Properties

Label 5.9.c.a.3.1
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 3.1
Root \(3.70505 + 3.70505i\) of defining polynomial
Character \(\chi\) \(=\) 5.3
Dual form 5.9.c.a.2.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-11.8649 + 11.8649i) q^{2} +(-90.9660 - 90.9660i) q^{3} -25.5528i q^{4} +(-434.373 + 449.383i) q^{5} +2158.61 q^{6} +(508.219 - 508.219i) q^{7} +(-2734.24 - 2734.24i) q^{8} +9988.61i q^{9} +O(q^{10})\) \(q+(-11.8649 + 11.8649i) q^{2} +(-90.9660 - 90.9660i) q^{3} -25.5528i q^{4} +(-434.373 + 449.383i) q^{5} +2158.61 q^{6} +(508.219 - 508.219i) q^{7} +(-2734.24 - 2734.24i) q^{8} +9988.61i q^{9} +(-178.084 - 10485.7i) q^{10} -7021.93 q^{11} +(-2324.44 + 2324.44i) q^{12} +(-8073.75 - 8073.75i) q^{13} +12060.0i q^{14} +(80391.7 - 1365.33i) q^{15} +71424.6 q^{16} +(-102958. + 102958. i) q^{17} +(-118514. - 118514. i) q^{18} -59599.0i q^{19} +(11483.0 + 11099.5i) q^{20} -92461.2 q^{21} +(83314.7 - 83314.7i) q^{22} +(132866. + 132866. i) q^{23} +497445. i q^{24} +(-13264.5 - 390400. i) q^{25} +191589. q^{26} +(311796. - 311796. i) q^{27} +(-12986.4 - 12986.4i) q^{28} -392047. i q^{29} +(-937642. + 970041. i) q^{30} -507883. q^{31} +(-147482. + 147482. i) q^{32} +(638757. + 638757. i) q^{33} -2.44319e6i q^{34} +(7628.00 + 449141. i) q^{35} +255237. q^{36} +(-61012.9 + 61012.9i) q^{37} +(707137. + 707137. i) q^{38} +1.46887e6i q^{39} +(2.41640e6 - 41038.9i) q^{40} -1.81765e6 q^{41} +(1.09705e6 - 1.09705e6i) q^{42} +(1.47723e6 + 1.47723e6i) q^{43} +179430. i q^{44} +(-4.48871e6 - 4.33879e6i) q^{45} -3.15288e6 q^{46} +(-1.79287e6 + 1.79287e6i) q^{47} +(-6.49721e6 - 6.49721e6i) q^{48} +5.24823e6i q^{49} +(4.78945e6 + 4.47468e6i) q^{50} +1.87314e7 q^{51} +(-206307. + 206307. i) q^{52} +(-5.66320e6 - 5.66320e6i) q^{53} +7.39887e6i q^{54} +(3.05014e6 - 3.15553e6i) q^{55} -2.77918e6 q^{56} +(-5.42148e6 + 5.42148e6i) q^{57} +(4.65161e6 + 4.65161e6i) q^{58} -1.74855e7i q^{59} +(-34888.1 - 2.05424e6i) q^{60} -1.96459e7 q^{61} +(6.02599e6 - 6.02599e6i) q^{62} +(5.07640e6 + 5.07640e6i) q^{63} +1.47850e7i q^{64} +(7.13522e6 - 121181. i) q^{65} -1.51576e7 q^{66} +(-1.12859e7 + 1.12859e7i) q^{67} +(2.63088e6 + 2.63088e6i) q^{68} -2.41725e7i q^{69} +(-5.41953e6 - 5.23852e6i) q^{70} +3.01001e7 q^{71} +(2.73112e7 - 2.73112e7i) q^{72} +(2.52645e7 + 2.52645e7i) q^{73} -1.44783e6i q^{74} +(-3.43065e7 + 3.67197e7i) q^{75} -1.52292e6 q^{76} +(-3.56868e6 + 3.56868e6i) q^{77} +(-1.74281e7 - 1.74281e7i) q^{78} -8.14025e6i q^{79} +(-3.10249e7 + 3.20970e7i) q^{80} +8.80962e6 q^{81} +(2.15663e7 - 2.15663e7i) q^{82} +(-1.99635e7 - 1.99635e7i) q^{83} +2.36265e6i q^{84} +(-1.54533e6 - 9.09902e7i) q^{85} -3.50545e7 q^{86} +(-3.56630e7 + 3.56630e7i) q^{87} +(1.91996e7 + 1.91996e7i) q^{88} +8.20905e7i q^{89} +(1.04738e8 - 1.77881e6i) q^{90} -8.20646e6 q^{91} +(3.39509e6 - 3.39509e6i) q^{92} +(4.62000e7 + 4.62000e7i) q^{93} -4.25446e7i q^{94} +(2.67827e7 + 2.58882e7i) q^{95} +2.68317e7 q^{96} +(3.37379e7 - 3.37379e7i) q^{97} +(-6.22698e7 - 6.22698e7i) q^{98} -7.01393e7i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.8649 + 11.8649i −0.741558 + 0.741558i −0.972878 0.231320i \(-0.925696\pi\)
0.231320 + 0.972878i \(0.425696\pi\)
\(3\) −90.9660 90.9660i −1.12304 1.12304i −0.991282 0.131754i \(-0.957939\pi\)
−0.131754 0.991282i \(-0.542061\pi\)
\(4\) 25.5528i 0.0998158i
\(5\) −434.373 + 449.383i −0.694997 + 0.719012i
\(6\) 2158.61 1.66559
\(7\) 508.219 508.219i 0.211670 0.211670i −0.593307 0.804976i \(-0.702178\pi\)
0.804976 + 0.593307i \(0.202178\pi\)
\(8\) −2734.24 2734.24i −0.667539 0.667539i
\(9\) 9988.61i 1.52242i
\(10\) −178.084 10485.7i −0.0178084 1.04857i
\(11\) −7021.93 −0.479607 −0.239804 0.970821i \(-0.577083\pi\)
−0.239804 + 0.970821i \(0.577083\pi\)
\(12\) −2324.44 + 2324.44i −0.112097 + 0.112097i
\(13\) −8073.75 8073.75i −0.282684 0.282684i 0.551494 0.834179i \(-0.314058\pi\)
−0.834179 + 0.551494i \(0.814058\pi\)
\(14\) 12060.0i 0.313930i
\(15\) 80391.7 1365.33i 1.58798 0.0269695i
\(16\) 71424.6 1.08985
\(17\) −102958. + 102958.i −1.23273 + 1.23273i −0.269813 + 0.962913i \(0.586962\pi\)
−0.962913 + 0.269813i \(0.913038\pi\)
\(18\) −118514. 118514.i −1.12896 1.12896i
\(19\) 59599.0i 0.457324i −0.973506 0.228662i \(-0.926565\pi\)
0.973506 0.228662i \(-0.0734351\pi\)
\(20\) 11483.0 + 11099.5i 0.0717688 + 0.0693717i
\(21\) −92461.2 −0.475425
\(22\) 83314.7 83314.7i 0.355657 0.355657i
\(23\) 132866. + 132866.i 0.474790 + 0.474790i 0.903461 0.428671i \(-0.141018\pi\)
−0.428671 + 0.903461i \(0.641018\pi\)
\(24\) 497445.i 1.49934i
\(25\) −13264.5 390400.i −0.0339572 0.999423i
\(26\) 191589. 0.419254
\(27\) 311796. 311796.i 0.586699 0.586699i
\(28\) −12986.4 12986.4i −0.0211280 0.0211280i
\(29\) 392047.i 0.554302i −0.960826 0.277151i \(-0.910610\pi\)
0.960826 0.277151i \(-0.0893902\pi\)
\(30\) −937642. + 970041.i −1.15758 + 1.19758i
\(31\) −507883. −0.549942 −0.274971 0.961453i \(-0.588668\pi\)
−0.274971 + 0.961453i \(0.588668\pi\)
\(32\) −147482. + 147482.i −0.140650 + 0.140650i
\(33\) 638757. + 638757.i 0.538617 + 0.538617i
\(34\) 2.44319e6i 1.82827i
\(35\) 7628.00 + 449141.i 0.00508321 + 0.299303i
\(36\) 255237. 0.151962
\(37\) −61012.9 + 61012.9i −0.0325548 + 0.0325548i −0.723197 0.690642i \(-0.757328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(38\) 707137. + 707137.i 0.339132 + 0.339132i
\(39\) 1.46887e6i 0.634930i
\(40\) 2.41640e6 41038.9i 0.943906 0.0160308i
\(41\) −1.81765e6 −0.643242 −0.321621 0.946868i \(-0.604228\pi\)
−0.321621 + 0.946868i \(0.604228\pi\)
\(42\) 1.09705e6 1.09705e6i 0.352555 0.352555i
\(43\) 1.47723e6 + 1.47723e6i 0.432090 + 0.432090i 0.889339 0.457249i \(-0.151165\pi\)
−0.457249 + 0.889339i \(0.651165\pi\)
\(44\) 179430.i 0.0478724i
\(45\) −4.48871e6 4.33879e6i −1.09464 1.05808i
\(46\) −3.15288e6 −0.704168
