Properties

Label 950.2.e.l.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.39075800976.1
Defining polynomial: \(x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(-1.63248 + 2.82754i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.l.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.63248 + 2.82754i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.63248 - 2.82754i) q^{6} +2.62013 q^{7} +1.00000 q^{8} +(-3.82998 - 6.63372i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.63248 + 2.82754i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.63248 - 2.82754i) q^{6} +2.62013 q^{7} +1.00000 q^{8} +(-3.82998 - 6.63372i) q^{9} +5.03983 q^{11} +3.26496 q^{12} +(2.32241 + 4.02254i) q^{13} +(-1.31007 + 2.26910i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.82998 + 3.16962i) q^{17} +7.65996 q^{18} +(0.697500 + 4.30273i) q^{19} +(-4.27731 + 7.40852i) q^{21} +(-2.51991 + 4.36462i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(-1.63248 + 2.82754i) q^{24} -4.64483 q^{26} +15.2146 q^{27} +(-1.31007 - 2.26910i) q^{28} +(4.01991 + 6.96270i) q^{29} -3.28009 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.22742 + 14.2503i) q^{33} +(-1.82998 - 3.16962i) q^{34} +(-3.82998 + 6.63372i) q^{36} +5.75505 q^{37} +(-4.07502 - 1.54731i) q^{38} -15.1652 q^{39} +(2.90735 - 5.03568i) q^{41} +(-4.27731 - 7.40852i) q^{42} +(-0.290150 + 0.502555i) q^{43} +(-2.51991 - 4.36462i) q^{44} +4.68466 q^{46} +(2.31007 + 4.00115i) q^{47} +(-1.63248 - 2.82754i) q^{48} -0.134919 q^{49} +(-5.97481 - 10.3487i) q^{51} +(2.32241 - 4.02254i) q^{52} +(-2.31007 - 4.00115i) q^{53} +(-7.60729 + 13.1762i) q^{54} +2.62013 q^{56} +(-13.3048 - 5.05191i) q^{57} -8.03983 q^{58} +(1.88743 - 3.26913i) q^{59} +(-0.0650203 - 0.112618i) q^{61} +(1.64004 - 2.84064i) q^{62} +(-10.0350 - 17.3812i) q^{63} +1.00000 q^{64} +(-8.22742 - 14.2503i) q^{66} +(0.189935 + 0.328977i) q^{67} +3.65996 q^{68} +15.2952 q^{69} +(4.56746 - 7.91107i) q^{71} +(-3.82998 - 6.63372i) q^{72} +(-4.25261 + 7.36574i) q^{73} +(-2.87752 + 4.98402i) q^{74} +(3.37752 - 2.75542i) q^{76} +13.2050 q^{77} +(7.58259 - 13.1334i) q^{78} +(3.98237 - 6.89767i) q^{79} +(-13.3475 + 23.1186i) q^{81} +(2.90735 + 5.03568i) q^{82} -7.86996 q^{83} +8.55462 q^{84} +(-0.290150 - 0.502555i) q^{86} -26.2497 q^{87} +5.03983 q^{88} +(4.14483 + 7.17905i) q^{89} +(6.08503 + 10.5396i) q^{91} +(-2.34233 + 4.05703i) q^{92} +(5.35468 - 9.27458i) q^{93} -4.62013 q^{94} +3.26496 q^{96} +(-8.09494 + 14.0208i) q^{97} +(0.0674593 - 0.116843i) q^{98} +(-19.3024 - 33.4328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + q^{3} - 4q^{4} + q^{6} + 12q^{7} + 8q^{8} - 11q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + q^{3} - 4q^{4} + q^{6} + 12q^{7} + 8q^{8} - 11q^{9} + 10q^{11} - 2q^{12} + 9q^{13} - 6q^{14} - 4q^{16} + 5q^{17} + 22q^{18} - q^{21} - 5q^{22} + 6q^{23} + q^{24} - 18q^{26} + 16q^{27} - 6q^{28} + 17q^{29} + 22q^{31} - 4q^{32} - 4q^{33} + 5q^{34} - 11q^{36} - 8q^{37} - 36q^{39} + 7q^{41} - q^{42} - 13q^{43} - 5q^{44} - 12q^{46} + 14q^{47} + q^{48} + 44q^{49} - 9q^{51} + 9q^{52} - 14q^{53} - 8q^{54} + 12q^{56} - 48q^{57} - 34q^{58} + 14q^{59} - 9q^{61} - 11q^{62} - 45q^{63} + 8q^{64} - 4q^{66} + 6q^{67} - 10q^{68} + 54q^{69} + 14q^{71} - 11q^{72} - 11q^{73} + 4q^{74} - 10q^{77} + 18q^{78} - 17q^{79} - 36q^{81} + 7q^{82} - 46q^{83} + 2q^{84} - 13q^{86} - 2q^{87} + 10q^{88} + 14q^{89} - 25q^{91} + 6q^{92} + 13q^{93} - 28q^{94} - 2q^{96} - 17q^{97} - 22q^{98} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.63248 + 2.82754i −0.942513 + 1.63248i −0.181856 + 0.983325i \(0.558210\pi\)
−0.760657 + 0.649154i \(0.775123\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −1.63248 2.82754i −0.666457 1.15434i
\(7\) 2.62013 0.990316 0.495158 0.868803i \(-0.335110\pi\)
0.495158 + 0.868803i \(0.335110\pi\)
\(8\) 1.00000 0.353553
\(9\) −3.82998 6.63372i −1.27666 2.21124i
\(10\) 0 0
\(11\) 5.03983 1.51957 0.759783 0.650177i \(-0.225305\pi\)
0.759783 + 0.650177i \(0.225305\pi\)
\(12\) 3.26496 0.942513
\(13\) 2.32241 + 4.02254i 0.644122 + 1.11565i 0.984504 + 0.175365i \(0.0561104\pi\)
−0.340382 + 0.940287i \(0.610556\pi\)
\(14\) −1.31007 + 2.26910i −0.350130 + 0.606442i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.82998 + 3.16962i −0.443835 + 0.768745i −0.997970 0.0636816i \(-0.979716\pi\)
0.554135 + 0.832427i \(0.313049\pi\)
\(18\) 7.65996 1.80547
\(19\) 0.697500 + 4.30273i 0.160017 + 0.987114i
\(20\) 0 0
\(21\) −4.27731 + 7.40852i −0.933385 + 1.61667i
\(22\) −2.51991 + 4.36462i −0.537248 + 0.930540i
\(23\) −2.34233 4.05703i −0.488409 0.845950i 0.511502 0.859282i \(-0.329089\pi\)
−0.999911 + 0.0133324i \(0.995756\pi\)
\(24\) −1.63248 + 2.82754i −0.333229 + 0.577169i
\(25\) 0 0
\(26\) −4.64483 −0.910926
\(27\) 15.2146 2.92805
\(28\) −1.31007 2.26910i −0.247579 0.428819i
\(29\) 4.01991 + 6.96270i 0.746479 + 1.29294i 0.949500 + 0.313766i \(0.101591\pi\)
−0.203021 + 0.979174i \(0.565076\pi\)
\(30\) 0 0
\(31\) −3.28009 −0.589121 −0.294561 0.955633i \(-0.595173\pi\)
−0.294561 + 0.955633i \(0.595173\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −8.22742 + 14.2503i −1.43221 + 2.48066i
