Properties

Label 912.2.cc.c.497.2
Level $912$
Weight $2$
Character 912.497
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 497.2
Root \(-1.73189 - 0.0237018i\) of defining polynomial
Character \(\chi\) \(=\) 912.497
Dual form 912.2.cc.c.545.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.324081 + 1.70146i) q^{3} +(2.22841 + 0.392929i) q^{5} +(1.16829 + 2.02354i) q^{7} +(-2.78994 + 1.10282i) q^{9} +O(q^{10})\) \(q+(0.324081 + 1.70146i) q^{3} +(2.22841 + 0.392929i) q^{5} +(1.16829 + 2.02354i) q^{7} +(-2.78994 + 1.10282i) q^{9} +(-2.52163 - 1.45586i) q^{11} +(-0.451929 + 1.24167i) q^{13} +(0.0536321 + 3.91889i) q^{15} +(-3.72112 + 4.43466i) q^{17} +(1.79800 + 3.97079i) q^{19} +(-3.06435 + 2.64359i) q^{21} +(8.06194 - 1.42154i) q^{23} +(0.112953 + 0.0411116i) q^{25} +(-2.78058 - 4.38958i) q^{27} +(1.64718 - 1.38215i) q^{29} +(-5.27928 + 3.04799i) q^{31} +(1.65988 - 4.76227i) q^{33} +(1.80832 + 4.96833i) q^{35} +2.98954i q^{37} +(-2.25911 - 0.366540i) q^{39} +(8.52555 - 3.10304i) q^{41} +(0.0666074 - 0.377749i) q^{43} +(-6.65047 + 1.36129i) q^{45} +(-6.57494 - 7.83571i) q^{47} +(0.770194 - 1.33401i) q^{49} +(-8.75134 - 4.89415i) q^{51} +(-0.494197 - 2.80273i) q^{53} +(-5.04717 - 4.23508i) q^{55} +(-6.17345 + 4.34609i) q^{57} +(2.53779 + 2.12946i) q^{59} +(1.01879 + 5.77787i) q^{61} +(-5.49107 - 4.35714i) q^{63} +(-1.49497 + 2.58936i) q^{65} +(10.4361 + 12.4373i) q^{67} +(5.03141 + 13.2564i) q^{69} +(-2.29622 + 13.0225i) q^{71} +(5.84733 - 2.12826i) q^{73} +(-0.0333438 + 0.205509i) q^{75} -6.80348i q^{77} +(-1.77569 - 4.87866i) q^{79} +(6.56756 - 6.15363i) q^{81} +(1.62533 - 0.938386i) q^{83} +(-10.0347 + 8.42009i) q^{85} +(2.88550 + 2.35469i) q^{87} +(-5.82289 - 2.11936i) q^{89} +(-3.04054 + 0.536130i) q^{91} +(-6.89696 - 7.99469i) q^{93} +(2.44644 + 9.55504i) q^{95} +(6.13336 - 7.30946i) q^{97} +(8.64076 + 1.28086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.324081 + 1.70146i 0.187108 + 0.982339i
\(4\) 0 0
\(5\) 2.22841 + 0.392929i 0.996575 + 0.175723i 0.648067 0.761583i \(-0.275577\pi\)
0.348508 + 0.937306i \(0.386689\pi\)
\(6\) 0 0
\(7\) 1.16829 + 2.02354i 0.441572 + 0.764826i 0.997806 0.0661999i \(-0.0210875\pi\)
−0.556234 + 0.831026i \(0.687754\pi\)
\(8\) 0 0
\(9\) −2.78994 + 1.10282i −0.929981 + 0.367608i
\(10\) 0 0
\(11\) −2.52163 1.45586i −0.760299 0.438959i 0.0691039 0.997609i \(-0.477986\pi\)
−0.829403 + 0.558650i \(0.811319\pi\)
\(12\) 0 0
\(13\) −0.451929 + 1.24167i −0.125343 + 0.344376i −0.986453 0.164041i \(-0.947547\pi\)
0.861111 + 0.508417i \(0.169769\pi\)
\(14\) 0 0
\(15\) 0.0536321 + 3.91889i 0.0138478 + 1.01185i
\(16\) 0 0
\(17\) −3.72112 + 4.43466i −0.902504 + 1.07556i 0.0942898 + 0.995545i \(0.469942\pi\)
−0.996793 + 0.0800172i \(0.974502\pi\)
\(18\) 0 0
\(19\) 1.79800 + 3.97079i 0.412489 + 0.910962i
\(20\) 0 0
\(21\) −3.06435 + 2.64359i −0.668697 + 0.576879i
\(22\) 0 0
\(23\) 8.06194 1.42154i 1.68103 0.296411i 0.750023 0.661412i \(-0.230042\pi\)
0.931007 + 0.365001i \(0.118931\pi\)
\(24\) 0 0
\(25\) 0.112953 + 0.0411116i 0.0225906 + 0.00822231i
\(26\) 0 0
\(27\) −2.78058 4.38958i −0.535123 0.844774i
\(28\) 0 0
\(29\) 1.64718 1.38215i 0.305875 0.256659i −0.476910 0.878952i \(-0.658243\pi\)
0.782784 + 0.622293i \(0.213799\pi\)
\(30\) 0 0
\(31\) −5.27928 + 3.04799i −0.948186 + 0.547436i −0.892517 0.451014i \(-0.851063\pi\)
−0.0556692 + 0.998449i \(0.517729\pi\)
\(32\) 0 0
\(33\) 1.65988 4.76227i 0.288948 0.829005i
\(34\) 0 0
\(35\) 1.80832 + 4.96833i 0.305662 + 0.839801i
\(36\) 0 0
\(37\) 2.98954i 0.491477i 0.969336 + 0.245738i \(0.0790304\pi\)
−0.969336 + 0.245738i \(0.920970\pi\)
\(38\) 0 0
\(39\) −2.25911 0.366540i −0.361747 0.0586934i
\(40\) 0 0
\(41\) 8.52555 3.10304i 1.33147 0.484614i 0.424352 0.905497i \(-0.360502\pi\)
0.907115 + 0.420883i \(0.138280\pi\)
\(42\) 0 0
\(43\) 0.0666074 0.377749i 0.0101575 0.0576062i −0.979308 0.202377i \(-0.935133\pi\)
0.989465 + 0.144771i \(0.0462445\pi\)
\(44\) 0 0
\(45\) −6.65047 + 1.36129i −0.991393 + 0.202929i
\(46\) 0 0
\(47\) −6.57494 7.83571i −0.959054 1.14296i −0.989661 0.143424i \(-0.954189\pi\)
0.0306076 0.999531i \(-0.490256\pi\)
\(48\) 0 0
\(49\) 0.770194 1.33401i 0.110028 0.190574i
\(50\) 0 0
\(51\) −8.75134 4.89415i −1.22543 0.685318i
\(52\) 0 0
\(53\) −0.494197 2.80273i −0.0678832 0.384985i −0.999754 0.0221937i \(-0.992935\pi\)
0.931870 0.362791i \(-0.118176\pi\)
\(54\) 0 0
