Properties

Label 38.6.e.a.5.4
Level $38$
Weight $6$
Character 38.5
Analytic conductor $6.095$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,6,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), 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: \(6.09458515289\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 38.5
Dual form 38.6.e.a.23.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.75877 - 1.36808i) q^{2} +(4.62861 - 26.2502i) q^{3} +(12.2567 - 10.2846i) q^{4} +(14.7431 + 12.3709i) q^{5} +(-18.5145 - 105.001i) q^{6} +(4.52908 + 7.84460i) q^{7} +(32.0000 - 55.4256i) q^{8} +(-439.302 - 159.893i) q^{9} +(72.3402 + 26.3297i) q^{10} +(-79.1353 + 137.066i) q^{11} +(-213.241 - 369.344i) q^{12} +(-12.8004 - 72.5945i) q^{13} +(27.7558 + 23.2899i) q^{14} +(392.978 - 329.748i) q^{15} +(44.4539 - 252.111i) q^{16} +(1772.70 - 645.211i) q^{17} -1869.98 q^{18} +(1207.77 + 1008.66i) q^{19} +307.931 q^{20} +(226.885 - 82.5795i) q^{21} +(-109.934 + 623.464i) q^{22} +(-2360.76 + 1980.91i) q^{23} +(-1306.82 - 1096.55i) q^{24} +(-478.332 - 2712.75i) q^{25} +(-147.429 - 255.354i) q^{26} +(-2991.98 + 5182.25i) q^{27} +(136.190 + 49.5692i) q^{28} +(6285.20 + 2287.62i) q^{29} +(1025.99 - 1777.07i) q^{30} +(3473.21 + 6015.78i) q^{31} +(-177.816 - 1008.44i) q^{32} +(3231.73 + 2711.74i) q^{33} +(5780.48 - 4850.40i) q^{34} +(-30.2722 + 171.682i) q^{35} +(-7028.83 + 2558.29i) q^{36} -10596.4 q^{37} +(5919.65 + 2139.01i) q^{38} -1964.86 q^{39} +(1157.44 - 421.275i) q^{40} +(1287.12 - 7299.63i) q^{41} +(739.834 - 620.795i) q^{42} +(7515.14 + 6305.95i) q^{43} +(439.734 + 2493.86i) q^{44} +(-4498.64 - 7791.88i) q^{45} +(-6163.50 + 10675.5i) q^{46} +(-7974.91 - 2902.63i) q^{47} +(-6412.19 - 2333.85i) q^{48} +(8362.47 - 14484.2i) q^{49} +(-5509.20 - 9542.22i) q^{50} +(-8731.74 - 49520.2i) q^{51} +(-903.495 - 758.123i) q^{52} +(-20682.6 + 17354.8i) q^{53} +(-4156.41 + 23572.2i) q^{54} +(-2862.33 + 1041.80i) q^{55} +579.722 q^{56} +(32067.8 - 27035.4i) q^{57} +26754.3 q^{58} +(-14404.4 + 5242.76i) q^{59} +(1425.30 - 8083.25i) q^{60} +(5949.25 - 4992.01i) q^{61} +(21285.1 + 17860.3i) q^{62} +(-735.339 - 4170.31i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(709.343 - 1228.62i) q^{65} +(15857.2 + 5771.55i) q^{66} +(-32752.5 - 11920.9i) q^{67} +(15091.8 - 26139.7i) q^{68} +(41072.2 + 71139.2i) q^{69} +(121.089 + 686.729i) q^{70} +(8827.63 + 7407.26i) q^{71} +(-22919.8 + 19232.0i) q^{72} +(-14590.3 + 82745.9i) q^{73} +(-39829.4 + 14496.7i) q^{74} -73424.3 q^{75} +(25176.9 - 58.5136i) q^{76} -1433.64 q^{77} +(-7385.47 + 2688.09i) q^{78} +(-14109.0 + 80016.3i) q^{79} +(3774.23 - 3166.95i) q^{80} +(35162.6 + 29505.0i) q^{81} +(-5148.49 - 29198.5i) q^{82} +(-32758.7 - 56739.7i) q^{83} +(1931.57 - 3345.58i) q^{84} +(34116.9 + 12417.5i) q^{85} +(36874.7 + 13421.3i) q^{86} +(89142.3 - 154399. i) q^{87} +(5064.66 + 8772.24i) q^{88} +(3382.52 + 19183.2i) q^{89} +(-27569.3 - 23133.4i) q^{90} +(511.500 - 429.200i) q^{91} +(-8562.25 + 48558.9i) q^{92} +(173991. - 63327.7i) q^{93} -33946.9 q^{94} +(5328.12 + 29811.9i) q^{95} -27294.8 q^{96} +(-104024. + 37861.5i) q^{97} +(11617.0 - 65883.4i) q^{98} +(56680.2 - 47560.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22}+ \cdots + 656436 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.75877 1.36808i 0.664463 0.241845i
\(3\) 4.62861 26.2502i 0.296926 1.68395i −0.362346 0.932044i \(-0.618024\pi\)
0.659271 0.751905i \(-0.270865\pi\)
\(4\) 12.2567 10.2846i 0.383022 0.321394i
\(5\) 14.7431 + 12.3709i 0.263732 + 0.221298i 0.765059 0.643961i \(-0.222710\pi\)
−0.501326 + 0.865258i \(0.667154\pi\)
\(6\) −18.5145 105.001i −0.209958 1.19073i
\(7\) 4.52908 + 7.84460i 0.0349353 + 0.0605098i 0.882964 0.469440i \(-0.155544\pi\)
−0.848029 + 0.529950i \(0.822211\pi\)
\(8\) 32.0000 55.4256i 0.176777 0.306186i
\(9\) −439.302 159.893i −1.80783 0.657995i
\(10\) 72.3402 + 26.3297i 0.228760 + 0.0832618i
\(11\) −79.1353 + 137.066i −0.197192 + 0.341546i −0.947617 0.319410i \(-0.896515\pi\)
0.750425 + 0.660955i \(0.229849\pi\)
\(12\) −213.241 369.344i −0.427482 0.740420i
\(13\) −12.8004 72.5945i −0.0210070 0.119137i 0.972501 0.232899i \(-0.0748210\pi\)
−0.993508 + 0.113762i \(0.963710\pi\)
\(14\) 27.7558 + 23.2899i 0.0378472 + 0.0317576i
\(15\) 392.978 329.748i 0.450963 0.378403i
\(16\) 44.4539 252.111i 0.0434120 0.246202i
\(17\) 1772.70 645.211i 1.48769 0.541476i 0.534853 0.844945i \(-0.320367\pi\)
0.952841 + 0.303469i \(0.0981449\pi\)
\(18\) −1869.98 −1.36037
\(19\) 1207.77 + 1008.66i 0.767536 + 0.641006i
\(20\) 307.931 0.172139
\(21\) 226.885 82.5795i 0.112269 0.0408624i
\(22\) −109.934 + 623.464i −0.0484254 + 0.274634i
\(23\) −2360.76 + 1980.91i −0.930533 + 0.780810i −0.975913 0.218160i \(-0.929995\pi\)
0.0453798 + 0.998970i \(0.485550\pi\)
\(24\) −1306.82 1096.55i −0.463112 0.388597i
\(25\) −478.332 2712.75i −0.153066 0.868081i
\(26\) −147.429 255.354i −0.0427709 0.0740814i
\(27\) −2991.98 + 5182.25i −0.789857 + 1.36807i
\(28\) 136.190 + 49.5692i 0.0328285 + 0.0119486i
\(29\) 6285.20 + 2287.62i 1.38779 + 0.505114i 0.924530 0.381108i \(-0.124457\pi\)
0.463260 + 0.886223i \(0.346680\pi\)
\(30\) 1025.99 1777.07i 0.208133 0.360497i
\(31\) 3473.21 + 6015.78i 0.649123 + 1.12431i 0.983333 + 0.181816i \(0.0581974\pi\)
−0.334209 + 0.942499i \(0.608469\pi\)
\(32\) −177.816 1008.44i −0.0306970 0.174091i
\(33\) 3231.73 + 2711.74i 0.516595 + 0.433474i
\(34\) 5780.48 4850.40i 0.857564 0.719582i
\(35\) −30.2722 + 171.682i −0.00417709 + 0.0236895i
\(36\) −7028.83 + 2558.29i −0.903914 + 0.328998i
\(37\) −10596.4 −1.27249 −0.636243 0.771489i \(-0.719513\pi\)
−0.636243 + 0.771489i \(0.719513\pi\)
\(38\) 5919.65 + 2139.01i 0.665023 + 0.240300i
\(39\) −1964.86 −0.206857
\(40\) 1157.44 421.275i 0.114380 0.0416309i
\(41\) 1287.12 7299.63i 0.119580 0.678174i −0.864800 0.502117i \(-0.832555\pi\)
0.984380 0.176057i \(-0.0563343\pi\)
\(42\) 739.834 620.795i 0.0647159 0.0543031i
\(43\) 7515.14 + 6305.95i 0.619820 + 0.520091i 0.897747 0.440511i \(-0.145203\pi\)
−0.277927 + 0.960602i \(0.589647\pi\)
\(44\) 439.734 + 2493.86i 0.0342420 + 0.194196i
\(45\) −4498.64 7791.88i −0.331169 0.573602i
\(46\) −6163.50 + 10675.5i −0.429470 + 0.743864i
\(47\) −7974.91 2902.63i −0.526601 0.191667i 0.0650192 0.997884i \(-0.479289\pi\)
−0.591620 + 0.806217i \(0.701511\pi\)
\(48\) −6412.19 2333.85i −0.401701 0.146207i
\(49\) 8362.47 14484.2i 0.497559 0.861798i
\(50\) −5509.20 9542.22i −0.311648 0.539790i
\(51\) −8731.74 49520.2i −0.470084 2.66598i
\(52\) −903.495 758.123i −0.0463359 0.0388804i
\(53\) −20682.6 + 17354.8i −1.01138 + 0.848653i −0.988521 0.151086i \(-0.951723\pi\)
−0.0228643 + 0.999739i \(0.507279\pi\)
\(54\) −4156.41 + 23572.2i −0.193970 + 1.10006i
\(55\) −2862.33 + 1041.80i −0.127589 + 0.0464386i
\(56\) 579.722 0.0247030
\(57\) 32067.8 27035.4i 1.30732 1.10216i
\(58\) 26754.3 1.04429
\(59\) −14404.4 + 5242.76i −0.538721 + 0.196078i −0.597028 0.802220i \(-0.703652\pi\)
0.0583072 + 0.998299i \(0.481430\pi\)
\(60\) 1425.30 8083.25i 0.0511125 0.289873i
\(61\) 5949.25 4992.01i 0.204709 0.171771i −0.534669 0.845061i \(-0.679564\pi\)
0.739379 + 0.673290i \(0.235119\pi\)
\(62\) 21285.1 + 17860.3i 0.703228 + 0.590078i
\(63\) −735.339 4170.31i −0.0233419 0.132378i
\(64\) −2048.00 3547.24i −0.0625000 0.108253i
\(65\) 709.343 1228.62i 0.0208244 0.0360689i
\(66\) 15857.2 + 5771.55i 0.448091 + 0.163092i
\(67\) −32752.5 11920.9i −0.891369 0.324432i −0.144581 0.989493i \(-0.546183\pi\)
−0.746789 + 0.665061i \(0.768405\pi\)
\(68\) 15091.8 26139.7i 0.395793 0.685533i
\(69\) 41072.2 + 71139.2i 1.03855 + 1.79881i
\(70\) 121.089 + 686.729i 0.00295365 + 0.0167510i
\(71\) 8827.63 + 7407.26i 0.207825 + 0.174386i 0.740759 0.671771i \(-0.234466\pi\)
−0.532934 + 0.846157i \(0.678910\pi\)
\(72\) −22919.8 + 19232.0i −0.521051 + 0.437213i
\(73\) −14590.3 + 82745.9i −0.320449 + 1.81735i 0.219450 + 0.975624i \(0.429574\pi\)
−0.539899 + 0.841730i \(0.681537\pi\)
