Properties

Label 105.4.b.b.41.6
Level $105$
Weight $4$
Character 105.41
Analytic conductor $6.195$
Analytic rank $0$
Dimension $16$
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] = [105,4,Mod(41,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.41");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + 13209792 x^{2} + 5760000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.6
Root \(-1.80256i\) of defining polynomial
Character \(\chi\) \(=\) 105.41
Dual form 105.4.b.b.41.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.80256i q^{2} +(1.60858 + 4.94090i) q^{3} +4.75076 q^{4} +5.00000 q^{5} +(8.90629 - 2.89956i) q^{6} +(2.01165 + 18.4107i) q^{7} -22.9841i q^{8} +(-21.8250 + 15.8956i) q^{9} +O(q^{10})\) \(q-1.80256i q^{2} +(1.60858 + 4.94090i) q^{3} +4.75076 q^{4} +5.00000 q^{5} +(8.90629 - 2.89956i) q^{6} +(2.01165 + 18.4107i) q^{7} -22.9841i q^{8} +(-21.8250 + 15.8956i) q^{9} -9.01282i q^{10} +11.3844i q^{11} +(7.64196 + 23.4730i) q^{12} +25.5766i q^{13} +(33.1865 - 3.62613i) q^{14} +(8.04288 + 24.7045i) q^{15} -3.42420 q^{16} +88.9065 q^{17} +(28.6529 + 39.3409i) q^{18} -54.2454i q^{19} +23.7538 q^{20} +(-87.7294 + 39.5544i) q^{21} +20.5211 q^{22} +25.4319i q^{23} +(113.562 - 36.9716i) q^{24} +25.0000 q^{25} +46.1034 q^{26} +(-113.646 - 82.2656i) q^{27} +(9.55687 + 87.4647i) q^{28} -231.306i q^{29} +(44.5315 - 14.4978i) q^{30} +117.898i q^{31} -177.700i q^{32} +(-56.2490 + 18.3126i) q^{33} -160.260i q^{34} +(10.0583 + 92.0534i) q^{35} +(-103.685 + 75.5163i) q^{36} +392.122 q^{37} -97.7808 q^{38} +(-126.371 + 41.1419i) q^{39} -114.920i q^{40} -478.312 q^{41} +(71.2993 + 158.138i) q^{42} -253.291 q^{43} +54.0844i q^{44} +(-109.125 + 79.4781i) q^{45} +45.8426 q^{46} -313.715 q^{47} +(-5.50809 - 16.9186i) q^{48} +(-334.907 + 74.0717i) q^{49} -45.0641i q^{50} +(143.013 + 439.278i) q^{51} +121.508i q^{52} -558.456i q^{53} +(-148.289 + 204.854i) q^{54} +56.9219i q^{55} +(423.152 - 46.2359i) q^{56} +(268.021 - 87.2578i) q^{57} -416.944 q^{58} -258.035 q^{59} +(38.2098 + 117.365i) q^{60} -457.766i q^{61} +212.519 q^{62} +(-336.554 - 369.836i) q^{63} -347.710 q^{64} +127.883i q^{65} +(33.0097 + 101.393i) q^{66} +751.160 q^{67} +422.373 q^{68} +(-125.656 + 40.9091i) q^{69} +(165.932 - 18.1307i) q^{70} -297.427i q^{71} +(365.346 + 501.626i) q^{72} -302.448i q^{73} -706.826i q^{74} +(40.2144 + 123.522i) q^{75} -257.707i q^{76} +(-209.594 + 22.9014i) q^{77} +(74.1609 + 227.792i) q^{78} -488.855 q^{79} -17.1210 q^{80} +(223.658 - 693.843i) q^{81} +862.188i q^{82} +918.367 q^{83} +(-416.781 + 187.913i) q^{84} +444.532 q^{85} +456.574i q^{86} +(1142.86 - 372.073i) q^{87} +261.659 q^{88} +61.4984 q^{89} +(143.265 + 196.705i) q^{90} +(-470.882 + 51.4511i) q^{91} +120.821i q^{92} +(-582.522 + 189.648i) q^{93} +565.491i q^{94} -271.227i q^{95} +(877.999 - 285.844i) q^{96} -175.695i q^{97} +(133.519 + 603.691i) q^{98} +(-180.962 - 248.464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.80256i 0.637303i −0.947872 0.318651i \(-0.896770\pi\)
0.947872 0.318651i \(-0.103230\pi\)
\(3\) 1.60858 + 4.94090i 0.309571 + 0.950876i
\(4\) 4.75076 0.593845
\(5\) 5.00000 0.447214
\(6\) 8.90629 2.89956i 0.605996 0.197290i
\(7\) 2.01165 + 18.4107i 0.108619 + 0.994083i
\(8\) 22.9841i 1.01576i
\(9\) −21.8250 + 15.8956i −0.808332 + 0.588727i
\(10\) 9.01282i 0.285011i
\(11\) 11.3844i 0.312047i 0.987753 + 0.156024i \(0.0498676\pi\)
−0.987753 + 0.156024i \(0.950132\pi\)
\(12\) 7.64196 + 23.4730i 0.183837 + 0.564673i
\(13\) 25.5766i 0.545666i 0.962061 + 0.272833i \(0.0879607\pi\)
−0.962061 + 0.272833i \(0.912039\pi\)
\(14\) 33.1865 3.62613i 0.633532 0.0692232i
\(15\) 8.04288 + 24.7045i 0.138444 + 0.425245i
\(16\) −3.42420 −0.0535031
\(17\) 88.9065 1.26841 0.634205 0.773165i \(-0.281327\pi\)
0.634205 + 0.773165i \(0.281327\pi\)
\(18\) 28.6529 + 39.3409i 0.375197 + 0.515152i
\(19\) 54.2454i 0.654986i −0.944854 0.327493i \(-0.893796\pi\)
0.944854 0.327493i \(-0.106204\pi\)
\(20\) 23.7538 0.265576
\(21\) −87.7294 + 39.5544i −0.911625 + 0.411022i
\(22\) 20.5211 0.198869
\(23\) 25.4319i 0.230561i 0.993333 + 0.115281i \(0.0367767\pi\)
−0.993333 + 0.115281i \(0.963223\pi\)
\(24\) 113.562 36.9716i 0.965864 0.314450i
\(25\) 25.0000 0.200000
\(26\) 46.1034 0.347755
\(27\) −113.646 82.2656i −0.810043 0.586371i
\(28\) 9.55687 + 87.4647i 0.0645028 + 0.590331i
\(29\) 231.306i 1.48112i −0.671991 0.740559i \(-0.734561\pi\)
0.671991 0.740559i \(-0.265439\pi\)
\(30\) 44.5315 14.4978i 0.271010 0.0882309i
\(31\) 117.898i 0.683068i 0.939869 + 0.341534i \(0.110947\pi\)
−0.939869 + 0.341534i \(0.889053\pi\)
\(32\) 177.700i 0.981664i
\(33\) −56.2490 + 18.3126i −0.296718 + 0.0966007i
\(34\) 160.260i 0.808362i
\(35\) 10.0583 + 92.0534i 0.0485759 + 0.444568i
\(36\) −103.685 + 75.5163i −0.480024 + 0.349613i
\(37\) 392.122 1.74228 0.871142 0.491031i \(-0.163380\pi\)
0.871142 + 0.491031i \(0.163380\pi\)
\(38\) −97.7808 −0.417425
\(39\) −126.371 + 41.1419i −0.518861 + 0.168922i
\(40\) 114.920i 0.454263i
\(41\) −478.312 −1.82195 −0.910973 0.412466i \(-0.864667\pi\)
−0.910973 + 0.412466i \(0.864667\pi\)
\(42\) 71.2993 + 158.138i 0.261946 + 0.580981i
\(43\) −253.291 −0.898293 −0.449146 0.893458i \(-0.648272\pi\)
−0.449146 + 0.893458i \(0.648272\pi\)
\(44\) 54.0844i 0.185308i
\(45\) −109.125 + 79.4781i −0.361497 + 0.263287i
\(46\) 45.8426 0.146937
\(47\) −313.715 −0.973617 −0.486809 0.873509i \(-0.661839\pi\)
−0.486809 + 0.873509i \(0.661839\pi\)
\(48\) −5.50809 16.9186i −0.0165630 0.0508749i
\(49\) −334.907 + 74.0717i −0.976404 + 0.215953i
\(50\) 45.0641i 0.127461i
\(51\) 143.013 + 439.278i 0.392663 + 1.20610i
\(52\) 121.508i 0.324041i
\(53\) 558.456i 1.44736i −0.690138 0.723678i \(-0.742450\pi\)
0.690138 0.723678i \(-0.257550\pi\)
\(54\) −148.289 + 204.854i −0.373696 + 0.516242i
\(55\) 56.9219i 0.139552i
\(56\) 423.152 46.2359i 1.00975 0.110331i
\(57\) 268.021 87.2578i 0.622811 0.202765i
\(58\) −416.944 −0.943921
\(59\) −258.035 −0.569377 −0.284689 0.958620i \(-0.591890\pi\)
−0.284689 + 0.958620i \(0.591890\pi\)
\(60\) 38.2098 + 117.365i 0.0822144 + 0.252530i
\(61\) 457.766i 0.960836i −0.877040 0.480418i \(-0.840485\pi\)
0.877040 0.480418i \(-0.159515\pi\)
\(62\) 212.519 0.435321
\(63\) −336.554 369.836i −0.673044 0.739602i
\(64\) −347.710 −0.679121
\(65\) 127.883i 0.244029i
\(66\) 33.0097 + 101.393i 0.0615639 + 0.189099i
\(67\) 751.160 1.36968 0.684842 0.728692i \(-0.259871\pi\)
