Properties

Label 115.4.b.a.24.9
Level $115$
Weight $4$
Character 115.24
Analytic conductor $6.785$
Analytic rank $0$
Dimension $34$
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] = [115,4,Mod(24,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.24");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 115.b (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: \(6.78521965066\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 24.9
Character \(\chi\) \(=\) 115.24
Dual form 115.4.b.a.24.26

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.13266i q^{2} -8.19196i q^{3} -1.81356 q^{4} +(-9.71296 + 5.53701i) q^{5} -25.6626 q^{6} +13.4923i q^{7} -19.3800i q^{8} -40.1082 q^{9} +O(q^{10})\) \(q-3.13266i q^{2} -8.19196i q^{3} -1.81356 q^{4} +(-9.71296 + 5.53701i) q^{5} -25.6626 q^{6} +13.4923i q^{7} -19.3800i q^{8} -40.1082 q^{9} +(17.3456 + 30.4274i) q^{10} -51.7973 q^{11} +14.8566i q^{12} -3.31182i q^{13} +42.2669 q^{14} +(45.3589 + 79.5681i) q^{15} -75.2195 q^{16} -95.2632i q^{17} +125.645i q^{18} +144.212 q^{19} +(17.6150 - 10.0417i) q^{20} +110.529 q^{21} +162.263i q^{22} +23.0000i q^{23} -158.760 q^{24} +(63.6831 - 107.561i) q^{25} -10.3748 q^{26} +107.382i q^{27} -24.4691i q^{28} -161.482 q^{29} +(249.260 - 142.094i) q^{30} -226.933 q^{31} +80.5968i q^{32} +424.321i q^{33} -298.427 q^{34} +(-74.7071 - 131.050i) q^{35} +72.7384 q^{36} -187.053i q^{37} -451.768i q^{38} -27.1303 q^{39} +(107.307 + 188.237i) q^{40} +205.405 q^{41} -346.249i q^{42} -232.530i q^{43} +93.9372 q^{44} +(389.569 - 222.079i) q^{45} +72.0512 q^{46} -322.333i q^{47} +616.195i q^{48} +160.957 q^{49} +(-336.953 - 199.498i) q^{50} -780.392 q^{51} +6.00618i q^{52} +553.632i q^{53} +336.390 q^{54} +(503.105 - 286.802i) q^{55} +261.482 q^{56} -1181.38i q^{57} +505.868i q^{58} -531.694 q^{59} +(-82.2609 - 144.301i) q^{60} +97.5357 q^{61} +710.904i q^{62} -541.153i q^{63} -349.273 q^{64} +(18.3376 + 32.1676i) q^{65} +1329.25 q^{66} +97.6135i q^{67} +172.765i q^{68} +188.415 q^{69} +(-410.536 + 234.032i) q^{70} +583.010 q^{71} +777.298i q^{72} -58.9911i q^{73} -585.973 q^{74} +(-881.139 - 521.689i) q^{75} -261.537 q^{76} -698.866i q^{77} +84.9901i q^{78} +242.740 q^{79} +(730.603 - 416.491i) q^{80} -203.255 q^{81} -643.465i q^{82} -1117.40i q^{83} -200.450 q^{84} +(527.473 + 925.287i) q^{85} -728.436 q^{86} +1322.85i q^{87} +1003.83i q^{88} +455.487 q^{89} +(-695.699 - 1220.39i) q^{90} +44.6842 q^{91} -41.7118i q^{92} +1859.03i q^{93} -1009.76 q^{94} +(-1400.73 + 798.505i) q^{95} +660.245 q^{96} +431.300i q^{97} -504.223i q^{98} +2077.49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.13266i 1.10756i −0.832662 0.553781i \(-0.813184\pi\)
0.832662 0.553781i \(-0.186816\pi\)
\(3\) 8.19196i 1.57654i −0.615328 0.788272i \(-0.710976\pi\)
0.615328 0.788272i \(-0.289024\pi\)
\(4\) −1.81356 −0.226694
\(5\) −9.71296 + 5.53701i −0.868753 + 0.495245i
\(6\) −25.6626 −1.74612
\(7\) 13.4923i 0.728517i 0.931298 + 0.364259i \(0.118678\pi\)
−0.931298 + 0.364259i \(0.881322\pi\)
\(8\) 19.3800i 0.856484i
\(9\) −40.1082 −1.48549
\(10\) 17.3456 + 30.4274i 0.548515 + 0.962199i
\(11\) −51.7973 −1.41977 −0.709885 0.704318i \(-0.751253\pi\)
−0.709885 + 0.704318i \(0.751253\pi\)
\(12\) 14.8566i 0.357394i
\(13\) 3.31182i 0.0706565i −0.999376 0.0353283i \(-0.988752\pi\)
0.999376 0.0353283i \(-0.0112477\pi\)
\(14\) 42.2669 0.806879
\(15\) 45.3589 + 79.5681i 0.780775 + 1.36963i
\(16\) −75.2195 −1.17530
\(17\) 95.2632i 1.35910i −0.733629 0.679551i \(-0.762175\pi\)
0.733629 0.679551i \(-0.237825\pi\)
\(18\) 125.645i 1.64527i
\(19\) 144.212 1.74129 0.870647 0.491909i \(-0.163701\pi\)
0.870647 + 0.491909i \(0.163701\pi\)
\(20\) 17.6150 10.0417i 0.196942 0.112269i
\(21\) 110.529 1.14854
\(22\) 162.263i 1.57248i
\(23\) 23.0000i 0.208514i
\(24\) −158.760 −1.35028
\(25\) 63.6831 107.561i 0.509465 0.860491i
\(26\) −10.3748 −0.0782565
\(27\) 107.382i 0.765393i
\(28\) 24.4691i 0.165151i
\(29\) −161.482 −1.03402 −0.517008 0.855980i \(-0.672954\pi\)
−0.517008 + 0.855980i \(0.672954\pi\)
\(30\) 249.260 142.094i 1.51695 0.864757i
\(31\) −226.933 −1.31479 −0.657393 0.753548i \(-0.728341\pi\)
−0.657393 + 0.753548i \(0.728341\pi\)
\(32\) 80.5968i 0.445238i
\(33\) 424.321i 2.23833i
\(34\) −298.427 −1.50529
\(35\) −74.7071 131.050i −0.360795 0.632902i
\(36\) 72.7384 0.336752
\(37\) 187.053i 0.831116i −0.909567 0.415558i \(-0.863586\pi\)
0.909567 0.415558i \(-0.136414\pi\)
\(38\) 451.768i 1.92859i
\(39\) −27.1303 −0.111393
\(40\) 107.307 + 188.237i 0.424169 + 0.744074i
\(41\) 205.405 0.782413 0.391206 0.920303i \(-0.372058\pi\)
0.391206 + 0.920303i \(0.372058\pi\)
\(42\) 346.249i 1.27208i
\(43\) 232.530i 0.824661i −0.911034 0.412331i \(-0.864715\pi\)
0.911034 0.412331i \(-0.135285\pi\)
\(44\) 93.9372 0.321854
\(45\) 389.569 222.079i 1.29052 0.735680i
\(46\) 72.0512 0.230943
\(47\) 322.333i 1.00036i −0.865920 0.500182i \(-0.833266\pi\)
0.865920 0.500182i \(-0.166734\pi\)
\(48\) 616.195i 1.85292i
\(49\) 160.957 0.469262
\(50\) −336.953 199.498i −0.953048 0.564264i
\(51\) −780.392 −2.14268
\(52\) 6.00618i 0.0160174i
\(53\) 553.632i 1.43485i 0.696635 + 0.717426i \(0.254680\pi\)
−0.696635 + 0.717426i \(0.745320\pi\)
\(54\) 336.390 0.847721
\(55\) 503.105 286.802i 1.23343 0.703133i
\(56\) 261.482 0.623964
\(57\) 1181.38i 2.74522i
\(58\) 505.868i 1.14524i
\(59\) −531.694 −1.17323 −0.586616 0.809866i \(-0.699540\pi\)
−0.586616 + 0.809866i \(0.699540\pi\)
\(60\) −82.2609 144.301i −0.176997 0.310487i
\(61\) 97.5357 0.204724 0.102362 0.994747i \(-0.467360\pi\)
0.102362 + 0.994747i \(0.467360\pi\)
\(62\) 710.904i 1.45621i
\(63\) 541.153i 1.08220i
\(64\) −349.273 −0.682175
\(65\) 18.3376 + 32.1676i 0.0349923 + 0.0613831i
\(66\) 1329.25 2.47909
