Properties

Label 1900.2.s.c.349.1
Level $1900$
Weight $2$
Character 1900.349
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 9 x^{10} + 59 x^{8} - 180 x^{6} + 403 x^{4} - 198 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.1
Root \(-0.617942 - 0.356769i\) of defining polynomial
Character \(\chi\) \(=\) 1900.349
Dual form 1900.2.s.c.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.77509 + 1.60220i) q^{3} +2.20440i q^{7} +(3.63409 - 6.29444i) q^{9} +O(q^{10})\) \(q+(-2.77509 + 1.60220i) q^{3} +2.20440i q^{7} +(3.63409 - 6.29444i) q^{9} -1.20440 q^{11} +(0.866025 + 0.500000i) q^{13} +(1.85383 - 1.07031i) q^{17} +(-4.30660 + 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(8.02649 + 4.63409i) q^{23} +13.6770i q^{27} +(4.16599 - 7.21570i) q^{29} +8.26819 q^{31} +(3.34233 - 1.92969i) q^{33} +2.20440i q^{37} -3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(2.03084 - 1.17251i) q^{43} +(-7.21570 - 4.16599i) q^{47} +2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(-0.232259 - 0.134095i) q^{53} +(10.8726 - 8.76819i) q^{57} +(-4.16599 - 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(13.8755 + 8.01100i) q^{63} +(-1.84253 - 1.06379i) q^{67} -29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(-4.20835 + 2.42969i) q^{73} -2.65498i q^{77} +(8.20440 + 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} -5.73181i q^{83} +26.6990i q^{87} +(-5.40880 + 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(-22.9450 + 13.2473i) q^{93} +(-13.6319 + 7.87039i) q^{97} +(-4.37691 + 7.58103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 16q^{9} + O(q^{10}) \) \( 12q + 16q^{9} + 20q^{11} - 32q^{21} + 12q^{29} + 44q^{31} - 4q^{39} - 12q^{41} + 12q^{49} - 48q^{51} - 12q^{59} - 14q^{61} - 60q^{69} + 18q^{71} + 64q^{79} - 46q^{81} + 4q^{89} + 4q^{91} + 6q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −2.77509 + 1.60220i −1.60220 + 0.925031i −0.611155 + 0.791511i \(0.709295\pi\)
−0.991046 + 0.133520i \(0.957372\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.20440i 0.833185i 0.909093 + 0.416593i \(0.136776\pi\)
−0.909093 + 0.416593i \(0.863224\pi\)
\(8\) 0 0
\(9\) 3.63409 6.29444i 1.21136 2.09815i
\(10\) 0 0
\(11\) −1.20440 −0.363141 −0.181570 0.983378i \(-0.558118\pi\)
−0.181570 + 0.983378i \(0.558118\pi\)
\(12\) 0 0
\(13\) 0.866025 + 0.500000i 0.240192 + 0.138675i 0.615265 0.788320i \(-0.289049\pi\)
−0.375073 + 0.926995i \(0.622382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.85383 1.07031i 0.449619 0.259588i −0.258050 0.966131i \(-0.583080\pi\)
0.707669 + 0.706544i \(0.249747\pi\)
\(18\) 0 0
\(19\) −4.30660 + 0.673184i −0.988002 + 0.154439i
\(20\) 0 0
\(21\) −3.53189 6.11742i −0.770722 1.33493i
\(22\) 0 0
\(23\) 8.02649 + 4.63409i 1.67364 + 0.966276i 0.965574 + 0.260127i \(0.0837645\pi\)
0.708064 + 0.706148i \(0.249569\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 13.6770i 2.63214i
\(28\) 0 0
\(29\) 4.16599 7.21570i 0.773605 1.33992i −0.161971 0.986796i \(-0.551785\pi\)
0.935575 0.353127i \(-0.114882\pi\)
\(30\) 0 0
\(31\) 8.26819 1.48501 0.742505 0.669840i \(-0.233637\pi\)
0.742505 + 0.669840i \(0.233637\pi\)
\(32\) 0 0
\(33\) 3.34233 1.92969i 0.581824 0.335916i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.20440i 0.362401i 0.983446 + 0.181201i \(0.0579984\pi\)
−0.983446 + 0.181201i \(0.942002\pi\)
\(38\) 0 0
\(39\) −3.20440 −0.513115
\(40\) 0 0
\(41\) 3.30660 + 5.72720i 0.516405 + 0.894439i 0.999819 + 0.0190471i \(0.00606323\pi\)
−0.483414 + 0.875392i \(0.660603\pi\)
\(42\) 0 0
\(43\) 2.03084 1.17251i 0.309701 0.178806i −0.337092 0.941472i \(-0.609443\pi\)
0.646793 + 0.762666i \(0.276110\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.21570 4.16599i −1.05252 0.607672i −0.129165 0.991623i \(-0.541230\pi\)
−0.923353 + 0.383951i \(0.874563\pi\)
\(48\) 0 0
\(49\) 2.14061 0.305802
\(50\) 0 0
\(51\) −3.42969 + 5.94040i −0.480253 + 0.831823i
