Properties

Label 72.8.d.b.37.5
Level $72$
Weight $8$
Character 72.37
Analytic conductor $22.492$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 72.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.4917218349\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.5
Root \(-4.85268 - 2.90715i\) of defining polynomial
Character \(\chi\) \(=\) 72.37
Dual form 72.8.d.b.37.6

$q$-expansion

\(f(q)\) \(=\) \(q+(9.70536 - 5.81430i) q^{2} +(60.3879 - 112.860i) q^{4} +324.492i q^{5} -956.960 q^{7} +(-70.1132 - 1446.46i) q^{8} +O(q^{10})\) \(q+(9.70536 - 5.81430i) q^{2} +(60.3879 - 112.860i) q^{4} +324.492i q^{5} -956.960 q^{7} +(-70.1132 - 1446.46i) q^{8} +(1886.69 + 3149.31i) q^{10} +5452.20i q^{11} +6289.38i q^{13} +(-9287.64 + 5564.05i) q^{14} +(-9090.60 - 13630.7i) q^{16} -34587.3 q^{17} +14595.6i q^{19} +(36622.0 + 19595.4i) q^{20} +(31700.7 + 52915.6i) q^{22} +24667.5 q^{23} -27169.8 q^{25} +(36568.3 + 61040.6i) q^{26} +(-57788.8 + 108002. i) q^{28} +171116. i q^{29} +111688. q^{31} +(-167481. - 79435.5i) q^{32} +(-335682. + 201101. i) q^{34} -310526. i q^{35} +103636. i q^{37} +(84863.4 + 141656. i) q^{38} +(469363. - 22751.1i) q^{40} -71691.3 q^{41} +328419. i q^{43} +(615334. + 329247. i) q^{44} +(239406. - 143424. i) q^{46} -119043. q^{47} +92230.3 q^{49} +(-263693. + 157973. i) q^{50} +(709817. + 379802. i) q^{52} -1.04011e6i q^{53} -1.76919e6 q^{55} +(67095.6 + 1.38420e6i) q^{56} +(994918. + 1.66074e6i) q^{58} -225984. i q^{59} -1.55268e6i q^{61} +(1.08398e6 - 649390. i) q^{62} +(-2.08732e6 + 202831. i) q^{64} -2.04085e6 q^{65} -316375. i q^{67} +(-2.08865e6 + 3.90351e6i) q^{68} +(-1.80549e6 - 3.01376e6i) q^{70} -538965. q^{71} -2.68512e6 q^{73} +(602570. + 1.00582e6i) q^{74} +(1.64726e6 + 881400. i) q^{76} -5.21754e6i q^{77} +8.22632e6 q^{79} +(4.42305e6 - 2.94982e6i) q^{80} +(-695790. + 416834. i) q^{82} -5.89510e6i q^{83} -1.12233e7i q^{85} +(1.90952e6 + 3.18742e6i) q^{86} +(7.88638e6 - 382271. i) q^{88} -437005. q^{89} -6.01868e6i q^{91} +(1.48962e6 - 2.78396e6i) q^{92} +(-1.15536e6 + 692152. i) q^{94} -4.73616e6 q^{95} -7.84322e6 q^{97} +(895128. - 536254. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.70536 5.81430i 0.857840 0.513916i
\(3\) 0 0
\(4\) 60.3879 112.860i 0.471781 0.881716i
\(5\) 324.492i 1.16094i 0.814283 + 0.580468i \(0.197130\pi\)
−0.814283 + 0.580468i \(0.802870\pi\)
\(6\) 0 0
\(7\) −956.960 −1.05451 −0.527255 0.849707i \(-0.676779\pi\)
−0.527255 + 0.849707i \(0.676779\pi\)
\(8\) −70.1132 1446.46i −0.0484155 0.998827i
\(9\) 0 0
\(10\) 1886.69 + 3149.31i 0.596624 + 0.995898i
\(11\) 5452.20i 1.23509i 0.786537 + 0.617544i \(0.211872\pi\)
−0.786537 + 0.617544i \(0.788128\pi\)
\(12\) 0 0
\(13\) 6289.38i 0.793973i 0.917824 + 0.396987i \(0.129944\pi\)
−0.917824 + 0.396987i \(0.870056\pi\)
\(14\) −9287.64 + 5564.05i −0.904602 + 0.541930i
\(15\) 0 0
\(16\) −9090.60 13630.7i −0.554846 0.831953i
\(17\) −34587.3 −1.70744 −0.853720 0.520733i \(-0.825659\pi\)
−0.853720 + 0.520733i \(0.825659\pi\)
\(18\) 0 0
\(19\) 14595.6i 0.488186i 0.969752 + 0.244093i \(0.0784903\pi\)
−0.969752 + 0.244093i \(0.921510\pi\)
\(20\) 36622.0 + 19595.4i 1.02362 + 0.547707i
\(21\) 0 0
\(22\) 31700.7 + 52915.6i 0.634731 + 1.05951i
\(23\) 24667.5 0.422743 0.211372 0.977406i \(-0.432207\pi\)
0.211372 + 0.977406i \(0.432207\pi\)
\(24\) 0 0
\(25\) −27169.8 −0.347774
\(26\) 36568.3 + 61040.6i 0.408036 + 0.681102i
\(27\) 0 0
\(28\) −57788.8 + 108002.i −0.497497 + 0.929779i
\(29\) 171116.i 1.30286i 0.758710 + 0.651429i \(0.225830\pi\)
−0.758710 + 0.651429i \(0.774170\pi\)
\(30\) 0 0
\(31\) 111688. 0.673352 0.336676 0.941620i \(-0.390697\pi\)
0.336676 + 0.941620i \(0.390697\pi\)
\(32\) −167481. 79435.5i −0.903524 0.428539i
\(33\) 0 0
\(34\) −335682. + 201101.i −1.46471 + 0.877480i
\(35\) 310526.i 1.22422i
\(36\) 0 0
\(37\) 103636.i 0.336360i 0.985756 + 0.168180i \(0.0537890\pi\)
−0.985756 + 0.168180i \(0.946211\pi\)
\(38\) 84863.4 + 141656.i 0.250887 + 0.418786i
\(39\) 0 0
\(40\) 469363. 22751.1i 1.15958 0.0562074i
\(41\) −71691.3 −0.162451 −0.0812256 0.996696i \(-0.525883\pi\)
−0.0812256 + 0.996696i \(0.525883\pi\)
\(42\) 0 0
\(43\) 328419.i 0.629925i 0.949104 + 0.314962i \(0.101992\pi\)
−0.949104 + 0.314962i \(0.898008\pi\)
\(44\) 615334. + 329247.i 1.08900 + 0.582690i
\(45\) 0 0
\(46\) 239406. 143424.i 0.362646 0.217255i
\(47\) −119043. −0.167248 −0.0836241 0.996497i \(-0.526650\pi\)
−0.0836241 + 0.996497i \(0.526650\pi\)
\(48\) 0 0
\(49\) 92230.3 0.111992
\(50\) −263693. + 157973.i −0.298334 + 0.178727i
