Properties

Label 135.4.e.b.46.1
Level $135$
Weight $4$
Character 135.46
Analytic conductor $7.965$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [135,4,Mod(46,135)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(135, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("135.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.96525785077\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.15759792.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.1
Root \(0.500000 + 2.88506i\) of defining polynomial
Character \(\chi\) \(=\) 135.46
Dual form 135.4.e.b.91.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.28679 + 3.96084i) q^{2} +(-6.45882 - 11.1870i) q^{4} +(2.50000 + 4.33013i) q^{5} +(10.0573 - 17.4197i) q^{7} +22.4912 q^{8} +O(q^{10})\) \(q+(-2.28679 + 3.96084i) q^{2} +(-6.45882 - 11.1870i) q^{4} +(2.50000 + 4.33013i) q^{5} +(10.0573 - 17.4197i) q^{7} +22.4912 q^{8} -22.8679 q^{10} +(33.1708 - 57.4535i) q^{11} +(23.4003 + 40.5305i) q^{13} +(45.9977 + 79.6704i) q^{14} +(0.237854 - 0.411975i) q^{16} +47.6233 q^{17} -9.95276 q^{19} +(32.2941 - 55.9350i) q^{20} +(151.709 + 262.768i) q^{22} +(4.79602 + 8.30695i) q^{23} +(-12.5000 + 21.6506i) q^{25} -214.046 q^{26} -259.832 q^{28} +(-89.3675 + 154.789i) q^{29} +(-77.0186 - 133.400i) q^{31} +(91.0527 + 157.708i) q^{32} +(-108.905 + 188.628i) q^{34} +100.573 q^{35} +248.864 q^{37} +(22.7599 - 39.4213i) q^{38} +(56.2280 + 97.3898i) q^{40} +(124.832 + 216.216i) q^{41} +(106.122 - 183.809i) q^{43} -856.976 q^{44} -43.8700 q^{46} +(237.847 - 411.963i) q^{47} +(-30.7973 - 53.3425i) q^{49} +(-57.1698 - 99.0209i) q^{50} +(302.277 - 523.559i) q^{52} +546.314 q^{53} +331.708 q^{55} +(226.200 - 391.790i) q^{56} +(-408.729 - 707.940i) q^{58} +(-209.648 - 363.121i) q^{59} +(272.605 - 472.165i) q^{61} +704.502 q^{62} -829.068 q^{64} +(-117.002 + 202.653i) q^{65} +(223.938 + 387.872i) q^{67} +(-307.590 - 532.762i) q^{68} +(-229.989 + 398.352i) q^{70} -409.542 q^{71} -358.548 q^{73} +(-569.100 + 985.710i) q^{74} +(64.2831 + 111.342i) q^{76} +(-667.215 - 1155.65i) q^{77} +(325.776 - 564.260i) q^{79} +2.37854 q^{80} -1141.86 q^{82} +(-406.571 + 704.202i) q^{83} +(119.058 + 206.215i) q^{85} +(485.359 + 840.667i) q^{86} +(746.051 - 1292.20i) q^{88} +201.000 q^{89} +941.373 q^{91} +(61.9532 - 107.306i) q^{92} +(1087.81 + 1884.14i) q^{94} +(-24.8819 - 43.0967i) q^{95} +(-126.074 + 218.367i) q^{97} +281.708 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8} - 10 q^{10} + 14 q^{11} - 40 q^{13} - 27 q^{14} + 13 q^{16} + 332 q^{17} - 328 q^{19} + 55 q^{20} + 376 q^{22} + 171 q^{23} - 75 q^{25} - 868 q^{26} - 1034 q^{28} - 335 q^{29} + 352 q^{31} - 77 q^{32} + 52 q^{34} + 430 q^{35} + 804 q^{37} - 178 q^{38} + 135 q^{40} + 187 q^{41} + 602 q^{43} - 1964 q^{44} - 402 q^{46} + 665 q^{47} - 430 q^{49} - 25 q^{50} + 456 q^{52} + 1460 q^{53} + 140 q^{55} + 705 q^{56} - 217 q^{58} - 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 3138 q^{64} + 200 q^{65} + 1849 q^{67} - 710 q^{68} + 135 q^{70} - 140 q^{71} - 736 q^{73} - 320 q^{74} - 204 q^{76} - 948 q^{77} + 382 q^{79} + 130 q^{80} - 1150 q^{82} - 831 q^{83} + 830 q^{85} + 1580 q^{86} + 1428 q^{88} - 3438 q^{89} - 1420 q^{91} - 1623 q^{92} + 2077 q^{94} - 820 q^{95} + 282 q^{97} - 4328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(82\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28679 + 3.96084i −0.808502 + 1.40037i 0.105398 + 0.994430i \(0.466388\pi\)
−0.913901 + 0.405937i \(0.866945\pi\)
\(3\) 0 0
\(4\) −6.45882 11.1870i −0.807352 1.39838i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 10.0573 17.4197i 0.543041 0.940575i −0.455686 0.890141i \(-0.650606\pi\)
0.998727 0.0504348i \(-0.0160607\pi\)
\(8\) 22.4912 0.993981
\(9\) 0 0
\(10\) −22.8679 −0.723147
\(11\) 33.1708 57.4535i 0.909215 1.57481i 0.0940582 0.995567i \(-0.470016\pi\)
0.815157 0.579240i \(-0.196651\pi\)
\(12\) 0 0
\(13\) 23.4003 + 40.5305i 0.499237 + 0.864703i 1.00000 0.000881222i \(-0.000280502\pi\)
−0.500763 + 0.865584i \(0.666947\pi\)
\(14\) 45.9977 + 79.6704i 0.878101 + 1.52092i
\(15\) 0 0
\(16\) 0.237854 0.411975i 0.00371647 0.00643711i
\(17\) 47.6233 0.679432 0.339716 0.940528i \(-0.389669\pi\)
0.339716 + 0.940528i \(0.389669\pi\)
\(18\) 0 0
\(19\) −9.95276 −0.120175 −0.0600874 0.998193i \(-0.519138\pi\)
−0.0600874 + 0.998193i \(0.519138\pi\)
\(20\) 32.2941 55.9350i 0.361059 0.625373i
\(21\) 0 0
\(22\) 151.709 + 262.768i 1.47021 + 2.54647i
\(23\) 4.79602 + 8.30695i 0.0434800 + 0.0753095i 0.886946 0.461872i \(-0.152822\pi\)
−0.843466 + 0.537182i \(0.819489\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −214.046 −1.61454
\(27\) 0 0
\(28\) −259.832 −1.75370
\(29\) −89.3675 + 154.789i −0.572246 + 0.991158i 0.424089 + 0.905620i \(0.360594\pi\)
−0.996335 + 0.0855380i \(0.972739\pi\)
\(30\) 0 0
\(31\) −77.0186 133.400i −0.446224 0.772883i 0.551912 0.833902i \(-0.313898\pi\)
−0.998137 + 0.0610190i \(0.980565\pi\)
\(32\) 91.0527 + 157.708i 0.503000 + 0.871222i
\(33\) 0 0
\(34\) −108.905 + 188.628i −0.549323 + 0.951455i
\(35\) 100.573 0.485711
\(36\) 0 0
\(37\) 248.864 1.10576 0.552878 0.833262i \(-0.313529\pi\)
0.552878 + 0.833262i \(0.313529\pi\)
\(38\) 22.7599 39.4213i 0.0971616 0.168289i
\(39\) 0 0
\(40\) 56.2280 + 97.3898i 0.222261 + 0.384967i
\(41\) 124.832 + 216.216i 0.475500 + 0.823590i 0.999606 0.0280628i \(-0.00893383\pi\)
−0.524106 + 0.851653i \(0.675600\pi\)
\(42\) 0 0
\(43\) 106.122 183.809i 0.376361 0.651876i −0.614169 0.789175i \(-0.710509\pi\)
0.990530 + 0.137299i \(0.0438420\pi\)
\(44\) −856.976 −2.93623
\(45\) 0 0
\(46\) −43.8700 −0.140615
\(47\) 237.847 411.963i 0.738160 1.27853i −0.215163 0.976578i \(-0.569028\pi\)
0.953323 0.301953i \(-0.0976384\pi\)
\(48\) 0 0
\(49\) −30.7973 53.3425i −0.0897880 0.155517i
\(50\) −57.1698 99.0209i −0.161700 0.280073i
\(51\) 0 0
\(52\) 302.277 523.559i 0.806120 1.39624i
\(53\) 546.314 1.41589 0.707944 0.706269i \(-0.249623\pi\)
