Properties

Label 3330.2.e.b.739.2
Level $3330$
Weight $2$
Character 3330.739
Analytic conductor $26.590$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1110)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 739.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 3330.739
Dual form 3330.2.e.b.739.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +(-2.00000 + 1.00000i) q^{10} +3.00000 q^{11} -4.00000 q^{13} +3.00000i q^{14} +1.00000 q^{16} -7.00000 q^{17} -4.00000i q^{19} +(-2.00000 + 1.00000i) q^{20} +3.00000 q^{22} -6.00000 q^{23} +(3.00000 - 4.00000i) q^{25} -4.00000 q^{26} +3.00000i q^{28} +9.00000i q^{29} -5.00000i q^{31} +1.00000 q^{32} -7.00000 q^{34} +(-3.00000 - 6.00000i) q^{35} +(6.00000 - 1.00000i) q^{37} -4.00000i q^{38} +(-2.00000 + 1.00000i) q^{40} -7.00000 q^{41} +1.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} -8.00000i q^{47} -2.00000 q^{49} +(3.00000 - 4.00000i) q^{50} -4.00000 q^{52} -1.00000i q^{53} +(-6.00000 + 3.00000i) q^{55} +3.00000i q^{56} +9.00000i q^{58} -6.00000i q^{59} -5.00000i q^{61} -5.00000i q^{62} +1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} -7.00000 q^{68} +(-3.00000 - 6.00000i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(6.00000 - 1.00000i) q^{74} -4.00000i q^{76} +9.00000i q^{77} -4.00000i q^{79} +(-2.00000 + 1.00000i) q^{80} -7.00000 q^{82} +14.0000i q^{83} +(14.0000 - 7.00000i) q^{85} +1.00000 q^{86} +3.00000 q^{88} -6.00000i q^{89} -12.0000i q^{91} -6.00000 q^{92} -8.00000i q^{94} +(4.00000 + 8.00000i) q^{95} +7.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} - 4q^{5} + 2q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} - 4q^{5} + 2q^{8} - 4q^{10} + 6q^{11} - 8q^{13} + 2q^{16} - 14q^{17} - 4q^{20} + 6q^{22} - 12q^{23} + 6q^{25} - 8q^{26} + 2q^{32} - 14q^{34} - 6q^{35} + 12q^{37} - 4q^{40} - 14q^{41} + 2q^{43} + 6q^{44} - 12q^{46} - 4q^{49} + 6q^{50} - 8q^{52} - 12q^{55} + 2q^{64} + 16q^{65} - 14q^{68} - 6q^{70} - 24q^{71} + 12q^{74} - 4q^{80} - 14q^{82} + 28q^{85} + 2q^{86} + 6q^{88} - 12q^{92} + 8q^{95} + 14q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 0 0
\(7\) 3.00000i 1.13389i 0.823754 + 0.566947i \(0.191875\pi\)
−0.823754 + 0.566947i \(0.808125\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 3.00000i 0.801784i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −7.00000 −1.69775 −0.848875 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 3.00000i 0.566947i
\(29\) 9.00000i 1.67126i 0.549294 + 0.835629i \(0.314897\pi\)
−0.549294 + 0.835629i \(0.685103\pi\)
\(30\) 0 0
\(31\) 5.00000i 0.898027i −0.893525 0.449013i \(-0.851776\pi\)
0.893525 0.449013i \(-0.148224\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) −3.00000 6.00000i −0.507093 1.01419i
\(36\) 0 0
\(37\) 6.00000 1.00000i 0.986394 0.164399i
\(38\) 4.00000i 0.648886i
\(39\) 0 0
\(40\) −2.00000 + 1.00000i −0.316228 + 0.158114i
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 0 0
\(49\) −2.00000 −0.285714
\(50\) 3.00000 4.00000i 0.424264 0.565685i
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) 1.00000i 0.137361i −0.997639 0.0686803i \(-0.978121\pi\)
0.997639 0.0686803i \(-0.0218788\pi\)
\(54\) 0 0
\(55\) −6.00000 + 3.00000i −0.809040 + 0.404520i
\(56\) 3.00000i 0.400892i
\(57\) 0 0
\(58\) 9.00000i 1.18176i
