Properties

Label 5.9.c.a.3.3
Level 5
Weight 9
Character 5.3
Analytic conductor 2.037
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.03689305031\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} - 30 x^{3} + 1089 x^{2} - 3168 x + 4608\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.3
Root \(1.52966 + 1.52966i\) of defining polynomial
Character \(\chi\) \(=\) 5.3
Dual form 5.9.c.a.2.3

$q$-expansion

\(f(q)\) \(=\) \(q+(15.2610 - 15.2610i) q^{2} +(-20.3321 - 20.3321i) q^{3} -209.796i q^{4} +(558.542 + 280.457i) q^{5} -620.576 q^{6} +(-2415.21 + 2415.21i) q^{7} +(705.116 + 705.116i) q^{8} -5734.21i q^{9} +O(q^{10})\) \(q+(15.2610 - 15.2610i) q^{2} +(-20.3321 - 20.3321i) q^{3} -209.796i q^{4} +(558.542 + 280.457i) q^{5} -620.576 q^{6} +(-2415.21 + 2415.21i) q^{7} +(705.116 + 705.116i) q^{8} -5734.21i q^{9} +(12804.0 - 4243.86i) q^{10} -981.878 q^{11} +(-4265.60 + 4265.60i) q^{12} +(-26582.1 - 26582.1i) q^{13} +73717.1i q^{14} +(-5654.06 - 17058.6i) q^{15} +75229.4 q^{16} +(-18503.9 + 18503.9i) q^{17} +(-87509.8 - 87509.8i) q^{18} +50374.1i q^{19} +(58838.8 - 117180. i) q^{20} +98212.6 q^{21} +(-14984.4 + 14984.4i) q^{22} +(13652.5 + 13652.5i) q^{23} -28673.0i q^{24} +(233313. + 313294. i) q^{25} -811340. q^{26} +(-249988. + 249988. i) q^{27} +(506702. + 506702. i) q^{28} -1.05137e6i q^{29} +(-346618. - 174045. i) q^{30} +1.09477e6 q^{31} +(967566. - 967566. i) q^{32} +(19963.6 + 19963.6i) q^{33} +564775. i q^{34} +(-2.02636e6 + 671634. i) q^{35} -1.20302e6 q^{36} +(77885.1 - 77885.1i) q^{37} +(768759. + 768759. i) q^{38} +1.08094e6i q^{39} +(196082. + 591591. i) q^{40} +554897. q^{41} +(1.49882e6 - 1.49882e6i) q^{42} +(-1.07414e6 - 1.07414e6i) q^{43} +205994. i q^{44} +(1.60820e6 - 3.20280e6i) q^{45} +416702. q^{46} +(-4.06986e6 + 4.06986e6i) q^{47} +(-1.52957e6 - 1.52957e6i) q^{48} -5.90168e6i q^{49} +(8.34176e6 + 1.22058e6i) q^{50} +752445. q^{51} +(-5.57683e6 + 5.57683e6i) q^{52} +(1.88025e6 + 1.88025e6i) q^{53} +7.63012e6i q^{54} +(-548420. - 275374. i) q^{55} -3.40601e6 q^{56} +(1.02421e6 - 1.02421e6i) q^{57} +(-1.60450e7 - 1.60450e7i) q^{58} +1.27248e7i q^{59} +(-3.57883e6 + 1.18620e6i) q^{60} +1.40038e7 q^{61} +(1.67073e7 - 1.67073e7i) q^{62} +(1.38493e7 + 1.38493e7i) q^{63} -1.02733e7i q^{64} +(-7.39210e6 - 2.23024e7i) q^{65} +609330. q^{66} +(-9.54151e6 + 9.54151e6i) q^{67} +(3.88204e6 + 3.88204e6i) q^{68} -555168. i q^{69} +(-2.06744e7 + 4.11741e7i) q^{70} -2.82034e7 q^{71} +(4.04328e6 - 4.04328e6i) q^{72} +(1.11578e7 + 1.11578e7i) q^{73} -2.37721e6i q^{74} +(1.62617e6 - 1.11137e7i) q^{75} +1.05683e7 q^{76} +(2.37144e6 - 2.37144e6i) q^{77} +(1.64963e7 + 1.64963e7i) q^{78} -6.87542e7i q^{79} +(4.20188e7 + 2.10986e7i) q^{80} -2.74566e7 q^{81} +(8.46828e6 - 8.46828e6i) q^{82} +(-3.29194e6 - 3.29194e6i) q^{83} -2.06046e7i q^{84} +(-1.55247e7 + 5.14565e6i) q^{85} -3.27850e7 q^{86} +(-2.13766e7 + 2.13766e7i) q^{87} +(-692338. - 692338. i) q^{88} +7.97635e7i q^{89} +(-2.43352e7 - 7.34206e7i) q^{90} +1.28403e8 q^{91} +(2.86424e6 - 2.86424e6i) q^{92} +(-2.22591e7 - 2.22591e7i) q^{93} +1.24220e8i q^{94} +(-1.41278e7 + 2.81360e7i) q^{95} -3.93453e7 q^{96} +(-1.96546e7 + 1.96546e7i) q^{97} +(-9.00656e7 - 9.00656e7i) q^{98} +5.63029e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{2} - 72q^{3} + 220q^{5} + 1752q^{6} - 2352q^{7} - 8220q^{8} + O(q^{10}) \) \( 6q - 2q^{2} - 72q^{3} + 220q^{5} + 1752q^{6} - 2352q^{7} - 8220q^{8} + 30870q^{10} + 23192q^{11} - 45912q^{12} - 119142q^{13} + 241440q^{15} + 218616q^{16} - 265502q^{17} - 454062q^{18} + 412260q^{20} + 231672q^{21} - 35664q^{22} + 28888q^{23} - 340350q^{25} - 801388q^{26} + 392040q^{27} + 1305192q^{28} - 2549760q^{30} - 747648q^{31} + 3033928q^{32} + 4269096q^{33} - 4971680q^{35} - 3972804q^{36} - 454002q^{37} + 1443720q^{38} + 2683500q^{40} + 2489432q^{41} + 4223856q^{42} + 792648q^{43} + 210690q^{45} - 3149928q^{46} - 15313352q^{47} - 21677712q^{48} + 29537650q^{50} + 35567712q^{51} - 735732q^{52} - 13509122q^{53} + 4448040q^{55} - 18454800q^{56} - 34625520q^{57} - 23903520q^{58} + 13688520q^{60} + 24111192q^{61} + 53913416q^{62} + 44837688q^{63} - 30943610q^{65} - 55047936q^{66} - 32827752q^{67} + 8118692q^{68} - 44156280q^{70} - 13992928q^{71} + 82596420q^{72} + 111859638q^{73} - 126793200q^{75} - 56470800q^{76} + 26260136q^{77} + 31125576q^{78} + 23045920q^{80} + 65834226q^{81} + 38023056q^{82} - 14768432q^{83} - 19713030q^{85} - 135560008q^{86} - 133207680q^{87} - 44555040q^{88} + 135147990q^{90} + 167542032q^{91} + 69931048q^{92} - 96798024q^{93} + 239661000q^{95} + 184867872q^{96} - 186656202q^{97} - 345959698q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.2610 15.2610i 0.953812 0.953812i −0.0451670 0.998979i \(-0.514382\pi\)
0.998979 + 0.0451670i \(0.0143820\pi\)
\(3\) −20.3321 20.3321i −0.251014 0.251014i 0.570373 0.821386i \(-0.306799\pi\)
−0.821386 + 0.570373i \(0.806799\pi\)
\(4\) 209.796i 0.819516i
\(5\) 558.542 + 280.457i 0.893667 + 0.448731i
\(6\) −620.576 −0.478840
\(7\) −2415.21 + 2415.21i −1.00592 + 1.00592i −0.00593626 + 0.999982i \(0.501890\pi\)
−0.999982 + 0.00593626i \(0.998110\pi\)
\(8\) 705.116 + 705.116i 0.172147 + 0.172147i
\(9\) 5734.21i 0.873984i
\(10\) 12804.0 4243.86i 1.28040 0.424386i
\(11\) −981.878 −0.0670636 −0.0335318 0.999438i \(-0.510675\pi\)
−0.0335318 + 0.999438i \(0.510675\pi\)
\(12\) −4265.60 + 4265.60i −0.205710 + 0.205710i
\(13\) −26582.1 26582.1i −0.930715 0.930715i 0.0670358 0.997751i \(-0.478646\pi\)
−0.997751 + 0.0670358i \(0.978646\pi\)
\(14\) 73717.1i 1.91892i
\(15\) −5654.06 17058.6i −0.111685 0.336960i
\(16\) 75229.4 1.14791
\(17\) −18503.9 + 18503.9i −0.221547 + 0.221547i −0.809150 0.587602i \(-0.800072\pi\)
0.587602 + 0.809150i \(0.300072\pi\)
\(18\) −87509.8 87509.8i −0.833617 0.833617i
\(19\) 50374.1i 0.386539i 0.981146 + 0.193269i \(0.0619091\pi\)
−0.981146 + 0.193269i \(0.938091\pi\)
\(20\) 58838.8 117180.i 0.367742 0.732375i
\(21\) 98212.6 0.504999
\(22\) −14984.4 + 14984.4i −0.0639661 + 0.0639661i
