Properties

Label 525.3.l.e.43.2
Level $525$
Weight $3$
Character 525.43
Analytic conductor $14.305$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,3,Mod(43,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.l (of order \(4\), degree \(2\), 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: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.2
Character \(\chi\) \(=\) 525.43
Dual form 525.3.l.e.232.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.41688 + 2.41688i) q^{2} +(-1.22474 - 1.22474i) q^{3} -7.68258i q^{4} +5.92011 q^{6} +(1.87083 - 1.87083i) q^{7} +(8.90034 + 8.90034i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-2.41688 + 2.41688i) q^{2} +(-1.22474 - 1.22474i) q^{3} -7.68258i q^{4} +5.92011 q^{6} +(1.87083 - 1.87083i) q^{7} +(8.90034 + 8.90034i) q^{8} +3.00000i q^{9} -20.9312 q^{11} +(-9.40920 + 9.40920i) q^{12} +(9.34319 + 9.34319i) q^{13} +9.04312i q^{14} -12.2917 q^{16} +(-7.08868 + 7.08868i) q^{17} +(-7.25063 - 7.25063i) q^{18} +14.9507i q^{19} -4.58258 q^{21} +(50.5882 - 50.5882i) q^{22} +(-12.9691 - 12.9691i) q^{23} -21.8013i q^{24} -45.1627 q^{26} +(3.67423 - 3.67423i) q^{27} +(-14.3728 - 14.3728i) q^{28} -39.6296i q^{29} +12.8776 q^{31} +(-5.89378 + 5.89378i) q^{32} +(25.6354 + 25.6354i) q^{33} -34.2649i q^{34} +23.0477 q^{36} +(31.7205 - 31.7205i) q^{37} +(-36.1341 - 36.1341i) q^{38} -22.8861i q^{39} +69.4519 q^{41} +(11.0755 - 11.0755i) q^{42} +(-4.46880 - 4.46880i) q^{43} +160.806i q^{44} +62.6895 q^{46} +(4.41044 - 4.41044i) q^{47} +(15.0542 + 15.0542i) q^{48} -7.00000i q^{49} +17.3636 q^{51} +(71.7798 - 71.7798i) q^{52} +(48.5314 + 48.5314i) q^{53} +17.7603i q^{54} +33.3020 q^{56} +(18.3108 - 18.3108i) q^{57} +(95.7797 + 95.7797i) q^{58} -29.4254i q^{59} +7.09295 q^{61} +(-31.1235 + 31.1235i) q^{62} +(5.61249 + 5.61249i) q^{63} -77.6560i q^{64} -123.915 q^{66} +(1.39800 - 1.39800i) q^{67} +(54.4593 + 54.4593i) q^{68} +31.7677i q^{69} -15.9437 q^{71} +(-26.7010 + 26.7010i) q^{72} +(-32.4160 - 32.4160i) q^{73} +153.329i q^{74} +114.860 q^{76} +(-39.1588 + 39.1588i) q^{77} +(55.3128 + 55.3128i) q^{78} +66.1155i q^{79} -9.00000 q^{81} +(-167.857 + 167.857i) q^{82} +(83.6744 + 83.6744i) q^{83} +35.2060i q^{84} +21.6011 q^{86} +(-48.5361 + 48.5361i) q^{87} +(-186.295 - 186.295i) q^{88} -62.7487i q^{89} +34.9590 q^{91} +(-99.6363 + 99.6363i) q^{92} +(-15.7717 - 15.7717i) q^{93} +21.3190i q^{94} +14.4368 q^{96} +(85.4547 - 85.4547i) q^{97} +(16.9181 + 16.9181i) q^{98} -62.7937i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41688 + 2.41688i −1.20844 + 1.20844i −0.236905 + 0.971533i \(0.576133\pi\)
−0.971533 + 0.236905i \(0.923867\pi\)
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 7.68258i 1.92065i
\(5\) 0 0
\(6\) 5.92011 0.986686
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) 8.90034 + 8.90034i 1.11254 + 1.11254i
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −20.9312 −1.90284 −0.951420 0.307897i \(-0.900375\pi\)
−0.951420 + 0.307897i \(0.900375\pi\)
\(12\) −9.40920 + 9.40920i −0.784100 + 0.784100i
\(13\) 9.34319 + 9.34319i 0.718707 + 0.718707i 0.968340 0.249633i \(-0.0803101\pi\)
−0.249633 + 0.968340i \(0.580310\pi\)
\(14\) 9.04312i 0.645937i
\(15\) 0 0
\(16\) −12.2917 −0.768233
\(17\) −7.08868 + 7.08868i −0.416981 + 0.416981i −0.884162 0.467181i \(-0.845270\pi\)
0.467181 + 0.884162i \(0.345270\pi\)
\(18\) −7.25063 7.25063i −0.402813 0.402813i
\(19\) 14.9507i 0.786881i 0.919350 + 0.393440i \(0.128715\pi\)
−0.919350 + 0.393440i \(0.871285\pi\)
\(20\) 0 0
\(21\) −4.58258 −0.218218
\(22\) 50.5882 50.5882i 2.29946 2.29946i
\(23\) −12.9691 12.9691i −0.563874 0.563874i 0.366531 0.930406i \(-0.380545\pi\)
−0.930406 + 0.366531i \(0.880545\pi\)
\(24\) 21.8013i 0.908388i
\(25\) 0 0
\(26\) −45.1627 −1.73703
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −14.3728 14.3728i −0.513314 0.513314i
\(29\) 39.6296i 1.36654i −0.730168 0.683268i \(-0.760558\pi\)
0.730168 0.683268i \(-0.239442\pi\)
\(30\) 0 0
\(31\) 12.8776 0.415405 0.207703 0.978192i \(-0.433401\pi\)
0.207703 + 0.978192i \(0.433401\pi\)
\(32\) −5.89378 + 5.89378i −0.184181 + 0.184181i
\(33\) 25.6354 + 25.6354i 0.776831 + 0.776831i
\(34\) 34.2649i 1.00779i
\(35\) 0 0
\(36\) 23.0477 0.640215
\(37\) 31.7205 31.7205i 0.857312 0.857312i −0.133709 0.991021i \(-0.542689\pi\)
0.991021 + 0.133709i \(0.0426887\pi\)
\(38\) −36.1341 36.1341i −0.950897 0.950897i
\(39\) 22.8861i 0.586822i
\(40\) 0 0
\(41\) 69.4519 1.69395 0.846974 0.531634i \(-0.178422\pi\)
0.846974 + 0.531634i \(0.178422\pi\)
\(42\) 11.0755 11.0755i 0.263703 0.263703i
\(43\) −4.46880 4.46880i −0.103926 0.103926i 0.653232 0.757158i \(-0.273413\pi\)
−0.757158 + 0.653232i \(0.773413\pi\)
\(44\) 160.806i 3.65468i
\(45\) 0 0
\(46\) 62.6895 1.36281
\(47\) 4.41044 4.41044i 0.0938392 0.0938392i −0.658629 0.752468i \(-0.728863\pi\)
0.752468 + 0.658629i \(0.228863\pi\)
\(48\) 15.0542 + 15.0542i 0.313630 + 0.313630i
\(49\) 7.00000i 0.142857i
\(50\) 0 0
\(51\) 17.3636 0.340464
\(52\) 71.7798 71.7798i 1.38038 1.38038i
\(53\) 48.5314 + 48.5314i 0.915687 + 0.915687i 0.996712 0.0810246i \(-0.0258192\pi\)
−0.0810246 + 0.996712i \(0.525819\pi\)
\(54\) 17.7603i 0.328895i
\(55\) 0 0
\(56\) 33.3020 0.594679
\(57\) 18.3108 18.3108i 0.321243 0.321243i
\(58\) 95.7797 + 95.7797i 1.65137 + 1.65137i
\(59\) 29.4254i 0.498736i −0.968409 0.249368i \(-0.919777\pi\)
0.968409 0.249368i \(-0.0802229\pi\)
\(60\) 0 0
\(61\) 7.09295 0.116278 0.0581389 0.998309i \(-0.481483\pi\)
0.0581389 + 0.998309i \(0.481483\pi\)
\(62\) −31.1235 + 31.1235i −0.501992 + 0.501992i
\(63\) 5.61249 + 5.61249i 0.0890871 + 0.0890871i
\(64\) 77.6560i 1.21338i
\(65\) 0 0
\(66\) −123.915 −1.87750
\(67\) 1.39800 1.39800i 0.0208657 0.0208657i −0.696597 0.717463i \(-0.745303\pi\)
0.717463 + 0.696597i \(0.245303\pi\)
\(68\) 54.4593 + 54.4593i 0.800873 + 0.800873i
\(69\) 31.7677i 0.460402i
\(70\) 0 0
\(71\) −15.9437 −0.224559 −0.112279 0.993677i \(-0.535815\pi\)
