Properties

Label 640.3.e.i.319.8
Level $640$
Weight $3$
Character 640.319
Analytic conductor $17.439$
Analytic rank $0$
Dimension $16$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [640,3,Mod(319,640)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(640, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("640.319");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 640.e (of order \(2\), degree \(1\), 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: \(17.4387369191\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 16x^{14} + 104x^{12} - 208x^{10} - 352x^{8} + 2312x^{6} + 2497x^{4} - 9072x^{2} + 5184 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{38} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 319.8
Root \(-0.973371 + 0.130814i\) of defining polynomial
Character \(\chi\) \(=\) 640.319
Dual form 640.3.e.i.319.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.20837i q^{3} +(3.50932 + 3.56155i) q^{5} +0.620058 q^{7} +4.12311 q^{9} +O(q^{10})\) \(q-2.20837i q^{3} +(3.50932 + 3.56155i) q^{5} +0.620058 q^{7} +4.12311 q^{9} +17.6757 q^{11} -17.9786 q^{13} +(7.86522 - 7.74988i) q^{15} +10.9600i q^{17} +2.17598 q^{19} -1.36932i q^{21} +13.8703 q^{23} +(-0.369317 + 24.9973i) q^{25} -28.9807i q^{27} +14.7386i q^{29} +55.2032i q^{31} -39.0346i q^{33} +(2.17598 + 2.20837i) q^{35} +7.01864 q^{37} +39.7034i q^{39} +48.3542 q^{41} -58.7769i q^{43} +(14.4693 + 14.6847i) q^{45} +54.1646 q^{47} -48.6155 q^{49} +24.2037 q^{51} +3.94134 q^{53} +(62.0299 + 62.9531i) q^{55} -4.80537i q^{57} +72.8789 q^{59} -79.3390i q^{61} +2.55656 q^{63} +(-63.0928 - 64.0318i) q^{65} -26.7723i q^{67} -30.6307i q^{69} -46.4993i q^{71} +95.1837i q^{73} +(55.2032 + 0.815588i) q^{75} +10.9600 q^{77} +24.2037i q^{79} -26.8920 q^{81} -107.361i q^{83} +(-39.0346 + 38.4621i) q^{85} +32.5483 q^{87} +44.2462 q^{89} -11.1478 q^{91} +121.909 q^{93} +(7.63623 + 7.74988i) q^{95} -123.258i q^{97} +72.8789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 192 q^{25} + 48 q^{41} - 448 q^{49} + 112 q^{65} - 1024 q^{81} + 576 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(3\) 2.20837i 0.736123i −0.929801 0.368062i \(-0.880022\pi\)
0.929801 0.368062i \(-0.119978\pi\)
\(4\) 0 0
\(5\) 3.50932 + 3.56155i 0.701864 + 0.712311i
\(6\) 0 0
\(7\) 0.620058 0.0885797 0.0442899 0.999019i \(-0.485897\pi\)
0.0442899 + 0.999019i \(0.485897\pi\)
\(8\) 0 0
\(9\) 4.12311 0.458123
\(10\) 0 0
\(11\) 17.6757 1.60689 0.803443 0.595382i \(-0.202999\pi\)
0.803443 + 0.595382i \(0.202999\pi\)
\(12\) 0 0
\(13\) −17.9786 −1.38297 −0.691486 0.722390i \(-0.743043\pi\)
−0.691486 + 0.722390i \(0.743043\pi\)
\(14\) 0 0
\(15\) 7.86522 7.74988i 0.524348 0.516659i
\(16\) 0 0
\(17\) 10.9600i 0.644705i 0.946620 + 0.322352i \(0.104474\pi\)
−0.946620 + 0.322352i \(0.895526\pi\)
\(18\) 0 0
\(19\) 2.17598 0.114525 0.0572627 0.998359i \(-0.481763\pi\)
0.0572627 + 0.998359i \(0.481763\pi\)
\(20\) 0 0
\(21\) 1.36932i 0.0652056i
\(22\) 0 0
\(23\) 13.8703 0.603055 0.301528 0.953457i \(-0.402503\pi\)
0.301528 + 0.953457i \(0.402503\pi\)
\(24\) 0 0
\(25\) −0.369317 + 24.9973i −0.0147727 + 0.999891i
\(26\) 0 0
\(27\) 28.9807i 1.07336i
\(28\) 0 0
\(29\) 14.7386i 0.508229i 0.967174 + 0.254114i \(0.0817840\pi\)
−0.967174 + 0.254114i \(0.918216\pi\)
\(30\) 0 0
\(31\) 55.2032i 1.78075i 0.455229 + 0.890374i \(0.349557\pi\)
−0.455229 + 0.890374i \(0.650443\pi\)
\(32\) 0 0
\(33\) 39.0346i 1.18287i
\(34\) 0 0
\(35\) 2.17598 + 2.20837i 0.0621709 + 0.0630963i
\(36\) 0 0
\(37\) 7.01864 0.189693 0.0948465 0.995492i \(-0.469764\pi\)
0.0948465 + 0.995492i \(0.469764\pi\)
\(38\) 0 0
\(39\) 39.7034i 1.01804i
\(40\) 0 0
\(41\) 48.3542 1.17937 0.589685 0.807633i \(-0.299252\pi\)
0.589685 + 0.807633i \(0.299252\pi\)
\(42\) 0 0
\(43\) 58.7769i 1.36690i −0.729995 0.683452i \(-0.760478\pi\)
0.729995 0.683452i \(-0.239522\pi\)
\(44\) 0 0
\(45\) 14.4693 + 14.6847i 0.321540 + 0.326326i
\(46\) 0 0
\(47\) 54.1646 1.15244 0.576220 0.817295i \(-0.304527\pi\)
0.576220 + 0.817295i \(0.304527\pi\)
\(48\) 0 0
\(49\) −48.6155 −0.992154
\(50\) 0 0
\(51\) 24.2037 0.474582
\(52\) 0 0
\(53\) 3.94134 0.0743649 0.0371824 0.999308i \(-0.488162\pi\)
0.0371824 + 0.999308i \(0.488162\pi\)
\(54\) 0 0
\(55\) 62.0299 + 62.9531i 1.12782 + 1.14460i
\(56\) 0 0
\(57\) 4.80537i 0.0843048i
\(58\) 0 0
\(59\) 72.8789 1.23524 0.617618 0.786478i \(-0.288098\pi\)
0.617618 + 0.786478i \(0.288098\pi\)
\(60\) 0 0
\(61\) 79.3390i 1.30064i −0.759661 0.650320i \(-0.774635\pi\)
0.759661 0.650320i \(-0.225365\pi\)
\(62\) 0 0
\(63\) 2.55656 0.0405804
\(64\) 0 0
\(65\) −63.0928 64.0318i −0.970658 0.985105i
\(66\) 0 0