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) 0 0
\(61\) 5.00000i 0.640184i −0.947386 0.320092i \(-0.896286\pi\)
0.947386 0.320092i \(-0.103714\pi\)
\(62\) 5.00000i 0.635001i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.00000 4.00000i 0.992278 0.496139i
\(66\) 0 0
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) −7.00000 −0.848875
\(69\) 0 0
\(70\) −3.00000 6.00000i −0.358569 0.717137i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 6.00000 1.00000i 0.697486 0.116248i
\(75\) 0 0
\(76\) 4.00000i 0.458831i
\(77\) 9.00000i 1.02565i
\(78\) 0 0
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 0 0
\(82\) −7.00000 −0.773021
\(83\) 14.0000i 1.53670i 0.640030 + 0.768350i \(0.278922\pi\)
−0.640030 + 0.768350i \(0.721078\pi\)
\(84\) 0 0
\(85\) 14.0000 7.00000i 1.51851 0.759257i
\(86\) 1.00000 0.107833
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) 6.00000i 0.635999i −0.948091 0.317999i \(-0.896989\pi\)
0.948091 0.317999i \(-0.103011\pi\)
\(90\) 0 0
\(91\) 12.0000i 1.25794i
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) 8.00000i 0.825137i
\(95\) 4.00000 + 8.00000i 0.410391 + 0.820783i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 1.00000i 0.0971286i
\(107\) 18.0000i 1.74013i −0.492941 0.870063i \(-0.664078\pi\)
0.492941 0.870063i \(-0.335922\pi\)
\(108\) 0 0
\(109\) 11.0000i 1.05361i 0.849987 + 0.526804i \(0.176610\pi\)
−0.849987 + 0.526804i \(0.823390\pi\)
\(110\) −6.00000 + 3.00000i −0.572078 + 0.286039i
\(111\) 0 0
\(112\) 3.00000i 0.283473i
\(113\) −1.00000 −0.0940721 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) 12.0000 6.00000i 1.11901 0.559503i
\(116\) 9.00000i 0.835629i
\(117\) 0 0
\(118\) 6.00000i 0.552345i
\(119\) 21.0000i 1.92507i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 5.00000i 0.452679i
\(123\) 0 0
\(124\) 5.00000i 0.449013i
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 8.00000 4.00000i 0.701646 0.350823i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 12.0000 1.04053
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) 12.0000i 1.02523i 0.858619 + 0.512615i \(0.171323\pi\)
−0.858619 + 0.512615i \(0.828677\pi\)
\(138\) 0 0
\(139\) −15.0000 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(140\) −3.00000 6.00000i −0.253546 0.507093i
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) −9.00000 18.0000i −0.747409 1.49482i
\(146\) 4.00000i 0.331042i
\(147\) 0 0
\(148\) 6.00000 1.00000i 0.493197 0.0821995i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 4.00000i 0.324443i
\(153\) 0 0
\(154\) 9.00000i 0.725241i
\(155\) 5.00000 + 10.0000i 0.401610 + 0.803219i
\(156\) 0 0
\(157\) 7.00000i 0.558661i −0.960195 0.279330i \(-0.909888\pi\)
0.960195 0.279330i \(-0.0901125\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 18.0000i 1.41860i
\(162\) 0 0
\(163\) −9.00000 −0.704934 −0.352467 0.935824i \(-0.614657\pi\)
−0.352467 + 0.935824i \(0.614657\pi\)
\(164\) −7.00000 −0.546608
\(165\) 0 0
\(166\) 14.0000i 1.08661i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 14.0000 7.00000i 1.07375 0.536875i
\(171\) 0 0
\(172\) 1.00000 0.0762493
\(173\) 9.00000i 0.684257i 0.939653 + 0.342129i \(0.111148\pi\)
−0.939653 + 0.342129i \(0.888852\pi\)
\(174\) 0 0
\(175\) 12.0000 + 9.00000i 0.907115 + 0.680336i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 6.00000i 0.449719i
