Properties

Label 76.5.j.a.29.2
Level $76$
Weight $5$
Character 76.29
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.2
Character \(\chi\) \(=\) 76.29
Dual form 76.5.j.a.21.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.77177 - 9.26203i) q^{3} +(42.9478 + 15.6317i) q^{5} +(2.15264 - 3.72849i) q^{7} +(-11.3194 + 64.1954i) q^{9} +O(q^{10})\) \(q+(-7.77177 - 9.26203i) q^{3} +(42.9478 + 15.6317i) q^{5} +(2.15264 - 3.72849i) q^{7} +(-11.3194 + 64.1954i) q^{9} +(-53.2761 - 92.2769i) q^{11} +(157.331 - 187.500i) q^{13} +(-188.999 - 519.270i) q^{15} +(-15.1100 - 85.6928i) q^{17} +(-115.998 - 341.856i) q^{19} +(-51.2632 + 9.03909i) q^{21} +(55.9483 - 20.3635i) q^{23} +(1121.39 + 940.954i) q^{25} +(-165.590 + 95.6032i) q^{27} +(-226.682 - 39.9702i) q^{29} +(581.855 + 335.934i) q^{31} +(-440.622 + 1210.60i) q^{33} +(150.734 - 126.481i) q^{35} -2475.69i q^{37} -2959.37 q^{39} +(-650.315 - 775.016i) q^{41} +(2564.45 + 933.382i) q^{43} +(-1489.63 + 2580.11i) q^{45} +(-270.376 + 1533.38i) q^{47} +(1191.23 + 2063.27i) q^{49} +(-676.259 + 805.934i) q^{51} +(1048.86 + 2881.73i) q^{53} +(-845.645 - 4795.89i) q^{55} +(-2264.77 + 3731.21i) q^{57} +(4897.42 - 863.548i) q^{59} +(-5548.86 + 2019.62i) q^{61} +(214.985 + 180.394i) q^{63} +(9687.97 - 5593.35i) q^{65} +(698.565 + 123.176i) q^{67} +(-623.424 - 359.934i) q^{69} +(-149.426 + 410.545i) q^{71} +(-4824.78 + 4048.47i) q^{73} -17699.2i q^{75} -458.738 q^{77} +(-5317.06 - 6336.63i) q^{79} +(7134.02 + 2596.57i) q^{81} +(-6604.82 + 11439.9i) q^{83} +(690.587 - 3916.51i) q^{85} +(1391.52 + 2410.18i) q^{87} +(5164.02 - 6154.24i) q^{89} +(-360.414 - 990.228i) q^{91} +(-1410.61 - 7999.97i) q^{93} +(361.918 - 16495.2i) q^{95} +(-14459.8 + 2549.65i) q^{97} +(6526.80 - 2375.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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
\(3\) −7.77177 9.26203i −0.863530 1.02911i −0.999264 0.0383696i \(-0.987784\pi\)
0.135734 0.990745i \(-0.456661\pi\)
\(4\) 0 0
\(5\) 42.9478 + 15.6317i 1.71791 + 0.625269i 0.997655 0.0684387i \(-0.0218018\pi\)
0.720257 + 0.693708i \(0.244024\pi\)
\(6\) 0 0
\(7\) 2.15264 3.72849i 0.0439315 0.0760916i −0.843224 0.537563i \(-0.819345\pi\)
0.887155 + 0.461471i \(0.152678\pi\)
\(8\) 0 0
\(9\) −11.3194 + 64.1954i −0.139745 + 0.792536i
\(10\) 0 0
\(11\) −53.2761 92.2769i −0.440298 0.762619i 0.557413 0.830235i \(-0.311794\pi\)
−0.997711 + 0.0676161i \(0.978461\pi\)
\(12\) 0 0
\(13\) 157.331 187.500i 0.930954 1.10947i −0.0628174 0.998025i \(-0.520009\pi\)
0.993771 0.111442i \(-0.0355470\pi\)
\(14\) 0 0
\(15\) −188.999 519.270i −0.839995 2.30787i
\(16\) 0 0
\(17\) −15.1100 85.6928i −0.0522836 0.296515i 0.947442 0.319927i \(-0.103658\pi\)
−0.999726 + 0.0234117i \(0.992547\pi\)
\(18\) 0 0
\(19\) −115.998 341.856i −0.321325 0.946969i
\(20\) 0 0
\(21\) −51.2632 + 9.03909i −0.116243 + 0.0204968i
\(22\) 0 0
\(23\) 55.9483 20.3635i 0.105762 0.0384943i −0.288597 0.957451i \(-0.593189\pi\)
0.394359 + 0.918956i \(0.370967\pi\)
\(24\) 0 0
\(25\) 1121.39 + 940.954i 1.79422 + 1.50553i
\(26\) 0 0
\(27\) −165.590 + 95.6032i −0.227146 + 0.131143i
\(28\) 0 0
\(29\) −226.682 39.9702i −0.269539 0.0475270i 0.0372449 0.999306i \(-0.488142\pi\)
−0.306784 + 0.951779i \(0.599253\pi\)
\(30\) 0 0
\(31\) 581.855 + 335.934i 0.605469 + 0.349567i 0.771190 0.636605i \(-0.219662\pi\)
−0.165721 + 0.986173i \(0.552995\pi\)
\(32\) 0 0
\(33\) −440.622 + 1210.60i −0.404612 + 1.11166i
\(34\) 0 0
\(35\) 150.734 126.481i 0.123048 0.103250i
\(36\) 0 0
\(37\) 2475.69i 1.80839i −0.427117 0.904196i \(-0.640471\pi\)
0.427117 0.904196i \(-0.359529\pi\)
\(38\) 0 0
\(39\) −2959.37 −1.94568
\(40\) 0 0
\(41\) −650.315 775.016i −0.386862 0.461045i 0.537105 0.843515i \(-0.319518\pi\)
−0.923968 + 0.382471i \(0.875073\pi\)
\(42\) 0 0
\(43\) 2564.45 + 933.382i 1.38694 + 0.504804i 0.924274 0.381731i \(-0.124672\pi\)
0.462663 + 0.886534i \(0.346894\pi\)
\(44\) 0 0
\(45\) −1489.63 + 2580.11i −0.735618 + 1.27413i
\(46\) 0 0
\(47\) −270.376 + 1533.38i −0.122398 + 0.694151i 0.860422 + 0.509582i \(0.170200\pi\)
−0.982820 + 0.184569i \(0.940911\pi\)
\(48\) 0 0
\(49\) 1191.23 + 2063.27i 0.496140 + 0.859340i
\(50\) 0 0
\(51\) −676.259 + 805.934i −0.259999 + 0.309855i
\(52\) 0 0
\(53\) 1048.86 + 2881.73i 0.373394 + 1.02589i 0.974040 + 0.226377i \(0.0726880\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(54\) 0 0
