Properties

Label 126.4.g.a.37.1
Level $126$
Weight $4$
Character 126.37
Analytic conductor $7.434$
Analytic rank $0$
Dimension $2$
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] = [126,4,Mod(37,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), 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: \(7.43424066072\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.37
Dual form 126.4.g.a.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} +(17.5000 + 6.06218i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} +(17.5000 + 6.06218i) q^{7} +8.00000 q^{8} +(-15.0000 - 25.9808i) q^{10} +(-4.50000 - 7.79423i) q^{11} -88.0000 q^{13} +(-28.0000 + 24.2487i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(-52.0000 + 90.0666i) q^{19} +60.0000 q^{20} +18.0000 q^{22} +(-42.0000 + 72.7461i) q^{23} +(-50.0000 - 86.6025i) q^{25} +(88.0000 - 152.420i) q^{26} +(-14.0000 - 72.7461i) q^{28} -51.0000 q^{29} +(-92.5000 - 160.215i) q^{31} +(-16.0000 - 27.7128i) q^{32} +168.000 q^{34} +(-210.000 + 181.865i) q^{35} +(-22.0000 + 38.1051i) q^{37} +(-104.000 - 180.133i) q^{38} +(-60.0000 + 103.923i) q^{40} +168.000 q^{41} +326.000 q^{43} +(-18.0000 + 31.1769i) q^{44} +(-84.0000 - 145.492i) q^{46} +(-69.0000 + 119.512i) q^{47} +(269.500 + 212.176i) q^{49} +200.000 q^{50} +(176.000 + 304.841i) q^{52} +(319.500 + 553.390i) q^{53} +135.000 q^{55} +(140.000 + 48.4974i) q^{56} +(51.0000 - 88.3346i) q^{58} +(79.5000 + 137.698i) q^{59} +(-361.000 + 625.270i) q^{61} +370.000 q^{62} +64.0000 q^{64} +(660.000 - 1143.15i) q^{65} +(83.0000 + 143.760i) q^{67} +(-168.000 + 290.985i) q^{68} +(-105.000 - 545.596i) q^{70} -1086.00 q^{71} +(-109.000 - 188.794i) q^{73} +(-44.0000 - 76.2102i) q^{74} +416.000 q^{76} +(-31.5000 - 163.679i) q^{77} +(291.500 - 504.893i) q^{79} +(-120.000 - 207.846i) q^{80} +(-168.000 + 290.985i) q^{82} +597.000 q^{83} +1260.00 q^{85} +(-326.000 + 564.649i) q^{86} +(-36.0000 - 62.3538i) q^{88} +(-519.000 + 898.934i) q^{89} +(-1540.00 - 533.472i) q^{91} +336.000 q^{92} +(-138.000 - 239.023i) q^{94} +(-780.000 - 1351.00i) q^{95} -169.000 q^{97} +(-637.000 + 254.611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{4} - 15 q^{5} + 35 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{4} - 15 q^{5} + 35 q^{7} + 16 q^{8} - 30 q^{10} - 9 q^{11} - 176 q^{13} - 56 q^{14} - 16 q^{16} - 84 q^{17} - 104 q^{19} + 120 q^{20} + 36 q^{22} - 84 q^{23} - 100 q^{25} + 176 q^{26} - 28 q^{28} - 102 q^{29} - 185 q^{31} - 32 q^{32} + 336 q^{34} - 420 q^{35} - 44 q^{37} - 208 q^{38} - 120 q^{40} + 336 q^{41} + 652 q^{43} - 36 q^{44} - 168 q^{46} - 138 q^{47} + 539 q^{49} + 400 q^{50} + 352 q^{52} + 639 q^{53} + 270 q^{55} + 280 q^{56} + 102 q^{58} + 159 q^{59} - 722 q^{61} + 740 q^{62} + 128 q^{64} + 1320 q^{65} + 166 q^{67} - 336 q^{68} - 210 q^{70} - 2172 q^{71} - 218 q^{73} - 88 q^{74} + 832 q^{76} - 63 q^{77} + 583 q^{79} - 240 q^{80} - 336 q^{82} + 1194 q^{83} + 2520 q^{85} - 652 q^{86} - 72 q^{88} - 1038 q^{89} - 3080 q^{91} + 672 q^{92} - 276 q^{94} - 1560 q^{95} - 338 q^{97} - 1274 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −7.50000 + 12.9904i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) 17.5000 + 6.06218i 0.944911 + 0.327327i
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −15.0000 25.9808i −0.474342 0.821584i
\(11\) −4.50000 7.79423i −0.123346 0.213641i 0.797739 0.603002i \(-0.206029\pi\)
−0.921085 + 0.389362i \(0.872696\pi\)
\(12\) 0 0
\(13\) −88.0000 −1.87745 −0.938723 0.344671i \(-0.887990\pi\)
−0.938723 + 0.344671i \(0.887990\pi\)
\(14\) −28.0000 + 24.2487i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −42.0000 72.7461i −0.599206 1.03785i −0.992939 0.118630i \(-0.962150\pi\)
0.393733 0.919225i \(-0.371183\pi\)
\(18\) 0 0
\(19\) −52.0000 + 90.0666i −0.627875 + 1.08751i 0.360103 + 0.932913i \(0.382742\pi\)
−0.987977 + 0.154598i \(0.950592\pi\)
\(20\) 60.0000 0.670820
\(21\) 0 0
\(22\) 18.0000 0.174437
\(23\) −42.0000 + 72.7461i −0.380765 + 0.659505i −0.991172 0.132583i \(-0.957673\pi\)
0.610406 + 0.792088i \(0.291006\pi\)
\(24\) 0 0
\(25\) −50.0000 86.6025i −0.400000 0.692820i
\(26\) 88.0000 152.420i 0.663778 1.14970i
\(27\) 0 0
\(28\) −14.0000 72.7461i −0.0944911 0.490990i
\(29\) −51.0000 −0.326568 −0.163284 0.986579i \(-0.552209\pi\)
−0.163284 + 0.986579i \(0.552209\pi\)
\(30\) 0 0
\(31\) −92.5000 160.215i −0.535919 0.928239i −0.999118 0.0419848i \(-0.986632\pi\)
0.463199 0.886254i \(-0.346701\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 168.000 0.847405
\(35\) −210.000 + 181.865i −1.01419 + 0.878310i
\(36\) 0 0
\(37\) −22.0000 + 38.1051i −0.0977507 + 0.169309i −0.910753 0.412951i \(-0.864498\pi\)
0.813003 + 0.582260i \(0.197831\pi\)
\(38\) −104.000 180.133i −0.443974 0.768986i
\(39\) 0 0
\(40\) −60.0000 + 103.923i −0.237171 + 0.410792i
\(41\) 168.000 0.639932 0.319966 0.947429i \(-0.396329\pi\)
0.319966 + 0.947429i \(0.396329\pi\)
\(42\) 0 0
\(43\) 326.000 1.15615 0.578076 0.815983i \(-0.303804\pi\)
0.578076 + 0.815983i \(0.303804\pi\)
\(44\) −18.0000 + 31.1769i −0.0616728 + 0.106820i
\(45\) 0 0
\(46\) −84.0000 145.492i −0.269242 0.466341i
\(47\) −69.0000 + 119.512i −0.214142 + 0.370905i −0.953007 0.302949i \(-0.902029\pi\)
0.738865 + 0.673854i \(0.235362\pi\)
\(48\) 0 0
\(49\) 269.500 + 212.176i 0.785714 + 0.618590i
\(50\) 200.000 0.565685
\(51\) 0 0
\(52\) 176.000 + 304.841i 0.469362 + 0.812958i
\(53\) 319.500 + 553.390i 0.828051 + 1.43423i 0.899565 + 0.436787i \(0.143884\pi\)
−0.0715141 + 0.997440i \(0.522783\pi\)
\(54\) 0 0
\(55\) 135.000 0.330971
\(56\) 140.000 + 48.4974i 0.334077 + 0.115728i
\(57\) 0 0
\(58\) 51.0000 88.3346i 0.115459 0.199981i
\(59\) 79.5000 + 137.698i 0.175424 + 0.303843i 0.940308 0.340325i \(-0.110537\pi\)
−0.764884 + 0.644168i \(0.777204\pi\)
\(60\) 0 0
\(61\) −361.000 + 625.270i −0.757726 + 1.31242i 0.186281 + 0.982497i \(0.440357\pi\)
−0.944007 + 0.329924i \(0.892977\pi\)
\(62\) 370.000 0.757904
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 660.000 1143.15i 1.25943 2.18140i
