Properties

Label 108.6.b.c.107.6
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 107.6
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.107.5

$q$-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 \(0.343854\pi\)
−0.471108 + 0.882076i \(0.656146\pi\)
\(6\) 0 0
\(7\) 67.7266i 0.522413i 0.965283 + 0.261207i \(0.0841204\pi\)
−0.965283 + 0.261207i \(0.915880\pi\)
\(8\) 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 \(0.0621531\pi\)
−0.980997 + 0.194021i \(0.937847\pi\)
\(18\) 0 0
\(19\) 1958.86i 1.24486i 0.782676 + 0.622430i \(0.213854\pi\)
−0.782676 + 0.622430i \(0.786146\pi\)
\(20\) 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 \(0.172193\pi\)
−0.857214 + 0.514960i \(0.827807\pi\)
\(30\) 0 0
\(31\) 8849.55i 1.65393i −0.562254 0.826965i \(-0.690066\pi\)
0.562254 0.826965i \(-0.309934\pi\)
\(32\) 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 \(-0.919690\pi\)
0.968341 0.249633i \(-0.0803098\pi\)
\(42\) 0 0
\(43\) 1880.14i 0.155067i 0.996990 + 0.0775335i \(0.0247045\pi\)
−0.996990 + 0.0775335i \(0.975296\pi\)
\(44\) 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 \(0.284876\pi\)
−0.625547 + 0.780186i \(0.715124\pi\)
\(54\) 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 \(-0.919314\pi\)
0.968045 0.250776i \(-0.0806859\pi\)
\(68\) 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 \(-0.673115\pi\)
0.517440 0.855720i \(-0.326885\pi\)
\(80\) 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 \(0.0442226\pi\)
−0.990365 + 0.138483i \(0.955777\pi\)
\(90\) 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 \(0.0670020\pi\)
−0.977928 + 0.208942i \(0.932998\pi\)
\(102\) 0 0
\(103\) 92957.3i 0.863357i 0.902027 + 0.431679i \(0.142079\pi\)
−0.902027 + 0.431679i \(0.857921\pi\)
\(104\) 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 \(-0.931614\pi\)
0.977010 0.213192i \(-0.0683860\pi\)
\(114\) 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 \(0.190631\pi\)
−0.825965 + 0.563721i \(0.809369\pi\)
\(128\) −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 \(0.104202\pi\)
−0.946895 + 0.321544i \(0.895798\pi\)
\(138\) 0 0
\(139\) 202692.i 0.889816i −0.895576 0.444908i \(-0.853236\pi\)
0.895576 0.444908i \(-0.146764\pi\)
\(140\) −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 \(-0.983563\pi\)
0.998667 0.0516153i \(-0.0164370\pi\)
\(150\) 0 0
\(151\) 26904.4i 0.0960242i −0.998847 0.0480121i \(-0.984711\pi\)
0.998847 0.0480121i \(-0.0152886\pi\)
\(152\) −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 \(0.0567868\pi\)
−0.984129 + 0.177456i \(0.943213\pi\)
\(164\) −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 \(0.0290060\pi\)
−0.995851 + 0.0909989i \(0.970994\pi\)
\(174\) 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 \(-0.917448\pi\)
0.966558 0.256446i \(-0.0825517\pi\)
\(198\) 0 0
\(199\) 50473.8i 0.0903510i −0.998979 0.0451755i \(-0.985615\pi\)
0.998979 0.0451755i \(-0.0143847\pi\)
\(200\) −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 \(0.200740\pi\)
−0.807647 + 0.589666i \(0.799260\pi\)
\(212\) 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 \(0.273217\pi\)
−0.653697 + 0.756756i \(0.726783\pi\)
\(224\) 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 \(0.0988867\pi\)
−0.952132 + 0.305689i \(0.901113\pi\)
\(234\) 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 \(-0.937848\pi\)
0.980998 0.194018i \(-0.0621520\pi\)
\(258\) 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 \(-0.905586\pi\)
0.956333 0.292279i \(-0.0944136\pi\)
\(270\) 0 0
\(271\) 34964.4i 0.0289203i −0.999895 0.0144602i \(-0.995397\pi\)
0.999895 0.0144602i \(-0.00460297\pi\)
\(272\) 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 \(0.247402\pi\)
−0.712854 + 0.701313i \(0.752598\pi\)
\(282\) 0 0
\(283\) 70998.4i 0.0526966i −0.999653 0.0263483i \(-0.991612\pi\)
0.999653 0.0263483i \(-0.00838789\pi\)
\(284\) −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 \(0.297856\pi\)
−0.593221 + 0.805039i \(0.702144\pi\)
\(294\) 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 \(0.00191860\pi\)
−0.999982 + 0.00602741i \(0.998081\pi\)
\(308\) 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 \(-0.814716\pi\)
