Properties

Label 405.4.e.q.271.2
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: \( x^{6} - x^{5} + 13x^{4} - 4x^{3} + 152x^{2} - 96x + 64 \) Copy content Toggle raw display
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 271.2
Root \(-1.66402 - 2.88216i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.q.136.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.06306 - 1.84127i) q^{2} +(1.73981 - 3.01344i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-15.3500 - 26.5870i) q^{7} -24.4070 q^{8} +O(q^{10})\) \(q+(-1.06306 - 1.84127i) q^{2} +(1.73981 - 3.01344i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-15.3500 - 26.5870i) q^{7} -24.4070 q^{8} +10.6306 q^{10} +(-25.0774 - 43.4353i) q^{11} +(7.97962 - 13.8211i) q^{13} +(-32.6360 + 56.5272i) q^{14} +(12.0277 + 20.8325i) q^{16} +105.668 q^{17} -21.3040 q^{19} +(8.69904 + 15.0672i) q^{20} +(-53.3175 + 92.3487i) q^{22} +(-68.0684 + 117.898i) q^{23} +(-12.5000 - 21.6506i) q^{25} -33.9312 q^{26} -106.824 q^{28} +(112.162 + 194.270i) q^{29} +(112.991 - 195.706i) q^{31} +(-72.0559 + 124.804i) q^{32} +(-112.332 - 194.564i) q^{34} +153.500 q^{35} -416.386 q^{37} +(22.6474 + 39.2264i) q^{38} +(61.0176 - 105.686i) q^{40} +(-38.0706 + 65.9402i) q^{41} +(-15.8686 - 27.4852i) q^{43} -174.519 q^{44} +289.443 q^{46} +(-30.4013 - 52.6566i) q^{47} +(-299.746 + 519.176i) q^{49} +(-26.5765 + 46.0318i) q^{50} +(-27.7660 - 48.0921i) q^{52} -466.532 q^{53} +250.774 q^{55} +(374.649 + 648.910i) q^{56} +(238.469 - 413.040i) q^{58} +(-47.7119 + 82.6395i) q^{59} +(178.587 + 309.322i) q^{61} -480.464 q^{62} +498.842 q^{64} +(39.8981 + 69.1055i) q^{65} +(-43.9172 + 76.0668i) q^{67} +(183.842 - 318.424i) q^{68} +(-163.180 - 282.636i) q^{70} +412.693 q^{71} -331.133 q^{73} +(442.643 + 766.680i) q^{74} +(-37.0648 + 64.1981i) q^{76} +(-769.877 + 1333.47i) q^{77} +(124.062 + 214.881i) q^{79} -120.277 q^{80} +161.885 q^{82} +(276.253 + 478.484i) q^{83} +(-264.171 + 457.557i) q^{85} +(-33.7386 + 58.4369i) q^{86} +(612.065 + 1060.13i) q^{88} -291.478 q^{89} -489.949 q^{91} +(236.852 + 410.240i) q^{92} +(-64.6368 + 111.954i) q^{94} +(53.2599 - 92.2489i) q^{95} +(-99.3032 - 171.998i) q^{97} +1274.59 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + 50 q^{10} - 5 q^{11} - 7 q^{13} - 60 q^{14} - 161 q^{16} + 310 q^{17} - 100 q^{19} - 85 q^{20} + 229 q^{22} - 285 q^{23} - 75 q^{25} + 370 q^{26} - 668 q^{28} - 115 q^{29} + 115 q^{31} - 775 q^{32} - 413 q^{34} - 40 q^{35} - 768 q^{37} + 1150 q^{38} - 375 q^{40} - 580 q^{41} + 797 q^{43} - 2830 q^{44} - 570 q^{46} + 145 q^{47} - 577 q^{49} - 125 q^{50} - 825 q^{52} - 800 q^{53} + 50 q^{55} + 2190 q^{56} + 59 q^{58} - 380 q^{59} + 152 q^{61} - 2010 q^{62} + 5874 q^{64} - 35 q^{65} - 2 q^{67} - 475 q^{68} - 300 q^{70} + 80 q^{71} - 1960 q^{73} + 2720 q^{74} + 3276 q^{76} - 1950 q^{77} - 1013 q^{79} + 1610 q^{80} + 8 q^{82} - 270 q^{83} - 775 q^{85} + 1555 q^{86} + 5193 q^{88} + 2040 q^{89} - 1264 q^{91} + 1215 q^{92} - 3833 q^{94} + 250 q^{95} - 720 q^{97} - 610 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06306 1.84127i −0.375848 0.650988i 0.614605 0.788835i \(-0.289315\pi\)
−0.990454 + 0.137846i \(0.955982\pi\)
\(3\) 0 0
\(4\) 1.73981 3.01344i 0.217476 0.376679i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −15.3500 26.5870i −0.828823 1.43556i −0.898962 0.438027i \(-0.855678\pi\)
0.0701387 0.997537i \(-0.477656\pi\)
\(8\) −24.4070 −1.07865
\(9\) 0 0
\(10\) 10.6306 0.336169
\(11\) −25.0774 43.4353i −0.687375 1.19057i −0.972684 0.232132i \(-0.925430\pi\)
0.285310 0.958435i \(-0.407904\pi\)
\(12\) 0 0
\(13\) 7.97962 13.8211i 0.170242 0.294868i −0.768262 0.640135i \(-0.778878\pi\)
0.938504 + 0.345267i \(0.112212\pi\)
\(14\) −32.6360 + 56.5272i −0.623024 + 1.07911i
\(15\) 0 0
\(16\) 12.0277 + 20.8325i 0.187932 + 0.325508i
\(17\) 105.668 1.50755 0.753774 0.657134i \(-0.228231\pi\)
0.753774 + 0.657134i \(0.228231\pi\)
\(18\) 0 0
\(19\) −21.3040 −0.257235 −0.128618 0.991694i \(-0.541054\pi\)
−0.128618 + 0.991694i \(0.541054\pi\)
\(20\) 8.69904 + 15.0672i 0.0972582 + 0.168456i
\(21\) 0 0
\(22\) −53.3175 + 92.3487i −0.516697 + 0.894946i
\(23\) −68.0684 + 117.898i −0.617098 + 1.06884i 0.372915 + 0.927866i \(0.378358\pi\)
−0.990013 + 0.140979i \(0.954975\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −33.9312 −0.255941
\(27\) 0 0
\(28\) −106.824 −0.720997
\(29\) 112.162 + 194.270i 0.718203 + 1.24396i 0.961711 + 0.274065i \(0.0883685\pi\)
−0.243508 + 0.969899i \(0.578298\pi\)
\(30\) 0 0
\(31\) 112.991 195.706i 0.654638 1.13387i −0.327347 0.944904i \(-0.606155\pi\)
0.981985 0.188961i \(-0.0605121\pi\)
\(32\) −72.0559 + 124.804i −0.398056 + 0.689454i
