Properties

Label 245.4.e.f.226.1
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $2$
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] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.f.116.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(2.50000 - 4.33013i) q^{5} -8.00000 q^{6} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\) \(q+(2.00000 - 3.46410i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(2.50000 - 4.33013i) q^{5} -8.00000 q^{6} +(11.5000 - 19.9186i) q^{9} +(-10.0000 - 17.3205i) q^{10} +(-16.0000 - 27.7128i) q^{11} +(-8.00000 + 13.8564i) q^{12} -38.0000 q^{13} -10.0000 q^{15} +(32.0000 - 55.4256i) q^{16} +(-13.0000 - 22.5167i) q^{17} +(-46.0000 - 79.6743i) q^{18} +(-50.0000 + 86.6025i) q^{19} -40.0000 q^{20} -128.000 q^{22} +(39.0000 - 67.5500i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-76.0000 + 131.636i) q^{26} -100.000 q^{27} -50.0000 q^{29} +(-20.0000 + 34.6410i) q^{30} +(54.0000 + 93.5307i) q^{31} +(-128.000 - 221.703i) q^{32} +(-32.0000 + 55.4256i) q^{33} -104.000 q^{34} -184.000 q^{36} +(-133.000 + 230.363i) q^{37} +(200.000 + 346.410i) q^{38} +(38.0000 + 65.8179i) q^{39} +22.0000 q^{41} +442.000 q^{43} +(-128.000 + 221.703i) q^{44} +(-57.5000 - 99.5929i) q^{45} +(-156.000 - 270.200i) q^{46} +(257.000 - 445.137i) q^{47} -128.000 q^{48} -100.000 q^{50} +(-26.0000 + 45.0333i) q^{51} +(152.000 + 263.272i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-200.000 + 346.410i) q^{54} -160.000 q^{55} +200.000 q^{57} +(-100.000 + 173.205i) q^{58} +(-250.000 - 433.013i) q^{59} +(40.0000 + 69.2820i) q^{60} +(259.000 - 448.601i) q^{61} +432.000 q^{62} -512.000 q^{64} +(-95.0000 + 164.545i) q^{65} +(128.000 + 221.703i) q^{66} +(-63.0000 - 109.119i) q^{67} +(-104.000 + 180.133i) q^{68} -156.000 q^{69} +412.000 q^{71} +(439.000 + 760.370i) q^{73} +(532.000 + 921.451i) q^{74} +(-25.0000 + 43.3013i) q^{75} +800.000 q^{76} +304.000 q^{78} +(-300.000 + 519.615i) q^{79} +(-160.000 - 277.128i) q^{80} +(-210.500 - 364.597i) q^{81} +(44.0000 - 76.2102i) q^{82} +282.000 q^{83} -130.000 q^{85} +(884.000 - 1531.13i) q^{86} +(50.0000 + 86.6025i) q^{87} +(75.0000 - 129.904i) q^{89} -460.000 q^{90} -624.000 q^{92} +(108.000 - 187.061i) q^{93} +(-1028.00 - 1780.55i) q^{94} +(250.000 + 433.013i) q^{95} +(-256.000 + 443.405i) q^{96} +386.000 q^{97} -736.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} + 5 q^{5} - 16 q^{6} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} + 5 q^{5} - 16 q^{6} + 23 q^{9} - 20 q^{10} - 32 q^{11} - 16 q^{12} - 76 q^{13} - 20 q^{15} + 64 q^{16} - 26 q^{17} - 92 q^{18} - 100 q^{19} - 80 q^{20} - 256 q^{22} + 78 q^{23} - 25 q^{25} - 152 q^{26} - 200 q^{27} - 100 q^{29} - 40 q^{30} + 108 q^{31} - 256 q^{32} - 64 q^{33} - 208 q^{34} - 368 q^{36} - 266 q^{37} + 400 q^{38} + 76 q^{39} + 44 q^{41} + 884 q^{43} - 256 q^{44} - 115 q^{45} - 312 q^{46} + 514 q^{47} - 256 q^{48} - 200 q^{50} - 52 q^{51} + 304 q^{52} - 2 q^{53} - 400 q^{54} - 320 q^{55} + 400 q^{57} - 200 q^{58} - 500 q^{59} + 80 q^{60} + 518 q^{61} + 864 q^{62} - 1024 q^{64} - 190 q^{65} + 256 q^{66} - 126 q^{67} - 208 q^{68} - 312 q^{69} + 824 q^{71} + 878 q^{73} + 1064 q^{74} - 50 q^{75} + 1600 q^{76} + 608 q^{78} - 600 q^{79} - 320 q^{80} - 421 q^{81} + 88 q^{82} + 564 q^{83} - 260 q^{85} + 1768 q^{86} + 100 q^{87} + 150 q^{89} - 920 q^{90} - 1248 q^{92} + 216 q^{93} - 2056 q^{94} + 500 q^{95} - 512 q^{96} + 772 q^{97} - 1472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 3.46410i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) −1.00000 1.73205i −0.192450 0.333333i 0.753612 0.657320i \(-0.228310\pi\)
−0.946062 + 0.323987i \(0.894977\pi\)
\(4\) −4.00000 6.92820i −0.500000 0.866025i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) −8.00000 −0.544331
\(7\) 0 0
\(8\) 0 0
\(9\) 11.5000 19.9186i 0.425926 0.737725i
\(10\) −10.0000 17.3205i −0.316228 0.547723i
\(11\) −16.0000 27.7128i −0.438562 0.759612i 0.559017 0.829156i \(-0.311179\pi\)
−0.997579 + 0.0695447i \(0.977845\pi\)
\(12\) −8.00000 + 13.8564i −0.192450 + 0.333333i
\(13\) −38.0000 −0.810716 −0.405358 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) −10.0000 −0.172133
\(16\) 32.0000 55.4256i 0.500000 0.866025i
\(17\) −13.0000 22.5167i −0.185468 0.321241i 0.758266 0.651945i \(-0.226047\pi\)
−0.943734 + 0.330705i \(0.892714\pi\)
\(18\) −46.0000 79.6743i −0.602350 1.04330i
\(19\) −50.0000 + 86.6025i −0.603726 + 1.04568i 0.388526 + 0.921438i \(0.372984\pi\)
−0.992251 + 0.124246i \(0.960349\pi\)
\(20\) −40.0000 −0.447214
\(21\) 0 0
\(22\) −128.000 −1.24044
\(23\) 39.0000 67.5500i 0.353568 0.612398i −0.633304 0.773903i \(-0.718302\pi\)
0.986872 + 0.161506i \(0.0516350\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −76.0000 + 131.636i −0.573263 + 0.992920i
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) −50.0000 −0.320164 −0.160082 0.987104i \(-0.551176\pi\)
−0.160082 + 0.987104i \(0.551176\pi\)
\(30\) −20.0000 + 34.6410i −0.121716 + 0.210819i
\(31\) 54.0000 + 93.5307i 0.312861 + 0.541891i 0.978980 0.203954i \(-0.0653793\pi\)
−0.666120 + 0.745845i \(0.732046\pi\)
\(32\) −128.000 221.703i −0.707107 1.22474i
\(33\) −32.0000 + 55.4256i −0.168803 + 0.292375i
\(34\) −104.000 −0.524584
\(35\) 0 0
\(36\) −184.000 −0.851852
\(37\) −133.000 + 230.363i −0.590948 + 1.02355i 0.403157 + 0.915131i \(0.367913\pi\)
−0.994105 + 0.108421i \(0.965421\pi\)
\(38\) 200.000 + 346.410i 0.853797 + 1.47882i
\(39\) 38.0000 + 65.8179i 0.156022 + 0.270239i
\(40\) 0 0
\(41\) 22.0000 0.0838006 0.0419003 0.999122i \(-0.486659\pi\)
0.0419003 + 0.999122i \(0.486659\pi\)
\(42\) 0 0
\(43\) 442.000 1.56754 0.783772 0.621049i \(-0.213293\pi\)
0.783772 + 0.621049i \(0.213293\pi\)
\(44\) −128.000 + 221.703i −0.438562 + 0.759612i
\(45\) −57.5000 99.5929i −0.190480 0.329921i
\(46\) −156.000 270.200i −0.500021 0.866061i
\(47\) 257.000 445.137i 0.797602 1.38149i −0.123571 0.992336i \(-0.539435\pi\)
0.921174 0.389152i \(-0.127232\pi\)
\(48\) −128.000 −0.384900
\(49\) 0 0
\(50\) −100.000 −0.282843
\(51\) −26.0000 + 45.0333i −0.0713868 + 0.123646i
\(52\) 152.000 + 263.272i 0.405358 + 0.702100i
\(53\) −1.00000 1.73205i −0.00259171 0.00448897i 0.864727 0.502243i \(-0.167492\pi\)
−0.867318 + 0.497754i \(0.834158\pi\)
\(54\) −200.000 + 346.410i −0.504010 + 0.872971i
\(55\) −160.000 −0.392262
\(56\) 0 0
\(57\) 200.000 0.464748
\(58\) −100.000 + 173.205i −0.226390 + 0.392120i
\(59\) −250.000 433.013i −0.551648 0.955482i −0.998156 0.0607026i \(-0.980666\pi\)
0.446508 0.894780i \(-0.352667\pi\)
\(60\) 40.0000 + 69.2820i 0.0860663 + 0.149071i
\(61\) 259.000 448.601i 0.543632 0.941598i −0.455060 0.890461i \(-0.650382\pi\)
