Properties

Label 169.4.c.i.22.2
Level $169$
Weight $4$
Character 169.22
Analytic conductor $9.971$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.22
Dual form 169.4.c.i.146.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 - 3.00000i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-2.00000 - 3.46410i) q^{4} -13.8564 q^{5} +(-12.1244 - 21.0000i) q^{6} +(-11.2583 - 19.5000i) q^{7} +13.8564 q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})\) \(q+(1.73205 - 3.00000i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-2.00000 - 3.46410i) q^{4} -13.8564 q^{5} +(-12.1244 - 21.0000i) q^{6} +(-11.2583 - 19.5000i) q^{7} +13.8564 q^{8} +(-11.0000 - 19.0526i) q^{9} +(-24.0000 + 41.5692i) q^{10} +(-11.2583 + 19.5000i) q^{11} -28.0000 q^{12} -78.0000 q^{14} +(-48.4974 + 84.0000i) q^{15} +(40.0000 - 69.2820i) q^{16} +(13.5000 + 23.3827i) q^{17} -76.2102 q^{18} +(-44.1673 - 76.5000i) q^{19} +(27.7128 + 48.0000i) q^{20} -157.617 q^{21} +(39.0000 + 67.5500i) q^{22} +(28.5000 - 49.3634i) q^{23} +(48.4974 - 84.0000i) q^{24} +67.0000 q^{25} +35.0000 q^{27} +(-45.0333 + 78.0000i) q^{28} +(34.5000 - 59.7558i) q^{29} +(168.000 + 290.985i) q^{30} +72.7461 q^{31} +(-83.1384 - 144.000i) q^{32} +(78.8083 + 136.500i) q^{33} +93.5307 q^{34} +(156.000 + 270.200i) q^{35} +(-44.0000 + 76.2102i) q^{36} +(-19.9186 + 34.5000i) q^{37} -306.000 q^{38} -192.000 q^{40} +(196.588 - 340.500i) q^{41} +(-273.000 + 472.850i) q^{42} +(-42.5000 - 73.6122i) q^{43} +90.0666 q^{44} +(152.420 + 264.000i) q^{45} +(-98.7269 - 171.000i) q^{46} -342.946 q^{47} +(-280.000 - 484.974i) q^{48} +(-82.0000 + 142.028i) q^{49} +(116.047 - 201.000i) q^{50} +189.000 q^{51} +426.000 q^{53} +(60.6218 - 105.000i) q^{54} +(156.000 - 270.200i) q^{55} +(-156.000 - 270.200i) q^{56} -618.342 q^{57} +(-119.512 - 207.000i) q^{58} +(9.52628 + 16.5000i) q^{59} +387.979 q^{60} +(8.50000 + 14.7224i) q^{61} +(126.000 - 218.238i) q^{62} +(-247.683 + 429.000i) q^{63} +64.0000 q^{64} +546.000 q^{66} +(-82.2724 + 142.500i) q^{67} +(54.0000 - 93.5307i) q^{68} +(-199.500 - 345.544i) q^{69} +1080.80 q^{70} +(291.851 + 505.500i) q^{71} +(-152.420 - 264.000i) q^{72} +1004.59 q^{73} +(69.0000 + 119.512i) q^{74} +(234.500 - 406.166i) q^{75} +(-176.669 + 306.000i) q^{76} +507.000 q^{77} -1244.00 q^{79} +(-554.256 + 960.000i) q^{80} +(419.500 - 726.595i) q^{81} +(-681.000 - 1179.53i) q^{82} +426.084 q^{83} +(315.233 + 546.000i) q^{84} +(-187.061 - 324.000i) q^{85} -294.449 q^{86} +(-241.500 - 418.290i) q^{87} +(-156.000 + 270.200i) q^{88} +(153.286 - 265.500i) q^{89} +1056.00 q^{90} -228.000 q^{92} +(254.611 - 441.000i) q^{93} +(-594.000 + 1028.84i) q^{94} +(612.000 + 1060.02i) q^{95} -1163.94 q^{96} +(617.476 + 1069.50i) q^{97} +(284.056 + 492.000i) q^{98} +495.367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 