Properties

Label 43.7.f.a.22.1
Level $43$
Weight $7$
Character 43.22
Analytic conductor $9.892$
Analytic rank $0$
Dimension $126$
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(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), 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: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(126\)
Relative dimension: \(21\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 22.1
Character \(\chi\) \(=\) 43.22
Dual form 43.7.f.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.68851 + 13.8888i) q^{2} +(4.36630 + 9.06671i) q^{3} +(-108.260 - 135.754i) q^{4} +(1.12402 - 0.256549i) q^{5} -155.130 q^{6} -114.871i q^{7} +(1647.71 - 376.078i) q^{8} +(391.383 - 490.779i) q^{9} +O(q^{10})\) \(q+(-6.68851 + 13.8888i) q^{2} +(4.36630 + 9.06671i) q^{3} +(-108.260 - 135.754i) q^{4} +(1.12402 - 0.256549i) q^{5} -155.130 q^{6} -114.871i q^{7} +(1647.71 - 376.078i) q^{8} +(391.383 - 490.779i) q^{9} +(-3.95482 + 17.3272i) q^{10} +(-143.971 + 180.533i) q^{11} +(758.145 - 1574.30i) q^{12} +(-474.002 - 2076.74i) q^{13} +(1595.43 + 768.317i) q^{14} +(7.23385 + 9.07095i) q^{15} +(-3324.60 + 14566.0i) q^{16} +(-265.325 + 1162.46i) q^{17} +(4198.58 + 8718.44i) q^{18} +(-1735.46 + 1383.99i) q^{19} +(-156.513 - 124.815i) q^{20} +(1041.50 - 501.562i) q^{21} +(-1544.45 - 3207.08i) q^{22} +(10598.8 - 13290.5i) q^{23} +(10604.2 + 13297.2i) q^{24} +(-14076.4 + 6778.86i) q^{25} +(32013.8 + 7306.94i) q^{26} +(13310.9 + 3038.12i) q^{27} +(-15594.2 + 12436.0i) q^{28} +(15411.2 - 32001.6i) q^{29} +(-174.369 + 39.7985i) q^{30} +(20994.6 + 10110.5i) q^{31} +(-95501.7 - 76160.1i) q^{32} +(-2265.46 - 517.077i) q^{33} +(-14370.6 - 11460.2i) q^{34} +(-29.4701 - 129.117i) q^{35} -108996. q^{36} -52619.2i q^{37} +(-7614.28 - 33360.4i) q^{38} +(16759.5 - 13365.3i) q^{39} +(1755.57 - 845.436i) q^{40} +(72824.9 + 35070.6i) q^{41} +17820.0i q^{42} +(78782.3 - 10710.5i) q^{43} +40094.3 q^{44} +(314.012 - 652.053i) q^{45} +(113699. + 236099. i) q^{46} +(-113860. - 142776. i) q^{47} +(-146582. + 33456.5i) q^{48} +104454. q^{49} -240846. i q^{50} +(-11698.2 + 2670.04i) q^{51} +(-230609. + 289175. i) q^{52} +(-23546.0 + 103162. i) q^{53} +(-131226. + 164552. i) q^{54} +(-115.509 + 239.858i) q^{55} +(-43200.5 - 189274. i) q^{56} +(-20125.8 - 9692.05i) q^{57} +(341387. + 428086. i) q^{58} +(9340.51 - 40923.5i) q^{59} +(448.280 - 1964.04i) q^{60} +(-173626. - 360538. i) q^{61} +(-280845. + 223966. i) q^{62} +(-56376.4 - 44958.7i) q^{63} +(835031. - 402130. i) q^{64} +(-1065.57 - 2212.68i) q^{65} +(22334.1 - 28006.1i) q^{66} +(99720.3 + 125045. i) q^{67} +(186533. - 89829.4i) q^{68} +(166779. + 38066.2i) q^{69} +(1990.39 + 454.295i) q^{70} +(23567.9 - 18794.8i) q^{71} +(460313. - 955851. i) q^{72} +(-466171. + 106400. i) q^{73} +(730819. + 351944. i) q^{74} +(-122924. - 98028.5i) q^{75} +(375763. + 85765.4i) q^{76} +(20738.1 + 16538.1i) q^{77} +(73531.8 + 322164. i) q^{78} -226642. q^{79} +17225.4i q^{80} +(-71255.6 - 312191. i) q^{81} +(-974179. + 776882. i) q^{82} +(-649105. + 312592. i) q^{83} +(-180842. - 87089.0i) q^{84} +1374.70i q^{85} +(-378180. + 1.16583e6i) q^{86} +357439. q^{87} +(-169327. + 351610. i) q^{88} +(-467543. - 970862. i) q^{89} +(6955.98 + 8722.52i) q^{90} +(-238557. + 54449.1i) q^{91} -2.95167e6 q^{92} +234497. i q^{93} +(2.74455e6 - 626426. i) q^{94} +(-1595.63 + 2000.85i) q^{95} +(273532. - 1.19842e6i) q^{96} +(-91309.4 + 114498. i) q^{97} +(-698639. + 1.45074e6i) q^{98} +(32254.4 + 141316. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.68851 + 13.8888i −0.836063 + 1.73610i −0.176720 + 0.984261i \(0.556549\pi\)
−0.659343 + 0.751842i \(0.729166\pi\)
\(3\) 4.36630 + 9.06671i 0.161715 + 0.335804i 0.966043 0.258381i \(-0.0831890\pi\)
−0.804328 + 0.594185i \(0.797475\pi\)
\(4\) −108.260 135.754i −1.69156 2.12115i
\(5\) 1.12402 0.256549i 0.00899213 0.00205239i −0.218023 0.975944i \(-0.569961\pi\)
0.227015 + 0.973891i \(0.427103\pi\)
\(6\) −155.130 −0.718194
\(7\) 114.871i 0.334901i −0.985880 0.167451i \(-0.946446\pi\)
0.985880 0.167451i \(-0.0535535\pi\)
\(8\) 1647.71 376.078i 3.21818 0.734528i
\(9\) 391.383 490.779i 0.536877 0.673223i
\(10\) −3.95482 + 17.3272i −0.00395482 + 0.0173272i
\(11\) −143.971 + 180.533i −0.108167 + 0.135637i −0.832968 0.553321i \(-0.813360\pi\)
0.724801 + 0.688958i \(0.241932\pi\)
\(12\) 758.145 1574.30i 0.438741 0.911055i
\(13\) −474.002 2076.74i −0.215749 0.945260i −0.960579 0.278006i \(-0.910327\pi\)
0.744830 0.667254i \(-0.232531\pi\)
\(14\) 1595.43 + 768.317i 0.581423 + 0.279999i
\(15\) 7.23385 + 9.07095i 0.00214336 + 0.00268769i
\(16\) −3324.60 + 14566.0i −0.811671 + 3.55616i
\(17\) −265.325 + 1162.46i −0.0540046 + 0.236610i −0.994726 0.102572i \(-0.967293\pi\)
0.940721 + 0.339181i \(0.110150\pi\)
\(18\) 4198.58 + 8718.44i 0.719921 + 1.49493i
\(19\) −1735.46 + 1383.99i −0.253020 + 0.201777i −0.741783 0.670640i \(-0.766020\pi\)
0.488763 + 0.872416i \(0.337448\pi\)
\(20\) −156.513 124.815i −0.0195642 0.0156019i
\(21\) 1041.50 501.562i 0.112461 0.0541585i
\(22\) −1544.45 3207.08i −0.145046 0.301191i
\(23\) 10598.8 13290.5i 0.871112 1.09234i −0.123871 0.992298i \(-0.539531\pi\)
0.994983 0.100042i \(-0.0318978\pi\)
\(24\) 10604.2 + 13297.2i 0.767084 + 0.961893i
\(25\) −14076.4 + 6778.86i −0.900892 + 0.433847i
\(26\) 32013.8 + 7306.94i 1.82145 + 0.415734i
\(27\) 13310.9 + 3038.12i 0.676261 + 0.154352i
\(28\) −15594.2 + 12436.0i −0.710377 + 0.566507i
\(29\) 15411.2 32001.6i 0.631890 1.31213i −0.301567 0.953445i \(-0.597510\pi\)
0.933457 0.358688i \(-0.116776\pi\)
\(30\) −174.369 + 39.7985i −0.00645809 + 0.00147402i
\(31\) 20994.6 + 10110.5i 0.704729 + 0.339380i 0.751690 0.659517i \(-0.229239\pi\)
−0.0469602 + 0.998897i \(0.514953\pi\)
\(32\) −95501.7 76160.1i −2.91448 2.32422i
\(33\) −2265.46 517.077i −0.0630398 0.0143884i
\(34\) −14370.6 11460.2i −0.365627 0.291578i
\(35\) −29.4701 129.117i −0.000687350 0.00301148i
\(36\) −108996. −2.33617
\(37\) 52619.2i 1.03882i −0.854526 0.519408i \(-0.826152\pi\)
0.854526 0.519408i \(-0.173848\pi\)
\(38\) −7614.28 33360.4i −0.138764 0.607967i
\(39\) 16759.5 13365.3i 0.282532 0.225312i
\(40\) 1755.57 845.436i 0.0274307 0.0132099i
\(41\) 72824.9 + 35070.6i 1.05664 + 0.508852i 0.879779 0.475383i \(-0.157691\pi\)
0.176864 + 0.984235i \(0.443405\pi\)
\(42\) 17820.0i 0.240524i
\(43\) 78782.3 10710.5i 0.990885 0.134711i
\(44\) 40094.3 0.470679
\(45\) 314.012 652.053i 0.00344595 0.00715559i
\(46\) 113699. + 236099.i 1.16811 + 2.42561i
\(47\) −113860. 142776.i −1.09668 1.37519i −0.920459 0.390840i \(-0.872185\pi\)
−0.176219 0.984351i \(-0.556387\pi\)
\(48\) −146582. + 33456.5i −1.32543 + 0.302521i
\(49\) 104454. 0.887841
\(50\) 240846.i 1.92677i
\(51\) −11698.2 + 2670.04i −0.0881878 + 0.0201283i
\(52\) −230609. + 289175.i −1.64009 + 2.05660i
\(53\) −23546.0 + 103162.i −0.158158 + 0.692934i 0.832209 + 0.554462i \(0.187076\pi\)
−0.990366 + 0.138471i \(0.955781\pi\)
\(54\) −131226. + 164552.i −0.833369 + 1.04501i
\(55\) −115.509 + 239.858i −0.000694272 + 0.00144167i
\(56\) −43200.5 189274.i −0.245994 1.07777i
\(57\) −20125.8 9692.05i −0.108674 0.0523349i
\(58\) 341387. + 428086.i 1.74970 + 2.19405i
\(59\) 9340.51 40923.5i 0.0454794 0.199258i −0.947084 0.320985i \(-0.895986\pi\)
0.992564 + 0.121727i \(0.0388432\pi\)
\(60\) 448.280 1964.04i 0.00207537 0.00909279i
\(61\) −173626. 360538.i −0.764936 1.58841i −0.807893 0.589329i \(-0.799392\pi\)
0.0429568 0.999077i \(-0.486322\pi\)
\(62\) −280845. + 223966.i −1.17840 + 0.939740i
\(63\) −56376.4 44958.7i −0.225463 0.179801i
\(64\) 835031. 402130.i 3.18539 1.53400i
\(65\) −1065.57 2212.68i −0.00388009 0.00805709i
\(66\) 22334.1 28006.1i 0.0776851 0.0974140i
\(67\) 99720.3 + 125045.i 0.331558 + 0.415760i 0.919467 0.393166i \(-0.128620\pi\)
−0.587910 + 0.808927i \(0.700049\pi\)
\(68\) 186533. 89829.4i 0.593237 0.285688i
\(69\) 166779. + 38066.2i 0.507684 + 0.115876i
\(70\) 1990.39 + 454.295i 0.00580290 + 0.00132447i
