Properties

Label 315.3.ca.b.37.15
Level $315$
Weight $3$
Character 315.37
Analytic conductor $8.583$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,3,Mod(37,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.15
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.18498 - 0.853412i) q^{2} +(5.95167 - 3.43620i) q^{4} +(4.91224 - 0.932701i) q^{5} +(5.00478 + 4.89410i) q^{7} +(6.69718 - 6.69718i) q^{8} +O(q^{10})\) \(q+(3.18498 - 0.853412i) q^{2} +(5.95167 - 3.43620i) q^{4} +(4.91224 - 0.932701i) q^{5} +(5.00478 + 4.89410i) q^{7} +(6.69718 - 6.69718i) q^{8} +(14.8494 - 7.16279i) q^{10} +(0.581984 + 1.00803i) q^{11} +(-14.6930 + 14.6930i) q^{13} +(20.1168 + 11.3165i) q^{14} +(1.87012 - 3.23914i) q^{16} +(6.97229 - 26.0209i) q^{17} +(-24.9464 - 14.4028i) q^{19} +(26.0311 - 22.4305i) q^{20} +(2.71387 + 2.71387i) q^{22} +(-3.19577 - 11.9268i) q^{23} +(23.2601 - 9.16329i) q^{25} +(-34.2576 + 59.3359i) q^{26} +(46.6039 + 11.9307i) q^{28} -12.5542i q^{29} +(8.24013 + 14.2723i) q^{31} +(-6.61339 + 24.6815i) q^{32} -88.8263i q^{34} +(29.1494 + 19.3730i) q^{35} +(13.6641 - 3.66129i) q^{37} +(-91.7452 - 24.5830i) q^{38} +(26.6517 - 39.1446i) q^{40} -48.3009 q^{41} +(-0.357576 + 0.357576i) q^{43} +(6.92755 + 3.99962i) q^{44} +(-20.3569 - 35.2592i) q^{46} +(-27.3656 + 7.33258i) q^{47} +(1.09559 + 48.9878i) q^{49} +(66.2630 - 49.0354i) q^{50} +(-36.9597 + 137.936i) q^{52} +(45.5418 + 12.2029i) q^{53} +(3.79903 + 4.40884i) q^{55} +(66.2945 - 0.741234i) q^{56} +(-10.7139 - 39.9849i) q^{58} +(-49.5210 + 28.5910i) q^{59} +(6.30786 - 10.9255i) q^{61} +(38.4248 + 38.4248i) q^{62} +99.2149i q^{64} +(-58.4712 + 85.8794i) q^{65} +(12.0537 - 44.9851i) q^{67} +(-47.9163 - 178.826i) q^{68} +(109.373 + 36.8262i) q^{70} -19.0442 q^{71} +(-118.629 - 31.7865i) q^{73} +(40.3953 - 23.3222i) q^{74} -197.963 q^{76} +(-2.02068 + 7.89323i) q^{77} +(74.1583 + 42.8153i) q^{79} +(6.16532 - 17.6557i) q^{80} +(-153.837 + 41.2206i) q^{82} +(-18.0900 + 18.0900i) q^{83} +(9.97979 - 134.324i) q^{85} +(-0.833713 + 1.44403i) q^{86} +(10.6486 + 2.85328i) q^{88} +(78.1616 + 45.1266i) q^{89} +(-145.444 + 1.62620i) q^{91} +(-60.0029 - 60.0029i) q^{92} +(-80.9010 + 46.7082i) q^{94} +(-135.976 - 47.4824i) q^{95} +(84.2362 + 84.2362i) q^{97} +(45.2962 + 155.090i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.18498 0.853412i 1.59249 0.426706i 0.649726 0.760169i \(-0.274884\pi\)
0.942763 + 0.333463i \(0.108217\pi\)
\(3\) 0 0
\(4\) 5.95167 3.43620i 1.48792 0.859049i
\(5\) 4.91224 0.932701i 0.982447 0.186540i
\(6\) 0 0
\(7\) 5.00478 + 4.89410i 0.714968 + 0.699157i
\(8\) 6.69718 6.69718i 0.837147 0.837147i
\(9\) 0 0
\(10\) 14.8494 7.16279i 1.48494 0.716279i
\(11\) 0.581984 + 1.00803i 0.0529076 + 0.0916387i 0.891266 0.453480i \(-0.149818\pi\)
−0.838359 + 0.545119i \(0.816484\pi\)
\(12\) 0 0
\(13\) −14.6930 + 14.6930i −1.13023 + 1.13023i −0.140089 + 0.990139i \(0.544739\pi\)
−0.990139 + 0.140089i \(0.955261\pi\)
\(14\) 20.1168 + 11.3165i 1.43691 + 0.808318i
\(15\) 0 0
\(16\) 1.87012 3.23914i 0.116882 0.202446i
\(17\) 6.97229 26.0209i 0.410135 1.53064i −0.384251 0.923229i \(-0.625540\pi\)
0.794385 0.607414i \(-0.207793\pi\)
\(18\) 0 0
\(19\) −24.9464 14.4028i −1.31297 0.758042i −0.330381 0.943848i \(-0.607177\pi\)
−0.982586 + 0.185806i \(0.940510\pi\)
\(20\) 26.0311 22.4305i 1.30155 1.12153i
\(21\) 0 0
\(22\) 2.71387 + 2.71387i 0.123358 + 0.123358i
\(23\) −3.19577 11.9268i −0.138946 0.518555i −0.999950 0.00995696i \(-0.996831\pi\)
0.861004 0.508598i \(-0.169836\pi\)
\(24\) 0 0
\(25\) 23.2601 9.16329i 0.930406 0.366532i
\(26\) −34.2576 + 59.3359i −1.31760 + 2.28215i
\(27\) 0 0
\(28\) 46.6039 + 11.9307i 1.66442 + 0.426095i
\(29\) 12.5542i 0.432905i −0.976293 0.216452i \(-0.930551\pi\)
0.976293 0.216452i \(-0.0694486\pi\)
\(30\) 0 0
\(31\) 8.24013 + 14.2723i 0.265811 + 0.460398i 0.967776 0.251814i \(-0.0810271\pi\)
−0.701965 + 0.712211i \(0.747694\pi\)
\(32\) −6.61339 + 24.6815i −0.206668 + 0.771297i
\(33\) 0 0
\(34\) 88.8263i 2.61254i
\(35\) 29.1494 + 19.3730i 0.832839 + 0.553515i
\(36\) 0 0
\(37\) 13.6641 3.66129i 0.369300 0.0989538i −0.0693957 0.997589i \(-0.522107\pi\)
0.438696 + 0.898635i \(0.355440\pi\)
\(38\) −91.7452 24.5830i −2.41435 0.646922i
\(39\) 0 0
\(40\) 26.6517 39.1446i 0.666292 0.978615i
\(41\) −48.3009 −1.17807 −0.589036 0.808107i \(-0.700492\pi\)
−0.589036 + 0.808107i \(0.700492\pi\)
\(42\) 0 0
\(43\) −0.357576 + 0.357576i −0.00831573 + 0.00831573i −0.711252 0.702937i \(-0.751872\pi\)
0.702937 + 0.711252i \(0.251872\pi\)
\(44\) 6.92755 + 3.99962i 0.157444 + 0.0909005i
\(45\) 0 0
\(46\) −20.3569 35.2592i −0.442541 0.766504i
\(47\) −27.3656 + 7.33258i −0.582246 + 0.156012i −0.537907 0.843004i \(-0.680785\pi\)
−0.0443391 + 0.999017i \(0.514118\pi\)
\(48\) 0 0
\(49\) 1.09559 + 48.9878i 0.0223590 + 0.999750i
\(50\) 66.2630 49.0354i 1.32526 0.980707i
\(51\) 0 0
\(52\) −36.9597 + 137.936i −0.710764 + 2.65261i
\(53\) 45.5418 + 12.2029i 0.859280 + 0.230243i 0.661447 0.749992i \(-0.269943\pi\)
0.197834 + 0.980236i \(0.436609\pi\)
\(54\) 0 0
\(55\) 3.79903 + 4.40884i 0.0690732 + 0.0801608i
\(56\) 66.2945 0.741234i 1.18383 0.0132363i
\(57\) 0 0
\(58\) −10.7139 39.9849i −0.184723 0.689396i
\(59\) −49.5210 + 28.5910i −0.839340 + 0.484593i −0.857040 0.515250i \(-0.827699\pi\)
0.0177000 + 0.999843i \(0.494366\pi\)
\(60\) 0 0
\(61\) 6.30786 10.9255i 0.103408 0.179107i −0.809679 0.586873i \(-0.800359\pi\)
0.913086 + 0.407766i \(0.133692\pi\)
\(62\) 38.4248 + 38.4248i 0.619755 + 0.619755i
\(63\) 0 0
\(64\) 99.2149i 1.55023i
\(65\) −58.4712 + 85.8794i −0.899556 + 1.32122i
\(66\) 0 0
\(67\) 12.0537 44.9851i 0.179906 0.671419i −0.815758 0.578394i \(-0.803680\pi\)
0.995664 0.0930251i \(-0.0296537\pi\)
\(68\) −47.9163 178.826i −0.704652 2.62980i
\(69\) 0 0
\(70\) 109.373 + 36.8262i 1.56248 + 0.526088i
\(71\) −19.0442 −0.268228 −0.134114 0.990966i \(-0.542819\pi\)
−0.134114 + 0.990966i \(0.542819\pi\)
\(72\) 0 0
\(73\) −118.629 31.7865i −1.62505 0.435432i −0.672573 0.740031i \(-0.734811\pi\)
−0.952481 + 0.304599i \(0.901477\pi\)
\(74\) 40.3953 23.3222i 0.545883 0.315165i
\(75\) 0 0
\(76\) −197.963 −2.60478
\(77\) −2.02068 + 7.89323i −0.0262426 + 0.102509i
