Properties

Label 147.4.c.b.146.4
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,4,Mod(146,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.146");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (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: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.4
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.22

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.84485i q^{2} +(5.11673 - 0.905040i) q^{3} -15.4725 q^{4} +17.3012 q^{5} +(-4.38478 - 24.7898i) q^{6} +36.2033i q^{8} +(25.3618 - 9.26169i) q^{9} +O(q^{10})\) \(q-4.84485i q^{2} +(5.11673 - 0.905040i) q^{3} -15.4725 q^{4} +17.3012 q^{5} +(-4.38478 - 24.7898i) q^{6} +36.2033i q^{8} +(25.3618 - 9.26169i) q^{9} -83.8216i q^{10} -27.8490i q^{11} +(-79.1688 + 14.0033i) q^{12} +16.3036i q^{13} +(88.5254 - 15.6583i) q^{15} +51.6191 q^{16} -40.8263 q^{17} +(-44.8715 - 122.874i) q^{18} -68.1627i q^{19} -267.693 q^{20} -134.924 q^{22} +71.7749i q^{23} +(32.7654 + 185.242i) q^{24} +174.331 q^{25} +78.9883 q^{26} +(121.387 - 70.3430i) q^{27} +216.426i q^{29} +(-75.8619 - 428.892i) q^{30} +157.351i q^{31} +39.5396i q^{32} +(-25.2044 - 142.496i) q^{33} +197.797i q^{34} +(-392.412 + 143.302i) q^{36} -348.489 q^{37} -330.238 q^{38} +(14.7554 + 83.4209i) q^{39} +626.360i q^{40} -153.371 q^{41} +427.584 q^{43} +430.894i q^{44} +(438.789 - 160.238i) q^{45} +347.738 q^{46} -16.8103 q^{47} +(264.121 - 46.7174i) q^{48} -844.606i q^{50} +(-208.897 + 36.9495i) q^{51} -252.258i q^{52} -192.526i q^{53} +(-340.801 - 588.103i) q^{54} -481.820i q^{55} +(-61.6899 - 348.770i) q^{57} +1048.55 q^{58} +287.422 q^{59} +(-1369.71 + 242.273i) q^{60} -224.297i q^{61} +762.340 q^{62} +604.516 q^{64} +282.071i q^{65} +(-690.370 + 122.112i) q^{66} -172.206 q^{67} +631.687 q^{68} +(64.9591 + 367.252i) q^{69} +1068.78i q^{71} +(335.304 + 918.181i) q^{72} -1078.22i q^{73} +1688.38i q^{74} +(892.004 - 157.776i) q^{75} +1054.65i q^{76} +(404.161 - 71.4875i) q^{78} +52.0336 q^{79} +893.072 q^{80} +(557.442 - 469.786i) q^{81} +743.059i q^{82} +1023.07 q^{83} -706.344 q^{85} -2071.58i q^{86} +(195.874 + 1107.39i) q^{87} +1008.23 q^{88} -668.570 q^{89} +(-776.329 - 2125.87i) q^{90} -1110.54i q^{92} +(142.409 + 805.121i) q^{93} +81.4431i q^{94} -1179.29i q^{95} +(35.7849 + 202.313i) q^{96} +1358.39i q^{97} +(-257.929 - 706.300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.84485i 1.71291i −0.516220 0.856456i \(-0.672661\pi\)
0.516220 0.856456i \(-0.327339\pi\)
\(3\) 5.11673 0.905040i 0.984715 0.174175i
\(4\) −15.4725 −1.93407
\(5\) 17.3012 1.54746 0.773732 0.633513i \(-0.218388\pi\)
0.773732 + 0.633513i \(0.218388\pi\)
\(6\) −4.38478 24.7898i −0.298346 1.68673i
\(7\) 0 0
\(8\) 36.2033i 1.59998i
\(9\) 25.3618 9.26169i 0.939326 0.343025i
\(10\) 83.8216i 2.65067i
\(11\) 27.8490i 0.763344i −0.924298 0.381672i \(-0.875348\pi\)
0.924298 0.381672i \(-0.124652\pi\)
\(12\) −79.1688 + 14.0033i −1.90450 + 0.336866i
\(13\) 16.3036i 0.347830i 0.984761 + 0.173915i \(0.0556419\pi\)
−0.984761 + 0.173915i \(0.944358\pi\)
\(14\) 0 0
\(15\) 88.5254 15.6583i 1.52381 0.269530i
\(16\) 51.6191 0.806549
\(17\) −40.8263 −0.582461 −0.291231 0.956653i \(-0.594065\pi\)
−0.291231 + 0.956653i \(0.594065\pi\)
\(18\) −44.8715 122.874i −0.587572 1.60898i
\(19\) 68.1627i 0.823031i −0.911403 0.411515i \(-0.865000\pi\)
0.911403 0.411515i \(-0.135000\pi\)
\(20\) −267.693 −2.99290
\(21\) 0 0
\(22\) −134.924 −1.30754
\(23\) 71.7749i 0.650700i 0.945594 + 0.325350i \(0.105482\pi\)
−0.945594 + 0.325350i \(0.894518\pi\)
\(24\) 32.7654 + 185.242i 0.278676 + 1.57552i
\(25\) 174.331 1.39465
\(26\) 78.9883 0.595803
\(27\) 121.387 70.3430i 0.865222 0.501389i
\(28\) 0 0
\(29\) 216.426i 1.38584i 0.721014 + 0.692920i \(0.243676\pi\)
−0.721014 + 0.692920i \(0.756324\pi\)
\(30\) −75.8619 428.892i −0.461681 2.61015i
\(31\) 157.351i 0.911646i 0.890070 + 0.455823i \(0.150655\pi\)
−0.890070 + 0.455823i \(0.849345\pi\)
\(32\) 39.5396i 0.218428i
\(33\) −25.2044 142.496i −0.132955 0.751676i
\(34\) 197.797i 0.997705i
\(35\) 0 0
\(36\) −392.412 + 143.302i −1.81672 + 0.663434i
\(37\) −348.489 −1.54841 −0.774207 0.632933i \(-0.781851\pi\)
−0.774207 + 0.632933i \(0.781851\pi\)
\(38\) −330.238 −1.40978
\(39\) 14.7554 + 83.4209i 0.0605834 + 0.342514i
\(40\) 626.360i 2.47590i
\(41\) −153.371 −0.584208 −0.292104 0.956387i \(-0.594355\pi\)
−0.292104 + 0.956387i \(0.594355\pi\)
\(42\) 0 0
\(43\) 427.584 1.51642 0.758208 0.652012i \(-0.226075\pi\)
0.758208 + 0.652012i \(0.226075\pi\)
\(44\) 430.894i 1.47636i
\(45\) 438.789 160.238i 1.45357 0.530820i
\(46\) 347.738 1.11459
\(47\) −16.8103 −0.0521708 −0.0260854 0.999660i \(-0.508304\pi\)
−0.0260854 + 0.999660i \(0.508304\pi\)
\(48\) 264.121 46.7174i 0.794221 0.140481i
\(49\) 0 0
\(50\) 844.606i 2.38891i
\(51\) −208.897 + 36.9495i −0.573558 + 0.101450i
\(52\) 252.258i 0.672727i
\(53\) 192.526i 0.498971i −0.968379 0.249486i \(-0.919738\pi\)
0.968379 0.249486i \(-0.0802615\pi\)
\(54\) −340.801 588.103i −0.858836 1.48205i
\(55\) 481.820i 1.18125i
\(56\) 0 0
\(57\) −61.6899 348.770i −0.143351 0.810451i
\(58\) 1048.55 2.37382
\(59\) 287.422 0.634224 0.317112 0.948388i \(-0.397287\pi\)
0.317112 + 0.948388i \(0.397287\pi\)
\(60\) −1369.71 + 242.273i −2.94715 + 0.521289i
\(61\) 224.297i 0.470792i −0.971900 0.235396i \(-0.924361\pi\)
0.971900 0.235396i \(-0.0756387\pi\)
\(62\) 762.340 1.56157
\(63\) 0 0
\(64\) 604.516 1.18070
\(65\) 282.071i 0.538255i
\(66\) −690.370 + 122.112i −1.28755 + 0.227741i
\(67\) −172.206 −0.314004 −0.157002 0.987598i \(-0.550183\pi\)
−0.157002 + 0.987598i \(0.550183\pi\)
\(68\) 631.687 1.12652
\(69\) 64.9591 + 367.252i 0.113336 + 0.640754i
\(70\) 0 0
\(71\) 1068.78i 1.78649i 0.449569 + 0.893246i \(0.351578\pi\)
