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Properties

Label 74.8.f.b.7.10
Level $74$
Weight $8$
Character 74.7
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 7.10
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(65.8840 + 23.9798i) q^{3} +(49.0268 - 41.1384i) q^{4} +(42.5352 + 241.229i) q^{5} +560.898 q^{6} +(44.8916 + 254.593i) q^{7} +(256.000 - 443.405i) q^{8} +(2090.33 + 1754.00i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(65.8840 + 23.9798i) q^{3} +(49.0268 - 41.1384i) q^{4} +(42.5352 + 241.229i) q^{5} +560.898 q^{6} +(44.8916 + 254.593i) q^{7} +(256.000 - 443.405i) q^{8} +(2090.33 + 1754.00i) q^{9} +(979.802 + 1697.07i) q^{10} +(-2364.74 + 4095.85i) q^{11} +(4216.58 - 1534.71i) q^{12} +(6256.90 - 5250.17i) q^{13} +(1034.08 + 1791.08i) q^{14} +(-2982.24 + 16913.1i) q^{15} +(711.263 - 4033.77i) q^{16} +(29894.9 + 25084.8i) q^{17} +(20513.4 + 7466.25i) q^{18} +(-55776.6 - 20301.0i) q^{19} +(12009.1 + 10076.9i) q^{20} +(-3147.45 + 17850.1i) q^{21} +(-6570.13 + 37261.1i) q^{22} +(11773.4 + 20392.1i) q^{23} +(27499.1 - 23074.5i) q^{24} +(17031.3 - 6198.87i) q^{25} +(32671.2 - 56588.2i) q^{26} +(18991.1 + 32893.5i) q^{27} +(12674.4 + 10635.1i) q^{28} +(75400.9 - 130598. i) q^{29} +(23857.9 + 135305. i) q^{30} -233484. q^{31} +(-5690.10 - 32270.2i) q^{32} +(-254016. + 213145. i) q^{33} +(293372. + 106779. i) q^{34} +(-59505.8 + 21658.3i) q^{35} +174639. q^{36} +(1855.28 + 308105. i) q^{37} -474850. q^{38} +(538128. - 195862. i) q^{39} +(117851. + 42894.3i) q^{40} +(554583. - 465351. i) q^{41} +(25179.6 + 142801. i) q^{42} +354593. q^{43} +(52561.0 + 298088. i) q^{44} +(-334202. + 578855. i) q^{45} +(144303. + 121085. i) q^{46} +(85724.9 + 148480. i) q^{47} +(143590. - 248705. i) q^{48} +(711075. - 258810. i) q^{49} +(111072. - 93200.5i) q^{50} +(1.36807e6 + 2.36956e6i) q^{51} +(90772.8 - 514798. i) q^{52} +(70227.5 - 398280. i) q^{53} +(232768. + 195316. i) q^{54} +(-1.08862e6 - 396227. i) q^{55} +(124380. + 45270.6i) q^{56} +(-3.18797e6 - 2.67503e6i) q^{57} +(209492. - 1.18809e6i) q^{58} +(95991.0 - 544392. i) q^{59} +(549569. + 951882. i) q^{60} +(-121715. + 102131. i) q^{61} +(-1.75522e6 + 638849. i) q^{62} +(-352717. + 610923. i) q^{63} +(-131072. - 227023. i) q^{64} +(1.53263e6 + 1.28603e6i) q^{65} +(-1.32638e6 + 2.29736e6i) q^{66} +(-187148. - 1.06137e6i) q^{67} +2.49760e6 q^{68} +(286679. + 1.62584e6i) q^{69} +(-388076. + 325635. i) q^{70} +(-2.12125e6 - 772073. i) q^{71} +(1.31286e6 - 477840. i) q^{72} -5.61552e6 q^{73} +(856971. + 2.31111e6i) q^{74} +1.27074e6 q^{75} +(-3.56970e6 + 1.29927e6i) q^{76} +(-1.14893e6 - 418177. i) q^{77} +(3.50949e6 - 2.94481e6i) q^{78} +(-1.26976e6 - 7.20116e6i) q^{79} +1.00332e6 q^{80} +(-573859. - 3.25452e6i) q^{81} +(2.89583e6 - 5.01572e6i) q^{82} +(-2.84698e6 - 2.38890e6i) q^{83} +(580015. + 1.00462e6i) q^{84} +(-4.77960e6 + 8.27851e6i) q^{85} +(2.66567e6 - 970223. i) q^{86} +(8.09944e6 - 6.79623e6i) q^{87} +(1.21075e6 + 2.09708e6i) q^{88} +(202740. - 1.14979e6i) q^{89} +(-928537. + 5.26600e6i) q^{90} +(1.61754e6 + 1.35728e6i) q^{91} +(1.41611e6 + 515423. i) q^{92} +(-1.53828e7 - 5.59890e6i) q^{93} +(1.05071e6 + 881647. i) q^{94} +(2.52473e6 - 1.43184e7i) q^{95} +(398946. - 2.26254e6i) q^{96} +(-36258.9 - 62802.3i) q^{97} +(4.63739e6 - 3.89123e6i) q^{98} +(-1.21272e7 + 4.41394e6i) 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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.51754 − 2.73616i 0.664463 − 0.241845i
\(3\) 65.8840 + 23.9798i 1.40882 + 0.512769i 0.930783 − 0.365571i \(-0.119126\pi\)
0.478037 + 0.878340i \(0.341349\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) 42.5352 + 241.229i 0.152179 + 0.863047i 0.961320 + 0.275434i \(0.0888214\pi\)
−0.809142 + 0.587614i \(0.800067\pi\)
\(6\) 560.898 1.06012
\(7\) 44.8916 + 254.593i 0.0494677 + 0.280545i 0.999500 − 0.0316049i \(-0.0100618\pi\)
−0.950033 + 0.312150i \(0.898951\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) 2090.33 + 1754.00i 0.955798 + 0.802010i
\(10\) 979.802 + 1697.07i 0.309841 + 0.536660i
\(11\) −2364.74 + 4095.85i −0.535685 + 0.927833i 0.463445 + 0.886126i \(0.346613\pi\)
−0.999130 + 0.0417077i \(0.986720\pi\)
\(12\) 4216.58 − 1534.71i 0.704410 − 0.256384i
\(13\) 6256.90 − 5250.17i 0.789874 − 0.662783i −0.155840 − 0.987782i \(-0.549809\pi\)
0.945714 + 0.324999i \(0.105364\pi\)
\(14\) 1034.08 + 1791.08i 0.100718 + 0.174449i
\(15\) −2982.24 + 16913.1i −0.228151 + 1.29391i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) 29894.9 + 25084.8i 1.47579 + 1.23834i 0.910539 + 0.413423i \(0.135667\pi\)
0.565256 + 0.824916i \(0.308777\pi\)
\(18\) 20513.4 + 7466.25i 0.829054 + 0.301751i
\(19\) −55776.6 − 20301.0i −1.86558 − 0.679017i −0.974166 − 0.225831i \(-0.927490\pi\)
−0.891416 − 0.453185i \(-0.850288\pi\)
\(20\) 12009.1 + 10076.9i 0.335666 + 0.281657i
\(21\) −3147.45 + 17850.1i −0.0741638 + 0.420604i
\(22\) −6570.13 + 37261.1i −0.131551 + 0.746064i
\(23\) 11773.4 + 20392.1i 0.201769 + 0.349474i 0.949098 − 0.314980i \(-0.101998\pi\)
−0.747329 + 0.664454i \(0.768664\pi\)
\(24\) 27499.1 − 23074.5i 0.406049 − 0.340716i
\(25\) 17031.3 − 6198.87i 0.218000 − 0.0793456i
\(26\) 32671.2 − 56588.2i 0.364551 − 0.631421i
\(27\) 18991.1 + 32893.5i 0.185685 + 0.321615i
\(28\) 12674.4 + 10635.1i 0.109113 + 0.0915565i
\(29\) 75400.9 − 130598.i 0.574095 − 0.994362i −0.422044 − 0.906575i \(-0.638687\pi\)
0.996139 − 0.0877864i \(-0.0279793\pi\)
\(30\) 23857.9 + 135305.i 0.161327 + 0.914933i
\(31\) −233484. −1.40764 −0.703819 − 0.710379i \(-0.748523\pi\)
−0.703819 + 0.710379i \(0.748523\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) −254016. + 213145.i −1.23045 + 1.03247i
\(34\) 293372. + 106779.i 1.28010 + 0.465917i
\(35\) −59505.8 + 21658.3i −0.234596 + 0.0853860i
\(36\) 174639. 0.623853
\(37\) 1855.28 + 308105.i 0.00602149 + 0.999982i
\(38\) −474850. −1.40383
\(39\) 538128. − 195862.i 1.45264 − 0.528719i
\(40\) 117851. + 42894.3i 0.291155 + 0.105972i
\(41\) 554583. − 465351.i 1.25668 − 1.05448i 0.260648 − 0.965434i \(-0.416064\pi\)
0.996028 − 0.0890425i \(-0.0283807\pi\)
\(42\) 25179.6 + 142801.i 0.0524417 + 0.297412i
\(43\) 354593. 0.680127 0.340064 − 0.940402i \(-0.389551\pi\)
0.340064 + 0.940402i \(0.389551\pi\)
\(44\) 52561.0 + 298088.i 0.0930207 + 0.527547i
\(45\) −334202. + 578855.i −0.546721 + 0.946948i
\(46\) 144303. + 121085.i 0.218587 + 0.183416i
\(47\) 85724.9 + 148480.i 0.120438 + 0.208605i 0.919941 − 0.392058i \(-0.128237\pi\)