\(52\) 0 0
\(53\) −0.232259 0.134095i −0.0319032 0.0184193i 0.483964 0.875088i \(-0.339197\pi\)
−0.515867 + 0.856669i \(0.672530\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 10.8726 8.76819i 1.44012 1.16138i
\(58\) 0 0
\(59\) −4.16599 7.21570i −0.542366 0.939405i −0.998768 0.0496310i \(-0.984195\pi\)
0.456402 0.889774i \(-0.349138\pi\)
\(60\) 0 0
\(61\) 1.70440 2.95211i 0.218226 0.377979i −0.736040 0.676939i \(-0.763306\pi\)
0.954266 + 0.298960i \(0.0966396\pi\)
\(62\) 0 0
\(63\) 13.8755 + 8.01100i 1.74814 + 1.00929i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.84253 1.06379i −0.225101 0.129962i 0.383209 0.923662i \(-0.374819\pi\)
−0.608310 + 0.793699i \(0.708152\pi\)
\(68\) 0 0
\(69\) −29.6990 −3.57534
\(70\) 0 0
\(71\) 5.23630 + 9.06953i 0.621434 + 1.07636i 0.989219 + 0.146444i \(0.0467829\pi\)
−0.367785 + 0.929911i \(0.619884\pi\)
\(72\) 0 0
\(73\) −4.20835 + 2.42969i −0.492550 + 0.284374i −0.725632 0.688083i \(-0.758452\pi\)
0.233082 + 0.972457i \(0.425119\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.65498i 0.302564i
\(78\) 0 0
\(79\) 8.20440 + 14.2104i 0.923067 + 1.59880i 0.794640 + 0.607080i \(0.207659\pi\)
0.128427 + 0.991719i \(0.459007\pi\)
\(80\) 0 0
\(81\) −11.0110 19.0716i −1.22344 2.11907i
\(82\) 0 0
\(83\) 5.73181i 0.629148i −0.949233 0.314574i \(-0.898138\pi\)
0.949233 0.314574i \(-0.101862\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 26.6990i 2.86243i
\(88\) 0 0
\(89\) −5.40880 + 9.36832i −0.573332 + 0.993040i 0.422889 + 0.906182i \(0.361016\pi\)
−0.996221 + 0.0868585i \(0.972317\pi\)
\(90\) 0 0
\(91\) −1.10220 + 1.90907i −0.115542 + 0.200125i
\(92\) 0 0
\(93\) −22.9450 + 13.2473i −2.37929 + 1.37368i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −13.6319 + 7.87039i −1.38411 + 0.799117i −0.992643 0.121075i \(-0.961366\pi\)
−0.391468 + 0.920192i \(0.628033\pi\)
\(98\) 0 0
\(99\) −4.37691 + 7.58103i −0.439896 + 0.761922i
\(100\) 0 0
\(101\) 5.27471 9.13606i 0.524853 0.909072i −0.474728 0.880133i \(-0.657454\pi\)
0.999581 0.0289397i \(-0.00921308\pi\)
\(102\) 0 0
\(103\) 0.731811i 0.0721075i −0.999350 0.0360537i \(-0.988521\pi\)
0.999350 0.0360537i \(-0.0114787\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.3958i 1.29502i 0.762058 + 0.647509i \(0.224189\pi\)
−0.762058 + 0.647509i \(0.775811\pi\)
\(108\) 0 0
\(109\) 2.96811 + 5.14091i 0.284293 + 0.492410i 0.972437 0.233164i \(-0.0749078\pi\)
−0.688144 + 0.725574i \(0.741574\pi\)
\(110\) 0 0
\(111\) −3.53189 6.11742i −0.335233 0.580640i
\(112\) 0 0
\(113\) 15.6132i 1.46877i 0.678735 + 0.734383i \(0.262529\pi\)
−0.678735 + 0.734383i \(0.737471\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 6.29444 3.63409i 0.581921 0.335972i
\(118\) 0 0
\(119\) 2.35939 + 4.08658i 0.216285 + 0.374616i
\(120\) 0 0
\(121\) −9.54942 −0.868129
\(122\) 0 0
\(123\) −18.3523 10.5957i −1.65477 0.955380i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −13.2969 7.67699i −1.17991 0.681223i −0.223918 0.974608i \(-0.571885\pi\)
−0.955994 + 0.293385i \(0.905218\pi\)
\(128\) 0 0
\(129\) −3.75719 + 6.50764i −0.330802 + 0.572965i
\(130\) 0 0
\(131\) 3.89780 + 6.75119i 0.340552 + 0.589854i 0.984535 0.175186i \(-0.0560526\pi\)
−0.643983 + 0.765040i \(0.722719\pi\)
\(132\) 0 0
\(133\) −1.48397 9.49348i −0.128676 0.823189i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.2657 + 8.23630i 1.21880 + 0.703674i 0.964661 0.263494i \(-0.0848748\pi\)
0.254138 + 0.967168i \(0.418208\pi\)
\(138\) 0 0
\(139\) −9.76819 + 16.9190i −0.828527 + 1.43505i 0.0706667 + 0.997500i \(0.477487\pi\)
−0.899194 + 0.437551i \(0.855846\pi\)
\(140\) 0 0
\(141\) 26.6990 2.24846
\(142\) 0 0
\(143\) −1.04304 0.602201i −0.0872236 0.0503586i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −5.94040 + 3.42969i −0.489956 + 0.282876i
\(148\) 0 0
\(149\) −2.83850 4.91642i −0.232539 0.402769i 0.726016 0.687678i \(-0.241370\pi\)