\(66\) 0 0
\(67\) 83.0000 + 143.760i 0.151344 + 0.262136i 0.931722 0.363173i \(-0.118306\pi\)
−0.780378 + 0.625309i \(0.784973\pi\)
\(68\) −168.000 + 290.985i −0.299603 + 0.518927i
\(69\) 0 0
\(70\) −105.000 545.596i −0.179284 0.931589i
\(71\) −1086.00 −1.81527 −0.907637 0.419755i \(-0.862116\pi\)
−0.907637 + 0.419755i \(0.862116\pi\)
\(72\) 0 0
\(73\) −109.000 188.794i −0.174760 0.302693i 0.765318 0.643652i \(-0.222582\pi\)
−0.940078 + 0.340959i \(0.889248\pi\)
\(74\) −44.0000 76.2102i −0.0691202 0.119720i
\(75\) 0 0
\(76\) 416.000 0.627875
\(77\) −31.5000 163.679i −0.0466202 0.242246i
\(78\) 0 0
\(79\) 291.500 504.893i 0.415143 0.719049i −0.580300 0.814403i \(-0.697065\pi\)
0.995443 + 0.0953535i \(0.0303981\pi\)
\(80\) −120.000 207.846i −0.167705 0.290474i
\(81\) 0 0
\(82\) −168.000 + 290.985i −0.226250 + 0.391876i
\(83\) 597.000 0.789509 0.394755 0.918787i \(-0.370830\pi\)
0.394755 + 0.918787i \(0.370830\pi\)
\(84\) 0 0
\(85\) 1260.00 1.60784
\(86\) −326.000 + 564.649i −0.408761 + 0.707996i
\(87\) 0 0
\(88\) −36.0000 62.3538i −0.0436092 0.0755334i
\(89\) −519.000 + 898.934i −0.618134 + 1.07064i 0.371692 + 0.928356i \(0.378778\pi\)
−0.989826 + 0.142283i \(0.954556\pi\)
\(90\) 0 0
\(91\) −1540.00 533.472i −1.77402 0.614539i
\(92\) 336.000 0.380765
\(93\) 0 0
\(94\) −138.000 239.023i −0.151421 0.262270i
\(95\) −780.000 1351.00i −0.842382 1.45905i
\(96\) 0 0
\(97\) −169.000 −0.176901 −0.0884503 0.996081i \(-0.528191\pi\)
−0.0884503 + 0.996081i \(0.528191\pi\)
\(98\) −637.000 + 254.611i −0.656599 + 0.262445i
\(99\) 0 0
\(100\) −200.000 + 346.410i −0.200000 + 0.346410i
\(101\) 321.000 + 555.988i 0.316244 + 0.547752i 0.979701 0.200463i \(-0.0642447\pi\)
−0.663457 + 0.748215i \(0.730911\pi\)
\(102\) 0 0
\(103\) −232.000 + 401.836i −0.221938 + 0.384408i −0.955396 0.295326i \(-0.904572\pi\)
0.733458 + 0.679735i \(0.237905\pi\)
\(104\) −704.000 −0.663778
\(105\) 0 0
\(106\) −1278.00 −1.17104
\(107\) 196.500 340.348i 0.177536 0.307502i −0.763500 0.645808i \(-0.776521\pi\)
0.941036 + 0.338306i \(0.109854\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.00615118 0.0106542i 0.862933 0.505318i \(-0.168625\pi\)
−0.869085 + 0.494663i \(0.835291\pi\)
\(110\) −135.000 + 233.827i −0.117016 + 0.202677i
\(111\) 0 0
\(112\) −224.000 + 193.990i −0.188982 + 0.163663i
\(113\) 2184.00 1.81817 0.909086 0.416608i \(-0.136781\pi\)
0.909086 + 0.416608i \(0.136781\pi\)
\(114\) 0 0
\(115\) −630.000 1091.19i −0.510850 0.884819i
\(116\) 102.000 + 176.669i 0.0816419 + 0.141408i
\(117\) 0 0
\(118\) −318.000 −0.248087
\(119\) −294.000 1527.67i −0.226478 1.17682i
\(120\) 0 0
\(121\) 625.000 1082.53i 0.469572 0.813322i
\(122\) −722.000 1250.54i −0.535794 0.928022i
\(123\) 0 0
\(124\) −370.000 + 640.859i −0.267960 + 0.464120i
\(125\) −375.000 −0.268328
\(126\) 0 0
\(127\) −373.000 −0.260617 −0.130309 0.991473i \(-0.541597\pi\)
−0.130309 + 0.991473i \(0.541597\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 1320.00 + 2286.31i 0.890551 + 1.54248i
\(131\) −586.500 + 1015.85i −0.391166 + 0.677519i −0.992604 0.121400i \(-0.961261\pi\)
0.601438 + 0.798920i \(0.294595\pi\)
\(132\) 0 0
\(133\) −1456.00 + 1260.93i −0.949257 + 0.822081i
\(134\) −332.000 −0.214033
\(135\) 0 0
\(136\) −336.000 581.969i −0.211851 0.366937i
\(137\) 15.0000 + 25.9808i 0.00935428 + 0.0162021i 0.870665 0.491877i \(-0.163689\pi\)
−0.861310 + 0.508079i \(0.830356\pi\)
\(138\) 0 0
\(139\) −82.0000 −0.0500370 −0.0250185 0.999687i \(-0.507964\pi\)
−0.0250185 + 0.999687i \(0.507964\pi\)
\(140\) 1050.00 + 363.731i 0.633866 + 0.219578i
\(141\) 0 0
\(142\) 1086.00 1881.01i 0.641796 1.11162i
\(143\) 396.000 + 685.892i 0.231575 + 0.401099i
\(144\) 0 0
\(145\) 382.500 662.509i 0.219068 0.379437i
\(146\) 436.000 0.247148
\(147\) 0 0
\(148\) 176.000 0.0977507
\(149\) −717.000 + 1241.88i −0.394221 + 0.682811i −0.993001 0.118102i \(-0.962319\pi\)
0.598780 + 0.800913i \(0.295652\pi\)
\(150\) 0 0
\(151\) 1335.50 + 2313.15i 0.719745 + 1.24663i 0.961101 + 0.276198i \(0.0890745\pi\)
−0.241356 + 0.970437i \(0.577592\pi\)
\(152\) −416.000 + 720.533i −0.221987 + 0.384493i
\(153\) 0 0
\(154\) 315.000 + 109.119i 0.164827 + 0.0570979i
\(155\) 2775.00 1.43802
\(156\) 0 0
\(157\) −1126.00 1950.29i −0.572386 0.991401i −0.996320 0.0857085i \(-0.972685\pi\)
0.423934 0.905693i \(-0.360649\pi\)
\(158\) 583.000 + 1009.79i 0.293551 + 0.508444i
\(159\) 0 0
\(160\) 480.000 0.237171
\(161\) −1176.00 + 1018.45i −0.575663 + 0.498539i
\(162\) 0 0
\(163\) −838.000 + 1451.46i −0.402682 + 0.697466i −0.994049 0.108937i \(-0.965255\pi\)
0.591366 + 0.806403i \(0.298589\pi\)
\(164\) −336.000 581.969i −0.159983 0.277098i
\(165\) 0 0
\(166\) −597.000 + 1034.03i −0.279134 + 0.483474i
\(167\) −3030.00 −1.40400 −0.702001 0.712176i \(-0.747710\pi\)
−0.702001 + 0.712176i \(0.747710\pi\)
\(168\) 0 0
\(169\) 5547.00 2.52481
\(170\) −1260.00 + 2182.38i −0.568456 + 0.984595i
\(171\) 0 0
\(172\) −652.000 1129.30i −0.289038 0.500628i
\(173\) 1719.00 2977.40i 0.755452 1.30848i −0.189698 0.981843i \(-0.560751\pi\)
0.945149 0.326638i \(-0.105916\pi\)
\(174\) 0 0
\(175\) −350.000 1818.65i −0.151186 0.785584i
\(176\) 144.000 0.0616728
\(177\) 0 0
\(178\) −1038.00 1797.87i −0.437086 0.757056i
\(179\) −606.000 1049.62i −0.253042 0.438282i 0.711320 0.702869i \(-0.248098\pi\)
−0.964362 + 0.264587i \(0.914765\pi\)
\(180\) 0 0
\(181\) 3032.00 1.24512 0.622560 0.782572i \(-0.286093\pi\)
0.622560 + 0.782572i \(0.286093\pi\)
\(182\) 2464.00 2133.89i 1.00354 0.869089i
\(183\) 0 0
\(184\) −336.000 + 581.969i −0.134621 + 0.233170i
\(185\) −330.000 571.577i −0.131146 0.227152i
\(186\) 0 0
\(187\) −378.000 + 654.715i −0.147819 + 0.256030i
\(188\) 552.000 0.214142
\(189\) 0 0
\(190\) 3120.00 1.19131
\(191\) 1260.00 2182.38i 0.477332 0.826763i −0.522331 0.852743i \(-0.674937\pi\)
0.999662 + 0.0259799i \(0.00827060\pi\)
\(192\) 0 0
\(193\) −182.500 316.099i −0.0680655 0.117893i 0.829984 0.557787i \(-0.188349\pi\)
