Properties

Label 43.6.c.a.6.16
Level $43$
Weight $6$
Character 43.6
Analytic conductor $6.897$
Analytic rank $0$
Dimension $34$
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] = [43,6,Mod(6,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.6");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.16
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.70119 q^{2} +(7.50728 - 13.0030i) q^{3} +62.1131 q^{4} +(-9.53861 + 16.5214i) q^{5} +(72.8296 - 126.145i) q^{6} +(-13.4501 - 23.2962i) q^{7} +292.133 q^{8} +(8.78143 + 15.2099i) q^{9} +O(q^{10})\) \(q+9.70119 q^{2} +(7.50728 - 13.0030i) q^{3} +62.1131 q^{4} +(-9.53861 + 16.5214i) q^{5} +(72.8296 - 126.145i) q^{6} +(-13.4501 - 23.2962i) q^{7} +292.133 q^{8} +(8.78143 + 15.2099i) q^{9} +(-92.5359 + 160.277i) q^{10} -218.352 q^{11} +(466.301 - 807.657i) q^{12} +(-136.773 - 236.897i) q^{13} +(-130.482 - 226.001i) q^{14} +(143.218 + 248.061i) q^{15} +846.420 q^{16} +(386.269 + 669.037i) q^{17} +(85.1903 + 147.554i) q^{18} +(-605.204 + 1048.24i) q^{19} +(-592.473 + 1026.19i) q^{20} -403.895 q^{21} -2118.27 q^{22} +(-422.115 + 731.124i) q^{23} +(2193.13 - 3798.61i) q^{24} +(1380.53 + 2391.15i) q^{25} +(-1326.86 - 2298.19i) q^{26} +3912.24 q^{27} +(-835.427 - 1447.00i) q^{28} +(-3608.91 - 6250.81i) q^{29} +(1389.39 + 2406.49i) q^{30} +(-100.481 + 174.038i) q^{31} -1136.98 q^{32} +(-1639.23 + 2839.23i) q^{33} +(3747.27 + 6490.45i) q^{34} +513.181 q^{35} +(545.442 + 944.733i) q^{36} +(1834.25 - 3177.02i) q^{37} +(-5871.20 + 10169.2i) q^{38} -4107.17 q^{39} +(-2786.54 + 4826.44i) q^{40} -14604.4 q^{41} -3918.26 q^{42} +(-11825.4 + 2677.49i) q^{43} -13562.5 q^{44} -335.050 q^{45} +(-4095.02 + 7092.78i) q^{46} +23450.9 q^{47} +(6354.31 - 11006.0i) q^{48} +(8041.69 - 13928.6i) q^{49} +(13392.8 + 23197.0i) q^{50} +11599.3 q^{51} +(-8495.39 - 14714.4i) q^{52} +(15577.4 - 26980.8i) q^{53} +37953.4 q^{54} +(2082.77 - 3607.47i) q^{55} +(-3929.22 - 6805.61i) q^{56} +(9086.87 + 15738.9i) q^{57} +(-35010.7 - 60640.3i) q^{58} +34542.5 q^{59} +(8895.72 + 15407.8i) q^{60} +(2226.37 + 3856.19i) q^{61} +(-974.787 + 1688.38i) q^{62} +(236.222 - 409.149i) q^{63} -38115.5 q^{64} +5218.49 q^{65} +(-15902.5 + 27543.9i) q^{66} +(18556.3 - 32140.4i) q^{67} +(23992.3 + 41556.0i) q^{68} +(6337.87 + 10977.5i) q^{69} +4978.46 q^{70} +(4558.20 + 7895.03i) q^{71} +(2565.35 + 4443.31i) q^{72} +(-15744.3 - 27270.0i) q^{73} +(17794.5 - 30820.9i) q^{74} +41456.1 q^{75} +(-37591.1 + 65109.7i) q^{76} +(2936.85 + 5086.78i) q^{77} -39844.4 q^{78} +(17569.3 + 30431.0i) q^{79} +(-8073.67 + 13984.0i) q^{80} +(27236.4 - 47174.8i) q^{81} -141680. q^{82} +(-16623.8 + 28793.3i) q^{83} -25087.2 q^{84} -14737.9 q^{85} +(-114720. + 25974.9i) q^{86} -108372. q^{87} -63787.8 q^{88} +(2143.02 - 3711.82i) q^{89} -3250.39 q^{90} +(-3679.22 + 6372.59i) q^{91} +(-26218.9 + 45412.4i) q^{92} +(1508.68 + 2613.11i) q^{93} +227501. q^{94} +(-11545.6 - 19997.6i) q^{95} +(-8535.62 + 14784.1i) q^{96} -4932.36 q^{97} +(78014.0 - 135124. i) q^{98} +(-1917.44 - 3321.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.70119 1.71494 0.857472 0.514530i \(-0.172034\pi\)
0.857472 + 0.514530i \(0.172034\pi\)
\(3\) 7.50728 13.0030i 0.481592 0.834142i −0.518184 0.855269i \(-0.673392\pi\)
0.999777 + 0.0211264i \(0.00672525\pi\)
\(4\) 62.1131 1.94104
\(5\) −9.53861 + 16.5214i −0.170632 + 0.295543i −0.938641 0.344896i \(-0.887914\pi\)
0.768009 + 0.640439i \(0.221248\pi\)
\(6\) 72.8296 126.145i 0.825904 1.43051i
\(7\) −13.4501 23.2962i −0.103748 0.179697i 0.809478 0.587150i \(-0.199750\pi\)
−0.913226 + 0.407453i \(0.866417\pi\)
\(8\) 292.133 1.61382
\(9\) 8.78143 + 15.2099i 0.0361376 + 0.0625921i
\(10\) −92.5359 + 160.277i −0.292624 + 0.506840i
\(11\) −218.352 −0.544096 −0.272048 0.962284i \(-0.587701\pi\)
−0.272048 + 0.962284i \(0.587701\pi\)
\(12\) 466.301 807.657i 0.934788 1.61910i
\(13\) −136.773 236.897i −0.224461 0.388778i 0.731696 0.681631i \(-0.238729\pi\)
−0.956158 + 0.292852i \(0.905396\pi\)
\(14\) −130.482 226.001i −0.177922 0.308170i
\(15\) 143.218 + 248.061i 0.164350 + 0.284662i
\(16\) 846.420 0.826582
\(17\) 386.269 + 669.037i 0.324166 + 0.561471i 0.981343 0.192264i \(-0.0615831\pi\)
−0.657177 + 0.753736i \(0.728250\pi\)
\(18\) 85.1903 + 147.554i 0.0619739 + 0.107342i
\(19\) −605.204 + 1048.24i −0.384607 + 0.666160i −0.991715 0.128460i \(-0.958996\pi\)
0.607107 + 0.794620i \(0.292330\pi\)
\(20\) −592.473 + 1026.19i −0.331202 + 0.573659i
\(21\) −403.895 −0.199857
\(22\) −2118.27 −0.933094
\(23\) −422.115 + 731.124i −0.166384 + 0.288185i −0.937146 0.348938i \(-0.886542\pi\)
0.770762 + 0.637123i \(0.219876\pi\)
\(24\) 2193.13 3798.61i 0.777205 1.34616i
\(25\) 1380.53 + 2391.15i 0.441770 + 0.765167i
\(26\) −1326.86 2298.19i −0.384939 0.666733i
\(27\) 3912.24 1.03280
\(28\) −835.427 1447.00i −0.201379 0.348798i
\(29\) −3608.91 6250.81i −0.796857 1.38020i −0.921653 0.388015i \(-0.873161\pi\)
0.124796 0.992182i \(-0.460172\pi\)
\(30\) 1389.39 + 2406.49i 0.281851 + 0.488180i
\(31\) −100.481 + 174.038i −0.0187793 + 0.0325268i −0.875262 0.483648i \(-0.839311\pi\)
0.856483 + 0.516175i \(0.172645\pi\)
\(32\) −1136.98 −0.196280
\(33\) −1639.23 + 2839.23i −0.262032 + 0.453853i
\(34\) 3747.27 + 6490.45i 0.555926 + 0.962892i
\(35\) 513.181 0.0708109
\(36\) 545.442 + 944.733i 0.0701443 + 0.121493i
\(37\) 1834.25 3177.02i 0.220270 0.381519i −0.734620 0.678479i \(-0.762640\pi\)
0.954890 + 0.296960i \(0.0959728\pi\)
\(38\) −5871.20 + 10169.2i −0.659580 + 1.14243i
\(39\) −4107.17 −0.432395
\(40\) −2786.54 + 4826.44i −0.275370 + 0.476954i
\(41\) −14604.4 −1.35683 −0.678414 0.734680i \(-0.737332\pi\)
−0.678414 + 0.734680i \(0.737332\pi\)
\(42\) −3918.26 −0.342744
\(43\) −11825.4 + 2677.49i −0.975312 + 0.220830i
\(44\) −13562.5 −1.05611
\(45\) −335.050 −0.0246649
\(46\) −4095.02 + 7092.78i −0.285339 + 0.494222i
\(47\) 23450.9 1.54851 0.774255 0.632873i \(-0.218125\pi\)
0.774255 + 0.632873i \(0.218125\pi\)
\(48\) 6354.31 11006.0i 0.398076 0.689487i
\(49\) 8041.69 13928.6i 0.478473 0.828739i
\(50\) 13392.8 + 23197.0i 0.757610 + 1.31222i
\(51\) 11599.3 0.624463
\(52\) −8495.39 14714.4i −0.435687 0.754632i
\(53\) 15577.4 26980.8i 0.761736 1.31937i −0.180219 0.983626i \(-0.557681\pi\)
0.941955 0.335739i \(-0.108986\pi\)
\(54\) 37953.4 1.77119
\(55\) 2082.77 3607.47i 0.0928400 0.160804i
\(56\) −3929.22 6805.61i −0.167431 0.289999i
\(57\) 9086.87 + 15738.9i 0.370448 + 0.641635i
\(58\) −35010.7 60640.3i −1.36657 2.36696i
\(59\) 34542.5 1.29189 0.645943 0.763386i \(-0.276464\pi\)
0.645943 + 0.763386i \(0.276464\pi\)
\(60\) 8895.72 + 15407.8i 0.319009 + 0.552540i
\(61\) 2226.37 + 3856.19i 0.0766078 + 0.132689i 0.901784 0.432186i \(-0.142258\pi\)
−0.825177 + 0.564875i \(0.808924\pi\)
\(62\) −974.787 + 1688.38i −0.0322055 + 0.0557816i
\(63\) 236.222 409.149i 0.00749841 0.0129876i
\(64\) −38115.5 −1.16319
\(65\) 5218.49 0.153201
\(66\) −15902.5 + 27543.9i −0.449371 + 0.778333i
\(67\) 18556.3 32140.4i 0.505014 0.874710i −0.494969 0.868911i \(-0.664821\pi\)
0.999983 0.00579951i \(-0.00184605\pi\)
\(68\) 23992.3 + 41556.0i 0.629217 + 1.08984i
\(69\) 6337.87 + 10977.5i 0.160258 + 0.277576i
\(70\) 4978.46 0.121437
\(71\) 4558.20 + 7895.03i 0.107312 + 0.185869i 0.914680 0.404178i \(-0.132442\pi\)
