Properties

Label 117.4.q.e.82.3
Level $117$
Weight $4$
Character 117.82
Analytic conductor $6.903$
Analytic rank $0$
Dimension $10$
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] = [117,4,Mod(10,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.10");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 82.3
Root \(0.917374i\) of defining polynomial
Character \(\chi\) \(=\) 117.82
Dual form 117.4.q.e.10.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.794469 + 0.458687i) q^{2} +(-3.57921 - 6.19938i) q^{4} +15.4704i q^{5} +(17.8257 - 10.2917i) q^{7} -13.9059i q^{8} +O(q^{10})\) \(q+(0.794469 + 0.458687i) q^{2} +(-3.57921 - 6.19938i) q^{4} +15.4704i q^{5} +(17.8257 - 10.2917i) q^{7} -13.9059i q^{8} +(-7.09608 + 12.2908i) q^{10} +(57.0209 + 32.9210i) q^{11} +(19.2429 + 42.7400i) q^{13} +18.8826 q^{14} +(-22.2552 + 38.5472i) q^{16} +(-22.1478 - 38.3611i) q^{17} +(127.352 - 73.5266i) q^{19} +(95.9069 - 55.3719i) q^{20} +(30.2009 + 52.3094i) q^{22} +(-26.5793 + 46.0367i) q^{23} -114.334 q^{25} +(-4.31639 + 42.7821i) q^{26} +(-127.604 - 73.6721i) q^{28} +(-19.3128 + 33.4508i) q^{29} +88.3894i q^{31} +(-131.705 + 76.0401i) q^{32} -40.6357i q^{34} +(159.216 + 275.771i) q^{35} +(68.3803 + 39.4794i) q^{37} +134.903 q^{38} +215.131 q^{40} +(-307.410 - 177.483i) q^{41} +(-203.923 - 353.205i) q^{43} -471.325i q^{44} +(-42.2329 + 24.3832i) q^{46} -67.9674i q^{47} +(40.3369 - 69.8656i) q^{49} +(-90.8345 - 52.4433i) q^{50} +(196.087 - 272.270i) q^{52} -226.572 q^{53} +(-509.302 + 882.136i) q^{55} +(-143.115 - 247.883i) q^{56} +(-30.6869 + 17.7171i) q^{58} +(123.002 - 71.0154i) q^{59} +(-133.416 - 231.083i) q^{61} +(-40.5431 + 70.2227i) q^{62} +216.569 q^{64} +(-661.206 + 297.696i) q^{65} +(356.098 + 205.593i) q^{67} +(-158.543 + 274.605i) q^{68} +292.122i q^{70} +(79.2458 - 45.7526i) q^{71} -63.1328i q^{73} +(36.2173 + 62.7303i) q^{74} +(-911.638 - 526.335i) q^{76} +1355.25 q^{77} -287.115 q^{79} +(-596.341 - 344.298i) q^{80} +(-162.818 - 282.010i) q^{82} +373.812i q^{83} +(593.463 - 342.636i) q^{85} -374.147i q^{86} +(457.798 - 792.929i) q^{88} +(-103.406 - 59.7013i) q^{89} +(782.885 + 563.829i) q^{91} +380.532 q^{92} +(31.1758 - 53.9980i) q^{94} +(1137.49 + 1970.18i) q^{95} +(480.341 - 277.325i) q^{97} +(64.0928 - 37.0040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.794469 + 0.458687i 0.280887 + 0.162170i 0.633825 0.773476i \(-0.281484\pi\)
−0.352938 + 0.935647i \(0.614817\pi\)
\(3\) 0 0
\(4\) −3.57921 6.19938i −0.447402 0.774922i
\(5\) 15.4704i 1.38372i 0.722034 + 0.691858i \(0.243208\pi\)
−0.722034 + 0.691858i \(0.756792\pi\)
\(6\) 0 0
\(7\) 17.8257 10.2917i 0.962497 0.555698i 0.0655563 0.997849i \(-0.479118\pi\)
0.896941 + 0.442151i \(0.145784\pi\)
\(8\) 13.9059i 0.614562i
\(9\) 0 0
\(10\) −7.09608 + 12.2908i −0.224398 + 0.388668i
\(11\) 57.0209 + 32.9210i 1.56295 + 0.902369i 0.996957 + 0.0779583i \(0.0248401\pi\)
0.565992 + 0.824411i \(0.308493\pi\)
\(12\) 0 0
\(13\) 19.2429 + 42.7400i 0.410540 + 0.911842i
\(14\) 18.8826 0.360471
\(15\) 0 0
\(16\) −22.2552 + 38.5472i −0.347738 + 0.602300i
\(17\) −22.1478 38.3611i −0.315979 0.547291i 0.663666 0.748029i \(-0.268999\pi\)
−0.979645 + 0.200738i \(0.935666\pi\)
\(18\) 0 0
\(19\) 127.352 73.5266i 1.53771 0.887798i 0.538738 0.842473i \(-0.318901\pi\)
0.998972 0.0453247i \(-0.0144322\pi\)
\(20\) 95.9069 55.3719i 1.07227 0.619077i
\(21\) 0 0
\(22\) 30.2009 + 52.3094i 0.292675 + 0.506928i
\(23\) −26.5793 + 46.0367i −0.240964 + 0.417362i −0.960989 0.276586i \(-0.910797\pi\)
0.720025 + 0.693948i \(0.244130\pi\)
\(24\) 0 0
\(25\) −114.334 −0.914669
\(26\) −4.31639 + 42.7821i −0.0325582 + 0.322702i
\(27\) 0 0
\(28\) −127.604 73.6721i −0.861245 0.497240i
\(29\) −19.3128 + 33.4508i −0.123666 + 0.214195i −0.921211 0.389064i \(-0.872798\pi\)
0.797545 + 0.603260i \(0.206132\pi\)
\(30\) 0 0
\(31\) 88.3894i 0.512104i 0.966663 + 0.256052i \(0.0824218\pi\)
−0.966663 + 0.256052i \(0.917578\pi\)
\(32\) −131.705 + 76.0401i −0.727576 + 0.420066i
\(33\) 0 0
\(34\) 40.6357i 0.204969i
\(35\) 159.216 + 275.771i 0.768928 + 1.33182i
\(36\) 0 0
\(37\) 68.3803 + 39.4794i 0.303828 + 0.175415i 0.644161 0.764890i \(-0.277206\pi\)
−0.340333 + 0.940305i \(0.610540\pi\)
\(38\) 134.903 0.575898
\(39\) 0 0
\(40\) 215.131 0.850379
\(41\) −307.410 177.483i −1.17096 0.676054i −0.217053 0.976160i \(-0.569645\pi\)
−0.953906 + 0.300106i \(0.902978\pi\)
\(42\) 0 0
\(43\) −203.923 353.205i −0.723208 1.25263i −0.959707 0.281002i \(-0.909333\pi\)
0.236499 0.971632i \(-0.424000\pi\)
\(44\) 471.325i 1.61489i
\(45\) 0 0
\(46\) −42.2329 + 24.3832i −0.135367 + 0.0781544i
\(47\) 67.9674i 0.210938i −0.994423 0.105469i \(-0.966366\pi\)
0.994423 0.105469i \(-0.0336343\pi\)
\(48\) 0 0
\(49\) 40.3369 69.8656i 0.117600 0.203690i
\(50\) −90.8345 52.4433i −0.256919 0.148332i
\(51\) 0 0
\(52\) 196.087 272.270i 0.522931 0.726097i
\(53\) −226.572 −0.587209 −0.293604 0.955927i \(-0.594855\pi\)
−0.293604 + 0.955927i \(0.594855\pi\)
\(54\) 0 0
\(55\) −509.302 + 882.136i −1.24862 + 2.16268i
\(56\) −143.115 247.883i −0.341511 0.591514i
\(57\) 0 0
\(58\) −30.6869 + 17.7171i −0.0694722 + 0.0401098i
\(59\) 123.002 71.0154i 0.271416 0.156702i −0.358115 0.933677i \(-0.616580\pi\)
0.629531 + 0.776976i \(0.283247\pi\)
\(60\) 0 0
\(61\) −133.416 231.083i −0.280035 0.485034i 0.691358 0.722512i \(-0.257013\pi\)
−0.971393 + 0.237478i \(0.923679\pi\)
\(62\) −40.5431 + 70.2227i −0.0830480 + 0.143843i
\(63\) 0 0
\(64\) 216.569 0.422987
\(65\) −661.206 + 297.696i −1.26173 + 0.568071i
\(66\) 0 0
\(67\) 356.098 + 205.593i 0.649318 + 0.374884i 0.788195 0.615426i \(-0.211016\pi\)
−0.138877 + 0.990310i \(0.544349\pi\)
\(68\) −158.543 + 274.605i −0.282739 + 0.489718i
\(69\) 0 0
\(70\) 292.122i 0.498789i
\(71\) 79.2458 45.7526i 0.132461 0.0764765i −0.432305 0.901727i \(-0.642300\pi\)
0.564766 + 0.825251i \(0.308966\pi\)
\(72\) 0 0
