Properties

Label 108.6.b.b.107.6
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{30}\cdot 3^{32}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.6
Root \(-1.73205 - 3.22829i\) of \(x^{16} + 30 x^{14} + 619 x^{12} + 5604 x^{10} + 40971 x^{8} - 4866 x^{6} + 568069 x^{4} - 7909632 x^{2} + 20340100\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.b.107.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.82945 + 4.16357i) q^{2} +(-2.67058 - 31.8884i) q^{4} -46.0468i q^{5} +134.772i q^{7} +(142.996 + 110.996i) q^{8} +O(q^{10})\) \(q+(-3.82945 + 4.16357i) q^{2} +(-2.67058 - 31.8884i) q^{4} -46.0468i q^{5} +134.772i q^{7} +(142.996 + 110.996i) q^{8} +(191.719 + 176.334i) q^{10} +471.524 q^{11} -987.091 q^{13} +(-561.131 - 516.102i) q^{14} +(-1009.74 + 170.321i) q^{16} -1467.20i q^{17} +308.416i q^{19} +(-1468.36 + 122.972i) q^{20} +(-1805.68 + 1963.22i) q^{22} -2118.55 q^{23} +1004.70 q^{25} +(3780.02 - 4109.82i) q^{26} +(4297.65 - 359.919i) q^{28} -5196.05i q^{29} -6363.26i q^{31} +(3157.59 - 4856.34i) q^{32} +(6108.79 + 5618.57i) q^{34} +6205.80 q^{35} -8747.55 q^{37} +(-1284.11 - 1181.07i) q^{38} +(5111.00 - 6584.51i) q^{40} -1393.48i q^{41} -9414.92i q^{43} +(-1259.24 - 15036.1i) q^{44} +(8112.88 - 8820.71i) q^{46} -11122.7 q^{47} -1356.43 q^{49} +(-3847.44 + 4183.12i) q^{50} +(2636.11 + 31476.7i) q^{52} -28464.4i q^{53} -21712.2i q^{55} +(-14959.1 + 19271.9i) q^{56} +(21634.1 + 19898.0i) q^{58} +15062.9 q^{59} -37841.4 q^{61} +(26493.9 + 24367.8i) q^{62} +(8127.84 + 31744.0i) q^{64} +45452.3i q^{65} -65223.3i q^{67} +(-46786.6 + 3918.28i) q^{68} +(-23764.8 + 25838.3i) q^{70} +9860.03 q^{71} -54858.1 q^{73} +(33498.3 - 36421.0i) q^{74} +(9834.89 - 823.651i) q^{76} +63548.2i q^{77} +91648.1i q^{79} +(7842.73 + 46495.1i) q^{80} +(5801.85 + 5336.27i) q^{82} -45138.1 q^{83} -67559.8 q^{85} +(39199.7 + 36054.0i) q^{86} +(67426.2 + 52337.3i) q^{88} +73149.6i q^{89} -133032. i q^{91} +(5657.75 + 67557.0i) q^{92} +(42593.8 - 46310.0i) q^{94} +14201.6 q^{95} -11422.1 q^{97} +(5194.40 - 5647.60i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 94q^{4} + O(q^{10}) \) \( 16q + 94q^{4} + 1454q^{10} + 896q^{13} + 178q^{16} + 30q^{22} + 9888q^{25} + 11454q^{28} - 6172q^{34} - 71008q^{37} - 16618q^{40} + 35304q^{46} - 49376q^{49} + 14876q^{52} - 10492q^{58} + 77888q^{61} + 89206q^{64} + 229398q^{70} - 38032q^{73} + 48960q^{76} - 224488q^{82} - 371264q^{85} + 249102q^{88} + 68772q^{94} - 976q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.82945 + 4.16357i −0.676958 + 0.736022i
\(3\) 0 0
\(4\) −2.67058 31.8884i −0.0834557 0.996511i
\(5\) 46.0468i 0.823709i −0.911250 0.411855i \(-0.864881\pi\)
0.911250 0.411855i \(-0.135119\pi\)
\(6\) 0 0
\(7\) 134.772i 1.03957i 0.854297 + 0.519785i \(0.173988\pi\)
−0.854297 + 0.519785i \(0.826012\pi\)
\(8\) 142.996 + 110.996i 0.789950 + 0.613171i
\(9\) 0 0
\(10\) 191.719 + 176.334i 0.606268 + 0.557617i
\(11\) 471.524 1.17496 0.587479 0.809239i \(-0.300120\pi\)
0.587479 + 0.809239i \(0.300120\pi\)
\(12\) 0 0
\(13\) −987.091 −1.61994 −0.809970 0.586471i \(-0.800517\pi\)
−0.809970 + 0.586471i \(0.800517\pi\)
\(14\) −561.131 516.102i −0.765146 0.703745i
\(15\) 0 0
\(16\) −1009.74 + 170.321i −0.986070 + 0.166329i
\(17\) 1467.20i 1.23131i −0.788016 0.615654i \(-0.788892\pi\)
0.788016 0.615654i \(-0.211108\pi\)
\(18\) 0 0
\(19\) 308.416i 0.195999i 0.995186 + 0.0979994i \(0.0312443\pi\)
−0.995186 + 0.0979994i \(0.968756\pi\)
\(20\) −1468.36 + 122.972i −0.820836 + 0.0687432i
\(21\) 0 0
\(22\) −1805.68 + 1963.22i −0.795397 + 0.864795i
\(23\) −2118.55 −0.835062 −0.417531 0.908663i \(-0.637104\pi\)
−0.417531 + 0.908663i \(0.637104\pi\)
\(24\) 0 0
\(25\) 1004.70 0.321503
\(26\) 3780.02 4109.82i 1.09663 1.19231i
\(27\) 0 0
\(28\) 4297.65 359.919i 1.03594 0.0867580i
\(29\) 5196.05i 1.14730i −0.819100 0.573651i \(-0.805526\pi\)
0.819100 0.573651i \(-0.194474\pi\)
\(30\) 0 0
\(31\) 6363.26i 1.18926i −0.804001 0.594628i \(-0.797299\pi\)
0.804001 0.594628i \(-0.202701\pi\)
\(32\) 3157.59 4856.34i 0.545106 0.838367i
\(33\) 0 0
\(34\) 6108.79 + 5618.57i 0.906270 + 0.833544i
\(35\) 6205.80 0.856304
\(36\) 0 0
\(37\) −8747.55 −1.05047 −0.525233 0.850958i \(-0.676022\pi\)
−0.525233 + 0.850958i \(0.676022\pi\)
\(38\) −1284.11 1181.07i −0.144259 0.132683i
\(39\) 0 0
\(40\) 5111.00 6584.51i 0.505075 0.650689i
\(41\) 1393.48i 0.129462i −0.997903 0.0647308i \(-0.979381\pi\)
0.997903 0.0647308i \(-0.0206189\pi\)
\(42\) 0 0