−0.958555 + 0.284909i \(0.908037\pi\)
\(150\) 0 0
\(151\) −14.2264 −1.15773 −0.578864 0.815424i \(-0.696504\pi\)
−0.578864 + 0.815424i \(0.696504\pi\)
\(152\) 0 0
\(153\) 15.5584i 1.25782i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.567233 0.327492i 0.0452701 0.0261367i −0.477194 0.878798i \(-0.658346\pi\)
0.522464 + 0.852661i \(0.325013\pi\)
\(158\) 0 0
\(159\) 0.859386 0.0681538
\(160\) 0 0
\(161\) −10.2154 + 17.6936i −0.805087 + 1.39445i
\(162\) 0 0
\(163\) 12.6770i 0.992939i −0.868054 0.496469i \(-0.834630\pi\)
0.868054 0.496469i \(-0.165370\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.75119 3.89780i −0.522422 0.301621i 0.215503 0.976503i \(-0.430861\pi\)
−0.737925 + 0.674882i \(0.764194\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −11.4133 + 29.5540i −0.872796 + 2.26005i
\(172\) 0 0
\(173\) −9.30179 + 5.37039i −0.707202 + 0.408303i −0.810024 0.586397i \(-0.800546\pi\)
0.102822 + 0.994700i \(0.467213\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 23.1220 + 13.3495i 1.73796 + 1.00341i
\(178\) 0 0
\(179\) 1.54942 0.115809 0.0579044 0.998322i \(-0.481558\pi\)
0.0579044 + 0.998322i \(0.481558\pi\)
\(180\) 0 0
\(181\) 4.11320 7.12428i 0.305732 0.529544i −0.671692 0.740831i \(-0.734432\pi\)
0.977424 + 0.211287i \(0.0677655\pi\)
\(182\) 0 0
\(183\) 10.9232i 0.807464i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.23275 + 1.28908i −0.163275 + 0.0942668i
\(188\) 0 0
\(189\) −30.1496 −2.19306
\(190\) 0 0
\(191\) 16.2812 1.17807 0.589034 0.808108i \(-0.299508\pi\)
0.589034 + 0.808108i \(0.299508\pi\)
\(192\) 0 0
\(193\) 14.9072 8.60669i 1.07304 0.619523i 0.144033 0.989573i \(-0.453993\pi\)
0.929012 + 0.370050i \(0.120659\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.2044i 0.727034i 0.931588 + 0.363517i \(0.118424\pi\)
−0.931588 + 0.363517i \(0.881576\pi\)
\(198\) 0 0
\(199\) 5.03189 8.71550i 0.356701 0.617825i −0.630706 0.776022i \(-0.717235\pi\)
0.987408 + 0.158197i \(0.0505680\pi\)
\(200\) 0 0
\(201\) 6.81761 0.480877
\(202\) 0 0
\(203\) 15.9063 + 9.18351i 1.11640 + 0.644556i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 58.3380 33.6815i 4.05477 2.34102i
\(208\) 0 0
\(209\) 5.18688 0.810784i 0.358784 0.0560831i
\(210\) 0 0
\(211\) 6.12758 + 10.6133i 0.421840 + 0.730648i 0.996119 0.0880113i \(-0.0280512\pi\)
−0.574280 + 0.818659i \(0.694718\pi\)
\(212\) 0 0
\(213\) −29.0624 16.7792i −1.99132 1.14969i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 18.2264i 1.23729i
\(218\) 0 0
\(219\) 7.78571 13.4852i 0.526110 0.911249i
\(220\) 0 0
\(221\) 2.14061 0.143993
\(222\) 0 0
\(223\) −17.4501 + 10.0748i −1.16854 + 0.674658i −0.953336 0.301911i \(-0.902376\pi\)
−0.215206 + 0.976569i \(0.569042\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.25515i 0.547914i 0.961742 + 0.273957i \(0.0883325\pi\)
−0.961742 + 0.273957i \(0.911667\pi\)
\(228\) 0 0
\(229\) 26.6860 1.76346 0.881729 0.471756i \(-0.156380\pi\)
0.881729 + 0.471756i \(0.156380\pi\)
\(230\) 0 0
\(231\) 4.25382 + 7.36783i 0.279881 + 0.484768i
\(232\) 0 0
\(233\) 12.1321 7.00448i 0.794802 0.458879i −0.0468485 0.998902i \(-0.514918\pi\)
0.841650 + 0.540023i \(0.181584\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −45.5360 26.2902i −2.95788 1.70773i
\(238\) 0 0
\(239\) 12.2682 0.793563 0.396782 0.917913i \(-0.370127\pi\)
0.396782 + 0.917913i \(0.370127\pi\)
\(240\) 0 0
\(241\) −4.93621 + 8.54977i −0.317969 + 0.550739i −0.980064 0.198681i \(-0.936334\pi\)
0.662095 + 0.749420i \(0.269668\pi\)
\(242\) 0 0
\(243\) 25.5793 + 14.7682i 1.64091 + 0.947380i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.06622 1.57031i −0.258727 0.0999162i
\(248\) 0 0
\(249\) 9.18351 + 15.9063i 0.581981 + 1.00802i
\(250\) 0 0
\(251\) −14.4198 + 24.9758i −0.910170 + 1.57646i −0.0963474 + 0.995348i \(0.530716\pi\)
−0.813823 + 0.581113i \(0.802617\pi\)
\(252\) 0 0
