i \(0.951395\pi\)
\(398\) 0 0
\(399\) 142825. 37342.0i 0.897135 0.234559i
\(400\) 0 0
\(401\) −210749. + 121676.i −1.31062 + 0.756687i −0.982199 0.187845i \(-0.939850\pi\)
−0.328421 + 0.944531i \(0.606517\pi\)
\(402\) 0 0
\(403\) 5669.86 9820.49i 0.0349110 0.0604677i
\(404\) 0 0
\(405\) 98267.0 170203.i 0.599098 1.03767i
\(406\) 0 0
\(407\) 261970.i 1.58148i
\(408\) 0 0
\(409\) 36346.9 + 20984.9i 0.217280 + 0.125447i 0.604690 0.796461i \(-0.293297\pi\)
−0.387410 + 0.921908i \(0.626630\pi\)
\(410\) 0 0
\(411\) 454586.i 2.69112i
\(412\) 0 0
\(413\) 10071.8 5814.93i 0.0590480 0.0340914i
\(414\) 0 0
\(415\) 143999. + 249413.i 0.836108 + 1.44818i
\(416\) 0 0
\(417\) 231881.i 1.33350i
\(418\) 0 0
\(419\) −213970. −1.21878 −0.609390 0.792871i \(-0.708586\pi\)
−0.609390 + 0.792871i \(0.708586\pi\)
\(420\) 0 0
\(421\) −160145. + 92459.6i −0.903542 + 0.521660i −0.878348 0.478022i \(-0.841354\pi\)
−0.0251947 + 0.999683i \(0.508021\pi\)
\(422\) 0 0
\(423\) −309126. 535422.i −1.72765 2.99237i
\(424\) 0 0
\(425\) −6203.45 −0.0343444
\(426\) 0 0
\(427\) 70880.3 122768.i 0.388750 0.673334i
\(428\) 0 0
\(429\) 70304.7 0.382006
\(430\) 0 0
\(431\) −262233. 151400.i −1.41167 0.815028i −0.416124 0.909308i \(-0.636612\pi\)
−0.995546 + 0.0942797i \(0.969945\pi\)
\(432\) 0 0
\(433\) 97747.5 + 56434.5i 0.521350 + 0.301002i 0.737487 0.675361i \(-0.236012\pi\)
−0.216137 + 0.976363i \(0.569346\pi\)
\(434\) 0 0
\(435\) 368096. + 637560.i 1.94528 + 3.36932i
\(436\) 0 0
\(437\) 59898.1 59175.2i 0.313654 0.309868i
\(438\) 0 0
\(439\) 122771. 70881.7i 0.637038 0.367794i −0.146435 0.989220i \(-0.546780\pi\)
0.783473 + 0.621426i \(0.213446\pi\)
\(440\) 0 0
\(441\) −139727. + 242014.i −0.718462 + 1.24441i
\(442\) 0 0
\(443\) 21949.9 38018.3i 0.111847 0.193725i −0.804668 0.593725i \(-0.797657\pi\)
0.916515 + 0.400000i \(0.130990\pi\)
\(444\) 0 0
\(445\) 117818.i 0.594964i
\(446\) 0 0
\(447\) −138652. 80050.6i −0.693921 0.400635i
\(448\) 0 0
\(449\) 341964.i 1.69624i 0.529803 + 0.848121i \(0.322266\pi\)
−0.529803 + 0.848121i \(0.677734\pi\)
\(450\) 0 0
\(451\) −385490. + 222563.i −1.89522 + 1.09421i
\(452\) 0 0
\(453\) 128533. + 222625.i 0.626351 + 1.08487i
\(454\) 0 0
\(455\) 22493.9i 0.108653i
\(456\) 0 0
\(457\) −310982. −1.48903 −0.744514 0.667606i \(-0.767319\pi\)
−0.744514 + 0.667606i \(0.767319\pi\)
\(458\) 0 0
\(459\) −32038.4 + 18497.4i −0.152070 + 0.0877979i
\(460\) 0 0
\(461\) 8617.64 + 14926.2i 0.0405496 + 0.0702340i 0.885588 0.464472i \(-0.153756\pi\)
−0.845038 + 0.534706i \(0.820422\pi\)
\(462\) 0 0
\(463\) −41988.4 −0.195870 −0.0979350 0.995193i \(-0.531224\pi\)
−0.0979350 + 0.995193i \(0.531224\pi\)
\(464\) 0 0
\(465\) −86534.2 + 149882.i −0.400205 + 0.693175i
\(466\) 0 0
\(467\) −127467. −0.584471 −0.292235 0.956346i \(-0.594399\pi\)
−0.292235 + 0.956346i \(0.594399\pi\)
\(468\) 0 0
\(469\) 70677.2 + 40805.5i 0.321317 + 0.185513i