\(47\) −1.79287e6 + 1.79287e6i −0.367416 + 0.367416i −0.866534 0.499118i \(-0.833657\pi\)
0.499118 + 0.866534i \(0.333657\pi\)
\(48\) −6.49721e6 6.49721e6i −1.22394 1.22394i
\(49\) 5.24823e6i 0.910392i
\(50\) 4.78945e6 + 4.47468e6i 0.766311 + 0.715949i
\(51\) 1.87314e7 2.76879
\(52\) −206307. + 206307.i −0.0282164 + 0.0282164i
\(53\) −5.66320e6 5.66320e6i −0.717725 0.717725i 0.250414 0.968139i \(-0.419433\pi\)
−0.968139 + 0.250414i \(0.919433\pi\)
\(54\) 7.39887e6i 0.870143i
\(55\) 3.05014e6 3.15553e6i 0.333326 0.344844i
\(56\) −2.77918e6 −0.282595
\(57\) −5.42148e6 + 5.42148e6i −0.513592 + 0.513592i
\(58\) 4.65161e6 + 4.65161e6i 0.411047 + 0.411047i
\(59\) 1.74855e7i 1.44301i −0.692410 0.721504i \(-0.743451\pi\)
0.692410 0.721504i \(-0.256549\pi\)
\(60\) −34888.1 2.05424e6i −0.00269199 0.158506i
\(61\) −1.96459e7 −1.41890 −0.709452 0.704754i \(-0.751057\pi\)
−0.709452 + 0.704754i \(0.751057\pi\)
\(62\) 6.02599e6 6.02599e6i 0.407814 0.407814i
\(63\) 5.07640e6 + 5.07640e6i 0.322251 + 0.322251i
\(64\) 1.47850e7i 0.881252i
\(65\) 7.13522e6 121181.i 0.399718 0.00678862i
\(66\) −1.51576e7 −0.798831
\(67\) −1.12859e7 + 1.12859e7i −0.560061 + 0.560061i −0.929325 0.369264i \(-0.879610\pi\)
0.369264 + 0.929325i \(0.379610\pi\)
\(68\) 2.63088e6 + 2.63088e6i 0.123045 + 0.123045i
\(69\) 2.41725e7i 1.06641i
\(70\) −5.41953e6 5.23852e6i −0.225720 0.218181i
\(71\) 3.01001e7 1.18450 0.592249 0.805755i \(-0.298240\pi\)
0.592249 + 0.805755i \(0.298240\pi\)
\(72\) 2.73112e7 2.73112e7i 1.01628 1.01628i
\(73\) 2.52645e7 + 2.52645e7i 0.889649 + 0.889649i 0.994489 0.104840i \(-0.0334331\pi\)
−0.104840 + 0.994489i \(0.533433\pi\)
\(74\) 1.44783e6i 0.0482825i
\(75\) −3.43065e7 + 3.67197e7i −1.08425 + 1.16052i
\(76\) −1.52292e6 −0.0456482
\(77\) −3.56868e6 + 3.56868e6i −0.101518 + 0.101518i
\(78\) −1.74281e7 1.74281e7i −0.470837 0.470837i
\(79\) 8.14025e6i 0.208992i −0.994525 0.104496i \(-0.966677\pi\)
0.994525 0.104496i \(-0.0333229\pi\)
\(80\) −3.10249e7 + 3.20970e7i −0.757445 + 0.783617i
\(81\) 8.80962e6 0.204653
\(82\) 2.15663e7 2.15663e7i 0.477001 0.477001i
\(83\) −1.99635e7 1.99635e7i −0.420652 0.420652i 0.464776 0.885428i \(-0.346135\pi\)
−0.885428 + 0.464776i \(0.846135\pi\)
\(84\) 2.36265e6i 0.0474550i
\(85\) −1.54533e6 9.09902e7i −0.0296037 1.74309i
\(86\) −3.50545e7 −0.640840
\(87\) −3.56630e7 + 3.56630e7i −0.622501 + 0.622501i
\(88\) 1.91996e7 + 1.91996e7i 0.320156 + 0.320156i
\(89\) 8.20905e7i 1.30838i 0.756332 + 0.654189i \(0.226990\pi\)
−0.756332 + 0.654189i \(0.773010\pi\)
\(90\) 1.04738e8 1.77881e6i 1.59637 0.0271119i
\(91\) −8.20646e6 −0.119671
\(92\) 3.39509e6 3.39509e6i 0.0473915 0.0473915i
\(93\) 4.62000e7 + 4.62000e7i 0.617605 + 0.617605i
\(94\) 4.25446e7i 0.544920i
\(95\) 2.67827e7 + 2.58882e7i 0.328822 + 0.317839i
\(96\) 2.68317e7 0.315910
\(97\) 3.37379e7 3.37379e7i 0.381093 0.381093i −0.490403 0.871496i \(-0.663150\pi\)
0.871496 + 0.490403i \(0.163150\pi\)
\(98\) −6.22698e7 6.22698e7i −0.675108 0.675108i
\(99\) 7.01393e7i 0.730165i
\(100\) −9.97582e6 + 338947.i −0.0997582 + 0.00338947i
\(101\) −1.91592e7 −0.184116 −0.0920582 0.995754i \(-0.529345\pi\)
−0.0920582 + 0.995754i \(0.529345\pi\)
\(102\) −2.22247e8 + 2.22247e8i −2.05322 + 2.05322i
\(103\) −1.35177e8 1.35177e8i −1.20103 1.20103i −0.973854 0.227173i \(-0.927052\pi\)
−0.227173 0.973854i \(-0.572948\pi\)
\(104\) 4.41511e7i 0.377405i
\(105\) 4.01627e7 4.15505e7i 0.330419 0.341837i
\(106\) 1.34387e8 1.06447
\(107\) 1.22825e8 1.22825e8i 0.937029 0.937029i −0.0611024 0.998132i \(-0.519462\pi\)
0.998132 + 0.0611024i \(0.0194616\pi\)
\(108\) −7.96728e6 7.96728e6i −0.0585619 0.0585619i
\(109\) 1.66780e8i 1.18151i 0.806850 + 0.590757i \(0.201171\pi\)
−0.806850 + 0.590757i \(0.798829\pi\)
\(110\) 1.25049e6 + 7.36298e7i 0.00854104 + 0.502902i
\(111\) 1.11002e7 0.0731204
\(112\) 3.62993e7 3.62993e7i 0.230689 0.230689i
\(113\) 3.23356e7 + 3.23356e7i 0.198320 + 0.198320i 0.799280 0.600959i \(-0.205215\pi\)
−0.600959 + 0.799280i \(0.705215\pi\)
\(114\) 1.28651e8i 0.761716i
\(115\) −1.17421e8 + 1.99422e6i −0.671357 + 0.0114020i
\(116\) −1.00179e7 −0.0553281
\(117\) 8.06456e7 8.06456e7i 0.430365 0.430365i
\(118\) 2.07464e8 + 2.07464e8i 1.07007 + 1.07007i
\(119\) 1.04651e8i 0.521861i
\(120\) −2.23543e8 2.16077e8i −1.07804 1.04204i
\(121\) −1.65051e8 −0.769977
\(122\) 2.33097e8 2.33097e8i 1.05220 1.05220i
\(123\) 1.65344e8 + 1.65344e8i 0.722385 + 0.722385i
\(124\) 1.29778e7i 0.0548929i
\(125\) 1.81201e8 + 1.63618e8i 0.742198 + 0.670181i
\(126\) −1.20462e8 −0.477935
\(127\) −2.93412e8 + 2.93412e8i −1.12788 + 1.12788i −0.137357 + 0.990522i \(0.543861\pi\)
−0.990522 + 0.137357i \(0.956139\pi\)
\(128\) −2.13178e8 2.13178e8i −0.794150 0.794150i
\(129\) 2.68756e8i 0.970507i
\(130\) −8.32211e7 + 8.60967e7i −0.291380 + 0.301448i
\(131\) −3.37671e8 −1.14659 −0.573295 0.819349i \(-0.694335\pi\)
−0.573295 + 0.819349i \(0.694335\pi\)
\(132\) 1.63220e7 1.63220e7i 0.0537624 0.0537624i
\(133\) −3.02893e7 3.02893e7i −0.0968017 0.0968017i
\(134\) 2.67812e8i 0.830635i
\(135\) 4.67983e6 + 2.75552e8i 0.0140895 + 0.829599i
\(136\) 5.63026e8 1.64578
\(137\) 1.06123e8 1.06123e8i 0.301249 0.301249i −0.540253 0.841502i \(-0.681672\pi\)
0.841502 + 0.540253i \(0.181672\pi\)
\(138\) 2.86805e8 + 2.86805e8i 0.790806 + 0.790806i
\(139\) 5.86652e8i 1.57153i −0.618528 0.785763i \(-0.712271\pi\)
0.618528 0.785763i \(-0.287729\pi\)
\(140\) 1.14768e7 194917.i 0.0298751 0.000507385i
\(141\) 3.26181e8 0.825243
\(142\) −3.57135e8 + 3.57135e8i −0.878373 + 0.878373i
\(143\) 5.66933e7 + 5.66933e7i 0.135577 + 0.135577i
\(144\) 7.13432e8i 1.65922i
\(145\) 1.76179e8 + 1.70295e8i 0.398550 + 0.385238i
\(146\) −5.99522e8 −1.31945
\(147\) 4.77410e8 4.77410e8i 1.02240 1.02240i
\(148\) 1.55905e6 + 1.55905e6i 0.00324948 + 0.00324948i
\(149\) 5.45945e8i 1.10765i 0.832632 + 0.553827i \(0.186833\pi\)