\(43\) 9414.92i 0.776508i −0.921552 0.388254i \(-0.873078\pi\)
0.921552 0.388254i \(-0.126922\pi\)
\(44\) −1259.24 15036.1i −0.0980569 1.17086i
\(45\) 0 0
\(46\) 8112.88 8820.71i 0.565302 0.614623i
\(47\) −11122.7 −0.734454 −0.367227 0.930131i \(-0.619693\pi\)
−0.367227 + 0.930131i \(0.619693\pi\)
\(48\) 0 0
\(49\) −1356.43 −0.0807064
\(50\) −3847.44 + 4183.12i −0.217644 + 0.236633i
\(51\) 0 0
\(52\) 2636.11 + 31476.7i 0.135193 + 1.61429i
\(53\) 28464.4i 1.39191i −0.718084 0.695957i \(-0.754981\pi\)
0.718084 0.695957i \(-0.245019\pi\)
\(54\) 0 0
\(55\) 21712.2i 0.967824i
\(56\) −14959.1 + 19271.9i −0.637435 + 0.821209i
\(57\) 0 0
\(58\) 21634.1 + 19898.0i 0.844439 + 0.776676i
\(59\) 15062.9 0.563351 0.281676 0.959510i \(-0.409110\pi\)
0.281676 + 0.959510i \(0.409110\pi\)
\(60\) 0 0
\(61\) −37841.4 −1.30209 −0.651047 0.759037i \(-0.725670\pi\)
−0.651047 + 0.759037i \(0.725670\pi\)
\(62\) 26493.9 + 24367.8i 0.875319 + 0.805077i
\(63\) 0 0
\(64\) 8127.84 + 31744.0i 0.248042 + 0.968749i
\(65\) 45452.3i 1.33436i
\(66\) 0 0
\(67\) 65223.3i 1.77507i −0.460740 0.887535i \(-0.652416\pi\)
0.460740 0.887535i \(-0.347584\pi\)
\(68\) −46786.6 + 3918.28i −1.22701 + 0.102760i
\(69\) 0 0
\(70\) −23764.8 + 25838.3i −0.579682 + 0.630258i
\(71\) 9860.03 0.232131 0.116065 0.993242i \(-0.462972\pi\)
0.116065 + 0.993242i \(0.462972\pi\)
\(72\) 0 0
\(73\) −54858.1 −1.20485 −0.602426 0.798175i \(-0.705799\pi\)
−0.602426 + 0.798175i \(0.705799\pi\)
\(74\) 33498.3 36421.0i 0.711122 0.773166i
\(75\) 0 0
\(76\) 9834.89 823.651i 0.195315 0.0163572i
\(77\) 63548.2i 1.22145i
\(78\) 0 0
\(79\) 91648.1i 1.65217i 0.563543 + 0.826087i \(0.309438\pi\)
−0.563543 + 0.826087i \(0.690562\pi\)
\(80\) 7842.73 + 46495.1i 0.137007 + 0.812235i
\(81\) 0 0
\(82\) 5801.85 + 5336.27i 0.0952866 + 0.0876401i
\(83\) −45138.1 −0.719197 −0.359598 0.933107i \(-0.617086\pi\)
−0.359598 + 0.933107i \(0.617086\pi\)
\(84\) 0 0
\(85\) −67559.8 −1.01424
\(86\) 39199.7 + 36054.0i 0.571526 + 0.525663i
\(87\) 0 0
\(88\) 67426.2 + 52337.3i 0.928158 + 0.720451i
\(89\) 73149.6i 0.978896i 0.872032 + 0.489448i \(0.162802\pi\)
−0.872032 + 0.489448i \(0.837198\pi\)
\(90\) 0 0
\(91\) 133032.i 1.68404i
\(92\) 5657.75 + 67557.0i 0.0696906 + 0.832148i
\(93\) 0 0
\(94\) 42593.8 46310.0i 0.497194 0.540574i
\(95\) 14201.6 0.161446
\(96\) 0 0
\(97\) −11422.1 −0.123259 −0.0616293 0.998099i \(-0.519630\pi\)
−0.0616293 + 0.998099i \(0.519630\pi\)
\(98\) 5194.40 5647.60i 0.0546349 0.0594017i
\(99\) 0 0
\(100\) −2683.12 32038.1i −0.0268312 0.320381i
\(101\) 78611.4i 0.766800i −0.923582 0.383400i \(-0.874753\pi\)
0.923582 0.383400i \(-0.125247\pi\)
\(102\) 0 0
\(103\) 101937.i 0.946758i −0.880859 0.473379i \(-0.843034\pi\)
0.880859 0.473379i \(-0.156966\pi\)
\(104\) −141150. 109563.i −1.27967 0.993301i
\(105\) 0 0
\(106\) 118513. + 109003.i 1.02448 + 0.942267i
\(107\) −135660. −1.14550 −0.572748 0.819731i \(-0.694123\pi\)
−0.572748 + 0.819731i \(0.694123\pi\)
\(108\) 0 0
\(109\) 225285. 1.81621 0.908106 0.418741i \(-0.137529\pi\)
0.908106 + 0.418741i \(0.137529\pi\)
\(110\) 90400.1 + 83145.7i 0.712340 + 0.655176i
\(111\) 0 0
\(112\) −22954.5 136084.i −0.172911 1.02509i
\(113\) 59823.0i 0.440730i 0.975418 + 0.220365i \(0.0707248\pi\)
−0.975418 + 0.220365i \(0.929275\pi\)
\(114\) 0 0
\(115\) 97552.2i 0.687848i
\(116\) −165693. + 13876.5i −1.14330 + 0.0957489i
\(117\) 0 0
\(118\) −57682.8 + 62715.5i −0.381365 + 0.414639i
\(119\) 197737. 1.28003
\(120\) 0 0
\(121\) 61284.2 0.380527
\(122\) 144912. 157555.i 0.881463 0.958369i
\(123\) 0 0
\(124\) −202914. + 16993.6i −1.18511 + 0.0992502i
\(125\) 190159.i 1.08853i
\(126\) 0 0
\(127\) 75992.2i 0.418080i 0.977907 + 0.209040i \(0.0670339\pi\)
−0.977907 + 0.209040i \(0.932966\pi\)
\(128\) −163293. 87721.3i −0.880934 0.473238i
\(129\) 0 0
\(130\) −189244. 174058.i −0.982118 0.903306i
\(131\) 371533. 1.89156 0.945778 0.324815i \(-0.105302\pi\)
0.945778 + 0.324815i \(0.105302\pi\)
\(132\) 0 0
\(133\) −41565.8 −0.203754
\(134\) 271561. + 249769.i 1.30649 + 1.20165i
\(135\) 0 0
\(136\) 162853. 209804.i 0.755003 0.972672i
\(137\) 389370.i 1.77240i −0.463304 0.886199i \(-0.653336\pi\)
0.463304 0.886199i \(-0.346664\pi\)
\(138\) 0 0
\(139\) 104310.i 0.457918i 0.973436 + 0.228959i \(0.0735322\pi\)
−0.973436 + 0.228959i \(0.926468\pi\)
\(140\) −16573.1 197893.i −0.0714634 0.853317i
\(141\) 0 0
\(142\) −37758.5 + 41052.9i −0.157143 + 0.170853i
\(143\) −465438. −1.90336
\(144\) 0 0
\(145\) −239261. −0.945044
\(146\) 210077. 228405.i 0.815634 0.886797i
