Properties

Label 912.2.cc.c.401.3
Level $912$
Weight $2$
Character 912.401
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 401.3
Root \(1.47158 + 0.913487i\) of defining polynomial
Character \(\chi\) \(=\) 912.401
Dual form 912.2.cc.c.257.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.69526 - 0.355087i) q^{3} +(-0.882820 - 2.42553i) q^{5} +(1.58376 + 2.74316i) q^{7} +(2.74783 - 1.20393i) q^{9} +O(q^{10})\) \(q+(1.69526 - 0.355087i) q^{3} +(-0.882820 - 2.42553i) q^{5} +(1.58376 + 2.74316i) q^{7} +(2.74783 - 1.20393i) q^{9} +(2.16590 + 1.25049i) q^{11} +(2.71907 + 3.24046i) q^{13} +(-2.35788 - 3.79843i) q^{15} +(1.32278 + 0.233243i) q^{17} +(-3.14841 + 3.01455i) q^{19} +(3.65896 + 4.08800i) q^{21} +(1.30503 - 3.58554i) q^{23} +(-1.27359 + 1.06867i) q^{25} +(4.23078 - 3.01670i) q^{27} +(-1.32242 - 7.49981i) q^{29} +(-6.89193 + 3.97906i) q^{31} +(4.11581 + 1.35082i) q^{33} +(5.25543 - 6.26318i) q^{35} -4.10469i q^{37} +(5.76019 + 4.52793i) q^{39} +(4.95792 + 4.16019i) q^{41} +(11.7465 - 4.27537i) q^{43} +(-5.34601 - 5.60207i) q^{45} +(-6.16940 + 1.08783i) q^{47} +(-1.51662 + 2.62686i) q^{49} +(2.32529 - 0.0742967i) q^{51} +(-3.46508 - 1.26118i) q^{53} +(1.12098 - 6.35742i) q^{55} +(-4.26694 + 6.22842i) q^{57} +(1.54335 - 8.75275i) q^{59} +(-0.133301 - 0.0485177i) q^{61} +(7.65449 + 5.63098i) q^{63} +(5.45938 - 9.45593i) q^{65} +(4.48795 - 0.791347i) q^{67} +(0.939187 - 6.54182i) q^{69} +(-8.59275 + 3.12750i) q^{71} +(-1.67672 - 1.40694i) q^{73} +(-1.77960 + 2.26391i) q^{75} +7.92190i q^{77} +(-6.41515 + 7.64528i) q^{79} +(6.10110 - 6.61639i) q^{81} +(-12.3308 + 7.11920i) q^{83} +(-0.602044 - 3.41436i) q^{85} +(-4.90493 - 12.2446i) q^{87} +(-12.7492 + 10.6978i) q^{89} +(-4.58274 + 12.5910i) q^{91} +(-10.2707 + 9.19278i) q^{93} +(10.0914 + 4.97524i) q^{95} +(0.538573 + 0.0949649i) q^{97} +(7.45703 + 0.828515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 1.69526 0.355087i 0.978760 0.205010i
\(4\) 0 0
\(5\) −0.882820 2.42553i −0.394809 1.08473i −0.964779 0.263063i \(-0.915267\pi\)
0.569970 0.821666i \(-0.306955\pi\)
\(6\) 0 0
\(7\) 1.58376 + 2.74316i 0.598607 + 1.03682i 0.993027 + 0.117887i \(0.0376121\pi\)
−0.394420 + 0.918930i \(0.629055\pi\)
\(8\) 0 0
\(9\) 2.74783 1.20393i 0.915942 0.401311i
\(10\) 0 0
\(11\) 2.16590 + 1.25049i 0.653045 + 0.377036i 0.789622 0.613594i \(-0.210277\pi\)
−0.136577 + 0.990629i \(0.543610\pi\)
\(12\) 0 0
\(13\) 2.71907 + 3.24046i 0.754135 + 0.898743i 0.997462 0.0712015i \(-0.0226833\pi\)
−0.243327 + 0.969944i \(0.578239\pi\)
\(14\) 0 0
\(15\) −2.35788 3.79843i −0.608803 0.980749i
\(16\) 0 0
\(17\) 1.32278 + 0.233243i 0.320822 + 0.0565696i 0.331740 0.943371i \(-0.392364\pi\)
−0.0109180 + 0.999940i \(0.503475\pi\)
\(18\) 0 0
\(19\) −3.14841 + 3.01455i −0.722294 + 0.691586i
\(20\) 0 0
\(21\) 3.65896 + 4.08800i 0.798450 + 0.892075i
\(22\) 0 0
\(23\) 1.30503 3.58554i 0.272117 0.747636i −0.726080 0.687611i \(-0.758660\pi\)
0.998197 0.0600255i \(-0.0191182\pi\)
\(24\) 0 0
\(25\) −1.27359 + 1.06867i −0.254718 + 0.213734i
\(26\) 0 0
\(27\) 4.23078 3.01670i 0.814215 0.580564i
\(28\) 0 0
\(29\) −1.32242 7.49981i −0.245567 1.39268i −0.819172 0.573547i \(-0.805567\pi\)
0.573606 0.819132i \(-0.305544\pi\)
\(30\) 0 0
\(31\) −6.89193 + 3.97906i −1.23783 + 0.714660i −0.968650 0.248431i \(-0.920085\pi\)
−0.269177 + 0.963091i \(0.586752\pi\)
\(32\) 0 0
\(33\) 4.11581 + 1.35082i 0.716470 + 0.235147i
\(34\) 0 0
\(35\) 5.25543 6.26318i 0.888330 1.05867i
\(36\) 0 0
\(37\) 4.10469i 0.674806i −0.941360 0.337403i \(-0.890451\pi\)
0.941360 0.337403i \(-0.109549\pi\)
\(38\) 0 0
\(39\) 5.76019 + 4.52793i 0.922368 + 0.725048i
\(40\) 0 0
\(41\) 4.95792 + 4.16019i 0.774297 + 0.649712i 0.941805 0.336158i \(-0.109128\pi\)
−0.167509 + 0.985871i \(0.553572\pi\)
\(42\) 0 0
\(43\) 11.7465 4.27537i 1.79132 0.651987i 0.792191 0.610273i \(-0.208940\pi\)
0.999130 0.0417144i \(-0.0132820\pi\)
\(44\) 0 0
\(45\) −5.34601 5.60207i −0.796935 0.835108i
\(46\) 0 0
\(47\) −6.16940 + 1.08783i −0.899899 + 0.158676i −0.604414 0.796671i \(-0.706593\pi\)
−0.295486 + 0.955347i \(0.595481\pi\)
\(48\) 0 0
\(49\) −1.51662 + 2.62686i −0.216660 + 0.375266i
\(50\) 0 0
\(51\) 2.32529 0.0742967i 0.325605 0.0104036i
\(52\) 0 0
\(53\) −3.46508 1.26118i −0.475965 0.173237i 0.0928877 0.995677i \(-0.470390\pi\)
−0.568853 + 0.822440i \(0.692612\pi\)
\(54\) 0 0
