Properties

Label 405.4.e.q.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.84779568.3
Defining polynomial: \(x^{6} - x^{5} + 13 x^{4} - 4 x^{3} + 152 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.327167 + 0.566669i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.q.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.72938 - 4.72742i) q^{2} +(-10.8990 + 18.8776i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(5.90326 + 10.2247i) q^{7} +75.3201 q^{8} +O(q^{10})\) \(q+(-2.72938 - 4.72742i) q^{2} +(-10.8990 + 18.8776i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(5.90326 + 10.2247i) q^{7} +75.3201 q^{8} +27.2938 q^{10} +(28.1188 + 48.7032i) q^{11} +(-17.2980 + 29.9611i) q^{13} +(32.2245 - 55.8144i) q^{14} +(-118.385 - 205.049i) q^{16} +39.2675 q^{17} -146.561 q^{19} +(-54.4951 - 94.3882i) q^{20} +(153.494 - 265.859i) q^{22} +(11.7889 - 20.4189i) q^{23} +(-12.5000 - 21.6506i) q^{25} +188.851 q^{26} -257.359 q^{28} +(-80.5013 - 139.432i) q^{29} +(14.7733 - 25.5880i) q^{31} +(-344.954 + 597.478i) q^{32} +(-107.176 - 185.634i) q^{34} -59.0326 q^{35} -217.688 q^{37} +(400.020 + 692.855i) q^{38} +(-188.300 + 326.146i) q^{40} +(-71.1449 + 123.227i) q^{41} +(234.015 + 405.326i) q^{43} -1225.87 q^{44} -128.705 q^{46} +(-197.159 - 341.490i) q^{47} +(101.803 - 176.328i) q^{49} +(-68.2345 + 118.186i) q^{50} +(-377.063 - 653.092i) q^{52} -134.780 q^{53} -281.188 q^{55} +(444.634 + 770.129i) q^{56} +(-439.437 + 761.128i) q^{58} +(65.5977 - 113.619i) q^{59} +(-129.901 - 224.994i) q^{61} -161.287 q^{62} +1871.88 q^{64} +(-86.4901 - 149.805i) q^{65} +(-222.622 + 385.593i) q^{67} +(-427.977 + 741.278i) q^{68} +(161.122 + 279.072i) q^{70} +560.841 q^{71} -88.6681 q^{73} +(594.152 + 1029.10i) q^{74} +(1597.37 - 2766.72i) q^{76} +(-331.985 + 575.015i) q^{77} +(-225.171 - 390.008i) q^{79} +1183.85 q^{80} +776.726 q^{82} +(-142.148 - 246.207i) q^{83} +(-98.1687 + 170.033i) q^{85} +(1277.43 - 2212.57i) q^{86} +(2117.91 + 3668.33i) q^{88} +625.305 q^{89} -408.459 q^{91} +(256.974 + 445.092i) q^{92} +(-1076.24 + 1864.11i) q^{94} +(366.402 - 634.627i) q^{95} +(96.6307 + 167.369i) q^{97} -1111.44 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + O(q^{10}) \) \( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + 50 q^{10} - 5 q^{11} - 7 q^{13} - 60 q^{14} - 161 q^{16} + 310 q^{17} - 100 q^{19} - 85 q^{20} + 229 q^{22} - 285 q^{23} - 75 q^{25} + 370 q^{26} - 668 q^{28} - 115 q^{29} + 115 q^{31} - 775 q^{32} - 413 q^{34} - 40 q^{35} - 768 q^{37} + 1150 q^{38} - 375 q^{40} - 580 q^{41} + 797 q^{43} - 2830 q^{44} - 570 q^{46} + 145 q^{47} - 577 q^{49} - 125 q^{50} - 825 q^{52} - 800 q^{53} + 50 q^{55} + 2190 q^{56} + 59 q^{58} - 380 q^{59} + 152 q^{61} - 2010 q^{62} + 5874 q^{64} - 35 q^{65} - 2 q^{67} - 475 q^{68} - 300 q^{70} + 80 q^{71} - 1960 q^{73} + 2720 q^{74} + 3276 q^{76} - 1950 q^{77} - 1013 q^{79} + 1610 q^{80} + 8 q^{82} - 270 q^{83} - 775 q^{85} + 1555 q^{86} + 5193 q^{88} + 2040 q^{89} - 1264 q^{91} + 1215 q^{92} - 3833 q^{94} + 250 q^{95} - 720 q^{97} - 610 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72938 4.72742i −0.964981 1.67140i −0.709666 0.704538i \(-0.751154\pi\)
−0.255315 0.966858i \(-0.582179\pi\)
\(3\) 0 0
\(4\) −10.8990 + 18.8776i −1.36238 + 2.35971i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 5.90326 + 10.2247i 0.318746 + 0.552084i 0.980227 0.197878i \(-0.0634050\pi\)
−0.661481 + 0.749962i \(0.730072\pi\)
\(8\) 75.3201 3.32871
\(9\) 0 0
\(10\) 27.2938 0.863105
\(11\) 28.1188 + 48.7032i 0.770740 + 1.33496i 0.937158 + 0.348905i \(0.113446\pi\)
−0.166418 + 0.986055i \(0.553220\pi\)
\(12\) 0 0
\(13\) −17.2980 + 29.9611i −0.369047 + 0.639208i −0.989417 0.145101i \(-0.953649\pi\)
0.620370 + 0.784309i \(0.286983\pi\)
\(14\) 32.2245 55.8144i 0.615168 1.06550i
\(15\) 0 0
\(16\) −118.385 205.049i −1.84976 3.20389i
\(17\) 39.2675 0.560221 0.280111 0.959968i \(-0.409629\pi\)
0.280111 + 0.959968i \(0.409629\pi\)
\(18\) 0 0
\(19\) −146.561 −1.76965 −0.884825 0.465924i \(-0.845722\pi\)
−0.884825 + 0.465924i \(0.845722\pi\)
\(20\) −54.4951 94.3882i −0.609273 1.05529i
\(21\) 0 0
\(22\) 153.494 265.859i 1.48750 2.57642i
\(23\) 11.7889 20.4189i 0.106876 0.185115i −0.807627 0.589693i \(-0.799249\pi\)
0.914503 + 0.404579i \(0.132582\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 188.851 1.42449
\(27\) 0 0
\(28\) −257.359 −1.73701
\(29\) −80.5013 139.432i −0.515473 0.892826i −0.999839 0.0179601i \(-0.994283\pi\)
0.484365 0.874866i \(-0.339051\pi\)
\(30\) 0 0
\(31\) 14.7733 25.5880i 0.0855921 0.148250i −0.820051 0.572290i \(-0.806055\pi\)
0.905643 + 0.424040i \(0.139388\pi\)