−0.449569 + 0.893246i \(0.648422\pi\)
\(72\) 335.304 + 918.181i 0.548832 + 1.50290i
\(73\) 1078.22i 1.72871i −0.502881 0.864356i \(-0.667726\pi\)
0.502881 0.864356i \(-0.332274\pi\)
\(74\) 1688.38i 2.65230i
\(75\) 892.004 157.776i 1.37333 0.242913i
\(76\) 1054.65i 1.59180i
\(77\) 0 0
\(78\) 404.161 71.4875i 0.586696 0.103774i
\(79\) 52.0336 0.0741043 0.0370521 0.999313i \(-0.488203\pi\)
0.0370521 + 0.999313i \(0.488203\pi\)
\(80\) 893.072 1.24811
\(81\) 557.442 469.786i 0.764667 0.644426i
\(82\) 743.059i 1.00070i
\(83\) 1023.07 1.35298 0.676488 0.736454i \(-0.263501\pi\)
0.676488 + 0.736454i \(0.263501\pi\)
\(84\) 0 0
\(85\) −706.344 −0.901338
\(86\) 2071.58i 2.59749i
\(87\) 195.874 + 1107.39i 0.241379 + 1.36466i
\(88\) 1008.23 1.22133
\(89\) −668.570 −0.796272 −0.398136 0.917326i \(-0.630343\pi\)
−0.398136 + 0.917326i \(0.630343\pi\)
\(90\) −776.329 2125.87i −0.909247 2.48984i
\(91\) 0 0
\(92\) 1110.54i 1.25850i
\(93\) 142.409 + 805.121i 0.158786 + 0.897711i
\(94\) 81.4431i 0.0893640i
\(95\) 1179.29i 1.27361i
\(96\) 35.7849 + 202.313i 0.0380446 + 0.215089i
\(97\) 1358.39i 1.42190i 0.703244 + 0.710949i \(0.251734\pi\)
−0.703244 + 0.710949i \(0.748266\pi\)
\(98\) 0 0
\(99\) −257.929 706.300i −0.261846 0.717029i
\(100\) −2697.34 −2.69734
\(101\) −29.0959 −0.0286649 −0.0143324 0.999897i \(-0.504562\pi\)
−0.0143324 + 0.999897i \(0.504562\pi\)
\(102\) 179.015 + 1012.08i 0.173775 + 0.982455i
\(103\) 300.909i 0.287859i 0.989588 + 0.143929i \(0.0459738\pi\)
−0.989588 + 0.143929i \(0.954026\pi\)
\(104\) −590.243 −0.556520
\(105\) 0 0
\(106\) −932.759 −0.854694
\(107\) 523.431i 0.472916i 0.971642 + 0.236458i \(0.0759866\pi\)
−0.971642 + 0.236458i \(0.924013\pi\)
\(108\) −1878.17 + 1088.38i −1.67340 + 0.969721i
\(109\) −62.6812 −0.0550805 −0.0275402 0.999621i \(-0.508767\pi\)
−0.0275402 + 0.999621i \(0.508767\pi\)
\(110\) −2334.35 −2.02337
\(111\) −1783.13 + 315.397i −1.52475 + 0.269695i
\(112\) 0 0
\(113\) 84.9426i 0.0707144i −0.999375 0.0353572i \(-0.988743\pi\)
0.999375 0.0353572i \(-0.0112569\pi\)
\(114\) −1689.74 + 298.878i −1.38823 + 0.245548i
\(115\) 1241.79i 1.00693i
\(116\) 3348.66i 2.68031i
\(117\) 150.998 + 413.488i 0.119315 + 0.326726i
\(118\) 1392.52i 1.08637i
\(119\) 0 0
\(120\) 566.881 + 3204.91i 0.431241 + 2.43806i
\(121\) 555.434 0.417306
\(122\) −1086.69 −0.806425
\(123\) −784.758 + 138.807i −0.575278 + 0.101754i
\(124\) 2434.62i 1.76318i
\(125\) 853.482 0.610702
\(126\) 0 0
\(127\) −1842.84 −1.28760 −0.643802 0.765192i \(-0.722644\pi\)
−0.643802 + 0.765192i \(0.722644\pi\)
\(128\) 2612.47i 1.80400i
\(129\) 2187.83 386.981i 1.49324 0.264122i
\(130\) 1366.59 0.921984
\(131\) 97.8698 0.0652742 0.0326371 0.999467i \(-0.489609\pi\)
0.0326371 + 0.999467i \(0.489609\pi\)
\(132\) 389.977 + 2204.77i 0.257145 + 1.45379i
\(133\) 0 0
\(134\) 834.310i 0.537861i
\(135\) 2100.14 1217.02i 1.33890 0.775882i
\(136\) 1478.05i 0.931924i
\(137\) 1693.85i 1.05631i 0.849147 + 0.528157i \(0.177117\pi\)
−0.849147 + 0.528157i \(0.822883\pi\)
\(138\) 1779.28 314.717i 1.09755 0.194134i
\(139\) 1821.25i 1.11134i −0.831402 0.555672i \(-0.812461\pi\)
0.831402 0.555672i \(-0.187539\pi\)
\(140\) 0 0
\(141\) −86.0135 + 15.2139i −0.0513733 + 0.00908685i
\(142\) 5178.08 3.06010
\(143\) 454.038 0.265514
\(144\) 1309.15 478.080i 0.757613 0.276667i
\(145\) 3744.43i 2.14454i
\(146\) −5223.80 −2.96113
\(147\) 0 0
\(148\) 5392.02 2.99474
\(149\) 1798.00i 0.988574i 0.869299 + 0.494287i \(0.164571\pi\)
−0.869299 + 0.494287i \(0.835429\pi\)
\(150\) −764.402 4321.62i −0.416088 2.35239i
\(151\) −2089.84 −1.12628 −0.563141 0.826361i \(-0.690407\pi\)
−0.563141 + 0.826361i \(0.690407\pi\)
\(152\) 2467.71 1.31683
\(153\) −1035.43 + 378.121i −0.547121 + 0.199799i
\(154\) 0 0
\(155\) 2722.35i 1.41074i
\(156\) −228.303 1290.73i −0.117172 0.662445i
\(157\) 1090.34i 0.554258i 0.960833 + 0.277129i \(0.0893829\pi\)
−0.960833 + 0.277129i \(0.910617\pi\)
\(158\) 252.095i 0.126934i
\(159\) −174.244 985.103i −0.0869083 0.491344i
\(160\) 684.082i 0.338009i
\(161\) 0 0
\(162\) −2276.04 2700.72i −1.10384 1.30981i
\(163\) −1940.53 −0.932478 −0.466239 0.884659i \(-0.654391\pi\)
−0.466239 + 0.884659i \(0.654391\pi\)
\(164\) 2373.04 1.12990
\(165\) −436.067 2465.34i −0.205744 1.16319i
\(166\) 4956.64i 2.31753i
\(167\) 2664.87 1.23481 0.617406 0.786645i \(-0.288184\pi\)
0.617406 + 0.786645i \(0.288184\pi\)
\(168\) 0 0
\(169\) 1931.19 0.879014
\(170\) 3422.13i 1.54391i
\(171\) −631.301 1728.73i −0.282320 0.773094i
\(172\) −6615.81 −2.93285
\(173\) −3096.19 −1.36069 −0.680343 0.732894i \(-0.738169\pi\)
−0.680343 + 0.732894i \(0.738169\pi\)
\(174\) 5365.16 948.982i 2.33754 0.413461i
\(175\) 0 0
\(176\) 1437.54i 0.615674i
\(177\) 1470.66 260.129i 0.624529 0.110466i
\(178\) 3239.12i 1.36394i
\(179\) 902.641i 0.376908i 0.982082 + 0.188454i \(0.0603476\pi\)
−0.982082 + 0.188454i \(0.939652\pi\)
\(180\) −6789.18 + 2479.29i −2.81131 + 1.02664i
\(181\) 3496.01i 1.43567i −0.696213 0.717835i \(-0.745133\pi\)
0.696213 0.717835i \(-0.254867\pi\)
\(182\) 0 0
\(183\) −202.998 1147.67i −0.0820002 0.463596i
\(184\) −2598.49 −1.04110
\(185\) −6029.28 −2.39612
\(186\) 3900.69 689.948i 1.53770 0.271986i
\(187\) 1136.97i 0.444618i
\(188\) 260.097 0.100902
\(189\) 0 0
\(190\) −5713.50 −2.18158
\(191\) 354.514i 0.134302i 0.997743 + 0.0671512i \(0.0213910\pi\)
−0.997743 + 0.0671512i \(0.978609\pi\)
\(192\) 3093.15 547.112i 1.16265 0.205648i
\(193\) 2839.88 1.05917 0.529584 0.848258i \(-0.322348\pi\)
0.529584 + 0.848258i \(0.322348\pi\)
\(194\) 6581.21 2.43559
\(195\) 255.285 + 1443.28i 0.0937506 + 0.530028i
\(196\) 0 0
\(197\) 3058.25i 1.10605i −0.833165 0.553024i \(-0.813474\pi\)
0.833165 0.553024i \(-0.186526\pi\)
\(198\) −3421.92 + 1249.62i −1.22821 + 0.448520i