\(179\) 4.00000i 0.298974i 0.988764 + 0.149487i \(0.0477622\pi\)
−0.988764 + 0.149487i \(0.952238\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 12.0000i 0.889499i
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) −11.0000 + 8.00000i −0.808736 + 0.588172i
\(186\) 0 0
\(187\) −21.0000 −1.53567
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 4.00000 + 8.00000i 0.290191 + 0.580381i
\(191\) 15.0000i 1.08536i 0.839939 + 0.542681i \(0.182591\pi\)
−0.839939 + 0.542681i \(0.817409\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 7.00000 0.502571
\(195\) 0 0
\(196\) −2.00000 −0.142857
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) 16.0000i 1.13421i 0.823646 + 0.567105i \(0.191937\pi\)
−0.823646 + 0.567105i \(0.808063\pi\)
\(200\) 3.00000 4.00000i 0.212132 0.282843i
\(201\) 0 0
\(202\) −2.00000 −0.140720
\(203\) −27.0000 −1.89503
\(204\) 0 0
\(205\) 14.0000 7.00000i 0.977802 0.488901i
\(206\) −14.0000 −0.975426
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 12.0000i 0.830057i
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 1.00000i 0.0686803i
\(213\) 0 0
\(214\) 18.0000i 1.23045i
\(215\) −2.00000 + 1.00000i −0.136399 + 0.0681994i
\(216\) 0 0
\(217\) 15.0000 1.01827
\(218\) 11.0000i 0.745014i
\(219\) 0 0
\(220\) −6.00000 + 3.00000i −0.404520 + 0.202260i
\(221\) 28.0000 1.88348
\(222\) 0 0
\(223\) 11.0000i 0.736614i 0.929704 + 0.368307i \(0.120063\pi\)
−0.929704 + 0.368307i \(0.879937\pi\)
\(224\) 3.00000i 0.200446i
\(225\) 0 0
\(226\) −1.00000 −0.0665190
\(227\) 13.0000 0.862840 0.431420 0.902151i \(-0.358013\pi\)
0.431420 + 0.902151i \(0.358013\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 12.0000 6.00000i 0.791257 0.395628i
\(231\) 0 0
\(232\) 9.00000i 0.590879i
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 0 0
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) 6.00000i 0.390567i
\(237\) 0 0
\(238\) 21.0000i 1.36123i
\(239\) 9.00000i 0.582162i 0.956698 + 0.291081i \(0.0940149\pi\)
−0.956698 + 0.291081i \(0.905985\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) 5.00000i 0.320092i
\(245\) 4.00000 2.00000i 0.255551 0.127775i
\(246\) 0 0
\(247\) 16.0000i 1.01806i
\(248\) 5.00000i 0.317500i
\(249\) 0 0
\(250\) −2.00000 + 11.0000i −0.126491 + 0.695701i
\(251\) 20.0000i 1.26239i −0.775625 0.631194i \(-0.782565\pi\)
0.775625 0.631194i \(-0.217435\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 8.00000i 0.501965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 3.00000 + 18.0000i 0.186411 + 1.11847i
\(260\) 8.00000 4.00000i 0.496139 0.248069i
\(261\) 0 0
\(262\) 0 0
\(263\) 31.0000i 1.91154i −0.294112 0.955771i \(-0.595024\pi\)
0.294112 0.955771i \(-0.404976\pi\)
\(264\) 0 0
\(265\) 1.00000 + 2.00000i 0.0614295 + 0.122859i
\(266\) 12.0000 0.735767
\(267\) 0 0
\(268\) 2.00000i 0.122169i
\(269\) −20.0000 −1.21942 −0.609711 0.792624i \(-0.708714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) 0 0
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) −7.00000 −0.424437
\(273\) 0 0
\(274\) 12.0000i 0.724947i
\(275\) 9.00000 12.0000i 0.542720 0.723627i
\(276\) 0 0
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) −15.0000 −0.899640
\(279\) 0 0
\(280\) −3.00000 6.00000i −0.179284 0.358569i
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) 21.0000i 1.23959i
