Properties

Label 1900.2.i.e.201.6
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + 14 x^{3} + 145 x^{2} + 33 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.6
Root \(1.42323 - 2.46510i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.e.501.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.923228 - 1.59908i) q^{3} +1.72830 q^{7} +(-0.204702 - 0.354554i) q^{9} +O(q^{10})\) \(q+(0.923228 - 1.59908i) q^{3} +1.72830 q^{7} +(-0.204702 - 0.354554i) q^{9} +2.66366 q^{11} +(-0.544662 - 0.943382i) q^{13} +(-0.660249 + 1.14358i) q^{17} +(2.41510 + 3.62868i) q^{19} +(1.59561 - 2.76368i) q^{21} +(-0.704108 - 1.21955i) q^{23} +4.78343 q^{27} +(0.0446618 + 0.0773564i) q^{29} +8.90368 q^{31} +(2.45917 - 4.25940i) q^{33} +3.32732 q^{37} -2.01139 q^{39} +(-0.296903 + 0.514251i) q^{41} +(1.31334 - 2.27477i) q^{43} +(-3.51092 - 6.08109i) q^{47} -4.01299 q^{49} +(1.21912 + 2.11158i) q^{51} +(0.275627 + 0.477400i) q^{53} +(8.03223 - 0.511833i) q^{57} +(-4.07268 + 7.05408i) q^{59} +(-0.207276 - 0.359013i) q^{61} +(-0.353785 - 0.612774i) q^{63} +(-2.11271 - 3.65932i) q^{67} -2.60021 q^{69} +(1.36672 - 2.36723i) q^{71} +(4.53139 - 7.84860i) q^{73} +4.60359 q^{77} +(-5.86470 + 10.1580i) q^{79} +(5.03030 - 8.71273i) q^{81} +7.76556 q^{83} +0.164932 q^{87} +(-0.132475 - 0.229454i) q^{89} +(-0.941337 - 1.63044i) q^{91} +(8.22013 - 14.2377i) q^{93} +(-0.843674 + 1.46129i) q^{97} +(-0.545256 - 0.944410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{3} - 3 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.923228 1.59908i 0.533026 0.923228i −0.466230 0.884664i \(-0.654388\pi\)
0.999256 0.0385649i \(-0.0122786\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.72830 0.653234 0.326617 0.945157i \(-0.394091\pi\)
0.326617 + 0.945157i \(0.394091\pi\)
\(8\) 0 0
\(9\) −0.204702 0.354554i −0.0682339 0.118185i
\(10\) 0 0
\(11\) 2.66366 0.803123 0.401562 0.915832i \(-0.368468\pi\)
0.401562 + 0.915832i \(0.368468\pi\)
\(12\) 0 0
\(13\) −0.544662 0.943382i −0.151062 0.261647i 0.780556 0.625086i \(-0.214936\pi\)
−0.931618 + 0.363439i \(0.881603\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.660249 + 1.14358i −0.160134 + 0.277360i −0.934917 0.354868i \(-0.884526\pi\)
0.774783 + 0.632228i \(0.217859\pi\)
\(18\) 0 0
\(19\) 2.41510 + 3.62868i 0.554061 + 0.832476i
\(20\) 0 0
\(21\) 1.59561 2.76368i 0.348191 0.603085i
\(22\) 0 0
\(23\) −0.704108 1.21955i −0.146817 0.254294i 0.783233 0.621729i \(-0.213569\pi\)
−0.930049 + 0.367435i \(0.880236\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.78343 0.920571
\(28\) 0 0
\(29\) 0.0446618 + 0.0773564i 0.00829348 + 0.0143647i 0.870142 0.492800i \(-0.164027\pi\)
−0.861849 + 0.507165i \(0.830693\pi\)
\(30\) 0 0
\(31\) 8.90368 1.59915 0.799574 0.600568i \(-0.205059\pi\)
0.799574 + 0.600568i \(0.205059\pi\)
\(32\) 0 0
\(33\) 2.45917 4.25940i 0.428086 0.741466i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.32732 0.547008 0.273504 0.961871i \(-0.411817\pi\)
0.273504 + 0.961871i \(0.411817\pi\)
\(38\) 0 0
\(39\) −2.01139 −0.322080
\(40\) 0 0
\(41\) −0.296903 + 0.514251i −0.0463685 + 0.0803126i −0.888278 0.459306i \(-0.848098\pi\)
0.841910 + 0.539618i \(0.181432\pi\)
\(42\) 0 0
\(43\) 1.31334 2.27477i 0.200282 0.346898i −0.748337 0.663318i \(-0.769148\pi\)
0.948619 + 0.316420i \(0.102481\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.51092 6.08109i −0.512120 0.887018i −0.999901 0.0140521i \(-0.995527\pi\)
0.487781 0.872966i \(-0.337806\pi\)
\(48\) 0 0
\(49\) −4.01299 −0.573285
\(50\) 0 0
\(51\) 1.21912 + 2.11158i 0.170711 + 0.295680i
\(52\) 0 0
\(53\) 0.275627 + 0.477400i 0.0378602 + 0.0655759i 0.884335 0.466854i \(-0.154612\pi\)
−0.846474 + 0.532429i \(0.821279\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.03223 0.511833i 1.06389 0.0677939i
\(58\) 0 0
\(59\) −4.07268 + 7.05408i −0.530217 + 0.918364i 0.469161 + 0.883113i \(0.344556\pi\)
