Properties

Label 95.4.e.a.11.1
Level $95$
Weight $4$
Character 95.11
Analytic conductor $5.605$
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] = [95,4,Mod(11,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.11");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 95.e (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: \(5.60518145055\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 95.11
Dual form 95.4.e.a.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(2.50000 - 4.33013i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-2.50000 - 4.33013i) q^{6} +22.0000 q^{7} +15.0000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(2.50000 - 4.33013i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-2.50000 - 4.33013i) q^{6} +22.0000 q^{7} +15.0000 q^{8} +(1.00000 + 1.73205i) q^{9} +(2.50000 + 4.33013i) q^{10} +9.00000 q^{11} +35.0000 q^{12} +(-27.0000 - 46.7654i) q^{13} +(11.0000 - 19.0526i) q^{14} +(12.5000 + 21.6506i) q^{15} +(-20.5000 + 35.5070i) q^{16} +(27.0000 - 46.7654i) q^{17} +2.00000 q^{18} +(-66.5000 - 49.3634i) q^{19} -35.0000 q^{20} +(55.0000 - 95.2628i) q^{21} +(4.50000 - 7.79423i) q^{22} +(46.0000 + 79.6743i) q^{23} +(37.5000 - 64.9519i) q^{24} +(-12.5000 - 21.6506i) q^{25} -54.0000 q^{26} +145.000 q^{27} +(77.0000 + 133.368i) q^{28} +(67.0000 + 116.047i) q^{29} +25.0000 q^{30} -252.000 q^{31} +(80.5000 + 139.430i) q^{32} +(22.5000 - 38.9711i) q^{33} +(-27.0000 - 46.7654i) q^{34} +(-55.0000 + 95.2628i) q^{35} +(-7.00000 + 12.1244i) q^{36} -236.000 q^{37} +(-76.0000 + 32.9090i) q^{38} -270.000 q^{39} +(-37.5000 + 64.9519i) q^{40} +(121.500 - 210.444i) q^{41} +(-55.0000 - 95.2628i) q^{42} +(-248.000 + 429.549i) q^{43} +(31.5000 + 54.5596i) q^{44} -10.0000 q^{45} +92.0000 q^{46} +(-251.000 - 434.745i) q^{47} +(102.500 + 177.535i) q^{48} +141.000 q^{49} -25.0000 q^{50} +(-135.000 - 233.827i) q^{51} +(189.000 - 327.358i) q^{52} +(-31.0000 - 53.6936i) q^{53} +(72.5000 - 125.574i) q^{54} +(-22.5000 + 38.9711i) q^{55} +330.000 q^{56} +(-380.000 + 164.545i) q^{57} +134.000 q^{58} +(-340.500 + 589.763i) q^{59} +(-87.5000 + 151.554i) q^{60} +(71.0000 + 122.976i) q^{61} +(-126.000 + 218.238i) q^{62} +(22.0000 + 38.1051i) q^{63} -167.000 q^{64} +270.000 q^{65} +(-22.5000 - 38.9711i) q^{66} +(-27.5000 - 47.6314i) q^{67} +378.000 q^{68} +460.000 q^{69} +(55.0000 + 95.2628i) q^{70} +(487.000 - 843.509i) q^{71} +(15.0000 + 25.9808i) q^{72} +(-347.500 + 601.888i) q^{73} +(-118.000 + 204.382i) q^{74} -125.000 q^{75} +(66.5000 - 575.907i) q^{76} +198.000 q^{77} +(-135.000 + 233.827i) q^{78} +(368.000 - 637.395i) q^{79} +(-102.500 - 177.535i) q^{80} +(335.500 - 581.103i) q^{81} +(-121.500 - 210.444i) q^{82} -63.0000 q^{83} +770.000 q^{84} +(135.000 + 233.827i) q^{85} +(248.000 + 429.549i) q^{86} +670.000 q^{87} +135.000 q^{88} +(-363.000 - 628.734i) q^{89} +(-5.00000 + 8.66025i) q^{90} +(-594.000 - 1028.84i) q^{91} +(-322.000 + 557.720i) q^{92} +(-630.000 + 1091.19i) q^{93} -502.000 q^{94} +(380.000 - 164.545i) q^{95} +805.000 q^{96} +(583.500 - 1010.65i) q^{97} +(70.5000 - 122.110i) q^{98} +(9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 5 q^{3} + 7 q^{4} - 5 q^{5} - 5 q^{6} + 44 q^{7} + 30 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 5 q^{3} + 7 q^{4} - 5 q^{5} - 5 q^{6} + 44 q^{7} + 30 q^{8} + 2 q^{9} + 5 q^{10} + 18 q^{11} + 70 q^{12} - 54 q^{13} + 22 q^{14} + 25 q^{15} - 41 q^{16} + 54 q^{17} + 4 q^{18} - 133 q^{19} - 70 q^{20} + 110 q^{21} + 9 q^{22} + 92 q^{23} + 75 q^{24} - 25 q^{25} - 108 q^{26} + 290 q^{27} + 154 q^{28} + 134 q^{29} + 50 q^{30} - 504 q^{31} + 161 q^{32} + 45 q^{33} - 54 q^{34} - 110 q^{35} - 14 q^{36} - 472 q^{37} - 152 q^{38} - 540 q^{39} - 75 q^{40} + 243 q^{41} - 110 q^{42} - 496 q^{43} + 63 q^{44} - 20 q^{45} + 184 q^{46} - 502 q^{47} + 205 q^{48} + 282 q^{49} - 50 q^{50} - 270 q^{51} + 378 q^{52} - 62 q^{53} + 145 q^{54} - 45 q^{55} + 660 q^{56} - 760 q^{57} + 268 q^{58} - 681 q^{59} - 175 q^{60} + 142 q^{61} - 252 q^{62} + 44 q^{63} - 334 q^{64} + 540 q^{65} - 45 q^{66} - 55 q^{67} + 756 q^{68} + 920 q^{69} + 110 q^{70} + 974 q^{71} + 30 q^{72} - 695 q^{73} - 236 q^{74} - 250 q^{75} + 133 q^{76} + 396 q^{77} - 270 q^{78} + 736 q^{79} - 205 q^{80} + 671 q^{81} - 243 q^{82} - 126 q^{83} + 1540 q^{84} + 270 q^{85} + 496 q^{86} + 1340 q^{87} + 270 q^{88} - 726 q^{89} - 10 q^{90} - 1188 q^{91} - 644 q^{92} - 1260 q^{93} - 1004 q^{94} + 760 q^{95} + 1610 q^{96} + 1167 q^{97} + 141 q^{98} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.176777 0.306186i −0.763998 0.645219i \(-0.776766\pi\)
0.940775 + 0.339032i \(0.110100\pi\)
\(3\) 2.50000 4.33013i 0.481125 0.833333i −0.518640 0.854993i \(-0.673562\pi\)
0.999765 + 0.0216593i \(0.00689490\pi\)
\(4\) 3.50000 + 6.06218i 0.437500 + 0.757772i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) −2.50000 4.33013i −0.170103 0.294628i
\(7\) 22.0000 1.18789 0.593944 0.804506i \(-0.297570\pi\)
0.593944 + 0.804506i \(0.297570\pi\)
\(8\) 15.0000 0.662913
\(9\) 1.00000 + 1.73205i 0.0370370 + 0.0641500i
\(10\) 2.50000 + 4.33013i 0.0790569 + 0.136931i
\(11\) 9.00000 0.246691 0.123346 0.992364i \(-0.460638\pi\)
0.123346 + 0.992364i \(0.460638\pi\)
\(12\) 35.0000 0.841969
\(13\) −27.0000 46.7654i −0.576035 0.997722i −0.995928 0.0901482i \(-0.971266\pi\)
0.419894 0.907573i \(-0.362067\pi\)
\(14\) 11.0000 19.0526i 0.209991 0.363715i
\(15\) 12.5000 + 21.6506i 0.215166 + 0.372678i
\(16\) −20.5000 + 35.5070i −0.320312 + 0.554798i
\(17\) 27.0000 46.7654i 0.385204 0.667192i −0.606594 0.795012i \(-0.707465\pi\)
0.991797 + 0.127820i \(0.0407979\pi\)
\(18\) 2.00000 0.0261891
\(19\) −66.5000 49.3634i −0.802955 0.596040i
\(20\) −35.0000 −0.391312
\(21\) 55.0000 95.2628i 0.571523 0.989907i
\(22\) 4.50000 7.79423i 0.0436092 0.0755334i
\(23\) 46.0000 + 79.6743i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 37.5000 64.9519i 0.318944 0.552427i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −54.0000 −0.407318
\(27\) 145.000 1.03353
\(28\) 77.0000 + 133.368i 0.519701 + 0.900149i
\(29\) 67.0000 + 116.047i 0.429020 + 0.743085i 0.996786 0.0801050i \(-0.0255256\pi\)
−0.567766 + 0.823190i \(0.692192\pi\)
\(30\) 25.0000 0.152145
\(31\) −252.000 −1.46002 −0.730009 0.683438i \(-0.760484\pi\)
−0.730009 + 0.683438i \(0.760484\pi\)
\(32\) 80.5000 + 139.430i 0.444704 + 0.770250i
\(33\) 22.5000 38.9711i 0.118689 0.205576i
\(34\) −27.0000 46.7654i −0.136190 0.235888i
\(35\) −55.0000 + 95.2628i −0.265620 + 0.460067i
\(36\) −7.00000 + 12.1244i −0.0324074 + 0.0561313i
\(37\) −236.000 −1.04860 −0.524299 0.851534i \(-0.675673\pi\)
−0.524299 + 0.851534i \(0.675673\pi\)
\(38\) −76.0000 + 32.9090i −0.324443 + 0.140488i
\(39\) −270.000 −1.10858
\(40\) −37.5000 + 64.9519i −0.148232 + 0.256745i
\(41\) 121.500 210.444i 0.462808 0.801606i −0.536292 0.844033i \(-0.680175\pi\)
0.999100 + 0.0424262i \(0.0135087\pi\)
\(42\) −55.0000 95.2628i −0.202064 0.349985i
\(43\) −248.000 + 429.549i −0.879527 + 1.52338i −0.0276654 + 0.999617i \(0.508807\pi\)
−0.851861 + 0.523768i \(0.824526\pi\)
\(44\) 31.5000 + 54.5596i 0.107927 + 0.186936i
\(45\) −10.0000 −0.0331269
\(46\) 92.0000 0.294884
\(47\) −251.000 434.745i −0.778981 1.34923i −0.932530 0.361094i \(-0.882403\pi\)
0.153548 0.988141i \(-0.450930\pi\)