\(33\) 0 0
\(34\) −112.332 194.564i −0.566609 0.981396i
\(35\) 153.500 0.741322
\(36\) 0 0
\(37\) −416.386 −1.85009 −0.925046 0.379854i \(-0.875974\pi\)
−0.925046 + 0.379854i \(0.875974\pi\)
\(38\) 22.6474 + 39.2264i 0.0966814 + 0.167457i
\(39\) 0 0
\(40\) 61.0176 105.686i 0.241193 0.417759i
\(41\) −38.0706 + 65.9402i −0.145015 + 0.251174i −0.929379 0.369128i \(-0.879656\pi\)
0.784363 + 0.620302i \(0.212990\pi\)
\(42\) 0 0
\(43\) −15.8686 27.4852i −0.0562777 0.0974758i 0.836514 0.547945i \(-0.184590\pi\)
−0.892792 + 0.450470i \(0.851257\pi\)
\(44\) −174.519 −0.597950
\(45\) 0 0
\(46\) 289.443 0.927741
\(47\) −30.4013 52.6566i −0.0943507 0.163420i 0.814987 0.579480i \(-0.196744\pi\)
−0.909337 + 0.416059i \(0.863411\pi\)
\(48\) 0 0
\(49\) −299.746 + 519.176i −0.873896 + 1.51363i
\(50\) −26.5765 + 46.0318i −0.0751697 + 0.130198i
\(51\) 0 0
\(52\) −27.7660 48.0921i −0.0740471 0.128253i
\(53\) −466.532 −1.20911 −0.604557 0.796562i \(-0.706650\pi\)
−0.604557 + 0.796562i \(0.706650\pi\)
\(54\) 0 0
\(55\) 250.774 0.614806
\(56\) 374.649 + 648.910i 0.894009 + 1.54847i
\(57\) 0 0
\(58\) 238.469 413.040i 0.539871 0.935084i
\(59\) −47.7119 + 82.6395i −0.105281 + 0.182352i −0.913853 0.406045i \(-0.866907\pi\)
0.808572 + 0.588397i \(0.200241\pi\)
\(60\) 0 0
\(61\) 178.587 + 309.322i 0.374848 + 0.649256i 0.990304 0.138915i \(-0.0443616\pi\)
−0.615456 + 0.788171i \(0.711028\pi\)
\(62\) −480.464 −0.984178
\(63\) 0 0
\(64\) 498.842 0.974300
\(65\) 39.8981 + 69.1055i 0.0761346 + 0.131869i
\(66\) 0 0
\(67\) −43.9172 + 76.0668i −0.0800797 + 0.138702i −0.903284 0.429043i \(-0.858851\pi\)
0.823204 + 0.567745i \(0.192184\pi\)
\(68\) 183.842 318.424i 0.327855 0.567862i
\(69\) 0 0
\(70\) −163.180 282.636i −0.278625 0.482592i
\(71\) 412.693 0.689826 0.344913 0.938635i \(-0.387908\pi\)
0.344913 + 0.938635i \(0.387908\pi\)
\(72\) 0 0
\(73\) −331.133 −0.530906 −0.265453 0.964124i \(-0.585522\pi\)
−0.265453 + 0.964124i \(0.585522\pi\)
\(74\) 442.643 + 766.680i 0.695354 + 1.20439i
\(75\) 0 0
\(76\) −37.0648 + 64.1981i −0.0559424 + 0.0968952i
\(77\) −769.877 + 1333.47i −1.13942 + 1.97354i
\(78\) 0 0
\(79\) 124.062 + 214.881i 0.176684 + 0.306025i 0.940743 0.339121i \(-0.110130\pi\)
−0.764059 + 0.645146i \(0.776796\pi\)
\(80\) −120.277 −0.168092
\(81\) 0 0
\(82\) 161.885 0.218015
\(83\) 276.253 + 478.484i 0.365333 + 0.632776i 0.988830 0.149050i \(-0.0476217\pi\)
−0.623496 + 0.781826i \(0.714288\pi\)
\(84\) 0 0
\(85\) −264.171 + 457.557i −0.337098 + 0.583871i
\(86\) −33.7386 + 58.4369i −0.0423038 + 0.0732723i
\(87\) 0 0
\(88\) 612.065 + 1060.13i 0.741436 + 1.28420i
\(89\) −291.478 −0.347153 −0.173577 0.984820i \(-0.555532\pi\)
−0.173577 + 0.984820i \(0.555532\pi\)
\(90\) 0 0
\(91\) −489.949 −0.564402
\(92\) 236.852 + 410.240i 0.268408 + 0.464896i
\(93\) 0 0
\(94\) −64.6368 + 111.954i −0.0709231 + 0.122842i
\(95\) 53.2599 92.2489i 0.0575195 0.0996267i
\(96\) 0 0
\(97\) −99.3032 171.998i −0.103946 0.180039i 0.809361 0.587311i \(-0.199813\pi\)
−0.913307 + 0.407272i \(0.866480\pi\)
\(98\) 1274.59 1.31381
\(99\) 0 0
\(100\) −86.9904 −0.0869904
\(101\) −408.117 706.880i −0.402071 0.696408i 0.591904 0.806008i \(-0.298376\pi\)
−0.993976 + 0.109600i \(0.965043\pi\)
\(102\) 0 0
\(103\) 701.186 1214.49i 0.670776 1.16182i −0.306908 0.951739i \(-0.599294\pi\)
0.977684 0.210079i \(-0.0673722\pi\)
\(104\) −194.759 + 337.332i −0.183631 + 0.318059i
\(105\) 0 0
\(106\) 495.951 + 859.013i 0.454444 + 0.787120i
\(107\) −978.996 −0.884515 −0.442258 0.896888i \(-0.645822\pi\)
−0.442258 + 0.896888i \(0.645822\pi\)
\(108\) 0 0
\(109\) 2122.96 1.86553 0.932766 0.360484i \(-0.117388\pi\)
0.932766 + 0.360484i \(0.117388\pi\)
\(110\) −266.588 461.743i −0.231074 0.400232i
\(111\) 0 0
\(112\) 369.250 639.560i 0.311525 0.539578i
\(113\) −897.399 + 1554.34i −0.747082 + 1.29398i 0.202134 + 0.979358i \(0.435212\pi\)
−0.949216 + 0.314626i \(0.898121\pi\)
\(114\) 0 0
\(115\) −340.342 589.490i −0.275975 0.478002i
\(116\) 780.559 0.624768
\(117\) 0 0
\(118\) 202.883 0.158278
\(119\) −1622.01 2809.40i −1.24949 2.16418i
\(120\) 0 0
\(121\) −592.252 + 1025.81i −0.444968 + 0.770706i
\(122\) 379.697 657.655i 0.281772 0.488043i
\(123\) 0 0
\(124\) −393.165 680.982i −0.284736 0.493177i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −748.894 −0.523257 −0.261628 0.965169i \(-0.584259\pi\)
−0.261628 + 0.965169i \(0.584259\pi\)
\(128\) 46.1486 + 79.9317i 0.0318672 + 0.0551955i
\(129\) 0 0
\(130\) 84.8281 146.927i 0.0572301 0.0991255i
\(131\) 1198.05 2075.09i 0.799042 1.38398i −0.121198 0.992628i \(-0.538674\pi\)
0.920240 0.391353i \(-0.127993\pi\)
\(132\) 0 0
\(133\) 327.016 + 566.409i 0.213202 + 0.369277i
