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Properties

Label 74.8.f.b.7.1
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 7.1
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(-83.1185 - 30.2527i) q^{3} +(49.0268 - 41.1384i) q^{4} +(77.4784 + 439.402i) q^{5} -707.623 q^{6} +(-71.3442 - 404.613i) q^{7} +(256.000 - 443.405i) q^{8} +(4318.12 + 3623.33i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(-83.1185 - 30.2527i) q^{3} +(49.0268 - 41.1384i) q^{4} +(77.4784 + 439.402i) q^{5} -707.623 q^{6} +(-71.3442 - 404.613i) q^{7} +(256.000 - 443.405i) q^{8} +(4318.12 + 3623.33i) q^{9} +(1784.72 + 3091.23i) q^{10} +(3194.65 - 5533.29i) q^{11} +(-5319.58 + 1936.17i) q^{12} +(-8360.35 + 7015.17i) q^{13} +(-1643.42 - 2846.49i) q^{14} +(6853.18 - 38866.3i) q^{15} +(711.263 - 4033.77i) q^{16} +(6936.33 + 5820.27i) q^{17} +(42375.7 + 15423.5i) q^{18} +(-2221.38 - 808.516i) q^{19} +(21874.8 + 18355.1i) q^{20} +(-6310.60 + 35789.2i) q^{21} +(8875.91 - 50337.8i) q^{22} +(-50849.4 - 88073.8i) q^{23} +(-34692.5 + 29110.5i) q^{24} +(-113657. + 41367.9i) q^{25} +(-43654.6 + 75612.1i) q^{26} +(-152577. - 264271. i) q^{27} +(-20142.9 - 16901.9i) q^{28} +(82240.6 - 142445. i) q^{29} +(-54825.4 - 310931. i) q^{30} -193872. q^{31} +(-5690.10 - 32270.2i) q^{32} +(-432931. + 363272. i) q^{33} +(68069.4 + 24775.2i) q^{34} +(172260. - 62697.5i) q^{35} +360762. q^{36} +(-70479.1 - 299941. i) q^{37} -18911.5 q^{38} +(907127. - 330167. i) q^{39} +(214667. + 78132.5i) q^{40} +(294703. - 247285. i) q^{41} +(50484.8 + 286313. i) q^{42} +182247. q^{43} +(-71007.3 - 402702. i) q^{44} +(-1.25754e6 + 2.17812e6i) q^{45} +(-623247. - 522966. i) q^{46} +(131588. + 227917. i) q^{47} +(-181151. + 313763. i) q^{48} +(615256. - 223935. i) q^{49} +(-741235. + 621970. i) q^{50} +(-400459. - 693615. i) q^{51} +(-121289. + 687863. i) q^{52} +(131560. - 746111. i) q^{53} +(-1.87009e6 - 1.56919e6i) q^{54} +(2.67885e6 + 975023. i) q^{55} +(-197672. - 71946.5i) q^{56} +(160178. + 134405. i) q^{57} +(228495. - 1.29586e6i) q^{58} +(-14916.6 + 84596.4i) q^{59} +(-1.26291e6 - 2.18742e6i) q^{60} +(2.33188e6 - 1.95668e6i) q^{61} +(-1.45744e6 + 530464. i) q^{62} +(1.15797e6 - 2.00567e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-3.73022e6 - 3.13003e6i) q^{65} +(-2.26060e6 + 3.91548e6i) q^{66} +(-68051.3 - 385938. i) q^{67} +579503. q^{68} +(1.56206e6 + 8.85889e6i) q^{69} +(1.12342e6 - 942662. i) q^{70} +(-5.49184e6 - 1.99886e6i) q^{71} +(2.71204e6 - 987103. i) q^{72} -845393. q^{73} +(-1.35052e6 - 2.06198e6i) q^{74} +1.06985e7 q^{75} +(-142168. + 51745.0i) q^{76} +(-2.46676e6 - 897827. i) q^{77} +(5.91597e6 - 4.96409e6i) q^{78} +(457665. + 2.59555e6i) q^{79} +1.82755e6 q^{80} +(2.54635e6 + 1.44410e7i) q^{81} +(1.53883e6 - 2.66533e6i) q^{82} +(-850370. - 713545. i) q^{83} +(1.16292e6 + 2.01424e6i) q^{84} +(-2.02002e6 + 3.49878e6i) q^{85} +(1.37005e6 - 498658. i) q^{86} +(-1.11450e7 + 9.35180e6i) q^{87} +(-1.63566e6 - 2.83304e6i) q^{88} +(10332.7 - 58599.4i) q^{89} +(-3.49391e6 + 1.98149e7i) q^{90} +(3.43489e6 + 2.88221e6i) q^{91} +(-6.11620e6 - 2.22612e6i) q^{92} +(1.61143e7 + 5.86513e6i) q^{93} +(1.61284e6 + 1.35333e6i) q^{94} +(183154. - 1.03872e6i) q^{95} +(-503306. + 2.85439e6i) q^{96} +(-8.35118e6 - 1.44647e7i) q^{97} +(4.01249e6 - 3.36688e6i) q^{98} +(3.38438e7 - 1.23181e7i) 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
\(3\) −83.1185 − 30.2527i −1.77735 − 0.646903i −0.999837 − 0.0180369i \(-0.994258\pi\)
−0.777514 − 0.628866i \(-0.783519\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) 77.4784 + 439.402i 0.277195 + 1.57205i 0.731902 + 0.681410i \(0.238633\pi\)
−0.454707 + 0.890641i \(0.650256\pi\)
\(6\) −707.623 −1.33743
\(7\) −71.3442 − 404.613i −0.0786168 − 0.445858i −0.998552 − 0.0537884i \(-0.982870\pi\)
0.919936 − 0.392070i \(-0.128241\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) 4318.12 + 3623.33i 1.97445 + 1.65676i
\(10\) 1784.72 + 3091.23i 0.564378 + 0.977532i
\(11\) 3194.65 − 5533.29i 0.723683 − 1.25346i −0.235831 − 0.971794i \(-0.575781\pi\)
0.959514 − 0.281662i \(-0.0908856\pi\)
\(12\) −5319.58 + 1936.17i −0.888676 + 0.323451i
\(13\) −8360.35 + 7015.17i −1.05541 + 0.885597i −0.993652 − 0.112494i \(-0.964116\pi\)
−0.0617612 + 0.998091i \(0.519672\pi\)
\(14\) −1643.42 − 2846.49i −0.160066 − 0.277243i
\(15\) 6853.18 − 38866.3i 0.524291 − 2.97340i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) 6936.33 + 5820.27i 0.342420 + 0.287324i 0.797738 − 0.603005i \(-0.206030\pi\)
−0.455318 + 0.890329i \(0.650474\pi\)
\(18\) 42375.7 + 15423.5i 1.71263 + 0.623345i
\(19\) −2221.38 − 808.516i −0.0742994 − 0.0270428i 0.304603 − 0.952479i \(-0.401476\pi\)
−0.378902 + 0.925437i \(0.623698\pi\)
\(20\) 21874.8 + 18355.1i 0.611419 + 0.513042i
\(21\) −6310.60 + 35789.2i −0.148697 + 0.843304i
\(22\) 8875.91 − 50337.8i 0.177719 − 1.00789i
\(23\) −50849.4 − 88073.8i −0.871442 − 1.50938i −0.860505 − 0.509442i \(-0.829852\pi\)
−0.0109373 − 0.999940i \(-0.503482\pi\)
\(24\) −34692.5 + 29110.5i −0.512267 + 0.429843i
\(25\) −113657. + 41367.9i −1.45481 + 0.529509i
\(26\) −43654.6 + 75612.1i −0.487106 + 0.843693i
\(27\) −152577. − 264271.i −1.49182 − 2.58390i
\(28\) −20142.9 − 16901.9i −0.173408 − 0.145507i
\(29\) 82240.6 − 142445.i 0.626171 − 1.08456i −0.362142 − 0.932123i \(-0.617954\pi\)
0.988313 − 0.152437i \(-0.0487122\pi\)
\(30\) −54825.4 − 310931.i −0.370730 − 2.10251i
\(31\) −193872. −1.16882 −0.584411 − 0.811458i \(-0.698674\pi\)
−0.584411 + 0.811458i \(0.698674\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) −432931. + 363272.i −2.09710 + 1.75968i
\(34\) 68069.4 + 24775.2i 0.297013 + 0.108104i
\(35\) 172260. − 62697.5i 0.679119 − 0.247179i
\(36\) 360762. 1.28873
\(37\) −70479.1 − 299941.i −0.228746 − 0.973486i
\(38\) −18911.5 −0.0559093
\(39\) 907127. − 330167.i 2.44874 − 0.891267i
\(40\) 214667. + 78132.5i 0.530342 + 0.193029i
\(41\) 294703. − 247285.i 0.667792 − 0.560344i −0.244619 − 0.969619i \(-0.578663\pi\)
0.912411 + 0.409275i \(0.134218\pi\)
\(42\) 50484.8 + 286313.i 0.105145 + 0.596306i
\(43\) 182247. 0.349560 0.174780 − 0.984608i \(-0.444079\pi\)
0.174780 + 0.984608i \(0.444079\pi\)
\(44\) −71007.3 − 402702.i −0.125666 − 0.712689i
\(45\) −1.25754e6 + 2.17812e6i −2.05720 + 3.56318i
\(46\) −623247. − 522966.i −0.944077 − 0.792175i
\(47\) 131588. + 227917.i 0.184873 + 0.320210i 0.943534 − 0.331276i \(-0.107479\pi\)
−0.758660 + 0.651486i \(0.774146\pi\)