−0.799502 + 0.600663i \(0.794903\pi\)
\(48\) 143590. − 248705.i 0.187404 − 0.324594i
\(49\) 711075. − 258810.i 0.863434 − 0.314264i
\(50\) 111072. − 93200.5i 0.125664 − 0.105444i
\(51\) 1.36807e6 + 2.36956e6i 1.44415 + 2.50134i
\(52\) 90772.8 − 514798.i 0.0895249 − 0.507721i
\(53\) 70227.5 − 398280.i 0.0647950 − 0.367471i −0.935119 − 0.354335i \(-0.884707\pi\)
0.999914 − 0.0131361i \(-0.00418147\pi\)
\(54\) 232768. + 195316.i 0.201162 + 0.168795i
\(55\) −1.08862e6 − 396227.i −0.882284 − 0.321125i
\(56\) 124380. + 45270.6i 0.0946439 + 0.0344476i
\(57\) −3.18797e6 − 2.67503e6i −2.28009 − 1.91322i
\(58\) 209492. − 1.18809e6i 0.140984 − 0.799558i
\(59\) 95991.0 − 544392.i 0.0608483 − 0.345088i −0.939150 − 0.343506i \(-0.888385\pi\)
0.999999 − 0.00158178i \(-0.000503495\pi\)
\(60\) 549569. + 951882.i 0.328468 + 0.568923i
\(61\) −121715. + 102131.i −0.0686576 + 0.0576105i −0.676471 − 0.736470i \(-0.736491\pi\)
0.607813 + 0.794080i \(0.292047\pi\)
\(62\) −1.75522e6 + 638849.i −0.935323 + 0.340430i
\(63\) −352717. + 610923.i −0.177719 + 0.307818i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) 1.53263e6 + 1.28603e6i 0.692215 + 0.580837i
\(66\) −1.32638e6 + 2.29736e6i −0.567890 + 0.983614i
\(67\) −187148. − 1.06137e6i −0.0760191 − 0.431126i −0.998936 − 0.0461256i \(-0.985313\pi\)
0.922917 − 0.385000i \(-0.125799\pi\)
\(68\) 2.49760e6 0.963257
\(69\) 286679. + 1.62584e6i 0.105057 + 0.595807i
\(70\) −388076. + 325635.i −0.135230 + 0.113472i
\(71\) −2.12125e6 − 772073.i −0.703377 − 0.256008i −0.0345252 − 0.999404i \(-0.510992\pi\)
−0.668852 + 0.743395i \(0.733214\pi\)
\(72\) 1.31286e6 − 477840.i 0.414527 − 0.150876i
\(73\) −5.61552e6 −1.68951 −0.844753 − 0.535156i \(-0.820253\pi\)
−0.844753 + 0.535156i \(0.820253\pi\)
\(74\) 856971. + 2.31111e6i 0.245841 + 0.662995i
\(75\) 1.27074e6 0.347809
\(76\) −3.56970e6 + 1.29927e6i −0.932791 + 0.339508i
\(77\) −1.14893e6 − 418177.i −0.286799 − 0.104386i
\(78\) 3.50949e6 − 2.94481e6i 0.837360 − 0.702629i
\(79\) −1.26976e6 − 7.20116e6i −0.289752 − 1.64326i −0.687800 − 0.725900i \(-0.741423\pi\)
0.398048 − 0.917365i \(-0.369688\pi\)
\(80\) 1.00332e6 0.219090
\(81\) −573859. − 3.25452e6i −0.119980 − 0.680439i
\(82\) 2.89583e6 − 5.01572e6i 0.579995 − 1.00458i
\(83\) −2.84698e6 − 2.38890e6i −0.546526 − 0.458590i 0.327236 − 0.944942i \(-0.393883\pi\)
−0.873763 + 0.486353i \(0.838327\pi\)
\(84\) 580015. + 1.00462e6i 0.106773 + 0.184936i
\(85\) −4.77960e6 + 8.27851e6i −0.844161 + 1.46213i
\(86\) 2.66567e6 − 970223.i 0.451920 − 0.164485i
\(87\) 8.09944e6 − 6.79623e6i 1.31867 − 1.10650i
\(88\) 1.21075e6 + 2.09708e6i 0.189393 + 0.328039i
\(89\) 202740. − 1.14979e6i 0.0304841 − 0.172884i −0.965765 − 0.259420i \(-0.916469\pi\)
0.996249 + 0.0865359i \(0.0275797\pi\)
\(90\) −928537. + 5.26600e6i −0.134261 + 0.761433i
\(91\) 1.61754e6 + 1.35728e6i 0.225014 + 0.188809i
\(92\) 1.41611e6 + 515423.i 0.189601 + 0.0690091i
\(93\) −1.53828e7 − 5.59890e6i −1.98311 − 0.721792i
\(94\) 1.05071e6 + 881647.i 0.130477 + 0.109483i
\(95\) 2.52473e6 − 1.43184e7i 0.302122 − 1.71342i
\(96\) 398946. − 2.26254e6i 0.0460219 − 0.261003i
\(97\) −36258.9 − 62802.3i −0.00403379 − 0.00698674i 0.864001 − 0.503489i \(-0.167951\pi\)
−0.868035 + 0.496503i \(0.834617\pi\)
\(98\) 4.63739e6 − 3.89123e6i 0.497717 − 0.417634i
\(99\) −1.21272e7 + 4.41394e6i −1.25614 + 0.457197i
\(100\) 579977. − 1.00455e6i 0.0579977 − 0.100455i
\(101\) −2.49641e6 − 4.32391e6i −0.241096 − 0.417591i 0.719930 − 0.694046i \(-0.244174\pi\)
−0.961027 + 0.276455i \(0.910840\pi\)
\(102\) 1.67680e7 + 1.40700e7i 1.56452 + 1.31279i
\(103\) −1.87475e6 + 3.24717e6i −0.169049 + 0.292802i −0.938086 − 0.346403i \(-0.887403\pi\)
0.769037 + 0.639205i \(0.220736\pi\)
\(104\) −726182. − 4.11838e6i −0.0633037 − 0.359013i
\(105\) −4.43984e6 −0.374287
\(106\) −561820. − 3.18624e6i −0.0458170 − 0.259841i
\(107\) −2.68945e6 + 2.25672e6i −0.212237 + 0.178088i −0.742709 − 0.669615i \(-0.766459\pi\)
0.530472 + 0.847703i \(0.322015\pi\)
\(108\) 2.28426e6 + 831402.i 0.174487 + 0.0635079i
\(109\) −5.21153e6 + 1.89684e6i −0.385454 + 0.140294i −0.527477 − 0.849570i \(-0.676862\pi\)
0.142022 + 0.989863i \(0.454640\pi\)
\(110\) −9.26791e6 −0.663907
\(111\) −7.26606e6 + 2.03437e7i −0.504276 + 1.41188i
\(112\) 1.05890e6 0.0712183
\(113\) 422357. − 153725.i 0.0275363 − 0.0100224i −0.328215 − 0.944603i \(-0.606447\pi\)
0.355752 + 0.934581i \(0.384225\pi\)
\(114\) −3.12850e7 − 1.13868e7i −1.97774 − 0.719839i
\(115\) −4.41839e6 + 3.70747e6i −0.270908 + 0.227319i
\(116\) −1.67593e6 − 9.50469e6i −0.0996905 − 0.565373i
\(117\) 2.22878e7 1.28652
\(118\) −767928. − 4.35514e6i −0.0430262 − 0.244014i
\(119\) −5.04438e6 + 8.73713e6i −0.274406 + 0.475285i
\(120\) 6.73591e6 + 5.65210e6i 0.355846 + 0.298590i
\(121\) −1.44042e6 − 2.49489e6i −0.0739165 − 0.128027i
\(122\) −635549. + 1.10080e6i −0.0316876 + 0.0548845i
\(123\) 4.76972e7 − 1.73604e7i 2.31113 − 0.841184i
\(124\) −1.14470e7 + 9.60515e6i −0.539157 + 0.452406i
\(125\) 1.17882e7 + 2.04177e7i 0.539835 + 0.935021i
\(126\) −979978. + 5.55773e6i −0.0436435 + 0.247514i
\(127\) 6.34121e6 − 3.59628e7i 0.274700 − 1.55790i −0.465212 − 0.885200i \(-0.654022\pi\)
0.739912 − 0.672704i \(-0.234867\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) 2.33620e7 + 8.50307e6i 0.958177 + 0.348748i
\(130\) 1.50404e7 + 5.47426e6i 0.600424 + 0.218536i
\(131\) 2.05272e7 + 1.72244e7i 0.797775 + 0.669413i 0.947657 − 0.319291i \(-0.103445\pi\)
−0.149882 + 0.988704i \(0.547889\pi\)
\(132\) −3.68517e6 + 2.08997e7i −0.139460 + 0.790916i
\(133\) 2.66460e6 − 1.51117e7i 0.0982089 − 0.556970i
\(134\) −4.31096e6 − 7.46681e6i −0.154777 − 0.268082i
\(135\) −7.12708e6 + 5.98033e6i −0.249312 + 0.209198i
\(136\) 1.87758e7 − 6.83384e6i 0.640048 − 0.232959i
\(137\) −2.33383e7 + 4.04231e7i −0.775437 + 1.34310i 0.159111 + 0.987261i \(0.449137\pi\)
−0.934548 + 0.355836i \(0.884196\pi\)
\(138\) 6.60368e6 + 1.14379e7i 0.213899 + 0.370484i
\(139\) 7.24761e6 + 6.08146e6i 0.228898 + 0.192069i 0.750022 − 0.661412i \(-0.230043\pi\)
−0.521124 + 0.853481i \(0.674487\pi\)
\(140\) −2.02639e6 + 3.50981e6i −0.0624130 + 0.108102i
\(141\) 2.08738e6 + 1.18381e7i 0.0627097 + 0.355644i
\(142\) −1.80591e7 −0.529283
\(143\) 6.70794e6 + 3.80426e7i 0.191829 + 1.08791i
\(144\) 8.56199e6 − 7.18437e6i 0.238950 − 0.200502i
\(145\) 3.47113e7 + 1.26339e7i 0.945546 + 0.344151i
\(146\) −4.22149e7 + 1.53650e7i −1.12261 + 0.408598i
\(147\) 5.30547e7 1.37757