\(134\) 186.746 0.120391
\(135\) 0 0
\(136\) −2579.05 −1.62611
\(137\) −502.238 869.901i −0.313205 0.542486i 0.665850 0.746086i \(-0.268069\pi\)
−0.979054 + 0.203600i \(0.934736\pi\)
\(138\) 0 0
\(139\) −1201.51 + 2081.08i −0.733172 + 1.26989i 0.222348 + 0.974967i \(0.428628\pi\)
−0.955521 + 0.294924i \(0.904706\pi\)
\(140\) 267.061 462.563i 0.161220 0.279241i
\(141\) 0 0
\(142\) −438.717 759.881i −0.259270 0.449069i
\(143\) −800.432 −0.468080
\(144\) 0 0
\(145\) −1121.62 −0.642380
\(146\) 352.014 + 609.706i 0.199540 + 0.345614i
\(147\) 0 0
\(148\) −724.432 + 1254.75i −0.402351 + 0.696892i
\(149\) −254.824 + 441.368i −0.140107 + 0.242673i −0.927537 0.373732i \(-0.878078\pi\)
0.787429 + 0.616405i \(0.211411\pi\)
\(150\) 0 0
\(151\) −721.648 1249.93i −0.388920 0.673629i 0.603385 0.797450i \(-0.293818\pi\)
−0.992305 + 0.123821i \(0.960485\pi\)
\(152\) 519.967 0.277466
\(153\) 0 0
\(154\) 3273.70 1.71300
\(155\) 564.955 + 978.530i 0.292763 + 0.507080i
\(156\) 0 0
\(157\) 1077.82 1866.84i 0.547895 0.948981i −0.450524 0.892764i \(-0.648763\pi\)
0.998419 0.0562170i \(-0.0179039\pi\)
\(158\) 263.770 456.863i 0.132813 0.230038i
\(159\) 0 0
\(160\) −360.279 624.022i −0.178016 0.308333i
\(161\) 4179.41 2.04586
\(162\) 0 0
\(163\) −529.909 −0.254636 −0.127318 0.991862i \(-0.540637\pi\)
−0.127318 + 0.991862i \(0.540637\pi\)
\(164\) 132.471 + 229.446i 0.0630747 + 0.109249i
\(165\) 0 0
\(166\) 587.346 1017.31i 0.274620 0.475656i
\(167\) 1489.64 2580.13i 0.690250 1.19555i −0.281506 0.959559i \(-0.590834\pi\)
0.971756 0.235988i \(-0.0758327\pi\)
\(168\) 0 0
\(169\) 971.151 + 1682.08i 0.442035 + 0.765628i
\(170\) 1123.32 0.506791
\(171\) 0 0
\(172\) −110.433 −0.0489562
\(173\) −889.939 1541.42i −0.391103 0.677410i 0.601493 0.798878i \(-0.294573\pi\)
−0.992595 + 0.121469i \(0.961240\pi\)
\(174\) 0 0
\(175\) −383.751 + 664.675i −0.165765 + 0.287113i
\(176\) 603.246 1044.85i 0.258360 0.447492i
\(177\) 0 0
\(178\) 309.859 + 536.692i 0.130477 + 0.225993i
\(179\) −2836.26 −1.18431 −0.592157 0.805823i \(-0.701724\pi\)
−0.592157 + 0.805823i \(0.701724\pi\)
\(180\) 0 0
\(181\) 811.890 0.333410 0.166705 0.986007i \(-0.446687\pi\)
0.166705 + 0.986007i \(0.446687\pi\)
\(182\) 520.845 + 902.130i 0.212130 + 0.367419i
\(183\) 0 0
\(184\) 1661.35 2877.54i 0.665632 1.15291i
\(185\) 1040.96 1803.00i 0.413693 0.716538i
\(186\) 0 0
\(187\) −2649.88 4589.73i −1.03625 1.79484i
\(188\) −211.570 −0.0820761
\(189\) 0 0
\(190\) −226.474 −0.0864745
\(191\) −574.231 994.597i −0.217539 0.376788i 0.736516 0.676420i \(-0.236469\pi\)
−0.954055 + 0.299632i \(0.903136\pi\)
\(192\) 0 0
\(193\) 1075.47 1862.76i 0.401107 0.694739i −0.592752 0.805385i \(-0.701959\pi\)
0.993860 + 0.110646i \(0.0352921\pi\)
\(194\) −211.131 + 365.689i −0.0781355 + 0.135335i
\(195\) 0 0
\(196\) 1043.00 + 1806.53i 0.380103 + 0.658357i
\(197\) −5057.51 −1.82910 −0.914551 0.404471i \(-0.867456\pi\)
−0.914551 + 0.404471i \(0.867456\pi\)
\(198\) 0 0
\(199\) −3554.12 −1.26605 −0.633027 0.774130i \(-0.718188\pi\)
−0.633027 + 0.774130i \(0.718188\pi\)
\(200\) 305.088 + 528.428i 0.107865 + 0.186827i
\(201\) 0 0
\(202\) −867.707 + 1502.91i −0.302236 + 0.523488i
\(203\) 3443.37 5964.09i 1.19053 2.06205i
\(204\) 0 0
\(205\) −190.353 329.701i −0.0648528 0.112328i
\(206\) −2981.61 −1.00844
\(207\) 0 0
\(208\) 383.905 0.127976
\(209\) 534.248 + 925.345i 0.176817 + 0.306256i
\(210\) 0 0
\(211\) 53.9547 93.4523i 0.0176038 0.0304906i −0.857089 0.515168i \(-0.827730\pi\)
0.874693 + 0.484677i \(0.161063\pi\)
\(212\) −811.676 + 1405.86i −0.262953 + 0.455449i
\(213\) 0 0
\(214\) 1040.73 + 1802.60i 0.332444 + 0.575809i
\(215\) 158.686 0.0503363
\(216\) 0 0
\(217\) −6937.65 −2.17032
\(218\) −2256.84 3908.95i −0.701157 1.21444i
\(219\) 0 0
\(220\) 436.299 755.691i 0.133706 0.231585i
\(221\) 843.192 1460.45i 0.256648 0.444528i
\(222\) 0 0
\(223\) 971.013 + 1681.84i 0.291587 + 0.505043i 0.974185 0.225751i \(-0.0724834\pi\)
−0.682598 + 0.730794i \(0.739150\pi\)
\(224\) 4424.24 1.31967
\(225\) 0 0
\(226\) 3815.96 1.12316
\(227\) −1721.99 2982.58i −0.503492 0.872074i −0.999992 0.00403708i \(-0.998715\pi\)
0.496500 0.868037i \(-0.334618\pi\)
\(228\) 0 0
\(229\) −1034.70 + 1792.15i −0.298579 + 0.517155i −0.975811 0.218615i \(-0.929846\pi\)
0.677232 + 0.735770i \(0.263179\pi\)
\(230\) −723.608 + 1253.33i −0.207449 + 0.359313i
\(231\) 0 0
\(232\) −2737.53 4741.55i −0.774689 1.34180i
\(233\) −2769.24 −0.778622 −0.389311 0.921106i \(-0.627287\pi\)
−0.389311 + 0.921106i \(0.627287\pi\)
\(234\) 0 0
\(235\) 304.013 0.0843898
\(236\) 166.019 + 287.554i 0.0457921 + 0.0793142i
\(237\) 0 0
\(238\) −3448.59 + 5973.13i −0.939238 + 1.62681i