\(147\) 0 0
\(148\) 23361.1 + 278945.i 0.0876674 + 1.04680i
\(149\) 227251.i 0.838570i 0.907855 + 0.419285i \(0.137719\pi\)
−0.907855 + 0.419285i \(0.862281\pi\)
\(150\) 0 0
\(151\) 488350.i 1.74296i 0.490427 + 0.871482i \(0.336841\pi\)
−0.490427 + 0.871482i \(0.663159\pi\)
\(152\) −34232.9 + 44102.4i −0.120181 + 0.154829i
\(153\) 0 0
\(154\) −264587. 243355.i −0.899015 0.826872i
\(155\) −293008. −0.979602
\(156\) 0 0
\(157\) 307615. 0.995998 0.497999 0.867178i \(-0.334068\pi\)
0.497999 + 0.867178i \(0.334068\pi\)
\(158\) −381583. 350962.i −1.21604 1.11845i
\(159\) 0 0
\(160\) −223619. 145397.i −0.690571 0.449009i
\(161\) 285520.i 0.868105i
\(162\) 0 0
\(163\) 409730.i 1.20789i 0.797024 + 0.603947i \(0.206406\pi\)
−0.797024 + 0.603947i \(0.793594\pi\)
\(164\) −44435.8 + 3721.40i −0.129010 + 0.0108043i
\(165\) 0 0
\(166\) 172854. 187935.i 0.486866 0.529344i
\(167\) 107694. 0.298814 0.149407 0.988776i \(-0.452264\pi\)
0.149407 + 0.988776i \(0.452264\pi\)
\(168\) 0 0
\(169\) 603056. 1.62421
\(170\) 258717. 281290.i 0.686598 0.746503i
\(171\) 0 0
\(172\) −300227. + 25143.3i −0.773799 + 0.0648040i
\(173\) 299962.i 0.761994i 0.924576 + 0.380997i \(0.124419\pi\)
−0.924576 + 0.380997i \(0.875581\pi\)
\(174\) 0 0
\(175\) 135405.i 0.334225i
\(176\) −476115. + 80310.5i −1.15859 + 0.195430i
\(177\) 0 0
\(178\) −304563. 280123.i −0.720489 0.662672i
\(179\) 539891. 1.25943 0.629714 0.776827i \(-0.283172\pi\)
0.629714 + 0.776827i \(0.283172\pi\)
\(180\) 0 0
\(181\) 25867.6 0.0586894 0.0293447 0.999569i \(-0.490658\pi\)
0.0293447 + 0.999569i \(0.490658\pi\)
\(182\) 553888. + 509440.i 1.23949 + 1.14003i
\(183\) 0 0
\(184\) −302944. 235150.i −0.659657 0.512036i
\(185\) 402796.i 0.865279i
\(186\) 0 0
\(187\) 691821.i 1.44674i
\(188\) 29704.0 + 354684.i 0.0612943 + 0.731892i
\(189\) 0 0
\(190\) −54384.2 + 59129.2i −0.109292 + 0.118828i
\(191\) −519499. −1.03039 −0.515194 0.857073i \(-0.672280\pi\)
−0.515194 + 0.857073i \(0.672280\pi\)
\(192\) 0 0
\(193\) 259328. 0.501137 0.250569 0.968099i \(-0.419382\pi\)
0.250569 + 0.968099i \(0.419382\pi\)
\(194\) 43740.5 47556.8i 0.0834410 0.0907211i
\(195\) 0 0
\(196\) 3622.46 + 43254.4i 0.00673541 + 0.0804249i
\(197\) 372151.i 0.683209i −0.939844 0.341604i \(-0.889030\pi\)
0.939844 0.341604i \(-0.110970\pi\)
\(198\) 0 0
\(199\) 2717.29i 0.00486412i 0.999997 + 0.00243206i \(0.000774149\pi\)
−0.999997 + 0.00243206i \(0.999226\pi\)
\(200\) 143668. + 111517.i 0.253971 + 0.197136i
\(201\) 0 0
\(202\) 327304. + 301039.i 0.564382 + 0.519092i
\(203\) 700280. 1.19270
\(204\) 0 0
\(205\) −64165.2 −0.106639
\(206\) 424422. + 390363.i 0.696835 + 0.640916i
\(207\) 0 0
\(208\) 996702. 168122.i 1.59737 0.269443i
\(209\) 145426.i 0.230290i
\(210\) 0 0
\(211\) 693979.i 1.07310i 0.843868 + 0.536550i \(0.180273\pi\)
−0.843868 + 0.536550i \(0.819727\pi\)
\(212\) −907683. + 76016.5i −1.38706 + 0.116163i
\(213\) 0 0
\(214\) 519505. 564832.i 0.775453 0.843110i
\(215\) −433527. −0.639617
\(216\) 0 0
\(217\) 857588. 1.23632
\(218\) −862719. + 937990.i −1.22950 + 1.33677i
\(219\) 0 0
\(220\) −692366. + 57984.1i −0.964448 + 0.0807704i
\(221\) 1.44826e6i 1.99465i
\(222\) 0 0
\(223\) 609819.i 0.821180i −0.911820 0.410590i \(-0.865323\pi\)
0.911820 0.410590i \(-0.134677\pi\)
\(224\) 654498. + 425555.i 0.871541 + 0.566676i
\(225\) 0 0
\(226\) −249077. 229089.i −0.324387 0.298356i
\(227\) −165538. −0.213223 −0.106611 0.994301i \(-0.534000\pi\)
−0.106611 + 0.994301i \(0.534000\pi\)
\(228\) 0 0
\(229\) −793320. −0.999677 −0.499839 0.866119i \(-0.666607\pi\)
−0.499839 + 0.866119i \(0.666607\pi\)
\(230\) −406165. 373572.i −0.506271 0.465644i
\(231\) 0 0
\(232\) 576740. 743015.i 0.703493 0.906312i
\(233\) 523254.i 0.631426i −0.948855 0.315713i \(-0.897756\pi\)
0.948855 0.315713i \(-0.102244\pi\)
\(234\) 0 0
\(235\) 512163.i 0.604977i
\(236\) −40226.8 480332.i −0.0470149 0.561386i
\(237\) 0 0
\(238\) −757225. + 823292.i −0.866528 + 0.942131i
\(239\) 521703. 0.590784 0.295392 0.955376i \(-0.404550\pi\)
0.295392 + 0.955376i \(0.404550\pi\)
\(240\) 0 0
\(241\) −1.08959e6 −1.20842 −0.604212 0.796824i \(-0.706512\pi\)
−0.604212 + 0.796824i \(0.706512\pi\)
\(242\) −234685. + 255161.i −0.257601 + 0.280076i
\(243\) 0 0
\(244\) 101058. + 1.20670e6i 0.108667 + 1.29755i
\(245\) 62459.3i 0.0664786i
\(246\) 0 0
\(247\) 304435.i 0.317506i
\(248\) 706296. 909923.i 0.729218 0.939453i
\(249\) 0 0
\(250\) 791740. + 728205.i 0.801185 + 0.736892i
\(251\) −1.15105e6 −1.15321 −0.576606 0.817022i \(-0.695623\pi\)