\(78\) 0 0
\(79\) 74.1583 + 42.8153i 0.938712 + 0.541966i 0.889556 0.456825i \(-0.151014\pi\)
0.0491557 + 0.998791i \(0.484347\pi\)
\(80\) 6.16532 17.6557i 0.0770665 0.220696i
\(81\) 0 0
\(82\) −153.837 + 41.2206i −1.87607 + 0.502690i
\(83\) −18.0900 + 18.0900i −0.217952 + 0.217952i −0.807635 0.589683i \(-0.799253\pi\)
0.589683 + 0.807635i \(0.299253\pi\)
\(84\) 0 0
\(85\) 9.97979 134.324i 0.117409 1.58028i
\(86\) −0.833713 + 1.44403i −0.00969433 + 0.0167911i
\(87\) 0 0
\(88\) 10.6486 + 2.85328i 0.121007 + 0.0324236i
\(89\) 78.1616 + 45.1266i 0.878220 + 0.507041i 0.870071 0.492926i \(-0.164073\pi\)
0.00814896 + 0.999967i \(0.497406\pi\)
\(90\) 0 0
\(91\) −145.444 + 1.62620i −1.59828 + 0.0178703i
\(92\) −60.0029 60.0029i −0.652205 0.652205i
\(93\) 0 0
\(94\) −80.9010 + 46.7082i −0.860649 + 0.496896i
\(95\) −135.976 47.4824i −1.43133 0.499815i
\(96\) 0 0
\(97\) 84.2362 + 84.2362i 0.868414 + 0.868414i 0.992297 0.123883i \(-0.0395347\pi\)
−0.123883 + 0.992297i \(0.539535\pi\)
\(98\) 45.2962 + 155.090i 0.462206 + 1.58255i
\(99\) 0 0
\(100\) 106.950 134.463i 1.06950 1.34463i
\(101\) −37.0883 64.2388i −0.367211 0.636028i 0.621917 0.783083i \(-0.286354\pi\)
−0.989128 + 0.147055i \(0.953021\pi\)
\(102\) 0 0
\(103\) 24.8309 + 92.6702i 0.241077 + 0.899711i 0.975315 + 0.220819i \(0.0708729\pi\)
−0.734238 + 0.678892i \(0.762460\pi\)
\(104\) 196.803i 1.89233i
\(105\) 0 0
\(106\) 155.464 1.46664
\(107\) 42.6823 11.4367i 0.398900 0.106885i −0.0537912 0.998552i \(-0.517131\pi\)
0.452692 + 0.891667i \(0.350464\pi\)
\(108\) 0 0
\(109\) 117.615 67.9052i 1.07904 0.622984i 0.148403 0.988927i \(-0.452587\pi\)
0.930637 + 0.365943i \(0.119254\pi\)
\(110\) 15.8624 + 10.7999i 0.144203 + 0.0981812i
\(111\) 0 0
\(112\) 25.2122 7.05863i 0.225109 0.0630235i
\(113\) 4.59841 4.59841i 0.0406939 0.0406939i −0.686467 0.727161i \(-0.740839\pi\)
0.727161 + 0.686467i \(0.240839\pi\)
\(114\) 0 0
\(115\) −26.8225 55.6064i −0.233239 0.483534i
\(116\) −43.1388 74.7186i −0.371886 0.644126i
\(117\) 0 0
\(118\) −133.324 + 133.324i −1.12986 + 1.12986i
\(119\) 162.244 96.1059i 1.36339 0.807613i
\(120\) 0 0
\(121\) 59.8226 103.616i 0.494402 0.856329i
\(122\) 10.7664 40.1808i 0.0882492 0.329351i
\(123\) 0 0
\(124\) 98.0851 + 56.6294i 0.791009 + 0.456689i
\(125\) 105.713 66.7070i 0.845702 0.533656i
\(126\) 0 0
\(127\) 16.6949 + 16.6949i 0.131456 + 0.131456i 0.769773 0.638317i \(-0.220369\pi\)
−0.638317 + 0.769773i \(0.720369\pi\)
\(128\) 58.2177 + 217.271i 0.454825 + 1.69743i
\(129\) 0 0
\(130\) −112.939 + 323.424i −0.868760 + 2.48788i
\(131\) 63.4004 109.813i 0.483973 0.838266i −0.515858 0.856674i \(-0.672527\pi\)
0.999831 + 0.0184088i \(0.00586002\pi\)
\(132\) 0 0
\(133\) −54.3623 194.173i −0.408739 1.45995i
\(134\) 153.563i 1.14599i
\(135\) 0 0
\(136\) −127.572 220.961i −0.938031 1.62472i
\(137\) −41.8269 + 156.100i −0.305306 + 1.13942i 0.627377 + 0.778716i \(0.284129\pi\)
−0.932682 + 0.360700i \(0.882538\pi\)
\(138\) 0 0
\(139\) 92.5186i 0.665601i 0.942997 + 0.332801i \(0.107994\pi\)
−0.942997 + 0.332801i \(0.892006\pi\)
\(140\) 240.057 + 15.1387i 1.71469 + 0.108134i
\(141\) 0 0
\(142\) −60.6552 + 16.2525i −0.427149 + 0.114454i
\(143\) −23.3619 6.25981i −0.163370 0.0437749i
\(144\) 0 0
\(145\) −11.7093 61.6694i −0.0807541 0.425306i
\(146\) −404.957 −2.77368
\(147\) 0 0
\(148\) 68.7434 68.7434i 0.464482 0.464482i
\(149\) 140.299 + 81.0014i 0.941601 + 0.543634i 0.890462 0.455058i \(-0.150381\pi\)
0.0511394 + 0.998692i \(0.483715\pi\)
\(150\) 0 0
\(151\) 143.434 + 248.435i 0.949893 + 1.64526i 0.745645 + 0.666344i \(0.232142\pi\)
0.204248 + 0.978919i \(0.434525\pi\)
\(152\) −263.528 + 70.6122i −1.73374 + 0.464554i
\(153\) 0 0
\(154\) 0.300367 + 26.8642i 0.00195043 + 0.174443i
\(155\) 53.7893 + 62.4235i 0.347028 + 0.402732i
\(156\) 0 0
\(157\) 74.0497 276.357i 0.471654 1.76024i −0.162174 0.986762i \(-0.551851\pi\)
0.633828 0.773474i \(-0.281483\pi\)
\(158\) 272.731 + 73.0782i 1.72615 + 0.462520i
\(159\) 0 0
\(160\) −9.46607 + 127.410i −0.0591630 + 0.796310i
\(161\) 42.3767 75.3312i 0.263209 0.467896i
\(162\) 0 0
\(163\) −2.63680 9.84068i −0.0161767 0.0603722i 0.957366 0.288879i \(-0.0932824\pi\)
−0.973542 + 0.228507i \(0.926616\pi\)
\(164\) −287.471 + 165.972i −1.75287 + 1.01202i
\(165\) 0 0
\(166\) −42.1781 + 73.0547i −0.254085 + 0.440088i
\(167\) 71.1342 + 71.1342i 0.425954 + 0.425954i 0.887247 0.461294i \(-0.152615\pi\)
−0.461294 + 0.887247i \(0.652615\pi\)
\(168\) 0 0
\(169\) 262.766i 1.55483i
\(170\) −82.8484 436.336i −0.487343 2.56668i
\(171\) 0 0
\(172\) −0.899473 + 3.35688i −0.00522949 + 0.0195167i
\(173\) −77.4717 289.128i −0.447813 1.67126i −0.708401 0.705811i \(-0.750583\pi\)
0.260588 0.965450i \(-0.416084\pi\)
\(174\) 0 0
\(175\) 161.258 + 67.9772i 0.921474 + 0.388441i
\(176\) 4.35351 0.0247359
\(177\) 0 0
\(178\) 287.455 + 77.0232i 1.61491 + 0.432715i
\(179\) −280.191 + 161.768i −1.56531 + 0.903733i −0.568608 + 0.822609i \(0.692518\pi\)
−0.996704 + 0.0811241i \(0.974149\pi\)
\(180\) 0 0
\(181\) 43.2716 0.239069 0.119535 0.992830i \(-0.461860\pi\)
0.119535 + 0.992830i \(0.461860\pi\)
\(182\) −461.847 + 129.303i −2.53762 + 0.710456i
\(183\) 0 0
\(184\) −101.278 58.4731i −0.550426 0.317788i
\(185\) 63.7065 30.7296i 0.344359 0.166106i
\(186\) 0 0
\(187\) 30.2875 8.11552i 0.161965 0.0433985i
\(188\) −137.675 + 137.675i −0.732312 + 0.732312i
\(189\) 0 0
\(190\) −473.603 35.1870i −2.49265 0.185195i
\(191\) 19.2949 33.4198i 0.101021 0.174973i −0.811085 0.584929i \(-0.801123\pi\)
0.912105 + 0.409956i \(0.134456\pi\)
\(192\) 0 0
\(193\) −233.231 62.4940i −1.20845 0.323803i −0.402296 0.915509i \(-0.631788\pi\)
−0.806154 + 0.591706i \(0.798455\pi\)
\(194\) 340.178 + 196.402i 1.75350 + 1.01238i
\(195\) 0 0
\(196\) 174.852 + 287.794i 0.892103 + 1.46834i
\(197\) −217.403 217.403i −1.10357 1.10357i −0.993976 0.109594i \(-0.965045\pi\)
−0.109594 0.993976i \(-0.534955\pi\)
\(198\) 0 0
\(199\) −168.448 + 97.2533i −0.846470 + 0.488710i −0.859458 0.511206i \(-0.829199\pi\)
0.0129880 + 0.999916i \(0.495866\pi\)
\(200\) 94.4091 217.145i 0.472045 1.08573i
\(201\) 0 0
\(202\) −172.948 172.948i −0.856177 0.856177i