\(23\) 13652.5 + 13652.5i 0.0487866 + 0.0487866i 0.731079 0.682293i \(-0.239017\pi\)
−0.682293 + 0.731079i \(0.739017\pi\)
\(24\) 28673.0i 0.0864227i
\(25\) 233313. + 313294.i 0.597281 + 0.802032i
\(26\) −811340. −1.77545
\(27\) −249988. + 249988.i −0.470396 + 0.470396i
\(28\) 506702. + 506702.i 0.824367 + 0.824367i
\(29\) 1.05137e6i 1.48650i −0.669015 0.743249i \(-0.733284\pi\)
0.669015 0.743249i \(-0.266716\pi\)
\(30\) −346618. 174045.i −0.427923 0.214870i
\(31\) 1.09477e6 1.18543 0.592717 0.805411i \(-0.298055\pi\)
0.592717 + 0.805411i \(0.298055\pi\)
\(32\) 967566. 967566.i 0.922743 0.922743i
\(33\) 19963.6 + 19963.6i 0.0168339 + 0.0168339i
\(34\) 564775.i 0.422629i
\(35\) −2.02636e6 + 671634.i −1.35034 + 0.447570i
\(36\) −1.20302e6 −0.716244
\(37\) 77885.1 77885.1i 0.0415573 0.0415573i −0.686023 0.727580i \(-0.740645\pi\)
0.727580 + 0.686023i \(0.240645\pi\)
\(38\) 768759. + 768759.i 0.368685 + 0.368685i
\(39\) 1.08094e6i 0.467244i
\(40\) 196082. + 591591.i 0.0765947 + 0.231090i
\(41\) 554897. 0.196371 0.0981854 0.995168i \(-0.468696\pi\)
0.0981854 + 0.995168i \(0.468696\pi\)
\(42\) 1.49882e6 1.49882e6i 0.481674 0.481674i
\(43\) −1.07414e6 1.07414e6i −0.314187 0.314187i 0.532342 0.846529i \(-0.321312\pi\)
−0.846529 + 0.532342i \(0.821312\pi\)
\(44\) 205994.i 0.0549597i
\(45\) 1.60820e6 3.20280e6i 0.392184 0.781051i
\(46\) 416702. 0.0930666
\(47\) −4.06986e6 + 4.06986e6i −0.834043 + 0.834043i −0.988067 0.154024i \(-0.950777\pi\)
0.154024 + 0.988067i \(0.450777\pi\)
\(48\) −1.52957e6 1.52957e6i −0.288141 0.288141i
\(49\) 5.90168e6i 1.02374i
\(50\) 8.34176e6 + 1.22058e6i 1.33468 + 0.195293i
\(51\) 752445. 0.111223
\(52\) −5.57683e6 + 5.57683e6i −0.762736 + 0.762736i
\(53\) 1.88025e6 + 1.88025e6i 0.238294 + 0.238294i 0.816143 0.577850i \(-0.196108\pi\)
−0.577850 + 0.816143i \(0.696108\pi\)
\(54\) 7.63012e6i 0.897338i
\(55\) −548420. 275374.i −0.0599325 0.0300935i
\(56\) −3.40601e6 −0.346333
\(57\) 1.02421e6 1.02421e6i 0.0970265 0.0970265i
\(58\) −1.60450e7 1.60450e7i −1.41784 1.41784i
\(59\) 1.27248e7i 1.05013i 0.851063 + 0.525063i \(0.175958\pi\)
−0.851063 + 0.525063i \(0.824042\pi\)
\(60\) −3.57883e6 + 1.18620e6i −0.276144 + 0.0915277i
\(61\) 1.40038e7 1.01141 0.505705 0.862707i \(-0.331233\pi\)
0.505705 + 0.862707i \(0.331233\pi\)
\(62\) 1.67073e7 1.67073e7i 1.13068 1.13068i
\(63\) 1.38493e7 + 1.38493e7i 0.879157 + 0.879157i
\(64\) 1.02733e7i 0.612338i
\(65\) −7.39210e6 2.23024e7i −0.414109 1.24939i
\(66\) 609330. 0.0321127
\(67\) −9.54151e6 + 9.54151e6i −0.473498 + 0.473498i −0.903045 0.429547i \(-0.858673\pi\)
0.429547 + 0.903045i \(0.358673\pi\)
\(68\) 3.88204e6 + 3.88204e6i 0.181562 + 0.181562i
\(69\) 555168.i 0.0244922i
\(70\) −2.06744e7 + 4.11741e7i −0.861076 + 1.71487i
\(71\) −2.82034e7 −1.10986 −0.554930 0.831897i \(-0.687255\pi\)
−0.554930 + 0.831897i \(0.687255\pi\)
\(72\) 4.04328e6 4.04328e6i 0.150454 0.150454i
\(73\) 1.11578e7 + 1.11578e7i 0.392905 + 0.392905i 0.875721 0.482817i \(-0.160386\pi\)
−0.482817 + 0.875721i \(0.660386\pi\)
\(74\) 2.37721e6i 0.0792758i
\(75\) 1.62617e6 1.11137e7i 0.0513951 0.351247i
\(76\) 1.05683e7 0.316775
\(77\) 2.37144e6 2.37144e6i 0.0674605 0.0674605i
\(78\) 1.64963e7 + 1.64963e7i 0.445663 + 0.445663i
\(79\) 6.87542e7i 1.76519i −0.470136 0.882594i \(-0.655795\pi\)
0.470136 0.882594i \(-0.344205\pi\)
\(80\) 4.20188e7 + 2.10986e7i 1.02585 + 0.515102i
\(81\) −2.74566e7 −0.637833
\(82\) 8.46828e6 8.46828e6i 0.187301 0.187301i
\(83\) −3.29194e6 3.29194e6i −0.0693649 0.0693649i 0.671573 0.740938i \(-0.265619\pi\)
−0.740938 + 0.671573i \(0.765619\pi\)
\(84\) 2.06046e7i 0.413855i
\(85\) −1.55247e7 + 5.14565e6i −0.297405 + 0.0985745i
\(86\) −3.27850e7 −0.599351
\(87\) −2.13766e7 + 2.13766e7i −0.373131 + 0.373131i
\(88\) −692338. 692338.i −0.0115448 0.0115448i
\(89\) 7.97635e7i 1.27129i 0.771982 + 0.635645i \(0.219266\pi\)
−0.771982 + 0.635645i \(0.780734\pi\)
\(90\) −2.43352e7 7.34206e7i −0.370906 1.11905i
\(91\) 1.28403e8 1.87245
\(92\) 2.86424e6 2.86424e6i 0.0399814 0.0399814i
\(93\) −2.22591e7 2.22591e7i −0.297560 0.297560i
\(94\) 1.24220e8i 1.59104i
\(95\) −1.41278e7 + 2.81360e7i −0.173452 + 0.345437i
\(96\) −3.93453e7 −0.463242
\(97\) −1.96546e7 + 1.96546e7i −0.222012 + 0.222012i −0.809345 0.587333i \(-0.800178\pi\)
0.587333 + 0.809345i \(0.300178\pi\)
\(98\) −9.00656e7 9.00656e7i −0.976460 0.976460i
\(99\) 5.63029e6i 0.0586125i
\(100\) 6.57278e7 4.89482e7i 0.657278 0.489482i
\(101\) 3.02468e7 0.290666 0.145333 0.989383i \(-0.453575\pi\)
0.145333 + 0.989383i \(0.453575\pi\)
\(102\) 1.14831e7 1.14831e7i 0.106086 0.106086i
\(103\) −4.28162e7 4.28162e7i −0.380416 0.380416i 0.490836 0.871252i \(-0.336691\pi\)
−0.871252 + 0.490836i \(0.836691\pi\)
\(104\) 3.74870e7i 0.320440i
\(105\) 5.48559e7 + 2.75444e7i 0.451301 + 0.226608i
\(106\) 5.73890e7 0.454575
\(107\) 8.84746e7 8.84746e7i 0.674969 0.674969i −0.283888 0.958857i \(-0.591625\pi\)
0.958857 + 0.283888i \(0.0916246\pi\)
\(108\) 5.24464e7 + 5.24464e7i 0.385497 + 0.385497i
\(109\) 4.49302e7i 0.318297i −0.987255 0.159148i \(-0.949125\pi\)
0.987255 0.159148i \(-0.0508749\pi\)
\(110\) −1.25719e7 + 4.16695e6i −0.0858679 + 0.0284608i
\(111\) −3.16714e6 −0.0208629
\(112\) −1.81695e8 + 1.81695e8i −1.15470 + 1.15470i
\(113\) 9.24017e6 + 9.24017e6i 0.0566717 + 0.0566717i 0.734875 0.678203i \(-0.237241\pi\)
−0.678203 + 0.734875i \(0.737241\pi\)
\(114\) 3.12610e7i 0.185090i
\(115\) 3.79656e6 + 1.14544e7i 0.0217069 + 0.0654911i
\(116\) −2.20574e8 −1.21821
\(117\) −1.52428e8 + 1.52428e8i −0.813430 + 0.813430i
\(118\) 1.94193e8 + 1.94193e8i 1.00162 + 1.00162i
\(119\) 8.93815e7i 0.445717i
\(120\) 8.04153e6 1.60151e7i 0.0387805 0.0772331i
\(121\) −2.13395e8 −0.995502
\(122\) 2.13712e8 2.13712e8i 0.964695 0.964695i
\(123\) −1.12822e7 1.12822e7i −0.0492917 0.0492917i
\(124\) 2.29679e8i 0.971483i
\(125\) 4.24498e7 + 2.40422e8i 0.173874 + 0.984768i
\(126\) 4.22709e8 1.67710
\(127\) 2.89529e8 2.89529e8i 1.11295 1.11295i 0.120204 0.992749i \(-0.461645\pi\)
0.992749 0.120204i \(-0.0383548\pi\)
