Properties

Label 20.8.e.b.7.1
Level $20$
Weight $8$
Character 20.7
Analytic conductor $6.248$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,8,Mod(3,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.3");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.24770050968\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Character \(\chi\) \(=\) 20.7
Dual form 20.8.e.b.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.3062 - 0.411421i) q^{2} +(-2.83352 - 2.83352i) q^{3} +(127.661 + 9.30323i) q^{4} +(-150.277 + 235.673i) q^{5} +(30.8707 + 33.2022i) q^{6} +(411.746 - 411.746i) q^{7} +(-1439.54 - 157.707i) q^{8} -2170.94i q^{9} +O(q^{10})\) \(q+(-11.3062 - 0.411421i) q^{2} +(-2.83352 - 2.83352i) q^{3} +(127.661 + 9.30323i) q^{4} +(-150.277 + 235.673i) q^{5} +(30.8707 + 33.2022i) q^{6} +(411.746 - 411.746i) q^{7} +(-1439.54 - 157.707i) q^{8} -2170.94i q^{9} +(1796.03 - 2602.74i) q^{10} -7801.51i q^{11} +(-335.370 - 388.092i) q^{12} +(-2238.68 + 2238.68i) q^{13} +(-4824.70 + 4485.90i) q^{14} +(1093.60 - 241.971i) q^{15} +(16210.9 + 2375.33i) q^{16} +(-18584.8 - 18584.8i) q^{17} +(-893.171 + 24545.2i) q^{18} +34833.9 q^{19} +(-21377.1 + 28688.3i) q^{20} -2333.38 q^{21} +(-3209.70 + 88205.6i) q^{22} +(7263.46 + 7263.46i) q^{23} +(3632.11 + 4525.84i) q^{24} +(-32958.5 - 70832.6i) q^{25} +(26232.1 - 24390.0i) q^{26} +(-12348.3 + 12348.3i) q^{27} +(56394.7 - 48733.6i) q^{28} +35580.6i q^{29} +(-12464.0 + 2285.85i) q^{30} -201719. i q^{31} +(-182307. - 33525.5i) q^{32} +(-22105.7 + 22105.7i) q^{33} +(202477. + 217770. i) q^{34} +(35161.4 + 158914. i) q^{35} +(20196.8 - 277146. i) q^{36} +(80900.2 + 80900.2i) q^{37} +(-393840. - 14331.4i) q^{38} +12686.7 q^{39} +(253498. - 315561. i) q^{40} +52398.8 q^{41} +(26381.8 + 960.003i) q^{42} +(-250428. - 250428. i) q^{43} +(72579.3 - 995952. i) q^{44} +(511632. + 326243. i) q^{45} +(-79134.0 - 85110.7i) q^{46} +(-890845. + 890845. i) q^{47} +(-39203.4 - 52664.5i) q^{48} +484473. i q^{49} +(343494. + 814409. i) q^{50} +105321. i q^{51} +(-306620. + 264966. i) q^{52} +(354485. - 354485. i) q^{53} +(144693. - 134533. i) q^{54} +(1.83861e6 + 1.17239e6i) q^{55} +(-657662. + 527791. i) q^{56} +(-98702.6 - 98702.6i) q^{57} +(14638.6 - 402282. i) q^{58} -858580. q^{59} +(141861. - 20716.3i) q^{60} -1.30963e6 q^{61} +(-82991.4 + 2.28068e6i) q^{62} +(-893878. - 893878. i) q^{63} +(2.04741e6 + 454052. i) q^{64} +(-191174. - 864020. i) q^{65} +(259027. - 240838. i) q^{66} +(1.97721e6 - 1.97721e6i) q^{67} +(-2.19966e6 - 2.54546e6i) q^{68} -41162.4i q^{69} +(-332162. - 1.81118e6i) q^{70} -4.95750e6i q^{71} +(-342373. + 3.12516e6i) q^{72} +(638724. - 638724. i) q^{73} +(-881392. - 947960. i) q^{74} +(-107317. + 294094. i) q^{75} +(4.44695e6 + 324068. i) q^{76} +(-3.21224e6 - 3.21224e6i) q^{77} +(-143439. - 5219.57i) q^{78} +503348. q^{79} +(-2.99593e6 + 3.46351e6i) q^{80} -4.67787e6 q^{81} +(-592432. - 21557.9i) q^{82} +(4.22137e6 + 4.22137e6i) q^{83} +(-297883. - 21708.0i) q^{84} +(7.17279e6 - 1.58706e6i) q^{85} +(2.72837e6 + 2.93443e6i) q^{86} +(100818. - 100818. i) q^{87} +(-1.23035e6 + 1.12306e7i) q^{88} +8.63243e6i q^{89} +(-5.65041e6 - 3.89908e6i) q^{90} +1.84354e6i q^{91} +(859691. + 994838. i) q^{92} +(-571575. + 571575. i) q^{93} +(1.04386e7 - 9.70558e6i) q^{94} +(-5.23475e6 + 8.20941e6i) q^{95} +(421575. + 611565. i) q^{96} +(-3.20292e6 - 3.20292e6i) q^{97} +(199322. - 5.47756e6i) q^{98} -1.69366e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8} + 390 q^{10} + 10960 q^{12} - 28564 q^{13} - 12104 q^{16} - 27012 q^{17} + 95298 q^{18} + 97180 q^{20} - 2352 q^{21} - 191320 q^{22} - 112580 q^{25} + 604628 q^{26} - 142800 q^{28} - 252760 q^{30} - 73976 q^{32} - 248080 q^{33} - 328580 q^{36} - 108732 q^{37} - 406560 q^{38} - 680660 q^{40} + 2019472 q^{41} + 1616840 q^{42} - 827660 q^{45} - 2690616 q^{46} + 549280 q^{48} + 1343690 q^{50} - 6025332 q^{52} + 5672196 q^{53} + 4064064 q^{56} - 1796160 q^{57} + 3463736 q^{58} + 3280240 q^{60} - 5624928 q^{61} + 2750760 q^{62} + 75940 q^{65} - 2175120 q^{66} - 5673084 q^{68} - 11417280 q^{70} + 4328964 q^{72} - 22930604 q^{73} - 4045600 q^{76} + 10982160 q^{77} + 27127080 q^{78} + 34488560 q^{80} + 21593004 q^{81} - 13289192 q^{82} - 28299060 q^{85} - 2245656 q^{86} - 38612320 q^{88} - 38642970 q^{90} - 22809360 q^{92} + 31343120 q^{93} + 49033664 q^{96} - 11169292 q^{97} + 45095638 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.3062 0.411421i −0.999339 0.0363648i
\(3\) −2.83352 2.83352i −0.0605901 0.0605901i 0.676162 0.736753i \(-0.263642\pi\)
−0.736753 + 0.676162i \(0.763642\pi\)
\(4\) 127.661 + 9.30323i 0.997355 + 0.0726815i
\(5\) −150.277 + 235.673i −0.537648 + 0.843169i
\(6\) 30.8707 + 33.2022i 0.0583467 + 0.0627534i
\(7\) 411.746 411.746i 0.453719 0.453719i −0.442868 0.896587i \(-0.646039\pi\)
0.896587 + 0.442868i \(0.146039\pi\)
\(8\) −1439.54 157.707i −0.994052 0.108902i
\(9\) 2170.94i 0.992658i
\(10\) 1796.03 2602.74i 0.567954 0.823060i
\(11\) 7801.51i 1.76728i −0.468171 0.883638i \(-0.655087\pi\)
0.468171 0.883638i \(-0.344913\pi\)
\(12\) −335.370 388.092i −0.0560261 0.0648337i
\(13\) −2238.68 + 2238.68i −0.282612 + 0.282612i −0.834150 0.551538i \(-0.814041\pi\)
0.551538 + 0.834150i \(0.314041\pi\)
\(14\) −4824.70 + 4485.90i −0.469918 + 0.436919i
\(15\) 1093.60 241.971i 0.0836639 0.0185116i
\(16\) 16210.9 + 2375.33i 0.989435 + 0.144979i
\(17\) −18584.8 18584.8i −0.917457 0.917457i 0.0793869 0.996844i \(-0.474704\pi\)
−0.996844 + 0.0793869i \(0.974704\pi\)
\(18\) −893.171 + 24545.2i −0.0360978 + 0.992001i
\(19\) 34833.9 1.16510 0.582552 0.812793i \(-0.302054\pi\)
0.582552 + 0.812793i \(0.302054\pi\)
\(20\) −21377.1 + 28688.3i −0.597509 + 0.801862i
\(21\) −2333.38 −0.0549818
\(22\) −3209.70 + 88205.6i −0.0642666 + 1.76611i
\(23\) 7263.46 + 7263.46i 0.124479 + 0.124479i 0.766602 0.642123i \(-0.221946\pi\)
−0.642123 + 0.766602i \(0.721946\pi\)
\(24\) 3632.11 + 4525.84i 0.0536314 + 0.0668282i
\(25\) −32958.5 70832.6i −0.421869 0.906657i
\(26\) 26232.1 24390.0i 0.292702 0.272148i
\(27\) −12348.3 + 12348.3i −0.120735 + 0.120735i
\(28\) 56394.7 48733.6i 0.485496 0.419542i
\(29\) 35580.6i 0.270907i 0.990784 + 0.135453i \(0.0432491\pi\)
−0.990784 + 0.135453i \(0.956751\pi\)
\(30\) −12464.0 + 2285.85i −0.0842818 + 0.0154569i
\(31\) 201719.i 1.21613i −0.793886 0.608067i \(-0.791945\pi\)
0.793886 0.608067i \(-0.208055\pi\)
\(32\) −182307. 33525.5i −0.983508 0.180863i
\(33\) −22105.7 + 22105.7i −0.107079 + 0.107079i
\(34\) 202477. + 217770.i 0.883487 + 0.950213i
\(35\) 35161.4 + 158914.i 0.138621 + 0.626503i
\(36\) 20196.8 277146.i 0.0721478 0.990032i
\(37\) 80900.2 + 80900.2i 0.262569 + 0.262569i 0.826097 0.563528i \(-0.190556\pi\)
−0.563528 + 0.826097i \(0.690556\pi\)
\(38\) −393840. 14331.4i −1.16433 0.0423688i
\(39\) 12686.7 0.0342470
\(40\) 253498. 315561.i 0.626273 0.779604i
\(41\) 52398.8 0.118735 0.0593673 0.998236i \(-0.481092\pi\)
0.0593673 + 0.998236i \(0.481092\pi\)
\(42\) 26381.8 + 960.003i 0.0549454 + 0.00199940i
\(43\) −250428. 250428.i −0.480334 0.480334i 0.424904 0.905238i \(-0.360308\pi\)
−0.905238 + 0.424904i \(0.860308\pi\)
\(44\) 72579.3 995952.i 0.128448 1.76260i
\(45\) 511632. + 326243.i 0.836978 + 0.533701i
\(46\) −79134.0 85110.7i −0.119870 0.128923i
\(47\) −890845. + 890845.i −1.25158 + 1.25158i −0.296572 + 0.955010i \(0.595844\pi\)
−0.955010 + 0.296572i \(0.904156\pi\)
\(48\) −39203.4 52664.5i −0.0511657 0.0687343i
\(49\) 484473.i 0.588279i
\(50\) 343494. + 814409.i 0.388619 + 0.921398i
\(51\) 105321.i 0.111178i
\(52\) −306620. + 264966.i −0.302405 + 0.261324i
\(53\) 354485. 354485.i 0.327064 0.327064i −0.524405 0.851469i \(-0.675712\pi\)
0.851469 + 0.524405i \(0.175712\pi\)
\(54\) 144693. 134533.i 0.125046 0.116265i
\(55\) 1.83861e6 + 1.17239e6i 1.49011 + 0.950173i
\(56\) −657662. + 527791.i −0.500431 + 0.401609i
\(57\) −98702.6 98702.6i −0.0705938 0.0705938i
\(58\) 14638.6 402282.i 0.00985148 0.270728i
\(59\) −858580. −0.544251 −0.272125 0.962262i \(-0.587727\pi\)
−0.272125 + 0.962262i \(0.587727\pi\)
\(60\) 141861. 20716.3i 0.0847881 0.0123818i