−0.999378 + 0.0352509i \(0.988777\pi\)
\(60\) 0 0
\(61\) −0.207276 0.359013i −0.0265390 0.0459669i 0.852451 0.522807i \(-0.175115\pi\)
−0.878990 + 0.476840i \(0.841782\pi\)
\(62\) 0 0
\(63\) −0.353785 0.612774i −0.0445727 0.0772022i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.11271 3.65932i −0.258108 0.447057i 0.707627 0.706586i \(-0.249766\pi\)
−0.965735 + 0.259529i \(0.916433\pi\)
\(68\) 0 0
\(69\) −2.60021 −0.313028
\(70\) 0 0
\(71\) 1.36672 2.36723i 0.162200 0.280939i −0.773457 0.633848i \(-0.781474\pi\)
0.935657 + 0.352910i \(0.114808\pi\)
\(72\) 0 0
\(73\) 4.53139 7.84860i 0.530359 0.918609i −0.469013 0.883191i \(-0.655390\pi\)
0.999373 0.0354182i \(-0.0112763\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.60359 0.524628
\(78\) 0 0
\(79\) −5.86470 + 10.1580i −0.659831 + 1.14286i 0.320829 + 0.947137i \(0.396039\pi\)
−0.980659 + 0.195723i \(0.937295\pi\)
\(80\) 0 0
\(81\) 5.03030 8.71273i 0.558922 0.968082i
\(82\) 0 0
\(83\) 7.76556 0.852381 0.426190 0.904633i \(-0.359855\pi\)
0.426190 + 0.904633i \(0.359855\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.164932 0.0176826
\(88\) 0 0
\(89\) −0.132475 0.229454i −0.0140423 0.0243221i 0.858919 0.512112i \(-0.171137\pi\)
−0.872961 + 0.487790i \(0.837803\pi\)
\(90\) 0 0
\(91\) −0.941337 1.63044i −0.0986789 0.170917i
\(92\) 0 0
\(93\) 8.22013 14.2377i 0.852387 1.47638i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.843674 + 1.46129i −0.0856621 + 0.148371i −0.905673 0.423977i \(-0.860634\pi\)
0.820011 + 0.572348i \(0.193967\pi\)
\(98\) 0 0
\(99\) −0.545256 0.944410i −0.0548002 0.0949168i
\(100\) 0 0
\(101\) −4.80562 8.32358i −0.478177 0.828227i 0.521510 0.853245i \(-0.325369\pi\)
−0.999687 + 0.0250179i \(0.992036\pi\)
\(102\) 0 0
\(103\) 5.41108 0.533169 0.266585 0.963812i \(-0.414105\pi\)
0.266585 + 0.963812i \(0.414105\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.99613 −0.676341 −0.338171 0.941085i \(-0.609808\pi\)
−0.338171 + 0.941085i \(0.609808\pi\)
\(108\) 0 0
\(109\) −2.05095 + 3.55235i −0.196445 + 0.340253i −0.947373 0.320131i \(-0.896273\pi\)
0.750928 + 0.660384i \(0.229607\pi\)
\(110\) 0 0
\(111\) 3.07187 5.32064i 0.291569 0.505013i
\(112\) 0 0
\(113\) 12.9414 1.21742 0.608710 0.793393i \(-0.291687\pi\)
0.608710 + 0.793393i \(0.291687\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.222986 + 0.386224i −0.0206151 + 0.0357064i
\(118\) 0 0
\(119\) −1.14110 + 1.97645i −0.104605 + 0.181181i
\(120\) 0 0
\(121\) −3.90492 −0.354993
\(122\) 0 0
\(123\) 0.548219 + 0.949543i 0.0494312 + 0.0856174i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −5.90009 10.2192i −0.523548 0.906812i −0.999624 0.0274077i \(-0.991275\pi\)
0.476076 0.879404i \(-0.342059\pi\)
\(128\) 0 0
\(129\) −2.42502 4.20026i −0.213511 0.369812i
\(130\) 0 0
\(131\) −2.25635 + 3.90811i −0.197138 + 0.341453i −0.947599 0.319461i \(-0.896498\pi\)
0.750461 + 0.660915i \(0.229831\pi\)
\(132\) 0 0
\(133\) 4.17400 + 6.27143i 0.361932 + 0.543802i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.63770 + 2.83658i 0.139918 + 0.242345i 0.927465 0.373909i \(-0.121983\pi\)
−0.787547 + 0.616254i \(0.788649\pi\)
\(138\) 0 0
\(139\) −3.84162 6.65388i −0.325842 0.564375i 0.655840 0.754900i \(-0.272314\pi\)
−0.981682 + 0.190525i \(0.938981\pi\)
\(140\) 0 0
\(141\) −12.9655 −1.09189
\(142\) 0 0
\(143\) −1.45079 2.51285i −0.121321 0.210135i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.70491 + 6.41709i −0.305576 + 0.529273i
\(148\) 0 0
\(149\) 1.15941 2.00816i 0.0949828 0.164515i −0.814619 0.579997i \(-0.803054\pi\)
0.909601 + 0.415482i \(0.136387\pi\)
\(150\) 0 0
\(151\) 3.18280 0.259012 0.129506 0.991579i \(-0.458661\pi\)
0.129506 + 0.991579i \(0.458661\pi\)
\(152\) 0 0
\(153\) 0.540616 0.0437062
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.981487 1.69999i 0.0783312 0.135674i −0.824199 0.566300i \(-0.808374\pi\)
