Properties

Label 245.4.e.k.116.1
Level $245$
Weight $4$
Character 245.116
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{11})\)
Defining polynomial: \( x^{4} + 11x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.1
Root \(-1.65831 - 2.87228i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.4.e.k.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.15831 - 3.73831i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-5.31662 + 9.20866i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.5831 q^{6} +11.3668 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-2.15831 - 3.73831i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-5.31662 + 9.20866i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.5831 q^{6} +11.3668 q^{8} +(1.00000 + 1.73205i) q^{9} +(10.7916 - 18.6915i) q^{10} +(-9.86675 + 17.0897i) q^{11} +(26.5831 + 46.0433i) q^{12} -71.3325 q^{13} +25.0000 q^{15} +(18.0000 + 31.1769i) q^{16} +(-15.6662 + 27.1347i) q^{17} +(4.31662 - 7.47661i) q^{18} +(68.1662 + 118.067i) q^{19} -53.1662 q^{20} +85.1821 q^{22} +(50.4327 + 87.3521i) q^{23} +(28.4169 - 49.2195i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(153.958 + 266.663i) q^{26} +145.000 q^{27} -288.198 q^{29} +(-53.9578 - 93.4577i) q^{30} +(-104.499 + 180.997i) q^{31} +(123.166 - 213.330i) q^{32} +(49.3338 + 85.4486i) q^{33} +135.251 q^{34} -21.2665 q^{36} +(-154.966 - 268.409i) q^{37} +(294.248 - 509.653i) q^{38} +(-178.331 + 308.879i) q^{39} +(28.4169 + 49.2195i) q^{40} +181.662 q^{41} -18.2005 q^{43} +(-104.916 - 181.719i) q^{44} +(-5.00000 + 8.66025i) q^{45} +(217.699 - 377.066i) q^{46} +(-73.8325 - 127.882i) q^{47} +180.000 q^{48} +107.916 q^{50} +(78.3312 + 135.674i) q^{51} +(379.248 - 656.877i) q^{52} +(63.9975 - 110.847i) q^{53} +(-312.955 - 542.054i) q^{54} -98.6675 q^{55} +681.662 q^{57} +(622.021 + 1077.37i) q^{58} +(161.332 - 279.436i) q^{59} +(-132.916 + 230.217i) q^{60} +(170.501 + 295.317i) q^{61} +902.164 q^{62} -775.325 q^{64} +(-178.331 - 308.879i) q^{65} +(212.955 - 368.849i) q^{66} +(42.1980 - 73.0891i) q^{67} +(-166.583 - 288.530i) q^{68} +504.327 q^{69} -315.736 q^{71} +(11.3668 + 19.6878i) q^{72} +(-546.662 + 946.847i) q^{73} +(-668.929 + 1158.62i) q^{74} +(62.5000 + 108.253i) q^{75} -1449.66 q^{76} +1539.58 q^{78} +(-616.593 - 1067.97i) q^{79} +(-90.0000 + 155.885i) q^{80} +(335.500 - 581.103i) q^{81} +(-392.084 - 679.110i) q^{82} +643.325 q^{83} -156.662 q^{85} +(39.2824 + 68.0391i) q^{86} +(-720.495 + 1247.93i) q^{87} +(-112.153 + 194.255i) q^{88} +(570.159 + 987.544i) q^{89} +43.1662 q^{90} -1072.53 q^{92} +(522.494 + 904.986i) q^{93} +(-318.707 + 552.017i) q^{94} +(-340.831 + 590.337i) q^{95} +(-615.831 - 1066.65i) q^{96} -1411.99 q^{97} -39.4670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9} + 10 q^{10} - 66 q^{11} + 40 q^{12} - 20 q^{13} + 100 q^{15} + 72 q^{16} + 70 q^{17} + 4 q^{18} + 140 q^{19} - 80 q^{20} - 44 q^{22} + 16 q^{23} + 180 q^{24} - 50 q^{25} + 450 q^{26} + 580 q^{27} - 516 q^{29} - 50 q^{30} - 20 q^{31} + 360 q^{32} + 330 q^{33} + 740 q^{34} - 32 q^{36} - 328 q^{37} + 580 q^{38} - 50 q^{39} + 180 q^{40} - 600 q^{41} - 232 q^{43} - 88 q^{44} - 20 q^{45} + 632 q^{46} - 30 q^{47} + 720 q^{48} + 100 q^{50} - 350 q^{51} + 920 q^{52} - 540 q^{53} - 290 q^{54} - 660 q^{55} + 1400 q^{57} + 1314 q^{58} + 380 q^{59} - 200 q^{60} + 1080 q^{61} + 2680 q^{62} - 448 q^{64} - 50 q^{65} - 110 q^{66} - 468 q^{67} - 600 q^{68} + 160 q^{69} - 2112 q^{71} + 72 q^{72} - 860 q^{73} - 1296 q^{74} + 250 q^{75} - 2880 q^{76} + 4500 q^{78} - 158 q^{79} - 360 q^{80} + 1342 q^{81} - 1900 q^{82} - 80 q^{83} + 700 q^{85} - 148 q^{86} - 1290 q^{87} - 1364 q^{88} - 240 q^{89} + 40 q^{90} - 2592 q^{92} + 100 q^{93} - 910 q^{94} - 700 q^{95} - 1800 q^{96} - 3260 q^{97} - 264 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15831 3.73831i −0.763079 1.32169i −0.941256 0.337693i \(-0.890354\pi\)
0.178178 0.983998i \(-0.442980\pi\)
\(3\) 2.50000 4.33013i 0.481125 0.833333i −0.518640 0.854993i \(-0.673562\pi\)
0.999765 + 0.0216593i \(0.00689490\pi\)
\(4\) −5.31662 + 9.20866i −0.664578 + 1.15108i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) −21.5831 −1.46855
\(7\) 0 0
\(8\) 11.3668 0.502344
\(9\) 1.00000 + 1.73205i 0.0370370 + 0.0641500i
\(10\) 10.7916 18.6915i 0.341259 0.591078i
\(11\) −9.86675 + 17.0897i −0.270449 + 0.468431i −0.968977 0.247152i \(-0.920505\pi\)
0.698528 + 0.715583i \(0.253839\pi\)
\(12\) 26.5831 + 46.0433i 0.639491 + 1.10763i
\(13\) −71.3325 −1.52185 −0.760926 0.648839i \(-0.775255\pi\)
−0.760926 + 0.648839i \(0.775255\pi\)
\(14\) 0 0
\(15\) 25.0000 0.430331
\(16\) 18.0000 + 31.1769i 0.281250 + 0.487139i
\(17\) −15.6662 + 27.1347i −0.223507 + 0.387126i −0.955871 0.293788i \(-0.905084\pi\)
0.732363 + 0.680914i \(0.238417\pi\)
\(18\) 4.31662 7.47661i 0.0565243 0.0979030i
\(19\) 68.1662 + 118.067i 0.823074 + 1.42561i 0.903382 + 0.428836i \(0.141076\pi\)
−0.0803080 + 0.996770i \(0.525590\pi\)
\(20\) −53.1662 −0.594417
\(21\) 0 0
\(22\) 85.1821 0.825495
\(23\) 50.4327 + 87.3521i 0.457215 + 0.791920i 0.998813 0.0487178i \(-0.0155135\pi\)
−0.541597 + 0.840638i \(0.682180\pi\)
\(24\) 28.4169 49.2195i 0.241690 0.418620i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 153.958 + 266.663i 1.16129 + 2.01142i