\(55\) −5.04717 4.23508i −0.680560 0.571058i
\(56\) 0 0
\(57\) −6.17345 + 4.34609i −0.817694 + 0.575653i
\(58\) 0 0
\(59\) 2.53779 + 2.12946i 0.330392 + 0.277232i 0.792860 0.609404i \(-0.208591\pi\)
−0.462468 + 0.886636i \(0.653036\pi\)
\(60\) 0 0
\(61\) 1.01879 + 5.77787i 0.130443 + 0.739780i 0.977925 + 0.208956i \(0.0670064\pi\)
−0.847482 + 0.530824i \(0.821882\pi\)
\(62\) 0 0
\(63\) −5.49107 4.35714i −0.691810 0.548948i
\(64\) 0 0
\(65\) −1.49497 + 2.58936i −0.185428 + 0.321171i
\(66\) 0 0
\(67\) 10.4361 + 12.4373i 1.27497 + 1.51945i 0.735668 + 0.677342i \(0.236868\pi\)
0.539305 + 0.842111i \(0.318687\pi\)
\(68\) 0 0
\(69\) 5.03141 + 13.2564i 0.605711 + 1.59588i
\(70\) 0 0
\(71\) −2.29622 + 13.0225i −0.272511 + 1.54549i 0.474247 + 0.880392i \(0.342720\pi\)
−0.746758 + 0.665095i \(0.768391\pi\)
\(72\) 0 0
\(73\) 5.84733 2.12826i 0.684379 0.249093i 0.0236522 0.999720i \(-0.492471\pi\)
0.660726 + 0.750627i \(0.270248\pi\)
\(74\) 0 0
\(75\) −0.0333438 + 0.205509i −0.00385021 + 0.0237301i
\(76\) 0 0
\(77\) 6.80348i 0.775329i
\(78\) 0 0
\(79\) −1.77569 4.87866i −0.199781 0.548893i 0.798832 0.601554i \(-0.205452\pi\)
−0.998612 + 0.0526618i \(0.983229\pi\)
\(80\) 0 0
\(81\) 6.56756 6.15363i 0.729729 0.683736i
\(82\) 0 0
\(83\) 1.62533 0.938386i 0.178403 0.103001i −0.408139 0.912920i \(-0.633822\pi\)
0.586542 + 0.809919i \(0.300489\pi\)
\(84\) 0 0
\(85\) −10.0347 + 8.42009i −1.08841 + 0.913288i
\(86\) 0 0
\(87\) 2.88550 + 2.35469i 0.309358 + 0.252450i
\(88\) 0 0
\(89\) −5.82289 2.11936i −0.617225 0.224651i 0.0144367 0.999896i \(-0.495405\pi\)
−0.631661 + 0.775244i \(0.717627\pi\)
\(90\) 0 0
\(91\) −3.04054 + 0.536130i −0.318735 + 0.0562017i
\(92\) 0 0
\(93\) −6.89696 7.99469i −0.715181 0.829011i
\(94\) 0 0
\(95\) 2.44644 + 9.55504i 0.251000 + 0.980326i
\(96\) 0 0
\(97\) 6.13336 7.30946i 0.622748 0.742163i −0.358792 0.933418i \(-0.616811\pi\)
0.981540 + 0.191255i \(0.0612557\pi\)
\(98\) 0 0
\(99\) 8.64076 + 1.28086i 0.868429 + 0.128732i
\(100\) 0 0
\(101\) −4.28105 + 11.7621i −0.425980 + 1.17037i 0.522251 + 0.852792i \(0.325092\pi\)
−0.948232 + 0.317580i \(0.897130\pi\)
\(102\) 0 0
\(103\) −7.59279 4.38370i −0.748140 0.431939i 0.0768818 0.997040i \(-0.475504\pi\)
−0.825021 + 0.565102i \(0.808837\pi\)
\(104\) 0 0
\(105\) −7.86738 + 4.68693i −0.767777 + 0.457398i
\(106\) 0 0
\(107\) −4.04583 7.00758i −0.391125 0.677449i 0.601473 0.798893i \(-0.294581\pi\)
−0.992598 + 0.121444i \(0.961247\pi\)
\(108\) 0 0
\(109\) 7.26213 + 1.28051i 0.695586 + 0.122651i 0.510252 0.860025i \(-0.329552\pi\)
0.185334 + 0.982676i \(0.440663\pi\)
\(110\) 0 0
\(111\) −5.08658 + 0.968852i −0.482797 + 0.0919594i
\(112\) 0 0
\(113\) −14.8779 −1.39960 −0.699799 0.714340i \(-0.746727\pi\)
−0.699799 + 0.714340i \(0.746727\pi\)
\(114\) 0 0
\(115\) 18.5239 1.72736
\(116\) 0 0
\(117\) −0.108480 3.96257i −0.0100290 0.366340i
\(118\) 0 0
\(119\) −13.3210 2.34886i −1.22114 0.215320i
\(120\) 0 0
\(121\) −1.26093 2.18399i −0.114630 0.198545i
\(122\) 0 0
\(123\) 8.04268 + 13.5002i 0.725184 + 1.21728i
\(124\) 0 0
\(125\) −9.56260 5.52097i −0.855305 0.493811i
\(126\) 0 0
\(127\) 2.54056 6.98012i 0.225438 0.619386i −0.774475 0.632605i \(-0.781986\pi\)
0.999913 + 0.0132192i \(0.00420794\pi\)
\(128\) 0 0
\(129\) 0.664312 0.00909146i 0.0584894 0.000800458i
\(130\) 0 0
\(131\) 11.4406 13.6344i 0.999574 1.19125i 0.0180637 0.999837i \(-0.494250\pi\)
0.981510 0.191409i \(-0.0613057\pi\)
\(132\) 0 0
\(133\) −5.93447 + 8.27736i −0.514584 + 0.717738i
\(134\) 0 0
\(135\) −4.47148 10.8743i −0.384843 0.935915i
\(136\) 0 0
\(137\) 16.1747 2.85204i 1.38190 0.243666i 0.567215 0.823570i \(-0.308021\pi\)
0.814685 + 0.579904i \(0.196910\pi\)
\(138\) 0 0
\(139\) 18.1680 + 6.61260i 1.54099 + 0.560873i 0.966282 0.257487i \(-0.0828944\pi\)
0.574705 + 0.818360i \(0.305117\pi\)
\(140\) 0 0
\(141\) 11.2013 13.7264i 0.943323 1.15597i
\(142\) 0 0
\(143\) 2.94729 2.47307i 0.246465 0.206809i
\(144\) 0 0
\(145\) 4.21369 2.43277i 0.349928 0.202031i
\(146\) 0 0
\(147\) 2.51938 + 0.878126i 0.207795 + 0.0724266i
\(148\) 0 0
\(149\) −2.20295 6.05256i −0.180473 0.495845i 0.816161 0.577824i \(-0.196098\pi\)
−0.996634 + 0.0819794i \(0.973876\pi\)
\(150\) 0 0
\(151\) 3.02833i 0.246442i 0.992379 + 0.123221i \(0.0393223\pi\)
−0.992379 + 0.123221i \(0.960678\pi\)
\(152\) 0 0
\(153\) 5.49107 16.4762i 0.443926 1.33202i
\(154\) 0 0
\(155\) −12.9620 + 4.71780i −1.04114 + 0.378942i