\(73\) 63.1328i 0.101221i −0.998718 0.0506105i \(-0.983883\pi\)
0.998718 0.0506105i \(-0.0161167\pi\)
\(74\) 36.2173 + 62.7303i 0.0568943 + 0.0985439i
\(75\) 0 0
\(76\) −911.638 526.335i −1.37595 0.794404i
\(77\) 1355.25 2.00578
\(78\) 0 0
\(79\) −287.115 −0.408899 −0.204449 0.978877i \(-0.565540\pi\)
−0.204449 + 0.978877i \(0.565540\pi\)
\(80\) −596.341 344.298i −0.833412 0.481170i
\(81\) 0 0
\(82\) −162.818 282.010i −0.219272 0.379790i
\(83\) 373.812i 0.494352i 0.968971 + 0.247176i \(0.0795026\pi\)
−0.968971 + 0.247176i \(0.920497\pi\)
\(84\) 0 0
\(85\) 593.463 342.636i 0.757295 0.437224i
\(86\) 374.147i 0.469132i
\(87\) 0 0
\(88\) 457.798 792.929i 0.554561 0.960528i
\(89\) −103.406 59.7013i −0.123157 0.0711047i 0.437156 0.899386i \(-0.355986\pi\)
−0.560313 + 0.828281i \(0.689319\pi\)
\(90\) 0 0
\(91\) 782.885 + 563.829i 0.901853 + 0.649509i
\(92\) 380.532 0.431231
\(93\) 0 0
\(94\) 31.1758 53.9980i 0.0342078 0.0592497i
\(95\) 1137.49 + 1970.18i 1.22846 + 2.12775i
\(96\) 0 0
\(97\) 480.341 277.325i 0.502796 0.290290i −0.227071 0.973878i \(-0.572915\pi\)
0.729868 + 0.683589i \(0.239582\pi\)
\(98\) 64.0928 37.0040i 0.0660648 0.0381426i
\(99\) 0 0
\(100\) 409.224 + 708.797i 0.409224 + 0.708797i
\(101\) 231.282 400.593i 0.227856 0.394658i −0.729317 0.684176i \(-0.760162\pi\)
0.957172 + 0.289518i \(0.0934952\pi\)
\(102\) 0 0
\(103\) −1122.07 −1.07341 −0.536704 0.843771i \(-0.680331\pi\)
−0.536704 + 0.843771i \(0.680331\pi\)
\(104\) 594.340 267.591i 0.560383 0.252302i
\(105\) 0 0
\(106\) −180.005 103.926i −0.164939 0.0952279i
\(107\) 301.378 522.002i 0.272293 0.471625i −0.697156 0.716920i \(-0.745551\pi\)
0.969449 + 0.245295i \(0.0788848\pi\)
\(108\) 0 0
\(109\) 1421.89i 1.24947i 0.780837 + 0.624735i \(0.214793\pi\)
−0.780837 + 0.624735i \(0.785207\pi\)
\(110\) −809.249 + 467.220i −0.701444 + 0.404979i
\(111\) 0 0
\(112\) 916.174i 0.772949i
\(113\) −198.359 343.569i −0.165134 0.286020i 0.771569 0.636145i \(-0.219472\pi\)
−0.936703 + 0.350126i \(0.886139\pi\)
\(114\) 0 0
\(115\) −712.207 411.193i −0.577510 0.333426i
\(116\) 276.499 0.221313
\(117\) 0 0
\(118\) 130.295 0.101650
\(119\) −789.600 455.876i −0.608257 0.351177i
\(120\) 0 0
\(121\) 1502.09 + 2601.69i 1.12854 + 1.95469i
\(122\) 244.784i 0.181653i
\(123\) 0 0
\(124\) 547.960 316.365i 0.396841 0.229116i
\(125\) 165.013i 0.118074i
\(126\) 0 0
\(127\) 218.934 379.205i 0.152970 0.264952i −0.779348 0.626592i \(-0.784449\pi\)
0.932318 + 0.361639i \(0.117783\pi\)
\(128\) 1225.70 + 707.659i 0.846388 + 0.488662i
\(129\) 0 0
\(130\) −661.857 66.7764i −0.446528 0.0450514i
\(131\) −1657.44 −1.10543 −0.552715 0.833370i \(-0.686408\pi\)
−0.552715 + 0.833370i \(0.686408\pi\)
\(132\) 0 0
\(133\) 1513.42 2621.33i 0.986695 1.70901i
\(134\) 188.606 + 326.675i 0.121590 + 0.210600i
\(135\) 0 0
\(136\) −533.448 + 307.986i −0.336344 + 0.194188i
\(137\) 1703.84 983.711i 1.06254 0.613460i 0.136410 0.990653i \(-0.456444\pi\)
0.926135 + 0.377192i \(0.123110\pi\)
\(138\) 0 0
\(139\) −1412.57 2446.64i −0.861960 1.49296i −0.870035 0.492990i \(-0.835904\pi\)
0.00807518 0.999967i \(-0.497430\pi\)
\(140\) 1139.74 1974.08i 0.688039 1.19172i
\(141\) 0 0
\(142\) 83.9445 0.0496089
\(143\) −309.797 + 3070.57i −0.181165 + 1.79562i
\(144\) 0 0
\(145\) −517.498 298.777i −0.296385 0.171118i
\(146\) 28.9582 50.1571i 0.0164150 0.0284317i
\(147\) 0 0
\(148\) 565.220i 0.313924i
\(149\) −690.792 + 398.829i −0.379811 + 0.219284i −0.677736 0.735305i \(-0.737039\pi\)
0.297925 + 0.954589i \(0.403706\pi\)
\(150\) 0 0
\(151\) 161.987i 0.0873003i 0.999047 + 0.0436501i \(0.0138987\pi\)
−0.999047 + 0.0436501i \(0.986101\pi\)
\(152\) −1022.46 1770.95i −0.545606 0.945018i
\(153\) 0 0
\(154\) 1076.70 + 621.635i 0.563397 + 0.325278i
\(155\) −1367.42 −0.708606
\(156\) 0 0
\(157\) −342.000 −0.173851 −0.0869255 0.996215i \(-0.527704\pi\)
−0.0869255 + 0.996215i \(0.527704\pi\)
\(158\) −228.104 131.696i −0.114854 0.0663112i
\(159\) 0 0
\(160\) −1176.37 2037.54i −0.581252 1.00676i
\(161\) 1094.18i 0.535613i
\(162\) 0 0
\(163\) 482.027 278.299i 0.231628 0.133730i −0.379695 0.925112i \(-0.623971\pi\)
0.611323 + 0.791381i \(0.290638\pi\)
\(164\) 2541.00i 1.20987i
\(165\) 0 0
\(166\) −171.463 + 296.982i −0.0801693 + 0.138857i
\(167\) −2716.22 1568.21i −1.25861 0.726658i −0.285805 0.958288i \(-0.592261\pi\)
−0.972804 + 0.231630i \(0.925594\pi\)
\(168\) 0 0
\(169\) −1456.42 + 1644.89i −0.662913 + 0.748696i
\(170\) 628.650 0.283619
\(171\) 0 0
\(172\) −1459.77 + 2528.39i −0.647129 + 1.12086i
\(173\) −1662.10 2878.84i −0.730444 1.26517i −0.956693 0.291097i \(-0.905980\pi\)
0.226249 0.974070i \(-0.427354\pi\)
\(174\) 0 0
\(175\) −2038.08 + 1176.68i −0.880366 + 0.508280i
\(176\) −2538.02 + 1465.33i −1.08699 + 0.627576i
\(177\) 0 0
\(178\) −54.7684 94.8616i −0.0230622 0.0399448i
\(179\) 1656.62 2869.36i 0.691743 1.19813i −0.279524 0.960139i \(-0.590177\pi\)
0.971266 0.237995i \(-0.0764900\pi\)
\(180\) 0 0
\(181\) −76.0118 −0.0312150 −0.0156075 0.999878i \(-0.504968\pi\)
−0.0156075 + 0.999878i \(0.504968\pi\)
\(182\) 363.357 + 807.044i 0.147988 + 0.328693i
\(183\) 0 0
\(184\) 640.184 + 369.610i 0.256494 + 0.148087i
\(185\) −610.762 + 1057.87i −0.242725 + 0.420412i
\(186\) 0 0
\(187\) 2916.51i 1.14052i
\(188\) −421.356 + 243.270i −0.163460 + 0.0943738i
\(189\) 0 0
\(190\) 2087.00i 0.796879i
\(191\) −2036.70 3527.66i −0.771572 1.33640i −0.936701 0.350130i \(-0.886138\pi\)
0.165129 0.986272i \(-0.447196\pi\)
\(192\) 0 0
\(193\) 751.347 + 433.791i 0.280224 + 0.161787i 0.633525 0.773723i \(-0.281608\pi\)
−0.353301 + 0.935510i \(0.614941\pi\)
\(194\) 508.821 0.188305
\(195\) 0 0
\(196\) −577.497 −0.210458
\(197\) −1634.79 943.846i −0.591238 0.341352i 0.174349 0.984684i \(-0.444218\pi\)
−0.765587 + 0.643332i \(0.777551\pi\)
\(198\) 0 0
\(199\) 1393.11 + 2412.94i 0.496256 + 0.859540i 0.999991 0.00431832i \(-0.00137457\pi\)