\(55\) −845.645 4795.89i −0.279552 1.58542i
\(56\) 0 0
\(57\) −2264.77 + 3731.21i −0.697066 + 1.14842i
\(58\) 0 0
\(59\) 4897.42 863.548i 1.40690 0.248075i 0.581925 0.813242i \(-0.302300\pi\)
0.824976 + 0.565168i \(0.191189\pi\)
\(60\) 0 0
\(61\) −5548.86 + 2019.62i −1.49123 + 0.542763i −0.953773 0.300528i \(-0.902837\pi\)
−0.537457 + 0.843291i \(0.680615\pi\)
\(62\) 0 0
\(63\) 214.985 + 180.394i 0.0541661 + 0.0454507i
\(64\) 0 0
\(65\) 9687.97 5593.35i 2.29301 1.32387i
\(66\) 0 0
\(67\) 698.565 + 123.176i 0.155617 + 0.0274395i 0.250914 0.968009i \(-0.419269\pi\)
−0.0952968 + 0.995449i \(0.530380\pi\)
\(68\) 0 0
\(69\) −623.424 359.934i −0.130944 0.0756006i
\(70\) 0 0
\(71\) −149.426 + 410.545i −0.0296422 + 0.0814412i −0.953631 0.300978i \(-0.902687\pi\)
0.923989 + 0.382419i \(0.124909\pi\)
\(72\) 0 0
\(73\) −4824.78 + 4048.47i −0.905383 + 0.759706i −0.971235 0.238123i \(-0.923468\pi\)
0.0658524 + 0.997829i \(0.479023\pi\)
\(74\) 0 0
\(75\) 17699.2i 3.14652i
\(76\) 0 0
\(77\) −458.738 −0.0773719
\(78\) 0 0
\(79\) −5317.06 6336.63i −0.851957 1.01532i −0.999654 0.0262899i \(-0.991631\pi\)
0.147698 0.989033i \(-0.452814\pi\)
\(80\) 0 0
\(81\) 7134.02 + 2596.57i 1.08734 + 0.395758i
\(82\) 0 0
\(83\) −6604.82 + 11439.9i −0.958749 + 1.66060i −0.233202 + 0.972428i \(0.574920\pi\)
−0.725546 + 0.688173i \(0.758413\pi\)
\(84\) 0 0
\(85\) 690.587 3916.51i 0.0955829 0.542078i
\(86\) 0 0
\(87\) 1391.52 + 2410.18i 0.183844 + 0.318428i
\(88\) 0 0
\(89\) 5164.02 6154.24i 0.651940 0.776952i −0.334265 0.942479i \(-0.608488\pi\)
0.986205 + 0.165527i \(0.0529325\pi\)
\(90\) 0 0
\(91\) −360.414 990.228i −0.0435230 0.119578i
\(92\) 0 0
\(93\) −1410.61 7999.97i −0.163095 0.924959i
\(94\) 0 0
\(95\) 361.918 16495.2i 0.0401018 1.82772i
\(96\) 0 0
\(97\) −14459.8 + 2549.65i −1.53680 + 0.270980i −0.877012 0.480469i \(-0.840467\pi\)
−0.659791 + 0.751449i \(0.729355\pi\)
\(98\) 0 0
\(99\) 6526.80 2375.56i 0.665933 0.242380i
\(100\) 0 0
\(101\) 9128.80 + 7659.97i 0.894893 + 0.750904i 0.969185 0.246332i \(-0.0792255\pi\)
−0.0742928 + 0.997236i \(0.523670\pi\)
\(102\) 0 0
\(103\) 5202.88 3003.89i 0.490421 0.283145i −0.234328 0.972158i \(-0.575289\pi\)
0.724749 + 0.689013i \(0.241956\pi\)
\(104\) 0 0
\(105\) −2342.94 413.124i −0.212512 0.0374715i
\(106\) 0 0
\(107\) 13797.3 + 7965.87i 1.20511 + 0.695770i 0.961687 0.274151i \(-0.0883967\pi\)
0.243422 + 0.969920i \(0.421730\pi\)
\(108\) 0 0
\(109\) −1127.50 + 3097.78i −0.0948994 + 0.260734i −0.978055 0.208346i \(-0.933192\pi\)
0.883156 + 0.469080i \(0.155414\pi\)
\(110\) 0 0
\(111\) −22929.9 + 19240.5i −1.86104 + 1.56160i
\(112\) 0 0
\(113\) 5176.20i 0.405372i 0.979244 + 0.202686i \(0.0649671\pi\)
−0.979244 + 0.202686i \(0.935033\pi\)
\(114\) 0 0
\(115\) 2721.17 0.205760
\(116\) 0 0
\(117\) 10255.7 + 12222.3i 0.749196 + 0.892857i
\(118\) 0 0
\(119\) −352.031 128.129i −0.0248592 0.00904800i
\(120\) 0 0
\(121\) 1643.81 2847.17i 0.112275 0.194465i
\(122\) 0 0
\(123\) −2124.12 + 12046.5i −0.140401 + 0.796252i
\(124\) 0 0
\(125\) 19169.8 + 33203.0i 1.22687 + 2.12499i
\(126\) 0 0
\(127\) −8203.83 + 9776.94i −0.508638 + 0.606172i −0.957855 0.287251i \(-0.907259\pi\)
0.449217 + 0.893423i \(0.351703\pi\)
\(128\) 0 0
\(129\) −11285.3 31006.0i −0.678160 1.86323i
\(130\) 0 0
\(131\) −907.345 5145.81i −0.0528725 0.299855i 0.946892 0.321552i \(-0.104204\pi\)
−0.999765 + 0.0216966i \(0.993093\pi\)
\(132\) 0 0
\(133\) −1524.31 303.395i −0.0861727 0.0171516i
\(134\) 0 0
\(135\) −8606.15 + 1517.50i −0.472217 + 0.0832646i
\(136\) 0 0
\(137\) −26335.1 + 9585.18i −1.40311 + 0.510692i −0.929101 0.369826i \(-0.879417\pi\)
−0.474013 + 0.880518i \(0.657195\pi\)
\(138\) 0 0
\(139\) −6235.78 5232.44i −0.322746 0.270816i 0.466990 0.884263i \(-0.345338\pi\)
−0.789737 + 0.613446i \(0.789783\pi\)
\(140\) 0 0
\(141\) 16303.5 9412.84i 0.820056 0.473459i
\(142\) 0 0
\(143\) −25683.9 4528.77i −1.25600 0.221466i
\(144\) 0 0
\(145\) −9110.71 5260.07i −0.433327 0.250182i
\(146\) 0 0
\(147\) 9852.14 27068.5i 0.455928 1.25265i
\(148\) 0 0
\(149\) 11571.2 9709.39i 0.521202 0.437340i −0.343849 0.939025i \(-0.611731\pi\)
0.865050 + 0.501685i \(0.167286\pi\)
\(150\) 0 0
\(151\) 16283.8i 0.714172i 0.934072 + 0.357086i \(0.116230\pi\)
−0.934072 + 0.357086i \(0.883770\pi\)
\(152\) 0 0
\(153\) 5672.12 0.242305