\(470\) 0 0
\(471\) 285728. + 164965.i 1.28799 + 0.743620i
\(472\) 0 0
\(473\) −40150.5 69542.7i −0.179460 0.310834i
\(474\) 0 0
\(475\) 55088.5 54423.6i 0.244159 0.241213i
\(476\) 0 0
\(477\) −407619. + 235339.i −1.79150 + 1.03433i
\(478\) 0 0
\(479\) 199847. 346146.i 0.871019 1.50865i 0.0100742 0.999949i \(-0.496793\pi\)
0.860944 0.508699i \(-0.169873\pi\)
\(480\) 0 0
\(481\) −25578.7 + 44303.5i −0.110557 + 0.191491i
\(482\) 0 0
\(483\) 95379.5i 0.408847i
\(484\) 0 0
\(485\) −403384. 232894.i −1.71489 0.990091i
\(486\) 0 0
\(487\) 148836.i 0.627551i 0.949497 + 0.313776i \(0.101594\pi\)
−0.949497 + 0.313776i \(0.898406\pi\)
\(488\) 0 0
\(489\) 32011.5 18481.9i 0.133872 0.0772908i
\(490\) 0 0
\(491\) −40416.6 70003.6i −0.167647 0.290374i 0.769945 0.638110i \(-0.220284\pi\)
−0.937592 + 0.347737i \(0.886950\pi\)
\(492\) 0 0
\(493\) 47048.8i 0.193577i
\(494\) 0 0
\(495\) −716669. −2.92488
\(496\) 0 0
\(497\) 9962.55 5751.88i 0.0403327 0.0232861i
\(498\) 0 0
\(499\) 177011. + 306591.i 0.710883 + 1.23129i 0.964526 + 0.263987i \(0.0850378\pi\)
−0.253643 + 0.967298i \(0.581629\pi\)
\(500\) 0 0
\(501\) 683746. 2.72408
\(502\) 0 0
\(503\) −112647. + 195110.i −0.445229 + 0.771160i −0.998068 0.0621282i \(-0.980211\pi\)
0.552839 + 0.833288i \(0.313545\pi\)
\(504\) 0 0
\(505\) −133298. −0.522684
\(506\) 0 0
\(507\) 374405. + 216163.i 1.45655 + 0.840941i
\(508\) 0 0
\(509\) 26520.7 + 15311.7i 0.102365 + 0.0591002i 0.550308 0.834962i \(-0.314510\pi\)
−0.447944 + 0.894062i \(0.647844\pi\)
\(510\) 0 0
\(511\) 42482.0 + 73581.0i 0.162691 + 0.281789i
\(512\) 0 0
\(513\) 122230. 445338.i 0.464456 1.69221i
\(514\) 0 0
\(515\) −190788. + 110151.i −0.719343 + 0.415313i
\(516\) 0 0
\(517\) −288100. + 499004.i −1.07786 + 1.86691i
\(518\) 0 0
\(519\) −117303. + 203175.i −0.435488 + 0.754287i
\(520\) 0 0
\(521\) 258518.i 0.952390i 0.879340 + 0.476195i \(0.157984\pi\)
−0.879340 + 0.476195i \(0.842016\pi\)
\(522\) 0 0
\(523\) −378631. 218603.i −1.38424 0.799194i −0.391586 0.920142i \(-0.628073\pi\)
−0.992659 + 0.120948i \(0.961407\pi\)
\(524\) 0 0
\(525\) 87720.8i 0.318261i
\(526\) 0 0
\(527\) 9578.69 5530.26i 0.0344893 0.0199124i
\(528\) 0 0
\(529\) 112720. + 195237.i 0.402802 + 0.697673i
\(530\) 0 0
\(531\) 72357.6i 0.256623i
\(532\) 0 0
\(533\) 86923.8 0.305974
\(534\) 0 0
\(535\) 556573. 321338.i 1.94453 1.12267i
\(536\) 0 0
\(537\) 214169. + 370952.i 0.742691 + 1.28638i
\(538\) 0 0
\(539\) 260447. 0.896481
\(540\) 0 0
\(541\) −141527. + 245131.i −0.483552 + 0.837537i −0.999822 0.0188890i \(-0.993987\pi\)
0.516269 + 0.856426i \(0.327320\pi\)
\(542\) 0 0
\(543\) 838976. 2.84544
\(544\) 0 0
\(545\) −77302.4 44630.5i −0.260255 0.150259i
\(546\) 0 0
\(547\) −44577.7 25736.9i −0.148985 0.0860166i 0.423654 0.905824i \(-0.360747\pi\)
−0.572639 + 0.819807i \(0.694080\pi\)
\(548\) 0 0
\(549\) −440996. 763828.i −1.46315 2.53426i
\(550\) 0 0