−0.807369 + 0.590047i \(0.799109\pi\)
\(72\) 2565.35 + 4443.31i 0.0583196 + 0.101013i
\(73\) −15744.3 27270.0i −0.345793 0.598932i 0.639704 0.768621i \(-0.279057\pi\)
−0.985498 + 0.169690i \(0.945724\pi\)
\(74\) 17794.5 30820.9i 0.377751 0.654284i
\(75\) 41456.1 0.851011
\(76\) −37591.1 + 65109.7i −0.746536 + 1.29304i
\(77\) 2936.85 + 5086.78i 0.0564489 + 0.0977724i
\(78\) −39844.4 −0.741534
\(79\) 17569.3 + 30431.0i 0.316729 + 0.548590i 0.979803 0.199963i \(-0.0640822\pi\)
−0.663075 + 0.748553i \(0.730749\pi\)
\(80\) −8073.67 + 13984.0i −0.141041 + 0.244291i
\(81\) 27236.4 47174.8i 0.461251 0.798909i
\(82\) −141680. −2.32688
\(83\) −16623.8 + 28793.3i −0.264872 + 0.458771i −0.967530 0.252756i \(-0.918663\pi\)
0.702658 + 0.711527i \(0.251996\pi\)
\(84\) −25087.2 −0.387930
\(85\) −14737.9 −0.221252
\(86\) −114720. + 25974.9i −1.67261 + 0.378710i
\(87\) −108372. −1.53504
\(88\) −63787.8 −0.878074
\(89\) 2143.02 3711.82i 0.0286781 0.0496720i −0.851330 0.524630i \(-0.824204\pi\)
0.880008 + 0.474958i \(0.157537\pi\)
\(90\) −3250.39 −0.0422989
\(91\) −3679.22 + 6372.59i −0.0465749 + 0.0806701i
\(92\) −26218.9 + 45412.4i −0.322957 + 0.559378i
\(93\) 1508.68 + 2613.11i 0.0180880 + 0.0313293i
\(94\) 227501. 2.65561
\(95\) −11545.6 19997.6i −0.131252 0.227336i
\(96\) −8535.62 + 14784.1i −0.0945272 + 0.163726i
\(97\) −4932.36 −0.0532262 −0.0266131 0.999646i \(-0.508472\pi\)
−0.0266131 + 0.999646i \(0.508472\pi\)
\(98\) 78014.0 135124.i 0.820554 1.42124i
\(99\) −1917.44 3321.11i −0.0196623 0.0340561i
\(100\) 85749.0 + 148522.i 0.857490 + 1.48522i
\(101\) 2725.57 + 4720.83i 0.0265861 + 0.0460484i 0.879012 0.476799i \(-0.158203\pi\)
−0.852426 + 0.522847i \(0.824870\pi\)
\(102\) 112527. 1.07092
\(103\) 76854.6 + 133116.i 0.713801 + 1.23634i 0.963420 + 0.267995i \(0.0863611\pi\)
−0.249620 + 0.968344i \(0.580306\pi\)
\(104\) −39955.9 69205.6i −0.362241 0.627419i
\(105\) 3852.59 6672.89i 0.0341020 0.0590664i
\(106\) 151119. 261746.i 1.30633 2.26264i
\(107\) −170219. −1.43730 −0.718652 0.695370i \(-0.755241\pi\)
−0.718652 + 0.695370i \(0.755241\pi\)
\(108\) 243001. 2.00470
\(109\) −18065.7 + 31290.7i −0.145642 + 0.252260i −0.929612 0.368539i \(-0.879858\pi\)
0.783970 + 0.620799i \(0.213192\pi\)
\(110\) 20205.4 34996.7i 0.159215 0.275769i
\(111\) −27540.5 47701.6i −0.212161 0.367473i
\(112\) −11384.4 19718.4i −0.0857563 0.148534i
\(113\) −12789.5 −0.0942235 −0.0471117 0.998890i \(-0.515002\pi\)
−0.0471117 + 0.998890i \(0.515002\pi\)
\(114\) 88153.5 + 152686.i 0.635298 + 1.10037i
\(115\) −8052.78 13947.8i −0.0567807 0.0983471i
\(116\) −224160. 388257.i −1.54673 2.67901i
\(117\) 2402.12 4160.60i 0.0162230 0.0280990i
\(118\) 335104. 2.21551
\(119\) 10390.7 17997.2i 0.0672632 0.116503i
\(120\) 41838.7 + 72466.8i 0.265232 + 0.459395i
\(121\) −113373. −0.703960
\(122\) 21598.4 + 37409.6i 0.131378 + 0.227554i
\(123\) −109640. + 189901.i −0.653438 + 1.13179i
\(124\) −6241.20 + 10810.1i −0.0364514 + 0.0631356i
\(125\) −112290. −0.642783
\(126\) 2291.64 3969.23i 0.0128594 0.0222731i
\(127\) −48266.3 −0.265543 −0.132771 0.991147i \(-0.542388\pi\)
−0.132771 + 0.991147i \(0.542388\pi\)
\(128\) −333382. −1.79853
\(129\) −53961.0 + 173866.i −0.285500 + 0.919899i
\(130\) 50625.6 0.262731
\(131\) −295377. −1.50383 −0.751915 0.659260i \(-0.770870\pi\)
−0.751915 + 0.659260i \(0.770870\pi\)
\(132\) −101818. + 176353.i −0.508614 + 0.880945i
\(133\) 32560.2 0.159609
\(134\) 180018. 311800.i 0.866071 1.50008i
\(135\) −37317.3 + 64635.5i −0.176228 + 0.305236i
\(136\) 112842. + 195448.i 0.523146 + 0.906116i
\(137\) 42056.8 0.191441 0.0957205 0.995408i \(-0.469485\pi\)
0.0957205 + 0.995408i \(0.469485\pi\)
\(138\) 61484.9 + 106495.i 0.274834 + 0.476027i
\(139\) −32118.9 + 55631.5i −0.141001 + 0.244221i −0.927874 0.372894i \(-0.878366\pi\)
0.786873 + 0.617115i \(0.211699\pi\)
\(140\) 31875.3 0.137446
\(141\) 176052. 304931.i 0.745751 1.29168i
\(142\) 44220.0 + 76591.2i 0.184034 + 0.318756i
\(143\) 29864.6 + 51727.0i 0.122128 + 0.211533i
\(144\) 7432.78 + 12873.9i 0.0298707 + 0.0517375i
\(145\) 137696. 0.543877
\(146\) −152739. 264551.i −0.593016 1.02713i
\(147\) −120742. 209132.i −0.460858 0.798229i
\(148\) 113931. 197335.i 0.427552 0.740541i
\(149\) 87550.4 151642.i 0.323067 0.559568i −0.658052 0.752972i \(-0.728619\pi\)
0.981119 + 0.193404i \(0.0619528\pi\)
\(150\) 402174. 1.45944
\(151\) 199671. 0.712642 0.356321 0.934364i \(-0.384031\pi\)
0.356321 + 0.934364i \(0.384031\pi\)
\(152\) −176800. + 306227.i −0.620688 + 1.07506i
\(153\) −6783.98 + 11750.2i −0.0234291 + 0.0405804i
\(154\) 28491.0 + 49347.8i 0.0968068 + 0.167674i
\(155\) −1916.90 3320.17i −0.00640871 0.0111002i
\(156\) −255109. −0.839295
\(157\) 300483. + 520452.i 0.972905 + 1.68512i 0.686681 + 0.726959i \(0.259067\pi\)
0.286224 + 0.958163i \(0.407600\pi\)
\(158\) 170443. + 295217.i 0.543172 + 0.940801i
\(159\) −233887. 405105.i −0.733692 1.27079i
\(160\) 10845.2 18784.4i 0.0334917 0.0580093i
\(161\) 22709.9 0.0690480
\(162\) 264225. 457652.i 0.791019 1.37009i
\(163\) 211370. + 366103.i 0.623123 + 1.07928i 0.988901 + 0.148579i \(0.0474698\pi\)
−0.365777 + 0.930702i \(0.619197\pi\)
\(164\) −907126. −2.63365
\(165\) −31271.9 54164.6i −0.0894221 0.154884i
\(166\) −161271. + 279329.i −0.454240 + 0.786767i
\(167\) −177087. + 306724.i −0.491355 + 0.851052i −0.999950 0.00995388i \(-0.996832\pi\)
0.508596 + 0.861006i \(0.330165\pi\)
\(168\) −117991. −0.322534
\(169\) 148233. 256747.i 0.399234 0.691494i
\(170\) −142975. −0.379435
\(171\) −21258.2 −0.0555951
\(172\) −734511. + 166307.i −1.89312 + 0.428638i
\(173\) 535409. 1.36010 0.680050 0.733166i \(-0.261958\pi\)
0.680050 + 0.733166i \(0.261958\pi\)
\(174\) −1.05134e6 −2.63251
\(175\) 37136.5 64322.3i 0.0916655 0.158769i
\(176\) −184817. −0.449740
\(177\) 259321. 449156.i 0.622163 1.07762i
\(178\) 20789.8 36009.1i 0.0491814 0.0851847i
\(179\) −237346. 411095.i −0.553667 0.958980i −0.998006 0.0631211i \(-0.979895\pi\)
0.444338 0.895859i \(-0.353439\pi\)
\(180\) −20811.0 −0.0478754
\(181\) 343639. + 595199.i 0.779660 + 1.35041i 0.932138 + 0.362104i \(0.117942\pi\)
−0.152477 + 0.988307i \(0.548725\pi\)
\(182\) −35692.8 + 61821.7i −0.0798733 + 0.138345i
\(183\) 66856.0 0.147575
\(184\) −123314. + 213586.i −0.268514 + 0.465080i
\(185\) 34992.5 + 60608.7i 0.0751701 + 0.130198i
\(186\) 14636.0 + 25350.3i 0.0310199 + 0.0537280i
\(187\) −84342.5 146085.i −0.176377 0.305494i
\(188\) 1.45661e6 3.00571
\(189\) −52620.0 91140.5i −0.107151 0.185591i
\(190\) −112006. 194000.i −0.225091 0.389869i
\(191\) −398997. + 691083.i −0.791382 + 1.37071i 0.133730 + 0.991018i \(0.457305\pi\)
−0.925112 + 0.379695i \(0.876029\pi\)
\(192\) −286144. + 495615.i −0.560185 + 0.970268i
\(193\) 408554. 0.789506 0.394753 0.918787i \(-0.370830\pi\)
0.394753 + 0.918787i \(0.370830\pi\)
\(194\) −47849.8 −0.0912800
\(195\) 39176.7 67856.0i 0.0737804 0.127791i
\(196\) 499494. 865150.i 0.928732 1.60861i
\(197\) −322760. 559036.i −0.592535 1.02630i −0.993890 0.110378i \(-0.964794\pi\)
0.401355 0.915923i \(-0.368539\pi\)
\(198\) −18601.5 32218.7i −0.0337197 0.0584043i
\(199\) 289218. 0.517717 0.258858 0.965915i \(-0.416654\pi\)
0.258858 + 0.965915i \(0.416654\pi\)
\(200\) 403299. + 698534.i 0.712938 + 1.23484i
\(201\) −278614. 482574.i −0.486422 0.842507i