\(128\) 9.09157e7 + 9.09157e7i 0.338687 + 0.338687i
\(129\) 4.36792e7i 0.157731i
\(130\) −4.53167e8 2.27546e8i −1.58667 0.796701i
\(131\) −1.84509e8 −0.626516 −0.313258 0.949668i \(-0.601420\pi\)
−0.313258 + 0.949668i \(0.601420\pi\)
\(132\) 4.18830e6 4.18830e6i 0.0137956 0.0137956i
\(133\) −1.21664e8 1.21664e8i −0.388826 0.388826i
\(134\) 2.91226e8i 0.903256i
\(135\) −2.09739e8 + 6.95178e7i −0.631458 + 0.209296i
\(136\) −2.60947e7 −0.0762777
\(137\) 1.60104e8 1.60104e8i 0.454484 0.454484i −0.442356 0.896840i \(-0.645857\pi\)
0.896840 + 0.442356i \(0.145857\pi\)
\(138\) −8.47242e6 8.47242e6i −0.0233610 0.0233610i
\(139\) 2.86303e8i 0.766949i 0.923551 + 0.383475i \(0.125273\pi\)
−0.923551 + 0.383475i \(0.874727\pi\)
\(140\) 1.40906e8 + 4.25122e8i 0.366791 + 1.10663i
\(141\) 1.65498e8 0.418712
\(142\) −4.30412e8 + 4.30412e8i −1.05860 + 1.05860i
\(143\) 2.61004e7 + 2.61004e7i 0.0624171 + 0.0624171i
\(144\) 4.31381e8i 1.00325i
\(145\) 2.94864e8 5.87235e8i 0.667037 1.32843i
\(146\) 3.40558e8 0.749515
\(147\) −1.19994e8 + 1.19994e8i −0.256974 + 0.256974i
\(148\) −1.63400e7 1.63400e7i −0.0340569 0.0340569i
\(149\) 1.84894e8i 0.375127i 0.982253 + 0.187563i \(0.0600590\pi\)
−0.982253 + 0.187563i \(0.939941\pi\)
\(150\) −1.44789e8 1.94423e8i −0.286002 0.384045i
\(151\) −6.16679e8 −1.18618 −0.593091 0.805135i \(-0.702093\pi\)
−0.593091 + 0.805135i \(0.702093\pi\)
\(152\) −3.55196e7 + 3.55196e7i −0.0665416 + 0.0665416i
\(153\) 1.06105e8 + 1.06105e8i 0.193629 + 0.193629i
\(154\) 7.23811e7i 0.128689i
\(155\) 6.11477e8 + 3.07037e8i 1.05938 + 0.531941i
\(156\) 2.26778e8 0.382914
\(157\) 2.91004e8 2.91004e8i 0.478961 0.478961i −0.425838 0.904799i \(-0.640021\pi\)
0.904799 + 0.425838i \(0.140021\pi\)
\(158\) −1.04926e9 1.04926e9i −1.68366 1.68366i
\(159\) 7.64589e7i 0.119630i
\(160\) 8.11786e8 2.69066e8i 1.23869 0.410562i
\(161\) −6.59473e7 −0.0981508
\(162\) −4.19015e8 + 4.19015e8i −0.608373 + 0.608373i
\(163\) 7.65254e8 + 7.65254e8i 1.08406 + 1.08406i 0.996126 + 0.0879389i \(0.0280280\pi\)
0.0879389 + 0.996126i \(0.471972\pi\)
\(164\) 1.16415e8i 0.160929i
\(165\) 5.55159e6 + 1.67495e7i 0.00749000 + 0.0225978i
\(166\) −1.00477e8 −0.132322
\(167\) −4.23551e8 + 4.23551e8i −0.544552 + 0.544552i −0.924860 0.380308i \(-0.875818\pi\)
0.380308 + 0.924860i \(0.375818\pi\)
\(168\) 6.92513e7 + 6.92513e7i 0.0869342 + 0.0869342i
\(169\) 5.97490e8i 0.732460i
\(170\) −1.58395e8 + 3.15450e8i −0.189647 + 0.377690i
\(171\) 2.88856e8 0.337829
\(172\) −2.25351e8 + 2.25351e8i −0.257482 + 0.257482i
\(173\) −1.22912e9 1.22912e9i −1.37217 1.37217i −0.857217 0.514955i \(-0.827809\pi\)
−0.514955 0.857217i \(-0.672191\pi\)
\(174\) 6.52457e8i 0.711795i
\(175\) −1.32017e9 1.93170e8i −1.40760 0.205962i
\(176\) −7.38661e7 −0.0769829
\(177\) 2.58721e8 2.58721e8i 0.263596 0.263596i
\(178\) 1.21727e9 + 1.21727e9i 1.21257 + 1.21257i
\(179\) 4.39309e8i 0.427916i −0.976843 0.213958i \(-0.931364\pi\)
0.976843 0.213958i \(-0.0686355\pi\)
\(180\) −6.71935e8 3.37394e8i −0.640084 0.321401i
\(181\) 1.68623e9 1.57110 0.785549 0.618799i \(-0.212380\pi\)
0.785549 + 0.618799i \(0.212380\pi\)
\(182\) 1.95956e9 1.95956e9i 1.78596 1.78596i
\(183\) −2.84727e8 2.84727e8i −0.253877 0.253877i
\(184\) 1.92532e7i 0.0167970i
\(185\) 6.53455e7 2.16587e7i 0.0557865 0.0184904i
\(186\) −6.79391e8 −0.567633
\(187\) 1.81685e7 1.81685e7i 0.0148578 0.0148578i
\(188\) 8.53842e8 + 8.53842e8i 0.683512 + 0.683512i
\(189\) 1.20755e9i 0.946359i
\(190\) 2.13780e8 + 6.44988e8i 0.164041 + 0.494922i
\(191\) −1.52273e9 −1.14416 −0.572082 0.820196i \(-0.693864\pi\)
−0.572082 + 0.820196i \(0.693864\pi\)
\(192\) −2.08878e8 + 2.08878e8i −0.153705 + 0.153705i
\(193\) −1.96356e8 1.96356e8i −0.141519 0.141519i 0.632798 0.774317i \(-0.281906\pi\)
−0.774317 + 0.632798i \(0.781906\pi\)
\(194\) 5.99897e8i 0.423516i
\(195\) −3.03157e8 + 6.03751e8i −0.209667 + 0.417561i
\(196\) −1.23815e9 −0.838976
\(197\) −1.25390e9 + 1.25390e9i −0.832525 + 0.832525i −0.987862 0.155337i \(-0.950354\pi\)
0.155337 + 0.987862i \(0.450354\pi\)
\(198\) 8.59239e7 + 8.59239e7i 0.0559053 + 0.0559053i
\(199\) 1.10010e9i 0.701489i −0.936471 0.350745i \(-0.885929\pi\)
0.936471 0.350745i \(-0.114071\pi\)
\(200\) −5.63956e7 + 3.85421e8i −0.0352473 + 0.240888i
\(201\) 3.87998e8 0.237709
\(202\) 4.61597e8 4.61597e8i 0.277241 0.277241i
\(203\) 2.53928e9 + 2.53928e9i 1.49530 + 1.49530i
\(204\) 1.57860e8i 0.0911490i
\(205\) 3.09933e8 + 1.55625e8i 0.175490 + 0.0881176i
\(206\) −1.30684e9 −0.725691
\(207\) 7.82863e7 7.82863e7i 0.0426388 0.0426388i
\(208\) −1.99976e9 1.99976e9i −1.06838 1.06838i
\(209\) 4.94612e7i 0.0259227i
\(210\) 1.25751e9 4.16800e8i 0.646598 0.214314i
\(211\) 2.62708e9 1.32539 0.662695 0.748889i \(-0.269412\pi\)
0.662695 + 0.748889i \(0.269412\pi\)
\(212\) 3.94470e8 3.94470e8i 0.195286 0.195286i
\(213\) 5.73434e8 + 5.73434e8i 0.278590 + 0.278590i
\(214\) 2.70042e9i 1.28759i
\(215\) −2.98703e8 9.01205e8i −0.139793 0.421764i
\(216\) −3.52540e8 −0.161955
\(217\) −2.64411e9 + 2.64411e9i −1.19245 + 1.19245i
\(218\) −6.85680e8 6.85680e8i −0.303596 0.303596i
\(219\) 4.53723e8i 0.197249i
\(220\) −5.77725e7 + 1.15056e8i −0.0246621 + 0.0491157i
\(221\) 9.83745e8 0.412395
\(222\) −4.83337e7 + 4.83337e7i −0.0198993 + 0.0198993i
\(223\) −2.23974e9 2.23974e9i −0.905687 0.905687i 0.0902332 0.995921i \(-0.471239\pi\)
−0.995921 + 0.0902332i \(0.971239\pi\)
\(224\) 4.67375e9i 1.85641i
\(225\) 1.79649e9 1.33787e9i 0.700963 0.522015i
\(226\) 2.82028e8 0.108108
\(227\) 2.86595e9 2.86595e9i 1.07936 1.07936i 0.0827897 0.996567i \(-0.473617\pi\)
0.996567 0.0827897i \(-0.0263830\pi\)
\(228\) −2.14876e8 2.14876e8i −0.0795148 0.0795148i
\(229\) 4.21694e9i 1.53340i 0.642005 + 0.766701i \(0.278103\pi\)
−0.642005 + 0.766701i \(0.721897\pi\)
\(230\) 2.32745e8 + 1.16867e8i 0.0831705 + 0.0417618i
\(231\) −9.64328e7 −0.0338670
\(232\) 7.41339e8 7.41339e8i 0.255897 0.255897i
\(233\) −1.39423e9 1.39423e9i −0.473052 0.473052i 0.429849 0.902901i \(-0.358567\pi\)
−0.902901 + 0.429849i \(0.858567\pi\)
