Properties

Label 405.4.e.o.271.2
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.o.136.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 + 0.633975i) q^{2} +(3.73205 - 6.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.46410 + 6.00000i) q^{7} +11.3205 q^{8} +O(q^{10})\) \(q+(0.366025 + 0.633975i) q^{2} +(3.73205 - 6.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.46410 + 6.00000i) q^{7} +11.3205 q^{8} -3.66025 q^{10} +(-18.7487 - 32.4737i) q^{11} +(19.4641 - 33.7128i) q^{13} +(-2.53590 + 4.39230i) q^{14} +(-25.7128 - 44.5359i) q^{16} -80.9948 q^{17} +112.779 q^{19} +(18.6603 + 32.3205i) q^{20} +(13.7250 - 23.7724i) q^{22} +(-6.71281 + 11.6269i) q^{23} +(-12.5000 - 21.6506i) q^{25} +28.4974 q^{26} +51.7128 q^{28} +(21.7154 + 37.6122i) q^{29} +(74.8923 - 129.717i) q^{31} +(64.1051 - 111.033i) q^{32} +(-29.6462 - 51.3487i) q^{34} -34.6410 q^{35} -218.344 q^{37} +(41.2801 + 71.4993i) q^{38} +(-28.3013 + 49.0192i) q^{40} +(186.069 - 322.281i) q^{41} +(-230.100 - 398.545i) q^{43} -279.885 q^{44} -9.82824 q^{46} +(107.144 + 185.578i) q^{47} +(147.500 - 255.477i) q^{49} +(9.15064 - 15.8494i) q^{50} +(-145.282 - 251.636i) q^{52} -445.205 q^{53} +187.487 q^{55} +(39.2154 + 67.9230i) q^{56} +(-15.8968 + 27.5340i) q^{58} +(200.749 - 347.707i) q^{59} +(-0.723122 - 1.25248i) q^{61} +109.650 q^{62} -317.549 q^{64} +(97.3205 + 168.564i) q^{65} +(408.033 - 706.734i) q^{67} +(-302.277 + 523.559i) q^{68} +(-12.6795 - 21.9615i) q^{70} -147.518 q^{71} +432.651 q^{73} +(-79.9193 - 138.424i) q^{74} +(420.899 - 729.018i) q^{76} +(129.895 - 224.985i) q^{77} +(-192.067 - 332.669i) q^{79} +257.128 q^{80} +272.424 q^{82} +(630.615 + 1092.26i) q^{83} +(202.487 - 350.718i) q^{85} +(168.445 - 291.755i) q^{86} +(-212.245 - 367.619i) q^{88} -513.000 q^{89} +269.703 q^{91} +(50.1051 + 86.7846i) q^{92} +(-78.4346 + 135.853i) q^{94} +(-281.949 + 488.349i) q^{95} +(548.051 + 949.252i) q^{97} +215.955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + O(q^{10}) \) \( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + 20 q^{10} + 22 q^{11} + 64 q^{13} - 24 q^{14} + 8 q^{16} + 64 q^{17} - 20 q^{19} + 40 q^{20} + 190 q^{22} + 84 q^{23} - 50 q^{25} - 80 q^{26} + 96 q^{28} + 170 q^{29} + 258 q^{31} + 104 q^{32} - 368 q^{34} + 152 q^{37} + 418 q^{38} + 60 q^{40} + 578 q^{41} - 380 q^{43} - 496 q^{44} - 552 q^{46} + 484 q^{47} + 590 q^{49} - 50 q^{50} - 304 q^{52} - 1088 q^{53} - 220 q^{55} + 240 q^{56} + 314 q^{58} + 706 q^{59} - 668 q^{61} - 372 q^{62} + 448 q^{64} + 320 q^{65} + 1452 q^{67} - 544 q^{68} - 120 q^{70} - 1948 q^{71} + 2368 q^{73} - 964 q^{74} + 776 q^{76} + 672 q^{77} - 408 q^{79} - 80 q^{80} - 580 q^{82} + 444 q^{83} - 160 q^{85} + 556 q^{86} - 1812 q^{88} - 2052 q^{89} + 192 q^{91} + 48 q^{92} + 580 q^{94} + 50 q^{95} + 668 q^{97} - 1180 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 + 0.633975i 0.129410 + 0.224144i 0.923448 0.383724i \(-0.125358\pi\)
−0.794038 + 0.607868i \(0.792025\pi\)
\(3\) 0 0
\(4\) 3.73205 6.46410i 0.466506 0.808013i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 3.46410 + 6.00000i 0.187044 + 0.323970i 0.944263 0.329191i \(-0.106776\pi\)
−0.757219 + 0.653161i \(0.773443\pi\)
\(8\) 11.3205 0.500301
\(9\) 0 0
\(10\) −3.66025 −0.115747
\(11\) −18.7487 32.4737i −0.513904 0.890109i −0.999870 0.0161306i \(-0.994865\pi\)
0.485965 0.873978i \(-0.338468\pi\)
\(12\) 0 0
\(13\) 19.4641 33.7128i 0.415259 0.719250i −0.580196 0.814477i \(-0.697024\pi\)
0.995456 + 0.0952265i \(0.0303575\pi\)
\(14\) −2.53590 + 4.39230i −0.0484105 + 0.0838495i
\(15\) 0 0
\(16\) −25.7128 44.5359i −0.401763 0.695873i
\(17\) −80.9948 −1.15554 −0.577769 0.816201i \(-0.696076\pi\)
−0.577769 + 0.816201i \(0.696076\pi\)
\(18\) 0 0
\(19\) 112.779 1.36176 0.680878 0.732396i \(-0.261598\pi\)
0.680878 + 0.732396i \(0.261598\pi\)
\(20\) 18.6603 + 32.3205i 0.208628 + 0.361354i
\(21\) 0 0
\(22\) 13.7250 23.7724i 0.133008 0.230377i
\(23\) −6.71281 + 11.6269i −0.0608573 + 0.105408i −0.894849 0.446369i \(-0.852717\pi\)
0.833992 + 0.551777i \(0.186050\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 28.4974 0.214954
\(27\) 0 0
\(28\) 51.7128 0.349029
\(29\) 21.7154 + 37.6122i 0.139050 + 0.240841i 0.927137 0.374722i \(-0.122262\pi\)
−0.788087 + 0.615563i \(0.788928\pi\)
\(30\) 0 0
\(31\) 74.8923 129.717i 0.433905 0.751546i −0.563301 0.826252i \(-0.690469\pi\)
0.997206 + 0.0747066i \(0.0238020\pi\)
\(32\) 64.1051 111.033i 0.354134 0.613378i
\(33\) 0 0
\(34\) −29.6462 51.3487i −0.149538 0.259007i
\(35\) −34.6410 −0.167297
\(36\) 0 0
\(37\) −218.344 −0.970147 −0.485074 0.874473i \(-0.661207\pi\)
−0.485074 + 0.874473i \(0.661207\pi\)