0.902530 + 0.430627i \(0.141708\pi\)
\(158\) 0 0
\(159\) 1.01787 0.0807220
\(160\) 0 0
\(161\) −1.21691 2.10774i −0.0959057 0.166114i
\(162\) 0 0
\(163\) 1.63601 0.128142 0.0640711 0.997945i \(-0.479592\pi\)
0.0640711 + 0.997945i \(0.479592\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.5824 21.7934i −0.973658 1.68642i −0.684295 0.729205i \(-0.739890\pi\)
−0.289363 0.957219i \(-0.593443\pi\)
\(168\) 0 0
\(169\) 5.90669 10.2307i 0.454361 0.786976i
\(170\) 0 0
\(171\) 0.792187 1.59908i 0.0605800 0.122285i
\(172\) 0 0
\(173\) 7.01277 12.1465i 0.533171 0.923479i −0.466079 0.884743i \(-0.654334\pi\)
0.999249 0.0387355i \(-0.0123330\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 7.52002 + 13.0251i 0.565240 + 0.979024i
\(178\) 0 0
\(179\) −23.7004 −1.77145 −0.885727 0.464207i \(-0.846339\pi\)
−0.885727 + 0.464207i \(0.846339\pi\)
\(180\) 0 0
\(181\) −3.91555 6.78193i −0.291040 0.504097i 0.683016 0.730404i \(-0.260668\pi\)
−0.974056 + 0.226307i \(0.927335\pi\)
\(182\) 0 0
\(183\) −0.765453 −0.0565839
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.75868 + 3.04612i −0.128607 + 0.222754i
\(188\) 0 0
\(189\) 8.26717 0.601348
\(190\) 0 0
\(191\) 6.03698 0.436820 0.218410 0.975857i \(-0.429913\pi\)
0.218410 + 0.975857i \(0.429913\pi\)
\(192\) 0 0
\(193\) −7.51822 + 13.0219i −0.541173 + 0.937339i 0.457664 + 0.889125i \(0.348686\pi\)
−0.998837 + 0.0482141i \(0.984647\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.45409 0.103599 0.0517996 0.998657i \(-0.483504\pi\)
0.0517996 + 0.998657i \(0.483504\pi\)
\(198\) 0 0
\(199\) 12.0696 + 20.9051i 0.855590 + 1.48193i 0.876096 + 0.482136i \(0.160139\pi\)
−0.0205062 + 0.999790i \(0.506528\pi\)
\(200\) 0 0
\(201\) −7.80205 −0.550314
\(202\) 0 0
\(203\) 0.0771887 + 0.133695i 0.00541759 + 0.00938354i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.288264 + 0.499288i −0.0200357 + 0.0347029i
\(208\) 0 0
\(209\) 6.43300 + 9.66556i 0.444980 + 0.668581i
\(210\) 0 0
\(211\) −7.63568 + 13.2254i −0.525662 + 0.910473i 0.473891 + 0.880583i \(0.342849\pi\)
−0.999553 + 0.0298898i \(0.990484\pi\)
\(212\) 0 0
\(213\) −2.52359 4.37099i −0.172914 0.299496i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 15.3882 1.04462
\(218\) 0 0
\(219\) −8.36702 14.4921i −0.565391 0.979286i
\(220\) 0 0
\(221\) 1.43845 0.0967605
\(222\) 0 0
\(223\) −1.72194 + 2.98248i −0.115309 + 0.199722i −0.917903 0.396804i \(-0.870119\pi\)
0.802594 + 0.596526i \(0.203453\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −24.9955 −1.65901 −0.829504 0.558501i \(-0.811377\pi\)
−0.829504 + 0.558501i \(0.811377\pi\)
\(228\) 0 0
\(229\) 5.35855 0.354103 0.177051 0.984202i \(-0.443344\pi\)
0.177051 + 0.984202i \(0.443344\pi\)
\(230\) 0 0
\(231\) 4.25017 7.36150i 0.279640 0.484351i
\(232\) 0 0
\(233\) −6.50466 + 11.2664i −0.426135 + 0.738087i −0.996526 0.0832864i \(-0.973458\pi\)
0.570391 + 0.821373i \(0.306792\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.8289 + 18.7562i 0.703414 + 1.21835i
\(238\) 0 0
\(239\) −8.48487 −0.548841 −0.274420 0.961610i \(-0.588486\pi\)
−0.274420 + 0.961610i \(0.588486\pi\)
\(240\) 0 0
\(241\) 0.0131746 + 0.0228190i 0.000848648 + 0.00146990i 0.866449 0.499265i \(-0.166397\pi\)
−0.865601 + 0.500735i \(0.833063\pi\)
\(242\) 0 0
\(243\) −2.11309 3.65999i −0.135555 0.234788i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.10782 4.25476i 0.134117 0.270724i
\(248\) 0 0
\(249\) 7.16939 12.4177i 0.454341 0.786942i
\(250\) 0 0
\(251\) 9.82041 + 17.0094i 0.619859 + 1.07363i 0.989511 + 0.144457i \(0.0461434\pi\)
−0.369653 + 0.929170i \(0.620523\pi\)
\(252\) 0 0
\(253\) −1.87550 3.24847i −0.117912 0.204229i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.76869 8.25962i −0.297463 0.515221i 0.678092 0.734977i \(-0.262807\pi\)
−0.975555 + 0.219756i \(0.929474\pi\)
\(258\) 0 0
\(259\) 5.75059 0.357324
\(260\) 0 0
\(261\) 0.0182847 0.0316700i 0.00113179 0.00196032i