−0.898050 + 0.439894i \(0.855016\pi\)
\(194\) 169.000 292.717i 0.0625438 0.108329i
\(195\) 0 0
\(196\) 196.000 1357.93i 0.0714286 0.494872i
\(197\) 1590.00 0.575040 0.287520 0.957775i \(-0.407169\pi\)
0.287520 + 0.957775i \(0.407169\pi\)
\(198\) 0 0
\(199\) 2690.00 + 4659.22i 0.958236 + 1.65971i 0.726782 + 0.686868i \(0.241015\pi\)
0.231455 + 0.972846i \(0.425652\pi\)
\(200\) −400.000 692.820i −0.141421 0.244949i
\(201\) 0 0
\(202\) −1284.00 −0.447237
\(203\) −892.500 309.171i −0.308577 0.106894i
\(204\) 0 0
\(205\) −1260.00 + 2182.38i −0.429279 + 0.743533i
\(206\) −464.000 803.672i −0.156934 0.271818i
\(207\) 0 0
\(208\) 704.000 1219.36i 0.234681 0.406479i
\(209\) 936.000 0.309782
\(210\) 0 0
\(211\) −5362.00 −1.74946 −0.874728 0.484614i \(-0.838960\pi\)
−0.874728 + 0.484614i \(0.838960\pi\)
\(212\) 1278.00 2213.56i 0.414025 0.717113i
\(213\) 0 0
\(214\) 393.000 + 680.696i 0.125537 + 0.217437i
\(215\) −2445.00 + 4234.86i −0.775570 + 1.34333i
\(216\) 0 0
\(217\) −647.500 3364.51i −0.202558 1.05252i
\(218\) 28.0000 0.00869908
\(219\) 0 0
\(220\) −270.000 467.654i −0.0827427 0.143315i
\(221\) 3696.00 + 6401.66i 1.12498 + 1.94852i
\(222\) 0 0
\(223\) −1573.00 −0.472358 −0.236179 0.971710i \(-0.575895\pi\)
−0.236179 + 0.971710i \(0.575895\pi\)
\(224\) −112.000 581.969i −0.0334077 0.173591i
\(225\) 0 0
\(226\) −2184.00 + 3782.80i −0.642821 + 1.11340i
\(227\) 460.500 + 797.609i 0.134645 + 0.233212i 0.925462 0.378841i \(-0.123677\pi\)
−0.790817 + 0.612053i \(0.790344\pi\)
\(228\) 0 0
\(229\) −2026.00 + 3509.13i −0.584637 + 1.01262i 0.410284 + 0.911958i \(0.365430\pi\)
−0.994921 + 0.100663i \(0.967904\pi\)
\(230\) 2520.00 0.722452
\(231\) 0 0
\(232\) −408.000 −0.115459
\(233\) −234.000 + 405.300i −0.0657933 + 0.113957i −0.897046 0.441938i \(-0.854291\pi\)
0.831252 + 0.555895i \(0.187624\pi\)
\(234\) 0 0
\(235\) −1035.00 1792.67i −0.287302 0.497622i
\(236\) 318.000 550.792i 0.0877120 0.151922i
\(237\) 0 0
\(238\) 2940.00 + 1018.45i 0.800722 + 0.277378i
\(239\) −4932.00 −1.33483 −0.667415 0.744686i \(-0.732599\pi\)
−0.667415 + 0.744686i \(0.732599\pi\)
\(240\) 0 0
\(241\) 768.500 + 1331.08i 0.205408 + 0.355778i 0.950263 0.311449i \(-0.100814\pi\)
−0.744854 + 0.667227i \(0.767481\pi\)
\(242\) 1250.00 + 2165.06i 0.332037 + 0.575106i
\(243\) 0 0
\(244\) 2888.00 0.757726
\(245\) −4777.50 + 1909.59i −1.24581 + 0.497955i
\(246\) 0 0
\(247\) 4576.00 7925.86i 1.17880 2.04174i
\(248\) −740.000 1281.72i −0.189476 0.328182i
\(249\) 0 0
\(250\) 375.000 649.519i 0.0948683 0.164317i
\(251\) −5319.00 −1.33758 −0.668789 0.743452i \(-0.733187\pi\)
−0.668789 + 0.743452i \(0.733187\pi\)
\(252\) 0 0
\(253\) 756.000 0.187863
\(254\) 373.000 646.055i 0.0921421 0.159595i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2673.00 4629.77i 0.648783 1.12372i −0.334631 0.942349i \(-0.608612\pi\)
0.983414 0.181375i \(-0.0580549\pi\)
\(258\) 0 0
\(259\) −616.000 + 533.472i −0.147785 + 0.127986i
\(260\) −5280.00 −1.25943
\(261\) 0 0
\(262\) −1173.00 2031.70i −0.276596 0.479079i
\(263\) 387.000 + 670.304i 0.0907355 + 0.157159i 0.907821 0.419358i \(-0.137745\pi\)
−0.817085 + 0.576517i \(0.804412\pi\)
\(264\) 0 0
\(265\) −9585.00 −2.22189
\(266\) −728.000 3782.80i −0.167807 0.871948i
\(267\) 0 0
\(268\) 332.000 575.041i 0.0756721 0.131068i
\(269\) 1207.50 + 2091.45i 0.273690 + 0.474045i 0.969804 0.243887i \(-0.0784225\pi\)
−0.696114 + 0.717931i \(0.745089\pi\)
\(270\) 0 0
\(271\) 237.500 411.362i 0.0532365 0.0922084i −0.838179 0.545395i \(-0.816380\pi\)
0.891416 + 0.453187i \(0.149713\pi\)
\(272\) 1344.00 0.299603
\(273\) 0 0
\(274\) −60.0000 −0.0132290
\(275\) −450.000 + 779.423i −0.0986764 + 0.170913i
\(276\) 0 0
\(277\) −1864.00 3228.54i −0.404321 0.700304i 0.589921 0.807461i \(-0.299159\pi\)
−0.994242 + 0.107156i \(0.965825\pi\)
\(278\) 82.0000 142.028i 0.0176908 0.0306413i
\(279\) 0 0
\(280\) −1680.00 + 1454.92i −0.358569 + 0.310530i
\(281\) −1602.00 −0.340097 −0.170049 0.985436i \(-0.554392\pi\)
−0.170049 + 0.985436i \(0.554392\pi\)
\(282\) 0 0
\(283\) −343.000 594.093i −0.0720468 0.124789i 0.827751 0.561095i \(-0.189620\pi\)
−0.899798 + 0.436306i \(0.856286\pi\)
\(284\) 2172.00 + 3762.01i 0.453819 + 0.786037i
\(285\) 0 0
\(286\) −1584.00 −0.327496
\(287\) 2940.00 + 1018.45i 0.604678 + 0.209467i
\(288\) 0 0
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) 765.000 + 1325.02i 0.154905 + 0.268303i
\(291\) 0 0
\(292\) −436.000 + 755.174i −0.0873800 + 0.151347i
\(293\) 1101.00 0.219526 0.109763 0.993958i \(-0.464991\pi\)
0.109763 + 0.993958i \(0.464991\pi\)
\(294\) 0 0
\(295\) −2385.00 −0.470712
\(296\) −176.000 + 304.841i −0.0345601 + 0.0598599i
\(297\) 0 0
\(298\) −1434.00 2483.76i −0.278756 0.482820i
\(299\) 3696.00 6401.66i 0.714867 1.23819i
\(300\) 0 0
\(301\) 5705.00 + 1976.27i 1.09246 + 0.378440i
\(302\) −5342.00 −1.01787
\(303\) 0 0
\(304\) −832.000 1441.07i −0.156969 0.271878i
\(305\) −5415.00 9379.06i −1.01660 1.76080i
\(306\) 0 0
\(307\) 2780.00 0.516818 0.258409 0.966036i \(-0.416802\pi\)
0.258409 + 0.966036i \(0.416802\pi\)
\(308\) −504.000 + 436.477i −0.0932405 + 0.0807486i
\(309\) 0 0
\(310\) −2775.00 + 4806.44i −0.508417 + 0.880605i
\(311\) 2148.00 + 3720.45i 0.391646 + 0.678351i 0.992667 0.120883i \(-0.0385725\pi\)
−0.601021 + 0.799233i \(0.705239\pi\)
\(312\) 0 0
\(313\) −2744.50 + 4753.61i −0.495618 + 0.858435i −0.999987 0.00505298i \(-0.998392\pi\)
0.504370 + 0.863488i \(0.331725\pi\)
\(314\) 4504.00 0.809476
\(315\) 0 0
\(316\) −2332.00 −0.415143
\(317\) 2245.50 3889.32i 0.397854 0.689104i −0.595607 0.803276i \(-0.703088\pi\)
0.993461 + 0.114172i \(0.0364216\pi\)
\(318\) 0 0
\(319\) 229.500 + 397.506i 0.0402807 + 0.0697682i
\(320\) −480.000 + 831.384i −0.0838525 + 0.145237i
\(321\) 0 0
\(322\) −588.000 3055.34i −0.101764 0.528780i
\(323\) 8736.00 1.50490
\(324\) 0 0
\(325\) 4400.00 + 7621.02i 0.750979 + 1.30073i
\(326\) −1676.00 2902.92i −0.284739 0.493183i
\(327\) 0 0
\(328\) 1344.00 0.226250
\(329\) −1932.00 + 1673.16i −0.323753 + 0.280378i