−0.112279 + 0.993677i \(0.535815\pi\)
\(72\) −26.7010 + 26.7010i −0.370848 + 0.370848i
\(73\) −32.4160 32.4160i −0.444055 0.444055i 0.449317 0.893372i \(-0.351667\pi\)
−0.893372 + 0.449317i \(0.851667\pi\)
\(74\) 153.329i 2.07202i
\(75\) 0 0
\(76\) 114.860 1.51132
\(77\) −39.1588 + 39.1588i −0.508555 + 0.508555i
\(78\) 55.3128 + 55.3128i 0.709138 + 0.709138i
\(79\) 66.1155i 0.836905i 0.908239 + 0.418453i \(0.137427\pi\)
−0.908239 + 0.418453i \(0.862573\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) −167.857 + 167.857i −2.04703 + 2.04703i
\(83\) 83.6744 + 83.6744i 1.00812 + 1.00812i 0.999967 + 0.00815803i \(0.00259681\pi\)
0.00815803 + 0.999967i \(0.497403\pi\)
\(84\) 35.2060i 0.419119i
\(85\) 0 0
\(86\) 21.6011 0.251175
\(87\) −48.5361 + 48.5361i −0.557886 + 0.557886i
\(88\) −186.295 186.295i −2.11699 2.11699i
\(89\) 62.7487i 0.705042i −0.935804 0.352521i \(-0.885325\pi\)
0.935804 0.352521i \(-0.114675\pi\)
\(90\) 0 0
\(91\) 34.9590 0.384165
\(92\) −99.6363 + 99.6363i −1.08300 + 1.08300i
\(93\) −15.7717 15.7717i −0.169589 0.169589i
\(94\) 21.3190i 0.226798i
\(95\) 0 0
\(96\) 14.4368 0.150383
\(97\) 85.4547 85.4547i 0.880976 0.880976i −0.112658 0.993634i \(-0.535936\pi\)
0.993634 + 0.112658i \(0.0359364\pi\)
\(98\) 16.9181 + 16.9181i 0.172634 + 0.172634i
\(99\) 62.7937i 0.634280i
\(100\) 0 0
\(101\) 145.641 1.44199 0.720997 0.692938i \(-0.243684\pi\)
0.720997 + 0.692938i \(0.243684\pi\)
\(102\) −41.9658 + 41.9658i −0.411429 + 0.411429i
\(103\) −62.2547 62.2547i −0.604414 0.604414i 0.337067 0.941481i \(-0.390565\pi\)
−0.941481 + 0.337067i \(0.890565\pi\)
\(104\) 166.315i 1.59918i
\(105\) 0 0
\(106\) −234.589 −2.21310
\(107\) 4.15809 4.15809i 0.0388607 0.0388607i −0.687409 0.726270i \(-0.741252\pi\)
0.726270 + 0.687409i \(0.241252\pi\)
\(108\) −28.2276 28.2276i −0.261367 0.261367i
\(109\) 78.6347i 0.721419i −0.932678 0.360710i \(-0.882535\pi\)
0.932678 0.360710i \(-0.117465\pi\)
\(110\) 0 0
\(111\) −77.6991 −0.699992
\(112\) −22.9957 + 22.9957i −0.205319 + 0.205319i
\(113\) 107.343 + 107.343i 0.949938 + 0.949938i 0.998805 0.0488672i \(-0.0155611\pi\)
−0.0488672 + 0.998805i \(0.515561\pi\)
\(114\) 88.5100i 0.776404i
\(115\) 0 0
\(116\) −304.457 −2.62463
\(117\) −28.0296 + 28.0296i −0.239569 + 0.239569i
\(118\) 71.1176 + 71.1176i 0.602692 + 0.602692i
\(119\) 26.5234i 0.222886i
\(120\) 0 0
\(121\) 317.117 2.62080
\(122\) −17.1428 + 17.1428i −0.140515 + 0.140515i
\(123\) −85.0608 85.0608i −0.691552 0.691552i
\(124\) 98.9329i 0.797846i
\(125\) 0 0
\(126\) −27.1294 −0.215312
\(127\) 116.651 116.651i 0.918514 0.918514i −0.0784074 0.996921i \(-0.524983\pi\)
0.996921 + 0.0784074i \(0.0249835\pi\)
\(128\) 164.110 + 164.110i 1.28211 + 1.28211i
\(129\) 10.9463i 0.0848548i
\(130\) 0 0
\(131\) 139.820 1.06733 0.533664 0.845697i \(-0.320815\pi\)
0.533664 + 0.845697i \(0.320815\pi\)
\(132\) 196.946 196.946i 1.49202 1.49202i
\(133\) 27.9703 + 27.9703i 0.210303 + 0.210303i
\(134\) 6.75760i 0.0504298i
\(135\) 0 0
\(136\) −126.183 −0.927819
\(137\) 161.119 161.119i 1.17605 1.17605i 0.195313 0.980741i \(-0.437428\pi\)
0.980741 0.195313i \(-0.0625723\pi\)
\(138\) −76.7786 76.7786i −0.556367 0.556367i
\(139\) 201.129i 1.44697i 0.690340 + 0.723485i \(0.257461\pi\)
−0.690340 + 0.723485i \(0.742539\pi\)
\(140\) 0 0
\(141\) −10.8033 −0.0766194
\(142\) 38.5339 38.5339i 0.271365 0.271365i
\(143\) −195.565 195.565i −1.36758 1.36758i
\(144\) 36.8752i 0.256078i
\(145\) 0 0
\(146\) 156.691 1.07323
\(147\) −8.57321 + 8.57321i −0.0583212 + 0.0583212i
\(148\) −243.696 243.696i −1.64659 1.64659i
\(149\) 23.2371i 0.155954i −0.996955 0.0779768i \(-0.975154\pi\)
0.996955 0.0779768i \(-0.0248460\pi\)
\(150\) 0 0
\(151\) −39.3517 −0.260607 −0.130304 0.991474i \(-0.541595\pi\)
−0.130304 + 0.991474i \(0.541595\pi\)
\(152\) −133.067 + 133.067i −0.875439 + 0.875439i
\(153\) −21.2660 21.2660i −0.138994 0.138994i
\(154\) 189.284i 1.22912i
\(155\) 0 0
\(156\) −175.824 −1.12708
\(157\) −51.1623 + 51.1623i −0.325874 + 0.325874i −0.851015 0.525141i \(-0.824013\pi\)
0.525141 + 0.851015i \(0.324013\pi\)
\(158\) −159.793 159.793i −1.01135 1.01135i
\(159\) 118.877i 0.747656i
\(160\) 0 0
\(161\) −48.5260 −0.301404
\(162\) 21.7519 21.7519i 0.134271 0.134271i
\(163\) 40.2804 + 40.2804i 0.247119 + 0.247119i 0.819787 0.572668i \(-0.194092\pi\)
−0.572668 + 0.819787i \(0.694092\pi\)
\(164\) 533.570i 3.25347i
\(165\) 0 0
\(166\) −404.461 −2.43651
\(167\) 66.9974 66.9974i 0.401182 0.401182i −0.477467 0.878649i \(-0.658445\pi\)
0.878649 + 0.477467i \(0.158445\pi\)
\(168\) −40.7865 40.7865i −0.242777 0.242777i
\(169\) 5.59045i 0.0330796i
\(170\) 0 0
\(171\) −44.8522 −0.262294
\(172\) −34.3319 + 34.3319i −0.199604 + 0.199604i
\(173\) −221.843 221.843i −1.28233 1.28233i −0.939339 0.342991i \(-0.888560\pi\)
−0.342991 0.939339i \(-0.611440\pi\)
\(174\) 234.611i 1.34834i
\(175\) 0 0
\(176\) 257.281 1.46182
\(177\) −36.0387 + 36.0387i −0.203608 + 0.203608i
\(178\) 151.656 + 151.656i 0.851999 + 0.851999i
\(179\) 129.207i 0.721827i −0.932599 0.360914i \(-0.882465\pi\)
0.932599 0.360914i \(-0.117535\pi\)
\(180\) 0 0
\(181\) 28.8400 0.159337 0.0796685 0.996821i \(-0.474614\pi\)
0.0796685 + 0.996821i \(0.474614\pi\)
\(182\) −84.4916 + 84.4916i −0.464240 + 0.464240i
\(183\) −8.68705 8.68705i −0.0474702 0.0474702i
\(184\) 230.859i 1.25467i
\(185\) 0 0
\(186\) 76.2366 0.409874
\(187\) 148.375 148.375i 0.793448 0.793448i
\(188\) −33.8836 33.8836i −0.180232 0.180232i
\(189\) 13.7477i 0.0727393i
\(190\) 0 0
\(191\) 29.9221 0.156660 0.0783302 0.996927i \(-0.475041\pi\)
0.0783302 + 0.996927i \(0.475041\pi\)
\(192\) −95.1088 + 95.1088i −0.495358 + 0.495358i
\(193\) 42.5417 + 42.5417i 0.220423 + 0.220423i 0.808677 0.588253i \(-0.200184\pi\)
−0.588253 + 0.808677i \(0.700184\pi\)
\(194\) 413.067i 2.12921i
\(195\) 0 0
\(196\) −53.7781 −0.274378
\(197\) −249.093 + 249.093i −1.26443 + 1.26443i −0.315509 + 0.948922i \(0.602175\pi\)