\(202\) 26441.3 + 45797.6i 0.0455936 + 0.0789704i
\(203\) −97080.2 + 168148.i −0.165345 + 0.286386i
\(204\) 720469. 1.21210
\(205\) 139306. 241285.i 0.231518 0.401001i
\(206\) 745581. + 1.29138e6i 1.22413 + 2.12025i
\(207\) −14827.1 −0.0240508
\(208\) −115767. 200515.i −0.185536 0.321357i
\(209\) 132147. 228886.i 0.209263 0.362455i
\(210\) 37374.7 64734.9i 0.0584830 0.101296i
\(211\) −675422. −1.04441 −0.522203 0.852821i \(-0.674890\pi\)
−0.522203 + 0.852821i \(0.674890\pi\)
\(212\) 967559. 1.67586e6i 1.47856 2.56093i
\(213\) 136879. 0.206722
\(214\) −1.65133e6 −2.46490
\(215\) 68561.8 220911.i 0.101155 0.325927i
\(216\) 1.14289e6 1.66675
\(217\) 5405.92 0.00779329
\(218\) −175259. + 303557.i −0.249769 + 0.432612i
\(219\) −472788. −0.666126
\(220\) 129368. 224071.i 0.180206 0.312126i
\(221\) 105662. 183012.i 0.145525 0.252057i
\(222\) −267176. 462762.i −0.363844 0.630196i
\(223\) −4792.23 −0.00645320 −0.00322660 0.999995i \(-0.501027\pi\)
−0.00322660 + 0.999995i \(0.501027\pi\)
\(224\) 15292.5 + 26487.3i 0.0203637 + 0.0352710i
\(225\) −24246.0 + 41995.4i −0.0319290 + 0.0553026i
\(226\) −124074. −0.161588
\(227\) −146116. + 253080.i −0.188206 + 0.325982i −0.944652 0.328074i \(-0.893601\pi\)
0.756446 + 0.654056i \(0.226934\pi\)
\(228\) 564414. + 977594.i 0.719053 + 1.24544i
\(229\) −116174. 201219.i −0.146393 0.253560i 0.783499 0.621393i \(-0.213433\pi\)
−0.929892 + 0.367833i \(0.880100\pi\)
\(230\) −78121.5 135310.i −0.0973758 0.168660i
\(231\) 88191.2 0.108741
\(232\) −1.05428e6 1.82607e6i −1.28599 2.22739i
\(233\) 473517. + 820156.i 0.571408 + 0.989707i 0.996422 + 0.0845204i \(0.0269358\pi\)
−0.425014 + 0.905187i \(0.639731\pi\)
\(234\) 23303.4 40362.7i 0.0278215 0.0481882i
\(235\) −223689. + 387440.i −0.264225 + 0.457651i
\(236\) 2.14554e6 2.50760
\(237\) 527591. 0.610136
\(238\) 100802. 174594.i 0.115353 0.199797i
\(239\) 432126. 748465.i 0.489346 0.847572i −0.510579 0.859831i \(-0.670569\pi\)
0.999925 + 0.0122588i \(0.00390220\pi\)
\(240\) 121223. + 209964.i 0.135849 + 0.235297i
\(241\) 166478. + 288348.i 0.184635 + 0.319797i 0.943453 0.331505i \(-0.107556\pi\)
−0.758818 + 0.651302i \(0.774223\pi\)
\(242\) −1.09986e6 −1.20725
\(243\) 66394.4 + 114999.i 0.0721300 + 0.124933i
\(244\) 138287. + 239520.i 0.148698 + 0.257553i
\(245\) 153413. + 265719.i 0.163285 + 0.282818i
\(246\) −1.06363e6 + 1.84227e6i −1.12061 + 1.94095i
\(247\) 331102. 0.345318
\(248\) −29353.9 + 50842.4i −0.0303065 + 0.0524925i
\(249\) 249599. + 432319.i 0.255120 + 0.441882i
\(250\) −1.08934e6 −1.10234
\(251\) −614278. 1.06396e6i −0.615433 1.06596i −0.990308 0.138886i \(-0.955648\pi\)
0.374876 0.927075i \(-0.377685\pi\)
\(252\) 14672.5 25413.5i 0.0145547 0.0252094i
\(253\) 92169.6 159642.i 0.0905287 0.156800i
\(254\) −468240. −0.455391
\(255\) −110641. + 191636.i −0.106553 + 0.184556i
\(256\) −2.01451e6 −1.92119
\(257\) −1.76419e6 −1.66614 −0.833070 0.553168i \(-0.813419\pi\)
−0.833070 + 0.553168i \(0.813419\pi\)
\(258\) −523486. + 1.68671e6i −0.489616 + 1.57758i
\(259\) −98683.6 −0.0914104
\(260\) 324137. 0.297368
\(261\) 63382.7 109782.i 0.0575930 0.0997539i
\(262\) −2.86551e6 −2.57899
\(263\) −1.03465e6 + 1.79206e6i −0.922363 + 1.59758i −0.126616 + 0.991952i \(0.540412\pi\)
−0.795748 + 0.605628i \(0.792922\pi\)
\(264\) −478873. + 829433.i −0.422874 + 0.732439i
\(265\) 297173. + 514718.i 0.259953 + 0.450251i
\(266\) 315873. 0.273721
\(267\) −32176.5 55731.3i −0.0276223 0.0478433i
\(268\) 1.15259e6 1.99634e6i 0.980250 1.69784i
\(269\) −216488. −0.182412 −0.0912059 0.995832i \(-0.529072\pi\)
−0.0912059 + 0.995832i \(0.529072\pi\)
\(270\) −362022. + 627041.i −0.302222 + 0.523464i
\(271\) 1.03032e6 + 1.78457e6i 0.852216 + 1.47608i 0.879204 + 0.476446i \(0.158075\pi\)
−0.0269875 + 0.999636i \(0.508591\pi\)
\(272\) 326945. + 566286.i 0.267950 + 0.464102i
\(273\) 55241.8 + 95681.6i 0.0448602 + 0.0777002i
\(274\) 408001. 0.328311
\(275\) −301441. 522112.i −0.240365 0.416324i
\(276\) 393665. + 681848.i 0.311067 + 0.538784i
\(277\) 1.16701e6 2.02132e6i 0.913852 1.58284i 0.105280 0.994443i \(-0.466426\pi\)
0.808573 0.588396i \(-0.200240\pi\)
\(278\) −311591. + 539692.i −0.241809 + 0.418826i
\(279\) −3529.47 −0.00271456
\(280\) 149917. 0.114276
\(281\) 961404. 1.66520e6i 0.726340 1.25806i −0.232080 0.972697i \(-0.574553\pi\)
0.958420 0.285361i \(-0.0921135\pi\)
\(282\) 1.70792e6 2.95820e6i 1.27892 2.21516i
\(283\) 1397.26 + 2420.12i 0.00103708 + 0.00179627i 0.866543 0.499102i \(-0.166337\pi\)
−0.865506 + 0.500898i \(0.833003\pi\)
\(284\) 283124. + 490385.i 0.208296 + 0.360779i
\(285\) −346704. −0.252841
\(286\) 289722. + 501814.i 0.209443 + 0.362767i
\(287\) 196431. + 340228.i 0.140768 + 0.243818i
\(288\) −9984.29 17293.3i −0.00709310 0.0122856i
\(289\) 411522. 712777.i 0.289833 0.502006i
\(290\) 1.33581e6 0.932718
\(291\) −37028.6 + 64135.5i −0.0256333 + 0.0443982i
\(292\) −977929. 1.69382e6i −0.671197 1.16255i
\(293\) 333287. 0.226803 0.113402 0.993549i \(-0.463825\pi\)
0.113402 + 0.993549i \(0.463825\pi\)
\(294\) −1.17135e6 2.02883e6i −0.790345 1.36892i
\(295\) −329488. + 570689.i −0.220437 + 0.381808i
\(296\) 535847. 928113.i 0.355477 0.615704i
\(297\) −854245. −0.561942
\(298\) 849343. 1.47111e6i 0.554042 0.959629i
\(299\) 230935. 0.149387
\(300\) 2.57497e6 1.65184
\(301\) 221428. + 239474.i 0.140869 + 0.152350i
\(302\) 1.93704e6 1.22214
\(303\) 81846.5 0.0512146
\(304\) −512257. + 887255.i −0.317910 + 0.550636i
\(305\) −84945.9 −0.0522869
\(306\) −65812.7 + 113991.i −0.0401796 + 0.0695932i
\(307\) −523370. + 906504.i −0.316930 + 0.548939i −0.979846 0.199755i \(-0.935985\pi\)
0.662916 + 0.748694i \(0.269319\pi\)
\(308\) 182417. + 315956.i 0.109569 + 0.189780i
\(309\) 2.30788e6 1.37504
\(310\) −18596.2 32209.6i −0.0109906 0.0190362i
\(311\) 1.41589e6 2.45240e6i 0.830099 1.43777i −0.0678598 0.997695i \(-0.521617\pi\)
0.897959 0.440079i \(-0.145050\pi\)
\(312\) −1.19984e6 −0.697810
\(313\) 632268. 1.09512e6i 0.364788 0.631831i −0.623954 0.781461i \(-0.714475\pi\)
0.988742 + 0.149630i \(0.0478082\pi\)
\(314\) 2.91504e6 + 5.04900e6i 1.66848 + 2.88989i
\(315\) 4506.46 + 7805.42i 0.00255893 + 0.00443220i
\(316\) 1.09129e6 + 1.89016e6i 0.614781 + 1.06483i
\(317\) −3.22703e6 −1.80366 −0.901831 0.432089i \(-0.857776\pi\)
−0.901831 + 0.432089i \(0.857776\pi\)
\(318\) −2.26899e6 3.93000e6i −1.25824 2.17934i
\(319\) 788011. + 1.36488e6i 0.433567 + 0.750959i
\(320\) 363569. 629719.i 0.198478 0.343773i
\(321\) −1.27788e6 + 2.21336e6i −0.692195 + 1.19892i
\(322\) 220314. 0.118414
\(323\) −935085. −0.498706
\(324\) 1.69174e6 2.93017e6i 0.895304 1.55071i
\(325\) 377638. 654088.i 0.198320 0.343501i
\(326\) 2.05054e6 + 3.55164e6i 1.06862 + 1.85091i
\(327\) 271248. + 469816.i 0.140281 + 0.242973i
\(328\) −4.26644e6 −2.18968
\(329\) −315416. 546317.i −0.160655 0.278263i
\(330\) −303375. 525461.i −0.153354 0.265617i
\(331\) −749788. 1.29867e6i −0.376156 0.651522i 0.614343 0.789039i \(-0.289421\pi\)
−0.990499 + 0.137517i \(0.956088\pi\)
\(332\) −1.03256e6 + 1.78844e6i −0.514125 + 0.890491i
\(333\) 64429.5 0.0318401
\(334\) −1.71795e6 + 2.97558e6i −0.842646 + 1.45951i
\(335\) 354002. + 613149.i 0.172343 + 0.298507i
\(336\) −341865. −0.165198
\(337\) 438472. + 759456.i 0.210313 + 0.364274i 0.951813 0.306680i \(-0.0992182\pi\)
