Properties

Label 108.6.b.c.107.5
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 20
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: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{50}\cdot 3^{40} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.5
Root \(-1.31722 - 0.760496i\) of \(x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} - 32033996800 x^{2} + 41943040000\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.c.107.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.10571 - 3.89142i) q^{2} +(1.71366 + 31.9541i) q^{4} -98.6190i q^{5} -67.7266i q^{7} +(117.311 - 137.863i) q^{8} +O(q^{10})\) \(q+(-4.10571 - 3.89142i) q^{2} +(1.71366 + 31.9541i) q^{4} -98.6190i q^{5} -67.7266i q^{7} +(117.311 - 137.863i) q^{8} +(-383.768 + 404.901i) q^{10} +403.224 q^{11} +525.857 q^{13} +(-263.553 + 278.066i) q^{14} +(-1018.13 + 109.517i) q^{16} -462.383i q^{17} -1958.86i q^{19} +(3151.28 - 169.000i) q^{20} +(-1655.52 - 1569.11i) q^{22} -696.614 q^{23} -6600.72 q^{25} +(-2159.02 - 2046.33i) q^{26} +(2164.14 - 116.060i) q^{28} -4664.43i q^{29} +8849.55i q^{31} +(4606.31 + 3512.32i) q^{32} +(-1799.33 + 1898.41i) q^{34} -6679.13 q^{35} -14878.3 q^{37} +(-7622.77 + 8042.52i) q^{38} +(-13595.9 - 11569.1i) q^{40} +5373.92i q^{41} -1880.14i q^{43} +(690.989 + 12884.6i) q^{44} +(2860.09 + 2710.82i) q^{46} -25776.3 q^{47} +12220.1 q^{49} +(27100.6 + 25686.2i) q^{50} +(901.142 + 16803.3i) q^{52} -31909.4i q^{53} -39765.5i q^{55} +(-9336.97 - 7945.08i) q^{56} +(-18151.3 + 19150.8i) q^{58} +5011.77 q^{59} +21451.5 q^{61} +(34437.3 - 36333.7i) q^{62} +(-5244.24 - 32345.6i) q^{64} -51859.6i q^{65} +18429.1i q^{67} +(14775.0 - 792.368i) q^{68} +(27422.6 + 25991.3i) q^{70} -67791.2 q^{71} +52806.9 q^{73} +(61085.9 + 57897.7i) q^{74} +(62593.7 - 3356.83i) q^{76} -27309.0i q^{77} +94935.6i q^{79} +(10800.5 + 100407. i) q^{80} +(20912.2 - 22063.7i) q^{82} +82255.2 q^{83} -45599.8 q^{85} +(-7316.42 + 7719.31i) q^{86} +(47302.6 - 55589.5i) q^{88} -20696.7i q^{89} -35614.5i q^{91} +(-1193.76 - 22259.7i) q^{92} +(105830. + 100307. i) q^{94} -193181. q^{95} +19858.5 q^{97} +(-50172.2 - 47553.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 20q^{4} + O(q^{10}) \) \( 20q + 20q^{4} + 184q^{10} - 116q^{13} - 4168q^{16} + 696q^{22} - 15228q^{25} - 4764q^{28} - 16520q^{34} - 6452q^{37} + 1504q^{40} - 9336q^{46} - 44464q^{49} + 8236q^{52} - 58736q^{58} + 84604q^{61} - 6496q^{64} + 138696q^{70} + 85420q^{73} + 89172q^{76} + 221200q^{82} + 180320q^{85} - 85824q^{88} - 60936q^{94} - 219908q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.10571 3.89142i −0.725793 0.687913i
\(3\) 0 0
\(4\) 1.71366 + 31.9541i 0.0535519 + 0.998565i
\(5\) 98.6190i 1.76415i −0.471108 0.882076i \(-0.656146\pi\)
0.471108 0.882076i \(-0.343854\pi\)
\(6\) 0 0
\(7\) 67.7266i 0.522413i −0.965283 0.261207i \(-0.915880\pi\)
0.965283 0.261207i \(-0.0841204\pi\)
\(8\) 117.311 137.863i 0.648058 0.761591i
\(9\) 0 0
\(10\) −383.768 + 404.901i −1.21358 + 1.28041i
\(11\) 403.224 1.00476 0.502382 0.864646i \(-0.332457\pi\)
0.502382 + 0.864646i \(0.332457\pi\)
\(12\) 0 0
\(13\) 525.857 0.862998 0.431499 0.902114i \(-0.357985\pi\)
0.431499 + 0.902114i \(0.357985\pi\)
\(14\) −263.553 + 278.066i −0.359375 + 0.379164i
\(15\) 0 0
\(16\) −1018.13 + 109.517i −0.994264 + 0.106950i
\(17\) 462.383i 0.388043i −0.980997 0.194021i \(-0.937847\pi\)
0.980997 0.194021i \(-0.0621531\pi\)
\(18\) 0 0
\(19\) 1958.86i 1.24486i −0.782676 0.622430i \(-0.786146\pi\)
0.782676 0.622430i \(-0.213854\pi\)
\(20\) 3151.28 169.000i 1.76162 0.0944737i
\(21\) 0 0
\(22\) −1655.52 1569.11i −0.729252 0.691191i
\(23\) −696.614 −0.274582 −0.137291 0.990531i \(-0.543840\pi\)
−0.137291 + 0.990531i \(0.543840\pi\)
\(24\) 0 0
\(25\) −6600.72 −2.11223
\(26\) −2159.02 2046.33i −0.626358 0.593667i
\(27\) 0 0
\(28\) 2164.14 116.060i 0.521664 0.0279762i
\(29\) 4664.43i 1.02992i −0.857214 0.514960i \(-0.827807\pi\)
0.857214 0.514960i \(-0.172193\pi\)
\(30\) 0 0
\(31\) 8849.55i 1.65393i 0.562254 + 0.826965i \(0.309934\pi\)
−0.562254 + 0.826965i \(0.690066\pi\)
\(32\) 4606.31 + 3512.32i 0.795203 + 0.606343i
\(33\) 0 0
\(34\) −1799.33 + 1898.41i −0.266939 + 0.281639i
\(35\) −6679.13 −0.921616
\(36\) 0 0
\(37\) −14878.3 −1.78669 −0.893343 0.449375i \(-0.851647\pi\)
−0.893343 + 0.449375i \(0.851647\pi\)
\(38\) −7622.77 + 8042.52i −0.856355 + 0.903511i
\(39\) 0 0
\(40\) −13595.9 11569.1i −1.34356 1.14327i
\(41\) 5373.92i 0.499265i 0.968341 + 0.249633i \(0.0803098\pi\)