\(67\) 97.6135i 0.177991i 0.996032 + 0.0889954i \(0.0283656\pi\)
−0.996032 + 0.0889954i \(0.971634\pi\)
\(68\) 172.765i 0.308101i
\(69\) 188.415 0.328732
\(70\) −410.536 + 234.032i −0.700978 + 0.399602i
\(71\) 583.010 0.974514 0.487257 0.873259i \(-0.337997\pi\)
0.487257 + 0.873259i \(0.337997\pi\)
\(72\) 777.298i 1.27230i
\(73\) 58.9911i 0.0945806i −0.998881 0.0472903i \(-0.984941\pi\)
0.998881 0.0472903i \(-0.0150586\pi\)
\(74\) −585.973 −0.920513
\(75\) −881.139 521.689i −1.35660 0.803193i
\(76\) −261.537 −0.394741
\(77\) 698.866i 1.03433i
\(78\) 84.9901i 0.123375i
\(79\) 242.740 0.345701 0.172851 0.984948i \(-0.444702\pi\)
0.172851 + 0.984948i \(0.444702\pi\)
\(80\) 730.603 416.491i 1.02105 0.582063i
\(81\) −203.255 −0.278813
\(82\) 643.465i 0.866571i
\(83\) 1117.40i 1.47772i −0.673859 0.738860i \(-0.735365\pi\)
0.673859 0.738860i \(-0.264635\pi\)
\(84\) −200.450 −0.260367
\(85\) 527.473 + 925.287i 0.673088 + 1.18072i
\(86\) −728.436 −0.913364
\(87\) 1322.85i 1.63017i
\(88\) 1003.83i 1.21601i
\(89\) 455.487 0.542489 0.271244 0.962510i \(-0.412565\pi\)
0.271244 + 0.962510i \(0.412565\pi\)
\(90\) −695.699 1220.39i −0.814812 1.42933i
\(91\) 44.6842 0.0514745
\(92\) 41.7118i 0.0472691i
\(93\) 1859.03i 2.07282i
\(94\) −1009.76 −1.10797
\(95\) −1400.73 + 798.505i −1.51275 + 0.862367i
\(96\) 660.245 0.701937
\(97\) 431.300i 0.451463i 0.974190 + 0.225731i \(0.0724772\pi\)
−0.974190 + 0.225731i \(0.927523\pi\)
\(98\) 504.223i 0.519737i
\(99\) 2077.49 2.10905
\(100\) −115.493 + 195.069i −0.115493 + 0.195069i
\(101\) 484.213 0.477039 0.238520 0.971138i \(-0.423338\pi\)
0.238520 + 0.971138i \(0.423338\pi\)
\(102\) 2444.70i 2.37315i
\(103\) 1715.24i 1.64085i 0.571756 + 0.820424i \(0.306262\pi\)
−0.571756 + 0.820424i \(0.693738\pi\)
\(104\) −64.1832 −0.0605162
\(105\) −1073.56 + 611.998i −0.997797 + 0.568808i
\(106\) 1734.34 1.58919
\(107\) 1595.48i 1.44150i −0.693193 0.720752i \(-0.743797\pi\)
0.693193 0.720752i \(-0.256203\pi\)
\(108\) 194.743i 0.173510i
\(109\) 1533.25 1.34733 0.673663 0.739039i \(-0.264720\pi\)
0.673663 + 0.739039i \(0.264720\pi\)
\(110\) −898.452 1576.06i −0.778764 1.36610i
\(111\) −1532.33 −1.31029
\(112\) 1014.89i 0.856230i
\(113\) 966.953i 0.804985i −0.915423 0.402492i \(-0.868144\pi\)
0.915423 0.402492i \(-0.131856\pi\)
\(114\) −3700.87 −3.04051
\(115\) −127.351 223.398i −0.103266 0.181148i
\(116\) 292.857 0.234406
\(117\) 132.831i 0.104959i
\(118\) 1665.62i 1.29943i
\(119\) 1285.32 0.990129
\(120\) 1542.03 879.057i 1.17306 0.668721i
\(121\) 1351.96 1.01574
\(122\) 305.546i 0.226745i
\(123\) 1682.67i 1.23351i
\(124\) 411.556 0.298055
\(125\) −22.9830 + 1397.35i −0.0164453 + 0.999865i
\(126\) −1695.25 −1.19861
\(127\) 1049.29i 0.733147i −0.930389 0.366573i \(-0.880531\pi\)
0.930389 0.366573i \(-0.119469\pi\)
\(128\) 1738.93i 1.20079i
\(129\) −1904.87 −1.30011
\(130\) 100.770 57.4454i 0.0679856 0.0387561i
\(131\) −648.199 −0.432316 −0.216158 0.976358i \(-0.569353\pi\)
−0.216158 + 0.976358i \(0.569353\pi\)
\(132\) 769.529i 0.507416i
\(133\) 1945.76i 1.26856i
\(134\) 305.790 0.197136
\(135\) −594.573 1042.99i −0.379057 0.664938i
\(136\) −1846.20 −1.16405
\(137\) 158.366i 0.0987599i 0.998780 + 0.0493799i \(0.0157245\pi\)
−0.998780 + 0.0493799i \(0.984275\pi\)
\(138\) 590.240i 0.364091i
\(139\) −272.315 −0.166169 −0.0830843 0.996543i \(-0.526477\pi\)
−0.0830843 + 0.996543i \(0.526477\pi\)
\(140\) 135.486 + 237.667i 0.0817901 + 0.143475i
\(141\) −2640.54 −1.57712
\(142\) 1826.37i 1.07934i
\(143\) 171.543i 0.100316i
\(144\) 3016.92 1.74590
\(145\) 1568.47 894.128i 0.898305 0.512091i
\(146\) −184.799 −0.104754
\(147\) 1318.55i 0.739812i
\(148\) 339.231i 0.188409i
\(149\) 2826.23 1.55392 0.776958 0.629552i \(-0.216762\pi\)
0.776958 + 0.629552i \(0.216762\pi\)
\(150\) −1634.28 + 2760.31i −0.889587 + 1.50252i
\(151\) 2065.22 1.11302 0.556508 0.830842i \(-0.312141\pi\)
0.556508 + 0.830842i \(0.312141\pi\)
\(152\) 2794.84i 1.49139i
\(153\) 3820.83i 2.01893i
\(154\) −2189.31 −1.14558
\(155\) 2204.19 1256.53i 1.14223 0.651142i
\(156\) 49.2023 0.0252522
\(157\) 137.317i 0.0698031i 0.999391 + 0.0349015i \(0.0111118\pi\)
−0.999391 + 0.0349015i \(0.988888\pi\)
\(158\) 760.422i 0.382886i
\(159\) 4535.33 2.26211
\(160\) −446.265 782.833i −0.220502 0.386802i
\(161\) −310.324 −0.151906
\(162\) 636.728i 0.308803i
\(163\) 3089.75i 1.48471i −0.670007 0.742355i \(-0.733709\pi\)
0.670007 0.742355i \(-0.266291\pi\)
\(164\) −372.514 −0.177369
\(165\) −2349.47 4121.41i −1.10852 1.94455i
\(166\) −3500.44 −1.63667
\(167\) 199.002i 0.0922108i 0.998937 + 0.0461054i \(0.0146810\pi\)
−0.998937 + 0.0461054i \(0.985319\pi\)
\(168\) 2142.05i 0.983706i
\(169\) 2186.03 0.995008
\(170\) 2898.61 1652.39i 1.30773 0.745487i
\(171\) −5784.09 −2.58667
\(172\) 421.705i 0.186946i
\(173\) 29.5998i 0.0130083i 0.999979 + 0.00650413i \(0.00207034\pi\)
−0.999979 + 0.00650413i \(0.997930\pi\)
\(174\) 4144.05 1.80552
\(175\) 1451.25 + 859.234i 0.626883 + 0.371154i
\(176\) 3896.16 1.66866
\(177\) 4355.61i 1.84965i
\(178\) 1426.89i 0.600840i
\(179\) 329.858 0.137736 0.0688681 0.997626i \(-0.478061\pi\)
0.0688681 + 0.997626i \(0.478061\pi\)
\(180\) −706.505 + 402.753i −0.292554 + 0.166775i
\(181\) −3600.84 −1.47872 −0.739360 0.673310i \(-0.764872\pi\)
−0.739360 + 0.673310i \(0.764872\pi\)
\(182\) 139.980i 0.0570112i
\(183\) 799.009i 0.322756i
\(184\) 445.741 0.178589
\(185\) 1035.71 + 1816.84i 0.411606 + 0.722035i
\(186\) 5823.70 2.29578
\(187\) 4934.37i 1.92961i
\(188\) 584.569i 0.226777i
\(189\) −1448.83 −0.557602
\(190\) 2501.44 + 4388.00i 0.955125 + 1.67547i
\(191\) 2766.29 1.04797 0.523984 0.851728i \(-0.324445\pi\)
0.523984 + 0.851728i \(0.324445\pi\)
\(192\) 2861.23i 1.07548i
\(193\) 342.533i 0.127752i 0.997958 + 0.0638758i \(0.0203462\pi\)