\(34\) −1.82998 3.16962i −0.313839 0.543585i
\(35\) 0 0
\(36\) −3.82998 + 6.63372i −0.638330 + 1.10562i
\(37\) 5.75505 0.946124 0.473062 0.881029i \(-0.343149\pi\)
0.473062 + 0.881029i \(0.343149\pi\)
\(38\) −4.07502 1.54731i −0.661056 0.251007i
\(39\) −15.1652 −2.42837
\(40\) 0 0
\(41\) 2.90735 5.03568i 0.454052 0.786441i −0.544581 0.838708i \(-0.683311\pi\)
0.998633 + 0.0522673i \(0.0166448\pi\)
\(42\) −4.27731 7.40852i −0.660003 1.14316i
\(43\) −0.290150 + 0.502555i −0.0442475 + 0.0766390i −0.887301 0.461191i \(-0.847422\pi\)
0.843053 + 0.537830i \(0.180756\pi\)
\(44\) −2.51991 4.36462i −0.379891 0.657991i
\(45\) 0 0
\(46\) 4.68466 0.690715
\(47\) 2.31007 + 4.00115i 0.336958 + 0.583628i 0.983859 0.178946i \(-0.0572688\pi\)
−0.646901 + 0.762574i \(0.723935\pi\)
\(48\) −1.63248 2.82754i −0.235628 0.408120i
\(49\) −0.134919 −0.0192741
\(50\) 0 0
\(51\) −5.97481 10.3487i −0.836641 1.44910i
\(52\) 2.32241 4.02254i 0.322061 0.557826i
\(53\) −2.31007 4.00115i −0.317312 0.549600i 0.662614 0.748961i \(-0.269447\pi\)
−0.979926 + 0.199361i \(0.936114\pi\)
\(54\) −7.60729 + 13.1762i −1.03522 + 1.79306i
\(55\) 0 0
\(56\) 2.62013 0.350130
\(57\) −13.3048 5.05191i −1.76226 0.669142i
\(58\) −8.03983 −1.05568
\(59\) 1.88743 3.26913i 0.245723 0.425605i −0.716612 0.697472i \(-0.754308\pi\)
0.962335 + 0.271868i \(0.0876413\pi\)
\(60\) 0 0
\(61\) −0.0650203 0.112618i −0.00832500 0.0144193i 0.861833 0.507192i \(-0.169317\pi\)
−0.870158 + 0.492773i \(0.835983\pi\)
\(62\) 1.64004 2.84064i 0.208286 0.360762i
\(63\) −10.0350 17.3812i −1.26430 2.18983i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −8.22742 14.2503i −1.01273 1.75409i
\(67\) 0.189935 + 0.328977i 0.0232043 + 0.0401909i 0.877394 0.479770i \(-0.159280\pi\)
−0.854190 + 0.519961i \(0.825947\pi\)
\(68\) 3.65996 0.443835
\(69\) 15.2952 1.84133
\(70\) 0 0
\(71\) 4.56746 7.91107i 0.542058 0.938871i −0.456728 0.889606i \(-0.650979\pi\)
0.998786 0.0492651i \(-0.0156879\pi\)
\(72\) −3.82998 6.63372i −0.451367 0.781791i
\(73\) −4.25261 + 7.36574i −0.497730 + 0.862094i −0.999997 0.00261883i \(-0.999166\pi\)
0.502266 + 0.864713i \(0.332500\pi\)
\(74\) −2.87752 + 4.98402i −0.334505 + 0.579380i
\(75\) 0 0
\(76\) 3.37752 2.75542i 0.387429 0.316068i
\(77\) 13.2050 1.50485
\(78\) 7.58259 13.1334i 0.858559 1.48707i
\(79\) 3.98237 6.89767i 0.448052 0.776049i −0.550207 0.835028i \(-0.685451\pi\)
0.998259 + 0.0589793i \(0.0187846\pi\)
\(80\) 0 0
\(81\) −13.3475 + 23.1186i −1.48306 + 2.56874i
\(82\) 2.90735 + 5.03568i 0.321063 + 0.556098i
\(83\) −7.86996 −0.863840 −0.431920 0.901912i \(-0.642164\pi\)
−0.431920 + 0.901912i \(0.642164\pi\)
\(84\) 8.55462 0.933385
\(85\) 0 0
\(86\) −0.290150 0.502555i −0.0312877 0.0541919i
\(87\) −26.2497 −2.81426
\(88\) 5.03983 0.537248
\(89\) 4.14483 + 7.17905i 0.439351 + 0.760978i 0.997640 0.0686686i \(-0.0218751\pi\)
−0.558289 + 0.829647i \(0.688542\pi\)
\(90\) 0 0
\(91\) 6.08503 + 10.5396i 0.637884 + 1.10485i
\(92\) −2.34233 + 4.05703i −0.244205 + 0.422975i
\(93\) 5.35468 9.27458i 0.555254 0.961729i
\(94\) −4.62013 −0.476530
\(95\) 0 0
\(96\) 3.26496 0.333229
\(97\) −8.09494 + 14.0208i −0.821917 + 1.42360i 0.0823367 + 0.996605i \(0.473762\pi\)
−0.904253 + 0.426997i \(0.859572\pi\)
\(98\) 0.0674593 0.116843i 0.00681442 0.0118029i
\(99\) −19.3024 33.4328i −1.93997 3.36012i
\(100\) 0 0
\(101\) −4.23270 7.33124i −0.421169 0.729486i 0.574885 0.818234i \(-0.305047\pi\)
−0.996054 + 0.0887481i \(0.971713\pi\)
\(102\) 11.9496 1.18319
\(103\) −11.8498 −1.16760 −0.583800 0.811898i \(-0.698435\pi\)
−0.583800 + 0.811898i \(0.698435\pi\)
\(104\) 2.32241 + 4.02254i 0.227731 + 0.394443i
\(105\) 0 0
\(106\) 4.62013 0.448747
\(107\) −16.8100 −1.62508 −0.812542 0.582902i \(-0.801917\pi\)
−0.812542 + 0.582902i \(0.801917\pi\)
\(108\) −7.60729 13.1762i −0.732012 1.26788i
\(109\) −10.0023 + 17.3245i −0.958045 + 1.65938i −0.230806 + 0.973000i \(0.574136\pi\)
−0.727240 + 0.686384i \(0.759197\pi\)
\(110\) 0 0
\(111\) −9.39500 + 16.2726i −0.891734 + 1.54453i
\(112\) −1.31007 + 2.26910i −0.123790 + 0.214410i
\(113\) 14.3505 1.34998 0.674990 0.737827i \(-0.264148\pi\)
0.674990 + 0.737827i \(0.264148\pi\)
\(114\) 11.0275 8.99633i 1.03282 0.842583i
\(115\) 0 0
\(116\) 4.01991 6.96270i 0.373240 0.646470i
\(117\) 17.7896 30.8125i 1.64465 2.84862i
\(118\) 1.88743 + 3.26913i 0.173752 + 0.300948i
\(119\) −4.79478 + 8.30481i −0.439537 + 0.761301i
\(120\) 0 0
\(121\) 14.3999 1.30908
\(122\) 0.130041 0.0117733
\(123\) 9.49238 + 16.4413i 0.855899 + 1.48246i
\(124\) 1.64004 + 2.84064i 0.147280 + 0.255097i
\(125\) 0 0
\(126\) 20.0701 1.78799
\(127\) 3.94254 + 6.82869i 0.349844 + 0.605948i 0.986222 0.165430i \(-0.0529012\pi\)
−0.636377 + 0.771378i \(0.719568\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −0.947329 1.64082i −0.0834077 0.144466i
\(130\) 0 0
\(131\) −1.20228 + 2.08242i −0.105044 + 0.181942i −0.913756 0.406263i \(-0.866832\pi\)
0.808712 + 0.588205i \(0.200165\pi\)
\(132\) 16.4548 1.43221
\(133\) 1.82754 + 11.2737i 0.158468 + 0.977555i
\(134\) −0.379870 −0.0328158
\(135\) 0 0
