Properties

Label 8.8.b.a.5.2
Level $8$
Weight $8$
Character 8.5
Analytic conductor $2.499$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(2.49908020387\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(-4.85268 - 2.90715i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.8.b.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.70536 + 5.81430i) q^{2} -40.2163i q^{3} +(60.3879 - 112.860i) q^{4} -324.492i q^{5} +(233.829 + 390.313i) q^{6} -956.960 q^{7} +(70.1132 + 1446.46i) q^{8} +569.651 q^{9} +O(q^{10})\) \(q+(-9.70536 + 5.81430i) q^{2} -40.2163i q^{3} +(60.3879 - 112.860i) q^{4} -324.492i q^{5} +(233.829 + 390.313i) q^{6} -956.960 q^{7} +(70.1132 + 1446.46i) q^{8} +569.651 q^{9} +(1886.69 + 3149.31i) q^{10} -5452.20i q^{11} +(-4538.80 - 2428.58i) q^{12} +6289.38i q^{13} +(9287.64 - 5564.05i) q^{14} -13049.8 q^{15} +(-9090.60 - 13630.7i) q^{16} +34587.3 q^{17} +(-5528.66 + 3312.12i) q^{18} +14595.6i q^{19} +(-36622.0 - 19595.4i) q^{20} +38485.4i q^{21} +(31700.7 + 52915.6i) q^{22} -24667.5 q^{23} +(58171.1 - 2819.69i) q^{24} -27169.8 q^{25} +(-36568.3 - 61040.6i) q^{26} -110862. i q^{27} +(-57788.8 + 108002. i) q^{28} -171116. i q^{29} +(126653. - 75875.7i) q^{30} +111688. q^{31} +(167481. + 79435.5i) q^{32} -219267. q^{33} +(-335682. + 201101. i) q^{34} +310526. i q^{35} +(34400.0 - 64290.6i) q^{36} +103636. i q^{37} +(-84863.4 - 141656. i) q^{38} +252935. q^{39} +(469363. - 22751.1i) q^{40} +71691.3 q^{41} +(-223765. - 373514. i) q^{42} +328419. i q^{43} +(-615334. - 329247. i) q^{44} -184847. i q^{45} +(239406. - 143424. i) q^{46} +119043. q^{47} +(-548177. + 365590. i) q^{48} +92230.3 q^{49} +(263693. - 157973. i) q^{50} -1.39097e6i q^{51} +(709817. + 379802. i) q^{52} +1.04011e6i q^{53} +(644586. + 1.07596e6i) q^{54} -1.76919e6 q^{55} +(-67095.6 - 1.38420e6i) q^{56} +586982. q^{57} +(994918. + 1.66074e6i) q^{58} +225984. i q^{59} +(-788053. + 1.47280e6i) q^{60} -1.55268e6i q^{61} +(-1.08398e6 + 649390. i) q^{62} -545133. q^{63} +(-2.08732e6 + 202831. i) q^{64} +2.04085e6 q^{65} +(2.12807e6 - 1.27489e6i) q^{66} -316375. i q^{67} +(2.08865e6 - 3.90351e6i) q^{68} +992033. i q^{69} +(-1.80549e6 - 3.01376e6i) q^{70} +538965. q^{71} +(39940.0 + 823975. i) q^{72} -2.68512e6 q^{73} +(-602570. - 1.00582e6i) q^{74} +1.09267e6i q^{75} +(1.64726e6 + 881400. i) q^{76} +5.21754e6i q^{77} +(-2.45483e6 + 1.47064e6i) q^{78} +8.22632e6 q^{79} +(-4.42305e6 + 2.94982e6i) q^{80} -3.21264e6 q^{81} +(-695790. + 416834. i) q^{82} +5.89510e6i q^{83} +(4.34345e6 + 2.32405e6i) q^{84} -1.12233e7i q^{85} +(-1.90952e6 - 3.18742e6i) q^{86} -6.88164e6 q^{87} +(7.88638e6 - 382271. i) q^{88} +437005. q^{89} +(1.07475e6 + 1.79400e6i) q^{90} -6.01868e6i q^{91} +(-1.48962e6 + 2.78396e6i) q^{92} -4.49169e6i q^{93} +(-1.15536e6 + 692152. i) q^{94} +4.73616e6 q^{95} +(3.19460e6 - 6.73545e6i) q^{96} -7.84322e6 q^{97} +(-895128. + 536254. i) q^{98} -3.10585e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9} - 1656 q^{10} - 4088 q^{12} + 12048 q^{14} + 17872 q^{15} + 35344 q^{16} + 1452 q^{17} - 89062 q^{18} - 114768 q^{20} + 152860 q^{22} - 1296 q^{23} + 282512 q^{24} - 39314 q^{25} - 316968 q^{26} - 480800 q^{28} + 821648 q^{30} - 89280 q^{31} + 817056 q^{32} + 53880 q^{33} - 1009108 q^{34} - 1253556 q^{36} + 974124 q^{38} - 328208 q^{39} + 954464 q^{40} + 521244 q^{41} - 1093088 q^{42} - 1096344 q^{44} + 929840 q^{46} + 1566432 q^{47} + 853920 q^{48} - 511050 q^{49} - 148626 q^{50} + 823952 q^{52} - 1077064 q^{54} - 3270256 q^{55} - 2468928 q^{56} - 1889896 q^{57} + 3130744 q^{58} + 5715168 q^{60} - 7055808 q^{62} + 5776816 q^{63} - 4792768 q^{64} + 1416480 q^{65} + 7926264 q^{66} + 6608040 q^{68} - 7406912 q^{70} - 7597104 q^{71} - 11363944 q^{72} + 2089564 q^{73} + 7744200 q^{74} + 9241288 q^{76} - 9471184 q^{78} + 16015904 q^{79} - 12600384 q^{80} - 723058 q^{81} + 10715932 q^{82} + 4220608 q^{84} - 5639076 q^{86} - 37453776 q^{87} + 1541200 q^{88} + 2169084 q^{89} - 121864 q^{90} + 669600 q^{92} + 15503712 q^{94} + 48537936 q^{95} + 21402176 q^{96} - 1088308 q^{97} - 14983242 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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
\(3\) 40.2163i 0.859959i −0.902839 0.429979i \(-0.858521\pi\)
0.902839 0.429979i \(-0.141479\pi\)
\(4\) 60.3879 112.860i 0.471781 0.881716i
\(5\) 324.492i 1.16094i −0.814283 0.580468i \(-0.802870\pi\)
0.814283 0.580468i \(-0.197130\pi\)
\(6\) 233.829 + 390.313i 0.441947 + 0.737707i
\(7\) −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
\(9\) 569.651 0.260471
\(10\) 1886.69 + 3149.31i 0.596624 + 0.995898i
\(11\) 5452.20i 1.23509i −0.786537 0.617544i \(-0.788128\pi\)
0.786537 0.617544i \(-0.211872\pi\)
\(12\) −4538.80 2428.58i −0.758239 0.405712i
\(13\) 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
\(15\) −13049.8 −0.998357