−0.997958 + 0.0638758i \(0.979654\pi\)
\(194\) 1351.12 0.500023
\(195\) 263.516 150.221i 0.0967731 0.0551668i
\(196\) −291.904 −0.106379
\(197\) 390.005i 0.141049i −0.997510 0.0705246i \(-0.977533\pi\)
0.997510 0.0705246i \(-0.0224673\pi\)
\(198\) 6508.08i 2.33590i
\(199\) −3859.22 −1.37474 −0.687368 0.726309i \(-0.741234\pi\)
−0.687368 + 0.726309i \(0.741234\pi\)
\(200\) −2084.54 1234.18i −0.736997 0.436349i
\(201\) 799.646 0.280610
\(202\) 1516.87i 0.528351i
\(203\) 2178.77i 0.753299i
\(204\) 1415.28 0.485734
\(205\) −1995.09 + 1137.33i −0.679724 + 0.387486i
\(206\) 5373.25 1.81734
\(207\) 922.488i 0.309746i
\(208\) 249.114i 0.0830429i
\(209\) −7469.80 −2.47223
\(210\) 1917.18 + 3363.10i 0.629991 + 1.10512i
\(211\) −5016.57 −1.63675 −0.818376 0.574683i \(-0.805125\pi\)
−0.818376 + 0.574683i \(0.805125\pi\)
\(212\) 1004.04i 0.325273i
\(213\) 4775.99i 1.53636i
\(214\) −4998.10 −1.59656
\(215\) 1287.52 + 2258.55i 0.408409 + 0.716427i
\(216\) 2081.06 0.655547
\(217\) 3061.86i 0.957845i
\(218\) 4803.14i 1.49225i
\(219\) −483.252 −0.149110
\(220\) −912.408 + 520.131i −0.279612 + 0.159396i
\(221\) −315.495 −0.0960293
\(222\) 4800.27i 1.45123i
\(223\) 429.979i 0.129119i 0.997914 + 0.0645595i \(0.0205642\pi\)
−0.997914 + 0.0645595i \(0.979436\pi\)
\(224\) −1087.44 −0.324364
\(225\) −2554.21 + 4314.09i −0.756804 + 1.27825i
\(226\) −3029.13 −0.891571
\(227\) 699.886i 0.204639i −0.994752 0.102320i \(-0.967374\pi\)
0.994752 0.102320i \(-0.0326264\pi\)
\(228\) 2142.50i 0.622327i
\(229\) −934.970 −0.269802 −0.134901 0.990859i \(-0.543072\pi\)
−0.134901 + 0.990859i \(0.543072\pi\)
\(230\) −699.830 + 398.948i −0.200632 + 0.114373i
\(231\) −5725.08 −1.63066
\(232\) 3129.53i 0.885619i
\(233\) 852.267i 0.239630i 0.992796 + 0.119815i \(0.0382302\pi\)
−0.992796 + 0.119815i \(0.961770\pi\)
\(234\) 416.115 0.116249
\(235\) 1784.76 + 3130.81i 0.495425 + 0.869070i
\(236\) 964.256 0.265965
\(237\) 1988.52i 0.545013i
\(238\) 4026.48i 1.09663i
\(239\) −2397.28 −0.648816 −0.324408 0.945917i \(-0.605165\pi\)
−0.324408 + 0.945917i \(0.605165\pi\)
\(240\) −3411.87 5985.07i −0.917648 1.60973i
\(241\) −1284.37 −0.343293 −0.171646 0.985159i \(-0.554909\pi\)
−0.171646 + 0.985159i \(0.554909\pi\)
\(242\) 4235.22i 1.12500i
\(243\) 4564.36i 1.20495i
\(244\) −176.886 −0.0464098
\(245\) −1563.37 + 891.220i −0.407673 + 0.232400i
\(246\) −5271.24 −1.36619
\(247\) 477.606i 0.123034i
\(248\) 4397.97i 1.12609i
\(249\) −9153.70 −2.32969
\(250\) 4377.43 + 71.9981i 1.10741 + 0.0182142i
\(251\) 5446.42 1.36962 0.684810 0.728722i \(-0.259885\pi\)
0.684810 + 0.728722i \(0.259885\pi\)
\(252\) 981.411i 0.245330i
\(253\) 1191.34i 0.296042i
\(254\) −3287.07 −0.812006
\(255\) 7579.92 4321.04i 1.86146 1.06115i
\(256\) 2653.28 0.647774
\(257\) 4124.52i 1.00109i 0.865710 + 0.500546i \(0.166867\pi\)
−0.865710 + 0.500546i \(0.833133\pi\)
\(258\) 5967.32i 1.43996i
\(259\) 2523.78 0.605483
\(260\) −33.2562 58.3377i −0.00793255 0.0139152i
\(261\) 6476.75 1.53602
\(262\) 2030.59i 0.478817i
\(263\) 3653.14i 0.856512i 0.903658 + 0.428256i \(0.140872\pi\)
−0.903658 + 0.428256i \(0.859128\pi\)
\(264\) 8223.35 1.91709
\(265\) −3065.46 5377.40i −0.710603 1.24653i
\(266\) 6095.41 1.40501
\(267\) 3731.33i 0.855257i
\(268\) 177.027i 0.0403495i
\(269\) −7453.46 −1.68939 −0.844694 0.535250i \(-0.820217\pi\)
−0.844694 + 0.535250i \(0.820217\pi\)
\(270\) −3267.34 + 1862.59i −0.736460 + 0.419829i
\(271\) 7506.57 1.68263 0.841313 0.540548i \(-0.181783\pi\)
0.841313 + 0.540548i \(0.181783\pi\)
\(272\) 7165.65i 1.59736i
\(273\) 366.051i 0.0811518i
\(274\) 496.106 0.109383
\(275\) −3298.61 + 5571.39i −0.723323 + 1.22170i
\(276\) −341.701 −0.0745217
\(277\) 4672.32i 1.01347i −0.862101 0.506737i \(-0.830852\pi\)
0.862101 0.506737i \(-0.169148\pi\)
\(278\) 853.069i 0.184042i
\(279\) 9101.87 1.95310
\(280\) −2539.76 + 1447.83i −0.542071 + 0.309015i
\(281\) 1695.47 0.359941 0.179970 0.983672i \(-0.442400\pi\)
0.179970 + 0.983672i \(0.442400\pi\)
\(282\) 8271.91i 1.74676i
\(283\) 2210.76i 0.464369i 0.972672 + 0.232184i \(0.0745872\pi\)
−0.972672 + 0.232184i \(0.925413\pi\)
\(284\) −1057.32 −0.220917
\(285\) 6541.32 + 11474.7i 1.35956 + 2.38492i
\(286\) 537.387 0.111106
\(287\) 2771.40i 0.570002i
\(288\) 3232.59i 0.661396i
\(289\) −4162.08 −0.847156
\(290\) −2801.00 4913.48i −0.567173 0.994929i
\(291\) 3533.19 0.711750
\(292\) 106.984i 0.0214409i
\(293\) 944.327i 0.188287i −0.995559 0.0941436i \(-0.969989\pi\)
0.995559 0.0941436i \(-0.0300113\pi\)
\(294\) −4130.58 −0.819388
\(295\) 5164.32 2943.99i 1.01925 0.581037i
\(296\) −3625.09 −0.711838
\(297\) 5562.08i 1.08668i
\(298\) 8853.60i 1.72106i
\(299\) 76.1719 0.0147329
\(300\) 1597.99 + 946.113i 0.307534 + 0.182079i
\(301\) 3137.37 0.600780
\(302\) 6469.64i 1.23274i
\(303\) 3966.65i 0.752073i
\(304\) −10847.6 −2.04655
\(305\) −947.360 + 540.056i −0.177855 + 0.101389i
\(306\) 11969.4 2.23609
\(307\) 4124.18i 0.766708i −0.923601 0.383354i \(-0.874769\pi\)
0.923601 0.383354i \(-0.125231\pi\)
\(308\) 1267.43i 0.234476i
\(309\) 14051.1 2.58687
\(310\) −3936.28 6904.98i −0.721180 1.26509i
\(311\) −1043.49 −0.190260 −0.0951299 0.995465i \(-0.530327\pi\)
−0.0951299 + 0.995465i \(0.530327\pi\)
\(312\) 525.786i 0.0954064i
\(313\) 10692.6i 1.93093i 0.260540 + 0.965463i \(0.416099\pi\)
−0.260540 + 0.965463i \(0.583901\pi\)
\(314\) 430.167 0.0773113
\(315\) 2996.37 + 5256.20i 0.535956 + 0.940168i
\(316\) −440.223 −0.0783686
\(317\) 5607.47i 0.993524i 0.867887 + 0.496762i \(0.165478\pi\)
−0.867887 + 0.496762i \(0.834522\pi\)
\(318\) 14207.6i 2.50542i
\(319\) 8364.33 1.46806
\(320\) 3392.48 1933.93i 0.592642 0.337844i
\(321\) −13070.1 −2.27259
\(322\) 972.138i 0.168246i
\(323\) 13738.1i 2.36659i
\(324\) 368.614 0.0632054