\(136\) −1.82998 + 3.16962i −0.156919 + 0.271792i
\(137\) −8.71751 15.0992i −0.744787 1.29001i −0.950294 0.311353i \(-0.899218\pi\)
0.205507 0.978656i \(-0.434116\pi\)
\(138\) −7.64761 + 13.2460i −0.651008 + 1.12758i
\(139\) −4.78487 8.28764i −0.405848 0.702949i 0.588572 0.808445i \(-0.299690\pi\)
−0.994420 + 0.105496i \(0.966357\pi\)
\(140\) 0 0
\(141\) −15.0845 −1.27035
\(142\) 4.56746 + 7.91107i 0.383293 + 0.663882i
\(143\) 11.7046 + 20.2729i 0.978786 + 1.69531i
\(144\) 7.65996 0.638330
\(145\) 0 0
\(146\) −4.25261 7.36574i −0.351948 0.609593i
\(147\) 0.220252 0.381488i 0.0181661 0.0314646i
\(148\) −2.87752 4.98402i −0.236531 0.409684i
\(149\) 8.56218 14.8301i 0.701441 1.21493i −0.266519 0.963830i \(-0.585874\pi\)
0.967961 0.251102i \(-0.0807931\pi\)
\(150\) 0 0
\(151\) −5.44440 −0.443059 −0.221529 0.975154i \(-0.571105\pi\)
−0.221529 + 0.975154i \(0.571105\pi\)
\(152\) 0.697500 + 4.30273i 0.0565747 + 0.348998i
\(153\) 28.0351 2.26651
\(154\) −6.60250 + 11.4359i −0.532045 + 0.921529i
\(155\) 0 0
\(156\) 7.58259 + 13.1334i 0.607093 + 1.05152i
\(157\) 0.0123496 0.0213902i 0.000985608 0.00170712i −0.865532 0.500853i \(-0.833020\pi\)
0.866518 + 0.499146i \(0.166353\pi\)
\(158\) 3.98237 + 6.89767i 0.316821 + 0.548749i
\(159\) 15.0845 1.19628
\(160\) 0 0
\(161\) −6.13721 10.6300i −0.483680 0.837758i
\(162\) −13.3475 23.1186i −1.04868 1.81637i
\(163\) −10.8347 −0.848640 −0.424320 0.905512i \(-0.639487\pi\)
−0.424320 + 0.905512i \(0.639487\pi\)
\(164\) −5.81470 −0.454052
\(165\) 0 0
\(166\) 3.93498 6.81558i 0.305414 0.528992i
\(167\) 3.14239 + 5.44278i 0.243165 + 0.421175i 0.961614 0.274405i \(-0.0884809\pi\)
−0.718449 + 0.695580i \(0.755148\pi\)
\(168\) −4.27731 + 7.40852i −0.330002 + 0.571579i
\(169\) −4.28722 + 7.42568i −0.329786 + 0.571206i
\(170\) 0 0
\(171\) 25.8717 21.1064i 1.97846 1.61405i
\(172\) 0.580301 0.0442475
\(173\) 0.187589 0.324914i 0.0142622 0.0247028i −0.858806 0.512301i \(-0.828793\pi\)
0.873068 + 0.487598i \(0.162127\pi\)
\(174\) 13.1249 22.7329i 0.994993 1.72338i
\(175\) 0 0
\(176\) −2.51991 + 4.36462i −0.189946 + 0.328996i
\(177\) 6.16240 + 10.6736i 0.463194 + 0.802276i
\(178\) −8.28966 −0.621336
\(179\) −8.04940 −0.601640 −0.300820 0.953681i \(-0.597260\pi\)
−0.300820 + 0.953681i \(0.597260\pi\)
\(180\) 0 0
\(181\) 10.5251 + 18.2301i 0.782327 + 1.35503i 0.930583 + 0.366081i \(0.119301\pi\)
−0.148256 + 0.988949i \(0.547366\pi\)
\(182\) −12.1701 −0.902105
\(183\) 0.424577 0.0313857
\(184\) −2.34233 4.05703i −0.172679 0.299088i
\(185\) 0 0
\(186\) 5.35468 + 9.27458i 0.392624 + 0.680045i
\(187\) −9.22278 + 15.9743i −0.674437 + 1.16816i
\(188\) 2.31007 4.00115i 0.168479 0.291814i
\(189\) 39.8642 2.89969
\(190\) 0 0
\(191\) 8.03983 0.581742 0.290871 0.956762i \(-0.406055\pi\)
0.290871 + 0.956762i \(0.406055\pi\)
\(192\) −1.63248 + 2.82754i −0.117814 + 0.204060i
\(193\) 10.1224 17.5325i 0.728628 1.26202i −0.228836 0.973465i \(-0.573492\pi\)
0.957463 0.288555i \(-0.0931748\pi\)
\(194\) −8.09494 14.0208i −0.581183 1.00664i
\(195\) 0 0
\(196\) 0.0674593 + 0.116843i 0.00481852 + 0.00834593i
\(197\) −2.92004 −0.208044 −0.104022 0.994575i \(-0.533171\pi\)
−0.104022 + 0.994575i \(0.533171\pi\)
\(198\) 38.6049 2.74353
\(199\) 7.80244 + 13.5142i 0.553101 + 0.957998i 0.998049 + 0.0624418i \(0.0198888\pi\)
−0.444948 + 0.895556i \(0.646778\pi\)
\(200\) 0 0
\(201\) −1.24026 −0.0874812
\(202\) 8.46539 0.595623
\(203\) 10.5327 + 18.2432i 0.739251 + 1.28042i
\(204\) −5.97481 + 10.3487i −0.418320 + 0.724552i
\(205\) 0 0
\(206\) 5.92492 10.2623i 0.412809 0.715006i
\(207\) −17.9421 + 31.0767i −1.24707 + 2.15998i
\(208\) −4.64483 −0.322061
\(209\) 3.51528 + 21.6850i 0.243157 + 1.49998i
\(210\) 0 0
\(211\) −0.572585 + 0.991747i −0.0394184 + 0.0682747i −0.885062 0.465474i \(-0.845884\pi\)
0.845643 + 0.533749i \(0.179217\pi\)
\(212\) −2.31007 + 4.00115i −0.158656 + 0.274800i
\(213\) 14.9126 + 25.8293i 1.02179 + 1.76980i
\(214\) 8.40500 14.5579i 0.574554 0.995157i
\(215\) 0 0
\(216\) 15.2146 1.03522
\(217\) −8.59426 −0.583416
\(218\) −10.0023 17.3245i −0.677440 1.17336i
\(219\) −13.8846 24.0488i −0.938234 1.62507i
\(220\) 0 0
\(221\) −16.9999 −1.14354
\(222\) −9.39500 16.2726i −0.630551 1.09215i
\(223\) 7.66474 13.2757i 0.513269 0.889008i −0.486612 0.873618i \(-0.661768\pi\)
0.999882 0.0153903i \(-0.00489909\pi\)
\(224\) −1.31007 2.26910i −0.0875324 0.151611i
\(225\) 0 0
\(226\) −7.17524 + 12.4279i −0.477290 + 0.826690i
\(227\) 19.2850 1.27999 0.639994 0.768380i \(-0.278937\pi\)
0.639994 + 0.768380i \(0.278937\pi\)
\(228\) 2.27731 + 14.0482i 0.150818 + 0.930368i
\(229\) 14.3752 0.949939 0.474969 0.880002i \(-0.342459\pi\)
0.474969 + 0.880002i \(0.342459\pi\)
\(230\) 0 0
\(231\) −21.5569 + 37.3377i −1.41834 + 2.45664i
\(232\) 4.01991 + 6.96270i 0.263920 + 0.457123i
\(233\) 6.91272 11.9732i 0.452867 0.784389i −0.545695 0.837984i \(-0.683734\pi\)
0.998563 + 0.0535944i \(0.0170678\pi\)
\(234\) 17.7896 + 30.8125i 1.16294 + 2.01428i
\(235\) 0 0
\(236\) −3.77487 −0.245723
\(237\) 13.0023 + 22.5206i 0.844589 + 1.46287i
\(238\) −4.79478 8.30481i −0.310800 0.538321i