−0.741499 + 0.670954i \(0.765885\pi\)
\(338\) 1.43804e6 2.49075e6i 0.684665 1.18587i
\(339\) −96014.8 + 166302.i −0.0453773 + 0.0785958i
\(340\) −915414. −0.429458
\(341\) 21940.3 38001.6i 0.0102178 0.0176977i
\(342\) −206230. −0.0953425
\(343\) −884757. −0.406059
\(344\) −3.45458e6 + 782185.i −1.57398 + 0.356380i
\(345\) −241818. −0.109381
\(346\) 5.19411e6 2.33250
\(347\) 864304. 1.49702e6i 0.385339 0.667426i −0.606477 0.795101i \(-0.707418\pi\)
0.991816 + 0.127674i \(0.0407512\pi\)
\(348\) −6.73134e6 −2.97957
\(349\) −1.44102e6 + 2.49592e6i −0.633294 + 1.09690i 0.353579 + 0.935404i \(0.384964\pi\)
−0.986874 + 0.161493i \(0.948369\pi\)
\(350\) 360268. 624003.i 0.157201 0.272281i
\(351\) −535088. 926799.i −0.231823 0.401530i
\(352\) 248261. 0.106795
\(353\) −1.10269e6 1.90992e6i −0.470997 0.815792i 0.528452 0.848963i \(-0.322773\pi\)
−0.999450 + 0.0331715i \(0.989439\pi\)
\(354\) 2.51572e6 4.35735e6i 1.06697 1.84805i
\(355\) −173915. −0.0732432
\(356\) 133110. 230553.i 0.0556653 0.0964151i
\(357\) −156012. 270220.i −0.0647869 0.112214i
\(358\) −2.30254e6 3.98811e6i −0.949509 1.64460i
\(359\) 1.28587e6 + 2.22718e6i 0.526574 + 0.912053i 0.999521 + 0.0309619i \(0.00985707\pi\)
−0.472946 + 0.881091i \(0.656810\pi\)
\(360\) −97879.3 −0.0398047
\(361\) 505506. + 875562.i 0.204154 + 0.353606i
\(362\) 3.33370e6 + 5.77414e6i 1.33707 + 2.31588i
\(363\) −851126. + 1.47419e6i −0.339022 + 0.587203i
\(364\) −228528. + 395821.i −0.0904035 + 0.156583i
\(365\) 600715. 0.236013
\(366\) 648583. 0.253083
\(367\) 1.52376e6 2.63922e6i 0.590541 1.02285i −0.403619 0.914927i \(-0.632248\pi\)
0.994160 0.107920i \(-0.0344189\pi\)
\(368\) −357287. + 618838.i −0.137530 + 0.238209i
\(369\) −128248. 222131.i −0.0490324 0.0849267i
\(370\) 339469. + 587977.i 0.128913 + 0.223283i
\(371\) −838068. −0.316115
\(372\) 93708.9 + 162309.i 0.0351094 + 0.0608113i
\(373\) −1.02592e6 1.77695e6i −0.381805 0.661306i 0.609515 0.792774i \(-0.291364\pi\)
−0.991320 + 0.131469i \(0.958031\pi\)
\(374\) −818223. 1.41720e6i −0.302477 0.523906i
\(375\) −842990. + 1.46010e6i −0.309560 + 0.536173i
\(376\) 6.85078e6 2.49902
\(377\) −987200. + 1.70988e6i −0.357727 + 0.619602i
\(378\) −510476. 884171.i −0.183758 0.318278i
\(379\) 2.08546e6 0.745769 0.372884 0.927878i \(-0.378369\pi\)
0.372884 + 0.927878i \(0.378369\pi\)
\(380\) −717133. 1.24211e6i −0.254766 0.441267i
\(381\) −362349. + 627606.i −0.127883 + 0.221501i
\(382\) −3.87074e6 + 6.70433e6i −1.35718 + 2.35070i
\(383\) −1.53676e6 −0.535314 −0.267657 0.963514i \(-0.586249\pi\)
−0.267657 + 0.963514i \(0.586249\pi\)
\(384\) −2.50280e6 + 4.33497e6i −0.866158 + 1.50023i
\(385\) −112054. −0.0385279
\(386\) 3.96346e6 1.35396
\(387\) −144568. 156350.i −0.0490676 0.0530666i
\(388\) −306364. −0.103314
\(389\) −581673. −0.194897 −0.0974484 0.995241i \(-0.531068\pi\)
−0.0974484 + 0.995241i \(0.531068\pi\)
\(390\) 380060. 658284.i 0.126529 0.219155i
\(391\) −652199. −0.215744
\(392\) 2.34924e6 4.06901e6i 0.772170 1.33744i
\(393\) −2.21748e6 + 3.84079e6i −0.724233 + 1.25441i
\(394\) −3.13116e6 5.42332e6i −1.01616 1.76005i
\(395\) −670347. −0.216176
\(396\) −119098. 206284.i −0.0381652 0.0661041i
\(397\) 369051. 639215.i 0.117520 0.203550i −0.801265 0.598310i \(-0.795839\pi\)
0.918784 + 0.394760i \(0.129172\pi\)
\(398\) 2.80576e6 0.887856
\(399\) 244439. 423380.i 0.0768666 0.133137i
\(400\) 1.16851e6 + 2.02392e6i 0.365159 + 0.632474i
\(401\) −3.04184e6 5.26862e6i −0.944659 1.63620i −0.756433 0.654072i \(-0.773060\pi\)
−0.188226 0.982126i \(-0.560274\pi\)
\(402\) −2.70289e6 4.68154e6i −0.834187 1.44485i
\(403\) 54972.4 0.0168609
\(404\) 169294. + 293225.i 0.0516045 + 0.0893815i
\(405\) 519594. + 899964.i 0.157408 + 0.272639i
\(406\) −941794. + 1.63124e6i −0.283557 + 0.491136i
\(407\) −400513. + 693709.i −0.119848 + 0.207583i
\(408\) 3.38854e6 1.00777
\(409\) 4.27147e6 1.26261 0.631304 0.775535i \(-0.282520\pi\)
0.631304 + 0.775535i \(0.282520\pi\)
\(410\) 1.35143e6 2.34075e6i 0.397040 0.687694i
\(411\) 315732. 546864.i 0.0921965 0.159689i
\(412\) 4.77368e6 + 8.26826e6i 1.38551 + 2.39978i
\(413\) −464600. 804712.i −0.134031 0.232148i
\(414\) −143840. −0.0412458
\(415\) −317136. 549296.i −0.0903911 0.156562i
\(416\) 155508. + 269347.i 0.0440574 + 0.0763096i
\(417\) 482251. + 835283.i 0.135810 + 0.235230i
\(418\) 1.28199e6 2.22047e6i 0.358875 0.621589i
\(419\) −1.43550e6 −0.399456 −0.199728 0.979851i \(-0.564006\pi\)
−0.199728 + 0.979851i \(0.564006\pi\)
\(420\) 239297. 414474.i 0.0661932 0.114650i
\(421\) 2.74777e6 + 4.75929e6i 0.755572 + 1.30869i 0.945089 + 0.326812i \(0.105974\pi\)
−0.189517 + 0.981877i \(0.560692\pi\)
\(422\) −6.55240e6 −1.79110
\(423\) 205932. + 356685.i 0.0559594 + 0.0969245i
\(424\) 4.55067e6 7.88199e6i 1.22931 2.12922i
\(425\) −1.06651e6 + 1.84725e6i −0.286413 + 0.496082i
\(426\) 1.32789e6 0.354517
\(427\) 59889.8 103732.i 0.0158958 0.0275324i
\(428\) −1.05728e7 −2.78986
\(429\) 896808. 0.235264
\(430\) 665131. 2.14310e6i 0.173475 0.558947i
\(431\) −1.71842e6 −0.445591 −0.222795 0.974865i \(-0.571518\pi\)
−0.222795 + 0.974865i \(0.571518\pi\)
\(432\) 3.31140e6 0.853693
\(433\) −3.37501e6 + 5.84569e6i −0.865078 + 1.49836i 0.00189188 + 0.999998i \(0.499398\pi\)
−0.866970 + 0.498361i \(0.833936\pi\)
\(434\) 52443.9 0.0133651
\(435\) 1.03372e6 1.79046e6i 0.261927 0.453671i
\(436\) −1.12212e6 + 1.94356e6i −0.282697 + 0.489646i
\(437\) −510931. 884959.i −0.127985 0.221676i
\(438\) −4.58661e6 −1.14237
\(439\) 1.03603e6 + 1.79446e6i 0.256574 + 0.444399i 0.965322 0.261063i \(-0.0840730\pi\)
−0.708748 + 0.705462i \(0.750740\pi\)
\(440\) 608447. 1.05386e6i 0.149827 0.259509i
\(441\) 282470. 0.0691633
\(442\) 1.02505e6 1.77544e6i 0.249568 0.432264i
\(443\) 687784. + 1.19128e6i 0.166511 + 0.288406i 0.937191 0.348817i \(-0.113417\pi\)
−0.770680 + 0.637223i \(0.780083\pi\)
\(444\) −1.71063e6 2.96290e6i −0.411811 0.713278i
\(445\) 40882.8 + 70811.1i 0.00978681 + 0.0169512i
\(446\) −46490.3 −0.0110669
\(447\) −1.31453e6 2.27683e6i −0.311173 0.538968i
\(448\) 512657. + 887948.i 0.120679 + 0.209022i
\(449\) −534198. + 925258.i −0.125051 + 0.216594i −0.921753 0.387778i \(-0.873243\pi\)
0.796702 + 0.604372i \(0.206576\pi\)
\(450\) −235216. + 407405.i −0.0547564 + 0.0948408i
\(451\) 3.18890e6 0.738244
\(452\) −794399. −0.182891
\(453\) 1.49898e6 2.59631e6i 0.343203 0.594445i
\(454\) −1.41750e6 + 2.45518e6i −0.322763 + 0.559041i
\(455\) −70189.2 121571.i −0.0158943 0.0275298i
\(456\) 2.65458e6 + 4.59786e6i 0.597838 + 1.03548i
\(457\) −3.15223e6 −0.706036 −0.353018 0.935616i \(-0.614845\pi\)
−0.353018 + 0.935616i \(0.614845\pi\)
\(458\) −1.12702e6 1.95206e6i −0.251056 0.434841i
\(459\) 1.51117e6 + 2.61743e6i 0.334798 + 0.579887i
\(460\) −500183. 866343.i −0.110213 0.190895i
\(461\) 2.41406e6 4.18128e6i 0.529050 0.916341i −0.470377 0.882466i \(-0.655882\pi\)
0.999426 0.0338749i \(-0.0107848\pi\)
\(462\) 855559. 0.186486
\(463\) 2.68183e6 4.64507e6i 0.581406 1.00702i −0.413907 0.910319i \(-0.635836\pi\)
0.995313 0.0967054i \(-0.0308305\pi\)
\(464\) −3.05465e6 5.29081e6i −0.658668 1.14085i
\(465\) −57562.9 −0.0123455
\(466\) 4.59368e6 + 7.95649e6i 0.979933 + 1.69729i
\(467\) 2.84727e6 4.93162e6i 0.604138 1.04640i −0.388049 0.921639i \(-0.626851\pi\)
0.992187 0.124759i \(-0.0398159\pi\)