14 q^{3} - 8 q^{4} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 14 q^{3} - 8 q^{4} - 44 q^{9} - 96 q^{10} - 112 q^{12} - 312 q^{14} + 160 q^{16} + 54 q^{17} + 156 q^{22} + 114 q^{23} + 268 q^{25} + 140 q^{27} + 138 q^{29} + 672 q^{30} + 624 q^{35} - 176 q^{36} - 1224 q^{38} - 768 q^{40} - 1092 q^{42} - 170 q^{43} - 1120 q^{48} - 328 q^{49} + 756 q^{51} + 1704 q^{53} + 624 q^{55} - 624 q^{56} + 34 q^{61} + 504 q^{62} + 256 q^{64} + 2184 q^{66} + 216 q^{68} - 798 q^{69} + 276 q^{74} + 938 q^{75} + 2028 q^{77} - 4976 q^{79} + 1678 q^{81} - 2724 q^{82} - 966 q^{87} - 624 q^{88} + 4224 q^{90} - 912 q^{92} - 2376 q^{94} + 2448 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 3.00000i 0.612372 1.06066i −0.378467 0.925615i \(-0.623549\pi\)
0.990839 0.135045i \(-0.0431180\pi\)
\(3\) 3.50000 6.06218i 0.673575 1.16667i −0.303308 0.952893i \(-0.598091\pi\)
0.976883 0.213774i \(-0.0685756\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −13.8564 −1.23935 −0.619677 0.784857i \(-0.712737\pi\)
−0.619677 + 0.784857i \(0.712737\pi\)
\(6\) −12.1244 21.0000i −0.824958 1.42887i
\(7\) −11.2583 19.5000i −0.607893 1.05290i −0.991587 0.129441i \(-0.958682\pi\)
0.383694 0.923460i \(-0.374652\pi\)
\(8\) 13.8564 0.612372
\(9\) −11.0000 19.0526i −0.407407 0.705650i
\(10\) −24.0000 + 41.5692i −0.758947 + 1.31453i
\(11\) −11.2583 + 19.5000i −0.308592 + 0.534497i −0.978055 0.208349i \(-0.933191\pi\)
0.669462 + 0.742846i \(0.266525\pi\)
\(12\) −28.0000 −0.673575
\(13\) 0 0
\(14\) −78.0000 −1.48903
\(15\) −48.4974 + 84.0000i −0.834799 + 1.44591i
\(16\) 40.0000 69.2820i 0.625000 1.08253i
\(17\) 13.5000 + 23.3827i 0.192602 + 0.333596i 0.946112 0.323840i \(-0.104974\pi\)
−0.753510 + 0.657437i \(0.771641\pi\)
\(18\) −76.2102 −0.997940
\(19\) −44.1673 76.5000i −0.533299 0.923700i −0.999244 0.0388865i \(-0.987619\pi\)
0.465945 0.884814i \(-0.345714\pi\)
\(20\) 27.7128 + 48.0000i 0.309839 + 0.536656i
\(21\) −157.617 −1.63785
\(22\) 39.0000 + 67.5500i 0.377947 + 0.654623i
\(23\) 28.5000 49.3634i 0.258377 0.447521i −0.707431 0.706783i \(-0.750146\pi\)
0.965807 + 0.259261i \(0.0834791\pi\)
\(24\) 48.4974 84.0000i 0.412479 0.714435i
\(25\) 67.0000 0.536000
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) −45.0333 + 78.0000i −0.303946 + 0.526451i
\(29\) 34.5000 59.7558i 0.220913 0.382633i −0.734172 0.678963i \(-0.762430\pi\)
0.955086 + 0.296330i \(0.0957628\pi\)
\(30\) 168.000 + 290.985i 1.02242 + 1.77088i
\(31\) 72.7461 0.421471 0.210735 0.977543i \(-0.432414\pi\)
0.210735 + 0.977543i \(0.432414\pi\)
\(32\) −83.1384 144.000i −0.459279 0.795495i
\(33\) 78.8083 + 136.500i 0.415720 + 0.720048i
\(34\) 93.5307 0.471776
\(35\) 156.000 + 270.200i 0.753395 + 1.30492i
\(36\) −44.0000 + 76.2102i −0.203704 + 0.352825i