\(262\) 0 0
\(263\) −5.64831 + 9.78317i −0.348290 + 0.603256i −0.985946 0.167065i \(-0.946571\pi\)
0.637656 + 0.770321i \(0.279904\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.489220 −0.0299398
\(268\) 0 0
\(269\) −8.18113 + 14.1701i −0.498812 + 0.863968i −0.999999 0.00137116i \(-0.999564\pi\)
0.501187 + 0.865339i \(0.332897\pi\)
\(270\) 0 0
\(271\) 2.25370 3.90352i 0.136903 0.237122i −0.789420 0.613853i \(-0.789619\pi\)
0.926323 + 0.376731i \(0.122952\pi\)
\(272\) 0 0
\(273\) −3.47628 −0.210394
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 26.7914 1.60974 0.804871 0.593450i \(-0.202235\pi\)
0.804871 + 0.593450i \(0.202235\pi\)
\(278\) 0 0
\(279\) −1.82260 3.15683i −0.109116 0.188995i
\(280\) 0 0
\(281\) 9.65081 + 16.7157i 0.575719 + 0.997174i 0.995963 + 0.0897633i \(0.0286111\pi\)
−0.420244 + 0.907411i \(0.638056\pi\)
\(282\) 0 0
\(283\) 1.15440 1.99948i 0.0686221 0.118857i −0.829673 0.558250i \(-0.811473\pi\)
0.898295 + 0.439393i \(0.144806\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.513136 + 0.888778i −0.0302895 + 0.0524629i
\(288\) 0 0
\(289\) 7.62814 + 13.2123i 0.448714 + 0.777196i
\(290\) 0 0
\(291\) 1.55781 + 2.69820i 0.0913203 + 0.158171i
\(292\) 0 0
\(293\) −20.5156 −1.19854 −0.599268 0.800549i \(-0.704541\pi\)
−0.599268 + 0.800549i \(0.704541\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 12.7414 0.739332
\(298\) 0 0
\(299\) −0.767001 + 1.32849i −0.0443568 + 0.0768283i
\(300\) 0 0
\(301\) 2.26983 3.93147i 0.130831 0.226606i
\(302\) 0 0
\(303\) −17.7468 −1.01952
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.03655 3.52742i 0.116232 0.201320i −0.802039 0.597271i \(-0.796252\pi\)
0.918272 + 0.395951i \(0.129585\pi\)
\(308\) 0 0
\(309\) 4.99566 8.65274i 0.284193 0.492237i
\(310\) 0 0
\(311\) 11.1999 0.635087 0.317543 0.948244i \(-0.397142\pi\)
0.317543 + 0.948244i \(0.397142\pi\)
\(312\) 0 0
\(313\) 13.0281 + 22.5654i 0.736393 + 1.27547i 0.954110 + 0.299458i \(0.0968057\pi\)
−0.217717 + 0.976012i \(0.569861\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.9315 24.1300i −0.782469 1.35528i −0.930499 0.366294i \(-0.880627\pi\)
0.148030 0.988983i \(-0.452707\pi\)
\(318\) 0 0
\(319\) 0.118964 + 0.206051i 0.00666069 + 0.0115367i
\(320\) 0 0
\(321\) −6.45902 + 11.1874i −0.360508 + 0.624417i
\(322\) 0 0
\(323\) −5.74426 + 0.366038i −0.319619 + 0.0203669i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 3.78699 + 6.55926i 0.209421 + 0.362728i
\(328\) 0 0
\(329\) −6.06791 10.5099i −0.334534 0.579431i
\(330\) 0 0
\(331\) −20.9379 −1.15085 −0.575426 0.817854i \(-0.695164\pi\)
−0.575426 + 0.817854i \(0.695164\pi\)
\(332\) 0 0
\(333\) −0.681108 1.17971i −0.0373245 0.0646479i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −7.75456 + 13.4313i −0.422418 + 0.731649i −0.996175 0.0873761i \(-0.972152\pi\)
0.573758 + 0.819025i \(0.305485\pi\)
\(338\) 0 0
\(339\) 11.9478 20.6942i 0.648917 1.12396i
\(340\) 0 0
\(341\) 23.7164 1.28431
\(342\) 0 0
\(343\) −19.0337 −1.02772
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17.5770 + 30.4443i −0.943584 + 1.63434i −0.185023 + 0.982734i \(0.559236\pi\)
−0.758561 + 0.651602i \(0.774097\pi\)
\(348\) 0 0
\(349\) 29.5120 1.57974 0.789870 0.613274i \(-0.210148\pi\)
0.789870 + 0.613274i \(0.210148\pi\)
\(350\) 0 0
\(351\) −2.60535 4.51260i −0.139063 0.240865i
\(352\) 0 0
\(353\) −31.0179 −1.65092 −0.825458 0.564463i \(-0.809083\pi\)
−0.825458 + 0.564463i \(0.809083\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.10700 + 3.64943i 0.111514 + 0.193148i
\(358\) 0 0
\(359\) 16.5956 28.7444i 0.875882 1.51707i 0.0200625 0.999799i \(-0.493613\pi\)
0.855820 0.517274i \(-0.173053\pi\)
\(360\) 0 0
\(361\) −7.33460 + 17.5272i −0.386032 + 0.922485i
\(362\) 0 0
\(363\) −3.60513 + 6.24428i −0.189220 + 0.327739i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 7.46462 + 12.9291i 0.389650 + 0.674894i 0.992402 0.123035i \(-0.0392626\pi\)