\(32\) −344.954 + 597.478i −1.90562 + 3.30063i
\(33\) 0 0
\(34\) −107.176 185.634i −0.540603 0.936352i
\(35\) −59.0326 −0.285095
\(36\) 0 0
\(37\) −217.688 −0.967233 −0.483617 0.875280i \(-0.660677\pi\)
−0.483617 + 0.875280i \(0.660677\pi\)
\(38\) 400.020 + 692.855i 1.70768 + 2.95779i
\(39\) 0 0
\(40\) −188.300 + 326.146i −0.744322 + 1.28920i
\(41\) −71.1449 + 123.227i −0.270999 + 0.469385i −0.969118 0.246597i \(-0.920687\pi\)
0.698119 + 0.715982i \(0.254021\pi\)
\(42\) 0 0
\(43\) 234.015 + 405.326i 0.829929 + 1.43748i 0.898093 + 0.439805i \(0.144952\pi\)
−0.0681645 + 0.997674i \(0.521714\pi\)
\(44\) −1225.87 −4.20015
\(45\) 0 0
\(46\) −128.705 −0.412533
\(47\) −197.159 341.490i −0.611886 1.05982i −0.990922 0.134435i \(-0.957078\pi\)
0.379037 0.925382i \(-0.376255\pi\)
\(48\) 0 0
\(49\) 101.803 176.328i 0.296802 0.514076i
\(50\) −68.2345 + 118.186i −0.192996 + 0.334279i
\(51\) 0 0
\(52\) −377.063 653.092i −1.00556 1.74168i
\(53\) −134.780 −0.349311 −0.174655 0.984630i \(-0.555881\pi\)
−0.174655 + 0.984630i \(0.555881\pi\)
\(54\) 0 0
\(55\) −281.188 −0.689371
\(56\) 444.634 + 770.129i 1.06101 + 1.83773i
\(57\) 0 0
\(58\) −439.437 + 761.128i −0.994844 + 1.72312i
\(59\) 65.5977 113.619i 0.144747 0.250710i −0.784531 0.620089i \(-0.787096\pi\)
0.929279 + 0.369379i \(0.120430\pi\)
\(60\) 0 0
\(61\) −129.901 224.994i −0.272657 0.472255i 0.696885 0.717183i \(-0.254569\pi\)
−0.969541 + 0.244928i \(0.921236\pi\)
\(62\) −161.287 −0.330379
\(63\) 0 0
\(64\) 1871.88 3.65602
\(65\) −86.4901 149.805i −0.165043 0.285863i
\(66\) 0 0
\(67\) −222.622 + 385.593i −0.405935 + 0.703100i −0.994430 0.105401i \(-0.966387\pi\)
0.588495 + 0.808501i \(0.299721\pi\)
\(68\) −427.977 + 741.278i −0.763233 + 1.32196i
\(69\) 0 0
\(70\) 161.122 + 279.072i 0.275111 + 0.476507i
\(71\) 560.841 0.937459 0.468729 0.883342i \(-0.344712\pi\)
0.468729 + 0.883342i \(0.344712\pi\)
\(72\) 0 0
\(73\) −88.6681 −0.142162 −0.0710809 0.997471i \(-0.522645\pi\)
−0.0710809 + 0.997471i \(0.522645\pi\)
\(74\) 594.152 + 1029.10i 0.933362 + 1.61663i
\(75\) 0 0
\(76\) 1597.37 2766.72i 2.41093 4.17585i
\(77\) −331.985 + 575.015i −0.491340 + 0.851027i
\(78\) 0 0
\(79\) −225.171 390.008i −0.320680 0.555434i 0.659948 0.751311i \(-0.270578\pi\)
−0.980629 + 0.195877i \(0.937245\pi\)
\(80\) 1183.85 1.65448
\(81\) 0 0
\(82\) 776.726 1.04604
\(83\) −142.148 246.207i −0.187985 0.325599i 0.756594 0.653886i \(-0.226862\pi\)
−0.944578 + 0.328286i \(0.893529\pi\)
\(84\) 0 0
\(85\) −98.1687 + 170.033i −0.125269 + 0.216973i
\(86\) 1277.43 2212.57i 1.60173 2.77428i
\(87\) 0 0
\(88\) 2117.91 + 3668.33i 2.56557 + 4.44369i
\(89\) 625.305 0.744744 0.372372 0.928083i \(-0.378545\pi\)
0.372372 + 0.928083i \(0.378545\pi\)
\(90\) 0 0
\(91\) −408.459 −0.470529
\(92\) 256.974 + 445.092i 0.291211 + 0.504392i
\(93\) 0 0
\(94\) −1076.24 + 1864.11i −1.18092 + 2.04541i
\(95\) 366.402 634.627i 0.395706 0.685382i
\(96\) 0 0
\(97\) 96.6307 + 167.369i 0.101148 + 0.175193i 0.912158 0.409839i \(-0.134415\pi\)
−0.811010 + 0.585032i \(0.801082\pi\)
\(98\) −1111.44 −1.14563
\(99\) 0 0
\(100\) 544.951 0.544951
\(101\) −687.429 1190.66i −0.677245 1.17302i −0.975807 0.218633i \(-0.929840\pi\)
0.298562 0.954390i \(-0.403493\pi\)
\(102\) 0 0
\(103\) −1014.80 + 1757.69i −0.970789 + 1.68146i −0.277605 + 0.960695i \(0.589541\pi\)
−0.693184 + 0.720761i \(0.743793\pi\)
\(104\) −1302.89 + 2256.67i −1.22845 + 2.12774i
\(105\) 0 0
\(106\) 367.866 + 637.162i 0.337078 + 0.583836i
\(107\) −823.062 −0.743630 −0.371815 0.928307i \(-0.621264\pi\)
−0.371815 + 0.928307i \(0.621264\pi\)
\(108\) 0 0
\(109\) −829.868 −0.729238 −0.364619 0.931157i \(-0.618801\pi\)
−0.364619 + 0.931157i \(0.618801\pi\)
\(110\) 767.469 + 1329.29i 0.665230 + 1.15221i
\(111\) 0 0
\(112\) 1397.71 2420.91i 1.17921 2.04245i
\(113\) 751.683 1301.95i 0.625773 1.08387i −0.362618 0.931938i \(-0.618117\pi\)
0.988391 0.151933i \(-0.0485498\pi\)
\(114\) 0 0
\(115\) 58.9443 + 102.095i 0.0477964 + 0.0827858i
\(116\) 3509.54 2.80908
\(117\) 0 0
\(118\) −716.164 −0.558714
\(119\) 231.806 + 401.500i 0.178568 + 0.309289i
\(120\) 0 0
\(121\) −915.834 + 1586.27i −0.688080 + 1.19179i
\(122\) −709.095 + 1228.19i −0.526217 + 0.911435i
\(123\) 0 0
\(124\) 322.028 + 557.768i 0.233217 + 0.403944i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −576.348 −0.402698 −0.201349 0.979520i \(-0.564532\pi\)
−0.201349 + 0.979520i \(0.564532\pi\)
\(128\) −2349.44 4069.36i −1.62237 2.81003i
\(129\) 0 0
\(130\) −472.129 + 817.751i −0.318526 + 0.551704i
\(131\) −1195.02 + 2069.83i −0.797017 + 1.38047i 0.124534 + 0.992215i \(0.460257\pi\)
−0.921551 + 0.388258i \(0.873077\pi\)
\(132\) 0 0