−0.503735 + 0.863858i \(0.668041\pi\)
\(200\) 1589.92i 0.562120i
\(201\) 0 0
\(202\) 367.493 212.172i 0.128004 0.0739029i
\(203\) 795.045i 0.274883i
\(204\) 0 0
\(205\) 2745.74 4755.75i 0.935466 1.62027i
\(206\) −891.451 514.680i −0.301507 0.174075i
\(207\) 0 0
\(208\) −2075.76 209.429i −0.691963 0.0698139i
\(209\) 9682.28 3.20448
\(210\) 0 0
\(211\) −354.395 + 613.830i −0.115628 + 0.200274i −0.918031 0.396509i \(-0.870221\pi\)
0.802403 + 0.596783i \(0.203555\pi\)
\(212\) 810.950 + 1404.61i 0.262718 + 0.455041i
\(213\) 0 0
\(214\) 478.871 276.476i 0.152967 0.0883156i
\(215\) 5464.22 3154.77i 1.73329 1.00071i
\(216\) 0 0
\(217\) 909.675 + 1575.60i 0.284575 + 0.492898i
\(218\) −652.202 + 1129.65i −0.202627 + 0.350960i
\(219\) 0 0
\(220\) 7291.59 2.23454
\(221\) 1213.37 1684.78i 0.369321 0.512808i
\(222\) 0 0
\(223\) −4673.62 2698.32i −1.40345 0.810281i −0.408703 0.912667i \(-0.634019\pi\)
−0.994745 + 0.102386i \(0.967352\pi\)
\(224\) −1565.16 + 2710.94i −0.466860 + 0.808625i
\(225\) 0 0
\(226\) 363.940i 0.107119i
\(227\) −2755.51 + 1590.90i −0.805682 + 0.465160i −0.845454 0.534048i \(-0.820670\pi\)
0.0397724 + 0.999209i \(0.487337\pi\)
\(228\) 0 0
\(229\) 2034.00i 0.586945i −0.955967 0.293473i \(-0.905189\pi\)
0.955967 0.293473i \(-0.0948110\pi\)
\(230\) −377.218 653.360i −0.108143 0.187310i
\(231\) 0 0
\(232\) 465.165 + 268.563i 0.131636 + 0.0760001i
\(233\) −2794.22 −0.785645 −0.392823 0.919614i \(-0.628501\pi\)
−0.392823 + 0.919614i \(0.628501\pi\)
\(234\) 0 0
\(235\) 1051.48 0.291878
\(236\) −880.502 508.358i −0.242864 0.140217i
\(237\) 0 0
\(238\) −418.209 724.359i −0.113901 0.197282i
\(239\) 5493.81i 1.48688i 0.668800 + 0.743442i \(0.266808\pi\)
−0.668800 + 0.743442i \(0.733192\pi\)
\(240\) 0 0
\(241\) −3517.16 + 2030.63i −0.940084 + 0.542758i −0.889987 0.455986i \(-0.849287\pi\)
−0.0500976 + 0.998744i \(0.515953\pi\)
\(242\) 2755.95i 0.732062i
\(243\) 0 0
\(244\) −955.046 + 1654.19i −0.250576 + 0.434010i
\(245\) 1080.85 + 624.028i 0.281849 + 0.162725i
\(246\) 0 0
\(247\) 5593.15 + 4028.15i 1.44082 + 1.03767i
\(248\) 1229.14 0.314719
\(249\) 0 0
\(250\) −75.6894 + 131.098i −0.0191481 + 0.0331654i
\(251\) 1785.44 + 3092.47i 0.448988 + 0.777670i 0.998320 0.0579336i \(-0.0184512\pi\)
−0.549332 + 0.835604i \(0.685118\pi\)
\(252\) 0 0
\(253\) −3031.15 + 1750.04i −0.753228 + 0.434877i
\(254\) 347.872 200.844i 0.0859348 0.0496145i
\(255\) 0 0
\(256\) −217.089 376.010i −0.0530003 0.0917993i
\(257\) 3759.13 6511.01i 0.912405 1.58033i 0.101749 0.994810i \(-0.467556\pi\)
0.810656 0.585522i \(-0.199111\pi\)
\(258\) 0 0
\(259\) 1625.23 0.389912
\(260\) 4212.13 + 3033.55i 1.00471 + 0.723587i
\(261\) 0 0
\(262\) −1316.79 760.246i −0.310501 0.179268i
\(263\) −2330.09 + 4035.84i −0.546310 + 0.946237i 0.452213 + 0.891910i \(0.350635\pi\)
−0.998523 + 0.0543273i \(0.982699\pi\)
\(264\) 0 0
\(265\) 3505.16i 0.812530i
\(266\) 2404.73 1388.37i 0.554300 0.320025i
\(267\) 0 0
\(268\) 2943.45i 0.670895i
\(269\) 2673.72 + 4631.02i 0.606021 + 1.04966i 0.991889 + 0.127105i \(0.0405684\pi\)
−0.385869 + 0.922554i \(0.626098\pi\)
\(270\) 0 0
\(271\) 2574.76 + 1486.54i 0.577143 + 0.333214i 0.759997 0.649926i \(-0.225200\pi\)
−0.182854 + 0.983140i \(0.558534\pi\)
\(272\) 1971.62 0.439511
\(273\) 0 0
\(274\) 1804.86 0.397940
\(275\) −6519.40 3763.98i −1.42958 0.825369i
\(276\) 0 0
\(277\) −382.076 661.776i −0.0828764 0.143546i 0.821608 0.570053i \(-0.193077\pi\)
−0.904484 + 0.426507i \(0.859744\pi\)
\(278\) 2591.70i 0.559137i
\(279\) 0 0
\(280\) 3834.85 2214.05i 0.818487 0.472554i
\(281\) 7040.34i 1.49463i −0.664469 0.747316i \(-0.731342\pi\)
0.664469 0.747316i \(-0.268658\pi\)
\(282\) 0 0
\(283\) −4517.58 + 7824.68i −0.948913 + 1.64357i −0.201194 + 0.979551i \(0.564482\pi\)
−0.747720 + 0.664015i \(0.768851\pi\)
\(284\) −567.275 327.517i −0.118527 0.0684314i
\(285\) 0 0
\(286\) −1654.55 + 2297.37i −0.342083 + 0.474988i
\(287\) −7306.39 −1.50273
\(288\) 0 0
\(289\) 1475.45 2555.55i 0.300315 0.520161i
\(290\) −274.091 474.739i −0.0555005 0.0961297i
\(291\) 0 0
\(292\) −391.384 + 225.966i −0.0784384 + 0.0452865i
\(293\) 1546.06 892.617i 0.308265 0.177977i −0.337885 0.941188i \(-0.609711\pi\)
0.646150 + 0.763211i \(0.276378\pi\)
\(294\) 0 0
\(295\) 1098.64 + 1902.89i 0.216831 + 0.375562i
\(296\) 548.998 950.892i 0.107804 0.186721i
\(297\) 0 0
\(298\) −731.751 −0.142246
\(299\) −2479.07 250.120i −0.479494 0.0483773i
\(300\) 0 0
\(301\) −7270.13 4197.41i −1.39217 0.803771i
\(302\) −74.3015 + 128.694i −0.0141575 + 0.0245215i
\(303\) 0 0
\(304\) 6545.40i 1.23488i
\(305\) 3574.94 2063.99i 0.671150 0.387488i
\(306\) 0 0
\(307\) 5323.13i 0.989600i −0.869007 0.494800i \(-0.835241\pi\)
0.869007 0.494800i \(-0.164759\pi\)
\(308\) −4850.72 8401.70i −0.897388 1.55432i
\(309\) 0 0
\(310\) −1086.37 627.218i −0.199038 0.114915i
\(311\) 6265.64 1.14242 0.571209 0.820805i \(-0.306475\pi\)
0.571209 + 0.820805i \(0.306475\pi\)
\(312\) 0 0
\(313\) 7193.77 1.29909 0.649547 0.760322i \(-0.274959\pi\)
0.649547 + 0.760322i \(0.274959\pi\)
\(314\) −271.709 156.871i −0.0488325 0.0281935i
\(315\) 0 0
\(316\) 1027.65 + 1779.94i 0.182942 + 0.316865i
\(317\) 9576.87i 1.69682i 0.529343 + 0.848408i \(0.322439\pi\)
−0.529343 + 0.848408i \(0.677561\pi\)
\(318\) 0 0
\(319\) −2202.47 + 1271.60i −0.386566 + 0.223184i
\(320\) 3350.41i 0.585293i
\(321\) 0 0
\(322\) −501.887 + 869.294i −0.0868604 + 0.150447i
\(323\) −5641.13 3256.91i −0.971767 0.561050i
\(324\) 0 0
\(325\) −2200.11 4886.62i −0.375509 0.834034i
\(326\) 510.608 0.0867483
\(327\) 0 0
\(328\) −2468.07 + 4274.82i −0.415477 + 0.719627i
\(329\) −699.498 1211.57i −0.117218 0.203027i
\(330\) 0 0
\(331\) 4999.68 2886.56i 0.830233 0.479335i −0.0236996 0.999719i \(-0.507545\pi\)
0.853932 + 0.520384i \(0.174211\pi\)
\(332\) 2317.40 1337.95i 0.383085 0.221174i
\(333\) 0 0
\(334\) −1438.64 2491.79i −0.235685 0.408218i