\(239\) −14.9696 −0.968305 −0.484152 0.874984i \(-0.660872\pi\)
−0.484152 + 0.874984i \(0.660872\pi\)
\(240\) 0 0
\(241\) 9.66469 + 16.7397i 0.622557 + 1.07830i 0.989008 + 0.147863i \(0.0472395\pi\)
−0.366451 + 0.930437i \(0.619427\pi\)
\(242\) −7.19994 + 12.4707i −0.462830 + 0.801644i
\(243\) −20.7573 35.9528i −1.33158 2.30637i
\(244\) −0.0650203 + 0.112618i −0.00416250 + 0.00720966i
\(245\) 0 0
\(246\) −18.9848 −1.21042
\(247\) −15.6880 + 12.7984i −0.998205 + 0.814346i
\(248\) −3.28009 −0.208286
\(249\) 12.8475 22.2526i 0.814180 1.41020i
\(250\) 0 0
\(251\) −5.16246 8.94164i −0.325851 0.564391i 0.655833 0.754906i \(-0.272318\pi\)
−0.981684 + 0.190515i \(0.938984\pi\)
\(252\) −10.0350 + 17.3812i −0.632148 + 1.09491i
\(253\) −11.8049 20.4468i −0.742170 1.28548i
\(254\) −7.88509 −0.494755
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −14.3846 24.9149i −0.897287 1.55415i −0.830949 0.556349i \(-0.812202\pi\)
−0.0663376 0.997797i \(-0.521131\pi\)
\(258\) 1.89466 0.117956
\(259\) 15.0790 0.936962
\(260\) 0 0
\(261\) 30.7924 53.3340i 1.90600 3.30129i
\(262\) −1.20228 2.08242i −0.0742774 0.128652i
\(263\) 4.56746 7.91107i 0.281642 0.487818i −0.690148 0.723669i \(-0.742454\pi\)
0.971789 + 0.235851i \(0.0757877\pi\)
\(264\) −8.22742 + 14.2503i −0.506363 + 0.877046i
\(265\) 0 0
\(266\) −10.6771 4.05416i −0.654655 0.248577i
\(267\) −27.0654 −1.65638
\(268\) 0.189935 0.328977i 0.0116021 0.0200955i
\(269\) −8.45474 + 14.6440i −0.515495 + 0.892863i 0.484343 + 0.874878i \(0.339059\pi\)
−0.999838 + 0.0179853i \(0.994275\pi\)
\(270\) 0 0
\(271\) 7.94483 13.7609i 0.482614 0.835912i −0.517187 0.855873i \(-0.673021\pi\)
0.999801 + 0.0199603i \(0.00635399\pi\)
\(272\) −1.82998 3.16962i −0.110959 0.192186i
\(273\) −39.7347 −2.40486
\(274\) 17.4350 1.05329
\(275\) 0 0
\(276\) −7.64761 13.2460i −0.460332 0.797318i
\(277\) 11.4852 0.690079 0.345040 0.938588i \(-0.387865\pi\)
0.345040 + 0.938588i \(0.387865\pi\)
\(278\) 9.56975 0.573955
\(279\) 12.5627 + 21.7592i 0.752108 + 1.30269i
\(280\) 0 0
\(281\) 7.14483 + 12.3752i 0.426225 + 0.738243i 0.996534 0.0831872i \(-0.0265099\pi\)
−0.570309 + 0.821430i \(0.693177\pi\)
\(282\) 7.54227 13.0636i 0.449136 0.777926i
\(283\) −1.58215 + 2.74037i −0.0940493 + 0.162898i −0.909211 0.416335i \(-0.863314\pi\)
0.815162 + 0.579233i \(0.196648\pi\)
\(284\) −9.13492 −0.542058
\(285\) 0 0
\(286\) −23.4091 −1.38421
\(287\) 7.61763 13.1941i 0.449655 0.778825i
\(288\) −3.82998 + 6.63372i −0.225684 + 0.390896i
\(289\) 1.80235 + 3.12176i 0.106021 + 0.183633i
\(290\) 0 0
\(291\) −26.4296 45.7775i −1.54933 2.68352i
\(292\) 8.50522 0.497730
\(293\) 14.7094 0.859330 0.429665 0.902988i \(-0.358632\pi\)
0.429665 + 0.902988i \(0.358632\pi\)
\(294\) 0.220252 + 0.381488i 0.0128454 + 0.0222488i
\(295\) 0 0
\(296\) 5.75505 0.334505
\(297\) 76.6789 4.44936
\(298\) 8.56218 + 14.8301i 0.495994 + 0.859087i
\(299\) 10.8797 18.8442i 0.629190 1.08979i
\(300\) 0 0
\(301\) −0.760232 + 1.31676i −0.0438190 + 0.0758968i
\(302\) 2.72220 4.71499i 0.156645 0.271317i
\(303\) 27.6392 1.58783
\(304\) −4.07502 1.54731i −0.233719 0.0887445i
\(305\) 0 0
\(306\) −14.0176 + 24.2791i −0.801331 + 1.38795i
\(307\) 13.0727 22.6425i 0.746097 1.29228i −0.203583 0.979058i \(-0.565259\pi\)
0.949680 0.313221i \(-0.101408\pi\)
\(308\) −6.60250 11.4359i −0.376213 0.651619i
\(309\) 19.3446 33.5059i 1.10048 1.90608i
\(310\) 0 0
\(311\) 6.65039 0.377109 0.188555 0.982063i \(-0.439620\pi\)
0.188555 + 0.982063i \(0.439620\pi\)
\(312\) −15.1652 −0.858559
\(313\) 8.68988 + 15.0513i 0.491181 + 0.850750i 0.999948 0.0101536i \(-0.00323205\pi\)
−0.508768 + 0.860904i \(0.669899\pi\)
\(314\) 0.0123496 + 0.0213902i 0.000696930 + 0.00120712i
\(315\) 0 0
\(316\) −7.96475 −0.448052
\(317\) −0.687647 1.19104i −0.0386221 0.0668954i 0.846068 0.533075i \(-0.178964\pi\)
−0.884690 + 0.466179i \(0.845630\pi\)
\(318\) −7.54227 + 13.0636i −0.422949 + 0.732570i
\(319\) 20.2597 + 35.0908i 1.13432 + 1.96471i
\(320\) 0 0
\(321\) 27.4420 47.5309i 1.53166 2.65292i
\(322\) 12.2744 0.684026
\(323\) −14.9144 5.66310i −0.829861 0.315103i
\(324\) 26.6951 1.48306
\(325\) 0 0
\(326\) 5.41735 9.38313i 0.300039 0.519684i
\(327\) −32.6571 56.5637i −1.80594 3.12798i
\(328\) 2.90735 5.03568i 0.160532 0.278049i
\(329\) 6.05267 + 10.4835i 0.333695 + 0.577976i
\(330\) 0 0
\(331\) 11.7399 0.645284 0.322642 0.946521i \(-0.395429\pi\)
0.322642 + 0.946521i \(0.395429\pi\)
\(332\) 3.93498 + 6.81558i 0.215960 + 0.374054i
\(333\) −22.0417 38.1774i −1.20788 2.09211i
\(334\) −6.28478 −0.343888
\(335\) 0 0
\(336\) −4.27731 7.40852i −0.233346 0.404168i
\(337\) −6.44005 + 11.1545i −0.350812 + 0.607624i −0.986392 0.164411i \(-0.947428\pi\)
0.635580 + 0.772035i \(0.280761\pi\)
\(338\) −4.28722 7.42568i −0.233194 0.403904i
\(339\) −23.4269 + 40.5765i −1.27237 + 2.20381i
\(340\) 0 0
\(341\) −16.5311 −0.895209
\(342\) 5.34282 + 32.9587i 0.288907 + 1.78220i
\(343\) −18.6944 −1.00940
\(344\) −0.290150 + 0.502555i −0.0156439 + 0.0270960i
\(345\) 0 0
\(346\) 0.187589 + 0.324914i 0.0100849 + 0.0174675i
\(347\) 2.46724 4.27339i 0.132449 0.229408i −0.792171 0.610299i \(-0.791049\pi\)