−0.576606 + 0.817022i \(0.695623\pi\)
\(252\) 0 0
\(253\) −998947. −0.981162
\(254\) −316399. 291008.i −0.307716 0.283023i
\(255\) 0 0
\(256\) 990558. 343958.i 0.944669 0.328024i
\(257\) 1.26233e6i 1.19218i 0.802918 + 0.596090i \(0.203280\pi\)
−0.802918 + 0.596090i \(0.796720\pi\)
\(258\) 0 0
\(259\) 1.17892e6i 1.09203i
\(260\) 1.44940e6 121384.i 1.32970 0.111360i
\(261\) 0 0
\(262\) −1.42277e6 + 1.54690e6i −1.28050 + 1.39223i
\(263\) −243029. −0.216655 −0.108328 0.994115i \(-0.534550\pi\)
−0.108328 + 0.994115i \(0.534550\pi\)
\(264\) 0 0
\(265\) −1.31069e6 −1.14653
\(266\) 159174. 173062.i 0.137933 0.149968i
\(267\) 0 0
\(268\) −2.07986e6 + 174184.i −1.76888 + 0.148140i
\(269\) 813756.i 0.685667i −0.939396 0.342834i \(-0.888613\pi\)
0.939396 0.342834i \(-0.111387\pi\)
\(270\) 0 0
\(271\) 1.85687e6i 1.53589i −0.640518 0.767943i \(-0.721280\pi\)
0.640518 0.767943i \(-0.278720\pi\)
\(272\) 249895. + 1.48148e6i 0.204802 + 1.21416i
\(273\) 0 0
\(274\) 1.62117e6 + 1.49108e6i 1.30452 + 1.19984i
\(275\) 473739. 0.377752
\(276\) 0 0
\(277\) 634180. 0.496607 0.248304 0.968682i \(-0.420127\pi\)
0.248304 + 0.968682i \(0.420127\pi\)
\(278\) −434301. 399449.i −0.337038 0.309991i
\(279\) 0 0
\(280\) 887406. + 688818.i 0.676437 + 0.525061i
\(281\) 2.12892e6i 1.60840i −0.594361 0.804198i \(-0.702595\pi\)
0.594361 0.804198i \(-0.297405\pi\)
\(282\) 0 0
\(283\) 1.03774e6i 0.770234i 0.922868 + 0.385117i \(0.125839\pi\)
−0.922868 + 0.385117i \(0.874161\pi\)
\(284\) −26332.0 314420.i −0.0193726 0.231321i
\(285\) 0 0
\(286\) 1.78237e6 1.93788e6i 1.28850 1.40092i
\(287\) 187802. 0.134584
\(288\) 0 0
\(289\) −732819. −0.516121
\(290\) 916239. 996179.i 0.639755 0.695573i
\(291\) 0 0
\(292\) 146503. + 1.74934e6i 0.100552 + 1.20065i
\(293\) 2.07720e6i 1.41354i −0.707442 0.706771i \(-0.750151\pi\)
0.707442 0.706771i \(-0.249849\pi\)
\(294\) 0 0
\(295\) 693599.i 0.464038i
\(296\) −1.25087e6 970942.i −0.829816 0.644116i
\(297\) 0 0
\(298\) −946173. 870246.i −0.617206 0.567677i
\(299\) 2.09120e6 1.35275
\(300\) 0 0
\(301\) 1.26887e6 0.807234
\(302\) −2.03328e6 1.87011e6i −1.28286 1.17991i
\(303\) 0 0
\(304\) −52529.8 311419.i −0.0326003 0.193269i
\(305\) 1.74247e6i 1.07255i
\(306\) 0 0
\(307\) 277720.i 0.168175i −0.996458 0.0840876i \(-0.973202\pi\)
0.996458 0.0840876i \(-0.0267976\pi\)
\(308\) 2.02645e6 169711.i 1.21719 0.101937i
\(309\) 0 0
\(310\) 1.12206e6 1.21996e6i 0.663149 0.721008i
\(311\) −752701. −0.441287 −0.220644 0.975354i \(-0.570816\pi\)
−0.220644 + 0.975354i \(0.570816\pi\)
\(312\) 0 0
\(313\) −1.71292e6 −0.988274 −0.494137 0.869384i \(-0.664516\pi\)
−0.494137 + 0.869384i \(0.664516\pi\)
\(314\) −1.17800e6 + 1.28078e6i −0.674249 + 0.733076i
\(315\) 0 0
\(316\) 2.92251e6 244754.i 1.64641 0.137883i
\(317\) 738922.i 0.413000i −0.978447 0.206500i \(-0.933793\pi\)
0.978447 0.206500i \(-0.0662074\pi\)
\(318\) 0 0
\(319\) 2.45006e6i 1.34803i
\(320\) 1.46171e6 374261.i 0.797968 0.204315i
\(321\) 0 0
\(322\) 1.18878e6 + 1.09339e6i 0.638944 + 0.587671i
\(323\) 452508. 0.241335
\(324\) 0 0
\(325\) −991727. −0.520815
\(326\) −1.70594e6 1.56904e6i −0.889036 0.817694i
\(327\) 0 0
\(328\) 154671. 199262.i 0.0793822 0.102268i
\(329\) 1.49902e6i 0.763517i
\(330\) 0 0
\(331\) 1.07446e6i 0.539038i −0.962995 0.269519i \(-0.913135\pi\)
0.962995 0.269519i \(-0.0868647\pi\)
\(332\) 120545. + 1.43938e6i 0.0600210 + 0.716688i
\(333\) 0 0
\(334\) −412410. + 448392.i −0.202285 + 0.219934i
\(335\) −3.00332e6 −1.46214
\(336\) 0 0
\(337\) 125481. 0.0601871 0.0300935 0.999547i \(-0.490419\pi\)
0.0300935 + 0.999547i \(0.490419\pi\)
\(338\) −2.30938e6 + 2.51086e6i −1.09952 + 1.19545i
\(339\) 0 0
\(340\) 180424. + 2.15437e6i 0.0846441 + 1.01070i
\(341\) 3.00043e6i 1.39733i
\(342\) 0 0
\(343\) 2.08230e6i 0.955670i
\(344\) 1.04502e6 1.34630e6i 0.476132 0.613402i
\(345\) 0 0
\(346\) −1.24891e6 1.14869e6i −0.560844 0.515838i
\(347\) 2.54277e6 1.13366 0.566830 0.823835i \(-0.308170\pi\)
0.566830 + 0.823835i \(0.308170\pi\)
\(348\) 0 0
\(349\) 554946. 0.243886 0.121943 0.992537i \(-0.461087\pi\)
0.121943 + 0.992537i \(0.461087\pi\)
\(350\) −563767. 518526.i −0.245997 0.226256i
\(351\) 0 0
\(352\) 1.48888e6 2.28988e6i 0.640477 0.985046i
\(353\) 2.07681e6i 0.887075i 0.896256 + 0.443538i \(0.146277\pi\)
−0.896256 + 0.443538i \(0.853723\pi\)
\(354\) 0 0
\(355\) 454022.i 0.191208i
\(356\) 2.33262e6 195352.i 0.975482 0.0816945i
\(357\) 0 0
\(358\) −2.06749e6 + 2.24787e6i −0.852579 + 0.926966i
