Properties

Label 225.4.e.e.76.7
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.7
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.e.151.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.238017 + 0.412258i) q^{2} +(-3.09012 + 4.17746i) q^{3} +(3.88670 - 6.73195i) q^{4} +(-2.45769 - 0.279619i) q^{6} +(6.34045 + 10.9820i) q^{7} +7.50869 q^{8} +(-7.90234 - 25.8177i) q^{9} +O(q^{10})\) \(q+(0.238017 + 0.412258i) q^{2} +(-3.09012 + 4.17746i) q^{3} +(3.88670 - 6.73195i) q^{4} +(-2.45769 - 0.279619i) q^{6} +(6.34045 + 10.9820i) q^{7} +7.50869 q^{8} +(-7.90234 - 25.8177i) q^{9} +(0.794994 + 1.37697i) q^{11} +(16.1121 + 37.0390i) q^{12} +(5.36718 - 9.29622i) q^{13} +(-3.01828 + 5.22781i) q^{14} +(-29.3064 - 50.7601i) q^{16} +69.7787 q^{17} +(8.76266 - 9.40287i) q^{18} +98.5661 q^{19} +(-65.4695 - 7.44864i) q^{21} +(-0.378445 + 0.655486i) q^{22} +(-15.7777 + 27.3278i) q^{23} +(-23.2027 + 31.3672i) q^{24} +5.10993 q^{26} +(132.272 + 46.7680i) q^{27} +98.5736 q^{28} +(150.627 + 260.893i) q^{29} +(58.6364 - 101.561i) q^{31} +(43.9856 - 76.1853i) q^{32} +(-8.20886 - 0.933944i) q^{33} +(16.6086 + 28.7669i) q^{34} +(-204.517 - 47.1473i) q^{36} +169.562 q^{37} +(23.4605 + 40.6347i) q^{38} +(22.2494 + 51.1476i) q^{39} +(-70.9376 + 122.868i) q^{41} +(-12.5121 - 28.7633i) q^{42} +(150.121 + 260.018i) q^{43} +12.3596 q^{44} -15.0215 q^{46} +(243.712 + 422.122i) q^{47} +(302.608 + 34.4286i) q^{48} +(91.0974 - 157.785i) q^{49} +(-215.625 + 291.498i) q^{51} +(-41.7212 - 72.2632i) q^{52} -459.166 q^{53} +(12.2024 + 65.6616i) q^{54} +(47.6084 + 82.4602i) q^{56} +(-304.581 + 411.756i) q^{57} +(-71.7037 + 124.194i) q^{58} +(250.099 - 433.185i) q^{59} +(-290.915 - 503.880i) q^{61} +55.8259 q^{62} +(233.425 - 250.479i) q^{63} -427.024 q^{64} +(-1.56883 - 3.60647i) q^{66} +(250.468 - 433.823i) q^{67} +(271.209 - 469.747i) q^{68} +(-65.4059 - 150.357i) q^{69} +1066.69 q^{71} +(-59.3362 - 193.857i) q^{72} -435.288 q^{73} +(40.3588 + 69.9034i) q^{74} +(383.096 - 663.542i) q^{76} +(-10.0812 + 17.4612i) q^{77} +(-15.7903 + 21.3465i) q^{78} +(-187.644 - 325.009i) q^{79} +(-604.106 + 408.040i) q^{81} -67.5375 q^{82} +(-646.617 - 1119.97i) q^{83} +(-304.604 + 411.787i) q^{84} +(-71.4630 + 123.778i) q^{86} +(-1555.33 - 176.954i) q^{87} +(5.96936 + 10.3392i) q^{88} -403.296 q^{89} +136.121 q^{91} +(122.646 + 212.430i) q^{92} +(243.074 + 558.787i) q^{93} +(-116.016 + 200.945i) q^{94} +(182.340 + 419.170i) q^{96} +(-790.735 - 1369.59i) q^{97} +86.7311 q^{98} +(29.2679 - 31.4062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9} - 29 q^{11} - 77 q^{12} + 24 q^{13} + 69 q^{14} - 192 q^{16} + 158 q^{17} + 125 q^{18} - 150 q^{19} - 60 q^{21} - 18 q^{22} - 318 q^{23} + 342 q^{24} - 308 q^{26} - 394 q^{27} - 192 q^{28} - 106 q^{29} - 60 q^{31} - 914 q^{32} - 80 q^{33} + 108 q^{34} + 1303 q^{36} + 168 q^{37} - 640 q^{38} - 410 q^{39} + 353 q^{41} + 1521 q^{42} - 426 q^{43} + 1142 q^{44} + 540 q^{46} - 1210 q^{47} + 2680 q^{48} - 666 q^{49} - 1369 q^{51} - 75 q^{52} + 896 q^{53} - 2128 q^{54} + 570 q^{56} + 1544 q^{57} + 594 q^{58} - 482 q^{59} - 402 q^{61} + 5088 q^{62} - 1038 q^{63} + 1950 q^{64} + 2041 q^{66} - 201 q^{67} - 3437 q^{68} + 2856 q^{69} - 1888 q^{71} - 5493 q^{72} + 906 q^{73} - 10 q^{74} + 462 q^{76} - 2652 q^{77} - 4589 q^{78} - 258 q^{79} + 3071 q^{81} - 1746 q^{82} - 3012 q^{83} - 2703 q^{84} - 1952 q^{86} + 2708 q^{87} - 216 q^{88} - 1476 q^{89} - 1236 q^{91} - 5232 q^{92} + 3024 q^{93} - 63 q^{94} - 10424 q^{96} - 318 q^{97} + 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.238017 + 0.412258i 0.0841519 + 0.145755i 0.905030 0.425349i \(-0.139849\pi\)
−0.820878 + 0.571104i \(0.806515\pi\)
\(3\) −3.09012 + 4.17746i −0.594694 + 0.803953i
\(4\) 3.88670 6.73195i 0.485837 0.841494i
\(5\) 0 0
\(6\) −2.45769 0.279619i −0.167225 0.0190256i
\(7\) 6.34045 + 10.9820i 0.342352 + 0.592971i 0.984869 0.173300i \(-0.0554431\pi\)
−0.642517 + 0.766271i \(0.722110\pi\)
\(8\) 7.50869 0.331840
\(9\) −7.90234 25.8177i −0.292679 0.956211i
\(10\) 0 0
\(11\) 0.794994 + 1.37697i 0.0217909 + 0.0377429i 0.876715 0.481010i \(-0.159730\pi\)
−0.854924 + 0.518753i \(0.826397\pi\)
\(12\) 16.1121 + 37.0390i 0.387597 + 0.891021i
\(13\) 5.36718 9.29622i 0.114507 0.198331i −0.803076 0.595877i \(-0.796805\pi\)
0.917582 + 0.397546i \(0.130138\pi\)
\(14\) −3.01828 + 5.22781i −0.0576191 + 0.0997993i
\(15\) 0 0
\(16\) −29.3064 50.7601i −0.457912 0.793127i
\(17\) 69.7787 0.995519 0.497760 0.867315i \(-0.334156\pi\)
0.497760 + 0.867315i \(0.334156\pi\)
\(18\) 8.76266 9.40287i 0.114743 0.123127i
\(19\) 98.5661 1.19014 0.595069 0.803675i \(-0.297125\pi\)
0.595069 + 0.803675i \(0.297125\pi\)
\(20\) 0 0
\(21\) −65.4695 7.44864i −0.680315 0.0774013i
\(22\) −0.378445 + 0.655486i −0.00366749 + 0.00635227i
\(23\) −15.7777 + 27.3278i −0.143038 + 0.247750i −0.928639 0.370984i \(-0.879021\pi\)
0.785601 + 0.618734i \(0.212354\pi\)
\(24\) −23.2027 + 31.3672i −0.197343 + 0.266784i
\(25\) 0 0
\(26\) 5.10993 0.0385438
\(27\) 132.272 + 46.7680i 0.942802 + 0.333352i
\(28\) 98.5736 0.665309
\(29\) 150.627 + 260.893i 0.964507 + 1.67058i 0.710933 + 0.703260i \(0.248273\pi\)
0.253574 + 0.967316i \(0.418394\pi\)
\(30\) 0 0
\(31\) 58.6364 101.561i 0.339723 0.588417i −0.644658 0.764471i \(-0.723000\pi\)
0.984380 + 0.176054i \(0.0563334\pi\)