0.924620 + 0.380891i \(0.124383\pi\)
\(348\) 13.1249 + 22.7329i 0.703566 + 1.21861i
\(349\) 1.26594 0.0677644 0.0338822 0.999426i \(-0.489213\pi\)
0.0338822 + 0.999426i \(0.489213\pi\)
\(350\) 0 0
\(351\) 35.3346 + 61.2012i 1.88602 + 3.26668i
\(352\) −2.51991 4.36462i −0.134312 0.232635i
\(353\) −2.16060 −0.114997 −0.0574986 0.998346i \(-0.518312\pi\)
−0.0574986 + 0.998346i \(0.518312\pi\)
\(354\) −12.3248 −0.655056
\(355\) 0 0
\(356\) 4.14483 7.17905i 0.219676 0.380489i
\(357\) −15.6548 27.1149i −0.828539 1.43507i
\(358\) 4.02470 6.97098i 0.212712 0.368428i
\(359\) 2.36981 4.10463i 0.125074 0.216634i −0.796688 0.604391i \(-0.793417\pi\)
0.921762 + 0.387757i \(0.126750\pi\)
\(360\) 0 0
\(361\) −18.0270 + 6.00231i −0.948789 + 0.315911i
\(362\) −21.0503 −1.10638
\(363\) −23.5075 + 40.7162i −1.23382 + 2.13705i
\(364\) 6.08503 10.5396i 0.318942 0.552424i
\(365\) 0 0
\(366\) −0.212289 + 0.367695i −0.0110965 + 0.0192197i
\(367\) −11.4472 19.8271i −0.597538 1.03497i −0.993183 0.116563i \(-0.962812\pi\)
0.395645 0.918403i \(-0.370521\pi\)
\(368\) 4.68466 0.244205
\(369\) −44.5404 −2.31868
\(370\) 0 0
\(371\) −6.05267 10.4835i −0.314239 0.544278i
\(372\) −10.7094 −0.555254
\(373\) −19.2393 −0.996172 −0.498086 0.867128i \(-0.665964\pi\)
−0.498086 + 0.867128i \(0.665964\pi\)
\(374\) −9.22278 15.9743i −0.476899 0.826013i
\(375\) 0 0
\(376\) 2.31007 + 4.00115i 0.119133 + 0.206344i
\(377\) −18.6718 + 32.3405i −0.961647 + 1.66562i
\(378\) −19.9321 + 34.5234i −1.02520 + 1.77569i
\(379\) −6.45953 −0.331804 −0.165902 0.986142i \(-0.553053\pi\)
−0.165902 + 0.986142i \(0.553053\pi\)
\(380\) 0 0
\(381\) −25.7445 −1.31893
\(382\) −4.01991 + 6.96270i −0.205677 + 0.356243i
\(383\) 4.56746 7.91107i 0.233386 0.404237i −0.725416 0.688310i \(-0.758353\pi\)
0.958802 + 0.284074i \(0.0916860\pi\)
\(384\) −1.63248 2.82754i −0.0833071 0.144292i
\(385\) 0 0
\(386\) 10.1224 + 17.5325i 0.515218 + 0.892383i
\(387\) 4.44508 0.225956
\(388\) 16.1899 0.821917
\(389\) 13.3424 + 23.1098i 0.676488 + 1.17171i 0.976032 + 0.217629i \(0.0698321\pi\)
−0.299544 + 0.954082i \(0.596835\pi\)
\(390\) 0 0
\(391\) 17.1457 0.867093
\(392\) −0.134919 −0.00681442
\(393\) −3.92541 6.79901i −0.198011 0.342965i
\(394\) 1.46002 2.52883i 0.0735548 0.127401i
\(395\) 0 0
\(396\) −19.3024 + 33.4328i −0.969984 + 1.68006i
\(397\) −7.37459 + 12.7732i −0.370120 + 0.641067i −0.989584 0.143958i \(-0.954017\pi\)
0.619464 + 0.785025i \(0.287350\pi\)
\(398\) −15.6049 −0.782202
\(399\) −34.8603 13.2367i −1.74520 0.662662i
\(400\) 0 0
\(401\) −5.82720 + 10.0930i −0.290996 + 0.504021i −0.974046 0.226352i \(-0.927320\pi\)
0.683049 + 0.730372i \(0.260653\pi\)
\(402\) 0.620130 1.07410i 0.0309293 0.0535711i
\(403\) −7.61773 13.1943i −0.379466 0.657254i
\(404\) −4.23270 + 7.33124i −0.210584 + 0.364743i
\(405\) 0 0
\(406\) −21.0654 −1.04546
\(407\) 29.0045 1.43770
\(408\) −5.97481 10.3487i −0.295797 0.512336i
\(409\) −19.7824 34.2641i −0.978176 1.69425i −0.669030 0.743235i \(-0.733290\pi\)
−0.309145 0.951015i \(-0.600043\pi\)
\(410\) 0 0
\(411\) 56.9246 2.80788
\(412\) 5.92492 + 10.2623i 0.291900 + 0.505585i
\(413\) 4.94532 8.56555i 0.243344 0.421483i
\(414\) −17.9421 31.0767i −0.881808 1.52734i
\(415\) 0 0
\(416\) 2.32241 4.02254i 0.113866 0.197221i
\(417\) 31.2448 1.53007
\(418\) −20.5374 7.79819i −1.00452 0.381422i
\(419\) 17.3292 0.846586 0.423293 0.905993i \(-0.360874\pi\)
0.423293 + 0.905993i \(0.360874\pi\)
\(420\) 0 0
\(421\) −12.1652 + 21.0707i −0.592895 + 1.02692i 0.400946 + 0.916102i \(0.368682\pi\)
−0.993840 + 0.110822i \(0.964652\pi\)
\(422\) −0.572585 0.991747i −0.0278730 0.0482775i
\(423\) 17.6950 30.6486i 0.860361 1.49019i
\(424\) −2.31007 4.00115i −0.112187 0.194313i
\(425\) 0 0
\(426\) −29.8251 −1.44503
\(427\) −0.170362 0.295075i −0.00824438 0.0142797i
\(428\) 8.40500 + 14.5579i 0.406271 + 0.703682i
\(429\) −76.4299 −3.69007
\(430\) 0 0
\(431\) −14.1173 24.4519i −0.680006 1.17781i −0.974978 0.222299i \(-0.928644\pi\)
0.294972 0.955506i \(-0.404690\pi\)
\(432\) −7.60729 + 13.1762i −0.366006 + 0.633941i
\(433\) 11.6899 + 20.2475i 0.561780 + 0.973031i 0.997341 + 0.0728720i \(0.0232165\pi\)
−0.435562 + 0.900159i \(0.643450\pi\)
\(434\) 4.29713 7.44285i 0.206269 0.357268i
\(435\) 0 0
\(436\) 20.0046 0.958045
\(437\) 15.8225 12.9082i 0.756895 0.617483i
\(438\) 27.7692 1.32686
\(439\) −13.3775 + 23.1705i −0.638472 + 1.10587i 0.347297 + 0.937755i \(0.387100\pi\)
−0.985768 + 0.168110i \(0.946234\pi\)
\(440\) 0 0
\(441\) 0.516736 + 0.895013i 0.0246065 + 0.0426197i
\(442\) 8.49994 14.7223i 0.404301 0.700270i
\(443\) 8.84989 + 15.3285i 0.420471 + 0.728277i 0.995986 0.0895142i \(-0.0285315\pi\)
−0.575514 + 0.817792i \(0.695198\pi\)
\(444\) 18.7900 0.891734
\(445\) 0 0
\(446\) 7.66474 + 13.2757i 0.362936 + 0.628624i
\(447\) 27.9552 + 48.4198i 1.32223 + 2.29018i
\(448\) 2.62013 0.123790
\(449\) 28.3541 1.33811 0.669056 0.743212i \(-0.266699\pi\)
0.669056 + 0.743212i \(0.266699\pi\)
\(450\) 0 0
\(451\) 14.6525 25.3790i 0.689961 1.19505i
\(452\) −7.17524 12.4279i −0.337495 0.584558i
\(453\) 8.88787 15.3942i 0.417589 0.723285i
\(454\) −9.64248 + 16.7013i −0.452544 + 0.783830i