\(74\) −39829.4 + 14496.7i −0.845520 + 0.307744i
\(75\) −73424.3 −1.50725
\(76\) 25176.9 58.5136i 0.499999 0.00116204i
\(77\) −1433.64 −0.0275558
\(78\) −7385.47 + 2688.09i −0.137449 + 0.0500274i
\(79\) −14109.0 + 80016.3i −0.254349 + 1.44248i 0.543390 + 0.839480i \(0.317141\pi\)
−0.797739 + 0.603003i \(0.793971\pi\)
\(80\) 3774.23 3166.95i 0.0659330 0.0553244i
\(81\) 35162.6 + 29505.0i 0.595482 + 0.499669i
\(82\) −5148.49 29198.5i −0.0845561 0.479542i
\(83\) −32758.7 56739.7i −0.521952 0.904048i −0.999674 0.0255367i \(-0.991871\pi\)
0.477722 0.878511i \(-0.341463\pi\)
\(84\) 1931.57 3345.58i 0.0298684 0.0517336i
\(85\) 34116.9 + 12417.5i 0.512180 + 0.186418i
\(86\) 36874.7 + 13421.3i 0.537629 + 0.195681i
\(87\) 89142.3 154399.i 1.26266 2.18699i
\(88\) 5064.66 + 8772.24i 0.0697178 + 0.120755i
\(89\) 3382.52 + 19183.2i 0.0452652 + 0.256712i 0.999040 0.0438109i \(-0.0139499\pi\)
−0.953775 + 0.300523i \(0.902839\pi\)
\(90\) −27569.3 23133.4i −0.358772 0.301046i
\(91\) 511.500 429.200i 0.00647504 0.00543320i
\(92\) −8562.25 + 48558.9i −0.105467 + 0.598135i
\(93\) 173991. 63327.7i 2.08603 0.759253i
\(94\) −33946.9 −0.396260
\(95\) 5328.12 + 29811.9i 0.0605710 + 0.338908i
\(96\) −27294.8 −0.302275
\(97\) −104024. + 37861.5i −1.12254 + 0.408572i −0.835580 0.549369i \(-0.814868\pi\)
−0.286963 + 0.957942i \(0.592646\pi\)
\(98\) 11617.0 65883.4i 0.122188 0.692965i
\(99\) 56680.2 47560.3i 0.581224 0.487705i
\(100\) −33762.4 28330.0i −0.337624 0.283300i
\(101\) −22509.1 127656.i −0.219561 1.24519i −0.872814 0.488052i \(-0.837707\pi\)
0.653253 0.757139i \(-0.273404\pi\)
\(102\) −100568. 174189.i −0.957106 1.65776i
\(103\) −49142.4 + 85117.1i −0.456419 + 0.790540i −0.998769 0.0496125i \(-0.984201\pi\)
0.542350 + 0.840153i \(0.317535\pi\)
\(104\) −4433.20 1613.55i −0.0401915 0.0146285i
\(105\) 4366.57 + 1589.30i 0.0386516 + 0.0140680i
\(106\) −53998.6 + 93528.3i −0.466786 + 0.808497i
\(107\) −79543.1 137773.i −0.671650 1.16333i −0.977436 0.211232i \(-0.932253\pi\)
0.305786 0.952100i \(-0.401081\pi\)
\(108\) 16625.6 + 94288.7i 0.137157 + 0.777858i
\(109\) 64477.4 + 54103.0i 0.519806 + 0.436169i 0.864564 0.502523i \(-0.167595\pi\)
−0.344758 + 0.938692i \(0.612039\pi\)
\(110\) −9333.58 + 7831.80i −0.0735472 + 0.0617135i
\(111\) −49046.5 + 278157.i −0.377834 + 2.14280i
\(112\) 2179.04 793.107i 0.0164142 0.00597429i
\(113\) −75222.9 −0.554184 −0.277092 0.960843i \(-0.589371\pi\)
−0.277092 + 0.960843i \(0.589371\pi\)
\(114\) 83549.1 145491.i 0.602115 1.04851i
\(115\) −59310.5 −0.418203
\(116\) 100563. 36602.0i 0.693895 0.252557i
\(117\) −5984.11 + 33937.6i −0.0404143 + 0.229201i
\(118\) −46970.2 + 39412.6i −0.310540 + 0.260574i
\(119\) 13090.1 + 10983.9i 0.0847377 + 0.0711034i
\(120\) −5701.18 32333.0i −0.0361420 0.204971i
\(121\) 68000.7 + 117781.i 0.422231 + 0.731325i
\(122\) 15532.4 26902.9i 0.0944797 0.163644i
\(123\) −185659. 67574.3i −1.10650 0.402735i
\(124\) 104440. + 38013.1i 0.609976 + 0.222013i
\(125\) 56578.6 97997.0i 0.323875 0.560967i
\(126\) −8469.30 14669.3i −0.0475249 0.0823155i
\(127\) 1304.20 + 7396.46i 0.00717519 + 0.0406925i 0.988185 0.153265i \(-0.0489788\pi\)
−0.981010 + 0.193957i \(0.937868\pi\)
\(128\) −12550.9 10531.4i −0.0677094 0.0568149i
\(129\) 200317. 168086.i 1.05985 0.889317i
\(130\) 985.408 5588.53i 0.00511397 0.0290027i
\(131\) 52347.1 19052.8i 0.266511 0.0970019i −0.205309 0.978697i \(-0.565820\pi\)
0.471819 + 0.881695i \(0.343598\pi\)
\(132\) 67499.5 0.337183
\(133\) −2442.48 + 14042.8i −0.0119730 + 0.0688372i
\(134\) −139418. −0.670744
\(135\) −108220. + 39388.9i −0.511062 + 0.186011i
\(136\) 20965.3 118900.i 0.0971970 0.551232i
\(137\) 277466. 232821.i 1.26301 1.05979i 0.267658 0.963514i \(-0.413750\pi\)
0.995354 0.0962792i \(-0.0306942\pi\)
\(138\) 251705. + 211206.i 1.12511 + 0.944078i
\(139\) 66136.0 + 375076.i 0.290336 + 1.64658i 0.685577 + 0.728000i \(0.259550\pi\)
−0.395241 + 0.918578i \(0.629339\pi\)
\(140\) 1394.65 + 2415.60i 0.00601373 + 0.0104161i
\(141\) −113107. + 195908.i −0.479119 + 0.829858i
\(142\) 43314.8 + 15765.3i 0.180267 + 0.0656117i
\(143\) 10963.2 + 3990.28i 0.0448330 + 0.0163179i
\(144\) −59839.4 + 103645.i −0.240481 + 0.416526i
\(145\) 64363.1 + 111480.i 0.254224 + 0.440329i
\(146\) 58361.4 + 330984.i 0.226591 + 1.28506i
\(147\) −341507. 286558.i −1.30349 1.09375i
\(148\) −129877. + 108980.i −0.487391 + 0.408969i
\(149\) 79709.6 452055.i 0.294134 1.66811i −0.376569 0.926389i \(-0.622896\pi\)
0.670703 0.741726i \(-0.265993\pi\)
\(150\) −275985. + 100450.i −1.00151 + 0.364521i
\(151\) 250490. 0.894020 0.447010 0.894529i \(-0.352489\pi\)
0.447010 + 0.894529i \(0.352489\pi\)
\(152\) 94554.3 34664.0i 0.331950 0.121694i
\(153\) −881916. −3.04578
\(154\) −5388.72 + 1961.33i −0.0183098 + 0.00666423i
\(155\) −23214.8 + 131658.i −0.0776134 + 0.440167i
\(156\) −24082.8 + 20207.8i −0.0792310 + 0.0664827i
\(157\) −443.254 371.935i −0.00143517 0.00120425i 0.642070 0.766646i \(-0.278076\pi\)
−0.643505 + 0.765442i \(0.722520\pi\)
\(158\) 56436.2 + 320065.i 0.179852 + 1.01999i
\(159\) 359835. + 623252.i 1.12878 + 1.95511i
\(160\) 9853.81 17067.3i 0.0304301 0.0527066i
\(161\) −26231.5 9547.49i −0.0797551 0.0290285i
\(162\) 172533. + 62797.0i 0.516518 + 0.187997i
\(163\) 134948. 233737.i 0.397831 0.689064i −0.595627 0.803261i \(-0.703096\pi\)
0.993458 + 0.114198i \(0.0364297\pi\)
\(164\) −59297.9 102707.i −0.172159 0.298188i
\(165\) 14098.9 + 79958.8i 0.0403158 + 0.228642i
\(166\) −200757. 168455.i −0.565457 0.474475i
\(167\) 323202. 271199.i 0.896774 0.752483i −0.0727829 0.997348i \(-0.523188\pi\)
0.969557 + 0.244865i \(0.0787436\pi\)
\(168\) 2683.31 15217.8i 0.00733496 0.0415986i
\(169\) 343795. 125131.i 0.925940 0.337015i
\(170\) 145226. 0.385409
\(171\) −369296. 636221.i −0.965794 1.66386i
\(172\) 156965. 0.404559
\(173\) −105352. + 38345.1i −0.267626 + 0.0974081i −0.472348 0.881412i \(-0.656593\pi\)
0.204721 + 0.978820i \(0.434371\pi\)
\(174\) 123835. 702304.i 0.310078 1.75854i
\(175\) 19114.1 16038.6i 0.0471800 0.0395887i
\(176\) 31038.0 + 26044.0i 0.0755288 + 0.0633762i
\(177\) 70951.1 + 402383.i 0.170226 + 0.965399i
\(178\) 38958.3 + 67477.7i 0.0921615 + 0.159628i
\(179\) 97892.9 169555.i 0.228359 0.395530i −0.728963 0.684553i \(-0.759997\pi\)
0.957322 + 0.289024i \(0.0933306\pi\)
\(180\) −135275. 49236.0i −0.311197 0.113267i
\(181\) −350476. 127563.i −0.795174 0.289420i −0.0876887 0.996148i \(-0.527948\pi\)
−0.707485 + 0.706728i \(0.750170\pi\)
\(182\) 1335.43 2313.04i 0.00298843 0.00517612i
\(183\) −103504. 179275.i −0.228471 0.395723i
\(184\) 34249.0 + 194236.i 0.0745767 + 0.422946i
\(185\) −156223. 131087.i −0.335596 0.281598i
\(186\) 567356. 476069.i 1.20247 1.00899i
\(187\) −51846.6 + 294037.i −0.108422 + 0.614890i
\(188\) −127599. + 46442.1i −0.263300 + 0.0958335i
\(189\) −54203.6 −0.110376
\(190\) 60812.3 + 104767.i 0.122210 + 0.210543i
\(191\) −734089. −1.45601 −0.728006 0.685570i \(-0.759553\pi\)
−0.728006 + 0.685570i \(0.759553\pi\)
\(192\) −102595. + 37341.5i −0.200851 + 0.0731037i
\(193\) 100706. 571133.i 0.194609 1.10368i −0.718366 0.695666i \(-0.755110\pi\)
0.912975 0.408016i \(-0.133779\pi\)
\(194\) −339204. + 284626.i −0.647077 + 0.542962i
\(195\) −28968.1 24307.2i −0.0545549 0.0457770i
\(196\) −46468.1 263534.i −0.0864002 0.490000i
\(197\) 489549. + 847923.i 0.898732 + 1.55665i 0.829117 + 0.559076i \(0.188844\pi\)
0.0696155 + 0.997574i \(0.477823\pi\)
\(198\) 147981. 256311.i 0.268253 0.464628i
\(199\) −360554. 131231.i −0.645412 0.234911i −0.00148643 0.999999i \(-0.500473\pi\)
−0.643926 + 0.765088i \(0.722695\pi\)
\(200\) −165663. 60296.3i −0.292853 0.106590i
\(201\) −464526. + 804582.i −0.810997 + 1.40469i
\(202\) −259250. 449034.i −0.447033 0.774284i
\(203\) 10520.7 + 59665.7i 0.0179186 + 0.101621i
\(204\) −616318. 517152.i −1.03688 0.870047i
\(205\) 109279. 91696.1i 0.181615 0.152393i
\(206\) −68267.9 + 387167.i −0.112085 + 0.635667i