\(330\) 0 0
\(331\) 1982.00 3432.92i 0.329126 0.570062i −0.653213 0.757174i \(-0.726579\pi\)
0.982339 + 0.187112i \(0.0599127\pi\)
\(332\) −1194.00 2068.07i −0.197377 0.341868i
\(333\) 0 0
\(334\) 3030.00 5248.11i 0.496390 0.859773i
\(335\) −2490.00 −0.406099
\(336\) 0 0
\(337\) 161.000 0.0260244 0.0130122 0.999915i \(-0.495858\pi\)
0.0130122 + 0.999915i \(0.495858\pi\)
\(338\) −5547.00 + 9607.69i −0.892654 + 1.54612i
\(339\) 0 0
\(340\) −2520.00 4364.77i −0.401959 0.696214i
\(341\) −832.500 + 1441.93i −0.132206 + 0.228988i
\(342\) 0 0
\(343\) 3430.00 + 5346.84i 0.539949 + 0.841698i
\(344\) 2608.00 0.408761
\(345\) 0 0
\(346\) 3438.00 + 5954.79i 0.534185 + 0.925236i
\(347\) −2958.00 5123.41i −0.457619 0.792619i 0.541216 0.840884i \(-0.317964\pi\)
−0.998835 + 0.0482646i \(0.984631\pi\)
\(348\) 0 0
\(349\) −142.000 −0.0217796 −0.0108898 0.999941i \(-0.503466\pi\)
−0.0108898 + 0.999941i \(0.503466\pi\)
\(350\) 3500.00 + 1212.44i 0.534522 + 0.185164i
\(351\) 0 0
\(352\) −144.000 + 249.415i −0.0218046 + 0.0377667i
\(353\) −2220.00 3845.15i −0.334727 0.579764i 0.648705 0.761040i \(-0.275311\pi\)
−0.983432 + 0.181275i \(0.941977\pi\)
\(354\) 0 0
\(355\) 8145.00 14107.6i 1.21772 2.10916i
\(356\) 4152.00 0.618134
\(357\) 0 0
\(358\) 2424.00 0.357856
\(359\) 1143.00 1979.73i 0.168037 0.291048i −0.769693 0.638415i \(-0.779591\pi\)
0.937730 + 0.347366i \(0.112924\pi\)
\(360\) 0 0
\(361\) −1978.50 3426.86i −0.288453 0.499615i
\(362\) −3032.00 + 5251.58i −0.440217 + 0.762477i
\(363\) 0 0
\(364\) 1232.00 + 6401.66i 0.177402 + 0.921808i
\(365\) 3270.00 0.468930
\(366\) 0 0
\(367\) 1434.50 + 2484.63i 0.204033 + 0.353396i 0.949824 0.312784i \(-0.101262\pi\)
−0.745791 + 0.666180i \(0.767928\pi\)
\(368\) −672.000 1163.94i −0.0951914 0.164876i
\(369\) 0 0
\(370\) 1320.00 0.185469
\(371\) 2236.50 + 11621.2i 0.312974 + 1.62626i
\(372\) 0 0
\(373\) 1532.00 2653.50i 0.212665 0.368346i −0.739883 0.672736i \(-0.765119\pi\)
0.952548 + 0.304390i \(0.0984524\pi\)
\(374\) −756.000 1309.43i −0.104524 0.181040i
\(375\) 0 0
\(376\) −552.000 + 956.092i −0.0757107 + 0.131135i
\(377\) 4488.00 0.613113
\(378\) 0 0
\(379\) −6040.00 −0.818612 −0.409306 0.912397i \(-0.634229\pi\)
−0.409306 + 0.912397i \(0.634229\pi\)
\(380\) −3120.00 + 5404.00i −0.421191 + 0.729524i
\(381\) 0 0
\(382\) 2520.00 + 4364.77i 0.337525 + 0.584610i
\(383\) 921.000 1595.22i 0.122874 0.212825i −0.798026 0.602623i \(-0.794122\pi\)
0.920900 + 0.389799i \(0.127455\pi\)
\(384\) 0 0
\(385\) 2362.50 + 818.394i 0.312738 + 0.108336i
\(386\) 730.000 0.0962591
\(387\) 0 0
\(388\) 338.000 + 585.433i 0.0442251 + 0.0766002i
\(389\) 3915.00 + 6780.98i 0.510279 + 0.883828i 0.999929 + 0.0119097i \(0.00379105\pi\)
−0.489650 + 0.871919i \(0.662876\pi\)
\(390\) 0 0
\(391\) 7056.00 0.912627
\(392\) 2156.00 + 1697.41i 0.277792 + 0.218704i
\(393\) 0 0
\(394\) −1590.00 + 2753.96i −0.203307 + 0.352138i
\(395\) 4372.50 + 7573.39i 0.556973 + 0.964706i
\(396\) 0 0
\(397\) 7382.00 12786.0i 0.933229 1.61640i 0.155467 0.987841i \(-0.450312\pi\)
0.777762 0.628559i \(-0.216355\pi\)
\(398\) −10760.0 −1.35515
\(399\) 0 0
\(400\) 1600.00 0.200000
\(401\) 3132.00 5424.78i 0.390036 0.675563i −0.602417 0.798181i \(-0.705796\pi\)
0.992454 + 0.122618i \(0.0391291\pi\)
\(402\) 0 0
\(403\) 8140.00 + 14098.9i 1.00616 + 1.74272i
\(404\) 1284.00 2223.95i 0.158122 0.273876i
\(405\) 0 0
\(406\) 1428.00 1236.68i 0.174558 0.151171i
\(407\) 396.000 0.0482285
\(408\) 0 0
\(409\) −2375.50 4114.49i −0.287191 0.497429i 0.685948 0.727651i \(-0.259388\pi\)
−0.973138 + 0.230222i \(0.926055\pi\)
\(410\) −2520.00 4364.77i −0.303546 0.525757i
\(411\) 0 0
\(412\) 1856.00 0.221938
\(413\) 556.500 + 2891.66i 0.0663041 + 0.344526i
\(414\) 0 0
\(415\) −4477.50 + 7755.26i −0.529619 + 0.917327i
\(416\) 1408.00 + 2438.73i 0.165944 + 0.287424i
\(417\) 0 0
\(418\) −936.000 + 1621.20i −0.109525 + 0.189702i
\(419\) 4704.00 0.548462 0.274231 0.961664i \(-0.411577\pi\)
0.274231 + 0.961664i \(0.411577\pi\)
\(420\) 0 0
\(421\) −4474.00 −0.517932 −0.258966 0.965886i \(-0.583382\pi\)
−0.258966 + 0.965886i \(0.583382\pi\)
\(422\) 5362.00 9287.26i 0.618526 1.07132i
\(423\) 0 0
\(424\) 2556.00 + 4427.12i 0.292760 + 0.507076i
\(425\) −4200.00 + 7274.61i −0.479365 + 0.830284i
\(426\) 0 0
\(427\) −10108.0 + 8753.78i −1.14557 + 0.992097i
\(428\) −1572.00 −0.177536
\(429\) 0 0
\(430\) −4890.00 8469.73i −0.548411 0.949876i
\(431\) −6402.00 11088.6i −0.715484 1.23925i −0.962773 0.270312i \(-0.912873\pi\)
0.247289 0.968942i \(-0.420460\pi\)
\(432\) 0 0
\(433\) −5074.00 −0.563143 −0.281571 0.959540i \(-0.590856\pi\)
−0.281571 + 0.959540i \(0.590856\pi\)
\(434\) 6475.00 + 2243.01i 0.716152 + 0.248082i
\(435\) 0 0
\(436\) −28.0000 + 48.4974i −0.00307559 + 0.00532708i
\(437\) −4368.00 7565.60i −0.478146 0.828173i
\(438\) 0 0
\(439\) 633.500 1097.25i 0.0688731 0.119292i −0.829532 0.558459i \(-0.811393\pi\)
0.898406 + 0.439167i \(0.144726\pi\)
\(440\) 1080.00 0.117016
\(441\) 0 0
\(442\) −14784.0 −1.59096
\(443\) −3466.50 + 6004.15i −0.371780 + 0.643941i −0.989839 0.142190i \(-0.954586\pi\)
0.618060 + 0.786131i \(0.287919\pi\)
\(444\) 0 0
\(445\) −7785.00 13484.0i −0.829313 1.43641i
\(446\) 1573.00 2724.52i 0.167004 0.289259i
\(447\) 0 0
\(448\) 1120.00 + 387.979i 0.118114 + 0.0409159i
\(449\) −11688.0 −1.22849 −0.614244 0.789116i \(-0.710539\pi\)
−0.614244 + 0.789116i \(0.710539\pi\)
\(450\) 0 0
\(451\) −756.000 1309.43i −0.0789327 0.136715i
\(452\) −4368.00 7565.60i −0.454543 0.787292i
\(453\) 0 0
\(454\) −1842.00 −0.190417
\(455\) 18480.0 16004.1i 1.90408 1.64898i
\(456\) 0 0
\(457\) −275.500 + 477.180i −0.0281999 + 0.0488436i −0.879781 0.475379i \(-0.842311\pi\)
0.851581 + 0.524223i \(0.175644\pi\)
\(458\) −4052.00 7018.27i −0.413401 0.716031i
\(459\) 0 0
\(460\) −2520.00 + 4364.77i −0.255425 + 0.442409i
\(461\) −13386.0 −1.35238 −0.676191 0.736726i \(-0.736371\pi\)
−0.676191 + 0.736726i \(0.736371\pi\)
\(462\) 0 0
\(463\) −6376.00 −0.639995 −0.319998 0.947418i \(-0.603682\pi\)