0.707944 + 0.706269i \(0.249623\pi\)
\(54\) 0 0
\(55\) 331.708 0.813227
\(56\) 226.200 391.790i 0.539773 0.934914i
\(57\) 0 0
\(58\) −408.729 707.940i −0.925324 1.60271i
\(59\) −209.648 363.121i −0.462608 0.801261i 0.536482 0.843912i \(-0.319753\pi\)
−0.999090 + 0.0426512i \(0.986420\pi\)
\(60\) 0 0
\(61\) 272.605 472.165i 0.572188 0.991059i −0.424153 0.905591i \(-0.639428\pi\)
0.996341 0.0854682i \(-0.0272386\pi\)
\(62\) 704.502 1.44309
\(63\) 0 0
\(64\) −829.068 −1.61927
\(65\) −117.002 + 202.653i −0.223265 + 0.386707i
\(66\) 0 0
\(67\) 223.938 + 387.872i 0.408335 + 0.707256i 0.994703 0.102788i \(-0.0327764\pi\)
−0.586369 + 0.810044i \(0.699443\pi\)
\(68\) −307.590 532.762i −0.548541 0.950102i
\(69\) 0 0
\(70\) −229.989 + 398.352i −0.392699 + 0.680174i
\(71\) −409.542 −0.684559 −0.342279 0.939598i \(-0.611199\pi\)
−0.342279 + 0.939598i \(0.611199\pi\)
\(72\) 0 0
\(73\) −358.548 −0.574861 −0.287431 0.957801i \(-0.592801\pi\)
−0.287431 + 0.957801i \(0.592801\pi\)
\(74\) −569.100 + 985.710i −0.894007 + 1.54847i
\(75\) 0 0
\(76\) 64.2831 + 111.342i 0.0970234 + 0.168049i
\(77\) −667.215 1155.65i −0.987483 1.71037i
\(78\) 0 0
\(79\) 325.776 564.260i 0.463958 0.803598i −0.535196 0.844728i \(-0.679762\pi\)
0.999154 + 0.0411297i \(0.0130957\pi\)
\(80\) 2.37854 0.00332411
\(81\) 0 0
\(82\) −1141.86 −1.53777
\(83\) −406.571 + 704.202i −0.537675 + 0.931280i 0.461354 + 0.887216i \(0.347364\pi\)
−0.999029 + 0.0440636i \(0.985970\pi\)
\(84\) 0 0
\(85\) 119.058 + 206.215i 0.151926 + 0.263143i
\(86\) 485.359 + 840.667i 0.608577 + 1.05409i
\(87\) 0 0
\(88\) 746.051 1292.20i 0.903743 1.56533i
\(89\) 201.000 0.239393 0.119696 0.992811i \(-0.461808\pi\)
0.119696 + 0.992811i \(0.461808\pi\)
\(90\) 0 0
\(91\) 941.373 1.08442
\(92\) 61.9532 107.306i 0.0702073 0.121603i
\(93\) 0 0
\(94\) 1087.81 + 1884.14i 1.19361 + 2.06739i
\(95\) −24.8819 43.0967i −0.0268719 0.0465435i
\(96\) 0 0
\(97\) −126.074 + 218.367i −0.131968 + 0.228576i −0.924435 0.381339i \(-0.875463\pi\)
0.792467 + 0.609915i \(0.208796\pi\)
\(98\) 281.708 0.290375
\(99\) 0 0
\(100\) 322.941 0.322941
\(101\) 21.8013 37.7610i 0.0214783 0.0372016i −0.855086 0.518485i \(-0.826496\pi\)
0.876565 + 0.481284i \(0.159829\pi\)
\(102\) 0 0
\(103\) 720.176 + 1247.38i 0.688942 + 1.19328i 0.972180 + 0.234233i \(0.0752579\pi\)
−0.283238 + 0.959050i \(0.591409\pi\)
\(104\) 526.301 + 911.581i 0.496232 + 0.859498i
\(105\) 0 0
\(106\) −1249.31 + 2163.86i −1.14475 + 1.98276i
\(107\) −355.755 −0.321422 −0.160711 0.987002i \(-0.551379\pi\)
−0.160711 + 0.987002i \(0.551379\pi\)
\(108\) 0 0
\(109\) −1522.51 −1.33789 −0.668946 0.743311i \(-0.733254\pi\)
−0.668946 + 0.743311i \(0.733254\pi\)
\(110\) −758.546 + 1313.84i −0.657496 + 1.13882i
\(111\) 0 0
\(112\) −4.78432 8.28669i −0.00403639 0.00699124i
\(113\) −406.499 704.077i −0.338409 0.586142i 0.645725 0.763570i \(-0.276555\pi\)
−0.984134 + 0.177429i \(0.943222\pi\)
\(114\) 0 0
\(115\) −23.9801 + 41.5347i −0.0194448 + 0.0336794i
\(116\) 2308.83 1.84802
\(117\) 0 0
\(118\) 1917.69 1.49608
\(119\) 478.960 829.584i 0.368960 0.639057i
\(120\) 0 0
\(121\) −1535.10 2658.87i −1.15334 1.99765i
\(122\) 1246.78 + 2159.49i 0.925231 + 1.60255i
\(123\) 0 0
\(124\) −994.899 + 1723.22i −0.720521 + 1.24798i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −864.662 −0.604144 −0.302072 0.953285i \(-0.597678\pi\)
−0.302072 + 0.953285i \(0.597678\pi\)
\(128\) 1167.48 2022.14i 0.806187 1.39636i
\(129\) 0 0
\(130\) −535.116 926.848i −0.361021 0.625307i
\(131\) −1089.26 1886.65i −0.726482 1.25830i −0.958361 0.285559i \(-0.907821\pi\)
0.231879 0.972745i \(-0.425513\pi\)
\(132\) 0 0
\(133\) −100.098 + 173.374i −0.0652599 + 0.113033i
\(134\) −2048.40 −1.32056
\(135\) 0 0
\(136\) 1071.11 0.675343
\(137\) −1149.58 + 1991.13i −0.716900 + 1.24171i 0.245322 + 0.969442i \(0.421106\pi\)
−0.962222 + 0.272266i \(0.912227\pi\)
\(138\) 0 0
\(139\) 1066.98 + 1848.06i 0.651077 + 1.12770i 0.982862 + 0.184343i \(0.0590157\pi\)
−0.331785 + 0.943355i \(0.607651\pi\)
\(140\) −649.581 1125.11i −0.392140 0.679206i
\(141\) 0 0
\(142\) 936.536 1622.13i 0.553467 0.958634i
\(143\) 3104.83 1.81565
\(144\) 0 0
\(145\) −893.675 −0.511832
\(146\) 819.924 1420.15i 0.464777 0.805017i
\(147\) 0 0
\(148\) −1607.37 2784.04i −0.892735 1.54626i
\(149\) 875.309 + 1516.08i 0.481263 + 0.833572i 0.999769 0.0215024i \(-0.00684497\pi\)
−0.518506 + 0.855074i \(0.673512\pi\)
\(150\) 0 0
\(151\) −437.977 + 758.598i −0.236040 + 0.408833i −0.959574 0.281455i \(-0.909183\pi\)
0.723534 + 0.690288i \(0.242516\pi\)
\(152\) −223.850 −0.119451
\(153\) 0 0
\(154\) 6103.12 3.19353
\(155\) 385.093 667.001i 0.199558 0.345644i
\(156\) 0 0
\(157\) 129.697 + 224.642i 0.0659298 + 0.114194i 0.897106 0.441815i \(-0.145665\pi\)
−0.831176 + 0.556009i \(0.812332\pi\)
\(158\) 1489.96 + 2580.69i 0.750222 + 1.29942i
\(159\) 0 0
\(160\) −455.264 + 788.540i −0.224948 + 0.389622i
\(161\) 192.939 0.0944457
\(162\) 0 0
\(163\) −1201.80 −0.577498 −0.288749 0.957405i \(-0.593239\pi\)
−0.288749 + 0.957405i \(0.593239\pi\)
\(164\) 1612.54 2792.99i 0.767792 1.32986i
\(165\) 0 0
\(166\) −1859.49 3220.72i −0.869422 1.50588i
\(167\) −839.452 1453.97i −0.388975 0.673724i 0.603337 0.797486i \(-0.293837\pi\)
−0.992312 + 0.123762i \(0.960504\pi\)
\(168\) 0 0
\(169\) 3.35162 5.80518i 0.00152554 0.00264232i
\(170\) −1089.05 −0.491329
\(171\) 0 0
\(172\) −2741.70 −1.21542
\(173\) 465.899 806.961i 0.204749 0.354636i −0.745303 0.666725i \(-0.767695\pi\)
0.950053 + 0.312089i \(0.101029\pi\)
\(174\) 0 0
\(175\) 251.432 + 435.493i 0.108608 + 0.188115i
\(176\) −15.7796 27.3311i −0.00675814 0.0117054i
\(177\) 0 0
\(178\) −459.644 + 796.127i −0.193549 + 0.335237i
\(179\) −1023.40 −0.427333 −0.213667 0.976907i \(-0.568541\pi\)
−0.213667 + 0.976907i \(0.568541\pi\)
\(180\) 0 0
\(181\) 2639.93 1.08411 0.542056 0.840342i \(-0.317646\pi\)
0.542056 + 0.840342i \(0.317646\pi\)
\(182\) −2152.72 + 3728.62i −0.876760 + 1.51859i
\(183\) 0 0