\(148\) 1.27659e7 + 1.50291e7i 0.323694 + 0.381080i
\(149\) 1.76911e7 0.438130 0.219065 − 0.975710i \(-0.429699\pi\)
0.219065 + 0.975710i \(0.429699\pi\)
\(150\) 9.55280e6 − 3.47694e6i 0.231106 − 0.0841158i
\(151\) 3.48128e7 + 1.26708e7i 0.822847 + 0.299492i 0.718920 − 0.695093i \(-0.244637\pi\)
0.103927 + 0.994585i \(0.466859\pi\)
\(152\) −2.32804e7 + 1.95346e7i −0.537697 + 0.451181i
\(153\) 1.84916e7 + 1.04871e8i 0.417402 + 2.36720i
\(154\) −9.78135e6 −0.215812
\(155\) −9.93128e6 − 5.63231e7i −0.214212 − 1.21486i
\(156\) 1.83252e7 − 3.17402e7i 0.386468 − 0.669382i
\(157\) −2.96814e7 − 2.49057e7i −0.612119 − 0.513629i 0.283196 − 0.959062i \(-0.408605\pi\)
−0.895315 + 0.445433i \(0.853050\pi\)
\(158\) −2.92490e7 − 5.06607e7i −0.589944 − 1.02181i
\(159\) 1.41775e7 − 2.45562e7i 0.279712 − 0.484475i
\(160\) 7.54248e6 − 2.74524e6i 0.145577 − 0.0529858i
\(161\) −4.66316e6 + 3.91286e6i −0.0880623 + 0.0738931i
\(162\) −1.32189e7 − 2.28958e7i −0.244283 − 0.423110i
\(163\) −1.20897e7 + 6.85639e7i −0.218654 + 1.24005i 0.655798 + 0.754937i \(0.272333\pi\)
−0.874452 + 0.485113i \(0.838779\pi\)
\(164\) 8.04569e6 − 4.56294e7i 0.142433 − 0.807776i
\(165\) −6.22214e7 − 5.22100e7i −1.07832 − 0.904815i
\(166\) −2.79387e7 − 1.01689e7i −0.474054 − 0.172542i
\(167\) −7.67006e7 − 2.79167e7i −1.27436 − 0.463828i −0.385795 − 0.922585i \(-0.626073\pi\)
−0.888562 + 0.458757i \(0.848295\pi\)
\(168\) 7.10907e6 + 5.96522e6i 0.115673 + 0.0970608i
\(169\) 688437. − 3.90432e6i 0.0109714 − 0.0622217i
\(170\) −1.32795e7 + 7.53118e7i −0.207305 + 1.17569i
\(171\) −8.09836e7 − 1.40268e8i −1.23854 − 2.14522i
\(172\) 1.73846e7 − 1.45874e7i 0.260504 − 0.218589i
\(173\) 6.40725e7 − 2.33205e7i 0.940828 − 0.342434i 0.174335 − 0.984686i \(-0.444222\pi\)
0.766493 + 0.642253i \(0.222000\pi\)
\(174\) 4.22923e7 − 7.32523e7i 0.608609 − 1.05414i
\(175\) 2.34275e6 + 4.05776e6i 0.0330440 + 0.0572339i
\(176\) 1.48398e7 + 1.24521e7i 0.205179 + 0.172166i
\(177\) 1.93787e7 − 3.35649e7i 0.262675 − 0.454966i
\(178\) −1.62192e6 − 9.19835e6i −0.0215555 − 0.122248i
\(179\) −1.33913e8 −1.74516 −0.872582 − 0.488468i \(-0.837556\pi\)
−0.872582 + 0.488468i \(0.837556\pi\)
\(180\) 7.42830e6 + 4.21280e7i 0.0949370 + 0.538415i
\(181\) 7.47893e7 − 6.27557e7i 0.937485 − 0.786644i −0.0396605 − 0.999213i \(-0.512628\pi\)
0.977146 + 0.212570i \(0.0681832\pi\)
\(182\) 1.58736e7 + 5.77753e6i 0.195176 + 0.0710382i
\(183\) −1.04681e7 + 3.81008e6i −0.126267 + 0.0459574i
\(184\) 1.20560e7 0.142672
\(185\) −7.42449e7 + 1.35528e7i −0.862115 + 0.157373i
\(186\) −1.30961e8 −1.49226
\(187\) −1.73437e8 + 6.31261e7i −1.93953 + 0.705932i
\(188\) 1.03111e7 + 3.75292e6i 0.113175 + 0.0411923i
\(189\) −7.52191e6 + 6.31163e6i −0.0810423 + 0.0680026i
\(190\) −2.01978e7 − 1.14548e8i −0.213632 − 1.21157i
\(191\) 8.32053e7 0.864040 0.432020 − 0.901864i \(-0.357801\pi\)
0.432020 + 0.901864i \(0.357801\pi\)
\(192\) −3.19157e6 − 1.81003e7i −0.0325424 − 0.184557i
\(193\) 6.63362e7 − 1.14898e8i 0.664201 − 1.15043i −0.315300 − 0.948992i \(-0.602105\pi\)
0.979501 − 0.201438i \(-0.0645615\pi\)
\(194\) −444415. − 372909.i −0.00437001 − 0.00366688i
\(195\) 7.01371e7 + 1.21481e8i 0.677371 + 1.17324i
\(196\) 2.42147e7 − 4.19411e7i 0.229712 − 0.397872i
\(197\) −7.12455e7 + 2.59312e7i −0.663935 + 0.241653i −0.651934 − 0.758275i \(-0.726042\pi\)
−0.0120006 + 0.999928i \(0.503820\pi\)
\(198\) −7.90895e7 + 6.63640e7i −0.724087 + 0.607581i
\(199\) 1.66449e7 + 2.88298e7i 0.149726 + 0.259332i 0.931126 − 0.364698i \(-0.118828\pi\)
−0.781400 + 0.624030i \(0.785494\pi\)
\(200\) 1.61139e6 − 9.13866e6i 0.0142428 − 0.0807751i
\(201\) 1.31214e7 − 7.44149e7i 0.113970 − 0.646359i
\(202\) −3.05978e7 − 2.56746e7i −0.261192 − 0.219166i
\(203\) 3.66343e7 + 1.33338e7i 0.307363 + 0.111871i
\(204\) 1.64552e8 + 5.98920e7i 1.35706 + 0.493928i
\(205\) 1.35845e8 + 1.13988e8i 1.10130 + 0.924102i
\(206\) −5.20876e6 + 2.95403e7i −0.0415144 + 0.235440i
\(207\) −1.11574e7 + 6.32768e7i −0.0874313 + 0.495847i
\(208\) −1.67277e7 − 2.89732e7i −0.128888 − 0.223241i
\(209\) 2.15047e8 − 1.80446e8i 1.62938 − 1.36721i
\(210\) −3.33767e7 + 1.21481e7i −0.248700 + 0.0905194i
\(211\) −8.38209e7 + 1.45182e8i −0.614276 + 1.06396i 0.376235 + 0.926524i \(0.377219\pi\)
−0.990511 + 0.137433i \(0.956115\pi\)
\(212\) −1.29416e7 − 2.24154e7i −0.0932849 − 0.161574i
\(213\) −1.21243e8 − 1.01735e8i −0.859659 − 0.721340i
\(214\) −1.40433e7 + 2.43238e7i −0.0979540 + 0.169661i
\(215\) 1.50827e7 + 8.55381e7i 0.103501 + 0.586982i
\(216\) 1.94469e7 0.131299
\(217\) −1.04815e7 − 5.94433e7i −0.0696327 − 0.394906i
\(218\) −3.39878e7 + 2.85192e7i −0.222191 + 0.186440i
\(219\) −3.69973e8 − 1.34659e8i −2.38021 − 0.866326i
\(220\) −6.96719e7 + 2.53585e7i −0.441142 + 0.160563i
\(221\) 3.18749e8 1.98644
\(222\) 1.04062e6 + 1.72815e8i 0.00638349 + 1.06010i
\(223\) 2.48139e8 1.49840 0.749200 − 0.662344i \(-0.230438\pi\)
0.749200 + 0.662344i \(0.230438\pi\)
\(224\) 7.96032e6 − 2.89732e6i 0.0473220 − 0.0172238i
\(225\) 4.64738e7 + 1.69151e7i 0.272000 + 0.0989999i
\(226\) 2.75447e6 − 2.31128e6i 0.0158730 − 0.0133190i
\(227\) 1.45024e7 + 8.22471e7i 0.0822903 + 0.466692i 0.997908 + 0.0646426i \(0.0205907\pi\)
−0.915618 + 0.402049i \(0.868298\pi\)
\(228\) −2.66342e8 −1.48822
\(229\) 5.75309e7 + 3.26274e8i 0.316575 + 1.79539i 0.563248 + 0.826288i \(0.309551\pi\)
−0.246673 + 0.969099i \(0.579337\pi\)
\(230\) −2.30712e7 + 3.99605e7i −0.125032 + 0.216562i
\(231\) −6.56685e7 − 5.51024e7i −0.350522 − 0.294123i
\(232\) −3.86053e7 − 6.68663e7i −0.202973 − 0.351560i
\(233\) −7.25562e6 + 1.25671e7i −0.0375776 + 0.0650863i −0.884203 − 0.467104i \(-0.845297\pi\)
0.846625 + 0.532190i \(0.178631\pi\)
\(234\) 1.67549e8 − 6.09829e7i 0.854844 − 0.311138i
\(235\) −3.21714e7 + 2.69950e7i −0.161708 + 0.135689i
\(236\) −1.76893e7 − 3.06387e7i −0.0876029 − 0.151733i
\(237\) 8.90257e7 − 5.04890e8i 0.434406 − 2.46364i
\(238\) −1.40152e7 + 7.94840e7i −0.0673875 + 0.382173i
\(239\) 1.25052e8 + 1.04931e8i 0.592514 + 0.497179i 0.889030 − 0.457849i \(-0.151380\pi\)
−0.296515 + 0.955028i \(0.595825\pi\)
\(240\) 6.61025e7 + 2.40594e7i 0.308659 + 0.112343i
\(241\) 1.26199e8 + 4.59329e7i 0.580762 + 0.211380i 0.615661 − 0.788011i \(-0.288889\pi\)
−0.0348997 + 0.999391i \(0.511111\pi\)
\(242\) −1.76548e7 − 1.48142e7i −0.0800774 − 0.0671930i
\(243\) 5.46590e7 − 3.09987e8i 0.244365 − 1.38587i
\(244\) −1.76579e6 + 1.00143e7i −0.00778170 + 0.0441322i
\(245\) 9.26782e7 + 1.60523e8i 0.402621 + 0.697360i