\(55\) 1.12098 6.35742i 0.151153 0.857234i
\(56\) 0 0
\(57\) −4.26694 + 6.22842i −0.565170 + 0.824974i
\(58\) 0 0
\(59\) 1.54335 8.75275i 0.200927 1.13951i −0.702796 0.711392i \(-0.748065\pi\)
0.903722 0.428119i \(-0.140824\pi\)
\(60\) 0 0
\(61\) −0.133301 0.0485177i −0.0170675 0.00621206i 0.333472 0.942760i \(-0.391780\pi\)
−0.350540 + 0.936548i \(0.614002\pi\)
\(62\) 0 0
\(63\) 7.65449 + 5.63098i 0.964375 + 0.709437i
\(64\) 0 0
\(65\) 5.45938 9.45593i 0.677153 1.17286i
\(66\) 0 0
\(67\) 4.48795 0.791347i 0.548291 0.0966784i 0.107361 0.994220i \(-0.465760\pi\)
0.440930 + 0.897542i \(0.354649\pi\)
\(68\) 0 0
\(69\) 0.939187 6.54182i 0.113065 0.787543i
\(70\) 0 0
\(71\) −8.59275 + 3.12750i −1.01977 + 0.371166i −0.797178 0.603745i \(-0.793675\pi\)
−0.222594 + 0.974911i \(0.571452\pi\)
\(72\) 0 0
\(73\) −1.67672 1.40694i −0.196245 0.164670i 0.539370 0.842069i \(-0.318662\pi\)
−0.735615 + 0.677399i \(0.763107\pi\)
\(74\) 0 0
\(75\) −1.77960 + 2.26391i −0.205490 + 0.261414i
\(76\) 0 0
\(77\) 7.92190i 0.902784i
\(78\) 0 0
\(79\) −6.41515 + 7.64528i −0.721760 + 0.860161i −0.994801 0.101842i \(-0.967526\pi\)
0.273040 + 0.962003i \(0.411971\pi\)
\(80\) 0 0
\(81\) 6.10110 6.61639i 0.677900 0.735155i
\(82\) 0 0
\(83\) −12.3308 + 7.11920i −1.35348 + 0.781433i −0.988735 0.149673i \(-0.952178\pi\)
−0.364747 + 0.931107i \(0.618844\pi\)
\(84\) 0 0
\(85\) −0.602044 3.41436i −0.0653008 0.370339i
\(86\) 0 0
\(87\) −4.90493 12.2446i −0.525864 1.31275i
\(88\) 0 0
\(89\) −12.7492 + 10.6978i −1.35141 + 1.13397i −0.372879 + 0.927880i \(0.621629\pi\)
−0.978533 + 0.206089i \(0.933926\pi\)
\(90\) 0 0
\(91\) −4.58274 + 12.5910i −0.480402 + 1.31989i
\(92\) 0 0
\(93\) −10.2707 + 9.19278i −1.06502 + 0.953247i
\(94\) 0 0
\(95\) 10.0914 + 4.97524i 1.03535 + 0.510448i
\(96\) 0 0
\(97\) 0.538573 + 0.0949649i 0.0546838 + 0.00964223i 0.200923 0.979607i \(-0.435606\pi\)
−0.146239 + 0.989249i \(0.546717\pi\)
\(98\) 0 0
\(99\) 7.45703 + 0.828515i 0.749460 + 0.0832689i
\(100\) 0 0
\(101\) 7.56338 + 9.01368i 0.752584 + 0.896895i 0.997355 0.0726860i \(-0.0231571\pi\)
−0.244771 + 0.969581i \(0.578713\pi\)
\(102\) 0 0
\(103\) −6.77528 3.91171i −0.667588 0.385432i 0.127574 0.991829i \(-0.459281\pi\)
−0.795162 + 0.606397i \(0.792614\pi\)
\(104\) 0 0
\(105\) 6.68536 12.4839i 0.652424 1.21830i
\(106\) 0 0
\(107\) −2.82951 4.90085i −0.273539 0.473783i 0.696227 0.717822i \(-0.254861\pi\)
−0.969765 + 0.244039i \(0.921528\pi\)
\(108\) 0 0
\(109\) 5.64501 + 15.5095i 0.540694 + 1.48554i 0.845944 + 0.533271i \(0.179038\pi\)
−0.305251 + 0.952272i \(0.598740\pi\)
\(110\) 0 0
\(111\) −1.45752 6.95852i −0.138342 0.660473i
\(112\) 0 0
\(113\) 5.15697 0.485127 0.242564 0.970136i \(-0.422012\pi\)
0.242564 + 0.970136i \(0.422012\pi\)
\(114\) 0 0
\(115\) −9.84893 −0.918417
\(116\) 0 0
\(117\) 11.3728 + 5.63065i 1.05142 + 0.520554i
\(118\) 0 0
\(119\) 1.45516 + 3.99801i 0.133394 + 0.366497i
\(120\) 0 0
\(121\) −2.37257 4.10941i −0.215688 0.373583i
\(122\) 0 0
\(123\) 9.88220 + 5.29211i 0.891048 + 0.477174i
\(124\) 0 0
\(125\) −7.46045 4.30729i −0.667283 0.385256i
\(126\) 0 0
\(127\) −5.03745 6.00340i −0.447001 0.532715i 0.494746 0.869038i \(-0.335261\pi\)
−0.941747 + 0.336322i \(0.890817\pi\)
\(128\) 0 0
\(129\) 18.3952 11.4189i 1.61961 1.00538i
\(130\) 0 0
\(131\) 4.43285 + 0.781631i 0.387300 + 0.0682914i 0.363908 0.931435i \(-0.381442\pi\)
0.0233919 + 0.999726i \(0.492553\pi\)
\(132\) 0 0
\(133\) −13.2557 3.86224i −1.14942 0.334898i
\(134\) 0 0
\(135\) −11.0521 7.59868i −0.951214 0.653990i
\(136\) 0 0
\(137\) −2.69063 + 7.39245i −0.229876 + 0.631580i −0.999980 0.00633905i \(-0.997982\pi\)
0.770104 + 0.637919i \(0.220204\pi\)
\(138\) 0 0
\(139\) 5.76780 4.83976i 0.489219 0.410503i −0.364528 0.931193i \(-0.618770\pi\)
0.853746 + 0.520689i \(0.174325\pi\)
\(140\) 0 0
\(141\) −10.0725 + 4.03483i −0.848255 + 0.339794i
\(142\) 0 0
\(143\) 1.83710 + 10.4187i 0.153626 + 0.871255i
\(144\) 0 0
\(145\) −17.0235 + 9.82854i −1.41373 + 0.816216i
\(146\) 0 0
\(147\) −1.63830 + 4.99175i −0.135125 + 0.411713i
\(148\) 0 0
\(149\) 8.79633 10.4831i 0.720624 0.858806i −0.274068 0.961710i \(-0.588369\pi\)
0.994691 + 0.102905i \(0.0328137\pi\)
\(150\) 0 0
\(151\) 8.63653i 0.702831i −0.936220 0.351415i \(-0.885700\pi\)
0.936220 0.351415i \(-0.114300\pi\)
\(152\) 0 0
\(153\) 3.91559 0.951632i 0.316557 0.0769349i
\(154\) 0 0
\(155\) 15.7356 + 13.2038i 1.26392 + 1.06055i