0.684842 + 0.728692i \(0.259871\pi\)
\(68\) 422.373 0.753239
\(69\) −125.656 + 40.9091i −0.219235 + 0.0713750i
\(70\) 165.932 18.1307i 0.283324 0.0309575i
\(71\) 297.427i 0.497156i −0.968612 0.248578i \(-0.920037\pi\)
0.968612 0.248578i \(-0.0799632\pi\)
\(72\) 365.346 + 501.626i 0.598007 + 0.821073i
\(73\) 302.448i 0.484916i −0.970162 0.242458i \(-0.922046\pi\)
0.970162 0.242458i \(-0.0779536\pi\)
\(74\) 706.826i 1.11036i
\(75\) 40.2144 + 123.522i 0.0619141 + 0.190175i
\(76\) 257.707i 0.388960i
\(77\) −209.594 + 22.9014i −0.310201 + 0.0338942i
\(78\) 74.1609 + 227.792i 0.107655 + 0.330672i
\(79\) −488.855 −0.696208 −0.348104 0.937456i \(-0.613174\pi\)
−0.348104 + 0.937456i \(0.613174\pi\)
\(80\) −17.1210 −0.0239273
\(81\) 223.658 693.843i 0.306801 0.951774i
\(82\) 862.188i 1.16113i
\(83\) 918.367 1.21451 0.607253 0.794509i \(-0.292272\pi\)
0.607253 + 0.794509i \(0.292272\pi\)
\(84\) −416.781 + 187.913i −0.541364 + 0.244084i
\(85\) 444.532 0.567251
\(86\) 456.574i 0.572484i
\(87\) 1142.86 372.073i 1.40836 0.458511i
\(88\) 261.659 0.316966
\(89\) 61.4984 0.0732451 0.0366225 0.999329i \(-0.488340\pi\)
0.0366225 + 0.999329i \(0.488340\pi\)
\(90\) 143.265 + 196.705i 0.167793 + 0.230383i
\(91\) −470.882 + 51.4511i −0.542438 + 0.0592697i
\(92\) 120.821i 0.136918i
\(93\) −582.522 + 189.648i −0.649514 + 0.211458i
\(94\) 565.491i 0.620489i
\(95\) 271.227i 0.292919i
\(96\) 877.999 285.844i 0.933441 0.303895i
\(97\) 175.695i 0.183909i −0.995763 0.0919545i \(-0.970689\pi\)
0.995763 0.0919545i \(-0.0293114\pi\)
\(98\) 133.519 + 603.691i 0.137627 + 0.622265i
\(99\) −180.962 248.464i −0.183711 0.252238i
\(100\) 118.769 0.118769
\(101\) −218.123 −0.214891 −0.107446 0.994211i \(-0.534267\pi\)
−0.107446 + 0.994211i \(0.534267\pi\)
\(102\) 791.827 257.790i 0.768652 0.250245i
\(103\) 344.306i 0.329374i 0.986346 + 0.164687i \(0.0526614\pi\)
−0.986346 + 0.164687i \(0.947339\pi\)
\(104\) 587.854 0.554267
\(105\) −438.647 + 197.772i −0.407691 + 0.183815i
\(106\) −1006.65 −0.922404
\(107\) 1799.20i 1.62557i 0.582566 + 0.812783i \(0.302049\pi\)
−0.582566 + 0.812783i \(0.697951\pi\)
\(108\) −539.904 390.824i −0.481040 0.348214i
\(109\) −759.911 −0.667764 −0.333882 0.942615i \(-0.608359\pi\)
−0.333882 + 0.942615i \(0.608359\pi\)
\(110\) 102.605 0.0889367
\(111\) 630.759 + 1937.44i 0.539360 + 1.65670i
\(112\) −6.88830 63.0419i −0.00581145 0.0531866i
\(113\) 1030.58i 0.857957i 0.903315 + 0.428978i \(0.141126\pi\)
−0.903315 + 0.428978i \(0.858874\pi\)
\(114\) −157.288 483.125i −0.129222 0.396919i
\(115\) 127.159i 0.103110i
\(116\) 1098.88i 0.879555i
\(117\) −406.556 558.208i −0.321249 0.441080i
\(118\) 465.124i 0.362866i
\(119\) 178.849 + 1636.83i 0.137773 + 1.26091i
\(120\) 567.810 184.858i 0.431948 0.140626i
\(121\) 1201.40 0.902627
\(122\) −825.154 −0.612344
\(123\) −769.401 2363.29i −0.564021 1.73245i
\(124\) 560.105i 0.405637i
\(125\) 125.000 0.0894427
\(126\) −666.653 + 606.660i −0.471351 + 0.428933i
\(127\) 789.585 0.551688 0.275844 0.961202i \(-0.411043\pi\)
0.275844 + 0.961202i \(0.411043\pi\)
\(128\) 794.832i 0.548859i
\(129\) −407.439 1251.49i −0.278085 0.854165i
\(130\) 230.517 0.155521
\(131\) −1156.88 −0.771583 −0.385792 0.922586i \(-0.626072\pi\)
−0.385792 + 0.922586i \(0.626072\pi\)
\(132\) −267.226 + 86.9990i −0.176205 + 0.0573658i
\(133\) 998.694 109.123i 0.651111 0.0711439i
\(134\) 1354.01i 0.872903i
\(135\) −568.229 411.328i −0.362262 0.262233i
\(136\) 2043.43i 1.28840i
\(137\) 127.823i 0.0797125i −0.999205 0.0398563i \(-0.987310\pi\)
0.999205 0.0398563i \(-0.0126900\pi\)
\(138\) 73.7413 + 226.504i 0.0454875 + 0.139719i
\(139\) 1296.63i 0.791216i −0.918420 0.395608i \(-0.870534\pi\)
0.918420 0.395608i \(-0.129466\pi\)
\(140\) 47.7844 + 437.324i 0.0288465 + 0.264004i
\(141\) −504.634 1550.03i −0.301403 0.925790i
\(142\) −536.131 −0.316839
\(143\) −291.173 −0.170274
\(144\) 74.7331 54.4298i 0.0432483 0.0314987i
\(145\) 1156.53i 0.662376i
\(146\) −545.182 −0.309038
\(147\) −904.704 1535.59i −0.507610 0.861587i
\(148\) 1862.88 1.03465
\(149\) 2573.40i 1.41491i 0.706760 + 0.707453i \(0.250156\pi\)
−0.706760 + 0.707453i \(0.749844\pi\)
\(150\) 222.657 72.4891i 0.121199 0.0394581i
\(151\) 1400.07 0.754541 0.377271 0.926103i \(-0.376863\pi\)
0.377271 + 0.926103i \(0.376863\pi\)
\(152\) −1246.78 −0.665310
\(153\) −1940.38 + 1413.22i −1.02530 + 0.746748i
\(154\) 41.2812 + 377.807i 0.0216009 + 0.197692i
\(155\) 589.490i 0.305477i
\(156\) −600.359 + 195.455i −0.308123 + 0.100314i
\(157\) 2959.00i 1.50417i 0.659068 + 0.752083i \(0.270951\pi\)
−0.659068 + 0.752083i \(0.729049\pi\)
\(158\) 881.192i 0.443695i
\(159\) 2759.28 898.320i 1.37626 0.448059i
\(160\) 888.501i 0.439014i
\(161\) −468.218 + 51.1600i −0.229197 + 0.0250433i
\(162\) −1250.70 403.158i −0.606568 0.195525i
\(163\) −3819.48 −1.83537 −0.917684 0.397312i \(-0.869943\pi\)
−0.917684 + 0.397312i \(0.869943\pi\)
\(164\) −2272.35 −1.08195
\(165\) −281.245 + 91.5632i −0.132696 + 0.0432011i
\(166\) 1655.42i 0.774008i
\(167\) 1801.35 0.834687 0.417343 0.908749i \(-0.362961\pi\)
0.417343 + 0.908749i \(0.362961\pi\)
\(168\) 909.120 + 2016.38i 0.417501 + 0.925994i
\(169\) 1542.84 0.702248
\(170\) 801.298i 0.361510i
\(171\) 862.264 + 1183.90i 0.385608 + 0.529446i
\(172\) −1203.33 −0.533446
\(173\) −1586.98 −0.697434 −0.348717 0.937228i \(-0.613383\pi\)
−0.348717 + 0.937228i \(0.613383\pi\)
\(174\) −670.686 2060.08i −0.292210 0.897552i
\(175\) 50.2913 + 460.267i 0.0217238 + 0.198817i
\(176\) 38.9824i 0.0166955i
\(177\) −415.068 1274.92i −0.176262 0.541407i
\(178\) 110.855i 0.0466793i
\(179\) 1270.55i 0.530531i −0.964175 0.265266i \(-0.914540\pi\)
0.964175 0.265266i \(-0.0854596\pi\)
\(180\) −518.426 + 377.582i −0.214673 + 0.156352i
\(181\) 1213.15i 0.498193i −0.968479 0.249097i \(-0.919866\pi\)
0.968479 0.249097i \(-0.0801336\pi\)
\(182\) 92.7440 + 848.796i 0.0377728 + 0.345697i
\(183\) 2261.78 736.352i 0.913636 0.297447i
\(184\) 584.528 0.234195
\(185\) 1960.61 0.779173
\(186\) 341.853 + 1050.03i 0.134763 + 0.413937i
\(187\) 1012.14i 0.395804i
\(188\) −1490.38 −0.578178
\(189\) 1285.95 2257.79i 0.494916 0.868941i
\(190\) −488.904 −0.186678
\(191\) 2654.34i 1.00555i 0.864416 + 0.502777i \(0.167688\pi\)
−0.864416 + 0.502777i \(0.832312\pi\)
\(192\) −559.318 1718.00i −0.210236 0.645760i
\(193\) −841.332 −0.313784 −0.156892 0.987616i \(-0.550148\pi\)
−0.156892 + 0.987616i \(0.550148\pi\)
\(194\) −316.703 −0.117206