\(207\) 1.35382e6 492750.i 2.19601 0.799283i
\(208\) −18870.9 −0.0302436
\(209\) −233831. + 85723.3i −0.370284 + 0.135748i
\(210\) 18587.2 0.0290848
\(211\) 320989. 116830.i 0.496345 0.180655i −0.0817042 0.996657i \(-0.526036\pi\)
0.578049 + 0.816002i \(0.303814\pi\)
\(212\) −75014.0 + 425426.i −0.114631 + 0.650106i
\(213\) 235302. 197441.i 0.355366 0.298187i
\(214\) −487468. 409035.i −0.727632 0.610556i
\(215\) 32785.9 + 185938.i 0.0483717 + 0.274329i
\(216\) 191486. + 331664.i 0.279257 + 0.483687i
\(217\) −31460.9 + 54491.9i −0.0453547 + 0.0785566i
\(218\) 316373. + 115150.i 0.450877 + 0.164106i
\(219\) 2.10456e6 + 765998.i 2.96518 + 1.07924i
\(220\) −24368.2 + 42207.0i −0.0339443 + 0.0587933i
\(221\) −69530.0 120429.i −0.0957616 0.165864i
\(222\) 196186. + 1.11263e6i 0.267169 + 1.51519i
\(223\) 132986. + 111589.i 0.179079 + 0.150265i 0.727921 0.685661i \(-0.240487\pi\)
−0.548842 + 0.835926i \(0.684931\pi\)
\(224\) 7105.49 5962.21i 0.00946180 0.00793939i
\(225\) −223618. + 1.26820e6i −0.294476 + 1.67006i
\(226\) −282745. + 102911.i −0.368235 + 0.134026i
\(227\) −90943.8 −0.117141 −0.0585704 0.998283i \(-0.518654\pi\)
−0.0585704 + 0.998283i \(0.518654\pi\)
\(228\) 114998. 661170.i 0.146506 0.842317i
\(229\) −846676. −1.06691 −0.533456 0.845828i \(-0.679107\pi\)
−0.533456 + 0.845828i \(0.679107\pi\)
\(230\) −222935. + 81141.6i −0.277880 + 0.101140i
\(231\) −6635.76 + 37633.3i −0.00818203 + 0.0464026i
\(232\) 327919. 275157.i 0.399988 0.335630i
\(233\) −1.03867e6 871550.i −1.25340 1.05173i −0.996353 0.0853265i \(-0.972807\pi\)
−0.257045 0.966399i \(-0.582749\pi\)
\(234\) 23936.4 + 135750.i 0.0285772 + 0.162069i
\(235\) −81666.6 141451.i −0.0964661 0.167084i
\(236\) −122630. + 212402.i −0.143324 + 0.248244i
\(237\) 2.03514e6 + 740729.i 2.35355 + 0.856621i
\(238\) 64229.7 + 23377.7i 0.0735010 + 0.0267522i
\(239\) −271684. + 470570.i −0.307659 + 0.532880i −0.977850 0.209308i \(-0.932879\pi\)
0.670191 + 0.742189i \(0.266212\pi\)
\(240\) −65663.6 113733.i −0.0735862 0.127455i
\(241\) 47957.9 + 271983.i 0.0531885 + 0.301647i 0.999784 0.0207762i \(-0.00661376\pi\)
−0.946596 + 0.322423i \(0.895503\pi\)
\(242\) 416733. + 349680.i 0.457424 + 0.383824i
\(243\) −176641. + 148220.i −0.191901 + 0.161024i
\(244\) 21577.4 122371.i 0.0232019 0.131585i
\(245\) 302472. 110091.i 0.321936 0.117175i
\(246\) −790297. −0.832631
\(247\) 57763.4 100588.i 0.0602436 0.104907i
\(248\) 444571. 0.458999
\(249\) −1.64105e6 + 597294.i −1.67735 + 0.610506i
\(250\) 78598.1 445752.i 0.0795357 0.451070i
\(251\) −306256. + 256979.i −0.306831 + 0.257462i −0.783181 0.621794i \(-0.786404\pi\)
0.476350 + 0.879256i \(0.341960\pi\)
\(252\) −51902.9 43551.7i −0.0514861 0.0432020i
\(253\) −84697.0 480340.i −0.0831891 0.471789i
\(254\) 15021.1 + 26017.3i 0.0146089 + 0.0253034i
\(255\) 483877. 838099.i 0.465998 0.807133i
\(256\) −61583.7 22414.6i −0.0587308 0.0213763i
\(257\) −294028. 107018.i −0.277688 0.101070i 0.199422 0.979914i \(-0.436093\pi\)
−0.477110 + 0.878844i \(0.658316\pi\)
\(258\) 522990. 905845.i 0.489152 0.847237i
\(259\) −47991.8 83124.3i −0.0444547 0.0769979i
\(260\) −3941.63 22354.1i −0.00361612 0.0205080i
\(261\) −2.39532e6 2.00992e6i −2.17652 1.82632i
\(262\) 170695. 143230.i 0.153627 0.128908i
\(263\) −292760. + 1.66032e6i −0.260989 + 1.48014i 0.519231 + 0.854634i \(0.326219\pi\)
−0.780219 + 0.625506i \(0.784893\pi\)
\(264\) 253715. 92344.8i 0.224046 0.0815460i
\(265\) −519621. −0.454539
\(266\) 10030.9 + 56125.0i 0.00869232 + 0.0486354i
\(267\) 519219. 0.445730
\(268\) −524040. + 190735.i −0.445685 + 0.162216i
\(269\) 336999. 1.91121e6i 0.283954 1.61038i −0.425046 0.905172i \(-0.639742\pi\)
0.708999 0.705209i \(-0.249147\pi\)
\(270\) −352887. + 296108.i −0.294596 + 0.247195i
\(271\) 405862. + 340558.i 0.335703 + 0.281688i 0.795019 0.606585i \(-0.207461\pi\)
−0.459316 + 0.888273i \(0.651905\pi\)
\(272\) −83861.0 475600.i −0.0687287 0.389780i
\(273\) −8899.03 15413.6i −0.00722663 0.0125169i
\(274\) 724411. 1.25472e6i 0.582920 1.00965i
\(275\) 409680. + 149111.i 0.326673 + 0.118899i
\(276\) 1.23505e6 + 449521.i 0.975913 + 0.355203i
\(277\) 938112. 1.62486e6i 0.734607 1.27238i −0.220288 0.975435i \(-0.570700\pi\)
0.954895 0.296942i \(-0.0959668\pi\)
\(278\) 761724. + 1.31935e6i 0.591134 + 1.02387i
\(279\) −563909. 3.19809e6i −0.433709 2.45969i
\(280\) 8546.89 + 7171.69i 0.00651498 + 0.00546672i
\(281\) −575513. + 482913.i −0.434800 + 0.364840i −0.833759 0.552128i \(-0.813816\pi\)
0.398959 + 0.916969i \(0.369371\pi\)
\(282\) −157127. + 891112.i −0.117660 + 0.667282i
\(283\) −804694. + 292885.i −0.597262 + 0.217385i −0.622920 0.782285i \(-0.714054\pi\)
0.0256586 + 0.999671i \(0.491832\pi\)
\(284\) 184379. 0.135648
\(285\) 807230. 1876.08i 0.588688 0.00136817i
\(286\) 46667.2 0.0337363
\(287\) 63092.1 22963.7i 0.0452138 0.0164565i
\(288\) −83128.0 + 471443.i −0.0590563 + 0.334925i
\(289\) 1.63850e6 1.37487e6i 1.15399 0.968314i
\(290\) 394440. + 330975.i 0.275414 + 0.231100i
\(291\) 512386. + 2.90589e6i 0.354703 + 2.01162i
\(292\) 672179. + 1.16425e6i 0.461347 + 0.799077i
\(293\) 148757. 257655.i 0.101230 0.175335i −0.810962 0.585099i \(-0.801056\pi\)
0.912192 + 0.409764i \(0.134389\pi\)
\(294\) −1.67568e6 609898.i −1.13064 0.411518i
\(295\) −277222. 100901.i −0.185470 0.0675054i
\(296\) −339084. + 587311.i −0.224946 + 0.389618i
\(297\) −473542. 820198.i −0.311506 0.539545i
\(298\) −318838. 1.80822e6i −0.207984 1.17954i
\(299\) 174022. + 146022.i 0.112571 + 0.0944581i
\(300\) −899940. + 755139.i −0.577312 + 0.484422i
\(301\) −15431.0 + 87513.3i −0.00981695 + 0.0556747i
\(302\) 941533. 342690.i 0.594043 0.216214i
\(303\) −3.45517e6 −2.16203
\(304\) 307985. 259652.i 0.191137 0.161142i
\(305\) 149466. 0.0920010
\(306\) −3.31492e6 + 1.20653e6i −2.02381 + 0.736606i
\(307\) −50094.5 + 284100.i −0.0303350 + 0.172039i −0.996211 0.0869652i \(-0.972283\pi\)
0.965876 + 0.259004i \(0.0833942\pi\)
\(308\) −17571.7 + 14744.4i −0.0105545 + 0.00885627i
\(309\) 2.00688e6 + 1.68397e6i 1.19571 + 1.00332i
\(310\) 92859.4 + 526632.i 0.0548809 + 0.311245i
\(311\) −425699. 737332.i −0.249575 0.432277i 0.713833 0.700316i \(-0.246958\pi\)
−0.963408 + 0.268039i \(0.913624\pi\)
\(312\) −62875.7 + 108904.i −0.0365676 + 0.0633369i
\(313\) 361508. + 131578.i 0.208572 + 0.0759141i 0.444194 0.895931i \(-0.353490\pi\)
−0.235621 + 0.971845i \(0.575712\pi\)
\(314\) −2174.93 791.609i −0.00124486 0.000453092i
\(315\) 40749.4 70580.1i 0.0231390 0.0400780i
\(316\) 650006. + 1.12584e6i 0.366184 + 0.634249i
\(317\) −51082.4 289703.i −0.0285511 0.161922i 0.967199 0.254021i \(-0.0817533\pi\)
−0.995750 + 0.0920996i \(0.970642\pi\)
\(318\) 2.20519e6 + 1.85038e6i 1.22287 + 1.02611i
\(319\) −810937. + 680457.i −0.446180 + 0.374390i
\(320\) 13688.8 77632.8i 0.00747290 0.0423809i
\(321\) −3.98473e6 + 1.45032e6i −2.15842 + 0.785601i
\(322\) −111660. −0.0600147
\(323\) 2.79181e6 + 1.00879e6i 1.48895 + 0.538017i
\(324\) 734425. 0.388673
\(325\) −190808. + 69448.5i −0.100205 + 0.0364715i
\(326\) 187468. 1.06319e6i 0.0976976 0.554071i
\(327\) 1.71865e6 1.44212e6i 0.888830 0.745817i
\(328\) −363399. 304928.i −0.186509 0.156499i
\(329\) −13349.1 75706.2i −0.00679924 0.0385604i
\(330\) 162385. + 281258.i 0.0820843 + 0.142174i
\(331\) −66717.8 + 115559.i −0.0334712 + 0.0579739i −0.882276 0.470733i \(-0.843990\pi\)
0.848805 + 0.528707i \(0.177323\pi\)
\(332\) −985058. 358532.i −0.490475 0.178518i
\(333\) 4.65501e6 + 1.69429e6i 2.30044 + 0.837290i
\(334\) 843821. 1.46154e6i 0.413889 0.716877i
\(335\) −335400. 580930.i −0.163287 0.282821i
\(336\) −10733.2 60871.2i −0.00518660 0.0294147i
\(337\) −150344. 126154.i −0.0721126 0.0605097i 0.606019 0.795450i \(-0.292766\pi\)
−0.678131 + 0.734941i \(0.737210\pi\)
\(338\) 1.12106e6 940679.i 0.533748 0.447868i
\(339\) −348177. + 1.97461e6i −0.164551 + 0.933217i
\(340\) 545871. 198681.i 0.256090 0.0932091i
\(341\) −1.09941e6 −0.512007