\(253\) −9.66711 5.58131i −0.607766 0.350894i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.15311 2.39780i −0.259064 0.149571i 0.364844 0.931069i \(-0.381122\pi\)
−0.623907 + 0.781498i \(0.714456\pi\)
\(258\) 0 0
\(259\) −4.85939 −0.301948
\(260\) 0 0
\(261\) −30.2792 52.4451i −1.87424 3.24627i
\(262\) 0 0
\(263\) 17.6745 10.2044i 1.08986 0.629230i 0.156320 0.987706i \(-0.450037\pi\)
0.933539 + 0.358476i \(0.116704\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 34.6640i 2.12140i
\(268\) 0 0
\(269\) 0.563788 + 0.976509i 0.0343747 + 0.0595388i 0.882701 0.469935i \(-0.155723\pi\)
−0.848326 + 0.529474i \(0.822389\pi\)
\(270\) 0 0
\(271\) −9.83850 17.0408i −0.597646 1.03515i −0.993168 0.116697i \(-0.962769\pi\)
0.395522 0.918457i \(-0.370564\pi\)
\(272\) 0 0
\(273\) 7.06379i 0.427520i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.35398i 0.441858i −0.975290 0.220929i \(-0.929091\pi\)
0.975290 0.220929i \(-0.0709089\pi\)
\(278\) 0 0
\(279\) 30.0474 52.0436i 1.79889 3.11577i
\(280\) 0 0
\(281\) −6.73630 + 11.6676i −0.401854 + 0.696031i −0.993950 0.109836i \(-0.964967\pi\)
0.592096 + 0.805867i \(0.298301\pi\)
\(282\) 0 0
\(283\) 18.4627 10.6595i 1.09750 0.633640i 0.161934 0.986802i \(-0.448227\pi\)
0.935562 + 0.353162i \(0.114894\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.6251 + 7.28908i −0.745233 + 0.430261i
\(288\) 0 0
\(289\) −6.20889 + 10.7541i −0.365229 + 0.632594i
\(290\) 0 0
\(291\) 25.2199 43.6821i 1.47842 2.56069i
\(292\) 0 0
\(293\) 8.08580i 0.472377i 0.971707 + 0.236189i \(0.0758983\pi\)
−0.971707 + 0.236189i \(0.924102\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 16.4726i 0.955837i
\(298\) 0 0
\(299\) 4.63409 + 8.02649i 0.267997 + 0.464184i
\(300\) 0 0
\(301\) 2.58468 + 4.47679i 0.148978 + 0.258038i
\(302\) 0 0
\(303\) 33.8046i 1.94202i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −24.7549 + 14.2922i −1.41284 + 0.815701i −0.995655 0.0931229i \(-0.970315\pi\)
−0.417180 + 0.908824i \(0.636982\pi\)
\(308\) 0 0
\(309\) 1.17251 + 2.03084i 0.0667016 + 0.115531i
\(310\) 0 0
\(311\) −10.7408 −0.609054 −0.304527 0.952504i \(-0.598498\pi\)
−0.304527 + 0.952504i \(0.598498\pi\)
\(312\) 0 0
\(313\) −9.89160 5.71092i −0.559107 0.322800i 0.193680 0.981065i \(-0.437958\pi\)
−0.752787 + 0.658264i \(0.771291\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.81128 + 1.62309i 0.157897 + 0.0911619i 0.576867 0.816838i \(-0.304275\pi\)
−0.418970 + 0.908000i \(0.637609\pi\)
\(318\) 0 0
\(319\) −5.01752 + 8.69060i −0.280927 + 0.486580i
\(320\) 0 0
\(321\) −21.4627 37.1745i −1.19793 2.07488i
\(322\) 0 0
\(323\) −7.26318 + 5.85735i −0.404134 + 0.325912i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −16.4735 9.51100i −0.910989 0.525960i
\(328\) 0 0
\(329\) 9.18351 15.9063i 0.506303 0.876943i
\(330\) 0 0
\(331\) 35.1208 1.93042 0.965208 0.261483i \(-0.0842116\pi\)
0.965208 + 0.261483i \(0.0842116\pi\)
\(332\) 0 0
\(333\) 13.8755 + 8.01100i 0.760371 + 0.439000i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −13.7459 + 7.93621i −0.748788 + 0.432313i −0.825256 0.564759i \(-0.808969\pi\)
0.0764677 + 0.997072i \(0.475636\pi\)
\(338\) 0 0
\(339\) −25.0155 43.3281i −1.35865 2.35326i
\(340\) 0 0
\(341\) −9.95822 −0.539268
\(342\) 0 0
\(343\) 20.1496i 1.08798i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.2707 16.3221i 1.51765 0.876216i 0.517866 0.855462i \(-0.326727\pi\)
0.999785 0.0207537i \(-0.00660660\pi\)
\(348\) 0 0
\(349\) 21.7538 1.16446 0.582228 0.813026i \(-0.302181\pi\)
0.582228 + 0.813026i \(0.302181\pi\)
\(350\) 0 0
\(351\) −6.83850 + 11.8446i −0.365012 + 0.632219i
\(352\) 0 0
\(353\) 8.67699i 0.461830i 0.972974 + 0.230915i \(0.0741719\pi\)
−0.972974 + 0.230915i \(0.925828\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −13.0950 7.56042i −0.693063 0.400140i
\(358\) 0 0
\(359\) 5.81109 + 10.0651i 0.306697 + 0.531216i 0.977638 0.210296i \(-0.0674427\pi\)
−0.670940 + 0.741511i \(0.734109\pi\)
\(360\) 0 0
