Properties

Label 43.7.h.a.29.14
Level $43$
Weight $7$
Character 43.29
Analytic conductor $9.892$
Analytic rank $0$
Dimension $252$
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] = [43,7,Mod(3,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\), degree \(12\), 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: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(252\)
Relative dimension: \(21\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 29.14
Character \(\chi\) \(=\) 43.29
Dual form 43.7.h.a.3.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.66970 + 5.54370i) q^{2} +(-33.1314 + 2.48285i) q^{3} +(16.2981 - 20.4372i) q^{4} +(-16.0047 - 51.8861i) q^{5} +(-102.215 - 177.042i) q^{6} +(211.134 + 121.898i) q^{7} +(540.730 + 123.418i) q^{8} +(370.667 - 55.8691i) q^{9} +O(q^{10})\) \(q+(2.66970 + 5.54370i) q^{2} +(-33.1314 + 2.48285i) q^{3} +(16.2981 - 20.4372i) q^{4} +(-16.0047 - 51.8861i) q^{5} +(-102.215 - 177.042i) q^{6} +(211.134 + 121.898i) q^{7} +(540.730 + 123.418i) q^{8} +(370.667 - 55.8691i) q^{9} +(244.913 - 227.246i) q^{10} +(250.917 + 314.640i) q^{11} +(-489.236 + 717.578i) q^{12} +(1651.29 + 1532.17i) q^{13} +(-112.102 + 1495.90i) q^{14} +(659.085 + 1679.32i) q^{15} +(387.125 + 1696.11i) q^{16} +(5161.89 + 1592.23i) q^{17} +(1299.29 + 1905.71i) q^{18} +(-169.021 + 1121.38i) q^{19} +(-1321.25 - 518.553i) q^{20} +(-7297.83 - 3514.45i) q^{21} +(-1074.39 + 2231.00i) q^{22} +(72.1719 - 183.891i) q^{23} +(-18221.6 - 2746.46i) q^{24} +(10474.0 - 7141.03i) q^{25} +(-4085.44 + 13244.7i) q^{26} +(11471.3 - 2618.24i) q^{27} +(5932.35 - 2328.27i) q^{28} +(20778.9 + 1557.16i) q^{29} +(-7550.09 + 8137.06i) q^{30} +(2538.77 + 1730.90i) q^{31} +(19383.2 - 15457.6i) q^{32} +(-9094.44 - 9801.47i) q^{33} +(4953.86 + 32866.7i) q^{34} +(2945.68 - 12905.9i) q^{35} +(4899.36 - 8485.95i) q^{36} +(-3922.38 + 2264.59i) q^{37} +(-6667.84 + 2056.76i) q^{38} +(-58513.5 - 46663.0i) q^{39} +(-2250.56 - 30031.6i) q^{40} +(-42574.1 + 20502.6i) q^{41} -49839.5i q^{42} +(-44842.4 - 65654.6i) q^{43} +10519.8 q^{44} +(-8831.26 - 18338.3i) q^{45} +(1212.11 - 90.8354i) q^{46} +(-35826.9 + 44925.6i) q^{47} +(-17037.2 - 55233.2i) q^{48} +(-29106.1 - 50413.2i) q^{49} +(67550.1 + 39000.0i) q^{50} +(-174974. - 39936.7i) q^{51} +(58226.0 - 8776.16i) q^{52} +(-89105.7 + 82678.0i) q^{53} +(45139.5 + 56603.2i) q^{54} +(12309.6 - 18054.8i) q^{55} +(99122.1 + 91971.9i) q^{56} +(2815.68 - 37572.6i) q^{57} +(46841.0 + 119349. i) q^{58} +(32710.0 + 143312. i) q^{59} +(45062.4 + 13899.9i) q^{60} +(118117. + 173246. i) q^{61} +(-2817.84 + 18695.2i) q^{62} +(85070.9 + 33387.9i) q^{63} +(237756. + 114497. i) q^{64} +(53069.9 - 110201. i) q^{65} +(30056.9 - 76583.8i) q^{66} +(144364. + 21759.4i) q^{67} +(116670. - 79544.1i) q^{68} +(-1934.58 + 6271.76i) q^{69} +(79410.4 - 18124.9i) q^{70} +(-466218. + 182977. i) q^{71} +(207326. + 15536.9i) q^{72} +(362592. - 390781. i) q^{73} +(-23025.8 - 15698.7i) q^{74} +(-329287. + 262598. i) q^{75} +(20163.2 + 21730.7i) q^{76} +(14623.1 + 97017.7i) q^{77} +(102472. - 448958. i) q^{78} +(-3158.67 + 5470.98i) q^{79} +(81808.6 - 47232.2i) q^{80} +(-634686. + 195775. i) q^{81} +(-227320. - 181282. i) q^{82} +(44832.5 + 598249. i) q^{83} +(-190766. + 91868.1i) q^{84} -293314. i q^{85} +(244253. - 423871. i) q^{86} -692300. q^{87} +(96846.0 + 201103. i) q^{88} +(560834. - 42028.7i) q^{89} +(78085.1 - 97915.6i) q^{90} +(161874. + 524782. i) q^{91} +(-2581.95 - 4472.07i) q^{92} +(-88410.6 - 51043.9i) q^{93} +(-344701. - 78675.7i) q^{94} +(60889.3 - 9177.59i) q^{95} +(-603814. + 560258. i) q^{96} +(-549117. - 688571. i) q^{97} +(201771. - 295943. i) q^{98} +(110585. + 102608. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9} + 967 q^{10} + 4090 q^{11} - 484 q^{12} + 1527 q^{13} + 7812 q^{14} - 8923 q^{15} - 13760 q^{16} - 3655 q^{17} + 5596 q^{18} + 38605 q^{19} + 26085 q^{20} + 24873 q^{21} - 25214 q^{22} + 27991 q^{23} - 20480 q^{24} - 24146 q^{25} - 34923 q^{26} - 14 q^{27} - 77634 q^{28} - 112735 q^{29} + 375072 q^{30} + 290647 q^{31} - 344064 q^{32} - 152174 q^{33} - 198311 q^{34} - 182471 q^{35} - 930891 q^{36} + 282762 q^{37} + 487342 q^{38} + 857290 q^{39} + 745459 q^{40} + 27674 q^{41} + 148802 q^{43} - 1255832 q^{44} - 191310 q^{45} - 1344785 q^{46} + 69166 q^{47} - 871241 q^{48} + 1786604 q^{49} + 837705 q^{50} - 182756 q^{51} + 2906416 q^{52} + 7779 q^{53} + 487154 q^{54} - 529592 q^{55} - 2464007 q^{56} - 767855 q^{57} - 1523780 q^{58} + 1531338 q^{59} - 1858647 q^{60} + 646957 q^{61} - 448559 q^{62} - 2007847 q^{63} + 3937366 q^{64} - 1473542 q^{65} + 1513319 q^{66} - 575523 q^{67} + 2717157 q^{68} + 967041 q^{69} + 4624473 q^{70} - 2149319 q^{71} - 9986371 q^{72} - 514565 q^{73} - 882972 q^{74} - 6655138 q^{75} + 1152658 q^{76} - 341803 q^{77} + 6322388 q^{78} - 2476742 q^{79} + 10750038 q^{80} + 4308941 q^{81} + 5079172 q^{82} + 2318609 q^{83} + 5578407 q^{84} + 585292 q^{86} - 1990710 q^{87} - 2864890 q^{88} - 4561993 q^{89} - 17681545 q^{90} - 4648506 q^{91} - 1991714 q^{92} - 8868294 q^{93} - 10200218 q^{94} + 10091737 q^{95} + 6250318 q^{96} - 1676750 q^{97} + 7512700 q^{98} + 18452884 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{41}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.66970 + 5.54370i 0.333713 + 0.692962i 0.998539 0.0540362i \(-0.0172086\pi\)
−0.664826 + 0.746998i \(0.731494\pi\)
\(3\) −33.1314 + 2.48285i −1.22709 + 0.0919576i −0.672456 0.740137i \(-0.734760\pi\)
−0.554633 + 0.832095i \(0.687141\pi\)
\(4\) 16.2981 20.4372i 0.254658 0.319331i
\(5\) −16.0047 51.8861i −0.128038 0.415089i 0.868743 0.495263i \(-0.164928\pi\)
−0.996781 + 0.0801745i \(0.974452\pi\)
\(6\) −102.215 177.042i −0.473218 0.819638i
\(7\) 211.134 + 121.898i 0.615552 + 0.355389i 0.775135 0.631795i \(-0.217682\pi\)
−0.159583 + 0.987184i \(0.551015\pi\)
\(8\) 540.730 + 123.418i 1.05611 + 0.241051i
\(9\) 370.667 55.8691i 0.508460 0.0766380i
\(10\) 244.913 227.246i 0.244913 0.227246i
\(11\) 250.917 + 314.640i 0.188518 + 0.236394i 0.867104 0.498127i \(-0.165979\pi\)
−0.678587 + 0.734520i \(0.737407\pi\)
\(12\) −489.236 + 717.578i −0.283123 + 0.415265i
\(13\) 1651.29 + 1532.17i 0.751609 + 0.697391i 0.959796 0.280698i \(-0.0905658\pi\)
−0.208187 + 0.978089i \(0.566756\pi\)
\(14\) −112.102 + 1495.90i −0.0408535 + 0.545152i
\(15\) 659.085 + 1679.32i 0.195284 + 0.497577i
\(16\) 387.125 + 1696.11i 0.0945131 + 0.414089i
\(17\) 5161.89 + 1592.23i 1.05066 + 0.324086i 0.771547 0.636173i \(-0.219483\pi\)
0.279113 + 0.960258i \(0.409960\pi\)
\(18\) 1299.29 + 1905.71i 0.222787 + 0.326768i
\(19\) −169.021 + 1121.38i −0.0246423 + 0.163491i −0.997767 0.0667868i \(-0.978725\pi\)
0.973125 + 0.230277i \(0.0739634\pi\)
\(20\) −1321.25 518.553i −0.165157 0.0648192i
\(21\) −7297.83 3514.45i −0.788017 0.379489i
\(22\) −1074.39 + 2231.00i −0.100901 + 0.209523i
\(23\) 72.1719 183.891i 0.00593178 0.0151139i −0.927877 0.372886i \(-0.878368\pi\)
0.933809 + 0.357772i \(0.116464\pi\)
\(24\) −18221.6 2746.46i −1.31811 0.198673i
\(25\) 10474.0 7141.03i 0.670334 0.457026i
\(26\) −4085.44 + 13244.7i −0.232444 + 0.753565i
\(27\) 11471.3 2618.24i 0.582800 0.133020i
\(28\) 5932.35 2328.27i 0.270242 0.106062i
\(29\) 20778.9 + 1557.16i 0.851978 + 0.0638469i 0.493557 0.869713i \(-0.335696\pi\)
0.358421 + 0.933560i \(0.383315\pi\)
\(30\) −7550.09 + 8137.06i −0.279633 + 0.301372i
\(31\) 2538.77 + 1730.90i 0.0852193 + 0.0581016i 0.605180 0.796089i \(-0.293101\pi\)
−0.519961 + 0.854190i \(0.674053\pi\)
\(32\) 19383.2 15457.6i 0.591529 0.471729i
\(33\) −9094.44 9801.47i −0.253066 0.272740i
\(34\) 4953.86 + 32866.7i 0.126040 + 0.836219i
\(35\) 2945.68 12905.9i 0.0687040 0.301012i
\(36\) 4899.36 8485.95i 0.105010 0.181883i
\(37\) −3922.38 + 2264.59i −0.0774362 + 0.0447078i −0.538218 0.842806i \(-0.680902\pi\)
0.460782 + 0.887513i \(0.347569\pi\)
\(38\) −6667.84 + 2056.76i −0.121516 + 0.0374828i
\(39\) −58513.5 46663.0i −0.986422 0.786645i
\(40\) −2250.56 30031.6i −0.0351650 0.469244i
\(41\) −42574.1 + 20502.6i −0.617723 + 0.297480i −0.716454 0.697634i \(-0.754236\pi\)
0.0987308 + 0.995114i \(0.468522\pi\)
\(42\) 49839.5i 0.672706i
\(43\) −44842.4 65654.6i −0.564005 0.825771i
\(44\) 10519.8 0.123495
\(45\) −8831.26 18338.3i −0.0969137 0.201243i
\(46\) 1212.11 90.8354i 0.0124529 0.000933215i
\(47\) −35826.9 + 44925.6i −0.345077 + 0.432713i −0.923838 0.382785i \(-0.874965\pi\)
0.578761 + 0.815498i \(0.303537\pi\)
\(48\) −17037.2 55233.2i −0.154055 0.499432i
\(49\) −29106.1 50413.2i −0.247397 0.428505i