\(342\) −2.25850e6 1.88618e6i −1.04413 0.872003i
\(343\) 303738. 0.139400
\(344\) 589995. 214741.i 0.268814 0.0978404i
\(345\) −274525. + 1.55691e6i −0.124175 + 0.704232i
\(346\) −343536. + 288261.i −0.154270 + 0.129448i
\(347\) 60397.4 + 50679.4i 0.0269274 + 0.0225948i 0.656152 0.754629i \(-0.272183\pi\)
−0.629225 + 0.777223i \(0.716627\pi\)
\(348\) −495340. 2.80922e6i −0.219258 1.24347i
\(349\) 187158. + 324167.i 0.0822517 + 0.142464i 0.904217 0.427074i \(-0.140456\pi\)
−0.821965 + 0.569538i \(0.807122\pi\)
\(350\) 49903.3 86435.0i 0.0217750 0.0377155i
\(351\) 414501. + 150866.i 0.179580 + 0.0653618i
\(352\) 152295. + 55430.9i 0.0655133 + 0.0238449i
\(353\) 396930. 687504.i 0.169542 0.293656i −0.768717 0.639589i \(-0.779104\pi\)
0.938259 + 0.345934i \(0.112438\pi\)
\(354\) 817182. + 1.41540e6i 0.346586 + 0.600304i
\(355\) 38511.9 + 218412.i 0.0162190 + 0.0919824i
\(356\) 238750. + 200335.i 0.0998432 + 0.0837784i
\(357\) 348919. 292778.i 0.144895 0.121582i
\(358\) 135991. 771246.i 0.0560795 0.318042i
\(359\) −727448. + 264769.i −0.297897 + 0.108426i −0.486645 0.873600i \(-0.661779\pi\)
0.188748 + 0.982026i \(0.439557\pi\)
\(360\) −575826. −0.234172
\(361\) 441300. + 2.43646e6i 0.178224 + 0.983990i
\(362\) −1.49188e6 −0.598358
\(363\) 3.40651e6 1.23987e6i 1.35689 0.493866i
\(364\) 1855.16 10521.2i 0.000733886 0.00416208i
\(365\) −1.23875e6 + 1.03943e6i −0.486688 + 0.408380i
\(366\) −634311. 532250.i −0.247514 0.207689i
\(367\) −408385. 2.31607e6i −0.158272 0.897607i −0.955733 0.294236i \(-0.904935\pi\)
0.797460 0.603371i \(-0.206176\pi\)
\(368\) 394464. + 683232.i 0.151841 + 0.262996i
\(369\) −1.73259e6 + 3.00094e6i −0.662416 + 1.14734i
\(370\) −766545. 278999.i −0.291094 0.105950i
\(371\) −229815. 83645.7i −0.0866849 0.0315507i
\(372\) 1.48126e6 2.56562e6i 0.554977 0.961248i
\(373\) 989355. + 1.71361e6i 0.368197 + 0.637735i 0.989284 0.146006i \(-0.0466420\pi\)
−0.621087 + 0.783742i \(0.713309\pi\)
\(374\) 207386. + 1.17615e6i 0.0766657 + 0.434793i
\(375\) −2.31056e6 1.93879e6i −0.848474 0.711954i
\(376\) −416077. + 349130.i −0.151777 + 0.127356i
\(377\) 85616.0 485553.i 0.0310243 0.175947i
\(378\) −203739. + 74154.9i −0.0733406 + 0.0266938i
\(379\) −3.20152e6 −1.14487 −0.572437 0.819949i \(-0.694002\pi\)
−0.572437 + 0.819949i \(0.694002\pi\)
\(380\) 371909. + 310599.i 0.132123 + 0.110342i
\(381\) 200195. 0.0706546
\(382\) −2.75927e6 + 1.00429e6i −0.967467 + 0.352129i
\(383\) 657287. 3.72766e6i 0.228959 1.29849i −0.626011 0.779814i \(-0.715313\pi\)
0.854970 0.518678i \(-0.173575\pi\)
\(384\) −334545. + 280717.i −0.115778 + 0.0971494i
\(385\) −21136.3 17735.4i −0.00726735 0.00609803i
\(386\) −402825. 2.28453e6i −0.137609 0.780421i
\(387\) −2.29314e6 3.97183e6i −0.778310 1.34807i
\(388\) −885598. + 1.53390e6i −0.298646 + 0.517271i
\(389\) 2.36395e6 + 860409.i 0.792073 + 0.288291i 0.706197 0.708015i \(-0.250409\pi\)
0.0858753 + 0.996306i \(0.472631\pi\)
\(390\) −142139. 51734.3i −0.0473207 0.0172233i
\(391\) −2.90682e6 + 5.03475e6i −0.961558 + 1.66547i
\(392\) −535198. 926991.i −0.175914 0.304691i
\(393\) −257844. 1.46231e6i −0.0842125 0.477593i
\(394\) 3.00013e6 + 2.51741e6i 0.973642 + 0.816982i
\(395\) −1.19789e6 + 1.00515e6i −0.386298 + 0.324143i
\(396\) 205574. 1.16587e6i 0.0658764 0.373603i
\(397\) 4.36439e6 1.58851e6i 1.38978 0.505840i 0.464654 0.885492i \(-0.346179\pi\)
0.925129 + 0.379653i \(0.123957\pi\)
\(398\) −1.53477e6 −0.485664
\(399\) 357319. + 129114.i 0.112363 + 0.0406014i
\(400\) −705178. −0.220368
\(401\) 4.43442e6 1.61400e6i 1.37713 0.501236i 0.455825 0.890069i \(-0.349344\pi\)
0.921308 + 0.388834i \(0.127122\pi\)
\(402\) −645312. + 3.65975e6i −0.199161 + 1.12950i
\(403\) 392254. 329140.i 0.120311 0.100953i
\(404\) −1.58877e6 1.33314e6i −0.484294 0.406371i
\(405\) 153402. + 869987.i 0.0464723 + 0.263558i
\(406\) 121172. + 209876.i 0.0364828 + 0.0631900i
\(407\) 838547. 1.45241e6i 0.250924 0.434612i
\(408\) −3.02410e6 1.10068e6i −0.899386 0.327350i
\(409\) −417529. 151968.i −0.123418 0.0449205i 0.279573 0.960124i \(-0.409807\pi\)
−0.402991 + 0.915204i \(0.632029\pi\)
\(410\) 285308. 494168.i 0.0838212 0.145183i
\(411\) −4.82732e6 8.36116e6i −1.40962 2.44153i
\(412\) 273072. + 1.54867e6i 0.0792562 + 0.449485i
\(413\) −106366. 89251.5i −0.0306850 0.0257478i
\(414\) 4.41457e6 3.70427e6i 1.26587 1.06219i
\(415\) 218958. 1.24177e6i 0.0624080 0.353933i
\(416\) −70931.3 + 25816.9i −0.0200958 + 0.00731426i
\(417\) 1.01519e7 2.85896
\(418\) −761639. + 642113.i −0.213210 + 0.179751i
\(419\) −1.62507e6 −0.452208 −0.226104 0.974103i \(-0.572599\pi\)
−0.226104 + 0.974103i \(0.572599\pi\)
\(420\) 69865.1 25428.8i 0.0193258 0.00703401i
\(421\) 197213. 1.11845e6i 0.0542289 0.307547i −0.945614 0.325292i \(-0.894537\pi\)
0.999843 + 0.0177445i \(0.00564854\pi\)
\(422\) 1.04669e6 878277.i 0.286113 0.240077i
\(423\) 3.03929e6 + 2.55026e6i 0.825887 + 0.693001i
\(424\) 300056. + 1.70170e6i 0.0810565 + 0.459694i
\(425\) −2.59824e6 4.50028e6i −0.697761 1.20856i
\(426\) 614329. 1.06405e6i 0.164012 0.284078i
\(427\) 66104.9 + 24060.2i 0.0175454 + 0.00638601i
\(428\) −2.39187e6 870571.i −0.631145 0.229718i
\(429\) 155490. 269317.i 0.0407905 0.0706513i
\(430\) 377613. + 654045.i 0.0984863 + 0.170583i
\(431\) 1.08482e6 + 6.15234e6i 0.281297 + 1.59532i 0.718219 + 0.695817i \(0.244958\pi\)
−0.436922 + 0.899500i \(0.643931\pi\)
\(432\) 1.17350e6 + 984681.i 0.302533 + 0.253855i
\(433\) −4.05424e6 + 3.40192e6i −1.03918 + 0.871974i −0.991914 0.126908i \(-0.959495\pi\)
−0.0472642 + 0.998882i \(0.515050\pi\)
\(434\) −43705.0 + 247864.i −0.0111380 + 0.0631667i
\(435\) 3.22429e6 1.17354e6i 0.816978 0.297356i
\(436\) 1.34671e6 0.339279
\(437\) −4.84931e6 + 11270.3i −1.21472 + 0.00282313i
\(438\) 8.95851e6 2.23126
\(439\) 691388. 251645.i 0.171222 0.0623199i −0.254987 0.966945i \(-0.582071\pi\)
0.426209 + 0.904625i \(0.359849\pi\)
\(440\) −33852.0 + 191984.i −0.00833590 + 0.0472753i
\(441\) −5.98958e6 + 5.02585e6i −1.46656 + 1.23059i
\(442\) −426104. 357544.i −0.103743 0.0870510i
\(443\) 703257. + 3.98837e6i 0.170257 + 0.965575i 0.943477 + 0.331437i \(0.107534\pi\)
−0.773220 + 0.634137i \(0.781355\pi\)
\(444\) 2.25958e6 + 3.91371e6i 0.543965 + 0.942174i
\(445\) −187445. + 324664.i −0.0448718 + 0.0777203i
\(446\) 652528. + 237501.i 0.155332 + 0.0565363i
\(447\) −1.14976e7 4.18478e6i −2.72168 0.990612i
\(448\) 18551.1 32131.5i 0.00436692 0.00756372i
\(449\) 1.50956e6 + 2.61463e6i 0.353374 + 0.612061i 0.986838 0.161711i \(-0.0517011\pi\)
−0.633465 + 0.773772i \(0.718368\pi\)
\(450\) 894471. + 5.07280e6i 0.208226 + 1.18091i
\(451\) 898677. + 754079.i 0.208047 + 0.174572i
\(452\) −921985. + 773637.i −0.212265 + 0.178111i
\(453\) 1.15942e6 6.57539e6i 0.265457 1.50548i
\(454\) −341837. + 124418.i −0.0778358 + 0.0283299i
\(455\) 12850.7 0.00291003
\(456\) −472281. 2.64251e6i −0.106362 0.595120i
\(457\) −7.75813e6 −1.73767 −0.868833 0.495105i \(-0.835130\pi\)
−0.868833 + 0.495105i \(0.835130\pi\)
\(458\) −3.18246e6 + 1.15832e6i −0.708924 + 0.258027i
\(459\) −1.96024e6 + 1.11170e7i −0.434287 + 2.46296i
\(460\) −726952. + 609985.i −0.160181 + 0.134408i
\(461\) 671886. + 563780.i 0.147246 + 0.123554i 0.713435 0.700721i \(-0.247138\pi\)
−0.566189 + 0.824275i \(0.691583\pi\)
\(462\) 26543.1 + 150533.i 0.00578557 + 0.0328116i
\(463\) 2.52329e6 + 4.37046e6i 0.547033 + 0.947490i 0.998476 + 0.0551895i \(0.0175763\pi\)
−0.451442 + 0.892300i \(0.649090\pi\)
\(464\) 856136. 1.48287e6i 0.184607 0.319749i
\(465\) 3.34859e6 + 1.21879e6i 0.718174 + 0.261394i
\(466\) −5.09648e6 1.85497e6i −1.08719 0.395705i
\(467\) −3.02566e6 + 5.24059e6i −0.641989 + 1.11196i 0.342999 + 0.939336i \(0.388557\pi\)
−0.984988 + 0.172622i \(0.944776\pi\)
\(468\) 275689. + 477507.i 0.0581841 + 0.100778i
\(469\) −54823.8 310921.i −0.0115090 0.0652707i
\(470\) −500482. 419954.i −0.104507 0.0876914i
\(471\) −11815.0 + 9913.96i −0.00245404 + 0.00205918i
\(472\) −170356. + 966139.i −0.0351968 + 0.199611i