\(359\) −3.54117e6 −1.45014 −0.725071 0.688674i \(-0.758193\pi\)
−0.725071 + 0.688674i \(0.758193\pi\)
\(360\) 0 0
\(361\) 2.38098e6 0.961585
\(362\) −99058.7 + 107701.i −0.0397302 + 0.0431966i
\(363\) 0 0
\(364\) −4.24217e6 + 355273.i −1.67817 + 0.140543i
\(365\) 2.52604e6i 0.992448i
\(366\) 0 0
\(367\) 1.66740e6i 0.646211i 0.946363 + 0.323105i \(0.104727\pi\)
−0.946363 + 0.323105i \(0.895273\pi\)
\(368\) 2.13917e6 360833.i 0.823429 0.138895i
\(369\) 0 0
\(370\) −1.67707e6 1.54249e6i −0.636864 0.585758i
\(371\) 3.83620e6 1.44699
\(372\) 0 0
\(373\) 304727. 0.113407 0.0567034 0.998391i \(-0.481941\pi\)
0.0567034 + 0.998391i \(0.481941\pi\)
\(374\) 2.88044e6 + 2.64929e6i 1.06483 + 0.979380i
\(375\) 0 0
\(376\) −1.59050e6 1.23457e6i −0.580182 0.450346i
\(377\) 5.12897e6i 1.85856i
\(378\) 0 0
\(379\) 805622.i 0.288093i −0.989571 0.144047i \(-0.953988\pi\)
0.989571 0.144047i \(-0.0460115\pi\)
\(380\) −37926.4 452865.i −0.0134736 0.160883i
\(381\) 0 0
\(382\) 1.98940e6 2.16297e6i 0.697530 0.758389i
\(383\) −1.84820e6 −0.643800 −0.321900 0.946774i \(-0.604321\pi\)
−0.321900 + 0.946774i \(0.604321\pi\)
\(384\) 0 0
\(385\) 2.92619e6 1.00612
\(386\) −993086. + 1.07973e6i −0.339249 + 0.368848i
\(387\) 0 0
\(388\) 30503.7 + 364233.i 0.0102866 + 0.122829i
\(389\) 3.65126e6i 1.22340i 0.791090 + 0.611700i \(0.209514\pi\)
−0.791090 + 0.611700i \(0.790486\pi\)
\(390\) 0 0
\(391\) 3.10833e6i 1.02822i
\(392\) −193965. 150558.i −0.0637540 0.0494869i
\(393\) 0 0
\(394\) 1.54947e6 + 1.42513e6i 0.502856 + 0.462504i
\(395\) 4.22010e6 1.36091
\(396\) 0 0
\(397\) −1.73747e6 −0.553274 −0.276637 0.960974i \(-0.589220\pi\)
−0.276637 + 0.960974i \(0.589220\pi\)
\(398\) −11313.6 10405.8i −0.00358010 0.00329280i
\(399\) 0 0
\(400\) −1.01448e6 + 171121.i −0.317024 + 0.0534753i
\(401\) 2.93873e6i 0.912640i −0.889816 0.456320i \(-0.849167\pi\)
0.889816 0.456320i \(-0.150833\pi\)
\(402\) 0 0
\(403\) 6.28112e6i 1.92652i
\(404\) −2.50679e6 + 209938.i −0.764125 + 0.0639938i
\(405\) 0 0
\(406\) −2.68169e6 + 2.91566e6i −0.807409 + 0.877854i
\(407\) −4.12469e6 −1.23425
\(408\) 0 0
\(409\) −1.82104e6 −0.538285 −0.269142 0.963100i \(-0.586740\pi\)
−0.269142 + 0.963100i \(0.586740\pi\)
\(410\) 245718. 267156.i 0.0721900 0.0784884i
\(411\) 0 0
\(412\) −3.25061e6 + 272231.i −0.943456 + 0.0790124i
\(413\) 2.03006e6i 0.585643i
\(414\) 0 0
\(415\) 2.07846e6i 0.592409i
\(416\) −3.11683e6 + 4.79365e6i −0.883040 + 1.35810i
\(417\) 0 0
\(418\) −605490. 556901.i −0.169499 0.155897i
\(419\) −5.56903e6 −1.54969 −0.774845 0.632151i \(-0.782172\pi\)
−0.774845 + 0.632151i \(0.782172\pi\)
\(420\) 0 0
\(421\) 220888. 0.0607390 0.0303695 0.999539i \(-0.490332\pi\)
0.0303695 + 0.999539i \(0.490332\pi\)
\(422\) −2.88943e6 2.65756e6i −0.789825 0.726444i
\(423\) 0 0
\(424\) 3.15943e6 4.07030e6i 0.853481 1.09954i
\(425\) 1.47409e6i 0.395869i
\(426\) 0 0
\(427\) 5.09995e6i 1.35362i
\(428\) 362292. + 4.32599e6i 0.0955982 + 1.14150i
\(429\) 0 0
\(430\) 1.66017e6 1.80502e6i 0.432994 0.470772i
\(431\) 2.90126e6 0.752304 0.376152 0.926558i \(-0.377247\pi\)
0.376152 + 0.926558i \(0.377247\pi\)
\(432\) 0 0
\(433\) 1.33580e6 0.342392 0.171196 0.985237i \(-0.445237\pi\)
0.171196 + 0.985237i \(0.445237\pi\)
\(434\) −3.28409e6 + 3.57063e6i −0.836934 + 0.909955i
\(435\) 0 0
\(436\) −601642. 7.18398e6i −0.151573 1.80988i
\(437\) 653394.i 0.163671i
\(438\) 0 0
\(439\) 8.00279e6i 1.98189i 0.134262 + 0.990946i \(0.457134\pi\)
−0.134262 + 0.990946i \(0.542866\pi\)
\(440\) 2.40996e6 3.10476e6i 0.593442 0.764533i
\(441\) 0 0
\(442\) −6.02993e6 5.54604e6i −1.46810 1.35029i
\(443\) 4.46062e6 1.07991 0.539953 0.841695i \(-0.318442\pi\)
0.539953 + 0.841695i \(0.318442\pi\)
\(444\) 0 0
\(445\) 3.36830e6 0.806326
\(446\) 2.53902e6 + 2.33527e6i 0.604407 + 0.555905i
\(447\) 0 0
\(448\) −4.27819e6 + 1.09540e6i −1.00708 + 0.257857i
\(449\) 394596.i 0.0923712i −0.998933 0.0461856i \(-0.985293\pi\)
0.998933 0.0461856i \(-0.0147066\pi\)
\(450\) 0 0
\(451\) 657060.i 0.152112i
\(452\) 1.90766e6 159762.i 0.439192 0.0367814i
\(453\) 0 0
\(454\) 633920. 689229.i 0.144343 0.156936i
\(455\) −6.12569e6 −1.38716
\(456\) 0 0
\(457\) 3.29879e6 0.738863 0.369431 0.929258i \(-0.379552\pi\)
0.369431 + 0.929258i \(0.379552\pi\)
\(458\) 3.03798e6 3.30304e6i 0.676739 0.735784i
\(459\) 0 0
\(460\) 3.11078e6 260521.i 0.685448 0.0574048i
\(461\) 574515.i 0.125907i 0.998016 + 0.0629534i \(0.0200519\pi\)
−0.998016 + 0.0629534i \(0.979948\pi\)
\(462\) 0 0