\(133\) −865.186 1498.55i −0.564069 0.976996i
\(134\) 2430.48 1.56688
\(135\) 0 0
\(136\) 2957.63 1.86481
\(137\) −501.230 868.155i −0.312576 0.541398i 0.666343 0.745645i \(-0.267859\pi\)
−0.978919 + 0.204248i \(0.934525\pi\)
\(138\) 0 0
\(139\) −65.9084 + 114.157i −0.0402178 + 0.0696593i −0.885434 0.464766i \(-0.846139\pi\)
0.845216 + 0.534425i \(0.179472\pi\)
\(140\) 643.397 1114.40i 0.388407 0.672740i
\(141\) 0 0
\(142\) −1530.75 2651.33i −0.904630 1.56687i
\(143\) −1945.60 −1.13776
\(144\) 0 0
\(145\) 805.013 0.461053
\(146\) 242.009 + 419.171i 0.137183 + 0.237609i
\(147\) 0 0
\(148\) 2372.58 4109.43i 1.31774 2.28239i
\(149\) −509.743 + 882.900i −0.280267 + 0.485436i −0.971450 0.237243i \(-0.923756\pi\)
0.691184 + 0.722679i \(0.257090\pi\)
\(150\) 0 0
\(151\) −1411.19 2444.25i −0.760537 1.31729i −0.942574 0.333997i \(-0.891603\pi\)
0.182037 0.983292i \(-0.441731\pi\)
\(152\) −11039.0 −5.89065
\(153\) 0 0
\(154\) 3624.45 1.89654
\(155\) 73.8663 + 127.940i 0.0382779 + 0.0662993i
\(156\) 0 0
\(157\) −238.250 + 412.661i −0.121111 + 0.209770i −0.920206 0.391434i \(-0.871979\pi\)
0.799095 + 0.601205i \(0.205312\pi\)
\(158\) −1229.15 + 2128.96i −0.618900 + 1.07197i
\(159\) 0 0
\(160\) −1724.77 2987.39i −0.852219 1.47609i
\(161\) 278.371 0.136265
\(162\) 0 0
\(163\) −2242.26 −1.07747 −0.538734 0.842476i \(-0.681097\pi\)
−0.538734 + 0.842476i \(0.681097\pi\)
\(164\) −1550.82 2686.10i −0.738406 1.27896i
\(165\) 0 0
\(166\) −775.949 + 1343.98i −0.362803 + 0.628394i
\(167\) −47.5195 + 82.3062i −0.0220190 + 0.0381380i −0.876825 0.480810i \(-0.840343\pi\)
0.854806 + 0.518948i \(0.173676\pi\)
\(168\) 0 0
\(169\) 500.056 + 866.123i 0.227609 + 0.394230i
\(170\) 1071.76 0.483530
\(171\) 0 0
\(172\) −10202.1 −4.52270
\(173\) 1066.88 + 1847.89i 0.468864 + 0.812096i 0.999367 0.0355875i \(-0.0113302\pi\)
−0.530503 + 0.847683i \(0.677997\pi\)
\(174\) 0 0
\(175\) 147.581 255.619i 0.0637492 0.110417i
\(176\) 6657.68 11531.4i 2.85137 4.93872i
\(177\) 0 0
\(178\) −1706.70 2956.08i −0.718664 1.24476i
\(179\) −1704.68 −0.711808 −0.355904 0.934523i \(-0.615827\pi\)
−0.355904 + 0.934523i \(0.615827\pi\)
\(180\) 0 0
\(181\) −1360.98 −0.558902 −0.279451 0.960160i \(-0.590152\pi\)
−0.279451 + 0.960160i \(0.590152\pi\)
\(182\) 1114.84 + 1930.96i 0.454051 + 0.786440i
\(183\) 0 0
\(184\) 887.938 1537.95i 0.355759 0.616193i
\(185\) 544.219 942.615i 0.216280 0.374608i
\(186\) 0 0
\(187\) 1104.15 + 1912.45i 0.431785 + 0.747873i
\(188\) 8595.36 3.33447
\(189\) 0 0
\(190\) −4000.20 −1.52739
\(191\) 548.421 + 949.892i 0.207761 + 0.359852i 0.951009 0.309164i \(-0.100049\pi\)
−0.743248 + 0.669016i \(0.766716\pi\)
\(192\) 0 0
\(193\) 1433.63 2483.13i 0.534691 0.926111i −0.464488 0.885580i \(-0.653762\pi\)
0.999178 0.0405316i \(-0.0129052\pi\)
\(194\) 527.483 913.628i 0.195212 0.338117i
\(195\) 0 0
\(196\) 2219.11 + 3843.61i 0.808712 + 1.40073i
\(197\) 724.139 0.261892 0.130946 0.991389i \(-0.458199\pi\)
0.130946 + 0.991389i \(0.458199\pi\)
\(198\) 0 0
\(199\) −1693.65 −0.603315 −0.301658 0.953416i \(-0.597540\pi\)
−0.301658 + 0.953416i \(0.597540\pi\)
\(200\) −941.501 1630.73i −0.332871 0.576549i
\(201\) 0 0
\(202\) −3752.51 + 6499.53i −1.30706 + 2.26389i
\(203\) 950.440 1646.21i 0.328610 0.569169i
\(204\) 0 0
\(205\) −355.725 616.133i −0.121195 0.209915i
\(206\) 11079.1 3.74717
\(207\) 0 0
\(208\) 8191.30 2.73060
\(209\) −4121.11 7137.98i −1.36394 2.36241i
\(210\) 0 0
\(211\) −473.726 + 820.517i −0.154562 + 0.267710i −0.932900 0.360137i \(-0.882730\pi\)
0.778337 + 0.627846i \(0.216063\pi\)
\(212\) 1468.97 2544.33i 0.475893 0.824270i
\(213\) 0 0
\(214\) 2246.45 + 3890.96i 0.717589 + 1.24290i
\(215\) −2340.15 −0.742311
\(216\) 0 0
\(217\) 348.841 0.109129
\(218\) 2265.02 + 3923.14i 0.703701 + 1.21885i
\(219\) 0 0
\(220\) 3064.67 5308.17i 0.939183 1.62671i
\(221\) −679.250 + 1176.50i −0.206748 + 0.358098i
\(222\) 0 0
\(223\) −55.9328 96.8784i −0.0167961 0.0290918i 0.857505 0.514475i \(-0.172013\pi\)
−0.874301 + 0.485384i \(0.838680\pi\)
\(224\) −8145.41 −2.42964
\(225\) 0 0
\(226\) −8206.51 −2.41544
\(227\) −600.350 1039.84i −0.175536 0.304037i 0.764811 0.644255i \(-0.222832\pi\)
−0.940347 + 0.340218i \(0.889499\pi\)
\(228\) 0 0
\(229\) −411.190 + 712.202i −0.118656 + 0.205518i −0.919235 0.393709i \(-0.871192\pi\)
0.800579 + 0.599227i \(0.204525\pi\)
\(230\) 321.763 557.309i 0.0922452 0.159773i
\(231\) 0 0
\(232\) −6063.37 10502.1i −1.71586 2.97196i
\(233\) −5329.21 −1.49840 −0.749202 0.662341i \(-0.769563\pi\)
−0.749202 + 0.662341i \(0.769563\pi\)
\(234\) 0 0
\(235\) 1971.59 0.547287
\(236\) 1429.90 + 2476.66i 0.394401 + 0.683123i
\(237\) 0 0
\(238\) 1265.37 2191.69i 0.344630 0.596917i