\(473\) −1.45905e6 + 531049.i −0.299858 + 0.109139i
\(474\) 8.66299e6 1.77101
\(475\) 2.15854e6 3.75885e6i 0.438961 0.764400i
\(476\) 273407. 0.0553086
\(477\) 1.18608e7 4.31699e6i 2.38682 0.868731i
\(478\) −377419. + 2.14045e6i −0.0755535 + 0.428485i
\(479\) 5.78623e6 4.85522e6i 1.15228 0.966875i 0.152507 0.988302i \(-0.451265\pi\)
0.999770 + 0.0214273i \(0.00682103\pi\)
\(480\) −402410. 337662.i −0.0797197 0.0668928i
\(481\) 135637. + 769238.i 0.0267311 + 0.151600i
\(482\) 552357. + 956710.i 0.108293 + 0.187570i
\(483\) −372039. + 644390.i −0.0725638 + 0.125684i
\(484\) 2.04479e6 + 744244.i 0.396767 + 0.144411i
\(485\) −2.00201e6 728672.i −0.386467 0.140662i
\(486\) −461177. + 798782.i −0.0885681 + 0.153404i
\(487\) 3.67077e6 + 6.35795e6i 0.701349 + 1.21477i 0.967993 + 0.250977i \(0.0807520\pi\)
−0.266644 + 0.963795i \(0.585915\pi\)
\(488\) −86309.4 489485.i −0.0164062 0.0930443i
\(489\) −5.51102e6 4.62430e6i −1.04222 0.874528i
\(490\) 986309. 827611.i 0.185576 0.155717i
\(491\) 1.19842e6 6.79657e6i 0.224339 1.27229i −0.639605 0.768704i \(-0.720902\pi\)
0.863944 0.503587i \(-0.167987\pi\)
\(492\) −2.97054e6 + 1.08119e6i −0.553252 + 0.201367i
\(493\) 1.26178e7 2.33811
\(494\) 79506.5 457114.i 0.0146584 0.0842766i
\(495\) 1.42400e6 0.261215
\(496\) 1.67104e6 608209.i 0.304988 0.111007i
\(497\) −18125.9 + 102797.i −0.00329162 + 0.0186677i
\(498\) −5.35119e6 + 4.49018e6i −0.966891 + 0.811318i
\(499\) −4.44897e6 3.73313e6i −0.799849 0.671153i 0.148313 0.988940i \(-0.452616\pi\)
−0.948162 + 0.317788i \(0.897060\pi\)
\(500\) −314393. 1.78301e6i −0.0562403 0.318954i
\(501\) −5.62304e6 9.73939e6i −1.00087 1.73355i
\(502\) −799576. + 1.38491e6i −0.141612 + 0.245280i
\(503\) −1.03504e6 376724.i −0.182405 0.0663901i 0.249203 0.968451i \(-0.419831\pi\)
−0.431608 + 0.902061i \(0.642054\pi\)
\(504\) −254673. 92693.4i −0.0446588 0.0162545i
\(505\) 1.24736e6 2.16049e6i 0.217653 0.376985i
\(506\) −975501. 1.68962e6i −0.169376 0.293367i
\(507\) −1.69342e6 9.60387e6i −0.292580 1.65930i
\(508\) 92054.8 + 77243.1i 0.0158266 + 0.0132801i
\(509\) 4.22636e6 3.54634e6i 0.723057 0.606717i −0.205172 0.978726i \(-0.565775\pi\)
0.928229 + 0.372009i \(0.121331\pi\)
\(510\) 672195. 3.81220e6i 0.114438 0.649009i
\(511\) −715189. + 260308.i −0.121163 + 0.0440996i
\(512\) −262144. −0.0441942
\(513\) −8.84075e6 + 3.24106e6i −1.48319 + 0.543743i
\(514\) −1.25159e6 −0.208956
\(515\) −1.77749e6 + 646952.i −0.295317 + 0.107487i
\(516\) 726530. 4.12036e6i 0.120124 0.681256i
\(517\) 1.02895e6 863392.i 0.169304 0.142063i
\(518\) −294111. 246789.i −0.0481601 0.0404111i
\(519\) 518931. + 2.94300e6i 0.0845651 + 0.479592i
\(520\) −45397.9 78631.5i −0.00736254 0.0127523i
\(521\) −4.50988e6 + 7.81135e6i −0.727899 + 1.26076i 0.229871 + 0.973221i \(0.426170\pi\)
−0.957770 + 0.287537i \(0.907164\pi\)
\(522\) −1.17532e7 4.27781e6i −1.88790 0.687141i
\(523\) −1.01710e7 3.70196e6i −1.62597 0.591803i −0.641460 0.767156i \(-0.721671\pi\)
−0.984506 + 0.175353i \(0.943893\pi\)
\(524\) 445653. 771894.i 0.0709037 0.122809i
\(525\) −332544. 575984.i −0.0526564 0.0912036i
\(526\) 1.17104e6 + 6.64129e6i 0.184547 + 1.04662i
\(527\) 1.00384e7 + 8.42323e6i 1.57449 + 1.32115i
\(528\) 827322. 694206.i 0.129149 0.108369i
\(529\) 531510. 3.01434e6i 0.0825796 0.468332i
\(530\) −1.95313e6 + 710883.i −0.302025 + 0.109928i
\(531\) 7.16614e6 1.10293
\(532\) 114487. + 197238.i 0.0175379 + 0.0302142i
\(533\) −546388. −0.0833074
\(534\) 1.95162e6 710333.i 0.296171 0.107798i
\(535\) 531663. 3.01521e6i 0.0803068 0.455443i
\(536\) −1.70881e6 + 1.43386e6i −0.256910 + 0.215573i
\(537\) −3.99775e6 3.35451e6i −0.598246 0.501988i
\(538\) −1.34799e6 7.64486e6i −0.200786 1.13871i
\(539\) 1.32353e6 + 2.29243e6i 0.196229 + 0.339878i
\(540\) −921323. + 1.59578e6i −0.135965 + 0.235499i
\(541\) 3.08233e6 + 1.12187e6i 0.452778 + 0.164798i 0.558335 0.829616i \(-0.311440\pi\)
−0.105557 + 0.994413i \(0.533663\pi\)
\(542\) 1.99145e6 + 724829.i 0.291187 + 0.105983i
\(543\) −4.97077e6 + 8.60962e6i −0.723475 + 1.25310i
\(544\) −965873. 1.67294e6i −0.139934 0.242373i
\(545\) 281292. + 1.59529e6i 0.0405664 + 0.230064i
\(546\) −54536.4 45761.5i −0.00782898 0.00656929i
\(547\) 3.60466e6 3.02466e6i 0.515105 0.432224i −0.347817 0.937563i \(-0.613077\pi\)
0.862921 + 0.505339i \(0.168632\pi\)
\(548\) 1.00634e6 5.70724e6i 0.143151 0.811849i
\(549\) −3.41170e6 + 1.24176e6i −0.483104 + 0.175835i
\(550\) 1.74389e6 0.245817
\(551\) 5.28361e6 + 9.10256e6i 0.741398 + 1.27727i
\(552\) 5.25724e6 0.734362
\(553\) −691597. + 251721.i −0.0961701 + 0.0350031i
\(554\) 1.30321e6 7.39088e6i 0.180402 1.02311i
\(555\) −4.16415e6 + 3.49414e6i −0.573844 + 0.481512i
\(556\) 4.66812e6 + 3.91702e6i 0.640405 + 0.537364i
\(557\) −989245. 5.61029e6i −0.135103 0.766209i −0.974788 0.223134i \(-0.928371\pi\)
0.839684 0.543075i \(-0.182740\pi\)
\(558\) −6.49484e6 1.12494e7i −0.883046 1.52948i
\(559\) 361580. 626276.i 0.0489413 0.0847688i
\(560\) 41937.2 + 15263.9i 0.00565106 + 0.00205682i
\(561\) 7.47854e6 + 2.72196e6i 1.00325 + 0.365153i
\(562\) −1.50256e6 + 2.60251e6i −0.200674 + 0.347577i
\(563\) −2.34633e6 4.06397e6i −0.311974 0.540355i 0.666815 0.745223i \(-0.267657\pi\)
−0.978790 + 0.204868i \(0.934324\pi\)
\(564\) 628508. + 3.56445e6i 0.0831981 + 0.471840i
\(565\) −1.10902e6 930575.i −0.146156 0.122639i
\(566\) −2.62397e6 + 2.20177e6i −0.344285 + 0.288889i
\(567\) −72200.1 + 409467.i −0.00943148 + 0.0534886i
\(568\) 693036. 252245.i 0.0901333 0.0328058i
\(569\) −8.15298e6 −1.05569 −0.527844 0.849341i \(-0.677000\pi\)
−0.527844 + 0.849341i \(0.677000\pi\)
\(570\) 3.03163e6 1.11141e6i 0.390831 0.143280i
\(571\) 9.63131e6 1.23622 0.618109 0.786092i \(-0.287899\pi\)
0.618109 + 0.786092i \(0.287899\pi\)
\(572\) 175411. 63844.5i 0.0224165 0.00815894i
\(573\) −3.39781e6 + 1.92700e7i −0.432328 + 2.45185i
\(574\) 205733. 172630.i 0.0260630 0.0218694i
\(575\) 6.50295e6 + 5.45662e6i 0.820240 + 0.688263i
\(576\) 332512. + 1.88577e6i 0.0417591 + 0.236828i
\(577\) 4.00252e6 + 6.93256e6i 0.500488 + 0.866870i 1.00000 0.000563384i \(0.000179331\pi\)
−0.499512 + 0.866307i \(0.666487\pi\)
\(578\) 4.27783e6 7.40942e6i 0.532603 0.922496i
\(579\) −1.45262e7 5.28711e6i −1.80076 0.655423i
\(580\) 1.93541e6 + 704431.i 0.238893 + 0.0869498i
\(581\) 296733. 513957.i 0.0364692 0.0631664i
\(582\) 5.90143e6 + 1.02216e7i 0.722187 + 1.25086i
\(583\) −742032. 4.20827e6i −0.0904172 0.512782i
\(584\) 4.11935e6 + 3.45655e6i 0.499801 + 0.419383i
\(585\) −508063. + 426315.i −0.0613801 + 0.0515040i
\(586\) 206651. 1.17198e6i 0.0248596 0.140986i
\(587\) 1.37165e7 4.99238e6i 1.64303 0.598016i 0.655469 0.755222i \(-0.272471\pi\)
0.987566 + 0.157206i \(0.0502487\pi\)
\(588\) −7.13289e6 −0.850789
\(589\) −1.87306e6 + 1.07690e7i −0.222466 + 1.27904i
\(590\) −1.18005e6 −0.139564
\(591\) 2.45241e7 8.92603e6i 2.88818 1.05121i
\(592\) −471051. + 2.67146e6i −0.0552412 + 0.313289i
\(593\) 394969. 331419.i 0.0461240 0.0387026i −0.619434 0.785049i \(-0.712638\pi\)
0.665558 + 0.746346i \(0.268194\pi\)
\(594\) −2.90203e6 2.43509e6i −0.337471 0.283171i
\(595\) 57107.7 + 323874.i 0.00661305 + 0.0375045i
\(596\) −3.67223e6 6.36049e6i −0.423462 0.733458i
\(597\) −5.11369e6 + 8.85717e6i −0.587217 + 1.01709i
\(598\) 853877. + 310786.i 0.0976433 + 0.0355392i
\(599\) −9.15679e6 3.33280e6i −1.04274 0.379526i −0.236822 0.971553i \(-0.576106\pi\)
−0.805918 + 0.592027i \(0.798328\pi\)
\(600\) −2.34958e6 + 4.06959e6i −0.266447 + 0.461500i
\(601\) 985891. + 1.70761e6i 0.111338 + 0.192843i 0.916310 0.400470i \(-0.131153\pi\)
−0.804972 + 0.593313i \(0.797820\pi\)
\(602\) 61723.9 + 350053.i 0.00694164 + 0.0393680i
\(603\) 1.24822e7 + 1.04738e7i 1.39797 + 1.17303i
\(604\) 3.07018e6 2.57619e6i 0.342430 0.287333i
\(605\) −454515. + 2.57768e6i −0.0504847 + 0.286313i
\(606\) −1.29872e7 + 4.72694e6i −1.43659 + 0.522876i
\(607\) −1.72940e7 −1.90513 −0.952565 0.304334i \(-0.901566\pi\)