\(71\) 23567.9 18794.8i 0.0658485 0.0525125i −0.590012 0.807394i \(-0.700877\pi\)
0.655861 + 0.754882i \(0.272306\pi\)
\(72\) 460313. 955851.i 1.23326 2.56090i
\(73\) −466171. + 106400.i −1.19833 + 0.273511i −0.774703 0.632326i \(-0.782100\pi\)
−0.423627 + 0.905837i \(0.639243\pi\)
\(74\) 730819. + 351944.i 1.80349 + 0.868517i
\(75\) −122924. 98028.5i −0.291375 0.232364i
\(76\) 375763. + 85765.4i 0.855998 + 0.195376i
\(77\) 20738.1 + 16538.1i 0.0454252 + 0.0362254i
\(78\) 73531.8 + 322164.i 0.154950 + 0.678880i
\(79\) −226642. −0.459684 −0.229842 0.973228i \(-0.573821\pi\)
−0.229842 + 0.973228i \(0.573821\pi\)
\(80\) 17225.4i 0.0336433i
\(81\) −71255.6 312191.i −0.134080 0.587442i
\(82\) −974179. + 776882.i −1.76684 + 1.40901i
\(83\) −649105. + 312592.i −1.13522 + 0.546694i −0.904562 0.426341i \(-0.859802\pi\)
−0.230659 + 0.973035i \(0.574088\pi\)
\(84\) −180842. 87089.0i −0.305114 0.146935i
\(85\) 1374.70i 0.00223846i
\(86\) −378180. + 1.16583e6i −0.594570 + 1.83291i
\(87\) 357439. 0.542806
\(88\) −169327. + 351610.i −0.248472 + 0.515957i
\(89\) −467543. 970862.i −0.663210 1.37717i −0.912635 0.408776i \(-0.865956\pi\)
0.249425 0.968394i \(-0.419759\pi\)
\(90\) 6955.98 + 8722.52i 0.00954180 + 0.0119650i
\(91\) −238557. + 54449.1i −0.316569 + 0.0722548i
\(92\) −2.95167e6 −3.79056
\(93\) 234497.i 0.291534i
\(94\) 2.74455e6 626426.i 3.30437 0.754200i
\(95\) −1595.63 + 2000.85i −0.00186106 + 0.00233370i
\(96\) 273532. 1.19842e6i 0.309168 1.35456i
\(97\) −91309.4 + 114498.i −0.100046 + 0.125454i −0.829334 0.558753i \(-0.811280\pi\)
0.729288 + 0.684207i \(0.239851\pi\)
\(98\) −698639. + 1.45074e6i −0.742291 + 1.54138i
\(99\) 32254.4 + 141316.i 0.0332417 + 0.145641i
\(100\) 2.44417e6 + 1.17705e6i 2.44417 + 1.17705i
\(101\) 767188. + 962023.i 0.744625 + 0.933730i 0.999447 0.0332581i \(-0.0105883\pi\)
−0.254822 + 0.966988i \(0.582017\pi\)
\(102\) 41159.8 180333.i 0.0387858 0.169932i
\(103\) −787.998 + 3452.44i −0.000721130 + 0.00315948i −0.975287 0.220941i \(-0.929087\pi\)
0.974566 + 0.224100i \(0.0719443\pi\)
\(104\) −1.56203e6 3.24359e6i −1.38864 2.88354i
\(105\) 1041.99 830.960i 0.000900111 0.000717815i
\(106\) −1.27531e6 1.01703e6i −1.07077 0.853914i
\(107\) 1.62781e6 783913.i 1.32878 0.639906i 0.371328 0.928502i \(-0.378903\pi\)
0.957451 + 0.288595i \(0.0931882\pi\)
\(108\) −1.02860e6 2.13591e6i −0.816534 1.69555i
\(109\) 565030. 708526.i 0.436307 0.547112i −0.514259 0.857635i \(-0.671933\pi\)
0.950566 + 0.310523i \(0.100504\pi\)
\(110\) −2558.76 3208.58i −0.00192243 0.00241066i
\(111\) 477083. 229751.i 0.348839 0.167992i
\(112\) 1.67322e6 + 381901.i 1.19096 + 0.271830i
\(113\) −1.94947e6 444954.i −1.35108 0.308375i −0.515098 0.857131i \(-0.672245\pi\)
−0.835983 + 0.548756i \(0.815102\pi\)
\(114\) 269222. 214698.i 0.181717 0.144915i
\(115\) 8503.58 17657.9i 0.00559124 0.0116103i
\(116\) −6.01275e6 + 1.37237e6i −3.85212 + 0.879220i
\(117\) −1.20474e6 580170.i −0.752201 0.362241i
\(118\) 505905. + 403446.i 0.307909 + 0.245549i
\(119\) 133534. + 30478.2i 0.0792409 + 0.0180862i
\(120\) 15330.6 + 12225.8i 0.00887190 + 0.00707510i
\(121\) 382345. + 1.67516e6i 0.215824 + 0.945585i
\(122\) 6.16875e6 3.39717
\(123\) 813411.i 0.437114i
\(124\) −900342. 3.94465e6i −0.472218 2.06892i
\(125\) −28167.3 + 22462.6i −0.0144216 + 0.0115009i
\(126\) 1.00150e6 482296.i 0.500654 0.241102i
\(127\) 1.76275e6 + 848894.i 0.860555 + 0.414422i 0.811485 0.584374i \(-0.198660\pi\)
0.0490707 + 0.998795i \(0.484374\pi\)
\(128\) 6.46956e6i 3.08493i
\(129\) 441096. + 667531.i 0.205477 + 0.310958i
\(130\) 37858.6 0.0172320
\(131\) 654391. 1.35886e6i 0.291087 0.604449i −0.703223 0.710969i \(-0.748257\pi\)
0.994311 + 0.106520i \(0.0339709\pi\)
\(132\) 175064. + 363524.i 0.0761158 + 0.158056i
\(133\) 158980. + 199355.i 0.0675753 + 0.0847367i
\(134\) −2.40371e6 + 548632.i −0.999006 + 0.228017i
\(135\) 15741.0 0.00639782
\(136\) 2.01518e6i 0.801119i
\(137\) 2.24073e6 511431.i 0.871419 0.198896i 0.236648 0.971596i \(-0.423951\pi\)
0.634772 + 0.772700i \(0.281094\pi\)
\(138\) −1.64420e6 + 2.06176e6i −0.625628 + 0.784513i
\(139\) 184760. 809484.i 0.0687959 0.301414i −0.928811 0.370553i \(-0.879168\pi\)
0.997607 + 0.0691390i \(0.0220252\pi\)
\(140\) −14337.7 + 17978.9i −0.00522510 + 0.00655207i
\(141\) 797364. 1.65574e6i 0.284446 0.590658i
\(142\) 103403. + 453040.i 0.0361135 + 0.158224i
\(143\) 443163. + 213416.i 0.151550 + 0.0729825i
\(144\) 5.84752e6 + 7.33255e6i 1.95832 + 2.45566i
\(145\) 9112.40 39924.0i 0.00298902 0.0130958i
\(146\) 1.64021e6 7.18622e6i 0.527036 2.30910i
\(147\) 456076. + 947051.i 0.143577 + 0.298141i
\(148\) −7.14325e6 + 5.69655e6i −2.20349 + 1.75722i
\(149\) 3.00345e6 + 2.39517e6i 0.907949 + 0.724065i 0.961588 0.274495i \(-0.0885108\pi\)
−0.0536395 + 0.998560i \(0.517082\pi\)
\(150\) 2.18368e6 1.05160e6i 0.647016 0.311586i
\(151\) −911094. 1.89191e6i −0.264626 0.549501i 0.725741 0.687968i \(-0.241497\pi\)
−0.990367 + 0.138467i \(0.955783\pi\)
\(152\) −2.33905e6 + 2.93307e6i −0.666052 + 0.835203i
\(153\) 466669. + 585185.i 0.130297 + 0.163387i
\(154\) −368401. + 177413.i −0.100869 + 0.0485761i
\(155\) 26192.1 + 5978.17i 0.00703356 + 0.00160536i
\(156\) −3.62877e6 828244.i −0.955842 0.218165i
\(157\) −5.46992e6 + 4.36211e6i −1.41345 + 1.12719i −0.440083 + 0.897957i \(0.645051\pi\)
−0.973371 + 0.229235i \(0.926378\pi\)
\(158\) 1.51590e6 3.14779e6i 0.384325 0.798058i
\(159\) −1.03815e6 + 236950.i −0.258266 + 0.0589476i
\(160\) −126884. 61104.2i −0.0309776 0.0149180i
\(161\) −1.52670e6 1.21750e6i −0.365826 0.291737i
\(162\) 4.81256e6 + 1.09844e6i 1.13196 + 0.258362i
\(163\) −312394. 249126.i −0.0721340 0.0575249i 0.586759 0.809762i \(-0.300404\pi\)
−0.658893 + 0.752237i \(0.728975\pi\)
\(164\) −3.12305e6 1.36830e7i −0.708024 3.10206i
\(165\) −2679.07 −0.000596393
\(166\) 1.11061e7i 2.42793i
\(167\) −607628. 2.66219e6i −0.130463 0.571597i −0.997328 0.0730537i \(-0.976726\pi\)
0.866865 0.498543i \(-0.166132\pi\)
\(168\) 1.52747e6 1.21811e6i 0.322139 0.256897i
\(169\) 260648. 125522.i 0.0540001 0.0260051i
\(170\) −19092.9 9194.66i −0.00388620 0.00187150i
\(171\) 1.39340e6i 0.278668i
\(172\) −9.98296e6 9.53548e6i −1.96189 1.87395i
\(173\) 4.38233e6 0.846382 0.423191 0.906040i \(-0.360910\pi\)
0.423191 + 0.906040i \(0.360910\pi\)
\(174\) −2.39073e6 + 4.96441e6i −0.453820 + 0.942366i
\(175\) 778695. + 1.61698e6i 0.145296 + 0.301710i
\(176\) −2.15101e6 2.69728e6i −0.394553 0.494753i
\(177\) 411825. 93996.3i 0.0742664 0.0169508i
\(178\) 1.66113e7 2.94539
\(179\) 7.85496e6i 1.36957i 0.728744 + 0.684786i \(0.240104\pi\)
−0.728744 + 0.684786i \(0.759896\pi\)
\(180\) −122514. + 27962.9i −0.0210071 + 0.00479474i
\(181\) −7.00741e6 + 8.78701e6i −1.18174 + 1.48185i −0.341295 + 0.939956i \(0.610866\pi\)
−0.840444 + 0.541898i \(0.817706\pi\)
\(182\) 839357. 3.67746e6i 0.139230 0.610006i
\(183\) 2.51079e6 3.14843e6i 0.409692 0.513737i
\(184\) 1.24655e7 2.58848e7i 2.00104 4.15520i
\(185\) −13499.4 59144.8i −0.00213206 0.00934117i
\(186\) −3.25689e6 1.56844e6i −0.506133 0.243741i
\(187\) −171664. 215260.i −0.0262516 0.0329185i
\(188\) −7.05591e6 + 3.09140e7i −1.06189 + 4.65244i
\(189\) 348992. 1.52903e6i 0.0516928 0.226481i
\(190\) −17117.1 35544.1i −0.00249557 0.00518211i
\(191\) 252002. 200965.i 0.0361662 0.0288416i −0.605240 0.796043i \(-0.706923\pi\)
0.641406 + 0.767202i \(0.278351\pi\)
\(192\) 7.29198e6 + 5.81516e6i 1.03025 + 0.821596i
\(193\) −7.37076e6 + 3.54957e6i −1.02528 + 0.493747i −0.869441 0.494037i \(-0.835521\pi\)
−0.155834 + 0.987783i \(0.549807\pi\)
\(194\) −979525. 2.03400e6i −0.134156 0.278578i
\(195\) 15409.1 19322.4i 0.00207814 0.00260590i
\(196\) −1.13081e7 1.41800e7i −1.50184 1.88325i
\(197\) −1.10934e7 + 5.34230e6i −1.45099 + 0.698762i −0.982767 0.184846i \(-0.940821\pi\)
−0.468227 + 0.883608i \(0.655107\pi\)
\(198\) −2.17844e6 497215.i −0.280640 0.0640543i
\(199\) 7.65792e6 + 1.74787e6i 0.971744 + 0.221794i 0.678790 0.734332i \(-0.262505\pi\)
0.292954 + 0.956127i \(0.405362\pi\)
\(200\) −2.06445e7 + 1.64634e7i −2.58056 + 2.05793i