\(27\) 145.000 1.03353
\(28\) 0 0
\(29\) −288.198 −1.84541 −0.922707 0.385501i \(-0.874029\pi\)
−0.922707 + 0.385501i \(0.874029\pi\)
\(30\) −53.9578 93.4577i −0.328377 0.568765i
\(31\) −104.499 + 180.997i −0.605436 + 1.04865i 0.386546 + 0.922270i \(0.373668\pi\)
−0.991982 + 0.126376i \(0.959665\pi\)
\(32\) 123.166 213.330i 0.680404 1.17849i
\(33\) 49.3338 + 85.4486i 0.260240 + 0.450748i
\(34\) 135.251 0.682214
\(35\) 0 0
\(36\) −21.2665 −0.0984560
\(37\) −154.966 268.409i −0.688546 1.19260i −0.972308 0.233702i \(-0.924916\pi\)
0.283762 0.958895i \(-0.408417\pi\)
\(38\) 294.248 509.653i 1.25614 2.17570i
\(39\) −178.331 + 308.879i −0.732201 + 1.26821i
\(40\) 28.4169 + 49.2195i 0.112328 + 0.194557i
\(41\) 181.662 0.691973 0.345987 0.938239i \(-0.387544\pi\)
0.345987 + 0.938239i \(0.387544\pi\)
\(42\) 0 0
\(43\) −18.2005 −0.0645477 −0.0322738 0.999479i \(-0.510275\pi\)
−0.0322738 + 0.999479i \(0.510275\pi\)
\(44\) −104.916 181.719i −0.359469 0.622618i
\(45\) −5.00000 + 8.66025i −0.0165635 + 0.0286888i
\(46\) 217.699 377.066i 0.697783 1.20860i
\(47\) −73.8325 127.882i −0.229140 0.396882i 0.728414 0.685138i \(-0.240258\pi\)
−0.957553 + 0.288256i \(0.906925\pi\)
\(48\) 180.000 0.541266
\(49\) 0 0
\(50\) 107.916 0.305231
\(51\) 78.3312 + 135.674i 0.215070 + 0.372512i
\(52\) 379.248 656.877i 1.01139 1.75178i
\(53\) 63.9975 110.847i 0.165863 0.287283i −0.771099 0.636716i \(-0.780292\pi\)
0.936961 + 0.349433i \(0.113626\pi\)
\(54\) −312.955 542.054i −0.788663 1.36601i
\(55\) −98.6675 −0.241897
\(56\) 0 0
\(57\) 681.662 1.58401
\(58\) 622.021 + 1077.37i 1.40820 + 2.43907i
\(59\) 161.332 279.436i 0.355995 0.616601i −0.631293 0.775545i \(-0.717475\pi\)
0.987288 + 0.158943i \(0.0508087\pi\)
\(60\) −132.916 + 230.217i −0.285989 + 0.495347i
\(61\) 170.501 + 295.317i 0.357876 + 0.619860i 0.987606 0.156955i \(-0.0501676\pi\)
−0.629730 + 0.776814i \(0.716834\pi\)
\(62\) 902.164 1.84798
\(63\) 0 0
\(64\) −775.325 −1.51431
\(65\) −178.331 308.879i −0.340296 0.589411i
\(66\) 212.955 368.849i 0.397166 0.687912i
\(67\) 42.1980 73.0891i 0.0769449 0.133272i −0.824986 0.565154i \(-0.808817\pi\)
0.901930 + 0.431881i \(0.142150\pi\)
\(68\) −166.583 288.530i −0.297076 0.514551i
\(69\) 504.327 0.879911
\(70\) 0 0
\(71\) −315.736 −0.527760 −0.263880 0.964555i \(-0.585002\pi\)
−0.263880 + 0.964555i \(0.585002\pi\)
\(72\) 11.3668 + 19.6878i 0.0186053 + 0.0322254i
\(73\) −546.662 + 946.847i −0.876466 + 1.51808i −0.0212727 + 0.999774i \(0.506772\pi\)
−0.855193 + 0.518310i \(0.826561\pi\)
\(74\) −668.929 + 1158.62i −1.05083 + 1.82009i
\(75\) 62.5000 + 108.253i 0.0962250 + 0.166667i
\(76\) −1449.66 −2.18799
\(77\) 0 0
\(78\) 1539.58 2.23491
\(79\) −616.593 1067.97i −0.878128 1.52096i −0.853393 0.521268i \(-0.825459\pi\)
−0.0247348 0.999694i \(-0.507874\pi\)
\(80\) −90.0000 + 155.885i −0.125779 + 0.217855i
\(81\) 335.500 581.103i 0.460219 0.797124i
\(82\) −392.084 679.110i −0.528030 0.914575i
\(83\) 643.325 0.850772 0.425386 0.905012i \(-0.360138\pi\)
0.425386 + 0.905012i \(0.360138\pi\)
\(84\) 0 0
\(85\) −156.662 −0.199911
\(86\) 39.2824 + 68.0391i 0.0492550 + 0.0853121i
\(87\) −720.495 + 1247.93i −0.887876 + 1.53785i
\(88\) −112.153 + 194.255i −0.135858 + 0.235314i
\(89\) 570.159 + 987.544i 0.679064 + 1.17617i 0.975263 + 0.221047i \(0.0709475\pi\)
−0.296199 + 0.955126i \(0.595719\pi\)
\(90\) 43.1662 0.0505569
\(91\) 0 0
\(92\) −1072.53 −1.21542
\(93\) 522.494 + 904.986i 0.582581 + 1.00906i
\(94\) −318.707 + 552.017i −0.349704 + 0.605704i
\(95\) −340.831 + 590.337i −0.368090 + 0.637551i
\(96\) −615.831 1066.65i −0.654719 1.13401i
\(97\) −1411.99 −1.47800 −0.739001 0.673705i \(-0.764702\pi\)
−0.739001 + 0.673705i \(0.764702\pi\)
\(98\) 0 0
\(99\) −39.4670 −0.0400665
\(100\) −132.916 230.217i −0.132916 0.230217i
\(101\) −272.836 + 472.566i −0.268794 + 0.465565i −0.968551 0.248816i \(-0.919959\pi\)
0.699756 + 0.714381i \(0.253292\pi\)
\(102\) 338.127 585.652i 0.328231 0.568512i
\(103\) 390.495 + 676.357i 0.373559 + 0.647024i 0.990110 0.140291i \(-0.0448039\pi\)
−0.616551 + 0.787315i \(0.711471\pi\)
\(104\) −810.819 −0.764493
\(105\) 0 0
\(106\) −552.506 −0.506266
\(107\) 310.330 + 537.507i 0.280381 + 0.485634i 0.971478 0.237128i \(-0.0762060\pi\)
−0.691098 + 0.722761i \(0.742873\pi\)
\(108\) −770.911 + 1335.26i −0.686860 + 1.18968i
\(109\) −2.09397 + 3.62686i −0.00184005 + 0.00318707i −0.866944 0.498406i \(-0.833919\pi\)
0.865104 + 0.501593i \(0.167252\pi\)
\(110\) 212.955 + 368.849i 0.184586 + 0.319713i
\(111\) −1549.66 −1.32511
\(112\) 0 0
\(113\) 1413.53 1.17676 0.588379 0.808585i \(-0.299766\pi\)
0.588379 + 0.808585i \(0.299766\pi\)
\(114\) −1471.24 2548.26i −1.20872 2.09357i
\(115\) −252.164 + 436.760i −0.204473 + 0.354158i
\(116\) 1532.24 2653.92i 1.22642 2.12423i
\(117\) −71.3325 123.552i −0.0563649 0.0976268i
\(118\) −1392.82 −1.08661
\(119\) 0 0
\(120\) 284.169 0.216175
\(121\) 470.794 + 815.440i 0.353715 + 0.612652i
\(122\) 735.990 1274.77i 0.546175 0.946004i
\(123\) 454.156 786.622i 0.332926 0.576645i
\(124\) −1111.16 1924.59i −0.804720 1.39382i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2046.26 −1.42974 −0.714868 0.699259i \(-0.753513\pi\)
−0.714868 + 0.699259i \(0.753513\pi\)
\(128\) 688.063 + 1191.76i 0.475131 + 0.822951i
