Properties

Label 1512.2.j.c.323.8
Level 1512
Weight 2
Character 1512.323
Analytic conductor 12.073
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.8
Character \(\chi\) = 1512.323
Dual form 1512.2.j.c.323.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16953 + 0.795104i) q^{2} +(0.735620 - 1.85980i) q^{4} +2.09311 q^{5} +1.00000i q^{7} +(0.618402 + 2.76000i) q^{8} +O(q^{10})\) \(q+(-1.16953 + 0.795104i) q^{2} +(0.735620 - 1.85980i) q^{4} +2.09311 q^{5} +1.00000i q^{7} +(0.618402 + 2.76000i) q^{8} +(-2.44797 + 1.66424i) q^{10} -0.961211i q^{11} -4.60210i q^{13} +(-0.795104 - 1.16953i) q^{14} +(-2.91773 - 2.73622i) q^{16} +3.28066i q^{17} +3.66977 q^{19} +(1.53974 - 3.89278i) q^{20} +(0.764262 + 1.12417i) q^{22} +2.40322 q^{23} -0.618872 q^{25} +(3.65914 + 5.38231i) q^{26} +(1.85980 + 0.735620i) q^{28} +9.31771 q^{29} -1.84927i q^{31} +(5.58795 + 0.880204i) q^{32} +(-2.60847 - 3.83684i) q^{34} +2.09311i q^{35} -2.29364i q^{37} +(-4.29193 + 2.91785i) q^{38} +(1.29439 + 5.77699i) q^{40} -0.314406i q^{41} -8.64261 q^{43} +(-1.78766 - 0.707086i) q^{44} +(-2.81064 + 1.91081i) q^{46} +2.34305 q^{47} -1.00000 q^{49} +(0.723792 - 0.492067i) q^{50} +(-8.55899 - 3.38540i) q^{52} +7.73354 q^{53} -2.01192i q^{55} +(-2.76000 + 0.618402i) q^{56} +(-10.8974 + 7.40855i) q^{58} +7.99530i q^{59} -10.6321i q^{61} +(1.47036 + 2.16278i) q^{62} +(-7.23516 + 3.41357i) q^{64} -9.63272i q^{65} +4.12203 q^{67} +(6.10138 + 2.41332i) q^{68} +(-1.66424 - 2.44797i) q^{70} -6.79440 q^{71} +16.0267 q^{73} +(1.82368 + 2.68249i) q^{74} +(2.69956 - 6.82505i) q^{76} +0.961211 q^{77} -1.26231i q^{79} +(-6.10713 - 5.72721i) q^{80} +(0.249985 + 0.367709i) q^{82} -2.99495i q^{83} +6.86680i q^{85} +(10.1078 - 6.87177i) q^{86} +(2.65294 - 0.594415i) q^{88} -12.8990i q^{89} +4.60210 q^{91} +(1.76785 - 4.46950i) q^{92} +(-2.74028 + 1.86297i) q^{94} +7.68126 q^{95} +4.98346 q^{97} +(1.16953 - 0.795104i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 8q^{4} + O(q^{10}) \) \( 32q + 8q^{4} - 8q^{10} - 8q^{16} - 64q^{19} + 24q^{22} - 16q^{25} - 8q^{28} + 8q^{34} - 24q^{40} - 48q^{43} - 8q^{46} - 32q^{49} - 24q^{52} - 96q^{58} - 40q^{64} + 16q^{67} - 16q^{70} - 16q^{73} + 16q^{76} + 24q^{82} + 72q^{88} + 16q^{91} - 56q^{94} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16953 + 0.795104i −0.826986 + 0.562223i
\(3\) 0 0
\(4\) 0.735620 1.85980i 0.367810 0.929901i
\(5\) 2.09311 0.936069 0.468035 0.883710i \(-0.344962\pi\)
0.468035 + 0.883710i \(0.344962\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0.618402 + 2.76000i 0.218638 + 0.975806i
\(9\) 0 0
\(10\) −2.44797 + 1.66424i −0.774116 + 0.526280i
\(11\) 0.961211i 0.289816i −0.989445 0.144908i \(-0.953711\pi\)
0.989445 0.144908i \(-0.0462886\pi\)
\(12\) 0 0
\(13\) 4.60210i 1.27639i −0.769874 0.638196i \(-0.779681\pi\)
0.769874 0.638196i \(-0.220319\pi\)
\(14\) −0.795104 1.16953i −0.212500 0.312571i
\(15\) 0 0
\(16\) −2.91773 2.73622i −0.729431 0.684054i
\(17\) 3.28066i 0.795677i 0.917455 + 0.397839i \(0.130240\pi\)
−0.917455 + 0.397839i \(0.869760\pi\)
\(18\) 0 0
\(19\) 3.66977 0.841904 0.420952 0.907083i \(-0.361696\pi\)
0.420952 + 0.907083i \(0.361696\pi\)
\(20\) 1.53974 3.89278i 0.344296 0.870452i
\(21\) 0 0
\(22\) 0.764262 + 1.12417i 0.162941 + 0.239674i
\(23\) 2.40322 0.501105 0.250553 0.968103i \(-0.419388\pi\)
0.250553 + 0.968103i \(0.419388\pi\)
\(24\) 0 0
\(25\) −0.618872 −0.123774
\(26\) 3.65914 + 5.38231i 0.717617 + 1.05556i
\(27\) 0 0
\(28\) 1.85980 + 0.735620i 0.351470 + 0.139019i
\(29\) 9.31771 1.73026 0.865128 0.501552i \(-0.167237\pi\)
0.865128 + 0.501552i \(0.167237\pi\)
\(30\) 0 0
\(31\) 1.84927i 0.332138i −0.986114 0.166069i \(-0.946892\pi\)
0.986114 0.166069i \(-0.0531075\pi\)
\(32\) 5.58795 + 0.880204i 0.987820 + 0.155600i
\(33\) 0 0
\(34\) −2.60847 3.83684i −0.447348 0.658013i
\(35\) 2.09311i 0.353801i
\(36\) 0 0
\(37\) 2.29364i 0.377072i −0.982066 0.188536i \(-0.939626\pi\)
0.982066 0.188536i \(-0.0603742\pi\)
\(38\) −4.29193 + 2.91785i −0.696242 + 0.473338i
\(39\) 0 0
\(40\) 1.29439 + 5.77699i 0.204660 + 0.913422i
\(41\) 0.314406i 0.0491020i −0.999699 0.0245510i \(-0.992184\pi\)
0.999699 0.0245510i \(-0.00781561\pi\)
\(42\) 0 0
\(43\) −8.64261 −1.31799 −0.658993 0.752149i \(-0.729017\pi\)
−0.658993 + 0.752149i \(0.729017\pi\)
\(44\) −1.78766 0.707086i −0.269500 0.106597i
\(45\) 0 0