\(184\) 107.868 + 186.833i 0.0432182 + 0.0748562i
\(185\) 622.160 + 1077.61i 0.247255 + 0.428258i
\(186\) 0 0
\(187\) 1579.70 2736.13i 0.617750 1.06997i
\(188\) −6144.84 −2.38382
\(189\) 0 0
\(190\) 227.599 0.0869039
\(191\) −406.640 + 704.322i −0.154050 + 0.266822i −0.932713 0.360621i \(-0.882565\pi\)
0.778663 + 0.627442i \(0.215898\pi\)
\(192\) 0 0
\(193\) 407.121 + 705.154i 0.151840 + 0.262995i 0.931904 0.362705i \(-0.118147\pi\)
−0.780064 + 0.625700i \(0.784813\pi\)
\(194\) −576.612 998.720i −0.213393 0.369608i
\(195\) 0 0
\(196\) −397.828 + 689.059i −0.144981 + 0.251115i
\(197\) −4078.41 −1.47500 −0.737499 0.675348i \(-0.763994\pi\)
−0.737499 + 0.675348i \(0.763994\pi\)
\(198\) 0 0
\(199\) −1342.49 −0.478224 −0.239112 0.970992i \(-0.576856\pi\)
−0.239112 + 0.970992i \(0.576856\pi\)
\(200\) −281.140 + 486.949i −0.0993981 + 0.172163i
\(201\) 0 0
\(202\) 99.7101 + 172.703i 0.0347306 + 0.0601551i
\(203\) 1797.58 + 3113.51i 0.621506 + 1.07648i
\(204\) 0 0
\(205\) −624.161 + 1081.08i −0.212650 + 0.368321i
\(206\) −6587.56 −2.22805
\(207\) 0 0
\(208\) 22.2634 0.00742159
\(209\) −330.141 + 571.821i −0.109265 + 0.189252i
\(210\) 0 0
\(211\) 1477.49 + 2559.08i 0.482059 + 0.834950i 0.999788 0.0205943i \(-0.00655583\pi\)
−0.517729 + 0.855545i \(0.673222\pi\)
\(212\) −3528.55 6111.62i −1.14312 1.97994i
\(213\) 0 0
\(214\) 813.536 1409.09i 0.259870 0.450108i
\(215\) 1061.22 0.336627
\(216\) 0 0
\(217\) −3098.39 −0.969273
\(218\) 3481.66 6030.42i 1.08169 1.87354i
\(219\) 0 0
\(220\) −2142.44 3710.82i −0.656561 1.13720i
\(221\) 1114.40 + 1930.20i 0.339198 + 0.587507i
\(222\) 0 0
\(223\) −1753.43 + 3037.03i −0.526539 + 0.911993i 0.472982 + 0.881072i \(0.343177\pi\)
−0.999522 + 0.0309212i \(0.990156\pi\)
\(224\) 3662.97 1.09260
\(225\) 0 0
\(226\) 3718.31 1.09442
\(227\) 326.413 565.364i 0.0954396 0.165306i −0.814352 0.580371i \(-0.802908\pi\)
0.909792 + 0.415064i \(0.136241\pi\)
\(228\) 0 0
\(229\) −2291.78 3969.47i −0.661331 1.14546i −0.980266 0.197682i \(-0.936659\pi\)
0.318935 0.947776i \(-0.396675\pi\)
\(230\) −109.675 189.962i −0.0314424 0.0544598i
\(231\) 0 0
\(232\) −2009.98 + 3481.39i −0.568801 + 0.985192i
\(233\) −317.527 −0.0892785 −0.0446392 0.999003i \(-0.514214\pi\)
−0.0446392 + 0.999003i \(0.514214\pi\)
\(234\) 0 0
\(235\) 2378.47 0.660230
\(236\) −2708.16 + 4690.67i −0.746975 + 1.29380i
\(237\) 0 0
\(238\) 2190.56 + 3794.17i 0.596610 + 1.03336i
\(239\) 928.835 + 1608.79i 0.251386 + 0.435414i 0.963908 0.266236i \(-0.0857802\pi\)
−0.712521 + 0.701650i \(0.752447\pi\)
\(240\) 0 0
\(241\) 1633.47 2829.25i 0.436602 0.756217i −0.560823 0.827936i \(-0.689515\pi\)
0.997425 + 0.0717190i \(0.0228485\pi\)
\(242\) 14041.8 3.72993
\(243\) 0 0
\(244\) −7042.82 −1.84783
\(245\) 153.986 266.712i 0.0401544 0.0695495i
\(246\) 0 0
\(247\) −232.898 403.390i −0.0599956 0.103915i
\(248\) −1732.24 3000.33i −0.443538 0.768231i
\(249\) 0 0
\(250\) 285.849 495.105i 0.0723147 0.125253i
\(251\) 5641.37 1.41865 0.709323 0.704884i \(-0.249001\pi\)
0.709323 + 0.704884i \(0.249001\pi\)
\(252\) 0 0
\(253\) 636.351 0.158131
\(254\) 1977.30 3424.78i 0.488452 0.846024i
\(255\) 0 0
\(256\) 2023.31 + 3504.47i 0.493971 + 0.855584i
\(257\) −586.731 1016.25i −0.142410 0.246661i 0.785994 0.618234i \(-0.212152\pi\)
−0.928404 + 0.371574i \(0.878818\pi\)
\(258\) 0 0
\(259\) 2502.89 4335.14i 0.600472 1.04005i
\(260\) 3022.77 0.721016
\(261\) 0 0
\(262\) 9963.64 2.34945
\(263\) −1448.98 + 2509.71i −0.339726 + 0.588423i −0.984381 0.176051i \(-0.943668\pi\)
0.644655 + 0.764474i \(0.277001\pi\)
\(264\) 0 0
\(265\) 1365.79 + 2365.61i 0.316602 + 0.548371i
\(266\) −457.804 792.940i −0.105526 0.182776i
\(267\) 0 0
\(268\) 2892.75 5010.40i 0.659340 1.14201i
\(269\) −2930.13 −0.664138 −0.332069 0.943255i \(-0.607747\pi\)
−0.332069 + 0.943255i \(0.607747\pi\)
\(270\) 0 0
\(271\) −668.881 −0.149932 −0.0749661 0.997186i \(-0.523885\pi\)
−0.0749661 + 0.997186i \(0.523885\pi\)
\(272\) 11.3274 19.6196i 0.00252509 0.00437358i
\(273\) 0 0
\(274\) −5257.70 9106.60i −1.15923 2.00785i
\(275\) 829.270 + 1436.34i 0.181843 + 0.314961i
\(276\) 0 0
\(277\) 316.315 547.874i 0.0686121 0.118840i −0.829679 0.558241i \(-0.811476\pi\)
0.898291 + 0.439402i \(0.144810\pi\)
\(278\) −9759.80 −2.10559
\(279\) 0 0
\(280\) 2262.00 0.482787
\(281\) −1797.65 + 3113.62i −0.381633 + 0.661007i −0.991296 0.131653i \(-0.957971\pi\)
0.609663 + 0.792661i \(0.291305\pi\)
\(282\) 0 0
\(283\) −252.184 436.796i −0.0529710 0.0917485i 0.838324 0.545172i \(-0.183536\pi\)
−0.891295 + 0.453424i \(0.850202\pi\)
\(284\) 2645.16 + 4581.55i 0.552680 + 0.957270i
\(285\) 0 0
\(286\) −7100.08 + 12297.7i −1.46796 + 2.54258i
\(287\) 5021.88 1.03286
\(288\) 0 0
\(289\) −2645.02 −0.538372
\(290\) 2043.65 3539.70i 0.413817 0.716753i
\(291\) 0 0
\(292\) 2315.80 + 4011.08i 0.464116 + 0.803872i
\(293\) 3099.25 + 5368.06i 0.617953 + 1.07033i 0.989859 + 0.142055i \(0.0453710\pi\)
−0.371906 + 0.928270i \(0.621296\pi\)
\(294\) 0 0
\(295\) 1048.24 1815.61i 0.206885 0.358335i
\(296\) 5597.26 1.09910
\(297\) 0 0
\(298\) −8006.60 −1.55641
\(299\) −224.457 + 388.770i −0.0434136 + 0.0751945i
\(300\) 0 0
\(301\) −2134.60 3697.24i −0.408759 0.707991i
\(302\) −2003.12 3469.51i −0.381678 0.661086i
\(303\) 0 0
\(304\) −2.36730 + 4.10029i −0.000446626 + 0.000773578i
\(305\) 2726.05 0.511781
\(306\) 0 0
\(307\) −1966.79 −0.365636 −0.182818 0.983147i \(-0.558522\pi\)
−0.182818 + 0.983147i \(0.558522\pi\)
\(308\) −8618.84 + 14928.3i −1.59449 + 2.76174i
\(309\) 0 0
\(310\) 1761.25 + 3050.58i 0.322686 + 0.558908i
\(311\) −1153.05 1997.15i −0.210237 0.364141i 0.741552 0.670896i \(-0.234090\pi\)
−0.951789 + 0.306755i \(0.900757\pi\)
\(312\) 0 0
\(313\) −5151.20 + 8922.14i −0.930234 + 1.61121i −0.147314 + 0.989090i \(0.547063\pi\)
−0.782920 + 0.622122i \(0.786271\pi\)
\(314\) −1186.36 −0.213218
\(315\) 0 0
\(316\) −8416.51 −1.49831
\(317\) −850.916 + 1473.83i −0.150764 + 0.261131i −0.931509 0.363719i \(-0.881507\pi\)