\(129\) −45.5013 + 78.8105i −0.0310555 + 0.0537897i
\(130\) −769.789 + 1333.31i −0.519346 + 0.899533i
\(131\) 570.159 + 987.544i 0.380267 + 0.658642i 0.991100 0.133117i \(-0.0424987\pi\)
−0.610833 + 0.791759i \(0.709165\pi\)
\(132\) −1049.16 −0.691798
\(133\) 0 0
\(134\) −364.306 −0.234860
\(135\) 362.500 + 627.868i 0.231104 + 0.400284i
\(136\) −178.074 + 308.434i −0.112278 + 0.194470i
\(137\) 245.171 424.649i 0.152893 0.264819i −0.779397 0.626531i \(-0.784474\pi\)
0.932290 + 0.361712i \(0.117808\pi\)
\(138\) −1088.50 1885.33i −0.671442 1.16297i
\(139\) −2800.00 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) −738.325 −0.440980
\(142\) 681.457 + 1180.32i 0.402723 + 0.697536i
\(143\) 703.820 1219.05i 0.411583 0.712883i
\(144\) −36.0000 + 62.3538i −0.0208333 + 0.0360844i
\(145\) −720.495 1247.93i −0.412647 0.714726i
\(146\) 4719.47 2.67525
\(147\) 0 0
\(148\) 3295.58 1.83037
\(149\) −583.058 1009.89i −0.320577 0.555256i 0.660030 0.751239i \(-0.270544\pi\)
−0.980607 + 0.195983i \(0.937210\pi\)
\(150\) 269.789 467.288i 0.146855 0.254360i
\(151\) −479.791 + 831.022i −0.258575 + 0.447865i −0.965860 0.259063i \(-0.916586\pi\)
0.707285 + 0.706928i \(0.249920\pi\)
\(152\) 774.829 + 1342.04i 0.413467 + 0.716145i
\(153\) −62.6650 −0.0331122
\(154\) 0 0
\(155\) −1044.99 −0.541519
\(156\) −1896.24 3284.39i −0.973210 1.68565i
\(157\) −510.330 + 883.917i −0.259419 + 0.449327i −0.966086 0.258219i \(-0.916864\pi\)
0.706667 + 0.707546i \(0.250198\pi\)
\(158\) −2661.60 + 4610.03i −1.34016 + 2.32123i
\(159\) −319.987 554.234i −0.159602 0.276438i
\(160\) 1231.66 0.608572
\(161\) 0 0
\(162\) −2896.46 −1.40473
\(163\) 783.008 + 1356.21i 0.376257 + 0.651696i 0.990514 0.137410i \(-0.0438777\pi\)
−0.614257 + 0.789106i \(0.710544\pi\)
\(164\) −965.831 + 1672.87i −0.459870 + 0.796519i
\(165\) −246.669 + 427.243i −0.116383 + 0.201581i
\(166\) −1388.50 2404.95i −0.649206 1.12446i
\(167\) 1130.30 0.523746 0.261873 0.965102i \(-0.415660\pi\)
0.261873 + 0.965102i \(0.415660\pi\)
\(168\) 0 0
\(169\) 2891.32 1.31603
\(170\) 338.127 + 585.652i 0.152548 + 0.264221i
\(171\) −136.332 + 236.135i −0.0609685 + 0.105600i
\(172\) 96.7652 167.602i 0.0428970 0.0742997i
\(173\) 1271.67 + 2202.59i 0.558862 + 0.967978i 0.997592 + 0.0693588i \(0.0220953\pi\)
−0.438729 + 0.898619i \(0.644571\pi\)
\(174\) 6220.21 2.71008
\(175\) 0 0
\(176\) −710.406 −0.304255
\(177\) −806.662 1397.18i −0.342556 0.593325i
\(178\) 2461.16 4262.86i 1.03636 1.79503i
\(179\) 605.325 1048.45i 0.252760 0.437794i −0.711524 0.702661i \(-0.751995\pi\)
0.964285 + 0.264868i \(0.0853282\pi\)
\(180\) −53.1662 92.0866i −0.0220154 0.0381319i
\(181\) 3031.32 1.24484 0.622421 0.782683i \(-0.286149\pi\)
0.622421 + 0.782683i \(0.286149\pi\)
\(182\) 0 0
\(183\) 1705.01 0.688733
\(184\) 573.256 + 992.909i 0.229679 + 0.397817i
\(185\) 774.829 1342.04i 0.307927 0.533346i
\(186\) 2255.41 3906.48i 0.889111 1.53999i
\(187\) −309.150 535.463i −0.120895 0.209396i
\(188\) 1570.16 0.609125
\(189\) 0 0
\(190\) 2942.48 1.12353
\(191\) 1084.32 + 1878.10i 0.410778 + 0.711488i 0.994975 0.100124i \(-0.0319239\pi\)
−0.584197 + 0.811612i \(0.698591\pi\)
\(192\) −1938.31 + 3357.26i −0.728571 + 1.26192i
\(193\) −745.240 + 1290.79i −0.277946 + 0.481416i −0.970874 0.239590i \(-0.922987\pi\)
0.692928 + 0.721006i \(0.256320\pi\)
\(194\) 3047.52 + 5278.46i 1.12783 + 1.95346i
\(195\) −1783.31 −0.654901
\(196\) 0 0
\(197\) 3380.57 1.22262 0.611308 0.791393i \(-0.290644\pi\)
0.611308 + 0.791393i \(0.290644\pi\)
\(198\) 85.1821 + 147.540i 0.0305739 + 0.0529555i
\(199\) 2297.66 3979.67i 0.818478 1.41765i −0.0883251 0.996092i \(-0.528151\pi\)
0.906803 0.421554i \(-0.138515\pi\)
\(200\) −142.084 + 246.097i −0.0502344 + 0.0870086i
\(201\) −210.990 365.445i −0.0740402 0.128241i
\(202\) 2355.46 0.820445
\(203\) 0 0
\(204\) −1665.83 −0.571723
\(205\) 454.156 + 786.622i 0.154730 + 0.268000i
\(206\) 1685.62 2919.58i 0.570110 0.987460i
\(207\) −100.865 + 174.704i −0.0338678 + 0.0586608i
\(208\) −1283.98 2223.93i −0.428021 0.741354i
\(209\) −2690.32 −0.890398
\(210\) 0 0
\(211\) −4988.66 −1.62765 −0.813824 0.581112i \(-0.802618\pi\)
−0.813824 + 0.581112i \(0.802618\pi\)
\(212\) 680.501 + 1178.66i 0.220458 + 0.381844i
\(213\) −789.340 + 1367.18i −0.253919 + 0.439800i
\(214\) 1339.58 2320.22i 0.427905 0.741153i
\(215\) −45.5013 78.8105i −0.0144333 0.0249992i
\(216\) 1648.18 0.519187
\(217\) 0 0
\(218\) 18.0778 0.00561643
\(219\) 2733.31 + 4734.24i 0.843380 + 1.46078i
\(220\) 524.578 908.596i 0.160759 0.278443i
\(221\) 1117.51 1935.59i 0.340145 0.589148i
\(222\) 3344.64 + 5793.09i 1.01116 + 1.75138i
\(223\) −3792.97 −1.13900 −0.569498 0.821993i \(-0.692862\pi\)
−0.569498 + 0.821993i \(0.692862\pi\)
\(224\) 0 0
\(225\) −50.0000 −0.0148148
\(226\) −3050.84 5284.21i −0.897960 1.55531i
\(227\) 1955.48 3386.99i 0.571762 0.990320i −0.424623 0.905370i \(-0.639593\pi\)
0.996385 0.0849504i \(-0.0270732\pi\)
\(228\) −3624.14 + 6277.20i −1.05270 + 1.82332i
\(229\) 177.164 + 306.857i 0.0511236 + 0.0885487i 0.890455 0.455072i \(-0.150386\pi\)
−0.839331 + 0.543621i \(0.817053\pi\)
\(230\) 2176.99 0.624116
\(231\) 0 0
\(232\) −3275.87 −0.927033
\(233\) −3246.24 5622.65i −0.912739 1.58091i −0.810178 0.586184i \(-0.800630\pi\)