\(156\) 0 0
\(157\) −3.22785 + 1.17484i −0.257610 + 0.0937625i −0.467597 0.883942i \(-0.654880\pi\)
0.209987 + 0.977704i \(0.432658\pi\)
\(158\) 0 0
\(159\) −6.32204 0.907634i −0.501371 0.0719800i
\(160\) 0 0
\(161\) 11.9026 2.09874i 0.938053 0.165404i
\(162\) 0 0
\(163\) −3.83308 + 6.63909i −0.300230 + 0.520014i −0.976188 0.216926i \(-0.930397\pi\)
0.675958 + 0.736940i \(0.263730\pi\)
\(164\) 0 0
\(165\) −0.357076 11.1755i −0.0277983 0.870014i
\(166\) 0 0
\(167\) 2.20429 + 0.802294i 0.170573 + 0.0620834i 0.425895 0.904773i \(-0.359959\pi\)
−0.255322 + 0.966856i \(0.582182\pi\)
\(168\) 0 0
\(169\) −0.849826 + 4.81960i −0.0653712 + 0.370739i
\(170\) 0 0
\(171\) −5.02195 + 12.0739i −0.384038 + 0.923317i
\(172\) 0 0
\(173\) 2.59056 14.6918i 0.196956 1.11700i −0.712649 0.701521i \(-0.752505\pi\)
0.909605 0.415474i \(-0.136384\pi\)
\(174\) 0 0
\(175\) −4.94860 1.80114i −0.374079 0.136154i
\(176\) 0 0
\(177\) −0.491615 15.3862i −0.0369520 1.15650i
\(178\) 0 0
\(179\) 0.0974666 0.168817i 0.00728500 0.0126180i −0.862360 0.506296i \(-0.831014\pi\)
0.869645 + 0.493678i \(0.164348\pi\)
\(180\) 0 0
\(181\) −7.00507 + 1.23518i −0.520683 + 0.0918105i −0.427812 0.903868i \(-0.640715\pi\)
−0.0928709 + 0.995678i \(0.529604\pi\)
\(182\) 0 0
\(183\) −0.243209 0.0349166i −0.0179785 0.00258111i
\(184\) 0 0
\(185\) −9.95603 + 3.62370i −0.731982 + 0.266420i
\(186\) 0 0
\(187\) 2.57336 + 2.15930i 0.188183 + 0.157904i
\(188\) 0 0
\(189\) 14.9759 + 6.82798i 1.08933 + 0.496662i
\(190\) 0 0
\(191\) 11.2480i 0.813878i 0.913455 + 0.406939i \(0.133404\pi\)
−0.913455 + 0.406939i \(0.866596\pi\)
\(192\) 0 0
\(193\) −10.3664 + 12.3541i −0.746187 + 0.889271i −0.996891 0.0787930i \(-0.974893\pi\)
0.250704 + 0.968064i \(0.419338\pi\)
\(194\) 0 0
\(195\) 5.89740 17.9688i 0.422322 1.28677i
\(196\) 0 0
\(197\) −19.7987 + 11.4308i −1.41060 + 0.814411i −0.995445 0.0953383i \(-0.969607\pi\)
−0.415157 + 0.909750i \(0.636273\pi\)
\(198\) 0 0
\(199\) −0.0579780 0.328809i −0.00410995 0.0233087i 0.982684 0.185290i \(-0.0593226\pi\)
−0.986794 + 0.161982i \(0.948211\pi\)
\(200\) 0 0
\(201\) 7.32726 2.93516i 0.516825 0.207030i
\(202\) 0 0
\(203\) 18.4788 15.5055i 1.29696 1.08827i
\(204\) 0 0
\(205\) 5.71370 15.6983i 0.399062 1.09641i
\(206\) 0 0
\(207\) −0.730751 11.4236i −0.0507907 0.793995i
\(208\) 0 0
\(209\) −10.5888 + 2.59220i −0.732443 + 0.179306i
\(210\) 0 0
\(211\) −2.52603 0.445407i −0.173899 0.0306631i 0.0860206 0.996293i \(-0.472585\pi\)
−0.259919 + 0.965630i \(0.583696\pi\)
\(212\) 0 0
\(213\) −13.4564 + 8.35311i −0.922019 + 0.572346i
\(214\) 0 0
\(215\) −20.7400 24.7170i −1.41446 1.68569i
\(216\) 0 0
\(217\) −21.8304 12.6038i −1.48194 0.855600i
\(218\) 0 0
\(219\) −3.34207 1.78974i −0.225836 0.120940i
\(220\) 0 0
\(221\) 2.84093 + 4.92064i 0.191102 + 0.330998i
\(222\) 0 0
\(223\) −2.28294 6.27232i −0.152877 0.420026i 0.839486 0.543382i \(-0.182856\pi\)
−0.992362 + 0.123356i \(0.960634\pi\)
\(224\) 0 0
\(225\) −2.21300 + 4.46983i −0.147533 + 0.297989i
\(226\) 0 0
\(227\) −20.0547 −1.33108 −0.665539 0.746363i \(-0.731798\pi\)
−0.665539 + 0.746363i \(0.731798\pi\)
\(228\) 0 0
\(229\) 16.5068 1.09080 0.545400 0.838176i \(-0.316378\pi\)
0.545400 + 0.838176i \(0.316378\pi\)
\(230\) 0 0
\(231\) 2.81297 + 13.4297i 0.185080 + 0.883609i
\(232\) 0 0
\(233\) −2.12137 5.82843i −0.138976 0.381833i 0.850606 0.525803i \(-0.176235\pi\)
−0.989582 + 0.143970i \(0.954013\pi\)
\(234\) 0 0
\(235\) 8.08503 + 14.0037i 0.527409 + 0.913500i
\(236\) 0 0
\(237\) −8.16062 + 15.2387i −0.530089 + 0.989859i
\(238\) 0 0
\(239\) 0.498666 + 0.287905i 0.0322560 + 0.0186230i 0.516041 0.856564i \(-0.327405\pi\)
−0.483785 + 0.875187i \(0.660738\pi\)
\(240\) 0 0
\(241\) −1.09166 1.30099i −0.0703198 0.0838039i 0.729738 0.683727i \(-0.239642\pi\)
−0.800058 + 0.599923i \(0.795198\pi\)
\(242\) 0 0
\(243\) 7.99356 13.3829i 0.512787 0.858516i
\(244\) 0 0
\(245\) 7.71043 + 1.35956i 0.492601 + 0.0868589i
\(246\) 0 0
\(247\) −18.3293 2.00550i −1.16627 0.127607i
\(248\) 0 0
\(249\) −18.3760 + 16.4474i −1.16453 + 1.04231i
\(250\) 0 0
\(251\) −2.05161 + 5.63675i −0.129496 + 0.355789i −0.987449 0.157941i \(-0.949514\pi\)
0.857952 + 0.513730i \(0.171737\pi\)
\(252\) 0 0
\(253\) 7.31023 6.13401i 0.459590 0.385642i
\(254\) 0 0
\(255\) −2.23302 5.57446i −0.139837 0.349086i
\(256\) 0 0
\(257\) 3.23144 + 18.3264i 0.201572 + 1.14317i 0.902744 + 0.430178i \(0.141549\pi\)