\(551\) 412764. + 417807.i 1.35956 + 1.37617i
\(552\) 0 0
\(553\) 61059.7 35252.8i 0.199666 0.115277i
\(554\) 0 0
\(555\) 390385. 676167.i 1.26738 2.19517i
\(556\) 0 0
\(557\) 114117. 197657.i 0.367825 0.637092i −0.621400 0.783494i \(-0.713436\pi\)
0.989225 + 0.146401i \(0.0467691\pi\)
\(558\) 0 0
\(559\) 15681.1i 0.0501826i
\(560\) 0 0
\(561\) 59386.5 + 34286.8i 0.188696 + 0.108944i
\(562\) 0 0
\(563\) 506715.i 1.59863i −0.600914 0.799313i \(-0.705197\pi\)
0.600914 0.799313i \(-0.294803\pi\)
\(564\) 0 0
\(565\) −362246. + 209143.i −1.13477 + 0.655158i
\(566\) 0 0
\(567\) −88804.4 153814.i −0.276228 0.478442i
\(568\) 0 0
\(569\) 596850.i 1.84349i −0.387797 0.921745i \(-0.626764\pi\)
0.387797 0.921745i \(-0.373236\pi\)
\(570\) 0 0
\(571\) −266256. −0.816635 −0.408317 0.912840i \(-0.633884\pi\)
−0.408317 + 0.912840i \(0.633884\pi\)
\(572\) 0 0
\(573\) −781837. + 451394.i −2.38126 + 1.37482i
\(574\) 0 0
\(575\) −25016.0 43329.0i −0.0756628 0.131052i
\(576\) 0 0
\(577\) 459755. 1.38094 0.690470 0.723361i \(-0.257404\pi\)
0.690470 + 0.723361i \(0.257404\pi\)
\(578\) 0 0
\(579\) −242520. + 420056.i −0.723419 + 1.25300i
\(580\) 0 0
\(581\) 260265. 0.771015
\(582\) 0 0
\(583\) 379894. + 219332.i 1.11770 + 0.645305i
\(584\) 0 0
\(585\) 121201. + 69975.2i 0.354155 + 0.204471i
\(586\) 0 0
\(587\) 75602.9 + 130948.i 0.219413 + 0.380034i 0.954629 0.297799i \(-0.0962525\pi\)
−0.735216 + 0.677833i \(0.762919\pi\)
\(588\) 0 0
\(589\) −36543.9 + 133145.i −0.105338 + 0.383791i
\(590\) 0 0
\(591\) −266796. + 154035.i −0.763842 + 0.441005i
\(592\) 0 0
\(593\) −85790.0 + 148593.i −0.243965 + 0.422559i −0.961840 0.273612i \(-0.911781\pi\)
0.717875 + 0.696172i \(0.245115\pi\)
\(594\) 0 0
\(595\) −10970.0 + 19000.7i −0.0309866 + 0.0536704i
\(596\) 0 0
\(597\) 1.10583e6i 3.10270i
\(598\) 0 0
\(599\) 19875.7 + 11475.2i 0.0553947 + 0.0319821i 0.527442 0.849591i \(-0.323151\pi\)
−0.472047 + 0.881573i \(0.656485\pi\)
\(600\) 0 0
\(601\) 107019.i 0.296287i −0.988966 0.148144i \(-0.952670\pi\)
0.988966 0.148144i \(-0.0473298\pi\)
\(602\) 0 0
\(603\) 439733. 253880.i 1.20936 0.698222i
\(604\) 0 0
\(605\) 121855. + 211059.i 0.332915 + 0.576625i
\(606\) 0 0
\(607\) 264918.i 0.719010i 0.933143 + 0.359505i \(0.117054\pi\)
−0.933143 + 0.359505i \(0.882946\pi\)
\(608\) 0 0
\(609\) 665300. 1.79384
\(610\) 0 0
\(611\) 97445.2 56260.0i 0.261023 0.150701i
\(612\) 0 0
\(613\) 267953. + 464108.i 0.713079 + 1.23509i 0.963696 + 0.267003i \(0.0860335\pi\)
−0.250616 + 0.968087i \(0.580633\pi\)
\(614\) 0 0
\(615\) −1.32664e6 −3.50755
\(616\) 0 0
\(617\) −92145.4 + 159601.i −0.242049 + 0.419241i −0.961298 0.275511i \(-0.911153\pi\)
0.719249 + 0.694753i \(0.244486\pi\)
\(618\) 0 0
\(619\) −400704. −1.04578 −0.522892 0.852399i \(-0.675147\pi\)
−0.522892 + 0.852399i \(0.675147\pi\)
\(620\) 0 0
\(621\) −258395. 149185.i −0.670041 0.386849i
\(622\) 0 0