\(38\) 41.2801 + 71.4993i 0.176224 + 0.305229i
\(39\) 0 0
\(40\) −28.3013 + 49.0192i −0.111871 + 0.193766i
\(41\) 186.069 322.281i 0.708759 1.22761i −0.256558 0.966529i \(-0.582589\pi\)
0.965318 0.261078i \(-0.0840781\pi\)
\(42\) 0 0
\(43\) −230.100 398.545i −0.816045 1.41343i −0.908575 0.417721i \(-0.862829\pi\)
0.0925309 0.995710i \(-0.470504\pi\)
\(44\) −279.885 −0.958959
\(45\) 0 0
\(46\) −9.82824 −0.0315021
\(47\) 107.144 + 185.578i 0.332521 + 0.575944i 0.983006 0.183576i \(-0.0587673\pi\)
−0.650484 + 0.759520i \(0.725434\pi\)
\(48\) 0 0
\(49\) 147.500 255.477i 0.430029 0.744832i
\(50\) 9.15064 15.8494i 0.0258819 0.0448288i
\(51\) 0 0
\(52\) −145.282 251.636i −0.387442 0.671070i
\(53\) −445.205 −1.15384 −0.576921 0.816800i \(-0.695746\pi\)
−0.576921 + 0.816800i \(0.695746\pi\)
\(54\) 0 0
\(55\) 187.487 0.459650
\(56\) 39.2154 + 67.9230i 0.0935782 + 0.162082i
\(57\) 0 0
\(58\) −15.8968 + 27.5340i −0.0359888 + 0.0623344i
\(59\) 200.749 347.707i 0.442970 0.767247i −0.554938 0.831892i \(-0.687258\pi\)
0.997908 + 0.0646445i \(0.0205913\pi\)
\(60\) 0 0
\(61\) −0.723122 1.25248i −0.00151781 0.00262892i 0.865266 0.501314i \(-0.167150\pi\)
−0.866783 + 0.498685i \(0.833816\pi\)
\(62\) 109.650 0.224606
\(63\) 0 0
\(64\) −317.549 −0.620212
\(65\) 97.3205 + 168.564i 0.185710 + 0.321658i
\(66\) 0 0
\(67\) 408.033 706.734i 0.744018 1.28868i −0.206634 0.978418i \(-0.566251\pi\)
0.950652 0.310259i \(-0.100416\pi\)
\(68\) −302.277 + 523.559i −0.539066 + 0.933689i
\(69\) 0 0
\(70\) −12.6795 21.9615i −0.0216498 0.0374986i
\(71\) −147.518 −0.246580 −0.123290 0.992371i \(-0.539345\pi\)
−0.123290 + 0.992371i \(0.539345\pi\)
\(72\) 0 0
\(73\) 432.651 0.693671 0.346836 0.937926i \(-0.387256\pi\)
0.346836 + 0.937926i \(0.387256\pi\)
\(74\) −79.9193 138.424i −0.125546 0.217453i
\(75\) 0 0
\(76\) 420.899 729.018i 0.635268 1.10032i
\(77\) 129.895 224.985i 0.192245 0.332979i
\(78\) 0 0
\(79\) −192.067 332.669i −0.273534 0.473775i 0.696230 0.717819i \(-0.254859\pi\)
−0.969764 + 0.244044i \(0.921526\pi\)
\(80\) 257.128 0.359347
\(81\) 0 0
\(82\) 272.424 0.366881
\(83\) 630.615 + 1092.26i 0.833964 + 1.44447i 0.894871 + 0.446325i \(0.147267\pi\)
−0.0609071 + 0.998143i \(0.519399\pi\)
\(84\) 0 0
\(85\) 202.487 350.718i 0.258386 0.447538i
\(86\) 168.445 291.755i 0.211208 0.365823i
\(87\) 0 0
\(88\) −212.245 367.619i −0.257107 0.445322i
\(89\) −513.000 −0.610988 −0.305494 0.952194i \(-0.598822\pi\)
−0.305494 + 0.952194i \(0.598822\pi\)
\(90\) 0 0
\(91\) 269.703 0.310687
\(92\) 50.1051 + 86.7846i 0.0567806 + 0.0983470i
\(93\) 0 0
\(94\) −78.4346 + 135.853i −0.0860628 + 0.149065i
\(95\) −281.949 + 488.349i −0.304498 + 0.527406i
\(96\) 0 0
\(97\) 548.051 + 949.252i 0.573672 + 0.993629i 0.996185 + 0.0872717i \(0.0278148\pi\)
−0.422513 + 0.906357i \(0.638852\pi\)
\(98\) 215.955 0.222599
\(99\) 0 0
\(100\) −186.603 −0.186603
\(101\) −597.043 1034.11i −0.588198 1.01879i −0.994468 0.105036i \(-0.966504\pi\)
0.406270 0.913753i \(-0.366829\pi\)
\(102\) 0 0
\(103\) −90.7513 + 157.186i −0.0868154 + 0.150369i −0.906163 0.422928i \(-0.861002\pi\)
0.819348 + 0.573297i \(0.194336\pi\)
\(104\) 220.344 381.646i 0.207754 0.359841i
\(105\) 0 0
\(106\) −162.956 282.249i −0.149318 0.258627i
\(107\) 611.667 0.552636 0.276318 0.961066i \(-0.410886\pi\)
0.276318 + 0.961066i \(0.410886\pi\)
\(108\) 0 0
\(109\) 550.467 0.483717 0.241859 0.970312i \(-0.422243\pi\)
0.241859 + 0.970312i \(0.422243\pi\)
\(110\) 68.6250 + 118.862i 0.0594831 + 0.103028i
\(111\) 0 0
\(112\) 178.144 308.554i 0.150295 0.260318i
\(113\) 237.951 412.144i 0.198094 0.343108i −0.749817 0.661646i \(-0.769858\pi\)
0.947910 + 0.318538i \(0.103192\pi\)
\(114\) 0 0
\(115\) −33.5641 58.1347i −0.0272162 0.0471399i
\(116\) 324.172 0.259471
\(117\) 0 0
\(118\) 293.917 0.229298
\(119\) −280.574 485.969i −0.216136 0.374359i
\(120\) 0 0
\(121\) −37.5284 + 65.0010i −0.0281956 + 0.0488362i
\(122\) 0.529362 0.916883i 0.000392838 0.000680415i
\(123\) 0 0
\(124\) −559.004 968.223i −0.404839 0.701202i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1645.91 −1.15001 −0.575003 0.818152i \(-0.694999\pi\)
−0.575003 + 0.818152i \(0.694999\pi\)
\(128\) −629.072 1089.58i −0.434395 0.752395i
\(129\) 0 0
\(130\) −71.2436 + 123.397i −0.0480652 + 0.0832513i
\(131\) −193.354 + 334.898i −0.128957 + 0.223360i −0.923273 0.384145i \(-0.874496\pi\)
0.794316 + 0.607505i \(0.207830\pi\)
\(132\) 0 0
\(133\) 390.679 + 676.677i 0.254708 + 0.441168i
\(134\) 597.402 0.385132
\(135\) 0 0
\(136\) −916.903 −0.578116
\(137\) 1486.61 + 2574.88i 0.927078 + 1.60575i 0.788185 + 0.615439i \(0.211021\pi\)
0.138893 + 0.990307i \(0.455646\pi\)
\(138\) 0 0
\(139\) −1173.68 + 2032.87i −0.716187 + 1.24047i 0.246313 + 0.969190i \(0.420781\pi\)