\(201\) −698341. + 1.45012e6i −0.0859962 + 0.178573i
\(202\) −1.84927e7 + 4.22084e6i −2.24360 + 0.512088i
\(203\) −3.67606e6 1.77030e6i −0.439435 0.211621i
\(204\) 1.62892e6 + 1.29902e6i 0.191870 + 0.153012i
\(205\) 90853.6 + 20736.7i 0.0105458 + 0.00240702i
\(206\) −42679.9 34036.1i −0.00488226 0.00389348i
\(207\) −2.37450e6 1.04034e7i −0.267708 1.17291i
\(208\) 3.18257e7 3.53662
\(209\) 512562.i 0.0561446i
\(210\) 4571.70 + 20029.9i 0.000493651 + 0.00216282i
\(211\) −3.12358e6 + 2.49097e6i −0.332510 + 0.265168i −0.775485 0.631366i \(-0.782495\pi\)
0.442975 + 0.896534i \(0.353923\pi\)
\(212\) 1.65537e7 7.97184e6i 1.73735 0.836664i
\(213\) 273311. + 131620.i 0.0282826 + 0.0136202i
\(214\) 2.78516e7i 2.84190i
\(215\) 85804.8 32250.3i 0.00863368 0.00324503i
\(216\) 2.30749e7 2.28970
\(217\) 1.16140e6 2.41167e6i 0.113659 0.236015i
\(218\) 6.06138e6 + 1.25866e7i 0.585062 + 1.21489i
\(219\) −3.00014e6 3.76206e6i −0.285634 0.358173i
\(220\) 45066.7 10286.2i 0.00423241 0.000966019i
\(221\) 2.53989e6 0.235309
\(222\) 8.16281e6i 0.746072i
\(223\) 1.47677e6 337062.i 0.133167 0.0303946i −0.155418 0.987849i \(-0.549672\pi\)
0.288585 + 0.957454i \(0.406815\pi\)
\(224\) −8.74860e6 + 1.09704e7i −0.778385 + 0.976064i
\(225\) −2.18236e6 + 9.56156e6i −0.191593 + 0.839423i
\(226\) 1.92189e7 2.40998e7i 1.66496 2.08779i
\(227\) 4.26801e6 8.86262e6i 0.364878 0.757678i −0.635012 0.772502i \(-0.719005\pi\)
0.999890 + 0.0148249i \(0.00471908\pi\)
\(228\) 863082. + 3.78141e6i 0.0728194 + 0.319043i
\(229\) 4.89383e6 + 2.35674e6i 0.407514 + 0.196248i 0.626399 0.779502i \(-0.284528\pi\)
−0.218886 + 0.975750i \(0.570242\pi\)
\(230\) 188371. + 236209.i 0.0154821 + 0.0194139i
\(231\) −59397.2 + 260236.i −0.00481871 + 0.0211121i
\(232\) 1.33580e7 5.85251e7i 1.06974 4.68682i
\(233\) 184983. + 384121.i 0.0146239 + 0.0303669i 0.908153 0.418639i \(-0.137493\pi\)
−0.893529 + 0.449006i \(0.851778\pi\)
\(234\) 1.61158e7 1.28519e7i 1.25778 1.00304i
\(235\) −164610. 131272.i −0.0126839 0.0101151i
\(236\) −6.56672e6 + 3.16236e6i −0.499588 + 0.240589i
\(237\) −989586. 2.05490e6i −0.0743376 0.154364i
\(238\) −1.31645e6 + 1.65077e6i −0.0976499 + 0.122449i
\(239\) −1.22896e7 1.54106e7i −0.900208 1.12883i −0.991120 0.132967i \(-0.957550\pi\)
0.0909120 0.995859i \(-0.471022\pi\)
\(240\) −156178. + 75211.2i −0.0112976 + 0.00544062i
\(241\) −1.10439e7 2.52069e6i −0.788988 0.180081i −0.191004 0.981589i \(-0.561174\pi\)
−0.597984 + 0.801508i \(0.704031\pi\)
\(242\) −2.58233e7 5.89401e6i −1.82208 0.415877i
\(243\) 1.03011e7 8.21487e6i 0.717902 0.572508i
\(244\) −3.01476e7 + 6.26022e7i −2.07531 + 4.30943i
\(245\) 117408. 26797.5i 0.00798358 0.00182220i
\(246\) −1.12973e7 5.44050e6i −0.758875 0.365455i
\(247\) 3.69679e6 + 2.94809e6i 0.245320 + 0.195636i
\(248\) 3.83952e7 + 8.76346e6i 2.51723 + 0.574541i
\(249\) −5.66837e6 4.52037e6i −0.367164 0.292803i
\(250\) −123583. 541452.i −0.00790930 0.0346529i
\(251\) 3.04247e7 1.92400 0.962000 0.273050i \(-0.0880324\pi\)
0.962000 + 0.273050i \(0.0880324\pi\)
\(252\) 1.25205e7i 0.782386i
\(253\) 873461. + 3.82688e6i 0.0539364 + 0.236311i
\(254\) −2.35803e7 + 1.88047e7i −1.43896 + 1.14753i
\(255\) −12464.0 + 6002.33i −0.000751685 + 0.000361992i
\(256\) −3.64126e7 1.75354e7i −2.17036 1.04519i
\(257\) 6.84569e6i 0.403290i 0.979459 + 0.201645i \(0.0646288\pi\)
−0.979459 + 0.201645i \(0.935371\pi\)
\(258\) −1.22215e7 + 1.66152e6i −0.711648 + 0.0967488i
\(259\) −6.04443e6 −0.347901
\(260\) −185021. + 384200.i −0.0105269 + 0.0218593i
\(261\) −9.67405e6 2.00884e7i −0.544110 1.12986i
\(262\) 1.44960e7 + 1.81774e7i 0.806018 + 1.01072i
\(263\) 2.94880e7 6.73044e6i 1.62098 0.369978i 0.686819 0.726828i \(-0.259006\pi\)
0.934162 + 0.356850i \(0.116149\pi\)
\(264\) −3.92728e6 −0.213442
\(265\) 121996.i 0.00655555i
\(266\) −3.83214e6 + 874662.i −0.203609 + 0.0464724i
\(267\) 6.76110e6 8.47815e6i 0.355208 0.445417i
\(268\) 6.17965e6 2.70748e7i 0.321040 1.40657i
\(269\) −2.76405e6 + 3.46601e6i −0.142000 + 0.178063i −0.847746 0.530403i \(-0.822041\pi\)
0.705745 + 0.708465i \(0.250612\pi\)
\(270\) −105284. + 218625.i −0.00534898 + 0.0111073i
\(271\) 3.42519e6 + 1.50068e7i 0.172099 + 0.754013i 0.985132 + 0.171797i \(0.0549572\pi\)
−0.813034 + 0.582216i \(0.802186\pi\)
\(272\) −1.60504e7 7.72946e6i −0.797588 0.384098i
\(273\) −1.53529e6 1.92519e6i −0.0754573 0.0946205i
\(274\) −7.88393e6 + 3.45418e7i −0.383258 + 1.67916i
\(275\) 802783. 3.51722e6i 0.0386012 0.169123i
\(276\) −1.28878e7 2.67619e7i −0.612990 1.27289i
\(277\) −6.74300e6 + 5.37736e6i −0.317259 + 0.253006i −0.769151 0.639067i \(-0.779321\pi\)
0.451892 + 0.892073i \(0.350749\pi\)
\(278\) 1.00070e7 + 7.98033e6i 0.465769 + 0.371438i
\(279\) 1.31789e7 6.34664e6i 0.606831 0.292235i
\(280\) −97116.2 201664.i −0.00442402 0.00918658i
\(281\) 3.40085e6 4.26453e6i 0.153274 0.192200i −0.699266 0.714862i \(-0.746490\pi\)
0.852540 + 0.522662i \(0.175061\pi\)
\(282\) 1.76632e7 + 2.21489e7i 0.787628 + 0.987654i
\(283\) 2.34453e7 1.12906e7i 1.03442 0.498149i 0.161938 0.986801i \(-0.448226\pi\)
0.872479 + 0.488652i \(0.162511\pi\)
\(284\) −5.10293e6 1.16471e6i −0.222774 0.0508467i
\(285\) −25108.2 5730.77i −0.00108463 0.000247559i
\(286\) −5.92819e6 + 4.72757e6i −0.253410 + 0.202088i
\(287\) 4.02860e6 8.36548e6i 0.170415 0.353871i
\(288\) −7.47556e7 + 1.70625e7i −3.12944 + 0.714273i
\(289\) 2.04663e7 + 9.85604e6i 0.847901 + 0.408328i
\(290\) 493550. + 393593.i 0.0202366 + 0.0161381i
\(291\) −1.43681e6 327942.i −0.0583069 0.0133082i
\(292\) 6.49119e7 + 5.17655e7i 2.60721 + 2.07918i
\(293\) −3.43227e6 1.50377e7i −0.136451 0.597833i −0.996198 0.0871127i \(-0.972236\pi\)
0.859747 0.510720i \(-0.170621\pi\)
\(294\) −1.62039e7 −0.637642
\(295\) 48394.9i 0.00188510i
\(296\) −1.97889e7 8.67010e7i −0.763040 3.34310i
\(297\) −2.46485e6 + 1.96565e6i −0.0940853 + 0.0750305i
\(298\) −5.33547e7 + 2.56943e7i −2.01615 + 0.970929i
\(299\) −3.26247e7 1.57112e7i −1.22049 0.587756i
\(300\) 2.72999e7i 1.01111i
\(301\) −1.23033e6 9.04981e6i −0.0451150 0.331849i
\(302\) 3.23702e7 1.17523
\(303\) −5.37261e6 + 1.11563e7i −0.193134 + 0.401046i
\(304\) −1.43895e7 2.98800e7i −0.512182 1.06356i
\(305\) −287654. 360707.i −0.0101384 0.0127132i
\(306\) −1.12488e7 + 2.56748e6i −0.392594 + 0.0896070i
\(307\) −2.50492e7 −0.865724 −0.432862 0.901460i \(-0.642496\pi\)
−0.432862 + 0.901460i \(0.642496\pi\)
\(308\) 4.60568e6i 0.157631i
\(309\) −34742.9 + 7929.85i −0.00117758 + 0.000268775i
\(310\) −258216. + 323792.i −0.00866758 + 0.0108688i
\(311\) 9.21445e6 4.03711e7i 0.306329 1.34212i −0.554060 0.832477i \(-0.686922\pi\)
0.860389 0.509639i \(-0.170221\pi\)
\(312\) 2.25884e7 2.83250e7i 0.743741 0.932621i
\(313\) −1.13967e7 + 2.36655e7i −0.371661 + 0.771761i −0.999981 0.00619355i \(-0.998029\pi\)
0.628320 + 0.777955i \(0.283743\pi\)
\(314\) −2.39991e7 1.05147e8i −0.775185 3.39631i
\(315\) −74902.1 36070.9i −0.00239642 0.00115405i
\(316\) 2.45363e7 + 3.07675e7i 0.777584 + 0.975059i
\(317\) 1.38147e6 6.05262e6i 0.0433675 0.190005i −0.948604 0.316465i \(-0.897504\pi\)
0.991972 + 0.126459i \(0.0403613\pi\)
\(318\) 3.65269e6 1.60035e7i 0.113588 0.497661i
\(319\) 3.55861e6 + 7.38952e6i 0.109625 + 0.227638i
\(320\) 835421. 666226.i 0.0254950 0.0203316i
\(321\) 1.42150e7 + 1.13361e7i 0.429766 + 0.342727i
\(322\) 2.71210e7 1.30608e7i 0.812339 0.391202i
\(323\) −1.14837e6 2.38462e6i −0.0340781 0.0707638i
\(324\) −3.46670e7 + 4.34710e7i −1.01925 + 1.27810i
\(325\) 2.07502e7 + 2.60199e7i 0.604465 + 0.757975i
\(326\) 5.54951e6 2.67250e6i 0.160178 0.0771375i
\(327\) 8.89109e6 + 2.02933e6i 0.254280 + 0.0580377i
\(328\) 1.33183e8 + 3.03982e7i 3.77423 + 0.861443i
\(329\) −1.64009e7 + 1.30793e7i −0.460553 + 0.367279i
\(330\) 17919.0 37209.2i 0.000498622 0.00103540i
\(331\) −1.67994e7 + 3.83435e6i −0.463243 + 0.105732i −0.447771 0.894148i \(-0.647782\pi\)
−0.0154719 + 0.999880i \(0.504925\pi\)
\(332\) 1.12708e8 + 5.42771e7i 3.07992 + 1.48321i
\(333\) −2.58244e7 2.05943e7i −0.699355 0.557717i
\(334\) 4.10389e7 + 9.36685e6i 1.10143 + 0.251394i