−0.602752 + 0.797928i \(0.705929\pi\)
\(368\) 0 0
\(369\) 0.243106 0.0126556
\(370\) 0 0
\(371\) 0.476365 + 0.825088i 0.0247316 + 0.0428364i
\(372\) 0 0
\(373\) −0.129504 −0.00670546 −0.00335273 0.999994i \(-0.501067\pi\)
−0.00335273 + 0.999994i \(0.501067\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.0486511 0.0842662i 0.00250566 0.00433993i
\(378\) 0 0
\(379\) 9.91054 0.509070 0.254535 0.967064i \(-0.418078\pi\)
0.254535 + 0.967064i \(0.418078\pi\)
\(380\) 0 0
\(381\) −21.7885 −1.11626
\(382\) 0 0
\(383\) −18.1930 + 31.5112i −0.929619 + 1.61015i −0.145659 + 0.989335i \(0.546530\pi\)
−0.783960 + 0.620812i \(0.786803\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.07537 −0.0546641
\(388\) 0 0
\(389\) 11.3433 + 19.6472i 0.575129 + 0.996153i 0.996028 + 0.0890454i \(0.0283816\pi\)
−0.420898 + 0.907108i \(0.638285\pi\)
\(390\) 0 0
\(391\) 1.85954 0.0940412
\(392\) 0 0
\(393\) 4.16625 + 7.21616i 0.210160 + 0.364007i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.67149 + 16.7515i −0.485398 + 0.840734i −0.999859 0.0167797i \(-0.994659\pi\)
0.514461 + 0.857514i \(0.327992\pi\)
\(398\) 0 0
\(399\) 13.8821 0.884599i 0.694973 0.0442853i
\(400\) 0 0
\(401\) −1.11006 + 1.92268i −0.0554337 + 0.0960140i −0.892411 0.451224i \(-0.850987\pi\)
0.836977 + 0.547238i \(0.184321\pi\)
\(402\) 0 0
\(403\) −4.84949 8.39957i −0.241570 0.418412i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8.86284 0.439315
\(408\) 0 0
\(409\) −5.19101 8.99110i −0.256679 0.444581i 0.708671 0.705539i \(-0.249295\pi\)
−0.965350 + 0.260958i \(0.915962\pi\)
\(410\) 0 0
\(411\) 6.04788 0.298320
\(412\) 0 0
\(413\) −7.03879 + 12.1915i −0.346356 + 0.599907i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −14.1868 −0.694730
\(418\) 0 0
\(419\) −15.0958 −0.737479 −0.368740 0.929533i \(-0.620211\pi\)
−0.368740 + 0.929533i \(0.620211\pi\)
\(420\) 0 0
\(421\) −6.47485 + 11.2148i −0.315565 + 0.546574i −0.979557 0.201165i \(-0.935527\pi\)
0.663993 + 0.747739i \(0.268861\pi\)
\(422\) 0 0
\(423\) −1.43738 + 2.48962i −0.0698879 + 0.121049i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.358235 0.620480i −0.0173362 0.0300272i
\(428\) 0 0
\(429\) −5.35765 −0.258670
\(430\) 0 0
\(431\) 15.0654 + 26.0940i 0.725674 + 1.25690i 0.958696 + 0.284433i \(0.0918053\pi\)
−0.233022 + 0.972472i \(0.574861\pi\)
\(432\) 0 0
\(433\) 12.9281 + 22.3922i 0.621287 + 1.07610i 0.989246 + 0.146259i \(0.0467232\pi\)
−0.367959 + 0.929842i \(0.619943\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.72487 5.50031i 0.130348 0.263116i
\(438\) 0 0
\(439\) 4.35016 7.53469i 0.207622 0.359611i −0.743343 0.668910i \(-0.766761\pi\)
0.950965 + 0.309299i \(0.100094\pi\)
\(440\) 0 0
\(441\) 0.821467 + 1.42282i 0.0391175 + 0.0677534i
\(442\) 0 0
\(443\) −15.0822 26.1231i −0.716575 1.24114i −0.962349 0.271817i \(-0.912375\pi\)
0.245774 0.969327i \(-0.420958\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.14081 3.70798i −0.101257 0.175382i
\(448\) 0 0
\(449\) 23.7821 1.12235 0.561173 0.827699i \(-0.310350\pi\)
0.561173 + 0.827699i \(0.310350\pi\)
\(450\) 0 0
\(451\) −0.790849 + 1.36979i −0.0372396 + 0.0645009i
\(452\) 0 0
\(453\) 2.93845 5.08954i 0.138060 0.239128i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.5258 1.24082 0.620412 0.784276i \(-0.286966\pi\)
0.620412 + 0.784276i \(0.286966\pi\)
\(458\) 0 0
\(459\) −3.15825 + 5.47025i −0.147414 + 0.255329i
\(460\) 0 0
\(461\) 7.34402 12.7202i 0.342045 0.592439i −0.642767 0.766061i \(-0.722214\pi\)
0.984812 + 0.173622i \(0.0555472\pi\)
\(462\) 0 0
\(463\) 9.22167 0.428567 0.214284 0.976771i \(-0.431258\pi\)
0.214284 + 0.976771i \(0.431258\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −31.3069 −1.44871 −0.724355 0.689427i \(-0.757862\pi\)
−0.724355 + 0.689427i \(0.757862\pi\)
\(468\) 0 0
\(469\) −3.65139 6.32439i −0.168605 0.292033i
\(470\) 0 0