−0.948922 + 0.315509i \(0.897825\pi\)
\(198\) 151.765 + 151.765i 0.766488 + 0.766488i
\(199\) 16.7548i 0.0841949i −0.999114 0.0420974i \(-0.986596\pi\)
0.999114 0.0420974i \(-0.0134040\pi\)
\(200\) 0 0
\(201\) −3.42439 −0.0170368
\(202\) −351.997 + 351.997i −1.74256 + 1.74256i
\(203\) −74.1401 74.1401i −0.365222 0.365222i
\(204\) 133.398i 0.653910i
\(205\) 0 0
\(206\) 300.924 1.46079
\(207\) 38.9073 38.9073i 0.187958 0.187958i
\(208\) −114.844 114.844i −0.552135 0.552135i
\(209\) 312.937i 1.49731i
\(210\) 0 0
\(211\) 77.0276 0.365060 0.182530 0.983200i \(-0.441571\pi\)
0.182530 + 0.983200i \(0.441571\pi\)
\(212\) 372.847 372.847i 1.75871 1.75871i
\(213\) 19.5269 + 19.5269i 0.0916758 + 0.0916758i
\(214\) 20.0992i 0.0939214i
\(215\) 0 0
\(216\) 65.4039 0.302796
\(217\) 24.0917 24.0917i 0.111022 0.111022i
\(218\) 190.050 + 190.050i 0.871791 + 0.871791i
\(219\) 79.4027i 0.362570i
\(220\) 0 0
\(221\) −132.462 −0.599374
\(222\) 187.789 187.789i 0.845897 0.845897i
\(223\) 44.1625 + 44.1625i 0.198038 + 0.198038i 0.799158 0.601120i \(-0.205279\pi\)
−0.601120 + 0.799158i \(0.705279\pi\)
\(224\) 22.0525i 0.0984487i
\(225\) 0 0
\(226\) −518.869 −2.29588
\(227\) 176.500 176.500i 0.777533 0.777533i −0.201878 0.979411i \(-0.564704\pi\)
0.979411 + 0.201878i \(0.0647044\pi\)
\(228\) −140.674 140.674i −0.616993 0.616993i
\(229\) 296.743i 1.29582i −0.761716 0.647911i \(-0.775643\pi\)
0.761716 0.647911i \(-0.224357\pi\)
\(230\) 0 0
\(231\) 95.9190 0.415234
\(232\) 352.717 352.717i 1.52033 1.52033i
\(233\) 88.1651 + 88.1651i 0.378391 + 0.378391i 0.870521 0.492131i \(-0.163782\pi\)
−0.492131 + 0.870521i \(0.663782\pi\)
\(234\) 135.488i 0.579009i
\(235\) 0 0
\(236\) −226.063 −0.957895
\(237\) 80.9746 80.9746i 0.341665 0.341665i
\(238\) −64.1038 64.1038i −0.269344 0.269344i
\(239\) 370.319i 1.54945i 0.632297 + 0.774726i \(0.282112\pi\)
−0.632297 + 0.774726i \(0.717888\pi\)
\(240\) 0 0
\(241\) −202.313 −0.839471 −0.419736 0.907646i \(-0.637877\pi\)
−0.419736 + 0.907646i \(0.637877\pi\)
\(242\) −766.431 + 766.431i −3.16707 + 3.16707i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 54.4921i 0.223328i
\(245\) 0 0
\(246\) 411.163 1.67139
\(247\) −139.688 + 139.688i −0.565537 + 0.565537i
\(248\) 114.615 + 114.615i 0.462156 + 0.462156i
\(249\) 204.959i 0.823130i
\(250\) 0 0
\(251\) −358.910 −1.42992 −0.714960 0.699165i \(-0.753555\pi\)
−0.714960 + 0.699165i \(0.753555\pi\)
\(252\) 43.1184 43.1184i 0.171105 0.171105i
\(253\) 271.459 + 271.459i 1.07296 + 1.07296i
\(254\) 563.863i 2.21993i
\(255\) 0 0
\(256\) −482.642 −1.88532
\(257\) 157.946 157.946i 0.614576 0.614576i −0.329559 0.944135i \(-0.606900\pi\)
0.944135 + 0.329559i \(0.106900\pi\)
\(258\) −26.4558 26.4558i −0.102542 0.102542i
\(259\) 118.687i 0.458252i
\(260\) 0 0
\(261\) 118.889 0.455512
\(262\) −337.927 + 337.927i −1.28980 + 1.28980i
\(263\) −9.79809 9.79809i −0.0372551 0.0372551i 0.688234 0.725489i \(-0.258386\pi\)
−0.725489 + 0.688234i \(0.758386\pi\)
\(264\) 456.328i 1.72852i
\(265\) 0 0
\(266\) −135.201 −0.508276
\(267\) −76.8512 + 76.8512i −0.287832 + 0.287832i
\(268\) −10.7403 10.7403i −0.0400756 0.0400756i
\(269\) 143.504i 0.533473i 0.963770 + 0.266736i \(0.0859453\pi\)
−0.963770 + 0.266736i \(0.914055\pi\)
\(270\) 0 0
\(271\) −29.4732 −0.108757 −0.0543785 0.998520i \(-0.517318\pi\)
−0.0543785 + 0.998520i \(0.517318\pi\)
\(272\) 87.1321 87.1321i 0.320339 0.320339i
\(273\) −42.8159 42.8159i −0.156835 0.156835i
\(274\) 778.811i 2.84238i
\(275\) 0 0
\(276\) 244.058 0.884268
\(277\) −189.827 + 189.827i −0.685295 + 0.685295i −0.961188 0.275894i \(-0.911026\pi\)
0.275894 + 0.961188i \(0.411026\pi\)
\(278\) −486.103 486.103i −1.74857 1.74857i
\(279\) 38.6327i 0.138468i
\(280\) 0 0
\(281\) −61.2502 −0.217972 −0.108986 0.994043i \(-0.534760\pi\)
−0.108986 + 0.994043i \(0.534760\pi\)
\(282\) 26.1103 26.1103i 0.0925898 0.0925898i
\(283\) 176.415 + 176.415i 0.623375 + 0.623375i 0.946393 0.323018i \(-0.104697\pi\)
−0.323018 + 0.946393i \(0.604697\pi\)
\(284\) 122.489i 0.431298i
\(285\) 0 0
\(286\) 945.310 3.30528
\(287\) 129.933 129.933i 0.452727 0.452727i
\(288\) −17.6813 17.6813i −0.0613935 0.0613935i
\(289\) 188.501i 0.652254i
\(290\) 0 0
\(291\) −209.320 −0.719314
\(292\) −249.039 + 249.039i −0.852873 + 0.852873i
\(293\) 92.7415 + 92.7415i 0.316524 + 0.316524i 0.847430 0.530907i \(-0.178148\pi\)
−0.530907 + 0.847430i \(0.678148\pi\)
\(294\) 41.4408i 0.140955i
\(295\) 0 0
\(296\) 564.647 1.90759
\(297\) −76.9063 + 76.9063i −0.258944 + 0.258944i
\(298\) 56.1612 + 56.1612i 0.188460 + 0.188460i
\(299\) 242.346i 0.810521i
\(300\) 0 0
\(301\) −16.7207 −0.0555505
\(302\) 95.1081 95.1081i 0.314927 0.314927i
\(303\) −178.374 178.374i −0.588692 0.588692i
\(304\) 183.770i 0.604508i
\(305\) 0 0
\(306\) 102.795 0.335931
\(307\) 228.867 228.867i 0.745494 0.745494i −0.228135 0.973629i \(-0.573263\pi\)
0.973629 + 0.228135i \(0.0732628\pi\)
\(308\) 300.840 + 300.840i 0.976754 + 0.976754i
\(309\) 152.492i 0.493502i
\(310\) 0 0
\(311\) 291.118 0.936070 0.468035 0.883710i \(-0.344962\pi\)
0.468035 + 0.883710i \(0.344962\pi\)
\(312\) 203.694 203.694i 0.652864 0.652864i
\(313\) −251.667 251.667i −0.804049 0.804049i 0.179677 0.983726i \(-0.442495\pi\)
−0.983726 + 0.179677i \(0.942495\pi\)
\(314\) 247.306i 0.787598i
\(315\) 0 0
\(316\) 507.938 1.60740
\(317\) −30.4080 + 30.4080i −0.0959244 + 0.0959244i −0.753440 0.657516i \(-0.771607\pi\)
0.657516 + 0.753440i \(0.271607\pi\)
\(318\) 287.312 + 287.312i 0.903496 + 0.903496i
\(319\) 829.495i 2.60030i
\(320\) 0 0
\(321\) −10.1852 −0.0317296
\(322\) 117.281 117.281i 0.364228 0.364228i
\(323\) −105.981 105.981i −0.328114 0.328114i
\(324\) 69.1432i 0.213405i
\(325\) 0 0
\(326\) −194.705 −0.597255
\(327\) −96.3075 + 96.3075i −0.294518 + 0.294518i
\(328\) 618.146 + 618.146i 1.88459 + 1.88459i
\(329\) 16.5024i 0.0501592i
\(330\) 0 0