\(203\) 61.4416 62.8311i 0.302668 0.309513i
\(204\) 0 0
\(205\) −237.266 + 45.0503i −1.15739 + 0.219758i
\(206\) 158.172 + 273.962i 0.767824 + 1.32991i
\(207\) 0 0
\(208\) 20.1150 + 75.0701i 0.0967066 + 0.360914i
\(209\) 33.5288i 0.160425i
\(210\) 0 0
\(211\) −67.4406 −0.319624 −0.159812 0.987147i \(-0.551089\pi\)
−0.159812 + 0.987147i \(0.551089\pi\)
\(212\) 312.982 83.8632i 1.47633 0.395581i
\(213\) 0 0
\(214\) 126.182 72.8513i 0.589636 0.340426i
\(215\) −1.42299 + 2.09001i −0.00661855 + 0.00972098i
\(216\) 0 0
\(217\) −28.6101 + 111.758i −0.131844 + 0.515013i
\(218\) 316.651 316.651i 1.45253 1.45253i
\(219\) 0 0
\(220\) 37.7602 + 13.1858i 0.171637 + 0.0599353i
\(221\) 279.881 + 484.768i 1.26643 + 2.19352i
\(222\) 0 0
\(223\) 17.6765 17.6765i 0.0792670 0.0792670i −0.666362 0.745629i \(-0.732149\pi\)
0.745629 + 0.666362i \(0.232149\pi\)
\(224\) −153.892 + 91.1588i −0.687019 + 0.406959i
\(225\) 0 0
\(226\) 10.7215 18.5702i 0.0474402 0.0821689i
\(227\) 83.0011 309.764i 0.365644 1.36460i −0.500903 0.865504i \(-0.666999\pi\)
0.866546 0.499097i \(-0.166335\pi\)
\(228\) 0 0
\(229\) 290.289 + 167.598i 1.26764 + 0.731870i 0.974540 0.224213i \(-0.0719813\pi\)
0.293096 + 0.956083i \(0.405315\pi\)
\(230\) −132.884 154.215i −0.577757 0.670498i
\(231\) 0 0
\(232\) −84.0779 84.0779i −0.362405 0.362405i
\(233\) −71.7786 267.882i −0.308063 1.14971i −0.930277 0.366859i \(-0.880433\pi\)
0.622214 0.782847i \(-0.286233\pi\)
\(234\) 0 0
\(235\) −127.587 + 61.5433i −0.542924 + 0.261886i
\(236\) −196.489 + 340.328i −0.832579 + 1.44207i
\(237\) 0 0
\(238\) 434.725 444.556i 1.82657 1.86788i
\(239\) 57.1966i 0.239316i −0.992815 0.119658i \(-0.961820\pi\)
0.992815 0.119658i \(-0.0381799\pi\)
\(240\) 0 0
\(241\) −4.95051 8.57453i −0.0205415 0.0355790i 0.855572 0.517684i \(-0.173206\pi\)
−0.876113 + 0.482105i \(0.839872\pi\)
\(242\) 102.107 381.067i 0.421928 1.57466i
\(243\) 0 0
\(244\) 86.7002i 0.355329i
\(245\) 51.0727 + 239.618i 0.208460 + 0.978031i
\(246\) 0 0
\(247\) 578.156 154.916i 2.34071 0.627192i
\(248\) 150.770 + 40.3987i 0.607943 + 0.162898i
\(249\) 0 0
\(250\) 279.764 302.677i 1.11906 1.21071i
\(251\) 187.727 0.747915 0.373957 0.927446i \(-0.378001\pi\)
0.373957 + 0.927446i \(0.378001\pi\)
\(252\) 0 0
\(253\) 10.1626 10.1626i 0.0401684 0.0401684i
\(254\) 67.4206 + 38.9253i 0.265436 + 0.153249i
\(255\) 0 0
\(256\) 172.414 + 298.630i 0.673493 + 1.16652i
\(257\) 119.767 32.0914i 0.466018 0.124869i −0.0181666 0.999835i \(-0.505783\pi\)
0.484185 + 0.874966i \(0.339116\pi\)
\(258\) 0 0
\(259\) 86.3046 + 48.5496i 0.333222 + 0.187450i
\(260\) −52.9023 + 712.044i −0.203470 + 2.73863i
\(261\) 0 0
\(262\) 108.213 403.858i 0.413028 1.54144i
\(263\) −11.8632 3.17875i −0.0451074 0.0120865i 0.236195 0.971706i \(-0.424100\pi\)
−0.281302 + 0.959619i \(0.590766\pi\)
\(264\) 0 0
\(265\) 235.094 + 17.4666i 0.887147 + 0.0659118i
\(266\) −338.852 572.043i −1.27388 2.15054i
\(267\) 0 0
\(268\) −82.8379 309.155i −0.309097 1.15356i
\(269\) −16.4548 + 9.50018i −0.0611703 + 0.0353167i −0.530273 0.847827i \(-0.677911\pi\)
0.469103 + 0.883143i \(0.344577\pi\)
\(270\) 0 0
\(271\) 49.9304 86.4820i 0.184245 0.319122i −0.759077 0.651001i \(-0.774349\pi\)
0.943322 + 0.331879i \(0.107683\pi\)
\(272\) −71.2465 71.2465i −0.261935 0.261935i
\(273\) 0 0
\(274\) 532.870i 1.94478i
\(275\) 22.7739 + 18.1139i 0.0828140 + 0.0658688i
\(276\) 0 0
\(277\) 18.4218 68.7510i 0.0665046 0.248199i −0.924668 0.380773i \(-0.875658\pi\)
0.991173 + 0.132575i \(0.0423245\pi\)
\(278\) 78.9565 + 294.670i 0.284016 + 1.05996i
\(279\) 0 0
\(280\) 324.963 65.4741i 1.16058 0.233836i
\(281\) 121.502 0.432393 0.216196 0.976350i \(-0.430635\pi\)
0.216196 + 0.976350i \(0.430635\pi\)
\(282\) 0 0
\(283\) 255.612 + 68.4910i 0.903223 + 0.242018i 0.680400 0.732841i \(-0.261806\pi\)
0.222823 + 0.974859i \(0.428473\pi\)
\(284\) −113.345 + 65.4395i −0.399100 + 0.230421i
\(285\) 0 0
\(286\) −79.7495 −0.278844
\(287\) −241.735 236.390i −0.842284 0.823657i
\(288\) 0 0
\(289\) −378.195 218.351i −1.30863 0.755539i
\(290\) −89.9234 186.423i −0.310081 0.642837i
\(291\) 0 0
\(292\) −815.265 + 218.449i −2.79200 + 0.748115i
\(293\) −59.1809 + 59.1809i −0.201983 + 0.201983i −0.800849 0.598866i \(-0.795618\pi\)
0.598866 + 0.800849i \(0.295618\pi\)
\(294\) 0 0
\(295\) −216.592 + 186.634i −0.734211 + 0.632658i
\(296\) 66.9907 116.031i 0.226320 0.391998i
\(297\) 0 0
\(298\) 515.976 + 138.255i 1.73146 + 0.463944i
\(299\) 222.195 + 128.284i 0.743127 + 0.429044i
\(300\) 0 0
\(301\) −3.53960 + 0.0395760i −0.0117595 + 0.000131482i
\(302\) 668.851 + 668.851i 2.21474 + 2.21474i
\(303\) 0 0
\(304\) −93.3054 + 53.8699i −0.306926 + 0.177204i
\(305\) 20.7954 59.5521i 0.0681818 0.195253i
\(306\) 0 0
\(307\) −100.076 100.076i −0.325979 0.325979i 0.525076 0.851055i \(-0.324037\pi\)
−0.851055 + 0.525076i \(0.824037\pi\)
\(308\) 15.0963 + 53.9213i 0.0490139 + 0.175069i
\(309\) 0 0
\(310\) 224.591 + 152.913i 0.724486 + 0.493267i
\(311\) 141.092 + 244.378i 0.453671 + 0.785781i 0.998611 0.0526944i \(-0.0167809\pi\)
−0.544940 + 0.838475i \(0.683448\pi\)
\(312\) 0 0
\(313\) −51.1230 190.794i −0.163332 0.609564i −0.998247 0.0591850i \(-0.981150\pi\)
0.834915 0.550379i \(-0.185517\pi\)
\(314\) 943.386i 3.00441i
\(315\) 0 0
\(316\) 588.487 1.86230
\(317\) −151.390 + 40.5648i −0.477571 + 0.127965i −0.489571 0.871963i \(-0.662847\pi\)
0.0120003 + 0.999928i \(0.496180\pi\)
\(318\) 0 0
\(319\) 12.6550 7.30636i 0.0396708 0.0229039i
\(320\) 92.5378 + 487.367i 0.289181 + 1.52302i
\(321\) 0 0
\(322\) 70.6802 276.093i 0.219504 0.857432i
\(323\) −548.708 + 548.708i −1.69878 + 1.69878i
\(324\) 0 0
\(325\) −207.124 + 476.396i −0.637306 + 1.46583i
\(326\) −16.7963 29.0921i −0.0515224 0.0892394i
\(327\) 0 0
\(328\) −323.480 + 323.480i −0.986219 + 0.986219i
\(329\) −172.845 97.2319i −0.525365 0.295538i
\(330\) 0 0
\(331\) −245.598 + 425.389i −0.741989 + 1.28516i 0.209599 + 0.977787i \(0.432784\pi\)
−0.951588 + 0.307375i \(0.900549\pi\)
\(332\) −45.5050 + 169.827i −0.137063 + 0.511527i
\(333\) 0 0
\(334\) 287.268 + 165.854i 0.860083 + 0.496569i
\(335\) 17.2531 232.220i 0.0515018 0.693194i
\(336\) 0 0