\(16\) −9090.60 13630.7i −0.554846 0.831953i
\(17\) 34587.3 1.70744 0.853720 0.520733i \(-0.174341\pi\)
0.853720 + 0.520733i \(0.174341\pi\)
\(18\) −5528.66 + 3312.12i −0.223443 + 0.133860i
\(19\) 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
\(21\) 38485.4i 0.906835i
\(22\) 31700.7 + 52915.6i 0.634731 + 1.05951i
\(23\) −24667.5 −0.422743 −0.211372 0.977406i \(-0.567793\pi\)
−0.211372 + 0.977406i \(0.567793\pi\)
\(24\) 58171.1 2819.69i 0.858950 0.0416354i
\(25\) −27169.8 −0.347774
\(26\) −36568.3 61040.6i −0.408036 0.681102i
\(27\) 110862.i 1.08395i
\(28\) −57788.8 + 108002.i −0.497497 + 0.929779i
\(29\) 171116.i 1.30286i −0.758710 0.651429i \(-0.774170\pi\)
0.758710 0.651429i \(-0.225830\pi\)
\(30\) 126653. 75875.7i 0.856431 0.513072i
\(31\) 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
\(33\) −219267. −1.06212
\(34\) −335682. + 201101.i −1.46471 + 0.877480i
\(35\) 310526.i 1.22422i
\(36\) 34400.0 64290.6i 0.122885 0.229662i
\(37\) 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
\(39\) 252935. 0.682784
\(40\) 469363. 22751.1i 1.15958 0.0562074i
\(41\) 71691.3 0.162451 0.0812256 0.996696i \(-0.474117\pi\)
0.0812256 + 0.996696i \(0.474117\pi\)
\(42\) −223765. 373514.i −0.466037 0.777920i
\(43\) 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
\(45\) 184847.i 0.302391i
\(46\) 239406. 143424.i 0.362646 0.217255i
\(47\) 119043. 0.167248 0.0836241 0.996497i \(-0.473350\pi\)
0.0836241 + 0.996497i \(0.473350\pi\)
\(48\) −548177. + 365590.i −0.715445 + 0.477145i
\(49\) 92230.3 0.111992
\(50\) 263693. 157973.i 0.298334 0.178727i
\(51\) 1.39097e6i 1.46833i
\(52\) 709817. + 379802.i 0.700059 + 0.374581i
\(53\) 1.04011e6i 0.959648i 0.877365 + 0.479824i \(0.159300\pi\)
−0.877365 + 0.479824i \(0.840700\pi\)
\(54\) 644586. + 1.07596e6i 0.557061 + 0.929859i
\(55\) −1.76919e6 −1.43386
\(56\) −67095.6 1.38420e6i −0.0510547 1.05327i
\(57\) 586982. 0.419820
\(58\) 994918. + 1.66074e6i 0.669559 + 1.11764i
\(59\) 225984.i 0.143250i 0.997432 + 0.0716250i \(0.0228185\pi\)
−0.997432 + 0.0716250i \(0.977182\pi\)
\(60\) −788053. + 1.47280e6i −0.471006 + 0.880268i
\(61\) 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
\(63\) −545133. −0.274670
\(64\) −2.08732e6 + 202831.i −0.995312 + 0.0967175i
\(65\) 2.04085e6 0.921753
\(66\) 2.12807e6 1.27489e6i 0.911133 0.545843i
\(67\) 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
\(69\) 992033.i 0.363542i
\(70\) −1.80549e6 3.01376e6i −0.629146 1.05019i
\(71\) 538965. 0.178713 0.0893566 0.996000i \(-0.471519\pi\)
0.0893566 + 0.996000i \(0.471519\pi\)
\(72\) 39940.0 + 823975.i 0.0126109 + 0.260166i
\(73\) −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
\(75\) 1.09267e6i 0.299071i
\(76\) 1.64726e6 + 881400.i 0.430442 + 0.230317i
\(77\) 5.21754e6i 1.30241i
\(78\) −2.45483e6 + 1.47064e6i −0.585720 + 0.350894i
\(79\) 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
\(81\) −3.21264e6 −0.671684
\(82\) −695790. + 416834.i −0.139357 + 0.0834863i
\(83\) 5.89510e6i 1.13167i 0.824520 + 0.565833i \(0.191445\pi\)
−0.824520 + 0.565833i \(0.808555\pi\)
\(84\) 4.34345e6 + 2.32405e6i 0.799571 + 0.427827i
\(85\) 1.12233e7i 1.98223i
\(86\) −1.90952e6 3.18742e6i −0.323728 0.540375i
\(87\) −6.88164e6 −1.12040
\(88\) 7.88638e6 382271.i 1.23364 0.0597974i
\(89\) 437005. 0.0657085 0.0328542 0.999460i \(-0.489540\pi\)
0.0328542 + 0.999460i \(0.489540\pi\)
\(90\) 1.07475e6 + 1.79400e6i 0.155403 + 0.259403i
\(91\) 6.01868e6i 0.837253i
\(92\) −1.48962e6 + 2.78396e6i −0.199442 + 0.372740i
\(93\) 4.49169e6i 0.579055i
\(94\) −1.15536e6 + 692152.i −0.143472 + 0.0859516i
\(95\) 4.73616e6 0.566753
\(96\) 3.19460e6 6.73545e6i 0.368525 0.776993i
\(97\) −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
\(99\) 3.10585e6i 0.321705i
\(100\) −1.64073e6 + 3.06638e6i −0.164073 + 0.306638i
\(101\) 6.19757e6i 0.598545i 0.954168 + 0.299272i \(0.0967439\pi\)
−0.954168 + 0.299272i \(0.903256\pi\)
\(102\) 8.08752e6 + 1.34999e7i 0.754597 + 1.25959i
\(103\) −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
\(105\) 1.24882e7 1.05278
\(106\) −6.04748e6 1.00946e7i −0.493179 0.823225i
\(107\) 512845.i 0.0404709i −0.999795 0.0202354i \(-0.993558\pi\)
0.999795 0.0202354i \(-0.00644158\pi\)
\(108\) −1.25119e7 6.69474e6i −0.955739 0.511388i
\(109\) 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
\(111\) 4.16785e6 0.289256
\(112\) 8.69934e6 + 1.30441e7i 0.585091 + 0.877303i
\(113\) 1.88876e7 1.23141 0.615705 0.787977i \(-0.288871\pi\)
0.615705 + 0.787977i \(0.288871\pi\)
\(114\) −5.69687e6 + 3.41289e6i −0.360139 + 0.215752i
\(115\) 8.00438e6i 0.490778i
\(116\) −1.93121e7 1.03333e7i −1.14875 0.614663i
\(117\) 3.58275e6i 0.206807i
\(118\) −1.31394e6 2.19325e6i −0.0736185 0.122886i
\(119\) −3.30987e7 −1.80051
\(120\) −914967. 1.88760e7i −0.0483360 0.997187i
\(121\) −1.02394e7 −0.525441
