Properties

Label 354.4.c.a.353.20
Level $354$
Weight $4$
Character 354.353
Analytic conductor $20.887$
Analytic rank $0$
Dimension $30$
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] = [354,4,Mod(353,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.353");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 354.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(20.8866761420\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.20
Character \(\chi\) \(=\) 354.353
Dual form 354.4.c.a.353.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +(2.99142 + 4.24869i) q^{3} +4.00000 q^{4} -19.3201i q^{5} +(-5.98284 - 8.49739i) q^{6} +6.85976 q^{7} -8.00000 q^{8} +(-9.10280 + 25.4193i) q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +(2.99142 + 4.24869i) q^{3} +4.00000 q^{4} -19.3201i q^{5} +(-5.98284 - 8.49739i) q^{6} +6.85976 q^{7} -8.00000 q^{8} +(-9.10280 + 25.4193i) q^{9} +38.6403i q^{10} -4.18926 q^{11} +(11.9657 + 16.9948i) q^{12} -24.0853i q^{13} -13.7195 q^{14} +(82.0854 - 57.7947i) q^{15} +16.0000 q^{16} -81.9283i q^{17} +(18.2056 - 50.8385i) q^{18} +122.854 q^{19} -77.2806i q^{20} +(20.5204 + 29.1450i) q^{21} +8.37851 q^{22} -216.823 q^{23} +(-23.9314 - 33.9896i) q^{24} -248.268 q^{25} +48.1705i q^{26} +(-135.229 + 37.3647i) q^{27} +27.4391 q^{28} -136.479i q^{29} +(-164.171 + 115.589i) q^{30} +342.041i q^{31} -32.0000 q^{32} +(-12.5318 - 17.7989i) q^{33} +163.857i q^{34} -132.532i q^{35} +(-36.4112 + 101.677i) q^{36} -346.028i q^{37} -245.708 q^{38} +(102.331 - 72.0492i) q^{39} +154.561i q^{40} -280.955i q^{41} +(-41.0409 - 58.2901i) q^{42} -353.238i q^{43} -16.7570 q^{44} +(491.104 + 175.868i) q^{45} +433.647 q^{46} -88.0361 q^{47} +(47.8627 + 67.9791i) q^{48} -295.944 q^{49} +496.536 q^{50} +(348.088 - 245.082i) q^{51} -96.3411i q^{52} -89.3036i q^{53} +(270.458 - 74.7294i) q^{54} +80.9370i q^{55} -54.8781 q^{56} +(367.509 + 521.970i) q^{57} +272.957i q^{58} +(359.580 + 275.828i) q^{59} +(328.342 - 231.179i) q^{60} -198.413i q^{61} -684.082i q^{62} +(-62.4431 + 174.370i) q^{63} +64.0000 q^{64} -465.331 q^{65} +(25.0637 + 35.5977i) q^{66} -856.105i q^{67} -327.713i q^{68} +(-648.610 - 921.217i) q^{69} +265.063i q^{70} +384.378i q^{71} +(72.8224 - 203.354i) q^{72} -586.003i q^{73} +692.057i q^{74} +(-742.674 - 1054.82i) q^{75} +491.417 q^{76} -28.7373 q^{77} +(-204.662 + 144.098i) q^{78} +417.338 q^{79} -309.122i q^{80} +(-563.278 - 462.773i) q^{81} +561.911i q^{82} +1265.56 q^{83} +(82.0818 + 116.580i) q^{84} -1582.87 q^{85} +706.475i q^{86} +(579.855 - 408.265i) q^{87} +33.5140 q^{88} +329.519 q^{89} +(-982.208 - 351.735i) q^{90} -165.219i q^{91} -867.294 q^{92} +(-1453.23 + 1023.19i) q^{93} +176.072 q^{94} -2373.56i q^{95} +(-95.7255 - 135.958i) q^{96} +49.9128i q^{97} +591.887 q^{98} +(38.1340 - 106.488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 2.99142 + 4.24869i 0.575699 + 0.817662i
\(4\) 4.00000 0.500000
\(5\) 19.3201i 1.72805i −0.503452 0.864023i \(-0.667937\pi\)
0.503452 0.864023i \(-0.332063\pi\)
\(6\) −5.98284 8.49739i −0.407081 0.578174i
\(7\) 6.85976 0.370392 0.185196 0.982702i \(-0.440708\pi\)
0.185196 + 0.982702i \(0.440708\pi\)
\(8\) −8.00000 −0.353553
\(9\) −9.10280 + 25.4193i −0.337141 + 0.941454i
\(10\) 38.6403i 1.22191i
\(11\) −4.18926 −0.114828 −0.0574140 0.998350i \(-0.518285\pi\)
−0.0574140 + 0.998350i \(0.518285\pi\)
\(12\) 11.9657 + 16.9948i 0.287850 + 0.408831i
\(13\) 24.0853i 0.513850i −0.966431 0.256925i \(-0.917291\pi\)
0.966431 0.256925i \(-0.0827093\pi\)
\(14\) −13.7195 −0.261907
\(15\) 82.0854 57.7947i 1.41296 0.994835i
\(16\) 16.0000 0.250000
\(17\) 81.9283i 1.16885i −0.811446 0.584427i \(-0.801319\pi\)
0.811446 0.584427i \(-0.198681\pi\)
\(18\) 18.2056 50.8385i 0.238395 0.665709i
\(19\) 122.854 1.48340 0.741702 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(20\) 77.2806i 0.864023i
\(21\) 20.5204 + 29.1450i 0.213235 + 0.302856i
\(22\) 8.37851 0.0811957
\(23\) −216.823 −1.96569 −0.982844 0.184439i \(-0.940953\pi\)
−0.982844 + 0.184439i \(0.940953\pi\)
\(24\) −23.9314 33.9896i −0.203540 0.289087i
\(25\) −248.268 −1.98615
\(26\) 48.1705i 0.363347i
\(27\) −135.229 + 37.3647i −0.963883 + 0.266327i
\(28\) 27.4391 0.185196
\(29\) 136.479i 0.873911i −0.899483 0.436956i \(-0.856057\pi\)
0.899483 0.436956i \(-0.143943\pi\)
\(30\) −164.171 + 115.589i −0.999112 + 0.703455i
\(31\) 342.041i 1.98169i 0.135002 + 0.990845i \(0.456896\pi\)
−0.135002 + 0.990845i \(0.543104\pi\)
\(32\) −32.0000 −0.176777
\(33\) −12.5318 17.7989i −0.0661064 0.0938904i
\(34\) 163.857i 0.826505i
\(35\) 132.532i 0.640055i
\(36\) −36.4112 + 101.677i −0.168570 + 0.470727i
\(37\) 346.028i 1.53748i −0.639562 0.768740i \(-0.720884\pi\)
0.639562 0.768740i \(-0.279116\pi\)
\(38\) −245.708 −1.04893
\(39\) 102.331 72.0492i 0.420155 0.295823i
\(40\) 154.561i 0.610957i
\(41\) 280.955i 1.07019i −0.844791 0.535096i \(-0.820276\pi\)
0.844791 0.535096i \(-0.179724\pi\)
\(42\) −41.0409 58.2901i −0.150780 0.214151i
\(43\) 353.238i 1.25275i −0.779522 0.626375i \(-0.784538\pi\)
0.779522 0.626375i \(-0.215462\pi\)
\(44\) −16.7570 −0.0574140
\(45\) 491.104 + 175.868i 1.62688 + 0.582595i
\(46\) 433.647 1.38995
\(47\) −88.0361 −0.273221 −0.136610 0.990625i \(-0.543621\pi\)
−0.136610 + 0.990625i \(0.543621\pi\)
\(48\) 47.8627 + 67.9791i 0.143925 + 0.204415i
\(49\) −295.944 −0.862809
\(50\) 496.536 1.40442
\(51\) 348.088 245.082i 0.955728 0.672909i
\(52\) 96.3411i 0.256925i
\(53\) 89.3036i 0.231449i −0.993281 0.115724i \(-0.963081\pi\)
0.993281 0.115724i \(-0.0369190\pi\)
\(54\) 270.458 74.7294i 0.681568 0.188322i
\(55\) 80.9370i 0.198428i
\(56\) −54.8781 −0.130954
\(57\) 367.509 + 521.970i 0.853995 + 1.21292i
\(58\) 272.957i 0.617948i
\(59\) 359.580 + 275.828i 0.793446 + 0.608640i
\(60\) 328.342 231.179i 0.706479 0.497418i
\(61\) 198.413i 0.416462i −0.978080 0.208231i \(-0.933229\pi\)
0.978080 0.208231i \(-0.0667706\pi\)
\(62\) 684.082i 1.40127i
\(63\) −62.4431 + 174.370i −0.124874 + 0.348708i
\(64\) 64.0000 0.125000
\(65\) −465.331 −0.887957
\(66\) 25.0637 + 35.5977i 0.0467443 + 0.0663906i
\(67\) 856.105i 1.56104i −0.625129 0.780521i \(-0.714954\pi\)
0.625129 0.780521i \(-0.285046\pi\)