\(337\) −250.219 250.219i −0.742489 0.742489i 0.230567 0.973056i \(-0.425942\pi\)
−0.973056 + 0.230567i \(0.925942\pi\)
\(338\) −224.248 836.904i −0.663455 2.47605i
\(339\) 0 0
\(340\) −402.168 833.745i −1.18285 2.45219i
\(341\) −9.59124 + 16.6125i −0.0281268 + 0.0487171i
\(342\) 0 0
\(343\) −234.268 + 250.535i −0.682996 + 0.730422i
\(344\) 4.78951i 0.0139230i
\(345\) 0 0
\(346\) −493.491 854.751i −1.42627 2.47038i
\(347\) 160.644 599.530i 0.462950 1.72775i −0.200649 0.979663i \(-0.564305\pi\)
0.663598 0.748089i \(-0.269028\pi\)
\(348\) 0 0
\(349\) 69.6374i 0.199534i 0.995011 + 0.0997671i \(0.0318098\pi\)
−0.995011 + 0.0997671i \(0.968190\pi\)
\(350\) 571.615 + 78.8864i 1.63319 + 0.225390i
\(351\) 0 0
\(352\) −28.7285 + 7.69777i −0.0816149 + 0.0218687i
\(353\) 55.0131 + 14.7407i 0.155845 + 0.0417584i 0.335898 0.941898i \(-0.390960\pi\)
−0.180053 + 0.983657i \(0.557627\pi\)
\(354\) 0 0
\(355\) −93.5494 + 17.7625i −0.263519 + 0.0500352i
\(356\) 620.256 1.74229
\(357\) 0 0
\(358\) −754.346 + 754.346i −2.10711 + 2.10711i
\(359\) −52.7945 30.4809i −0.147060 0.0849051i 0.424665 0.905351i \(-0.360392\pi\)
−0.571725 + 0.820446i \(0.693725\pi\)
\(360\) 0 0
\(361\) 234.381 + 405.960i 0.649255 + 1.12454i
\(362\) 137.819 36.9285i 0.380715 0.102012i
\(363\) 0 0
\(364\) −860.045 + 509.452i −2.36276 + 1.39959i
\(365\) −612.380 45.4976i −1.67775 0.124651i
\(366\) 0 0
\(367\) −93.2748 + 348.106i −0.254155 + 0.948519i 0.714404 + 0.699734i \(0.246698\pi\)
−0.968559 + 0.248785i \(0.919969\pi\)
\(368\) −44.6089 11.9529i −0.121220 0.0324808i
\(369\) 0 0
\(370\) 176.679 152.241i 0.477510 0.411463i
\(371\) 168.205 + 283.959i 0.453382 + 0.765388i
\(372\) 0 0
\(373\) −4.66229 17.3999i −0.0124994 0.0466485i 0.959394 0.282068i \(-0.0910203\pi\)
−0.971894 + 0.235419i \(0.924354\pi\)
\(374\) 89.5392 51.6955i 0.239410 0.138223i
\(375\) 0 0
\(376\) −134.164 + 232.380i −0.356820 + 0.618031i
\(377\) 184.459 + 184.459i 0.489281 + 0.489281i
\(378\) 0 0
\(379\) 93.7813i 0.247444i −0.992317 0.123722i \(-0.960517\pi\)
0.992317 0.123722i \(-0.0394831\pi\)
\(380\) −972.443 + 184.641i −2.55906 + 0.485896i
\(381\) 0 0
\(382\) 32.9330 122.908i 0.0862122 0.321748i
\(383\) −107.167 399.952i −0.279809 1.04426i −0.952550 0.304382i \(-0.901550\pi\)
0.672741 0.739878i \(-0.265117\pi\)
\(384\) 0 0
\(385\) −2.56402 + 40.6581i −0.00665980 + 0.105605i
\(386\) −796.168 −2.06261
\(387\) 0 0
\(388\) 790.798 + 211.894i 2.03814 + 0.546118i
\(389\) −142.385 + 82.2062i −0.366029 + 0.211327i −0.671722 0.740803i \(-0.734445\pi\)
0.305693 + 0.952130i \(0.401112\pi\)
\(390\) 0 0
\(391\) −332.627 −0.850710
\(392\) 335.417 + 320.742i 0.855656 + 0.818220i
\(393\) 0 0
\(394\) −877.960 506.890i −2.22832 1.28652i
\(395\) 404.217 + 141.151i 1.02333 + 0.357345i
\(396\) 0 0
\(397\) −564.572 + 151.277i −1.42210 + 0.381050i −0.886227 0.463251i \(-0.846683\pi\)
−0.535870 + 0.844301i \(0.680016\pi\)
\(398\) −453.505 + 453.505i −1.13946 + 1.13946i
\(399\) 0 0
\(400\) 13.8180 92.4793i 0.0345451 0.231198i
\(401\) 80.2339 138.969i 0.200084 0.346556i −0.748471 0.663168i \(-0.769212\pi\)
0.948555 + 0.316611i \(0.102545\pi\)
\(402\) 0 0
\(403\) −330.775 88.6308i −0.820781 0.219928i
\(404\) −441.475 254.886i −1.09276 0.630905i
\(405\) 0 0
\(406\) 142.069 252.551i 0.349925 0.622046i
\(407\) 11.6430 + 11.6430i 0.0286068 + 0.0286068i
\(408\) 0 0
\(409\) −143.273 + 82.7185i −0.350300 + 0.202246i −0.664817 0.747006i \(-0.731491\pi\)
0.314518 + 0.949252i \(0.398157\pi\)
\(410\) −717.239 + 345.970i −1.74936 + 0.843828i
\(411\) 0 0
\(412\) 466.219 + 466.219i 1.13160 + 1.13160i
\(413\) −387.769 99.2694i −0.938908 0.240362i
\(414\) 0 0
\(415\) −71.9900 + 105.735i −0.173470 + 0.254784i
\(416\) −265.474 459.814i −0.638159 1.10532i
\(417\) 0 0
\(418\) −28.6139 106.788i −0.0684542 0.255475i
\(419\) 572.116i 1.36543i 0.730684 + 0.682716i \(0.239201\pi\)
−0.730684 + 0.682716i \(0.760799\pi\)
\(420\) 0 0
\(421\) 259.398 0.616148 0.308074 0.951362i \(-0.400316\pi\)
0.308074 + 0.951362i \(0.400316\pi\)
\(422\) −214.797 + 57.5546i −0.508997 + 0.136385i
\(423\) 0 0
\(424\) 386.727 223.277i 0.912092 0.526596i
\(425\) −76.2610 669.140i −0.179438 1.57445i
\(426\) 0 0
\(427\) 85.0401 23.8086i 0.199157 0.0557578i
\(428\) 214.732 214.732i 0.501711 0.501711i
\(429\) 0 0
\(430\) −2.74854 + 7.87104i −0.00639196 + 0.0183047i
\(431\) 310.336 + 537.517i 0.720036 + 1.24714i 0.960985 + 0.276602i \(0.0892082\pi\)
−0.240948 + 0.970538i \(0.577458\pi\)
\(432\) 0 0
\(433\) 334.651 334.651i 0.772865 0.772865i −0.205741 0.978606i \(-0.565961\pi\)
0.978606 + 0.205741i \(0.0659605\pi\)
\(434\) 4.25280 + 380.362i 0.00979908 + 0.876411i
\(435\) 0 0
\(436\) 466.672 808.299i 1.07035 1.85390i
\(437\) −92.0560 + 343.558i −0.210654 + 0.786173i
\(438\) 0 0
\(439\) 568.777 + 328.383i 1.29562 + 0.748026i 0.979644 0.200741i \(-0.0643351\pi\)
0.315975 + 0.948768i \(0.397668\pi\)
\(440\) 54.9696 + 4.08404i 0.124931 + 0.00928191i
\(441\) 0 0
\(442\) 1305.12 + 1305.12i 2.95276 + 2.95276i
\(443\) 154.454 + 576.431i 0.348655 + 1.30120i 0.888283 + 0.459296i \(0.151898\pi\)
−0.539628 + 0.841904i \(0.681435\pi\)
\(444\) 0 0
\(445\) 426.038 + 148.771i 0.957388 + 0.334317i
\(446\) 41.2140 71.3847i 0.0924081 0.160055i
\(447\) 0 0
\(448\) −485.567 + 496.548i −1.08386 + 1.10837i
\(449\) 162.638i 0.362223i 0.983463 + 0.181111i \(0.0579694\pi\)
−0.983463 + 0.181111i \(0.942031\pi\)
\(450\) 0 0
\(451\) −28.1104 48.6886i −0.0623290 0.107957i
\(452\) 11.5672 43.1693i 0.0255911 0.0955072i
\(453\) 0 0
\(454\) 1057.43i 2.32913i
\(455\) −712.938 + 143.644i −1.56690 + 0.315701i
\(456\) 0 0
\(457\) 486.828 130.445i 1.06527 0.285438i 0.316721 0.948519i \(-0.397418\pi\)
0.748548 + 0.663081i \(0.230751\pi\)
\(458\) 1067.59 + 286.061i 2.33099 + 0.624587i
\(459\) 0 0
\(460\) −350.713 238.784i −0.762420 0.519095i
\(461\) −323.423 −0.701568 −0.350784 0.936456i \(-0.614085\pi\)
−0.350784 + 0.936456i \(0.614085\pi\)
\(462\) 0 0
\(463\) 108.492 108.492i 0.234324 0.234324i −0.580171 0.814495i \(-0.697014\pi\)
0.814495 + 0.580171i \(0.197014\pi\)
\(464\) −40.6649 23.4779i −0.0876399 0.0505989i
\(465\) 0 0
\(466\) −457.227 791.940i −0.981173 1.69944i
