Properties

Label 912.2.cc.c.257.3
Level $912$
Weight $2$
Character 912.257
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 257.3
Root \(1.47158 - 0.913487i\) of defining polynomial
Character \(\chi\) \(=\) 912.257
Dual form 912.2.cc.c.401.3

$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\) \(-1\) \(1\)

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 0.569970 + 0.821666i \(0.306955\pi\)
−0.964779 + 0.263063i \(0.915267\pi\)
\(6\) 0 0
\(7\) 1.58376 2.74316i 0.598607 1.03682i −0.394420 0.918930i \(-0.629055\pi\)
0.993027 0.117887i \(-0.0376121\pi\)
\(8\) 0 0
\(9\) 2.74783 + 1.20393i 0.915942 + 0.401311i
\(10\) 0 0
\(11\) 2.16590 1.25049i 0.653045 0.377036i −0.136577 0.990629i \(-0.543610\pi\)
0.789622 + 0.613594i \(0.210277\pi\)
\(12\) 0 0
\(13\) 2.71907 3.24046i 0.754135 0.898743i −0.243327 0.969944i \(-0.578239\pi\)
0.997462 + 0.0712015i \(0.0226833\pi\)
\(14\) 0 0
\(15\) −2.35788 + 3.79843i −0.608803 + 0.980749i
\(16\) 0 0
\(17\) 1.32278 0.233243i 0.320822 0.0565696i −0.0109180 0.999940i \(-0.503475\pi\)
0.331740 + 0.943371i \(0.392364\pi\)
\(18\) 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 0.998197 + 0.0600255i \(0.0191182\pi\)
−0.726080 + 0.687611i \(0.758660\pi\)
\(24\) 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 0.573606 + 0.819132i \(0.305544\pi\)
−0.819172 + 0.573547i \(0.805567\pi\)
\(30\) 0 0
\(31\) −6.89193 3.97906i −1.23783 0.714660i −0.269177 0.963091i \(-0.586752\pi\)
−0.968650 + 0.248431i \(0.920085\pi\)
\(32\) 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 \(0.109549\pi\)
−0.941360 + 0.337403i \(0.890451\pi\)
\(38\) 0 0
\(39\) 5.76019 4.52793i 0.922368 0.725048i
\(40\) 0 0
\(41\) 4.95792 4.16019i 0.774297 0.649712i −0.167509 0.985871i \(-0.553572\pi\)
0.941805 + 0.336158i \(0.109128\pi\)
\(42\) 0 0
\(43\) 11.7465 + 4.27537i 1.79132 + 0.651987i 0.999130 + 0.0417144i \(0.0132820\pi\)
0.792191 + 0.610273i \(0.208940\pi\)
\(44\) 0 0
\(45\) −5.34601 + 5.60207i −0.796935 + 0.835108i
\(46\) 0 0
\(47\) −6.16940 1.08783i −0.899899 0.158676i −0.295486 0.955347i \(-0.595481\pi\)
−0.604414 + 0.796671i \(0.706593\pi\)
\(48\) 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 −0.568853 0.822440i \(-0.692612\pi\)
0.0928877 + 0.995677i \(0.470390\pi\)
\(54\) 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 0.903722 + 0.428119i \(0.140824\pi\)
−0.702796 + 0.711392i \(0.748065\pi\)
\(60\) 0 0
\(61\) −0.133301 + 0.0485177i −0.0170675 + 0.00621206i −0.350540 0.936548i \(-0.614002\pi\)
0.333472 + 0.942760i \(0.391780\pi\)
\(62\) 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 0.440930 0.897542i \(-0.354649\pi\)
0.107361 + 0.994220i \(0.465760\pi\)
\(68\) 0 0
\(69\) 0.939187 + 6.54182i 0.113065 + 0.787543i
\(70\) 0 0
\(71\) −8.59275 3.12750i −1.01977 0.371166i −0.222594 0.974911i \(-0.571452\pi\)
−0.797178 + 0.603745i \(0.793675\pi\)
\(72\) 0 0
\(73\) −1.67672 + 1.40694i −0.196245 + 0.164670i −0.735615 0.677399i \(-0.763107\pi\)
0.539370 + 0.842069i \(0.318662\pi\)
\(74\) 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 0.273040 0.962003i \(-0.411971\pi\)
−0.994801 + 0.101842i \(0.967526\pi\)
\(80\) 0 0
\(81\) 6.10110 + 6.61639i 0.677900 + 0.735155i
\(82\) 0 0