\(48\) −181151. + 313763.i −0.236427 + 0.409504i
\(49\) 615256. − 223935.i 0.747084 − 0.271916i
\(50\) −741235. + 621970.i −0.838611 + 0.703679i
\(51\) −400459. − 693615.i −0.422729 − 0.732188i
\(52\) −121289. + 687863.i −0.119621 + 0.678407i
\(53\) 131560. − 746111.i 0.121383 − 0.688396i −0.862008 − 0.506895i \(-0.830793\pi\)
0.983391 − 0.181501i \(-0.0580956\pi\)
\(54\) −1.87009e6 − 1.56919e6i −1.61616 − 1.35612i
\(55\) 2.67885e6 + 975023.i 2.17110 + 0.790215i
\(56\) −197672. − 71946.5i −0.150413 − 0.0547459i
\(57\) 160178. + 134405.i 0.114562 + 0.0961290i
\(58\) 228495. − 1.29586e6i 0.153772 − 0.872086i
\(59\) −14916.6 + 84596.4i −0.00945559 + 0.0536253i −0.989170 − 0.146771i \(-0.953112\pi\)
0.979715 + 0.200396i \(0.0642230\pi\)
\(60\) −1.26291e6 − 2.18742e6i −0.754819 − 1.30738i
\(61\) 2.33188e6 − 1.95668e6i 1.31538 − 1.10374i 0.328121 − 0.944636i \(-0.393585\pi\)
0.987262 − 0.159102i \(-0.0508599\pi\)
\(62\) −1.45744e6 + 530464.i −0.776639 + 0.282674i
\(63\) 1.15797e6 − 2.00567e6i 0.583455 − 1.01057i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) −3.73022e6 − 3.13003e6i −1.68476 − 1.41368i
\(66\) −2.26060e6 + 3.91548e6i −0.967879 + 1.67641i
\(67\) −68051.3 − 385938.i −0.0276423 − 0.156767i 0.967862 − 0.251481i \(-0.0809176\pi\)
−0.995505 + 0.0947136i \(0.969806\pi\)
\(68\) 579503. 0.223499
\(69\) 1.56206e6 + 8.85889e6i 0.572435 + 3.24644i
\(70\) 1.12342e6 − 942662.i 0.391471 − 0.328483i
\(71\) −5.49184e6 − 1.99886e6i −1.82101 − 0.662795i −0.995085 − 0.0990203i \(-0.968429\pi\)
−0.825929 − 0.563775i \(-0.809349\pi\)
\(72\) 2.71204e6 − 987103.i 0.856313 − 0.311673i
\(73\) −845393. −0.254348 −0.127174 − 0.991880i \(-0.540591\pi\)
−0.127174 + 0.991880i \(0.540591\pi\)
\(74\) −1.35052e6 − 2.06198e6i −0.387426 − 0.591524i
\(75\) 1.06985e7 2.92826
\(76\) −142168. + 51745.0i −0.0371497 + 0.0135214i
\(77\) −2.46676e6 − 897827.i −0.615757 − 0.224117i
\(78\) 5.91597e6 − 4.96409e6i 1.41155 − 1.18443i
\(79\) 457665. + 2.59555e6i 0.104437 + 0.592290i 0.991444 + 0.130534i \(0.0416693\pi\)
−0.887007 + 0.461756i \(0.847220\pi\)
\(80\) 1.82755e6 0.399076
\(81\) 2.54635e6 + 1.44410e7i 0.532378 + 3.01926i
\(82\) 1.53883e6 − 2.66533e6i 0.308207 − 0.533830i
\(83\) −850370. − 713545.i −0.163243 − 0.136977i 0.557507 − 0.830172i \(-0.311758\pi\)
−0.720750 + 0.693195i \(0.756202\pi\)
\(84\) 1.16292e6 + 2.01424e6i 0.214078 + 0.370794i
\(85\) −2.02002e6 + 3.49878e6i −0.356771 + 0.617946i
\(86\) 1.37005e6 − 498658.i 0.232270 − 0.0845393i
\(87\) −1.11450e7 + 9.35180e6i −1.81453 + 1.52257i
\(88\) −1.63566e6 − 2.83304e6i −0.255861 − 0.443164i
\(89\) 10332.7 − 58599.4i 0.00155363 − 0.00881106i −0.984021 − 0.178052i \(-0.943020\pi\)
0.985575 + 0.169241i \(0.0541316\pi\)
\(90\) −3.49391e6 + 1.98149e7i −0.505199 + 2.86512i
\(91\) 3.43489e6 + 2.88221e6i 0.477824 + 0.400942i
\(92\) −6.11620e6 − 2.22612e6i −0.818888 − 0.298051i
\(93\) 1.61143e7 + 5.86513e6i 2.07741 + 0.756114i
\(94\) 1.61284e6 + 1.35333e6i 0.200283 + 0.168057i
\(95\) 183154. − 1.03872e6i 0.0219172 − 0.124299i
\(96\) −503306. + 2.85439e6i −0.0580607 + 0.329279i
\(97\) −8.35118e6 − 1.44647e7i −0.929067 − 1.60919i −0.784887 − 0.619639i \(-0.787279\pi\)
−0.144180 − 0.989551i \(-0.546054\pi\)
\(98\) 4.01249e6 − 3.36688e6i 0.430648 − 0.361357i
\(99\) 3.38438e7 − 1.23181e7i 3.50555 − 1.27592i
\(100\) −3.87045e6 + 6.70382e6i −0.387045 + 0.670382i
\(101\) 1.59559e6 + 2.76364e6i 0.154098 + 0.266905i 0.932730 − 0.360575i \(-0.117420\pi\)
−0.778632 + 0.627480i \(0.784086\pi\)
\(102\) −4.90831e6 − 4.11856e6i −0.457964 − 0.384277i
\(103\) −733800. + 1.27098e6i −0.0661679 + 0.114606i −0.897211 − 0.441601i \(-0.854411\pi\)
0.831044 + 0.556207i \(0.187744\pi\)
\(104\) 970310. + 5.50290e6i 0.0845851 + 0.479706i
\(105\) −1.62148e7 −1.36693
\(106\) −1.05248e6 − 5.96889e6i −0.0858306 − 0.486769i
\(107\) 2.59024e6 − 2.17347e6i 0.204408 − 0.171518i −0.534837 − 0.844955i \(-0.679627\pi\)
0.739245 + 0.673437i \(0.235183\pi\)
\(108\) −1.83521e7 − 6.67960e6i −1.40185 − 0.510232i
\(109\) −4.30866e6 + 1.56822e6i −0.318676 + 0.115989i −0.496405 − 0.868091i \(-0.665347\pi\)
0.177729 + 0.984079i \(0.443125\pi\)
\(110\) 2.28062e7 1.63372
\(111\) −3.21590e6 + 2.70628e7i −0.223188 + 1.87820i
\(112\) −1.68286e6 −0.113184
\(113\) 8.06111e6 − 2.93400e6i 0.525558 − 0.191287i −0.0655961 − 0.997846i \(-0.520895\pi\)
0.591154 + 0.806559i \(0.298673\pi\)
\(114\) 1.57190e6 + 572124.i 0.0993705 + 0.0361679i
\(115\) 3.47600e7 − 2.91671e7i 2.13127 − 1.78834i
\(116\) −1.82796e6 − 1.03669e7i −0.108733 − 0.616658i
\(117\) −6.15193e7 −3.55108
\(118\) 119333. + 676771.i 0.00668611 + 0.0379188i
\(119\) 1.86009e6 − 3.22177e6i 0.101186 − 0.175259i
\(120\) −1.54791e7 − 1.29885e7i −0.817733 − 0.686159i
\(121\) −1.06680e7 − 1.84774e7i −0.547435 − 0.948185i
\(122\) 1.21762e7 − 2.10898e7i 0.607090 − 1.05151i
\(123\) −3.19763e7 + 1.16384e7i −1.54939 + 0.563932i
\(124\) −9.50492e6 + 7.97557e6i −0.447685 + 0.375652i
\(125\) −9.55420e6 − 1.65484e7i −0.437531 − 0.757827i
\(126\) 3.21728e6 − 1.82461e7i 0.143282 − 0.812594i
\(127\) −2.71077e6 + 1.53735e7i −0.117430 + 0.665978i 0.868088 + 0.496410i \(0.165349\pi\)
−0.985518 + 0.169569i \(0.945763\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) −1.51481e7 − 5.51347e6i −0.621291 − 0.226131i
\(130\) −3.66063e7 − 1.33236e7i −1.46135 − 0.531888i
\(131\) −3.51296e6 − 2.94772e6i −0.136529 − 0.114561i 0.571966 − 0.820277i \(-0.306181\pi\)
−0.708495 + 0.705716i \(0.750625\pi\)
\(132\) −6.28080e6 + 3.56202e7i −0.237687 + 1.34799i
\(133\) −168654. + 956482.i −0.00621605 + 0.0352530i
\(134\) −1.56757e6 − 2.71511e6i −0.0562807 − 0.0974810i
\(135\) 1.04300e8 − 8.75178e7i 3.64850 − 3.06146i
\(136\) 4.35644e6 − 1.58561e6i 0.148506 − 0.0540519i
\(137\) −1.33834e7 + 2.31807e7i −0.444676 + 0.770201i −0.998030 − 0.0627451i \(-0.980014\pi\)
0.553354 + 0.832946i \(0.313348\pi\)
\(138\) 3.59822e7 + 6.23230e7i 1.16550 + 2.01870i
\(139\) −4.43650e6 − 3.72266e6i −0.140116 − 0.117571i 0.570036 − 0.821620i \(-0.306929\pi\)
−0.710152 + 0.704048i \(0.751374\pi\)
\(140\) 5.86609e6 − 1.01604e7i 0.180676 − 0.312940i
\(141\) −4.04230e6 − 2.29250e7i −0.121440 − 0.688721i
\(142\) −4.67543e7 −1.37029
\(143\) 1.21086e7 + 6.86712e7i 0.346272 + 1.96381i
\(144\) 1.76870e7 − 1.48412e7i 0.493612 − 0.414190i
\(145\) 6.89624e7 + 2.51002e7i 1.87856 + 0.683738i
\(146\) −6.35528e6 + 2.31313e6i −0.169005 + 0.0615128i
\(147\) −5.79137e7 −1.50373
\(148\) −1.57945e7 − 1.18058e7i −0.400487 − 0.299349i