\(234\) 4.65240e9i 1.55172i
\(235\) −3.41461e9 + 1.13177e9i −1.11962 + 0.371096i
\(236\) 2.66961e9 0.860596
\(237\) −1.39792e9 + 1.39792e9i −0.443086 + 0.443086i
\(238\) −1.36405e9 1.36405e9i −0.425131 0.425131i
\(239\) 2.78614e9i 0.853907i −0.904274 0.426954i \(-0.859587\pi\)
0.904274 0.426954i \(-0.140413\pi\)
\(240\) −4.25351e8 1.28331e9i −0.128204 0.386800i
\(241\) −1.82461e9 −0.540881 −0.270441 0.962737i \(-0.587169\pi\)
−0.270441 + 0.962737i \(0.587169\pi\)
\(242\) −3.25662e9 + 3.25662e9i −0.949523 + 0.949523i
\(243\) 2.19842e9 + 2.19842e9i 0.630500 + 0.630500i
\(244\) 2.93795e9i 0.828866i
\(245\) 1.65517e9 3.29634e9i 0.459386 0.914887i
\(246\) −3.44356e8 −0.0940301
\(247\) 1.33905e9 1.33905e9i 0.359757 0.359757i
\(248\) 7.71943e8 + 7.71943e8i 0.204070 + 0.204070i
\(249\) 1.33864e8i 0.0348230i
\(250\) 4.31690e9 + 3.02125e9i 1.10513 + 0.773440i
\(251\) −1.08818e9 −0.274162 −0.137081 0.990560i \(-0.543772\pi\)
−0.137081 + 0.990560i \(0.543772\pi\)
\(252\) 2.90554e9 2.90554e9i 0.720484 0.720484i
\(253\) −1.34051e7 1.34051e7i −0.00327181 0.00327181i
\(254\) 8.83700e9i 2.12310i
\(255\) 4.20272e8 + 2.11028e8i 0.0993962 + 0.0499091i
\(256\) 5.40490e9 1.25843
\(257\) −1.38793e9 + 1.38793e9i −0.318151 + 0.318151i −0.848057 0.529905i \(-0.822227\pi\)
0.529905 + 0.848057i \(0.322227\pi\)
\(258\) 6.66588e8 + 6.66588e8i 0.150445 + 0.150445i
\(259\) 3.76218e8i 0.0836066i
\(260\) −4.67896e9 + 1.55083e9i −1.02390 + 0.339369i
\(261\) −6.02879e9 −1.29918
\(262\) −2.81579e9 + 2.81579e9i −0.597578 + 0.597578i
\(263\) 3.30796e9 + 3.30796e9i 0.691412 + 0.691412i 0.962543 0.271130i \(-0.0873974\pi\)
−0.271130 + 0.962543i \(0.587397\pi\)
\(264\) 2.81534e7i 0.00579582i
\(265\) 5.22870e8 + 1.57753e9i 0.106025 + 0.319885i
\(266\) −3.71343e9 −0.741735
\(267\) 1.62176e9 1.62176e9i 0.319111 0.319111i
\(268\) 2.00177e9 + 2.00177e9i 0.388039 + 0.388039i
\(269\) 4.82096e9i 0.920713i 0.887734 + 0.460356i \(0.152278\pi\)
−0.887734 + 0.460356i \(0.847722\pi\)
\(270\) −2.13992e9 + 4.26174e9i −0.402663 + 0.801922i
\(271\) −5.54038e9 −1.02722 −0.513609 0.858025i \(-0.671692\pi\)
−0.513609 + 0.858025i \(0.671692\pi\)
\(272\) −1.39203e9 + 1.39203e9i −0.254316 + 0.254316i
\(273\) −2.61070e9 2.61070e9i −0.470010 0.470010i
\(274\) 4.88668e9i 0.866985i
\(275\) −2.29085e8 3.07616e8i −0.0400558 0.0537871i
\(276\) −1.16472e8 −0.0200718
\(277\) 6.27804e9 6.27804e9i 1.06636 1.06636i 0.0687272 0.997635i \(-0.478106\pi\)
0.997635 0.0687272i \(-0.0218938\pi\)
\(278\) 4.36927e9 + 4.36927e9i 0.731526 + 0.731526i
\(279\) 6.27766e9i 1.03605i
\(280\) −1.90240e9 9.55238e8i −0.309506 0.155410i
\(281\) 9.60308e9 1.54023 0.770114 0.637906i \(-0.220199\pi\)
0.770114 + 0.637906i \(0.220199\pi\)
\(282\) 2.52566e9 2.52566e9i 0.399373 0.399373i
\(283\) 2.69661e9 + 2.69661e9i 0.420409 + 0.420409i 0.885344 0.464936i \(-0.153923\pi\)
−0.464936 + 0.885344i \(0.653923\pi\)
\(284\) 5.91696e9i 0.909548i
\(285\) 8.59312e8 2.84818e8i 0.130248 0.0431706i
\(286\) 7.96637e8 0.119068
\(287\) −1.34019e9 + 1.34019e9i −0.197533 + 0.197533i
\(288\) −5.54823e9 5.54823e9i −0.806463 0.806463i
\(289\) 6.29097e9i 0.901833i
\(290\) −4.46187e9 1.34617e10i −0.630849 1.90331i
\(291\) 7.99238e8 0.111456
\(292\) 2.34086e9 2.34086e9i 0.321992 0.321992i
\(293\) −6.28799e9 6.28799e9i −0.853182 0.853182i 0.137342 0.990524i \(-0.456144\pi\)
−0.990524 + 0.137342i \(0.956144\pi\)
\(294\) 3.66245e9i 0.490210i
\(295\) −3.56875e9 + 7.10731e9i −0.471224 + 0.938464i
\(296\) 1.09836e8 0.0143080
\(297\) 2.45457e8 2.45457e8i 0.0315464 0.0315464i
\(298\) 2.82167e9 + 2.82167e9i 0.357800 + 0.357800i
\(299\) 7.25825e8i 0.0908129i
\(300\) −2.33160e9 3.41165e8i −0.287852 0.0421192i
\(301\) 5.18856e9 0.632093
\(302\) −9.41114e9 + 9.41114e9i −1.13140 + 1.13140i
\(303\) −6.14981e8 6.14981e8i −0.0729611 0.0729611i
\(304\) 3.78961e9i 0.443711i
\(305\) 7.82171e9 + 3.92746e9i 0.903863 + 0.453850i
\(306\) 3.23854e9 0.369371
\(307\) −4.34115e8 + 4.34115e8i −0.0488710 + 0.0488710i −0.731120 0.682249i \(-0.761002\pi\)
0.682249 + 0.731120i \(0.261002\pi\)
\(308\) −4.97519e8 4.97519e8i −0.0552850 0.0552850i
\(309\) 1.74109e9i 0.190979i
\(310\) 1.40174e10 4.64606e9i 1.51783 0.503082i
\(311\) −5.29907e9 −0.566445 −0.283223 0.959054i \(-0.591404\pi\)
−0.283223 + 0.959054i \(0.591404\pi\)
\(312\) −7.62190e8 + 7.62190e8i −0.0804349 + 0.0804349i
\(313\) −5.51999e9 5.51999e9i −0.575123 0.575123i 0.358433 0.933556i \(-0.383311\pi\)
−0.933556 + 0.358433i \(0.883311\pi\)
\(314\) 8.88202e9i 0.913678i
\(315\) 3.85129e9 + 1.16196e10i 0.391169 + 1.18018i
\(316\) −1.44244e10 −1.44660
\(317\) −3.86039e9 + 3.86039e9i −0.382291 + 0.382291i −0.871927 0.489636i \(-0.837130\pi\)
0.489636 + 0.871927i \(0.337130\pi\)
\(318\) −1.16684e9 1.16684e9i −0.114104 0.114104i
\(319\) 1.03232e9i 0.0996899i
\(320\) 2.88122e9 5.73808e9i 0.274775 0.547226i
\(321\) −3.59775e9 −0.338853
\(322\) −1.00642e9 + 1.00642e9i −0.0936174 + 0.0936174i
\(323\) −9.32115e8 9.32115e8i −0.0856366 0.0856366i
\(324\) 5.76029e9i 0.522715i
\(325\) 2.12606e9 1.45300e10i 0.190564 1.30236i
\(326\) 2.33571e10 2.06799
\(327\) −9.13526e8 + 9.13526e8i −0.0798969 + 0.0798969i
\(328\) 3.91267e8 + 3.91267e8i 0.0338047 + 0.0338047i
\(329\) 1.96591e10i 1.67796i
\(330\) 3.40336e8 + 1.70891e8i 0.0286981 + 0.0144100i
\(331\) −4.43747e9 −0.369678 −0.184839 0.982769i \(-0.559176\pi\)
−0.184839 + 0.982769i \(0.559176\pi\)
\(332\) −6.90636e8 + 6.90636e8i −0.0568456 + 0.0568456i
\(333\) −4.46610e8 4.46610e8i −0.0363204 0.0363204i
\(334\) 1.29276e10i 1.03880i
\(335\) −8.00532e9 + 2.65335e9i −0.635622 + 0.210676i
\(336\) 7.38848e9 0.579693
\(337\) 5.03851e9 5.03851e9i 0.390645 0.390645i −0.484272 0.874917i \(-0.660916\pi\)
0.874917 + 0.484272i \(0.160916\pi\)
\(338\) 9.11830e9 + 9.11830e9i 0.698630 + 0.698630i
\(339\) 3.75744e8i 0.0284507i
\(340\) 1.07954e9 + 3.25703e9i 0.0807834 + 0.243728i
\(341\) −1.07493e9 −0.0794995
\(342\) 4.40823e9 4.40823e9i 0.322225 0.322225i
\(343\) 3.30601e8 + 3.30601e8i 0.0238852 + 0.0238852i
\(344\) 1.51479e9i 0.108173i