−0.962500 + 0.271282i \(0.912552\pi\)
\(140\) −129.282 + 223.923i −0.0780452 + 0.135178i
\(141\) 0 0
\(142\) −53.9954 93.5227i −0.0319098 0.0552694i
\(143\) −1459.71 −0.853614
\(144\) 0 0
\(145\) −217.154 −0.124370
\(146\) 158.361 + 274.290i 0.0897677 + 0.155482i
\(147\) 0 0
\(148\) −814.869 + 1411.39i −0.452580 + 0.783891i
\(149\) −701.046 + 1214.25i −0.385449 + 0.667618i −0.991831 0.127556i \(-0.959287\pi\)
0.606382 + 0.795173i \(0.292620\pi\)
\(150\) 0 0
\(151\) 1470.63 + 2547.21i 0.792571 + 1.37277i 0.924370 + 0.381497i \(0.124591\pi\)
−0.131799 + 0.991276i \(0.542075\pi\)
\(152\) 1276.72 0.681288
\(153\) 0 0
\(154\) 190.179 0.0995135
\(155\) 374.462 + 648.586i 0.194048 + 0.336101i
\(156\) 0 0
\(157\) −1275.99 + 2210.08i −0.648631 + 1.12346i 0.334819 + 0.942282i \(0.391325\pi\)
−0.983450 + 0.181179i \(0.942009\pi\)
\(158\) 140.603 243.531i 0.0707958 0.122622i
\(159\) 0 0
\(160\) 320.526 + 555.167i 0.158374 + 0.274311i
\(161\) −93.0155 −0.0455320
\(162\) 0 0
\(163\) 351.559 0.168934 0.0844669 0.996426i \(-0.473081\pi\)
0.0844669 + 0.996426i \(0.473081\pi\)
\(164\) −1388.84 2405.54i −0.661281 1.14537i
\(165\) 0 0
\(166\) −461.642 + 799.588i −0.215846 + 0.373856i
\(167\) 10.4947 18.1773i 0.00486288 0.00842276i −0.863584 0.504205i \(-0.831785\pi\)
0.868447 + 0.495783i \(0.165119\pi\)
\(168\) 0 0
\(169\) 340.797 + 590.279i 0.155119 + 0.268675i
\(170\) 296.462 0.133750
\(171\) 0 0
\(172\) −3434.98 −1.52276
\(173\) −2262.30 3918.43i −0.994219 1.72204i −0.590098 0.807332i \(-0.700911\pi\)
−0.404121 0.914706i \(-0.632423\pi\)
\(174\) 0 0
\(175\) 86.6025 150.000i 0.0374088 0.0647939i
\(176\) −964.164 + 1669.98i −0.412935 + 0.715225i
\(177\) 0 0
\(178\) −187.771 325.229i −0.0790676 0.136949i
\(179\) −3626.79 −1.51441 −0.757204 0.653179i \(-0.773435\pi\)
−0.757204 + 0.653179i \(0.773435\pi\)
\(180\) 0 0
\(181\) 3551.41 1.45842 0.729210 0.684289i \(-0.239888\pi\)
0.729210 + 0.684289i \(0.239888\pi\)
\(182\) 98.7180 + 170.985i 0.0402058 + 0.0696386i
\(183\) 0 0
\(184\) −75.9925 + 131.623i −0.0304469 + 0.0527357i
\(185\) 545.859 945.455i 0.216932 0.375736i
\(186\) 0 0
\(187\) 1518.55 + 2630.20i 0.593836 + 1.02855i
\(188\) 1599.46 0.620493
\(189\) 0 0
\(190\) −412.801 −0.157620
\(191\) −139.825 242.185i −0.0529707 0.0917479i 0.838324 0.545172i \(-0.183536\pi\)
−0.891295 + 0.453424i \(0.850202\pi\)
\(192\) 0 0
\(193\) −133.080 + 230.501i −0.0496336 + 0.0859679i −0.889775 0.456400i \(-0.849139\pi\)
0.840141 + 0.542368i \(0.182472\pi\)
\(194\) −401.201 + 694.901i −0.148477 + 0.257170i
\(195\) 0 0
\(196\) −1100.95 1906.91i −0.401223 0.694938i
\(197\) 4731.12 1.71106 0.855528 0.517756i \(-0.173232\pi\)
0.855528 + 0.517756i \(0.173232\pi\)
\(198\) 0 0
\(199\) 2879.69 1.02581 0.512904 0.858446i \(-0.328570\pi\)
0.512904 + 0.858446i \(0.328570\pi\)
\(200\) −141.506 245.096i −0.0500301 0.0866546i
\(201\) 0 0
\(202\) 437.066 757.021i 0.152237 0.263682i
\(203\) −150.449 + 260.585i −0.0520169 + 0.0900959i
\(204\) 0 0
\(205\) 930.346 + 1611.41i 0.316967 + 0.549003i
\(206\) −132.869 −0.0449390
\(207\) 0 0
\(208\) −2001.91 −0.667343
\(209\) −2114.47 3662.37i −0.699813 1.21211i
\(210\) 0 0
\(211\) −1364.10 + 2362.69i −0.445065 + 0.770875i −0.998057 0.0623117i \(-0.980153\pi\)
0.552992 + 0.833187i \(0.313486\pi\)
\(212\) −1661.53 + 2877.85i −0.538275 + 0.932319i
\(213\) 0 0
\(214\) 223.886 + 387.781i 0.0715164 + 0.123870i
\(215\) 2301.00 0.729892
\(216\) 0 0
\(217\) 1037.74 0.324637
\(218\) 201.485 + 348.982i 0.0625976 + 0.108422i
\(219\) 0 0
\(220\) 699.711 1211.94i 0.214430 0.371403i
\(221\) −1576.49 + 2730.56i −0.479848 + 0.831120i
\(222\) 0 0
\(223\) 1837.42 + 3182.51i 0.551762 + 0.955680i 0.998148 + 0.0608392i \(0.0193777\pi\)
−0.446386 + 0.894841i \(0.647289\pi\)
\(224\) 888.267 0.264954
\(225\) 0 0
\(226\) 348.385 0.102541
\(227\) 2886.96 + 5000.36i 0.844115 + 1.46205i 0.886388 + 0.462943i \(0.153207\pi\)
−0.0422732 + 0.999106i \(0.513460\pi\)
\(228\) 0 0
\(229\) −2409.14 + 4172.75i −0.695198 + 1.20412i 0.274916 + 0.961468i \(0.411350\pi\)
−0.970114 + 0.242650i \(0.921983\pi\)
\(230\) 24.5706 42.5575i 0.00704408 0.0122007i
\(231\) 0 0
\(232\) 245.829 + 425.789i 0.0695667 + 0.120493i
\(233\) −91.0828 −0.0256096 −0.0128048 0.999918i \(-0.504076\pi\)
−0.0128048 + 0.999918i \(0.504076\pi\)
\(234\) 0 0
\(235\) −1071.44 −0.297416
\(236\) −1498.41 2595.32i −0.413297 0.715851i
\(237\) 0 0
\(238\) 205.395 355.754i 0.0559402 0.0968912i
\(239\) 2743.42 4751.74i 0.742498 1.28604i −0.208856 0.977946i \(-0.566974\pi\)
0.951354 0.308098i \(-0.0996926\pi\)
\(240\) 0 0
\(241\) −1508.60 2612.97i −0.403225 0.698406i 0.590888 0.806754i \(-0.298778\pi\)