\(68\) 327.713i 0.584427i
\(69\) −648.610 921.217i −1.13164 1.60727i
\(70\) 265.063i 0.452588i
\(71\) 384.378i 0.642497i 0.946995 + 0.321249i \(0.104103\pi\)
−0.946995 + 0.321249i \(0.895897\pi\)
\(72\) 72.8224 203.354i 0.119197 0.332854i
\(73\) 586.003i 0.939540i −0.882789 0.469770i \(-0.844337\pi\)
0.882789 0.469770i \(-0.155663\pi\)
\(74\) 692.057i 1.08716i
\(75\) −742.674 1054.82i −1.14342 1.62399i
\(76\) 491.417 0.741702
\(77\) −28.7373 −0.0425314
\(78\) −204.662 + 144.098i −0.297095 + 0.209178i
\(79\) 417.338 0.594357 0.297179 0.954822i \(-0.403954\pi\)
0.297179 + 0.954822i \(0.403954\pi\)
\(80\) 309.122i 0.432012i
\(81\) −563.278 462.773i −0.772672 0.634805i
\(82\) 561.911i 0.756740i
\(83\) 1265.56 1.67366 0.836828 0.547465i \(-0.184407\pi\)
0.836828 + 0.547465i \(0.184407\pi\)
\(84\) 82.0818 + 116.580i 0.106617 + 0.151428i
\(85\) −1582.87 −2.01984
\(86\) 706.475i 0.885828i
\(87\) 579.855 408.265i 0.714564 0.503110i
\(88\) 33.5140 0.0405978
\(89\) 329.519 0.392460 0.196230 0.980558i \(-0.437130\pi\)
0.196230 + 0.980558i \(0.437130\pi\)
\(90\) −982.208 351.735i −1.15038 0.411957i
\(91\) 165.219i 0.190326i
\(92\) −867.294 −0.982844
\(93\) −1453.23 + 1023.19i −1.62035 + 1.14086i
\(94\) 176.072 0.193196
\(95\) 2373.56i 2.56339i
\(96\) −95.7255 135.958i −0.101770 0.144544i
\(97\) 49.9128i 0.0522462i 0.999659 + 0.0261231i \(0.00831618\pi\)
−0.999659 + 0.0261231i \(0.991684\pi\)
\(98\) 591.887 0.610098
\(99\) 38.1340 106.488i 0.0387132 0.108105i
\(100\) −993.073 −0.993073
\(101\) −351.292 −0.346088 −0.173044 0.984914i \(-0.555360\pi\)
−0.173044 + 0.984914i \(0.555360\pi\)
\(102\) −696.177 + 490.164i −0.675801 + 0.475818i
\(103\) 1144.52i 1.09488i 0.836844 + 0.547441i \(0.184398\pi\)
−0.836844 + 0.547441i \(0.815602\pi\)
\(104\) 192.682i 0.181673i
\(105\) 563.087 396.458i 0.523349 0.368479i
\(106\) 178.607i 0.163659i
\(107\) 372.797i 0.336819i −0.985717 0.168409i \(-0.946137\pi\)
0.985717 0.168409i \(-0.0538630\pi\)
\(108\) −540.916 + 149.459i −0.481941 + 0.133164i
\(109\) 1401.55i 1.23160i −0.787904 0.615798i \(-0.788834\pi\)
0.787904 0.615798i \(-0.211166\pi\)
\(110\) 161.874i 0.140310i
\(111\) 1470.17 1035.12i 1.25714 0.885125i
\(112\) 109.756 0.0925981
\(113\) 1636.81 1.36264 0.681319 0.731987i \(-0.261407\pi\)
0.681319 + 0.731987i \(0.261407\pi\)
\(114\) −735.017 1043.94i −0.603865 0.857666i
\(115\) 4189.06i 3.39680i
\(116\) 545.914i 0.436956i
\(117\) 612.230 + 219.243i 0.483766 + 0.173240i
\(118\) −719.160 551.657i −0.561051 0.430374i
\(119\) 562.009i 0.432935i
\(120\) −656.683 + 462.358i −0.499556 + 0.351727i
\(121\) −1313.45 −0.986815
\(122\) 396.826i 0.294483i
\(123\) 1193.69 840.456i 0.875054 0.616108i
\(124\) 1368.16i 0.990845i
\(125\) 2381.56i 1.70410i
\(126\) 124.886 348.740i 0.0882996 0.246573i
\(127\) −2385.37 −1.66667 −0.833337 0.552765i \(-0.813573\pi\)
−0.833337 + 0.552765i \(0.813573\pi\)
\(128\) −128.000 −0.0883883
\(129\) 1500.80 1056.68i 1.02433 0.721207i
\(130\) 930.662 0.627880
\(131\) −613.343 −0.409069 −0.204535 0.978859i \(-0.565568\pi\)
−0.204535 + 0.978859i \(0.565568\pi\)
\(132\) −50.1273 71.1955i −0.0330532 0.0469452i
\(133\) 842.751 0.549442
\(134\) 1712.21i 1.10382i
\(135\) 721.891 + 2612.64i 0.460226 + 1.66563i
\(136\) 655.426i 0.413253i
\(137\) 1818.42i 1.13400i 0.823716 + 0.567002i \(0.191897\pi\)
−0.823716 + 0.567002i \(0.808103\pi\)
\(138\) 1297.22 + 1842.43i 0.800194 + 1.13651i
\(139\) 1979.15 1.20769 0.603847 0.797100i \(-0.293634\pi\)
0.603847 + 0.797100i \(0.293634\pi\)
\(140\) 530.127i 0.320028i
\(141\) −263.353 374.038i −0.157293 0.223402i
\(142\) 768.757i 0.454314i
\(143\) 100.899i 0.0590044i
\(144\) −145.645 + 406.708i −0.0842852 + 0.235364i
\(145\) −2636.79 −1.51016
\(146\) 1172.01i 0.664355i
\(147\) −885.292 1257.37i −0.496719 0.705486i
\(148\) 1384.11i 0.768740i
\(149\) −2341.67 −1.28750 −0.643749 0.765237i \(-0.722622\pi\)
−0.643749 + 0.765237i \(0.722622\pi\)
\(150\) 1485.35 + 2109.63i 0.808522 + 1.14834i
\(151\) 58.6798i 0.0316245i −0.999875 0.0158122i \(-0.994967\pi\)
0.999875 0.0158122i \(-0.00503340\pi\)
\(152\) −982.834 −0.524463
\(153\) 2082.56 + 745.777i 1.10042 + 0.394069i
\(154\) 57.4746 0.0300743
\(155\) 6608.29 3.42445
\(156\) 409.324 288.197i 0.210078 0.147912i
\(157\) 816.575i 0.415094i 0.978225 + 0.207547i \(0.0665480\pi\)
−0.978225 + 0.207547i \(0.933452\pi\)
\(158\) −834.676 −0.420274
\(159\) 379.424 267.145i 0.189247 0.133245i
\(160\) 618.245i 0.305478i
\(161\) −1487.36 −0.728076
\(162\) 1126.56 + 925.546i 0.546362 + 0.448875i
\(163\) 743.864 0.357447 0.178724 0.983899i \(-0.442803\pi\)
0.178724 + 0.983899i \(0.442803\pi\)
\(164\) 1123.82i 0.535096i
\(165\) −343.877 + 242.117i −0.162247 + 0.114235i
\(166\) −2531.12 −1.18345
\(167\) 3395.96i 1.57358i 0.617224 + 0.786788i \(0.288257\pi\)
−0.617224 + 0.786788i \(0.711743\pi\)
\(168\) −164.164 233.160i −0.0753898 0.107076i
\(169\) 1616.90 0.735958
\(170\) 3165.73 1.42824
\(171\) −1118.32 + 3122.86i −0.500116 + 1.39656i
\(172\) 1412.95i 0.626375i
\(173\) 3561.30 1.56509 0.782545 0.622594i \(-0.213921\pi\)
0.782545 + 0.622594i \(0.213921\pi\)
\(174\) −1159.71 + 816.529i −0.505273 + 0.355752i
\(175\) −1703.06 −0.735653
\(176\) −67.0281 −0.0287070
\(177\) −96.2552 + 2352.86i −0.0408756 + 0.999164i
\(178\) −659.038 −0.277511
\(179\) −439.482 −0.183511 −0.0917553 0.995782i \(-0.529248\pi\)
−0.0917553 + 0.995782i \(0.529248\pi\)
\(180\) 1964.42 + 703.470i 0.813438 + 0.291298i
\(181\) −1254.06 −0.514990 −0.257495 0.966280i \(-0.582897\pi\)
−0.257495 + 0.966280i \(0.582897\pi\)
\(182\) 330.439i 0.134581i
\(183\) 842.996 593.537i 0.340525 0.239757i
\(184\) 1734.59 0.694976
\(185\) −6685.32 −2.65684
\(186\) 2906.46 2046.38i 1.14576 0.806708i
\(187\) 343.219i 0.134217i
\(188\) −352.144 −0.136610
\(189\) −927.639 + 256.313i −0.357015 + 0.0986456i
\(190\) 4747.12i 1.81259i
\(191\) −1864.36 −0.706283 −0.353141 0.935570i \(-0.614887\pi\)
−0.353141 + 0.935570i \(0.614887\pi\)
\(192\) 191.451 + 271.916i 0.0719624 + 0.102208i
\(193\) 2674.19 0.997369 0.498684 0.866784i \(-0.333817\pi\)
0.498684 + 0.866784i \(0.333817\pi\)
\(194\) 99.8256i 0.0369436i
\(195\) −1392.00 1977.05i −0.511196 0.726048i