\(335\) −3180.61 + 5508.98i −0.518733 + 0.898471i
\(336\) 0 0
\(337\) −1238.09 −0.200127 −0.100063 0.994981i \(-0.531905\pi\)
−0.100063 + 0.994981i \(0.531905\pi\)
\(338\) −1911.57 + 638.770i −0.307620 + 0.102794i
\(339\) 0 0
\(340\) −4248.26 2452.73i −0.677630 0.391230i
\(341\) −2909.87 + 5040.04i −0.462106 + 0.800392i
\(342\) 0 0
\(343\) 5399.55i 0.849995i
\(344\) −4911.65 + 2835.74i −0.769820 + 0.444456i
\(345\) 0 0
\(346\) 3049.53i 0.473826i
\(347\) 2724.98 + 4719.81i 0.421570 + 0.730181i 0.996093 0.0883076i \(-0.0281459\pi\)
−0.574523 + 0.818488i \(0.694813\pi\)
\(348\) 0 0
\(349\) −1189.95 687.016i −0.182511 0.105373i 0.405961 0.913890i \(-0.366937\pi\)
−0.588472 + 0.808518i \(0.700270\pi\)
\(350\) −2158.92 −0.329711
\(351\) 0 0
\(352\) −10013.3 −1.51622
\(353\) −5170.55 2985.22i −0.779606 0.450106i 0.0566848 0.998392i \(-0.481947\pi\)
−0.836291 + 0.548287i \(0.815280\pi\)
\(354\) 0 0
\(355\) 707.811 + 1225.97i 0.105822 + 0.183289i
\(356\) 854.734i 0.127249i
\(357\) 0 0
\(358\) 2632.27 1519.74i 0.388603 0.224360i
\(359\) 7813.71i 1.14872i −0.818602 0.574362i \(-0.805250\pi\)
0.818602 0.574362i \(-0.194750\pi\)
\(360\) 0 0
\(361\) 7382.82 12787.4i 1.07637 1.86433i
\(362\) −60.3891 34.8656i −0.00876790 0.00506215i
\(363\) 0 0
\(364\) 693.279 6871.46i 0.0998288 0.989457i
\(365\) 976.690 0.140061
\(366\) 0 0
\(367\) −844.195 + 1462.19i −0.120073 + 0.207972i −0.919796 0.392397i \(-0.871646\pi\)
0.799724 + 0.600368i \(0.204979\pi\)
\(368\) −1183.06 2049.12i −0.167585 0.290265i
\(369\) 0 0
\(370\) −970.463 + 560.297i −0.136357 + 0.0787256i
\(371\) −4038.80 + 2331.81i −0.565187 + 0.326311i
\(372\) 0 0
\(373\) −935.307 1620.00i −0.129835 0.224880i 0.793778 0.608208i \(-0.208111\pi\)
−0.923612 + 0.383328i \(0.874778\pi\)
\(374\) 1337.77 2317.08i 0.184958 0.320357i
\(375\) 0 0
\(376\) −945.151 −0.129634
\(377\) −1801.32 181.740i −0.246082 0.0248278i
\(378\) 0 0
\(379\) 10103.9 + 5833.52i 1.36941 + 0.790627i 0.990852 0.134952i \(-0.0430882\pi\)
0.378554 + 0.925579i \(0.376421\pi\)
\(380\) 8142.61 14103.4i 1.09923 1.90392i
\(381\) 0 0
\(382\) 3736.82i 0.500504i
\(383\) −5782.11 + 3338.30i −0.771415 + 0.445376i −0.833379 0.552702i \(-0.813597\pi\)
0.0619643 + 0.998078i \(0.480263\pi\)
\(384\) 0 0
\(385\) 20966.3i 2.77543i
\(386\) 397.948 + 689.266i 0.0524742 + 0.0908879i
\(387\) 0 0
\(388\) −3438.48 1985.21i −0.449904 0.259752i
\(389\) 14285.3 1.86194 0.930969 0.365099i \(-0.118965\pi\)
0.930969 + 0.365099i \(0.118965\pi\)
\(390\) 0 0
\(391\) 2354.69 0.304558
\(392\) −971.547 560.923i −0.125180 0.0722726i
\(393\) 0 0
\(394\) −865.860 1499.71i −0.110714 0.191763i
\(395\) 4441.79i 0.565800i
\(396\) 0 0
\(397\) 3091.09 1784.64i 0.390774 0.225614i −0.291721 0.956503i \(-0.594228\pi\)
0.682496 + 0.730890i \(0.260895\pi\)
\(398\) 2556.00i 0.321912i
\(399\) 0 0
\(400\) 2544.52 4407.24i 0.318065 0.550905i
\(401\) 432.448 + 249.674i 0.0538540 + 0.0310926i 0.526685 0.850060i \(-0.323435\pi\)
−0.472831 + 0.881153i \(0.656768\pi\)
\(402\) 0 0
\(403\) −3777.77 + 1700.87i −0.466958 + 0.210239i
\(404\) −3311.23 −0.407772
\(405\) 0 0
\(406\) −364.677 + 631.639i −0.0445778 + 0.0772111i
\(407\) 2599.40 + 4502.30i 0.316579 + 0.548331i
\(408\) 0 0
\(409\) −9056.46 + 5228.75i −1.09490 + 0.632140i −0.934876 0.354974i \(-0.884490\pi\)
−0.160022 + 0.987114i \(0.551156\pi\)
\(410\) 4362.80 2518.87i 0.525521 0.303410i
\(411\) 0 0
\(412\) 4016.13 + 6956.15i 0.480245 + 0.831808i
\(413\) 1461.73 2531.80i 0.174158 0.301650i
\(414\) 0 0
\(415\) −5783.03 −0.684043
\(416\) −5784.35 4165.86i −0.681734 0.490981i
\(417\) 0 0
\(418\) 7692.27 + 4441.13i 0.900099 + 0.519672i
\(419\) −852.710 + 1476.94i −0.0994215 + 0.172203i −0.911445 0.411421i \(-0.865033\pi\)
0.812024 + 0.583624i \(0.198366\pi\)
\(420\) 0 0
\(421\) 8765.57i 1.01475i 0.861727 + 0.507373i \(0.169383\pi\)
−0.861727 + 0.507373i \(0.830617\pi\)
\(422\) −563.111 + 325.112i −0.0649569 + 0.0375029i
\(423\) 0 0
\(424\) 3150.70i 0.360876i
\(425\) 2532.24 + 4385.97i 0.289016 + 0.500590i
\(426\) 0 0
\(427\) −4756.45 2746.14i −0.539065 0.311229i
\(428\) −4314.79 −0.487297
\(429\) 0 0
\(430\) 5788.21 0.649145
\(431\) 6997.81 + 4040.18i 0.782071 + 0.451529i 0.837164 0.546953i \(-0.184212\pi\)
−0.0550930 + 0.998481i \(0.517546\pi\)
\(432\) 0 0
\(433\) −2062.24 3571.91i −0.228880 0.396432i 0.728596 0.684943i \(-0.240173\pi\)
−0.957476 + 0.288511i \(0.906840\pi\)
\(434\) 1669.02i 0.184598i
\(435\) 0 0
\(436\) 8814.83 5089.24i 0.968242 0.559015i
\(437\) 7817.14i 0.855709i
\(438\) 0 0
\(439\) −3057.76 + 5296.19i −0.332435 + 0.575794i −0.982989 0.183666i \(-0.941203\pi\)
0.650554 + 0.759460i \(0.274537\pi\)
\(440\) 12266.9 + 7082.32i 1.32910 + 0.767355i
\(441\) 0 0
\(442\) 1736.77 781.948i 0.186900 0.0841482i
\(443\) 11058.8 1.18605 0.593025 0.805184i \(-0.297933\pi\)
0.593025 + 0.805184i \(0.297933\pi\)
\(444\) 0 0
\(445\) 923.603 1599.73i 0.0983887 0.170414i
\(446\) −2475.37 4287.46i −0.262807 0.455195i
\(447\) 0 0
\(448\) 3860.50 2228.86i 0.407123 0.235053i
\(449\) −209.588 + 121.006i −0.0220291 + 0.0127185i −0.510974 0.859596i \(-0.670715\pi\)
0.488945 + 0.872315i \(0.337382\pi\)
\(450\) 0 0
\(451\) −11685.8 20240.5i −1.22010 2.11327i
\(452\) −1419.94 + 2459.41i −0.147762 + 0.255931i
\(453\) 0 0
\(454\) −2918.89 −0.301741
\(455\) −8722.67 + 12111.5i −0.898736 + 1.24791i
\(456\) 0 0
\(457\) 9571.46 + 5526.08i 0.979724 + 0.565644i 0.902187 0.431346i \(-0.141961\pi\)
0.0775372 + 0.996989i \(0.475294\pi\)
\(458\) 932.969 1615.95i 0.0951851 0.164865i
\(459\) 0 0
\(460\) 5886.99i 0.596700i
\(461\) −237.086 + 136.882i −0.0239527 + 0.0138291i −0.511929 0.859028i \(-0.671069\pi\)
0.487976 + 0.872857i \(0.337735\pi\)
\(462\) 0 0
\(463\) 11579.2i 1.16227i −0.813808 0.581134i \(-0.802609\pi\)
0.813808 0.581134i \(-0.197391\pi\)
\(464\) −859.623 1488.91i −0.0860064 0.148968i
\(465\) 0 0
\(466\) −2219.92 1281.67i −0.220678 0.127408i