\(156\) 0 0
\(157\) 3.32082 18.8333i 0.265030 1.50306i −0.503918 0.863751i \(-0.668109\pi\)
0.768949 0.639311i \(-0.220780\pi\)
\(158\) 0 0
\(159\) 4.60858 1.74917i 0.365484 0.138718i
\(160\) 0 0
\(161\) 12.2952 + 14.6529i 0.968999 + 1.15481i
\(162\) 0 0
\(163\) 3.09435 5.35958i 0.242368 0.419794i −0.719020 0.694989i \(-0.755409\pi\)
0.961388 + 0.275195i \(0.0887424\pi\)
\(164\) 0 0
\(165\) 5.57013 9.96007i 0.433634 0.775391i
\(166\) 0 0
\(167\) −0.758731 4.30298i −0.0587124 0.332975i 0.941277 0.337636i \(-0.109627\pi\)
−0.999989 + 0.00466148i \(0.998516\pi\)
\(168\) 0 0
\(169\) 8.62108 + 7.23395i 0.663160 + 0.556458i
\(170\) 0 0
\(171\) −9.39540 9.09541i −0.718484 0.695543i
\(172\) 0 0
\(173\) 11.4117 + 9.57556i 0.867616 + 0.728016i 0.963595 0.267367i \(-0.0861536\pi\)
−0.0959786 + 0.995383i \(0.530598\pi\)
\(174\) 0 0
\(175\) 0.0487712 + 0.276595i 0.00368676 + 0.0209086i
\(176\) 0 0
\(177\) −2.80074 + 5.00807i −0.210517 + 0.376429i
\(178\) 0 0
\(179\) −1.68012 + 2.91005i −0.125578 + 0.217507i −0.921959 0.387288i \(-0.873412\pi\)
0.796381 + 0.604796i \(0.206745\pi\)
\(180\) 0 0
\(181\) 12.7706 + 15.2194i 0.949231 + 1.13125i 0.991232 + 0.132132i \(0.0421822\pi\)
−0.0420013 + 0.999118i \(0.513373\pi\)
\(182\) 0 0
\(183\) −9.50065 + 3.60593i −0.702308 + 0.266558i
\(184\) 0 0
\(185\) −1.17467 + 6.66191i −0.0863638 + 0.489794i
\(186\) 0 0
\(187\) 15.8395 5.76511i 1.15830 0.421587i
\(188\) 0 0
\(189\) 5.63396 10.7549i 0.409810 0.782305i
\(190\) 0 0
\(191\) 10.2346i 0.740548i −0.928923 0.370274i \(-0.879264\pi\)
0.928923 0.370274i \(-0.120736\pi\)
\(192\) 0 0
\(193\) −0.784644 2.15579i −0.0564799 0.155177i 0.908244 0.418441i \(-0.137423\pi\)
−0.964724 + 0.263264i \(0.915201\pi\)
\(194\) 0 0
\(195\) −4.89019 1.70447i −0.350194 0.122060i
\(196\) 0 0
\(197\) 5.46822 3.15708i 0.389595 0.224933i −0.292390 0.956299i \(-0.594450\pi\)
0.681984 + 0.731367i \(0.261117\pi\)
\(198\) 0 0
\(199\) 7.96251 6.68134i 0.564447 0.473628i −0.315351 0.948975i \(-0.602122\pi\)
0.879798 + 0.475348i \(0.157678\pi\)
\(200\) 0 0
\(201\) −17.7794 + 21.7873i −1.25406 + 1.53676i
\(202\) 0 0
\(203\) 4.72123 + 1.71839i 0.331365 + 0.120607i
\(204\) 0 0
\(205\) 20.2177 3.56492i 1.41206 0.248985i
\(206\) 0 0
\(207\) −20.9246 + 12.8569i −1.45436 + 0.893616i
\(208\) 0 0
\(209\) 1.24704 12.6305i 0.0862598 0.873670i
\(210\) 0 0
\(211\) 3.58388 4.27111i 0.246725 0.294035i −0.628442 0.777856i \(-0.716307\pi\)
0.875167 + 0.483821i \(0.160752\pi\)
\(212\) 0 0
\(213\) −22.9015 + 0.313418i −1.56918 + 0.0214751i
\(214\) 0 0
\(215\) 0.296857 0.815608i 0.0202455 0.0556240i
\(216\) 0 0
\(217\) −12.3355 7.12188i −0.837386 0.483465i
\(218\) 0 0
\(219\) 5.51615 + 9.25929i 0.372747 + 0.625685i
\(220\) 0 0
\(221\) −3.82468 6.62453i −0.257276 0.445614i
\(222\) 0 0
\(223\) −5.10735 0.900564i −0.342014 0.0603062i 3.40741e−6 1.00000i \(-0.499999\pi\)
−0.342017 + 0.939694i \(0.611110\pi\)
\(224\) 0 0
\(225\) −0.360471 + 0.00986833i −0.0240314 + 0.000657889i
\(226\) 0 0
\(227\) 17.0369 1.13078 0.565391 0.824823i \(-0.308725\pi\)
0.565391 + 0.824823i \(0.308725\pi\)
\(228\) 0 0
\(229\) 24.5203 1.62035 0.810173 0.586191i \(-0.199373\pi\)
0.810173 + 0.586191i \(0.199373\pi\)
\(230\) 0 0
\(231\) 11.5759 2.20488i 0.761636 0.145070i
\(232\) 0 0
\(233\) −22.4936 3.96623i −1.47360 0.259836i −0.621585 0.783346i \(-0.713511\pi\)
−0.852019 + 0.523510i \(0.824622\pi\)
\(234\) 0 0
\(235\) −11.5728 20.0447i −0.754925 1.30757i
\(236\) 0 0
\(237\) 7.72539 4.60235i 0.501818 0.298955i
\(238\) 0 0
\(239\) −2.62883 1.51775i −0.170045 0.0981753i 0.412562 0.910929i \(-0.364634\pi\)
−0.582607 + 0.812754i \(0.697967\pi\)
\(240\) 0 0
\(241\) −1.35157 + 3.71341i −0.0870624 + 0.239202i −0.975582 0.219638i \(-0.929512\pi\)
0.888519 + 0.458840i \(0.151735\pi\)
\(242\) 0 0
\(243\) 12.5986 + 9.18018i 0.808199 + 0.588909i
\(244\) 0 0
\(245\) 2.24048 2.67010i 0.143139 0.170586i
\(246\) 0 0
\(247\) −5.74296 + 0.437996i −0.365416 + 0.0278690i
\(248\) 0 0
\(249\) 2.12337 + 2.46133i 0.134563 + 0.155980i
\(250\) 0 0
\(251\) −7.14276 + 1.25946i −0.450847 + 0.0794965i −0.394461 0.918913i \(-0.629069\pi\)
−0.0563857 + 0.998409i \(0.517958\pi\)
\(252\) 0 0
\(253\) −22.3988 8.15248i −1.40820 0.512542i
\(254\) 0 0
\(255\) −17.5785 14.3448i −1.10081 0.898308i
\(256\) 0 0
\(257\) 7.10091 5.95837i 0.442942 0.371673i −0.393867 0.919168i \(-0.628863\pi\)