\(196\) −1183.77 −0.431405
\(197\) 1280.49i 0.463104i −0.972823 0.231552i \(-0.925620\pi\)
0.972823 0.231552i \(-0.0743803\pi\)
\(198\) −76.2679 + 212.976i −0.0273744 + 0.0764420i
\(199\) −1491.41 −0.531271 −0.265635 0.964074i \(-0.585582\pi\)
−0.265635 + 0.964074i \(0.585582\pi\)
\(200\) 1986.15 0.702208
\(201\) 3637.33 2560.97i 1.27640 0.898691i
\(202\) 702.584 0.244721
\(203\) 936.210i 0.323690i
\(204\) 1392.35 980.328i 0.477864 0.336454i
\(205\) −5428.10 −1.84934
\(206\) 2289.04i 0.774199i
\(207\) 1973.70 5511.49i 0.662714 1.85061i
\(208\) 385.364i 0.128463i
\(209\) −514.668 −0.170336
\(210\) −1126.17 + 792.916i −0.370063 + 0.260554i
\(211\) 1360.50i 0.443889i 0.975059 + 0.221945i \(0.0712404\pi\)
−0.975059 + 0.221945i \(0.928760\pi\)
\(212\) 357.214i 0.115724i
\(213\) −1633.11 + 1149.84i −0.525345 + 0.369885i
\(214\) 745.593i 0.238167i
\(215\) −6824.61 −2.16481
\(216\) 1081.83 298.917i 0.340784 0.0941609i
\(217\) 2346.32i 0.734003i
\(218\) 2803.10i 0.870870i
\(219\) 2489.75 1752.98i 0.768226 0.540892i
\(220\) 323.748i 0.0992141i
\(221\) −1973.26 −0.600616
\(222\) −2940.34 + 2070.23i −0.888930 + 0.625878i
\(223\) −4065.57 −1.22086 −0.610428 0.792072i \(-0.709003\pi\)
−0.610428 + 0.792072i \(0.709003\pi\)
\(224\) −219.512 −0.0654768
\(225\) 2259.94 6310.79i 0.669611 1.86986i
\(226\) −3273.62 −0.963530
\(227\) −1176.48 −0.343990 −0.171995 0.985098i \(-0.555021\pi\)
−0.171995 + 0.985098i \(0.555021\pi\)
\(228\) 1470.03 + 2087.88i 0.426997 + 0.606461i
\(229\) 4445.18i 1.28273i 0.767235 + 0.641367i \(0.221632\pi\)
−0.767235 + 0.641367i \(0.778368\pi\)
\(230\) 8378.12i 2.40190i
\(231\) −85.9654 122.096i −0.0244853 0.0347763i
\(232\) 1091.83i 0.308974i
\(233\) −452.890 −0.127338 −0.0636691 0.997971i \(-0.520280\pi\)
−0.0636691 + 0.997971i \(0.520280\pi\)
\(234\) −1224.46 438.487i −0.342074 0.122499i
\(235\) 1700.87i 0.472138i
\(236\) 1438.32 + 1103.31i 0.396723 + 0.304320i
\(237\) 1248.43 + 1773.14i 0.342171 + 0.485983i
\(238\) 1124.02i 0.306131i
\(239\) 2596.48i 0.702729i 0.936239 + 0.351364i \(0.114282\pi\)
−0.936239 + 0.351364i \(0.885718\pi\)
\(240\) 1313.37 924.715i 0.353239 0.248709i
\(241\) 4352.05 1.16324 0.581618 0.813462i \(-0.302420\pi\)
0.581618 + 0.813462i \(0.302420\pi\)
\(242\) 2626.90 0.697783
\(243\) 281.180 3777.54i 0.0742293 0.997241i
\(244\) 793.652i 0.208231i
\(245\) 5717.67i 1.49097i
\(246\) −2387.39 + 1680.91i −0.618757 + 0.435654i
\(247\) 2958.98i 0.762247i
\(248\) 2736.33i 0.700633i
\(249\) 3785.83 + 5376.99i 0.963523 + 1.36848i
\(250\) 4763.12i 1.20498i
\(251\) 4403.08i 1.10725i −0.832766 0.553625i \(-0.813244\pi\)
0.832766 0.553625i \(-0.186756\pi\)
\(252\) −249.772 + 697.481i −0.0624372 + 0.174354i
\(253\) 908.329 0.225716
\(254\) 4770.75 1.17852
\(255\) −4735.02 6725.12i −1.16282 1.65154i
\(256\) 256.000 0.0625000
\(257\) 883.840i 0.214523i −0.994231 0.107262i \(-0.965792\pi\)
0.994231 0.107262i \(-0.0342082\pi\)
\(258\) −3001.60 + 2113.37i −0.724307 + 0.509970i
\(259\) 2373.67i 0.569471i
\(260\) −1861.32 −0.443978
\(261\) 3469.18 + 1242.34i 0.822747 + 0.294631i
\(262\) 1226.69 0.289256
\(263\) 4860.77i 1.13965i 0.821766 + 0.569825i \(0.192989\pi\)
−0.821766 + 0.569825i \(0.807011\pi\)
\(264\) 100.255 + 142.391i 0.0233721 + 0.0331953i
\(265\) −1725.36 −0.399955
\(266\) −1685.50 −0.388514
\(267\) 985.731 + 1400.03i 0.225939 + 0.320900i
\(268\) 3424.42i 0.780521i
\(269\) 3635.08 0.823921 0.411960 0.911202i \(-0.364844\pi\)
0.411960 + 0.911202i \(0.364844\pi\)
\(270\) −1443.78 5225.29i −0.325429 1.17778i
\(271\) −1565.65 −0.350947 −0.175473 0.984484i \(-0.556146\pi\)
−0.175473 + 0.984484i \(0.556146\pi\)
\(272\) 1310.85i 0.292214i
\(273\) 701.966 494.240i 0.155622 0.109571i
\(274\) 3636.85i 0.801862i
\(275\) 1040.06 0.228065
\(276\) −2594.44 3684.87i −0.565822 0.803634i
\(277\) 5463.54 1.18510 0.592549 0.805534i \(-0.298122\pi\)
0.592549 + 0.805534i \(0.298122\pi\)
\(278\) −3958.30 −0.853968
\(279\) −8694.43 3113.53i −1.86567 0.668109i
\(280\) 1060.25i 0.226294i
\(281\) 2307.25i 0.489818i −0.969546 0.244909i \(-0.921242\pi\)
0.969546 0.244909i \(-0.0787581\pi\)
\(282\) 526.706 + 748.077i 0.111223 + 0.157969i
\(283\) 1493.24i 0.313653i 0.987626 + 0.156827i \(0.0501264\pi\)
−0.987626 + 0.156827i \(0.949874\pi\)
\(284\) 1537.51i 0.321249i
\(285\) 10084.5 7100.32i 2.09599 1.47574i
\(286\) 201.799i 0.0417224i
\(287\) 1927.29i 0.396391i
\(288\) 291.290 813.416i 0.0595987 0.166427i
\(289\) −1799.25 −0.366221
\(290\) 5273.57 1.06784
\(291\) −212.064 + 149.310i −0.0427197 + 0.0300781i
\(292\) 2344.01i 0.469770i
\(293\) 34.7500i 0.00692874i 0.999994 + 0.00346437i \(0.00110274\pi\)
−0.999994 + 0.00346437i \(0.998897\pi\)
\(294\) 1770.58 + 2514.75i 0.351233 + 0.498854i
\(295\) 5329.04 6947.14i 1.05176 1.37111i
\(296\) 2768.23i 0.543581i
\(297\) 566.509 156.530i 0.110681 0.0305818i
\(298\) 4683.34 0.910399
\(299\) 5222.25i 1.01007i
\(300\) −2970.70 4219.26i −0.571711 0.811997i
\(301\) 2423.13i 0.464009i
\(302\) 117.360i 0.0223619i
\(303\) −1050.86 1492.53i −0.199242 0.282983i
\(304\) 1965.67 0.370851
\(305\) −3833.37 −0.719666
\(306\) −4165.11 1491.55i −0.778117 0.278649i
\(307\) 5355.26 0.995573 0.497786 0.867300i \(-0.334146\pi\)
0.497786 + 0.867300i \(0.334146\pi\)
\(308\) −114.949 −0.0212657
\(309\) −4862.72 + 3423.74i −0.895244 + 0.630323i
\(310\) −13216.6 −2.42145
\(311\) 6528.18i 1.19029i 0.803620 + 0.595143i \(0.202905\pi\)
−0.803620 + 0.595143i \(0.797095\pi\)
\(312\) −818.647 + 576.393i −0.148547 + 0.104589i
\(313\) 528.968i 0.0955240i −0.998859 0.0477620i \(-0.984791\pi\)
0.998859 0.0477620i \(-0.0152089\pi\)
\(314\) 1633.15i 0.293516i
\(315\) 3368.86 + 1206.41i 0.602583 + 0.215789i
\(316\) 1669.35 0.297179
\(317\) 1736.12i 0.307603i −0.988102 0.153802i \(-0.950848\pi\)
0.988102 0.153802i \(-0.0491516\pi\)
\(318\) −758.847 + 534.289i −0.133818 + 0.0942184i
\(319\) 571.743i 0.100349i
\(320\) 1236.49i 0.216006i
\(321\) 1583.90 1115.19i 0.275404 0.193906i
\(322\) 2974.72 0.514827
\(323\) 10065.2i 1.73388i
\(324\) −2253.11 1851.09i −0.386336 0.317403i
\(325\) 5979.60i 1.02058i
\(326\) −1487.73 −0.252754
\(327\) 5954.75 4192.62i 1.00703 0.709029i