\(468\) 149203. 258428.i 0.0314893 0.0545412i
\(469\) −998334. −0.209577
\(470\) −2.17005e6 + 3.75863e6i −0.453132 + 0.784847i
\(471\) 9.02324e6 1.87417
\(472\) 1.00910e7 2.08488
\(473\) 2.58209e6 584636.i 0.530663 0.120152i
\(474\) 5.11826e6 1.04635
\(475\) −3.34201e6 −0.679631
\(476\) 645399. 1.11786e6i 0.130560 0.226137i
\(477\) 547166. 0.110109
\(478\) 4.19214e6 7.26100e6i 0.839201 1.45354i
\(479\) −1.04650e6 + 1.81259e6i −0.208401 + 0.360961i −0.951211 0.308541i \(-0.900159\pi\)
0.742810 + 0.669502i \(0.233493\pi\)
\(480\) −162836. 282040.i −0.0322587 0.0558737i
\(481\) −1.00350e6 −0.197768
\(482\) 1.61503e6 + 2.79732e6i 0.316639 + 0.548435i
\(483\) 170490. 295297.i 0.0332530 0.0575959i
\(484\) −7.04198e6 −1.36641
\(485\) 47047.9 81489.3i 0.00908208 0.0157306i
\(486\) 644105. + 1.11562e6i 0.123699 + 0.214253i
\(487\) −2.05270e6 3.55538e6i −0.392196 0.679304i 0.600543 0.799593i \(-0.294951\pi\)
−0.992739 + 0.120289i \(0.961618\pi\)
\(488\) 650397. + 1.12652e6i 0.123631 + 0.214136i
\(489\) 6.34725e6 1.20037
\(490\) 1.48829e6 + 2.57779e6i 0.280025 + 0.485018i
\(491\) 786609. + 1.36245e6i 0.147250 + 0.255044i 0.930210 0.367027i \(-0.119624\pi\)
−0.782960 + 0.622072i \(0.786291\pi\)
\(492\) −6.81005e6 + 1.17954e7i −1.26835 + 2.19684i
\(493\) 2.78801e6 4.82898e6i 0.516628 0.894825i
\(494\) 3.21208e6 0.592201
\(495\) 73158.9 0.0134200
\(496\) −85049.3 + 147310.i −0.0155227 + 0.0268861i
\(497\) 122616. 212378.i 0.0222668 0.0385672i
\(498\) 2.42141e6 + 4.19401e6i 0.437517 + 0.757802i
\(499\) −2.03361e6 3.52231e6i −0.365608 0.633252i 0.623266 0.782010i \(-0.285806\pi\)
−0.988874 + 0.148759i \(0.952472\pi\)
\(500\) −6.97466e6 −1.24766
\(501\) 2.65888e6 + 4.60532e6i 0.473266 + 0.819720i
\(502\) −5.95923e6 1.03217e7i −1.05543 1.82806i
\(503\) −2.51936e6 4.36365e6i −0.443986 0.769007i 0.553995 0.832520i \(-0.313103\pi\)
−0.997981 + 0.0635134i \(0.979769\pi\)
\(504\) 69008.3 119526.i 0.0121011 0.0209597i
\(505\) −103993. −0.0181457
\(506\) 894155. 1.54872e6i 0.155252 0.268904i
\(507\) −2.22565e6 3.85494e6i −0.384536 0.666036i
\(508\) −2.99797e6 −0.515428
\(509\) −1.04539e6 1.81068e6i −0.178849 0.309775i 0.762638 0.646826i \(-0.223904\pi\)
−0.941486 + 0.337051i \(0.890571\pi\)
\(510\) −1.07335e6 + 1.85910e6i −0.182733 + 0.316503i
\(511\) −423525. + 733567.i −0.0717508 + 0.124276i
\(512\) −8.87492e6 −1.49620
\(513\) −2.36770e6 + 4.10098e6i −0.397222 + 0.688009i
\(514\) −1.71147e7 −2.85734
\(515\) −2.93234e6 −0.487188
\(516\) −3.35169e6 + 1.07994e7i −0.554165 + 1.78556i
\(517\) −5.12054e6 −0.842538
\(518\) −957348. −0.156764
\(519\) 4.01947e6 6.96192e6i 0.655014 1.13452i
\(520\) 1.52449e6 0.247239
\(521\) −506310. + 876954.i −0.0817188 + 0.141541i −0.903988 0.427557i \(-0.859374\pi\)
0.822270 + 0.569098i \(0.192708\pi\)
\(522\) 614888. 1.06502e6i 0.0987687 0.171072i
\(523\) 1.31129e6 + 2.27122e6i 0.209626 + 0.363082i 0.951597 0.307350i \(-0.0994421\pi\)
−0.741971 + 0.670432i \(0.766109\pi\)
\(524\) −1.83468e7 −2.91899
\(525\) −557589. 965772.i −0.0882908 0.152924i
\(526\) −1.00373e7 + 1.73851e7i −1.58180 + 2.73976i
\(527\) −155251. −0.0243505
\(528\) −1.38748e6 + 2.40318e6i −0.216591 + 0.375147i
\(529\) 2.86181e6 + 4.95680e6i 0.444633 + 0.770127i
\(530\) 2.88293e6 + 4.99338e6i 0.445805 + 0.772156i
\(531\) 303333. + 525388.i 0.0466856 + 0.0808619i
\(532\) 2.02242e6 0.309807
\(533\) 1.99749e6 + 3.45975e6i 0.304555 + 0.527505i
\(534\) −312150. 540660.i −0.0473708 0.0820486i
\(535\) 1.62365e6 2.81225e6i 0.245250 0.424785i
\(536\) 5.42090e6 9.38927e6i 0.815003 1.41163i
\(537\) −7.12729e6 −1.06657
\(538\) −2.10019e6 −0.312826
\(539\) −1.75592e6 + 3.04134e6i −0.260335 + 0.450913i
\(540\) −2.31789e6 + 4.01471e6i −0.342065 + 0.592475i
\(541\) −3.00801e6 5.21003e6i −0.441862 0.765328i 0.555966 0.831205i \(-0.312349\pi\)
−0.997828 + 0.0658777i \(0.979015\pi\)
\(542\) 9.99535e6 + 1.73125e7i 1.46150 + 2.53140i
\(543\) 1.03192e7 1.50191
\(544\) −439179. 760680.i −0.0636274 0.110206i
\(545\) −344643. 596939.i −0.0497024 0.0860872i
\(546\) 535911. + 928226.i 0.0769328 + 0.133251i
\(547\) −28069.5 + 48617.8i −0.00401113 + 0.00694747i −0.868024 0.496522i \(-0.834610\pi\)
0.864013 + 0.503470i \(0.167943\pi\)
\(548\) 2.61228e6 0.371594
\(549\) −39101.4 + 67725.6i −0.00553684 + 0.00959008i
\(550\) −2.92434e6 5.06511e6i −0.412213 0.713973i
\(551\) 8.73649e6 1.22591
\(552\) 1.85150e6 + 3.20690e6i 0.258629 + 0.447958i
\(553\) 472618. 818598.i 0.0657200 0.113830i
\(554\) 1.13214e7 1.96093e7i 1.56721 2.71448i
\(555\) 1.05079e6 0.144805
\(556\) −1.99500e6 + 3.45545e6i −0.273688 + 0.474042i
\(557\) 3.39535e6 0.463710 0.231855 0.972750i \(-0.425520\pi\)
0.231855 + 0.972750i \(0.425520\pi\)
\(558\) −34240.1 −0.00465532
\(559\) 2.25168e6 + 2.43519e6i 0.304774 + 0.329613i
\(560\) 434366. 0.0585310
\(561\) −2.53273e6 −0.339768
\(562\) 9.32676e6 1.61544e7i 1.24563 2.15750i
\(563\) 1.14249e7 1.51908 0.759542 0.650458i \(-0.225423\pi\)
0.759542 + 0.650458i \(0.225423\pi\)
\(564\) 1.09352e7 1.89402e7i 1.44753 2.50719i
\(565\) 121994. 211301.i 0.0160775 0.0278471i
\(566\) 13555.1 + 23478.1i 0.00177853 + 0.00308050i
\(567\) −1.46533e6 −0.191416
\(568\) 1.33160e6 + 2.30640e6i 0.173182 + 0.299960i
\(569\) −6.93642e6 + 1.20142e7i −0.898162 + 1.55566i −0.0683210 + 0.997663i \(0.521764\pi\)
−0.829841 + 0.557999i \(0.811569\pi\)
\(570\) −3.36345e6 −0.433608
\(571\) 3.46572e6 6.00280e6i 0.444839 0.770484i −0.553202 0.833047i \(-0.686594\pi\)
0.998041 + 0.0625632i \(0.0199275\pi\)
\(572\) 1.85498e6 + 3.21293e6i 0.237056 + 0.410592i
\(573\) 5.99076e6 + 1.03763e7i 0.762247 + 1.32025i
\(574\) 1.90561e6 + 3.30062e6i 0.241410 + 0.418134i
\(575\) −2.33097e6 −0.294013
\(576\) −334708. 579732.i −0.0420349 0.0728066i
\(577\) −6.03914e6 1.04601e7i −0.755154 1.30797i −0.945298 0.326209i \(-0.894229\pi\)
0.190144 0.981756i \(-0.439105\pi\)
\(578\) 3.99225e6 6.91478e6i 0.497048 0.860912i
\(579\) 3.06713e6 5.31242e6i 0.380220 0.658561i
\(580\) 8.55271e6 1.05568
\(581\) 894368. 0.109920
\(582\) −359222. + 622190.i −0.0439598 + 0.0761405i
\(583\) −3.40135e6 + 5.89131e6i −0.414457 + 0.717861i
\(584\) −4.59944e6 7.96646e6i −0.558049 0.966570i
\(585\) 45825.8 + 79372.6i 0.00553631 + 0.00958917i
\(586\) 3.23328e6 0.388955
\(587\) 6.81822e6 + 1.18095e7i 0.816725 + 1.41461i 0.908082 + 0.418791i \(0.137546\pi\)
−0.0913572 + 0.995818i \(0.529121\pi\)
\(588\) −7.49969e6 1.29898e7i −0.894541 1.54939i
\(589\) −121623. 210657.i −0.0144453 0.0250201i
\(590\) −3.19642e6 + 5.53637e6i −0.378037 + 0.654779i
\(591\) −9.69220e6 −1.14144
\(592\) 1.55255e6 2.68910e6i 0.182071 0.315357i
\(593\) −3.42044e6 5.92438e6i −0.399435 0.691841i 0.594222 0.804301i \(-0.297460\pi\)
−0.993656 + 0.112460i \(0.964127\pi\)
\(594\) −8.28719e6 −0.963699
\(595\) 198226. + 343337.i 0.0229545 + 0.0397583i
\(596\) 5.43803e6 9.41894e6i 0.627084 1.08614i
\(597\) 2.17124e6 3.76070e6i 0.249328 0.431850i
\(598\) 2.24035e6 0.256190
\(599\) −3.74140e6 + 6.48029e6i −0.426056 + 0.737951i −0.996518 0.0833728i \(-0.973431\pi\)
0.570462 + 0.821324i \(0.306764\pi\)
\(600\) 1.21107e7 1.37338
\(601\) −1.61098e7 −1.81930 −0.909652 0.415372i \(-0.863651\pi\)
−0.909652 + 0.415372i \(0.863651\pi\)
\(602\) 2.14812e6 + 2.32319e6i 0.241583 + 0.261272i
\(603\) 651802. 0.0729999