0.836809 + 0.547495i \(0.184418\pi\)
\(258\) 0 0
\(259\) −6.04944 + 3.49265i −0.375894 + 0.217023i
\(260\) 0 0
\(261\) −3.07128 + 5.67268i −0.190108 + 0.351130i
\(262\) 0 0
\(263\) −1.21399 3.33541i −0.0748578 0.205670i 0.896620 0.442801i \(-0.146015\pi\)
−0.971478 + 0.237131i \(0.923793\pi\)
\(264\) 0 0
\(265\) 6.43982i 0.395595i
\(266\) 0 0
\(267\) 1.71892 10.5943i 0.105196 0.648358i
\(268\) 0 0
\(269\) −4.70855 + 1.71377i −0.287086 + 0.104491i −0.481549 0.876419i \(-0.659926\pi\)
0.194463 + 0.980910i \(0.437703\pi\)
\(270\) 0 0
\(271\) 1.60600 9.10806i 0.0975574 0.553275i −0.896376 0.443294i \(-0.853810\pi\)
0.993934 0.109981i \(-0.0350791\pi\)
\(272\) 0 0
\(273\) −1.89759 4.99962i −0.114847 0.302591i
\(274\) 0 0
\(275\) −0.224973 0.268112i −0.0135664 0.0161678i
\(276\) 0 0
\(277\) 3.80040 6.58248i 0.228344 0.395503i −0.728974 0.684542i \(-0.760002\pi\)
0.957317 + 0.289039i \(0.0933356\pi\)
\(278\) 0 0
\(279\) 11.3675 14.3258i 0.680554 0.857665i
\(280\) 0 0
\(281\) 2.50185 + 14.1887i 0.149248 + 0.846425i 0.963858 + 0.266417i \(0.0858397\pi\)
−0.814610 + 0.580009i \(0.803049\pi\)
\(282\) 0 0
\(283\) −7.59307 6.37134i −0.451361 0.378737i 0.388579 0.921415i \(-0.372966\pi\)
−0.839941 + 0.542678i \(0.817410\pi\)
\(284\) 0 0
\(285\) −15.4647 + 7.25913i −0.916049 + 0.429994i
\(286\) 0 0
\(287\) 16.2394 + 13.6265i 0.958584 + 0.804348i
\(288\) 0 0
\(289\) −2.86743 16.2620i −0.168673 0.956589i
\(290\) 0 0
\(291\) 14.4245 + 8.06682i 0.845577 + 0.472886i
\(292\) 0 0
\(293\) −4.11218 + 7.12251i −0.240236 + 0.416102i −0.960782 0.277306i \(-0.910558\pi\)
0.720545 + 0.693408i \(0.243892\pi\)
\(294\) 0 0
\(295\) 4.81851 + 5.74247i 0.280544 + 0.334340i
\(296\) 0 0
\(297\) 0.620963 + 15.1170i 0.0360319 + 0.877178i
\(298\) 0 0
\(299\) −1.87835 + 10.6527i −0.108628 + 0.616059i
\(300\) 0 0
\(301\) 0.842207 0.306538i 0.0485440 0.0176686i
\(302\) 0 0
\(303\) −21.4001 3.47217i −1.22941 0.199471i
\(304\) 0 0
\(305\) 13.2758i 0.760168i
\(306\) 0 0
\(307\) 3.47152 + 9.53794i 0.198130 + 0.544359i 0.998476 0.0551795i \(-0.0175731\pi\)
−0.800346 + 0.599538i \(0.795351\pi\)
\(308\) 0 0
\(309\) 4.99801 14.3395i 0.284327 0.815746i
\(310\) 0 0
\(311\) −9.98316 + 5.76378i −0.566093 + 0.326834i −0.755587 0.655048i \(-0.772648\pi\)
0.189494 + 0.981882i \(0.439315\pi\)
\(312\) 0 0
\(313\) 2.29638 1.92690i 0.129799 0.108915i −0.575577 0.817748i \(-0.695222\pi\)
0.705376 + 0.708833i \(0.250778\pi\)
\(314\) 0 0
\(315\) −10.5243 11.8671i −0.592977 0.668635i
\(316\) 0 0
\(317\) −15.4509 5.62366i −0.867808 0.315856i −0.130529 0.991445i \(-0.541667\pi\)
−0.737279 + 0.675588i \(0.763890\pi\)
\(318\) 0 0
\(319\) −6.16581 + 1.08720i −0.345219 + 0.0608714i
\(320\) 0 0
\(321\) 10.6120 9.15485i 0.592302 0.510974i
\(322\) 0 0
\(323\) −24.2997 6.80228i −1.35207 0.378489i
\(324\) 0 0
\(325\) −0.102094 + 0.121670i −0.00566313 + 0.00674906i
\(326\) 0 0
\(327\) 0.174781 + 12.7712i 0.00966540 + 0.706250i
\(328\) 0 0
\(329\) 8.17442 22.4590i 0.450670 1.23821i
\(330\) 0 0
\(331\) −1.51206 0.872986i −0.0831101 0.0479837i 0.457869 0.889020i \(-0.348613\pi\)
−0.540979 + 0.841036i \(0.681946\pi\)
\(332\) 0 0
\(333\) −3.29693 8.34064i −0.180671 0.457064i
\(334\) 0 0
\(335\) 18.3689 + 31.8160i 1.00360 + 1.73829i
\(336\) 0 0
\(337\) −14.3139 2.52392i −0.779727 0.137487i −0.230402 0.973096i \(-0.574004\pi\)
−0.549325 + 0.835609i \(0.685115\pi\)
\(338\) 0 0
\(339\) −4.82166 25.3142i −0.261876 1.37488i
\(340\) 0 0
\(341\) 17.7498 0.961207
\(342\) 0 0
\(343\) 19.9553 1.07749
\(344\) 0 0
\(345\) 6.00323 + 31.5176i 0.323203 + 1.69685i
\(346\) 0 0
\(347\) 5.30901 + 0.936123i 0.285003 + 0.0502537i 0.314322 0.949316i \(-0.398223\pi\)
−0.0293192 + 0.999570i \(0.509334\pi\)
\(348\) 0 0
\(349\) −1.57657 2.73070i −0.0843920 0.146171i 0.820740 0.571302i \(-0.193561\pi\)
−0.905132 + 0.425131i \(0.860228\pi\)
\(350\) 0 0
\(351\) 6.70701 1.46877i 0.357994 0.0783971i
\(352\) 0 0
\(353\) 19.6094 + 11.3215i 1.04370 + 0.602582i 0.920880 0.389847i \(-0.127472\pi\)
0.122822 + 0.992429i \(0.460805\pi\)
\(354\) 0 0
\(355\) −10.2338 + 28.1172i −0.543155 + 1.49231i
\(356\) 0 0
\(357\) −0.320603 23.4265i −0.0169681 1.23986i
\(358\) 0 0
\(359\) 10.4708 12.4786i 0.552628 0.658596i −0.415341 0.909666i \(-0.636338\pi\)
0.967969 + 0.251069i \(0.0807822\pi\)
\(360\) 0 0
\(361\) −12.5344 + 14.2790i −0.659705 + 0.751525i
\(362\) 0 0
\(363\) 3.30734 2.85321i 0.173590 0.149755i