\(195\) −631.856 + 205.709i −0.232042 + 0.0755444i
\(196\) −1591.06 + 351.897i −0.579833 + 0.128242i
\(197\) 1201.46i 0.434522i −0.976114 0.217261i \(-0.930288\pi\)
0.976114 0.217261i \(-0.0697122\pi\)
\(198\) −447.872 + 326.195i −0.160752 + 0.117079i
\(199\) 4524.30i 1.61165i 0.592151 + 0.805827i \(0.298279\pi\)
−0.592151 + 0.805827i \(0.701721\pi\)
\(200\) 574.602i 0.203152i
\(201\) 1208.30 + 3711.40i 0.424014 + 1.30240i
\(202\) 393.180i 0.136951i
\(203\) 4258.50 465.307i 1.47236 0.160878i
\(204\) 679.420 + 2086.90i 0.233181 + 0.716238i
\(205\) −2391.56 −0.814799
\(206\) 620.635 0.209911
\(207\) −404.255 555.049i −0.135738 0.186370i
\(208\) 87.5793i 0.0291949i
\(209\) 617.550 0.204387
\(210\) 356.497 + 790.690i 0.117146 + 0.259823i
\(211\) 2948.59 0.962033 0.481017 0.876711i \(-0.340268\pi\)
0.481017 + 0.876711i \(0.340268\pi\)
\(212\) 2653.09i 0.859505i
\(213\) 1469.56 478.434i 0.472734 0.153905i
\(214\) 3243.18 1.03598
\(215\) −1266.46 −0.401729
\(216\) −1890.80 + 2612.04i −0.595614 + 0.822810i
\(217\) −2170.58 + 237.170i −0.679027 + 0.0741942i
\(218\) 1369.79i 0.425568i
\(219\) 1494.36 486.511i 0.461095 0.150116i
\(220\) 270.422i 0.0828721i
\(221\) 2273.92i 0.692129i
\(222\) 3492.36 1136.98i 1.05582 0.343736i
\(223\) 554.664i 0.166561i −0.996526 0.0832804i \(-0.973460\pi\)
0.996526 0.0832804i \(-0.0265397\pi\)
\(224\) 3271.58 357.471i 0.975856 0.106627i
\(225\) −545.624 + 397.391i −0.161666 + 0.117745i
\(226\) 1857.69 0.546778
\(227\) 5416.25 1.58365 0.791826 0.610746i \(-0.209130\pi\)
0.791826 + 0.610746i \(0.209130\pi\)
\(228\) 1273.30 414.541i 0.369853 0.120411i
\(229\) 681.437i 0.196640i 0.995155 + 0.0983201i \(0.0313469\pi\)
−0.995155 + 0.0983201i \(0.968653\pi\)
\(230\) 229.213 0.0657124
\(231\) −450.302 998.745i −0.128258 0.284470i
\(232\) −5316.35 −1.50446
\(233\) 4345.48i 1.22181i −0.791704 0.610905i \(-0.790806\pi\)
0.791704 0.610905i \(-0.209194\pi\)
\(234\) −1006.21 + 732.843i −0.281101 + 0.204733i
\(235\) −1568.57 −0.435415
\(236\) −1225.86 −0.338122
\(237\) −786.360 2415.38i −0.215526 0.662008i
\(238\) 2950.49 322.387i 0.803579 0.0878034i
\(239\) 1368.95i 0.370502i 0.982691 + 0.185251i \(0.0593099\pi\)
−0.982691 + 0.185251i \(0.940690\pi\)
\(240\) −27.5404 84.5932i −0.00740720 0.0227519i
\(241\) 4526.16i 1.20978i −0.796311 0.604888i \(-0.793218\pi\)
0.796311 0.604888i \(-0.206782\pi\)
\(242\) 2165.59i 0.575247i
\(243\) 3787.98 11.0286i 0.999996 0.00291146i
\(244\) 2174.74i 0.570588i
\(245\) −1674.53 + 370.359i −0.436661 + 0.0965769i
\(246\) −4259.99 + 1386.90i −1.10409 + 0.359452i
\(247\) 1387.41 0.357404
\(248\) 2709.78 0.693835
\(249\) 1477.26 + 4537.56i 0.375975 + 1.15484i
\(250\) 225.321i 0.0570021i
\(251\) 6278.33 1.57882 0.789411 0.613865i \(-0.210386\pi\)
0.789411 + 0.613865i \(0.210386\pi\)
\(252\) −1598.89 1757.00i −0.399684 0.439209i
\(253\) −289.526 −0.0719460
\(254\) 1423.28i 0.351592i
\(255\) 715.064 + 2196.39i 0.175604 + 0.539385i
\(256\) −4214.42 −1.02891
\(257\) −7065.00 −1.71480 −0.857398 0.514655i \(-0.827920\pi\)
−0.857398 + 0.514655i \(0.827920\pi\)
\(258\) −2255.89 + 734.435i −0.544362 + 0.177224i
\(259\) 788.813 + 7219.24i 0.189245 + 1.73198i
\(260\) 607.541i 0.144916i
\(261\) 3676.75 + 5048.24i 0.871974 + 1.19724i
\(262\) 2085.36i 0.491732i
\(263\) 4457.41i 1.04508i 0.852616 + 0.522539i \(0.175015\pi\)
−0.852616 + 0.522539i \(0.824985\pi\)
\(264\) 420.899 + 1292.83i 0.0981233 + 0.301395i
\(265\) 2792.28i 0.647277i
\(266\) −196.701 1800.21i −0.0453402 0.414955i
\(267\) 98.9248 + 303.857i 0.0226745 + 0.0696470i
\(268\) 3568.58 0.813380
\(269\) −4733.36 −1.07286 −0.536428 0.843946i \(-0.680227\pi\)
−0.536428 + 0.843946i \(0.680227\pi\)
\(270\) −741.445 + 1024.27i −0.167122 + 0.230871i
\(271\) 5052.32i 1.13250i −0.824234 0.566249i \(-0.808394\pi\)
0.824234 0.566249i \(-0.191606\pi\)
\(272\) −304.434 −0.0678640
\(273\) −1011.66 2243.82i −0.224281 0.497443i
\(274\) −230.408 −0.0508010
\(275\) 284.609i 0.0624094i
\(276\) −596.963 + 194.349i −0.130192 + 0.0423857i
\(277\) −7257.22 −1.57417 −0.787084 0.616846i \(-0.788410\pi\)
−0.787084 + 0.616846i \(0.788410\pi\)
\(278\) −2337.26 −0.504244
\(279\) −1874.06 2573.12i −0.402141 0.552146i
\(280\) 2115.76 231.180i 0.451575 0.0493415i
\(281\) 599.316i 0.127232i −0.997974 0.0636160i \(-0.979737\pi\)
0.997974 0.0636160i \(-0.0202633\pi\)
\(282\) −2794.03 + 909.636i −0.590008 + 0.192085i
\(283\) 4328.08i 0.909108i −0.890719 0.454554i \(-0.849799\pi\)
0.890719 0.454554i \(-0.150201\pi\)
\(284\) 1413.00i 0.295234i
\(285\) 1340.10 436.289i 0.278530 0.0906791i
\(286\) 524.859i 0.108516i
\(287\) −962.197 8806.05i −0.197898 1.81117i
\(288\) 2824.66 + 3878.30i 0.577932 + 0.793511i
\(289\) 2991.36 0.608866
\(290\) −2084.72 −0.422134
\(291\) 868.094 282.620i 0.174875 0.0569328i
\(292\) 1436.86i 0.287965i
\(293\) −2719.51 −0.542236 −0.271118 0.962546i \(-0.587393\pi\)
−0.271118 + 0.962546i \(0.587393\pi\)
\(294\) −2768.00 + 1630.79i −0.549092 + 0.323502i
\(295\) −1290.17 −0.254633
\(296\) 9012.57i 1.76975i
\(297\) 936.542 1293.79i 0.182975 0.252771i
\(298\) 4638.72 0.901724
\(299\) −650.460 −0.125810
\(300\) 191.049 + 586.826i 0.0367674 + 0.112935i
\(301\) −509.534 4663.27i −0.0975716 0.892978i
\(302\) 2523.71i 0.480871i
\(303\) −350.867 1077.72i −0.0665241 0.204335i
\(304\) 185.747i 0.0350438i
\(305\) 2288.83i 0.429699i
\(306\) 2547.43 + 3497.66i 0.475905 + 0.653425i
\(307\) 7761.41i 1.44289i 0.692472 + 0.721444i \(0.256521\pi\)
−0.692472 + 0.721444i \(0.743479\pi\)
\(308\) −995.731 + 108.799i −0.184211 + 0.0201279i
\(309\) −1701.18 + 553.843i −0.313194 + 0.101965i
\(310\) 1062.59 0.194682
\(311\) −4886.92 −0.891034 −0.445517 0.895273i \(-0.646980\pi\)
−0.445517 + 0.895273i \(0.646980\pi\)
\(312\) 945.608 + 2904.53i 0.171585 + 0.527040i
\(313\) 6512.69i 1.17610i 0.808825 + 0.588050i \(0.200104\pi\)
−0.808825 + 0.588050i \(0.799896\pi\)
\(314\) 5333.79 0.958610
\(315\) −1682.77 1849.18i −0.300994 0.330760i
\(316\) −2322.43 −0.413440
\(317\) 4297.71i 0.761462i 0.924686 + 0.380731i \(0.124328\pi\)
−0.924686 + 0.380731i \(0.875672\pi\)
\(318\) −1619.28 4973.77i −0.285549 0.877092i
\(319\) 2633.27 0.462179
\(320\) −1738.55 −0.303712
\(321\) −8889.68 + 2894.16i −1.54571 + 0.503228i
\(322\) 92.2193 + 843.993i 0.0159602 + 0.146068i
\(323\) 4822.76i 0.830792i
\(324\) 1062.55 3296.28i 0.182192 0.565206i
\(325\) 639.414i 0.109133i
\(326\) 6884.86i 1.16969i