\(239\) 3542.81 6136.32i 0.958850 1.66078i 0.233548 0.972345i \(-0.424966\pi\)
0.725302 0.688431i \(-0.241700\pi\)
\(240\) 0 0
\(241\) 3280.05 + 5681.21i 0.876707 + 1.51850i 0.854933 + 0.518738i \(0.173598\pi\)
0.0217738 + 0.999763i \(0.493069\pi\)
\(242\) 9998.63 2.65593
\(243\) 0 0
\(244\) 5663.15 1.48584
\(245\) 509.015 + 881.641i 0.132734 + 0.229902i
\(246\) 0 0
\(247\) 2535.21 4391.12i 0.653084 1.13117i
\(248\) 1112.72 1927.29i 0.284911 0.493481i
\(249\) 0 0
\(250\) −341.172 590.928i −0.0863105 0.149494i
\(251\) 714.222 0.179607 0.0898033 0.995960i \(-0.471376\pi\)
0.0898033 + 0.995960i \(0.471376\pi\)
\(252\) 0 0
\(253\) 1325.95 0.329494
\(254\) 1573.07 + 2724.64i 0.388595 + 0.673067i
\(255\) 0 0
\(256\) −5337.51 + 9244.85i −1.30310 + 2.25704i
\(257\) −2198.29 + 3807.56i −0.533563 + 0.924159i 0.465668 + 0.884959i \(0.345814\pi\)
−0.999231 + 0.0391993i \(0.987519\pi\)
\(258\) 0 0
\(259\) −1285.07 2225.80i −0.308302 0.533994i
\(260\) 3770.63 0.899402
\(261\) 0 0
\(262\) 13046.6 3.07643
\(263\) 3775.15 + 6538.76i 0.885118 + 1.53307i 0.845579 + 0.533851i \(0.179256\pi\)
0.0395390 + 0.999218i \(0.487411\pi\)
\(264\) 0 0
\(265\) 336.950 583.615i 0.0781082 0.135287i
\(266\) −4722.84 + 8180.20i −1.08863 + 1.88556i
\(267\) 0 0
\(268\) −4852.72 8405.17i −1.10607 1.91577i
\(269\) −5536.86 −1.25497 −0.627487 0.778627i \(-0.715917\pi\)
−0.627487 + 0.778627i \(0.715917\pi\)
\(270\) 0 0
\(271\) 3058.25 0.685518 0.342759 0.939423i \(-0.388639\pi\)
0.342759 + 0.939423i \(0.388639\pi\)
\(272\) −4648.68 8051.75i −1.03628 1.79489i
\(273\) 0 0
\(274\) −2736.09 + 4739.05i −0.603260 + 1.04488i
\(275\) 702.970 1217.58i 0.154148 0.266992i
\(276\) 0 0
\(277\) 2035.09 + 3524.88i 0.441433 + 0.764584i 0.997796 0.0663552i \(-0.0211371\pi\)
−0.556363 + 0.830939i \(0.687804\pi\)
\(278\) 719.556 0.155238
\(279\) 0 0
\(280\) −4446.34 −0.948998
\(281\) −3723.09 6448.59i −0.790396 1.36901i −0.925722 0.378204i \(-0.876542\pi\)
0.135326 0.990801i \(-0.456792\pi\)
\(282\) 0 0
\(283\) 387.326 670.868i 0.0813573 0.140915i −0.822476 0.568800i \(-0.807408\pi\)
0.903833 + 0.427885i \(0.140741\pi\)
\(284\) −6112.61 + 10587.4i −1.27717 + 2.21213i
\(285\) 0 0
\(286\) 5310.28 + 9197.67i 1.09791 + 1.90164i
\(287\) −1679.95 −0.345520
\(288\) 0 0
\(289\) −3371.06 −0.686152
\(290\) −2197.19 3805.64i −0.444908 0.770603i
\(291\) 0 0
\(292\) 966.394 1673.84i 0.193678 0.335460i
\(293\) −3374.62 + 5845.01i −0.672857 + 1.16542i 0.304233 + 0.952598i \(0.401600\pi\)
−0.977090 + 0.212825i \(0.931733\pi\)
\(294\) 0 0
\(295\) 327.989 + 568.093i 0.0647330 + 0.112121i
\(296\) −16396.3 −3.21964
\(297\) 0 0
\(298\) 5565.12 1.08181
\(299\) 407.848 + 706.413i 0.0788845 + 0.136632i
\(300\) 0 0
\(301\) −2762.90 + 4785.48i −0.529073 + 0.916381i
\(302\) −7703.35 + 13342.6i −1.46781 + 2.54232i
\(303\) 0 0
\(304\) 17350.6 + 30052.1i 3.27343 + 5.66975i
\(305\) 1299.01 0.243872
\(306\) 0 0
\(307\) −2204.39 −0.409808 −0.204904 0.978782i \(-0.565688\pi\)
−0.204904 + 0.978782i \(0.565688\pi\)
\(308\) −7236.62 12534.2i −1.33878 2.31884i
\(309\) 0 0
\(310\) 403.218 698.394i 0.0738750 0.127955i
\(311\) 3016.49 5224.71i 0.549998 0.952625i −0.448276 0.893895i \(-0.647962\pi\)
0.998274 0.0587296i \(-0.0187050\pi\)
\(312\) 0 0
\(313\) 2886.48 + 4999.53i 0.521257 + 0.902844i 0.999694 + 0.0247221i \(0.00787008\pi\)
−0.478437 + 0.878122i \(0.658797\pi\)
\(314\) 2601.09 0.467479
\(315\) 0 0
\(316\) 9816.57 1.74755
\(317\) 1651.04 + 2859.68i 0.292528 + 0.506674i 0.974407 0.224791i \(-0.0721701\pi\)
−0.681879 + 0.731465i \(0.738837\pi\)
\(318\) 0 0
\(319\) 4527.20 7841.35i 0.794592 1.37627i
\(320\) −4679.71 + 8105.49i −0.817511 + 1.41597i
\(321\) 0 0
\(322\) −759.779 1315.98i −0.131493 0.227753i
\(323\) −5755.07 −0.991395
\(324\) 0 0
\(325\) 864.901 0.147619
\(326\) 6119.97 + 10600.1i 1.03974 + 1.80087i
\(327\) 0 0
\(328\) −5358.64 + 9281.44i −0.902078 + 1.56244i
\(329\) 2327.76 4031.80i 0.390072 0.675625i
\(330\) 0 0
\(331\) −4026.58 6974.23i −0.668642 1.15812i −0.978284 0.207269i \(-0.933542\pi\)
0.309642 0.950853i \(-0.399791\pi\)
\(332\) 6197.08 1.02442
\(333\) 0 0
\(334\) 518.795 0.0849916
\(335\) −1113.11 1927.96i −0.181540 0.314436i
\(336\) 0 0
\(337\) −1730.16 + 2996.73i −0.279668 + 0.484398i −0.971302 0.237849i \(-0.923558\pi\)
0.691635 + 0.722248i \(0.256891\pi\)
\(338\) 2729.69 4727.96i 0.439276 0.760849i
\(339\) 0 0
\(340\) −2139.88 3706.39i −0.341328 0.591197i
\(341\) 1661.62 0.263877
\(342\) 0 0
\(343\) 6453.51 1.01591
\(344\) 17626.0 + 30529.2i 2.76259 + 4.78495i
\(345\) 0 0
\(346\) 5823.84 10087.2i 0.904889 1.56731i
\(347\) 4664.14 8078.52i 0.721568 1.24979i −0.238804 0.971068i \(-0.576755\pi\)