−0.102561 0.994727i \(-0.532704\pi\)
\(234\) −307.916 + 533.325i −0.0860217 + 0.148994i
\(235\) 369.162 639.408i 0.102474 0.177491i
\(236\) 1715.49 + 2971.31i 0.473173 + 0.819559i
\(237\) −6165.93 −1.68996
\(238\) 0 0
\(239\) −342.688 −0.0927474 −0.0463737 0.998924i \(-0.514766\pi\)
−0.0463737 + 0.998924i \(0.514766\pi\)
\(240\) 450.000 + 779.423i 0.121031 + 0.209631i
\(241\) 1156.83 2003.69i 0.309204 0.535557i −0.668984 0.743277i \(-0.733271\pi\)
0.978189 + 0.207719i \(0.0666040\pi\)
\(242\) 2032.24 3519.95i 0.539825 0.935003i
\(243\) 280.000 + 484.974i 0.0739177 + 0.128029i
\(244\) −3625.96 −0.951347
\(245\) 0 0
\(246\) −3920.84 −1.01619
\(247\) −4862.47 8422.04i −1.25260 2.16956i
\(248\) −1187.81 + 2057.35i −0.304137 + 0.526781i
\(249\) 1608.31 2785.68i 0.409328 0.708977i
\(250\) 269.789 + 467.288i 0.0682518 + 0.118216i
\(251\) −3989.29 −1.00319 −0.501597 0.865101i \(-0.667254\pi\)
−0.501597 + 0.865101i \(0.667254\pi\)
\(252\) 0 0
\(253\) −1990.43 −0.494614
\(254\) 4416.48 + 7649.56i 1.09100 + 1.88967i
\(255\) −391.656 + 678.368i −0.0961822 + 0.166592i
\(256\) −131.188 + 227.224i −0.0320283 + 0.0554747i
\(257\) 1145.66 + 1984.34i 0.278071 + 0.481633i 0.970905 0.239463i \(-0.0769715\pi\)
−0.692834 + 0.721097i \(0.743638\pi\)
\(258\) 392.824 0.0947912
\(259\) 0 0
\(260\) 3792.48 0.904614
\(261\) −288.198 499.174i −0.0683487 0.118383i
\(262\) 2461.16 4262.86i 0.580348 1.00519i
\(263\) −3180.24 + 5508.33i −0.745634 + 1.29148i 0.204264 + 0.978916i \(0.434520\pi\)
−0.949898 + 0.312560i \(0.898813\pi\)
\(264\) 560.764 + 971.273i 0.130730 + 0.226431i
\(265\) 639.975 0.148352
\(266\) 0 0
\(267\) 5701.59 1.30686
\(268\) 448.702 + 777.174i 0.102272 + 0.177140i
\(269\) −495.673 + 858.530i −0.112348 + 0.194593i −0.916717 0.399538i \(-0.869171\pi\)
0.804368 + 0.594131i \(0.202504\pi\)
\(270\) 1564.78 2710.27i 0.352701 0.610896i
\(271\) 365.489 + 633.045i 0.0819257 + 0.141899i 0.904077 0.427370i \(-0.140560\pi\)
−0.822151 + 0.569269i \(0.807226\pi\)
\(272\) −1127.97 −0.251446
\(273\) 0 0
\(274\) −2116.62 −0.466679
\(275\) −246.669 427.243i −0.0540898 0.0936862i
\(276\) −2681.32 + 4644.18i −0.584770 + 1.01285i
\(277\) 1769.31 3064.54i 0.383783 0.664731i −0.607817 0.794077i \(-0.707954\pi\)
0.991600 + 0.129346i \(0.0412878\pi\)
\(278\) 6043.27 + 10467.3i 1.30378 + 2.25822i
\(279\) −417.995 −0.0896943
\(280\) 0 0
\(281\) −4663.20 −0.989975 −0.494988 0.868900i \(-0.664827\pi\)
−0.494988 + 0.868900i \(0.664827\pi\)
\(282\) 1593.54 + 2760.09i 0.336502 + 0.582839i
\(283\) −1052.47 + 1822.94i −0.221071 + 0.382906i −0.955134 0.296176i \(-0.904289\pi\)
0.734062 + 0.679082i \(0.237622\pi\)
\(284\) 1678.65 2907.51i 0.350738 0.607496i
\(285\) 1704.16 + 2951.69i 0.354195 + 0.613483i
\(286\) −6076.25 −1.25628
\(287\) 0 0
\(288\) 492.665 0.100801
\(289\) 1965.64 + 3404.58i 0.400089 + 0.692975i
\(290\) −3110.11 + 5386.86i −0.629765 + 1.09078i
\(291\) −3529.98 + 6114.11i −0.711104 + 1.23167i
\(292\) −5812.80 10068.1i −1.16496 2.01777i
\(293\) 6594.66 1.31489 0.657447 0.753501i \(-0.271636\pi\)
0.657447 + 0.753501i \(0.271636\pi\)
\(294\) 0 0
\(295\) 1613.32 0.318412
\(296\) −1761.46 3050.93i −0.345887 0.599094i
\(297\) −1430.68 + 2478.01i −0.279517 + 0.484137i
\(298\) −2516.84 + 4359.30i −0.489251 + 0.847408i
\(299\) −3597.49 6231.04i −0.695814 1.20519i
\(300\) −1329.16 −0.255796
\(301\) 0 0
\(302\) 4142.15 0.789252
\(303\) 1364.18 + 2362.83i 0.258647 + 0.447990i
\(304\) −2453.98 + 4250.43i −0.462979 + 0.801904i
\(305\) −852.506 + 1476.58i −0.160047 + 0.277210i
\(306\) 135.251 + 234.261i 0.0252672 + 0.0437641i
\(307\) 2672.97 0.496920 0.248460 0.968642i \(-0.420076\pi\)
0.248460 + 0.968642i \(0.420076\pi\)
\(308\) 0 0
\(309\) 3904.95 0.718915
\(310\) 2255.41 + 3906.48i 0.413221 + 0.715721i
\(311\) −427.849 + 741.056i −0.0780099 + 0.135117i −0.902391 0.430918i \(-0.858190\pi\)
0.824381 + 0.566035i \(0.191523\pi\)
\(312\) −2027.05 + 3510.95i −0.367817 + 0.637078i
\(313\) −1674.99 2901.17i −0.302480 0.523911i 0.674217 0.738533i \(-0.264481\pi\)
−0.976697 + 0.214622i \(0.931148\pi\)
\(314\) 4405.81 0.791828
\(315\) 0 0
\(316\) 13112.8 2.33434
\(317\) −3816.53 6610.42i −0.676206 1.17122i −0.976115 0.217256i \(-0.930289\pi\)
0.299908 0.953968i \(-0.403044\pi\)
\(318\) −1381.27 + 2392.42i −0.243577 + 0.421888i
\(319\) 2843.58 4925.22i 0.499090 0.864450i
\(320\) −1938.31 3357.26i −0.338609 0.586488i
\(321\) 3103.30 0.539593
\(322\) 0 0
\(323\) −4271.64 −0.735852
\(324\) 3567.46 + 6179.01i 0.611704 + 1.05950i
\(325\) 891.656 1544.39i 0.152185 0.263592i
\(326\) 3379.95 5854.24i 0.574227 0.994591i
\(327\) 10.4698 + 18.1343i 0.00177059 + 0.00306676i
\(328\) 2064.91 0.347609
\(329\) 0 0
\(330\) 2129.55 0.355236
\(331\) 1660.85 + 2876.68i 0.275796 + 0.477693i 0.970336 0.241761i \(-0.0777251\pi\)
−0.694539 + 0.719455i \(0.744392\pi\)
\(332\) −3420.32 + 5924.16i −0.565405 + 0.979309i
\(333\) 309.931 536.817i 0.0510034 0.0883405i
\(334\) −2439.55 4225.43i −0.399660 0.692231i
\(335\) 421.980 0.0688216
\(336\) 0 0
\(337\) −2233.98 −0.361107 −0.180553 0.983565i \(-0.557789\pi\)
−0.180553 + 0.983565i \(0.557789\pi\)
\(338\) −6240.38 10808.7i −1.00424 1.73939i
\(339\) 3533.83 6120.77i 0.566168 0.980632i
\(340\) 832.916 1442.65i 0.132856 0.230114i