\(327\) −1222.37 3754.64i −0.206720 0.634961i
\(328\) 10993.6i 1.85066i
\(329\) −631.085 5775.70i −0.105753 0.967857i
\(330\) 165.049 + 506.963i 0.0275322 + 0.0845678i
\(331\) 3047.66 0.506086 0.253043 0.967455i \(-0.418569\pi\)
0.253043 + 0.967455i \(0.418569\pi\)
\(332\) 4362.94 0.721228
\(333\) −8558.06 + 6233.03i −1.40834 + 1.02573i
\(334\) 3247.05i 0.531948i
\(335\) 3755.80 0.612541
\(336\) 300.403 135.442i 0.0487748 0.0219910i
\(337\) 3571.60 0.577322 0.288661 0.957431i \(-0.406790\pi\)
0.288661 + 0.957431i \(0.406790\pi\)
\(338\) 2781.07i 0.447545i
\(339\) −5092.01 + 1657.77i −0.815811 + 0.265598i
\(340\) 2111.87 0.336859
\(341\) −1342.20 −0.213149
\(342\) 2134.06 1554.29i 0.337418 0.245749i
\(343\) −2037.43 6016.85i −0.320731 0.947170i
\(344\) 5821.67i 0.912451i
\(345\) −628.281 + 204.545i −0.0980450 + 0.0319199i
\(346\) 2860.64i 0.444477i
\(347\) 11138.9i 1.72325i 0.507543 + 0.861626i \(0.330554\pi\)
−0.507543 + 0.861626i \(0.669446\pi\)
\(348\) 5429.45 1767.63i 0.836348 0.272284i
\(349\) 10991.7i 1.68587i −0.538013 0.842937i \(-0.680825\pi\)
0.538013 0.842937i \(-0.319175\pi\)
\(350\) 829.661 90.6533i 0.126706 0.0138446i
\(351\) 2104.07 2906.67i 0.319963 0.442013i
\(352\) 2023.01 0.306326
\(353\) −10085.8 −1.52072 −0.760359 0.649503i \(-0.774977\pi\)
−0.760359 + 0.649503i \(0.774977\pi\)
\(354\) −2298.13 + 748.188i −0.345040 + 0.112333i
\(355\) 1487.13i 0.222335i
\(356\) 292.164 0.0434962
\(357\) −7799.71 + 3516.64i −1.15632 + 0.521345i
\(358\) −2290.24 −0.338109
\(359\) 640.876i 0.0942176i 0.998890 + 0.0471088i \(0.0150007\pi\)
−0.998890 + 0.0471088i \(0.984999\pi\)
\(360\) 1826.73 + 2508.13i 0.267437 + 0.367195i
\(361\) 3916.44 0.570993
\(362\) −2186.79 −0.317500
\(363\) 1932.54 + 5935.98i 0.279427 + 0.858286i
\(364\) −2237.05 + 244.432i −0.322124 + 0.0351970i
\(365\) 1512.24i 0.216861i
\(366\) −1327.32 4077.00i −0.189564 0.582263i
\(367\) 4440.20i 0.631544i −0.948835 0.315772i \(-0.897737\pi\)
0.948835 0.315772i \(-0.102263\pi\)
\(368\) 87.0838i 0.0123358i
\(369\) 10439.1 7603.07i 1.47274 1.07263i
\(370\) 3534.13i 0.496569i
\(371\) 10281.6 1123.42i 1.43879 0.157210i
\(372\) −2767.42 + 900.973i −0.385710 + 0.125573i
\(373\) −3346.57 −0.464554 −0.232277 0.972650i \(-0.574618\pi\)
−0.232277 + 0.972650i \(0.574618\pi\)
\(374\) 1824.46 0.252247
\(375\) 201.072 + 617.612i 0.0276888 + 0.0850490i
\(376\) 7210.44i 0.988963i
\(377\) 5916.01 0.808197
\(378\) −4069.81 2318.01i −0.553779 0.315411i
\(379\) −5731.50 −0.776800 −0.388400 0.921491i \(-0.626972\pi\)
−0.388400 + 0.921491i \(0.626972\pi\)
\(380\) 1288.53i 0.173948i
\(381\) 1270.11 + 3901.26i 0.170786 + 0.524587i
\(382\) 4784.61 0.640843
\(383\) −2978.01 −0.397309 −0.198654 0.980070i \(-0.563657\pi\)
−0.198654 + 0.980070i \(0.563657\pi\)
\(384\) 3927.19 1278.55i 0.521897 0.169911i
\(385\) −1047.97 + 114.507i −0.138726 + 0.0151580i
\(386\) 1516.56i 0.199976i
\(387\) 5528.08 4026.23i 0.726119 0.528849i
\(388\) 834.687i 0.109213i
\(389\) 8663.36i 1.12918i 0.825373 + 0.564588i \(0.190965\pi\)
−0.825373 + 0.564588i \(0.809035\pi\)
\(390\) 370.804 + 1138.96i 0.0481447 + 0.147881i
\(391\) 2261.06i 0.292446i
\(392\) 1702.47 + 7697.52i 0.219356 + 0.991794i
\(393\) −1860.94 5716.05i −0.238860 0.733680i
\(394\) −2165.72 −0.276922
\(395\) −2444.27 −0.311354
\(396\) −859.706 1180.39i −0.109096 0.149790i
\(397\) 4560.17i 0.576494i 0.957556 + 0.288247i \(0.0930724\pi\)
−0.957556 + 0.288247i \(0.906928\pi\)
\(398\) 8155.34 1.02711
\(399\) 2145.64 + 4758.92i 0.269214 + 0.597102i
\(400\) −85.6050 −0.0107006
\(401\) 4033.10i 0.502253i −0.967954 0.251127i \(-0.919199\pi\)
0.967954 0.251127i \(-0.0808011\pi\)
\(402\) 6690.05 2178.04i 0.830023 0.270225i
\(403\) −3015.43 −0.372727
\(404\) −1036.25 −0.127612
\(405\) 1118.29 3469.22i 0.137206 0.425646i
\(406\) −838.746 7676.22i −0.102528 0.938336i
\(407\) 4464.07i 0.543675i
\(408\) 10096.4 3287.02i 1.22511 0.398852i
\(409\) 1829.12i 0.221135i 0.993869 + 0.110568i \(0.0352669\pi\)
−0.993869 + 0.110568i \(0.964733\pi\)
\(410\) 4310.94i 0.519274i
\(411\) 631.558 205.612i 0.0757968 0.0246767i
\(412\) 1635.72i 0.195597i
\(413\) −519.076 4750.59i −0.0618451 0.566008i
\(414\) −1000.51 + 728.697i −0.118774 + 0.0865060i
\(415\) 4591.84 0.543143
\(416\) 4544.96 0.535661
\(417\) 6406.53 2085.73i 0.752348 0.244937i
\(418\) 1113.17i 0.130256i
\(419\) 4125.47 0.481008 0.240504 0.970648i \(-0.422687\pi\)
0.240504 + 0.970648i \(0.422687\pi\)
\(420\) −2083.91 + 939.566i −0.242105 + 0.109157i
\(421\) 4892.88 0.566424 0.283212 0.959057i \(-0.408600\pi\)
0.283212 + 0.959057i \(0.408600\pi\)
\(422\) 5315.02i 0.613107i
\(423\) 6846.81 4986.69i 0.787006 0.573195i
\(424\) −12835.6 −1.47017
\(425\) 2222.66 0.253682
\(426\) −862.408 2648.97i −0.0980841 0.301275i
\(427\) 8427.79 920.866i 0.955151 0.104365i
\(428\) 8547.59i 0.965334i
\(429\) −468.375 1438.66i −0.0527117 0.161909i
\(430\) 2282.87i 0.256023i
\(431\) 3994.63i 0.446437i −0.974768 0.223219i \(-0.928344\pi\)
0.974768 0.223219i \(-0.0716564\pi\)
\(432\) 389.146 + 281.694i 0.0433398 + 0.0313727i
\(433\) 13895.6i 1.54221i 0.636705 + 0.771107i \(0.280297\pi\)
−0.636705 + 0.771107i \(0.719703\pi\)
\(434\) 427.514 + 3912.62i 0.0472842 + 0.432746i
\(435\) 5714.30 1860.37i 0.629838 0.205052i
\(436\) −3610.15 −0.396548
\(437\) 1379.56 0.151014
\(438\) −876.967 2693.69i −0.0956692 0.293857i
\(439\) 4224.83i 0.459317i 0.973271 + 0.229658i \(0.0737609\pi\)
−0.973271 + 0.229658i \(0.926239\pi\)
\(440\) 1308.30 0.141751
\(441\) 6131.91 6940.16i 0.662121 0.749397i
\(442\) 4098.89 0.441096
\(443\) 14223.7i 1.52548i 0.646706 + 0.762739i \(0.276146\pi\)
−0.646706 + 0.762739i \(0.723854\pi\)
\(444\) 2996.58 + 9204.30i 0.320296 + 0.983821i
\(445\) 307.492 0.0327562
\(446\) −999.818 −0.106150
\(447\) −12714.9 + 4139.51i −1.34540 + 0.438013i
\(448\) −699.471 6401.57i −0.0737654 0.675103i
\(449\) 16223.9i 1.70524i −0.522531 0.852620i \(-0.675012\pi\)
0.522531 0.852620i \(-0.324988\pi\)
\(450\) 716.323 + 983.523i 0.0750395 + 0.103030i
\(451\) 5445.28i 0.568533i
\(452\) 4896.05i 0.509493i
\(453\) 2252.11 + 6917.58i 0.233584 + 0.717476i
\(454\) 9763.14i 1.00927i
\(455\) −2354.41 + 257.256i −0.242586 + 0.0265062i
\(456\) −2005.54 6160.21i −0.205961 0.632628i
\(457\) 4257.18 0.435761 0.217880 0.975975i \(-0.430086\pi\)
0.217880 + 0.975975i \(0.430086\pi\)
\(458\) 1228.33 0.125319
\(459\) −10103.8 7313.94i −1.02747 0.743760i
\(460\) 604.103i 0.0612314i