−0.701172 + 0.712992i \(0.747340\pi\)
\(258\) 0 0
\(259\) 11.2598 6.50086i 0.699651 0.403944i
\(260\) 0 0
\(261\) −12.6630 19.0161i −0.783822 1.17706i
\(262\) 0 0
\(263\) 1.37946 1.64398i 0.0850614 0.101372i −0.721835 0.692065i \(-0.756701\pi\)
0.806896 + 0.590693i \(0.201146\pi\)
\(264\) 0 0
\(265\) 9.51804i 0.584688i
\(266\) 0 0
\(267\) −17.8146 + 22.6627i −1.09023 + 1.38694i
\(268\) 0 0
\(269\) 19.9247 + 16.7188i 1.21483 + 1.01936i 0.999079 + 0.0429154i \(0.0136646\pi\)
0.215752 + 0.976448i \(0.430780\pi\)
\(270\) 0 0
\(271\) −4.62857 + 1.68466i −0.281166 + 0.102336i −0.478754 0.877949i \(-0.658911\pi\)
0.197588 + 0.980285i \(0.436689\pi\)
\(272\) 0 0
\(273\) −3.29805 + 22.9723i −0.199607 + 1.39035i
\(274\) 0 0
\(275\) −4.09483 + 0.722029i −0.246928 + 0.0435400i
\(276\) 0 0
\(277\) −0.845901 + 1.46514i −0.0508252 + 0.0880319i −0.890319 0.455338i \(-0.849518\pi\)
0.839493 + 0.543370i \(0.182852\pi\)
\(278\) 0 0
\(279\) −14.1473 + 19.2312i −0.846977 + 1.15134i
\(280\) 0 0
\(281\) −28.0317 10.2027i −1.67223 0.608642i −0.680017 0.733196i \(-0.738028\pi\)
−0.992213 + 0.124555i \(0.960250\pi\)
\(282\) 0 0
\(283\) −4.10223 + 23.2649i −0.243852 + 1.38296i 0.579290 + 0.815121i \(0.303330\pi\)
−0.823143 + 0.567834i \(0.807781\pi\)
\(284\) 0 0
\(285\) 18.8741 + 4.85101i 1.11801 + 0.287349i
\(286\) 0 0
\(287\) −3.55989 + 20.1891i −0.210134 + 1.19173i
\(288\) 0 0
\(289\) −14.2794 5.19728i −0.839966 0.305723i
\(290\) 0 0
\(291\) 0.946743 0.0302500i 0.0554991 0.00177328i
\(292\) 0 0
\(293\) 4.63502 8.02810i 0.270781 0.469006i −0.698281 0.715824i \(-0.746051\pi\)
0.969062 + 0.246817i \(0.0793847\pi\)
\(294\) 0 0
\(295\) −22.5925 + 3.98367i −1.31539 + 0.231938i
\(296\) 0 0
\(297\) 12.9358 1.24335i 0.750612 0.0721463i
\(298\) 0 0
\(299\) 15.1673 5.52043i 0.877146 0.319255i
\(300\) 0 0
\(301\) 30.3317 + 25.4513i 1.74829 + 1.46699i
\(302\) 0 0
\(303\) 16.0226 + 12.5949i 0.920472 + 0.723558i
\(304\) 0 0
\(305\) 0.366159i 0.0209662i
\(306\) 0 0
\(307\) −1.76414 + 2.10242i −0.100685 + 0.119991i −0.814034 0.580818i \(-0.802733\pi\)
0.713349 + 0.700809i \(0.247177\pi\)
\(308\) 0 0
\(309\) −12.8749 4.22555i −0.732425 0.240383i
\(310\) 0 0
\(311\) −19.8290 + 11.4483i −1.12440 + 0.649172i −0.942520 0.334148i \(-0.891551\pi\)
−0.181879 + 0.983321i \(0.558218\pi\)
\(312\) 0 0
\(313\) −2.33240 13.2277i −0.131835 0.747673i −0.977012 0.213186i \(-0.931616\pi\)
0.845177 0.534487i \(-0.179495\pi\)
\(314\) 0 0
\(315\) 6.90057 23.5373i 0.388803 1.32618i
\(316\) 0 0
\(317\) 15.9117 13.3515i 0.893689 0.749894i −0.0752579 0.997164i \(-0.523978\pi\)
0.968947 + 0.247270i \(0.0795336\pi\)
\(318\) 0 0
\(319\) 6.51417 17.8975i 0.364723 1.00207i
\(320\) 0 0
\(321\) −6.53699 7.30350i −0.364859 0.407642i
\(322\) 0 0
\(323\) −4.86778 + 3.25326i −0.270851 + 0.181016i
\(324\) 0 0
\(325\) −6.92597 1.22124i −0.384184 0.0677419i
\(326\) 0 0
\(327\) 15.0770 + 24.2882i 0.833760 + 1.34314i
\(328\) 0 0
\(329\) −12.7550 15.2008i −0.703204 0.838046i
\(330\) 0 0
\(331\) −7.79345 4.49955i −0.428367 0.247318i 0.270284 0.962781i \(-0.412882\pi\)
−0.698651 + 0.715463i \(0.746216\pi\)
\(332\) 0 0
\(333\) −4.94176 11.2790i −0.270807 0.618083i
\(334\) 0 0
\(335\) −5.88149 10.1870i −0.321340 0.556577i
\(336\) 0 0
\(337\) 4.39017 + 12.0619i 0.239148 + 0.657053i 0.999967 + 0.00808963i \(0.00257504\pi\)
−0.760819 + 0.648964i \(0.775203\pi\)
\(338\) 0 0
\(339\) 8.74242 1.83117i 0.474823 0.0994558i
\(340\) 0 0
\(341\) −19.9030 −1.07781
\(342\) 0 0
\(343\) 12.5648 0.678437
\(344\) 0 0
\(345\) −16.6965 + 3.49723i −0.898910 + 0.188284i
\(346\) 0 0
\(347\) −4.73541 13.0104i −0.254210 0.698436i −0.999498 0.0316932i \(-0.989910\pi\)
0.745288 0.666743i \(-0.232312\pi\)
\(348\) 0 0
\(349\) −10.3158 17.8674i −0.552190 0.956421i −0.998116 0.0613514i \(-0.980459\pi\)
0.445926 0.895070i \(-0.352874\pi\)
\(350\) 0 0
\(351\) 21.2793 + 5.50708i 1.13581 + 0.293946i
\(352\) 0 0
\(353\) 19.7460 + 11.4004i 1.05098 + 0.606781i 0.922922 0.384987i \(-0.125794\pi\)
0.128053 + 0.991767i \(0.459127\pi\)
\(354\) 0 0
\(355\) 15.1717 + 18.0809i 0.805230 + 0.959636i
\(356\) 0 0
\(357\) 3.88651 + 6.26097i 0.205696 + 0.331366i
\(358\) 0 0
\(359\) −7.31056 1.28905i −0.385837 0.0680334i −0.0226346 0.999744i \(-0.507205\pi\)
−0.363202 + 0.931710i \(0.618317\pi\)
\(360\) 0 0
\(361\) 0.824917 18.9821i 0.0434167 0.999057i
\(362\) 0 0