\(83\) −12.3308 7.11920i −1.35348 0.781433i −0.364747 0.931107i \(-0.618844\pi\)
−0.988735 + 0.149673i \(0.952178\pi\)
\(84\) 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 −0.978533 0.206089i \(-0.933926\pi\)
−0.372879 0.927880i \(-0.621629\pi\)
\(90\) 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 −0.146239 0.989249i \(-0.546717\pi\)
0.200923 + 0.979607i \(0.435606\pi\)
\(98\) 0 0
\(99\) 7.45703 0.828515i 0.749460 0.0832689i
\(100\) 0 0
\(101\) 7.56338 9.01368i 0.752584 0.896895i −0.244771 0.969581i \(-0.578713\pi\)
0.997355 + 0.0726860i \(0.0231571\pi\)
\(102\) 0 0
\(103\) −6.77528 + 3.91171i −0.667588 + 0.385432i −0.795162 0.606397i \(-0.792614\pi\)
0.127574 + 0.991829i \(0.459281\pi\)
\(104\) 0 0
\(105\) 6.68536 + 12.4839i 0.652424 + 1.21830i
\(106\) 0 0
\(107\) −2.82951 + 4.90085i −0.273539 + 0.473783i −0.969765 0.244039i \(-0.921528\pi\)
0.696227 + 0.717822i \(0.254861\pi\)
\(108\) 0 0
\(109\) 5.64501 15.5095i 0.540694 1.48554i −0.305251 0.952272i \(-0.598740\pi\)
0.845944 0.533271i \(-0.179038\pi\)
\(110\) 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 −0.941747 0.336322i \(-0.890817\pi\)
0.494746 + 0.869038i \(0.335261\pi\)
\(128\) 0 0
\(129\) 18.3952 + 11.4189i 1.61961 + 1.00538i
\(130\) 0 0
\(131\) 4.43285 0.781631i 0.387300 0.0682914i 0.0233919 0.999726i \(-0.492553\pi\)
0.363908 + 0.931435i \(0.381442\pi\)
\(132\) 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 0.770104 0.637919i \(-0.220204\pi\)
−0.999980 + 0.00633905i \(0.997982\pi\)
\(138\) 0 0
\(139\) 5.76780 + 4.83976i 0.489219 + 0.410503i 0.853746 0.520689i \(-0.174325\pi\)
−0.364528 + 0.931193i \(0.618770\pi\)
\(140\) 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 0.994691 0.102905i \(-0.0328137\pi\)
−0.274068 + 0.961710i \(0.588369\pi\)
\(150\) 0 0
\(151\) 8.63653i 0.702831i 0.936220 + 0.351415i \(0.114300\pi\)
−0.936220 + 0.351415i \(0.885700\pi\)
\(152\) 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 0.209987 0.977704i \(-0.432658\pi\)
−0.467597 + 0.883942i \(0.654880\pi\)
\(158\) 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 0.675958 0.736940i \(-0.263730\pi\)
−0.976188 + 0.216926i \(0.930397\pi\)
\(164\) 0 0
\(165\) −0.357076 + 11.1755i −0.0277983 + 0.870014i
\(166\) 0 0
\(167\) 2.20429 0.802294i 0.170573 0.0620834i −0.255322 0.966856i \(-0.582182\pi\)
0.425895 + 0.904773i \(0.359959\pi\)
\(168\) 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 0.909605 + 0.415474i \(0.136384\pi\)
−0.712649 + 0.701521i \(0.752505\pi\)
\(174\) 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 0.869645 0.493678i \(-0.164348\pi\)
−0.862360 + 0.506296i \(0.831014\pi\)
\(180\) 0 0
\(181\) −7.00507 1.23518i −0.520683 0.0918105i −0.0928709 0.995678i \(-0.529604\pi\)
−0.427812 + 0.903868i \(0.640715\pi\)
\(182\) 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 \(-0.866596\pi\)
0.913455 0.406939i \(-0.133404\pi\)
\(192\) 0 0
\(193\) −10.3664 12.3541i −0.746187 0.889271i 0.250704 0.968064i \(-0.419338\pi\)
−0.996891 + 0.0787930i \(0.974893\pi\)
\(194\) 0 0
\(195\) 5.89740 + 17.9688i 0.422322 + 1.28677i
\(196\) 0 0
\(197\) −19.7987 11.4308i −1.41060 0.814411i −0.415157 0.909750i \(-0.636273\pi\)
−0.995445 + 0.0953383i \(0.969607\pi\)