\(335\) 144167. + 114970.i 0.00383471 + 0.00305808i
\(336\) 3.84318e6 + 1.68381e7i 0.101315 + 0.443889i
\(337\) −3.55032e7 −0.927637 −0.463818 0.885930i \(-0.653521\pi\)
−0.463818 + 0.885930i \(0.653521\pi\)
\(338\) 4.45965e6i 0.115492i
\(339\) −4.47770e6 1.96181e7i −0.114936 0.503567i
\(340\) 186620. 148825.i 0.00474812 0.00378650i
\(341\) −4.84788e6 + 2.33462e6i −0.122261 + 0.0588779i
\(342\) −1.93527e7 9.31976e6i −0.483796 0.232984i
\(343\) 2.55132e7i 0.632241i
\(344\) 1.25782e8 4.72760e7i 3.08989 1.16136i
\(345\) 197228. 0.00480298
\(346\) −2.93112e7 + 6.08654e7i −0.707629 + 1.46941i
\(347\) 2.24218e7 + 4.65594e7i 0.536640 + 1.11434i 0.976348 + 0.216204i \(0.0693675\pi\)
−0.439709 + 0.898141i \(0.644918\pi\)
\(348\) −3.86964e7 4.85237e7i −0.918190 1.15137i
\(349\) −2.04138e7 + 4.65931e6i −0.480228 + 0.109609i −0.455780 0.890092i \(-0.650640\pi\)
−0.0244474 + 0.999701i \(0.507783\pi\)
\(350\) −2.76662e7 −0.645276
\(351\) 2.90832e7i 0.672544i
\(352\) 2.74989e7 6.27644e6i 0.630503 0.143908i
\(353\) −4.15892e7 + 5.21512e7i −0.945489 + 1.18561i 0.0370059 + 0.999315i \(0.488218\pi\)
−0.982495 + 0.186290i \(0.940353\pi\)
\(354\) −1.44899e6 + 6.34846e6i −0.0326630 + 0.143106i
\(355\) 21668.9 27172.0i 0.000484342 0.000607346i
\(356\) −8.11820e7 + 1.68576e8i −1.79933 + 3.73634i
\(357\) 306710. + 1.34379e6i 0.00674099 + 0.0295342i
\(358\) −1.09096e8 5.25379e7i −2.37772 1.14505i
\(359\) 2.47703e7 + 3.10610e7i 0.535363 + 0.671324i 0.973792 0.227442i \(-0.0730363\pi\)
−0.438429 + 0.898766i \(0.644465\pi\)
\(360\) 272177. 1.19248e6i 0.00583369 0.0255591i
\(361\) −9.37228e6 + 4.10626e7i −0.199216 + 0.872821i
\(362\) −7.51722e7 1.56097e8i −1.58464 3.29055i
\(363\) −1.35188e7 + 1.07809e7i −0.282629 + 0.225389i
\(364\) 3.32179e7 + 2.64904e7i 0.688760 + 0.549267i
\(365\) −496686. + 239192.i −0.0102142 + 0.00491889i
\(366\) 2.69346e7 + 5.59302e7i 0.549373 + 1.14078i
\(367\) −3.97723e7 + 4.98729e7i −0.804605 + 1.00894i 0.194999 + 0.980803i \(0.437530\pi\)
−0.999604 + 0.0281390i \(0.991042\pi\)
\(368\) 1.58353e8 + 1.98569e8i 3.17748 + 3.98444i
\(369\) 4.57144e7 2.20149e7i 0.909858 0.438164i
\(370\) 911743. + 208099.i 0.0179998 + 0.00410833i
\(371\) 1.18503e7 + 2.70476e6i 0.232064 + 0.0529672i
\(372\) 3.18339e7 2.53867e7i 0.618388 0.493148i
\(373\) 4.78277e6 9.93152e6i 0.0921622 0.191377i −0.849792 0.527118i \(-0.823273\pi\)
0.941954 + 0.335741i \(0.108987\pi\)
\(374\) 4.13789e6 944447.i 0.0790978 0.0180536i
\(375\) −326649. 157306.i −0.00619423 0.00298298i
\(376\) −2.41304e8 1.92433e8i −4.53942 3.62007i
\(377\) −7.37638e7 1.68361e7i −1.37664 0.314208i
\(378\) 1.89022e7 + 1.50740e7i 0.349976 + 0.279096i
\(379\) 1.77148e7 + 7.76136e7i 0.325401 + 1.42567i 0.827793 + 0.561034i \(0.189596\pi\)
−0.502392 + 0.864640i \(0.667546\pi\)
\(380\) 444366. 0.00809823
\(381\) 1.96888e7i 0.355996i
\(382\) 1.10565e6 + 4.84416e6i 0.0198348 + 0.0869017i
\(383\) 2.45008e7 1.95387e7i 0.436098 0.347777i −0.380702 0.924698i \(-0.624318\pi\)
0.816800 + 0.576921i \(0.195746\pi\)
\(384\) −5.86576e7 + 2.82480e7i −1.03593 + 0.498878i
\(385\) 27552.8 + 13268.7i 0.000482818 + 0.000232513i
\(386\) 1.26113e8i 2.19279i
\(387\) 2.55776e7 4.28566e7i 0.441293 0.739409i
\(388\) 2.54288e7 0.435341
\(389\) −3.91537e6 + 8.13034e6i −0.0665156 + 0.138121i −0.931576 0.363547i \(-0.881566\pi\)
0.865060 + 0.501668i \(0.167280\pi\)
\(390\) 165302. + 343253.i 0.00278666 + 0.00578656i
\(391\) 1.26376e7 + 1.58470e7i 0.211414 + 0.265105i
\(392\) 1.72109e8 3.92827e7i 2.85723 0.652144i
\(393\) 1.51776e7 0.250050
\(394\) 1.89806e8i 3.10328i
\(395\) −254749. + 58144.8i −0.00413353 + 0.000943452i
\(396\) 1.56923e7 1.96775e7i 0.252697 0.316872i
\(397\) −1.37131e7 + 6.00809e7i −0.219161 + 0.960207i 0.738939 + 0.673773i \(0.235327\pi\)
−0.958100 + 0.286435i \(0.907530\pi\)
\(398\) −7.54959e7 + 9.46689e7i −1.19750 + 1.50161i
\(399\) −1.11334e6 + 2.31187e6i −0.0175270 + 0.0363952i
\(400\) −5.19425e7 2.27575e8i −0.811602 3.55586i
\(401\) −1.24317e7 5.98679e6i −0.192796 0.0928455i 0.334995 0.942220i \(-0.391265\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(402\) −1.54696e7 1.93983e7i −0.238123 0.298597i
\(403\) 1.10453e7 4.83926e7i 0.168757 0.739374i
\(404\) 4.75425e7 2.08297e8i 0.721004 3.15893i
\(405\) −160185. 332627.i −0.00241133 0.00500717i
\(406\) 4.91747e7 3.92155e7i 0.734791 0.585976i
\(407\) 9.49952e6 + 7.57561e6i 0.140902 + 0.112366i
\(408\) −1.82711e7 + 8.79888e6i −0.269019 + 0.129553i
\(409\) −1.55172e7 3.22218e7i −0.226800 0.470956i 0.756252 0.654280i \(-0.227028\pi\)
−0.983052 + 0.183325i \(0.941314\pi\)
\(410\) −895684. + 1.12315e6i −0.0129958 + 0.0162962i
\(411\) 1.44207e7 + 1.80830e7i 0.207711 + 0.260462i
\(412\) 553991. 266788.i 0.00792156 0.00381482i
\(413\) −4.70093e6 1.07296e6i −0.0667319 0.0152311i
\(414\) 1.60372e8 + 3.66040e7i 2.26011 + 0.515854i
\(415\) −649408. + 517886.i −0.00908602 + 0.00724586i
\(416\) −1.12896e8 + 2.34432e8i −1.56820 + 3.25639i
\(417\) 8.14608e6 1.85929e6i 0.112342 0.0256412i
\(418\) 7.11889e6 + 3.42828e6i 0.0974728 + 0.0469404i
\(419\) 9.60288e7 + 7.65804e7i 1.30545 + 1.04106i 0.995927 + 0.0901675i \(0.0287402\pi\)
0.309521 + 0.950893i \(0.399831\pi\)
\(420\) −225612. 51494.5i −0.00304519 0.000695045i
\(421\) 3.39158e7 + 2.70470e7i 0.454523 + 0.362470i 0.823830 0.566837i \(-0.191833\pi\)
−0.369306 + 0.929308i \(0.620405\pi\)
\(422\) −1.37046e7 6.00436e7i −0.182359 0.798969i
\(423\) −1.14635e8 −1.51459
\(424\) 1.78836e8i 2.34615i
\(425\) −4.14534e6 1.81619e7i −0.0540000 0.236589i
\(426\) −3.65609e6 + 2.91563e6i −0.0472920 + 0.0377142i
\(427\) −4.14154e7 + 1.99446e7i −0.531959 + 0.256178i
\(428\) −2.82646e8 1.36115e8i −3.60505 1.73610i
\(429\) 4.94986e6i 0.0626933i
\(430\) −125987. + 1.40743e6i −0.00158460 + 0.0177020i
\(431\) 2.44738e7 0.305682 0.152841 0.988251i \(-0.451158\pi\)
0.152841 + 0.988251i \(0.451158\pi\)
\(432\) −8.85067e7 + 1.83786e8i −1.09780 + 2.27961i
\(433\) −2.70297e7 5.61278e7i −0.332949 0.691376i 0.665538 0.746364i \(-0.268202\pi\)
−0.998487 + 0.0549881i \(0.982488\pi\)
\(434\) 2.57273e7 + 3.22610e7i 0.314720 + 0.394647i
\(435\) 401767. 91700.7i 0.00488098 0.00111405i
\(436\) −1.57355e8 −1.89855
\(437\) 3.77338e7i 0.452154i
\(438\) 7.23170e7 1.65059e7i 0.860634 0.196434i
\(439\) 9.68237e7 1.21413e8i 1.14443 1.43507i 0.261718 0.965144i \(-0.415711\pi\)
0.882708 0.469921i \(-0.155718\pi\)
\(440\) −100120. + 438656.i −0.00117534 + 0.00514951i
\(441\) 4.08814e7 5.12637e7i 0.476662 0.597715i
\(442\) −1.69881e7 + 3.52761e7i −0.196733 + 0.408521i
\(443\) 4.17760e6 + 1.83033e7i 0.0480525 + 0.210532i 0.993255 0.115954i \(-0.0369926\pi\)
−0.945202 + 0.326486i \(0.894135\pi\)
\(444\) −8.28386e7 3.98930e7i −0.946419 0.455772i
\(445\) −774599. 971317.i −0.00879017 0.0110225i
\(446\) −5.19596e6 + 2.27650e7i −0.0585681 + 0.256604i
\(447\) −8.60237e6 + 3.76894e7i −0.0963153 + 0.421985i
\(448\) −4.61931e7 9.59209e7i −0.513740 1.06679i
\(449\) 6.54068e7 5.21602e7i 0.722577 0.576236i −0.191638 0.981466i \(-0.561380\pi\)
0.914215 + 0.405230i \(0.132809\pi\)
\(450\) −1.18202e8 9.42630e7i −1.29714 1.03444i
\(451\) −1.68161e7 + 8.09818e6i −0.183313 + 0.0882791i
\(452\) 1.50646e8 + 3.12819e8i 1.63133 + 3.38749i
\(453\) 1.31753e7 1.65212e7i 0.141731 0.177725i
\(454\) 9.45447e7 + 1.18555e8i 1.01035 + 1.26693i
\(455\) −254173. + 122403.i −0.00269833 + 0.00129945i
\(456\) −3.68063e7 8.40080e6i −0.388175 0.0885984i
\(457\) −829990. 189440.i −0.00869610 0.00198483i 0.218171 0.975911i \(-0.429991\pi\)
−0.226867 + 0.973926i \(0.572848\pi\)
\(458\) −6.54648e7 + 5.22064e7i −0.681414 + 0.543410i
\(459\) −7.06339e6 + 1.46673e7i −0.0730425 + 0.151674i
\(460\) −3.31772e6 + 757248.i −0.0340852 + 0.00777973i
\(461\) 6.66907e7 + 3.21166e7i 0.680711 + 0.327813i 0.742089 0.670301i \(-0.233835\pi\)
−0.0613779 + 0.998115i \(0.519549\pi\)
\(462\) −3.21710e6 2.56555e6i −0.0326241 0.0260168i
\(463\) 1.79636e8 + 4.10008e7i 1.80988 + 0.413094i 0.987730 0.156171i \(-0.0499152\pi\)
0.822154 + 0.569265i \(0.192772\pi\)