\(471\) −1.81227 3.13895i −0.0835051 0.144635i
\(472\) 0 0
\(473\) 3.49828 6.05920i 0.160851 0.278602i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.112843 0.195449i 0.00516671 0.00894900i
\(478\) 0 0
\(479\) −16.0062 27.7236i −0.731344 1.26672i −0.956309 0.292357i \(-0.905560\pi\)
0.224966 0.974367i \(-0.427773\pi\)
\(480\) 0 0
\(481\) −1.81226 3.13893i −0.0826321 0.143123i
\(482\) 0 0
\(483\) −4.49393 −0.204481
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 2.19899 0.0996456 0.0498228 0.998758i \(-0.484134\pi\)
0.0498228 + 0.998758i \(0.484134\pi\)
\(488\) 0 0
\(489\) 1.51041 2.61611i 0.0683031 0.118304i
\(490\) 0 0
\(491\) −6.78283 + 11.7482i −0.306105 + 0.530189i −0.977507 0.210904i \(-0.932359\pi\)
0.671402 + 0.741094i \(0.265693\pi\)
\(492\) 0 0
\(493\) −0.117951 −0.00531227
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.36210 4.09128i 0.105955 0.183519i
\(498\) 0 0
\(499\) −6.20880 + 10.7540i −0.277944 + 0.481413i −0.970874 0.239592i \(-0.922986\pi\)
0.692930 + 0.721005i \(0.256320\pi\)
\(500\) 0 0
\(501\) −46.4658 −2.07594
\(502\) 0 0
\(503\) 8.43957 + 14.6178i 0.376302 + 0.651774i 0.990521 0.137361i \(-0.0438622\pi\)
−0.614219 + 0.789136i \(0.710529\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −10.9064 18.8905i −0.484372 0.838957i
\(508\) 0 0
\(509\) 12.4081 + 21.4915i 0.549981 + 0.952594i 0.998275 + 0.0587085i \(0.0186983\pi\)
−0.448295 + 0.893886i \(0.647968\pi\)
\(510\) 0 0
\(511\) 7.83159 13.5647i 0.346449 0.600067i
\(512\) 0 0
\(513\) 11.5524 + 17.3575i 0.510053 + 0.766353i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9.35189 16.1979i −0.411296 0.712385i
\(518\) 0 0
\(519\) −12.9488 22.4279i −0.568388 0.984477i
\(520\) 0 0
\(521\) −32.6549 −1.43064 −0.715318 0.698799i \(-0.753718\pi\)
−0.715318 + 0.698799i \(0.753718\pi\)
\(522\) 0 0
\(523\) −1.72603 2.98957i −0.0754741 0.130725i 0.825818 0.563936i \(-0.190714\pi\)
−0.901292 + 0.433211i \(0.857380\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.87864 + 10.1821i −0.256078 + 0.443539i
\(528\) 0 0
\(529\) 10.5085 18.2012i 0.456890 0.791356i
\(530\) 0 0
\(531\) 3.33474 0.144715
\(532\) 0 0
\(533\) 0.646847 0.0280181
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −21.8809 + 37.8989i −0.944231 + 1.63546i
\(538\) 0 0
\(539\) −10.6892 −0.460418
\(540\) 0 0
\(541\) −3.69787 6.40490i −0.158984 0.275368i 0.775519 0.631325i \(-0.217488\pi\)
−0.934503 + 0.355956i \(0.884155\pi\)
\(542\) 0 0
\(543\) −14.4598 −0.620529
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.74778 6.49134i −0.160243 0.277550i 0.774713 0.632314i \(-0.217895\pi\)
−0.934956 + 0.354764i \(0.884561\pi\)
\(548\) 0 0
\(549\) −0.0848596 + 0.146981i −0.00362172 + 0.00627300i
\(550\) 0 0
\(551\) −0.172839 + 0.348887i −0.00736319 + 0.0148631i
\(552\) 0 0
\(553\) −10.1359 + 17.5560i −0.431024 + 0.746556i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13.1744 22.8187i −0.558217 0.966859i −0.997645 0.0685820i \(-0.978153\pi\)
0.439429 0.898277i \(-0.355181\pi\)
\(558\) 0 0
\(559\) −2.86130 −0.121020
\(560\) 0 0
\(561\) 3.24732 + 5.62453i 0.137102 + 0.237468i
\(562\) 0 0
\(563\) −10.8731 −0.458247 −0.229123 0.973397i \(-0.573586\pi\)
−0.229123 + 0.973397i \(0.573586\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 8.69385 15.0582i 0.365107 0.632384i
\(568\) 0 0
\(569\) −18.8171 −0.788853 −0.394427 0.918927i \(-0.629057\pi\)
−0.394427 + 0.918927i \(0.629057\pi\)
\(570\) 0 0
\(571\) −29.0661 −1.21638 −0.608189 0.793792i \(-0.708104\pi\)
−0.608189 + 0.793792i \(0.708104\pi\)
\(572\) 0 0
\(573\) 5.57351 9.65360i 0.232837 0.403285i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 17.6665 0.735468 0.367734 0.929931i \(-0.380134\pi\)
0.367734 + 0.929931i \(0.380134\pi\)
\(578\) 0 0
\(579\) 13.8821 + 24.0444i 0.576919 + 0.999253i
\(580\) 0 0
\(581\) 13.4212 0.556804
\(582\) 0 0