\(239\) 1471.92 2549.44i 0.398371 0.689999i −0.595154 0.803612i \(-0.702909\pi\)
0.993525 + 0.113613i \(0.0362423\pi\)
\(240\) 0 0
\(241\) −2237.27 3875.06i −0.597988 1.03575i −0.993118 0.117120i \(-0.962634\pi\)
0.395130 0.918625i \(-0.370700\pi\)
\(242\) 2518.40 0.668961
\(243\) 0 0
\(244\) 1242.83 0.326082
\(245\) −1498.73 2595.88i −0.390818 0.676917i
\(246\) 0 0
\(247\) −169.997 + 294.444i −0.0437922 + 0.0758504i
\(248\) −2757.77 + 4776.60i −0.706124 + 1.22304i
\(249\) 0 0
\(250\) −132.882 230.159i −0.0336169 0.0582262i
\(251\) −2121.41 −0.533474 −0.266737 0.963769i \(-0.585945\pi\)
−0.266737 + 0.963769i \(0.585945\pi\)
\(252\) 0 0
\(253\) 6827.92 1.69671
\(254\) 796.119 + 1378.92i 0.196665 + 0.340634i
\(255\) 0 0
\(256\) 2093.48 3626.02i 0.511104 0.885259i
\(257\) −2274.12 + 3938.89i −0.551967 + 0.956035i 0.446165 + 0.894951i \(0.352789\pi\)
−0.998133 + 0.0610849i \(0.980544\pi\)
\(258\) 0 0
\(259\) 6391.53 + 11070.5i 1.53340 + 2.65593i
\(260\) 277.660 0.0662298
\(261\) 0 0
\(262\) −5094.42 −1.20127
\(263\) 1749.92 + 3030.95i 0.410284 + 0.710632i 0.994921 0.100663i \(-0.0320964\pi\)
−0.584637 + 0.811295i \(0.698763\pi\)
\(264\) 0 0
\(265\) 1166.33 2020.14i 0.270366 0.468288i
\(266\) 695.276 1204.25i 0.160264 0.277585i
\(267\) 0 0
\(268\) 152.815 + 264.683i 0.0348308 + 0.0603287i
\(269\) 2594.25 0.588008 0.294004 0.955804i \(-0.405012\pi\)
0.294004 + 0.955804i \(0.405012\pi\)
\(270\) 0 0
\(271\) 8518.20 1.90939 0.954693 0.297593i \(-0.0961838\pi\)
0.954693 + 0.297593i \(0.0961838\pi\)
\(272\) 1270.94 + 2201.34i 0.283317 + 0.490720i
\(273\) 0 0
\(274\) −1067.82 + 1849.51i −0.235435 + 0.407785i
\(275\) −626.935 + 1085.88i −0.137475 + 0.238114i
\(276\) 0 0
\(277\) 945.248 + 1637.22i 0.205034 + 0.355130i 0.950144 0.311813i \(-0.100936\pi\)
−0.745109 + 0.666942i \(0.767603\pi\)
\(278\) 5109.12 1.10225
\(279\) 0 0
\(280\) −3746.49 −0.799626
\(281\) −1569.34 2718.18i −0.333164 0.577057i 0.649967 0.759963i \(-0.274783\pi\)
−0.983130 + 0.182906i \(0.941450\pi\)
\(282\) 0 0
\(283\) −2034.55 + 3523.94i −0.427354 + 0.740199i −0.996637 0.0819429i \(-0.973888\pi\)
0.569283 + 0.822142i \(0.307221\pi\)
\(284\) 718.007 1243.62i 0.150021 0.259843i
\(285\) 0 0
\(286\) 850.907 + 1473.81i 0.175927 + 0.304715i
\(287\) 2337.54 0.480768
\(288\) 0 0
\(289\) 6252.77 1.27270
\(290\) 1192.35 + 2065.20i 0.241438 + 0.418182i
\(291\) 0 0
\(292\) −576.108 + 997.848i −0.115459 + 0.199982i
\(293\) −1818.97 + 3150.56i −0.362681 + 0.628182i −0.988401 0.151865i \(-0.951472\pi\)
0.625720 + 0.780048i \(0.284805\pi\)
\(294\) 0 0
\(295\) −238.560 413.197i −0.0470830 0.0815501i
\(296\) 10162.7 1.99560
\(297\) 0 0
\(298\) 1083.57 0.210637
\(299\) 1086.32 + 1881.56i 0.210112 + 0.363925i
\(300\) 0 0
\(301\) −487.167 + 843.798i −0.0932885 + 0.161580i
\(302\) −1534.31 + 2657.50i −0.292350 + 0.506365i
\(303\) 0 0
\(304\) −256.237 443.816i −0.0483428 0.0837322i
\(305\) −1785.87 −0.335274
\(306\) 0 0
\(307\) −6829.07 −1.26956 −0.634781 0.772692i \(-0.718910\pi\)
−0.634781 + 0.772692i \(0.718910\pi\)
\(308\) 2678.88 + 4639.95i 0.495595 + 0.858395i
\(309\) 0 0
\(310\) 1201.16 2080.47i 0.220069 0.381171i
\(311\) −3300.51 + 5716.66i −0.601785 + 1.04232i 0.390766 + 0.920490i \(0.372210\pi\)
−0.992551 + 0.121831i \(0.961123\pi\)
\(312\) 0 0
\(313\) −1383.30 2395.94i −0.249803 0.432672i 0.713668 0.700484i \(-0.247033\pi\)
−0.963471 + 0.267812i \(0.913699\pi\)
\(314\) −4583.15 −0.823701
\(315\) 0 0
\(316\) 863.373 0.153698
\(317\) −2282.21 3952.90i −0.404358 0.700368i 0.589889 0.807485i \(-0.299172\pi\)
−0.994247 + 0.107116i \(0.965838\pi\)
\(318\) 0 0
\(319\) 5625.44 9743.55i 0.987349 1.71014i
\(320\) −1247.10 + 2160.05i −0.217860 + 0.377345i
\(321\) 0 0
\(322\) −4442.96 7695.43i −0.768933 1.33183i
\(323\) −2251.15 −0.387794
\(324\) 0 0
\(325\) −398.981 −0.0680968
\(326\) 563.325 + 975.707i 0.0957045 + 0.165765i
\(327\) 0 0
\(328\) 929.190 1609.40i 0.156421 0.270928i
\(329\) −933.321 + 1616.56i −0.156400 + 0.270893i
\(330\) 0 0
\(331\) 2332.81 + 4040.54i 0.387380 + 0.670962i 0.992096 0.125479i \(-0.0400468\pi\)
−0.604716 + 0.796441i \(0.706713\pi\)
\(332\) 1922.51 0.317805
\(333\) 0 0
\(334\) −6334.30 −1.03772
\(335\) −219.586 380.334i −0.0358127 0.0620295i
\(336\) 0 0
\(337\) 1903.53 3297.01i 0.307691 0.532937i −0.670166 0.742212i \(-0.733777\pi\)
0.977857 + 0.209275i \(0.0671103\pi\)
\(338\) 2064.78 3576.31i 0.332276 0.575520i
\(339\) 0 0
\(340\) 919.212 + 1592.12i 0.146621 + 0.253956i
\(341\) −11334.1 −1.79993
\(342\) 0 0
\(343\) 7874.33 1.23957
\(344\) 387.306 + 670.833i 0.0607039 + 0.105142i
\(345\) 0 0
\(346\) −1892.12 + 3277.24i −0.293991 + 0.509207i
\(347\) −1155.63 + 2001.61i −0.178783 + 0.309660i −0.941464 0.337114i \(-0.890549\pi\)