\(67\) 26.7723i 0.399586i −0.979838 0.199793i \(-0.935973\pi\)
0.979838 0.199793i \(-0.0640270\pi\)
\(68\) 0 0
\(69\) 30.6307i 0.443923i
\(70\) 0 0
\(71\) 46.4993i 0.654919i −0.944865 0.327460i \(-0.893807\pi\)
0.944865 0.327460i \(-0.106193\pi\)
\(72\) 0 0
\(73\) 95.1837i 1.30389i 0.758268 + 0.651943i \(0.226046\pi\)
−0.758268 + 0.651943i \(0.773954\pi\)
\(74\) 0 0
\(75\) 55.2032 + 0.815588i 0.736043 + 0.0108745i
\(76\) 0 0
\(77\) 10.9600 0.142337
\(78\) 0 0
\(79\) 24.2037i 0.306376i 0.988197 + 0.153188i \(0.0489540\pi\)
−0.988197 + 0.153188i \(0.951046\pi\)
\(80\) 0 0
\(81\) −26.8920 −0.332001
\(82\) 0 0
\(83\) 107.361i 1.29351i −0.762699 0.646753i \(-0.776126\pi\)
0.762699 0.646753i \(-0.223874\pi\)
\(84\) 0 0
\(85\) −39.0346 + 38.4621i −0.459230 + 0.452495i
\(86\) 0 0
\(87\) 32.5483 0.374119
\(88\) 0 0
\(89\) 44.2462 0.497148 0.248574 0.968613i \(-0.420038\pi\)
0.248574 + 0.968613i \(0.420038\pi\)
\(90\) 0 0
\(91\) −11.1478 −0.122503
\(92\) 0 0
\(93\) 121.909 1.31085
\(94\) 0 0
\(95\) 7.63623 + 7.74988i 0.0803813 + 0.0815777i
\(96\) 0 0
\(97\) 123.258i 1.27070i −0.772223 0.635352i \(-0.780855\pi\)
0.772223 0.635352i \(-0.219145\pi\)
\(98\) 0 0
\(99\) 72.8789 0.736151
\(100\) 0 0
\(101\) 32.7083i 0.323845i −0.986803 0.161922i \(-0.948231\pi\)
0.986803 0.161922i \(-0.0517694\pi\)
\(102\) 0 0
\(103\) −70.2862 −0.682390 −0.341195 0.939993i \(-0.610832\pi\)
−0.341195 + 0.939993i \(0.610832\pi\)
\(104\) 0 0
\(105\) 4.87689 4.80537i 0.0464466 0.0457655i
\(106\) 0 0
\(107\) 87.7576i 0.820164i 0.912049 + 0.410082i \(0.134500\pi\)
−0.912049 + 0.410082i \(0.865500\pi\)
\(108\) 0 0
\(109\) 81.8617i 0.751025i 0.926817 + 0.375513i \(0.122533\pi\)
−0.926817 + 0.375513i \(0.877467\pi\)
\(110\) 0 0
\(111\) 15.4998i 0.139637i
\(112\) 0 0
\(113\) 12.3092i 0.108931i −0.998516 0.0544656i \(-0.982654\pi\)
0.998516 0.0544656i \(-0.0173455\pi\)
\(114\) 0 0
\(115\) 48.6753 + 49.3997i 0.423263 + 0.429563i
\(116\) 0 0
\(117\) −74.1278 −0.633571
\(118\) 0 0
\(119\) 6.79583i 0.0571078i
\(120\) 0 0
\(121\) 191.432 1.58208
\(122\) 0 0
\(123\) 106.784i 0.868161i
\(124\) 0 0
\(125\) −90.3252 + 86.4081i −0.722601 + 0.691265i
\(126\) 0 0
\(127\) 175.897 1.38501 0.692507 0.721411i \(-0.256506\pi\)
0.692507 + 0.721411i \(0.256506\pi\)
\(128\) 0 0
\(129\) −129.801 −1.00621
\(130\) 0 0
\(131\) −15.2319 −0.116274 −0.0581370 0.998309i \(-0.518516\pi\)
−0.0581370 + 0.998309i \(0.518516\pi\)
\(132\) 0 0
\(133\) 1.34924 0.0101446
\(134\) 0 0
\(135\) 103.216 101.702i 0.764564 0.753352i
\(136\) 0 0
\(137\) 249.973i 1.82462i 0.409502 + 0.912309i \(0.365702\pi\)
−0.409502 + 0.912309i \(0.634298\pi\)
\(138\) 0 0
\(139\) −225.433 −1.62182 −0.810909 0.585172i \(-0.801027\pi\)
−0.810909 + 0.585172i \(0.801027\pi\)
\(140\) 0 0
\(141\) 119.616i 0.848337i
\(142\) 0 0
\(143\) −317.786 −2.22228
\(144\) 0 0
\(145\) −52.4924 + 51.7226i −0.362017 + 0.356708i
\(146\) 0 0
\(147\) 107.361i 0.730347i
\(148\) 0 0
\(149\) 77.3693i 0.519257i 0.965709 + 0.259629i \(0.0836001\pi\)
−0.965709 + 0.259629i \(0.916400\pi\)
\(150\) 0 0
\(151\) 163.702i 1.08412i 0.840341 + 0.542058i \(0.182355\pi\)
−0.840341 + 0.542058i \(0.817645\pi\)
\(152\) 0 0
\(153\) 45.1892i 0.295354i
\(154\) 0 0
\(155\) −196.609 + 193.726i −1.26845 + 1.24984i
\(156\) 0 0
\(157\) −58.7413 −0.374148 −0.187074 0.982346i \(-0.559900\pi\)
−0.187074 + 0.982346i \(0.559900\pi\)
\(158\) 0 0
\(159\) 8.70393i 0.0547417i
\(160\) 0 0
\(161\) 8.60037 0.0534185
\(162\) 0 0
\(163\) 112.560i 0.690551i −0.938501 0.345276i \(-0.887785\pi\)
0.938501 0.345276i \(-0.112215\pi\)
\(164\) 0 0
\(165\) 139.024 136.985i 0.842568 0.830211i
\(166\) 0 0
\(167\) −237.035 −1.41937 −0.709685 0.704519i \(-0.751163\pi\)
−0.709685 + 0.704519i \(0.751163\pi\)
\(168\) 0 0
\(169\) 154.231 0.912610
\(170\) 0 0
\(171\) 8.97181 0.0524667
\(172\) 0 0
\(173\) −292.949 −1.69334 −0.846672 0.532115i \(-0.821398\pi\)
−0.846672 + 0.532115i \(0.821398\pi\)
\(174\) 0 0
\(175\) −0.228998 + 15.4998i −0.00130856 + 0.0885700i
\(176\) 0 0
\(177\) 160.944i 0.909286i
\(178\) 0 0
\(179\) −180.841 −1.01029 −0.505144 0.863035i \(-0.668561\pi\)
−0.505144 + 0.863035i \(0.668561\pi\)
\(180\) 0 0
\(181\) 259.231i 1.43222i 0.697990 + 0.716108i \(0.254078\pi\)
−0.697990 + 0.716108i \(0.745922\pi\)
\(182\) 0 0
\(183\) −175.210 −0.957431
\(184\) 0 0
\(185\) 24.6307 + 24.9973i 0.133139 + 0.135120i
\(186\) 0 0
\(187\) 193.726i 1.03597i
\(188\) 0 0
\(189\) 17.9697i 0.0950777i
\(190\) 0 0
\(191\) 269.220i 1.40953i −0.709441 0.704765i \(-0.751052\pi\)
0.709441 0.704765i \(-0.248948\pi\)
\(192\) 0 0
\(193\) 145.178i 0.752219i −0.926575 0.376109i \(-0.877262\pi\)
0.926575 0.376109i \(-0.122738\pi\)
\(194\) 0 0