\(623\) −92207.9 53236.2i −0.237570 0.137161i
\(624\) 0 0
\(625\) 239340. + 414548.i 0.612709 + 1.06124i
\(626\) 0 0
\(627\) −828172. + 216528.i −2.10662 + 0.550781i
\(628\) 0 0
\(629\) −43212.7 + 24948.9i −0.109222 + 0.0630593i
\(630\) 0 0
\(631\) −91315.6 + 158163.i −0.229343 + 0.397235i −0.957614 0.288056i \(-0.906991\pi\)
0.728270 + 0.685290i \(0.240325\pi\)
\(632\) 0 0
\(633\) 9374.42 16237.0i 0.0233958 0.0405226i
\(634\) 0 0
\(635\) 275860.i 0.684133i
\(636\) 0 0
\(637\) −44045.9 25429.9i −0.108549 0.0626709i
\(638\) 0 0
\(639\) 71572.9i 0.175286i
\(640\) 0 0
\(641\) −141458. + 81670.6i −0.344279 + 0.198770i −0.662163 0.749360i \(-0.730361\pi\)
0.317884 + 0.948130i \(0.397028\pi\)
\(642\) 0 0
\(643\) −138596. 240055.i −0.335219 0.580616i 0.648308 0.761378i \(-0.275477\pi\)
−0.983527 + 0.180762i \(0.942144\pi\)
\(644\) 0 0
\(645\) 239327.i 0.575271i
\(646\) 0 0
\(647\) −624788. −1.49253 −0.746267 0.665647i \(-0.768156\pi\)
−0.746267 + 0.665647i \(0.768156\pi\)
\(648\) 0 0
\(649\) −58401.3 + 33718.0i −0.138654 + 0.0800521i
\(650\) 0 0
\(651\) 78201.4 + 135449.i 0.184524 + 0.319605i
\(652\) 0 0
\(653\) 32974.6 0.0773308 0.0386654 0.999252i \(-0.487689\pi\)
0.0386654 + 0.999252i \(0.487689\pi\)
\(654\) 0 0
\(655\) −375306. + 650049.i −0.874788 + 1.51518i
\(656\) 0 0
\(657\) 528621. 1.22465
\(658\) 0 0
\(659\) 245158. + 141542.i 0.564514 + 0.325922i 0.754955 0.655776i \(-0.227659\pi\)
−0.190441 + 0.981699i \(0.560992\pi\)
\(660\) 0 0
\(661\) −469830. 271257.i −1.07532 0.620837i −0.145691 0.989330i \(-0.546540\pi\)
−0.929630 + 0.368493i \(0.879874\pi\)
\(662\) 0 0
\(663\) −6695.51 11597.0i −0.0152320 0.0263826i
\(664\) 0 0
\(665\) −69278.0 264973.i −0.156658 0.599181i
\(666\) 0 0
\(667\) 328620. 189729.i 0.738655 0.426463i
\(668\) 0 0
\(669\) 534247. 925343.i 1.19369 2.06752i
\(670\) 0 0
\(671\) −411001. + 711874.i −0.912846 + 1.58110i
\(672\) 0 0
\(673\) 278225.i 0.614279i −0.951664 0.307140i \(-0.900628\pi\)
0.951664 0.307140i \(-0.0993719\pi\)
\(674\) 0 0
\(675\) −237647. 137206.i −0.521585 0.301137i
\(676\) 0 0
\(677\) 107959.i 0.235550i −0.993040 0.117775i \(-0.962424\pi\)
0.993040 0.117775i \(-0.0375761\pi\)
\(678\) 0 0
\(679\) −364540. + 210468.i −0.790690 + 0.456505i
\(680\) 0 0
\(681\) 707173. + 1.22486e6i 1.52487 + 2.64114i
\(682\) 0 0
\(683\) 344624.i 0.738761i −0.929278 0.369381i \(-0.879570\pi\)
0.929278 0.369381i \(-0.120430\pi\)
\(684\) 0 0
\(685\) 843362. 1.79735
\(686\) 0 0
\(687\) 530361. 306204.i 1.12372 0.648780i
\(688\) 0 0
\(689\) −42831.0 74185.4i −0.0902235 0.156272i
\(690\) 0 0
\(691\) 143967. 0.301513 0.150757 0.988571i \(-0.451829\pi\)
0.150757 + 0.988571i \(0.451829\pi\)
\(692\) 0 0
\(693\) −323828. + 560887.i −0.674293 + 1.16791i
\(694\) 0 0
\(695\) 430192. 0.890621
\(696\) 0 0
\(697\) 73424.7 + 42391.8i 0.151139 + 0.0872602i
\(698\) 0 0
\(699\) 553211. + 319397.i 1.13223 + 0.653696i
\(700\) 0 0