\(199\) 1839.48i 0.655264i −0.944805 0.327632i \(-0.893749\pi\)
0.944805 0.327632i \(-0.106251\pi\)
\(200\) 6311.35i 2.23140i
\(201\) −881.129 + 155.853i −0.309204 + 0.0546916i
\(202\) 140.965i 0.0491004i
\(203\) 0 0
\(204\) 3232.17 571.702i 1.10930 0.196212i
\(205\) −2653.50 −0.904041
\(206\) 1457.86 0.493077
\(207\) 664.756 + 1820.34i 0.223207 + 0.611219i
\(208\) 841.576i 0.280542i
\(209\) −1898.26 −0.628256
\(210\) 0 0
\(211\) −644.694 −0.210344 −0.105172 0.994454i \(-0.533539\pi\)
−0.105172 + 0.994454i \(0.533539\pi\)
\(212\) 2978.86i 0.965044i
\(213\) 967.289 + 5468.66i 0.311162 + 1.75918i
\(214\) 2535.94 0.810063
\(215\) 7397.71 2.34660
\(216\) 2546.65 + 4394.62i 0.802210 + 1.38433i
\(217\) 0 0
\(218\) 303.681i 0.0943480i
\(219\) −975.831 5516.95i −0.301098 1.70229i
\(220\) 7454.98i 2.28461i
\(221\) 665.615i 0.202598i
\(222\) 1528.05 + 8638.97i 0.461964 + 2.61176i
\(223\) 3760.55i 1.12926i 0.825344 + 0.564630i \(0.190981\pi\)
−0.825344 + 0.564630i \(0.809019\pi\)
\(224\) 0 0
\(225\) 4421.35 1614.60i 1.31003 0.478399i
\(226\) −411.534 −0.121128
\(227\) 2836.86 0.829467 0.414733 0.909943i \(-0.363875\pi\)
0.414733 + 0.909943i \(0.363875\pi\)
\(228\) 954.500 + 5396.35i 0.277251 + 1.56747i
\(229\) 5207.86i 1.50282i −0.659837 0.751409i \(-0.729375\pi\)
0.659837 0.751409i \(-0.270625\pi\)
\(230\) 6016.28 1.72479
\(231\) 0 0
\(232\) −7835.35 −2.21731
\(233\) 2185.90i 0.614604i −0.951612 0.307302i \(-0.900574\pi\)
0.951612 0.307302i \(-0.0994262\pi\)
\(234\) 2003.28 731.565i 0.559653 0.204376i
\(235\) −290.837 −0.0807325
\(236\) −4447.15 −1.22663
\(237\) 266.242 47.0925i 0.0729716 0.0129071i
\(238\) 0 0
\(239\) 1921.87i 0.520148i 0.965589 + 0.260074i \(0.0837469\pi\)
−0.965589 + 0.260074i \(0.916253\pi\)
\(240\) 4569.61 808.266i 1.22903 0.217389i
\(241\) 4476.26i 1.19644i −0.801333 0.598218i \(-0.795876\pi\)
0.801333 0.598218i \(-0.204124\pi\)
\(242\) 2690.99i 0.714809i
\(243\) 2427.11 2908.28i 0.640736 0.767761i
\(244\) 3470.45i 0.910543i
\(245\) 0 0
\(246\) 672.498 + 3802.03i 0.174296 + 0.985401i
\(247\) 1111.29 0.286275
\(248\) −5696.62 −1.45861
\(249\) 5234.79 925.923i 1.33230 0.235655i
\(250\) 4134.99i 1.04608i
\(251\) −3296.51 −0.828980 −0.414490 0.910054i \(-0.636040\pi\)
−0.414490 + 0.910054i \(0.636040\pi\)
\(252\) 0 0
\(253\) 1998.86 0.496708
\(254\) 8928.28i 2.20555i
\(255\) −3614.17 + 639.270i −0.887561 + 0.156991i
\(256\) −7820.90 −1.90940
\(257\) −7110.67 −1.72588 −0.862940 0.505307i \(-0.831379\pi\)
−0.862940 + 0.505307i \(0.831379\pi\)
\(258\) −1874.86 10599.7i −0.452418 2.55779i
\(259\) 0 0
\(260\) 4364.35i 1.04102i
\(261\) 2004.47 + 5488.96i 0.475378 + 1.30176i
\(262\) 474.164i 0.111809i
\(263\) 6808.88i 1.59640i 0.602391 + 0.798201i \(0.294215\pi\)
−0.602391 + 0.798201i \(0.705785\pi\)
\(264\) 5158.81 912.484i 1.20266 0.212725i
\(265\) 3330.93i 0.772140i
\(266\) 0 0
\(267\) −3420.89 + 605.082i −0.784101 + 0.138691i
\(268\) 2664.46 0.607305
\(269\) −3603.91 −0.816856 −0.408428 0.912791i \(-0.633923\pi\)
−0.408428 + 0.912791i \(0.633923\pi\)
\(270\) −5896.26 10174.9i −1.32902 2.29342i
\(271\) 3376.15i 0.756777i −0.925647 0.378388i \(-0.876478\pi\)
0.925647 0.378388i \(-0.123522\pi\)
\(272\) −2107.42 −0.469784
\(273\) 0 0
\(274\) 8206.42 1.80937
\(275\) 4854.94i 1.06460i
\(276\) −1005.08 5682.33i −0.219199 1.23926i
\(277\) −6940.10 −1.50538 −0.752690 0.658375i \(-0.771244\pi\)
−0.752690 + 0.658375i \(0.771244\pi\)
\(278\) −8823.70 −1.90363
\(279\) 1457.33 + 3990.70i 0.312718 + 0.856333i
\(280\) 0 0
\(281\) 3834.00i 0.813940i −0.913441 0.406970i \(-0.866585\pi\)
0.913441 0.406970i \(-0.133415\pi\)
\(282\) 73.7093 + 416.722i 0.0155650 + 0.0879980i
\(283\) 6443.70i 1.35349i −0.736217 0.676746i \(-0.763390\pi\)
0.736217 0.676746i \(-0.236610\pi\)
\(284\) 16536.7i 3.45519i
\(285\) −1067.31 6034.13i −0.221831 1.25414i
\(286\) 2199.74i 0.454802i
\(287\) 0 0
\(288\) 366.203 + 1002.80i 0.0749262 + 0.205175i
\(289\) −3246.21 −0.660739
\(290\) 18141.2 3.67341
\(291\) 1229.40 + 6950.54i 0.247659 + 1.40016i
\(292\) 16682.8i 3.34344i
\(293\) −1443.22 −0.287760 −0.143880 0.989595i \(-0.545958\pi\)
−0.143880 + 0.989595i \(0.545958\pi\)
\(294\) 0 0
\(295\) 4972.74 0.981439
\(296\) 12616.5i 2.47742i
\(297\) −1958.98 3380.51i −0.382733 0.660462i
\(298\) 8711.01 1.69334
\(299\) −1170.19 −0.226333
\(300\) −13801.6 + 2441.20i −2.65611 + 0.469809i
\(301\) 0 0
\(302\) 10124.9i 1.92922i
\(303\) −148.876 + 26.3330i −0.0282267 + 0.00499271i
\(304\) 3518.50i 0.663815i
\(305\) 3880.61i 0.728534i
\(306\) 1831.94 + 5016.50i 0.342238 + 0.937170i
\(307\) 5504.32i 1.02328i −0.859199 0.511642i \(-0.829038\pi\)
0.859199 0.511642i \(-0.170962\pi\)
\(308\) 0 0
\(309\) 272.335 + 1539.67i 0.0501378 + 0.283459i
\(310\) 13189.4 2.41647
\(311\) 2419.45 0.441140 0.220570 0.975371i \(-0.429208\pi\)
0.220570 + 0.975371i \(0.429208\pi\)
\(312\) −3020.11 + 534.193i −0.548013 + 0.0969319i
\(313\) 1190.38i 0.214966i 0.994207 + 0.107483i \(0.0342791\pi\)
−0.994207 + 0.107483i \(0.965721\pi\)
\(314\) 5282.52 0.949395
\(315\) 0 0
\(316\) −805.092 −0.143323
\(317\) 6628.17i 1.17437i −0.809453 0.587185i \(-0.800236\pi\)
0.809453 0.587185i \(-0.199764\pi\)
\(318\) −4772.67 + 844.184i −0.841629 + 0.148866i
\(319\) 6027.25 1.05787
\(320\) 10458.8 1.82709
\(321\) 473.726 + 2678.25i 0.0823701 + 0.465687i
\(322\) 0 0
\(323\) 2782.83i 0.479384i
\(324\) −8625.05 + 7268.78i −1.47892 + 1.24636i
\(325\) 2842.21i 0.485101i
\(326\) 9401.56i 1.59725i
\(327\) −320.723 + 56.7290i −0.0542385 + 0.00959364i
\(328\) 5552.54i 0.934718i
\(329\) 0 0
\(330\) −11944.2 + 2112.68i −1.99245 + 0.352421i
\(331\) −7185.16 −1.19315 −0.596574 0.802558i \(-0.703472\pi\)
−0.596574 + 0.802558i \(0.703472\pi\)
\(332\) −15829.6 −2.61675