\(363\) −5.48133 6.12406i −0.287695 0.321430i
\(364\) 0 0
\(365\) −1.93232 + 5.30901i −0.101142 + 0.277886i
\(366\) 0 0
\(367\) 15.2065 12.7597i 0.793771 0.666053i −0.152904 0.988241i \(-0.548863\pi\)
0.946676 + 0.322188i \(0.104418\pi\)
\(368\) 0 0
\(369\) 18.6321 + 5.46248i 0.969947 + 0.284365i
\(370\) 0 0
\(371\) −2.02823 11.5027i −0.105301 0.597189i
\(372\) 0 0
\(373\) 16.5145 9.53467i 0.855090 0.493687i −0.00727484 0.999974i \(-0.502316\pi\)
0.862365 + 0.506287i \(0.168982\pi\)
\(374\) 0 0
\(375\) −14.1769 4.65288i −0.732091 0.240274i
\(376\) 0 0
\(377\) 20.7071 24.6778i 1.06647 1.27097i
\(378\) 0 0
\(379\) 30.0894i 1.54559i −0.634656 0.772795i \(-0.718858\pi\)
0.634656 0.772795i \(-0.281142\pi\)
\(380\) 0 0
\(381\) −10.6715 8.38860i −0.546719 0.429761i
\(382\) 0 0
\(383\) 4.60213 + 3.86165i 0.235158 + 0.197321i 0.752750 0.658307i \(-0.228727\pi\)
−0.517592 + 0.855628i \(0.673171\pi\)
\(384\) 0 0
\(385\) 19.2148 6.99361i 0.979276 0.356427i
\(386\) 0 0
\(387\) 27.1300 25.8899i 1.37910 1.31606i
\(388\) 0 0
\(389\) −20.4701 + 3.60942i −1.03787 + 0.183005i −0.666520 0.745487i \(-0.732217\pi\)
−0.371353 + 0.928492i \(0.621106\pi\)
\(390\) 0 0
\(391\) 2.56257 4.43850i 0.129595 0.224465i
\(392\) 0 0
\(393\) 7.79238 0.248979i 0.393074 0.0125593i
\(394\) 0 0
\(395\) 24.2072 + 8.81072i 1.21800 + 0.443315i
\(396\) 0 0
\(397\) 1.82838 10.3692i 0.0917636 0.520417i −0.903928 0.427686i \(-0.859329\pi\)
0.995691 0.0927316i \(-0.0295599\pi\)
\(398\) 0 0
\(399\) −23.8434 1.84056i −1.19366 0.0921432i
\(400\) 0 0
\(401\) 1.59795 9.06241i 0.0797977 0.452555i −0.918561 0.395280i \(-0.870648\pi\)
0.998358 0.0572753i \(-0.0182413\pi\)
\(402\) 0 0
\(403\) −31.6336 11.5137i −1.57578 0.573538i
\(404\) 0 0
\(405\) −21.4344 8.95729i −1.06508 0.445092i
\(406\) 0 0
\(407\) 5.13285 8.89036i 0.254426 0.440679i
\(408\) 0 0
\(409\) 23.2080 4.09220i 1.14756 0.202346i 0.432651 0.901561i \(-0.357578\pi\)
0.714911 + 0.699215i \(0.246467\pi\)
\(410\) 0 0
\(411\) −1.93636 + 13.4875i −0.0955136 + 0.665292i
\(412\) 0 0
\(413\) 26.4545 9.62865i 1.30174 0.473795i
\(414\) 0 0
\(415\) 28.1537 + 23.6238i 1.38201 + 1.15964i
\(416\) 0 0
\(417\) 8.05940 10.2527i 0.394670 0.502079i
\(418\) 0 0
\(419\) 20.4238i 0.997766i −0.866669 0.498883i \(-0.833744\pi\)
0.866669 0.498883i \(-0.166256\pi\)
\(420\) 0 0
\(421\) −0.259039 + 0.308710i −0.0126248 + 0.0150456i −0.772320 0.635234i \(-0.780904\pi\)
0.759695 + 0.650279i \(0.225348\pi\)
\(422\) 0 0
\(423\) −15.6428 + 10.4167i −0.760577 + 0.506478i
\(424\) 0 0
\(425\) −1.93394 + 1.11656i −0.0938101 + 0.0541613i
\(426\) 0 0
\(427\) −0.0780261 0.442508i −0.00377595 0.0214144i
\(428\) 0 0
\(429\) 6.81391 + 17.0101i 0.328979 + 0.821255i
\(430\) 0 0
\(431\) 7.15165 6.00095i 0.344483 0.289055i −0.454087 0.890957i \(-0.650035\pi\)
0.798570 + 0.601902i \(0.205590\pi\)
\(432\) 0 0
\(433\) −7.03421 + 19.3263i −0.338043 + 0.928765i 0.647907 + 0.761720i \(0.275645\pi\)
−0.985949 + 0.167045i \(0.946577\pi\)
\(434\) 0 0
\(435\) −25.3694 + 22.7068i −1.21637 + 1.08871i
\(436\) 0 0
\(437\) 6.70004 + 15.2228i 0.320506 + 0.728206i
\(438\) 0 0
\(439\) 25.2438 + 4.45116i 1.20482 + 0.212442i 0.739781 0.672847i \(-0.234929\pi\)
0.465040 + 0.885290i \(0.346040\pi\)
\(440\) 0 0
\(441\) −1.00484 + 9.04407i −0.0478497 + 0.430670i
\(442\) 0 0
\(443\) −17.0745 20.3486i −0.811235 0.966792i 0.188649 0.982045i \(-0.439589\pi\)
−0.999884 + 0.0152527i \(0.995145\pi\)
\(444\) 0 0
\(445\) 37.2032 + 21.4793i 1.76360 + 1.01821i
\(446\) 0 0
\(447\) 11.1897 20.8950i 0.529254 0.988300i
\(448\) 0 0
\(449\) −5.66925 9.81944i −0.267549 0.463408i 0.700680 0.713476i \(-0.252880\pi\)
−0.968228 + 0.250068i \(0.919547\pi\)
\(450\) 0 0
\(451\) 5.53612 + 15.2104i 0.260686 + 0.716229i
\(452\) 0 0
\(453\) −3.06672 14.6412i −0.144087 0.687903i
\(454\) 0 0
\(455\) 34.5855 1.62139
\(456\) 0 0
\(457\) −21.3688 −0.999591 −0.499796 0.866143i \(-0.666592\pi\)
−0.499796 + 0.866143i \(0.666592\pi\)
\(458\) 0 0
\(459\) 6.30004 3.00364i 0.294061 0.140198i
\(460\) 0 0
\(461\) 9.40832 + 25.8492i 0.438189 + 1.20392i 0.940669 + 0.339326i \(0.110199\pi\)
−0.502480 + 0.864589i \(0.667579\pi\)
\(462\) 0 0
\(463\) 4.52654 + 7.84019i 0.210366 + 0.364365i 0.951829 0.306629i \(-0.0992011\pi\)
−0.741463 + 0.670994i \(0.765868\pi\)
\(464\) 0 0
\(465\) 31.3645 + 16.7963i 1.45450 + 0.778911i
\(466\) 0 0
