Properties

Label 33.7.h.a.5.13
Level $33$
Weight $7$
Character 33.5
Analytic conductor $7.592$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [33,7,Mod(5,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\), degree \(4\), 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: \(7.59178475946\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 5.13
Character \(\chi\) \(=\) 33.5
Dual form 33.7.h.a.20.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.46608 - 1.12620i) q^{2} +(20.0067 - 18.1310i) q^{3} +(-41.0317 + 29.8113i) q^{4} +(-207.457 - 67.4069i) q^{5} +(48.9257 - 85.3748i) q^{6} +(-309.326 + 224.739i) q^{7} +(-245.744 + 338.237i) q^{8} +(71.5354 - 725.482i) q^{9} +O(q^{10})\) \(q+(3.46608 - 1.12620i) q^{2} +(20.0067 - 18.1310i) q^{3} +(-41.0317 + 29.8113i) q^{4} +(-207.457 - 67.4069i) q^{5} +(48.9257 - 85.3748i) q^{6} +(-309.326 + 224.739i) q^{7} +(-245.744 + 338.237i) q^{8} +(71.5354 - 725.482i) q^{9} -794.976 q^{10} +(1315.45 - 202.875i) q^{11} +(-280.401 + 1340.37i) q^{12} +(-49.3913 - 152.011i) q^{13} +(-819.049 + 1127.32i) q^{14} +(-5372.68 + 2412.81i) q^{15} +(532.209 - 1637.97i) q^{16} +(-2813.90 - 914.290i) q^{17} +(-569.088 - 2595.14i) q^{18} +(-8908.01 - 6472.05i) q^{19} +(10521.8 - 3418.74i) q^{20} +(-2113.86 + 10104.7i) q^{21} +(4330.97 - 2184.63i) q^{22} -3868.12i q^{23} +(1216.05 + 11222.6i) q^{24} +(25853.9 + 18783.9i) q^{25} +(-342.388 - 471.257i) q^{26} +(-11722.5 - 15811.5i) q^{27} +(5992.44 - 18442.8i) q^{28} +(650.406 + 895.207i) q^{29} +(-15904.8 + 14413.7i) q^{30} +(9410.07 + 28961.2i) q^{31} -33034.1i q^{32} +(22639.4 - 27909.2i) q^{33} -10782.8 q^{34} +(79320.9 - 25772.9i) q^{35} +(18692.3 + 31900.3i) q^{36} +(-32265.8 + 23442.5i) q^{37} +(-38164.7 - 12400.5i) q^{38} +(-3744.26 - 2145.72i) q^{39} +(73780.7 - 53604.8i) q^{40} +(-3524.47 + 4851.01i) q^{41} +(4053.03 + 37404.2i) q^{42} -88867.7 q^{43} +(-47927.1 + 47539.5i) q^{44} +(-63743.0 + 145684. i) q^{45} +(-4356.27 - 13407.2i) q^{46} +(62872.8 - 86536.9i) q^{47} +(-19050.3 - 42419.9i) q^{48} +(8819.78 - 27144.5i) q^{49} +(110766. + 35990.0i) q^{50} +(-72873.7 + 32726.8i) q^{51} +(6558.25 + 4764.85i) q^{52} +(-15515.5 + 5041.29i) q^{53} +(-58438.0 - 41602.0i) q^{54} +(-286574. - 46582.4i) q^{55} -159854. i q^{56} +(-295564. + 32026.7i) q^{57} +(3262.54 + 2370.37i) q^{58} +(-31753.6 - 43705.1i) q^{59} +(148521. - 259168. i) q^{60} +(-115051. + 354089. i) q^{61} +(65232.1 + 89784.3i) q^{62} +(140916. + 240487. i) q^{63} +(-3141.46 - 9668.43i) q^{64} +34865.0i q^{65} +(47038.8 - 122232. i) q^{66} +372987. q^{67} +(142715. - 46371.0i) q^{68} +(-70132.8 - 77388.3i) q^{69} +(245907. - 178662. i) q^{70} +(64896.3 + 21086.1i) q^{71} +(227805. + 202478. i) q^{72} +(41200.9 - 29934.2i) q^{73} +(-85434.9 + 117591. i) q^{74} +(857821. - 92951.4i) q^{75} +558451. q^{76} +(-361309. + 358387. i) q^{77} +(-15394.4 - 3220.46i) q^{78} +(-224316. - 690373. i) q^{79} +(-220821. + 303934. i) q^{80} +(-521206. - 103795. i) q^{81} +(-6752.88 + 20783.2i) q^{82} +(-696592. - 226336. i) q^{83} +(-214498. - 477629. i) q^{84} +(522133. + 379352. i) q^{85} +(-308022. + 100082. i) q^{86} +(29243.5 + 6117.64i) q^{87} +(-254643. + 494788. i) q^{88} -1.34220e6i q^{89} +(-56868.9 + 576740. i) q^{90} +(49440.8 + 35920.8i) q^{91} +(115314. + 158716. i) q^{92} +(713360. + 408805. i) q^{93} +(120464. - 370751. i) q^{94} +(1.41177e6 + 1.94313e6i) q^{95} +(-598940. - 660903. i) q^{96} +(-196405. - 604473. i) q^{97} -104018. i q^{98} +(-53080.9 - 968846. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24} + 68152 q^{25} + 65385 q^{27} - 37986 q^{28} + 20928 q^{30} + 96222 q^{31} - 67159 q^{33} - 186548 q^{34} - 107169 q^{36} - 112854 q^{37} - 257545 q^{39} + 246958 q^{40} - 130324 q^{42} + 40328 q^{43} + 505478 q^{45} - 30630 q^{46} + 647882 q^{48} - 327700 q^{49} + 88197 q^{51} - 132630 q^{52} - 1639642 q^{54} - 216226 q^{55} + 174477 q^{57} + 1571894 q^{58} + 772854 q^{60} + 559626 q^{61} + 1129495 q^{63} + 1406654 q^{64} + 34620 q^{66} - 3229336 q^{67} - 2492844 q^{69} - 2066360 q^{70} - 2672882 q^{72} + 1068798 q^{73} - 1207057 q^{75} + 913268 q^{76} + 6763180 q^{78} - 255558 q^{79} + 3363409 q^{81} - 3580072 q^{82} - 2958906 q^{84} - 2098978 q^{85} + 365046 q^{87} + 2251838 q^{88} - 813500 q^{90} + 7887166 q^{91} + 4000307 q^{93} + 11260802 q^{94} + 4588186 q^{96} + 3850038 q^{97} - 1274785 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.46608 1.12620i 0.433260 0.140775i −0.0842641 0.996443i \(-0.526854\pi\)
0.517524 + 0.855669i \(0.326854\pi\)
\(3\) 20.0067 18.1310i 0.740989 0.671518i
\(4\) −41.0317 + 29.8113i −0.641121 + 0.465801i
\(5\) −207.457 67.4069i −1.65966 0.539255i −0.678856 0.734271i \(-0.737524\pi\)
−0.980800 + 0.195016i \(0.937524\pi\)
\(6\) 48.9257 85.3748i 0.226508 0.395254i
\(7\) −309.326 + 224.739i −0.901826 + 0.655215i −0.938934 0.344096i \(-0.888185\pi\)
0.0371081 + 0.999311i \(0.488185\pi\)
\(8\) −245.744 + 338.237i −0.479968 + 0.660619i
\(9\) 71.5354 725.482i 0.0981281 0.995174i
\(10\) −794.976 −0.794976
\(11\) 1315.45 202.875i 0.988315 0.152423i
\(12\) −280.401 + 1340.37i −0.162269 + 0.775677i
\(13\) −49.3913 152.011i −0.0224812 0.0691902i 0.939186 0.343408i \(-0.111581\pi\)
−0.961668 + 0.274217i \(0.911581\pi\)
\(14\) −819.049 + 1127.32i −0.298487 + 0.410833i
\(15\) −5372.68 + 2412.81i −1.59191 + 0.714907i
\(16\) 532.209 1637.97i 0.129934 0.399896i
\(17\) −2813.90 914.290i −0.572745 0.186096i 0.00830293 0.999966i \(-0.497357\pi\)
−0.581048 + 0.813869i \(0.697357\pi\)
\(18\) −569.088 2595.14i −0.0975802 0.444983i
\(19\) −8908.01 6472.05i −1.29873 0.943585i −0.298791 0.954318i \(-0.596583\pi\)
−0.999942 + 0.0107333i \(0.996583\pi\)
\(20\) 10521.8 3418.74i 1.31523 0.427343i
\(21\) −2113.86 + 10104.7i −0.228254 + 1.09110i
\(22\) 4330.97 2184.63i 0.406740 0.205168i
\(23\) 3868.12i 0.317919i −0.987285 0.158960i \(-0.949186\pi\)
0.987285 0.158960i \(-0.0508139\pi\)
\(24\) 1216.05 + 11222.6i 0.0879667 + 0.811818i
\(25\) 25853.9 + 18783.9i 1.65465 + 1.20217i
\(26\) −342.388 471.257i −0.0194804 0.0268125i
\(27\) −11722.5 15811.5i −0.595565 0.803307i
\(28\) 5992.44 18442.8i 0.272979 0.840144i
\(29\) 650.406 + 895.207i 0.0266680 + 0.0367054i 0.822143 0.569281i \(-0.192778\pi\)
−0.795475 + 0.605987i \(0.792778\pi\)
\(30\) −15904.8 + 14413.7i −0.589068 + 0.533840i
\(31\) 9410.07 + 28961.2i 0.315870 + 0.972147i 0.975395 + 0.220465i \(0.0707573\pi\)
−0.659525 + 0.751682i \(0.729243\pi\)
\(32\) 33034.1i 1.00812i
\(33\) 22639.4 27909.2i 0.629976 0.776615i
\(34\) −10782.8 −0.274345
\(35\) 79320.9 25772.9i 1.85005 0.601118i
\(36\) 18692.3 + 31900.3i 0.400641 + 0.683735i
\(37\) −32265.8 + 23442.5i −0.636997 + 0.462805i −0.858817 0.512282i \(-0.828800\pi\)
0.221820 + 0.975088i \(0.428800\pi\)
\(38\) −38164.7 12400.5i −0.695522 0.225989i
\(39\) −3744.26 2145.72i −0.0631208 0.0361726i
\(40\) 73780.7 53604.8i 1.15282 0.837576i
\(41\) −3524.47 + 4851.01i −0.0511378 + 0.0703851i −0.833820 0.552036i \(-0.813851\pi\)
0.782682 + 0.622421i \(0.213851\pi\)
\(42\) 4053.03 + 37404.2i 0.0547056 + 0.504862i
\(43\) −88867.7 −1.11773 −0.558867 0.829257i \(-0.688764\pi\)
−0.558867 + 0.829257i \(0.688764\pi\)
\(44\) −47927.1 + 47539.5i −0.562631 + 0.558080i
\(45\) −63743.0 + 145684.i −0.699511 + 1.59873i
\(46\) −4356.27 13407.2i −0.0447549 0.137742i
\(47\) 62872.8 86536.9i 0.605576 0.833504i −0.390628 0.920549i \(-0.627742\pi\)
0.996204 + 0.0870442i \(0.0277421\pi\)
\(48\) −19050.3 42419.9i −0.172257 0.383571i
\(49\) 8819.78 27144.5i 0.0749669 0.230724i
\(50\) 110766. + 35990.0i 0.886127 + 0.287920i
\(51\) −72873.7 + 32726.8i −0.549364 + 0.246713i
\(52\) 6558.25 + 4764.85i 0.0466421 + 0.0338874i
\(53\) −15515.5 + 5041.29i −0.104217 + 0.0338621i −0.360661 0.932697i \(-0.617449\pi\)
0.256444 + 0.966559i \(0.417449\pi\)
\(54\) −58438.0 41602.0i −0.371119 0.264200i
\(55\) −286574. 46582.4i −1.72246 0.279985i
\(56\) 159854.i 0.910246i
\(57\) −295564. + 32026.7i −1.59598 + 0.172937i
\(58\) 3262.54 + 2370.37i 0.0167214 + 0.0121488i
\(59\) −31753.6 43705.1i −0.154610 0.212802i 0.724685 0.689081i \(-0.241985\pi\)
−0.879295 + 0.476278i \(0.841985\pi\)
\(60\) 148521. 259168.i 0.687599 1.19985i