\(46\) −2.81064 + 1.91081i −0.414407 + 0.281733i
\(47\) 2.34305 0.341769 0.170884 0.985291i \(-0.445338\pi\)
0.170884 + 0.985291i \(0.445338\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0.723792 0.492067i 0.102360 0.0695888i
\(51\) 0 0
\(52\) −8.55899 3.38540i −1.18692 0.469470i
\(53\) 7.73354 1.06228 0.531142 0.847283i \(-0.321763\pi\)
0.531142 + 0.847283i \(0.321763\pi\)
\(54\) 0 0
\(55\) 2.01192i 0.271288i
\(56\) −2.76000 + 0.618402i −0.368820 + 0.0826374i
\(57\) 0 0
\(58\) −10.8974 + 7.40855i −1.43090 + 0.972790i
\(59\) 7.99530i 1.04090i 0.853892 + 0.520450i \(0.174236\pi\)
−0.853892 + 0.520450i \(0.825764\pi\)
\(60\) 0 0
\(61\) 10.6321i 1.36130i −0.732610 0.680649i \(-0.761698\pi\)
0.732610 0.680649i \(-0.238302\pi\)
\(62\) 1.47036 + 2.16278i 0.186736 + 0.274674i
\(63\) 0 0
\(64\) −7.23516 + 3.41357i −0.904395 + 0.426697i
\(65\) 9.63272i 1.19479i
\(66\) 0 0
\(67\) 4.12203 0.503586 0.251793 0.967781i \(-0.418980\pi\)
0.251793 + 0.967781i \(0.418980\pi\)
\(68\) 6.10138 + 2.41332i 0.739901 + 0.292658i
\(69\) 0 0
\(70\) −1.66424 2.44797i −0.198915 0.292588i
\(71\) −6.79440 −0.806347 −0.403174 0.915124i \(-0.632093\pi\)
−0.403174 + 0.915124i \(0.632093\pi\)
\(72\) 0 0
\(73\) 16.0267 1.87579 0.937894 0.346922i \(-0.112773\pi\)
0.937894 + 0.346922i \(0.112773\pi\)
\(74\) 1.82368 + 2.68249i 0.211999 + 0.311833i
\(75\) 0 0
\(76\) 2.69956 6.82505i 0.309661 0.782887i
\(77\) 0.961211 0.109540
\(78\) 0 0
\(79\) 1.26231i 0.142021i −0.997476 0.0710106i \(-0.977378\pi\)
0.997476 0.0710106i \(-0.0226224\pi\)
\(80\) −6.10713 5.72721i −0.682798 0.640322i
\(81\) 0 0
\(82\) 0.249985 + 0.367709i 0.0276063 + 0.0406066i
\(83\) 2.99495i 0.328738i −0.986399 0.164369i \(-0.947441\pi\)
0.986399 0.164369i \(-0.0525589\pi\)
\(84\) 0 0
\(85\) 6.86680i 0.744809i
\(86\) 10.1078 6.87177i 1.08995 0.741002i
\(87\) 0 0
\(88\) 2.65294 0.594415i 0.282804 0.0633648i
\(89\) 12.8990i 1.36729i −0.729815 0.683645i \(-0.760394\pi\)
0.729815 0.683645i \(-0.239606\pi\)
\(90\) 0 0
\(91\) 4.60210 0.482431
\(92\) 1.76785 4.46950i 0.184312 0.465978i
\(93\) 0 0
\(94\) −2.74028 + 1.86297i −0.282638 + 0.192150i
\(95\) 7.68126 0.788080
\(96\) 0 0
\(97\) 4.98346 0.505994 0.252997 0.967467i \(-0.418584\pi\)
0.252997 + 0.967467i \(0.418584\pi\)
\(98\) 1.16953 0.795104i 0.118141 0.0803176i
\(99\) 0 0
\(100\) −0.455255 + 1.15098i −0.0455255 + 0.115098i
\(101\) −3.18764 −0.317182 −0.158591 0.987344i \(-0.550695\pi\)
−0.158591 + 0.987344i \(0.550695\pi\)
\(102\) 0 0
\(103\) 0.535425i 0.0527570i 0.999652 + 0.0263785i \(0.00839750\pi\)
−0.999652 + 0.0263785i \(0.991602\pi\)
\(104\) 12.7018 2.84595i 1.24551 0.279068i
\(105\) 0 0
\(106\) −9.04464 + 6.14897i −0.878493 + 0.597240i
\(107\) 9.70673i 0.938385i 0.883096 + 0.469193i \(0.155455\pi\)
−0.883096 + 0.469193i \(0.844545\pi\)
\(108\) 0 0
\(109\) 8.03576i 0.769686i −0.922982 0.384843i \(-0.874256\pi\)
0.922982 0.384843i \(-0.125744\pi\)
\(110\) 1.59969 + 2.35301i 0.152524 + 0.224351i
\(111\) 0 0
\(112\) 2.73622 2.91773i 0.258548 0.275699i
\(113\) 12.7809i 1.20233i −0.799126 0.601163i \(-0.794704\pi\)
0.799126 0.601163i \(-0.205296\pi\)
\(114\) 0 0
\(115\) 5.03021 0.469069
\(116\) 6.85430 17.3291i 0.636406 1.60897i
\(117\) 0 0
\(118\) −6.35709 9.35078i −0.585218 0.860809i
\(119\) −3.28066 −0.300738
\(120\) 0 0
\(121\) 10.0761 0.916007
\(122\) 8.45360 + 12.4346i 0.765353 + 1.12577i
\(123\) 0 0
\(124\) −3.43927 1.36036i −0.308856 0.122164i
\(125\) −11.7609 −1.05193
\(126\) 0 0
\(127\) 16.6260i 1.47532i 0.675175 + 0.737658i \(0.264068\pi\)
−0.675175 + 0.737658i \(0.735932\pi\)
\(128\) 5.74762 9.74499i 0.508023 0.861344i
\(129\) 0 0
\(130\) 7.65901 + 11.2658i 0.671739 + 0.988075i
\(131\) 14.5603i 1.27214i 0.771632 + 0.636069i \(0.219440\pi\)
−0.771632 + 0.636069i \(0.780560\pi\)
\(132\) 0 0
\(133\) 3.66977i 0.318210i
\(134\) −4.82086 + 3.27744i −0.416459 + 0.283128i
\(135\) 0 0
\(136\) −9.05461 + 2.02877i −0.776426 + 0.173965i
\(137\) 17.2672i 1.47524i 0.675216 + 0.737620i \(0.264050\pi\)
−0.675216 + 0.737620i \(0.735950\pi\)
\(138\) 0 0
\(139\) 14.5580 1.23480 0.617398 0.786651i \(-0.288187\pi\)
0.617398 + 0.786651i \(0.288187\pi\)
\(140\) 3.89278 + 1.53974i 0.329000 + 0.130132i
\(141\) 0 0
\(142\) 7.94629 5.40225i 0.666837 0.453347i
\(143\) −4.42358 −0.369919
\(144\) 0 0
\(145\) 19.5030 1.61964
\(146\) −18.7438 + 12.7429i −1.55125 + 1.05461i
\(147\) 0 0