\(467\) 902.915 0.0894688 0.0447344 0.998999i \(-0.485756\pi\)
0.0447344 + 0.998999i \(0.485756\pi\)
\(468\) 0 0
\(469\) 8463.59 0.833289
\(470\) 835.372 + 482.302i 0.0819847 + 0.0473339i
\(471\) 0 0
\(472\) −987.535 1710.46i −0.0963030 0.166802i
\(473\) 26853.4i 2.61040i
\(474\) 0 0
\(475\) −14560.6 + 8406.56i −1.40650 + 0.812041i
\(476\) 6526.71i 0.628469i
\(477\) 0 0
\(478\) −2519.94 + 4364.67i −0.241128 + 0.417647i
\(479\) 10451.9 + 6034.38i 0.996988 + 0.575611i 0.907356 0.420364i \(-0.138097\pi\)
0.0896324 + 0.995975i \(0.471431\pi\)
\(480\) 0 0
\(481\) −371.514 + 3682.27i −0.0352174 + 0.349059i
\(482\) −3725.70 −0.352077
\(483\) 0 0
\(484\) 10752.6 18624.0i 1.00982 1.74906i
\(485\) 4290.33 + 7431.07i 0.401678 + 0.695727i
\(486\) 0 0
\(487\) 9952.82 5746.26i 0.926089 0.534678i 0.0405163 0.999179i \(-0.487100\pi\)
0.885572 + 0.464501i \(0.153766\pi\)
\(488\) −3213.42 + 1855.27i −0.298084 + 0.172099i
\(489\) 0 0
\(490\) 572.467 + 991.543i 0.0527785 + 0.0914150i
\(491\) −7852.08 + 13600.2i −0.721710 + 1.25004i 0.238605 + 0.971117i \(0.423310\pi\)
−0.960314 + 0.278921i \(0.910023\pi\)
\(492\) 0 0
\(493\) 1710.95 0.156303
\(494\) 2595.92 + 5765.75i 0.236429 + 0.525128i
\(495\) 0 0
\(496\) −3407.16 1967.13i −0.308440 0.178078i
\(497\) 941.741 1631.14i 0.0849957 0.147217i
\(498\) 0 0
\(499\) 9019.80i 0.809181i 0.914498 + 0.404591i \(0.132586\pi\)
−0.914498 + 0.404591i \(0.867414\pi\)
\(500\) 1022.98 590.617i 0.0914980 0.0528264i
\(501\) 0 0
\(502\) 3275.83i 0.291250i
\(503\) −3016.92 5225.46i −0.267431 0.463204i 0.700767 0.713391i \(-0.252841\pi\)
−0.968198 + 0.250186i \(0.919508\pi\)
\(504\) 0 0
\(505\) 6197.33 + 3578.03i 0.546094 + 0.315288i
\(506\) −3210.87 −0.282096
\(507\) 0 0
\(508\) −3134.44 −0.273757
\(509\) 19443.6 + 11225.8i 1.69317 + 0.977551i 0.951934 + 0.306304i \(0.0990926\pi\)
0.741234 + 0.671246i \(0.234241\pi\)
\(510\) 0 0
\(511\) −649.742 1125.39i −0.0562483 0.0974249i
\(512\) 11720.8i 1.01170i
\(513\) 0 0
\(514\) 5973.03 3448.53i 0.512566 0.295930i
\(515\) 17358.9i 1.48529i
\(516\) 0 0
\(517\) 2237.56 3875.56i 0.190344 0.329685i
\(518\) 1291.20 + 745.474i 0.109521 + 0.0632321i
\(519\) 0 0
\(520\) 4139.74 + 9194.69i 0.349115 + 0.775411i
\(521\) −15674.7 −1.31808 −0.659040 0.752108i \(-0.729037\pi\)
−0.659040 + 0.752108i \(0.729037\pi\)
\(522\) 0 0
\(523\) −6755.39 + 11700.7i −0.564804 + 0.978270i 0.432264 + 0.901747i \(0.357715\pi\)
−0.997068 + 0.0765223i \(0.975618\pi\)
\(524\) 5932.33 + 10275.1i 0.494571 + 0.856622i
\(525\) 0 0
\(526\) −3702.37 + 2137.57i −0.306903 + 0.177191i
\(527\) 3390.72 1957.63i 0.280270 0.161814i
\(528\) 0 0
\(529\) 4670.58 + 8089.68i 0.383873 + 0.664887i
\(530\) 1607.77 2784.74i 0.131768 0.228229i
\(531\) 0 0
\(532\) −21667.4 −1.76580
\(533\) 1670.17 16554.0i 0.135728 1.34528i
\(534\) 0 0
\(535\) 8075.59 + 4662.44i 0.652595 + 0.376776i
\(536\) 2858.97 4951.88i 0.230389 0.399046i
\(537\) 0 0
\(538\) 4905.60i 0.393114i
\(539\) 4600.09 2655.86i 0.367607 0.212238i
\(540\) 0 0
\(541\) 12103.6i 0.961875i −0.876755 0.480937i \(-0.840296\pi\)
0.876755 0.480937i \(-0.159704\pi\)
\(542\) 1363.71 + 2362.02i 0.108075 + 0.187191i
\(543\) 0 0
\(544\) 5833.97 + 3368.25i 0.459797 + 0.265464i
\(545\) −21997.2 −1.72891
\(546\) 0 0
\(547\) −15228.6 −1.19036 −0.595181 0.803592i \(-0.702920\pi\)
−0.595181 + 0.803592i \(0.702920\pi\)
\(548\) −12196.8 7041.82i −0.950768 0.548926i
\(549\) 0 0
\(550\) −3452.98 5980.73i −0.267701 0.463671i
\(551\) 5680.03i 0.439160i
\(552\) 0 0
\(553\) −5118.03 + 2954.90i −0.393564 + 0.227224i
\(554\) 701.014i 0.0537603i
\(555\) 0 0
\(556\) −10111.8 + 17514.1i −0.771284 + 1.33590i
\(557\) −20435.5 11798.5i −1.55454 0.897516i −0.997763 0.0668564i \(-0.978703\pi\)
−0.556781 0.830660i \(-0.687964\pi\)
\(558\) 0 0
\(559\) 11171.9 15512.4i 0.845298 1.17371i
\(560\) −14173.6 −1.06954
\(561\) 0 0
\(562\) 3229.31 5593.33i 0.242385 0.419823i
\(563\) −3970.81 6877.64i −0.297246 0.514846i 0.678259 0.734823i \(-0.262735\pi\)
−0.975505 + 0.219978i \(0.929402\pi\)
\(564\) 0 0
\(565\) 5315.15 3068.70i 0.395770 0.228498i
\(566\) −7178.16 + 4144.31i −0.533075 + 0.307771i
\(567\) 0 0
\(568\) −636.233 1101.99i −0.0469995 0.0814056i
\(569\) −1137.33 + 1969.91i −0.0837948 + 0.145137i −0.904877 0.425673i \(-0.860037\pi\)
0.821082 + 0.570810i \(0.193371\pi\)
\(570\) 0 0
\(571\) 4499.84 0.329794 0.164897 0.986311i \(-0.447271\pi\)
0.164897 + 0.986311i \(0.447271\pi\)
\(572\) 20144.5 9069.67i 1.47252 0.662975i
\(573\) 0 0
\(574\) −5804.70 3351.34i −0.422097 0.243698i
\(575\) 3038.91 5263.55i 0.220402 0.381748i
\(576\) 0 0
\(577\) 25253.3i 1.82202i −0.412381 0.911011i \(-0.635303\pi\)
0.412381 0.911011i \(-0.364697\pi\)
\(578\) 2344.40 1353.54i 0.168709 0.0974044i
\(579\) 0 0
\(580\) 4277.55i 0.306234i
\(581\) 3847.15 + 6663.47i 0.274711 + 0.475813i
\(582\) 0 0
\(583\) −12919.3 7458.98i −0.917777 0.529879i
\(584\) −877.921 −0.0622066
\(585\) 0 0
\(586\) 1637.73 0.115450
\(587\) −9773.25 5642.59i −0.687198 0.396754i 0.115363 0.993323i \(-0.463197\pi\)
−0.802562 + 0.596569i \(0.796530\pi\)
\(588\) 0 0
\(589\) 6498.97 + 11256.6i 0.454644 + 0.787467i
\(590\) 2015.72i 0.140654i
\(591\) 0 0
\(592\) −3043.64 + 1757.24i −0.211305 + 0.121997i
\(593\) 12824.5i 0.888090i 0.896005 + 0.444045i \(0.146457\pi\)
−0.896005 + 0.444045i \(0.853543\pi\)
\(594\) 0 0
\(595\) 7052.59 12215.4i 0.485929 0.841654i
\(596\) 4944.99 + 2854.99i 0.339857 + 0.196216i
\(597\) 0 0
\(598\) −1854.82 1335.83i −0.126838 0.0913482i
\(599\) 26180.3 1.78581 0.892905 0.450245i \(-0.148664\pi\)
0.892905 + 0.450245i \(0.148664\pi\)
\(600\) 0 0
\(601\) −8006.28 + 13867.3i −0.543399 + 0.941195i 0.455307 + 0.890335i \(0.349530\pi\)
−0.998706 + 0.0508602i \(0.983804\pi\)
\(602\) −3850.60 6669.43i −0.260695 0.451538i
\(603\) 0 0
\(604\) 1004.22 579.787i 0.0676509 0.0390583i
\(605\) −40249.2 + 23237.9i −2.70473 + 1.56158i