\(701\) −371742. 643876.i −0.756494 1.31029i −0.944628 0.328142i \(-0.893577\pi\)
0.188134 0.982143i \(-0.439756\pi\)
\(702\) 0 0
\(703\) 164862. 600663.i 0.333587 1.21540i
\(704\) 0 0
\(705\) −1.48722e6 + 858648.i −2.99225 + 1.72758i
\(706\) 0 0
\(707\) −60230.8 + 104323.i −0.120498 + 0.208709i
\(708\) 0 0
\(709\) −167187. + 289576.i −0.332590 + 0.576063i −0.983019 0.183504i \(-0.941256\pi\)
0.650429 + 0.759567i \(0.274589\pi\)
\(710\) 0 0
\(711\) 438665.i 0.867748i
\(712\) 0 0
\(713\) 77254.0 + 44602.6i 0.151964 + 0.0877367i
\(714\) 0 0
\(715\) 130431.i 0.255135i
\(716\) 0 0
\(717\) 1.18585e6 684651.i 2.30670 1.33177i
\(718\) 0 0
\(719\) 166066. + 287634.i 0.321234 + 0.556394i 0.980743 0.195303i \(-0.0625689\pi\)
−0.659509 + 0.751697i \(0.729236\pi\)
\(720\) 0 0
\(721\) 199089.i 0.382980i
\(722\) 0 0
\(723\) −633927. −1.21273
\(724\) 0 0
\(725\) 302232. 174494.i 0.574996 0.331974i
\(726\) 0 0
\(727\) −88406.6 153125.i −0.167269 0.289719i 0.770190 0.637815i \(-0.220162\pi\)
−0.937459 + 0.348096i \(0.886828\pi\)
\(728\) 0 0
\(729\) 513253. 0.965776
\(730\) 0 0
\(731\) −7647.50 + 13245.9i −0.0143115 + 0.0247882i
\(732\) 0 0
\(733\) −534132. −0.994124 −0.497062 0.867715i \(-0.665588\pi\)
−0.497062 + 0.867715i \(0.665588\pi\)
\(734\) 0 0
\(735\) 672234. + 388115.i 1.24436 + 0.718432i
\(736\) 0 0
\(737\) −409823. 236612.i −0.754504 0.435613i
\(738\) 0 0
\(739\) −221075. 382913.i −0.404810 0.701151i 0.589490 0.807776i \(-0.299329\pi\)
−0.994299 + 0.106625i \(0.965996\pi\)
\(740\) 0 0
\(741\) 161200. + 44243.9i 0.293581 + 0.0805781i
\(742\) 0 0
\(743\) −18451.4 + 10652.9i −0.0334235 + 0.0192971i −0.516619 0.856216i \(-0.672809\pi\)
0.483195 + 0.875513i \(0.339476\pi\)
\(744\) 0 0
\(745\) −148512. + 257231.i −0.267578 + 0.463458i
\(746\) 0 0
\(747\) 809644. 1.40235e6i 1.45095 2.51312i
\(748\) 0 0
\(749\) 580789.i 1.03527i
\(750\) 0 0
\(751\) 345107. + 199248.i 0.611891 + 0.353275i 0.773705 0.633546i \(-0.218401\pi\)
−0.161814 + 0.986821i \(0.551735\pi\)
\(752\) 0 0
\(753\) 432635.i 0.763013i
\(754\) 0 0
\(755\) 413021. 238458.i 0.724567 0.418329i
\(756\) 0 0
\(757\) −200807. 347808.i −0.350419 0.606943i 0.635904 0.771768i \(-0.280627\pi\)
−0.986323 + 0.164825i \(0.947294\pi\)
\(758\) 0 0
\(759\) 553060.i 0.960038i
\(760\) 0 0
\(761\) −383128. −0.661568 −0.330784 0.943706i \(-0.607313\pi\)
−0.330784 + 0.943706i \(0.607313\pi\)
\(762\) 0 0
\(763\) −69858.5 + 40332.8i −0.119997 + 0.0692803i
\(764\) 0 0
\(765\) 68252.3 + 118216.i 0.116626 + 0.202002i
\(766\) 0 0
\(767\) 13168.9 0.0223850
\(768\) 0 0
\(769\) 86027.4 149004.i 0.145474 0.251968i −0.784076 0.620665i \(-0.786863\pi\)
0.929550 + 0.368697i \(0.120196\pi\)
\(770\) 0 0
\(771\) 1.34301e6 2.25927
\(772\) 0 0
\(773\) 145779. + 84165.8i 0.243971 + 0.140856i 0.617000 0.786963i \(-0.288348\pi\)
−0.373030 + 0.927819i \(0.621681\pi\)
\(774\) 0 0