\(198\) 0 0
\(199\) −0.0579780 + 0.328809i −0.00410995 + 0.0233087i −0.986794 0.161982i \(-0.948211\pi\)
0.982684 + 0.185290i \(0.0593226\pi\)
\(200\) 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 −0.259919 0.965630i \(-0.583696\pi\)
0.0860206 + 0.996293i \(0.472585\pi\)
\(212\) 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 −0.992362 0.123356i \(-0.960634\pi\)
0.839486 + 0.543382i \(0.182856\pi\)
\(224\) 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 −0.989582 0.143970i \(-0.954013\pi\)
0.850606 + 0.525803i \(0.176235\pi\)
\(234\) 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 −0.483785 0.875187i \(-0.660738\pi\)
0.516041 + 0.856564i \(0.327405\pi\)
\(240\) 0 0
\(241\) −1.09166 + 1.30099i −0.0703198 + 0.0838039i −0.800058 0.599923i \(-0.795198\pi\)
0.729738 + 0.683727i \(0.239642\pi\)
\(242\) 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 0.857952 0.513730i \(-0.171737\pi\)
−0.987449 + 0.157941i \(0.949514\pi\)
\(252\) 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 −0.701172 0.712992i \(-0.747340\pi\)
0.902744 0.430178i \(-0.141549\pi\)
\(258\) 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 0.806896 0.590693i \(-0.201146\pi\)
−0.721835 + 0.692065i \(0.756701\pi\)
\(264\) 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 0.215752 0.976448i \(-0.430780\pi\)
0.999079 0.0429154i \(-0.0136646\pi\)
\(270\) 0 0
\(271\) −4.62857 1.68466i −0.281166 0.102336i 0.197588 0.980285i \(-0.436689\pi\)
−0.478754 + 0.877949i \(0.658911\pi\)
\(272\) 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 0.839493 0.543370i \(-0.182852\pi\)
−0.890319 + 0.455338i \(0.849518\pi\)
\(278\) 0 0
\(279\) −14.1473 19.2312i −0.846977 1.15134i
\(280\) 0 0
\(281\) −28.0317 + 10.2027i −1.67223 + 0.608642i −0.992213 0.124555i \(-0.960250\pi\)
−0.680017 + 0.733196i \(0.738028\pi\)
\(282\) 0 0
\(283\) −4.10223 23.2649i −0.243852 1.38296i −0.823143 0.567834i \(-0.807781\pi\)
0.579290 0.815121i \(-0.303330\pi\)
\(284\) 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 0.969062 0.246817i \(-0.0793847\pi\)
−0.698281 + 0.715824i \(0.746051\pi\)
\(294\) 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 0.713349 0.700809i \(-0.247177\pi\)
−0.814034 + 0.580818i \(0.802733\pi\)
\(308\) 0 0
\(309\) −12.8749 + 4.22555i −0.732425 + 0.240383i
\(310\) 0 0
\(311\) −19.8290 11.4483i −1.12440 0.649172i −0.181879 0.983321i \(-0.558218\pi\)
−0.942520 + 0.334148i \(0.891551\pi\)
\(312\) 0 0
\(313\) −2.33240 + 13.2277i −0.131835 + 0.747673i 0.845177 + 0.534487i \(0.179495\pi\)
−0.977012 + 0.213186i \(0.931616\pi\)
\(314\) 0 0
\(315\) 6.90057 + 23.5373i 0.388803 + 1.32618i
\(316\) 0 0
\(317\) 15.9117 + 13.3515i 0.893689 + 0.749894i 0.968947 0.247270i \(-0.0795336\pi\)
−0.0752579 + 0.997164i \(0.523978\pi\)
\(318\) 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 −0.698651 0.715463i \(-0.746216\pi\)
0.270284 + 0.962781i \(0.412882\pi\)
\(332\) 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 −0.760819 0.648964i \(-0.775203\pi\)
0.999967 0.00808963i \(-0.00257504\pi\)
\(338\) 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 0.745288 + 0.666743i \(0.232312\pi\)
−0.999498 + 0.0316932i \(0.989910\pi\)