\(51\) 0 0
\(52\) 709817. + 379802.i 0.700059 + 0.374581i
\(53\) 1.04011e6i 0.959648i −0.877365 0.479824i \(-0.840700\pi\)
0.877365 0.479824i \(-0.159300\pi\)
\(54\) 0 0
\(55\) −1.76919e6 −1.43386
\(56\) 67095.6 + 1.38420e6i 0.0510547 + 1.05327i
\(57\) 0 0
\(58\) 994918. + 1.66074e6i 0.669559 + 1.11764i
\(59\) 225984.i 0.143250i −0.997432 0.0716250i \(-0.977182\pi\)
0.997432 0.0716250i \(-0.0228185\pi\)
\(60\) 0 0
\(61\) 1.55268e6i 0.875843i −0.899013 0.437922i \(-0.855715\pi\)
0.899013 0.437922i \(-0.144285\pi\)
\(62\) 1.08398e6 649390.i 0.577629 0.346047i
\(63\) 0 0
\(64\) −2.08732e6 + 202831.i −0.995312 + 0.0967175i
\(65\) −2.04085e6 −0.921753
\(66\) 0 0
\(67\) 316375.i 0.128511i −0.997933 0.0642555i \(-0.979533\pi\)
0.997933 0.0642555i \(-0.0204673\pi\)
\(68\) −2.08865e6 + 3.90351e6i −0.805537 + 1.50548i
\(69\) 0 0
\(70\) −1.80549e6 3.01376e6i −0.629146 1.05019i
\(71\) −538965. −0.178713 −0.0893566 0.996000i \(-0.528481\pi\)
−0.0893566 + 0.996000i \(0.528481\pi\)
\(72\) 0 0
\(73\) −2.68512e6 −0.807856 −0.403928 0.914791i \(-0.632355\pi\)
−0.403928 + 0.914791i \(0.632355\pi\)
\(74\) 602570. + 1.00582e6i 0.172861 + 0.288543i
\(75\) 0 0
\(76\) 1.64726e6 + 881400.i 0.430442 + 0.230317i
\(77\) 5.21754e6i 1.30241i
\(78\) 0 0
\(79\) 8.22632e6 1.87720 0.938600 0.345007i \(-0.112123\pi\)
0.938600 + 0.345007i \(0.112123\pi\)
\(80\) 4.42305e6 2.94982e6i 0.965845 0.644141i
\(81\) 0 0
\(82\) −695790. + 416834.i −0.139357 + 0.0834863i
\(83\) 5.89510e6i 1.13167i −0.824520 0.565833i \(-0.808555\pi\)
0.824520 0.565833i \(-0.191445\pi\)
\(84\) 0 0
\(85\) 1.12233e7i 1.98223i
\(86\) 1.90952e6 + 3.18742e6i 0.323728 + 0.540375i
\(87\) 0 0
\(88\) 7.88638e6 382271.i 1.23364 0.0597974i
\(89\) −437005. −0.0657085 −0.0328542 0.999460i \(-0.510460\pi\)
−0.0328542 + 0.999460i \(0.510460\pi\)
\(90\) 0 0
\(91\) 6.01868e6i 0.837253i
\(92\) 1.48962e6 2.78396e6i 0.199442 0.372740i
\(93\) 0 0
\(94\) −1.15536e6 + 692152.i −0.143472 + 0.0859516i
\(95\) −4.73616e6 −0.566753
\(96\) 0 0
\(97\) −7.84322e6 −0.872556 −0.436278 0.899812i \(-0.643704\pi\)
−0.436278 + 0.899812i \(0.643704\pi\)
\(98\) 895128. 536254.i 0.0960713 0.0575545i
\(99\) 0 0
\(100\) −1.64073e6 + 3.06638e6i −0.164073 + 0.306638i
\(101\) 6.19757e6i 0.598545i −0.954168 0.299272i \(-0.903256\pi\)
0.954168 0.299272i \(-0.0967439\pi\)
\(102\) 0 0
\(103\) −6.59816e6 −0.594966 −0.297483 0.954727i \(-0.596147\pi\)
−0.297483 + 0.954727i \(0.596147\pi\)
\(104\) 9.09731e6 440968.i 0.793042 0.0384406i
\(105\) 0 0
\(106\) −6.04748e6 1.00946e7i −0.493179 0.823225i
\(107\) 512845.i 0.0404709i 0.999795 + 0.0202354i \(0.00644158\pi\)
−0.999795 + 0.0202354i \(0.993558\pi\)
\(108\) 0 0
\(109\) 1.95882e7i 1.44878i 0.689393 + 0.724388i \(0.257877\pi\)
−0.689393 + 0.724388i \(0.742123\pi\)
\(110\) −1.71707e7 + 1.02866e7i −1.23002 + 0.736883i
\(111\) 0 0
\(112\) 8.69934e6 + 1.30441e7i 0.585091 + 0.877303i
\(113\) −1.88876e7 −1.23141 −0.615705 0.787977i \(-0.711129\pi\)
−0.615705 + 0.787977i \(0.711129\pi\)
\(114\) 0 0
\(115\) 8.00438e6i 0.490778i
\(116\) 1.93121e7 + 1.03333e7i 1.14875 + 0.614663i
\(117\) 0 0
\(118\) −1.31394e6 2.19325e6i −0.0736185 0.122886i
\(119\) 3.30987e7 1.80051
\(120\) 0 0
\(121\) −1.02394e7 −0.525441
\(122\) −9.02772e6 1.50693e7i −0.450110 0.751334i
\(123\) 0 0
\(124\) 6.74463e6 1.26051e7i 0.317675 0.593706i
\(125\) 1.65345e7i 0.757193i
\(126\) 0 0
\(127\) 3.96314e7 1.71683 0.858413 0.512959i \(-0.171451\pi\)
0.858413 + 0.512959i \(0.171451\pi\)
\(128\) −1.90789e7 + 1.41048e7i −0.804114 + 0.594475i
\(129\) 0 0
\(130\) −1.98072e7 + 1.18661e7i −0.790717 + 0.473703i
\(131\) 3.65337e7i 1.41986i 0.704274 + 0.709928i \(0.251273\pi\)
−0.704274 + 0.709928i \(0.748727\pi\)
\(132\) 0 0
\(133\) 1.39675e7i 0.514797i
\(134\) −1.83950e6 3.07053e6i −0.0660439 0.110242i
\(135\) 0 0
\(136\) 2.42503e6 + 5.00290e7i 0.0826666 + 1.70544i
\(137\) 2.56967e7 0.853799 0.426899 0.904299i \(-0.359606\pi\)
0.426899 + 0.904299i \(0.359606\pi\)
\(138\) 0 0
\(139\) 5.23001e7i 1.65177i 0.563836 + 0.825886i \(0.309325\pi\)
−0.563836 + 0.825886i \(0.690675\pi\)
\(140\) −3.50458e7 1.87520e7i −1.07941 0.577563i
\(141\) 0 0
\(142\) −5.23085e6 + 3.13370e6i −0.153307 + 0.0918436i
\(143\) −3.42910e7 −0.980626
\(144\) 0 0
\(145\) −5.55256e7 −1.51254
\(146\) −2.60601e7 + 1.56121e7i −0.693011 + 0.415170i
\(147\) 0 0
\(148\) 1.16963e7 + 6.25836e6i 0.296574 + 0.158688i
\(149\) 1.80406e7i 0.446785i −0.974729 0.223392i \(-0.928287\pi\)
0.974729 0.223392i \(-0.0717131\pi\)