\(333\) −8838.32 + 3227.60i −1.45447 + 0.531145i
\(334\) 12910.9i 2.11512i
\(335\) −2979.36 −0.485910
\(336\) 0 0
\(337\) −7214.56 −1.16618 −0.583090 0.812408i \(-0.698156\pi\)
−0.583090 + 0.812408i \(0.698156\pi\)
\(338\) 9356.34i 1.50567i
\(339\) −76.8764 434.628i −0.0123167 0.0696335i
\(340\) 10928.9 1.74325
\(341\) 4382.06 0.695899
\(342\) −8375.42 + 3058.56i −1.32424 + 0.483590i
\(343\) 0 0
\(344\) 15479.9i 2.42623i
\(345\) 1123.87 + 6353.90i 0.175383 + 0.991543i
\(346\) 15000.6i 2.33074i
\(347\) 8151.04i 1.26101i −0.776185 0.630505i \(-0.782848\pi\)
0.776185 0.630505i \(-0.217152\pi\)
\(348\) −3030.68 17134.2i −0.466843 2.63934i
\(349\) 491.916i 0.0754489i 0.999288 + 0.0377245i \(0.0120109\pi\)
−0.999288 + 0.0377245i \(0.987989\pi\)
\(350\) 0 0
\(351\) 1146.84 + 1979.04i 0.174398 + 0.300950i
\(352\) 1101.14 0.166735
\(353\) 2923.64 0.440820 0.220410 0.975407i \(-0.429260\pi\)
0.220410 + 0.975407i \(0.429260\pi\)
\(354\) −1260.28 7125.13i −0.189218 1.06976i
\(355\) 18491.2i 2.76453i
\(356\) 10344.5 1.54004
\(357\) 0 0
\(358\) 4373.16 0.645610
\(359\) 4802.16i 0.705985i −0.935626 0.352992i \(-0.885164\pi\)
0.935626 0.352992i \(-0.114836\pi\)
\(360\) 5801.15 + 15885.6i 0.849298 + 2.32568i
\(361\) 2212.85 0.322620
\(362\) −16937.6 −2.45918
\(363\) 2842.01 502.690i 0.410927 0.0726843i
\(364\) 0 0
\(365\) 18654.5i 2.67512i
\(366\) −5560.27 + 983.494i −0.794099 + 0.140459i
\(367\) 8957.91i 1.27411i 0.770817 + 0.637056i \(0.219848\pi\)
−0.770817 + 0.637056i \(0.780152\pi\)
\(368\) 3704.96i 0.524821i
\(369\) −3889.77 + 1420.47i −0.548762 + 0.200398i
\(370\) 29210.9i 4.10434i
\(371\) 0 0
\(372\) −2203.42 12457.3i −0.307103 1.73623i
\(373\) −5072.83 −0.704186 −0.352093 0.935965i \(-0.614530\pi\)
−0.352093 + 0.935965i \(0.614530\pi\)
\(374\) 5508.45 0.761592
\(375\) 4367.04 772.435i 0.601367 0.106369i
\(376\) 608.587i 0.0834720i
\(377\) −3528.52 −0.482037
\(378\) 0 0
\(379\) −855.835 −0.115993 −0.0579964 0.998317i \(-0.518471\pi\)
−0.0579964 + 0.998317i \(0.518471\pi\)
\(380\) 18246.7i 2.46325i
\(381\) −9429.31 + 1667.84i −1.26792 + 0.224268i
\(382\) 1717.57 0.230048
\(383\) 7080.61 0.944653 0.472326 0.881424i \(-0.343414\pi\)
0.472326 + 0.881424i \(0.343414\pi\)
\(384\) −2364.39 13367.3i −0.314212 1.77643i
\(385\) 0 0
\(386\) 13758.8i 1.81426i
\(387\) 10844.3 3960.15i 1.42441 0.520170i
\(388\) 21017.8i 2.75005i
\(389\) 2073.59i 0.270270i −0.990827 0.135135i \(-0.956853\pi\)
0.990827 0.135135i \(-0.0431468\pi\)
\(390\) 6992.47 1236.82i 0.907891 0.160587i
\(391\) 2930.31i 0.379007i
\(392\) 0 0
\(393\) 500.773 88.5761i 0.0642765 0.0113691i
\(394\) −14816.8 −1.89456
\(395\) 900.243 0.114674
\(396\) 3990.81 + 10928.3i 0.506429 + 1.38678i
\(397\) 5722.06i 0.723380i −0.932298 0.361690i \(-0.882200\pi\)
0.932298 0.361690i \(-0.117800\pi\)
\(398\) −8912.01 −1.12241
\(399\) 0 0
\(400\) 8998.81 1.12485
\(401\) 11728.9i 1.46064i 0.683107 + 0.730319i \(0.260628\pi\)
−0.683107 + 0.730319i \(0.739372\pi\)
\(402\) 755.084 + 4268.94i 0.0936820 + 0.529640i
\(403\) −2565.38 −0.317098
\(404\) 450.188 0.0554398
\(405\) 9644.41 8127.86i 1.18330 0.997226i
\(406\) 0 0
\(407\) 9705.08i 1.18197i
\(408\) −1337.69 7562.77i −0.162318 0.917679i
\(409\) 2623.53i 0.317176i −0.987345 0.158588i \(-0.949306\pi\)
0.987345 0.158588i \(-0.0506942\pi\)
\(410\) 12855.8i 1.54854i
\(411\) 1533.00 + 8666.95i 0.183983 + 1.04017i
\(412\) 4655.83i 0.556738i
\(413\) 0 0
\(414\) 8819.27 3220.64i 1.04696 0.382333i
\(415\) 17700.4 2.09368
\(416\) −644.637 −0.0759757
\(417\) −1648.31 9318.86i −0.193568 1.09436i
\(418\) 9196.78i 1.07615i
\(419\) 2183.62 0.254598 0.127299 0.991864i \(-0.459369\pi\)
0.127299 + 0.991864i \(0.459369\pi\)
\(420\) 0 0
\(421\) −12921.5 −1.49586 −0.747929 0.663778i \(-0.768952\pi\)
−0.747929 + 0.663778i \(0.768952\pi\)
\(422\) 3123.44i 0.360300i
\(423\) −426.338 + 155.691i −0.0490054 + 0.0178959i
\(424\) 6970.07 0.798341
\(425\) −7117.29 −0.812328
\(426\) 26494.8 4686.37i 3.01333 0.532993i
\(427\) 0 0
\(428\) 8098.81i 0.914651i
\(429\) 2323.19 410.922i 0.261456 0.0462459i
\(430\) 35840.8i 4.01952i
\(431\) 12619.8i 1.41038i 0.709018 + 0.705190i \(0.249138\pi\)
−0.709018 + 0.705190i \(0.750862\pi\)
\(432\) 6265.91 3631.04i 0.697844 0.404395i
\(433\) 14180.4i 1.57382i 0.617066 + 0.786912i \(0.288321\pi\)
−0.617066 + 0.786912i \(0.711679\pi\)
\(434\) 0 0
\(435\) 3388.86 + 19159.2i 0.373525 + 2.11176i
\(436\) 969.837 0.106529
\(437\) 4892.36 0.535546
\(438\) −26728.8 + 4727.75i −2.91587 + 0.515755i
\(439\) 7467.03i 0.811804i 0.913917 + 0.405902i \(0.133043\pi\)
−0.913917 + 0.405902i \(0.866957\pi\)
\(440\) 17443.5 1.88997
\(441\) 0 0
\(442\) −3224.80 −0.347032
\(443\) 363.788i 0.0390160i 0.999810 + 0.0195080i \(0.00620998\pi\)
−0.999810 + 0.0195080i \(0.993790\pi\)
\(444\) 27589.5 4879.99i 2.94896 0.521608i
\(445\) −11567.0 −1.23220
\(446\) 18219.3 1.93432
\(447\) 1627.26 + 9199.85i 0.172185 + 0.973463i
\(448\) 0 0
\(449\) 5444.69i 0.572273i 0.958189 + 0.286136i \(0.0923711\pi\)
−0.958189 + 0.286136i \(0.907629\pi\)
\(450\) −7822.48 21420.7i −0.819456 2.24396i
\(451\) 4271.23i 0.445952i
\(452\) 1314.28i 0.136766i
\(453\) −10693.1 + 1891.39i −1.10907 + 0.196170i
\(454\) 13744.1i 1.42080i
\(455\) 0 0
\(456\) 12626.6 2233.38i 1.29670 0.229359i
\(457\) 2305.66 0.236005 0.118003 0.993013i \(-0.462351\pi\)
0.118003 + 0.993013i \(0.462351\pi\)
\(458\) −25231.3 −2.57419
\(459\) −4955.80 + 2871.85i −0.503958 + 0.292040i
\(460\) 19213.6i 1.94748i
\(461\) −585.754 −0.0591785 −0.0295892 0.999562i \(-0.509420\pi\)
−0.0295892 + 0.999562i \(0.509420\pi\)
\(462\) 0 0
\(463\) 11321.6 1.13641 0.568205 0.822887i \(-0.307638\pi\)
0.568205 + 0.822887i \(0.307638\pi\)
\(464\) 11171.7i 1.11775i
\(465\) 2463.84 + 13929.5i 0.245716 + 1.38918i
