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Properties

Label 74.8.f.b.9.3
Level $74$
Weight $8$
Character 74.9
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.3
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(-8.32711 + 47.2254i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-300.074 - 251.792i) q^{5} +383.631 q^{6} +(-303.488 - 254.657i) q^{7} +(256.000 + 443.405i) q^{8} +(-105.789 - 38.5041i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(-8.32711 + 47.2254i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-300.074 - 251.792i) q^{5} +383.631 q^{6} +(-303.488 - 254.657i) q^{7} +(256.000 + 443.405i) q^{8} +(-105.789 - 38.5041i) q^{9} +(-1566.88 + 2713.91i) q^{10} +(-3219.34 - 5576.06i) q^{11} +(-532.935 - 3022.43i) q^{12} +(207.811 - 75.6371i) q^{13} +(-1584.70 + 2744.79i) q^{14} +(14389.7 - 12074.4i) q^{15} +(3137.72 - 2632.86i) q^{16} +(12591.0 + 4582.74i) q^{17} +(-156.392 + 886.946i) q^{18} +(-8748.46 + 49615.0i) q^{19} +(23558.1 + 8574.46i) q^{20} +(14553.5 - 12211.8i) q^{21} +(-39458.5 + 33109.6i) q^{22} +(1788.29 - 3097.41i) q^{23} +(-23071.7 + 8397.42i) q^{24} +(13079.0 + 74174.7i) q^{25} +(-884.592 - 1532.16i) q^{26} +(-49738.3 + 86149.3i) q^{27} +(23826.1 + 8672.01i) q^{28} +(71144.6 + 123226. i) q^{29} +(-115118. - 96595.4i) q^{30} +111397. q^{31} +(-25101.7 - 21062.9i) q^{32} +(290140. - 105602. i) q^{33} +(18613.7 - 105564. i) q^{34} +(26948.4 + 152832. i) q^{35} +7205.03 q^{36} +(-163048. + 261433. i) q^{37} +403043. q^{38} +(1841.52 + 10443.8i) q^{39} +(34826.9 - 197513. i) q^{40} +(488103. - 177655. i) q^{41} +(-116428. - 97694.4i) q^{42} +904263. q^{43} +(315668. + 264877. i) q^{44} +(22049.6 + 38191.0i) q^{45} +(-26887.1 - 9786.09i) q^{46} +(470180. - 814376. i) q^{47} +(98209.6 + 170104. i) q^{48} +(-115752. - 656461. i) q^{49} +(566214. - 206085. i) q^{50} +(-321268. + 556452. i) q^{51} +(-10842.2 + 9097.68i) q^{52} +(-1.30764e6 + 1.09724e6i) q^{53} +(747820. + 272184. i) q^{54} +(-437968. + 2.48384e6i) q^{55} +(35223.1 - 199760. i) q^{56} +(-2.27024e6 - 826299. i) q^{57} +(871999. - 731694. i) q^{58} +(1.19893e6 - 1.00602e6i) q^{59} +(-601103. + 1.04114e6i) q^{60} +(-1.84795e6 + 672597. i) q^{61} +(-154751. - 877638. i) q^{62} +(22300.5 + 38625.5i) q^{63} +(-131072. + 227023. i) q^{64} +(-81403.6 - 29628.5i) q^{65} +(-1.23504e6 - 2.13915e6i) q^{66} +(2.24890e6 + 1.88705e6i) q^{67} -857538. q^{68} +(131385. + 110245. i) q^{69} +(1.16665e6 - 424624. i) q^{70} +(-636995. + 3.61258e6i) q^{71} +(-10009.1 - 56764.5i) q^{72} -588716. q^{73} +(2.28619e6 + 921392. i) q^{74} -3.61184e6 q^{75} +(-559901. - 3.17536e6i) q^{76} +(-442951. + 2.51210e6i) q^{77} +(79722.9 - 29016.8i) q^{78} +(-928283. - 778922. i) q^{79} -1.60448e6 q^{80} +(-3.84287e6 - 3.22455e6i) q^{81} +(-2.07771e6 - 3.59871e6i) q^{82} +(1.94636e6 + 708417. i) q^{83} +(-607942. + 1.05299e6i) q^{84} +(-2.62433e6 - 4.54547e6i) q^{85} +(-1.25619e6 - 7.12420e6i) q^{86} +(-6.41183e6 + 2.33371e6i) q^{87} +(1.64830e6 - 2.85494e6i) q^{88} +(2.89787e6 - 2.43160e6i) q^{89} +(270256. - 226771. i) q^{90} +(-82329.8 - 29965.6i) q^{91} +(-39748.2 + 225423. i) q^{92} +(-927616. + 5.26077e6i) q^{93} +(-7.06920e6 - 2.57298e6i) q^{94} +(1.51179e7 - 1.26854e7i) q^{95} +(1.20373e6 - 1.01005e6i) q^{96} +(-2.63919e6 + 4.57122e6i) q^{97} +(-5.01110e6 + 1.82389e6i) q^{98} +(125870. + 713845. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38919 − 7.87846i −0.122788 − 0.696364i
\(3\) −8.32711 + 47.2254i −0.178061 + 1.00984i 0.756489 + 0.654006i \(0.226913\pi\)
−0.934551 + 0.355830i \(0.884198\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) −300.074 − 251.792i −1.07358 − 0.900840i −0.0782068 − 0.996937i \(-0.524919\pi\)
−0.995372 + 0.0960977i \(0.969364\pi\)
\(6\) 383.631 0.725078
\(7\) −303.488 − 254.657i −0.334425 − 0.280616i 0.460075 − 0.887880i \(-0.347823\pi\)
−0.794500 + 0.607264i \(0.792267\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) −105.789 − 38.5041i −0.0483718 − 0.0176059i
\(10\) −1566.88 + 2713.91i −0.495490 + 0.858214i
\(11\) −3219.34 − 5576.06i −0.729277 − 1.26315i −0.957189 − 0.289463i \(-0.906523\pi\)
0.227912 − 0.973682i \(-0.426810\pi\)
\(12\) −532.935 − 3022.43i −0.0890307 − 0.504918i
\(13\) 207.811 − 75.6371i 0.0262342 − 0.00954845i −0.328870 − 0.944375i \(-0.606668\pi\)
0.355104 + 0.934827i \(0.384445\pi\)
\(14\) −1584.70 + 2744.79i −0.154348 + 0.267338i
\(15\) 14389.7 − 12074.4i 1.10086 − 0.923734i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) 12591.0 + 4582.74i 0.621567 + 0.226232i 0.633557 − 0.773696i \(-0.281594\pi\)
−0.0119897 + 0.999928i \(0.503817\pi\)
\(18\) −156.392 + 886.946i −0.00632066 + 0.0358462i
\(19\) −8748.46 + 49615.0i −0.292613 + 1.65949i 0.384134 + 0.923277i \(0.374500\pi\)
−0.676748 + 0.736215i \(0.736611\pi\)
\(20\) 23558.1 + 8574.46i 0.658470 + 0.239663i
\(21\) 14553.5 − 12211.8i 0.342925 − 0.287748i
\(22\) −39458.5 + 33109.6i −0.790063 + 0.662941i
\(23\) 1788.29 − 3097.41i 0.0306472 − 0.0530824i −0.850295 − 0.526306i \(-0.823577\pi\)
0.880942 + 0.473224i \(0.156910\pi\)
\(24\) −23071.7 + 8397.42i −0.340675 + 0.123996i
\(25\) 13079.0 + 74174.7i 0.167411 + 0.949436i
\(26\) −884.592 − 1532.16i −0.00987044 − 0.0170961i
\(27\) −49738.3 + 86149.3i −0.486315 + 0.842323i
\(28\) 23826.1 + 8672.01i 0.205117 + 0.0746563i
\(29\) 71144.6 + 123226.i 0.541688 + 0.938231i 0.998807 + 0.0488254i \(0.0155478\pi\)
−0.457120 + 0.889405i \(0.651119\pi\)
\(30\) −115118. − 96595.4i −0.778428 − 0.653179i
\(31\) 111397. 0.671596 0.335798 − 0.941934i \(-0.390994\pi\)
0.335798 + 0.941934i \(0.390994\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) 290140. − 105602.i 1.40543 − 0.511533i
\(34\) 18613.7 − 105564.i 0.0812189 − 0.460616i
\(35\) 26948.4 + 152832.i 0.106242 + 0.602527i
\(36\) 7205.03 0.0257381
\(37\) −163048. + 261433.i −0.529189 + 0.848504i
\(38\) 403043. 1.19154
\(39\) 1841.52 + 10443.8i 0.00497109 + 0.0281924i
\(40\) 34826.9 − 197513.i 0.0860409 − 0.487962i
\(41\) 488103. − 177655.i 1.10603 − 0.402563i 0.276496 − 0.961015i \(-0.410827\pi\)
0.829537 + 0.558452i \(0.188604\pi\)
\(42\) −116428. − 97694.4i −0.242484 − 0.203468i
\(43\) 904263. 1.73442 0.867211 − 0.497940i \(-0.165910\pi\)
0.867211 + 0.497940i \(0.165910\pi\)
\(44\) 315668. + 264877.i 0.558659 + 0.468770i
\(45\) 22049.6 + 38191.0i 0.0360709 + 0.0624766i
\(46\) −26887.1 − 9786.09i −0.0407278 − 0.0148237i
\(47\) 470180. − 814376.i 0.660575 − 1.14415i −0.319890 − 0.947455i \(-0.603646\pi\)