\(345\) 1.55701e8 3.10085e8i 0.0109904 0.0218879i
\(346\) −3.75151e10 −2.61759
\(347\) −2.80674e9 + 2.80674e9i −0.193590 + 0.193590i −0.797246 0.603655i \(-0.793710\pi\)
0.603655 + 0.797246i \(0.293710\pi\)
\(348\) 4.48473e9 + 4.48473e9i 0.305787 + 0.305787i
\(349\) 1.32267e10i 0.891561i 0.895142 + 0.445780i \(0.147074\pi\)
−0.895142 + 0.445780i \(0.852926\pi\)
\(350\) −2.30951e10 + 1.71992e10i −1.53903 + 1.14613i
\(351\) 1.32904e10 0.875608
\(352\) −9.50031e8 + 9.50031e8i −0.0618824 + 0.0618824i
\(353\) −1.16376e9 1.16376e9i −0.0749489 0.0749489i 0.668639 0.743587i \(-0.266877\pi\)
−0.743587 + 0.668639i \(0.766877\pi\)
\(354\) 7.89669e9i 0.502843i
\(355\) −1.57528e10 7.90983e9i −0.991845 0.498028i
\(356\) 1.67341e10 1.04184
\(357\) −1.81731e9 + 1.81731e9i −0.111881 + 0.111881i
\(358\) −6.70430e9 6.70430e9i −0.408151 0.408151i
\(359\) 1.99414e10i 1.20054i 0.799797 + 0.600270i \(0.204940\pi\)
−0.799797 + 0.600270i \(0.795060\pi\)
\(360\) 3.39231e9 1.12438e9i 0.201969 0.0669425i
\(361\) 1.44460e10 0.850588
\(362\) 2.57336e10 2.57336e10i 1.49853 1.49853i
\(363\) 4.33877e9 + 4.33877e9i 0.249885 + 0.249885i
\(364\) 2.69385e10i 1.53450i
\(365\) 3.10282e9 + 9.36138e9i 0.174817 + 0.527434i
\(366\) −8.69043e9 −0.484303
\(367\) 2.26918e10 2.26918e10i 1.25085 1.25085i 0.295506 0.955341i \(-0.404512\pi\)
0.955341 0.295506i \(-0.0954881\pi\)
\(368\) 1.02707e9 + 1.02707e9i 0.0560026 + 0.0560026i
\(369\) 3.18190e9i 0.171625i
\(370\) 6.66704e8 1.32777e9i 0.0355735 0.0708461i
\(371\) −9.08241e9 −0.479408
\(372\) −4.66987e9 + 4.66987e9i −0.243856 + 0.243856i
\(373\) 1.70421e10 + 1.70421e10i 0.880417 + 0.880417i 0.993577 0.113160i \(-0.0360971\pi\)
−0.113160 + 0.993577i \(0.536097\pi\)
\(374\) 5.54540e8i 0.0283430i
\(375\) 4.02519e9 5.75138e9i 0.203545 0.290835i
\(376\) −5.73945e9 −0.287157
\(377\) −2.79477e10 + 2.79477e10i −1.38351 + 1.38351i
\(378\) −1.84283e10 1.84283e10i −0.902649 0.902649i
\(379\) 2.63026e10i 1.27480i −0.770534 0.637399i \(-0.780010\pi\)
0.770534 0.637399i \(-0.219990\pi\)
\(380\) 5.90283e9 + 2.96395e9i 0.283091 + 0.142147i
\(381\) −1.17735e10 −0.558733
\(382\) −2.32383e10 + 2.32383e10i −1.09132 + 1.09132i
\(383\) 2.24947e10 + 2.24947e10i 1.04541 + 1.04541i 0.998919 + 0.0464865i \(0.0148024\pi\)
0.0464865 + 0.998919i \(0.485198\pi\)
\(384\) 3.69702e9i 0.170030i
\(385\) 1.98964e9 6.59463e8i 0.0905588 0.0300156i
\(386\) −5.99317e9 −0.269965
\(387\) −6.15936e9 + 6.15936e9i −0.274595 + 0.274595i
\(388\) 4.12345e9 + 4.12345e9i 0.181943 + 0.181943i
\(389\) 5.72221e9i 0.249900i −0.992163 0.124950i \(-0.960123\pi\)
0.992163 0.124950i \(-0.0398770\pi\)
\(390\) 4.58736e9 + 1.38403e10i 0.198292 + 0.598257i
\(391\) −5.05248e8 −0.0216171
\(392\) 4.16137e9 4.16137e9i 0.176235 0.176235i
\(393\) 3.75145e9 + 3.75145e9i 0.157264 + 0.157264i
\(394\) 3.82715e10i 1.58814i
\(395\) 1.92826e10 3.84021e10i 0.792094 1.57749i
\(396\) 1.18121e9 0.0480339
\(397\) 2.97350e9 2.97350e9i 0.119703 0.119703i −0.644718 0.764421i \(-0.723025\pi\)
0.764421 + 0.644718i \(0.223025\pi\)
\(398\) −1.67887e10 1.67887e10i −0.669089 0.669089i
\(399\) 4.94737e9i 0.195201i
\(400\) 1.75520e10 + 2.35689e10i 0.685625 + 0.920660i
\(401\) −1.77762e10 −0.687481 −0.343741 0.939065i \(-0.611694\pi\)
−0.343741 + 0.939065i \(0.611694\pi\)
\(402\) 5.92124e9 5.92124e9i 0.226730 0.226730i
\(403\) −2.91014e10 2.91014e10i −1.10330 1.10330i
\(404\) 6.34567e9i 0.238205i
\(405\) −1.53357e10 7.70039e9i −0.570010 0.286215i
\(406\) 7.75040e10 2.85246
\(407\) −7.64737e7 + 7.64737e7i −0.00278698 + 0.00278698i
\(408\) 5.30561e8 + 5.30561e8i 0.0191467 + 0.0191467i
\(409\) 2.57868e10i 0.921519i 0.887525 + 0.460759i \(0.152423\pi\)
−0.887525 + 0.460759i \(0.847577\pi\)
\(410\) 7.10487e9 2.35490e9i 0.251432 0.0833369i
\(411\) −6.51048e9 −0.228163
\(412\) −8.98267e9 + 8.98267e9i −0.311757 + 0.311757i
\(413\) −3.07330e10 3.07330e10i −1.05634 1.05634i
\(414\) 2.38945e9i 0.0813387i
\(415\) −9.15439e8 2.76193e9i −0.0308629 0.0931152i
\(416\) −5.14399e10 −1.71762
\(417\) 5.82114e9 5.82114e9i 0.192515 0.192515i
\(418\) −7.54827e8 7.54827e8i −0.0247254 0.0247254i
\(419\) 2.80387e9i 0.0909707i 0.998965 + 0.0454853i \(0.0144834\pi\)
−0.998965 + 0.0454853i \(0.985517\pi\)
\(420\) 5.77871e9 1.15086e10i 0.185709 0.369848i
\(421\) 3.39054e10 1.07929 0.539647 0.841891i \(-0.318558\pi\)
0.539647 + 0.841891i \(0.318558\pi\)
\(422\) 4.00919e10 4.00919e10i 1.26417 1.26417i
\(423\) 2.33374e10 + 2.33374e10i 0.728940 + 0.728940i
\(424\) 2.65159e9i 0.0820433i
\(425\) −1.01143e10 1.47995e9i −0.310014 0.0453619i
\(426\) 1.75024e10 0.531445
\(427\) −3.38221e10 + 3.38221e10i −1.01740 + 1.01740i
\(428\) −1.85616e10 1.85616e10i −0.553148 0.553148i
\(429\) 1.06135e9i 0.0313351i
\(430\) −1.83118e10 9.19477e9i −0.535620 0.268947i
\(431\) 4.74314e10 1.37454 0.687269 0.726403i \(-0.258810\pi\)
0.687269 + 0.726403i \(0.258810\pi\)
\(432\) −1.88064e10 + 1.88064e10i −0.539971 + 0.539971i
\(433\) 2.85545e10 + 2.85545e10i 0.812313 + 0.812313i 0.984980 0.172667i \(-0.0552384\pi\)
−0.172667 + 0.984980i \(0.555238\pi\)
\(434\) 8.07035e10i 2.27475i
\(435\) −1.79349e10 + 5.94452e9i −0.500891 + 0.166020i
\(436\) −9.42619e9 −0.260850
\(437\) −6.87732e8 + 6.87732e8i −0.0188579 + 0.0188579i
\(438\) −6.92427e9 6.92427e9i −0.188138 0.188138i
\(439\) 4.70888e10i 1.26783i −0.773404 0.633913i \(-0.781448\pi\)
0.773404 0.633913i \(-0.218552\pi\)
\(440\) −1.92529e8 5.80870e8i −0.00513671 0.0154977i
\(441\) −3.38415e10 −0.894737
\(442\) 1.50129e10 1.50129e10i 0.393347 0.393347i
\(443\) −2.13908e10 2.13908e10i −0.555407 0.555407i 0.372589 0.927996i \(-0.378470\pi\)
−0.927996 + 0.372589i \(0.878470\pi\)
\(444\) 6.64453e8i 0.0170975i
\(445\) −2.23702e10 + 4.45513e10i −0.570467 + 1.13611i
\(446\) −6.83614e10 −1.72771
\(447\) 3.75928e9 3.75928e9i 0.0941619 0.0941619i
\(448\) 2.48122e10 + 2.48122e10i 0.615962 + 0.615962i
\(449\) 1.99035e9i 0.0489717i −0.999700 0.0244858i \(-0.992205\pi\)
0.999700 0.0244858i \(-0.00779487\pi\)
\(450\) 6.99909e9 4.78334e10i 0.170683 1.16649i