−0.968341 + 0.249633i \(0.919690\pi\)
\(42\) 0 0
\(43\) 1880.14i 0.155067i −0.996990 0.0775335i \(-0.975296\pi\)
0.996990 0.0775335i \(-0.0247045\pi\)
\(44\) 690.989 + 12884.6i 0.0538071 + 1.00332i
\(45\) 0 0
\(46\) 2860.09 + 2710.82i 0.199290 + 0.188889i
\(47\) −25776.3 −1.70207 −0.851034 0.525111i \(-0.824024\pi\)
−0.851034 + 0.525111i \(0.824024\pi\)
\(48\) 0 0
\(49\) 12220.1 0.727084
\(50\) 27100.6 + 25686.2i 1.53304 + 1.45303i
\(51\) 0 0
\(52\) 901.142 + 16803.3i 0.0462152 + 0.861759i
\(53\) 31909.4i 1.56037i −0.625547 0.780186i \(-0.715124\pi\)
0.625547 0.780186i \(-0.284876\pi\)
\(54\) 0 0
\(55\) 39765.5i 1.77256i
\(56\) −9336.97 7945.08i −0.397865 0.338554i
\(57\) 0 0
\(58\) −18151.3 + 19150.8i −0.708495 + 0.747509i
\(59\) 5011.77 0.187439 0.0937197 0.995599i \(-0.470124\pi\)
0.0937197 + 0.995599i \(0.470124\pi\)
\(60\) 0 0
\(61\) 21451.5 0.738132 0.369066 0.929403i \(-0.379678\pi\)
0.369066 + 0.929403i \(0.379678\pi\)
\(62\) 34437.3 36333.7i 1.13776 1.20041i
\(63\) 0 0
\(64\) −5244.24 32345.6i −0.160042 0.987110i
\(65\) 51859.6i 1.52246i
\(66\) 0 0
\(67\) 18429.1i 0.501553i 0.968045 + 0.250776i \(0.0806859\pi\)
−0.968045 + 0.250776i \(0.919314\pi\)
\(68\) 14775.0 792.368i 0.387486 0.0207804i
\(69\) 0 0
\(70\) 27422.6 + 25991.3i 0.668903 + 0.633991i
\(71\) −67791.2 −1.59598 −0.797990 0.602671i \(-0.794103\pi\)
−0.797990 + 0.602671i \(0.794103\pi\)
\(72\) 0 0
\(73\) 52806.9 1.15980 0.579901 0.814687i \(-0.303091\pi\)
0.579901 + 0.814687i \(0.303091\pi\)
\(74\) 61085.9 + 57897.7i 1.29677 + 1.22908i
\(75\) 0 0
\(76\) 62593.7 3356.83i 1.24307 0.0666646i
\(77\) 27309.0i 0.524902i
\(78\) 0 0
\(79\) 94935.6i 1.71144i 0.517440 + 0.855720i \(0.326885\pi\)
−0.517440 + 0.855720i \(0.673115\pi\)
\(80\) 10800.5 + 100407.i 0.188676 + 1.75403i
\(81\) 0 0
\(82\) 20912.2 22063.7i 0.343451 0.362363i
\(83\) 82255.2 1.31059 0.655297 0.755371i \(-0.272543\pi\)
0.655297 + 0.755371i \(0.272543\pi\)
\(84\) 0 0
\(85\) −45599.8 −0.684566
\(86\) −7316.42 + 7719.31i −0.106673 + 0.112547i
\(87\) 0 0
\(88\) 47302.6 55589.5i 0.651146 0.765220i
\(89\) 20696.7i 0.276966i −0.990365 0.138483i \(-0.955777\pi\)
0.990365 0.138483i \(-0.0442226\pi\)
\(90\) 0 0
\(91\) 35614.5i 0.450841i
\(92\) −1193.76 22259.7i −0.0147044 0.274188i
\(93\) 0 0
\(94\) 105830. + 100307.i 1.23535 + 1.17087i
\(95\) −193181. −2.19612
\(96\) 0 0
\(97\) 19858.5 0.214298 0.107149 0.994243i \(-0.465828\pi\)
0.107149 + 0.994243i \(0.465828\pi\)
\(98\) −50172.2 47553.6i −0.527713 0.500171i
\(99\) 0 0
\(100\) −11311.4 210920.i −0.113114 2.10920i
\(101\) 42840.9i 0.417884i −0.977928 0.208942i \(-0.932998\pi\)
0.977928 0.208942i \(-0.0670020\pi\)
\(102\) 0 0
\(103\) 92957.3i 0.863357i −0.902027 0.431679i \(-0.857921\pi\)
0.902027 0.431679i \(-0.142079\pi\)
\(104\) 61688.9 72496.1i 0.559273 0.657251i
\(105\) 0 0
\(106\) −124173. + 131010.i −1.07340 + 1.13251i
\(107\) 48825.7 0.412277 0.206139 0.978523i \(-0.433910\pi\)
0.206139 + 0.978523i \(0.433910\pi\)
\(108\) 0 0
\(109\) 104798. 0.844863 0.422432 0.906395i \(-0.361177\pi\)
0.422432 + 0.906395i \(0.361177\pi\)
\(110\) −154745. + 163266.i −1.21936 + 1.28651i
\(111\) 0 0
\(112\) 7417.21 + 68954.3i 0.0558722 + 0.519417i
\(113\) 57875.8i 0.426384i 0.977010 + 0.213192i \(0.0683860\pi\)
−0.977010 + 0.213192i \(0.931614\pi\)
\(114\) 0 0
\(115\) 68699.4i 0.484405i
\(116\) 149048. 7993.26i 1.02844 0.0551542i
\(117\) 0 0
\(118\) −20576.8 19502.9i −0.136042 0.128942i
\(119\) −31315.6 −0.202719
\(120\) 0 0
\(121\) 1538.38 0.00955215
\(122\) −88073.8 83477.0i −0.535731 0.507770i
\(123\) 0 0
\(124\) −282779. + 15165.1i −1.65156 + 0.0885711i
\(125\) 342772.i 1.96214i
\(126\) 0 0
\(127\) 204929.i 1.12744i −0.825965 0.563721i \(-0.809369\pi\)
0.825965 0.563721i \(-0.190631\pi\)
\(128\) −104339. + 153209.i −0.562889 + 0.826533i
\(129\) 0 0
\(130\) −201807. + 212920.i −1.04732 + 1.10499i
\(131\) 106839. 0.543938 0.271969 0.962306i \(-0.412325\pi\)
0.271969 + 0.962306i \(0.412325\pi\)
\(132\) 0 0
\(133\) −132667. −0.650331
\(134\) 71715.3 75664.4i 0.345025 0.364024i
\(135\) 0 0
\(136\) −63745.3 54242.6i −0.295530 0.251474i
\(137\) 141277.i 0.643089i −0.946895 0.321544i \(-0.895798\pi\)
0.946895 0.321544i \(-0.104202\pi\)
\(138\) 0 0
\(139\) 202692.i 0.889816i 0.895576 + 0.444908i \(0.146764\pi\)
−0.895576 + 0.444908i \(0.853236\pi\)
\(140\) −11445.8 213426.i −0.0493543 0.920293i
\(141\) 0 0
\(142\) 278331. + 263804.i 1.15835 + 1.09789i
\(143\) 212038. 0.867110
\(144\) 0 0
\(145\) −460002. −1.81693