\(341\) −2062.13 3571.71i −0.327479 0.567211i
\(342\) 1176.99 0.186095
\(343\) 0 0
\(344\) −206.881 −0.0324252
\(345\) 1260.82 + 2183.80i 0.196754 + 0.340788i
\(346\) 5489.32 9507.78i 0.852912 1.47729i
\(347\) −1264.31 + 2189.84i −0.195595 + 0.338781i −0.947095 0.320952i \(-0.895997\pi\)
0.751500 + 0.659733i \(0.229330\pi\)
\(348\) −7661.20 13269.6i −1.18013 2.04404i
\(349\) −1291.00 −0.198011 −0.0990054 0.995087i \(-0.531566\pi\)
−0.0990054 + 0.995087i \(0.531566\pi\)
\(350\) 0 0
\(351\) −10343.2 −1.57288
\(352\) 2430.50 + 4209.75i 0.368029 + 0.637445i
\(353\) −3884.32 + 6727.84i −0.585670 + 1.01441i 0.409121 + 0.912480i \(0.365835\pi\)
−0.994792 + 0.101930i \(0.967498\pi\)
\(354\) −3482.06 + 6031.10i −0.522795 + 0.905507i
\(355\) −789.340 1367.18i −0.118011 0.204401i
\(356\) −12125.3 −1.80516
\(357\) 0 0
\(358\) −5225.92 −0.771504
\(359\) 1142.07 + 1978.12i 0.167900 + 0.290811i 0.937681 0.347496i \(-0.112968\pi\)
−0.769781 + 0.638308i \(0.779635\pi\)
\(360\) −56.8338 + 98.4389i −0.00832056 + 0.0144116i
\(361\) −5863.77 + 10156.4i −0.854902 + 1.48073i
\(362\) −6542.54 11332.0i −0.949912 1.64530i
\(363\) 4707.94 0.680725
\(364\) 0 0
\(365\) −5466.62 −0.783935
\(366\) −3679.95 6373.86i −0.525558 0.910292i
\(367\) 5353.50 9272.54i 0.761446 1.31886i −0.180660 0.983546i \(-0.557823\pi\)
0.942105 0.335317i \(-0.108843\pi\)
\(368\) −1815.58 + 3144.67i −0.257184 + 0.445455i
\(369\) 181.662 + 314.649i 0.0256286 + 0.0443901i
\(370\) −6689.29 −0.939891
\(371\) 0 0
\(372\) −11111.6 −1.54868
\(373\) 415.215 + 719.173i 0.0576381 + 0.0998321i 0.893405 0.449253i \(-0.148310\pi\)
−0.835767 + 0.549085i \(0.814976\pi\)
\(374\) −1334.48 + 2311.39i −0.184504 + 0.319570i
\(375\) −312.500 + 541.266i −0.0430331 + 0.0745356i
\(376\) −839.236 1453.60i −0.115107 0.199371i
\(377\) 20557.9 2.80845
\(378\) 0 0
\(379\) 5253.17 0.711972 0.355986 0.934491i \(-0.384145\pi\)
0.355986 + 0.934491i \(0.384145\pi\)
\(380\) −3624.14 6277.20i −0.489249 0.847404i
\(381\) −5115.66 + 8860.58i −0.687882 + 1.19145i
\(382\) 4680.60 8107.03i 0.626911 1.08584i
\(383\) −5621.95 9737.51i −0.750048 1.29912i −0.947799 0.318869i \(-0.896697\pi\)
0.197750 0.980252i \(-0.436636\pi\)
\(384\) 6880.63 0.914390
\(385\) 0 0
\(386\) 6433.84 0.848378
\(387\) −18.2005 31.5242i −0.00239066 0.00414074i
\(388\) 7507.03 13002.6i 0.982247 1.70130i
\(389\) 4253.43 7367.15i 0.554389 0.960230i −0.443562 0.896244i \(-0.646285\pi\)
0.997951 0.0639860i \(-0.0203813\pi\)
\(390\) 3848.95 + 6666.57i 0.499741 + 0.865576i
\(391\) −3160.37 −0.408764
\(392\) 0 0
\(393\) 5701.59 0.731824
\(394\) −7296.32 12637.6i −0.932952 1.61592i
\(395\) 3082.96 5339.85i 0.392711 0.680195i
\(396\) 209.831 363.438i 0.0266273 0.0461199i
\(397\) 1561.62 + 2704.80i 0.197419 + 0.341940i 0.947691 0.319190i \(-0.103411\pi\)
−0.750272 + 0.661130i \(0.770077\pi\)
\(398\) −19836.3 −2.49825
\(399\) 0 0
\(400\) −900.000 −0.112500
\(401\) 5627.67 + 9747.40i 0.700828 + 1.21387i 0.968176 + 0.250270i \(0.0805195\pi\)
−0.267348 + 0.963600i \(0.586147\pi\)
\(402\) −910.764 + 1577.49i −0.112997 + 0.195717i
\(403\) 7454.16 12911.0i 0.921385 1.59588i
\(404\) −2901.14 5024.92i −0.357270 0.618809i
\(405\) 3355.00 0.411633
\(406\) 0 0
\(407\) 6116.03 0.744866
\(408\) 890.372 + 1542.17i 0.108039 + 0.187129i
\(409\) −3959.96 + 6858.86i −0.478747 + 0.829214i −0.999703 0.0243694i \(-0.992242\pi\)
0.520956 + 0.853584i \(0.325576\pi\)
\(410\) 1960.42 3395.55i 0.236142 0.409010i
\(411\) −1225.86 2123.25i −0.147122 0.254822i
\(412\) −8304.46 −0.993037
\(413\) 0 0
\(414\) 870.797 0.103375
\(415\) 1608.31 + 2785.68i 0.190238 + 0.329503i
\(416\) −8785.76 + 15217.4i −1.03547 + 1.79349i
\(417\) −7000.00 + 12124.4i −0.822042 + 1.42382i
\(418\) 5806.55 + 10057.2i 0.679444 + 1.17683i
\(419\) 5257.28 0.612972 0.306486 0.951875i \(-0.400847\pi\)
0.306486 + 0.951875i \(0.400847\pi\)
\(420\) 0 0
\(421\) 1457.36 0.168711 0.0843556 0.996436i \(-0.473117\pi\)
0.0843556 + 0.996436i \(0.473117\pi\)
\(422\) 10767.1 + 18649.2i 1.24202 + 2.15125i
\(423\) 147.665 255.763i 0.0169733 0.0293987i
\(424\) 727.443 1259.97i 0.0833202 0.144315i
\(425\) −391.656 678.368i −0.0447014 0.0774252i
\(426\) 6814.57 0.775040
\(427\) 0 0
\(428\) −6599.63 −0.745339
\(429\) −3519.10 6095.26i −0.396046 0.685972i
\(430\) −196.412 + 340.195i −0.0220275 + 0.0381527i
\(431\) 7645.59 13242.6i 0.854467 1.47998i −0.0226716 0.999743i \(-0.507217\pi\)
0.877139 0.480237i \(-0.159449\pi\)
\(432\) 2610.00 + 4520.65i 0.290680 + 0.503472i
\(433\) −187.260 −0.0207832 −0.0103916 0.999946i \(-0.503308\pi\)
−0.0103916 + 0.999946i \(0.503308\pi\)
\(434\) 0 0
\(435\) −7204.95 −0.794140
\(436\) −22.2657 38.5653i −0.00244572 0.00423611i
\(437\) −6875.62 + 11908.9i −0.752644 + 1.30362i
\(438\) 11798.7 20435.9i 1.28713 2.22937i
\(439\) 1793.96 + 3107.23i 0.195037 + 0.337813i 0.946912 0.321491i \(-0.104184\pi\)
−0.751876 + 0.659305i \(0.770851\pi\)
\(440\) −1121.53 −0.121515
\(441\) 0 0
\(442\) −9647.76 −1.03823
\(443\) −2457.82 4257.08i −0.263600 0.456568i 0.703596 0.710600i \(-0.251577\pi\)
−0.967196 + 0.254032i \(0.918243\pi\)
\(444\) 8238.95 14270.3i 0.880638 1.52531i
\(445\) −2850.79 + 4937.72i −0.303687 + 0.526001i
\(446\) 8186.41 + 14179.3i 0.869143 + 1.50540i
\(447\) −5830.58 −0.616951
\(448\) 0 0