\(361\) 18.0936 5.79827i 0.952297 0.305172i
\(362\) 0 0
\(363\) 26.5005 15.3001i 1.39092 0.803046i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 26.5083 + 15.3046i 1.38372 + 0.798892i 0.992598 0.121446i \(-0.0387532\pi\)
0.391123 + 0.920338i \(0.372087\pi\)
\(368\) 0 0
\(369\) 48.0660 2.50222
\(370\) 0 0
\(371\) 0.295598 0.511992i 0.0153467 0.0265813i
\(372\) 0 0
\(373\) 4.70980i 0.243864i 0.992538 + 0.121932i \(0.0389090\pi\)
−0.992538 + 0.121932i \(0.961091\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7.21570 4.16599i 0.371628 0.214559i
\(378\) 0 0
\(379\) −10.0638 −0.516942 −0.258471 0.966019i \(-0.583219\pi\)
−0.258471 + 0.966019i \(0.583219\pi\)
\(380\) 0 0
\(381\) 49.2003 2.52061
\(382\) 0 0
\(383\) 23.7671 13.7219i 1.21444 0.701158i 0.250717 0.968060i \(-0.419334\pi\)
0.963723 + 0.266903i \(0.0860003\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 17.0440i 0.866396i
\(388\) 0 0
\(389\) 0.257185 0.445458i 0.0130398 0.0225856i −0.859432 0.511250i \(-0.829183\pi\)
0.872472 + 0.488665i \(0.162516\pi\)
\(390\) 0 0
\(391\) 19.8396 1.00333
\(392\) 0 0
\(393\) −21.6335 12.4901i −1.09127 0.630043i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2.68950 + 1.55278i −0.134982 + 0.0779320i −0.565970 0.824426i \(-0.691498\pi\)
0.430988 + 0.902358i \(0.358165\pi\)
\(398\) 0 0
\(399\) 19.3286 + 23.9677i 0.967641 + 1.19988i
\(400\) 0 0
\(401\) 6.51752 + 11.2887i 0.325470 + 0.563730i 0.981607 0.190911i \(-0.0611443\pi\)
−0.656138 + 0.754641i \(0.727811\pi\)
\(402\) 0 0
\(403\) 7.16046 + 4.13409i 0.356688 + 0.205934i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.65498i 0.131603i
\(408\) 0 0
\(409\) 13.7747 23.8585i 0.681115 1.17973i −0.293525 0.955951i \(-0.594828\pi\)
0.974641 0.223775i \(-0.0718382\pi\)
\(410\) 0 0
\(411\) −52.7848 −2.60368
\(412\) 0 0
\(413\) 15.9063 9.18351i 0.782698 0.451891i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 62.6024i 3.06565i
\(418\) 0 0
\(419\) −16.5494 −0.808492 −0.404246 0.914650i \(-0.632466\pi\)
−0.404246 + 0.914650i \(0.632466\pi\)
\(420\) 0 0
\(421\) 7.93418 + 13.7424i 0.386688 + 0.669764i 0.992002 0.126223i \(-0.0402856\pi\)
−0.605314 + 0.795987i \(0.706952\pi\)
\(422\) 0 0
\(423\) −52.4451 + 30.2792i −2.54997 + 1.47222i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.50764 + 3.75719i 0.314927 + 0.181823i
\(428\) 0 0
\(429\) 3.85939 0.186333
\(430\) 0 0
\(431\) −11.4472 + 19.8272i −0.551393 + 0.955041i 0.446781 + 0.894643i \(0.352570\pi\)
−0.998174 + 0.0603975i \(0.980763\pi\)
\(432\) 0 0
\(433\) 18.4740 + 10.6660i 0.887805 + 0.512575i 0.873224 0.487319i \(-0.162025\pi\)
0.0145814 + 0.999894i \(0.495358\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −37.6865 14.5539i −1.80279 0.696208i
\(438\) 0 0
\(439\) −5.08783 8.81238i −0.242829 0.420592i 0.718690 0.695331i \(-0.244742\pi\)
−0.961519 + 0.274739i \(0.911409\pi\)
\(440\) 0 0
\(441\) 7.77919 13.4740i 0.370438 0.641617i
\(442\) 0 0
\(443\) 5.72720 + 3.30660i 0.272108 + 0.157101i 0.629845 0.776721i \(-0.283118\pi\)
−0.357737 + 0.933822i \(0.616452\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.7542 + 9.09568i 0.745147 + 0.430211i
\(448\) 0 0
\(449\) −10.9870 −0.518507 −0.259253 0.965809i \(-0.583476\pi\)
−0.259253 + 0.965809i \(0.583476\pi\)
\(450\) 0 0
\(451\) −3.98248 6.89785i −0.187528 0.324807i
\(452\) 0 0
\(453\) 39.4796 22.7936i 1.85491 1.07094i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.5494i 0.587037i −0.955953 0.293518i \(-0.905174\pi\)
0.955953 0.293518i \(-0.0948262\pi\)
\(458\) 0 0
\(459\) 14.6386 + 25.3548i 0.683270 + 1.18346i
\(460\) 0 0
\(461\) 11.6386 + 20.1586i 0.542063 + 0.938880i 0.998785 + 0.0492710i \(0.0156898\pi\)
−0.456723 + 0.889609i \(0.650977\pi\)
\(462\) 0 0
\(463\) 23.3958i 1.08729i −0.839314 0.543647i \(-0.817043\pi\)
0.839314 0.543647i \(-0.182957\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.6352i 0.584688i 0.956313 + 0.292344i \(0.0944352\pi\)