\(154\) 0 0
\(155\) 19738.2 + 23523.0i 0.821568 + 0.979107i
\(156\) 0 0
\(157\) 149.451 + 54.3957i 0.00606316 + 0.00220681i 0.345050 0.938584i \(-0.387862\pi\)
−0.338987 + 0.940791i \(0.610084\pi\)
\(158\) 0 0
\(159\) 18539.2 32110.8i 0.733324 1.27015i
\(160\) 0 0
\(161\) 44.5116 252.438i 0.00171720 0.00973874i
\(162\) 0 0
\(163\) 21107.9 + 36559.9i 0.794454 + 1.37603i 0.923185 + 0.384355i \(0.125576\pi\)
−0.128731 + 0.991680i \(0.541090\pi\)
\(164\) 0 0
\(165\) −37847.5 + 45104.9i −1.39018 + 1.65675i
\(166\) 0 0
\(167\) 9351.36 + 25692.7i 0.335307 + 0.921247i 0.986706 + 0.162513i \(0.0519598\pi\)
−0.651400 + 0.758735i \(0.725818\pi\)
\(168\) 0 0
\(169\) −5443.58 30872.1i −0.190595 1.08092i
\(170\) 0 0
\(171\) 23258.6 3576.97i 0.795410 0.122327i
\(172\) 0 0
\(173\) 20255.6 3571.61i 0.676788 0.119336i 0.175319 0.984512i \(-0.443904\pi\)
0.501469 + 0.865176i \(0.332793\pi\)
\(174\) 0 0
\(175\) 5922.28 2155.53i 0.193381 0.0703848i
\(176\) 0 0
\(177\) −46059.9 38648.8i −1.47020 1.23364i
\(178\) 0 0
\(179\) −23621.9 + 13638.1i −0.737239 + 0.425645i −0.821064 0.570836i \(-0.806619\pi\)
0.0838258 + 0.996480i \(0.473286\pi\)
\(180\) 0 0
\(181\) 938.228 + 165.435i 0.0286386 + 0.00504975i 0.187949 0.982179i \(-0.439816\pi\)
−0.159311 + 0.987229i \(0.550927\pi\)
\(182\) 0 0
\(183\) 61830.3 + 35697.7i 1.84629 + 1.06595i
\(184\) 0 0
\(185\) 38699.3 106325.i 1.13073 3.10666i
\(186\) 0 0
\(187\) −7102.47 + 5959.68i −0.203108 + 0.170427i
\(188\) 0 0
\(189\) 823.199i 0.0230452i
\(190\) 0 0
\(191\) 30843.6 0.845471 0.422736 0.906253i \(-0.361070\pi\)
0.422736 + 0.906253i \(0.361070\pi\)
\(192\) 0 0
\(193\) −16809.0 20032.1i −0.451259 0.537790i 0.491671 0.870781i \(-0.336386\pi\)
−0.942930 + 0.332991i \(0.891942\pi\)
\(194\) 0 0
\(195\) −127099. 46260.1i −3.34250 1.21657i
\(196\) 0 0
\(197\) 20383.7 35305.7i 0.525232 0.909728i −0.474336 0.880344i \(-0.657312\pi\)
0.999568 0.0293847i \(-0.00935479\pi\)
\(198\) 0 0
\(199\) 9655.08 54756.7i 0.243809 1.38271i −0.579433 0.815020i \(-0.696726\pi\)
0.823242 0.567690i \(-0.192163\pi\)
\(200\) 0 0
\(201\) −4288.23 7427.43i −0.106142 0.183843i
\(202\) 0 0
\(203\) −636.995 + 759.141i −0.0154577 + 0.0184217i
\(204\) 0 0
\(205\) −15814.8 43450.8i −0.376319 1.03393i
\(206\) 0 0
\(207\) 673.943 + 3822.12i 0.0157283 + 0.0891998i
\(208\) 0 0
\(209\) −25365.5 + 28916.7i −0.580698 + 0.661998i
\(210\) 0 0
\(211\) −55860.4 + 9849.70i −1.25470 + 0.221237i −0.761204 0.648512i \(-0.775392\pi\)
−0.493494 + 0.869749i \(0.664281\pi\)
\(212\) 0 0
\(213\) 4963.79 1806.67i 0.109409 0.0398217i
\(214\) 0 0
\(215\) 95546.9 + 80173.4i 2.06700 + 1.73442i
\(216\) 0 0
\(217\) 2505.05 1446.29i 0.0531983 0.0307140i
\(218\) 0 0
\(219\) 74994.2 + 13223.5i 1.56365 + 0.275714i
\(220\) 0 0
\(221\) −18444.7 10649.0i −0.377647 0.218035i
\(222\) 0 0
\(223\) −3325.90 + 9137.83i −0.0668804 + 0.183752i −0.968631 0.248505i \(-0.920061\pi\)
0.901750 + 0.432258i \(0.142283\pi\)
\(224\) 0 0
\(225\) −73098.3 + 61336.7i −1.44392 + 1.21159i
\(226\) 0 0
\(227\) 46967.0i 0.911468i 0.890116 + 0.455734i \(0.150623\pi\)
−0.890116 + 0.455734i \(0.849377\pi\)
\(228\) 0 0
\(229\) 64077.4 1.22190 0.610948 0.791671i \(-0.290788\pi\)
0.610948 + 0.791671i \(0.290788\pi\)
\(230\) 0 0
\(231\) 3565.21 + 4248.85i 0.0668130 + 0.0796246i
\(232\) 0 0
\(233\) 16649.0 + 6059.75i 0.306674 + 0.111620i 0.490773 0.871287i \(-0.336714\pi\)
−0.184099 + 0.982908i \(0.558937\pi\)
\(234\) 0 0
\(235\) −35581.4 + 61628.9i −0.644300 + 1.11596i
\(236\) 0 0
\(237\) −17367.1 + 98493.6i −0.309193 + 1.75352i
\(238\) 0 0
\(239\) −16641.4 28823.7i −0.291335 0.504607i 0.682791 0.730614i \(-0.260766\pi\)
−0.974126 + 0.226007i \(0.927433\pi\)
\(240\) 0 0
\(241\) 2883.17 3436.03i 0.0496405 0.0591593i −0.740653 0.671888i \(-0.765484\pi\)
0.790293 + 0.612729i \(0.209928\pi\)
\(242\) 0 0
\(243\) −26097.3 71701.8i −0.441960 1.21428i
\(244\) 0 0
\(245\) 18908.3 + 107234.i 0.315007 + 1.78649i
\(246\) 0 0
\(247\) −82348.1 32034.9i −1.34977 0.525084i
\(248\) 0 0
\(249\) 157288. 27734.1i 2.53686 0.447317i
\(250\) 0 0
\(251\) 49755.7 18109.6i 0.789760 0.287449i 0.0845238 0.996421i \(-0.473063\pi\)
0.705236 + 0.708972i \(0.250841\pi\)
\(252\) 0 0
\(253\) −4859.79 4077.85i −0.0759235 0.0637074i
\(254\) 0 0
\(255\) −41641.9 + 24042.0i −0.640399 + 0.369735i
\(256\) 0 0