\(146\) −216810. 205494.i −0.841776 0.797843i
\(147\) 0 0
\(148\) −25496.3 475422.i −0.0956805 1.78412i
\(149\) 27975.3i 0.103231i 0.998667 + 0.0516153i \(0.0164370\pi\)
−0.998667 + 0.0516153i \(0.983563\pi\)
\(150\) 0 0
\(151\) 26904.4i 0.0960242i 0.998847 + 0.0480121i \(0.0152886\pi\)
−0.998847 + 0.0480121i \(0.984711\pi\)
\(152\) −270054. 229796.i −0.948074 0.806741i
\(153\) 0 0
\(154\) −106271. + 112123.i −0.361087 + 0.380971i
\(155\) 872734. 2.91778
\(156\) 0 0
\(157\) −169696. −0.549442 −0.274721 0.961524i \(-0.588585\pi\)
−0.274721 + 0.961524i \(0.588585\pi\)
\(158\) 369435. 389778.i 1.17732 1.24215i
\(159\) 0 0
\(160\) 346381. 454270.i 1.06968 1.40286i
\(161\) 47179.3i 0.143445i
\(162\) 0 0
\(163\) 120390.i 0.354912i −0.984129 0.177456i \(-0.943213\pi\)
0.984129 0.177456i \(-0.0567868\pi\)
\(164\) −171719. + 9209.08i −0.498549 + 0.0267366i
\(165\) 0 0
\(166\) −337716. 320090.i −0.951220 0.901574i
\(167\) −252246. −0.699896 −0.349948 0.936769i \(-0.613801\pi\)
−0.349948 + 0.936769i \(0.613801\pi\)
\(168\) 0 0
\(169\) −94767.0 −0.255235
\(170\) 187219. + 177448.i 0.496853 + 0.470922i
\(171\) 0 0
\(172\) 60078.2 3221.93i 0.154844 0.00830414i
\(173\) 71644.3i 0.181998i −0.995851 0.0909989i \(-0.970994\pi\)
0.995851 0.0909989i \(-0.0290060\pi\)
\(174\) 0 0
\(175\) 447044.i 1.10346i
\(176\) −410533. + 44159.9i −0.999002 + 0.107460i
\(177\) 0 0
\(178\) −80539.7 + 84974.7i −0.190528 + 0.201020i
\(179\) −472794. −1.10291 −0.551455 0.834205i \(-0.685927\pi\)
−0.551455 + 0.834205i \(0.685927\pi\)
\(180\) 0 0
\(181\) 142613. 0.323566 0.161783 0.986826i \(-0.448275\pi\)
0.161783 + 0.986826i \(0.448275\pi\)
\(182\) −138591. + 146223.i −0.310139 + 0.327218i
\(183\) 0 0
\(184\) −81720.5 + 96037.1i −0.177945 + 0.209119i
\(185\) 1.46728e6i 3.15199i
\(186\) 0 0
\(187\) 186444.i 0.389892i
\(188\) −44171.9 823659.i −0.0911490 1.69962i
\(189\) 0 0
\(190\) 793146. + 751750.i 1.59393 + 1.51074i
\(191\) 762070. 1.51151 0.755755 0.654854i \(-0.227270\pi\)
0.755755 + 0.654854i \(0.227270\pi\)
\(192\) 0 0
\(193\) 766564. 1.48134 0.740670 0.671869i \(-0.234508\pi\)
0.740670 + 0.671869i \(0.234508\pi\)
\(194\) −81533.3 77277.9i −0.155536 0.147418i
\(195\) 0 0
\(196\) 20941.1 + 390482.i 0.0389368 + 0.726041i
\(197\) 279378.i 0.512893i 0.966558 + 0.256446i \(0.0825517\pi\)
−0.966558 + 0.256446i \(0.917448\pi\)
\(198\) 0 0
\(199\) 50473.8i 0.0903510i 0.998979 + 0.0451755i \(0.0143847\pi\)
−0.998979 + 0.0451755i \(0.985615\pi\)
\(200\) −774337. + 909993.i −1.36885 + 1.60865i
\(201\) 0 0
\(202\) −166712. + 175892.i −0.287468 + 0.303297i
\(203\) −315906. −0.538044
\(204\) 0 0
\(205\) 529970. 0.880779
\(206\) −361736. + 381656.i −0.593915 + 0.626619i
\(207\) 0 0
\(208\) −535389. + 57590.3i −0.858048 + 0.0922978i
\(209\) 789861.i 1.25079i
\(210\) 0 0
\(211\) 762679.i 1.17933i −0.807647 0.589666i \(-0.799260\pi\)
0.807647 0.589666i \(-0.200740\pi\)
\(212\) 1.01963e6 54681.8i 1.55813 0.0835610i
\(213\) 0 0
\(214\) −200464. 190001.i −0.299228 0.283611i
\(215\) −185418. −0.273562
\(216\) 0 0
\(217\) 599350. 0.864034
\(218\) −430269. 407813.i −0.613196 0.581192i
\(219\) 0 0
\(220\) 1.27067e6 68144.7i 1.77001 0.0949239i
\(221\) 243147.i 0.334880i
\(222\) 0 0
\(223\) 1.12395e6i 1.51351i −0.653697 0.756756i \(-0.726783\pi\)
0.653697 0.756756i \(-0.273217\pi\)
\(224\) 237877. 311969.i 0.316762 0.415424i
\(225\) 0 0
\(226\) 225219. 237621.i 0.293315 0.309467i
\(227\) −630849. −0.812570 −0.406285 0.913746i \(-0.633176\pi\)
−0.406285 + 0.913746i \(0.633176\pi\)
\(228\) 0 0
\(229\) 551782. 0.695311 0.347655 0.937622i \(-0.386978\pi\)
0.347655 + 0.937622i \(0.386978\pi\)
\(230\) 267338. 282060.i 0.333228 0.351578i
\(231\) 0 0
\(232\) −643051. 547189.i −0.784378 0.667448i
\(233\) 506640.i 0.611377i −0.952132 0.305689i \(-0.901113\pi\)
0.952132 0.305689i \(-0.0988867\pi\)
\(234\) 0 0
\(235\) 2.54204e6i 3.00270i
\(236\) 8588.47 + 160146.i 0.0100377 + 0.187170i
\(237\) 0 0
\(238\) 128573. + 121862.i 0.147132 + 0.139453i
\(239\) 843448. 0.955132 0.477566 0.878596i \(-0.341519\pi\)
0.477566 + 0.878596i \(0.341519\pi\)
\(240\) 0 0
\(241\) −160398. −0.177892 −0.0889460 0.996036i \(-0.528350\pi\)
−0.0889460 + 0.996036i \(0.528350\pi\)
\(242\) −6316.15 5986.50i −0.00693289 0.00657105i
\(243\) 0 0
\(244\) 36760.7 + 685464.i 0.0395284 + 0.737073i
\(245\) 1.20514e6i 1.28269i
\(246\) 0 0
\(247\) 1.03008e6i 1.07431i
\(248\) 1.22002e6 + 1.03815e6i 1.25962 + 1.07184i
\(249\) 0 0
\(250\) 1.33387e6 1.40732e6i 1.34978 1.42411i