\(37\) −19.9186 + 34.5000i −0.0885026 + 0.153291i −0.906878 0.421393i \(-0.861541\pi\)
0.818376 + 0.574683i \(0.194875\pi\)
\(38\) −306.000 −1.30631
\(39\) 0 0
\(40\) −192.000 −0.758947
\(41\) 196.588 340.500i 0.748826 1.29700i −0.199560 0.979886i \(-0.563951\pi\)
0.948386 0.317118i \(-0.102715\pi\)
\(42\) −273.000 + 472.850i −1.00297 + 1.73720i
\(43\) −42.5000 73.6122i −0.150725 0.261064i 0.780769 0.624820i \(-0.214828\pi\)
−0.931494 + 0.363756i \(0.881494\pi\)
\(44\) 90.0666 0.308592
\(45\) 152.420 + 264.000i 0.504922 + 0.874551i
\(46\) −98.7269 171.000i −0.316445 0.548099i
\(47\) −342.946 −1.06434 −0.532168 0.846639i \(-0.678623\pi\)
−0.532168 + 0.846639i \(0.678623\pi\)
\(48\) −280.000 484.974i −0.841969 1.45833i
\(49\) −82.0000 + 142.028i −0.239067 + 0.414076i
\(50\) 116.047 201.000i 0.328232 0.568514i
\(51\) 189.000 0.518927
\(52\) 0 0
\(53\) 426.000 1.10407 0.552034 0.833822i \(-0.313852\pi\)
0.552034 + 0.833822i \(0.313852\pi\)
\(54\) 60.6218 105.000i 0.152770 0.264605i
\(55\) 156.000 270.200i 0.382455 0.662432i
\(56\) −156.000 270.200i −0.372257 0.644768i
\(57\) −618.342 −1.43687
\(58\) −119.512 207.000i −0.270563 0.468628i
\(59\) 9.52628 + 16.5000i 0.0210206 + 0.0364088i 0.876344 0.481685i \(-0.159975\pi\)
−0.855324 + 0.518094i \(0.826642\pi\)
\(60\) 387.979 0.834799
\(61\) 8.50000 + 14.7224i 0.0178412 + 0.0309019i 0.874808 0.484469i \(-0.160987\pi\)
−0.856967 + 0.515371i \(0.827654\pi\)
\(62\) 126.000 218.238i 0.258097 0.447037i
\(63\) −247.683 + 429.000i −0.495320 + 0.857919i
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 546.000 1.01830
\(67\) −82.2724 + 142.500i −0.150018 + 0.259838i −0.931234 0.364423i \(-0.881266\pi\)
0.781216 + 0.624261i \(0.214600\pi\)
\(68\) 54.0000 93.5307i 0.0963009 0.166798i
\(69\) −199.500 345.544i −0.348072 0.602879i
\(70\) 1080.80 1.84543
\(71\) 291.851 + 505.500i 0.487835 + 0.844955i 0.999902 0.0139904i \(-0.00445341\pi\)
−0.512067 + 0.858945i \(0.671120\pi\)
\(72\) −152.420 264.000i −0.249485 0.432121i
\(73\) 1004.59 1.61066 0.805331 0.592826i \(-0.201988\pi\)
0.805331 + 0.592826i \(0.201988\pi\)
\(74\) 69.0000 + 119.512i 0.108393 + 0.187742i
\(75\) 234.500 406.166i 0.361036 0.625333i
\(76\) −176.669 + 306.000i −0.266649 + 0.461850i
\(77\) 507.000 0.750364
\(78\) 0 0
\(79\) −1244.00 −1.77166 −0.885829 0.464012i \(-0.846409\pi\)
−0.885829 + 0.464012i \(0.846409\pi\)
\(80\) −554.256 + 960.000i −0.774597 + 1.34164i
\(81\) 419.500 726.595i 0.575446 0.996701i
\(82\) −681.000 1179.53i −0.917120 1.58850i
\(83\) 426.084 0.563480 0.281740 0.959491i \(-0.409088\pi\)
0.281740 + 0.959491i \(0.409088\pi\)
\(84\) 315.233 + 546.000i 0.409462 + 0.709208i
\(85\) −187.061 324.000i −0.238702 0.413444i
\(86\) −294.449 −0.369200
\(87\) −241.500 418.290i −0.297604 0.515465i
\(88\) −156.000 + 270.200i −0.188973 + 0.327311i