\(449\) 7091.12 0.745324 0.372662 0.927967i \(-0.378445\pi\)
0.372662 + 0.927967i \(0.378445\pi\)
\(450\) 107.916 + 186.915i 0.0113049 + 0.0195806i
\(451\) −1792.42 + 3104.56i −0.187143 + 0.324142i
\(452\) −7515.21 + 13016.7i −0.782048 + 1.35455i
\(453\) 2398.95 + 4155.11i 0.248814 + 0.430958i
\(454\) −16882.2 −1.74520
\(455\) 0 0
\(456\) 7748.29 0.795717
\(457\) −2525.91 4375.00i −0.258549 0.447820i 0.707304 0.706909i \(-0.249911\pi\)
−0.965853 + 0.259089i \(0.916578\pi\)
\(458\) 764.749 1324.58i 0.0780227 0.135139i
\(459\) −2271.61 + 3934.54i −0.231001 + 0.400106i
\(460\) −2681.32 4644.18i −0.271776 0.470731i
\(461\) 16681.3 1.68531 0.842653 0.538456i \(-0.180992\pi\)
0.842653 + 0.538456i \(0.180992\pi\)
\(462\) 0 0
\(463\) 15569.6 1.56280 0.781402 0.624027i \(-0.214505\pi\)
0.781402 + 0.624027i \(0.214505\pi\)
\(464\) −5187.56 8985.12i −0.519023 0.898974i
\(465\) −2612.47 + 4524.93i −0.260538 + 0.451266i
\(466\) −14012.8 + 24270.9i −1.39298 + 2.41272i
\(467\) 1664.18 + 2882.44i 0.164901 + 0.285617i 0.936620 0.350346i \(-0.113936\pi\)
−0.771719 + 0.635964i \(0.780603\pi\)
\(468\) 1516.99 0.149835
\(469\) 0 0
\(470\) −3187.07 −0.312784
\(471\) 2551.65 + 4419.59i 0.249626 + 0.432365i
\(472\) 1833.83 3176.28i 0.178832 0.309746i
\(473\) 179.580 311.041i 0.0174568 0.0302361i
\(474\) 13308.0 + 23050.1i 1.28957 + 2.23360i
\(475\) −3408.31 −0.329230
\(476\) 0 0
\(477\) 255.990 0.0245723
\(478\) 739.627 + 1281.07i 0.0707735 + 0.122583i
\(479\) −7303.75 + 12650.5i −0.696695 + 1.20671i 0.272911 + 0.962039i \(0.412014\pi\)
−0.969606 + 0.244672i \(0.921320\pi\)
\(480\) 3079.16 5333.25i 0.292799 0.507143i
\(481\) 11054.1 + 19146.3i 1.04787 + 1.81496i
\(482\) −9987.23 −0.943789
\(483\) 0 0
\(484\) −10012.2 −0.940285
\(485\) −3529.98 6114.11i −0.330491 0.572427i
\(486\) 1208.65 2093.45i 0.112810 0.195393i
\(487\) 939.744 1627.68i 0.0874412 0.151453i −0.818988 0.573811i \(-0.805464\pi\)
0.906429 + 0.422359i \(0.138798\pi\)
\(488\) 1938.05 + 3356.79i 0.179777 + 0.311383i
\(489\) 7830.08 0.724107
\(490\) 0 0
\(491\) 3221.13 0.296064 0.148032 0.988983i \(-0.452706\pi\)
0.148032 + 0.988983i \(0.452706\pi\)
\(492\) 4829.16 + 8364.34i 0.442511 + 0.766451i
\(493\) 4514.98 7820.18i 0.412464 0.714408i
\(494\) −20989.5 + 36354.8i −1.91166 + 3.31109i
\(495\) −98.6675 170.897i −0.00895914 0.0155177i
\(496\) −7523.91 −0.681116
\(497\) 0 0
\(498\) −13885.0 −1.24940
\(499\) −4856.91 8412.41i −0.435721 0.754692i 0.561633 0.827387i \(-0.310173\pi\)
−0.997354 + 0.0726950i \(0.976840\pi\)
\(500\) 664.578 1151.08i 0.0594417 0.102956i
\(501\) 2825.76 4894.36i 0.251988 0.436455i
\(502\) 8610.13 + 14913.2i 0.765516 + 1.32591i
\(503\) −2078.32 −0.184230 −0.0921152 0.995748i \(-0.529363\pi\)
−0.0921152 + 0.995748i \(0.529363\pi\)
\(504\) 0 0
\(505\) −2728.36 −0.240417
\(506\) 4295.97 + 7440.84i 0.377429 + 0.653726i
\(507\) 7228.31 12519.8i 0.633177 1.09669i
\(508\) 10879.2 18843.4i 0.950172 1.64575i
\(509\) −9487.23 16432.4i −0.826158 1.43095i −0.901031 0.433754i \(-0.857189\pi\)
0.0748736 0.997193i \(-0.476145\pi\)
\(510\) 3381.27 0.293578
\(511\) 0 0
\(512\) 12141.6 1.04802
\(513\) 9884.11 + 17119.8i 0.850670 + 1.47340i
\(514\) 4945.38 8565.66i 0.424380 0.735048i
\(515\) −1952.47 + 3381.79i −0.167061 + 0.289358i
\(516\) −483.826 838.012i −0.0412776 0.0714950i
\(517\) 2913.95 0.247883
\(518\) 0 0
\(519\) 12716.7 1.07553
\(520\) −2027.05 3510.95i −0.170946 0.296087i
\(521\) 8761.78 15175.9i 0.736777 1.27613i −0.217163 0.976135i \(-0.569680\pi\)
0.953939 0.299999i \(-0.0969865\pi\)
\(522\) −1244.04 + 2154.74i −0.104311 + 0.180672i
\(523\) 7609.29 + 13179.7i 0.636197 + 1.10193i 0.986260 + 0.165199i \(0.0528268\pi\)
−0.350063 + 0.936726i \(0.613840\pi\)
\(524\) −12125.3 −1.01087
\(525\) 0 0
\(526\) 27455.8 2.27591
\(527\) −3274.21 5671.09i −0.270639 0.468760i
\(528\) −1776.02 + 3076.15i −0.146385 + 0.253546i
\(529\) 996.576 1726.12i 0.0819081 0.141869i
\(530\) −1381.27 2392.42i −0.113204 0.196076i
\(531\) 645.330 0.0527400
\(532\) 0 0
\(533\) −12958.4 −1.05308
\(534\) −12305.8 21314.3i −0.997237 1.72726i
\(535\) −1551.65 + 2687.54i −0.125390 + 0.217182i
\(536\) 479.654 830.785i 0.0386528 0.0669486i
\(537\) −3026.62 5242.27i −0.243219 0.421267i
\(538\) 4279.26 0.342922
\(539\) 0 0
\(540\) −7709.11 −0.614346
\(541\) 7779.63 + 13474.7i 0.618249 + 1.07084i 0.989805 + 0.142428i \(0.0454909\pi\)
−0.371557 + 0.928410i \(0.621176\pi\)
\(542\) 1577.68 2732.62i 0.125031 0.216561i
\(543\) 7578.30 13126.0i 0.598924 1.03737i
\(544\) 3859.11 + 6684.17i 0.304150 + 0.526804i
\(545\) −20.9397 −0.00164579
\(546\) 0 0
\(547\) −8690.70 −0.679319 −0.339660 0.940548i \(-0.610312\pi\)
−0.339660 + 0.940548i \(0.610312\pi\)
\(548\) 2606.97 + 4515.40i 0.203219 + 0.351986i
\(549\) −341.003 + 590.634i −0.0265093 + 0.0459155i
\(550\) −1064.78 + 1844.25i −0.0825495 + 0.142980i
\(551\) −19645.4 34026.8i −1.51891 2.63083i
\(552\) 5732.56 0.442018
\(553\) 0 0
\(554\) −15274.9 −1.17143
\(555\) −3874.14 6710.21i −0.296303 0.513212i
\(556\) 14886.5 25784.3i 1.13549 1.96672i
\(557\) 3688.13 6388.03i 0.280559 0.485942i −0.690964 0.722889i \(-0.742814\pi\)
0.971522 + 0.236948i \(0.0761469\pi\)
\(558\) 902.164 + 1562.59i 0.0684438 + 0.118548i
\(559\) 1298.29 0.0982320
\(560\) 0 0
\(561\) −3091.50 −0.232662