0.998692 0.0511373i \(-0.0162846\pi\)
\(62\) 432.000 0.884904
\(63\) 0 0
\(64\) −512.000 −1.00000
\(65\) −95.0000 + 164.545i −0.181282 + 0.313989i
\(66\) 128.000 + 221.703i 0.238723 + 0.413480i
\(67\) −63.0000 109.119i −0.114876 0.198971i 0.802854 0.596175i \(-0.203314\pi\)
−0.917730 + 0.397205i \(0.869980\pi\)
\(68\) −104.000 + 180.133i −0.185468 + 0.321241i
\(69\) −156.000 −0.272177
\(70\) 0 0
\(71\) 412.000 0.688668 0.344334 0.938847i \(-0.388105\pi\)
0.344334 + 0.938847i \(0.388105\pi\)
\(72\) 0 0
\(73\) 439.000 + 760.370i 0.703850 + 1.21910i 0.967105 + 0.254378i \(0.0818707\pi\)
−0.263255 + 0.964726i \(0.584796\pi\)
\(74\) 532.000 + 921.451i 0.835726 + 1.44752i
\(75\) −25.0000 + 43.3013i −0.0384900 + 0.0666667i
\(76\) 800.000 1.20745
\(77\) 0 0
\(78\) 304.000 0.441298
\(79\) −300.000 + 519.615i −0.427249 + 0.740016i −0.996627 0.0820590i \(-0.973850\pi\)
0.569379 + 0.822075i \(0.307184\pi\)
\(80\) −160.000 277.128i −0.223607 0.387298i
\(81\) −210.500 364.597i −0.288752 0.500133i
\(82\) 44.0000 76.2102i 0.0592559 0.102634i
\(83\) 282.000 0.372934 0.186467 0.982461i \(-0.440296\pi\)
0.186467 + 0.982461i \(0.440296\pi\)
\(84\) 0 0
\(85\) −130.000 −0.165888
\(86\) 884.000 1531.13i 1.10842 1.91984i
\(87\) 50.0000 + 86.6025i 0.0616157 + 0.106721i
\(88\) 0 0
\(89\) 75.0000 129.904i 0.0893257 0.154717i −0.817901 0.575360i \(-0.804862\pi\)
0.907226 + 0.420643i \(0.138195\pi\)
\(90\) −460.000 −0.538758
\(91\) 0 0
\(92\) −624.000 −0.707136
\(93\) 108.000 187.061i 0.120420 0.208574i
\(94\) −1028.00 1780.55i −1.12798 1.95372i
\(95\) 250.000 + 433.013i 0.269994 + 0.467644i
\(96\) −256.000 + 443.405i −0.272166 + 0.471405i
\(97\) 386.000 0.404045 0.202022 0.979381i \(-0.435249\pi\)
0.202022 + 0.979381i \(0.435249\pi\)
\(98\) 0 0
\(99\) −736.000 −0.747180
\(100\) −100.000 + 173.205i −0.100000 + 0.173205i
\(101\) −351.000 607.950i −0.345800 0.598943i 0.639699 0.768626i \(-0.279059\pi\)
−0.985499 + 0.169682i \(0.945726\pi\)
\(102\) 104.000 + 180.133i 0.100956 + 0.174861i
\(103\) 299.000 517.883i 0.286032 0.495423i −0.686827 0.726821i \(-0.740997\pi\)
0.972859 + 0.231399i \(0.0743301\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −8.00000 −0.00733046
\(107\) 597.000 1034.03i 0.539385 0.934242i −0.459552 0.888151i \(-0.651990\pi\)
0.998937 0.0460912i \(-0.0146765\pi\)
\(108\) 400.000 + 692.820i 0.356389 + 0.617284i
\(109\) 275.000 + 476.314i 0.241653 + 0.418556i 0.961185 0.275903i \(-0.0889770\pi\)
−0.719532 + 0.694459i \(0.755644\pi\)
\(110\) −320.000 + 554.256i −0.277371 + 0.480421i
\(111\) 532.000 0.454912
\(112\) 0 0
\(113\) 1562.00 1.30036 0.650180 0.759781i \(-0.274694\pi\)
0.650180 + 0.759781i \(0.274694\pi\)
\(114\) 400.000 692.820i 0.328627 0.569198i
\(115\) −195.000 337.750i −0.158120 0.273873i
\(116\) 200.000 + 346.410i 0.160082 + 0.277270i
\(117\) −437.000 + 756.906i −0.345305 + 0.598085i
\(118\) −2000.00 −1.56030
\(119\) 0 0
\(120\) 0 0
\(121\) 153.500 265.870i 0.115327 0.199752i
\(122\) −1036.00 1794.40i −0.768812 1.33162i
\(123\) −22.0000 38.1051i −0.0161274 0.0279335i
\(124\) 432.000 748.246i 0.312861 0.541891i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1846.00 1.28981 0.644906 0.764262i \(-0.276897\pi\)
0.644906 + 0.764262i \(0.276897\pi\)
\(128\) 0 0
\(129\) −442.000 765.566i −0.301674 0.522514i
\(130\) 380.000 + 658.179i 0.256371 + 0.444047i
\(131\) 1104.00 1912.18i 0.736312 1.27533i −0.217833 0.975986i \(-0.569899\pi\)
0.954145 0.299344i \(-0.0967680\pi\)
\(132\) 512.000 0.337605
\(133\) 0 0
\(134\) −504.000 −0.324918
\(135\) −250.000 + 433.013i −0.159382 + 0.276058i
\(136\) 0 0
\(137\) 1167.00 + 2021.30i 0.727763 + 1.26052i 0.957827 + 0.287347i \(0.0927733\pi\)
−0.230064 + 0.973176i \(0.573893\pi\)
\(138\) −312.000 + 540.400i −0.192458 + 0.333347i
\(139\) −700.000 −0.427146 −0.213573 0.976927i \(-0.568510\pi\)
−0.213573 + 0.976927i \(0.568510\pi\)
\(140\) 0 0
\(141\) −1028.00 −0.613994
\(142\) 824.000 1427.21i 0.486962 0.843442i
\(143\) 608.000 + 1053.09i 0.355549 + 0.615829i
\(144\) −736.000 1274.79i −0.425926 0.737725i
\(145\) −125.000 + 216.506i −0.0715909 + 0.123999i
\(146\) 3512.00 1.99079
\(147\) 0 0
\(148\) 2128.00 1.18190
\(149\) −1025.00 + 1775.35i −0.563566 + 0.976124i 0.433616 + 0.901098i \(0.357237\pi\)
−0.997182 + 0.0750264i \(0.976096\pi\)
\(150\) 100.000 + 173.205i 0.0544331 + 0.0942809i
\(151\) −926.000 1603.88i −0.499052 0.864383i 0.500948 0.865478i \(-0.332985\pi\)
−0.999999 + 0.00109462i \(0.999652\pi\)
\(152\) 0 0
\(153\) −598.000 −0.315983
\(154\) 0 0
\(155\) 540.000 0.279831
\(156\) 304.000 526.543i 0.156022 0.270239i
\(157\) 1247.00 + 2159.87i 0.633894 + 1.09794i 0.986748 + 0.162259i \(0.0518780\pi\)
−0.352854 + 0.935678i \(0.614789\pi\)
\(158\) 1200.00 + 2078.46i 0.604221 + 1.04654i
\(159\) −2.00000 + 3.46410i −0.000997549 + 0.00172781i
\(160\) −1280.00 −0.632456
\(161\) 0 0
\(162\) −1684.00 −0.816713
\(163\) −1381.00 + 2391.96i −0.663609 + 1.14940i 0.316051 + 0.948742i \(0.397643\pi\)
−0.979660 + 0.200662i \(0.935691\pi\)
\(164\) −88.0000 152.420i −0.0419003 0.0725734i
\(165\) 160.000 + 277.128i 0.0754908 + 0.130754i
\(166\) 564.000 976.877i 0.263704 0.456749i
\(167\) 3126.00 1.44849 0.724243 0.689545i \(-0.242189\pi\)
0.724243 + 0.689545i \(0.242189\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) −260.000 + 450.333i −0.117301 + 0.203170i
\(171\) 1150.00 + 1991.86i 0.514285 + 0.890767i
\(172\) −1768.00 3062.27i −0.783772 1.35753i
\(173\) 39.0000 67.5500i 0.0171394 0.0296863i −0.857328 0.514770i \(-0.827877\pi\)
0.874468 + 0.485083i \(0.161211\pi\)
\(174\) 400.000 0.174275
\(175\) 0 0
\(176\) −2048.00 −0.877124
\(177\) −500.000 + 866.025i −0.212329 + 0.367765i
\(178\) −300.000 519.615i −0.126326 0.218802i
\(179\) 650.000 + 1125.83i 0.271415 + 0.470105i 0.969224 0.246179i \(-0.0791751\pi\)
−0.697809 + 0.716283i \(0.745842\pi\)
\(180\) −460.000 + 796.743i −0.190480 + 0.329921i
\(181\) 1742.00 0.715369 0.357685 0.933842i \(-0.383566\pi\)
0.357685 + 0.933842i \(0.383566\pi\)
\(182\) 0 0
\(183\) −1036.00 −0.418488
\(184\) 0 0
\(185\) 665.000 + 1151.81i 0.264280 + 0.457746i
\(186\) −432.000 748.246i −0.170300 0.294968i
\(187\) −416.000 + 720.533i −0.162679 + 0.281768i
\(188\) −4112.00 −1.59520
\(189\) 0 0
\(190\) 2000.00 0.763659
\(191\) −1886.00 + 3266.65i −0.714483 + 1.23752i 0.248676 + 0.968587i \(0.420004\pi\)
−0.963159 + 0.268933i \(0.913329\pi\)
\(192\) 512.000 + 886.810i 0.192450 + 0.333333i
\(193\) 179.000 + 310.037i 0.0667601 + 0.115632i 0.897473 0.441069i \(-0.145400\pi\)
−0.830713 + 0.556700i \(0.812067\pi\)
\(194\) 772.000 1337.14i 0.285703 0.494852i