\(89\) 153.286 265.500i 0.182566 0.316213i −0.760188 0.649703i \(-0.774893\pi\)
0.942753 + 0.333490i \(0.108226\pi\)
\(90\) 1056.00 1.23680
\(91\) 0 0
\(92\) −228.000 −0.258377
\(93\) 254.611 441.000i 0.283892 0.491716i
\(94\) −594.000 + 1028.84i −0.651770 + 1.12890i
\(95\) 612.000 + 1060.02i 0.660946 + 1.14479i
\(96\) −1163.94 −1.23744
\(97\) 617.476 + 1069.50i 0.646342 + 1.11950i 0.983990 + 0.178225i \(0.0570355\pi\)
−0.337647 + 0.941273i \(0.609631\pi\)
\(98\) 284.056 + 492.000i 0.292796 + 0.507138i
\(99\) 495.367 0.502891
\(100\) −134.000 232.095i −0.134000 0.232095i
\(101\) 979.500 1696.54i 0.964989 1.67141i 0.255345 0.966850i \(-0.417811\pi\)
0.709645 0.704560i \(-0.248856\pi\)
\(102\) 327.358 567.000i 0.317777 0.550406i
\(103\) −1856.00 −1.77551 −0.887753 0.460320i \(-0.847735\pi\)
−0.887753 + 0.460320i \(0.847735\pi\)
\(104\) 0 0
\(105\) 2184.00 2.02987
\(106\) 737.854 1278.00i 0.676101 1.17104i
\(107\) 127.500 220.836i 0.115195 0.199524i −0.802663 0.596433i \(-0.796584\pi\)
0.917858 + 0.396909i \(0.129917\pi\)
\(108\) −70.0000 121.244i −0.0623681 0.108025i
\(109\) 609.682 0.535752 0.267876 0.963453i \(-0.413678\pi\)
0.267876 + 0.963453i \(0.413678\pi\)
\(110\) −540.400 936.000i −0.468410 0.811310i
\(111\) 139.430 + 241.500i 0.119226 + 0.206506i
\(112\) −1801.33 −1.51973
\(113\) −205.500 355.936i −0.171078 0.296316i 0.767719 0.640787i \(-0.221392\pi\)
−0.938797 + 0.344471i \(0.888058\pi\)
\(114\) −1071.00 + 1855.03i −0.879898 + 1.52403i
\(115\) −394.908 + 684.000i −0.320220 + 0.554638i
\(116\) −276.000 −0.220913
\(117\) 0 0
\(118\) 66.0000 0.0514898
\(119\) 303.975 526.500i 0.234162 0.405581i
\(120\) −672.000 + 1163.94i −0.511208 + 0.885438i
\(121\) 412.000 + 713.605i 0.309542 + 0.536142i
\(122\) 58.8897 0.0437018
\(123\) −1376.11 2383.50i −1.00878 1.74726i
\(124\) −145.492 252.000i −0.105368 0.182502i
\(125\) 803.672 0.575061
\(126\) 858.000 + 1486.10i 0.606641 + 1.05073i
\(127\) −1121.50 + 1942.49i −0.783599 + 1.35723i 0.146234 + 0.989250i \(0.453285\pi\)
−0.929833 + 0.367983i \(0.880049\pi\)
\(128\) 775.959 1344.00i 0.535826 0.928078i
\(129\) −595.000 −0.406099
\(130\) 0 0
\(131\) −372.000 −0.248105 −0.124053 0.992276i \(-0.539589\pi\)
−0.124053 + 0.992276i \(0.539589\pi\)
\(132\) 315.233 546.000i 0.207860 0.360024i
\(133\) −994.500 + 1722.52i −0.648377 + 1.12302i
\(134\) 285.000 + 493.634i 0.183733 + 0.318235i
\(135\) −484.974 −0.309185
\(136\) 187.061 + 324.000i 0.117944 + 0.204285i
\(137\) 594.959 + 1030.50i 0.371028 + 0.642639i 0.989724 0.142991i \(-0.0456721\pi\)
−0.618696 + 0.785630i \(0.712339\pi\)
\(138\) −1382.18 −0.852599
\(139\) 1272.50 + 2204.03i 0.776490 + 1.34492i 0.933953 + 0.357395i \(0.116335\pi\)
−0.157464 + 0.987525i \(0.550332\pi\)
\(140\) 624.000 1080.80i 0.376697 0.652459i
\(141\) −1200.31 + 2079.00i −0.716911 + 1.24173i