\(61\) −1.30963e6 −0.738746 −0.369373 0.929281i \(-0.620428\pi\)
−0.369373 + 0.929281i \(0.620428\pi\)
\(62\) −82991.4 + 2.28068e6i −0.0442244 + 1.21533i
\(63\) −893878. 893878.i −0.450387 0.450387i
\(64\) 2.04741e6 + 454052.i 0.976281 + 0.216509i
\(65\) −191174. 864020.i −0.0863440 0.390236i
\(66\) 259027. 240838.i 0.110903 0.103115i
\(67\) 1.97721e6 1.97721e6i 0.803140 0.803140i −0.180445 0.983585i \(-0.557754\pi\)
0.983585 + 0.180445i \(0.0577539\pi\)
\(68\) −2.19966e6 2.54546e6i −0.848348 0.981713i
\(69\) 41162.4i 0.0150844i
\(70\) −332162. 1.81118e6i −0.115746 0.631129i
\(71\) 4.95750e6i 1.64384i −0.569605 0.821919i \(-0.692904\pi\)
0.569605 0.821919i \(-0.307096\pi\)
\(72\) −342373. + 3.12516e6i −0.108102 + 0.986754i
\(73\) 638724. 638724.i 0.192169 0.192169i −0.604464 0.796633i \(-0.706613\pi\)
0.796633 + 0.604464i \(0.206613\pi\)
\(74\) −881392. 947960.i −0.252847 0.271944i
\(75\) −107317. + 294094.i −0.0293734 + 0.0804956i
\(76\) 4.44695e6 + 324068.i 1.16202 + 0.0846815i
\(77\) −3.21224e6 3.21224e6i −0.801846 0.801846i
\(78\) −143439. 5219.57i −0.0342244 0.00124539i
\(79\) 503348. 0.114861 0.0574306 0.998349i \(-0.481709\pi\)
0.0574306 + 0.998349i \(0.481709\pi\)
\(80\) −2.99593e6 + 3.46351e6i −0.654209 + 0.756314i
\(81\) −4.67787e6 −0.978027
\(82\) −592432. 21557.9i −0.118656 0.00431776i
\(83\) 4.22137e6 + 4.22137e6i 0.810363 + 0.810363i 0.984688 0.174325i \(-0.0557744\pi\)
−0.174325 + 0.984688i \(0.555774\pi\)
\(84\) −297883. 21708.0i −0.0548364 0.00399616i
\(85\) 7.17279e6 1.58706e6i 1.26684 0.280302i
\(86\) 2.72837e6 + 2.93443e6i 0.462549 + 0.497484i
\(87\) 100818. 100818.i 0.0164143 0.0164143i
\(88\) −1.23035e6 + 1.12306e7i −0.192460 + 1.75676i
\(89\) 8.63243e6i 1.29798i 0.760797 + 0.648990i \(0.224808\pi\)
−0.760797 + 0.648990i \(0.775192\pi\)
\(90\) −5.65041e6 3.89908e6i −0.817017 0.563784i
\(91\) 1.84354e6i 0.256453i
\(92\) 859691. + 994838.i 0.115103 + 0.133197i
\(93\) −571575. + 571575.i −0.0736857 + 0.0736857i
\(94\) 1.04386e7 9.70558e6i 1.29627 1.20524i
\(95\) −5.23475e6 + 8.20941e6i −0.626416 + 0.982380i
\(96\) 421575. + 611565.i 0.0486324 + 0.0705494i
\(97\) −3.20292e6 3.20292e6i −0.356324 0.356324i 0.506132 0.862456i \(-0.331075\pi\)
−0.862456 + 0.506132i \(0.831075\pi\)
\(98\) 199322. 5.47756e6i 0.0213926 0.587889i
\(99\) −1.69366e7 −1.75430
\(100\) −3.54856e6 9.34921e6i −0.354856 0.934921i
\(101\) 1.36177e7 1.31516 0.657579 0.753386i \(-0.271581\pi\)
0.657579 + 0.753386i \(0.271581\pi\)
\(102\) 43331.1 1.19078e6i 0.00404295 0.111104i
\(103\) 5.48497e6 + 5.48497e6i 0.494588 + 0.494588i 0.909748 0.415160i \(-0.136274\pi\)
−0.415160 + 0.909748i \(0.636274\pi\)
\(104\) 3.57573e6 2.86962e6i 0.311708 0.250154i
\(105\) 350655. 549916.i 0.0295608 0.0463589i
\(106\) −4.15373e6 + 3.86205e6i −0.338741 + 0.314954i
\(107\) 1.06402e7 1.06402e7i 0.839668 0.839668i −0.149147 0.988815i \(-0.547653\pi\)
0.988815 + 0.149147i \(0.0476528\pi\)
\(108\) −1.69128e6 + 1.46153e6i −0.129191 + 0.111641i
\(109\) 1.60681e7i 1.18843i 0.804308 + 0.594213i \(0.202536\pi\)
−0.804308 + 0.594213i \(0.797464\pi\)
\(110\) −2.03053e7 1.40117e7i −1.45457 1.00373i
\(111\) 458465.i 0.0318182i
\(112\) 7.65281e6 5.69675e6i 0.514705 0.383146i
\(113\) 8.05564e6 8.05564e6i 0.525201 0.525201i −0.393937 0.919137i \(-0.628887\pi\)
0.919137 + 0.393937i \(0.128887\pi\)
\(114\) 1.07535e6 + 1.15656e6i 0.0679800 + 0.0731143i
\(115\) −2.80334e6 + 620269.i −0.171883 + 0.0380310i
\(116\) −331014. + 4.54227e6i −0.0196899 + 0.270190i
\(117\) 4.86005e6 + 4.86005e6i 0.280537 + 0.280537i
\(118\) 9.70730e6 + 353238.i 0.543891 + 0.0197916i
\(119\) −1.53044e7 −0.832535
\(120\) −1.61244e6 + 175859.i −0.0851823 + 0.00929030i
\(121\) −4.13764e7 −2.12326
\(122\) 1.48070e7 + 538810.i 0.738258 + 0.0268644i
\(123\) −148473. 148473.i −0.00719415 0.00719415i
\(124\) 1.87664e6 2.57518e7i 0.0883904 1.21292i
\(125\) 2.16462e7 + 2.87709e6i 0.991282 + 0.131756i
\(126\) 9.73862e6 + 1.04741e7i 0.433711 + 0.466468i
\(127\) 2.13662e7 2.13662e7i 0.925579 0.925579i −0.0718370 0.997416i \(-0.522886\pi\)
0.997416 + 0.0718370i \(0.0228862\pi\)
\(128\) −2.29617e7 5.97596e6i −0.967762 0.251868i
\(129\) 1.41919e6i 0.0582071i
\(130\) 1.80598e6 + 9.84746e6i 0.0720960 + 0.393117i
\(131\) 1.30799e7i 0.508340i 0.967160 + 0.254170i \(0.0818023\pi\)
−0.967160 + 0.254170i \(0.918198\pi\)
\(132\) −3.02771e6 + 2.61640e6i −0.114579 + 0.0990136i
\(133\) 1.43427e7 1.43427e7i 0.528630 0.528630i
\(134\) −2.31683e7 + 2.15413e7i −0.831815 + 0.773402i
\(135\) −1.05449e6 4.76584e6i −0.0368872 0.166714i
\(136\) 2.38226e7 + 2.96845e7i 0.812087 + 1.01191i
\(137\) −3.05794e7 3.05794e7i −1.01603 1.01603i −0.999869 0.0161626i \(-0.994855\pi\)
−0.0161626 0.999869i \(-0.505145\pi\)
\(138\) −16935.0 + 465391.i −0.000548542 + 0.0150744i
\(139\) −394230. −0.0124508 −0.00622541 0.999981i \(-0.501982\pi\)
−0.00622541 + 0.999981i \(0.501982\pi\)
\(140\) 3.01035e6 + 2.06143e7i 0.0927189 + 0.634921i
\(141\) 5.04845e6 0.151667
\(142\) −2.03962e6 + 5.60507e7i −0.0597778 + 1.64275i
\(143\) 1.74651e7 + 1.74651e7i 0.499454 + 0.499454i
\(144\) 5.15670e6 3.51929e7i 0.143914 0.982170i
\(145\) −8.38538e6 5.34695e6i −0.228420 0.145653i
\(146\) −7.48435e6 + 6.95878e6i −0.199030 + 0.185054i
\(147\) 1.37276e6 1.37276e6i 0.0356439 0.0356439i
\(148\) 9.57520e6 + 1.10805e7i 0.242791 + 0.280958i
\(149\) 2.76465e7i 0.684681i −0.939576 0.342341i \(-0.888780\pi\)
0.939576 0.342341i \(-0.111220\pi\)
\(150\) 1.33435e6 3.28094e6i 0.0322811 0.0793742i
\(151\) 2.31256e7i 0.546605i −0.961928 0.273302i \(-0.911884\pi\)
0.961928 0.273302i \(-0.0881160\pi\)
\(152\) −5.01449e7 5.49355e6i −1.15817 0.126882i
\(153\) −4.03464e7 + 4.03464e7i −0.910721 + 0.910721i
\(154\) 3.49968e7 + 3.76399e7i 0.772157 + 0.830475i
\(155\) 4.75397e7 + 3.03138e7i 1.02541 + 0.653852i
\(156\) 1.61960e6 + 118027.i 0.0341564 + 0.00248912i
\(157\) 1.48337e7 + 1.48337e7i 0.305915 + 0.305915i 0.843323 0.537407i \(-0.180596\pi\)
−0.537407 + 0.843323i \(0.680596\pi\)
\(158\) −5.69097e6 207088.i −0.114785 0.00417691i
\(159\) −2.00888e6 −0.0396337
\(160\) 3.52976e7 3.79267e7i 0.681280 0.732023i
\(161\) 5.98141e6 0.112957
\(162\) 5.28891e7 + 1.92457e6i 0.977380 + 0.0355657i
\(163\) −4.56028e7 4.56028e7i −0.824774 0.824774i 0.162014 0.986788i \(-0.448201\pi\)
−0.986788 + 0.162014i \(0.948201\pi\)
\(164\) 6.68930e6 + 487478.i 0.118421 + 0.00862981i
\(165\) −1.88774e6 8.53172e6i −0.0327150 0.147857i
\(166\) −4.59910e7 4.94645e7i −0.780358 0.839296i
\(167\) −3.29811e7 + 3.29811e7i −0.547972 + 0.547972i −0.925854 0.377882i \(-0.876652\pi\)
0.377882 + 0.925854i \(0.376652\pi\)
\(168\) 3.35900e6 + 367991.i 0.0546548 + 0.00598763i
\(169\) 5.27251e7i 0.840261i
\(170\) −8.17501e7 + 1.49926e7i −1.27620 + 0.234049i
\(171\) 7.56224e7i 1.15655i
\(172\) −2.96402e7 3.42998e7i −0.444153 0.513975i
\(173\) 5.87038e7 5.87038e7i 0.861996 0.861996i −0.129574 0.991570i \(-0.541361\pi\)
0.991570 + 0.129574i \(0.0413609\pi\)
\(174\) −1.18135e6 + 1.09840e6i −0.0170003 + 0.0158065i
\(175\) −4.27356e7 1.55945e7i −0.602777 0.219957i
\(176\) 1.85311e7 1.26470e8i 0.256217 1.74860i
\(177\) 2.43281e6 + 2.43281e6i 0.0329762 + 0.0329762i
\(178\) 3.55156e6 9.76002e7i 0.0472008 1.29712i
\(179\) 8.56864e7 1.11667 0.558337 0.829614i \(-0.311440\pi\)
0.558337 + 0.829614i \(0.311440\pi\)
\(180\) 6.22806e7 + 4.64085e7i 0.795975 + 0.593122i
\(181\) 7.60781e7 0.953641 0.476820 0.879001i \(-0.341789\pi\)
0.476820 + 0.879001i \(0.341789\pi\)
\(182\) 758470. 2.08435e7i 0.00932585 0.256283i
\(183\) 3.71087e6 + 3.71087e6i 0.0447607 + 0.0447607i
\(184\) −9.31056e6 1.16016e7i −0.110183 0.137295i
\(185\) −3.12234e7 + 6.90853e6i −0.362560 + 0.0802204i
\(186\) 6.69752e6 6.22720e6i 0.0763165 0.0709574i
\(187\) −1.44989e8 + 1.44989e8i −1.62140 + 1.62140i
\(188\) −1.22014e8 + 1.05439e8i −1.33924 + 1.15731i
\(189\) 1.01688e7i 0.109560i
\(190\) 6.25627e7 9.06638e7i 0.661726 0.958951i
\(191\) 7.27447e7i 0.755413i 0.925925 + 0.377707i \(0.123287\pi\)
−0.925925 + 0.377707i \(0.876713\pi\)
\(192\) −4.51481e6 7.08794e6i −0.0460347 0.0722713i