0.980465 − 0.196694i \(-0.0630207\pi\)
\(48\) 98209.6 + 170104.i 0.128177 + 0.222009i
\(49\) −115752. − 656461.i −0.140553 − 0.797118i
\(50\) 566214. − 206085.i 0.640598 − 0.233158i
\(51\) −321268. + 556452.i −0.339134 + 0.587398i
\(52\) −10842.2 + 9097.68i −0.0106931 + 0.00897261i
\(53\) −1.30764e6 + 1.09724e6i −1.20649 + 1.01236i −0.207068 + 0.978326i \(0.566392\pi\)
−0.999421 + 0.0340379i \(0.989163\pi\)
\(54\) 747820. + 272184.i 0.646277 + 0.235226i
\(55\) −437968. + 2.48384e6i −0.354955 + 2.01305i
\(56\) 35223.1 − 199760.i 0.0268022 − 0.152003i
\(57\) −2.27024e6 − 826299.i −1.62371 − 0.590983i
\(58\) 871999. − 731694.i 0.586838 − 0.492415i
\(59\) 1.19893e6 − 1.00602e6i 0.759994 − 0.637711i −0.178131 − 0.984007i \(-0.557005\pi\)
0.938125 + 0.346296i \(0.112561\pi\)
\(60\) −601103. + 1.04114e6i −0.359269 + 0.622272i
\(61\) −1.84795e6 + 672597.i −1.04240 + 0.379403i −0.805790 − 0.592201i \(-0.798259\pi\)
−0.236611 + 0.971604i \(0.576037\pi\)
\(62\) −154751. − 877638.i −0.0824638 − 0.467675i
\(63\) 22300.5 + 38625.5i 0.0112363 + 0.0194618i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) −81403.6 − 29628.5i −0.0367661 − 0.0133818i
\(66\) −1.23504e6 − 2.13915e6i −0.528783 − 0.915879i
\(67\) 2.24890e6 + 1.88705e6i 0.913499 + 0.766517i 0.972781 − 0.231724i \(-0.0744367\pi\)
−0.0592822 + 0.998241i \(0.518881\pi\)
\(68\) −857538. −0.330729
\(69\) 131385. + 110245.i 0.0481475 + 0.0404006i
\(70\) 1.16665e6 − 424624.i 0.406533 − 0.147966i
\(71\) −636995. + 3.61258e6i −0.211218 + 1.19788i 0.676131 + 0.736781i \(0.263655\pi\)
−0.887349 + 0.461098i \(0.847456\pi\)
\(72\) −10009.1 − 56764.5i −0.00316033 − 0.0179231i
\(73\) −588716. −0.177123 −0.0885617 − 0.996071i \(-0.528227\pi\)
−0.0885617 + 0.996071i \(0.528227\pi\)
\(74\) 2.28619e6 + 921392.i 0.655846 + 0.264322i
\(75\) −3.61184e6 −0.988585
\(76\) −559901. − 3.17536e6i −0.146307 − 0.829746i
\(77\) −442951. + 2.51210e6i −0.110570 + 0.627074i
\(78\) 79722.9 − 29016.8i 0.0190218 − 0.00692337i
\(79\) −928283. − 778922.i −0.211829 − 0.177746i 0.530700 − 0.847560i \(-0.321929\pi\)
−0.742529 + 0.669814i \(0.766374\pi\)
\(80\) −1.60448e6 −0.350364
\(81\) −3.84287e6 − 3.22455e6i −0.803448 − 0.674173i
\(82\) −2.07771e6 − 3.59871e6i −0.416138 − 0.720772i
\(83\) 1.94636e6 + 708417.i 0.373637 + 0.135993i 0.522011 − 0.852939i \(-0.325182\pi\)
−0.148374 + 0.988931i \(0.547404\pi\)
\(84\) −607942. + 1.05299e6i −0.111914 + 0.193841i
\(85\) −2.62433e6 − 4.54547e6i −0.463502 − 0.802810i
\(86\) −1.25619e6 − 7.12420e6i −0.212966 − 1.20779i
\(87\) −6.41183e6 + 2.33371e6i −1.04391 + 0.379953i
\(88\) 1.64830e6 − 2.85494e6i 0.257838 − 0.446589i
\(89\) 2.89787e6 − 2.43160e6i 0.435726 − 0.365618i −0.398381 − 0.917220i \(-0.630428\pi\)
0.834107 + 0.551602i \(0.185983\pi\)
\(90\) 270256. − 226771.i 0.0390774 − 0.0327898i
\(91\) −82329.8 − 29965.6i −0.0114528 − 0.00416848i
\(92\) −39748.2 + 225423.i −0.00532182 + 0.0301816i
\(93\) −927616. + 5.26077e6i −0.119585 + 0.678202i
\(94\) −7.06920e6 − 2.57298e6i −0.877855 − 0.319513i
\(95\) 1.51179e7 − 1.26854e7i 1.80908 − 1.51800i
\(96\) 1.20373e6 − 1.01005e6i 0.138860 − 0.116518i
\(97\) −2.63919e6 + 4.57122e6i −0.293610 + 0.508547i −0.974661 − 0.223689i \(-0.928190\pi\)
0.681051 + 0.732236i \(0.261523\pi\)
\(98\) −5.01110e6 + 1.82389e6i −0.537826 + 0.195753i
\(99\) 125870. + 713845.i 0.0130377 + 0.0739403i
\(100\) −2.41021e6 − 4.17460e6i −0.241021 − 0.417460i
\(101\) −1.73860e6 + 3.01135e6i −0.167909 + 0.290828i −0.937685 − 0.347487i \(-0.887035\pi\)
0.769775 + 0.638315i \(0.220368\pi\)
\(102\) 4.83029e6 + 1.75808e6i 0.450685 + 0.164036i
\(103\) 1.36128e6 + 2.35780e6i 0.122748 + 0.212607i 0.920851 − 0.389916i \(-0.127496\pi\)
−0.798102 + 0.602522i \(0.794162\pi\)
\(104\) 86737.5 + 72781.4i 0.00756119 + 0.00634459i
\(105\) −7.44196e6 −0.627371
\(106\) 1.04611e7 + 8.77794e6i 0.853116 + 0.715850i
\(107\) 1.53231e7 − 5.57716e6i 1.20922 − 0.440119i 0.342784 − 0.939414i \(-0.388630\pi\)
0.866432 + 0.499295i \(0.166408\pi\)
\(108\) 1.10553e6 − 6.26978e6i 0.0844478 − 0.478927i
\(109\) 1.67027e6 + 9.47260e6i 0.123536 + 0.700610i 0.982166 + 0.188014i \(0.0602051\pi\)
−0.858630 + 0.512596i \(0.828684\pi\)
\(110\) 2.01772e7 1.44540
\(111\) −1.09885e7 − 9.87701e6i −0.762623 − 0.685480i
\(112\) −1.62274e6 −0.109140
\(113\) −1.15423e6 − 6.54598e6i −0.0752522 − 0.426776i −0.999037 − 0.0438654i \(-0.986033\pi\)
0.923785 − 0.382911i \(-0.125078\pi\)
\(114\) −3.35618e6 + 1.90339e7i −0.212167 + 1.20326i
\(115\) −1.31652e6 + 479175.i −0.0807209 + 0.0293800i
\(116\) −6.97599e6 − 5.85355e6i −0.414957 − 0.348190i
\(117\) −24896.5 −0.00143710
\(118\) −9.59140e6 − 8.04814e6i −0.537397 − 0.450929i
\(119\) −2.65419e6 − 4.59718e6i −0.144383 − 0.250079i
\(120\) 9.03764e6 + 3.28943e6i 0.477442 + 0.173775i
\(121\) −1.09847e7 + 1.90261e7i −0.563690 + 0.976340i
\(122\) 7.86617e6 + 1.36246e7i 0.392197 + 0.679305i
\(123\) 4.32534e6 + 2.45302e7i 0.209581 + 1.18859i
\(124\) −6.69946e6 + 2.43840e6i −0.315547 + 0.114850i
\(125\) −549584. + 951908.i −0.0251680 + 0.0435923i
\(126\) 273330. − 229351.i 0.0121728 − 0.0102142i
\(127\) −2.63543e6 + 2.21139e6i −0.114167 + 0.0957971i −0.698084 − 0.716016i \(-0.745964\pi\)
0.583917 + 0.811813i \(0.301519\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) −7.52990e6 + 4.27042e7i −0.308834 + 1.75148i
\(130\) −120342. + 682495.i −0.00480415 + 0.0272457i
\(131\) −2.98096e7 − 1.08498e7i −1.15853 − 0.421670i −0.309956 − 0.950751i \(-0.600314\pi\)
−0.848571 + 0.529081i \(0.822537\pi\)
\(132\) −1.51375e7 + 1.27019e7i −0.572857 + 0.480684i
\(133\) 1.52899e7 − 1.28297e7i 0.563537 − 0.472864i
\(134\) 1.17429e7 − 2.03393e7i 0.421608 − 0.730247i
\(135\) 3.66169e7 − 1.33275e7i 1.28090 − 0.466208i
\(136\) 1.19128e6 + 6.75608e6i 0.0406095 + 0.230308i
\(137\) 74443.4 + 128940.i 0.00247346 + 0.00428415i 0.867259 − 0.497856i \(-0.165879\pi\)
−0.864786 + 0.502141i \(0.832546\pi\)
\(138\) 686044. − 1.18826e6i 0.0222216 − 0.0384889i
\(139\) 1.17650e7 + 4.28210e6i 0.371569 + 0.135240i 0.521053 − 0.853524i \(-0.325539\pi\)
−0.149485 + 0.988764i \(0.547761\pi\)
\(140\) −4.96607e6 − 8.60149e6i −0.152955 − 0.264927i
\(141\) 3.45440e7 + 2.89859e7i 1.03778 + 0.870802i
\(142\) 2.93465e7 0.860095
\(143\) −1.09077e6 − 915267.i −0.0311931 − 0.0261741i
\(144\) −433313. + 157713.i −0.0120930 + 0.00440148i
\(145\) 9.67870e6 − 5.48906e7i 0.263651 − 1.49524i
\(146\) 817836. + 4.63818e6i 0.0217486 + 0.123342i
\(147\) 3.19655e7 0.829986
\(148\) 4.08321e6 − 1.92917e7i 0.103535 − 0.489163i