0.780745 + 0.624850i \(0.214840\pi\)
\(318\) 0 0
\(319\) 5928.78 + 10268.9i 1.04059 + 1.80235i
\(320\) −2072.67 3589.97i −0.362081 0.627142i
\(321\) 0 0
\(322\) −441.212 + 764.201i −0.0763596 + 0.132259i
\(323\) −473.983 −0.0816506
\(324\) 0 0
\(325\) −1170.02 −0.199695
\(326\) 2748.26 4760.13i 0.466908 0.808709i
\(327\) 0 0
\(328\) 2807.63 + 4862.95i 0.472638 + 0.818633i
\(329\) −4784.18 8286.44i −0.801703 1.38859i
\(330\) 0 0
\(331\) 4175.74 7232.60i 0.693413 1.20103i −0.277300 0.960783i \(-0.589440\pi\)
0.970713 0.240243i \(-0.0772271\pi\)
\(332\) 10503.9 1.73637
\(333\) 0 0
\(334\) 7678.61 1.25795
\(335\) −1119.69 + 1939.36i −0.182613 + 0.316295i
\(336\) 0 0
\(337\) 3928.71 + 6804.73i 0.635046 + 1.09993i 0.986505 + 0.163729i \(0.0523523\pi\)
−0.351459 + 0.936203i \(0.614314\pi\)
\(338\) 15.3289 + 26.5504i 0.00246681 + 0.00427264i
\(339\) 0 0
\(340\) 1537.95 2663.81i 0.245315 0.424898i
\(341\) −10219.1 −1.62286
\(342\) 0 0
\(343\) 5660.34 0.891048
\(344\) 2386.82 4134.10i 0.374095 0.647952i
\(345\) 0 0
\(346\) 2130.83 + 3690.70i 0.331081 + 0.573449i
\(347\) 606.088 + 1049.78i 0.0937652 + 0.162406i 0.909093 0.416594i \(-0.136776\pi\)
−0.815327 + 0.579000i \(0.803443\pi\)
\(348\) 0 0
\(349\) −699.332 + 1211.28i −0.107262 + 0.185783i −0.914660 0.404224i \(-0.867542\pi\)
0.807398 + 0.590007i \(0.200875\pi\)
\(350\) −2299.89 −0.351240
\(351\) 0 0
\(352\) 12081.2 1.82934
\(353\) 1314.21 2276.28i 0.198154 0.343214i −0.749776 0.661692i \(-0.769839\pi\)
0.947930 + 0.318479i \(0.103172\pi\)
\(354\) 0 0
\(355\) −1023.85 1773.37i −0.153072 0.265128i
\(356\) −1298.22 2248.59i −0.193274 0.334761i
\(357\) 0 0
\(358\) 2340.31 4053.53i 0.345500 0.598424i
\(359\) −3677.48 −0.540640 −0.270320 0.962770i \(-0.587130\pi\)
−0.270320 + 0.962770i \(0.587130\pi\)
\(360\) 0 0
\(361\) −6759.94 −0.985558
\(362\) −6036.96 + 10456.3i −0.876507 + 1.51815i
\(363\) 0 0
\(364\) −6080.16 10531.1i −0.875513 1.51643i
\(365\) −896.370 1552.56i −0.128543 0.222643i
\(366\) 0 0
\(367\) −5714.88 + 9898.47i −0.812846 + 1.40789i 0.0980185 + 0.995185i \(0.468750\pi\)
−0.910864 + 0.412706i \(0.864584\pi\)
\(368\) 4.56301 0.000646368
\(369\) 0 0
\(370\) −5691.00 −0.799624
\(371\) 5494.43 9516.63i 0.768886 1.33175i
\(372\) 0 0
\(373\) −1129.95 1957.13i −0.156854 0.271679i 0.776879 0.629650i \(-0.216802\pi\)
−0.933733 + 0.357971i \(0.883469\pi\)
\(374\) 7224.90 + 12513.9i 0.998905 + 1.73015i
\(375\) 0 0
\(376\) 5349.47 9265.55i 0.733717 1.27084i
\(377\) −8364.90 −1.14274
\(378\) 0 0
\(379\) −11815.8 −1.60142 −0.800709 0.599053i \(-0.795544\pi\)
−0.800709 + 0.599053i \(0.795544\pi\)
\(380\) −321.415 + 556.708i −0.0433902 + 0.0751540i
\(381\) 0 0
\(382\) −1859.80 3221.27i −0.249099 0.431452i
\(383\) −4040.11 6997.68i −0.539008 0.933589i −0.998958 0.0456440i \(-0.985466\pi\)
0.459950 0.887945i \(-0.347867\pi\)
\(384\) 0 0
\(385\) 3336.07 5778.25i 0.441616 0.764901i
\(386\) −3724.00 −0.491054
\(387\) 0 0
\(388\) 3257.17 0.426180
\(389\) 1550.22 2685.05i 0.202054 0.349968i −0.747136 0.664671i \(-0.768572\pi\)
0.949190 + 0.314703i \(0.101905\pi\)
\(390\) 0 0
\(391\) 228.402 + 395.604i 0.0295417 + 0.0511677i
\(392\) −692.669 1199.74i −0.0892476 0.154581i
\(393\) 0 0
\(394\) 9326.47 16153.9i 1.19254 2.06554i
\(395\) 3257.76 0.414976
\(396\) 0 0
\(397\) −11990.1 −1.51578 −0.757890 0.652382i \(-0.773770\pi\)
−0.757890 + 0.652382i \(0.773770\pi\)
\(398\) 3069.99 5317.38i 0.386645 0.669689i
\(399\) 0 0
\(400\) 5.94635 + 10.2994i 0.000743294 + 0.00128742i
\(401\) 6426.63 + 11131.3i 0.800326 + 1.38620i 0.919402 + 0.393320i \(0.128673\pi\)
−0.119076 + 0.992885i \(0.537993\pi\)
\(402\) 0 0
\(403\) 3604.52 6243.21i 0.445543 0.771703i
\(404\) −563.243 −0.0693623
\(405\) 0 0
\(406\) −16442.8 −2.00996
\(407\) 8255.02 14298.1i 1.00537 1.74135i
\(408\) 0 0
\(409\) −1112.54 1926.98i −0.134503 0.232966i 0.790904 0.611940i \(-0.209610\pi\)
−0.925408 + 0.378974i \(0.876277\pi\)
\(410\) −2854.65 4944.40i −0.343856 0.595576i
\(411\) 0 0
\(412\) 9302.97 16113.2i 1.11244 1.92680i
\(413\) −8433.95 −1.00486
\(414\) 0 0
\(415\) −4065.71 −0.480911
\(416\) −4261.32 + 7380.83i −0.502232 + 0.869891i
\(417\) 0 0
\(418\) −1509.93 2615.27i −0.176682 0.306021i
\(419\) 4838.33 + 8380.23i 0.564123 + 0.977090i 0.997131 + 0.0756998i \(0.0241191\pi\)
−0.433007 + 0.901390i \(0.642548\pi\)
\(420\) 0 0
\(421\) 4981.30 8627.87i 0.576660 0.998804i −0.419199 0.907894i \(-0.637689\pi\)
0.995859 0.0909098i \(-0.0289775\pi\)
\(422\) −13514.8 −1.55898
\(423\) 0 0
\(424\) 12287.3 1.40737
\(425\) −595.291 + 1031.08i −0.0679432 + 0.117681i
\(426\) 0 0
\(427\) −5483.32 9497.39i −0.621444 1.07637i
\(428\) 2297.76 + 3979.83i 0.259500 + 0.449468i
\(429\) 0 0
\(430\) −2426.80 + 4203.33i −0.272164 + 0.471402i
\(431\) 2461.47 0.275092 0.137546 0.990495i \(-0.456078\pi\)
0.137546 + 0.990495i \(0.456078\pi\)
\(432\) 0 0
\(433\) 7818.49 0.867743 0.433871 0.900975i \(-0.357147\pi\)
0.433871 + 0.900975i \(0.357147\pi\)
\(434\) 7085.36 12272.2i 0.783660 1.35734i
\(435\) 0 0
\(436\) 9833.63 + 17032.3i 1.08015 + 1.87087i
\(437\) −47.7336 82.6770i −0.00522519 0.00905030i
\(438\) 0 0
\(439\) −3105.91 + 5379.60i −0.337670 + 0.584862i −0.983994 0.178201i \(-0.942972\pi\)
0.646324 + 0.763063i \(0.276306\pi\)
\(440\) 7460.51 0.808332
\(441\) 0 0
\(442\) −10193.6 −1.09697
\(443\) 1492.17 2584.52i 0.160034 0.277188i −0.774846 0.632150i \(-0.782173\pi\)
0.934881 + 0.354962i \(0.115506\pi\)
\(444\) 0 0
\(445\) 502.499 + 870.355i 0.0535298 + 0.0927163i
\(446\) −8019.45 13890.1i −0.851417 1.47470i
\(447\) 0 0
\(448\) −8338.16 + 14442.1i −0.879333 + 1.52305i
\(449\) 810.476 0.0851865 0.0425932 0.999092i \(-0.486438\pi\)
0.0425932 + 0.999092i \(0.486438\pi\)
\(450\) 0 0
\(451\) 16563.1 1.72933
\(452\) −5251.01 + 9095.01i −0.546431 + 0.946446i
\(453\) 0 0
\(454\) 1492.88 + 2585.74i 0.154326 + 0.267301i
\(455\) 2353.43 + 4076.26i 0.242485 + 0.419996i
\(456\) 0 0