\(193\) −9.24429e7 + 9.24429e7i −0.925599 + 0.925599i −0.997418 0.0718188i \(-0.977120\pi\)
0.0718188 + 0.997418i \(0.477120\pi\)
\(194\) 3.48952e7 + 3.75307e7i 0.343131 + 0.369046i
\(195\) −1.90652e6 + 2.98991e6i −0.0184128 + 0.0288760i
\(196\) −4.50716e6 + 6.18485e7i −0.0427570 + 0.586723i
\(197\) 1.26447e8 + 1.26447e8i 1.17836 + 1.17836i 0.980163 + 0.198195i \(0.0635080\pi\)
0.198195 + 0.980163i \(0.436492\pi\)
\(198\) 1.91489e8 + 6.96808e6i 1.75314 + 0.0637948i
\(199\) 4.23032e7 0.380529 0.190264 0.981733i \(-0.439066\pi\)
0.190264 + 0.981733i \(0.439066\pi\)
\(200\) 3.62744e7 + 1.07164e8i 0.320623 + 0.947207i
\(201\) −1.12049e7 −0.0973247
\(202\) −1.53964e8 5.60259e6i −1.31429 0.0478254i
\(203\) 1.46502e7 + 1.46502e7i 0.122916 + 0.122916i
\(204\) −979822. + 1.34454e7i −0.00808056 + 0.110884i
\(205\) −7.87434e6 + 1.23490e7i −0.0638375 + 0.100113i
\(206\) −5.97576e7 6.42709e7i −0.476275 0.512247i
\(207\) 1.57686e7 1.57686e7i 0.123565 0.123565i
\(208\) −4.16087e7 + 3.09735e7i −0.320599 + 0.238654i
\(209\) 2.71757e8i 2.05906i
\(210\) −4.19083e6 + 6.07320e6i −0.0312271 + 0.0452533i
\(211\) 5.94925e7i 0.435987i 0.975950 + 0.217994i \(0.0699512\pi\)
−0.975950 + 0.217994i \(0.930049\pi\)
\(212\) 4.85520e7 4.19563e7i 0.349970 0.302427i
\(213\) −1.40472e7 + 1.40472e7i −0.0996003 + 0.0996003i
\(214\) −1.24678e8 + 1.15923e8i −0.869647 + 0.808578i
\(215\) 9.66528e7 2.13855e7i 0.663254 0.146752i
\(216\) 1.97233e7 1.58285e7i 0.133166 0.106869i
\(217\) −8.30571e7 8.30571e7i −0.551782 0.551782i
\(218\) 6.61075e6 1.81670e8i 0.0432169 1.18764i
\(219\) −3.61968e6 −0.0232871
\(220\) 2.23812e8 + 1.66774e8i 1.41711 + 1.05596i
\(221\) 8.32107e7 0.518569
\(222\) −188622. + 5.18350e6i −0.00115706 + 0.0317971i
\(223\) −1.47527e8 1.47527e8i −0.890850 0.890850i 0.103753 0.994603i \(-0.466915\pi\)
−0.994603 + 0.103753i \(0.966915\pi\)
\(224\) −8.88682e7 + 6.12602e7i −0.528297 + 0.364175i
\(225\) −1.53773e8 + 7.15510e7i −0.900000 + 0.418771i
\(226\) −9.43931e7 + 8.77646e7i −0.543952 + 0.505754i
\(227\) 1.65384e8 1.65384e8i 0.938432 0.938432i −0.0597791 0.998212i \(-0.519040\pi\)
0.998212 + 0.0597791i \(0.0190396\pi\)
\(228\) −1.16823e7 1.35188e7i −0.0652763 0.0755380i
\(229\) 3.76350e7i 0.207094i −0.994625 0.103547i \(-0.966981\pi\)
0.994625 0.103547i \(-0.0330192\pi\)
\(230\) 3.19503e7 5.85955e6i 0.173152 0.0317553i
\(231\) 1.82039e7i 0.0971680i
\(232\) 5.61131e6 5.12197e7i 0.0295023 0.269296i
\(233\) 2.27130e7 2.27130e7i 0.117633 0.117633i −0.645840 0.763473i \(-0.723493\pi\)
0.763473 + 0.645840i \(0.223493\pi\)
\(234\) −5.29493e7 5.69484e7i −0.270150 0.290553i
\(235\) −7.60744e7 3.43822e8i −0.382385 1.72821i
\(236\) −1.09608e8 7.98757e6i −0.542811 0.0395569i
\(237\) −1.42625e6 1.42625e6i −0.00695946 0.00695946i
\(238\) 1.73035e8 + 6.29655e6i 0.831984 + 0.0302750i
\(239\) 1.99420e8 0.944880 0.472440 0.881363i \(-0.343373\pi\)
0.472440 + 0.881363i \(0.343373\pi\)
\(240\) 1.83030e7 1.32491e6i 0.0854638 0.00618652i
\(241\) −1.65531e8 −0.761762 −0.380881 0.924624i \(-0.624379\pi\)
−0.380881 + 0.924624i \(0.624379\pi\)
\(242\) 4.67811e8 + 1.70231e7i 2.12186 + 0.0772121i
\(243\) 4.02606e7 + 4.02606e7i 0.179994 + 0.179994i
\(244\) −1.67190e8 1.21838e7i −0.736793 0.0536932i
\(245\) −1.14177e8 7.28052e7i −0.496018 0.316287i
\(246\) 1.61758e6 + 1.73975e6i 0.00692778 + 0.00745100i
\(247\) −7.79821e7 + 7.79821e7i −0.329273 + 0.329273i
\(248\) −3.18125e7 + 2.90383e8i −0.132439 + 1.20890i
\(249\) 2.39227e7i 0.0982000i
\(250\) −2.43554e8 4.14348e7i −0.985835 0.167716i
\(251\) 2.30813e8i 0.921303i 0.887581 + 0.460652i \(0.152384\pi\)
−0.887581 + 0.460652i \(0.847616\pi\)
\(252\) −1.05798e8 1.22430e8i −0.416461 0.481931i
\(253\) 5.66660e7 5.66660e7i 0.219989 0.219989i
\(254\) −2.50361e8 + 2.32780e8i −0.958626 + 0.891309i
\(255\) −2.48212e7 1.58273e7i −0.0937416 0.0597745i
\(256\) 2.57151e8 + 7.70124e7i 0.957962 + 0.286894i
\(257\) 1.46979e8 + 1.46979e8i 0.540117 + 0.540117i 0.923563 0.383446i \(-0.125263\pi\)
−0.383446 + 0.923563i \(0.625263\pi\)
\(258\) 583883. 1.60456e7i 0.00211669 0.0581686i
\(259\) 6.66207e7 0.238265
\(260\) −1.63674e7 1.12081e8i −0.0577527 0.395479i
\(261\) 7.72434e7 0.268918
\(262\) 5.38134e6 1.47884e8i 0.0184857 0.508004i
\(263\) 5.89163e7 + 5.89163e7i 0.199706 + 0.199706i 0.799874 0.600168i \(-0.204900\pi\)
−0.600168 + 0.799874i \(0.704900\pi\)
\(264\) 3.53084e7 2.83359e7i 0.118104 0.0947815i
\(265\) 3.02715e7 + 1.36814e8i 0.0999249 + 0.451616i
\(266\) −1.68063e8 + 1.56261e8i −0.547504 + 0.509057i
\(267\) 2.44602e7 2.44602e7i 0.0786448 0.0786448i
\(268\) 2.70808e8 2.34019e8i 0.859389 0.742642i
\(269\) 8.61462e7i 0.269838i −0.990857 0.134919i \(-0.956923\pi\)
0.990857 0.134919i \(-0.0430774\pi\)
\(270\) 9.96158e6 + 5.43175e7i 0.0308003 + 0.167945i
\(271\) 1.59798e8i 0.487730i 0.969809 + 0.243865i \(0.0784154\pi\)
−0.969809 + 0.243865i \(0.921585\pi\)
\(272\) −2.57131e8 3.45421e8i −0.774752 1.04078i
\(273\) 5.22371e6 5.22371e6i 0.0155385 0.0155385i
\(274\) 3.33157e8 + 3.58319e8i 0.978412 + 1.05231i
\(275\) −5.52601e8 + 2.57126e8i −1.60231 + 0.745559i
\(276\) 382943. 5.25485e6i 0.00109636 0.0150445i
\(277\) 4.29400e7 + 4.29400e7i 0.121390 + 0.121390i 0.765192 0.643802i \(-0.222644\pi\)
−0.643802 + 0.765192i \(0.722644\pi\)
\(278\) 4.45725e6 + 162194.i 0.0124426 + 0.000452771i
\(279\) −4.37921e8 −1.20720
\(280\) −2.55545e7 2.34308e8i −0.0695688 0.637873i
\(281\) 5.50346e8 1.47966 0.739832 0.672791i \(-0.234905\pi\)
0.739832 + 0.672791i \(0.234905\pi\)
\(282\) −5.70790e7 2.07704e6i −0.151567 0.00551535i
\(283\) 3.43398e8 + 3.43398e8i 0.900627 + 0.900627i 0.995490 0.0948631i \(-0.0302414\pi\)
−0.0948631 + 0.995490i \(0.530241\pi\)
\(284\) 4.61208e7 6.32882e8i 0.119477 1.63949i
\(285\) 3.80943e7 8.42879e6i 0.0974772 0.0215679i
\(286\) −1.90279e8 2.04650e8i −0.480961 0.517286i
\(287\) 2.15750e7 2.15750e7i 0.0538721 0.0538721i
\(288\) −7.27819e7 + 3.95778e8i −0.179535 + 0.976287i
\(289\) 2.80448e8i 0.683455i
\(290\) 9.26072e7 + 6.39038e7i 0.222973 + 0.153863i
\(291\) 1.81511e7i 0.0431794i
\(292\) 8.74827e7 7.55983e7i 0.205628 0.177694i
\(293\) −4.91649e8 + 4.91649e8i −1.14187 + 1.14187i −0.153768 + 0.988107i \(0.549141\pi\)
−0.988107 + 0.153768i \(0.950859\pi\)
\(294\) −1.60856e7 + 1.49560e7i −0.0369165 + 0.0343241i
\(295\) 1.29025e8 2.02344e8i 0.292615 0.458895i
\(296\) −1.03701e8 1.29218e8i −0.232413 0.289602i
\(297\) 9.63356e7 + 9.63356e7i 0.213373 + 0.213373i
\(298\) −1.13743e7 + 3.12578e8i −0.0248983 + 0.684228i
\(299\) −3.25212e7 −0.0703586
\(300\) −1.64363e7 + 3.65461e7i −0.0351462 + 0.0781478i
\(301\) −2.06226e8 −0.435873
\(302\) −9.51435e6 + 2.61463e8i −0.0198772 + 0.546243i
\(303\) −3.85859e7 3.85859e7i −0.0796856 0.0796856i
\(304\) 5.64689e8 + 8.27420e7i 1.15279 + 0.168915i
\(305\) 1.96808e8 3.08645e8i 0.397186 0.622888i
\(306\) 4.72765e8 4.39567e8i 0.943236 0.877000i
\(307\) 2.19109e6 2.19109e6i 0.00432192 0.00432192i −0.704943 0.709264i \(-0.749027\pi\)
0.709264 + 0.704943i \(0.249027\pi\)
\(308\) −3.80196e8 4.39964e8i −0.741446 0.858005i
\(309\) 3.10835e7i 0.0599343i
\(310\) −5.25023e8 3.62293e8i −1.00095 0.690708i
\(311\) 4.25742e8i 0.802573i −0.915953 0.401287i \(-0.868563\pi\)
0.915953 0.401287i \(-0.131437\pi\)
\(312\) −1.82630e7 2.00078e6i −0.0340433 0.00372957i
\(313\) 4.44768e8 4.44768e8i 0.819839 0.819839i −0.166246 0.986084i \(-0.553164\pi\)
0.986084 + 0.166246i \(0.0531645\pi\)
\(314\) −1.61610e8 1.73816e8i −0.294588 0.316838i
\(315\) 3.44992e8 7.63334e7i 0.621903 0.137603i
\(316\) 6.42582e7 + 4.68276e6i 0.114558 + 0.00834829i
\(317\) −5.33839e8 5.33839e8i −0.941245 0.941245i 0.0571220 0.998367i \(-0.481808\pi\)
−0.998367 + 0.0571220i \(0.981808\pi\)
\(318\) 2.27129e7 + 826496.i 0.0396075 + 0.00144127i
\(319\) 2.77582e8 0.478767
\(320\) −4.14687e8 + 4.14285e8i −0.707449 + 0.706764i
\(321\) −6.02986e7 −0.101751
\(322\) −6.76272e7 2.46088e6i −0.112882 0.00410766i
\(323\) −6.47380e8 6.47380e8i −1.06893 1.06893i
\(324\) −5.97184e8 4.35193e7i −0.975440 0.0710845i
\(325\) 2.32355e8 + 8.47880e7i 0.375457 + 0.137007i
\(326\) 4.96834e8 + 5.34358e8i 0.794236 + 0.854221i
\(327\) 4.55293e7 4.55293e7i 0.0720069 0.0720069i