\(149\) 7.39130e7 1.83050 0.915248 − 0.402890i \(-0.131994\pi\)
0.915248 + 0.402890i \(0.131994\pi\)
\(150\) 5.01752e6 + 2.84558e7i 0.121386 + 0.688416i
\(151\) −4.21771e6 + 2.39198e7i −0.0996914 + 0.565378i 0.893517 + 0.449029i \(0.148230\pi\)
−0.993208 + 0.116349i \(0.962881\pi\)
\(152\) −2.42391e7 + 8.82233e6i −0.559841 + 0.203765i
\(153\) −1.15553e6 − 969609.i −0.0260833 − 0.0218865i
\(154\) 2.04068e7 0.450249
\(155\) −3.34274e7 − 2.80489e7i −0.721011 − 0.605000i
\(156\) −339357. − 587784.i −0.00715684 − 0.0123960i
\(157\) 4.05322e6 + 1.47525e6i 0.0835894 + 0.0304240i 0.383476 − 0.923551i \(-0.374727\pi\)
−0.299887 + 0.953975i \(0.596949\pi\)
\(158\) −4.84715e6 + 8.39551e6i −0.0977657 + 0.169335i
\(159\) −4.09288e7 − 7.08908e7i −0.807494 − 1.39862i
\(160\) 2.22892e6 + 1.26409e7i 0.0430205 + 0.243981i
\(161\) −1.33150e6 + 484627.i −0.0251450 + 0.00915202i
\(162\) −2.00660e7 + 3.47554e7i −0.370816 + 0.642272i
\(163\) 6.97862e7 − 5.85576e7i 1.26216 − 1.05907i 0.266707 − 0.963778i \(-0.414064\pi\)
0.995449 − 0.0952974i \(-0.0303802\pi\)
\(164\) −2.54660e7 + 2.13685e7i −0.450823 + 0.378286i
\(165\) −1.13653e8 − 4.13664e7i −1.96965 − 0.716892i
\(166\) 2.87738e6 − 1.63184e7i 0.0488224 − 0.276886i
\(167\) −6.52382e6 + 3.69984e7i −0.108391 + 0.614718i 0.881420 + 0.472333i \(0.156588\pi\)
−0.989811 + 0.142384i \(0.954523\pi\)
\(168\) 9.14046e6 + 3.32685e6i 0.148725 + 0.0541317i
\(169\) −4.80307e7 + 4.03025e7i −0.765447 + 0.642287i
\(170\) −3.21656e7 + 2.69902e7i −0.502136 + 0.421342i
\(171\) 2.83588e6 − 4.91188e6i 0.0433711 − 0.0751210i
\(172\) −5.43827e7 + 1.97937e7i −0.814912 + 0.296604i
\(173\) −3.30317e6 − 1.87332e7i −0.0485030 − 0.275074i 0.950905 − 0.309484i \(-0.100156\pi\)
−0.999408 + 0.0344092i \(0.989045\pi\)
\(174\) 2.72933e7 + 4.72734e7i 0.392766 + 0.680290i
\(175\) 1.49198e7 − 2.58418e7i 0.210440 − 0.364494i
\(176\) −2.47824e7 − 9.02004e6i −0.342648 − 0.124714i
\(177\) 3.75260e7 + 6.49969e7i 0.508658 + 0.881021i
\(178\) −2.31829e7 − 1.94528e7i −0.308105 − 0.258531i
\(179\) 668268. 0.00870893 0.00435447 − 0.999991i \(-0.498614\pi\)
0.00435447 + 0.999991i \(0.498614\pi\)
\(180\) −2.16204e6 − 1.81417e6i −0.0276319 − 0.0231859i
\(181\) −864146. + 314523.i −0.0108321 + 0.00394256i −0.347431 − 0.937706i \(-0.612946\pi\)
0.336598 + 0.941648i \(0.390724\pi\)
\(182\) −121711. + 690260.i −0.00149652 + 0.00848717i
\(183\) −1.63756e7 − 9.28708e7i −0.197524 − 1.12021i
\(184\) 1.83121e6 0.0216708
\(185\) 1.14753e8 − 3.73949e7i 1.33249 − 0.434222i
\(186\) 4.27354e7 0.486959
\(187\) −1.49810e7 − 8.49614e7i −0.167531 − 0.950115i
\(188\) −1.04507e7 + 5.92688e7i −0.114708 + 0.650539i
\(189\) 3.70335e7 − 1.34791e7i 0.399005 − 0.145226i
\(190\) −1.20943e8 − 1.01483e8i −1.27921 − 1.07339i
\(191\) −5.40542e7 −0.561323 −0.280662 − 0.959807i \(-0.590554\pi\)
−0.280662 + 0.959807i \(0.590554\pi\)
\(192\) −9.62982e6 − 8.08038e6i −0.0981892 − 0.0823905i
\(193\) 96010.7 + 166295.i 0.000961323 + 0.00166506i 0.866506 − 0.499167i \(-0.166361\pi\)
−0.865544 + 0.500832i \(0.833027\pi\)
\(194\) 3.96805e7 + 1.44425e7i 0.390186 + 0.142016i
\(195\) 2.07707e6 − 3.59760e6i 0.0200600 − 0.0347449i
\(196\) 2.13308e7 + 3.69460e7i 0.202354 + 0.350487i
\(197\) 1.01618e7 + 5.76303e7i 0.0946973 + 0.537055i 0.994840 + 0.101459i \(0.0323512\pi\)
−0.900142 + 0.435596i \(0.856538\pi\)
\(198\) 5.44915e6 − 1.98333e6i 0.0498885 − 0.0181579i
\(199\) −5.81980e7 + 1.00802e8i −0.523507 + 0.906741i 0.476119 + 0.879381i \(0.342043\pi\)
−0.999626 + 0.0273597i \(0.991290\pi\)
\(200\) −2.95412e7 + 2.47880e7i −0.261110 + 0.219097i
\(201\) −1.07844e8 + 9.04915e7i −0.936716 + 0.785998i
\(202\) 2.61400e7 + 9.51419e6i 0.223139 + 0.0812161i
\(203\) 9.78882e6 − 5.55151e7i 0.0821285 − 0.465774i
\(204\) 7.14081e6 − 4.04976e7i 0.0588901 − 0.333982i
\(205\) −1.91199e8 − 6.95909e7i −1.55006 − 0.564175i
\(206\) 1.66848e7 − 1.40002e7i 0.132980 − 0.111583i
\(207\) −308445. + 258816.i −0.00241702 + 0.00202812i
\(208\) 452911. − 784465.i 0.00348973 − 0.00604438i
\(209\) 3.04821e8 − 1.10946e8i 2.30958 − 0.840617i
\(210\) 1.03383e7 + 5.86312e7i 0.0770335 + 0.436879i
\(211\) 1.01350e8 + 1.75543e8i 0.742736 + 1.28646i 0.951245 + 0.308436i \(0.0998055\pi\)
−0.208509 + 0.978020i \(0.566861\pi\)
\(212\) 5.46242e7 − 9.46118e7i 0.393740 − 0.681977i
\(213\) −1.65301e8 − 6.01647e7i −1.17205 − 0.426592i
\(214\) −6.52261e7 − 1.12975e8i −0.454960 − 0.788014i
\(215\) −2.71346e8 − 2.27686e8i −1.86204 − 1.56244i
\(216\) −5.09320e7 −0.343877
\(217\) −3.38077e7 − 2.83680e7i −0.224598 − 0.188460i
\(218\) 7.23092e7 − 2.63184e7i 0.472711 − 0.172053i
\(219\) 4.90230e6 − 2.78023e7i 0.0315388 − 0.178866i
\(220\) −2.80299e7 − 1.58966e8i −0.177477 − 1.00652i
\(221\) 2.96317e6 0.0184665
\(222\) −6.25505e7 + 1.00294e8i −0.383703 + 0.615232i
\(223\) −2.28898e8 −1.38222 −0.691108 − 0.722752i \(-0.742877\pi\)
−0.691108 + 0.722752i \(0.742877\pi\)
\(224\) 2.25428e6 + 1.27847e7i 0.0134011 + 0.0760014i
\(225\) 1.47242e6 − 8.35048e6i 0.00861770 − 0.0488734i
\(226\) −4.99688e7 + 1.81872e7i −0.287952 + 0.104806i
\(227\) 2.50960e8 + 2.10580e8i 1.42401 + 1.19489i 0.949148 + 0.314831i \(0.101948\pi\)
0.474866 + 0.880058i \(0.342497\pi\)
\(228\) 1.54620e8 0.863960
\(229\) −6.58412e6 − 5.52473e6i −0.0362304 − 0.0304009i 0.624493 − 0.781031i \(-0.285306\pi\)
−0.660723 + 0.750630i \(0.729750\pi\)
\(230\) 5.60406e6 + 9.70651e6i 0.0303707 + 0.0526036i
\(231\) −1.14946e8 − 4.18370e7i −0.613554 − 0.223316i
\(232\) −3.64260e7 + 6.30917e7i −0.191516 + 0.331715i
\(233\) 1.42757e8 + 2.47262e8i 0.739351 + 1.28059i 0.952788 + 0.303636i \(0.0982007\pi\)
−0.213438 + 0.976957i \(0.568466\pi\)
\(234\) 34585.9 + 196146.i 0.000176459 + 0.00100075i
\(235\) −3.46143e8 + 1.25986e8i −1.73987 + 0.633262i
\(236\) −5.00827e7 + 8.67459e7i −0.248025 + 0.429593i
\(237\) 4.45148e7 − 3.73523e7i 0.217213 − 0.182263i
\(238\) −3.25316e7 + 2.72972e7i −0.156418 + 0.131250i
\(239\) 3.61434e8 + 1.31551e8i 1.71252 + 0.623308i 0.997151 − 0.0754343i \(-0.0240343\pi\)
0.715374 + 0.698742i \(0.246257\pi\)
\(240\) 1.33607e7 − 7.57723e7i 0.0623864 − 0.353811i
\(241\) −3.68218e6 + 2.08827e7i −0.0169452 + 0.0961008i −0.992107 − 0.125391i \(-0.959981\pi\)
0.975162 + 0.221492i \(0.0710926\pi\)
\(242\) 1.65156e8 + 6.01120e7i 0.749103 + 0.272651i
\(243\) 1.76233e7 − 1.47877e7i 0.0787891 − 0.0661119i
\(244\) 9.64134e7 − 8.09004e7i 0.424887 − 0.356522i
\(245\) −1.30558e8 + 2.26132e8i −0.567180 + 0.982385i
\(246\) 1.87252e8 − 6.81541e7i 0.801961 − 0.291890i