\(251\) −793734. −0.795227 −0.397613 0.917553i \(-0.630161\pi\)
−0.397613 + 0.917553i \(0.630161\pi\)
\(252\) 0 0
\(253\) −280891. −0.275891
\(254\) −797465. + 841379.i −0.775582 + 0.818290i
\(255\) 0 0
\(256\) 1.02459e6 223004.i 0.977123 0.212674i
\(257\) 410870.i 0.388036i 0.980998 + 0.194018i \(0.0621520\pi\)
−0.980998 + 0.194018i \(0.937848\pi\)
\(258\) 0 0
\(259\) 1.00766e6i 0.933389i
\(260\) 1.65712e6 88869.7i 1.52027 0.0815306i
\(261\) 0 0
\(262\) −438648. 415754.i −0.394787 0.374182i
\(263\) 808668. 0.720910 0.360455 0.932777i \(-0.382621\pi\)
0.360455 + 0.932777i \(0.382621\pi\)
\(264\) 0 0
\(265\) −3.14687e6 −2.75273
\(266\) 544693. + 516264.i 0.472006 + 0.447371i
\(267\) 0 0
\(268\) −588884. + 31581.2i −0.500833 + 0.0268591i
\(269\) 693759.i 0.584558i 0.956333 + 0.292279i \(0.0944136\pi\)
−0.956333 + 0.292279i \(0.905586\pi\)
\(270\) 0 0
\(271\) 34964.4i 0.0289203i 0.999895 + 0.0144602i \(0.00460297\pi\)
−0.999895 + 0.0144602i \(0.995397\pi\)
\(272\) 50638.8 + 470764.i 0.0415012 + 0.385817i
\(273\) 0 0
\(274\) −549769. + 580043.i −0.442389 + 0.466749i
\(275\) −2.66157e6 −2.12229
\(276\) 0 0
\(277\) −348977. −0.273274 −0.136637 0.990621i \(-0.543629\pi\)
−0.136637 + 0.990621i \(0.543629\pi\)
\(278\) 788761. 832195.i 0.612116 0.645822i
\(279\) 0 0
\(280\) −783536. + 920803.i −0.597261 + 0.701894i
\(281\) 1.85655e6i 1.40263i −0.712854 0.701313i \(-0.752598\pi\)
0.712854 0.701313i \(-0.247402\pi\)
\(282\) 0 0
\(283\) 70998.4i 0.0526966i 0.999653 + 0.0263483i \(0.00838789\pi\)
−0.999653 + 0.0263483i \(0.991612\pi\)
\(284\) −116171. 2.16620e6i −0.0854678 1.59369i
\(285\) 0 0
\(286\) −870567. 825130.i −0.629342 0.596496i
\(287\) 363957. 0.260823
\(288\) 0 0
\(289\) 1.20606e6 0.849423
\(290\) 1.88863e6 + 1.79006e6i 1.31872 + 1.24989i
\(291\) 0 0
\(292\) 90493.2 + 1.68740e6i 0.0621096 + 1.15814i
\(293\) 2.36601e6i 1.61008i −0.593221 0.805039i \(-0.702144\pi\)
0.593221 0.805039i \(-0.297856\pi\)
\(294\) 0 0
\(295\) 494256.i 0.330671i
\(296\) −1.74539e6 + 2.05116e6i −1.15788 + 1.36072i
\(297\) 0 0
\(298\) 108864. 114858.i 0.0710137 0.0749241i
\(299\) −366320. −0.236964
\(300\) 0 0
\(301\) −127336. −0.0810090
\(302\) 104696. 110461.i 0.0660562 0.0696937i
\(303\) 0 0
\(304\) 214529. + 1.99437e6i 0.133138 + 1.23772i
\(305\) 2.11553e6i 1.30218i
\(306\) 0 0
\(307\) 19907.0i 0.0120548i −0.999982 0.00602741i \(-0.998081\pi\)
0.999982 0.00602741i \(-0.00191860\pi\)
\(308\) 872633. 46798.3i 0.524149 0.0281095i
\(309\) 0 0
\(310\) −3.58319e6 3.39618e6i −2.11771 2.00718i
\(311\) −2.54109e6 −1.48977 −0.744885 0.667193i \(-0.767495\pi\)
−0.744885 + 0.667193i \(0.767495\pi\)
\(312\) 0 0
\(313\) 964745. 0.556611 0.278306 0.960493i \(-0.410227\pi\)
0.278306 + 0.960493i \(0.410227\pi\)
\(314\) 696721. + 660358.i 0.398781 + 0.377968i
\(315\) 0 0
\(316\) −3.03358e6 + 162688.i −1.70898 + 0.0916509i
\(317\) 1.96724e6i 1.09954i 0.835317 + 0.549769i \(0.185284\pi\)
−0.835317 + 0.549769i \(0.814716\pi\)
\(318\) 0 0
\(319\) 1.88081e6i 1.03483i
\(320\) −3.18990e6 + 517182.i −1.74141 + 0.282337i
\(321\) 0 0
\(322\) 183595. 193704.i 0.0986779 0.104112i
\(323\) −905745. −0.483059
\(324\) 0 0
\(325\) −3.47104e6 −1.82285
\(326\) −468488. + 494286.i −0.244149 + 0.257593i
\(327\) 0 0
\(328\) 740863. + 630420.i 0.380236 + 0.323553i
\(329\) 1.74574e6i 0.889182i
\(330\) 0 0
\(331\) 2.34318e6i 1.17554i −0.809029 0.587769i \(-0.800007\pi\)
0.809029 0.587769i \(-0.199993\pi\)
\(332\) 140958. + 2.62839e6i 0.0701849 + 1.30871i
\(333\) 0 0
\(334\) 1.03565e6 + 981597.i 0.507980 + 0.481467i
\(335\) 1.81746e6 0.884815
\(336\) 0 0
\(337\) 3.39138e6 1.62668 0.813338 0.581791i \(-0.197648\pi\)
0.813338 + 0.581791i \(0.197648\pi\)
\(338\) 389086. + 368779.i 0.185248 + 0.175580i
\(339\) 0 0
\(340\) −78142.6 1.45710e6i −0.0366598 0.683584i
\(341\) 3.56835e6i 1.66181i
\(342\) 0 0
\(343\) 1.96591e6i 0.902252i
\(344\) −259201. 220561.i −0.118098 0.100492i
\(345\) 0 0
\(346\) −278798. + 294150.i −0.125199 + 0.132093i
\(347\) 952624. 0.424715 0.212358 0.977192i \(-0.431886\pi\)
0.212358 + 0.977192i \(0.431886\pi\)
\(348\) 0 0
\(349\) −1.24091e6 −0.545350 −0.272675 0.962106i \(-0.587908\pi\)
−0.272675 + 0.962106i \(0.587908\pi\)
\(350\) 1.73964e6 1.83543e6i 0.759082 0.800881i
\(351\) 0 0
\(352\) 1.85737e6 + 1.41625e6i 0.798992 + 0.609233i
\(353\) 322727.i 0.137847i 0.997622 + 0.0689236i \(0.0219565\pi\)
−0.997622 + 0.0689236i \(0.978044\pi\)
\(354\) 0 0
\(355\) 6.68550e6i 2.81555i
\(356\) 661345. 35467.2i 0.276569 0.0148321i