\(467\) −454.466 + 121.774i −0.973161 + 0.260758i −0.710162 0.704038i \(-0.751378\pi\)
−0.262999 + 0.964796i \(0.584712\pi\)
\(468\) 0 0
\(469\) 280.488 166.148i 0.598055 0.354261i
\(470\) −353.840 + 304.898i −0.752851 + 0.648720i
\(471\) 0 0
\(472\) −140.172 + 523.130i −0.296975 + 1.10833i
\(473\) −0.568550 0.152342i −0.00120201 0.000322077i
\(474\) 0 0
\(475\) −712.233 106.420i −1.49944 0.224042i
\(476\) 635.382 1129.49i 1.33484 2.37288i
\(477\) 0 0
\(478\) −48.8123 182.170i −0.102118 0.381109i
\(479\) 79.9576 46.1636i 0.166926 0.0963749i −0.414209 0.910182i \(-0.635942\pi\)
0.581136 + 0.813807i \(0.302609\pi\)
\(480\) 0 0
\(481\) −146.971 + 254.561i −0.305553 + 0.529234i
\(482\) −23.0849 23.0849i −0.0478939 0.0478939i
\(483\) 0 0
\(484\) 822.249i 1.69886i
\(485\) 492.355 + 335.221i 1.01517 + 0.691177i
\(486\) 0 0
\(487\) −206.367 + 770.171i −0.423751 + 1.58146i 0.342884 + 0.939378i \(0.388596\pi\)
−0.766635 + 0.642083i \(0.778071\pi\)
\(488\) −30.9254 115.415i −0.0633717 0.236506i
\(489\) 0 0
\(490\) 367.158 + 719.591i 0.749302 + 1.46855i
\(491\) −442.461 −0.901143 −0.450572 0.892740i \(-0.648780\pi\)
−0.450572 + 0.892740i \(0.648780\pi\)
\(492\) 0 0
\(493\) −326.673 87.5317i −0.662622 0.177549i
\(494\) 1709.21 986.810i 3.45993 1.99759i
\(495\) 0 0
\(496\) 61.6401 0.124274
\(497\) −95.3118 93.2040i −0.191774 0.187533i
\(498\) 0 0
\(499\) 59.9751 + 34.6267i 0.120191 + 0.0693921i 0.558890 0.829242i \(-0.311227\pi\)
−0.438699 + 0.898634i \(0.644561\pi\)
\(500\) 399.949 760.268i 0.799897 1.52054i
\(501\) 0 0
\(502\) 597.905 160.208i 1.19105 0.319140i
\(503\) −570.214 + 570.214i −1.13363 + 1.13363i −0.144057 + 0.989569i \(0.546015\pi\)
−0.989569 + 0.144057i \(0.953985\pi\)
\(504\) 0 0
\(505\) −242.102 280.964i −0.479410 0.556365i
\(506\) 23.6948 41.0405i 0.0468276 0.0811078i
\(507\) 0 0
\(508\) 156.730 + 41.9956i 0.308523 + 0.0826685i
\(509\) 252.827 + 145.970i 0.496713 + 0.286778i 0.727355 0.686261i \(-0.240749\pi\)
−0.230642 + 0.973039i \(0.574083\pi\)
\(510\) 0 0
\(511\) −438.145 739.666i −0.857426 1.44749i
\(512\) 167.775 + 167.775i 0.327686 + 0.327686i
\(513\) 0 0
\(514\) 354.067 204.421i 0.688846 0.397706i
\(515\) 208.409 + 432.058i 0.404677 + 0.838948i
\(516\) 0 0
\(517\) −23.3177 23.3177i −0.0451020 0.0451020i
\(518\) 316.311 + 80.9760i 0.610639 + 0.156324i
\(519\) 0 0
\(520\) 183.558 + 966.742i 0.352996 + 1.85912i
\(521\) −204.719 354.584i −0.392935 0.680583i 0.599900 0.800075i \(-0.295207\pi\)
−0.992835 + 0.119491i \(0.961874\pi\)
\(522\) 0 0
\(523\) −37.0443 138.251i −0.0708305 0.264343i 0.921425 0.388556i \(-0.127026\pi\)
−0.992256 + 0.124213i \(0.960359\pi\)
\(524\) 871.426i 1.66303i
\(525\) 0 0
\(526\) −40.4970 −0.0769904
\(527\) 428.832 114.905i 0.813723 0.218036i
\(528\) 0 0
\(529\) 326.093 188.270i 0.616432 0.355897i
\(530\) 763.675 145.001i 1.44090 0.273587i
\(531\) 0 0
\(532\) −990.763 968.853i −1.86234 1.82115i
\(533\) 709.684 709.684i 1.33149 1.33149i
\(534\) 0 0
\(535\) 198.999 95.9896i 0.371960 0.179420i
\(536\) −220.547 381.999i −0.411469 0.712685i
\(537\) 0 0
\(538\) −44.3006 + 44.3006i −0.0823431 + 0.0823431i
\(539\) −48.7433 + 29.6145i −0.0904328 + 0.0549433i
\(540\) 0 0
\(541\) −97.2826 + 168.498i −0.179820 + 0.311457i −0.941819 0.336121i \(-0.890885\pi\)
0.761999 + 0.647578i \(0.224218\pi\)
\(542\) 85.2224 318.054i 0.157237 0.586816i
\(543\) 0 0
\(544\) 596.125 + 344.173i 1.09582 + 0.632671i
\(545\) 514.419 443.267i 0.943888 0.813333i
\(546\) 0 0
\(547\) −170.750 170.750i −0.312158 0.312158i 0.533587 0.845745i \(-0.320844\pi\)
−0.845745 + 0.533587i \(0.820844\pi\)
\(548\) 287.451 + 1072.78i 0.524545 + 1.95763i
\(549\) 0 0
\(550\) 87.9929 + 38.2570i 0.159987 + 0.0695581i
\(551\) −180.816 + 313.183i −0.328160 + 0.568389i
\(552\) 0 0
\(553\) 161.603 + 577.219i 0.292230 + 1.04380i
\(554\) 234.692i 0.423631i
\(555\) 0 0
\(556\) 317.912 + 550.640i 0.571785 + 0.990360i
\(557\) −150.676 + 562.331i −0.270514 + 1.00957i 0.688275 + 0.725450i \(0.258368\pi\)
−0.958789 + 0.284121i \(0.908298\pi\)
\(558\) 0 0
\(559\) 10.5077i 0.0187973i
\(560\) 117.265 58.1891i 0.209401 0.103909i
\(561\) 0 0
\(562\) 386.982 103.692i 0.688581 0.184505i
\(563\) −403.835 108.207i −0.717291 0.192197i −0.118328 0.992975i \(-0.537754\pi\)
−0.598963 + 0.800777i \(0.704420\pi\)
\(564\) 0 0
\(565\) 18.2995 26.8774i 0.0323886 0.0475706i
\(566\) 872.570 1.54164
\(567\) 0 0
\(568\) −127.542 + 127.542i −0.224546 + 0.224546i
\(569\) −424.932 245.335i −0.746806 0.431168i 0.0777329 0.996974i \(-0.475232\pi\)
−0.824539 + 0.565806i \(0.808565\pi\)
\(570\) 0 0
\(571\) 105.483 + 182.702i 0.184734 + 0.319969i 0.943487 0.331410i \(-0.107524\pi\)
−0.758753 + 0.651379i \(0.774191\pi\)
\(572\) −160.553 + 43.0199i −0.280686 + 0.0752096i
\(573\) 0 0
\(574\) −971.660 546.595i −1.69279 0.952257i
\(575\) −183.622 248.135i −0.319343 0.431538i
\(576\) 0 0
\(577\) 18.3165 68.3580i 0.0317443 0.118471i −0.948236 0.317568i \(-0.897134\pi\)
0.979980 + 0.199096i \(0.0638006\pi\)
\(578\) −1390.89 372.687i −2.40638 0.644787i
\(579\) 0 0
\(580\) −281.598 326.800i −0.485514 0.563448i
\(581\) −179.071 + 2.00218i −0.308212 + 0.00344609i
\(582\) 0 0
\(583\) 14.2038 + 53.0092i 0.0243633 + 0.0909249i
\(584\) −1007.36 + 581.599i −1.72493 + 0.995888i
\(585\) 0 0
\(586\) −137.984 + 238.996i −0.235468 + 0.407842i
\(587\) 716.384 + 716.384i 1.22042 + 1.22042i 0.967484 + 0.252932i \(0.0813949\pi\)
0.252932 + 0.967484i \(0.418605\pi\)
\(588\) 0 0
\(589\) 474.724i 0.805982i
\(590\) −530.566 + 779.268i −0.899264 + 1.32079i
\(591\) 0 0
\(592\) 13.6941 51.1070i 0.0231319 0.0863294i
\(593\) 181.380 + 676.921i 0.305869 + 1.14152i 0.932194 + 0.361958i \(0.117892\pi\)
−0.626325 + 0.779562i \(0.715442\pi\)
\(594\) 0 0
\(595\) 707.342 623.420i 1.18881 1.04776i
\(596\) 1113.35 1.86803
\(597\) 0 0
\(598\) 817.165 + 218.959i 1.36650 + 0.366152i
\(599\) −39.4905 + 22.7998i −0.0659273 + 0.0380632i −0.532601 0.846366i \(-0.678785\pi\)
0.466674 + 0.884429i \(0.345452\pi\)
\(600\) 0 0
\(601\) 1084.31 1.80418 0.902092 0.431544i \(-0.142031\pi\)
0.902092 + 0.431544i \(0.142031\pi\)
\(602\) −11.2398 + 3.14679i −0.0186707 + 0.00522723i
\(603\) 0 0
\(604\) 1707.34 + 985.734i 2.82672 + 1.63201i