\(325\) −356.225 210.907i −0.0607993 0.0359970i
\(326\) −9679.13 −1.64441
\(327\) 12560.3i 2.12412i
\(328\) 3980.76i 0.670124i
\(329\) 4349.03 0.728783
\(330\) −12911.0 + 7360.08i −2.15372 + 1.22776i
\(331\) −5714.38 −0.948914 −0.474457 0.880279i \(-0.657356\pi\)
−0.474457 + 0.880279i \(0.657356\pi\)
\(332\) 2026.47i 0.334991i
\(333\) 7502.35i 1.23461i
\(334\) 623.404 0.102129
\(335\) −540.486 948.116i −0.0881490 0.154630i
\(336\) −8313.90 −1.34988
\(337\) 6359.17i 1.02791i 0.857817 + 0.513956i \(0.171820\pi\)
−0.857817 + 0.513956i \(0.828180\pi\)
\(338\) 6848.09i 1.10203i
\(339\) −7921.24 −1.26909
\(340\) −956.601 1678.06i −0.152585 0.267663i
\(341\) 11754.5 1.86669
\(342\) 18119.6i 2.86490i
\(343\) 6799.55i 1.07038i
\(344\) −4506.43 −0.706309
\(345\) −1830.07 + 1043.26i −0.285587 + 0.162803i
\(346\) 92.7259 0.0144074
\(347\) 8649.58i 1.33814i −0.743200 0.669069i \(-0.766693\pi\)
0.743200 0.669069i \(-0.233307\pi\)
\(348\) 2399.07i 0.369551i
\(349\) −6134.27 −0.940859 −0.470429 0.882438i \(-0.655901\pi\)
−0.470429 + 0.882438i \(0.655901\pi\)
\(350\) 2691.69 4546.29i 0.411076 0.694312i
\(351\) 355.629 0.0540800
\(352\) 4174.69i 0.632136i
\(353\) 3494.07i 0.526828i −0.964683 0.263414i \(-0.915151\pi\)
0.964683 0.263414i \(-0.0848485\pi\)
\(354\) 13644.7 2.04860
\(355\) −5662.75 + 3228.13i −0.846613 + 0.482623i
\(356\) −826.051 −0.122979
\(357\) 10529.3i 1.56098i
\(358\) 1033.33i 0.152551i
\(359\) −11003.2 −1.61763 −0.808814 0.588064i \(-0.799890\pi\)
−0.808814 + 0.588064i \(0.799890\pi\)
\(360\) −4303.90 7549.86i −0.630099 1.10531i
\(361\) 13938.2 2.03210
\(362\) 11280.2i 1.63777i
\(363\) 11075.2i 1.60136i
\(364\) −81.0373 −0.0116690
\(365\) 326.634 + 572.978i 0.0468405 + 0.0821672i
\(366\) −2503.02 −0.357473
\(367\) 6441.75i 0.916231i −0.888893 0.458115i \(-0.848525\pi\)
0.888893 0.458115i \(-0.151475\pi\)
\(368\) 1730.05i 0.245068i
\(369\) −8238.44 −1.16227
\(370\) 5691.53 3244.54i 0.799699 0.455879i
\(371\) −7469.78 −1.04531
\(372\) 3371.45i 0.469896i
\(373\) 7432.01i 1.03168i −0.856686 0.515838i \(-0.827481\pi\)
0.856686 0.515838i \(-0.172519\pi\)
\(374\) 15457.7 2.13716
\(375\) 11447.1 + 188.276i 1.57633 + 0.0259268i
\(376\) −6246.82 −0.856796
\(377\) 534.800i 0.0730600i
\(378\) 4538.69i 0.617579i
\(379\) 7399.24 1.00283 0.501416 0.865206i \(-0.332813\pi\)
0.501416 + 0.865206i \(0.332813\pi\)
\(380\) 2540.30 1448.13i 0.342933 0.195494i
\(381\) −8595.76 −1.15584
\(382\) 8665.84i 1.16069i
\(383\) 5510.66i 0.735200i 0.929984 + 0.367600i \(0.119820\pi\)
−0.929984 + 0.367600i \(0.880180\pi\)
\(384\) 14245.2 1.89310
\(385\) 3869.62 + 6788.05i 0.512245 + 0.898575i
\(386\) 1073.04 0.141493
\(387\) 9326.34i 1.22502i
\(388\) 782.186i 0.102344i
\(389\) −7779.10 −1.01392 −0.506962 0.861969i \(-0.669231\pi\)
−0.506962 + 0.861969i \(0.669231\pi\)
\(390\) −470.591 825.505i −0.0611007 0.107182i
\(391\) 2191.05 0.283392
\(392\) 3119.35i 0.401916i
\(393\) 5310.02i 0.681565i
\(394\) −1221.75 −0.156221
\(395\) −2357.73 + 1344.05i −0.300329 + 0.171207i
\(396\) −3767.65 −0.478110
\(397\) 4722.18i 0.596976i −0.954413 0.298488i \(-0.903518\pi\)
0.954413 0.298488i \(-0.0964823\pi\)
\(398\) 12089.6i 1.52261i
\(399\) 15939.6 1.99994
\(400\) −4790.21 + 8090.71i −0.598776 + 1.01134i
\(401\) 10838.3 1.34972 0.674862 0.737944i \(-0.264203\pi\)
0.674862 + 0.737944i \(0.264203\pi\)
\(402\) 2505.02i 0.310793i
\(403\) 751.562i 0.0928982i
\(404\) −878.146 −0.108142
\(405\) 1974.20 1125.42i 0.242220 0.138081i
\(406\) −6825.35 −0.834326
\(407\) 9688.82i 1.17999i
\(408\) 15124.0i 1.83517i
\(409\) 8904.96 1.07658 0.538291 0.842759i \(-0.319070\pi\)
0.538291 + 0.842759i \(0.319070\pi\)
\(410\) 3562.87 + 6249.95i 0.429165 + 0.752837i
\(411\) 1297.33 0.155699
\(412\) 3110.68i 0.371971i
\(413\) 7173.79i 0.854719i
\(414\) −2889.84 −0.343063
\(415\) 6187.06 + 10853.3i 0.731833 + 1.28377i
\(416\) 266.922 0.0314590
\(417\) 2230.79i 0.261972i
\(418\) 23400.3i 2.73815i
\(419\) −15917.0 −1.85584 −0.927919 0.372781i \(-0.878404\pi\)
−0.927919 + 0.372781i \(0.878404\pi\)
\(420\) 1946.96 1109.89i 0.226195 0.128946i
\(421\) −1869.26 −0.216395 −0.108197 0.994129i \(-0.534508\pi\)
−0.108197 + 0.994129i \(0.534508\pi\)
\(422\) 15715.2i 1.81281i
\(423\) 12928.2i 1.48603i
\(424\) 10729.4 1.22893
\(425\) −10246.6 6066.66i −1.16949 0.692414i
\(426\) −14961.6 −1.70162
\(427\) 1315.98i 0.149145i
\(428\) 2893.49i 0.326781i
\(429\) 1405.28 0.158152
\(430\) 7075.27 4033.35i 0.793488 0.452339i
\(431\) −6903.88 −0.771573 −0.385787 0.922588i \(-0.626070\pi\)
−0.385787 + 0.922588i \(0.626070\pi\)
\(432\) 8077.19i 0.899570i
\(433\) 1991.39i 0.221016i 0.993875 + 0.110508i \(0.0352478\pi\)
−0.993875 + 0.110508i \(0.964752\pi\)
\(434\) −9591.75 −1.06087
\(435\) −7324.66 12848.8i −0.807334 1.41622i
\(436\) −2780.63 −0.305431
\(437\) 3316.88i 0.363085i
\(438\) 1513.86i 0.165149i
\(439\) 7051.99 0.766681 0.383341 0.923607i \(-0.374774\pi\)
0.383341 + 0.923607i \(0.374774\pi\)
\(440\) −5558.23 9750.18i −0.602223 1.05641i
\(441\) −6455.69 −0.697084
\(442\) 988.338i 0.106358i
\(443\) 241.640i 0.0259157i 0.999916 + 0.0129579i \(0.00412473\pi\)
−0.999916 + 0.0129579i \(0.995875\pi\)
\(444\) 2778.96 0.297036
\(445\) −4424.13 + 2522.03i −0.471289 + 0.268665i
\(446\) 1346.98 0.143007
\(447\) 23152.3i 2.44982i
\(448\) 4712.51i 0.496976i
\(449\) 12453.4 1.30894 0.654468 0.756089i \(-0.272893\pi\)
0.654468 + 0.756089i \(0.272893\pi\)
\(450\) 13514.6 + 8001.48i 1.41574 + 0.838208i
\(451\) −10639.4 −1.11085
\(452\) 1753.62i 0.182486i
\(453\) 16918.2i 1.75472i
\(454\) −2192.50 −0.226650
\(455\) −434.016 + 247.417i −0.0447186 + 0.0254925i
\(456\) −22895.2 −2.35124
\(457\) 4700.39i 0.481127i 0.970633 + 0.240564i \(0.0773323\pi\)
−0.970633 + 0.240564i \(0.922668\pi\)