\(357\) 0 0
\(358\) 1.94116e6 + 1.83984e6i 0.800484 + 0.758705i
\(359\) −2.01638e6 −0.825725 −0.412862 0.910793i \(-0.635471\pi\)
−0.412862 + 0.910793i \(0.635471\pi\)
\(360\) 0 0
\(361\) −1.36105e6 −0.549675
\(362\) −585528. 554968.i −0.234842 0.222585i
\(363\) 0 0
\(364\) 1.13803e6 61031.3i 0.450194 0.0241434i
\(365\) 5.20777e6i 2.04607i
\(366\) 0 0
\(367\) 2.80423e6i 1.08680i 0.839475 + 0.543398i \(0.182862\pi\)
−0.839475 + 0.543398i \(0.817138\pi\)
\(368\) 709241. 76291.1i 0.273007 0.0293666i
\(369\) 0 0
\(370\) 5.70981e6 6.02423e6i 2.16829 2.28769i
\(371\) −2.16111e6 −0.815159
\(372\) 0 0
\(373\) 793282. 0.295227 0.147613 0.989045i \(-0.452841\pi\)
0.147613 + 0.989045i \(0.452841\pi\)
\(374\) −725531. + 765483.i −0.268211 + 0.282981i
\(375\) 0 0
\(376\) −3.02385e6 + 3.55360e6i −1.10304 + 1.29628i
\(377\) 2.45282e6i 0.888819i
\(378\) 0 0
\(379\) 875935.i 0.313237i −0.987659 0.156619i \(-0.949941\pi\)
0.987659 0.156619i \(-0.0500594\pi\)
\(380\) −331048. 6.17293e6i −0.117607 2.19297i
\(381\) 0 0
\(382\) −3.12883e6 2.96554e6i −1.09704 1.03979i
\(383\) 5.68554e6 1.98050 0.990250 0.139305i \(-0.0444867\pi\)
0.990250 + 0.139305i \(0.0444867\pi\)
\(384\) 0 0
\(385\) −2.69318e6 −0.926007
\(386\) −3.14729e6 2.98302e6i −1.07515 1.01903i
\(387\) 0 0
\(388\) 34030.8 + 634561.i 0.0114761 + 0.213990i
\(389\) 2.56686e6i 0.860059i 0.902815 + 0.430029i \(0.141497\pi\)
−0.902815 + 0.430029i \(0.858503\pi\)
\(390\) 0 0
\(391\) 322102.i 0.106550i
\(392\) 1.43355e6 1.68470e6i 0.471193 0.553741i
\(393\) 0 0
\(394\) 1.08718e6 1.14704e6i 0.352825 0.372254i
\(395\) 9.36246e6 3.01924
\(396\) 0 0
\(397\) 6.13240e6 1.95278 0.976392 0.216004i \(-0.0693025\pi\)
0.976392 + 0.216004i \(0.0693025\pi\)
\(398\) 196415. 207231.i 0.0621536 0.0655762i
\(399\) 0 0
\(400\) 6.72037e6 722891.i 2.10011 0.225903i
\(401\) 5.63051e6i 1.74858i 0.485401 + 0.874292i \(0.338674\pi\)
−0.485401 + 0.874292i \(0.661326\pi\)
\(402\) 0 0
\(403\) 4.65360e6i 1.42734i
\(404\) 1.36894e6 73414.9i 0.417284 0.0223785i
\(405\) 0 0
\(406\) 1.29702e6 + 1.22932e6i 0.390509 + 0.370127i
\(407\) −5.99928e6 −1.79520
\(408\) 0 0
\(409\) 2.86885e6 0.848008 0.424004 0.905660i \(-0.360624\pi\)
0.424004 + 0.905660i \(0.360624\pi\)
\(410\) −2.17590e6 2.06234e6i −0.639264 0.605899i
\(411\) 0 0
\(412\) 2.97037e6 159297.i 0.862118 0.0462345i
\(413\) 339430.i 0.0979208i
\(414\) 0 0
\(415\) 8.11193e6i 2.31209i
\(416\) 2.42226e6 + 1.84698e6i 0.686258 + 0.523273i
\(417\) 0 0
\(418\) −3.07368e6 + 3.24294e6i −0.860435 + 0.907816i
\(419\) 5.25000e6 1.46091 0.730456 0.682960i \(-0.239308\pi\)
0.730456 + 0.682960i \(0.239308\pi\)
\(420\) 0 0
\(421\) 3.82887e6 1.05285 0.526423 0.850223i \(-0.323533\pi\)
0.526423 + 0.850223i \(0.323533\pi\)
\(422\) −2.96791e6 + 3.13134e6i −0.811277 + 0.855951i
\(423\) 0 0
\(424\) −4.39911e6 3.74332e6i −1.18837 1.01121i
\(425\) 3.05206e6i 0.819635i
\(426\) 0 0
\(427\) 1.45284e6i 0.385610i
\(428\) 83670.8 + 1.56018e6i 0.0220782 + 0.411685i
\(429\) 0 0
\(430\) 761271. + 721539.i 0.198549 + 0.188186i
\(431\) −763450. −0.197965 −0.0989823 0.995089i \(-0.531559\pi\)
−0.0989823 + 0.995089i \(0.531559\pi\)
\(432\) 0 0
\(433\) −126626. −0.0324566 −0.0162283 0.999868i \(-0.505166\pi\)
−0.0162283 + 0.999868i \(0.505166\pi\)
\(434\) −2.46075e6 2.33232e6i −0.627110 0.594380i
\(435\) 0 0
\(436\) 179588. + 3.34872e6i 0.0452441 + 0.843651i
\(437\) 1.36457e6i 0.341816i
\(438\) 0 0
\(439\) 6.36482e6i 1.57625i −0.615516 0.788124i \(-0.711052\pi\)
0.615516 0.788124i \(-0.288948\pi\)
\(440\) −5.48218e6 4.66494e6i −1.34996 1.14872i
\(441\) 0 0
\(442\) −946189. + 998292.i −0.230368 + 0.243054i
\(443\) 5.00344e6 1.21132 0.605661 0.795723i \(-0.292909\pi\)
0.605661 + 0.795723i \(0.292909\pi\)
\(444\) 0 0
\(445\) −2.04109e6 −0.488610
\(446\) −4.37378e6 + 4.61462e6i −1.04116 + 1.09850i
\(447\) 0 0
\(448\) −2.19066e6 + 355175.i −0.515679 + 0.0836078i
\(449\) 2.33255e6i 0.546028i 0.962010 + 0.273014i \(0.0880205\pi\)
−0.962010 + 0.273014i \(0.911979\pi\)
\(450\) 0 0
\(451\) 2.16689e6i 0.501644i
\(452\) −1.84937e6 + 99179.6i −0.425772 + 0.0228337i
\(453\) 0 0
\(454\) 2.59008e6 + 2.45490e6i 0.589758 + 0.558978i
\(455\) −3.51227e6 −0.795352
\(456\) 0 0
\(457\) 3.50222e6 0.784429 0.392214 0.919874i \(-0.371709\pi\)
0.392214 + 0.919874i \(0.371709\pi\)
\(458\) −2.26546e6 2.14722e6i −0.504652 0.478313i
\(459\) 0 0
\(460\) −2.19523e6 + 117728.i −0.483710 + 0.0259408i
\(461\) 4.55640e6i 0.998550i 0.866444 + 0.499275i \(0.166400\pi\)