\(61\) −115051. + 354089.i −0.506873 + 1.55999i 0.290726 + 0.956806i \(0.406103\pi\)
−0.797599 + 0.603188i \(0.793897\pi\)
\(62\) 65232.1 + 89784.3i 0.273707 + 0.376726i
\(63\) 140916. + 240487.i 0.563559 + 0.961769i
\(64\) −3141.46 9668.43i −0.0119837 0.0368821i
\(65\) 34865.0i 0.126955i
\(66\) 47038.8 122232.i 0.163615 0.425160i
\(67\) 372987. 1.24013 0.620067 0.784549i \(-0.287105\pi\)
0.620067 + 0.784549i \(0.287105\pi\)
\(68\) 142715. 46371.0i 0.453882 0.147475i
\(69\) −70132.8 77388.3i −0.213488 0.235574i
\(70\) 245907. 178662.i 0.716930 0.520880i
\(71\) 64896.3 + 21086.1i 0.181320 + 0.0589143i 0.398270 0.917268i \(-0.369611\pi\)
−0.216950 + 0.976183i \(0.569611\pi\)
\(72\) 227805. + 202478.i 0.610332 + 0.542477i
\(73\) 41200.9 29934.2i 0.105910 0.0769483i −0.533570 0.845756i \(-0.679150\pi\)
0.639480 + 0.768808i \(0.279150\pi\)
\(74\) −85434.9 + 117591.i −0.210834 + 0.290188i
\(75\) 857821. 92951.4i 2.03335 0.220329i
\(76\) 558451. 1.27217
\(77\) −361309. + 358387.i −0.791419 + 0.785018i
\(78\) −15394.4 3220.46i −0.0324399 0.00678631i
\(79\) −224316. 690373.i −0.454966 1.40024i −0.871175 0.490972i \(-0.836642\pi\)
0.416210 0.909269i \(-0.363358\pi\)
\(80\) −220821. + 303934.i −0.431291 + 0.593622i
\(81\) −521206. 103795.i −0.980742 0.195309i
\(82\) −6752.88 + 20783.2i −0.0122475 + 0.0376939i
\(83\) −696592. 226336.i −1.21827 0.395840i −0.371819 0.928305i \(-0.621266\pi\)
−0.846452 + 0.532465i \(0.821266\pi\)
\(84\) −214498. 477629.i −0.361897 0.805847i
\(85\) 522133. + 379352.i 0.850206 + 0.617711i
\(86\) −308022. + 100082.i −0.484269 + 0.157349i
\(87\) 29243.5 + 6117.64i 0.0444090 + 0.00929022i
\(88\) −254643. + 494788.i −0.373666 + 0.726058i
\(89\) 1.34220e6i 1.90392i −0.306223 0.951960i \(-0.599065\pi\)
0.306223 0.951960i \(-0.400935\pi\)
\(90\) −56868.9 + 576740.i −0.0780094 + 0.791139i
\(91\) 49440.8 + 35920.8i 0.0656086 + 0.0476675i
\(92\) 115314. + 158716.i 0.148087 + 0.203824i
\(93\) 713360. + 408805.i 0.886870 + 0.508238i
\(94\) 120464. 370751.i 0.145036 0.446374i
\(95\) 1.41177e6 + 1.94313e6i 1.64662 + 2.26638i
\(96\) −598940. 660903.i −0.676970 0.747005i
\(97\) −196405. 604473.i −0.215198 0.662311i −0.999139 0.0414764i \(-0.986794\pi\)
0.783942 0.620835i \(-0.213206\pi\)
\(98\) 104018.i 0.110517i
\(99\) −53080.9 968846.i −0.0547057 0.998503i
\(100\) −1.62080e6 −1.62080
\(101\) −412435. + 134008.i −0.400305 + 0.130067i −0.502249 0.864723i \(-0.667494\pi\)
0.101944 + 0.994790i \(0.467494\pi\)
\(102\) −215729. + 195504.i −0.203286 + 0.184227i
\(103\) −1.19483e6 + 868094.i −1.09344 + 0.794429i −0.979976 0.199114i \(-0.936194\pi\)
−0.113461 + 0.993542i \(0.536194\pi\)
\(104\) 63553.3 + 20649.7i 0.0564986 + 0.0183575i
\(105\) 1.11966e6 1.95380e6i 0.967205 1.68776i
\(106\) −48100.4 + 34947.0i −0.0403860 + 0.0293422i
\(107\) −962640. + 1.32496e6i −0.785801 + 1.08156i 0.208817 + 0.977955i \(0.433039\pi\)
−0.994618 + 0.103608i \(0.966961\pi\)
\(108\) 952356. + 299310.i 0.756011 + 0.237602i
\(109\) −40045.6 −0.0309226 −0.0154613 0.999880i \(-0.504922\pi\)
−0.0154613 + 0.999880i \(0.504922\pi\)
\(110\) −1.04575e6 + 161280.i −0.785687 + 0.121172i
\(111\) −220497. + 1.05402e6i −0.161225 + 0.770688i
\(112\) 203490. + 626276.i 0.144840 + 0.445771i
\(113\) 707211. 973392.i 0.490133 0.674610i −0.490280 0.871565i \(-0.663105\pi\)
0.980412 + 0.196955i \(0.0631054\pi\)
\(114\) −988381. + 443871.i −0.667129 + 0.299600i
\(115\) −260738. + 802469.i −0.171439 + 0.527636i
\(116\) −53374.6 17342.4i −0.0341948 0.0111106i
\(117\) −113814. + 24958.3i −0.0710623 + 0.0155833i
\(118\) −159281. 115724.i −0.0969434 0.0704335i
\(119\) 1.07589e6 349577.i 0.638449 0.207445i
\(120\) 504200. 2.41017e6i 0.291783 1.39478i
\(121\) 1.68924e6 533742.i 0.953535 0.301284i
\(122\) 1.35687e6i 0.747237i
\(123\) 17440.7 + 160955.i 0.00937234 + 0.0864945i
\(124\) −1.24948e6 907803.i −0.655338 0.476131i
\(125\) −2.09403e6 2.88219e6i −1.07214 1.47568i
\(126\) 759262. + 674849.i 0.379560 + 0.337361i
\(127\) 382203. 1.17630e6i 0.186588 0.574258i −0.813385 0.581726i \(-0.802377\pi\)
0.999972 + 0.00746889i \(0.00237744\pi\)
\(128\) 1.22091e6 + 1.68043e6i 0.582174 + 0.801294i
\(129\) −1.77795e6 + 1.61126e6i −0.828228 + 0.750578i
\(130\) 39264.9 + 120845.i 0.0178720 + 0.0550045i
\(131\) 3.93038e6i 1.74832i −0.485641 0.874159i \(-0.661414\pi\)
0.485641 0.874159i \(-0.338586\pi\)
\(132\) −96925.7 + 1.82007e6i −0.0421422 + 0.791347i
\(133\) 4.21001e6 1.78948
\(134\) 1.29280e6 420056.i 0.537300 0.174579i
\(135\) 1.36611e6 + 4.07038e6i 0.555246 + 1.65438i
\(136\) 1.00074e6 727083.i 0.397838 0.289046i
\(137\) 642804. + 208860.i 0.249987 + 0.0812256i 0.431330 0.902194i \(-0.358045\pi\)
−0.181343 + 0.983420i \(0.558045\pi\)
\(138\) −330240. 189250.i −0.125659 0.0720112i
\(139\) −1.65296e6 + 1.20095e6i −0.615485 + 0.447176i −0.851342 0.524612i \(-0.824211\pi\)
0.235856 + 0.971788i \(0.424211\pi\)
\(140\) −2.48635e6 + 3.42217e6i −0.906104 + 1.24714i
\(141\) −311123. 2.87126e6i −0.110988 1.02427i
\(142\) 248683. 0.0868521
\(143\) −95810.8 189942.i −0.0327647 0.0649551i
\(144\) −1.15025e6 503281.i −0.385215 0.168548i
\(145\) −74588.2 229559.i −0.0244662 0.0752992i
\(146\) 109094. 150154.i 0.0350543 0.0482480i
\(147\) −315701. 702982.i −0.0993858 0.221306i
\(148\) 625071. 1.92377e6i 0.192816 0.593428i
\(149\) 3.54942e6 + 1.15328e6i 1.07300 + 0.348638i 0.791654 0.610970i \(-0.209220\pi\)
0.281343 + 0.959607i \(0.409220\pi\)
\(150\) 2.86859e6 1.28825e6i 0.849953 0.381704i
\(151\) 4.33906e6 + 3.15252e6i 1.26027 + 0.915643i 0.998771 0.0495591i \(-0.0157816\pi\)
0.261504 + 0.965202i \(0.415782\pi\)
\(152\) 4.37817e6 1.42255e6i 1.24670 0.405078i
\(153\) −864594. + 1.97603e6i −0.241400 + 0.551719i
\(154\) −848711. + 1.64910e6i −0.232379 + 0.451528i
\(155\) 6.64252e6i 1.78376i
\(156\) 217600. 23578.6i 0.0573173 0.00621076i
\(157\) −3.22672e6 2.34435e6i −0.833800 0.605791i 0.0868317 0.996223i \(-0.472326\pi\)
−0.920632 + 0.390432i \(0.872326\pi\)
\(158\) −1.55499e6 2.14026e6i −0.394237 0.542620i
\(159\) −219010. + 382170.i −0.0544845 + 0.0950749i
\(160\) −2.22672e6 + 6.85315e6i −0.543634 + 1.67313i
\(161\) 869317. + 1.19651e6i 0.208305 + 0.286708i
\(162\) −1.92344e6 + 227219.i −0.452410 + 0.0534440i
\(163\) −796849. 2.45245e6i −0.183998 0.566288i 0.815932 0.578148i \(-0.196225\pi\)
−0.999930 + 0.0118608i \(0.996225\pi\)
\(164\) 304114.i 0.0689454i
\(165\) −6.57798e6 + 4.26391e6i −1.46434 + 0.949196i
\(166\) −2.66934e6 −0.583552
\(167\) −574555. + 186684.i −0.123362 + 0.0400828i −0.370048 0.929013i \(-0.620659\pi\)
0.246685 + 0.969096i \(0.420659\pi\)
\(168\) −2.89830e6 3.19814e6i −0.611246 0.674482i
\(169\) 3.88430e6 2.82211e6i 0.804735 0.584674i
\(170\) 2.23698e6 + 726838.i 0.455318 + 0.147942i
\(171\) −5.33259e6 + 5.99962e6i −1.06647 + 1.19987i
\(172\) 3.64639e6 2.64926e6i 0.716602 0.520642i
\(173\) −1.99625e6 + 2.74760e6i −0.385546 + 0.530658i −0.957043 0.289946i \(-0.906363\pi\)
0.571497 + 0.820604i \(0.306363\pi\)
\(174\) 108250. 11729.7i 0.0205485 0.00222658i
\(175\) −1.22188e7 −2.27988
\(176\) 367791. 2.26264e6i 0.0674625 0.415028i
\(177\) −1.42770e6 298671.i −0.257465 0.0538608i
\(178\) −1.51159e6 4.65218e6i −0.268024 0.824892i
\(179\) −2.60302e6 + 3.58274e6i −0.453856 + 0.624679i −0.973220 0.229874i \(-0.926169\pi\)
0.519365 + 0.854553i \(0.326169\pi\)
\(180\) −1.72755e6 7.87794e6i −0.296220 1.35081i
\(181\) −2355.00 + 7247.94i −0.000397151 + 0.00122230i −0.951255 0.308406i \(-0.900205\pi\)
0.950858 + 0.309628i \(0.100205\pi\)
\(182\) 211819. + 68824.3i 0.0351359 + 0.0114164i
\(183\) 4.11820e6 + 9.17013e6i 0.671977 + 1.49631i
\(184\) 1.30834e6 + 950566.i 0.210023 + 0.152591i
\(185\) 8.27395e6 2.68837e6i 1.30677 0.424594i
\(186\) 2.93295e6 + 613565.i 0.455792 + 0.0953502i
\(187\) −3.88702e6 631832.i −0.594418 0.0966222i
\(188\) 5.42508e6i 0.816455i
\(189\) 7.17954e6 + 2.25641e6i 1.06344 + 0.334220i
\(190\) 7.08165e6 + 5.14512e6i 1.03246 + 0.750127i
\(191\) −2.09680e6 2.88600e6i −0.300925 0.414187i 0.631600 0.775295i \(-0.282399\pi\)
−0.932524 + 0.361108i \(0.882399\pi\)
\(192\) −238148. 136475.i −0.0336468 0.0192819i
\(193\) 1.53164e6 4.71391e6i 0.213052 0.655706i −0.786234 0.617928i \(-0.787972\pi\)
0.999286 0.0377776i \(-0.0120279\pi\)