−0.832632 + 0.553827i \(0.813167\pi\)
\(150\) −2.86329e7 8.42720e8i −0.0565589 1.66463i
\(151\) 8.88293e7 0.170863 0.0854316 0.996344i \(-0.472773\pi\)
0.0854316 + 0.996344i \(0.472773\pi\)
\(152\) −1.62958e8 + 1.62958e8i −0.305282 + 0.305282i
\(153\) −1.02841e9 1.02841e9i −1.87673 1.87673i
\(154\) 8.46841e7i 0.150563i
\(155\) 2.20611e8 2.28234e8i 0.382208 0.395415i
\(156\) 3.75339e7 0.0633760
\(157\) −3.21072e8 + 3.21072e8i −0.528450 + 0.528450i −0.920110 0.391660i \(-0.871901\pi\)
0.391660 + 0.920110i \(0.371901\pi\)
\(158\) 9.65834e7 + 9.65834e7i 0.154979 + 0.154979i
\(159\) 1.03032e9i 1.61206i
\(160\) −2.21360e6 1.30338e8i −0.00337769 0.198881i
\(161\) 1.35050e8 0.200997
\(162\) −1.04526e8 + 1.04526e8i −0.151762 + 0.151762i
\(163\) 2.14053e8 + 2.14053e8i 0.303229 + 0.303229i 0.842276 0.539047i \(-0.181215\pi\)
−0.539047 + 0.842276i \(0.681215\pi\)
\(164\) 4.64461e7i 0.0642057i
\(165\) −5.64505e8 + 9.58728e6i −0.761609 + 0.0129348i
\(166\) 4.73730e8 0.623876
\(167\) 6.91005e8 6.91005e8i 0.888414 0.888414i −0.105957 0.994371i \(-0.533791\pi\)
0.994371 + 0.105957i \(0.0337906\pi\)
\(168\) 2.52811e8 + 2.52811e8i 0.317365 + 0.317365i
\(169\) 6.85360e8i 0.840179i
\(170\) 1.09793e9 + 1.06126e9i 1.31455 + 1.27065i
\(171\) 5.95311e8 0.696241
\(172\) 3.77475e7 3.77475e7i 0.0431294 0.0431294i
\(173\) −3.40367e8 3.40367e8i −0.379982 0.379982i 0.491114 0.871095i \(-0.336590\pi\)
−0.871095 + 0.491114i \(0.836590\pi\)
\(174\) 8.46276e8i 0.923241i
\(175\) −2.05150e8 1.91667e8i −0.218735 0.204360i
\(176\) −5.01538e8 −0.522701
\(177\) −1.59058e9 + 1.59058e9i −1.62055 + 1.62055i
\(178\) −9.73998e8 9.73998e8i −0.970237 0.970237i
\(179\) 7.51587e7i 0.0732094i −0.999330 0.0366047i \(-0.988346\pi\)
0.999330 0.0366047i \(-0.0116542\pi\)
\(180\) −1.10868e8 + 1.14699e8i −0.105613 + 0.109262i
\(181\) 1.46153e8 0.136174 0.0680870 0.997679i \(-0.478310\pi\)
0.0680870 + 0.997679i \(0.478310\pi\)
\(182\) 9.73690e7 9.73690e7i 0.0887432 0.0887432i
\(183\) 1.78711e9 + 1.78711e9i 1.59348 + 1.59348i
\(184\) 7.26573e8i 0.633881i
\(185\) −915760. 5.39205e7i −0.000781798 0.0460328i
\(186\) −1.09632e9 −0.915979
\(187\) 7.22967e8 7.22967e8i 0.591224 0.591224i
\(188\) 4.58130e7 + 4.58130e7i 0.0366739 + 0.0366739i
\(189\) 3.16921e8i 0.248373i
\(190\) −6.24937e8 + 1.06136e7i −0.479537 + 0.00814421i
\(191\) −2.54450e9 −1.91191 −0.955957 0.293506i \(-0.905178\pi\)
−0.955957 + 0.293506i \(0.905178\pi\)
\(192\) 1.34493e9 1.34493e9i 0.989679 0.989679i
\(193\) 9.46964e8 + 9.46964e8i 0.682503 + 0.682503i 0.960563 0.278061i \(-0.0896917\pi\)
−0.278061 + 0.960563i \(0.589692\pi\)
\(194\) 8.00595e8i 0.565205i
\(195\) −6.60086e8 6.38039e8i −0.456522 0.441275i
\(196\) 1.34107e8 0.0908715
\(197\) 6.42356e8 6.42356e8i 0.426492 0.426492i −0.460940 0.887432i \(-0.652487\pi\)
0.887432 + 0.460940i \(0.152487\pi\)
\(198\) 8.32198e8 + 8.32198e8i 0.541459 + 0.541459i
\(199\) 3.47565e8i 0.221628i 0.993841 + 0.110814i \(0.0353457\pi\)
−0.993841 + 0.110814i \(0.964654\pi\)
\(200\) −1.03118e9 + 1.10371e9i −0.644486 + 0.689821i
\(201\) 2.05326e9 1.25794
\(202\) 2.27323e8 2.27323e8i 0.136533 0.136533i
\(203\) −1.99246e8 1.99246e8i −0.117329 0.117329i
\(204\) 4.78641e8i 0.276369i
\(205\) 7.89538e8 8.16820e8i 0.447052 0.462499i
\(206\) 3.20772e9 1.78126
\(207\) −1.32714e9 + 1.32714e9i −0.722831 + 0.722831i
\(208\) −5.76664e8 5.76664e8i −0.308084 0.308084i
\(209\) 4.18500e8i 0.219336i
\(210\) 1.64659e7 + 9.69520e8i 0.00846656 + 0.498517i
\(211\) −1.32439e9 −0.668168 −0.334084 0.942543i \(-0.608427\pi\)
−0.334084 + 0.942543i \(0.608427\pi\)
\(212\) −1.44711e8 + 1.44711e8i −0.0716403 + 0.0716403i
\(213\) −2.73808e9 2.73808e9i −1.33023 1.33023i
\(214\) 2.91463e9i 1.38972i
\(215\) −1.30551e9 + 2.21722e7i −0.610980 + 0.0103766i
\(216\) −1.70505e9 −0.783289
\(217\) −2.58115e8 + 2.58115e8i −0.116406 + 0.116406i
\(218\) −1.97883e9 1.97883e9i −0.876160 0.876160i
\(219\) 4.59641e9i 1.99822i
\(220\) −8.06328e7 7.79397e7i −0.0344208 0.0332712i
\(221\) 1.66252e9 0.696945
\(222\) −1.31703e8 + 1.31703e8i −0.0542230 + 0.0542230i
\(223\) 2.96426e9 + 2.96426e9i 1.19866 + 1.19866i 0.974567 + 0.224096i \(0.0719429\pi\)
0.224096 + 0.974567i \(0.428057\pi\)
\(224\) 1.49906e8i 0.0595427i
\(225\) 3.89955e9 1.32494e8i 1.52154 0.0516972i
\(226\) −7.67318e8 −0.294132
\(227\) −8.37535e8 + 8.37535e8i −0.315428 + 0.315428i −0.847008 0.531580i \(-0.821598\pi\)
0.531580 + 0.847008i \(0.321598\pi\)
\(228\) 1.38534e8 + 1.38534e8i 0.0512646 + 0.0512646i
\(229\) 2.66676e9i 0.969709i 0.874595 + 0.484854i \(0.161127\pi\)
−0.874595 + 0.484854i \(0.838873\pi\)
\(230\) 1.36953e9 1.41685e9i 0.489395 0.506305i
\(231\) 6.49256e8 0.228017
\(232\) −1.07195e9 + 1.07195e9i −0.370018 + 0.370018i
\(233\) 9.91964e8 + 9.91964e8i 0.336568 + 0.336568i 0.855074 0.518506i \(-0.173512\pi\)
−0.518506 + 0.855074i \(0.673512\pi\)
\(234\) 1.91371e9i 0.638281i
\(235\) −2.69097e7 1.58446e9i −0.00882343 0.519529i
\(236\) −4.46803e8 −0.144035
\(237\) −7.40485e8 + 7.40485e8i −0.234705 + 0.234705i
\(238\) −1.24167e9 1.24167e9i −0.386990 0.386990i
\(239\) 1.26088e9i 0.386440i −0.981155 0.193220i \(-0.938107\pi\)
0.981155 0.193220i \(-0.0618931\pi\)
\(240\) 5.74194e9 9.75184e7i 1.73067 0.0293928i
\(241\) −1.40173e9 −0.415524 −0.207762 0.978179i \(-0.566618\pi\)
−0.207762 + 0.978179i \(0.566618\pi\)
\(242\) 1.95832e9 1.95832e9i 0.570982 0.570982i
\(243\) −2.84707e9 2.84707e9i −0.816532 0.816532i
\(244\) 5.02009e8i 0.141629i
\(245\) −2.35846e9 2.27969e9i −0.654583 0.632720i
\(246\) −3.92359e9 −1.07138
\(247\) −4.81187e8 + 4.81187e8i −0.129278 + 0.129278i
\(248\) 1.38867e9 + 1.38867e9i 0.367107 + 0.367107i
\(249\) 3.63199e9i 0.944816i
\(250\) −4.09125e9 + 2.08612e8i −1.04736 + 0.0534046i
\(251\) 5.24024e9 1.32025 0.660126 0.751155i \(-0.270503\pi\)
0.660126 + 0.751155i \(0.270503\pi\)