\(458\) 2928.94i 0.298822i
\(459\) 10229.5 1.04025
\(460\) 230.958 + 405.145i 0.0234098 + 0.0410651i
\(461\) 9555.28 0.965366 0.482683 0.875795i \(-0.339662\pi\)
0.482683 + 0.875795i \(0.339662\pi\)
\(462\) 17934.7i 1.80606i
\(463\) 16057.0i 1.61173i −0.592098 0.805866i \(-0.701700\pi\)
0.592098 0.805866i \(-0.298300\pi\)
\(464\) 12146.6 1.21528
\(465\) −10293.4 18056.6i −1.02655 1.80077i
\(466\) 2669.86 0.265406
\(467\) 18657.5i 1.84875i 0.381484 + 0.924375i \(0.375413\pi\)
−0.381484 + 0.924375i \(0.624587\pi\)
\(468\) 240.897i 0.0237937i
\(469\) −1317.03 −0.129669
\(470\) 9807.76 5591.05i 0.962549 0.548714i
\(471\) 1124.89 0.110048
\(472\) 10304.2i 1.00485i
\(473\) 12044.4i 1.17083i
\(474\) −6229.35 −0.603636
\(475\) 9183.89 15511.7i 0.887128 1.49837i
\(476\) −2331.00 −0.224457
\(477\) 22205.2i 2.13146i
\(478\) 7509.85i 0.718604i
\(479\) −12059.8 −1.15037 −0.575184 0.818024i \(-0.695069\pi\)
−0.575184 + 0.818024i \(0.695069\pi\)
\(480\) −6412.93 + 3655.78i −0.609811 + 0.347631i
\(481\) −619.486 −0.0587238
\(482\) 4023.50i 0.380218i
\(483\) 2542.16i 0.239487i
\(484\) −2451.85 −0.230264
\(485\) −2388.11 4189.20i −0.223585 0.392210i
\(486\) 14298.6 1.33456
\(487\) 19826.9i 1.84485i −0.386178 0.922424i \(-0.626205\pi\)
0.386178 0.922424i \(-0.373795\pi\)
\(488\) 1890.24i 0.175343i
\(489\) −25311.1 −2.34071
\(490\) 2791.89 + 4897.50i 0.257397 + 0.451524i
\(491\) −1218.93 −0.112036 −0.0560178 0.998430i \(-0.517840\pi\)
−0.0560178 + 0.998430i \(0.517840\pi\)
\(492\) 3051.62i 0.279629i
\(493\) 15383.3i 1.40533i
\(494\) −1496.18 −0.136268
\(495\) −20178.6 + 11503.1i −1.83224 + 1.04450i
\(496\) 17069.8 1.54527
\(497\) 7866.16i 0.709951i
\(498\) 28675.4i 2.58028i
\(499\) −10445.2 −0.937061 −0.468531 0.883447i \(-0.655216\pi\)
−0.468531 + 0.883447i \(0.655216\pi\)
\(500\) 41.6810 2534.18i 0.00372806 0.226664i
\(501\) 1630.21 0.145374
\(502\) 17061.8i 1.51694i
\(503\) 6597.00i 0.584783i 0.956299 + 0.292391i \(0.0944510\pi\)
−0.956299 + 0.292391i \(0.905549\pi\)
\(504\) −10487.6 −0.926891
\(505\) −4703.14 + 2681.09i −0.414429 + 0.236251i
\(506\) −3732.05 −0.327885
\(507\) 17907.9i 1.56867i
\(508\) 1902.95i 0.166200i
\(509\) 20547.8 1.78932 0.894662 0.446744i \(-0.147417\pi\)
0.894662 + 0.446744i \(0.147417\pi\)
\(510\) −13536.3 23745.3i −1.17529 2.06169i
\(511\) 795.927 0.0689036
\(512\) 5599.60i 0.483339i
\(513\) 15485.8i 1.33277i
\(514\) 12920.7 1.10877
\(515\) −9497.28 16660.0i −0.812621 1.42549i
\(516\) 3454.59 0.294729
\(517\) 16696.0i 1.42029i
\(518\) 7906.14i 0.670610i
\(519\) 242.480 0.0205081
\(520\) 623.409 355.383i 0.0525736 0.0299703i
\(521\) 7024.25 0.590668 0.295334 0.955394i \(-0.404569\pi\)
0.295334 + 0.955394i \(0.404569\pi\)
\(522\) 20289.5i 1.70124i
\(523\) 8773.19i 0.733508i −0.930318 0.366754i \(-0.880469\pi\)
0.930318 0.366754i \(-0.119531\pi\)
\(524\) 1175.54 0.0980036
\(525\) 7038.81 11888.6i 0.585140 0.988308i
\(526\) 11444.1 0.948640
\(527\) 21618.4i 1.78693i
\(528\) 31917.2i 2.63072i
\(529\) −529.000 −0.0434783
\(530\) −16845.6 + 9603.05i −1.38061 + 0.787037i
\(531\) 21325.3 1.74282
\(532\) 3528.74i 0.287576i
\(533\) 680.266i 0.0552826i
\(534\) −11689.0 −0.947251
\(535\) 8834.19 + 15496.8i 0.713897 + 1.25231i
\(536\) 1891.75 0.152446
\(537\) 2702.19i 0.217147i
\(538\) 23349.1i 1.87110i
\(539\) −8337.13 −0.666244
\(540\) 1078.29 + 1891.53i 0.0859301 + 0.150738i
\(541\) 1418.43 0.112723 0.0563615 0.998410i \(-0.482050\pi\)
0.0563615 + 0.998410i \(0.482050\pi\)
\(542\) 23515.5i 1.86361i
\(543\) 29497.9i 2.33127i
\(544\) 7677.90 0.605124
\(545\) −14892.4 + 8489.61i −1.17049 + 0.667256i
\(546\) −1146.71 −0.0898806
\(547\) 9882.41i 0.772470i −0.922400 0.386235i \(-0.873775\pi\)
0.922400 0.386235i \(-0.126225\pi\)
\(548\) 287.205i 0.0223883i
\(549\) −3911.98 −0.304115
\(550\) 17453.3 + 10333.4i 1.35311 + 0.801125i
\(551\) −23287.7 −1.80053
\(552\) 3651.49i 0.281554i
\(553\) 3275.13i 0.251849i
\(554\) −14636.8 −1.12249
\(555\) 14883.4 8484.52i 1.13832 0.648915i
\(556\) 493.858 0.0376695
\(557\) 5932.82i 0.451313i 0.974207 + 0.225657i \(0.0724527\pi\)
−0.974207 + 0.225657i \(0.927547\pi\)
\(558\) 28513.1i 2.16318i
\(559\) −770.097 −0.0582677
\(560\) 5619.43 + 9857.54i 0.424043 + 0.743852i
\(561\) 40422.2 3.04211
\(562\) 5311.34i 0.398657i
\(563\) 5347.11i 0.400273i 0.979768 + 0.200137i \(0.0641386\pi\)
−0.979768 + 0.200137i \(0.935861\pi\)
\(564\) 4788.76 0.357524
\(565\) 5354.02 + 9391.97i 0.398665 + 0.699333i
\(566\) 6925.57 0.514317
\(567\) 2742.38i 0.203120i
\(568\) 11298.7i 0.834656i
\(569\) 13568.8 0.999709 0.499854 0.866109i \(-0.333387\pi\)
0.499854 + 0.866109i \(0.333387\pi\)
\(570\) 35946.4 20491.7i 2.64145 1.50580i
\(571\) 5528.45 0.405181 0.202590 0.979264i \(-0.435064\pi\)
0.202590 + 0.979264i \(0.435064\pi\)
\(572\) 311.103i 0.0227411i
\(573\) 22661.3i 1.65217i
\(574\) 8681.85 0.631312
\(575\) 2473.91 + 1464.71i 0.179425 + 0.106231i
\(576\) 14008.7 1.01336
\(577\) 13634.6i 0.983734i −0.870670 0.491867i \(-0.836315\pi\)
0.870670 0.491867i \(-0.163685\pi\)
\(578\) 13038.4i 0.938278i
\(579\) 2806.02 0.201406
\(580\) −2844.51 + 1621.55i −0.203641 + 0.116088i
\(581\) 15076.3 1.07654
\(582\) 11068.3i 0.788308i
\(583\) 28676.6i 2.03716i
\(584\) −1143.25 −0.0810068
\(585\) −735.487 1290.18i −0.0519806 0.0911838i
\(586\) −2958.25 −0.208540
\(587\) 25831.5i 1.81632i −0.418622 0.908160i \(-0.637487\pi\)
0.418622 0.908160i \(-0.362513\pi\)
\(588\) 2391.27i 0.167711i
\(589\) −32726.6 −2.28943
\(590\) −9222.53 16178.1i −0.643534 1.12888i
\(591\) −3194.90 −0.222370
\(592\) 14070.0i 0.976814i
\(593\) 19241.9i 1.33250i 0.745731 + 0.666248i \(0.232101\pi\)
−0.745731 + 0.666248i \(0.767899\pi\)
\(594\) −17424.1 −1.20357
\(595\) −12484.3 + 7116.84i −0.860178 + 0.490356i
\(596\) −5125.52 −0.352264