−0.952565 + 0.304334i \(0.901566\pi\)
\(608\) 802419. 1.39732e6i 0.0880323 0.153298i
\(609\) 1.61493e6 0.176445
\(610\) 561808. 204481.i 0.0611312 0.0222500i
\(611\) −108633. + 616089.i −0.0117722 + 0.0667637i
\(612\) −1.08094e7 + 9.07016e6i −1.16660 + 0.978895i
\(613\) −6.34057e6 5.32037e6i −0.681517 0.571861i 0.234932 0.972012i \(-0.424513\pi\)
−0.916449 + 0.400151i \(0.868958\pi\)
\(614\) 200378. + 1.13640e6i 0.0214501 + 0.121650i
\(615\) −1.90123e6 3.29302e6i −0.202697 0.351081i
\(616\) −45876.5 + 79460.4i −0.00487123 + 0.00843721i
\(617\) 7.25416e6 + 2.64030e6i 0.767139 + 0.279216i 0.695799 0.718236i \(-0.255050\pi\)
0.0713396 + 0.997452i \(0.477273\pi\)
\(618\) 9.84720e6 + 3.58409e6i 1.03715 + 0.377492i
\(619\) 1.10533e6 1.91449e6i 0.115949 0.200829i −0.802210 0.597042i \(-0.796343\pi\)
0.918159 + 0.396213i \(0.129676\pi\)
\(620\) 1.06951e6 + 1.85245e6i 0.111739 + 0.193538i
\(621\) −3.20225e6 1.81609e7i −0.333217 1.88977i
\(622\) −2.60883e6 2.18907e6i −0.270377 0.226874i
\(623\) −135165. + 113417.i −0.0139522 + 0.0117073i
\(624\) −87346.0 + 495364.i −0.00898010 + 0.0509287i
\(625\) −6.04254e6 + 2.19931e6i −0.618757 + 0.225209i
\(626\) 1.53883e6 0.156948
\(627\) 1.16794e6 + 6.53487e6i 0.118646 + 0.663847i
\(628\) −9258.04 −0.000936742
\(629\) −1.87842e7 + 6.83690e6i −1.89307 + 0.689021i
\(630\) 56608.5 321043.i 0.00568238 0.0322264i
\(631\) 1.04955e7 8.80676e6i 1.04937 0.880527i 0.0563440 0.998411i \(-0.482056\pi\)
0.993027 + 0.117884i \(0.0376112\pi\)
\(632\) 3.98347e6 + 3.34253e6i 0.396706 + 0.332876i
\(633\) −1.58108e6 8.96678e6i −0.156836 0.889461i
\(634\) −588344. 1.01904e6i −0.0581311 0.100686i
\(635\) −72273.1 + 125181.i −0.00711283 + 0.0123198i
\(636\) 1.08203e7 + 3.93826e6i 1.06071 + 0.386066i
\(637\) −1.15852e6 421666.i −0.113124 0.0411737i
\(638\) −2.11721e6 + 3.66711e6i −0.205926 + 0.356674i
\(639\) −2.69363e6 4.66550e6i −0.260967 0.452008i
\(640\) −54755.1 310531.i −0.00528414 0.0299678i
\(641\) −1.26124e6 1.05831e6i −0.121242 0.101734i 0.580151 0.814509i \(-0.302994\pi\)
−0.701393 + 0.712775i \(0.747438\pi\)
\(642\) −1.29935e7 + 1.09029e7i −1.24420 + 1.04401i
\(643\) 2.59707e6 1.47287e7i 0.247717 1.40488i −0.566378 0.824145i \(-0.691656\pi\)
0.814096 0.580730i \(-0.197233\pi\)
\(644\) −419704. + 152760.i −0.0398776 + 0.0145142i
\(645\) 5.03266e6 0.476319
\(646\) 1.18739e7 27596.0i 1.11947 0.00260175i
\(647\) 5.38213e6 0.505468 0.252734 0.967536i \(-0.418670\pi\)
0.252734 + 0.967536i \(0.418670\pi\)
\(648\) 2.76053e6 1.00475e6i 0.258259 0.0939986i
\(649\) 421287. 2.38924e6i 0.0392615 0.222663i
\(650\) −622193. + 522082.i −0.0577619 + 0.0484680i
\(651\) 1.28480e6 + 1.07808e6i 0.118818 + 0.0997004i
\(652\) −749873. 4.25274e6i −0.0690826 0.391787i
\(653\) −1.68049e6 2.91069e6i −0.154224 0.267124i 0.778552 0.627580i \(-0.215954\pi\)
−0.932776 + 0.360456i \(0.882621\pi\)
\(654\) 4.48708e6 7.77186e6i 0.410223 0.710527i
\(655\) 1.00746e6 + 366685.i 0.0917537 + 0.0333956i
\(656\) −1.78310e6 648995.i −0.161777 0.0588819i
\(657\) 1.96400e7 3.40176e7i 1.77513 3.07461i
\(658\) −153748. 266300.i −0.0138435 0.0239776i
\(659\) −2.48701e6 1.41046e7i −0.223082 1.26516i −0.866318 0.499493i \(-0.833520\pi\)
0.643236 0.765668i \(-0.277592\pi\)
\(660\) 995150. + 835030.i 0.0889260 + 0.0746178i
\(661\) −1.29547e7 + 1.08703e7i −1.15325 + 0.967693i −0.999791 0.0204621i \(-0.993486\pi\)
−0.153461 + 0.988155i \(0.549042\pi\)
\(662\) −92683.4 + 525634.i −0.00821972 + 0.0466164i
\(663\) −3.48312e6 + 1.26775e6i −0.307740 + 0.112008i
\(664\) −4.19311e6 −0.369076
\(665\) −209731. + 176818.i −0.0183912 + 0.0155050i
\(666\) 1.98150e7 1.73105
\(667\) −1.93694e7 + 7.04989e6i −1.68578 + 0.613575i
\(668\) 1.17222e6 6.64801e6i 0.101641 0.576435i
\(669\) 3.54477e6 2.97441e6i 0.306212 0.256943i
\(670\) −2.05545e6 1.72473e6i −0.176897 0.148434i
\(671\) 213441. + 1.21049e6i 0.0183009 + 0.103789i
\(672\) −123621. 214117.i −0.0105601 0.0182906i
\(673\) −2.39454e6 + 4.14746e6i −0.203791 + 0.352976i −0.949747 0.313019i \(-0.898660\pi\)
0.745956 + 0.665995i \(0.231993\pi\)
\(674\) −737697. 268500.i −0.0625501 0.0227664i
\(675\) 1.54893e7 + 5.63766e6i 1.30850 + 0.476255i
\(676\) 2.92687e6 5.06949e6i 0.246341 0.426676i
\(677\) 6.26061e6 + 1.08437e7i 0.524982 + 0.909296i 0.999577 + 0.0290915i \(0.00926142\pi\)
−0.474594 + 0.880205i \(0.657405\pi\)
\(678\) 1.39271e6 + 7.89845e6i 0.116355 + 0.659884i
\(679\) −768140. 644546.i −0.0639390 0.0536512i
\(680\) 1.77999e6 1.49359e6i 0.147620 0.123868i
\(681\) −420944. + 2.38729e6i −0.0347821 + 0.197259i
\(682\) −4.13245e6 + 1.50409e6i −0.340209 + 0.123826i
\(683\) −7.82961e6 −0.642227 −0.321113 0.947041i \(-0.604057\pi\)
−0.321113 + 0.947041i \(0.604057\pi\)
\(684\) −1.10696e7 3.99991e6i −0.904676 0.326896i
\(685\) 6.97090e6 0.567627
\(686\) 1.14168e6 415538.i 0.0926263 0.0337132i
\(687\) −3.91894e6 + 2.22254e7i −0.316794 + 1.79663i
\(688\) 1.92387e6 1.61432e6i 0.154955 0.130023i
\(689\) 1.52461e6 + 1.27930e6i 0.122352 + 0.102665i
\(690\) 1.09810e6 + 6.22764e6i 0.0878051 + 0.497967i
\(691\) −4.14150e6 7.17329e6i −0.329961 0.571510i 0.652543 0.757752i \(-0.273702\pi\)
−0.982504 + 0.186242i \(0.940369\pi\)
\(692\) −896909. + 1.55349e6i −0.0712005 + 0.123323i
\(693\) 629801. + 229229.i 0.0498161 + 0.0181316i
\(694\) 296353. + 107864.i 0.0233567 + 0.00850114i
\(695\) −3.66498e6 + 6.34794e6i −0.287813 + 0.498506i
\(696\) −5.70510e6 9.88153e6i −0.446417 0.773217i
\(697\) −2.42812e6 1.37705e7i −0.189316 1.07367i
\(698\) 1.14697e6 + 962422.i 0.0891074 + 0.0747700i
\(699\) −2.76860e7 + 2.32313e7i −2.14322 + 1.79837i
\(700\) 69324.9 393161.i 0.00534742 0.0303267i
\(701\) −1.44089e7 + 5.24440e6i −1.10748 + 0.403089i −0.830068 0.557663i \(-0.811698\pi\)
−0.277410 + 0.960752i \(0.589476\pi\)
\(702\) 1.76441e6 0.135132
\(703\) −1.27979e7 1.06882e7i −0.976680 0.815671i
\(704\) 648276. 0.0492979
\(705\) −4.09111e6 + 1.48904e6i −0.310004 + 0.112832i
\(706\) 551410. 3.12720e6i 0.0416354 0.236126i
\(707\) 899461. 754737.i 0.0676758 0.0567868i
\(708\) 5.00798e6 + 4.20219e6i 0.375474 + 0.315060i
\(709\) −3.16956e6 1.79755e7i −0.236801 1.34297i −0.838787 0.544460i \(-0.816735\pi\)
0.601986 0.798507i \(-0.294376\pi\)
\(710\) 443562. + 768272.i 0.0330224 + 0.0571965i
\(711\) 1.89922e7 3.28954e7i 1.40897 2.44040i
\(712\) 1.17148e6 + 426384.i 0.0866035 + 0.0315211i
\(713\) −2.01161e7 7.32168e6i −1.48191 0.539370i
\(714\) 910963. 1.57783e6i 0.0668737 0.115829i
\(715\) 112268. + 194454.i 0.00821280 + 0.0142250i
\(716\) −543966. 3.08498e6i −0.0396542 0.224890i
\(717\) 1.10950e7 + 9.30983e6i 0.805992 + 0.676307i
\(718\) −2.37208e6 + 1.99042e6i −0.171719 + 0.144090i
\(719\) −4.53757e6 + 2.57339e7i −0.327342 + 1.85645i 0.165338 + 0.986237i \(0.447129\pi\)
−0.492680 + 0.870211i \(0.663983\pi\)
\(720\) −2.16440e6 + 787777.i −0.155599 + 0.0566333i
\(721\) −890279. −0.0637805
\(722\) 4.99201e6 + 8.55435e6i 0.356396 + 0.610722i
\(723\) 7.36157e6 0.523751
\(724\) −5.60762e6 + 2.04101e6i −0.397587 + 0.144710i
\(725\) 3.19935e6 1.81444e7i 0.226057 1.28203i
\(726\) 1.11081e7 9.32077e6i 0.782162 0.656312i
\(727\) 6.09162e6 + 5.11148e6i 0.427461 + 0.358683i 0.830993 0.556283i \(-0.187773\pi\)
−0.403531 + 0.914966i \(0.632217\pi\)
\(728\) −7420.65 42084.6i −0.000518936 0.00294303i
\(729\) 8.65022e6 + 1.49826e7i 0.602849 + 1.04416i
\(730\) −3.23414e6 + 5.60170e6i −0.224622 + 0.389057i
\(731\) 1.73908e7 + 6.32972e6i 1.20372 + 0.438118i
\(732\) −3.11239e6 1.13282e6i −0.214692 0.0781416i
\(733\) −5.13849e6 + 8.90013e6i −0.353245 + 0.611838i −0.986816 0.161847i \(-0.948255\pi\)
0.633571 + 0.773684i \(0.281588\pi\)
\(734\) −4.70360e6 8.14687e6i −0.322248 0.558149i
\(735\) −1.48987e6 8.44950e6i −0.101726 0.576916i
\(736\) 2.41742e6 + 2.02845e6i 0.164497 + 0.138029i
\(737\) 4.22584e6 3.54590e6i 0.286579 0.240468i
\(738\) −2.40689e6 + 1.36502e7i −0.162673 + 0.922566i
\(739\) 2.65872e7 9.67695e6i 1.79086 0.651820i 0.791696 0.610915i \(-0.209198\pi\)