\(247\) 1.93470e6 + 1.09723e7i 0.00816912 + 0.0463294i
\(248\) 2.85177e7 + 4.93940e7i 0.118722 + 0.205633i
\(249\) −4.96628e7 + 8.60185e7i −0.203861 + 0.353097i
\(250\) 8.26304e6 + 3.00750e6i 0.0334465 + 0.0121735i
\(251\) 7.65697e7 + 1.32623e8i 0.305632 + 0.529370i 0.977402 − 0.211390i \(-0.0677990\pi\)
−0.671770 + 0.740760i \(0.734466\pi\)
\(252\) −2.18664e6 − 1.83481e6i −0.00860747 − 0.00722253i
\(253\) −2.30284e7 −0.0894011
\(254\) 2.10835e7 + 1.76911e7i 0.0807279 + 0.0677388i
\(255\) 2.36515e8 − 8.60843e7i 0.893239 − 0.325112i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) −5.42937e7 − 3.07915e8i −0.199519 − 1.13153i −0.905835 − 0.423630i \(-0.860756\pi\)
0.706316 − 0.707896i \(-0.250356\pi\)
\(258\) 3.46904e8 1.25759
\(259\) 1.16059e8 − 3.78204e7i 0.415078 − 0.135262i
\(260\) 5.54419e6 0.0195628
\(261\) −2.78162e6 − 1.57754e7i −0.00968403 − 0.0549209i
\(262\) −4.40687e7 + 2.49926e8i −0.151383 + 0.858533i
\(263\) 1.55401e8 − 5.65614e7i 0.526756 − 0.191723i −0.0649334 − 0.997890i \(-0.520683\pi\)
0.591689 + 0.806166i \(0.298461\pi\)
\(264\) 1.21100e8 + 1.01615e8i 0.405071 + 0.339895i
\(265\) 6.68667e8 2.20724
\(266\) −1.22319e8 − 1.02638e8i −0.398481 − 0.334365i
\(267\) 9.07024e7 + 1.57101e8i 0.291628 + 0.505115i
\(268\) −1.76556e8 − 6.42610e7i −0.560286 − 0.203928i
\(269\) −2.77693e8 + 4.80979e8i −0.869826 + 1.50658i −0.00765101 + 0.999971i \(0.502435\pi\)
−0.862175 + 0.506611i \(0.830898\pi\)
\(270\) −1.55868e8 − 2.69971e8i −0.481929 − 0.834725i
\(271\) −1.09828e8 − 6.22866e8i −0.335213 − 1.90109i −0.425118 − 0.905138i \(-0.639767\pi\)
0.0899046 − 0.995950i \(-0.471344\pi\)
\(272\) 5.15726e7 − 1.87709e7i 0.155392 − 0.0565580i
\(273\) 2.10071e6 − 3.63853e6i 0.00624879 − 0.0108232i
\(274\) 912431. − 765620.i 0.00267962 − 0.00224847i
\(275\) 3.71497e8 − 3.11723e8i 1.07719 − 0.903867i
\(276\) −1.03147e7 − 3.75425e6i −0.0295308 − 0.0107483i
\(277\) −6.40450e7 + 3.63217e8i −0.181053 + 1.02680i 0.749869 + 0.661586i \(0.230116\pi\)
−0.930922 + 0.365217i \(0.880995\pi\)
\(278\) 1.73926e7 − 9.86385e7i 0.0485522 − 0.275353i
\(279\) −1.17846e7 − 4.28925e6i −0.0324863 − 0.0118241i
\(280\) −6.08677e7 + 5.10741e7i −0.165704 + 0.139042i
\(281\) −2.18828e8 + 1.83619e8i −0.588344 + 0.493680i −0.887675 − 0.460470i \(-0.847681\pi\)
0.299331 + 0.954149i \(0.403237\pi\)
\(282\) 1.80376e8 − 3.12420e8i 0.478968 − 0.829597i
\(283\) 1.60223e8 − 5.83163e7i 0.420215 − 0.152946i −0.123254 − 0.992375i \(-0.539333\pi\)
0.543469 + 0.839430i \(0.317111\pi\)
\(284\) −4.07677e7 − 2.31205e8i −0.105609 − 0.598940i
\(285\) 4.73184e8 + 8.19580e8i 1.21080 + 2.09717i
\(286\) −5.69561e6 + 9.86508e6i −0.0143966 + 0.0249356i
\(287\) −1.93375e8 − 7.03827e7i −0.482851 − 0.175743i
\(288\) 1.84449e6 + 3.19475e6i 0.00454990 + 0.00788066i
\(289\) −1.76807e8 − 1.48358e8i −0.430880 − 0.361551i
\(290\) −4.45899e8 −1.07360
\(291\) −1.93901e8 − 1.62702e8i −0.461269 − 0.387050i
\(292\) 3.54056e7 − 1.28866e7i 0.0832208 − 0.0302899i
\(293\) −9.36063e7 + 5.30868e8i −0.217404 + 1.23296i 0.659281 + 0.751897i \(0.270861\pi\)
−0.876685 + 0.481065i \(0.840250\pi\)
\(294\) −4.44060e7 − 2.51839e8i −0.101912 − 0.577973i
\(295\) −6.13074e8 −1.39039
\(296\) −1.57661e8 − 5.36972e6i −0.353349 − 0.0120346i
\(297\) 6.40498e8 1.41863
\(298\) −1.02679e8 − 5.82321e8i −0.224763 − 1.27469i
\(299\) 137348. − 778937.i 0.000297147 − 0.00168521i
\(300\) 2.17217e8 − 7.90606e7i 0.464483 − 0.169058i
\(301\) −2.74433e8 − 2.30277e8i −0.580035 − 0.486707i
\(302\) 1.94311e8 0.405950
\(303\) −1.27734e8 − 1.07182e8i −0.263790 − 0.221346i
\(304\) 1.03179e8 + 1.78711e8i 0.210637 + 0.364833i
\(305\) 7.23876e8 + 2.63469e8i 1.46088 + 0.531717i
\(306\) −6.03377e6 + 1.04508e7i −0.0120383 + 0.0208509i
\(307\) −1.40229e8 − 2.42883e8i −0.276600 − 0.479085i 0.693937 − 0.720035i \(-0.255874\pi\)
−0.970538 + 0.240950i \(0.922541\pi\)
\(308\) −2.83488e7 − 1.60774e8i −0.0552850 − 0.313537i
\(309\) −1.22684e8 + 4.46532e7i −0.236555 + 0.0860989i
\(310\) −1.74546e8 + 3.02322e8i −0.332769 + 0.576373i
\(311\) −5.12759e8 + 4.30256e8i −0.966611 + 0.811083i −0.982016 − 0.188798i \(-0.939541\pi\)
0.0154046 + 0.999881i \(0.495096\pi\)
\(312\) −4.15940e6 + 3.49015e6i −0.00775336 + 0.00650584i
\(313\) 9.63202e7 + 3.50577e7i 0.177547 + 0.0646217i 0.429264 − 0.903179i \(-0.358773\pi\)
−0.251717 + 0.967801i \(0.580995\pi\)
\(314\) 5.99203e6 − 3.39825e7i 0.0109225 − 0.0619443i
\(315\) 3.03381e6 − 1.72056e7i 0.00546892 − 0.0310158i
\(316\) 7.28773e7 + 2.65252e7i 0.129923 + 0.0472882i
\(317\) −5.07527e7 + 4.25865e7i −0.0894852 + 0.0750870i −0.686433 − 0.727193i \(-0.740824\pi\)
0.596948 + 0.802280i \(0.296380\pi\)
\(318\) −5.01652e8 + 4.20936e8i −0.874799 + 0.734043i
\(319\) 4.58078e8 − 7.93414e8i 0.790081 − 1.36846i
\(320\) 9.64941e7 − 3.51210e7i 0.164617 − 0.0599158i
\(321\) 1.35786e8 + 7.70082e8i 0.229133 + 1.29948i
\(322\) 5.66781e6 + 9.81694e6i 0.00946063 + 0.0163863i
\(323\) −3.37524e8 + 5.84609e8i −0.557309 + 0.965287i
\(324\) 3.01694e8 + 1.09808e8i 0.492787 + 0.179360i
\(325\) 8.32832e6 + 1.44251e7i 0.0134575 + 0.0233091i
\(326\) −5.58290e8 − 4.68461e8i −0.892479 − 0.748879i
\(327\) −4.61256e8 −0.729499
\(328\) 2.03728e8 + 1.70948e8i 0.318780 + 0.267488i
\(329\) −3.50081e8 + 1.27419e8i −0.541979 + 0.197264i
\(330\) −1.68018e8 + 9.52878e8i −0.257370 + 1.45962i
\(331\) −2.02088e8 − 1.14610e9i −0.306297 − 1.73710i −0.617334 − 0.786701i \(-0.711787\pi\)
0.311037 − 0.950398i \(-0.399324\pi\)
\(332\) −1.32561e8 −0.198808
\(333\) 2.73150e7 − 2.13787e7i 0.0405365 − 0.0317269i
\(334\) 3.00554e8 0.441376
\(335\) −1.99692e8 − 1.13251e9i −0.290205 − 1.64583i
\(336\) 1.35127e7 − 7.66344e7i 0.0194337 − 0.110214i
\(337\) −1.08398e9 + 3.94537e8i −1.54283 + 0.561544i −0.966722 − 0.255831i \(-0.917651\pi\)
−0.576107 + 0.817375i \(0.695429\pi\)
\(338\) 3.84246e8 + 3.22420e8i 0.541253 + 0.454165i
\(339\) 3.18748e8 0.444374
\(340\) 2.57325e8 + 2.15921e8i 0.355063 + 0.297934i
\(341\) −3.58625e8 − 6.21157e8i −0.489779 − 0.848323i
\(342\) −4.26376e7 − 1.55188e7i −0.0576370 − 0.0209782i
\(343\) −2.95177e8 + 5.11261e8i −0.394960 + 0.684091i
\(344\) 2.31491e8 + 4.00955e8i 0.306606 + 0.531056i
\(345\) −1.16664e7 − 6.61635e7i −0.0152957 − 0.0867464i
\(346\) −1.43000e8 + 5.20477e7i −0.185596 + 0.0675516i
\(347\) −5.97210e7 + 1.03440e8i −0.0767315 + 0.132903i −0.901838 − 0.432074i \(-0.857782\pi\)
0.825106 + 0.564977i \(0.191115\pi\)
\(348\) 3.34526e8 − 2.80701e8i 0.425503 − 0.357039i
\(349\) −8.55219e7 + 7.17614e7i −0.107693 + 0.0903653i −0.695044 − 0.718967i \(-0.744615\pi\)