−0.319998 + 0.947418i \(0.603682\pi\)
\(464\) 408.000 706.677i 0.0408210 0.0707040i
\(465\) 0 0
\(466\) −468.000 810.600i −0.0465229 0.0805801i
\(467\) 2850.00 4936.34i 0.282403 0.489137i −0.689573 0.724216i \(-0.742202\pi\)
0.971976 + 0.235080i \(0.0755351\pi\)
\(468\) 0 0
\(469\) 581.000 + 3018.96i 0.0572027 + 0.297234i
\(470\) 4140.00 0.406306
\(471\) 0 0
\(472\) 636.000 + 1101.58i 0.0620218 + 0.107425i
\(473\) −1467.00 2540.92i −0.142606 0.247001i
\(474\) 0 0
\(475\) 10400.0 1.00460
\(476\) −4704.00 + 4073.78i −0.452957 + 0.392272i
\(477\) 0 0
\(478\) 4932.00 8542.47i 0.471934 0.817414i
\(479\) 9897.00 + 17142.1i 0.944062 + 1.63516i 0.757619 + 0.652697i \(0.226362\pi\)
0.186442 + 0.982466i \(0.440304\pi\)
\(480\) 0 0
\(481\) 1936.00 3353.25i 0.183522 0.317869i
\(482\) −3074.00 −0.290491
\(483\) 0 0
\(484\) −5000.00 −0.469572
\(485\) 1267.50 2195.37i 0.118668 0.205540i
\(486\) 0 0
\(487\) −7967.50 13800.1i −0.741359 1.28407i −0.951877 0.306482i \(-0.900848\pi\)
0.210517 0.977590i \(-0.432485\pi\)
\(488\) −2888.00 + 5002.16i −0.267897 + 0.464011i
\(489\) 0 0
\(490\) 1470.00 10184.5i 0.135526 0.938953i
\(491\) −9963.00 −0.915731 −0.457865 0.889021i \(-0.651386\pi\)
−0.457865 + 0.889021i \(0.651386\pi\)
\(492\) 0 0
\(493\) 2142.00 + 3710.05i 0.195681 + 0.338930i
\(494\) 9152.00 + 15851.7i 0.833538 + 1.44373i
\(495\) 0 0
\(496\) 2960.00 0.267960
\(497\) −19005.0 6583.53i −1.71527 0.594188i
\(498\) 0 0
\(499\) −9571.00 + 16577.5i −0.858631 + 1.48719i 0.0146043 + 0.999893i \(0.495351\pi\)
−0.873235 + 0.487299i \(0.837982\pi\)
\(500\) 750.000 + 1299.04i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 5319.00 9212.78i 0.472906 0.819096i
\(503\) 12192.0 1.08074 0.540372 0.841426i \(-0.318283\pi\)
0.540372 + 0.841426i \(0.318283\pi\)
\(504\) 0 0
\(505\) −9630.00 −0.848573
\(506\) −756.000 + 1309.43i −0.0664196 + 0.115042i
\(507\) 0 0
\(508\) 746.000 + 1292.11i 0.0651543 + 0.112851i
\(509\) −9904.50 + 17155.1i −0.862494 + 1.49388i 0.00702091 + 0.999975i \(0.497765\pi\)
−0.869515 + 0.493907i \(0.835568\pi\)
\(510\) 0 0
\(511\) −763.000 3964.66i −0.0660531 0.343222i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 5346.00 + 9259.54i 0.458759 + 0.794593i
\(515\) −3480.00 6027.54i −0.297761 0.515738i
\(516\) 0 0
\(517\) 1242.00 0.105654
\(518\) −308.000 1600.41i −0.0261250 0.135749i
\(519\) 0 0
\(520\) 5280.00 9145.23i 0.445276 0.771240i
\(521\) −897.000 1553.65i −0.0754286 0.130646i 0.825844 0.563899i \(-0.190699\pi\)
−0.901273 + 0.433253i \(0.857366\pi\)
\(522\) 0 0
\(523\) 3224.00 5584.13i 0.269552 0.466878i −0.699194 0.714932i \(-0.746458\pi\)
0.968746 + 0.248054i \(0.0797911\pi\)
\(524\) 4692.00 0.391166
\(525\) 0 0
\(526\) −1548.00 −0.128319
\(527\) −7770.00 + 13458.0i −0.642251 + 1.11241i
\(528\) 0 0
\(529\) 2555.50 + 4426.26i 0.210035 + 0.363792i
\(530\) 9585.00 16601.7i 0.785558 1.36063i
\(531\) 0 0
\(532\) 7280.00 + 2521.87i 0.593286 + 0.205520i
\(533\) −14784.0 −1.20144
\(534\) 0 0
\(535\) 2947.50 + 5105.22i 0.238190 + 0.412557i
\(536\) 664.000 + 1150.08i 0.0535083 + 0.0926790i
\(537\) 0 0
\(538\) −4830.00 −0.387056
\(539\) 441.000 3055.34i 0.0352416 0.244161i
\(540\) 0 0
\(541\) −3631.00 + 6289.08i −0.288556 + 0.499794i −0.973465 0.228835i \(-0.926509\pi\)
0.684909 + 0.728628i \(0.259842\pi\)
\(542\) 475.000 + 822.724i 0.0376439 + 0.0652012i
\(543\) 0 0
\(544\) −1344.00 + 2327.88i −0.105926 + 0.183469i
\(545\) 210.000 0.0165053
\(546\) 0 0
\(547\) 14204.0 1.11027 0.555136 0.831759i \(-0.312666\pi\)
0.555136 + 0.831759i \(0.312666\pi\)
\(548\) 60.0000 103.923i 0.00467714 0.00810104i
\(549\) 0 0
\(550\) −900.000 1558.85i −0.0697748 0.120853i
\(551\) 2652.00 4593.40i 0.205044 0.355146i
\(552\) 0 0
\(553\) 8162.00 7068.50i 0.627638 0.543550i
\(554\) 7456.00 0.571796
\(555\) 0 0
\(556\) 164.000 + 284.056i 0.0125093 + 0.0216667i
\(557\) 7912.50 + 13704.9i 0.601909 + 1.04254i 0.992532 + 0.121986i \(0.0389264\pi\)
−0.390623 + 0.920551i \(0.627740\pi\)
\(558\) 0 0
\(559\) −28688.0 −2.17061
\(560\) −840.000 4364.77i −0.0633866 0.329366i
\(561\) 0 0
\(562\) 1602.00 2774.75i 0.120243 0.208266i
\(563\) 529.500 + 917.121i 0.0396372 + 0.0686537i 0.885163 0.465280i \(-0.154046\pi\)
−0.845526 + 0.533934i \(0.820713\pi\)
\(564\) 0 0
\(565\) −16380.0 + 28371.0i −1.21967 + 2.11252i
\(566\) 1372.00 0.101890
\(567\) 0 0
\(568\) −8688.00 −0.641796
\(569\) 1980.00 3429.46i 0.145880 0.252672i −0.783821 0.620987i \(-0.786732\pi\)
0.929701 + 0.368315i \(0.120065\pi\)
\(570\) 0 0
\(571\) 1265.00 + 2191.04i 0.0927121 + 0.160582i 0.908651 0.417555i \(-0.137113\pi\)
−0.815939 + 0.578138i \(0.803780\pi\)
\(572\) 1584.00 2743.57i 0.115787 0.200550i
\(573\) 0 0
\(574\) −4704.00 + 4073.78i −0.342058 + 0.296231i
\(575\) 8400.00 0.609225
\(576\) 0 0
\(577\) −5915.50 10245.9i −0.426803 0.739245i 0.569784 0.821795i \(-0.307027\pi\)
−0.996587 + 0.0825498i \(0.973694\pi\)
\(578\) −2143.00 3711.78i −0.154216 0.267111i
\(579\) 0 0
\(580\) −3060.00 −0.219068
\(581\) 10447.5 + 3619.12i 0.746016 + 0.258428i
\(582\) 0 0
\(583\) 2875.50 4980.51i 0.204273 0.353811i
\(584\) −872.000 1510.35i −0.0617870 0.107018i
\(585\) 0 0
\(586\) −1101.00 + 1906.99i −0.0776141 + 0.134432i
\(587\) −4809.00 −0.338141 −0.169070 0.985604i \(-0.554077\pi\)
−0.169070 + 0.985604i \(0.554077\pi\)
\(588\) 0 0
\(589\) 19240.0 1.34596
\(590\) 2385.00 4130.94i 0.166422 0.288251i
\(591\) 0 0
\(592\) −352.000 609.682i −0.0244377 0.0423273i
\(593\) 10902.0 18882.8i 0.754960 1.30763i −0.190434 0.981700i \(-0.560989\pi\)
0.945394 0.325930i \(-0.105677\pi\)
\(594\) 0 0
\(595\) 22050.0 + 7638.34i 1.51926 + 0.526288i
\(596\) 5736.00 0.394221
\(597\) 0 0
\(598\) 7392.00 + 12803.3i 0.505487 + 0.875530i
\(599\) 7083.00 + 12268.1i 0.483144 + 0.836831i 0.999813 0.0193549i \(-0.00616125\pi\)
−0.516668 + 0.856186i \(0.672828\pi\)
\(600\) 0 0
\(601\) 5891.00 0.399832 0.199916 0.979813i \(-0.435933\pi\)
0.199916 + 0.979813i \(0.435933\pi\)
\(602\) −9128.00 + 7905.08i −0.617989 + 0.535194i