\(257\) 59276.0 + 10452.0i 0.897455 + 0.158245i 0.603302 0.797513i \(-0.293851\pi\)
0.294153 + 0.955758i \(0.404963\pi\)
\(258\) 0 0
\(259\) −9230.58 5329.28i −0.137603 0.0794454i
\(260\) 0 0
\(261\) 5131.81 14099.5i 0.0753337 0.206978i
\(262\) 0 0
\(263\) −22538.1 + 18911.8i −0.325842 + 0.273414i −0.791003 0.611812i \(-0.790441\pi\)
0.465161 + 0.885226i \(0.345996\pi\)
\(264\) 0 0
\(265\) 140160.i 1.99586i
\(266\) 0 0
\(267\) −97134.3 −1.36254
\(268\) 0 0
\(269\) −40065.0 47747.6i −0.553682 0.659853i 0.414514 0.910043i \(-0.363951\pi\)
−0.968197 + 0.250190i \(0.919507\pi\)
\(270\) 0 0
\(271\) −98266.8 35766.2i −1.33804 0.487006i −0.428844 0.903379i \(-0.641079\pi\)
−0.909194 + 0.416373i \(0.863301\pi\)
\(272\) 0 0
\(273\) −6370.48 + 11034.0i −0.0854765 + 0.148050i
\(274\) 0 0
\(275\) 27085.3 153608.i 0.358153 2.03118i
\(276\) 0 0
\(277\) 22345.6 + 38703.8i 0.291228 + 0.504422i 0.974100 0.226116i \(-0.0726028\pi\)
−0.682872 + 0.730538i \(0.739269\pi\)
\(278\) 0 0
\(279\) −28151.7 + 33549.9i −0.361656 + 0.431005i
\(280\) 0 0
\(281\) −20650.9 56738.0i −0.261533 0.718557i −0.999065 0.0432439i \(-0.986231\pi\)
0.737531 0.675313i \(-0.235991\pi\)
\(282\) 0 0
\(283\) −5636.27 31964.9i −0.0703751 0.399117i −0.999564 0.0295128i \(-0.990604\pi\)
0.929189 0.369604i \(-0.120507\pi\)
\(284\) 0 0
\(285\) −155592. + 124845.i −1.91557 + 1.53703i
\(286\) 0 0
\(287\) −4289.54 + 756.361i −0.0520771 + 0.00918259i
\(288\) 0 0
\(289\) 71369.1 25976.2i 0.854505 0.311014i
\(290\) 0 0
\(291\) 135993. + 114112.i 1.60595 + 1.34755i
\(292\) 0 0
\(293\) 80889.4 46701.5i 0.942229 0.543996i 0.0515704 0.998669i \(-0.483577\pi\)
0.890658 + 0.454673i \(0.150244\pi\)
\(294\) 0 0
\(295\) 223832. + 39467.7i 2.57205 + 0.453521i
\(296\) 0 0
\(297\) 17643.9 + 10186.7i 0.200024 + 0.115484i
\(298\) 0 0
\(299\) 4984.25 13694.1i 0.0557516 0.153176i
\(300\) 0 0
\(301\) 9000.44 7552.27i 0.0993415 0.0833574i
\(302\) 0 0
\(303\) 144083.i 1.56938i
\(304\) 0 0
\(305\) −269882. −2.90117
\(306\) 0 0
\(307\) −57343.3 68339.1i −0.608424 0.725091i 0.370610 0.928788i \(-0.379149\pi\)
−0.979034 + 0.203697i \(0.934704\pi\)
\(308\) 0 0
\(309\) −68257.7 24843.8i −0.714882 0.260196i
\(310\) 0 0
\(311\) 28338.0 49082.9i 0.292987 0.507469i −0.681528 0.731792i \(-0.738684\pi\)
0.974515 + 0.224324i \(0.0720174\pi\)
\(312\) 0 0
\(313\) 25753.8 146057.i 0.262877 1.49085i −0.512136 0.858904i \(-0.671146\pi\)
0.775013 0.631945i \(-0.217743\pi\)
\(314\) 0 0
\(315\) 6413.27 + 11108.1i 0.0646336 + 0.111949i
\(316\) 0 0
\(317\) −118529. + 141258.i −1.17952 + 1.40570i −0.285092 + 0.958500i \(0.592024\pi\)
−0.894433 + 0.447203i \(0.852420\pi\)
\(318\) 0 0
\(319\) 8388.43 + 23047.0i 0.0824326 + 0.226482i
\(320\) 0 0
\(321\) −33449.2 189700.i −0.324620 1.84101i
\(322\) 0 0
\(323\) −27541.8 + 15105.7i −0.263990 + 0.144789i
\(324\) 0 0
\(325\) 352858. 62218.3i 3.34066 0.589049i
\(326\) 0 0
\(327\) 37454.4 13632.3i 0.350274 0.127489i
\(328\) 0 0
\(329\) 5135.17 + 4308.92i 0.0474420 + 0.0398085i
\(330\) 0 0
\(331\) −24255.8 + 14004.1i −0.221391 + 0.127820i −0.606594 0.795012i \(-0.707465\pi\)
0.385203 + 0.922832i \(0.374131\pi\)
\(332\) 0 0
\(333\) 158928. + 28023.3i 1.43322 + 0.252715i
\(334\) 0 0
\(335\) 28076.4 + 16209.9i 0.250179 + 0.144441i
\(336\) 0 0
\(337\) −25143.3 + 69080.7i −0.221392 + 0.608271i −0.999810 0.0194757i \(-0.993800\pi\)
0.778418 + 0.627746i \(0.216023\pi\)
\(338\) 0 0
\(339\) 47942.2 40228.2i 0.417175 0.350051i
\(340\) 0 0
\(341\) 71589.1i 0.615656i
\(342\) 0 0
\(343\) 20594.2 0.175048
\(344\) 0 0
\(345\) −21148.3 25203.6i −0.177680 0.211750i
\(346\) 0 0
\(347\) −71229.0 25925.2i −0.591559 0.215310i 0.0288561 0.999584i \(-0.490814\pi\)
−0.620415 + 0.784274i \(0.713036\pi\)
\(348\) 0 0
\(349\) −21076.6 + 36505.7i −0.173041 + 0.299716i −0.939482 0.342599i \(-0.888693\pi\)
0.766440 + 0.642315i \(0.222026\pi\)
\(350\) 0 0
\(351\) −8126.81 + 46089.4i −0.0659638 + 0.374099i
\(352\) 0 0
\(353\) −24819.5 42988.7i −0.199179 0.344988i 0.749083 0.662476i \(-0.230494\pi\)
−0.948263 + 0.317487i \(0.897161\pi\)
\(354\) 0 0
\(355\) −12835.0 + 15296.2i −0.101845 + 0.121374i
\(356\) 0 0
\(357\) 1549.17 + 4256.31i 0.0121552 + 0.0333962i
\(358\) 0 0
\(359\) 14713.1 + 83442.1i 0.114160 + 0.647435i 0.987163 + 0.159719i \(0.0510588\pi\)
−0.873002 + 0.487716i \(0.837830\pi\)
\(360\) 0 0
\(361\) −103410. + 79309.4i −0.793500 + 0.608570i