\(466\) −10590.3 −1.05276
\(467\) 9958.30 0.986756 0.493378 0.869815i \(-0.335762\pi\)
0.493378 + 0.869815i \(0.335762\pi\)
\(468\) −2336.33 6397.71i −0.230763 0.631910i
\(469\) 0 0
\(470\) 1409.06i 0.138288i
\(471\) 986.800 + 5578.97i 0.0965379 + 0.545786i
\(472\) 10405.6i 1.01474i
\(473\) 11907.8i 1.15755i
\(474\) −228.156 1289.90i −0.0221088 0.124994i
\(475\) 11882.9i 1.14784i
\(476\) 0 0
\(477\) −1783.11 4882.81i −0.171160 0.468697i
\(478\) 9311.16 0.890967
\(479\) 13832.0 1.31942 0.659709 0.751521i \(-0.270680\pi\)
0.659709 + 0.751521i \(0.270680\pi\)
\(480\) 619.122 + 3500.26i 0.0588727 + 0.332842i
\(481\) 5681.62i 0.538585i
\(482\) −21686.8 −2.04939
\(483\) 0 0
\(484\) −8593.98 −0.807098
\(485\) 23501.8i 2.20034i
\(486\) −14090.1 11759.0i −1.31511 1.09752i
\(487\) 456.178 0.0424464 0.0212232 0.999775i \(-0.493244\pi\)
0.0212232 + 0.999775i \(0.493244\pi\)
\(488\) 8120.30 0.753256
\(489\) −9929.15 + 1756.26i −0.918224 + 0.162414i
\(490\) 0 0
\(491\) 17039.5i 1.56616i −0.621922 0.783079i \(-0.713648\pi\)
0.621922 0.783079i \(-0.286352\pi\)
\(492\) 12142.2 2147.70i 1.11263 0.196800i
\(493\) 8835.90i 0.807198i
\(494\) 5384.05i 0.490364i
\(495\) −4462.47 12219.8i −0.405198 1.10958i
\(496\) 8122.31i 0.735287i
\(497\) 0 0
\(498\) −4485.96 25361.8i −0.403656 2.28210i
\(499\) −1855.54 −0.166463 −0.0832317 0.996530i \(-0.526524\pi\)
−0.0832317 + 0.996530i \(0.526524\pi\)
\(500\) −13205.5 −1.18114
\(501\) 13635.4 2411.81i 1.21594 0.215073i
\(502\) 15971.1i 1.41997i
\(503\) −5860.64 −0.519509 −0.259754 0.965675i \(-0.583642\pi\)
−0.259754 + 0.965675i \(0.583642\pi\)
\(504\) 0 0
\(505\) −503.394 −0.0443579
\(506\) 9684.15i 0.850816i
\(507\) 9881.39 1747.81i 0.865578 0.153102i
\(508\) 28513.4 2.49031
\(509\) −5456.88 −0.475191 −0.237595 0.971364i \(-0.576359\pi\)
−0.237595 + 0.971364i \(0.576359\pi\)
\(510\) 3097.16 + 17510.1i 0.268911 + 1.52031i
\(511\) 0 0
\(512\) 16991.3i 1.46663i
\(513\) −4794.76 8274.08i −0.412659 0.712104i
\(514\) 34450.1i 2.95628i
\(515\) 5206.08i 0.445451i
\(516\) −33851.3 + 5987.57i −2.88802 + 0.510830i
\(517\) 468.148i 0.0398243i
\(518\) 0 0
\(519\) −15842.4 + 2802.17i −1.33989 + 0.236998i
\(520\) −10211.9 −0.861195
\(521\) 7285.24 0.612614 0.306307 0.951933i \(-0.400907\pi\)
0.306307 + 0.951933i \(0.400907\pi\)
\(522\) 26593.2 9711.36i 2.22979 0.814281i
\(523\) 3415.29i 0.285545i 0.989756 + 0.142772i \(0.0456017\pi\)
−0.989756 + 0.142772i \(0.954398\pi\)
\(524\) −1514.29 −0.126245
\(525\) 0 0
\(526\) 32988.0 2.73450
\(527\) 6424.06i 0.530999i
\(528\) −1301.03 7355.50i −0.107235 0.606264i
\(529\) 7015.37 0.576590
\(530\) −16137.8 −1.32261
\(531\) 7289.55 2662.01i 0.595743 0.217555i
\(532\) 0 0
\(533\) 2500.49i 0.203205i
\(534\) 2931.53 + 16573.7i 0.237565 + 1.34310i
\(535\) 9055.98i 0.731821i
\(536\) 6234.41i 0.502398i
\(537\) 816.926 + 4618.57i 0.0656480 + 0.371147i
\(538\) 17460.4i 1.39920i
\(539\) 0 0
\(540\) −32494.5 + 18830.3i −2.58952 + 1.50061i
\(541\) −2381.89 −0.189289 −0.0946447 0.995511i \(-0.530172\pi\)
−0.0946447 + 0.995511i \(0.530172\pi\)
\(542\) −16356.9 −1.29629
\(543\) −3164.03 17888.1i −0.250058 1.41373i
\(544\) 1614.26i 0.127226i
\(545\) −1084.46 −0.0852351
\(546\) 0 0
\(547\) −1376.55 −0.107600 −0.0537998 0.998552i \(-0.517133\pi\)
−0.0537998 + 0.998552i \(0.517133\pi\)
\(548\) 26208.1i 2.04298i
\(549\) −2077.37 5688.58i −0.161494 0.442227i
\(550\) −23521.4 −1.82356
\(551\) 14752.2 1.14059
\(552\) −13295.8 + 2351.73i −1.02519 + 0.181334i
\(553\) 0 0
\(554\) 33623.7i 2.57858i
\(555\) −30850.2 + 5456.74i −2.35949 + 0.417344i
\(556\) 28179.4i 2.14941i
\(557\) 2037.41i 0.154987i 0.996993 + 0.0774935i \(0.0246917\pi\)
−0.996993 + 0.0774935i \(0.975308\pi\)
\(558\) 19334.3 7060.56i 1.46682 0.535658i
\(559\) 6971.14i 0.527456i
\(560\) 0 0
\(561\) 1029.01 + 5817.58i 0.0774414 + 0.437822i
\(562\) −18575.1 −1.39421
\(563\) −2394.19 −0.179224 −0.0896118 0.995977i \(-0.528563\pi\)
−0.0896118 + 0.995977i \(0.528563\pi\)
\(564\) 1330.85 235.398i 0.0993595 0.0175746i
\(565\) 1469.61i 0.109428i
\(566\) −31218.7 −2.31841
\(567\) 0 0
\(568\) −38693.4 −2.85834
\(569\) 7635.14i 0.562534i −0.959630 0.281267i \(-0.909245\pi\)
0.959630 0.281267i \(-0.0907546\pi\)
\(570\) −29234.4 + 5170.95i −2.14824 + 0.379977i
\(571\) 2512.52 0.184143 0.0920715 0.995752i \(-0.470651\pi\)
0.0920715 + 0.995752i \(0.470651\pi\)
\(572\) −7025.11 −0.513522
\(573\) 320.850 + 1813.95i 0.0233921 + 0.132249i
\(574\) 0 0
\(575\) 12512.6i 0.907496i
\(576\) 15331.6 5598.84i 1.10906 0.405009i
\(577\) 10906.9i 0.786929i −0.919340 0.393465i \(-0.871276\pi\)
0.919340 0.393465i \(-0.128724\pi\)
\(578\) 15727.4i 1.13179i
\(579\) 14530.9 2570.21i 1.04298 0.184480i
\(580\) 57935.9i 4.14768i
\(581\) 0 0
\(582\) 33674.3 5956.26i 2.39836 0.424218i
\(583\) −5361.65 −0.380887
\(584\) 39035.1 2.76590
\(585\) 2612.45 + 7153.83i 0.184635 + 0.505597i
\(586\) 6992.18i 0.492908i
\(587\) 25367.7 1.78371 0.891855 0.452321i \(-0.149404\pi\)
0.891855 + 0.452321i \(0.149404\pi\)
\(588\) 0 0
\(589\) 10725.4 0.750313
\(590\) 24092.2i 1.68112i
\(591\) −2767.84 15648.2i −0.192646 1.08914i
\(592\) −17988.7 −1.24887
\(593\) 9834.38 0.681028 0.340514 0.940239i \(-0.389399\pi\)
0.340514 + 0.940239i \(0.389399\pi\)
\(594\) −16378.1 + 9490.96i −1.13131 + 0.655587i
\(595\) 0 0
\(596\) 27819.5i 1.91197i
\(597\) −1664.81 9412.13i −0.114131 0.645248i
\(598\) 5669.37i 0.387689i
\(599\) 6922.43i 0.472192i −0.971730 0.236096i \(-0.924132\pi\)
0.971730 0.236096i \(-0.0758679\pi\)
\(600\) 5712.03 + 32293.5i 0.388654 + 2.19729i
\(601\) 15144.9i 1.02791i −0.857817 0.513955i \(-0.828180\pi\)
0.857817 0.513955i \(-0.171820\pi\)
\(602\) 0 0
\(603\) −4367.44 + 1594.91i −0.294952 + 0.107711i
\(604\) 32335.1 2.17830