\(195\) 380.000 0.139551
\(196\) 0 0
\(197\) −2214.00 −0.800716 −0.400358 0.916359i \(-0.631114\pi\)
−0.400358 + 0.916359i \(0.631114\pi\)
\(198\) −1472.00 + 2549.58i −0.528336 + 0.915104i
\(199\) 1300.00 + 2251.67i 0.463088 + 0.802092i 0.999113 0.0421099i \(-0.0134080\pi\)
−0.536025 + 0.844202i \(0.680075\pi\)
\(200\) 0 0
\(201\) −126.000 + 218.238i −0.0442157 + 0.0765838i
\(202\) −2808.00 −0.978070
\(203\) 0 0
\(204\) 416.000 0.142774
\(205\) 55.0000 95.2628i 0.0187384 0.0324558i
\(206\) −1196.00 2071.53i −0.404511 0.700634i
\(207\) −897.000 1553.65i −0.301187 0.521672i
\(208\) −1216.00 + 2106.17i −0.405358 + 0.702100i
\(209\) 3200.00 1.05908
\(210\) 0 0
\(211\) −1168.00 −0.381083 −0.190541 0.981679i \(-0.561024\pi\)
−0.190541 + 0.981679i \(0.561024\pi\)
\(212\) −8.00000 + 13.8564i −0.00259171 + 0.00448897i
\(213\) −412.000 713.605i −0.132534 0.229556i
\(214\) −2388.00 4136.14i −0.762805 1.32122i
\(215\) 1105.00 1913.92i 0.350513 0.607107i
\(216\) 0 0
\(217\) 0 0
\(218\) 2200.00 0.683499
\(219\) 878.000 1520.74i 0.270912 0.469233i
\(220\) 640.000 + 1108.51i 0.196131 + 0.339709i
\(221\) 494.000 + 855.633i 0.150362 + 0.260435i
\(222\) 1064.00 1842.90i 0.321671 0.557151i
\(223\) −6478.00 −1.94529 −0.972643 0.232303i \(-0.925374\pi\)
−0.972643 + 0.232303i \(0.925374\pi\)
\(224\) 0 0
\(225\) −575.000 −0.170370
\(226\) 3124.00 5410.93i 0.919493 1.59261i
\(227\) −323.000 559.452i −0.0944417 0.163578i 0.814934 0.579554i \(-0.196773\pi\)
−0.909375 + 0.415976i \(0.863440\pi\)
\(228\) −800.000 1385.64i −0.232374 0.402484i
\(229\) −1875.00 + 3247.60i −0.541063 + 0.937149i 0.457780 + 0.889065i \(0.348645\pi\)
−0.998843 + 0.0480836i \(0.984689\pi\)
\(230\) −1560.00 −0.447232
\(231\) 0 0
\(232\) 0 0
\(233\) −741.000 + 1283.45i −0.208346 + 0.360865i −0.951194 0.308595i \(-0.900141\pi\)
0.742848 + 0.669460i \(0.233475\pi\)
\(234\) 1748.00 + 3027.62i 0.488335 + 0.845821i
\(235\) −1285.00 2225.69i −0.356699 0.617820i
\(236\) −2000.00 + 3464.10i −0.551648 + 0.955482i
\(237\) 1200.00 0.328896
\(238\) 0 0
\(239\) 1400.00 0.378906 0.189453 0.981890i \(-0.439329\pi\)
0.189453 + 0.981890i \(0.439329\pi\)
\(240\) −320.000 + 554.256i −0.0860663 + 0.149071i
\(241\) −1511.00 2617.13i −0.403867 0.699519i 0.590321 0.807168i \(-0.299001\pi\)
−0.994189 + 0.107649i \(0.965668\pi\)
\(242\) −614.000 1063.48i −0.163097 0.282492i
\(243\) −1771.00 + 3067.46i −0.467530 + 0.809785i
\(244\) −4144.00 −1.08726
\(245\) 0 0
\(246\) −176.000 −0.0456152
\(247\) 1900.00 3290.90i 0.489450 0.847752i
\(248\) 0 0
\(249\) −282.000 488.438i −0.0717712 0.124311i
\(250\) −250.000 + 433.013i −0.0632456 + 0.109545i
\(251\) −1248.00 −0.313837 −0.156918 0.987612i \(-0.550156\pi\)
−0.156918 + 0.987612i \(0.550156\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) 3692.00 6394.73i 0.912034 1.57969i
\(255\) 130.000 + 225.167i 0.0319252 + 0.0552960i
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) −1053.00 + 1823.85i −0.255581 + 0.442679i −0.965053 0.262054i \(-0.915600\pi\)
0.709472 + 0.704734i \(0.248933\pi\)
\(258\) −3536.00 −0.853263
\(259\) 0 0
\(260\) 1520.00 0.362563
\(261\) −575.000 + 995.929i −0.136366 + 0.236193i
\(262\) −4416.00 7648.74i −1.04130 1.80359i
\(263\) 1819.00 + 3150.60i 0.426480 + 0.738686i 0.996557 0.0829055i \(-0.0264200\pi\)
−0.570077 + 0.821591i \(0.693087\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.00231809
\(266\) 0 0
\(267\) −300.000 −0.0687629
\(268\) −504.000 + 872.954i −0.114876 + 0.198971i
\(269\) 3275.00 + 5672.47i 0.742306 + 1.28571i 0.951443 + 0.307825i \(0.0996012\pi\)
−0.209137 + 0.977886i \(0.567065\pi\)
\(270\) 1000.00 + 1732.05i 0.225400 + 0.390405i
\(271\) 2194.00 3800.12i 0.491793 0.851811i −0.508162 0.861262i \(-0.669675\pi\)
0.999955 + 0.00945040i \(0.00300820\pi\)
\(272\) −1664.00 −0.370937
\(273\) 0 0
\(274\) 9336.00 2.05842
\(275\) −400.000 + 692.820i −0.0877124 + 0.151922i
\(276\) 624.000 + 1080.80i 0.136088 + 0.235712i
\(277\) −273.000 472.850i −0.0592165 0.102566i 0.834897 0.550406i \(-0.185527\pi\)
−0.894114 + 0.447840i \(0.852194\pi\)
\(278\) −1400.00 + 2424.87i −0.302037 + 0.523144i
\(279\) 2484.00 0.533022
\(280\) 0 0
\(281\) −6858.00 −1.45592 −0.727961 0.685619i \(-0.759532\pi\)
−0.727961 + 0.685619i \(0.759532\pi\)
\(282\) −2056.00 + 3561.10i −0.434160 + 0.751987i
\(283\) −4641.00 8038.45i −0.974837 1.68847i −0.680473 0.732774i \(-0.738225\pi\)
−0.294364 0.955693i \(-0.595108\pi\)
\(284\) −1648.00 2854.42i −0.344334 0.596404i
\(285\) 500.000 866.025i 0.103921 0.179996i
\(286\) 4864.00 1.00564
\(287\) 0 0
\(288\) −5888.00 −1.20470
\(289\) 2118.50 3669.35i 0.431203 0.746865i
\(290\) 500.000 + 866.025i 0.101245 + 0.175361i
\(291\) −386.000 668.572i −0.0777585 0.134682i
\(292\) 3512.00 6082.96i 0.703850 1.21910i
\(293\) 4842.00 0.965436 0.482718 0.875776i \(-0.339650\pi\)
0.482718 + 0.875776i \(0.339650\pi\)
\(294\) 0 0
\(295\) −2500.00 −0.493409
\(296\) 0 0
\(297\) 1600.00 + 2771.28i 0.312597 + 0.541435i
\(298\) 4100.00 + 7101.41i 0.797002 + 1.38045i
\(299\) −1482.00 + 2566.90i −0.286643 + 0.496480i
\(300\) 400.000 0.0769800
\(301\) 0 0
\(302\) −7408.00 −1.41153
\(303\) −702.000 + 1215.90i −0.133099 + 0.230533i
\(304\) 3200.00 + 5542.56i 0.603726 + 1.04568i
\(305\) −1295.00 2243.01i −0.243120 0.421096i
\(306\) −1196.00 + 2071.53i −0.223434 + 0.386999i
\(307\) −2594.00 −0.482239 −0.241120 0.970495i \(-0.577515\pi\)
−0.241120 + 0.970495i \(0.577515\pi\)
\(308\) 0 0
\(309\) −1196.00 −0.220188
\(310\) 1080.00 1870.61i 0.197871 0.342722i
\(311\) −3666.00 6349.70i −0.668424 1.15774i −0.978345 0.206982i \(-0.933636\pi\)
0.309921 0.950762i \(-0.399697\pi\)
\(312\) 0 0
\(313\) −781.000 + 1352.73i −0.141037 + 0.244284i −0.927888 0.372860i \(-0.878377\pi\)
0.786850 + 0.617144i \(0.211710\pi\)
\(314\) 9976.00 1.79292
\(315\) 0 0
\(316\) 4800.00 0.854497
\(317\) −713.000 + 1234.95i −0.126328 + 0.218807i −0.922251 0.386591i \(-0.873653\pi\)
0.795923 + 0.605398i \(0.206986\pi\)
\(318\) 8.00000 + 13.8564i 0.00141075 + 0.00244349i
\(319\) 800.000 + 1385.64i 0.140412 + 0.243201i
\(320\) −1280.00 + 2217.03i −0.223607 + 0.387298i
\(321\) −2388.00 −0.415219
\(322\) 0 0
\(323\) 2600.00 0.447888
\(324\) −1684.00 + 2916.77i −0.288752 + 0.500133i
\(325\) 475.000 + 822.724i 0.0810716 + 0.140420i
\(326\) 5524.00 + 9567.85i 0.938485 + 1.62550i
\(327\) 550.000 952.628i 0.0930124 0.161102i
\(328\) 0 0
\(329\) 0 0
\(330\) 1280.00 0.213520
\(331\) 2004.00 3471.03i 0.332779 0.576390i −0.650277 0.759697i \(-0.725347\pi\)
0.983056 + 0.183308i \(0.0586804\pi\)
\(332\) −1128.00 1953.75i −0.186467 0.322970i
\(333\) 3059.00 + 5298.34i 0.503400 + 0.871914i