\(32\) 43.9856 76.1853i 0.242988 0.420868i
\(33\) −8.20886 0.933944i −0.0433024 0.00492663i
\(34\) 16.6086 + 28.7669i 0.0837748 + 0.145102i
\(35\) 0 0
\(36\) −204.517 47.1473i −0.946840 0.218275i
\(37\) 169.562 0.753402 0.376701 0.926335i \(-0.377059\pi\)
0.376701 + 0.926335i \(0.377059\pi\)
\(38\) 23.4605 + 40.6347i 0.100152 + 0.173469i
\(39\) 22.2494 + 51.1476i 0.0913526 + 0.210004i
\(40\) 0 0
\(41\) −70.9376 + 122.868i −0.270210 + 0.468017i −0.968915 0.247392i \(-0.920426\pi\)
0.698706 + 0.715409i \(0.253760\pi\)
\(42\) −12.5121 28.7633i −0.0459682 0.105673i
\(43\) 150.121 + 260.018i 0.532402 + 0.922147i 0.999284 + 0.0378277i \(0.0120438\pi\)
−0.466882 + 0.884319i \(0.654623\pi\)
\(44\) 12.3596 0.0423472
\(45\) 0 0
\(46\) −15.0215 −0.0481478
\(47\) 243.712 + 422.122i 0.756364 + 1.31006i 0.944694 + 0.327954i \(0.106359\pi\)
−0.188330 + 0.982106i \(0.560307\pi\)
\(48\) 302.608 + 34.4286i 0.909953 + 0.103528i
\(49\) 91.0974 157.785i 0.265590 0.460016i
\(50\) 0 0
\(51\) −215.625 + 291.498i −0.592029 + 0.800350i
\(52\) −41.7212 72.2632i −0.111263 0.192713i
\(53\) −459.166 −1.19002 −0.595012 0.803717i \(-0.702853\pi\)
−0.595012 + 0.803717i \(0.702853\pi\)
\(54\) 12.2024 + 65.6616i 0.0307508 + 0.165471i
\(55\) 0 0
\(56\) 47.6084 + 82.4602i 0.113606 + 0.196772i
\(57\) −304.581 + 411.756i −0.707767 + 0.956814i
\(58\) −71.7037 + 124.194i −0.162330 + 0.281164i
\(59\) 250.099 433.185i 0.551867 0.955862i −0.446273 0.894897i \(-0.647249\pi\)
0.998140 0.0609650i \(-0.0194178\pi\)
\(60\) 0 0
\(61\) −290.915 503.880i −0.610621 1.05763i −0.991136 0.132852i \(-0.957587\pi\)
0.380515 0.924775i \(-0.375747\pi\)
\(62\) 55.8259 0.114353
\(63\) 233.425 250.479i 0.466806 0.500911i
\(64\) −427.024 −0.834032
\(65\) 0 0
\(66\) −1.56883 3.60647i −0.00292589 0.00672614i
\(67\) 250.468 433.823i 0.456709 0.791044i −0.542075 0.840330i \(-0.682361\pi\)
0.998785 + 0.0492862i \(0.0156946\pi\)
\(68\) 271.209 469.747i 0.483660 0.837724i
\(69\) −65.4059 150.357i −0.114115 0.262331i
\(70\) 0 0
\(71\) 1066.69 1.78299 0.891495 0.453031i \(-0.149657\pi\)
0.891495 + 0.453031i \(0.149657\pi\)
\(72\) −59.3362 193.857i −0.0971227 0.317309i
\(73\) −435.288 −0.697899 −0.348950 0.937141i \(-0.613462\pi\)
−0.348950 + 0.937141i \(0.613462\pi\)
\(74\) 40.3588 + 69.9034i 0.0634002 + 0.109812i
\(75\) 0 0
\(76\) 383.096 663.542i 0.578213 1.00149i
\(77\) −10.0812 + 17.4612i −0.0149203 + 0.0258427i
\(78\) −15.7903 + 21.3465i −0.0229218 + 0.0309874i
\(79\) −187.644 325.009i −0.267236 0.462866i 0.700911 0.713248i \(-0.252777\pi\)
−0.968147 + 0.250383i \(0.919444\pi\)
\(80\) 0 0
\(81\) −604.106 + 408.040i −0.828678 + 0.559726i
\(82\) −67.5375 −0.0909546
\(83\) −646.617 1119.97i −0.855126 1.48112i −0.876528 0.481351i \(-0.840146\pi\)
0.0214014 0.999771i \(-0.493187\pi\)
\(84\) −304.604 + 411.787i −0.395655 + 0.534877i
\(85\) 0 0
\(86\) −71.4630 + 123.778i −0.0896053 + 0.155201i
\(87\) −1555.33 176.954i −1.91665 0.218062i
\(88\) 5.96936 + 10.3392i 0.00723109 + 0.0125246i
\(89\) −403.296 −0.480330 −0.240165 0.970732i \(-0.577201\pi\)
−0.240165 + 0.970732i \(0.577201\pi\)
\(90\) 0 0
\(91\) 136.121 0.156806
\(92\) 122.646 + 212.430i 0.138987 + 0.240732i
\(93\) 243.074 + 558.787i 0.271028 + 0.623049i
\(94\) −116.016 + 200.945i −0.127299 + 0.220488i
\(95\) 0 0
\(96\) 182.340 + 419.170i 0.193854 + 0.445639i
\(97\) −790.735 1369.59i −0.827700 1.43362i −0.899838 0.436225i \(-0.856315\pi\)
0.0721373 0.997395i \(-0.477018\pi\)
\(98\) 86.7311 0.0893996
\(99\) 29.2679 31.4062i 0.0297124 0.0318832i
\(100\) 0 0
\(101\) 577.422 + 1000.12i 0.568867 + 0.985307i 0.996678 + 0.0814388i \(0.0259515\pi\)
−0.427811 + 0.903868i \(0.640715\pi\)
\(102\) −171.495 19.5114i −0.166476 0.0189404i
\(103\) −725.615 + 1256.80i −0.694145 + 1.20229i 0.276323 + 0.961065i \(0.410884\pi\)
−0.970468 + 0.241230i \(0.922449\pi\)
\(104\) 40.3004 69.8024i 0.0379979 0.0658143i
\(105\) 0 0
\(106\) −109.290 189.295i −0.100143 0.173452i
\(107\) −136.728 −0.123533 −0.0617664 0.998091i \(-0.519673\pi\)
−0.0617664 + 0.998091i \(0.519673\pi\)
\(108\) 828.939 708.673i 0.738562 0.631408i
\(109\) 40.1176 0.0352529 0.0176265 0.999845i \(-0.494389\pi\)
0.0176265 + 0.999845i \(0.494389\pi\)
\(110\) 0 0
\(111\) −523.967 + 708.339i −0.448043 + 0.605699i
\(112\) 371.631 643.684i 0.313534 0.543057i
\(113\) −989.231 + 1713.40i −0.823531 + 1.42640i 0.0795054 + 0.996834i \(0.474666\pi\)
−0.903037 + 0.429564i \(0.858667\pi\)
\(114\) −242.245 27.5609i −0.199021 0.0226431i
\(115\) 0 0
\(116\) 2341.76 1.87437
\(117\) −282.420 65.1062i −0.223160 0.0514450i
\(118\) 238.112 0.185763
\(119\) 442.428 + 766.309i 0.340818 + 0.590314i
\(120\) 0 0
\(121\) 664.236 1150.49i 0.499050 0.864381i
\(122\) 138.486 239.865i 0.102770 0.178003i
\(123\) −294.069 676.014i −0.215571 0.495562i
\(124\) −455.804 789.475i −0.330100 0.571750i
\(125\) 0 0
\(126\) 158.821 + 36.6130i 0.112293 + 0.0258869i
\(127\) −1318.35 −0.921142 −0.460571 0.887623i \(-0.652355\pi\)
−0.460571 + 0.887623i \(0.652355\pi\)
\(128\) −453.524 785.527i −0.313174 0.542433i
\(129\) −1550.11 176.360i −1.05798 0.120369i
\(130\) 0 0
\(131\) −792.463 + 1372.59i −0.528533 + 0.915446i 0.470913 + 0.882179i \(0.343924\pi\)
−0.999447 + 0.0332667i \(0.989409\pi\)
\(132\) −38.1926 + 51.6317i −0.0251836 + 0.0340452i
\(133\) 624.953 + 1082.45i 0.407446 + 0.705717i