\(122\) 9.02772e6 + 1.50693e7i 0.450110 + 0.751334i
\(123\) 2.88316e6i 0.139701i
\(124\) 6.74463e6 1.26051e7i 0.317675 0.593706i
\(125\) 1.65345e7i 0.757193i
\(126\) 5.29071e6 3.16957e6i 0.235623 0.141157i
\(127\) 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
\(129\) 1.32078e7 0.541709
\(130\) −1.98072e7 + 1.18661e7i −0.790717 + 0.473703i
\(131\) 3.65337e7i 1.41986i −0.704274 0.709928i \(-0.748727\pi\)
0.704274 0.709928i \(-0.251273\pi\)
\(132\) −1.32411e7 + 2.47464e7i −0.501090 + 0.936492i
\(133\) 1.39675e7i 0.514797i
\(134\) 1.83950e6 + 3.07053e6i 0.0660439 + 0.110242i
\(135\) −3.59739e7 −1.25840
\(136\) 2.42503e6 + 5.00290e7i 0.0826666 + 1.70544i
\(137\) −2.56967e7 −0.853799 −0.426899 0.904299i \(-0.640394\pi\)
−0.426899 + 0.904299i \(0.640394\pi\)
\(138\) −5.76798e6 9.62804e6i −0.186830 0.311861i
\(139\) 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
\(141\) 4.78747e6i 0.143827i
\(142\) −5.23085e6 + 3.13370e6i −0.153307 + 0.0918436i
\(143\) 3.42910e7 0.980626
\(144\) −5.17847e6 7.76475e6i −0.144521 0.216700i
\(145\) −5.55256e7 −1.51254
\(146\) 2.60601e7 1.56121e7i 0.693011 0.415170i
\(147\) 3.70916e6i 0.0963085i
\(148\) 1.16963e7 + 6.25836e6i 0.296574 + 0.158688i
\(149\) 1.80406e7i 0.446785i 0.974729 + 0.223392i \(0.0717131\pi\)
−0.974729 + 0.223392i \(0.928287\pi\)
\(150\) −6.35311e6 1.06047e7i −0.153697 0.256555i
\(151\) 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
\(153\) 1.97027e7 0.444739
\(154\) −3.03363e7 5.06381e7i −0.669331 1.11726i
\(155\) 3.62420e7i 0.781719i
\(156\) 1.52742e7 2.85462e7i 0.322124 0.602022i
\(157\) 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
\(159\) 4.18292e7 0.825258
\(160\) 2.57762e7 5.43460e7i 0.497506 1.04893i
\(161\) 2.36058e7 0.445787
\(162\) 3.11798e7 1.86793e7i 0.576197 0.345189i
\(163\) 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
\(165\) 7.11504e7i 1.23306i
\(166\) −3.42759e7 5.72141e7i −0.581581 0.970789i
\(167\) −1.05871e8 −1.75901 −0.879503 0.475893i \(-0.842125\pi\)
−0.879503 + 0.475893i \(0.842125\pi\)
\(168\) −5.56674e7 + 2.69833e6i −0.905772 + 0.0439049i
\(169\) 2.31923e7 0.369606
\(170\) 6.52555e7 + 1.08926e8i 1.01870 + 1.70044i
\(171\) 8.31441e6i 0.127158i
\(172\) 3.70652e7 + 1.98325e7i 0.555415 + 0.297186i
\(173\) 1.98148e7i 0.290956i −0.989361 0.145478i \(-0.953528\pi\)
0.989361 0.145478i \(-0.0464720\pi\)
\(174\) 6.67888e7 4.00119e7i 0.961128 0.575793i
\(175\) 2.60005e7 0.366731
\(176\) −7.43175e7 + 4.95638e7i −1.02753 + 0.685284i
\(177\) 9.08822e6 0.123189
\(178\) −4.24129e6 + 2.54088e6i −0.0563674 + 0.0337686i
\(179\) 2.97800e7i 0.388096i −0.980992 0.194048i \(-0.937838\pi\)
0.980992 0.194048i \(-0.0621618\pi\)
\(180\) −2.08617e7 1.11625e7i −0.266623 0.142662i
\(181\) 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
\(183\) −6.24429e7 −0.753189
\(184\) −1.72951e6 3.56804e7i −0.0204674 0.422248i
\(185\) 3.36290e7 0.390493
\(186\) 2.61160e7 + 4.35935e7i 0.297586 + 0.496737i
\(187\) 1.88577e8i 2.10884i
\(188\) 7.18876e6 1.34352e7i 0.0789045 0.147465i
\(189\) 1.06091e8i 1.14304i
\(190\) −4.59662e7 + 2.75375e7i −0.486184 + 0.291264i
\(191\) −4.80105e7 −0.498562 −0.249281 0.968431i \(-0.580194\pi\)
−0.249281 + 0.968431i \(0.580194\pi\)
\(192\) 8.15712e6 + 8.39443e7i 0.0831731 + 0.855927i
\(193\) −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
\(195\) 8.20754e7i 0.792669i
\(196\) 5.56959e6 1.04091e7i 0.0528357 0.0987452i
\(197\) 1.14882e8i 1.07058i −0.844668 0.535290i \(-0.820202\pi\)
0.844668 0.535290i \(-0.179798\pi\)
\(198\) 1.80583e7 + 3.01434e7i 0.165329 + 0.275971i
\(199\) 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
\(201\) −1.27234e7 −0.110514
\(202\) −3.60345e7 6.01496e7i −0.307602 0.513456i
\(203\) 1.63751e8i 1.37388i
\(204\) −1.56985e8 8.39979e7i −1.29465 0.692728i
\(205\) 2.32632e7i 0.188596i
\(206\) 6.40375e7 3.83636e7i 0.510386 0.305763i
\(207\) −1.40518e7 −0.110112
\(208\) 8.57287e7 5.71742e7i 0.660548 0.440533i
\(209\) 7.95784e7 0.602953
\(210\) −1.21202e8 + 7.26100e7i −0.903116 + 0.541040i
\(211\) 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
\(213\) 2.16752e7i 0.153686i
\(214\) 2.98183e6 + 4.97734e6i 0.0207986 + 0.0347176i
\(215\) 1.06569e8 0.731302
\(216\) 1.60357e8 7.77291e6i 1.08268 0.0524802i
\(217\) −1.06881e8 −0.710057
\(218\) −1.13891e8 1.90110e8i −0.744549 1.24282i
\(219\) 1.07986e8i 0.694723i
\(220\) −1.06838e8 + 1.99671e8i −0.676466 + 1.26426i
\(221\) 2.17532e8i 1.35566i
\(222\) −4.04505e7 + 2.42331e7i −0.248135 + 0.148653i
\(223\) 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
\(225\) −1.54773e7 −0.0905851
\(226\) −1.83311e8 + 1.09818e8i −1.05635 + 0.632841i
\(227\) 1.61144e8i 0.914374i −0.889371 0.457187i \(-0.848857\pi\)
0.889371 0.457187i \(-0.151143\pi\)
\(228\) 3.54466e7 6.62466e7i 0.198063 0.370162i
\(229\) 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