0.762681 + 0.646775i \(0.223883\pi\)
\(348\) 0 0
\(349\) 5436.61 + 9416.49i 0.833854 + 1.44428i 0.894960 + 0.446147i \(0.147204\pi\)
−0.0611053 + 0.998131i \(0.519463\pi\)
\(350\) 1631.80 0.249209
\(351\) 0 0
\(352\) 7227.89 1.09445
\(353\) 1446.87 + 2506.05i 0.218156 + 0.377857i 0.954244 0.299029i \(-0.0966626\pi\)
−0.736088 + 0.676885i \(0.763329\pi\)
\(354\) 0 0
\(355\) −1031.73 + 1787.01i −0.154250 + 0.267168i
\(356\) −507.117 + 878.352i −0.0754975 + 0.130766i
\(357\) 0 0
\(358\) 3015.12 + 5222.34i 0.445123 + 0.770975i
\(359\) −9875.47 −1.45183 −0.725915 0.687784i \(-0.758584\pi\)
−0.725915 + 0.687784i \(0.758584\pi\)
\(360\) 0 0
\(361\) −6405.14 −0.933830
\(362\) −863.087 1494.91i −0.125312 0.217046i
\(363\) 0 0
\(364\) −852.417 + 1476.43i −0.122744 + 0.212599i
\(365\) 827.832 1433.85i 0.118714 0.205619i
\(366\) 0 0
\(367\) −5361.08 9285.66i −0.762523 1.32073i −0.941546 0.336884i \(-0.890627\pi\)
0.179023 0.983845i \(-0.442706\pi\)
\(368\) −3274.82 −0.463891
\(369\) 0 0
\(370\) −4426.43 −0.621944
\(371\) 7161.27 + 12403.7i 1.00214 + 1.73576i
\(372\) 0 0
\(373\) −2087.95 + 3616.44i −0.289839 + 0.502016i −0.973771 0.227530i \(-0.926935\pi\)
0.683932 + 0.729546i \(0.260268\pi\)
\(374\) −5633.97 + 9758.32i −0.778946 + 1.34917i
\(375\) 0 0
\(376\) 742.005 + 1285.19i 0.101771 + 0.176273i
\(377\) 3580.03 0.489074
\(378\) 0 0
\(379\) 1715.14 0.232457 0.116228 0.993223i \(-0.462920\pi\)
0.116228 + 0.993223i \(0.462920\pi\)
\(380\) −185.324 320.991i −0.0250182 0.0433328i
\(381\) 0 0
\(382\) −1220.88 + 2114.63i −0.163523 + 0.283230i
\(383\) −2569.53 + 4450.56i −0.342812 + 0.593768i −0.984954 0.172818i \(-0.944713\pi\)
0.642142 + 0.766586i \(0.278046\pi\)
\(384\) 0 0
\(385\) −3849.39 6667.33i −0.509566 0.882594i
\(386\) −4573.14 −0.603022
\(387\) 0 0
\(388\) −691.074 −0.0904226
\(389\) −4498.27 7791.23i −0.586301 1.01550i −0.994712 0.102705i \(-0.967250\pi\)
0.408411 0.912798i \(-0.366083\pi\)
\(390\) 0 0
\(391\) −7192.67 + 12458.1i −0.930304 + 1.61133i
\(392\) 7315.92 12671.5i 0.942627 1.63268i
\(393\) 0 0
\(394\) 5376.44 + 9312.27i 0.687465 + 1.19072i
\(395\) −1240.62 −0.158031
\(396\) 0 0
\(397\) −105.823 −0.0133781 −0.00668905 0.999978i \(-0.502129\pi\)
−0.00668905 + 0.999978i \(0.502129\pi\)
\(398\) 3778.24 + 6544.10i 0.475844 + 0.824186i
\(399\) 0 0
\(400\) 300.692 520.814i 0.0375865 0.0651017i
\(401\) −7240.91 + 12541.6i −0.901730 + 1.56184i −0.0764824 + 0.997071i \(0.524369\pi\)
−0.825248 + 0.564771i \(0.808964\pi\)
\(402\) 0 0
\(403\) −1803.25 3123.32i −0.222894 0.386063i
\(404\) −2840.18 −0.349763
\(405\) 0 0
\(406\) −14642.0 −1.78983
\(407\) 10441.9 + 18085.9i 1.27171 + 2.20266i
\(408\) 0 0
\(409\) 430.532 745.704i 0.0520500 0.0901533i −0.838826 0.544399i \(-0.816758\pi\)
0.890876 + 0.454246i \(0.150091\pi\)
\(410\) −404.713 + 700.983i −0.0487496 + 0.0844368i
\(411\) 0 0
\(412\) −2439.86 4225.96i −0.291755 0.505335i
\(413\) 2929.52 0.349037
\(414\) 0 0
\(415\) −2762.53 −0.326764
\(416\) 1149.96 + 1991.78i 0.135532 + 0.234748i
\(417\) 0 0
\(418\) 1135.88 1967.39i 0.132913 0.230211i
\(419\) 6508.87 11273.7i 0.758900 1.31445i −0.184512 0.982830i \(-0.559070\pi\)
0.943412 0.331623i \(-0.107596\pi\)
\(420\) 0 0
\(421\) −7273.28 12597.7i −0.841991 1.45837i −0.888209 0.459439i \(-0.848050\pi\)
0.0462188 0.998931i \(-0.485283\pi\)
\(422\) −229.428 −0.0264654
\(423\) 0 0
\(424\) 11386.7 1.30421
\(425\) −1320.85 2287.78i −0.150755 0.261115i
\(426\) 0 0
\(427\) 5482.63 9496.19i 0.621365 1.07624i
\(428\) −1703.27 + 2950.14i −0.192361 + 0.333179i
\(429\) 0 0
\(430\) −168.693 292.185i −0.0189188 0.0327683i
\(431\) −3539.94 −0.395622 −0.197811 0.980240i \(-0.563383\pi\)
−0.197811 + 0.980240i \(0.563383\pi\)
\(432\) 0 0
\(433\) 669.471 0.0743019 0.0371509 0.999310i \(-0.488172\pi\)
0.0371509 + 0.999310i \(0.488172\pi\)
\(434\) 7375.14 + 12774.1i 0.815710 + 1.41285i
\(435\) 0 0
\(436\) 3693.55 6397.41i 0.405708 0.702707i
\(437\) 1450.13 2511.70i 0.158739 0.274944i
\(438\) 0 0
\(439\) −6284.27 10884.7i −0.683216 1.18337i −0.973994 0.226575i \(-0.927247\pi\)
0.290777 0.956791i \(-0.406086\pi\)
\(440\) −6120.65 −0.663160
\(441\) 0 0
\(442\) −3585.45 −0.385843
\(443\) −5530.17 9578.53i −0.593106 1.02729i −0.993811 0.111083i \(-0.964568\pi\)
0.400705 0.916207i \(-0.368765\pi\)
\(444\) 0 0
\(445\) 728.696 1262.14i 0.0776259 0.134452i
\(446\) 2064.49 3575.80i 0.219185 0.379639i
\(447\) 0 0
\(448\) −7657.23 13262.7i −0.807522 1.39867i
\(449\) 18553.9 1.95014 0.975072 0.221891i \(-0.0712228\pi\)
0.975072 + 0.221891i \(0.0712228\pi\)
\(450\) 0 0
\(451\) 3818.84 0.398719
\(452\) 3122.60 + 5408.51i 0.324945 + 0.562821i
\(453\) 0 0