\(134\) 238.463 0.153732
\(135\) 0 0
\(136\) 523.947 0.330353
\(137\) 190.760 + 330.406i 0.118961 + 0.206047i 0.919356 0.393426i \(-0.128710\pi\)
−0.800395 + 0.599473i \(0.795377\pi\)
\(138\) 46.4182 62.7517i 0.0286332 0.0387086i
\(139\) 1231.19 2132.49i 0.751283 1.30126i −0.195918 0.980620i \(-0.562769\pi\)
0.947201 0.320641i \(-0.103898\pi\)
\(140\) 0 0
\(141\) −2516.50 286.309i −1.50303 0.171004i
\(142\) 253.890 + 439.750i 0.150042 + 0.259880i
\(143\) 17.0675 0.00998080
\(144\) −1078.92 + 1157.75i −0.624375 + 0.669992i
\(145\) 0 0
\(146\) −103.606 179.451i −0.0587295 0.101723i
\(147\) 377.640 + 868.131i 0.211886 + 0.487090i
\(148\) 659.037 1141.48i 0.366030 0.633983i
\(149\) −192.172 + 332.852i −0.105660 + 0.183008i −0.914008 0.405697i \(-0.867029\pi\)
0.808348 + 0.588705i \(0.200362\pi\)
\(150\) 0 0
\(151\) −398.550 690.308i −0.214792 0.372030i 0.738417 0.674345i \(-0.235574\pi\)
−0.953208 + 0.302315i \(0.902241\pi\)
\(152\) 740.102 0.394935
\(153\) −551.415 1801.53i −0.291368 0.951926i
\(154\) −9.59804 −0.00502229
\(155\) 0 0
\(156\) 430.800 + 49.0133i 0.221100 + 0.0251551i
\(157\) −435.496 + 754.300i −0.221378 + 0.383438i −0.955227 0.295875i \(-0.904389\pi\)
0.733849 + 0.679313i \(0.237722\pi\)
\(158\) 89.3252 154.716i 0.0449768 0.0779021i
\(159\) 1418.88 1918.15i 0.707700 0.956723i
\(160\) 0 0
\(161\) −400.152 −0.195878
\(162\) −312.006 151.927i −0.151318 0.0736822i
\(163\) 31.2604 0.0150215 0.00751074 0.999972i \(-0.497609\pi\)
0.00751074 + 0.999972i \(0.497609\pi\)
\(164\) 551.426 + 955.097i 0.262556 + 0.454759i
\(165\) 0 0
\(166\) 307.813 533.147i 0.143921 0.249278i
\(167\) −18.6415 + 32.2881i −0.00863787 + 0.0149612i −0.870312 0.492501i \(-0.836083\pi\)
0.861674 + 0.507462i \(0.169416\pi\)
\(168\) −491.590 55.9295i −0.225756 0.0256849i
\(169\) 1040.89 + 1802.87i 0.473776 + 0.820605i
\(170\) 0 0
\(171\) −778.903 2544.75i −0.348329 1.13802i
\(172\) 2333.90 1.03464
\(173\) −590.590 1022.93i −0.259548 0.449550i 0.706573 0.707640i \(-0.250240\pi\)
−0.966121 + 0.258090i \(0.916907\pi\)
\(174\) −297.244 683.315i −0.129506 0.297712i
\(175\) 0 0
\(176\) 46.5967 80.7079i 0.0199566 0.0345658i
\(177\) 1036.78 + 2383.37i 0.440276 + 1.01212i
\(178\) −95.9916 166.262i −0.0404206 0.0700106i
\(179\) −429.484 −0.179336 −0.0896680 0.995972i \(-0.528581\pi\)
−0.0896680 + 0.995972i \(0.528581\pi\)
\(180\) 0 0
\(181\) −1787.97 −0.734246 −0.367123 0.930172i \(-0.619657\pi\)
−0.367123 + 0.930172i \(0.619657\pi\)
\(182\) 32.3992 + 56.1171i 0.0131956 + 0.0228554i
\(183\) 3003.90 + 341.762i 1.21341 + 0.138053i
\(184\) −118.470 + 205.196i −0.0474659 + 0.0822134i
\(185\) 0 0
\(186\) −172.509 + 233.211i −0.0680051 + 0.0919346i
\(187\) 55.4736 + 96.0832i 0.0216932 + 0.0375738i
\(188\) 3788.94 1.46988
\(189\) 325.056 + 1749.13i 0.125102 + 0.673178i
\(190\) 0 0
\(191\) −392.583 679.974i −0.148724 0.257598i 0.782032 0.623238i \(-0.214183\pi\)
−0.930756 + 0.365640i \(0.880850\pi\)
\(192\) 1319.56 1783.88i 0.495994 0.670522i
\(193\) −238.539 + 413.162i −0.0889659 + 0.154093i −0.907074 0.420971i \(-0.861690\pi\)
0.818108 + 0.575064i \(0.195023\pi\)
\(194\) 376.417 651.974i 0.139305 0.241284i
\(195\) 0 0
\(196\) −708.136 1226.53i −0.258067 0.446985i
\(197\) 4628.37 1.67390 0.836949 0.547281i \(-0.184337\pi\)
0.836949 + 0.547281i \(0.184337\pi\)
\(198\) 19.9137 + 4.59070i 0.00714751 + 0.00164771i
\(199\) 2533.85 0.902611 0.451305 0.892370i \(-0.350958\pi\)
0.451305 + 0.892370i \(0.350958\pi\)
\(200\) 0 0
\(201\) 1038.30 + 2386.88i 0.364359 + 0.837601i
\(202\) −274.873 + 476.094i −0.0957425 + 0.165831i
\(203\) −1910.08 + 3308.36i −0.660402 + 1.14385i
\(204\) 1124.28 + 2584.54i 0.385861 + 0.887029i
\(205\) 0 0
\(206\) −690.836 −0.233654
\(207\) 830.222 + 191.391i 0.278765 + 0.0642636i
\(208\) −629.170 −0.209736
\(209\) 78.3594 + 135.722i 0.0259341 + 0.0449192i
\(210\) 0 0
\(211\) −1382.70 + 2394.90i −0.451131 + 0.781382i −0.998457 0.0555378i \(-0.982313\pi\)
0.547325 + 0.836920i \(0.315646\pi\)
\(212\) −1784.64 + 3091.08i −0.578158 + 1.00140i
\(213\) −3296.18 + 4456.03i −1.06033 + 1.43344i
\(214\) −32.5437 56.3673i −0.0103955 0.0180056i
\(215\) 0 0
\(216\) 993.185 + 351.166i 0.312860 + 0.110620i
\(217\) 1487.12 0.465219
\(218\) 9.54869 + 16.5388i 0.00296660 + 0.00513830i
\(219\) 1345.09 1818.40i 0.415036 0.561078i
\(220\) 0 0
\(221\) 374.515 648.679i 0.113994 0.197443i
\(222\) −416.732 47.4128i −0.125988 0.0143339i
\(223\) 234.694 + 406.502i 0.0704767 + 0.122069i 0.899110 0.437722i \(-0.144215\pi\)
−0.828634 + 0.559791i \(0.810881\pi\)
\(224\) 1115.55 0.332750
\(225\) 0 0
\(226\) −941.817 −0.277207
\(227\) −2143.99 3713.50i −0.626879 1.08579i −0.988174 0.153335i \(-0.950999\pi\)
0.361295 0.932452i \(-0.382335\pi\)
\(228\) 1588.11 + 3650.79i 0.461294 + 1.06044i
\(229\) −2052.30 + 3554.69i −0.592227 + 1.02577i 0.401705 + 0.915769i \(0.368418\pi\)
−0.993932 + 0.109998i \(0.964916\pi\)
\(230\) 0 0
\(231\) −41.7913 96.0711i −0.0119033 0.0273637i
\(232\) 1131.01 + 1958.97i 0.320062 + 0.554364i
\(233\) 4272.57 1.20131 0.600656 0.799508i \(-0.294906\pi\)
0.600656 + 0.799508i \(0.294906\pi\)
\(234\) −40.3804 131.927i −0.0112810 0.0368560i
\(235\) 0 0
\(236\) −1944.12 3367.31i −0.536235 0.928786i
\(237\) 1937.56 + 220.441i 0.531045 + 0.0604185i
\(238\) −210.611 + 364.790i −0.0573610 + 0.0993521i