\(362\) 0 0
\(363\) −39145.9 + 6902.48i −0.297080 + 0.0523831i
\(364\) 0 0
\(365\) −270498. + 98453.4i −2.03039 + 0.739001i
\(366\) 0 0
\(367\) 38648.6 + 32430.0i 0.286947 + 0.240777i 0.774887 0.632100i \(-0.217807\pi\)
−0.487940 + 0.872877i \(0.662251\pi\)
\(368\) 0 0
\(369\) 57113.6 32974.6i 0.419456 0.242173i
\(370\) 0 0
\(371\) 13002.3 + 2292.66i 0.0944655 + 0.0166568i
\(372\) 0 0
\(373\) −42536.7 24558.6i −0.305735 0.176516i 0.339281 0.940685i \(-0.389816\pi\)
−0.645017 + 0.764169i \(0.723150\pi\)
\(374\) 0 0
\(375\) 158544. 435597.i 1.12743 3.09758i
\(376\) 0 0
\(377\) −43158.6 + 36214.4i −0.303658 + 0.254799i
\(378\) 0 0
\(379\) 46677.4i 0.324959i 0.986712 + 0.162479i \(0.0519491\pi\)
−0.986712 + 0.162479i \(0.948051\pi\)
\(380\) 0 0
\(381\) 154313. 1.06304
\(382\) 0 0
\(383\) −74647.5 88961.5i −0.508883 0.606463i 0.449032 0.893516i \(-0.351769\pi\)
−0.957915 + 0.287053i \(0.907325\pi\)
\(384\) 0 0
\(385\) −19701.8 7170.86i −0.132918 0.0483782i
\(386\) 0 0
\(387\) −88946.7 + 154060.i −0.593893 + 1.02865i
\(388\) 0 0
\(389\) −37952.9 + 215242.i −0.250811 + 1.42242i 0.555791 + 0.831322i \(0.312416\pi\)
−0.806601 + 0.591096i \(0.798695\pi\)
\(390\) 0 0
\(391\) −2590.38 4486.67i −0.0169438 0.0293475i
\(392\) 0 0
\(393\) −40609.0 + 48395.9i −0.262928 + 0.313346i
\(394\) 0 0
\(395\) −129304. 355259.i −0.828737 2.27694i
\(396\) 0 0
\(397\) −6390.11 36240.1i −0.0405441 0.229937i 0.957802 0.287429i \(-0.0928006\pi\)
−0.998346 + 0.0574924i \(0.981689\pi\)
\(398\) 0 0
\(399\) 9036.52 + 16476.1i 0.0567617 + 0.103493i
\(400\) 0 0
\(401\) −67077.2 + 11827.5i −0.417144 + 0.0735537i −0.378281 0.925691i \(-0.623485\pi\)
−0.0388629 + 0.999245i \(0.512374\pi\)
\(402\) 0 0
\(403\) 154532. 56244.9i 0.951497 0.346316i
\(404\) 0 0
\(405\) 265802. + 223034.i 1.62049 + 1.35976i
\(406\) 0 0
\(407\) −228449. + 131895.i −1.37911 + 0.796232i
\(408\) 0 0
\(409\) 44057.4 + 7768.52i 0.263374 + 0.0464399i 0.303776 0.952744i \(-0.401753\pi\)
−0.0404018 + 0.999184i \(0.512864\pi\)
\(410\) 0 0
\(411\) 293448. + 169422.i 1.73719 + 1.00297i
\(412\) 0 0
\(413\) 7322.68 20118.9i 0.0429309 0.117952i
\(414\) 0 0
\(415\) −462488. + 388073.i −2.68537 + 2.25329i
\(416\) 0 0
\(417\) 98421.4i 0.566001i
\(418\) 0 0
\(419\) 203865. 1.16122 0.580612 0.814181i \(-0.302814\pi\)
0.580612 + 0.814181i \(0.302814\pi\)
\(420\) 0 0
\(421\) 146420. + 174497.i 0.826108 + 0.984517i 1.00000 0.000248007i \(-7.89430e-5\pi\)
−0.173892 + 0.984765i \(0.555634\pi\)
\(422\) 0 0
\(423\) −95375.4 34713.8i −0.533035 0.194009i
\(424\) 0 0
\(425\) 63688.9 110312.i 0.352603 0.610726i
\(426\) 0 0
\(427\) −4414.59 + 25036.4i −0.0242122 + 0.137314i
\(428\) 0 0
\(429\) 157664. + 273082.i 0.856678 + 1.48381i
\(430\) 0 0
\(431\) 34977.2 41684.2i 0.188292 0.224397i −0.663638 0.748054i \(-0.730988\pi\)
0.851929 + 0.523657i \(0.175433\pi\)
\(432\) 0 0
\(433\) 27973.5 + 76856.7i 0.149201 + 0.409926i 0.991668 0.128822i \(-0.0411196\pi\)
−0.842467 + 0.538748i \(0.818897\pi\)
\(434\) 0 0
\(435\) 22087.4 + 125264.i 0.116725 + 0.661983i
\(436\) 0 0
\(437\) −13451.3 16764.1i −0.0704370 0.0877844i
\(438\) 0 0
\(439\) −320915. + 56585.9i −1.66518 + 0.293616i −0.925331 0.379160i \(-0.876213\pi\)
−0.739846 + 0.672776i \(0.765102\pi\)
\(440\) 0 0
\(441\) −145937. + 53116.6i −0.750391 + 0.273120i
\(442\) 0 0
\(443\) 1195.82 + 1003.41i 0.00609337 + 0.00511295i 0.645829 0.763482i \(-0.276512\pi\)
−0.639736 + 0.768595i \(0.720956\pi\)
\(444\) 0 0
\(445\) 317984. 183588.i 1.60578 0.927097i
\(446\) 0 0
\(447\) −179857. 31713.7i −0.900147 0.158720i
\(448\) 0 0
\(449\) 179448. + 103604.i 0.890113 + 0.513907i 0.873979 0.485963i \(-0.161531\pi\)
0.0161336 + 0.999870i \(0.494864\pi\)
\(450\) 0 0
\(451\) −36869.8 + 101299.i −0.181267 + 0.498026i
\(452\) 0 0
\(453\) 150821. 126554.i 0.734965 0.616709i
\(454\) 0 0
\(455\) 48162.0i 0.232639i
\(456\) 0 0
\(457\) −115293. −0.552040 −0.276020 0.961152i \(-0.589016\pi\)
−0.276020 + 0.961152i \(0.589016\pi\)
\(458\) 0 0
\(459\) 10694.6 + 12745.3i 0.0507619 + 0.0604956i
\(460\) 0 0
\(461\) −299131. 108875.i −1.40754 0.512302i −0.477131 0.878832i \(-0.658323\pi\)
−0.930406 + 0.366530i \(0.880546\pi\)
\(462\) 0 0
\(463\) 54789.1 94897.4i 0.255583 0.442683i −0.709471 0.704735i \(-0.751066\pi\)
0.965054 + 0.262052i \(0.0843993\pi\)
\(464\) 0 0