−0.994113 + 0.108347i \(0.965444\pi\)
\(242\) −54.9453 −0.0145951
\(243\) 0 0
\(244\) −10.7949 −0.00283227
\(245\) 737.500 + 1277.39i 0.192315 + 0.333099i
\(246\) 0 0
\(247\) 2195.15 3802.11i 0.565482 0.979444i
\(248\) 847.819 1468.47i 0.217083 0.375999i
\(249\) 0 0
\(250\) 45.7532 + 79.2468i 0.0115747 + 0.0200480i
\(251\) 2740.98 0.689280 0.344640 0.938735i \(-0.388001\pi\)
0.344640 + 0.938735i \(0.388001\pi\)
\(252\) 0 0
\(253\) 503.426 0.125099
\(254\) −602.444 1043.46i −0.148822 0.257767i
\(255\) 0 0
\(256\) −809.682 + 1402.41i −0.197676 + 0.342385i
\(257\) −1260.70 + 2183.60i −0.305993 + 0.529996i −0.977482 0.211019i \(-0.932322\pi\)
0.671489 + 0.741015i \(0.265655\pi\)
\(258\) 0 0
\(259\) −756.364 1310.06i −0.181460 0.314298i
\(260\) 1452.82 0.346539
\(261\) 0 0
\(262\) −283.089 −0.0667531
\(263\) −2243.86 3886.48i −0.526092 0.911219i −0.999538 0.0303955i \(-0.990323\pi\)
0.473446 0.880823i \(-0.343010\pi\)
\(264\) 0 0
\(265\) 1113.01 1927.79i 0.258007 0.446881i
\(266\) −285.997 + 495.362i −0.0659234 + 0.114183i
\(267\) 0 0
\(268\) −3045.60 5275.14i −0.694178 1.20235i
\(269\) −8531.47 −1.93373 −0.966864 0.255291i \(-0.917829\pi\)
−0.966864 + 0.255291i \(0.917829\pi\)
\(270\) 0 0
\(271\) −123.097 −0.0275927 −0.0137964 0.999905i \(-0.504392\pi\)
−0.0137964 + 0.999905i \(0.504392\pi\)
\(272\) 2082.61 + 3607.18i 0.464252 + 0.804108i
\(273\) 0 0
\(274\) −1088.27 + 1884.95i −0.239945 + 0.415598i
\(275\) −468.718 + 811.843i −0.102781 + 0.178022i
\(276\) 0 0
\(277\) 3278.79 + 5679.03i 0.711204 + 1.23184i 0.964405 + 0.264428i \(0.0851831\pi\)
−0.253201 + 0.967414i \(0.581484\pi\)
\(278\) −1718.38 −0.370726
\(279\) 0 0
\(280\) −392.154 −0.0836989
\(281\) 3542.02 + 6134.96i 0.751954 + 1.30242i 0.946874 + 0.321604i \(0.104222\pi\)
−0.194920 + 0.980819i \(0.562445\pi\)
\(282\) 0 0
\(283\) −1036.47 + 1795.21i −0.217709 + 0.377082i −0.954107 0.299466i \(-0.903192\pi\)
0.736399 + 0.676548i \(0.236525\pi\)
\(284\) −550.545 + 953.572i −0.115031 + 0.199240i
\(285\) 0 0
\(286\) −534.290 925.417i −0.110466 0.191332i
\(287\) 2578.25 0.530276
\(288\) 0 0
\(289\) 1647.16 0.335267
\(290\) −79.4838 137.670i −0.0160947 0.0278768i
\(291\) 0 0
\(292\) 1614.68 2796.70i 0.323602 0.560495i
\(293\) 3564.20 6173.38i 0.710658 1.23090i −0.253952 0.967217i \(-0.581730\pi\)
0.964610 0.263680i \(-0.0849362\pi\)
\(294\) 0 0
\(295\) 1003.74 + 1738.53i 0.198102 + 0.343123i
\(296\) −2471.76 −0.485365
\(297\) 0 0
\(298\) −1026.40 −0.199523
\(299\) 261.318 + 452.616i 0.0505431 + 0.0875433i
\(300\) 0 0
\(301\) 1594.18 2761.20i 0.305272 0.528747i
\(302\) −1076.58 + 1864.68i −0.205132 + 0.355300i
\(303\) 0 0
\(304\) −2899.88 5022.73i −0.547103 0.947610i
\(305\) 7.23122 0.00135757
\(306\) 0 0
\(307\) −6334.70 −1.17766 −0.588828 0.808259i \(-0.700410\pi\)
−0.588828 + 0.808259i \(0.700410\pi\)
\(308\) −969.549 1679.31i −0.179367 0.310673i
\(309\) 0 0
\(310\) −274.125 + 474.798i −0.0502234 + 0.0869894i
\(311\) 3696.95 6403.30i 0.674067 1.16752i −0.302674 0.953094i \(-0.597879\pi\)
0.976741 0.214423i \(-0.0687872\pi\)
\(312\) 0 0
\(313\) 466.528 + 808.050i 0.0842482 + 0.145922i 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(314\) −1868.18 −0.335756
\(315\) 0 0
\(316\) −2867.21 −0.510421
\(317\) 4367.34 + 7564.45i 0.773799 + 1.34026i 0.935467 + 0.353413i \(0.114979\pi\)
−0.161669 + 0.986845i \(0.551688\pi\)
\(318\) 0 0
\(319\) 814.271 1410.36i 0.142917 0.247539i
\(320\) 793.872 1375.03i 0.138684 0.240207i
\(321\) 0 0
\(322\) −34.0460 58.9694i −0.00589227 0.0102057i
\(323\) −9134.55 −1.57356
\(324\) 0 0
\(325\) −973.205 −0.166104
\(326\) 128.679 + 222.879i 0.0218617 + 0.0378655i
\(327\) 0 0
\(328\) 2106.40 3648.39i 0.354593 0.614172i
\(329\) −742.313 + 1285.72i −0.124392 + 0.215454i
\(330\) 0 0
\(331\) 645.266 + 1117.63i 0.107151 + 0.185591i 0.914615 0.404326i \(-0.132494\pi\)
−0.807464 + 0.589917i \(0.799160\pi\)
\(332\) 9413.95 1.55620
\(333\) 0 0
\(334\) 15.3652 0.00251721
\(335\) 2040.17 + 3533.67i 0.332735 + 0.576314i
\(336\) 0 0
\(337\) 5000.66 8661.40i 0.808318 1.40005i −0.105710 0.994397i \(-0.533711\pi\)
0.914028 0.405651i \(-0.132955\pi\)
\(338\) −249.481 + 432.114i −0.0401479 + 0.0695382i
\(339\) 0 0
\(340\) −1511.38 2617.79i −0.241077 0.417558i
\(341\) −5616.54 −0.891943
\(342\) 0 0
\(343\) 4420.19 0.695825
\(344\) −2604.85 4511.73i −0.408267 0.707140i
\(345\) 0 0
\(346\) 1656.12 2868.49i 0.257323 0.445696i
\(347\) 3234.18 5601.77i 0.500346 0.866625i −0.499654 0.866225i \(-0.666539\pi\)
1.00000 0.000399827i \(-0.000127269\pi\)
\(348\) 0 0
\(349\) −5584.89 9673.32i −0.856597 1.48367i −0.875155 0.483842i \(-0.839241\pi\)
0.0185577 0.999828i \(-0.494093\pi\)