0.835317 0.549769i \(-0.185284\pi\)
\(318\) 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 \(0.199993\pi\)
−0.809029 + 0.587769i \(0.800007\pi\)
\(332\) 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 \(-0.978044\pi\)
0.997622 0.0689236i \(-0.0219565\pi\)
\(354\) 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 \(-0.817138\pi\)
0.839475 0.543398i \(-0.182862\pi\)
\(368\) 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 \(0.0500594\pi\)
−0.987659 + 0.156619i \(0.949941\pi\)
\(380\) −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 \(-0.858503\pi\)
0.902815 0.430029i \(-0.141497\pi\)
\(390\) 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 \(-0.661326\pi\)
0.485401 0.874292i \(-0.338674\pi\)
\(402\) 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 \(0.288948\pi\)
−0.615516 + 0.788124i \(0.711052\pi\)
\(440\) −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 \(-0.911979\pi\)
0.962010 0.273014i \(-0.0880205\pi\)
\(450\) 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 \(-0.833600\pi\)
0.866444 0.499275i \(-0.166400\pi\)
\(462\) 0 0
\(463\) 3.28727e6i 0.712660i 0.934360 + 0.356330i \(0.115972\pi\)
−0.934360 + 0.356330i \(0.884028\pi\)
\(464\) 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 \(-0.937938\pi\)
0.981053 0.193740i \(-0.0620618\pi\)
\(488\) 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 \(0.0165922\pi\)
−0.998642 + 0.0521024i \(0.983408\pi\)
\(500\) −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 \(0.0633665\pi\)
−0.980251 + 0.197759i \(0.936634\pi\)
\(510\) 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 \(0.0688355\pi\)
−0.976708 + 0.214571i \(0.931165\pi\)
\(522\) 0 0
\(523\) 3.85731e6i 0.616638i −0.951283 0.308319i \(-0.900234\pi\)
0.951283 0.308319i \(-0.0997664\pi\)
\(524\) 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 \(0.0565258\pi\)
−0.984274 + 0.176649i \(0.943474\pi\)
\(548\) 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 \(0.130785\pi\)
−0.916772 + 0.399410i \(0.869215\pi\)
\(558\) 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 \(0.102198\pi\)
−0.948900 + 0.315575i \(0.897802\pi\)
\(570\) 0 0
\(571\) 1.04563e7i 1.34211i −0.741409 0.671054i \(-0.765842\pi\)
0.741409 0.671054i \(-0.234158\pi\)
\(572\) 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 \(0.120253\pi\)
−0.929483 + 0.368864i \(0.879747\pi\)
\(594\) 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 \(0.134984\pi\)
−0.911424 + 0.411468i \(0.865016\pi\)
\(608\) 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 \(0.163538\pi\)
−0.870897 + 0.491465i \(0.836462\pi\)
\(618\) 0 0
\(619\) 3.38720e6i 0.355316i −0.984092 0.177658i \(-0.943148\pi\)
0.984092 0.177658i \(-0.0568520\pi\)
\(620\) 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 \(0.0201375\pi\)
−0.998000 + 0.0632216i \(0.979863\pi\)
\(632\) 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 \(-0.829280\pi\)
0.859588 0.510987i \(-0.170720\pi\)
\(642\) 0 0
\(643\) 1.49352e7i 1.42457i −0.701893 0.712283i \(-0.747661\pi\)
0.701893 0.712283i \(-0.252339\pi\)
\(644\) −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 \(-0.884497\pi\)
0.934884 0.354952i \(-0.115503\pi\)
\(654\) 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 \(0.318930\pi\)
−0.538661 + 0.842522i \(0.681070\pi\)
\(678\) 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 \(0.00681597\pi\)
−0.999771 + 0.0214114i \(0.993184\pi\)
\(692\) 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 \(0.172261\pi\)
−0.857104 + 0.515143i \(0.827739\pi\)
\(702\) 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 \(-0.954222\pi\)
0.989676 0.143321i \(-0.0457780\pi\)
\(728\) −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 \(-0.774056\pi\)
0.758477 0.651699i \(-0.225944\pi\)
\(740\) −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 \(0.178284\pi\)
−0.847205 + 0.531267i \(0.821716\pi\)
\(752\) 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 \(-0.751377\pi\)
0.710159 0.704041i \(-0.248623\pi\)
\(762\) 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 \(0.164062\pi\)
−0.870088 + 0.492896i \(0.835938\pi\)
\(774\) 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 0