\(583\) 0.734176 + 1.27163i 0.0304065 + 0.0526655i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.2815 + 26.4684i −0.630736 + 1.09247i 0.356666 + 0.934232i \(0.383913\pi\)
−0.987402 + 0.158234i \(0.949420\pi\)
\(588\) 0 0
\(589\) 21.5032 + 32.3086i 0.886026 + 1.33125i
\(590\) 0 0
\(591\) 1.34245 2.32520i 0.0552211 0.0956458i
\(592\) 0 0
\(593\) 11.0606 + 19.1576i 0.454206 + 0.786707i 0.998642 0.0520949i \(-0.0165898\pi\)
−0.544437 + 0.838802i \(0.683257\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 44.5719 1.82421
\(598\) 0 0
\(599\) −14.0909 24.4062i −0.575740 0.997210i −0.995961 0.0897885i \(-0.971381\pi\)
0.420221 0.907422i \(-0.361952\pi\)
\(600\) 0 0
\(601\) −32.7927 −1.33764 −0.668821 0.743424i \(-0.733201\pi\)
−0.668821 + 0.743424i \(0.733201\pi\)
\(602\) 0 0
\(603\) −0.864950 + 1.49814i −0.0352235 + 0.0610089i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −38.2403 −1.55213 −0.776063 0.630656i \(-0.782786\pi\)
−0.776063 + 0.630656i \(0.782786\pi\)
\(608\) 0 0
\(609\) 0.285051 0.0115509
\(610\) 0 0
\(611\) −3.82453 + 6.62427i −0.154724 + 0.267989i
\(612\) 0 0
\(613\) −3.72203 + 6.44674i −0.150331 + 0.260381i −0.931349 0.364127i \(-0.881367\pi\)
0.781018 + 0.624509i \(0.214701\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.23294 7.33167i −0.170412 0.295162i 0.768152 0.640267i \(-0.221176\pi\)
−0.938564 + 0.345106i \(0.887843\pi\)
\(618\) 0 0
\(619\) −35.1940 −1.41457 −0.707283 0.706931i \(-0.750079\pi\)
−0.707283 + 0.706931i \(0.750079\pi\)
\(620\) 0 0
\(621\) −3.36805 5.83363i −0.135155 0.234095i
\(622\) 0 0
\(623\) −0.228956 0.396564i −0.00917294 0.0158880i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 21.3951 1.36335i 0.854439 0.0544469i
\(628\) 0 0
\(629\) −2.19686 + 3.80507i −0.0875944 + 0.151718i
\(630\) 0 0
\(631\) −5.23316 9.06410i −0.208329 0.360836i 0.742859 0.669447i \(-0.233469\pi\)
−0.951188 + 0.308611i \(0.900136\pi\)
\(632\) 0 0
\(633\) 14.0990 + 24.4201i 0.560383 + 0.970612i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.18572 + 3.78579i 0.0866016 + 0.149998i
\(638\) 0 0
\(639\) −1.11908 −0.0442702
\(640\) 0 0
\(641\) 2.85836 4.95082i 0.112898 0.195546i −0.804039 0.594576i \(-0.797320\pi\)
0.916938 + 0.399030i \(0.130653\pi\)
\(642\) 0 0
\(643\) 17.5249 30.3540i 0.691114 1.19705i −0.280359 0.959895i \(-0.590453\pi\)
0.971473 0.237150i \(-0.0762133\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.40523 0.330444 0.165222 0.986256i \(-0.447166\pi\)
0.165222 + 0.986256i \(0.447166\pi\)
\(648\) 0 0
\(649\) −10.8482 + 18.7897i −0.425830 + 0.737559i
\(650\) 0 0
\(651\) 14.2068 24.6069i 0.556809 0.964421i
\(652\) 0 0
\(653\) −0.586740 −0.0229609 −0.0114805 0.999934i \(-0.503654\pi\)
−0.0114805 + 0.999934i \(0.503654\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.71034 −0.144754
\(658\) 0 0
\(659\) −4.16313 7.21076i −0.162173 0.280891i 0.773475 0.633827i \(-0.218517\pi\)
−0.935648 + 0.352936i \(0.885183\pi\)
\(660\) 0 0
\(661\) 0.564657 + 0.978014i 0.0219626 + 0.0380403i 0.876798 0.480859i \(-0.159675\pi\)
−0.854835 + 0.518900i \(0.826342\pi\)
\(662\) 0 0
\(663\) 1.32802 2.30019i 0.0515759 0.0893321i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.0628934 0.108935i 0.00243524 0.00421796i
\(668\) 0 0
\(669\) 3.17948 + 5.50703i 0.122926 + 0.212914i
\(670\) 0 0
\(671\) −0.552113 0.956288i −0.0213141 0.0369171i
\(672\) 0 0
\(673\) 9.90978 0.381994 0.190997 0.981591i \(-0.438828\pi\)
0.190997 + 0.981591i \(0.438828\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −32.9039 −1.26460 −0.632301 0.774723i \(-0.717889\pi\)
−0.632301 + 0.774723i \(0.717889\pi\)
\(678\) 0 0
\(679\) −1.45812 + 2.52553i −0.0559574 + 0.0969211i
\(680\) 0 0
\(681\) −23.0765 + 39.9697i −0.884295 + 1.53164i
\(682\) 0 0
\(683\) 3.22470 0.123390 0.0616949 0.998095i \(-0.480349\pi\)
0.0616949 + 0.998095i \(0.480349\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.94716 8.56874i 0.188746 0.326918i