\(48\) 102.500 + 177.535i 0.308221 + 0.533854i
\(49\) 141.000 0.411079
\(50\) −25.0000 −0.0707107
\(51\) −135.000 233.827i −0.370662 0.642006i
\(52\) 189.000 327.358i 0.504030 0.873006i
\(53\) −31.0000 53.6936i −0.0803430 0.139158i 0.823054 0.567963i \(-0.192268\pi\)
−0.903397 + 0.428805i \(0.858935\pi\)
\(54\) 72.5000 125.574i 0.182704 0.316452i
\(55\) −22.5000 + 38.9711i −0.0551618 + 0.0955431i
\(56\) 330.000 0.787466
\(57\) −380.000 + 164.545i −0.883022 + 0.382360i
\(58\) 134.000 0.303363
\(59\) −340.500 + 589.763i −0.751344 + 1.30137i 0.195827 + 0.980639i \(0.437261\pi\)
−0.947171 + 0.320728i \(0.896072\pi\)
\(60\) −87.5000 + 151.554i −0.188270 + 0.326093i
\(61\) 71.0000 + 122.976i 0.149027 + 0.258122i 0.930868 0.365356i \(-0.119053\pi\)
−0.781841 + 0.623477i \(0.785719\pi\)
\(62\) −126.000 + 218.238i −0.258097 + 0.447037i
\(63\) 22.0000 + 38.1051i 0.0439959 + 0.0762031i
\(64\) −167.000 −0.326172
\(65\) 270.000 0.515221
\(66\) −22.5000 38.9711i −0.0419630 0.0726821i
\(67\) −27.5000 47.6314i −0.0501442 0.0868523i 0.839864 0.542797i \(-0.182635\pi\)
−0.890008 + 0.455945i \(0.849301\pi\)
\(68\) 378.000 0.674106
\(69\) 460.000 0.802572
\(70\) 55.0000 + 95.2628i 0.0939108 + 0.162658i
\(71\) 487.000 843.509i 0.814032 1.40994i −0.0959890 0.995382i \(-0.530601\pi\)
0.910021 0.414562i \(-0.136065\pi\)
\(72\) 15.0000 + 25.9808i 0.0245523 + 0.0425259i
\(73\) −347.500 + 601.888i −0.557148 + 0.965009i 0.440585 + 0.897711i \(0.354771\pi\)
−0.997733 + 0.0672976i \(0.978562\pi\)
\(74\) −118.000 + 204.382i −0.185368 + 0.321067i
\(75\) −125.000 −0.192450
\(76\) 66.5000 575.907i 0.100369 0.869224i
\(77\) 198.000 0.293041
\(78\) −135.000 + 233.827i −0.195971 + 0.339432i
\(79\) 368.000 637.395i 0.524092 0.907753i −0.475515 0.879708i \(-0.657738\pi\)
0.999607 0.0280457i \(-0.00892838\pi\)
\(80\) −102.500 177.535i −0.143248 0.248113i
\(81\) 335.500 581.103i 0.460219 0.797124i
\(82\) −121.500 210.444i −0.163627 0.283411i
\(83\) −63.0000 −0.0833150 −0.0416575 0.999132i \(-0.513264\pi\)
−0.0416575 + 0.999132i \(0.513264\pi\)
\(84\) 770.000 1.00017
\(85\) 135.000 + 233.827i 0.172268 + 0.298377i
\(86\) 248.000 + 429.549i 0.310960 + 0.538598i
\(87\) 670.000 0.825650
\(88\) 135.000 0.163535
\(89\) −363.000 628.734i −0.432336 0.748828i 0.564738 0.825270i \(-0.308977\pi\)
−0.997074 + 0.0764421i \(0.975644\pi\)
\(90\) −5.00000 + 8.66025i −0.00585607 + 0.0101430i
\(91\) −594.000 1028.84i −0.684265 1.18518i
\(92\) −322.000 + 557.720i −0.364900 + 0.632026i
\(93\) −630.000 + 1091.19i −0.702451 + 1.21668i
\(94\) −502.000 −0.550823
\(95\) 380.000 164.545i 0.410391 0.177705i
\(96\) 805.000 0.855833
\(97\) 583.500 1010.65i 0.610778 1.05790i −0.380332 0.924850i \(-0.624190\pi\)
0.991110 0.133048i \(-0.0424765\pi\)
\(98\) 70.5000 122.110i 0.0726691 0.125867i
\(99\) 9.00000 + 15.5885i 0.00913671 + 0.0158252i
\(100\) 87.5000 151.554i 0.0875000 0.151554i
\(101\) 15.0000 + 25.9808i 0.0147778 + 0.0255959i 0.873320 0.487147i \(-0.161963\pi\)
−0.858542 + 0.512743i \(0.828629\pi\)
\(102\) −270.000 −0.262098
\(103\) −602.000 −0.575891 −0.287946 0.957647i \(-0.592972\pi\)
−0.287946 + 0.957647i \(0.592972\pi\)
\(104\) −405.000 701.481i −0.381861 0.661402i
\(105\) 275.000 + 476.314i 0.255593 + 0.442700i
\(106\) −62.0000 −0.0568111
\(107\) 660.000 0.596305 0.298152 0.954518i \(-0.403630\pi\)
0.298152 + 0.954518i \(0.403630\pi\)
\(108\) 507.500 + 879.016i 0.452169 + 0.783179i
\(109\) 60.0000 103.923i 0.0527244 0.0913213i −0.838459 0.544965i \(-0.816543\pi\)
0.891183 + 0.453644i \(0.149876\pi\)
\(110\) 22.5000 + 38.9711i 0.0195026 + 0.0337796i
\(111\) −590.000 + 1021.91i −0.504507 + 0.873832i
\(112\) −451.000 + 781.155i −0.380495 + 0.659038i
\(113\) 1059.00 0.881614 0.440807 0.897602i \(-0.354692\pi\)
0.440807 + 0.897602i \(0.354692\pi\)
\(114\) −47.5000 + 411.362i −0.0390244 + 0.337961i
\(115\) −460.000 −0.373002
\(116\) −469.000 + 812.332i −0.375393 + 0.650199i
\(117\) 54.0000 93.5307i 0.0426692 0.0739053i
\(118\) 340.500 + 589.763i 0.265640 + 0.460103i
\(119\) 594.000 1028.84i 0.457579 0.792550i
\(120\) 187.500 + 324.760i 0.142636 + 0.247053i
\(121\) −1250.00 −0.939144
\(122\) 142.000 0.105378
\(123\) −607.500 1052.22i −0.445337 0.771346i
\(124\) −882.000 1527.67i −0.638758 1.10636i
\(125\) 125.000 0.0894427
\(126\) 44.0000 0.0311098
\(127\) −59.0000 102.191i −0.0412236 0.0714015i 0.844677 0.535276i \(-0.179792\pi\)
−0.885901 + 0.463874i \(0.846459\pi\)
\(128\) −727.500 + 1260.07i −0.502363 + 0.870119i
\(129\) 1240.00 + 2147.74i 0.846325 + 1.46588i
\(130\) 135.000 233.827i 0.0910791 0.157754i
\(131\) −333.500 + 577.639i −0.222428 + 0.385256i −0.955545 0.294847i \(-0.904731\pi\)
0.733117 + 0.680103i \(0.238065\pi\)
\(132\) 315.000 0.207706
\(133\) −1463.00 1086.00i −0.953821 0.708028i
\(134\) −55.0000 −0.0354573
\(135\) −362.500 + 627.868i −0.231104 + 0.400284i
\(136\) 405.000 701.481i 0.255356 0.442290i
\(137\) 525.500 + 910.193i 0.327712 + 0.567613i 0.982057 0.188582i \(-0.0603892\pi\)
−0.654346 + 0.756196i \(0.727056\pi\)
\(138\) 230.000 398.372i 0.141876 0.245737i
\(139\) 417.500 + 723.131i 0.254762 + 0.441260i 0.964831 0.262872i \(-0.0846696\pi\)
−0.710069 + 0.704132i \(0.751336\pi\)
\(140\) −770.000 −0.464835
\(141\) −2510.00 −1.49915
\(142\) −487.000 843.509i −0.287804 0.498491i
\(143\) −243.000 420.888i −0.142103 0.246129i
\(144\) −82.0000 −0.0474537
\(145\) −670.000 −0.383727
\(146\) 347.500 + 601.888i 0.196982 + 0.341182i
\(147\) 352.500 610.548i 0.197780 0.342566i
\(148\) −826.000 1430.67i −0.458762 0.794599i
\(149\) −1368.00 + 2369.45i −0.752154 + 1.30277i 0.194623 + 0.980878i \(0.437652\pi\)
−0.946777 + 0.321891i \(0.895682\pi\)
\(150\) −62.5000 + 108.253i −0.0340207 + 0.0589256i
\(151\) −376.000 −0.202639 −0.101319 0.994854i \(-0.532306\pi\)
−0.101319 + 0.994854i \(0.532306\pi\)
\(152\) −997.500 740.452i −0.532289 0.395122i
\(153\) 108.000 0.0570672
\(154\) 99.0000 171.473i 0.0518029 0.0897253i
\(155\) 630.000 1091.19i 0.326470 0.565462i
\(156\) −945.000 1636.79i −0.485004 0.840051i
\(157\) 496.000 859.097i 0.252134 0.436710i −0.711979 0.702201i \(-0.752201\pi\)
0.964113 + 0.265491i \(0.0855341\pi\)
\(158\) −368.000 637.395i −0.185294 0.320939i
\(159\) −310.000 −0.154620
\(160\) −805.000 −0.397755
\(161\) 1012.00 + 1752.84i 0.495384 + 0.858030i
\(162\) −335.500 581.103i −0.162712 0.281826i
\(163\) 3047.00 1.46417 0.732084 0.681214i \(-0.238548\pi\)
0.732084 + 0.681214i \(0.238548\pi\)
\(164\) 1701.00 0.809913
\(165\) 112.500 + 194.856i 0.0530795 + 0.0919363i
\(166\) −31.5000 + 54.5596i −0.0147282 + 0.0255099i
\(167\) 652.000 + 1129.30i 0.302115 + 0.523279i 0.976615 0.214996i \(-0.0689739\pi\)
−0.674500 + 0.738275i \(0.735641\pi\)
\(168\) 825.000 1428.94i 0.378870 0.656222i
\(169\) −359.500 + 622.672i −0.163632 + 0.283419i
\(170\) 270.000 0.121812
\(171\) 19.0000 164.545i 0.00849688 0.0735851i
\(172\) −3472.00 −1.53917
\(173\) −99.0000 + 171.473i −0.0435077 + 0.0753575i −0.886959 0.461848i \(-0.847187\pi\)
0.843452 + 0.537205i \(0.180520\pi\)
\(174\) 335.000 580.237i 0.145956 0.252803i
\(175\) −275.000 476.314i −0.118789 0.205748i
\(176\) −184.500 + 319.563i −0.0790182 + 0.136864i
\(177\) 1702.50 + 2948.82i 0.722982 + 1.25224i
\(178\) −726.000 −0.305708
\(179\) −1265.00 −0.528215 −0.264108 0.964493i \(-0.585077\pi\)