\(457\) −785.887 + 1361.20i −0.0804425 + 0.139331i −0.903440 0.428714i \(-0.858967\pi\)
0.822998 + 0.568045i \(0.192300\pi\)
\(458\) 20963.2 2.13875
\(459\) 0 0
\(460\) 619.532 0.0627953
\(461\) 1031.35 1786.34i 0.104196 0.180474i −0.809213 0.587515i \(-0.800106\pi\)
0.913410 + 0.407042i \(0.133440\pi\)
\(462\) 0 0
\(463\) −1391.62 2410.35i −0.139684 0.241940i 0.787693 0.616068i \(-0.211275\pi\)
−0.927377 + 0.374128i \(0.877942\pi\)
\(464\) 42.5128 + 73.6344i 0.00425347 + 0.00736722i
\(465\) 0 0
\(466\) 726.118 1257.67i 0.0721819 0.125023i
\(467\) −10939.7 −1.08400 −0.541999 0.840379i \(-0.682332\pi\)
−0.541999 + 0.840379i \(0.682332\pi\)
\(468\) 0 0
\(469\) 9008.83 0.886970
\(470\) −5439.06 + 9420.72i −0.533798 + 0.924565i
\(471\) 0 0
\(472\) −4715.24 8167.04i −0.459823 0.796438i
\(473\) −7040.33 12194.2i −0.684386 1.18539i
\(474\) 0 0
\(475\) 124.409 215.484i 0.0120175 0.0208149i
\(476\) −12374.1 −1.19152
\(477\) 0 0
\(478\) −8496.21 −0.812986
\(479\) 7311.85 12664.5i 0.697467 1.20805i −0.271875 0.962333i \(-0.587644\pi\)
0.969342 0.245716i \(-0.0790230\pi\)
\(480\) 0 0
\(481\) 5823.49 + 10086.6i 0.552034 + 0.956151i
\(482\) 7470.81 + 12939.8i 0.705987 + 1.22281i
\(483\) 0 0
\(484\) −19829.9 + 34346.4i −1.86231 + 3.22562i
\(485\) −1260.74 −0.118036
\(486\) 0 0
\(487\) 16473.6 1.53284 0.766419 0.642341i \(-0.222037\pi\)
0.766419 + 0.642341i \(0.222037\pi\)
\(488\) 6131.22 10619.6i 0.568744 0.985093i
\(489\) 0 0
\(490\) 704.270 + 1219.83i 0.0649299 + 0.112462i
\(491\) 10264.6 + 17778.8i 0.943450 + 1.63410i 0.758825 + 0.651295i \(0.225774\pi\)
0.184626 + 0.982809i \(0.440893\pi\)
\(492\) 0 0
\(493\) −4255.97 + 7371.56i −0.388802 + 0.673425i
\(494\) 2130.35 0.194026
\(495\) 0 0
\(496\) −73.2768 −0.00663352
\(497\) −4118.87 + 7134.10i −0.371744 + 0.643879i
\(498\) 0 0
\(499\) 7202.31 + 12474.8i 0.646131 + 1.11913i 0.984039 + 0.177953i \(0.0569475\pi\)
−0.337908 + 0.941179i \(0.609719\pi\)
\(500\) 807.352 + 1398.38i 0.0722118 + 0.125075i
\(501\) 0 0
\(502\) −12900.6 + 22344.5i −1.14698 + 1.98663i
\(503\) 2953.63 0.261821 0.130910 0.991394i \(-0.458210\pi\)
0.130910 + 0.991394i \(0.458210\pi\)
\(504\) 0 0
\(505\) 218.013 0.0192108
\(506\) −1455.20 + 2520.48i −0.127849 + 0.221441i
\(507\) 0 0
\(508\) 5584.69 + 9672.98i 0.487757 + 0.844821i
\(509\) −8684.44 15041.9i −0.756250 1.30986i −0.944750 0.327790i \(-0.893696\pi\)
0.188500 0.982073i \(-0.439637\pi\)
\(510\) 0 0
\(511\) −3606.02 + 6245.80i −0.312174 + 0.540701i
\(512\) 172.223 0.0148657
\(513\) 0 0
\(514\) 5366.92 0.460554
\(515\) −3600.88 + 6236.91i −0.308104 + 0.533652i
\(516\) 0 0
\(517\) −15779.1 27330.3i −1.34229 2.32492i
\(518\) 11447.2 + 19827.1i 0.970966 + 1.68176i
\(519\) 0 0
\(520\) −2631.51 + 4557.90i −0.221922 + 0.384379i
\(521\) 6146.30 0.516841 0.258421 0.966033i \(-0.416798\pi\)
0.258421 + 0.966033i \(0.416798\pi\)
\(522\) 0 0
\(523\) −4554.68 −0.380807 −0.190404 0.981706i \(-0.560980\pi\)
−0.190404 + 0.981706i \(0.560980\pi\)
\(524\) −14070.7 + 24371.1i −1.17305 + 2.03179i
\(525\) 0 0
\(526\) −6627.03 11478.4i −0.549339 0.951483i
\(527\) −3667.88 6352.96i −0.303179 0.525122i
\(528\) 0 0
\(529\) 6037.50 10457.3i 0.496219 0.859476i
\(530\) −12493.1 −1.02389
\(531\) 0 0
\(532\) 2586.05 0.210751
\(533\) −5842.22 + 10119.0i −0.474774 + 0.822333i
\(534\) 0 0
\(535\) −889.387 1540.46i −0.0718720 0.124486i
\(536\) 5036.64 + 8723.72i 0.405877 + 0.702999i
\(537\) 0 0
\(538\) 6700.59 11605.8i 0.536957 0.930037i
\(539\) −4086.28 −0.326547
\(540\) 0 0
\(541\) 18091.8 1.43776 0.718879 0.695135i \(-0.244655\pi\)
0.718879 + 0.695135i \(0.244655\pi\)
\(542\) 1529.59 2649.33i 0.121221 0.209960i
\(543\) 0 0
\(544\) 4336.23 + 7510.58i 0.341754 + 0.591936i
\(545\) −3806.28 6592.67i −0.299162 0.518163i
\(546\) 0 0
\(547\) −7890.69 + 13667.1i −0.616786 + 1.06830i 0.373283 + 0.927718i \(0.378232\pi\)
−0.990068 + 0.140586i \(0.955101\pi\)
\(548\) 29699.7 2.31516
\(549\) 0 0
\(550\) −7585.46 −0.588082
\(551\) 889.453 1540.58i 0.0687694 0.119112i
\(552\) 0 0
\(553\) −6552.83 11349.8i −0.503896 0.872774i
\(554\) 1446.69 + 2505.75i 0.110946 + 0.192164i
\(555\) 0 0
\(556\) 13782.8 23872.5i 1.05130 1.82090i
\(557\) 13954.5 1.06153 0.530766 0.847519i \(-0.321904\pi\)
0.530766 + 0.847519i \(0.321904\pi\)
\(558\) 0 0
\(559\) 9933.18 0.751572
\(560\) 23.9216 41.4335i 0.00180513 0.00312658i
\(561\) 0 0
\(562\) −8221.69 14240.4i −0.617102 1.06885i
\(563\) −6801.97 11781.4i −0.509181 0.881927i −0.999943 0.0106339i \(-0.996615\pi\)
0.490762 0.871293i \(-0.336718\pi\)
\(564\) 0 0
\(565\) 2032.50 3520.39i 0.151341 0.262131i
\(566\) 2306.77 0.171309
\(567\) 0 0
\(568\) −9211.10 −0.680438
\(569\) −6229.30 + 10789.5i −0.458956 + 0.794935i −0.998906 0.0467619i \(-0.985110\pi\)
0.539950 + 0.841697i \(0.318443\pi\)
\(570\) 0 0
\(571\) 6728.56 + 11654.2i 0.493137 + 0.854139i 0.999969 0.00790629i \(-0.00251668\pi\)
−0.506831 + 0.862045i \(0.669183\pi\)
\(572\) −20053.5 34733.7i −1.46587 2.53897i
\(573\) 0 0
\(574\) −11484.0 + 19890.8i −0.835074 + 1.44639i
\(575\) −239.801 −0.0173920
\(576\) 0 0
\(577\) 3722.70 0.268592 0.134296 0.990941i \(-0.457123\pi\)
0.134296 + 0.990941i \(0.457123\pi\)
\(578\) 6048.61 10476.5i 0.435275 0.753918i
\(579\) 0 0
\(580\) 5772.08 + 9997.54i 0.413229 + 0.715733i
\(581\) 8177.99 + 14164.7i 0.583959 + 1.01145i
\(582\) 0 0
\(583\) 18121.7 31387.7i 1.28735 2.22975i
\(584\) −8064.19 −0.571401
\(585\) 0 0
\(586\) −28349.3 −1.99847
\(587\) −8770.16 + 15190.4i −0.616667 + 1.06810i 0.373423 + 0.927661i \(0.378184\pi\)
−0.990090 + 0.140437i \(0.955149\pi\)
\(588\) 0 0
\(589\) 766.548 + 1327.70i 0.0536249 + 0.0928810i
\(590\) 4794.21 + 8303.82i 0.334533 + 0.579429i
\(591\) 0 0
\(592\) 59.1933 102.526i 0.00410951 0.00711788i
\(593\) 22350.6 1.54777 0.773886 0.633325i \(-0.218310\pi\)
0.773886 + 0.633325i \(0.218310\pi\)
\(594\) 0 0
\(595\) 4789.60 0.330008
\(596\) 11306.9 19584.2i 0.777097 1.34597i
\(597\) 0 0
\(598\) −1026.57 1778.07i −0.0702000 0.121590i