\(195\) −141.406 + 139.332i −0.725159 + 0.714524i
\(196\) 0 0
\(197\) 272.378 1.38263 0.691314 0.722554i \(-0.257032\pi\)
0.691314 + 0.722554i \(0.257032\pi\)
\(198\) 0 0
\(199\) 329.311i 1.65483i −0.561591 0.827415i \(-0.689811\pi\)
0.561591 0.827415i \(-0.310189\pi\)
\(200\) 0 0
\(201\) −59.1231 −0.294145
\(202\) 0 0
\(203\) 9.13881i 0.0450188i
\(204\) 0 0
\(205\) 169.690 + 172.216i 0.827758 + 0.840078i
\(206\) 0 0
\(207\) 57.1886 0.276273
\(208\) 0 0
\(209\) 38.4621 0.184029
\(210\) 0 0
\(211\) −6.52795 −0.0309381 −0.0154691 0.999880i \(-0.504924\pi\)
−0.0154691 + 0.999880i \(0.504924\pi\)
\(212\) 0 0
\(213\) −102.688 −0.482101
\(214\) 0 0
\(215\) 209.337 206.267i 0.973661 0.959382i
\(216\) 0 0
\(217\) 34.2292i 0.157738i
\(218\) 0 0
\(219\) 210.201 0.959821
\(220\) 0 0
\(221\) 197.045i 0.891608i
\(222\) 0 0
\(223\) −365.597 −1.63945 −0.819724 0.572759i \(-0.805873\pi\)
−0.819724 + 0.572759i \(0.805873\pi\)
\(224\) 0 0
\(225\) −1.52273 + 103.066i −0.00676770 + 0.458073i
\(226\) 0 0
\(227\) 224.066i 0.987074i 0.869725 + 0.493537i \(0.164296\pi\)
−0.869725 + 0.493537i \(0.835704\pi\)
\(228\) 0 0
\(229\) 247.723i 1.08176i −0.841099 0.540881i \(-0.818091\pi\)
0.841099 0.540881i \(-0.181909\pi\)
\(230\) 0 0
\(231\) 24.2037i 0.104778i
\(232\) 0 0
\(233\) 260.933i 1.11988i −0.828532 0.559941i \(-0.810824\pi\)
0.828532 0.559941i \(-0.189176\pi\)
\(234\) 0 0
\(235\) 190.081 + 192.910i 0.808856 + 0.820895i
\(236\) 0 0
\(237\) 53.4507 0.225530
\(238\) 0 0
\(239\) 183.017i 0.765764i −0.923797 0.382882i \(-0.874932\pi\)
0.923797 0.382882i \(-0.125068\pi\)
\(240\) 0 0
\(241\) −204.725 −0.849483 −0.424741 0.905315i \(-0.639635\pi\)
−0.424741 + 0.905315i \(0.639635\pi\)
\(242\) 0 0
\(243\) 201.438i 0.828965i
\(244\) 0 0
\(245\) −170.608 173.147i −0.696357 0.706722i
\(246\) 0 0
\(247\) −39.1212 −0.158385
\(248\) 0 0
\(249\) −237.093 −0.952180
\(250\) 0 0
\(251\) −322.247 −1.28385 −0.641927 0.766766i \(-0.721865\pi\)
−0.641927 + 0.766766i \(0.721865\pi\)
\(252\) 0 0
\(253\) 245.167 0.969041
\(254\) 0 0
\(255\) 84.9385 + 86.2027i 0.333092 + 0.338050i
\(256\) 0 0
\(257\) 234.207i 0.911313i 0.890156 + 0.455656i \(0.150595\pi\)
−0.890156 + 0.455656i \(0.849405\pi\)
\(258\) 0 0
\(259\) 4.35197 0.0168030
\(260\) 0 0
\(261\) 60.7689i 0.232831i
\(262\) 0 0
\(263\) −448.361 −1.70479 −0.852397 0.522896i \(-0.824852\pi\)
−0.852397 + 0.522896i \(0.824852\pi\)
\(264\) 0 0
\(265\) 13.8314 + 14.0373i 0.0521941 + 0.0529709i
\(266\) 0 0
\(267\) 97.7120i 0.365962i
\(268\) 0 0
\(269\) 16.6610i 0.0619368i 0.999520 + 0.0309684i \(0.00985912\pi\)
−0.999520 + 0.0309684i \(0.990141\pi\)
\(270\) 0 0
\(271\) 148.202i 0.546870i −0.961890 0.273435i \(-0.911840\pi\)
0.961890 0.273435i \(-0.0881598\pi\)
\(272\) 0 0
\(273\) 24.6184i 0.0901774i
\(274\) 0 0
\(275\) −6.52795 + 441.845i −0.0237380 + 1.60671i
\(276\) 0 0
\(277\) −373.716 −1.34916 −0.674578 0.738204i \(-0.735674\pi\)
−0.674578 + 0.738204i \(0.735674\pi\)
\(278\) 0 0
\(279\) 227.609i 0.815802i
\(280\) 0 0
\(281\) −250.756 −0.892369 −0.446184 0.894941i \(-0.647217\pi\)
−0.446184 + 0.894941i \(0.647217\pi\)
\(282\) 0 0
\(283\) 463.657i 1.63836i −0.573533 0.819182i \(-0.694428\pi\)
0.573533 0.819182i \(-0.305572\pi\)
\(284\) 0 0
\(285\) 17.1146 16.8636i 0.0600512 0.0591705i
\(286\) 0 0
\(287\) 29.9824 0.104468
\(288\) 0 0
\(289\) 168.879 0.584356
\(290\) 0 0
\(291\) −272.200 −0.935395
\(292\) 0 0
\(293\) 275.455 0.940120 0.470060 0.882634i \(-0.344232\pi\)
0.470060 + 0.882634i \(0.344232\pi\)
\(294\) 0 0
\(295\) 255.756 + 259.562i 0.866968 + 0.879872i
\(296\) 0 0
\(297\) 512.255i 1.72476i
\(298\) 0 0
\(299\) −249.368 −0.834008
\(300\) 0 0
\(301\) 36.4451i 0.121080i
\(302\) 0 0
\(303\) −72.2321 −0.238390
\(304\) 0 0
\(305\) 282.570 278.426i 0.926459 0.912873i
\(306\) 0 0
\(307\) 131.620i 0.428728i 0.976754 + 0.214364i \(0.0687679\pi\)
−0.976754 + 0.214364i \(0.931232\pi\)
\(308\) 0 0
\(309\) 155.218i 0.502323i
\(310\) 0 0
\(311\) 353.515i 1.13670i −0.822786 0.568352i \(-0.807581\pi\)
0.822786 0.568352i \(-0.192419\pi\)
\(312\) 0 0
\(313\) 281.503i 0.899372i 0.893187 + 0.449686i \(0.148464\pi\)
−0.893187 + 0.449686i \(0.851536\pi\)
\(314\) 0 0
\(315\) 8.97181 + 9.10534i 0.0284819 + 0.0289058i
\(316\) 0 0
\(317\) 216.229 0.682110 0.341055 0.940043i \(-0.389216\pi\)
0.341055 + 0.940043i \(0.389216\pi\)
\(318\) 0 0
\(319\) 260.516i 0.816665i
\(320\) 0 0
\(321\) 193.801 0.603742
\(322\) 0 0
\(323\) 23.8487i 0.0738351i
\(324\) 0 0
\(325\) 6.63981 449.417i 0.0204302 1.38282i
\(326\) 0 0
\(327\) 180.781 0.552847
\(328\) 0 0
\(329\) 33.5852 0.102083
\(330\) 0 0
\(331\) 333.395 1.00724 0.503618 0.863926i \(-0.332002\pi\)