\(149\) 5.37887e7 1.33211 0.666054 − 0.745904i \(-0.267982\pi\)
0.666054 + 0.745904i \(0.267982\pi\)
\(150\) 8.04265e7 − 2.92729e7i 1.94572 − 0.708184i
\(151\) −5.33854e6 − 1.94307e6i −0.126184 − 0.0459271i 0.278156 − 0.960536i \(-0.410277\pi\)
−0.404340 + 0.914609i \(0.632499\pi\)
\(152\) −927173. + 777991.i −0.0214145 + 0.0179689i
\(153\) 8.86312e6 + 5.02653e7i 0.200063 + 1.13461i
\(154\) −2.10006e7 −0.463349
\(155\) −1.50209e7 − 8.51875e7i −0.323992 − 1.83745i
\(156\) 3.08910e7 − 5.35048e7i 0.651473 − 1.12838i
\(157\) −2.54370e7 − 2.13442e7i −0.524586 − 0.440180i 0.341641 − 0.939831i \(-0.389017\pi\)
−0.866227 + 0.499651i \(0.833462\pi\)
\(158\) 1.05424e7 + 1.82599e7i 0.212637 + 0.368297i
\(159\) −3.35069e7 + 5.80356e7i −0.661065 + 1.14500i
\(160\) 1.37387e7 − 5.00048e6i 0.265171 − 0.0965143i
\(161\) −3.20080e7 + 2.68579e7i −0.604460 + 0.507202i
\(162\) 5.86553e7 + 1.01594e8i 1.08394 + 1.87744i
\(163\) −3.85465e6 + 2.18608e7i −0.0697153 + 0.395375i 0.929904 + 0.367801i \(0.119889\pi\)
−0.999620 + 0.0275741i \(0.991222\pi\)
\(164\) 4.27544e6 − 2.42472e7i 0.0756881 − 0.429248i
\(165\) −1.93165e8 − 1.62085e8i −3.34761 − 2.80898i
\(166\) −8.34507e6 − 3.03736e6i −0.141596 − 0.0515368i
\(167\) −8.35030e7 − 3.03926e7i −1.38738 − 0.504964i −0.462971 − 0.886374i \(-0.653217\pi\)
−0.924406 + 0.381410i \(0.875439\pi\)
\(168\) 1.42536e7 + 1.19602e7i 0.231922 + 0.194605i
\(169\) 9.78672e6 − 5.55032e7i 0.155967 − 0.884535i
\(170\) −5.61237e6 + 3.18293e7i −0.0876143 + 0.496885i
\(171\) −6.66266e6 − 1.15401e7i −0.101897 − 0.176491i
\(172\) 8.93501e6 − 7.49737e6i 0.133889 − 0.112346i
\(173\) 9.52044e7 − 3.46516e7i 1.39796 − 0.508817i 0.470390 − 0.882459i \(-0.344113\pi\)
0.927573 + 0.373641i \(0.121891\pi\)
\(174\) −5.81953e7 + 1.00797e8i −0.837463 + 1.45053i
\(175\) 2.48468e7 + 4.30359e7i 0.350459 + 0.607012i
\(176\) −2.00478e7 − 1.68221e7i −0.277187 − 0.232587i
\(177\) 3.79911e6 − 6.58026e6i 0.0514963 − 0.0891941i
\(178\) −82661.2 − 468795.i −0.00109858 − 0.00623036i
\(179\) 5.65712e7 0.737242 0.368621 − 0.929580i \(-0.379830\pi\)
0.368621 + 0.929580i \(0.379830\pi\)
\(180\) 2.79512e7 + 1.58519e8i 0.357230 + 2.02595i
\(181\) −2.90654e7 + 2.43888e7i −0.364336 + 0.305714i −0.806516 − 0.591212i \(-0.798650\pi\)
0.442180 + 0.896926i \(0.354205\pi\)
\(182\) 3.37081e7 + 1.22688e7i 0.414462 + 0.150852i
\(183\) −2.53017e8 + 9.20908e7i −3.05191 + 1.11080i
\(184\) −5.20698e7 −0.616203
\(185\) 1.26334e8 − 5.42075e7i 1.46696 − 0.629446i
\(186\) 1.37188e8 1.56322
\(187\) 5.43644e7 − 1.97870e7i 0.607951 − 0.221276i
\(188\) 1.58275e7 + 5.76074e6i 0.173724 + 0.0632304i
\(189\) −9.60420e7 + 8.05888e7i −1.03477 + 0.868277i
\(190\) −1.46524e6 − 8.30976e6i −0.0154978 − 0.0878923i
\(191\) 3.03908e7 0.315592 0.157796 − 0.987472i \(-0.449561\pi\)
0.157796 + 0.987472i \(0.449561\pi\)
\(192\) 4.02645e6 + 2.28351e7i 0.0410551 + 0.232835i
\(193\) −4.84973e7 + 8.39998e7i −0.485587 + 0.841061i −0.999863 − 0.0165637i \(-0.994727\pi\)
0.514276 + 0.857625i \(0.328061\pi\)
\(194\) −1.02358e8 − 8.58886e7i −1.00650 − 0.844558i
\(195\) 2.15359e8 + 3.73012e8i 2.07989 + 3.60248i
\(196\) 2.09517e7 − 3.62895e7i 0.198757 − 0.344258i
\(197\) 1.01038e8 − 3.67747e7i 0.941569 − 0.342703i 0.174784 − 0.984607i \(-0.444077\pi\)
0.766785 + 0.641904i \(0.221855\pi\)
\(198\) 2.20718e8 − 1.85204e8i 2.02074 − 1.69560i
\(199\) −6.88836e7 − 1.19310e8i −0.619626 − 1.07322i −0.989554 − 0.144164i \(-0.953951\pi\)
0.369927 − 0.929061i \(-0.379383\pi\)
\(200\) −1.07536e7 + 6.09864e7i −0.0950489 + 0.539049i
\(201\) −6.01933e6 + 3.41373e7i −0.0522832 + 0.296513i
\(202\) 1.95567e7 + 1.64100e7i 0.166942 + 0.140081i
\(203\) −6.35024e7 − 2.31130e7i −0.532788 − 0.193919i
\(204\) −4.81674e7 − 1.75315e7i −0.397235 − 0.144582i
\(205\) 1.31491e8 + 1.10334e8i 1.06600 + 0.894479i
\(206\) −2.03877e6 + 1.15624e7i −0.0162492 + 0.0921540i
\(207\) 9.95467e7 − 5.64558e8i 0.780065 − 4.42397i
\(208\) 2.23512e7 + 3.87134e7i 0.172218 + 0.298290i
\(209\) −1.15703e7 + 9.70862e6i −0.0876661 + 0.0735606i
\(210\) −1.21895e8 + 4.43662e7i −0.908277 + 0.330586i
\(211\) −3.80768e7 + 6.59510e7i −0.279044 + 0.483318i −0.971147 − 0.238480i \(-0.923351\pi\)
0.692104 + 0.721798i \(0.256684\pi\)
\(212\) −2.42439e7 − 4.19916e7i −0.174754 − 0.302683i
\(213\) 3.96002e8 + 3.32285e8i 2.80782 + 2.35604i
\(214\) 1.35253e7 − 2.34265e7i 0.0943404 − 0.163402i
\(215\) 1.41202e7 + 8.00798e7i 0.0968963 + 0.549526i
\(216\) −1.56239e8 −1.05487
\(217\) 1.38316e7 + 7.84430e7i 0.0918891 + 0.521129i
\(218\) −2.80996e7 + 2.35784e7i −0.183697 + 0.154140i
\(219\) 7.02678e7 + 2.55754e7i 0.452066 + 0.164539i
\(220\) 1.71447e8 − 6.24015e7i 1.08555 − 0.395108i
\(221\) −9.88203e7 −0.615848
\(222\) 4.98726e7 + 2.12245e8i 0.305933 + 1.30197i
\(223\) 4.77682e6 0.0288451 0.0144225 − 0.999896i \(-0.495409\pi\)
0.0144225 + 0.999896i \(0.495409\pi\)
\(224\) −1.26510e7 + 4.60458e6i −0.0752066 + 0.0273730i
\(225\) −6.40676e8 − 2.33187e8i −3.74973 − 1.36479i
\(226\) 5.25718e7 − 4.41130e7i 0.302952 − 0.254207i
\(227\) −2.93195e6 − 1.66279e7i −0.0166366 − 0.0943511i 0.975359 − 0.220624i \(-0.0708095\pi\)
−0.991995 + 0.126273i \(0.959698\pi\)
\(228\) 1.33822e7 0.0747751
\(229\) −3.95599e7 − 2.24356e8i −0.217686 − 1.23456i −0.876183 − 0.481978i \(-0.839919\pi\)
0.658497 − 0.752583i \(-0.271193\pi\)
\(230\) 1.81504e8 − 3.14374e8i 0.983646 − 1.70372i
\(231\) 1.77872e8 + 1.49252e8i 0.949434 + 0.796670i
\(232\) −4.21072e7 − 7.29318e7i −0.221385 − 0.383450i
\(233\) −9.85319e7 + 1.70662e8i −0.510306 + 0.883876i 0.489622 + 0.871935i \(0.337135\pi\)
−0.999929 + 0.0119418i \(0.996199\pi\)
\(234\) −4.62474e8 + 1.68327e8i −2.35956 + 0.858810i
\(235\) −8.99520e7 + 7.54787e7i −0.452141 + 0.379391i
\(236\) 2.74885e6 + 4.76114e6i 0.0136131 + 0.0235787i
\(237\) 4.04818e7 − 2.29584e8i 0.197533 − 1.12027i
\(238\) 5.16802e6 − 2.93093e7i 0.0248488 − 0.140924i
\(239\) 2.02769e8 + 1.70144e8i 0.960747 + 0.806163i 0.981075 − 0.193631i \(-0.0620263\pi\)
−0.0203271 + 0.999793i \(0.506471\pi\)
\(240\) −1.51903e8 − 5.52883e7i −0.709297 − 0.258163i
\(241\) 1.86468e8 + 6.78689e7i 0.858115 + 0.312328i 0.733345 − 0.679857i \(-0.237958\pi\)
0.124771 + 0.992186i \(0.460180\pi\)
\(242\) −1.30754e8 − 1.09716e8i −0.593064 − 0.497639i
\(243\) 1.09344e8 − 6.20119e8i 0.488845 − 2.77238i
\(244\) 3.38301e7 − 1.91860e8i 0.149087 − 0.845512i
\(245\) 1.46066e8 + 2.52994e8i 0.634554 + 1.09908i
\(246\) −2.08539e8 + 1.74985e8i −0.893128 + 0.749423i