0.587351 + 0.809332i \(0.300171\pi\)
\(350\) −2.24320e8 − 8.16459e7i −0.279660 − 0.101788i
\(351\) −3.82010e6 + 2.16648e7i −0.00471519 + 0.0267412i
\(352\) −3.66368e7 + 2.07777e8i −0.0447732 + 0.253921i
\(353\) −1.06274e9 − 3.86807e8i −1.28593 − 0.468040i −0.393541 − 0.919307i \(-0.628750\pi\)
−0.892389 + 0.451267i \(0.850972\pi\)
\(354\) 4.59945e8 − 3.85940e8i 0.551055 − 0.462390i
\(355\) 1.10077e9 − 9.23652e8i 1.30586 − 1.09574i
\(356\) −1.21053e8 + 2.09669e8i −0.142200 + 0.246298i
\(357\) 2.39206e8 − 8.70637e7i 0.278248 − 0.101274i
\(358\) −928348. − 5.26492e6i −0.00106935 − 0.00606459i
\(359\) 3.64957e8 + 6.32123e8i 0.416304 + 0.721060i 0.995564 − 0.0940828i \(-0.0299918\pi\)
−0.579260 + 0.815143i \(0.696659\pi\)
\(360\) −1.12894e7 + 1.95538e7i −0.0127530 + 0.0220888i
\(361\) −1.54515e9 − 5.62387e8i −1.72860 − 0.629159i
\(362\) 3.67842e6 + 6.37121e6i 0.00407550 + 0.00705898i
\(363\) −8.07044e8 − 6.77191e8i −0.885573 − 0.743084i
\(364\) 5.60726e6 0.00609391
\(365\) 1.76659e8 + 1.48234e8i 0.190156 + 0.159560i
\(366\) −7.08930e8 + 2.58029e8i −0.755822 + 0.275097i
\(367\) 2.78678e8 − 1.58046e9i 0.294287 − 1.66899i −0.375798 − 0.926702i \(-0.622631\pi\)
0.670085 − 0.742284i \(-0.266258\pi\)
\(368\) −2.54389e6 − 1.44271e7i −0.00266091 − 0.0150908i
\(369\) −5.84765e7 −0.0605884
\(370\) −4.54028e8 − 8.52132e8i −0.465990 − 0.874583i
\(371\) 6.76274e8 0.687566
\(372\) −5.93674e7 − 3.36689e8i −0.0597927 − 0.339101i
\(373\) −1.39307e8 + 7.90050e8i −0.138993 + 0.788268i 0.833003 + 0.553269i \(0.186620\pi\)
−0.971996 + 0.234999i \(0.924491\pi\)
\(374\) −6.48554e8 + 2.36054e8i −0.641055 + 0.233325i
\(375\) −4.03778e7 − 3.38810e7i −0.0395397 − 0.0331777i
\(376\) 4.81465e8 0.467097
\(377\) 2.41051e7 + 2.02266e7i 0.0231694 + 0.0194414i
\(378\) −1.57641e8 − 2.73042e8i −0.150123 − 0.260021i
\(379\) 1.02154e9 + 3.71810e8i 0.963868 + 0.350819i 0.775548 − 0.631289i \(-0.217474\pi\)
0.188320 + 0.982108i \(0.439696\pi\)
\(380\) −6.31519e8 + 1.09382e9i −0.590396 + 1.02260i
\(381\) −8.24882e7 − 1.42874e8i −0.0764108 − 0.132347i
\(382\) 7.50914e7 + 4.25864e8i 0.0689236 + 0.390885i
\(383\) 1.27115e9 − 4.62660e8i 1.15611 − 0.420791i 0.308406 − 0.951255i \(-0.400205\pi\)
0.847707 + 0.530464i \(0.177982\pi\)
\(384\) −5.02833e7 + 8.70933e7i −0.0453174 + 0.0784920i
\(385\) 7.65445e8 − 6.42284e8i 0.683599 − 0.573608i
\(386\) 1.17678e6 − 987432.i 0.00104145 − 0.000873880i
\(387\) −9.56613e7 − 3.48179e7i −0.0838972 − 0.0305361i
\(388\) 5.86613e7 − 3.32685e8i 0.0509848 − 0.289149i
\(389\) 1.77879e8 − 1.00880e9i 0.153215 − 0.868925i −0.807185 − 0.590299i \(-0.799010\pi\)
0.960400 − 0.278626i \(-0.0898789\pi\)
\(390\) −3.12290e7 − 1.13664e7i −0.0266583 − 0.00970281i
\(391\) 3.67109e7 − 3.08041e7i 0.0310582 − 0.0260609i
\(392\) 2.61446e8 − 2.19379e8i 0.219220 − 0.183947i
\(393\) 7.60614e8 − 1.31742e9i 0.632107 − 1.09484i
\(394\) 4.39921e8 − 1.60118e8i 0.362358 − 0.131888i
\(395\) 8.24274e7 + 4.67469e8i 0.0672948 + 0.381648i
\(396\) −2.31954e7 − 4.01757e7i −0.0187702 − 0.0325110i
\(397\) 1.22636e8 − 2.12412e8i 0.0983677 − 0.170378i −0.812641 − 0.582764i \(-0.801971\pi\)
0.911009 + 0.412386i \(0.135305\pi\)
\(398\) 8.75012e8 + 3.18478e8i 0.695702 + 0.253215i
\(399\) 4.78568e8 + 8.28904e8i 0.377171 + 0.653280i
\(400\) 2.36330e8 + 1.98304e8i 0.184633 + 0.154925i
\(401\) 4.62036e8 0.357825 0.178912 − 0.983865i \(-0.442742\pi\)
0.178912 + 0.983865i \(0.442742\pi\)
\(402\) 8.62748e8 + 7.23932e8i 0.662358 + 0.555785i
\(403\) 2.31496e7 − 8.42575e6i 0.0176188 − 0.00641270i
\(404\) 3.86438e7 − 2.19160e8i 0.0291572 − 0.165359i
\(405\) 3.41229e8 + 1.93521e9i 0.255243 + 1.44755i
\(406\) −4.50972e8 −0.334433
\(407\) 1.98267e9 + 6.75271e7i 1.45771 + 0.0496476i
\(408\) −3.28978e8 −0.239804
\(409\) −6.04550e7 − 3.42857e8i −0.0436918 − 0.247789i 0.955137 − 0.296163i \(-0.0957071\pi\)
−0.998829 + 0.0483741i \(0.984596\pi\)
\(410\) −2.82658e8 + 1.60303e9i −0.202543 + 1.14868i
\(411\) −6.70913e6 + 2.44192e6i −0.00476672 + 0.00173494i
\(412\) −1.33478e8 − 1.12001e8i −0.0940308 − 0.0789012i
\(413\) −6.20049e8 −0.433113
\(414\) 2.46756e6 + 2.07053e6i 0.00170909 + 0.00143410i
\(415\) −4.05679e8 − 7.02656e8i −0.278621 − 0.482586i
\(416\) −6.80956e6 − 2.47848e6i −0.00463759 − 0.00168794i
\(417\) −3.00192e8 + 5.19948e8i −0.202732 + 0.351143i
\(418\) −1.29753e9 − 2.24739e9i −0.868963 − 1.50509i
\(419\) 8.85668e7 + 5.02288e8i 0.0588196 + 0.333583i 0.999991 − 0.00434830i \(-0.00138411\pi\)
−0.941171 + 0.337931i \(0.890273\pi\)
\(420\) 4.47562e8 − 1.62899e8i 0.294768 − 0.107287i
\(421\) −7.49025e8 + 1.29735e9i −0.489225 + 0.847363i −0.999923 − 0.0123972i \(-0.996054\pi\)
0.510698 + 0.859760i \(0.329387\pi\)
\(422\) 1.24222e9 − 1.04234e9i 0.804643 − 0.675176i
\(423\) −8.10969e7 + 6.80484e7i −0.0520970 + 0.0437146i
\(424\) −8.21279e8 − 2.98921e8i −0.523251 − 0.190448i
\(425\) −1.75246e8 + 9.93869e8i −0.110735 + 0.628012i
\(426\) −2.44371e8 + 1.38590e9i −0.153150 + 0.868556i
\(427\) 7.32112e8 + 2.66467e8i 0.455072 + 0.165633i
\(428\) −7.99457e8 + 6.70824e8i −0.492881 + 0.413576i
\(429\) 5.23068e7 − 4.38906e7i 0.0319858 − 0.0268393i
\(430\) −1.41687e9 + 2.45409e9i −0.859389 + 1.48851i
\(431\) 5.69848e8 − 2.07408e8i 0.342838 − 0.124783i −0.164862 − 0.986317i \(-0.552718\pi\)
0.507700 + 0.861534i \(0.330496\pi\)
\(432\) 7.07540e7 + 4.01266e8i 0.0422239 + 0.239464i
\(433\) 1.42019e9 + 2.45984e9i 0.840696 + 1.45613i 0.889307 + 0.457311i \(0.151187\pi\)
−0.0486106 + 0.998818i \(0.515479\pi\)
\(434\) −1.76531e8 + 3.05761e8i −0.103659 + 0.179543i
\(435\) 2.51164e9 + 9.14161e8i 1.46300 + 0.532489i
\(436\) −3.07799e8 − 5.33124e8i −0.177855 − 0.308053i
\(437\) 1.38033e8 + 1.15823e8i 0.0791221 + 0.0663914i
\(438\) −2.25850e8 −0.128428
\(439\) −1.36707e8 − 1.14711e8i −0.0771196 − 0.0647110i 0.603413 − 0.797429i \(-0.293807\pi\)
−0.680533 + 0.732718i \(0.738252\pi\)
\(440\) −1.21347e9 + 4.41666e8i −0.679115 + 0.247178i
\(441\) −1.30312e7 + 7.39034e7i −0.00723516 + 0.0410326i
\(442\) −4.11639e6 − 2.33452e7i −0.00226746 − 0.0128594i
\(443\) −1.87420e9 −1.02425 −0.512123 − 0.858912i \(-0.671141\pi\)
−0.512123 + 0.858912i \(0.671141\pi\)
\(444\) 8.77055e8 + 3.53475e8i 0.475539 + 0.191654i
\(445\) −1.48183e9 −0.797149
\(446\) 3.17982e8 + 1.80337e9i 0.169719 + 0.962525i
\(447\) −6.15482e8 + 3.49057e9i −0.325941 + 1.84850i
\(448\) 9.75919e7 − 3.55205e7i 0.0512791 − 0.0186641i
\(449\) 1.44640e8 + 1.21367e8i 0.0754094 + 0.0632760i 0.679713 − 0.733478i \(-0.262104\pi\)