\(455\) 0 0
\(456\) −13.3048 5.05191i −0.623054 0.236578i
\(457\) 11.5898 0.542146 0.271073 0.962559i \(-0.412622\pi\)
0.271073 + 0.962559i \(0.412622\pi\)
\(458\) −7.18759 + 12.4493i −0.335854 + 0.581716i
\(459\) −27.8424 + 48.2244i −1.29957 + 2.25092i
\(460\) 0 0
\(461\) −17.8899 + 30.9862i −0.833214 + 1.44317i 0.0622614 + 0.998060i \(0.480169\pi\)
−0.895476 + 0.445110i \(0.853165\pi\)
\(462\) −21.5569 37.3377i −1.00292 1.73711i
\(463\) 23.5039 1.09232 0.546160 0.837681i \(-0.316089\pi\)
0.546160 + 0.837681i \(0.316089\pi\)
\(464\) −8.03983 −0.373240
\(465\) 0 0
\(466\) 6.91272 + 11.9732i 0.320226 + 0.554647i
\(467\) −1.12047 −0.0518492 −0.0259246 0.999664i \(-0.508253\pi\)
−0.0259246 + 0.999664i \(0.508253\pi\)
\(468\) −35.5792 −1.64465
\(469\) 0.497654 + 0.861963i 0.0229795 + 0.0398017i
\(470\) 0 0
\(471\) 0.0403210 + 0.0698381i 0.00185790 + 0.00321797i
\(472\) 1.88743 3.26913i 0.0868762 0.150474i
\(473\) −1.46231 + 2.53279i −0.0672370 + 0.116458i
\(474\) −26.0046 −1.19443
\(475\) 0 0
\(476\) 9.58957 0.439537
\(477\) −17.6950 + 30.6486i −0.810199 + 1.40331i
\(478\) 7.48481 12.9641i 0.342347 0.592963i
\(479\) −13.6547 23.6506i −0.623898 1.08062i −0.988753 0.149559i \(-0.952215\pi\)
0.364854 0.931065i \(-0.381119\pi\)
\(480\) 0 0
\(481\) 13.3656 + 23.1499i 0.609419 + 1.05555i
\(482\) −19.3294 −0.880429
\(483\) 40.0755 1.82350
\(484\) −7.19994 12.4707i −0.327270 0.566848i
\(485\) 0 0
\(486\) 41.5147 1.88314
\(487\) 6.32003 0.286388 0.143194 0.989695i \(-0.454263\pi\)
0.143194 + 0.989695i \(0.454263\pi\)
\(488\) −0.0650203 0.112618i −0.00294333 0.00509800i
\(489\) 17.6874 30.6355i 0.799854 1.38539i
\(490\) 0 0
\(491\) 12.9025 22.3478i 0.582282 1.00854i −0.412926 0.910764i \(-0.635493\pi\)
0.995208 0.0977776i \(-0.0311734\pi\)
\(492\) 9.49238 16.4413i 0.427949 0.741230i
\(493\) −29.4254 −1.32526
\(494\) −3.23977 19.9855i −0.145764 0.899188i
\(495\) 0 0
\(496\) 1.64004 2.84064i 0.0736402 0.127549i
\(497\) 11.9673 20.7280i 0.536808 0.929779i
\(498\) 12.8475 + 22.2526i 0.575712 + 0.997163i
\(499\) 14.4572 25.0406i 0.647192 1.12097i −0.336598 0.941648i \(-0.609276\pi\)
0.983790 0.179322i \(-0.0573903\pi\)
\(500\) 0 0
\(501\) −20.5196 −0.916746
\(502\) 10.3249 0.460823
\(503\) 0.575024 + 0.995971i 0.0256391 + 0.0444082i 0.878560 0.477632i \(-0.158505\pi\)
−0.852921 + 0.522040i \(0.825171\pi\)
\(504\) −10.0350 17.3812i −0.446996 0.774220i
\(505\) 0 0
\(506\) 23.6099 1.04959
\(507\) −13.9976 24.2445i −0.621655 1.07674i
\(508\) 3.94254 6.82869i 0.174922 0.302974i
\(509\) −20.3673 35.2772i −0.902765 1.56364i −0.823889 0.566751i \(-0.808200\pi\)
−0.0788760 0.996884i \(-0.525133\pi\)
\(510\) 0 0
\(511\) −11.1424 + 19.2992i −0.492910 + 0.853746i
\(512\) 1.00000 0.0441942
\(513\) 10.6122 + 65.4642i 0.468539 + 2.89032i
\(514\) 28.7692 1.26895
\(515\) 0 0
\(516\) −0.947329 + 1.64082i −0.0417038 + 0.0722332i
\(517\) 11.6423 + 20.1651i 0.512029 + 0.886861i
\(518\) −7.53949 + 13.0588i −0.331266 + 0.573770i
\(519\) 0.612472 + 1.06083i 0.0268845 + 0.0465654i
\(520\) 0 0
\(521\) −11.4246 −0.500520 −0.250260 0.968179i \(-0.580516\pi\)
−0.250260 + 0.968179i \(0.580516\pi\)
\(522\) 30.7924 + 53.3340i 1.34775 + 2.33436i
\(523\) 6.55696 + 11.3570i 0.286716 + 0.496607i 0.973024 0.230704i \(-0.0741031\pi\)
−0.686308 + 0.727311i \(0.740770\pi\)
\(524\) 2.40457 0.105044
\(525\) 0 0
\(526\) 4.56746 + 7.91107i 0.199151 + 0.344939i
\(527\) 6.00250 10.3966i 0.261473 0.452884i
\(528\) −8.22742 14.2503i −0.358052 0.620165i
\(529\) 0.526988 0.912769i 0.0229125 0.0396856i
\(530\) 0 0
\(531\) −28.9153 −1.25482
\(532\) 8.84955 7.21955i 0.383677 0.313007i
\(533\) 27.0083 1.16986
\(534\) 13.5327 23.4393i 0.585617 1.01432i
\(535\) 0 0
\(536\) 0.189935 + 0.328977i 0.00820394 + 0.0142096i
\(537\) 13.1405 22.7600i 0.567054 0.982166i
\(538\) −8.45474 14.6440i −0.364510 0.631350i
\(539\) −0.679967 −0.0292883
\(540\) 0 0
\(541\) 14.4949 + 25.1059i 0.623183 + 1.07939i 0.988889 + 0.148655i \(0.0474943\pi\)
−0.365706 + 0.930730i \(0.619172\pi\)
\(542\) 7.94483 + 13.7609i 0.341260 + 0.591079i
\(543\) −68.7283 −2.94941
\(544\) 3.65996 0.156919
\(545\) 0 0
\(546\) 19.8674 34.4113i 0.850245 1.47267i
\(547\) −17.8242 30.8724i −0.762108 1.32001i −0.941762 0.336280i \(-0.890831\pi\)
0.179654 0.983730i \(-0.442502\pi\)
\(548\) −8.71751 + 15.0992i −0.372393 + 0.645004i
\(549\) −0.498053 + 0.862653i −0.0212564 + 0.0368171i
\(550\) 0 0
\(551\) −27.1547 + 22.1531i −1.15683 + 0.943753i
\(552\) 15.2952 0.651008
\(553\) 10.4343 18.0728i 0.443713 0.768534i
\(554\) −5.74261 + 9.94648i −0.243980 + 0.422586i
\(555\) 0 0
\(556\) −4.78487 + 8.28764i −0.202924 + 0.351474i
\(557\) 6.27731 + 10.8726i 0.265978 + 0.460688i 0.967819 0.251646i \(-0.0809718\pi\)
−0.701841 + 0.712333i \(0.747638\pi\)
\(558\) −25.1253 −1.06364
\(559\) −2.69540 −0.114003
\(560\) 0 0
\(561\) −30.1120 52.1555i −1.27133 2.20201i
\(562\) −14.2897 −0.602773
\(563\) 2.88509 0.121592 0.0607960 0.998150i \(-0.480636\pi\)
0.0607960 + 0.998150i \(0.480636\pi\)
\(564\) 7.54227 + 13.0636i 0.317587 + 0.550076i
\(565\) 0 0
\(566\) −1.58215 2.74037i −0.0665029 0.115186i