\(334\) 6252.00 10828.8i 1.02423 1.77403i
\(335\) −630.000 −0.102748
\(336\) 0 0
\(337\) 8866.00 1.43312 0.716561 0.697525i \(-0.245715\pi\)
0.716561 + 0.697525i \(0.245715\pi\)
\(338\) −1506.00 + 2608.47i −0.242354 + 0.419769i
\(339\) −1562.00 2705.46i −0.250254 0.433453i
\(340\) 520.000 + 900.666i 0.0829440 + 0.143663i
\(341\) 1728.00 2992.98i 0.274418 0.475305i
\(342\) 9200.00 1.45462
\(343\) 0 0
\(344\) 0 0
\(345\) −390.000 + 675.500i −0.0608606 + 0.105414i
\(346\) −156.000 270.200i −0.0242388 0.0419828i
\(347\) 857.000 + 1484.37i 0.132583 + 0.229640i 0.924671 0.380766i \(-0.124340\pi\)
−0.792089 + 0.610406i \(0.791006\pi\)
\(348\) 400.000 692.820i 0.0616157 0.106721i
\(349\) 1150.00 0.176384 0.0881921 0.996103i \(-0.471891\pi\)
0.0881921 + 0.996103i \(0.471891\pi\)
\(350\) 0 0
\(351\) 3800.00 0.577860
\(352\) −4096.00 + 7094.48i −0.620220 + 1.07425i
\(353\) 2199.00 + 3808.78i 0.331561 + 0.574280i 0.982818 0.184577i \(-0.0590915\pi\)
−0.651257 + 0.758857i \(0.725758\pi\)
\(354\) 2000.00 + 3464.10i 0.300279 + 0.520099i
\(355\) 1030.00 1784.01i 0.153991 0.266720i
\(356\) −1200.00 −0.178651
\(357\) 0 0
\(358\) 5200.00 0.767677
\(359\) −900.000 + 1558.85i −0.132312 + 0.229172i −0.924568 0.381018i \(-0.875574\pi\)
0.792255 + 0.610190i \(0.208907\pi\)
\(360\) 0 0
\(361\) −1570.50 2720.19i −0.228969 0.396586i
\(362\) 3484.00 6034.47i 0.505842 0.876145i
\(363\) −614.000 −0.0887786
\(364\) 0 0
\(365\) 4390.00 0.629543
\(366\) −2072.00 + 3588.81i −0.295916 + 0.512541i
\(367\) 2937.00 + 5087.03i 0.417739 + 0.723545i 0.995712 0.0925111i \(-0.0294894\pi\)
−0.577973 + 0.816056i \(0.696156\pi\)
\(368\) −2496.00 4323.20i −0.353568 0.612398i
\(369\) 253.000 438.209i 0.0356928 0.0618218i
\(370\) 5320.00 0.747496
\(371\) 0 0
\(372\) −1728.00 −0.240840
\(373\) 1039.00 1799.60i 0.144229 0.249812i −0.784856 0.619678i \(-0.787263\pi\)
0.929085 + 0.369866i \(0.120597\pi\)
\(374\) 1664.00 + 2882.13i 0.230063 + 0.398480i
\(375\) 125.000 + 216.506i 0.0172133 + 0.0298142i
\(376\) 0 0
\(377\) 1900.00 0.259562
\(378\) 0 0
\(379\) 7900.00 1.07070 0.535351 0.844630i \(-0.320179\pi\)
0.535351 + 0.844630i \(0.320179\pi\)
\(380\) 2000.00 3464.10i 0.269994 0.467644i
\(381\) −1846.00 3197.37i −0.248224 0.429937i
\(382\) 7544.00 + 13066.6i 1.01043 + 1.75012i
\(383\) 3759.00 6510.78i 0.501504 0.868630i −0.498495 0.866893i \(-0.666114\pi\)
0.999998 0.00173723i \(-0.000552976\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1432.00 0.188826
\(387\) 5083.00 8804.01i 0.667657 1.15642i
\(388\) −1544.00 2674.29i −0.202022 0.349913i
\(389\) 975.000 + 1688.75i 0.127081 + 0.220111i 0.922544 0.385891i \(-0.126106\pi\)
−0.795464 + 0.606001i \(0.792773\pi\)
\(390\) 760.000 1316.36i 0.0986772 0.170914i
\(391\) −2028.00 −0.262303
\(392\) 0 0
\(393\) −4416.00 −0.566814
\(394\) −4428.00 + 7669.52i −0.566191 + 0.980672i
\(395\) 1500.00 + 2598.08i 0.191071 + 0.330945i
\(396\) 2944.00 + 5099.16i 0.373590 + 0.647077i
\(397\) −6893.00 + 11939.0i −0.871410 + 1.50933i −0.0108715 + 0.999941i \(0.503461\pi\)
−0.860538 + 0.509385i \(0.829873\pi\)
\(398\) 10400.0 1.30981
\(399\) 0 0
\(400\) −1600.00 −0.200000
\(401\) −3201.00 + 5544.29i −0.398629 + 0.690446i −0.993557 0.113333i \(-0.963847\pi\)
0.594928 + 0.803779i \(0.297181\pi\)
\(402\) 504.000 + 872.954i 0.0625304 + 0.108306i
\(403\) −2052.00 3554.17i −0.253641 0.439319i
\(404\) −2808.00 + 4863.60i −0.345800 + 0.598943i
\(405\) −2105.00 −0.258267
\(406\) 0 0
\(407\) 8512.00 1.03667
\(408\) 0 0
\(409\) −5575.00 9656.18i −0.674000 1.16740i −0.976760 0.214335i \(-0.931241\pi\)
0.302760 0.953067i \(-0.402092\pi\)
\(410\) −220.000 381.051i −0.0265001 0.0458995i
\(411\) 2334.00 4042.61i 0.280116 0.485175i
\(412\) −4784.00 −0.572065
\(413\) 0 0
\(414\) −7176.00 −0.851887
\(415\) 705.000 1221.10i 0.0833906 0.144437i
\(416\) 4864.00 + 8424.70i 0.573263 + 0.992920i
\(417\) 700.000 + 1212.44i 0.0822042 + 0.142382i
\(418\) 6400.00 11085.1i 0.748886 1.29711i
\(419\) −13700.0 −1.59735 −0.798674 0.601764i \(-0.794465\pi\)
−0.798674 + 0.601764i \(0.794465\pi\)
\(420\) 0 0
\(421\) −5438.00 −0.629529 −0.314765 0.949170i \(-0.601926\pi\)
−0.314765 + 0.949170i \(0.601926\pi\)
\(422\) −2336.00 + 4046.07i −0.269466 + 0.466729i
\(423\) −5911.00 10238.2i −0.679439 1.17682i
\(424\) 0 0
\(425\) −325.000 + 562.917i −0.0370937 + 0.0642481i
\(426\) −3296.00 −0.374863
\(427\) 0 0
\(428\) −9552.00 −1.07877
\(429\) 1216.00 2106.17i 0.136851 0.237033i
\(430\) −4420.00 7655.66i −0.495701 0.858579i
\(431\) −3846.00 6661.47i −0.429827 0.744482i 0.567031 0.823697i \(-0.308092\pi\)
−0.996858 + 0.0792149i \(0.974759\pi\)
\(432\) −3200.00 + 5542.56i −0.356389 + 0.617284i
\(433\) −1118.00 −0.124082 −0.0620412 0.998074i \(-0.519761\pi\)
−0.0620412 + 0.998074i \(0.519761\pi\)
\(434\) 0 0
\(435\) 500.000 0.0551107
\(436\) 2200.00 3810.51i 0.241653 0.418556i
\(437\) 3900.00 + 6755.00i 0.426916 + 0.739440i
\(438\) −3512.00 6082.96i −0.383128 0.663596i
\(439\) 1300.00 2251.67i 0.141334 0.244798i −0.786665 0.617380i \(-0.788194\pi\)
0.927999 + 0.372582i \(0.121528\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3952.00 0.425288
\(443\) 5979.00 10355.9i 0.641243 1.11067i −0.343912 0.939002i \(-0.611752\pi\)
0.985155 0.171664i \(-0.0549145\pi\)
\(444\) −2128.00 3685.80i −0.227456 0.393965i
\(445\) −375.000 649.519i −0.0399477 0.0691914i
\(446\) −12956.0 + 22440.5i −1.37553 + 2.38248i
\(447\) 4100.00 0.433833
\(448\) 0 0
\(449\) −17050.0 −1.79207 −0.896035 0.443984i \(-0.853565\pi\)
−0.896035 + 0.443984i \(0.853565\pi\)
\(450\) −1150.00 + 1991.86i −0.120470 + 0.208660i
\(451\) −352.000 609.682i −0.0367517 0.0636559i
\(452\) −6248.00 10821.9i −0.650180 1.12614i
\(453\) −1852.00 + 3207.76i −0.192085 + 0.332701i
\(454\) −2584.00 −0.267121
\(455\) 0 0
\(456\) 0 0
\(457\) 4747.00 8222.05i 0.485898 0.841600i −0.513971 0.857808i \(-0.671826\pi\)
0.999869 + 0.0162080i \(0.00515939\pi\)
\(458\) 7500.00 + 12990.4i 0.765179 + 1.32533i
\(459\) 1300.00 + 2251.67i 0.132198 + 0.228973i
\(460\) −1560.00 + 2702.00i −0.158120 + 0.273873i
\(461\) −11418.0 −1.15356 −0.576778 0.816901i \(-0.695690\pi\)
−0.576778 + 0.816901i \(0.695690\pi\)
\(462\) 0 0
\(463\) 7962.00 0.799191 0.399596 0.916692i \(-0.369151\pi\)
0.399596 + 0.916692i \(0.369151\pi\)
\(464\) −1600.00 + 2771.28i −0.160082 + 0.277270i
\(465\) −540.000 935.307i −0.0538535 0.0932771i
\(466\) 2964.00 + 5133.80i 0.294645 + 0.510340i
\(467\) −3263.00 + 5651.68i −0.323327 + 0.560019i −0.981172 0.193134i \(-0.938135\pi\)
0.657845 + 0.753153i \(0.271468\pi\)
\(468\) 6992.00 0.690610
\(469\) 0 0
\(470\) −10280.0 −1.00890
\(471\) 2494.00 4319.73i 0.243986 0.422596i
\(472\) 0 0