\(605\) 9609.67 0.645766
\(606\) 127.579 + 721.281i 0.00855207 + 0.0483499i
\(607\) 27601.0i 1.84562i −0.385259 0.922809i \(-0.625888\pi\)
0.385259 0.922809i \(-0.374112\pi\)
\(608\) 2695.12 0.179773
\(609\) 0 0
\(610\) −18800.9 −1.24791
\(611\) 274.067i 0.0181466i
\(612\) 16020.7 5850.49i 1.05817 0.386425i
\(613\) 12162.1 0.801342 0.400671 0.916222i \(-0.368777\pi\)
0.400671 + 0.916222i \(0.368777\pi\)
\(614\) −26667.6 −1.75279
\(615\) −13577.2 + 2401.52i −0.890223 + 0.157461i
\(616\) 0 0
\(617\) 17715.1i 1.15589i 0.816077 + 0.577944i \(0.196145\pi\)
−0.816077 + 0.577944i \(0.803855\pi\)
\(618\) 7459.46 1319.42i 0.485540 0.0858816i
\(619\) 4569.82i 0.296731i −0.988933 0.148366i \(-0.952599\pi\)
0.988933 0.148366i \(-0.0474013\pi\)
\(620\) 42121.7i 2.72847i
\(621\) 5048.86 + 8712.55i 0.326254 + 0.563000i
\(622\) 11721.9i 0.755634i
\(623\) 0 0
\(624\) 761.660 + 4306.11i 0.0488635 + 0.276254i
\(625\) −7025.11 −0.449607
\(626\) 5767.21 0.368218
\(627\) −9712.88 + 1718.00i −0.618652 + 0.109426i
\(628\) 16870.3i 1.07197i
\(629\) 14227.6 0.901891
\(630\) 0 0
\(631\) −1677.26 −0.105817 −0.0529086 0.998599i \(-0.516849\pi\)
−0.0529086 + 0.998599i \(0.516849\pi\)
\(632\) 1883.79i 0.118565i
\(633\) −3298.72 + 583.474i −0.207129 + 0.0366366i
\(634\) −32112.5 −2.01159
\(635\) −31883.3 −1.99252
\(636\) 2695.99 + 15242.0i 0.168087 + 0.950293i
\(637\) 0 0
\(638\) 29201.1i 1.81204i
\(639\) 9898.71 + 27106.2i 0.612812 + 1.67810i
\(640\) 45198.9i 2.79163i
\(641\) 27279.5i 1.68093i −0.541868 0.840464i \(-0.682283\pi\)
0.541868 0.840464i \(-0.317717\pi\)
\(642\) 12975.7 2295.13i 0.797681 0.141093i
\(643\) 19330.9i 1.18559i 0.805353 + 0.592796i \(0.201976\pi\)
−0.805353 + 0.592796i \(0.798024\pi\)
\(644\) 0 0
\(645\) 37852.0 6695.22i 2.31073 0.408719i
\(646\) 13482.4 0.821142
\(647\) −19942.3 −1.21177 −0.605884 0.795553i \(-0.707181\pi\)
−0.605884 + 0.795553i \(0.707181\pi\)
\(648\) 17007.8 + 20181.3i 1.03106 + 1.22345i
\(649\) 8004.42i 0.484131i
\(650\) 13770.1 0.830935
\(651\) 0 0
\(652\) 30024.9 1.80347
\(653\) 12834.9i 0.769171i 0.923089 + 0.384586i \(0.125656\pi\)
−0.923089 + 0.384586i \(0.874344\pi\)
\(654\) 274.843 + 1553.85i 0.0164331 + 0.0929059i
\(655\) 1693.26 0.101010
\(656\) −7916.88 −0.471193
\(657\) −9986.12 27345.6i −0.592992 1.62382i
\(658\) 0 0
\(659\) 11112.6i 0.656880i −0.944525 0.328440i \(-0.893477\pi\)
0.944525 0.328440i \(-0.106523\pi\)
\(660\) 6747.06 + 38145.1i 0.397922 + 2.24969i
\(661\) 3297.94i 0.194062i −0.995281 0.0970312i \(-0.969065\pi\)
0.995281 0.0970312i \(-0.0309346\pi\)
\(662\) 34811.0i 2.04376i
\(663\) −602.408 3405.77i −0.0352875 0.199501i
\(664\) 37038.7i 2.16473i
\(665\) 0 0
\(666\) 15637.2 + 42820.3i 0.909805 + 2.49137i
\(667\) −15534.0 −0.901766
\(668\) −41232.2 −2.38821
\(669\) 3403.45 + 19241.7i 0.196689 + 1.11200i
\(670\) 14434.5i 0.832321i
\(671\) −6246.45 −0.359376
\(672\) 0 0
\(673\) 527.753 0.0302279 0.0151140 0.999886i \(-0.495189\pi\)
0.0151140 + 0.999886i \(0.495189\pi\)
\(674\) 34953.5i 1.99756i
\(675\) 21161.5 12263.0i 1.20668 0.699261i
\(676\) −29880.5 −1.70007
\(677\) −214.998 −0.0122054 −0.00610269 0.999981i \(-0.501943\pi\)
−0.00610269 + 0.999981i \(0.501943\pi\)
\(678\) −2105.71 + 372.454i −0.119276 + 0.0210974i
\(679\) 0 0
\(680\) 25572.0i 1.44212i
\(681\) 14515.4 2567.47i 0.816788 0.144472i
\(682\) 21230.4i 1.19201i
\(683\) 7314.04i 0.409757i 0.978787 + 0.204878i \(0.0656799\pi\)
−0.978787 + 0.204878i \(0.934320\pi\)
\(684\) 9767.83 + 26747.8i 0.546027 + 1.49522i
\(685\) 29305.5i 1.63461i
\(686\) 0 0
\(687\) −4713.32 26647.2i −0.261753 1.47985i
\(688\) 22071.5 1.22306
\(689\) 3138.86 0.173557
\(690\) 30783.7 5444.98i 1.69843 0.300415i
\(691\) 31412.9i 1.72938i −0.502302 0.864692i \(-0.667514\pi\)
0.502302 0.864692i \(-0.332486\pi\)
\(692\) 47905.9 2.63166
\(693\) 0 0
\(694\) −39490.5 −2.16000
\(695\) 31509.9i 1.71977i
\(696\) −40091.3 + 7091.30i −2.18342 + 0.386200i
\(697\) 6261.58 0.340279
\(698\) 2383.26 0.129237
\(699\) −1978.32 11184.6i −0.107049 0.605210i
\(700\) 0 0
\(701\) 11496.6i 0.619430i 0.950829 + 0.309715i \(0.100234\pi\)
−0.950829 + 0.309715i \(0.899766\pi\)
\(702\) 9588.17 5556.27i 0.515502 0.298729i
\(703\) 23754.0i 1.27439i
\(704\) 16835.2i 0.901277i
\(705\) −1488.13 + 263.219i −0.0794984 + 0.0140616i
\(706\) 14164.6i 0.755087i
\(707\) 0 0
\(708\) −22754.9 + 4024.85i −1.20788 + 0.213649i
\(709\) 21068.2 1.11598 0.557992 0.829847i \(-0.311572\pi\)
0.557992 + 0.829847i \(0.311572\pi\)
\(710\) 89586.8 4.73540
\(711\) 1319.67 481.919i 0.0696081 0.0254197i
\(712\) 24204.4i 1.27402i
\(713\) −11293.8 −0.593208
\(714\) 0 0
\(715\) 7855.39 0.410874
\(716\) 13966.1i 0.728966i
\(717\) 1739.37 + 9833.68i 0.0905968 + 0.512197i
\(718\) −23265.7 −1.20929
\(719\) 7492.00 0.388602 0.194301 0.980942i \(-0.437756\pi\)
0.194301 + 0.980942i \(0.437756\pi\)
\(720\) 22649.9 8271.35i 1.17238 0.428132i
\(721\) 0 0
\(722\) 10720.9i 0.552620i
\(723\) −4051.19 22903.8i −0.208389 1.17815i
\(724\) 54092.1i 2.77668i
\(725\) 37729.8i 1.93276i
\(726\) −2435.46 13769.1i −0.124502 0.703882i
\(727\) 19637.5i 1.00181i −0.865503 0.500904i \(-0.833001\pi\)
0.865503 0.500904i \(-0.166999\pi\)
\(728\) 0 0
\(729\) 9786.73 17077.5i 0.497217 0.867626i
\(730\) −90378.0 −4.58225
\(731\) −17456.7 −0.883254
\(732\) 3140.89 + 17757.3i 0.158594 + 0.896626i
\(733\) 28892.7i 1.45590i 0.685629 + 0.727951i \(0.259527\pi\)
−0.685629 + 0.727951i \(0.740473\pi\)
\(734\) 43399.7 2.18244
\(735\) 0 0
\(736\) −2837.95 −0.142131
\(737\) 4795.75i 0.239693i
\(738\) 6881.98 + 18845.3i 0.343265 + 0.939981i
\(739\) −4114.53 −0.204811 −0.102406 0.994743i \(-0.532654\pi\)
−0.102406 + 0.994743i \(0.532654\pi\)
\(740\) 93288.3 4.63425
\(741\) 5686.19 1005.77i 0.281899 0.0498620i
\(742\) 0 0