\(50\) 67550.1 + 39000.0i 0.540401 + 0.312000i
\(51\) −174974. 39936.7i −1.31905 0.301066i
\(52\) 58226.0 8776.16i 0.414102 0.0624158i
\(53\) −89105.7 + 82678.0i −0.598519 + 0.555345i −0.920173 0.391513i \(-0.871952\pi\)
0.321653 + 0.946857i \(0.395761\pi\)
\(54\) 45139.5 + 56603.2i 0.286666 + 0.359468i
\(55\) 12309.6 18054.8i 0.0739870 0.108519i
\(56\) 99122.1 + 91971.9i 0.564425 + 0.523710i
\(57\) 2815.68 37572.6i 0.0152040 0.202884i
\(58\) 46841.0 + 119349.i 0.240073 + 0.611695i
\(59\) 32710.0 + 143312.i 0.159267 + 0.697793i 0.989994 + 0.141113i \(0.0450680\pi\)
−0.830727 + 0.556680i \(0.812075\pi\)
\(60\) 45062.4 + 13899.9i 0.208622 + 0.0643515i
\(61\) 118117. + 173246.i 0.520382 + 0.763260i 0.993014 0.118000i \(-0.0376483\pi\)
−0.472632 + 0.881260i \(0.656696\pi\)
\(62\) −2817.84 + 18695.2i −0.0118234 + 0.0784430i
\(63\) 85070.9 + 33387.9i 0.340220 + 0.133526i
\(64\) 237756. + 114497.i 0.906967 + 0.436772i
\(65\) 53069.9 110201.i 0.193245 0.401277i
\(66\) 30056.9 76583.8i 0.104547 0.266382i
\(67\) 144364. + 21759.4i 0.479992 + 0.0723472i 0.384582 0.923091i \(-0.374346\pi\)
0.0954103 + 0.995438i \(0.469584\pi\)
\(68\) 116670. 79544.1i 0.371049 0.252977i
\(69\) −1934.58 + 6271.76i −0.00588898 + 0.0190916i
\(70\) 79410.4 18124.9i 0.231517 0.0528423i
\(71\) −466218. + 182977.i −1.30261 + 0.511236i −0.912328 0.409461i \(-0.865717\pi\)
−0.390280 + 0.920696i \(0.627622\pi\)
\(72\) 207326. + 15536.9i 0.555464 + 0.0416263i
\(73\) 362592. 390781.i 0.932072 1.00453i −0.0679047 0.997692i \(-0.521631\pi\)
0.999977 0.00684275i \(-0.00217813\pi\)
\(74\) −23025.8 15698.7i −0.0568223 0.0387408i
\(75\) −329287. + 262598.i −0.780532 + 0.622453i
\(76\) 20163.2 + 21730.7i 0.0459323 + 0.0495032i
\(77\) 14623.1 + 97017.7i 0.0320307 + 0.212510i
\(78\) 102472. 448958.i 0.215933 0.946066i
\(79\) −3158.67 + 5470.98i −0.00640653 + 0.0110964i −0.869211 0.494442i \(-0.835373\pi\)
0.862804 + 0.505538i \(0.168706\pi\)
\(80\) 81808.6 47232.2i 0.159782 0.0922504i
\(81\) −634686. + 195775.i −1.19427 + 0.368385i
\(82\) −227320. 181282.i −0.412284 0.328786i
\(83\) 44832.5 + 598249.i 0.0784078 + 1.04628i 0.888168 + 0.459518i \(0.151978\pi\)
−0.809760 + 0.586761i \(0.800403\pi\)
\(84\) −190766. + 91868.1i −0.321857 + 0.154998i
\(85\) 293314.i 0.477612i
\(86\) 244253. 423871.i 0.384012 0.666405i
\(87\) −692300. −1.05132
\(88\) 96846.0 + 201103.i 0.142113 + 0.295101i
\(89\) 560834. 42028.7i 0.795544 0.0596178i 0.329244 0.944245i \(-0.393206\pi\)
0.466299 + 0.884627i \(0.345587\pi\)
\(90\) 78085.1 97915.6i 0.107113 0.134315i
\(91\) 161874. + 524782.i 0.214809 + 0.696394i
\(92\) −2581.95 4472.07i −0.00331577 0.00574308i
\(93\) −88410.6 51043.9i −0.109915 0.0634592i
\(94\) −344701. 78675.7i −0.415010 0.0947234i
\(95\) 60889.3 9177.59i 0.0710183 0.0107043i
\(96\) −603814. + 560258.i −0.682480 + 0.633249i
\(97\) −549117. 688571.i −0.601658 0.754456i 0.383977 0.923343i \(-0.374554\pi\)
−0.985635 + 0.168887i \(0.945983\pi\)
\(98\) 201771. 295943.i 0.214378 0.314435i
\(99\) 110585. + 102608.i 0.113970 + 0.105749i
\(100\) 24763.3 330443.i 0.0247633 0.330443i
\(101\) −85711.7 218390.i −0.0831909 0.211967i 0.883225 0.468949i \(-0.155367\pi\)
−0.966416 + 0.256982i \(0.917272\pi\)
\(102\) −245732. 1.07662e6i −0.231559 1.01452i
\(103\) −295107. 91028.6i −0.270065 0.0833040i 0.156765 0.987636i \(-0.449894\pi\)
−0.426830 + 0.904332i \(0.640370\pi\)
\(104\) 703802. + 1.03229e6i 0.625677 + 0.917700i
\(105\) −65551.2 + 434904.i −0.0566256 + 0.375686i
\(106\) −696228. 273249.i −0.584566 0.229425i
\(107\) −1.61915e6 779743.i −1.32171 0.636503i −0.365947 0.930636i \(-0.619255\pi\)
−0.955764 + 0.294133i \(0.904969\pi\)
\(108\) 133450. 277112.i 0.105937 0.219981i
\(109\) 784414. 1.99866e6i 0.605712 1.54333i −0.217778 0.975998i \(-0.569881\pi\)
0.823490 0.567330i \(-0.192024\pi\)
\(110\) 132953. + 20039.5i 0.0998899 + 0.0150560i
\(111\) 124331. 84767.6i 0.0909099 0.0619813i
\(112\) −125017. + 405296.i −0.0889849 + 0.288482i
\(113\) 1.12382e6 256504.i 0.778861 0.177770i 0.185433 0.982657i \(-0.440631\pi\)
0.593428 + 0.804887i \(0.297774\pi\)
\(114\) 215808. 84698.5i 0.145664 0.0571691i
\(115\) −10696.5 801.591i −0.00703311 0.000527059i
\(116\) 370480. 399283.i 0.237351 0.255804i
\(117\) 697678. + 475669.i 0.435610 + 0.296994i
\(118\) −707152. + 563935.i −0.430394 + 0.343228i
\(119\) 895761. + 965401.i 0.531559 + 0.572884i
\(120\) 149128. + 989402.i 0.0863011 + 0.572571i
\(121\) 358170. 1.56925e6i 0.202178 0.885799i
\(122\) −645084. + 1.11732e6i −0.355252 + 0.615315i
\(123\) 1.35963e6 784985.i 0.730646 0.421838i
\(124\) 76751.9 23674.8i 0.0402554 0.0124171i
\(125\) −1.20147e6 958140.i −0.615152 0.490568i
\(126\) 42021.9 + 560743.i 0.0210070 + 0.280319i
\(127\) −2.08515e6 + 1.00415e6i −1.01795 + 0.490218i −0.866992 0.498322i \(-0.833950\pi\)
−0.150957 + 0.988540i \(0.548235\pi\)
\(128\) 37026.4i 0.0176556i
\(129\) 1.64870e6 + 2.06389e6i 0.768021 + 0.961430i
\(130\) 752600. 0.342558
\(131\) 1.36258e6 + 2.82943e6i 0.606105 + 1.25859i 0.947826 + 0.318789i \(0.103276\pi\)
−0.341720 + 0.939802i \(0.611010\pi\)
\(132\) −348536. + 26119.2i −0.151540 + 0.0113563i
\(133\) −172381. + 216159.i −0.0732714 + 0.0918794i
\(134\) 264782. + 858401.i 0.110046 + 0.356760i
\(135\) −319445. 553294.i −0.129836 0.224882i
\(136\) 2.59468e6 + 1.49804e6i 1.03149 + 0.595533i
\(137\) −132666. 30280.1i −0.0515938 0.0117759i 0.196646 0.980475i \(-0.436995\pi\)
−0.248240 + 0.968699i \(0.579852\pi\)
\(138\) −39933.5 + 6019.01i −0.0151950 + 0.00229027i
\(139\) −2.35221e6 + 2.18253e6i −0.875854 + 0.812673i −0.983386 0.181528i \(-0.941896\pi\)
0.107532 + 0.994202i \(0.465705\pi\)
\(140\) −215751. 270543.i −0.0786264 0.0985943i
\(141\) 1.07545e6 1.57740e6i 0.383649 0.562710i
\(142\) −2.25903e6 2.09607e6i −0.788964 0.732052i
\(143\) −67746.0 + 904008.i −0.0231673 + 0.309146i
\(144\) 238255. + 607063.i 0.0797910 + 0.203304i
\(145\) −251766. 1.10306e6i −0.0825834 0.361821i
\(146\) 3.13438e6 + 966829.i 1.00715 + 0.310664i
\(147\) 1.08949e6 + 1.59799e6i 0.342983 + 0.503063i
\(148\) −17645.6 + 117071.i −0.00544315 + 0.0361130i
\(149\) 1.58366e6 + 621540.i 0.478743 + 0.187893i 0.592427 0.805624i \(-0.298170\pi\)
−0.113684 + 0.993517i \(0.536265\pi\)
\(150\) −2.33486e6 1.12441e6i −0.691810 0.333158i
\(151\) 788221. 1.63676e6i 0.228938 0.475394i −0.754579 0.656209i \(-0.772159\pi\)
0.983517 + 0.180815i \(0.0578734\pi\)
\(152\) −229794. + 585505.i −0.0654346 + 0.166725i
\(153\) 2.00230e6 + 301798.i 0.559055 + 0.0842640i
\(154\) −498797. + 340074.i −0.136572 + 0.0931133i
\(155\) 49177.5 159430.i 0.0132060 0.0428128i
\(156\) −1.90732e6 + 435333.i −0.502400 + 0.114670i
\(157\) −3.23299e6 + 1.26885e6i −0.835420 + 0.327878i −0.744203 0.667953i \(-0.767171\pi\)
−0.0912164 + 0.995831i \(0.529075\pi\)
\(158\) −38762.1 2904.82i −0.00982735 0.000736458i
\(159\) 2.74692e6 2.96048e6i 0.683368 0.736496i
\(160\) −1.11226e6 758325.i −0.271548 0.185138i
\(161\) 37654.0 30028.1i 0.00902264 0.00719531i
\(162\) −2.77974e6 2.99584e6i −0.653821 0.704651i
\(163\) −818595. 5.43102e6i −0.189019 1.25406i −0.859114 0.511785i \(-0.828984\pi\)
0.670094 0.742276i \(-0.266254\pi\)
\(164\) −274862. + 1.20425e6i −0.0623136 + 0.273014i
\(165\) −363006. + 628745.i −0.0808094 + 0.139966i
\(166\) −3.19682e6 + 1.84568e6i −0.698866 + 0.403490i
\(167\) −105478. + 32535.5i −0.0226470 + 0.00698568i −0.306058 0.952013i \(-0.599010\pi\)
0.283411 + 0.958999i \(0.408534\pi\)
\(168\) −3.51241e6 2.80105e6i −0.740759 0.590736i
\(169\) 18494.0 + 246785.i 0.00383151 + 0.0511280i
\(170\) 1.62604e6 783061.i 0.330967 0.159385i
\(171\) 425103.i 0.0850169i
\(172\) −2.07264e6 153593.i −0.407323 0.0301847i
\(173\) 7.33488e6 1.41662 0.708312 0.705900i \(-0.249457\pi\)
0.708312 + 0.705900i \(0.249457\pi\)
\(174\) −1.84823e6 3.83790e6i −0.350840 0.728527i
\(175\) 3.08189e6 230956.i 0.575047 0.0430938i
\(176\) −436527. + 547387.i −0.0800706 + 0.100405i
\(177\) −1.43955e6 4.66691e6i −0.259602 0.841608i
\(178\) 1.73025e6 + 2.99689e6i 0.306796 + 0.531386i
\(179\) 9.19205e6 + 5.30703e6i 1.60270 + 0.925321i 0.990944 + 0.134277i \(0.0428713\pi\)
0.611760 + 0.791044i \(0.290462\pi\)
\(180\) −518716. 118393.i −0.0889430 0.0203007i
\(181\) 3.27902e6 494233.i 0.552979 0.0833482i 0.133392 0.991063i \(-0.457413\pi\)
0.419587 + 0.907715i \(0.362175\pi\)
\(182\) −2.47708e6 + 2.29839e6i −0.410890 + 0.381250i
\(183\) −4.34352e6 5.44660e6i −0.708742 0.888735i
\(184\) 61721.0 90528.1i 0.00990785 0.0145321i
\(185\) 180277. + 167273.i 0.0284725 + 0.0264186i