−0.264108 + 0.964493i \(0.585077\pi\)
\(180\) −35.0000 60.6218i −0.0144930 0.0251027i
\(181\) 2038.00 + 3529.92i 0.836925 + 1.44960i 0.892454 + 0.451139i \(0.148982\pi\)
−0.0555292 + 0.998457i \(0.517685\pi\)
\(182\) −1188.00 −0.483848
\(183\) 710.000 0.286802
\(184\) 690.000 + 1195.12i 0.276454 + 0.478832i
\(185\) 590.000 1021.91i 0.234474 0.406121i
\(186\) 630.000 + 1091.19i 0.248354 + 0.430162i
\(187\) 243.000 420.888i 0.0950263 0.164590i
\(188\) 1757.00 3043.21i 0.681608 1.18058i
\(189\) 3190.00 1.22772
\(190\) 47.5000 411.362i 0.0181369 0.157070i
\(191\) 3292.00 1.24712 0.623562 0.781774i \(-0.285685\pi\)
0.623562 + 0.781774i \(0.285685\pi\)
\(192\) −417.500 + 723.131i −0.156930 + 0.271810i
\(193\) −969.000 + 1678.36i −0.361400 + 0.625963i −0.988191 0.153224i \(-0.951034\pi\)
0.626792 + 0.779187i \(0.284368\pi\)
\(194\) −583.500 1010.65i −0.215943 0.374024i
\(195\) 675.000 1169.13i 0.247886 0.429351i
\(196\) 493.500 + 854.767i 0.179847 + 0.311504i
\(197\) 4524.00 1.63615 0.818075 0.575111i \(-0.195041\pi\)
0.818075 + 0.575111i \(0.195041\pi\)
\(198\) 18.0000 0.00646063
\(199\) −2141.00 3708.32i −0.762671 1.32098i −0.941469 0.337099i \(-0.890554\pi\)
0.178799 0.983886i \(-0.442779\pi\)
\(200\) −187.500 324.760i −0.0662913 0.114820i
\(201\) −275.000 −0.0965025
\(202\) 30.0000 0.0104495
\(203\) 1474.00 + 2553.04i 0.509628 + 0.882702i
\(204\) 945.000 1636.79i 0.324330 0.561755i
\(205\) 607.500 + 1052.22i 0.206974 + 0.358489i
\(206\) −301.000 + 521.347i −0.101804 + 0.176330i
\(207\) −92.0000 + 159.349i −0.0308910 + 0.0535048i
\(208\) 2214.00 0.738045
\(209\) −598.500 444.271i −0.198082 0.147038i
\(210\) 550.000 0.180731
\(211\) 970.000 1680.09i 0.316481 0.548162i −0.663270 0.748380i \(-0.730832\pi\)
0.979751 + 0.200219i \(0.0641652\pi\)
\(212\) 217.000 375.855i 0.0703001 0.121763i
\(213\) −2435.00 4217.54i −0.783303 1.35672i
\(214\) 330.000 571.577i 0.105413 0.182580i
\(215\) −1240.00 2147.74i −0.393336 0.681278i
\(216\) 2175.00 0.685139
\(217\) −5544.00 −1.73434
\(218\) −60.0000 103.923i −0.0186409 0.0322870i
\(219\) 1737.50 + 3009.44i 0.536116 + 0.928580i
\(220\) −315.000 −0.0965332
\(221\) −2916.00 −0.887563
\(222\) 590.000 + 1021.91i 0.178370 + 0.308946i
\(223\) 2078.00 3599.20i 0.624005 1.08081i −0.364727 0.931114i \(-0.618838\pi\)
0.988732 0.149694i \(-0.0478290\pi\)
\(224\) 1771.00 + 3067.46i 0.528259 + 0.914971i
\(225\) 25.0000 43.3013i 0.00740741 0.0128300i
\(226\) 529.500 917.121i 0.155849 0.269938i
\(227\) 2093.00 0.611970 0.305985 0.952036i \(-0.401014\pi\)
0.305985 + 0.952036i \(0.401014\pi\)
\(228\) −2327.50 1727.72i −0.676063 0.501847i
\(229\) −4312.00 −1.24430 −0.622151 0.782898i \(-0.713741\pi\)
−0.622151 + 0.782898i \(0.713741\pi\)
\(230\) −230.000 + 398.372i −0.0659380 + 0.114208i
\(231\) 495.000 857.365i 0.140990 0.244201i
\(232\) 1005.00 + 1740.71i 0.284403 + 0.492600i
\(233\) 2114.50 3662.42i 0.594530 1.02976i −0.399083 0.916915i \(-0.630671\pi\)
0.993613 0.112841i \(-0.0359952\pi\)
\(234\) −54.0000 93.5307i −0.0150859 0.0261295i
\(235\) 2510.00 0.696742
\(236\) −4767.00 −1.31485
\(237\) −1840.00 3186.97i −0.504307 0.873486i
\(238\) −594.000 1028.84i −0.161779 0.280209i
\(239\) −5556.00 −1.50371 −0.751857 0.659326i \(-0.770842\pi\)
−0.751857 + 0.659326i \(0.770842\pi\)
\(240\) −1025.00 −0.275681
\(241\) 2209.50 + 3826.97i 0.590566 + 1.02289i 0.994156 + 0.107950i \(0.0344288\pi\)
−0.403590 + 0.914940i \(0.632238\pi\)
\(242\) −625.000 + 1082.53i −0.166019 + 0.287553i
\(243\) 280.000 + 484.974i 0.0739177 + 0.128029i
\(244\) −497.000 + 860.829i −0.130398 + 0.225856i
\(245\) −352.500 + 610.548i −0.0919200 + 0.159210i
\(246\) −1215.00 −0.314901
\(247\) −513.000 + 4442.71i −0.132151 + 1.14447i
\(248\) −3780.00 −0.967864
\(249\) −157.500 + 272.798i −0.0400850 + 0.0694292i
\(250\) 62.5000 108.253i 0.0158114 0.0273861i
\(251\) 1978.50 + 3426.86i 0.497537 + 0.861760i 0.999996 0.00284158i \(-0.000904504\pi\)
−0.502459 + 0.864601i \(0.667571\pi\)
\(252\) −154.000 + 266.736i −0.0384964 + 0.0666777i
\(253\) 414.000 + 717.069i 0.102877 + 0.178189i
\(254\) −118.000 −0.0291495
\(255\) 1350.00 0.331531
\(256\) 59.5000 + 103.057i 0.0145264 + 0.0251604i
\(257\) 438.500 + 759.504i 0.106431 + 0.184345i 0.914322 0.404988i \(-0.132724\pi\)
−0.807891 + 0.589332i \(0.799391\pi\)
\(258\) 2480.00 0.598442
\(259\) −5192.00 −1.24562
\(260\) 945.000 + 1636.79i 0.225409 + 0.390420i
\(261\) −134.000 + 232.095i −0.0317793 + 0.0550433i
\(262\) 333.500 + 577.639i 0.0786401 + 0.136209i
\(263\) 1215.00 2104.44i 0.284867 0.493405i −0.687710 0.725986i \(-0.741384\pi\)
0.972577 + 0.232581i \(0.0747171\pi\)
\(264\) 337.500 584.567i 0.0786806 0.136279i
\(265\) 310.000 0.0718609
\(266\) −1672.00 + 723.997i −0.385402 + 0.166884i
\(267\) −3630.00 −0.832031
\(268\) 192.500 333.420i 0.0438762 0.0759957i
\(269\) −2346.00 + 4063.39i −0.531740 + 0.921001i 0.467573 + 0.883954i \(0.345128\pi\)
−0.999314 + 0.0370469i \(0.988205\pi\)
\(270\) 362.500 + 627.868i 0.0817076 + 0.141522i
\(271\) 4381.00 7588.11i 0.982018 1.70090i 0.327513 0.944847i \(-0.393790\pi\)
0.654505 0.756058i \(-0.272877\pi\)
\(272\) 1107.00 + 1917.38i 0.246771 + 0.427420i
\(273\) −5940.00 −1.31687
\(274\) 1051.00 0.231727
\(275\) −112.500 194.856i −0.0246691 0.0427282i
\(276\) 1610.00 + 2788.60i 0.351125 + 0.608167i
\(277\) 5014.00 1.08759 0.543794 0.839219i \(-0.316987\pi\)
0.543794 + 0.839219i \(0.316987\pi\)
\(278\) 835.000 0.180144
\(279\) −252.000 436.477i −0.0540747 0.0936602i
\(280\) −825.000 + 1428.94i −0.176083 + 0.304984i
\(281\) 1932.50 + 3347.19i 0.410261 + 0.710593i 0.994918 0.100688i \(-0.0321043\pi\)
−0.584657 + 0.811280i \(0.698771\pi\)
\(282\) −1255.00 + 2173.72i −0.265015 + 0.459019i
\(283\) 296.500 513.553i 0.0622795 0.107871i −0.833204 0.552965i \(-0.813496\pi\)
0.895484 + 0.445094i \(0.146830\pi\)
\(284\) 6818.00 1.42456
\(285\) 237.500 2056.81i 0.0493624 0.427491i
\(286\) −486.000 −0.100482
\(287\) 2673.00 4629.77i 0.549764 0.952219i
\(288\) −161.000 + 278.860i −0.0329410 + 0.0570555i
\(289\) 998.500 + 1729.45i 0.203236 + 0.352016i
\(290\) −335.000 + 580.237i −0.0678341 + 0.117492i
\(291\) −2917.50 5053.26i −0.587721 1.01796i
\(292\) −4865.00 −0.975009
\(293\) −5838.00 −1.16403 −0.582013 0.813180i \(-0.697735\pi\)
−0.582013 + 0.813180i \(0.697735\pi\)
\(294\) −352.500 610.548i −0.0699259 0.121115i
\(295\) −1702.50 2948.82i −0.336011 0.581989i
\(296\) −3540.00 −0.695129
\(297\) 1305.00 0.254962
\(298\) 1368.00 + 2369.45i 0.265927 + 0.460598i
\(299\) 2484.00 4302.41i 0.480446 0.832157i
\(300\) −437.500 757.772i −0.0841969 0.145833i
\(301\) −5456.00 + 9450.07i −1.04478 + 1.80961i
\(302\) −188.000 + 325.626i −0.0358218 + 0.0620452i
\(303\) 150.000 0.0284399
\(304\) 3116.00 1349.27i 0.587878 0.254559i
\(305\) −710.000 −0.133293
\(306\) 54.0000 93.5307i 0.0100882 0.0174732i
\(307\) −123.500 + 213.908i −0.0229593 + 0.0397667i −0.877277 0.479985i \(-0.840642\pi\)
0.854317 + 0.519752i \(0.173975\pi\)
\(308\) 693.000 + 1200.31i 0.128206 + 0.222059i
\(309\) −1505.00 + 2606.74i −0.277076 + 0.479910i
\(310\) −630.000 1091.19i −0.115425 0.199921i
\(311\) −10220.0 −1.86342 −0.931709 0.363206i \(-0.881682\pi\)
−0.931709 + 0.363206i \(0.881682\pi\)
\(312\) −4050.00 −0.734891
\(313\) 3917.50 + 6785.31i 0.707445 + 1.22533i 0.965802 + 0.259281i \(0.0834855\pi\)