\(467\) 17.7092 + 10.2244i 0.819486 + 0.473130i 0.850239 0.526397i \(-0.176457\pi\)
−0.0307535 + 0.999527i \(0.509791\pi\)
\(468\) 0 0
\(469\) 9.27865 + 11.0579i 0.428448 + 0.510605i
\(470\) 0 0
\(471\) −5.05488 + 3.13783i −0.232916 + 0.144584i
\(472\) 0 0
\(473\) 30.7880 + 5.42876i 1.41564 + 0.249615i
\(474\) 0 0
\(475\) 0.788217 7.20391i 0.0361659 0.330538i
\(476\) 0 0
\(477\) −11.0398 + 0.706200i −0.505478 + 0.0323347i
\(478\) 0 0
\(479\) 3.36367 9.24160i 0.153690 0.422259i −0.838822 0.544405i \(-0.816755\pi\)
0.992512 + 0.122146i \(0.0389776\pi\)
\(480\) 0 0
\(481\) 13.3011 11.1609i 0.606477 0.508895i
\(482\) 0 0
\(483\) 19.4327 7.78437i 0.884220 0.354201i
\(484\) 0 0
\(485\) −0.245123 1.39016i −0.0111305 0.0631239i
\(486\) 0 0
\(487\) 6.75564 3.90037i 0.306127 0.176743i −0.339065 0.940763i \(-0.610111\pi\)
0.645192 + 0.764020i \(0.276777\pi\)
\(488\) 0 0
\(489\) −4.14062 + 12.6161i −0.187245 + 0.570519i
\(490\) 0 0
\(491\) −18.0754 + 21.5414i −0.815729 + 0.972148i −0.999942 0.0107379i \(-0.996582\pi\)
0.184213 + 0.982886i \(0.441026\pi\)
\(492\) 0 0
\(493\) 10.2291i 0.460694i
\(494\) 0 0
\(495\) −4.57363 18.8187i −0.205569 0.845836i
\(496\) 0 0
\(497\) −22.1881 18.6181i −0.995274 0.835134i
\(498\) 0 0
\(499\) 12.8477 4.67618i 0.575142 0.209334i −0.0380402 0.999276i \(-0.512112\pi\)
0.613182 + 0.789942i \(0.289889\pi\)
\(500\) 0 0
\(501\) 4.02173 + 0.577385i 0.179677 + 0.0257957i
\(502\) 0 0
\(503\) 25.8762 4.56267i 1.15376 0.203439i 0.436144 0.899877i \(-0.356344\pi\)
0.717618 + 0.696437i \(0.245233\pi\)
\(504\) 0 0
\(505\) 15.1858 26.3026i 0.675761 1.17045i
\(506\) 0 0
\(507\) 0.270702 + 8.47225i 0.0120223 + 0.376266i
\(508\) 0 0
\(509\) −25.0043 9.10082i −1.10830 0.403387i −0.277928 0.960602i \(-0.589648\pi\)
−0.830368 + 0.557215i \(0.811870\pi\)
\(510\) 0 0
\(511\) 1.20392 6.82777i 0.0532583 0.302043i
\(512\) 0 0
\(513\) −4.22622 + 22.2517i −0.186592 + 0.982437i
\(514\) 0 0
\(515\) −3.50661 + 19.8869i −0.154520 + 0.876324i
\(516\) 0 0
\(517\) −14.7226 5.35860i −0.647501 0.235671i
\(518\) 0 0
\(519\) −0.825191 25.8263i −0.0362219 1.13365i
\(520\) 0 0
\(521\) −10.2977 + 17.8362i −0.451151 + 0.781417i −0.998458 0.0555154i \(-0.982320\pi\)
0.547307 + 0.836932i \(0.315653\pi\)
\(522\) 0 0
\(523\) −7.47024 + 1.31720i −0.326651 + 0.0575973i −0.334569 0.942371i \(-0.608591\pi\)
0.00791816 + 0.999969i \(0.497480\pi\)
\(524\) 0 0
\(525\) −9.02874 1.29622i −0.394046 0.0565719i
\(526\) 0 0
\(527\) −10.0446 + 3.65594i −0.437550 + 0.159255i
\(528\) 0 0
\(529\) 6.46604 + 5.42566i 0.281132 + 0.235898i
\(530\) 0 0
\(531\) −6.29687 25.9091i −0.273261 1.12436i
\(532\) 0 0
\(533\) 27.3778i 1.18586i
\(534\) 0 0
\(535\) −9.38920 + 11.1896i −0.405931 + 0.483769i
\(536\) 0 0
\(537\) 0.105287 0.320799i 0.00454345 0.0138435i
\(538\) 0 0
\(539\) −6.56971 + 3.79302i −0.282977 + 0.163377i
\(540\) 0 0
\(541\) 7.39225 + 41.9235i 0.317818 + 1.80243i 0.555966 + 0.831205i \(0.312349\pi\)
−0.238148 + 0.971229i \(0.576540\pi\)
\(542\) 0 0
\(543\) −11.4368 + 4.58137i −0.490802 + 0.196605i
\(544\) 0 0
\(545\) 32.6353 27.3842i 1.39794 1.17301i
\(546\) 0 0
\(547\) 0.418676 1.15030i 0.0179013 0.0491833i −0.930420 0.366495i \(-0.880558\pi\)
0.948321 + 0.317311i \(0.102780\pi\)
\(548\) 0 0
\(549\) −0.424701 + 0.0271675i −0.0181258 + 0.00115948i
\(550\) 0 0
\(551\) 26.7721 + 19.6259i 1.14053 + 0.836093i
\(552\) 0 0
\(553\) −31.1323 5.48946i −1.32388 0.233436i
\(554\) 0 0
\(555\) −15.5914 + 9.67838i −0.661816 + 0.410824i
\(556\) 0 0
\(557\) −13.8808 16.5425i −0.588147 0.700927i 0.387101 0.922037i \(-0.373476\pi\)
−0.975249 + 0.221110i \(0.929032\pi\)
\(558\) 0 0
\(559\) 45.7937 + 26.4390i 1.93687 + 1.11825i
\(560\) 0 0
\(561\) 5.12926 + 2.74682i 0.216557 + 0.115971i
\(562\) 0 0
\(563\) 13.0149 + 22.5424i 0.548512 + 0.950051i 0.998377 + 0.0569541i \(0.0181389\pi\)
−0.449865 + 0.893097i \(0.648528\pi\)
\(564\) 0 0
\(565\) −4.55268 12.5084i −0.191533 0.526231i
\(566\) 0 0
\(567\) 27.8125 + 6.25748i 1.16802 + 0.262789i
\(568\) 0 0
\(569\) −4.80544 −0.201455 −0.100727 0.994914i \(-0.532117\pi\)
−0.100727 + 0.994914i \(0.532117\pi\)
\(570\) 0 0
\(571\) 46.6475 1.95214 0.976068 0.217466i \(-0.0697792\pi\)
0.976068 + 0.217466i \(0.0697792\pi\)
\(572\) 0 0
\(573\) 3.99403 + 19.0683i 0.166853 + 0.796591i
\(574\) 0 0
\(575\) 2.16968 + 5.96115i 0.0904820 + 0.248597i
\(576\) 0 0
\(577\) 23.3103 + 40.3745i 0.970418 + 1.68081i 0.694293 + 0.719692i \(0.255717\pi\)