\(194\) −1.36151e6 1.87396e6i −0.186473 0.256658i
\(195\) 632137. + 697534.i 0.0852525 + 0.0940722i
\(196\) 447321. + 1.37671e6i 0.0594089 + 0.182842i
\(197\) 944276.i 0.123509i −0.998091 0.0617547i \(-0.980330\pi\)
0.998091 0.0617547i \(-0.0196697\pi\)
\(198\) −1.27509e6 3.29832e6i −0.164266 0.424910i
\(199\) 2.53844e6 0.322113 0.161056 0.986945i \(-0.448510\pi\)
0.161056 + 0.986945i \(0.448510\pi\)
\(200\) −1.27068e7 + 4.12870e6i −1.58835 + 0.516088i
\(201\) 7.46223e6 6.76261e6i 0.918925 0.832772i
\(202\) −1.27861e6 + 928965.i −0.155126 + 0.112706i
\(203\) −402376. 130740.i −0.0480998 0.0156286i
\(204\) 2.01451e6 3.51529e6i 0.237289 0.414068i
\(205\) 1.05817e6 768803.i 0.122827 0.0892388i
\(206\) −3.16372e6 + 4.35449e6i −0.361907 + 0.498122i
\(207\) −2.80625e6 276707.i −0.316385 0.0311968i
\(208\) −275276. −0.0305899
\(209\) −1.30310e7 6.70643e6i −1.42738 0.734603i
\(210\) 1.68047e6 8.03297e6i 0.181457 0.867397i
\(211\) 4.19422e6 + 1.29085e7i 0.446482 + 1.37413i 0.880850 + 0.473395i \(0.156972\pi\)
−0.434368 + 0.900735i \(0.643028\pi\)
\(212\) 486340. 669389.i 0.0510425 0.0702540i
\(213\) 1.68067e6 754770.i 0.173918 0.0781045i
\(214\) −1.84442e6 + 5.67654e6i −0.188199 + 0.579218i
\(215\) 1.84362e7 + 5.99029e6i 1.85505 + 0.602744i
\(216\) 8.22876e6 79412.3i 0.816532 0.00788001i
\(217\) −9.41950e6 6.84367e6i −0.921825 0.669745i
\(218\) −138801. + 45099.2i −0.0133975 + 0.00435311i
\(219\) 281557. 1.34590e6i 0.0268061 0.128138i
\(220\) 1.31473e7 6.63178e6i 1.23472 0.622820i
\(221\) 472900.i 0.0438120i
\(222\) 422771. + 3.90163e6i 0.0386408 + 0.356604i
\(223\) 7.71030e6 + 5.60186e6i 0.695275 + 0.505147i 0.878390 0.477944i \(-0.158618\pi\)
−0.183115 + 0.983092i \(0.558618\pi\)
\(224\) 7.42404e6 + 1.02183e7i 0.660536 + 0.909149i
\(225\) 1.54769e7 1.74128e7i 1.35874 1.52869i
\(226\) 1.35502e6 4.17031e6i 0.117387 0.361279i
\(227\) −4.06858e6 5.59992e6i −0.347829 0.478745i 0.598879 0.800840i \(-0.295613\pi\)
−0.946707 + 0.322095i \(0.895613\pi\)
\(228\) 1.11728e7 1.01253e7i 0.942662 0.854283i
\(229\) 1.20973e6 + 3.72315e6i 0.100735 + 0.310030i 0.988706 0.149869i \(-0.0478853\pi\)
−0.887971 + 0.459900i \(0.847885\pi\)
\(230\) 3.07506e6i 0.252738i
\(231\) −730695. + 1.37210e7i −0.0592789 + 1.11314i
\(232\) −462625. −0.0370481
\(233\) −4.89707e6 + 1.59115e6i −0.387141 + 0.125790i −0.496119 0.868255i \(-0.665242\pi\)
0.108978 + 0.994044i \(0.465242\pi\)
\(234\) −366381. + 214685.i −0.0285947 + 0.0167554i
\(235\) −1.88766e7 + 1.37146e7i −1.45452 + 1.05677i
\(236\) 2.60581e6 + 846680.i 0.198247 + 0.0644144i
\(237\) −1.70050e7 9.74502e6i −1.27741 0.732045i
\(238\) 3.33542e6 2.42332e6i 0.247411 0.179755i
\(239\) −5.99476e6 + 8.25107e6i −0.439115 + 0.604389i −0.970015 0.243045i \(-0.921854\pi\)
0.530901 + 0.847434i \(0.321854\pi\)
\(240\) 1.09272e6 + 1.00844e7i 0.0790455 + 0.729487i
\(241\) 9.72929e6 0.695072 0.347536 0.937667i \(-0.387018\pi\)
0.347536 + 0.937667i \(0.387018\pi\)
\(242\) 5.25395e6 3.75241e6i 0.370715 0.264767i
\(243\) −1.23095e7 + 7.37338e6i −0.857872 + 0.513864i
\(244\) −5.83513e6 1.79587e7i −0.401681 1.23625i
\(245\) −3.65945e6 + 5.03680e6i −0.248838 + 0.342497i
\(246\) 241717. + 538240.i 0.0162369 + 0.0361552i
\(247\) −543843. + 1.67378e6i −0.0360897 + 0.111073i
\(248\) −1.21082e7 3.93420e6i −0.793826 0.257930i
\(249\) −1.80402e7 + 8.10164e6i −1.16854 + 0.524777i
\(250\) −1.05040e7 7.63159e6i −0.672255 0.488422i
\(251\) −7.98571e6 + 2.59471e6i −0.505001 + 0.164085i −0.550428 0.834883i \(-0.685535\pi\)
0.0454265 + 0.998968i \(0.485535\pi\)
\(252\) −1.29513e7 5.66672e6i −0.809302 0.354104i
\(253\) −784744. 5.08831e6i −0.0484581 0.314204i
\(254\) 4.50758e6i 0.275069i
\(255\) 1.73242e7 1.87721e6i 1.04480 0.113212i
\(256\) 6.65062e6 + 4.83196e6i 0.396408 + 0.288007i
\(257\) 524020. + 721251.i 0.0308708 + 0.0424900i 0.824173 0.566338i \(-0.191640\pi\)
−0.793303 + 0.608828i \(0.791640\pi\)
\(258\) −4.34791e6 + 7.58706e6i −0.253175 + 0.441789i
\(259\) 4.71223e6 1.45028e7i 0.271224 0.834740i
\(260\) −1.03937e6 1.43057e6i −0.0591358 0.0813935i
\(261\) 695984. 407819.i 0.0391451 0.0229375i
\(262\) −4.42638e6 1.36230e7i −0.246119 0.757475i
\(263\) 484859.i 0.0266532i 0.999911 + 0.0133266i \(0.00424211\pi\)
−0.999911 + 0.0133266i \(0.995758\pi\)
\(264\) 3.87643e6 + 1.45160e7i 0.210678 + 0.788924i
\(265\) 3.55861e6 0.191224
\(266\) 1.45922e7 4.74129e6i 0.775311 0.251914i
\(267\) −2.43355e7 2.68531e7i −1.27852 1.41078i
\(268\) −1.53043e7 + 1.11192e7i −0.795076 + 0.577656i
\(269\) −2.07946e7 6.75658e6i −1.06830 0.347112i −0.278475 0.960443i \(-0.589829\pi\)
−0.789826 + 0.613331i \(0.789829\pi\)
\(270\) 9.31911e6 + 1.25698e7i 0.473460 + 0.638610i
\(271\) −8.35231e6 + 6.06831e6i −0.419661 + 0.304902i −0.777501 0.628881i \(-0.783513\pi\)
0.357840 + 0.933783i \(0.383513\pi\)
\(272\) −2.99516e6 + 4.12249e6i −0.148838 + 0.204858i
\(273\) 1.64043e6 177753.i 0.0806248 0.00873631i
\(274\) 2.46322e6 0.119744
\(275\) 3.78202e7 + 1.94642e7i 1.81855 + 0.935918i
\(276\) 5.18472e6 + 1.08463e6i 0.246603 + 0.0515885i
\(277\) −5.38374e6 1.65694e7i −0.253306 0.779594i −0.994159 0.107927i \(-0.965579\pi\)
0.740853 0.671667i \(-0.234421\pi\)
\(278\) −4.37678e6 + 6.02413e6i −0.203714 + 0.280388i
\(279\) 2.16840e7 4.75508e6i 0.998451 0.218950i
\(280\) −1.07752e7 + 3.31628e7i −0.490855 + 1.51070i
\(281\) −1.24707e7 4.05197e6i −0.562045 0.182620i 0.0141960 0.999899i \(-0.495481\pi\)
−0.576241 + 0.817280i \(0.695481\pi\)
\(282\) −4.31198e6 9.60163e6i −0.192278 0.428152i
\(283\) 2.86918e7 + 2.08458e7i 1.26590 + 0.919727i 0.999031 0.0440065i \(-0.0140122\pi\)
0.266865 + 0.963734i \(0.414012\pi\)
\(284\) −3.29141e6 + 1.06944e6i −0.143690 + 0.0466877i
\(285\) 6.34758e7 + 1.32789e7i 2.74204 + 0.573625i
\(286\) −546000. 550452.i −0.0233397 0.0235300i
\(287\) 2.29263e6i 0.0969814i
\(288\) −2.39656e7 2.36310e6i −1.00325 0.0989249i
\(289\) −1.24456e7 9.04227e6i −0.515612 0.374614i
\(290\) −517057. 711668.i −0.0212004 0.0291799i
\(291\) −1.48891e7 8.53249e6i −0.604213 0.346256i
\(292\) −798166. + 2.45650e6i −0.0320586 + 0.0986662i
\(293\) 6.16978e6 + 8.49197e6i 0.245282 + 0.337602i 0.913852 0.406047i \(-0.133093\pi\)
−0.668570 + 0.743650i \(0.733093\pi\)
\(294\) −1.88594e6 2.08105e6i −0.0742141 0.0818918i
\(295\) 3.64149e6 + 1.12073e7i 0.141845 + 0.436553i
\(296\) 1.66743e7i 0.642944i
\(297\) −1.86281e7 1.84210e7i −0.711048 0.703143i
\(298\) 1.36014e7 0.513965
\(299\) −587996. + 191052.i −0.0219969 + 0.00714722i
\(300\) −3.24269e7 + 2.93867e7i −1.20099 + 1.08840i
\(301\) 2.74891e7 1.99720e7i 1.00800 0.732356i
\(302\) 1.85899e7 + 6.04022e6i 0.674926 + 0.219297i
\(303\) −5.82176e6 + 1.01589e7i −0.209279 + 0.365190i
\(304\) −1.53420e7 + 1.11466e7i −0.546085 + 0.396754i
\(305\) 4.77361e7 6.57031e7i 1.68247 2.31572i
\(306\) −771355. + 7.82276e6i −0.0269209 + 0.273021i
\(307\) −83874.7 −0.00289879 −0.00144939 0.999999i \(-0.500461\pi\)
−0.00144939 + 0.999999i \(0.500461\pi\)
\(308\) 4.14116e6 2.54763e7i 0.141733 0.871935i
\(309\) −8.16518e6 + 3.90311e7i −0.276752 + 1.32293i
\(310\) −7.48078e6 2.30235e7i −0.251109 0.772833i
\(311\) 1.95846e7 2.69558e7i 0.651077 0.896131i −0.348068 0.937469i \(-0.613162\pi\)
0.999145 + 0.0413382i \(0.0131621\pi\)
\(312\) 1.64589e6 739150.i 0.0541922 0.0243371i
\(313\) 1.55391e6 4.78244e6i 0.0506749 0.155961i −0.922517 0.385957i \(-0.873871\pi\)
0.973192 + 0.229996i \(0.0738713\pi\)
\(314\) −1.38242e7 4.49177e6i −0.446532 0.145087i
\(315\) −1.30235e7 5.93895e7i −0.416675 1.90011i
\(316\) 2.97850e7 + 2.16401e7i 0.943922 + 0.685799i
\(317\) −4.44954e7 + 1.44574e7i −1.39681 + 0.453851i −0.908158 0.418627i \(-0.862511\pi\)
−0.488653 + 0.872478i \(0.662511\pi\)
\(318\) −328707. + 1.57128e6i −0.0102218 + 0.0488621i
\(319\) 1.03719e6 + 1.04565e6i 0.0319511 + 0.0322117i
\(320\) 2.21754e6i 0.0676740i
\(321\) 4.76358e6 + 4.39617e7i 0.144019 + 1.32910i
\(322\) 4.36063e6 + 3.16818e6i 0.130612 + 0.0948948i
\(323\) 1.91489e7 + 2.63562e7i 0.568245 + 0.782123i
\(324\) 2.44803e7 1.12789e7i 0.719749 0.331614i
\(325\) 1.57840e6 4.85783e6i 0.0459799 0.141512i
\(326\) −5.52388e6 7.60297e6i −0.159438 0.219447i
\(327\) −801180. + 726066.i −0.0229133 + 0.0207650i
\(328\) −774677. 2.38421e6i −0.0219533 0.0675652i