−0.866444 + 0.499275i \(0.833600\pi\)
\(462\) 0 0
\(463\) 3.28727e6i 0.712660i −0.934360 0.356330i \(-0.884028\pi\)
0.934360 0.356330i \(-0.115972\pi\)
\(464\) 510834. + 4.74898e6i 0.110150 + 1.02401i
\(465\) 0 0
\(466\) −1.97155e6 + 2.08011e6i −0.420574 + 0.443734i
\(467\) −4.27154e6 −0.906343 −0.453171 0.891423i \(-0.649707\pi\)
−0.453171 + 0.891423i \(0.649707\pi\)
\(468\) 0 0
\(469\) 1.24814e6 0.262018
\(470\) 9.89215e6 1.04369e7i 2.06560 2.17934i
\(471\) 0 0
\(472\) 587935. 690935.i 0.121472 0.142752i
\(473\) 758117.i 0.155806i
\(474\) 0 0
\(475\) 1.29299e7i 2.62943i
\(476\) −53664.4 1.00066e6i −0.0108560 0.202428i
\(477\) 0 0
\(478\) −3.46295e6 3.28221e6i −0.693228 0.657048i
\(479\) −2.08964e6 −0.416134 −0.208067 0.978115i \(-0.566717\pi\)
−0.208067 + 0.978115i \(0.566717\pi\)
\(480\) 0 0
\(481\) −7.82385e6 −1.54191
\(482\) 658547. + 624176.i 0.129113 + 0.122374i
\(483\) 0 0
\(484\) 2636.27 + 49157.6i 0.000511536 + 0.00953845i
\(485\) 1.95843e6i 0.378054i
\(486\) 0 0
\(487\) 2.02802e6i 0.387480i 0.981053 + 0.193740i \(0.0620618\pi\)
−0.981053 + 0.193740i \(0.937938\pi\)
\(488\) 2.51650e6 2.95737e6i 0.478352 0.562155i
\(489\) 0 0
\(490\) −4.68969e6 + 4.94793e6i −0.882377 + 0.930966i
\(491\) 7.39231e6 1.38381 0.691905 0.721988i \(-0.256772\pi\)
0.691905 + 0.721988i \(0.256772\pi\)
\(492\) 0 0
\(493\) −2.15675e6 −0.399653
\(494\) −4.00849e6 + 4.22922e6i −0.739032 + 0.779728i
\(495\) 0 0
\(496\) −969176. 9.00996e6i −0.176888 1.64444i
\(497\) 4.59127e6i 0.833761i
\(498\) 0 0
\(499\) 579614.i 0.104205i −0.998642 0.0521024i \(-0.983408\pi\)
0.998642 0.0521024i \(-0.0165922\pi\)
\(500\) −1.09530e7 + 587395.i −1.95933 + 0.105076i
\(501\) 0 0
\(502\) 3.25884e6 + 3.08876e6i 0.577170 + 0.547047i
\(503\) 1.39449e6 0.245750 0.122875 0.992422i \(-0.460789\pi\)
0.122875 + 0.992422i \(0.460789\pi\)
\(504\) 0 0
\(505\) −4.22493e6 −0.737210
\(506\) 1.15326e6 + 1.09307e6i 0.200240 + 0.189789i
\(507\) 0 0
\(508\) 6.54832e6 351179.i 1.12582 0.0603767i
\(509\) 2.31186e6i 0.395519i −0.980251 0.197759i \(-0.936634\pi\)
0.980251 0.197759i \(-0.0633665\pi\)
\(510\) 0 0
\(511\) 3.57643e6i 0.605896i
\(512\) −5.07446e6 3.07151e6i −0.855490 0.517819i
\(513\) 0 0
\(514\) 1.59887e6 1.68691e6i 0.266935 0.281634i
\(515\) −9.16736e6 −1.52309
\(516\) 0 0
\(517\) −1.03936e7 −1.71018
\(518\) 3.92121e6 4.13714e6i 0.642090 0.677447i
\(519\) 0 0
\(520\) −7.14950e6 6.08370e6i −1.15949 0.986641i
\(521\) 2.65886e6i 0.429143i −0.976708 0.214571i \(-0.931165\pi\)
0.976708 0.214571i \(-0.0688355\pi\)
\(522\) 0 0
\(523\) 3.85731e6i 0.616638i 0.951283 + 0.308319i \(0.0997664\pi\)
−0.951283 + 0.308319i \(0.900234\pi\)
\(524\) 183085. + 3.41393e6i 0.0291290 + 0.543158i
\(525\) 0 0
\(526\) −3.32016e6 3.14687e6i −0.523232 0.495923i
\(527\) 4.09188e6 0.641795
\(528\) 0 0
\(529\) −5.95107e6 −0.924605
\(530\) 1.29201e7 + 1.22458e7i 1.99792 + 1.89364i
\(531\) 0 0
\(532\) −227347. 4.23926e6i −0.0348265 0.649398i
\(533\) 2.82591e6i 0.430865i
\(534\) 0 0
\(535\) 4.81515e6i 0.727319i
\(536\) 2.54068e6 + 2.16193e6i 0.381978 + 0.325035i
\(537\) 0 0
\(538\) 2.69971e6 2.84837e6i 0.402125 0.424268i
\(539\) 4.92744e6 0.730549
\(540\) 0 0
\(541\) −7.07371e6 −1.03909 −0.519546 0.854442i \(-0.673899\pi\)
−0.519546 + 0.854442i \(0.673899\pi\)
\(542\) 136061. 143554.i 0.0198947 0.0209902i
\(543\) 0 0
\(544\) 1.62403e6 2.12988e6i 0.235287 0.308573i
\(545\) 1.03351e7i 1.49047i
\(546\) 0 0
\(547\) 2.47235e6i 0.353298i −0.984274 0.176649i \(-0.943474\pi\)
0.984274 0.176649i \(-0.0565258\pi\)
\(548\) 4.51438e6 242101.i 0.642166 0.0344386i
\(549\) 0 0
\(550\) 1.09276e7 + 1.03573e7i 1.54035 + 1.45995i
\(551\) −9.13699e6 −1.28211
\(552\) 0 0
\(553\) 6.42967e6 0.894079
\(554\) 1.43280e6 + 1.35802e6i 0.198340 + 0.187988i
\(555\) 0 0
\(556\) −6.47684e6 + 347346.i −0.888539 + 0.0476514i
\(557\) 5.84907e6i 0.798820i −0.916772 0.399410i \(-0.869215\pi\)
0.916772 0.399410i \(-0.130785\pi\)
\(558\) 0 0
\(559\) 988686.i 0.133822i
\(560\) 6.80020e6 731478.i 0.916330 0.0985670i
\(561\) 0 0
\(562\) −7.22464e6 + 7.62247e6i −0.964884 + 1.01802i
\(563\) 310076. 0.0412284 0.0206142 0.999788i \(-0.493438\pi\)
0.0206142 + 0.999788i \(0.493438\pi\)
\(564\) 0 0
\(565\) 5.70766e6 0.752206
\(566\) 276285. 291498.i 0.0362506 0.0382468i
\(567\) 0 0
\(568\) −7.95265e6 + 9.34587e6i −1.03429 + 1.21548i
\(569\) 4.87432e6i 0.631151i −0.948900 0.315575i \(-0.897802\pi\)
0.948900 0.315575i \(-0.102198\pi\)
\(570\) 0 0
\(571\) 1.04563e7i 1.34211i 0.741409 + 0.671054i \(0.234158\pi\)