\(465\) 64470.7 365631.i 0.298165 1.69098i
\(466\) 0 0
\(467\) 159310. + 275933.i 0.730482 + 1.26523i 0.956677 + 0.291151i \(0.0940380\pi\)
−0.226195 + 0.974082i \(0.572629\pi\)
\(468\) 0 0
\(469\) 1963.02 2339.44i 0.00892440 0.0106357i
\(470\) 0 0
\(471\) −657.683 1806.97i −0.00296466 0.00814534i
\(472\) 0 0
\(473\) −50494.1 286366.i −0.225693 1.27997i
\(474\) 0 0
\(475\) 191592. 492501.i 0.849160 2.18283i
\(476\) 0 0
\(477\) −196866. + 34712.8i −0.865236 + 0.152564i
\(478\) 0 0
\(479\) 335823. 122229.i 1.46366 0.532727i 0.517286 0.855812i \(-0.326942\pi\)
0.946370 + 0.323085i \(0.104720\pi\)
\(480\) 0 0
\(481\) −464192. 389503.i −2.00635 1.68353i
\(482\) 0 0
\(483\) −2684.02 + 1549.62i −0.0115051 + 0.00664249i
\(484\) 0 0
\(485\) −660871. 116529.i −2.80953 0.495396i
\(486\) 0 0
\(487\) −213167. 123072.i −0.898800 0.518922i −0.0219892 0.999758i \(-0.507000\pi\)
−0.876811 + 0.480836i \(0.840333\pi\)
\(488\) 0 0
\(489\) 174573. 479637.i 0.730063 2.00583i
\(490\) 0 0
\(491\) −37914.8 + 31814.3i −0.157270 + 0.131965i −0.718027 0.696015i \(-0.754955\pi\)
0.560757 + 0.827980i \(0.310510\pi\)
\(492\) 0 0
\(493\) 20029.0i 0.0824072i
\(494\) 0 0
\(495\) 317446. 1.29557
\(496\) 0 0
\(497\) 1209.05 + 1440.89i 0.00489476 + 0.00583335i
\(498\) 0 0
\(499\) 170320. + 61991.4i 0.684013 + 0.248960i 0.660570 0.750765i \(-0.270315\pi\)
0.0234434 + 0.999725i \(0.492537\pi\)
\(500\) 0 0
\(501\) 165290. 286290.i 0.658522 1.14059i
\(502\) 0 0
\(503\) −72462.0 + 410952.i −0.286401 + 1.62426i 0.413838 + 0.910350i \(0.364188\pi\)
−0.700239 + 0.713909i \(0.746923\pi\)
\(504\) 0 0
\(505\) 272323. + 471678.i 1.06783 + 1.84954i
\(506\) 0 0
\(507\) −243632. + 290349.i −0.947804 + 1.12955i
\(508\) 0 0
\(509\) 14428.3 + 39641.3i 0.0556902 + 0.153007i 0.964418 0.264381i \(-0.0851677\pi\)
−0.908728 + 0.417389i \(0.862945\pi\)
\(510\) 0 0
\(511\) 4708.65 + 26704.1i 0.0180324 + 0.102267i
\(512\) 0 0
\(513\) 51890.6 + 45518.0i 0.197176 + 0.172961i
\(514\) 0 0
\(515\) 270408. 47680.3i 1.01954 0.179773i
\(516\) 0 0
\(517\) 155900. 56743.0i 0.583265 0.212291i
\(518\) 0 0
\(519\) −190502. 159850.i −0.707237 0.593443i
\(520\) 0 0
\(521\) 237664. 137216.i 0.875566 0.505508i 0.00637184 0.999980i \(-0.497972\pi\)
0.869194 + 0.494472i \(0.164638\pi\)
\(522\) 0 0
\(523\) 188131. + 33172.6i 0.687793 + 0.121276i 0.506613 0.862174i \(-0.330897\pi\)
0.181180 + 0.983450i \(0.442008\pi\)
\(524\) 0 0
\(525\) −65991.2 38100.0i −0.239424 0.138231i
\(526\) 0 0
\(527\) 19995.3 54936.8i 0.0719959 0.197807i
\(528\) 0 0
\(529\) −211655. + 177600.i −0.756341 + 0.634645i
\(530\) 0 0
\(531\) 324167.i 1.14969i
\(532\) 0 0
\(533\) −247630. −0.871665
\(534\) 0 0
\(535\) 468043. + 557792.i 1.63523 + 1.94879i
\(536\) 0 0
\(537\) 309900. + 112794.i 1.07467 + 0.391146i
\(538\) 0 0
\(539\) 126928. 219847.i 0.436899 0.756732i
\(540\) 0 0
\(541\) 92745.0 525983.i 0.316881 1.79712i −0.244593 0.969626i \(-0.578654\pi\)
0.561474 0.827495i \(-0.310235\pi\)
\(542\) 0 0
\(543\) −5759.43 9975.62i −0.0195335 0.0338330i
\(544\) 0 0
\(545\) −96847.3 + 115418.i −0.326058 + 0.388581i
\(546\) 0 0
\(547\) −143720. 394868.i −0.480334 1.31971i −0.909208 0.416343i \(-0.863312\pi\)
0.428873 0.903365i \(-0.358911\pi\)
\(548\) 0 0
\(549\) −66840.7 379072.i −0.221767 1.25770i
\(550\) 0 0
\(551\) 12630.7 + 82129.2i 0.0416031 + 0.270517i
\(552\) 0 0
\(553\) −35071.8 + 6184.10i −0.114685 + 0.0202221i
\(554\) 0 0
\(555\) −1.28555e6 + 467903.i −4.17353 + 1.51904i
\(556\) 0 0
\(557\) −99053.6 83115.8i −0.319271 0.267900i 0.469040 0.883177i \(-0.344600\pi\)
−0.788311 + 0.615276i \(0.789044\pi\)
\(558\) 0 0
\(559\) 578476. 333983.i 1.85124 1.06881i
\(560\) 0 0
\(561\) 110398. + 19466.1i 0.350779 + 0.0618518i
\(562\) 0 0
\(563\) 261889. + 151202.i 0.826229 + 0.477024i 0.852560 0.522630i \(-0.175049\pi\)
−0.0263308 + 0.999653i \(0.508382\pi\)
\(564\) 0 0
\(565\) −80912.9 + 222306.i −0.253467 + 0.696394i
\(566\) 0 0
\(567\) 25038.3 21009.6i 0.0778823 0.0653510i
\(568\) 0 0
\(569\) 360748.i 1.11424i −0.830431 0.557121i \(-0.811906\pi\)
0.830431 0.557121i \(-0.188094\pi\)
\(570\) 0 0
\(571\) 232100. 0.711872 0.355936 0.934510i \(-0.384162\pi\)
0.355936 + 0.934510i \(0.384162\pi\)
\(572\) 0 0
\(573\) −239710. 285675.i −0.730090 0.870087i
\(574\) 0 0
\(575\) 81900.7 + 29809.4i 0.247715 + 0.0901608i
\(576\) 0 0