0.503618 + 0.863926i \(0.332002\pi\)
\(332\) 0 0
\(333\) 28.9386 0.0869027
\(334\) 0 0
\(335\) 95.3509 93.9526i 0.284630 0.280456i
\(336\) 0 0
\(337\) 243.818i 0.723496i 0.932276 + 0.361748i \(0.117820\pi\)
−0.932276 + 0.361748i \(0.882180\pi\)
\(338\) 0 0
\(339\) −27.1833 −0.0801867
\(340\) 0 0
\(341\) 975.758i 2.86146i
\(342\) 0 0
\(343\) −60.5273 −0.176464
\(344\) 0 0
\(345\) 109.093 107.493i 0.316211 0.311574i
\(346\) 0 0
\(347\) 221.109i 0.637201i 0.947889 + 0.318601i \(0.103213\pi\)
−0.947889 + 0.318601i \(0.896787\pi\)
\(348\) 0 0
\(349\) 39.1704i 0.112236i −0.998424 0.0561181i \(-0.982128\pi\)
0.998424 0.0561181i \(-0.0178723\pi\)
\(350\) 0 0
\(351\) 521.033i 1.48442i
\(352\) 0 0
\(353\) 646.473i 1.83137i 0.401899 + 0.915684i \(0.368350\pi\)
−0.401899 + 0.915684i \(0.631650\pi\)
\(354\) 0 0
\(355\) 165.610 163.181i 0.466506 0.459665i
\(356\) 0 0
\(357\) 15.0077 0.0420383
\(358\) 0 0
\(359\) 256.700i 0.715042i 0.933905 + 0.357521i \(0.116378\pi\)
−0.933905 + 0.357521i \(0.883622\pi\)
\(360\) 0 0
\(361\) −356.265 −0.986884
\(362\) 0 0
\(363\) 422.752i 1.16461i
\(364\) 0 0
\(365\) −339.002 + 334.030i −0.928772 + 0.915152i
\(366\) 0 0
\(367\) 551.424 1.50252 0.751259 0.660008i \(-0.229447\pi\)
0.751259 + 0.660008i \(0.229447\pi\)
\(368\) 0 0
\(369\) 199.369 0.540296
\(370\) 0 0
\(371\) 2.44386 0.00658722
\(372\) 0 0
\(373\) −261.418 −0.700852 −0.350426 0.936590i \(-0.613963\pi\)
−0.350426 + 0.936590i \(0.613963\pi\)
\(374\) 0 0
\(375\) 190.821 + 199.471i 0.508856 + 0.531923i
\(376\) 0 0
\(377\) 264.980i 0.702866i
\(378\) 0 0
\(379\) 344.007 0.907671 0.453835 0.891086i \(-0.350055\pi\)
0.453835 + 0.891086i \(0.350055\pi\)
\(380\) 0 0
\(381\) 388.445i 1.01954i
\(382\) 0 0
\(383\) −374.736 −0.978422 −0.489211 0.872165i \(-0.662715\pi\)
−0.489211 + 0.872165i \(0.662715\pi\)
\(384\) 0 0
\(385\) 38.4621 + 39.0346i 0.0999016 + 0.101388i
\(386\) 0 0
\(387\) 242.343i 0.626210i
\(388\) 0 0
\(389\) 692.358i 1.77984i −0.456116 0.889920i \(-0.650760\pi\)
0.456116 0.889920i \(-0.349240\pi\)
\(390\) 0 0
\(391\) 152.018i 0.388793i
\(392\) 0 0
\(393\) 33.6376i 0.0855919i
\(394\) 0 0
\(395\) −86.2027 + 84.9385i −0.218235 + 0.215034i
\(396\) 0 0
\(397\) −427.546 −1.07694 −0.538471 0.842644i \(-0.680998\pi\)
−0.538471 + 0.842644i \(0.680998\pi\)
\(398\) 0 0
\(399\) 2.97961i 0.00746770i
\(400\) 0 0
\(401\) 179.261 0.447036 0.223518 0.974700i \(-0.428246\pi\)
0.223518 + 0.974700i \(0.428246\pi\)
\(402\) 0 0
\(403\) 992.478i 2.46272i
\(404\) 0 0
\(405\) −94.3729 95.7775i −0.233019 0.236488i
\(406\) 0 0
\(407\) 124.060 0.304815
\(408\) 0 0
\(409\) −89.7368 −0.219405 −0.109703 0.993964i \(-0.534990\pi\)
−0.109703 + 0.993964i \(0.534990\pi\)
\(410\) 0 0
\(411\) 552.032 1.34314
\(412\) 0 0
\(413\) 45.1892 0.109417
\(414\) 0 0
\(415\) 382.372 376.764i 0.921378 0.907866i
\(416\) 0 0
\(417\) 497.839i 1.19386i
\(418\) 0 0
\(419\) 203.673 0.486093 0.243046 0.970015i \(-0.421853\pi\)
0.243046 + 0.970015i \(0.421853\pi\)
\(420\) 0 0
\(421\) 388.384i 0.922528i 0.887263 + 0.461264i \(0.152604\pi\)
−0.887263 + 0.461264i \(0.847396\pi\)
\(422\) 0 0
\(423\) 223.327 0.527959
\(424\) 0 0
\(425\) −273.970 4.04771i −0.644635 0.00952402i
\(426\) 0 0
\(427\) 49.1948i 0.115210i
\(428\) 0 0
\(429\) 701.788i 1.63587i
\(430\) 0 0
\(431\) 617.011i 1.43158i 0.698316 + 0.715790i \(0.253933\pi\)
−0.698316 + 0.715790i \(0.746067\pi\)
\(432\) 0 0
\(433\) 210.938i 0.487155i −0.969881 0.243578i \(-0.921679\pi\)
0.969881 0.243578i \(-0.0783210\pi\)
\(434\) 0 0
\(435\) 114.223 + 115.923i 0.262581 + 0.266489i
\(436\) 0 0
\(437\) 30.1815 0.0690652
\(438\) 0 0
\(439\) 159.885i 0.364203i −0.983280 0.182102i \(-0.941710\pi\)
0.983280 0.182102i \(-0.0582900\pi\)
\(440\) 0 0
\(441\) −200.447 −0.454528
\(442\) 0 0
\(443\) 121.460i 0.274177i −0.990559 0.137088i \(-0.956226\pi\)
0.990559 0.137088i \(-0.0437744\pi\)
\(444\) 0 0
\(445\) 155.274 + 157.585i 0.348931 + 0.354124i
\(446\) 0 0
\(447\) 170.860 0.382237
\(448\) 0 0
\(449\) 533.002 1.18709 0.593543 0.804802i \(-0.297729\pi\)
0.593543 + 0.804802i \(0.297729\pi\)
\(450\) 0 0
\(451\) 854.696 1.89511
\(452\) 0 0
\(453\) 361.513 0.798043
\(454\) 0 0
\(455\) −39.1212 39.7034i −0.0859806 0.0872603i
\(456\) 0 0
\(457\) 103.445i 0.226357i −0.993575 0.113179i \(-0.963897\pi\)
0.993575 0.113179i \(-0.0361032\pi\)
\(458\) 0 0
\(459\) 317.628 0.691999
\(460\) 0 0
\(461\) 420.337i 0.911794i −0.890032 0.455897i \(-0.849318\pi\)
0.890032 0.455897i \(-0.150682\pi\)
\(462\) 0 0
\(463\) 63.3035 0.136725 0.0683623 0.997661i \(-0.478223\pi\)
0.0683623 + 0.997661i \(0.478223\pi\)
\(464\) 0 0
\(465\) 427.818 + 434.186i 0.920039 + 0.933732i
\(466\) 0 0