\(331\) −600.898 −1.81540 −0.907701 0.419617i \(-0.862164\pi\)
−0.907701 + 0.419617i \(0.862164\pi\)
\(332\) 642.835 642.835i 1.93625 1.93625i
\(333\) 95.1616 + 95.1616i 0.285771 + 0.285771i
\(334\) 323.849i 0.969607i
\(335\) 0 0
\(336\) 56.3278 0.167642
\(337\) 18.3744 18.3744i 0.0545235 0.0545235i −0.679319 0.733843i \(-0.737725\pi\)
0.733843 + 0.679319i \(0.237725\pi\)
\(338\) −13.5114 13.5114i −0.0399746 0.0399746i
\(339\) 262.936i 0.775621i
\(340\) 0 0
\(341\) −269.543 −0.790450
\(342\) 108.402 108.402i 0.316966 0.316966i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) 79.5477i 0.231243i
\(345\) 0 0
\(346\) 1072.33 3.09923
\(347\) −274.252 + 274.252i −0.790351 + 0.790351i −0.981551 0.191200i \(-0.938762\pi\)
0.191200 + 0.981551i \(0.438762\pi\)
\(348\) 372.882 + 372.882i 1.07150 + 1.07150i
\(349\) 218.995i 0.627494i 0.949507 + 0.313747i \(0.101584\pi\)
−0.949507 + 0.313747i \(0.898416\pi\)
\(350\) 0 0
\(351\) 68.6582 0.195607
\(352\) 123.364 123.364i 0.350466 0.350466i
\(353\) −77.0417 77.0417i −0.218248 0.218248i 0.589512 0.807760i \(-0.299320\pi\)
−0.807760 + 0.589512i \(0.799320\pi\)
\(354\) 174.202i 0.492096i
\(355\) 0 0
\(356\) −482.072 −1.35413
\(357\) 32.4844 32.4844i 0.0909927 0.0909927i
\(358\) 312.277 + 312.277i 0.872283 + 0.872283i
\(359\) 532.713i 1.48388i −0.670466 0.741940i \(-0.733906\pi\)
0.670466 0.741940i \(-0.266094\pi\)
\(360\) 0 0
\(361\) 137.476 0.380819
\(362\) −69.7027 + 69.7027i −0.192549 + 0.192549i
\(363\) −388.387 388.387i −1.06994 1.06994i
\(364\) 268.576i 0.737845i
\(365\) 0 0
\(366\) 41.9910 0.114730
\(367\) −367.459 + 367.459i −1.00125 + 1.00125i −0.00125078 + 0.999999i \(0.500398\pi\)
−0.999999 + 0.00125078i \(0.999602\pi\)
\(368\) 159.413 + 159.413i 0.433187 + 0.433187i
\(369\) 208.356i 0.564649i
\(370\) 0 0
\(371\) 181.588 0.489456
\(372\) −121.168 + 121.168i −0.325719 + 0.325719i
\(373\) −30.1723 30.1723i −0.0808908 0.0808908i 0.665504 0.746395i \(-0.268217\pi\)
−0.746395 + 0.665504i \(0.768217\pi\)
\(374\) 717.207i 1.91767i
\(375\) 0 0
\(376\) 78.5089 0.208800
\(377\) 370.267 370.267i 0.982139 0.982139i
\(378\) 33.2266 + 33.2266i 0.0879009 + 0.0879009i
\(379\) 254.898i 0.672555i −0.941763 0.336277i \(-0.890832\pi\)
0.941763 0.336277i \(-0.109168\pi\)
\(380\) 0 0
\(381\) −285.736 −0.749964
\(382\) −72.3181 + 72.3181i −0.189314 + 0.189314i
\(383\) −104.737 104.737i −0.273465 0.273465i 0.557028 0.830493i \(-0.311941\pi\)
−0.830493 + 0.557028i \(0.811941\pi\)
\(384\) 401.985i 1.04684i
\(385\) 0 0
\(386\) −205.636 −0.532736
\(387\) 13.4064 13.4064i 0.0346418 0.0346418i
\(388\) −656.512 656.512i −1.69204 1.69204i
\(389\) 667.039i 1.71475i 0.514689 + 0.857377i \(0.327908\pi\)
−0.514689 + 0.857377i \(0.672092\pi\)
\(390\) 0 0
\(391\) 183.868 0.470250
\(392\) 62.3024 62.3024i 0.158935 0.158935i
\(393\) −171.244 171.244i −0.435735 0.435735i
\(394\) 1204.05i 3.05598i
\(395\) 0 0
\(396\) −482.418 −1.21823
\(397\) 171.665 171.665i 0.432406 0.432406i −0.457040 0.889446i \(-0.651090\pi\)
0.889446 + 0.457040i \(0.151090\pi\)
\(398\) 40.4942 + 40.4942i 0.101744 + 0.101744i
\(399\) 68.5129i 0.171711i
\(400\) 0 0
\(401\) 686.098 1.71097 0.855484 0.517829i \(-0.173260\pi\)
0.855484 + 0.517829i \(0.173260\pi\)
\(402\) 8.27633 8.27633i 0.0205879 0.0205879i
\(403\) 120.318 + 120.318i 0.298555 + 0.298555i
\(404\) 1118.90i 2.76956i
\(405\) 0 0
\(406\) 358.375 0.882697
\(407\) −663.950 + 663.950i −1.63133 + 1.63133i
\(408\) 154.542 + 154.542i 0.378780 + 0.378780i
\(409\) 556.252i 1.36003i 0.733198 + 0.680015i \(0.238027\pi\)
−0.733198 + 0.680015i \(0.761973\pi\)
\(410\) 0 0
\(411\) −394.660 −0.960244
\(412\) −478.277 + 478.277i −1.16087 + 1.16087i
\(413\) −55.0499 55.0499i −0.133293 0.133293i
\(414\) 188.068i 0.454272i
\(415\) 0 0
\(416\) −110.133 −0.264744
\(417\) 246.331 246.331i 0.590723 0.590723i
\(418\) 756.331 + 756.331i 1.80940 + 1.80940i
\(419\) 143.631i 0.342794i −0.985202 0.171397i \(-0.945172\pi\)
0.985202 0.171397i \(-0.0548280\pi\)
\(420\) 0 0
\(421\) 110.369 0.262159 0.131080 0.991372i \(-0.458156\pi\)
0.131080 + 0.991372i \(0.458156\pi\)
\(422\) −186.166 + 186.166i −0.441152 + 0.441152i
\(423\) 13.2313 + 13.2313i 0.0312797 + 0.0312797i
\(424\) 863.893i 2.03748i
\(425\) 0 0
\(426\) −94.3884 −0.221569
\(427\) 13.2697 13.2697i 0.0310766 0.0310766i
\(428\) −31.9449 31.9449i −0.0746376 0.0746376i
\(429\) 479.033i 1.11663i
\(430\) 0 0
\(431\) 439.840 1.02051 0.510255 0.860023i \(-0.329551\pi\)
0.510255 + 0.860023i \(0.329551\pi\)
\(432\) −45.1627 + 45.1627i −0.104543 + 0.104543i
\(433\) 118.543 + 118.543i 0.273770 + 0.273770i 0.830616 0.556846i \(-0.187989\pi\)
−0.556846 + 0.830616i \(0.687989\pi\)
\(434\) 116.453i 0.268326i
\(435\) 0 0
\(436\) −604.118 −1.38559
\(437\) 193.898 193.898i 0.443702 0.443702i
\(438\) −191.907 191.907i −0.438143 0.438143i
\(439\) 351.519i 0.800727i −0.916356 0.400363i \(-0.868884\pi\)
0.916356 0.400363i \(-0.131116\pi\)
\(440\) 0 0
\(441\) 21.0000 0.0476190
\(442\) 320.144 320.144i 0.724307 0.724307i
\(443\) 41.1332 + 41.1332i 0.0928514 + 0.0928514i 0.752007 0.659155i \(-0.229086\pi\)
−0.659155 + 0.752007i \(0.729086\pi\)
\(444\) 596.930i 1.34444i
\(445\) 0 0
\(446\) −213.470 −0.478633
\(447\) −28.4595 + 28.4595i −0.0636678 + 0.0636678i
\(448\) −145.281 145.281i −0.324288 0.324288i
\(449\) 209.909i 0.467503i −0.972296 0.233751i \(-0.924900\pi\)
0.972296 0.233751i \(-0.0751002\pi\)
\(450\) 0 0
\(451\) −1453.71 −3.22331
\(452\) 824.671 824.671i 1.82449 1.82449i
\(453\) 48.1957 + 48.1957i 0.106392 + 0.106392i
\(454\) 853.157i 1.87920i
\(455\) 0 0
\(456\) 325.945 0.714793
\(457\) 156.842 156.842i 0.343199 0.343199i −0.514370 0.857568i \(-0.671974\pi\)
0.857568 + 0.514370i \(0.171974\pi\)
\(458\) 717.192 + 717.192i 1.56592 + 1.56592i
\(459\) 52.0909i 0.113488i
\(460\) 0 0
\(461\) 274.147 0.594680 0.297340 0.954772i \(-0.403901\pi\)
0.297340 + 0.954772i \(0.403901\pi\)
\(462\) −231.824 + 231.824i −0.501784 + 0.501784i