\(577\) −310604. + 537982.i −0.932944 + 1.61591i −0.154685 + 0.987964i \(0.549436\pi\)
−0.778259 + 0.627943i \(0.783897\pi\)
\(578\) 0 0
\(579\) −54903.0 + 311370.i −0.163772 + 0.928796i
\(580\) 0 0
\(581\) 28435.7 + 49252.0i 0.0842386 + 0.145905i
\(582\) 0 0
\(583\) 210038. 250313.i 0.617960 0.736456i
\(584\) 0 0
\(585\) 249406. + 685236.i 0.728777 + 2.00230i
\(586\) 0 0
\(587\) −103359. 586178.i −0.299966 1.70119i −0.646302 0.763082i \(-0.723685\pi\)
0.346336 0.938111i \(-0.387426\pi\)
\(588\) 0 0
\(589\) 47346.8 237878.i 0.136477 0.685685i
\(590\) 0 0
\(591\) −485420. + 85592.6i −1.38977 + 0.245054i
\(592\) 0 0
\(593\) 426488. 155229.i 1.21282 0.441431i 0.345140 0.938551i \(-0.387831\pi\)
0.867682 + 0.497120i \(0.165609\pi\)
\(594\) 0 0
\(595\) −13116.1 11005.7i −0.0370485 0.0310874i
\(596\) 0 0
\(597\) −582196. + 336131.i −1.63350 + 0.943104i
\(598\) 0 0
\(599\) −318910. 56232.5i −0.888822 0.156723i −0.289449 0.957193i \(-0.593472\pi\)
−0.599373 + 0.800470i \(0.704583\pi\)
\(600\) 0 0
\(601\) −146181. 84397.6i −0.404708 0.233658i 0.283805 0.958882i \(-0.408403\pi\)
−0.688513 + 0.725224i \(0.741736\pi\)
\(602\) 0 0
\(603\) −15814.6 + 43450.4i −0.0434935 + 0.119497i
\(604\) 0 0
\(605\) 115104. 96583.9i 0.314471 0.263872i
\(606\) 0 0
\(607\) 259583.i 0.704529i 0.935900 + 0.352265i \(0.114588\pi\)
−0.935900 + 0.352265i \(0.885412\pi\)
\(608\) 0 0
\(609\) 11981.8 0.0323062
\(610\) 0 0
\(611\) 244970. + 291944.i 0.656192 + 0.782019i
\(612\) 0 0
\(613\) 111054. + 40420.2i 0.295537 + 0.107567i 0.485533 0.874218i \(-0.338625\pi\)
−0.189997 + 0.981785i \(0.560848\pi\)
\(614\) 0 0
\(615\) −279534. + 484167.i −0.739067 + 1.28010i
\(616\) 0 0
\(617\) −108570. + 615731.i −0.285193 + 1.61741i 0.419400 + 0.907801i \(0.362240\pi\)
−0.704594 + 0.709611i \(0.748871\pi\)
\(618\) 0 0
\(619\) −244052. 422710.i −0.636943 1.10322i −0.986100 0.166154i \(-0.946865\pi\)
0.349157 0.937064i \(-0.386468\pi\)
\(620\) 0 0
\(621\) −7317.63 + 8720.82i −0.0189753 + 0.0226138i
\(622\) 0 0
\(623\) −11829.7 32501.9i −0.0304788 0.0837398i
\(624\) 0 0
\(625\) 145406. + 824637.i 0.372239 + 2.11107i
\(626\) 0 0
\(627\) 464962. + 10201.6i 1.18272 + 0.0259499i
\(628\) 0 0
\(629\) −212149. + 37407.5i −0.536215 + 0.0945492i
\(630\) 0 0
\(631\) 135771. 49416.5i 0.340994 0.124112i −0.165846 0.986152i \(-0.553036\pi\)
0.506840 + 0.862040i \(0.330813\pi\)
\(632\) 0 0
\(633\) 525363. + 440832.i 1.31115 + 1.10018i
\(634\) 0 0
\(635\) −505167. + 291658.i −1.25282 + 0.723314i
\(636\) 0 0
\(637\) 574282. + 101261.i 1.41529 + 0.249554i
\(638\) 0 0
\(639\) −24663.7 14239.6i −0.0604027 0.0348735i
\(640\) 0 0
\(641\) −221079. + 607409.i −0.538061 + 1.47831i 0.311205 + 0.950343i \(0.399268\pi\)
−0.849265 + 0.527966i \(0.822955\pi\)
\(642\) 0 0
\(643\) −162219. + 136118.i −0.392355 + 0.329225i −0.817530 0.575886i \(-0.804657\pi\)
0.425175 + 0.905111i \(0.360213\pi\)
\(644\) 0 0
\(645\) 1.50805e6i 3.62490i
\(646\) 0 0
\(647\) 417859. 0.998208 0.499104 0.866542i \(-0.333663\pi\)
0.499104 + 0.866542i \(0.333663\pi\)
\(648\) 0 0
\(649\) −340601. 405913.i −0.808643 0.963703i
\(650\) 0 0
\(651\) −32864.3 11961.6i −0.0775466 0.0282247i
\(652\) 0 0
\(653\) −84288.8 + 145993.i −0.197671 + 0.342377i −0.947773 0.318946i \(-0.896671\pi\)
0.750102 + 0.661323i \(0.230005\pi\)
\(654\) 0 0
\(655\) 41469.4 235185.i 0.0966596 0.548184i
\(656\) 0 0
\(657\) −205280. 355555.i −0.475571 0.823713i
\(658\) 0 0
\(659\) 439281. 523515.i 1.01151 1.20548i 0.0329657 0.999456i \(-0.489505\pi\)
0.978548 0.206019i \(-0.0660508\pi\)
\(660\) 0 0
\(661\) 46527.5 + 127833.i 0.106490 + 0.292578i 0.981481 0.191561i \(-0.0613551\pi\)
−0.874991 + 0.484139i \(0.839133\pi\)
\(662\) 0 0
\(663\) 44716.0 + 253597.i 0.101727 + 0.576922i
\(664\) 0 0
\(665\) −60723.1 36857.7i −0.137313 0.0833461i
\(666\) 0 0
\(667\) −13496.4 + 2379.78i −0.0303366 + 0.00534916i
\(668\) 0 0
\(669\) 110483. 40212.5i 0.246856 0.0898481i
\(670\) 0 0
\(671\) 481986. + 404435.i 1.07051 + 0.898263i
\(672\) 0 0
\(673\) 102257. 59038.0i 0.225768 0.130347i −0.382850 0.923810i \(-0.625057\pi\)
0.608618 + 0.793463i \(0.291724\pi\)
\(674\) 0 0
\(675\) −275648. 48604.2i −0.604989 0.106676i
\(676\) 0 0
\(677\) 464689. + 268288.i 1.01388 + 0.585361i 0.912324 0.409469i \(-0.134286\pi\)
0.101551 + 0.994830i \(0.467619\pi\)
\(678\) 0 0
\(679\) −21620.4 + 59401.6i −0.0468948 + 0.128842i