\(328\) 2247.64i 0.378370i
\(329\) −603.907 −0.101199
\(330\) 687.753 484.233i 0.114726 0.0807763i
\(331\) −4528.41 −0.751975 −0.375988 0.926625i \(-0.622697\pi\)
−0.375988 + 0.926625i \(0.622697\pi\)
\(332\) 5062.25 0.836828
\(333\) 8795.79 + 3149.83i 1.44747 + 0.518347i
\(334\) 6791.92i 1.11269i
\(335\) −16540.1 −2.69755
\(336\) 328.327 + 466.321i 0.0533087 + 0.0757139i
\(337\) 2199.10i 0.355467i 0.984079 + 0.177734i \(0.0568766\pi\)
−0.984079 + 0.177734i \(0.943123\pi\)
\(338\) −3233.80 −0.520401
\(339\) 4896.38 + 6954.30i 0.784469 + 1.11418i
\(340\) −6331.47 −1.00992
\(341\) 1432.90i 0.227554i
\(342\) 2236.64 6245.73i 0.353636 0.987515i
\(343\) −4383.00 −0.689971
\(344\) 2825.90i 0.442914i
\(345\) −17798.0 + 12531.2i −2.77743 + 1.95554i
\(346\) −7122.60 −1.10669
\(347\) 3235.70 0.500580 0.250290 0.968171i \(-0.419474\pi\)
0.250290 + 0.968171i \(0.419474\pi\)
\(348\) 2319.42 1633.06i 0.357282 0.251555i
\(349\) 3400.91i 0.521623i 0.965390 + 0.260812i \(0.0839901\pi\)
−0.965390 + 0.260812i \(0.916010\pi\)
\(350\) 3406.12 0.520185
\(351\) 899.938 + 3257.03i 0.136852 + 0.495291i
\(352\) 134.056 0.0202989
\(353\) 11542.1 1.74029 0.870144 0.492798i \(-0.164026\pi\)
0.870144 + 0.492798i \(0.164026\pi\)
\(354\) 192.510 4705.73i 0.0289034 0.706516i
\(355\) 7426.25 1.11027
\(356\) 1318.08 0.196230
\(357\) 2387.80 1681.20i 0.353994 0.249240i
\(358\) 878.963 0.129762
\(359\) 6857.58i 1.00816i 0.863657 + 0.504079i \(0.168168\pi\)
−0.863657 + 0.504079i \(0.831832\pi\)
\(360\) −3928.83 1406.94i −0.575188 0.205979i
\(361\) 8234.15 1.20049
\(362\) 2508.11 0.364153
\(363\) −3929.08 5580.45i −0.568108 0.806880i
\(364\) 660.877i 0.0951631i
\(365\) −11321.7 −1.62357
\(366\) −1685.99 + 1187.07i −0.240787 + 0.169534i
\(367\) 5058.19i 0.719443i −0.933060 0.359722i \(-0.882872\pi\)
0.933060 0.359722i \(-0.117128\pi\)
\(368\) −3469.18 −0.491422
\(369\) 7141.68 + 2557.48i 1.00754 + 0.360805i
\(370\) 13370.6 1.87867
\(371\) 612.602i 0.0857269i
\(372\) −5812.91 + 4092.76i −0.810176 + 0.570429i
\(373\) 11615.2 1.61237 0.806185 0.591663i \(-0.201528\pi\)
0.806185 + 0.591663i \(0.201528\pi\)
\(374\) 686.437i 0.0949059i
\(375\) −10118.5 + 7124.24i −1.39338 + 0.981052i
\(376\) 704.289 0.0965982
\(377\) −3287.12 −0.449059
\(378\) 1855.28 512.626i 0.252448 0.0697530i
\(379\) 5801.94 0.786347 0.393174 0.919464i \(-0.371377\pi\)
0.393174 + 0.919464i \(0.371377\pi\)
\(380\) 9494.25i 1.28170i
\(381\) −7135.65 10134.7i −0.959503 1.36278i
\(382\) 3728.71 0.499417
\(383\) 7103.14i 0.947659i −0.880616 0.473830i \(-0.842871\pi\)
0.880616 0.473830i \(-0.157129\pi\)
\(384\) −382.902 543.833i −0.0508851 0.0722718i
\(385\) 555.209i 0.0734963i
\(386\) −5348.37 −0.705246
\(387\) 8979.04 + 3215.45i 1.17941 + 0.422353i
\(388\) 199.651i 0.0261231i
\(389\) 10123.9i 1.31954i 0.751466 + 0.659771i \(0.229347\pi\)
−0.751466 + 0.659771i \(0.770653\pi\)
\(390\) 2784.00 + 3954.10i 0.361470 + 0.513394i
\(391\) 17764.0i 2.29760i
\(392\) 2367.55 0.305049
\(393\) −1834.77 2605.91i −0.235501 0.334480i
\(394\) 2560.99i 0.327464i
\(395\) 8063.04i 1.02708i
\(396\) 152.536 425.951i 0.0193566 0.0540527i
\(397\) 12298.8i 1.55480i −0.629003 0.777402i \(-0.716537\pi\)
0.629003 0.777402i \(-0.283463\pi\)
\(398\) 2982.81 0.375665
\(399\) 2521.02 + 3580.59i 0.316313 + 0.449258i
\(400\) −3972.29 −0.496536
\(401\) 366.551 0.0456476 0.0228238 0.999740i \(-0.492734\pi\)
0.0228238 + 0.999740i \(0.492734\pi\)
\(402\) −7274.65 + 5121.94i −0.902554 + 0.635470i
\(403\) 8238.15 1.01829
\(404\) −1405.17 −0.173044
\(405\) −8940.85 + 10882.6i −1.09697 + 1.33521i
\(406\) 1872.42i 0.228883i
\(407\) 1449.60i 0.176546i
\(408\) −2784.71 + 1960.66i −0.337901 + 0.237909i
\(409\) 8767.45i 1.05996i 0.848011 + 0.529979i \(0.177800\pi\)
−0.848011 + 0.529979i \(0.822200\pi\)
\(410\) 10856.2 1.30768
\(411\) −7725.93 + 5439.67i −0.927231 + 0.652845i
\(412\) 4578.08i 0.547441i
\(413\) 2466.63 + 1892.12i 0.293886 + 0.225436i
\(414\) −3947.40 + 11023.0i −0.468609 + 1.30858i
\(415\) 24450.9i 2.89216i
\(416\) 770.728i 0.0908367i
\(417\) 5920.47 + 8408.81i 0.695268 + 0.987485i
\(418\) 1029.34 0.120446
\(419\) 4236.17 0.493915 0.246958 0.969026i \(-0.420569\pi\)
0.246958 + 0.969026i \(0.420569\pi\)
\(420\) 2252.35 1585.83i 0.261674 0.184240i
\(421\) 4501.94i 0.521167i −0.965451 0.260583i \(-0.916085\pi\)
0.965451 0.260583i \(-0.0839149\pi\)
\(422\) 2721.00i 0.313877i
\(423\) 801.375 2237.81i 0.0921139 0.257225i
\(424\) 714.429i 0.0818295i
\(425\) 20340.2i 2.32152i
\(426\) 3266.21 2299.67i 0.371475 0.261548i
\(427\) 1361.07i 0.154254i
\(428\) 1491.19i 0.168409i
\(429\) −428.690 + 301.832i −0.0482456 + 0.0339688i
\(430\) 13649.2 1.53075
\(431\) 11871.0 1.32669 0.663347 0.748312i \(-0.269136\pi\)
0.663347 + 0.748312i \(0.269136\pi\)
\(432\) −2163.66 + 597.835i −0.240971 + 0.0665818i
\(433\) −4824.35 −0.535435 −0.267718 0.963497i \(-0.586269\pi\)
−0.267718 + 0.963497i \(0.586269\pi\)
\(434\) 4692.64i 0.519019i
\(435\) −7887.73 11202.9i −0.869397 1.23480i
\(436\) 5606.20i 0.615798i
\(437\) −26637.7 −2.91591
\(438\) −4979.49 + 3505.96i −0.543218 + 0.382469i
\(439\) −8521.83 −0.926480 −0.463240 0.886233i \(-0.653313\pi\)
−0.463240 + 0.886233i \(0.653313\pi\)
\(440\) 647.496i 0.0701549i
\(441\) 2693.92 7522.67i 0.290888 0.812296i
\(442\) 3946.53 0.424700
\(443\) −6506.99 −0.697870 −0.348935 0.937147i \(-0.613457\pi\)
−0.348935 + 0.937147i \(0.613457\pi\)
\(444\) 5880.68 4140.47i 0.628569 0.442563i
\(445\) 6366.36i 0.678190i
\(446\) 8131.15 0.863276
\(447\) −7004.93 9949.05i −0.741212 1.05274i
\(448\) 439.025 0.0462991
\(449\) 3008.46i 0.316210i −0.987422 0.158105i \(-0.949462\pi\)
0.987422 0.158105i \(-0.0505384\pi\)
\(450\) −4519.87 + 12621.6i −0.473486 + 1.32219i
\(451\) 1176.99i 0.122888i
\(452\) 6547.24 0.681319
\(453\) 249.313 175.536i 0.0258581 0.0182062i
\(454\) 2352.96 0.243238
\(455\) −3192.06 −0.328893
\(456\) −2940.07 4175.76i −0.301933 0.428833i
\(457\) 6371.84i 0.652215i 0.945333 + 0.326107i \(0.105737\pi\)
−0.945333 + 0.326107i \(0.894263\pi\)
\(458\) 8890.36i 0.907029i
\(459\) 3061.22 + 11079.1i 0.311298 + 1.12664i
\(460\) 16756.2i 1.69840i
\(461\) 12246.1i 1.23722i −0.785699 0.618609i \(-0.787696\pi\)