−0.956313 + 0.292344i \(0.905565\pi\)
\(468\) 0 0
\(469\) 2.34502 4.06169i 0.108283 0.187551i
\(470\) 0 0
\(471\) −1.04942 + 1.81764i −0.0483546 + 0.0837526i
\(472\) 0 0
\(473\) −2.44595 + 1.41217i −0.112465 + 0.0649316i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.68810 + 0.974625i −0.0772928 + 0.0446250i
\(478\) 0 0
\(479\) 2.01752 3.49445i 0.0921830 0.159666i −0.816246 0.577704i \(-0.803949\pi\)
0.908429 + 0.418038i \(0.137282\pi\)
\(480\) 0 0
\(481\) −1.10220 + 1.90907i −0.0502560 + 0.0870460i
\(482\) 0 0
\(483\) 65.4685i 2.97892i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.54942i 0.296782i −0.988929 0.148391i \(-0.952591\pi\)
0.988929 0.148391i \(-0.0474095\pi\)
\(488\) 0 0
\(489\) 20.3111 + 35.1798i 0.918499 + 1.59089i
\(490\) 0 0
\(491\) −1.04290 1.80635i −0.0470653 0.0815195i 0.841533 0.540206i \(-0.181654\pi\)
−0.888598 + 0.458686i \(0.848320\pi\)
\(492\) 0 0
\(493\) 17.8355i 0.803273i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −19.9929 + 11.5429i −0.896803 + 0.517770i
\(498\) 0 0
\(499\) −12.0539 20.8780i −0.539607 0.934626i −0.998925 0.0463546i \(-0.985240\pi\)
0.459318 0.888272i \(-0.348094\pi\)
\(500\) 0 0
\(501\) 24.9802 1.11603
\(502\) 0 0
\(503\) 7.16823 + 4.13858i 0.319616 + 0.184530i 0.651221 0.758888i \(-0.274257\pi\)
−0.331606 + 0.943418i \(0.607590\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 33.3011 + 19.2264i 1.47895 + 0.853875i
\(508\) 0 0
\(509\) −2.86591 + 4.96389i −0.127029 + 0.220021i −0.922524 0.385939i \(-0.873877\pi\)
0.795495 + 0.605960i \(0.207211\pi\)
\(510\) 0 0
\(511\) −5.35602 9.27690i −0.236936 0.410386i
\(512\) 0 0
\(513\) −9.20713 58.9014i −0.406505 2.60056i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.69060 + 5.01752i 0.382212 + 0.220670i
\(518\) 0 0
\(519\) 17.2089 29.8067i 0.755386 1.30837i
\(520\) 0 0
\(521\) 14.8086 0.648778 0.324389 0.945924i \(-0.394841\pi\)
0.324389 + 0.945924i \(0.394841\pi\)
\(522\) 0 0
\(523\) −13.4988 7.79356i −0.590263 0.340789i 0.174938 0.984579i \(-0.444027\pi\)
−0.765202 + 0.643791i \(0.777361\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15.3278 8.84950i 0.667689 0.385490i
\(528\) 0 0
\(529\) 31.4497 + 54.4724i 1.36738 + 2.36837i
\(530\) 0 0
\(531\) −60.5584 −2.62801
\(532\) 0 0
\(533\) 6.61320i 0.286450i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.29978 + 2.48248i −0.185549 + 0.107127i
\(538\) 0 0
\(539\) −2.57816 −0.111049
\(540\) 0 0
\(541\) −14.0539 + 24.3421i −0.604224 + 1.04655i 0.387949 + 0.921681i \(0.373184\pi\)
−0.992174 + 0.124867i \(0.960150\pi\)
\(542\) 0 0
\(543\) 26.3607i 1.13125i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −37.5569 21.6835i −1.60582 0.927120i −0.990292 0.139004i \(-0.955610\pi\)
−0.615527 0.788116i \(-0.711057\pi\)
\(548\) 0 0
\(549\) −12.3879 21.4565i −0.528703 0.915741i
\(550\) 0 0
\(551\) −13.0838 + 33.8796i −0.557387 + 1.44332i
\(552\) 0 0
\(553\) −31.3255 + 18.0858i −1.33210 + 0.769086i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.9963 + 8.65814i 0.635415 + 0.366857i 0.782846 0.622215i \(-0.213767\pi\)
−0.147431 + 0.989072i \(0.547100\pi\)
\(558\) 0 0
\(559\) 2.34502 0.0991836
\(560\) 0 0
\(561\) 4.13073 7.15463i 0.174399 0.302069i
\(562\) 0 0
\(563\) 8.35398i 0.352078i 0.984383 + 0.176039i \(0.0563286\pi\)
−0.984383 + 0.176039i \(0.943671\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 42.0415 24.2727i 1.76558 1.01936i
\(568\) 0 0
\(569\) 10.6640 0.447056 0.223528 0.974697i \(-0.428243\pi\)
0.223528 + 0.974697i \(0.428243\pi\)
\(570\) 0 0
\(571\) −2.56512 −0.107347 −0.0536735 0.998559i \(-0.517093\pi\)
−0.0536735 + 0.998559i \(0.517093\pi\)
\(572\) 0 0
\(573\) −45.1819 + 26.0858i −1.88750 + 1.08975i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 20.4218i 0.850172i −0.905153 0.425086i \(-0.860244\pi\)
0.905153 0.425086i \(-0.139756\pi\)
\(578\) 0 0
\(579\) −27.5793 + 47.7687i −1.14616 + 1.98520i