\(464\) 4.14901e8 + 3.30872e8i 4.15327 + 3.31212i
\(465\) 60160.1 + 263579.i 0.000598342 + 0.00262151i
\(466\) −6.57224e6 −0.0649465
\(467\) 7.31844e7i 0.718568i −0.933228 0.359284i \(-0.883021\pi\)
0.933228 0.359284i \(-0.116979\pi\)
\(468\) 5.16644e7 + 2.26357e8i 0.504027 + 2.20829i
\(469\) 1.43641e7 1.14550e7i 0.139239 0.111039i
\(470\) 2.92421e6 1.40823e6i 0.0281654 0.0135637i
\(471\) −6.34333e7 3.05479e7i −0.607092 0.292360i
\(472\) 7.09426e7i 0.674654i
\(473\) −9.40873e6 + 1.57648e7i −0.0889094 + 0.148972i
\(474\) 3.51590e7 0.330142
\(475\) 1.50473e7 3.12461e7i 0.140404 0.291551i
\(476\) −1.03188e7 2.14272e7i −0.0956773 0.198676i
\(477\) 4.14142e7 + 5.19317e7i 0.381587 + 0.478495i
\(478\) 2.96235e8 6.76136e7i 2.71239 0.619085i
\(479\) −8.57154e7 −0.779924 −0.389962 0.920831i \(-0.627512\pi\)
−0.389962 + 0.920831i \(0.627512\pi\)
\(480\) 1.41722e6i 0.0128149i
\(481\) −1.09276e8 + 2.49416e7i −0.981952 + 0.224124i
\(482\) 1.08876e8 1.36527e8i 0.972284 1.21921i
\(483\) 4.37271e6 1.91581e7i 0.0388069 0.170024i
\(484\) 1.86017e8 2.33258e8i 1.64065 2.05731i
\(485\) −73258.8 + 152123.i −0.000642147 + 0.00133343i
\(486\) 4.51958e7 + 1.98016e8i 0.393721 + 1.72501i
\(487\) −1.03846e8 5.00094e7i −0.899086 0.432977i −0.0735275 0.997293i \(-0.523426\pi\)
−0.825559 + 0.564316i \(0.809140\pi\)
\(488\) −4.21675e8 5.28764e8i −3.62843 4.54990i
\(489\) 894747. 3.92014e6i 0.00765198 0.0335255i
\(490\) −413095. + 1.80989e6i −0.00351125 + 0.0153838i
\(491\) −4.62842e7 9.61102e7i −0.391010 0.811942i −0.999826 0.0186301i \(-0.994069\pi\)
0.608816 0.793311i \(-0.291645\pi\)
\(492\) 1.10424e8 8.80598e7i 0.927185 0.739405i
\(493\) 3.31117e7 + 2.64057e7i 0.276338 + 0.220372i
\(494\) −6.56715e7 + 3.16257e7i −0.544748 + 0.262337i
\(495\) 72508.8 + 150566.i 0.000597826 + 0.00124140i
\(496\) −2.17068e8 + 2.72195e8i −1.77890 + 2.23067i
\(497\) −2.15898e6 2.70727e6i −0.0175865 0.0220528i
\(498\) 1.00696e8 4.84924e7i 0.815309 0.392632i
\(499\) −2.21595e8 5.05777e7i −1.78344 0.407059i −0.801769 0.597634i \(-0.796107\pi\)
−0.981673 + 0.190576i \(0.938965\pi\)
\(500\) 6.09878e6 + 1.39201e6i 0.0487902 + 0.0111360i
\(501\) 2.14842e7 1.71331e7i 0.170847 0.136246i
\(502\) −2.03496e8 + 4.22563e8i −1.60859 + 3.34026i
\(503\) 1.00241e8 2.28794e7i 0.787667 0.179780i 0.190277 0.981730i \(-0.439061\pi\)
0.597390 + 0.801951i \(0.296204\pi\)
\(504\) −1.09800e8 5.28767e7i −0.857649 0.413022i
\(505\) 1.10914e6 + 884507.i 0.00861214 + 0.00686795i
\(506\) −5.89931e7 1.34648e7i −0.455354 0.103932i
\(507\) 2.27614e6 + 1.81516e6i 0.0174652 + 0.0139281i
\(508\) −7.55944e7 3.31201e8i −0.576632 2.52639i
\(509\) 1.33991e8 1.01607 0.508033 0.861337i \(-0.330373\pi\)
0.508033 + 0.861337i \(0.330373\pi\)
\(510\) 213256.i 0.00160765i
\(511\) 1.22223e7 + 5.35496e7i 0.0915992 + 0.401322i
\(512\) 1.63373e8 1.30286e8i 1.21722 0.970704i
\(513\) −2.73052e7 + 1.31495e7i −0.202252 + 0.0973996i
\(514\) −9.50786e7 4.57874e7i −0.700154 0.337176i
\(515\) 4082.76i 2.98904e-5i
\(516\) 4.28668e7 1.32147e8i 0.312013 0.961854i
\(517\) 4.21685e7 0.305152
\(518\) 4.04282e7 8.39500e7i 0.290867 0.603992i
\(519\) 1.91345e7 + 3.97333e7i 0.136872 + 0.284219i
\(520\) −2.58789e6 3.24511e6i −0.0184050 0.0230791i
\(521\) 1.47771e8 3.37279e7i 1.04491 0.238493i 0.334581 0.942367i \(-0.391405\pi\)
0.710325 + 0.703874i \(0.248548\pi\)
\(522\) 3.43709e8 2.41646
\(523\) 1.02568e8i 0.716980i 0.933534 + 0.358490i \(0.116708\pi\)
−0.933534 + 0.358490i \(0.883292\pi\)
\(524\) −2.55314e8 + 5.82738e7i −1.77452 + 0.405023i
\(525\) −1.12607e7 + 1.41204e7i −0.0778190 + 0.0975819i
\(526\) −1.03753e8 + 4.54570e8i −0.712922 + 3.12352i
\(527\) −1.73234e7 + 2.17229e7i −0.118359 + 0.148418i
\(528\) 1.50635e7 3.12797e7i 0.102335 0.212501i
\(529\) −3.13614e7 1.37403e8i −0.211850 0.928175i
\(530\) −1.69439e6 815973.i −0.0113811 0.00548085i
\(531\) −1.64287e7 2.06009e7i −0.109728 0.137595i
\(532\) 9.85197e6 4.31643e7i 0.0654317 0.286675i
\(533\) 3.83133e7 1.67862e8i 0.253028 1.10859i
\(534\) 7.25299e7 + 1.50610e8i 0.476314 + 0.989076i
\(535\) 1.62857e6 1.29874e6i 0.0106352 0.00848130i
\(536\) 2.11337e8 + 1.68535e8i 1.37240 + 1.09445i
\(537\) −7.12186e7 + 3.42971e7i −0.459908 + 0.221480i
\(538\) −2.96515e7 6.15719e7i −0.190414 0.395399i
\(539\) −1.50382e7 + 1.88574e7i −0.0960353 + 0.120424i
\(540\) −1.70412e6 2.13691e6i −0.0108223 0.0135708i
\(541\) −1.13048e6 + 544410.i −0.00713955 + 0.00343823i −0.437450 0.899243i \(-0.644118\pi\)
0.430311 + 0.902681i \(0.358404\pi\)
\(542\) −2.31336e8 5.28008e7i −1.45293 0.331622i
\(543\) −1.10266e8 2.51674e7i −0.688717 0.157195i
\(544\) 1.13872e8 9.08101e7i 0.707328 0.564076i
\(545\) 453331. 941352.i 0.00280044 0.00581517i
\(546\) 3.70074e7 8.44669e6i 0.227358 0.0518930i
\(547\) −5.58408e7 2.68915e7i −0.341185 0.164306i 0.255443 0.966824i \(-0.417779\pi\)
−0.596628 + 0.802518i \(0.703493\pi\)
\(548\) −3.12010e8 2.48819e8i −1.89595 1.51197i
\(549\) −2.44899e8 5.58966e7i −1.48003 0.337807i
\(550\) 4.34807e7 + 3.46747e7i 0.261341 + 0.208413i
\(551\) 1.75443e7 + 7.68665e7i 0.104877 + 0.459496i
\(552\) 2.89118e8 1.71893
\(553\) 2.60346e7i 0.153949i
\(554\) −2.95847e7 1.29619e8i −0.173995 0.762323i
\(555\) 477306. 380639.i 0.00279202 0.00222656i
\(556\) −1.29893e8 + 6.25530e7i −0.755719 + 0.363935i
\(557\) 1.23337e8 + 5.93960e7i 0.713720 + 0.343710i 0.755258 0.655427i \(-0.227511\pi\)
−0.0415379 + 0.999137i \(0.513226\pi\)
\(558\) 2.25490e8i 1.29785i
\(559\) −5.95858e7 1.58533e8i −0.341120 0.907580i
\(560\) 1.97870e6 0.0112672
\(561\) 1.20217e6 2.49632e6i 0.00680888 0.0141388i
\(562\) 3.64827e7 + 7.57572e7i 0.205531 + 0.426791i
\(563\) 4.69001e7 + 5.88108e7i 0.262814 + 0.329558i 0.895677 0.444706i \(-0.146692\pi\)
−0.632863 + 0.774264i \(0.718120\pi\)
\(564\) −3.11096e8 + 7.10056e7i −1.73403 + 0.395782i
\(565\) −2.30539e6 −0.0127820
\(566\) 4.01144e8i 2.21234i
\(567\) −3.58617e7 + 8.18521e6i −0.196735 + 0.0449035i
\(568\) 3.17647e7 3.98317e7i 0.173340 0.217362i
\(569\) 2.22747e6 9.75918e6i 0.0120914 0.0529757i −0.968522 0.248927i \(-0.919922\pi\)
0.980614 + 0.195951i \(0.0627793\pi\)
\(570\) 247530. 310392.i 0.00133660 0.00167605i
\(571\) 2.60687e7 5.41323e7i 0.140027 0.290769i −0.819148 0.573582i \(-0.805553\pi\)
0.959175 + 0.282813i \(0.0912676\pi\)
\(572\) −1.90048e7 8.32654e7i −0.101549 0.444914i
\(573\) 2.92240e6 + 1.40735e6i 0.0155337 + 0.00748066i
\(574\) 8.92413e7 + 1.11905e8i 0.471879 + 0.591717i
\(575\) −5.90993e7 + 2.58931e8i −0.310870 + 1.36201i
\(576\) 1.29460e8 5.67202e8i 0.677437 2.96805i
\(577\) 8.27096e7 + 1.71748e8i 0.430555 + 0.894056i 0.997525 + 0.0703177i \(0.0224013\pi\)
−0.566970 + 0.823739i \(0.691884\pi\)
\(578\) −2.73778e8 + 2.18330e8i −1.41780 + 1.13066i
\(579\) −6.43659e7 5.13301e7i −0.331604 0.264446i
\(580\) −6.40635e6 + 3.08513e6i −0.0328342 + 0.0158121i
\(581\) 3.59078e7 + 7.45634e7i 0.183088 + 0.380187i
\(582\) 1.41648e7 1.77621e7i 0.0718526 0.0901003i
\(583\) −1.52342e7 1.91031e7i −0.0768803 0.0964048i
\(584\) −7.28097e8 + 3.50633e8i −3.65553 + 1.76041i
\(585\) −1.50298e6 343046.i −0.00750735 0.00171350i
\(586\) 2.31813e8 + 5.29099e7i 1.15198 + 0.262932i
\(587\) −8.83194e7 + 7.04324e7i −0.436658 + 0.348223i −0.817015 0.576616i \(-0.804373\pi\)
0.380357 + 0.924840i \(0.375801\pi\)
\(588\) 7.91909e7 1.64442e8i 0.389532 0.808872i
\(589\) −5.04281e7 + 1.15099e7i −0.246790 + 0.0563281i
\(590\) 672149. + 323690.i 0.00327272 + 0.00157606i
\(591\) −9.68741e7 7.72545e7i −0.469294 0.374250i
\(592\) 7.66453e8 + 1.74938e8i 3.69420 + 0.843177i
\(593\) −2.25368e8 1.79725e8i −1.08076 0.861876i −0.0897882 0.995961i \(-0.528619\pi\)
−0.990970 + 0.134085i \(0.957190\pi\)
\(594\) −1.08145e7 4.73812e7i −0.0515995 0.226072i
\(595\) 157913. 0.000749664
\(596\) 6.67031e8i 3.15070i
\(597\) 1.75893e7 + 7.70639e7i 0.0826659 + 0.362183i
\(598\) 4.36421e8 3.48035e8i 2.04081 1.62749i
\(599\) 2.97054e8 1.43054e8i 1.38215 0.665608i 0.412692 0.910871i \(-0.364589\pi\)
0.969457 + 0.245263i \(0.0788743\pi\)
\(600\) −2.39409e8 1.15293e8i −1.10837 0.533765i