\(329\) 4.08981e7i 1.14846i
\(330\) −1.79978e7 + 2.21871e7i −0.500815 + 0.617390i
\(331\) 4.72394e7 1.30263 0.651314 0.758808i \(-0.274218\pi\)
0.651314 + 0.758808i \(0.274218\pi\)
\(332\) 3.53297e7 1.14793e7i 0.965442 0.313691i
\(333\) 1.46989e7 + 2.50852e7i 0.398064 + 0.679337i
\(334\) −1.78121e6 + 1.29412e6i −0.0478052 + 0.0347325i
\(335\) −7.73787e7 2.51419e7i −2.05820 0.668749i
\(336\) 1.54262e7 + 8.84025e6i 0.406668 + 0.233049i
\(337\) −1.94858e7 + 1.41573e7i −0.509130 + 0.369904i −0.812493 0.582971i \(-0.801890\pi\)
0.303364 + 0.952875i \(0.401890\pi\)
\(338\) 1.02850e7 1.41561e7i 0.266352 0.366602i
\(339\) −3.49960e6 3.22968e7i −0.0898296 0.829011i
\(340\) −3.27330e7 −0.832816
\(341\) 1.82540e7 + 3.61879e7i 0.460356 + 0.912642i
\(342\) −1.17264e7 + 2.68007e7i −0.293148 + 0.669989i
\(343\) −1.05283e7 3.24026e7i −0.260900 0.802968i
\(344\) 2.18387e7 3.00583e7i 0.536476 0.738396i
\(345\) 9.33304e6 + 2.07822e7i 0.227283 + 0.506097i
\(346\) −3.82481e6 + 1.17716e7i −0.0923382 + 0.284188i
\(347\) 5.43954e7 + 1.76741e7i 1.30189 + 0.423009i 0.876238 0.481879i \(-0.160045\pi\)
0.425650 + 0.904888i \(0.360045\pi\)
\(348\) −1.38228e6 + 620768.i −0.0327989 + 0.0147296i
\(349\) −4.60533e7 3.34597e7i −1.08339 0.787129i −0.105119 0.994460i \(-0.533522\pi\)
−0.978271 + 0.207331i \(0.933522\pi\)
\(350\) −4.23512e7 + 1.37607e7i −0.987782 + 0.320950i
\(351\) −1.82453e6 + 2.56290e6i −0.0421919 + 0.0592666i
\(352\) −6.70178e6 4.34546e7i −0.153660 0.996341i
\(353\) 1.83600e7i 0.417397i −0.977980 0.208698i \(-0.933077\pi\)
0.977980 0.208698i \(-0.0669227\pi\)
\(354\) −5.28489e6 + 572658.i −0.119131 + 0.0129088i
\(355\) −1.20418e7 8.74891e6i −0.269158 0.195555i
\(356\) 4.00128e7 + 5.50730e7i 0.886848 + 1.22064i
\(357\) 1.51868e7 2.65008e7i 0.333781 0.582444i
\(358\) −4.98738e6 + 1.53496e7i −0.108698 + 0.334539i
\(359\) −9.52770e6 1.31138e7i −0.205923 0.283429i 0.693547 0.720412i \(-0.256047\pi\)
−0.899470 + 0.436983i \(0.856047\pi\)
\(360\) −3.36114e7 5.73612e7i −0.720409 1.22945i
\(361\) 2.29273e7 + 7.05630e7i 0.487339 + 1.49988i
\(362\) 27774.1i 0.000585484i
\(363\) 2.41189e7 4.13061e7i 0.504241 0.863563i
\(364\) −3.09949e6 −0.0642666
\(365\) −1.05652e7 + 3.43284e6i −0.217269 + 0.0705951i
\(366\) 2.46014e7 + 2.71465e7i 0.501783 + 0.553694i
\(367\) −5.15642e7 + 3.74636e7i −1.04316 + 0.757899i −0.970900 0.239487i \(-0.923021\pi\)
−0.0722588 + 0.997386i \(0.523021\pi\)
\(368\) −6.33588e6 2.05865e6i −0.127134 0.0413085i
\(369\) 3.26720e6 + 2.90395e6i 0.0650274 + 0.0577977i
\(370\) 2.56505e7 1.86362e7i 0.506397 0.367919i
\(371\) 3.66638e6 5.04634e6i 0.0717985 0.0988222i
\(372\) −4.14574e7 + 4.49222e6i −0.805328 + 0.0872635i
\(373\) −1.00775e8 −1.94190 −0.970951 0.239277i \(-0.923090\pi\)
−0.970951 + 0.239277i \(0.923090\pi\)
\(374\) −1.41843e7 + 2.18757e6i −0.271139 + 0.0418164i
\(375\) −9.41515e7 1.96962e7i −1.78539 0.373498i
\(376\) 1.38194e7 + 4.25318e7i 0.259972 + 0.800111i
\(377\) 103957. 143084.i 0.00194012 0.00267035i
\(378\) 2.74260e7 264677.i 0.507793 0.00490050i
\(379\) −2.32596e6 + 7.15856e6i −0.0427252 + 0.131495i −0.970144 0.242530i \(-0.922023\pi\)
0.927419 + 0.374025i \(0.122023\pi\)
\(380\) −1.15855e8 3.76435e7i −2.11136 0.686023i
\(381\) −1.36808e7 3.04636e7i −0.247365 0.550815i
\(382\) −1.05179e7 7.64170e6i −0.188686 0.137088i
\(383\) −2.25089e7 + 7.31358e6i −0.400643 + 0.130177i −0.502406 0.864632i \(-0.667552\pi\)
0.101763 + 0.994809i \(0.467552\pi\)
\(384\) 5.48942e7 + 1.14837e7i 0.969467 + 0.202809i
\(385\) 9.91138e7 4.99951e7i 1.73681 0.876084i
\(386\) 1.80637e7i 0.314083i
\(387\) −6.35718e6 + 6.44719e7i −0.109681 + 1.11234i
\(388\) 2.60790e7 + 1.89475e7i 0.446473 + 0.324382i
\(389\) −3.35805e7 4.62195e7i −0.570477 0.785194i 0.422134 0.906533i \(-0.361281\pi\)
−0.992611 + 0.121339i \(0.961281\pi\)
\(390\) 2.97660e6 + 1.70580e6i 0.0501795 + 0.0287563i
\(391\) −3.53658e6 + 1.08845e7i −0.0591635 + 0.182087i
\(392\) 7.01386e6 + 9.65376e6i 0.116439 + 0.160265i
\(393\) −7.12616e7 7.86338e7i −1.17403 1.29548i
\(394\) −1.06344e6 3.27293e6i −0.0173870 0.0535117i
\(395\) 1.58343e8i 2.56926i
\(396\) 3.10605e7 + 3.81710e7i 0.500177 + 0.614679i
\(397\) 1.09438e7 0.174903 0.0874517 0.996169i \(-0.472128\pi\)
0.0874517 + 0.996169i \(0.472128\pi\)
\(398\) 8.79843e6 2.85878e6i 0.139558 0.0453453i
\(399\) 8.42283e7 7.63315e7i 1.32599 1.20167i
\(400\) 4.45272e7 3.23509e7i 0.695738 0.505483i
\(401\) 9.21794e7 + 2.99509e7i 1.42955 + 0.464490i 0.918624 0.395132i \(-0.129301\pi\)
0.510930 + 0.859622i \(0.329301\pi\)
\(402\) 1.82486e7 3.18437e7i 0.280900 0.490168i
\(403\) 3.93764e6 2.86087e6i 0.0601619 0.0437102i
\(404\) 1.29280e7 1.77938e7i 0.196058 0.269851i
\(405\) 1.01131e8 + 5.66659e7i 1.52237 + 0.853016i
\(406\) −1.54190e6 −0.0230398
\(407\) −3.76881e7 + 3.73833e7i −0.559012 + 0.554490i
\(408\) 6.83884e6 3.26910e7i 0.100694 0.481335i
\(409\) −1.74781e7 5.37921e7i −0.255461 0.786228i −0.993739 0.111731i \(-0.964361\pi\)
0.738278 0.674497i \(-0.235639\pi\)
\(410\) 2.80186e6 3.85644e6i 0.0406533 0.0559544i
\(411\) 1.66472e7 7.47607e6i 0.239782 0.107683i
\(412\) 2.31469e7 7.12388e7i 0.330979 1.01865i
\(413\) 1.96445e7 + 6.38288e6i 0.278863 + 0.0906080i
\(414\) −1.00383e7 + 2.20130e6i −0.141468 + 0.0310226i
\(415\) 1.29256e8 + 9.39101e7i 1.80845 + 1.31392i
\(416\) −5.02154e6 + 1.63160e6i −0.0697520 + 0.0226638i
\(417\) −1.12959e7 + 5.39967e7i −0.155781 + 0.744662i
\(418\) −5.27194e7 8.56950e6i −0.721841 0.117335i
\(419\) 3.11166e7i 0.423009i 0.977377 + 0.211505i \(0.0678364\pi\)
−0.977377 + 0.211505i \(0.932164\pi\)
\(420\) 1.23036e7 + 1.13546e8i 0.166067 + 1.53258i
\(421\) 4.65757e7 + 3.38392e7i 0.624184 + 0.453497i 0.854381 0.519648i \(-0.173937\pi\)
−0.230196 + 0.973144i \(0.573937\pi\)
\(422\) 2.90750e7 + 4.00183e7i 0.386885 + 0.532502i
\(423\) −5.82833e7 5.18035e7i −0.770058 0.684444i
\(424\) 2.10768e6 6.48678e6i 0.0276508 0.0851003i
\(425\) −5.55761e7 7.64939e7i −0.723971 0.996460i
\(426\) 4.97532e6 4.50886e6i 0.0643564 0.0583227i
\(427\) −4.39894e7 1.35385e8i −0.565021 1.73895i
\(428\) 8.30629e7i 1.05944i
\(429\) −5.36069e6 2.06297e6i −0.0678968 0.0261289i
\(430\) 7.06476e7 0.888571
\(431\) −1.10184e7 + 3.58011e6i −0.137622 + 0.0447161i −0.377018 0.926206i \(-0.623051\pi\)
0.239396 + 0.970922i \(0.423051\pi\)
\(432\) −3.21376e7 + 1.07861e7i −0.398623 + 0.133787i
\(433\) 4.92410e7 3.57757e7i 0.606545 0.440681i −0.241651 0.970363i \(-0.577689\pi\)
0.848196 + 0.529682i \(0.177689\pi\)
\(434\) −4.03560e7 1.31125e7i −0.493673 0.160404i
\(435\) −5.65439e6 3.24036e6i −0.0686939 0.0393664i
\(436\) 1.64314e6 1.19381e6i 0.0198251 0.0144038i
\(437\) −2.50347e7 + 3.44573e7i −0.299984 + 0.412892i
\(438\) −539845. 4.98207e6i −0.00642461 0.0592908i
\(439\) −7.09201e7 −0.838255 −0.419127 0.907928i \(-0.637664\pi\)
−0.419127 + 0.907928i \(0.637664\pi\)
\(440\) 8.61796e7 8.54826e7i 1.01169 1.00351i
\(441\) −1.90619e7 8.34038e6i −0.222254 0.0972456i
\(442\) 532579. + 1.63911e6i 0.00616761 + 0.0189820i
\(443\) −9.52462e7 + 1.31095e8i −1.09556 + 1.50791i −0.254421 + 0.967094i \(0.581885\pi\)
−0.841140 + 0.540817i \(0.818115\pi\)
\(444\) −2.23742e7 4.98214e7i −0.255623 0.569203i
\(445\) −9.04738e7 + 2.78450e8i −1.02670 + 3.15985i
\(446\) 3.30333e7 + 1.07332e7i 0.372347 + 0.120983i
\(447\) 9.19221e7 4.12812e7i 1.02919 0.462200i
\(448\) 3.14461e6 + 2.28469e6i 0.0349730 + 0.0254094i
\(449\) 4.13085e7 1.34220e7i 0.456353 0.148278i −0.0718152 0.997418i \(-0.522879\pi\)
0.528168 + 0.849140i \(0.322879\pi\)
\(450\) 3.40338e7 7.77840e7i 0.373484 0.853597i
\(451\) −3.65210e6 + 7.09628e6i −0.0398120 + 0.0773572i
\(452\) 6.10228e7i 0.660810i
\(453\) 1.43969e8 1.56001e7i 1.54872 0.167816i
\(454\) −2.04086e7 1.48277e7i −0.218095 0.158455i
\(455\) −7.83553e6 1.07847e7i −0.0831829 0.114491i
\(456\) 6.18005e7 1.07841e8i 0.651774 1.13734i
\(457\) −3.37792e7 + 1.03962e8i −0.353917 + 1.08924i 0.602718 + 0.797954i \(0.294084\pi\)
−0.956635 + 0.291290i \(0.905916\pi\)
\(458\) 8.38600e6 + 1.15423e7i 0.0872888 + 0.120143i
\(459\) 1.85296e7 + 5.52097e7i 0.191614 + 0.570922i
\(460\) −1.32241e7 4.06996e7i −0.135860 0.418135i
\(461\) 1.53088e8i 1.56257i −0.624176 0.781284i \(-0.714565\pi\)