−0.741409 + 0.671054i \(0.765842\pi\)
\(572\) 363362. + 6.77549e6i 0.0464354 + 0.865865i
\(573\) 0 0
\(574\) −1.49430e6 1.41631e6i −0.189303 0.179423i
\(575\) 4.59815e6 0.579981
\(576\) 0 0
\(577\) 9.62808e6 1.20393 0.601963 0.798524i \(-0.294385\pi\)
0.601963 + 0.798524i \(0.294385\pi\)
\(578\) −4.95173e6 4.69329e6i −0.616506 0.584329i
\(579\) 0 0
\(580\) −788287. 1.46989e7i −0.0973004 1.81433i
\(581\) 5.57086e6i 0.684672i
\(582\) 0 0
\(583\) 1.28666e7i 1.56781i
\(584\) 6.19484e6 7.28011e6i 0.751619 0.883295i
\(585\) 0 0
\(586\) −9.20714e6 + 9.71414e6i −1.10759 + 1.16858i
\(587\) −584872. −0.0700593 −0.0350296 0.999386i \(-0.511153\pi\)
−0.0350296 + 0.999386i \(0.511153\pi\)
\(588\) 0 0
\(589\) 1.73351e7 2.05891
\(590\) −1.92336e6 + 2.02927e6i −0.227473 + 0.239999i
\(591\) 0 0
\(592\) 1.51480e7 1.62942e6i 1.77644 0.191086i
\(593\) 6.31733e6i 0.737728i −0.929483 0.368864i \(-0.879747\pi\)
0.929483 0.368864i \(-0.120253\pi\)
\(594\) 0 0
\(595\) 3.08832e6i 0.357626i
\(596\) −893924. + 47940.2i −0.103083 + 0.00552820i
\(597\) 0 0
\(598\) 1.50400e6 + 1.42550e6i 0.171987 + 0.163010i
\(599\) −9.48535e6 −1.08016 −0.540078 0.841615i \(-0.681605\pi\)
−0.540078 + 0.841615i \(0.681605\pi\)
\(600\) 0 0
\(601\) −1.10737e7 −1.25057 −0.625284 0.780397i \(-0.715017\pi\)
−0.625284 + 0.780397i \(0.715017\pi\)
\(602\) 522802. + 495516.i 0.0587958 + 0.0557271i
\(603\) 0 0
\(604\) −859705. + 46105.0i −0.0958864 + 0.00514228i
\(605\) 151714.i 0.0168514i
\(606\) 0 0
\(607\) 7.47030e6i 0.822936i −0.911424 0.411468i \(-0.865016\pi\)
0.911424 0.411468i \(-0.134984\pi\)
\(608\) 6.88015e6 9.02313e6i 0.754812 0.989916i
\(609\) 0 0
\(610\) −8.23242e6 + 8.68575e6i −0.895784 + 0.945111i
\(611\) −1.35547e7 −1.46888
\(612\) 0 0
\(613\) 527227. 0.0566692 0.0283346 0.999598i \(-0.490980\pi\)
0.0283346 + 0.999598i \(0.490980\pi\)
\(614\) −77466.7 + 81732.5i −0.00829266 + 0.00874931i
\(615\) 0 0
\(616\) −3.76489e6 3.20364e6i −0.399761 0.340167i
\(617\) 9.29470e6i 0.982929i −0.870897 0.491465i \(-0.836462\pi\)
0.870897 0.491465i \(-0.163538\pi\)
\(618\) 0 0
\(619\) 3.38720e6i 0.355316i 0.984092 + 0.177658i \(0.0568520\pi\)
−0.984092 + 0.177658i \(0.943148\pi\)
\(620\) 1.49557e6 + 2.78874e7i 0.156253 + 2.91359i
\(621\) 0 0
\(622\) 1.04330e7 + 9.88845e6i 1.08126 + 1.02483i
\(623\) −1.40172e6 −0.144691
\(624\) 0 0
\(625\) 1.31766e7 1.34928
\(626\) −3.96096e6 3.75423e6i −0.403985 0.382900i
\(627\) 0 0
\(628\) −290801. 5.42247e6i −0.0294237 0.548653i
\(629\) 6.87946e6i 0.693311i
\(630\) 0 0
\(631\) 1.26464e6i 0.126443i −0.998000 0.0632216i \(-0.979863\pi\)
0.998000 0.0632216i \(-0.0201375\pi\)
\(632\) 1.30881e7 + 1.11370e7i 1.30342 + 1.10911i
\(633\) 0 0
\(634\) 7.65538e6 8.07693e6i 0.756386 0.798037i
\(635\) −2.02099e7 −1.98898
\(636\) 0 0
\(637\) 6.42603e6 0.627472
\(638\) −7.31902e6 + 7.72205e6i −0.711871 + 0.751071i
\(639\) 0 0
\(640\) 1.51093e7 + 1.02898e7i 1.45813 + 0.993021i
\(641\) 1.06313e7i 1.02197i 0.859588 + 0.510987i \(0.170720\pi\)
−0.859588 + 0.510987i \(0.829280\pi\)
\(642\) 0 0
\(643\) 1.49352e7i 1.42457i 0.701893 + 0.712283i \(0.252339\pi\)
−0.701893 + 0.712283i \(0.747661\pi\)
\(644\) −1.50757e6 + 80849.3i −0.143240 + 0.00768178i
\(645\) 0 0
\(646\) 3.71873e6 + 3.52464e6i 0.350601 + 0.332302i
\(647\) 4.38900e6 0.412197 0.206099 0.978531i \(-0.433923\pi\)
0.206099 + 0.978531i \(0.433923\pi\)
\(648\) 0 0
\(649\) 2.02086e6 0.188332
\(650\) 1.42511e7 + 1.35073e7i 1.32301 + 1.25396i
\(651\) 0 0
\(652\) 3.84695e6 206308.i 0.354403 0.0190062i
\(653\) 7.73540e6i 0.709905i 0.934884 + 0.354952i \(0.115503\pi\)
−0.934884 + 0.354952i \(0.884497\pi\)
\(654\) 0 0
\(655\) 1.05363e7i 0.959589i
\(656\) −588535. 5.47133e6i −0.0533965 0.496402i
\(657\) 0 0
\(658\) 6.79343e6 7.16751e6i 0.611680 0.645363i
\(659\) −1.45433e6 −0.130452 −0.0652258 0.997871i \(-0.520777\pi\)
−0.0652258 + 0.997871i \(0.520777\pi\)
\(660\) 0 0
\(661\) −1.13463e7 −1.01007 −0.505034 0.863100i \(-0.668520\pi\)
−0.505034 + 0.863100i \(0.668520\pi\)
\(662\) −9.11832e6 + 9.62043e6i −0.808667 + 0.853197i
\(663\) 0 0
\(664\) 9.64944e6 1.13399e7i 0.849341 0.998137i
\(665\) 1.30835e7i 1.14728i
\(666\) 0 0
\(667\) 3.24931e6i 0.282798i
\(668\) −432265. 8.06030e6i −0.0374808 0.698892i
\(669\) 0 0
\(670\) −7.46195e6 7.07250e6i −0.642193 0.608675i
\(671\) 8.64977e6 0.741649
\(672\) 0 0
\(673\) 2.63098e6 0.223913 0.111957 0.993713i \(-0.464288\pi\)
0.111957 + 0.993713i \(0.464288\pi\)
\(674\) −1.39240e7 1.31973e7i −1.18063 1.11901i
\(675\) 0 0