\(148\) −4.26571 1.68725i −0.350640 0.138691i
\(149\) 20.1739 1.65271 0.826356 0.563148i \(-0.190410\pi\)
0.826356 + 0.563148i \(0.190410\pi\)
\(150\) 0 0
\(151\) 11.9560i 0.972966i −0.873690 0.486483i \(-0.838280\pi\)
0.873690 0.486483i \(-0.161720\pi\)
\(152\) 2.26940 + 10.1286i 0.184072 + 0.821535i
\(153\) 0 0
\(154\) −1.12417 + 0.764262i −0.0905881 + 0.0615860i
\(155\) 3.87073i 0.310905i
\(156\) 0 0
\(157\) 22.1011i 1.76386i 0.471381 + 0.881930i \(0.343756\pi\)
−0.471381 + 0.881930i \(0.656244\pi\)
\(158\) 1.00367 + 1.47632i 0.0798476 + 0.117450i
\(159\) 0 0
\(160\) 11.6962 + 1.84237i 0.924668 + 0.145652i
\(161\) 2.40322i 0.189400i
\(162\) 0 0
\(163\) 11.2054 0.877674 0.438837 0.898567i \(-0.355391\pi\)
0.438837 + 0.898567i \(0.355391\pi\)
\(164\) −0.584733 0.231284i −0.0456600 0.0180602i
\(165\) 0 0
\(166\) 2.38130 + 3.50270i 0.184824 + 0.271862i
\(167\) −1.76628 −0.136679 −0.0683395 0.997662i \(-0.521770\pi\)
−0.0683395 + 0.997662i \(0.521770\pi\)
\(168\) 0 0
\(169\) −8.17930 −0.629177
\(170\) −5.45982 8.03095i −0.418749 0.615946i
\(171\) 0 0
\(172\) −6.35768 + 16.0735i −0.484768 + 1.22560i
\(173\) −4.37240 −0.332428 −0.166214 0.986090i \(-0.553154\pi\)
−0.166214 + 0.986090i \(0.553154\pi\)
\(174\) 0 0
\(175\) 0.618872i 0.0467823i
\(176\) −2.63008 + 2.80455i −0.198250 + 0.211401i
\(177\) 0 0
\(178\) 10.2560 + 15.0858i 0.768722 + 1.13073i
\(179\) 17.0068i 1.27115i 0.772041 + 0.635573i \(0.219236\pi\)
−0.772041 + 0.635573i \(0.780764\pi\)
\(180\) 0 0
\(181\) 8.50624i 0.632264i −0.948715 0.316132i \(-0.897616\pi\)
0.948715 0.316132i \(-0.102384\pi\)
\(182\) −5.38231 + 3.65914i −0.398963 + 0.271234i
\(183\) 0 0
\(184\) 1.48615 + 6.63287i 0.109561 + 0.488981i
\(185\) 4.80085i 0.352965i
\(186\) 0 0
\(187\) 3.15341 0.230600
\(188\) 1.72359 4.35761i 0.125706 0.317811i
\(189\) 0 0
\(190\) −8.98349 + 6.10739i −0.651731 + 0.443077i
\(191\) 0.725194 0.0524732 0.0262366 0.999656i \(-0.491648\pi\)
0.0262366 + 0.999656i \(0.491648\pi\)
\(192\) 0 0
\(193\) −15.7648 −1.13478 −0.567388 0.823450i \(-0.692046\pi\)
−0.567388 + 0.823450i \(0.692046\pi\)
\(194\) −5.82833 + 3.96237i −0.418450 + 0.284481i
\(195\) 0 0
\(196\) −0.735620 + 1.85980i −0.0525443 + 0.132843i
\(197\) −5.76032 −0.410406 −0.205203 0.978719i \(-0.565785\pi\)
−0.205203 + 0.978719i \(0.565785\pi\)
\(198\) 0 0
\(199\) 11.7773i 0.834872i −0.908706 0.417436i \(-0.862929\pi\)
0.908706 0.417436i \(-0.137071\pi\)
\(200\) −0.382712 1.70808i −0.0270618 0.120780i
\(201\) 0 0
\(202\) 3.72805 2.53450i 0.262305 0.178327i
\(203\) 9.31771i 0.653975i
\(204\) 0 0
\(205\) 0.658088i 0.0459629i
\(206\) −0.425718 0.626197i −0.0296612 0.0436292i
\(207\) 0 0
\(208\) −12.5923 + 13.4277i −0.873121 + 0.931040i
\(209\) 3.52742i 0.243997i
\(210\) 0 0
\(211\) 19.9971 1.37666 0.688328 0.725399i \(-0.258345\pi\)
0.688328 + 0.725399i \(0.258345\pi\)
\(212\) 5.68895 14.3829i 0.390719 0.987818i
\(213\) 0 0
\(214\) −7.71786 11.3524i −0.527582 0.776031i
\(215\) −18.0900 −1.23373
\(216\) 0 0
\(217\) 1.84927 0.125537
\(218\) 6.38926 + 9.39810i 0.432735 + 0.636519i
\(219\) 0 0
\(220\) −3.74178 1.48001i −0.252271 0.0997824i
\(221\) 15.0979 1.01560
\(222\) 0 0
\(223\) 6.84047i 0.458071i 0.973418 + 0.229036i \(0.0735573\pi\)
−0.973418 + 0.229036i \(0.926443\pi\)
\(224\) −0.880204 + 5.58795i −0.0588111 + 0.373361i
\(225\) 0 0
\(226\) 10.1621 + 14.9477i 0.675976 + 0.994307i
\(227\) 13.9061i 0.922981i 0.887145 + 0.461490i \(0.152685\pi\)
−0.887145 + 0.461490i \(0.847315\pi\)
\(228\) 0 0
\(229\) 3.87934i 0.256354i 0.991751 + 0.128177i \(0.0409126\pi\)
−0.991751 + 0.128177i \(0.959087\pi\)
\(230\) −5.88300 + 3.99953i −0.387913 + 0.263722i
\(231\) 0 0
\(232\) 5.76209 + 25.7168i 0.378300 + 1.68839i
\(233\) 21.8307i 1.43017i −0.699035 0.715087i \(-0.746387\pi\)
0.699035 0.715087i \(-0.253613\pi\)
\(234\) 0 0
\(235\) 4.90427 0.319919
\(236\) 14.8697 + 5.88151i 0.967933 + 0.382853i
\(237\) 0 0
\(238\) 3.83684 2.60847i 0.248706 0.169082i
\(239\) −27.8956 −1.80441 −0.902207 0.431303i \(-0.858054\pi\)
−0.902207 + 0.431303i \(0.858054\pi\)
\(240\) 0 0
\(241\) −6.17606 −0.397835 −0.198918 0.980016i \(-0.563743\pi\)
−0.198918 + 0.980016i \(0.563743\pi\)
\(242\) −11.7843 + 8.01152i −0.757524 + 0.515000i
\(243\) 0 0
\(244\) −19.7736 7.82117i −1.26587 0.500699i
\(245\) −2.09311 −0.133724
\(246\) 0 0
\(247\) 16.8887i 1.07460i