\(604\) 1.24022e7 1.38326
\(605\) 1.08142e6 1.87308e6i 0.120118 0.208050i
\(606\) 794008. 0.0878301
\(607\) −5.39955e6 + 9.35230e6i −0.594821 + 1.03026i 0.398752 + 0.917059i \(0.369444\pi\)
−0.993572 + 0.113200i \(0.963890\pi\)
\(608\) 688103. 1.19183e6i 0.0754909 0.130754i
\(609\) 1.45762e6 + 2.52467e6i 0.159258 + 0.275842i
\(610\) −824076. −0.0896691
\(611\) −3.20744e6 5.55545e6i −0.347581 0.602028i
\(612\) −421374. + 729841.i −0.0454767 + 0.0787680i
\(613\) −4.53519e6 −0.487466 −0.243733 0.969842i \(-0.578372\pi\)
−0.243733 + 0.969842i \(0.578372\pi\)
\(614\) −5.07732e6 + 8.79417e6i −0.543517 + 0.941399i
\(615\) −2.09162e6 3.62279e6i −0.222995 0.386238i
\(616\) 857953. + 1.48602e6i 0.0910986 + 0.157787i
\(617\) −501748. 869053.i −0.0530607 0.0919038i 0.838275 0.545248i \(-0.183564\pi\)
−0.891336 + 0.453344i \(0.850231\pi\)
\(618\) 2.23892e7 2.35812
\(619\) 5.73770e6 + 9.93798e6i 0.601881 + 1.04249i 0.992536 + 0.121952i \(0.0389153\pi\)
−0.390655 + 0.920537i \(0.627751\pi\)
\(620\) −119065. 206226.i −0.0124395 0.0215459i
\(621\) −1.65141e6 + 2.86033e6i −0.171841 + 0.297637i
\(622\) 1.37359e7 2.37912e7i 1.42357 2.46570i
\(623\) −115295. −0.0119012
\(624\) −3.47639e6 −0.357410
\(625\) −3.24307e6 + 5.61716e6i −0.332090 + 0.575197i
\(626\) 6.13375e6 1.06240e7i 0.625591 1.08356i
\(627\) −1.98414e6 3.43662e6i −0.201559 0.349111i
\(628\) 1.86639e7 + 3.23269e7i 1.88844 + 3.27088i
\(629\) 2.83406e6 0.285616
\(630\) 43718.0 + 75721.8i 0.00438843 + 0.00760098i
\(631\) −5.97711e6 1.03526e7i −0.597610 1.03509i −0.993173 0.116651i \(-0.962784\pi\)
0.395563 0.918439i \(-0.370549\pi\)
\(632\) 5.13258e6 + 8.88989e6i 0.511144 + 0.885327i
\(633\) −5.07058e6 + 8.78251e6i −0.502978 + 0.871183i
\(634\) −3.13061e7 −3.09318
\(635\) 460393. 797424.i 0.0453100 0.0784793i
\(636\) −1.45275e7 2.51623e7i −1.42412 2.46665i
\(637\) −4.39954e6 −0.429594
\(638\) 7.64465e6 + 1.32409e7i 0.743543 + 1.28785i
\(639\) −80055.0 + 138659.i −0.00775597 + 0.0134337i
\(640\) 3.18000e6 5.50793e6i 0.306886 0.531543i
\(641\) −7.44664e6 −0.715839 −0.357919 0.933753i \(-0.616514\pi\)
−0.357919 + 0.933753i \(0.616514\pi\)
\(642\) −1.23970e7 + 2.14722e7i −1.18708 + 2.05608i
\(643\) −1.01638e7 −0.969460 −0.484730 0.874664i \(-0.661082\pi\)
−0.484730 + 0.874664i \(0.661082\pi\)
\(644\) 1.41059e6 0.134025
\(645\) −2.35779e6 2.54995e6i −0.223154 0.241341i
\(646\) −9.07144e6 −0.855253
\(647\) −9.18915e6 −0.863008 −0.431504 0.902111i \(-0.642017\pi\)
−0.431504 + 0.902111i \(0.642017\pi\)
\(648\) 7.95665e6 1.37813e7i 0.744377 1.28930i
\(649\) −7.54243e6 −0.702910
\(650\) 3.66354e6 6.34543e6i 0.340108 0.589085i
\(651\) 40583.8 70293.2i 0.00375319 0.00650071i
\(652\) 1.31288e7 + 2.27398e7i 1.20950 + 2.09492i
\(653\) −1.14604e7 −1.05176 −0.525879 0.850559i \(-0.676264\pi\)
−0.525879 + 0.850559i \(0.676264\pi\)
\(654\) 2.63143e6 + 4.55777e6i 0.240573 + 0.416685i
\(655\) 2.81749e6 4.88003e6i 0.256601 0.444447i
\(656\) −1.23615e7 −1.12153
\(657\) 276515. 478938.i 0.0249923 0.0432879i
\(658\) −3.05992e6 5.29993e6i −0.275515 0.477205i
\(659\) 7.75611e6 + 1.34340e7i 0.695714 + 1.20501i 0.969939 + 0.243346i \(0.0782451\pi\)
−0.274226 + 0.961665i \(0.588422\pi\)
\(660\) −1.94240e6 3.36433e6i −0.173571 0.300635i
\(661\) 1.90205e7 1.69324 0.846619 0.532200i \(-0.178635\pi\)
0.846619 + 0.532200i \(0.178635\pi\)
\(662\) −7.27384e6 1.25987e7i −0.645087 1.11732i
\(663\) −1.58647e6 2.74785e6i −0.140168 0.242778i
\(664\) −4.85637e6 + 8.41148e6i −0.427456 + 0.740376i
\(665\) −310579. + 537938.i −0.0272344 + 0.0471714i
\(666\) 625043. 0.0546040
\(667\) 6.09349e6 0.530337
\(668\) −1.09994e7 + 1.90516e7i −0.953737 + 1.65192i
\(669\) −35976.6 + 62313.3i −0.00310781 + 0.00538289i
\(670\) 3.43424e6 + 5.94828e6i 0.295559 + 0.511922i
\(671\) −486132. 842006.i −0.0416820 0.0721953i
\(672\) 459219. 0.0392281
\(673\) 407802. + 706334.i 0.0347066 + 0.0601136i 0.882857 0.469642i \(-0.155617\pi\)
−0.848150 + 0.529756i \(0.822284\pi\)
\(674\) 4.25370e6 + 7.36763e6i 0.360676 + 0.624709i
\(675\) 5.40096e6 + 9.35474e6i 0.456259 + 0.790264i
\(676\) 9.20721e6 1.59474e7i 0.774928 1.34221i
\(677\) −1.04057e7 −0.872567 −0.436284 0.899809i \(-0.643706\pi\)
−0.436284 + 0.899809i \(0.643706\pi\)
\(678\) −931458. + 1.61333e6i −0.0778196 + 0.134787i
\(679\) 66340.7 + 114906.i 0.00552212 + 0.00956459i
\(680\) −4.30542e6 −0.357061
\(681\) 2.19387e6 + 3.79989e6i 0.181277 + 0.313981i
\(682\) 212847. 368661.i 0.0175229 0.0303505i
\(683\) 6.68197e6 1.15735e7i 0.548091 0.949322i −0.450314 0.892870i \(-0.648688\pi\)
0.998405 0.0564516i \(-0.0179787\pi\)
\(684\) −1.32041e6 −0.107912
\(685\) −401163. + 694835.i −0.0326659 + 0.0565790i
\(686\) −8.58320e6 −0.696368
\(687\) −3.48860e6 −0.282007
\(688\) −1.00092e7 + 2.26628e6i −0.806176 + 0.182534i
\(689\) −8.52224e6 −0.683921
\(690\) −2.34592e6 −0.187582
\(691\) −7.97022e6 + 1.38048e7i −0.635002 + 1.09986i 0.351512 + 0.936183i \(0.385668\pi\)
−0.986515 + 0.163673i \(0.947666\pi\)
\(692\) 3.32559e7 2.64000
\(693\) −51579.5 + 89338.4i −0.00407985 + 0.00706651i
\(694\) 8.38478e6 1.45229e7i 0.660835 1.14460i
\(695\) −612738. 1.06129e6i −0.0481186 0.0833439i
\(696\) −3.16591e7 −2.47729
\(697\) −5.64123e6 9.77089e6i −0.439837 0.761820i
\(698\) −1.39796e7 + 2.42134e7i −1.08606 + 1.88112i
\(699\) 1.42193e7 1.10074
\(700\) 2.30667e6 3.99526e6i 0.177926 0.308177i
\(701\) −5.52424e6 9.56827e6i −0.424598 0.735425i 0.571785 0.820404i \(-0.306251\pi\)
−0.996383 + 0.0849785i \(0.972918\pi\)
\(702\) −5.19099e6 8.99106e6i −0.397564 0.688602i
\(703\) 2.22020e6 + 3.84549e6i 0.169435 + 0.293470i
\(704\) 8.32259e6 0.632888
\(705\) 3.35859e6 + 5.81724e6i 0.254498 + 0.440803i
\(706\) −1.06975e7 1.85285e7i −0.807735 1.39904i
\(707\) 73318.3 126991.i 0.00551651 0.00955487i
\(708\) 1.61072e7 2.78985e7i 1.20764 2.09169i
\(709\) 1.51125e7 1.12907 0.564536 0.825408i \(-0.309055\pi\)
0.564536 + 0.825408i \(0.309055\pi\)
\(710\) −1.68719e6 −0.125608
\(711\) −308567. + 534454.i −0.0228916 + 0.0396494i
\(712\) 626047. 1.08435e6i 0.0462814 0.0801618i
\(713\) −84829.2 146928.i −0.00624916 0.0108239i
\(714\) −1.51350e6 2.62146e6i −0.111106 0.192441i
\(715\) −1.13947e6 −0.0833560
\(716\) −1.47423e7 2.55344e7i −1.07469 1.86141i
\(717\) −6.48819e6 1.12379e7i −0.471331 0.816369i
\(718\) 1.24744e7 + 2.16063e7i 0.903045 + 1.56412i
\(719\) −932291. + 1.61478e6i −0.0672557 + 0.116490i −0.897692 0.440623i \(-0.854758\pi\)
0.830437 + 0.557113i \(0.188091\pi\)
\(720\) −283593. −0.0203875
\(721\) 2.06740e6 3.58085e6i 0.148111 0.256536i
\(722\) 4.90401e6 + 8.49400e6i 0.350113 + 0.606414i
\(723\) 4.99919e6 0.355675
\(724\) 2.13445e7 + 3.69697e7i 1.51335 + 2.62120i
\(725\) 9.96440e6 1.72589e7i 0.704055 1.21946i
\(726\) −8.25694e6 + 1.43014e7i −0.581403 + 1.00702i
\(727\) 4.41487e6 0.309801 0.154900 0.987930i \(-0.450494\pi\)
0.154900 + 0.987930i \(0.450494\pi\)
\(728\) −1.07482e6 + 1.86164e6i −0.0751636 + 0.130187i
\(729\) 1.52307e7 1.06145
\(730\) 5.82765e6 0.404750
\(731\) −6.35911e6 6.87738e6i −0.440152 0.476025i
\(732\) 4.15263e6 0.286448
\(733\) 2.75979e7 1.89721 0.948605 0.316462i \(-0.102495\pi\)
0.948605 + 0.316462i \(0.102495\pi\)
\(734\) 1.47822e7 2.56036e7i 1.01275 1.75413i
\(735\) 4.60686e6 0.314548
\(736\) 479935. 831272.i 0.0326579 0.0565651i
\(737\) −4.05180e6 + 7.01792e6i −0.274776 + 0.475926i