\(328\) −7.54302e7 8.26365e6i −0.118028 0.0129304i
\(329\) 7.33604e8i 1.13573i
\(330\) 1.78330e7 + 9.72382e7i 0.0273166 + 0.148949i
\(331\) 6.51795e8i 0.987900i −0.869490 0.493950i \(-0.835553\pi\)
0.869490 0.493950i \(-0.164447\pi\)
\(332\) 4.99633e8 + 5.78178e8i 0.749321 + 0.867118i
\(333\) 1.75630e8 1.75630e8i 0.260641 0.260641i
\(334\) 3.86461e8 3.59323e8i 0.567536 0.527682i
\(335\) 1.68845e8 + 7.63105e8i 0.245376 + 1.10899i
\(336\) −3.78263e7 5.54255e6i −0.0544009 0.00797118i
\(337\) −1.98324e8 1.98324e8i −0.282273 0.282273i 0.551742 0.834015i \(-0.313963\pi\)
−0.834015 + 0.551742i \(0.813963\pi\)
\(338\) 2.16922e7 5.96122e8i 0.0305559 0.839705i
\(339\) −4.56516e7 −0.0636440
\(340\) 9.30454e8 1.35876e8i 1.28386 0.187485i
\(341\) −1.57371e9 −2.14924
\(342\) −3.11126e7 + 8.55004e8i −0.0420577 + 1.15578i
\(343\) 5.38571e8 + 5.38571e8i 0.720632 + 0.720632i
\(344\) 3.21008e8 + 3.99996e8i 0.425168 + 0.529787i
\(345\) 9.70085e6 + 6.18576e6i 0.0127187 + 0.00811011i
\(346\) −6.87871e8 + 6.39567e8i −0.892772 + 0.830079i
\(347\) 1.75405e7 1.75405e7i 0.0225366 0.0225366i −0.695749 0.718285i \(-0.744927\pi\)
0.718285 + 0.695749i \(0.244927\pi\)
\(348\) 1.38086e7 1.19327e7i 0.0175639 0.0151779i
\(349\) 5.34547e8i 0.673127i −0.941661 0.336564i \(-0.890735\pi\)
0.941661 0.336564i \(-0.109265\pi\)
\(350\) 4.76763e8 + 1.93897e8i 0.594380 + 0.241732i
\(351\) 5.52879e7i 0.0682426i
\(352\) −2.61550e8 + 1.42227e9i −0.319635 + 1.73813i
\(353\) 5.88714e8 5.88714e8i 0.712349 0.712349i −0.254677 0.967026i \(-0.581969\pi\)
0.967026 + 0.254677i \(0.0819691\pi\)
\(354\) −2.65049e7 2.85067e7i −0.0317552 0.0341536i
\(355\) 1.16835e9 + 7.45000e8i 1.38603 + 0.883806i
\(356\) −8.03095e7 + 1.10203e9i −0.0943392 + 1.29455i
\(357\) 4.33654e7 + 4.33654e7i 0.0504434 + 0.0504434i
\(358\) −9.68789e8 3.52531e7i −1.11593 0.0406076i
\(359\) −6.52439e8 −0.744233 −0.372117 0.928186i \(-0.621368\pi\)
−0.372117 + 0.928186i \(0.621368\pi\)
\(360\) −6.85065e8 5.50329e8i −0.773879 0.621675i
\(361\) 3.19531e8 0.357468
\(362\) −8.60157e8 3.13001e7i −0.953010 0.0346790i
\(363\) 1.17241e8 + 1.17241e8i 0.128649 + 0.128649i
\(364\) −1.71509e7 + 2.35349e8i −0.0186394 + 0.255775i
\(365\) 5.45443e7 + 2.46516e8i 0.0587117 + 0.265350i
\(366\) −4.04292e7 4.34827e7i −0.0431034 0.0463589i
\(367\) 2.40601e8 2.40601e8i 0.254077 0.254077i −0.568563 0.822640i \(-0.692500\pi\)
0.822640 + 0.568563i \(0.192500\pi\)
\(368\) 1.00494e8 + 1.35000e8i 0.105117 + 0.141211i
\(369\) 1.13755e8i 0.117863i
\(370\) 3.55862e8 6.52634e7i 0.365237 0.0669829i
\(371\) 2.91916e8i 0.296790i
\(372\) −7.82856e7 + 6.76506e7i −0.0788464 + 0.0681352i
\(373\) −5.35238e8 + 5.35238e8i −0.534030 + 0.534030i −0.921769 0.387739i \(-0.873256\pi\)
0.387739 + 0.921769i \(0.373256\pi\)
\(374\) 1.69893e9 1.57963e9i 1.67929 1.56137i
\(375\) −5.31828e7 6.94874e7i −0.0520788 0.0680450i
\(376\) 1.42290e9 1.14192e9i 1.38044 1.10784i
\(377\) −7.96536e7 7.96536e7i −0.0765616 0.0765616i
\(378\) 4.18364e6 1.14970e8i 0.00398412 0.109487i
\(379\) −6.90665e8 −0.651674 −0.325837 0.945426i \(-0.605646\pi\)
−0.325837 + 0.945426i \(0.605646\pi\)
\(380\) −7.44649e8 + 9.99326e8i −0.696160 + 0.934253i
\(381\) −1.21083e8 −0.112162
\(382\) 2.99287e7 8.22468e8i 0.0274705 0.754914i
\(383\) −1.11082e9 1.11082e9i −1.01029 1.01029i −0.999946 0.0103446i \(-0.996707\pi\)
−0.0103446 0.999946i \(-0.503293\pi\)
\(384\) 4.81293e7 + 8.19953e7i 0.0433761 + 0.0738975i
\(385\) 1.23977e9 2.74312e8i 1.10720 0.244981i
\(386\) 1.08321e9 1.00715e9i 0.958646 0.891327i
\(387\) −5.43665e8 + 5.43665e8i −0.476808 + 0.476808i
\(388\) −3.79092e8 4.38687e8i −0.329483 0.381280i
\(389\) 1.83379e9i 1.57953i 0.613412 + 0.789763i \(0.289796\pi\)
−0.613412 + 0.789763i \(0.710204\pi\)
\(390\) 2.27857e7 3.30203e7i 0.0194507 0.0281874i
\(391\) 2.69979e8i 0.228408i
\(392\) 7.64047e7 6.97419e8i 0.0640647 0.584780i
\(393\) 3.70621e7 3.70621e7i 0.0308004 0.0308004i
\(394\) −1.37762e9 1.48166e9i −1.13473 1.22043i
\(395\) −7.56418e7 + 1.18626e8i −0.0617550 + 0.0968475i
\(396\) −2.16216e9 1.57565e8i −1.74966 0.127505i
\(397\) −7.65356e7 7.65356e7i −0.0613898 0.0613898i 0.675745 0.737135i \(-0.263822\pi\)
−0.737135 + 0.675745i \(0.763822\pi\)
\(398\) −4.78289e8 1.74044e7i −0.380277 0.0138378i
\(399\) −8.12809e7 −0.0640595
\(400\) −3.66036e8 1.22655e9i −0.285966 0.958240i
\(401\) 8.24997e8 0.638921 0.319460 0.947600i \(-0.396498\pi\)
0.319460 + 0.947600i \(0.396498\pi\)
\(402\) 1.26686e8 + 4.60994e6i 0.0972603 + 0.00353919i
\(403\) 4.51585e8 + 4.51585e8i 0.343694 + 0.343694i
\(404\) 1.73845e9 + 1.26688e8i 1.31168 + 0.0955876i
\(405\) 7.02978e8 1.10245e9i 0.525834 0.824642i
\(406\) −1.59611e8 1.71666e8i −0.118364 0.127304i
\(407\) 6.31144e8 6.31144e8i 0.464032 0.464032i
\(408\) 1.66098e7 1.51613e8i 0.0121075 0.110516i
\(409\) 6.73253e8i 0.486572i 0.969955 + 0.243286i \(0.0782253\pi\)
−0.969955 + 0.243286i \(0.921775\pi\)
\(410\) 9.41097e7 1.36381e8i 0.0674358 0.0977258i
\(411\) 1.73295e8i 0.123123i
\(412\) 6.49191e8 + 7.51247e8i 0.457333 + 0.529227i
\(413\) −3.53517e8 + 3.53517e8i −0.246937 + 0.246937i
\(414\) −1.84770e8 + 1.71795e8i −0.127977 + 0.118990i
\(415\) −1.62924e9 + 3.60487e8i −1.11896 + 0.247583i
\(416\) 4.83180e8 3.33074e8i 0.329065 0.226837i
\(417\) 1.11706e6 + 1.11706e6i 0.000754397 + 0.000754397i
\(418\) −1.11807e8 + 3.07255e9i −0.0748773 + 2.05770i
\(419\) 1.99512e8 0.132501 0.0662505 0.997803i \(-0.478896\pi\)
0.0662505 + 0.997803i \(0.478896\pi\)
\(420\) 4.98811e7 6.69408e7i 0.0328521 0.0440878i
\(421\) −5.02691e8 −0.328333 −0.164166 0.986433i \(-0.552493\pi\)
−0.164166 + 0.986433i \(0.552493\pi\)
\(422\) 2.44765e7 6.72636e8i 0.0158546 0.435699i
\(423\) 1.93397e9 + 1.93397e9i 1.24239 + 1.24239i
\(424\) −5.66201e8 + 4.54392e8i −0.360737 + 0.289501i
\(425\) −7.03880e8 + 1.92893e9i −0.444772 + 1.21887i
\(426\) 1.64600e8 1.53041e8i 0.103156 0.0959125i
\(427\) −5.39237e8 + 5.39237e8i −0.335183 + 0.335183i
\(428\) 1.45734e9 1.25936e9i 0.898476 0.776419i
\(429\) 9.89755e7i 0.0605239i
\(430\) −1.10158e9 + 2.02024e8i −0.668152 + 0.122536i
\(431\) 5.28235e8i 0.317802i 0.987295 + 0.158901i \(0.0507951\pi\)
−0.987295 + 0.158901i \(0.949205\pi\)
\(432\) −2.29509e8 + 1.70846e8i −0.136964 + 0.101956i
\(433\) 1.14007e9 1.14007e9i 0.674874 0.674874i −0.283962 0.958836i \(-0.591649\pi\)
0.958836 + 0.283962i \(0.0916489\pi\)
\(434\) 9.04891e8 + 9.73234e8i 0.531352 + 0.571483i
\(435\) 8.60946e6 + 3.89109e7i 0.00501491 + 0.0226651i
\(436\) −1.49485e8 + 2.05128e9i −0.0863766 + 1.18528i
\(437\) 2.53015e8 + 2.53015e8i 0.145031 + 0.145031i
\(438\) 4.09249e7 + 1.48921e6i 0.0232717 + 0.000846831i
\(439\) −4.88680e8 −0.275676 −0.137838 0.990455i \(-0.544015\pi\)
−0.137838 + 0.990455i \(0.544015\pi\)
\(440\) −2.46186e9 1.97766e9i −1.37777 1.10680i
\(441\) 1.05176e9 0.583959
\(442\) −9.40799e8 3.42346e7i −0.518226 0.0188577i
\(443\) −8.53170e8 8.53170e8i −0.466254 0.466254i 0.434445 0.900699i \(-0.356945\pi\)
−0.900699 + 0.434445i \(0.856945\pi\)
\(444\) 4.26520e6 5.85283e7i 0.00231259 0.0317340i
\(445\) −2.03443e9 1.29726e9i −1.09442 0.697857i
\(446\) 1.60728e9 + 1.72867e9i 0.857865 + 0.922657i
\(447\) −7.83370e7 + 7.83370e7i −0.0414849 + 0.0414849i
\(448\) 1.02997e9 6.56059e8i 0.541191 0.344723i
\(449\) 1.33866e9i 0.697923i −0.937137 0.348961i \(-0.886534\pi\)
0.937137 0.348961i \(-0.113466\pi\)
\(450\) 1.76803e9 7.45706e8i 0.914633 0.385766i
\(451\) 4.08789e8i 0.209837i
\(452\) 1.10334e9 9.53451e8i 0.561984 0.485639i
\(453\) −6.55268e7 + 6.55268e7i −0.0331189 + 0.0331189i
\(454\) −1.93791e9 + 1.80183e9i −0.971938 + 0.903686i
\(455\) −4.34472e8 2.77042e8i −0.216233 0.137881i
\(456\) 1.26520e8 + 1.57653e8i 0.0624862 + 0.0778618i
\(457\) −3.23503e7 3.23503e7i −0.0158552 0.0158552i 0.699135 0.714990i \(-0.253569\pi\)
−0.714990 + 0.699135i \(0.753569\pi\)
\(458\) −1.54838e7 + 4.25510e8i −0.00753094 + 0.206957i
\(459\) 4.58981e8 0.221539
\(460\) −3.63648e8 + 5.31044e7i −0.174192 + 0.0254377i
\(461\) −6.23343e8 −0.296329 −0.148164 0.988963i \(-0.547336\pi\)
−0.148164 + 0.988963i \(0.547336\pi\)