\(680\) 0 0
\(681\) 435010. 365017.i 0.938005 0.787080i
\(682\) 0 0
\(683\) 231574.i 0.496420i 0.968706 + 0.248210i \(0.0798423\pi\)
−0.968706 + 0.248210i \(0.920158\pi\)
\(684\) 0 0
\(685\) −1.28087e6 −2.72975
\(686\) 0 0
\(687\) −497995. 593487.i −1.05514 1.25747i
\(688\) 0 0
\(689\) 705343. + 256724.i 1.48581 + 0.540789i
\(690\) 0 0
\(691\) 111751. 193558.i 0.234043 0.405374i −0.724951 0.688800i \(-0.758138\pi\)
0.958994 + 0.283426i \(0.0914711\pi\)
\(692\) 0 0
\(693\) 5192.63 29448.9i 0.0108124 0.0613200i
\(694\) 0 0
\(695\) −186021. 322198.i −0.385117 0.667042i
\(696\) 0 0
\(697\) −56587.0 + 67437.8i −0.116480 + 0.138815i
\(698\) 0 0
\(699\) −73266.8 201299.i −0.149952 0.411990i
\(700\) 0 0
\(701\) 20429.4 + 115861.i 0.0415737 + 0.235776i 0.998513 0.0545114i \(-0.0173601\pi\)
−0.956939 + 0.290288i \(0.906249\pi\)
\(702\) 0 0
\(703\) −846329. + 287176.i −1.71249 + 0.581082i
\(704\) 0 0
\(705\) 847339. 149409.i 1.70482 0.300606i
\(706\) 0 0
\(707\) 48211.2 17547.4i 0.0964515 0.0351055i
\(708\) 0 0
\(709\) −57886.1 48572.2i −0.115155 0.0966264i 0.583392 0.812191i \(-0.301725\pi\)
−0.698547 + 0.715564i \(0.746170\pi\)
\(710\) 0 0
\(711\) 466968. 269604.i 0.923736 0.533319i
\(712\) 0 0
\(713\) 39394.6 + 6946.33i 0.0774921 + 0.0136639i
\(714\) 0 0
\(715\) −1.03228e6 595984.i −2.01922 1.16580i
\(716\) 0 0
\(717\) −137633. + 378144.i −0.267722 + 0.735561i
\(718\) 0 0
\(719\) 422817. 354785.i 0.817889 0.686291i −0.134587 0.990902i \(-0.542971\pi\)
0.952477 + 0.304611i \(0.0985265\pi\)
\(720\) 0 0
\(721\) 25865.2i 0.0497559i
\(722\) 0 0
\(723\) −54232.0 −0.103748
\(724\) 0 0
\(725\) −216588. 258120.i −0.412058 0.491072i
\(726\) 0 0
\(727\) 170252. + 61966.5i 0.322123 + 0.117243i 0.498021 0.867165i \(-0.334060\pi\)
−0.175897 + 0.984409i \(0.556283\pi\)
\(728\) 0 0
\(729\) −153812. + 266410.i −0.289424 + 0.501297i
\(730\) 0 0
\(731\) 41235.4 233858.i 0.0771678 0.437640i
\(732\) 0 0
\(733\) −340098. 589067.i −0.632989 1.09637i −0.986937 0.161105i \(-0.948494\pi\)
0.353948 0.935265i \(-0.384839\pi\)
\(734\) 0 0
\(735\) 846255. 1.00853e6i 1.56649 1.86687i
\(736\) 0 0
\(737\) −25850.5 71023.7i −0.0475921 0.130758i
\(738\) 0 0
\(739\) −18375.1 104210.i −0.0336466 0.190819i 0.963352 0.268241i \(-0.0864424\pi\)
−0.996998 + 0.0774216i \(0.975331\pi\)
\(740\) 0 0
\(741\) 343282. + 1.01168e6i 0.625195 + 1.84249i
\(742\) 0 0
\(743\) 621964. 109669.i 1.12665 0.198658i 0.420889 0.907112i \(-0.361718\pi\)
0.705757 + 0.708454i \(0.250607\pi\)
\(744\) 0 0
\(745\) 648732. 236119.i 1.16883 0.425421i
\(746\) 0 0
\(747\) −659625. 553491.i −1.18211 0.991904i
\(748\) 0 0
\(749\) 59401.3 34295.4i 0.105884 0.0611324i
\(750\) 0 0
\(751\) −987429. 174110.i −1.75076 0.308706i −0.795825 0.605527i \(-0.792962\pi\)
−0.954933 + 0.296822i \(0.904073\pi\)
\(752\) 0 0
\(753\) −554421. 320095.i −0.977800 0.564533i
\(754\) 0 0
\(755\) −254544. + 699355.i −0.446549 + 1.22688i
\(756\) 0 0
\(757\) 180218. 151221.i 0.314489 0.263888i −0.471855 0.881676i \(-0.656416\pi\)
0.786344 + 0.617788i \(0.211971\pi\)
\(758\) 0 0
\(759\) 76703.6i 0.133147i
\(760\) 0 0
\(761\) −448159. −0.773861 −0.386931 0.922109i \(-0.626465\pi\)
−0.386931 + 0.922109i \(0.626465\pi\)
\(762\) 0 0
\(763\) 9122.94 + 10872.3i 0.0156706 + 0.0186755i
\(764\) 0 0
\(765\) 243605. + 88664.9i 0.416259 + 0.151506i
\(766\) 0 0
\(767\) 608602. 1.05413e6i 1.03453 1.79186i
\(768\) 0 0
\(769\) 7459.51 42305.0i 0.0126141 0.0715383i −0.977851 0.209303i \(-0.932881\pi\)
0.990465 + 0.137764i \(0.0439917\pi\)
\(770\) 0 0
\(771\) −363873. 630247.i −0.612126 1.06023i
\(772\) 0 0
\(773\) 11898.2 14179.7i 0.0199124 0.0237306i −0.755996 0.654576i \(-0.772847\pi\)
0.775909 + 0.630845i \(0.217292\pi\)
\(774\) 0 0
\(775\) 336385. + 924211.i 0.560059 + 1.53875i
\(776\) 0 0
\(777\) 22378.0 + 126912.i 0.0370663 + 0.210213i
\(778\) 0 0
\(779\) −189508. + 312215.i −0.312286 + 0.514492i
\(780\) 0 0
\(781\) 45844.7 8083.65i 0.0751600 0.0132527i
\(782\) 0 0
\(783\) 41357.5 15052.9i 0.0674576 0.0245526i
\(784\) 0 0
\(785\) 5568.29 + 4672.35i 0.00903613 + 0.00758221i
\(786\) 0 0
\(787\) −146996. + 84868.4i −0.237332 + 0.137024i −0.613950 0.789345i \(-0.710420\pi\)
0.376618 + 0.926369i \(0.377087\pi\)
\(788\) 0 0
\(789\) 350323. + 61771.3i 0.562748 + 0.0992277i
\(790\) 0 0
\(791\) 19299.4 + 11142.5i 0.0308454 + 0.0178086i
\(792\) 0 0