\(738\) −1.24416e6 2.15494e6i −0.0840879 0.145645i
\(739\) 9.00737e6 0.606718 0.303359 0.952876i \(-0.401892\pi\)
0.303359 + 0.952876i \(0.401892\pi\)
\(740\) 2.17349e6 + 3.76460e6i 0.145908 + 0.252720i
\(741\) 2.48567e6 4.30531e6i 0.166302 0.288044i
\(742\) −8.13026e6 −0.542119
\(743\) 29536.9 51159.4i 0.00196288 0.00339980i −0.865042 0.501699i \(-0.832709\pi\)
0.867005 + 0.498299i \(0.166042\pi\)
\(744\) 440736. + 763377.i 0.0291908 + 0.0505599i
\(745\) 1.67022e6 + 2.89290e6i 0.110251 + 0.190960i
\(746\) −9.95265e6 1.72385e7i −0.654774 1.13410i
\(747\) −583924. −0.0382873
\(748\) −5.23877e6 9.07382e6i −0.342354 0.592975i
\(749\) 2.28946e6 + 3.96547e6i 0.149118 + 0.258279i
\(750\) −8.17801e6 + 1.41647e7i −0.530877 + 0.919507i
\(751\) 1.72832e6 2.99353e6i 0.111821 0.193680i −0.804684 0.593704i \(-0.797665\pi\)
0.916504 + 0.400024i \(0.130998\pi\)
\(752\) 1.98493e7 1.27997
\(753\) −1.84462e7 −1.18555
\(754\) −9.57702e6 + 1.65879e7i −0.613482 + 1.06258i
\(755\) −1.90458e6 + 3.29883e6i −0.121599 + 0.210616i
\(756\) −3.26839e6 5.66102e6i −0.207984 0.360238i
\(757\) −1.34214e6 2.32466e6i −0.0851254 0.147441i 0.820319 0.571906i \(-0.193796\pi\)
−0.905445 + 0.424464i \(0.860462\pi\)
\(758\) 2.02315e7 1.27895
\(759\) −1.38389e6 2.39696e6i −0.0871959 0.151028i
\(760\) −3.37285e6 5.84195e6i −0.211818 0.366880i
\(761\) −1.49439e6 2.58836e6i −0.0935411 0.162018i 0.815458 0.578817i \(-0.196485\pi\)
−0.908999 + 0.416799i \(0.863152\pi\)
\(762\) −3.51521e6 + 6.08853e6i −0.219313 + 0.379861i
\(763\) 971940. 0.0604405
\(764\) −2.47829e7 + 4.29253e7i −1.53610 + 2.66060i
\(765\) −129419. 224161.i −0.00799550 0.0138486i
\(766\) −1.49084e7 −0.918033
\(767\) −4.72448e6 8.18304e6i −0.289978 0.502257i
\(768\) −1.51235e7 + 2.61947e7i −0.925229 + 1.60254i
\(769\) −2.96623e6 + 5.13767e6i −0.180880 + 0.313293i −0.942180 0.335106i \(-0.891228\pi\)
0.761301 + 0.648399i \(0.224561\pi\)
\(770\) −1.08706e6 −0.0660732
\(771\) −1.32442e7 + 2.29397e7i −0.802400 + 1.38980i
\(772\) 2.53765e7 1.53246
\(773\) 1.41823e7 0.853687 0.426844 0.904325i \(-0.359625\pi\)
0.426844 + 0.904325i \(0.359625\pi\)
\(774\) −1.40248e6 1.51678e6i −0.0841482 0.0910063i
\(775\) −554869. −0.0331846
\(776\) −1.44091e6 −0.0858977
\(777\) −740846. + 1.28318e6i −0.0440225 + 0.0762493i
\(778\) −5.64292e6 −0.334237
\(779\) 8.83865e6 1.53090e7i 0.521846 0.903864i
\(780\) 2.43339e6 4.21475e6i 0.143210 0.248048i
\(781\) −995291. 1.72390e6i −0.0583879 0.101131i
\(782\) −6.32711e6 −0.369989
\(783\) −1.41189e7 2.44546e7i −0.822993 1.42547i
\(784\) 6.80665e6 1.17895e7i 0.395497 0.685021i
\(785\) −1.14648e7 −0.664034
\(786\) −2.15122e7 + 3.72602e7i −1.24202 + 2.15124i
\(787\) −1.02103e7 1.76848e7i −0.587629 1.01780i −0.994542 0.104336i \(-0.966728\pi\)
0.406913 0.913467i \(-0.366605\pi\)
\(788\) −2.00476e7 3.47235e7i −1.15013 1.99209i
\(789\) 1.55347e7 + 2.69070e7i 0.888406 + 1.53876i
\(790\) −6.50317e6 −0.370730
\(791\) 172021. + 297949.i 0.00977551 + 0.0169317i
\(792\) −560148. 970205.i −0.0317315 0.0549605i
\(793\) 609014. 1.05484e6i 0.0343910 0.0595669i
\(794\) 3.58023e6 6.20115e6i 0.201540 0.349077i
\(795\) 8.92384e6 0.500765
\(796\) 1.79642e7 1.00491
\(797\) 6.51515e6 1.12846e7i 0.363311 0.629273i −0.625193 0.780471i \(-0.714980\pi\)
0.988504 + 0.151197i \(0.0483129\pi\)
\(798\) 2.37135e6 4.10729e6i 0.131822 0.228322i
\(799\) 9.05833e6 + 1.56895e7i 0.501974 + 0.869445i
\(800\) −1.56963e6 2.71868e6i −0.0867108 0.150187i
\(801\) 75275.1 0.00414543
\(802\) −2.95094e7 5.11119e7i −1.62004 2.80599i
\(803\) 3.43780e6 + 5.95445e6i 0.188145 + 0.325876i
\(804\) −1.73056e7 2.99742e7i −0.944162 1.63534i
\(805\) −216621. + 375199.i −0.0117818 + 0.0204067i
\(806\) 533298. 0.0289156
\(807\) −1.62524e6 + 2.81499e6i −0.0878482 + 0.152157i
\(808\) 796229. + 1.37911e6i 0.0429052 + 0.0743140i
\(809\) 3.31770e7 1.78224 0.891119 0.453770i \(-0.149921\pi\)
0.891119 + 0.453770i \(0.149921\pi\)
\(810\) 5.04068e6 + 8.73072e6i 0.269946 + 0.467560i
\(811\) 8.53077e6 1.47757e7i 0.455445 0.788854i −0.543268 0.839559i \(-0.682813\pi\)
0.998714 + 0.0507048i \(0.0161468\pi\)
\(812\) −6.02996e6 + 1.04442e7i −0.320940 + 0.555885i
\(813\) 3.09397e7 1.64168
\(814\) −3.88545e6 + 6.72980e6i −0.205533 + 0.355993i
\(815\) −8.06469e6 −0.425298
\(816\) 9.81789e6 0.516170
\(817\) 4.35010e6 1.40163e7i 0.228005 0.734646i
\(818\) 4.14383e7 2.16530
\(819\) −129235. −0.00673241
\(820\) 8.65272e6 1.49870e7i 0.449384 0.778357i
\(821\) 2.68197e7 1.38866 0.694330 0.719657i \(-0.255701\pi\)
0.694330 + 0.719657i \(0.255701\pi\)
\(822\) 3.06298e6 5.30524e6i 0.158112 0.273858i
\(823\) −1.77702e7 + 3.07788e7i −0.914518 + 1.58399i −0.106912 + 0.994269i \(0.534096\pi\)
−0.807606 + 0.589722i \(0.799237\pi\)
\(824\) 2.24518e7 + 3.88876e7i 1.15195 + 1.99523i
\(825\) −9.05202e6 −0.463032
\(826\) −4.50718e6 7.80666e6i −0.229855 0.398121i
\(827\) −1.70824e7 + 2.95876e7i −0.868532 + 1.50434i −0.00503531 + 0.999987i \(0.501603\pi\)
−0.863497 + 0.504354i \(0.831731\pi\)
\(828\) −920957. −0.0466835
\(829\) 1.08028e7 1.87110e7i 0.545946 0.945606i −0.452601 0.891713i \(-0.649504\pi\)
0.998547 0.0538925i \(-0.0171628\pi\)
\(830\) −3.07660e6 5.32883e6i −0.155016 0.268495i
\(831\) −1.75222e7 3.03493e7i −0.880209 1.52457i
\(832\) 5.21316e6 + 9.02946e6i 0.261092 + 0.452224i
\(833\) 1.24250e7 0.620418
\(834\) 4.67841e6 + 8.10324e6i 0.232907 + 0.403407i
\(835\) −3.37833e6 5.85143e6i −0.167682 0.290433i
\(836\) 8.20809e6 1.42168e7i 0.406187 0.703537i
\(837\) −393106. + 680880.i −0.0193953 + 0.0335936i
\(838\) −1.39261e7 −0.685045
\(839\) 1.67006e7 0.819081 0.409540 0.912292i \(-0.365689\pi\)
0.409540 + 0.912292i \(0.365689\pi\)
\(840\) 1.12547e6 1.94937e6i 0.0550346 0.0953227i
\(841\) −1.57928e7 + 2.73540e7i −0.769963 + 1.33361i
\(842\) 2.66567e7 + 4.61707e7i 1.29576 + 2.24433i
\(843\) −1.44351e7 2.50022e7i −0.699600 1.21174i
\(844\) −4.19526e7 −2.02723
\(845\) 2.82787e6 + 4.89802e6i 0.136244 + 0.235982i
\(846\) 1.99779e6 + 3.46027e6i 0.0959673 + 0.166220i
\(847\) 1.52488e6 + 2.64118e6i 0.0730345 + 0.126499i
\(848\) 1.31850e7 2.28371e7i 0.629637 1.09056i
\(849\) 41958.5 0.00199779
\(850\) −1.03464e7 + 1.79205e7i −0.491183 + 0.850753i
\(851\) 1.54853e6 + 2.68214e6i 0.0732987 + 0.126957i
\(852\) 8.50196e6 0.401255
\(853\) −7.49511e6 1.29819e7i −0.352700 0.610894i 0.634022 0.773315i \(-0.281403\pi\)
−0.986722 + 0.162421i \(0.948070\pi\)
\(854\) 581002. 1.00633e6i 0.0272605 0.0472165i
\(855\) 202774. 351214.i 0.00948629 0.0164307i
\(856\) −4.97266e7 −2.31955
\(857\) 1.76802e6 3.06231e6i 0.0822311 0.142428i −0.821977 0.569521i \(-0.807129\pi\)
0.904208 + 0.427092i \(0.140462\pi\)
\(858\) 8.70011e6 0.403466
\(859\) 7.76090e6 0.358863 0.179432 0.983770i \(-0.442574\pi\)
0.179432 + 0.983770i \(0.442574\pi\)
\(860\) 4.25859e6 1.37215e7i 0.196345 0.632636i
\(861\) 5.89865e6 0.271172
\(862\) −1.66707e7 −0.764164
\(863\) −1.94627e7 + 3.37104e7i −0.889561 + 1.54077i −0.0491669 + 0.998791i \(0.515657\pi\)
−0.840395 + 0.541975i \(0.817677\pi\)
\(864\) −4.44813e6 −0.202718
\(865\) −5.10706e6 + 8.84569e6i −0.232076 + 0.401968i
\(866\) −3.27416e7 + 5.67101e7i −1.48356 + 2.56960i
\(867\) −6.17882e6 1.07020e7i −0.279163 0.483524i
\(868\) 335779. 0.0151270
\(869\) −3.83629e6 6.64466e6i −0.172331 0.298485i