−0.604304 + 0.796754i \(0.706549\pi\)
\(450\) −6.78344e7 −0.0350919
\(451\) −2.56199e9 − 2.14976e9i −1.31510 − 1.10350i
\(452\) 2.12703e8 + 3.68412e8i 0.108340 + 0.187650i
\(453\) −1.09450e9 − 3.98366e8i −0.553189 − 0.201344i
\(454\) 1.31042e9 − 2.26971e9i 0.657227 − 1.13835i
\(455\) 1.71600e7 + 2.97219e7i 0.00854036 + 0.0147923i
\(456\) −2.14796e8 − 1.21817e9i −0.106084 − 0.601631i
\(457\) 3.54606e9 − 1.29066e9i 1.73796 − 0.632564i 0.738812 − 0.673912i \(-0.235387\pi\)
0.999145 + 0.0413473i \(0.0131650\pi\)
\(458\) −3.43798e7 + 5.95476e7i −0.0167215 + 0.0289624i
\(459\) −1.02105e9 + 8.56765e8i −0.492838 + 0.413540i
\(460\) 6.86873e7 − 5.76355e7i 0.0329021 − 0.0276082i
\(461\) 1.58057e9 + 5.75281e8i 0.751382 + 0.273481i 0.689187 − 0.724583i \(-0.257968\pi\)
0.0621949 + 0.998064i \(0.480190\pi\)
\(462\) −1.69930e8 + 9.63719e8i −0.0801719 + 0.454678i
\(463\) 5.10268e8 − 2.89388e9i 0.238927 − 1.35502i −0.595257 − 0.803535i \(-0.702950\pi\)
0.834184 − 0.551486i \(-0.185939\pi\)
\(464\) 5.47668e8 + 1.99335e8i 0.254510 + 0.0926341i
\(465\) 1.60298e9 − 1.34506e9i 0.739336 − 0.620376i
\(466\) 1.74973e9 − 1.46819e9i 0.800976 − 0.672098i
\(467\) 6.42984e8 − 1.11368e9i 0.292140 − 0.506002i −0.682175 − 0.731189i \(-0.738966\pi\)
0.974316 + 0.225187i \(0.0722993\pi\)
\(468\) 1.49729e6 − 544967.i 0.000675218 − 0.000245759i
\(469\) −2.01964e8 − 1.14540e9i −0.0904002 − 0.512685i
\(470\) 1.47343e9 + 2.55206e9i 0.654616 + 1.13383i
\(471\) −1.03421e8 + 1.79130e8i −0.0456074 + 0.0789943i
\(472\) 7.52998e8 + 2.74069e8i 0.329607 + 0.119967i
\(473\) −2.91113e9 − 5.04223e9i −1.26488 − 2.19083i
\(474\) −3.56118e8 − 2.98819e8i −0.153593 − 0.128879i
\(475\) −3.79460e9 −1.62457
\(476\) 2.60253e8 + 2.18378e8i 0.110604 + 0.0928078i
\(477\) 1.80583e8 − 6.57268e7i 0.0761837 − 0.0277286i
\(478\) 5.34323e8 − 3.03030e9i 0.223772 − 1.26908i
\(479\) 5.41931e8 + 3.07344e9i 0.225305 + 1.27777i 0.862102 + 0.506734i \(0.169148\pi\)
−0.636798 + 0.771031i \(0.719741\pi\)
\(480\) −6.15530e8 −0.254042
\(481\) −1.41093e7 + 6.66612e7i −0.00578092 + 0.0273127i
\(482\) 1.69639e8 0.0690018
\(483\) −1.17991e7 − 6.69162e7i −0.00476469 − 0.0270219i
\(484\) 2.44157e8 − 1.38468e9i 0.0978838 − 0.555127i
\(485\) 1.94295e9 − 7.07177e8i 0.773332 − 0.281470i
\(486\) −1.40987e8 − 1.18302e8i −0.0557123 − 0.0467482i
\(487\) −3.33279e9 −1.30754 −0.653772 − 0.756691i \(-0.726815\pi\)
−0.653772 + 0.756691i \(0.726815\pi\)
\(488\) −7.71307e8 − 6.47204e8i −0.300440 − 0.252099i
\(489\) 2.18429e9 + 3.78330e9i 0.844751 + 1.46315i
\(490\) 1.96294e9 + 7.14453e8i 0.753740 + 0.274339i
\(491\) 4.06002e8 − 7.03217e8i 0.154790 − 0.268104i −0.778192 − 0.628026i \(-0.783863\pi\)
0.932983 + 0.359921i \(0.117197\pi\)
\(492\) −7.97077e8 − 1.38058e9i −0.301733 − 0.522616i
\(493\) 3.31067e8 + 1.87757e9i 0.124438 + 0.705720i
\(494\) 8.37568e7 − 3.04850e7i 0.0312591 − 0.0113774i
\(495\) 1.41970e8 − 2.45900e8i 0.0526113 − 0.0911255i
\(496\) 3.49533e8 − 2.93293e8i 0.128618 − 0.107923i
\(497\) 1.11329e9 − 9.34160e8i 0.406781 − 0.341330i
\(498\) 7.46685e8 + 2.71771e8i 0.270916 + 0.0986053i
\(499\) −7.92330e8 + 4.49353e9i −0.285466 + 1.61896i 0.418151 + 0.908378i \(0.362678\pi\)
−0.703617 + 0.710580i \(0.748433\pi\)
\(500\) 1.22156e7 − 6.92781e7i 0.00437038 − 0.0247857i
\(501\) −1.69294e9 − 6.16180e8i −0.601464 − 0.218915i
\(502\) 9.38492e8 − 7.87489e8i 0.331107 − 0.277831i
\(503\) 3.23464e9 − 2.71418e9i 1.13328 − 0.950935i 0.134082 − 0.990970i \(-0.457191\pi\)
0.999198 + 0.0400350i \(0.0127469\pi\)
\(504\) −1.14178e7 + 1.97763e7i −0.00397262 + 0.00688078i
\(505\) 1.27994e9 − 4.65861e8i 0.442253 − 0.160967i
\(506\) 3.19908e7 + 1.81429e8i 0.0109774 + 0.0622557i
\(507\) −1.50335e9 − 2.60387e9i −0.512308 − 0.887343i
\(508\) 1.10090e8 − 1.90681e8i 0.0372585 − 0.0645336i
\(509\) 1.07690e9 + 3.91961e8i 0.361963 + 0.131744i 0.516598 − 0.856228i \(-0.327198\pi\)
−0.154635 + 0.987972i \(0.549420\pi\)
\(510\) −1.00677e9 − 1.74379e9i −0.336075 − 0.582100i
\(511\) 1.78668e8 + 1.49921e8i 0.0592345 + 0.0497036i
\(512\) −1.34218e8 −0.0441942
\(513\) −3.83916e9 − 3.22144e9i −1.25553 − 1.05351i
\(514\) −2.35047e9 + 8.55502e8i −0.763456 + 0.277875i
\(515\) 1.85192e8 − 1.05027e9i 0.0597443 − 0.338827i
\(516\) −4.81913e8 − 2.73307e9i −0.154417 − 0.875742i
\(517\) −6.05468e9 −1.92697
\(518\) −4.59194e8 − 8.61827e8i −0.145158 − 0.272437i
\(519\) 9.12188e8 0.286417
\(520\) −7.70191e6 − 4.36797e7i −0.00240207 − 0.0136228i
\(521\) −1.05843e9 + 6.00266e9i −0.327892 + 1.85957i 0.160628 + 0.987015i \(0.448648\pi\)
−0.488520 + 0.872553i \(0.662463\pi\)
\(522\) −1.20421e8 + 4.38298e7i −0.0370558 + 0.0134872i
\(523\) −2.33572e9 − 1.95990e9i −0.713945 − 0.599071i 0.211758 − 0.977322i \(-0.432081\pi\)
−0.925703 + 0.378251i \(0.876526\pi\)
\(524\) 2.03025e9 0.616440
\(525\) 1.09615e9 + 9.19780e8i 0.330608 + 0.277413i
\(526\) −6.61498e8 − 1.14575e9i −0.198189 − 0.343273i
\(527\) 1.40260e9 + 5.10504e8i 0.417442 + 0.151936i
\(528\) 6.32341e8 − 1.09525e9i 0.186953 − 0.323812i
\(529\) 1.69602e9 + 2.93759e9i 0.498122 + 0.862772i
\(530\) −9.28902e8 − 5.26807e9i −0.271022 − 1.53704i
\(531\) −1.65569e8 + 6.02623e7i −0.0479898 + 0.0174669i
\(532\) −6.38704e8 + 1.10627e9i −0.183911 + 0.318544i
\(533\) 8.79960e7 − 7.38374e7i 0.0251720 − 0.0211218i
\(534\) 1.11171e9 − 9.32838e8i 0.315935 − 0.265101i
\(535\) −6.00236e9 − 2.18468e9i −1.69467 − 0.616808i
\(536\) −2.61009e8 + 1.48026e9i −0.0732115 + 0.415203i
\(537\) −5.56474e6 + 3.15592e7i −0.00155073 + 0.00879460i
\(538\) 4.17514e9 + 1.51963e9i 1.15593 + 0.420726i
\(539\) −3.28782e9 + 2.75881e9i −0.904373 + 0.758859i
\(540\) −1.91043e9 + 1.60304e9i −0.522098 + 0.438092i
\(541\) −3.59543e9 + 6.22748e9i −0.976250 + 1.69091i −0.300502 + 0.953781i \(0.597154\pi\)
−0.675748 + 0.737133i \(0.736179\pi\)
\(542\) −4.75466e9 + 1.73055e9i −1.28269 + 0.466861i
\(543\) −7.65765e6 − 4.34287e7i −0.00205256 − 0.0116407i
\(544\) −2.19530e8 − 3.80237e8i −0.0584652 − 0.101265i
\(545\) 1.88392e9 − 3.26305e9i 0.498511 − 0.863447i
\(546\) −3.15843e7 − 1.14957e7i −0.00830418 − 0.00302247i
\(547\) 1.38143e8 + 2.39271e8i 0.0360889 + 0.0625079i 0.883506 − 0.468420i \(-0.155177\pi\)
−0.847417 + 0.530928i \(0.821843\pi\)
\(548\) −7.29945e6 − 6.12496e6i −0.00189478 − 0.00158991i
\(549\) 2.21391e8 0.0571026
\(550\) −2.97198e9 − 2.49378e9i −0.761686 − 0.639131i
\(551\) −6.73627e9 + 2.45180e9i −1.71549 + 0.624388i
\(552\) −1.52487e7 + 8.64795e7i −0.00385874 + 0.0218840i
\(553\) 8.33651e7 + 4.72787e8i 0.0209627 + 0.118885i