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) −9.00000 18.0000i −0.528498 1.05700i
\(291\) 0 0
\(292\) 4.00000i 0.234082i
\(293\) 29.0000i 1.69420i 0.531435 + 0.847099i \(0.321653\pi\)
−0.531435 + 0.847099i \(0.678347\pi\)
\(294\) 0 0
\(295\) 6.00000 + 12.0000i 0.349334 + 0.698667i
\(296\) 6.00000 1.00000i 0.348743 0.0581238i
\(297\) 0 0
\(298\) 0 0
\(299\) 24.0000 1.38796
\(300\) 0 0
\(301\) 3.00000i 0.172917i
\(302\) 2.00000 0.115087
\(303\) 0 0
\(304\) 4.00000i 0.229416i
\(305\) 5.00000 + 10.0000i 0.286299 + 0.572598i
\(306\) 0 0
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) 9.00000i 0.512823i
\(309\) 0 0
\(310\) 5.00000 + 10.0000i 0.283981 + 0.567962i
\(311\) 15.0000i 0.850572i −0.905059 0.425286i \(-0.860174\pi\)
0.905059 0.425286i \(-0.139826\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 7.00000i 0.395033i
\(315\) 0 0
\(316\) 4.00000i 0.225018i
\(317\) 27.0000i 1.51647i 0.651981 + 0.758236i \(0.273938\pi\)
−0.651981 + 0.758236i \(0.726062\pi\)
\(318\) 0 0
\(319\) 27.0000i 1.51171i
\(320\) −2.00000 + 1.00000i −0.111803 + 0.0559017i
\(321\) 0 0
\(322\) 18.0000i 1.00310i
\(323\) 28.0000i 1.55796i
\(324\) 0 0
\(325\) −12.0000 + 16.0000i −0.665640 + 0.887520i
\(326\) −9.00000 −0.498464
\(327\) 0 0
\(328\) −7.00000 −0.386510
\(329\) 24.0000 1.32316
\(330\) 0 0
\(331\) 20.0000i 1.09930i −0.835395 0.549650i \(-0.814761\pi\)
0.835395 0.549650i \(-0.185239\pi\)
\(332\) 14.0000i 0.768350i
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) 2.00000 + 4.00000i 0.109272 + 0.218543i
\(336\) 0 0
\(337\) 18.0000i 0.980522i 0.871576 + 0.490261i \(0.163099\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 3.00000 0.163178
\(339\) 0 0
\(340\) 14.0000 7.00000i 0.759257 0.379628i
\(341\) 15.0000i 0.812296i
\(342\) 0 0
\(343\) 15.0000i 0.809924i
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) 9.00000i 0.483843i
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 12.0000 + 9.00000i 0.641427 + 0.481070i
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) −31.0000 −1.64996 −0.824982 0.565159i \(-0.808815\pi\)
−0.824982 + 0.565159i \(0.808815\pi\)
\(354\) 0 0
\(355\) 24.0000 12.0000i 1.27379 0.636894i
\(356\) 6.00000i 0.317999i
\(357\) 0 0
\(358\) 4.00000i 0.211407i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) −18.0000 −0.946059
\(363\) 0 0
\(364\) 12.0000i 0.628971i
\(365\) 4.00000 + 8.00000i 0.209370 + 0.418739i
\(366\) 0 0
\(367\) 23.0000i 1.20059i 0.799779 + 0.600295i \(0.204950\pi\)
−0.799779 + 0.600295i \(0.795050\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) −11.0000 + 8.00000i −0.571863 + 0.415900i
\(371\) 3.00000 0.155752
\(372\) 0 0
\(373\) 14.0000i 0.724893i −0.932005 0.362446i \(-0.881942\pi\)
0.932005 0.362446i \(-0.118058\pi\)
\(374\) −21.0000 −1.08588
\(375\) 0 0
\(376\) 8.00000i 0.412568i
\(377\) 36.0000i 1.85409i
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 4.00000 + 8.00000i 0.205196 + 0.410391i
\(381\) 0 0
\(382\) 15.0000i 0.767467i
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) −9.00000 18.0000i −0.458682 0.917365i
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) 7.00000 0.355371
\(389\) 31.0000i 1.57176i −0.618378 0.785881i \(-0.712210\pi\)
0.618378 0.785881i \(-0.287790\pi\)
\(390\) 0 0
\(391\) 42.0000 2.12403
