Properties

Label 950.2.e.m.501.4
Level $950$
Weight $2$
Character 950.501
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 501.4
Root \(-1.63248 - 2.82754i\) of defining polynomial
Character \(\chi\) \(=\) 950.501
Dual form 950.2.e.m.201.4

$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

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

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 0.760657 + 0.649154i \(0.224877\pi\)
0.181856 + 0.983325i \(0.441790\pi\)
\(4\) −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 \(-0.664890\pi\)
−0.495158 + 0.868803i \(0.664890\pi\)
\(8\) −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 0.340382 + 0.940287i \(0.389444\pi\)
−0.984504 + 0.175365i \(0.943890\pi\)
\(14\) −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 \(-0.0202842\pi\)
−0.554135 + 0.832427i \(0.686951\pi\)
\(18\) −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 \(-0.670911\pi\)
0.999911 + 0.0133324i \(0.00424395\pi\)
\(24\) −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 −0.203021 0.979174i \(-0.565076\pi\)
0.949500 0.313766i \(-0.101591\pi\)
\(30\) 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 \(-0.656851\pi\)
−0.473062 + 0.881029i \(0.656851\pi\)
\(38\) 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 0.998633 0.0522673i \(-0.0166448\pi\)
−0.544581 + 0.838708i \(0.683311\pi\)
\(42\) 4.27731 7.40852i 0.660003 1.14316i
\(43\) 0.290150 + 0.502555i 0.0442475 + 0.0766390i 0.887301 0.461191i \(-0.152578\pi\)
−0.843053 + 0.537830i \(0.819244\pi\)
\(44\) −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 \(-0.942731\pi\)
0.646901 + 0.762574i \(0.276065\pi\)
\(48\) 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 \(-0.730553\pi\)
0.979926 + 0.199361i \(0.0638865\pi\)
\(54\) −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 0.962335 0.271868i \(-0.0876413\pi\)
−0.716612 + 0.697472i \(0.754308\pi\)
\(60\) 0 0
\(61\) −0.0650203 + 0.112618i −0.00832500 + 0.0144193i −0.870158 0.492773i \(-0.835983\pi\)
0.861833 + 0.507192i \(0.169317\pi\)
\(62\) −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 \(-0.840720\pi\)
0.854190 + 0.519961i \(0.174053\pi\)
\(68\) −3.65996 −0.443835
\(69\) 15.2952 1.84133
\(70\) 0 0
\(71\) 4.56746 + 7.91107i 0.542058 + 0.938871i 0.998786 + 0.0492651i \(0.0156879\pi\)
−0.456728 + 0.889606i \(0.650979\pi\)
\(72\) 3.82998 6.63372i 0.451367 0.781791i
\(73\) 4.25261 + 7.36574i 0.497730 + 0.862094i 0.999997 0.00261883i \(-0.000833600\pi\)
−0.502266 + 0.864713i \(0.667500\pi\)
\(74\) −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 0.998259 0.0589793i \(-0.0187846\pi\)
−0.550207 + 0.835028i \(0.685451\pi\)
\(80\) 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 \(-0.357836\pi\)
0.431920 + 0.901912i \(0.357836\pi\)
\(84\) 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 −0.558289 0.829647i \(-0.688542\pi\)
0.997640 + 0.0686686i \(0.0218751\pi\)
\(90\) 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 0.904253 + 0.426997i \(0.140428\pi\)
−0.0823367 + 0.996605i \(0.526238\pi\)
\(98\) −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 −0.996054 0.0887481i \(-0.971713\pi\)
0.574885 + 0.818234i \(0.305047\pi\)
\(102\) −11.9496 −1.18319
\(103\) 11.8498 1.16760 0.583800 0.811898i \(-0.301565\pi\)
0.583800 + 0.811898i \(0.301565\pi\)
\(104\) 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 \(-0.198083\pi\)
0.812542 + 0.582902i \(0.198083\pi\)
\(108\) 7.60729 13.1762i 0.732012 1.26788i
\(109\) −10.0023 17.3245i −0.958045 1.65938i −0.727240 0.686384i \(-0.759197\pi\)
−0.230806 0.973000i \(-0.574136\pi\)
\(110\) 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 \(-0.735852\pi\)
−0.674990 + 0.737827i \(0.735852\pi\)
\(114\) 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 \(-0.947099\pi\)
0.636377 + 0.771378i \(0.280432\pi\)