\(364\) 0 0
\(365\) 13.8665 2.44504i 0.725806 0.127979i
\(366\) 0 0
\(367\) −13.5022 4.91441i −0.704811 0.256530i −0.0353474 0.999375i \(-0.511254\pi\)
−0.669464 + 0.742845i \(0.733476\pi\)
\(368\) 0 0
\(369\) −20.3637 + 18.0595i −1.06009 + 0.940139i
\(370\) 0 0
\(371\) 5.09407 4.27443i 0.264471 0.221918i
\(372\) 0 0
\(373\) −31.7907 + 18.3543i −1.64606 + 0.950352i −0.667441 + 0.744663i \(0.732610\pi\)
−0.978617 + 0.205689i \(0.934056\pi\)
\(374\) 0 0
\(375\) 6.29466 18.0596i 0.325055 0.932596i
\(376\) 0 0
\(377\) 0.971760 + 2.66989i 0.0500482 + 0.137506i
\(378\) 0 0
\(379\) 26.0481i 1.33800i 0.743263 + 0.669000i \(0.233277\pi\)
−0.743263 + 0.669000i \(0.766723\pi\)
\(380\) 0 0
\(381\) 12.6998 + 2.06053i 0.650628 + 0.105564i
\(382\) 0 0
\(383\) −2.22943 + 0.811445i −0.113918 + 0.0414629i −0.398350 0.917233i \(-0.630417\pi\)
0.284432 + 0.958696i \(0.408195\pi\)
\(384\) 0 0
\(385\) 2.67328 15.1609i 0.136243 0.772673i
\(386\) 0 0
\(387\) 0.230760 + 1.12735i 0.0117302 + 0.0573067i
\(388\) 0 0
\(389\) −15.0557 17.9426i −0.763353 0.909728i 0.234702 0.972067i \(-0.424588\pi\)
−0.998055 + 0.0623389i \(0.980144\pi\)
\(390\) 0 0
\(391\) −23.6954 + 41.0416i −1.19833 + 2.07556i
\(392\) 0 0
\(393\) 26.9062 + 15.0472i 1.35724 + 0.759029i
\(394\) 0 0
\(395\) −2.03999 11.5694i −0.102643 0.582119i
\(396\) 0 0
\(397\) 5.26511 + 4.41795i 0.264248 + 0.221731i 0.765279 0.643699i \(-0.222601\pi\)
−0.501031 + 0.865430i \(0.667046\pi\)
\(398\) 0 0
\(399\) −16.0069 7.41473i −0.801345 0.371201i
\(400\) 0 0
\(401\) −23.7988 19.9695i −1.18845 0.997231i −0.999885 0.0151712i \(-0.995171\pi\)
−0.188569 0.982060i \(-0.560385\pi\)
\(402\) 0 0
\(403\) −1.39873 7.93257i −0.0696755 0.395150i
\(404\) 0 0
\(405\) 17.0532 11.1322i 0.847378 0.553164i
\(406\) 0 0
\(407\) 4.35235 7.53850i 0.215738 0.373670i
\(408\) 0 0
\(409\) −5.64702 6.72985i −0.279227 0.332770i 0.608143 0.793827i \(-0.291915\pi\)
−0.887370 + 0.461057i \(0.847470\pi\)
\(410\) 0 0
\(411\) 10.0946 + 26.5964i 0.497928 + 1.31190i
\(412\) 0 0
\(413\) −1.34417 + 7.62314i −0.0661420 + 0.375110i
\(414\) 0 0
\(415\) 3.99063 1.45247i 0.195892 0.0712989i
\(416\) 0 0
\(417\) −5.36319 + 33.0551i −0.262637 + 1.61872i
\(418\) 0 0
\(419\) 0.268652i 0.0131245i −0.999978 0.00656225i \(-0.997911\pi\)
0.999978 0.00656225i \(-0.00208885\pi\)
\(420\) 0 0
\(421\) 6.44528 + 17.7083i 0.314124 + 0.863048i 0.991813 + 0.127699i \(0.0407592\pi\)
−0.677689 + 0.735348i \(0.737019\pi\)
\(422\) 0 0
\(423\) 26.9851 + 14.6102i 1.31206 + 0.710372i
\(424\) 0 0
\(425\) −0.602627 + 0.347927i −0.0292317 + 0.0168769i
\(426\) 0 0
\(427\) −10.5015 + 8.81180i −0.508203 + 0.426433i
\(428\) 0 0
\(429\) 5.16300 + 4.21323i 0.249272 + 0.203417i
\(430\) 0 0
\(431\) −8.09752 2.94726i −0.390044 0.141964i 0.139551 0.990215i \(-0.455434\pi\)
−0.529595 + 0.848250i \(0.677656\pi\)
\(432\) 0 0
\(433\) 8.52374 1.50296i 0.409625 0.0722279i 0.0349610 0.999389i \(-0.488869\pi\)
0.374664 + 0.927161i \(0.377758\pi\)
\(434\) 0 0
\(435\) 5.50485 + 6.38102i 0.263937 + 0.305946i
\(436\) 0 0
\(437\) 20.1400 + 29.4564i 0.963426 + 1.40909i
\(438\) 0 0
\(439\) 16.0959 19.1824i 0.768216 0.915524i −0.230122 0.973162i \(-0.573912\pi\)
0.998338 + 0.0576380i \(0.0183569\pi\)
\(440\) 0 0
\(441\) −0.677615 + 4.57121i −0.0322674 + 0.217677i
\(442\) 0 0
\(443\) 2.20842 6.06757i 0.104925 0.288279i −0.876110 0.482112i \(-0.839870\pi\)
0.981035 + 0.193833i \(0.0620920\pi\)
\(444\) 0 0
\(445\) −12.1430 7.01078i −0.575634 0.332343i
\(446\) 0 0
\(447\) 9.58426 5.70975i 0.453320 0.270062i
\(448\) 0 0
\(449\) −11.3528 19.6637i −0.535774 0.927988i −0.999125 0.0418133i \(-0.986687\pi\)
0.463351 0.886175i \(-0.346647\pi\)
\(450\) 0 0
\(451\) −26.0159 4.58730i −1.22504 0.216007i
\(452\) 0 0
\(453\) −5.15258 + 0.981423i −0.242089 + 0.0461113i
\(454\) 0 0
\(455\) −6.98624 −0.327520
\(456\) 0 0
\(457\) 9.08970 0.425198 0.212599 0.977140i \(-0.431807\pi\)
0.212599 + 0.977140i \(0.431807\pi\)
\(458\) 0 0
\(459\) 29.8131 + 4.00323i 1.39156 + 0.186855i
\(460\) 0 0
\(461\) −19.6634 3.46719i −0.915818 0.161483i −0.304174 0.952617i \(-0.598380\pi\)
−0.611644 + 0.791133i \(0.709491\pi\)
\(462\) 0 0
\(463\) −0.304139 0.526785i −0.0141346 0.0244818i 0.858872 0.512191i \(-0.171166\pi\)
−0.873006 + 0.487709i \(0.837833\pi\)
\(464\) 0 0
\(465\) −12.2279 20.5255i −0.567055 0.951845i
\(466\) 0 0