\(392\) −2.00000 −0.101015
\(393\) 0 0
\(394\) 18.0000i 0.906827i
\(395\) 4.00000 + 8.00000i 0.201262 + 0.402524i
\(396\) 0 0
\(397\) 38.0000i 1.90717i 0.301131 + 0.953583i \(0.402636\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 10.0000i 0.499376i 0.968326 + 0.249688i \(0.0803281\pi\)
−0.968326 + 0.249688i \(0.919672\pi\)
\(402\) 0 0
\(403\) 20.0000i 0.996271i
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) −27.0000 −1.33999
\(407\) 18.0000 3.00000i 0.892227 0.148704i
\(408\) 0 0
\(409\) 14.0000i 0.692255i −0.938187 0.346128i \(-0.887496\pi\)
0.938187 0.346128i \(-0.112504\pi\)
\(410\) 14.0000 7.00000i 0.691411 0.345705i
\(411\) 0 0
\(412\) −14.0000 −0.689730
\(413\) 18.0000 0.885722
\(414\) 0 0
\(415\) −14.0000 28.0000i −0.687233 1.37447i
\(416\) −4.00000 −0.196116
\(417\) 0 0
\(418\) 12.0000i 0.586939i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 30.0000i 1.46211i 0.682318 + 0.731055i \(0.260972\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) −13.0000 −0.632830
\(423\) 0 0
\(424\) 1.00000i 0.0485643i
\(425\) −21.0000 + 28.0000i −1.01865 + 1.35820i
\(426\) 0 0
\(427\) 15.0000 0.725901
\(428\) 18.0000i 0.870063i
\(429\) 0 0
\(430\) −2.00000 + 1.00000i −0.0964486 + 0.0482243i
\(431\) 25.0000i 1.20421i 0.798418 + 0.602104i \(0.205671\pi\)
−0.798418 + 0.602104i \(0.794329\pi\)
\(432\) 0 0
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) 15.0000 0.720023
\(435\) 0 0
\(436\) 11.0000i 0.526804i
\(437\) 24.0000i 1.14808i
\(438\) 0 0
\(439\) 9.00000i 0.429547i −0.976664 0.214773i \(-0.931099\pi\)
0.976664 0.214773i \(-0.0689013\pi\)
\(440\) −6.00000 + 3.00000i −0.286039 + 0.143019i
\(441\) 0 0
\(442\) 28.0000 1.33182
\(443\) 36.0000i 1.71041i −0.518289 0.855206i \(-0.673431\pi\)
0.518289 0.855206i \(-0.326569\pi\)
\(444\) 0 0
\(445\) 6.00000 + 12.0000i 0.284427 + 0.568855i
\(446\) 11.0000i 0.520865i
\(447\) 0 0
\(448\) 3.00000i 0.141737i
\(449\) 6.00000i 0.283158i −0.989927 0.141579i \(-0.954782\pi\)
0.989927 0.141579i \(-0.0452178\pi\)
\(450\) 0 0
\(451\) −21.0000 −0.988851
\(452\) −1.00000 −0.0470360
\(453\) 0 0
\(454\) 13.0000 0.610120
\(455\) 12.0000 + 24.0000i 0.562569 + 1.12514i
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) 12.0000 6.00000i 0.559503 0.279751i
\(461\) 25.0000i 1.16437i −0.813058 0.582183i \(-0.802199\pi\)
0.813058 0.582183i \(-0.197801\pi\)
\(462\) 0 0
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) 9.00000i 0.417815i
\(465\) 0 0
\(466\) 6.00000i 0.277945i
\(467\) 23.0000 1.06431 0.532157 0.846646i \(-0.321382\pi\)
0.532157 + 0.846646i \(0.321382\pi\)
\(468\) 0 0
\(469\) 6.00000 0.277054
\(470\) 8.00000 + 16.0000i 0.369012 + 0.738025i
\(471\) 0 0
\(472\) 6.00000i 0.276172i
\(473\) 3.00000 0.137940
\(474\) 0 0
\(475\) −16.0000 12.0000i −0.734130 0.550598i
\(476\) 21.0000i 0.962533i
\(477\) 0 0
\(478\) 9.00000i 0.411650i
\(479\) 24.0000i 1.09659i 0.836286 + 0.548294i \(0.184723\pi\)
−0.836286 + 0.548294i \(0.815277\pi\)
\(480\) 0 0
\(481\) −24.0000 + 4.00000i −1.09431 + 0.182384i
\(482\) 0 0
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −14.0000 + 7.00000i −0.635707 + 0.317854i
\(486\) 0 0
\(487\) 22.0000 0.996915 0.498458 0.866914i \(-0.333900\pi\)
0.498458 + 0.866914i \(0.333900\pi\)
\(488\) 5.00000i 0.226339i
\(489\) 0 0