\(142\) 2022.00 1.19495
\(143\) 0 0
\(144\) −1760.00 −1.01852
\(145\) −478.046 + 828.000i −0.273790 + 0.474218i
\(146\) 1740.00 3013.77i 0.986325 1.70836i
\(147\) 574.000 + 994.197i 0.322059 + 0.557823i
\(148\) 159.349 0.0885026
\(149\) 652.117 + 1129.50i 0.358547 + 0.621022i 0.987718 0.156245i \(-0.0499389\pi\)
−0.629171 + 0.777267i \(0.716606\pi\)
\(150\) −812.332 1407.00i −0.442177 0.765874i
\(151\) −86.6025 −0.0466729 −0.0233365 0.999728i \(-0.507429\pi\)
−0.0233365 + 0.999728i \(0.507429\pi\)
\(152\) −612.000 1060.02i −0.326577 0.565649i
\(153\) 297.000 514.419i 0.156935 0.271819i
\(154\) 878.150 1521.00i 0.459502 0.795881i
\(155\) −1008.00 −0.522352
\(156\) 0 0
\(157\) −1534.00 −0.779787 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(158\) −2154.67 + 3732.00i −1.08491 + 1.87913i
\(159\) 1491.00 2582.49i 0.743673 1.28808i
\(160\) 1152.00 + 1995.32i 0.569210 + 0.985901i
\(161\) −1283.45 −0.628261
\(162\) −1453.19 2517.00i −0.704774 1.22070i
\(163\) 816.662 + 1414.50i 0.392429 + 0.679707i 0.992769 0.120038i \(-0.0383016\pi\)
−0.600340 + 0.799745i \(0.704968\pi\)
\(164\) −1572.70 −0.748826
\(165\) −1092.00 1891.40i −0.515225 0.892395i
\(166\) 738.000 1278.25i 0.345060 0.597661i
\(167\) 813.198 1408.50i 0.376809 0.652653i −0.613787 0.789472i \(-0.710355\pi\)
0.990596 + 0.136819i \(0.0436879\pi\)
\(168\) −2184.00 −1.00297
\(169\) 0 0
\(170\) −1296.00 −0.584698
\(171\) −971.681 + 1683.00i −0.434540 + 0.752645i
\(172\) −170.000 + 294.449i −0.0753627 + 0.130532i
\(173\) −436.500 756.040i −0.191829 0.332258i 0.754027 0.656843i \(-0.228109\pi\)
−0.945857 + 0.324585i \(0.894775\pi\)
\(174\) −1673.16 −0.728977
\(175\) −754.308 1306.50i −0.325830 0.564355i
\(176\) 900.666 + 1560.00i 0.385740 + 0.668122i
\(177\) 133.368 0.0566359
\(178\) −531.000 919.719i −0.223596 0.387280i
\(179\) −643.500 + 1114.57i −0.268701 + 0.465403i −0.968527 0.248910i \(-0.919928\pi\)
0.699826 + 0.714314i \(0.253261\pi\)
\(180\) 609.682 1056.00i 0.252461 0.437276i
\(181\) −2.00000 −0.000821319 −0.000410660 1.00000i \(-0.500131\pi\)
−0.000410660 1.00000i \(0.500131\pi\)
\(182\) 0 0
\(183\) 119.000 0.0480696
\(184\) 394.908 684.000i 0.158223 0.274050i
\(185\) 276.000 478.046i 0.109686 0.189982i
\(186\) −882.000 1527.67i −0.347696 0.602226i
\(187\) −607.950 −0.237742
\(188\) 685.892 + 1188.00i 0.266084 + 0.460871i
\(189\) −394.042 682.500i −0.151652 0.262670i
\(190\) 4240.06 1.61898
\(191\) 1420.50 + 2460.38i 0.538135 + 0.932077i 0.999005 + 0.0446092i \(0.0142043\pi\)
−0.460870 + 0.887468i \(0.652462\pi\)
\(192\) 224.000 387.979i 0.0841969 0.145833i
\(193\) −2122.63 + 3676.50i −0.791659 + 1.37119i 0.133281 + 0.991078i \(0.457449\pi\)
−0.924939 + 0.380115i \(0.875885\pi\)
\(194\) 4278.00 1.58321
\(195\) 0 0
\(196\) 656.000 0.239067