\(597\) 31614.5i 2.16733i
\(598\) 238.621i 0.0163176i
\(599\) 5609.23 0.382616 0.191308 0.981530i \(-0.438727\pi\)
0.191308 + 0.981530i \(0.438727\pi\)
\(600\) −10110.4 + 17076.5i −0.687922 + 1.16191i
\(601\) 6750.84 0.458191 0.229095 0.973404i \(-0.426423\pi\)
0.229095 + 0.973404i \(0.426423\pi\)
\(602\) 9828.30i 0.665401i
\(603\) 3915.10i 0.264403i
\(604\) −3745.40 −0.252315
\(605\) −13131.5 + 7485.79i −0.882431 + 0.503042i
\(606\) −12426.2 −0.832967
\(607\) 11132.1i 0.744378i −0.928157 0.372189i \(-0.878607\pi\)
0.928157 0.372189i \(-0.121393\pi\)
\(608\) 11623.0i 0.775291i
\(609\) −17848.4 −1.18761
\(610\) 1691.81 + 2967.76i 0.112294 + 0.196985i
\(611\) −1067.51 −0.0706822
\(612\) 6929.29i 0.457680i
\(613\) 8300.26i 0.546891i −0.961888 0.273445i \(-0.911837\pi\)
0.961888 0.273445i \(-0.0881633\pi\)
\(614\) −12919.7 −0.849177
\(615\) 9316.97 + 16343.7i 0.610889 + 1.07161i
\(616\) −13544.0 −0.885884
\(617\) 6597.54i 0.430482i −0.976561 0.215241i \(-0.930946\pi\)
0.976561 0.215241i \(-0.0690536\pi\)
\(618\) 44017.5i 2.86512i
\(619\) 27992.2 1.81761 0.908805 0.417221i \(-0.136996\pi\)
0.908805 + 0.417221i \(0.136996\pi\)
\(620\) −3997.42 + 2278.79i −0.258936 + 0.147610i
\(621\) −2469.78 −0.159595
\(622\) 3268.90i 0.210725i
\(623\) 6145.58i 0.395213i
\(624\) 2040.73 0.130921
\(625\) −7513.92 13699.7i −0.480891 0.876780i
\(626\) 33496.2 2.13862
\(627\) 61192.3i 3.89758i
\(628\) 249.032i 0.0158240i
\(629\) −17819.3 −1.12957
\(630\) 16465.9 9386.60i 1.04130 0.593605i
\(631\) −447.361 −0.0282237 −0.0141119 0.999900i \(-0.504492\pi\)
−0.0141119 + 0.999900i \(0.504492\pi\)
\(632\) 4704.31i 0.296088i
\(633\) 41095.5i 2.58041i
\(634\) 17566.3 1.10039
\(635\) 5809.94 + 10191.7i 0.363087 + 0.636924i
\(636\) −8225.06 −0.512807
\(637\) 533.061i 0.0331564i
\(638\) 26202.6i 1.62597i
\(639\) −23383.5 −1.44763
\(640\) −9628.46 16890.1i −0.594685 1.04319i
\(641\) 20751.5 1.27868 0.639341 0.768924i \(-0.279207\pi\)
0.639341 + 0.768924i \(0.279207\pi\)
\(642\) 40944.2i 2.51704i
\(643\) 3579.70i 0.219549i 0.993957 + 0.109774i \(0.0350128\pi\)
−0.993957 + 0.109774i \(0.964987\pi\)
\(644\) 562.789 0.0344363
\(645\) 18501.9 10547.3i 1.12948 0.643875i
\(646\) −43036.9 −2.62115
\(647\) 547.886i 0.0332916i 0.999861 + 0.0166458i \(0.00529876\pi\)
−0.999861 + 0.0166458i \(0.994701\pi\)
\(648\) 3939.08i 0.238799i
\(649\) 27540.3 1.66572
\(650\) −660.701 + 1115.93i −0.0398689 + 0.0673390i
\(651\) −25082.6 −1.51008
\(652\) 5603.43i 0.336575i
\(653\) 6388.75i 0.382866i 0.981506 + 0.191433i \(0.0613134\pi\)
−0.981506 + 0.191433i \(0.938687\pi\)
\(654\) −39347.2 −2.35259
\(655\) 6295.93 3589.08i 0.375576 0.214102i
\(656\) −15450.5 −0.919573
\(657\) 2366.02i 0.140498i
\(658\) 13624.0i 0.807172i
\(659\) 10862.4 0.642092 0.321046 0.947064i \(-0.395966\pi\)
0.321046 + 0.947064i \(0.395966\pi\)
\(660\) 4260.89 + 7474.41i 0.251295 + 0.440820i
\(661\) 7995.73 0.470496 0.235248 0.971935i \(-0.424410\pi\)
0.235248 + 0.971935i \(0.424410\pi\)
\(662\) 17901.2i 1.05098i
\(663\) 2584.52i 0.151394i
\(664\) −21655.3 −1.26564
\(665\) −10773.7 18899.1i −0.628249 1.10207i
\(666\) 23502.3 1.36741
\(667\) 3714.09i 0.215607i
\(668\) 360.901i 0.0209037i
\(669\) 3522.37 0.203562
\(670\) −2970.12 + 1693.16i −0.171263 + 0.0976306i
\(671\) −5052.08 −0.290661
\(672\) 8908.25i 0.511374i
\(673\) 16061.3i 0.919935i 0.887936 + 0.459967i \(0.152139\pi\)
−0.887936 + 0.459967i \(0.847861\pi\)
\(674\) 19921.1 1.13848
\(675\) 11550.1 + 6838.40i 0.658614 + 0.389941i
\(676\) −3964.49 −0.225563
\(677\) 12848.3i 0.729393i −0.931127 0.364696i \(-0.881173\pi\)
0.931127 0.364696i \(-0.118827\pi\)
\(678\) 24814.5i 1.40560i
\(679\) −5819.24 −0.328898
\(680\) 17932.1 10222.4i 1.01127 0.576489i
\(681\) −5733.44 −0.322622
\(682\) 36822.9i 2.06748i
\(683\) 31534.0i 1.76664i −0.468770 0.883320i \(-0.655303\pi\)
0.468770 0.883320i \(-0.344697\pi\)
\(684\) 10489.8 0.586384
\(685\) −876.872 1538.20i −0.0489103 0.0857980i
\(686\) 21300.7 1.18552
\(687\) 7659.24i 0.425354i
\(688\) 17490.7i 0.969227i
\(689\) 1833.53 0.101382
\(690\) 3268.16 + 5732.98i 0.180314 + 0.316305i
\(691\) −11002.1 −0.605702 −0.302851 0.953038i \(-0.597938\pi\)
−0.302851 + 0.953038i \(0.597938\pi\)
\(692\) 53.6808i 0.00294890i
\(693\) 28030.2i 1.53648i
\(694\) −27096.2 −1.48207
\(695\) 2644.98 1507.81i 0.144359 0.0822941i
\(696\) 25637.0 1.39622
\(697\) 19567.6i 1.06338i
\(698\) 19216.6i 1.04206i
\(699\) 6981.74 0.377788
\(700\) −2631.93 1558.27i −0.142111 0.0841386i
\(701\) −21688.3 −1.16855 −0.584277 0.811554i \(-0.698622\pi\)
−0.584277 + 0.811554i \(0.698622\pi\)
\(702\) 1114.07i 0.0598970i
\(703\) 26975.3i 1.44722i
\(704\) 18091.4 0.968531
\(705\) 25647.4 14620.7i 1.37013 0.781059i
\(706\) −10945.7 −0.583495
\(707\) 6533.16i 0.347531i
\(708\) 7899.15i 0.419305i
\(709\) 21156.7 1.12067 0.560335 0.828266i \(-0.310672\pi\)
0.560335 + 0.828266i \(0.310672\pi\)
\(710\) 10112.6 + 17739.5i 0.534535 + 0.937676i
\(711\) −9735.87 −0.513535
\(712\) 8827.35i 0.464633i
\(713\) 5219.46i 0.274152i
\(714\) −32984.7 −1.72888
\(715\) −949.837 1666.19i −0.0496810 0.0871498i
\(716\) −598.216 −0.0312240
\(717\) 19638.4i 1.02289i
\(718\) 34469.4i 1.79162i
\(719\) 3485.09 0.180767 0.0903837 0.995907i \(-0.471191\pi\)
0.0903837 + 0.995907i \(0.471191\pi\)
\(720\) −29303.2 + 16704.7i −1.51676 + 0.864648i
\(721\) −23142.5 −1.19539
\(722\) 43663.6i 2.25068i
\(723\) 10521.5i 0.541216i
\(724\) 6530.32 0.335218
\(725\) −10283.7 + 17369.2i −0.526795 + 0.889762i
\(726\) −34694.7 −1.77361
\(727\) 11214.0i 0.572082i −0.958217 0.286041i \(-0.907661\pi\)
0.958217 0.286041i \(-0.0923393\pi\)
\(728\) 865.981i 0.0440871i
\(729\) 31903.2 1.62085
\(730\) 1794.94 1023.23i 0.0910053 0.0518788i
\(731\) −22151.5 −1.12080