\(580\) 0 0
\(581\) 12.6352 0.524197
\(582\) 0 0
\(583\) 0.279733 + 0.161504i 0.0115853 + 0.00668880i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.62850 4.40432i 0.314862 0.181786i −0.334238 0.942489i \(-0.608479\pi\)
0.649100 + 0.760703i \(0.275146\pi\)
\(588\) 0 0
\(589\) −35.6078 + 5.56601i −1.46719 + 0.229343i
\(590\) 0 0
\(591\) −16.3495 28.3182i −0.672529 1.16485i
\(592\) 0 0
\(593\) −28.5314 16.4726i −1.17164 0.676448i −0.217576 0.976043i \(-0.569815\pi\)
−0.954066 + 0.299595i \(0.903148\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 32.2484i 1.31984i
\(598\) 0 0
\(599\) −9.56379 + 16.5650i −0.390766 + 0.676826i −0.992551 0.121832i \(-0.961123\pi\)
0.601785 + 0.798658i \(0.294456\pi\)
\(600\) 0 0
\(601\) 19.3100 0.787670 0.393835 0.919181i \(-0.371148\pi\)
0.393835 + 0.919181i \(0.371148\pi\)
\(602\) 0 0
\(603\) −13.3919 + 7.73181i −0.545360 + 0.314864i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 36.8773i 1.49680i −0.663245 0.748402i \(-0.730821\pi\)
0.663245 0.748402i \(-0.269179\pi\)
\(608\) 0 0
\(609\) −58.8553 −2.38494
\(610\) 0 0
\(611\) −4.16599 7.21570i −0.168538 0.291916i
\(612\) 0 0
\(613\) −24.6996 + 14.2603i −0.997609 + 0.575970i −0.907540 0.419966i \(-0.862042\pi\)
−0.0900688 + 0.995936i \(0.528709\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.78112 5.64713i −0.393773 0.227345i 0.290021 0.957020i \(-0.406338\pi\)
−0.683794 + 0.729675i \(0.739671\pi\)
\(618\) 0 0
\(619\) −27.2044 −1.09344 −0.546719 0.837316i \(-0.684123\pi\)
−0.546719 + 0.837316i \(0.684123\pi\)
\(620\) 0 0
\(621\) −63.3805 + 109.778i −2.54337 + 4.40525i
\(622\) 0 0
\(623\) −20.6515 11.9232i −0.827387 0.477692i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −13.0950 + 10.5604i −0.522965 + 0.421743i
\(628\) 0 0
\(629\) 2.35939 + 4.08658i 0.0940749 + 0.162942i
\(630\) 0 0
\(631\) −4.19136 + 7.25965i −0.166856 + 0.289002i −0.937313 0.348490i \(-0.886695\pi\)
0.770457 + 0.637492i \(0.220028\pi\)
\(632\) 0 0
\(633\) −34.0092 19.6352i −1.35174 0.780430i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.85383 + 1.07031i 0.0734513 + 0.0424071i
\(638\) 0 0
\(639\) 76.1168 3.01113
\(640\) 0 0
\(641\) −9.55594 16.5514i −0.377437 0.653740i 0.613252 0.789888i \(-0.289861\pi\)
−0.990689 + 0.136148i \(0.956528\pi\)
\(642\) 0 0
\(643\) −41.7618 + 24.1112i −1.64692 + 0.950852i −0.668638 + 0.743588i \(0.733123\pi\)
−0.978285 + 0.207264i \(0.933544\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.0817i 1.18263i 0.806439 + 0.591317i \(0.201392\pi\)
−0.806439 + 0.591317i \(0.798608\pi\)
\(648\) 0 0
\(649\) 5.01752 + 8.69060i 0.196955 + 0.341136i
\(650\) 0 0
\(651\) −29.2024 50.5800i −1.14453 1.98239i
\(652\) 0 0
\(653\) 41.9124i 1.64016i 0.572250 + 0.820079i \(0.306071\pi\)
−0.572250 + 0.820079i \(0.693929\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 35.3189i 1.37792i
\(658\) 0 0
\(659\) −20.0936 + 34.8032i −0.782737 + 1.35574i 0.147604 + 0.989047i \(0.452844\pi\)
−0.930341 + 0.366694i \(0.880489\pi\)
\(660\) 0 0
\(661\) 0.757185 1.31148i 0.0294511 0.0510108i −0.850924 0.525289i \(-0.823957\pi\)
0.880375 + 0.474278i \(0.157291\pi\)
\(662\) 0 0
\(663\) −5.94040 + 3.42969i −0.230706 + 0.133198i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 66.8765 38.6112i 2.58947 1.49503i
\(668\) 0 0
\(669\) 32.2837 55.9170i 1.24816 2.16187i
\(670\) 0 0
\(671\) −2.05278 + 3.55553i −0.0792468 + 0.137260i
\(672\) 0 0
\(673\) 7.76686i 0.299390i −0.988732 0.149695i \(-0.952171\pi\)
0.988732 0.149695i \(-0.0478292\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.19136i 0.237953i −0.992897 0.118977i \(-0.962039\pi\)
0.992897 0.118977i \(-0.0379614\pi\)
\(678\) 0 0
\(679\) −17.3495 30.0502i −0.665813 1.15322i
\(680\) 0 0
\(681\) −13.2264 22.9088i −0.506837 0.877868i
\(682\) 0 0
\(683\) 2.92317i 0.111852i 0.998435 + 0.0559261i \(0.0178111\pi\)