\(246\) 3.11065e8 − 2.61014e8i 1.33223 − 1.11787i
\(247\) −4.55573e8 + 1.65815e8i −1.92362 + 0.700139i
\(248\) −5.97719e7 + 1.03528e8i −0.248838 + 0.430999i
\(249\) −1.30285e8 − 2.25660e8i −0.534807 − 0.926312i
\(250\) 1.44484e8 + 1.21236e8i 0.584830 + 0.490731i
\(251\) −9.41717e7 + 1.63110e8i −0.375891 + 0.651063i −0.990460 − 0.137800i \(-0.955997\pi\)
0.614569 + 0.788863i \(0.289330\pi\)
\(252\) 7.83982e6 + 4.44618e7i 0.0308606 + 0.175019i
\(253\) −1.11364e8 −0.432338
\(254\) −5.07297e7 − 2.87702e8i −0.194243 − 1.10160i
\(255\) −5.13416e8 + 4.30807e8i −1.93900 + 1.62702i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) −3.64158e8 + 1.32543e8i −1.33821 + 0.487069i −0.909248 − 0.416254i \(-0.863343\pi\)
−0.428962 + 0.903323i \(0.641121\pi\)
\(258\) 1.98890e8 0.721016
\(259\) −7.83580e7 + 1.43037e7i −0.280243 + 0.0511561i
\(260\) 1.28045e8 0.451811
\(261\) 3.86682e8 − 1.40741e8i 1.34621 − 0.489979i
\(262\) 2.01443e8 + 7.33192e7i 0.691986 + 0.251862i
\(263\) 2.78903e7 − 2.34027e7i 0.0945384 − 0.0793271i −0.594294 − 0.804248i \(-0.702568\pi\)
0.688832 + 0.724921i \(0.258124\pi\)
\(264\) 2.94814e7 + 1.67197e8i 0.0986130 + 0.559262i
\(265\) 9.90638e7 0.327005
\(266\) −2.13168e7 − 1.20893e8i −0.0694442 − 0.393837i
\(267\) 4.09291e7 − 7.08914e7i 0.131596 − 0.227931i
\(268\) −5.28382e7 − 4.43365e7i −0.167678 − 0.140699i
\(269\) −2.68641e8 − 4.65300e8i −0.841472 − 1.45747i −0.888650 − 0.458585i \(-0.848356\pi\)
0.0471785 − 0.998886i \(-0.484977\pi\)
\(270\) −3.72150e7 + 6.44582e7i −0.115065 + 0.199299i
\(271\) 3.04689e6 − 1.10898e6i 0.00929959 − 0.00338477i −0.337366 − 0.941374i \(-0.609536\pi\)
0.346666 + 0.937989i \(0.387314\pi\)
\(272\) 1.22450e8 − 1.02747e8i 0.368949 − 0.309585i
\(273\) 7.40226e7 + 1.28211e8i 0.220189 + 0.381378i
\(274\) −6.48424e7 + 3.67739e8i −0.190428 + 1.07997i
\(275\) −1.48849e7 + 8.44163e7i −0.0431599 + 0.244772i
\(276\) 8.09394e7 + 6.79162e7i 0.231728 + 0.194443i
\(277\) 3.63829e8 + 1.32423e8i 1.02853 + 0.374355i 0.800522 − 0.599303i \(-0.204556\pi\)
0.228011 + 0.973659i \(0.426778\pi\)
\(278\) 7.11241e7 + 2.58870e7i 0.198545 + 0.0722646i
\(279\) −4.88058e8 − 4.09530e8i −1.34542 − 1.12894i
\(280\) −5.63006e6 + 3.19297e7i −0.0153271 + 0.0869244i
\(281\) −5.68830e7 + 3.22600e8i −0.152936 + 0.867345i 0.807712 + 0.589577i \(0.200706\pi\)
−0.960648 + 0.277768i \(0.910406\pi\)
\(282\) 4.80830e7 + 8.32822e7i 0.127679 + 0.221147i
\(283\) 6.18459e7 − 5.18949e7i 0.162203 − 0.136104i −0.558074 − 0.829791i \(-0.688459\pi\)
0.720277 + 0.693687i \(0.244015\pi\)
\(284\) −1.35760e8 + 4.94127e7i −0.351689 + 0.128004i
\(285\) 5.09693e8 − 8.82814e8i 1.30422 − 2.25898i
\(286\) 1.54518e8 + 2.67633e8i 0.390569 + 0.676486i
\(287\) 1.43371e8 + 1.20303e8i 0.357994 + 0.300392i
\(288\) 4.47076e7 − 7.74358e7i 0.110283 − 0.191015i
\(289\) 1.93203e8 + 1.09571e9i 0.470839 + 2.67026i
\(290\) 2.95512e8 0.711511
\(291\) −882895. − 5.00715e6i −0.00210031 − 0.0119115i
\(292\) −2.75311e8 + 2.31014e8i −0.647119 + 0.542997i
\(293\) 3.43800e8 + 1.25133e8i 0.798489 + 0.290626i 0.708860 − 0.705349i \(-0.249210\pi\)
0.0896291 + 0.995975i \(0.471432\pi\)
\(294\) 3.98841e8 − 1.45166e8i 0.915343 − 0.333158i
\(295\) 1.35406e8 0.307087
\(296\) 1.37090e8 + 7.80521e7i 0.307245 + 0.174930i
\(297\) −1.79636e8 −0.397874
\(298\) 1.32994e8 − 4.84057e7i 0.291121 − 0.105959i
\(299\) 1.80727e8 + 6.57793e7i 0.390997 + 0.142311i
\(300\) 6.23001e7 − 5.22760e7i 0.133219 − 0.111784i
\(301\) 1.59182e7 + 9.02768e7i 0.0336444 + 0.190807i
\(302\) 2.96376e8 0.619182
\(303\) −6.07869e7 − 3.44740e8i −0.125534 − 0.711938i
\(304\) −1.21562e8 + 2.10551e8i −0.248164 + 0.429833i
\(305\) −2.98141e7 − 2.50170e7i −0.0601688 − 0.0504876i
\(306\) 4.25956e8 + 7.37777e8i 0.849844 + 1.47197i
\(307\) −2.21120e8 + 3.82991e8i −0.436158 + 0.755448i −0.997389 − 0.0722109i \(-0.976995\pi\)
0.561231 + 0.827659i \(0.310328\pi\)
\(308\) −7.35317e7 + 2.67633e7i −0.143399 + 0.0521931i
\(309\) −2.01383e8 + 1.68980e8i −0.388300 + 0.325822i
\(310\) −2.28768e8 − 3.96238e8i −0.436143 − 0.755422i
\(311\) 7.13888e7 − 4.04866e8i 0.134576 − 0.763220i −0.840578 − 0.541691i \(-0.817784\pi\)
0.975154 − 0.221529i \(-0.0711046\pi\)
\(312\) 5.09143e7 − 2.88749e8i 0.0949071 − 0.538245i
\(313\) −3.93402e8 − 3.30103e8i −0.725156 − 0.608478i 0.203650 − 0.979044i \(-0.434719\pi\)
−0.928806 + 0.370566i \(0.879164\pi\)
\(314\) −2.91277e8 − 1.06016e8i −0.530949 − 0.193250i
\(315\) −1.62375e8 − 5.90998e7i −0.292707 − 0.106537i
\(316\) −3.58496e8 − 3.00814e8i −0.639117 − 0.536282i
\(317\) −6.91330e7 + 3.92073e8i −0.121893 + 0.691289i 0.861212 + 0.508246i \(0.169706\pi\)
−0.983105 + 0.183043i \(0.941405\pi\)
\(318\) 3.93905e7 − 2.23394e8i 0.0686904 − 0.389563i
\(319\) 3.56607e8 + 6.17662e8i 0.615068 + 1.06533i
\(320\) 4.91895e7 − 4.12749e7i 0.0839165 − 0.0704143i
\(321\) −2.31308e8 + 8.41891e7i −0.390322 + 0.142065i
\(322\) −2.43493e7 + 4.21743e7i −0.0406435 + 0.0703966i
\(323\) −1.15819e9 − 2.00604e9i −1.91236 − 3.31231i
\(324\) −1.62020e8 − 1.35951e8i −0.264644 − 0.222062i
\(325\) 7.40178e7 − 1.28203e8i 0.119604 − 0.207160i
\(326\) 9.67173e7 + 5.48511e8i 0.154612 + 0.876847i
\(327\) −3.88843e8 −0.614974
\(328\) −6.43655e7 − 3.65035e8i −0.100715 − 0.571184i
\(329\) −3.39536e7 + 2.84905e7i −0.0525655 + 0.0441077i
\(330\) −6.10607e8 − 2.22243e8i −0.935326 − 0.340431i
\(331\) 3.60095e8 − 1.31064e8i 0.545782 − 0.198648i −0.0543893 − 0.998520i \(-0.517321\pi\)
0.600172 + 0.799871i \(0.295099\pi\)
\(332\) −2.37854e8 −0.356720
\(333\) −5.36536e8 + 6.47295e8i −0.796240 + 0.960610i
\(334\) −6.52984e8 −0.958937
\(335\) 2.48072e8 − 9.02909e7i 0.360513 − 0.131216i
\(336\) 6.97646e7 + 2.53922e7i 0.100334 + 0.0365185i
\(337\) −6.31331e8 + 5.29750e8i −0.898571 + 0.753991i −0.969911 − 0.243462i \(-0.921717\pi\)
0.0713396 + 0.997452i \(0.477273\pi\)
\(338\) −5.50750e6 − 3.12346e7i −0.00775793 − 0.0439974i
\(339\) 3.15129e7 0.0439328
\(340\) 1.06236e8 + 6.02494e8i 0.146587 + 0.831336i
\(341\) 5.52129e8 − 9.56316e8i 0.754050 − 1.30605i
\(342\) −9.92593e8 − 8.32885e8i −1.34178 − 1.12588i
\(343\) 2.04264e8 + 3.53795e8i 0.273314 + 0.473394i
\(344\) 9.07757e7 − 1.57228e8i 0.120231 − 0.208246i
\(345\) −3.80006e8 + 1.38311e8i −0.498222 + 0.181338i
\(346\) 4.17859e8 − 3.50625e8i 0.542330 − 0.455069i
\(347\) −3.37572e8 − 5.84692e8i −0.433724 − 0.751232i 0.563467 − 0.826139i \(-0.309467\pi\)
−0.997191 + 0.0749070i \(0.976134\pi\)
\(348\) 1.17504e8 − 6.66396e8i 0.149460 − 0.847627i
\(349\) 8.09078e7 − 4.58851e8i 0.101883 − 0.577807i −0.890537 − 0.454911i \(-0.849671\pi\)