\(606\) 0 0
\(607\) 4765.74 + 8254.50i 0.318674 + 0.551960i 0.980212 0.197952i \(-0.0634290\pi\)
−0.661537 + 0.749912i \(0.730096\pi\)
\(608\) −11181.9 + 19367.7i −0.745868 + 1.29188i
\(609\) 0 0
\(610\) 3786.91 0.251356
\(611\) 2904.93 1307.89i 0.192342 0.0865984i
\(612\) 0 0
\(613\) −8822.27 5093.54i −0.581286 0.335605i 0.180359 0.983601i \(-0.442274\pi\)
−0.761644 + 0.647996i \(0.775608\pi\)
\(614\) 2441.65 4229.06i 0.160484 0.277966i
\(615\) 0 0
\(616\) 18846.0i 1.23267i
\(617\) −6939.13 + 4006.31i −0.452770 + 0.261407i −0.708999 0.705209i \(-0.750853\pi\)
0.256230 + 0.966616i \(0.417520\pi\)
\(618\) 0 0
\(619\) 1886.59i 0.122501i −0.998122 0.0612506i \(-0.980491\pi\)
0.998122 0.0612506i \(-0.0195089\pi\)
\(620\) 4894.29 + 8477.16i 0.317031 + 0.549114i
\(621\) 0 0
\(622\) 4977.86 + 2873.97i 0.320891 + 0.185266i
\(623\) −2457.70 −0.158051
\(624\) 0 0
\(625\) −16844.5 −1.07805
\(626\) 5715.23 + 3299.69i 0.364899 + 0.210674i
\(627\) 0 0
\(628\) 1224.09 + 2120.19i 0.0777812 + 0.134721i
\(629\) 3497.53i 0.221710i
\(630\) 0 0
\(631\) −12952.3 + 7478.04i −0.817154 + 0.471784i −0.849434 0.527695i \(-0.823057\pi\)
0.0322798 + 0.999479i \(0.489723\pi\)
\(632\) 3992.61i 0.251293i
\(633\) 0 0
\(634\) −4392.79 + 7608.53i −0.275173 + 0.476614i
\(635\) 5866.45 + 3387.00i 0.366619 + 0.211667i
\(636\) 0 0
\(637\) 3762.26 + 379.583i 0.234013 + 0.0236101i
\(638\) −2333.06 −0.144775
\(639\) 0 0
\(640\) −10947.8 + 18962.1i −0.676170 + 1.17116i
\(641\) −11845.9 20517.6i −0.729927 1.26427i −0.956913 0.290373i \(-0.906221\pi\)
0.226986 0.973898i \(-0.427113\pi\)
\(642\) 0 0
\(643\) 11822.4 6825.65i 0.725083 0.418627i −0.0915374 0.995802i \(-0.529178\pi\)
0.816621 + 0.577175i \(0.195845\pi\)
\(644\) 6783.25 3916.31i 0.415058 0.239634i
\(645\) 0 0
\(646\) −2987.80 5175.02i −0.181971 0.315184i
\(647\) 9066.14 15703.0i 0.550892 0.954172i −0.447319 0.894375i \(-0.647621\pi\)
0.998211 0.0597977i \(-0.0190456\pi\)
\(648\) 0 0
\(649\) 9351.59 0.565612
\(650\) 493.509 4891.43i 0.0297800 0.295166i
\(651\) 0 0
\(652\) −3450.56 1992.18i −0.207261 0.119662i
\(653\) 3181.74 5510.93i 0.190675 0.330259i −0.754799 0.655956i \(-0.772266\pi\)
0.945474 + 0.325697i \(0.105599\pi\)
\(654\) 0 0
\(655\) 25641.3i 1.52960i
\(656\) 13682.9 7899.85i 0.814374 0.470179i
\(657\) 0 0
\(658\) 1283.40i 0.0760369i
\(659\) −525.717 910.568i −0.0310759 0.0538250i 0.850069 0.526671i \(-0.176560\pi\)
−0.881145 + 0.472846i \(0.843227\pi\)
\(660\) 0 0
\(661\) 7031.91 + 4059.87i 0.413781 + 0.238897i 0.692413 0.721501i \(-0.256548\pi\)
−0.278632 + 0.960398i \(0.589881\pi\)
\(662\) 5296.12 0.310936
\(663\) 0 0
\(664\) 5198.21 0.303810
\(665\) 40553.0 + 23413.3i 2.36478 + 1.36530i
\(666\) 0 0
\(667\) −1026.64 1778.20i −0.0595979 0.103227i
\(668\) 22451.9i 1.30043i
\(669\) 0 0
\(670\) −5053.80 + 2917.81i −0.291411 + 0.168246i
\(671\) 17568.7i 1.01078i
\(672\) 0 0
\(673\) −95.1322 + 164.774i −0.00544885 + 0.00943769i −0.868737 0.495274i \(-0.835068\pi\)
0.863288 + 0.504711i \(0.168401\pi\)
\(674\) −983.620 567.893i −0.0562131 0.0324547i
\(675\) 0 0
\(676\) 15410.1 + 3141.51i 0.876770 + 0.178738i
\(677\) −4861.93 −0.276010 −0.138005 0.990431i \(-0.544069\pi\)
−0.138005 + 0.990431i \(0.544069\pi\)
\(678\) 0 0
\(679\) 5708.27 9887.02i 0.322627 0.558806i
\(680\) −4764.67 8252.66i −0.268701 0.465404i
\(681\) 0 0
\(682\) −4623.60 + 2669.44i −0.259600 + 0.149880i
\(683\) −12591.7 + 7269.80i −0.705426 + 0.407278i −0.809365 0.587306i \(-0.800189\pi\)
0.103939 + 0.994584i \(0.466855\pi\)
\(684\) 0 0
\(685\) 15218.4 + 26359.1i 0.848855 + 1.47026i
\(686\) −2476.70 + 4289.77i −0.137844 + 0.238753i
\(687\) 0 0
\(688\) 18153.4 1.00595
\(689\) −4359.91 9683.70i −0.241073 0.535442i
\(690\) 0 0
\(691\) 19144.8 + 11053.2i 1.05398 + 0.608517i 0.923762 0.382968i \(-0.125098\pi\)
0.130221 + 0.991485i \(0.458431\pi\)
\(692\) −11898.0 + 20607.9i −0.653604 + 1.13208i
\(693\) 0 0
\(694\) 4999.66i 0.273465i
\(695\) 37850.5 21853.0i 2.06583 1.19271i
\(696\) 0 0
\(697\) 15723.4i 0.854474i
\(698\) −630.251 1091.63i −0.0341767 0.0591958i
\(699\) 0 0
\(700\) 14589.4 + 8423.20i 0.787754 + 0.454810i
\(701\) 229.971 0.0123907 0.00619535 0.999981i \(-0.498028\pi\)
0.00619535 + 0.999981i \(0.498028\pi\)
\(702\) 0 0
\(703\) 11611.1 0.622934
\(704\) 12349.0 + 7129.68i 0.661107 + 0.381690i
\(705\) 0 0
\(706\) −2738.56 4743.33i −0.145988 0.252858i
\(707\) 9521.12i 0.506476i
\(708\) 0 0
\(709\) 4158.85 2401.11i 0.220294 0.127187i −0.385792 0.922586i \(-0.626072\pi\)
0.606087 + 0.795399i \(0.292738\pi\)
\(710\) 1298.66i 0.0686446i
\(711\) 0 0
\(712\) −830.202 + 1437.95i −0.0436982 + 0.0756876i
\(713\) −4069.16 2349.33i −0.213732 0.123398i
\(714\) 0 0
\(715\) −47503.0 4792.69i −2.48463 0.250681i
\(716\) −23717.6 −1.23795
\(717\) 0 0
\(718\) 3584.05 6207.75i 0.186289 0.322662i
\(719\) 5508.46 + 9540.94i 0.285718 + 0.494878i 0.972783 0.231718i \(-0.0744347\pi\)
−0.687065 + 0.726596i \(0.741101\pi\)
\(720\) 0 0
\(721\) −20001.7 + 11548.0i −1.03315 + 0.596491i
\(722\) 11730.8 6772.81i 0.604677 0.349110i
\(723\) 0 0
\(724\) 272.063 + 471.226i 0.0139656 + 0.0241892i
\(725\) 2208.11 3824.55i 0.113113 0.195918i
\(726\) 0 0
\(727\) 13498.2 0.688612 0.344306 0.938857i \(-0.388114\pi\)
0.344306 + 0.938857i \(0.388114\pi\)
\(728\) 7840.57 10886.7i 0.399163 0.554244i
\(729\) 0 0
\(730\) 775.950 + 447.995i 0.0393414 + 0.0227138i
\(731\) −9032.89 + 15645.4i −0.457037 + 0.791610i
\(732\) 0 0
\(733\) 17014.7i 0.857368i −0.903455 0.428684i \(-0.858977\pi\)
0.903455 0.428684i \(-0.141023\pi\)
\(734\) −1341.37 + 774.442i −0.0674537 + 0.0389444i
\(735\) 0 0
\(736\) 8084.38i 0.404883i
\(737\) 13536.7 + 23446.2i 0.676567 + 1.17185i
\(738\) 0 0
\(739\) 11598.3 + 6696.31i 0.577337 + 0.333326i 0.760074 0.649836i \(-0.225162\pi\)
−0.182737 + 0.983162i \(0.558496\pi\)
\(740\) 8744.19 0.434382
\(741\) 0 0
\(742\) −4278.27 −0.211672