\(605\) 197.220 564.782i 0.325984 0.933524i
\(606\) 0 0
\(607\) 409.938 109.843i 0.675351 0.180960i 0.0951869 0.995459i \(-0.469655\pi\)
0.580164 + 0.814500i \(0.302988\pi\)
\(608\) 520.462 520.462i 0.856024 0.856024i
\(609\) 0 0
\(610\) 15.4105 207.419i 0.0252631 0.340032i
\(611\) 294.344 509.819i 0.481741 0.834400i
\(612\) 0 0
\(613\) −558.097 149.542i −0.910435 0.243950i −0.226943 0.973908i \(-0.572873\pi\)
−0.683492 + 0.729958i \(0.739540\pi\)
\(614\) −404.144 233.333i −0.658215 0.380021i
\(615\) 0 0
\(616\) 39.3295 + 66.3952i 0.0638466 + 0.107784i
\(617\) −23.3244 23.3244i −0.0378030 0.0378030i 0.687953 0.725756i \(-0.258510\pi\)
−0.725756 + 0.687953i \(0.758510\pi\)
\(618\) 0 0
\(619\) −534.066 + 308.343i −0.862788 + 0.498131i −0.864945 0.501867i \(-0.832647\pi\)
0.00215709 + 0.999998i \(0.499313\pi\)
\(620\) 534.635 + 186.693i 0.862315 + 0.301118i
\(621\) 0 0
\(622\) 657.928 + 657.928i 1.05776 + 1.05776i
\(623\) 170.327 + 608.379i 0.273398 + 0.976532i
\(624\) 0 0
\(625\) 457.068 426.279i 0.731309 0.682046i
\(626\) −325.651 564.044i −0.520210 0.901029i
\(627\) 0 0
\(628\) −508.899 1899.24i −0.810348 3.02426i
\(629\) 381.081i 0.605852i
\(630\) 0 0
\(631\) 524.168 0.830695 0.415347 0.909663i \(-0.363660\pi\)
0.415347 + 0.909663i \(0.363660\pi\)
\(632\) 783.393 209.909i 1.23955 0.332135i
\(633\) 0 0
\(634\) −447.555 + 258.396i −0.705923 + 0.407565i
\(635\) 97.5808 + 66.4381i 0.153671 + 0.104627i
\(636\) 0 0
\(637\) −735.873 703.678i −1.15522 1.10467i
\(638\) 34.0705 34.0705i 0.0534020 0.0534020i
\(639\) 0 0
\(640\) 488.628 + 1012.99i 0.763481 + 1.58279i
\(641\) −29.7943 51.6052i −0.0464809 0.0805074i 0.841849 0.539713i \(-0.181467\pi\)
−0.888330 + 0.459206i \(0.848134\pi\)
\(642\) 0 0
\(643\) −282.054 + 282.054i −0.438653 + 0.438653i −0.891558 0.452906i \(-0.850387\pi\)
0.452906 + 0.891558i \(0.350387\pi\)
\(644\) −6.64103 593.961i −0.0103122 0.922300i
\(645\) 0 0
\(646\) −1279.35 + 2215.89i −1.98041 + 3.43018i
\(647\) −113.319 + 422.913i −0.175145 + 0.653652i 0.821381 + 0.570379i \(0.193204\pi\)
−0.996527 + 0.0832724i \(0.973463\pi\)
\(648\) 0 0
\(649\) −57.6409 33.2790i −0.0888149 0.0512773i
\(650\) −253.124 + 1694.07i −0.389422 + 2.60627i
\(651\) 0 0
\(652\) −49.5079 49.5079i −0.0759323 0.0759323i
\(653\) −121.826 454.660i −0.186563 0.696263i −0.994291 0.106707i \(-0.965969\pi\)
0.807727 0.589556i \(-0.200697\pi\)
\(654\) 0 0
\(655\) 209.016 598.560i 0.319108 0.913832i
\(656\) −90.3285 + 156.454i −0.137696 + 0.238496i
\(657\) 0 0
\(658\) −633.486 162.173i −0.962745 0.246464i
\(659\) 1076.98i 1.63426i −0.576454 0.817129i \(-0.695564\pi\)
0.576454 0.817129i \(-0.304436\pi\)
\(660\) 0 0
\(661\) −36.2193 62.7337i −0.0547948 0.0949073i 0.837327 0.546702i \(-0.184117\pi\)
−0.892122 + 0.451795i \(0.850784\pi\)
\(662\) −419.193 + 1564.45i −0.633222 + 2.36322i
\(663\) 0 0
\(664\) 242.305i 0.364916i
\(665\) −448.146 903.119i −0.673904 1.35807i
\(666\) 0 0
\(667\) −149.731 + 40.1204i −0.224485 + 0.0601505i
\(668\) 667.799 + 178.936i 0.999699 + 0.267868i
\(669\) 0 0
\(670\) −143.229 754.339i −0.213774 1.12588i
\(671\) 14.6843 0.0218842
\(672\) 0 0
\(673\) −217.067 + 217.067i −0.322537 + 0.322537i −0.849740 0.527203i \(-0.823241\pi\)
0.527203 + 0.849740i \(0.323241\pi\)
\(674\) −1010.48 583.402i −1.49923 0.865581i
\(675\) 0 0
\(676\) −902.916 1563.90i −1.33568 2.31346i
\(677\) 712.265 190.851i 1.05209 0.281907i 0.308975 0.951070i \(-0.400014\pi\)
0.743115 + 0.669164i \(0.233348\pi\)
\(678\) 0 0
\(679\) 9.32314 + 833.843i 0.0137307 + 1.22805i
\(680\) −832.756 966.428i −1.22464 1.42122i
\(681\) 0 0
\(682\) −16.3706 + 61.0958i −0.0240038 + 0.0895833i
\(683\) −447.760 119.977i −0.655579 0.175662i −0.0843288 0.996438i \(-0.526875\pi\)
−0.571250 + 0.820776i \(0.693541\pi\)
\(684\) 0 0
\(685\) −59.8689 + 805.812i −0.0873998 + 1.17637i
\(686\) −532.328 + 997.874i −0.775988 + 1.45463i
\(687\) 0 0
\(688\) 0.489530 + 1.82695i 0.000711526 + 0.00265545i
\(689\) −848.441 + 489.848i −1.23141 + 0.710955i
\(690\) 0 0
\(691\) 206.290 357.305i 0.298538 0.517084i −0.677263 0.735741i \(-0.736834\pi\)
0.975802 + 0.218657i \(0.0701676\pi\)
\(692\) −1454.59 1454.59i −2.10200 2.10200i
\(693\) 0 0
\(694\) 2046.58i 2.94897i
\(695\) 86.2922 + 454.473i 0.124161 + 0.653918i
\(696\) 0 0
\(697\) −336.768 + 1256.84i −0.483168 + 1.80321i
\(698\) 59.4294 + 221.794i 0.0851424 + 0.317756i
\(699\) 0 0
\(700\) 1193.34 149.536i 1.70477 0.213623i
\(701\) 946.008 1.34951 0.674756 0.738041i \(-0.264249\pi\)
0.674756 + 0.738041i \(0.264249\pi\)
\(702\) 0 0
\(703\) −393.603 105.466i −0.559890 0.150022i
\(704\) −100.011 + 57.7415i −0.142061 + 0.0820191i
\(705\) 0 0
\(706\) 187.795 0.265999
\(707\) 128.772 503.015i 0.182139 0.711478i
\(708\) 0 0
\(709\) −66.1749 38.2061i −0.0933355 0.0538873i 0.452606 0.891711i \(-0.350495\pi\)
−0.545941 + 0.837823i \(0.683828\pi\)
\(710\) −282.794 + 136.409i −0.398301 + 0.192126i
\(711\) 0 0
\(712\) 825.683 221.241i 1.15967 0.310732i
\(713\) 143.889 143.889i 0.201808 0.201808i
\(714\) 0 0
\(715\) −120.598 8.95999i −0.168668 0.0125315i
\(716\) −1111.74 + 1925.58i −1.55270 + 2.68936i
\(717\) 0 0
\(718\) −194.162 52.0256i −0.270421 0.0724591i
\(719\) −726.346 419.356i −1.01022 0.583249i −0.0989618 0.995091i \(-0.531552\pi\)
−0.911255 + 0.411842i \(0.864886\pi\)
\(720\) 0 0
\(721\) −329.264 + 585.319i −0.456677 + 0.811815i
\(722\) 1092.95 + 1092.95i 1.51378 + 1.51378i
\(723\) 0 0
\(724\) 257.538 148.690i 0.355715 0.205372i
\(725\) −115.038 292.013i −0.158673 0.402777i
\(726\) 0 0
\(727\) 325.814 + 325.814i 0.448162 + 0.448162i 0.894743 0.446581i \(-0.147359\pi\)
−0.446581 + 0.894743i \(0.647359\pi\)
\(728\) −963.172 + 984.954i −1.32304 + 1.35296i
\(729\) 0 0
\(730\) −1989.25 + 377.704i −2.72500 + 0.517403i
\(731\) 6.81135 + 11.7976i 0.00931785 + 0.0161390i
\(732\) 0 0
\(733\) −176.158 657.430i −0.240324 0.896903i −0.975676 0.219217i \(-0.929650\pi\)
0.735352 0.677686i \(-0.237017\pi\)
\(734\) 1188.31i 1.61896i
\(735\) 0 0
\(736\) 315.505 0.428676
\(737\) 52.3612 14.0301i 0.0710464 0.0190368i
\(738\) 0 0
\(739\) −1219.14 + 703.869i −1.64971 + 0.952461i −0.672526 + 0.740074i \(0.734791\pi\)