\(688\) 0 0
\(689\) 0.300247 0.520043i 0.0114385 0.0198120i
\(690\) 0 0
\(691\) −8.98569 −0.341832 −0.170916 0.985286i \(-0.554673\pi\)
−0.170916 + 0.985286i \(0.554673\pi\)
\(692\) 0 0
\(693\) −0.942363 1.63222i −0.0357974 0.0620029i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.392060 0.679067i −0.0148503 0.0257215i
\(698\) 0 0
\(699\) 12.0106 + 20.8029i 0.454282 + 0.786839i
\(700\) 0 0
\(701\) 7.62340 13.2041i 0.287932 0.498713i −0.685384 0.728182i \(-0.740366\pi\)
0.973316 + 0.229469i \(0.0736990\pi\)
\(702\) 0 0
\(703\) 8.03580 + 12.0738i 0.303076 + 0.455371i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.30554 14.3856i −0.312362 0.541027i
\(708\) 0 0
\(709\) −17.6736 30.6116i −0.663746 1.14964i −0.979624 0.200841i \(-0.935632\pi\)
0.315878 0.948800i \(-0.397701\pi\)
\(710\) 0 0
\(711\) 4.80206 0.180091
\(712\) 0 0
\(713\) −6.26915 10.8585i −0.234781 0.406653i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −7.83347 + 13.5680i −0.292546 + 0.506705i
\(718\) 0 0
\(719\) 14.9566 25.9056i 0.557787 0.966115i −0.439894 0.898050i \(-0.644984\pi\)
0.997681 0.0680651i \(-0.0216826\pi\)
\(720\) 0 0
\(721\) 9.35194 0.348284
\(722\) 0 0
\(723\) 0.0486525 0.00180941
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −19.1230 + 33.1220i −0.709232 + 1.22843i 0.255911 + 0.966700i \(0.417625\pi\)
−0.965142 + 0.261725i \(0.915709\pi\)
\(728\) 0 0
\(729\) 22.3783 0.828827
\(730\) 0 0
\(731\) 1.73426 + 3.00382i 0.0641438 + 0.111100i
\(732\) 0 0
\(733\) 1.55553 0.0574549 0.0287274 0.999587i \(-0.490855\pi\)
0.0287274 + 0.999587i \(0.490855\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.62754 9.74718i −0.207293 0.359042i
\(738\) 0 0
\(739\) 13.5945 23.5464i 0.500083 0.866169i −0.499917 0.866073i \(-0.666636\pi\)
1.00000 9.57964e-5i \(-3.04929e-5\pi\)
\(740\) 0 0
\(741\) −4.85770 7.29868i −0.178452 0.268124i
\(742\) 0 0
\(743\) 9.54725 16.5363i 0.350255 0.606659i −0.636039 0.771657i \(-0.719428\pi\)
0.986294 + 0.164998i \(0.0527617\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.58962 2.75331i −0.0581613 0.100738i
\(748\) 0 0
\(749\) −12.0914 −0.441809
\(750\) 0 0
\(751\) −1.08150 1.87321i −0.0394644 0.0683544i 0.845619 0.533788i \(-0.179232\pi\)
−0.885083 + 0.465433i \(0.845899\pi\)
\(752\) 0 0
\(753\) 36.2659 1.32160
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 24.1677 41.8598i 0.878392 1.52142i 0.0252862 0.999680i \(-0.491950\pi\)
0.853105 0.521739i \(-0.174716\pi\)
\(758\) 0 0
\(759\) −6.92607 −0.251401
\(760\) 0 0
\(761\) 49.4377 1.79211 0.896057 0.443939i \(-0.146419\pi\)
0.896057 + 0.443939i \(0.146419\pi\)
\(762\) 0 0
\(763\) −3.54465 + 6.13951i −0.128325 + 0.222265i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.87293 0.320383
\(768\) 0 0
\(769\) 10.7781 + 18.6682i 0.388667 + 0.673192i 0.992271 0.124093i \(-0.0396022\pi\)
−0.603603 + 0.797285i \(0.706269\pi\)
\(770\) 0 0
\(771\) −17.6104 −0.634222
\(772\) 0 0
\(773\) −22.9699 39.7850i −0.826169 1.43097i −0.901022 0.433772i \(-0.857182\pi\)
0.0748533 0.997195i \(-0.476151\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 5.30911 9.19564i 0.190463 0.329892i
\(778\) 0 0
\(779\) −2.58310 + 0.164602i −0.0925493 + 0.00589746i
\(780\) 0 0
\(781\) 3.64048 6.30550i 0.130267 0.225629i
\(782\) 0 0
\(783\) 0.213636 + 0.370029i 0.00763473 + 0.0132237i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 43.7925 1.56103 0.780517 0.625135i \(-0.214956\pi\)
0.780517 + 0.625135i \(0.214956\pi\)
\(788\) 0 0
\(789\) 10.4294 + 18.0642i 0.371295 + 0.643102i
\(790\) 0 0
\(791\) 22.3665 0.795261
\(792\) 0 0
\(793\) −0.225791 + 0.391081i −0.00801807 + 0.0138877i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −44.8269 −1.58785 −0.793925 0.608016i \(-0.791966\pi\)
−0.793925 + 0.608016i \(0.791966\pi\)
\(798\) 0 0
\(799\) 9.27232 0.328031
\(800\) 0 0
\(801\) −0.0542358 + 0.0939392i −0.00191633 +