\(743\) 10216.1 + 5898.26i 0.504431 + 0.291233i 0.730541 0.682868i \(-0.239268\pi\)
−0.226111 + 0.974102i \(0.572601\pi\)
\(744\) 0 0
\(745\) −6170.05 10686.8i −0.303427 0.525551i
\(746\) 1716.05i 0.0842214i
\(747\) 0 0
\(748\) −18080.6 + 10438.8i −0.883812 + 0.510269i
\(749\) 12406.7i 0.605250i
\(750\) 0 0
\(751\) −6225.26 + 10782.5i −0.302480 + 0.523911i −0.976697 0.214622i \(-0.931148\pi\)
0.674217 + 0.738534i \(0.264481\pi\)
\(752\) 2619.95 + 1512.63i 0.127048 + 0.0733510i
\(753\) 0 0
\(754\) −1347.73 970.630i −0.0650949 0.0468810i
\(755\) −2506.01 −0.120799
\(756\) 0 0
\(757\) 3514.92 6088.02i 0.168761 0.292302i −0.769224 0.638980i \(-0.779357\pi\)
0.937984 + 0.346677i \(0.112690\pi\)
\(758\) 5351.51 + 9269.10i 0.256432 + 0.444154i
\(759\) 0 0
\(760\) 27397.3 15817.8i 1.30764 0.754964i
\(761\) 15363.8 8870.29i 0.731849 0.422533i −0.0872491 0.996187i \(-0.527808\pi\)
0.819098 + 0.573653i \(0.194474\pi\)
\(762\) 0 0
\(763\) 14633.6 + 25346.2i 0.694328 + 1.20261i
\(764\) −14579.5 + 25252.5i −0.690405 + 1.19582i
\(765\) 0 0
\(766\) −6124.94 −0.288907
\(767\) 5402.12 + 3890.58i 0.254314 + 0.183156i
\(768\) 0 0
\(769\) −27692.4 15988.2i −1.29859 0.749741i −0.318429 0.947947i \(-0.603155\pi\)
−0.980160 + 0.198206i \(0.936489\pi\)
\(770\) −9616.95 + 16657.0i −0.450092 + 0.779582i
\(771\) 0 0
\(772\) 6210.51i 0.289535i
\(773\) 1849.06 1067.56i 0.0860364 0.0496732i −0.456365 0.889793i \(-0.650849\pi\)
0.542401 + 0.840120i \(0.317515\pi\)
\(774\) 0 0
\(775\) 10105.9i 0.468405i
\(776\) −3856.47 6679.59i −0.178401 0.308999i
\(777\) 0 0
\(778\) 11349.2 + 6552.48i 0.522994 + 0.301951i
\(779\) −52198.9 −2.40080
\(780\) 0 0
\(781\) 6024.89 0.276040
\(782\) 1870.73 + 1080.07i 0.0855464 + 0.0493902i
\(783\) 0 0
\(784\) 1795.41 + 3109.75i 0.0817882 + 0.141661i
\(785\) 5290.89i 0.240560i
\(786\) 0 0
\(787\) 10136.3 5852.18i 0.459109 0.265067i −0.252560 0.967581i \(-0.581273\pi\)
0.711670 + 0.702514i \(0.247939\pi\)
\(788\) 13512.9i 0.610885i
\(789\) 0 0
\(790\) 2037.39 3528.87i 0.0917559 0.158926i
\(791\) −7071.79 4082.90i −0.317881 0.183529i
\(792\) 0 0
\(793\) 7309.17 10148.9i 0.327309 0.454474i
\(794\) 3274.37 0.146351
\(795\) 0 0
\(796\) 9972.46 17272.8i 0.444051 0.769119i
\(797\) 74.8667 + 129.673i 0.00332737 + 0.00576317i 0.867684 0.497116i \(-0.165608\pi\)
−0.864357 + 0.502879i \(0.832274\pi\)
\(798\) 0 0
\(799\) −2607.31 + 1505.33i −0.115444 + 0.0666518i
\(800\) 15058.4 8693.94i 0.665491 0.384222i
\(801\) 0 0
\(802\) 229.045 + 396.717i 0.0100846 + 0.0174670i
\(803\) 2078.40 3599.89i 0.0913387 0.158203i
\(804\) 0 0
\(805\) −16927.4 −0.741135
\(806\) −3781.49 381.524i −0.165257 0.0166732i
\(807\) 0 0
\(808\) −5570.62 3216.20i −0.242542 0.140031i
\(809\) 11760.4 20369.6i 0.511093 0.885239i −0.488825 0.872382i \(-0.662574\pi\)
0.999917 0.0128565i \(-0.00409245\pi\)
\(810\) 0 0
\(811\) 29604.8i 1.28183i 0.767612 + 0.640915i \(0.221445\pi\)
−0.767612 + 0.640915i \(0.778555\pi\)
\(812\) 4928.79 2845.64i 0.213013 0.122983i
\(813\) 0 0
\(814\) 4769.25i 0.205359i
\(815\) 4305.39 + 7457.16i 0.185045 + 0.320507i
\(816\) 0 0
\(817\) −51939.9 29987.5i −2.22417 1.28413i
\(818\) −9593.44 −0.410057
\(819\) 0 0
\(820\) −39310.3 −1.67412
\(821\) 37269.2 + 21517.4i 1.58429 + 0.914691i 0.994223 + 0.107338i \(0.0342326\pi\)
0.590068 + 0.807353i \(0.299101\pi\)
\(822\) 0 0
\(823\) 2792.47 + 4836.71i 0.118274 + 0.204857i 0.919084 0.394062i \(-0.128931\pi\)
−0.800810 + 0.598919i \(0.795597\pi\)
\(824\) 15603.5i 0.659675i
\(825\) 0 0
\(826\) 2322.60 1340.96i 0.0978374 0.0564865i
\(827\) 4788.13i 0.201330i −0.994920 0.100665i \(-0.967903\pi\)
0.994920 0.100665i \(-0.0320970\pi\)
\(828\) 0 0
\(829\) −16196.1 + 28052.5i −0.678546 + 1.17528i 0.296873 + 0.954917i \(0.404056\pi\)
−0.975419 + 0.220359i \(0.929277\pi\)
\(830\) −4594.44 2652.60i −0.192139 0.110931i
\(831\) 0 0
\(832\) 4167.42 + 9256.17i 0.173653 + 0.385697i
\(833\) −3573.50 −0.148637
\(834\) 0 0
\(835\) 24260.9 42021.1i 1.00549 1.74156i
\(836\) −34654.9 60024.1i −1.43369 2.48323i
\(837\) 0 0
\(838\) −1354.90 + 782.254i −0.0558525 + 0.0322464i
\(839\) 11777.0 6799.43i 0.484607 0.279788i −0.237727 0.971332i \(-0.576402\pi\)
0.722335 + 0.691544i \(0.243069\pi\)
\(840\) 0 0
\(841\) 11448.5 + 19829.4i 0.469414 + 0.813048i
\(842\) −4020.65 + 6963.97i −0.164562 + 0.285029i
\(843\) 0 0
\(844\) 5073.82 0.206929
\(845\) −25447.1 22531.4i −1.03598 0.917284i
\(846\) 0 0
\(847\) 53551.4 + 30917.9i 2.17243 + 1.25425i
\(848\) 5042.41 8733.72i 0.204195 0.353676i
\(849\) 0 0
\(850\) 4646.02i 0.187479i
\(851\) −3635.00 + 2098.67i −0.146423 + 0.0845375i
\(852\) 0 0
\(853\) 41037.0i 1.64722i −0.567155 0.823611i \(-0.691956\pi\)
0.567155 0.823611i \(-0.308044\pi\)
\(854\) −2519.24 4363.44i −0.100944 0.174841i
\(855\) 0 0
\(856\) −7258.93 4190.95i −0.289843 0.167341i
\(857\) −39959.3 −1.59275 −0.796374 0.604804i \(-0.793251\pi\)
−0.796374 + 0.604804i \(0.793251\pi\)
\(858\) 0 0
\(859\) −32570.5 −1.29371 −0.646853 0.762615i \(-0.723915\pi\)
−0.646853 + 0.762615i \(0.723915\pi\)
\(860\) −39115.2 22583.2i −1.55095 0.895442i
\(861\) 0 0
\(862\) 3706.36 + 6419.60i 0.146449 + 0.253657i
\(863\) 16951.8i 0.668652i 0.942457 + 0.334326i \(0.108509\pi\)
−0.942457 + 0.334326i \(0.891491\pi\)
\(864\) 0 0
\(865\) 44536.8 25713.3i 1.75063 1.01073i
\(866\) 3783.69i 0.148470i
\(867\) 0 0
\(868\) 6511.84 11278.8i 0.254639 0.441047i
\(869\) −16371.6 9452.13i −0.639088 0.368978i
\(870\) 0 0
\(871\) −1934.70 + 19175.9i −0.0752639 + 0.745981i
\(872\) 19772.7 0.767876
\(873\) 0 0
\(874\) −3585.62 + 6210.48i −0.138771 + 0.240358i
\(875\) 1698.26 + 2941.47i 0.0656134 + 0.113646i
\(876\) 0 0
\(877\) −39784.5 + 22969.6i −1.53184 + 0.884411i −0.532568 + 0.846388i \(0.678773\pi\)
−0.999277 + 0.0380232i \(0.987894\pi\)
\(878\) −4858.59 + 2805.11i −0.186753 + 0.107822i
\(879\) 0 0
\(880\) −22669.2 39264.3i −0.868386 1.50409i