\(231\) 2.09830e8 1.12002
\(232\) 2.47511e8 1.19975e7i 1.30133 0.0630786i
\(233\) −1.79423e8 −0.929249 −0.464625 0.885508i \(-0.653811\pi\)
−0.464625 + 0.885508i \(0.653811\pi\)
\(234\) −2.08312e7 3.47718e7i −0.106282 0.177408i
\(235\) 3.86285e7i 0.194165i
\(236\) 2.55044e7 + 1.36467e7i 0.126306 + 0.0675826i
\(237\) 3.30832e8i 1.61431i
\(238\) 3.21234e8 1.92445e8i 1.54455 0.925312i
\(239\) −8.42441e7 −0.399160 −0.199580 0.979882i \(-0.563958\pi\)
−0.199580 + 0.979882i \(0.563958\pi\)
\(240\) 1.18631e8 + 1.77879e8i 0.553935 + 0.830586i
\(241\) −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
\(243\) 1.13255e8i 0.506333i
\(244\) −1.75234e8 9.37629e7i −0.772245 0.413206i
\(245\) 2.99280e7i 0.130016i
\(246\) 1.67635e7 + 2.79821e7i 0.0717947 + 0.119841i
\(247\) −9.17975e7 −0.387607
\(248\) 7.83083e6 + 1.61552e8i 0.0326007 + 0.672563i
\(249\) 2.37079e8 0.973186
\(250\) 9.61366e7 + 1.60473e8i 0.389134 + 0.649551i
\(251\) 1.18102e8i 0.471411i 0.971825 + 0.235706i \(0.0757401\pi\)
−0.971825 + 0.235706i \(0.924260\pi\)
\(252\) −3.29194e7 + 6.15235e7i −0.129584 + 0.242181i
\(253\) 1.34492e8i 0.522125i
\(254\) −3.84637e8 + 2.30429e8i −1.47276 + 0.882304i
\(255\) −4.51359e8 −1.70463
\(256\) −1.03157e8 + 2.47823e8i −0.384291 + 0.923212i
\(257\) 1.27463e8 0.468402 0.234201 0.972188i \(-0.424753\pi\)
0.234201 + 0.972188i \(0.424753\pi\)
\(258\) −1.28186e8 + 7.67940e7i −0.464700 + 0.278393i
\(259\) 9.91755e7i 0.354695i
\(260\) 1.23243e8 2.30330e8i 0.434865 0.812724i
\(261\) 9.74762e7i 0.339357i
\(262\) 2.12418e8 + 3.54573e8i 0.729687 + 1.21801i
\(263\) 4.33125e8 1.46814 0.734071 0.679073i \(-0.237618\pi\)
0.734071 + 0.679073i \(0.237618\pi\)
\(264\) −1.53735e7 3.17161e8i −0.0514233 1.06088i
\(265\) 3.37506e8 1.11409
\(266\) 8.12109e7 + 1.35559e8i 0.264563 + 0.441614i
\(267\) 1.75747e7i 0.0565066i
\(268\) −3.57060e7 1.91052e7i −0.113310 0.0606290i
\(269\) 3.44748e8i 1.07986i 0.841709 + 0.539931i \(0.181550\pi\)
−0.841709 + 0.539931i \(0.818450\pi\)
\(270\) 3.49139e8 2.09163e8i 1.07951 0.646712i
\(271\) −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
\(273\) −2.42049e8 −0.720003
\(274\) 2.49396e8 1.49408e8i 0.732423 0.438781i
\(275\) 1.48135e8i 0.429531i
\(276\) 1.11961e8 + 5.99068e7i 0.320541 + 0.171512i
\(277\) 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
\(279\) 6.36234e7 0.175389
\(280\) −4.49162e8 + 2.17719e7i −1.22278 + 0.0592713i
\(281\) 1.28497e8 0.345478 0.172739 0.984968i \(-0.444738\pi\)
0.172739 + 0.984968i \(0.444738\pi\)
\(282\) 2.78358e7 + 4.64641e7i 0.0739148 + 0.123380i
\(283\) 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
\(285\) 1.90471e8i 0.487384i
\(286\) −3.32806e8 + 1.99378e8i −0.841221 + 0.503960i
\(287\) −6.86057e7 −0.171306
\(288\) 9.54054e7 + 4.52505e7i 0.235342 + 0.111622i
\(289\) 7.85942e8 1.91535
\(290\) 5.38896e8 3.22842e8i 1.29751 0.777316i
\(291\) 3.15425e8i 0.750362i
\(292\) −1.62149e8 + 3.03042e8i −0.381131 + 0.712299i
\(293\) 2.00958e8i 0.466732i 0.972389 + 0.233366i \(0.0749741\pi\)
−0.972389 + 0.233366i \(0.925026\pi\)
\(294\) 2.15662e7 + 3.59987e7i 0.0494945 + 0.0826174i
\(295\) 7.33298e7 0.166304
\(296\) −1.49905e8 + 7.26625e6i −0.335965 + 0.0162850i
\(297\) −6.04444e8 −1.33878
\(298\) −1.04893e8 1.75090e8i −0.229610 0.383270i
\(299\) 1.55143e8i 0.335647i
\(300\) 1.23318e8 + 6.59840e7i 0.263696 + 0.141096i
\(301\) 3.14284e8i 0.664262i
\(302\) −3.75971e8 + 2.25237e8i −0.785470 + 0.470560i
\(303\) 2.49243e8 0.514724
\(304\) 1.98949e8 1.32683e8i 0.406148 0.270868i
\(305\) −5.03830e8 −1.01680
\(306\) −1.91221e8 + 1.14557e8i −0.381515 + 0.228558i
\(307\) 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
\(309\) 2.65353e8i 0.511646i
\(310\) 2.10722e8 + 3.51741e8i 0.401738 + 0.670591i
\(311\) 4.87710e8 0.919391 0.459695 0.888077i \(-0.347959\pi\)
0.459695 + 0.888077i \(0.347959\pi\)
\(312\) 1.77341e7 + 3.65860e8i 0.0330574 + 0.681983i
\(313\) −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
\(315\) 1.76891e8i 0.318874i
\(316\) 4.96770e8 9.28419e8i 0.885627 1.65516i
\(317\) 1.06084e9i 1.87043i −0.354086 0.935213i \(-0.615208\pi\)
0.354086 0.935213i \(-0.384792\pi\)
\(318\) −4.05967e8 + 2.43207e8i −0.707939 + 0.424113i
\(319\) −9.32958e8 −1.60914
\(320\) 6.58171e7 + 6.77318e8i 0.112283 + 1.15549i
\(321\) −2.06247e7 −0.0348033
\(322\) −2.29102e8 + 1.37251e8i −0.382414 + 0.229097i
\(323\) 5.04824e8i 0.833548i
\(324\) −1.94005e8 + 3.62578e8i −0.316887 + 0.592234i
\(325\) 1.70881e8i 0.276123i
\(326\) −4.98618e8 8.32304e8i −0.797088 1.33052i
\(327\) 7.87763e8 1.24589
\(328\) 5.02651e6 + 1.03698e8i 0.00786516 + 0.162261i
\(329\) −1.13919e8 −0.176365
\(330\) −4.13690e8 6.90540e8i −0.633689 1.05777i
\(331\) 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
\(333\) 5.90363e7i 0.0876121i
\(334\) 1.02751e9 6.15563e8i 1.50895 0.903982i