\(463\) −483.190 483.190i −1.04361 1.04361i −0.999005 0.0446032i \(-0.985798\pi\)
−0.0446032 0.999005i \(-0.514202\pi\)
\(464\) 487.116i 1.04982i
\(465\) 0 0
\(466\) −426.168 −0.914524
\(467\) −8.70901 + 8.70901i −0.0186489 + 0.0186489i −0.716370 0.697721i \(-0.754198\pi\)
0.697721 + 0.716370i \(0.254198\pi\)
\(468\) 215.339 + 215.339i 0.460127 + 0.460127i
\(469\) 5.23085i 0.0111532i
\(470\) 0 0
\(471\) 125.321 0.266075
\(472\) 261.896 261.896i 0.554865 0.554865i
\(473\) 93.5374 + 93.5374i 0.197754 + 0.197754i
\(474\) 391.411i 0.825762i
\(475\) 0 0
\(476\) 203.768 0.428084
\(477\) −145.594 + 145.594i −0.305229 + 0.305229i
\(478\) −895.015 895.015i −1.87242 1.87242i
\(479\) 806.280i 1.68326i −0.540056 0.841629i \(-0.681597\pi\)
0.540056 0.841629i \(-0.318403\pi\)
\(480\) 0 0
\(481\) 592.742 1.23231
\(482\) 488.965 488.965i 1.01445 1.01445i
\(483\) 59.4319 + 59.4319i 0.123047 + 0.123047i
\(484\) 2436.27i 5.03362i
\(485\) 0 0
\(486\) −53.2810 −0.109632
\(487\) 153.496 153.496i 0.315186 0.315186i −0.531729 0.846915i \(-0.678457\pi\)
0.846915 + 0.531729i \(0.178457\pi\)
\(488\) 63.1297 + 63.1297i 0.129364 + 0.129364i
\(489\) 98.6663i 0.201772i
\(490\) 0 0
\(491\) −180.954 −0.368543 −0.184271 0.982875i \(-0.558993\pi\)
−0.184271 + 0.982875i \(0.558993\pi\)
\(492\) −653.487 + 653.487i −1.32823 + 1.32823i
\(493\) 280.921 + 280.921i 0.569820 + 0.569820i
\(494\) 675.215i 1.36683i
\(495\) 0 0
\(496\) −158.288 −0.319128
\(497\) −29.8279 + 29.8279i −0.0600159 + 0.0600159i
\(498\) 495.362 + 495.362i 0.994702 + 0.994702i
\(499\) 13.9603i 0.0279765i −0.999902 0.0139883i \(-0.995547\pi\)
0.999902 0.0139883i \(-0.00445275\pi\)
\(500\) 0 0
\(501\) −164.109 −0.327564
\(502\) 867.441 867.441i 1.72797 1.72797i
\(503\) −358.510 358.510i −0.712743 0.712743i 0.254365 0.967108i \(-0.418134\pi\)
−0.967108 + 0.254365i \(0.918134\pi\)
\(504\) 99.9061i 0.198226i
\(505\) 0 0
\(506\) −1312.17 −2.59322
\(507\) 6.84688 6.84688i 0.0135047 0.0135047i
\(508\) −896.183 896.183i −1.76414 1.76414i
\(509\) 446.506i 0.877223i 0.898677 + 0.438611i \(0.144530\pi\)
−0.898677 + 0.438611i \(0.855470\pi\)
\(510\) 0 0
\(511\) −121.290 −0.237357
\(512\) 510.047 510.047i 0.996186 0.996186i
\(513\) 54.9325 + 54.9325i 0.107081 + 0.107081i
\(514\) 763.472i 1.48535i
\(515\) 0 0
\(516\) 84.0956 0.162976
\(517\) −92.3160 + 92.3160i −0.178561 + 0.178561i
\(518\) 286.853 + 286.853i 0.553770 + 0.553770i
\(519\) 543.402i 1.04702i
\(520\) 0 0
\(521\) −682.112 −1.30924 −0.654618 0.755960i \(-0.727171\pi\)
−0.654618 + 0.755960i \(0.727171\pi\)
\(522\) −287.339 + 287.339i −0.550458 + 0.550458i
\(523\) 252.224 + 252.224i 0.482263 + 0.482263i 0.905854 0.423591i \(-0.139231\pi\)
−0.423591 + 0.905854i \(0.639231\pi\)
\(524\) 1074.18i 2.04996i
\(525\) 0 0
\(526\) 47.3615 0.0900410
\(527\) −91.2849 + 91.2849i −0.173216 + 0.173216i
\(528\) −315.104 315.104i −0.596787 0.596787i
\(529\) 192.604i 0.364091i
\(530\) 0 0
\(531\) 88.2763 0.166245
\(532\) 214.884 214.884i 0.403917 0.403917i
\(533\) 648.902 + 648.902i 1.21745 + 1.21745i
\(534\) 371.479i 0.695654i
\(535\) 0 0
\(536\) 24.8854 0.0464280
\(537\) −158.246 + 158.246i −0.294685 + 0.294685i
\(538\) −346.832 346.832i −0.644669 0.644669i
\(539\) 146.519i 0.271834i
\(540\) 0 0
\(541\) 225.356 0.416554 0.208277 0.978070i \(-0.433214\pi\)
0.208277 + 0.978070i \(0.433214\pi\)
\(542\) 71.2330 71.2330i 0.131426 0.131426i
\(543\) −35.3217 35.3217i −0.0650491 0.0650491i
\(544\) 83.5582i 0.153600i
\(545\) 0 0
\(546\) 206.961 0.379050
\(547\) −211.802 + 211.802i −0.387207 + 0.387207i −0.873690 0.486483i \(-0.838280\pi\)
0.486483 + 0.873690i \(0.338280\pi\)
\(548\) −1237.81 1237.81i −2.25878 2.25878i
\(549\) 21.2788i 0.0387593i
\(550\) 0 0
\(551\) 592.491 1.07530
\(552\) −282.743 + 282.743i −0.512216 + 0.512216i
\(553\) 123.691 + 123.691i 0.223672 + 0.223672i
\(554\) 917.575i 1.65627i
\(555\) 0 0
\(556\) 1545.19 2.77912
\(557\) 74.4003 74.4003i 0.133573 0.133573i −0.637159 0.770732i \(-0.719891\pi\)
0.770732 + 0.637159i \(0.219891\pi\)
\(558\) −93.3704 93.3704i −0.167331 0.167331i
\(559\) 83.5057i 0.149384i
\(560\) 0 0
\(561\) −363.442 −0.647848
\(562\) 148.034 148.034i 0.263406 0.263406i
\(563\) 340.172 + 340.172i 0.604214 + 0.604214i 0.941428 0.337214i \(-0.109485\pi\)
−0.337214 + 0.941428i \(0.609485\pi\)
\(564\) 82.9975i 0.147159i
\(565\) 0 0
\(566\) −852.747 −1.50662
\(567\) −16.8375 + 16.8375i −0.0296957 + 0.0296957i
\(568\) −141.904 141.904i −0.249831 0.249831i
\(569\) 672.360i 1.18165i −0.806799 0.590826i \(-0.798802\pi\)
0.806799 0.590826i \(-0.201198\pi\)
\(570\) 0 0
\(571\) 613.562 1.07454 0.537269 0.843411i \(-0.319456\pi\)
0.537269 + 0.843411i \(0.319456\pi\)
\(572\) −1502.44 + 1502.44i −2.62664 + 2.62664i
\(573\) −36.6470 36.6470i −0.0639563 0.0639563i
\(574\) 628.062i 1.09418i
\(575\) 0 0
\(576\) 232.968 0.404458
\(577\) 81.3337 81.3337i 0.140960 0.140960i −0.633106 0.774065i \(-0.718220\pi\)
0.774065 + 0.633106i \(0.218220\pi\)
\(578\) −455.584 455.584i −0.788208 0.788208i
\(579\) 104.205i 0.179975i
\(580\) 0 0
\(581\) 313.081 0.538865
\(582\) 505.901 505.901i 0.869246 0.869246i
\(583\) −1015.82 1015.82i −1.74241 1.74241i
\(584\) 577.028i 0.988061i
\(585\) 0 0
\(586\) −448.289 −0.764999
\(587\) −819.321 + 819.321i −1.39578 + 1.39578i −0.584082 + 0.811694i \(0.698546\pi\)
−0.811694 + 0.584082i \(0.801454\pi\)
\(588\) 65.8644 + 65.8644i 0.112014 + 0.112014i
\(589\) 192.529i 0.326874i
\(590\) 0 0
\(591\) 610.151 1.03240
\(592\) −389.900 + 389.900i −0.658615 + 0.658615i
\(593\) 308.110 + 308.110i 0.519578 + 0.519578i 0.917444 0.397865i \(-0.130249\pi\)
−0.397865 + 0.917444i \(0.630249\pi\)
\(594\) 371.746i 0.625835i
\(595\) 0 0
\(596\) −178.521 −0.299532
\(597\) −20.5203 + 20.5203i −0.0343724 + 0.0343724i
\(598\) 585.720 + 585.720i 0.979464 + 0.979464i
\(599\) 458.753i 0.765864i −0.923776 0.382932i \(-0.874914\pi\)
0.923776 0.382932i \(-0.125086\pi\)
\(600\) 0 0