\(239\) 780.619 1352.07i 0.211272 0.365934i −0.740841 0.671681i \(-0.765573\pi\)
0.952113 + 0.305747i \(0.0989061\pi\)
\(240\) 0 0
\(241\) 2410.77 + 4175.58i 0.644362 + 1.11607i 0.984448 + 0.175674i \(0.0562105\pi\)
−0.340086 + 0.940394i \(0.610456\pi\)
\(242\) 632.399 0.167984
\(243\) 162.187 3784.52i 0.0428161 0.999083i
\(244\) −4522.80 −1.18665
\(245\) 0 0
\(246\) 208.699 282.135i 0.0540901 0.0731232i
\(247\) 529.021 916.292i 0.136279 0.236042i
\(248\) 440.282 762.591i 0.112734 0.195260i
\(249\) 6676.77 + 759.634i 1.69929 + 0.193333i
\(250\) 0 0
\(251\) −3487.72 −0.877063 −0.438532 0.898716i \(-0.644501\pi\)
−0.438532 + 0.898716i \(0.644501\pi\)
\(252\) −778.962 2544.94i −0.194722 0.636176i
\(253\) −50.1728 −0.0124677
\(254\) −313.791 543.503i −0.0775158 0.134261i
\(255\) 0 0
\(256\) −1492.20 + 2584.57i −0.364308 + 0.631000i
\(257\) −2460.87 + 4262.35i −0.597295 + 1.03454i 0.395924 + 0.918283i \(0.370424\pi\)
−0.993219 + 0.116261i \(0.962909\pi\)
\(258\) −296.247 681.021i −0.0714865 0.164335i
\(259\) 1075.10 + 1862.13i 0.257929 + 0.446745i
\(260\) 0 0
\(261\) 5545.36 5950.51i 1.31513 1.41121i
\(262\) −754.480 −0.177908
\(263\) −2758.58 4777.99i −0.646772 1.12024i −0.983889 0.178780i \(-0.942785\pi\)
0.337117 0.941463i \(-0.390548\pi\)
\(264\) −61.6377 7.01269i −0.0143695 0.00163485i
\(265\) 0 0
\(266\) −297.500 + 515.284i −0.0685747 + 0.118775i
\(267\) 1246.23 1684.75i 0.285649 0.386162i
\(268\) −1946.98 3372.28i −0.443772 0.768636i
\(269\) −7844.13 −1.77794 −0.888969 0.457968i \(-0.848577\pi\)
−0.888969 + 0.457968i \(0.848577\pi\)
\(270\) 0 0
\(271\) 4301.35 0.964164 0.482082 0.876126i \(-0.339881\pi\)
0.482082 + 0.876126i \(0.339881\pi\)
\(272\) −2044.96 3541.98i −0.455860 0.789573i
\(273\) −420.631 + 568.641i −0.0932517 + 0.126065i
\(274\) −90.8083 + 157.285i −0.0200216 + 0.0346785i
\(275\) 0 0
\(276\) −1266.41 144.083i −0.276192 0.0314231i
\(277\) 925.922 + 1603.74i 0.200842 + 0.347869i 0.948800 0.315877i \(-0.102299\pi\)
−0.747958 + 0.663746i \(0.768966\pi\)
\(278\) 1172.18 0.252888
\(279\) −3085.44 711.285i −0.662081 0.152629i
\(280\) 0 0
\(281\) −3470.93 6011.82i −0.736862 1.27628i −0.953902 0.300119i \(-0.902974\pi\)
0.217040 0.976163i \(-0.430360\pi\)
\(282\) −480.937 1105.59i −0.101558 0.233465i
\(283\) 3216.21 5570.64i 0.675562 1.17011i −0.300743 0.953705i \(-0.597235\pi\)
0.976304 0.216402i \(-0.0694321\pi\)
\(284\) 4145.88 7180.87i 0.866242 1.50038i
\(285\) 0 0
\(286\) 4.06236 + 7.03621i 0.000839903 + 0.00145476i
\(287\) −1799.10 −0.370027
\(288\) −2314.52 533.564i −0.473556 0.109169i
\(289\) −43.9287 −0.00894133
\(290\) 0 0
\(291\) 8164.88 + 928.941i 1.64479 + 0.187132i
\(292\) −1691.83 + 2930.34i −0.339065 + 0.587278i
\(293\) −3820.89 + 6617.98i −0.761840 + 1.31955i 0.180062 + 0.983655i \(0.442370\pi\)
−0.941901 + 0.335890i \(0.890963\pi\)
\(294\) −268.009 + 362.316i −0.0531654 + 0.0718731i
\(295\) 0 0
\(296\) 1273.19 0.250009
\(297\) 40.7569 + 219.314i 0.00796281 + 0.0428481i
\(298\) −182.961 −0.0355660
\(299\) 169.364 + 293.347i 0.0327577 + 0.0567380i
\(300\) 0 0
\(301\) −1903.67 + 3297.26i −0.364538 + 0.631398i
\(302\) 189.724 328.611i 0.0361502 0.0626140i
\(303\) −5962.28 678.344i −1.13044 0.128613i
\(304\) −2888.61 5003.23i −0.544978 0.943930i
\(305\) 0 0
\(306\) 611.448 656.120i 0.114229 0.122575i
\(307\) −4517.66 −0.839857 −0.419929 0.907557i \(-0.637945\pi\)
−0.419929 + 0.907557i \(0.637945\pi\)
\(308\) 78.3654 + 135.733i 0.0144977 + 0.0251107i
\(309\) −3008.00 6914.89i −0.553784 1.27306i
\(310\) 0 0
\(311\) −1966.54 + 3406.15i −0.358560 + 0.621044i −0.987721 0.156231i \(-0.950066\pi\)
0.629160 + 0.777275i \(0.283399\pi\)
\(312\) 167.064 + 384.051i 0.0303145 + 0.0696879i
\(313\) −1583.09 2742.00i −0.285884 0.495165i 0.686939 0.726715i \(-0.258954\pi\)
−0.972823 + 0.231549i \(0.925620\pi\)
\(314\) −414.622 −0.0745175
\(315\) 0 0
\(316\) −2917.26 −0.519332
\(317\) −3920.86 6791.13i −0.694692 1.20324i −0.970284 0.241967i \(-0.922207\pi\)
0.275592 0.961275i \(-0.411126\pi\)
\(318\) 1128.49 + 128.391i 0.199002 + 0.0226410i
\(319\) −239.495 + 414.817i −0.0420349 + 0.0728066i
\(320\) 0 0
\(321\) 422.506 571.176i 0.0734641 0.0993145i
\(322\) −95.2431 164.966i −0.0164835 0.0285503i
\(323\) 6877.82 1.18480
\(324\) 398.932 + 5652.74i 0.0684040 + 0.969263i
\(325\) 0 0
\(326\) 7.44051 + 12.8873i 0.00126409 + 0.00218946i
\(327\) −123.968 + 167.590i −0.0209647 + 0.0283417i
\(328\) −532.648 + 922.574i −0.0896664 + 0.155307i
\(329\) −3090.49 + 5352.89i −0.517885 + 0.897004i
\(330\) 0 0
\(331\) 5426.53 + 9399.03i 0.901115 + 1.56078i 0.826049 + 0.563599i \(0.190584\pi\)
0.0750663 + 0.997179i \(0.476083\pi\)
\(332\) −10052.8 −1.66181
\(333\) −1339.94 4377.70i −0.220505 0.720411i
\(334\) −17.7480 −0.00290757
\(335\) 0 0
\(336\) 1540.58 + 3541.53i 0.250135 + 0.575019i
\(337\) −3258.64 + 5644.13i −0.526735 + 0.912331i 0.472780 + 0.881180i \(0.343251\pi\)
−0.999515 + 0.0311507i \(0.990083\pi\)
\(338\) −495.499 + 858.229i −0.0797384 + 0.138111i
\(339\) −4100.81 9427.08i −0.657008 1.51035i
\(340\) 0 0
\(341\) 186.462 0.0296114
\(342\) 863.701 926.804i 0.136560 0.146537i
\(343\) 6659.94 1.04841
\(344\) 1127.21 + 1952.39i 0.176672 + 0.306005i
\(345\) 0 0
\(346\) 281.142 486.952i 0.0436829 0.0756609i
\(347\) 2969.27 5142.93i 0.459363 0.795640i −0.539564 0.841944i \(-0.681411\pi\)