\(601\) 2.36278e8i 1.08843i −0.838946 0.544214i \(-0.816828\pi\)
0.838946 0.544214i \(-0.183172\pi\)
\(602\) 1.33920e8 + 4.34420e7i 0.613843 + 0.199122i
\(603\) 1.00399e8 0.457905
\(604\) −1.58198e8 + 3.28502e8i −0.717945 + 1.49083i
\(605\) 859523. + 1.78482e6i 0.00388143 + 0.00805986i
\(606\) −1.19014e8 1.49239e8i −0.534785 0.670599i
\(607\) −2.32483e8 + 5.30627e7i −1.03950 + 0.237259i −0.708012 0.706200i \(-0.750408\pi\)
−0.331488 + 0.943459i \(0.607551\pi\)
\(608\) 2.71144e8 1.20640
\(609\) 4.10595e7i 0.181786i
\(610\) 6.93377e6 1.58259e6i 0.0305478 0.00697234i
\(611\) −2.42539e8 + 3.04134e8i −1.06331 + 1.33334i
\(612\) 2.89194e7 1.26704e8i 0.126164 0.552760i
\(613\) 1.09104e8 1.36812e8i 0.473653 0.593942i −0.486408 0.873732i \(-0.661693\pi\)
0.960061 + 0.279790i \(0.0902647\pi\)
\(614\) 1.67542e8 3.47905e8i 0.723800 1.50299i
\(615\) 208680. + 914286.i 0.000897130 + 0.00393058i
\(616\) 4.03899e7 + 1.94507e7i 0.172795 + 0.0832135i
\(617\) 4.96337e6 + 6.22386e6i 0.0211310 + 0.0264975i 0.792285 0.610152i \(-0.208891\pi\)
−0.771154 + 0.636649i \(0.780320\pi\)
\(618\) 122242. 535577.i 0.000517911 0.00226912i
\(619\) −5.78770e7 + 2.53576e8i −0.244025 + 1.06914i 0.693290 + 0.720659i \(0.256161\pi\)
−0.937315 + 0.348484i \(0.886697\pi\)
\(620\) −2.02400e6 4.20287e6i −0.00849248 0.0176348i
\(621\) 1.81458e8 1.44708e8i 0.757705 0.604250i
\(622\) 4.99077e8 + 3.98001e8i 2.07394 + 1.65391i
\(623\) −1.11524e8 + 5.37072e7i −0.461216 + 0.222110i
\(624\) 1.38960e8 + 2.88554e8i 0.571923 + 1.18761i
\(625\) 1.52180e8 1.90828e8i 0.623331 0.781632i
\(626\) −2.52459e8 3.16574e8i −1.02913 1.29048i
\(627\) 4.64726e6 2.23800e6i 0.0188536 0.00907941i
\(628\) 1.18435e9 + 2.70319e8i 4.78189 + 1.09144i
\(629\) 6.11679e7 + 1.39612e7i 0.245794 + 0.0561009i
\(630\) 1.00197e6 799041.i 0.00400711 0.00319556i
\(631\) 1.18234e8 2.45516e8i 0.470603 0.977218i −0.521670 0.853147i \(-0.674691\pi\)
0.992273 0.124070i \(-0.0395949\pi\)
\(632\) −3.73439e8 + 8.52351e7i −1.47934 + 0.337650i
\(633\) −3.62233e7 1.74442e7i −0.142816 0.0687767i
\(634\) 7.48238e7 + 5.96700e7i 0.293611 + 0.234147i
\(635\) 2.19914e6 + 501939.i 0.00858878 + 0.00196033i
\(636\) 1.44557e8 + 1.15280e8i 0.561911 + 0.448109i
\(637\) −4.95112e7 2.16923e8i −0.191551 0.839241i
\(638\) −1.26434e8 −0.486856
\(639\) 1.89226e7i 0.0725235i
\(640\) 1.65976e6 + 7.27188e6i 0.00633148 + 0.0277400i
\(641\) −1.76524e8 + 1.40773e8i −0.670240 + 0.534498i −0.898429 0.439118i \(-0.855291\pi\)
0.228189 + 0.973617i \(0.426719\pi\)
\(642\) −2.52522e8 + 1.21608e8i −0.954322 + 0.459577i
\(643\) 2.04712e8 + 9.85839e7i 0.770033 + 0.370828i 0.777288 0.629145i \(-0.216595\pi\)
−0.00725462 + 0.999974i \(0.502309\pi\)
\(644\) 3.39061e8i 1.26946i
\(645\) 667053. + 637153.i 0.00248589 + 0.00237446i
\(646\) 4.08004e7 0.151345
\(647\) −8.74152e7 + 1.81520e8i −0.322756 + 0.670210i −0.997709 0.0676510i \(-0.978450\pi\)
0.674953 + 0.737861i \(0.264164\pi\)
\(648\) −2.34816e8 4.87601e8i −0.862985 1.79201i
\(649\) 6.04329e6 + 7.57805e6i 0.0221075 + 0.0277219i
\(650\) −5.00173e8 + 1.14161e8i −1.82129 + 0.415699i
\(651\) 2.69370e7 0.0976351
\(652\) 6.93790e7i 0.250314i
\(653\) 3.13024e8 7.14456e7i 1.12418 0.256588i 0.380278 0.924872i \(-0.375828\pi\)
0.743906 + 0.668284i \(0.232971\pi\)
\(654\) −8.76531e7 + 1.09914e8i −0.313353 + 0.392933i
\(655\) 386932. 1.69526e6i 0.00137693 0.00603271i
\(656\) −7.52954e8 + 9.44174e8i −2.66721 + 3.34457i
\(657\) −1.30232e8 + 2.70430e8i −0.459222 + 0.953584i
\(658\) −7.19583e7 3.15270e8i −0.252583 1.10664i
\(659\) 3.14354e8 + 1.51385e8i 1.09841 + 0.528964i 0.893157 0.449746i \(-0.148485\pi\)
0.205249 + 0.978710i \(0.434200\pi\)
\(660\) 290036. + 363694.i 0.00100884 + 0.00126504i
\(661\) 6.04597e7 2.64891e8i 0.209345 0.917199i −0.755660 0.654965i \(-0.772684\pi\)
0.965004 0.262234i \(-0.0844593\pi\)
\(662\) 5.91081e7 2.58970e8i 0.203739 0.892637i
\(663\) 1.10899e7 + 2.30285e7i 0.0380529 + 0.0790177i
\(664\) −9.51974e8 + 7.59174e8i −3.25178 + 2.59321i
\(665\) 229841. + 183292.i 0.000781559 + 0.000623272i
\(666\) 4.58757e8 2.20926e8i 1.55296 0.747866i
\(667\) −2.61977e8 5.44002e8i −0.882849 1.83325i
\(668\) −2.95621e8 + 3.70697e8i −0.991758 + 1.24363i
\(669\) 9.50405e6 + 1.19177e7i 0.0317417 + 0.0398029i
\(670\) −2.56106e6 + 1.23334e6i −0.00851521 + 0.00410071i
\(671\) 9.00862e7 + 2.05616e7i 0.298188 + 0.0680595i
\(672\) −1.37664e8 3.14210e7i −0.453642 0.103541i
\(673\) −4.14595e7 + 3.30628e7i −0.136012 + 0.108466i −0.689133 0.724635i \(-0.742008\pi\)
0.553120 + 0.833101i \(0.313437\pi\)
\(674\) 2.37463e8 4.93098e8i 0.775563 1.61047i
\(675\) −2.07964e8 + 4.74665e7i −0.676204 + 0.154339i
\(676\) −4.52578e7 2.17950e7i −0.146505 0.0705533i
\(677\) 2.34682e8 + 1.87153e8i 0.756335 + 0.603157i 0.923869 0.382710i \(-0.125009\pi\)
−0.167534 + 0.985866i \(0.553580\pi\)
\(678\) 3.02421e8 + 6.90257e7i 0.970339 + 0.221473i
\(679\) 1.31526e7 + 1.04888e7i 0.0420147 + 0.0335056i
\(680\) 516993. + 2.26509e6i 0.00164421 + 0.00720377i
\(681\) 9.89902e7 0.313437
\(682\) 8.29465e7i 0.261484i
\(683\) −1.08659e7 4.76065e7i −0.0341038 0.149419i 0.955009 0.296576i \(-0.0958448\pi\)
−0.989113 + 0.147157i \(0.952988\pi\)
\(684\) 1.89159e8 1.50849e8i 0.591097 0.471384i
\(685\) 2.38740e6 1.14971e6i 0.00742770 0.00357699i
\(686\) 3.54348e8 + 1.70645e8i 1.09763 + 0.528593i
\(687\) 5.46612e7i 0.168581i
\(688\) −1.05911e8 + 1.18315e9i −0.325218 + 3.63309i
\(689\) 2.25401e8 0.689125
\(690\) −1.31916e6 + 2.73926e6i −0.00401560 + 0.00833847i
\(691\) 1.60332e8 + 3.32933e8i 0.485944 + 1.00907i 0.989422 + 0.145065i \(0.0463392\pi\)
−0.503478 + 0.864008i \(0.667947\pi\)
\(692\) −4.74431e8 5.94917e8i −1.43171 1.79531i
\(693\) 1.62331e7 3.70510e6i 0.0487755 0.0111327i
\(694\) −7.96625e8 −2.38328
\(695\) 957273.i 0.00285155i
\(696\) 5.88955e8 1.34425e8i 1.74684 0.398706i
\(697\) −6.00905e7 + 7.53511e7i −0.177463 + 0.222531i
\(698\) 7.18253e7 3.14687e8i 0.211209 0.925365i
\(699\) −2.67502e6 + 3.35437e6i −0.00783241 + 0.00982154i
\(700\) 1.35209e8 2.80765e8i 0.394196 0.818556i
\(701\) 5.88728e7 + 2.57939e8i 0.170907 + 0.748794i 0.985627 + 0.168939i \(0.0540340\pi\)
−0.814719 + 0.579856i \(0.803109\pi\)
\(702\) 4.03932e8 + 1.94523e8i 1.16761 + 0.562290i
\(703\) 7.28242e7 + 9.13187e7i 0.209609 + 0.262841i
\(704\) −4.76220e7 + 2.08646e8i −0.136487 + 0.597987i
\(705\) 471470. 2.06565e6i 0.00134551 0.00589506i
\(706\) −4.46149e8 9.26439e8i −1.26785 2.63271i
\(707\) 1.10509e8 8.81277e7i 0.312707 0.249376i
\(708\) −5.73445e7 4.57307e7i −0.161582 0.128857i
\(709\) 3.66320e8 1.76411e8i 1.02783 0.494978i 0.157540 0.987513i \(-0.449644\pi\)
0.870293 + 0.492535i \(0.163929\pi\)
\(710\) 232454. + 482696.i 0.000649474 + 0.00134865i
\(711\) −8.87039e7 + 1.11231e8i −0.246794 + 0.309469i
\(712\) −1.13549e9 1.42386e9i −3.14590 3.94483i
\(713\) 3.56891e8 1.71870e8i 0.984617 0.474167i
\(714\) −2.07150e7 4.72807e6i −0.0569104 0.0129894i
\(715\) 552873. + 126190.i 0.00151254 + 0.000345228i
\(716\) 1.06634e9 8.50378e8i 2.90507 2.31672i
\(717\) 8.60639e7 1.78713e8i 0.233487 0.484841i
\(718\) −5.97077e8 + 1.36279e8i −1.61308 + 0.368176i
\(719\) −7.09078e7 3.41474e7i −0.190769 0.0918694i 0.336061 0.941840i \(-0.390905\pi\)
−0.526830 + 0.849971i \(0.676619\pi\)
\(720\) 8.45386e6 + 6.74173e6i 0.0226495 + 0.0180623i
\(721\) 396586. + 90518.2i 0.00105811 + 0.000241507i
\(722\) −5.07625e8 4.04818e8i −1.34875 1.07559i
\(723\) −2.53665e7 1.11138e8i −0.0671189 0.294067i
\(724\) 1.95149e9 5.14223
\(725\) 5.54939e8i 1.45623i
\(726\) −5.93131e7 2.59868e8i −0.155003 0.679114i
\(727\) −5.87787e8 + 4.68744e8i −1.52974 + 1.21992i −0.635693 + 0.771942i \(0.719286\pi\)
−0.894043 + 0.447982i \(0.852143\pi\)
\(728\) −3.72595e8 + 1.79432e8i −0.965701 + 0.465057i
\(729\) −9.08627e7 4.37572e7i −0.234532 0.112945i
\(730\) 8.49822e6i 0.0218454i
\(731\) −8.45234e6 + 9.44232e7i −0.0216384 + 0.241728i
\(732\) −6.99230e8 −1.78273
\(733\) 2.43406e8 5.05437e8i 0.618043 1.28338i −0.323417 0.946257i \(-0.604832\pi\)
0.941460 0.337124i \(-0.109454\pi\)