\(461\) −4912.62 −0.496320 −0.248160 0.968719i \(-0.579826\pi\)
−0.248160 + 0.968719i \(0.579826\pi\)
\(462\) −1800.30 + 811.698i −0.181294 + 0.0817394i
\(463\) −15697.6 −1.57566 −0.787830 0.615893i \(-0.788795\pi\)
−0.787830 + 0.615893i \(0.788795\pi\)
\(464\) 792.038i 0.0792445i
\(465\) −2912.61 + 948.240i −0.290471 + 0.0945669i
\(466\) −7833.01 −0.778663
\(467\) −1451.66 −0.143844 −0.0719219 0.997410i \(-0.522913\pi\)
−0.0719219 + 0.997410i \(0.522913\pi\)
\(468\) −1931.45 2651.91i −0.190772 0.261933i
\(469\) 1511.07 + 13829.4i 0.148774 + 1.36158i
\(470\) 2827.46i 0.277491i
\(471\) −14620.1 + 4759.78i −1.43028 + 0.465646i
\(472\) 5930.69i 0.578352i
\(473\) 2883.56i 0.280310i
\(474\) −4353.88 + 1417.47i −0.421900 + 0.137355i
\(475\) 1356.13i 0.130997i
\(476\) 849.668 + 7776.18i 0.0818161 + 0.748783i
\(477\) 8877.01 + 12188.3i 0.852098 + 1.16994i
\(478\) 2467.62 0.236122
\(479\) −12161.8 −1.16009 −0.580047 0.814583i \(-0.696966\pi\)
−0.580047 + 0.814583i \(0.696966\pi\)
\(480\) 4389.99 1429.22i 0.417448 0.135906i
\(481\) 10029.1i 0.950706i
\(482\) −8158.70 −0.770993
\(483\) −1005.94 2231.12i −0.0947658 0.210185i
\(484\) 5707.54 0.536020
\(485\) 878.477i 0.0822466i
\(486\) −19.8797 6828.08i −0.00185548 0.637300i
\(487\) −699.290 −0.0650675 −0.0325337 0.999471i \(-0.510358\pi\)
−0.0325337 + 0.999471i \(0.510358\pi\)
\(488\) −10521.3 −0.975981
\(489\) −6143.93 18871.7i −0.568176 1.74521i
\(490\) 667.596 + 3018.45i 0.0615488 + 0.278285i
\(491\) 15982.5i 1.46900i 0.678607 + 0.734501i \(0.262584\pi\)
−0.678607 + 0.734501i \(0.737416\pi\)
\(492\) −3655.24 11227.4i −0.334941 1.02880i
\(493\) 20564.6i 1.87867i
\(494\) 2500.90i 0.227775i
\(495\) −904.809 1242.32i −0.0821579 0.112804i
\(496\) 403.707i 0.0365463i
\(497\) 5475.83 598.319i 0.494215 0.0540006i
\(498\) 8179.25 2662.87i 0.735986 0.239610i
\(499\) −20926.5 −1.87735 −0.938675 0.344804i \(-0.887946\pi\)
−0.938675 + 0.344804i \(0.887946\pi\)
\(500\) 593.845 0.0531151
\(501\) 2897.61 + 8900.29i 0.258395 + 0.793684i
\(502\) 11317.1i 1.00619i
\(503\) −8664.19 −0.768026 −0.384013 0.923328i \(-0.625458\pi\)
−0.384013 + 0.923328i \(0.625458\pi\)
\(504\) −8500.34 + 7735.37i −0.751260 + 0.683653i
\(505\) −1090.61 −0.0961023
\(506\) 521.889i 0.0458514i
\(507\) 2481.78 + 7623.01i 0.217395 + 0.667751i
\(508\) 3751.13 0.327617
\(509\) 532.494 0.0463701 0.0231850 0.999731i \(-0.492619\pi\)
0.0231850 + 0.999731i \(0.492619\pi\)
\(510\) 3959.13 1288.95i 0.343752 0.111913i
\(511\) 5568.27 608.420i 0.482047 0.0526710i
\(512\) 1238.10i 0.106869i
\(513\) −4462.53 + 6164.76i −0.384065 + 0.530567i
\(514\) 12735.1i 1.09284i
\(515\) 1721.53i 0.147301i
\(516\) −1935.64 5945.52i −0.165139 0.507242i
\(517\) 3571.45i 0.303814i
\(518\) 13013.1 1421.89i 1.10379 0.120606i
\(519\) −2552.79 7841.13i −0.215905 0.663174i
\(520\) 2939.27 0.247876
\(521\) 3128.28 0.263056 0.131528 0.991312i \(-0.458012\pi\)
0.131528 + 0.991312i \(0.458012\pi\)
\(522\) 9099.79 6627.59i 0.763002 0.555712i
\(523\) 11087.0i 0.926961i −0.886107 0.463480i \(-0.846600\pi\)
0.886107 0.463480i \(-0.153400\pi\)
\(524\) −5496.08 −0.458201
\(525\) −2193.24 + 988.859i −0.182325 + 0.0822045i
\(526\) 8034.76 0.666031
\(527\) 10481.9i 0.866411i
\(528\) 192.608 62.7062i 0.0158754 0.00516844i
\(529\) 11520.2 0.946841
\(530\) −5033.27 −0.412512
\(531\) 5631.60 4101.62i 0.460246 0.335208i
\(532\) 4744.56 518.416i 0.386659 0.0422485i
\(533\) 12233.6i 0.994175i
\(534\) 547.722 178.318i 0.0443863 0.0144505i
\(535\) 8996.02i 0.726975i
\(536\) 17264.7i 1.39127i
\(537\) 6277.64 2043.77i 0.504470 0.164237i
\(538\) 8532.19i 0.683734i
\(539\) −843.260 3812.70i −0.0673874 0.304684i
\(540\) −2699.52 1954.12i −0.215127 0.155726i
\(541\) −14971.8 −1.18981 −0.594907 0.803795i \(-0.702811\pi\)
−0.594907 + 0.803795i \(0.702811\pi\)
\(542\) −9107.14 −0.721744
\(543\) 5994.07 1951.45i 0.473720 0.154226i
\(544\) 15798.7i 1.24515i
\(545\) −3799.55 −0.298633
\(546\) −4044.63 + 1823.59i −0.317022 + 0.142935i
\(547\) 18296.5 1.43017 0.715085 0.699037i \(-0.246388\pi\)
0.715085 + 0.699037i \(0.246388\pi\)
\(548\) 607.254i 0.0473369i
\(549\) 7276.49 + 9990.74i 0.565670 + 0.776674i
\(550\) 513.027 0.0397737
\(551\) −12547.3 −0.970112
\(552\) 940.258 + 2888.09i 0.0725000 + 0.222691i
\(553\) −983.405 9000.15i −0.0756214 0.692089i
\(554\) 13081.6i 1.00322i
\(555\) 3153.79 + 9687.18i 0.241209 + 0.740897i
\(556\) 6159.99i 0.469859i
\(557\) 20277.9i 1.54255i −0.636500 0.771277i \(-0.719618\pi\)
0.636500 0.771277i \(-0.280382\pi\)
\(558\) −4638.22 + 3378.12i −0.351884 + 0.256285i
\(559\) 6478.33i 0.490168i
\(560\) −34.4415 315.209i −0.00259896 0.0237858i
\(561\) −5000.90 + 1628.11i −0.376361 + 0.122529i
\(562\) −1080.31 −0.0810853
\(563\) 11663.5 0.873107 0.436554 0.899678i \(-0.356199\pi\)
0.436554 + 0.899678i \(0.356199\pi\)
\(564\) −2397.40 7363.83i −0.178987 0.549775i
\(565\) 5152.92i 0.383690i
\(566\) −7801.65 −0.579377
\(567\) 13224.0 + 2721.93i 0.979467 + 0.201605i
\(568\) −6836.08 −0.504992
\(569\) 4152.37i 0.305934i −0.988231 0.152967i \(-0.951117\pi\)
0.988231 0.152967i \(-0.0488828\pi\)
\(570\) −786.440 2415.63i −0.0577900 0.177508i
\(571\) −4908.94 −0.359777 −0.179889 0.983687i \(-0.557574\pi\)
−0.179889 + 0.983687i \(0.557574\pi\)
\(572\) −1383.29 −0.101116
\(573\) −13114.8 + 4269.70i −0.956158 + 0.311290i
\(574\) −15873.5 + 1734.42i −1.15426 + 0.126121i
\(575\) 635.797i 0.0461123i
\(576\) 7588.75 5527.07i 0.548955 0.399817i
\(577\) 19077.9i 1.37647i −0.725488 0.688235i \(-0.758386\pi\)
0.725488 0.688235i \(-0.241614\pi\)
\(578\) 5392.12i 0.388032i
\(579\) −1353.35 4156.94i −0.0971385 0.298370i
\(580\) 5494.40i 0.393349i
\(581\) 1847.43 + 16907.8i 0.131918 + 1.20732i
\(582\) −509.440 1564.80i −0.0362835 0.111448i
\(583\) 6357.68 0.451643
\(584\) −6951.48 −0.492559
\(585\) −2032.78 2791.04i −0.143667 0.197257i
\(586\) 4902.09i 0.345569i
\(587\) 13746.4 0.966570 0.483285 0.875463i \(-0.339444\pi\)
0.483285 + 0.875463i \(0.339444\pi\)
\(588\) −4298.03 7295.22i −0.301442 0.511649i
\(589\) 6395.42 0.447400
\(590\) 2325.62i 0.162278i
\(591\) 5936.31 1932.65i 0.413176 0.134515i
\(592\) −1342.71 −0.0932177
\(593\) 22547.2 1.56139 0.780693 0.624914i \(-0.214866\pi\)
0.780693 + 0.624914i \(0.214866\pi\)
\(594\) −2332.13 1688.18i −0.161092 0.116611i
\(595\) 894.244 + 8184.14i 0.0616142 + 0.563894i
\(596\) 12225.6i 0.840235i
\(597\) −22354.1 + 7277.68i −1.53248 + 0.498921i