0.785699 0.618609i \(-0.212304\pi\)
\(462\) 171.931 + 244.192i 0.0173137 + 0.0245906i
\(463\) 8205.00i 0.823582i −0.911278 0.411791i \(-0.864903\pi\)
0.911278 0.411791i \(-0.135097\pi\)
\(464\) 2183.66i 0.218478i
\(465\) 19768.2 + 28076.6i 1.97146 + 2.80004i
\(466\) 905.780 0.0900418
\(467\) 6329.50 0.627183 0.313592 0.949558i \(-0.398468\pi\)
0.313592 + 0.949558i \(0.398468\pi\)
\(468\) 2448.92 + 876.974i 0.241883 + 0.0866199i
\(469\) 5872.68i 0.578198i
\(470\) 3401.74i 0.333852i
\(471\) −3469.38 + 2442.72i −0.339406 + 0.238969i
\(472\) −2876.64 2206.63i −0.280526 0.215187i
\(473\) 1479.80i 0.143851i
\(474\) −2496.87 3546.28i −0.241951 0.343642i
\(475\) −30500.8 −2.94626
\(476\) 2248.04i 0.216467i
\(477\) 2270.03 + 812.913i 0.217899 + 0.0780309i
\(478\) 5192.95i 0.496904i
\(479\) 4833.02i 0.461015i −0.973071 0.230508i \(-0.925961\pi\)
0.973071 0.230508i \(-0.0740386\pi\)
\(480\) −2626.73 + 1849.43i −0.249778 + 0.175864i
\(481\) −8334.19 −0.790034
\(482\) −8704.10 −0.822533
\(483\) −4449.31 6319.33i −0.419153 0.595320i
\(484\) −5253.80 −0.493407
\(485\) 964.323 0.0902838
\(486\) −562.361 + 7555.09i −0.0524881 + 0.705156i
\(487\) 16547.6 1.53972 0.769858 0.638215i \(-0.220327\pi\)
0.769858 + 0.638215i \(0.220327\pi\)
\(488\) 1587.30i 0.147242i
\(489\) 2225.21 + 3160.45i 0.205782 + 0.292271i
\(490\) 11435.3i 1.05428i
\(491\) 12716.8i 1.16884i −0.811451 0.584421i \(-0.801322\pi\)
0.811451 0.584421i \(-0.198678\pi\)
\(492\) 4774.77 3361.82i 0.437527 0.308054i
\(493\) −11181.5 −1.02148
\(494\) 5917.95i 0.538990i
\(495\) −2057.36 736.754i −0.186811 0.0668982i
\(496\) 5472.66i 0.495423i
\(497\) 2636.74i 0.237976i
\(498\) −7571.66 10754.0i −0.681314 0.967665i
\(499\) −2473.28 −0.221883 −0.110941 0.993827i \(-0.535387\pi\)
−0.110941 + 0.993827i \(0.535387\pi\)
\(500\) 9526.24i 0.852052i
\(501\) −14428.4 + 10158.7i −1.28665 + 0.905906i
\(502\) 8806.16i 0.782944i
\(503\) 6251.46 0.554153 0.277076 0.960848i \(-0.410635\pi\)
0.277076 + 0.960848i \(0.410635\pi\)
\(504\) 499.545 1394.96i 0.0441498 0.123287i
\(505\) 6787.02i 0.598056i
\(506\) −1816.66 −0.159605
\(507\) 4836.83 + 6869.71i 0.423690 + 0.601765i
\(508\) −9541.49 −0.833337
\(509\) 7718.65 0.672148 0.336074 0.941836i \(-0.390901\pi\)
0.336074 + 0.941836i \(0.390901\pi\)
\(510\) 9470.04 + 13450.2i 0.822236 + 1.16782i
\(511\) 4019.84i 0.347999i
\(512\) −512.000 −0.0441942
\(513\) −16613.4 + 4590.41i −1.42983 + 0.395071i
\(514\) 1767.68i 0.151691i
\(515\) 22112.3 1.89201
\(516\) 6003.20 4226.73i 0.512163 0.360604i
\(517\) 368.806 0.0313734
\(518\) 4747.35i 0.402677i
\(519\) 10653.3 + 15130.9i 0.901021 + 1.27971i
\(520\) 3722.65 0.313940
\(521\) 8059.77i 0.677745i 0.940832 + 0.338872i \(0.110045\pi\)
−0.940832 + 0.338872i \(0.889955\pi\)
\(522\) −6938.37 2484.67i −0.581770 0.208336i
\(523\) 12070.8 1.00922 0.504608 0.863349i \(-0.331637\pi\)
0.504608 + 0.863349i \(0.331637\pi\)
\(524\) −2453.37 −0.204535
\(525\) −5094.57 7235.79i −0.423515 0.601515i
\(526\) 9721.54i 0.805854i
\(527\) 28022.8 2.31631
\(528\) −200.509 284.782i −0.0165266 0.0234726i
\(529\) 34845.4 2.86393
\(530\) 3450.72 0.282811
\(531\) −10284.5 + 6629.45i −0.840510 + 0.541796i
\(532\) 3371.00 0.274721
\(533\) −6766.88 −0.549918
\(534\) −1971.46 2800.05i −0.159763 0.226910i
\(535\) −7202.48 −0.582038
\(536\) 6848.84i 0.551912i
\(537\) −1314.67 1867.22i −0.105647 0.150050i
\(538\) −7270.16 −0.582600
\(539\) 1239.78 0.0990747
\(540\) 2887.56 + 10450.6i 0.230113 + 0.832817i
\(541\) 18578.4i 1.47643i 0.674568 + 0.738213i \(0.264330\pi\)
−0.674568 + 0.738213i \(0.735670\pi\)
\(542\) 3131.30 0.248157
\(543\) −3751.41 5328.10i −0.296480 0.421088i
\(544\) 2621.71i 0.206626i
\(545\) −27078.1 −2.12826
\(546\) −1403.93 + 988.481i −0.110042 + 0.0774781i
\(547\) −22992.7 −1.79725 −0.898627 0.438714i \(-0.855434\pi\)
−0.898627 + 0.438714i \(0.855434\pi\)
\(548\) 7273.70i 0.567002i
\(549\) 5043.51 + 1806.11i 0.392080 + 0.140406i
\(550\) −2080.12 −0.161266
\(551\) 16767.0i 1.29636i
\(552\) 5188.88 + 7369.73i 0.400097 + 0.568255i
\(553\) 2862.84 0.220145
\(554\) −10927.1 −0.837991
\(555\) −19998.6 28403.9i −1.52954 2.17239i
\(556\) 7916.60 0.603847
\(557\) 6008.06i 0.457037i 0.973540 + 0.228519i \(0.0733882\pi\)
−0.973540 + 0.228519i \(0.926612\pi\)
\(558\) 17388.9 + 6227.07i 1.31923 + 0.472424i
\(559\) −8507.82 −0.643726
\(560\) 2120.51i 0.160014i
\(561\) −1458.23 + 1026.71i −0.109744 + 0.0772688i
\(562\) 4614.50i 0.346354i
\(563\) −17932.4 −1.34238 −0.671189 0.741286i \(-0.734216\pi\)
−0.671189 + 0.741286i \(0.734216\pi\)
\(564\) −1053.41 1496.15i −0.0786465 0.111701i
\(565\) 31623.4i 2.35470i
\(566\) 2986.48i 0.221786i
\(567\) −3863.95 3174.51i −0.286192 0.235127i
\(568\) 3075.03i 0.227157i
\(569\) 9814.15 0.723077 0.361538 0.932357i \(-0.382252\pi\)
0.361538 + 0.932357i \(0.382252\pi\)
\(570\) −20169.1 + 14200.6i −1.48209 + 1.04351i
\(571\) 23326.3i 1.70959i −0.518969 0.854793i \(-0.673684\pi\)
0.518969 0.854793i \(-0.326316\pi\)
\(572\) 403.597i 0.0295022i
\(573\) −5577.07 7921.08i −0.406607 0.577500i
\(574\) 3854.57i 0.280291i
\(575\) 53830.4 3.90414
\(576\) −582.579 + 1626.83i −0.0421426 + 0.117682i
\(577\) 4534.05 0.327132 0.163566 0.986532i \(-0.447700\pi\)
0.163566 + 0.986532i \(0.447700\pi\)
\(578\) 3598.49 0.258958
\(579\) 7999.62 + 11361.8i 0.574184 + 0.815510i
\(580\) −10547.1 −0.755080
\(581\) 8681.46 0.619910
\(582\) 424.129 298.620i 0.0302074 0.0212684i
\(583\) 374.116i 0.0265768i
\(584\) 4688.02i 0.332178i
\(585\) 4235.82 11828.4i 0.299367 0.835971i
\(586\) 69.5001i 0.00489936i
\(587\) 14774.7 1.03887 0.519437 0.854509i \(-0.326142\pi\)
0.519437 + 0.854509i \(0.326142\pi\)
\(588\) −3541.17 5029.50i −0.248359 0.352743i
\(589\) 42021.2i 2.93965i
\(590\) −10658.1 + 13894.3i −0.743706 + 0.969523i
\(591\) 5440.43 3830.50i 0.378662 0.266608i
\(592\) 5536.46i 0.384370i
\(593\) 810.843i 0.0561507i −0.999606 0.0280753i \(-0.991062\pi\)
0.999606 0.0280753i \(-0.00893783\pi\)
\(594\) −1133.02 + 313.060i −0.0782631 + 0.0216246i
\(595\) −10858.1 −0.748132
\(596\) −9366.69 −0.643749
\(597\) −4461.42 6336.52i −0.305852 0.434400i
\(598\) 10444.5i 0.714227i