\(462\) 7.48947e6 2.05818e8i 0.00353349 0.0971037i
\(463\) 8.17939e8 + 8.17939e8i 0.382990 + 0.382990i 0.872178 0.489188i \(-0.162707\pi\)
−0.489188 + 0.872178i \(0.662707\pi\)
\(464\) −8.45156e7 + 5.76793e8i −0.0392757 + 0.268045i
\(465\) −4.88101e7 2.20600e8i −0.0225125 0.101746i
\(466\) −2.66143e8 + 2.47454e8i −0.121833 + 0.113277i
\(467\) 3.01352e9 3.01352e9i 1.36919 1.36919i 0.507600 0.861593i \(-0.330533\pi\)
0.861593 0.507600i \(-0.169467\pi\)
\(468\) 5.75227e8 + 6.65655e8i 0.259405 + 0.300185i
\(469\) 1.62822e9i 0.728799i
\(470\) 7.18658e8 + 3.91862e9i 0.319286 + 1.74097i
\(471\) 8.40633e7i 0.0370709i
\(472\) 1.23596e9 + 1.35404e8i 0.541014 + 0.0592700i
\(473\) −1.95372e9 + 1.95372e9i −0.848883 + 0.848883i
\(474\) 1.55387e7 + 1.67123e7i 0.00670178 + 0.00720794i
\(475\) −1.14807e9 2.46738e9i −0.491521 1.05635i
\(476\) −1.95378e9 1.42381e8i −0.830333 0.0605099i
\(477\) −7.69567e8 7.69567e8i −0.324663 0.324663i
\(478\) −2.25469e9 8.20457e7i −0.944255 0.0343604i
\(479\) 2.62303e9 1.09051 0.545254 0.838271i \(-0.316433\pi\)
0.545254 + 0.838271i \(0.316433\pi\)
\(480\) −2.07483e8 + 7.44948e6i −0.0856322 + 0.00307455i
\(481\) −3.62220e8 −0.148410
\(482\) 1.87153e9 + 6.81028e7i 0.761258 + 0.0277013i
\(483\) −1.69485e7 1.69485e7i −0.00684408 0.00684408i
\(484\) −5.28217e9 3.84934e8i −2.11765 0.154322i
\(485\) 1.23617e9 2.73516e8i 0.492018 0.108865i
\(486\) −4.38632e8 4.71760e8i −0.173330 0.186421i
\(487\) −2.89549e8 + 2.89549e8i −0.113598 + 0.113598i −0.761621 0.648023i \(-0.775596\pi\)
0.648023 + 0.761621i \(0.275596\pi\)
\(488\) 1.88527e9 + 2.06538e8i 0.734353 + 0.0804510i
\(489\) 2.58433e8i 0.0999464i
\(490\) 1.26096e9 + 8.70127e8i 0.484189 + 0.334115i
\(491\) 4.72022e9i 1.79960i 0.436298 + 0.899802i \(0.356289\pi\)
−0.436298 + 0.899802i \(0.643711\pi\)
\(492\) −1.75730e7 2.03356e7i −0.00665224 0.00769800i
\(493\) 6.61257e8 6.61257e8i 0.248545 0.248545i
\(494\) 9.13767e8 8.49600e8i 0.341029 0.317081i
\(495\) 2.54519e9 3.99151e9i 0.943196 1.47917i
\(496\) 4.79149e8 3.27005e9i 0.176313 1.20328i
\(497\) −2.04123e9 2.04123e9i −0.745840 0.745840i
\(498\) −9.84227e6 + 2.70475e8i −0.00357102 + 0.0981351i
\(499\) −1.70138e9 −0.612983 −0.306492 0.951873i \(-0.599155\pi\)
−0.306492 + 0.951873i \(0.599155\pi\)
\(500\) 2.73662e9 + 5.68674e8i 0.979084 + 0.203455i
\(501\) 1.86905e8 0.0664033
\(502\) 9.49613e7 2.60963e9i 0.0335030 0.920694i
\(503\) −3.46811e9 3.46811e9i −1.21508 1.21508i −0.969334 0.245746i \(-0.920967\pi\)
−0.245746 0.969334i \(-0.579033\pi\)
\(504\) 1.14580e9 + 1.42775e9i 0.398661 + 0.496757i
\(505\) −2.04642e9 + 3.20931e9i −0.707092 + 1.10890i
\(506\) −6.63992e8 + 6.17365e8i −0.227843 + 0.211844i
\(507\) 1.49398e8 1.49398e8i 0.0509115 0.0509115i
\(508\) 2.92641e9 2.52886e9i 0.990404 0.855859i
\(509\) 3.22836e9i 1.08510i −0.840023 0.542551i \(-0.817459\pi\)
0.840023 0.542551i \(-0.182541\pi\)
\(510\) 2.74123e8 + 1.89159e8i 0.0915059 + 0.0631438i
\(511\) 5.25985e8i 0.174381i
\(512\) −2.87572e9 9.76517e8i −0.946896 0.321540i
\(513\) −4.30140e8 + 4.30140e8i −0.140669 + 0.140669i
\(514\) −1.60130e9 1.72224e9i −0.520119 0.559401i
\(515\) −2.11692e9 + 4.68393e8i −0.682936 + 0.151107i
\(516\) −1.32030e7 + 1.81176e8i −0.00423058 + 0.0580531i
\(517\) 6.94994e9 + 6.94994e9i 2.21189 + 2.21189i
\(518\) −7.53229e8 2.74091e7i −0.238107 0.00866446i
\(519\) −3.32677e8 −0.104457
\(520\) 1.38941e8 + 1.27394e9i 0.0433330 + 0.397318i
\(521\) 1.61238e9 0.499500 0.249750 0.968310i \(-0.419652\pi\)
0.249750 + 0.968310i \(0.419652\pi\)
\(522\) −8.73331e8 3.17795e7i −0.268740 0.00977914i
\(523\) 1.61920e9 + 1.61920e9i 0.494930 + 0.494930i 0.909855 0.414925i \(-0.136192\pi\)
−0.414925 + 0.909855i \(0.636192\pi\)
\(524\) −1.21685e8 + 1.66980e9i −0.0369469 + 0.506996i
\(525\) 7.69049e7 + 1.65280e8i 0.0231951 + 0.0498496i
\(526\) −6.41881e8 6.90360e8i −0.192311 0.206836i
\(527\) −3.74890e9 + 3.74890e9i −1.11575 + 1.11575i
\(528\) −4.10862e8 + 3.05846e8i −0.121472 + 0.0904240i
\(529\) 3.29931e9i 0.969010i
\(530\) −2.85969e8 1.55930e9i −0.0834359 0.454951i
\(531\) 1.86393e9i 0.540255i
\(532\) 1.96445e9 1.69758e9i 0.565653 0.488810i
\(533\) −1.17304e8 + 1.17304e8i −0.0335558 + 0.0335558i
\(534\) −2.86616e8 + 2.66489e8i −0.0814527 + 0.0757329i
\(535\) 9.08630e8 + 4.10660e9i 0.256536 + 1.15943i
\(536\) −3.15810e9 + 2.53446e9i −0.885827 + 0.710899i
\(537\) −2.42794e8 2.42794e8i −0.0676594 0.0676594i
\(538\) −3.54423e7 + 9.73989e8i −0.00981261 + 0.269660i
\(539\) 3.77962e9 1.03965
\(540\) −9.02806e7 6.18224e8i −0.0246727 0.168954i
\(541\) 1.93493e9 0.525382 0.262691 0.964880i \(-0.415390\pi\)
0.262691 + 0.964880i \(0.415390\pi\)
\(542\) 6.57443e7 1.80672e9i 0.0177362 0.487408i
\(543\) −2.15569e8 2.15569e8i −0.0577812 0.0577812i
\(544\) 2.76507e9 + 4.01119e9i 0.736392 + 1.06826i
\(545\) −3.78682e9 2.41467e9i −1.00204 0.638955i
\(546\) −6.12095e7 + 5.69113e7i −0.0160933 + 0.0149632i
\(547\) −3.25133e9 + 3.25133e9i −0.849386 + 0.849386i −0.990056 0.140671i \(-0.955074\pi\)
0.140671 + 0.990056i \(0.455074\pi\)
\(548\) −3.61933e9 4.18830e9i −0.939498 1.08719i
\(549\) 2.84314e9i 0.733322i
\(550\) 6.35362e9 2.67977e9i 1.62837 0.686798i
\(551\) 1.23941e9i 0.315635i
\(552\) −6.49159e6 + 5.92549e7i −0.00164272 + 0.0149947i
\(553\) 2.07252e8 2.07252e8i 0.0521147 0.0521147i
\(554\) −4.67823e8 5.03155e8i −0.116895 0.125724i
\(555\) 1.08048e8 + 6.88968e7i 0.0268281 + 0.0171070i
\(556\) −5.03280e7 3.66761e6i −0.0124179 0.000904944i
\(557\) 3.15200e9 + 3.15200e9i 0.772846 + 0.772846i 0.978603 0.205757i \(-0.0659656\pi\)
−0.205757 + 0.978603i \(0.565966\pi\)
\(558\) 4.95123e9 + 1.80170e8i 1.20641 + 0.0438997i
\(559\) 1.12126e9 0.271497
\(560\) 1.92526e8 + 2.65965e9i 0.0463267 + 0.639981i
\(561\) 8.21660e8 0.196482
\(562\) −6.22233e9 2.26424e8i −1.47869 0.0538077i
\(563\) −9.58862e7 9.58862e7i −0.0226452 0.0226452i 0.695694 0.718339i \(-0.255097\pi\)
−0.718339 + 0.695694i \(0.755097\pi\)
\(564\) 6.44493e8 + 4.69669e7i 0.151266 + 0.0110234i
\(565\) 6.87917e8 + 3.10907e9i 0.160460 + 0.725206i
\(566\) −3.74125e9 4.02381e9i −0.867280 0.932783i
\(567\) −1.92610e9 + 1.92610e9i −0.443749 + 0.443749i
\(568\) −7.81833e8 + 7.13653e9i −0.179017 + 1.63406i
\(569\) 5.59524e9i 1.27329i 0.771159 + 0.636643i \(0.219677\pi\)
−0.771159 + 0.636643i \(0.780323\pi\)
\(570\) −4.34171e8 + 7.96250e7i −0.0981970 + 0.0180089i
\(571\) 7.02795e9i 1.57980i −0.613235 0.789900i \(-0.710132\pi\)
0.613235 0.789900i \(-0.289868\pi\)
\(572\) 2.06714e9 + 2.39210e9i 0.461832 + 0.534434i
\(573\) 2.06124e8 2.06124e8i 0.0457706 0.0457706i
\(574\) −2.52808e8 + 2.35055e8i −0.0557956 + 0.0518775i
\(575\) 2.75097e8 7.53883e8i 0.0603460 0.165374i
\(576\) 9.85720e8 4.44481e9i 0.214919 0.969113i
\(577\) −5.27941e9 5.27941e9i −1.14412 1.14412i −0.987690 0.156427i \(-0.950002\pi\)
−0.156427 0.987690i \(-0.549998\pi\)
\(578\) 1.15382e8 3.17081e9i 0.0248537 0.683002i
\(579\) 5.23877e8 0.112164
\(580\) −1.02075e9 7.60611e8i −0.217230 0.161869i
\(581\) 3.47626e9 0.735354
\(582\) 7.46773e6 2.05220e8i 0.00157021 0.0431509i
\(583\) −2.76552e9 2.76552e9i −0.578012 0.578012i
\(584\) −1.02020e9 + 8.18739e8i −0.211954 + 0.170099i
\(585\) −1.87574e9 + 4.15028e8i −0.387370 + 0.0857100i
\(586\) 5.76097e9 5.35642e9i 1.18264 1.09960i
\(587\) −1.36796e9 + 1.36796e9i −0.279152 + 0.279152i −0.832771 0.553618i \(-0.813247\pi\)
0.553618 + 0.832771i \(0.313247\pi\)
\(588\) 1.88020e8 1.62478e8i 0.0381403 0.0329590i
\(589\) 7.02667e9i 1.41692i
\(590\) −1.54204e9 + 2.23467e9i −0.309109 + 0.447951i
\(591\) 7.16581e8i 0.142794i
\(592\) 1.11930e9 + 1.50363e9i 0.221728 + 0.297862i
\(593\) −1.73951e8 + 1.73951e8i −0.0342560 + 0.0342560i −0.724027 0.689771i \(-0.757711\pi\)
0.689771 + 0.724027i \(0.257711\pi\)
\(594\) −1.04956e9 1.12883e9i −0.205472 0.220991i
\(595\) 2.29991e9 3.60684e9i 0.447611 0.701968i
\(596\) 2.57202e8 3.52939e9i 0.0497637 0.682870i
\(597\) −1.19867e8 1.19867e8i −0.0230563 0.0230563i
\(598\) 3.67692e8 + 1.33799e7i 0.0703121 + 0.00255858i
\(599\) 6.55496e9 1.24617 0.623083 0.782156i \(-0.285880\pi\)
0.623083 + 0.782156i \(0.285880\pi\)
\(600\) 2.00868e8 4.06436e8i 0.0379648 0.0768180i