\(186\) 46941.7 626393.i 0.00729491 0.0973438i
\(187\) 794226. + 2.02366e6i 0.121456 + 0.309465i
\(188\) 334240. + 1.46440e6i 0.0503020 + 0.220387i
\(189\) 2.74113e6 + 845527.i 0.406017 + 0.125240i
\(190\) 213434. + 313050.i 0.0311174 + 0.0456408i
\(191\) 373625. 2.47884e6i 0.0536211 0.355753i −0.945890 0.324487i \(-0.894808\pi\)
0.999511 0.0312654i \(-0.00995372\pi\)
\(192\) −8.16146e6 3.20314e6i −1.15309 0.452556i
\(193\) −6.45013e6 3.10622e6i −0.897215 0.432076i −0.0723326 0.997381i \(-0.523044\pi\)
−0.824882 + 0.565305i \(0.808759\pi\)
\(194\) 2.35125e6 4.88242e6i 0.322028 0.668698i
\(195\) −1.48467e6 + 3.78287e6i −0.200228 + 0.510173i
\(196\) −1.50468e6 226793.i −0.199836 0.0301205i
\(197\) −9.28792e6 + 6.33240e6i −1.21484 + 0.828266i −0.989290 0.145965i \(-0.953371\pi\)
−0.225553 + 0.974231i \(0.572419\pi\)
\(198\) −273599. + 886985.i −0.0352467 + 0.114267i
\(199\) −9.43143e6 + 2.15266e6i −1.19679 + 0.273160i −0.774070 0.633100i \(-0.781782\pi\)
−0.422721 + 0.906260i \(0.638925\pi\)
\(200\) 6.54492e6 2.56869e6i 0.818114 0.321086i
\(201\) −4.83700e6 362483.i −0.595646 0.0446375i
\(202\) 981862. 1.05820e6i 0.119123 0.128384i
\(203\) 4.19732e6 + 2.86168e6i 0.501746 + 0.342085i
\(204\) −3.66794e6 + 2.92508e6i −0.432047 + 0.344546i
\(205\) 1.74519e6 + 1.88087e6i 0.202573 + 0.218321i
\(206\) −283214. 1.87900e6i −0.0323977 0.214944i
\(207\) 16477.9 72194.6i 0.00185777 0.00813942i
\(208\) −1.95947e6 + 3.39390e6i −0.217745 + 0.377146i
\(209\) −395242. + 228193.i −0.0432937 + 0.0249956i
\(210\) −2.58598e6 + 797668.i −0.279233 + 0.0861320i
\(211\) −7.00409e6 5.58557e6i −0.745597 0.594594i 0.175247 0.984524i \(-0.443928\pi\)
−0.920844 + 0.389931i \(0.872499\pi\)
\(212\) 237451. + 3.16856e6i 0.0249211 + 0.332548i
\(213\) 1.49921e7 7.21983e6i 1.55140 0.747116i
\(214\) 1.10578e7i 1.12830i
\(215\) −2.68887e6 + 3.37748e6i −0.270554 + 0.339842i
\(216\) 6.52598e6 0.647567
\(217\) 325027. + 674925.i 0.0318083 + 0.0660505i
\(218\) 1.31741e7 987262.i 1.27160 0.0952934i
\(219\) −1.10429e7 + 1.38474e7i −1.05136 + 1.31836i
\(220\) −168367. 545833.i −0.0158121 0.0512615i
\(221\) 6.08419e6 + 1.05381e7i 0.563671 + 0.976307i
\(222\) 801853. + 462950.i 0.0732885 + 0.0423131i
\(223\) 9.20356e6 + 2.10065e6i 0.829929 + 0.189426i 0.616323 0.787494i \(-0.288622\pi\)
0.213607 + 0.976920i \(0.431479\pi\)
\(224\) 5.97672e6 900846.i 0.531764 0.0801505i
\(225\) 3.48339e6 3.23212e6i 0.305812 0.283752i
\(226\) 4.42223e6 + 5.54530e6i 0.383104 + 0.480397i
\(227\) 1.66193e6 2.43760e6i 0.142081 0.208394i −0.748602 0.663020i \(-0.769275\pi\)
0.890683 + 0.454626i \(0.150227\pi\)
\(228\) −721988. 669907.i −0.0609152 0.0565210i
\(229\) 73598.1 982098.i 0.00612858 0.0817802i −0.993301 0.115557i \(-0.963135\pi\)
0.999429 + 0.0337771i \(0.0107536\pi\)
\(230\) −24112.7 61438.1i −0.00198181 0.00504957i
\(231\) −725363. 3.17802e6i −0.0588464 0.257823i
\(232\) 1.10436e7 + 3.40649e6i 0.884394 + 0.272800i
\(233\) −2.78422e6 4.08370e6i −0.220108 0.322839i 0.700263 0.713885i \(-0.253066\pi\)
−0.920371 + 0.391046i \(0.872113\pi\)
\(234\) −774370. + 5.13761e6i −0.0604367 + 0.400972i
\(235\) 2.90441e6 + 1.13990e6i 0.223797 + 0.0878340i
\(236\) 3.46200e6 + 1.66721e6i 0.263385 + 0.126840i
\(237\) 91067.5 189104.i 0.00684098 0.0142054i
\(238\) −2.96047e6 + 7.54316e6i −0.219599 + 0.559529i
\(239\) −5.25797e6 792511.i −0.385145 0.0580512i −0.0463838 0.998924i \(-0.514770\pi\)
−0.338761 + 0.940872i \(0.610008\pi\)
\(240\) −2.59316e6 + 1.76799e6i −0.187584 + 0.127893i
\(241\) −7.41698e6 + 2.40452e7i −0.529878 + 1.71782i 0.153859 + 0.988093i \(0.450830\pi\)
−0.683737 + 0.729729i \(0.739646\pi\)
\(242\) 9.65564e6 2.20384e6i 0.681294 0.155501i
\(243\) 1.25573e7 4.92837e6i 0.875139 0.343467i
\(244\) 5.46573e6 + 409600.i 0.376252 + 0.0281962i
\(245\) −2.14991e6 + 2.31705e6i −0.146191 + 0.157557i
\(246\) 7.98154e6 + 5.44172e6i 0.536144 + 0.365537i
\(247\) −1.99725e6 + 1.59275e6i −0.132538 + 0.105696i
\(248\) 1.15916e6 + 1.24928e6i 0.0759958 + 0.0819040i
\(249\) −2.97073e6 1.97095e7i −0.192427 1.27667i
\(250\) 2.10407e6 9.21853e6i 0.134660 0.589986i
\(251\) −1.38333e7 + 2.39600e7i −0.874793 + 1.51519i −0.0178105 + 0.999841i \(0.505670\pi\)
−0.856983 + 0.515345i \(0.827664\pi\)
\(252\) 2.06885e6 1.19445e6i 0.129279 0.0746391i
\(253\) 75968.7 23433.2i 0.00469108 0.00144701i
\(254\) −1.11335e7 8.87864e6i −0.679405 0.541808i
\(255\) 728255. + 9.71789e6i 0.0439201 + 0.586073i
\(256\) 1.50111e7 7.22897e6i 0.894732 0.430880i
\(257\) 1.99535e7i 1.17549i −0.809046 0.587745i \(-0.800016\pi\)
0.809046 0.587745i \(-0.199984\pi\)
\(258\) −7.04004e6 + 1.46499e7i −0.409936 + 0.853051i
\(259\) −1.10420e6 −0.0635547
\(260\) −1.38725e6 2.88066e6i −0.0789288 0.163897i
\(261\) 7.78905e6 583708.i 0.438089 0.0328303i
\(262\) −1.20478e7 + 1.51075e7i −0.669890 + 0.840016i
\(263\) −7.78467e6 2.52373e7i −0.427930 1.38732i −0.871200 0.490927i \(-0.836658\pi\)
0.443270 0.896388i \(-0.353818\pi\)
\(264\) −3.70795e6 6.42236e6i −0.201522 0.349046i
\(265\) 5.71596e6 + 3.30011e6i 0.307151 + 0.177333i
\(266\) −1.65852e6 378547.i −0.0881205 0.0201129i
\(267\) −1.84769e7 + 2.78494e6i −0.970721 + 0.146313i
\(268\) 2.79756e6 2.59575e6i 0.145336 0.134853i
\(269\) −1.98818e7 2.49310e7i −1.02141 1.28081i −0.959196 0.282742i \(-0.908756\pi\)
−0.0622120 0.998063i \(-0.519815\pi\)
\(270\) 2.21447e6 3.24803e6i 0.112507 0.165017i
\(271\) −2.52220e7 2.34026e7i −1.26728 1.17586i −0.975651 0.219330i \(-0.929613\pi\)
−0.291627 0.956532i \(-0.594197\pi\)
\(272\) −702298. + 9.37152e6i −0.0348991 + 0.465697i
\(273\) −6.66607e6 1.69849e7i −0.327629 0.834784i
\(274\) −186315. 816297.i −0.00905722 0.0396823i
\(275\) 4.87495e6 + 1.50372e6i 0.234408 + 0.0723052i
\(276\) 96647.0 + 141755.i 0.00459686 + 0.00674236i
\(277\) 4.63957e6 3.07816e7i 0.218292 1.44828i −0.564212 0.825630i \(-0.690820\pi\)
0.782504 0.622645i \(-0.213942\pi\)
\(278\) −1.83790e7 7.21322e6i −0.855435 0.335734i
\(279\) 1.03774e6 + 499750.i 0.0477834 + 0.0230113i
\(280\) 3.18564e6 6.61505e6i 0.145118 0.301341i
\(281\) −9.87680e6 + 2.51657e7i −0.445141 + 1.13420i 0.515619 + 0.856818i \(0.327562\pi\)
−0.960760 + 0.277382i \(0.910533\pi\)
\(282\) 1.16158e7 + 1.75079e6i 0.517965 + 0.0780707i
\(283\) −9.97328e6 + 6.79967e6i −0.440026 + 0.300005i −0.762994 0.646405i \(-0.776272\pi\)
0.322968 + 0.946410i \(0.395319\pi\)
\(284\) −3.85893e6 + 1.25103e7i −0.168466 + 0.546153i
\(285\) −1.99456e6 + 455246.i −0.0861614 + 0.0196658i
\(286\) −5.19241e6 + 2.03787e6i −0.221958 + 0.0871120i
\(287\) −1.14881e7 860913.i −0.485962 0.0364178i
\(288\) 6.32112e6 6.81255e6i 0.264616 0.285189i
\(289\) 4.16652e6 + 2.84069e6i 0.172616 + 0.117687i
\(290\) 5.44288e6 4.34055e6i 0.223169 0.177972i
\(291\) 1.99026e7 + 2.14499e7i 0.807666 + 0.870457i
\(292\) −2.07690e6 1.37793e7i −0.0834194 0.553452i
\(293\) −2.22497e6 + 9.74823e6i −0.0884547 + 0.387546i −0.999705 0.0243087i \(-0.992262\pi\)
0.911250 + 0.411854i \(0.135119\pi\)
\(294\) −5.95016e6 + 1.03060e7i −0.234146 + 0.405553i
\(295\) 6.91238e6 3.99087e6i 0.269254 0.155454i
\(296\) −2.40044e6 + 740437.i −0.0925582 + 0.0285504i
\(297\) 3.70213e6 + 2.95235e6i 0.141313 + 0.112694i
\(298\) 782268. + 1.04386e7i 0.0295602 + 0.394453i
\(299\) 400929. 193077.i 0.0149987 0.00722299i
\(300\) 1.10095e7i 0.407761i
\(301\) −1.46457e6 1.93281e7i −0.0537046 0.708746i
\(302\) 1.11780e7 0.405830
\(303\) 3.38198e6 + 7.02275e6i 0.121575 + 0.252452i
\(304\) −1.96742e6 + 147438.i −0.0700287 + 0.00524792i
\(305\) 7.09861e6 8.90137e6i 0.250192 0.313731i
\(306\) 3.67247e6 + 1.19059e7i 0.128172 + 0.415524i
\(307\) 2.05872e7 + 3.56580e7i 0.711510 + 1.23237i 0.964290 + 0.264848i \(0.0853219\pi\)
−0.252780 + 0.967524i \(0.581345\pi\)
\(308\) 2.22109e6 + 1.28235e6i 0.0760177 + 0.0438889i
\(309\) 1.00033e7 + 2.28319e6i 0.339054 + 0.0773869i
\(310\) 1.01512e6 153004.i 0.0340747 0.00513593i
\(311\) −1.73798e7 + 1.61261e7i −0.577781 + 0.536102i −0.914017 0.405676i \(-0.867036\pi\)
0.336237 + 0.941778i \(0.390846\pi\)
\(312\) −2.58810e7 3.24537e7i −0.852151 1.06856i
\(313\) 3.20251e7 4.69722e7i 1.04438 1.53182i 0.212265 0.977212i \(-0.431916\pi\)
0.832112 0.554607i \(-0.187131\pi\)
\(314\) −1.56652e7 1.45352e7i −0.505997 0.469497i
\(315\) 370828. 4.94836e6i 0.0118643 0.158318i
\(316\) 60331.0 + 153721.i 0.00191196 + 0.00487160i
\(317\) −3.24206e6 1.42044e7i −0.101775 0.445907i −0.999980 0.00632951i \(-0.997985\pi\)
0.898205 0.439578i \(-0.144872\pi\)
\(318\) 2.37454e7 + 7.32450e6i 0.738412 + 0.227770i