\(451\) −5.44841e8 −0.0131693
\(452\) 1.93855e9 1.93855e9i 0.0464434 0.0464434i
\(453\) 1.25384e10 + 1.25384e10i 0.297748 + 0.297748i
\(454\) 8.74745e10i 2.05901i
\(455\) 7.17184e10 + 3.60115e10i 1.67334 + 0.840224i
\(456\) 1.44438e9 0.0334057
\(457\) 1.28799e10 1.28799e10i 0.295290 0.295290i −0.543876 0.839166i \(-0.683044\pi\)
0.839166 + 0.543876i \(0.183044\pi\)
\(458\) 6.43548e10 + 6.43548e10i 1.46258 + 1.46258i
\(459\) 9.25147e9i 0.208430i
\(460\) 2.40310e9 7.96503e8i 0.0536710 0.0177892i
\(461\) 2.95032e10 0.653229 0.326615 0.945158i \(-0.394092\pi\)
0.326615 + 0.945158i \(0.394092\pi\)
\(462\) −1.47166e9 + 1.47166e9i −0.0323028 + 0.0323028i
\(463\) −2.68794e10 2.68794e10i −0.584919 0.584919i 0.351332 0.936251i \(-0.385729\pi\)
−0.936251 + 0.351332i \(0.885729\pi\)
\(464\) 7.90941e10i 1.70636i
\(465\) −6.18991e9 1.86753e10i −0.132395 0.399444i
\(466\) −4.25545e10 −0.902407
\(467\) 2.41860e10 2.41860e10i 0.508507 0.508507i −0.405561 0.914068i \(-0.632924\pi\)
0.914068 + 0.405561i \(0.132924\pi\)
\(468\) 3.19787e10 + 3.19787e10i 0.666619 + 0.666619i
\(469\) 4.60895e10i 0.952601i
\(470\) −3.48384e10 + 6.93822e10i −0.713949 + 1.42186i
\(471\) −1.18334e10 −0.240451
\(472\) −8.97244e9 + 8.97244e9i −0.180777 + 0.180777i
\(473\) 1.05468e9 + 1.05468e9i 0.0210705 + 0.0210705i
\(474\) 4.26672e10i 0.845242i
\(475\) −1.57819e10 + 1.17529e10i −0.310016 + 0.230872i
\(476\) −1.87519e10 −0.365273
\(477\) 1.07818e10 1.07818e10i 0.208265 0.208265i
\(478\) −4.25192e10 4.25192e10i −0.814467 0.814467i
\(479\) 1.00060e11i 1.90073i 0.311144 + 0.950363i \(0.399288\pi\)
−0.311144 + 0.950363i \(0.600712\pi\)
\(480\) −2.19760e10 1.10347e10i −0.413984 0.207871i
\(481\) −4.14071e9 −0.0773560
\(482\) −2.78454e10 + 2.78454e10i −0.515899 + 0.515899i
\(483\) 1.34085e9 + 1.34085e9i 0.0246372 + 0.0246372i
\(484\) 4.47694e10i 0.815831i
\(485\) −1.64902e10 + 5.46564e9i −0.298029 + 0.0987812i
\(486\) 6.71001e10 1.20276
\(487\) −4.35298e10 + 4.35298e10i −0.773875 + 0.773875i −0.978782 0.204907i \(-0.934311\pi\)
0.204907 + 0.978782i \(0.434311\pi\)
\(488\) 9.87431e9 + 9.87431e9i 0.174112 + 0.174112i
\(489\) 3.11185e10i 0.544230i
\(490\) −2.50459e10 7.55649e10i −0.434463 1.31080i
\(491\) −1.74821e10 −0.300794 −0.150397 0.988626i \(-0.548055\pi\)
−0.150397 + 0.988626i \(0.548055\pi\)
\(492\) −2.36697e9 + 2.36697e9i −0.0403954 + 0.0403954i
\(493\) 1.94544e10 + 1.94544e10i 0.329330 + 0.329330i
\(494\) 4.08705e10i 0.686282i
\(495\) −1.57905e9 + 3.14475e9i −0.0263012 + 0.0523801i
\(496\) 8.23592e10 1.36077
\(497\) 6.81171e10 6.81171e10i 1.11643 1.11643i
\(498\) 2.04290e9 + 2.04290e9i 0.0332147 + 0.0332147i
\(499\) 6.18997e10i 0.998358i 0.866499 + 0.499179i \(0.166365\pi\)
−0.866499 + 0.499179i \(0.833635\pi\)
\(500\) 5.04396e10 8.90581e9i 0.807033 0.142493i
\(501\) 1.72234e10 0.273380
\(502\) −1.66068e10 + 1.66068e10i −0.261499 + 0.261499i
\(503\) −5.48962e10 5.48962e10i −0.857571 0.857571i 0.133480 0.991051i \(-0.457385\pi\)
−0.991051 + 0.133480i \(0.957385\pi\)
\(504\) 1.95308e10i 0.302689i
\(505\) 1.68941e10 + 8.48292e9i 0.259759 + 0.130431i
\(506\) −4.09150e8 −0.00624138
\(507\) 1.21482e10 1.21482e10i 0.183857 0.183857i
\(508\) −6.07420e10 6.07420e10i −0.912083 0.912083i
\(509\) 2.78975e9i 0.0415618i 0.999784 + 0.0207809i \(0.00661524\pi\)
−0.999784 + 0.0207809i \(0.993385\pi\)
\(510\) 9.63427e9 3.19327e9i 0.142409 0.0472014i
\(511\) −5.38969e10 −0.790460
\(512\) 5.92097e10 5.92097e10i 0.861615 0.861615i
\(513\) −1.25929e10 1.25929e10i −0.181826 0.181826i
\(514\) 4.23623e10i 0.606914i
\(515\) −1.19065e10 3.59227e10i −0.169261 0.510670i
\(516\) 9.16373e9 0.129263
\(517\) 3.99611e9 3.99611e9i 0.0559339 0.0559339i
\(518\) 5.74146e9 + 5.74146e9i 0.0797450 + 0.0797450i
\(519\) 4.99810e10i 0.688868i
\(520\) 1.05135e10 2.09381e10i 0.143791 0.286367i
\(521\) −7.48087e10 −1.01532 −0.507658 0.861559i \(-0.669489\pi\)
−0.507658 + 0.861559i \(0.669489\pi\)
\(522\) −9.20053e10 + 9.20053e10i −1.23917 + 1.23917i
\(523\) −1.13284e10 1.13284e10i −0.151412 0.151412i 0.627336 0.778748i \(-0.284145\pi\)
−0.778748 + 0.627336i \(0.784145\pi\)
\(524\) 3.87093e10i 0.513440i
\(525\) 2.29143e10 + 3.07694e10i 0.301626 + 0.405025i
\(526\) 1.00966e11 1.31896
\(527\) −2.02575e10 + 2.02575e10i −0.262630 + 0.262630i
\(528\) 1.50185e9 + 1.50185e9i 0.0193238 + 0.0193238i
\(529\) 7.79382e10i 0.995240i
\(530\) 3.20542e10 + 1.60951e10i 0.406239 + 0.203982i
\(531\) 7.29665e10 0.917794
\(532\) −2.55247e10 + 2.55247e10i −0.318650 + 0.318650i
\(533\) −1.47503e10 1.47503e10i −0.182765 0.182765i
\(534\) 4.94994e10i 0.608744i
\(535\) 7.42301e10 2.46035e10i 0.906077 0.300318i
\(536\) −1.34557e10 −0.163023
\(537\) −8.93208e9 + 8.93208e9i −0.107413 + 0.107413i
\(538\) 7.35726e10 + 7.35726e10i 0.878187 + 0.878187i
\(539\) 5.79473e9i 0.0686560i
\(540\) 1.45846e10 + 4.40025e10i 0.171522 + 0.517490i
\(541\) −1.41419e11 −1.65090 −0.825448 0.564479i \(-0.809077\pi\)
−0.825448 + 0.564479i \(0.809077\pi\)
\(542\) −8.45517e10 + 8.45517e10i −0.979773 + 0.979773i
\(543\) −3.42847e10 3.42847e10i −0.394367 0.394367i
\(544\) 3.58074e10i 0.408863i
\(545\) 1.26010e10 2.50954e10i 0.142830 0.284452i
\(546\) −7.96839e10 −0.896602
\(547\) −2.99290e10 + 2.99290e10i −0.334305 + 0.334305i −0.854219 0.519914i \(-0.825964\pi\)
0.519914 + 0.854219i \(0.325964\pi\)
\(548\) −3.35891e10 3.35891e10i −0.372457 0.372457i
\(549\) 8.03008e10i 0.883956i
\(550\) −8.19059e9 1.19846e9i −0.0895086 0.0130971i
\(551\) 5.29619e10 0.574589
\(552\) 3.91458e8 3.91458e8i 0.00421627 0.00421627i
\(553\) 1.66056e11 + 1.66056e11i 1.77564 + 1.77564i
\(554\) 1.91618e11i 2.03422i
\(555\) −1.76898e9 8.88245e8i −0.0186445 0.00936183i
\(556\) 6.00653e10 0.628527
\(557\) 5.59400e10 5.59400e10i 0.581168 0.581168i −0.354056 0.935224i \(-0.615198\pi\)
0.935224 + 0.354056i \(0.115198\pi\)
\(558\) −9.58034e10 9.58034e10i −0.988199 0.988199i
\(559\) 5.71061e10i 0.584837i
\(560\) −1.52442e11 + 5.05266e10i −1.55007 + 0.513769i
\(561\) −7.38809e8 −0.00745900