\(350\) 126.795 0.0193642
\(351\) 0 0
\(352\) −4807.55 −0.727964
\(353\) 908.387 + 1573.37i 0.136965 + 0.237230i 0.926346 0.376673i \(-0.122932\pi\)
−0.789382 + 0.613903i \(0.789599\pi\)
\(354\) 0 0
\(355\) 368.795 638.772i 0.0551369 0.0955000i
\(356\) −1914.54 + 3316.08i −0.285030 + 0.493686i
\(357\) 0 0
\(358\) −1327.50 2299.29i −0.195979 0.339445i
\(359\) −918.073 −0.134969 −0.0674847 0.997720i \(-0.521497\pi\)
−0.0674847 + 0.997720i \(0.521497\pi\)
\(360\) 0 0
\(361\) 5860.21 0.854382
\(362\) 1299.91 + 2251.50i 0.188734 + 0.326896i
\(363\) 0 0
\(364\) 1006.54 1743.38i 0.144937 0.251039i
\(365\) −1081.63 + 1873.44i −0.155110 + 0.268658i
\(366\) 0 0
\(367\) −3677.14 6368.99i −0.523011 0.905881i −0.999641 0.0267777i \(-0.991475\pi\)
0.476630 0.879104i \(-0.341858\pi\)
\(368\) 690.421 0.0978008
\(369\) 0 0
\(370\) 799.193 0.112292
\(371\) −1542.24 2671.23i −0.215819 0.373810i
\(372\) 0 0
\(373\) 301.303 521.873i 0.0418255 0.0724438i −0.844355 0.535784i \(-0.820016\pi\)
0.886180 + 0.463341i \(0.153349\pi\)
\(374\) −1111.66 + 1925.44i −0.153696 + 0.266209i
\(375\) 0 0
\(376\) 1212.92 + 2100.84i 0.166361 + 0.288145i
\(377\) 1690.68 0.230967
\(378\) 0 0
\(379\) 13319.0 1.80515 0.902575 0.430533i \(-0.141674\pi\)
0.902575 + 0.430533i \(0.141674\pi\)
\(380\) 2104.49 + 3645.09i 0.284101 + 0.492077i
\(381\) 0 0
\(382\) 102.359 177.291i 0.0137098 0.0237461i
\(383\) −4268.87 + 7393.91i −0.569528 + 0.986452i 0.427084 + 0.904212i \(0.359541\pi\)
−0.996613 + 0.0822399i \(0.973793\pi\)
\(384\) 0 0
\(385\) 649.474 + 1124.92i 0.0859748 + 0.148913i
\(386\) −194.842 −0.0256922
\(387\) 0 0
\(388\) 8181.42 1.07049
\(389\) −6319.99 10946.5i −0.823744 1.42677i −0.902875 0.429902i \(-0.858548\pi\)
0.0791316 0.996864i \(-0.474785\pi\)
\(390\) 0 0
\(391\) 543.703 941.722i 0.0703229 0.121803i
\(392\) 1669.77 2892.14i 0.215144 0.372640i
\(393\) 0 0
\(394\) 1731.71 + 2999.41i 0.221427 + 0.383523i
\(395\) 1920.67 0.244656
\(396\) 0 0
\(397\) 5473.94 0.692013 0.346006 0.938232i \(-0.387538\pi\)
0.346006 + 0.938232i \(0.387538\pi\)
\(398\) 1054.04 + 1825.65i 0.132749 + 0.229929i
\(399\) 0 0
\(400\) −642.820 + 1113.40i −0.0803525 + 0.139175i
\(401\) 6522.82 11297.9i 0.812305 1.40695i −0.0989419 0.995093i \(-0.531546\pi\)
0.911247 0.411860i \(-0.135121\pi\)
\(402\) 0 0
\(403\) −2915.42 5049.66i −0.360366 0.624172i
\(404\) −8912.79 −1.09759
\(405\) 0 0
\(406\) −220.272 −0.0269259
\(407\) 4093.66 + 7090.43i 0.498563 + 0.863537i
\(408\) 0 0
\(409\) 3591.36 6220.41i 0.434184 0.752029i −0.563045 0.826426i \(-0.690370\pi\)
0.997229 + 0.0743978i \(0.0237035\pi\)
\(410\) −681.061 + 1179.63i −0.0820370 + 0.142092i
\(411\) 0 0
\(412\) 677.377 + 1173.25i 0.0809999 + 0.140296i
\(413\) 2781.66 0.331420
\(414\) 0 0
\(415\) −6306.15 −0.745920
\(416\) −2495.50 4322.33i −0.294115 0.509422i
\(417\) 0 0
\(418\) 1547.90 2681.04i 0.181125 0.313718i
\(419\) 4360.20 7552.09i 0.508376 0.880534i −0.491577 0.870834i \(-0.663579\pi\)
0.999953 0.00969927i \(-0.00308742\pi\)
\(420\) 0 0
\(421\) −3276.51 5675.09i −0.379305 0.656976i 0.611656 0.791124i \(-0.290504\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(422\) −1997.18 −0.230383
\(423\) 0 0
\(424\) −5039.95 −0.577268
\(425\) 1012.44 + 1753.59i 0.115554 + 0.200145i
\(426\) 0 0
\(427\) 5.00994 8.67747i 0.000567794 0.000983448i
\(428\) 2282.77 3953.88i 0.257808 0.446537i
\(429\) 0 0
\(430\) 842.224 + 1458.78i 0.0944550 + 0.163601i
\(431\) −5217.70 −0.583127 −0.291564 0.956551i \(-0.594176\pi\)
−0.291564 + 0.956551i \(0.594176\pi\)
\(432\) 0 0
\(433\) 3377.56 0.374862 0.187431 0.982278i \(-0.439984\pi\)
0.187431 + 0.982278i \(0.439984\pi\)
\(434\) 379.839 + 657.900i 0.0420111 + 0.0727654i
\(435\) 0 0
\(436\) 2054.37 3558.27i 0.225657 0.390850i
\(437\) −757.067 + 1311.28i −0.0828729 + 0.143540i
\(438\) 0 0
\(439\) −1069.46 1852.36i −0.116270 0.201386i 0.802017 0.597302i \(-0.203761\pi\)
−0.918287 + 0.395916i \(0.870427\pi\)
\(440\) 2122.45 0.229963
\(441\) 0 0
\(442\) −2308.14 −0.248387
\(443\) 4256.31 + 7372.15i 0.456486 + 0.790658i 0.998772 0.0495363i \(-0.0157744\pi\)
−0.542286 + 0.840194i \(0.682441\pi\)
\(444\) 0 0
\(445\) 1282.50 2221.36i 0.136621 0.236634i
\(446\) −1345.09 + 2329.76i −0.142807 + 0.247348i
\(447\) 0 0
\(448\) −1100.02 1905.29i −0.116007 0.200930i
\(449\) 4542.67 0.477465 0.238733 0.971085i \(-0.423268\pi\)
0.238733 + 0.971085i \(0.423268\pi\)
\(450\) 0 0
\(451\) −13954.2 −1.45694
\(452\) −1776.09 3076.28i −0.184824 0.320124i
\(453\) 0 0
\(454\) −2113.40 + 3660.51i −0.218473 + 0.378406i
\(455\) −674.256 + 1167.85i −0.0694717 + 0.120329i
\(456\) 0 0
\(457\) 8971.10 + 15538.4i 0.918272 + 1.59049i 0.802039 + 0.597271i \(0.203748\pi\)