\(335\) −1.02661e8 −0.149193
\(336\) 5.24583e8 3.49855e8i 0.754444 0.503154i
\(337\) −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
\(339\) 7.59590e8i 1.05896i
\(340\) −1.26666e9 6.77751e8i −1.74776 0.935177i
\(341\) 6.08948e8i 0.831649i
\(342\) −4.83425e7 8.06944e7i −0.0653488 0.109082i
\(343\) 6.99837e8 0.936414
\(344\) −4.75044e8 + 2.30265e7i −0.629186 + 0.0304981i
\(345\) 3.21907e8 0.422049
\(346\) 1.15209e8 + 1.92309e8i 0.149527 + 0.249594i
\(347\) 1.10651e9i 1.42168i 0.703352 + 0.710841i \(0.251686\pi\)
−0.703352 + 0.710841i \(0.748314\pi\)
\(348\) −4.15568e8 + 7.76659e8i −0.528585 + 0.987878i
\(349\) 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
\(351\) 6.97254e8 0.860630
\(352\) 4.33099e8 9.13138e8i 0.529283 1.11593i
\(353\) −2.47617e8 −0.299618 −0.149809 0.988715i \(-0.547866\pi\)
−0.149809 + 0.988715i \(0.547866\pi\)
\(354\) −8.82044e7 + 5.28416e7i −0.105677 + 0.0633089i
\(355\) 1.74890e8i 0.207475i
\(356\) 2.63898e7 4.93202e7i 0.0310000 0.0579362i
\(357\) 1.33111e9i 1.54837i
\(358\) 1.73150e8 + 2.89026e8i 0.199449 + 0.332925i
\(359\) −1.38641e9 −1.58148 −0.790738 0.612155i \(-0.790303\pi\)
−0.790738 + 0.612155i \(0.790303\pi\)
\(360\) 2.67373e8 1.29602e7i 0.302036 0.0146404i
\(361\) 6.80839e8 0.761674
\(362\) 2.30378e7 + 3.84552e7i 0.0255247 + 0.0426064i
\(363\) 4.11789e8i 0.451858i
\(364\) −6.79267e8 3.63456e8i −0.738219 0.395000i
\(365\) 8.71299e8i 0.937869i
\(366\) 6.06030e8 3.63061e8i 0.646116 0.387076i
\(367\) −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
\(369\) 4.08390e7 0.0423139
\(370\) −3.26381e8 + 1.95529e8i −0.334980 + 0.200680i
\(371\) 9.95340e8i 1.01196i
\(372\) −5.06931e8 2.71244e8i −0.510562 0.273187i
\(373\) 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
\(375\) −6.64957e8 −0.651155
\(376\) 8.34649e6 + 1.72191e8i 0.00809741 + 0.167052i
\(377\) 1.07621e9 1.03443
\(378\) −6.16843e8 1.02965e9i −0.587426 0.980546i
\(379\) 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
\(381\) 1.59383e9i 1.47640i
\(382\) 4.65959e8 2.79147e8i 0.427687 0.256219i
\(383\) 4.80285e8 0.436820 0.218410 0.975857i \(-0.429913\pi\)
0.218410 + 0.975857i \(0.429913\pi\)
\(384\) −5.67245e8 7.67281e8i −0.511224 0.691505i
\(385\) 1.69305e9 1.51202
\(386\) 4.58580e7 2.74726e7i 0.0405844 0.0243134i
\(387\) 1.87084e8i 0.164077i
\(388\) −4.73636e8 + 8.85183e8i −0.411655 + 0.769346i
\(389\) 1.07150e9i 0.922928i −0.887159 0.461464i \(-0.847324\pi\)
0.887159 0.461464i \(-0.152676\pi\)
\(390\) 4.77211e8 + 7.96571e8i 0.407365 + 0.679984i
\(391\) −8.53180e8 −0.721809
\(392\) 6.46656e6 + 1.33407e8i 0.00542216 + 0.111861i
\(393\) −1.46925e9 −1.22102
\(394\) 6.67957e8 + 1.11497e9i 0.550189 + 0.918387i
\(395\) 2.66937e9i 2.17931i
\(396\) −3.50525e8 1.87556e8i −0.283652 0.151774i
\(397\) 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
\(399\) −5.61719e8 −0.442705
\(400\) 2.46990e8 + 3.70344e8i 0.192961 + 0.289331i
\(401\) −2.57759e9 −1.99622 −0.998111 0.0614301i \(-0.980434\pi\)
−0.998111 + 0.0614301i \(0.980434\pi\)
\(402\) 1.23485e8 7.39778e7i 0.0948035 0.0567950i
\(403\) 7.02451e8i 0.534624i
\(404\) 6.99455e8 + 3.74258e8i 0.527746 + 0.282382i
\(405\) 1.04248e9i 0.779782i
\(406\) −9.52097e8 1.58926e9i −0.706057 1.17857i
\(407\) 5.65044e8 0.415434
\(408\) 2.01198e9 9.75255e7i 1.46661 0.0710899i
\(409\) 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
\(411\) 1.03343e9i 0.734232i
\(412\) −3.98449e8 + 7.44666e8i −0.280693 + 0.524591i
\(413\) 2.16257e8i 0.151059i
\(414\) 1.36378e8 8.17015e7i 0.0944590 0.0565886i
\(415\) 1.91291e9 1.31379
\(416\) −4.99600e8 + 1.05335e9i −0.340248 + 0.717374i
\(417\) 2.10331e9 1.42046
\(418\) −7.72337e8 + 4.62692e8i −0.517237 + 0.309867i
\(419\) 5.80021e7i 0.0385207i 0.999815 + 0.0192604i \(0.00613114\pi\)
−0.999815 + 0.0192604i \(0.993869\pi\)
\(420\) 7.54136e8 1.40941e9i 0.496680 0.928251i
\(421\) 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
\(423\) 6.78129e7 0.0435633
\(424\) −1.50447e9 + 7.29251e7i −0.958523 + 0.0464619i
\(425\) −9.39731e8 −0.593803
\(426\) 1.26026e8 + 2.10365e8i 0.0789817 + 0.131838i
\(427\) 1.48585e9i 0.923586i
\(428\) −5.78795e7 3.09696e7i −0.0356838 0.0190934i
\(429\) 1.37906e9i 0.843298i
\(430\) −1.03429e9 + 6.19625e8i −0.627341 + 0.375828i
\(431\) 2.42923e9 1.46150 0.730749 0.682646i \(-0.239171\pi\)
0.730749 + 0.682646i \(0.239171\pi\)
\(432\) −1.51113e9 + 1.00780e9i −0.901798 + 0.601427i
\(433\) −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
\(435\) 2.23303e9i 1.30072i
\(436\) 2.21071e9 + 1.18289e9i 1.27741 + 0.683504i
\(437\) 3.60037e8i 0.206378i
\(438\) −6.27860e8 1.04804e9i −0.357029 0.595961i
\(439\) −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
\(441\) 5.25390e7 0.0291707
\(442\) −1.26480e9 2.11123e9i −0.696696 1.16294i
\(443\) 5.02643e8i 0.274692i 0.990523 + 0.137346i \(0.0438573\pi\)