\(601\) 829.765 1.38064 0.690320 0.723504i \(-0.257470\pi\)
0.690320 + 0.723504i \(0.257470\pi\)
\(602\) 40.4119 40.4119i 0.0671294 0.0671294i
\(603\) 4.19401 + 4.19401i 0.00695524 + 0.00695524i
\(604\) 302.322i 0.500534i
\(605\) 0 0
\(606\) 862.214 1.42279
\(607\) 249.775 249.775i 0.411490 0.411490i −0.470767 0.882258i \(-0.656023\pi\)
0.882258 + 0.470767i \(0.156023\pi\)
\(608\) −88.1163 88.1163i −0.144928 0.144928i
\(609\) 181.605i 0.298203i
\(610\) 0 0
\(611\) 82.4152 0.134886
\(612\) −163.378 + 163.378i −0.266958 + 0.266958i
\(613\) −90.9769 90.9769i −0.148413 0.148413i 0.628996 0.777409i \(-0.283466\pi\)
−0.777409 + 0.628996i \(0.783466\pi\)
\(614\) 1106.29i 1.80177i
\(615\) 0 0
\(616\) −697.053 −1.13158
\(617\) 445.593 445.593i 0.722193 0.722193i −0.246858 0.969052i \(-0.579398\pi\)
0.969052 + 0.246858i \(0.0793983\pi\)
\(618\) −368.555 368.555i −0.596367 0.596367i
\(619\) 943.969i 1.52499i −0.646994 0.762495i \(-0.723974\pi\)
0.646994 0.762495i \(-0.276026\pi\)
\(620\) 0 0
\(621\) −95.3031 −0.153467
\(622\) −703.595 + 703.595i −1.13118 + 1.13118i
\(623\) −117.392 117.392i −0.188430 0.188430i
\(624\) 281.309i 0.450816i
\(625\) 0 0
\(626\) 1216.50 1.94329
\(627\) −383.268 + 383.268i −0.611273 + 0.611273i
\(628\) 393.058 + 393.058i 0.625889 + 0.625889i
\(629\) 449.713i 0.714965i
\(630\) 0 0
\(631\) −1001.49 −1.58714 −0.793570 0.608478i \(-0.791780\pi\)
−0.793570 + 0.608478i \(0.791780\pi\)
\(632\) −588.451 + 588.451i −0.931093 + 0.931093i
\(633\) −94.3392 94.3392i −0.149035 0.149035i
\(634\) 146.985i 0.231837i
\(635\) 0 0
\(636\) −913.284 −1.43598
\(637\) 65.4023 65.4023i 0.102672 0.102672i
\(638\) −2004.79 2004.79i −3.14230 3.14230i
\(639\) 47.8310i 0.0748529i
\(640\) 0 0
\(641\) −878.051 −1.36981 −0.684907 0.728630i \(-0.740157\pi\)
−0.684907 + 0.728630i \(0.740157\pi\)
\(642\) 24.6164 24.6164i 0.0383433 0.0383433i
\(643\) 551.380 + 551.380i 0.857511 + 0.857511i 0.991044 0.133533i \(-0.0426323\pi\)
−0.133533 + 0.991044i \(0.542632\pi\)
\(644\) 372.805i 0.578889i
\(645\) 0 0
\(646\) 512.286 0.793012
\(647\) −315.391 + 315.391i −0.487466 + 0.487466i −0.907506 0.420039i \(-0.862016\pi\)
0.420039 + 0.907506i \(0.362016\pi\)
\(648\) −80.1031 80.1031i −0.123616 0.123616i
\(649\) 615.911i 0.949015i
\(650\) 0 0
\(651\) −59.0124 −0.0906489
\(652\) 309.457 309.457i 0.474628 0.474628i
\(653\) 825.176 + 825.176i 1.26367 + 1.26367i 0.949301 + 0.314368i \(0.101793\pi\)
0.314368 + 0.949301i \(0.398207\pi\)
\(654\) 465.526i 0.711814i
\(655\) 0 0
\(656\) −853.684 −1.30135
\(657\) 97.2481 97.2481i 0.148018 0.148018i
\(658\) 39.8842 + 39.8842i 0.0606143 + 0.0606143i
\(659\) 956.471i 1.45140i 0.688012 + 0.725699i \(0.258483\pi\)
−0.688012 + 0.725699i \(0.741517\pi\)
\(660\) 0 0
\(661\) 18.2815 0.0276573 0.0138286 0.999904i \(-0.495598\pi\)
0.0138286 + 0.999904i \(0.495598\pi\)
\(662\) 1452.30 1452.30i 2.19380 2.19380i
\(663\) 162.232 + 162.232i 0.244694 + 0.244694i
\(664\) 1489.46i 2.24316i
\(665\) 0 0
\(666\) −459.988 −0.690672
\(667\) −513.960 + 513.960i −0.770555 + 0.770555i
\(668\) −514.713 514.713i −0.770528 0.770528i
\(669\) 108.176i 0.161697i
\(670\) 0 0
\(671\) −148.464 −0.221258
\(672\) 27.0087 27.0087i 0.0401915 0.0401915i
\(673\) 829.059 + 829.059i 1.23189 + 1.23189i 0.963239 + 0.268647i \(0.0865764\pi\)
0.268647 + 0.963239i \(0.413424\pi\)
\(674\) 88.8173i 0.131776i
\(675\) 0 0
\(676\) 42.9491 0.0635342
\(677\) 421.712 421.712i 0.622913 0.622913i −0.323362 0.946275i \(-0.604813\pi\)
0.946275 + 0.323362i \(0.104813\pi\)
\(678\) 635.483 + 635.483i 0.937290 + 0.937290i
\(679\) 319.742i 0.470901i
\(680\) 0 0
\(681\) −432.335 −0.634853
\(682\) 651.453 651.453i 0.955209 0.955209i
\(683\) 40.2821 + 40.2821i 0.0589782 + 0.0589782i 0.735981 0.677003i \(-0.236721\pi\)
−0.677003 + 0.735981i \(0.736721\pi\)
\(684\) 344.581i 0.503773i
\(685\) 0 0
\(686\) 63.3019 0.0922768
\(687\) −363.435 + 363.435i −0.529017 + 0.529017i
\(688\) 54.9293 + 54.9293i 0.0798390 + 0.0798390i
\(689\) 906.877i 1.31622i
\(690\) 0 0
\(691\) 499.429 0.722763 0.361381 0.932418i \(-0.382305\pi\)
0.361381 + 0.932418i \(0.382305\pi\)
\(692\) −1704.33 + 1704.33i −2.46290 + 2.46290i
\(693\) −117.476 117.476i −0.169518 0.169518i
\(694\) 1325.67i 1.91018i
\(695\) 0 0
\(696\) −863.976 −1.24134
\(697\) −492.322 + 492.322i −0.706344 + 0.706344i
\(698\) −529.285 529.285i −0.758287 0.758287i
\(699\) 215.959i 0.308955i
\(700\) 0 0
\(701\) 29.9935 0.0427867 0.0213934 0.999771i \(-0.493190\pi\)
0.0213934 + 0.999771i \(0.493190\pi\)
\(702\) −165.938 + 165.938i −0.236379 + 0.236379i
\(703\) 474.245 + 474.245i 0.674602 + 0.674602i
\(704\) 1625.44i 2.30886i
\(705\) 0 0
\(706\) 372.401 0.527480
\(707\) 272.470 272.470i 0.385389 0.385389i
\(708\) 276.870 + 276.870i 0.391059 + 0.391059i
\(709\) 983.508i 1.38718i 0.720372 + 0.693588i \(0.243971\pi\)
−0.720372 + 0.693588i \(0.756029\pi\)
\(710\) 0 0
\(711\) −198.347 −0.278968
\(712\) 558.485 558.485i 0.784389 0.784389i
\(713\) −167.011 167.011i −0.234236 0.234236i
\(714\) 157.022i 0.219918i
\(715\) 0 0
\(716\) −992.644 −1.38637
\(717\) 453.546 453.546i 0.632561 0.632561i
\(718\) 1287.50 + 1287.50i 1.79318 + 1.79318i
\(719\) 59.3020i 0.0824784i −0.999149 0.0412392i \(-0.986869\pi\)
0.999149 0.0412392i \(-0.0131306\pi\)
\(720\) 0 0
\(721\) −232.936 −0.323073
\(722\) −332.261 + 332.261i −0.460196 + 0.460196i
\(723\) 247.781 + 247.781i 0.342713 + 0.342713i
\(724\) 221.566i 0.306030i
\(725\) 0 0
\(726\) 1877.37 2.58590
\(727\) 25.0937 25.0937i 0.0345168 0.0345168i −0.689638 0.724155i \(-0.742230\pi\)
0.724155 + 0.689638i \(0.242230\pi\)
\(728\) 311.147 + 311.147i 0.427400 + 0.427400i
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 63.3557 0.0866699
\(732\) −66.7390 + 66.7390i −0.0911734 + 0.0911734i
\(733\) −611.839 611.839i −0.834706 0.834706i 0.153451 0.988156i \(-0.450961\pi\)
−0.988156 + 0.153451i \(0.950961\pi\)
\(734\) 1776.20i 2.41990i
\(735\) 0 0