0.624176 0.781284i \(-0.285435\pi\)
\(462\) 1.29199e7 + 4.83810e7i 0.131019 + 0.490624i
\(463\) 6.58998e7 0.663959 0.331979 0.943287i \(-0.392284\pi\)
0.331979 + 0.943287i \(0.392284\pi\)
\(464\) 1.81248e6 588910.i 0.0181434 0.00589515i
\(465\) −1.20435e8 1.32895e8i −1.19783 1.32175i
\(466\) −1.51817e7 + 1.10301e7i −0.150024 + 0.108999i
\(467\) −2.63332e7 8.55617e6i −0.258555 0.0840095i 0.176871 0.984234i \(-0.443402\pi\)
−0.435426 + 0.900224i \(0.643402\pi\)
\(468\) 3.92596e6 4.41703e6i 0.0383008 0.0430917i
\(469\) −1.15375e8 + 8.38246e7i −1.11839 + 0.812555i
\(470\) −4.99823e7 + 6.87947e7i −0.481418 + 0.662616i
\(471\) −1.07061e8 + 1.16009e7i −1.02464 + 0.111027i
\(472\) 2.25859e7 0.214789
\(473\) −1.16901e8 + 1.80290e7i −1.10467 + 0.170368i
\(474\) −6.99153e7 1.46261e7i −0.656504 0.137338i
\(475\) −1.08736e8 3.34655e8i −1.01459 3.12260i
\(476\) −3.37242e7 + 4.64174e7i −0.312695 + 0.430388i
\(477\) 2.54746e6 + 1.16168e7i 0.0234721 + 0.107037i
\(478\) −1.14860e7 + 3.53501e7i −0.105168 + 0.323674i
\(479\) 1.30471e8 + 4.23926e7i 1.18716 + 0.385731i 0.835021 0.550218i \(-0.185456\pi\)
0.352136 + 0.935949i \(0.385456\pi\)
\(480\) 7.97050e7 + 1.77482e8i 0.720712 + 1.60483i
\(481\) 5.15716e6 + 3.74690e6i 0.0463421 + 0.0336695i
\(482\) 3.37225e7 1.09571e7i 0.301147 0.0978485i
\(483\) 3.90861e7 + 8.17668e6i 0.346881 + 0.0725664i
\(484\) −5.34011e7 + 7.22589e7i −0.470992 + 0.637317i
\(485\) 1.38641e8i 1.21526i
\(486\) −3.43619e7 + 3.94197e7i −0.299342 + 0.343403i
\(487\) −8.74638e7 6.35461e7i −0.757254 0.550177i 0.140813 0.990036i \(-0.455028\pi\)
−0.898067 + 0.439859i \(0.855028\pi\)
\(488\) −9.14931e7 1.25929e8i −0.787279 1.08360i
\(489\) −6.04076e7 3.46177e7i −0.516612 0.296055i
\(490\) −7.01151e6 + 2.15792e7i −0.0595968 + 0.183420i
\(491\) −3.35087e7 4.61208e7i −0.283082 0.389630i 0.643669 0.765304i \(-0.277411\pi\)
−0.926752 + 0.375674i \(0.877411\pi\)
\(492\) −5.51389e6 6.08432e6i −0.0462980 0.0510877i
\(493\) −1.01170e6 3.11368e6i −0.00844324 0.0259856i
\(494\) 6.41392e6i 0.0532038i
\(495\) −5.42949e7 + 2.04572e8i −0.447655 + 1.68667i
\(496\) 5.24458e7 0.429799
\(497\) −2.48130e7 + 8.06223e6i −0.202120 + 0.0656729i
\(498\) −5.34046e7 + 4.83977e7i −0.432405 + 0.391865i
\(499\) −1.58778e7 + 1.15359e7i −0.127788 + 0.0928432i −0.649843 0.760068i \(-0.725165\pi\)
0.522055 + 0.852912i \(0.325165\pi\)
\(500\) 1.71843e8 + 5.58353e7i 1.37475 + 0.446682i
\(501\) −8.11017e6 + 1.41522e7i −0.0644937 + 0.112541i
\(502\) −2.47569e7 + 1.79870e7i −0.195698 + 0.142183i
\(503\) 9.97880e7 1.37346e8i 0.784105 1.07923i −0.210712 0.977548i \(-0.567578\pi\)
0.994817 0.101680i \(-0.0324217\pi\)
\(504\) −1.15971e8 1.14352e7i −0.905853 0.0893207i
\(505\) 9.45956e7 0.734508
\(506\) −8.45042e6 1.67527e7i −0.0652269 0.129310i
\(507\) 2.65444e7 1.26887e8i 0.203680 0.973631i
\(508\) 1.93846e7 + 5.96595e7i 0.147865 + 0.455081i
\(509\) 1.03715e8 1.42752e8i 0.786484 1.08250i −0.208053 0.978118i \(-0.566713\pi\)
0.994537 0.104385i \(-0.0332874\pi\)
\(510\) 5.79328e7 2.60170e7i 0.436731 0.196131i
\(511\) −6.01715e6 + 1.85189e7i −0.0450949 + 0.138788i
\(512\) −9.79367e7 3.18216e7i −0.729686 0.237089i
\(513\) 2.09145e6 + 2.16718e8i 0.0154916 + 1.60525i
\(514\) 2.62856e6 + 1.90976e6i 0.0193566 + 0.0140634i
\(515\) 3.06391e8 9.95525e7i 2.24313 0.728837i
\(516\) 2.49186e7 1.19116e8i 0.181374 0.867001i
\(517\) 6.51497e7 1.26590e8i 0.471455 0.916069i
\(518\) 5.55746e7i 0.399841i
\(519\) 9.87834e6 + 9.11643e7i 0.0706614 + 0.652113i
\(520\) −1.17926e7 8.56786e6i −0.0838689 0.0609343i
\(521\) −3.63593e7 5.00442e7i −0.257100 0.353868i 0.660882 0.750490i \(-0.270182\pi\)
−0.917982 + 0.396622i \(0.870182\pi\)
\(522\) 1.95305e6 2.19735e6i 0.0137310 0.0154485i
\(523\) 4.41511e7 1.35883e8i 0.308629 0.949863i −0.669669 0.742660i \(-0.733564\pi\)
0.978298 0.207203i \(-0.0664360\pi\)
\(524\) 1.17170e8 + 1.61270e8i 0.814368 + 1.12088i
\(525\) −2.44457e8 + 2.21538e8i −1.68937 + 1.53098i
\(526\) 546047. + 1.68056e6i 0.00375209 + 0.0115477i
\(527\) 9.00974e7i 0.615574i
\(528\) −3.36656e7 5.19363e7i −0.228710 0.352833i
\(529\) 1.33074e8 0.898927
\(530\) 1.23344e7 4.00770e6i 0.0828498 0.0269195i
\(531\) −3.39788e7 + 1.99102e7i −0.226947 + 0.132982i
\(532\) −1.72744e8 + 1.25506e8i −1.14727 + 0.833544i
\(533\) 911484. + 296159.i 0.00601960 + 0.00195589i
\(534\) −1.14590e8 6.56683e7i −0.752532 0.431253i
\(535\) 2.89018e8 2.09984e8i 1.88740 1.37127i
\(536\) −9.16590e7 + 1.26158e8i −0.595225 + 0.819256i
\(537\) 1.28809e7 + 1.18874e8i 0.0831810 + 0.767652i
\(538\) −7.96849e7 −0.511716
\(539\) 6.09503e6 3.74965e7i 0.0389233 0.239455i
\(540\) −1.77397e8 1.26289e8i −1.12659 0.802020i
\(541\) −314786. 968811.i −0.00198803 0.00611853i 0.950058 0.312075i \(-0.101024\pi\)
−0.952046 + 0.305956i \(0.901024\pi\)
\(542\) −2.21156e7 + 3.04396e7i −0.138900 + 0.191179i
\(543\) 84296.6 + 187706.i 0.000526514 + 0.00117241i
\(544\) −3.02027e7 + 9.29544e7i −0.187607 + 0.577396i
\(545\) 8.30775e6 + 2.69935e6i 0.0513208 + 0.0166751i
\(546\) 5.48566e6 2.46355e6i 0.0337016 0.0151350i
\(547\) 1.28221e8 + 9.31579e7i 0.783423 + 0.569190i 0.906004 0.423268i \(-0.139117\pi\)
−0.122581 + 0.992458i \(0.539117\pi\)
\(548\) −3.26017e7 + 1.05929e7i −0.198107 + 0.0643687i
\(549\) 2.48655e8 + 1.08797e8i 1.50273 + 0.657506i
\(550\) 1.53008e8 + 2.48714e7i 0.919658 + 0.149490i
\(551\) 1.21840e7i 0.0728341i
\(552\) 4.34103e7 4.70383e6i 0.258092 0.0279663i
\(553\) 2.24541e8 + 1.63138e8i 1.32776 + 0.964673i
\(554\) −3.73209e7 5.13678e7i −0.219494 0.302108i
\(555\) 1.16792e8 2.03800e8i 0.683176 1.19214i
\(556\) 3.20220e7 9.85537e7i 0.186305 0.573388i
\(557\) −6.05923e7 8.33981e7i −0.350632 0.482604i 0.596877 0.802333i \(-0.296408\pi\)
−0.947509 + 0.319729i \(0.896408\pi\)
\(558\) 6.98032e7 4.09019e7i 0.401766 0.235419i
\(559\) 4.38929e6 + 1.35088e7i 0.0251281 + 0.0773362i
\(560\) 1.43642e8i 0.817933i
\(561\) −8.92221e7 + 5.78346e7i −0.505340 + 0.327566i
\(562\) −4.77877e7 −0.269220
\(563\) −1.20241e8 + 3.90686e7i −0.673794 + 0.218929i −0.625876 0.779922i \(-0.715259\pi\)
−0.0479177 + 0.998851i \(0.515259\pi\)
\(564\) 9.83619e7 + 1.08538e8i 0.548264 + 0.604984i
\(565\) −2.12329e8 + 1.54266e8i −1.17724 + 0.855314i
\(566\) 1.22924e8 + 3.99405e7i 0.677936 + 0.220275i
\(567\) 1.84550e8 8.50287e7i 1.01243 0.466462i
\(568\) −2.30799e7 + 1.67686e7i −0.125947 + 0.0915062i
\(569\) −1.68568e8 + 2.32014e8i −0.915035 + 1.25944i 0.0503828 + 0.998730i \(0.483956\pi\)
−0.965418 + 0.260708i \(0.916044\pi\)
\(570\) 2.34967e8 2.54604e7i 1.26877 0.137480i
\(571\) −1.02775e8 −0.552049 −0.276025 0.961151i \(-0.589017\pi\)
−0.276025 + 0.961151i \(0.589017\pi\)
\(572\) 9.59370e6 + 4.93740e6i 0.0512623 + 0.0263822i
\(573\) −9.42762e7 1.97223e7i −0.501116 0.104832i
\(574\) −2.58195e6 7.94643e6i −0.0136525 0.0420181i
\(575\) 7.26585e7 1.00006e8i 0.382193 0.526044i
\(576\) −7.23899e6 + 1.58744e6i −0.0378801 + 0.00830672i
\(577\) −6.60850e6 + 2.03389e7i −0.0344013 + 0.105876i −0.966783 0.255600i \(-0.917727\pi\)
0.932381 + 0.361476i \(0.117727\pi\)
\(578\) −5.33209e7 1.73250e7i −0.276130 0.0897201i
\(579\) −5.48247e7 1.22080e8i −0.282449 0.628939i
\(580\) 9.90393e6 + 7.19563e6i 0.0507602 + 0.0368795i
\(581\) 2.66341e8 8.65394e7i 1.35803 0.441251i
\(582\) −6.12161e7 1.28062e7i −0.310525 0.0649608i
\(583\) −1.93871e7 + 9.77925e6i −0.0978377 + 0.0493515i
\(584\) 2.12918e7i 0.106899i
\(585\) 2.52939e7 + 2.49408e6i 0.126342 + 0.0124579i
\(586\) 3.09485e7 + 2.24854e7i 0.153797 + 0.111740i
\(587\) −1.76594e8 2.43061e8i −0.873096 1.20171i −0.978286 0.207261i \(-0.933545\pi\)
0.105190 0.994452i \(-0.466455\pi\)
\(588\) 3.39106e7 + 1.94331e7i 0.166803 + 0.0955895i
\(589\) 1.03613e8 3.18890e8i 0.507073 1.56061i
\(590\) 2.52434e7 + 3.47445e7i 0.122911 + 0.169173i
\(591\) −1.71206e7 1.88918e7i −0.0829388 0.0915191i
\(592\) 2.12260e7 + 6.53268e7i 0.102306 + 0.314866i
\(593\) 2.18279e8i 1.04676i 0.852099 + 0.523380i \(0.175329\pi\)
−0.852099 + 0.523380i \(0.824671\pi\)
\(594\) −8.53121e7 4.28697e7i −0.407053 0.204546i
\(595\) −2.46765e8 −1.17147
\(596\) −1.80019e8 + 5.84918e7i −0.850316 + 0.276284i
\(597\) 5.07858e7 4.60244e7i 0.238682 0.216304i
\(598\) −1.82288e6 + 1.32440e6i −0.00852421 + 0.00619320i