\(150\) 0 0
\(151\) 3.87385e7 0.915637 0.457818 0.889046i \(-0.348631\pi\)
0.457818 + 0.889046i \(0.348631\pi\)
\(152\) 2.11120e7 1.02335e6i 0.487614 0.0236358i
\(153\) 0 0
\(154\) −3.03363e7 5.06381e7i −0.669331 1.11726i
\(155\) 3.62420e7i 0.781719i
\(156\) 0 0
\(157\) 5.12341e7i 1.05660i −0.849058 0.528300i \(-0.822830\pi\)
0.849058 0.528300i \(-0.177170\pi\)
\(158\) 7.98393e7 4.78302e7i 1.61034 0.964723i
\(159\) 0 0
\(160\) 2.57762e7 5.43460e7i 0.497506 1.04893i
\(161\) −2.36058e7 −0.445787
\(162\) 0 0
\(163\) 8.57572e7i 1.55101i 0.631343 + 0.775504i \(0.282504\pi\)
−0.631343 + 0.775504i \(0.717496\pi\)
\(164\) −4.32929e6 + 8.09105e6i −0.0766413 + 0.143236i
\(165\) 0 0
\(166\) −3.42759e7 5.72141e7i −0.581581 0.970789i
\(167\) 1.05871e8 1.75901 0.879503 0.475893i \(-0.157875\pi\)
0.879503 + 0.475893i \(0.157875\pi\)
\(168\) 0 0
\(169\) 2.31923e7 0.369606
\(170\) −6.52555e7 1.08926e8i −1.01870 1.70044i
\(171\) 0 0
\(172\) 3.70652e7 + 1.98325e7i 0.555415 + 0.297186i
\(173\) 1.98148e7i 0.290956i 0.989361 + 0.145478i \(0.0464720\pi\)
−0.989361 + 0.145478i \(0.953528\pi\)
\(174\) 0 0
\(175\) 2.60005e7 0.366731
\(176\) 7.43175e7 4.95638e7i 1.02753 0.685284i
\(177\) 0 0
\(178\) −4.24129e6 + 2.54088e6i −0.0563674 + 0.0337686i
\(179\) 2.97800e7i 0.388096i 0.980992 + 0.194048i \(0.0621618\pi\)
−0.980992 + 0.194048i \(0.937838\pi\)
\(180\) 0 0
\(181\) 3.96227e6i 0.0496671i −0.999692 0.0248335i \(-0.992094\pi\)
0.999692 0.0248335i \(-0.00790558\pi\)
\(182\) −3.49944e7 5.84135e7i −0.430278 0.718230i
\(183\) 0 0
\(184\) −1.72951e6 3.56804e7i −0.0204674 0.422248i
\(185\) −3.36290e7 −0.390493
\(186\) 0 0
\(187\) 1.88577e8i 2.10884i
\(188\) −7.18876e6 + 1.34352e7i −0.0789045 + 0.147465i
\(189\) 0 0
\(190\) −4.59662e7 + 2.75375e7i −0.486184 + 0.291264i
\(191\) 4.80105e7 0.498562 0.249281 0.968431i \(-0.419806\pi\)
0.249281 + 0.968431i \(0.419806\pi\)
\(192\) 0 0
\(193\) −4.72502e6 −0.0473100 −0.0236550 0.999720i \(-0.507530\pi\)
−0.0236550 + 0.999720i \(0.507530\pi\)
\(194\) −7.61212e7 + 4.56028e7i −0.748514 + 0.448420i
\(195\) 0 0
\(196\) 5.56959e6 1.04091e7i 0.0528357 0.0987452i
\(197\) 1.14882e8i 1.07058i 0.844668 + 0.535290i \(0.179798\pi\)
−0.844668 + 0.535290i \(0.820202\pi\)
\(198\) 0 0
\(199\) 1.20933e7 0.108782 0.0543911 0.998520i \(-0.482678\pi\)
0.0543911 + 0.998520i \(0.482678\pi\)
\(200\) 1.90496e6 + 3.93000e7i 0.0168377 + 0.347366i
\(201\) 0 0
\(202\) −3.60345e7 6.01496e7i −0.307602 0.513456i
\(203\) 1.63751e8i 1.37388i
\(204\) 0 0
\(205\) 2.32632e7i 0.188596i
\(206\) −6.40375e7 + 3.83636e7i −0.510386 + 0.305763i
\(207\) 0 0
\(208\) 8.57287e7 5.71742e7i 0.660548 0.440533i
\(209\) −7.95784e7 −0.602953
\(210\) 0 0
\(211\) 1.95850e8i 1.43527i 0.696418 + 0.717636i \(0.254776\pi\)
−0.696418 + 0.717636i \(0.745224\pi\)
\(212\) −1.17386e8 6.28098e7i −0.846137 0.452743i
\(213\) 0 0
\(214\) 2.98183e6 + 4.97734e6i 0.0207986 + 0.0347176i
\(215\) −1.06569e8 −0.731302
\(216\) 0 0
\(217\) −1.06881e8 −0.710057
\(218\) 1.13891e8 + 1.90110e8i 0.744549 + 1.24282i
\(219\) 0 0
\(220\) −1.06838e8 + 1.99671e8i −0.676466 + 1.26426i
\(221\) 2.17532e8i 1.35566i
\(222\) 0 0
\(223\) 1.08024e8 0.652311 0.326156 0.945316i \(-0.394247\pi\)
0.326156 + 0.945316i \(0.394247\pi\)
\(224\) 1.60272e8 + 7.60167e7i 0.952775 + 0.451898i
\(225\) 0 0
\(226\) −1.83311e8 + 1.09818e8i −1.05635 + 0.632841i
\(227\) 1.61144e8i 0.914374i 0.889371 + 0.457187i \(0.151143\pi\)
−0.889371 + 0.457187i \(0.848857\pi\)
\(228\) 0 0
\(229\) 5.27173e7i 0.290088i −0.989425 0.145044i \(-0.953668\pi\)
0.989425 0.145044i \(-0.0463323\pi\)
\(230\) 4.65399e7 + 7.76854e7i 0.252219 + 0.421010i
\(231\) 0 0
\(232\) 2.47511e8 1.19975e7i 1.30133 0.0630786i
\(233\) 1.79423e8 0.929249 0.464625 0.885508i \(-0.346189\pi\)
0.464625 + 0.885508i \(0.346189\pi\)
\(234\) 0 0
\(235\) 3.86285e7i 0.194165i
\(236\) −2.55044e7 1.36467e7i −0.126306 0.0675826i
\(237\) 0 0
\(238\) 3.21234e8 1.92445e8i 1.54455 0.925312i
\(239\) 8.42441e7 0.399160 0.199580 0.979882i \(-0.436042\pi\)
0.199580 + 0.979882i \(0.436042\pi\)
\(240\) 0 0
\(241\) −2.12302e8 −0.977000 −0.488500 0.872564i \(-0.662456\pi\)
−0.488500 + 0.872564i \(0.662456\pi\)
\(242\) −9.93766e7 + 5.95347e7i −0.450745 + 0.270033i
\(243\) 0 0
\(244\) −1.75234e8 9.37629e7i −0.772245 0.413206i
\(245\) 2.99280e7i 0.130016i
\(246\) 0 0
\(247\) −9.17975e7 −0.387607
\(248\) −7.83083e6 1.61552e8i −0.0326007 0.672563i
\(249\) 0 0
\(250\) 9.61366e7 + 1.60473e8i 0.389134 + 0.649551i
\(251\) 1.18102e8i 0.471411i −0.971825 0.235706i \(-0.924260\pi\)