\(319\) 4.72383e6 + 6.92859e6i 0.145520 + 0.213438i
\(320\) 2.13559e6 1.41687e7i 0.0651731 0.432395i
\(321\) 5.55808e7 + 2.18139e7i 1.68039 + 0.659504i
\(322\) 266991. + 128576.i 0.00799705 + 0.00385118i
\(323\) −2.65797e6 + 5.51933e6i −0.0788756 + 0.163787i
\(324\) −6.34309e6 + 1.61619e7i −0.186494 + 0.475180i
\(325\) 2.82368e7 + 4.25601e6i 0.822555 + 0.123980i
\(326\) 2.79225e7 1.90373e7i 0.805938 0.549479i
\(327\) −2.10264e7 + 6.81658e7i −0.601341 + 1.94950i
\(328\) −2.55515e7 + 5.83196e6i −0.724093 + 0.165270i
\(329\) −1.30406e7 + 5.11808e6i −0.366194 + 0.143721i
\(330\) −4.45469e6 333833.i −0.123958 0.00928939i
\(331\) 1.78559e7 1.92441e7i 0.492377 0.530656i −0.437161 0.899383i \(-0.644016\pi\)
0.929538 + 0.368727i \(0.120206\pi\)
\(332\) 1.29572e7 + 8.83407e6i 0.354076 + 0.241405i
\(333\) −1.32738e6 + 1.05855e6i −0.0359469 + 0.0286667i
\(334\) −461961. 497876.i −0.0123984 0.0133623i
\(335\) −1.18150e6 7.83874e6i −0.0314267 0.208503i
\(336\) 3.13571e6 1.37384e7i 0.0826643 0.362176i
\(337\) −9.13150e6 + 1.58162e7i −0.238590 + 0.413250i −0.960310 0.278935i \(-0.910019\pi\)
0.721720 + 0.692185i \(0.243352\pi\)
\(338\) −1.31873e6 + 761368.i −0.0341511 + 0.0197172i
\(339\) −3.65967e7 + 1.12886e7i −0.939384 + 0.289762i
\(340\) −5.99450e6 4.78046e6i −0.152516 0.121628i
\(341\) 92408.9 + 1.23311e6i 0.00233051 + 0.0310985i
\(342\) −2.35664e6 + 1.13490e6i −0.0589135 + 0.0283712i
\(343\) 4.28744e7i 1.06247i
\(344\) −1.61447e7 4.10357e7i −0.396601 1.00806i
\(345\) 356380. 0.00867872
\(346\) 1.95819e7 + 4.06623e7i 0.472746 + 0.981666i
\(347\) −5.63351e7 + 4.22174e6i −1.34831 + 0.101042i −0.729222 0.684277i \(-0.760118\pi\)
−0.619091 + 0.785319i \(0.712499\pi\)
\(348\) −1.12832e7 + 1.41486e7i −0.267728 + 0.335720i
\(349\) 2.97103e6 + 9.63184e6i 0.0698925 + 0.226586i 0.983779 0.179383i \(-0.0574102\pi\)
−0.913887 + 0.405969i \(0.866934\pi\)
\(350\) 9.50809e6 + 1.64685e7i 0.221763 + 0.384105i
\(351\) 2.29539e7 + 1.32524e7i 0.530805 + 0.306460i
\(352\) 9.72716e6 + 2.22016e6i 0.223027 + 0.0509046i
\(353\) −1.97099e7 + 2.97078e6i −0.448084 + 0.0675378i −0.369208 0.929347i \(-0.620371\pi\)
−0.0788756 + 0.996884i \(0.525133\pi\)
\(354\) 2.20288e7 2.04397e7i 0.496570 0.460749i
\(355\) 1.69557e7 + 2.12617e7i 0.378991 + 0.475240i
\(356\) 8.28158e6 1.21468e7i 0.183554 0.269224i
\(357\) −3.20748e7 2.97610e7i −0.704951 0.654099i
\(358\) −4.88053e6 + 6.51261e7i −0.106370 + 1.41940i
\(359\) −3.39658e6 8.65434e6i −0.0734105 0.187047i 0.889458 0.457016i \(-0.151082\pi\)
−0.962869 + 0.269969i \(0.912987\pi\)
\(360\) −2.51205e6 1.10060e7i −0.0538419 0.235897i
\(361\) 4.37268e7 + 1.34879e7i 0.929451 + 0.286698i
\(362\) 1.14939e7 + 1.68584e7i 0.242293 + 0.355379i
\(363\) −7.97047e6 + 5.28806e7i −0.166634 + 1.10555i
\(364\) 1.33633e7 + 5.24471e6i 0.277083 + 0.108747i
\(365\) −2.60793e7 1.25591e7i −0.536312 0.258274i
\(366\) 1.85984e7 3.86200e7i 0.379343 0.787714i
\(367\) 6.11614e6 1.55837e7i 0.123731 0.315262i −0.855565 0.517696i \(-0.826790\pi\)
0.979296 + 0.202434i \(0.0648851\pi\)
\(368\) 339839. + 51222.4i 0.00681914 + 0.00102782i
\(369\) −1.46354e7 + 9.97822e6i −0.291289 + 0.198598i
\(370\) −446023. + 1.44597e6i −0.00880546 + 0.0285466i
\(371\) −2.88916e7 + 6.59432e6i −0.565783 + 0.129136i
\(372\) −2.48412e6 + 974944.i −0.0482551 + 0.0189387i
\(373\) 4.02506e7 + 3.01636e6i 0.775614 + 0.0581243i 0.456655 0.889644i \(-0.349048\pi\)
0.318960 + 0.947768i \(0.396667\pi\)
\(374\) −9.09818e6 + 9.80551e6i −0.173916 + 0.187437i
\(375\) 4.21853e7 + 2.87614e7i 0.799958 + 0.545402i
\(376\) −2.49173e7 + 1.98709e7i −0.468746 + 0.373813i
\(377\) 3.19260e7 + 3.44081e7i 0.595828 + 0.642150i
\(378\) 2.63066e6 + 1.74533e7i 0.0487068 + 0.323149i
\(379\) −8.45478e6 + 3.70428e7i −0.155305 + 0.680435i 0.835987 + 0.548750i \(0.184896\pi\)
−0.991292 + 0.131685i \(0.957961\pi\)
\(380\) 804816. 1.39398e6i 0.0146672 0.0254043i
\(381\) 6.65907e7 3.84462e7i 1.20403 0.695149i
\(382\) 1.47394e7 4.54650e6i 0.264417 0.0815619i
\(383\) −4.82140e7 3.84494e7i −0.858177 0.684374i 0.0921096 0.995749i \(-0.470639\pi\)
−0.950287 + 0.311375i \(0.899210\pi\)
\(384\) −91931.3 1.22674e6i −0.00162356 0.0216650i
\(385\) 4.79983e6 2.31148e6i 0.0841092 0.0405049i
\(386\) 4.40502e7i 0.765925i
\(387\) −2.02897e7 2.18307e7i −0.350059 0.376647i
\(388\) −2.30220e7 −0.394138
\(389\) −6.35621e6 1.31988e7i −0.107982 0.224226i 0.839975 0.542624i \(-0.182569\pi\)
−0.947957 + 0.318398i \(0.896855\pi\)
\(390\) −2.49347e7 + 1.86860e6i −0.420349 + 0.0315008i
\(391\) 665341. 834311.i 0.0111305 0.0139572i
\(392\) −9.51661e6 3.08521e7i −0.157988 0.512185i
\(393\) −5.21692e7 9.03598e7i −0.859482 1.48867i
\(394\) −5.99009e7 3.45838e7i −0.979365 0.565437i
\(395\) 334421. + 76329.5i 0.00542629 + 0.00123851i
\(396\) 3.89935e6 587733.i 0.0627924 0.00946443i
\(397\) −2.74600e6 + 2.54792e6i −0.0438863 + 0.0407206i −0.701811 0.712363i \(-0.747625\pi\)
0.657925 + 0.753084i \(0.271434\pi\)
\(398\) −3.71128e7 4.65380e7i −0.588674 0.738173i
\(399\) 5.17453e6 7.58964e6i 0.0814614 0.119482i
\(400\) 1.61667e7 + 1.50005e7i 0.252605 + 0.234383i
\(401\) 6.09511e6 8.13336e7i 0.0945253 1.26135i −0.725177 0.688563i \(-0.758242\pi\)
0.819702 0.572790i \(-0.194139\pi\)
\(402\) −1.09039e7 2.77826e7i −0.167843 0.427656i
\(403\) 1.54020e6 + 6.74804e6i 0.0235321 + 0.103101i
\(404\) −5.86021e6 1.80764e6i −0.0888728 0.0274136i
\(405\) 2.03160e7 + 2.97980e7i 0.305825 + 0.448562i
\(406\) −4.65871e6 + 3.09085e7i −0.0696125 + 0.461849i
\(407\) −1.69672e6 665914.i −0.0251667 0.00987722i
\(408\) −8.96847e7 4.31899e7i −1.32050 0.635919i
\(409\) 2.88184e7 5.98420e7i 0.421211 0.874654i −0.577107 0.816669i \(-0.695818\pi\)
0.998317 0.0579847i \(-0.0184675\pi\)
\(410\) −5.76781e6 + 1.46961e7i −0.0836873 + 0.213232i
\(411\) 4.47058e6 + 673832.i 0.0643930 + 0.00970568i
\(412\) −6.67005e6 + 4.54757e6i −0.0953757 + 0.0650261i
\(413\) −1.05633e7 + 3.42454e7i −0.149951 + 0.486129i
\(414\) 444216. 101389.i 0.00626027 0.00142887i
\(415\) 3.03233e7 1.19010e7i 0.424260 0.166510i
\(416\) 5.56909e7 + 4.17346e6i 0.773578 + 0.0579717i
\(417\) 7.25131e7 7.81505e7i 1.00002 1.07776i
\(418\) −2.32021e6 1.58189e6i −0.0317687 0.0216595i
\(419\) −4.66820e7 + 3.72276e7i −0.634611 + 0.506085i −0.887138 0.461505i \(-0.847310\pi\)
0.252527 + 0.967590i \(0.418738\pi\)
\(420\) 7.81984e6 + 8.42779e6i 0.105548 + 0.113754i
\(421\) 2.06866e6 + 1.37247e7i 0.0277232 + 0.183931i 0.998407 0.0564306i \(-0.0179720\pi\)
−0.970683 + 0.240362i \(0.922734\pi\)
\(422\) 1.22659e7 5.37403e7i 0.163216 0.715094i
\(423\) −1.07699e7 + 1.86540e7i −0.142296 + 0.246463i
\(424\) −5.83861e7 + 3.37092e7i −0.765970 + 0.442233i
\(425\) 6.54357e7 2.01842e7i 0.852408 0.262933i
\(426\) 8.00491e7 + 6.38370e7i 1.03545 + 0.825741i
\(427\) 3.82015e6 + 5.09763e7i 0.0490678 + 0.654764i
\(428\) −4.23249e7 + 2.03826e7i −0.539839 + 0.259973i
\(429\) 3.01192e7i 0.381480i
\(430\) −2.59022e7 5.88940e6i −0.325785 0.0740740i
\(431\) 6.69534e7 0.836259 0.418129 0.908387i \(-0.362686\pi\)
0.418129 + 0.908387i \(0.362686\pi\)
\(432\) 8.88163e6 + 1.84429e7i 0.110164 + 0.228759i
\(433\) 3.31460e6 248395.i 0.0408289 0.00305970i −0.0543000 0.998525i \(-0.517293\pi\)
0.0951289 + 0.995465i \(0.469674\pi\)
\(434\) −2.87385e6 + 3.60370e6i −0.0351557 + 0.0440838i
\(435\) 1.10801e7 + 3.59207e7i 0.134609 + 0.436393i
\(436\) −2.80624e7 4.86055e7i −0.338583 0.586443i
\(437\) 194014. + 112014.i 0.00232481 + 0.00134223i
\(438\) −1.06247e8 2.42502e7i −1.26443 0.288598i
\(439\) −8.30638e7 + 1.25199e7i −0.981789 + 0.147981i −0.620274 0.784385i \(-0.712979\pi\)
−0.361515 + 0.932366i \(0.617740\pi\)
\(440\) 8.88445e6 8.24356e6i 0.104297 0.0967736i
\(441\) −1.36052e7 1.70604e7i −0.158631 0.198917i
\(442\) −4.21772e7 + 6.18625e7i −0.488439 + 0.716409i
\(443\) 5.30406e7 + 4.92145e7i 0.610095 + 0.566085i 0.923531 0.383524i \(-0.125290\pi\)
−0.313436 + 0.949609i \(0.601480\pi\)
\(444\) 293953. 3.92253e6i 0.00335837 0.0448144i
\(445\) −1.11567e7 2.84268e7i −0.126606 0.322588i
\(446\) 1.29254e7 + 5.66298e7i 0.145693 + 0.638323i
\(447\) −5.40120e7 1.66605e7i −0.604739 0.186537i
\(448\) 3.62414e7 + 5.31563e7i 0.403061 + 0.591182i
\(449\) −1.13348e7 + 7.52017e7i −0.125221 + 0.830784i 0.834739 + 0.550646i \(0.185619\pi\)
−0.959960 + 0.280139i \(0.909620\pi\)
\(450\) 2.72175e7 + 1.06821e7i 0.298683 + 0.117224i
\(451\) −1.71335e7 8.25106e6i −0.186774 0.0899457i
\(452\) 1.30739e7 2.71481e7i 0.141576 0.293985i
\(453\) −2.20510e7 + 5.61851e7i −0.237211 + 0.604403i
\(454\) 1.79502e7 + 2.70555e6i 0.191823 + 0.0289127i