\(252\) 1.29716e8 1.29716e8i 0.0321657 0.0321657i
\(253\) −9.32973e8 9.32973e8i −0.227713 0.227713i
\(254\) 6.96261e9i 1.67277i
\(255\) −8.13644e9 + 8.41758e9i −1.92430 + 1.99080i
\(256\) 1.27373e9 0.296563
\(257\) −2.38954e9 + 2.38954e9i −0.547749 + 0.547749i −0.925789 0.378040i \(-0.876598\pi\)
0.378040 + 0.925789i \(0.376598\pi\)
\(258\) 3.18876e9 + 3.18876e9i 0.719687 + 0.719687i
\(259\) 6.20158e7i 0.0137817i
\(260\) −3.09652e6 1.82325e8i −0.000677612 0.0398982i
\(261\) 3.91601e9 0.843882
\(262\) 4.00644e9 4.00644e9i 0.850263 0.850263i
\(263\) −1.29445e9 1.29445e9i −0.270559 0.270559i 0.558766 0.829325i \(-0.311275\pi\)
−0.829325 + 0.558766i \(0.811275\pi\)
\(264\) 3.49303e9i 0.719095i
\(265\) 5.00488e9 8.50005e7i 1.01487 0.0172361i
\(266\) 7.18761e8 0.143568
\(267\) 7.46744e9 7.46744e9i 1.46936 1.46936i
\(268\) 2.88386e8 + 2.88386e8i 0.0559029 + 0.0559029i
\(269\) 6.14346e9i 1.17329i 0.809845 + 0.586643i \(0.199551\pi\)
−0.809845 + 0.586643i \(0.800449\pi\)
\(270\) −3.32493e9 3.21387e9i −0.625643 0.604747i
\(271\) −5.21208e9 −0.966349 −0.483174 0.875524i \(-0.660516\pi\)
−0.483174 + 0.875524i \(0.660516\pi\)
\(272\) −7.35377e9 + 7.35377e9i −1.34349 + 1.34349i
\(273\) 7.46509e8 + 7.46509e8i 0.134395 + 0.134395i
\(274\) 2.51828e9i 0.446787i
\(275\) 9.31427e7 + 2.74136e9i 0.0162861 + 0.479331i
\(276\) −6.17676e8 −0.106445
\(277\) 5.42598e9 5.42598e9i 0.921635 0.921635i −0.0755097 0.997145i \(-0.524058\pi\)
0.997145 + 0.0755097i \(0.0240584\pi\)
\(278\) 6.96058e9 + 6.96058e9i 1.16538 + 1.16538i
\(279\) 5.07304e9i 0.837243i
\(280\) 1.20720e9 1.24892e9i 0.196403 0.203189i
\(281\) −7.13397e9 −1.14421 −0.572106 0.820180i \(-0.693873\pi\)
−0.572106 + 0.820180i \(0.693873\pi\)
\(282\) −3.87011e9 + 3.87011e9i −0.611965 + 0.611965i
\(283\) 2.63941e9 + 2.63941e9i 0.411492 + 0.411492i 0.882258 0.470766i \(-0.156022\pi\)
−0.470766 + 0.882258i \(0.656022\pi\)
\(284\) 7.69142e8i 0.118232i
\(285\) −8.13725e7 4.79126e9i −0.0123338 0.726224i
\(286\) −1.34532e9 −0.201077
\(287\) −9.23763e8 + 9.23763e8i −0.136155 + 0.136155i
\(288\) −1.47314e9 1.47314e9i −0.214129 0.214129i
\(289\) 1.42251e10i 2.03923i
\(290\) −4.11089e9 + 6.98173e7i −0.581224 + 0.00987123i
\(291\) −6.13800e9 −0.855963
\(292\) 6.45579e8 6.45579e8i 0.0888010 0.0888010i
\(293\) −2.26873e9 2.26873e9i −0.307831 0.307831i 0.536237 0.844068i \(-0.319845\pi\)
−0.844068 + 0.536237i \(0.819845\pi\)
\(294\) 1.13289e10i 1.51634i
\(295\) 7.85766e9 + 7.59522e9i 1.03754 + 1.00289i
\(296\) 3.33648e8 0.0434631
\(297\) −2.18941e9 + 2.18941e9i −0.281385 + 0.281385i
\(298\) −6.47760e9 6.47760e9i −0.821390 0.821390i
\(299\) 2.14545e9i 0.268431i
\(300\) 9.38293e8 + 8.76628e8i 0.115839 + 0.108226i
\(301\) 1.50151e9 0.182921
\(302\) −1.05395e9 + 1.05395e9i −0.126705 + 0.126705i
\(303\) 1.74284e9 + 1.74284e9i 0.206769 + 0.206769i
\(304\) 4.25683e9i 0.498416i
\(305\) 8.53366e9 8.82853e9i 0.986134 1.02021i
\(306\) 2.44041e10 2.78341
\(307\) −5.16937e9 + 5.16937e9i −0.581948 + 0.581948i −0.935438 0.353490i \(-0.884995\pi\)
0.353490 + 0.935438i \(0.384995\pi\)
\(308\) 9.11898e7 + 9.11898e7i 0.0101331 + 0.0101331i
\(309\) 2.45930e10i 2.69760i
\(310\) 9.04458e7 + 5.32550e9i 0.00979358 + 0.576652i
\(311\) 1.32155e10 1.41268 0.706340 0.707873i \(-0.250345\pi\)
0.706340 + 0.707873i \(0.250345\pi\)
\(312\) 4.01625e9 4.01625e9i 0.423840 0.423840i
\(313\) −9.02814e9 9.02814e9i −0.940635 0.940635i 0.0576992 0.998334i \(-0.481624\pi\)
−0.998334 + 0.0576992i \(0.981624\pi\)
\(314\) 7.61899e9i 0.783753i
\(315\) −4.48630e9 + 7.61931e7i −0.455665 + 0.00773880i
\(316\) −2.08006e8 −0.0208607
\(317\) −4.91807e9 + 4.91807e9i −0.487032 + 0.487032i −0.907369 0.420336i \(-0.861912\pi\)
0.420336 + 0.907369i \(0.361912\pi\)
\(318\) −1.22246e10 1.22246e10i −1.19544 1.19544i
\(319\) 2.75293e9i 0.265847i
\(320\) −6.64410e9 6.42219e9i −0.633631 0.612468i
\(321\) −2.23459e10 −2.10464
\(322\) −1.60235e9 + 1.60235e9i −0.149051 + 0.149051i
\(323\) 6.13622e9 + 6.13622e9i 0.563756 + 0.563756i
\(324\) 2.25111e8i 0.0204276i
\(325\) −3.04489e9 + 3.25908e9i −0.272922 + 0.292121i
\(326\) −5.07944e9 −0.449723
\(327\) 1.51713e10 1.51713e10i 1.32688 1.32688i
\(328\) 4.96989e9 + 4.96989e9i 0.429389 + 0.429389i
\(329\) 1.82234e9i 0.155541i
\(330\) 6.58406e9 6.81156e9i 0.555185 0.574369i
\(331\) 1.72045e9 0.143327 0.0716637 0.997429i \(-0.477169\pi\)
0.0716637 + 0.997429i \(0.477169\pi\)
\(332\) −5.10123e8 + 5.10123e8i −0.0419877 + 0.0419877i
\(333\) −6.09434e8 6.09434e8i −0.0495621 0.0495621i
\(334\) 1.63974e10i 1.31762i
\(335\) −1.69393e8 9.97394e9i −0.0134498 0.791932i
\(336\) −6.60400e9 −0.518144
\(337\) −5.92808e9 + 5.92808e9i −0.459615 + 0.459615i −0.898529 0.438914i \(-0.855363\pi\)
0.438914 + 0.898529i \(0.355363\pi\)
\(338\) 8.13174e9 + 8.13174e9i 0.623041 + 0.623041i
\(339\) 5.88287e9i 0.445442i
\(340\) −2.32506e9 + 3.94876e7i −0.173988 + 0.00295492i
\(341\) 3.56632e9 0.263756
\(342\) −7.06332e9 + 7.06332e9i −0.516303 + 0.516303i
\(343\) 5.59703e9 + 5.59703e9i 0.404372 + 0.404372i
\(344\) 8.07820e9i 0.576874i
\(345\) 1.08627e10 + 1.04999e10i 0.766764 + 0.741154i
\(346\) 8.07685e9 0.563557
\(347\) 4.12838e9 4.12838e9i 0.284749 0.284749i −0.550251 0.834999i \(-0.685468\pi\)
0.834999 + 0.550251i \(0.185468\pi\)
\(348\) 9.11290e8 + 9.11290e8i 0.0621355 + 0.0621355i
\(349\) 3.79762e9i 0.255983i −0.991775 0.127991i \(-0.959147\pi\)
0.991775 0.127991i \(-0.0408530\pi\)
\(350\) 4.70820e9 1.59970e8i 0.313749 0.0106602i
\(351\) −5.03473e9 −0.331702
\(352\) 1.03561e9 1.03561e9i 0.0674568 0.0674568i
\(353\) −4.46363e9 4.46363e9i −0.287468 0.287468i 0.548610 0.836078i \(-0.315157\pi\)
−0.836078 + 0.548610i \(0.815157\pi\)
\(354\) 3.77443e10i 2.40347i
\(355\) −1.30747e10 + 1.35265e10i −0.823223 + 0.851668i
\(356\) 2.09765e9 0.130597
\(357\) 9.51967e9 9.51967e9i 0.586069 0.586069i