−0.258357 + 0.966049i \(0.583181\pi\)
\(314\) −496.000 859.097i −0.0891430 0.154400i
\(315\) −220.000 −0.0393511
\(316\) 5152.00 0.917160
\(317\) 1887.00 + 3268.38i 0.334336 + 0.579087i 0.983357 0.181684i \(-0.0581547\pi\)
−0.649021 + 0.760770i \(0.724821\pi\)
\(318\) −155.000 + 268.468i −0.0273332 + 0.0473425i
\(319\) 603.000 + 1044.43i 0.105835 + 0.183312i
\(320\) 417.500 723.131i 0.0729342 0.126326i
\(321\) 1650.00 2857.88i 0.286897 0.496921i
\(322\) 2024.00 0.350289
\(323\) −4104.00 + 1777.08i −0.706974 + 0.306129i
\(324\) 4697.00 0.805384
\(325\) −675.000 + 1169.13i −0.115207 + 0.199544i
\(326\) 1523.50 2638.78i 0.258831 0.448308i
\(327\) −300.000 519.615i −0.0507341 0.0878740i
\(328\) 1822.50 3156.66i 0.306801 0.531395i
\(329\) −5522.00 9564.38i −0.925343 1.60274i
\(330\) 225.000 0.0375329
\(331\) −5.00000 −0.000830287 −0.000415143 1.00000i \(-0.500132\pi\)
−0.000415143 1.00000i \(0.500132\pi\)
\(332\) −220.500 381.917i −0.0364503 0.0631338i
\(333\) −236.000 408.764i −0.0388370 0.0672677i
\(334\) 1304.00 0.213628
\(335\) 275.000 0.0448503
\(336\) 2255.00 + 3905.77i 0.366132 + 0.634159i
\(337\) 3178.50 5505.32i 0.513780 0.889893i −0.486092 0.873908i \(-0.661578\pi\)
0.999872 0.0159858i \(-0.00508865\pi\)
\(338\) 359.500 + 622.672i 0.0578527 + 0.100204i
\(339\) 2647.50 4585.60i 0.424167 0.734678i
\(340\) −945.000 + 1636.79i −0.150735 + 0.261080i
\(341\) −2268.00 −0.360173
\(342\) −133.000 98.7269i −0.0210287 0.0156098i
\(343\) −4444.00 −0.699573
\(344\) −3720.00 + 6443.23i −0.583049 + 1.00987i
\(345\) −1150.00 + 1991.86i −0.179461 + 0.310835i
\(346\) 99.0000 + 171.473i 0.0153823 + 0.0266429i
\(347\) 6279.50 10876.4i 0.971473 1.68264i 0.280359 0.959895i \(-0.409546\pi\)
0.691114 0.722746i \(-0.257120\pi\)
\(348\) 2345.00 + 4061.66i 0.361222 + 0.625655i
\(349\) 7336.00 1.12518 0.562589 0.826737i \(-0.309805\pi\)
0.562589 + 0.826737i \(0.309805\pi\)
\(350\) −550.000 −0.0839964
\(351\) −3915.00 6780.98i −0.595348 1.03117i
\(352\) 724.500 + 1254.87i 0.109704 + 0.190014i
\(353\) 10451.0 1.57578 0.787890 0.615816i \(-0.211173\pi\)
0.787890 + 0.615816i \(0.211173\pi\)
\(354\) 3405.00 0.511225
\(355\) 2435.00 + 4217.54i 0.364046 + 0.630546i
\(356\) 2541.00 4401.14i 0.378294 0.655225i
\(357\) −2970.00 5144.19i −0.440306 0.762632i
\(358\) −632.500 + 1095.52i −0.0933762 + 0.161732i
\(359\) −3650.00 + 6321.99i −0.536601 + 0.929420i 0.462483 + 0.886628i \(0.346958\pi\)
−0.999084 + 0.0427916i \(0.986375\pi\)
\(360\) −150.000 −0.0219603
\(361\) 1985.50 + 6565.34i 0.289474 + 0.957186i
\(362\) 4076.00 0.591795
\(363\) −3125.00 + 5412.66i −0.451846 + 0.782620i
\(364\) 4158.00 7201.87i 0.598732 1.03703i
\(365\) −1737.50 3009.44i −0.249164 0.431565i
\(366\) 355.000 614.878i 0.0506999 0.0878147i
\(367\) 316.000 + 547.328i 0.0449457 + 0.0778482i 0.887623 0.460571i \(-0.152355\pi\)
−0.842677 + 0.538419i \(0.819022\pi\)
\(368\) −3772.00 −0.534318
\(369\) 486.000 0.0685641
\(370\) −590.000 1021.91i −0.0828990 0.143585i
\(371\) −682.000 1181.26i −0.0954385 0.165304i
\(372\) −8820.00 −1.22929
\(373\) −96.0000 −0.0133263 −0.00666313 0.999978i \(-0.502121\pi\)
−0.00666313 + 0.999978i \(0.502121\pi\)
\(374\) −243.000 420.888i −0.0335969 0.0581915i
\(375\) 312.500 541.266i 0.0430331 0.0745356i
\(376\) −3765.00 6521.17i −0.516396 0.894425i
\(377\) 3618.00 6266.56i 0.494261 0.856086i
\(378\) 1595.00 2762.62i 0.217032 0.375910i
\(379\) 10964.0 1.48597 0.742985 0.669308i \(-0.233409\pi\)
0.742985 + 0.669308i \(0.233409\pi\)
\(380\) 2327.50 + 1727.72i 0.314206 + 0.233237i
\(381\) −590.000 −0.0793349
\(382\) 1646.00 2850.96i 0.220463 0.381852i
\(383\) −1009.00 + 1747.64i −0.134615 + 0.233160i −0.925450 0.378869i \(-0.876313\pi\)
0.790835 + 0.612029i \(0.209646\pi\)
\(384\) 3637.50 + 6300.33i 0.483399 + 0.837272i
\(385\) −495.000 + 857.365i −0.0655261 + 0.113494i
\(386\) 969.000 + 1678.36i 0.127774 + 0.221311i
\(387\) −992.000 −0.130300
\(388\) 8169.00 1.06886
\(389\) −4364.00 7558.67i −0.568801 0.985192i −0.996685 0.0813585i \(-0.974074\pi\)
0.427884 0.903834i \(-0.359259\pi\)
\(390\) −675.000 1169.13i −0.0876409 0.151799i
\(391\) 4968.00 0.642564
\(392\) 2115.00 0.272509
\(393\) 1667.50 + 2888.19i 0.214031 + 0.370713i
\(394\) 2262.00 3917.90i 0.289233 0.500967i
\(395\) 1840.00 + 3186.97i 0.234381 + 0.405960i
\(396\) −63.0000 + 109.119i −0.00799462 + 0.0138471i
\(397\) −4782.00 + 8282.67i −0.604538 + 1.04709i 0.387586 + 0.921834i \(0.373309\pi\)
−0.992124 + 0.125257i \(0.960024\pi\)
\(398\) −4282.00 −0.539290
\(399\) −8360.00 + 3619.99i −1.04893 + 0.454200i
\(400\) 1025.00 0.128125
\(401\) 2933.50 5080.97i 0.365317 0.632747i −0.623510 0.781815i \(-0.714294\pi\)
0.988827 + 0.149068i \(0.0476274\pi\)
\(402\) −137.500 + 238.157i −0.0170594 + 0.0295477i
\(403\) 6804.00 + 11784.9i 0.841021 + 1.45669i
\(404\) −105.000 + 181.865i −0.0129306 + 0.0223964i
\(405\) 1677.50 + 2905.52i 0.205816 + 0.356484i
\(406\) 2948.00 0.360362
\(407\) −2124.00 −0.258680
\(408\) −2025.00 3507.40i −0.245717 0.425594i
\(409\) 417.500 + 723.131i 0.0504744 + 0.0874243i 0.890159 0.455651i \(-0.150593\pi\)
−0.839684 + 0.543075i \(0.817260\pi\)
\(410\) 1215.00 0.146353
\(411\) 5255.00 0.630681
\(412\) −2107.00 3649.43i −0.251953 0.436395i
\(413\) −7491.00 + 12974.8i −0.892513 + 1.54588i
\(414\) 92.0000 + 159.349i 0.0109216 + 0.0189168i
\(415\) 157.500 272.798i 0.0186298 0.0322678i
\(416\) 4347.00 7529.22i 0.512330 0.887381i
\(417\) 4175.00 0.490289
\(418\) −684.000 + 296.181i −0.0800372 + 0.0346571i
\(419\) 756.000 0.0881456 0.0440728 0.999028i \(-0.485967\pi\)
0.0440728 + 0.999028i \(0.485967\pi\)
\(420\) −1925.00 + 3334.20i −0.223644 + 0.387362i
\(421\) 1950.00 3377.50i 0.225742 0.390996i −0.730800 0.682592i \(-0.760853\pi\)
0.956542 + 0.291596i \(0.0941862\pi\)
\(422\) −970.000 1680.09i −0.111893 0.193804i
\(423\) 502.000 869.490i 0.0577023 0.0999433i
\(424\) −465.000 805.404i −0.0532604 0.0922497i
\(425\) −1350.00 −0.154081
\(426\) −4870.00 −0.553879
\(427\) 1562.00 + 2705.46i 0.177027 + 0.306620i
\(428\) 2310.00 + 4001.04i 0.260883 + 0.451863i
\(429\) −2430.00 −0.273477
\(430\) −2480.00 −0.278131
\(431\) −7353.00 12735.8i −0.821767 1.42334i −0.904365 0.426759i \(-0.859655\pi\)
0.0825984 0.996583i \(-0.473678\pi\)
\(432\) −2972.50 + 5148.52i −0.331052 + 0.573399i
\(433\) −3919.00 6787.91i −0.434954 0.753363i 0.562338 0.826908i \(-0.309902\pi\)
−0.997292 + 0.0735450i \(0.976569\pi\)
\(434\) −2772.00 + 4801.24i −0.306590 + 0.531030i
\(435\) −1675.00 + 2901.19i −0.184621 + 0.319773i
\(436\) 840.000 0.0922677
\(437\) 874.000 7569.06i 0.0956730 0.828552i
\(438\) 3475.00 0.379091
\(439\) −8814.00 + 15266.3i −0.958244 + 1.65973i −0.231482 + 0.972839i \(0.574357\pi\)
−0.726763 + 0.686889i \(0.758976\pi\)
\(440\) −337.500 + 584.567i −0.0365675 + 0.0633367i
\(441\) 141.000 + 244.219i 0.0152251 + 0.0263707i
\(442\) −1458.00 + 2525.33i −0.156900 + 0.271760i
\(443\) −4633.50 8025.46i −0.496940 0.860725i 0.503054 0.864255i \(-0.332210\pi\)
−0.999994 + 0.00353028i \(0.998876\pi\)
\(444\) −8260.00 −0.882888
\(445\) 3630.00 0.386693
\(446\) −2078.00 3599.20i −0.220619 0.382124i
\(447\) 6840.00 + 11847.2i 0.723760 + 1.25359i
\(448\) −3674.00 −0.387456
\(449\) −9371.00 −0.984955 −0.492478 0.870325i \(-0.663909\pi\)