0.960371 0.278724i \(-0.0899114\pi\)
\(348\) 0 0
\(349\) −4449.71 7707.13i −0.682486 1.18210i −0.974220 0.225601i \(-0.927566\pi\)
0.291734 0.956499i \(-0.405768\pi\)
\(350\) −1611.22 −0.246067
\(351\) 0 0
\(352\) −38798.8 −5.87495
\(353\) −1861.23 3223.74i −0.280632 0.486069i 0.690909 0.722942i \(-0.257211\pi\)
−0.971541 + 0.236873i \(0.923877\pi\)
\(354\) 0 0
\(355\) −1402.10 + 2428.51i −0.209622 + 0.363076i
\(356\) −6815.21 + 11804.3i −1.01462 + 1.75738i
\(357\) 0 0
\(358\) 4652.71 + 8058.73i 0.686881 + 1.18971i
\(359\) 11029.3 1.62145 0.810727 0.585425i \(-0.199072\pi\)
0.810727 + 0.585425i \(0.199072\pi\)
\(360\) 0 0
\(361\) 14621.1 2.13166
\(362\) 3714.64 + 6433.95i 0.539330 + 0.934146i
\(363\) 0 0
\(364\) 4451.80 7710.74i 0.641038 1.11031i
\(365\) 221.670 383.944i 0.0317883 0.0550590i
\(366\) 0 0
\(367\) 2426.56 + 4202.92i 0.345137 + 0.597794i 0.985379 0.170379i \(-0.0544992\pi\)
−0.640242 + 0.768173i \(0.721166\pi\)
\(368\) −5582.49 −0.790781
\(369\) 0 0
\(370\) −5941.52 −0.834824
\(371\) −795.641 1378.09i −0.111341 0.192849i
\(372\) 0 0
\(373\) 6186.89 10716.0i 0.858834 1.48754i −0.0142081 0.999899i \(-0.504523\pi\)
0.873042 0.487645i \(-0.162144\pi\)
\(374\) 6027.31 10439.6i 0.833328 1.44337i
\(375\) 0 0
\(376\) −14850.0 25721.0i −2.03679 3.52782i
\(377\) 5570.06 0.760935
\(378\) 0 0
\(379\) 11150.6 1.51127 0.755634 0.654994i \(-0.227329\pi\)
0.755634 + 0.654994i \(0.227329\pi\)
\(380\) 7986.84 + 13833.6i 1.07820 + 1.86750i
\(381\) 0 0
\(382\) 2993.69 5185.23i 0.400970 0.694501i
\(383\) −1099.80 + 1904.90i −0.146728 + 0.254141i −0.930016 0.367518i \(-0.880208\pi\)
0.783288 + 0.621659i \(0.213541\pi\)
\(384\) 0 0
\(385\) −1659.93 2875.07i −0.219734 0.380591i
\(386\) −15651.7 −2.06386
\(387\) 0 0
\(388\) −4212.72 −0.551207
\(389\) −4609.46 7983.82i −0.600794 1.04061i −0.992701 0.120601i \(-0.961518\pi\)
0.391907 0.920005i \(-0.371815\pi\)
\(390\) 0 0
\(391\) 462.919 801.799i 0.0598742 0.103705i
\(392\) 7667.82 13281.1i 0.987968 1.71121i
\(393\) 0 0
\(394\) −1976.45 3423.31i −0.252721 0.437726i
\(395\) 2251.71 0.286825
\(396\) 0 0
\(397\) 1119.36 0.141509 0.0707544 0.997494i \(-0.477459\pi\)
0.0707544 + 0.997494i \(0.477459\pi\)
\(398\) 4622.61 + 8006.60i 0.582188 + 1.00838i
\(399\) 0 0
\(400\) −2959.62 + 5126.22i −0.369953 + 0.640777i
\(401\) −6148.45 + 10649.4i −0.765683 + 1.32620i 0.174202 + 0.984710i \(0.444265\pi\)
−0.939885 + 0.341491i \(0.889068\pi\)
\(402\) 0 0
\(403\) 511.096 + 885.245i 0.0631750 + 0.109422i
\(404\) 29969.2 3.69065
\(405\) 0 0
\(406\) −10376.4 −1.26841
\(407\) −6121.12 10602.1i −0.745485 1.29122i
\(408\) 0 0
\(409\) −1250.11 + 2165.25i −0.151134 + 0.261772i −0.931645 0.363370i \(-0.881626\pi\)
0.780510 + 0.625143i \(0.214959\pi\)
\(410\) −1941.81 + 3363.32i −0.233901 + 0.405128i
\(411\) 0 0
\(412\) −22120.7 38314.1i −2.64516 4.58155i
\(413\) 1548.96 0.184551
\(414\) 0 0
\(415\) 1421.48 0.168139
\(416\) −11934.1 20670.4i −1.40653 2.43618i
\(417\) 0 0
\(418\) −22496.2 + 38964.5i −2.63235 + 4.55937i
\(419\) 4166.49 7216.57i 0.485790 0.841414i −0.514076 0.857744i \(-0.671865\pi\)
0.999867 + 0.0163308i \(0.00519849\pi\)
\(420\) 0 0
\(421\) −5687.10 9850.35i −0.658367 1.14032i −0.981038 0.193814i \(-0.937914\pi\)
0.322672 0.946511i \(-0.395419\pi\)
\(422\) 5171.91 0.596598
\(423\) 0 0
\(424\) −10151.6 −1.16275
\(425\) −490.844 850.166i −0.0560221 0.0970332i
\(426\) 0 0
\(427\) 1533.67 2656.40i 0.173816 0.301059i
\(428\) 8970.56 15537.5i 1.01310 1.75475i
\(429\) 0 0
\(430\) 6387.15 + 11062.9i 0.716316 + 1.24070i
\(431\) −10030.2 −1.12097 −0.560484 0.828165i \(-0.689385\pi\)
−0.560484 + 0.828165i \(0.689385\pi\)
\(432\) 0 0
\(433\) 7609.38 0.844535 0.422267 0.906471i \(-0.361234\pi\)
0.422267 + 0.906471i \(0.361234\pi\)
\(434\) −952.120 1649.12i −0.105307 0.182397i
\(435\) 0 0
\(436\) 9044.74 15666.0i 0.993497 1.72079i
\(437\) −1727.78 + 2992.61i −0.189133 + 0.327588i
\(438\) 0 0
\(439\) 6185.24 + 10713.2i 0.672450 + 1.16472i 0.977207 + 0.212287i \(0.0680913\pi\)
−0.304757 + 0.952430i \(0.598575\pi\)
\(440\) −21179.1 −2.29471
\(441\) 0 0
\(442\) 7415.72 0.798032
\(443\) 6042.21 + 10465.4i 0.648023 + 1.12241i 0.983594 + 0.180394i \(0.0577373\pi\)
−0.335572 + 0.942015i \(0.608929\pi\)
\(444\) 0 0
\(445\) −1563.26 + 2707.65i −0.166530 + 0.288438i
\(446\) −305.324 + 528.836i −0.0324159 + 0.0561460i
\(447\) 0 0
\(448\) 11050.2 + 19139.5i 1.16534 + 2.01843i
\(449\) −625.550 −0.0657495 −0.0328747 0.999459i \(-0.510466\pi\)
−0.0328747 + 0.999459i \(0.510466\pi\)
\(450\) 0 0
\(451\) −8002.04 −0.835480
\(452\) 16385.2 + 28380.0i 1.70508 + 2.95328i
\(453\) 0 0
\(454\) −3277.16 + 5676.22i −0.338777 + 0.586780i