\(455\) 2.46382e7 1.67980e7i 0.261562 0.178330i
\(456\) 6.15966e6 1.99691e7i 0.0649624 0.210603i
\(457\) −1.62492e8 + 3.70876e7i −1.70248 + 0.388580i −0.959716 0.280973i \(-0.909343\pi\)
−0.742765 + 0.669553i \(0.766486\pi\)
\(458\) 5.64094e6 2.21390e6i 0.0587158 0.0230442i
\(459\) 6.33822e7 + 4.74984e6i 0.655434 + 0.0491180i
\(460\) −190715. + 205542.i −0.00195934 + 0.00211167i
\(461\) 1.15895e8 + 7.90157e7i 1.18294 + 0.806512i 0.984805 0.173664i \(-0.0555606\pi\)
0.198130 + 0.980176i \(0.436513\pi\)
\(462\) 1.56815e7 1.25056e7i 0.159024 0.126817i
\(463\) 6.32295e7 + 6.81452e7i 0.637055 + 0.686582i 0.966228 0.257688i \(-0.0829606\pi\)
−0.329174 + 0.944269i \(0.606770\pi\)
\(464\) 5.40292e6 + 3.58460e7i 0.0540847 + 0.358829i
\(465\) −1.23348e6 + 5.40422e6i −0.0122680 + 0.0537495i
\(466\) 1.52057e7 2.63371e7i 0.150262 0.260262i
\(467\) 1.06453e8 6.14605e7i 1.04522 0.603456i 0.123910 0.992293i \(-0.460457\pi\)
0.921306 + 0.388838i \(0.127123\pi\)
\(468\) 2.10922e7 6.50607e6i 0.205771 0.0634718i
\(469\) 2.78277e7 + 2.21919e7i 0.269749 + 0.215117i
\(470\) 1.43467e6 + 1.91444e7i 0.0138184 + 0.184394i
\(471\) 1.03963e8 5.00659e7i 0.994983 0.479159i
\(472\) 8.15301e7i 0.775339i
\(473\) 9.40584e6 3.05831e7i 0.0888821 0.289000i
\(474\) 1.29146e6 0.0121268
\(475\) 6.23750e6 + 1.29523e7i 0.0582009 + 0.120855i
\(476\) 3.43293e7 2.57262e6i 0.318305 0.0238537i
\(477\) −2.84094e7 + 3.56243e7i −0.261762 + 0.328240i
\(478\) −9.64377e6 3.12643e7i −0.0883005 0.286263i
\(479\) −9.51310e7 1.64772e8i −0.865597 1.49926i −0.866454 0.499258i \(-0.833606\pi\)
0.000857036 1.00000i \(-0.499727\pi\)
\(480\) 3.87335e7 + 2.23628e7i 0.350238 + 0.202210i
\(481\) −9.94669e6 2.27027e6i −0.0893806 0.0204005i
\(482\) −1.53101e8 + 2.30762e7i −1.36721 + 0.206074i
\(483\) −1.17297e6 + 1.08836e6i −0.0104099 + 0.00965899i
\(484\) −2.62335e7 3.28957e7i −0.231377 0.290137i
\(485\) −2.69388e7 + 3.95120e7i −0.236131 + 0.346341i
\(486\) 6.08456e7 + 5.64565e7i 0.530054 + 0.491819i
\(487\) 1.46865e7 1.95978e8i 0.127155 1.69676i −0.460510 0.887654i \(-0.652334\pi\)
0.587665 0.809105i \(-0.300047\pi\)
\(488\) 4.24877e7 + 1.08257e8i 0.365598 + 0.931527i
\(489\) 4.06056e7 + 1.77905e8i 0.347264 + 1.52146i
\(490\) −1.85846e7 5.73260e6i −0.157967 0.0487263i
\(491\) −4.29043e7 6.29290e7i −0.362456 0.531626i 0.601085 0.799185i \(-0.294735\pi\)
−0.963541 + 0.267559i \(0.913783\pi\)
\(492\) 6.11658e6 4.05808e7i 0.0513586 0.340742i
\(493\) 1.04779e8 + 4.11227e7i 0.874447 + 0.343195i
\(494\) −1.41618e7 6.81997e6i −0.117473 0.0565720i
\(495\) 3.55405e6 7.38006e6i 0.0293027 0.0608477i
\(496\) −1.95298e6 + 4.97610e6i −0.0160049 + 0.0407797i
\(497\) −1.20739e8 1.81985e7i −0.983510 0.148240i
\(498\) 1.01333e8 6.90873e7i 0.820466 0.559385i
\(499\) 3.87360e7 1.25579e8i 0.311755 1.01068i −0.655140 0.755508i \(-0.727390\pi\)
0.966894 0.255176i \(-0.0821336\pi\)
\(500\) −3.91633e7 + 8.93878e6i −0.313307 + 0.0715102i
\(501\) 3.41384e6 1.33983e6i 0.0271475 0.0106546i
\(502\) −1.69758e8 1.27216e7i −1.34190 0.100561i
\(503\) 9.51789e7 1.02578e8i 0.747889 0.806032i −0.238382 0.971172i \(-0.576617\pi\)
0.986270 + 0.165139i \(0.0528074\pi\)
\(504\) 4.18797e7 + 2.85531e7i 0.327124 + 0.223029i
\(505\) −9.95961e6 + 7.94252e6i −0.0773336 + 0.0616715i
\(506\) 332720. + 358587.i 0.00256819 + 0.00276786i
\(507\) −1.22546e6 8.13042e6i −0.00940322 0.0623863i
\(508\) −1.34619e7 + 5.89804e7i −0.102687 + 0.449900i
\(509\) −7.86375e7 + 1.36204e8i −0.596316 + 1.03285i 0.397044 + 0.917800i \(0.370036\pi\)
−0.993360 + 0.115050i \(0.963297\pi\)
\(510\) −5.19288e7 + 2.99811e7i −0.391469 + 0.226015i
\(511\) 1.24191e8 3.83079e7i 0.930739 0.287095i
\(512\) 8.20031e7 + 6.53953e7i 0.610971 + 0.487233i
\(513\) 997162. + 1.33062e7i 0.00738607 + 0.0985603i
\(514\) 1.10616e8 5.32699e7i 0.814570 0.392276i
\(515\) 1.67689e7i 0.122767i
\(516\) 6.90508e7 57299.1i 0.502597 0.000417060i
\(517\) −2.31250e7 −0.167344
\(518\) −2.94788e6 6.12133e6i −0.0212090 0.0440410i
\(519\) −2.43015e8 + 1.82114e7i −1.73832 + 0.130269i
\(520\) 4.22972e7 5.30390e7i 0.300817 0.377212i
\(521\) 1.23273e7 + 3.99641e7i 0.0871674 + 0.282590i 0.988653 0.150220i \(-0.0479983\pi\)
−0.901485 + 0.432810i \(0.857522\pi\)
\(522\) 2.40303e7 + 4.16218e7i 0.168946 + 0.292623i
\(523\) 2.78872e7 + 1.61007e7i 0.194939 + 0.112548i 0.594293 0.804249i \(-0.297432\pi\)
−0.399354 + 0.916797i \(0.630765\pi\)
\(524\) 8.00329e7 + 1.82670e7i 0.556256 + 0.126962i
\(525\) −1.01534e8 + 1.53038e7i −0.701671 + 0.105760i
\(526\) 1.19125e8 1.10532e8i 0.818551 0.759504i
\(527\) 1.03489e7 + 1.29770e7i 0.0707067 + 0.0886633i
\(528\) 1.31037e7 1.92195e7i 0.0890207 0.130569i
\(529\) 1.08489e8 + 1.00663e8i 0.732859 + 0.679993i
\(530\) −3.03489e6 + 4.04978e7i −0.0203852 + 0.272022i
\(531\) 2.01312e7 + 5.12936e7i 0.134458 + 0.342594i
\(532\) 1.60819e6 + 7.04596e6i 0.0106808 + 0.0467956i
\(533\) −1.01715e8 3.13751e7i −0.671746 0.207206i
\(534\) −6.47666e7 9.49951e7i −0.425331 0.623846i
\(535\) −1.45437e7 + 9.64911e7i −0.0949759 + 0.630124i
\(536\) 7.53764e7 + 2.95830e7i 0.489487 + 0.192109i
\(537\) −3.17722e8 1.53007e8i −2.05175 0.988070i
\(538\) 8.51314e7 1.76777e8i 0.546692 1.13522i
\(539\) 8.55879e6 2.18075e7i 0.0546571 0.139264i
\(540\) −1.65141e7 2.48910e6i −0.104875 0.0158074i
\(541\) −2.00427e8 + 1.36649e8i −1.26580 + 0.863006i −0.995024 0.0996367i \(-0.968232\pi\)
−0.270774 + 0.962643i \(0.587280\pi\)
\(542\) 6.24017e7 2.02301e8i 0.391921 1.27058i
\(543\) −1.07411e8 + 2.45160e7i −0.670890 + 0.153126i
\(544\) 1.24666e8 4.89279e7i 0.774376 0.303920i
\(545\) −1.16257e8 8.71224e6i −0.718173 0.0538196i
\(546\) 7.63625e7 8.22992e7i 0.469140 0.505612i
\(547\) −1.60785e8 1.09622e8i −0.982392 0.669784i −0.0382315 0.999269i \(-0.512172\pi\)
−0.944161 + 0.329485i \(0.893125\pi\)
\(548\) −2.78104e6 + 2.21780e6i −0.0168992 + 0.0134766i
\(549\) 5.34611e7 + 5.76174e7i 0.323088 + 0.348206i
\(550\) 4.67849e6 + 3.10397e7i 0.0281201 + 0.186565i
\(551\) −5.25825e6 + 2.30379e7i −0.0314330 + 0.137717i
\(552\) −1.82013e6 + 3.15257e6i −0.0108215 + 0.0187433i
\(553\) −1.33381e6 + 770074.i −0.00788710 + 0.00455362i
\(554\) 1.83030e8 5.64572e7i 1.07645 0.332040i
\(555\) −6.38815e6 5.09438e6i −0.0373677 0.0297997i
\(556\) 6.26822e6 + 8.36436e7i 0.0364687 + 0.486641i
\(557\) −2.37408e8 + 1.14330e8i −1.37382 + 0.661596i −0.967672 0.252211i \(-0.918842\pi\)
−0.406147 + 0.913808i \(0.633128\pi\)
\(558\) 7.08711e6i 0.0407912i
\(559\) 2.65463e7 1.77121e8i 0.151974 1.01399i
\(560\) 2.30301e7 0.131139
\(561\) −3.13383e7 6.50746e7i −0.177495 0.368572i
\(562\) −1.65879e8 + 1.24309e7i −0.934507 + 0.0700316i
\(563\) −9.70356e7 + 1.21679e8i −0.543759 + 0.681852i −0.975463 0.220163i \(-0.929341\pi\)
0.431704 + 0.902015i \(0.357912\pi\)
\(564\) −1.47097e7 4.76878e7i −0.0819913 0.265809i
\(565\) −3.12954e7 5.42052e7i −0.173514 0.300535i
\(566\) −6.43210e7 3.71357e7i −0.354734 0.204806i
\(567\) −1.57869e8 3.60325e7i −0.866057 0.197672i
\(568\) −2.74680e8 + 4.14014e7i −1.49893 + 0.225928i
\(569\) 1.11937e8 1.03863e8i 0.607629 0.563798i −0.315191 0.949028i \(-0.602069\pi\)
0.922820 + 0.385231i \(0.125878\pi\)
\(570\) −7.84863e6 9.84187e6i −0.0423808 0.0531438i
\(571\) −2.18322e7 + 3.20219e7i −0.117270 + 0.172004i −0.880386 0.474258i \(-0.842716\pi\)
0.763115 + 0.646262i \(0.223669\pi\)
\(572\) 1.73712e7 + 1.61181e7i 0.0928202 + 0.0861246i
\(573\) −6.22412e6 + 8.30551e7i −0.0330837 + 0.441471i
\(574\) −2.58971e7 6.59848e7i −0.136936 0.348906i
\(575\) −557245. 2.44145e6i −0.00293118 0.0128423i
\(576\) 9.45251e7 + 2.91571e7i 0.494629 + 0.152573i
\(577\) −1.83701e8 2.69439e8i −0.956276 1.40260i −0.915001 0.403451i \(-0.867811\pi\)
−0.0412745 0.999148i \(-0.513142\pi\)
\(578\) −4.62453e6 + 3.06817e7i −0.0239488 + 0.158890i
\(579\) 2.21414e8 + 8.68986e7i 1.14069 + 0.447690i
\(580\) −2.66467e7 1.28324e7i −0.136571 0.0657692i
\(581\) −6.34599e7 + 1.31776e8i −0.323572 + 0.671904i
\(582\) −6.57778e7 + 1.67599e8i −0.333665 + 0.850165i
\(583\) −4.83720e7 7.29090e6i −0.244111 0.0367939i
\(584\) 2.44294e8 1.66557e8i 1.22652 0.836225i
\(585\) 1.35144e7 4.38128e7i 0.0675042 0.218843i
\(586\) −5.99812e7 + 1.36903e7i −0.298073 + 0.0680332i
\(587\) 2.43537e8 9.55811e7i 1.20407 0.472561i 0.323383 0.946268i \(-0.395180\pi\)
0.880682 + 0.473707i \(0.157084\pi\)
\(588\) 5.04151e7 + 3.77809e6i 0.247987 + 0.0185840i
\(589\) −2.37011e6 + 2.55437e6i −0.0115991 + 0.0125008i
\(590\) 4.05782e7 + 2.76657e7i 0.197577 + 0.134706i
\(591\) 2.91999e8 2.32862e8i 1.41455 1.12807i
\(592\) −5.35943e6 5.77609e6i −0.0258317 0.0278400i