0.971825 0.235706i \(-0.0757401\pi\)
\(252\) 0 0
\(253\) 1.34492e8i 0.522125i
\(254\) 3.84637e8 2.30429e8i 1.47276 0.882304i
\(255\) 0 0
\(256\) −1.03157e8 + 2.47823e8i −0.384291 + 0.923212i
\(257\) −1.27463e8 −0.468402 −0.234201 0.972188i \(-0.575247\pi\)
−0.234201 + 0.972188i \(0.575247\pi\)
\(258\) 0 0
\(259\) 9.91755e7i 0.354695i
\(260\) −1.23243e8 + 2.30330e8i −0.434865 + 0.812724i
\(261\) 0 0
\(262\) 2.12418e8 + 3.54573e8i 0.729687 + 1.21801i
\(263\) −4.33125e8 −1.46814 −0.734071 0.679073i \(-0.762382\pi\)
−0.734071 + 0.679073i \(0.762382\pi\)
\(264\) 0 0
\(265\) 3.37506e8 1.11409
\(266\) −8.12109e7 1.35559e8i −0.264563 0.441614i
\(267\) 0 0
\(268\) −3.57060e7 1.91052e7i −0.113310 0.0606290i
\(269\) 3.44748e8i 1.07986i −0.841709 0.539931i \(-0.818450\pi\)
0.841709 0.539931i \(-0.181550\pi\)
\(270\) 0 0
\(271\) −4.42513e8 −1.35062 −0.675311 0.737533i \(-0.735990\pi\)
−0.675311 + 0.737533i \(0.735990\pi\)
\(272\) 3.14419e8 + 4.71450e8i 0.947366 + 1.42051i
\(273\) 0 0
\(274\) 2.49396e8 1.49408e8i 0.732423 0.438781i
\(275\) 1.48135e8i 0.429531i
\(276\) 0 0
\(277\) 3.18148e8i 0.899395i 0.893181 + 0.449697i \(0.148468\pi\)
−0.893181 + 0.449697i \(0.851532\pi\)
\(278\) 3.04088e8 + 5.07591e8i 0.848873 + 1.41696i
\(279\) 0 0
\(280\) −4.49162e8 + 2.17719e7i −1.22278 + 0.0592713i
\(281\) −1.28497e8 −0.345478 −0.172739 0.984968i \(-0.555262\pi\)
−0.172739 + 0.984968i \(0.555262\pi\)
\(282\) 0 0
\(283\) 3.98970e8i 1.04637i −0.852218 0.523187i \(-0.824743\pi\)
0.852218 0.523187i \(-0.175257\pi\)
\(284\) −3.25470e7 + 6.08274e7i −0.0843134 + 0.157574i
\(285\) 0 0
\(286\) −3.32806e8 + 1.99378e8i −0.841221 + 0.503960i
\(287\) 6.86057e7 0.171306
\(288\) 0 0
\(289\) 7.85942e8 1.91535
\(290\) −5.38896e8 + 3.22842e8i −1.29751 + 0.777316i
\(291\) 0 0
\(292\) −1.62149e8 + 3.03042e8i −0.381131 + 0.712299i
\(293\) 2.00958e8i 0.466732i −0.972389 0.233366i \(-0.925026\pi\)
0.972389 0.233366i \(-0.0749741\pi\)
\(294\) 0 0
\(295\) 7.33298e7 0.166304
\(296\) 1.49905e8 7.26625e6i 0.335965 0.0162850i
\(297\) 0 0
\(298\) −1.04893e8 1.75090e8i −0.229610 0.383270i
\(299\) 1.55143e8i 0.335647i
\(300\) 0 0
\(301\) 3.14284e8i 0.664262i
\(302\) 3.75971e8 2.25237e8i 0.785470 0.470560i
\(303\) 0 0
\(304\) 1.98949e8 1.32683e8i 0.406148 0.270868i
\(305\) 5.03830e8 1.01680
\(306\) 0 0
\(307\) 1.58918e7i 0.0313465i 0.999877 + 0.0156733i \(0.00498916\pi\)
−0.999877 + 0.0156733i \(0.995011\pi\)
\(308\) −5.88850e8 3.15077e8i −1.14836 0.614453i
\(309\) 0 0
\(310\) 2.10722e8 + 3.51741e8i 0.401738 + 0.670591i
\(311\) −4.87710e8 −0.919391 −0.459695 0.888077i \(-0.652041\pi\)
−0.459695 + 0.888077i \(0.652041\pi\)
\(312\) 0 0
\(313\) −3.24731e8 −0.598576 −0.299288 0.954163i \(-0.596749\pi\)
−0.299288 + 0.954163i \(0.596749\pi\)
\(314\) −2.97890e8 4.97245e8i −0.543003 0.906394i
\(315\) 0 0
\(316\) 4.96770e8 9.28419e8i 0.885627 1.65516i
\(317\) 1.06084e9i 1.87043i 0.354086 + 0.935213i \(0.384792\pi\)
−0.354086 + 0.935213i \(0.615208\pi\)
\(318\) 0 0
\(319\) −9.32958e8 −1.60914
\(320\) −6.58171e7 6.77318e8i −0.112283 1.15549i
\(321\) 0 0
\(322\) −2.29102e8 + 1.37251e8i −0.382414 + 0.229097i
\(323\) 5.04824e8i 0.833548i
\(324\) 0 0
\(325\) 1.70881e8i 0.276123i
\(326\) 4.98618e8 + 8.32304e8i 0.797088 + 1.33052i
\(327\) 0 0
\(328\) 5.02651e6 + 1.03698e8i 0.00786516 + 0.162261i
\(329\) 1.13919e8 0.176365
\(330\) 0 0
\(331\) 2.88487e8i 0.437249i −0.975809 0.218624i \(-0.929843\pi\)
0.975809 0.218624i \(-0.0701569\pi\)
\(332\) −6.65319e8 3.55993e8i −0.997808 0.533898i
\(333\) 0 0
\(334\) 1.02751e9 6.15563e8i 1.50895 0.903982i
\(335\) 1.02661e8 0.149193
\(336\) 0 0
\(337\) −1.10595e8 −0.157410 −0.0787051 0.996898i \(-0.525079\pi\)
−0.0787051 + 0.996898i \(0.525079\pi\)
\(338\) 2.25089e8 1.34847e8i 0.317063 0.189947i
\(339\) 0 0
\(340\) −1.26666e9 6.77751e8i −1.74776 0.935177i
\(341\) 6.08948e8i 0.831649i
\(342\) 0 0
\(343\) 6.99837e8 0.936414
\(344\) 4.75044e8 2.30265e7i 0.629186 0.0304981i
\(345\) 0 0
\(346\) 1.15209e8 + 1.92309e8i 0.149527 + 0.249594i
\(347\) 1.10651e9i 1.42168i −0.703352 0.710841i \(-0.748314\pi\)
0.703352 0.710841i \(-0.251686\pi\)
\(348\) 0 0
\(349\) 1.38337e9i 1.74201i 0.491278 + 0.871003i \(0.336530\pi\)
−0.491278 + 0.871003i \(0.663470\pi\)
\(350\) 2.52344e8 1.51174e8i 0.314597 0.188469i
\(351\) 0 0
\(352\) 4.33099e8 9.13138e8i 0.529283 1.11593i
\(353\) 2.47617e8 0.299618 0.149809 0.988715i \(-0.452134\pi\)
0.149809 + 0.988715i \(0.452134\pi\)
\(354\) 0 0
\(355\) 1.74890e8i 0.207475i