0.276125 + 0.961122i \(0.410950\pi\)
\(578\) 0 0
\(579\) −13.1869 + 24.6245i −0.548028 + 1.02336i
\(580\) 0 0
\(581\) −39.0582 22.5503i −1.62041 0.935543i
\(582\) 0 0
\(583\) −5.92793 7.06463i −0.245510 0.292587i
\(584\) 0 0
\(585\) 3.61714 32.5560i 0.149550 1.34602i
\(586\) 0 0
\(587\) 14.9298 + 2.63253i 0.616220 + 0.108656i 0.473041 0.881040i \(-0.343156\pi\)
0.143180 + 0.989697i \(0.454267\pi\)
\(588\) 0 0
\(589\) 9.70350 33.3038i 0.399826 1.37226i
\(590\) 0 0
\(591\) −29.5051 + 26.4085i −1.21368 + 1.08630i
\(592\) 0 0
\(593\) 0.398860 1.09586i 0.0163792 0.0450015i −0.931234 0.364423i \(-0.881266\pi\)
0.947613 + 0.319421i \(0.103489\pi\)
\(594\) 0 0
\(595\) 8.41264 7.05905i 0.344885 0.289393i
\(596\) 0 0
\(597\) −0.215044 0.536831i −0.00880116 0.0219710i
\(598\) 0 0
\(599\) −4.45202 25.2486i −0.181905 1.03163i −0.929868 0.367892i \(-0.880079\pi\)
0.747964 0.663739i \(-0.231032\pi\)
\(600\) 0 0
\(601\) −26.4639 + 15.2789i −1.07948 + 0.623240i −0.930757 0.365639i \(-0.880851\pi\)
−0.148726 + 0.988878i \(0.547517\pi\)
\(602\) 0 0
\(603\) 11.3794 7.57767i 0.463404 0.308587i
\(604\) 0 0
\(605\) −7.87294 + 9.38261i −0.320081 + 0.381457i
\(606\) 0 0
\(607\) 7.82667i 0.317675i 0.987305 + 0.158837i \(0.0507745\pi\)
−0.987305 + 0.158837i \(0.949225\pi\)
\(608\) 0 0
\(609\) 25.8205 32.8475i 1.04630 1.33105i
\(610\) 0 0
\(611\) −20.3001 17.0338i −0.821254 0.689114i
\(612\) 0 0
\(613\) 30.3824 11.0583i 1.22713 0.446640i 0.354519 0.935049i \(-0.384645\pi\)
0.872615 + 0.488408i \(0.162422\pi\)
\(614\) 0 0
\(615\) 4.11197 28.6415i 0.165810 1.15494i
\(616\) 0 0
\(617\) 24.5040 4.32072i 0.986495 0.173946i 0.342950 0.939354i \(-0.388574\pi\)
0.643545 + 0.765408i \(0.277463\pi\)
\(618\) 0 0
\(619\) 3.60285 6.24032i 0.144811 0.250820i −0.784492 0.620140i \(-0.787076\pi\)
0.929302 + 0.369320i \(0.120409\pi\)
\(620\) 0 0
\(621\) −5.29519 19.1065i −0.212489 0.766718i
\(622\) 0 0
\(623\) −49.5376 18.0302i −1.98468 0.722366i
\(624\) 0 0
\(625\) −5.30472 + 30.0846i −0.212189 + 1.20338i
\(626\) 0 0
\(627\) −17.0303 + 8.15441i −0.680126 + 0.325656i
\(628\) 0 0
\(629\) 0.957388 5.42961i 0.0381735 0.216493i
\(630\) 0 0
\(631\) −23.7099 8.62969i −0.943876 0.343543i −0.176180 0.984358i \(-0.556374\pi\)
−0.767695 + 0.640815i \(0.778596\pi\)
\(632\) 0 0
\(633\) −4.44044 + 0.141879i −0.176492 + 0.00563919i
\(634\) 0 0
\(635\) −10.1142 + 17.5184i −0.401372 + 0.695196i
\(636\) 0 0
\(637\) −12.6361 + 2.22808i −0.500659 + 0.0882796i
\(638\) 0 0
\(639\) −19.8461 + 18.9389i −0.785099 + 0.749212i
\(640\) 0 0
\(641\) −8.36361 + 3.04411i −0.330343 + 0.120235i −0.501867 0.864945i \(-0.667353\pi\)
0.171524 + 0.985180i \(0.445131\pi\)
\(642\) 0 0
\(643\) −5.41716 4.54553i −0.213632 0.179258i 0.529692 0.848190i \(-0.322307\pi\)
−0.743324 + 0.668932i \(0.766752\pi\)
\(644\) 0 0
\(645\) −43.9365 34.5373i −1.73000 1.35990i
\(646\) 0 0
\(647\) 7.87198i 0.309479i −0.987955 0.154740i \(-0.950546\pi\)
0.987955 0.154740i \(-0.0494539\pi\)
\(648\) 0 0
\(649\) 14.2879 17.0277i 0.560850 0.668395i
\(650\) 0 0
\(651\) −41.4837 13.6150i −1.62587 0.533614i
\(652\) 0 0
\(653\) −1.40402 + 0.810613i −0.0549437 + 0.0317217i −0.527220 0.849729i \(-0.676766\pi\)
0.472277 + 0.881450i \(0.343432\pi\)
\(654\) 0 0
\(655\) −2.01754 11.4420i −0.0788318 0.447077i
\(656\) 0 0
\(657\) −6.30120 1.84736i −0.245833 0.0720723i
\(658\) 0 0
\(659\) 9.29693 7.80105i 0.362157 0.303886i −0.443493 0.896278i \(-0.646261\pi\)
0.805650 + 0.592392i \(0.201816\pi\)
\(660\) 0 0
\(661\) −10.0965 + 27.7400i −0.392710 + 1.07896i 0.573050 + 0.819521i \(0.305760\pi\)
−0.965759 + 0.259440i \(0.916462\pi\)
\(662\) 0 0
\(663\) 6.56338 + 7.33299i 0.254900 + 0.284790i
\(664\) 0 0
\(665\) 2.33447 + 35.5618i 0.0905268 + 1.37903i
\(666\) 0 0
\(667\) −28.6166 5.04588i −1.10804 0.195377i
\(668\) 0 0
\(669\) −6.09740 9.82258i −0.235739 0.379763i
\(670\) 0 0
\(671\) −0.228047 0.271776i −0.00880367 0.0104918i
\(672\) 0 0
\(673\) −3.84411 2.21940i −0.148180 0.0855516i 0.424077 0.905626i \(-0.360599\pi\)
−0.572257 + 0.820075i \(0.693932\pi\)
\(674\) 0 0
\(675\) −2.16443 + 8.36335i −0.0833091 + 0.321905i
\(676\) 0 0
\(677\) 0.610403 + 1.05725i 0.0234597 + 0.0406334i 0.877517 0.479546i \(-0.159199\pi\)
−0.854057 + 0.520179i \(0.825865\pi\)
\(678\) 0 0
\(679\) 0.592469 + 1.62779i 0.0227369 + 0.0624690i
\(680\) 0 0
\(681\) −33.9980 + 7.12117i −1.30281 + 0.272884i