\(593\) 3.70948e7 + 2.46108e8i 0.177889 + 1.18022i 0.882392 + 0.470516i \(0.155932\pi\)
−0.704503 + 0.709701i \(0.748830\pi\)
\(594\) −6.48335e6 + 2.84054e7i −0.0309343 + 0.135532i
\(595\) 3.57545e7 6.19286e7i 0.169738 0.293995i
\(596\) 3.85131e7 2.22356e7i 0.181916 0.105029i
\(597\) 3.07132e8 9.47375e7i 1.44345 0.445245i
\(598\) 2.14072e6 + 1.70717e6i 0.0100105 + 0.00798312i
\(599\) 1.62322e7 + 2.16604e8i 0.0755263 + 1.00783i 0.898278 + 0.439428i \(0.144819\pi\)
−0.822752 + 0.568401i \(0.807562\pi\)
\(600\) −2.10465e8 + 1.01354e8i −0.974373 + 0.469233i
\(601\) 2.16600e7i 0.0997778i −0.998755 0.0498889i \(-0.984113\pi\)
0.998755 0.0498889i \(-0.0158867\pi\)
\(602\) 1.03239e8 5.97196e7i 0.473212 0.273733i
\(603\) 5.47266e7 0.249601
\(604\) −2.06042e7 4.27851e7i −0.0935072 0.194170i
\(605\) −8.71545e7 + 6.53133e6i −0.393572 + 0.0294941i
\(606\) −2.99031e7 + 3.74973e7i −0.134369 + 0.168493i
\(607\) 8.56879e7 + 2.77793e8i 0.383136 + 1.24210i 0.917803 + 0.397035i \(0.129961\pi\)
−0.534667 + 0.845063i \(0.679563\pi\)
\(608\) 1.40577e7 + 2.43487e7i 0.0625466 + 0.108334i
\(609\) −1.46168e8 8.43902e7i −0.647144 0.373629i
\(610\) 6.82977e7 + 1.55885e7i 0.300896 + 0.0686775i
\(611\) −1.27994e8 + 1.92920e7i −0.561133 + 0.0845773i
\(612\) 3.88016e7 3.60026e7i 0.169276 0.157065i
\(613\) 1.49469e8 + 1.87428e8i 0.648887 + 0.813679i 0.992083 0.125585i \(-0.0400808\pi\)
−0.343196 + 0.939264i \(0.611509\pi\)
\(614\) −1.42716e8 + 2.09325e8i −0.616547 + 0.904308i
\(615\) −6.24904e7 5.79826e7i −0.268651 0.249271i
\(616\) −4.06661e6 + 5.42651e7i −0.0173976 + 0.232155i
\(617\) 3.83993e7 + 9.78399e7i 0.163481 + 0.416543i 0.989016 0.147808i \(-0.0472217\pi\)
−0.825535 + 0.564351i \(0.809126\pi\)
\(618\) 1.40486e7 + 6.15509e7i 0.0595206 + 0.260777i
\(619\) 2.35615e8 + 7.26775e7i 0.993414 + 0.306428i 0.748513 0.663120i \(-0.230768\pi\)
0.244901 + 0.969548i \(0.421244\pi\)
\(620\) −2.45679e6 3.60345e6i −0.0103084 0.0151197i
\(621\) 346432. 2.29842e6i 0.00144658 0.00959744i
\(622\) −1.35797e8 5.32963e7i −0.564311 0.221476i
\(623\) 1.23534e8 + 5.94911e7i 0.510886 + 0.246030i
\(624\) 5.64934e7 1.17310e8i 0.232511 0.482814i
\(625\) 4.18793e7 1.06707e8i 0.171538 0.437071i
\(626\) 3.45897e8 + 5.21356e7i 1.41001 + 0.212526i
\(627\) 1.25284e7 8.54168e6i 0.0508266 0.0346530i
\(628\) −2.67597e7 + 8.67530e7i −0.108045 + 0.350272i
\(629\) −2.38526e7 + 5.44421e6i −0.0958483 + 0.0218767i
\(630\) 2.84222e7 1.11549e7i 0.113667 0.0446112i
\(631\) 6.40203e7 + 4.79766e6i 0.254818 + 0.0190960i 0.201527 0.979483i \(-0.435410\pi\)
0.0532913 + 0.998579i \(0.483029\pi\)
\(632\) −2.38320e6 + 2.56848e6i −0.00944083 + 0.0101748i
\(633\) 2.45923e8 + 1.67668e8i 0.969591 + 0.661056i
\(634\) 7.00894e7 5.58945e7i 0.275033 0.219331i
\(635\) 8.54739e7 + 9.21190e7i 0.333820 + 0.359773i
\(636\) −1.57342e7 1.04389e8i −0.0611607 0.405775i
\(637\) 2.91791e7 1.27842e8i 0.112889 0.494601i
\(638\) −2.57988e7 + 4.46848e7i −0.0993429 + 0.172067i
\(639\) −1.62589e8 + 9.38707e7i −0.623143 + 0.359772i
\(640\) 1.92116e6 592599.i 0.00732863 0.00226058i
\(641\) 3.69376e8 + 2.94567e8i 1.40247 + 1.11843i 0.976946 + 0.213488i \(0.0684824\pi\)
0.425526 + 0.904946i \(0.360089\pi\)
\(642\) 2.74549e7 + 3.66360e8i 0.103756 + 1.38453i
\(643\) 2.18714e8 1.05327e8i 0.822702 0.396193i 0.0253292 0.999679i \(-0.491937\pi\)
0.797373 + 0.603487i \(0.206222\pi\)
\(644\) 1.25894e6i 0.00471355i
\(645\) 8.07002e7 1.18577e8i 0.300743 0.441896i
\(646\) −3.76935e7 −0.139820
\(647\) −1.50974e8 3.13500e8i −0.557428 1.15751i −0.969212 0.246229i \(-0.920809\pi\)
0.411784 0.911281i \(-0.364906\pi\)
\(648\) −3.67356e8 + 2.75295e7i −1.35009 + 0.101175i
\(649\) −3.68842e7 + 4.62513e7i −0.134929 + 0.169196i
\(650\) 5.17898e7 + 1.67898e8i 0.188584 + 0.611373i
\(651\) −1.24443e7 2.15542e7i −0.0451054 0.0781249i
\(652\) −1.24336e8 7.17856e7i −0.448596 0.258997i
\(653\) −3.23308e8 7.37929e7i −1.16112 0.265018i −0.401794 0.915730i \(-0.631613\pi\)
−0.759325 + 0.650712i \(0.774470\pi\)
\(654\) −4.34025e8 + 6.54187e7i −1.55161 + 0.233867i
\(655\) 1.25000e8 1.15983e8i 0.444823 0.412735i
\(656\) −5.12561e7 6.42732e7i −0.181566 0.227676i
\(657\) 1.12568e8 1.65107e8i 0.396935 0.582197i
\(658\) −6.31877e7 5.86296e7i −0.221797 0.205797i
\(659\) 4.42729e6 5.90781e7i 0.0154697 0.206429i −0.984113 0.177543i \(-0.943185\pi\)
0.999583 0.0288857i \(-0.00919588\pi\)
\(660\) 6.93346e6 + 1.76662e7i 0.0241167 + 0.0614484i
\(661\) 8.00106e7 + 3.50549e8i 0.277040 + 1.21379i 0.901515 + 0.432748i \(0.142456\pi\)
−0.624474 + 0.781045i \(0.714687\pi\)
\(662\) 1.54353e8 + 4.76117e7i 0.532037 + 0.164112i
\(663\) −2.27742e8 3.34037e8i −0.781453 1.14618i
\(664\) −4.95924e7 + 3.29024e8i −0.169399 + 1.12389i
\(665\) 1.39746e7 + 5.48461e6i 0.0475196 + 0.0186501i
\(666\) −9.41196e6 4.53256e6i −0.0318609 0.0153434i
\(667\) 1.78600e6 3.70867e6i 0.00601872 0.0124980i
\(668\) −1.05415e6 + 2.68593e6i −0.00353650 + 0.00901085i
\(669\) −3.10142e8 4.67464e7i −1.03582 0.156124i
\(670\) 4.03013e7 2.74770e7i 0.133997 0.0913575i
\(671\) −2.48725e7 + 8.06345e7i −0.0823287 + 0.266903i
\(672\) −1.95780e8 + 4.46856e7i −0.645151 + 0.147252i
\(673\) 1.85131e8 7.26584e7i 0.607342 0.238364i −0.0416835 0.999131i \(-0.513272\pi\)
0.649025 + 0.760767i \(0.275177\pi\)
\(674\) −1.12059e8 8.39764e6i −0.365987 0.0274269i
\(675\) 1.01453e8 1.09340e8i 0.329877 0.355523i
\(676\) 5.34501e6 + 3.64416e6i 0.0173025 + 0.0117966i
\(677\) 7.92654e7 6.32120e7i 0.255457 0.203720i −0.487385 0.873187i \(-0.662049\pi\)
0.742841 + 0.669467i \(0.233478\pi\)
\(678\) −1.60283e8 1.72744e8i −0.514278 0.554260i
\(679\) −3.20017e7 2.12318e8i −0.102227 0.678229i
\(680\) 3.62002e7 1.58603e8i 0.115129 0.504413i
\(681\) −4.90098e7 + 8.48874e7i −0.155182 + 0.268783i
\(682\) −6.58929e6 + 3.80433e6i −0.0207723 + 0.0119929i
\(683\) −1.72203e8 + 5.31175e7i −0.540477 + 0.166715i −0.552961 0.833207i \(-0.686502\pi\)
0.0124840 + 0.999922i \(0.496026\pi\)
\(684\) 8.68790e6 + 6.92837e6i 0.0271485 + 0.0216502i
\(685\) 552165. + 7.36813e6i 0.00171790 + 0.0229238i
\(686\) 2.37683e8 1.14462e8i 0.736249 0.354559i
\(687\) 3.27210e7i 0.100915i
\(688\) 9.39976e7 1.01474e8i 0.288637 0.311594i
\(689\) −2.73816e8 −0.837145
\(690\) 951428. + 1.97566e6i 0.00289620 + 0.00601402i
\(691\) −3.31711e8 + 2.48583e7i −1.00537 + 0.0753420i −0.567225 0.823563i \(-0.691983\pi\)
−0.438144 + 0.898905i \(0.644364\pi\)
\(692\) 1.19545e8 1.49904e8i 0.360754 0.452372i
\(693\) 1.08406e7 + 3.51443e7i 0.0325726 + 0.105598i
\(694\) −1.73802e8 3.01034e8i −0.519968 0.900611i
\(695\) 1.50890e8 + 8.71161e7i 0.449474 + 0.259504i
\(696\) −3.74347e8 8.54423e7i −1.11032 0.253422i
\(697\) −2.52408e8 + 3.80444e7i −0.745426 + 0.112355i
\(698\) −4.54642e7 + 4.21846e7i −0.133691 + 0.124048i
\(699\) 1.02384e8 + 1.28386e8i 0.299779 + 0.375911i
\(700\) 4.55089e7 6.67493e7i 0.132679 0.194604i
\(701\) −2.25220e8 2.08973e8i −0.653811 0.606648i 0.281888 0.959447i \(-0.409039\pi\)
−0.935699 + 0.352799i \(0.885230\pi\)
\(702\) −1.21874e7 + 1.62629e8i −0.0352289 + 0.470097i
\(703\) −1.87650e6 4.78125e6i −0.00540111 0.0137618i
\(704\) 2.36316e7 + 1.03537e8i 0.0677291 + 0.296740i
\(705\) −9.90575e7 3.05552e7i −0.282696 0.0872002i
\(706\) −6.90886e7 1.01334e8i −0.196332 0.287967i
\(707\) 8.52470e6 5.65577e7i 0.0241224 0.160042i
\(708\) −1.18840e8 4.66414e7i −0.334861 0.131423i
\(709\) 4.36522e8 + 2.10218e8i 1.22481 + 0.589835i 0.930646 0.365921i \(-0.119246\pi\)
0.294159 + 0.955756i \(0.404960\pi\)
\(710\) −7.26019e7 + 1.50759e8i −0.202849 + 0.421220i
\(711\) −865157. + 2.20438e6i −0.00240705 + 0.00613308i
\(712\) 3.08447e8 + 4.64908e7i 0.854555 + 0.128803i
\(713\) 501526. 341934.i 0.00138364 0.000943353i
\(714\) 7.93560e7 2.57266e8i 0.218014 0.706786i
\(715\) 4.79897e7 1.09533e7i 0.131289 0.0299660i
\(716\) 2.58274e8 1.01365e8i 0.703625 0.276152i
\(717\) 1.76171e8 + 1.32022e7i 0.477945 + 0.0358170i
\(718\) 3.89092e7 4.19341e7i 0.105118 0.113291i
\(719\) 2.63222e8 + 1.79462e8i 0.708168 + 0.482821i 0.863054 0.505112i \(-0.168549\pi\)
−0.154886 + 0.987932i \(0.549501\pi\)
\(720\) 2.76849e7 2.20780e7i 0.0741730 0.0591510i
\(721\) −5.12110e7 5.51924e7i −0.136634 0.147256i
\(722\) 4.19646e7 + 2.78417e8i 0.111499 + 0.739749i
\(723\) 1.86034e8 8.15068e8i 0.492240 2.15665i
\(724\) 4.33411e7 7.50690e7i 0.114205 0.197809i
\(725\) 2.28757e8 1.32073e8i 0.600289 0.346577i
\(726\) −3.14433e8 + 9.69897e7i −0.821709 + 0.253464i
\(727\) 3.85352e8 + 3.07308e8i 1.00289 + 0.799781i 0.979806 0.199953i \(-0.0640788\pi\)