\(248\) 5.10397 1.14359i 0.324103 0.0726181i
\(249\) 0 0
\(250\) 13.7548 9.35117i 0.869931 0.591420i
\(251\) 18.6366i 1.17633i −0.808740 0.588167i \(-0.799850\pi\)
0.808740 0.588167i \(-0.200150\pi\)
\(252\) 0 0
\(253\) 2.31000i 0.145228i
\(254\) −13.2194 19.4446i −0.829456 1.22006i
\(255\) 0 0
\(256\) 1.02624 + 15.9671i 0.0641402 + 0.997941i
\(257\) 8.25845i 0.515148i −0.966259 0.257574i \(-0.917077\pi\)
0.966259 0.257574i \(-0.0829231\pi\)
\(258\) 0 0
\(259\) 2.29364 0.142520
\(260\) −17.9149 7.08602i −1.11104 0.439456i
\(261\) 0 0
\(262\) −11.5769 17.0287i −0.715225 1.05204i
\(263\) −9.34158 −0.576027 −0.288013 0.957626i \(-0.592995\pi\)
−0.288013 + 0.957626i \(0.592995\pi\)
\(264\) 0 0
\(265\) 16.1872 0.994371
\(266\) −2.91785 4.29193i −0.178905 0.263155i
\(267\) 0 0
\(268\) 3.03225 7.66616i 0.185224 0.468286i
\(269\) 11.9972 0.731484 0.365742 0.930716i \(-0.380815\pi\)
0.365742 + 0.930716i \(0.380815\pi\)
\(270\) 0 0
\(271\) 23.7030i 1.43986i −0.694049 0.719928i \(-0.744175\pi\)
0.694049 0.719928i \(-0.255825\pi\)
\(272\) 8.97660 9.57207i 0.544286 0.580392i
\(273\) 0 0
\(274\) −13.7292 20.1946i −0.829414 1.22000i
\(275\) 0.594866i 0.0358718i
\(276\) 0 0
\(277\) 13.7688i 0.827284i −0.910440 0.413642i \(-0.864256\pi\)
0.910440 0.413642i \(-0.135744\pi\)
\(278\) −17.0261 + 11.5751i −1.02116 + 0.694230i
\(279\) 0 0
\(280\) −5.77699 + 1.29439i −0.345241 + 0.0773544i
\(281\) 8.69078i 0.518448i −0.965817 0.259224i \(-0.916533\pi\)
0.965817 0.259224i \(-0.0834669\pi\)
\(282\) 0 0
\(283\) −32.7518 −1.94689 −0.973447 0.228913i \(-0.926483\pi\)
−0.973447 + 0.228913i \(0.926483\pi\)
\(284\) −4.99810 + 12.6362i −0.296583 + 0.749823i
\(285\) 0 0
\(286\) 5.17353 3.51721i 0.305917 0.207977i
\(287\) 0.314406 0.0185588
\(288\) 0 0
\(289\) 6.23727 0.366898
\(290\) −22.8095 + 15.5069i −1.33942 + 0.910599i
\(291\) 0 0
\(292\) 11.7896 29.8066i 0.689934 1.74430i
\(293\) 12.3629 0.722249 0.361124 0.932518i \(-0.382393\pi\)
0.361124 + 0.932518i \(0.382393\pi\)
\(294\) 0 0
\(295\) 16.7351i 0.974354i
\(296\) 6.33044 1.41839i 0.367949 0.0824423i
\(297\) 0 0
\(298\) −23.5941 + 16.0404i −1.36677 + 0.929193i
\(299\) 11.0598i 0.639607i
\(300\) 0 0
\(301\) 8.64261i 0.498152i
\(302\) 9.50627 + 13.9830i 0.547024 + 0.804629i
\(303\) 0 0
\(304\) −10.7074 10.0413i −0.614111 0.575908i
\(305\) 22.2542i 1.27427i
\(306\) 0 0
\(307\) 15.2600 0.870935 0.435468 0.900204i \(-0.356583\pi\)
0.435468 + 0.900204i \(0.356583\pi\)
\(308\) 0.707086 1.78766i 0.0402900 0.101861i
\(309\) 0 0
\(310\) 3.07763 + 4.52695i 0.174798 + 0.257114i
\(311\) −5.12076 −0.290372 −0.145186 0.989404i \(-0.546378\pi\)
−0.145186 + 0.989404i \(0.546378\pi\)
\(312\) 0 0
\(313\) −11.7058 −0.661649 −0.330825 0.943692i \(-0.607327\pi\)
−0.330825 + 0.943692i \(0.607327\pi\)
\(314\) −17.5727 25.8480i −0.991683 1.45869i
\(315\) 0 0
\(316\) −2.34765 0.928583i −0.132066 0.0522369i
\(317\) −18.5302 −1.04076 −0.520379 0.853935i \(-0.674209\pi\)
−0.520379 + 0.853935i \(0.674209\pi\)
\(318\) 0 0
\(319\) 8.95628i 0.501456i
\(320\) −15.1440 + 7.14500i −0.846576 + 0.399418i
\(321\) 0 0
\(322\) −1.91081 2.81064i −0.106485 0.156631i
\(323\) 12.0393i 0.669883i
\(324\) 0 0
\(325\) 2.84811i 0.157985i
\(326\) −13.1051 + 8.90945i −0.725824 + 0.493449i
\(327\) 0 0
\(328\) 0.867760 0.194429i 0.0479140 0.0107356i
\(329\) 2.34305i 0.129176i
\(330\) 0 0
\(331\) −20.4688 −1.12507 −0.562534 0.826774i \(-0.690174\pi\)
−0.562534 + 0.826774i \(0.690174\pi\)
\(332\) −5.57001 2.20315i −0.305694 0.120913i
\(333\) 0 0
\(334\) 2.06573 1.40438i 0.113032 0.0768442i
\(335\) 8.62789 0.471392
\(336\) 0 0
\(337\) −19.9419 −1.08631 −0.543153 0.839634i \(-0.682769\pi\)
−0.543153 + 0.839634i \(0.682769\pi\)
\(338\) 9.56597 6.50339i 0.520320 0.353738i
\(339\) 0 0
\(340\) 12.7709 + 5.05136i 0.692598 + 0.273948i
\(341\) −1.77754 −0.0962590
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −5.34461 23.8536i −0.288162 1.28610i
\(345\) 0 0
\(346\) 5.11367 3.47651i 0.274913 0.186898i
\(347\) 10.1743i 0.546187i 0.961987 + 0.273094i \(0.0880469\pi\)
−0.961987 + 0.273094i \(0.911953\pi\)
\(348\) 0 0
\(349\) 31.9386i 1.70963i 0.518930 + 0.854817i \(0.326331\pi\)
−0.518930 + 0.854817i \(0.673669\pi\)
\(350\) 0.492067 + 0.723792i 0.0263021 + 0.0386883i
\(351\) 0 0
\(352\) 0.846062 5.37120i 0.0450952 0.286286i
\(353\) 24.3932i 1.29832i 0.760653 + 0.649159i \(0.224879\pi\)