\(601\) −4.90759e9 −0.922163 −0.461081 0.887358i \(-0.652538\pi\)
−0.461081 + 0.887358i \(0.652538\pi\)
\(602\) 2.33164e9 + 8.48456e7i 0.435585 + 0.0158504i
\(603\) −4.29241e9 4.29241e9i −0.797243 0.797243i
\(604\) 2.15143e8 2.95225e9i 0.0397281 0.545159i
\(605\) 6.21793e9 9.75130e9i 1.14157 1.79027i
\(606\) 4.20386e8 + 4.52136e8i 0.0767351 + 0.0825306i
\(607\) 3.30338e9 3.30338e9i 0.599512 0.599512i −0.340670 0.940183i \(-0.610654\pi\)
0.940183 + 0.340670i \(0.110654\pi\)
\(608\) −6.35046e9 1.16782e9i −1.14589 0.210725i
\(609\) 8.30232e7i 0.0148949i
\(610\) −2.35214e9 + 3.40864e9i −0.419574 + 0.608033i
\(611\) 3.98864e9i 0.707425i
\(612\) −5.52604e9 + 4.77533e9i −0.974505 + 0.842119i
\(613\) −5.27313e9 + 5.27313e9i −0.924606 + 0.924606i −0.997351 0.0727449i \(-0.976824\pi\)
0.0727449 + 0.997351i \(0.476824\pi\)
\(614\) −2.56745e7 + 2.38715e7i −0.00447623 + 0.00416190i
\(615\) 5.73032e7 1.26790e7i 0.00993381 0.00219796i
\(616\) 4.11757e9 + 5.13075e9i 0.709755 + 0.884400i
\(617\) −1.16802e9 1.16802e9i −0.200194 0.200194i 0.599889 0.800083i \(-0.295211\pi\)
−0.800083 + 0.599889i \(0.795211\pi\)
\(618\) −1.27884e7 + 3.51437e8i −0.00217950 + 0.0598947i
\(619\) 2.75694e9 0.467208 0.233604 0.972332i \(-0.424948\pi\)
0.233604 + 0.972332i \(0.424948\pi\)
\(620\) 5.78698e9 + 4.31218e9i 0.975171 + 0.726650i
\(621\) −1.79383e8 −0.0300581
\(622\) −1.75159e8 + 4.81353e9i −0.0291854 + 0.802042i
\(623\) 3.55437e9 + 3.55437e9i 0.588918 + 0.588918i
\(624\) 2.05663e8 + 3.01351e7i 0.0338852 + 0.00496508i
\(625\) −3.93099e9 + 4.66907e9i −0.644053 + 0.764981i
\(626\) −5.21163e9 + 4.84566e9i −0.849110 + 0.789483i
\(627\) −7.70030e8 + 7.70030e8i −0.124759 + 0.124759i
\(628\) 1.75569e9 + 2.03170e9i 0.282872 + 0.327341i
\(629\) 3.00702e9i 0.481792i
\(630\) −3.93197e9 + 7.21105e8i −0.626495 + 0.114896i
\(631\) 5.29415e7i 0.00838868i 0.999991 + 0.00419434i \(0.00133510\pi\)
−0.999991 + 0.00419434i \(0.998665\pi\)
\(632\) −7.24591e8 7.93815e7i −0.114178 0.0125086i
\(633\) 1.68573e8 1.68573e8i 0.0264165 0.0264165i
\(634\) 5.81607e9 + 6.25534e9i 0.906395 + 0.974851i
\(635\) 1.82458e9 + 8.24628e9i 0.282784 + 1.27806i
\(636\) −2.56457e8 1.86891e7i −0.0395289 0.00288064i
\(637\) −1.08458e9 1.08458e9i −0.166255 0.166255i
\(638\) −3.13841e9 1.14203e8i −0.478451 0.0174103i
\(639\) −1.07625e10 −1.63177
\(640\) 4.85899e9 4.51339e9i 0.732682 0.680571i
\(641\) 6.65348e8 0.0997805 0.0498903 0.998755i \(-0.484113\pi\)
0.0498903 + 0.998755i \(0.484113\pi\)
\(642\) 6.81749e8 + 2.48081e7i 0.101684 + 0.00370016i
\(643\) 8.14853e9 + 8.14853e9i 1.20876 + 1.20876i 0.971428 + 0.237334i \(0.0762735\pi\)
0.237334 + 0.971428i \(0.423726\pi\)
\(644\) 7.63596e8 + 5.56465e7i 0.112658 + 0.00820988i
\(645\) −3.34464e8 2.13272e8i −0.0490784 0.0312949i
\(646\) 7.05308e9 + 7.58577e9i 1.02935 + 1.10710i
\(647\) 6.73119e9 6.73119e9i 0.977073 0.977073i −0.0226697 0.999743i \(-0.507217\pi\)
0.999743 + 0.0226697i \(0.00721661\pi\)
\(648\) 6.73399e9 + 7.37733e8i 0.972210 + 0.106509i
\(649\) 6.69822e9i 0.961841i
\(650\) −2.59218e9 1.05423e9i −0.370227 0.150570i
\(651\) 4.70688e8i 0.0668651i
\(652\) −5.39747e9 6.24598e9i −0.762647 0.882539i
\(653\) 4.89097e9 4.89097e9i 0.687383 0.687383i −0.274270 0.961653i \(-0.588436\pi\)
0.961653 + 0.274270i \(0.0884362\pi\)
\(654\) −5.33496e8 + 4.96033e8i −0.0745778 + 0.0693407i
\(655\) −3.08258e9 1.96561e9i −0.428617 0.273308i
\(656\) 8.49431e8 + 1.24464e8i 0.117480 + 0.0172140i
\(657\) −1.38663e9 1.38663e9i −0.190758 0.190758i
\(658\) 3.01820e8 8.29430e9i 0.0413007 1.13498i
\(659\) −6.95092e9 −0.946114 −0.473057 0.881032i \(-0.656850\pi\)
−0.473057 + 0.881032i \(0.656850\pi\)
\(660\) −1.61619e8 1.10673e9i −0.0218820 0.149844i
\(661\) −8.50689e9 −1.14569 −0.572843 0.819665i \(-0.694160\pi\)
−0.572843 + 0.819665i \(0.694160\pi\)
\(662\) −2.68162e8 + 7.36934e9i −0.0359248 + 0.987246i
\(663\) −2.35779e8 2.35779e8i −0.0314202 0.0314202i
\(664\) −5.41109e9 6.74257e9i −0.717293 0.893794i
\(665\) 1.22481e9 + 5.53559e9i 0.161508 + 0.729941i
\(666\) −2.05797e9 + 1.91345e9i −0.269947 + 0.250991i
\(667\) −2.58438e8 + 2.58438e8i −0.0337222 + 0.0337222i
\(668\) −4.51725e9 + 3.90359e9i −0.586350 + 0.506695i
\(669\) 8.36042e8i 0.107953i
\(670\) −1.59505e9 8.69730e9i −0.204886 1.11718i
\(671\) 1.02171e10i 1.30557i
\(672\) 4.25392e8 + 7.82279e7i 0.0540750 + 0.00994418i
\(673\) 1.05812e10 1.05812e10i 1.33808 1.33808i 0.440160 0.897920i \(-0.354922\pi\)
0.897920 0.440160i \(-0.145078\pi\)
\(674\) 2.16070e9 + 2.32389e9i 0.271822 + 0.292351i
\(675\) 1.28165e9 + 4.67681e8i 0.160400 + 0.0585311i
\(676\) −4.90514e8 + 6.73097e9i −0.0610714 + 0.838038i
\(677\) 4.36544e9 + 4.36544e9i 0.540714 + 0.540714i 0.923738 0.383024i \(-0.125117\pi\)
−0.383024 + 0.923738i \(0.625117\pi\)
\(678\) 5.16147e8 + 1.87820e7i 0.0636019 + 0.00231440i
\(679\) −2.63758e9 −0.323342
\(680\) −1.05758e10 + 1.15344e9i −1.28983 + 0.140674i
\(681\) −9.37238e8 −0.113720
\(682\) 1.77928e10 + 6.47459e8i 2.14782 + 0.0781568i
\(683\) −6.42877e9 6.42877e9i −0.772067 0.772067i 0.206400 0.978468i \(-0.433825\pi\)
−0.978468 + 0.206400i \(0.933825\pi\)
\(684\) 7.03533e8 9.65407e9i 0.0840598 1.15349i
\(685\) 1.18021e10 2.61135e9i 1.40295 0.310419i
\(686\) −5.86762e9 6.31078e9i −0.693950 0.746361i
\(687\) −1.06640e8 + 1.06640e8i −0.0125479 + 0.0125479i
\(688\) −3.46482e9 4.65452e9i −0.405621 0.544898i
\(689\) 1.58716e9i 0.184864i
\(690\) −1.07135e8 7.39288e7i −0.0124154 0.00856726i
\(691\) 2.26489e9i 0.261140i −0.991439 0.130570i \(-0.958319\pi\)
0.991439 0.130570i \(-0.0416807\pi\)
\(692\) 8.04035e9 6.94808e9i 0.922367 0.797065i
\(693\) −6.97360e9 + 6.97360e9i −0.795959 + 0.795959i
\(694\) −2.05533e8 + 1.91100e8i −0.0233412 + 0.0217022i
\(695\) 5.92438e7 9.29093e7i 0.00669416 0.0104981i
\(696\) −1.61032e8 + 1.29232e8i −0.0181042 + 0.0145291i
\(697\) −9.73818e8 9.73818e8i −0.108934 0.108934i
\(698\) −2.19924e8 + 6.04371e9i −0.0244781 + 0.672682i
\(699\) −1.28716e8 −0.0142548
\(700\) −5.31061e9 2.38840e9i −0.585196 0.263186i
\(701\) −1.24128e9 −0.136100 −0.0680499 0.997682i \(-0.521678\pi\)
−0.0680499 + 0.997682i \(0.521678\pi\)
\(702\) −2.27466e7 + 6.25098e8i −0.00248163 + 0.0681974i
\(703\) 2.81807e9 + 2.81807e9i 0.305920 + 0.305920i
\(704\) 3.54229e9 1.59729e10i 0.382631 1.72536i
\(705\) −7.58668e8 + 1.18978e9i −0.0815436 + 0.127881i
\(706\) −6.89834e9 + 6.41393e9i −0.737783 + 0.685974i
\(707\) 5.60702e9 5.60702e9i 0.596712 0.596712i
\(708\) 2.87943e8 + 3.33208e8i 0.0304922 + 0.0352858i
\(709\) 1.53303e10i 1.61544i 0.589568 + 0.807718i \(0.299298\pi\)
−0.589568 + 0.807718i \(0.700702\pi\)
\(710\) −1.29031e10 8.90382e9i −1.35298 0.933625i
\(711\) 1.09274e9i 0.114018i
\(712\) 1.36140e9 1.24267e10i 0.141353 1.29026i
\(713\) 1.46518e9 1.46518e9i 0.151383 0.151383i
\(714\) −4.72457e8 5.08140e8i −0.0485757 0.0522444i
\(715\) −6.74066e9 + 1.49145e9i −0.689654 + 0.152594i
\(716\) 1.09388e10 + 7.97160e8i 1.11372 + 0.0811615i
\(717\) −5.65062e8 5.65062e8i −0.0572504 0.0572504i
\(718\) 7.37662e9 + 2.68427e8i 0.743741 + 0.0270639i
\(719\) −1.20575e10 −1.20978 −0.604888 0.796311i \(-0.706782\pi\)
−0.604888 + 0.796311i \(0.706782\pi\)
\(720\) 7.51909e9 + 6.50399e9i 0.750760 + 0.649406i
\(721\) 4.51683e9 0.448808
\(722\) −3.61269e9 1.31462e8i −0.357232 0.0129993i
\(723\) 4.69035e8 + 4.69035e8i 0.0461552 + 0.0461552i
\(724\) 9.71225e9 + 7.07772e8i 0.951119 + 0.0693120i
\(725\) 2.52026e9 1.17268e9i 0.245620 0.114287i
\(726\) −1.27732e9 1.37379e9i −0.123885 0.133242i
\(727\) 1.25078e9 1.25078e9i 0.120728 0.120728i −0.644161 0.764890i \(-0.722793\pi\)
0.764890 + 0.644161i \(0.222793\pi\)
\(728\) 2.90739e8 2.65385e9i 0.0279282 0.254928i
\(729\) 1.00023e10i 0.956215i
\(730\) −5.15269e8 2.80960e9i −0.0490235 0.267310i
\(731\) 9.30830e9i 0.881372i
\(732\) 4.39212e8 + 5.08259e8i 0.0413891 + 0.0478956i
\(733\) −6.17582e8 + 6.17582e8i −0.0579203 + 0.0579203i −0.735474 0.677553i \(-0.763040\pi\)
0.677553 + 0.735474i \(0.263040\pi\)
\(734\) −2.81927e9 + 2.62130e9i −0.263149 + 0.244670i
\(735\) 1.17228e8 + 5.29818e8i 0.0108900 + 0.0492177i
\(736\) −1.08067e9 1.56769e9i −0.0999125 0.144940i