\(598\) 1172.50i 0.0801788i
\(599\) 879.555i 0.0599961i 0.999550 + 0.0299980i \(0.00955010\pi\)
−0.999550 + 0.0299980i \(0.990450\pi\)
\(600\) 2839.05 924.291i 0.193173 0.0628900i
\(601\) 28491.1i 1.93374i 0.255270 + 0.966870i \(0.417836\pi\)
−0.255270 + 0.966870i \(0.582164\pi\)
\(602\) −8405.84 + 918.468i −0.569097 + 0.0621827i
\(603\) −16394.0 + 11940.2i −1.10716 + 0.806370i
\(604\) 6651.38 0.448081
\(605\) 6006.98 0.403667
\(606\) −1942.66 + 632.461i −0.130223 + 0.0423960i
\(607\) 1139.02i 0.0761636i −0.999275 0.0380818i \(-0.987875\pi\)
0.999275 0.0380818i \(-0.0121247\pi\)
\(608\) −9639.41 −0.642977
\(609\) 9149.16 + 20292.3i 0.608773 + 1.35023i
\(610\) −4125.77 −0.273848
\(611\) 8023.75i 0.531270i
\(612\) −9218.28 + 6713.89i −0.608868 + 0.443452i
\(613\) 25123.6 1.65535 0.827676 0.561206i \(-0.189663\pi\)
0.827676 + 0.561206i \(0.189663\pi\)
\(614\) 13990.4 0.919557
\(615\) −3847.01 11816.5i −0.252238 0.774773i
\(616\) 526.367 + 4817.33i 0.0344285 + 0.315090i
\(617\) 22839.2i 1.49023i −0.666937 0.745114i \(-0.732395\pi\)
0.666937 0.745114i \(-0.267605\pi\)
\(618\) 998.338 + 3066.49i 0.0649823 + 0.199599i
\(619\) 16035.4i 1.04122i 0.853795 + 0.520610i \(0.174295\pi\)
−0.853795 + 0.520610i \(0.825705\pi\)
\(620\) 2800.53i 0.181406i
\(621\) 2092.17 2890.22i 0.135194 0.186764i
\(622\) 8808.99i 0.567859i
\(623\) 123.713 + 1132.23i 0.00795580 + 0.0728117i
\(624\) 432.721 140.878i 0.0277607 0.00903788i
\(625\) 625.000 0.0400000
\(626\) 11739.6 0.749532
\(627\) 993.376 + 3051.25i 0.0632721 + 0.194346i
\(628\) 14057.5i 0.893242i
\(629\) 34862.2 2.20993
\(630\) −3333.27 + 3033.30i −0.210794 + 0.191825i
\(631\) 10777.3 0.679932 0.339966 0.940438i \(-0.389584\pi\)
0.339966 + 0.940438i \(0.389584\pi\)
\(632\) 11235.9i 0.707182i
\(633\) 4743.03 + 14568.7i 0.297817 + 0.914775i
\(634\) 7746.91 0.485282
\(635\) 3947.93 0.246722
\(636\) 13108.7 4267.70i 0.817283 0.266078i
\(637\) −1894.50 8565.76i −0.117838 0.532791i
\(638\) 4746.65i 0.294548i
\(639\) 4727.79 + 6491.33i 0.292689 + 0.401867i
\(640\) 3974.16i 0.245457i
\(641\) 16244.6i 1.00097i −0.865745 0.500485i \(-0.833155\pi\)
0.865745 0.500485i \(-0.166845\pi\)
\(642\) 5216.91 + 16024.2i 0.320709 + 0.985087i
\(643\) 15497.6i 0.950490i 0.879854 + 0.475245i \(0.157641\pi\)
−0.879854 + 0.475245i \(0.842359\pi\)
\(644\) −2224.39 + 243.049i −0.136108 + 0.0148719i
\(645\) −2037.19 6257.44i −0.124363 0.381994i
\(646\) −8693.35 −0.529466
\(647\) −19665.2 −1.19493 −0.597464 0.801896i \(-0.703825\pi\)
−0.597464 + 0.801896i \(0.703825\pi\)
\(648\) −15947.3 5140.57i −0.966776 0.311637i
\(649\) 2937.56i 0.177672i
\(650\) 1152.59 0.0695510
\(651\) −4663.38 10343.1i −0.280756 0.622702i
\(652\) −18145.4 −1.08992
\(653\) 22325.5i 1.33792i 0.743298 + 0.668961i \(0.233261\pi\)
−0.743298 + 0.668961i \(0.766739\pi\)
\(654\) −6767.99 + 2203.41i −0.404662 + 0.131743i
\(655\) −5784.42 −0.345063
\(656\) 1637.84 0.0974798
\(657\) 4807.60 + 6600.91i 0.285483 + 0.391973i
\(658\) −10411.1 + 1137.57i −0.616818 + 0.0673969i
\(659\) 14557.3i 0.860505i −0.902709 0.430253i \(-0.858424\pi\)
0.902709 0.430253i \(-0.141576\pi\)
\(660\) −1336.13 + 434.995i −0.0788011 + 0.0256548i
\(661\) 3927.35i 0.231098i 0.993302 + 0.115549i \(0.0368628\pi\)
−0.993302 + 0.115549i \(0.963137\pi\)
\(662\) 5493.60i 0.322530i
\(663\) −11235.2 + 3657.78i −0.658129 + 0.214263i
\(664\) 21107.8i 1.23365i
\(665\) 4993.47 545.614i 0.291186 0.0318165i
\(666\) 11235.4 + 15426.5i 0.653701 + 0.897542i
\(667\) 5882.54 0.341489
\(668\) 8557.78 0.495675
\(669\) 2740.54 892.220i 0.158379 0.0515623i
\(670\) 6770.07i 0.390374i
\(671\) 5211.38 0.299826
\(672\) 7028.82 + 15589.5i 0.403486 + 0.894910i
\(673\) 2999.78 0.171817 0.0859086 0.996303i \(-0.472621\pi\)
0.0859086 + 0.996303i \(0.472621\pi\)
\(674\) 6438.04i 0.367929i
\(675\) −2841.15 2056.64i −0.162009 0.117274i
\(676\) 7329.66 0.417027
\(677\) 25090.8 1.42440 0.712200 0.701977i \(-0.247699\pi\)
0.712200 + 0.701977i \(0.247699\pi\)
\(678\) 2988.24 + 9178.67i 0.169267 + 0.519919i
\(679\) 3234.67 353.438i 0.182821 0.0199760i
\(680\) 10217.2i 0.576192i
\(681\) 8712.45 + 26761.1i 0.490252 + 1.50586i
\(682\) 2419.39i 0.135841i
\(683\) 19494.4i 1.09214i −0.837738 0.546072i \(-0.816123\pi\)
0.837738 0.546072i \(-0.183877\pi\)
\(684\) 4096.41 + 5624.44i 0.228991 + 0.314409i
\(685\) 639.113i 0.0356485i
\(686\) −10845.8 + 3672.59i −0.603634 + 0.204403i
\(687\) −3366.91 + 1096.14i −0.186980 + 0.0608740i
\(688\) 867.321 0.0480615
\(689\) 14283.4 0.789774
\(690\) 368.707 + 1132.52i 0.0203426 + 0.0624844i
\(691\) 359.818i 0.0198091i −0.999951 0.00990456i \(-0.996847\pi\)
0.999951 0.00990456i \(-0.00315277\pi\)
\(692\) −7539.38 −0.414168
\(693\) 4210.35 3831.45i 0.230791 0.210021i
\(694\) 20078.6 1.09823
\(695\) 6483.16i 0.353842i
\(696\) −8551.76 26267.6i −0.465738 1.43056i
\(697\) −42525.0 −2.31098
\(698\) −19813.2 −1.07441
\(699\) 21470.6 6990.04i 1.16179 0.378237i
\(700\) 238.922 + 2186.62i 0.0129006 + 0.118066i
\(701\) 29342.5i 1.58096i −0.612489 0.790479i \(-0.709832\pi\)
0.612489 0.790479i \(-0.290168\pi\)
\(702\) −5239.46 3792.73i −0.281696 0.203913i
\(703\) 21270.8i 1.14117i
\(704\) 3958.46i 0.211918i
\(705\) −2523.17 7750.16i −0.134792 0.414026i
\(706\) 18180.3i 0.969158i
\(707\) −438.787 4015.79i −0.0233413 0.213620i
\(708\) −1971.89 6056.85i −0.104673 0.321512i
\(709\) 6480.14 0.343254 0.171627 0.985162i \(-0.445098\pi\)
0.171627 + 0.985162i \(0.445098\pi\)
\(710\) −2680.66 −0.141695
\(711\) 10669.2 7770.65i 0.562767 0.409877i
\(712\) 1413.48i 0.0743996i
\(713\) −2998.37 −0.157489
\(714\) 6338.97 + 14059.5i 0.332255 + 0.736923i
\(715\) −1455.87 −0.0761487
\(716\) 6036.06i 0.315053i
\(717\) −6763.85 + 2202.06i −0.352302 + 0.114697i
\(718\) 1155.22 0.0600452
\(719\) −31658.4 −1.64208 −0.821042 0.570868i \(-0.806607\pi\)
−0.821042 + 0.570868i \(0.806607\pi\)
\(720\) 373.665 272.149i 0.0193412 0.0140867i
\(721\) −6338.92 + 692.624i −0.327425 + 0.0357762i
\(722\) 7059.64i 0.363895i
\(723\) 22363.3 7280.68i 1.15035 0.374511i
\(724\) 5763.40i 0.295849i
\(725\) 5782.65i 0.296224i
\(726\) 10700.0 3483.52i 0.546988 0.178080i
\(727\) 21956.9i 1.12013i −0.828447 0.560067i \(-0.810775\pi\)
0.828447 0.560067i \(-0.189225\pi\)
\(728\) 1182.56 + 10822.8i 0.0602039 + 0.550988i
\(729\) 6147.75 + 18698.3i 0.312338 + 0.949971i
\(730\) −2725.91 −0.138206
\(731\) −22519.2 −1.13940
\(732\) 10745.2 3498.23i 0.542558 0.176637i