\(567\) −34.9723 + 60.5738i −1.46870 + 2.54386i
\(568\) 4.56746 7.91107i 0.191646 0.331941i
\(569\) −10.9249 −0.457996 −0.228998 0.973427i \(-0.573545\pi\)
−0.228998 + 0.973427i \(0.573545\pi\)
\(570\) 0 0
\(571\) 6.27911 0.262772 0.131386 0.991331i \(-0.458057\pi\)
0.131386 + 0.991331i \(0.458057\pi\)
\(572\) 11.7046 20.2729i 0.489393 0.847653i
\(573\) −13.1249 + 22.7329i −0.548299 + 0.949681i
\(574\) 7.61763 + 13.1941i 0.317954 + 0.550712i
\(575\) 0 0
\(576\) −3.82998 6.63372i −0.159582 0.276405i
\(577\) 25.9848 1.08176 0.540880 0.841100i \(-0.318091\pi\)
0.540880 + 0.841100i \(0.318091\pi\)
\(578\) −3.60470 −0.149936
\(579\) 33.0493 + 57.2430i 1.37348 + 2.37894i
\(580\) 0 0
\(581\) −20.6203 −0.855475
\(582\) 52.8593 2.19109
\(583\) −11.6423 20.1651i −0.482176 0.835154i
\(584\) −4.25261 + 7.36574i −0.175974 + 0.304796i
\(585\) 0 0
\(586\) −7.35468 + 12.7387i −0.303819 + 0.526230i
\(587\) 18.1547 31.4448i 0.749324 1.29787i −0.198823 0.980035i \(-0.563712\pi\)
0.948147 0.317832i \(-0.102955\pi\)
\(588\) −0.440504 −0.0181661
\(589\) −2.28786 14.1133i −0.0942697 0.581530i
\(590\) 0 0
\(591\) 4.76691 8.25652i 0.196084 0.339628i
\(592\) −2.87752 + 4.98402i −0.118266 + 0.204842i
\(593\) −15.8646 27.4783i −0.651482 1.12840i −0.982763 0.184868i \(-0.940814\pi\)
0.331281 0.943532i \(-0.392519\pi\)
\(594\) −38.3394 + 66.4058i −1.57309 + 2.72466i
\(595\) 0 0
\(596\) −17.1244 −0.701441
\(597\) −50.9493 −2.08522
\(598\) 10.8797 + 18.8442i 0.444905 + 0.770598i
\(599\) 0.174654 + 0.302510i 0.00713619 + 0.0123602i 0.869571 0.493807i \(-0.164395\pi\)
−0.862435 + 0.506167i \(0.831062\pi\)
\(600\) 0 0
\(601\) 33.7305 1.37590 0.687949 0.725759i \(-0.258511\pi\)
0.687949 + 0.725759i \(0.258511\pi\)
\(602\) −0.760232 1.31676i −0.0309847 0.0536671i
\(603\) 1.45489 2.51995i 0.0592479 0.102620i
\(604\) 2.72220 + 4.71499i 0.110765 + 0.191850i
\(605\) 0 0
\(606\) −13.8196 + 23.9362i −0.561382 + 0.972342i
\(607\) −28.0561 −1.13876 −0.569382 0.822073i \(-0.692817\pi\)
−0.569382 + 0.822073i \(0.692817\pi\)
\(608\) 3.37752 2.75542i 0.136977 0.111747i
\(609\) −68.7777 −2.78701
\(610\) 0 0
\(611\) −10.7299 + 18.5847i −0.434084 + 0.751855i
\(612\) −14.0176 24.2791i −0.566627 0.981426i
\(613\) 20.7251 35.8969i 0.837078 1.44986i −0.0552496 0.998473i \(-0.517595\pi\)
0.892327 0.451389i \(-0.149071\pi\)
\(614\) 13.0727 + 22.6425i 0.527570 + 0.913779i
\(615\) 0 0
\(616\) 13.2050 0.532045
\(617\) −2.94440 5.09985i −0.118537 0.205312i 0.800651 0.599131i \(-0.204487\pi\)
−0.919188 + 0.393819i \(0.871154\pi\)
\(618\) 19.3446 + 33.5059i 0.778155 + 1.34780i
\(619\) 13.7152 0.551261 0.275631 0.961264i \(-0.411113\pi\)
0.275631 + 0.961264i \(0.411113\pi\)
\(620\) 0 0
\(621\) −35.6375 61.7260i −1.43009 2.47698i
\(622\) −3.32519 + 5.75941i −0.133328 + 0.230931i
\(623\) 10.8600 + 18.8101i 0.435096 + 0.753609i
\(624\) 7.58259 13.1334i 0.303547 0.525758i
\(625\) 0 0
\(626\) −17.3798 −0.694635
\(627\) −67.0539 25.4608i −2.67787 1.01681i
\(628\) −0.0246993 −0.000985608
\(629\) −10.5316 + 18.2413i −0.419923 + 0.727328i
\(630\) 0 0
\(631\) 8.14468 + 14.1070i 0.324235 + 0.561591i 0.981357 0.192193i \(-0.0615600\pi\)
−0.657123 + 0.753784i \(0.728227\pi\)
\(632\) 3.98237 6.89767i 0.158410 0.274375i
\(633\) −1.86947 3.23801i −0.0743047 0.128699i
\(634\) 1.37529 0.0546199
\(635\) 0 0
\(636\) −7.54227 13.0636i −0.299070 0.518005i
\(637\) −0.313337 0.542716i −0.0124149 0.0215032i
\(638\) −40.5194 −1.60418
\(639\) −69.9731 −2.76809
\(640\) 0 0
\(641\) −14.8124 + 25.6559i −0.585056 + 1.01335i 0.409812 + 0.912170i \(0.365594\pi\)
−0.994868 + 0.101177i \(0.967739\pi\)
\(642\) 27.4420 + 47.5309i 1.08305 + 1.87590i
\(643\) 6.01050 10.4105i 0.237031 0.410549i −0.722830 0.691026i \(-0.757159\pi\)
0.959861 + 0.280476i \(0.0904924\pi\)
\(644\) −6.13721 + 10.6300i −0.241840 + 0.418879i
\(645\) 0 0
\(646\) 12.3616 10.0847i 0.486361 0.396778i
\(647\) 3.16079 0.124263 0.0621317 0.998068i \(-0.480210\pi\)
0.0621317 + 0.998068i \(0.480210\pi\)
\(648\) −13.3475 + 23.1186i −0.524341 + 0.908186i
\(649\) 9.51235 16.4759i 0.373392 0.646735i
\(650\) 0 0
\(651\) 14.0300 24.3006i 0.549877 0.952415i
\(652\) 5.41735 + 9.38313i 0.212160 + 0.367472i
\(653\) −19.6097 −0.767387 −0.383693 0.923461i \(-0.625348\pi\)
−0.383693 + 0.923461i \(0.625348\pi\)
\(654\) 65.3141 2.55398
\(655\) 0 0
\(656\) 2.90735 + 5.03568i 0.113513 + 0.196610i
\(657\) 65.1496 2.54173
\(658\) −12.1053 −0.471915
\(659\) 9.03748 + 15.6534i 0.352050 + 0.609769i 0.986609 0.163106i \(-0.0521512\pi\)
−0.634558 + 0.772875i \(0.718818\pi\)
\(660\) 0 0
\(661\) 7.26715 + 12.5871i 0.282660 + 0.489581i 0.972039 0.234820i \(-0.0754500\pi\)
−0.689379 + 0.724400i \(0.742117\pi\)
\(662\) −5.86996 + 10.1671i −0.228142 + 0.395154i
\(663\) 27.7520 48.0678i 1.07780 1.86680i
\(664\) −7.86996 −0.305414
\(665\) 0 0
\(666\) 44.0834 1.70820
\(667\) 18.8319 32.6179i 0.729175 1.26297i
\(668\) 3.14239 5.44278i 0.121583 0.210587i
\(669\) 25.0251 + 43.3447i 0.967525 + 1.67580i
\(670\) 0 0
\(671\) −0.327691 0.567578i −0.0126504 0.0219111i
\(672\) 8.55462 0.330002
\(673\) 6.13522 0.236495 0.118248 0.992984i \(-0.462272\pi\)