\(467\) 13.6575 + 7.88518i 0.631995 + 0.364883i 0.781524 0.623875i \(-0.214442\pi\)
−0.149529 + 0.988757i \(0.547776\pi\)
\(468\) 0 0
\(469\) −12.9749 + 35.6482i −0.599124 + 1.64608i
\(470\) 0 0
\(471\) 33.1204 0.453270i 1.52611 0.0208856i
\(472\) 0 0
\(473\) −0.717910 + 0.855572i −0.0330095 + 0.0393392i
\(474\) 0 0
\(475\) 0.0398441 + 0.522432i 0.00182817 + 0.0239708i
\(476\) 0 0
\(477\) 4.46970 + 7.27445i 0.204653 + 0.333074i
\(478\) 0 0
\(479\) −9.47350 + 1.67043i −0.432855 + 0.0763241i −0.385831 0.922570i \(-0.626085\pi\)
−0.0470248 + 0.998894i \(0.514974\pi\)
\(480\) 0 0
\(481\) −3.71200 1.35106i −0.169253 0.0616030i
\(482\) 0 0
\(483\) −20.9467 + 25.6686i −0.953106 + 1.16796i
\(484\) 0 0
\(485\) 16.5397 13.8785i 0.751031 0.630190i
\(486\) 0 0
\(487\) −28.7513 + 16.5996i −1.30285 + 0.752198i −0.980891 0.194557i \(-0.937673\pi\)
−0.321954 + 0.946755i \(0.604340\pi\)
\(488\) 0 0
\(489\) 10.1219 + 3.52798i 0.457730 + 0.159541i
\(490\) 0 0
\(491\) 3.75074 + 10.3051i 0.169268 + 0.465061i 0.995102 0.0988527i \(-0.0315173\pi\)
−0.825834 + 0.563914i \(0.809295\pi\)
\(492\) 0 0
\(493\) 12.4478i 0.560623i
\(494\) 0 0
\(495\) 18.7519 + 6.24949i 0.842833 + 0.280894i
\(496\) 0 0
\(497\) −29.0342 + 10.5676i −1.30236 + 0.474021i
\(498\) 0 0
\(499\) 5.30316 30.0757i 0.237402 1.34637i −0.600094 0.799930i \(-0.704870\pi\)
0.837496 0.546444i \(-0.184019\pi\)
\(500\) 0 0
\(501\) 7.07546 2.68547i 0.316108 0.119978i
\(502\) 0 0
\(503\) −10.7776 12.8442i −0.480550 0.572697i 0.470238 0.882540i \(-0.344168\pi\)
−0.950788 + 0.309843i \(0.899724\pi\)
\(504\) 0 0
\(505\) −14.1616 + 24.5286i −0.630182 + 1.09151i
\(506\) 0 0
\(507\) −9.51436 + 17.0128i −0.422547 + 0.755566i
\(508\) 0 0
\(509\) 7.27364 + 41.2508i 0.322398 + 1.82841i 0.527360 + 0.849642i \(0.323182\pi\)
−0.204962 + 0.978770i \(0.565707\pi\)
\(510\) 0 0
\(511\) 11.1380 + 9.34588i 0.492716 + 0.413438i
\(512\) 0 0
\(513\) 12.4306 18.9336i 0.548825 0.835937i
\(514\) 0 0
\(515\) −15.1974 12.7521i −0.669676 0.561925i
\(516\) 0 0
\(517\) 5.17184 + 29.3310i 0.227457 + 1.28997i
\(518\) 0 0
\(519\) −12.5941 + 22.5198i −0.552821 + 0.988511i
\(520\) 0 0
\(521\) 5.82256 10.0850i 0.255091 0.441831i −0.709829 0.704374i \(-0.751228\pi\)
0.964920 + 0.262543i \(0.0845612\pi\)
\(522\) 0 0
\(523\) −1.24233 1.48055i −0.0543231 0.0647398i 0.738199 0.674583i \(-0.235677\pi\)
−0.792522 + 0.609844i \(0.791232\pi\)
\(524\) 0 0
\(525\) −0.454810 + 0.172622i −0.0198495 + 0.00753382i
\(526\) 0 0
\(527\) 6.12802 34.7537i 0.266941 1.51390i
\(528\) 0 0
\(529\) 41.3611 15.0542i 1.79831 0.654531i
\(530\) 0 0
\(531\) −9.42870 3.14233i −0.409171 0.136366i
\(532\) 0 0
\(533\) 11.9882i 0.519268i
\(534\) 0 0
\(535\) −6.26229 17.2055i −0.270742 0.743858i
\(536\) 0 0
\(537\) −5.49583 1.91557i −0.237163 0.0826627i
\(538\) 0 0
\(539\) −3.88428 + 2.24259i −0.167308 + 0.0965953i
\(540\) 0 0
\(541\) −7.95720 + 6.67688i −0.342107 + 0.287062i −0.797611 0.603172i \(-0.793903\pi\)
0.455505 + 0.890233i \(0.349459\pi\)
\(542\) 0 0
\(543\) −21.7565 + 26.6610i −0.933662 + 1.14413i
\(544\) 0 0
\(545\) 15.6798 + 5.70700i 0.671651 + 0.244461i
\(546\) 0 0
\(547\) −24.0156 + 4.23461i −1.02683 + 0.181059i −0.661600 0.749857i \(-0.730122\pi\)
−0.365235 + 0.930915i \(0.619011\pi\)
\(548\) 0 0
\(549\) −9.21434 14.9964i −0.393258 0.640029i
\(550\) 0 0
\(551\) 8.44988 + 4.05552i 0.359977 + 0.172771i
\(552\) 0 0
\(553\) 7.79765 9.29287i 0.331590 0.395173i
\(554\) 0 0
\(555\) −11.7157 + 0.160335i −0.497303 + 0.00680585i
\(556\) 0 0
\(557\) −6.96784 + 19.1440i −0.295237 + 0.811156i 0.700042 + 0.714101i \(0.253164\pi\)
−0.995279 + 0.0970547i \(0.969058\pi\)
\(558\) 0 0
\(559\) 0.438936 + 0.253420i 0.0185650 + 0.0107185i
\(560\) 0 0
\(561\) 14.9424 + 25.0820i 0.630869 + 1.05896i
\(562\) 0 0
\(563\) −0.391026 0.677277i −0.0164798 0.0285438i 0.857668 0.514204i \(-0.171913\pi\)
−0.874148 + 0.485660i \(0.838579\pi\)
\(564\) 0 0
\(565\) −33.1541 5.84597i −1.39481 0.245942i
\(566\) 0 0
\(567\) 20.1249 + 6.10050i 0.845167 + 0.256197i
\(568\) 0 0
\(569\) 12.5732 0.527098 0.263549 0.964646i \(-0.415107\pi\)
0.263549 + 0.964646i \(0.415107\pi\)
\(570\) 0 0
\(571\) 2.14694 0.0898468 0.0449234 0.998990i \(-0.485696\pi\)
0.0449234 + 0.998990i \(0.485696\pi\)
\(572\) 0 0
\(573\) 17.4137 3.31683i 0.727469 0.138563i
\(574\) 0 0
\(575\) 0.969062 + 0.170872i 0.0404127 + 0.00712585i
\(576\) 0 0
\(577\) −19.9348 34.5282i −0.829898 1.43743i −0.898117 0.439756i \(-0.855065\pi\)