\(473\) −7072.00 12249.1i −0.687465 1.19072i
\(474\) 2400.00 4156.92i 0.232565 0.402814i
\(475\) 2500.00 0.241490
\(476\) 0 0
\(477\) −46.0000 −0.00441550
\(478\) 2800.00 4849.74i 0.267927 0.464063i
\(479\) −8700.00 15068.8i −0.829881 1.43740i −0.898131 0.439728i \(-0.855075\pi\)
0.0682495 0.997668i \(-0.478259\pi\)
\(480\) 1280.00 + 2217.03i 0.121716 + 0.210819i
\(481\) 5054.00 8753.78i 0.479091 0.829809i
\(482\) −12088.0 −1.14231
\(483\) 0 0
\(484\) −2456.00 −0.230654
\(485\) 965.000 1671.43i 0.0903472 0.156486i
\(486\) 7084.00 + 12269.8i 0.661187 + 1.14521i
\(487\) −583.000 1009.79i −0.0542469 0.0939584i 0.837627 0.546243i \(-0.183942\pi\)
−0.891874 + 0.452285i \(0.850609\pi\)
\(488\) 0 0
\(489\) 5524.00 0.510846
\(490\) 0 0
\(491\) 7072.00 0.650010 0.325005 0.945712i \(-0.394634\pi\)
0.325005 + 0.945712i \(0.394634\pi\)
\(492\) −176.000 + 304.841i −0.0161274 + 0.0279335i
\(493\) 650.000 + 1125.83i 0.0593804 + 0.102850i
\(494\) −7600.00 13163.6i −0.692187 1.19890i
\(495\) −1840.00 + 3186.97i −0.167074 + 0.289381i
\(496\) 6912.00 0.625722
\(497\) 0 0
\(498\) −2256.00 −0.203000
\(499\) −50.0000 + 86.6025i −0.00448559 + 0.00776926i −0.868259 0.496110i \(-0.834761\pi\)
0.863774 + 0.503880i \(0.168094\pi\)
\(500\) 500.000 + 866.025i 0.0447214 + 0.0774597i
\(501\) −3126.00 5414.39i −0.278761 0.482829i
\(502\) −2496.00 + 4323.20i −0.221916 + 0.384370i
\(503\) 2602.00 0.230651 0.115325 0.993328i \(-0.463209\pi\)
0.115325 + 0.993328i \(0.463209\pi\)
\(504\) 0 0
\(505\) −3510.00 −0.309293
\(506\) −4992.00 + 8646.40i −0.438580 + 0.759643i
\(507\) 753.000 + 1304.23i 0.0659604 + 0.114247i
\(508\) −7384.00 12789.5i −0.644906 1.11701i
\(509\) −5575.00 + 9656.18i −0.485476 + 0.840870i −0.999861 0.0166899i \(-0.994687\pi\)
0.514384 + 0.857560i \(0.328021\pi\)
\(510\) 1040.00 0.0902980
\(511\) 0 0
\(512\) −16384.0 −1.41421
\(513\) 5000.00 8660.25i 0.430322 0.745340i
\(514\) 4212.00 + 7295.40i 0.361446 + 0.626043i
\(515\) −1495.00 2589.42i −0.127918 0.221560i
\(516\) −3536.00 + 6124.53i −0.301674 + 0.522514i
\(517\) −16448.0 −1.39919
\(518\) 0 0
\(519\) −156.000 −0.0131939
\(520\) 0 0
\(521\) 1819.00 + 3150.60i 0.152959 + 0.264933i 0.932314 0.361650i \(-0.117786\pi\)
−0.779355 + 0.626583i \(0.784453\pi\)
\(522\) 2300.00 + 3983.72i 0.192851 + 0.334028i
\(523\) 1039.00 1799.60i 0.0868686 0.150461i −0.819317 0.573340i \(-0.805647\pi\)
0.906186 + 0.422879i \(0.138981\pi\)
\(524\) −17664.0 −1.47262
\(525\) 0 0
\(526\) 14552.0 1.20627
\(527\) 1404.00 2431.80i 0.116052 0.201007i
\(528\) 2048.00 + 3547.24i 0.168803 + 0.292375i
\(529\) 3041.50 + 5268.03i 0.249979 + 0.432977i
\(530\) −20.0000 + 34.6410i −0.00163914 + 0.00283907i
\(531\) −11500.0 −0.939845
\(532\) 0 0
\(533\) −836.000 −0.0679384
\(534\) −600.000 + 1039.23i −0.0486227 + 0.0842170i
\(535\) −2985.00 5170.17i −0.241220 0.417806i
\(536\) 0 0
\(537\) 1300.00 2251.67i 0.104468 0.180943i
\(538\) 26200.0 2.09956
\(539\) 0 0
\(540\) 4000.00 0.318764
\(541\) −2811.00 + 4868.79i −0.223391 + 0.386924i −0.955835 0.293903i \(-0.905046\pi\)
0.732445 + 0.680826i \(0.238379\pi\)
\(542\) −8776.00 15200.5i −0.695501 1.20464i
\(543\) −1742.00 3017.23i −0.137673 0.238456i
\(544\) −3328.00 + 5764.27i −0.262292 + 0.454303i
\(545\) 2750.00 0.216141
\(546\) 0 0
\(547\) 16486.0 1.28865 0.644324 0.764753i \(-0.277139\pi\)
0.644324 + 0.764753i \(0.277139\pi\)
\(548\) 9336.00 16170.4i 0.727763 1.26052i
\(549\) −5957.00 10317.8i −0.463094 0.802102i
\(550\) 1600.00 + 2771.28i 0.124044 + 0.214851i
\(551\) 2500.00 4330.13i 0.193291 0.334791i
\(552\) 0 0
\(553\) 0 0
\(554\) −2184.00 −0.167490
\(555\) 1330.00 2303.63i 0.101721 0.176187i
\(556\) 2800.00 + 4849.74i 0.213573 + 0.369919i
\(557\) −5853.00 10137.7i −0.445242 0.771181i 0.552827 0.833296i \(-0.313549\pi\)
−0.998069 + 0.0621147i \(0.980216\pi\)
\(558\) 4968.00 8604.83i 0.376904 0.652816i
\(559\) −16796.0 −1.27083
\(560\) 0 0
\(561\) 1664.00 0.125230
\(562\) −13716.0 + 23756.8i −1.02949 + 1.78313i
\(563\) 12519.0 + 21683.5i 0.937146 + 1.62318i 0.770763 + 0.637123i \(0.219875\pi\)
0.166383 + 0.986061i \(0.446791\pi\)
\(564\) 4112.00 + 7122.19i 0.306997 + 0.531735i
\(565\) 3905.00 6763.66i 0.290769 0.503627i
\(566\) −37128.0 −2.75725
\(567\) 0 0
\(568\) 0 0
\(569\) −8775.00 + 15198.7i −0.646515 + 1.11980i 0.337434 + 0.941349i \(0.390441\pi\)
−0.983949 + 0.178448i \(0.942892\pi\)
\(570\) −2000.00 3464.10i −0.146966 0.254553i
\(571\) −5356.00 9276.86i −0.392542 0.679903i 0.600242 0.799819i \(-0.295071\pi\)
−0.992784 + 0.119915i \(0.961738\pi\)
\(572\) 4864.00 8424.70i 0.355549 0.615829i
\(573\) 7544.00 0.550009
\(574\) 0 0
\(575\) −1950.00 −0.141427
\(576\) −5888.00 + 10198.3i −0.425926 + 0.737725i
\(577\) 6827.00 + 11824.7i 0.492568 + 0.853153i 0.999963 0.00856059i \(-0.00272495\pi\)
−0.507395 + 0.861713i \(0.669392\pi\)
\(578\) −8474.00 14677.4i −0.609813 1.05623i
\(579\) 358.000 620.074i 0.0256960 0.0445067i
\(580\) 2000.00 0.143182
\(581\) 0 0
\(582\) −3088.00 −0.219934
\(583\) −32.0000 + 55.4256i −0.00227325 + 0.00393738i
\(584\) 0 0
\(585\) 2185.00 + 3784.53i 0.154425 + 0.267472i
\(586\) 9684.00 16773.2i 0.682666 1.18241i
\(587\) 14166.0 0.996071 0.498035 0.867157i \(-0.334055\pi\)
0.498035 + 0.867157i \(0.334055\pi\)
\(588\) 0 0
\(589\) −10800.0 −0.755528
\(590\) −5000.00 + 8660.25i −0.348893 + 0.604300i
\(591\) 2214.00 + 3834.76i 0.154098 + 0.266905i
\(592\) 8512.00 + 14743.2i 0.590948 + 1.02355i
\(593\) −8921.00 + 15451.6i −0.617777 + 1.07002i 0.372114 + 0.928187i \(0.378633\pi\)
−0.989891 + 0.141833i \(0.954700\pi\)
\(594\) 12800.0 0.884159
\(595\) 0 0
\(596\) 16400.0 1.12713
\(597\) 2600.00 4503.33i 0.178243 0.308725i
\(598\) 5928.00 + 10267.6i 0.405374 + 0.702129i
\(599\) 8800.00 + 15242.0i 0.600264 + 1.03969i 0.992781 + 0.119943i \(0.0382712\pi\)
−0.392517 + 0.919745i \(0.628395\pi\)
\(600\) 0 0
\(601\) 27302.0 1.85303 0.926516 0.376256i \(-0.122789\pi\)
0.926516 + 0.376256i \(0.122789\pi\)
\(602\) 0 0
\(603\) −2898.00 −0.195714
\(604\) −7408.00 + 12831.0i −0.499052 + 0.864383i
\(605\) −767.500 1329.35i −0.0515757 0.0893318i
\(606\) 2808.00 + 4863.60i 0.188230 + 0.326023i
\(607\) 1897.00 3285.70i 0.126848 0.219708i −0.795606 0.605815i \(-0.792847\pi\)
0.922454 + 0.386107i \(0.126181\pi\)
\(608\) 25600.0 1.70759
\(609\) 0 0
\(610\) −10360.0 −0.687646
\(611\) −9766.00 + 16915.2i −0.646629 + 1.11999i
\(612\) 2392.00 + 4143.07i 0.157992 + 0.273650i
\(613\) 6619.00 + 11464.4i 0.436116 + 0.755374i 0.997386 0.0722581i \(-0.0230205\pi\)
−0.561270 + 0.827633i \(0.689687\pi\)
\(614\) −5188.00 + 8985.88i −0.340995 + 0.590620i
\(615\) −220.000 −0.0144248
\(616\) 0 0