\(348\) 0 0
\(349\) −10.3158 + 17.8674i −0.552190 + 0.956421i 0.445926 + 0.895070i \(0.352874\pi\)
−0.998116 + 0.0613514i \(0.980459\pi\)
\(350\) 0 0
\(351\) 21.2793 5.50708i 1.13581 0.293946i
\(352\) 0 0
\(353\) 19.7460 11.4004i 1.05098 0.606781i 0.128053 0.991767i \(-0.459127\pi\)
0.922922 + 0.384987i \(0.125794\pi\)
\(354\) 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 −0.363202 0.931710i \(-0.618317\pi\)
−0.0226346 + 0.999744i \(0.507205\pi\)
\(360\) 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 0.946676 0.322188i \(-0.104418\pi\)
−0.152904 + 0.988241i \(0.548863\pi\)
\(368\) 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 0.862365 0.506287i \(-0.168982\pi\)
−0.00727484 + 0.999974i \(0.502316\pi\)
\(374\) 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 \(0.281142\pi\)
−0.634656 + 0.772795i \(0.718858\pi\)
\(380\) 0 0
\(381\) −10.6715 + 8.38860i −0.546719 + 0.429761i
\(382\) 0 0
\(383\) 4.60213 3.86165i 0.235158 0.197321i −0.517592 0.855628i \(-0.673171\pi\)
0.752750 + 0.658307i \(0.228727\pi\)
\(384\) 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 −0.371353 0.928492i \(-0.621106\pi\)
−0.666520 + 0.745487i \(0.732217\pi\)
\(390\) 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 0.995691 + 0.0927316i \(0.0295599\pi\)
−0.903928 + 0.427686i \(0.859329\pi\)
\(398\) 0 0
\(399\) −23.8434 + 1.84056i −1.19366 + 0.0921432i
\(400\) 0 0
\(401\) 1.59795 + 9.06241i 0.0797977 + 0.452555i 0.998358 + 0.0572753i \(0.0182413\pi\)
−0.918561 + 0.395280i \(0.870648\pi\)
\(402\) 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 0.714911 0.699215i \(-0.246467\pi\)
0.432651 + 0.901561i \(0.357578\pi\)
\(410\) 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 \(0.166256\pi\)
−0.866669 + 0.498883i \(0.833744\pi\)
\(420\) 0 0
\(421\) −0.259039 0.308710i −0.0126248 0.0150456i 0.759695 0.650279i \(-0.225348\pi\)
−0.772320 + 0.635234i \(0.780904\pi\)
\(422\) 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 0.798570 0.601902i \(-0.205590\pi\)
−0.454087 + 0.890957i \(0.650035\pi\)
\(432\) 0 0
\(433\) −7.03421 19.3263i −0.338043 0.928765i −0.985949 0.167045i \(-0.946577\pi\)
0.647907 0.761720i \(-0.275645\pi\)
\(434\) 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 0.465040 0.885290i \(-0.346040\pi\)
0.739781 + 0.672847i \(0.234929\pi\)
\(440\) 0 0
\(441\) −1.00484 9.04407i −0.0478497 0.430670i
\(442\) 0 0
\(443\) −17.0745 + 20.3486i −0.811235 + 0.966792i −0.999884 0.0152527i \(-0.995145\pi\)
0.188649 + 0.982045i \(0.439589\pi\)
\(444\) 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 −0.968228 0.250068i \(-0.919547\pi\)
0.700680 + 0.713476i \(0.252880\pi\)
\(450\) 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 −0.502480 0.864589i \(-0.667579\pi\)
0.940669 0.339326i \(-0.110199\pi\)
\(462\) 0 0
\(463\) 4.52654 7.84019i 0.210366 0.364365i −0.741463 0.670994i \(-0.765868\pi\)
0.951829 + 0.306629i \(0.0992011\pi\)
\(464\) 0 0
\(465\) 31.3645 16.7963i 1.45450 0.778911i
\(466\) 0 0
\(467\) 17.7092 10.2244i 0.819486 0.473130i −0.0307535 0.999527i \(-0.509791\pi\)
0.850239 + 0.526397i \(0.176457\pi\)
\(468\) 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 0.992512 0.122146i \(-0.0389776\pi\)