0.0230878 + 0.999733i \(0.492650\pi\)
\(728\) 2.27624e7 + 3.03744e8i 0.0589963 + 0.787251i
\(729\) 3.24430e7 1.56237e7i 0.0837410 0.0403275i
\(730\) 1.78105e8i 0.457833i
\(731\) −1.26934e8 4.10301e8i −0.324957 1.05039i
\(732\) −1.82104e8 −0.464287
\(733\) 2.68454e8 + 5.57451e8i 0.681645 + 1.41545i 0.898379 + 0.439220i \(0.144745\pi\)
−0.216734 + 0.976231i \(0.569540\pi\)
\(734\) 1.02719e8 7.69775e6i 0.259755 0.0194660i
\(735\) 6.54765e7 8.21050e7i 0.164901 0.206780i
\(736\) −1.44359e6 4.68001e6i −0.00362085 0.0117385i
\(737\) 2.93770e7 + 5.08825e7i 0.0733846 + 0.127106i
\(738\) −9.43882e7 5.44951e7i −0.234827 0.135578i
\(739\) −5.26805e8 1.20240e8i −1.30532 0.297931i −0.487357 0.873203i \(-0.662039\pi\)
−0.817962 + 0.575272i \(0.804896\pi\)
\(740\) 6.35676e6 958127.i 0.0156870 0.00236444i
\(741\) 6.22171e7 5.77290e7i 0.152917 0.141886i
\(742\) −1.13689e8 1.42561e8i −0.278296 0.348972i
\(743\) −1.79592e8 + 2.63414e8i −0.437846 + 0.642203i −0.980214 0.197938i \(-0.936575\pi\)
0.542368 + 0.840141i \(0.317528\pi\)
\(744\) −4.15065e7 3.85124e7i −0.100785 0.0935151i
\(745\) 6.90325e6 9.21174e7i 0.0166949 0.222778i
\(746\) 9.07353e7 + 2.31190e8i 0.218555 + 0.556868i
\(747\) 5.00416e7 + 2.19246e8i 0.120052 + 0.525982i
\(748\) 5.43022e7 + 1.67500e7i 0.129752 + 0.0400230i
\(749\) −2.46809e8 3.62003e8i −0.587376 0.861522i
\(750\) −4.68225e7 + 3.10647e8i −0.110987 + 0.736348i
\(751\) −5.60970e7 2.20164e7i −0.132440 0.0519789i 0.298195 0.954505i \(-0.403615\pi\)
−0.430636 + 0.902526i \(0.641711\pi\)
\(752\) −9.00681e7 4.33745e7i −0.211796 0.101996i
\(753\) 3.98828e8 8.28175e8i 0.934116 1.93971i
\(754\) −1.05515e8 + 2.68848e8i −0.246150 + 0.627180i
\(755\) −9.75403e7 1.47018e7i −0.226644 0.0341610i
\(756\) 6.19554e7 4.22405e7i 0.143388 0.0977606i
\(757\) −8.99361e7 + 2.91566e8i −0.207322 + 0.672123i 0.790868 + 0.611987i \(0.209630\pi\)
−0.998190 + 0.0601357i \(0.980847\pi\)
\(758\) −2.27926e8 + 5.20226e7i −0.523343 + 0.119450i
\(759\) −2.45877e6 + 964995.i −0.00562331 + 0.00220699i
\(760\) 3.40573e7 + 2.55224e6i 0.0775836 + 0.00581409i
\(761\) −2.46283e8 + 2.65430e8i −0.558831 + 0.602276i −0.947757 0.318993i \(-0.896655\pi\)
0.388927 + 0.921269i \(0.372846\pi\)
\(762\) 3.90911e8 + 2.66519e8i 0.883514 + 0.602370i
\(763\) 4.09250e8 3.26366e8i 0.921329 0.734735i
\(764\) −4.45711e7 4.80362e7i −0.0999478 0.107718i
\(765\) −1.63872e7 1.08722e8i −0.0366032 0.242847i
\(766\) 8.44347e7 3.69932e8i 0.187860 0.823069i
\(767\) −1.65565e8 + 2.86766e8i −0.366928 + 0.635539i
\(768\) −4.79391e8 + 2.76776e8i −1.05829 + 0.611006i
\(769\) −5.27625e8 + 1.62751e8i −1.16024 + 0.357885i −0.814340 0.580388i \(-0.802901\pi\)
−0.345896 + 0.938273i \(0.612425\pi\)
\(770\) 2.56282e7 + 2.04378e7i 0.0561367 + 0.0447675i
\(771\) 4.95416e7 + 6.61086e8i 0.108095 + 1.44243i
\(772\) −1.68607e8 + 8.11969e7i −0.366458 + 0.176477i
\(773\) 6.85694e8i 1.48454i −0.670101 0.742270i \(-0.733749\pi\)
0.670101 0.742270i \(-0.266251\pi\)
\(774\) 6.68553e7 1.70761e8i 0.144183 0.368270i
\(775\) 3.89514e7 0.0836793
\(776\) −2.11942e8 4.40102e8i −0.453557 0.941820i
\(777\) 3.65836e7 2.74156e6i 0.0779872 0.00584433i
\(778\) 5.62010e7 7.04738e7i 0.119345 0.149654i
\(779\) −1.57953e7 5.12072e7i −0.0334131 0.108323i
\(780\) 5.31139e7 + 9.19960e7i 0.111924 + 0.193859i
\(781\) −1.74554e8 1.00779e8i −0.366417 0.211551i
\(782\) 6.40143e6 + 1.46109e6i 0.0133862 + 0.00305531i
\(783\) 2.42437e8 3.65415e7i 0.505026 0.0761203i
\(784\) 7.42384e7 6.88832e7i 0.154057 0.142944i
\(785\) 1.17579e8 + 1.47439e8i 0.243064 + 0.304793i
\(786\) 3.61651e8 5.30444e8i 0.744769 1.09238i
\(787\) −3.85729e8 3.57904e8i −0.791330 0.734247i 0.176921 0.984225i \(-0.443386\pi\)
−0.968252 + 0.249978i \(0.919577\pi\)
\(788\) −2.19592e7 + 2.93025e8i −0.0448784 + 0.598861i
\(789\) 3.20577e8 + 8.16818e8i 0.652682 + 1.66301i
\(790\) 469658. + 2.05771e6i 0.000952578 + 0.00417352i
\(791\) 2.68543e8 + 8.28347e7i 0.542607 + 0.167372i
\(792\) 4.71331e7 + 6.91315e7i 0.0948747 + 0.139156i
\(793\) −7.03969e7 + 4.67053e8i −0.141167 + 0.936583i
\(794\) −2.14559e7 8.42082e6i −0.0428633 0.0168226i
\(795\) −1.97571e8 9.51453e7i −0.393208 0.189359i
\(796\) −1.09720e8 + 2.27836e8i −0.217544 + 0.451734i
\(797\) −4.77737e7 + 1.21725e8i −0.0943656 + 0.240440i −0.970261 0.242062i \(-0.922176\pi\)
0.875895 + 0.482501i \(0.160272\pi\)
\(798\) 5.58891e7 + 8.42393e6i 0.109981 + 0.0165770i
\(799\) −2.56467e8 + 1.74856e8i −0.502795 + 0.342800i
\(800\) 9.26360e7 3.00319e8i 0.180930 0.586560i
\(801\) 2.05535e8 4.69119e7i 0.399933 0.0912821i
\(802\) 4.67161e8 1.83347e8i 0.905614 0.355427i
\(803\) 2.13936e8 + 1.60323e7i 0.413178 + 0.0309634i
\(804\) −8.62421e7 + 9.29469e7i −0.165940 + 0.178841i
\(805\) −2.16068e6 1.47313e6i −0.00414193 0.00282392i
\(806\) −3.32972e7 + 2.65536e7i −0.0635920 + 0.0507130i
\(807\) 7.20612e8 + 7.76636e8i 1.37114 + 1.47774i
\(808\) −1.93936e7 1.28668e8i −0.0367642 0.243914i
\(809\) 1.24010e8 5.43323e8i 0.234213 1.02615i −0.711891 0.702290i \(-0.752161\pi\)
0.946104 0.323863i \(-0.104982\pi\)
\(810\) −1.10954e8 + 1.92177e8i −0.208779 + 0.361616i
\(811\) −5.06928e8 + 2.92675e8i −0.950351 + 0.548685i −0.893190 0.449679i \(-0.851538\pi\)
−0.0571612 + 0.998365i \(0.518205\pi\)
\(812\) 1.26893e8 3.91413e7i 0.237012 0.0731084i
\(813\) 8.93746e8 + 7.12739e8i 1.66319 + 1.32635i
\(814\) −838117. 1.11839e7i −0.00155393 0.0207358i
\(815\) −2.68693e8 + 1.29396e8i −0.496345 + 0.239027i
\(816\) 3.12235e8i 0.574660i
\(817\) 8.12032e7 3.91884e7i 0.148904 0.0718608i
\(818\) 4.08682e8 0.746665
\(819\) 8.93205e7 + 1.85476e8i 0.162592 + 0.337626i
\(820\) 6.68828e7 5.01217e6i 0.121303 0.00909043i
\(821\) −6.09257e7 + 7.63984e7i −0.110096 + 0.138056i −0.833826 0.552027i \(-0.813855\pi\)
0.723730 + 0.690083i \(0.242426\pi\)
\(822\) 8.19961e6 + 2.65825e7i 0.0147631 + 0.0478608i
\(823\) −9.71037e7 1.68189e8i −0.174195 0.301715i 0.765687 0.643213i \(-0.222399\pi\)
−0.939882 + 0.341498i \(0.889066\pi\)
\(824\) −1.48339e8 8.56434e7i −0.265139 0.153078i
\(825\) −1.65247e8 3.77166e7i −0.294288 0.0671694i
\(826\) −2.18047e8 + 3.28653e7i −0.386910 + 0.0583172i
\(827\) −3.52245e8 + 3.26836e8i −0.622771 + 0.577847i −0.927144 0.374706i \(-0.877744\pi\)
0.304373 + 0.952553i \(0.401553\pi\)
\(828\) −1.20689e6 1.51340e6i −0.00212607 0.00266601i
\(829\) −2.43793e8 + 3.57579e8i −0.427916 + 0.627637i −0.978280 0.207287i \(-0.933537\pi\)
0.550364 + 0.834925i \(0.314489\pi\)
\(830\) 1.46930e8 + 1.36331e8i 0.256966 + 0.238429i
\(831\) −7.72894e7 + 1.03136e9i −0.134684 + 1.79724i
\(832\) 2.17174e8 + 5.53350e8i 0.377083 + 0.960793i
\(833\) −6.99728e7 3.06571e8i −0.121058 0.530391i
\(834\) 6.26831e8 + 1.93352e8i 1.08057 + 0.333311i
\(835\) 3.37629e6 + 4.95210e6i 0.00579936 + 0.00850609i
\(836\) −1.77807e6 + 1.17967e7i −0.00304320 + 0.0201903i
\(837\) 3.36548e7 + 1.32085e7i 0.0573945 + 0.0225257i
\(838\) −3.31006e8 1.59404e8i −0.562475 0.270874i
\(839\) 1.78333e8 3.70311e8i 0.301957 0.627020i −0.693685 0.720278i \(-0.744014\pi\)
0.995642 + 0.0932587i \(0.0297284\pi\)
\(840\) −8.91204e7 + 2.27075e8i −0.150362 + 0.383117i
\(841\) −1.58842e8 2.39416e7i −0.267041 0.0402500i
\(842\) −7.05627e7 + 4.81088e7i −0.118206 + 0.0805914i
\(843\) 2.64749e8 8.58297e8i 0.441929 1.43270i
\(844\) −2.28307e8 + 5.21095e7i −0.379744 + 0.0866741i
\(845\) 1.25087e7 4.90931e6i 0.0207321 0.00813674i
\(846\) −1.32165e8 9.90438e6i −0.218275 0.0163575i
\(847\) 2.66911e8 2.87661e8i 0.439254 0.473403i
\(848\) −1.74726e8 1.19126e8i −0.286530 0.195353i
\(849\) 3.13546e8 2.50045e8i 0.512364 0.408596i
\(850\) 2.86589e8 + 3.08869e8i 0.466662 + 0.502942i
\(851\) 133352. + 884730.i 0.000216376 + 0.00143556i
\(852\) 9.67904e7 4.24066e8i 0.156500 0.685670i
\(853\) −5.63636e8 + 9.76246e8i −0.908137 + 1.57294i −0.0914880 + 0.995806i \(0.529162\pi\)
−0.816649 + 0.577134i \(0.804171\pi\)
\(854\) −2.72399e8 + 1.57269e8i −0.437352 + 0.252505i
\(855\) 2.20569e7 6.80366e6i 0.0352896 0.0108854i
\(856\) −7.79290e8 6.21463e8i −1.24245 0.990818i
\(857\) −4.77047e7 6.36574e8i −0.0757911 1.01136i −0.897373 0.441272i \(-0.854527\pi\)
0.821582 0.570090i \(-0.193092\pi\)
\(858\) 1.66972e8 8.04094e7i 0.264351 0.127305i
\(859\) 3.00288e8i 0.473760i −0.971539 0.236880i \(-0.923875\pi\)
0.971539 0.236880i \(-0.0761248\pi\)
\(860\) 2.52027e7 + 1.09999e8i 0.0396234 + 0.172940i
\(861\) 3.82754e8 0.599667
\(862\) 1.78746e8 + 3.71169e8i 0.279070 + 0.579496i
\(863\) 4.42018e8 3.31247e7i 0.687714 0.0515371i 0.273710 0.961812i \(-0.411749\pi\)
0.414004 + 0.910275i \(0.364130\pi\)