\(617\) −11574.0 −0.755189 −0.377595 0.925971i \(-0.623249\pi\)
−0.377595 + 0.925971i \(0.623249\pi\)
\(618\) −2392.00 + 4143.07i −0.155696 + 0.269674i
\(619\) −4150.00 7188.01i −0.269471 0.466738i 0.699254 0.714873i \(-0.253516\pi\)
−0.968725 + 0.248135i \(0.920182\pi\)
\(620\) −2160.00 3741.23i −0.139916 0.242341i
\(621\) −3900.00 + 6755.00i −0.252015 + 0.436504i
\(622\) −29328.0 −1.89059
\(623\) 0 0
\(624\) 4864.00 0.312045
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 3124.00 + 5410.93i 0.199457 + 0.345470i
\(627\) −3200.00 5542.56i −0.203821 0.353028i
\(628\) 9976.00 17278.9i 0.633894 1.09794i
\(629\) 6916.00 0.438409
\(630\) 0 0
\(631\) −7508.00 −0.473675 −0.236837 0.971549i \(-0.576111\pi\)
−0.236837 + 0.971549i \(0.576111\pi\)
\(632\) 0 0
\(633\) 1168.00 + 2023.04i 0.0733394 + 0.127028i
\(634\) 2852.00 + 4939.81i 0.178655 + 0.309440i
\(635\) 4615.00 7993.41i 0.288411 0.499542i
\(636\) 32.0000 0.00199510
\(637\) 0 0
\(638\) 6400.00 0.397145
\(639\) 4738.00 8206.46i 0.293321 0.508048i
\(640\) 0 0
\(641\) 13689.0 + 23710.0i 0.843499 + 1.46098i 0.886918 + 0.461927i \(0.152842\pi\)
−0.0434190 + 0.999057i \(0.513825\pi\)
\(642\) −4776.00 + 8272.27i −0.293604 + 0.508537i
\(643\) 1842.00 0.112973 0.0564863 0.998403i \(-0.482010\pi\)
0.0564863 + 0.998403i \(0.482010\pi\)
\(644\) 0 0
\(645\) −4420.00 −0.269825
\(646\) 5200.00 9006.66i 0.316705 0.548549i
\(647\) 5057.00 + 8758.98i 0.307282 + 0.532227i 0.977767 0.209696i \(-0.0672473\pi\)
−0.670485 + 0.741923i \(0.733914\pi\)
\(648\) 0 0
\(649\) −8000.00 + 13856.4i −0.483864 + 0.838076i
\(650\) 3800.00 0.229305
\(651\) 0 0
\(652\) 22096.0 1.32722
\(653\) −5201.00 + 9008.40i −0.311686 + 0.539856i −0.978727 0.205165i \(-0.934227\pi\)
0.667042 + 0.745020i \(0.267560\pi\)
\(654\) −2200.00 3810.51i −0.131539 0.227833i
\(655\) −5520.00 9560.92i −0.329289 0.570345i
\(656\) 704.000 1219.36i 0.0419003 0.0725734i
\(657\) 20194.0 1.19915
\(658\) 0 0
\(659\) 7100.00 0.419692 0.209846 0.977734i \(-0.432704\pi\)
0.209846 + 0.977734i \(0.432704\pi\)
\(660\) 1280.00 2217.03i 0.0754908 0.130754i
\(661\) 3559.00 + 6164.37i 0.209424 + 0.362732i 0.951533 0.307546i \(-0.0995079\pi\)
−0.742109 + 0.670279i \(0.766175\pi\)
\(662\) −8016.00 13884.1i −0.470620 0.815138i
\(663\) 988.000 1711.27i 0.0578744 0.100241i
\(664\) 0 0
\(665\) 0 0
\(666\) 24472.0 1.42383
\(667\) −1950.00 + 3377.50i −0.113200 + 0.196068i
\(668\) −12504.0 21657.6i −0.724243 1.25443i
\(669\) 6478.00 + 11220.2i 0.374371 + 0.648429i
\(670\) −1260.00 + 2182.38i −0.0726538 + 0.125840i
\(671\) −16576.0 −0.953665
\(672\) 0 0
\(673\) −31278.0 −1.79150 −0.895749 0.444560i \(-0.853360\pi\)
−0.895749 + 0.444560i \(0.853360\pi\)
\(674\) 17732.0 30712.7i 1.01337 1.75521i
\(675\) 1250.00 + 2165.06i 0.0712778 + 0.123457i
\(676\) 3012.00 + 5216.94i 0.171370 + 0.296822i
\(677\) 15027.0 26027.5i 0.853079 1.47758i −0.0253367 0.999679i \(-0.508066\pi\)
0.878416 0.477897i \(-0.158601\pi\)
\(678\) −12496.0 −0.707826
\(679\) 0 0
\(680\) 0 0
\(681\) −646.000 + 1118.90i −0.0363506 + 0.0629611i
\(682\) −6912.00 11971.9i −0.388085 0.672183i
\(683\) 2259.00 + 3912.70i 0.126557 + 0.219203i 0.922340 0.386378i \(-0.126274\pi\)
−0.795784 + 0.605581i \(0.792941\pi\)
\(684\) 9200.00 15934.9i 0.514285 0.890767i
\(685\) 11670.0 0.650931
\(686\) 0 0
\(687\) 7500.00 0.416511
\(688\) 14144.0 24498.1i 0.783772 1.35753i
\(689\) 38.0000 + 65.8179i 0.00210114 + 0.00363928i
\(690\) 1560.00 + 2702.00i 0.0860698 + 0.149077i
\(691\) −14636.0 + 25350.3i −0.805759 + 1.39562i 0.110018 + 0.993930i \(0.464909\pi\)
−0.915777 + 0.401686i \(0.868424\pi\)
\(692\) −624.000 −0.0342788
\(693\) 0 0
\(694\) 6856.00 0.375000
\(695\) −1750.00 + 3031.09i −0.0955126 + 0.165433i
\(696\) 0 0
\(697\) −286.000 495.367i −0.0155424 0.0269202i
\(698\) 2300.00 3983.72i 0.124722 0.216026i
\(699\) 2964.00 0.160385
\(700\) 0 0
\(701\) −5798.00 −0.312393 −0.156196 0.987726i \(-0.549923\pi\)
−0.156196 + 0.987726i \(0.549923\pi\)
\(702\) 7600.00 13163.6i 0.408609 0.707732i
\(703\) −13300.0 23036.3i −0.713541 1.23589i
\(704\) 8192.00 + 14189.0i 0.438562 + 0.759612i
\(705\) −2570.00 + 4451.37i −0.137293 + 0.237799i
\(706\) 17592.0 0.937796
\(707\) 0 0
\(708\) 8000.00 0.424659
\(709\) −4475.00 + 7750.93i −0.237041 + 0.410567i −0.959864 0.280466i \(-0.909511\pi\)
0.722823 + 0.691033i \(0.242844\pi\)
\(710\) −4120.00 7136.05i −0.217776 0.377199i
\(711\) 6900.00 + 11951.2i 0.363952 + 0.630384i
\(712\) 0 0
\(713\) 8424.00 0.442470
\(714\) 0 0
\(715\) 6080.00 0.318013
\(716\) 5200.00 9006.66i 0.271415 0.470105i
\(717\) −1400.00 2424.87i −0.0729204 0.126302i
\(718\) 3600.00 + 6235.38i 0.187118 + 0.324098i
\(719\) −3900.00 + 6755.00i −0.202289 + 0.350374i −0.949265 0.314476i \(-0.898171\pi\)
0.746977 + 0.664850i \(0.231505\pi\)
\(720\) −7360.00 −0.380960
\(721\) 0 0
\(722\) −12564.0 −0.647623
\(723\) −3022.00 + 5234.26i −0.155449 + 0.269245i
\(724\) −6968.00 12068.9i −0.357685 0.619528i
\(725\) 625.000 + 1082.53i 0.0320164 + 0.0554541i
\(726\) −1228.00 + 2126.96i −0.0627760 + 0.108731i
\(727\) −8554.00 −0.436383 −0.218191 0.975906i \(-0.570016\pi\)
−0.218191 + 0.975906i \(0.570016\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 8780.00 15207.4i 0.445154 0.771029i
\(731\) −5746.00 9952.36i −0.290730 0.503559i
\(732\) 4144.00 + 7177.62i 0.209244 + 0.362421i
\(733\) −1441.00 + 2495.89i −0.0726119 + 0.125768i −0.900045 0.435796i \(-0.856467\pi\)
0.827433 + 0.561564i \(0.189800\pi\)
\(734\) 23496.0 1.18154
\(735\) 0 0
\(736\) −19968.0 −1.00004
\(737\) −2016.00 + 3491.81i −0.100760 + 0.174522i
\(738\) −1012.00 1752.84i −0.0504773 0.0874292i
\(739\) −9350.00 16194.7i −0.465420 0.806131i 0.533800 0.845610i \(-0.320763\pi\)
−0.999220 + 0.0394795i \(0.987430\pi\)
\(740\) 5320.00 9214.51i 0.264280 0.457746i
\(741\) −7600.00 −0.376779
\(742\) 0 0
\(743\) 12242.0 0.604462 0.302231 0.953235i \(-0.402269\pi\)
0.302231 + 0.953235i \(0.402269\pi\)
\(744\) 0 0
\(745\) 5125.00 + 8876.76i 0.252034 + 0.436536i
\(746\) −4156.00 7198.40i −0.203970 0.353287i
\(747\) 3243.00 5617.04i 0.158842 0.275123i
\(748\) 6656.00 0.325358
\(749\) 0 0
\(750\) 1000.00 0.0486864
\(751\) 15574.0 26975.0i 0.756729 1.31069i −0.187781 0.982211i \(-0.560130\pi\)
0.944510 0.328482i \(-0.106537\pi\)
\(752\) −16448.0 28488.8i −0.797602 1.38149i
\(753\) 1248.00 + 2161.60i 0.0603979 + 0.104612i
\(754\) 3800.00 6581.79i 0.183538 0.317898i
\(755\) −9260.00 −0.446365
\(756\) 0 0
\(757\) −7694.00 −0.369410 −0.184705 0.982794i \(-0.559133\pi\)
−0.184705 + 0.982794i \(0.559133\pi\)
\(758\) 15800.0 27366.4i 0.757100 1.31134i
\(759\) 2496.00 + 4323.20i 0.119366 + 0.206749i
\(760\) 0 0