\(358\) 8.91752e8 + 8.91752e8i 0.0542890 + 0.0542890i
\(359\) 9.04307e8i 0.0544425i 0.999629 + 0.0272213i \(0.00866586\pi\)
−0.999629 + 0.0272213i \(0.991334\pi\)
\(360\) 4.09922e8 + 2.41365e10i 0.0244057 + 1.43702i
\(361\) 1.34315e10 0.790854
\(362\) −1.73410e9 + 1.73410e9i −0.100981 + 0.100981i
\(363\) 1.50141e10 + 1.50141e10i 0.864712 + 0.864712i
\(364\) 2.09698e8i 0.0119451i
\(365\) −2.23276e10 + 3.79201e8i −1.25797 + 0.0213648i
\(366\) −4.24078e10 −2.36332
\(367\) −9.88793e9 + 9.88793e9i −0.545056 + 0.545056i −0.925007 0.379951i \(-0.875941\pi\)
0.379951 + 0.925007i \(0.375941\pi\)
\(368\) 9.48987e9 + 9.48987e9i 0.517451 + 0.517451i
\(369\) 1.81558e10i 0.979287i
\(370\) 6.50628e8 + 6.28897e8i 0.0347157 + 0.0335562i
\(371\) −5.75629e9 −0.303841
\(372\) 1.18054e9 1.18054e9i 0.0616467 0.0616467i
\(373\) −1.56902e10 1.56902e10i −0.810575 0.810575i 0.174145 0.984720i \(-0.444284\pi\)
−0.984720 + 0.174145i \(0.944284\pi\)
\(374\) 1.71559e10i 0.876854i
\(375\) −1.59938e9 3.13668e10i −0.0808775 1.58615i
\(376\) 9.80428e9 0.490528
\(377\) −3.16529e9 + 3.16529e9i −0.156692 + 0.156692i
\(378\) 3.76025e9 + 3.76025e9i 0.184183 + 0.184183i
\(379\) 4.03797e8i 0.0195707i 0.999952 + 0.00978534i \(0.00311482\pi\)
−0.999952 + 0.00978534i \(0.996885\pi\)
\(380\) 6.61517e8 6.84375e8i 0.0317254 0.0328216i
\(381\) 5.33809e10 2.53330
\(382\) 3.01903e10 3.01903e10i 1.41779 1.41779i
\(383\) −1.94253e10 1.94253e10i −0.902761 0.902761i 0.0929130 0.995674i \(-0.470382\pi\)
−0.995674 + 0.0929130i \(0.970382\pi\)
\(384\) 3.87839e10i 1.78372i
\(385\) −5.35633e7 3.15384e9i −0.00243795 0.143548i
\(386\) −2.24713e10 −1.01223
\(387\) −1.47555e10 + 1.47555e10i −0.657824 + 0.657824i
\(388\) −8.62099e8 8.62099e8i −0.0380391 0.0380391i
\(389\) 1.00547e10i 0.439109i 0.975600 + 0.219555i \(0.0704604\pi\)
−0.975600 + 0.219555i \(0.929540\pi\)
\(390\) 1.54022e10 2.61583e8i 0.665768 0.0113071i
\(391\) −2.73593e10 −1.17057
\(392\) 1.43499e10 1.43499e10i 0.607722 0.607722i
\(393\) 3.07165e10 + 3.07165e10i 1.28766 + 1.28766i
\(394\) 1.52430e10i 0.632537i
\(395\) 3.65809e9 + 3.53591e9i 0.150268 + 0.145249i
\(396\) −1.79226e9 −0.0728820
\(397\) 4.59921e9 4.59921e9i 0.185149 0.185149i −0.608446 0.793595i \(-0.708207\pi\)
0.793595 + 0.608446i \(0.208207\pi\)
\(398\) −4.12383e9 4.12383e9i −0.164350 0.164350i
\(399\) 5.51059e9i 0.217424i
\(400\) −9.47414e8 2.78841e10i −0.0370084 1.08922i
\(401\) 3.93282e10 1.52099 0.760496 0.649343i \(-0.224956\pi\)
0.760496 + 0.649343i \(0.224956\pi\)
\(402\) −2.43617e10 + 2.43617e10i −0.932834 + 0.932834i
\(403\) 4.10052e9 + 4.10052e9i 0.155460 + 0.155460i
\(404\) 4.89572e8i 0.0183777i
\(405\) −3.82667e9 + 3.95889e9i −0.142233 + 0.147148i
\(406\) 4.72807e9 0.174012
\(407\) 4.28428e8 4.28428e8i 0.0156135 0.0156135i
\(408\) −5.12162e10 5.12162e10i −1.84828 1.84828i
\(409\) 3.53396e10i 1.26290i −0.775417 0.631450i \(-0.782460\pi\)
0.775417 0.631450i \(-0.217540\pi\)
\(410\) 3.23694e8 + 1.90593e10i 0.0114551 + 0.674485i
\(411\) −1.93071e10 −0.676628
\(412\) −3.45415e9 + 3.45415e9i −0.119881 + 0.119881i
\(413\) −8.88644e9 8.88644e9i −0.305441 0.305441i
\(414\) 3.14929e10i 1.07204i
\(415\) 1.76428e10 2.99637e8i 0.594806 0.0101019i
\(416\) 2.38147e9 0.0795191
\(417\) −5.33654e10 + 5.33654e10i −1.76488 + 1.76488i
\(418\) −4.96547e9 4.96547e9i −0.162650 0.162650i
\(419\) 1.65282e10i 0.536251i 0.963384 + 0.268126i \(0.0864042\pi\)
−0.963384 + 0.268126i \(0.913596\pi\)
\(420\) −1.06173e9 1.02627e9i −0.0341207 0.0329811i
\(421\) −2.05277e10 −0.653449 −0.326725 0.945120i \(-0.605945\pi\)
−0.326725 + 0.945120i \(0.605945\pi\)
\(422\) 1.57138e10 1.57138e10i 0.495485 0.495485i
\(423\) −1.79083e10 1.79083e10i −0.559362 0.559362i
\(424\) 3.09691e10i 0.958219i
\(425\) 4.15607e10 + 3.88293e10i 1.27387 + 1.19015i
\(426\) 6.49743e10 1.97289
\(427\) −9.98442e9 + 9.98442e9i −0.300339 + 0.300339i
\(428\) −3.13854e9 3.13854e9i −0.0935303 0.0935303i
\(429\) 1.03143e10i 0.304517i
\(430\) 1.52267e10 1.57529e10i 0.445382 0.460772i
\(431\) 2.06955e9 0.0599745 0.0299873 0.999550i \(-0.490453\pi\)
0.0299873 + 0.999550i \(0.490453\pi\)
\(432\) 2.22699e10 2.22699e10i 0.639416 0.639416i
\(433\) 2.90398e10 + 2.90398e10i 0.826118 + 0.826118i 0.986977 0.160860i \(-0.0514266\pi\)
−0.160860 + 0.986977i \(0.551427\pi\)
\(434\) 6.12504e9i 0.172643i
\(435\) −5.35275e8 3.15173e10i −0.0149493 0.880223i
\(436\) 4.26171e9 0.117934
\(437\) 7.91866e9 7.91866e9i 0.217133 0.217133i
\(438\) 5.45361e10 + 5.45361e10i 1.48179 + 1.48179i
\(439\) 1.56289e10i 0.420795i −0.977616 0.210398i \(-0.932524\pi\)
0.977616 0.210398i \(-0.0674758\pi\)
\(440\) −1.69678e10 + 2.88173e8i −0.452704 + 0.00768851i
\(441\) −5.24225e10 −1.38600
\(442\) −1.97257e10 + 1.97257e10i −0.516825 + 0.516825i
\(443\) 7.72628e9 + 7.72628e9i 0.200611 + 0.200611i 0.800262 0.599651i \(-0.204694\pi\)
−0.599651 + 0.800262i \(0.704694\pi\)
\(444\) 2.83641e8i 0.00729857i
\(445\) −3.68901e10 3.56579e10i −0.940739 0.909319i
\(446\) −7.03415e10 −1.77776
\(447\) 4.96625e10 4.96625e10i 1.24394 1.24394i
\(448\) 7.51399e9 + 7.51399e9i 0.186534 + 0.186534i
\(449\) 1.21836e10i 0.299771i 0.988703 + 0.149886i \(0.0478905\pi\)
−0.988703 + 0.149886i \(0.952109\pi\)
\(450\) −4.46958e10 + 4.78399e10i −1.08998 + 1.16665i
\(451\) 1.27634e10 0.308504
\(452\) 8.26266e8 8.26266e8i 0.0197955 0.0197955i
\(453\) −8.08045e9 8.08045e9i −0.191886 0.191886i
\(454\) 1.98746e10i 0.467816i
\(455\) 3.56467e9 3.68784e9i 0.0831713 0.0860452i
\(456\) 2.96472e10 0.685685
\(457\) 4.53311e10 4.53311e10i 1.03928 1.03928i 0.0400801 0.999196i \(-0.487239\pi\)
0.999196 0.0400801i \(-0.0127613\pi\)
\(458\) −3.16409e10 3.16409e10i −0.719095 0.719095i
\(459\) 6.42041e10i 1.44648i
\(460\) 5.09579e7 + 3.00043e9i 0.00113810 + 0.0670120i
\(461\) −3.53353e9 −0.0782357 −0.0391178 0.999235i \(-0.512455\pi\)