\(682\) 0 0
\(683\) −40.7336 −1.55863 −0.779313 0.626635i \(-0.784432\pi\)
−0.779313 + 0.626635i \(0.784432\pi\)
\(684\) 0 0
\(685\) 20.3059 0.775850
\(686\) 0 0
\(687\) 27.9834 5.86136i 1.06763 0.223625i
\(688\) 0 0
\(689\) −5.33497 14.6577i −0.203246 0.558414i
\(690\) 0 0
\(691\) −18.9023 32.7397i −0.719077 1.24548i −0.961366 0.275274i \(-0.911231\pi\)
0.242289 0.970204i \(-0.422102\pi\)
\(692\) 0 0
\(693\) 9.53743 + 21.7680i 0.362297 + 0.826898i
\(694\) 0 0
\(695\) −16.8309 9.71733i −0.638433 0.368599i
\(696\) 0 0
\(697\) 5.58792 + 6.65943i 0.211658 + 0.252244i
\(698\) 0 0
\(699\) −5.66589 9.12744i −0.214304 0.345231i
\(700\) 0 0
\(701\) 23.1182 + 4.07636i 0.873162 + 0.153962i 0.592233 0.805767i \(-0.298246\pi\)
0.280929 + 0.959729i \(0.409358\pi\)
\(702\) 0 0
\(703\) 12.3738 + 12.9232i 0.466687 + 0.487408i
\(704\) 0 0
\(705\) 18.6788 + 20.8690i 0.703483 + 0.785973i
\(706\) 0 0
\(707\) −12.7474 + 35.0231i −0.479414 + 1.31718i
\(708\) 0 0
\(709\) 21.3882 17.9469i 0.803252 0.674009i −0.145735 0.989324i \(-0.546555\pi\)
0.948987 + 0.315315i \(0.102110\pi\)
\(710\) 0 0
\(711\) −8.42332 + 28.7313i −0.315899 + 1.07751i
\(712\) 0 0
\(713\) 5.27289 + 29.9041i 0.197471 + 1.11992i
\(714\) 0 0
\(715\) 23.6490 13.6538i 0.884423 0.510622i
\(716\) 0 0
\(717\) 0.947601 + 0.311004i 0.0353888 + 0.0116147i
\(718\) 0 0
\(719\) 26.4940 31.5743i 0.988060 1.17752i 0.00394505 0.999992i \(-0.498744\pi\)
0.984115 0.177532i \(-0.0568113\pi\)
\(720\) 0 0
\(721\) 24.7809i 0.922889i
\(722\) 0 0
\(723\) −2.31261 1.81788i −0.0860069 0.0676077i
\(724\) 0 0
\(725\) 9.69903 + 8.13846i 0.360213 + 0.302255i
\(726\) 0 0
\(727\) −4.13772 + 1.50601i −0.153460 + 0.0558548i −0.417608 0.908627i \(-0.637131\pi\)
0.264148 + 0.964482i \(0.414909\pi\)
\(728\) 0 0
\(729\) 8.79906 25.5260i 0.325891 0.945407i
\(730\) 0 0
\(731\) 16.5352 2.91561i 0.611578 0.107838i
\(732\) 0 0
\(733\) 11.3991 19.7438i 0.421034 0.729253i −0.575007 0.818149i \(-0.695001\pi\)
0.996041 + 0.0888960i \(0.0283339\pi\)
\(734\) 0 0
\(735\) 13.5540 0.433071i 0.499945 0.0159741i
\(736\) 0 0
\(737\) 10.7100 + 3.89814i 0.394510 + 0.143590i
\(738\) 0 0
\(739\) 8.91510 50.5600i 0.327947 1.85988i −0.160151 0.987093i \(-0.551198\pi\)
0.488098 0.872789i \(-0.337691\pi\)
\(740\) 0 0
\(741\) −31.7851 + 3.10865i −1.16765 + 0.114199i
\(742\) 0 0
\(743\) 0.154876 0.878343i 0.00568183 0.0322233i −0.981835 0.189737i \(-0.939237\pi\)
0.987517 + 0.157513i \(0.0503477\pi\)
\(744\) 0 0
\(745\) −33.1925 12.0811i −1.21608 0.442617i
\(746\) 0 0
\(747\) −25.3119 + 34.4078i −0.926114 + 1.25891i
\(748\) 0 0
\(749\) 8.96255 15.5236i 0.327484 0.567220i
\(750\) 0 0
\(751\) 10.0009 1.76342i 0.364936 0.0643481i 0.0118266 0.999930i \(-0.496235\pi\)
0.353110 + 0.935582i \(0.385124\pi\)
\(752\) 0 0
\(753\) −1.47648 + 10.2843i −0.0538058 + 0.374780i
\(754\) 0 0
\(755\) −20.9481 + 7.62450i −0.762381 + 0.277484i
\(756\) 0 0
\(757\) 16.0181 + 13.4408i 0.582187 + 0.488513i 0.885664 0.464326i \(-0.153703\pi\)
−0.303478 + 0.952839i \(0.598148\pi\)
\(758\) 0 0
\(759\) 10.2146 12.9945i 0.370768 0.471672i
\(760\) 0 0
\(761\) 23.9282i 0.867396i −0.901058 0.433698i \(-0.857209\pi\)
0.901058 0.433698i \(-0.142791\pi\)
\(762\) 0 0
\(763\) −33.6048 + 40.0486i −1.21657 + 1.44986i
\(764\) 0 0
\(765\) −5.76497 8.65725i −0.208433 0.313003i
\(766\) 0 0
\(767\) 32.5594 18.7982i 1.17565 0.678764i
\(768\) 0 0
\(769\) −3.21910 18.2564i −0.116084 0.658344i −0.986208 0.165511i \(-0.947073\pi\)
0.870124 0.492833i \(-0.164039\pi\)
\(770\) 0 0
\(771\) 11.9856 + 29.9206i 0.431651 + 1.07756i
\(772\) 0 0
\(773\) −27.0855 + 22.7275i −0.974199 + 0.817450i −0.983204 0.182509i \(-0.941578\pi\)
0.00900488 + 0.999959i \(0.497134\pi\)
\(774\) 0 0
\(775\) 4.52520 12.4329i 0.162550 0.446602i
\(776\) 0 0
\(777\) 16.7800 15.0189i 0.601978 0.538799i
\(778\) 0 0
\(779\) −28.1507 + 1.84796i −1.00860 + 0.0662100i
\(780\) 0 0
\(781\) −22.5220 3.97123i −0.805900 0.142102i
\(782\) 0 0
\(783\) −28.2195 27.7407i −1.00848 0.991372i
\(784\) 0 0
\(785\) 5.69922 + 6.79206i 0.203414 + 0.242419i
\(786\) 0 0
\(787\) −6.19829 3.57858i −0.220945 0.127563i 0.385443 0.922732i \(-0.374049\pi\)
−0.606388 + 0.795169i \(0.707382\pi\)
\(788\) 0 0
\(789\) 1.75480 3.27681i 0.0624724 0.116658i
\(790\) 0 0
\(791\) 8.16743 + 14.1464i 0.290400 + 0.502988i
\(792\) 0 0
\(793\) −0.205236 0.563881i −0.00728815 0.0200240i