0.998927 + 0.0463041i \(0.0147443\pi\)
\(348\) −7236.33 + 9782.62i −1.11468 + 1.50691i
\(349\) 3648.27 + 6318.99i 0.559563 + 0.969192i 0.997533 + 0.0702022i \(0.0223644\pi\)
−0.437970 + 0.898990i \(0.644302\pi\)
\(350\) 0 0
\(351\) 1144.69 978.613i 0.174071 0.148816i
\(352\) 139.873 0.0211797
\(353\) 625.356 + 1083.15i 0.0942900 + 0.163315i 0.909312 0.416115i \(-0.136609\pi\)
−0.815022 + 0.579430i \(0.803275\pi\)
\(354\) −735.795 + 994.704i −0.110472 + 0.149344i
\(355\) 0 0
\(356\) −1567.49 + 2714.97i −0.233362 + 0.404195i
\(357\) −4568.38 519.757i −0.677267 0.0770545i
\(358\) −102.225 177.058i −0.0150915 0.0261392i
\(359\) −10928.3 −1.60661 −0.803303 0.595570i \(-0.796926\pi\)
−0.803303 + 0.595570i \(0.796926\pi\)
\(360\) 0 0
\(361\) 2856.27 0.416427
\(362\) −425.567 737.104i −0.0617882 0.107020i
\(363\) 2753.56 + 6329.97i 0.398139 + 0.915254i
\(364\) 529.062 916.362i 0.0761823 0.131952i
\(365\) 0 0
\(366\) 574.087 + 1319.73i 0.0819891 + 0.188479i
\(367\) −3215.66 5569.68i −0.457373 0.792194i 0.541448 0.840734i \(-0.317876\pi\)
−0.998821 + 0.0485405i \(0.984543\pi\)
\(368\) 1849.55 0.261996
\(369\) 3732.73 + 860.504i 0.526607 + 0.121398i
\(370\) 0 0
\(371\) −2911.32 5042.55i −0.407407 0.705650i
\(372\) 4706.49 + 535.470i 0.655968 + 0.0746312i
\(373\) 2455.85 4253.66i 0.340909 0.590472i −0.643693 0.765284i \(-0.722598\pi\)
0.984602 + 0.174812i \(0.0559317\pi\)
\(374\) −26.4074 + 45.7389i −0.00365105 + 0.00632381i
\(375\) 0 0
\(376\) 1829.96 + 3169.58i 0.250992 + 0.434731i
\(377\) 3233.76 0.441770
\(378\) −643.726 + 550.331i −0.0875918 + 0.0748836i
\(379\) 4805.81 0.651340 0.325670 0.945483i \(-0.394410\pi\)
0.325670 + 0.945483i \(0.394410\pi\)
\(380\) 0 0
\(381\) 4073.87 5507.37i 0.547797 0.740554i
\(382\) 186.883 323.691i 0.0250308 0.0433547i
\(383\) −2116.08 + 3665.15i −0.282314 + 0.488983i −0.971954 0.235170i \(-0.924435\pi\)
0.689640 + 0.724152i \(0.257769\pi\)
\(384\) 4682.95 + 532.792i 0.622333 + 0.0708045i
\(385\) 0 0
\(386\) −227.106 −0.0299466
\(387\) 5526.75 5930.53i 0.725944 0.778982i
\(388\) −12293.4 −1.60851
\(389\) 1758.54 + 3045.89i 0.229208 + 0.396999i 0.957573 0.288189i \(-0.0930532\pi\)
−0.728366 + 0.685188i \(0.759720\pi\)
\(390\) 0 0
\(391\) −1100.95 + 1906.90i −0.142398 + 0.246640i
\(392\) 684.022 1184.76i 0.0881335 0.152652i
\(393\) −3285.12 7551.94i −0.421660 0.969325i
\(394\) 1101.63 + 1908.09i 0.140862 + 0.243980i
\(395\) 0 0
\(396\) −97.6697 319.096i −0.0123942 0.0404929i
\(397\) −3925.05 −0.496203 −0.248101 0.968734i \(-0.579807\pi\)
−0.248101 + 0.968734i \(0.579807\pi\)
\(398\) 603.100 + 1044.60i 0.0759564 + 0.131560i
\(399\) −6453.07 734.184i −0.809669 0.0921182i
\(400\) 0 0
\(401\) −403.676 + 699.188i −0.0502709 + 0.0870718i −0.890066 0.455832i \(-0.849342\pi\)
0.839795 + 0.542904i \(0.182675\pi\)
\(402\) −736.879 + 996.169i −0.0914233 + 0.123593i
\(403\) −629.424 1090.19i −0.0778011 0.134755i
\(404\) 8977.05 1.10551
\(405\) 0 0
\(406\) −1818.53 −0.222296
\(407\) 134.801 + 233.482i 0.0164173 + 0.0284356i
\(408\) −1619.06 + 2188.77i −0.196459 + 0.265588i
\(409\) −404.224 + 700.137i −0.0488694 + 0.0846444i −0.889425 0.457080i \(-0.848895\pi\)
0.840556 + 0.541725i \(0.182228\pi\)
\(410\) 0 0
\(411\) −1969.73 224.101i −0.236398 0.0268956i
\(412\) 5640.49 + 9769.61i 0.674482 + 1.16824i
\(413\) 6342.97 0.755732
\(414\) 118.705 + 387.821i 0.0140919 + 0.0460395i
\(415\) 0 0
\(416\) −472.157 817.800i −0.0556476 0.0963844i
\(417\) 5103.85 + 11732.9i 0.599369 + 1.37785i
\(418\) −37.3018 + 64.6086i −0.00436481 + 0.00756008i
\(419\) −880.089 + 1524.36i −0.102614 + 0.177732i −0.912761 0.408495i \(-0.866054\pi\)
0.810147 + 0.586227i \(0.199387\pi\)
\(420\) 0 0
\(421\) −7287.86 12622.9i −0.843678 1.46129i −0.886765 0.462221i \(-0.847053\pi\)
0.0430868 0.999071i \(-0.486281\pi\)
\(422\) −1316.42 −0.151854
\(423\) 8972.32 9627.84i 1.03132 1.10667i
\(424\) −3447.73 −0.394898
\(425\) 0 0
\(426\) −2621.59 298.265i −0.298160 0.0339225i
\(427\) 3689.07 6389.65i 0.418095 0.724161i
\(428\) −531.421 + 920.447i −0.0600168 + 0.103952i
\(429\) −52.7405 + 71.2987i −0.00593552 + 0.00802409i
\(430\) 0 0
\(431\) 5715.34 0.638743 0.319371 0.947630i \(-0.396528\pi\)
0.319371 + 0.947630i \(0.396528\pi\)
\(432\) −1502.45 8084.72i −0.167330 0.900408i
\(433\) 12751.4 1.41523 0.707614 0.706599i \(-0.249772\pi\)
0.707614 + 0.706599i \(0.249772\pi\)
\(434\) 353.962 + 613.079i 0.0391491 + 0.0678082i
\(435\) 0 0
\(436\) 155.925 270.070i 0.0171272 0.0296651i
\(437\) −1555.15 + 2693.60i −0.170235 + 0.294856i
\(438\) 1069.81 + 121.715i 0.116706 + 0.0132780i
\(439\) −2420.51 4192.44i −0.263154 0.455796i 0.703924 0.710275i \(-0.251429\pi\)
−0.967078 + 0.254479i \(0.918096\pi\)
\(440\) 0 0
\(441\) −4793.54 1105.05i −0.517605 0.119323i
\(442\) 356.564 0.0383711
\(443\) −4472.98 7747.43i −0.479724 0.830907i 0.520005 0.854163i \(-0.325930\pi\)
−0.999730 + 0.0232564i \(0.992597\pi\)
\(444\) 2732.01 + 6280.42i 0.292016 + 0.671297i
\(445\) 0 0
\(446\) −111.723 + 193.509i −0.0118615 + 0.0205447i
\(447\) −796.640 1831.34i −0.0842948 0.193780i
\(448\) −2707.53 4689.57i −0.285533 0.494557i
\(449\) −2743.57 −0.288367 −0.144184 0.989551i \(-0.546056\pi\)
−0.144184 + 0.989551i \(0.546056\pi\)
\(450\) 0 0
\(451\) −225.580 −0.0235524
\(452\) 7689.68 + 13318.9i 0.800204 + 1.38599i