−0.990523 + 0.137346i \(0.956143\pi\)
\(444\) 2.51688e8 4.70382e8i 0.136465 0.255041i
\(445\) 1.41805e8i 0.0762834i
\(446\) −1.04842e9 + 6.28086e8i −0.559579 + 0.335233i
\(447\) 7.25525e8 0.384217
\(448\) 1.99748e9 1.94102e8i 1.04957 0.101990i
\(449\) 3.14785e9 1.64116 0.820580 0.571531i \(-0.193650\pi\)
0.820580 + 0.571531i \(0.193650\pi\)
\(450\) 1.50213e8 8.99897e7i 0.0777075 0.0465531i
\(451\) 3.90876e8i 0.200641i
\(452\) 1.14058e9 2.13165e9i 0.580955 1.08575i
\(453\) 1.55792e9i 0.787410i
\(454\) 9.36939e8 + 1.56396e9i 0.469911 + 0.784387i
\(455\) −1.95301e9 −0.971998
\(456\) 4.11552e7 + 8.49044e8i 0.0203258 + 0.419328i
\(457\) −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
\(459\) 3.83442e9i 1.85078i
\(460\) 9.03372e8 + 4.83368e8i 0.432727 + 0.231540i
\(461\) 1.30434e9i 0.620065i 0.950726 + 0.310033i \(0.100340\pi\)
−0.950726 + 0.310033i \(0.899660\pi\)
\(462\) −2.03648e9 + 1.22002e9i −0.960799 + 0.575597i
\(463\) 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
\(465\) −1.45752e9 −0.672246
\(466\) 1.74136e9 1.04322e9i 0.797148 0.477556i
\(467\) 5.96519e8i 0.271029i 0.990775 + 0.135514i \(0.0432687\pi\)
−0.990775 + 0.135514i \(0.956731\pi\)
\(468\) 4.04348e8 + 2.16355e8i 0.182345 + 0.0975676i
\(469\) 3.02758e8i 0.135516i
\(470\) 2.24597e8 + 3.74903e8i 0.0997843 + 0.166562i
\(471\) −2.06045e9 −0.908632
\(472\) −3.26875e8 + 1.58444e7i −0.143082 + 0.00693553i
\(473\) 1.79061e9 0.778012
\(474\) 1.92355e9 + 3.21084e9i 0.829622 + 1.38482i
\(475\) 3.96561e8i 0.169778i
\(476\) −1.99876e9 + 3.73550e9i −0.849447 + 1.58754i
\(477\) 5.92497e8i 0.249961i
\(478\) 8.17619e8 4.89820e8i 0.342416 0.205135i
\(479\) −2.16068e9 −0.898289 −0.449144 0.893459i \(-0.648271\pi\)
−0.449144 + 0.893459i \(0.648271\pi\)
\(480\) −2.18560e9 1.03662e9i −0.902039 0.427835i
\(481\) −6.51805e8 −0.267061
\(482\) 2.06047e9 1.23439e9i 0.838110 0.502096i
\(483\) 9.49337e8i 0.383359i
\(484\) −6.18334e8 + 1.15561e9i −0.247893 + 0.463290i
\(485\) 2.54506e9i 1.01298i
\(486\) 6.58499e8 + 1.09918e9i 0.260213 + 0.434353i
\(487\) 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
\(489\) 3.44884e9 1.33380
\(490\) 1.74010e8 + 2.90462e8i 0.0668172 + 0.111533i
\(491\) 2.38677e9i 0.909966i 0.890500 + 0.454983i \(0.150355\pi\)
−0.890500 + 0.454983i \(0.849645\pi\)
\(492\) −3.25392e8 1.74108e8i −0.123177 0.0659084i
\(493\) 5.91843e9i 2.22455i
\(494\) 8.90927e8 5.33738e8i 0.332505 0.199197i
\(495\) −1.00782e9 −0.373479
\(496\) −1.01532e9 1.52239e9i −0.373607 0.560197i
\(497\) −5.15769e8 −0.188455
\(498\) −2.30094e9 + 1.37845e9i −0.834838 + 0.500136i
\(499\) 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
\(501\) 4.25772e9i 1.51267i
\(502\) −6.86681e8 1.14622e9i −0.242266 0.404396i
\(503\) −3.63292e9 −1.27282 −0.636411 0.771350i \(-0.719582\pi\)
−0.636411 + 0.771350i \(0.719582\pi\)
\(504\) −3.82210e7 7.88511e8i −0.0132983 0.274347i
\(505\) 2.01106e9 0.694872
\(506\) −7.81976e8 1.30529e9i −0.268328 0.447900i
\(507\) 9.32706e8i 0.317846i
\(508\) 2.39326e9 4.47278e9i 0.809965 1.51375i
\(509\) 2.58693e9i 0.869505i 0.900550 + 0.434753i \(0.143164\pi\)
−0.900550 + 0.434753i \(0.856836\pi\)
\(510\) 4.38060e9 2.62433e9i 1.46230 0.876039i
\(511\) 2.56955e9 0.851892
\(512\) −4.39735e8 3.00500e9i −0.144793 0.989462i
\(513\) 1.61811e9 0.529171
\(514\) −1.23708e9 + 7.41108e8i −0.401814 + 0.240719i
\(515\) 2.14105e9i 0.690718i
\(516\) 7.97591e8 1.49063e9i 0.255568 0.477633i
\(517\) 6.49047e8i 0.206566i
\(518\) 5.76636e8 + 9.62533e8i 0.182283 + 0.304272i
\(519\) −7.96876e8 −0.250210
\(520\) 1.43091e8 + 2.95200e9i 0.0446272 + 0.920672i
\(521\) 1.08542e8 0.0336253 0.0168127 0.999859i \(-0.494648\pi\)
0.0168127 + 0.999859i \(0.494648\pi\)
\(522\) 5.66755e8 + 9.46041e8i 0.174401 + 0.291114i
\(523\) 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
\(525\) 1.04564e9i 0.315374i
\(526\) −4.20363e9 + 2.51832e9i −1.25943 + 0.754502i
\(527\) 3.86300e9 1.14971
\(528\) 1.99327e9 + 2.98877e9i 0.589315 + 0.883637i
\(529\) −2.79634e9 −0.821288
\(530\) −3.27561e9 + 1.96236e9i −0.955712 + 0.572549i
\(531\) 1.28732e8i 0.0373125i
\(532\) −1.57636e9 8.43465e8i −0.453905 0.242871i
\(533\) 4.50894e8i 0.128982i
\(534\) 1.02185e8 + 1.70569e8i 0.0290396 + 0.0484736i
\(535\) −1.66414e8 −0.0469841
\(536\) 4.57623e8 2.21821e7i 0.128360 0.00622193i
\(537\) −1.19764e9 −0.333747
\(538\) −2.00446e9 3.34590e9i −0.554958 0.926349i
\(539\) 5.02858e8i 0.138320i
\(540\) −2.17239e9 + 4.06000e9i −0.593689 + 1.10955i
\(541\) 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
\(543\) −1.59348e8 −0.0427116
\(544\) 5.79270e9 + 2.74746e9i 1.54271 + 0.731704i
\(545\) 6.35620e9 1.68194
\(546\) 2.34917e9 1.40735e9i 0.617648 0.370021i
\(547\) 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
\(549\) 8.84483e8i 0.228132i
\(550\) −8.61304e8 1.43771e9i −0.220743 0.368469i
\(551\) 2.49754e9 0.636037