−0.838822 + 0.544405i \(0.816755\pi\)
\(480\) 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 0.645192 0.764020i \(-0.276777\pi\)
−0.339065 + 0.940763i \(0.610111\pi\)
\(488\) 0 0
\(489\) −4.14062 12.6161i −0.187245 0.570519i
\(490\) 0 0
\(491\) −18.0754 21.5414i −0.815729 0.972148i 0.184213 0.982886i \(-0.441026\pi\)
−0.999942 + 0.0107379i \(0.996582\pi\)
\(492\) 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 0.613182 0.789942i \(-0.289889\pi\)
−0.0380402 + 0.999276i \(0.512112\pi\)
\(500\) 0 0
\(501\) 4.02173 0.577385i 0.179677 0.0257957i
\(502\) 0 0
\(503\) 25.8762 + 4.56267i 1.15376 + 0.203439i 0.717618 0.696437i \(-0.245233\pi\)
0.436144 + 0.899877i \(0.356344\pi\)
\(504\) 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 −0.830368 0.557215i \(-0.811870\pi\)
−0.277928 + 0.960602i \(0.589648\pi\)
\(510\) 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 0.547307 0.836932i \(-0.315653\pi\)
−0.998458 + 0.0555154i \(0.982320\pi\)
\(522\) 0 0
\(523\) −7.47024 1.31720i −0.326651 0.0575973i 0.00791816 0.999969i \(-0.497480\pi\)
−0.334569 + 0.942371i \(0.608591\pi\)
\(524\) 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 −0.238148 0.971229i \(-0.576540\pi\)
0.555966 0.831205i \(-0.312349\pi\)
\(542\) 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 0.948321 0.317311i \(-0.102780\pi\)
−0.930420 + 0.366495i \(0.880558\pi\)
\(548\) 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 −0.975249 0.221110i \(-0.929032\pi\)
0.387101 + 0.922037i \(0.373476\pi\)
\(558\) 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 −0.449865 0.893097i \(-0.648528\pi\)
0.998377 0.0569541i \(-0.0181389\pi\)
\(564\) 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 0.276125 0.961122i \(-0.410950\pi\)
0.694293 0.719692i \(-0.255717\pi\)
\(578\) 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 0.143180 0.989697i \(-0.454267\pi\)
0.473041 + 0.881040i \(0.343156\pi\)
\(588\) 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 0.947613 0.319421i \(-0.103489\pi\)
−0.931234 + 0.364423i \(0.881266\pi\)
\(594\) 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 0.747964 + 0.663739i \(0.231032\pi\)
−0.929868 + 0.367892i \(0.880079\pi\)
\(600\) 0 0
\(601\) −26.4639 15.2789i −1.07948 0.623240i −0.148726 0.988878i \(-0.547517\pi\)
−0.930757 + 0.365639i \(0.880851\pi\)
\(602\) 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 \(-0.949225\pi\)
0.987305 0.158837i \(-0.0507745\pi\)
\(608\) 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 0.872615 0.488408i \(-0.162422\pi\)
0.354519 + 0.935049i \(0.384645\pi\)
\(614\) 0 0
\(615\) 4.11197 + 28.6415i 0.165810 + 1.15494i
\(616\) 0 0
\(617\) 24.5040 + 4.32072i 0.986495 + 0.173946i 0.643545 0.765408i \(-0.277463\pi\)
0.342950 + 0.939354i \(0.388574\pi\)
\(618\) 0 0
\(619\) 3.60285 + 6.24032i 0.144811 + 0.250820i 0.929302 0.369320i \(-0.120409\pi\)
−0.784492 + 0.620140i \(0.787076\pi\)
\(620\) 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 −0.767695 0.640815i \(-0.778596\pi\)
−0.176180 + 0.984358i \(0.556374\pi\)
\(632\) 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 0.171524 0.985180i \(-0.445131\pi\)
−0.501867 + 0.864945i \(0.667353\pi\)