0.999163 0.0409048i \(-0.0130240\pi\)
\(740\) −3.26296e6 −0.219044
\(741\) −2.37310e6 1.98188e6i −0.158771 0.132597i
\(742\) −978255. −0.0652293
\(743\) 8.14086e6 2.96303e6i 0.541001 0.196908i −0.0570426 0.998372i \(-0.518167\pi\)
0.598044 + 0.801463i \(0.295945\pi\)
\(744\) 2.05775e6 1.16701e7i 0.136289 0.772932i
\(745\) 6.76750e6 5.67861e6i 0.446722 0.374844i
\(746\) 6.06312e6 + 5.08756e6i 0.398886 + 0.334705i
\(747\) 5.31868e6 + 3.01637e7i 0.348740 + 1.97780i
\(748\) 2.38858e6 + 4.13714e6i 0.156094 + 0.270363i
\(749\) 720514. 1.24797e6i 0.0469286 0.0812828i
\(750\) −1.13373e7 4.12643e6i −0.735962 0.267868i
\(751\) 8.54607e6 + 3.11051e6i 0.552925 + 0.201248i 0.603346 0.797480i \(-0.293834\pi\)
−0.0504205 + 0.998728i \(0.516056\pi\)
\(752\) −1.08630e6 + 1.88153e6i −0.0700496 + 0.121329i
\(753\) 5.32820e6 + 9.22872e6i 0.342447 + 0.593135i
\(754\) −342464. 1.94221e6i −0.0219375 0.124414i
\(755\) 3.69299e6 + 3.09878e6i 0.235782 + 0.197844i
\(756\) −664358. + 557462.i −0.0422763 + 0.0354741i
\(757\) 1.54211e6 8.74573e6i 0.0978082 0.554698i −0.896042 0.443969i \(-0.853570\pi\)
0.993851 0.110729i \(-0.0353187\pi\)
\(758\) −1.20338e7 + 4.37993e6i −0.760727 + 0.276882i
\(759\) −1.30010e7 −0.819170
\(760\) 1.82285e6 + 658668.i 0.114476 + 0.0413650i
\(761\) 3.96760e6 0.248351 0.124176 0.992260i \(-0.460371\pi\)
0.124176 + 0.992260i \(0.460371\pi\)
\(762\) 752487. 273883.i 0.0469474 0.0170874i
\(763\) −132393. + 750836.i −0.00823289 + 0.0466910i
\(764\) −8.99751e6 + 7.54981e6i −0.557685 + 0.467953i
\(765\) −1.30022e7 1.09101e7i −0.803271 0.674024i
\(766\) −2.62915e6 1.49106e7i −0.161899 0.918172i
\(767\) 564976. + 978567.i 0.0346770 + 0.0600623i
\(768\) −873435. + 1.51283e6i −0.0534352 + 0.0925525i
\(769\) 2.46990e7 + 8.98971e6i 1.50614 + 0.548189i 0.957641 0.287965i \(-0.0929787\pi\)
0.548495 + 0.836154i \(0.315201\pi\)
\(770\) −103710. 37747.3i −0.00630366 0.00229435i
\(771\) −4.17017e6 + 7.22295e6i −0.252649 + 0.437602i
\(772\) −4.63955e6 8.03594e6i −0.280177 0.485281i
\(773\) 3.57135e6 + 2.02541e7i 0.214973 + 1.21917i 0.880953 + 0.473203i \(0.156902\pi\)
−0.665980 + 0.745969i \(0.731987\pi\)
\(774\) −1.40532e7 1.17920e7i −0.843183 0.707514i
\(775\) 1.46580e7 1.22995e7i 0.876637 0.735586i
\(776\) −1.23026e6 + 6.97715e6i −0.0733402 + 0.415933i
\(777\) −2.40416e6 + 875044.i −0.142860 + 0.0519969i
\(778\) 1.00627e7 0.596025
\(779\) 8.91741e6 7.51798e6i 0.526496 0.443872i
\(780\) −605044. −0.0356082
\(781\) −1.71386e6 + 623795.i −0.100542 + 0.0365944i
\(782\) −4.03811e6 + 2.29012e7i −0.236135 + 1.33919i
\(783\) −3.06602e7 + 2.57270e7i −1.78719 + 1.49963i
\(784\) −3.27989e6 2.75215e6i −0.190576 0.159912i
\(785\) −1933.76 10966.9i −0.000112003 0.000635200i
\(786\) −2.96973e6 5.14373e6i −0.171459 0.296976i
\(787\) −4.24313e6 + 7.34932e6i −0.244202 + 0.422971i −0.961907 0.273377i \(-0.911859\pi\)
0.717705 + 0.696347i \(0.245193\pi\)
\(788\) 1.47208e7 + 5.35794e6i 0.844532 + 0.307384i
\(789\) 4.22287e7 + 1.53700e7i 2.41499 + 0.878983i
\(790\) −3.12746e6 + 5.41691e6i −0.178289 + 0.308805i
\(791\) −340690. 590093.i −0.0193606 0.0335335i
\(792\) −822295. 4.66347e6i −0.0465816 0.264178i
\(793\) −438545. 367983.i −0.0247646 0.0207799i
\(794\) 1.42315e7 1.19417e7i 0.801125 0.672223i
\(795\) −2.40512e6 + 1.36401e7i −0.134964 + 0.765421i
\(796\) −5.76886e6 + 2.09969e6i −0.322706 + 0.117455i
\(797\) −1.53268e7 −0.854682 −0.427341 0.904090i \(-0.640550\pi\)
−0.427341 + 0.904090i \(0.640550\pi\)
\(798\) 1.51972e6 3531.97i 0.0844804 0.000196340i
\(799\) −1.60100e7 −0.887204
\(800\) −2.65060e6 + 964741.i −0.146427 + 0.0532949i
\(801\) 1.58131e6 8.96806e6i 0.0870835 0.493875i
\(802\) 1.44599e7 1.21333e7i 0.793833 0.666105i
\(803\) −1.01871e7 8.54797e6i −0.557520 0.467815i
\(804\) 2.58125e6 + 1.46390e7i 0.140828 + 0.798676i
\(805\) −268622. 465267.i −0.0146101 0.0253054i
\(806\) 1.02410e6 1.77380e6i 0.0555272 0.0961759i
\(807\) −4.86099e7 1.76925e7i −2.62749 0.956327i
\(808\) −7.79568e6 2.83740e6i −0.420074 0.152894i
\(809\) −7.57937e6 + 1.31279e7i −0.407157 + 0.705217i −0.994570 0.104071i \(-0.966813\pi\)
0.587413 + 0.809287i \(0.300146\pi\)
\(810\) 1.76682e6 + 3.06022e6i 0.0946191 + 0.163885i
\(811\) 4.64283e6 + 2.63308e7i 0.247874 + 1.40576i 0.813723 + 0.581253i \(0.197437\pi\)
−0.565849 + 0.824509i \(0.691452\pi\)
\(812\) 742586. + 623104.i 0.0395236 + 0.0331643i
\(813\) 1.08183e7 9.07763e6i 0.574027 0.481666i
\(814\) 1.16490e6 6.60646e6i 0.0616207 0.349468i
\(815\) 4.88110e6 1.77657e6i 0.257409 0.0936892i
\(816\) −1.28727e7 −0.676776
\(817\) 2.71596e6 + 1.51963e7i 0.142353 + 0.796497i
\(818\) −1.77730e6 −0.0928705
\(819\) −293329. + 106763.i −0.0152808 + 0.00556175i
\(820\) 396345. 2.24779e6i 0.0205844 0.116740i
\(821\) 4.80990e6 4.03598e6i 0.249045 0.208974i −0.509716 0.860343i \(-0.670250\pi\)
0.758761 + 0.651369i \(0.225805\pi\)
\(822\) −2.95835e7 2.48235e7i −1.52711 1.28140i
\(823\) −3.01319e6 1.70886e7i −0.155069 0.879443i −0.958722 0.284344i \(-0.908224\pi\)
0.803653 0.595098i \(-0.202887\pi\)
\(824\) 3.14511e6 + 5.44750e6i 0.161368 + 0.279498i
\(825\) 5.81045e6 1.00640e7i 0.297218 0.514796i
\(826\) −521908. 189959.i −0.0266161 0.00968745i
\(827\) −107887. 39267.6i −0.00548536 0.00199651i 0.339276 0.940687i \(-0.389818\pi\)
−0.344761 + 0.938690i \(0.612040\pi\)
\(828\) 1.15256e7 1.99630e7i 0.584237 1.01193i
\(829\) 1.00562e7 + 1.74179e7i 0.508217 + 0.880258i 0.999955 + 0.00951459i \(0.00302863\pi\)
−0.491737 + 0.870743i \(0.663638\pi\)
\(830\) −875831. 4.96709e6i −0.0441291 0.250269i
\(831\) −3.83106e7 3.21464e7i −1.92449 1.61484i
\(832\) −231295. + 194079.i −0.0115840 + 0.00972011i
\(833\) 5.47880e6 3.10718e7i 0.273573 1.55151i
\(834\) 3.81588e7 1.38887e7i 1.89967 0.691425i
\(835\) 8.11997e6 0.403031
\(836\) −1.98436e6 + 3.45554e6i −0.0981986 + 0.171002i
\(837\) −4.15671e7 −2.05086
\(838\) −6.10828e6 + 2.22323e6i −0.300475 + 0.109364i
\(839\) 2.38339e6 1.35169e7i 0.116894 0.662936i −0.868902 0.494985i \(-0.835174\pi\)
0.985795 0.167952i \(-0.0537152\pi\)
\(840\) 227818. 191162.i 0.0111401 0.00934768i
\(841\) 1.85580e7 + 1.55720e7i 0.904777 + 0.759198i
\(842\) −788853. 4.47381e6i −0.0383456 0.217469i
\(843\) 1.00127e7 + 1.73425e7i 0.485269 + 0.840511i
\(844\) 2.73271e6 4.73320e6i 0.132050 0.228717i
\(845\) 6.61658e6 + 2.40824e6i 0.318781 + 0.116027i
\(846\) 1.49129e7 + 5.42787e6i 0.716370 + 0.260737i
\(847\) −615961. + 1.06688e6i −0.0295016 + 0.0510982i
\(848\) 3.45591e6 + 5.98581e6i 0.165034 + 0.285847i
\(849\) 3.96365e6 + 2.24790e7i 0.188724 + 1.07031i
\(850\) −1.59229e7 1.33609e7i −0.755920 0.634292i
\(851\) 2.50155e7 2.09905e7i 1.18409 0.993570i
\(852\) 853417. 4.83997e6i 0.0402775 0.228425i
\(853\) 8.43002e6 3.06828e6i 0.396694 0.144385i −0.135967 0.990713i \(-0.543414\pi\)
0.532661 + 0.846328i \(0.321192\pi\)
\(854\) 281389. 0.0132027
\(855\) 2.42606e6 1.39484e7i 0.113498 0.652542i
\(856\) −1.01815e7 −0.474928
\(857\) −5.10273e6 + 1.85724e6i −0.237329 + 0.0863807i −0.457947 0.888980i \(-0.651415\pi\)
0.220618 + 0.975360i \(0.429193\pi\)
\(858\) 216005. 1.22502e6i 0.0100172 0.0568101i
\(859\) −1.94984e6 + 1.63611e6i −0.0901605 + 0.0756536i −0.686754 0.726890i \(-0.740965\pi\)
0.596593 + 0.802544i \(0.296521\pi\)
\(860\) 2.31415e6 + 1.94180e6i 0.106695 + 0.0895279i
\(861\) −310771. 1.76247e6i −0.0142867 0.0810240i
\(862\) 1.24945e7 + 2.16411e7i 0.572731 + 0.991999i
\(863\) 7.04130e6 1.21959e7i 0.321829 0.557425i −0.659036 0.752111i \(-0.729036\pi\)
0.980866 + 0.194686i \(0.0623689\pi\)
\(864\) 5.75803e6 + 2.09575e6i 0.262415 + 0.0955114i
\(865\) −2.02758e6 737979.i −0.0921379 0.0335354i
\(866\) −1.05849e7 + 1.83336e7i −0.479613 + 0.830715i
\(867\) −2.85065e7 4.93747e7i −1.28794 2.23078i
\(868\) 174820. + 991454.i 0.00787576 + 0.0446656i
\(869\) −9.85102e6 8.26599e6i −0.442519 0.371317i
\(870\) 1.05138e7 8.82217e6i 0.470938 0.395164i
\(871\) −446150. + 2.53024e6i −0.0199267 + 0.113010i
\(872\) 5.06197e6 1.84241e6i 0.225438 0.0820529i