\(562\) 1.46553e11 1.46553e11i 1.46909 1.46909i
\(563\) 5.76816e9 + 5.76816e9i 0.0574121 + 0.0574121i 0.735230 0.677818i \(-0.237074\pi\)
−0.677818 + 0.735230i \(0.737074\pi\)
\(564\) 3.47208e10i 0.343141i
\(565\) 2.56955e9 + 7.75249e9i 0.0252153 + 0.0760759i
\(566\) 8.23058e10 0.801982
\(567\) 6.63135e10 6.63135e10i 0.641608 0.641608i
\(568\) −1.98867e10 1.98867e10i −0.191059 0.191059i
\(569\) 1.53674e11i 1.46606i 0.680196 + 0.733031i \(0.261895\pi\)
−0.680196 + 0.733031i \(0.738105\pi\)
\(570\) 8.76735e9 1.74606e10i 0.0830556 0.165409i
\(571\) −3.33206e10 −0.313450 −0.156725 0.987642i \(-0.550094\pi\)
−0.156725 + 0.987642i \(0.550094\pi\)
\(572\) 5.47577e9 5.47577e9i 0.0511518 0.0511518i
\(573\) 3.09602e10 + 3.09602e10i 0.287201 + 0.287201i
\(574\) 4.09054e10i 0.376819i
\(575\) −1.09194e9 + 7.46255e9i −0.00998908 + 0.0682678i
\(576\) −5.89094e10 −0.535173
\(577\) 6.01902e10 6.01902e10i 0.543029 0.543029i −0.381387 0.924416i \(-0.624553\pi\)
0.924416 + 0.381387i \(0.124553\pi\)
\(578\) 9.60065e10 + 9.60065e10i 0.860180 + 0.860180i
\(579\) 7.98465e9i 0.0710464i
\(580\) −1.23200e11 6.18614e10i −1.08867 0.546648i
\(581\) 1.59015e10 0.139551
\(582\) 1.21972e10 1.21972e10i 0.106308 0.106308i
\(583\) −1.84618e9 1.84618e9i −0.0159808 0.0159808i
\(584\) 1.57351e10i 0.135275i
\(585\) −1.27887e11 + 4.23879e10i −1.09195 + 0.361925i
\(586\) −1.91922e11 −1.62755
\(587\) −1.49796e11 + 1.49796e11i −1.26168 + 1.26168i −0.311397 + 0.950280i \(0.600797\pi\)
−0.950280 + 0.311397i \(0.899203\pi\)
\(588\) 2.51742e10 + 2.51742e10i 0.210594 + 0.210594i
\(589\) 5.51482e10i 0.458216i
\(590\) 5.40021e10 + 1.62927e11i 0.445659 + 1.34458i
\(591\) 5.09887e10 0.417950
\(592\) 5.85925e9 5.85925e9i 0.0477040 0.0477040i
\(593\) −9.15532e10 9.15532e10i −0.740381 0.740381i 0.232271 0.972651i \(-0.425384\pi\)
−0.972651 + 0.232271i \(0.925384\pi\)
\(594\) 7.49184e9i 0.0601787i
\(595\) 2.50676e10 4.99233e10i 0.200007 0.398323i
\(596\) 3.87901e10 0.307422
\(597\) −2.23674e10 + 2.23674e10i −0.176083 + 0.176083i
\(598\) −1.10768e10 1.10768e10i −0.0866185 0.0866185i
\(599\) 1.74821e11i 1.35796i −0.734158 0.678979i \(-0.762423\pi\)
0.734158 0.678979i \(-0.237577\pi\)
\(600\) 8.98307e9 6.68978e9i 0.0693138 0.0516187i
\(601\) 6.55639e10 0.502536 0.251268 0.967918i \(-0.419153\pi\)
0.251268 + 0.967918i \(0.419153\pi\)
\(602\) 7.91827e10 7.91827e10i 0.602899 0.602899i
\(603\) 5.47130e10 + 5.47130e10i 0.413830 + 0.413830i
\(604\) 1.29377e11i 0.972096i
\(605\) −1.19190e11 5.98480e10i −0.889648 0.446713i
\(606\) −1.87705e10 −0.139182
\(607\) 8.22746e10 8.22746e10i 0.606054 0.606054i −0.335859 0.941912i \(-0.609026\pi\)
0.941912 + 0.335859i \(0.109026\pi\)
\(608\) 4.87402e10 + 4.87402e10i 0.356676 + 0.356676i
\(609\) 1.03258e11i 0.750679i
\(610\) 1.79304e11 5.94302e10i 1.29500 0.429228i
\(611\) 2.16371e11 1.55251
\(612\) 2.22604e10 2.22604e10i 0.158682 0.158682i
\(613\) 3.09061e10 + 3.09061e10i 0.218878 + 0.218878i 0.808026 0.589148i \(-0.200536\pi\)
−0.589148 + 0.808026i \(0.700536\pi\)
\(614\) 1.32501e10i 0.0932276i
\(615\) −3.13742e9 9.46577e9i −0.0219317 0.0661691i
\(616\) 3.34428e9 0.0232263
\(617\) −1.72051e11 + 1.72051e11i −1.18718 + 1.18718i −0.209337 + 0.977844i \(0.567130\pi\)
−0.977844 + 0.209337i \(0.932870\pi\)
\(618\) 2.65707e10 + 2.65707e10i 0.182158 + 0.182158i
\(619\) 2.58123e11i 1.75818i −0.476652 0.879092i \(-0.658150\pi\)
0.476652 0.879092i \(-0.341850\pi\)
\(620\) 6.44151e10 1.28286e11i 0.435934 0.868182i
\(621\) −6.82591e9 −0.0458980
\(622\) −8.08691e10 + 8.08691e10i −0.540283 + 0.540283i
\(623\) −1.92646e11 1.92646e11i −1.27881 1.27881i
\(624\) 8.13186e10i 0.536354i
\(625\) −4.37179e10 + 1.46191e11i −0.286510 + 0.958077i
\(626\) −1.68481e11 −1.09712
\(627\) −1.00565e9 + 1.00565e9i −0.00650694 + 0.00650694i
\(628\) −6.10515e10 6.10515e10i −0.392516 0.392516i
\(629\) 2.88235e9i 0.0184138i
\(630\) 2.36101e11 + 1.18552e11i 1.49877 + 0.752567i
\(631\) −2.49622e11 −1.57458 −0.787292 0.616580i \(-0.788518\pi\)
−0.787292 + 0.616580i \(0.788518\pi\)
\(632\) 4.84797e10 4.84797e10i 0.303873 0.303873i
\(633\) −5.34141e10 5.34141e10i −0.332691 0.332691i
\(634\) 1.17827e11i 0.729267i
\(635\) 2.42914e11 8.05136e10i 1.49403 0.495193i
\(636\) −1.60408e10 −0.0980387
\(637\) −1.56879e11 + 1.56879e11i −0.952814 + 0.952814i
\(638\) 1.57542e10 + 1.57542e10i 0.0950854 + 0.0950854i
\(639\) 1.61724e11i 0.970000i
\(640\) 2.52823e10 + 7.62781e10i 0.150694 + 0.454653i
\(641\) 1.95384e11 1.15733 0.578666 0.815565i \(-0.303573\pi\)
0.578666 + 0.815565i \(0.303573\pi\)
\(642\) −5.49053e10 + 5.49053e10i −0.323202 + 0.323202i
\(643\) 4.31377e10 + 4.31377e10i 0.252355 + 0.252355i 0.821936 0.569580i \(-0.192894\pi\)
−0.569580 + 0.821936i \(0.692894\pi\)
\(644\) 1.38355e10i 0.0804362i
\(645\) −1.22501e10 + 2.43967e10i −0.0707785 + 0.140959i
\(646\) −2.84500e10 −0.163363
\(647\) −5.34194e10 + 5.34194e10i −0.304847 + 0.304847i −0.842907 0.538060i \(-0.819158\pi\)
0.538060 + 0.842907i \(0.319158\pi\)
\(648\) −1.93601e10 1.93601e10i −0.109801 0.109801i
\(649\) 1.24942e10i 0.0704252i
\(650\) −1.89296e11 2.54188e11i −1.06045 1.42397i
\(651\) 1.07521e11 0.598643
\(652\) 1.60547e11 1.60547e11i 0.888409 0.888409i
\(653\) 1.68747e11 + 1.68747e11i 0.928074 + 0.928074i 0.997581 0.0695077i \(-0.0221429\pi\)
−0.0695077 + 0.997581i \(0.522143\pi\)
\(654\) 2.78826e10i 0.152413i
\(655\) −1.03056e11 5.17467e10i −0.559896 0.281137i
\(656\) 4.17445e10 0.225416
\(657\) 6.39812e10 6.39812e10i 0.343392 0.343392i
\(658\) −3.00018e11 3.00018e11i −1.60046 1.60046i
\(659\) 2.23769e11i 1.18647i 0.805028 + 0.593237i \(0.202150\pi\)
−0.805028 + 0.593237i \(0.797850\pi\)
\(660\) 3.51397e9 1.16470e9i 0.0185192 0.00613818i
\(661\) 1.49226e11 0.781700 0.390850 0.920454i \(-0.372181\pi\)
0.390850 + 0.920454i \(0.372181\pi\)
\(662\) −6.77202e10 + 6.77202e10i −0.352603 + 0.352603i
\(663\) −2.00016e10 2.00016e10i −0.103517 0.103517i
\(664\) 4.64240e9i 0.0238820i
\(665\) −3.38330e10 1.02076e11i −0.173003 0.521960i
\(666\) −1.36314e10 −0.0692858