0.116232 + 0.993222i \(0.462918\pi\)
\(458\) −3527.22 −0.359861
\(459\) 0 0
\(460\) −501.051 −0.0507862
\(461\) −2590.44 4486.78i −0.261711 0.453297i 0.704985 0.709222i \(-0.250954\pi\)
−0.966697 + 0.255924i \(0.917620\pi\)
\(462\) 0 0
\(463\) −7096.44 + 12291.4i −0.712310 + 1.23376i 0.251677 + 0.967811i \(0.419018\pi\)
−0.963988 + 0.265947i \(0.914315\pi\)
\(464\) 1116.73 1934.23i 0.111730 0.193522i
\(465\) 0 0
\(466\) −33.3386 57.7442i −0.00331413 0.00574023i
\(467\) 11886.3 1.17780 0.588901 0.808205i \(-0.299561\pi\)
0.588901 + 0.808205i \(0.299561\pi\)
\(468\) 0 0
\(469\) 5653.88 0.556656
\(470\) −392.173 679.263i −0.0384885 0.0666640i
\(471\) 0 0
\(472\) 2272.58 3936.22i 0.221618 0.383854i
\(473\) −8628.16 + 14944.4i −0.838738 + 1.45274i
\(474\) 0 0
\(475\) −1409.74 2441.75i −0.136176 0.235863i
\(476\) −4188.47 −0.403316
\(477\) 0 0
\(478\) 4016.65 0.384345
\(479\) −2159.73 3740.76i −0.206014 0.356826i 0.744442 0.667688i \(-0.232716\pi\)
−0.950455 + 0.310861i \(0.899382\pi\)
\(480\) 0 0
\(481\) −4249.86 + 7360.97i −0.402863 + 0.697779i
\(482\) 1104.37 1912.82i 0.104362 0.180761i
\(483\) 0 0
\(484\) 280.115 + 485.174i 0.0263069 + 0.0455648i
\(485\) −5480.51 −0.513108
\(486\) 0 0
\(487\) −6436.94 −0.598944 −0.299472 0.954105i \(-0.596810\pi\)
−0.299472 + 0.954105i \(0.596810\pi\)
\(488\) −8.18611 14.1788i −0.000759361 0.00131525i
\(489\) 0 0
\(490\) −539.887 + 935.113i −0.0497748 + 0.0862124i
\(491\) −1448.87 + 2509.51i −0.133170 + 0.230657i −0.924897 0.380218i \(-0.875849\pi\)
0.791727 + 0.610875i \(0.209182\pi\)
\(492\) 0 0
\(493\) −1758.83 3046.39i −0.160677 0.278301i
\(494\) 3213.92 0.292715
\(495\) 0 0
\(496\) −7702.77 −0.697307
\(497\) −511.017 885.108i −0.0461213 0.0798844i
\(498\) 0 0
\(499\) −7527.29 + 13037.6i −0.675286 + 1.16963i 0.301099 + 0.953593i \(0.402646\pi\)
−0.976385 + 0.216037i \(0.930687\pi\)
\(500\) 466.506 808.013i 0.0417256 0.0722709i
\(501\) 0 0
\(502\) 1003.27 + 1737.71i 0.0891994 + 0.154498i
\(503\) −15582.5 −1.38129 −0.690646 0.723193i \(-0.742674\pi\)
−0.690646 + 0.723193i \(0.742674\pi\)
\(504\) 0 0
\(505\) 5970.43 0.526101
\(506\) 184.267 + 319.160i 0.0161891 + 0.0280403i
\(507\) 0 0
\(508\) −6142.61 + 10639.3i −0.536485 + 0.929219i
\(509\) 2035.51 3525.60i 0.177254 0.307013i −0.763685 0.645589i \(-0.776612\pi\)
0.940939 + 0.338576i \(0.109945\pi\)
\(510\) 0 0
\(511\) 1498.75 + 2595.91i 0.129747 + 0.224728i
\(512\) −11250.6 −0.971116
\(513\) 0 0
\(514\) −1845.79 −0.158394
\(515\) −453.756 785.929i −0.0388250 0.0672469i
\(516\) 0 0
\(517\) 4017.61 6958.70i 0.341768 0.591960i
\(518\) 553.697 959.031i 0.0469653 0.0813464i
\(519\) 0 0
\(520\) 1101.72 + 1908.23i 0.0929106 + 0.160926i
\(521\) 18597.9 1.56389 0.781947 0.623345i \(-0.214227\pi\)
0.781947 + 0.623345i \(0.214227\pi\)
\(522\) 0 0
\(523\) −12073.5 −1.00944 −0.504722 0.863282i \(-0.668405\pi\)
−0.504722 + 0.863282i \(0.668405\pi\)
\(524\) 1443.21 + 2499.72i 0.120319 + 0.208398i
\(525\) 0 0
\(526\) 1642.62 2845.10i 0.136163 0.235841i
\(527\) −6065.89 + 10506.4i −0.501393 + 0.868439i
\(528\) 0 0
\(529\) 5993.38 + 10380.8i 0.492593 + 0.853196i
\(530\) 1629.56 0.133554
\(531\) 0 0
\(532\) 5832.14 0.475292
\(533\) −7243.34 12545.8i −0.588638 1.01955i
\(534\) 0 0
\(535\) −1529.17 + 2648.59i −0.123573 + 0.214035i
\(536\) 4619.14 8000.59i 0.372233 0.644726i
\(537\) 0 0
\(538\) −3122.74 5408.74i −0.250243 0.433433i
\(539\) −11061.7 −0.883976
\(540\) 0 0
\(541\) 1802.04 0.143208 0.0716041 0.997433i \(-0.477188\pi\)
0.0716041 + 0.997433i \(0.477188\pi\)
\(542\) −45.0567 78.0405i −0.00357076 0.00618474i
\(543\) 0 0
\(544\) −5192.18 + 8993.13i −0.409215 + 0.708781i
\(545\) −1376.17 + 2383.59i −0.108162 + 0.187343i
\(546\) 0 0
\(547\) −3294.86 5706.87i −0.257547 0.446084i 0.708037 0.706175i \(-0.249581\pi\)
−0.965584 + 0.260091i \(0.916248\pi\)
\(548\) 22192.4 1.72995
\(549\) 0 0
\(550\) −686.250 −0.0532033
\(551\) 2449.05 + 4241.88i 0.189352 + 0.327968i
\(552\) 0 0
\(553\) 1330.68 2304.80i 0.102326 0.177233i
\(554\) −2400.24 + 4157.34i −0.184073 + 0.318824i
\(555\) 0 0
\(556\) 8760.44 + 15173.5i 0.668211 + 1.15738i
\(557\) 21128.6 1.60727 0.803633 0.595125i \(-0.202897\pi\)
0.803633 + 0.595125i \(0.202897\pi\)
\(558\) 0 0
\(559\) −17914.8 −1.35548
\(560\) 890.718 + 1542.77i 0.0672138 + 0.116418i
\(561\) 0 0
\(562\) −2592.94 + 4491.10i −0.194620 + 0.337092i
\(563\) 55.2137 95.6330i 0.00413318 0.00715888i −0.863951 0.503575i \(-0.832018\pi\)
0.868085 + 0.496416i \(0.165351\pi\)
\(564\) 0 0
\(565\) 1189.76 + 2060.72i 0.0885901 + 0.153443i
\(566\) −1517.49 −0.112694
\(567\) 0 0
\(568\) −1669.98 −0.123364
\(569\) 3465.04 + 6001.63i 0.255294 + 0.442182i 0.964975 0.262341i \(-0.0844945\pi\)