\(676\) −162399. 3.02819e6i −0.0136683 0.254869i
\(677\) 2.00948e7i 1.68504i −0.538661 0.842522i \(-0.681070\pi\)
0.538661 0.842522i \(-0.318930\pi\)
\(678\) 0 0
\(679\) 1.34495e6i 0.111952i
\(680\) −5.34935e6 + 6.28651e6i −0.443638 + 0.521359i
\(681\) 0 0
\(682\) 1.38859e7 1.46506e7i 1.14318 1.20613i
\(683\) −9.59174e6 −0.786766 −0.393383 0.919375i \(-0.628695\pi\)
−0.393383 + 0.919375i \(0.628695\pi\)
\(684\) 0 0
\(685\) −1.39326e7 −1.13451
\(686\) −7.65018e6 + 8.07144e6i −0.620670 + 0.654848i
\(687\) 0 0
\(688\) 205907. + 1.91422e6i 0.0165844 + 0.154178i
\(689\) 1.67798e7i 1.34660i
\(690\) 0 0
\(691\) 537489.i 0.0428227i −0.999771 0.0214114i \(-0.993184\pi\)
0.999771 0.0214114i \(-0.00681597\pi\)
\(692\) 2.28933e6 122774.i 0.181737 0.00974634i
\(693\) 0 0
\(694\) −3.91120e6 3.70706e6i −0.308256 0.292167i
\(695\) 1.99893e7 1.56977
\(696\) 0 0
\(697\) 2.48481e6 0.193736
\(698\) 5.09480e6 + 4.82889e6i 0.395811 + 0.375153i
\(699\) 0 0
\(700\) −1.42849e7 + 766082.i −1.10187 + 0.0590922i
\(701\) 1.34046e7i 1.03029i −0.857104 0.515143i \(-0.827739\pi\)
0.857104 0.515143i \(-0.172261\pi\)
\(702\) 0 0
\(703\) 2.91445e7i 2.22417i
\(704\) −2.11460e6 1.30425e7i −0.160804 0.991814i
\(705\) 0 0
\(706\) 1.25587e6 1.32502e6i 0.0948269 0.100049i
\(707\) −2.90147e6 −0.218308
\(708\) 0 0
\(709\) 1.75400e7 1.31043 0.655217 0.755441i \(-0.272577\pi\)
0.655217 + 0.755441i \(0.272577\pi\)
\(710\) 2.60161e7 2.74487e7i 1.93685 2.04351i
\(711\) 0 0
\(712\) −2.85331e6 2.42795e6i −0.210935 0.179490i
\(713\) 6.16472e6i 0.454140i
\(714\) 0 0
\(715\) 2.09110e7i 1.52971i
\(716\) −810210. 1.51077e7i −0.0590629 1.10133i
\(717\) 0 0
\(718\) 8.27865e6 + 7.84657e6i 0.599305 + 0.568026i
\(719\) 9.18586e6 0.662670 0.331335 0.943513i \(-0.392501\pi\)
0.331335 + 0.943513i \(0.392501\pi\)
\(720\) 0 0
\(721\) −6.29568e6 −0.451029
\(722\) 5.58808e6 + 5.29642e6i 0.398951 + 0.378129i
\(723\) 0 0
\(724\) 244391. + 4.55707e6i 0.0173276 + 0.323102i
\(725\) 3.07886e7i 2.17543i
\(726\) 0 0
\(727\) 4.08483e6i 0.286641i 0.989676 + 0.143321i \(0.0457780\pi\)
−0.989676 + 0.143321i \(0.954222\pi\)
\(728\) −4.90991e6 4.17798e6i −0.343357 0.292171i
\(729\) 0 0
\(730\) −2.02656e7 + 2.13816e7i −1.40751 + 1.48502i
\(731\) −869345. −0.0601726
\(732\) 0 0
\(733\) −1.95584e7 −1.34454 −0.672269 0.740307i \(-0.734680\pi\)
−0.672269 + 0.740307i \(0.734680\pi\)
\(734\) 1.09124e7 1.15133e7i 0.747621 0.788789i
\(735\) 0 0
\(736\) −3.20882e6 2.44673e6i −0.218349 0.166491i
\(737\) 7.43104e6i 0.503942i
\(738\) 0 0
\(739\) 1.93503e7i 1.30340i 0.758477 + 0.651699i \(0.225944\pi\)
−0.758477 + 0.651699i \(0.774056\pi\)
\(740\) −4.68856e7 + 2.51443e6i −3.14746 + 0.168795i
\(741\) 0 0
\(742\) 8.87289e6 + 8.40980e6i 0.591637 + 0.560758i
\(743\) 1.80071e7 1.19666 0.598330 0.801249i \(-0.295831\pi\)
0.598330 + 0.801249i \(0.295831\pi\)
\(744\) 0 0
\(745\) 2.75890e6 0.182115
\(746\) −3.25699e6 3.08700e6i −0.214274 0.203090i
\(747\) 0 0
\(748\) 5.95764e6 319502.i 0.389332 0.0208794i
\(749\) 3.30680e6i 0.215379i
\(750\) 0 0
\(751\) 1.64226e7i 1.06253i −0.847205 0.531267i \(-0.821716\pi\)
0.847205 0.531267i \(-0.178284\pi\)
\(752\) 2.62436e7 2.82295e6i 1.69230 0.182036i
\(753\) 0 0
\(754\) −9.54498e6 + 1.00706e7i −0.611430 + 0.645099i
\(755\) 2.65328e6 0.169401
\(756\) 0 0
\(757\) 2.25867e7 1.43256 0.716279 0.697814i \(-0.245844\pi\)
0.716279 + 0.697814i \(0.245844\pi\)
\(758\) −3.40863e6 + 3.59633e6i −0.215480 + 0.227346i
\(759\) 0 0
\(760\) −2.26623e7 + 2.66325e7i −1.42321 + 1.67255i
\(761\) 2.24952e7i 1.40808i 0.710159 + 0.704041i \(0.248623\pi\)
−0.710159 + 0.704041i \(0.751377\pi\)
\(762\) 0 0
\(763\) 7.09760e6i 0.441368i
\(764\) 1.30593e6 + 2.43512e7i 0.0809443 + 1.50934i
\(765\) 0 0
\(766\) −2.33432e7 2.21248e7i −1.43743 1.36241i
\(767\) 2.63547e6 0.161760
\(768\) 0 0
\(769\) −1.86118e7 −1.13494 −0.567468 0.823395i \(-0.692077\pi\)
−0.567468 + 0.823395i \(0.692077\pi\)
\(770\) 1.10574e7 + 1.04803e7i 0.672090 + 0.637012i
\(771\) 0 0
\(772\) 1.31363e6 + 2.44948e7i 0.0793287 + 1.47921i
\(773\) 1.63770e7i 0.985793i −0.870088 0.492896i \(-0.835938\pi\)
0.870088 0.492896i \(-0.164062\pi\)
\(774\) 0 0
\(775\) 5.84134e7i 3.49348i
\(776\) 2.32962e6 2.73775e6i 0.138877 0.163207i
\(777\) 0 0
\(778\) 9.98873e6 1.05388e7i 0.591645 0.624225i
\(779\) 1.05268e7 0.621515
\(780\) 0 0
\(781\) −2.73350e7 −1.60358
\(782\) 1.25344e6 1.32246e6i 0.0732969 0.0773330i
\(783\) 0 0
\(784\) −1.24416e7 + 1.33831e6i −0.722914 + 0.0777618i
\(785\) 1.67352e7i 0.969298i
\(786\) 0