−0.0391178 + 0.999235i \(0.512455\pi\)
\(462\) −7.70337e9 + 7.70337e9i −0.169088 + 0.169088i
\(463\) 1.72557e10 + 1.72557e10i 0.375499 + 0.375499i 0.869475 0.493976i \(-0.164457\pi\)
−0.493976 + 0.869475i \(0.664457\pi\)
\(464\) 2.80018e10i 0.604107i
\(465\) −4.08296e10 + 6.93429e8i −0.873299 + 0.0148317i
\(466\) −2.35392e10 −0.499169
\(467\) −2.45996e10 + 2.45996e10i −0.517203 + 0.517203i −0.916724 0.399521i \(-0.869177\pi\)
0.399521 + 0.916724i \(0.369177\pi\)
\(468\) −2.06072e9 2.06072e9i −0.0429572 0.0429572i
\(469\) 1.14714e10i 0.237096i
\(470\) 1.91188e10 + 1.84802e10i 0.391804 + 0.378718i
\(471\) 5.84133e10 1.18694
\(472\) −4.78094e10 + 4.78094e10i −0.963264 + 0.963264i
\(473\) −1.03730e10 1.03730e10i −0.207234 0.207234i
\(474\) 1.75716e10i 0.348095i
\(475\) −2.32674e10 + 7.90553e8i −0.457061 + 0.0155295i
\(476\) 2.67413e9 0.0520900
\(477\) 5.65675e10 5.65675e10i 1.09268 1.09268i
\(478\) 1.49602e10 + 1.49602e10i 0.286568 + 0.286568i
\(479\) 7.37614e10i 1.40116i −0.713575 0.700579i \(-0.752925\pi\)
0.713575 0.700579i \(-0.247075\pi\)
\(480\) −1.16550e10 + 1.20577e10i −0.219557 + 0.227143i
\(481\) 9.85206e8 0.0184055
\(482\) 1.66314e10 1.66314e10i 0.308135 0.308135i
\(483\) −1.22849e10 1.22849e10i −0.225727 0.225727i
\(484\) 4.21753e9i 0.0768558i
\(485\) 5.06382e8 + 2.98161e10i 0.00915189 + 0.538869i
\(486\) 6.75605e10 1.21101
\(487\) −2.80441e10 + 2.80441e10i −0.498569 + 0.498569i −0.910992 0.412423i \(-0.864682\pi\)
0.412423 + 0.910992i \(0.364682\pi\)
\(488\) 5.37166e10 + 5.37166e10i 0.947173 + 0.947173i
\(489\) 3.89430e10i 0.681074i
\(490\) 5.50313e10 9.34625e8i 0.954610 0.0162126i
\(491\) −1.16769e10 −0.200911 −0.100455 0.994942i \(-0.532030\pi\)
−0.100455 + 0.994942i \(0.532030\pi\)
\(492\) 4.22501e9 4.22501e9i 0.0721054 0.0721054i
\(493\) 4.03646e10 + 4.03646e10i 0.683302 + 0.683302i
\(494\) 1.14185e10i 0.191735i
\(495\) 3.15194e10 + 3.04667e10i 0.524997 + 0.507463i
\(496\) −3.62753e10 −0.599355
\(497\) 1.52974e10 1.52974e10i 0.250722 0.250722i
\(498\) −4.30933e10 4.30933e10i −0.700635 0.700635i
\(499\) 7.08522e10i 1.14275i 0.820689 + 0.571375i \(0.193590\pi\)
−0.820689 + 0.571375i \(0.806410\pi\)
\(500\) 4.18091e9 4.63019e9i 0.0668946 0.0740830i
\(501\) −1.25716e11 −1.99544
\(502\) −6.21751e10 + 6.21751e10i −0.979043 + 0.979043i
\(503\) −7.32217e10 7.32217e10i −1.14385 1.14385i −0.987740 0.156107i \(-0.950106\pi\)
−0.156107 0.987740i \(-0.549894\pi\)
\(504\) 2.77602e10i 0.430229i
\(505\) 8.32225e9 8.60982e9i 0.127960 0.132382i
\(506\) 2.21393e10 0.337724
\(507\) −6.23444e10 + 6.23444e10i −0.943552 + 0.943552i
\(508\) 7.49750e9 + 7.49750e9i 0.112580 + 0.112580i
\(509\) 1.10598e11i 1.64769i 0.566813 + 0.823846i \(0.308176\pi\)
−0.566813 + 0.823846i \(0.691824\pi\)
\(510\) −3.33577e9 1.96412e11i −0.0493077 2.90327i
\(511\) 2.56797e10 0.376623
\(512\) 3.94608e10 3.94608e10i 0.574231 0.574231i
\(513\) −1.85827e10 1.85827e10i −0.268312 0.268312i
\(514\) 5.67034e10i 0.812376i
\(515\) 1.19463e11 2.02890e9i 1.69826 0.0288425i
\(516\) −6.86747e9 −0.0968719
\(517\) 1.25894e10 1.25894e10i 0.176215 0.176215i
\(518\) −7.35813e8 7.35813e8i −0.0102199 0.0102199i
\(519\) 6.19236e10i 0.853467i
\(520\) −1.98407e10 1.91781e10i −0.271359 0.262296i
\(521\) −8.07216e10 −1.09557 −0.547783 0.836620i \(-0.684528\pi\)
−0.547783 + 0.836620i \(0.684528\pi\)
\(522\) −4.64631e10 + 4.64631e10i −0.625787 + 0.625787i
\(523\) −3.77792e10 3.77792e10i −0.504948 0.504948i 0.408024 0.912971i \(-0.366218\pi\)
−0.912971 + 0.408024i \(0.866218\pi\)
\(524\) 8.62844e9i 0.114448i
\(525\) 1.22646e9 + 3.60968e10i 0.0161441 + 0.475151i
\(526\) 3.07170e10 0.401270
\(527\) 5.22908e10 5.22908e10i 0.677927 0.677927i
\(528\) 4.56229e10 + 4.56229e10i 0.587013 + 0.587013i
\(529\) 4.30044e10i 0.549149i
\(530\) −5.83741e10 + 6.03911e10i −0.739804 + 0.765367i
\(531\) 1.74655e11 2.19687
\(532\) −7.73978e8 + 7.73978e8i −0.00966233 + 0.00966233i
\(533\) 1.46752e10 + 1.46752e10i 0.181835 + 0.181835i
\(534\) 1.77201e11i 2.17922i
\(535\) 1.84352e9 + 1.08548e11i 0.0225026 + 1.32497i
\(536\) 6.17164e10 0.747725
\(537\) −6.83688e9 + 6.83688e9i −0.0822169 + 0.0822169i
\(538\) −7.28917e10 7.28917e10i −0.870060 0.870060i
\(539\) 3.68527e10i 0.436631i
\(540\) 7.04113e9 1.19583e8i 0.0828070 0.00140635i
\(541\) 7.53948e10 0.880141 0.440071 0.897963i \(-0.354953\pi\)
0.440071 + 0.897963i \(0.354953\pi\)
\(542\) 6.18409e10 6.18409e10i 0.716604 0.716604i
\(543\) −1.32950e10 1.32950e10i −0.152928 0.152928i
\(544\) 3.03691e10i 0.346766i
\(545\) −7.49481e10 7.24449e10i −0.849522 0.821149i
\(546\) −1.77145e10 −0.199324
\(547\) 2.20178e10 2.20178e10i 0.245937 0.245937i −0.573364 0.819301i \(-0.694362\pi\)
0.819301 + 0.573364i \(0.194362\pi\)
\(548\) −2.71174e9 2.71174e9i −0.0300694 0.0300694i
\(549\) 1.96235e11i 2.16017i
\(550\) −3.36312e10 3.14209e10i −0.367529 0.343374i
\(551\) −2.33656e10 −0.253496
\(552\) −6.60934e10 + 6.60934e10i −0.711871 + 0.711871i
\(553\) −4.13703e9 4.13703e9i −0.0442372 0.0442372i
\(554\) 1.28758e11i 1.36689i
\(555\) −4.82163e9 + 4.98823e9i −0.0508185 + 0.0525745i
\(556\) −1.49906e10 −0.156863
\(557\) −1.03428e11 + 1.03428e11i −1.07453 + 1.07453i −0.0775357 + 0.996990i \(0.524705\pi\)
−0.996990 + 0.0775357i \(0.975295\pi\)
\(558\) 6.01913e10 + 6.01913e10i 0.620864 + 0.620864i
\(559\) 2.38536e10i 0.244290i
\(560\) 5.44826e8 + 3.20797e10i 0.00553995 + 0.326196i
\(561\) −1.31531e11 −1.32793
\(562\) 8.46441e10 8.46441e10i 0.848499 0.848499i
\(563\) −7.70545e10 7.70545e10i −0.766945 0.766945i 0.210623 0.977567i \(-0.432451\pi\)
−0.977567 + 0.210623i \(0.932451\pi\)
\(564\) 8.33484e9i 0.0823722i
\(565\) −2.85768e10 + 4.85334e8i −0.280427 + 0.00476263i
\(566\) −6.26329e10 −0.610290
\(567\) 4.47721e9 4.47721e9i 0.0433187 0.0433187i
\(568\) −8.23008e10 8.23008e10i −0.790698 0.790698i