−0.760653 + 0.649159i \(0.775121\pi\)
\(354\) 0 0
\(355\) −14.2215 −0.754797
\(356\) −23.9895 9.48875i −1.27144 0.502903i
\(357\) 0 0
\(358\) −13.5222 19.8900i −0.714668 1.05122i
\(359\) −8.59571 −0.453664 −0.226832 0.973934i \(-0.572837\pi\)
−0.226832 + 0.973934i \(0.572837\pi\)
\(360\) 0 0
\(361\) −5.53276 −0.291198
\(362\) 6.76335 + 9.94834i 0.355474 + 0.522873i
\(363\) 0 0
\(364\) 3.38540 8.55899i 0.177443 0.448613i
\(365\) 33.5458 1.75587
\(366\) 0 0
\(367\) 29.1285i 1.52050i 0.649632 + 0.760249i \(0.274923\pi\)
−0.649632 + 0.760249i \(0.725077\pi\)
\(368\) −7.01192 6.57572i −0.365522 0.342783i
\(369\) 0 0
\(370\) 3.81717 + 5.61476i 0.198445 + 0.291897i
\(371\) 7.73354i 0.401505i
\(372\) 0 0
\(373\) 4.56533i 0.236384i 0.992991 + 0.118192i \(0.0377098\pi\)
−0.992991 + 0.118192i \(0.962290\pi\)
\(374\) −3.68802 + 2.50728i −0.190703 + 0.129649i
\(375\) 0 0
\(376\) 1.44895 + 6.46680i 0.0747237 + 0.333500i
\(377\) 42.8810i 2.20848i
\(378\) 0 0
\(379\) 15.5673 0.799641 0.399820 0.916593i \(-0.369072\pi\)
0.399820 + 0.916593i \(0.369072\pi\)
\(380\) 5.65049 14.2856i 0.289864 0.732836i
\(381\) 0 0
\(382\) −0.848139 + 0.576604i −0.0433946 + 0.0295016i
\(383\) 3.08947 0.157865 0.0789323 0.996880i \(-0.474849\pi\)
0.0789323 + 0.996880i \(0.474849\pi\)
\(384\) 0 0
\(385\) 2.01192 0.102537
\(386\) 18.4375 12.5347i 0.938444 0.637998i
\(387\) 0 0
\(388\) 3.66594 9.26825i 0.186110 0.470524i
\(389\) −30.6022 −1.55160 −0.775798 0.630982i \(-0.782652\pi\)
−0.775798 + 0.630982i \(0.782652\pi\)
\(390\) 0 0
\(391\) 7.88413i 0.398718i
\(392\) −0.618402 2.76000i −0.0312340 0.139401i
\(393\) 0 0
\(394\) 6.73689 4.58005i 0.339400 0.230740i
\(395\) 2.64216i 0.132942i
\(396\) 0 0
\(397\) 0.403742i 0.0202632i −0.999949 0.0101316i \(-0.996775\pi\)
0.999949 0.0101316i \(-0.00322505\pi\)
\(398\) 9.36419 + 13.7740i 0.469385 + 0.690427i
\(399\) 0 0
\(400\) 1.80570 + 1.69337i 0.0902849 + 0.0846684i
\(401\) 30.3779i 1.51700i −0.651672 0.758501i \(-0.725932\pi\)
0.651672 0.758501i \(-0.274068\pi\)
\(402\) 0 0
\(403\) −8.51051 −0.423939
\(404\) −2.34489 + 5.92838i −0.116663 + 0.294948i
\(405\) 0 0
\(406\) −7.40855 10.8974i −0.367680 0.540828i
\(407\) −2.20467 −0.109281
\(408\) 0 0
\(409\) −17.8549 −0.882869 −0.441434 0.897293i \(-0.645530\pi\)
−0.441434 + 0.897293i \(0.645530\pi\)
\(410\) 0.523248 + 0.769656i 0.0258414 + 0.0380106i
\(411\) 0 0
\(412\) 0.995784 + 0.393869i 0.0490587 + 0.0194045i
\(413\) −7.99530 −0.393423
\(414\) 0 0
\(415\) 6.26877i 0.307722i
\(416\) 4.05079 25.7163i 0.198606 1.26085i
\(417\) 0 0
\(418\) 2.80467 + 4.12544i 0.137181 + 0.201782i
\(419\) 31.1609i 1.52231i 0.648569 + 0.761156i \(0.275368\pi\)
−0.648569 + 0.761156i \(0.724632\pi\)
\(420\) 0 0
\(421\) 7.19292i 0.350562i 0.984518 + 0.175281i \(0.0560833\pi\)
−0.984518 + 0.175281i \(0.943917\pi\)
\(422\) −23.3873 + 15.8998i −1.13848 + 0.773988i
\(423\) 0 0
\(424\) 4.78244 + 21.3445i 0.232256 + 1.03658i
\(425\) 2.03031i 0.0984844i
\(426\) 0 0
\(427\) 10.6321 0.514522
\(428\) 18.0526 + 7.14047i 0.872605 + 0.345148i
\(429\) 0 0
\(430\) 21.1568 14.3834i 1.02027 0.693629i
\(431\) −25.7598 −1.24081 −0.620404 0.784283i \(-0.713031\pi\)
−0.620404 + 0.784283i \(0.713031\pi\)
\(432\) 0 0
\(433\) −3.66449 −0.176104 −0.0880521 0.996116i \(-0.528064\pi\)
−0.0880521 + 0.996116i \(0.528064\pi\)
\(434\) −2.16278 + 1.47036i −0.103817 + 0.0705796i
\(435\) 0 0
\(436\) −14.9449 5.91127i −0.715732 0.283098i
\(437\) 8.81926 0.421882
\(438\) 0 0
\(439\) 39.4350i 1.88213i −0.338227 0.941064i \(-0.609827\pi\)
0.338227 0.941064i \(-0.390173\pi\)
\(440\) 5.55290 1.24418i 0.264724 0.0593138i
\(441\) 0 0
\(442\) −17.6575 + 12.0044i −0.839883 + 0.570992i
\(443\) 36.1437i 1.71724i −0.512612 0.858620i \(-0.671322\pi\)
0.512612 0.858620i \(-0.328678\pi\)
\(444\) 0 0
\(445\) 26.9990i 1.27988i
\(446\) −5.43888 8.00016i −0.257538 0.378819i
\(447\) 0 0
\(448\) −3.41357 7.23516i −0.161276 0.341829i
\(449\) 24.9465i 1.17730i 0.808389 + 0.588649i \(0.200340\pi\)
−0.808389 + 0.588649i \(0.799660\pi\)
\(450\) 0 0
\(451\) −0.302210 −0.0142305
\(452\) −23.7700 9.40190i −1.11804 0.442228i
\(453\) 0 0
\(454\) −11.0568 16.2637i −0.518921 0.763292i
\(455\) 9.63272 0.451589
\(456\) 0 0
\(457\) 15.1856 0.710354 0.355177 0.934799i \(-0.384421\pi\)
0.355177 + 0.934799i \(0.384421\pi\)
\(458\) −3.08448 4.53702i −0.144128 0.212001i
\(459\) 0 0