\(454\) −3661.16 + 6341.32i −0.378473 + 0.655535i
\(455\) 1224.87 2121.54i 0.126204 0.218592i
\(456\) 0 0
\(457\) 3401.13 + 5890.93i 0.348136 + 0.602989i 0.985918 0.167228i \(-0.0534814\pi\)
−0.637782 + 0.770217i \(0.720148\pi\)
\(458\) 4399.78 0.448882
\(459\) 0 0
\(460\) −2368.52 −0.240071
\(461\) −7447.19 12898.9i −0.752386 1.30317i −0.946663 0.322224i \(-0.895569\pi\)
0.194277 0.980947i \(-0.437764\pi\)
\(462\) 0 0
\(463\) 7144.33 12374.3i 0.717117 1.24208i −0.245020 0.969518i \(-0.578794\pi\)
0.962137 0.272566i \(-0.0878722\pi\)
\(464\) −2698.09 + 4673.22i −0.269947 + 0.467562i
\(465\) 0 0
\(466\) 2943.87 + 5098.93i 0.292644 + 0.506874i
\(467\) 13115.1 1.29956 0.649780 0.760122i \(-0.274861\pi\)
0.649780 + 0.760122i \(0.274861\pi\)
\(468\) 0 0
\(469\) 2696.52 0.265488
\(470\) −323.184 559.771i −0.0317178 0.0549368i
\(471\) 0 0
\(472\) 1164.51 2016.99i 0.113561 0.196693i
\(473\) −795.887 + 1378.52i −0.0773677 + 0.134005i
\(474\) 0 0
\(475\) 266.300 + 461.244i 0.0257235 + 0.0445544i
\(476\) −11287.9 −1.08694
\(477\) 0 0
\(478\) −6258.96 −0.598908
\(479\) −3959.89 6858.74i −0.377729 0.654246i 0.613002 0.790081i \(-0.289962\pi\)
−0.990731 + 0.135835i \(0.956628\pi\)
\(480\) 0 0
\(481\) −3322.60 + 5754.91i −0.314964 + 0.545533i
\(482\) −4756.70 + 8238.85i −0.449506 + 0.778567i
\(483\) 0 0
\(484\) 2060.81 + 3569.43i 0.193540 + 0.335220i
\(485\) 993.032 0.0929717
\(486\) 0 0
\(487\) −17003.1 −1.58210 −0.791051 0.611751i \(-0.790466\pi\)
−0.791051 + 0.611751i \(0.790466\pi\)
\(488\) −4358.78 7549.63i −0.404329 0.700319i
\(489\) 0 0
\(490\) −3186.48 + 5519.15i −0.293777 + 0.508836i
\(491\) −3195.87 + 5535.41i −0.293743 + 0.508777i −0.974692 0.223554i \(-0.928234\pi\)
0.680949 + 0.732331i \(0.261568\pi\)
\(492\) 0 0
\(493\) 11851.9 + 20528.1i 1.08273 + 1.87534i
\(494\) 722.870 0.0658370
\(495\) 0 0
\(496\) 5436.07 0.492111
\(497\) −6334.85 10972.3i −0.571744 0.990289i
\(498\) 0 0
\(499\) 1337.06 2315.85i 0.119950 0.207759i −0.799798 0.600270i \(-0.795060\pi\)
0.919748 + 0.392510i \(0.128393\pi\)
\(500\) 217.476 376.679i 0.0194516 0.0336912i
\(501\) 0 0
\(502\) 2255.18 + 3906.09i 0.200505 + 0.347285i
\(503\) 1263.13 0.111969 0.0559843 0.998432i \(-0.482170\pi\)
0.0559843 + 0.998432i \(0.482170\pi\)
\(504\) 0 0
\(505\) 4081.17 0.359624
\(506\) −7258.48 12572.1i −0.637706 1.10454i
\(507\) 0 0
\(508\) −1302.93 + 2256.74i −0.113796 + 0.197100i
\(509\) −690.421 + 1195.84i −0.0601226 + 0.104135i −0.894520 0.447028i \(-0.852482\pi\)
0.834397 + 0.551163i \(0.185816\pi\)
\(510\) 0 0
\(511\) 5082.90 + 8803.84i 0.440028 + 0.762150i
\(512\) −8163.62 −0.704657
\(513\) 0 0
\(514\) 9670.09 0.829824
\(515\) 3505.93 + 6072.45i 0.299980 + 0.519581i
\(516\) 0 0
\(517\) −1524.77 + 2640.98i −0.129709 + 0.224662i
\(518\) 13589.2 23537.1i 1.15265 1.99645i
\(519\) 0 0
\(520\) −973.794 1686.66i −0.0821225 0.142240i
\(521\) 2689.80 0.226185 0.113092 0.993584i \(-0.463924\pi\)
0.113092 + 0.993584i \(0.463924\pi\)
\(522\) 0 0
\(523\) 7144.18 0.597310 0.298655 0.954361i \(-0.403462\pi\)
0.298655 + 0.954361i \(0.403462\pi\)
\(524\) −4168.77 7220.52i −0.347545 0.601966i
\(525\) 0 0
\(526\) 3720.54 6444.16i 0.308409 0.534180i
\(527\) 11939.6 20679.9i 0.986897 1.70936i
\(528\) 0 0
\(529\) −3183.13 5513.34i −0.261620 0.453138i
\(530\) −4959.51 −0.406467
\(531\) 0 0
\(532\) 2275.78 0.185466
\(533\) 607.577 + 1052.35i 0.0493754 + 0.0855207i
\(534\) 0 0
\(535\) 2447.49 4239.18i 0.197784 0.342571i
\(536\) 1071.89 1856.57i 0.0863779 0.149611i
\(537\) 0 0
\(538\) −2757.84 4776.72i −0.221002 0.382786i
\(539\) 30067.4 2.40278
\(540\) 0 0
\(541\) −3310.57 −0.263091 −0.131546 0.991310i \(-0.541994\pi\)
−0.131546 + 0.991310i \(0.541994\pi\)
\(542\) −9055.35 15684.3i −0.717640 1.24299i
\(543\) 0 0
\(544\) −7614.02 + 13187.9i −0.600089 + 1.03938i
\(545\) −5307.41 + 9192.70i −0.417145 + 0.722517i
\(546\) 0 0
\(547\) −1143.26 1980.18i −0.0893643 0.154784i 0.817878 0.575391i \(-0.195150\pi\)
−0.907243 + 0.420608i \(0.861817\pi\)
\(548\) −3495.19 −0.272458
\(549\) 0 0
\(550\) 2665.88 0.206679
\(551\) −2389.49 4138.71i −0.184747 0.319991i
\(552\) 0 0
\(553\) 3808.70 6596.85i 0.292879 0.507282i
\(554\) 2009.71 3480.92i 0.154124 0.266950i
\(555\) 0 0
\(556\) 4180.80 + 7241.36i 0.318895 + 0.552342i
\(557\) −13846.6 −1.05332 −0.526658 0.850077i \(-0.676555\pi\)
−0.526658 + 0.850077i \(0.676555\pi\)
\(558\) 0 0
\(559\) −506.502 −0.0383233
\(560\) 1846.25 + 3197.80i 0.139318 + 0.241307i
\(561\) 0 0
\(562\) −3336.61 + 5779.17i −0.250438 + 0.433772i
\(563\) −8082.21 + 13998.8i −0.605017 + 1.04792i 0.387032 + 0.922066i \(0.373500\pi\)
−0.992049 + 0.125853i \(0.959833\pi\)
\(564\) 0 0