\(247\) 2.42434e7 − 8.82387e6i 0.102366 − 0.0372580i
\(248\) −4.96311e7 + 8.59637e7i −0.206621 + 0.357877i
\(249\) 4.90948e7 + 8.50348e7i 0.201529 + 0.349059i
\(250\) −1.17103e8 − 9.82612e7i −0.474000 − 0.397733i
\(251\) −7.33816e7 + 1.27101e8i −0.292907 + 0.507329i −0.974496 − 0.224406i \(-0.927956\pi\)
0.681589 + 0.731735i \(0.261289\pi\)
\(252\) −2.57383e7 − 1.45969e8i −0.101316 − 0.574591i
\(253\) −6.49784e8 −2.52259
\(254\) 2.16861e7 + 1.22988e8i 0.0830355 + 0.470918i
\(255\) 2.73749e8 − 2.29702e8i 1.03386 − 0.867510i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) −3.12582e8 + 1.13771e8i −1.14868 + 0.418085i −0.845040 − 0.534703i \(-0.820424\pi\)
−0.303638 + 0.952787i \(0.598201\pi\)
\(258\) −1.28962e8 −0.467513
\(259\) −1.16332e8 + 4.99158e7i −0.416053 + 0.178521i
\(260\) −3.11645e8 −1.09965
\(261\) 8.71250e8 − 3.17109e8i 3.03320 − 1.10399i
\(262\) −3.44742e7 − 1.25476e7i −0.118424 − 0.0431029i
\(263\) −2.51816e8 + 2.11299e8i −0.853570 + 0.716230i −0.960573 − 0.278029i \(-0.910319\pi\)
0.107003 + 0.994259i \(0.465875\pi\)
\(264\) 5.02464e7 + 2.84961e8i 0.168070 + 0.953174i
\(265\) 3.38036e8 1.11584
\(266\) 1.34923e6 + 7.65186e6i 0.00439541 + 0.0249276i
\(267\) −2.63162e6 + 4.55810e6i −0.00846124 + 0.0146553i
\(268\) −1.92132e7 − 1.61218e7i −0.0609717 − 0.0511613i
\(269\) −1.12505e8 − 1.94864e8i −0.352402 − 0.610378i 0.634268 − 0.773113i \(-0.281302\pi\)
−0.986670 + 0.162736i \(0.947968\pi\)
\(270\) 5.44614e8 − 9.43300e8i 1.68390 − 2.91660i
\(271\) 5.04570e8 − 1.83648e8i 1.54003 − 0.560524i 0.573976 − 0.818872i \(-0.305400\pi\)
0.966052 + 0.258347i \(0.0831779\pi\)
\(272\) 2.84112e7 − 2.38398e7i 0.0856049 − 0.0718310i
\(273\) −1.98308e8 − 3.43480e8i −0.589890 − 1.02172i
\(274\) −3.71840e7 + 2.10881e8i −0.109202 + 0.619313i
\(275\) −1.34195e8 + 7.61055e8i −0.389108 + 2.20674i
\(276\) 4.41024e8 + 3.70063e8i 1.26264 + 1.05948i
\(277\) 2.94739e8 + 1.07276e8i 0.833217 + 0.303266i 0.723179 − 0.690661i \(-0.242680\pi\)
0.110039 + 0.993927i \(0.464903\pi\)
\(278\) −4.35374e7 − 1.58463e7i −0.121536 − 0.0442355i
\(279\) −8.37161e8 − 7.02462e8i −2.30778 − 1.93646i
\(280\) 1.62982e7 − 9.24315e7i 0.0443696 − 0.251633i
\(281\) 4.54330e7 − 2.57663e8i 0.122152 − 0.692756i −0.860807 − 0.508931i \(-0.830041\pi\)
0.982959 − 0.183825i \(-0.0588480\pi\)
\(282\) −9.31148e7 − 1.61280e8i −0.247256 − 0.428260i
\(283\) −7.06251e7 + 5.92615e7i −0.185228 + 0.155425i −0.730687 − 0.682713i \(-0.760800\pi\)
0.545459 + 0.838138i \(0.316356\pi\)
\(284\) −3.51477e8 + 1.27927e8i −0.910507 + 0.331397i
\(285\) −4.66476e7 + 8.07960e7i −0.119364 + 0.206744i
\(286\) 2.78922e8 + 4.83108e8i 0.705021 + 1.22113i
\(287\) −1.21080e8 − 1.01598e8i −0.302334 − 0.253688i
\(288\) 9.23551e7 − 1.59964e8i 0.227817 − 0.394591i
\(289\) −5.70174e7 − 3.23362e8i −0.138952 − 0.788037i
\(290\) 5.87106e8 1.41359
\(291\) 2.56543e8 + 1.45493e9i 0.610288 + 3.46111i
\(292\) −4.14469e7 + 3.47781e7i −0.0974210 + 0.0817459i
\(293\) −6.67027e8 − 2.42778e8i −1.54920 − 0.563862i −0.580968 − 0.813926i \(-0.697326\pi\)
−0.968229 + 0.250065i \(0.919548\pi\)
\(294\) −4.35369e8 + 1.58461e8i −0.999175 + 0.363670i
\(295\) −3.83275e7 −0.0869228
\(296\) −1.51038e8 − 4.55341e7i −0.338505 − 0.102051i
\(297\) −1.94972e9 −4.31841
\(298\) 4.04359e8 − 1.47175e8i 0.885136 − 0.322163i
\(299\) 1.04297e9 + 3.79610e8i 2.25644 + 0.821276i
\(300\) 5.24515e8 − 4.40120e8i 1.12159 − 0.941124i
\(301\) −1.30023e7 − 7.37397e7i −0.0274813 − 0.155854i
\(302\) −4.54493e7 −0.0949517
\(303\) −4.90154e7 − 2.77980e8i −0.101224 − 0.574070i
\(304\) −4.84136e6 + 8.38547e6i −0.00988347 + 0.0171187i
\(305\) 1.04044e9 + 8.73033e8i 2.09975 + 1.76190i
\(306\) 2.04163e8 + 3.53620e8i 0.407335 + 0.705525i
\(307\) −1.22257e8 + 2.11756e8i −0.241152 + 0.417688i −0.961043 − 0.276400i \(-0.910859\pi\)
0.719891 + 0.694087i \(0.244192\pi\)
\(308\) −1.57873e8 + 5.74610e7i −0.307879 + 0.112059i
\(309\) 9.94429e7 − 8.34425e7i 0.191743 − 0.160891i
\(310\) −3.46007e8 − 5.99301e8i −0.659658 − 1.14256i
\(311\) −498011. + 2.82436e6i −0.000938810 + 0.00532426i −0.985274 − 0.170985i \(-0.945305\pi\)
0.984335 + 0.176310i \(0.0564160\pi\)
\(312\) 8.58267e7 − 4.86747e8i 0.159986 − 0.907324i
\(313\) 5.31677e8 + 4.46130e8i 0.980037 + 0.822349i 0.984095 − 0.177643i \(-0.0568472\pi\)
−0.00405771 + 0.999992i \(0.501292\pi\)
\(314\) −2.49625e8 − 9.08559e7i −0.455023 − 0.165615i
\(315\) 9.71013e8 + 3.53420e8i 1.75040 + 0.637095i
\(316\) 1.29215e8 + 1.08424e8i 0.230360 + 0.193295i
\(317\) 2.24011e7 − 1.27043e8i 0.0394969 − 0.223998i −0.958670 − 0.284521i \(-0.908166\pi\)
0.998167 + 0.0605226i \(0.0192767\pi\)
\(318\) −9.30946e7 + 5.27965e8i −0.162341 + 0.920684i
\(319\) −5.25459e8 − 9.10122e8i −0.906299 − 1.56976i
\(320\) 8.95992e7 − 7.51826e7i 0.152855 − 0.128260i
\(321\) −2.81050e8 + 1.02294e8i −0.474260 + 0.172616i
\(322\) −1.67134e8 + 2.89484e8i −0.278977 + 0.483203i
\(323\) −1.07024e7 − 1.85372e7i −0.0176715 − 0.0306080i
\(324\) 7.18921e8 + 6.03246e8i 1.17428 + 0.985342i
\(325\) 6.60013e8 − 1.14318e9i 1.06650 − 1.84723i
\(326\) 3.08372e7 + 1.74886e8i 0.0492962 + 0.279573i
\(327\) 4.05572e8 0.641432
\(328\) −3.42035e7 − 1.93978e8i −0.0535196 − 0.303525i
\(329\) 8.28303e7 − 6.95029e7i 0.128234 − 0.107601i
\(330\) −1.89562e9 − 6.89948e8i −2.90370 − 1.05686i
\(331\) 1.15821e9 − 4.21552e8i 1.75545 − 0.638931i 0.755577 − 0.655059i \(-0.227356\pi\)
0.999870 + 0.0161289i \(0.00513420\pi\)
\(332\) −7.10451e7 −0.106549
\(333\) 7.82449e8 − 1.55055e9i 1.16118 − 2.30108i
\(334\) −7.10896e8 −1.04398
\(335\) 1.64309e8 − 5.98037e7i 0.238784 − 0.0869103i
\(336\) 1.39877e8 + 5.09110e7i 0.201168 + 0.0732191i
\(337\) −7.79177e8 + 6.53807e8i −1.10900 + 0.930562i −0.997997 − 0.0632586i \(-0.979851\pi\)
−0.111003 + 0.993820i \(0.535406\pi\)
\(338\) −7.82938e7 − 4.44026e8i −0.110286 − 0.625461i
\(339\) −7.58789e8 −1.05784
\(340\) 4.48990e7 + 2.54635e8i 0.0619527 + 0.351351i
\(341\) −6.19352e8 + 1.07275e9i −0.845857 + 1.46507i
\(342\) −8.16623e7 − 6.85228e7i −0.110390 − 0.0926283i
\(343\) −3.03680e8 − 5.25989e8i −0.406337 − 0.703797i
\(344\) 4.66553e7 − 8.08094e7i 0.0617941 − 0.107030i
\(345\) −3.77158e9 + 1.37274e9i −4.94489 + 1.79979i
\(346\) 6.20891e8 − 5.20989e8i 0.805840 − 0.676180i
\(347\) −8.70849e7 − 1.50836e8i −0.111890 − 0.193799i 0.804642 − 0.593760i \(-0.202357\pi\)
−0.916532 + 0.399961i \(0.869024\pi\)
\(348\) −1.61688e8 + 9.16979e8i −0.205660 + 1.16636i