−0.977185 + 0.212388i \(0.931876\pi\)
\(740\) 273.567 401.801i 0.369685 0.542974i
\(741\) 0 0
\(742\) 778.062 + 760.856i 1.04860 + 1.02541i
\(743\) 431.433 431.433i 0.580664 0.580664i −0.354422 0.935086i \(-0.615322\pi\)
0.935086 + 0.354422i \(0.115322\pi\)
\(744\) 0 0
\(745\) 764.730 + 267.042i 1.02648 + 0.358445i
\(746\) −29.6986 51.4394i −0.0398104 0.0689537i
\(747\) 0 0
\(748\) 152.375 152.375i 0.203710 0.203710i
\(749\) 269.588 + 151.653i 0.359931 + 0.202475i
\(750\) 0 0
\(751\) 98.6211 170.817i 0.131320 0.227452i −0.792866 0.609396i \(-0.791412\pi\)
0.924186 + 0.381944i \(0.124745\pi\)
\(752\) −27.4256 + 102.354i −0.0364702 + 0.136109i
\(753\) 0 0
\(754\) 744.917 + 430.078i 0.987953 + 0.570395i
\(755\) 936.296 + 1086.59i 1.24013 + 1.43919i
\(756\) 0 0
\(757\) −925.874 925.874i −1.22308 1.22308i −0.966530 0.256553i \(-0.917413\pi\)
−0.256553 0.966530i \(-0.582587\pi\)
\(758\) −80.0341 298.691i −0.105586 0.394052i
\(759\) 0 0
\(760\) −1228.65 + 592.657i −1.61665 + 0.779812i
\(761\) −148.294 + 256.852i −0.194867 + 0.337519i −0.946857 0.321655i \(-0.895761\pi\)
0.751990 + 0.659174i \(0.229094\pi\)
\(762\) 0 0
\(763\) 920.973 + 235.770i 1.20704 + 0.309004i
\(764\) 265.205i 0.347127i
\(765\) 0 0
\(766\) −682.647 1182.38i −0.891184 1.54358i
\(767\) 307.524 1147.70i 0.400945 1.49635i
\(768\) 0 0
\(769\) 483.085i 0.628199i −0.949390 0.314099i \(-0.898297\pi\)
0.949390 0.314099i \(-0.101703\pi\)
\(770\) 26.5318 + 131.683i 0.0344568 + 0.171017i
\(771\) 0 0
\(772\) −1602.85 + 429.484i −2.07624 + 0.556326i
\(773\) −309.472 82.9229i −0.400353 0.107274i 0.0530240 0.998593i \(-0.483114\pi\)
−0.453376 + 0.891319i \(0.649781\pi\)
\(774\) 0 0
\(775\) 322.448 + 256.470i 0.416062 + 0.330928i
\(776\) 1128.29 1.45398
\(777\) 0 0
\(778\) −383.338 + 383.338i −0.492723 + 0.492723i
\(779\) 1204.93 + 695.669i 1.54677 + 0.893028i
\(780\) 0 0
\(781\) −11.0834 19.1970i −0.0141913 0.0245800i
\(782\) −1059.41 + 283.868i −1.35475 + 0.363003i
\(783\) 0 0
\(784\) 160.727 + 88.0641i 0.205009 + 0.112327i
\(785\) 105.991 1426.60i 0.135020 1.81732i
\(786\) 0 0
\(787\) 219.064 817.557i 0.278353 1.03883i −0.675208 0.737627i \(-0.735946\pi\)
0.953561 0.301200i \(-0.0973870\pi\)
\(788\) −2040.95 546.872i −2.59004 0.694000i
\(789\) 0 0
\(790\) 1407.88 + 104.600i 1.78213 + 0.132406i
\(791\) 45.5191 0.508945i 0.0575463 0.000643420i
\(792\) 0 0
\(793\) 67.8473 + 253.209i 0.0855577 + 0.319306i
\(794\) −1669.05 + 963.626i −2.10208 + 1.21363i
\(795\) 0 0
\(796\) −668.363 + 1157.64i −0.839652 + 1.45432i
\(797\) −1003.28 1003.28i −1.25882 1.25882i −0.951658 0.307160i \(-0.900621\pi\)
−0.307160 0.951658i \(-0.599379\pi\)
\(798\) 0 0
\(799\) 763.203i 0.955197i
\(800\) 72.3355 + 634.695i 0.0904193 + 0.793369i
\(801\) 0 0
\(802\) 136.945 511.086i 0.170755 0.637265i
\(803\) −36.9985 138.080i −0.0460753 0.171955i
\(804\) 0 0
\(805\) 137.903 409.570i 0.171308 0.508782i
\(806\) −1129.15 −1.40093
\(807\) 0 0
\(808\) −678.606 181.832i −0.839859 0.225040i
\(809\) −331.791 + 191.559i −0.410124 + 0.236785i −0.690843 0.723005i \(-0.742760\pi\)
0.280719 + 0.959790i \(0.409427\pi\)
\(810\) 0 0
\(811\) 537.982 0.663357 0.331678 0.943393i \(-0.392385\pi\)
0.331678 + 0.943393i \(0.392385\pi\)
\(812\) 149.780 585.076i 0.184458 0.720537i
\(813\) 0 0
\(814\) 47.0188 + 27.1463i 0.0577627 + 0.0333493i
\(815\) −22.1310 45.8804i −0.0271546 0.0562950i
\(816\) 0 0
\(817\) 14.0703 3.77013i 0.0172220 0.00461461i
\(818\) −385.727 + 385.727i −0.471549 + 0.471549i
\(819\) 0 0
\(820\) −1257.32 + 1083.42i −1.53332 + 1.32124i
\(821\) 192.500 333.419i 0.234470 0.406114i −0.724649 0.689119i \(-0.757998\pi\)
0.959118 + 0.283005i \(0.0913312\pi\)
\(822\) 0 0
\(823\) 214.992 + 57.6069i 0.261230 + 0.0699963i 0.387057 0.922056i \(-0.373492\pi\)
−0.125827 + 0.992052i \(0.540158\pi\)
\(824\) 786.926 + 454.332i 0.955007 + 0.551374i
\(825\) 0 0
\(826\) −1319.75 + 14.7561i −1.59776 + 0.0178645i
\(827\) 542.598 + 542.598i 0.656104 + 0.656104i 0.954456 0.298352i \(-0.0964370\pi\)
−0.298352 + 0.954456i \(0.596437\pi\)
\(828\) 0 0
\(829\) −968.472 + 559.148i −1.16824 + 0.674485i −0.953265 0.302135i \(-0.902301\pi\)
−0.214976 + 0.976619i \(0.568967\pi\)
\(830\) −139.051 + 398.201i −0.167531 + 0.479761i
\(831\) 0 0
\(832\) −1457.76 1457.76i −1.75212 1.75212i
\(833\) 1282.35 + 313.048i 1.53943 + 0.375808i
\(834\) 0 0
\(835\) 415.775 + 283.081i 0.497934 + 0.339019i
\(836\) −115.212 199.552i −0.137813 0.238699i
\(837\) 0 0
\(838\) 488.251 + 1822.18i 0.582638 + 2.17444i
\(839\) 866.690i 1.03300i −0.856286 0.516502i \(-0.827234\pi\)
0.856286 0.516502i \(-0.172766\pi\)
\(840\) 0 0
\(841\) 683.391 0.812594
\(842\) 826.177 221.374i 0.981208 0.262914i
\(843\) 0 0
\(844\) −401.384 + 231.739i −0.475574 + 0.274573i
\(845\) −245.082 1290.77i −0.290038 1.52754i
\(846\) 0 0
\(847\) 806.505 225.796i 0.952190 0.266583i
\(848\) 124.696 124.696i 0.147047 0.147047i
\(849\) 0 0
\(850\) −813.942 2066.11i −0.957578 2.43072i
\(851\) −87.3347 151.268i −0.102626 0.177753i
\(852\) 0 0
\(853\) 846.282 846.282i 0.992124 0.992124i −0.00784512 0.999969i \(-0.502497\pi\)
0.999969 + 0.00784512i \(0.00249721\pi\)
\(854\) 250.532 148.404i 0.293363 0.173775i
\(855\) 0 0
\(856\) 209.258 362.445i 0.244460 0.423417i
\(857\) −251.985 + 940.421i −0.294032 + 1.09734i 0.647952 + 0.761681i \(0.275626\pi\)
−0.941983 + 0.335659i \(0.891041\pi\)
\(858\) 0 0
\(859\) −1270.34 733.431i −1.47886 0.853819i −0.479144 0.877736i \(-0.659053\pi\)
−0.999714 + 0.0239168i \(0.992386\pi\)
\(860\) −1.28746 + 17.3287i −0.00149705 + 0.0201497i
\(861\) 0 0
\(862\) 1447.14 + 1447.14i 1.67881 + 1.67881i
\(863\) −215.966 805.996i −0.250250 0.933946i −0.970672 0.240410i \(-0.922718\pi\)
0.720421 0.693537i \(-0.243948\pi\)
\(864\) 0 0
\(865\) −650.229 1348.01i −0.751710 1.55839i
\(866\) 780.260 1351.45i 0.900993 1.56057i
\(867\) 0 0
\(868\) 213.744 + 763.456i 0.246249 + 0.879557i
\(869\) 99.6712i 0.114696i
\(870\) 0 0
\(871\) 483.859 + 838.069i 0.555521 + 0.962191i
\(872\) 332.917 1242.46i 0.381786 1.42484i
\(873\) 0 0
\(874\) 1172.79i 1.34186i
\(875\) 855.539 + 183.515i 0.977759 + 0.209731i
\(876\) 0 0