\(460\) 3.70032 9.35518i 0.172528 0.436188i
\(461\) −9.29479 −0.432902 −0.216451 0.976294i \(-0.569448\pi\)
−0.216451 + 0.976294i \(0.569448\pi\)
\(462\) 0 0
\(463\) 2.13438i 0.0991930i 0.998769 + 0.0495965i \(0.0157935\pi\)
−0.998769 + 0.0495965i \(0.984206\pi\)
\(464\) −27.1865 25.4953i −1.26210 1.18359i
\(465\) 0 0
\(466\) 17.3576 + 25.5317i 0.804077 + 1.18273i
\(467\) 41.6077i 1.92538i 0.270612 + 0.962688i \(0.412774\pi\)
−0.270612 + 0.962688i \(0.587226\pi\)
\(468\) 0 0
\(469\) 4.12203i 0.190338i
\(470\) −5.73571 + 3.89940i −0.264569 + 0.179866i
\(471\) 0 0
\(472\) −22.0670 + 4.94431i −1.01572 + 0.227580i
\(473\) 8.30736i 0.381973i
\(474\) 0 0
\(475\) −2.27112 −0.104206
\(476\) −2.41332 + 6.10138i −0.110614 + 0.279656i
\(477\) 0 0
\(478\) 32.6248 22.1799i 1.49222 1.01448i
\(479\) −40.9442 −1.87079 −0.935394 0.353608i \(-0.884955\pi\)
−0.935394 + 0.353608i \(0.884955\pi\)
\(480\) 0 0
\(481\) −10.5556 −0.481292
\(482\) 7.22312 4.91061i 0.329004 0.223672i
\(483\) 0 0
\(484\) 7.41217 18.7395i 0.336917 0.851795i
\(485\) 10.4310 0.473645
\(486\) 0 0
\(487\) 14.2039i 0.643639i −0.946801 0.321820i \(-0.895706\pi\)
0.946801 0.321820i \(-0.104294\pi\)
\(488\) 29.3445 6.57490i 1.32836 0.297632i
\(489\) 0 0
\(490\) 2.44797 1.66424i 0.110588 0.0751828i
\(491\) 39.3013i 1.77364i −0.462113 0.886821i \(-0.652909\pi\)
0.462113 0.886821i \(-0.347091\pi\)
\(492\) 0 0
\(493\) 30.5682i 1.37672i
\(494\) 13.4282 + 19.7519i 0.604165 + 0.888678i
\(495\) 0 0
\(496\) −5.06000 + 5.39566i −0.227201 + 0.242272i
\(497\) 6.79440i 0.304771i
\(498\) 0 0
\(499\) −32.3257 −1.44710 −0.723548 0.690274i \(-0.757490\pi\)
−0.723548 + 0.690274i \(0.757490\pi\)
\(500\) −8.65159 + 21.8730i −0.386911 + 0.978191i
\(501\) 0 0
\(502\) 14.8180 + 21.7962i 0.661362 + 0.972810i
\(503\) 19.7861 0.882217 0.441108 0.897454i \(-0.354585\pi\)
0.441108 + 0.897454i \(0.354585\pi\)
\(504\) 0 0
\(505\) −6.67210 −0.296904
\(506\) 1.83669 + 2.70162i 0.0816507 + 0.120102i
\(507\) 0 0
\(508\) 30.9210 + 12.2304i 1.37190 + 0.542636i
\(509\) −33.7174 −1.49450 −0.747248 0.664545i \(-0.768625\pi\)
−0.747248 + 0.664545i \(0.768625\pi\)
\(510\) 0 0
\(511\) 16.0267i 0.708981i
\(512\) −13.8957 17.8580i −0.614109 0.789222i
\(513\) 0 0
\(514\) 6.56632 + 9.65854i 0.289628 + 0.426020i
\(515\) 1.12070i 0.0493842i
\(516\) 0 0
\(517\) 2.25216i 0.0990500i
\(518\) −2.68249 + 1.82368i −0.117862 + 0.0801279i
\(519\) 0 0
\(520\) 26.5863 5.95689i 1.16588 0.261227i
\(521\) 28.4958i 1.24842i 0.781255 + 0.624212i \(0.214580\pi\)
−0.781255 + 0.624212i \(0.785420\pi\)
\(522\) 0 0
\(523\) −4.42637 −0.193552 −0.0967758 0.995306i \(-0.530853\pi\)
−0.0967758 + 0.995306i \(0.530853\pi\)
\(524\) 27.0792 + 10.7108i 1.18296 + 0.467905i
\(525\) 0 0
\(526\) 10.9253 7.42753i 0.476366 0.323855i
\(527\) 6.06682 0.264275
\(528\) 0 0
\(529\) −17.2246 −0.748894
\(530\) −18.9315 + 12.8705i −0.822330 + 0.559058i
\(531\) 0 0
\(532\) 6.82505 + 2.69956i 0.295903 + 0.117041i
\(533\) −1.44693 −0.0626734
\(534\) 0 0
\(535\) 20.3173i 0.878394i
\(536\) 2.54907 + 11.3768i 0.110103 + 0.491403i
\(537\) 0 0
\(538\) −14.0312 + 9.53905i −0.604927 + 0.411258i
\(539\) 0.961211i 0.0414023i
\(540\) 0 0
\(541\) 33.7548i 1.45123i −0.688101 0.725615i \(-0.741555\pi\)
0.688101 0.725615i \(-0.258445\pi\)
\(542\) 18.8464 + 27.7215i 0.809520 + 1.19074i
\(543\) 0 0
\(544\) −2.88765 + 18.3322i −0.123807 + 0.785986i
\(545\) 16.8198i 0.720480i
\(546\) 0 0
\(547\) −14.6641 −0.626992 −0.313496 0.949589i \(-0.601500\pi\)
−0.313496 + 0.949589i \(0.601500\pi\)
\(548\) 32.1136 + 12.7021i 1.37183 + 0.542608i
\(549\) 0 0
\(550\) −0.472980 0.695716i −0.0201680 0.0296654i
\(551\) 34.1939 1.45671
\(552\) 0 0
\(553\) 1.26231 0.0536790
\(554\) 10.9476 + 16.1030i 0.465118 + 0.684152i
\(555\) 0 0
\(556\) 10.7092 27.0750i 0.454170 1.14824i
\(557\) 15.4373 0.654099 0.327050 0.945007i \(-0.393946\pi\)
0.327050 + 0.945007i \(0.393946\pi\)
\(558\) 0 0
\(559\) 39.7741i 1.68227i
\(560\) 5.72721 6.10713i 0.242019 0.258073i
\(561\) 0 0
\(562\) 6.91007 + 10.1642i 0.291484 + 0.428749i
\(563\) 26.9472i 1.13569i 0.823135 + 0.567845i \(0.192223\pi\)
−0.823135 + 0.567845i \(0.807777\pi\)
\(564\) 0 0
\(565\) 26.7519i 1.12546i
\(566\) 38.3044 26.0411i 1.61005 1.09459i
\(567\) 0 0
\(568\) −4.20167 18.7525i −0.176298 0.786838i
\(569\) 3.63013i 0.152183i 0.997101 + 0.0760915i \(0.0242441\pi\)
−0.997101 + 0.0760915i \(0.975756\pi\)