\(733\) 17572.2i 0.885464i 0.896654 + 0.442732i \(0.145991\pi\)
−0.896654 + 0.442732i \(0.854009\pi\)
\(734\) −8003.75 −0.402485
\(735\) −4523.52 7677.95i −0.227010 0.385313i
\(736\) 4519.25 0.226334
\(737\) 8551.49i 0.427406i
\(738\) −13705.0 18817.2i −0.683589 0.938580i
\(739\) 26316.8 1.30999 0.654993 0.755635i \(-0.272671\pi\)
0.654993 + 0.755635i \(0.272671\pi\)
\(740\) 9314.40 0.462708
\(741\) 2231.76 + 6855.05i 0.110642 + 0.339847i
\(742\) −2025.04 18533.2i −0.100191 0.916947i
\(743\) 9051.35i 0.446920i −0.974713 0.223460i \(-0.928265\pi\)
0.974713 0.223460i \(-0.0717353\pi\)
\(744\) 4358.89 + 13388.7i 0.214791 + 0.659751i
\(745\) 12867.0i 0.632765i
\(746\) 6032.40i 0.296062i
\(747\) −20043.3 + 14598.0i −0.981723 + 0.715012i
\(748\) 4808.46i 0.235046i
\(749\) −33124.6 + 3619.37i −1.61595 + 0.176567i
\(750\) 1113.29 362.445i 0.0542020 0.0176462i
\(751\) −8878.79 −0.431414 −0.215707 0.976458i \(-0.569206\pi\)
−0.215707 + 0.976458i \(0.569206\pi\)
\(752\) 1074.22 0.0520916
\(753\) 10099.2 + 31020.6i 0.488757 + 1.50127i
\(754\) 10664.0i 0.515066i
\(755\) 7000.33 0.337441
\(756\) 6109.24 10726.2i 0.293903 0.516016i
\(757\) −24510.4 −1.17681 −0.588405 0.808567i \(-0.700244\pi\)
−0.588405 + 0.808567i \(0.700244\pi\)
\(758\) 10331.4i 0.495057i
\(759\) −465.725 1430.52i −0.0222724 0.0684117i
\(760\) −6233.90 −0.297536
\(761\) 7443.90 0.354588 0.177294 0.984158i \(-0.443266\pi\)
0.177294 + 0.984158i \(0.443266\pi\)
\(762\) 7032.28 2289.45i 0.334321 0.108843i
\(763\) −1528.68 13990.5i −0.0725318 0.663813i
\(764\) 12610.1i 0.597144i
\(765\) −9701.90 + 7066.12i −0.458527 + 0.333956i
\(766\) 5368.06i 0.253206i
\(767\) 6599.64i 0.310690i
\(768\) −6779.21 20823.0i −0.318520 0.978366i
\(769\) 32340.6i 1.51656i −0.651930 0.758279i \(-0.726040\pi\)
0.651930 0.758279i \(-0.273960\pi\)
\(770\) 206.406 + 1889.03i 0.00966021 + 0.0884105i
\(771\) −11364.6 34907.4i −0.530850 1.63056i
\(772\) −3996.97 −0.186339
\(773\) 24198.8 1.12596 0.562982 0.826469i \(-0.309654\pi\)
0.562982 + 0.826469i \(0.309654\pi\)
\(774\) −7257.53 9964.71i −0.337037 0.462757i
\(775\) 2947.45i 0.136614i
\(776\) −4038.20 −0.186808
\(777\) −34400.7 + 15510.1i −1.58831 + 0.716118i
\(778\) 15616.3 0.719627
\(779\) 25946.2i 1.19335i
\(780\) −3001.80 + 977.276i −0.137797 + 0.0448617i
\(781\) 3386.02 0.155136
\(782\) 4075.70 0.186377
\(783\) −19028.5 + 26287.0i −0.868485 + 1.19977i
\(784\) 1146.79 253.637i 0.0522407 0.0115541i
\(785\) 14795.0i 0.672684i
\(786\) −10303.5 + 3354.46i −0.467577 + 0.152226i
\(787\) 30214.8i 1.36854i −0.729228 0.684271i \(-0.760121\pi\)
0.729228 0.684271i \(-0.239879\pi\)
\(788\) 5707.87i 0.258038i
\(789\) −22023.6 + 7170.08i −0.993740 + 0.323525i
\(790\) 4405.96i 0.198427i
\(791\) −18973.7 + 2073.17i −0.852881 + 0.0931904i
\(792\) −5710.70 + 4159.24i −0.256213 + 0.186606i
\(793\) 11708.1 0.524296
\(794\) 8220.00 0.367401
\(795\) 13796.4 4491.60i 0.615481 0.200378i
\(796\) 21493.9i 0.957073i
\(797\) −13957.5 −0.620327 −0.310163 0.950683i \(-0.600384\pi\)
−0.310163 + 0.950683i \(0.600384\pi\)
\(798\) 8578.25 3867.66i 0.380535 0.171571i
\(799\) −27891.3 −1.23495
\(800\) 4442.51i 0.196333i
\(801\) −1342.20 + 977.555i −0.0592063 + 0.0431214i
\(802\) −7269.93 −0.320087
\(803\) 3443.18 0.151317
\(804\) 5740.34 + 17632.0i 0.251799 + 0.773423i
\(805\) −2341.09 + 255.800i −0.102500 + 0.0111997i
\(806\) 5435.50i 0.237540i
\(807\) −7613.98 23387.1i −0.332125 1.02015i
\(808\) 5013.35i 0.218278i
\(809\) 21035.9i 0.914195i 0.889416 + 0.457098i \(0.151111\pi\)
−0.889416 + 0.457098i \(0.848889\pi\)
\(810\) −6253.49 2015.79i −0.271266 0.0874415i
\(811\) 12726.2i 0.551022i 0.961298 + 0.275511i \(0.0888471\pi\)
−0.961298 + 0.275511i \(0.911153\pi\)
\(812\) 20231.1 2210.56i 0.874351 0.0955363i
\(813\) 24963.0 8127.05i 1.07687 0.350588i
\(814\) 8046.77 0.346486
\(815\) −19097.4 −0.820801
\(816\) −489.705 1504.18i −0.0210087 0.0645302i
\(817\) 13739.9i 0.588369i
\(818\) 3297.11 0.140930
\(819\) 9459.14 8607.89i 0.403576 0.367258i
\(820\) −11361.7 −0.483864
\(821\) 26669.8i 1.13372i −0.823814 0.566860i \(-0.808158\pi\)
0.823814 0.566860i \(-0.191842\pi\)
\(822\) −370.630 1138.42i −0.0157265 0.0483055i
\(823\) 6265.72 0.265382 0.132691 0.991157i \(-0.457638\pi\)
0.132691 + 0.991157i \(0.457638\pi\)
\(824\) 7913.56 0.334566
\(825\) −1406.23 + 457.816i −0.0593436 + 0.0193201i
\(826\) −8563.25 + 935.667i −0.360719 + 0.0394141i
\(827\) 33183.6i 1.39529i 0.716442 + 0.697646i \(0.245769\pi\)
−0.716442 + 0.697646i \(0.754231\pi\)
\(828\) −1920.52 2636.91i −0.0806071 0.110675i
\(829\) 38711.3i 1.62183i 0.585162 + 0.810916i \(0.301031\pi\)
−0.585162 + 0.810916i \(0.698969\pi\)
\(830\) 8277.08i 0.346147i
\(831\) −11673.8 35857.2i −0.487316 1.49684i
\(832\) 8893.22i 0.370573i
\(833\) −29775.4 + 6585.46i −1.23848 + 0.273917i
\(834\) −3759.67 11548.2i −0.156099 0.479474i
\(835\) 9006.75 0.373283
\(836\) 2933.83 0.121374
\(837\) 9698.95 13398.6i 0.400532 0.553314i
\(838\) 7436.42i 0.306548i
\(839\) −21242.9 −0.874119 −0.437060 0.899432i \(-0.643980\pi\)
−0.437060 + 0.899432i \(0.643980\pi\)
\(840\) 4545.60 + 10081.9i 0.186712 + 0.414117i
\(841\) −29113.4 −1.19371
\(842\) 8819.74i 0.360984i
\(843\) 2961.16 964.045i 0.120982 0.0393873i
\(844\) 14008.0 0.571299
\(845\) 7714.20 0.314055
\(846\) −8988.84 12341.8i −0.365299 0.501561i
\(847\) 2416.79 + 22118.5i 0.0980423 + 0.897286i
\(848\) 1912.27i 0.0774381i
\(849\) 21384.6 6962.05i 0.864450 0.281433i
\(850\) 4006.49i 0.161672i
\(851\) 9972.40i 0.401703i
\(852\) 6981.51 2272.93i 0.280731 0.0913957i
\(853\) 16997.9i 0.682294i −0.940010 0.341147i \(-0.889185\pi\)
0.940010 0.341147i \(-0.110815\pi\)
\(854\) −1659.92 15191.6i −0.0665121 0.608721i
\(855\) 4311.32 + 5919.52i 0.172449 + 0.236776i
\(856\) 41353.0 1.65119
\(857\) −2698.89 −0.107576 −0.0537879 0.998552i \(-0.517129\pi\)
−0.0537879 + 0.998552i \(0.517129\pi\)
\(858\) −2593.27 + 844.275i −0.103185 + 0.0335933i
\(859\) 2431.69i 0.0965870i 0.998833 + 0.0482935i \(0.0153783\pi\)
−0.998833 + 0.0482935i \(0.984622\pi\)
\(860\) −6016.63 −0.238565
\(861\) 41962.0 18919.3i 1.66093 0.748860i
\(862\) −7200.57 −0.284516
\(863\) 725.483i 0.0286161i 0.999898 + 0.0143081i \(0.00455455\pi\)
−0.999898 + 0.0143081i \(0.995445\pi\)
\(864\) −14618.6 + 20194.9i −0.575620 + 0.795190i
\(865\) −7934.92 −0.311902
\(866\) 25047.7 0.982858
\(867\) 4811.83 + 14780.0i 0.188487 + 0.578957i
\(868\) −10311.9 + 1126.74i −0.403237 + 0.0440598i