\(552\) −1.43493e9 + 6.95546e7i −0.363116 + 0.0176011i
\(553\) −7.87226e9 −1.97953
\(554\) −1.84981e9 3.08774e9i −0.462213 0.771537i
\(555\) 1.35243e9i 0.335807i
\(556\) 5.90257e9 + 3.15829e9i 1.45639 + 0.779274i
\(557\) 5.57233e8i 0.136629i −0.997664 0.0683147i \(-0.978238\pi\)
0.997664 0.0683147i \(-0.0217622\pi\)
\(558\) −6.17488e8 + 3.69925e8i −0.150456 + 0.0901352i
\(559\) −2.06555e9 −0.500143
\(560\) 4.23269e9 2.82286e9i 1.01849 0.679254i
\(561\) −7.58386e9 −1.81351
\(562\) −1.24711e9 + 7.47119e8i −0.296365 + 0.177547i
\(563\) 1.17012e9i 0.276344i −0.990408 0.138172i \(-0.955877\pi\)
0.990408 0.138172i \(-0.0441227\pi\)
\(564\) −5.40312e8 2.89105e8i −0.126814 0.0678546i
\(565\) 6.12887e9i 1.42959i
\(566\) 2.31973e9 + 3.87214e9i 0.537749 + 0.897623i
\(567\) 3.07437e9 0.708297
\(568\) 3.77886e7 + 7.79590e8i 0.00865250 + 0.178504i
\(569\) −2.39181e9 −0.544295 −0.272147 0.962256i \(-0.587734\pi\)
−0.272147 + 0.962256i \(0.587734\pi\)
\(570\) 1.10745e9 + 1.84859e9i 0.250475 + 0.418098i
\(571\) 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
\(573\) 1.93080e9i 0.428743i
\(574\) 6.65843e8 3.98894e8i 0.146954 0.0880371i
\(575\) 6.70211e8 0.147019
\(576\) −1.18904e9 + 1.15543e8i −0.259250 + 0.0251921i
\(577\) 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
\(579\) 1.90023e8i 0.0406846i
\(580\) −3.35308e9 + 6.26660e9i −0.713585 + 1.33363i
\(581\) 5.64138e9i 1.19335i
\(582\) −1.83398e9 3.06131e9i −0.385623 0.643691i
\(583\) 5.67087e9 1.18525
\(584\) −1.88262e8 3.88391e9i −0.0391128 0.806908i
\(585\) 1.16257e9 0.240090
\(586\) −1.16843e9 1.95037e9i −0.239861 0.400382i
\(587\) 2.72240e9i 0.555544i −0.960647 0.277772i \(-0.910404\pi\)
0.960647 0.277772i \(-0.0895960\pi\)
\(588\) −4.18614e8 2.23988e8i −0.0849168 0.0454365i
\(589\) 1.63016e9i 0.328721i
\(590\) −7.11692e8 + 4.26361e8i −0.142662 + 0.0854664i
\(591\) −4.62012e9 −0.920655
\(592\) 1.41263e9 9.42113e8i 0.279836 0.186628i
\(593\) −2.29251e9 −0.451460 −0.225730 0.974190i \(-0.572477\pi\)
−0.225730 + 0.974190i \(0.572477\pi\)
\(594\) 5.86634e9 3.51441e9i 1.14846 0.688019i
\(595\) 1.07402e10i 2.09028i
\(596\) 2.03605e9 + 1.08943e9i 0.393937 + 0.210784i
\(597\) 4.86346e8i 0.0935482i
\(598\) 9.02047e8 + 1.50572e9i 0.172494 + 0.287932i
\(599\) −3.58734e9 −0.681991 −0.340995 0.940065i \(-0.610764\pi\)
−0.340995 + 0.940065i \(0.610764\pi\)
\(600\) −1.58050e9 + 7.66106e7i −0.298720 + 0.0144797i
\(601\) 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
\(603\) 1.80223e8i 0.0334734i
\(604\) 2.33934e9 4.37201e9i 0.431980 0.807332i
\(605\) 3.32259e9i 0.610004i
\(606\) −2.41899e9 + 1.44917e9i −0.441551 + 0.264525i
\(607\) −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
\(609\) 6.58546e9 1.18148
\(610\) 4.88985e9 2.92942e9i 0.872251 0.522549i
\(611\) 7.48707e8i 0.132791i
\(612\) 1.18980e9 2.22364e9i 0.209819 0.392133i
\(613\) 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
\(615\) −9.35561e8 −0.162184
\(616\) −7.54695e9 + 3.65819e8i −1.30089 + 0.0630570i
\(617\) −2.58089e9 −0.442355 −0.221178 0.975234i \(-0.570990\pi\)
−0.221178 + 0.975234i \(0.570990\pi\)
\(618\) −1.54284e9 2.57535e9i −0.262943 0.438911i
\(619\) 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
\(621\) 2.73469e9i 0.458234i
\(622\) −4.73340e9 + 2.83569e9i −0.788690 + 0.472490i
\(623\) −4.18197e8 −0.0692903
\(624\) −2.29933e9 3.44769e9i −0.378840 0.568044i
\(625\) −7.48796e9 −1.22683
\(626\) 3.15164e9 1.88809e9i 0.513483 0.307618i
\(627\) 3.20035e9i 0.518514i
\(628\) −5.78226e9 3.09392e9i −0.931621 0.498483i
\(629\) 3.58449e9i 0.574314i
\(630\) −1.02850e9 1.71679e9i −0.163874 0.273543i
\(631\) 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
\(633\) 7.87635e9 1.23428
\(634\) 6.16801e9 + 1.02958e10i 0.961242 + 1.60453i
\(635\) 1.28601e10i 1.99313i
\(636\) 2.52598e9 4.72083e9i 0.389341 0.727643i
\(637\) 5.80071e8i 0.0889187i
\(638\) 9.05469e9 5.42449e9i 1.38039 0.826965i
\(639\) 3.07022e8 0.0465496
\(640\) −4.57691e9 6.19093e9i −0.690148 0.933526i
\(641\) 4.26190e9 0.639146 0.319573 0.947562i \(-0.396460\pi\)
0.319573 + 0.947562i \(0.396460\pi\)
\(642\) 2.00170e8 1.19918e8i 0.0298557 0.0178860i
\(643\) 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
\(645\) 4.28582e9i 0.628890i
\(646\) −2.93519e9 4.89949e9i −0.428374 0.715052i
\(647\) −7.38061e9 −1.07134 −0.535670 0.844427i \(-0.679941\pi\)
−0.535670 + 0.844427i \(0.679941\pi\)
\(648\) −2.25249e8 4.64695e9i −0.0325199 0.670896i
\(649\) 1.23211e9 0.176926
\(650\) 9.93555e8 + 1.65846e9i 0.141904 + 0.236870i
\(651\) 4.29837e9i 0.610620i
\(652\) 9.67853e9 + 5.17870e9i 1.36755 + 0.731735i
\(653\) 3.21579e9i 0.451951i −0.974133 0.225975i \(-0.927443\pi\)
0.974133 0.225975i \(-0.0725569\pi\)
\(654\) −7.64552e9 + 4.58029e9i −1.06877 + 0.640281i
\(655\) −1.18549e10 −1.64836
\(656\) −6.51717e8 9.77204e8i −0.0901354 0.135152i