\(642\) 0 0
\(643\) −5.41716 + 4.54553i −0.213632 + 0.179258i −0.743324 0.668932i \(-0.766752\pi\)
0.529692 + 0.848190i \(0.322307\pi\)
\(644\) 0 0
\(645\) −43.9365 + 34.5373i −1.73000 + 1.35990i
\(646\) 0 0
\(647\) 7.87198i 0.309479i 0.987955 + 0.154740i \(0.0494539\pi\)
−0.987955 + 0.154740i \(0.950546\pi\)
\(648\) 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 0.472277 0.881450i \(-0.343432\pi\)
−0.527220 + 0.849729i \(0.676766\pi\)
\(654\) 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 0.805650 0.592392i \(-0.201816\pi\)
−0.443493 + 0.896278i \(0.646261\pi\)
\(660\) 0 0
\(661\) −10.0965 27.7400i −0.392710 1.07896i −0.965759 0.259440i \(-0.916462\pi\)
0.573050 0.819521i \(-0.305760\pi\)
\(662\) 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 −0.572257 0.820075i \(-0.693932\pi\)
0.424077 + 0.905626i \(0.360599\pi\)
\(674\) 0 0
\(675\) −2.16443 8.36335i −0.0833091 0.321905i
\(676\) 0 0
\(677\) 0.610403 1.05725i 0.0234597 0.0406334i −0.854057 0.520179i \(-0.825865\pi\)
0.877517 + 0.479546i \(0.159199\pi\)
\(678\) 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 0.242289 + 0.970204i \(0.422102\pi\)
−0.961366 + 0.275274i \(0.911231\pi\)
\(692\) 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 0.280929 0.959729i \(-0.409358\pi\)
0.592233 + 0.805767i \(0.298246\pi\)
\(702\) 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 0.948987 0.315315i \(-0.102110\pi\)
−0.145735 + 0.989324i \(0.546555\pi\)
\(710\) 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 0.984115 + 0.177532i \(0.0568113\pi\)
0.00394505 + 0.999992i \(0.498744\pi\)
\(720\) 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 0.264148 0.964482i \(-0.414909\pi\)
−0.417608 + 0.908627i \(0.637131\pi\)
\(728\) 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 0.996041 0.0888960i \(-0.0283339\pi\)
−0.575007 + 0.818149i \(0.695001\pi\)
\(734\) 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 0.488098 + 0.872789i \(0.337691\pi\)
−0.160151 + 0.987093i \(0.551198\pi\)
\(740\) 0 0
\(741\) −31.7851 3.10865i −1.16765 0.114199i
\(742\) 0 0
\(743\) 0.154876 + 0.878343i 0.00568183 + 0.0322233i 0.987517 0.157513i \(-0.0503477\pi\)
−0.981835 + 0.189737i \(0.939237\pi\)
\(744\) 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 0.353110 0.935582i \(-0.385124\pi\)
0.0118266 + 0.999930i \(0.496235\pi\)
\(752\) 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 −0.303478 0.952839i \(-0.598148\pi\)
0.885664 + 0.464326i \(0.153703\pi\)
\(758\) 0 0
\(759\) 10.2146 + 12.9945i 0.370768 + 0.471672i
\(760\) 0 0
\(761\) 23.9282i 0.867396i 0.901058 + 0.433698i \(0.142791\pi\)
−0.901058 + 0.433698i \(0.857209\pi\)
\(762\) 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 0.870124 + 0.492833i \(0.164039\pi\)
−0.986208 + 0.165511i \(0.947073\pi\)
\(770\) 0 0
\(771\) 11.9856 29.9206i 0.431651 1.07756i
\(772\) 0 0
\(773\) −27.0855 22.7275i −0.974199 0.817450i 0.00900488 0.999959i \(-0.497134\pi\)
−0.983204 + 0.182509i \(0.941578\pi\)
\(774\) 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 −0.606388 0.795169i \(-0.707382\pi\)
0.385443 + 0.922732i \(0.374049\pi\)
\(788\) 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
\(794\)