\(569\) 6.19669e10i 0.591168i 0.955317 + 0.295584i \(0.0955142\pi\)
−0.955317 + 0.295584i \(0.904486\pi\)
\(570\) 5.78135e10 + 5.58825e10i 0.547683 + 0.529391i
\(571\) 2.38428e10 0.224292 0.112146 0.993692i \(-0.464228\pi\)
0.112146 + 0.993692i \(0.464228\pi\)
\(572\) 1.44867e9 1.44867e9i 0.0135328 0.0135328i
\(573\) 2.31463e11 + 2.31463e11i 2.14715 + 2.14715i
\(574\) 2.19208e10i 0.201933i
\(575\) 5.01083e10 5.36331e10i 0.458393 0.490638i
\(576\) −1.47681e11 −1.34164
\(577\) 1.08821e11 1.08821e11i 0.981772 0.981772i −0.0180652 0.999837i \(-0.505751\pi\)
0.999837 + 0.0180652i \(0.00575065\pi\)
\(578\) 1.68780e11 + 1.68780e11i 1.51220 + 1.51220i
\(579\) 1.72283e11i 1.53295i
\(580\) 4.35152e9 4.50188e9i 0.0384529 0.0397816i
\(581\) −2.02916e10 −0.178079
\(582\) 7.28269e10 7.28269e10i 0.634746 0.634746i
\(583\) 3.97666e10 + 3.97666e10i 0.344226 + 0.344226i
\(584\) 1.38158e11i 1.18775i
\(585\) 1.21043e9 + 7.12710e10i 0.0103351 + 0.608540i
\(586\) 5.38366e10 0.456549
\(587\) −9.61187e10 + 9.61187e10i −0.809572 + 0.809572i −0.984569 0.174997i \(-0.944008\pi\)
0.174997 + 0.984569i \(0.444008\pi\)
\(588\) −1.21992e10 1.21992e10i −0.102052 0.102052i
\(589\) 3.02693e10i 0.251502i
\(590\) −1.83347e11 + 3.11388e9i −1.51310 + 0.0256977i
\(591\) −1.16865e11 −0.957932
\(592\) −4.35782e9 + 4.35782e9i −0.0354799 + 0.0354799i
\(593\) 1.01154e10 + 1.01154e10i 0.0818021 + 0.0818021i 0.746824 0.665022i \(-0.231578\pi\)
−0.665022 + 0.746824i \(0.731578\pi\)
\(594\) 5.19544e10i 0.417327i
\(595\) −4.70283e10 4.54575e10i −0.375225 0.362692i
\(596\) 1.39505e10 0.110561
\(597\) 3.16166e10 3.16166e10i 0.248896 0.248896i
\(598\) 2.54556e10 + 2.54556e10i 0.199057 + 0.199057i
\(599\) 1.61079e11i 1.25121i 0.780139 + 0.625606i \(0.215148\pi\)
−0.780139 + 0.625606i \(0.784852\pi\)
\(600\) 1.94202e11 6.59838e9i 1.49848 0.0509134i
\(601\) 2.16088e11 1.65627 0.828137 0.560526i \(-0.189401\pi\)
0.828137 + 0.560526i \(0.189401\pi\)
\(602\) −1.78153e10 + 1.78153e10i −0.135646 + 0.135646i
\(603\) −1.12730e11 1.12730e11i −0.852649 0.852649i
\(604\) 2.26984e9i 0.0170548i
\(605\) 7.16939e10 7.41712e10i 0.535132 0.553623i
\(606\) −4.13573e10 −0.306663
\(607\) −8.94773e10 + 8.94773e10i −0.659111 + 0.659111i −0.955170 0.296059i \(-0.904327\pi\)
0.296059 + 0.955170i \(0.404327\pi\)
\(608\) 8.78979e9 + 8.78979e9i 0.0643227 + 0.0643227i
\(609\) 3.62492e10i 0.263529i
\(610\) 3.49862e9 + 2.06001e11i 0.0252684 + 1.48782i
\(611\) 2.89504e10 0.207725
\(612\) −2.62789e10 + 2.62789e10i −0.187327 + 0.187327i
\(613\) −1.23726e11 1.23726e11i −0.876229 0.876229i 0.116913 0.993142i \(-0.462700\pi\)
−0.993142 + 0.116913i \(0.962700\pi\)
\(614\) 1.22668e11i 0.863096i
\(615\) −1.46124e11 + 2.48170e9i −1.02146 + 0.0173480i
\(616\) 1.95152e10 0.135535
\(617\) 1.10854e11 1.10854e11i 0.764908 0.764908i −0.212297 0.977205i \(-0.568094\pi\)
0.977205 + 0.212297i \(0.0680945\pi\)
\(618\) −2.91794e11 2.91794e11i −2.00042 2.00042i
\(619\) 1.30648e11i 0.889897i 0.895556 + 0.444949i \(0.146778\pi\)
−0.895556 + 0.444949i \(0.853222\pi\)
\(620\) −5.83202e9 5.63723e9i −0.0394686 0.0381504i
\(621\) 8.28540e10 0.557118
\(622\) −1.56801e11 + 1.56801e11i −1.04758 + 1.04758i
\(623\) 4.17199e10 + 4.17199e10i 0.276944 + 0.276944i
\(624\) 1.04914e11i 0.691980i
\(625\) −1.52236e11 + 1.03569e10i −0.997694 + 0.0678753i
\(626\) 2.14236e11 1.39507
\(627\) 3.80692e10 3.80692e10i 0.246323 0.246323i
\(628\) 8.20431e9 + 8.20431e9i 0.0527477 + 0.0527477i
\(629\) 1.25636e10i 0.0802622i
\(630\) 5.23256e10 5.41336e10i 0.332163 0.343641i
\(631\) −2.21106e11 −1.39470 −0.697352 0.716729i \(-0.745639\pi\)
−0.697352 + 0.716729i \(0.745639\pi\)
\(632\) −2.22574e10 + 2.22574e10i −0.139510 + 0.139510i
\(633\) 1.20474e11 + 1.20474e11i 0.750377 + 0.750377i
\(634\) 1.16705e11i 0.722325i
\(635\) −4.40390e9 2.59304e11i −0.0270858 1.59483i
\(636\) 2.63275e10 0.160909
\(637\) 4.23729e10 4.23729e10i 0.257354 0.257354i
\(638\) −3.26633e10 3.26633e10i −0.197141 0.197141i
\(639\) 3.00658e11i 1.80331i
\(640\) 1.88397e11 3.19965e9i 1.12294 0.0190714i
\(641\) 2.04377e11 1.21060 0.605298 0.795999i \(-0.293054\pi\)
0.605298 + 0.795999i \(0.293054\pi\)
\(642\) 2.65132e11 2.65132e11i 1.56071 1.56071i
\(643\) 1.72443e11 + 1.72443e11i 1.00879 + 1.00879i 0.999961 + 0.00882849i \(0.00281023\pi\)
0.00882849 + 0.999961i \(0.497190\pi\)
\(644\) 3.45090e9i 0.0200627i
\(645\) 1.20774e11 + 1.16740e11i 0.697806 + 0.674500i
\(646\) −1.45612e11 −0.836115
\(647\) −1.33246e11 + 1.33246e11i −0.760392 + 0.760392i −0.976393 0.216001i \(-0.930699\pi\)
0.216001 + 0.976393i \(0.430699\pi\)
\(648\) −2.40876e10 2.40876e10i −0.136614 0.136614i
\(649\) 1.22782e11i 0.692078i
\(650\) −2.54134e9 7.47962e10i −0.0142367 0.419012i
\(651\) 4.69594e10 0.261456
\(652\) 5.46966e9 5.46966e9i 0.0302670 0.0302670i
\(653\) −7.89023e10 7.89023e10i −0.433947 0.433947i 0.456022 0.889969i \(-0.349274\pi\)
−0.889969 + 0.456022i \(0.849274\pi\)
\(654\) 3.60013e11i 1.96792i
\(655\) 1.46675e11 1.51743e11i 0.796877 0.824412i
\(656\) −1.29825e11 −0.701039
\(657\) −2.52357e11 + 2.52357e11i −1.35442 + 1.35442i
\(658\) −2.16219e10 2.16219e10i −0.115343 0.115343i
\(659\) 3.33275e11i 1.76710i −0.468339 0.883549i \(-0.655147\pi\)
0.468339 0.883549i \(-0.344853\pi\)
\(660\) 2.44982e8 + 1.44247e10i 0.00129110 + 0.0760206i
\(661\) −2.67623e11 −1.40190 −0.700951 0.713209i \(-0.747241\pi\)
−0.700951 + 0.713209i \(0.747241\pi\)
\(662\) −2.04130e10 + 2.04130e10i −0.106286 + 0.106286i
\(663\) −1.51233e11 1.51233e11i −0.782694 0.782694i
\(664\) 1.09170e11i 0.561603i
\(665\) 2.67684e10 4.54621e8i 0.136879 0.00232468i
\(666\) 1.44618e10 0.0735064
\(667\) 5.20896e10 5.20896e10i 0.263177 0.263177i
\(668\) −1.76571e10 1.76571e10i −0.0886777 0.0886777i
\(669\) 5.39294e11i 2.69228i
\(670\) 1.20350e11 + 1.16330e11i 0.597237 + 0.577289i
\(671\) 1.37952e11 0.680517