\(467\) 129.206i 0.276673i 0.990385 + 0.138337i \(0.0441756\pi\)
−0.990385 + 0.138337i \(0.955824\pi\)
\(468\) 0 0
\(469\) 16.6004i 0.0353953i
\(470\) 0 0
\(471\) 129.722i 0.275419i
\(472\) 0 0
\(473\) 1038.93i 2.19646i
\(474\) 0 0
\(475\) −0.803627 + 54.3936i −0.00169185 + 0.114513i
\(476\) 0 0
\(477\) 16.2506 0.0340683
\(478\) 0 0
\(479\) 517.216i 1.07978i −0.841734 0.539892i \(-0.818465\pi\)
0.841734 0.539892i \(-0.181535\pi\)
\(480\) 0 0
\(481\) −126.186 −0.262340
\(482\) 0 0
\(483\) 18.9928i 0.0393226i
\(484\) 0 0
\(485\) 438.991 432.553i 0.905136 0.891862i
\(486\) 0 0
\(487\) 893.449 1.83460 0.917299 0.398199i \(-0.130365\pi\)
0.917299 + 0.398199i \(0.130365\pi\)
\(488\) 0 0
\(489\) −248.574 −0.508331
\(490\) 0 0
\(491\) −506.336 −1.03124 −0.515618 0.856819i \(-0.672437\pi\)
−0.515618 + 0.856819i \(0.672437\pi\)
\(492\) 0 0
\(493\) −161.535 −0.327658
\(494\) 0 0
\(495\) 255.756 + 259.562i 0.516678 + 0.524368i
\(496\) 0 0
\(497\) 28.8322i 0.0580126i
\(498\) 0 0
\(499\) 512.596 1.02725 0.513624 0.858016i \(-0.328303\pi\)
0.513624 + 0.858016i \(0.328303\pi\)
\(500\) 0 0
\(501\) 523.460i 1.04483i
\(502\) 0 0
\(503\) −389.856 −0.775061 −0.387530 0.921857i \(-0.626672\pi\)
−0.387530 + 0.921857i \(0.626672\pi\)
\(504\) 0 0
\(505\) 116.492 114.784i 0.230678 0.227295i
\(506\) 0 0
\(507\) 340.599i 0.671793i
\(508\) 0 0
\(509\) 80.1553i 0.157476i −0.996895 0.0787380i \(-0.974911\pi\)
0.996895 0.0787380i \(-0.0250891\pi\)
\(510\) 0 0
\(511\) 59.0194i 0.115498i
\(512\) 0 0
\(513\) 63.0614i 0.122927i
\(514\) 0 0
\(515\) −246.657 250.328i −0.478945 0.486073i
\(516\) 0 0
\(517\) 957.400 1.85184
\(518\) 0 0
\(519\) 646.939i 1.24651i
\(520\) 0 0
\(521\) −417.076 −0.800529 −0.400265 0.916400i \(-0.631082\pi\)
−0.400265 + 0.916400i \(0.631082\pi\)
\(522\) 0 0
\(523\) 28.2320i 0.0539809i 0.999636 + 0.0269904i \(0.00859237\pi\)
−0.999636 + 0.0269904i \(0.991408\pi\)
\(524\) 0 0
\(525\) 34.2292 + 0.505712i 0.0651985 + 0.000963261i
\(526\) 0 0
\(527\) −605.026 −1.14806
\(528\) 0 0
\(529\) −336.616 −0.636324
\(530\) 0 0
\(531\) 300.488 0.565890
\(532\) 0 0
\(533\) −869.341 −1.63103
\(534\) 0 0
\(535\) −312.553 + 307.970i −0.584212 + 0.575644i
\(536\) 0 0
\(537\) 399.365i 0.743696i
\(538\) 0 0
\(539\) −859.315 −1.59428
\(540\) 0 0
\(541\) 948.095i 1.75249i −0.481870 0.876243i \(-0.660042\pi\)
0.481870 0.876243i \(-0.339958\pi\)
\(542\) 0 0
\(543\) 572.478 1.05429
\(544\) 0 0
\(545\) −291.555 + 287.279i −0.534963 + 0.527118i
\(546\) 0 0
\(547\) 266.602i 0.487389i −0.969852 0.243695i \(-0.921641\pi\)
0.969852 0.243695i \(-0.0783595\pi\)
\(548\) 0 0
\(549\) 327.123i 0.595853i
\(550\) 0 0
\(551\) 32.0710i 0.0582051i
\(552\) 0 0
\(553\) 15.0077i 0.0271387i
\(554\) 0 0
\(555\) 55.2032 54.3936i 0.0994652 0.0980066i
\(556\) 0 0
\(557\) 23.5417 0.0422651 0.0211326 0.999777i \(-0.493273\pi\)
0.0211326 + 0.999777i \(0.493273\pi\)
\(558\) 0 0
\(559\) 1056.73i 1.89039i
\(560\) 0 0
\(561\) 427.818 0.762599
\(562\) 0 0
\(563\) 119.352i 0.211993i −0.994366 0.105997i \(-0.966197\pi\)
0.994366 0.105997i \(-0.0338033\pi\)
\(564\) 0 0
\(565\) 43.8399 43.1970i 0.0775928 0.0764549i
\(566\) 0 0
\(567\) −16.6746 −0.0294085
\(568\) 0 0
\(569\) −717.434 −1.26087 −0.630434 0.776243i \(-0.717123\pi\)
−0.630434 + 0.776243i \(0.717123\pi\)
\(570\) 0 0
\(571\) −389.134 −0.681496 −0.340748 0.940155i \(-0.610680\pi\)
−0.340748 + 0.940155i \(0.610680\pi\)
\(572\) 0 0
\(573\) −594.538 −1.03759
\(574\) 0 0
\(575\) −5.12253 + 346.719i −0.00890874 + 0.602990i
\(576\) 0 0
\(577\) 934.131i 1.61894i −0.587158 0.809472i \(-0.699753\pi\)
0.587158 0.809472i \(-0.300247\pi\)
\(578\) 0 0
\(579\) −320.607 −0.553726
\(580\) 0 0
\(581\) 66.5701i 0.114578i
\(582\) 0 0
\(583\) 69.6661 0.119496
\(584\) 0 0
\(585\) −260.138 264.010i −0.444681 0.451299i
\(586\) 0 0
\(587\) 372.365i 0.634353i 0.948366 + 0.317177i \(0.102735\pi\)
−0.948366 + 0.317177i \(0.897265\pi\)
\(588\) 0 0
\(589\) 120.121i 0.203941i
\(590\) 0 0
\(591\) 601.511i 1.01778i
\(592\) 0 0
\(593\) 446.495i 0.752942i 0.926428 + 0.376471i \(0.122863\pi\)
−0.926428 + 0.376471i \(0.877137\pi\)
\(594\) 0 0
\(595\) −24.2037 + 23.8487i −0.0406785 + 0.0400819i
\(596\) 0 0
\(597\) −727.241 −1.21816
\(598\) 0 0
\(599\) 677.938i 1.13178i −0.824480 0.565892i \(-0.808532\pi\)
0.824480 0.565892i \(-0.191468\pi\)
\(600\) 0 0
\(601\) 696.941 1.15964 0.579818 0.814746i \(-0.303124\pi\)
0.579818 + 0.814746i \(0.303124\pi\)
\(602\) 0 0
\(603\) 110.385i 0.183060i
\(604\) 0 0
\(605\) 671.796 + 681.794i 1.11041 + 1.12693i
\(606\) 0 0
\(607\) −372.628 −0.613884 −0.306942 0.951728i \(-0.599306\pi\)
−0.306942 + 0.951728i \(0.599306\pi\)
\(608\) 0 0