\(453\) 4115.30 + 468.209i 0.426829 + 0.0485615i
\(454\) 1020.61 1767.76i 0.105506 0.182742i
\(455\) 0 0
\(456\) −2287.00 + 3091.75i −0.234865 + 0.317509i
\(457\) 2806.35 + 4860.74i 0.287255 + 0.497540i 0.973153 0.230157i \(-0.0739240\pi\)
−0.685899 + 0.727697i \(0.740591\pi\)
\(458\) −1953.93 −0.199348
\(459\) 9229.74 + 3263.41i 0.938578 + 0.331858i
\(460\) 0 0
\(461\) −6273.50 10866.0i −0.633809 1.09779i −0.986766 0.162150i \(-0.948157\pi\)
0.352957 0.935640i \(-0.385176\pi\)
\(462\) 29.6591 40.0954i 0.00298672 0.00403768i
\(463\) −5361.12 + 9285.74i −0.538126 + 0.932062i 0.460879 + 0.887463i \(0.347534\pi\)
−0.999005 + 0.0445990i \(0.985799\pi\)
\(464\) 8828.65 15291.7i 0.883319 1.52995i
\(465\) 0 0
\(466\) 1016.95 + 1761.40i 0.101093 + 0.175098i
\(467\) 12798.4 1.26818 0.634089 0.773260i \(-0.281375\pi\)
0.634089 + 0.773260i \(0.281375\pi\)
\(468\) −1535.97 + 1648.19i −0.151710 + 0.162794i
\(469\) 6352.31 0.625421
\(470\) 0 0
\(471\) −1805.33 4150.14i −0.176614 0.406005i
\(472\) 1877.92 3252.65i 0.183132 0.317193i
\(473\) −238.691 + 413.425i −0.0232030 + 0.0401888i
\(474\) 370.293 + 851.242i 0.0358822 + 0.0824870i
\(475\) 0 0
\(476\) 6878.34 0.662328
\(477\) 3628.49 + 11854.6i 0.348296 + 1.13791i
\(478\) 743.203 0.0711158
\(479\) −1207.38 2091.25i −0.115171 0.199481i 0.802677 0.596413i \(-0.203408\pi\)
−0.917848 + 0.396932i \(0.870075\pi\)
\(480\) 0 0
\(481\) 910.070 1576.29i 0.0862695 0.149423i
\(482\) −1147.61 + 1987.72i −0.108449 + 0.187839i
\(483\) 1236.52 1671.62i 0.116487 0.157477i
\(484\) −5163.37 8943.21i −0.484914 0.839896i
\(485\) 0 0
\(486\) 1598.80 833.919i 0.149225 0.0778340i
\(487\) 16386.9 1.52477 0.762384 0.647125i \(-0.224029\pi\)
0.762384 + 0.647125i \(0.224029\pi\)
\(488\) −2184.39 3783.48i −0.202629 0.350963i
\(489\) −96.5982 + 130.589i −0.00893317 + 0.0120766i
\(490\) 0 0
\(491\) −7935.54 + 13744.8i −0.729381 + 1.26332i 0.227764 + 0.973716i \(0.426858\pi\)
−0.957145 + 0.289609i \(0.906475\pi\)
\(492\) −5693.85 647.805i −0.521745 0.0593604i
\(493\) 10510.6 + 18204.8i 0.960186 + 1.66309i
\(494\) 503.665 0.0458724
\(495\) 0 0
\(496\) −6873.68 −0.622252
\(497\) 6763.26 + 11714.3i 0.610410 + 1.05726i
\(498\) 1276.02 + 2933.36i 0.114819 + 0.263950i
\(499\) −5730.39 + 9925.33i −0.514083 + 0.890419i 0.485783 + 0.874079i \(0.338534\pi\)
−0.999867 + 0.0163392i \(0.994799\pi\)
\(500\) 0 0
\(501\) −77.2776 177.648i −0.00689123 0.0158418i
\(502\) −830.138 1437.84i −0.0738065 0.127837i
\(503\) −1038.52 −0.0920585 −0.0460293 0.998940i \(-0.514657\pi\)
−0.0460293 + 0.998940i \(0.514657\pi\)
\(504\) 1752.71 1880.77i 0.154905 0.166222i
\(505\) 0 0
\(506\) −11.9420 20.6841i −0.00104918 0.00181724i
\(507\) −10747.9 1222.81i −0.941479 0.107115i
\(508\) −5124.04 + 8875.10i −0.447525 + 0.775135i
\(509\) 2514.44 4355.14i 0.218960 0.379249i −0.735530 0.677492i \(-0.763067\pi\)
0.954490 + 0.298242i \(0.0964003\pi\)
\(510\) 0 0
\(511\) −2759.92 4780.33i −0.238927 0.413834i
\(512\) −8677.07 −0.748976
\(513\) 13037.5 + 4609.74i 1.12206 + 0.396735i
\(514\) −2342.92 −0.201054
\(515\) 0 0
\(516\) −7212.04 + 9749.79i −0.615295 + 0.831803i
\(517\) −387.499 + 671.169i −0.0329636 + 0.0570947i
\(518\) −511.785 + 886.438i −0.0434104 + 0.0751889i
\(519\) 6098.25 + 693.815i 0.515768 + 0.0586803i
\(520\) 0 0
\(521\) 7057.78 0.593487 0.296744 0.954957i \(-0.404099\pi\)
0.296744 + 0.954957i \(0.404099\pi\)
\(522\) 3773.04 + 869.797i 0.316363 + 0.0729310i
\(523\) −14453.5 −1.20843 −0.604215 0.796821i \(-0.706513\pi\)
−0.604215 + 0.796821i \(0.706513\pi\)
\(524\) 6160.13 + 10669.7i 0.513562 + 0.889515i
\(525\) 0 0
\(526\) 1313.18 2274.49i 0.108854 0.188541i
\(527\) 4091.57 7086.81i 0.338201 0.585781i
\(528\) 193.165 + 444.053i 0.0159212 + 0.0366002i
\(529\) 5585.63 + 9674.59i 0.459080 + 0.795150i
\(530\) 0 0
\(531\) −13160.2 3033.81i −1.07553 0.247940i
\(532\) 9716.01 0.791809
\(533\) 761.469 + 1318.90i 0.0618816 + 0.107182i
\(534\) 991.180 + 112.769i 0.0803231 + 0.00913858i
\(535\) 0 0
\(536\) 1880.68 3257.44i 0.151554 0.262500i
\(537\) 1327.16 1794.15i 0.106650 0.144178i
\(538\) −1867.04 3233.81i −0.149617 0.259144i
\(539\) 289.687 0.0231498
\(540\) 0 0
\(541\) 4101.59 0.325954 0.162977 0.986630i \(-0.447890\pi\)
0.162977 + 0.986630i \(0.447890\pi\)
\(542\) 1023.80 + 1773.27i 0.0811362 + 0.140532i
\(543\) 5525.03 7469.16i 0.436651 0.590299i
\(544\) 3069.26 5316.11i 0.241900 0.418982i
\(545\) 0 0
\(546\) −334.544 38.0620i −0.0262219 0.00298334i
\(547\) −8410.52 14567.4i −0.657418 1.13868i −0.981282 0.192578i \(-0.938315\pi\)
0.323863 0.946104i \(-0.395018\pi\)
\(548\) 2965.70 0.231183
\(549\) −10710.1 + 11492.6i −0.832598 + 0.893428i
\(550\) 0 0
\(551\) 14846.7 + 25715.2i 1.14790 + 1.98821i
\(552\) −491.112 1128.98i −0.0378680 0.0870521i
\(553\) 2379.50 4121.41i 0.182977 0.316926i
\(554\) −440.771 + 763.438i −0.0338025 + 0.0585476i
\(555\) 0 0
\(556\) −9570.54 16576.7i −0.730002 1.26440i
\(557\) 12248.8 0.931771 0.465885 0.884845i \(-0.345736\pi\)
0.465885 + 0.884845i \(0.345736\pi\)
\(558\) −441.156 1441.30i −0.0334688 0.109346i
\(559\) 3222.91 0.243854
\(560\) 0 0
\(561\) −572.804 65.1694i −0.0431084 0.00490455i
\(562\) 1652.28 2861.84i 0.124017 0.214803i
\(563\) 4422.86 7660.62i 0.331086 0.573457i −0.651639 0.758529i \(-0.725918\pi\)
0.982725 + 0.185072i \(0.0592517\pi\)