\(775\) 71050.7 + 41021.1i 0.118295 + 0.0682974i
\(776\) 0 0
\(777\) −352793. 611055.i −0.584356 1.01213i
\(778\) 0 0
\(779\) −1.02394e6 + 267712.i −1.68733 + 0.441157i
\(780\) 0 0
\(781\) −57768.0 + 33352.4i −0.0947077 + 0.0546795i
\(782\) 0 0
\(783\) 1.04061e6 1.80238e6i 1.69732 2.93984i
\(784\) 0 0
\(785\) 306049. 530092.i 0.496651 0.860225i
\(786\) 0 0
\(787\) 90783.2i 0.146574i 0.997311 + 0.0732868i \(0.0233489\pi\)
−0.997311 + 0.0732868i \(0.976651\pi\)
\(788\) 0 0
\(789\) −343339. 198227.i −0.551530 0.318426i
\(790\) 0 0
\(791\) 378007.i 0.604153i
\(792\) 0 0
\(793\) 139014. 80259.9i 0.221061 0.127630i
\(794\) 0 0
\(795\) 653692. + 1.13223e6i 1.03428 + 1.79143i
\(796\) 0 0
\(797\) 250407.i 0.394213i −0.980382 0.197106i \(-0.936846\pi\)
0.980382 0.197106i \(-0.0631544\pi\)
\(798\) 0 0
\(799\) 109750. 0.171913
\(800\) 0 0
\(801\) −573690. + 331220.i −0.894153 + 0.516240i
\(802\) 0 0
\(803\) −246333. 426661.i −0.382024 0.661685i
\(804\) 0 0
\(805\) −176951. −0.273062
\(806\) 0 0
\(807\) 310587. 537953.i 0.476910 0.826033i
\(808\) 0 0
\(809\) 366214. 0.559549 0.279775 0.960066i \(-0.409740\pi\)
0.279775 + 0.960066i \(0.409740\pi\)
\(810\) 0 0
\(811\) −379096. 218871.i −0.576379 0.332772i 0.183314 0.983054i \(-0.441317\pi\)
−0.759693 + 0.650282i \(0.774651\pi\)
\(812\) 0 0
\(813\) −148686. 85844.0i −0.224952 0.129876i
\(814\) 0 0
\(815\) −34288.1 59388.8i −0.0516212 0.0894106i
\(816\) 0 0
\(817\) −48295.5 184720.i −0.0723540 0.276738i
\(818\) 0 0
\(819\) 109530. 63237.0i 0.163292 0.0942765i
\(820\) 0 0
\(821\) 434018. 751741.i 0.643904 1.11527i −0.340649 0.940190i \(-0.610647\pi\)
0.984553 0.175084i \(-0.0560198\pi\)
\(822\) 0 0
\(823\) 310831. 538375.i 0.458907 0.794850i −0.539997 0.841667i \(-0.681575\pi\)
0.998903 + 0.0468175i \(0.0149079\pi\)
\(824\) 0 0
\(825\) 508651.i 0.747329i
\(826\) 0 0
\(827\) −543344. 313700.i −0.794445 0.458673i 0.0470803 0.998891i \(-0.485008\pi\)
−0.841525 + 0.540218i \(0.818342\pi\)
\(828\) 0 0
\(829\) 644642.i 0.938015i −0.883194 0.469007i \(-0.844612\pi\)
0.883194 0.469007i \(-0.155388\pi\)
\(830\) 0 0
\(831\) −1.02594e6 + 592325.i −1.48566 + 0.857744i
\(832\) 0 0
\(833\) −24803.8 42961.4i −0.0357460 0.0619139i
\(834\) 0 0
\(835\) 1.26851e6i 1.81936i
\(836\) 0 0
\(837\) 489265. 0.698382
\(838\) 0 0
\(839\) 673952. 389106.i 0.957426 0.552770i 0.0620460 0.998073i \(-0.480237\pi\)
0.895380 + 0.445303i \(0.146904\pi\)
\(840\) 0 0
\(841\) 969772. + 1.67969e6i 1.37113 + 2.37486i
\(842\) 0 0
\(843\) 1.70414e6 2.39800
\(844\) 0 0
\(845\) 401032. 694608.i 0.561650 0.972807i
\(846\) 0 0
\(847\) 220242. 0.306997
\(848\) 0 0
\(849\) −458322. 264613.i −0.635851 0.367109i
\(850\) 0 0
\(851\) −348518. 201217.i −0.481246 0.277847i
\(852\) 0 0
\(853\) 591661. + 1.02479e6i 0.813158 + 1.40843i 0.910643 + 0.413194i \(0.135587\pi\)
−0.0974854 + 0.995237i \(0.531080\pi\)
\(854\) 0 0
\(855\) −1.64323e6 451011.i −2.24784 0.616957i