\(737\) −1.54252e10 1.54252e10i −1.41937 1.41937i
\(738\) −4.68010e7 + 1.28614e9i −0.00428606 + 0.117785i
\(739\) −7.59769e9 −0.692510 −0.346255 0.938140i \(-0.612547\pi\)
−0.346255 + 0.938140i \(0.612547\pi\)
\(740\) −4.05030e9 + 5.91474e8i −0.367431 + 0.0536568i
\(741\) 4.41928e8 0.0399013
\(742\) −1.20100e8 + 3.30047e9i −0.0107927 + 0.296594i
\(743\) 9.79501e9 + 9.79501e9i 0.876080 + 0.876080i 0.993126 0.117046i \(-0.0373426\pi\)
−0.117046 + 0.993126i \(0.537343\pi\)
\(744\) 9.12948e8 7.32665e8i 0.0812720 0.0652229i
\(745\) 6.51554e9 + 4.15464e9i 0.577302 + 0.368118i
\(746\) 6.27173e9 5.83131e9i 0.553097 0.514257i
\(747\) 9.16434e9 9.16434e9i 0.804413 0.804413i
\(748\) −1.98584e10 + 1.71607e10i −1.73496 + 1.49927i
\(749\) 8.76215e9i 0.761946i
\(750\) 5.72708e8 + 8.07520e8i 0.0495700 + 0.0698938i
\(751\) 1.49232e10i 1.28565i −0.766015 0.642823i \(-0.777763\pi\)
0.766015 0.642823i \(-0.222237\pi\)
\(752\) −1.65574e10 + 1.23253e10i −1.41981 + 1.05691i
\(753\) 6.54014e8 6.54014e8i 0.0558219 0.0558219i
\(754\) 8.67811e8 + 9.33353e8i 0.0737268 + 0.0792951i
\(755\) 5.45008e9 + 3.47525e9i 0.460880 + 0.293881i
\(756\) −9.46023e7 + 1.29816e9i −0.00796297 + 0.109270i
\(757\) 7.59624e9 + 7.59624e9i 0.636448 + 0.636448i 0.949677 0.313230i \(-0.101411\pi\)
−0.313230 + 0.949677i \(0.601411\pi\)
\(758\) 7.80881e9 + 2.84154e8i 0.651243 + 0.0236980i
\(759\) −3.21129e8 −0.0266583
\(760\) 8.83032e9 1.09922e10i 0.729674 0.908319i
\(761\) 1.33749e10 1.10013 0.550066 0.835121i \(-0.314603\pi\)
0.550066 + 0.835121i \(0.314603\pi\)
\(762\) 1.36899e9 + 4.98160e7i 0.112088 + 0.00407875i
\(763\) 6.61599e9 + 6.61599e9i 0.539211 + 0.539211i
\(764\) −6.76761e8 + 9.28670e9i −0.0549046 + 0.753415i
\(765\) −3.44541e9 1.55717e10i −0.278244 1.25754i
\(766\) 1.21021e10 + 1.30162e10i 0.972884 + 1.04636i
\(767\) 1.92209e9 1.92209e9i 0.153812 0.153812i
\(768\) −5.10427e8 9.46859e8i −0.0406602 0.0754260i
\(769\) 1.23200e10i 0.976939i −0.872581 0.488469i \(-0.837555\pi\)
0.872581 0.488469i \(-0.162445\pi\)
\(770\) −1.41299e10 + 2.59137e9i −1.11538 + 0.204556i
\(771\) 8.32934e8i 0.0654516i
\(772\) −1.26614e10 + 1.09414e10i −0.990425 + 0.855877i
\(773\) −4.94826e9 + 4.94826e9i −0.385322 + 0.385322i −0.873015 0.487693i \(-0.837839\pi\)
0.487693 + 0.873015i \(0.337839\pi\)
\(774\) 6.37048e9 5.92313e9i 0.493831 0.459153i
\(775\) −1.42883e10 + 6.64836e9i −1.10262 + 0.513049i
\(776\) 4.10562e9 + 5.11586e9i 0.315400 + 0.393009i
\(777\) −1.88771e8 1.88771e8i −0.0144365 0.0144365i
\(778\) 7.54460e8 2.07333e10i 0.0574391 1.57848i
\(779\) 1.82525e9 0.138338
\(780\) −2.71205e8 + 3.63960e8i −0.0204629 + 0.0274614i
\(781\) −3.86760e10 −2.90511
\(782\) −1.11075e8 + 3.05245e9i −0.00830603 + 0.228257i
\(783\) −4.39360e8 4.39360e8i −0.0327081 0.0327081i
\(784\) −1.15078e9 + 7.85374e9i −0.0852878 + 0.582063i
\(785\) −5.72508e9 + 1.26674e9i −0.422413 + 0.0934636i
\(786\) −4.34281e8 + 4.03785e8i −0.0319001 + 0.0296600i
\(787\) −9.43553e9 + 9.43553e9i −0.690009 + 0.690009i −0.962234 0.272225i \(-0.912241\pi\)
0.272225 + 0.962234i \(0.412241\pi\)
\(788\) 1.49661e10 + 1.73188e10i 1.08960 + 1.26089i
\(789\) 3.33881e8i 0.0242004i
\(790\) 9.04028e8 1.31009e9i 0.0652360 0.0945378i
\(791\) 6.63376e9i 0.476587i
\(792\) 2.43810e10 + 2.67103e9i 1.74387 + 0.191047i
\(793\) 2.93185e9 2.93185e9i 0.208779 0.208779i
\(794\) 8.33840e8 + 8.96817e8i 0.0591168 + 0.0635817i
\(795\) 3.01889e8 4.73439e8i 0.0213090 0.0334179i
\(796\) 5.40049e9 + 3.93556e8i 0.379522 + 0.0276574i
\(797\) −3.20198e8 3.20198e8i −0.0224034 0.0224034i 0.695816 0.718220i \(-0.255043\pi\)
−0.718220 + 0.695816i \(0.755043\pi\)
\(798\) 9.18980e8 + 3.34407e7i 0.0640171 + 0.00232951i
\(799\) 3.31123e10 2.29655
\(800\) 3.63386e9 + 1.40182e10i 0.250931 + 0.968005i
\(801\) 1.87405e10 1.28845
\(802\) −9.32760e9 3.39421e8i −0.638498 0.0232342i
\(803\) −4.98301e9 4.98301e9i −0.339616 0.339616i
\(804\) −1.43044e9 1.04242e8i −0.0970673 0.00707370i
\(805\) −8.98870e8 + 1.40966e9i −0.0607311 + 0.0952419i
\(806\) −4.91993e9 5.29151e9i −0.330968 0.355965i
\(807\) −2.44097e8 + 2.44097e8i −0.0163495 + 0.0163495i
\(808\) −1.96032e10 2.14760e9i −1.30734 0.143223i
\(809\) 1.99620e10i 1.32552i 0.748834 + 0.662758i \(0.230614\pi\)
−0.748834 + 0.662758i \(0.769386\pi\)
\(810\) −8.40159e9 + 1.21753e10i −0.555475 + 0.804975i
\(811\) 9.87181e9i 0.649866i −0.945737 0.324933i \(-0.894658\pi\)
0.945737 0.324933i \(-0.105342\pi\)
\(812\) 1.73397e9 + 2.00656e9i 0.113657 + 0.131524i
\(813\) 4.52792e8 4.52792e8i 0.0295516 0.0295516i
\(814\) −7.39552e9 + 6.87619e9i −0.480599 + 0.446851i
\(815\) 1.76004e10 3.89429e9i 1.13886 0.251986i
\(816\) −2.50171e8 + 1.70734e9i −0.0161184 + 0.110003i
\(817\) −8.72340e9 8.72340e9i −0.559640 0.559640i
\(818\) 2.76990e8 7.61195e9i 0.0176941 0.486250i
\(819\) 4.00222e9 0.254570
\(820\) −1.12014e9 + 1.50323e9i −0.0709450 + 0.0952088i
\(821\) −1.10174e10 −0.694827 −0.347413 0.937712i \(-0.612940\pi\)
−0.347413 + 0.937712i \(0.612940\pi\)
\(822\) 7.12971e7 1.95931e9i 0.00447734 0.123042i
\(823\) −1.60177e10 1.60177e10i −1.00162 1.00162i −0.999999 0.00161632i \(-0.999486\pi\)
−0.00161632 0.999999i \(-0.500514\pi\)
\(824\) −7.03082e9 8.76086e9i −0.437785 0.545508i
\(825\) 2.29438e9 + 8.37234e8i 0.142258 + 0.0519109i
\(826\) 4.14239e9 3.85150e9i 0.255753 0.237794i
\(827\) 7.73791e8 7.73791e8i 0.0475724 0.0475724i −0.682920 0.730493i \(-0.739290\pi\)
0.730493 + 0.682920i \(0.239290\pi\)
\(828\) 2.15974e9 1.86634e9i 0.132219 0.114257i
\(829\) 1.26868e10i 0.773410i −0.922203 0.386705i \(-0.873613\pi\)
0.922203 0.386705i \(-0.126387\pi\)
\(830\) 1.85688e10 3.40544e9i 1.12723 0.206728i
\(831\) 2.43343e8i 0.0147101i
\(832\) −5.59998e9 + 3.56702e9i −0.337097 + 0.214721i
\(833\) 9.00381e9 9.00381e9i 0.539720 0.539720i
\(834\) −1.21701e7 1.30893e7i −0.000726464 0.000781331i
\(835\) −2.81645e9 1.27291e10i −0.167417 0.756649i
\(836\) 2.52822e9 3.46929e10i 0.149656 2.05361i
\(837\) 2.49089e9 + 2.49089e9i 0.146830 + 0.146830i
\(838\) −2.25572e9 8.20832e7i −0.132413 0.00481837i
\(839\) −1.30733e10 −0.764222 −0.382111 0.924117i \(-0.624803\pi\)
−0.382111 + 0.924117i \(0.624803\pi\)
\(840\) −5.91507e8 + 7.36326e8i −0.0344336 + 0.0428640i
\(841\) 1.59839e10 0.926609
\(842\) 5.68354e9 + 2.06818e8i 0.328115 + 0.0119398i
\(843\) −1.55942e9 1.55942e9i −0.0896531 0.0896531i
\(844\) −5.53473e8 + 7.59490e9i −0.0316882 + 0.434834i
\(845\) −1.24259e10 7.92339e9i −0.708482 0.451765i
\(846\) −2.10703e10 2.26616e10i −1.19639 1.28675i
\(847\) −1.70366e10 + 1.70366e10i −0.963365 + 0.963365i
\(848\) 6.58854e9 4.90451e9i 0.371026 0.276191i
\(849\) 1.94605e9i 0.109138i
\(850\) 8.75183e9 2.15193e10i 0.488802 1.20188i
\(851\) 1.17523e9i 0.0653687i
\(852\) −1.92397e9 + 1.66260e9i −0.106576 + 0.0920978i
\(853\) −3.67214e9 + 3.67214e9i −0.202581 + 0.202581i −0.801105 0.598524i \(-0.795754\pi\)
0.598524 + 0.801105i \(0.295754\pi\)
\(854\) 6.31859e9 5.87488e9i 0.347150 0.322773i
\(855\) 1.78222e10 + 1.13643e10i 0.975167 + 0.621817i
\(856\) −1.69951e10 + 1.36390e10i −0.926116 + 0.743233i
\(857\) 1.10924e10 + 1.10924e10i 0.601995 + 0.601995i 0.940842 0.338847i \(-0.110037\pi\)
−0.338847 + 0.940842i \(0.610037\pi\)
\(858\) −4.07206e7 + 1.11904e9i −0.00220094 + 0.0604839i
\(859\) −7.53633e9 −0.405680 −0.202840 0.979212i \(-0.565017\pi\)
−0.202840 + 0.979212i \(0.565017\pi\)
\(860\) 1.25378e10 1.83092e9i 0.672166 0.0981579i
\(861\) −1.22266e8 −0.00652824
\(862\) 2.17327e8 5.97234e9i 0.0115568 0.317592i
\(863\) −8.38017e9 8.38017e9i −0.443828 0.443828i 0.449468 0.893296i \(-0.351614\pi\)
−0.893296 + 0.449468i \(0.851614\pi\)
\(864\) 2.66517e9 1.83720e9i 0.140581 0.0969077i
\(865\) 5.01306e9 + 2.26568e10i 0.263358 + 1.19026i
\(866\) −1.33589e10 + 1.24208e10i −0.698969 + 0.649886i
\(867\) 7.94655e8 7.94655e8i 0.0414106 0.0414106i
\(868\) −9.83050e9 1.13759e10i −0.510219 0.590427i
\(869\) 3.92688e9i 0.202992i
\(870\) −8.13317e7 4.43477e8i −0.00418738 0.0228325i
\(871\) 8.85269e9i 0.453954i
\(872\) 2.53405e9 2.31307e10i 0.129422 1.18136i
\(873\) −6.95336e9 + 6.95336e9i −0.353708 + 0.353708i