\(761\) 2259.00 3912.70i 0.107607 0.186380i −0.807194 0.590287i \(-0.799015\pi\)
0.914800 + 0.403907i \(0.132348\pi\)
\(762\) −14768.0 −0.702084
\(763\) 0 0
\(764\) 30176.0 1.42897
\(765\) −1495.00 + 2589.42i −0.0706560 + 0.122380i
\(766\) −15036.0 26043.1i −0.709233 1.22843i
\(767\) 9500.00 + 16454.5i 0.447230 + 0.774624i
\(768\) −4096.00 + 7094.48i −0.192450 + 0.333333i
\(769\) −39550.0 −1.85463 −0.927314 0.374283i \(-0.877889\pi\)
−0.927314 + 0.374283i \(0.877889\pi\)
\(770\) 0 0
\(771\) 4212.00 0.196746
\(772\) 1432.00 2480.30i 0.0667601 0.115632i
\(773\) −11061.0 19158.2i −0.514666 0.891427i −0.999855 0.0170180i \(-0.994583\pi\)
0.485190 0.874409i \(-0.338751\pi\)
\(774\) −20332.0 35216.1i −0.944210 1.63542i
\(775\) 1350.00 2338.27i 0.0625722 0.108378i
\(776\) 0 0
\(777\) 0 0
\(778\) 7800.00 0.359439
\(779\) −1100.00 + 1905.26i −0.0505925 + 0.0876289i
\(780\) −1520.00 2632.72i −0.0697753 0.120854i
\(781\) −6592.00 11417.7i −0.302023 0.523120i
\(782\) −4056.00 + 7025.20i −0.185476 + 0.321254i
\(783\) 5000.00 0.228206
\(784\) 0 0
\(785\) 12470.0 0.566972
\(786\) −8832.00 + 15297.5i −0.400798 + 0.694202i
\(787\) 8317.00 + 14405.5i 0.376708 + 0.652477i 0.990581 0.136928i \(-0.0437228\pi\)
−0.613873 + 0.789405i \(0.710389\pi\)
\(788\) 8856.00 + 15339.0i 0.400358 + 0.693440i
\(789\) 3638.00 6301.20i 0.164152 0.284320i
\(790\) 12000.0 0.540431
\(791\) 0 0
\(792\) 0 0
\(793\) −9842.00 + 17046.8i −0.440731 + 0.763368i
\(794\) 27572.0 + 47756.1i 1.23236 + 2.13451i
\(795\) 10.0000 + 17.3205i 0.000446118 + 0.000772698i
\(796\) 10400.0 18013.3i 0.463088 0.802092i
\(797\) 27586.0 1.22603 0.613015 0.790071i \(-0.289956\pi\)
0.613015 + 0.790071i \(0.289956\pi\)
\(798\) 0 0
\(799\) −13364.0 −0.591720
\(800\) −3200.00 + 5542.56i −0.141421 + 0.244949i
\(801\) −1725.00 2987.79i −0.0760922 0.131796i
\(802\) 12804.0 + 22177.2i 0.563747 + 0.976438i
\(803\) 14048.0 24331.8i 0.617364 1.06931i
\(804\) 2016.00 0.0884314
\(805\) 0 0
\(806\) −16416.0 −0.717406
\(807\) 6550.00 11344.9i 0.285714 0.494871i
\(808\) 0 0
\(809\) −1925.00 3334.20i −0.0836581 0.144900i 0.821161 0.570697i \(-0.193327\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(810\) −4210.00 + 7291.93i −0.182623 + 0.316312i
\(811\) 10032.0 0.434366 0.217183 0.976131i \(-0.430313\pi\)
0.217183 + 0.976131i \(0.430313\pi\)
\(812\) 0 0
\(813\) −8776.00 −0.378583
\(814\) 17024.0 29486.4i 0.733035 1.26965i
\(815\) 6905.00 + 11959.8i 0.296775 + 0.514029i
\(816\) 1664.00 + 2882.13i 0.0713868 + 0.123646i
\(817\) −22100.0 + 38278.3i −0.946366 + 1.63915i
\(818\) −44600.0 −1.90636
\(819\) 0 0
\(820\) −880.000 −0.0374767
\(821\) −10281.0 + 17807.2i −0.437039 + 0.756975i −0.997460 0.0712339i \(-0.977306\pi\)
0.560420 + 0.828208i \(0.310640\pi\)
\(822\) −9336.00 16170.4i −0.396144 0.686142i
\(823\) −5161.00 8939.11i −0.218592 0.378612i 0.735786 0.677214i \(-0.236813\pi\)
−0.954378 + 0.298602i \(0.903480\pi\)
\(824\) 0 0
\(825\) 1600.00 0.0675210
\(826\) 0 0
\(827\) 8846.00 0.371954 0.185977 0.982554i \(-0.440455\pi\)
0.185977 + 0.982554i \(0.440455\pi\)
\(828\) −7176.00 + 12429.2i −0.301187 + 0.521672i
\(829\) 12675.0 + 21953.7i 0.531026 + 0.919765i 0.999344 + 0.0362048i \(0.0115269\pi\)
−0.468318 + 0.883560i \(0.655140\pi\)
\(830\) −2820.00 4884.38i −0.117932 0.204264i
\(831\) −546.000 + 945.700i −0.0227925 + 0.0394777i
\(832\) 19456.0 0.810716
\(833\) 0 0
\(834\) 5600.00 0.232509
\(835\) 7815.00 13536.0i 0.323891 0.560996i
\(836\) −12800.0 22170.3i −0.529542 0.917194i
\(837\) −5400.00 9353.07i −0.223000 0.386248i
\(838\) −27400.0 + 47458.2i −1.12950 + 1.95634i
\(839\) 46000.0 1.89284 0.946422 0.322932i \(-0.104669\pi\)
0.946422 + 0.322932i \(0.104669\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) −10876.0 + 18837.8i −0.445145 + 0.771013i
\(843\) 6858.00 + 11878.4i 0.280192 + 0.485307i
\(844\) 4672.00 + 8092.14i 0.190541 + 0.330027i
\(845\) −1882.50 + 3260.59i −0.0766390 + 0.132743i
\(846\) −47288.0 −1.92174
\(847\) 0 0
\(848\) −128.000 −0.00518342
\(849\) −9282.00 + 16076.9i −0.375215 + 0.649891i
\(850\) 1300.00 + 2251.67i 0.0524584 + 0.0908606i
\(851\) 10374.0 + 17968.3i 0.417880 + 0.723790i
\(852\) −3296.00 + 5708.84i −0.132534 + 0.229556i
\(853\) −16998.0 −0.682298 −0.341149 0.940009i \(-0.610816\pi\)
−0.341149 + 0.940009i \(0.610816\pi\)
\(854\) 0 0
\(855\) 11500.0 0.459990
\(856\) 0 0
\(857\) 13247.0 + 22944.5i 0.528015 + 0.914549i 0.999467 + 0.0326569i \(0.0103969\pi\)
−0.471452 + 0.881892i \(0.656270\pi\)
\(858\) −4864.00 8424.70i −0.193536 0.335215i
\(859\) 10750.0 18619.5i 0.426991 0.739570i −0.569613 0.821913i \(-0.692907\pi\)
0.996604 + 0.0823429i \(0.0262403\pi\)
\(860\) −17680.0 −0.701027
\(861\) 0 0
\(862\) −30768.0 −1.21573
\(863\) −12881.0 + 22310.5i −0.508082 + 0.880023i 0.491875 + 0.870666i \(0.336312\pi\)
−0.999956 + 0.00935699i \(0.997022\pi\)
\(864\) 12800.0 + 22170.3i 0.504010 + 0.872971i
\(865\) −195.000 337.750i −0.00766497 0.0132761i
\(866\) −2236.00 + 3872.87i −0.0877395 + 0.151969i
\(867\) −8474.00 −0.331940
\(868\) 0 0
\(869\) 19200.0 0.749500
\(870\) 1000.00 1732.05i 0.0389692 0.0674966i
\(871\) 2394.00 + 4146.53i 0.0931316 + 0.161309i
\(872\) 0 0
\(873\) 4439.00 7688.57i 0.172093 0.298074i
\(874\) 31200.0 1.20750
\(875\) 0 0
\(876\) −14048.0 −0.541824
\(877\) −15273.0 + 26453.6i −0.588064 + 1.01856i 0.406421 + 0.913686i \(0.366777\pi\)
−0.994486 + 0.104872i \(0.966557\pi\)
\(878\) −5200.00 9006.66i −0.199876 0.346196i
\(879\) −4842.00 8386.59i −0.185798 0.321812i
\(880\) −5120.00 + 8868.10i −0.196131 + 0.339709i
\(881\) 32942.0 1.25976 0.629878 0.776694i \(-0.283105\pi\)
0.629878 + 0.776694i \(0.283105\pi\)
\(882\) 0 0
\(883\) −27118.0 −1.03351 −0.516757 0.856132i \(-0.672861\pi\)
−0.516757 + 0.856132i \(0.672861\pi\)
\(884\) 3952.00 6845.06i 0.150362 0.260435i
\(885\) 2500.00 + 4330.13i 0.0949566 + 0.164470i
\(886\) −23916.0 41423.7i −0.906855 1.57072i
\(887\) 19317.0 33458.0i 0.731230 1.26653i −0.225127 0.974329i \(-0.572280\pi\)
0.956358 0.292199i \(-0.0943869\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −3000.00 −0.112989
\(891\) −6736.00 + 11667.1i −0.253271 + 0.438678i
\(892\) 25912.0 + 44880.9i 0.972643 + 1.68467i
\(893\) 25700.0 + 44513.7i 0.963066 + 1.66808i
\(894\) 8200.00 14202.8i 0.306766 0.531335i
\(895\) 6500.00 0.242761
\(896\) 0 0
\(897\) 5928.00 0.220658
\(898\) −34100.0 + 59062.9i −1.26718 + 2.19483i
\(899\) −2700.00 4676.54i −0.100167 0.173494i
\(900\) 2300.00 + 3983.72i 0.0851852 + 0.147545i
\(901\) −26.0000 + 45.0333i −0.000961360 + 0.00166512i
\(902\) −2816.00 −0.103950
\(903\) 0 0
\(904\) 0 0
\(905\) 4355.00 7543.08i 0.159961 0.277061i