\(356\) −2.63898e7 + 4.93202e7i −0.0310000 + 0.0579362i
\(357\) 0 0
\(358\) 1.73150e8 + 2.89026e8i 0.199449 + 0.332925i
\(359\) 1.38641e9 1.58148 0.790738 0.612155i \(-0.209697\pi\)
0.790738 + 0.612155i \(0.209697\pi\)
\(360\) 0 0
\(361\) 6.80839e8 0.761674
\(362\) −2.30378e7 3.84552e7i −0.0255247 0.0426064i
\(363\) 0 0
\(364\) −6.79267e8 3.63456e8i −0.738219 0.395000i
\(365\) 8.71299e8i 0.937869i
\(366\) 0 0
\(367\) −7.49367e8 −0.791341 −0.395670 0.918393i \(-0.629488\pi\)
−0.395670 + 0.918393i \(0.629488\pi\)
\(368\) −2.24242e8 3.36235e8i −0.234558 0.351703i
\(369\) 0 0
\(370\) −3.26381e8 + 1.95529e8i −0.334980 + 0.200680i
\(371\) 9.95340e8i 1.01196i
\(372\) 0 0
\(373\) 1.49519e9i 1.49181i −0.666051 0.745906i \(-0.732017\pi\)
0.666051 0.745906i \(-0.267983\pi\)
\(374\) −1.09644e9 1.83021e9i −1.08377 1.80905i
\(375\) 0 0
\(376\) 8.34649e6 + 1.72191e8i 0.00809741 + 0.167052i
\(377\) −1.07621e9 −1.03443
\(378\) 0 0
\(379\) 7.92096e7i 0.0747379i 0.999302 + 0.0373689i \(0.0118977\pi\)
−0.999302 + 0.0373689i \(0.988102\pi\)
\(380\) −2.86007e8 + 5.34522e8i −0.267383 + 0.499715i
\(381\) 0 0
\(382\) 4.65959e8 2.79147e8i 0.427687 0.256219i
\(383\) −4.80285e8 −0.436820 −0.218410 0.975857i \(-0.570087\pi\)
−0.218410 + 0.975857i \(0.570087\pi\)
\(384\) 0 0
\(385\) 1.69305e9 1.51202
\(386\) −4.58580e7 + 2.74726e7i −0.0405844 + 0.0243134i
\(387\) 0 0
\(388\) −4.73636e8 + 8.85183e8i −0.411655 + 0.769346i
\(389\) 1.07150e9i 0.922928i 0.887159 + 0.461464i \(0.152676\pi\)
−0.887159 + 0.461464i \(0.847324\pi\)
\(390\) 0 0
\(391\) −8.53180e8 −0.721809
\(392\) −6.46656e6 1.33407e8i −0.00542216 0.111861i
\(393\) 0 0
\(394\) 6.67957e8 + 1.11497e9i 0.550189 + 0.918387i
\(395\) 2.66937e9i 2.17931i
\(396\) 0 0
\(397\) 2.03185e9i 1.62976i 0.579627 + 0.814882i \(0.303198\pi\)
−0.579627 + 0.814882i \(0.696802\pi\)
\(398\) 1.17369e8 7.03138e7i 0.0933178 0.0559049i
\(399\) 0 0
\(400\) 2.46990e8 + 3.70344e8i 0.192961 + 0.289331i
\(401\) 2.57759e9 1.99622 0.998111 0.0614301i \(-0.0195661\pi\)
0.998111 + 0.0614301i \(0.0195661\pi\)
\(402\) 0 0
\(403\) 7.02451e8i 0.534624i
\(404\) −6.99455e8 3.74258e8i −0.527746 0.282382i
\(405\) 0 0
\(406\) −9.52097e8 1.58926e9i −0.706057 1.17857i
\(407\) −5.65044e8 −0.415434
\(408\) 0 0
\(409\) 3.30242e8 0.238672 0.119336 0.992854i \(-0.461923\pi\)
0.119336 + 0.992854i \(0.461923\pi\)
\(410\) −1.35259e8 2.25778e8i −0.0969223 0.161785i
\(411\) 0 0
\(412\) −3.98449e8 + 7.44666e8i −0.280693 + 0.524591i
\(413\) 2.16257e8i 0.151059i
\(414\) 0 0
\(415\) 1.91291e9 1.31379
\(416\) 4.99600e8 1.05335e9i 0.340248 0.717374i
\(417\) 0 0
\(418\) −7.72337e8 + 4.62692e8i −0.517237 + 0.309867i
\(419\) 5.80021e7i 0.0385207i −0.999815 0.0192604i \(-0.993869\pi\)
0.999815 0.0192604i \(-0.00613114\pi\)
\(420\) 0 0
\(421\) 1.90609e8i 0.124496i 0.998061 + 0.0622480i \(0.0198270\pi\)
−0.998061 + 0.0622480i \(0.980173\pi\)
\(422\) 1.13873e9 + 1.90079e9i 0.737610 + 1.23123i
\(423\) 0 0
\(424\) −1.50447e9 + 7.29251e7i −0.958523 + 0.0464619i
\(425\) 9.39731e8 0.593803
\(426\) 0 0
\(427\) 1.48585e9i 0.923586i
\(428\) 5.78795e7 + 3.09696e7i 0.0356838 + 0.0190934i
\(429\) 0 0
\(430\) −1.03429e9 + 6.19625e8i −0.627341 + 0.375828i
\(431\) −2.42923e9 −1.46150 −0.730749 0.682646i \(-0.760829\pi\)
−0.730749 + 0.682646i \(0.760829\pi\)
\(432\) 0 0
\(433\) −2.37902e9 −1.40828 −0.704141 0.710060i \(-0.748668\pi\)
−0.704141 + 0.710060i \(0.748668\pi\)
\(434\) −1.03732e9 + 6.21440e8i −0.609116 + 0.364910i
\(435\) 0 0
\(436\) 2.21071e9 + 1.18289e9i 1.27741 + 0.683504i
\(437\) 3.60037e8i 0.206378i
\(438\) 0 0
\(439\) −1.33161e9 −0.751194 −0.375597 0.926783i \(-0.622562\pi\)
−0.375597 + 0.926783i \(0.622562\pi\)
\(440\) 1.24044e8 + 2.55906e9i 0.0694210 + 1.43218i
\(441\) 0 0
\(442\) −1.26480e9 2.11123e9i −0.696696 1.16294i
\(443\) 5.02643e8i 0.274692i −0.990523 0.137346i \(-0.956143\pi\)
0.990523 0.137346i \(-0.0438573\pi\)
\(444\) 0 0
\(445\) 1.41805e8i 0.0762834i
\(446\) 1.04842e9 6.28086e8i 0.559579 0.335233i
\(447\) 0 0
\(448\) 1.99748e9 1.94102e8i 1.04957 0.101990i
\(449\) −3.14785e9 −1.64116 −0.820580 0.571531i \(-0.806350\pi\)
−0.820580 + 0.571531i \(0.806350\pi\)
\(450\) 0 0
\(451\) 3.90876e8i 0.200641i
\(452\) −1.14058e9 + 2.13165e9i −0.580955 + 1.08575i
\(453\) 0 0
\(454\) 9.36939e8 + 1.56396e9i 0.469911 + 0.784387i
\(455\) 1.95301e9 0.971998
\(456\) 0 0
\(457\) −2.68422e9 −1.31556 −0.657782 0.753209i \(-0.728505\pi\)
−0.657782 + 0.753209i \(0.728505\pi\)
\(458\) −3.06514e8 5.11641e8i −0.149081 0.248849i
\(459\) 0 0