\(874\) −2.75655e9 2.96474e9i −0.139661 0.150209i
\(875\) 1.00974e10 7.72813e9i 0.509543 0.389983i
\(876\) −4.62093e8 3.36747e7i −0.0232255 0.00169254i
\(877\) 2.03754e10 + 2.03754e10i 1.02002 + 1.02002i 0.999795 + 0.0202244i \(0.00643806\pi\)
0.0202244 + 0.999795i \(0.493562\pi\)
\(878\) 5.52513e9 + 2.01053e8i 0.275494 + 0.0100249i
\(879\) 2.78619e9 0.138373
\(880\) 2.70206e10 + 2.33728e10i 1.33661 + 1.15617i
\(881\) 3.11896e10 1.53672 0.768359 0.640019i \(-0.221073\pi\)
0.768359 + 0.640019i \(0.221073\pi\)
\(882\) −1.18915e10 4.32717e8i −0.583573 0.0212356i
\(883\) −3.04851e9 3.04851e9i −0.149014 0.149014i 0.628664 0.777677i \(-0.283602\pi\)
−0.777677 + 0.628664i \(0.783602\pi\)
\(884\) 1.06228e10 + 7.74129e8i 0.517197 + 0.0376904i
\(885\) −9.38942e8 + 2.07751e8i −0.0455341 + 0.0100749i
\(886\) 9.29512e9 + 9.99714e9i 0.448990 + 0.482901i
\(887\) −2.64384e10 + 2.64384e10i −1.27205 + 1.27205i −0.327034 + 0.945012i \(0.606049\pi\)
−0.945012 + 0.327034i \(0.893951\pi\)
\(888\) −7.23031e7 + 6.59979e8i −0.00346507 + 0.0316289i
\(889\) 1.75949e10i 0.839905i
\(890\) 2.24680e10 + 1.55041e10i 1.06832 + 0.737194i
\(891\) 3.64945e10i 1.72844i
\(892\) −1.74610e10 2.02060e10i −0.823746 0.953242i
\(893\) −3.10316e10 + 3.10316e10i −1.45822 + 1.45822i
\(894\) 9.17925e8 8.53466e8i 0.0429661 0.0399489i
\(895\) −1.28767e10 + 2.01940e10i −0.600377 + 0.941545i
\(896\) −1.19150e10 + 6.99380e9i −0.553369 + 0.324815i
\(897\) 9.21494e7 + 9.21494e7i 0.00426304 + 0.00426304i
\(898\) −5.50751e8 + 1.51352e10i −0.0253798 + 0.697461i
\(899\) 7.17728e9 0.329459
\(900\) −2.02966e10 + 7.70372e9i −0.928056 + 0.352250i
\(901\) −1.31760e10 −0.600134
\(902\) −1.68184e8 + 4.62187e9i −0.00763068 + 0.209698i
\(903\) 5.84345e8 + 5.84345e8i 0.0264096 + 0.0264096i
\(904\) −1.28669e10 + 1.03260e10i −0.579272 + 0.464882i
\(905\) −1.14328e10 + 1.79296e10i −0.512723 + 0.804081i
\(906\) 7.67820e8 7.13902e8i 0.0343013 0.0318926i
\(907\) −7.63813e9 + 7.63813e9i −0.339908 + 0.339908i −0.856333 0.516424i \(-0.827263\pi\)
0.516424 + 0.856333i \(0.327263\pi\)
\(908\) 2.26518e10 1.95746e10i 1.00416 0.867744i
\(909\) 2.95632e10i 1.30550i
\(910\) 4.79826e9 + 3.31105e9i 0.211076 + 0.145653i
\(911\) 1.41412e10i 0.619685i −0.950788 0.309843i \(-0.899724\pi\)
0.950788 0.309843i \(-0.100276\pi\)
\(912\) −1.36561e9 1.83451e9i −0.0596134 0.0800826i
\(913\) 3.29330e10 3.29330e10i 1.43214 1.43214i
\(914\) 3.52450e8 + 3.79069e8i 0.0152681 + 0.0164213i
\(915\) −1.43221e9 + 3.16893e8i −0.0618064 + 0.0136754i
\(916\) 3.50127e8 4.80454e9i 0.0150519 0.206546i
\(917\) 5.38560e9 + 5.38560e9i 0.230644 + 0.230644i
\(918\) −5.18934e9 1.88834e8i −0.221393 0.00805622i
\(919\) 3.28770e10 1.39729 0.698647 0.715467i \(-0.253786\pi\)
0.698647 + 0.715467i \(0.253786\pi\)
\(920\) 4.13334e9 4.50797e8i 0.175002 0.0190864i
\(921\) −1.24170e7 −0.000523731
\(922\) 7.04765e9 + 2.56456e8i 0.296133 + 0.0107759i
\(923\) 1.10983e10 + 1.10983e10i 0.464568 + 0.464568i
\(924\) −1.69355e8 + 2.32394e9i −0.00706231 + 0.0969110i
\(925\) 3.06402e9 8.39672e9i 0.127290 0.348830i
\(926\) −8.91129e9 9.58433e9i −0.368810 0.396664i
\(927\) 1.19075e10 1.19075e10i 0.490957 0.490957i
\(928\) 1.19286e9 6.48658e9i 0.0489971 0.266439i
\(929\) 1.07291e10i 0.439046i 0.975607 + 0.219523i \(0.0704501\pi\)
−0.975607 + 0.219523i \(0.929550\pi\)
\(930\) 4.61099e8 + 2.51423e9i 0.0187977 + 0.102498i
\(931\) 1.68761e10i 0.685406i
\(932\) 3.11088e9 2.68827e9i 0.125872 0.108772i
\(933\) −1.20635e9 + 1.20635e9i −0.0486280 + 0.0486280i
\(934\) −3.53113e10 + 3.28317e10i −1.41808 + 1.31850i
\(935\) −1.23815e10 5.59586e10i −0.495372 2.23886i
\(936\) −6.22978e9 7.76271e9i −0.248318 0.309420i
\(937\) −5.62209e7 5.62209e7i −0.00223259 0.00223259i 0.705990 0.708222i \(-0.250503\pi\)
−0.708222 + 0.705990i \(0.750503\pi\)
\(938\) −6.69883e8 + 1.84090e10i −0.0265026 + 0.728317i
\(939\) −2.52052e9 −0.0993483
\(940\) −6.51311e9 4.46005e10i −0.255765 1.75143i
\(941\) −9.09097e9 −0.355669 −0.177835 0.984060i \(-0.556909\pi\)
−0.177835 + 0.984060i \(0.556909\pi\)
\(942\) −3.45854e7 + 9.50438e8i −0.00134808 + 0.0370464i
\(943\) 3.80597e8 + 3.80597e8i 0.0147800 + 0.0147800i
\(944\) −1.39184e10 2.03941e9i −0.538500 0.0789046i
\(945\) −2.39650e9 1.52813e9i −0.0923775 0.0589046i
\(946\) 2.28930e10 2.12854e10i 0.879191 0.817452i
\(947\) 8.98425e8 8.98425e8i 0.0343761 0.0343761i −0.689710 0.724086i \(-0.742262\pi\)
0.724086 + 0.689710i \(0.242262\pi\)
\(948\) −1.68808e8 1.95346e8i −0.00643523 0.00744688i
\(949\) 2.85980e9i 0.108619i
\(950\) 1.19653e10 + 2.83691e10i 0.452782 + 1.07353i
\(951\) 3.02529e9i 0.114060i
\(952\) 2.20313e10 + 2.41361e9i 0.827583 + 0.0906647i
\(953\) −1.00058e10 + 1.00058e10i −0.374480 + 0.374480i −0.869106 0.494626i \(-0.835305\pi\)
0.494626 + 0.869106i \(0.335305\pi\)
\(954\) 8.38428e9 + 9.01752e9i 0.312642 + 0.336254i
\(955\) −1.71440e10 1.09319e10i −0.636941 0.406147i
\(956\) 2.54583e10 + 1.85525e9i 0.942381 + 0.0686753i
\(957\) −7.86535e8 7.86535e8i −0.0290086 0.0290086i
\(958\) −2.96566e10 1.07917e9i −1.08979 0.0396561i
\(959\) −2.51819e10 −0.921986
\(960\) 2.34891e9 + 1.13706e6i 0.0856874 + 4.14797e-5i
\(961\) −1.31780e10 −0.478980
\(962\) 4.09534e9 + 1.49025e8i 0.148312 + 0.00539691i
\(963\) −2.30993e10 2.30993e10i −0.833503 0.833503i
\(964\) −2.11319e10 1.53997e9i −0.759747 0.0553660i
\(965\) −7.89423e9 3.56783e10i −0.282790 1.27808i
\(966\) 1.84650e8 + 1.98596e8i 0.00659067 + 0.00708844i
\(967\) 2.63538e10 2.63538e10i 0.937241 0.937241i −0.0609028 0.998144i \(-0.519398\pi\)
0.998144 + 0.0609028i \(0.0193980\pi\)
\(968\) 5.95631e10 + 6.52535e9i 2.11064 + 0.231228i
\(969\) 3.66873e9i 0.129534i
\(970\) −1.40889e10 + 2.58385e9i −0.495652 + 0.0909004i
\(971\) 5.07351e10i 1.77845i −0.457471 0.889225i \(-0.651245\pi\)
0.457471 0.889225i \(-0.348755\pi\)
\(972\) 4.76518e9 + 5.51428e9i 0.166436 + 0.192600i
\(973\) −1.62323e8 + 1.62323e8i −0.00564917 + 0.00564917i
\(974\) 3.39284e9 3.15458e9i 0.117654 0.109392i
\(975\) −4.18135e8 8.98632e8i −0.0144477 0.0310503i
\(976\) −2.12303e10 3.11081e9i −0.730941 0.107102i
\(977\) −2.06830e10 2.06830e10i −0.709550 0.709550i 0.256891 0.966440i \(-0.417302\pi\)
−0.966440 + 0.256891i \(0.917302\pi\)
\(978\) 1.06325e8 2.92190e9i 0.00363453 0.0998803i
\(979\) 6.73460e10 2.29389
\(980\) −1.38987e10 1.03566e10i −0.471718 0.351502i
\(981\) 3.48829e10 1.17970
\(982\) 1.94200e9 5.33679e10i 0.0654422 1.79841i
\(983\) 2.03885e10 + 2.03885e10i 0.684618 + 0.684618i 0.961037 0.276419i \(-0.0891478\pi\)
−0.276419 + 0.961037i \(0.589148\pi\)
\(984\) 1.90318e8 + 2.37148e8i 0.00636790 + 0.00793482i
\(985\) −4.88023e10 + 1.07980e10i −1.62710 + 0.360013i
\(986\) −7.74837e9 + 7.20426e9i −0.257419 + 0.239343i
\(987\) 2.07868e9 2.07868e9i 0.0688142 0.0688142i
\(988\) −1.06808e10 + 9.22982e9i −0.352334 + 0.304470i
\(989\) 3.63795e9i 0.119583i
\(990\) −3.04187e10 + 4.40817e10i −0.996362 + 1.44389i
\(991\) 2.19271e10i 0.715688i 0.933781 + 0.357844i \(0.116488\pi\)
−0.933781 + 0.357844i \(0.883512\pi\)
\(992\) −6.76273e9 + 3.67748e10i −0.219954 + 1.19608i
\(993\) −1.84687e9 + 1.84687e9i −0.0598570 + 0.0598570i
\(994\) 2.22389e10 + 2.39185e10i 0.718224 + 0.772469i
\(995\) −6.35720e9 + 9.96972e9i −0.204590 + 0.320850i
\(996\) 2.22558e8 3.05400e9i 0.00713732 0.0979403i
\(997\) 7.81273e9 + 7.81273e9i 0.249672 + 0.249672i 0.820836 0.571164i \(-0.193508\pi\)
−0.571164 + 0.820836i \(0.693508\pi\)
\(998\) 1.92362e10 + 6.99982e8i 0.612578 + 0.0222910i
\(999\) −1.99796e9 −0.0634028
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 20.8.e.b.7.1 yes 36
4.3 odd 2 inner 20.8.e.b.7.8 yes 36
5.2 odd 4 100.8.e.e.43.11 36
5.3 odd 4 inner 20.8.e.b.3.8 yes 36
5.4 even 2 100.8.e.e.7.18 36
20.3 even 4 inner 20.8.e.b.3.1 36
20.7 even 4 100.8.e.e.43.18 36
20.19 odd 2 100.8.e.e.7.11 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.8.e.b.3.1 36 20.3 even 4 inner
20.8.e.b.3.8 yes 36 5.3 odd 4 inner
20.8.e.b.7.1 yes 36 1.1 even 1 trivial
20.8.e.b.7.8 yes 36 4.3 odd 2 inner
100.8.e.e.7.11 36 20.19 odd 2
100.8.e.e.7.18 36 5.4 even 2
100.8.e.e.43.11 36 5.2 odd 4
100.8.e.e.43.18 36 20.7 even 4