\(881\) −18980.3 + 32874.8i −0.725836 + 1.25718i 0.232793 + 0.972526i \(0.425213\pi\)
−0.958629 + 0.284658i \(0.908120\pi\)
\(882\) 0 0
\(883\) −43172.9 −1.64539 −0.822697 0.568480i \(-0.807532\pi\)
−0.822697 + 0.568480i \(0.807532\pi\)
\(884\) −14787.5 1491.95i −0.562621 0.0567642i
\(885\) 0 0
\(886\) 8785.89 + 5072.54i 0.333146 + 0.192342i
\(887\) 14353.1 24860.4i 0.543327 0.941071i −0.455383 0.890296i \(-0.650498\pi\)
0.998710 0.0507749i \(-0.0161691\pi\)
\(888\) 0 0
\(889\) 9012.78i 0.340021i
\(890\) 1467.55 847.289i 0.0552723 0.0319115i
\(891\) 0 0
\(892\) 38631.4i 1.45008i
\(893\) −4997.41 8655.78i −0.187270 0.324361i
\(894\) 0 0
\(895\) 44390.1 + 25628.7i 1.65788 + 0.957175i
\(896\) 29131.9 1.08619
\(897\) 0 0
\(898\) −222.015 −0.00825027
\(899\) −2956.70 1707.05i −0.109690 0.0633296i
\(900\) 0 0
\(901\) 5018.08 + 8691.57i 0.185545 + 0.321374i
\(902\) 21440.6i 0.791456i
\(903\) 0 0
\(904\) −4777.65 + 2758.38i −0.175777 + 0.101485i
\(905\) 1175.93i 0.0431927i
\(906\) 0 0
\(907\) −11178.0 + 19360.9i −0.409218 + 0.708786i −0.994802 0.101826i \(-0.967532\pi\)
0.585585 + 0.810611i \(0.300865\pi\)
\(908\) 19725.1 + 11388.3i 0.720926 + 0.416227i
\(909\) 0 0
\(910\) −12485.3 + 5621.28i −0.454817 + 0.204773i
\(911\) −6953.80 −0.252897 −0.126449 0.991973i \(-0.540358\pi\)
−0.126449 + 0.991973i \(0.540358\pi\)
\(912\) 0 0
\(913\) −12306.3 + 21315.1i −0.446088 + 0.772647i
\(914\) 5069.48 + 8780.60i 0.183461 + 0.317764i
\(915\) 0 0
\(916\) −12609.5 + 7280.12i −0.454837 + 0.262600i
\(917\) −29545.0 + 17057.8i −1.06397 + 0.614285i
\(918\) 0 0
\(919\) −20312.6 35182.4i −0.729108 1.26285i −0.957261 0.289227i \(-0.906602\pi\)
0.228153 0.973625i \(-0.426731\pi\)
\(920\) −5718.02 + 9903.91i −0.204911 + 0.354915i
\(921\) 0 0
\(922\) −251.143 −0.00897068
\(923\) 3480.39 + 2506.56i 0.124115 + 0.0893871i
\(924\) 0 0
\(925\) −7818.17 4513.82i −0.277902 0.160447i
\(926\) 5311.22 9199.30i 0.188485 0.326466i
\(927\) 0 0
\(928\) 5874.20i 0.207791i
\(929\) −37077.8 + 21406.9i −1.30946 + 0.756014i −0.982005 0.188854i \(-0.939523\pi\)
−0.327450 + 0.944869i \(0.606189\pi\)
\(930\) 0 0
\(931\) 11863.3i 0.417621i
\(932\) 10001.1 + 17322.4i 0.351499 + 0.608814i
\(933\) 0 0
\(934\) 717.338 + 414.155i 0.0251306 + 0.0145092i
\(935\) 45119.7 1.57815
\(936\) 0 0
\(937\) 43484.1 1.51608 0.758038 0.652210i \(-0.226158\pi\)
0.758038 + 0.652210i \(0.226158\pi\)
\(938\) 6724.06 + 3882.14i 0.234060 + 0.135135i
\(939\) 0 0
\(940\) −3763.49 6518.55i −0.130587 0.226183i
\(941\) 7108.58i 0.246263i 0.992390 + 0.123131i \(0.0392936\pi\)
−0.992390 + 0.123131i \(0.960706\pi\)
\(942\) 0 0
\(943\) 16341.5 9434.75i 0.564318 0.325809i
\(944\) 6321.85i 0.217965i
\(945\) 0 0
\(946\) 12317.3 21334.2i 0.423330 0.733229i
\(947\) −1679.22 969.496i −0.0576211 0.0332676i 0.470913 0.882180i \(-0.343925\pi\)
−0.528534 + 0.848912i \(0.677258\pi\)
\(948\) 0 0
\(949\) 2698.30 1214.86i 0.0922976 0.0415553i
\(950\) −15423.9 −0.526756
\(951\) 0 0
\(952\) −6339.39 + 10980.1i −0.215820 + 0.373811i
\(953\) 23903.3 + 41401.8i 0.812492 + 1.40728i 0.911115 + 0.412153i \(0.135223\pi\)
−0.0986228 + 0.995125i \(0.531444\pi\)
\(954\) 0 0
\(955\) 54574.4 31508.5i 1.84920 1.06764i
\(956\) 34058.2 19663.5i 1.15222 0.665234i
\(957\) 0 0
\(958\) 5535.78 + 9588.26i 0.186694 + 0.323364i
\(959\) 20248.1 35070.7i 0.681797 1.18091i
\(960\) 0 0
\(961\) 21978.3 0.737750
\(962\) −1984.17 + 2755.04i −0.0664991 + 0.0923349i
\(963\) 0 0
\(964\) 25177.3 + 14536.1i 0.841190 + 0.485662i
\(965\) −6710.92 + 11623.7i −0.223867 + 0.387750i
\(966\) 0 0
\(967\) 2832.71i 0.0942025i −0.998890 0.0471013i \(-0.985002\pi\)
0.998890 0.0471013i \(-0.0149983\pi\)
\(968\) 36178.9 20887.9i 1.20128 0.693557i
\(969\) 0 0
\(970\) 7871.68i 0.260561i
\(971\) −20638.1 35746.3i −0.682090 1.18142i −0.974342 0.225074i \(-0.927738\pi\)
0.292251 0.956342i \(-0.405596\pi\)
\(972\) 0 0
\(973\) −50360.0 29075.3i −1.65927 0.957978i
\(974\) 10542.9 0.346835
\(975\) 0 0
\(976\) 11876.8 0.389515
\(977\) 3705.63 + 2139.45i 0.121344 + 0.0700583i 0.559444 0.828868i \(-0.311015\pi\)
−0.438099 + 0.898927i \(0.644348\pi\)
\(978\) 0 0
\(979\) −3930.85 6808.43i −0.128325 0.222266i
\(980\) 8934.12i 0.291214i
\(981\) 0 0
\(982\) −12476.5 + 7203.29i −0.405438 + 0.234080i
\(983\) 22652.9i 0.735011i 0.930021 + 0.367505i \(0.119788\pi\)
−0.930021 + 0.367505i \(0.880212\pi\)
\(984\) 0 0
\(985\) 14601.7 25290.9i 0.472333 0.818105i
\(986\) 1359.30 + 784.790i 0.0439034 + 0.0253477i
\(987\) 0 0
\(988\) 4952.98 49091.7i 0.159489 1.58078i
\(989\) 21680.5 0.697068
\(990\) 0 0
\(991\) −11030.1 + 19104.7i −0.353565 + 0.612393i −0.986871 0.161508i \(-0.948364\pi\)
0.633306 + 0.773901i \(0.281697\pi\)
\(992\) −6721.15 11641.4i −0.215118 0.372594i
\(993\) 0 0
\(994\) 1496.37 863.929i 0.0477484 0.0275676i
\(995\) −37329.1 + 21552.0i −1.18936 + 0.686677i
\(996\) 0 0
\(997\) −17817.8 30861.3i −0.565992 0.980327i −0.996957 0.0779583i \(-0.975160\pi\)
0.430964 0.902369i \(-0.358173\pi\)
\(998\) −4137.26 + 7165.95i −0.131225 + 0.227289i
\(999\) 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 117.4.q.e.82.3 10
3.2 odd 2 39.4.j.c.4.3 10
12.11 even 2 624.4.bv.h.433.2 10
13.6 odd 12 1521.4.a.bk.1.5 10
13.7 odd 12 1521.4.a.bk.1.6 10
13.10 even 6 inner 117.4.q.e.10.3 10
39.17 odd 6 507.4.b.i.337.5 10
39.20 even 12 507.4.a.r.1.5 10
39.23 odd 6 39.4.j.c.10.3 yes 10
39.32 even 12 507.4.a.r.1.6 10
39.35 odd 6 507.4.b.i.337.6 10
156.23 even 6 624.4.bv.h.49.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.3 10 3.2 odd 2
39.4.j.c.10.3 yes 10 39.23 odd 6
117.4.q.e.10.3 10 13.10 even 6 inner
117.4.q.e.82.3 10 1.1 even 1 trivial
507.4.a.r.1.5 10 39.20 even 12
507.4.a.r.1.6 10 39.32 even 12
507.4.b.i.337.5 10 39.17 odd 6
507.4.b.i.337.6 10 39.35 odd 6
624.4.bv.h.49.4 10 156.23 even 6
624.4.bv.h.433.2 10 12.11 even 2
1521.4.a.bk.1.5 10 13.6 odd 12
1521.4.a.bk.1.6 10 13.7 odd 12