\(603\) 0 0
\(604\) 5342.00 9252.62i 0.359872 0.623317i
\(605\) 9375.00 + 16238.0i 0.629997 + 1.09119i
\(606\) 0 0
\(607\) 1368.50 2370.31i 0.0915086 0.158497i −0.816638 0.577151i \(-0.804164\pi\)
0.908146 + 0.418653i \(0.137498\pi\)
\(608\) 3328.00 0.221987
\(609\) 0 0
\(610\) 21660.0 1.43768
\(611\) 6072.00 10517.0i 0.402041 0.696355i
\(612\) 0 0
\(613\) 13094.0 + 22679.5i 0.862743 + 1.49432i 0.869271 + 0.494337i \(0.164589\pi\)
−0.00652719 + 0.999979i \(0.502078\pi\)
\(614\) −2780.00 + 4815.10i −0.182723 + 0.316485i
\(615\) 0 0
\(616\) −252.000 1309.43i −0.0164827 0.0856468i
\(617\) 2358.00 0.153857 0.0769283 0.997037i \(-0.475489\pi\)
0.0769283 + 0.997037i \(0.475489\pi\)
\(618\) 0 0
\(619\) −6883.00 11921.7i −0.446932 0.774110i 0.551252 0.834339i \(-0.314150\pi\)
−0.998185 + 0.0602291i \(0.980817\pi\)
\(620\) −5550.00 9612.88i −0.359505 0.622682i
\(621\) 0 0
\(622\) −8592.00 −0.553871
\(623\) −14532.0 + 12585.1i −0.934530 + 0.809327i
\(624\) 0 0
\(625\) 9062.50 15696.7i 0.580000 1.00459i
\(626\) −5489.00 9507.23i −0.350455 0.607005i
\(627\) 0 0
\(628\) −4504.00 + 7801.16i −0.286193 + 0.495701i
\(629\) 3696.00 0.234291
\(630\) 0 0
\(631\) 21287.0 1.34298 0.671491 0.741012i \(-0.265654\pi\)
0.671491 + 0.741012i \(0.265654\pi\)
\(632\) 2332.00 4039.14i 0.146775 0.254222i
\(633\) 0 0
\(634\) 4491.00 + 7778.64i 0.281326 + 0.487270i
\(635\) 2797.50 4845.41i 0.174827 0.302810i
\(636\) 0 0
\(637\) −23716.0 18671.5i −1.47514 1.16137i
\(638\) −918.000 −0.0569655
\(639\) 0 0
\(640\) −960.000 1662.77i −0.0592927 0.102698i
\(641\) 10713.0 + 18555.5i 0.660122 + 1.14336i 0.980583 + 0.196103i \(0.0628287\pi\)
−0.320462 + 0.947262i \(0.603838\pi\)
\(642\) 0 0
\(643\) 9962.00 0.610984 0.305492 0.952195i \(-0.401179\pi\)
0.305492 + 0.952195i \(0.401179\pi\)
\(644\) 5880.00 + 2036.89i 0.359790 + 0.124635i
\(645\) 0 0
\(646\) −8736.00 + 15131.2i −0.532064 + 0.921562i
\(647\) −9087.00 15739.1i −0.552159 0.956367i −0.998119 0.0613142i \(-0.980471\pi\)
0.445960 0.895053i \(-0.352863\pi\)
\(648\) 0 0
\(649\) 715.500 1239.28i 0.0432755 0.0749555i
\(650\) −17600.0 −1.06204
\(651\) 0 0
\(652\) 6704.00 0.402682
\(653\) −9583.50 + 16599.1i −0.574321 + 0.994752i 0.421795 + 0.906691i \(0.361400\pi\)
−0.996115 + 0.0880610i \(0.971933\pi\)
\(654\) 0 0
\(655\) −8797.50 15237.7i −0.524804 0.908988i
\(656\) −1344.00 + 2327.88i −0.0799914 + 0.138549i
\(657\) 0 0
\(658\) −966.000 5019.48i −0.0572319 0.297386i
\(659\) −13080.0 −0.773178 −0.386589 0.922252i \(-0.626347\pi\)
−0.386589 + 0.922252i \(0.626347\pi\)
\(660\) 0 0
\(661\) 7595.00 + 13154.9i 0.446916 + 0.774081i 0.998183 0.0602477i \(-0.0191891\pi\)
−0.551268 + 0.834328i \(0.685856\pi\)
\(662\) 3964.00 + 6865.85i 0.232727 + 0.403095i
\(663\) 0 0
\(664\) 4776.00 0.279134
\(665\) −5460.00 28371.0i −0.318391 1.65441i
\(666\) 0 0
\(667\) 2142.00 3710.05i 0.124346 0.215373i
\(668\) 6060.00 + 10496.2i 0.351001 + 0.607951i
\(669\) 0 0
\(670\) 2490.00 4312.81i 0.143578 0.248684i
\(671\) 6498.00 0.373849
\(672\) 0 0
\(673\) 4397.00 0.251845 0.125923 0.992040i \(-0.459811\pi\)
0.125923 + 0.992040i \(0.459811\pi\)
\(674\) −161.000 + 278.860i −0.00920102 + 0.0159366i
\(675\) 0 0
\(676\) −11094.0 19215.4i −0.631202 1.09327i
\(677\) 2014.50 3489.22i 0.114363 0.198082i −0.803162 0.595761i \(-0.796851\pi\)
0.917525 + 0.397679i \(0.130184\pi\)
\(678\) 0 0
\(679\) −2957.50 1024.51i −0.167155 0.0579043i
\(680\) 10080.0 0.568456
\(681\) 0 0
\(682\) −1665.00 2883.86i −0.0934841 0.161919i
\(683\) 7510.50 + 13008.6i 0.420763 + 0.728783i 0.996014 0.0891936i \(-0.0284290\pi\)
−0.575251 + 0.817977i \(0.695096\pi\)
\(684\) 0 0
\(685\) −450.000 −0.0251002
\(686\) −12691.0 + 594.093i −0.706333 + 0.0330650i
\(687\) 0 0
\(688\) −2608.00 + 4517.19i −0.144519 + 0.250314i
\(689\) −28116.0 48698.3i −1.55462 2.69268i
\(690\) 0 0
\(691\) 6992.00 12110.5i 0.384932 0.666722i −0.606828 0.794834i \(-0.707558\pi\)
0.991760 + 0.128111i \(0.0408915\pi\)
\(692\) −13752.0 −0.755452
\(693\) 0 0
\(694\) 11832.0 0.647171
\(695\) 615.000 1065.21i 0.0335659 0.0581378i
\(696\) 0 0
\(697\) −7056.00 12221.4i −0.383451 0.664156i
\(698\) 142.000 245.951i 0.00770026 0.0133372i
\(699\) 0 0
\(700\) −5600.00 + 4849.74i −0.302372 + 0.261861i
\(701\) 31053.0 1.67312 0.836559 0.547877i \(-0.184564\pi\)
0.836559 + 0.547877i \(0.184564\pi\)
\(702\) 0 0
\(703\) −2288.00 3962.93i −0.122750 0.212610i
\(704\) −288.000 498.831i −0.0154182 0.0267051i
\(705\) 0 0
\(706\) 8880.00 0.473376
\(707\) 2247.00 + 11675.8i 0.119529 + 0.621092i
\(708\) 0 0
\(709\) −7543.00 + 13064.9i −0.399553 + 0.692047i −0.993671 0.112332i \(-0.964168\pi\)
0.594117 + 0.804378i \(0.297501\pi\)
\(710\) 16290.0 + 28215.1i 0.861060 + 1.49140i
\(711\) 0 0
\(712\) −4152.00 + 7191.47i −0.218543 + 0.378528i
\(713\) 15540.0 0.816238
\(714\) 0 0
\(715\) −11880.0 −0.621380
\(716\) −2424.00 + 4198.49i −0.126521 + 0.219141i
\(717\) 0 0
\(718\) 2286.00 + 3959.47i 0.118820 + 0.205802i
\(719\) −3189.00 + 5523.51i −0.165410 + 0.286498i −0.936801 0.349863i \(-0.886228\pi\)
0.771391 + 0.636362i \(0.219561\pi\)
\(720\) 0 0
\(721\) −6496.00 + 5625.70i −0.335539 + 0.290585i
\(722\) 7914.00 0.407934
\(723\) 0 0
\(724\) −6064.00 10503.2i −0.311280 0.539153i
\(725\) 2550.00 + 4416.73i 0.130627 + 0.226253i
\(726\) 0 0
\(727\) −7363.00 −0.375624 −0.187812 0.982205i \(-0.560140\pi\)
−0.187812 + 0.982205i \(0.560140\pi\)
\(728\) −12320.0 4267.77i −0.627211 0.217272i
\(729\) 0 0
\(730\) −3270.00 + 5663.81i −0.165792 + 0.287160i
\(731\) −13692.0 23715.2i −0.692773 1.19992i
\(732\) 0 0
\(733\) −16405.0 + 28414.3i −0.826647 + 1.43180i 0.0740064 + 0.997258i \(0.476421\pi\)
−0.900654 + 0.434537i \(0.856912\pi\)
\(734\) −5738.00 −0.288547
\(735\) 0 0
\(736\) 2688.00 0.134621
\(737\) 747.000 1293.84i 0.0373353 0.0646666i
\(738\) 0 0
\(739\) 12017.0 + 20814.1i 0.598177 + 1.03607i 0.993090 + 0.117354i \(0.0374412\pi\)
−0.394914 + 0.918718i \(0.629225\pi\)
\(740\) −1320.00 + 2286.31i −0.0655732 + 0.113576i
\(741\) 0 0