\(490\) 4.00000 2.00000i 0.180702 0.0903508i
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) 0 0
\(493\) 63.0000i 2.83738i
\(494\) 16.0000i 0.719874i
\(495\) 0 0
\(496\) 5.00000i 0.224507i
\(497\) 36.0000i 1.61482i
\(498\) 0 0
\(499\) 24.0000i 1.07439i −0.843459 0.537194i \(-0.819484\pi\)
0.843459 0.537194i \(-0.180516\pi\)
\(500\) −2.00000 + 11.0000i −0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 20.0000i 0.892644i
\(503\) 14.0000 0.624229 0.312115 0.950044i \(-0.398963\pi\)
0.312115 + 0.950044i \(0.398963\pi\)
\(504\) 0 0
\(505\) 4.00000 2.00000i 0.177998 0.0889988i
\(506\) −18.0000 −0.800198
\(507\) 0 0
\(508\) 8.00000i 0.354943i
\(509\) 10.0000 0.443242 0.221621 0.975133i \(-0.428865\pi\)
0.221621 + 0.975133i \(0.428865\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) 28.0000 14.0000i 1.23383 0.616914i
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) 3.00000 + 18.0000i 0.131812 + 0.790875i
\(519\) 0 0
\(520\) 8.00000 4.00000i 0.350823 0.175412i
\(521\) −37.0000 −1.62100 −0.810500 0.585739i \(-0.800804\pi\)
−0.810500 + 0.585739i \(0.800804\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 31.0000i 1.35166i
\(527\) 35.0000i 1.52462i
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 1.00000 + 2.00000i 0.0434372 + 0.0868744i
\(531\) 0 0
\(532\) 12.0000 0.520266
\(533\) 28.0000 1.21281
\(534\) 0 0
\(535\) 18.0000 + 36.0000i 0.778208 + 1.55642i
\(536\) 2.00000i 0.0863868i
\(537\) 0 0
\(538\) −20.0000 −0.862261
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) 30.0000i 1.28980i 0.764267 + 0.644900i \(0.223101\pi\)
−0.764267 + 0.644900i \(0.776899\pi\)
\(542\) 22.0000 0.944981
\(543\) 0 0
\(544\) −7.00000 −0.300123
\(545\) −11.0000 22.0000i −0.471188 0.942376i
\(546\) 0 0
\(547\) −23.0000 −0.983409 −0.491704 0.870762i \(-0.663626\pi\)
−0.491704 + 0.870762i \(0.663626\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 0 0
\(550\) 9.00000 12.0000i 0.383761 0.511682i
\(551\) 36.0000 1.53365
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) −28.0000 −1.18961
\(555\) 0 0
\(556\) −15.0000 −0.636142
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) −3.00000 6.00000i −0.126773 0.253546i
\(561\) 0 0
\(562\) 30.0000i 1.26547i
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 0 0
\(565\) 2.00000 1.00000i 0.0841406 0.0420703i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 24.0000i 1.00613i 0.864248 + 0.503066i \(0.167795\pi\)
−0.864248 + 0.503066i \(0.832205\pi\)
\(570\) 0 0
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) −12.0000 −0.501745
\(573\) 0 0
\(574\) 21.0000i 0.876523i
\(575\) −18.0000 + 24.0000i −0.750652 + 1.00087i
\(576\) 0 0
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 32.0000 1.33102
\(579\) 0 0
\(580\) −9.00000 18.0000i −0.373705 0.747409i
\(581\) −42.0000 −1.74245
\(582\) 0 0
\(583\) 3.00000i 0.124247i
\(584\) 4.00000i 0.165521i
\(585\) 0 0
\(586\) 29.0000i 1.19798i
\(587\) −47.0000 −1.93990 −0.969949 0.243309i \(-0.921767\pi\)
−0.969949 + 0.243309i \(0.921767\pi\)
\(588\) 0 0
\(589\) −20.0000 −0.824086
\(590\) 6.00000 + 12.0000i 0.247016 + 0.494032i
\(591\) 0 0
\(592\) 6.00000 1.00000i 0.246598 0.0410997i
\(593\) 46.0000i 1.88899i −0.328521 0.944497i \(-0.606550\pi\)
0.328521 0.944497i \(-0.393450\pi\)
\(594\) 0 0
\(595\) 21.0000 + 42.0000i 0.860916 + 1.72183i