\(565\) −4487.00 7771.71i −0.334105 0.578687i
\(566\) 8651.37 0.642481
\(567\) 0 0
\(568\) −10072.6 −0.744080
\(569\) 248.167 + 429.838i 0.0182842 + 0.0316691i 0.875023 0.484082i \(-0.160846\pi\)
−0.856739 + 0.515751i \(0.827513\pi\)
\(570\) 0 0
\(571\) −2985.59 + 5171.20i −0.218815 + 0.378998i −0.954446 0.298384i \(-0.903552\pi\)
0.735631 + 0.677382i \(0.236886\pi\)
\(572\) −1392.60 + 2412.05i −0.101796 + 0.176316i
\(573\) 0 0
\(574\) −2484.94 4304.04i −0.180696 0.312974i
\(575\) 3403.42 0.246839
\(576\) 0 0
\(577\) 9571.82 0.690607 0.345304 0.938491i \(-0.387776\pi\)
0.345304 + 0.938491i \(0.387776\pi\)
\(578\) −6647.07 11513.1i −0.478342 0.828513i
\(579\) 0 0
\(580\) −1951.40 + 3379.92i −0.139702 + 0.241971i
\(581\) 8480.97 14689.5i 0.605594 1.04892i
\(582\) 0 0
\(583\) 11699.4 + 20264.0i 0.831115 + 1.43953i
\(584\) 8081.97 0.572662
\(585\) 0 0
\(586\) 7734.71 0.545253
\(587\) 2661.09 + 4609.14i 0.187112 + 0.324088i 0.944286 0.329125i \(-0.106754\pi\)
−0.757174 + 0.653213i \(0.773420\pi\)
\(588\) 0 0
\(589\) −2407.16 + 4169.31i −0.168396 + 0.291670i
\(590\) −507.206 + 878.507i −0.0353921 + 0.0613010i
\(591\) 0 0
\(592\) −5008.15 8674.38i −0.347692 0.602221i
\(593\) 11066.5 0.766354 0.383177 0.923675i \(-0.374830\pi\)
0.383177 + 0.923675i \(0.374830\pi\)
\(594\) 0 0
\(595\) 16220.1 1.11758
\(596\) 886.690 + 1535.79i 0.0609400 + 0.105551i
\(597\) 0 0
\(598\) 2309.65 4000.42i 0.157941 0.273561i
\(599\) 9192.50 15921.9i 0.627037 1.08606i −0.361106 0.932525i \(-0.617601\pi\)
0.988143 0.153536i \(-0.0490660\pi\)
\(600\) 0 0
\(601\) 308.915 + 535.057i 0.0209666 + 0.0363152i 0.876318 0.481733i \(-0.159992\pi\)
−0.855352 + 0.518048i \(0.826659\pi\)
\(602\) 2071.55 0.140249
\(603\) 0 0
\(604\) −5022.12 −0.338323
\(605\) −2961.26 5129.05i −0.198996 0.344670i
\(606\) 0 0
\(607\) −6919.89 + 11985.6i −0.462718 + 0.801451i −0.999095 0.0425272i \(-0.986459\pi\)
0.536377 + 0.843978i \(0.319792\pi\)
\(608\) 1535.08 2658.83i 0.102394 0.177352i
\(609\) 0 0
\(610\) 1898.49 + 3288.28i 0.126012 + 0.218260i
\(611\) −970.362 −0.0642498
\(612\) 0 0
\(613\) −25655.4 −1.69039 −0.845196 0.534457i \(-0.820516\pi\)
−0.845196 + 0.534457i \(0.820516\pi\)
\(614\) 7259.71 + 12574.2i 0.477163 + 0.826470i
\(615\) 0 0
\(616\) 18790.4 32546.0i 1.22904 2.12876i
\(617\) 2109.13 3653.12i 0.137618 0.238361i −0.788977 0.614423i \(-0.789389\pi\)
0.926594 + 0.376062i \(0.122722\pi\)
\(618\) 0 0
\(619\) −6091.28 10550.4i −0.395524 0.685067i 0.597644 0.801761i \(-0.296104\pi\)
−0.993168 + 0.116694i \(0.962770\pi\)
\(620\) 3931.65 0.254676
\(621\) 0 0
\(622\) 14034.6 0.904719
\(623\) 4474.20 + 7749.54i 0.287729 + 0.498361i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −2941.05 + 5094.05i −0.187776 + 0.325238i
\(627\) 0 0
\(628\) −3750.40 6495.89i −0.238308 0.412761i
\(629\) −43998.8 −2.78910
\(630\) 0 0
\(631\) 16673.2 1.05190 0.525951 0.850515i \(-0.323709\pi\)
0.525951 + 0.850515i \(0.323709\pi\)
\(632\) −3027.98 5244.61i −0.190580 0.330094i
\(633\) 0 0
\(634\) −4852.24 + 8404.33i −0.303954 + 0.526465i
\(635\) 1872.23 3242.81i 0.117004 0.202656i
\(636\) 0 0
\(637\) 4783.72 + 8285.65i 0.297548 + 0.515368i
\(638\) −23920.7 −1.48437
\(639\) 0 0
\(640\) −461.486 −0.0285028
\(641\) 13135.4 + 22751.2i 0.809388 + 1.40190i 0.913289 + 0.407313i \(0.133534\pi\)
−0.103901 + 0.994588i \(0.533133\pi\)
\(642\) 0 0
\(643\) −5778.17 + 10008.1i −0.354384 + 0.613810i −0.987012 0.160645i \(-0.948643\pi\)
0.632629 + 0.774455i \(0.281976\pi\)
\(644\) 7271.37 12594.4i 0.444925 0.770634i
\(645\) 0 0
\(646\) 2393.11 + 4144.99i 0.145752 + 0.252449i
\(647\) 25395.2 1.54310 0.771552 0.636166i \(-0.219481\pi\)
0.771552 + 0.636166i \(0.219481\pi\)
\(648\) 0 0
\(649\) 4785.96 0.289469
\(650\) 424.140 + 734.633i 0.0255941 + 0.0443303i
\(651\) 0 0
\(652\) −921.939 + 1596.85i −0.0553772 + 0.0959161i
\(653\) −3091.42 + 5354.50i −0.185263 + 0.320885i −0.943665 0.330902i \(-0.892647\pi\)
0.758402 + 0.651787i \(0.225980\pi\)
\(654\) 0 0
\(655\) 5990.27 + 10375.5i 0.357343 + 0.618935i
\(656\) −1831.60 −0.109012
\(657\) 0 0
\(658\) 3968.70 0.235131
\(659\) −4442.66 7694.91i −0.262612 0.454858i 0.704323 0.709880i \(-0.251251\pi\)
−0.966935 + 0.255022i \(0.917917\pi\)
\(660\) 0 0
\(661\) 3585.80 6210.79i 0.211001 0.365464i −0.741027 0.671475i \(-0.765661\pi\)
0.952028 + 0.306011i \(0.0989944\pi\)
\(662\) 4959.83 8590.68i 0.291192 0.504360i
\(663\) 0 0
\(664\) −6742.51 11678.4i −0.394066 0.682543i
\(665\) −3270.16 −0.190694
\(666\) 0 0
\(667\) −30538.7 −1.77281
\(668\) −5183.37 8977.86i −0.300226 0.520006i
\(669\) 0 0
\(670\) −466.866 + 808.636i −0.0269203 + 0.0466273i
\(671\) 8957.00 15514.0i 0.515322 0.892564i
\(672\) 0 0