\(734\) −4.26659e8 8.85966e8i −1.07893 2.24042i
\(735\) 755601. + 947494.i 0.00190296 + 0.00238624i
\(736\) −2.02441e9 + 4.62059e8i −5.07768 + 1.15895i
\(737\) −3.69316e7 −0.0922563
\(738\) 7.82165e8i 1.94594i
\(739\) 1.08425e8 2.47472e7i 0.268655 0.0613187i −0.0860713 0.996289i \(-0.527431\pi\)
0.354726 + 0.934970i \(0.384574\pi\)
\(740\) −6.56768e6 + 8.23561e6i −0.0162075 + 0.0203236i
\(741\) −1.05882e7 + 4.63899e7i −0.0260236 + 0.114017i
\(742\) −1.16827e8 + 1.46496e8i −0.285977 + 0.358604i
\(743\) −1.35249e8 + 2.80848e8i −0.329737 + 0.684706i −0.998259 0.0589864i \(-0.981213\pi\)
0.668522 + 0.743693i \(0.266927\pi\)
\(744\) 8.81893e7 + 3.86382e8i 0.214140 + 0.938207i
\(745\) 3.99040e6 + 1.92168e6i 0.00965046 + 0.00464742i
\(746\) 1.05948e8 + 1.32854e8i 0.255197 + 0.320006i
\(747\) −1.00635e8 + 4.40910e8i −0.241428 + 1.05776i
\(748\) −1.06380e7 + 4.66082e7i −0.0254188 + 0.111367i
\(749\) −9.00490e7 1.86989e8i −0.214306 0.445010i
\(750\) 4.36959e6 3.48463e6i 0.0103575 0.00825986i
\(751\) 2.99306e8 + 2.38689e8i 0.706637 + 0.563524i 0.909510 0.415681i \(-0.136457\pi\)
−0.202874 + 0.979205i \(0.565028\pi\)
\(752\) 2.45823e9 1.18382e9i 5.78054 2.78376i
\(753\) 1.32843e8 + 2.75852e8i 0.311139 + 0.646087i
\(754\) 7.27204e8 9.11885e8i 1.69645 2.12729i
\(755\) −1.50945e6 1.89279e6i −0.00350734 0.00439807i
\(756\) −2.45354e8 + 1.18156e8i −0.567842 + 0.273458i
\(757\) −5.14900e7 1.17523e7i −0.118696 0.0270915i 0.162760 0.986666i \(-0.447960\pi\)
−0.281456 + 0.959574i \(0.590817\pi\)
\(758\) −1.19645e9 2.73081e8i −2.74717 0.627025i
\(759\) −3.08835e7 + 2.46287e7i −0.0706318 + 0.0563270i
\(760\) −1.87665e6 + 3.89690e6i −0.00427506 + 0.00887725i
\(761\) −4.03034e8 + 9.19898e7i −0.914508 + 0.208730i −0.653783 0.756683i \(-0.726819\pi\)
−0.260725 + 0.965413i \(0.583962\pi\)
\(762\) −2.73455e8 1.31689e8i −0.618046 0.297635i
\(763\) −8.13892e7 6.49057e7i −0.183229 0.146120i
\(764\) −5.45634e7 1.24537e7i −0.122355 0.0279267i
\(765\) 674672. + 538033.i 0.00150698 + 0.00120178i
\(766\) 1.07496e8 + 4.70972e8i 0.239170 + 1.04787i
\(767\) −8.94147e7 −0.198163
\(768\) 4.06707e8i 0.897838i
\(769\) −6.03006e7 2.64194e8i −0.132600 0.580957i −0.996948 0.0780643i \(-0.975126\pi\)
0.864349 0.502893i \(-0.167731\pi\)
\(770\) −368574. + 293928.i −0.000807332 + 0.000643826i
\(771\) −6.20679e7 + 2.98903e7i −0.135427 + 0.0652180i
\(772\) 1.27983e9 + 6.16332e8i 2.78163 + 1.33956i
\(773\) 1.91045e7i 0.0413616i −0.999786 0.0206808i \(-0.993417\pi\)
0.999786 0.0206808i \(-0.00658337\pi\)
\(774\) 4.24152e8 + 6.41889e8i 0.914742 + 1.38432i
\(775\) −3.64067e8 −0.782124
\(776\) −1.07391e8 + 2.22999e8i −0.229817 + 0.477220i
\(777\) −2.63918e7 5.48031e7i −0.0562607 0.116827i
\(778\) −8.67329e7 1.08760e8i −0.184181 0.230956i
\(779\) −1.74922e8 + 3.99248e7i −0.370026 + 0.0844560i
\(780\) −4.29129e6 −0.00904281
\(781\) 6.96069e6i 0.0146117i
\(782\) −3.04623e8 + 6.95283e7i −0.637005 + 0.145392i
\(783\) 3.02360e8 3.79148e8i 0.629854 0.789811i
\(784\) −3.47267e8 + 1.52148e9i −0.720635 + 3.15731i
\(785\) −5.02917e6 + 6.30639e6i −0.0103965 + 0.0130368i
\(786\) −1.01516e8 + 2.10799e8i −0.209057 + 0.434112i
\(787\) −3.95157e7 1.73129e8i −0.0810672 0.355178i 0.918083 0.396387i \(-0.129736\pi\)
−0.999151 + 0.0412088i \(0.986879\pi\)
\(788\) 1.92621e9 + 9.27613e8i 3.93663 + 1.89578i
\(789\) 1.89776e8 + 2.37972e8i 0.386377 + 0.484501i
\(790\) 896328. 3.92707e6i 0.00181797 0.00796503i
\(791\) −5.11124e7 + 2.23938e8i −0.103275 + 0.452479i
\(792\) 1.06291e8 + 2.20716e8i 0.213955 + 0.444282i
\(793\) −6.66443e8 + 5.31471e8i −1.33642 + 1.06576i
\(794\) −7.42733e8 5.92310e8i −1.48379 1.18328i
\(795\) −1.10611e6 + 532672.i −0.00220138 + 0.00106013i
\(796\) −5.91767e8 1.22882e9i −1.17331 2.43640i
\(797\) 7.13596e6 8.94821e6i 0.0140954 0.0176751i −0.774734 0.632288i \(-0.782116\pi\)
0.788829 + 0.614612i \(0.210688\pi\)
\(798\) −2.46626e7 3.09259e7i −0.0485322 0.0608574i
\(799\) 1.96182e8 9.44764e7i 0.384609 0.185218i
\(800\) 1.86060e9 + 4.24670e8i 3.63399 + 0.829434i
\(801\) −6.59467e8 1.50519e8i −1.28320 0.292883i
\(802\) 1.66299e8 1.32619e8i 0.322379 0.257088i
\(803\) 4.79060e7 9.94779e7i 0.0925217 0.192123i
\(804\) 2.72462e8 6.21876e7i 0.524249 0.119656i
\(805\) −2.02838e6 976816.i −0.00388832 0.00187251i
\(806\) 5.98240e8 + 4.77081e8i 1.14254 + 0.911143i
\(807\) −4.34940e7 9.92723e6i −0.0827578 0.0188889i
\(808\) 1.62590e9 + 1.29661e9i 3.08218 + 2.45796i
\(809\) −9.40819e7 4.12200e8i −0.177689 0.778506i −0.982694 0.185238i \(-0.940694\pi\)
0.805005 0.593268i \(-0.202163\pi\)
\(810\) 5.69120e6 0.0107090
\(811\) 4.64400e8i 0.870622i −0.900280 0.435311i \(-0.856638\pi\)
0.900280 0.435311i \(-0.143362\pi\)
\(812\) 1.57646e8 + 6.90692e8i 0.294452 + 1.29008i
\(813\) −1.21106e8 + 9.65792e7i −0.225370 + 0.179726i
\(814\) −1.68754e8 + 8.12676e7i −0.312882 + 0.150676i
\(815\) −415049. 199877.i −0.000766701 0.000369224i
\(816\) 1.79273e8i 0.329948i
\(817\) −1.21901e8 + 1.27621e8i −0.223532 + 0.234022i
\(818\) 5.51310e8 1.00725
\(819\) −6.66448e7 + 1.38389e8i −0.121315 + 0.251913i
\(820\) −7.02072e6 1.45787e7i −0.0127333 0.0264409i
\(821\) 2.63716e8 + 3.30690e8i 0.476549 + 0.597573i 0.960761 0.277377i \(-0.0894653\pi\)
−0.484212 + 0.874950i \(0.660894\pi\)
\(822\) −3.47604e8 + 7.93383e7i −0.625848 + 0.142846i
\(823\) −2.72196e8 −0.488296 −0.244148 0.969738i \(-0.578508\pi\)
−0.244148 + 0.969738i \(0.578508\pi\)
\(824\) 5.98496e6i 0.0106974i
\(825\) 3.53948e7 8.07864e6i 0.0630345 0.0143872i
\(826\) 4.63443e7 5.81139e7i 0.0822349 0.103119i
\(827\) −1.57854e8 + 6.91603e8i −0.279086 + 1.22276i 0.619865 + 0.784709i \(0.287188\pi\)
−0.898951 + 0.438049i \(0.855670\pi\)
\(828\) −1.15523e9 + 1.44862e9i −2.03507 + 2.55189i
\(829\) 3.81735e8 7.92680e8i 0.670036 1.39134i −0.237508 0.971386i \(-0.576331\pi\)
0.907544 0.419958i \(-0.137955\pi\)
\(830\) −2.84926e6 1.24834e7i −0.00498307 0.0218323i
\(831\) −7.81970e7 3.76577e7i −0.136266 0.0656221i
\(832\) −1.23092e9 1.54353e9i −2.13728 2.68006i
\(833\) −2.77141e7 + 1.21423e8i −0.0479475 + 0.210072i
\(834\) −2.86617e7 + 1.25575e8i −0.0494088 + 0.216474i
\(835\) −1.36597e6 2.83646e6i −0.00234629 0.00487211i
\(836\) −6.95823e7 + 5.54900e7i −0.119091 + 0.0949721i
\(837\) 2.48739e8 + 1.98363e8i 0.424197 + 0.338286i
\(838\) −1.70590e9 + 8.21519e8i −2.89882 + 1.39600i
\(839\) 1.34540e8 + 2.79376e8i 0.227807 + 0.473046i 0.983272 0.182143i \(-0.0583034\pi\)
−0.755465 + 0.655189i \(0.772589\pi\)
\(840\) 1.40439e6 1.76105e6i 0.00236946 0.00297121i
\(841\) −4.15733e8 5.21313e8i −0.698919 0.876416i
\(842\) −6.02497e8 + 2.90147e8i −1.00930 + 0.486051i
\(843\) 5.35144e7 + 1.22143e7i 0.0893281 + 0.0203885i
\(844\) 6.76317e8 + 1.54365e8i 1.12492 + 0.256756i
\(845\) 260770. 207957.i 0.000432203 0.000344671i
\(846\) 7.66735e8 1.59214e9i 1.26629 2.62949i
\(847\) 1.92428e8 4.39204e7i 0.316678 0.0722796i
\(848\) −1.42438e9 6.85945e8i −2.33581 1.12487i
\(849\) 2.04738e8 + 1.63273e8i 0.334561 + 0.266803i
\(850\) 2.79974e8 + 6.39023e7i 0.455891 + 0.104054i
\(851\) −6.99336e8 5.57702e8i −1.13474 0.904926i
\(852\) −1.17208e7 5.13522e7i −0.0189513 0.0830310i
\(853\) −9.82643e8 −1.58325 −0.791624 0.611009i \(-0.790764\pi\)
−0.791624 + 0.611009i \(0.790764\pi\)
\(854\) 7.08611e8i 1.13772i
\(855\) 357475. + 1.56620e6i 0.000571937 + 0.00250582i
\(856\) 2.38734e9 1.90384e9i 3.80622 3.03536i
\(857\) −5.10999e7 + 2.46084e7i −0.0811853 + 0.0390968i −0.474036 0.880506i \(-0.657203\pi\)
0.392850 + 0.919602i \(0.371489\pi\)
\(858\) −6.87478e7 3.31072e7i −0.108842 0.0524156i
\(859\) 4.05303e8i 0.639441i −0.947512 0.319721i \(-0.896411\pi\)
0.947512 0.319721i \(-0.103589\pi\)
\(860\) −1.36673e7 8.15690e6i −0.0214876 0.0128242i
\(861\) 9.34374e7 0.146390
\(862\) −1.63693e8 + 3.39912e8i −0.255569 + 0.530695i
\(863\) 2.58026e7 + 5.35797e7i 0.0401450 + 0.0833619i 0.920077 0.391738i \(-0.128126\pi\)
−0.879932 + 0.475100i \(0.842412\pi\)
\(864\) −1.03983e9 1.30390e9i −1.61220 2.02164i
\(865\) 4.92580e6 1.12428e6i 0.00761077 0.00173711i