\(455\) 1021.15 1768.68i 0.105213 0.182235i
\(456\) 0 0
\(457\) −905.611 1568.56i −0.0926974 0.160557i 0.815948 0.578125i \(-0.196216\pi\)
−0.908645 + 0.417569i \(0.862882\pi\)
\(458\) 4489.17 0.458003
\(459\) 0 0
\(460\) −2569.74 −0.260467
\(461\) 5812.49 + 10067.5i 0.587233 + 1.01712i 0.994593 + 0.103850i \(0.0331163\pi\)
−0.407359 + 0.913268i \(0.633550\pi\)
\(462\) 0 0
\(463\) −3645.94 + 6314.96i −0.365964 + 0.633868i −0.988930 0.148380i \(-0.952594\pi\)
0.622966 + 0.782249i \(0.285927\pi\)
\(464\) −19060.3 + 33013.4i −1.90701 + 3.30303i
\(465\) 0 0
\(466\) 14545.4 + 25193.4i 1.44593 + 2.50443i
\(467\) −11637.6 −1.15316 −0.576579 0.817042i \(-0.695613\pi\)
−0.576579 + 0.817042i \(0.695613\pi\)
\(468\) 0 0
\(469\) −5256.78 −0.517560
\(470\) −5381.22 9320.55i −0.528122 0.914734i
\(471\) 0 0
\(472\) 4940.83 8557.76i 0.481822 0.834540i
\(473\) −13160.4 + 22794.5i −1.27932 + 2.21584i
\(474\) 0 0
\(475\) 1832.01 + 3173.13i 0.176965 + 0.306512i
\(476\) −10105.8 −0.973109
\(477\) 0 0
\(478\) −38678.6 −3.70109
\(479\) −6020.72 10428.2i −0.574309 0.994732i −0.996116 0.0880467i \(-0.971938\pi\)
0.421807 0.906685i \(-0.361396\pi\)
\(480\) 0 0
\(481\) 3765.57 6522.16i 0.356955 0.618263i
\(482\) 17905.0 31012.3i 1.69201 2.93065i
\(483\) 0 0
\(484\) −19963.4 34577.6i −1.87485 3.24733i
\(485\) −966.307 −0.0904695
\(486\) 0 0
\(487\) 7037.81 0.654853 0.327427 0.944877i \(-0.393819\pi\)
0.327427 + 0.944877i \(0.393819\pi\)
\(488\) −9784.12 16946.6i −0.907595 1.57200i
\(489\) 0 0
\(490\) 2778.59 4812.66i 0.256171 0.443702i
\(491\) −3301.53 + 5718.42i −0.303454 + 0.525599i −0.976916 0.213624i \(-0.931473\pi\)
0.673462 + 0.739222i \(0.264807\pi\)
\(492\) 0 0
\(493\) −3161.09 5475.16i −0.288779 0.500180i
\(494\) −27678.2 −2.52085
\(495\) 0 0
\(496\) −6995.72 −0.633301
\(497\) 3310.79 + 5734.46i 0.298811 + 0.517556i
\(498\) 0 0
\(499\) 18.3523 31.7872i 0.00164642 0.00285168i −0.865201 0.501425i \(-0.832809\pi\)
0.866847 + 0.498573i \(0.166143\pi\)
\(500\) −1362.38 + 2359.71i −0.121855 + 0.211059i
\(501\) 0 0
\(502\) −1949.38 3376.43i −0.173317 0.300194i
\(503\) 21242.5 1.88302 0.941508 0.336990i \(-0.109409\pi\)
0.941508 + 0.336990i \(0.109409\pi\)
\(504\) 0 0
\(505\) 6874.29 0.605746
\(506\) −3619.03 6268.35i −0.317956 0.550715i
\(507\) 0 0
\(508\) 6281.62 10880.1i 0.548626 0.950248i
\(509\) 5640.20 9769.12i 0.491155 0.850705i −0.508794 0.860889i \(-0.669908\pi\)
0.999948 + 0.0101839i \(0.00324171\pi\)
\(510\) 0 0
\(511\) −523.430 906.608i −0.0453135 0.0784853i
\(512\) 20681.3 1.78514
\(513\) 0 0
\(514\) 23999.9 2.05951
\(515\) −5074.00 8788.43i −0.434150 0.751970i
\(516\) 0 0
\(517\) 11087.8 19204.6i 0.943209 1.63369i
\(518\) −7014.87 + 12150.1i −0.595011 + 1.03059i
\(519\) 0 0
\(520\) −6514.45 11283.4i −0.549379 0.951553i
\(521\) −10239.3 −0.861023 −0.430511 0.902585i \(-0.641667\pi\)
−0.430511 + 0.902585i \(0.641667\pi\)
\(522\) 0 0
\(523\) −2822.00 −0.235942 −0.117971 0.993017i \(-0.537639\pi\)
−0.117971 + 0.993017i \(0.537639\pi\)
\(524\) −26049.0 45118.3i −2.17167 3.76145i
\(525\) 0 0
\(526\) 20607.6 35693.5i 1.70824 2.95876i
\(527\) 580.108 1004.78i 0.0479505 0.0830527i
\(528\) 0 0
\(529\) 5805.55 + 10055.5i 0.477155 + 0.826457i
\(530\) −3678.66 −0.301492
\(531\) 0 0
\(532\) 37718.7 3.07390
\(533\) −2461.33 4263.16i −0.200023 0.346450i
\(534\) 0 0
\(535\) 2057.65 3563.96i 0.166281 0.288007i
\(536\) −16767.9 + 29042.9i −1.35124 + 2.34041i
\(537\) 0 0
\(538\) 15112.2 + 26175.1i 1.21103 + 2.09756i
\(539\) 11450.3 0.915028
\(540\) 0 0
\(541\) −9409.63 −0.747785 −0.373892 0.927472i \(-0.621977\pi\)
−0.373892 + 0.927472i \(0.621977\pi\)
\(542\) −8347.12 14457.6i −0.661512 1.14577i
\(543\) 0 0
\(544\) −13545.5 + 23461.5i −1.06757 + 1.84908i
\(545\) 2074.67 3593.43i 0.163063 0.282433i
\(546\) 0 0
\(547\) 1918.21 + 3322.45i 0.149940 + 0.259703i 0.931205 0.364496i \(-0.118759\pi\)
−0.781265 + 0.624199i \(0.785425\pi\)
\(548\) 21851.6 1.70339
\(549\) 0 0
\(550\) −7674.69 −0.594999
\(551\) 11798.3 + 20435.3i 0.912207 + 1.57999i
\(552\) 0 0
\(553\) 2658.49 4604.63i 0.204431 0.354085i
\(554\) 11109.1 19241.5i 0.851948 1.47562i
\(555\) 0 0
\(556\) −1436.67 2488.39i −0.109584 0.189804i
\(557\) 6145.92 0.467524 0.233762 0.972294i \(-0.424896\pi\)
0.233762 + 0.972294i \(0.424896\pi\)
\(558\) 0 0
\(559\) −16192.0 −1.22513
\(560\) 6988.57 + 12104.6i 0.527359 + 0.913412i
\(561\) 0 0
\(562\) −20323.5 + 35201.3i −1.52543 + 2.64213i
\(563\) −6623.93 + 11473.0i −0.495854 + 0.858844i −0.999989 0.00478126i \(-0.998478\pi\)
0.504135 + 0.863625i \(0.331811\pi\)
\(564\) 0 0
\(565\) 3758.41 + 6509.76i 0.279854 + 0.484722i
\(566\) −4228.63 −0.314033