\(463\) 362906.i 0.0786760i −0.999226 0.0393380i \(-0.987475\pi\)
0.999226 0.0393380i \(-0.0125249\pi\)
\(464\) 884995. + 5.24663e6i 0.190830 + 1.13132i
\(465\) 0 0
\(466\) 2.17860e6 + 2.00378e6i 0.464743 + 0.427449i
\(467\) 9.20629e6 1.95340 0.976702 0.214598i \(-0.0688441\pi\)
0.976702 + 0.214598i \(0.0688441\pi\)
\(468\) 0 0
\(469\) 8.79026e6 1.84531
\(470\) −2.13243e6 1.96130e6i −0.445276 0.409544i
\(471\) 0 0
\(472\) 2.15394e6 + 1.67192e6i 0.445019 + 0.345431i
\(473\) 4.43937e6i 0.912364i
\(474\) 0 0
\(475\) 309865.i 0.0630141i
\(476\) −528073. 6.30551e6i −0.106826 1.27557i
\(477\) 0 0
\(478\) −1.99784e6 + 2.17215e6i −0.399936 + 0.434830i
\(479\) 2.27095e6 0.452240 0.226120 0.974099i \(-0.427396\pi\)
0.226120 + 0.974099i \(0.427396\pi\)
\(480\) 0 0
\(481\) 8.63463e6 1.70169
\(482\) 4.17252e6 4.53657e6i 0.818052 0.889426i
\(483\) 0 0
\(484\) −163665. 1.95425e6i −0.0317571 0.379199i
\(485\) 525952.i 0.101529i
\(486\) 0 0
\(487\) 6.09989e6i 1.16547i −0.812664 0.582733i \(-0.801984\pi\)
0.812664 0.582733i \(-0.198016\pi\)
\(488\) −5.41117e6 4.20024e6i −1.02859 0.798407i
\(489\) 0 0
\(490\) −260054. 239185.i −0.0489297 0.0450033i
\(491\) 536585. 0.100446 0.0502232 0.998738i \(-0.484007\pi\)
0.0502232 + 0.998738i \(0.484007\pi\)
\(492\) 0 0
\(493\) −7.62364e6 −1.41268
\(494\) 1.26754e6 + 1.16582e6i 0.233691 + 0.214938i
\(495\) 0 0
\(496\) 1.08380e6 + 6.42522e6i 0.197808 + 1.17269i
\(497\) 1.32885e6i 0.241316i
\(498\) 0 0
\(499\) 3.52841e6i 0.634348i 0.948367 + 0.317174i \(0.102734\pi\)
−0.948367 + 0.317174i \(0.897266\pi\)
\(500\) −6.06386e6 + 507835.i −1.08474 + 0.0908444i
\(501\) 0 0
\(502\) 4.40789e6 4.79247e6i 0.780676 0.848789i
\(503\) −3.34461e6 −0.589422 −0.294711 0.955586i \(-0.595223\pi\)
−0.294711 + 0.955586i \(0.595223\pi\)
\(504\) 0 0
\(505\) −3.61980e6 −0.631621
\(506\) 3.82542e6 4.15918e6i 0.664206 0.722157i
\(507\) 0 0
\(508\) 2.42327e6 202943.i 0.416622 0.0348912i
\(509\) 5.31062e6i 0.908553i −0.890861 0.454277i \(-0.849898\pi\)
0.890861 0.454277i \(-0.150102\pi\)
\(510\) 0 0
\(511\) 7.39332e6i 1.25253i
\(512\) −2.36120e6 + 5.44143e6i −0.398068 + 0.917356i
\(513\) 0 0
\(514\) −5.25581e6 4.83405e6i −0.877470 0.807055i
\(515\) −4.69387e6 −0.779854
\(516\) 0 0
\(517\) −5.24461e6 −0.862953
\(518\) 4.90853e6 + 4.51463e6i 0.803761 + 0.739261i
\(519\) 0 0
\(520\) −5.04502e6 + 6.49951e6i −0.818191 + 1.05408i
\(521\) 4.42521e6i 0.714232i −0.934060 0.357116i \(-0.883760\pi\)
0.934060 0.357116i \(-0.116240\pi\)
\(522\) 0 0
\(523\) 88509.2i 0.0141493i 0.999975 + 0.00707463i \(0.00225194\pi\)
−0.999975 + 0.00707463i \(0.997748\pi\)
\(524\) −992209. 1.18476e7i −0.157861 1.88496i
\(525\) 0 0
\(526\) 930669. 1.01187e6i 0.146667 0.159463i
\(527\) −9.33618e6 −1.46434
\(528\) 0 0
\(529\) −1.94810e6 −0.302672
\(530\) 5.01924e6 5.45716e6i 0.776154 0.843872i
\(531\) 0 0
\(532\) 111005. + 1.32547e6i 0.0170045 + 0.203044i
\(533\) 1.37549e6i 0.209720i
\(534\) 0 0
\(535\) 6.24672e6i 0.943557i
\(536\) 7.23951e6 9.32668e6i 1.08842 1.40222i
\(537\) 0 0
\(538\) 3.38813e6 + 3.11624e6i 0.504666 + 0.464168i
\(539\) −639591. −0.0948267
\(540\) 0 0
\(541\) −3.49057e6 −0.512747 −0.256373 0.966578i \(-0.582528\pi\)
−0.256373 + 0.966578i \(0.582528\pi\)
\(542\) 7.73122e6 + 7.11081e6i 1.13045 + 1.03973i
\(543\) 0 0
\(544\) −7.12522e6 4.63282e6i −1.03229 0.671194i
\(545\) 1.03737e7i 1.49603i
\(546\) 0 0
\(547\) 4.73741e6i 0.676975i 0.940971 + 0.338487i \(0.109915\pi\)
−0.940971 + 0.338487i \(0.890085\pi\)
\(548\) −1.24164e7 + 1.03984e6i −1.76622 + 0.147917i
\(549\) 0 0
\(550\) −1.81416e6 + 1.97244e6i −0.255723 + 0.278034i
\(551\) 1.60254e6 0.224870
\(552\) 0 0
\(553\) −1.23516e7 −1.71755
\(554\) −2.42856e6 + 2.64045e6i −0.336182 + 0.365514i
\(555\) 0 0
\(556\) 3.32627e6 278568.i 0.456321 0.0382159i
\(557\) 6.51222e6i 0.889388i 0.895683 + 0.444694i \(0.146688\pi\)
−0.895683 + 0.444694i \(0.853312\pi\)
\(558\) 0 0
\(559\) 9.29339e6i 1.25790i
\(560\) −6.26622e6 + 1.05698e6i −0.844376 + 0.142428i
\(561\) 0 0
\(562\) 8.86389e6 + 8.15259e6i 1.18381 + 1.08882i
\(563\) 1.30164e7 1.73069 0.865343 0.501180i \(-0.167100\pi\)
0.865343 + 0.501180i \(0.167100\pi\)
\(564\) 0 0
\(565\) 2.75466e6 0.363033
\(566\) −4.32070e6 3.97398e6i −0.566909 0.521416i
\(567\) 0 0
\(568\) 1.40995e6 + 1.09442e6i 0.183372 + 0.142336i
\(569\) 2.32444e6i 0.300980i 0.988612 + 0.150490i \(0.0480851\pi\)
−0.988612 + 0.150490i \(0.951915\pi\)
\(570\) 0 0
\(571\) 1.30746e7i 1.67818i −0.543992 0.839091i \(-0.683088\pi\)
0.543992 0.839091i \(-0.316912\pi\)