\(732\) 1449.05i 0.0731671i
\(733\) 33463.9i 1.68624i −0.537723 0.843122i \(-0.680715\pi\)
0.537723 0.843122i \(-0.319285\pi\)
\(734\) −20179.8 −1.01478
\(735\) 7300.84 + 12807.0i 0.366388 + 0.642714i
\(736\) −1853.73 −0.0928386
\(737\) 5056.11i 0.252706i
\(738\) 25808.2i 1.28728i
\(739\) −32656.2 −1.62555 −0.812773 0.582581i \(-0.802043\pi\)
−0.812773 + 0.582581i \(0.802043\pi\)
\(740\) −1878.32 3294.93i −0.0933088 0.163681i
\(741\) −3912.53 −0.193968
\(742\) 23400.3i 1.15775i
\(743\) 16670.6i 0.823129i 0.911381 + 0.411564i \(0.135017\pi\)
−0.911381 + 0.411564i \(0.864983\pi\)
\(744\) 36028.0 1.77534
\(745\) −27451.0 + 15648.8i −1.34997 + 0.769569i
\(746\) −23282.0 −1.14264
\(747\) 44816.9i 2.19513i
\(748\) 8948.76i 0.437432i
\(749\) 21526.8 1.05016
\(750\) 589.805 35859.7i 0.0287155 1.74588i
\(751\) 1939.32 0.0942303 0.0471152 0.998889i \(-0.484997\pi\)
0.0471152 + 0.998889i \(0.484997\pi\)
\(752\) 24245.7i 1.17573i
\(753\) 44616.8i 2.15927i
\(754\) 1675.35 0.0809185
\(755\) −20059.4 + 11435.2i −0.966937 + 0.551216i
\(756\) 2627.53 0.126405
\(757\) 3445.40i 0.165423i 0.996574 + 0.0827114i \(0.0263580\pi\)
−0.996574 + 0.0827114i \(0.973642\pi\)
\(758\) 23179.3i 1.11070i
\(759\) −9759.38 −0.466723
\(760\) 15475.0 + 27146.1i 0.738604 + 1.29565i
\(761\) −32261.4 −1.53676 −0.768381 0.639993i \(-0.778937\pi\)
−0.768381 + 0.639993i \(0.778937\pi\)
\(762\) 26927.6i 1.28016i
\(763\) 20687.1i 0.981551i
\(764\) −5016.82 −0.237568
\(765\) −21156.0 37111.6i −0.999864 1.75395i
\(766\) 17263.0 0.814280
\(767\) 1760.88i 0.0828964i
\(768\) 21735.6i 1.02124i
\(769\) 8322.06 0.390249 0.195124 0.980779i \(-0.437489\pi\)
0.195124 + 0.980779i \(0.437489\pi\)
\(770\) 21264.7 12122.2i 0.995228 0.567343i
\(771\) 33787.9 1.57827
\(772\) 621.203i 0.0289606i
\(773\) 11057.9i 0.514519i 0.966342 + 0.257260i \(0.0828196\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(774\) 29216.2 1.35679
\(775\) −14451.8 + 24409.3i −0.669838 + 1.13136i
\(776\) 8358.61 0.386671
\(777\) 20674.7i 0.954570i
\(778\) 24369.3i 1.12298i
\(779\) 29622.0 1.36241
\(780\) −477.900 + 272.434i −0.0219379 + 0.0125060i
\(781\) −30198.3 −1.38359
\(782\) 6863.82i 0.313875i
\(783\) 17340.2i 0.791429i
\(784\) −12107.1 −0.551526
\(785\) −760.325 1333.75i −0.0345696 0.0606417i
\(786\) 16634.5 0.754875
\(787\) 9092.33i 0.411826i −0.978570 0.205913i \(-0.933984\pi\)
0.978570 0.205913i \(-0.0660163\pi\)
\(788\) 707.295i 0.0319751i
\(789\) 29926.4 1.35033
\(790\) 4210.46 + 7385.95i 0.189622 + 0.332633i
\(791\) 13046.4 0.586445
\(792\) 40261.9i 1.80637i
\(793\) 323.021i 0.0144651i
\(794\) −14793.0 −0.661188
\(795\) −44051.4 + 25112.1i −1.96521 + 1.12030i
\(796\) 6998.90 0.311645
\(797\) 11969.9i 0.531988i −0.963975 0.265994i \(-0.914300\pi\)
0.963975 0.265994i \(-0.0857002\pi\)
\(798\) 49933.3i 2.21506i
\(799\) −30706.5 −1.35960
\(800\) 8669.10 + 5132.65i 0.383124 + 0.226833i
\(801\) −18268.8 −0.805861
\(802\) 33952.7i 1.49490i
\(803\) 3055.58i 0.134283i
\(804\) −1450.20 −0.0636128
\(805\) 3014.16 1718.26i 0.131969 0.0752309i
\(806\) 2354.39 0.102891
\(807\) 61058.4i 2.66339i
\(808\) 9384.05i 0.408576i
\(809\) 29216.4 1.26971 0.634854 0.772632i \(-0.281060\pi\)
0.634854 + 0.772632i \(0.281060\pi\)
\(810\) −3525.57 6184.51i −0.152933 0.268274i
\(811\) −6747.86 −0.292169 −0.146085 0.989272i \(-0.546667\pi\)
−0.146085 + 0.989272i \(0.546667\pi\)
\(812\) 3951.32i 0.170769i
\(813\) 61493.5i 2.65273i
\(814\) 30351.8 1.30692
\(815\) 17108.0 + 30010.6i 0.735295 + 1.28985i
\(816\) 58700.7 2.51830
\(817\) 33533.6i 1.43598i
\(818\) 27896.2i 1.19238i
\(819\) −1792.20 −0.0764648
\(820\) 3618.21 2062.61i 0.154090 0.0878409i
\(821\) 28219.7 1.19960 0.599801 0.800149i \(-0.295247\pi\)
0.599801 + 0.800149i \(0.295247\pi\)
\(822\) 4064.08i 0.172447i
\(823\) 13238.6i 0.560714i −0.959896 0.280357i \(-0.909547\pi\)
0.959896 0.280357i \(-0.0904529\pi\)
\(824\) 33241.3 1.40536
\(825\) 45640.6 + 27022.1i 1.92606 + 1.14035i
\(826\) −22473.0 −0.946655
\(827\) 26369.9i 1.10879i 0.832252 + 0.554397i \(0.187051\pi\)
−0.832252 + 0.554397i \(0.812949\pi\)
\(828\) 1672.98i 0.0702176i
\(829\) −2281.90 −0.0956013 −0.0478007 0.998857i \(-0.515221\pi\)
−0.0478007 + 0.998857i \(0.515221\pi\)
\(830\) 33999.6 19381.9i 1.42186 0.810551i
\(831\) −38275.4 −1.59779
\(832\) 1156.73i 0.0482001i
\(833\) 15333.3i 0.637775i
\(834\) 6988.31 0.290150
\(835\) −1101.87 1932.89i −0.0456670 0.0801085i
\(836\) 13546.9 0.560442
\(837\) 24368.5i 1.00633i
\(838\) 49862.5i 2.05546i
\(839\) −19587.9 −0.806019 −0.403010 0.915196i \(-0.632036\pi\)
−0.403010 + 0.915196i \(0.632036\pi\)
\(840\) 11860.5 + 20805.6i 0.487175 + 0.854598i
\(841\) 1687.47 0.0691899
\(842\) 5855.76i 0.239671i
\(843\) 13889.2i 0.567462i
\(844\) 9097.82 0.371043
\(845\) −21232.8 + 12104.1i −0.864416 + 0.492773i
\(846\) 40499.6 1.64587
\(847\) 18241.0i 0.739987i
\(848\) 41643.9i 1.68639i
\(849\) 18110.5 0.732097
\(850\) −19004.8 + 32099.3i −0.766892 + 1.29529i
\(851\) 4302.22 0.173300
\(852\) 8661.52i 0.348285i
\(853\) 45899.7i 1.84241i 0.389078 + 0.921205i \(0.372794\pi\)
−0.389078 + 0.921205i \(0.627206\pi\)
\(854\) 4122.53 0.165187
\(855\) 56180.7 32026.6i 2.24718 1.28104i
\(856\) −30920.4 −1.23463
\(857\) 6236.58i 0.248585i −0.992246 0.124293i \(-0.960334\pi\)
0.992246 0.124293i \(-0.0396661\pi\)
\(858\) 4402.25i 0.175164i
\(859\) −30799.6 −1.22336 −0.611681 0.791104i \(-0.709506\pi\)
−0.611681 + 0.791104i \(0.709506\pi\)
\(860\) −2334.98 4096.00i −0.0925841 0.162410i
\(861\) 22703.2 0.898632
\(862\) 21627.5i 0.854565i
\(863\) 36472.2i 1.43862i −0.694689 0.719310i \(-0.744458\pi\)
0.694689 0.719310i \(-0.255542\pi\)
\(864\) −8654.61 −0.340782
\(865\) −163.894 287.501i −0.00644227 0.0113010i
\(866\) 6238.34 0.244789
\(867\) 34095.6i 1.33558i