\(128\) 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 0.808712 0.588205i \(-0.200165\pi\)
−0.913756 + 0.406263i \(0.866832\pi\)
\(132\) −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 −0.205507 0.978656i \(-0.565884\pi\)
0.950294 0.311353i \(-0.100782\pi\)
\(138\) 7.64761 + 13.2460i 0.651008 + 1.12758i
\(139\) −4.78487 + 8.28764i −0.405848 + 0.702949i −0.994420 0.105496i \(-0.966357\pi\)
0.588572 + 0.808445i \(0.299690\pi\)
\(140\) 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 0.967961 + 0.251102i \(0.0807931\pi\)
−0.266519 + 0.963830i \(0.585874\pi\)
\(150\) 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 \(-0.166980\pi\)
−0.866518 + 0.499146i \(0.833647\pi\)
\(158\) −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 \(-0.360513\pi\)
0.424320 + 0.905512i \(0.360513\pi\)
\(164\) −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 \(-0.911519\pi\)
0.718449 + 0.695580i \(0.244852\pi\)
\(168\) 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 \(-0.171207\pi\)
−0.873068 + 0.487598i \(0.837873\pi\)
\(174\) 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 −0.148256 0.988949i \(-0.547366\pi\)
0.930583 0.366081i \(-0.119301\pi\)
\(182\) 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 −0.957463 0.288555i \(-0.906825\pi\)
0.228836 0.973465i \(-0.426508\pi\)
\(194\) −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 \(-0.466829\pi\)
0.104022 + 0.994575i \(0.466829\pi\)
\(198\) −38.6049 −2.74353
\(199\) 7.80244 13.5142i 0.553101 0.957998i −0.444948 0.895556i \(-0.646778\pi\)
0.998049 0.0624418i \(-0.0198888\pi\)
\(200\) 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 0.845643 0.533749i \(-0.179217\pi\)
−0.885062 + 0.465474i \(0.845884\pi\)
\(212\) 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 −0.999882 0.0153903i \(-0.995101\pi\)
0.486612 0.873618i \(-0.338232\pi\)
\(224\) −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 \(-0.721063\pi\)
−0.639994 + 0.768380i \(0.721063\pi\)
\(228\) −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 \(-0.316266\pi\)
−0.998563 + 0.0535944i \(0.982932\pi\)
\(234\) 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 −0.366451 0.930437i \(-0.619427\pi\)
0.989008 0.147863i \(-0.0472395\pi\)
\(242\) 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 −0.981684 0.190515i \(-0.938984\pi\)
0.655833 + 0.754906i \(0.272318\pi\)
\(252\) 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 0.0663376 0.997797i \(-0.478869\pi\)
0.830949 0.556349i \(-0.187798\pi\)
\(258\) −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 \(-0.257546\pi\)
−0.971789 + 0.235851i \(0.924212\pi\)
\(264\) −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 −0.999838 0.0179853i \(-0.994275\pi\)
0.484343 0.874878i \(-0.339059\pi\)
\(270\) 0 0
\(271\) 7.94483 + 13.7609i 0.482614 + 0.835912i 0.999801 0.0199603i \(-0.00635399\pi\)
−0.517187 + 0.855873i \(0.673021\pi\)
\(272\) 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 \(-0.612135\pi\)
−0.345040 + 0.938588i \(0.612135\pi\)
\(278\) −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 −0.570309 0.821430i \(-0.693177\pi\)
0.996534 + 0.0831872i \(0.0265099\pi\)
\(282\) −7.54227 13.0636i −0.449136 0.777926i
\(283\) 1.58215 + 2.74037i 0.0940493 + 0.162898i 0.909211 0.416335i \(-0.136686\pi\)
−0.815162 + 0.579233i \(0.803352\pi\)
\(284\) −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 \(-0.641368\pi\)
−0.429665 + 0.902988i \(0.641368\pi\)
\(294\) 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 −0.949680 0.313221i \(-0.898592\pi\)
0.203583 0.979058i \(-0.434741\pi\)
\(308\) 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 \(-0.996768\pi\)
0.508768 + 0.860904i \(0.330101\pi\)
\(314\) 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 \(-0.821036\pi\)
0.884690 + 0.466179i \(0.154370\pi\)
\(318\) 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 \(-0.0525724\pi\)