\(856\) 0 0
\(857\) 732946. 423166.i 0.997953 0.576168i 0.0903111 0.995914i \(-0.471214\pi\)
0.907642 + 0.419745i \(0.137881\pi\)
\(858\) 0 0
\(859\) −128900. + 223261.i −0.174689 + 0.302570i −0.940054 0.341027i \(-0.889225\pi\)
0.765365 + 0.643597i \(0.222559\pi\)
\(860\) 0 0
\(861\) −599447. + 1.03827e6i −0.808620 + 1.40057i
\(862\) 0 0
\(863\) 615296.i 0.826157i 0.910695 + 0.413079i \(0.135547\pi\)
−0.910695 + 0.413079i \(0.864453\pi\)
\(864\) 0 0
\(865\) 376937. + 217625.i 0.503775 + 0.290855i
\(866\) 0 0
\(867\) 1.29134e6i 1.71792i
\(868\) 0 0
\(869\) −354056. + 204414.i −0.468848 + 0.270689i
\(870\) 0 0
\(871\) 46205.3 + 80030.0i 0.0609054 + 0.105491i
\(872\) 0 0
\(873\) 2.61893e6i 3.43634i
\(874\) 0 0
\(875\) 311426. 0.406761
\(876\) 0 0
\(877\) 641044. 370107.i 0.833468 0.481203i −0.0215707 0.999767i \(-0.506867\pi\)
0.855039 + 0.518564i \(0.173533\pi\)
\(878\) 0 0
\(879\) 852663. + 1.47686e6i 1.10357 + 1.91144i
\(880\) 0 0
\(881\) −28024.1 −0.0361061 −0.0180530 0.999837i \(-0.505747\pi\)
−0.0180530 + 0.999837i \(0.505747\pi\)
\(882\) 0 0
\(883\) 518628. 898290.i 0.665173 1.15211i −0.314066 0.949401i \(-0.601691\pi\)
0.979238 0.202712i \(-0.0649754\pi\)
\(884\) 0 0
\(885\) −200985. −0.256612
\(886\) 0 0
\(887\) −785062. 453255.i −0.997830 0.576097i −0.0902243 0.995921i \(-0.528758\pi\)
−0.907605 + 0.419824i \(0.862092\pi\)
\(888\) 0 0
\(889\) −215896. 124648.i −0.273176 0.157718i
\(890\) 0 0
\(891\) 514934. + 891892.i 0.648629 + 1.12346i
\(892\) 0 0
\(893\) −974608. + 962846.i −1.22216 + 1.20741i
\(894\) 0 0
\(895\) 688201. 397333.i 0.859150 0.496031i
\(896\) 0 0
\(897\) 54000.5 93531.7i 0.0671140 0.116245i
\(898\) 0 0
\(899\) −311116. + 538869.i −0.384949 + 0.666751i
\(900\) 0 0
\(901\) 83552.8i 0.102923i
\(902\) 0 0
\(903\) −187305. 108141.i −0.229707 0.132621i
\(904\) 0 0
\(905\) 1.55649e6i 1.90042i
\(906\) 0 0
\(907\) 534950. 308854.i 0.650278 0.375438i −0.138285 0.990392i \(-0.544159\pi\)
0.788563 + 0.614954i \(0.210826\pi\)
\(908\) 0 0
\(909\) 374738. + 649066.i 0.453524 + 0.785526i
\(910\) 0 0
\(911\) 728686.i 0.878019i −0.898482 0.439009i \(-0.855329\pi\)
0.898482 0.439009i \(-0.144671\pi\)
\(912\) 0 0
\(913\) −1.50915e6 −1.81047
\(914\) 0 0
\(915\) −2.12165e6 + 1.22494e6i −2.53415 + 1.46309i
\(916\) 0 0
\(917\) 339166. + 587452.i 0.403342 + 0.698609i
\(918\) 0 0
\(919\) −545481. −0.645875 −0.322938 0.946420i \(-0.604670\pi\)
−0.322938 + 0.946420i \(0.604670\pi\)
\(920\) 0 0
\(921\) 1.18057e6 2.04480e6i 1.39178 2.41064i
\(922\) 0 0
\(923\) 13026.1 0.0152901
\(924\) 0 0
\(925\) −320533. 185060.i −0.374619 0.216286i
\(926\) 0 0
\(927\) 1.07272e6 + 619335.i 1.24832 + 0.720719i
\(928\) 0 0
\(929\) −450263. 779878.i −0.521717 0.903640i −0.999681 0.0252606i \(-0.991958\pi\)
0.477964 0.878379i \(-0.341375\pi\)
\(930\) 0 0
\(931\) 597170. + 163903.i 0.688967 + 0.189098i
\(932\) 0 0