\(567\) 0 0
\(568\) 42242.6 3.12053
\(569\) −3272.45 5668.04i −0.241104 0.417604i 0.719925 0.694052i \(-0.244176\pi\)
−0.961029 + 0.276448i \(0.910843\pi\)
\(570\) 0 0
\(571\) −10181.0 + 17634.1i −0.746170 + 1.29241i 0.203475 + 0.979080i \(0.434776\pi\)
−0.949646 + 0.313325i \(0.898557\pi\)
\(572\) 21205.1 36728.3i 1.55005 2.68477i
\(573\) 0 0
\(574\) 4585.21 + 7941.82i 0.333420 + 0.577500i
\(575\) −589.443 −0.0427504
\(576\) 0 0
\(577\) −26247.4 −1.89375 −0.946876 0.321600i \(-0.895779\pi\)
−0.946876 + 0.321600i \(0.895779\pi\)
\(578\) 9200.91 + 15936.4i 0.662124 + 1.14683i
\(579\) 0 0
\(580\) −8773.85 + 15196.8i −0.628128 + 1.08795i
\(581\) 1678.27 2906.85i 0.119839 0.207567i
\(582\) 0 0
\(583\) −3789.85 6564.22i −0.269228 0.466316i
\(584\) −6678.49 −0.473215
\(585\) 0 0
\(586\) 36842.4 2.59718
\(587\) 7049.08 + 12209.4i 0.495650 + 0.858492i 0.999987 0.00501514i \(-0.00159638\pi\)
−0.504337 + 0.863507i \(0.668263\pi\)
\(588\) 0 0
\(589\) −2165.18 + 3750.20i −0.151468 + 0.262350i
\(590\) 1790.41 3101.08i 0.124932 0.216389i
\(591\) 0 0
\(592\) 25770.9 + 44636.6i 1.78915 + 3.09891i
\(593\) 3476.71 0.240761 0.120380 0.992728i \(-0.461589\pi\)
0.120380 + 0.992728i \(0.461589\pi\)
\(594\) 0 0
\(595\) −2318.06 −0.159716
\(596\) −11111.4 19245.5i −0.763658 1.32269i
\(597\) 0 0
\(598\) 2226.34 3856.14i 0.152244 0.263694i
\(599\) 8089.48 14011.4i 0.551798 0.955743i −0.446347 0.894860i \(-0.647275\pi\)
0.998145 0.0608826i \(-0.0193915\pi\)
\(600\) 0 0
\(601\) −4056.08 7025.34i −0.275293 0.476821i 0.694916 0.719091i \(-0.255441\pi\)
−0.970209 + 0.242270i \(0.922108\pi\)
\(602\) 30164.0 2.04218
\(603\) 0 0
\(604\) 61522.3 4.14455
\(605\) −4579.17 7931.35i −0.307719 0.532984i
\(606\) 0 0
\(607\) −10569.6 + 18307.1i −0.706765 + 1.22415i 0.259286 + 0.965800i \(0.416513\pi\)
−0.966051 + 0.258352i \(0.916821\pi\)
\(608\) 50556.7 87566.8i 3.37228 5.84096i
\(609\) 0 0
\(610\) −3545.48 6140.95i −0.235331 0.407606i
\(611\) 13641.9 0.903258
\(612\) 0 0
\(613\) −11440.3 −0.753785 −0.376892 0.926257i \(-0.623007\pi\)
−0.376892 + 0.926257i \(0.623007\pi\)
\(614\) 6016.62 + 10421.1i 0.395457 + 0.684952i
\(615\) 0 0
\(616\) −25005.1 + 43310.2i −1.63553 + 2.83282i
\(617\) −10783.1 + 18676.9i −0.703584 + 1.21864i 0.263616 + 0.964628i \(0.415085\pi\)
−0.967200 + 0.254016i \(0.918249\pi\)
\(618\) 0 0
\(619\) 7599.14 + 13162.1i 0.493433 + 0.854651i 0.999971 0.00756612i \(-0.00240839\pi\)
−0.506538 + 0.862218i \(0.669075\pi\)
\(620\) −3220.28 −0.208596
\(621\) 0 0
\(622\) −32932.6 −2.12295
\(623\) 3691.34 + 6393.59i 0.237384 + 0.411162i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 15756.6 27291.2i 1.00601 1.74245i
\(627\) 0 0
\(628\) −5193.37 8995.19i −0.329997 0.571572i
\(629\) −8548.05 −0.541865
\(630\) 0 0
\(631\) −4929.66 −0.311009 −0.155504 0.987835i \(-0.549700\pi\)
−0.155504 + 0.987835i \(0.549700\pi\)
\(632\) −16959.9 29375.4i −1.06745 1.84888i
\(633\) 0 0
\(634\) 9012.61 15610.3i 0.564569 0.977862i
\(635\) 1440.87 2495.66i 0.0900459 0.155964i
\(636\) 0 0
\(637\) 3521.99 + 6100.26i 0.219068 + 0.379436i
\(638\) −49425.8 −3.06706
\(639\) 0 0
\(640\) 23494.4 1.45109
\(641\) 3767.86 + 6526.13i 0.232171 + 0.402132i 0.958447 0.285271i \(-0.0920838\pi\)
−0.726276 + 0.687403i \(0.758750\pi\)
\(642\) 0 0
\(643\) 7998.62 13854.0i 0.490568 0.849688i −0.509373 0.860546i \(-0.670123\pi\)
0.999941 + 0.0108576i \(0.00345614\pi\)
\(644\) −3033.97 + 5254.98i −0.185644 + 0.321546i
\(645\) 0 0
\(646\) 15707.8 + 27206.7i 0.956678 + 1.65701i
\(647\) 6020.46 0.365825 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(648\) 0 0
\(649\) 7378.12 0.446250
\(650\) −2360.64 4088.75i −0.142449 0.246729i
\(651\) 0 0
\(652\) 24438.4 42328.5i 1.46792 2.54251i
\(653\) −5474.34 + 9481.84i −0.328067 + 0.568228i −0.982128 0.188213i \(-0.939730\pi\)
0.654062 + 0.756441i \(0.273064\pi\)
\(654\) 0 0
\(655\) −5975.09 10349.2i −0.356437 0.617367i
\(656\) 33690.0 2.00514
\(657\) 0 0
\(658\) −25413.4 −1.50565
\(659\) 6169.14 + 10685.3i 0.364667 + 0.631622i 0.988723 0.149758i \(-0.0478495\pi\)
−0.624056 + 0.781380i \(0.714516\pi\)
\(660\) 0 0
\(661\) −10008.4 + 17335.0i −0.588928 + 1.02005i 0.405445 + 0.914119i \(0.367116\pi\)
−0.994373 + 0.105934i \(0.966217\pi\)
\(662\) −21980.1 + 38070.6i −1.29045 + 2.23513i
\(663\) 0 0
\(664\) −10706.6 18544.3i −0.625746 1.08382i
\(665\) 8651.86 0.504518
\(666\) 0 0
\(667\) −3796.08 −0.220367
\(668\) −1035.83 1794.11i −0.0599963 0.103917i
\(669\) 0 0
\(670\) −6076.20 + 10524.3i −0.350364 + 0.606849i
\(671\) 7305.29 12653.1i 0.420295 0.727972i
\(672\) 0 0
\(673\) 4209.61 + 7291.26i 0.241112 + 0.417619i 0.961031 0.276439i \(-0.0891544\pi\)