−0.998435 + 0.0559261i \(0.982189\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −74.0560 + 42.7563i −2.82541 + 1.63125i
\(688\) 0 0
\(689\) −0.134095 0.232259i −0.00510860 0.00884835i
\(690\) 0 0
\(691\) −2.35805 −0.0897046 −0.0448523 0.998994i \(-0.514282\pi\)
−0.0448523 + 0.998994i \(0.514282\pi\)
\(692\) 0 0
\(693\) −16.7116 9.64847i −0.634822 0.366515i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.2597 + 7.07816i 0.464370 + 0.268104i
\(698\) 0 0
\(699\) −22.4452 + 38.8762i −0.848955 + 1.47043i
\(700\) 0 0
\(701\) −12.2792 21.2682i −0.463779 0.803288i 0.535367 0.844620i \(-0.320173\pi\)
−0.999145 + 0.0413314i \(0.986840\pi\)
\(702\) 0 0
\(703\) −1.48397 9.49348i −0.0559689 0.358053i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 20.1396 + 11.6276i 0.757426 + 0.437300i
\(708\) 0 0
\(709\) 3.63858 6.30220i 0.136650 0.236684i −0.789577 0.613652i \(-0.789700\pi\)
0.926226 + 0.376968i \(0.123033\pi\)
\(710\) 0 0
\(711\) 119.262 4.47269
\(712\) 0 0
\(713\) 66.3645 + 38.3156i 2.48537 + 1.43493i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −34.0454 + 19.6561i −1.27145 + 0.734071i
\(718\) 0 0
\(719\) 16.4452 + 28.4839i 0.613302 + 1.06227i 0.990680 + 0.136211i \(0.0434924\pi\)
−0.377378 + 0.926059i \(0.623174\pi\)
\(720\) 0 0
\(721\) 1.61320 0.0600789
\(722\) 0 0
\(723\) 31.6352i 1.17653i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −24.1709 + 13.9551i −0.896449 + 0.517565i −0.876046 0.482227i \(-0.839828\pi\)
−0.0204023 + 0.999792i \(0.506495\pi\)
\(728\) 0 0
\(729\) −28.5804 −1.05853
\(730\) 0 0
\(731\) 2.50989 4.34725i 0.0928315 0.160789i
\(732\) 0 0
\(733\) 4.89710i 0.180878i −0.995902 0.0904392i \(-0.971173\pi\)
0.995902 0.0904392i \(-0.0288271\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.21915 + 1.28123i 0.0817435 + 0.0471946i
\(738\) 0 0
\(739\) −11.5936 20.0808i −0.426479 0.738684i 0.570078 0.821591i \(-0.306913\pi\)
−0.996557 + 0.0829069i \(0.973580\pi\)
\(740\) 0 0
\(741\) 13.8001 2.15715i 0.506959 0.0792449i
\(742\) 0 0
\(743\) 34.6239 19.9901i 1.27023 0.733366i 0.295197 0.955436i \(-0.404615\pi\)
0.975031 + 0.222070i \(0.0712815\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −36.0785 20.8299i −1.32004 0.762128i
\(748\) 0 0
\(749\) −29.5296 −1.07899
\(750\) 0 0
\(751\) 10.2936 17.8290i 0.375617 0.650589i −0.614802 0.788682i \(-0.710764\pi\)
0.990419 + 0.138093i \(0.0440973\pi\)
\(752\) 0 0
\(753\) 92.4137i 3.36774i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 29.9950 17.3176i 1.09019 0.629419i 0.156560 0.987668i \(-0.449960\pi\)
0.933626 + 0.358249i \(0.116626\pi\)
\(758\) 0 0
\(759\) 35.7695 1.29835
\(760\) 0 0
\(761\) 24.3890 0.884102 0.442051 0.896990i \(-0.354251\pi\)
0.442051 + 0.896990i \(0.354251\pi\)
\(762\) 0 0
\(763\) −11.3326 + 6.54290i −0.410269 + 0.236869i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.33198i 0.300850i
\(768\) 0 0
\(769\) 3.27471 5.67196i 0.118089 0.204536i −0.800921 0.598770i \(-0.795657\pi\)
0.919010 + 0.394233i \(0.128990\pi\)
\(770\) 0 0
\(771\) 15.3670 0.553430
\(772\) 0 0
\(773\) 32.4522 + 18.7363i 1.16723 + 0.673898i 0.953025 0.302892i \(-0.0979522\pi\)
0.214200 + 0.976790i \(0.431286\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 13.4852 7.78571i 0.483781 0.279311i
\(778\) 0 0
\(779\) −18.0957 22.4388i −0.648345 0.803955i
\(780\) 0 0
\(781\) −6.30660 10.9234i −0.225668 0.390868i
\(782\) 0 0
\(783\) 98.6891 + 56.9782i 3.52686 + 2.03623i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 12.8306i 0.457363i 0.973501 + 0.228682i \(0.0734415\pi\)
−0.973501 + 0.228682i \(0.926559\pi\)
\(788\) 0 0
\(789\) −32.6990 + 56.6363i −1.16412 + 2.01631i
\(790\) 0 0
\(791\) −34.4178 −1.22376
\(792\) 0 0
\(793\) 2.95211 1.70440i 0.104833 0.0605251i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.3032i 1.00255i 0.865287 + 0.501276i \(0.167136\pi\)
−0.865287 + 0.501276i \(0.832864\pi\)
\(798\) 0 0
\(799\) −17.8355 −0.630976
\(800\) 0