\(599\) −1280.81 2218.43i −0.0873665 0.151323i 0.819031 0.573750i \(-0.194512\pi\)
−0.906397 + 0.422427i \(0.861178\pi\)
\(600\) 0 0
\(601\) −6692.51 + 11591.8i −0.454232 + 0.786752i −0.998644 0.0520656i \(-0.983420\pi\)
0.544412 + 0.838818i \(0.316753\pi\)
\(602\) 19525.6 1.32193
\(603\) 0 0
\(604\) 11315.3 0.762270
\(605\) 7675.51 13294.4i 0.515791 0.893377i
\(606\) 0 0
\(607\) 14314.3 + 24793.1i 0.957166 + 1.65786i 0.729331 + 0.684161i \(0.239831\pi\)
0.227835 + 0.973700i \(0.426835\pi\)
\(608\) −906.226 1569.63i −0.0604479 0.104699i
\(609\) 0 0
\(610\) −6233.90 + 10797.4i −0.413776 + 0.716681i
\(611\) 22262.8 1.47407
\(612\) 0 0
\(613\) 7188.12 0.473614 0.236807 0.971557i \(-0.423899\pi\)
0.236807 + 0.971557i \(0.423899\pi\)
\(614\) 4497.63 7790.12i 0.295618 0.512025i
\(615\) 0 0
\(616\) −15006.5 25992.0i −0.981539 1.70008i
\(617\) 7766.88 + 13452.6i 0.506779 + 0.877767i 0.999969 + 0.00784559i \(0.00249736\pi\)
−0.493190 + 0.869922i \(0.664169\pi\)
\(618\) 0 0
\(619\) 11079.9 19191.0i 0.719450 1.24612i −0.241769 0.970334i \(-0.577728\pi\)
0.961218 0.275789i \(-0.0889392\pi\)
\(620\) −9948.99 −0.644453
\(621\) 0 0
\(622\) 10547.2 0.679908
\(623\) 2021.51 3501.36i 0.130000 0.225167i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −23559.4 40806.1i −1.50419 2.60534i
\(627\) 0 0
\(628\) 1675.38 2901.85i 0.106457 0.184389i
\(629\) 11851.7 0.751287
\(630\) 0 0
\(631\) −25582.8 −1.61400 −0.807002 0.590549i \(-0.798911\pi\)
−0.807002 + 0.590549i \(0.798911\pi\)
\(632\) 7327.10 12690.9i 0.461165 0.798761i
\(633\) 0 0
\(634\) −3891.73 6740.68i −0.243786 0.422250i
\(635\) −2161.65 3744.10i −0.135091 0.233984i
\(636\) 0 0
\(637\) 1441.33 2496.46i 0.0896510 0.155280i
\(638\) −54231.5 −3.36527
\(639\) 0 0
\(640\) 11674.8 0.721076
\(641\) 1905.34 3300.14i 0.117405 0.203351i −0.801334 0.598217i \(-0.795876\pi\)
0.918738 + 0.394867i \(0.129209\pi\)
\(642\) 0 0
\(643\) −13360.0 23140.3i −0.819391 1.41923i −0.906131 0.422996i \(-0.860978\pi\)
0.0867402 0.996231i \(-0.472355\pi\)
\(644\) −1246.16 2158.41i −0.0762509 0.132071i
\(645\) 0 0
\(646\) 1083.90 1877.37i 0.0660147 0.114341i
\(647\) −5114.23 −0.310759 −0.155380 0.987855i \(-0.549660\pi\)
−0.155380 + 0.987855i \(0.549660\pi\)
\(648\) 0 0
\(649\) −27816.8 −1.68244
\(650\) 2675.58 4634.24i 0.161454 0.279646i
\(651\) 0 0
\(652\) 7762.20 + 13444.5i 0.466244 + 0.807559i
\(653\) −4435.53 7682.56i −0.265813 0.460401i 0.701964 0.712213i \(-0.252307\pi\)
−0.967776 + 0.251812i \(0.918974\pi\)
\(654\) 0 0
\(655\) 5446.30 9433.27i 0.324893 0.562730i
\(656\) 118.767 0.00706872
\(657\) 0 0
\(658\) 43761.7 2.59272
\(659\) −12102.2 + 20961.7i −0.715382 + 1.23908i 0.247430 + 0.968906i \(0.420414\pi\)
−0.962812 + 0.270172i \(0.912920\pi\)
\(660\) 0 0
\(661\) −10689.8 18515.2i −0.629023 1.08950i −0.987748 0.156056i \(-0.950122\pi\)
0.358726 0.933443i \(-0.383211\pi\)
\(662\) 19098.1 + 33078.9i 1.12125 + 1.94207i
\(663\) 0 0
\(664\) −9144.28 + 15838.4i −0.534438 + 0.925674i
\(665\) −1000.98 −0.0583702
\(666\) 0 0
\(667\) −1714.43 −0.0995248
\(668\) −10843.7 + 18781.9i −0.628079 + 1.08787i
\(669\) 0 0
\(670\) −5121.00 8869.83i −0.295286 0.511450i
\(671\) −18085.0 31324.2i −1.04048 1.80217i
\(672\) 0 0
\(673\) −14850.7 + 25722.1i −0.850597 + 1.47328i 0.0300732 + 0.999548i \(0.490426\pi\)
−0.880670 + 0.473730i \(0.842907\pi\)
\(674\) −35936.6 −2.05375
\(675\) 0 0
\(676\) −86.5900 −0.00492661
\(677\) 1330.74 2304.91i 0.0755459 0.130849i −0.825778 0.563996i \(-0.809263\pi\)
0.901324 + 0.433147i \(0.142597\pi\)
\(678\) 0 0
\(679\) 2535.93 + 4392.36i 0.143328 + 0.248252i
\(680\) 2677.77 + 4638.03i 0.151011 + 0.261559i
\(681\) 0 0
\(682\) 23368.9 40476.1i 1.31208 2.27259i
\(683\) −28698.1 −1.60776 −0.803882 0.594789i \(-0.797235\pi\)
−0.803882 + 0.594789i \(0.797235\pi\)
\(684\) 0 0
\(685\) −11495.8 −0.641215
\(686\) −12944.0 + 22419.7i −0.720415 + 1.24780i
\(687\) 0 0
\(688\) −50.4833 87.4396i −0.00279747 0.00484535i
\(689\) 12783.9 + 22142.4i 0.706863 + 1.22432i
\(690\) 0 0
\(691\) −8412.62 + 14571.1i −0.463142 + 0.802186i −0.999116 0.0420492i \(-0.986611\pi\)
0.535973 + 0.844235i \(0.319945\pi\)
\(692\) −12036.6 −0.661220
\(693\) 0 0
\(694\) −5543.99 −0.303238
\(695\) −5334.88 + 9240.28i −0.291170 + 0.504322i
\(696\) 0 0
\(697\) 5944.92 + 10296.9i 0.323070 + 0.559574i
\(698\) −3198.45 5539.88i −0.173443 0.300412i
\(699\) 0 0
\(700\) 3247.90 5625.54i 0.175370 0.303750i
\(701\) 998.795 0.0538145 0.0269073 0.999638i \(-0.491434\pi\)
0.0269073 + 0.999638i \(0.491434\pi\)
\(702\) 0 0
\(703\) −2476.88 −0.132884
\(704\) −27500.8 + 47632.9i −1.47227 + 2.55004i
\(705\) 0 0
\(706\) 6010.66 + 10410.8i 0.320417 + 0.554978i
\(707\) −438.523 759.545i −0.0233272 0.0404040i
\(708\) 0 0
\(709\) −16626.9 + 28798.6i −0.880727 + 1.52546i −0.0301937 + 0.999544i \(0.509612\pi\)
−0.850534 + 0.525921i \(0.823721\pi\)
\(710\) 9365.36 0.495036
\(711\) 0 0
\(712\) 4520.73 0.237952
\(713\) 738.765 1279.58i 0.0388036 0.0672099i
\(714\) 0 0
\(715\) 7762.06 + 13444.3i 0.405993 + 0.703200i
\(716\) 6609.97 + 11448.8i 0.345009 + 0.597573i
\(717\) 0 0
\(718\) 8409.62 14565.9i 0.437109 0.757095i
\(719\) −1178.94 −0.0611503 −0.0305752 0.999532i \(-0.509734\pi\)
−0.0305752 + 0.999532i \(0.509734\pi\)
\(720\) 0 0
\(721\) 28972.0 1.49650
\(722\) 15458.6 26775.0i 0.796826 1.38014i
\(723\) 0 0
\(724\) −17050.8 29532.9i −0.875260 1.51600i
\(725\) −2234.19 3869.72i −0.114449 0.198232i
\(726\) 0 0
\(727\) −6338.35 + 10978.3i −0.323351 + 0.560061i −0.981177 0.193109i \(-0.938143\pi\)
0.657826 + 0.753170i \(0.271476\pi\)
\(728\) 21172.6 1.07790
\(729\) 0 0
\(730\) 8199.24 0.415709
\(731\) 5053.90 8753.61i 0.255712 0.442906i
\(732\) 0 0
\(733\) −4903.42 8492.98i −0.247083 0.427961i 0.715632 0.698478i \(-0.246139\pi\)
−0.962715 + 0.270517i \(0.912805\pi\)
\(734\) −26137.5 45271.4i −1.31438 2.27657i
\(735\) 0 0
\(736\) −873.381 + 1512.74i −0.0437408 + 0.0757613i
\(737\) 29712.8 1.48506
\(738\) 0 0