\(197\) −1376.11 + 2383.50i −0.497686 + 0.862017i −0.999996 0.00267023i \(-0.999150\pi\)
0.502311 + 0.864687i \(0.332483\pi\)
\(198\) 858.000 1486.10i 0.307957 0.533396i
\(199\) −842.500 1459.25i −0.300117 0.519818i 0.676045 0.736860i \(-0.263692\pi\)
−0.976162 + 0.217042i \(0.930359\pi\)
\(200\) 928.379 0.328232
\(201\) 575.907 + 997.500i 0.202096 + 0.350041i
\(202\) −3393.09 5877.00i −1.18187 2.04705i
\(203\) −1553.65 −0.537167
\(204\) −378.000 654.715i −0.129732 0.224702i
\(205\) −2724.00 + 4718.11i −0.928061 + 1.60745i
\(206\) −3214.69 + 5568.00i −1.08727 + 1.88321i
\(207\) −1254.00 −0.421058
\(208\) 0 0
\(209\) 1989.00 0.658287
\(210\) 3782.80 6552.00i 1.24304 2.15300i
\(211\) −840.500 + 1455.79i −0.274229 + 0.474979i −0.969940 0.243343i \(-0.921756\pi\)
0.695711 + 0.718322i \(0.255089\pi\)
\(212\) −852.000 1475.71i −0.276017 0.478075i
\(213\) 4085.91 1.31437
\(214\) −441.673 765.000i −0.141085 0.244366i
\(215\) 588.897 + 1020.00i 0.186802 + 0.323551i
\(216\) 484.974 0.152770
\(217\) −819.000 1418.55i −0.256209 0.443767i
\(218\) 1056.00 1829.05i 0.328080 0.568250i
\(219\) 3516.06 6090.00i 1.08490 1.87911i
\(220\) −1248.00 −0.382455
\(221\) 0 0
\(222\) 966.000 0.292044
\(223\) 2048.15 3547.50i 0.615042 1.06528i −0.375336 0.926889i \(-0.622473\pi\)
0.990377 0.138394i \(-0.0441941\pi\)
\(224\) −1872.00 + 3242.40i −0.558385 + 0.967151i
\(225\) −737.000 1276.52i −0.218370 0.378229i
\(226\) −1423.75 −0.419054
\(227\) 219.104 + 379.500i 0.0640638 + 0.110962i 0.896278 0.443492i \(-0.146261\pi\)
−0.832215 + 0.554454i \(0.812927\pi\)
\(228\) 1236.68 + 2142.00i 0.359217 + 0.622182i
\(229\) 180.133 0.0519805 0.0259903 0.999662i \(-0.491726\pi\)
0.0259903 + 0.999662i \(0.491726\pi\)
\(230\) 1368.00 + 2369.45i 0.392188 + 0.679290i
\(231\) 1774.50 3073.52i 0.505427 0.875424i
\(232\) 478.046 828.000i 0.135281 0.234314i
\(233\) 5778.00 1.62459 0.812295 0.583247i \(-0.198218\pi\)
0.812295 + 0.583247i \(0.198218\pi\)
\(234\) 0 0
\(235\) 4752.00 1.31909
\(236\) 38.1051 66.0000i 0.0105103 0.0182044i
\(237\) −4354.00 + 7541.35i −1.19334 + 2.06693i
\(238\) −1053.00 1823.85i −0.286789 0.496734i
\(239\) 1860.22 0.503464 0.251732 0.967797i \(-0.419000\pi\)
0.251732 + 0.967797i \(0.419000\pi\)
\(240\) 3879.79 + 6720.00i 1.04350 + 1.80739i
\(241\) −1029.70 1783.50i −0.275224 0.476703i 0.694967 0.719041i \(-0.255419\pi\)
−0.970192 + 0.242339i \(0.922085\pi\)
\(242\) 2854.42 0.758219
\(243\) −2464.00 4267.77i −0.650476 1.12666i
\(244\) 34.0000 58.8897i 0.00892060 0.0154509i
\(245\) 1136.23 1968.00i 0.296289 0.513187i
\(246\) −9534.00 −2.47100
\(247\) 0 0
\(248\) 1008.00 0.258097
\(249\) 1491.30 2583.00i 0.379546 0.657393i
\(250\) 1392.00 2411.01i 0.352151 0.609944i
\(251\) 2245.50 + 3889.32i 0.564680 + 0.978055i 0.997079 + 0.0763724i \(0.0243338\pi\)
−0.432399 + 0.901682i \(0.642333\pi\)
\(252\) 1981.47 0.495320