0.0682191 0.997670i \(-0.478268\pi\)
\(578\) 0 0
\(579\) 3.41371 2.03369i 0.141869 0.0845174i
\(580\) 0 0
\(581\) 3.79772 + 2.19262i 0.157556 + 0.0909650i
\(582\) 0 0
\(583\) −2.83421 + 7.78693i −0.117381 + 0.322502i
\(584\) 0 0
\(585\) 1.31527 8.87286i 0.0543798 0.366848i
\(586\) 0 0
\(587\) −28.9490 + 34.5001i −1.19485 + 1.42397i −0.314757 + 0.949172i \(0.601923\pi\)
−0.880095 + 0.474797i \(0.842521\pi\)
\(588\) 0 0
\(589\) −21.5951 15.4826i −0.889810 0.637951i
\(590\) 0 0
\(591\) 7.14380 + 8.28082i 0.293856 + 0.340627i
\(592\) 0 0
\(593\) 29.2417 5.15610i 1.20081 0.211736i 0.462763 0.886482i \(-0.346858\pi\)
0.738050 + 0.674746i \(0.235747\pi\)
\(594\) 0 0
\(595\) −28.7618 10.4684i −1.17912 0.429164i
\(596\) 0 0
\(597\) 13.9485 + 11.3826i 0.570876 + 0.465859i
\(598\) 0 0
\(599\) −23.2268 + 19.4896i −0.949023 + 0.796325i −0.979133 0.203222i \(-0.934859\pi\)
0.0301101 + 0.999547i \(0.490414\pi\)
\(600\) 0 0
\(601\) 19.5471 11.2855i 0.797343 0.460346i −0.0451983 0.998978i \(-0.514392\pi\)
0.842541 + 0.538632i \(0.181059\pi\)
\(602\) 0 0
\(603\) −42.8322 23.1901i −1.74426 0.944373i
\(604\) 0 0
\(605\) −1.95171 5.36229i −0.0793484 0.218008i
\(606\) 0 0
\(607\) 22.1708i 0.899886i 0.893057 + 0.449943i \(0.148556\pi\)
−0.893057 + 0.449943i \(0.851444\pi\)
\(608\) 0 0
\(609\) −1.39371 + 8.58989i −0.0564759 + 0.348080i
\(610\) 0 0
\(611\) 12.7007 4.62269i 0.513817 0.187014i
\(612\) 0 0
\(613\) −4.39349 + 24.9167i −0.177451 + 1.00638i 0.757825 + 0.652458i \(0.226262\pi\)
−0.935276 + 0.353919i \(0.884849\pi\)
\(614\) 0 0
\(615\) 12.6177 + 33.2443i 0.508797 + 1.34054i
\(616\) 0 0
\(617\) −3.45217 4.11414i −0.138979 0.165629i 0.692065 0.721835i \(-0.256701\pi\)
−0.831045 + 0.556206i \(0.812257\pi\)
\(618\) 0 0
\(619\) 10.8898 18.8617i 0.437699 0.758117i −0.559813 0.828619i \(-0.689127\pi\)
0.997512 + 0.0705023i \(0.0224602\pi\)
\(620\) 0 0
\(621\) −28.6568 31.4358i −1.14996 1.26148i
\(622\) 0 0
\(623\) −2.51422 14.2589i −0.100730 0.571269i
\(624\) 0 0
\(625\) −19.6004 16.4467i −0.784018 0.657869i
\(626\) 0 0
\(627\) 21.8945 1.97151i 0.874380 0.0787345i
\(628\) 0 0
\(629\) −13.2576 11.1244i −0.528614 0.443560i
\(630\) 0 0
\(631\) 2.49759 + 14.1646i 0.0994276 + 0.563882i 0.993300 + 0.115561i \(0.0368667\pi\)
−0.893873 + 0.448321i \(0.852022\pi\)
\(632\) 0 0
\(633\) 8.42859 + 4.71366i 0.335006 + 0.187351i
\(634\) 0 0
\(635\) 8.40409 14.5563i 0.333506 0.577650i
\(636\) 0 0
\(637\) 1.30833 + 1.55920i 0.0518378 + 0.0617779i
\(638\) 0 0
\(639\) −7.95520 38.8644i −0.314703 1.53745i
\(640\) 0 0
\(641\) 1.24354 7.05244i 0.0491167 0.278555i −0.950351 0.311180i \(-0.899276\pi\)
0.999468 + 0.0326255i \(0.0103869\pi\)
\(642\) 0 0
\(643\) −9.97359 + 3.63009i −0.393320 + 0.143157i −0.531106 0.847305i \(-0.678224\pi\)
0.137786 + 0.990462i \(0.456001\pi\)
\(644\) 0 0
\(645\) 1.48393 + 0.240768i 0.0584297 + 0.00948022i
\(646\) 0 0
\(647\) 25.2527i 0.992786i 0.868098 + 0.496393i \(0.165342\pi\)
−0.868098 + 0.496393i \(0.834658\pi\)
\(648\) 0 0
\(649\) −3.29916 9.06437i −0.129503 0.355808i
\(650\) 0 0
\(651\) 8.11992 23.2964i 0.318245 0.913057i
\(652\) 0 0
\(653\) 4.44155 2.56433i 0.173811 0.100350i −0.410570 0.911829i \(-0.634670\pi\)
0.584382 + 0.811479i \(0.301337\pi\)
\(654\) 0 0
\(655\) 30.8518 25.8877i 1.20548 1.01152i
\(656\) 0 0
\(657\) −13.9666 + 12.3863i −0.544890 + 0.483235i
\(658\) 0 0
\(659\) 39.0596 + 14.2165i 1.52154 + 0.553797i 0.961533 0.274688i \(-0.0885747\pi\)
0.560011 + 0.828485i \(0.310797\pi\)
\(660\) 0 0
\(661\) −46.7645 + 8.24585i −1.81893 + 0.320726i −0.976078 0.217421i \(-0.930236\pi\)
−0.842851 + 0.538147i \(0.819125\pi\)
\(662\) 0 0
\(663\) 10.0319 8.65443i 0.389606 0.336110i
\(664\) 0 0
\(665\) −16.4768 + 16.1135i −0.638944 + 0.624856i
\(666\) 0 0
\(667\) 11.3147 13.4844i 0.438108 0.522116i
\(668\) 0 0
\(669\) −0.122921 8.98182i −0.00475240 0.347257i
\(670\) 0 0
\(671\) 5.84276 16.0529i 0.225557 0.619713i
\(672\) 0 0
\(673\) −37.0622 21.3979i −1.42864 0.824827i −0.431629 0.902051i \(-0.642061\pi\)
−0.997014 + 0.0772240i \(0.975394\pi\)
\(674\) 0 0
\(675\) −0.133613 0.610130i −0.00514275 0.0234839i
\(676\) 0 0
\(677\) −16.0186 27.7451i −0.615646 1.06633i −0.990271 0.139153i \(-0.955562\pi\)
0.374625 0.927176i \(-0.377771\pi\)
\(678\) 0 0
\(679\) 21.9565 + 3.87153i 0.842614 + 0.148576i
\(680\) 0 0
\(681\) 5.52135 + 28.9877i 0.211578 + 1.11081i