\(742\) −22365.0 7747.46i −1.10653 0.383313i
\(743\) 8022.00 0.396095 0.198048 0.980192i \(-0.436540\pi\)
0.198048 + 0.980192i \(0.436540\pi\)
\(744\) 0 0
\(745\) −10755.0 18628.2i −0.528903 0.916087i
\(746\) 3064.00 + 5307.00i 0.150377 + 0.260460i
\(747\) 0 0
\(748\) 3024.00 0.147819
\(749\) 5502.00 4764.87i 0.268409 0.232449i
\(750\) 0 0
\(751\) −14759.5 + 25564.2i −0.717153 + 1.24215i 0.244970 + 0.969531i \(0.421222\pi\)
−0.962123 + 0.272615i \(0.912112\pi\)
\(752\) −1104.00 1912.18i −0.0535356 0.0927263i
\(753\) 0 0
\(754\) −4488.00 + 7773.44i −0.216768 + 0.375454i
\(755\) −40065.0 −1.93128
\(756\) 0 0
\(757\) −3742.00 −0.179664 −0.0898318 0.995957i \(-0.528633\pi\)
−0.0898318 + 0.995957i \(0.528633\pi\)
\(758\) 6040.00 10461.6i 0.289423 0.501295i
\(759\) 0 0
\(760\) −6240.00 10808.0i −0.297827 0.515852i
\(761\) −5448.00 + 9436.21i −0.259514 + 0.449491i −0.966112 0.258124i \(-0.916896\pi\)
0.706598 + 0.707615i \(0.250229\pi\)
\(762\) 0 0
\(763\) −49.0000 254.611i −0.00232493 0.0120807i
\(764\) −10080.0 −0.477332
\(765\) 0 0
\(766\) 1842.00 + 3190.44i 0.0868853 + 0.150490i
\(767\) −6996.00 12117.4i −0.329349 0.570450i
\(768\) 0 0
\(769\) 17285.0 0.810550 0.405275 0.914195i \(-0.367176\pi\)
0.405275 + 0.914195i \(0.367176\pi\)
\(770\) −3780.00 + 3273.58i −0.176911 + 0.153210i
\(771\) 0 0
\(772\) −730.000 + 1264.40i −0.0340327 + 0.0589464i
\(773\) 5913.00 + 10241.6i 0.275130 + 0.476540i 0.970168 0.242434i \(-0.0779456\pi\)
−0.695038 + 0.718973i \(0.744612\pi\)
\(774\) 0 0
\(775\) −9250.00 + 16021.5i −0.428735 + 0.742591i
\(776\) −1352.00 −0.0625438
\(777\) 0 0
\(778\) −15660.0 −0.721643
\(779\) −8736.00 + 15131.2i −0.401797 + 0.695932i
\(780\) 0 0
\(781\) 4887.00 + 8464.53i 0.223906 + 0.387817i
\(782\) −7056.00 + 12221.4i −0.322662 + 0.558868i
\(783\) 0 0
\(784\) −5096.00 + 2036.89i −0.232143 + 0.0927884i
\(785\) 33780.0 1.53587
\(786\) 0 0
\(787\) −8857.00 15340.8i −0.401166 0.694841i 0.592701 0.805423i \(-0.298062\pi\)
−0.993867 + 0.110582i \(0.964728\pi\)
\(788\) −3180.00 5507.92i −0.143760 0.248999i
\(789\) 0 0
\(790\) −17490.0 −0.787679
\(791\) 38220.0 + 13239.8i 1.71801 + 0.595136i
\(792\) 0 0
\(793\) 31768.0 55023.8i 1.42259 2.46400i
\(794\) 14764.0 + 25572.0i 0.659893 + 1.14297i
\(795\) 0 0
\(796\) 10760.0 18636.9i 0.479118 0.829857i
\(797\) 24939.0 1.10839 0.554194 0.832388i \(-0.313027\pi\)
0.554194 + 0.832388i \(0.313027\pi\)
\(798\) 0 0
\(799\) 11592.0 0.513261
\(800\) −1600.00 + 2771.28i −0.0707107 + 0.122474i
\(801\) 0 0
\(802\) 6264.00 + 10849.6i 0.275797 + 0.477695i
\(803\) −981.000 + 1699.14i −0.0431118 + 0.0746717i
\(804\) 0 0
\(805\) −4410.00 22915.0i −0.193083 1.00329i
\(806\) −32560.0 −1.42292
\(807\) 0 0
\(808\) 2568.00 + 4447.91i 0.111809 + 0.193659i
\(809\) −14532.0 25170.2i −0.631543 1.09386i −0.987236 0.159261i \(-0.949089\pi\)
0.355694 0.934602i \(-0.384245\pi\)
\(810\) 0 0
\(811\) −15370.0 −0.665492 −0.332746 0.943017i \(-0.607975\pi\)
−0.332746 + 0.943017i \(0.607975\pi\)
\(812\) 714.000 + 3710.05i 0.0308577 + 0.160342i
\(813\) 0 0
\(814\) −396.000 + 685.892i −0.0170513 + 0.0295338i
\(815\) −12570.0 21771.9i −0.540255 0.935749i
\(816\) 0 0
\(817\) −16952.0 + 29361.7i −0.725918 + 1.25733i
\(818\) 9502.00 0.406149
\(819\) 0 0
\(820\) 10080.0 0.429279
\(821\) 22015.5 38132.0i 0.935866 1.62097i 0.162785 0.986662i \(-0.447952\pi\)
0.773082 0.634306i \(-0.218714\pi\)
\(822\) 0 0
\(823\) 2096.00 + 3630.38i 0.0887752 + 0.153763i 0.906994 0.421144i \(-0.138371\pi\)
−0.818218 + 0.574907i \(0.805038\pi\)
\(824\) −1856.00 + 3214.69i −0.0784670 + 0.135909i
\(825\) 0 0
\(826\) −5565.00 1927.77i −0.234420 0.0812056i
\(827\) −33195.0 −1.39577 −0.697886 0.716209i \(-0.745876\pi\)
−0.697886 + 0.716209i \(0.745876\pi\)
\(828\) 0 0
\(829\) −8224.00 14244.4i −0.344549 0.596777i 0.640723 0.767773i \(-0.278635\pi\)
−0.985272 + 0.170996i \(0.945302\pi\)
\(830\) −8955.00 15510.5i −0.374497 0.648648i
\(831\) 0 0
\(832\) −5632.00 −0.234681
\(833\) 4116.00 28516.5i 0.171202 1.18612i
\(834\) 0 0
\(835\) 22725.0 39360.9i 0.941834 1.63130i
\(836\) −1872.00 3242.40i −0.0774455 0.134140i
\(837\) 0 0
\(838\) −4704.00 + 8147.57i −0.193910 + 0.335863i
\(839\) −16860.0 −0.693769 −0.346884 0.937908i \(-0.612760\pi\)
−0.346884 + 0.937908i \(0.612760\pi\)
\(840\) 0 0
\(841\) −21788.0 −0.893354
\(842\) 4474.00 7749.20i 0.183117 0.317167i
\(843\) 0 0
\(844\) 10724.0 + 18574.5i 0.437364 + 0.757537i
\(845\) −41602.5 + 72057.6i −1.69369 + 2.93356i
\(846\) 0 0
\(847\) 17500.0 15155.4i 0.709926 0.614814i
\(848\) −10224.0 −0.414025
\(849\) 0 0
\(850\) −8400.00 14549.2i −0.338962 0.587099i
\(851\) −1848.00 3200.83i −0.0744402 0.128934i
\(852\) 0 0
\(853\) 29054.0 1.16623 0.583113 0.812391i \(-0.301835\pi\)
0.583113 + 0.812391i \(0.301835\pi\)
\(854\) −5054.00 26261.4i −0.202511 1.05228i
\(855\) 0 0
\(856\) 1572.00 2722.78i 0.0627685 0.108718i
\(857\) 20979.0 + 36336.7i 0.836207 + 1.44835i 0.893044 + 0.449969i \(0.148565\pi\)
−0.0568378 + 0.998383i \(0.518102\pi\)
\(858\) 0 0
\(859\) −2773.00 + 4802.98i −0.110144 + 0.190775i −0.915828 0.401570i \(-0.868464\pi\)
0.805684 + 0.592345i \(0.201798\pi\)
\(860\) 19560.0 0.775570
\(861\) 0 0
\(862\) 25608.0 1.01185
\(863\) −16269.0 + 28178.7i −0.641719 + 1.11149i 0.343330 + 0.939215i \(0.388445\pi\)
−0.985049 + 0.172275i \(0.944888\pi\)
\(864\) 0 0
\(865\) 25785.0 + 44660.9i 1.01354 + 1.75551i
\(866\) 5074.00 8788.43i 0.199101 0.344853i
\(867\) 0 0
\(868\) −10360.0 + 8972.02i −0.405117 + 0.350841i
\(869\) −5247.00 −0.204824
\(870\) 0 0
\(871\) −7304.00 12650.9i −0.284141 0.492146i
\(872\) −56.0000 96.9948i −0.00217477 0.00376681i
\(873\) 0 0
\(874\) 17472.0 0.676200
\(875\) −6562.50 2273.32i −0.253546 0.0878310i
\(876\) 0 0
\(877\) −16048.0 + 27796.0i −0.617905 + 1.07024i 0.371963 + 0.928248i \(0.378685\pi\)
−0.989867 + 0.141995i \(0.954648\pi\)
\(878\) 1267.00 + 2194.51i 0.0487007 + 0.0843520i
\(879\) 0 0
\(880\) −1080.00 + 1870.61i −0.0413714 + 0.0716573i
\(881\) 8490.00 0.324671 0.162336 0.986736i \(-0.448097\pi\)
