Properties

Label 108.6.b.b.107.11
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 107.11
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.107.12

$q$-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 \(0.135119\pi\)
−0.911250 + 0.411855i \(0.864881\pi\)
\(6\) 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 \(-0.699880\pi\)
−0.587479 + 0.809239i \(0.699880\pi\)
\(12\) 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 \(0.211108\pi\)
−0.788016 + 0.615654i \(0.788892\pi\)
\(18\) 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 \(-0.362896\pi\)
0.417531 + 0.908663i \(0.362896\pi\)
\(24\) 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 \(0.194474\pi\)
−0.819100 + 0.573651i \(0.805526\pi\)
\(30\) 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 \(0.0206189\pi\)
−0.997903 + 0.0647308i \(0.979381\pi\)
\(42\) 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 \(-0.380307\pi\)
0.367227 + 0.930131i \(0.380307\pi\)
\(48\) 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 \(0.245019\pi\)
−0.718084 + 0.695957i \(0.754981\pi\)
\(54\) 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 \(-0.590890\pi\)
−0.281676 + 0.959510i \(0.590890\pi\)
\(60\) 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 \(-0.537028\pi\)
−0.116065 + 0.993242i \(0.537028\pi\)
\(72\) 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 \(-0.382914\pi\)
0.359598 + 0.933107i \(0.382914\pi\)
\(84\) 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 \(-0.837198\pi\)
0.872032 0.489448i \(-0.162802\pi\)
\(90\) 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 \(0.125247\pi\)
−0.923582 + 0.383400i \(0.874753\pi\)
\(102\) 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 \(-0.305877\pi\)
0.572748 + 0.819731i \(0.305877\pi\)
\(108\) 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 \(-0.929275\pi\)
0.975418 0.220365i \(-0.0707248\pi\)
\(114\) 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 \(-0.894698\pi\)
−0.945778 + 0.324815i \(0.894698\pi\)
\(132\) 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 \(0.346664\pi\)
−0.463304 + 0.886199i \(0.653336\pi\)
\(138\) 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 \(-0.862281\pi\)
0.907855 0.419285i \(-0.137719\pi\)
\(150\) 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 \(-0.547736\pi\)
−0.149407 + 0.988776i \(0.547736\pi\)
\(168\) 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 \(-0.875581\pi\)
0.924576 0.380997i \(-0.124419\pi\)
\(174\) 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 \(-0.716828\pi\)
−0.629714 + 0.776827i \(0.716828\pi\)
\(180\) 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 \(-0.327720\pi\)
0.515194 + 0.857073i \(0.327720\pi\)
\(192\) 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 \(0.110970\pi\)
−0.939844 + 0.341604i \(0.889030\pi\)
\(198\) 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 \(-0.466000\pi\)
0.106611 + 0.994301i \(0.466000\pi\)
\(228\) 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 \(0.102244\pi\)
−0.948855 + 0.315713i \(0.897756\pi\)
\(234\) 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 \(-0.595450\pi\)
−0.295392 + 0.955376i \(0.595450\pi\)
\(240\) 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 \(-0.304377\pi\)
0.576606 + 0.817022i \(0.304377\pi\)
\(252\) 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 \(-0.796720\pi\)
0.802918 0.596090i \(-0.203280\pi\)
\(258\) 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 \(-0.465450\pi\)
0.108328 + 0.994115i \(0.465450\pi\)
\(264\) 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 \(0.111387\pi\)
−0.939396 + 0.342834i \(0.888613\pi\)
\(270\) 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 \(0.297405\pi\)
−0.594361 + 0.804198i \(0.702595\pi\)
\(282\) 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 \(0.249849\pi\)
−0.707442 + 0.706771i \(0.750151\pi\)
\(294\) 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 \(-0.429184\pi\)
0.220644 + 0.975354i \(0.429184\pi\)
\(312\) 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 \(0.0662074\pi\)
−0.978447 + 0.206500i \(0.933793\pi\)