\(570\) 0 0
\(571\) −16.2293 −0.679174 −0.339587 0.940575i \(-0.610287\pi\)
−0.339587 + 0.940575i \(0.610287\pi\)
\(572\) −3.25408 + 8.22699i −0.136060 + 0.343988i
\(573\) 0 0
\(574\) −0.367709 + 0.249985i −0.0153479 + 0.0104342i
\(575\) −1.48728 −0.0620240
\(576\) 0 0
\(577\) 42.1511 1.75477 0.877386 0.479786i \(-0.159286\pi\)
0.877386 + 0.479786i \(0.159286\pi\)
\(578\) −7.29470 + 4.95927i −0.303419 + 0.206279i
\(579\) 0 0
\(580\) 14.3468 36.2718i 0.595720 1.50610i
\(581\) 2.99495 0.124251
\(582\) 0 0
\(583\) 7.43356i 0.307867i
\(584\) 9.91097 + 44.2337i 0.410119 + 1.83040i
\(585\) 0 0
\(586\) −14.4588 + 9.82979i −0.597289 + 0.406065i
\(587\) 22.7097i 0.937328i 0.883377 + 0.468664i \(0.155264\pi\)
−0.883377 + 0.468664i \(0.844736\pi\)
\(588\) 0 0
\(589\) 6.78640i 0.279629i
\(590\) −13.3061 19.5722i −0.547804 0.805777i
\(591\) 0 0
\(592\) −6.27589 + 6.69221i −0.257938 + 0.275048i
\(593\) 22.8921i 0.940068i 0.882648 + 0.470034i \(0.155758\pi\)
−0.882648 + 0.470034i \(0.844242\pi\)
\(594\) 0 0
\(595\) −6.86680 −0.281511
\(596\) 14.8404 37.5195i 0.607885 1.53686i
\(597\) 0 0
\(598\) 8.79371 + 12.9349i 0.359602 + 0.528945i
\(599\) −31.0216 −1.26751 −0.633755 0.773534i \(-0.718487\pi\)
−0.633755 + 0.773534i \(0.718487\pi\)
\(600\) 0 0
\(601\) −36.3657 −1.48339 −0.741693 0.670739i \(-0.765977\pi\)
−0.741693 + 0.670739i \(0.765977\pi\)
\(602\) 6.87177 + 10.1078i 0.280072 + 0.411964i
\(603\) 0 0
\(604\) −22.2358 8.79508i −0.904762 0.357867i
\(605\) 21.0904 0.857446
\(606\) 0 0
\(607\) 27.1019i 1.10003i 0.835154 + 0.550016i \(0.185378\pi\)
−0.835154 + 0.550016i \(0.814622\pi\)
\(608\) 20.5065 + 3.23015i 0.831649 + 0.131000i
\(609\) 0 0
\(610\) 17.6944 + 26.0270i 0.716424 + 1.05380i
\(611\) 10.7829i 0.436231i
\(612\) 0 0
\(613\) 21.7164i 0.877118i −0.898702 0.438559i \(-0.855489\pi\)
0.898702 0.438559i \(-0.144511\pi\)
\(614\) −17.8471 + 12.1333i −0.720251 + 0.489660i
\(615\) 0 0
\(616\) 0.594415 + 2.65294i 0.0239496 + 0.106890i
\(617\) 15.0335i 0.605224i −0.953114 0.302612i \(-0.902141\pi\)
0.953114 0.302612i \(-0.0978587\pi\)
\(618\) 0 0
\(619\) −12.2249 −0.491359 −0.245680 0.969351i \(-0.579011\pi\)
−0.245680 + 0.969351i \(0.579011\pi\)
\(620\) −7.19879 2.84739i −0.289110 0.114354i
\(621\) 0 0
\(622\) 5.98891 4.07154i 0.240133 0.163254i
\(623\) 12.8990 0.516787
\(624\) 0 0
\(625\) −21.5226 −0.860906
\(626\) 13.6903 9.30730i 0.547174 0.371995i
\(627\) 0 0
\(628\) 41.1037 + 16.2580i 1.64021 + 0.648765i
\(629\) 7.52465 0.300028
\(630\) 0 0
\(631\) 0.290118i 0.0115494i 0.999983 + 0.00577472i \(0.00183816\pi\)
−0.999983 + 0.00577472i \(0.998162\pi\)
\(632\) 3.48398 0.780617i 0.138585 0.0310513i
\(633\) 0 0
\(634\) 21.6717 14.7334i 0.860692 0.585138i
\(635\) 34.8000i 1.38100i
\(636\) 0 0
\(637\) 4.60210i 0.182342i
\(638\) 7.12117 + 10.4747i 0.281930 + 0.414696i
\(639\) 0 0
\(640\) 12.0304 20.3974i 0.475544 0.806277i
\(641\) 32.2612i 1.27424i 0.770764 + 0.637120i \(0.219875\pi\)
−0.770764 + 0.637120i \(0.780125\pi\)
\(642\) 0 0
\(643\) −25.2641 −0.996317 −0.498159 0.867086i \(-0.665990\pi\)
−0.498159 + 0.867086i \(0.665990\pi\)
\(644\) 4.46950 + 1.76785i 0.176123 + 0.0696632i
\(645\) 0 0
\(646\) −9.57248 14.0803i −0.376624 0.553984i
\(647\) −15.6735 −0.616188 −0.308094 0.951356i \(-0.599691\pi\)
−0.308094 + 0.951356i \(0.599691\pi\)
\(648\) 0 0
\(649\) 7.68517 0.301669
\(650\) −2.26454 3.33096i −0.0888226 0.130651i
\(651\) 0 0
\(652\) 8.24291 20.8398i 0.322817 0.816150i
\(653\) −17.4580 −0.683183 −0.341591 0.939849i \(-0.610966\pi\)
−0.341591 + 0.939849i \(0.610966\pi\)
\(654\) 0 0
\(655\) 30.4763i 1.19081i
\(656\) −0.860283 + 0.917351i −0.0335884 + 0.0358165i
\(657\) 0 0
\(658\) −1.86297 2.74028i −0.0726260 0.106827i
\(659\) 34.8692i 1.35831i −0.733995 0.679155i \(-0.762347\pi\)
0.733995 0.679155i \(-0.237653\pi\)
\(660\) 0 0
\(661\) 13.7607i 0.535230i 0.963526 + 0.267615i \(0.0862355\pi\)
−0.963526 + 0.267615i \(0.913765\pi\)
\(662\) 23.9390 16.2748i 0.930415 0.632540i
\(663\) 0 0
\(664\) 8.26605 1.85208i 0.320785 0.0718748i
\(665\) 7.68126i 0.297866i
\(666\) 0 0
\(667\) 22.3925 0.867040
\(668\) −1.29931 + 3.28494i −0.0502720 + 0.127098i
\(669\) 0 0
\(670\) −10.0906 + 6.86006i −0.389834 + 0.265027i
\(671\) −10.2197 −0.394526
\(672\) 0 0
\(673\) −8.50938 −0.328013 −0.164006 0.986459i \(-0.552442\pi\)
−0.164006 + 0.986459i \(0.552442\pi\)