\(460\) 9.03372e8 + 4.83368e8i 0.432727 + 0.231540i
\(461\) 1.30434e9i 0.620065i −0.950726 0.310033i \(-0.899660\pi\)
0.950726 0.310033i \(-0.100340\pi\)
\(462\) 0 0
\(463\) 2.86853e9 1.34315 0.671577 0.740934i \(-0.265617\pi\)
0.671577 + 0.740934i \(0.265617\pi\)
\(464\) 2.33243e9 1.55554e9i 1.08392 0.722886i
\(465\) 0 0
\(466\) 1.74136e9 1.04322e9i 0.797148 0.477556i
\(467\) 5.96519e8i 0.271029i −0.990775 0.135514i \(-0.956731\pi\)
0.990775 0.135514i \(-0.0432687\pi\)
\(468\) 0 0
\(469\) 3.02758e8i 0.135516i
\(470\) −2.24597e8 3.74903e8i −0.0997843 0.166562i
\(471\) 0 0
\(472\) −3.26875e8 + 1.58444e7i −0.143082 + 0.00693553i
\(473\) −1.79061e9 −0.778012
\(474\) 0 0
\(475\) 3.96561e8i 0.169778i
\(476\) 1.99876e9 3.73550e9i 0.849447 1.58754i
\(477\) 0 0
\(478\) 8.17619e8 4.89820e8i 0.342416 0.205135i
\(479\) 2.16068e9 0.898289 0.449144 0.893459i \(-0.351729\pi\)
0.449144 + 0.893459i \(0.351729\pi\)
\(480\) 0 0
\(481\) −6.51805e8 −0.267061
\(482\) −2.06047e9 + 1.23439e9i −0.838110 + 0.502096i
\(483\) 0 0
\(484\) −6.18334e8 + 1.15561e9i −0.247893 + 0.463290i
\(485\) 2.54506e9i 1.01298i
\(486\) 0 0
\(487\) 1.41934e8 0.0556847 0.0278424 0.999612i \(-0.491136\pi\)
0.0278424 + 0.999612i \(0.491136\pi\)
\(488\) −2.24588e9 + 1.08863e8i −0.874816 + 0.0424044i
\(489\) 0 0
\(490\) 1.74010e8 + 2.90462e8i 0.0668172 + 0.111533i
\(491\) 2.38677e9i 0.909966i −0.890500 0.454983i \(-0.849645\pi\)
0.890500 0.454983i \(-0.150355\pi\)
\(492\) 0 0
\(493\) 5.91843e9i 2.22455i
\(494\) −8.90927e8 + 5.33738e8i −0.332505 + 0.199197i
\(495\) 0 0
\(496\) −1.01532e9 1.52239e9i −0.373607 0.560197i
\(497\) 5.15769e8 0.188455
\(498\) 0 0
\(499\) 5.23900e9i 1.88754i −0.330601 0.943771i \(-0.607251\pi\)
0.330601 0.943771i \(-0.392749\pi\)
\(500\) 1.86608e9 + 9.98486e8i 0.667629 + 0.357229i
\(501\) 0 0
\(502\) −6.86681e8 1.14622e9i −0.242266 0.404396i
\(503\) 3.63292e9 1.27282 0.636411 0.771350i \(-0.280418\pi\)
0.636411 + 0.771350i \(0.280418\pi\)
\(504\) 0 0
\(505\) 2.01106e9 0.694872
\(506\) 7.81976e8 + 1.30529e9i 0.268328 + 0.447900i
\(507\) 0 0
\(508\) 2.39326e9 4.47278e9i 0.809965 1.51375i
\(509\) 2.58693e9i 0.869505i −0.900550 0.434753i \(-0.856836\pi\)
0.900550 0.434753i \(-0.143164\pi\)
\(510\) 0 0
\(511\) 2.56955e9 0.851892
\(512\) 4.39735e8 + 3.00500e9i 0.144793 + 0.989462i
\(513\) 0 0
\(514\) −1.23708e9 + 7.41108e8i −0.401814 + 0.240719i
\(515\) 2.14105e9i 0.690718i
\(516\) 0 0
\(517\) 6.49047e8i 0.206566i
\(518\) −5.76636e8 9.62533e8i −0.182283 0.304272i
\(519\) 0 0
\(520\) 1.43091e8 + 2.95200e9i 0.0446272 + 0.920672i
\(521\) −1.08542e8 −0.0336253 −0.0168127 0.999859i \(-0.505352\pi\)
−0.0168127 + 0.999859i \(0.505352\pi\)
\(522\) 0 0
\(523\) 6.10725e9i 1.86676i 0.358884 + 0.933382i \(0.383157\pi\)
−0.358884 + 0.933382i \(0.616843\pi\)
\(524\) 4.12318e9 + 2.20620e9i 1.25191 + 0.669861i
\(525\) 0 0
\(526\) −4.20363e9 + 2.51832e9i −1.25943 + 0.754502i
\(527\) −3.86300e9 −1.14971
\(528\) 0 0
\(529\) −2.79634e9 −0.821288
\(530\) 3.27561e9 1.96236e9i 0.955712 0.572549i
\(531\) 0 0
\(532\) −1.57636e9 8.43465e8i −0.453905 0.242871i
\(533\) 4.50894e8i 0.128982i
\(534\) 0 0
\(535\) −1.66414e8 −0.0469841
\(536\) −4.57623e8 + 2.21821e7i −0.128360 + 0.00622193i
\(537\) 0 0
\(538\) −2.00446e9 3.34590e9i −0.554958 0.926349i
\(539\) 5.02858e8i 0.138320i
\(540\) 0 0
\(541\) 5.39345e8i 0.146445i 0.997316 + 0.0732227i \(0.0233284\pi\)
−0.997316 + 0.0732227i \(0.976672\pi\)
\(542\) −4.29475e9 + 2.57290e9i −1.15862 + 0.694106i
\(543\) 0 0
\(544\) 5.79270e9 + 2.74746e9i 1.54271 + 0.731704i
\(545\) −6.35620e9 −1.68194
\(546\) 0 0
\(547\) 8.82287e7i 0.0230491i 0.999934 + 0.0115246i \(0.00366846\pi\)
−0.999934 + 0.0115246i \(0.996332\pi\)
\(548\) 1.55177e9 2.90012e9i 0.402806 0.752808i
\(549\) 0 0
\(550\) −8.61304e8 1.43771e9i −0.220743 0.368469i
\(551\) −2.49754e9 −0.636037
\(552\) 0 0
\(553\) −7.87226e9 −1.97953
\(554\) 1.84981e9 + 3.08774e9i 0.462213 + 0.771537i
\(555\) 0 0
\(556\) 5.90257e9 + 3.15829e9i 1.45639 + 0.779274i
\(557\) 5.57233e8i 0.136629i 0.997664 + 0.0683147i \(0.0217622\pi\)
−0.997664 + 0.0683147i \(0.978238\pi\)
\(558\) 0 0
\(559\) −2.06555e9 −0.500143
\(560\) −4.23269e9 + 2.82286e9i −1.01849 + 0.679254i
\(561\) 0 0
\(562\) −1.24711e9 + 7.47119e8i −0.296365 + 0.177547i
\(563\) 1.17012e9i 0.276344i 0.990408 + 0.138172i \(0.0441227\pi\)
−0.990408 + 0.138172i \(0.955877\pi\)
\(564\) 0 0
\(565\) 6.12887e9i 1.42959i
\(566\) −2.31973e9 3.87214e9i −0.537749 0.897623i
\(567\) 0 0
\(568\) 3.77886e7 + 7.79590e8i 0.00865250 + 0.178504i