0.992420 − 0.122895i \(-0.0392179\pi\)
\(350\) 2.87144e7 + 2.40942e7i 0.0357982 + 0.0300383i
\(351\) 2.91522e8 + 1.06105e8i 0.359829 + 0.130967i
\(352\) 1.45630e8 + 5.30048e7i 0.177971 + 0.0647763i
\(353\) 1.16618e8 + 9.78545e7i 0.141109 + 0.118405i 0.710610 − 0.703586i \(-0.248419\pi\)
−0.569501 + 0.821991i \(0.692863\pi\)
\(354\) 5.38412e7 − 3.05349e8i 0.0645065 − 0.365834i
\(355\) 9.60186e7 − 5.44548e8i 0.113908 − 0.646007i
\(356\) −3.73610e7 − 6.47112e7i −0.0438878 − 0.0760159i
\(357\) −5.41859e8 + 4.54674e8i −0.630300 + 0.528885i
\(358\) −1.00669e9 + 3.66407e8i −1.15960 + 0.422059i
\(359\) −1.65849e7 + 2.87258e7i −0.0189183 + 0.0327674i −0.875330 − 0.483527i \(-0.839356\pi\)
0.856411 + 0.516294i \(0.172689\pi\)
\(360\) 1.71111e8 + 2.96374e8i 0.193295 + 0.334797i
\(361\) 2.01415e9 + 1.69008e9i 2.25329 + 1.89074i
\(362\) 3.90522e8 − 6.76404e8i 0.432679 − 0.749422i
\(363\) −3.50739e7 − 1.98914e8i −0.0384868 − 0.218269i
\(364\) 1.35139e8 0.146867
\(365\) −2.38857e8 − 1.35463e9i −0.257107 − 1.45812i
\(366\) −6.82695e7 + 5.72849e7i −0.0727852 + 0.0610740i
\(367\) 2.31556e8 + 8.42794e7i 0.244526 + 0.0890001i 0.461376 − 0.887205i \(-0.347356\pi\)
−0.216850 + 0.976205i \(0.569578\pi\)
\(368\) 9.06312e7 − 3.29870e7i 0.0948004 − 0.0345045i
\(369\) 1.97549e9 2.04683
\(370\) −5.21056e8 + 3.05030e8i −0.534784 + 0.313066i
\(371\) 1.04552e8 0.106297
\(372\) −9.84502e8 + 3.58330e8i −0.991554 + 0.360896i
\(373\) −8.70904e8 − 3.16983e8i −0.868940 − 0.316268i −0.131202 − 0.991356i \(-0.541884\pi\)
−0.737738 + 0.675088i \(0.764106\pi\)
\(374\) −1.13110e9 + 9.49105e8i −1.11802 + 0.938132i
\(375\) 2.87038e8 + 1.62788e9i 0.281080 + 1.59409i
\(376\) 8.77823e7 0.0851628
\(377\) −2.13886e8 − 1.21301e9i −0.205583 − 1.16592i
\(378\) −3.92766e7 + 6.80291e7i −0.0374036 + 0.0647849i
\(379\) 4.43248e8 + 3.71929e8i 0.418224 + 0.350932i 0.827487 − 0.561485i \(-0.189770\pi\)
−0.409263 + 0.912417i \(0.634214\pi\)
\(380\) −4.65259e8 − 8.05852e8i −0.434963 − 0.753377i
\(381\) 1.28017e9 − 2.21731e9i 1.18585 − 2.05395i
\(382\) 6.25499e8 − 2.27663e8i 0.574123 − 0.208964i
\(383\) −1.17007e9 + 9.81808e8i −1.06419 + 0.892958i −0.994513 − 0.104612i \(-0.966640\pi\)
−0.0696726 + 0.997570i \(0.522195\pi\)
\(384\) −7.35181e7 − 1.27337e8i −0.0662575 − 0.114761i
\(385\) 5.20064e7 − 2.94943e8i 0.0464456 − 0.263406i
\(386\) 1.84306e8 − 1.04525e9i 0.163112 − 0.925052i
\(387\) 7.41216e8 + 6.21954e8i 0.650065 + 0.545469i
\(388\) −4.36125e6 − 1.58736e6i −0.00379053 − 0.00137964i
\(389\) −4.66334e8 − 1.69732e8i −0.401674 − 0.146197i 0.133280 − 0.991078i \(-0.457449\pi\)
−0.534954 + 0.844881i \(0.679671\pi\)
\(390\) 8.59650e8 + 7.21332e8i 0.733830 + 0.615757i
\(391\) −1.59568e8 + 9.04954e8i −0.134998 + 0.765610i
\(392\) 6.72775e7 − 3.81550e8i 0.0564116 − 0.319926i
\(393\) 9.39377e8 + 1.62705e9i 0.780667 + 1.35216i
\(394\) −4.64639e8 + 3.89878e8i −0.382718 + 0.321138i
\(395\) 1.68312e9 − 6.12605e8i 1.37412 − 0.500139i
\(396\) −4.12976e8 + 7.15295e8i −0.334189 + 0.578832i
\(397\) 5.63522e8 + 9.76049e8i 0.452006 + 0.782898i 0.998511 − 0.0545585i \(-0.0173751\pi\)
−0.546504 + 0.837456i \(0.684042\pi\)
\(398\) 2.04012e8 + 1.71186e8i 0.162205 + 0.136106i
\(399\) 5.37930e8 − 9.31721e8i 0.423956 − 0.734312i
\(400\) −1.28911e7 − 7.31093e7i −0.0100712 − 0.0571166i
\(401\) −1.01426e9 −0.785492 −0.392746 − 0.919647i \(-0.628475\pi\)
−0.392746 + 0.919647i \(0.628475\pi\)
\(402\) −1.04971e8 − 5.95319e8i −0.0805893 − 0.457045i
\(403\) −1.46089e9 + 1.22583e9i −1.11186 + 0.932958i
\(404\) −3.00270e8 − 1.09289e8i −0.226557 − 0.0824598i
\(405\) 7.60675e8 − 2.76863e8i 0.568993 − 0.207096i
\(406\) 3.11883e8 0.231287
\(407\) −1.26634e9 − 7.20989e8i −0.931042 − 0.530088i
\(408\) 1.40090e9 1.02117
\(409\) −7.27384e8 + 2.64746e8i −0.525693 + 0.191337i −0.591214 − 0.806515i \(-0.701351\pi\)
0.0655213 + 0.997851i \(0.479129\pi\)
\(410\) 1.33311e9 + 4.85213e8i 0.955264 + 0.347688i
\(411\) −2.50696e9 + 2.10359e9i −1.78115 + 1.49456i
\(412\) 4.16701e7 + 2.36323e8i 0.0293551 + 0.166481i
\(413\) 1.42908e8 0.0998229
\(414\) 8.92592e7 + 5.06214e8i 0.0618233 + 0.350617i
\(415\) 4.55175e8 − 7.88387e8i 0.312615 − 0.541466i
\(416\) −2.05026e8 − 1.72037e8i −0.139631 − 0.117165i
\(417\) 3.31669e8 + 5.74468e8i 0.223990 + 0.387962i
\(418\) 1.12290e9 − 1.94492e9i 0.752009 − 1.30252i
\(419\) 9.94604e8 − 3.62006e8i 0.660543 − 0.240418i 0.0100723 − 0.999949i \(-0.496794\pi\)
0.650471 + 0.759531i \(0.274572\pi\)
\(420\) −2.17671e8 + 1.82648e8i −0.143360 + 0.120294i
\(421\) −1.43292e9 − 2.48189e9i −0.935910 − 1.62104i −0.773003 − 0.634403i \(-0.781246\pi\)
−0.162908 − 0.986641i \(-0.552087\pi\)
\(422\) −2.32886e8 + 1.32076e9i −0.150851 + 0.855520i
\(423\) −8.12397e7 + 4.60733e8i −0.0521888 + 0.295977i
\(424\) −1.58621e8 − 1.33099e8i −0.101060 − 0.0847996i
\(425\) 6.64645e8 + 2.41911e8i 0.419980 + 0.152860i
\(426\) −1.18981e9 − 4.33055e8i −0.745664 − 0.271400i
\(427\) −3.14657e7 − 2.64029e7i −0.0195587 − 0.0164117i
\(428\) −3.90176e7 + 2.21280e8i −0.0240551 + 0.136423i
\(429\) −4.70309e8 + 2.66726e9i −0.287596 + 1.63104i
\(430\) 3.47431e8 + 6.01767e8i 0.210731 + 0.364997i
\(431\) 1.46369e9 − 1.22818e9i 0.880598 − 0.738910i −0.0857039 − 0.996321i \(-0.527314\pi\)
0.966302 + 0.257411i \(0.0828695\pi\)
\(432\) 1.46193e8 − 5.32097e7i 0.0872433 − 0.0317540i
\(433\) −4.48977e8 + 7.77651e8i −0.265776 + 0.460338i −0.967767 − 0.251848i \(-0.918962\pi\)
0.701990 + 0.712186i \(0.252295\pi\)
\(434\) −2.41441e8 − 4.18189e8i −0.141774 − 0.245560i
\(435\) 1.98396e9 + 1.66474e9i 1.15563 + 0.969693i
\(436\) −1.77472e8 + 3.07390e8i −0.102548 + 0.177618i
\(437\) −2.42699e8 − 1.37642e9i −0.139118 − 0.788977i
\(438\) −3.14974e9 −1.79108
\(439\) −2.15177e8 − 1.22033e9i −0.121386 − 0.688416i −0.983389 − 0.181512i \(-0.941901\pi\)
0.862002 − 0.506904i \(-0.169210\pi\)
\(440\) −4.54377e8 + 3.81267e8i −0.254291 + 0.213376i
\(441\) 1.94033e9 + 7.06224e8i 1.07731 + 0.392109i
\(442\) 2.39621e9 − 8.72148e8i 1.31992 − 0.480410i
\(443\) −1.38824e8 −0.0758666 −0.0379333 − 0.999280i \(-0.512077\pi\)
−0.0379333 + 0.999280i \(0.512077\pi\)
\(444\) 4.80674e8 + 1.29630e9i 0.260621 + 0.702854i
\(445\) 2.85987e8 0.153846
\(446\) 1.86539e9 − 6.78948e8i 0.995631 − 0.362380i
\(447\) 1.16556e9 + 4.24230e8i 0.617247 + 0.224659i
\(448\) 5.19145e7 − 4.35615e7i 0.0272782 − 0.0228891i
\(449\) −2.00550e7 − 1.13738e8i −0.0104559 − 0.0592982i 0.979133 − 0.203219i \(-0.0651402\pi\)