−0.492478 + 0.870325i \(0.663909\pi\)
\(450\) −25.0000 43.3013i −0.00261891 0.00453609i
\(451\) 1093.50 1894.00i 0.114171 0.197749i
\(452\) 3706.50 + 6419.85i 0.385706 + 0.668062i
\(453\) −940.000 + 1628.13i −0.0974946 + 0.168866i
\(454\) 1046.50 1812.59i 0.108182 0.187377i
\(455\) 5940.00 0.612025
\(456\) −5700.00 + 2468.17i −0.585366 + 0.253471i
\(457\) −4107.00 −0.420388 −0.210194 0.977660i \(-0.567410\pi\)
−0.210194 + 0.977660i \(0.567410\pi\)
\(458\) −2156.00 + 3734.30i −0.219963 + 0.380988i
\(459\) 3915.00 6780.98i 0.398119 0.689562i
\(460\) −1610.00 2788.60i −0.163188 0.282650i
\(461\) 2715.00 4702.52i 0.274295 0.475093i −0.695662 0.718369i \(-0.744889\pi\)
0.969957 + 0.243276i \(0.0782221\pi\)
\(462\) −495.000 857.365i −0.0498474 0.0863382i
\(463\) −14222.0 −1.42754 −0.713771 0.700379i \(-0.753014\pi\)
−0.713771 + 0.700379i \(0.753014\pi\)
\(464\) −5494.00 −0.549682
\(465\) −3150.00 5455.96i −0.314146 0.544116i
\(466\) −2114.50 3662.42i −0.210198 0.364074i
\(467\) −3885.00 −0.384960 −0.192480 0.981301i \(-0.561653\pi\)
−0.192480 + 0.981301i \(0.561653\pi\)
\(468\) 756.000 0.0746712
\(469\) −605.000 1047.89i −0.0595657 0.103171i
\(470\) 1255.00 2173.72i 0.123168 0.213333i
\(471\) −2480.00 4295.49i −0.242616 0.420224i
\(472\) −5107.50 + 8846.45i −0.498076 + 0.862692i
\(473\) −2232.00 + 3865.94i −0.216971 + 0.375805i
\(474\) −3680.00 −0.356599
\(475\) −237.500 + 2056.81i −0.0229416 + 0.198680i
\(476\) 8316.00 0.800763
\(477\) 62.0000 107.387i 0.00595133 0.0103080i
\(478\) −2778.00 + 4811.64i −0.265822 + 0.460417i
\(479\) −2190.00 3793.19i −0.208901 0.361827i 0.742467 0.669882i \(-0.233655\pi\)
−0.951369 + 0.308055i \(0.900322\pi\)
\(480\) −2012.50 + 3485.75i −0.191370 + 0.331463i
\(481\) 6372.00 + 11036.6i 0.604030 + 1.04621i
\(482\) 4419.00 0.417593
\(483\) 10120.0 0.953366
\(484\) −4375.00 7577.72i −0.410875 0.711657i
\(485\) 2917.50 + 5053.26i 0.273148 + 0.473106i
\(486\) 560.000 0.0522677
\(487\) −18856.0 −1.75451 −0.877256 0.480024i \(-0.840628\pi\)
−0.877256 + 0.480024i \(0.840628\pi\)
\(488\) 1065.00 + 1844.63i 0.0987916 + 0.171112i
\(489\) 7617.50 13193.9i 0.704448 1.22014i
\(490\) 352.500 + 610.548i 0.0324986 + 0.0562893i
\(491\) −794.000 + 1375.25i −0.0729791 + 0.126403i −0.900206 0.435465i \(-0.856584\pi\)
0.827227 + 0.561868i \(0.189917\pi\)
\(492\) 4252.50 7365.55i 0.389670 0.674928i
\(493\) 7236.00 0.661041
\(494\) 3591.00 + 2665.63i 0.327058 + 0.242778i
\(495\) −90.0000 −0.00817212
\(496\) 5166.00 8947.77i 0.467662 0.810014i
\(497\) 10714.0 18557.2i 0.966979 1.67486i
\(498\) 157.500 + 272.798i 0.0141722 + 0.0245469i
\(499\) −5578.50 + 9662.25i −0.500457 + 0.866817i 0.499543 + 0.866289i \(0.333501\pi\)
−1.00000 0.000527580i \(0.999832\pi\)
\(500\) 437.500 + 757.772i 0.0391312 + 0.0677772i
\(501\) 6520.00 0.581421
\(502\) 3957.00 0.351812
\(503\) 9024.00 + 15630.0i 0.799921 + 1.38550i 0.919667 + 0.392699i \(0.128459\pi\)
−0.119746 + 0.992805i \(0.538208\pi\)
\(504\) 330.000 + 571.577i 0.0291654 + 0.0505160i
\(505\) −150.000 −0.0132176
\(506\) 828.000 0.0727452
\(507\) 1797.50 + 3113.36i 0.157455 + 0.272720i
\(508\) 413.000 715.337i 0.0360707 0.0624763i
\(509\) 2094.00 + 3626.91i 0.182348 + 0.315835i 0.942680 0.333699i \(-0.108297\pi\)
−0.760332 + 0.649535i \(0.774964\pi\)
\(510\) 675.000 1169.13i 0.0586069 0.101510i
\(511\) −7645.00 + 13241.5i −0.661830 + 1.14632i
\(512\) −11521.0 −0.994455
\(513\) −9642.50 7157.70i −0.829877 0.616024i
\(514\) 877.000 0.0752584
\(515\) 1505.00 2606.74i 0.128773 0.223042i
\(516\) −8680.00 + 15034.2i −0.740534 + 1.28264i
\(517\) −2259.00 3912.70i −0.192168 0.332844i
\(518\) −2596.00 + 4496.40i −0.220196 + 0.381391i
\(519\) 495.000 + 857.365i 0.0418653 + 0.0725128i
\(520\) 4050.00 0.341547
\(521\) 20405.0 1.71585 0.857926 0.513773i \(-0.171753\pi\)
0.857926 + 0.513773i \(0.171753\pi\)
\(522\) 134.000 + 232.095i 0.0112357 + 0.0194608i
\(523\) −3604.00 6242.31i −0.301323 0.521907i 0.675113 0.737714i \(-0.264095\pi\)
−0.976436 + 0.215808i \(0.930762\pi\)
\(524\) −4669.00 −0.389248
\(525\) −2750.00 −0.228609
\(526\) −1215.00 2104.44i −0.100716 0.174445i
\(527\) −6804.00 + 11784.9i −0.562404 + 0.974112i
\(528\) 922.500 + 1597.82i 0.0760353 + 0.131697i
\(529\) 1851.50 3206.89i 0.152174 0.263573i
\(530\) 155.000 268.468i 0.0127033 0.0220028i
\(531\) −1362.00 −0.111310
\(532\) 1463.00 12670.0i 0.119228 1.03254i
\(533\) −13122.0 −1.06637
\(534\) −1815.00 + 3143.67i −0.147084 + 0.254757i
\(535\) −1650.00 + 2857.88i −0.133338 + 0.230948i
\(536\) −412.500 714.471i −0.0332412 0.0575755i
\(537\) −3162.50 + 5477.61i −0.254138 + 0.440179i
\(538\) 2346.00 + 4063.39i 0.187999 + 0.325623i
\(539\) 1269.00 0.101409
\(540\) −5075.00 −0.404432
\(541\) −1704.00 2951.41i −0.135417 0.234549i 0.790340 0.612669i \(-0.209904\pi\)
−0.925757 + 0.378120i \(0.876571\pi\)
\(542\) −4381.00 7588.11i −0.347196 0.601361i
\(543\) 20380.0 1.61066
\(544\) 8694.00 0.685206
\(545\) 300.000 + 519.615i 0.0235791 + 0.0408401i
\(546\) −2970.00 + 5144.19i −0.232792 + 0.403207i
\(547\) 4708.00 + 8154.50i 0.368006 + 0.637406i 0.989254 0.146209i \(-0.0467071\pi\)
−0.621247 + 0.783615i \(0.713374\pi\)
\(548\) −3678.50 + 6371.35i −0.286748 + 0.496662i
\(549\) −142.000 + 245.951i −0.0110390 + 0.0191201i
\(550\) −225.000 −0.0174437
\(551\) 1273.00 11024.5i 0.0984240 0.852377i
\(552\) 6900.00 0.532035
\(553\) 8096.00 14022.7i 0.622562 1.07831i
\(554\) 2507.00 4342.25i 0.192260 0.333005i
\(555\) −2950.00 5109.55i −0.225623 0.390790i
\(556\) −2922.50 + 5061.92i −0.222917 + 0.386103i
\(557\) 7956.00 + 13780.2i 0.605218 + 1.04827i 0.992017 + 0.126105i \(0.0402475\pi\)
−0.386799 + 0.922164i \(0.626419\pi\)
\(558\) −504.000 −0.0382366
\(559\) 26784.0 2.02655
\(560\) −2255.00 3905.77i −0.170163 0.294731i
\(561\) −1215.00 2104.44i −0.0914391 0.158377i
\(562\) 3865.00 0.290098
\(563\) 1533.00 0.114757 0.0573785 0.998352i \(-0.481726\pi\)
0.0573785 + 0.998352i \(0.481726\pi\)
\(564\) −8785.00 15216.1i −0.655878 1.13601i
\(565\) −2647.50 + 4585.60i −0.197135 + 0.341447i
\(566\) −296.500 513.553i −0.0220191 0.0381382i
\(567\) 7381.00 12784.3i 0.546689 0.946894i
\(568\) 7305.00 12652.6i 0.539632 0.934670i
\(569\) −16070.0 −1.18399 −0.591994 0.805942i \(-0.701659\pi\)
−0.591994 + 0.805942i \(0.701659\pi\)
\(570\) −1662.50 1234.09i −0.122166 0.0906845i
\(571\) −8097.00 −0.593431 −0.296715 0.954966i \(-0.595891\pi\)
−0.296715 + 0.954966i \(0.595891\pi\)
\(572\) 1701.00 2946.22i 0.124340 0.215363i
\(573\) 8230.00 14254.8i 0.600023 1.03927i
\(574\) −2673.00 4629.77i −0.194371 0.336660i
\(575\) 1150.00 1991.86i 0.0834058 0.144463i
\(576\) −167.000 289.252i −0.0120804 0.0209239i
\(577\) 17927.0 1.29343 0.646716 0.762731i \(-0.276142\pi\)
0.646716 + 0.762731i \(0.276142\pi\)
\(578\) 1997.00 0.143710
\(579\) 4845.00 + 8391.79i 0.347757 + 0.602333i
\(580\) −2345.00 4061.66i −0.167881 0.290778i
\(581\) −1386.00 −0.0989690
\(582\) −5835.00 −0.415582
\(583\) −279.000 483.242i −0.0198199 0.0343291i
\(584\) −5212.50 + 9028.31i −0.369340 + 0.639716i
\(585\) 270.000 + 467.654i 0.0190823 + 0.0330515i
\(586\) −2919.00 + 5055.86i −0.205773 + 0.356409i
\(587\) 9904.00 17154.2i 0.696392 1.20619i −0.273318 0.961924i \(-0.588121\pi\)
0.969709 0.244262i \(-0.0785456\pi\)
\(588\) 4935.00 0.346116