\(569\) 2.39181e9 0.544295 0.272147 0.962256i \(-0.412266\pi\)
0.272147 + 0.962256i \(0.412266\pi\)
\(570\) 0 0
\(571\) 3.15823e9i 0.709933i −0.934879 0.354966i \(-0.884492\pi\)
0.934879 0.354966i \(-0.115508\pi\)
\(572\) −2.07076e9 + 3.87007e9i −0.462640 + 0.864634i
\(573\) 0 0
\(574\) 6.65843e8 3.98894e8i 0.146954 0.0880371i
\(575\) −6.70211e8 −0.147019
\(576\) 0 0
\(577\) 4.03435e9 0.874296 0.437148 0.899390i \(-0.355989\pi\)
0.437148 + 0.899390i \(0.355989\pi\)
\(578\) 7.62785e9 4.56970e9i 1.64306 0.984329i
\(579\) 0 0
\(580\) −3.35308e9 + 6.26660e9i −0.713585 + 1.33363i
\(581\) 5.64138e9i 1.19335i
\(582\) 0 0
\(583\) 5.67087e9 1.18525
\(584\) 1.88262e8 + 3.88391e9i 0.0391128 + 0.806908i
\(585\) 0 0
\(586\) −1.16843e9 1.95037e9i −0.239861 0.400382i
\(587\) 2.72240e9i 0.555544i 0.960647 + 0.277772i \(0.0895960\pi\)
−0.960647 + 0.277772i \(0.910404\pi\)
\(588\) 0 0
\(589\) 1.63016e9i 0.328721i
\(590\) 7.11692e8 4.26361e8i 0.142662 0.0854664i
\(591\) 0 0
\(592\) 1.41263e9 9.42113e8i 0.279836 0.186628i
\(593\) 2.29251e9 0.451460 0.225730 0.974190i \(-0.427523\pi\)
0.225730 + 0.974190i \(0.427523\pi\)
\(594\) 0 0
\(595\) 1.07402e10i 2.09028i
\(596\) −2.03605e9 1.08943e9i −0.393937 0.210784i
\(597\) 0 0
\(598\) 9.02047e8 + 1.50572e9i 0.172494 + 0.287932i
\(599\) 3.58734e9 0.681991 0.340995 0.940065i \(-0.389236\pi\)
0.340995 + 0.940065i \(0.389236\pi\)
\(600\) 0 0
\(601\) 8.20369e9 1.54152 0.770759 0.637127i \(-0.219877\pi\)
0.770759 + 0.637127i \(0.219877\pi\)
\(602\) −1.82734e9 3.05024e9i −0.341375 0.569831i
\(603\) 0 0
\(604\) 2.33934e9 4.37201e9i 0.431980 0.807332i
\(605\) 3.32259e9i 0.610004i
\(606\) 0 0
\(607\) −4.60087e9 −0.834986 −0.417493 0.908680i \(-0.637091\pi\)
−0.417493 + 0.908680i \(0.637091\pi\)
\(608\) 1.15941e9 2.44449e9i 0.209207 0.441088i
\(609\) 0 0
\(610\) 4.88985e9 2.92942e9i 0.872251 0.522549i
\(611\) 7.48707e8i 0.132791i
\(612\) 0 0
\(613\) 8.55728e9i 1.50046i 0.661178 + 0.750229i \(0.270057\pi\)
−0.661178 + 0.750229i \(0.729943\pi\)
\(614\) 9.23998e7 + 1.54236e8i 0.0161095 + 0.0268903i
\(615\) 0 0
\(616\) −7.54695e9 + 3.65819e8i −1.30089 + 0.0630570i
\(617\) 2.58089e9 0.442355 0.221178 0.975234i \(-0.429010\pi\)
0.221178 + 0.975234i \(0.429010\pi\)
\(618\) 0 0
\(619\) 5.26641e9i 0.892478i 0.894914 + 0.446239i \(0.147237\pi\)
−0.894914 + 0.446239i \(0.852763\pi\)
\(620\) 4.09026e9 + 2.18858e9i 0.689255 + 0.368800i
\(621\) 0 0
\(622\) −4.73340e9 + 2.83569e9i −0.788690 + 0.472490i
\(623\) 4.18197e8 0.0692903
\(624\) 0 0
\(625\) −7.48796e9 −1.22683
\(626\) −3.15164e9 + 1.88809e9i −0.513483 + 0.307618i
\(627\) 0 0
\(628\) −5.78226e9 3.09392e9i −0.931621 0.498483i
\(629\) 3.58449e9i 0.574314i
\(630\) 0 0
\(631\) 8.32515e9 1.31914 0.659568 0.751645i \(-0.270739\pi\)
0.659568 + 0.751645i \(0.270739\pi\)
\(632\) −5.76773e8 1.18990e10i −0.0908857 1.87500i
\(633\) 0 0
\(634\) 6.16801e9 + 1.02958e10i 0.961242 + 1.60453i
\(635\) 1.28601e10i 1.99313i
\(636\) 0 0
\(637\) 5.80071e8i 0.0889187i
\(638\) −9.05469e9 + 5.42449e9i −1.38039 + 0.826965i
\(639\) 0 0
\(640\) −4.57691e9 6.19093e9i −0.690148 0.933526i
\(641\) −4.26190e9 −0.639146 −0.319573 0.947562i \(-0.603540\pi\)
−0.319573 + 0.947562i \(0.603540\pi\)
\(642\) 0 0
\(643\) 1.26588e10i 1.87782i −0.344167 0.938908i \(-0.611839\pi\)
0.344167 0.938908i \(-0.388161\pi\)
\(644\) −1.42550e9 + 2.66414e9i −0.210314 + 0.393058i
\(645\) 0 0
\(646\) −2.93519e9 4.89949e9i −0.428374 0.715052i
\(647\) 7.38061e9 1.07134 0.535670 0.844427i \(-0.320059\pi\)
0.535670 + 0.844427i \(0.320059\pi\)
\(648\) 0 0
\(649\) 1.23211e9 0.176926
\(650\) −9.93555e8 1.65846e9i −0.141904 0.236870i
\(651\) 0 0
\(652\) 9.67853e9 + 5.17870e9i 1.36755 + 0.731735i
\(653\) 3.21579e9i 0.451951i 0.974133 + 0.225975i \(0.0725569\pi\)
−0.974133 + 0.225975i \(0.927443\pi\)
\(654\) 0 0
\(655\) −1.18549e10 −1.64836
\(656\) 6.51717e8 + 9.77204e8i 0.0901354 + 0.135152i
\(657\) 0 0
\(658\) 1.10563e9 6.62362e8i 0.151293 0.0906368i
\(659\) 5.17004e9i 0.703711i −0.936054 0.351856i \(-0.885551\pi\)
0.936054 0.351856i \(-0.114449\pi\)
\(660\) 0 0
\(661\) 1.95604e9i 0.263435i −0.991287 0.131717i \(-0.957951\pi\)
0.991287 0.131717i \(-0.0420491\pi\)
\(662\) −1.67735e9 2.79987e9i −0.224709 0.375090i
\(663\) 0 0
\(664\) −8.52701e9 + 4.13325e8i −1.13034 + 0.0547902i
\(665\) 4.53232e9 0.597647
\(666\) 0 0
\(667\) 4.22099e9i 0.550775i
\(668\) 6.39330e9 1.19485e10i 0.829865 1.55094i
\(669\) 0 0
\(670\) 9.96362e8 5.96902e8i 0.127984 0.0766727i
\(671\) 8.46551e9 1.08174
\(672\) 0 0