−0.989589 + 0.143920i \(0.954029\pi\)
\(450\) 3.95651e8 0.204677
\(451\) 5.94562e8 + 3.37193e9i 0.305196 + 1.73085i
\(452\) 1.43828e7 − 2.49118e7i 0.00732588 − 0.0126888i
\(453\) 1.98976e9 + 1.66961e9i 1.00567 + 0.843860i
\(454\) 3.34063e8 + 5.78615e8i 0.167546 + 0.290198i
\(455\) −2.58612e8 + 4.47929e8i −0.128709 + 0.222930i
\(456\) −2.00224e9 + 7.28756e8i −0.988870 + 0.359919i
\(457\) −2.22632e9 + 1.86811e9i −1.09114 + 0.915577i −0.996798 − 0.0799625i \(-0.974520\pi\)
−0.0943444 + 0.995540i \(0.530075\pi\)
\(458\) 1.32523e9 + 2.29536e9i 0.644557 + 1.11641i
\(459\) −2.57391e8 + 1.45974e9i −0.124236 + 0.704579i
\(460\) −6.41003e7 + 3.63531e8i −0.0307049 + 0.174136i
\(461\) −4.59208e8 − 3.85321e8i −0.218301 − 0.183176i 0.527079 − 0.849817i \(-0.323287\pi\)
−0.745380 + 0.666640i \(0.767732\pi\)
\(462\) −6.44434e8 − 2.34555e8i −0.304041 − 0.110662i
\(463\) −1.99043e9 − 7.24456e8i −0.931994 − 0.339218i −0.168994 − 0.985617i \(-0.554052\pi\)
−0.762999 + 0.646399i \(0.776274\pi\)
\(464\) −4.73174e8 − 3.97040e8i −0.219891 − 0.184511i
\(465\) 6.96305e8 − 3.94894e9i 0.321155 − 1.82136i
\(466\) −2.01588e7 + 1.14326e8i −0.00922813 + 0.0523353i
\(467\) −9.48381e8 − 1.64264e9i −0.430897 − 0.746336i 0.566053 − 0.824369i \(-0.308470\pi\)
−0.996951 + 0.0780324i \(0.975136\pi\)
\(468\) 1.09270e9 − 9.16883e8i 0.492765 − 0.413479i
\(469\) 2.61815e8 − 9.52930e7i 0.117190 − 0.0426536i
\(470\) −1.67987e8 + 2.90962e8i −0.0746333 + 0.129269i
\(471\) −1.35830e9 − 2.35264e9i −0.598993 − 1.03749i
\(472\) −2.16812e8 − 1.81927e8i −0.0949046 − 0.0796344i
\(473\) −8.38520e8 + 1.45236e9i −0.364334 + 0.631045i
\(474\) −7.12205e8 − 4.03912e9i −0.307172 − 1.74206i
\(475\) −1.07579e9 −0.460574
\(476\) 1.12121e8 + 6.35872e8i 0.0476501 + 0.270237i
\(477\) 8.45380e8 − 7.09358e8i 0.356646 − 0.299262i
\(478\) 1.22719e9 + 4.46662e8i 0.513944 + 0.187060i
\(479\) 3.20707e9 − 1.16728e9i 1.33332 − 0.485289i 0.425617 − 0.904903i \(-0.360057\pi\)
0.907702 + 0.419615i \(0.137835\pi\)
\(480\) 5.62759e8 0.232262
\(481\) 1.62921e9 + 1.91804e9i 0.667527 + 0.785869i
\(482\) 1.07439e9 0.437016
\(483\) −4.01058e8 + 1.45973e8i −0.161954 + 0.0589464i
\(484\) −1.73255e8 − 6.30597e7i −0.0694588 − 0.0252809i
\(485\) 1.36075e7 − 1.14180e7i 0.00541603 − 0.00454459i
\(486\) −4.37272e8 − 2.47989e9i −0.172792 − 0.979955i
\(487\) −2.63360e9 −1.03324 −0.516618 − 0.856216i \(-0.672809\pi\)
−0.516618 + 0.856216i \(0.672809\pi\)
\(488\) 1.41263e7 + 8.01143e7i 0.00550249 + 0.0312062i
\(489\) −2.44067e9 + 4.22736e9i −0.943903 + 1.63489i
\(490\) 1.13593e9 + 9.53159e8i 0.436180 + 0.365998i
\(491\) 2.15078e8 + 3.72525e8i 0.0819993 + 0.142027i 0.904109 − 0.427303i \(-0.140536\pi\)
−0.822109 + 0.569330i \(0.807203\pi\)
\(492\) 1.62427e9 − 2.81331e9i 0.614864 − 1.06498i
\(493\) 5.53014e9 − 2.01280e9i 2.07860 − 0.756550i
\(494\) −2.97109e9 + 2.49304e9i −1.10885 + 0.930433i
\(495\) −1.58060e9 − 2.73769e9i −0.585740 − 1.01453i
\(496\) −1.66068e8 + 9.41821e8i −0.0611084 + 0.346563i
\(497\) 1.01338e8 − 5.74716e8i 0.0370275 − 0.209994i
\(498\) −1.59687e9 − 1.33993e9i −0.579383 − 0.486160i
\(499\) −2.19752e9 − 7.99834e8i −0.791739 − 0.288169i −0.0856800 − 0.996323i \(-0.527306\pi\)
−0.706059 + 0.708153i \(0.749528\pi\)
\(500\) 1.41789e9 + 5.16069e8i 0.507279 + 0.184634i
\(501\) −4.38390e9 − 3.67853e9i −1.55750 − 1.30690i
\(502\) −2.61644e8 + 1.48386e9i −0.0923097 + 0.523515i
\(503\) 1.12320e8 − 6.37001e8i 0.0393523 − 0.223178i −0.958789 − 0.284119i \(-0.908299\pi\)
0.998141 + 0.0609407i \(0.0194101\pi\)
\(504\) 1.80591e8 + 3.12793e8i 0.0628332 + 0.108830i
\(505\) 9.36867e8 − 7.86124e8i 0.323711 − 0.271626i
\(506\) −8.37185e8 + 3.04710e8i −0.287273 + 0.104559i
\(507\) 1.38982e8 − 2.40724e8i 0.0473620 − 0.0820335i
\(508\) −1.16856e9 − 2.02401e9i −0.395484 − 0.684999i
\(509\) 1.67939e9 + 1.40917e9i 0.564468 + 0.473645i 0.879805 − 0.475335i \(-0.157673\pi\)
−0.315337 + 0.948980i \(0.602118\pi\)
\(510\) −2.68087e9 + 4.64340e9i −0.894911 + 1.55003i
\(511\) −2.52090e8 − 1.42967e9i −0.0835761 − 0.473984i
\(512\) −1.34218e8 −0.0441942
\(513\) −3.91486e8 − 2.22023e9i −0.128028 − 0.726083i
\(514\) −2.37492e9 + 1.99279e9i −0.771396 + 0.647278i
\(515\) −8.63054e8 − 3.14126e8i −0.278428 − 0.101339i
\(516\) 1.49517e9 − 5.44196e8i 0.479089 − 0.174374i
\(517\) −8.10870e8 −0.258068
\(518\) −5.49922e8 + 3.21928e8i −0.173839 + 0.101767i
\(519\) 4.78057e9 1.50105
\(520\) 9.62586e8 − 3.50353e8i 0.300212 − 0.109268i
\(521\) 3.40142e9 + 1.23802e9i 1.05373 + 0.383526i 0.810069 − 0.586335i \(-0.199430\pi\)
0.243659 + 0.969861i \(0.421652\pi\)
\(522\) 2.52181e9 − 2.11605e9i 0.776006 − 0.651146i
\(523\) 6.76177e8 + 3.83479e9i 0.206683 + 1.17216i 0.894769 + 0.446528i \(0.147340\pi\)
−0.688087 + 0.725629i \(0.741549\pi\)
\(524\) 1.71497e9 0.520710
\(525\) 5.70454e7 + 3.23520e8i 0.0172053 + 0.0975762i
\(526\) 1.45633e8 − 2.52243e8i 0.0436324 − 0.0755736i
\(527\) −6.97998e9 − 5.85690e9i −2.07738 − 1.74313i
\(528\) 6.79106e8 + 1.17625e9i 0.200779 + 0.347760i
\(529\) 1.42519e9 − 2.46850e9i 0.418579 − 0.724999i
\(530\) 7.44716e8 − 2.71054e8i 0.217283 − 0.0790844i
\(531\) 1.15551e9 − 9.69592e8i 0.334923 − 0.281033i
\(532\) −4.91034e8 − 8.50495e8i −0.141391 − 0.244896i
\(533\) 1.02681e9 − 5.82331e9i 0.293727 − 1.66581i
\(534\) 1.13716e8 − 6.44918e8i 0.0323168 − 0.183278i
\(535\) −6.58783e8 − 5.52785e8i −0.185996 − 0.156069i
\(536\) −5.18525e8 − 1.88728e8i −0.145443 − 0.0529370i
\(537\) −8.82270e9 − 3.21120e9i −2.45862 − 0.894865i
\(538\) −3.29266e9 − 2.76287e9i −0.911609 − 0.764931i
\(539\) −6.21461e8 + 3.52448e9i −0.170944 + 0.969469i
\(540\) −1.03397e8 + 5.86393e8i −0.0282572 + 0.160255i
\(541\) −2.84236e9 − 4.92311e9i −0.771772 − 1.33675i −0.936591 − 0.350424i \(-0.886038\pi\)
0.164820 − 0.986324i \(-0.447296\pi\)
\(542\) 1.98708e7 − 1.66735e7i 0.00536064 − 0.00449811i
\(543\) 6.43229e9 − 2.34116e9i 1.72411 − 0.627526i
\(544\) 6.39386e8 − 1.10745e9i 0.170281 − 0.294936i
\(545\) −6.79247e8 − 1.17649e9i −0.179738 − 0.311315i
\(546\) 9.07274e8 + 7.61293e8i 0.238542 + 0.200160i
\(547\) −2.79007e9 + 4.83254e9i −0.728885 + 1.26247i 0.228469 + 0.973551i \(0.426628\pi\)
−0.957355 + 0.288915i \(0.906705\pi\)
\(548\) 5.18739e8 + 2.94191e9i 0.134653 + 0.763656i
\(549\) −4.33561e8 −0.111827
\(550\) 1.19079e8 + 6.75330e8i 0.0305187 + 0.173080i
\(551\) −6.85689e9 + 5.75361e9i −1.74621 + 1.46524i
\(552\) 7.94295e8 + 2.89100e8i 0.200999 + 0.0731578i
\(553\) 1.77636e9 − 6.46543e8i 0.446677 − 0.162577i
\(554\) 3.09743e9 0.773958