\(866\) 9.60338e8 1.47867
\(867\) 2.28596e8i 0.350761i
\(868\) −4.53127e8 + 1.03423e8i −0.692885 + 0.158146i
\(869\) 3.26298e7 4.09164e7i 0.0497227 0.0623503i
\(870\) −1.41361e6 + 6.19342e6i −0.00214670 + 0.00940530i
\(871\) 2.12419e8 2.66364e8i 0.321468 0.403108i
\(872\) 6.64543e8 1.37994e9i 1.00224 2.08118i
\(873\) 2.04565e7 + 8.96256e7i 0.0307459 + 0.134707i
\(874\) −5.24078e8 2.52383e8i −0.784986 0.378029i
\(875\) 2.58031e6 + 3.23561e6i 0.00385166 + 0.00482983i
\(876\) −1.85918e8 + 8.14561e8i −0.276573 + 1.21175i
\(877\) −1.66682e8 + 7.30283e8i −0.247110 + 1.08266i 0.687275 + 0.726397i \(0.258807\pi\)
−0.934385 + 0.356264i \(0.884050\pi\)
\(878\) 1.03868e9 + 2.15684e9i 1.53461 + 3.18665i
\(879\) 1.21357e8 9.67786e7i 0.178689 0.142499i
\(880\) −3.10976e6 2.47995e6i −0.00456330 0.00363911i
\(881\) 4.10161e8 1.97523e8i 0.599827 0.288862i −0.109226 0.994017i \(-0.534837\pi\)
0.709053 + 0.705155i \(0.249123\pi\)
\(882\) 4.38557e8 + 9.10672e8i 0.639175 + 1.32726i
\(883\) 7.08707e8 8.88691e8i 1.02940 1.29083i 0.0734517 0.997299i \(-0.476599\pi\)
0.955950 0.293530i \(-0.0948300\pi\)
\(884\) −2.74969e8 3.44800e8i −0.398040 0.499126i
\(885\) 438783. 211307.i 0.000633023 0.000304848i
\(886\) −2.82153e8 6.43995e7i −0.405679 0.0925937i
\(887\) 1.61395e8 + 3.68373e7i 0.231270 + 0.0527858i 0.336585 0.941653i \(-0.390728\pi\)
−0.105315 + 0.994439i \(0.533585\pi\)
\(888\) 6.99688e8 5.57983e8i 0.999230 0.796860i
\(889\) 9.75135e7 2.02489e8i 0.138790 0.288201i
\(890\) 1.86714e7 4.26162e6i 0.0264854 0.00604511i
\(891\) 6.66196e7 + 3.20823e7i 0.0941822 + 0.0453558i
\(892\) −2.05632e8 1.63986e8i −0.289732 0.231054i
\(893\) 3.95201e8 + 9.02021e7i 0.554963 + 0.126667i
\(894\) −4.65925e8 3.71563e8i −0.652084 0.520019i
\(895\) 2.01518e6 + 8.82910e6i 0.00281090 + 0.0123154i
\(896\) 7.43166e8 1.03315
\(897\) 3.64399e8i 0.504894i
\(898\) 2.86970e8 + 1.25730e9i 0.396285 + 1.73624i
\(899\) 6.47102e8 5.16047e8i 0.890623 0.710248i
\(900\) 1.53428e9 7.38870e8i 2.10464 1.01354i
\(901\) −1.13675e8 5.47428e7i −0.155414 0.0748432i
\(902\) 2.87720e8i 0.392058i
\(903\) 7.66801e7 5.06692e7i 0.104140 0.0688146i
\(904\) −3.37949e9 −4.57453
\(905\) −5.62214e6 + 1.16745e7i −0.00758500 + 0.0157504i
\(906\) 1.41338e8 + 2.93491e8i 0.190053 + 0.394649i
\(907\) 3.32834e8 + 4.17361e8i 0.446073 + 0.559358i 0.953133 0.302553i \(-0.0978390\pi\)
−0.507059 + 0.861911i \(0.669268\pi\)
\(908\) −1.66519e9 + 3.80068e8i −2.22436 + 0.507697i
\(909\) 7.72405e8 1.02838
\(910\) 4.34886e6i 0.00577100i
\(911\) −7.45785e8 + 1.70221e8i −0.986412 + 0.225142i −0.685152 0.728400i \(-0.740264\pi\)
−0.301260 + 0.953542i \(0.597407\pi\)
\(912\) 2.08085e8 2.60930e8i 0.274319 0.343985i
\(913\) 3.70186e7 1.62189e8i 0.0486416 0.213113i
\(914\) 8.18249e6 1.02605e7i 0.0107164 0.0134379i
\(915\) 2.01444e6 4.18303e6i 0.00262961 0.00546044i
\(916\) −2.09869e8 9.19496e8i −0.273062 1.19636i
\(917\) −1.56093e8 7.51706e7i −0.202431 0.0974855i
\(918\) −1.56468e8 1.96205e8i −0.202254 0.253618i
\(919\) 2.40634e8 1.05429e9i 0.310034 1.35835i −0.544415 0.838816i \(-0.683248\pi\)
0.854450 0.519534i \(-0.173894\pi\)
\(920\) 7.37066e6 3.22930e7i 0.00946549 0.0414710i
\(921\) −1.09372e8 2.27114e8i −0.140000 0.290714i
\(922\) −8.92123e8 + 7.11444e8i −1.13823 + 0.907712i
\(923\) −5.02030e7 4.00356e7i −0.0638447 0.0509145i
\(924\) 4.17584e7 2.01098e7i 0.0529332 0.0254913i
\(925\) 3.56698e8 + 7.40691e8i 0.450687 + 0.935862i
\(926\) −1.77095e9 + 2.22070e9i −2.23035 + 2.79677i
\(927\) 1.38598e6 + 1.73796e6i 0.00173987 + 0.00218173i
\(928\) −3.90904e9 + 1.88249e9i −4.89132 + 2.35553i
\(929\) −7.84485e8 1.79053e8i −0.978447 0.223324i −0.296747 0.954956i \(-0.595902\pi\)
−0.681700 + 0.731632i \(0.738759\pi\)
\(930\) −4.06318e6 927394.i −0.00505146 0.00115296i
\(931\) −1.81275e8 + 1.44562e8i −0.224641 + 0.179146i
\(932\) 3.21196e7 6.66970e7i 0.0396755 0.0823870i
\(933\) 4.06267e8 9.27277e7i 0.500226 0.114173i
\(934\) 1.01645e9 + 4.89494e8i 1.24751 + 0.600768i
\(935\) −248178. 197916.i −0.000303619 0.000242128i
\(936\) −2.20324e9 5.02875e8i −2.68679 0.613243i
\(937\) −2.92177e8 2.33003e8i −0.355162 0.283232i 0.429613 0.903013i \(-0.358650\pi\)
−0.784775 + 0.619781i \(0.787222\pi\)
\(938\) 6.30220e7 + 2.76117e8i 0.0763631 + 0.334569i
\(939\) −2.64330e8 −0.319264
\(940\) 3.65580e7i 0.0440148i
\(941\) 2.58523e8 + 1.13266e9i 0.310264 + 1.35935i 0.854076 + 0.520147i \(0.174123\pi\)
−0.543813 + 0.839207i \(0.683020\pi\)
\(942\) 8.48548e8 6.76694e8i 1.01513 0.809543i
\(943\) 1.23796e9 5.96172e8i 1.47629 0.710946i
\(944\) 5.65039e8 + 2.72109e8i 0.671681 + 0.323464i
\(945\) 1.80819e6i 0.00214264i
\(946\) −1.56025e8 2.36119e8i −0.184298 0.278906i
\(947\) 1.23373e9 1.45269 0.726343 0.687333i \(-0.241219\pi\)
0.726343 + 0.687333i \(0.241219\pi\)
\(948\) −1.71827e8 + 3.56803e8i −0.201682 + 0.418797i
\(949\) 4.41931e8 + 9.17680e8i 0.517078 + 1.07372i
\(950\) 3.33327e8 + 4.17979e8i 0.388776 + 0.487510i
\(951\) 6.09093e7 1.39021e7i 0.0708177 0.0161637i
\(952\) 2.31486e8 0.268296
\(953\) 9.31315e8i 1.07601i −0.842940 0.538007i \(-0.819177\pi\)
0.842940 0.538007i \(-0.180823\pi\)
\(954\) −9.98270e8 + 2.27849e8i −1.14975 + 0.262423i
\(955\) 231697. 290538.i 0.000266017 0.000333575i
\(956\) −7.61583e8 + 3.33671e9i −0.871652 + 3.81896i
\(957\) −5.14607e7 + 6.45297e7i −0.0587138 + 0.0736247i
\(958\) 5.73308e8 1.19049e9i 0.652066 1.35403i
\(959\) −5.87487e7 2.57395e8i −0.0666105 0.291840i
\(960\) 9.68818e6 + 4.66558e6i 0.0109504 + 0.00527342i
\(961\) −2.14798e8 2.69348e8i −0.242025 0.303490i
\(962\) 3.84485e8 1.68454e9i 0.431871 1.89215i
\(963\) 2.52370e8 1.10571e9i 0.282592 1.23812i
\(964\) 8.53417e8 + 1.77214e9i 0.952643 + 1.97818i
\(965\) −7.37421e6 + 5.88074e6i −0.00820604 + 0.00654410i
\(966\) 2.36836e8 + 1.88871e8i 0.262734 + 0.209524i
\(967\) −1.35527e9 + 6.52665e8i −1.49881 + 0.721790i −0.990259 0.139241i \(-0.955534\pi\)
−0.508553 + 0.861031i \(0.669820\pi\)
\(968\) 1.25998e9 + 2.61638e9i 1.38912 + 2.88453i
\(969\) 1.66065e7 2.08239e7i 0.0182519 0.0228871i
\(970\) −1.62282e6 2.03496e6i −0.00177810 0.00222967i
\(971\) 9.55056e8 4.59931e8i 1.04321 0.502383i 0.167828 0.985816i \(-0.446325\pi\)
0.875381 + 0.483433i \(0.160610\pi\)
\(972\) −2.23040e9 5.09074e8i −2.42875 0.554347i
\(973\) −9.29864e7 2.12235e7i −0.100944 0.0230398i
\(974\) 1.38914e9 1.10781e9i 1.50339 1.19891i
\(975\) −1.45313e8 + 3.01746e8i −0.156780 + 0.325558i
\(976\) 5.82885e9 1.33040e9i 6.26951 1.43097i
\(977\) −1.51471e9 7.29447e8i −1.62423 0.782186i −1.00000 0.000941452i \(-0.999700\pi\)
−0.624226 0.781244i \(-0.714585\pi\)
\(978\) 4.84617e7 + 3.86469e7i 0.0518062 + 0.0413141i
\(979\) 2.42585e8 + 5.53685e7i 0.258533 + 0.0590086i
\(980\) −1.63484e7 1.30374e7i −0.0173699 0.0138520i
\(981\) −1.26586e8 5.54610e8i −0.134085 0.587464i
\(982\) 1.64443e9 1.73652
\(983\) 1.40125e9i 1.47521i 0.675233 + 0.737605i \(0.264043\pi\)
−0.675233 + 0.737605i \(0.735957\pi\)
\(984\) 3.05906e8 + 1.34026e9i 0.321072 + 1.40671i
\(985\) −1.10986e7 + 8.85083e6i −0.0116134 + 0.00926137i
\(986\) −5.88213e8 + 2.83268e8i −0.613626 + 0.295507i
\(987\) −1.90197e8 9.15942e7i −0.197812 0.0952613i
\(988\) 8.21013e8i 0.851293i
\(989\) 6.92652e8 1.16058e9i 0.716022 1.19973i
\(990\) −2.57616e6 −0.00265502
\(991\) 4.22956e8 8.78276e8i 0.434584 0.902423i −0.562550 0.826763i \(-0.690180\pi\)
0.997134 0.0756595i \(-0.0241062\pi\)
\(992\) −1.23501e9 2.56452e9i −1.26513 2.62706i
\(993\) −1.08116e8 1.35573e8i −0.110419 0.138461i
\(994\) 5.20412e7 1.18781e7i 0.0529893 0.0120945i
\(995\) 9.05604e6 0.00919325
\(996\) 1.25888e9i 1.27411i
\(997\) −1.82840e7 + 4.17320e6i −0.0184495 + 0.00421098i −0.231736 0.972779i \(-0.574440\pi\)
0.213286 + 0.976990i \(0.431583\pi\)
\(998\) 2.18461e9 2.73941e9i 2.19777 2.75591i
\(999\) 1.59863e8 7.00406e8i 0.160344 0.702512i
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.f.a.22.1 yes 126
43.2 odd 14 inner 43.7.f.a.2.1 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.7.f.a.2.1 126 43.2 odd 14 inner
43.7.f.a.22.1 yes 126 1.1 even 1 trivial