\(599\) 1.38399e8 + 4.49685e7i 0.643950 + 0.209232i 0.612744 0.790281i \(-0.290066\pi\)
0.0312051 + 0.999513i \(0.490066\pi\)
\(600\) −1.79364e8 + 3.12989e8i −0.830390 + 1.44902i
\(601\) −1.77249e8 + 1.28779e8i −0.816509 + 0.593228i −0.915710 0.401839i \(-0.868371\pi\)
0.0992017 + 0.995067i \(0.468371\pi\)
\(602\) 7.27870e7 1.00183e8i 0.333629 0.459201i
\(603\) 2.66817e7 2.70595e8i 0.121692 1.23415i
\(604\) −2.72020e8 −1.23450
\(605\) −3.86424e8 3.13811e6i −1.74501 0.0141711i
\(606\) −8.73773e6 + 4.17680e7i −0.0392628 + 0.187683i
\(607\) 6.52798e7 + 2.00911e8i 0.291886 + 0.898332i 0.984250 + 0.176783i \(0.0565692\pi\)
−0.692364 + 0.721548i \(0.743431\pi\)
\(608\) −2.13798e8 + 2.94268e8i −0.951247 + 1.30928i
\(609\) −1.04206e7 + 4.67979e6i −0.0461363 + 0.0207193i
\(610\) 9.14623e7 2.81492e8i 0.402952 1.24016i
\(611\) −1.62599e7 5.28317e6i −0.0712844 0.0231617i
\(612\) −2.34321e7 1.06854e8i −0.102225 0.466163i
\(613\) −2.06810e8 1.50256e8i −0.897820 0.652305i 0.0400849 0.999196i \(-0.487237\pi\)
−0.937905 + 0.346892i \(0.887237\pi\)
\(614\) −290716. + 94459.5i −0.00125593 + 0.000408075i
\(615\) 7.23126e6 3.45668e7i 0.0310877 0.148605i
\(616\) −3.24303e7 2.10279e8i −0.138742 0.899610i
\(617\) 2.58334e8i 1.09983i −0.835221 0.549915i \(-0.814660\pi\)
0.835221 0.549915i \(-0.185340\pi\)
\(618\) 1.56556e7 + 1.44480e8i 0.0663289 + 0.612130i
\(619\) 2.16921e7 + 1.57602e7i 0.0914597 + 0.0664494i 0.632575 0.774499i \(-0.281998\pi\)
−0.541116 + 0.840948i \(0.681998\pi\)
\(620\) 1.98022e8 + 2.72554e8i 0.830880 + 1.14361i
\(621\) −6.11608e7 + 4.53441e7i −0.255387 + 0.189341i
\(622\) 3.75240e7 1.15487e8i 0.155933 0.479913i
\(623\) 3.01645e8 + 4.15179e8i 1.24748 + 1.71701i
\(624\) −5.50736e6 + 4.99102e6i −0.0226668 + 0.0205417i
\(625\) 8.58408e7 + 2.64191e8i 0.351604 + 1.08213i
\(626\) 1.83263e7i 0.0747055i
\(627\) −3.82302e8 + 1.02092e8i −1.55097 + 0.414180i
\(628\) 2.02286e8 0.816745
\(629\) 1.12226e8 3.64644e7i 0.450963 0.146527i
\(630\) −1.12025e8 1.91182e8i −0.448015 0.764583i
\(631\) −1.05284e7 + 7.64930e6i −0.0419056 + 0.0304462i −0.608541 0.793523i \(-0.708245\pi\)
0.566635 + 0.823969i \(0.308245\pi\)
\(632\) 2.88634e8 + 9.37828e7i 1.14339 + 0.371511i
\(633\) 3.17956e8 + 1.82211e8i 1.25359 + 0.718394i
\(634\) −1.37943e8 + 1.00221e8i −0.541291 + 0.393271i
\(635\) −1.58581e8 + 2.18268e8i −0.619343 + 0.852452i
\(636\) −2.40663e6 2.22101e7i −0.00935488 0.0863334i
\(637\) −4.56187e6 −0.0176492
\(638\) 4.77259e6 + 2.45621e6i 0.0183777 + 0.00945811i
\(639\) 1.99399e7 4.55727e7i 0.0764225 0.174663i
\(640\) −1.40013e8 4.30916e8i −0.534107 1.64381i
\(641\) 2.21951e8 3.05489e8i 0.842719 1.15990i −0.142702 0.989766i \(-0.545579\pi\)
0.985420 0.170137i \(-0.0544210\pi\)
\(642\) 6.60204e7 + 1.47010e8i 0.249502 + 0.555573i
\(643\) 6.63646e7 2.04249e8i 0.249634 0.768295i −0.745206 0.666835i \(-0.767649\pi\)
0.994840 0.101460i \(-0.0323513\pi\)
\(644\) −7.13391e7 2.31795e7i −0.267098 0.0867853i
\(645\) 4.77458e8 2.14421e8i 1.77933 0.799076i
\(646\) 9.60538e7 + 6.97871e7i 0.356301 + 0.258868i
\(647\) −3.34219e8 + 1.08594e8i −1.23401 + 0.400954i −0.852165 0.523273i \(-0.824711\pi\)
−0.381844 + 0.924227i \(0.624711\pi\)
\(648\) 1.63190e8 1.50784e8i 0.599749 0.554155i
\(649\) −5.06369e7 5.10498e7i −0.185239 0.186750i
\(650\) 1.86152e7i 0.0677841i
\(651\) −3.12535e8 + 3.38656e7i −1.13281 + 0.122748i
\(652\) 1.05807e8 + 7.68731e7i 0.381742 + 0.277352i
\(653\) −1.93093e8 2.65770e8i −0.693471 0.954480i −0.999997 0.00261804i \(-0.999167\pi\)
0.306526 0.951862i \(-0.400833\pi\)
\(654\) −1.95926e6 + 3.41889e6i −0.00700420 + 0.0122223i
\(655\) −2.64934e8 + 8.15384e8i −0.942789 + 2.90161i
\(656\) 6.07007e6 + 8.35473e6i 0.0215022 + 0.0295952i
\(657\) −1.87694e7 3.20318e7i −0.0661841 0.112950i
\(658\) 4.60593e7 + 1.41756e8i 0.161674 + 0.497581i
\(659\) 6.06012e7i 0.211751i 0.994379 + 0.105875i \(0.0337645\pi\)
−0.994379 + 0.105875i \(0.966236\pi\)
\(660\) 1.42793e8 3.71054e8i 0.496680 1.29064i
\(661\) −5.22966e7 −0.181080 −0.0905398 0.995893i \(-0.528859\pi\)
−0.0905398 + 0.995893i \(0.528859\pi\)
\(662\) 1.63735e8 5.32009e7i 0.564376 0.183377i
\(663\) 8.57415e6 + 9.46117e6i 0.0294205 + 0.0324642i
\(664\) 2.47738e8 1.79992e8i 0.846231 0.614822i
\(665\) −8.73395e8 2.83783e8i −2.96993 0.964988i
\(666\) 7.91986e7 + 7.03934e7i 0.268099 + 0.238292i
\(667\) 3.46277e6 2.51585e6i 0.0116693 0.00847827i
\(668\) 1.80097e7 2.47882e7i 0.0604194 0.0831602i
\(669\) 2.55825e8 2.77206e7i 0.854406 0.0925815i
\(670\) −2.96515e8 −0.985877
\(671\) −7.95072e7 + 4.89127e8i −0.263172 + 1.61903i
\(672\) 3.33798e8 + 6.98296e7i 1.09996 + 0.230108i
\(673\) 3.37658e7 + 1.03920e8i 0.110773 + 0.340923i 0.991042 0.133552i \(-0.0426382\pi\)
−0.880269 + 0.474474i \(0.842638\pi\)
\(674\) −5.15954e7 + 7.10150e7i −0.168512 + 0.231937i
\(675\) −6.07005e6 6.28983e8i −0.0197370 2.04516i
\(676\) −7.52488e7 + 2.31592e8i −0.243590 + 0.749693i
\(677\) 1.95576e8 + 6.35465e7i 0.630303 + 0.204798i 0.606709 0.794924i \(-0.292489\pi\)
0.0235936 + 0.999722i \(0.492489\pi\)
\(678\) −4.85024e7 1.08002e8i −0.155623 0.346531i
\(679\) 1.96602e8 + 1.42840e8i 0.628027 + 0.456289i
\(680\) −2.56622e8 + 8.33814e7i −0.816143 + 0.265181i
\(681\) −1.82931e8 3.82685e7i −0.579223 0.121172i
\(682\) 1.04024e8 + 1.04873e8i 0.327931 + 0.330604i
\(683\) 2.76878e8i 0.869015i 0.900668 + 0.434507i \(0.143077\pi\)
−0.900668 + 0.434507i \(0.856923\pi\)
\(684\) 3.99490e7 4.05146e8i 0.124835 1.26603i
\(685\) −1.19276e8 8.66588e7i −0.371091 0.269613i
\(686\) −7.29835e7 1.00453e8i −0.226075 0.311165i
\(687\) 9.17070e7 + 5.25544e7i 0.282834 + 0.162084i
\(688\) −4.72962e7 + 1.45563e8i −0.145232 + 0.446977i
\(689\) 1.53266e6 + 2.10953e6i 0.00468585 + 0.00644952i
\(690\) 5.57539e7 + 6.15218e7i 0.169718 + 0.187276i
\(691\) −1.63747e8 5.03962e8i −0.496295 1.52744i −0.814929 0.579561i \(-0.803224\pi\)
0.318634 0.947878i \(-0.396776\pi\)
\(692\) 1.72249e8i 0.519804i
\(693\) 2.34157e8 + 2.87760e8i 0.703569 + 0.864632i
\(694\) 2.08443e8 0.623605
\(695\) 4.23870e8 1.37724e8i 1.26264 0.410255i
\(696\) −9.25560e6 + 8.38785e6i −0.0274522 + 0.0248784i
\(697\) 1.43527e7 1.04279e7i 0.0423873 0.0307962i
\(698\) −1.97307e8 6.41088e7i −0.580197 0.188517i
\(699\) −6.91250e7 + 1.20622e8i −0.202397 + 0.353180i
\(700\) 5.01357e8 3.64257e8i 1.46168 1.06197i
\(701\) 2.46337e8 3.39053e8i 0.715114 0.984269i −0.284558 0.958659i \(-0.591847\pi\)
0.999672 0.0256108i \(-0.00815305\pi\)
\(702\) −3.43763e6 + 1.09380e7i −0.00993682 + 0.0316174i
\(703\) 4.39145e8 1.26399
\(704\) −6.09391e6 1.20810e7i −0.0174654 0.0346246i
\(705\) −1.28998e8 + 6.16635e8i −0.368143 + 1.75979i
\(706\) −2.06770e7 6.36372e7i −0.0587588 0.180841i
\(707\) 9.74602e7 1.34142e8i 0.275784 0.379584i
\(708\) 6.74848e7 3.03067e7i 0.190154 0.0853961i
\(709\) 2.93434e7 9.03097e7i 0.0823326 0.253394i −0.901413 0.432960i \(-0.857469\pi\)
0.983746 + 0.179566i \(0.0574693\pi\)
\(710\) −5.15910e7 1.67629e7i −0.144145 0.0468354i
\(711\) −5.16900e8 + 1.13351e8i −1.43813 + 0.315367i
\(712\) 4.53983e8 + 3.29838e8i 1.25777 + 0.913820i
\(713\) 1.12026e8 3.63993e7i 0.309064 0.100421i
\(714\) 2.27935e7 1.08957e8i 0.0626204 0.299337i
\(715\) 7.07323e6 + 4.58631e7i 0.0193508 + 0.125472i
\(716\) 2.24605e8i 0.611901i
\(717\) 2.96648e7 + 2.73767e8i 0.0804793 + 0.742719i
\(718\) −4.77924e7 3.47232e7i −0.129118 0.0938095i
\(719\) 4.15239e8 + 5.71528e8i 1.11715 + 1.53763i 0.810438 + 0.585824i \(0.199229\pi\)
0.306712 + 0.951802i \(0.400771\pi\)
\(720\) 2.04702e8 + 1.81944e8i 0.548435 + 0.487461i
\(721\) 1.74498e8 5.37049e8i 0.465569 1.43287i
\(722\) 1.58936e8 + 2.18756e8i 0.422289 + 0.581230i
\(723\) 1.94651e8 1.76402e8i 0.515041 0.466753i
\(724\) −119441. 367601.i −0.000314729 0.000968637i
\(725\) 3.53617e7i 0.0927939i
\(726\) 3.70793e7 1.70333e8i 0.0968995 0.445131i
\(727\) 2.90755e8 0.756700 0.378350 0.925663i \(-0.376492\pi\)
0.378350 + 0.925663i \(0.376492\pi\)
\(728\) −2.42995e7 + 7.89539e6i −0.0629801 + 0.0204635i
\(729\) −1.12586e8 + 3.70701e8i −0.290605 + 0.956843i
\(730\) −3.27537e7 + 2.37969e7i −0.0841960 + 0.0611720i
\(731\) 2.50064e8 + 8.12508e7i 0.640176 + 0.208006i
\(732\) −4.42350e8 2.53497e8i −1.12780 0.646309i
\(733\) −3.44314e8 + 2.50158e8i −0.874263 + 0.635190i −0.931728 0.363158i \(-0.881699\pi\)