\(596\) 0 0
\(597\) 0 0
\(598\) 24.0000 0.981433
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) −23.0000 −0.938190 −0.469095 0.883148i \(-0.655420\pi\)
−0.469095 + 0.883148i \(0.655420\pi\)
\(602\) 3.00000i 0.122271i
\(603\) 0 0
\(604\) 2.00000 0.0813788
\(605\) 4.00000 2.00000i 0.162623 0.0813116i
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 0 0
\(610\) 5.00000 + 10.0000i 0.202444 + 0.404888i
\(611\) 32.0000i 1.29458i
\(612\) 0 0
\(613\) 31.0000i 1.25208i 0.779792 + 0.626039i \(0.215325\pi\)
−0.779792 + 0.626039i \(0.784675\pi\)
\(614\) 18.0000i 0.726421i
\(615\) 0 0
\(616\) 9.00000i 0.362620i
\(617\) 8.00000i 0.322068i −0.986949 0.161034i \(-0.948517\pi\)
0.986949 0.161034i \(-0.0514829\pi\)
\(618\) 0 0
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) 5.00000 + 10.0000i 0.200805 + 0.401610i
\(621\) 0 0
\(622\) 15.0000i 0.601445i
\(623\) 18.0000 0.721155
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 7.00000i 0.279330i
\(629\) −42.0000 + 7.00000i −1.67465 + 0.279108i
\(630\) 0 0
\(631\) 25.0000i 0.995234i −0.867397 0.497617i \(-0.834208\pi\)
0.867397 0.497617i \(-0.165792\pi\)
\(632\) 4.00000i 0.159111i
\(633\) 0 0
\(634\) 27.0000i 1.07231i
\(635\) −8.00000 16.0000i −0.317470 0.634941i
\(636\) 0 0
\(637\) 8.00000 0.316972
\(638\) 27.0000i 1.06894i
\(639\) 0 0
\(640\) −2.00000 + 1.00000i −0.0790569 + 0.0395285i
\(641\) −17.0000 −0.671460 −0.335730 0.941958i \(-0.608983\pi\)
−0.335730 + 0.941958i \(0.608983\pi\)
\(642\) 0 0
\(643\) 31.0000 1.22252 0.611260 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 18.0000i 0.709299i
\(645\) 0 0
\(646\) 28.0000i 1.10165i
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) 0 0
\(649\) 18.0000i 0.706562i
\(650\) −12.0000 + 16.0000i −0.470679 + 0.627572i
\(651\) 0 0
\(652\) −9.00000 −0.352467
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −7.00000 −0.273304
\(657\) 0 0
\(658\) 24.0000 0.935617
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 35.0000i 1.36134i −0.732589 0.680671i \(-0.761688\pi\)
0.732589 0.680671i \(-0.238312\pi\)
\(662\) 20.0000i 0.777322i
\(663\) 0 0
\(664\) 14.0000i 0.543305i
\(665\) −24.0000 + 12.0000i −0.930680 + 0.465340i
\(666\) 0 0
\(667\) 54.0000i 2.09089i
\(668\) −12.0000 −0.464294
\(669\) 0 0
\(670\) 2.00000 + 4.00000i 0.0772667 + 0.154533i
\(671\) 15.0000i 0.579069i
\(672\) 0 0
\(673\) 26.0000i 1.00223i 0.865382 + 0.501113i \(0.167076\pi\)
−0.865382 + 0.501113i \(0.832924\pi\)
\(674\) 18.0000i 0.693334i
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 42.0000i 1.61419i 0.590421 + 0.807096i \(0.298962\pi\)
−0.590421 + 0.807096i \(0.701038\pi\)
\(678\) 0 0
\(679\) 21.0000i 0.805906i
\(680\) 14.0000 7.00000i 0.536875 0.268438i
\(681\) 0 0
\(682\) 15.0000i 0.574380i
\(683\) −1.00000 −0.0382639 −0.0191320 0.999817i \(-0.506090\pi\)
−0.0191320 + 0.999817i \(0.506090\pi\)
\(684\) 0 0
\(685\) −12.0000 24.0000i −0.458496 0.916993i
\(686\) 15.0000i 0.572703i
\(687\) 0 0
\(688\) 1.00000 0.0381246
\(689\) 4.00000i 0.152388i
\(690\) 0 0
\(691\) −43.0000 −1.63580 −0.817899 0.575362i \(-0.804861\pi\)
−0.817899 + 0.575362i \(0.804861\pi\)
\(692\) 9.00000i 0.342129i
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 30.0000 15.0000i 1.13796 0.568982i
\(696\) 0 0
\(697\) 49.0000 1.85601
\(698\) 0 0
\(699\) 0 0