0.118248 + 0.992984i \(0.462272\pi\)
\(674\) −6.44005 11.1545i −0.248061 0.429655i
\(675\) 0 0
\(676\) 8.57444 0.329786
\(677\) −13.6380 −0.524150 −0.262075 0.965047i \(-0.584407\pi\)
−0.262075 + 0.965047i \(0.584407\pi\)
\(678\) −23.4269 40.5765i −0.899703 1.55833i
\(679\) −21.2098 + 36.7364i −0.813957 + 1.40982i
\(680\) 0 0
\(681\) −31.4823 + 54.5290i −1.20640 + 2.08955i
\(682\) 8.26554 14.3163i 0.316504 0.548201i
\(683\) 16.7550 0.641114 0.320557 0.947229i \(-0.396130\pi\)
0.320557 + 0.947229i \(0.396130\pi\)
\(684\) −31.2145 11.8524i −1.19352 0.453186i
\(685\) 0 0
\(686\) 9.34721 16.1898i 0.356878 0.618131i
\(687\) −23.4672 + 40.6464i −0.895329 + 1.55076i
\(688\) −0.290150 0.502555i −0.0110619 0.0191597i
\(689\) 10.7299 18.5847i 0.408775 0.708019i
\(690\) 0 0
\(691\) 21.5889 0.821280 0.410640 0.911798i \(-0.365305\pi\)
0.410640 + 0.911798i \(0.365305\pi\)
\(692\) −0.375179 −0.0142622
\(693\) −50.5749 87.5983i −1.92118 3.32758i
\(694\) 2.46724 + 4.27339i 0.0936553 + 0.162216i
\(695\) 0 0
\(696\) −26.2497 −0.994993
\(697\) 10.6408 + 18.4304i 0.403048 + 0.698100i
\(698\) −0.632972 + 1.09634i −0.0239583 + 0.0414970i
\(699\) 22.5697 + 39.0919i 0.853666 + 1.47859i
\(700\) 0 0
\(701\) 18.8628 32.6713i 0.712437 1.23398i −0.251503 0.967857i \(-0.580925\pi\)
0.963940 0.266121i \(-0.0857419\pi\)
\(702\) −70.6691 −2.66723
\(703\) 4.01415 + 24.7624i 0.151396 + 0.933933i
\(704\) 5.03983 0.189946
\(705\) 0 0
\(706\) 1.08030 1.87114i 0.0406577 0.0704211i
\(707\) −11.0902 19.2088i −0.417090 0.722422i
\(708\) 6.16240 10.6736i 0.231597 0.401138i
\(709\) 10.4795 + 18.1511i 0.393567 + 0.681678i 0.992917 0.118809i \(-0.0379075\pi\)
−0.599350 + 0.800487i \(0.704574\pi\)
\(710\) 0 0
\(711\) −61.0096 −2.28804
\(712\) 4.14483 + 7.17905i 0.155334 + 0.269046i
\(713\) 7.68305 + 13.3074i 0.287732 + 0.498367i
\(714\) 31.3096 1.17173
\(715\) 0 0
\(716\) 4.02470 + 6.97098i 0.150410 + 0.260518i
\(717\) 24.4376 42.3272i 0.912639 1.58074i
\(718\) 2.36981 + 4.10463i 0.0884405 + 0.153183i
\(719\) 22.1401 38.3477i 0.825686 1.43013i −0.0757084 0.997130i \(-0.524122\pi\)
0.901394 0.433000i \(-0.142545\pi\)
\(720\) 0 0
\(721\) −31.0481 −1.15629
\(722\) 3.81534 18.6130i 0.141992 0.692704i
\(723\) −63.1096 −2.34707
\(724\) 10.5251 18.2301i 0.391164 0.677515i
\(725\) 0 0
\(726\) −23.5075 40.7162i −0.872445 1.51112i
\(727\) −24.2169 + 41.9448i −0.898154 + 1.55565i −0.0683017 + 0.997665i \(0.521758\pi\)
−0.829852 + 0.557983i \(0.811575\pi\)
\(728\) 6.08503 + 10.5396i 0.225526 + 0.390623i
\(729\) 55.4584 2.05402
\(730\) 0 0
\(731\) −1.06194 1.83933i −0.0392772 0.0680301i
\(732\) −0.212289 0.367695i −0.00784641 0.0135904i
\(733\) 9.62940 0.355670 0.177835 0.984060i \(-0.443091\pi\)
0.177835 + 0.984060i \(0.443091\pi\)
\(734\) 22.8944 0.845046
\(735\) 0 0
\(736\) −2.34233 + 4.05703i −0.0863394 + 0.149544i
\(737\) 0.957240 + 1.65799i 0.0352604 + 0.0610728i
\(738\) 22.2702 38.5731i 0.819777 1.41989i
\(739\) 20.3423 35.2338i 0.748303 1.29610i −0.200333 0.979728i \(-0.564202\pi\)
0.948636 0.316370i \(-0.102464\pi\)
\(740\) 0 0
\(741\) −10.5777 65.2517i −0.388582 2.39708i
\(742\) 12.1053 0.444401
\(743\) 1.43254 2.48123i 0.0525548 0.0910276i −0.838551 0.544823i \(-0.816597\pi\)
0.891106 + 0.453795i \(0.149930\pi\)
\(744\) 5.35468 9.27458i 0.196312 0.340022i
\(745\) 0 0
\(746\) 9.61964 16.6617i 0.352200 0.610028i
\(747\) 30.1418 + 52.2071i 1.10283 + 1.91016i
\(748\) 18.4456 0.674437
\(749\) −44.0444 −1.60935
\(750\) 0 0
\(751\) 13.1148 + 22.7155i 0.478566 + 0.828900i 0.999698 0.0245758i \(-0.00782351\pi\)
−0.521132 + 0.853476i \(0.674490\pi\)
\(752\) −4.62013 −0.168479
\(753\) 33.7104 1.22848
\(754\) −18.6718 32.3405i −0.679987 1.17777i
\(755\) 0 0
\(756\) −19.9321 34.5234i −0.724923 1.25560i
\(757\) 3.29195 5.70182i 0.119648 0.207236i −0.799980 0.600026i \(-0.795157\pi\)
0.919628 + 0.392790i \(0.128490\pi\)
\(758\) 3.22976 5.59412i 0.117310 0.203187i
\(759\) 77.0853 2.79802
\(760\) 0 0
\(761\) −27.7549 −1.00612 −0.503058 0.864253i \(-0.667792\pi\)
−0.503058 + 0.864253i \(0.667792\pi\)
\(762\) 12.8722 22.2954i 0.466312 0.807677i
\(763\) −26.2073 + 45.3924i −0.948768 + 1.64331i
\(764\) −4.01991 6.96270i −0.145435 0.251902i
\(765\) 0 0
\(766\) 4.56746 + 7.91107i 0.165029 + 0.285839i
\(767\) 17.5336 0.633103
\(768\) 3.26496 0.117814
\(769\) −8.32285 14.4156i −0.300130 0.519840i 0.676035 0.736869i \(-0.263697\pi\)
−0.976165 + 0.217029i \(0.930363\pi\)
\(770\) 0 0
\(771\) 93.9303 3.38282
\(772\) −20.2448 −0.728628
\(773\) −12.1049 20.9664i −0.435385 0.754108i 0.561942 0.827176i \(-0.310054\pi\)
−0.997327 + 0.0730682i \(0.976721\pi\)
\(774\) −2.22254 + 3.84955i −0.0798876 + 0.138369i
\(775\) 0 0
\(776\) −8.09494 + 14.0208i −0.290591 + 0.503319i
\(777\) −24.6161 + 42.6364i −0.883098 + 1.52957i
\(778\) −26.6848 −0.956698
\(779\) 23.6950 + 8.99716i 0.848963 + 0.322357i
\(780\) 0 0
\(781\) 23.0192 39.8704i 0.823692 1.42668i
\(782\) −8.57283 + 14.8486i −0.306564 + 0.530984i
\(783\) 61.1613 + 105.934i 2.18573 + 3.78579i
\(784\) 0.0674593 0.116843i 0.00240926 0.00417296i
\(785\) 0 0
\(786\) 7.85082