\(739\) −29970.4 −1.49185 −0.745927 0.666028i \(-0.767993\pi\)
−0.745927 + 0.666028i \(0.767993\pi\)
\(740\) 8036.84 13920.2i 0.399243 0.691510i
\(741\) 0 0
\(742\) 25129.2 + 43525.1i 1.24329 + 2.15345i
\(743\) 10848.8 + 18790.6i 0.535670 + 0.927808i 0.999131 + 0.0416904i \(0.0132743\pi\)
−0.463460 + 0.886118i \(0.653392\pi\)
\(744\) 0 0
\(745\) −4376.55 + 7580.40i −0.215227 + 0.372785i
\(746\) 10335.8 0.507267
\(747\) 0 0
\(748\) −40812.1 −1.99497
\(749\) −3577.92 + 6197.14i −0.174545 + 0.302321i
\(750\) 0 0
\(751\) −8512.10 14743.4i −0.413596 0.716370i 0.581684 0.813415i \(-0.302394\pi\)
−0.995280 + 0.0970452i \(0.969061\pi\)
\(752\) −113.146 195.974i −0.00548670 0.00950324i
\(753\) 0 0
\(754\) 19128.8 33132.0i 0.923911 1.60026i
\(755\) −4379.77 −0.211121
\(756\) 0 0
\(757\) 30745.2 1.47616 0.738080 0.674714i \(-0.235733\pi\)
0.738080 + 0.674714i \(0.235733\pi\)
\(758\) 27020.3 46800.5i 1.29475 2.24257i
\(759\) 0 0
\(760\) −559.624 969.298i −0.0267101 0.0462633i
\(761\) 10748.3 + 18616.6i 0.511992 + 0.886797i 0.999903 + 0.0139035i \(0.00442575\pi\)
−0.487911 + 0.872893i \(0.662241\pi\)
\(762\) 0 0
\(763\) −15312.3 + 26521.7i −0.726530 + 1.25839i
\(764\) 10505.7 0.497489
\(765\) 0 0
\(766\) 36955.5 1.74316
\(767\) 9811.66 16994.3i 0.461902 0.800037i
\(768\) 0 0
\(769\) −11028.7 19102.4i −0.517174 0.895772i −0.999801 0.0199457i \(-0.993651\pi\)
0.482627 0.875826i \(-0.339683\pi\)
\(770\) 15257.8 + 26427.3i 0.714095 + 1.23685i
\(771\) 0 0
\(772\) 5259.04 9108.93i 0.245178 0.424660i
\(773\) −30155.8 −1.40314 −0.701570 0.712601i \(-0.747517\pi\)
−0.701570 + 0.712601i \(0.747517\pi\)
\(774\) 0 0
\(775\) 3850.93 0.178490
\(776\) −2835.57 + 4911.35i −0.131174 + 0.227200i
\(777\) 0 0
\(778\) 7090.04 + 12280.3i 0.326723 + 0.565900i
\(779\) −1242.42 2151.94i −0.0571431 0.0989747i
\(780\) 0 0
\(781\) −13584.8 + 23529.6i −0.622411 + 1.07805i
\(782\) −2089.23 −0.0955381
\(783\) 0 0
\(784\) −29.3010 −0.00133478
\(785\) −648.487 + 1123.21i −0.0294847 + 0.0510690i
\(786\) 0 0
\(787\) 1624.36 + 2813.47i 0.0735733 + 0.127433i 0.900465 0.434929i \(-0.143226\pi\)
−0.826892 + 0.562361i \(0.809893\pi\)
\(788\) 26341.7 + 45625.2i 1.19084 + 2.06260i
\(789\) 0 0
\(790\) −7449.81 + 12903.4i −0.335509 + 0.581119i
\(791\) −16353.1 −0.735081
\(792\) 0 0
\(793\) 25516.1 1.14263
\(794\) 27418.8 47490.8i 1.22551 2.12265i
\(795\) 0 0
\(796\) 8670.90 + 15018.4i 0.386095 + 0.668737i
\(797\) −13855.1 23997.7i −0.615775 1.06655i −0.990248 0.139316i \(-0.955510\pi\)
0.374473 0.927238i \(-0.377824\pi\)
\(798\) 0 0
\(799\) 11327.1 19619.0i 0.501530 0.868675i
\(800\) −4552.64 −0.201200
\(801\) 0 0
\(802\) −58785.4 −2.58826
\(803\) −11893.3 + 20599.8i −0.522673 + 0.905296i
\(804\) 0 0
\(805\) 482.348 + 835.452i 0.0211187 + 0.0365786i
\(806\) 16485.6 + 28553.8i 0.720445 + 1.24785i
\(807\) 0 0
\(808\) 490.338 849.290i 0.0213491 0.0369776i
\(809\) 2244.10 0.0975259 0.0487630 0.998810i \(-0.484472\pi\)
0.0487630 + 0.998810i \(0.484472\pi\)
\(810\) 0 0
\(811\) −2739.73 −0.118625 −0.0593126 0.998239i \(-0.518891\pi\)
−0.0593126 + 0.998239i \(0.518891\pi\)
\(812\) 23220.6 40219.2i 1.00355 1.73820i
\(813\) 0 0
\(814\) 37755.0 + 65393.5i 1.62569 + 2.81578i
\(815\) −3004.50 5203.94i −0.129132 0.223664i
\(816\) 0 0
\(817\) −1056.21 + 1829.41i −0.0452290 + 0.0783390i
\(818\) 10176.6 0.434984
\(819\) 0 0
\(820\) 16125.4 0.686734
\(821\) −8616.06 + 14923.5i −0.366264 + 0.634388i −0.988978 0.148062i \(-0.952697\pi\)
0.622714 + 0.782449i \(0.286030\pi\)
\(822\) 0 0
\(823\) −9642.94 16702.1i −0.408422 0.707409i 0.586291 0.810101i \(-0.300588\pi\)
−0.994713 + 0.102692i \(0.967254\pi\)
\(824\) 16197.6 + 28055.1i 0.684795 + 1.18610i
\(825\) 0 0
\(826\) 19286.7 33405.5i 0.812433 1.40717i
\(827\) −26379.4 −1.10919 −0.554595 0.832120i \(-0.687127\pi\)
−0.554595 + 0.832120i \(0.687127\pi\)
\(828\) 0 0
\(829\) −8718.15 −0.365252 −0.182626 0.983182i \(-0.558460\pi\)
−0.182626 + 0.983182i \(0.558460\pi\)
\(830\) 9297.43 16103.6i 0.388818 0.673452i
\(831\) 0 0
\(832\) −19400.4 33602.6i −0.808401 1.40019i
\(833\) −1466.67 2540.35i −0.0610049 0.105664i
\(834\) 0 0
\(835\) 4197.26 7269.87i 0.173955 0.301299i
\(836\) 8529.28 0.352860
\(837\) 0 0
\(838\) −44256.9 −1.82438
\(839\) −6738.10 + 11670.7i −0.277265 + 0.480236i −0.970704 0.240279i \(-0.922761\pi\)
0.693439 + 0.720515i \(0.256095\pi\)
\(840\) 0 0
\(841\) −3778.58 6544.70i −0.154930 0.268346i
\(842\) 22782.4 + 39460.2i 0.932462 + 1.61507i
\(843\) 0 0
\(844\) 19085.6 33057.3i 0.778383 1.34820i
\(845\) 33.5162 0.00136449
\(846\) 0 0
\(847\) −61755.7 −2.50526
\(848\) 129.943 225.068i 0.00526210 0.00911423i
\(849\) 0 0
\(850\) −2722.61 4715.70i −0.109865 0.190291i
\(851\) 1193.56 + 2067.30i 0.0480783 + 0.0832740i
\(852\) 0 0
\(853\) 14118.3 24453.6i 0.566708 0.981567i −0.430181 0.902743i \(-0.641550\pi\)
0.996889 0.0788242i \(-0.0251166\pi\)
\(854\) 50156.8 2.00975
\(855\) 0 0
\(856\) −8001.36 −0.319487
\(857\) 4229.08 7324.98i 0.168568 0.291968i −0.769349 0.638829i \(-0.779419\pi\)
0.937917 + 0.346861i \(0.112752\pi\)
\(858\) 0 0
\(859\) 11527.2 + 19965.6i 0.457860 + 0.793036i 0.998848 0.0479940i \(-0.0152828\pi\)
−0.540988 + 0.841030i \(0.681950\pi\)
\(860\) −6854.25 11871.9i −0.271777 0.470731i
\(861\) 0 0
\(862\) −5628.86 + 9749.48i −0.222413 + 0.385230i
\(863\) 42314.4 1.66906 0.834529 0.550963i \(-0.185740\pi\)
0.834529 + 0.550963i \(0.185740\pi\)
\(864\) 0 0
\(865\) 4658.99 0.183133
\(866\) −17879.2 + 30967.8i −0.701572 + 1.21516i
\(867\) 0 0
\(868\) 20011.9 + 34661.7i 0.782545 + 1.35541i
\(869\) −21612.5 37433.9i −0.843674 1.46129i
\(870\) 0 0
\(871\) −10480.4 + 18152.7i −0.407711 + 0.706176i
\(872\) −34243.1 −1.32984
\(873\) 0 0
\(874\) 436.627 0.0168983
\(875\) −1257.16 + 2177.46i −0.0485711 + 0.0841276i
\(876\) 0 0
\(877\) 5090.00 + 8816.15i 0.195983 + 0.339453i 0.947222 0.320577i \(-0.103877\pi\)
−0.751239 + 0.660030i \(0.770544\pi\)
\(878\) −14205.2 24604.0i −0.546014 0.945725i