−0.709682 + 0.704523i \(0.751161\pi\)
\(570\) 0 0
\(571\) −10632.3 + 18415.7i −0.779244 + 1.34969i 0.153134 + 0.988205i \(0.451063\pi\)
−0.932378 + 0.361484i \(0.882270\pi\)
\(572\) −5447.70 + 9435.70i −0.398217 + 0.689731i
\(573\) 0 0
\(574\) 943.705 + 1634.55i 0.0686228 + 0.118858i
\(575\) 335.641 0.0243429
\(576\) 0 0
\(577\) 2927.39 0.211211 0.105606 0.994408i \(-0.466322\pi\)
0.105606 + 0.994408i \(0.466322\pi\)
\(578\) 602.904 + 1044.26i 0.0433867 + 0.0751480i
\(579\) 0 0
\(580\) −810.429 + 1403.70i −0.0580194 + 0.100493i
\(581\) −4369.03 + 7567.38i −0.311976 + 0.540358i
\(582\) 0 0
\(583\) 8347.02 + 14457.5i 0.592965 + 1.02704i
\(584\) 4897.83 0.347044
\(585\) 0 0
\(586\) 5218.35 0.367864
\(587\) −10875.2 18836.4i −0.764683 1.32447i −0.940414 0.340031i \(-0.889562\pi\)
0.175732 0.984438i \(-0.443771\pi\)
\(588\) 0 0
\(589\) 8446.31 14629.4i 0.590873 1.02342i
\(590\) −734.791 + 1272.70i −0.0512727 + 0.0888069i
\(591\) 0 0
\(592\) 5614.23 + 9724.12i 0.389769 + 0.675100i
\(593\) 5635.88 0.390283 0.195142 0.980775i \(-0.437483\pi\)
0.195142 + 0.980775i \(0.437483\pi\)
\(594\) 0 0
\(595\) 2805.74 0.193318
\(596\) 5232.68 + 9063.27i 0.359629 + 0.622896i
\(597\) 0 0
\(598\) −191.298 + 331.338i −0.0130815 + 0.0226579i
\(599\) −9162.20 + 15869.4i −0.624970 + 1.08248i 0.363576 + 0.931564i \(0.381556\pi\)
−0.988547 + 0.150916i \(0.951778\pi\)
\(600\) 0 0
\(601\) 1251.95 + 2168.44i 0.0849719 + 0.147176i 0.905379 0.424604i \(-0.139587\pi\)
−0.820407 + 0.571779i \(0.806253\pi\)
\(602\) 2334.04 0.158021
\(603\) 0 0
\(604\) 21953.9 1.47896
\(605\) −187.642 325.005i −0.0126095 0.0218402i
\(606\) 0 0
\(607\) −8733.32 + 15126.6i −0.583978 + 1.01148i 0.411024 + 0.911624i \(0.365171\pi\)
−0.995002 + 0.0998550i \(0.968162\pi\)
\(608\) 7229.74 12522.3i 0.482245 0.835272i
\(609\) 0 0
\(610\) 2.64681 + 4.58441i 0.000175682 + 0.000304291i
\(611\) 8341.82 0.552330
\(612\) 0 0
\(613\) −2244.45 −0.147883 −0.0739417 0.997263i \(-0.523558\pi\)
−0.0739417 + 0.997263i \(0.523558\pi\)
\(614\) −2318.66 4016.04i −0.152400 0.263964i
\(615\) 0 0
\(616\) 1470.48 2546.94i 0.0961805 0.166589i
\(617\) 2904.92 5031.47i 0.189542 0.328297i −0.755555 0.655085i \(-0.772633\pi\)
0.945098 + 0.326788i \(0.105966\pi\)
\(618\) 0 0
\(619\) 771.742 + 1336.70i 0.0501114 + 0.0867954i 0.889993 0.455974i \(-0.150709\pi\)
−0.839882 + 0.542770i \(0.817376\pi\)
\(620\) 5590.04 0.362099
\(621\) 0 0
\(622\) 5412.71 0.348922
\(623\) −1777.08 3078.00i −0.114281 0.197941i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −341.522 + 591.533i −0.0218050 + 0.0377675i
\(627\) 0 0
\(628\) 9524.11 + 16496.2i 0.605181 + 1.04820i
\(629\) 17684.7 1.12104
\(630\) 0 0
\(631\) 7992.93 0.504269 0.252134 0.967692i \(-0.418868\pi\)
0.252134 + 0.967692i \(0.418868\pi\)
\(632\) −2174.29 3765.98i −0.136849 0.237030i
\(633\) 0 0
\(634\) −3197.11 + 5537.56i −0.200274 + 0.346884i
\(635\) 4114.77 7126.99i 0.257149 0.445395i
\(636\) 0 0
\(637\) −5741.91 9945.28i −0.357147 0.618597i
\(638\) 1192.18 0.0739791
\(639\) 0 0
\(640\) 6290.72 0.388535
\(641\) −13064.9 22629.1i −0.805044 1.39438i −0.916261 0.400581i \(-0.868808\pi\)
0.111217 0.993796i \(-0.464525\pi\)
\(642\) 0 0
\(643\) 14386.1 24917.4i 0.882319 1.52822i 0.0335621 0.999437i \(-0.489315\pi\)
0.848756 0.528784i \(-0.177352\pi\)
\(644\) −347.138 + 601.261i −0.0212409 + 0.0367904i
\(645\) 0 0
\(646\) −3343.48 5791.08i −0.203634 0.352704i
\(647\) −7156.38 −0.434847 −0.217424 0.976077i \(-0.569765\pi\)
−0.217424 + 0.976077i \(0.569765\pi\)
\(648\) 0 0
\(649\) −15055.1 −0.910578
\(650\) −356.218 616.987i −0.0214954 0.0372311i
\(651\) 0 0
\(652\) 1312.04 2272.51i 0.0788087 0.136501i
\(653\) −7717.43 + 13367.0i −0.462491 + 0.801057i −0.999084 0.0427836i \(-0.986377\pi\)
0.536594 + 0.843841i \(0.319711\pi\)
\(654\) 0 0
\(655\) −966.768 1674.49i −0.0576714 0.0998898i
\(656\) −19137.5 −1.13901
\(657\) 0 0
\(658\) −1086.82 −0.0643901
\(659\) 3231.32 + 5596.81i 0.191008 + 0.330836i 0.945585 0.325376i \(-0.105491\pi\)
−0.754577 + 0.656212i \(0.772158\pi\)
\(660\) 0 0
\(661\) −873.801 + 1513.47i −0.0514174 + 0.0890576i −0.890589 0.454810i \(-0.849707\pi\)
0.839171 + 0.543867i \(0.183041\pi\)
\(662\) −472.368 + 818.165i −0.0277328 + 0.0480345i
\(663\) 0 0
\(664\) 7138.88 + 12364.9i 0.417233 + 0.722668i
\(665\) −3906.79 −0.227818
\(666\) 0 0
\(667\) −583.085 −0.0338488
\(668\) −78.3332 135.677i −0.00453713 0.00785854i
\(669\) 0 0
\(670\) −1493.51 + 2586.83i −0.0861181 + 0.149161i
\(671\) −27.1152 + 46.9650i −0.00156002 + 0.00270203i
\(672\) 0 0
\(673\) 2739.19 + 4744.42i 0.156892 + 0.271744i 0.933746 0.357936i \(-0.116519\pi\)
−0.776855 + 0.629680i \(0.783186\pi\)