\(589\) 16758.0 + 12439.6i 1.17233 + 0.870228i
\(590\) −3405.00 −0.237596
\(591\) 11310.0 19589.5i 0.787193 1.36346i
\(592\) 4838.00 8379.66i 0.335879 0.581760i
\(593\) 2790.50 + 4833.29i 0.193241 + 0.334704i 0.946323 0.323224i \(-0.104767\pi\)
−0.753081 + 0.657928i \(0.771433\pi\)
\(594\) 652.500 1130.16i 0.0450714 0.0780659i
\(595\) 2970.00 + 5144.19i 0.204636 + 0.354439i
\(596\) −19152.0 −1.31627
\(597\) −21410.0 −1.46776
\(598\) −2484.00 4302.41i −0.169863 0.294212i
\(599\) 12394.0 + 21467.0i 0.845418 + 1.46431i 0.885258 + 0.465100i \(0.153982\pi\)
−0.0398405 + 0.999206i \(0.512685\pi\)
\(600\) −1875.00 −0.127578
\(601\) −413.000 −0.0280310 −0.0140155 0.999902i \(-0.504461\pi\)
−0.0140155 + 0.999902i \(0.504461\pi\)
\(602\) 5456.00 + 9450.07i 0.369385 + 0.639794i
\(603\) 55.0000 95.2628i 0.00371438 0.00643350i
\(604\) −1316.00 2279.38i −0.0886544 0.153554i
\(605\) 3125.00 5412.66i 0.209999 0.363729i
\(606\) 75.0000 129.904i 0.00502750 0.00870789i
\(607\) −22778.0 −1.52311 −0.761557 0.648098i \(-0.775565\pi\)
−0.761557 + 0.648098i \(0.775565\pi\)
\(608\) 1529.50 13245.9i 0.102022 0.883537i
\(609\) 14740.0 0.980780
\(610\) −355.000 + 614.878i −0.0235632 + 0.0408126i
\(611\) −13554.0 + 23476.2i −0.897441 + 1.55441i
\(612\) 378.000 + 654.715i 0.0249669 + 0.0432439i
\(613\) 4729.00 8190.87i 0.311586 0.539684i −0.667120 0.744951i \(-0.732473\pi\)
0.978706 + 0.205267i \(0.0658063\pi\)
\(614\) 123.500 + 213.908i 0.00811735 + 0.0140597i
\(615\) 6075.00 0.398321
\(616\) 2970.00 0.194261
\(617\) 6314.50 + 10937.0i 0.412013 + 0.713628i 0.995110 0.0987749i \(-0.0314924\pi\)
−0.583097 + 0.812403i \(0.698159\pi\)
\(618\) 1505.00 + 2606.74i 0.0979611 + 0.169674i
\(619\) −4984.00 −0.323625 −0.161812 0.986822i \(-0.551734\pi\)
−0.161812 + 0.986822i \(0.551734\pi\)
\(620\) 8820.00 0.571322
\(621\) 6670.00 + 11552.8i 0.431011 + 0.746533i
\(622\) −5110.00 + 8850.78i −0.329409 + 0.570553i
\(623\) −7986.00 13832.2i −0.513567 0.889524i
\(624\) 5535.00 9586.90i 0.355092 0.615037i
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 7835.00 0.500239
\(627\) −3420.00 + 1480.90i −0.217834 + 0.0943247i
\(628\) 6944.00 0.441235
\(629\) −6372.00 + 11036.6i −0.403924 + 0.699617i
\(630\) −110.000 + 190.526i −0.00695636 + 0.0120488i
\(631\) 3077.00 + 5329.52i 0.194126 + 0.336236i 0.946614 0.322370i \(-0.104480\pi\)
−0.752488 + 0.658606i \(0.771146\pi\)
\(632\) 5520.00 9560.92i 0.347427 0.601761i
\(633\) −4850.00 8400.45i −0.304534 0.527469i
\(634\) 3774.00 0.236411
\(635\) 590.000 0.0368716
\(636\) −1085.00 1879.28i −0.0676463 0.117167i
\(637\) −3807.00 6593.92i −0.236796 0.410142i
\(638\) 1206.00 0.0748370
\(639\) 1948.00 0.120597
\(640\) −3637.50 6300.33i −0.224664 0.389129i
\(641\) −1350.50 + 2339.13i −0.0832161 + 0.144135i −0.904630 0.426198i \(-0.859853\pi\)
0.821414 + 0.570333i \(0.193186\pi\)
\(642\) −1650.00 2857.88i −0.101433 0.175688i
\(643\) 996.500 1725.99i 0.0611168 0.105857i −0.833848 0.551994i \(-0.813867\pi\)
0.894965 + 0.446137i \(0.147200\pi\)
\(644\) −7084.00 + 12269.8i −0.433461 + 0.750776i
\(645\) −12400.0 −0.756976
\(646\) −513.000 + 4442.71i −0.0312441 + 0.270582i
\(647\) 15638.0 0.950221 0.475111 0.879926i \(-0.342408\pi\)
0.475111 + 0.879926i \(0.342408\pi\)
\(648\) 5032.50 8716.55i 0.305085 0.528423i
\(649\) −3064.50 + 5307.87i −0.185350 + 0.321036i
\(650\) 675.000 + 1169.13i 0.0407318 + 0.0705496i
\(651\) −13860.0 + 24006.2i −0.834434 + 1.44528i
\(652\) 10664.5 + 18471.5i 0.640574 + 1.10951i
\(653\) 3180.00 0.190571 0.0952856 0.995450i \(-0.469624\pi\)
0.0952856 + 0.995450i \(0.469624\pi\)
\(654\) −600.000 −0.0358744
\(655\) −1667.50 2888.19i −0.0994727 0.172292i
\(656\) 4981.50 + 8628.21i 0.296486 + 0.513529i
\(657\) −1390.00 −0.0825404
\(658\) −11044.0 −0.654316
\(659\) −150.000 259.808i −0.00886672 0.0153576i 0.861558 0.507659i \(-0.169489\pi\)
−0.870425 + 0.492302i \(0.836156\pi\)
\(660\) −787.500 + 1363.99i −0.0464445 + 0.0804443i
\(661\) −895.000 1550.19i −0.0526648 0.0912182i 0.838491 0.544915i \(-0.183438\pi\)
−0.891156 + 0.453697i \(0.850105\pi\)
\(662\) −2.50000 + 4.33013i −0.000146775 + 0.000254222i
\(663\) −7290.00 + 12626.7i −0.427029 + 0.739636i
\(664\) −945.000 −0.0552306
\(665\) 8360.00 3619.99i 0.487499 0.211093i
\(666\) −472.000 −0.0274619
\(667\) −6164.00 + 10676.4i −0.357828 + 0.619776i
\(668\) −4564.00 + 7905.08i −0.264351 + 0.457869i
\(669\) −10390.0 17996.0i −0.600449 1.04001i
\(670\) 137.500 238.157i 0.00792849 0.0137325i
\(671\) 639.000 + 1106.78i 0.0367635 + 0.0636763i
\(672\) 17710.0 1.01663
\(673\) −13830.0 −0.792136 −0.396068 0.918221i \(-0.629625\pi\)
−0.396068 + 0.918221i \(0.629625\pi\)
\(674\) −3178.50 5505.32i −0.181649 0.314625i
\(675\) −1812.50 3139.34i −0.103353 0.179012i
\(676\) −5033.00 −0.286356
\(677\) −6090.00 −0.345728 −0.172864 0.984946i \(-0.555302\pi\)
−0.172864 + 0.984946i \(0.555302\pi\)
\(678\) −2647.50 4585.60i −0.149966 0.259748i
\(679\) 12837.0 22234.3i 0.725536 1.25666i
\(680\) 2025.00 + 3507.40i 0.114199 + 0.197798i
\(681\) 5232.50 9062.96i 0.294434 0.509975i
\(682\) −1134.00 + 1964.15i −0.0636702 + 0.110280i
\(683\) −21180.0 −1.18657 −0.593287 0.804991i \(-0.702170\pi\)
−0.593287 + 0.804991i \(0.702170\pi\)
\(684\) 1064.00 460.726i 0.0594782 0.0257548i
\(685\) −5255.00 −0.293114
\(686\) −2222.00 + 3848.62i −0.123668 + 0.214200i
\(687\) −10780.0 + 18671.5i −0.598665 + 1.03692i
\(688\) −10168.0 17611.5i −0.563447 0.975918i
\(689\) −1674.00 + 2899.45i −0.0925607 + 0.160320i
\(690\) 1150.00 + 1991.86i 0.0634489 + 0.109897i
\(691\) −14812.0 −0.815449 −0.407724 0.913105i \(-0.633678\pi\)
−0.407724 + 0.913105i \(0.633678\pi\)
\(692\) −1386.00 −0.0761385
\(693\) 198.000 + 342.946i 0.0108534 + 0.0187986i
\(694\) −6279.50 10876.4i −0.343468 0.594903i
\(695\) −4175.00 −0.227866
\(696\) 10050.0 0.547334
\(697\) −6561.00 11364.0i −0.356550 0.617563i
\(698\) 3668.00 6353.16i 0.198905 0.344514i
\(699\) −10572.5 18312.1i −0.572087 0.990883i
\(700\) 1925.00 3334.20i 0.103940 0.180030i
\(701\) −16593.0 + 28739.9i −0.894021 + 1.54849i −0.0590102 + 0.998257i \(0.518794\pi\)
−0.835011 + 0.550233i \(0.814539\pi\)
\(702\) −7830.00 −0.420975
\(703\) 15694.0 + 11649.8i 0.841978 + 0.625006i
\(704\) −1503.00 −0.0804637
\(705\) 6275.00 10868.6i 0.335220 0.580618i
\(706\) 5225.50 9050.83i 0.278561 0.482482i
\(707\) 330.000 + 571.577i 0.0175544 + 0.0304050i
\(708\) −11917.5 + 20641.7i −0.632609 + 1.09571i
\(709\) −15620.0 27054.6i −0.827393 1.43309i −0.900077 0.435731i \(-0.856490\pi\)
0.0726842 0.997355i \(-0.476843\pi\)
\(710\) 4870.00 0.257419
\(711\) 1472.00 0.0776432
\(712\) −5445.00 9431.02i −0.286601 0.496408i
\(713\) −11592.0 20077.9i −0.608869 1.05459i
\(714\) −5940.00 −0.311343
\(715\) 2430.00 0.127100
\(716\) −4427.50 7668.65i −0.231094 0.400267i
\(717\) −13890.0 + 24058.2i −0.723475 + 1.25310i
\(718\) 3650.00 + 6321.99i 0.189717 + 0.328599i
\(719\) −7113.00 + 12320.1i −0.368943 + 0.639028i −0.989401 0.145212i \(-0.953614\pi\)
0.620457 + 0.784240i \(0.286947\pi\)
\(720\) 205.000 355.070i 0.0106110 0.0183787i
\(721\) −13244.0 −0.684095
\(722\) 6678.50 + 1563.18i 0.344249 + 0.0805753i
\(723\) 22095.0 1.13654
\(724\) −14266.0 + 24709.4i −0.732309 + 1.26840i
\(725\) 1675.00 2901.19i 0.0858041 0.148617i
\(726\) 3125.00 + 5412.66i 0.159752 + 0.276698i