0.162336 + 0.986736i \(0.448097\pi\)
\(882\) 0 0
\(883\) −48352.0 −1.84278 −0.921390 0.388640i \(-0.872945\pi\)
−0.921390 + 0.388640i \(0.872945\pi\)
\(884\) 14784.0 25606.6i 0.562488 0.974258i
\(885\) 0 0
\(886\) −6933.00 12008.3i −0.262888 0.455335i
\(887\) 7746.00 13416.5i 0.293219 0.507870i −0.681350 0.731958i \(-0.738607\pi\)
0.974569 + 0.224088i \(0.0719402\pi\)
\(888\) 0 0
\(889\) −6527.50 2261.19i −0.246260 0.0853070i
\(890\) 31140.0 1.17283
\(891\) 0 0
\(892\) 3146.00 + 5449.03i 0.118090 + 0.204537i
\(893\) −7176.00 12429.2i −0.268909 0.465764i
\(894\) 0 0
\(895\) 18180.0 0.678984
\(896\) −1792.00 + 1551.92i −0.0668153 + 0.0578638i
\(897\) 0 0
\(898\) 11688.0 20244.2i 0.434336 0.752292i
\(899\) 4717.50 + 8170.95i 0.175014 + 0.303133i
\(900\) 0 0
\(901\) 26838.0 46484.8i 0.992346 1.71879i
\(902\) 3024.00 0.111628
\(903\) 0 0
\(904\) 17472.0 0.642821
\(905\) −22740.0 + 39386.8i −0.835252 + 1.44670i
\(906\) 0 0
\(907\) 4058.00 + 7028.66i 0.148560 + 0.257313i 0.930695 0.365795i \(-0.119203\pi\)
−0.782136 + 0.623108i \(0.785870\pi\)
\(908\) 1842.00 3190.44i 0.0673226 0.116606i
\(909\) 0 0
\(910\) 9240.00 + 48012.4i 0.336597 + 1.74901i
\(911\) 4446.00 0.161693 0.0808466 0.996727i \(-0.474238\pi\)
0.0808466 + 0.996727i \(0.474238\pi\)
\(912\) 0 0
\(913\) −2686.50 4653.15i −0.0973824 0.168671i
\(914\) −551.000 954.360i −0.0199403 0.0345377i
\(915\) 0 0
\(916\) 16208.0 0.584637
\(917\) −16422.0 + 14221.9i −0.591387 + 0.512156i
\(918\) 0 0
\(919\) −13252.0 + 22953.1i −0.475673 + 0.823889i −0.999612 0.0278666i \(-0.991129\pi\)
0.523939 + 0.851756i \(0.324462\pi\)
\(920\) −5040.00 8729.54i −0.180613 0.312831i
\(921\) 0 0
\(922\) 13386.0 23185.2i 0.478139 0.828162i
\(923\) 95568.0 3.40808
\(924\) 0 0
\(925\) 4400.00 0.156401
\(926\) 6376.00 11043.6i 0.226273 0.391916i
\(927\) 0 0
\(928\) 816.000 + 1413.35i 0.0288648 + 0.0499953i
\(929\) −2715.00 + 4702.52i −0.0958840 + 0.166076i −0.909977 0.414658i \(-0.863901\pi\)
0.814093 + 0.580734i \(0.197234\pi\)
\(930\) 0 0
\(931\) −33124.0 + 13239.8i −1.16605 + 0.466076i
\(932\) 1872.00 0.0657933
\(933\) 0 0
\(934\) 5700.00 + 9872.69i 0.199689 + 0.345872i
\(935\) −5670.00 9820.73i −0.198320 0.343500i
\(936\) 0 0
\(937\) 33803.0 1.17854 0.589272 0.807935i \(-0.299415\pi\)
0.589272 + 0.807935i \(0.299415\pi\)
\(938\) −5810.00 2012.64i −0.202242 0.0700588i
\(939\) 0 0
\(940\) −4140.00 + 7170.69i −0.143651 + 0.248811i
\(941\) −24241.5 41987.5i −0.839798 1.45457i −0.890063 0.455838i \(-0.849340\pi\)
0.0502645 0.998736i \(-0.483994\pi\)
\(942\) 0 0
\(943\) −7056.00 + 12221.4i −0.243664 + 0.422038i
\(944\) −2544.00 −0.0877120
\(945\) 0 0
\(946\) 5868.00 0.201676
\(947\) 18648.0 32299.3i 0.639893 1.10833i −0.345563 0.938396i \(-0.612312\pi\)
0.985456 0.169931i \(-0.0543546\pi\)
\(948\) 0 0
\(949\) 9592.00 + 16613.8i 0.328103 + 0.568291i
\(950\) −10400.0 + 18013.3i −0.355180 + 0.615189i
\(951\) 0 0
\(952\) −2352.00 12221.4i −0.0800722 0.416067i
\(953\) 38478.0 1.30790 0.653948 0.756540i \(-0.273112\pi\)
0.653948 + 0.756540i \(0.273112\pi\)
\(954\) 0 0
\(955\) 18900.0 + 32735.8i 0.640408 + 1.10922i
\(956\) 9864.00 + 17084.9i 0.333708 + 0.577999i
\(957\) 0 0
\(958\) −39588.0 −1.33510
\(959\) 105.000 + 545.596i 0.00353559 + 0.0183714i
\(960\) 0 0
\(961\) −2217.00 + 3839.96i −0.0744184 + 0.128897i
\(962\) 3872.00 + 6706.50i 0.129770 + 0.224767i
\(963\) 0 0
\(964\) 3074.00 5324.32i 0.102704 0.177889i
\(965\) 5475.00 0.182639
\(966\) 0 0
\(967\) 27257.0 0.906438 0.453219 0.891399i \(-0.350275\pi\)
0.453219 + 0.891399i \(0.350275\pi\)
\(968\) 5000.00 8660.25i 0.166019 0.287553i
\(969\) 0 0
\(970\) 2535.00 + 4390.75i 0.0839113 + 0.145339i
\(971\) 17170.5 29740.2i 0.567485 0.982912i −0.429329 0.903148i \(-0.641250\pi\)
0.996814 0.0797641i \(-0.0254167\pi\)
\(972\) 0 0
\(973\) −1435.00 497.099i −0.0472806 0.0163785i
\(974\) 31870.0 1.04844
\(975\) 0 0
\(976\) −5776.00 10004.3i −0.189432 0.328105i
\(977\) 13713.0 + 23751.6i 0.449046 + 0.777770i 0.998324 0.0578693i \(-0.0184307\pi\)
−0.549278 + 0.835639i \(0.685097\pi\)
\(978\) 0 0
\(979\) 9342.00 0.304976
\(980\) 16170.0 + 12730.6i 0.527073 + 0.414963i
\(981\) 0 0
\(982\) 9963.00 17256.4i 0.323760 0.560768i
\(983\) 6162.00 + 10672.9i 0.199936 + 0.346300i 0.948508 0.316755i \(-0.102593\pi\)
−0.748571 + 0.663054i \(0.769260\pi\)
\(984\) 0 0
\(985\) −11925.0 + 20654.7i −0.385748 + 0.668136i
\(986\) −8568.00 −0.276735
\(987\) 0 0
\(988\) −36608.0 −1.17880
\(989\) −13692.0 + 23715.2i −0.440223 + 0.762488i
\(990\) 0 0
\(991\) −23798.5 41220.2i −0.762850 1.32129i −0.941376 0.337360i \(-0.890466\pi\)
0.178526 0.983935i \(-0.442867\pi\)
\(992\) −2960.00 + 5126.87i −0.0947380 + 0.164091i
\(993\) 0 0
\(994\) 30408.0 26334.1i 0.970305 0.840309i
\(995\) −80700.0 −2.57122
\(996\) 0 0
\(997\) 5621.00 + 9735.86i 0.178555 + 0.309266i 0.941386 0.337332i \(-0.109525\pi\)
−0.762831 + 0.646598i \(0.776191\pi\)
\(998\) −19142.0 33154.9i −0.607144 1.05160i
\(999\) 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 126.4.g.a.37.1 2
3.2 odd 2 42.4.e.b.37.1 yes 2
7.2 even 3 882.4.a.r.1.1 1
7.3 odd 6 882.4.g.l.361.1 2
7.4 even 3 inner 126.4.g.a.109.1 2
7.5 odd 6 882.4.a.h.1.1 1
7.6 odd 2 882.4.g.l.667.1 2
12.11 even 2 336.4.q.d.289.1 2
21.2 odd 6 294.4.a.a.1.1 1
21.5 even 6 294.4.a.g.1.1 1
21.11 odd 6 42.4.e.b.25.1 2
21.17 even 6 294.4.e.e.67.1 2
21.20 even 2 294.4.e.e.79.1 2
84.11 even 6 336.4.q.d.193.1 2
84.23 even 6 2352.4.a.u.1.1 1
84.47 odd 6 2352.4.a.q.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.b.25.1 2 21.11 odd 6
42.4.e.b.37.1 yes 2 3.2 odd 2
126.4.g.a.37.1 2 1.1 even 1 trivial
126.4.g.a.109.1 2 7.4 even 3 inner
294.4.a.a.1.1 1 21.2 odd 6
294.4.a.g.1.1 1 21.5 even 6
294.4.e.e.67.1 2 21.17 even 6
294.4.e.e.79.1 2 21.20 even 2
336.4.q.d.193.1 2 84.11 even 6
336.4.q.d.289.1 2 12.11 even 2
882.4.a.h.1.1 1 7.5 odd 6
882.4.a.r.1.1 1 7.2 even 3
882.4.g.l.361.1 2 7.3 odd 6
882.4.g.l.667.1 2 7.6 odd 2
2352.4.a.q.1.1 1 84.47 odd 6
2352.4.a.u.1.1 1 84.23 even 6