\(564\) −11708.3 + 15828.1i −0.874127 + 1.18171i
\(565\) 0 0
\(566\) 3062.06 0.227399
\(567\) −8311.39 4047.12i −0.615601 0.299759i
\(568\) 8009.40 0.591667
\(569\) 4049.35 + 7013.68i 0.298344 + 0.516747i 0.975757 0.218856i \(-0.0702325\pi\)
−0.677413 + 0.735603i \(0.736899\pi\)
\(570\) 0 0
\(571\) 8189.02 14183.8i 0.600175 1.03953i −0.392619 0.919701i \(-0.628431\pi\)
0.992794 0.119832i \(-0.0382356\pi\)
\(572\) 66.3361 114.897i 0.00484904 0.00839879i
\(573\) 4053.69 + 461.200i 0.295542 + 0.0336246i
\(574\) −428.218 741.696i −0.0311385 0.0539334i
\(575\) 0 0
\(576\) 3374.49 + 11024.8i 0.244104 + 0.797510i
\(577\) −24920.9 −1.79804 −0.899020 0.437907i \(-0.855720\pi\)
−0.899020 + 0.437907i \(0.855720\pi\)
\(578\) −10.4558 18.1100i −0.000752430 0.00130325i
\(579\) −988.853 2273.21i −0.0709764 0.163163i
\(580\) 0 0
\(581\) 8199.69 14202.3i 0.585509 1.01413i
\(582\) 1560.42 + 3587.15i 0.111137 + 0.255484i
\(583\) −365.034 632.257i −0.0259317 0.0449150i
\(584\) −3268.44 −0.231591
\(585\) 0 0
\(586\) −3637.76 −0.256441
\(587\) −4182.25 7243.86i −0.294071 0.509346i 0.680697 0.732565i \(-0.261677\pi\)
−0.974768 + 0.223219i \(0.928344\pi\)
\(588\) 7311.99 + 831.905i 0.512826 + 0.0583456i
\(589\) 5779.56 10010.5i 0.404317 0.700297i
\(590\) 0 0
\(591\) −14302.2 + 19334.8i −0.995456 + 1.34573i
\(592\) −4969.25 8607.00i −0.344992 0.597543i
\(593\) −27169.7 −1.88150 −0.940749 0.339105i \(-0.889876\pi\)
−0.940749 + 0.339105i \(0.889876\pi\)
\(594\) −80.7132 + 69.0030i −0.00557526 + 0.00476637i
\(595\) 0 0
\(596\) 1493.83 + 2587.39i 0.102667 + 0.177825i
\(597\) −7829.88 + 10585.0i −0.536777 + 0.725656i
\(598\) −80.6231 + 139.643i −0.00551325 + 0.00954923i
\(599\) −10666.2 + 18474.4i −0.727560 + 1.26017i 0.230351 + 0.973108i \(0.426013\pi\)
−0.957911 + 0.287064i \(0.907321\pi\)
\(600\) 0 0
\(601\) −292.016 505.786i −0.0198196 0.0343285i 0.855946 0.517066i \(-0.172976\pi\)
−0.875765 + 0.482738i \(0.839643\pi\)
\(602\) −1812.43 −0.122706
\(603\) −13179.6 3038.28i −0.890074 0.205188i
\(604\) −6196.17 −0.417415
\(605\) 0 0
\(606\) −1139.47 2619.46i −0.0763827 0.175591i
\(607\) 5635.12 9760.32i 0.376808 0.652651i −0.613788 0.789471i \(-0.710355\pi\)
0.990596 + 0.136820i \(0.0436883\pi\)
\(608\) 4335.49 7509.29i 0.289190 0.500891i
\(609\) −7918.17 18202.5i −0.526864 1.21117i
\(610\) 0 0
\(611\) 5232.19 0.346435
\(612\) −14271.0 3289.88i −0.942598 0.217297i
\(613\) −4271.02 −0.281411 −0.140706 0.990051i \(-0.544937\pi\)
−0.140706 + 0.990051i \(0.544937\pi\)
\(614\) −1075.28 1862.44i −0.0706756 0.122414i
\(615\) 0 0
\(616\) −75.6968 + 131.111i −0.00495115 + 0.00857565i
\(617\) −3598.08 + 6232.06i −0.234770 + 0.406634i −0.959206 0.282708i \(-0.908767\pi\)
0.724436 + 0.689342i \(0.242100\pi\)
\(618\) 2134.76 2885.94i 0.138953 0.187847i
\(619\) −5128.24 8882.36i −0.332991 0.576757i 0.650106 0.759843i \(-0.274724\pi\)
−0.983097 + 0.183087i \(0.941391\pi\)
\(620\) 0 0
\(621\) −3365.01 + 2876.80i −0.217445 + 0.185897i
\(622\) −1872.28 −0.120694
\(623\) −2557.08 4428.99i −0.164442 0.284822i
\(624\) 1944.21 2628.33i 0.124729 0.168618i
\(625\) 0 0
\(626\) 753.607 1305.29i 0.0481153 0.0833382i
\(627\) −809.115 92.0552i −0.0515358 0.00586337i
\(628\) 3385.28 + 5863.47i 0.215107 + 0.372576i
\(629\) 11831.8 0.750026
\(630\) 0 0
\(631\) 15187.7 0.958183 0.479091 0.877765i \(-0.340966\pi\)
0.479091 + 0.877765i \(0.340966\pi\)
\(632\) −1408.96 2440.39i −0.0886795 0.153597i
\(633\) −5731.90 13176.7i −0.359909 0.827371i
\(634\) 1866.47 3232.81i 0.116919 0.202510i
\(635\) 0 0
\(636\) −7398.14 17007.1i −0.461250 1.06034i
\(637\) −977.872 1693.72i −0.0608237 0.105350i
\(638\) −228.016 −0.0141493
\(639\) −8429.31 27539.3i −0.521844 1.70491i
\(640\) 0 0
\(641\) 14196.7 + 24589.4i 0.874783 + 1.51517i 0.856994 + 0.515327i \(0.172329\pi\)
0.0177891 + 0.999842i \(0.494337\pi\)
\(642\) 336.036 + 38.2317i 0.0206578 + 0.00235029i
\(643\) −5844.00 + 10122.1i −0.358421 + 0.620804i −0.987697 0.156378i \(-0.950018\pi\)
0.629276 + 0.777182i \(0.283351\pi\)
\(644\) −1555.27 + 2693.80i −0.0951648 + 0.164830i
\(645\) 0 0
\(646\) 1637.04 + 2835.44i 0.0997036 + 0.172692i
\(647\) 12800.8 0.777822 0.388911 0.921275i \(-0.372851\pi\)
0.388911 + 0.921275i \(0.372851\pi\)
\(648\) −4536.04 + 3063.85i −0.274989 + 0.185740i
\(649\) 795.310 0.0481027
\(650\) 0 0
\(651\) −4595.39 + 6212.40i −0.276663 + 0.374014i
\(652\) 121.500 210.443i 0.00729799 0.0126405i
\(653\) −3079.46 + 5333.78i −0.184546 + 0.319643i −0.943423 0.331590i \(-0.892415\pi\)
0.758877 + 0.651233i \(0.225748\pi\)
\(654\) −98.5968 11.2176i −0.00589517 0.000670709i
\(655\) 0 0
\(656\) 8315.69 0.494929
\(657\) 3439.80 + 11238.1i 0.204261 + 0.667339i
\(658\) −2942.36 −0.174324
\(659\) −8289.10 14357.1i −0.489981 0.848672i 0.509953 0.860202i \(-0.329663\pi\)
−0.999934 + 0.0115307i \(0.996330\pi\)
\(660\) 0 0
\(661\) 11469.8 19866.4i 0.674925 1.16900i −0.301566 0.953445i \(-0.597509\pi\)
0.976491 0.215559i \(-0.0691573\pi\)
\(662\) −2583.22 + 4474.27i −0.151661 + 0.262685i
\(663\) 1552.53 + 3569.01i 0.0909433 + 0.209063i
\(664\) −4855.25 8409.53i −0.283765 0.491496i
\(665\) 0 0
\(666\) 1485.82 1594.37i 0.0864478 0.0927637i
\(667\) −9506.20 −0.551847
\(668\) 144.908 + 250.988i 0.00839319 + 0.0145374i
\(669\) −2423.38 275.715i −0.140050 0.0159338i
\(670\) 0 0