0.0574642 + 0.998348i \(0.481699\pi\)
\(734\) −1.36534e8 + 1.87923e8i −0.345265 + 0.475217i
\(735\) 1.81086e7 + 1.67119e8i 0.0456062 + 0.420886i
\(736\) −1.27780e8 −0.320501
\(737\) 4.90644e8 7.56696e7i 1.22564 0.189025i
\(738\) 1.45948e7 + 6.38582e6i 0.0363102 + 0.0158872i
\(739\) 1.64586e8 + 5.06545e8i 0.407813 + 1.25512i 0.918524 + 0.395366i \(0.129382\pi\)
−0.510711 + 0.859752i \(0.670618\pi\)
\(740\) −2.59351e8 + 3.56966e8i −0.640018 + 0.880909i
\(741\) 1.94667e7 + 4.33472e7i 0.0478452 + 0.106538i
\(742\) 7.02478e6 2.16201e7i 0.0171957 0.0529231i
\(743\) −1.94701e8 6.32621e7i −0.474680 0.154233i 0.0618998 0.998082i \(-0.480284\pi\)
−0.536580 + 0.843849i \(0.680284\pi\)
\(744\) −3.13576e8 + 1.40824e8i −0.761420 + 0.341945i
\(745\) −6.58613e8 4.78510e8i −1.59280 1.15724i
\(746\) −3.49295e8 + 1.13493e8i −0.841348 + 0.273371i
\(747\) −2.14034e8 + 4.89173e8i −0.513476 + 1.17355i
\(748\) 1.78327e8 8.99519e7i 0.426100 0.214934i
\(749\) 6.26188e8i 1.49025i
\(750\) −3.48518e8 + 3.77646e7i −0.826117 + 0.0895161i
\(751\) −3.66505e8 2.66282e8i −0.865287 0.628668i 0.0640309 0.997948i \(-0.479604\pi\)
−0.929318 + 0.369280i \(0.879604\pi\)
\(752\) −1.08284e8 1.49040e8i −0.254630 0.350468i
\(753\) −1.12723e8 + 1.96700e8i −0.264014 + 0.460702i
\(754\) 199181. 613017.i 0.000464659 0.00143007i
\(755\) −6.87668e8 9.46494e8i −1.59786 2.19926i
\(756\) −3.61855e8 + 1.21447e8i −0.837471 + 0.281074i
\(757\) −1.82178e8 5.60687e8i −0.419961 1.29251i −0.907737 0.419539i \(-0.862192\pi\)
0.487776 0.872969i \(-0.337808\pi\)
\(758\) 2.74316e7i 0.0629860i
\(759\) −1.07956e8 8.75721e7i −0.246901 0.200281i
\(760\) −1.00417e9 −2.28754
\(761\) 1.96925e8 6.39848e7i 0.446835 0.145185i −0.0769520 0.997035i \(-0.524519\pi\)
0.523787 + 0.851849i \(0.324519\pi\)
\(762\) −8.17268e7 9.01818e7i −0.184714 0.203823i
\(763\) 1.23872e7 8.99980e6i 0.0278868 0.0202609i
\(764\) 1.72071e8 + 5.59092e7i 0.385858 + 0.125373i
\(765\) 3.12564e8 3.51661e8i 0.698159 0.785488i
\(766\) −6.97810e7 + 5.06988e7i −0.155257 + 0.112801i
\(767\) −5.07530e6 + 6.98555e6i −0.0112480 + 0.0154815i
\(768\) 2.20665e8 2.39108e7i 0.487136 0.0527849i
\(769\) 2.79594e8 0.614822 0.307411 0.951577i \(-0.400537\pi\)
0.307411 + 0.951577i \(0.400537\pi\)
\(770\) 2.87232e8 2.84909e8i 0.629159 0.624070i
\(771\) 2.35609e7 + 4.92886e6i 0.0514077 + 0.0107543i
\(772\) 7.76818e7 + 2.39080e8i 0.168837 + 0.519626i
\(773\) 1.37905e8 1.89811e8i 0.298568 0.410943i −0.633206 0.773984i \(-0.718261\pi\)
0.931773 + 0.363040i \(0.118261\pi\)
\(774\) 5.05735e7 + 2.30624e8i 0.109069 + 0.497372i
\(775\) −3.00719e8 + 9.25517e8i −0.646034 + 1.98829i
\(776\) 2.52721e8 + 8.21139e7i 0.540823 + 0.175724i
\(777\) −1.68673e8 3.75590e8i −0.359569 0.800664i
\(778\) −1.68445e8 1.22382e8i −0.357700 0.259884i
\(779\) 6.27920e7 2.04024e7i 0.132829 0.0431587i
\(780\) −4.67320e7 9.77619e6i −0.0984761 0.0206009i
\(781\) 8.96455e7 + 1.45718e7i 0.188181 + 0.0305887i
\(782\) 4.17094e7i 0.0872195i
\(783\) 6.53018e6 2.07780e7i 0.0136032 0.0432830i
\(784\) −3.97679e7 2.88931e7i −0.0825249 0.0599578i
\(785\) 5.11380e8 + 7.03854e8i 1.05715 + 1.45504i
\(786\) −3.35555e8 1.92296e8i −0.691029 0.396007i
\(787\) 7.07075e7 2.17615e8i 0.145058 0.446442i −0.851961 0.523606i \(-0.824586\pi\)
0.997018 + 0.0771638i \(0.0245864\pi\)
\(788\) 2.81501e7 + 3.87453e7i 0.0575309 + 0.0791844i
\(789\) 8.79097e6 + 9.70043e6i 0.0178981 + 0.0197497i
\(790\) 1.78326e8 + 5.48830e8i 0.361687 + 1.11316i
\(791\) 4.60034e8i 0.929523i
\(792\) 3.40744e8 + 2.20134e8i 0.685887 + 0.443109i
\(793\) 5.95079e7 0.119331
\(794\) 3.79322e7 1.23249e7i 0.0757786 0.0246220i
\(795\) 7.11961e7 6.45212e7i 0.141695 0.128411i
\(796\) −1.04157e8 + 7.56742e7i −0.206513 + 0.150040i
\(797\) −1.65547e8 5.37896e7i −0.327000 0.106249i 0.140916 0.990021i \(-0.454995\pi\)
−0.467916 + 0.883773i \(0.654995\pi\)
\(798\) 2.05977e8 3.59429e8i 0.405332 0.707300i
\(799\) −2.56037e8 + 1.86022e8i −0.501953 + 0.364690i
\(800\) 6.20510e8 8.54058e8i 1.21193 1.66808i
\(801\) −9.73745e8 9.60151e7i −1.89473 0.186828i
\(802\) 3.53231e8 0.684757
\(803\) 4.81247e7 4.77355e7i 0.0929440 0.0921923i
\(804\) −1.04586e8 + 4.99940e8i −0.201236 + 0.961944i
\(805\) −9.96928e7 3.06823e8i −0.191107 0.588166i
\(806\) 1.04263e7 1.43505e7i 0.0199124 0.0274071i
\(807\) −5.38534e8 + 2.41850e8i −1.02469 + 0.460177i
\(808\) 5.60267e7 1.72432e8i 0.106209 0.326877i
\(809\) −8.08144e8 2.62582e8i −1.52631 0.495929i −0.578751 0.815504i \(-0.696460\pi\)
−0.947561 + 0.319576i \(0.896460\pi\)
\(810\) 4.14346e8 + 8.25146e7i 0.779666 + 0.155266i
\(811\) −5.09848e8 3.70426e8i −0.955825 0.694447i −0.00364741 0.999993i \(-0.501161\pi\)
−0.952177 + 0.305546i \(0.901161\pi\)
\(812\) 2.04077e7 6.63086e6i 0.0381176 0.0123852i
\(813\) −5.70777e7 + 2.72842e8i −0.106217 + 0.507738i
\(814\) −8.85289e7 + 1.72018e8i −0.164139 + 0.318933i
\(815\) 5.62491e8i 1.03906i
\(816\) 1.48214e7 + 1.36783e8i 0.0272785 + 0.251745i
\(817\) 7.91634e8 + 5.75156e8i 1.45164 + 1.05468i
\(818\) −1.21161e8 1.66764e8i −0.221362 0.304678i
\(819\) 2.95967e7 3.32988e7i 0.0538755 0.0606145i
\(820\) −2.04994e7 + 6.30906e7i −0.0371791 + 0.114426i
\(821\) 2.46244e8 + 3.38925e8i 0.444975 + 0.612455i 0.971309 0.237823i \(-0.0764337\pi\)
−0.526334 + 0.850278i \(0.676434\pi\)
\(822\) 4.92810e7 4.46607e7i 0.0887286 0.0804099i
\(823\) 1.66639e8 + 5.12862e8i 0.298935 + 0.920027i 0.981871 + 0.189549i \(0.0607027\pi\)
−0.682936 + 0.730478i \(0.739297\pi\)
\(824\) 6.17464e8i 1.10365i
\(825\) 1.10956e9 2.96303e8i 1.97601 0.527684i
\(826\) 7.52776e7 0.133575
\(827\) −2.11579e7 + 6.87462e6i −0.0374073 + 0.0121544i −0.327661 0.944795i \(-0.606260\pi\)
0.290254 + 0.956950i \(0.406260\pi\)
\(828\) 1.23394e8 7.23042e7i 0.217372 0.127372i
\(829\) 4.95978e8 3.60349e8i 0.870560 0.632499i −0.0601769 0.998188i \(-0.519166\pi\)
0.930737 + 0.365689i \(0.119166\pi\)
\(830\) 5.53773e8 + 1.79932e8i 0.968496 + 0.314683i
\(831\) −4.08131e8 2.33887e8i −0.711208 0.407571i
\(832\) −1.31454e6 + 955073.i −0.00228247 + 0.00165831i
\(833\) −4.96359e7 + 6.83179e7i −0.0858738 + 0.118195i
\(834\) 2.16583e7 + 1.99878e8i 0.0373359 + 0.344562i
\(835\) 1.31779e8 0.226354
\(836\) 7.34613e8 1.13296e8i 1.25730 0.193907i
\(837\) 3.47611e8 4.88286e8i 0.592812 0.832717i
\(838\) 3.50434e7 + 1.07853e8i 0.0595490 + 0.183273i
\(839\) 2.48132e8 3.41525e8i 0.420144 0.578278i −0.545512 0.838103i \(-0.683665\pi\)
0.965656 + 0.259825i \(0.0836648\pi\)
\(840\) 3.85697e8 + 8.58843e8i 0.650741 + 1.44903i
\(841\) 1.83432e8 5.64546e8i 0.308381 0.949099i
\(842\) 1.99544e8 + 6.48359e7i 0.334275 + 0.108612i
\(843\) −3.22963e8 + 1.45039e8i −0.539101 + 0.242104i
\(844\) −5.56915e8 4.04622e8i −0.926321 0.673011i
\(845\) −9.96056e8 + 3.23638e8i −1.65087 + 0.536401i
\(846\) −2.60355e8 1.13916e8i −0.429987 0.188137i
\(847\) −4.02575e8 + 5.44739e8i −0.662517 + 0.896476i
\(848\) 2.80970e7i 0.0460757i
\(849\) 9.51982e8 1.03155e8i 1.55563 0.168564i
\(850\) −2.78778e8 2.02544e8i −0.453944 0.329809i
\(851\) 9.06784e7 + 1.24808e8i 0.147135 + 0.202513i
\(852\) −4.64601e7 + 8.10725e7i −0.0751211 + 0.131086i
\(853\) 7.60262e7 2.33984e8i 0.122494 0.376999i −0.870942 0.491386i \(-0.836490\pi\)
0.993436 + 0.114387i \(0.0364904\pi\)
\(854\) −3.04941e8 4.19716e8i −0.489601 0.673878i
\(855\) 1.51070e9 8.85210e8i 2.41702 1.41628i
\(856\) −2.11588e8 6.51201e8i −0.337341 1.03823i
\(857\) 5.31034e8i 0.843684i 0.906669 + 0.421842i \(0.138616\pi\)
−0.906669 + 0.421842i \(0.861384\pi\)
\(858\) −2.09039e7 1.11321e6i −0.0330952 0.00176244i
\(859\) 9.75882e8 1.53964 0.769818 0.638264i \(-0.220347\pi\)
0.769818 + 0.638264i \(0.220347\pi\)
\(860\) −9.35048e8 + 3.03816e8i −1.47007 + 0.477655i
\(861\) −4.15676e7 4.58680e7i −0.0651247 0.0718621i
\(862\) −3.41588e7 + 2.48179e7i −0.0533312 + 0.0387474i
\(863\) −9.12434e8 2.96468e8i −1.41961 0.461259i −0.504131 0.863627i \(-0.668187\pi\)
−0.915478 + 0.402368i \(0.868187\pi\)
\(864\) −5.22318e8 + 3.87242e8i −0.809830 + 0.600401i
\(865\) 5.99343e8 4.35448e8i 0.926034 0.672803i
\(866\) 1.30383e8 1.79456e8i 0.200755 0.276315i
\(867\) −4.12941e8 + 4.47453e7i −0.633623 + 0.0686579i
\(868\) 5.90517e8 0.902969
\(869\) −4.35135e8 8.62642e8i −0.663078 1.31453i