\(562\) 10064.6 + 17432.5i 0.755429 + 1.30844i
\(563\) 6437.70 11150.4i 0.481913 0.834697i −0.517872 0.855458i \(-0.673276\pi\)
0.999784 + 0.0207610i \(0.00660892\pi\)
\(564\) 3925.40 6798.99i 0.293066 0.507605i
\(565\) 3533.83 + 6120.77i 0.263131 + 0.455757i
\(566\) 9086.28 0.674779
\(567\) 0 0
\(568\) −3588.89 −0.265117
\(569\) 6032.30 + 10448.2i 0.444441 + 0.769795i 0.998013 0.0630067i \(-0.0200689\pi\)
−0.553572 + 0.832801i \(0.686736\pi\)
\(570\) 7356.20 12741.3i 0.540557 0.936272i
\(571\) −11872.8 + 20564.3i −0.870158 + 1.50716i −0.00832580 + 0.999965i \(0.502650\pi\)
−0.861832 + 0.507193i \(0.830683\pi\)
\(572\) 7483.89 + 12962.5i 0.547058 + 0.947533i
\(573\) 10843.2 0.790542
\(574\) 0 0
\(575\) −2521.64 −0.182886
\(576\) −775.325 1342.90i −0.0560854 0.0971428i
\(577\) −4923.04 + 8526.95i −0.355197 + 0.615220i −0.987152 0.159786i \(-0.948920\pi\)
0.631954 + 0.775006i \(0.282253\pi\)
\(578\) 8484.92 14696.3i 0.610599 1.05759i
\(579\) 3726.20 + 6453.97i 0.267453 + 0.463243i
\(580\) 15322.4 1.09695
\(581\) 0 0
\(582\) 30475.2 2.17051
\(583\) 1262.89 + 2187.40i 0.0897148 + 0.155391i
\(584\) −6213.78 + 10762.6i −0.440287 + 0.762600i
\(585\) 356.662 617.758i 0.0252071 0.0436601i
\(586\) −14233.3 24652.9i −1.00337 1.73788i
\(587\) −10074.7 −0.708392 −0.354196 0.935171i \(-0.615245\pi\)
−0.354196 + 0.935171i \(0.615245\pi\)
\(588\) 0 0
\(589\) −28493.1 −1.99328
\(590\) −3482.06 6031.10i −0.242973 0.420842i
\(591\) 8451.42 14638.3i 0.588231 1.01885i
\(592\) 5578.77 9662.71i 0.387307 0.670836i
\(593\) −3693.62 6397.54i −0.255782 0.443028i 0.709325 0.704881i \(-0.249000\pi\)
−0.965108 + 0.261853i \(0.915666\pi\)
\(594\) 12351.4 0.853172
\(595\) 0 0
\(596\) 12399.6 0.852194
\(597\) −11488.3 19898.4i −0.787581 1.36413i
\(598\) −15529.0 + 26897.1i −1.06192 + 1.83930i
\(599\) −626.365 + 1084.90i −0.0427255 + 0.0740027i −0.886597 0.462542i \(-0.846937\pi\)
0.843872 + 0.536545i \(0.180271\pi\)
\(600\) 710.422 + 1230.49i 0.0483381 + 0.0837240i
\(601\) 1800.81 0.122224 0.0611120 0.998131i \(-0.480535\pi\)
0.0611120 + 0.998131i \(0.480535\pi\)
\(602\) 0 0
\(603\) 168.792 0.0113992
\(604\) −5101.73 8836.46i −0.343686 0.595282i
\(605\) −2353.97 + 4077.20i −0.158186 + 0.273986i
\(606\) 5888.66 10199.5i 0.394737 0.683704i
\(607\) 1248.53 + 2162.51i 0.0834863 + 0.144602i 0.904745 0.425953i \(-0.140061\pi\)
−0.821259 + 0.570556i \(0.806728\pi\)
\(608\) 33583.1 2.24009
\(609\) 0 0
\(610\) 7359.90 0.488514
\(611\) 5266.66 + 9122.12i 0.348717 + 0.603996i
\(612\) 333.166 577.061i 0.0220056 0.0381149i
\(613\) 9875.39 17104.7i 0.650674 1.12700i −0.332286 0.943179i \(-0.607820\pi\)
0.982960 0.183821i \(-0.0588468\pi\)
\(614\) −5769.10 9992.38i −0.379189 0.656775i
\(615\) 4541.56 0.297778
\(616\) 0 0
\(617\) 16797.4 1.09601 0.548004 0.836476i \(-0.315388\pi\)
0.548004 + 0.836476i \(0.315388\pi\)
\(618\) −8428.10 14597.9i −0.548589 0.950184i
\(619\) 13273.7 22990.7i 0.861897 1.49285i −0.00819917 0.999966i \(-0.502610\pi\)
0.870096 0.492883i \(-0.164057\pi\)
\(620\) 5555.81 9622.94i 0.359882 0.623333i
\(621\) 7312.75 + 12666.1i 0.472545 + 0.818472i
\(622\) 3693.73 0.238111
\(623\) 0 0
\(624\) −12839.8 −0.823727
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −7230.32 + 12523.3i −0.461632 + 0.799570i
\(627\) −6725.79 + 11649.4i −0.428393 + 0.741998i
\(628\) −5426.47 9398.91i −0.344808 0.597225i
\(629\) 9710.93 0.615580
\(630\) 0 0
\(631\) 5394.86 0.340358 0.170179 0.985413i \(-0.445565\pi\)
0.170179 + 0.985413i \(0.445565\pi\)
\(632\) −7008.66 12139.3i −0.441122 0.764046i
\(633\) −12471.7 + 21601.5i −0.783102 + 1.35637i
\(634\) −16474.5 + 28534.7i −1.03200 + 1.78747i
\(635\) −5115.66 8860.58i −0.319699 0.553735i
\(636\) 6805.01 0.424271
\(637\) 0 0
\(638\) −24549.3 −1.52338
\(639\) −315.736 546.871i −0.0195467 0.0338558i
\(640\) −3440.32 + 5958.80i −0.212485 + 0.368035i
\(641\) −1226.20 + 2123.85i −0.0755572 + 0.130869i −0.901328 0.433136i \(-0.857407\pi\)
0.825771 + 0.564005i \(0.190740\pi\)
\(642\) −6697.89 11601.1i −0.411752 0.713175i
\(643\) −7074.97 −0.433919 −0.216959 0.976181i \(-0.569614\pi\)
−0.216959 + 0.976181i \(0.569614\pi\)
\(644\) 0 0
\(645\) −455.013 −0.0277769
\(646\) 9219.53 + 15968.7i 0.561513 + 0.972569i
\(647\) 1670.69 2893.71i 0.101517 0.175832i −0.810793 0.585333i \(-0.800964\pi\)
0.912310 + 0.409501i \(0.134297\pi\)
\(648\) 3813.54 6605.25i 0.231189 0.400430i
\(649\) 3183.65 + 5514.25i 0.192557 + 0.333518i
\(650\) −7697.89 −0.464517
\(651\) 0 0
\(652\) −16651.8 −1.00021
\(653\) 11530.8 + 19971.9i 0.691019 + 1.19688i 0.971504 + 0.237022i \(0.0761712\pi\)
−0.280486 + 0.959858i \(0.590495\pi\)
\(654\) 45.1944 78.2790i 0.00270220 0.00468035i
\(655\) −2850.79 + 4937.72i −0.170061 + 0.294554i
\(656\) 3269.92 + 5663.68i 0.194618 + 0.337087i
\(657\) −2186.65 −0.129847
\(658\) 0 0
\(659\) 1742.64 0.103010 0.0515049 0.998673i \(-0.483598\pi\)
0.0515049 + 0.998673i \(0.483598\pi\)
\(660\) −2622.89 4542.98i −0.154691 0.267932i
\(661\) −6288.26 + 10891.6i −0.370023 + 0.640898i −0.989569 0.144062i \(-0.953983\pi\)
0.619546 + 0.784960i \(0.287317\pi\)
\(662\) 7169.27 12417.5i 0.420909 0.729035i
\(663\) −5587.56 9677.94i −0.327305 0.566908i
\(664\) 7312.51 0.427380
\(665\) 0 0
\(666\) −2675.72 −0.155679