\(572\) 1.24299e6 + 1.48420e7i 0.158846 + 1.89672i
\(573\) 0 0
\(574\) −719178. + 781925.i −0.0911081 + 0.0990571i
\(575\) −2.12850e6 −0.268475
\(576\) 0 0
\(577\) −9.92814e6 −1.24145 −0.620724 0.784029i \(-0.713161\pi\)
−0.620724 + 0.784029i \(0.713161\pi\)
\(578\) 2.80629e6 3.05114e6i 0.349393 0.379877i
\(579\) 0 0
\(580\) 638966. + 7.62964e6i 0.0788693 + 0.941747i
\(581\) 6.08334e6i 0.747656i
\(582\) 0 0
\(583\) 1.34217e7i 1.63544i
\(584\) −7.84450e6 6.08902e6i −0.951773 0.738780i
\(585\) 0 0
\(586\) 8.64855e6 + 7.95453e6i 1.04040 + 0.956909i
\(587\) 8.76459e6 1.04987 0.524936 0.851142i \(-0.324089\pi\)
0.524936 + 0.851142i \(0.324089\pi\)
\(588\) 0 0
\(589\) 1.96253e6 0.233093
\(590\) 2.88785e6 + 2.65610e6i 0.341542 + 0.314134i
\(591\) 0 0
\(592\) 8.83272e6 1.48989e6i 1.03583 0.174723i
\(593\) 6.94712e6i 0.811275i 0.914034 + 0.405637i \(0.132950\pi\)
−0.914034 + 0.405637i \(0.867050\pi\)
\(594\) 0 0
\(595\) 9.10515e6i 1.05437i
\(596\) 7.24665e6 606891.i 0.835645 0.0699834i
\(597\) 0 0
\(598\) −8.00815e6 + 8.70685e6i −0.915755 + 0.995653i
\(599\) −7.15594e6 −0.814892 −0.407446 0.913229i \(-0.633580\pi\)
−0.407446 + 0.913229i \(0.633580\pi\)
\(600\) 0 0
\(601\) 2.05362e6 0.231918 0.115959 0.993254i \(-0.463006\pi\)
0.115959 + 0.993254i \(0.463006\pi\)
\(602\) −4.85906e6 + 5.28301e6i −0.546464 + 0.594142i
\(603\) 0 0
\(604\) 1.55727e7 1.30418e6i 1.73688 0.145460i
\(605\) 2.82194e6i 0.313444i
\(606\) 0 0
\(607\) 1.85546e6i 0.204399i −0.994764 0.102200i \(-0.967412\pi\)
0.994764 0.102200i \(-0.0325881\pi\)
\(608\) 1.49777e6 + 973853.i 0.164319 + 0.106840i
\(609\) 0 0
\(610\) −7.25490e6 6.67272e6i −0.789418 0.726069i
\(611\) 1.09791e7 1.18977
\(612\) 0 0
\(613\) 527592. 0.0567083 0.0283542 0.999598i \(-0.490973\pi\)
0.0283542 + 0.999598i \(0.490973\pi\)
\(614\) 1.15631e6 + 1.06352e6i 0.123781 + 0.113848i
\(615\) 0 0
\(616\) −7.05358e6 + 9.08715e6i −0.748959 + 0.964886i
\(617\) 1.33503e7i 1.41182i 0.708301 + 0.705910i \(0.249462\pi\)
−0.708301 + 0.705910i \(0.750538\pi\)
\(618\) 0 0
\(619\) 1.22140e7i 1.28124i −0.767856 0.640622i \(-0.778676\pi\)
0.767856 0.640622i \(-0.221324\pi\)
\(620\) 782501. + 9.34353e6i 0.0817533 + 0.976185i
\(621\) 0 0
\(622\) 2.88243e6 3.13392e6i 0.298733 0.324797i
\(623\) −9.85850e6 −1.01763
\(624\) 0 0
\(625\) −5.61653e6 −0.575133
\(626\) 6.55956e6 7.13187e6i 0.669020 0.727391i
\(627\) 0 0
\(628\) −821511. 9.80934e6i −0.0831217 0.992524i
\(629\) 1.28344e7i 1.29345i
\(630\) 0 0
\(631\) 842912.i 0.0842770i −0.999112 0.0421385i \(-0.986583\pi\)
0.999112 0.0421385i \(-0.0134171\pi\)
\(632\) −1.01726e7 + 1.31053e7i −1.01307 + 1.30513i
\(633\) 0 0
\(634\) 3.07655e6 + 2.82967e6i 0.303977 + 0.279584i
\(635\) 3.49919e6 0.344377
\(636\) 0 0
\(637\) 1.33892e6 0.130740
\(638\) 1.02010e7 + 9.38240e6i 0.992181 + 0.912561i
\(639\) 0 0
\(640\) −4.03928e6 + 7.51913e6i −0.389811 + 0.725634i
\(641\) 4.62200e6i 0.444309i −0.975011 0.222155i \(-0.928691\pi\)
0.975011 0.222155i \(-0.0713090\pi\)
\(642\) 0 0
\(643\) 9.28181e6i 0.885330i 0.896687 + 0.442665i \(0.145967\pi\)
−0.896687 + 0.442665i \(0.854033\pi\)
\(644\) −9.10478e6 + 762505.i −0.865077 + 0.0724483i
\(645\) 0 0
\(646\) −1.73286e6 + 1.88405e6i −0.163374 + 0.177628i
\(647\) −1.74226e7 −1.63626 −0.818129 0.575034i \(-0.804989\pi\)
−0.818129 + 0.575034i \(0.804989\pi\)
\(648\) 0 0
\(649\) 7.10254e6 0.661914
\(650\) 3.79777e6 4.12912e6i 0.352570 0.383331i
\(651\) 0 0
\(652\) 1.30656e7 1.09422e6i 1.20368 0.100806i
\(653\) 3.94341e6i 0.361901i −0.983492 0.180950i \(-0.942083\pi\)
0.983492 0.180950i \(-0.0579173\pi\)
\(654\) 0 0
\(655\) 1.71079e7i 1.55809i
\(656\) 237339. + 1.40705e6i 0.0215332 + 0.127658i
\(657\) 0 0
\(658\) 6.24128e6 + 5.74044e6i 0.561965 + 0.516869i
\(659\) 1.46127e7 1.31074 0.655371 0.755307i \(-0.272512\pi\)
0.655371 + 0.755307i \(0.272512\pi\)
\(660\) 0 0
\(661\) 4.83511e6 0.430430 0.215215 0.976567i \(-0.430955\pi\)
0.215215 + 0.976567i \(0.430955\pi\)
\(662\) 4.47358e6 + 4.11459e6i 0.396744 + 0.364906i
\(663\) 0 0
\(664\) −6.45457e6 5.01014e6i −0.568129 0.440991i
\(665\) 1.91397e6i 0.167834i
\(666\) 0 0
\(667\) 1.10081e7i 0.958068i
\(668\) −287606. 3.43419e6i −0.0249377 0.297772i
\(669\) 0 0
\(670\) 1.15011e7 1.25045e7i 0.989809 1.07617i
\(671\) −1.78431e7 −1.52991
\(672\) 0 0
\(673\) −4.36686e6 −0.371648 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(674\) −480524. + 522448.i −0.0407441 + 0.0442990i
\(675\) 0 0
\(676\) −1.61051e6 1.92305e7i −0.135549 1.61854i