\(736\) 152.874 0.207709
\(737\) −29.2619 + 29.2619i −0.0397041 + 0.0397041i
\(738\) −503.570 503.570i −0.682344 0.682344i
\(739\) 566.278i 0.766277i −0.923691 0.383138i \(-0.874843\pi\)
0.923691 0.383138i \(-0.125157\pi\)
\(740\) 0 0
\(741\) 342.163 0.461759
\(742\) −438.876 + 438.876i −0.591477 + 0.591477i
\(743\) −65.5539 65.5539i −0.0882287 0.0882287i 0.661615 0.749844i \(-0.269871\pi\)
−0.749844 + 0.661615i \(0.769871\pi\)
\(744\) 280.748i 0.377349i
\(745\) 0 0
\(746\) 145.845 0.195503
\(747\) −251.023 + 251.023i −0.336042 + 0.336042i
\(748\) −1139.90 1139.90i −1.52393 1.52393i
\(749\) 15.5582i 0.0207719i
\(750\) 0 0
\(751\) −99.3347 −0.132270 −0.0661350 0.997811i \(-0.521067\pi\)
−0.0661350 + 0.997811i \(0.521067\pi\)
\(752\) −54.2120 + 54.2120i −0.0720904 + 0.0720904i
\(753\) 439.573 + 439.573i 0.583763 + 0.583763i
\(754\) 1789.78i 2.37371i
\(755\) 0 0
\(756\) −105.618 −0.139706
\(757\) −605.866 + 605.866i −0.800351 + 0.800351i −0.983150 0.182799i \(-0.941484\pi\)
0.182799 + 0.983150i \(0.441484\pi\)
\(758\) 616.058 + 616.058i 0.812741 + 0.812741i
\(759\) 664.937i 0.876070i
\(760\) 0 0
\(761\) 126.096 0.165698 0.0828489 0.996562i \(-0.473598\pi\)
0.0828489 + 0.996562i \(0.473598\pi\)
\(762\) 690.589 690.589i 0.906285 0.906285i
\(763\) −147.112 147.112i −0.192807 0.192807i
\(764\) 229.879i 0.300889i
\(765\) 0 0
\(766\) 506.273 0.660931
\(767\) 274.927 274.927i 0.358445 0.358445i
\(768\) 591.114 + 591.114i 0.769679 + 0.769679i
\(769\) 115.901i 0.150716i −0.997157 0.0753582i \(-0.975990\pi\)
0.997157 0.0753582i \(-0.0240100\pi\)
\(770\) 0 0
\(771\) −386.887 −0.501799
\(772\) 326.830 326.830i 0.423355 0.423355i
\(773\) −325.618 325.618i −0.421240 0.421240i 0.464391 0.885630i \(-0.346273\pi\)
−0.885630 + 0.464391i \(0.846273\pi\)
\(774\) 64.8032i 0.0837250i
\(775\) 0 0
\(776\) 1521.15 1.96025
\(777\) −145.362 + 145.362i −0.187081 + 0.187081i
\(778\) −1612.15 1612.15i −2.07217 2.07217i
\(779\) 1038.36i 1.33294i
\(780\) 0 0
\(781\) 333.721 0.427299
\(782\) −444.385 + 444.385i −0.568268 + 0.568268i
\(783\) −145.608 145.608i −0.185962 0.185962i
\(784\) 86.0421i 0.109748i
\(785\) 0 0
\(786\) 827.750 1.05312
\(787\) 140.660 140.660i 0.178730 0.178730i −0.612072 0.790802i \(-0.709664\pi\)
0.790802 + 0.612072i \(0.209664\pi\)
\(788\) 1913.68 + 1913.68i 2.42852 + 2.42852i
\(789\) 24.0003i 0.0304187i
\(790\) 0 0
\(791\) 401.641 0.507763
\(792\) 558.886 558.886i 0.705664 0.705664i
\(793\) 66.2708 + 66.2708i 0.0835697 + 0.0835697i
\(794\) 829.788i 1.04507i
\(795\) 0 0
\(796\) −128.720 −0.161709
\(797\) 533.305 533.305i 0.669141 0.669141i −0.288376 0.957517i \(-0.593115\pi\)
0.957517 + 0.288376i \(0.0931154\pi\)
\(798\) 165.587 + 165.587i 0.207503 + 0.207503i
\(799\) 62.5284i 0.0782584i
\(800\) 0 0
\(801\) 188.246 0.235014
\(802\) −1658.21 + 1658.21i −2.06760 + 2.06760i
\(803\) 678.507 + 678.507i 0.844966 + 0.844966i
\(804\) 26.3082i 0.0327216i
\(805\) 0 0
\(806\) −581.585 −0.721570
\(807\) 175.756 175.756i 0.217789 0.217789i
\(808\) 1296.26 + 1296.26i 1.60428 + 1.60428i
\(809\) 651.161i 0.804896i −0.915443 0.402448i \(-0.868159\pi\)
0.915443 0.402448i \(-0.131841\pi\)
\(810\) 0 0
\(811\) 94.9703 0.117103 0.0585513 0.998284i \(-0.481352\pi\)
0.0585513 + 0.998284i \(0.481352\pi\)
\(812\) −569.587 + 569.587i −0.701462 + 0.701462i
\(813\) 36.0971 + 36.0971i 0.0443999 + 0.0443999i
\(814\) 3209.37i 3.94271i
\(815\) 0 0
\(816\) −213.429 −0.261555
\(817\) 66.8118 66.8118i 0.0817770 0.0817770i
\(818\) −1344.39 1344.39i −1.64351 1.64351i
\(819\) 104.877i 0.128055i
\(820\) 0 0
\(821\) −368.589 −0.448952 −0.224476 0.974480i \(-0.572067\pi\)
−0.224476 + 0.974480i \(0.572067\pi\)
\(822\) 953.845 953.845i 1.16040 1.16040i
\(823\) −494.462 494.462i −0.600804 0.600804i 0.339722 0.940526i \(-0.389667\pi\)
−0.940526 + 0.339722i \(0.889667\pi\)
\(824\) 1108.18i 1.34487i
\(825\) 0 0
\(826\) 266.098 0.322152
\(827\) 191.666 191.666i 0.231761 0.231761i −0.581666 0.813427i \(-0.697599\pi\)
0.813427 + 0.581666i \(0.197599\pi\)
\(828\) −298.909 298.909i −0.361001 0.361001i
\(829\) 110.729i 0.133569i −0.997767 0.0667847i \(-0.978726\pi\)
0.997767 0.0667847i \(-0.0212741\pi\)
\(830\) 0 0
\(831\) 464.978 0.559541
\(832\) 725.555 725.555i 0.872061 0.872061i
\(833\) 49.6207 + 49.6207i 0.0595687 + 0.0595687i
\(834\) 1190.71i 1.42770i
\(835\) 0 0
\(836\) −2404.17 −2.87580
\(837\) 47.3152 47.3152i 0.0565295 0.0565295i
\(838\) 347.137 + 347.137i 0.414245 + 0.414245i
\(839\) 184.793i 0.220254i −0.993918 0.110127i \(-0.964874\pi\)
0.993918 0.110127i \(-0.0351258\pi\)
\(840\) 0 0
\(841\) −729.502 −0.867422
\(842\) −266.748 + 266.748i −0.316803 + 0.316803i
\(843\) 75.0159 + 75.0159i 0.0889869 + 0.0889869i
\(844\) 591.771i 0.701150i
\(845\) 0 0
\(846\) −63.9570 −0.0755993
\(847\) 593.271 593.271i 0.700438 0.700438i
\(848\) −596.535 596.535i −0.703462 0.703462i
\(849\) 432.127i 0.508984i
\(850\) 0 0
\(851\) −822.774 −0.966832
\(852\) 150.017 150.017i 0.176077 0.176077i
\(853\) −3.11065 3.11065i −0.00364672 0.00364672i 0.705281 0.708928i \(-0.250821\pi\)
−0.708928 + 0.705281i \(0.750821\pi\)
\(854\) 64.1424i 0.0751082i
\(855\) 0 0
\(856\) 74.0169 0.0864683
\(857\) −141.310 + 141.310i −0.164889 + 0.164889i −0.784729 0.619840i \(-0.787198\pi\)
0.619840 + 0.784729i \(0.287198\pi\)
\(858\) −1157.76 1157.76i −1.34938 1.34938i
\(859\) 1054.78i 1.22792i −0.789338 0.613959i \(-0.789576\pi\)
0.789338 0.613959i \(-0.210424\pi\)
\(860\) 0 0
\(861\) −318.269 −0.369650
\(862\) −1063.04 + 1063.04i −1.23322 + 1.23322i
\(863\) 227.600 + 227.600i 0.263732 + 0.263732i 0.826568 0.562837i \(-0.190290\pi\)
−0.562837 + 0.826568i \(0.690290\pi\)
\(864\) 43.3103i 0.0501276i
\(865\) 0 0
\(866\) −573.005 −0.661669
\(867\) 230.866 230.866i 0.266281 0.266281i
\(868\) −185.087 185.087i −0.213233 0.213233i
\(869\) 1383.88i 1.59250i
\(870\) 0 0
\(871\) 26.1236 0.0299927
\(872\) 699.876 699.876i 0.802610 0.802610i