\(667\) 1.43539e10 1.43539e10i 0.0725212 0.0725212i
\(668\) 8.88594e10 + 8.88594e10i 0.446270 + 0.446270i
\(669\) 9.10773e10i 0.454680i
\(670\) −8.16763e10 + 1.62662e11i −0.405319 + 0.807210i
\(671\) −1.37500e10 −0.0678287
\(672\) 9.50272e10 9.50272e10i 0.465984 0.465984i
\(673\) −1.20787e11 1.20787e11i −0.588791 0.588791i 0.348513 0.937304i \(-0.386687\pi\)
−0.937304 + 0.348513i \(0.886687\pi\)
\(674\) 1.53785e11i 0.745204i
\(675\) −1.36645e11 1.99942e10i −0.658231 0.0963137i
\(676\) 1.25351e11 0.600263
\(677\) 1.59570e11 1.59570e11i 0.759621 0.759621i −0.216632 0.976253i \(-0.569507\pi\)
0.976253 + 0.216632i \(0.0695072\pi\)
\(678\) −5.73423e9 5.73423e9i −0.0271367 0.0271367i
\(679\) 9.49399e10i 0.446652i
\(680\) −1.45750e10 7.31845e9i −0.0681668 0.0342281i
\(681\) −1.16542e11 −0.541867
\(682\) −1.64046e10 + 1.64046e10i −0.0758276 + 0.0758276i
\(683\) 2.73157e11 + 2.73157e11i 1.25525 + 1.25525i 0.953336 + 0.301913i \(0.0976252\pi\)
0.301913 + 0.953336i \(0.402375\pi\)
\(684\) 6.06008e10i 0.276856i
\(685\) 1.34327e11 4.45224e10i 0.610098 0.202216i
\(686\) 1.00906e10 0.0455639
\(687\) 8.57393e10 8.57393e10i 0.384905 0.384905i
\(688\) −8.08071e10 8.08071e10i −0.360658 0.360658i
\(689\) 9.99622e10i 0.443567i
\(690\) −2.35605e9 7.10835e9i −0.0103941 0.0313597i
\(691\) 1.64854e11 0.723082 0.361541 0.932356i \(-0.382251\pi\)
0.361541 + 0.932356i \(0.382251\pi\)
\(692\) −2.57864e11 + 2.57864e11i −1.12452 + 1.12452i
\(693\) −1.35983e10 1.35983e10i −0.0589594 0.0589594i
\(694\) 8.56672e10i 0.369298i
\(695\) −8.02956e10 + 1.59912e11i −0.344154 + 0.685397i
\(696\) −3.01460e10 −0.128467
\(697\) −1.02677e10 + 1.02677e10i −0.0435054 + 0.0435054i
\(698\) 2.01853e11 + 2.01853e11i 0.850382 + 0.850382i
\(699\) 5.66951e10i 0.237485i
\(700\) −4.05263e10 + 2.76967e11i −0.168789 + 1.15355i
\(701\) −4.11487e11 −1.70406 −0.852028 0.523496i \(-0.824627\pi\)
−0.852028 + 0.523496i \(0.824627\pi\)
\(702\) 2.02825e11 2.02825e11i 0.835166 0.835166i
\(703\) 3.92339e9 + 3.92339e9i 0.0160635 + 0.0160635i
\(704\) 1.00871e10i 0.0410655i
\(705\) 9.24374e10 + 4.64149e10i 0.374189 + 0.187889i
\(706\) −3.55203e10 −0.142974
\(707\) −7.30524e10 + 7.30524e10i −0.292386 + 0.292386i
\(708\) −5.42787e10 5.42787e10i −0.216021 0.216021i
\(709\) 3.55785e11i 1.40800i −0.710201 0.703999i \(-0.751396\pi\)
0.710201 0.703999i \(-0.248604\pi\)
\(710\) −3.61115e11 + 1.19691e11i −1.42106 + 0.471008i
\(711\) −3.94251e11 −1.54275
\(712\) −5.62426e10 + 5.62426e10i −0.218849 + 0.218849i
\(713\) 1.49464e10 + 1.49464e10i 0.0578334 + 0.0578334i
\(714\) 5.54680e10i 0.213427i
\(715\) 7.25814e9 + 2.18982e10i 0.0277716 + 0.0837885i
\(716\) −9.21654e10 −0.350684
\(717\) −5.66480e10 + 5.66480e10i −0.214342 + 0.214342i
\(718\) 3.04325e11 + 3.04325e11i 1.14509 + 1.14509i
\(719\) 1.68430e10i 0.0630238i −0.999503 0.0315119i \(-0.989968\pi\)
0.999503 0.0315119i \(-0.0100322\pi\)
\(720\) 1.20984e11 2.40944e11i 0.450191 0.896576i
\(721\) 2.06820e11 0.765335
\(722\) 2.20461e11 2.20461e11i 0.811301 0.811301i
\(723\) 3.70982e10 + 3.70982e10i 0.135769 + 0.135769i
\(724\) 3.53765e11i 1.28754i
\(725\) 3.29388e11 2.45299e11i 1.19222 0.887858i
\(726\) 1.32428e11 0.476686
\(727\) −7.96403e9 + 7.96403e9i −0.0285099 + 0.0285099i −0.721218 0.692708i \(-0.756417\pi\)
0.692708 + 0.721218i \(0.256417\pi\)
\(728\) 9.05390e10 + 9.05390e10i 0.322337 + 0.322337i
\(729\) 9.07459e10i 0.321304i
\(730\) 1.90216e11 + 9.55119e10i 0.669816 + 0.336330i
\(731\) 3.97516e10 0.139215
\(732\) −5.97346e10 + 5.97346e10i −0.208057 + 0.208057i
\(733\) −3.27099e10 3.27099e10i −0.113309 0.113309i 0.648179 0.761488i \(-0.275531\pi\)
−0.761488 + 0.648179i \(0.775531\pi\)
\(734\) 6.92598e11i 2.38615i
\(735\) −1.00675e11 + 3.33685e10i −0.344961 + 0.114337i
\(736\) 2.64194e10 0.0900350
\(737\) 9.36860e9 9.36860e9i 0.0317545 0.0317545i
\(738\) −4.85589e10 4.85589e10i −0.163698 0.163698i
\(739\) 2.49954e11i 0.838075i 0.907969 + 0.419038i \(0.137632\pi\)
−0.907969 + 0.419038i \(0.862368\pi\)
\(740\) −4.54391e9 1.37092e10i −0.0151532 0.0457179i
\(741\) −5.44515e10 −0.180608
\(742\) −1.38607e11 + 1.38607e11i −0.457265 + 0.457265i
\(743\) −2.19494e11 2.19494e11i −0.720224 0.720224i 0.248427 0.968651i \(-0.420086\pi\)
−0.968651 + 0.248427i \(0.920086\pi\)
\(744\) 3.13904e10i 0.102449i
\(745\) −5.18548e10 + 1.03271e11i −0.168331 + 0.335238i
\(746\) 5.20160e11 1.67951
\(747\) −1.88767e10 + 1.88767e10i −0.0606238 + 0.0606238i
\(748\) −3.81169e9 3.81169e9i −0.0121762 0.0121762i
\(749\) 4.27370e11i 1.35793i
\(750\) −2.63433e10 1.49200e11i −0.0832580 0.471546i
\(751\) −3.34163e11 −1.05051 −0.525253 0.850946i \(-0.676029\pi\)
−0.525253 + 0.850946i \(0.676029\pi\)
\(752\) −3.06173e11 + 3.06173e11i −0.957405 + 0.957405i
\(753\) 2.21250e10 + 2.21250e10i 0.0688183 + 0.0688183i
\(754\) 8.53020e11i 2.63921i
\(755\) −3.44441e11 1.72952e11i −1.06005 0.532276i
\(756\) −2.53338e11 −0.775557
\(757\) 3.61172e11 3.61172e11i 1.09984 1.09984i 0.105414 0.994428i \(-0.466383\pi\)
0.994428 0.105414i \(-0.0336168\pi\)
\(758\) −4.01403e11 4.01403e11i −1.21592 1.21592i
\(759\) 5.45107e8i 0.00164254i
\(760\) −2.98009e10 + 9.87747e9i −0.0893254 + 0.0296068i
\(761\) 1.43773e10 0.0428685 0.0214342 0.999770i \(-0.493177\pi\)
0.0214342 + 0.999770i \(0.493177\pi\)
\(762\) −1.79675e11 + 1.79675e11i −0.532926 + 0.532926i
\(763\) 1.08516e11 + 1.08516e11i 0.320181 + 0.320181i
\(764\) 3.19462e11i 0.937661i
\(765\) 2.95062e10 + 8.90220e10i 0.0861525 + 0.259927i
\(766\) 6.86583e11 1.99424
\(767\) 3.38252e11 3.38252e11i 0.977368 0.977368i
\(768\) −1.09893e11 1.09893e11i −0.315882 0.315882i
\(769\) 4.36097e10i 0.124703i 0.998054 + 0.0623517i \(0.0198600\pi\)
−0.998054 + 0.0623517i \(0.980140\pi\)
\(770\) 2.02998e10 4.04279e10i 0.0577469 0.115005i
\(771\) 5.64389e10 0.159721
\(772\) −4.11947e10 + 4.11947e10i −0.115977 + 0.115977i
\(773\) −4.23792e11 4.23792e11i −1.18696 1.18696i −0.977905 0.209051i \(-0.932963\pi\)
−0.209051 0.977905i \(-0.567037\pi\)
\(774\) 1.87996e11i 0.523824i
\(775\) 2.55425e11 + 3.42986e11i 0.708038 + 0.950756i