\(674\) 23.3227 15.8559i 0.898359 0.610746i
\(675\) 0 0
\(676\) −6.01686 + 15.2119i −0.231418 + 0.585072i
\(677\) 3.14515 0.120878 0.0604390 0.998172i \(-0.480750\pi\)
0.0604390 + 0.998172i \(0.480750\pi\)
\(678\) 0 0
\(679\) 4.98346i 0.191248i
\(680\) −18.9523 + 4.24644i −0.726789 + 0.162844i
\(681\) 0 0
\(682\) 2.07889 1.41333i 0.0796048 0.0541190i
\(683\) 9.12590i 0.349193i 0.984640 + 0.174596i \(0.0558621\pi\)
−0.984640 + 0.174596i \(0.944138\pi\)
\(684\) 0 0
\(685\) 36.1423i 1.38093i
\(686\) 0.795104 + 1.16953i 0.0303572 + 0.0446530i
\(687\) 0 0
\(688\) 25.2168 + 23.6480i 0.961380 + 0.901573i
\(689\) 35.5905i 1.35589i
\(690\) 0 0
\(691\) −15.6298 −0.594586 −0.297293 0.954786i \(-0.596084\pi\)
−0.297293 + 0.954786i \(0.596084\pi\)
\(692\) −3.21643 + 8.13180i −0.122270 + 0.309125i
\(693\) 0 0
\(694\) −8.08965 11.8992i −0.307079 0.451689i
\(695\) 30.4716 1.15585
\(696\) 0 0
\(697\) 1.03146 0.0390693
\(698\) −25.3945 37.3533i −0.961196 1.41384i
\(699\) 0 0
\(700\) −1.15098 0.455255i −0.0435029 0.0172070i
\(701\) 50.4853 1.90680 0.953402 0.301701i \(-0.0975546\pi\)
0.953402 + 0.301701i \(0.0975546\pi\)
\(702\) 0 0
\(703\) 8.41714i 0.317458i
\(704\) 3.28116 + 6.95451i 0.123664 + 0.262108i
\(705\) 0 0
\(706\) −19.3951 28.5286i −0.729944 1.07369i
\(707\) 3.18764i 0.119884i
\(708\) 0 0
\(709\) 28.7706i 1.08050i 0.841504 + 0.540251i \(0.181671\pi\)
−0.841504 + 0.540251i \(0.818329\pi\)
\(710\) 16.6325 11.3075i 0.624206 0.424364i
\(711\) 0 0
\(712\) 35.6011 7.97676i 1.33421 0.298942i
\(713\) 4.44419i 0.166436i
\(714\) 0 0
\(715\) −9.25907 −0.346270
\(716\) 31.6292 + 12.5105i 1.18204 + 0.467541i
\(717\) 0 0
\(718\) 10.0530 6.83448i 0.375174 0.255061i
\(719\) −0.582170 −0.0217113 −0.0108556 0.999941i \(-0.503456\pi\)
−0.0108556 + 0.999941i \(0.503456\pi\)
\(720\) 0 0
\(721\) −0.535425 −0.0199403
\(722\) 6.47076 4.39912i 0.240817 0.163718i
\(723\) 0 0
\(724\) −15.8199 6.25737i −0.587943 0.232553i
\(725\) −5.76647 −0.214161
\(726\) 0 0
\(727\) 6.92907i 0.256985i 0.991710 + 0.128492i \(0.0410138\pi\)
−0.991710 + 0.128492i \(0.958986\pi\)
\(728\) 2.84595 + 12.7018i 0.105478 + 0.470759i
\(729\) 0 0
\(730\) −39.2330 + 26.6724i −1.45208 + 0.987189i
\(731\) 28.3535i 1.04869i
\(732\) 0 0
\(733\) 1.86770i 0.0689850i −0.999405 0.0344925i \(-0.989019\pi\)
0.999405 0.0344925i \(-0.0109815\pi\)
\(734\) −23.1602 34.0668i −0.854859 1.25743i
\(735\) 0 0
\(736\) 13.4291 + 2.11532i 0.495002 + 0.0779717i
\(737\) 3.96214i 0.145947i
\(738\) 0 0
\(739\) −38.7036 −1.42373 −0.711867 0.702314i \(-0.752150\pi\)
−0.711867 + 0.702314i \(0.752150\pi\)
\(740\) −8.92863 3.53160i −0.328223 0.129824i
\(741\) 0 0
\(742\) −6.14897 9.04464i −0.225736 0.332039i
\(743\) −23.3088 −0.855118 −0.427559 0.903987i \(-0.640626\pi\)
−0.427559 + 0.903987i \(0.640626\pi\)
\(744\) 0 0
\(745\) 42.2263 1.54705
\(746\) −3.62991 5.33931i −0.132900 0.195486i
\(747\) 0 0
\(748\) 2.31971 5.86471i 0.0848170 0.214435i
\(749\) −9.70673 −0.354676
\(750\) 0 0
\(751\) 26.6345i 0.971908i 0.873984 + 0.485954i \(0.161528\pi\)
−0.873984 + 0.485954i \(0.838472\pi\)
\(752\) −6.83637 6.41109i −0.249297 0.233788i
\(753\) 0 0
\(754\) 34.0948 + 50.1508i 1.24166 + 1.82638i
\(755\) 25.0253i 0.910764i
\(756\) 0 0
\(757\) 26.4285i 0.960562i 0.877115 + 0.480281i \(0.159465\pi\)
−0.877115 + 0.480281i \(0.840535\pi\)
\(758\) −18.2065 + 12.3777i −0.661292 + 0.449577i
\(759\) 0 0
\(760\) 4.75010 + 21.2002i 0.172304 + 0.769013i
\(761\) 13.2617i 0.480736i 0.970682 + 0.240368i \(0.0772681\pi\)
−0.970682 + 0.240368i \(0.922732\pi\)
\(762\) 0 0
\(763\) 8.03576 0.290914
\(764\) 0.533467 1.34872i 0.0193002 0.0487949i
\(765\) 0 0
\(766\) −3.61324 + 2.45645i −0.130552 + 0.0887552i
\(767\) 36.7951 1.32860
\(768\) 0 0
\(769\) −4.34986 −0.156860 −0.0784300 0.996920i \(-0.524991\pi\)
−0.0784300 + 0.996920i \(0.524991\pi\)
\(770\) −2.35301 + 1.59969i −0.0847967 + 0.0576488i
\(771\) 0 0
\(772\) −11.5969 + 29.3194i −0.417382 + 1.05523i
\(773\) 34.8861 1.25477 0.627383 0.778711i \(-0.284126\pi\)
0.627383 + 0.778711i \(0.284126\pi\)
\(774\) 0 0
\(775\) 1.14446i 0.0411102i
\(776\) 3.08178 + 13.7543i 0.110630 + 0.493752i
\(777\) 0 0
\(778\) 35.7904 24.3320i 1.28315 0.872343i
\(779\) 1.15380i 0.0413391i
\(780\) 0 0
\(781\) 6.53085i 0.233692i
\(782\) −6.26870 9.22076i −0.224168 0.329734i
\(783\) 0 0
\(784\) 2.91773 + 2.73622i 0.104204 + 0.0977220i