\(873\) 256.364 + 256.364i 0.293659 + 0.293659i
\(874\) 937.254i 1.07237i
\(875\) 0 0
\(876\) 610.018 0.696368
\(877\) 71.4976 71.4976i 0.0815252 0.0815252i −0.665168 0.746693i \(-0.731640\pi\)
0.746693 + 0.665168i \(0.231640\pi\)
\(878\) 849.578 + 849.578i 0.967629 + 0.967629i
\(879\) 227.169i 0.258441i
\(880\) 0 0
\(881\) 932.073 1.05797 0.528986 0.848631i \(-0.322572\pi\)
0.528986 + 0.848631i \(0.322572\pi\)
\(882\) −50.7544 + 50.7544i −0.0575447 + 0.0575447i
\(883\) 616.640 + 616.640i 0.698346 + 0.698346i 0.964054 0.265708i \(-0.0856056\pi\)
−0.265708 + 0.964054i \(0.585606\pi\)
\(884\) 1017.65i 1.15119i
\(885\) 0 0
\(886\) −198.828 −0.224410
\(887\) 990.320 990.320i 1.11648 1.11648i 0.124229 0.992254i \(-0.460354\pi\)
0.992254 0.124229i \(-0.0396459\pi\)
\(888\) −691.549 691.549i −0.778771 0.778771i
\(889\) 436.469i 0.490966i
\(890\) 0 0
\(891\) 188.381 0.211427
\(892\) 339.282 339.282i 0.380361 0.380361i
\(893\) 65.9394 + 65.9394i 0.0738403 + 0.0738403i
\(894\) 137.566i 0.153877i
\(895\) 0 0
\(896\) 614.043 0.685316
\(897\) −296.812 + 296.812i −0.330894 + 0.330894i
\(898\) 507.323 + 507.323i 0.564948 + 0.564948i
\(899\) 510.332i 0.567666i
\(900\) 0 0
\(901\) −688.047 −0.763649
\(902\) 3513.45 3513.45i 3.89517 3.89517i
\(903\) 20.4786 + 20.4786i 0.0226784 + 0.0226784i
\(904\) 1910.78i 2.11369i
\(905\) 0 0
\(906\) −232.966 −0.257137
\(907\) 449.584 449.584i 0.495682 0.495682i −0.414409 0.910091i \(-0.636012\pi\)
0.910091 + 0.414409i \(0.136012\pi\)
\(908\) −1355.98 1355.98i −1.49336 1.49336i
\(909\) 436.924i 0.480665i
\(910\) 0 0
\(911\) 1065.29 1.16936 0.584680 0.811264i \(-0.301220\pi\)
0.584680 + 0.811264i \(0.301220\pi\)
\(912\) −225.072 + 225.072i −0.246789 + 0.246789i
\(913\) −1751.41 1751.41i −1.91830 1.91830i
\(914\) 758.134i 0.829468i
\(915\) 0 0
\(916\) −2279.75 −2.48881
\(917\) 261.579 261.579i 0.285255 0.285255i
\(918\) −125.897 125.897i −0.137143 0.137143i
\(919\) 1080.05i 1.17525i −0.809135 0.587623i \(-0.800064\pi\)
0.809135 0.587623i \(-0.199936\pi\)
\(920\) 0 0
\(921\) −560.607 −0.608694
\(922\) −662.580 + 662.580i −0.718634 + 0.718634i
\(923\) −148.965 148.965i −0.161392 0.161392i
\(924\) 736.905i 0.797516i
\(925\) 0 0
\(926\) 2335.62 2.52227
\(927\) 186.764 186.764i 0.201471 0.201471i
\(928\) 233.568 + 233.568i 0.251690 + 0.251690i
\(929\) 1513.19i 1.62884i −0.580278 0.814419i \(-0.697056\pi\)
0.580278 0.814419i \(-0.302944\pi\)
\(930\) 0 0
\(931\) 104.655 0.112412
\(932\) 677.335 677.335i 0.726755 0.726755i
\(933\) −356.545 356.545i −0.382149 0.382149i
\(934\) 42.0972i 0.0450720i
\(935\) 0 0
\(936\) −498.946 −0.533062
\(937\) −754.545 + 754.545i −0.805278 + 0.805278i −0.983915 0.178637i \(-0.942831\pi\)
0.178637 + 0.983915i \(0.442831\pi\)
\(938\) 12.6423 + 12.6423i 0.0134779 + 0.0134779i
\(939\) 616.457i 0.656503i
\(940\) 0 0
\(941\) 1377.61 1.46399 0.731993 0.681312i \(-0.238590\pi\)
0.731993 + 0.681312i \(0.238590\pi\)
\(942\) −302.886 + 302.886i −0.321535 + 0.321535i
\(943\) −900.729 900.729i −0.955174 0.955174i
\(944\) 361.690i 0.383146i
\(945\) 0 0
\(946\) −452.137 −0.477946
\(947\) −133.593 + 133.593i −0.141070 + 0.141070i −0.774115 0.633045i \(-0.781805\pi\)
0.633045 + 0.774115i \(0.281805\pi\)
\(948\) −622.094 622.094i −0.656217 0.656217i
\(949\) 605.738i 0.638291i
\(950\) 0 0
\(951\) 74.4842 0.0783219
\(952\) −236.067 + 236.067i −0.247970 + 0.247970i
\(953\) 498.927 + 498.927i 0.523533 + 0.523533i 0.918636 0.395104i \(-0.129291\pi\)
−0.395104 + 0.918636i \(0.629291\pi\)
\(954\) 703.767i 0.737701i
\(955\) 0 0
\(956\) 2845.01 2.97595
\(957\) 1015.92 1015.92i 1.06157 1.06157i
\(958\) 1948.68 + 1948.68i 2.03411 + 2.03411i
\(959\) 602.854i 0.628627i
\(960\) 0 0
\(961\) −795.168 −0.827438
\(962\) −1432.58 + 1432.58i −1.48917 + 1.48917i
\(963\) 12.4743 + 12.4743i 0.0129536 + 0.0129536i
\(964\) 1554.28i 1.61233i
\(965\) 0 0
\(966\) −287.279 −0.297391
\(967\) −506.991 + 506.991i −0.524293 + 0.524293i −0.918865 0.394572i \(-0.870893\pi\)
0.394572 + 0.918865i \(0.370893\pi\)
\(968\) 2822.45 + 2822.45i 2.91575 + 2.91575i
\(969\) 259.599i 0.267904i
\(970\) 0 0
\(971\) −74.6256 −0.0768543 −0.0384272 0.999261i \(-0.512235\pi\)
−0.0384272 + 0.999261i \(0.512235\pi\)
\(972\) 84.6828 84.6828i 0.0871222 0.0871222i
\(973\) 376.277 + 376.277i 0.386719 + 0.386719i
\(974\) 741.960i 0.761766i
\(975\) 0 0
\(976\) −87.1846 −0.0893285
\(977\) 291.427 291.427i 0.298288 0.298288i −0.542055 0.840343i \(-0.682354\pi\)
0.840343 + 0.542055i \(0.182354\pi\)
\(978\) 238.464 + 238.464i 0.243829 + 0.243829i
\(979\) 1313.41i 1.34158i
\(980\) 0 0
\(981\) 235.904 0.240473
\(982\) 437.345 437.345i 0.445361 0.445361i
\(983\) 932.709 + 932.709i 0.948839 + 0.948839i 0.998754 0.0499141i \(-0.0158948\pi\)
−0.0499141 + 0.998754i \(0.515895\pi\)
\(984\) 1514.14i 1.53876i
\(985\) 0 0
\(986\) −1357.90 −1.37718
\(987\) −20.2112 + 20.2112i −0.0204774 + 0.0204774i
\(988\) 1073.16 + 1073.16i 1.08620 + 1.08620i
\(989\) 115.913i 0.117202i
\(990\) 0 0
\(991\) 294.340 0.297013 0.148507 0.988911i \(-0.452553\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(992\) −75.8975 + 75.8975i −0.0765096 + 0.0765096i
\(993\) 735.947 + 735.947i 0.741135 + 0.741135i
\(994\) 144.181i 0.145051i
\(995\) 0 0
\(996\) −1574.62 −1.58094
\(997\) −678.292 + 678.292i −0.680333 + 0.680333i −0.960075 0.279742i \(-0.909751\pi\)
0.279742 + 0.960075i \(0.409751\pi\)
\(998\) 33.7403 + 33.7403i 0.0338079 + 0.0338079i
\(999\) 233.097i 0.233331i
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 525.3.l.e.43.2 24
5.2 odd 4 inner 525.3.l.e.232.2 24
5.3 odd 4 105.3.l.a.22.11 24
5.4 even 2 105.3.l.a.43.11 yes 24
15.8 even 4 315.3.o.b.127.2 24
15.14 odd 2 315.3.o.b.253.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.l.a.22.11 24 5.3 odd 4
105.3.l.a.43.11 yes 24 5.4 even 2
315.3.o.b.127.2 24 15.8 even 4
315.3.o.b.253.2 24 15.14 odd 2
525.3.l.e.43.2 24 1.1 even 1 trivial
525.3.l.e.232.2 24 5.2 odd 4 inner