\(671\) 462.552 801.163i 0.0266119 0.0460932i
\(672\) −3447.19 + 4660.18i −0.197884 + 0.267515i
\(673\) 1181.62 + 2046.62i 0.0676790 + 0.117223i 0.897879 0.440242i \(-0.145107\pi\)
−0.830200 + 0.557465i \(0.811774\pi\)
\(674\) −3102.46 −0.177303
\(675\) 0 0
\(676\) 16182.4 0.920712
\(677\) −7824.09 13551.7i −0.444172 0.769328i 0.553822 0.832635i \(-0.313169\pi\)
−0.997994 + 0.0633068i \(0.979835\pi\)
\(678\) 2910.33 3934.40i 0.164853 0.222861i
\(679\) 10027.2 17367.7i 0.566730 0.981605i
\(680\) 0 0
\(681\) 22138.2 + 2518.72i 1.24572 + 0.141729i
\(682\) 44.3813 + 76.8706i 0.00249186 + 0.00431602i
\(683\) −19626.7 −1.09955 −0.549777 0.835311i \(-0.685287\pi\)
−0.549777 + 0.835311i \(0.685287\pi\)
\(684\) −20158.5 4647.12i −1.12687 0.259777i
\(685\) 0 0
\(686\) 1585.18 + 2745.62i 0.0882253 + 0.152811i
\(687\) −8507.72 19557.8i −0.472474 1.08614i
\(688\) 8799.02 15240.3i 0.487586 0.844524i
\(689\) −2464.42 + 4268.51i −0.136266 + 0.236019i
\(690\) 0 0
\(691\) 51.5955 + 89.3660i 0.00284050 + 0.00491989i 0.867442 0.497538i \(-0.165763\pi\)
−0.864602 + 0.502458i \(0.832429\pi\)
\(692\) −9181.78 −0.504391
\(693\) 530.473 + 122.290i 0.0290779 + 0.00670332i
\(694\) 2826.96 0.154625
\(695\) 0 0
\(696\) −11678.5 1328.69i −0.636021 0.0723619i
\(697\) −4949.93 + 8573.54i −0.268999 + 0.465920i
\(698\) −1736.71 + 3008.06i −0.0941766 + 0.163119i
\(699\) −13202.8 + 17848.5i −0.714412 + 0.965797i
\(700\) 0 0
\(701\) −17977.8 −0.968631 −0.484316 0.874893i \(-0.660931\pi\)
−0.484316 + 0.874893i \(0.660931\pi\)
\(702\) 675.898 + 238.981i 0.0363392 + 0.0128487i
\(703\) 16713.1 0.896651
\(704\) −339.482 588.000i −0.0181743 0.0314788i
\(705\) 0 0
\(706\) −297.692 + 515.617i −0.0158694 + 0.0274865i
\(707\) −7322.22 + 12682.5i −0.389506 + 0.674644i
\(708\) 20074.4 + 2283.92i 1.06560 + 0.121236i
\(709\) −5385.10 9327.26i −0.285249 0.494066i 0.687421 0.726260i \(-0.258743\pi\)
−0.972670 + 0.232194i \(0.925410\pi\)
\(710\) 0 0
\(711\) −6908.16 + 7412.87i −0.364383 + 0.391005i
\(712\) −3028.23 −0.159393
\(713\) 1850.30 + 3204.81i 0.0971868 + 0.168333i
\(714\) −873.080 2007.06i −0.0457622 0.105200i
\(715\) 0 0
\(716\) −1669.27 + 2891.27i −0.0871280 + 0.150910i
\(717\) 3236.02 + 7439.06i 0.168551 + 0.387471i
\(718\) −2601.12 4505.27i −0.135199 0.234171i
\(719\) 24138.7 1.25205 0.626023 0.779804i \(-0.284681\pi\)
0.626023 + 0.779804i \(0.284681\pi\)
\(720\) 0 0
\(721\) −18402.9 −0.950568
\(722\) 679.843 + 1177.52i 0.0350431 + 0.0606964i
\(723\) −24892.9 2832.13i −1.28046 0.145682i
\(724\) −6949.28 + 12036.5i −0.356724 + 0.617864i
\(725\) 0 0
\(726\) −1954.19 + 2641.82i −0.0998991 + 0.135051i
\(727\) −5395.46 9345.20i −0.275250 0.476746i 0.694949 0.719059i \(-0.255427\pi\)
−0.970198 + 0.242313i \(0.922094\pi\)
\(728\) 1022.09 0.0520347
\(729\) 15308.5 + 12372.1i 0.777753 + 0.628570i
\(730\) 0 0
\(731\) 10475.3 + 18143.7i 0.530016 + 0.918015i
\(732\) 13976.0 18893.8i 0.705692 0.954009i
\(733\) −10492.9 + 18174.3i −0.528738 + 0.915801i 0.470700 + 0.882293i \(0.344001\pi\)
−0.999438 + 0.0335082i \(0.989332\pi\)
\(734\) 1530.77 2651.36i 0.0769776 0.133329i
\(735\) 0 0
\(736\) 1387.99 + 2404.06i 0.0695134 + 0.120401i
\(737\) 796.481 0.0398084
\(738\) 533.705 + 1743.66i 0.0266205 + 0.0869717i
\(739\) 1773.47 0.0882790 0.0441395 0.999025i \(-0.485945\pi\)
0.0441395 + 0.999025i \(0.485945\pi\)
\(740\) 0 0
\(741\) 2193.03 + 5041.42i 0.108722 + 0.249934i
\(742\) 1385.89 2400.43i 0.0685682 0.118764i
\(743\) −2640.39 + 4573.28i −0.130372 + 0.225811i −0.923820 0.382827i \(-0.874950\pi\)
0.793448 + 0.608638i \(0.208284\pi\)
\(744\) 1825.17 + 4195.76i 0.0899381 + 0.206753i
\(745\) 0 0
\(746\) 2338.14 0.114753
\(747\) −23805.4 + 25544.6i −1.16599 + 1.25117i
\(748\) 862.437 0.0421575
\(749\) −866.918 1501.55i −0.0422917 0.0732514i
\(750\) 0 0
\(751\) −5514.51 + 9551.40i −0.267946 + 0.464095i −0.968331 0.249669i \(-0.919678\pi\)
0.700386 + 0.713765i \(0.253011\pi\)
\(752\) 14284.6 24741.7i 0.692696 1.19978i
\(753\) 10777.5 14569.8i 0.521584 0.705117i
\(754\) 769.692 + 1333.15i 0.0371758 + 0.0643904i
\(755\) 0 0
\(756\) 13038.5 + 4610.09i 0.627255 + 0.221782i
\(757\) 19897.2 0.955318 0.477659 0.878545i \(-0.341486\pi\)
0.477659 + 0.878545i \(0.341486\pi\)
\(758\) 1143.87 + 1981.24i 0.0548115 + 0.0949363i
\(759\) 155.040 209.595i 0.00741448 0.0100235i
\(760\) 0 0
\(761\) 12636.2 21886.5i 0.601920 1.04256i −0.390610 0.920556i \(-0.627736\pi\)
0.992530 0.122000i \(-0.0389307\pi\)
\(762\) 3240.11 + 368.636i 0.154038 + 0.0175253i
\(763\) 254.364 + 440.571i 0.0120689 + 0.0209040i
\(764\) −6103.40 −0.289023
\(765\) 0 0
\(766\) −2014.65 −0.0950292
\(767\) −2684.65 4649.96i −0.126385 0.218905i
\(768\) −6185.87 14220.3i −0.290642 0.668137i
\(769\) −15167.1 + 26270.1i −0.711233 + 1.23189i 0.253162 + 0.967424i \(0.418529\pi\)
−0.964395 + 0.264467i \(0.914804\pi\)
\(770\) 0 0
\(771\) −10201.4 23451.3i −0.476517 1.09543i
\(772\) 1854.26 + 3211.67i 0.0864458 + 0.149729i
\(773\) −6671.36 −0.310417 −0.155208 0.987882i \(-0.549605\pi\)
−0.155208 + 0.987882i \(0.549605\pi\)
\(774\) 3760.37 + 866.877i 0.174630 + 0.0402574i
\(775\) 0 0
\(776\) −5937.38 10283.8i −0.274664 0.475732i
\(777\) −11101.2 1263.01i −0.512551 0.0583143i
\(778\) −837.129 + 1449.95i −0.0385765 + 0.0668165i
\(779\) −6992.04 + 12110.6i −0.321586 + 0.557004i
\(780\) 0