−0.635580 + 0.772035i \(0.719239\pi\)
\(338\) 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 \(-0.208951\pi\)
−0.924620 + 0.380891i \(0.875617\pi\)
\(348\) −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 \(-0.481688\pi\)
0.0574986 + 0.998346i \(0.481688\pi\)
\(354\) −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 0.921762 0.387757i \(-0.126750\pi\)
−0.796688 + 0.604391i \(0.793417\pi\)
\(360\) 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 −0.395645 0.918403i \(-0.629479\pi\)
0.993183 0.116563i \(-0.0371876\pi\)
\(368\) −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 \(-0.334036\pi\)
0.498086 + 0.867128i \(0.334036\pi\)
\(374\) −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 \(-0.241647\pi\)
−0.958802 + 0.284074i \(0.908314\pi\)
\(384\) −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 −0.299544 0.954082i \(-0.596835\pi\)
0.976032 0.217629i \(-0.0698321\pi\)
\(390\) 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 \(-0.0459832\pi\)
−0.619464 + 0.785025i \(0.712650\pi\)
\(398\) 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 0.683049 0.730372i \(-0.260653\pi\)
−0.974046 + 0.226352i \(0.927320\pi\)
\(402\) −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 −0.309145 + 0.951015i \(0.600043\pi\)
−0.669030 + 0.743235i \(0.733290\pi\)
\(410\) 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 −0.993840 0.110822i \(-0.964652\pi\)
0.400946 0.916102i \(-0.368682\pi\)
\(422\) 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 0.294972 + 0.955506i \(0.404690\pi\)
−0.974978 + 0.222299i \(0.928644\pi\)
\(432\) 7.60729 + 13.1762i 0.366006 + 0.633941i
\(433\) −11.6899 + 20.2475i −0.561780 + 0.973031i 0.435562 + 0.900159i \(0.356550\pi\)
−0.997341 + 0.0728720i \(0.976784\pi\)
\(434\) 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 −0.985768 0.168110i \(-0.946234\pi\)
0.347297 0.937755i \(-0.387100\pi\)
\(440\) 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 \(-0.971469\pi\)
0.575514 + 0.817792i \(0.304802\pi\)
\(444\) 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 \(-0.587378\pi\)
−0.271073 + 0.962559i \(0.587378\pi\)
\(458\) 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 −0.895476 0.445110i \(-0.853165\pi\)
0.0622614 0.998060i \(-0.480169\pi\)
\(462\) 21.5569 37.3377i 1.00292 1.73711i
\(463\) −23.5039 −1.09232 −0.546160 0.837681i \(-0.683911\pi\)
−0.546160 + 0.837681i \(0.683911\pi\)
\(464\) −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 \(-0.491747\pi\)
0.0259246 + 0.999664i \(0.491747\pi\)
\(468\) 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 0.364854 + 0.931065i \(0.381119\pi\)
−0.988753 + 0.149559i \(0.952215\pi\)
\(480\) 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 \(-0.545737\pi\)
−0.143194 + 0.989695i \(0.545737\pi\)
\(488\) 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 0.995208 + 0.0977776i \(0.0311734\pi\)
−0.412926 + 0.910764i \(0.635493\pi\)
\(492\) −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 0.983790 + 0.179322i \(0.0573903\pi\)
−0.336598 + 0.941648i \(0.609276\pi\)
\(500\) 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 \(-0.841495\pi\)
0.852921 + 0.522040i \(0.174829\pi\)
\(504\) −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 −0.0788760 + 0.996884i \(0.525133\pi\)
−0.823889 + 0.566751i \(0.808200\pi\)
\(510\) 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 \(-0.925897\pi\)
0.686308 + 0.727311i \(0.259230\pi\)
\(524\) 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 −0.365706 0.930730i \(-0.619172\pi\)
0.988889 0.148655i \(-0.0474943\pi\)
\(542\) −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 −0.179654 0.983730i \(-0.557498\pi\)
0.941762 0.336280i \(-0.109169\pi\)
\(548\) 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 \(-0.919028\pi\)
