Properties

Label 108.6.b.c.107.16
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 107.16
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.107.15

$q$-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 \(-0.915880\pi\)
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 \(-0.667543\pi\)
−0.502382 + 0.864646i \(0.667543\pi\)
\(12\) 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 \(-0.786146\pi\)
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 \(-0.456160\pi\)
0.137291 + 0.990531i \(0.456160\pi\)
\(24\) 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 \(0.309934\pi\)
−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 \(-0.919690\pi\)
0.968341 0.249633i \(-0.0803098\pi\)
\(42\) 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 \(-0.175976\pi\)
0.851034 + 0.525111i \(0.175976\pi\)
\(48\) 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 \(-0.529876\pi\)
−0.0937197 + 0.995599i \(0.529876\pi\)
\(60\) 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 \(-0.205897\pi\)
0.797990 + 0.602671i \(0.205897\pi\)
\(72\) 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 \(-0.727457\pi\)
−0.655297 + 0.755371i \(0.727457\pi\)
\(84\) 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 \(-0.857921\pi\)
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 \(-0.566090\pi\)
−0.206139 + 0.978523i \(0.566090\pi\)
\(108\) 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 \(-0.809369\pi\)
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 \(-0.587675\pi\)
−0.271969 + 0.962306i \(0.587675\pi\)
\(132\) 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 \(0.146764\pi\)
−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 \(-0.983563\pi\)
0.998667 0.0516153i \(-0.0164370\pi\)
\(150\) 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 \(-0.386199\pi\)
0.349948 + 0.936769i \(0.386199\pi\)
\(168\) 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 \(-0.314073\pi\)
0.551455 + 0.834205i \(0.314073\pi\)
\(180\) 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 \(-0.772730\pi\)
−0.755755 + 0.654854i \(0.772730\pi\)
\(192\) 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 \(0.0143847\pi\)
−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 \(-0.366824\pi\)
0.406285 + 0.913746i \(0.366824\pi\)
\(228\) 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 \(-0.658481\pi\)
−0.477566 + 0.878596i \(0.658481\pi\)
\(240\) 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 \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(252\) 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 \(-0.617379\pi\)
−0.360455 + 0.932777i \(0.617379\pi\)
\(264\) 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 \(0.00460297\pi\)
−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 \(0.247402\pi\)
−0.712854 + 0.701313i \(0.752598\pi\)
\(282\) 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 \(0.297856\pi\)
−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 \(-0.998081\pi\)
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 \(-0.232505\pi\)
0.744885 + 0.667193i \(0.232505\pi\)
\(312\) 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 \(-0.800007\pi\)
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 \(-0.568114\pi\)
−0.212358 + 0.977192i \(0.568114\pi\)
\(348\) 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 \(-0.364529\pi\)
0.412862 + 0.910793i \(0.364529\pi\)
\(360\) 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 \(-0.955513\pi\)
−0.990250 + 0.139305i \(0.955513\pi\)
\(384\) 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 \(-0.760692\pi\)
−0.730456 + 0.682960i \(0.760692\pi\)
\(420\) 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 \(-0.468441\pi\)
0.0989823 + 0.995089i \(0.468441\pi\)
\(432\) 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 \(-0.707091\pi\)
−0.605661 + 0.795723i \(0.707091\pi\)
\(444\) 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 \(-0.884028\pi\)
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 \(-0.350293\pi\)
0.453171 + 0.891423i \(0.350293\pi\)
\(468\) 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 \(-0.433283\pi\)
0.208067 + 0.978115i \(0.433283\pi\)
\(480\) 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 \(-0.743228\pi\)
−0.691905 + 0.721988i \(0.743228\pi\)
\(492\) 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 \(-0.539211\pi\)
−0.122875 + 0.992422i \(0.539211\pi\)
\(504\) 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 \(0.0997664\pi\)
−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 \(0.130785\pi\)
−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 \(-0.506562\pi\)
−0.0206142 + 0.999788i \(0.506562\pi\)
\(564\) 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 \(0.234158\pi\)
−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 \(-0.488847\pi\)
0.0350296 + 0.999386i \(0.488847\pi\)
\(588\) 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 \(-0.318395\pi\)
0.540078 + 0.841615i \(0.318395\pi\)
\(600\) 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 \(0.163538\pi\)
−0.870897 + 0.491465i \(0.836462\pi\)
\(618\) 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 \(-0.829280\pi\)
0.859588 0.510987i \(-0.170720\pi\)
\(642\) 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 \(-0.566077\pi\)
−0.206099 + 0.978531i \(0.566077\pi\)
\(648\) 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 \(-0.479223\pi\)
0.0652258 + 0.997871i \(0.479223\pi\)
\(660\) 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 \(-0.371305\pi\)
0.393383 + 0.919375i \(0.371305\pi\)
\(684\) 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 \(0.172261\pi\)
−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 \(-0.607499\pi\)
−0.331335 + 0.943513i \(0.607499\pi\)
\(720\) 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 \(-0.704169\pi\)
−0.598330 + 0.801249i \(0.704169\pi\)
\(744\) 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 \(-0.751377\pi\)
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