\(906\) 7408.00 + 12831.0i 0.271649 + 0.470510i
\(907\) 897.000 + 1553.65i 0.0328384 + 0.0568777i 0.881978 0.471291i \(-0.156212\pi\)
−0.849139 + 0.528169i \(0.822879\pi\)
\(908\) −2584.00 + 4475.62i −0.0944417 + 0.163578i
\(909\) −16146.0 −0.589141
\(910\) 0 0
\(911\) 41732.0 1.51772 0.758860 0.651254i \(-0.225757\pi\)
0.758860 + 0.651254i \(0.225757\pi\)
\(912\) 6400.00 11085.1i 0.232374 0.402484i
\(913\) −4512.00 7815.01i −0.163555 0.283285i
\(914\) −18988.0 32888.2i −0.687163 1.19020i
\(915\) −2590.00 + 4486.01i −0.0935768 + 0.162080i
\(916\) 30000.0 1.08213
\(917\) 0 0
\(918\) 10400.0 0.373912
\(919\) −14600.0 + 25287.9i −0.524058 + 0.907696i 0.475549 + 0.879689i \(0.342249\pi\)
−0.999608 + 0.0280066i \(0.991084\pi\)
\(920\) 0 0
\(921\) 2594.00 + 4492.94i 0.0928070 + 0.160746i
\(922\) −22836.0 + 39553.1i −0.815687 + 1.41281i
\(923\) −15656.0 −0.558314
\(924\) 0 0
\(925\) 6650.00 0.236379
\(926\) 15924.0 27581.2i 0.565114 0.978805i
\(927\) −6877.00 11911.3i −0.243657 0.422027i
\(928\) 6400.00 + 11085.1i 0.226390 + 0.392120i
\(929\) 24325.0 42132.1i 0.859071 1.48796i −0.0137443 0.999906i \(-0.504375\pi\)
0.872816 0.488050i \(-0.162292\pi\)
\(930\) −4320.00 −0.152321
\(931\) 0 0
\(932\) 11856.0 0.416691
\(933\) −7332.00 + 12699.4i −0.257276 + 0.445616i
\(934\) 13052.0 + 22606.7i 0.457253 + 0.791986i
\(935\) 2080.00 + 3602.67i 0.0727522 + 0.126010i
\(936\) 0 0
\(937\) −11334.0 −0.395161 −0.197580 0.980287i \(-0.563308\pi\)
−0.197580 + 0.980287i \(0.563308\pi\)
\(938\) 0 0
\(939\) 3124.00 0.108571
\(940\) −10280.0 + 17805.5i −0.356699 + 0.617820i
\(941\) 15589.0 + 27000.9i 0.540050 + 0.935394i 0.998901 + 0.0468803i \(0.0149279\pi\)
−0.458851 + 0.888513i \(0.651739\pi\)
\(942\) −9976.00 17278.9i −0.345048 0.597641i
\(943\) 858.000 1486.10i 0.0296292 0.0513193i
\(944\) −32000.0 −1.10330
\(945\) 0 0
\(946\) −56576.0 −1.94444
\(947\) −2343.00 + 4058.20i −0.0803984 + 0.139254i −0.903421 0.428754i \(-0.858953\pi\)
0.823023 + 0.568008i \(0.192286\pi\)
\(948\) −4800.00 8313.84i −0.164448 0.284832i
\(949\) −16682.0 28894.1i −0.570622 0.988347i
\(950\) 5000.00 8660.25i 0.170759 0.295764i
\(951\) 2852.00 0.0972476
\(952\) 0 0
\(953\) −598.000 −0.0203265 −0.0101632 0.999948i \(-0.503235\pi\)
−0.0101632 + 0.999948i \(0.503235\pi\)
\(954\) −92.0000 + 159.349i −0.00312223 + 0.00540787i
\(955\) 9430.00 + 16333.2i 0.319526 + 0.553436i
\(956\) −5600.00 9699.48i −0.189453 0.328142i
\(957\) 1600.00 2771.28i 0.0540446 0.0936079i
\(958\) −69600.0 −2.34726
\(959\) 0 0
\(960\) 5120.00 0.172133
\(961\) 9063.50 15698.4i 0.304236 0.526953i
\(962\) −20216.0 35015.1i −0.677536 1.17353i
\(963\) −13731.0 23782.8i −0.459476 0.795836i
\(964\) −12088.0 + 20937.0i −0.403867 + 0.699519i
\(965\) 1790.00 0.0597121
\(966\) 0 0
\(967\) 41726.0 1.38761 0.693804 0.720163i \(-0.255933\pi\)
0.693804 + 0.720163i \(0.255933\pi\)
\(968\) 0 0
\(969\) −2600.00 4503.33i −0.0861961 0.149296i
\(970\) −3860.00 6685.72i −0.127770 0.221305i
\(971\) −12156.0 + 21054.8i −0.401756 + 0.695861i −0.993938 0.109943i \(-0.964933\pi\)
0.592182 + 0.805804i \(0.298267\pi\)
\(972\) 28336.0 0.935059
\(973\) 0 0
\(974\) −4664.00 −0.153433
\(975\) 950.000 1645.45i 0.0312045 0.0540477i
\(976\) −16576.0 28710.5i −0.543632 0.941598i
\(977\) −20473.0 35460.3i −0.670409 1.16118i −0.977788 0.209595i \(-0.932785\pi\)
0.307380 0.951587i \(-0.400548\pi\)
\(978\) 11048.0 19135.7i 0.361223 0.625657i
\(979\) −4800.00 −0.156699
\(980\) 0 0
\(981\) 12650.0 0.411706
\(982\) 14144.0 24498.1i 0.459626 0.796096i
\(983\) −21141.0 36617.3i −0.685954 1.18811i −0.973136 0.230232i \(-0.926052\pi\)
0.287181 0.957876i \(-0.407282\pi\)
\(984\) 0 0
\(985\) −5535.00 + 9586.90i −0.179045 + 0.310116i
\(986\) 5200.00 0.167953
\(987\) 0 0
\(988\) −30400.0 −0.978900
\(989\) 17238.0 29857.1i 0.554233 0.959960i
\(990\) 7360.00 + 12747.9i 0.236279 + 0.409247i
\(991\) −586.000 1014.98i −0.0187840 0.0325348i 0.856481 0.516179i \(-0.172646\pi\)
−0.875265 + 0.483644i \(0.839313\pi\)
\(992\) 13824.0 23943.9i 0.442452 0.766349i
\(993\) −8016.00 −0.256173
\(994\) 0 0
\(995\) 13000.0 0.414199
\(996\) −2256.00 + 3907.51i −0.0717712 + 0.124311i
\(997\) 15807.0 + 27378.5i 0.502119 + 0.869696i 0.999997 + 0.00244862i \(0.000779421\pi\)
−0.497878 + 0.867247i \(0.665887\pi\)
\(998\) 200.000 + 346.410i 0.00634358 + 0.0109874i
\(999\) 13300.0 23036.3i 0.421215 0.729565i
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 245.4.e.f.226.1 2
7.2 even 3 5.4.a.a.1.1 1
7.3 odd 6 245.4.e.g.116.1 2
7.4 even 3 inner 245.4.e.f.116.1 2
7.5 odd 6 245.4.a.a.1.1 1
7.6 odd 2 245.4.e.g.226.1 2
21.2 odd 6 45.4.a.d.1.1 1
21.5 even 6 2205.4.a.q.1.1 1
28.23 odd 6 80.4.a.d.1.1 1
35.2 odd 12 25.4.b.a.24.1 2
35.9 even 6 25.4.a.c.1.1 1
35.19 odd 6 1225.4.a.k.1.1 1
35.23 odd 12 25.4.b.a.24.2 2
56.37 even 6 320.4.a.g.1.1 1
56.51 odd 6 320.4.a.h.1.1 1
63.2 odd 6 405.4.e.c.271.1 2
63.16 even 3 405.4.e.l.271.1 2
63.23 odd 6 405.4.e.c.136.1 2
63.58 even 3 405.4.e.l.136.1 2
77.65 odd 6 605.4.a.d.1.1 1
84.23 even 6 720.4.a.u.1.1 1
91.51 even 6 845.4.a.b.1.1 1
105.2 even 12 225.4.b.c.199.2 2
105.23 even 12 225.4.b.c.199.1 2
105.44 odd 6 225.4.a.b.1.1 1
112.37 even 12 1280.4.d.e.641.1 2
112.51 odd 12 1280.4.d.l.641.1 2
112.93 even 12 1280.4.d.e.641.2 2
112.107 odd 12 1280.4.d.l.641.2 2
119.16 even 6 1445.4.a.a.1.1 1
133.37 odd 6 1805.4.a.h.1.1 1
140.23 even 12 400.4.c.k.49.1 2
140.79 odd 6 400.4.a.m.1.1 1
140.107 even 12 400.4.c.k.49.2 2
280.149 even 6 1600.4.a.bi.1.1 1
280.219 odd 6 1600.4.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.4.a.a.1.1 1 7.2 even 3
25.4.a.c.1.1 1 35.9 even 6
25.4.b.a.24.1 2 35.2 odd 12
25.4.b.a.24.2 2 35.23 odd 12
45.4.a.d.1.1 1 21.2 odd 6
80.4.a.d.1.1 1 28.23 odd 6
225.4.a.b.1.1 1 105.44 odd 6
225.4.b.c.199.1 2 105.23 even 12
225.4.b.c.199.2 2 105.2 even 12
245.4.a.a.1.1 1 7.5 odd 6
245.4.e.f.116.1 2 7.4 even 3 inner
245.4.e.f.226.1 2 1.1 even 1 trivial
245.4.e.g.116.1 2 7.3 odd 6
245.4.e.g.226.1 2 7.6 odd 2
320.4.a.g.1.1 1 56.37 even 6
320.4.a.h.1.1 1 56.51 odd 6
400.4.a.m.1.1 1 140.79 odd 6
400.4.c.k.49.1 2 140.23 even 12
400.4.c.k.49.2 2 140.107 even 12
405.4.e.c.136.1 2 63.23 odd 6
405.4.e.c.271.1 2 63.2 odd 6
405.4.e.l.136.1 2 63.58 even 3
405.4.e.l.271.1 2 63.16 even 3
605.4.a.d.1.1 1 77.65 odd 6
720.4.a.u.1.1 1 84.23 even 6
845.4.a.b.1.1 1 91.51 even 6
1225.4.a.k.1.1 1 35.19 odd 6
1280.4.d.e.641.1 2 112.37 even 12
1280.4.d.e.641.2 2 112.93 even 12
1280.4.d.l.641.1 2 112.51 odd 12
1280.4.d.l.641.2 2 112.107 odd 12
1445.4.a.a.1.1 1 119.16 even 6
1600.4.a.s.1.1 1 280.219 odd 6
1600.4.a.bi.1.1 1 280.149 even 6
1805.4.a.h.1.1 1 133.37 odd 6
2205.4.a.q.1.1 1 21.5 even 6