\(864\) 1.81878e8 2.28068e8i 0.281994 0.353609i
\(865\) −1.17393e8 3.80578e8i −0.181382 0.588025i
\(866\) 1.02260e7 + 1.77120e7i 0.0157454 + 0.0272718i
\(867\) −1.45096e8 8.37711e7i −0.222637 0.128540i
\(868\) 1.90909e7 + 4.35737e6i 0.0291922 + 0.00666293i
\(869\) −2.51395e6 + 378917.i −0.00383087 + 0.000577411i
\(870\) −1.69553e8 + 1.57322e8i −0.257483 + 0.238909i
\(871\) 2.05047e8 + 2.57121e8i 0.310312 + 0.389119i
\(872\) 6.70826e8 9.83921e8i 1.01172 1.48392i
\(873\) −2.42010e8 2.24552e8i −0.363739 0.337500i
\(874\) −103012. + 1.37460e6i −0.000154295 + 0.00205893i
\(875\) −1.36876e8 3.48753e8i −0.204316 0.520588i
\(876\) 1.03023e8 + 4.51372e8i 0.153257 + 0.671463i
\(877\) 1.17631e9 + 3.62842e8i 1.74390 + 0.537922i 0.992534 0.121965i \(-0.0389196\pi\)
0.751365 + 0.659887i \(0.229396\pi\)
\(878\) −2.91162e8 4.27056e8i −0.430181 0.630960i
\(879\) 4.95129e7 3.28497e8i 0.0729041 0.483687i
\(880\) 3.53883e7 + 1.38889e7i 0.0519292 + 0.0203807i
\(881\) −1.15724e9 5.57297e8i −1.69237 0.815002i −0.995175 0.0981199i \(-0.968717\pi\)
−0.697194 0.716882i \(-0.745569\pi\)
\(882\) 5.82557e7 1.20969e8i 0.0849049 0.176307i
\(883\) 4.64269e8 1.18294e9i 0.674353 1.71822i −0.0212266 0.999775i \(-0.506757\pi\)
0.695580 0.718449i \(-0.255148\pi\)
\(884\) 3.14530e8 + 4.74078e7i 0.455308 + 0.0686267i
\(885\) −2.19108e8 + 1.49385e8i −0.316103 + 0.215515i
\(886\) −1.31228e8 + 4.25429e8i −0.188679 + 0.611682i
\(887\) −1.16794e9 + 2.66574e8i −1.67359 + 0.381985i −0.950975 0.309269i \(-0.899916\pi\)
−0.722612 + 0.691254i \(0.757058\pi\)
\(888\) 7.76914e7 3.04916e7i 0.110952 0.0435453i
\(889\) −5.62651e8 4.21649e7i −0.800818 0.0600130i
\(890\) 1.27805e8 1.37741e8i 0.181291 0.195385i
\(891\) −2.20852e8 1.50574e8i −0.312225 0.212872i
\(892\) 1.92932e8 1.53858e8i 0.271838 0.216783i
\(893\) −4.43232e7 4.77691e7i −0.0622410 0.0670799i
\(894\) −5.18353e7 3.43905e8i −0.0725459 0.481311i
\(895\) 1.28245e8 5.61877e8i 0.178884 0.783740i
\(896\) −4.51346e6 + 7.81755e6i −0.00627460 + 0.0108679i
\(897\) −1.28039e7 + 7.39236e6i −0.0177405 + 0.0102425i
\(898\) −4.47156e8 + 1.37929e8i −0.617490 + 0.190470i
\(899\) 5.00575e7 + 3.99195e7i 0.0688954 + 0.0549422i
\(900\) −9.28262e6 1.23868e8i −0.0127334 0.169915i
\(901\) −5.91597e8 + 2.84898e8i −0.808819 + 0.389507i
\(902\) 1.17011e8i 0.159443i
\(903\) 9.65124e7 + 6.36732e8i 0.131075 + 0.864756i
\(904\) 6.39338e8 0.865416
\(905\) −7.81237e7 1.62226e8i −0.105399 0.218864i
\(906\) −3.70343e8 + 2.77534e7i −0.497989 + 0.0373191i
\(907\) 6.42500e8 8.05670e8i 0.861096 1.07978i −0.134942 0.990853i \(-0.543085\pi\)
0.996038 0.0889264i \(-0.0283436\pi\)
\(908\) −2.27314e7 7.36934e7i −0.0303647 0.0984398i
\(909\) −4.39718e7 7.61613e7i −0.0585440 0.101401i
\(910\) 1.58900e8 + 9.17408e7i 0.210862 + 0.121741i
\(911\) −1.38433e9 3.15963e8i −1.83098 0.417909i −0.838981 0.544161i \(-0.816848\pi\)
−0.991998 + 0.126252i \(0.959705\pi\)
\(912\) 6.48172e7 9.76962e6i 0.0854488 0.0128793i
\(913\) −1.76984e8 + 1.64217e8i −0.232553 + 0.215777i
\(914\) −6.39407e8 8.01791e8i −0.837411 1.05008i
\(915\) −2.13086e8 + 3.12540e8i −0.278158 + 0.407983i
\(916\) −1.88718e7 1.75105e7i −0.0245543 0.0227830i
\(917\) −5.72153e7 + 7.63485e8i −0.0742001 + 0.990131i
\(918\) 1.42880e8 + 3.64052e8i 0.184690 + 0.470582i
\(919\) 3.02249e8 + 1.32424e9i 0.389420 + 1.70616i 0.666661 + 0.745361i \(0.267723\pi\)
−0.277240 + 0.960801i \(0.589420\pi\)
\(920\) −5.68498e6 1.75358e6i −0.00730071 0.00225197i
\(921\) −7.70615e8 1.13028e9i −0.986412 1.44680i
\(922\) −1.28634e8 + 8.53434e8i −0.164121 + 1.08887i
\(923\) −1.05021e9 4.12177e8i −1.33558 0.524178i
\(924\) −7.67719e7 3.69714e7i −0.0973164 0.0468651i
\(925\) −2.49114e7 + 5.17290e7i −0.0314755 + 0.0653595i
\(926\) −2.08972e8 + 5.32452e8i −0.263182 + 0.670576i
\(927\) −1.14472e8 1.72539e7i −0.143701 0.0216595i
\(928\) 4.26832e8 2.91009e8i 0.534088 0.364135i
\(929\) 1.03002e8 3.33923e8i 0.128469 0.416485i −0.868372 0.495913i \(-0.834833\pi\)
0.996841 + 0.0794286i \(0.0253096\pi\)
\(930\) −3.32524e7 + 7.58964e6i −0.0413403 + 0.00943566i
\(931\) 6.14520e7 2.41181e7i 0.0761530 0.0298878i
\(932\) −1.28837e8 9.65498e6i −0.159145 0.0119262i
\(933\) 5.35777e8 5.77431e8i 0.659689 0.710976i
\(934\) 6.24915e8 + 4.26060e8i 0.766974 + 0.522914i
\(935\) 9.22882e7 7.35974e7i 0.112905 0.0900384i
\(936\) 3.18549e8 + 3.43314e8i 0.388462 + 0.418663i
\(937\) −8.85209e7 5.87298e8i −0.107604 0.713904i −0.975958 0.217959i \(-0.930060\pi\)
0.868354 0.495944i \(-0.165178\pi\)
\(938\) −4.87332e7 + 2.13514e8i −0.0590496 + 0.258713i
\(939\) −9.44411e8 + 1.63577e9i −1.14068 + 1.97572i
\(940\) 7.06327e7 4.07798e7i 0.0850398 0.0490978i
\(941\) −1.06975e9 + 3.29974e8i −1.28385 + 0.396014i −0.860267 0.509844i \(-0.829703\pi\)
−0.423580 + 0.905859i \(0.639227\pi\)
\(942\) 5.55100e8 + 4.42678e8i 0.664078 + 0.529584i
\(943\) 697591. + 9.30871e6i 0.000831890 + 0.0111008i
\(944\) −2.30410e8 + 1.10959e8i −0.273895 + 0.131901i
\(945\) 1.55759e8i 0.184569i
\(946\) 1.94654e8 2.95046e7i 0.229927 0.0348511i
\(947\) 1.15987e9 1.36571 0.682854 0.730555i \(-0.260739\pi\)
0.682854 + 0.730555i \(0.260739\pi\)
\(948\) −2.38052e6 4.94319e6i −0.00279413 0.00580206i
\(949\) 1.19749e9 8.97391e7i 1.40111 0.104999i
\(950\) −5.51514e7 + 6.91576e7i −0.0643258 + 0.0806620i
\(951\) 1.42681e8 + 4.62561e8i 0.165892 + 0.537809i
\(952\) 3.65217e8 + 6.32574e8i 0.423292 + 0.733163i
\(953\) 1.17861e9 + 6.80469e8i 1.36173 + 0.786194i 0.989854 0.142089i \(-0.0453821\pi\)
0.371874 + 0.928283i \(0.378715\pi\)
\(954\) −2.73335e8 6.23869e7i −0.314811 0.0718536i
\(955\) −1.34597e8 + 2.02873e7i −0.154535 + 0.0232923i
\(956\) −1.01892e8 + 9.45415e7i −0.116618 + 0.108205i
\(957\) −1.73710e8 2.17825e8i −0.198193 0.248526i
\(958\) 6.59473e8 9.67269e8i 0.750067 1.10015i
\(959\) −2.43192e7 2.25649e7i −0.0275736 0.0255846i
\(960\) −3.55762e7 + 4.74732e8i −0.0402111 + 0.536580i
\(961\) −3.20792e8 8.17365e8i −0.361454 0.920971i
\(962\) −1.39690e7 6.12024e7i −0.0156907 0.0687453i
\(963\) −6.43730e8 1.98565e8i −0.720817 0.222343i
\(964\) 3.70534e8 + 5.43474e8i 0.413616 + 0.606663i
\(965\) −5.79369e7 + 3.84386e8i −0.0644723 + 0.427746i
\(966\) −9.16504e6 3.59701e6i −0.0101672 0.00399034i
\(967\) 6.18011e8 + 2.97618e8i 0.683466 + 0.329140i 0.743195 0.669075i \(-0.233309\pi\)
−0.0597292 + 0.998215i \(0.519024\pi\)
\(968\) 3.87347e8 8.04334e8i 0.427045 0.886769i
\(969\) 7.43586e7 1.89463e8i 0.0817259 0.208234i
\(970\) −2.90961e8 4.38553e7i −0.318801 0.0480515i
\(971\) 3.75539e6 2.56038e6i 0.00410202 0.00279671i −0.561267 0.827635i \(-0.689686\pi\)
0.565369 + 0.824838i \(0.308734\pi\)
\(972\) 1.03938e8 3.36958e8i 0.113181 0.366925i
\(973\) −7.62679e8 + 1.74077e8i −0.827948 + 0.188974i
\(974\) 1.12565e9 4.41785e8i 1.21822 0.478117i
\(975\) −9.46091e8 7.08997e7i −1.02075 0.0764946i
\(976\) −2.48117e8 + 2.67407e8i −0.266875 + 0.287622i
\(977\) −7.35711e8 5.01599e8i −0.788903 0.537865i 0.100528 0.994934i \(-0.467947\pi\)
−0.889431 + 0.457069i \(0.848899\pi\)
\(978\) −8.77845e8 + 7.00058e8i −0.938429 + 0.748372i
\(979\) 1.53947e8 + 1.65915e8i 0.164067 + 0.176823i
\(980\) 1.23145e7 + 8.17015e7i 0.0130840 + 0.0868064i
\(981\) 1.79094e8 7.84660e8i 0.189702 0.831141i
\(982\) 2.34318e8 4.05850e8i 0.247440 0.428579i
\(983\) 7.69362e8 4.44192e8i 0.809973 0.467638i −0.0369738 0.999316i \(-0.511772\pi\)
0.846946 + 0.531678i \(0.178438\pi\)
\(984\) 8.32076e8 2.56661e8i 0.873329 0.269386i
\(985\) 4.77214e8 + 3.80566e8i 0.499350 + 0.398218i
\(986\) 5.17569e7 + 6.90648e8i 0.0539930 + 0.720487i
\(987\) 4.19347e8 2.01947e8i 0.436137 0.210032i
\(988\) 6.67770e7i 0.0692398i
\(989\) −1.53097e7 + 3.50770e6i −0.0158262 + 0.00362605i
\(990\) 5.04011e7 0.0519439
\(991\) 1.01135e8 + 2.10010e8i 0.103916 + 0.215784i 0.946443 0.322870i \(-0.104648\pi\)
−0.842527 + 0.538653i \(0.818933\pi\)
\(992\) 7.59652e7 5.69280e6i 0.0778179 0.00583165i
\(993\) −5.43811e8 + 6.81917e8i −0.555393 + 0.696440i
\(994\) −2.21451e8 7.17925e8i −0.225485 0.731005i
\(995\) 2.62641e8 + 4.54907e8i 0.266620 + 0.461800i
\(996\) −4.51224e8 2.60514e8i −0.456682 0.263666i
\(997\) 6.12843e8 + 1.39877e8i 0.618392 + 0.141144i 0.520230 0.854026i \(-0.325846\pi\)
0.0981625 + 0.995170i \(0.468704\pi\)
\(998\) 7.99586e8 1.20518e8i 0.804402 0.121244i
\(999\) −3.90653e7 + 3.62473e7i −0.0391828 + 0.0363563i
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 43.7.h.a.29.14 yes 252
43.3 odd 42 inner 43.7.h.a.3.14 252
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.7.h.a.3.14 252 43.3 odd 42 inner
43.7.h.a.29.14 yes 252 1.1 even 1 trivial