\(554\) 2.95056e9 0.737261
\(555\) 8.10426e8 + 5.73067e9i 0.201228 + 1.42292i
\(556\) −8.01282e8 −0.197708
\(557\) −1.03184e9 − 5.85188e9i −0.253000 − 1.43484i −0.801154 − 0.598459i \(-0.795780\pi\)
0.548153 − 0.836378i \(-0.315331\pi\)
\(558\) −1.74217e7 + 9.88032e7i −0.00424493 + 0.0240742i
\(559\) 1.87916e8 − 6.83958e7i 0.0455011 − 0.0165611i
\(560\) 4.86942e8 + 4.08592e8i 0.117171 + 0.0983178i
\(561\) 4.13709e9 0.989292
\(562\) 1.75063e9 + 1.46895e9i 0.416022 + 0.349084i
\(563\) 5.30265e8 + 9.18445e8i 0.125231 + 0.216907i 0.921823 − 0.387610i \(-0.126699\pi\)
−0.796592 + 0.604517i \(0.793366\pi\)
\(564\) −2.71197e9 − 9.87075e8i −0.636513 − 0.231672i
\(565\) −1.30187e9 + 2.25491e9i −0.303668 + 0.525968i
\(566\) −6.82021e8 − 1.18130e9i −0.158103 − 0.273843i
\(567\) 3.45111e8 + 1.95722e9i 0.0795094 + 0.450920i
\(568\) −1.76491e9 + 6.42373e8i −0.404113 + 0.147085i
\(569\) 3.49120e9 − 6.04694e9i 0.794478 − 1.37608i −0.128692 − 0.991685i \(-0.541078\pi\)
0.923170 − 0.384391i \(-0.125589\pi\)
\(570\) 5.79969e9 − 4.86651e9i 1.31172 − 1.10067i
\(571\) 2.50119e9 − 2.09875e9i 0.562239 − 0.471774i −0.316821 − 0.948485i \(-0.602616\pi\)
0.879060 + 0.476711i \(0.158171\pi\)
\(572\) 8.56339e7 + 3.11682e7i 0.0191320 + 0.00696347i
\(573\) 4.50116e8 − 2.55273e9i 0.0999500 − 0.566845i
\(574\) −2.85874e8 + 1.62127e9i −0.0630932 + 0.357819i
\(575\) 2.53138e8 + 9.21348e7i 0.0555291 + 0.0202109i
\(576\) 2.26073e7 − 1.89698e7i 0.00492914 − 0.00413604i
\(577\) 3.47486e9 − 2.91576e9i 0.753047 − 0.631882i −0.183260 − 0.983065i \(-0.558665\pi\)
0.936307 + 0.351183i \(0.114220\pi\)
\(578\) −9.23219e8 + 1.59906e9i −0.198864 + 0.344443i
\(579\) −8.65286e6 + 3.14938e6i −0.00185261 + 0.000674296i
\(580\) 6.19437e8 + 3.51300e9i 0.131825 + 0.747619i
\(581\) −4.10294e8 − 7.10650e8i −0.0867918 − 0.150328i
\(582\) −1.01248e9 + 1.75366e9i −0.212890 + 0.368736i
\(583\) 1.03280e10 + 3.75910e9i 2.15863 + 0.785676i
\(584\) −1.50711e8 − 2.61040e8i −0.0313113 − 0.0542327i
\(585\) 7.47081e6 + 6.26875e6i 0.00154284 + 0.00129460i
\(586\) 4.31246e9 0.885285
\(587\) −3.01838e9 − 2.53273e9i −0.615944 − 0.516838i 0.280582 − 0.959830i \(-0.409473\pi\)
−0.896526 + 0.442992i \(0.853917\pi\)
\(588\) −1.92242e9 + 6.99702e8i −0.389966 + 0.141936i
\(589\) −9.74553e8 + 5.52697e9i −0.196518 + 1.11451i
\(590\) 8.51674e8 + 4.83008e9i 0.170723 + 0.968216i
\(591\) −2.80623e9 −0.559200
\(592\) 1.76715e8 + 1.24959e9i 0.0350064 + 0.247537i
\(593\) −4.57758e9 −0.901456 −0.450728 − 0.892661i \(-0.648835\pi\)
−0.450728 + 0.892661i \(0.648835\pi\)
\(594\) −8.89771e8 − 5.04614e9i −0.174191 − 0.987886i
\(595\) −3.61083e8 + 2.04780e9i −0.0702744 + 0.398546i
\(596\) −4.44515e9 + 1.61790e9i −0.860052 + 0.313033i
\(597\) −4.27579e9 − 3.58781e9i −0.822444 − 0.690112i
\(598\) −6.32762e6 −0.00121000
\(599\) 3.08952e9 + 2.59242e9i 0.587351 + 0.492846i 0.887352 − 0.461093i \(-0.152542\pi\)
−0.300001 + 0.953939i \(0.596987\pi\)
\(600\) −9.24631e8 − 1.60151e9i −0.174759 − 0.302691i
\(601\) 8.21531e9 + 2.99013e9i 1.54370 + 0.561861i 0.966930 − 0.255044i \(-0.0820899\pi\)
0.576772 + 0.816905i \(0.304312\pi\)
\(602\) −1.43299e9 + 2.48201e9i −0.267704 + 0.463677i
\(603\) −1.65250e8 − 2.86222e8i −0.0306924 − 0.0531608i
\(604\) −2.69934e8 − 1.53087e9i −0.0498457 − 0.282689i
\(605\) 8.08686e9 − 2.94338e9i 1.48469 − 0.540384i
\(606\) −6.66982e8 + 1.15525e9i −0.121747 + 0.210873i
\(607\) −3.90159e9 + 3.27383e9i −0.708079 + 0.594149i −0.924059 − 0.382249i \(-0.875150\pi\)
0.215980 + 0.976398i \(0.430705\pi\)
\(608\) 1.26464e9 − 1.06116e9i 0.228193 − 0.191477i
\(609\) 2.54021e9 + 9.24561e8i 0.455732 + 0.165873i
\(610\) 1.07014e9 − 6.06904e9i 0.190890 − 1.08259i
\(611\) 3.61117e7 − 2.04800e8i 0.00640477 − 0.0363233i
\(612\) 9.07183e7 + 3.30188e7i 0.0159980 + 0.00582278i
\(613\) −2.08809e9 + 1.75212e9i −0.366133 + 0.307222i −0.807229 − 0.590238i \(-0.799034\pi\)
0.441097 + 0.897460i \(0.354590\pi\)
\(614\) −1.71874e9 + 1.44220e9i −0.299655 + 0.251440i
\(615\) 4.87860e9 − 8.44998e9i 0.845731 − 1.46485i
\(616\) −1.22727e9 + 4.46690e8i −0.211548 + 0.0769971i
\(617\) −1.59542e9 − 9.04809e9i −0.273450 − 1.55081i −0.743843 − 0.668354i \(-0.766999\pi\)
0.470394 − 0.882457i \(-0.344112\pi\)
\(618\) 5.22228e8 + 9.04526e8i 0.0890022 + 0.154156i
\(619\) −7.71493e8 + 1.33627e9i −0.130742 + 0.226452i −0.923963 − 0.382482i \(-0.875069\pi\)
0.793221 + 0.608934i \(0.208403\pi\)
\(620\) 2.62431e9 + 9.55170e8i 0.442225 + 0.160957i
\(621\) 1.77893e8 + 3.08120e8i 0.0298084 + 0.0516296i
\(622\) 4.10207e9 + 3.44205e9i 0.683497 + 0.573522i
\(623\) −1.49869e9 −0.248316
\(624\) 3.32752e7 + 2.79212e7i 0.00548245 + 0.00460033i
\(625\) 5.93403e9 − 2.15981e9i 0.972231 − 0.353863i
\(626\) 1.42394e8 − 8.07557e8i 0.0231997 − 0.131572i
\(627\) 2.70118e9 + 1.53191e10i 0.437639 + 2.48198i
\(628\) −2.76054e8 −0.0444770
\(629\) −3.25102e9 + 2.54448e9i −0.520885 + 0.407683i
\(630\) −1.39768e8 −0.0222698
\(631\) 4.24557e8 + 2.40778e9i 0.0672718 + 0.381517i 0.999792 + 0.0203992i \(0.00649371\pi\)
−0.932520 + 0.361118i \(0.882395\pi\)
\(632\) 1.07737e8 − 6.11009e8i 0.0169768 − 0.0962804i
\(633\) −9.13404e9 + 3.32452e9i −1.43136 + 0.520974i
\(634\) 4.06021e8 + 3.40692e8i 0.0632756 + 0.0530946i
\(635\) 1.34764e9 0.208865
\(636\) 4.01322e9 + 3.36749e9i 0.618576 + 0.519047i
\(637\) −7.37073e7 − 1.27665e8i −0.0112985 − 0.0195696i
\(638\) −6.88723e9 − 2.50675e9i −1.04996 − 0.382154i
\(639\) 2.06486e8 − 3.57645e8i 0.0313068 − 0.0542249i
\(640\) −4.10747e8 − 7.11435e8i −0.0619363 − 0.107277i
\(641\) 7.68513e8 + 4.35846e9i 0.115252 + 0.653626i 0.986625 + 0.163006i \(0.0521188\pi\)
−0.871373 + 0.490621i \(0.836770\pi\)
\(642\) 5.87843e9 − 2.13957e9i 0.876776 − 0.319120i
\(643\) 5.89594e9 − 1.02121e10i 0.874610 − 1.51487i 0.0174333 − 0.999848i \(-0.494451\pi\)
0.857177 − 0.515022i \(-0.172216\pi\)
\(644\) 6.94688e7 − 5.82912e7i 0.0102492 − 0.00860008i
\(645\) 1.30121e10 − 1.09185e10i 1.90936 − 1.60215i
\(646\) 5.07470e9 + 1.84704e9i 0.740622 + 0.269564i
\(647\) 6.15570e8 − 3.49107e9i 0.0893536 − 0.506750i −0.906978 − 0.421177i \(-0.861617\pi\)
0.996332 − 0.0855723i \(-0.0272719\pi\)
\(648\) 4.46007e8 − 2.52943e9i 0.0643915 − 0.365183i
\(649\) −9.46937e9 − 3.44657e9i −1.35977 − 0.494915i
\(650\) 1.02078e8 − 8.56535e7i 0.0145792 − 0.0122334i
\(651\) 1.62121e9 − 1.36036e9i 0.230307 − 0.193250i
\(652\) −2.91518e9 + 5.04924e9i −0.411907 + 0.713444i
\(653\) 4.54478e9 − 1.65417e9i 0.638730 − 0.232479i −0.00229685 − 0.999997i \(-0.500731\pi\)