\(868\) 5552.85i 0.217138i
\(869\) −12573.3 −0.490816
\(870\) −40251.0 + 22945.7i −1.56855 + 0.894173i
\(871\) 323.279 0.0125762
\(872\) 29714.4i 1.15396i
\(873\) 17298.7i 0.670643i
\(874\) 10390.7 0.402139
\(875\) −18853.6 310.095i −0.728419 0.0119807i
\(876\) 876.405 0.0338025
\(877\) 2516.40i 0.0968903i −0.998826 0.0484451i \(-0.984573\pi\)
0.998826 0.0484451i \(-0.0154266\pi\)
\(878\) 22091.5i 0.849147i
\(879\) −7735.88 −0.296843
\(880\) −37843.3 + 21573.1i −1.44965 + 0.826396i
\(881\) −25947.3 −0.992266 −0.496133 0.868246i \(-0.665247\pi\)
−0.496133 + 0.868246i \(0.665247\pi\)
\(882\) 20223.5i 0.772064i
\(883\) 30869.7i 1.17650i −0.808680 0.588249i \(-0.799818\pi\)
0.808680 0.588249i \(-0.200182\pi\)
\(884\) 572.167 0.0217693
\(885\) −24117.1 42305.9i −0.916030 1.60689i
\(886\) 756.975 0.0287033
\(887\) 13920.9i 0.526965i 0.964664 + 0.263483i \(0.0848711\pi\)
−0.964664 + 0.263483i \(0.915129\pi\)
\(888\) 29696.6i 1.12224i
\(889\) 14157.4 0.534110
\(890\) 7900.67 + 13859.3i 0.297563 + 0.521982i
\(891\) 10528.0 0.395850
\(892\) 779.791i 0.0292705i
\(893\) 46484.4i 1.74193i
\(894\) −72528.4 −2.71332
\(895\) −3203.90 + 1826.43i −0.119659 + 0.0682131i
\(896\) −23462.2 −0.874796
\(897\) 623.997i 0.0232271i
\(898\) 39012.3i 1.44973i
\(899\) 36645.6 1.35951
\(900\) 4632.21 7823.85i 0.171563 0.289772i
\(901\) 52740.7 1.95011
\(902\) 33329.7i 1.23033i
\(903\) 25701.2i 0.947156i
\(904\) −18739.6 −0.689457
\(905\) 34974.8 19937.9i 1.28464 0.732328i
\(906\) −52999.0 −1.94346
\(907\) 16652.6i 0.609637i −0.952410 0.304818i \(-0.901404\pi\)
0.952410 0.304818i \(-0.0985958\pi\)
\(908\) 1269.28i 0.0463905i
\(909\) −19420.9 −0.708636
\(910\) 775.073 + 1359.62i 0.0282345 + 0.0495287i
\(911\) −3907.51 −0.142109 −0.0710547 0.997472i \(-0.522636\pi\)
−0.0710547 + 0.997472i \(0.522636\pi\)
\(912\) 88862.9i 3.22647i
\(913\) 57878.3i 2.09802i
\(914\) 14724.7 0.532879
\(915\) 4424.12 + 7760.74i 0.159843 + 0.280396i
\(916\) 1695.62 0.0611625
\(917\) 8745.71i 0.314950i
\(918\) 32045.6i 1.15214i
\(919\) 41052.1 1.47354 0.736770 0.676143i \(-0.236350\pi\)
0.736770 + 0.676143i \(0.236350\pi\)
\(920\) −4329.46 + 2468.07i −0.155150 + 0.0884454i
\(921\) −33785.1 −1.20875
\(922\) 29933.4i 1.06920i
\(923\) 1930.83i 0.0688558i
\(924\) 10382.7 0.369662
\(925\) −20119.7 11912.1i −0.715168 0.423425i
\(926\) −50301.1 −1.78509
\(927\) 68795.0i 2.43746i
\(928\) 13014.9i 0.460384i
\(929\) −53877.6 −1.90276 −0.951382 0.308014i \(-0.900336\pi\)
−0.951382 + 0.308014i \(0.900336\pi\)
\(930\) −56565.3 + 32245.9i −1.99446 + 1.13697i
\(931\) 23212.0 0.817123
\(932\) 1545.63i 0.0543229i
\(933\) 8548.22i 0.299953i
\(934\) 58447.6 2.04761
\(935\) −27321.7 47927.4i −0.955630 1.67636i
\(936\) 2574.27 0.0898961
\(937\) 22558.8i 0.786515i −0.919428 0.393257i \(-0.871348\pi\)
0.919428 0.393257i \(-0.128652\pi\)
\(938\) 4125.82i 0.143617i
\(939\) 87593.1 3.04419
\(940\) −3236.76 5677.89i −0.112310 0.197013i
\(941\) 54423.8 1.88540 0.942702 0.333637i \(-0.108276\pi\)
0.942702 + 0.333637i \(0.108276\pi\)
\(942\) 3523.91i 0.121885i
\(943\) 4724.32i 0.163144i
\(944\) 39993.7 1.37890
\(945\) 14072.4 8022.18i 0.484419 0.276150i
\(946\) 37731.0 1.29677
\(947\) 20381.8i 0.699387i 0.936864 + 0.349693i \(0.113714\pi\)
−0.936864 + 0.349693i \(0.886286\pi\)
\(948\) 3606.29i 0.123551i
\(949\) −195.368 −0.00668273
\(950\) −48592.8 28770.0i −1.65954 0.982549i
\(951\) 45936.2 1.56633
\(952\) 24909.6i 0.848030i
\(953\) 28702.1i 0.975605i 0.872954 + 0.487803i \(0.162201\pi\)
−0.872954 + 0.487803i \(0.837799\pi\)
\(954\) −69561.2 −2.36072
\(955\) −26868.9 + 15317.0i −0.910425 + 0.519000i
\(956\) 4347.59 0.147083
\(957\) 68520.2i 2.31447i
\(958\) 37779.2i 1.27410i
\(959\) −2136.72 −0.0719483
\(960\) −15842.7 27791.0i −0.532625 0.934325i
\(961\) 21707.6 0.728664
\(962\) 1940.64i 0.0650402i
\(963\) 63991.8i 2.14134i
\(964\) 2329.28 0.0778226
\(965\) −1896.61 3327.01i −0.0632684 0.110985i
\(966\) 7963.72 0.265247
\(967\) 5788.98i 0.192514i −0.995357 0.0962571i \(-0.969313\pi\)
0.995357 0.0962571i \(-0.0306871\pi\)
\(968\) 26200.9i 0.869969i
\(969\) −112542. −3.73104
\(970\) −13123.3 + 7481.14i −0.434397 + 0.247634i
\(971\) −34807.9 −1.15040 −0.575200 0.818013i \(-0.695076\pi\)
−0.575200 + 0.818013i \(0.695076\pi\)
\(972\) 8277.72i 0.273156i
\(973\) 3674.16i 0.121057i
\(974\) −62110.8 −2.04329
\(975\) −1727.74 + 2918.18i −0.0567508 + 0.0958528i
\(976\) −7336.58 −0.240613
\(977\) 32169.4i 1.05342i 0.850045 + 0.526710i \(0.176575\pi\)
−0.850045 + 0.526710i \(0.823425\pi\)
\(978\) 79291.0i 2.59248i
\(979\) −23593.0 −0.770209
\(980\) 2835.25 1616.28i 0.0924172 0.0526837i
\(981\) −61495.8 −2.00144
\(982\) 3818.49i 0.124086i
\(983\) 30095.0i 0.976481i 0.872709 + 0.488240i \(0.162361\pi\)
−0.872709 + 0.488240i \(0.837639\pi\)
\(984\) −32610.2 −1.05648
\(985\) 2159.46 + 3788.10i 0.0698539 + 0.122537i
\(986\) 48190.6 1.55649
\(987\) 35627.0i 1.14896i
\(988\) 866.165i 0.0278911i
\(989\) 5348.18 0.171954
\(990\) 36035.3 + 63212.7i 1.15684 + 2.02933i
\(991\) 40627.1 1.30228 0.651141 0.758957i \(-0.274291\pi\)
0.651141 + 0.758957i \(0.274291\pi\)
\(992\) 18290.1i 0.585394i
\(993\) 46811.9i 1.49600i
\(994\) 24642.0 0.786315
\(995\) 37484.4 21368.5i 1.19431 0.680831i
\(996\) 16600.7 0.528127
\(997\) 5694.87i 0.180901i −0.995901 0.0904505i \(-0.971169\pi\)
0.995901 0.0904505i \(-0.0288307\pi\)
\(998\) 32721.4i 1.03785i
\(999\) 20086.0 0.636131
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 115.4.b.a.24.9 34
5.2 odd 4 575.4.a.r.1.13 17
5.3 odd 4 575.4.a.q.1.5 17
5.4 even 2 inner 115.4.b.a.24.26 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.b.a.24.9 34 1.1 even 1 trivial
115.4.b.a.24.26 yes 34 5.4 even 2 inner
575.4.a.q.1.5 17 5.3 odd 4
575.4.a.r.1.13 17 5.2 odd 4