−0.719919 + 0.694058i \(0.755821\pi\)
\(674\) 18889.1 1.07950
\(675\) 0 0
\(676\) −21800.5 −1.24036
\(677\) 12853.5 + 22263.0i 0.729692 + 1.26386i 0.957013 + 0.290044i \(0.0936701\pi\)
−0.227321 + 0.973820i \(0.572997\pi\)
\(678\) 0 0
\(679\) −1140.87 + 1976.05i −0.0644810 + 0.111684i
\(680\) −7394.08 + 12806.9i −0.416985 + 0.722239i
\(681\) 0 0
\(682\) −4535.20 7855.20i −0.254636 0.441043i
\(683\) 19624.3 1.09942 0.549708 0.835357i \(-0.314739\pi\)
0.549708 + 0.835357i \(0.314739\pi\)
\(684\) 0 0
\(685\) 5012.30 0.279577
\(686\) −17614.1 30508.5i −0.980334 1.69799i
\(687\) 0 0
\(688\) 55407.7 95968.9i 3.07035 5.31799i
\(689\) 2331.43 4038.15i 0.128912 0.223282i
\(690\) 0 0
\(691\) −3636.61 6298.80i −0.200207 0.346769i 0.748388 0.663261i \(-0.230828\pi\)
−0.948595 + 0.316492i \(0.897495\pi\)
\(692\) −46511.8 −2.55508
\(693\) 0 0
\(694\) −50920.8 −2.78520
\(695\) −329.542 570.783i −0.0179860 0.0311526i
\(696\) 0 0
\(697\) −2793.68 + 4838.80i −0.151820 + 0.262959i
\(698\) −24289.9 + 42071.3i −1.31717 + 2.28141i
\(699\) 0 0
\(700\) 3216.98 + 5571.98i 0.173701 + 0.300859i
\(701\) −17644.3 −0.950664 −0.475332 0.879807i \(-0.657672\pi\)
−0.475332 + 0.879807i \(0.657672\pi\)
\(702\) 0 0
\(703\) 31904.5 1.71166
\(704\) 52635.1 + 91166.7i 2.81784 + 4.88064i
\(705\) 0 0
\(706\) −10160.0 + 17597.6i −0.541609 + 0.938094i
\(707\) 8116.14 14057.6i 0.431738 0.747793i
\(708\) 0 0
\(709\) −12152.2 21048.2i −0.643703 1.11493i −0.984600 0.174825i \(-0.944064\pi\)
0.340897 0.940101i \(-0.389269\pi\)
\(710\) 15307.5 0.809126
\(711\) 0 0
\(712\) 47098.1 2.47904
\(713\) −348.320 603.307i −0.0182955 0.0316887i
\(714\) 0 0
\(715\) 4864.00 8424.69i 0.254410 0.440651i
\(716\) 18579.3 32180.3i 0.969751 1.67966i
\(717\) 0 0
\(718\) −30103.0 52139.9i −1.56467 2.71009i
\(719\) 15170.2 0.786863 0.393431 0.919354i \(-0.371288\pi\)
0.393431 + 0.919354i \(0.371288\pi\)
\(720\) 0 0
\(721\) −23962.5 −1.23774
\(722\) −39906.4 69119.9i −2.05701 3.56285i
\(723\) 0 0
\(724\) 14833.4 25692.2i 0.761435 1.31884i
\(725\) −2012.53 + 3485.81i −0.103095 + 0.178565i
\(726\) 0 0
\(727\) 8743.52 + 15144.2i 0.446051 + 0.772583i 0.998125 0.0612123i \(-0.0194967\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(728\) −30765.2 −1.56625
\(729\) 0 0
\(730\) −2420.09 −0.122701
\(731\) 9189.18 + 15916.1i 0.464944 + 0.805306i
\(732\) 0 0
\(733\) −9349.02 + 16193.0i −0.471097 + 0.815964i −0.999453 0.0330590i \(-0.989475\pi\)
0.528357 + 0.849023i \(0.322808\pi\)
\(734\) 13246.0 22942.7i 0.666101 1.15372i
\(735\) 0 0
\(736\) 8133.23 + 14087.2i 0.407330 + 0.705516i
\(737\) −25039.5 −1.25148
\(738\) 0 0
\(739\) −35250.3 −1.75467 −0.877336 0.479876i \(-0.840682\pi\)
−0.877336 + 0.479876i \(0.840682\pi\)
\(740\) 11862.9 + 20547.2i 0.589310 + 1.02071i
\(741\) 0 0
\(742\) −4343.21 + 7522.67i −0.214885 + 0.372191i
\(743\) −5566.78 + 9641.94i −0.274866 + 0.476081i −0.970101 0.242701i \(-0.921967\pi\)
0.695236 + 0.718782i \(0.255300\pi\)
\(744\) 0 0
\(745\) −2548.71 4414.50i −0.125339 0.217094i
\(746\) −67545.5 −3.31503
\(747\) 0 0
\(748\) −48136.8 −2.35301
\(749\) −4858.75 8415.59i −0.237029 0.410546i
\(750\) 0 0
\(751\) −8598.81 + 14893.6i −0.417809 + 0.723667i −0.995719 0.0924337i \(-0.970535\pi\)
0.577909 + 0.816101i \(0.303869\pi\)
\(752\) −46681.3 + 80854.5i −2.26369 + 3.92082i
\(753\) 0 0
\(754\) −15202.8 26332.0i −0.734288 1.27182i
\(755\) 14111.9 0.680245
\(756\) 0 0
\(757\) 804.647 0.0386333 0.0193166 0.999813i \(-0.493851\pi\)
0.0193166 + 0.999813i \(0.493851\pi\)
\(758\) −30434.3 52713.8i −1.45834 2.52593i
\(759\) 0 0
\(760\) 27597.4 47800.1i 1.31719 2.28144i
\(761\) −13104.4 + 22697.5i −0.624225 + 1.08119i 0.364465 + 0.931217i \(0.381252\pi\)
−0.988690 + 0.149973i \(0.952081\pi\)
\(762\) 0 0
\(763\) −4898.93 8485.19i −0.232442 0.402601i
\(764\) −23909.0 −1.13219
\(765\) 0 0
\(766\) 12007.0 0.566360
\(767\) 2269.42 + 3930.76i 0.106837 + 0.185047i
\(768\) 0 0
\(769\) −18272.1 + 31648.2i −0.856837 + 1.48409i 0.0180924 + 0.999836i \(0.494241\pi\)
−0.874930 + 0.484250i \(0.839093\pi\)
\(770\) −9061.13 + 15694.3i −0.424078 + 0.734525i
\(771\) 0 0
\(772\) 31250.4 + 54127.3i 1.45690 + 2.52342i
\(773\) −42387.4 −1.97228 −0.986139 0.165923i \(-0.946940\pi\)
−0.986139 + 0.165923i \(0.946940\pi\)
\(774\) 0 0
\(775\) −738.663 −0.0342368
\(776\) 7278.23 + 12606.3i 0.336692 + 0.583168i
\(777\) 0 0
\(778\) −25161.9 + 43581.7i −1.15951 + 2.00833i
\(779\) 10427.1 18060.2i 0.479574 0.830646i
\(780\) 0 0
\(781\) 15770.2 + 27314.7i 0.722537 + 1.25147i
\(782\) −5053.92 −0.231110
\(783\) 0 0
\(784\) −48207.8 −2.19606
\(785\) −1191.25 2063.30i −0.0541624 0.0938120i
\(786\) 0 0
\(787\) −13424.7