\(599\) 10769.4i 0.734600i −0.930103 0.367300i \(-0.880282\pi\)
0.930103 0.367300i \(-0.119718\pi\)
\(600\) 5941.40 + 8438.52i 0.404261 + 0.574169i
\(601\) 8354.78i 0.567052i −0.958965 0.283526i \(-0.908496\pi\)
0.958965 0.283526i \(-0.0915043\pi\)
\(602\) 4846.26i 0.328104i
\(603\) 21761.5 + 7792.95i 1.46965 + 0.526291i
\(604\) 234.719i 0.0158122i
\(605\) 25376.1i 1.70526i
\(606\) 2101.72 + 2985.07i 0.140886 + 0.200099i
\(607\) 8150.29 0.544992 0.272496 0.962157i \(-0.412151\pi\)
0.272496 + 0.962157i \(0.412151\pi\)
\(608\) −3931.33 −0.262231
\(609\) 3977.67 2800.60i 0.264669 0.186348i
\(610\) 7666.74 0.508880
\(611\) 2120.37i 0.140395i
\(612\) 8330.23 + 2983.11i 0.550212 + 0.197034i
\(613\) 10034.8i 0.661180i −0.943774 0.330590i \(-0.892752\pi\)
0.943774 0.330590i \(-0.107248\pi\)
\(614\) −10710.5 −0.703976
\(615\) −16237.7 23062.3i −1.06466 1.51213i
\(616\) 229.898 0.0150371
\(617\) 16348.2i 1.06670i 0.845895 + 0.533350i \(0.179067\pi\)
−0.845895 + 0.533350i \(0.820933\pi\)
\(618\) 9725.43 6847.48i 0.633033 0.445706i
\(619\) 14628.1 0.949843 0.474922 0.880028i \(-0.342476\pi\)
0.474922 + 0.880028i \(0.342476\pi\)
\(620\) 26433.1 1.71223
\(621\) 29320.8 8101.54i 1.89469 0.523516i
\(622\) 13056.4i 0.841659i
\(623\) 2260.42 0.145364
\(624\) 1637.29 1152.79i 0.105039 0.0739558i
\(625\) 14978.6 0.958627
\(626\) 1057.94i 0.0675457i
\(627\) −1539.59 2186.67i −0.0980625 0.139278i
\(628\) 3266.30i 0.207547i
\(629\) −28349.5 −1.79709
\(630\) −6737.72 2412.82i −0.426090 0.152586i
\(631\) −3561.61 −0.224700 −0.112350 0.993669i \(-0.535838\pi\)
−0.112350 + 0.993669i \(0.535838\pi\)
\(632\) −3338.71 −0.210137
\(633\) −5780.34 + 4069.82i −0.362951 + 0.255547i
\(634\) 3472.24i 0.217508i
\(635\) 46085.8i 2.88009i
\(636\) 1517.69 1068.58i 0.0946234 0.0666225i
\(637\) 7127.88i 0.443355i
\(638\) 1143.49i 0.0709578i
\(639\) −9770.61 3498.92i −0.604882 0.216612i
\(640\) 2472.98i 0.152739i
\(641\) 14739.1i 0.908205i −0.890949 0.454103i \(-0.849960\pi\)
0.890949 0.454103i \(-0.150040\pi\)
\(642\) −3167.80 + 2230.38i −0.194740 + 0.137112i
\(643\) 15120.1 0.927340 0.463670 0.886008i \(-0.346532\pi\)
0.463670 + 0.886008i \(0.346532\pi\)
\(644\) −5949.43 −0.364038
\(645\) −20415.3 28995.7i −1.24628 1.77008i
\(646\) 20130.5i 1.22604i
\(647\) 16479.3i 1.00134i 0.865637 + 0.500672i \(0.166914\pi\)
−0.865637 + 0.500672i \(0.833086\pi\)
\(648\) 4506.22 + 3702.19i 0.273181 + 0.224438i
\(649\) −1506.37 1155.52i −0.0911098 0.0698890i
\(650\) 11959.2i 0.721660i
\(651\) −9968.80 + 7018.84i −0.600166 + 0.422565i
\(652\) 2975.46 0.178724
\(653\) 2442.19i 0.146356i 0.997319 + 0.0731779i \(0.0233141\pi\)
−0.997319 + 0.0731779i \(0.976686\pi\)
\(654\) −11909.5 + 8385.25i −0.712077 + 0.501359i
\(655\) 11849.9i 0.706891i
\(656\) 4495.29i 0.267548i
\(657\) 14895.8 + 5334.27i 0.884534 + 0.316757i
\(658\) 1207.81 0.0715585
\(659\) −16334.4 −0.965549 −0.482774 0.875745i \(-0.660371\pi\)
−0.482774 + 0.875745i \(0.660371\pi\)
\(660\) −1375.51 + 968.467i −0.0811235 + 0.0571175i
\(661\) −1213.17 −0.0713870 −0.0356935 0.999363i \(-0.511364\pi\)
−0.0356935 + 0.999363i \(0.511364\pi\)
\(662\) 9056.82 0.531727
\(663\) −5902.86 8383.80i −0.345774 0.491101i
\(664\) −10124.5 −0.591727
\(665\) 16282.1i 0.949461i
\(666\) −17591.6 6299.66i −1.02351 0.366527i
\(667\) 29591.7i 1.71784i
\(668\) 13583.8i 0.786788i
\(669\) −12161.8 17273.4i −0.702846 0.998247i
\(670\) 33080.1 1.90746
\(671\) 831.203i 0.0478215i
\(672\) −656.654 932.641i −0.0376949 0.0535378i
\(673\) 7012.56i 0.401656i −0.979627 0.200828i \(-0.935637\pi\)
0.979627 0.200828i \(-0.0643632\pi\)
\(674\) 4398.20i 0.251353i
\(675\) 33573.1 9276.46i 1.91441 0.528965i
\(676\) 6467.60 0.367979
\(677\) 13576.6i 0.770739i 0.922762 + 0.385370i \(0.125926\pi\)
−0.922762 + 0.385370i \(0.874074\pi\)
\(678\) −9792.77 13908.6i −0.554704 0.787842i
\(679\) 342.390i 0.0193516i
\(680\) 12662.9 0.714120
\(681\) −3519.35 4998.51i −0.198035 0.281268i
\(682\) 2865.80i 0.160905i
\(683\) −35104.8 −1.96669 −0.983345 0.181749i \(-0.941824\pi\)
−0.983345 + 0.181749i \(0.941824\pi\)
\(684\) −4473.27 + 12491.5i −0.250058 + 0.698279i
\(685\) 35132.2 1.95961
\(686\) 8766.01 0.487883
\(687\) −18886.2 + 13297.4i −1.04884 + 0.738468i
\(688\) 5651.80i 0.313187i
\(689\) −2150.90 −0.118930
\(690\) 35596.1 25062.5i 1.96394 1.38277i
\(691\) 13636.1i 0.750713i 0.926881 + 0.375356i \(0.122480\pi\)
−0.926881 + 0.375356i \(0.877520\pi\)
\(692\) 14245.2 0.782545
\(693\) 261.590 730.481i 0.0143391 0.0400414i
\(694\) −6471.40 −0.353964
\(695\) 38237.5i 2.08695i
\(696\) −4638.84 + 3266.12i −0.252636 + 0.177876i
\(697\) −23018.2 −1.25090
\(698\) 6801.82i 0.368843i
\(699\) −1354.78 1924.19i −0.0733085 0.104120i
\(700\) −6812.24 −0.367827
\(701\) 20921.4 1.12723 0.563616 0.826037i \(-0.309410\pi\)
0.563616 + 0.826037i \(0.309410\pi\)
\(702\) −1799.88 6514.05i −0.0967692 0.350224i
\(703\) 42511.0i 2.28070i
\(704\) −268.112 −0.0143535
\(705\) −7226.48 + 5088.02i −0.386049 + 0.271810i
\(706\) −23084.1 −1.23057
\(707\) −2409.78 −0.128188
\(708\) −385.021 + 9411.46i −0.0204378 + 0.499582i
\(709\) −12409.7 −0.657341 −0.328671 0.944445i \(-0.606601\pi\)
−0.328671 + 0.944445i \(0.606601\pi\)
\(710\) −14852.5 −0.785076
\(711\) −3798.95 + 10608.4i −0.200382 + 0.559560i
\(712\) −2636.15 −0.138756
\(713\) 74162.6i 3.89539i
\(714\) −4775.61 + 3362.41i −0.250312 + 0.176240i
\(715\) 1949.39 0.101962
\(716\) −1757.93 −0.0917553
\(717\) −11031.6 + 7767.15i −0.574594 + 0.404560i
\(718\) 13715.2i 0.712876i
\(719\) −31979.3 −1.65873 −0.829365 0.558707i \(-0.811298\pi\)
−0.829365 + 0.558707i \(0.811298\pi\)
\(720\) 7857.66 + 2813.88i 0.406719 + 0.145649i
\(721\) 7851.14i 0.405536i
\(722\) −16468.3 −0.848874
\(723\) 13018.8 + 18490.5i 0.669674 + 0.951134i
\(724\) −5016.23 −0.257495
\(725\) 33883.3i 1.73571i
\(726\) 7858.16 + 11160.9i 0.401713 + 0.570551i
\(727\) −10864.9 −0.554275 −0.277137 0.960830i \(-0.589386\pi\)
−0.277137 + 0.960830i \(0.589386\pi\)
\(728\) 1321.75i 0.0672905i
\(729\) 16890.8 10105.6i 0.858140 0.513416i
\(730\) 22643.3 1.14804
\(731\) −28940.2 −1.46428
\(732\) 3371.98 2374.15i 0.170262 0.119878i
\(733\) −4862.94 −0.245044 −0.122522 0.992466i \(-0.539098\pi\)