\(873\) 5.17516e7 2.29820
\(874\) −1.82120e7 + 6.67662e6i −0.806455 + 0.295650i
\(875\) 1.02500e6 0.0452587
\(876\) 3.36730e7 1.22560e7i 1.48259 0.539619i
\(877\) 7.30656e6 4.14376e7i 0.320785 1.81926i −0.216990 0.976174i \(-0.569624\pi\)
0.537775 0.843088i \(-0.319265\pi\)
\(878\) 2.25450e6 1.89175e6i 0.0986993 0.0828185i
\(879\) −6.07494e6 5.09748e6i −0.265198 0.222527i
\(880\) 135408. + 767937.i 0.00589437 + 0.0334287i
\(881\) −5.83783e6 1.01114e7i −0.253403 0.438907i 0.711057 0.703134i \(-0.248217\pi\)
−0.964461 + 0.264227i \(0.914883\pi\)
\(882\) −1.56377e7 + 2.70852e7i −0.676863 + 1.17236i
\(883\) −3.50071e7 1.27415e7i −1.51096 0.549946i −0.552092 0.833783i \(-0.686170\pi\)
−0.958872 + 0.283838i \(0.908392\pi\)
\(884\) −2.09078e6 760981.i −0.0899865 0.0327524i
\(885\) −3.93181e6 + 6.81010e6i −0.168746 + 0.292277i
\(886\) 8.09979e6 + 1.40292e7i 0.346649 + 0.600413i
\(887\) −942199. 5.34348e6i −0.0402100 0.228042i 0.958080 0.286501i \(-0.0924923\pi\)
−0.998290 + 0.0584594i \(0.981381\pi\)
\(888\) 1.38475e7 + 1.16195e7i 0.589304 + 0.494485i
\(889\) −52115.4 + 43730.0i −0.00221163 + 0.00185578i
\(890\) −260396. + 1.47678e6i −0.0110194 + 0.0624943i
\(891\) −6.82674e6 + 2.48473e6i −0.288084 + 0.104854i
\(892\) 2.77762e6 0.116886
\(893\) −6.70406e6 1.15497e7i −0.281326 0.484665i
\(894\) −4.89419e7 −2.04803
\(895\) 3.54080e6 1.28875e6i 0.147755 0.0537786i
\(896\) 25770.9 146154.i 0.00107241 0.00608193i
\(897\) 4.63857e6 3.89222e6i 0.192488 0.161516i
\(898\) 9.25111e6 + 7.76260e6i 0.382827 + 0.321230i
\(899\) 8.06798e6 + 4.57558e7i 0.332940 + 1.88819i
\(900\) 1.03021e7 + 1.78438e7i 0.423955 + 0.734312i
\(901\) −2.54667e7 + 4.41096e7i −1.04511 + 1.81018i
\(902\) 4.40956e6 + 1.60495e6i 0.180459 + 0.0656818i
\(903\) 2.22582e6 + 810131.i 0.0908385 + 0.0330625i
\(904\) −2.40713e6 + 4.16927e6i −0.0979668 + 0.169683i
\(905\) −3.58903e6 6.21638e6i −0.145665 0.252299i
\(906\) −4.63768e6 2.63016e7i −0.187707 1.06454i
\(907\) −2.36772e7 1.98675e7i −0.955680 0.801911i 0.0245649 0.999698i \(-0.492180\pi\)
−0.980245 + 0.197787i \(0.936624\pi\)
\(908\) −1.11467e6 + 935321.i −0.0448676 + 0.0376483i
\(909\) −1.05229e7 + 5.96784e7i −0.422402 + 2.39556i
\(910\) 48302.7 17580.8i 0.00193361 0.000703776i
\(911\) 7.30220e6 0.291513 0.145756 0.989321i \(-0.453438\pi\)
0.145756 + 0.989321i \(0.453438\pi\)
\(912\) −5.39036e6 9.28648e6i −0.214601 0.369712i
\(913\) 1.03695e7 0.411698
\(914\) −2.91610e7 + 1.06137e7i −1.15462 + 0.420246i
\(915\) 691820. 3.92350e6i 0.0273174 0.154925i
\(916\) −1.03775e7 + 8.70773e6i −0.408651 + 0.342899i
\(917\) 386546. + 324350.i 0.0151802 + 0.0127377i
\(918\) 7.84094e6 + 4.44682e7i 0.307087 + 1.74158i
\(919\) 1.52820e7 + 2.64692e7i 0.596886 + 1.03384i 0.993278 + 0.115756i \(0.0369289\pi\)
−0.396392 + 0.918082i \(0.629738\pi\)
\(920\) −1.89794e6 + 3.28732e6i −0.0739285 + 0.128048i
\(921\) 7.22581e6 + 2.62998e6i 0.280697 + 0.102165i
\(922\) 3.29676e6 + 1.19992e6i 0.127720 + 0.0464864i
\(923\) 424729. 735653.i 0.0164100 0.0284229i
\(924\) 305711. + 529506.i 0.0117796 + 0.0204029i
\(925\) 5.06858e6 + 2.87454e7i 0.194775 + 1.10462i
\(926\) 1.54636e7 + 1.29755e7i 0.592629 + 0.497275i
\(927\) 3.51980e7 2.95346e7i 1.34530 1.12884i
\(928\) 1.18933e6 6.74504e6i 0.0453350 0.257107i
\(929\) −1.10919e7 + 4.03714e6i −0.421666 + 0.153474i −0.544133 0.838999i \(-0.683141\pi\)
0.122468 + 0.992472i \(0.460919\pi\)
\(930\) 1.42540e7 0.540417
\(931\) 2.47096e7 9.05865e6i 0.934312 0.342523i
\(932\) −2.16943e7 −0.818098
\(933\) −2.13255e7 + 7.76184e6i −0.802038 + 0.291918i
\(934\) −4.20320e6 + 2.38375e7i −0.157657 + 0.894116i
\(935\) −4.40188e6 + 3.69362e6i −0.164668 + 0.138173i
\(936\) 1.68952e6 + 1.41768e6i 0.0630338 + 0.0528917i
\(937\) 4.28719e6 + 2.43139e7i 0.159523 + 0.904702i 0.954533 + 0.298105i \(0.0963545\pi\)
−0.795010 + 0.606597i \(0.792534\pi\)
\(938\) −631435. 1.09368e6i −0.0234327 0.0405866i
\(939\) 5.12722e6 8.88061e6i 0.189766 0.328684i
\(940\) −2.45573e6 893812.i −0.0906485 0.0329933i
\(941\) −2.60065e7 9.46559e6i −0.957431 0.348477i −0.184405 0.982850i \(-0.559036\pi\)
−0.773026 + 0.634374i \(0.781258\pi\)
\(942\) −30846.8 + 53428.2i −0.00113262 + 0.00196175i
\(943\) 1.14213e7 + 1.97823e7i 0.418252 + 0.724433i
\(944\) 681425. + 3.86455e6i 0.0248879 + 0.141146i
\(945\) −799127. 670548.i −0.0291096 0.0244259i
\(946\) −4.75770e6 + 3.99218e6i −0.172850 + 0.145038i
\(947\) 5.86481e6 3.32610e7i 0.212510 1.20520i −0.672666 0.739946i \(-0.734851\pi\)
0.885176 0.465256i \(-0.154038\pi\)
\(948\) 3.25622e7 1.18517e7i 1.17677 0.428310i
\(949\) 6.19366e6 0.223245
\(950\) 2.97105e6 1.70817e7i 0.106807 0.614076i
\(951\) −7.84119e6 −0.281145
\(952\) 1.02767e6 374043.i 0.0367505 0.0133761i
\(953\) 5.15305e6 2.92244e7i 0.183794 1.04235i −0.743700 0.668513i \(-0.766931\pi\)
0.927495 0.373836i \(-0.121958\pi\)
\(954\) 3.86762e7 3.24532e7i 1.37585 1.15448i
\(955\) −1.08227e7 9.08134e6i −0.383997 0.322212i
\(956\) 1.50968e6 + 8.56180e6i 0.0534244 + 0.302985i
\(957\) 1.41086e7 + 2.44368e7i 0.497971 + 0.862511i
\(958\) 1.51068e7 2.61657e7i 0.531812 0.921125i
\(959\) 3.08305e6 + 1.12214e6i 0.108252 + 0.0394004i
\(960\) −1.97452e6 718665.i −0.0691484 0.0251680i
\(961\) −9.81184e6 + 1.69946e7i −0.342722 + 0.593612i
\(962\) 1.56221e6 + 2.70583e6i 0.0544254 + 0.0942676i
\(963\) 1.29146e7 + 7.32422e7i 0.448760 + 2.54505i
\(964\) 3.38504e6 + 2.84039e6i 0.117320 + 0.0984430i
\(965\) 8.55015e6 7.17443e6i 0.295567 0.248010i
\(966\) −516831. + 2.93109e6i −0.0178199 + 0.101062i
\(967\) −4.38278e7 + 1.59520e7i −1.50724 + 0.548591i −0.957924 0.287022i \(-0.907335\pi\)
−0.549318 + 0.835613i \(0.685113\pi\)
\(968\) 8.70409e6 0.298562
\(969\) 3.94032e7 6.86162e7i 1.34810 2.34756i
\(970\) −8.52198e6 −0.290811
\(971\) −1.52651e7 + 5.55606e6i −0.519580 + 0.189112i −0.588480 0.808512i \(-0.700273\pi\)
0.0688996 + 0.997624i \(0.478051\pi\)
\(972\) −640661. + 3.63337e6i −0.0217502 + 0.123351i
\(973\) −2.64278e6 + 2.21756e6i −0.0894911 + 0.0750919i
\(974\) 2.24958e7 + 1.88762e7i 0.759807 + 0.637554i
\(975\) 939857. + 5.33019e6i 0.0316629 + 0.179569i
\(976\) −994072. 1.72178e6i −0.0334036 0.0578567i
\(977\) 1.47469e7 2.55424e7i 0.494270 0.856101i −0.505708 0.862705i \(-0.668769\pi\)
0.999978 + 0.00660354i \(0.00210199\pi\)
\(978\) −2.70411e7 9.84215e6i −0.904018 0.329036i
\(979\) −2.89705e6 1.05444e6i −0.0966048 0.0351613i
\(980\) 2.57507e6 4.46015e6i 0.0856493 0.148349i
\(981\) −1.96744e7 3.40770e7i −0.652722 1.13055i
\(982\) −4.79368e6 2.71863e7i −0.158632 0.899645i
\(983\) 6.78117e6 + 5.69008e6i 0.223831 + 0.187817i 0.747806 0.663917i \(-0.231107\pi\)
−0.523975 + 0.851734i \(0.675552\pi\)
\(984\) −9.68644e6 + 8.12789e6i −0.318916 + 0.267602i
\(985\) −3.27213e6 + 1.85572e7i −0.107458 + 0.609426i
\(986\) 4.74273e7 1.72621e7i 1.55359 0.565461i
\(987\) −2.04909e6 −0.0669527
\(988\) −326522. 1.82696e6i −0.0106419 0.0595437i
\(989\) −3.02329e7 −0.982855
\(990\) 5.35251e6 1.94815e6i 0.173568 0.0631735i
\(991\) −3.38259e6 + 1.91836e7i −0.109412 + 0.620507i 0.879954 + 0.475059i \(0.157573\pi\)
−0.989366 + 0.145448i \(0.953538\pi\)
\(992\) 5.44898e6 4.57224e6i 0.175807 0.147520i
\(993\) 2.72462e6 + 2.28623e6i 0.0876866 + 0.0735778i
\(994\) 72503.8 + 411189.i 0.00232753 + 0.0132001i
\(995\) −3.69222e6 6.39512e6i −0.118231 0.204782i
\(996\) −1.39710e7 + 2.41984e7i −0.446250 + 0.772928i
\(997\) 3.78155e7 + 1.37637e7i 1.20485 + 0.438528i 0.864913 0.501921i \(-0.167373\pi\)
0.339933 + 0.940450i \(0.389596\pi\)
\(998\) −2.18299e7 7.94542e6i −0.693785 0.252517i
\(999\) 3.17041e7 5.49131e7i 1.00508 1.74085i
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 38.6.e.a.5.4 24
19.2 odd 18 722.6.a.p.1.1 12
19.4 even 9 inner 38.6.e.a.23.4 yes 24
19.17 even 9 722.6.a.o.1.12 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.6.e.a.5.4 24 1.1 even 1 trivial
38.6.e.a.23.4 yes 24 19.4 even 9 inner
722.6.a.o.1.12 12 19.17 even 9
722.6.a.p.1.1 12 19.2 odd 18