\(869\) 5565.30i 0.217250i
\(870\) −3353.43 10300.4i −0.130680 0.401398i
\(871\) 19212.1i 0.747390i
\(872\) 17465.8i 0.678289i
\(873\) 2792.79 + 3834.55i 0.108272 + 0.148660i
\(874\) 2486.75i 0.0962420i
\(875\) 251.456 + 2301.34i 0.00971517 + 0.0889135i
\(876\) 7099.37 2311.30i 0.273819 0.0891455i
\(877\) 5541.59 0.213371 0.106685 0.994293i \(-0.465976\pi\)
0.106685 + 0.994293i \(0.465976\pi\)
\(878\) 7615.53 0.292724
\(879\) −4374.53 13436.8i −0.167861 0.515600i
\(880\) 194.912i 0.00746645i
\(881\) −13728.4 −0.524995 −0.262498 0.964933i \(-0.584546\pi\)
−0.262498 + 0.964933i \(0.584546\pi\)
\(882\) −12510.1 11053.2i −0.477593 0.421972i
\(883\) 10444.4 0.398053 0.199027 0.979994i \(-0.436222\pi\)
0.199027 + 0.979994i \(0.436222\pi\)
\(884\) 10802.9i 0.411018i
\(885\) −2075.34 6374.61i −0.0788270 0.242125i
\(886\) 25639.1 0.972192
\(887\) −10785.5 −0.408278 −0.204139 0.978942i \(-0.565439\pi\)
−0.204139 + 0.978942i \(0.565439\pi\)
\(888\) 44530.2 14497.4i 1.68281 0.547862i
\(889\) 1588.37 + 14536.8i 0.0599238 + 0.548424i
\(890\) 554.274i 0.0208756i
\(891\) 7898.97 + 2546.21i 0.296998 + 0.0957364i
\(892\) 2635.08i 0.0989113i
\(893\) 17017.6i 0.637706i
\(894\) 7461.73 + 22919.4i 0.279147 + 0.857428i
\(895\) 6352.73i 0.237261i
\(896\) 14633.4 1598.93i 0.545611 0.0596165i
\(897\) −1046.31 3213.86i −0.0389470 0.119629i
\(898\) −29244.6 −1.08675
\(899\) 27270.5 1.01171
\(900\) −2592.13 + 1887.91i −0.0960048 + 0.0699225i
\(901\) 49650.4i 1.83584i
\(902\) −9815.47 −0.362328
\(903\) 22221.1 10018.8i 0.818906 0.369218i
\(904\) 23687.0 0.871480
\(905\) 6065.76i 0.222799i
\(906\) 12469.4 4059.58i 0.457249 0.148864i
\(907\) 5164.52 0.189069 0.0945343 0.995522i \(-0.469864\pi\)
0.0945343 + 0.995522i \(0.469864\pi\)
\(908\) 25731.3 0.940444
\(909\) 4760.52 3467.20i 0.173703 0.126512i
\(910\) 463.720 + 4243.98i 0.0168925 + 0.154601i
\(911\) 47274.3i 1.71929i 0.510896 + 0.859643i \(0.329314\pi\)
−0.510896 + 0.859643i \(0.670686\pi\)
\(912\) −917.757 + 298.788i −0.0333223 + 0.0108485i
\(913\) 10455.0i 0.378983i
\(914\) 7673.85i 0.277712i
\(915\) 11308.9 3681.76i 0.408591 0.133022i
\(916\) 3237.34i 0.116774i
\(917\) −2327.25 21299.0i −0.0838086 0.767018i
\(918\) −13183.9 + 18212.8i −0.474000 + 0.654808i
\(919\) −32724.6 −1.17463 −0.587314 0.809359i \(-0.699815\pi\)
−0.587314 + 0.809359i \(0.699815\pi\)
\(920\) 2922.64 0.104735
\(921\) −38348.3 + 12484.8i −1.37201 + 0.446676i
\(922\) 8855.32i 0.316306i
\(923\) 7607.16 0.271281
\(924\) −2139.28 4744.80i −0.0761656 0.168931i
\(925\) 9803.06 0.348457
\(926\) 28296.0i 1.00417i
\(927\) −5472.97 7514.47i −0.193911 0.266243i
\(928\) −41103.1 −1.45396
\(929\) 14232.6 0.502642 0.251321 0.967904i \(-0.419135\pi\)
0.251321 + 0.967904i \(0.419135\pi\)
\(930\) 1709.26 + 5250.17i 0.0602677 + 0.185118i
\(931\) 4018.05 + 18167.1i 0.141446 + 0.639531i
\(932\) 20644.3i 0.725566i
\(933\) −7860.98 24145.8i −0.275838 0.847264i
\(934\) 2616.72i 0.0916720i
\(935\) 5060.72i 0.177009i
\(936\) −12829.9 + 9344.30i −0.448032 + 0.326312i
\(937\) 23436.1i 0.817101i −0.912736 0.408550i \(-0.866034\pi\)
0.912736 0.408550i \(-0.133966\pi\)
\(938\) 24928.3 2723.80i 0.867739 0.0948138i
\(939\) −32178.6 + 10476.2i −1.11833 + 0.364086i
\(940\) −7451.92 −0.258569
\(941\) 30270.7 1.04867 0.524333 0.851513i \(-0.324315\pi\)
0.524333 + 0.851513i \(0.324315\pi\)
\(942\) 8579.82 + 26353.7i 0.296757 + 0.911519i
\(943\) 12164.4i 0.420070i
\(944\) 883.562 0.0304635
\(945\) 6429.75 11288.9i 0.221333 0.388602i
\(946\) −5197.81 −0.178642
\(947\) 12968.3i 0.444997i 0.974933 + 0.222498i \(0.0714212\pi\)
−0.974933 + 0.222498i \(0.928579\pi\)
\(948\) −3735.81 11474.9i −0.127989 0.393130i
\(949\) 7735.58 0.264602
\(950\) −2444.52 −0.0834849
\(951\) −21234.6 + 6913.20i −0.724057 + 0.235726i
\(952\) 37621.0 4110.67i 1.28078 0.139945i
\(953\) 25435.7i 0.864577i 0.901735 + 0.432288i \(0.142294\pi\)
−0.901735 + 0.432288i \(0.857706\pi\)
\(954\) 21970.2 16001.4i 0.745609 0.543044i
\(955\) 13271.7i 0.449698i
\(956\) 6503.56i 0.220021i
\(957\) 4235.82 + 13010.7i 0.143077 + 0.439475i
\(958\) 21922.4i 0.739331i
\(959\) 2353.30 257.134i 0.0792409 0.00865829i
\(960\) −2796.59 8589.99i −0.0940204 0.288793i
\(961\) 15891.0 0.533418
\(962\) 18078.2 0.605888
\(963\) −28599.5 39267.6i −0.957015 1.31400i
\(964\) 21502.7i 0.718419i
\(965\) −4206.66 −0.140329
\(966\) −4021.74 + 1813.27i −0.133952 + 0.0603945i
\(967\) 23388.3 0.777785 0.388893 0.921283i \(-0.372858\pi\)
0.388893 + 0.921283i \(0.372858\pi\)
\(968\) 27613.0i 0.916854i
\(969\) 23828.8 7757.79i 0.789980 0.257189i
\(970\) −1583.51 −0.0524160
\(971\) 20436.8 0.675436 0.337718 0.941247i \(-0.390345\pi\)
0.337718 + 0.941247i \(0.390345\pi\)
\(972\) 17995.8 52.3941i 0.593842 0.00172895i
\(973\) 23871.9 2608.37i 0.786534 0.0859410i
\(974\) 1260.52i 0.0414677i
\(975\) −3159.28 + 1028.55i −0.103772 + 0.0337845i
\(976\) 1567.48i 0.0514077i
\(977\) 28876.4i 0.945587i 0.881173 + 0.472793i \(0.156754\pi\)
−0.881173 + 0.472793i \(0.843246\pi\)
\(978\) −34017.4 + 11074.8i −1.11223 + 0.362100i
\(979\) 700.120i 0.0228559i
\(980\) −7955.30 + 1759.49i −0.259309 + 0.0573517i
\(981\) 16585.0 12079.3i 0.539775 0.393131i
\(982\) 28809.5 0.936199
\(983\) −19964.0 −0.647766 −0.323883 0.946097i \(-0.604988\pi\)
−0.323883 + 0.946097i \(0.604988\pi\)
\(984\) −54318.0 + 17684.0i −1.75975 + 0.572911i
\(985\) 6007.32i 0.194324i
\(986\) −37069.0 −1.19728
\(987\) 27522.0 12408.8i 0.887574 0.400178i
\(988\) 6591.25 0.212243
\(989\) 6441.67i 0.207111i
\(990\) −2239.36 + 1630.98i −0.0718904 + 0.0523594i
\(991\) −27990.1 −0.897210 −0.448605 0.893730i \(-0.648079\pi\)
−0.448605 + 0.893730i \(0.648079\pi\)
\(992\) 20950.5 0.670544
\(993\) 4902.39 + 15058.2i 0.156669 + 0.481225i
\(994\) −1078.51 9870.54i −0.0344147 0.314964i
\(995\) 22621.5i 0.720754i
\(996\) 7018.13 + 21556.9i 0.223271 + 0.685799i
\(997\) 24576.1i 0.780676i 0.920672 + 0.390338i \(0.127642\pi\)
−0.920672 + 0.390338i \(0.872358\pi\)
\(998\) 37721.3i 1.19644i
\(999\) −44563.1 32258.2i −1.41132 1.02163i
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 105.4.b.b.41.6 yes 16
3.2 odd 2 105.4.b.a.41.11 yes 16
7.6 odd 2 105.4.b.a.41.6 16
21.20 even 2 inner 105.4.b.b.41.11 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.b.a.41.6 16 7.6 odd 2
105.4.b.a.41.11 yes 16 3.2 odd 2
105.4.b.b.41.6 yes 16 1.1 even 1 trivial
105.4.b.b.41.11 yes 16 21.20 even 2 inner