\(727\) −5188.00 + 8985.88i −0.264666 + 0.458415i −0.967476 0.252962i \(-0.918595\pi\)
0.702810 + 0.711378i \(0.251928\pi\)
\(728\) −8910.00 15432.6i −0.453608 0.785672i
\(729\) 20917.0 1.06269
\(730\) −3475.00 −0.176186
\(731\) 13392.0 + 23195.6i 0.677594 + 1.17363i
\(732\) 2485.00 + 4304.15i 0.125476 + 0.217330i
\(733\) −21868.0 −1.10193 −0.550964 0.834529i \(-0.685740\pi\)
−0.550964 + 0.834529i \(0.685740\pi\)
\(734\) 632.000 0.0317814
\(735\) 1762.50 + 3052.74i 0.0884501 + 0.153200i
\(736\) −7406.00 + 12827.6i −0.370909 + 0.642433i
\(737\) −247.500 428.683i −0.0123701 0.0214257i
\(738\) 243.000 420.888i 0.0121205 0.0209934i
\(739\) 10535.5 18248.0i 0.524431 0.908341i −0.475164 0.879897i \(-0.657611\pi\)
0.999595 0.0284443i \(-0.00905532\pi\)
\(740\) 8260.00 0.410329
\(741\) 17955.0 + 13328.1i 0.890140 + 0.660757i
\(742\) −1364.00 −0.0674852
\(743\) 7200.00 12470.8i 0.355508 0.615758i −0.631697 0.775216i \(-0.717641\pi\)
0.987205 + 0.159458i \(0.0509746\pi\)
\(744\) −9450.00 + 16367.9i −0.465664 + 0.806553i
\(745\) −6840.00 11847.2i −0.336373 0.582616i
\(746\) −48.0000 + 83.1384i −0.00235577 + 0.00408031i
\(747\) −63.0000 109.119i −0.00308574 0.00534466i
\(748\) 3402.00 0.166296
\(749\) 14520.0 0.708343
\(750\) −312.500 541.266i −0.0152145 0.0263523i
\(751\) −17293.0 29952.4i −0.840254 1.45536i −0.889680 0.456584i \(-0.849073\pi\)
0.0494264 0.998778i \(-0.484261\pi\)
\(752\) 20582.0 0.998070
\(753\) 19785.0 0.957511
\(754\) −3618.00 6266.56i −0.174748 0.302672i
\(755\) 940.000 1628.13i 0.0453114 0.0784816i
\(756\) 11165.0 + 19338.3i 0.537126 + 0.930329i
\(757\) 2839.00 4917.29i 0.136308 0.236093i −0.789788 0.613380i \(-0.789810\pi\)
0.926096 + 0.377287i \(0.123143\pi\)
\(758\) 5482.00 9495.10i 0.262685 0.454984i
\(759\) 4140.00 0.197987
\(760\) 5700.00 2468.17i 0.272054 0.117803i
\(761\) −12243.0 −0.583191 −0.291596 0.956542i \(-0.594186\pi\)
−0.291596 + 0.956542i \(0.594186\pi\)
\(762\) −295.000 + 510.955i −0.0140246 + 0.0242913i
\(763\) 1320.00 2286.31i 0.0626307 0.108480i
\(764\) 11522.0 + 19956.7i 0.545617 + 0.945036i
\(765\) −270.000 + 467.654i −0.0127606 + 0.0221020i
\(766\) 1009.00 + 1747.64i 0.0475935 + 0.0824344i
\(767\) 36774.0 1.73120
\(768\) 595.000 0.0279560
\(769\) 15625.0 + 27063.3i 0.732707 + 1.26909i 0.955722 + 0.294271i \(0.0950769\pi\)
−0.223015 + 0.974815i \(0.571590\pi\)
\(770\) 495.000 + 857.365i 0.0231670 + 0.0401264i
\(771\) 4385.00 0.204827
\(772\) −13566.0 −0.632450
\(773\) −15021.0 26017.1i −0.698923 1.21057i −0.968840 0.247687i \(-0.920329\pi\)
0.269917 0.962884i \(-0.413004\pi\)
\(774\) −496.000 + 859.097i −0.0230340 + 0.0398961i
\(775\) 3150.00 + 5455.96i 0.146002 + 0.252882i
\(776\) 8752.50 15159.8i 0.404892 0.701294i
\(777\) −12980.0 + 22482.0i −0.599298 + 1.03802i
\(778\) −8728.00 −0.402203
\(779\) −18468.0 + 7996.88i −0.849403 + 0.367802i
\(780\) 9450.00 0.433800
\(781\) 4383.00 7591.58i 0.200814 0.347821i
\(782\) 2484.00 4302.41i 0.113590 0.196744i
\(783\) 9715.00 + 16826.9i 0.443405 + 0.767999i
\(784\) −2890.50 + 5006.49i −0.131674 + 0.228065i
\(785\) 2480.00 + 4295.49i 0.112758 + 0.195303i
\(786\) 3335.00 0.151343
\(787\) −43141.0 −1.95402 −0.977008 0.213203i \(-0.931611\pi\)
−0.977008 + 0.213203i \(0.931611\pi\)
\(788\) 15834.0 + 27425.3i 0.715816 + 1.23983i
\(789\) −6075.00 10522.2i −0.274114 0.474779i
\(790\) 3680.00 0.165732
\(791\) 23298.0 1.04726
\(792\) 135.000 + 233.827i 0.00605684 + 0.0104908i
\(793\) 3834.00 6640.68i 0.171689 0.297374i
\(794\) 4782.00 + 8282.67i 0.213737 + 0.370203i
\(795\) 775.000 1342.34i 0.0345741 0.0598841i
\(796\) 14987.0 25958.2i 0.667337 1.15586i
\(797\) 8008.00 0.355907 0.177954 0.984039i \(-0.443052\pi\)
0.177954 + 0.984039i \(0.443052\pi\)
\(798\) −1045.00 + 9049.97i −0.0463566 + 0.401460i
\(799\) −27108.0 −1.20027
\(800\) 2012.50 3485.75i 0.0889408 0.154050i
\(801\) 726.000 1257.47i 0.0320249 0.0554688i
\(802\) −2933.50 5080.97i −0.129159 0.223710i
\(803\) −3127.50 + 5416.99i −0.137443 + 0.238059i
\(804\) −962.500 1667.10i −0.0422198 0.0731269i
\(805\) −10120.0 −0.443085
\(806\) 13608.0 0.594692
\(807\) 11730.0 + 20317.0i 0.511667 + 0.886234i
\(808\) 225.000 + 389.711i 0.00979638 + 0.0169678i
\(809\) 9053.00 0.393432 0.196716 0.980461i \(-0.436972\pi\)
0.196716 + 0.980461i \(0.436972\pi\)
\(810\) 3355.00 0.145534
\(811\) 1478.00 + 2559.97i 0.0639946 + 0.110842i 0.896248 0.443554i \(-0.146283\pi\)
−0.832253 + 0.554396i \(0.812949\pi\)
\(812\) −10318.0 + 17871.3i −0.445925 + 0.772364i
\(813\) −21905.0 37940.6i −0.944947 1.63670i
\(814\) −1062.00 + 1839.44i −0.0457286 + 0.0792043i
\(815\) −7617.50 + 13193.9i −0.327398 + 0.567070i
\(816\) 11070.0 0.474911
\(817\) 37696.0 16322.8i 1.61422 0.698977i
\(818\) 835.000 0.0356908
\(819\) 1188.00 2057.68i 0.0506863 0.0877912i
\(820\) −4252.50 + 7365.55i −0.181102 + 0.313678i
\(821\) −9453.00 16373.1i −0.401842 0.696010i 0.592107 0.805860i \(-0.298296\pi\)
−0.993948 + 0.109850i \(0.964963\pi\)
\(822\) 2627.50 4550.96i 0.111490 0.193106i
\(823\) 7375.00 + 12773.9i 0.312365 + 0.541032i 0.978874 0.204465i \(-0.0655455\pi\)
−0.666509 + 0.745497i \(0.732212\pi\)
\(824\) −9030.00 −0.381766
\(825\) −1125.00 −0.0474757
\(826\) 7491.00 + 12974.8i 0.315551 + 0.546551i
\(827\) −19543.5 33850.3i −0.821758 1.42333i −0.904372 0.426745i \(-0.859660\pi\)
0.0826135 0.996582i \(-0.473673\pi\)
\(828\) −1288.00 −0.0540593
\(829\) 168.000 0.00703846 0.00351923 0.999994i \(-0.498880\pi\)
0.00351923 + 0.999994i \(0.498880\pi\)
\(830\) −157.500 272.798i −0.00658663 0.0114084i
\(831\) 12535.0 21711.3i 0.523266 0.906324i
\(832\) 4509.00 + 7809.82i 0.187886 + 0.325429i
\(833\) 3807.00 6593.92i 0.158349 0.274269i
\(834\) 2087.50 3615.66i 0.0866717 0.150120i
\(835\) −6520.00 −0.270220
\(836\) 598.500 5183.16i 0.0247602 0.214430i
\(837\) −36540.0 −1.50897
\(838\) 378.000 654.715i 0.0155821 0.0269890i
\(839\) 15329.0 26550.6i 0.630770 1.09253i −0.356625 0.934248i \(-0.616073\pi\)
0.987395 0.158278i \(-0.0505941\pi\)
\(840\) 4125.00 + 7144.71i 0.169436 + 0.293471i
\(841\) 3216.50 5571.14i 0.131883 0.228428i
\(842\) −1950.00 3377.50i −0.0798117 0.138238i
\(843\) 19325.0 0.789547
\(844\) 13580.0 0.553842
\(845\) −1797.50 3113.36i −0.0731786 0.126749i
\(846\) −502.000 869.490i −0.0204008 0.0353353i
\(847\) −27500.0 −1.11560
\(848\) 2542.00 0.102939
\(849\) −1482.50 2567.77i −0.0599285 0.103799i
\(850\) −675.000 + 1169.13i −0.0272380 + 0.0471776i
\(851\) −10856.0 18803.1i −0.437296 0.757419i
\(852\) 17045.0 29522.8i 0.685390 1.18713i
\(853\) 14909.0 25823.1i 0.598446 1.03654i −0.394605 0.918851i \(-0.629118\pi\)
0.993051 0.117688i \(-0.0375482\pi\)
\(854\) 3124.00 0.125177
\(855\) 665.000 + 493.634i 0.0265994 + 0.0197450i
\(856\) 9900.00 0.395298
\(857\) 16235.5 28120.7i 0.647134 1.12087i −0.336670 0.941623i \(-0.609301\pi\)
0.983804 0.179247i \(-0.0573660\pi\)
\(858\) −1215.00 + 2104.44i −0.0483443 + 0.0837348i
\(859\) 17910.5 + 31021.9i 0.711407 + 1.23219i 0.964329 + 0.264706i \(0.0852749\pi\)
−0.252922 + 0.967487i \(0.581392\pi\)
\(860\) 8680.00 15034.2i 0.344169 0.596119i
\(861\) −13365.0 23148.9i −0.529010 0.916273i
\(862\) −14706.0 −0.581077
\(863\) 39300.0 1.55016 0.775080 0.631863i \(-0.217710\pi\)
0.775080 + 0.631863i \(0.217710\pi\)
\(864\) 11672.5 + 20217.4i 0.459614 + 0.796075i