\(673\) 1.54679e9 0.195605 0.0978024 0.995206i \(-0.468819\pi\)
0.0978024 + 0.995206i \(0.468819\pi\)
\(674\) −1.07337e9 + 6.43035e8i −0.135033 + 0.0808956i
\(675\) 0 0
\(676\) 1.40053e9 2.61747e9i 0.174373 0.325888i
\(677\) 8.55209e9i 1.05928i 0.848222 + 0.529642i \(0.177674\pi\)
−0.848222 + 0.529642i \(0.822326\pi\)
\(678\) 0 0
\(679\) 7.50565e9 0.920119
\(680\) −1.62340e10 + 7.86900e8i −1.97990 + 0.0959707i
\(681\) 0 0
\(682\) 3.54061e9 + 5.91006e9i 0.427398 + 0.713422i
\(683\) 7.26976e9i 0.873067i −0.899688 0.436534i \(-0.856206\pi\)
0.899688 0.436534i \(-0.143794\pi\)
\(684\) 0 0
\(685\) 8.33837e9i 0.991206i
\(686\) 6.79217e9 4.06906e9i 0.803293 0.481238i
\(687\) 0 0
\(688\) 4.47658e9 2.98552e9i 0.524068 0.349511i
\(689\) 6.54162e9 0.761935
\(690\) 0 0
\(691\) 5.19893e9i 0.599434i −0.954028 0.299717i \(-0.903108\pi\)
0.954028 0.299717i \(-0.0968922\pi\)
\(692\) 2.23629e9 + 1.19657e9i 0.256541 + 0.137268i
\(693\) 0 0
\(694\) −6.43358e9 1.07391e10i −0.730626 1.21958i
\(695\) −1.69709e10 −1.91760
\(696\) 0 0
\(697\) 2.47961e9 0.277376
\(698\) 8.04333e9 + 1.34261e10i 0.895245 + 1.49436i
\(699\) 0 0
\(700\) 1.57011e9 2.93440e9i 0.173017 0.323353i
\(701\) 1.35221e10i 1.48262i 0.671163 + 0.741310i \(0.265795\pi\)
−0.671163 + 0.741310i \(0.734205\pi\)
\(702\) 0 0
\(703\) −1.51263e9 −0.164206
\(704\) −1.10588e9 1.13805e10i −0.119455 1.22930i
\(705\) 0 0
\(706\) 2.40321e9 1.43972e9i 0.257025 0.153979i
\(707\) 5.93083e9i 0.631172i
\(708\) 0 0
\(709\) 1.05901e10i 1.11594i 0.829862 + 0.557969i \(0.188419\pi\)
−0.829862 + 0.557969i \(0.811581\pi\)
\(710\) −1.01686e9 1.69737e9i −0.106625 0.177980i
\(711\) 0 0
\(712\) 3.06398e7 + 6.32109e8i 0.00318131 + 0.0656314i
\(713\) 2.75507e9 0.284655
\(714\) 0 0
\(715\) 1.11271e10i 1.13845i
\(716\) 3.36096e9 + 1.79835e9i 0.342191 + 0.183096i
\(717\) 0 0
\(718\) 1.34556e10 8.06102e9i 1.35665 0.812746i
\(719\) −1.49161e10 −1.49659 −0.748297 0.663363i \(-0.769128\pi\)
−0.748297 + 0.663363i \(0.769128\pi\)
\(720\) 0 0
\(721\) 6.31417e9 0.627398
\(722\) 6.60779e9 3.95860e9i 0.653395 0.391437i
\(723\) 0 0
\(724\) −4.47180e8 2.39273e8i −0.0437923 0.0234320i
\(725\) 4.64919e9i 0.453100i
\(726\) 0 0
\(727\) −8.90159e9 −0.859206 −0.429603 0.903018i \(-0.641346\pi\)
−0.429603 + 0.903018i \(0.641346\pi\)
\(728\) −8.70577e9 + 4.21989e8i −0.836271 + 0.0405361i
\(729\) 0 0
\(730\) −5.06599e9 8.45627e9i −0.481986 0.804542i
\(731\) 1.13591e10i 1.07556i
\(732\) 0 0
\(733\) 7.99792e9i 0.750090i −0.927007 0.375045i \(-0.877627\pi\)
0.927007 0.375045i \(-0.122373\pi\)
\(734\) −7.27288e9 + 4.35704e9i −0.678844 + 0.406683i
\(735\) 0 0
\(736\) −4.13132e9 1.95947e9i −0.381959 0.181162i
\(737\) 1.72494e9 0.158722
\(738\) 0 0
\(739\) 1.03852e10i 0.946588i 0.880905 + 0.473294i \(0.156935\pi\)
−0.880905 + 0.473294i \(0.843065\pi\)
\(740\) −2.03078e9 + 3.79536e9i −0.184227 + 0.344304i
\(741\) 0 0
\(742\) 5.78720e9 + 9.66013e9i 0.520062 + 0.868099i
\(743\) 3.73477e9 0.334044 0.167022 0.985953i \(-0.446585\pi\)
0.167022 + 0.985953i \(0.446585\pi\)
\(744\) 0 0
\(745\) 5.85402e9 0.518689
\(746\) −8.69345e9 1.45113e10i −0.766666 1.27974i
\(747\) 0 0
\(748\) −2.12827e10 1.13878e10i −1.85940 0.994908i
\(749\) 4.90772e8i 0.0426770i
\(750\) 0 0
\(751\) −1.34330e10 −1.15726 −0.578631 0.815589i \(-0.696413\pi\)
−0.578631 + 0.815589i \(0.696413\pi\)
\(752\) 1.08217e9 + 1.62264e9i 0.0927970 + 0.139143i
\(753\) 0 0
\(754\) −1.04450e10 + 6.25741e9i −0.887379 + 0.531612i
\(755\) 1.25703e10i 1.06300i
\(756\) 0 0
\(757\) 6.78007e9i 0.568065i −0.958815 0.284033i \(-0.908328\pi\)
0.958815 0.284033i \(-0.0916724\pi\)
\(758\) 4.60548e8 + 7.68758e8i 0.0384090 + 0.0641132i
\(759\) 0 0
\(760\) 3.32068e8 + 6.85065e9i 0.0274397 + 0.566089i
\(761\) −8.01137e9 −0.658962 −0.329481 0.944162i \(-0.606874\pi\)
−0.329481 + 0.944162i \(0.606874\pi\)
\(762\) 0 0
\(763\) 1.87451e10i 1.52775i
\(764\) 2.89925e9 5.41845e9i 0.235212 0.439590i
\(765\) 0 0
\(766\) −4.66133e9 + 2.79252e9i −0.374722 + 0.224489i
\(767\) 1.42130e9 0.113737
\(768\) 0 0
\(769\) 1.46553e10 1.16213 0.581063 0.813858i \(-0.302637\pi\)
0.581063 + 0.813858i \(0.302637\pi\)
\(770\) 1.64316e10 9.84389e9i 1.29707 0.777051i
\(771\) 0 0
\(772\) −2.85334e8 + 5.33264e8i −0.0223199 + 0.0417140i
\(773\) 2.33296e10i 1.81668i −0.418233 0.908340i \(-0.637350\pi\)
0.418233 0.908340i \(-0.362650\pi\)
\(774\) 0 0
\(775\) −3.03456e9 −0.234174
\(776\) 5.49913e8 + 1.13449e10i 0.0422453 + 0.871533i
\(777\) 0 0
\(778\) 6.23001e9 + 1.03993e10i 0.474307 + 0.791725i
\(779\)