0.701841 + 0.712333i \(0.252362\pi\)
\(558\) 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 \(-0.519364\pi\)
−0.0607960 + 0.998150i \(0.519364\pi\)
\(564\) 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 \(-0.681909\pi\)
−0.540880 + 0.841100i \(0.681909\pi\)
\(578\) 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 −0.948147 0.317832i \(-0.897045\pi\)
0.198823 0.980035i \(-0.436288\pi\)
\(588\) 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 −0.331281 0.943532i \(-0.607481\pi\)
0.982763 0.184868i \(-0.0591858\pi\)
\(594\) −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 −0.862435 0.506167i \(-0.831062\pi\)
0.869571 + 0.493807i \(0.164395\pi\)
\(600\) 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 \(-0.307183\pi\)
0.569382 + 0.822073i \(0.307183\pi\)
\(608\) −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 −0.892327 0.451389i \(-0.850929\pi\)
0.0552496 0.998473i \(-0.482405\pi\)
\(614\) 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 \(-0.795513\pi\)
0.919188 + 0.393819i \(0.128846\pi\)
\(618\) −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 −0.657123 0.753784i \(-0.728227\pi\)
0.981357 + 0.192193i \(0.0615600\pi\)
\(632\) −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 −0.994868 0.101177i \(-0.967739\pi\)
0.409812 0.912170i \(-0.365594\pi\)
\(642\) −27.4420 + 47.5309i −1.08305 + 1.87590i
\(643\) −6.01050 10.4105i −0.237031 0.410549i 0.722830 0.691026i \(-0.242841\pi\)
−0.959861 + 0.280476i \(0.909508\pi\)
\(644\) −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 \(-0.519790\pi\)
−0.0621317 + 0.998068i \(0.519790\pi\)
\(648\) 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 \(-0.374652\pi\)
0.383693 + 0.923461i \(0.374652\pi\)
\(654\) 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 −0.634558 0.772875i \(-0.718818\pi\)
0.986609 + 0.163106i \(0.0521512\pi\)
\(660\) 0 0
\(661\) 7.26715 12.5871i 0.282660 0.489581i −0.689379 0.724400i \(-0.742117\pi\)
0.972039 + 0.234820i \(0.0754500\pi\)
\(662\) 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 \(-0.537728\pi\)
−0.118248 + 0.992984i \(0.537728\pi\)
\(674\) −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 \(-0.415593\pi\)
0.262075 + 0.965047i \(0.415593\pi\)
\(678\) 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 \(-0.603870\pi\)
−0.320557 + 0.947229i \(0.603870\pi\)
\(684\) −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 0.963940 + 0.266121i \(0.0857419\pi\)
−0.251503 + 0.967857i \(0.580925\pi\)
\(702\) 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 −0.599350 0.800487i \(-0.704574\pi\)
0.992917 + 0.118809i \(0.0379075\pi\)
\(710\) 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 0.901394 + 0.433000i \(0.142545\pi\)
−0.0757084 + 0.997130i \(0.524122\pi\)
\(720\) 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 0.829852 + 0.557983i \(0.188425\pi\)
0.0683017 + 0.997665i \(0.478242\pi\)
\(728\) −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 \(-0.556909\pi\)
−0.177835 + 0.984060i \(0.556909\pi\)
\(734\) 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 0.948636 + 0.316370i \(0.102464\pi\)
−0.200333 + 0.979728i \(0.564202\pi\)
\(740\) 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 \(-0.183403\pi\)
−0.891106 + 0.453795i \(0.850070\pi\)
\(744\) 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 −0.521132 0.853476i \(-0.674490\pi\)
0.999698 + 0.0245758i \(0.00782351\pi\)
\(752\) 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 \(-0.204843\pi\)
−0.919628 + 0.392790i \(0.871510\pi\)
\(758\) −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 −0.976165 0.217029i \(-0.930363\pi\)
0.676035 + 0.736869i \(0.263697\pi\)
\(770\) 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 \(-0.689946\pi\)
0.997327 + 0.0730682i \(0.0232791\pi\)
\(774\) −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