\(609\) 20.1819 0.0331393
\(610\) 0 0
\(611\) −973.806 −1.59379
\(612\) 0 0
\(613\) 569.647 0.929277 0.464638 0.885501i \(-0.346184\pi\)
0.464638 + 0.885501i \(0.346184\pi\)
\(614\) 0 0
\(615\) 380.316 374.739i 0.618400 0.609332i
\(616\) 0 0
\(617\) 126.714i 0.205372i 0.994714 + 0.102686i \(0.0327437\pi\)
−0.994714 + 0.102686i \(0.967256\pi\)
\(618\) 0 0
\(619\) 771.205 1.24589 0.622944 0.782266i \(-0.285936\pi\)
0.622944 + 0.782266i \(0.285936\pi\)
\(620\) 0 0
\(621\) 401.970i 0.647294i
\(622\) 0 0
\(623\) 27.4352 0.0440373
\(624\) 0 0
\(625\) −624.727 18.4638i −0.999564 0.0295421i
\(626\) 0 0
\(627\) 84.9385i 0.135468i
\(628\) 0 0
\(629\) 76.9242i 0.122296i
\(630\) 0 0
\(631\) 74.5192i 0.118097i 0.998255 + 0.0590485i \(0.0188067\pi\)
−0.998255 + 0.0590485i \(0.981193\pi\)
\(632\) 0 0
\(633\) 14.4161i 0.0227743i
\(634\) 0 0
\(635\) 617.279 + 626.466i 0.972092 + 0.986560i
\(636\) 0 0
\(637\) 874.040 1.37212
\(638\) 0 0
\(639\) 191.721i 0.300034i
\(640\) 0 0
\(641\) −32.9072 −0.0513373 −0.0256686 0.999671i \(-0.508171\pi\)
−0.0256686 + 0.999671i \(0.508171\pi\)
\(642\) 0 0
\(643\) 900.609i 1.40064i 0.713831 + 0.700318i \(0.246958\pi\)
−0.713831 + 0.700318i \(0.753042\pi\)
\(644\) 0 0
\(645\) −455.514 462.294i −0.706223 0.716734i
\(646\) 0 0
\(647\) −571.419 −0.883182 −0.441591 0.897217i \(-0.645586\pi\)
−0.441591 + 0.897217i \(0.645586\pi\)
\(648\) 0 0
\(649\) 1288.19 1.98488
\(650\) 0 0
\(651\) 75.5907 0.116115
\(652\) 0 0
\(653\) 1138.05 1.74280 0.871402 0.490570i \(-0.163212\pi\)
0.871402 + 0.490570i \(0.163212\pi\)
\(654\) 0 0
\(655\) −53.4536 54.2492i −0.0816085 0.0828231i
\(656\) 0 0
\(657\) 392.453i 0.597340i
\(658\) 0 0
\(659\) −260.248 −0.394914 −0.197457 0.980312i \(-0.563268\pi\)
−0.197457 + 0.980312i \(0.563268\pi\)
\(660\) 0 0
\(661\) 1012.05i 1.53109i 0.643385 + 0.765543i \(0.277529\pi\)
−0.643385 + 0.765543i \(0.722471\pi\)
\(662\) 0 0
\(663\) −435.149 −0.656334
\(664\) 0 0
\(665\) 4.73490 + 4.80537i 0.00712015 + 0.00722613i
\(666\) 0 0
\(667\) 204.429i 0.306490i
\(668\) 0 0
\(669\) 807.373i 1.20684i
\(670\) 0 0
\(671\) 1402.38i 2.08998i
\(672\) 0 0
\(673\) 597.070i 0.887177i −0.896231 0.443588i \(-0.853705\pi\)
0.896231 0.443588i \(-0.146295\pi\)
\(674\) 0 0
\(675\) 724.437 + 10.7030i 1.07324 + 0.0158564i
\(676\) 0 0
\(677\) −1112.46 −1.64322 −0.821611 0.570048i \(-0.806925\pi\)
−0.821611 + 0.570048i \(0.806925\pi\)
\(678\) 0 0
\(679\) 76.4273i 0.112559i
\(680\) 0 0
\(681\) 494.820 0.726608
\(682\) 0 0
\(683\) 1089.31i 1.59489i 0.603394 + 0.797443i \(0.293815\pi\)
−0.603394 + 0.797443i \(0.706185\pi\)
\(684\) 0 0
\(685\) −890.291 + 877.235i −1.29969 + 1.28063i
\(686\) 0 0
\(687\) −547.065 −0.796310
\(688\) 0 0
\(689\) −70.8599 −0.102845
\(690\) 0 0
\(691\) −837.556 −1.21209 −0.606046 0.795430i \(-0.707245\pi\)
−0.606046 + 0.795430i \(0.707245\pi\)
\(692\) 0 0
\(693\) 45.1892 0.0652080
\(694\) 0 0
\(695\) −791.116 802.890i −1.13830 1.15524i
\(696\) 0 0
\(697\) 529.961i 0.760346i
\(698\) 0 0
\(699\) −576.236 −0.824372
\(700\) 0 0
\(701\) 969.714i 1.38333i −0.722219 0.691665i \(-0.756878\pi\)
0.722219 0.691665i \(-0.243122\pi\)
\(702\) 0 0
\(703\) 15.2725 0.0217247
\(704\) 0 0
\(705\) 426.017 419.769i 0.604279 0.595418i
\(706\) 0 0
\(707\) 20.2811i 0.0286861i
\(708\) 0 0
\(709\) 636.769i 0.898123i −0.893501 0.449061i \(-0.851758\pi\)
0.893501 0.449061i \(-0.148242\pi\)
\(710\) 0 0
\(711\) 99.7944i 0.140358i
\(712\) 0 0
\(713\) 765.684i 1.07389i
\(714\) 0 0
\(715\) −1115.21 1131.81i −1.55974 1.58295i
\(716\) 0 0
\(717\) −404.170 −0.563696
\(718\) 0 0
\(719\) 955.862i 1.32943i −0.747096 0.664717i \(-0.768552\pi\)
0.747096 0.664717i \(-0.231448\pi\)
\(720\) 0 0
\(721\) −43.5815 −0.0604459
\(722\) 0 0
\(723\) 452.109i 0.625324i
\(724\) 0 0
\(725\) −368.426 5.44323i −0.508173 0.00750790i
\(726\) 0 0
\(727\) 334.899 0.460659 0.230330 0.973113i \(-0.426020\pi\)
0.230330 + 0.973113i \(0.426020\pi\)
\(728\) 0 0
\(729\) −686.879 −0.942221
\(730\) 0 0
\(731\) 644.194 0.881250
\(732\) 0 0
\(733\) −321.781 −0.438992 −0.219496 0.975613i \(-0.570441\pi\)
−0.219496 + 0.975613i \(0.570441\pi\)
\(734\) 0 0
\(735\) −382.372 + 376.764i −0.520234 + 0.512605i
\(736\) 0 0
\(737\) 473.220i 0.642090i
\(738\) 0 0
\(739\) −446.245 −0.603850 −0.301925 0.953332i \(-0.597629\pi\)
−0.301925 + 0.953332i \(0.597629\pi\)
\(740\) 0 0
\(741\) 86.3940i 0.116591i
\(742\) 0 0
\(743\) 436.894 0.588014 0.294007 0.955803i \(-0.405011\pi\)
0.294007 + 0.955803i \(0.405011\pi\)
\(744\) 0 0
\(745\) −275.555 + 271.514i −0.369872 + 0.364448i
\(746\) 0 0
\(747\) 442.661i 0.592585i
\(748\) 0 0
\(749\) 54.4148i 0.0726499i
\(750\) 0 0