\(349\) −1.84600e8 + 1.04692e9i −0.232457 + 1.31833i 0.615445 + 0.788180i \(0.288976\pi\)
−0.847903 + 0.530152i \(0.822135\pi\)
\(350\) 3.04540e8 + 2.55539e8i 0.379670 + 0.318581i
\(351\) 3.12950e9 + 1.13905e9i 3.86278 + 1.40594i
\(352\) −1.96738e8 − 7.16068e7i −0.240430 − 0.0875095i
\(353\) 1.03147e9 + 8.65504e8i 1.24808 + 1.04727i 0.996847 + 0.0793417i \(0.0252818\pi\)
0.251237 + 0.967926i \(0.419163\pi\)
\(354\) 1.05553e7 − 5.98623e7i 0.0126462 − 0.0717203i
\(355\) 4.52806e8 − 2.56799e9i 0.537171 − 3.04645i
\(356\) −1.90411e6 − 3.29801e6i −0.00223675 − 0.00387416i
\(357\) −2.52075e8 + 2.11516e8i −0.293218 + 0.246039i
\(358\) 4.25277e8 − 1.54788e8i 0.489870 − 0.178298i
\(359\) −6.84562e7 + 1.18570e8i −0.0780876 + 0.135252i −0.902425 − 0.430847i \(-0.858215\pi\)
0.824337 + 0.566099i \(0.191548\pi\)
\(360\) 6.43859e8 + 1.11520e9i 0.727331 + 1.25977i
\(361\) −6.80465e8 − 5.70978e8i −0.761255 − 0.638769i
\(362\) −1.51769e8 + 2.62871e8i −0.168152 + 0.291248i
\(363\) 3.27713e8 + 1.85855e9i 0.359600 + 2.03939i
\(364\) 2.86971e8 0.311877
\(365\) −6.54996e7 − 3.71467e8i −0.0705040 − 0.399848i
\(366\) −1.65009e9 + 1.38459e9i −1.75924 + 1.47618i
\(367\) −1.04472e9 − 3.80248e8i −1.10324 − 0.401547i −0.274730 − 0.961521i \(-0.588589\pi\)
−0.828510 + 0.559975i \(0.810811\pi\)
\(368\) −3.91437e8 + 1.42471e8i −0.409444 + 0.149025i
\(369\) 2.16856e9 2.24688
\(370\) 8.01400e8 − 7.53177e8i 0.822514 − 0.773021i
\(371\) −3.11272e8 −0.316470
\(372\) 1.03132e9 − 3.75368e8i 1.03870 − 0.378057i
\(373\) −1.02813e9 − 3.74208e8i −1.02581 − 0.373364i −0.226325 − 0.974052i \(-0.572671\pi\)
−0.799484 + 0.600688i \(0.794894\pi\)
\(374\) 3.54546e8 − 2.97499e8i 0.350447 − 0.294060i
\(375\) 2.93499e8 + 1.66451e9i 0.287407 + 1.62996i
\(376\) 1.34746e8 0.130725
\(377\) 3.11714e8 + 1.76782e9i 0.299614 + 1.69920i
\(378\) −5.01496e8 + 8.68616e8i −0.477580 + 0.827192i
\(379\) 1.12768e9 + 9.46233e8i 1.06401 + 0.892814i 0.994497 − 0.104767i \(-0.0334096\pi\)
0.0695175 + 0.997581i \(0.477854\pi\)
\(380\) −3.37518e7 − 5.84599e7i −0.0315540 − 0.0546532i
\(381\) 6.90404e8 − 1.19582e9i 0.639538 − 1.10771i
\(382\) 2.28464e8 − 8.31542e7i 0.209699 − 0.0763242i
\(383\) 1.53812e9 − 1.29064e9i 1.39893 − 1.17384i 0.437357 − 0.899288i \(-0.355915\pi\)
0.961572 − 0.274553i \(-0.0885298\pi\)
\(384\) 9.27495e7 + 1.60647e8i 0.0835896 + 0.144781i
\(385\) 2.03386e8 − 1.15346e9i 0.181639 − 1.03013i
\(386\) −1.34743e8 + 7.64168e8i −0.119248 + 0.676291i
\(387\) 7.86966e8 + 6.60343e8i 0.690188 + 0.579137i
\(388\) −1.00449e9 − 3.65603e8i −0.873037 − 0.317760i
\(389\) −7.31568e8 − 2.66269e8i −0.630132 − 0.229349i 0.00715694 − 0.999974i \(-0.497722\pi\)
−0.637289 + 0.770625i \(0.719944\pi\)
\(390\) 2.63959e9 + 2.21488e9i 2.25325 + 1.89070i
\(391\) 1.59905e8 − 9.06866e8i 0.135283 − 0.767228i
\(392\) 5.82117e7 − 3.30135e8i 0.0488100 − 0.276815i
\(393\) 2.02815e8 + 3.51286e8i 0.168549 + 0.291936i
\(394\) 6.58934e8 − 5.52911e8i 0.542757 − 0.455427i
\(395\) −1.10503e9 + 4.02198e8i −0.902161 + 0.328360i
\(396\) 1.15251e9 − 1.99620e9i 0.932632 − 1.61537i
\(397\) −1.02905e9 − 1.78236e9i −0.825408 − 1.42965i −0.901607 − 0.432556i \(-0.857612\pi\)
0.0761989 − 0.997093i \(-0.475722\pi\)
\(398\) −8.44286e8 − 7.08440e8i −0.671273 − 0.563265i
\(399\) 4.29543e7 − 7.43991e7i 0.0338534 − 0.0586358i
\(400\) 8.60284e7 + 4.87891e8i 0.0672097 + 0.381165i
\(401\) −1.55913e9 −1.20747 −0.603735 − 0.797185i \(-0.706321\pi\)
−0.603735 + 0.797185i \(0.706321\pi\)
\(402\) 4.81546e7 + 2.73099e8i 0.0369698 + 0.209666i
\(403\) 1.62083e9 − 1.36004e9i 1.23359 − 1.03511i
\(404\) 1.91918e8 + 6.98526e7i 0.144804 + 0.0527045i
\(405\) −6.14813e9 + 2.23774e9i −4.59886 + 1.67385i
\(406\) −5.40623e8 −0.400916
\(407\) −1.88482e9 − 5.68224e8i −1.38576 − 0.417772i
\(408\) −4.10070e8 −0.298915
\(409\) −2.15917e9 + 7.85875e8i −1.56047 + 0.567965i −0.970844 − 0.239711i \(-0.922947\pi\)
−0.589627 + 0.807676i \(0.700725\pi\)
\(410\) 1.29038e9 + 4.69659e8i 0.924641 + 0.336542i
\(411\) 1.81368e9 − 1.52186e9i 1.28859 − 1.08126i
\(412\) 1.63102e7 + 9.24995e7i 0.0114899 + 0.0651627i
\(413\) 3.52930e7 0.0246526
\(414\) −7.96374e8 − 4.51646e9i −0.551589 − 3.12822i
\(415\) 2.47648e8 − 4.28938e8i 0.170085 − 0.294596i
\(416\) 2.73952e8 + 2.29873e8i 0.186573 + 0.156553i
\(417\) 2.56134e8 + 4.43638e8i 0.172978 + 0.299607i
\(418\) −6.04157e7 + 1.04643e8i −0.0404607 + 0.0700799i
\(419\) 5.43547e8 − 1.97835e8i 0.360984 − 0.131387i −0.155160 − 0.987889i \(-0.549589\pi\)
0.516144 + 0.856502i \(0.327367\pi\)
\(420\) −7.94958e8 + 6.67049e8i −0.523566 + 0.439324i
\(421\) 2.00257e8 + 3.46856e8i 0.130798 + 0.226549i 0.923984 − 0.382430i \(-0.124913\pi\)
−0.793186 + 0.608979i \(0.791579\pi\)
\(422\) −1.05792e8 + 5.99974e8i −0.0685264 + 0.388632i
\(423\) −2.57607e8 + 1.46096e9i −0.165488 + 0.938529i
\(424\) −2.97150e8 − 2.49339e8i −0.189320 − 0.158858i
\(425\) −1.02914e9 − 3.74575e8i −0.650298 − 0.236689i
\(426\) 3.88615e9 + 1.41444e9i 2.43549 + 0.886445i
\(427\) −9.58065e8 − 8.03912e8i −0.595522 − 0.499702i
\(428\) 3.75782e7 − 2.13117e8i 0.0231677 − 0.131391i
\(429\) 1.07104e9 − 6.07416e9i 0.654945 − 3.71438i
\(430\) 3.25261e8 + 5.63368e8i 0.197284 + 0.341706i
\(431\) 1.27305e9 − 1.06822e9i 0.765906 − 0.642671i −0.173751 − 0.984790i \(-0.555589\pi\)
0.939657 + 0.342118i \(0.111144\pi\)
\(432\) −1.17453e9 + 4.27495e8i −0.700925 + 0.255116i
\(433\) −3.02448e8 + 5.23855e8i −0.179037 + 0.310101i −0.941551 − 0.336871i \(-0.890632\pi\)
0.762514 + 0.646972i \(0.223965\pi\)
\(434\) 3.18612e8 + 5.51853e8i 0.187089 + 0.324048i
\(435\) −4.97270e9 − 4.17259e9i −2.89654 − 2.43049i
\(436\) −1.46726e8 + 2.54136e8i −0.0847820 + 0.146847i
\(437\) 4.17468e7 + 2.36758e8i 0.0239298 + 0.135712i
\(438\) 5.98219e8 0.340174
\(439\) 5.91393e7 + 3.35396e8i 0.0333619 + 0.189205i 0.996934 − 0.0782428i \(-0.0249309\pi\)
−0.963572 + 0.267447i \(0.913820\pi\)
\(440\) 1.11812e9 − 9.38211e8i 0.625753 − 0.525069i
\(441\) 3.46814e9 + 1.26230e9i 1.92558 + 0.700853i
\(442\) −7.42886e8 + 2.70388e8i −0.409208 + 0.148940i
\(443\) −2.17652e9 −1.18946 −0.594729 − 0.803926i \(-0.702741\pi\)
−0.594729 + 0.803926i \(0.702741\pi\)
\(444\) 9.55656e8 + 1.45910e9i 0.518157 + 0.791125i
\(445\) 2.65492e7 0.0142821
\(446\) 3.59099e7 − 1.30701e7i 0.0191665 − 0.00697603i
\(447\) −4.47084e9 − 1.62725e9i −2.36762 − 0.861744i
\(448\) −8.25054e7 + 6.92302e7i −0.0433520 + 0.0363766i
\(449\) 3.71684e7 + 2.10792e8i 0.0193781 + 0.109899i 0.992963 − 0.118428i \(-0.0377856\pi\)
−0.973584 + 0.228327i \(0.926674\pi\)