\(877\) 1454.90 389.839i 1.65895 0.444514i 0.696852 0.717215i \(-0.254584\pi\)
0.962099 + 0.272701i \(0.0879170\pi\)
\(878\) 2091.79 + 560.493i 2.38245 + 0.638375i
\(879\) 0 0
\(880\) 21.3855 4.06053i 0.0243017 0.00461423i
\(881\) −381.409 −0.432928 −0.216464 0.976291i \(-0.569452\pi\)
−0.216464 + 0.976291i \(0.569452\pi\)
\(882\) 0 0
\(883\) 523.721 523.721i 0.593115 0.593115i −0.345356 0.938472i \(-0.612242\pi\)
0.938472 + 0.345356i \(0.112242\pi\)
\(884\) 3331.52 + 1923.45i 3.76869 + 2.17585i
\(885\) 0 0
\(886\) 983.867 + 1704.11i 1.11046 + 1.92337i
\(887\) 1068.20 286.223i 1.20428 0.322686i 0.399766 0.916617i \(-0.369091\pi\)
0.804516 + 0.593931i \(0.202425\pi\)
\(888\) 0 0
\(889\) 1.84777 + 165.261i 0.00207848 + 0.185895i
\(890\) 1483.88 + 110.247i 1.66729 + 0.123873i
\(891\) 0 0
\(892\) 44.4648 165.945i 0.0498485 0.186037i
\(893\) 788.281 + 211.219i 0.882734 + 0.236528i
\(894\) 0 0
\(895\) −1225.48 + 1055.98i −1.36925 + 1.17986i
\(896\) −771.981 + 1372.32i −0.861585 + 1.53160i
\(897\) 0 0
\(898\) 138.797 + 517.998i 0.154563 + 0.576835i
\(899\) 179.178 103.448i 0.199308 0.115071i
\(900\) 0 0
\(901\) 635.062 1099.96i 0.704841 1.22082i
\(902\) −131.082 131.082i −0.145324 0.145324i
\(903\) 0 0
\(904\) 61.5927i 0.0681336i
\(905\) 212.560 40.3594i 0.234873 0.0445960i
\(906\) 0 0
\(907\) 236.171 881.400i 0.260386 0.971776i −0.704628 0.709577i \(-0.748886\pi\)
0.965014 0.262198i \(-0.0844474\pi\)
\(908\) −570.416 2128.82i −0.628212 2.34452i
\(909\) 0 0
\(910\) −2148.10 + 1065.93i −2.36055 + 1.17135i
\(911\) −269.276 −0.295583 −0.147791 0.989019i \(-0.547216\pi\)
−0.147791 + 0.989019i \(0.547216\pi\)
\(912\) 0 0
\(913\) −28.7633 7.70711i −0.0315042 0.00844153i
\(914\) 1439.21 830.930i 1.57463 0.909113i
\(915\) 0 0
\(916\) 2303.60 2.51485
\(917\) 854.740 239.301i 0.932104 0.260960i
\(918\) 0 0
\(919\) 723.603 + 417.773i 0.787381 + 0.454595i 0.839040 0.544070i \(-0.183117\pi\)
−0.0516585 + 0.998665i \(0.516451\pi\)
\(920\) −552.041 192.771i −0.600045 0.209534i
\(921\) 0 0
\(922\) −1030.09 + 276.013i −1.11724 + 0.299363i
\(923\) 279.815 279.815i 0.303158 0.303158i
\(924\) 0 0
\(925\) 284.280 210.370i 0.307329 0.227427i
\(926\) 252.956 438.132i 0.273170 0.473145i
\(927\) 0 0
\(928\) 309.857 + 83.0260i 0.333898 + 0.0894676i
\(929\) 1433.61 + 827.695i 1.54318 + 0.890953i 0.998636 + 0.0522181i \(0.0166291\pi\)
0.544540 + 0.838735i \(0.316704\pi\)
\(930\) 0 0
\(931\) 678.230 1237.85i 0.728496 1.32959i
\(932\) −1347.70 1347.70i −1.44603 1.44603i
\(933\) 0 0
\(934\) −1343.54 + 775.694i −1.43848 + 0.830507i
\(935\) 141.210 68.1145i 0.151027 0.0728498i
\(936\) 0 0
\(937\) −260.635 260.635i −0.278159 0.278159i 0.554215 0.832374i \(-0.313019\pi\)
−0.832374 + 0.554215i \(0.813019\pi\)
\(938\) 751.554 768.550i 0.801230 0.819350i
\(939\) 0 0
\(940\) −547.881 + 804.699i −0.582852 + 0.856063i
\(941\) 398.010 + 689.374i 0.422965 + 0.732597i 0.996228 0.0867746i \(-0.0276560\pi\)
−0.573263 + 0.819371i \(0.694323\pi\)
\(942\) 0 0
\(943\) 154.359 + 576.074i 0.163689 + 0.610895i
\(944\) 213.874i 0.226562i
\(945\) 0 0
\(946\) −1.94083 −0.00205162
\(947\) −1564.71 + 419.263i −1.65228 + 0.442727i −0.960250 0.279142i \(-0.909950\pi\)
−0.692030 + 0.721869i \(0.743283\pi\)
\(948\) 0 0
\(949\) 2210.05 1275.97i 2.32882 1.34454i
\(950\) −2359.27 + 268.883i −2.48344 + 0.283035i
\(951\) 0 0
\(952\) 442.937 1730.21i 0.465270 1.81745i
\(953\) −935.909 + 935.909i −0.982066 + 0.982066i −0.999842 0.0177757i \(-0.994342\pi\)
0.0177757 + 0.999842i \(0.494342\pi\)
\(954\) 0 0
\(955\) 63.6106 182.162i 0.0666079 0.190746i
\(956\) −196.539 340.415i −0.205585 0.356083i
\(957\) 0 0
\(958\) 215.267 215.267i 0.224704 0.224704i
\(959\) −973.303 + 576.541i −1.01491 + 0.601190i
\(960\) 0 0
\(961\) 344.701 597.039i 0.358689 0.621268i
\(962\) −250.854 + 936.200i −0.260763 + 0.973180i
\(963\) 0 0
\(964\) −58.9276 34.0218i −0.0611282 0.0352924i
\(965\) −1203.97 89.4509i −1.24764 0.0926952i
\(966\) 0 0
\(967\) −469.949 469.949i −0.485987 0.485987i 0.421050 0.907037i \(-0.361662\pi\)
−0.907037 + 0.421050i \(0.861662\pi\)
\(968\) −293.291 1094.58i −0.302986 1.13076i
\(969\) 0 0
\(970\) 1854.22 + 647.489i 1.91157 + 0.667515i
\(971\) −313.617 + 543.200i −0.322983 + 0.559424i −0.981102 0.193490i \(-0.938019\pi\)
0.658119 + 0.752914i \(0.271352\pi\)
\(972\) 0 0
\(973\) −452.795 + 463.035i −0.465360 + 0.475884i
\(974\) 2629.09i 2.69928i
\(975\) 0 0
\(976\) −23.5929 40.8641i −0.0241730 0.0418689i
\(977\) −246.004 + 918.098i −0.251795 + 0.939712i 0.718050 + 0.695991i \(0.245035\pi\)
−0.969845 + 0.243721i \(0.921632\pi\)
\(978\) 0 0
\(979\) 105.052i 0.107305i
\(980\) 1127.34 + 1250.63i 1.15035 + 1.27615i
\(981\) 0 0
\(982\) −1409.23 + 377.602i −1.43506 + 0.384523i
\(983\) −1103.69 295.733i −1.12278 0.300847i −0.350770 0.936462i \(-0.614080\pi\)
−0.772007 + 0.635614i \(0.780747\pi\)
\(984\) 0 0
\(985\) −1270.71 865.165i −1.29006 0.878340i
\(986\) −1115.15 −1.13098
\(987\) 0 0
\(988\) 2908.67 2908.67i 2.94400 2.94400i
\(989\) 5.40746 + 3.12200i 0.00546761 + 0.00315672i
\(990\) 0 0
\(991\) −430.389 745.456i −0.434298 0.752226i 0.562940 0.826498i \(-0.309670\pi\)
−0.997238 + 0.0742715i \(0.976337\pi\)
\(992\) −406.757 + 108.990i −0.410038 + 0.109869i
\(993\) 0 0
\(994\) −383.107 215.512i −0.385420 0.216813i
\(995\) −736.746 + 634.842i −0.740449 + 0.638032i
\(996\) 0 0
\(997\) 92.4269 344.942i 0.0927050 0.345980i −0.903957 0.427624i \(-0.859351\pi\)
0.996661 + 0.0816447i \(0.0260173\pi\)
\(998\) 220.570 + 59.1016i 0.221012 + 0.0592201i
\(999\) 0 0
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 315.3.ca.b.37.15 64
3.2 odd 2 105.3.v.a.37.2 64
5.3 odd 4 inner 315.3.ca.b.163.2 64
7.4 even 3 inner 315.3.ca.b.172.2 64
15.8 even 4 105.3.v.a.58.15 yes 64
21.11 odd 6 105.3.v.a.67.15 yes 64
35.18 odd 12 inner 315.3.ca.b.298.15 64
105.53 even 12 105.3.v.a.88.2 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.v.a.37.2 64 3.2 odd 2
105.3.v.a.58.15 yes 64 15.8 even 4
105.3.v.a.67.15 yes 64 21.11 odd 6
105.3.v.a.88.2 yes 64 105.53 even 12
315.3.ca.b.37.15 64 1.1 even 1 trivial
315.3.ca.b.163.2 64 5.3 odd 4 inner
315.3.ca.b.172.2 64 7.4 even 3 inner
315.3.ca.b.298.15 64 35.18 odd 12 inner