\(751\) 273.036i 0.363564i −0.983339 0.181782i \(-0.941814\pi\)
0.983339 0.181782i \(-0.0581865\pi\)
\(752\) 0 0
\(753\) 711.641i 0.945075i
\(754\) 0 0
\(755\) −583.032 + 574.481i −0.772227 + 0.760902i
\(756\) 0 0
\(757\) 265.844 0.351182 0.175591 0.984463i \(-0.443816\pi\)
0.175591 + 0.984463i \(0.443816\pi\)
\(758\) 0 0
\(759\) 541.420i 0.713333i
\(760\) 0 0
\(761\) 475.322 0.624602 0.312301 0.949983i \(-0.398900\pi\)
0.312301 + 0.949983i \(0.398900\pi\)
\(762\) 0 0
\(763\) 50.7590i 0.0665256i
\(764\) 0 0
\(765\) −160.944 + 158.583i −0.210384 + 0.207298i
\(766\) 0 0
\(767\) −1310.26 −1.70830
\(768\) 0 0
\(769\) −768.098 −0.998828 −0.499414 0.866364i \(-0.666451\pi\)
−0.499414 + 0.866364i \(0.666451\pi\)
\(770\) 0 0
\(771\) 517.216 0.670838
\(772\) 0 0
\(773\) 628.494 0.813059 0.406529 0.913638i \(-0.366739\pi\)
0.406529 + 0.913638i \(0.366739\pi\)
\(774\) 0 0
\(775\) −1379.93 20.3875i −1.78055 0.0263064i
\(776\) 0 0
\(777\) 9.61075i 0.0123690i
\(778\) 0 0
\(779\) 105.218 0.135068
\(780\) 0 0
\(781\) 821.909i 1.05238i
\(782\) 0 0
\(783\) 427.135 0.545511
\(784\) 0 0
\(785\) −206.142 209.210i −0.262601 0.266510i
\(786\) 0 0
\(787\) 1051.87i 1.33655i 0.743914 + 0.668275i \(0.232967\pi\)
−0.743914 + 0.668275i \(0.767033\pi\)
\(788\) 0 0
\(789\) 990.146i 1.25494i
\(790\) 0 0
\(791\) 7.63243i 0.00964909i
\(792\) 0 0
\(793\) 1426.41i 1.79875i
\(794\) 0 0
\(795\) 30.9995 30.5449i 0.0389931 0.0384213i
\(796\) 0 0
\(797\) −783.662 −0.983265 −0.491632 0.870803i \(-0.663600\pi\)
−0.491632 + 0.870803i \(0.663600\pi\)
\(798\) 0 0
\(799\) 593.644i 0.742983i
\(800\) 0 0
\(801\) 182.432 0.227755
\(802\) 0 0
\(803\) 1682.44i 2.09520i
\(804\) 0 0
\(805\) 30.1815 + 30.6307i 0.0374925 + 0.0380505i
\(806\) 0 0
\(807\) 36.7936 0.0455931
\(808\) 0 0
\(809\) 860.712 1.06392 0.531960 0.846769i \(-0.321455\pi\)
0.531960 + 0.846769i \(0.321455\pi\)
\(810\) 0 0
\(811\) −489.765 −0.603903 −0.301951 0.953323i \(-0.597638\pi\)
−0.301951 + 0.953323i \(0.597638\pi\)
\(812\) 0 0
\(813\) −327.284 −0.402564
\(814\) 0 0
\(815\) 400.888 395.009i 0.491887 0.484674i
\(816\) 0 0
\(817\) 127.898i 0.156545i
\(818\) 0 0
\(819\) −45.9635 −0.0561215
\(820\) 0 0
\(821\) 296.634i 0.361309i −0.983547 0.180654i \(-0.942178\pi\)
0.983547 0.180654i \(-0.0578215\pi\)
\(822\) 0 0
\(823\) 544.661 0.661800 0.330900 0.943666i \(-0.392648\pi\)
0.330900 + 0.943666i \(0.392648\pi\)
\(824\) 0 0
\(825\) 975.758 + 14.4161i 1.18274 + 0.0174741i
\(826\) 0 0
\(827\) 187.749i 0.227024i −0.993537 0.113512i \(-0.963790\pi\)
0.993537 0.113512i \(-0.0362101\pi\)
\(828\) 0 0
\(829\) 153.430i 0.185078i −0.995709 0.0925392i \(-0.970502\pi\)
0.995709 0.0925392i \(-0.0294983\pi\)
\(830\) 0 0
\(831\) 825.303i 0.993145i
\(832\) 0 0
\(833\) 532.825i 0.639646i
\(834\) 0 0
\(835\) −831.831 844.212i −0.996205 1.01103i
\(836\) 0 0
\(837\) 1599.83 1.91138
\(838\) 0 0
\(839\) 826.140i 0.984672i −0.870405 0.492336i \(-0.836143\pi\)
0.870405 0.492336i \(-0.163857\pi\)
\(840\) 0 0
\(841\) 623.773 0.741704
\(842\) 0 0
\(843\) 553.761i 0.656893i
\(844\) 0 0
\(845\) 541.246 + 549.302i 0.640528 + 0.650062i
\(846\) 0 0
\(847\) 118.699 0.140140
\(848\) 0 0
\(849\) −1023.93 −1.20604
\(850\) 0 0
\(851\) 97.3505 0.114395
\(852\) 0 0
\(853\) −186.426 −0.218553 −0.109277 0.994011i \(-0.534853\pi\)
−0.109277 + 0.994011i \(0.534853\pi\)
\(854\) 0 0
\(855\) 31.4850 + 31.9536i 0.0368245 + 0.0373726i
\(856\) 0 0
\(857\) 1310.23i 1.52885i −0.644711 0.764426i \(-0.723022\pi\)
0.644711 0.764426i \(-0.276978\pi\)
\(858\) 0 0
\(859\) −655.375 −0.762951 −0.381475 0.924379i \(-0.624584\pi\)
−0.381475 + 0.924379i \(0.624584\pi\)
\(860\) 0 0
\(861\) 66.2122i 0.0769015i
\(862\) 0 0
\(863\) 170.869 0.197995 0.0989973 0.995088i \(-0.468436\pi\)
0.0989973 + 0.995088i \(0.468436\pi\)
\(864\) 0 0
\(865\) −1028.05 1043.35i −1.18850 1.20619i
\(866\) 0 0
\(867\) 372.947i 0.430158i
\(868\) 0 0
\(869\) 427.818i 0.492311i
\(870\) 0 0
\(871\) 481.329i 0.552617i
\(872\) 0 0
\(873\) 508.207i 0.582139i
\(874\) 0 0
\(875\) −56.0068 + 53.5781i −0.0640078 + 0.0612321i
\(876\) 0 0
\(877\) −303.743 −0.346343 −0.173171 0.984892i \(-0.555401\pi\)
−0.173171 + 0.984892i \(0.555401\pi\)
\(878\) 0 0
\(879\) 608.307i 0.692044i
\(880\) 0 0
\(881\) 2.32385 0.00263774 0.00131887 0.999999i \(-0.499580\pi\)
0.00131887 + 0.999999i \(0.499580\pi\)
\(882\) 0 0
\(883\) 260.688i 0.295230i −0.989045 0.147615i \(-0.952840\pi\)
0.989045 0.147615i \(-0.0471596\pi\)
\(884\) 0 0
\(885\) 573.209 564.803i 0.647694 0.638195i
\(886\) 0 0
\(887\) −452.710 −0.510384 −0.255192 0.966890i \(-0.582139\pi\)
−0.255192 + 0.966890i \(0.582139\pi\)
\(888\) 0 0
\(889\) 109.066 0.122684
\(890\) 0 0
\(891\) −475.337 −0.533487