\(450\) −5.45434e9 −2.82162
\(451\) −4.26829e8 − 2.42067e9i −0.219097 − 1.24256i
\(452\) 2.74511e8 − 4.75466e8i 0.139822 − 0.242178i
\(453\) 3.84949e8 + 3.23010e8i 0.194562 + 0.163257i
\(454\) −6.75376e7 − 1.16979e8i −0.0338727 − 0.0586693i
\(455\) −1.00032e9 + 1.73260e9i −0.497851 + 0.862303i
\(456\) 1.00602e8 − 3.66160e7i 0.0496853 − 0.0180840i
\(457\) 2.49520e9 − 2.09373e9i 1.22292 − 1.02615i 0.224257 − 0.974530i \(-0.428004\pi\)
0.998667 − 0.0516250i \(-0.0164401\pi\)
\(458\) −9.11266e8 − 1.57836e9i −0.443217 − 0.767674i
\(459\) 4.79805e8 − 2.72111e9i 0.231590 − 1.31341i
\(460\) 5.04285e8 − 2.85994e9i 0.241559 − 1.36995i
\(461\) −1.37656e8 − 1.15507e8i −0.0654397 − 0.0549104i 0.609481 − 0.792801i \(-0.291378\pi\)
−0.674921 + 0.737890i \(0.735822\pi\)
\(462\) 1.74554e9 + 6.35323e8i 0.823535 + 0.299742i
\(463\) 1.10640e9 + 4.02697e8i 0.518059 + 0.188558i 0.587799 − 0.809007i \(-0.299995\pi\)
−0.0697397 + 0.997565i \(0.522217\pi\)
\(464\) −5.16095e8 − 4.33055e8i −0.239837 − 0.201248i
\(465\) −1.32864e9 + 7.53508e9i −0.612803 + 3.47538i
\(466\) −2.73758e8 + 1.55256e9i −0.125319 + 0.710718i
\(467\) 5.30730e8 + 9.19251e8i 0.241137 + 0.417662i 0.961039 − 0.276415i \(-0.0891463\pi\)
−0.719901 + 0.694076i \(0.755813\pi\)
\(468\) −3.01610e9 + 2.53080e9i −1.36014 + 1.14130i
\(469\) −1.51300e8 + 5.50689e7i −0.0677229 + 0.0246491i
\(470\) −4.69696e8 + 8.13538e8i −0.208677 + 0.361439i
\(471\) 1.46857e9 + 2.54363e9i 0.647620 + 1.12171i
\(472\) 3.36918e7 + 2.82708e7i 0.0147478 + 0.0123749i
\(473\) 5.82216e8 − 1.00843e9i 0.252971 − 0.438158i
\(474\) −3.23854e8 − 1.83667e9i −0.139677 − 0.792149i
\(475\) 2.85923e8 0.122411
\(476\) −4.13442e7 − 2.34474e8i −0.0175707 − 0.0996486i
\(477\) 3.27150e9 − 2.74511e9i 1.38017 − 1.15810i
\(478\) 1.98987e9 + 7.24252e8i 0.833347 + 0.303314i
\(479\) −3.66192e9 + 1.33283e9i −1.52242 + 0.554115i −0.961751 − 0.273925i \(-0.911678\pi\)
−0.560668 + 0.828041i \(0.689456\pi\)
\(480\) −1.29322e9 −0.533737
\(481\) 2.69337e9 + 2.01319e9i 1.10354 + 0.824853i
\(482\) 1.58748e9 0.645721
\(483\) 3.47298e9 − 1.26406e9i 1.40245 − 0.510450i
\(484\) −1.28315e9 − 4.67028e8i −0.514420 − 0.187234i
\(485\) 5.70876e9 − 4.79022e9i 2.27220 − 1.90660i
\(486\) −8.74749e8 − 4.96095e9i −0.345666 − 1.96037i
\(487\) 3.48197e9 1.36607 0.683035 − 0.730385i \(-0.260660\pi\)
0.683035 + 0.730385i \(0.260660\pi\)
\(488\) −2.70641e8 − 1.53488e9i −0.105420 − 0.597867i
\(489\) 9.81740e8 − 1.70042e9i 0.379678 − 0.657622i
\(490\) 1.79029e9 + 1.50223e9i 0.687444 + 0.576834i
\(491\) 6.57798e8 + 1.13934e9i 0.250788 + 0.434378i 0.963743 − 0.266832i \(-0.0859768\pi\)
−0.712955 + 0.701210i \(0.752644\pi\)
\(492\) −1.08891e9 + 1.88605e9i −0.412206 + 0.713962i
\(493\) 1.39952e9 − 5.09382e8i 0.526034 − 0.191461i
\(494\) 1.58107e8 − 1.32668e8i 0.0590075 − 0.0495132i
\(495\) 8.03478e9 + 1.39166e10i 2.97753 + 5.15723i
\(496\) −1.37894e8 + 7.82034e8i −0.0507410 + 0.287766i
\(497\) −4.16956e8 + 2.36468e9i −0.152350 + 0.864021i
\(498\) 6.01741e8 + 5.04921e8i 0.218327 + 0.183198i
\(499\) −1.77082e9 − 6.44526e8i −0.638003 − 0.232214i 0.00270796 − 0.999996i \(-0.499138\pi\)
−0.640711 + 0.767782i \(0.721360\pi\)
\(500\) −1.14919e9 − 4.18269e8i −0.411145 − 0.149645i
\(501\) 6.02119e9 + 5.05237e9i 2.13919 + 1.79500i
\(502\) −2.03881e8 + 1.15627e9i −0.0719307 + 0.407940i
\(503\) −8.08576e8 + 4.58566e9i −0.283291 + 1.60662i 0.428035 + 0.903762i \(0.359206\pi\)
−0.711326 + 0.702862i \(0.751905\pi\)
\(504\) −5.92883e8 − 1.02690e9i −0.206282 − 0.357292i
\(505\) −1.09072e9 + 9.15226e8i −0.376873 + 0.316234i
\(506\) −4.88478e9 + 1.77791e9i −1.67617 + 0.610076i
\(507\) −2.49258e9 + 4.31727e9i −0.849417 + 1.47123i
\(508\) 4.99542e8 + 8.65232e8i 0.169063 + 0.292826i
\(509\) −1.15545e9 − 9.69541e8i −0.388365 − 0.325877i 0.427611 − 0.903963i \(-0.359355\pi\)
−0.815976 + 0.578086i \(0.803800\pi\)
\(510\) 1.42941e9 − 2.47582e9i 0.477158 − 0.826462i
\(511\) 6.03139e7 + 3.42057e8i 0.0199960 + 0.113403i
\(512\) −1.34218e8 −0.0441942
\(513\) 1.25264e8 + 7.10407e8i 0.0409652 + 0.232325i
\(514\) −2.03856e9 + 1.71055e9i −0.662143 + 0.555604i
\(515\) −6.15324e8 − 2.23960e8i −0.198508 − 0.0722511i
\(516\) −9.69480e8 + 3.52862e8i −0.310645 + 0.113066i
\(517\) 1.68151e9 0.535159
\(518\) −7.37951e8 + 6.93546e8i −0.233278 + 0.219241i
\(519\) −8.96155e9 −2.81383
\(520\) −2.34281e9 + 8.52712e8i −0.730676 + 0.265944i
\(521\) −1.64866e9 − 6.00063e8i −0.510739 − 0.185894i 0.0737788 − 0.997275i \(-0.476494\pi\)
−0.584518 + 0.811381i \(0.698716\pi\)
\(522\) 5.68199e9 − 4.76776e9i 1.74845 − 1.46713i
\(523\) −6.46788e8 − 3.66812e9i −0.197700 − 1.12121i −0.908521 − 0.417839i \(-0.862788\pi\)
0.710821 − 0.703372i \(-0.248323\pi\)
\(524\) −2.93494e8 −0.0891127
\(525\) −7.63277e8 − 4.32876e9i −0.230210 − 1.30559i
\(526\) −1.31489e9 + 2.27746e9i −0.393949 + 0.682340i
\(527\) −1.34476e9 − 1.12839e9i −0.400228 − 0.335831i
\(528\) 1.15743e9 + 2.00473e9i 0.342197 + 0.592702i
\(529\) −3.46891e9 + 6.00834e9i −1.01882 + 1.76465i
\(530\) 2.54120e9 − 9.24920e8i 0.741434 − 0.269860i
\(531\) −3.70933e8 + 3.11249e8i −0.107514 + 0.0902148i
\(532\) 3.10796e7 + 5.38314e7i 0.00894921 + 0.0155005i
\(533\) −7.29074e8 + 4.13478e9i −0.208558 + 1.18279i
\(534\) −7.31162e6 + 4.14663e7i −0.00207787 + 0.0117842i
\(535\) 1.15571e9 + 9.69759e8i 0.326296 + 0.273795i
\(536\) −1.88548e8 − 6.86259e7i −0.0528865 − 0.0192491i
\(537\) −4.70212e9 − 1.71143e9i −1.31034 − 0.476924i
\(538\) −1.37894e9 − 1.15707e9i −0.381775 − 0.320347i
\(539\) 7.26429e8 − 4.11978e9i 0.199817 − 1.13322i
\(540\) 1.51314e9 − 8.58145e9i 0.413524 − 2.34521i
\(541\) −3.38801e9 − 5.86820e9i −0.919929 − 1.59336i −0.799521 − 0.600638i \(-0.794913\pi\)
−0.120408 − 0.992725i \(-0.538420\pi\)
\(542\) 3.29063e9 − 2.76117e9i 0.887732 − 0.744896i
\(543\) 3.15370e9 − 1.14785e9i 0.845319 − 0.307671i
\(544\) 1.48353e8 − 2.56955e8i 0.0395093 − 0.0684322i
\(545\) −1.02291e9 − 1.77173e9i −0.270675 − 0.468823i
\(546\) −2.43061e9 − 2.03952e9i −0.639058 − 0.536233i
\(547\) −6.51630e8 + 1.12866e9i −0.170234 + 0.294853i −0.938502 − 0.345275i \(-0.887786\pi\)
0.768268 + 0.640129i \(0.221119\pi\)
\(548\) 2.97472e8 + 1.68705e9i 0.0772172 + 0.437920i
\(549\) 1.71591e10 4.42579
\(550\) 1.07356e9 + 6.08844e9i 0.275141 + 1.56040i
\(551\) −2.97856e8 + 2.49931e8i −0.0758536 + 0.0636488i
\(552\) 4.32796e9 + 1.57525e9i 1.09521 + 0.398623i
\(553\) 1.01754e9 − 3.70355e8i 0.255867 − 0.0931279i
\(554\) 2.50924e9 0.626985