\(933\) −860688. + 496918.i −0.988741 + 0.570850i
\(934\) 0 0
\(935\) 63610.0 110176.i 0.0727616 0.126027i
\(936\) 0 0
\(937\) 324708. 562411.i 0.369840 0.640582i −0.619700 0.784839i \(-0.712746\pi\)
0.989540 + 0.144256i \(0.0460790\pi\)
\(938\) 0 0
\(939\) 1.96021e6i 2.22317i
\(940\) 0 0
\(941\) −460050. 265610.i −0.519548 0.299961i 0.217202 0.976127i \(-0.430307\pi\)
−0.736750 + 0.676165i \(0.763640\pi\)
\(942\) 0 0
\(943\) 683795.i 0.768958i
\(944\) 0 0
\(945\) −840499. + 485262.i −0.941182 + 0.543392i
\(946\) 0 0
\(947\) −803821. 1.39226e6i −0.896313 1.55246i −0.832172 0.554518i \(-0.812903\pi\)
−0.0641411 0.997941i \(-0.520431\pi\)
\(948\) 0 0
\(949\) 96207.3i 0.106826i
\(950\) 0 0
\(951\) −1.23445e6 −1.36494
\(952\) 0 0
\(953\) −662976. + 382769.i −0.729982 + 0.421455i −0.818416 0.574627i \(-0.805147\pi\)
0.0884337 + 0.996082i \(0.471814\pi\)
\(954\) 0 0
\(955\) 837439. + 1.45049e6i 0.918219 + 1.59040i
\(956\) 0 0
\(957\) −3.85775e6 −4.21222
\(958\) 0 0
\(959\) 381075. 660042.i 0.414356 0.717686i
\(960\) 0 0
\(961\) 777243. 0.841608
\(962\) 0 0
\(963\) −3.12938e6 1.80675e6i −3.37447 1.94825i
\(964\) 0 0
\(965\) 779302. + 449930.i 0.836856 + 0.483159i
\(966\) 0 0
\(967\) −67077.0 116181.i −0.0717332 0.124246i 0.827928 0.560835i \(-0.189520\pi\)
−0.899661 + 0.436589i \(0.856186\pi\)
\(968\) 0 0
\(969\) 114588. + 115988.i 0.122037 + 0.123528i
\(970\) 0 0
\(971\) −362961. + 209555.i −0.384965 + 0.222260i −0.679976 0.733234i \(-0.738010\pi\)
0.295011 + 0.955494i \(0.404677\pi\)
\(972\) 0 0
\(973\) 194383. 336682.i 0.205321 0.355626i
\(974\) 0 0
\(975\) 49664.5 86021.4i 0.0522440 0.0904893i
\(976\) 0 0
\(977\) 1.26450e6i 1.32474i 0.749178 + 0.662369i \(0.230449\pi\)
−0.749178 + 0.662369i \(0.769551\pi\)
\(978\) 0 0
\(979\) 534669. + 308691.i 0.557853 + 0.322077i
\(980\) 0 0
\(981\) 501878.i 0.521507i
\(982\) 0 0
\(983\) 632772. 365331.i 0.654848 0.378076i −0.135463 0.990782i \(-0.543252\pi\)
0.790311 + 0.612706i \(0.209919\pi\)
\(984\) 0 0
\(985\) 285770. + 494967.i 0.294539 + 0.510157i
\(986\) 0 0
\(987\) 1.55193e6i 1.59308i
\(988\) 0 0
\(989\) −123357. −0.126116
\(990\) 0 0
\(991\) −228836. + 132118.i −0.233011 + 0.134529i −0.611960 0.790888i \(-0.709619\pi\)
0.378949 + 0.925417i \(0.376285\pi\)
\(992\) 0 0
\(993\) −398993. 691075.i −0.404638 0.700853i
\(994\) 0 0
\(995\) −2.05157e6 −2.07224
\(996\) 0 0
\(997\) 263686. 456717.i 0.265275 0.459469i −0.702361 0.711821i \(-0.747871\pi\)
0.967636 + 0.252352i \(0.0812040\pi\)
\(998\) 0 0
\(999\) −2.20724e6 −2.21166
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 304.5.r.d.145.2 40
4.3 odd 2 152.5.n.a.145.19 yes 40
19.8 odd 6 inner 304.5.r.d.65.2 40
76.27 even 6 152.5.n.a.65.19 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.5.n.a.65.19 40 76.27 even 6
152.5.n.a.145.19 yes 40 4.3 odd 2
304.5.r.d.65.2 40 19.8 odd 6 inner
304.5.r.d.145.2 40 1.1 even 1 trivial