\(667\) −14534.6 25174.7i −0.843752 1.46142i
\(668\) −6009.41 + 10408.6i −0.348070 + 0.602875i
\(669\) −9482.42 + 16424.0i −0.548000 + 0.949163i
\(670\) −910.764 1577.49i −0.0525163 0.0909608i
\(671\) −6729.17 −0.387149
\(672\) 0 0
\(673\) −10680.8 −0.611760 −0.305880 0.952070i \(-0.598951\pi\)
−0.305880 + 0.952070i \(0.598951\pi\)
\(674\) 4821.64 + 8351.32i 0.275553 + 0.477271i
\(675\) −1812.50 + 3139.34i −0.103353 + 0.179012i
\(676\) −15372.1 + 26625.2i −0.874607 + 1.51486i
\(677\) −14779.6 25599.0i −0.839032 1.45325i −0.890705 0.454582i \(-0.849789\pi\)
0.0516726 0.998664i \(-0.483545\pi\)
\(678\) −30508.4 −1.72812
\(679\) 0 0
\(680\) −1780.74 −0.100424
\(681\) −9777.41 16935.0i −0.550178 0.952936i
\(682\) −8901.42 + 15417.7i −0.499785 + 0.865652i
\(683\) −5125.21 + 8877.13i −0.287132 + 0.497327i −0.973124 0.230282i \(-0.926035\pi\)
0.685992 + 0.727609i \(0.259368\pi\)
\(684\) −1449.66 2510.88i −0.0810366 0.140360i
\(685\) 2451.71 0.136752
\(686\) 0 0
\(687\) 1771.64 0.0983875
\(688\) −327.609 567.436i −0.0181540 0.0314437i
\(689\) −4565.10 + 7906.99i −0.252419 + 0.437202i
\(690\) 5442.48 9426.65i 0.300278 0.520096i
\(691\) −4437.02 7685.14i −0.244272 0.423092i 0.717655 0.696399i \(-0.245216\pi\)
−0.961927 + 0.273307i \(0.911882\pi\)
\(692\) −27043.9 −1.48563
\(693\) 0 0
\(694\) 10915.1 0.597018
\(695\) −7000.00 12124.4i −0.382051 0.661731i
\(696\) −8189.69 + 14185.0i −0.446019 + 0.772528i
\(697\) −2845.97 + 4929.36i −0.154661 + 0.267881i
\(698\) 2786.39 + 4826.16i 0.151098 + 0.261709i
\(699\) −32462.4 −1.75657
\(700\) 0 0
\(701\) −22086.2 −1.18999 −0.594996 0.803729i \(-0.702846\pi\)
−0.594996 + 0.803729i \(0.702846\pi\)
\(702\) 22323.9 + 38666.1i 1.20023 + 2.07886i
\(703\) 21126.9 36592.8i 1.13345 1.96319i
\(704\) 7649.94 13250.1i 0.409542 0.709348i
\(705\) −1845.81 3197.04i −0.0986061 0.170791i
\(706\) 33534.3 1.78765
\(707\) 0 0
\(708\) 17154.9 0.910622
\(709\) 13939.4 + 24143.8i 0.738373 + 1.27890i 0.953228 + 0.302254i \(0.0977390\pi\)
−0.214854 + 0.976646i \(0.568928\pi\)
\(710\) −3407.28 + 5901.59i −0.180103 + 0.311948i
\(711\) 1233.19 2135.94i 0.0650465 0.112664i
\(712\) 6480.85 + 11225.2i 0.341124 + 0.590844i
\(713\) −21080.6 −1.10726
\(714\) 0 0
\(715\) 7038.20 0.368131
\(716\) 6436.57 + 11148.5i 0.335958 + 0.581896i
\(717\) −856.719 + 1483.88i −0.0446231 + 0.0772895i
\(718\) 4929.88 8538.80i 0.256242 0.443824i
\(719\) 12931.6 + 22398.3i 0.670750 + 1.16177i 0.977692 + 0.210044i \(0.0673608\pi\)
−0.306942 + 0.951728i \(0.599306\pi\)
\(720\) −360.000 −0.0186339
\(721\) 0 0
\(722\) 50623.4 2.60943
\(723\) −5784.17 10018.5i −0.297532 0.515340i
\(724\) −16116.4 + 27914.4i −0.827294 + 1.43292i
\(725\) 3602.47 6239.67i 0.184541 0.319635i
\(726\) −10161.2 17599.7i −0.519446 0.899708i
\(727\) −29157.0 −1.48744 −0.743722 0.668489i \(-0.766941\pi\)
−0.743722 + 0.668489i \(0.766941\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 11798.7 + 20435.9i 0.598204 + 1.03612i
\(731\) 285.134 493.866i 0.0144269 0.0249881i
\(732\) −9064.91 + 15700.9i −0.457717 + 0.792789i
\(733\) 5503.03 + 9531.52i 0.277297 + 0.480293i 0.970712 0.240246i \(-0.0772280\pi\)
−0.693415 + 0.720539i \(0.743895\pi\)
\(734\) −46218.1 −2.32417
\(735\) 0 0
\(736\) 24846.4 1.24436
\(737\) 832.714 + 1442.30i 0.0416193 + 0.0720867i
\(738\) 784.169 1358.22i 0.0391133 0.0677463i
\(739\) 18607.2 32228.6i 0.926221 1.60426i 0.136634 0.990622i \(-0.456371\pi\)
0.789586 0.613640i \(-0.210295\pi\)
\(740\) 8238.95 + 14270.3i 0.409283 + 0.708900i
\(741\) −48624.7 −2.41062
\(742\) 0 0
\(743\) 11214.5 0.553730 0.276865 0.960909i \(-0.410704\pi\)
0.276865 + 0.960909i \(0.410704\pi\)
\(744\) 5939.06 + 10286.7i 0.292656 + 0.506896i
\(745\) 2915.29 5049.43i 0.143367 0.248318i
\(746\) 1792.33 3104.40i 0.0879648 0.152359i
\(747\) 643.325 + 1114.27i 0.0315101 + 0.0545771i
\(748\) 6574.54 0.321375
\(749\) 0 0
\(750\) 2697.89 0.131351
\(751\) −3482.63 6032.09i −0.169218 0.293095i 0.768927 0.639337i \(-0.220791\pi\)
−0.938145 + 0.346242i \(0.887458\pi\)
\(752\) 2657.97 4603.74i 0.128891 0.223246i
\(753\) −9973.22 + 17274.1i −0.482662 + 0.835995i
\(754\) −44370.3 76851.7i −2.14307 3.71190i
\(755\) −4797.91 −0.231276
\(756\) 0 0
\(757\) −19352.8 −0.929180 −0.464590 0.885526i \(-0.653798\pi\)
−0.464590 + 0.885526i \(0.653798\pi\)
\(758\) −11338.0 19638.0i −0.543291 0.941007i
\(759\) −4976.07 + 8618.81i −0.237971 + 0.412178i
\(760\) −3874.14 + 6710.21i −0.184908 + 0.320270i
\(761\) 16191.8 + 28045.0i 0.771291 + 1.33591i 0.936856 + 0.349716i \(0.113722\pi\)
−0.165565 + 0.986199i \(0.552945\pi\)
\(762\) 44164.8 2.09963
\(763\) 0 0
\(764\) −23059.7 −1.09198
\(765\) −156.662 271.347i −0.00740411 0.0128243i
\(766\) −24267.9 + 42033.2i −1.14469 + 1.98266i
\(767\) −11508.2 + 19932.9i −0.541772 + 0.938376i
\(768\) 655.940 + 1136.12i 0.0308193 + 0.0533805i
\(769\) 25353.9 1.18893 0.594463 0.804123i \(-0.297365\pi\)
0.594463 + 0.804123i \(0.297365\pi\)
\(770\) 0 0
\(771\) 11456.6 0.535148
\(772\) −7924.32 13725.3i −0.369433 0.639877i
\(773\) 13058.5 22618.0i 0.607610 1.05241i −0.384023 0.923323i \(-0.625462\pi\)
0.991633 0.129088i \(-0.0412049\pi\)
\(774\) −78.5647 + 136.078i −0.00364852 + 0.00631941i
\(775\) −2612.47 4524.93i −0.121087 0.209729i
\(776\) −16049.8 −0.742465
\(777\) 0 0
\(778\) −36720