\(674\) 7321.47 0.418416
\(675\) 0 0
\(676\) 5087.49 0.289457
\(677\) 2009.27 + 3480.15i 0.114066 + 0.197567i 0.917406 0.397953i \(-0.130279\pi\)
−0.803340 + 0.595520i \(0.796946\pi\)
\(678\) 0 0
\(679\) −3797.01 + 6576.61i −0.214604 + 0.371704i
\(680\) 2292.26 3970.31i 0.129271 0.223903i
\(681\) 0 0
\(682\) −2055.80 3560.74i −0.115426 0.199924i
\(683\) 9894.95 0.554348 0.277174 0.960820i \(-0.410602\pi\)
0.277174 + 0.960820i \(0.410602\pi\)
\(684\) 0 0
\(685\) −14866.1 −0.829204
\(686\) 1617.90 + 2802.29i 0.0900464 + 0.155965i
\(687\) 0 0
\(688\) −11833.0 + 20495.4i −0.655713 + 1.13573i
\(689\) −8665.52 + 15009.1i −0.479144 + 0.829901i
\(690\) 0 0
\(691\) −10924.0 18920.9i −0.601400 1.04166i −0.992609 0.121354i \(-0.961276\pi\)
0.391209 0.920302i \(-0.372057\pi\)
\(692\) −33772.1 −1.85524
\(693\) 0 0
\(694\) 4735.18 0.258998
\(695\) −5868.38 10164.3i −0.320289 0.554756i
\(696\) 0 0
\(697\) −15070.6 + 26103.1i −0.818998 + 1.41855i
\(698\) 4088.43 7081.36i 0.221704 0.384002i
\(699\) 0 0
\(700\) −646.410 1119.62i −0.0349029 0.0604535i
\(701\) 15506.5 0.835480 0.417740 0.908567i \(-0.362822\pi\)
0.417740 + 0.908567i \(0.362822\pi\)
\(702\) 0 0
\(703\) −24624.7 −1.32110
\(704\) 5953.63 + 10312.0i 0.318730 + 0.552056i
\(705\) 0 0
\(706\) −664.986 + 1151.79i −0.0354491 + 0.0613996i
\(707\) 4136.44 7164.52i 0.220038 0.381117i
\(708\) 0 0
\(709\) −3199.85 5542.30i −0.169496 0.293576i 0.768747 0.639553i \(-0.220881\pi\)
−0.938243 + 0.345977i \(0.887547\pi\)
\(710\) 539.954 0.0285410
\(711\) 0 0
\(712\) −5807.42 −0.305677
\(713\) 1005.48 + 1741.54i 0.0528126 + 0.0914741i
\(714\) 0 0
\(715\) 3649.27 6320.72i 0.190874 0.330603i
\(716\) −13535.4 + 23443.9i −0.706481 + 1.22366i
\(717\) 0 0
\(718\) −336.038 582.035i −0.0174663 0.0302526i
\(719\) 1771.66 0.0918941 0.0459470 0.998944i \(-0.485369\pi\)
0.0459470 + 0.998944i \(0.485369\pi\)
\(720\) 0 0
\(721\) −1257.49 −0.0649532
\(722\) 2144.98 + 3715.22i 0.110565 + 0.191504i
\(723\) 0 0
\(724\) 13254.0 22956.7i 0.680363 1.17842i
\(725\) 542.885 940.304i 0.0278100 0.0481683i
\(726\) 0 0
\(727\) −4787.53 8292.25i −0.244236 0.423030i 0.717680 0.696373i \(-0.245204\pi\)
−0.961917 + 0.273343i \(0.911871\pi\)
\(728\) 3053.17 0.155437
\(729\) 0 0
\(730\) −1583.61 −0.0802907
\(731\) 18636.9 + 32280.1i 0.942970 + 1.63327i
\(732\) 0 0
\(733\) 9895.25 17139.1i 0.498622 0.863638i −0.501377 0.865229i \(-0.667173\pi\)
0.999999 + 0.00159099i \(0.000506428\pi\)
\(734\) 2691.85 4662.42i 0.135365 0.234459i
\(735\) 0 0
\(736\) 860.651 + 1490.69i 0.0431033 + 0.0746571i
\(737\) −30600.4 −1.52942
\(738\) 0 0
\(739\) −13106.5 −0.652407 −0.326203 0.945300i \(-0.605769\pi\)
−0.326203 + 0.945300i \(0.605769\pi\)
\(740\) −4074.35 7056.97i −0.202400 0.350567i
\(741\) 0 0
\(742\) 1128.99 1955.48i 0.0558581 0.0967491i
\(743\) 8534.44 14782.1i 0.421398 0.729882i −0.574679 0.818379i \(-0.694873\pi\)
0.996076 + 0.0884970i \(0.0282064\pi\)
\(744\) 0 0
\(745\) −3505.23 6071.24i −0.172378 0.298568i
\(746\) 441.139 0.0216505
\(747\) 0 0
\(748\) 22669.2 1.10811
\(749\) 2118.88 + 3670.00i 0.103367 + 0.179037i
\(750\) 0 0
\(751\) −2056.46 + 3561.90i −0.0999220 + 0.173070i −0.911652 0.410963i \(-0.865193\pi\)
0.811730 + 0.584033i \(0.198526\pi\)
\(752\) 5509.93 9543.47i 0.267189 0.462785i
\(753\) 0 0
\(754\) 618.833 + 1071.85i 0.0298893 + 0.0517698i
\(755\) −14706.3 −0.708897
\(756\) 0 0
\(757\) 17493.6 0.839915 0.419958 0.907544i \(-0.362045\pi\)
0.419958 + 0.907544i \(0.362045\pi\)
\(758\) 4875.10 + 8443.92i 0.233604 + 0.404613i
\(759\) 0 0
\(760\) −3191.80 + 5528.36i −0.152341 + 0.263862i
\(761\) −2606.02 + 4513.76i −0.124137 + 0.215011i −0.921395 0.388627i \(-0.872949\pi\)
0.797258 + 0.603638i \(0.206283\pi\)
\(762\) 0 0
\(763\) 1906.87 + 3302.80i 0.0904763 + 0.156710i
\(764\) −2087.34 −0.0988447
\(765\) 0 0
\(766\) −6250.07 −0.294809
\(767\) −7814.79 13535.6i −0.367895 0.637213i
\(768\) 0 0
\(769\) 11662.3 20199.7i 0.546885 0.947232i −0.451601 0.892220i \(-0.649147\pi\)
0.998486 0.0550119i \(-0.0175197\pi\)
\(770\) −475.448 + 823.501i −0.0222519 + 0.0385414i
\(771\) 0 0
\(772\) 993.321 + 1720.48i 0.0463088 + 0.0802092i
\(773\) −20455.0 −0.951765 −0.475883 0.879509i \(-0.657871\pi\)
−0.475883 + 0.879509i \(0.657871\pi\)
\(774\) 0 0
\(775\) −3744.62 −0.173562
\(776\) 6204.22 + 10746.0i 0.287008 + 0.497113i
\(777\) 0 0
\(778\) 4626.56 8013.43i 0.213201 0.369274i
\(779\) 20984.8 36346.7i 0.965158 1.67170i
\(780\) 0 0
\(781\) 2765.77 + 4790.46i 0.126718 + 0.219483i
\(782\) 796.037 0.0364018
\(783\) 0 0
\(784\) −15170.6 −0.691079
\(785\) −6379.95 11050.4i −0.290077 0.502427i
\(786\) 0 0
\(787\) −4555.49 + 7890.33i −0.206335 + 0.357382i −0.950557 0.310549i