\(677\) 3.80499e6i 0.319067i 0.987193 + 0.159534i \(0.0509990\pi\)
−0.987193 + 0.159534i \(0.949001\pi\)
\(678\) 0 0
\(679\) 1.53938e6i 0.128136i
\(680\) −9.66080e6 7.49886e6i −0.801199 0.621903i
\(681\) 0 0
\(682\) 1.24925e7 + 1.14900e7i 1.02846 + 0.945932i
\(683\) −8.23750e6 −0.675684 −0.337842 0.941203i \(-0.609697\pi\)
−0.337842 + 0.941203i \(0.609697\pi\)
\(684\) 0 0
\(685\) −1.79292e7 −1.45994
\(686\) −8.66980e6 7.97407e6i −0.703394 0.646949i
\(687\) 0 0
\(688\) 1.60356e6 + 9.50659e6i 0.129156 + 0.765691i
\(689\) 2.80969e7i 2.25482i
\(690\) 0 0
\(691\) 2.65718e6i 0.211703i −0.994382 0.105851i \(-0.966243\pi\)
0.994382 0.105851i \(-0.0337568\pi\)
\(692\) 9.56531e6 801074.i 0.759336 0.0635927i
\(693\) 0 0
\(694\) −9.73741e6 + 1.05870e7i −0.767440 + 0.834398i
\(695\) 4.80313e6 0.377191
\(696\) 0 0
\(697\) −2.04451e6 −0.159407
\(698\) −2.12514e6 + 2.31055e6i −0.165101 + 0.179505i
\(699\) 0 0
\(700\) 4.31784e6 361609.i 0.333059 0.0278930i
\(701\) 1.26405e7i 0.971561i −0.874081 0.485780i \(-0.838535\pi\)
0.874081 0.485780i \(-0.161465\pi\)
\(702\) 0 0
\(703\) 2.69789e6i 0.205890i
\(704\) 3.83247e6 + 1.49681e7i 0.291439 + 1.13824i
\(705\) 0 0
\(706\) −8.64695e6 7.95305e6i −0.652907 0.600513i
\(707\) 1.05946e7 0.797143
\(708\) 0 0
\(709\) −1.00735e7 −0.752599 −0.376300 0.926498i \(-0.622804\pi\)
−0.376300 + 0.926498i \(0.622804\pi\)
\(710\) 1.89035e6 + 1.73866e6i 0.140733 + 0.129440i
\(711\) 0 0
\(712\) −8.11930e6 + 1.04601e7i −0.600231 + 0.773279i
\(713\) 1.34809e7i 0.993103i
\(714\) 0 0
\(715\) 2.14319e7i 1.56782i
\(716\) −1.44182e6 1.72162e7i −0.105106 1.25503i
\(717\) 0 0
\(718\) 1.35607e7 1.47439e7i 0.981686 1.06734i
\(719\) 3.82437e6 0.275891 0.137946 0.990440i \(-0.455950\pi\)
0.137946 + 0.990440i \(0.455950\pi\)
\(720\) 0 0
\(721\) 1.37382e7 0.984222
\(722\) −9.11784e6 + 9.91336e6i −0.650952 + 0.707747i
\(723\) 0 0
\(724\) −69081.5 824875.i −0.00489796 0.0584846i
\(725\) 5.22045e6i 0.368861i
\(726\) 0 0
\(727\) 1.74022e6i 0.122115i 0.998134 + 0.0610575i \(0.0194473\pi\)
−0.998134 + 0.0610575i \(0.980553\pi\)
\(728\) 1.47660e7 1.90231e7i 1.03261 1.33031i
\(729\) 0 0
\(730\) −1.05173e7 9.67334e6i −0.730463 0.671845i
\(731\) −1.38136e7 −0.956121
\(732\) 0 0
\(733\) 2.39703e7 1.64783 0.823917 0.566711i \(-0.191784\pi\)
0.823917 + 0.566711i \(0.191784\pi\)
\(734\) −6.94233e6 6.38523e6i −0.475625 0.437458i
\(735\) 0 0
\(736\) −6.68951e6 + 1.02884e7i −0.455197 + 0.700088i
\(737\) 3.07544e7i 2.08563i
\(738\) 0 0
\(739\) 6.52306e6i 0.439380i 0.975570 + 0.219690i \(0.0705046\pi\)
−0.975570 + 0.219690i \(0.929495\pi\)
\(740\) 1.28445e7 1.07570e6i 0.862261 0.0722125i
\(741\) 0 0
\(742\) −1.46905e7 + 1.59723e7i −0.979553 + 1.06502i
\(743\) 2.51966e7 1.67444 0.837219 0.546868i \(-0.184180\pi\)
0.837219 + 0.546868i \(0.184180\pi\)
\(744\) 0 0
\(745\) 1.04642e7 0.690738
\(746\) −1.16694e6 + 1.26875e6i −0.0767716 + 0.0834698i
\(747\) 0 0
\(748\) −2.20610e7 + 1.84756e6i −1.44169 + 0.120738i
\(749\) 1.82832e7i 1.19082i
\(750\) 0 0
\(751\) 6.46901e6i 0.418541i 0.977858 + 0.209270i \(0.0671089\pi\)
−0.977858 + 0.209270i \(0.932891\pi\)
\(752\) 1.12310e7 1.89442e6i 0.724223 0.122161i
\(753\) 0 0
\(754\) −2.13548e7 1.96412e7i −1.36794 1.25817i
\(755\) 2.24869e7 1.43570
\(756\) 0 0
\(757\) −1.26991e7 −0.805440 −0.402720 0.915323i \(-0.631935\pi\)
−0.402720 + 0.915323i \(0.631935\pi\)
\(758\) 3.35426e6 + 3.08509e6i 0.212043 + 0.195027i
\(759\) 0 0
\(760\) 2.03077e6 + 1.57632e6i 0.127534 + 0.0989940i
\(761\) 1.71063e7i 1.07076i −0.844610 0.535382i \(-0.820167\pi\)
0.844610 0.535382i \(-0.179833\pi\)
\(762\) 0 0
\(763\) 3.03621e7i 1.88808i
\(764\) 1.38736e6 + 1.65660e7i 0.0859918 + 1.02679i
\(765\) 0 0
\(766\) 7.07758e6 7.69509e6i 0.435826 0.473851i
\(767\) −1.48685e7 −0.912596
\(768\) 0 0
\(769\) −7.68095e6 −0.468381 −0.234190 0.972191i \(-0.575244\pi\)
−0.234190 + 0.972191i \(0.575244\pi\)
\(770\) −1.12057e7 + 1.21834e7i −0.681102 + 0.740527i
\(771\) 0 0
\(772\) −692558. 8.26956e6i −0.0418228 0.499389i
\(773\) 2.27192e6i 0.136755i −0.997660 0.0683776i \(-0.978218\pi\)
0.997660 0.0683776i \(-0.0217823\pi\)
\(774\) 0 0
\(775\) 6.39315e6i 0.382349i
\(776\) −1.63332e6 1.26781e6i −0.0973682 0.0755787i
\(777\) 0 0
\(778\) −1.52022e7 1.39823e7i −0.900448 0.828190i
\(779\) 429772. 0.0253743
\(780\) 0 0
\(781\) 4.64924e6 0.272744
\(782\) −1.29417e7 1.19032e7i −0.756791 0.696061i
\(783\) 0 0
\(784\) 1.36964e6 231029.i 0.0795822 0.0134238i
\(785\) 1.41647e7i 0.820413i
\(786\) 0 0
\(787\)