\(555\) −1.21406e10 + 6.83713e8i −3.01450 + 0.169765i
\(556\) −3.70652e8 −0.0914544
\(557\) 2.68684e9 − 9.77929e8i 0.658792 − 0.239781i 0.00907718 − 0.999959i \(-0.497111\pi\)
0.649715 + 0.760178i \(0.274888\pi\)
\(558\) −8.21544e9 − 2.99018e9i −2.00176 − 0.728580i
\(559\) −1.52365e9 + 1.27850e9i −0.368930 + 0.309569i
\(560\) −1.30385e8 − 7.39452e8i −0.0313740 − 0.177931i
\(561\) −5.11730e9 −1.22369
\(562\) −3.63464e8 − 2.06131e9i −0.0863742 − 0.489852i
\(563\) −1.53221e9 + 2.65386e9i −0.361858 + 0.626757i −0.988267 − 0.152738i \(-0.951191\pi\)
0.626408 + 0.779495i \(0.284524\pi\)
\(564\) −1.14128e9 − 9.57648e8i −0.267865 − 0.224765i
\(565\) 1.91377e9 + 3.31474e9i 0.446395 + 0.773179i
\(566\) −3.68778e8 + 6.38743e8i −0.0854885 + 0.148070i
\(567\) 5.66137e9 − 2.06057e9i 1.30431 − 0.474730i
\(568\) −2.29222e9 + 1.92340e9i −0.524852 + 0.440403i
\(569\) 2.95230e9 + 5.11353e9i 0.671842 + 1.16366i 0.977381 + 0.211485i \(0.0678301\pi\)
−0.305539 + 0.952180i \(0.598837\pi\)
\(570\) −1.29604e8 + 7.35022e8i −0.0293128 + 0.166241i
\(571\) 2.67649e8 − 1.51791e9i 0.0601644 − 0.341209i −0.939835 − 0.341627i \(-0.889022\pi\)
1.00000 0.000417965i \(0.000133043\pi\)
\(572\) 3.41867e9 + 2.86861e9i 0.763785 + 0.640892i
\(573\) −2.52604e9 − 9.19403e8i −0.560917 − 0.204157i
\(574\) −1.18821e9 − 4.32475e8i −0.262243 − 0.0954485i
\(575\) 9.42284e9 + 7.90670e9i 2.06702 + 1.73443i
\(576\) 2.56597e8 − 1.45523e9i 0.0559464 − 0.317288i
\(577\) 1.29754e9 − 7.35871e9i 0.281194 − 1.59473i −0.437380 − 0.899277i \(-0.644094\pi\)
0.718574 − 0.695451i \(-0.244795\pi\)
\(578\) −1.31340e9 − 2.27488e9i −0.282911 − 0.490017i
\(579\) 6.57224e9 − 5.51476e9i 1.40714 − 1.18073i
\(580\) 4.41359e9 − 1.60642e9i 0.939278 − 0.341869i
\(581\) −2.28041e8 + 3.94978e8i −0.0482387 + 0.0835519i
\(582\) 5.90949e9 + 1.02355e10i 1.24257 + 2.15219i
\(583\) −3.70817e9 − 3.11152e9i −0.775031 − 0.650328i
\(584\) −2.16421e8 + 3.74851e8i −0.0449628 + 0.0778779i
\(585\) −4.76641e9 − 2.70317e10i −0.984342 − 5.58248i
\(586\) −5.67868e9 −1.16575
\(587\) 8.37379e7 + 4.74901e8i 0.0170879 + 0.0969103i 0.992159 − 0.124983i \(-0.0398875\pi\)
−0.975071 + 0.221893i \(0.928776\pi\)
\(588\) −2.83933e9 + 2.38248e9i −0.575963 + 0.483291i
\(589\) 4.30663e8 + 1.56748e8i 0.0868428 + 0.0316082i
\(590\) −2.88129e8 + 1.04870e8i −0.0577570 + 0.0210218i
\(591\) −9.51064e9 −1.89519
\(592\) −1.26002e9 + 7.09597e7i −0.249605 + 0.0140568i
\(593\) −3.34977e8 −0.0659665 −0.0329832 − 0.999456i \(-0.510501\pi\)
−0.0329832 + 0.999456i \(0.510501\pi\)
\(594\) −1.46571e10 + 5.33474e9i −2.86943 + 1.04439i
\(595\) 1.55977e9 + 5.67709e8i 0.303564 + 0.110488i
\(596\) 2.63709e9 − 2.21278e9i 0.510227 − 0.428131i
\(597\) 2.11606e9 + 1.20008e10i 0.407022 + 2.30833i
\(598\) 8.87925e9 1.69794
\(599\) 5.10224e8 + 2.89362e9i 0.0969989 + 0.550108i 0.994116 + 0.108316i \(0.0345459\pi\)
−0.897118 + 0.441792i \(0.854343\pi\)
\(600\) 2.73882e9 − 4.74378e9i 0.517648 − 0.896592i
\(601\) 2.64258e9 + 2.21739e9i 0.496556 + 0.416660i 0.856369 − 0.516365i \(-0.172715\pi\)
−0.359813 + 0.933024i \(0.617160\pi\)
\(602\) −2.99509e8 − 5.18765e8i −0.0559528 − 0.0969131i
\(603\) 1.10453e9 − 1.91310e9i 0.205148 − 0.355326i
\(604\) −3.41667e8 + 1.24357e8i −0.0630919 + 0.0229636i
\(605\) 7.29248e9 − 6.11912e9i 1.33885 − 1.12343i
\(606\) −1.12907e9 − 1.95561e9i −0.206095 − 0.356968i
\(607\) −1.77441e9 + 1.00632e10i −0.322028 + 1.82631i 0.207759 + 0.978180i \(0.433383\pi\)
−0.529787 + 0.848131i \(0.677728\pi\)
\(608\) −1.34511e7 + 7.62849e7i −0.00242714 + 0.0137650i
\(609\) 4.57899e9 + 3.84223e9i 0.821504 + 0.689324i
\(610\) 1.02103e10 + 3.71625e9i 1.82131 + 0.662903i
\(611\) −2.69900e9 − 9.82356e8i −0.478695 − 0.174231i
\(612\) 2.50236e9 + 2.09973e9i 0.441286 + 0.370283i
\(613\) 1.66973e7 − 9.46949e7i 0.00292775 − 0.0166041i −0.983309 − 0.181944i \(-0.941761\pi\)
0.986237 + 0.165340i \(0.0528721\pi\)
\(614\) −3.39676e8 + 1.92640e9i −0.0592211 + 0.335859i
\(615\) −7.59142e9 − 1.31487e10i −1.31601 − 2.27940i
\(616\) −1.02959e9 + 8.63930e8i −0.177473 + 0.148918i
\(617\) −1.64949e9 + 6.00367e8i −0.282717 + 0.102901i −0.479487 − 0.877549i \(-0.659177\pi\)
0.196769 + 0.980450i \(0.436955\pi\)
\(618\) 5.19254e8 − 8.99374e8i 0.0884953 − 0.153278i
\(619\) 3.95289e9 + 6.84661e9i 0.669881 + 1.16027i 0.977937 + 0.208900i \(0.0669883\pi\)
−0.308056 + 0.951368i \(0.599678\pi\)
\(620\) −4.24090e9 − 3.55854e9i −0.714640 − 0.599654i
\(621\) −1.55169e10 + 2.68761e10i −2.60007 + 4.50345i
\(622\) 3.98409e6 + 2.25949e7i 0.000663839 + 0.00376482i
\(623\) −2.44472e7 −0.00405062
\(624\) −6.86614e8 − 3.89398e9i −0.113127 − 0.641575i
\(625\) −7.07488e8 + 5.93653e8i −0.115915 + 0.0972641i
\(626\) 5.21759e9 + 1.89905e9i 0.850079 + 0.309404i
\(627\) 1.25542e9 − 4.56934e8i 0.203400 − 0.0740316i
\(628\) −2.12516e9 −0.342399
\(629\) 1.25687e9 − 2.49070e9i 0.201379 − 0.399065i
\(630\) 8.26664e9 1.31716
\(631\) −2.28944e9 + 8.33287e8i −0.362765 + 0.132036i −0.516971 − 0.856003i \(-0.672940\pi\)
0.154205 + 0.988039i \(0.450718\pi\)
\(632\) 1.26804e9 + 4.61530e8i 0.199813 + 0.0727260i
\(633\) 5.16008e9 − 4.32982e9i 0.808619 − 0.678512i
\(634\) −1.79209e8 − 1.01635e9i −0.0279285 − 0.158390i
\(635\) −6.96517e9 −1.07950
\(636\) 7.44756e8 + 4.22372e9i 0.114793 + 0.651022i
\(637\) −3.57281e9 + 6.18829e9i −0.547674 + 0.948599i
\(638\) −6.44040e9 − 5.40414e9i −0.981840 − 0.823861i
\(639\) −1.64719e10 − 2.85301e10i −2.49741 − 4.32564i
\(640\) 4.67854e8 − 8.10346e8i 0.0705473 − 0.122191i
\(641\) −1.36438e9 + 4.96593e8i −0.204612 + 0.0744728i −0.442293 − 0.896870i \(-0.645835\pi\)
0.237681 + 0.971343i \(0.423613\pi\)
\(642\) −1.83291e9 + 1.53800e9i −0.273382 + 0.229394i
\(643\) −2.77959e9 − 4.81439e9i −0.412328 − 0.714173i 0.582816 − 0.812604i \(-0.301951\pi\)
−0.995144 + 0.0984315i \(0.968617\pi\)
\(644\) −4.64360e8 + 2.63351e9i −0.0685100 + 0.388540i
\(645\) 1.24897e9 − 7.08329e9i 0.183271 − 1.03938i
\(646\) −1.31177e8 − 1.10070e8i −0.0191445 − 0.0160641i
\(647\) 1.53847e9 + 5.59956e8i 0.223318 + 0.0812809i 0.451256 − 0.892395i \(-0.350976\pi\)
−0.227938 + 0.973676i \(0.573198\pi\)
\(648\) 7.05509e9 + 2.56784e9i 1.01857 + 0.370729i
\(649\) 4.20443e8 + 3.52794e8i 0.0603741 + 0.0506599i
\(650\) 1.83376e9 − 1.03998e10i 0.261906 − 1.48534i
\(651\) 1.22345e9 − 6.93851e9i 0.173801 − 0.985672i
\(652\) 7.10337e8 + 1.23034e9i 0.100369 + 0.173844i
\(653\) 4.66377e9 − 3.91337e9i 0.655452 − 0.549990i −0.253267 − 0.967396i \(-0.581505\pi\)