\(870\) −2.32478e7 4.86337e6i −0.0353041 0.00738550i
\(871\) −1.84223e7 5.66980e7i −0.0278798 0.0858051i
\(872\) 9.84095e6 1.35449e7i 0.0148418 0.0204280i
\(873\) −4.52584e8 + 9.92472e7i −0.680231 + 0.149168i
\(874\) −4.79665e7 + 1.47626e8i −0.0718461 + 0.221120i
\(875\) 1.29548e9 + 4.20926e8i 1.93378 + 0.628322i
\(876\) 2.85701e7 + 6.36180e7i 0.0425011 + 0.0946385i
\(877\) 9.61188e8 + 6.98344e8i 1.42498 + 1.03531i 0.990924 + 0.134426i \(0.0429189\pi\)
0.434059 + 0.900885i \(0.357081\pi\)
\(878\) −2.45815e8 + 7.98700e7i −0.363182 + 0.118005i
\(879\) 2.77404e8 + 5.80321e7i 0.408457 + 0.0854480i
\(880\) −2.28818e8 + 4.44609e8i −0.335770 + 0.652424i
\(881\) 4.64513e7i 0.0679314i 0.999423 + 0.0339657i \(0.0108137\pi\)
−0.999423 + 0.0339657i \(0.989186\pi\)
\(882\) −7.54629e7 7.44094e6i −0.109984 0.0108448i
\(883\) −8.37482e8 6.08467e8i −1.21645 0.883801i −0.220648 0.975354i \(-0.570817\pi\)
−0.995800 + 0.0915524i \(0.970817\pi\)
\(884\) −1.40978e7 1.94039e7i −0.0204077 0.0280888i
\(885\) 2.76054e8 + 1.58198e8i 0.398258 + 0.228230i
\(886\) −1.82492e8 + 5.61652e8i −0.262387 + 0.807544i
\(887\) −1.88792e8 2.59850e8i −0.270529 0.372351i 0.652039 0.758185i \(-0.273914\pi\)
−0.922568 + 0.385834i \(0.873914\pi\)
\(888\) −3.02322e8 3.33598e8i −0.431748 0.476414i
\(889\) 1.46135e8 + 4.49756e8i 0.207993 + 0.640136i
\(890\) 1.06702e9i 1.51357i
\(891\) −7.06677e8 3.07975e7i −0.999052 0.0435394i
\(892\) −4.83366e8 −0.681054
\(893\) −1.12014e9 + 3.63956e8i −1.57296 + 0.511087i
\(894\) 2.72118e8 2.46606e8i 0.380843 0.345137i
\(895\) 7.81516e8 5.67804e8i 1.09011 0.792008i
\(896\) −7.55318e8 2.45418e8i −1.05004 0.341179i
\(897\) −8.29991e6 + 1.44833e7i −0.0114999 + 0.0200673i
\(898\) 1.28063e8 9.30430e7i 0.176845 0.128486i
\(899\) −1.98059e7 + 2.72605e7i −0.0272594 + 0.0375193i
\(900\) −1.15945e8 + 1.17586e9i −0.159046 + 1.61298i
\(901\) 4.82682e7 0.0659913
\(902\) −4.66667e6 + 2.87092e7i −0.00635898 + 0.0391203i
\(903\) 1.87854e8 8.97979e8i 0.255128 1.21956i
\(904\) 1.55445e8 + 4.78410e8i 0.210412 + 0.647582i
\(905\) 977123. 1.34489e6i 0.00131827 0.00181444i
\(906\) 4.81437e8 2.16208e8i 0.647374 0.290728i
\(907\) 8.63415e7 2.65732e8i 0.115717 0.356141i −0.876379 0.481622i \(-0.840048\pi\)
0.992096 + 0.125482i \(0.0400477\pi\)
\(908\) 3.33882e8 + 1.08485e8i 0.446000 + 0.144914i
\(909\) 6.77168e7 + 3.08800e8i 0.0901581 + 0.411136i
\(910\) −3.93042e7 2.85562e7i −0.0521573 0.0378945i
\(911\) 1.28587e9 4.17806e8i 1.70076 0.552611i 0.712009 0.702171i \(-0.247786\pi\)
0.988753 + 0.149560i \(0.0477857\pi\)
\(912\) −1.04843e8 + 5.01171e8i −0.138215 + 0.660696i
\(913\) −9.62248e8 1.56413e8i −1.26437 0.205523i
\(914\) 3.98382e8i 0.521748i
\(915\) −2.36220e8 2.18000e9i −0.308357 2.84573i
\(916\) −1.60629e8 1.16704e8i −0.208996 0.151844i
\(917\) 8.83308e8 + 1.21577e9i 1.14552 + 1.57668i
\(918\) 1.26402e8 + 1.70493e8i 0.163390 + 0.220383i
\(919\) −3.24415e8 + 9.98448e8i −0.417980 + 1.28641i 0.491579 + 0.870833i \(0.336420\pi\)
−0.909559 + 0.415576i \(0.863580\pi\)
\(920\) −2.07350e8 2.85393e8i −0.266281 0.366505i
\(921\) −1.67806e6 + 1.52073e6i −0.00214797 + 0.00194659i
\(922\) −1.72407e8 5.30615e8i −0.219970 0.676997i
\(923\) 1.09064e7i 0.0138700i
\(924\) −3.79059e8 5.84780e8i −0.480498 0.741270i
\(925\) −1.27454e9 −1.61038
\(926\) 2.28414e8 7.42161e7i 0.287667 0.0934685i
\(927\) 5.44314e8 + 9.28926e8i 0.683298 + 1.16612i
\(928\) 2.95724e7 2.14856e7i 0.0370034 0.0268846i
\(929\) 4.86695e8 + 1.58137e8i 0.607030 + 0.197236i 0.596373 0.802707i \(-0.296608\pi\)
0.0106564 + 0.999943i \(0.496608\pi\)
\(930\) −5.67104e8 3.24990e8i −0.705040 0.404037i
\(931\) −2.54247e8 + 1.84721e8i −0.315070 + 0.228912i
\(932\) 1.53501e8 2.11276e8i 0.189611 0.260977i
\(933\) −9.69134e7 8.94384e8i −0.119327 1.10123i
\(934\) −1.00909e8 −0.123848
\(935\) 7.63800e8 + 3.93090e8i 0.934425 + 0.480903i
\(936\) 1.95273e7 4.46295e7i 0.0238130 0.0544246i
\(937\) −3.60761e7 1.11031e8i −0.0438532 0.134966i 0.926733 0.375721i \(-0.122605\pi\)
−0.970586 + 0.240755i \(0.922605\pi\)
\(938\) −3.05494e8 + 4.20477e8i −0.370164 + 0.509488i
\(939\) −5.56218e7 1.23855e8i −0.0671813 0.149595i
\(940\) 3.65688e8 1.12547e9i 0.440278 1.35504i
\(941\) −5.12587e8 1.66550e8i −0.615175 0.199883i −0.0151784 0.999885i \(-0.504832\pi\)
−0.599997 + 0.800002i \(0.704832\pi\)
\(942\) −3.58018e8 + 1.60782e8i −0.428304 + 0.192346i
\(943\) 1.87643e7 + 1.36331e7i 0.0223768 + 0.0162577i
\(944\) −8.84874e7 + 2.87513e7i −0.105188 + 0.0341776i
\(945\) −1.33735e9 9.52059e8i −1.58471 1.12815i
\(946\) −3.84883e8 + 1.94143e8i −0.454627 + 0.229324i
\(947\) 1.46211e9i 1.72159i 0.508955 + 0.860793i \(0.330032\pi\)
−0.508955 + 0.860793i \(0.669968\pi\)
\(948\) 9.88254e8 1.07085e8i 1.15996 0.125691i
\(949\) −6.58528e6 4.78449e6i −0.00770506 0.00559805i
\(950\) −7.53774e8 1.03748e9i −0.879165 1.21007i
\(951\) −6.28079e8 + 1.09599e9i −0.730252 + 1.27428i
\(952\) −1.46153e8 + 4.49812e8i −0.169393 + 0.521339i
\(953\) −8.82706e8 1.21494e9i −1.01985 1.40371i −0.912307 0.409507i \(-0.865701\pi\)
−0.107546 0.994200i \(-0.534299\pi\)
\(954\) 2.19125e7 + 3.73959e7i 0.0252375 + 0.0430704i
\(955\) 2.40460e8 + 7.40061e8i 0.276079 + 0.849684i
\(956\) 5.17267e8i 0.592027i
\(957\) 3.97094e7 + 2.11467e6i 0.0453061 + 0.00241272i
\(958\) 4.99966e8 0.568648
\(959\) −2.45775e8 + 7.98572e7i −0.278665 + 0.0905437i
\(960\) 4.02062e7 + 4.43656e7i 0.0454443 + 0.0501456i
\(961\) −3.21978e7 + 2.33931e7i −0.0362791 + 0.0263583i
\(962\) 2.20949e7 + 7.17905e6i 0.0248180 + 0.00806384i
\(963\) 8.92372e8 + 7.93159e8i 0.999233 + 0.888140i
\(964\) −3.99210e8 + 2.90043e8i −0.445625 + 0.323766i
\(965\) −6.35500e8 + 8.74690e8i −0.707186 + 0.973357i
\(966\) 1.44684e8 1.56776e7i 0.160505 0.0173920i
\(967\) −2.39011e8 −0.264325 −0.132162 0.991228i \(-0.542192\pi\)
−0.132162 + 0.991228i \(0.542192\pi\)
\(968\) −2.34590e8 + 7.02529e8i −0.258632 + 0.774530i
\(969\) 8.60969e8 + 1.80112e8i 0.946273 + 0.197957i
\(970\) 1.56137e8 + 4.80541e8i 0.171077 + 0.526521i
\(971\) −7.14535e8 + 9.83473e8i −0.780487 + 1.07425i 0.214741 + 0.976671i \(0.431109\pi\)
−0.995228 + 0.0975775i \(0.968891\pi\)
\(972\) 2.85271e8 6.69505e8i 0.310641 0.729046i
\(973\) 2.41405e8 7.42968e8i 0.262064 0.806551i
\(974\) −3.74722e8 1.21754e8i −0.405538 0.131767i
\(975\) −5.64985e7 1.25807e8i −0.0609569 0.135735i
\(976\) 5.18757e8 + 3.76899e8i 0.557975 + 0.405392i
\(977\) 3.71553e8 1.20725e8i 0.398417 0.129453i −0.102954 0.994686i \(-0.532829\pi\)
0.501370 + 0.865233i \(0.332829\pi\)
\(978\) −2.48364e8 5.19569e7i −0.265504 0.0555426i
\(979\) −2.72299e8 1.76560e9i −0.290201 1.88167i
\(980\) 3.15761e8i 0.335491i
\(981\) −2.86468e6 + 2.90524e7i −0.00303437 + 0.0307733i
\(982\) −1.68085e8 1.22121e8i −0.177498 0.128960i
\(983\) −4.23112e8 5.82364e8i −0.445446 0.613103i 0.525966 0.850506i \(-0.323704\pi\)
−0.971411 + 0.237402i \(0.923704\pi\)
\(984\) −5.87268e7 3.36545e7i −0.0616383 0.0353230i
\(985\) −6.36507e7 + 1.95897e8i −0.0666031 + 0.204983i
\(986\) −7.01323e6 9.65289e6i −0.00731623 0.0100699i
\(987\) 7.41523e8 + 8.18236e8i 0.771211 + 0.850995i
\(988\) −2.75826e7 8.48906e7i −0.0285999 0.0880215i
\(989\) 3.43751e8i 0.355349i
\(990\) 4.21980e7 + 7.70209e8i 0.0434897 + 0.793785i
\(991\) −1.50206e8 −0.154335 −0.0771677 0.997018i \(-0.524588\pi\)
−0.0771677 + 0.997018i \(0.524588\pi\)
\(992\) 9.56708e8 3.10853e8i 0.980041 0.318435i
\(993\) 9.45104e8 8.56497e8i 0.965233 0.874738i
\(994\) −7.69241e7 + 5.58886e7i −0.0783255 + 0.0569068i
\(995\) −5.26617e8 1.71108e8i −0.534596 0.173701i
\(996\) 4.98700e8 8.70226e8i 0.504732 0.880752i
\(997\) 4.76479e8 3.46182e8i 0.480793 0.349316i −0.320840 0.947133i \(-0.603965\pi\)
0.801633 + 0.597817i \(0.203965\pi\)
\(998\) −4.20420e7 + 5.78659e7i −0.0422953 + 0.0582145i
\(999\) 7.48897e8 + 2.35366e8i 0.751148 + 0.236073i
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 33.7.h.a.5.13 yes 88
3.2 odd 2 inner 33.7.h.a.5.10 88
11.9 even 5 inner 33.7.h.a.20.10 yes 88
33.20 odd 10 inner 33.7.h.a.20.13 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.7.h.a.5.10 88 3.2 odd 2 inner
33.7.h.a.5.13 yes 88 1.1 even 1 trivial
33.7.h.a.20.10 yes 88 11.9 even 5 inner
33.7.h.a.20.13 yes 88 33.20 odd 10 inner