−0.122522 + 0.992466i \(0.539098\pi\)
\(734\) 10116.4i 0.508723i
\(735\) −24292.7 + 17104.0i −1.21911 + 0.858353i
\(736\) 6938.35 0.347488
\(737\) 3586.44i 0.179251i
\(738\) −14283.4 5114.96i −0.712436 0.255128i
\(739\) 20365.8i 1.01376i −0.862017 0.506879i \(-0.830799\pi\)
0.862017 0.506879i \(-0.169201\pi\)
\(740\) −26741.3 −1.32842
\(741\) 12571.8 8851.54i 0.623260 0.438825i
\(742\) 1225.20i 0.0606181i
\(743\) 35272.0i 1.74160i −0.491641 0.870798i \(-0.663603\pi\)
0.491641 0.870798i \(-0.336397\pi\)
\(744\) 11625.8 8185.51i 0.572881 0.403354i
\(745\) 45241.5i 2.22486i
\(746\) −23230.5 −1.14012
\(747\) −11520.2 + 32169.7i −0.564258 + 1.57567i
\(748\) 1372.87i 0.0671086i
\(749\) 2557.30i 0.124755i
\(750\) 20237.0 14248.5i 0.985269 0.693708i
\(751\) 5331.76i 0.259066i 0.991575 + 0.129533i \(0.0413478\pi\)
−0.991575 + 0.129533i \(0.958652\pi\)
\(752\) −1408.58 −0.0683052
\(753\) 18707.3 13171.5i 0.905356 0.637443i
\(754\) 6574.24 0.317533
\(755\) −1133.70 −0.0546486
\(756\) −3710.56 + 1025.25i −0.178507 + 0.0493228i
\(757\) −7086.43 −0.340239 −0.170119 0.985423i \(-0.554415\pi\)
−0.170119 + 0.985423i \(0.554415\pi\)
\(758\) −11603.9 −0.556032
\(759\) 2717.19 + 3859.21i 0.129945 + 0.184559i
\(760\) 18988.5i 0.906296i
\(761\) 4581.22i 0.218225i −0.994029 0.109112i \(-0.965199\pi\)
0.994029 0.109112i \(-0.0348008\pi\)
\(762\) 14271.3 + 20269.4i 0.678471 + 0.963628i
\(763\) 9614.30i 0.456174i
\(764\) −7457.42 −0.353141
\(765\) 14408.5 40235.3i 0.680969 1.90158i
\(766\) 14206.3i 0.670096i
\(767\) 6643.40 8660.58i 0.312750 0.407712i
\(768\) 765.804 + 1087.67i 0.0359812 + 0.0511038i
\(769\) 11328.6i 0.531235i 0.964079 + 0.265617i \(0.0855758\pi\)
−0.964079 + 0.265617i \(0.914424\pi\)
\(770\) 1110.42i 0.0519697i
\(771\) 3755.17 2643.94i 0.175407 0.123501i
\(772\) 10696.7 0.498684
\(773\) −17160.9 −0.798491 −0.399245 0.916844i \(-0.630728\pi\)
−0.399245 + 0.916844i \(0.630728\pi\)
\(774\) −17958.1 6430.91i −0.833966 0.298649i
\(775\) 84917.9i 3.93593i
\(776\) 399.303i 0.0184718i
\(777\) 10085.0 7100.66i 0.465634 0.327844i
\(778\) 20247.8i 0.933058i
\(779\) 34516.5i 1.58753i
\(780\) −5568.00 7908.19i −0.255598 0.363024i
\(781\) 1610.26i 0.0737767i
\(782\) 35528.0i 1.62465i
\(783\) 5099.48 + 18455.9i 0.232746 + 0.842348i
\(784\) −4735.10 −0.215702
\(785\) 15776.3 0.717302
\(786\) 3669.54 + 5211.82i 0.166524 + 0.236513i
\(787\) −26544.8 −1.20231 −0.601157 0.799131i \(-0.705293\pi\)
−0.601157 + 0.799131i \(0.705293\pi\)
\(788\) 5121.98i 0.231552i
\(789\) −20651.9 + 14540.6i −0.931848 + 0.656096i
\(790\) 16126.1i 0.726253i
\(791\) 11228.1 0.504711
\(792\) −305.072 + 851.902i −0.0136872 + 0.0382210i
\(793\) −4778.83 −0.213999
\(794\) 24597.5i 1.09941i
\(795\) −5161.27 7330.52i −0.230253 0.327027i
\(796\) −5965.62 −0.265635
\(797\) −6602.21 −0.293428 −0.146714 0.989179i \(-0.546870\pi\)
−0.146714 + 0.989179i \(0.546870\pi\)
\(798\) −5042.04 7161.18i −0.223667 0.317673i
\(799\) 7212.64i 0.319355i
\(800\) 7944.58 0.351104
\(801\) −2999.55 + 8376.14i −0.132314 + 0.369483i
\(802\) −733.103 −0.0322778
\(803\) 2454.91i 0.107885i
\(804\) 14549.3 10243.9i 0.638202 0.449345i
\(805\) 28736.0i 1.25815i
\(806\) −16476.3 −0.720041
\(807\) 10874.1 + 15444.3i 0.474331 + 0.673688i
\(808\) 2810.34 0.122361
\(809\) 27228.8 1.18333 0.591665 0.806184i \(-0.298471\pi\)
0.591665 + 0.806184i \(0.298471\pi\)
\(810\) 17881.7 21765.2i 0.775677 0.944138i
\(811\) 7065.46i 0.305921i −0.988232 0.152960i \(-0.951119\pi\)
0.988232 0.152960i \(-0.0488807\pi\)
\(812\) 3744.84i 0.161845i
\(813\) −4683.52 6651.97i −0.202040 0.286955i
\(814\) 2899.20i 0.124837i
\(815\) 14371.6i 0.617686i
\(816\) 5569.41 3921.31i 0.238932 0.168227i
\(817\) 43396.7i 1.85833i
\(818\) 17534.9i 0.749503i
\(819\) 4199.75 + 1503.96i 0.179183 + 0.0641667i
\(820\) −21712.4 −0.924670
\(821\) −14983.1 −0.636924 −0.318462 0.947936i \(-0.603166\pi\)
−0.318462 + 0.947936i \(0.603166\pi\)
\(822\) 15451.9 10879.3i 0.655652 0.461631i
\(823\) 26292.3i 1.11360i 0.830647 + 0.556800i \(0.187971\pi\)
−0.830647 + 0.556800i \(0.812029\pi\)
\(824\) 9156.16i 0.387100i
\(825\) 3111.25 + 4418.89i 0.131297 + 0.186480i
\(826\) −4933.27 3784.23i −0.207809 0.159407i
\(827\) 24569.6i 1.03310i −0.856258 0.516548i \(-0.827217\pi\)
0.856258 0.516548i \(-0.172783\pi\)
\(828\) 7894.81 22046.0i 0.331357 0.925303i
\(829\) 30899.9 1.29457 0.647285 0.762248i \(-0.275904\pi\)
0.647285 + 0.762248i \(0.275904\pi\)
\(830\) 48901.7i 2.04506i
\(831\) 16343.7 + 23212.9i 0.682260 + 0.969009i
\(832\) 1541.46i 0.0642313i
\(833\) 24246.2i 1.00850i
\(834\) −11840.9 16817.6i −0.491629 0.698257i
\(835\) 65610.4 2.71921
\(836\) −2058.67 −0.0851682
\(837\) −12780.3 46253.9i −0.527778 1.91012i
\(838\) −8472.34 −0.349251
\(839\) −4412.75 −0.181579 −0.0907897 0.995870i \(-0.528939\pi\)
−0.0907897 + 0.995870i \(0.528939\pi\)
\(840\) −4504.69 + 3171.66i −0.185032 + 0.130277i
\(841\) 5762.62 0.236279
\(842\) 9003.89i 0.368521i
\(843\) 9802.79 6901.95i 0.400505 0.281988i
\(844\) 5442.00i 0.221945i
\(845\) 31238.7i 1.27177i
\(846\) −1602.75 + 4475.62i −0.0651344 + 0.181885i
\(847\) −9009.96 −0.365509
\(848\) 1428.86i 0.0578622i
\(849\) −6344.32 + 4466.91i −0.256462 + 0.180570i
\(850\) 40680.4i 1.64156i
\(851\) 75027.1i 3.02220i
\(852\) −6532.42 + 4599.35i −0.262673 + 0.184943i
\(853\) 1603.41 0.0643607 0.0321803 0.999482i \(-0.489755\pi\)
0.0321803 + 0.999482i \(0.489755\pi\)
\(854\) 2722.13i 0.109074i
\(855\) 60334.2 + 21606.1i 2.41332 + 0.864224i
\(856\) 2982.37i 0.119083i
\(857\) 38885.4 1.54994 0.774970 0.631998i \(-0.217765\pi\)
0.774970 + 0.631998i \(0.217765\pi\)
\(858\) 857.381 603.665i 0.0341148 0.0240195i
\(859\) 23506.4i 0.933678i 0.884342 + 0.466839i \(0.154607\pi\)
−0.884342 + 0.466839i \(0.845393\pi\)
\(860\) −27298.4 −1.08241
\(861\) 8188.46 5765.33i 0.324114 0.228202i
\(862\) −23742.0 −0.938114
\(863\) 35138.2 1.38600 0.693001 0.720937i \(-0.256288\pi\)
0.693001 + 0.720937i \(0.256288\pi\)
\(864\) 4327.33 1195.67i 0.170392 0.0470805i
\(865\) 68804.8i 2.70455i
\(866\) 9648.70 0.378610
\(867\) −5382.30 7644.44i −0.210833 0.299445i
\(868\) 9385.29i 0.367002i
\(869\) −1748.34 −0.0682488
\(870\) 15775.5 + 22405.8i 0.614757 + 0.873135i