\(892\) 0 0
\(893\) 117.861 0.131984
\(894\) 0 0
\(895\) −634.631 644.077i −0.709085 0.719639i
\(896\) 0 0
\(897\) 550.698i 0.613933i
\(898\) 0 0
\(899\) −813.620 −0.905028
\(900\) 0 0
\(901\) 43.1970i 0.0479434i
\(902\) 0 0
\(903\) −80.4842 −0.0891298
\(904\) 0 0
\(905\) −923.265 + 909.725i −1.02018 + 1.00522i
\(906\) 0 0
\(907\) 417.248i 0.460031i 0.973187 + 0.230015i \(0.0738777\pi\)
−0.973187 + 0.230015i \(0.926122\pi\)
\(908\) 0 0
\(909\) 134.860i 0.148361i
\(910\) 0 0
\(911\) 673.050i 0.738804i 0.929270 + 0.369402i \(0.120437\pi\)
−0.929270 + 0.369402i \(0.879563\pi\)
\(912\) 0 0
\(913\) 1897.69i 2.07852i
\(914\) 0 0
\(915\) −614.868 624.019i −0.671987 0.681988i
\(916\) 0 0
\(917\) −9.44465 −0.0102995
\(918\) 0 0
\(919\) 1204.93i 1.31113i 0.755138 + 0.655566i \(0.227570\pi\)
−0.755138 + 0.655566i \(0.772430\pi\)
\(920\) 0 0
\(921\) 290.665 0.315597
\(922\) 0 0
\(923\) 835.993i 0.905735i
\(924\) 0 0
\(925\) −2.59210 + 175.447i −0.00280227 + 0.189672i
\(926\) 0 0
\(927\) −289.797 −0.312618
\(928\) 0 0
\(929\) 658.790 0.709139 0.354569 0.935030i \(-0.384628\pi\)
0.354569 + 0.935030i \(0.384628\pi\)
\(930\) 0 0
\(931\) −105.787 −0.113627
\(932\) 0 0
\(933\) −780.691 −0.836754
\(934\) 0 0
\(935\) −689.965 + 679.846i −0.737930 + 0.727108i
\(936\) 0 0
\(937\) 1690.80i 1.80448i 0.431237 + 0.902239i \(0.358077\pi\)
−0.431237 + 0.902239i \(0.641923\pi\)
\(938\) 0 0
\(939\) 621.664 0.662048
\(940\) 0 0
\(941\) 219.663i 0.233436i 0.993165 + 0.116718i \(0.0372373\pi\)
−0.993165 + 0.116718i \(0.962763\pi\)
\(942\) 0 0
\(943\) 670.685 0.711225
\(944\) 0 0
\(945\) 64.0000 63.0614i 0.0677249 0.0667317i
\(946\) 0 0
\(947\) 552.774i 0.583711i −0.956462 0.291855i \(-0.905727\pi\)
0.956462 0.291855i \(-0.0942726\pi\)
\(948\) 0 0
\(949\) 1711.27i 1.80324i
\(950\) 0 0
\(951\) 477.513i 0.502117i
\(952\) 0 0
\(953\) 15.7654i 0.0165429i 0.999966 + 0.00827144i \(0.00263291\pi\)
−0.999966 + 0.00827144i \(0.997367\pi\)
\(954\) 0 0
\(955\) 958.842 944.780i 1.00402 0.989299i
\(956\) 0 0
\(957\) 575.316 0.601166
\(958\) 0 0
\(959\) 154.998i 0.161624i
\(960\) 0 0
\(961\) −2086.39 −2.17107
\(962\) 0 0
\(963\) 361.834i 0.375736i
\(964\) 0 0
\(965\) 517.060 509.477i 0.535814 0.527956i
\(966\) 0 0
\(967\) 308.027 0.318538 0.159269 0.987235i \(-0.449086\pi\)
0.159269 + 0.987235i \(0.449086\pi\)
\(968\) 0 0
\(969\) 52.6668 0.0543517
\(970\) 0 0
\(971\) 41.8794 0.0431302 0.0215651 0.999767i \(-0.493135\pi\)
0.0215651 + 0.999767i \(0.493135\pi\)
\(972\) 0 0
\(973\) −139.781 −0.143660
\(974\) 0 0
\(975\) −992.478 14.6632i −1.01793 0.0150391i
\(976\) 0 0
\(977\) 586.276i 0.600078i −0.953927 0.300039i \(-0.903000\pi\)
0.953927 0.300039i \(-0.0969997\pi\)
\(978\) 0 0
\(979\) 782.085 0.798861
\(980\) 0 0
\(981\) 337.525i 0.344062i
\(982\) 0 0
\(983\) 1627.01 1.65515 0.827573 0.561358i \(-0.189721\pi\)
0.827573 + 0.561358i \(0.189721\pi\)
\(984\) 0 0
\(985\) 955.862 + 970.088i 0.970418 + 0.984861i
\(986\) 0 0
\(987\) 74.1686i 0.0751455i
\(988\) 0 0
\(989\) 815.252i 0.824319i
\(990\) 0 0
\(991\) 255.629i 0.257950i 0.991648 + 0.128975i \(0.0411687\pi\)
−0.991648 + 0.128975i \(0.958831\pi\)
\(992\) 0 0
\(993\) 736.260i 0.741450i
\(994\) 0 0
\(995\) 1172.86 1155.66i 1.17875 1.16147i
\(996\) 0 0
\(997\) −1001.35 −1.00436 −0.502180 0.864763i \(-0.667468\pi\)
−0.502180 + 0.864763i \(0.667468\pi\)
\(998\) 0 0
\(999\) 203.405i 0.203609i
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 640.3.e.i.319.8 yes 16
4.3 odd 2 inner 640.3.e.i.319.12 yes 16
5.4 even 2 inner 640.3.e.i.319.10 yes 16
8.3 odd 2 inner 640.3.e.i.319.5 16
8.5 even 2 inner 640.3.e.i.319.9 yes 16
16.3 odd 4 1280.3.h.l.1279.3 8
16.5 even 4 1280.3.h.h.1279.4 8
16.11 odd 4 1280.3.h.h.1279.6 8
16.13 even 4 1280.3.h.l.1279.5 8
20.19 odd 2 inner 640.3.e.i.319.6 yes 16
40.19 odd 2 inner 640.3.e.i.319.11 yes 16
40.29 even 2 inner 640.3.e.i.319.7 yes 16
80.19 odd 4 1280.3.h.l.1279.6 8
80.29 even 4 1280.3.h.l.1279.4 8
80.59 odd 4 1280.3.h.h.1279.3 8
80.69 even 4 1280.3.h.h.1279.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.3.e.i.319.5 16 8.3 odd 2 inner
640.3.e.i.319.6 yes 16 20.19 odd 2 inner
640.3.e.i.319.7 yes 16 40.29 even 2 inner
640.3.e.i.319.8 yes 16 1.1 even 1 trivial
640.3.e.i.319.9 yes 16 8.5 even 2 inner
640.3.e.i.319.10 yes 16 5.4 even 2 inner
640.3.e.i.319.11 yes 16 40.19 odd 2 inner
640.3.e.i.319.12 yes 16 4.3 odd 2 inner
1280.3.h.h.1279.3 8 80.59 odd 4
1280.3.h.h.1279.4 8 16.5 even 4
1280.3.h.h.1279.5 8 80.69 even 4
1280.3.h.h.1279.6 8 16.11 odd 4
1280.3.h.l.1279.3 8 16.3 odd 4
1280.3.h.l.1279.4 8 80.29 even 4
1280.3.h.l.1279.5 8 16.13 even 4
1280.3.h.l.1279.6 8 80.19 odd 4