\(865\) −495.000 857.365i −0.0194572 0.0337009i
\(866\) −7838.00 −0.307559
\(867\) 9985.00 0.391128
\(868\) −19404.0 33608.7i −0.758773 1.31423i
\(869\) 3312.00 5736.55i 0.129289 0.223935i
\(870\) 1675.00 + 2901.19i 0.0652734 + 0.113057i
\(871\) −1485.00 + 2572.10i −0.0577696 + 0.100060i
\(872\) 900.000 1558.85i 0.0349517 0.0605380i
\(873\) 2334.00 0.0904856
\(874\) −6118.00 4541.44i −0.236779 0.175762i
\(875\) 2750.00 0.106248
\(876\) −12162.5 + 21066.1i −0.469101 + 0.812507i
\(877\) −11427.0 + 19792.1i −0.439980 + 0.762068i −0.997687 0.0679700i \(-0.978348\pi\)
0.557707 + 0.830038i \(0.311681\pi\)
\(878\) 8814.00 + 15266.3i 0.338791 + 0.586802i
\(879\) −14595.0 + 25279.3i −0.560042 + 0.970022i
\(880\) −922.500 1597.82i −0.0353380 0.0612073i
\(881\) 25347.0 0.969310 0.484655 0.874705i \(-0.338945\pi\)
0.484655 + 0.874705i \(0.338945\pi\)
\(882\) 282.000 0.0107658
\(883\) 7434.50 + 12876.9i 0.283342 + 0.490762i 0.972206 0.234128i \(-0.0752236\pi\)
−0.688864 + 0.724891i \(0.741890\pi\)
\(884\) −10206.0 17677.3i −0.388309 0.672570i
\(885\) −17025.0 −0.646654
\(886\) −9267.00 −0.351389
\(887\) 4026.00 + 6973.24i 0.152401 + 0.263967i 0.932110 0.362176i \(-0.117966\pi\)
−0.779709 + 0.626143i \(0.784633\pi\)
\(888\) −8850.00 + 15328.6i −0.334444 + 0.579275i
\(889\) −1298.00 2248.20i −0.0489691 0.0848170i
\(890\) 1815.00 3143.67i 0.0683584 0.118400i
\(891\) 3019.50 5229.93i 0.113532 0.196643i
\(892\) 29092.0 1.09201
\(893\) −4769.00 + 41300.8i −0.178711 + 1.54768i
\(894\) 13680.0 0.511776
\(895\) 3162.50 5477.61i 0.118113 0.204577i
\(896\) −16005.0 + 27721.5i −0.596752 + 1.03360i
\(897\) −12420.0 21512.1i −0.462310 0.800744i
\(898\) −4685.50 + 8115.52i −0.174117 + 0.301580i
\(899\) −16884.0 29243.9i −0.626377 1.08492i
\(900\) 350.000 0.0129630
\(901\) −3348.00 −0.123794
\(902\) −1093.50 1894.00i −0.0403654 0.0699149i
\(903\) 27280.0 + 47250.3i 1.00534 + 1.74130i
\(904\) 15885.0 0.584433
\(905\) −20380.0 −0.748568
\(906\) 940.000 + 1628.13i 0.0344695 + 0.0597030i
\(907\) 2310.50 4001.90i 0.0845853 0.146506i −0.820629 0.571461i \(-0.806377\pi\)
0.905214 + 0.424955i \(0.139710\pi\)
\(908\) 7325.50 + 12688.1i 0.267737 + 0.463734i
\(909\) −30.0000 + 51.9615i −0.00109465 + 0.00189599i
\(910\) 2970.00 5144.19i 0.108192 0.187394i
\(911\) −41004.0 −1.49124 −0.745622 0.666369i \(-0.767847\pi\)
−0.745622 + 0.666369i \(0.767847\pi\)
\(912\) 1947.50 16865.8i 0.0707107 0.612373i
\(913\) −567.000 −0.0205531
\(914\) −2053.50 + 3556.77i −0.0743148 + 0.128717i
\(915\) −1775.00 + 3074.39i −0.0641308 + 0.111078i
\(916\) −15092.0 26140.1i −0.544382 0.942897i
\(917\) −7337.00 + 12708.1i −0.264219 + 0.457641i
\(918\) −3915.00 6780.98i −0.140756 0.243797i
\(919\) −45946.0 −1.64920 −0.824602 0.565713i \(-0.808601\pi\)
−0.824602 + 0.565713i \(0.808601\pi\)
\(920\) −6900.00 −0.247268
\(921\) 617.500 + 1069.54i 0.0220926 + 0.0382656i
\(922\) −2715.00 4702.52i −0.0969781 0.167971i
\(923\) −52596.0 −1.87564
\(924\) 6930.00 0.246732
\(925\) 2950.00 + 5109.55i 0.104860 + 0.181623i
\(926\) −7111.00 + 12316.6i −0.252356 + 0.437094i
\(927\) −602.000 1042.69i −0.0213293 0.0369435i
\(928\) −10787.0 + 18683.6i −0.381574 + 0.660905i
\(929\) 23305.5 40366.3i 0.823066 1.42559i −0.0803218 0.996769i \(-0.525595\pi\)
0.903388 0.428824i \(-0.141072\pi\)
\(930\) −6300.00 −0.222135
\(931\) −9376.50 6960.25i −0.330078 0.245019i
\(932\) 29603.0 1.04043
\(933\) −25550.0 + 44253.9i −0.896537 + 1.55285i
\(934\) −1942.50 + 3364.51i −0.0680520 + 0.117869i
\(935\) 1215.00 + 2104.44i 0.0424971 + 0.0736071i
\(936\) 810.000 1402.96i 0.0282860 0.0489928i
\(937\) 16678.5 + 28888.0i 0.581497 + 1.00718i 0.995302 + 0.0968171i \(0.0308662\pi\)
−0.413805 + 0.910366i \(0.635800\pi\)
\(938\) −1210.00 −0.0421193
\(939\) 39175.0 1.36148
\(940\) 8785.00 + 15216.1i 0.304825 + 0.527972i
\(941\) 20945.0 + 36277.8i 0.725598 + 1.25677i 0.958728 + 0.284327i \(0.0917700\pi\)
−0.233130 + 0.972446i \(0.574897\pi\)
\(942\) −4960.00 −0.171556
\(943\) 22356.0 0.772016
\(944\) −13960.5 24180.3i −0.481330 0.833688i
\(945\) −7975.00 + 13813.1i −0.274526 + 0.475492i
\(946\) 2232.00 + 3865.94i 0.0767110 + 0.132867i
\(947\) 5982.00 10361.1i 0.205268 0.355535i −0.744950 0.667120i \(-0.767527\pi\)
0.950218 + 0.311586i \(0.100860\pi\)
\(948\) 12880.0 22308.8i 0.441269 0.764300i
\(949\) 37530.0 1.28375
\(950\) 1662.50 + 1234.09i 0.0567775 + 0.0421464i
\(951\) 18870.0 0.643430
\(952\) 8910.00 15432.6i 0.303335 0.525391i
\(953\) −5536.50 + 9589.50i −0.188190 + 0.325954i −0.944647 0.328089i \(-0.893595\pi\)
0.756457 + 0.654043i \(0.226929\pi\)
\(954\) −62.0000 107.387i −0.00210411 0.00364443i
\(955\) −8230.00 + 14254.8i −0.278865 + 0.483009i
\(956\) −19446.0 33681.5i −0.657875 1.13947i
\(957\) 6030.00 0.203680
\(958\) −4380.00 −0.147715
\(959\) 11561.0 + 20024.2i 0.389285 + 0.674261i
\(960\) −2087.50 3615.66i −0.0701810 0.121557i
\(961\) 33713.0 1.13165
\(962\) 12744.0 0.427113
\(963\) 660.000 + 1143.15i 0.0220854 + 0.0382530i
\(964\) −15466.5 + 26788.8i −0.516745 + 0.895029i
\(965\) −4845.00 8391.79i −0.161623 0.279939i
\(966\) 5060.00 8764.18i 0.168533 0.291908i
\(967\) 7123.00 12337.4i 0.236877 0.410283i −0.722939 0.690911i \(-0.757209\pi\)
0.959817 + 0.280628i \(0.0905428\pi\)
\(968\) −18750.0 −0.622570
\(969\) −2565.00 + 22213.6i −0.0850358 + 0.736431i
\(970\) 5835.00 0.193145
\(971\) −15705.5 + 27202.7i −0.519066 + 0.899049i 0.480688 + 0.876892i \(0.340387\pi\)
−0.999754 + 0.0221577i \(0.992946\pi\)
\(972\) −1960.00 + 3394.82i −0.0646780 + 0.112026i
\(973\) 9185.00 + 15908.9i 0.302629 + 0.524168i
\(974\) −9428.00 + 16329.8i −0.310157 + 0.537207i
\(975\) 3375.00 + 5845.67i 0.110858 + 0.192012i
\(976\) −5822.00 −0.190940
\(977\) 18657.0 0.610942 0.305471 0.952201i \(-0.401186\pi\)
0.305471 + 0.952201i \(0.401186\pi\)
\(978\) −7617.50 13193.9i −0.249060 0.431385i
\(979\) −3267.00 5658.61i −0.106653 0.184729i
\(980\) −4935.00 −0.160860
\(981\) 240.000 0.00781102
\(982\) 794.000 + 1375.25i 0.0258020 + 0.0446904i
\(983\) 28706.0 49720.3i 0.931413 1.61326i 0.150505 0.988609i \(-0.451910\pi\)
0.780908 0.624646i \(-0.214757\pi\)
\(984\) −9112.50 15783.3i −0.295219 0.511335i
\(985\) −11310.0 + 19589.5i −0.365854 + 0.633678i
\(986\) 3618.00 6266.56i 0.116857 0.202402i
\(987\) −55220.0 −1.78082
\(988\) −28728.0 + 12439.6i −0.925060 + 0.400563i
\(989\) −45632.0 −1.46715
\(990\) −45.0000 + 77.9423i −0.00144464 + 0.00250219i
\(991\) −1312.00 + 2272.45i −0.0420556 + 0.0728424i −0.886287 0.463136i \(-0.846724\pi\)
0.844231 + 0.535979i \(0.180057\pi\)
\(992\) −20286.0 35136.4i −0.649275 1.12458i
\(993\) −12.5000 + 21.6506i −0.000399472 + 0.000691905i
\(994\) −10714.0 18557.2i −0.341879 0.592151i
\(995\) 21410.0 0.682153
\(996\) −2205.00 −0.0701487
\(997\) 6329.00 + 10962.1i 0.201045 + 0.348219i 0.948865 0.315681i \(-0.102233\pi\)
−0.747821 + 0.663901i \(0.768900\pi\)
\(998\) 5578.50 + 9662.25i 0.176938 + 0.306466i
\(999\) −34220.0 −1.08376
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 95.4.e.a.11.1 2
19.7 even 3 inner 95.4.e.a.26.1 yes 2
19.8 odd 6 1805.4.a.g.1.1 1
19.11 even 3 1805.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.4.e.a.11.1 2 1.1 even 1 trivial
95.4.e.a.26.1 yes 2 19.7 even 3 inner
1805.4.a.e.1.1 1 19.11 even 3
1805.4.a.g.1.1 1 19.8 odd 6