\(555\) −5.21654e9 − 8.87463e8i −1.29526 − 0.220356i
\(556\) 6.05509e8 0.149403
\(557\) −6.28689e9 + 2.28824e9i −1.54150 + 0.561059i −0.966404 − 0.257028i \(-0.917257\pi\)
−0.575094 + 0.818088i \(0.695034\pi\)
\(558\) −4.78954e9 − 1.74325e9i −1.16701 − 0.424756i
\(559\) 2.21865e9 − 1.86167e9i 0.537215 − 0.450777i
\(560\) 4.50405e7 + 2.55437e8i 0.0108379 + 0.0614648i
\(561\) −1.29405e10 −3.09443
\(562\) 4.55064e8 + 2.58080e9i 0.108142 + 0.613305i
\(563\) −5.45889e8 + 9.45508e8i −0.128921 + 0.223299i −0.923259 − 0.384178i \(-0.874485\pi\)
0.794338 + 0.607477i \(0.207818\pi\)
\(564\) 5.89339e8 + 4.94514e8i 0.138321 + 0.116065i
\(565\) 5.50481e7 + 9.53461e7i 0.0128402 + 0.0222399i
\(566\) 3.22936e8 − 5.59342e8i 0.0748617 − 0.129664i
\(567\) 8.02816e8 − 2.92201e8i 0.184959 − 0.0673196i
\(568\) −8.85382e8 + 7.42924e8i −0.202727 + 0.170108i
\(569\) 2.03324e9 + 3.52167e9i 0.462696 + 0.801413i 0.999094 − 0.0425523i \(-0.0135489\pi\)
−0.536398 + 0.843965i \(0.680216\pi\)
\(570\) 1.41612e9 − 8.03119e9i 0.320285 − 1.81643i
\(571\) −1.09954e9 + 6.23581e9i −0.247164 + 1.40174i 0.568248 + 0.822857i \(0.307621\pi\)
−0.815413 + 0.578880i \(0.803490\pi\)
\(572\) 1.89388e9 + 1.58916e9i 0.423123 + 0.355043i
\(573\) 5.48190e9 + 1.99525e9i 1.21728 + 0.443053i
\(574\) 1.40697e9 + 5.12094e8i 0.310522 + 0.113021i
\(575\) 3.26924e8 + 2.74322e8i 0.0717149 + 0.0601759i
\(576\) 1.24214e8 − 7.04454e8i 0.0270827 − 0.153594i
\(577\) −5.26551e8 + 2.98622e9i −0.114110 + 0.647152i 0.873076 + 0.487583i \(0.162121\pi\)
−0.987187 + 0.159569i \(0.948990\pi\)
\(578\) 4.45046e9 + 7.70842e9i 0.958644 + 1.66042i
\(579\) 7.12571e9 − 5.97918e9i 1.52564 − 1.28017i
\(580\) 2.22152e9 − 8.08568e8i 0.472773 − 0.172075i
\(581\) 4.80392e8 − 8.32062e8i 0.101620 − 0.176011i
\(582\) −2.03376e7 − 3.52257e7i −0.00427630 − 0.00740678i
\(583\) 1.46523e9 + 1.22947e9i 0.306242 + 0.256967i
\(584\) −1.43757e9 + 2.48995e9i −0.298665 + 0.517304i
\(585\) 9.48014e8 + 5.37646e9i 0.195780 + 1.11033i
\(586\) 2.92691e9 0.600853
\(587\) −3.14655e8 − 1.78449e9i −0.0642097 − 0.364151i −0.999935 − 0.0114211i \(-0.996364\pi\)
0.935725 − 0.352730i \(-0.114747\pi\)
\(588\) 2.60110e9 − 2.18259e9i 0.527639 − 0.442742i
\(589\) 1.30229e10 + 4.73996e9i 2.62606 + 0.955809i
\(590\) 1.01792e9 − 3.70493e8i 0.204048 − 0.0742674i
\(591\) −5.31576e9 −1.05928
\(592\) 1.24414e9 + 2.11660e8i 0.246459 + 0.0419288i
\(593\) 6.28364e9 1.23743 0.618714 − 0.785616i \(-0.287654\pi\)
0.618714 + 0.785616i \(0.287654\pi\)
\(594\) −1.35042e9 + 4.91513e8i −0.264373 + 0.0962237i
\(595\) −2.32221e9 − 8.45217e8i −0.451953 − 0.164497i
\(596\) 8.67339e8 − 7.27784e8i 0.167814 − 0.140812i
\(597\) 4.05299e8 + 2.29857e9i 0.0779589 + 0.442127i
\(598\) 1.53861e9 0.294221
\(599\) −9.20597e8 − 5.22096e9i −0.175015 − 0.992560i −0.938126 − 0.346293i \(-0.887440\pi\)
0.763111 − 0.646267i \(-0.223671\pi\)
\(600\) 3.25308e8 − 5.63450e8i 0.0614845 − 0.106494i
\(601\) −5.80655e9 − 4.87228e9i −1.09108 − 0.915527i −0.0942891 − 0.995545i \(-0.530058\pi\)
−0.996793 + 0.0800179i \(0.974502\pi\)
\(602\) 3.66678e8 + 6.35105e8i 0.0685010 + 0.118647i
\(603\) 1.47043e9 − 2.54686e9i 0.273108 − 0.473037i
\(604\) 2.22802e9 − 8.10932e8i 0.411423 − 0.149746i
\(605\) 5.40570e8 − 4.53592e8i 0.0992450 − 0.0832764i
\(606\) −1.40023e9 − 2.42527e9i −0.255591 − 0.442697i
\(607\) −4.51623e8 + 2.56128e9i −0.0819626 + 0.464833i 0.916008 + 0.401160i \(0.131393\pi\)
−0.997971 + 0.0636734i \(0.979718\pi\)
\(608\) −3.37743e8 + 1.91544e9i −0.0609430 + 0.345625i
\(609\) 2.09387e9 + 1.75697e9i 0.375655 + 0.315212i
\(610\) −2.92579e8 − 1.06490e8i −0.0521901 − 0.0189957i
\(611\) 1.31592e9 + 4.78955e8i 0.233391 + 0.0849474i
\(612\) 5.22081e9 + 4.38078e9i 0.920679 + 0.772541i
\(613\) 7.27695e8 − 4.12696e9i 0.127596 − 0.723634i −0.852136 − 0.523321i \(-0.824693\pi\)
0.979732 − 0.200313i \(-0.0641960\pi\)
\(614\) −6.14354e8 + 3.48417e9i −0.107110 + 0.607450i
\(615\) 6.21663e9 + 1.07675e10i 1.07769 + 1.86661i
\(616\) −4.79549e8 + 4.02389e8i −0.0826609 + 0.0693607i
\(617\) −8.09448e8 + 2.94615e8i −0.138736 + 0.0504959i −0.410455 − 0.911881i \(-0.634630\pi\)
0.271719 + 0.962377i \(0.412408\pi\)
\(618\) −1.05155e9 + 1.82133e9i −0.179212 + 0.310405i
\(619\) 2.75898e9 + 4.77869e9i 0.467553 + 0.809825i 0.999313 − 0.0370700i \(-0.0118024\pi\)
−0.531760 + 0.846895i \(0.678469\pi\)
\(620\) −2.80394e9 − 2.35279e9i −0.472496 − 0.396471i
\(621\) −4.47179e8 + 7.74536e8i −0.0749308 + 0.129784i
\(622\) −5.71110e8 − 3.23893e9i −0.0951598 − 0.539678i
\(623\) 3.01831e8 0.0500098
\(624\) −4.07314e8 − 2.30999e9i −0.0671095 − 0.380597i
\(625\) −3.33924e9 + 2.80195e9i −0.547101 + 0.459072i
\(626\) −3.86063e9 − 1.40515e9i −0.628996 − 0.228936i
\(627\) 1.84952e10 − 6.73172e9i 2.99656 − 1.09066i
\(628\) −2.47977e9 −0.399532
\(629\) −7.67328e9 + 9.25730e9i −1.22943 + 1.48322i
\(630\) −1.38237e9 −0.220258
\(631\) 7.57224e9 − 2.75607e9i 1.19983 − 0.436704i 0.336668 − 0.941623i \(-0.390700\pi\)
0.863167 + 0.504919i \(0.168478\pi\)
\(632\) −3.51809e9 − 1.28048e9i −0.554366 − 0.201773i
\(633\) −9.00389e9 + 7.55516e9i −1.41097 + 1.18394i
\(634\) 5.53064e8 + 3.13658e9i 0.0861913 + 0.488815i
\(635\) 8.94500e9 1.38635
\(636\) −3.15124e8 − 1.78716e9i −0.0485715 − 0.275462i
\(637\) 3.09033e9 − 5.35261e9i 0.473715 − 0.820498i
\(638\) 4.37083e9 + 3.66757e9i 0.666334 + 0.559121i
\(639\) −3.07991e9 − 5.33456e9i −0.466966 − 0.808808i
\(640\) 2.56849e8 − 4.44876e8i 0.0387301 − 0.0670824i
\(641\) −1.21194e9 + 4.41110e8i −0.181751 + 0.0661521i −0.431293 − 0.902212i \(-0.641942\pi\)
0.249541 + 0.968364i \(0.419720\pi\)
\(642\) −1.50851e9 + 1.26579e9i −0.224996 + 0.188794i
\(643\) −5.24040e9 − 9.07664e9i −0.777367 − 1.34644i −0.933455 − 0.358695i \(-0.883222\pi\)
0.156088 − 0.987743i \(-0.450112\pi\)
\(644\) −6.76514e7 + 3.83670e8i −0.00998105 + 0.0566054i
\(645\) −1.05748e9 + 5.99727e9i −0.155172 + 0.880024i
\(646\) −1.41956e10 − 1.19115e10i −2.07176 − 1.73841i
\(647\) 1.10665e9 + 4.02786e8i 0.160636 + 0.0584668i 0.421087 − 0.907020i \(-0.361649\pi\)
−0.260450 + 0.965487i \(0.583871\pi\)
\(648\) −1.58998e9 − 5.78705e8i −0.229551 − 0.0835496i
\(649\) 2.00276e9 + 1.68051e9i 0.287589 + 0.241315i
\(650\) 2.05649e8 − 1.16629e9i 0.0293718 − 0.166575i
\(651\) 7.34880e8 − 4.16771e9i 0.104396 − 0.592058i
\(652\) 2.22789e9 + 3.85882e9i 0.314795 + 0.545241i
\(653\) −6.01437e9 + 5.04665e9i −0.845267 + 0.709263i −0.958742 − 0.284278i \(-0.908246\pi\)
0.113475 + 0.993541i \(0.463802\pi\)