0.641026 + 0.767519i \(0.278509\pi\)
\(654\) 6.40770e8 + 3.63399e9i 0.0895736 + 0.507997i
\(655\) 6.21320e9 + 1.07616e10i 0.863914 + 1.49634i
\(656\) 1.06379e9 − 1.84254e9i 0.147127 − 0.254831i
\(657\) 6.22798e7 + 2.26680e7i 0.00856778 + 0.00311842i
\(658\) 1.49019e9 + 2.58109e9i 0.203916 + 0.353193i
\(659\) −1.46927e9 − 1.23286e9i −0.199987 − 0.167809i 0.537295 − 0.843395i \(-0.319446\pi\)
−0.737281 + 0.675586i \(0.763891\pi\)
\(660\) 7.74063e9 1.04803
\(661\) −7.98310e9 − 6.69861e9i −1.07514 − 0.902152i −0.0796348 − 0.996824i \(-0.525375\pi\)
−0.995509 + 0.0946718i \(0.969820\pi\)
\(662\) −8.74877e9 + 3.18429e9i −1.17204 + 0.426589i
\(663\) −2.46746e7 + 1.39937e8i −0.00328816 + 0.0186481i
\(664\) 1.84152e8 + 1.04438e9i 0.0244112 + 0.138443i
\(665\) −7.81852e9 −1.03098
\(666\) −2.06377e8 − 1.85501e8i −0.0270708 − 0.0243325i
\(667\) 5.08908e8 0.0664048
\(668\) −4.17525e8 − 2.36790e9i −0.0541956 − 0.307359i
\(669\) 1.90606e9 − 1.08098e10i 0.246119 − 1.39581i
\(670\) −8.64504e9 + 3.14654e9i −1.11047 + 0.404176i
\(671\) 9.69961e9 + 8.13894e9i 1.23944 + 1.04001i
\(672\) −6.22533e8 −0.0791352
\(673\) 9.76944e9 + 8.19753e9i 1.23543 + 1.03665i 0.997867 + 0.0652727i \(0.0207917\pi\)
0.237559 + 0.971373i \(0.423653\pi\)
\(674\) 4.61420e9 + 7.99203e9i 0.580479 + 1.00542i
\(675\) −7.04063e9 − 2.56258e9i −0.881147 − 0.320711i
\(676\) 2.00639e9 − 3.47517e9i 0.249805 − 0.432675i
\(677\) −3.19902e9 − 5.54086e9i −0.396238 − 0.686304i 0.597020 − 0.802226i \(-0.296351\pi\)
−0.993258 + 0.115922i \(0.963018\pi\)
\(678\) −4.42800e8 − 2.51124e9i −0.0545637 − 0.309446i
\(679\) 1.96506e9 − 7.15222e8i 0.240897 − 0.0876793i
\(680\) 1.34366e9 − 2.32728e9i 0.163873 − 0.283836i
\(681\) −1.20345e10 + 1.00982e10i −1.46020 + 1.22526i
\(682\) −4.39557e9 + 3.68832e9i −0.530603 + 0.445229i
\(683\) 1.33415e10 + 4.85590e9i 1.60225 + 0.583172i 0.979887 − 0.199554i \(-0.0639494\pi\)
0.622366 + 0.782727i \(0.286172\pi\)
\(684\) −6.30329e7 + 3.57477e8i −0.00753132 + 0.0427122i
\(685\) 1.01275e7 − 5.74358e7i 0.00120388 − 0.00682756i
\(686\) 4.43801e9 + 1.61530e9i 0.524872 + 0.191038i
\(687\) 3.15734e8 − 2.64933e8i 0.0371512 − 0.0311736i
\(688\) 2.83732e9 − 2.38080e9i 0.332161 − 0.278716i
\(689\) −1.88750e8 + 3.26925e8i −0.0219847 + 0.0380786i
\(690\) −5.05059e8 + 1.83827e8i −0.0585289 + 0.0213028i
\(691\) 2.09850e9 + 1.19012e10i 0.241956 + 1.37220i 0.827457 + 0.561529i \(0.189787\pi\)
−0.585501 + 0.810672i \(0.699102\pi\)
\(692\) 6.08710e8 + 1.05432e9i 0.0698295 + 0.120948i
\(693\) 1.43586e8 − 2.48697e8i 0.0163887 − 0.0283860i
\(694\) 8.97910e8 + 3.26812e8i 0.101971 + 0.0371142i
\(695\) −2.45217e9 − 4.24728e9i −0.277079 − 0.479915i
\(696\) −2.67621e9 − 2.24561e9i −0.300876 − 0.252465i
\(697\) 6.95984e9 0.778547
\(698\) 6.84175e8 + 5.74091e8i 0.0761506 + 0.0638979i
\(699\) −1.28658e10 + 4.68276e9i −1.42484 + 0.518599i
\(700\) −3.31622e8 + 1.88072e9i −0.0365426 + 0.207243i
\(701\) −1.10504e9 − 6.26697e9i −0.121161 − 0.687139i −0.983514 − 0.180831i \(-0.942121\pi\)
0.862353 − 0.506307i \(-0.168990\pi\)
\(702\) 1.75993e8 0.0192006
\(703\) −1.15446e10 − 1.03768e10i −1.25324 − 1.12647i
\(704\) 1.68786e9 0.182319
\(705\) −3.06735e9 − 1.73958e10i −0.329687 − 1.86975i
\(706\) −1.57110e9 + 8.91014e9i −0.168030 + 0.952945i
\(707\) 1.29451e9 − 4.71161e8i 0.137764 − 0.0501420i
\(708\) −3.67956e9 − 3.08752e9i −0.389655 − 0.326959i
\(709\) 4.81633e9 0.507522 0.253761 − 0.967267i \(-0.418332\pi\)
0.253761 + 0.967267i \(0.418332\pi\)
\(710\) −8.80612e9 − 7.38921e9i −0.923380 − 0.774808i
\(711\) 6.82106e7 + 1.18144e8i 0.00711719 + 0.0123273i
\(712\) 1.82004e9 + 6.62440e8i 0.188973 + 0.0687807i
\(713\) 1.99210e8 − 3.45042e8i 0.0205825 − 0.0356499i
\(714\) −1.01823e9 − 1.76362e9i −0.104689 − 0.181327i
\(715\) 9.68557e7 + 5.49296e8i 0.00990955 + 0.0561999i
\(716\) −4.01898e7 + 1.46279e7i −0.00409186 + 0.00148932i
\(717\) −9.22227e9 + 1.59734e10i −0.934374 + 1.61838i
\(718\) 4.47317e9 − 3.75343e9i 0.451003 − 0.378437i
\(719\) 8.41401e9 − 7.06020e9i 0.844213 − 0.708379i −0.114294 − 0.993447i \(-0.536461\pi\)
0.958507 + 0.285068i \(0.0920162\pi\)
\(720\) 1.69737e8 + 6.17792e7i 0.0169478 + 0.00616848i
\(721\) 1.87299e8 − 1.06222e9i 0.0186106 − 0.105546i
\(722\) −2.28425e9 + 1.29546e10i −0.225873 + 1.28099i
\(723\) −9.55532e8 − 3.47785e8i −0.0940289 − 0.0342237i
\(724\) 4.50853e7 − 3.78311e7i 0.00441520 − 0.00370479i
\(725\) −8.20976e9 + 6.88881e9i −0.800106 + 0.671368i
\(726\) −4.21409e9 + 7.29901e9i −0.408719 + 0.707923i
\(727\) −3.69487e9 + 1.34482e9i −0.356639 + 0.129806i −0.514125 − 0.857715i \(-0.671883\pi\)
0.157486 + 0.987521i \(0.449661\pi\)
\(728\) −7.78953e6 − 4.41766e7i −0.000748258 − 0.00424358i
\(729\) −4.93394e9 − 8.54584e9i −0.471680 − 0.816974i
\(730\) 9.22446e8 − 1.59772e9i 0.0877629 − 0.152010i
\(731\) 1.13855e10 + 4.14400e9i 1.07806 + 0.392382i
\(732\) 3.01771e9 + 5.22683e9i 0.284373 + 0.492549i
\(733\) −9.34393e9 − 7.84049e9i −0.876326 − 0.735325i 0.0890944 − 0.996023i \(-0.471603\pi\)
−0.965420 + 0.260698i \(0.916047\pi\)
\(734\) −1.28387e10 −1.19836
\(735\) −9.59203e9 − 8.04867e9i −0.891055 − 0.747684i
\(736\) −1.10129e8 + 4.00838e7i −0.0101820 + 0.00370593i
\(737\) 3.28234e9 − 1.86151e10i 0.302028 − 1.71289i
\(738\) 8.12347e7 + 4.60705e8i 0.00743951 + 0.0421916i
\(739\) −6.93670e9 −0.632262 −0.316131 − 0.948716i \(-0.602384\pi\)
−0.316131 + 0.948716i \(0.602384\pi\)
\(740\) −6.08276e9 + 4.76081e9i −0.551810 + 0.431887i
\(741\) −5.34280e8 −0.0482397
\(742\) −9.39470e8 − 5.32800e9i −0.0844247 − 0.478796i
\(743\) 2.15838e9 − 1.22408e10i 0.193049 − 1.09483i −0.722122 − 0.691766i \(-0.756833\pi\)
0.915170 − 0.403068i \(-0.132056\pi\)
\(744\) −2.57012e9 + 9.35448e8i −0.228796 + 0.0832750i
\(745\) −2.21794e10 − 1.86107e10i −1.96518 − 1.64898i
\(746\) 6.41790e9 0.565988
\(747\) −1.78627e8 − 1.49886e8i −0.0156792 − 0.0131564i
\(748\) 2.76071e9 + 4.78168e9i 0.241193 + 0.417759i
\(749\) −6.07065e9 − 2.20954e9i −0.527897 − 0.192139i
\(750\) −2.10838e8 + 3.65182e8i −0.0182488 + 0.0316078i
\(751\) 8.87320e9 + 1.53688e10i 0.764435 + 1.32404i 0.940545 + 0.339670i \(0.110315\pi\)
−0.176110 + 0.984371i \(0.556351\pi\)
\(752\) −6.68844e8 − 3.79320e9i −0.0573538 − 0.325270i
\(753\) −6.90076e9 + 2.51167e9i −0.588999 + 0.214378i
\(754\) 1.25868e8 − 2.18010e8i 0.0106934 − 0.0185215i
\(755\) 7.28846e9 − 6.11574e9i 0.616342 − 0.517172i
\(756\) −1.93216e9 + 1.62127e9i −0.162636 + 0.136468i
\(757\) 1.53035e9 + 5.57003e8i 0.128220 + 0.0466683i 0.405333 − 0.914169i \(-0.367155\pi\)