\(672\) 1.36364e10 1.36364e10i 0.0668686 0.0668686i
\(673\) −4.65870e10 4.65870e10i −0.227093 0.227093i 0.584384 0.811477i \(-0.301336\pi\)
−0.811477 + 0.584384i \(0.801336\pi\)
\(674\) 1.40672e11i 0.681662i
\(675\) −1.25861e11 1.17589e11i −0.606284 0.566438i
\(676\) −1.75129e10 −0.0838631
\(677\) −2.04905e11 + 2.04905e11i −0.975432 + 0.975432i −0.999705 0.0242736i \(-0.992273\pi\)
0.0242736 + 0.999705i \(0.492273\pi\)
\(678\) 6.97998e10 + 6.97998e10i 0.330321 + 0.330321i
\(679\) 3.42925e10i 0.161332i
\(680\) −2.44564e11 + 2.53014e11i −1.14382 + 1.18334i
\(681\) 1.52374e11 0.708473
\(682\) −4.23141e10 + 4.23141e10i −0.195590 + 0.195590i
\(683\) 2.26392e11 + 2.26392e11i 1.04035 + 1.04035i 0.999151 + 0.0411961i \(0.0131168\pi\)
0.0411961 + 0.999151i \(0.486883\pi\)
\(684\) 1.52119e10i 0.0694958i
\(685\) 1.59283e9 + 9.37866e10i 0.00723445 + 0.425969i
\(686\) −1.32817e11 −0.599730
\(687\) 2.42584e11 2.42584e11i 1.08902 1.08902i
\(688\) 1.05511e11 + 1.05511e11i 0.470915 + 0.470915i
\(689\) 9.14465e10i 0.405779i
\(690\) −2.53466e11 + 4.30473e9i −1.11821 + 0.0189911i
\(691\) −1.15111e11 −0.504900 −0.252450 0.967610i \(-0.581236\pi\)
−0.252450 + 0.967610i \(0.581236\pi\)
\(692\) −8.69734e9 + 8.69734e9i −0.0379282 + 0.0379282i
\(693\) −3.56461e10 3.56461e10i −0.154554 0.154554i
\(694\) 9.79658e10i 0.422315i
\(695\) 2.63631e11 + 2.54826e11i 1.12995 + 1.09221i
\(696\) 1.95022e11 0.831087
\(697\) 1.87142e11 1.87142e11i 0.792941 0.792941i
\(698\) 4.50585e10 + 4.50585e10i 0.189826 + 0.189826i
\(699\) 1.80470e11i 0.755956i
\(700\) −4.89764e9 + 5.24216e9i −0.0203983 + 0.0218332i
\(701\) 3.26439e10 0.135185 0.0675927 0.997713i \(-0.478468\pi\)
0.0675927 + 0.997713i \(0.478468\pi\)
\(702\) 5.97367e10 5.97367e10i 0.245976 0.245976i
\(703\) 3.63631e9 + 3.63631e9i 0.0148881 + 0.0148881i
\(704\) 1.03819e11i 0.422655i
\(705\) −1.41684e11 + 1.46580e11i −0.573542 + 0.593360i
\(706\) 1.05921e11 0.426349
\(707\) −9.73707e9 + 9.73707e9i −0.0389718 + 0.0389718i
\(708\) 4.06439e10 + 4.06439e10i 0.161757 + 0.161757i
\(709\) 1.10106e11i 0.435737i −0.975978 0.217869i \(-0.930090\pi\)
0.975978 0.217869i \(-0.0699104\pi\)
\(710\) −5.36034e9 3.15620e11i −0.0210940 1.24203i
\(711\) 8.13098e10 0.318174
\(712\) 2.24455e11 2.24455e11i 0.873392 0.873392i
\(713\) −6.74802e10 6.74802e10i −0.261107 0.261107i
\(714\) 2.25900e11i 0.869208i
\(715\) −5.01030e10 + 8.50926e8i −0.191708 + 0.00325587i
\(716\) −1.92052e9 −0.00730746
\(717\) −1.14697e11 + 1.14697e11i −0.433986 + 0.433986i
\(718\) −1.07295e10 1.07295e10i −0.0403723 0.0403723i
\(719\) 2.80995e11i 1.05144i 0.850658 + 0.525719i \(0.176204\pi\)
−0.850658 + 0.525719i \(0.823796\pi\)
\(720\) −3.20604e11 3.09896e11i −1.19300 1.15315i
\(721\) −1.37399e11 −0.508442
\(722\) −1.59364e11 + 1.59364e11i −0.586464 + 0.586464i
\(723\) 1.27510e11 + 1.27510e11i 0.466649 + 0.466649i
\(724\) 3.73463e9i 0.0135923i
\(725\) −1.53055e11 + 5.20033e9i −0.553982 + 0.0188226i
\(726\) −3.56281e11 −1.28247
\(727\) 7.91155e10 7.91155e10i 0.283220 0.283220i −0.551172 0.834392i \(-0.685819\pi\)
0.834392 + 0.551172i \(0.185819\pi\)
\(728\) 2.24384e10 + 2.24384e10i 0.0798853 + 0.0798853i
\(729\) 4.60173e11i 1.62934i
\(730\) 2.60416e11 2.69415e11i 0.917016 0.948702i
\(731\) −3.04187e11 −1.06530
\(732\) 4.56657e10 4.56657e10i 0.159055 0.159055i
\(733\) −1.00588e11 1.00588e11i −0.348441 0.348441i 0.511088 0.859529i \(-0.329243\pi\)
−0.859529 + 0.511088i \(0.829243\pi\)
\(734\) 2.34639e11i 0.808381i
\(735\) 7.16558e9 + 4.21914e11i 0.0245529 + 1.44569i
\(736\) −3.91906e10 −0.133558
\(737\) 7.92485e10 7.92485e10i 0.268609 0.268609i
\(738\) 2.15417e11 + 2.15417e11i 0.726197 + 0.726197i
\(739\) 1.06947e11i 0.358584i −0.983796 0.179292i \(-0.942619\pi\)
0.983796 0.179292i \(-0.0573806\pi\)
\(740\) −1.37782e9 + 2.34003e7i −0.00459480 + 7.80358e-5i
\(741\) 8.75433e10 0.290369
\(742\) 6.82979e10 6.82979e10i 0.225316 0.225316i
\(743\) 5.96783e10 + 5.96783e10i 0.195822 + 0.195822i 0.798206 0.602384i \(-0.205782\pi\)
−0.602384 + 0.798206i \(0.705782\pi\)
\(744\) 2.52644e11i 0.824550i
\(745\) −2.45338e11 2.37144e11i −0.796417 0.769817i
\(746\) 3.72326e11 1.20218
\(747\) 1.99407e11 1.99407e11i 0.640410 0.640410i
\(748\) −1.84739e10 1.84739e10i −0.0590135 0.0590135i
\(749\) 1.24844e11i 0.396681i
\(750\) 3.91141e11 + 3.53188e11i 1.23620 + 1.11625i
\(751\) −2.90374e11 −0.912846 −0.456423 0.889763i \(-0.650870\pi\)
−0.456423 + 0.889763i \(0.650870\pi\)
\(752\) −1.28055e11 + 1.28055e11i −0.400429 + 0.400429i
\(753\) −4.76684e11 4.76684e11i −1.48269 1.48269i
\(754\) 7.51119e10i 0.232393i
\(755\) −3.85851e10 + 3.99184e10i −0.118750 + 0.122853i
\(756\) −8.09824e9 −0.0247915
\(757\) −2.22407e11 + 2.22407e11i −0.677274 + 0.677274i −0.959383 0.282108i \(-0.908966\pi\)
0.282108 + 0.959383i \(0.408966\pi\)
\(758\) −4.79102e9 4.79102e9i −0.0145128 0.0145128i
\(759\) 1.69738e11i 0.511459i
\(760\) −2.44588e9 1.44015e11i −0.00733129 0.431671i
\(761\) 5.59405e11 1.66797 0.833984 0.551788i \(-0.186054\pi\)
0.833984 + 0.551788i \(0.186054\pi\)
\(762\) −6.33361e11 + 6.33361e11i −1.87859 + 1.87859i
\(763\) 8.47608e10 + 8.47608e10i 0.250090 + 0.250090i
\(764\) 6.50191e10i 0.190839i
\(765\) 9.08866e11 1.54357e10i 2.65371 0.0450694i
\(766\) 4.60960e11 1.33890
\(767\) −1.41173e11 + 1.41173e11i −0.407916 + 0.407916i
\(768\) −1.15866e11 1.15866e11i −0.333051 0.333051i
\(769\) 3.07549e10i 0.0879446i 0.999033 + 0.0439723i \(0.0140013\pi\)
−0.999033 + 0.0439723i \(0.985999\pi\)
\(770\) 3.80556e10 + 3.67845e10i 0.108257 + 0.104641i
\(771\) 4.34734e11 1.23029
\(772\) 2.41976e10 2.41976e10i 0.0681245 0.0681245i
\(773\) −1.21896e11 1.21896e11i −0.341405 0.341405i 0.515490 0.856896i \(-0.327610\pi\)
−0.856896 + 0.515490i \(0.827610\pi\)
\(774\) 3.50146e11i 0.975629i
\(775\) 6.73683e9 + 1.98277e11i 0.0186745 + 0.549625i