0.908720 + 0.417406i \(0.137061\pi\)
\(654\) 3.04890e9 − 1.10971e9i 0.426208 − 0.155127i
\(655\) 1.02306e9 − 1.77198e9i 0.142251 − 0.246386i
\(656\) −7.87881e8 − 1.36465e9i −0.108968 − 0.188737i
\(657\) −3.65051e9 − 3.06314e9i −0.502197 − 0.421394i
\(658\) 4.32509e8 − 7.49128e8i 0.0591840 − 0.102510i
\(659\) 3.14392e8 + 1.78300e9i 0.0427930 + 0.242691i 0.998700 − 0.0509795i \(-0.0162343\pi\)
−0.955907 + 0.293670i \(0.905123\pi\)
\(660\) −1.61382e10 −2.18500
\(661\) 2.65347e8 + 1.50486e9i 0.0357362 + 0.202670i 0.997448 − 0.0713914i \(-0.0227439\pi\)
−0.961712 + 0.274061i \(0.911633\pi\)
\(662\) 7.55342e9 − 6.33808e9i 1.01191 − 0.849091i
\(663\) 8.21380e9 + 2.98958e9i 1.09458 + 0.398394i
\(664\) −5.34084e8 + 1.94391e8i −0.0707981 + 0.0257684i
\(665\) −4.33347e8 −0.0571426
\(666\) 1.63954e9 − 1.37972e10i 0.215061 − 1.80981i
\(667\) −1.67275e10 −2.18269
\(668\) −5.34419e9 + 1.94513e9i −0.693688 + 0.252482i
\(669\) −3.97042e8 − 1.44511e8i −0.0512678 − 0.0186600i
\(670\) 1.07157e9 − 8.99153e8i 0.137644 − 0.115497i
\(671\) −3.37735e9 − 1.91539e10i −0.431566 − 2.44753i
\(672\) 1.19083e9 0.151376
\(673\) 1.33610e8 + 7.57740e8i 0.0168961 + 0.0958225i 0.992090 − 0.125531i \(-0.0400636\pi\)
−0.975194 + 0.221354i \(0.928952\pi\)
\(674\) −4.06857e9 + 7.04698e9i −0.511838 + 0.886530i
\(675\) 2.82738e10 + 2.37246e10i 3.53852 + 2.96917i
\(676\) −1.80350e9 − 3.12376e9i −0.224545 − 0.388923i
\(677\) 2.15443e9 − 3.73159e9i 0.266853 − 0.462204i −0.701194 − 0.712970i \(-0.747349\pi\)
0.968048 + 0.250767i \(0.0806827\pi\)
\(678\) −5.70422e9 + 2.07617e9i −0.702899 + 0.255834i
\(679\) −5.25679e9 + 4.41097e9i −0.644430 + 0.540741i
\(680\) 1.03425e9 + 1.79138e9i 0.126138 + 0.218477i
\(681\) −2.59339e8 + 1.47078e9i −0.0314668 + 0.178457i
\(682\) −1.72079e9 + 9.75908e9i −0.207722 + 1.17805i
\(683\) 5.42467e9 + 4.55183e9i 0.651479 + 0.546656i 0.907519 − 0.420010i \(-0.137974\pi\)
−0.256040 + 0.966666i \(0.582418\pi\)
\(684\) −8.01389e8 − 2.91682e8i −0.0957518 − 0.0348508i
\(685\) −1.12226e10 − 4.08467e9i −1.33406 − 0.485557i
\(686\) −3.72212e9 − 3.12323e9i −0.440206 − 0.369377i
\(687\) −3.49919e9 + 1.98449e10i −0.411736 + 2.33507i
\(688\) 1.29626e8 − 7.35145e8i 0.0151751 − 0.0860623i
\(689\) 4.13421e9 + 7.16066e9i 0.481532 + 0.834038i
\(690\) −2.45970e10 + 2.06393e10i −2.85043 + 2.39179i
\(691\) 1.37115e10 − 4.99057e9i 1.58092 − 0.575409i 0.605519 − 0.795831i \(-0.292965\pi\)
0.975405 + 0.220421i \(0.0707432\pi\)
\(692\) 3.24206e9 − 5.61542e9i 0.371920 − 0.644185i
\(693\) −7.39864e9 − 1.28148e10i −0.844473 − 1.46267i
\(694\) −1.06738e9 − 8.95634e8i −0.121216 − 0.101712i
\(695\) 1.29201e9 − 2.23783e9i 0.145989 − 0.252860i
\(696\) 1.29350e9 + 7.33583e9i 0.145424 + 0.824740i
\(697\) 3.48343e9 0.389665
\(698\) 1.47680e9 + 8.37536e9i 0.164372 + 0.932201i
\(699\) 1.33528e10 − 1.12043e10i 1.47878 − 1.24084i
\(700\) 2.98859e9 + 1.08776e9i 0.329324 + 0.119864i
\(701\) 9.80238e9 − 3.56777e9i 1.07478 − 0.391187i 0.256816 − 0.966460i \(-0.417327\pi\)
0.817961 + 0.575273i \(0.195104\pi\)
\(702\) 2.66428e10 2.90670
\(703\) −8.59463e7 + 7.23266e8i −0.00933004 + 0.0785154i
\(704\) −1.67492e9 −0.180921
\(705\) 9.76011e9 − 3.55239e9i 1.04904 − 0.381820i
\(706\) 1.01223e10 + 3.68420e9i 1.08258 + 0.394028i
\(707\) 1.00437e9 − 8.42765e8i 0.106887 − 0.0896889i
\(708\) −8.44428e7 − 4.78899e8i −0.00894223 − 0.0507139i
\(709\) 7.02863e9 0.740643 0.370321 − 0.928904i \(-0.379248\pi\)
0.370321 + 0.928904i \(0.379248\pi\)
\(710\) −3.62245e9 − 2.05439e10i −0.379838 − 2.15417i
\(711\) −7.42829e9 + 1.28662e10i −0.775077 + 1.34247i
\(712\) −2.33381e7 − 1.95830e7i −0.00242318 − 0.00203329i
\(713\) 9.85826e9 + 1.70750e10i 1.01856 + 1.76420i
\(714\) −1.31624e9 + 2.27980e9i −0.135329 + 0.234397i
\(715\) −2.92361e10 + 1.06411e10i −2.99122 + 1.08871i
\(716\) 2.77351e9 − 2.32725e9i 0.282380 − 0.236945i
\(717\) −1.17066e10 − 2.02764e10i −1.18608 − 2.05434i
\(718\) −1.90197e8 + 1.07866e9i −0.0191764 + 0.108755i
\(719\) 6.53104e8 − 3.70394e9i 0.0655287 − 0.371632i −0.934354 − 0.356345i \(-0.884023\pi\)
0.999883 − 0.0152867i \(-0.00486611\pi\)
\(720\) 7.89160e9 + 6.62183e9i 0.787954 + 0.661172i
\(721\) 5.66607e8 + 2.06228e8i 0.0563000 + 0.0204915i
\(722\) −6.67771e9 − 2.43049e9i −0.660309 − 0.240333i
\(723\) −1.34458e10 − 1.12823e10i −1.32313 − 1.11023i
\(724\) −4.21670e8 + 2.39141e9i −0.0412941 + 0.234190i
\(725\) −3.45460e9 + 1.95920e10i −0.336678 + 1.90940i
\(726\) 7.54889e9 + 1.30751e10i 0.732158 + 1.26813i
\(727\) 7.24267e8 − 6.07732e8i 0.0699082 − 0.0586600i −0.607164 − 0.794577i \(-0.707693\pi\)
0.677072 + 0.735917i \(0.263248\pi\)
\(728\) 2.15732e9 − 7.85200e8i 0.207231 − 0.0754259i
\(729\) −1.18138e10 + 2.04621e10i −1.12939 + 1.95616i
\(730\) −1.50879e9 − 2.61330e9i −0.143549 − 0.248633i
\(731\) 1.26413e9 + 1.06073e9i 0.119696 + 0.100437i
\(732\) −8.61618e9 + 1.49237e10i −0.811943 + 1.40633i
\(733\) −1.22146e9 − 6.92725e9i −0.114555 − 0.649677i −0.986969 − 0.160909i \(-0.948558\pi\)
0.872414 − 0.488768i \(-0.162554\pi\)
\(734\) −8.89417e9 −0.830174
\(735\) −4.48706e9 − 2.54474e10i −0.416827 − 2.36395i
\(736\) −2.55282e9 + 2.14207e9i −0.236019 + 0.198044i
\(737\) −2.35291e9 − 8.56388e8i −0.216505 − 0.0788015i
\(738\) 1.63022e10 − 5.93353e9i 1.49297 − 0.543395i
\(739\) 7.97177e9 0.726607 0.363303 − 0.931671i \(-0.381649\pi\)
0.363303 + 0.931671i \(0.381649\pi\)
\(740\) 3.96374e9 − 7.85480e9i 0.359579 − 0.712565i
\(741\) −2.28202e9 −0.206042
\(742\) −2.34000e9 + 8.51691e8i −0.210282 + 0.0765365i
\(743\) −1.30183e10 − 4.73828e9i −1.16438 − 0.423799i −0.313718 − 0.949516i \(-0.601575\pi\)
−0.850659 + 0.525718i \(0.823797\pi\)
\(744\) 6.72589e9 − 5.64370e9i 0.598749 − 0.502410i
\(745\) 4.16746e9 + 2.36348e10i 0.369253 + 2.09414i
\(746\) −8.75289e9 −0.771908
\(747\) −1.08659e9 − 6.16235e9i −0.0953768 − 0.540909i
\(748\) 1.85131e9 − 3.20656e9i 0.161742 − 0.280146i
\(749\) −1.06421e9 − 8.92980e8i −0.0925427 − 0.0776525i
\(750\) 6.76077e9 + 1.17100e10i 0.585170 + 1.01354i
\(751\) 6.97596e9 − 1.20827e10i 0.600986 − 1.04094i −0.391686 − 0.920099i \(-0.628108\pi\)
0.992672 − 0.120839i \(-0.0385585\pi\)
\(752\) 1.01296e9 − 3.68688e8i 0.0868621 − 0.0316152i
\(753\) 9.94450e9 − 8.34443e9i 0.848791 − 0.712220i
\(754\) 7.18037e9 + 1.24368e10i 0.610024 + 1.05659i
\(755\) 4.40167e8 − 2.49631e9i 0.0372223 − 0.211098i
\(756\) −1.39334e9 + 7.90203e9i −0.117282 + 0.665139i
\(757\) −1.29861e9 − 1.08966e9i −0.108803 − 0.0912969i 0.586763 − 0.809759i \(-0.300402\pi\)