\(682\) 0 0
\(683\) 8.09665 0.309810 0.154905 0.987929i \(-0.450493\pi\)
0.154905 + 0.987929i \(0.450493\pi\)
\(684\) 0 0
\(685\) 37.1646 1.41998
\(686\) 0 0
\(687\) 7.94656 + 41.7203i 0.303180 + 1.59173i
\(688\) 0 0
\(689\) 3.70340 + 0.653009i 0.141088 + 0.0248777i
\(690\) 0 0
\(691\) −14.6326 25.3445i −0.556652 0.964149i −0.997773 0.0667014i \(-0.978753\pi\)
0.441121 0.897447i \(-0.354581\pi\)
\(692\) 0 0
\(693\) 7.50304 + 18.9813i 0.285017 + 0.721041i
\(694\) 0 0
\(695\) 37.8874 + 21.8743i 1.43715 + 0.829740i
\(696\) 0 0
\(697\) −17.9636 + 49.3547i −0.680421 + 1.86944i
\(698\) 0 0
\(699\) −0.541363 39.5574i −0.0204762 1.49620i
\(700\) 0 0
\(701\) −6.18601 + 7.37220i −0.233642 + 0.278444i −0.870108 0.492861i \(-0.835951\pi\)
0.636466 + 0.771305i \(0.280396\pi\)
\(702\) 0 0
\(703\) −11.8708 + 5.37519i −0.447717 + 0.202729i
\(704\) 0 0
\(705\) 30.3547 26.1867i 1.14322 0.986250i
\(706\) 0 0
\(707\) −28.8025 + 5.07867i −1.08323 + 0.191003i
\(708\) 0 0
\(709\) 2.54680 + 0.926959i 0.0956471 + 0.0348127i 0.389400 0.921069i \(-0.372682\pi\)
−0.293753 + 0.955881i \(0.594904\pi\)
\(710\) 0 0
\(711\) 10.3344 + 11.6529i 0.387569 + 0.437019i
\(712\) 0 0
\(713\) −38.2284 + 32.0774i −1.43166 + 1.20131i
\(714\) 0 0
\(715\) 7.53951 4.35294i 0.281962 0.162791i
\(716\) 0 0
\(717\) 1.73045 4.96472i 0.0646247 0.185411i
\(718\) 0 0
\(719\) −3.02583 8.31341i −0.112845 0.310038i 0.870396 0.492353i \(-0.163863\pi\)
−0.983240 + 0.182315i \(0.941641\pi\)
\(720\) 0 0
\(721\) 20.4857i 0.762929i
\(722\) 0 0
\(723\) −6.75625 1.09620i −0.251268 0.0407681i
\(724\) 0 0
\(725\) 0.242877 0.0884000i 0.00902023 0.00328309i
\(726\) 0 0
\(727\) 6.48485 36.7774i 0.240510 1.36400i −0.590183 0.807269i \(-0.700945\pi\)
0.830693 0.556730i \(-0.187944\pi\)
\(728\) 0 0
\(729\) −11.5368 + 24.4111i −0.427288 + 0.904116i
\(730\) 0 0
\(731\) 1.42733 + 1.70103i 0.0527918 + 0.0629149i
\(732\) 0 0
\(733\) 17.5306 30.3638i 0.647506 1.12151i −0.336211 0.941787i \(-0.609146\pi\)
0.983717 0.179726i \(-0.0575211\pi\)
\(734\) 0 0
\(735\) 5.26917 + 2.94676i 0.194356 + 0.108693i
\(736\) 0 0
\(737\) −8.20902 46.5557i −0.302383 1.71490i
\(738\) 0 0
\(739\) −20.2995 17.0333i −0.746731 0.626581i 0.187905 0.982187i \(-0.439830\pi\)
−0.934636 + 0.355606i \(0.884275\pi\)
\(740\) 0 0
\(741\) −2.60642 9.62949i −0.0957492 0.353748i
\(742\) 0 0
\(743\) −24.2865 20.3788i −0.890984 0.747624i 0.0774234 0.996998i \(-0.475331\pi\)
−0.968407 + 0.249374i \(0.919775\pi\)
\(744\) 0 0
\(745\) −2.53085 14.3532i −0.0927233 0.525860i
\(746\) 0 0
\(747\) −3.49971 + 4.41050i −0.128048 + 0.161372i
\(748\) 0 0
\(749\) 9.45341 16.3738i 0.345420 0.598285i
\(750\) 0 0
\(751\) 1.60959 + 1.91823i 0.0587347 + 0.0699973i 0.794612 0.607118i \(-0.207674\pi\)
−0.735877 + 0.677115i \(0.763230\pi\)
\(752\) 0 0
\(753\) −4.45776 11.7450i −0.162450 0.428010i
\(754\) 0 0
\(755\) −1.18992 + 6.74835i −0.0433055 + 0.245598i
\(756\) 0 0
\(757\) −7.22987 + 2.63146i −0.262774 + 0.0956419i −0.470048 0.882641i \(-0.655763\pi\)
0.207273 + 0.978283i \(0.433541\pi\)
\(758\) 0 0
\(759\) 6.61212 40.7527i 0.240005 1.47923i
\(760\) 0 0
\(761\) 26.1918i 0.949453i −0.880133 0.474727i \(-0.842547\pi\)
0.880133 0.474727i \(-0.157453\pi\)
\(762\) 0 0
\(763\) 5.89312 + 16.1912i 0.213345 + 0.586161i
\(764\) 0 0
\(765\) 18.7103 34.5581i 0.676473 1.24945i
\(766\) 0 0
\(767\) −3.79097 + 2.18872i −0.136884 + 0.0790301i
\(768\) 0 0
\(769\) 35.3779 29.6856i 1.27576 1.07049i 0.281948 0.959430i \(-0.409020\pi\)
0.993814 0.111061i \(-0.0354249\pi\)
\(770\) 0 0
\(771\) 12.4392 + 10.1509i 0.447987 + 0.365577i
\(772\) 0 0
\(773\) 6.91607 + 2.51724i 0.248754 + 0.0905390i 0.463388 0.886156i \(-0.346634\pi\)
−0.214634 + 0.976695i \(0.568856\pi\)
\(774\) 0 0
\(775\) −0.721618 + 0.127241i −0.0259213 + 0.00457062i
\(776\) 0 0
\(777\) −7.90312 9.16100i −0.283523 0.328649i
\(778\) 0 0
\(779\) 27.6505 + 28.2739i 0.990681 + 1.01302i
\(780\) 0 0
\(781\) 24.7492 29.4949i 0.885596 1.05541i
\(782\) 0 0
\(783\) −10.6472 3.38726i −0.380500 0.121051i
\(784\) 0 0
\(785\) 14.8003 40.6635i 0.528245 1.45134i
\(786\) 0 0
\(787\) −15.0496 8.68891i −0.536462 0.309726i 0.207182 0.978302i \(-0.433571\pi\)
−0.743644 + 0.668576i \(0.766904\pi\)
\(788\) 0 0
\(789\) 5.28164 3.14650i 0.188031 0.112018i
\(790\) 0 0
\(791\) −17.3818 30.1061i −0.618024 1.07045i
\(792\) 0 0
\(793\) −7.63460 1.34619i −0.271113 0.0478045i