\(743\) 19095.9i 0.942881i 0.881898 + 0.471441i \(0.156266\pi\)
−0.881898 + 0.471441i \(0.843734\pi\)
\(744\) −29148.0 + 5155.67i −1.43632 + 0.254054i
\(745\) 31107.4i 1.52978i
\(746\) 24577.1i 1.20621i
\(747\) 25947.0 9475.40i 1.27089 0.464105i
\(748\) 17591.8i 0.859922i
\(749\) 0 0
\(750\) −3742.33 21157.6i −0.182201 1.03009i
\(751\) 27352.7 1.32905 0.664524 0.747267i \(-0.268634\pi\)
0.664524 + 0.747267i \(0.268634\pi\)
\(752\) −867.731 −0.0420783
\(753\) −16867.3 + 2983.47i −0.816308 + 0.144388i
\(754\) 17095.1i 0.825687i
\(755\) −36156.7 −1.74288
\(756\) 0 0
\(757\) 2016.86 0.0968349 0.0484174 0.998827i \(-0.484582\pi\)
0.0484174 + 0.998827i \(0.484582\pi\)
\(758\) 4146.39i 0.198686i
\(759\) 10227.6 1809.05i 0.489115 0.0865141i
\(760\) 42694.4 2.03775
\(761\) −28904.7 −1.37687 −0.688434 0.725299i \(-0.741701\pi\)
−0.688434 + 0.725299i \(0.741701\pi\)
\(762\) 8080.45 + 45683.6i 0.384152 + 2.17184i
\(763\) 0 0
\(764\) 5485.23i 0.259750i
\(765\) −17914.2 + 6541.94i −0.846651 + 0.309182i
\(766\) 34304.4i 1.61811i
\(767\) 4686.01i 0.220602i
\(768\) −40017.4 + 7078.23i −1.88021 + 0.332570i
\(769\) 16726.1i 0.784343i 0.919892 + 0.392171i \(0.128276\pi\)
−0.919892 + 0.392171i \(0.871724\pi\)
\(770\) 0 0
\(771\) −36383.3 + 6435.44i −1.69950 + 0.300605i
\(772\) −43940.2 −2.04850
\(773\) −15197.6 −0.707139 −0.353570 0.935408i \(-0.615032\pi\)
−0.353570 + 0.935408i \(0.615032\pi\)
\(774\) −19186.3 52539.0i −0.891005 2.43989i
\(775\) 27431.1i 1.27142i
\(776\) −49178.4 −2.27500
\(777\) 0 0
\(778\) −10046.2 −0.462949
\(779\) 10454.2i 0.480821i
\(780\) −3949.91 22331.2i −0.181320 1.02511i
\(781\) 29764.4 1.36371
\(782\) −14196.9 −0.649206
\(783\) 15224.1 + 26271.4i 0.694845 + 1.19906i
\(784\) 0 0
\(785\) 18864.1i 0.857694i
\(786\) −429.138 2426.17i −0.0194743 0.110100i
\(787\) 13333.2i 0.603910i 0.953322 + 0.301955i \(0.0976393\pi\)
−0.953322 + 0.301955i \(0.902361\pi\)
\(788\) 47318.9i 2.13917i
\(789\) 6162.31 + 34839.2i 0.278053 + 1.57200i
\(790\) 4361.54i 0.196426i
\(791\) 0 0
\(792\) 25570.4 9337.86i 1.14723 0.418948i
\(793\) 3656.84 0.163756
\(794\) −27722.5 −1.23909
\(795\) −3014.62 17043.4i −0.134488 0.760338i
\(796\) 28461.5i 1.26732i
\(797\) 31995.7 1.42202 0.711008 0.703183i \(-0.248239\pi\)
0.711008 + 0.703183i \(0.248239\pi\)
\(798\) 0 0
\(799\) 686.301 0.0303875
\(800\) 6892.97i 0.304629i
\(801\) −16956.1 + 6192.08i −0.747959 + 0.273142i
\(802\) 56824.9 2.50194
\(803\) −30027.3 −1.31960
\(804\) 13633.3 2411.44i 0.598022 0.105777i
\(805\) 0 0
\(806\) 12428.9i 0.543161i
\(807\) −18440.2 + 3261.68i −0.804370 + 0.142276i
\(808\) 1053.37i 0.0458631i
\(809\) 5450.03i 0.236852i 0.992963 + 0.118426i \(0.0377848\pi\)
−0.992963 + 0.118426i \(0.962215\pi\)
\(810\) −39378.2 46725.7i −1.70816 2.02688i
\(811\) 39222.9i 1.69828i −0.528171 0.849138i \(-0.677122\pi\)
0.528171 0.849138i \(-0.322878\pi\)
\(812\) 0 0
\(813\) −3055.55 17274.8i −0.131812 0.745209i
\(814\) 47019.6 2.02461
\(815\) −33573.4 −1.44298
\(816\) −10783.1 + 1907.30i −0.462603 + 0.0818246i
\(817\) 29145.3i 1.24806i
\(818\) −12710.6 −0.543295
\(819\) 0 0
\(820\) 41056.4 1.74848
\(821\) 14897.1i 0.633267i −0.948548 0.316634i \(-0.897447\pi\)
0.948548 0.316634i \(-0.102553\pi\)
\(822\) 41990.0 7427.14i 1.78172 0.315147i
\(823\) −33975.1 −1.43900 −0.719500 0.694492i \(-0.755629\pi\)
−0.719500 + 0.694492i \(0.755629\pi\)
\(824\) −10893.9 −0.460567
\(825\) −4393.91 24841.4i −0.185426 1.04832i
\(826\) 0 0
\(827\) 5008.85i 0.210610i −0.994440 0.105305i \(-0.966418\pi\)
0.994440 0.105305i \(-0.0335819\pi\)
\(828\) −10285.5 28165.3i −0.431696 1.18214i
\(829\) 33961.3i 1.42283i −0.702773 0.711414i \(-0.748055\pi\)
0.702773 0.711414i \(-0.251945\pi\)
\(830\) 85755.7i 3.58629i
\(831\) −35510.6 + 6281.07i −1.48237 + 0.262199i
\(832\) 9855.77i 0.410682i
\(833\) 0 0
\(834\) −45148.5 + 7985.80i −1.87454 + 0.331566i
\(835\) 46105.3 1.91083
\(836\) 29370.9 1.21509
\(837\) 11068.5 + 19100.4i 0.457090 + 0.788776i
\(838\) 10579.3i 0.436104i
\(839\) 31564.7 1.29885 0.649426 0.760425i \(-0.275009\pi\)
0.649426 + 0.760425i \(0.275009\pi\)
\(840\) 0 0
\(841\) −22451.4 −0.920553
\(842\) 62602.8i 2.56227i
\(843\) −3469.92 19617.5i −0.141768 0.801499i
\(844\) 9975.05 0.406819
\(845\) 33411.9 1.36024
\(846\) 754.300 + 2065.54i 0.0306541 + 0.0839419i
\(847\) 0 0
\(848\) 9938.02i 0.402445i
\(849\) −5831.80 32970.6i −0.235744 1.33280i
\(850\) 34482.2i 1.39145i
\(851\) 25012.8i 1.00755i
\(852\) −14966.4 84614.0i −0.601809 3.40238i
\(853\) 26673.5i 1.07067i 0.844639 + 0.535336i \(0.179815\pi\)
−0.844639 + 0.535336i \(0.820185\pi\)
\(854\) 0 0
\(855\) −10922.3 29909.0i −0.436881 1.19634i
\(856\) −18949.9 −0.756654
\(857\) −28604.9 −1.14017 −0.570084 0.821586i \(-0.693089\pi\)
−0.570084 + 0.821586i \(0.693089\pi\)
\(858\) −1990.86 11255.5i −0.0792152 0.447851i
\(859\) 42152.2i 1.67429i 0.546980 + 0.837146i \(0.315777\pi\)
−0.546980 + 0.837146i \(0.684223\pi\)
\(860\) −114461. −4.53849
\(861\) 0 0
\(862\) 61141.0 2.41586
\(863\) 33862.3i 1.33567i 0.744308 + 0.667836i \(0.232779\pi\)
−0.744308 + 0.667836i \(0.767221\pi\)
\(864\) 2781.33 + 4799.60i 0.109517 + 0.188988i
\(865\) −53567.7 −2.10561
\(866\) 68701.8 2.69582
\(867\) −16610.0 + 2937.95i −0.650639 + 0.115084i
\(868\) 0 0
\(869\) 1449.08i 0.0565671i
\(870\) 92823.6 16418.5i 3.61726 0.639816i
\(871\) 2807.56i 0.109220i
\(872\) 2269.27i 0.0881274i
\(873\) 12581.0 + 34451.3i 0.487747 + 1.33563i
\(874\) 23702.8i 0.917343i
\(875\) 0 0
\(876\) 15098.6 + 85361.2i 0.582345 + 3.29234i
\(877\) 14209.4 0.547111 0.273556 0.961856i \(-0.411800\pi\)
0.273556 + 0.961856i \(0.411800\pi\)
\(878\) 36176.6 1.39055
\(879\) −7384.56 + 1306.17i −0.283362 + 0.0501207i
\(880\) 24871.1i 0.952734i
\(881\) −40320.8 −1.54193 −0.770966 0.636877i \(-0.780226\pi\)