\(700\) 12.0000 + 9.00000i 0.453557 + 0.340168i
\(701\) 10.0000i 0.377695i 0.982006 + 0.188847i \(0.0604752\pi\)
−0.982006 + 0.188847i \(0.939525\pi\)
\(702\) 0 0
\(703\) −4.00000 24.0000i −0.150863 0.905177i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) −31.0000 −1.16670
\(707\) 6.00000i 0.225653i
\(708\) 0 0
\(709\) 11.0000i 0.413114i 0.978435 + 0.206557i \(0.0662258\pi\)
−0.978435 + 0.206557i \(0.933774\pi\)
\(710\) 24.0000 12.0000i 0.900704 0.450352i
\(711\) 0 0
\(712\) 6.00000i 0.224860i
\(713\) 30.0000i 1.12351i
\(714\) 0 0
\(715\) 24.0000 12.0000i 0.897549 0.448775i
\(716\) 4.00000i 0.149487i
\(717\) 0 0
\(718\) 0 0
\(719\) −50.0000 −1.86469 −0.932343 0.361576i \(-0.882239\pi\)
−0.932343 + 0.361576i \(0.882239\pi\)
\(720\) 0 0
\(721\) 42.0000i 1.56416i
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) −18.0000 −0.668965
\(725\) 36.0000 + 27.0000i 1.33701 + 1.00275i
\(726\) 0 0
\(727\) −18.0000 −0.667583 −0.333792 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 12.0000i 0.444750i
\(729\) 0 0
\(730\) 4.00000 + 8.00000i 0.148047 + 0.296093i
\(731\) −7.00000 −0.258904
\(732\) 0 0
\(733\) 11.0000i 0.406294i 0.979148 + 0.203147i \(0.0651170\pi\)
−0.979148 + 0.203147i \(0.934883\pi\)
\(734\) 23.0000i 0.848945i
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 6.00000i 0.221013i
\(738\) 0 0
\(739\) 5.00000 0.183928 0.0919640 0.995762i \(-0.470686\pi\)
0.0919640 + 0.995762i \(0.470686\pi\)
\(740\) −11.0000 + 8.00000i −0.404368 + 0.294086i
\(741\) 0 0
\(742\) 3.00000 0.110133
\(743\) 51.0000i 1.87101i −0.353315 0.935504i \(-0.614946\pi\)
0.353315 0.935504i \(-0.385054\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 14.0000i 0.512576i
\(747\) 0 0
\(748\) −21.0000 −0.767836
\(749\) 54.0000 1.97312
\(750\) 0 0
\(751\) −18.0000 −0.656829 −0.328415 0.944534i \(-0.606514\pi\)
−0.328415 + 0.944534i \(0.606514\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) 36.0000i 1.31104i
\(755\) −4.00000 + 2.00000i −0.145575 + 0.0727875i
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 4.00000 + 8.00000i 0.145095 + 0.290191i
\(761\) 13.0000 0.471250 0.235625 0.971844i \(-0.424286\pi\)
0.235625 + 0.971844i \(0.424286\pi\)
\(762\) 0 0
\(763\) −33.0000 −1.19468
\(764\) 15.0000i 0.542681i
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 24.0000i 0.866590i
\(768\) 0 0
\(769\) 26.0000i 0.937584i 0.883309 + 0.468792i \(0.155311\pi\)
−0.883309 + 0.468792i \(0.844689\pi\)
\(770\) −9.00000 18.0000i −0.324337 0.648675i
\(771\) 0 0
\(772\) −14.0000 −0.503871
\(773\) 11.0000i 0.395643i −0.980238 0.197821i \(-0.936613\pi\)
0.980238 0.197821i \(-0.0633866\pi\)
\(774\) 0 0
\(775\) −20.0000 15.0000i −0.718421 0.538816i
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) 31.0000i 1.11140i
\(779\) 28.0000i 1.00320i
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) 42.0000 1.50192
\(783\) 0 0
\(784\) −2.00000 −0.0714286
\(785\) 7.00000 + 14.0000i 0.249841 + 0.499681i
\(786\) 0 0
\(787\) 28.0000i 0.998092i 0.866575 + 0.499046i \(0.166316\pi\)
−0.866575 + 0.499046i \(0.833684\pi\)
\(788\) 18.0000i 0.641223i
\(789\) 0 0
\(790\) 4.00000 + 8.00000i 0.142314 + 0.284627i
\(791\) 3.00000i 0.106668i
\(792\) 0 0
\(793\) 20.0000i 0.710221i
\(794\) 38.0000i 1.34857i
\(795\) 0 0
\(796\) 16.0000i 0.567105i
\(797\) 28.0000