\(673\) 2125.26 + 3681.06i 0.121728 + 0.210839i 0.920449 0.390862i \(-0.127823\pi\)
−0.798721 + 0.601701i \(0.794490\pi\)
\(674\) −8094.27 −0.462581
\(675\) 0 0
\(676\) 6758.47 0.384528
\(677\) 1116.83 + 1934.40i 0.0634019 + 0.109815i 0.895984 0.444086i \(-0.146472\pi\)
−0.832582 + 0.553902i \(0.813138\pi\)
\(678\) 0 0
\(679\) −3048.61 + 5280.35i −0.172305 + 0.298441i
\(680\) 6447.62 11167.6i 0.363610 0.629791i
\(681\) 0 0
\(682\) 12048.8 + 20869.1i 0.676499 + 1.17173i
\(683\) 6071.62 0.340153 0.170076 0.985431i \(-0.445599\pi\)
0.170076 + 0.985431i \(0.445599\pi\)
\(684\) 0 0
\(685\) 5022.38 0.280139
\(686\) −8370.89 14498.8i −0.465892 0.806949i
\(687\) 0 0
\(688\) 381.725 661.167i 0.0211528 0.0366377i
\(689\) −3722.74 + 6447.98i −0.205842 + 0.356529i
\(690\) 0 0
\(691\) 382.892 + 663.188i 0.0210794 + 0.0365107i 0.876373 0.481634i \(-0.159956\pi\)
−0.855293 + 0.518144i \(0.826623\pi\)
\(692\) −6193.29 −0.340222
\(693\) 0 0
\(694\) 4914.02 0.268780
\(695\) −6007.56 10405.4i −0.327885 0.567913i
\(696\) 0 0
\(697\) −4022.85 + 6967.78i −0.218617 + 0.378656i
\(698\) 11558.9 20020.6i 0.626806 1.08566i
\(699\) 0 0
\(700\) 1335.30 + 2312.82i 0.0720997 + 0.124880i
\(701\) −23564.3 −1.26963 −0.634814 0.772665i \(-0.718923\pi\)
−0.634814 + 0.772665i \(0.718923\pi\)
\(702\) 0 0
\(703\) 8870.67 0.475909
\(704\) −12509.6 21667.3i −0.669709 1.15997i
\(705\) 0 0
\(706\) 3076.21 5328.16i 0.163987 0.284034i
\(707\) −12529.2 + 21701.3i −0.666492 + 1.15440i
\(708\) 0 0
\(709\) −12086.1 20933.8i −0.640204 1.10887i −0.985387 0.170331i \(-0.945516\pi\)
0.345183 0.938535i \(-0.387817\pi\)
\(710\) 4387.17 0.231898
\(711\) 0 0
\(712\) 7114.13 0.374457
\(713\) 15382.2 + 26642.8i 0.807951 + 1.39941i
\(714\) 0 0
\(715\) 2001.08 3465.97i 0.104666 0.181287i
\(716\) −4934.55 + 8546.90i −0.257560 + 0.446107i
\(717\) 0 0
\(718\) 10498.2 + 18183.4i 0.545668 + 0.945125i
\(719\) −12829.0 −0.665424 −0.332712 0.943028i \(-0.607964\pi\)
−0.332712 + 0.943028i \(0.607964\pi\)
\(720\) 0 0
\(721\) −43052.9 −2.22382
\(722\) 6809.05 + 11793.6i 0.350979 + 0.607913i
\(723\) 0 0
\(724\) 1412.53 2446.58i 0.0725088 0.125589i
\(725\) 2804.04 4856.74i 0.143641 0.248793i
\(726\) 0 0
\(727\) 12362.4 + 21412.2i 0.630666 + 1.09235i 0.987416 + 0.158146i \(0.0505517\pi\)
−0.356749 + 0.934200i \(0.616115\pi\)
\(728\) 11958.2 0.608792
\(729\) 0 0
\(730\) −3520.14 −0.178474
\(731\) −1676.81 2904.32i −0.0848413 0.146949i
\(732\) 0 0
\(733\) 10086.1 17469.7i 0.508239 0.880296i −0.491715 0.870756i \(-0.663630\pi\)
0.999954 0.00954010i \(-0.00303675\pi\)
\(734\) −11398.3 + 19742.4i −0.573186 + 0.992788i
\(735\) 0 0
\(736\) −9809.46 16990.5i −0.491279 0.850921i
\(737\) 4405.32 0.220179
\(738\) 0 0
\(739\) −16452.8 −0.818979 −0.409489 0.912315i \(-0.634293\pi\)
−0.409489 + 0.912315i \(0.634293\pi\)
\(740\) −3622.16 6273.76i −0.179937 0.311660i
\(741\) 0 0
\(742\) 15225.7 26371.7i 0.753307 1.30477i
\(743\) 10432.3 18069.3i 0.515107 0.892191i −0.484739 0.874659i \(-0.661086\pi\)
0.999846 0.0175328i \(-0.00558115\pi\)
\(744\) 0 0
\(745\) −1274.12 2206.84i −0.0626579 0.108527i
\(746\) 8878.47 0.435742
\(747\) 0 0
\(748\) −18441.2 −0.901438
\(749\) 15027.6 + 26028.6i 0.733107 + 1.26978i
\(750\) 0 0
\(751\) −7762.84 + 13445.6i −0.377191 + 0.653313i −0.990652 0.136411i \(-0.956443\pi\)
0.613462 + 0.789725i \(0.289777\pi\)
\(752\) 731.313 1266.67i 0.0354631 0.0614239i
\(753\) 0 0
\(754\) −3805.78 6591.81i −0.183818 0.318381i
\(755\) 7216.48 0.347861
\(756\) 0 0
\(757\) 30105.7 1.44546 0.722729 0.691132i \(-0.242888\pi\)
0.722729 + 0.691132i \(0.242888\pi\)
\(758\) −1823.30 3158.05i −0.0873684 0.151327i
\(759\) 0 0
\(760\) −1299.92 + 2251.52i −0.0620433 + 0.107462i
\(761\) −10869.9 + 18827.3i −0.517786 + 0.896831i 0.482001 + 0.876171i \(0.339910\pi\)
−0.999787 + 0.0206605i \(0.993423\pi\)
\(762\) 0 0
\(763\) −32587.5 56443.2i −1.54620 2.67809i
\(764\) −3996.21 −0.189238
\(765\) 0 0
\(766\) 10926.3 0.515381
\(767\) 761.446 + 1318.86i 0.0358464 + 0.0620878i
\(768\) 0 0
\(769\) −971.112 + 1682.02i −0.0455386 + 0.0788752i −0.887896 0.460044i \(-0.847834\pi\)
0.842358 + 0.538919i \(0.181167\pi\)
\(770\) −8184.25 + 14175.5i −0.383039 + 0.663443i
\(771\) 0 0
\(772\) −3742.21 6481.70i −0.174462 0.302178i
\(773\) −7921.02 −0.368563 −0.184282 0.982873i \(-0.558996\pi\)
−0.184282 + 0.982873i \(0.558996\pi\)
\(774\) 0 0
\(775\) −5649.55 −0.261855
\(776\) 2423.70 + 4197.97i 0.112121 + 0.194199i
\(777\) 0 0
\(778\) −9563.85 + 16565.1i −0.440721 + 0.763351i
\(779\) 811.054 1404.79i 0.0373030 0.0646107i
\(780\) 0 0
\(781\) −10349.3 17925.5i −0.474169 0.821285i
\(782\) 30585.0 1.39861
\(783\) 0 0
\(784\) −14421.0 −0.656933
\(785\) 5389.10