\(654\) −2.92314e9 + 1.06394e9i −0.408627 + 0.148728i
\(655\) −3.28189e9 + 5.68440e9i −0.456331 + 0.790388i
\(656\) −1.48266e9 − 2.56805e9i −0.205059 − 0.355173i
\(657\) −1.17383e10 − 9.84960e9i −1.61483 − 1.35500i
\(658\) −1.77293e8 + 3.07081e8i −0.0242606 + 0.0420206i
\(659\) −1.00441e9 − 5.69631e9i −0.136714 − 0.775344i −0.973651 − 0.228045i \(-0.926767\pi\)
0.836937 − 0.547300i \(-0.184344\pi\)
\(660\) −5.19836e9 −0.703821
\(661\) −1.92387e9 − 1.09108e10i −0.259103 − 1.46944i −0.785318 − 0.619092i \(-0.787501\pi\)
0.526216 − 0.850351i \(-0.323610\pi\)
\(662\) 2.34842e9 − 1.97056e9i 0.314610 − 0.263989i
\(663\) 2.10005e10 + 7.64354e9i 2.79854 + 1.01858i
\(664\) −1.78808e9 + 6.50807e8i −0.237027 + 0.0862708i
\(665\) 3.75872e9 0.495637
\(666\) −2.26233e9 + 6.33411e9i −0.296754 + 0.830856i
\(667\) 3.55090e9 0.463338
\(668\) −4.90884e9 + 1.78667e9i −0.637178 + 0.231914i
\(669\) 1.63484e10 + 5.95032e9i 2.11098 + 0.768332i
\(670\) 1.61784e9 − 1.35753e9i 0.207814 − 0.174377i
\(671\) −1.30489e8 − 7.40038e8i −0.0166742 − 0.0945639i
\(672\) 5.93935e8 0.0754999
\(673\) −1.81071e8 − 1.02690e9i −0.0228979 − 0.129861i 0.971216 − 0.238201i \(-0.0765576\pi\)
−0.994114 + 0.108340i \(0.965446\pi\)
\(674\) −3.29658e9 + 5.70984e9i −0.414719 + 0.718314i
\(675\) 5.27344e8 + 4.42494e8i 0.0659980 + 0.0553789i
\(676\) −1.26866e8 − 2.19738e8i −0.0157954 − 0.0273584i
\(677\) −6.31790e8 + 1.09429e9i −0.0782550 + 0.135542i −0.902497 − 0.430696i \(-0.858268\pi\)
0.824242 + 0.566238i \(0.191602\pi\)
\(678\) 2.36899e8 − 8.62244e7i 0.0291918 − 0.0106249i
\(679\) 1.43613e7 − 1.20506e7i 0.00176055 − 0.00147728i
\(680\) 2.44715e9 + 4.23860e9i 0.298456 + 0.516941i
\(681\) −1.01679e9 + 5.76653e9i −0.123373 + 0.699680i
\(682\) 1.53402e9 − 8.69985e9i 0.185176 − 1.05019i
\(683\) 1.83475e9 + 1.53954e9i 0.220345 + 0.184892i 0.746278 − 0.665635i \(-0.231839\pi\)
−0.525932 + 0.850526i \(0.676284\pi\)
\(684\) −9.74077e9 − 3.54535e9i −1.16385 − 0.423607i
\(685\) −1.07439e10 − 3.91047e9i −1.27716 − 0.464848i
\(686\) 2.50360e9 + 2.10077e9i 0.296095 + 0.248453i
\(687\) −4.03362e9 + 2.28758e10i −0.474620 + 2.69171i
\(688\) 2.52209e8 − 1.43035e9i 0.0295257 − 0.167449i
\(689\) −1.65163e9 − 2.86070e9i −0.192373 − 0.333200i
\(690\) −2.47827e9 + 2.07951e9i −0.287195 + 0.240985i
\(691\) −5.80736e9 + 2.11371e9i −0.669585 + 0.243709i −0.654369 − 0.756175i \(-0.727066\pi\)
−0.0152156 + 0.999884i \(0.504843\pi\)
\(692\) 2.18191e9 − 3.77917e9i 0.250302 − 0.433536i
\(693\) −1.66817e9 − 2.88935e9i −0.190403 − 0.329787i
\(694\) −4.13752e9 − 3.47179e9i −0.469875 − 0.394272i
\(695\) −1.15875e9 + 2.00701e9i −0.130931 + 0.226779i
\(696\) −9.40029e8 − 5.33117e9i −0.105684 − 0.599363i
\(697\) 2.82524e10 3.16040
\(698\) −6.47262e8 − 3.67081e9i −0.0720421 − 0.408571i
\(699\) −7.79386e8 + 6.53982e8i −0.0863142 + 0.0724262i
\(700\) 2.81787e8 + 1.02562e8i 0.0310512 + 0.0113017i
\(701\) −1.65343e10 + 6.01799e9i −1.81289 + 0.659839i −0.816275 + 0.577663i \(0.803965\pi\)
−0.996618 + 0.0821762i \(0.973813\pi\)
\(702\) 2.48185e9 0.270766
\(703\) 6.15136e9 − 1.72227e10i 0.667771 − 1.86964i
\(704\) 1.23981e9 0.133921
\(705\) −2.76691e9 + 1.00707e9i −0.297395 + 0.108243i
\(706\) 1.14443e9 + 4.16538e8i 0.122398 + 0.0445491i
\(707\) 9.88768e8 − 8.29675e8i 0.105227 − 0.0882958i
\(708\) −4.30730e8 − 2.44279e9i −0.0456130 − 0.258684i
\(709\) −1.75849e10 −1.85301 −0.926505 − 0.376282i \(-0.877202\pi\)
−0.926505 + 0.376282i \(0.877202\pi\)
\(710\) −7.68149e8 − 4.35639e9i −0.0805455 − 0.456796i
\(711\) 9.97659e9 − 1.72800e10i 1.04097 − 1.80301i
\(712\) −4.57923e8 − 3.84243e8i −0.0475458 − 0.0398957i
\(713\) −2.74890e9 − 4.76123e9i −0.284018 − 0.491933i
\(714\) −2.82939e9 + 4.90064e9i −0.290903 + 0.503859i
\(715\) −8.89167e9 + 3.23630e9i −0.909729 + 0.331114i
\(716\) −6.56532e9 + 5.50895e9i −0.668436 + 0.560885i
\(717\) 5.72271e9 + 9.91203e9i 0.579809 + 1.00426i
\(718\) −4.60789e7 + 2.61326e8i −0.00464586 + 0.0263480i
\(719\) 2.56412e9 − 1.45419e10i 0.257269 − 1.45905i −0.532911 − 0.846171i \(-0.678902\pi\)
0.790180 − 0.612874i \(-0.209987\pi\)
\(720\) 2.09726e9 + 1.75981e9i 0.209406 + 0.175713i
\(721\) −9.10866e8 − 3.31528e8i −0.0905068 − 0.0329418i
\(722\) 1.97658e10 + 7.19416e9i 1.95449 + 0.711377i
\(723\) 7.21307e9 + 6.05248e9i 0.709800 + 0.595593i
\(724\) 1.08502e9 − 6.15343e9i 0.106255 − 0.602604i
\(725\) 4.74611e8 − 2.69165e9i 0.0462546 − 0.262323i
\(726\) −8.07931e8 − 1.39938e9i −0.0783603 − 0.135724i
\(727\) −2.88848e9 + 2.42372e9i −0.278804 + 0.233944i −0.771457 − 0.636282i \(-0.780472\pi\)
0.492653 + 0.870226i \(0.336027\pi\)
\(728\) 1.01591e9 − 3.69762e8i 0.0975880 − 0.0355191i
\(729\) 7.42086e9 − 1.28533e10i 0.709427 − 1.22876i
\(730\) −5.50210e9 − 9.52991e9i −0.523478 − 0.906690i
\(731\) 1.06005e10 + 8.89489e9i 1.00373 + 0.842228i
\(732\) −3.56478e8 + 6.17438e8i −0.0335926 + 0.0581842i
\(733\) 1.50616e9 + 8.54186e9i 0.141256 + 0.801103i 0.970297 + 0.241916i \(0.0777757\pi\)
−0.829041 + 0.559188i \(0.811113\pi\)
\(734\) 1.97133e9 0.184002
\(735\) 2.25669e9 + 1.27983e10i 0.209636 + 1.18891i
\(736\) 5.91066e8 − 4.95963e8i 0.0546466 − 0.0458540i
\(737\) 4.78976e9 + 1.74333e9i 0.440735 + 0.160414i
\(738\) 1.48508e10 − 5.40525e9i 1.36004 − 0.495015i
\(739\) 1.84480e10 1.68149 0.840746 − 0.541430i \(-0.182117\pi\)
0.840746 + 0.541430i \(0.182117\pi\)
\(740\) −3.08245e9 + 3.71877e9i −0.279631 + 0.337356i
\(741\) −3.39912e10 −3.06904
\(742\) 7.85973e8 − 2.86071e8i 0.0706308 − 0.0257075i
\(743\) 1.12083e10 + 4.07948e9i 1.00249 + 0.364875i 0.790543 − 0.612407i \(-0.209799\pi\)
0.211943 + 0.977282i \(0.432021\pi\)
\(744\) −6.42059e9 + 5.38751e9i −0.571570 + 0.479604i
\(745\) 7.52495e8 + 4.26761e9i 0.0666740 + 0.378127i
\(746\) −7.41438e9 −0.653866
\(747\) −1.76101e9 − 9.98718e9i −0.154575 − 0.876639i
\(748\) −5.90618e9 + 1.02298e10i −0.516002 + 0.893742i
\(749\) −6.95279e8 − 5.83408e8i −0.0604606 − 0.0507325i
\(750\) 6.61195e9 + 1.14522e10i 0.572289 + 0.991234i
\(751\) 1.00998e10 − 1.74934e10i 0.870107 − 1.50707i 0.00822150 − 0.999966i \(-0.497383\pi\)
0.861885 − 0.507103i \(-0.169284\pi\)
\(752\) 6.59907e8 − 2.40187e8i 0.0565875 − 0.0205962i
\(753\) −1.01158e10 + 8.48813e9i −0.863408 + 0.724485i
\(754\) −4.92688e9 − 8.53361e9i −0.418574 − 0.724992i
\(755\) −1.57580e9 + 8.93680e9i −0.133256 + 0.755732i
\(756\) −1.09125e8 + 6.18879e8i −0.00918540 + 0.0520930i
\(757\) 4.27163e9 + 3.58433e9i 0.357897 + 0.300311i 0.803952 − 0.594694i \(-0.202727\pi\)
−0.446055 + 0.895006i \(0.647171\pi\)