\(318\) 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 \(-0.691830\pi\)
−0.566830 + 0.823835i \(0.691830\pi\)
\(348\) 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 \(-0.853723\pi\)
0.896256 0.443538i \(-0.146277\pi\)
\(354\) 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 \(-0.241807\pi\)
0.725071 + 0.688674i \(0.241807\pi\)
\(360\) 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 \(-0.395679\pi\)
0.321900 + 0.946774i \(0.395679\pi\)
\(384\) 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 \(-0.790486\pi\)
0.791090 0.611700i \(-0.209514\pi\)
\(390\) 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 \(0.150833\pi\)
−0.889816 + 0.456320i \(0.849167\pi\)
\(402\) 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 \(-0.217828\pi\)
0.774845 + 0.632151i \(0.217828\pi\)
\(420\) 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 \(-0.622753\pi\)
−0.376152 + 0.926558i \(0.622753\pi\)
\(432\) 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 \(-0.681558\pi\)
−0.539953 + 0.841695i \(0.681558\pi\)
\(444\) 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 \(0.0147066\pi\)
−0.998933 + 0.0461856i \(0.985293\pi\)
\(450\) 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 \(-0.979948\pi\)
0.998016 0.0629534i \(-0.0200519\pi\)
\(462\) 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 \(-0.931156\pi\)
−0.976702 + 0.214598i \(0.931156\pi\)
\(468\) 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 \(-0.572604\pi\)
−0.226120 + 0.974099i \(0.572604\pi\)
\(480\) 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 \(-0.515993\pi\)
−0.0502232 + 0.998738i \(0.515993\pi\)
\(492\) 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 \(-0.404777\pi\)
0.294711 + 0.955586i \(0.404777\pi\)
\(504\) 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 \(0.150102\pi\)
−0.890861 + 0.454277i \(0.849898\pi\)
\(510\) 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 \(0.116240\pi\)
−0.934060 + 0.357116i \(0.883760\pi\)
\(522\) 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 \(-0.853312\pi\)
0.895683 0.444694i \(-0.146688\pi\)
\(558\) 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 \(-0.832900\pi\)
−0.865343 + 0.501180i \(0.832900\pi\)
\(564\) 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 \(-0.951915\pi\)
0.988612 0.150490i \(-0.0480851\pi\)
\(570\) 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 \(-0.675911\pi\)
−0.524936 + 0.851142i \(0.675911\pi\)
\(588\) 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 \(-0.867050\pi\)
0.914034 0.405637i \(-0.132950\pi\)
\(594\) 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 \(-0.366420\pi\)
0.407446 + 0.913229i \(0.366420\pi\)
\(600\) 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 \(-0.750538\pi\)
0.708301 0.705910i \(-0.249462\pi\)
\(618\) 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 \(0.0713090\pi\)
−0.975011 + 0.222155i \(0.928691\pi\)
\(642\) 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 \(-0.195011\pi\)
0.818129 + 0.575034i \(0.195011\pi\)
\(648\) 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 \(0.0579173\pi\)
−0.983492 + 0.180950i \(0.942083\pi\)
\(654\) 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 \(-0.727488\pi\)
−0.655371 + 0.755307i \(0.727488\pi\)
\(660\) 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 \(-0.949001\pi\)
0.987193 0.159534i \(-0.0509990\pi\)
\(678\) 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 \(-0.390303\pi\)
0.337842 + 0.941203i \(0.390303\pi\)
\(684\) 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 \(0.161465\pi\)
−0.874081 + 0.485780i \(0.838535\pi\)
\(702\) 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 \(-0.544050\pi\)
−0.137946 + 0.990440i \(0.544050\pi\)
\(720\) 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 \(-0.815820\pi\)
−0.837219 + 0.546868i \(0.815820\pi\)
\(744\) 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 \(0.179833\pi\)
−0.844610 + 0.535382i \(0.820167\pi\)
\(762\) 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 \(0.0217823\pi\)
−0.997660 + 0.0683776i \(0.978218\pi\)
\(774\) 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
\(787\) 1.56436e7i