\(657\) −1.52958e9 −0.210423
\(658\) 1.10563e9 6.62362e8i 0.151293 0.0906368i
\(659\) 5.17004e9i 0.703711i 0.936054 + 0.351856i \(0.114449\pi\)
−0.936054 + 0.351856i \(0.885551\pi\)
\(660\) 8.03001e9 + 4.29663e9i 1.08721 + 0.581733i
\(661\) 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
\(663\) 8.74835e9 1.16581
\(664\) −8.52701e9 + 4.13325e8i −1.13034 + 0.0547902i
\(665\) −4.53232e9 −0.597647
\(666\) −3.43254e8 5.72968e8i −0.0450253 0.0751572i
\(667\) 4.22099e9i 0.550775i
\(668\) −6.39330e9 + 1.19485e10i −0.829865 + 1.55094i
\(669\) 4.34434e9i 0.560961i
\(670\) 9.96362e8 5.96902e8i 0.127984 0.0766727i
\(671\) −8.46551e9 −1.08174
\(672\) −3.05711e9 + 6.44555e9i −0.388614 + 0.819347i
\(673\) 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
\(675\) 3.01211e9i 0.376971i
\(676\) 1.40053e9 2.61747e9i 0.174373 0.325888i
\(677\) 8.55209e9i 1.05928i −0.848222 0.529642i \(-0.822326\pi\)
0.848222 0.529642i \(-0.177674\pi\)
\(678\) 4.41648e9 + 7.37209e9i 0.544217 + 0.908420i
\(679\) 7.50565e9 0.920119
\(680\) 1.62340e10 7.86900e8i 1.97990 0.0959707i
\(681\) −6.48061e9 −0.786323
\(682\) 3.54061e9 + 5.91006e9i 0.427398 + 0.713422i
\(683\) 7.26976e9i 0.873067i 0.899688 + 0.436534i \(0.143794\pi\)
−0.899688 + 0.436534i \(0.856206\pi\)
\(684\) 9.38362e8 + 5.02090e8i 0.112118 + 0.0599909i
\(685\) 8.33837e9i 0.991206i
\(686\) −6.79217e9 + 4.06906e9i −0.803293 + 0.481238i
\(687\) −2.12010e9 −0.249463
\(688\) 4.47658e9 2.98552e9i 0.524068 0.349511i
\(689\) −6.54162e9 −0.761935
\(690\) −3.12422e9 + 1.87166e9i −0.362051 + 0.216898i
\(691\) 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
\(693\) 2.97218e9i 0.339241i
\(694\) −6.43358e9 1.07391e10i −0.730626 1.21958i
\(695\) 1.69709e10 1.91760
\(696\) −4.82494e8 9.95399e9i −0.0542449 1.11909i
\(697\) 2.47961e9 0.277376
\(698\) −8.04333e9 1.34261e10i −0.895245 1.49436i
\(699\) 7.21572e9i 0.799116i
\(700\) 1.57011e9 2.93440e9i 0.173017 0.323353i
\(701\) 1.35221e10i 1.48262i −0.671163 0.741310i \(-0.734205\pi\)
0.671163 0.741310i \(-0.265795\pi\)
\(702\) −6.76710e9 + 4.05404e9i −0.738283 + 0.442291i
\(703\) −1.51263e9 −0.164206
\(704\) 1.10588e9 + 1.13805e10i 0.119455 + 1.22930i
\(705\) −1.55349e9 −0.166974
\(706\) 2.40321e9 1.43972e9i 0.257025 0.153979i
\(707\) 5.93083e9i 0.631172i
\(708\) 5.48819e8 1.02569e9i 0.0581182 0.108618i
\(709\) 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
\(711\) 4.68613e9 0.488957
\(712\) 3.06398e7 + 6.32109e8i 0.00318131 + 0.0656314i
\(713\) −2.75507e9 −0.284655
\(714\) −7.73944e9 1.29189e10i −0.795730 1.32825i
\(715\) 1.11271e10i 1.13845i
\(716\) −3.36096e9 1.79835e9i −0.342191 0.183096i
\(717\) 3.38799e9i 0.343261i
\(718\) 1.34556e10 8.06102e9i 1.35665 0.812746i
\(719\) 1.49161e10 1.49659 0.748297 0.663363i \(-0.230872\pi\)
0.748297 + 0.663363i \(0.230872\pi\)
\(720\) −2.51959e9 + 1.68037e9i −0.251575 + 0.167780i
\(721\) 6.31417e9 0.627398
\(722\) −6.60779e9 + 3.95860e9i −0.653395 + 0.391437i
\(723\) 8.53800e9i 0.840180i
\(724\) −4.47180e8 2.39273e8i −0.0437923 0.0234320i
\(725\) 4.64919e9i 0.453100i
\(726\) −2.39426e9 3.99656e9i −0.232217 0.387622i
\(727\) −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
\(729\) −1.15808e10 −1.10711
\(730\) −5.06599e9 8.45627e9i −0.481986 0.804542i
\(731\) 1.13591e10i 1.07556i
\(732\) −3.77079e9 + 7.04728e9i −0.355340 + 0.664099i
\(733\) 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
\(735\) −1.20359e9 −0.111808
\(736\) −4.13132e9 1.95947e9i −0.381959 0.181162i
\(737\) −1.72494e9 −0.158722
\(738\) −3.96357e8 + 2.37450e8i −0.0362985 + 0.0217458i
\(739\) 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
\(741\) 3.69175e9i 0.333326i
\(742\) 5.78720e9 + 9.66013e9i 0.520062 + 0.868099i
\(743\) −3.73477e9 −0.334044 −0.167022 0.985953i \(-0.553415\pi\)
−0.167022 + 0.985953i \(0.553415\pi\)
\(744\) 6.49704e9 3.14927e8i 0.578376 0.0280353i
\(745\) 5.85402e9 0.518689
\(746\) 8.69345e9 + 1.45113e10i 0.766666 + 1.27974i
\(747\) 3.35815e9i 0.294766i
\(748\) −2.12827e10 1.13878e10i −1.85940 0.994908i
\(749\) 4.90772e8i 0.0426770i
\(750\) 6.45365e9 3.86626e9i 0.558587 0.334639i
\(751\) −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
\(753\) 4.74963e9 0.405394
\(754\) −1.04450e10 + 6.25741e9i −0.887379 + 0.531612i
\(755\) 1.25703e10i 1.06300i
\(756\) 1.19734e10 + 6.40660e9i 1.00784 + 0.539264i
\(757\) 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
\(759\) 5.40877e9 0.449006
\(760\) 3.32068e8 + 6.85065e9i 0.0274397 + 0.566089i
\(761\) 8.01137e9 0.658962 0.329481 0.944162i \(-0.393126\pi\)
0.329481 + 0.944162i \(0.393126\pi\)
\(762\) 9.26698e9 + 1.54687e10i 0.758745 + 1.26652i
\(763\) 1.87451e10i 1.52775i
\(764\) −2.89925e9 + 5.41845e9i −0.235212 + 0.439590i
\(765\) 6.39335e9i 0.516314i
\(766\) −4.66133e9 + 2.79252e9i −0.374722 + 0.224489i
\(767\) −1.42130e9