\(871\) −20619.5 −0.802142
\(872\) 11212.4i 0.435435i
\(873\) −1268.75 454.347i −0.0491874 0.0176143i
\(874\) 53275.4 2.06186
\(875\) 16336.9i 0.631188i
\(876\) 9958.98 7011.92i 0.384113 0.270446i
\(877\) −10671.1 −0.410876 −0.205438 0.978670i \(-0.565862\pi\)
−0.205438 + 0.978670i \(0.565862\pi\)
\(878\) 17043.7 0.655121
\(879\) −147.642 + 103.952i −0.00566536 + 0.00398887i
\(880\) 1294.99i 0.0496070i
\(881\) −27854.9 −1.06522 −0.532609 0.846362i \(-0.678788\pi\)
−0.532609 + 0.846362i \(0.678788\pi\)
\(882\) −5387.83 + 15045.3i −0.205689 + 0.574380i
\(883\) −17898.9 −0.682160 −0.341080 0.940034i \(-0.610793\pi\)
−0.341080 + 0.940034i \(0.610793\pi\)
\(884\) −7893.06 −0.300308
\(885\) 45457.7 + 1859.66i 1.72660 + 0.0706349i
\(886\) 13014.0 0.493469
\(887\) 131.720 0.00498618 0.00249309 0.999997i \(-0.499206\pi\)
0.00249309 + 0.999997i \(0.499206\pi\)
\(888\) −11761.4 + 8280.93i −0.444465 + 0.312939i
\(889\) −16363.1 −0.617324
\(890\) 12732.7i 0.479553i
\(891\) 2359.71 + 1938.67i 0.0887244 + 0.0728934i
\(892\) −16262.3 −0.610428
\(893\) −10815.6 −0.405297
\(894\) 14009.9 + 19898.1i 0.524116 + 0.744398i
\(895\) 8490.85i 0.317115i
\(896\) −878.050 −0.0327384
\(897\) −22187.7 + 15622.0i −0.825894 + 0.581496i
\(898\) 6016.93i 0.223594i
\(899\) 46681.3 1.73182
\(900\) 9039.75 25243.2i 0.334805 0.934932i
\(901\) −7316.49 −0.270530
\(902\) 2353.99i 0.0868949i
\(903\) 10295.1 7248.59i 0.379402 0.267130i
\(904\) −13094.5 −0.481765
\(905\) 24228.6i 0.889928i
\(906\) −498.625 + 351.072i −0.0182844 + 0.0128737i
\(907\) −29776.4 −1.09009 −0.545043 0.838408i \(-0.683487\pi\)
−0.545043 + 0.838408i \(0.683487\pi\)
\(908\) −4705.92 −0.171995
\(909\) 3197.74 8929.59i 0.116680 0.325826i
\(910\) 6384.12 0.232562
\(911\) 1619.23i 0.0588886i −0.999566 0.0294443i \(-0.990626\pi\)
0.999566 0.0294443i \(-0.00937376\pi\)
\(912\) 5880.14 + 8351.52i 0.213499 + 0.303231i
\(913\) −5301.76 −0.192183
\(914\) 12743.7i 0.461185i
\(915\) −11467.2 16286.8i −0.414311 0.588443i
\(916\) 17780.7i 0.641367i
\(917\) −4207.39 −0.151516
\(918\) −6122.45 22158.2i −0.220121 0.796654i
\(919\) 17813.8i 0.639416i −0.947516 0.319708i \(-0.896415\pi\)
0.947516 0.319708i \(-0.103585\pi\)
\(920\) 33512.5i 1.20095i
\(921\) 16019.8 + 22752.9i 0.573150 + 0.814042i
\(922\) 24492.2i 0.874846i
\(923\) 9257.85 0.330147
\(924\) −343.861 488.384i −0.0122427 0.0173882i
\(925\) 85907.8i 3.05366i
\(926\) 16410.0i 0.582361i
\(927\) −29092.9 10418.3i −1.03078 0.369130i
\(928\) 4367.31i 0.154487i
\(929\) −15087.4 −0.532831 −0.266416 0.963858i \(-0.585839\pi\)
−0.266416 + 0.963858i \(0.585839\pi\)
\(930\) −39536.3 56153.2i −1.39403 1.97993i
\(931\) −36357.9 −1.27990
\(932\) −1811.56 −0.0636691
\(933\) −27736.2 + 19528.5i −0.973251 + 0.685247i
\(934\) −12659.0 −0.443485
\(935\) 6631.03 0.231934
\(936\) −4897.84 1753.95i −0.171037 0.0612495i
\(937\) 150.028i 0.00523072i −0.999997 0.00261536i \(-0.999168\pi\)
0.999997 0.00261536i \(-0.000832497\pi\)
\(938\) 11745.4i 0.408848i
\(939\) 2247.42 1582.36i 0.0781063 0.0549931i
\(940\) 6803.48i 0.236069i
\(941\) 22210.1 0.769423 0.384711 0.923037i \(-0.374301\pi\)
0.384711 + 0.923037i \(0.374301\pi\)
\(942\) 6938.75 4885.44i 0.239997 0.168977i
\(943\) 60917.7i 2.10366i
\(944\) 5753.28 + 4413.25i 0.198362 + 0.152160i
\(945\) 4952.00 + 17922.1i 0.170464 + 0.616938i
\(946\) 2959.61i 0.101718i
\(947\) 16355.4i 0.561223i −0.959822 0.280611i \(-0.909463\pi\)
0.959822 0.280611i \(-0.0905372\pi\)
\(948\) 4993.74 + 7092.57i 0.171085 + 0.242992i
\(949\) −14114.0 −0.482783
\(950\) 61001.6 2.08332
\(951\) 7376.24 5193.46i 0.251515 0.177087i
\(952\) 4496.07i 0.153066i
\(953\) 42907.8i 1.45847i −0.684264 0.729235i \(-0.739876\pi\)
0.684264 0.729235i \(-0.260124\pi\)
\(954\) −4540.06 1625.83i −0.154078 0.0551762i
\(955\) 36019.6i 1.22049i
\(956\) 10385.9i 0.351364i
\(957\) −2429.16 + 1710.32i −0.0820519 + 0.0577711i
\(958\) 9666.04i 0.325987i
\(959\) 12474.0i 0.420026i
\(960\) 5253.47 3698.86i 0.176620 0.124354i
\(961\) −87201.2 −2.92710
\(962\) 16668.4 0.558638
\(963\) 9476.21 + 3393.49i 0.317099 + 0.113555i
\(964\) 17408.2 0.581618
\(965\) 51665.7i 1.72350i
\(966\) 8898.63 + 12638.7i 0.296386 + 0.420955i
\(967\) 23064.3i 0.767009i 0.923539 + 0.383505i \(0.125283\pi\)
−0.923539 + 0.383505i \(0.874717\pi\)
\(968\) 10507.6 0.348892
\(969\) 42764.1 30109.4i 1.41773 0.998196i
\(970\) −1928.65 −0.0638403
\(971\) 4903.81i 0.162071i −0.996711 0.0810355i \(-0.974177\pi\)
0.996711 0.0810355i \(-0.0258227\pi\)
\(972\) 1124.72 15110.2i 0.0371147 0.498621i
\(973\) 13576.5 0.447321
\(974\) −33095.1 −1.08874
\(975\) −25405.5 + 17887.5i −0.834490 + 0.587548i
\(976\) 3174.61i 0.104115i
\(977\) −25816.5 −0.845386 −0.422693 0.906273i \(-0.638915\pi\)
−0.422693 + 0.906273i \(0.638915\pi\)
\(978\) −4450.42 6320.90i −0.145510 0.206667i
\(979\) −1380.44 −0.0450654
\(980\) 22870.7i 0.745487i
\(981\) 35626.3 + 12758.0i 1.15949 + 0.415222i
\(982\) 25433.6i 0.826496i
\(983\) 2380.07 0.0772252 0.0386126 0.999254i \(-0.487706\pi\)
0.0386126 + 0.999254i \(0.487706\pi\)
\(984\) −9549.55 + 6723.64i −0.309378 + 0.217827i
\(985\) −24739.3 −0.800265
\(986\) 22362.9 0.722292
\(987\) −1806.54 2565.81i −0.0582602 0.0827465i
\(988\) 11835.9i 0.381124i
\(989\) 76590.2i 2.46252i
\(990\) 4114.72 + 1473.51i 0.132095 + 0.0473042i
\(991\) 35380.6i 1.13411i 0.823680 + 0.567054i \(0.191917\pi\)
−0.823680 + 0.567054i \(0.808083\pi\)
\(992\) 10945.3i 0.350317i
\(993\) −13546.4 19239.8i −0.432912 0.614861i
\(994\) 5273.49i 0.168275i
\(995\) 28814.2i 0.918061i
\(996\) 15143.3 + 21508.0i 0.481761 + 0.684242i
\(997\) 16910.4 0.537169 0.268584 0.963256i \(-0.413444\pi\)
0.268584 + 0.963256i \(0.413444\pi\)
\(998\) 4946.57 0.156895
\(999\) 12929.2 + 46793.1i 0.409473 + 1.48195i
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 354.4.c.a.353.20 yes 30
3.2 odd 2 354.4.c.b.353.19 yes 30
59.58 odd 2 354.4.c.b.353.20 yes 30
177.176 even 2 inner 354.4.c.a.353.19 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.4.c.a.353.19 30 177.176 even 2 inner
354.4.c.a.353.20 yes 30 1.1 even 1 trivial
354.4.c.b.353.19 yes 30 3.2 odd 2
354.4.c.b.353.20 yes 30 59.58 odd 2