\(870\) 1.00283e7 1.73696e7i 0.449190 0.778020i
\(871\) −1.01520e7 −0.453424
\(872\) −5.27758e6 + 9.14104e6i −0.235041 + 0.407103i
\(873\) −43313.2 75020.6i −0.00192347 0.00333154i
\(874\) −4.95664e6 8.58515e6i −0.219487 0.380163i
\(875\) 1.51031e6 + 2.61593e6i 0.0666876 + 0.115506i
\(876\) −2.93663e7 −1.29297
\(877\) −1.24863e7 2.16270e7i −0.548197 0.949505i −0.998398 0.0565777i \(-0.981981\pi\)
0.450201 0.892927i \(-0.351352\pi\)
\(878\) 1.00508e7 + 1.74084e7i 0.440010 + 0.762120i
\(879\) 2.50208e6 4.33373e6i 0.109227 0.189186i
\(880\) 1.76290e6 3.05343e6i 0.0767399 0.132917i
\(881\) 3.41908e6 0.148412 0.0742061 0.997243i \(-0.476358\pi\)
0.0742061 + 0.997243i \(0.476358\pi\)
\(882\) 2.74030e6 0.118611
\(883\) −8.84755e6 + 1.53244e7i −0.381875 + 0.661427i −0.991330 0.131393i \(-0.958055\pi\)
0.609455 + 0.792821i \(0.291388\pi\)
\(884\) 6.56300e6 1.13675e7i 0.282470 0.489252i
\(885\) 4.94711e6 + 8.56865e6i 0.212321 + 0.367751i
\(886\) 6.67233e6 + 1.15568e7i 0.285557 + 0.494599i
\(887\) 3.81040e6 0.162616 0.0813078 0.996689i \(-0.474090\pi\)
0.0813078 + 0.996689i \(0.474090\pi\)
\(888\) −8.04550e6 1.39352e7i −0.342390 0.593036i
\(889\) 649186. + 1.12442e6i 0.0275496 + 0.0477173i
\(890\) 396612. + 686952.i 0.0167838 + 0.0290704i
\(891\) −5.94712e6 + 1.03007e7i −0.250964 + 0.434683i
\(892\) −297660. −0.0125259
\(893\) −1.41926e7 + 2.45822e7i −0.595569 + 1.03156i
\(894\) −1.27525e7 2.20880e7i −0.533645 0.924300i
\(895\) 9.05579e6 0.377893
\(896\) 4.48402e6 + 7.76656e6i 0.186594 + 0.323190i
\(897\) 1.73370e6 3.00285e6i 0.0719436 0.124610i
\(898\) −5.18236e6 + 8.97610e6i −0.214455 + 0.371447i
\(899\) 1.45051e6 0.0598578
\(900\) −1.50600e6 + 2.60846e6i −0.0619752 + 0.107344i
\(901\) 2.40682e7 0.987715
\(902\) 3.09362e7 1.26605
\(903\) 4.77621e6 1.08143e6i 0.194923 0.0441344i
\(904\) −3.73625e6 −0.152060
\(905\) −1.31113e7 −0.532139
\(906\) 1.45419e7 2.51873e7i 0.588574 1.01944i
\(907\) −4.40691e7 −1.77876 −0.889378 0.457173i \(-0.848862\pi\)
−0.889378 + 0.457173i \(0.848862\pi\)
\(908\) −9.07572e6 + 1.57196e7i −0.365314 + 0.632743i
\(909\) −47868.8 + 82911.2i −0.00192151 + 0.00332815i
\(910\) −680919. 1.17939e6i −0.0272579 0.0472120i
\(911\) −1.89199e7 −0.755308 −0.377654 0.925947i \(-0.623269\pi\)
−0.377654 + 0.925947i \(0.623269\pi\)
\(912\) 7.69131e6 + 1.33217e7i 0.306206 + 0.530364i
\(913\) 3.62984e6 6.28707e6i 0.144116 0.249615i
\(914\) −3.05804e7 −1.21081
\(915\) −637713. + 1.10455e6i −0.0251810 + 0.0436147i
\(916\) −7.21592e6 1.24983e7i −0.284154 0.492168i
\(917\) 3.97285e6 + 6.88118e6i 0.156020 + 0.270234i
\(918\) 1.46602e7 + 2.53922e7i 0.574160 + 0.994474i
\(919\) −2.52471e7 −0.986102 −0.493051 0.870000i \(-0.664118\pi\)
−0.493051 + 0.870000i \(0.664118\pi\)
\(920\) −2.35248e6 4.07462e6i −0.0916341 0.158715i
\(921\) 7.85818e6 + 1.36108e7i 0.305262 + 0.528729i
\(922\) 2.34193e7 4.05634e7i 0.907291 1.57147i
\(923\) 1.24688e6 2.15965e6i 0.0481747 0.0834410i
\(924\) 5.47783e6 0.211071
\(925\) 1.01290e7 0.389234
\(926\) 2.60170e7 4.50627e7i 0.997079 1.72699i
\(927\) −1.34979e6 + 2.33790e6i −0.0515900 + 0.0893566i
\(928\) 4.10325e6 + 7.10703e6i 0.156408 + 0.270906i
\(929\) −2.20283e7 3.81542e7i −0.837418 1.45045i −0.892046 0.451944i \(-0.850731\pi\)
0.0546285 0.998507i \(-0.482603\pi\)
\(930\) −558428. −0.0211719
\(931\) 9.73372e6 + 1.68593e7i 0.368048 + 0.637478i
\(932\) 2.94116e7 + 5.09425e7i 1.10912 + 1.92106i
\(933\) −2.12590e7 3.68217e7i −0.799539 1.38484i
\(934\) 2.76219e7 4.78426e7i 1.03606 1.79452i
\(935\) 3.21804e6 0.120382
\(936\) 701739. 1.21545e6i 0.0261810 0.0453468i
\(937\) 3.20035e6 + 5.54316e6i 0.119083 + 0.206257i 0.919404 0.393314i \(-0.128671\pi\)
−0.800322 + 0.599571i \(0.795338\pi\)
\(938\) −9.68503e6 −0.359413
\(939\) −9.49323e6 1.64428e7i −0.351358 0.608570i
\(940\) −1.38940e7 + 2.40651e7i −0.512870 + 0.888318i
\(941\) 1.14783e7 1.98810e7i 0.422575 0.731921i −0.573616 0.819125i \(-0.694460\pi\)
0.996191 + 0.0872034i \(0.0277930\pi\)
\(942\) 8.75362e7 3.21411
\(943\) 6.16474e6 1.06776e7i 0.225754 0.391018i
\(944\) 2.92375e7 1.06785
\(945\) 2.00768e6 0.0731334
\(946\) 2.50494e7 5.67166e6i 0.910058 0.206055i
\(947\) −1.54669e7 −0.560437 −0.280219 0.959936i \(-0.590407\pi\)
−0.280219 + 0.959936i \(0.590407\pi\)
\(948\) 3.27703e7 1.18430
\(949\) −4.30679e6 + 7.45958e6i −0.155234 + 0.268874i
\(950\) −3.24215e7 −1.16553
\(951\) −2.42262e7 + 4.19611e7i −0.868630 + 1.50451i
\(952\) 3.03547e6 5.25758e6i 0.108551 0.188016i
\(953\) −4.39274e6 7.60845e6i −0.156676 0.271371i 0.776992 0.629511i \(-0.216745\pi\)
−0.933668 + 0.358139i \(0.883411\pi\)
\(954\) 5.30816e6 0.188831
\(955\) −7.61175e6 1.31839e7i −0.270070 0.467775i
\(956\) 2.68407e7 4.64895e7i 0.949838 1.64517i
\(957\) 2.36633e7 0.835209
\(958\) −1.01523e7 + 1.75843e7i −0.357396 + 0.619028i
\(959\) −565668. 979766.i −0.0198616 0.0344014i
\(960\) −5.45882e6 9.45496e6i −0.191171 0.331117i
\(961\) 1.42944e7 + 2.47586e7i 0.499295 + 0.864804i
\(962\) −9.73519e6 −0.339162
\(963\) −1.49477e6 2.58901e6i −0.0519407 0.0899639i
\(964\) 1.03405e7 + 1.79102e7i 0.358383 + 0.620738i
\(965\) −3.89703e6 + 6.74986e6i −0.134715 + 0.233333i
\(966\) 1.65396e6 2.86474e6i 0.0570271 0.0987738i
\(967\) 9.97371e6 0.342997 0.171499 0.985184i \(-0.445139\pi\)
0.171499 + 0.985184i \(0.445139\pi\)
\(968\) −3.31201e7 −1.13607
\(969\) −7.01995e6 + 1.21589e7i −0.240173 + 0.415992i
\(970\) 456420. 790543.i 0.0155753 0.0269772i
\(971\) 82862.1 + 143521.i 0.00282038 + 0.00488504i 0.867432 0.497555i \(-0.165769\pi\)
−0.864612 + 0.502441i \(0.832436\pi\)
\(972\) 4.12396e6 + 7.14292e6i 0.140007 + 0.242499i
\(973\) 1.72801e6 0.0585145
\(974\) −1.99137e7 3.44915e7i −0.672595 1.16497i
\(975\) −5.67007e6 9.82085e6i −0.191019 0.330855i
\(976\) 1.88444e6 + 3.26395e6i 0.0633226 + 0.109678i
\(977\) −1.81566e7 + 3.14482e7i −0.608554 + 1.05405i 0.382925 + 0.923779i \(0.374917\pi\)
−0.991479 + 0.130267i \(0.958417\pi\)
\(978\) 6.15759e7 2.05856
\(979\) −467932. + 810483.i −0.0156037 + 0.0270263i
\(980\) 9.52896e6 + 1.65046e7i 0.316942 + 0.548960i
\(981\) −634569. −0.0210526
\(982\) 7.63105e6 + 1.32174e7i 0.252526 + 0.437387i
\(983\) 2.72724e7 4.72371e7i 0.900200 1.55919i 0.0729656 0.997334i \(-0.476754\pi\)
0.827234 0.561857i \(-0.189913\pi\)
\(984\) −3.20293e7 + 5.54764e7i −1.05453 + 1.82650i
\(985\) 1.23147e7 0.404421
\(986\) 2.70471e7 4.68469e7i 0.885988 1.53458i
\(987\) −9.47168e6 −0.309481
\(988\) 2.05658e7 0.670274
\(989\) 3.03409e6 9.77603e6i 0.0986364 0.317813i
\(990\) 709728. 0.0230146
\(991\) 4.88358e7 1.57963 0.789813 0.613348i \(-0.210178\pi\)
0.789813 + 0.613348i \(0.210178\pi\)
\(992\) 114245. 197878.i 0.00368602 0.00638437i
\(993\) −2.25155e7 −0.724616
\(994\) 1.18953e6 2.06032e6i 0.0381863 0.0661406i
\(995\) −2.75873e6 + 4.77827e6i −0.0883389 + 0.153008i
\(996\) 1.55034e7 + 2.68527e7i 0.495198 + 0.857708i
\(997\) 5.74163e7 1.82935 0.914676 0.404187i \(-0.132445\pi\)
0.914676 + 0.404187i \(0.132445\pi\)
\(998\) −1.97284e7 3.41706e7i −0.626997 1.08599i
\(999\) 7.17604e6 1.24293e7i 0.227495 0.394032i
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 43.6.c.a.6.16 34
43.36 even 3 inner 43.6.c.a.36.16 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.c.a.6.16 34 1.1 even 1 trivial
43.6.c.a.36.16 yes 34 43.36 even 3 inner