\(879\) 0 0
\(880\) 78.8980 136.655i 0.00302233 0.00523483i
\(881\) −6030.64 −0.230621 −0.115311 0.993329i \(-0.536786\pi\)
−0.115311 + 0.993329i \(0.536786\pi\)
\(882\) 0 0
\(883\) −30238.0 −1.15242 −0.576211 0.817301i \(-0.695469\pi\)
−0.576211 + 0.817301i \(0.695469\pi\)
\(884\) 14395.4 24933.6i 0.547704 0.948651i
\(885\) 0 0
\(886\) 6824.57 + 11820.5i 0.258776 + 0.448214i
\(887\) 9388.09 + 16260.7i 0.355379 + 0.615535i 0.987183 0.159594i \(-0.0510184\pi\)
−0.631804 + 0.775129i \(0.717685\pi\)
\(888\) 0 0
\(889\) −8696.14 + 15062.1i −0.328075 + 0.568243i
\(890\) −4596.44 −0.173116
\(891\) 0 0
\(892\) 45300.3 1.70041
\(893\) −2367.23 + 4100.17i −0.0887082 + 0.153647i
\(894\) 0 0
\(895\) −2558.51 4431.46i −0.0955547 0.165506i
\(896\) −23483.4 40674.4i −0.875586 1.51656i
\(897\) 0 0
\(898\) −1853.39 + 3210.16i −0.0688735 + 0.119292i
\(899\) 27531.8 1.02140
\(900\) 0 0
\(901\) 26017.3 0.962000
\(902\) −37876.4 + 65603.8i −1.39817 + 2.42169i
\(903\) 0 0
\(904\) −9142.66 15835.6i −0.336372 0.582614i
\(905\) 6599.82 + 11431.2i 0.242415 + 0.419875i
\(906\) 0 0
\(907\) 18826.3 32608.1i 0.689213 1.19375i −0.282880 0.959155i \(-0.591290\pi\)
0.972093 0.234597i \(-0.0753769\pi\)
\(908\) −8432.97 −0.308214
\(909\) 0 0
\(910\) −21527.2 −0.784198
\(911\) −23793.1 + 41210.8i −0.865312 + 1.49877i 0.00142411 + 0.999999i \(0.499547\pi\)
−0.866737 + 0.498766i \(0.833787\pi\)
\(912\) 0 0
\(913\) 26972.6 + 46717.9i 0.977724 + 1.69347i
\(914\) −3594.32 6225.54i −0.130076 0.225298i
\(915\) 0 0
\(916\) −29604.3 + 51276.2i −1.06785 + 1.84958i
\(917\) −43819.9 −1.57804
\(918\) 0 0
\(919\) 32177.3 1.15499 0.577493 0.816396i \(-0.304031\pi\)
0.577493 + 0.816396i \(0.304031\pi\)
\(920\) −539.341 + 934.167i −0.0193278 + 0.0334767i
\(921\) 0 0
\(922\) 4716.94 + 8169.99i 0.168486 + 0.291827i
\(923\) −9583.40 16598.9i −0.341757 0.591940i
\(924\) 0 0
\(925\) −3110.80 + 5388.07i −0.110576 + 0.191523i
\(926\) 12729.3 0.451741
\(927\) 0 0
\(928\) −32548.6 −1.15136
\(929\) 20321.8 35198.4i 0.717694 1.24308i −0.244218 0.969720i \(-0.578531\pi\)
0.961911 0.273362i \(-0.0881355\pi\)
\(930\) 0 0
\(931\) 306.518 + 530.905i 0.0107903 + 0.0186893i
\(932\) 2050.85 + 3552.18i 0.0720792 + 0.124845i
\(933\) 0 0
\(934\) 25016.7 43330.2i 0.876415 1.51799i
\(935\) 15797.0 0.552533
\(936\) 0 0
\(937\) 6077.87 0.211905 0.105953 0.994371i \(-0.466211\pi\)
0.105953 + 0.994371i \(0.466211\pi\)
\(938\) −20601.3 + 35682.5i −0.717118 + 1.24208i
\(939\) 0 0
\(940\) −15362.1 26607.9i −0.533039 0.923250i
\(941\) 732.293 + 1268.37i 0.0253688 + 0.0439401i 0.878431 0.477869i \(-0.158591\pi\)
−0.853062 + 0.521809i \(0.825257\pi\)
\(942\) 0 0
\(943\) −1197.39 + 2073.95i −0.0413494 + 0.0716193i
\(944\) −199.463 −0.00687707
\(945\) 0 0
\(946\) 64399.0 2.21331
\(947\) −5304.36 + 9187.43i −0.182015 + 0.315260i −0.942567 0.334018i \(-0.891595\pi\)
0.760551 + 0.649278i \(0.224929\pi\)
\(948\) 0 0
\(949\) −8390.14 14532.1i −0.286992 0.497085i
\(950\) 568.997 + 985.531i 0.0194323 + 0.0336577i
\(951\) 0 0
\(952\) 10772.4 18658.4i 0.366739 0.635211i
\(953\) 43623.4 1.48279 0.741396 0.671068i \(-0.234164\pi\)
0.741396 + 0.671068i \(0.234164\pi\)
\(954\) 0 0
\(955\) −4066.40 −0.137786
\(956\) 11998.4 20781.8i 0.405915 0.703065i
\(957\) 0 0
\(958\) 33441.3 + 57922.1i 1.12781 + 1.95342i
\(959\) 23123.3 + 40050.7i 0.778613 + 1.34860i
\(960\) 0 0
\(961\) 3031.76 5251.17i 0.101768 0.176267i
\(962\) −53268.4 −1.78528
\(963\) 0 0
\(964\) −42201.2 −1.40997
\(965\) −2035.61 + 3525.77i −0.0679051 + 0.117615i
\(966\) 0 0
\(967\) −2540.19 4399.73i −0.0844745 0.146314i 0.820693 0.571370i \(-0.193588\pi\)
−0.905167 + 0.425056i \(0.860254\pi\)
\(968\) −34526.3 59801.3i −1.14640 1.98563i
\(969\) 0 0
\(970\) 2883.06 4993.60i 0.0954324 0.165294i
\(971\) −9875.60 −0.326388 −0.163194 0.986594i \(-0.552180\pi\)
−0.163194 + 0.986594i \(0.552180\pi\)
\(972\) 0 0
\(973\) 42923.4 1.41425
\(974\) −37671.8 + 65249.4i −1.23930 + 2.14654i
\(975\) 0 0
\(976\) −129.680 224.613i −0.00425304 0.00736648i
\(977\) 12290.4 + 21287.6i 0.402461 + 0.697084i 0.994022 0.109177i \(-0.0348214\pi\)
−0.591561 + 0.806260i \(0.701488\pi\)
\(978\) 0 0
\(979\) 6667.32 11548.1i 0.217659 0.376997i
\(980\) −3978.28 −0.129675
\(981\) 0 0
\(982\) −93891.8 −3.05113
\(983\) −15930.3 + 27592.1i −0.516885 + 0.895270i 0.482923 + 0.875663i \(0.339575\pi\)
−0.999808 + 0.0196076i \(0.993758\pi\)
\(984\) 0 0
\(985\) −10196.0 17660.0i −0.329820 0.571265i
\(986\) −19465.0 33714.4i −0.628695 1.08893i
\(987\) 0 0
\(988\) −3008.49 + 5210.85i −0.0968752 + 0.167793i
\(989\) 2035.86 0.0654566
\(990\) 0 0
\(991\) −36921.3 −1.18350 −0.591748 0.806123i \(-0.701562\pi\)
−0.591748 + 0.806123i \(0.701562\pi\)
\(992\) 14025.5 24292.9i 0.448902 0.777520i
\(993\) 0 0
\(994\) −18838.0 32628.4i −0.601112 1.04116i
\(995\) −3356.22 5813.15i −0.106934 0.185215i
\(996\) 0 0
\(997\) 1867.06 3233.84i 0.0593083 0.102725i −0.834847 0.550482i \(-0.814444\pi\)
0.894155 + 0.447757i \(0.147777\pi\)
\(998\) −65880.7 −2.08959
\(999\) 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 135.4.e.b.46.1 6
3.2 odd 2 45.4.e.b.16.3 6
9.2 odd 6 405.4.a.h.1.1 3
9.4 even 3 inner 135.4.e.b.91.1 6
9.5 odd 6 45.4.e.b.31.3 yes 6
9.7 even 3 405.4.a.j.1.3 3
15.2 even 4 225.4.k.c.124.6 12
15.8 even 4 225.4.k.c.124.1 12
15.14 odd 2 225.4.e.c.151.1 6
45.14 odd 6 225.4.e.c.76.1 6
45.23 even 12 225.4.k.c.49.6 12
45.29 odd 6 2025.4.a.s.1.3 3
45.32 even 12 225.4.k.c.49.1 12
45.34 even 6 2025.4.a.q.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.b.16.3 6 3.2 odd 2
45.4.e.b.31.3 yes 6 9.5 odd 6
135.4.e.b.46.1 6 1.1 even 1 trivial
135.4.e.b.91.1 6 9.4 even 3 inner
225.4.e.c.76.1 6 45.14 odd 6
225.4.e.c.151.1 6 15.14 odd 2
225.4.k.c.49.1 12 45.32 even 12
225.4.k.c.49.6 12 45.23 even 12
225.4.k.c.124.1 12 15.8 even 4
225.4.k.c.124.6 12 15.2 even 4
405.4.a.h.1.1 3 9.2 odd 6
405.4.a.j.1.3 3 9.7 even 3
2025.4.a.q.1.1 3 45.34 even 6
2025.4.a.s.1.3 3 45.29 odd 6