−0.770966 + 0.636877i \(0.780226\pi\)
\(882\) 0 0
\(883\) 44671.9 1.70252 0.851262 0.524741i \(-0.175838\pi\)
0.851262 + 0.524741i \(0.175838\pi\)
\(884\) 10298.8i 0.391838i
\(885\) 25444.2 4500.53i 0.966437 0.170942i
\(886\) 1762.50 0.0668309
\(887\) 6917.18 0.261845 0.130922 0.991393i \(-0.458206\pi\)
0.130922 + 0.991393i \(0.458206\pi\)
\(888\) −11418.4 64555.0i −0.431505 2.43956i
\(889\) 0 0
\(890\) 56040.6i 2.11066i
\(891\) −13083.1 15524.2i −0.491918 0.583704i
\(892\) 58185.3i 2.18407i
\(893\) 1145.83i 0.0429382i
\(894\) 44571.9 7883.81i 1.66746 0.294938i
\(895\) 15616.8i 0.583252i
\(896\) 0 0
\(897\) −5987.52 + 1059.07i −0.222874 + 0.0394216i
\(898\) 26378.7 0.980253
\(899\) −34054.8 −1.26340
\(900\) −68409.4 + 24981.9i −2.53368 + 0.925257i
\(901\) 7860.13i 0.290631i
\(902\) 20693.4 0.763876
\(903\) 0 0
\(904\) 3075.20 0.113141
\(905\) 60485.1i 2.22165i
\(906\) 9163.48 + 51806.6i 0.336022 + 1.89973i
\(907\) 3716.85 0.136071 0.0680353 0.997683i \(-0.478327\pi\)
0.0680353 + 0.997683i \(0.478327\pi\)
\(908\) −43893.4 −1.60424
\(909\) −737.925 + 269.477i −0.0269257 + 0.00983278i
\(910\) 0 0
\(911\) 47943.1i 1.74361i −0.489855 0.871804i \(-0.662950\pi\)
0.489855 0.871804i \(-0.337050\pi\)
\(912\) −3184.38 18003.2i −0.115620 0.653668i
\(913\) 28491.6i 1.03279i
\(914\) 11170.6i 0.404256i
\(915\) −3512.10 19856.0i −0.126892 0.717398i
\(916\) 80578.8i 2.90655i
\(917\) 0 0
\(918\) 13913.7 + 24010.1i 0.500239 + 0.863236i
\(919\) −7853.69 −0.281904 −0.140952 0.990016i \(-0.545016\pi\)
−0.140952 + 0.990016i \(0.545016\pi\)
\(920\) −44956.9 −1.61107
\(921\) −4981.63 28164.1i −0.178230 1.00764i
\(922\) 2837.89i 0.101367i
\(923\) −17424.9 −0.621396
\(924\) 0 0
\(925\) −60752.5 −2.15949
\(926\) 54851.2i 1.94657i
\(927\) 2786.93 + 7631.60i 0.0987429 + 0.270393i
\(928\) −8557.41 −0.302706
\(929\) 19541.9 0.690148 0.345074 0.938575i \(-0.387854\pi\)
0.345074 + 0.938575i \(0.387854\pi\)
\(930\) 67486.5 11936.9i 2.37954 0.420889i
\(931\) 0 0
\(932\) 33821.4i 1.18869i
\(933\) 12379.7 2189.70i 0.434397 0.0768355i
\(934\) 48246.4i 1.69023i
\(935\) 19671.0i 0.688031i
\(936\) −14969.6 + 5466.64i −0.522754 + 0.190900i
\(937\) 8670.27i 0.302290i −0.988512 0.151145i \(-0.951704\pi\)
0.988512 0.151145i \(-0.0482960\pi\)
\(938\) 0 0
\(939\) 1077.34 + 6090.86i 0.0374417 + 0.211680i
\(940\) 4499.99 0.156142
\(941\) 49486.9 1.71437 0.857187 0.515006i \(-0.172210\pi\)
0.857187 + 0.515006i \(0.172210\pi\)
\(942\) 27029.2 4780.89i 0.934883 0.165361i
\(943\) 11008.2i 0.380144i
\(944\) 14836.5 0.511532
\(945\) 0 0
\(946\) −57691.3 −1.98278
\(947\) 34057.1i 1.16865i 0.811521 + 0.584323i \(0.198640\pi\)
−0.811521 + 0.584323i \(0.801360\pi\)
\(948\) −4119.44 + 728.641i −0.141132 + 0.0249632i
\(949\) 17578.8 0.601298
\(950\) −57570.6 −1.96614
\(951\) −5998.76 33914.6i −0.204546 1.15642i
\(952\) 0 0
\(953\) 28600.5i 0.972152i 0.873917 + 0.486076i \(0.161572\pi\)
−0.873917 + 0.486076i \(0.838428\pi\)
\(954\) −23656.4 + 8638.92i −0.802836 + 0.293182i
\(955\) 6133.51i 0.207828i
\(956\) 29736.2i 1.00600i
\(957\) 30839.8 5454.90i 1.04170 0.184255i
\(958\) 67014.0i 2.26005i
\(959\) 0 0
\(960\) 53515.1 9465.68i 1.79916 0.318233i
\(961\) 5031.75 0.168902
\(962\) −27526.6 −0.922549
\(963\) 4847.86 + 13275.2i 0.162222 + 0.444222i
\(964\) 69259.1i 2.31399i
\(965\) 49133.3 1.63902
\(966\) 0 0
\(967\) 10889.4 0.362131 0.181065 0.983471i \(-0.442045\pi\)
0.181065 + 0.983471i \(0.442045\pi\)
\(968\) 20108.6i 0.667679i
\(969\) 2518.57 + 14239.0i 0.0834967 + 0.472056i
\(970\) 113863. 3.76898
\(971\) −45497.2 −1.50368 −0.751841 0.659344i \(-0.770834\pi\)
−0.751841 + 0.659344i \(0.770834\pi\)
\(972\) −37553.5 + 44998.4i −1.23923 + 1.48490i
\(973\) 0 0
\(974\) 2210.11i 0.0727069i
\(975\) 2572.32 + 14542.8i 0.0844924 + 0.477686i
\(976\) 11578.0i 0.379717i
\(977\) 27429.6i 0.898210i 0.893479 + 0.449105i \(0.148257\pi\)
−0.893479 + 0.449105i \(0.851743\pi\)
\(978\) 8508.79 + 48105.2i 0.278201 + 1.57284i
\(979\) 18619.0i 0.607830i
\(980\) 0 0
\(981\) −1589.71 + 580.534i −0.0517385 + 0.0188940i
\(982\) −82553.9 −2.68269
\(983\) 25943.6 0.841783 0.420892 0.907111i \(-0.361717\pi\)
0.420892 + 0.907111i \(0.361717\pi\)
\(984\) −5025.27 28410.8i −0.162805 0.920431i
\(985\) 52911.4i 1.71157i
\(986\) −42808.6 −1.38266
\(987\) 0 0
\(988\) −17194.5 −0.553675
\(989\) 30689.8i 0.986732i
\(990\) −59203.2 + 21620.0i −1.90061 + 0.694069i
\(991\) 53486.9 1.71450 0.857250 0.514901i \(-0.172171\pi\)
0.857250 + 0.514901i \(0.172171\pi\)
\(992\) −6221.59 −0.199129
\(993\) −36764.5 + 6502.86i −1.17491 + 0.207817i
\(994\) 0 0
\(995\) 31825.2i 1.01400i
\(996\) −80995.5 + 14326.4i −2.57675 + 0.455772i
\(997\) 797.622i 0.0253369i −0.999920 0.0126685i \(-0.995967\pi\)
0.999920 0.0126685i \(-0.00403261\pi\)
\(998\) 8989.79i 0.285137i
\(999\) −42302.2 + 24513.8i −1.33972 + 0.776358i
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 147.4.c.b.146.4 yes 24
3.2 odd 2 inner 147.4.c.b.146.21 yes 24
7.2 even 3 147.4.g.e.80.3 48
7.3 odd 6 147.4.g.e.68.22 48
7.4 even 3 147.4.g.e.68.21 48
7.5 odd 6 147.4.g.e.80.4 48
7.6 odd 2 inner 147.4.c.b.146.3 24
21.2 odd 6 147.4.g.e.80.22 48
21.5 even 6 147.4.g.e.80.21 48
21.11 odd 6 147.4.g.e.68.4 48
21.17 even 6 147.4.g.e.68.3 48
21.20 even 2 inner 147.4.c.b.146.22 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.4.c.b.146.3 24 7.6 odd 2 inner
147.4.c.b.146.4 yes 24 1.1 even 1 trivial
147.4.c.b.146.21 yes 24 3.2 odd 2 inner
147.4.c.b.146.22 yes 24 21.20 even 2 inner
147.4.g.e.68.3 48 21.17 even 6
147.4.g.e.68.4 48 21.11 odd 6
147.4.g.e.68.21 48 7.4 even 3
147.4.g.e.68.22 48 7.3 odd 6
147.4.g.e.80.3 48 7.2 even 3
147.4.g.e.80.4 48 7.5 odd 6
147.4.g.e.80.21 48 21.5 even 6
147.4.g.e.80.22 48 21.2 odd 6