\(253\) 641.725 + 1111.50i 0.159466 + 0.276203i
\(254\) 3884.99 + 6729.00i 0.959708 + 1.66226i
\(255\) −2618.86 −0.643135
\(256\) −2432.00 4212.35i −0.593750 1.02841i
\(257\) 2725.50 4720.70i 0.661525 1.14580i −0.318690 0.947859i \(-0.603243\pi\)
0.980215 0.197936i \(-0.0634239\pi\)
\(258\) −1030.57 + 1785.00i −0.248684 + 0.430734i
\(259\) 897.000 0.215200
\(260\) 0 0
\(261\) −1518.00 −0.360007
\(262\) −644.323 + 1116.00i −0.151933 + 0.263155i
\(263\) 391.500 678.098i 0.0917906 0.158986i −0.816474 0.577382i \(-0.804074\pi\)
0.908265 + 0.418396i \(0.137408\pi\)
\(264\) 1092.00 + 1891.40i 0.254576 + 0.440938i
\(265\) −5902.83 −1.36833
\(266\) 3445.05 + 5967.00i 0.794096 + 1.37541i
\(267\) −1073.01 1858.50i −0.245943 0.425986i
\(268\) 658.179 0.150018
\(269\) 2542.50 + 4403.74i 0.576279 + 0.998144i 0.995901 + 0.0904453i \(0.0288290\pi\)
−0.419623 + 0.907699i \(0.637838\pi\)
\(270\) −840.000 + 1454.92i −0.189336 + 0.327940i
\(271\) −662.509 + 1147.50i −0.148504 + 0.257216i −0.930675 0.365848i \(-0.880779\pi\)
0.782171 + 0.623064i \(0.214112\pi\)
\(272\) 2160.00 0.481505
\(273\) 0 0
\(274\) 4122.00 0.908829
\(275\) −754.308 + 1306.50i −0.165405 + 0.286491i
\(276\) −798.000 + 1382.18i −0.174036 + 0.301439i
\(277\) −1710.50 2962.67i −0.371025 0.642635i 0.618698 0.785629i \(-0.287660\pi\)
−0.989724 + 0.142994i \(0.954327\pi\)
\(278\) 8816.14 1.90200
\(279\) −800.207 1386.00i −0.171710 0.297411i
\(280\) 2161.60 + 3744.00i 0.461358 + 0.799096i
\(281\) 810.600 0.172087 0.0860433 0.996291i \(-0.472578\pi\)
0.0860433 + 0.996291i \(0.472578\pi\)
\(282\) 4158.00 + 7201.87i 0.878033 + 1.52080i
\(283\) 3588.50 6215.46i 0.753760 1.30555i −0.192228 0.981350i \(-0.561571\pi\)
0.945988 0.324201i \(-0.105095\pi\)
\(284\) 1167.40 2022.00i 0.243918 0.422478i
\(285\) 8568.00 1.78079
\(286\) 0 0
\(287\) −8853.00 −1.82082
\(288\) −1829.05 + 3168.00i −0.374228 + 0.648181i
\(289\) 2092.00 3623.45i 0.425809 0.737523i
\(290\) 1656.00 + 2868.28i 0.335323 + 0.580796i
\(291\) 8644.67 1.74144
\(292\) −2009.18 3480.00i −0.402665 0.697437i
\(293\) −4656.62 8065.50i −0.928473 1.60816i −0.785878 0.618381i \(-0.787789\pi\)
−0.142595 0.989781i \(-0.545544\pi\)
\(294\) 3976.79 0.788881
\(295\) −132.000 228.631i −0.0260520 0.0451234i
\(296\) −276.000 + 478.046i −0.0541965 + 0.0938712i
\(297\) −394.042 + 682.500i −0.0769852 + 0.133342i
\(298\) 4518.00 0.878257
\(299\) 0 0
\(300\) −1876.00 −0.361036
\(301\) −956.958 + 1657.50i −0.183250 + 0.317398i
\(302\) −150.000 + 259.808i −0.0285812 + 0.0495041i
\(303\) −6856.50 11875.8i −1.29999 2.25164i
\(304\) −7066.77 −1.33325
\(305\) −117.779 204.000i −0.0221116 0.0382984i
\(306\) −1028.84 1782.00i −0.192205 0.332909i
\(307\) −4777.00 −0.888070 −0.444035 0.896009i \(-0.646453\pi\)
−0.444035 + 0.896009i \(0.646453\pi\)
\(308\) −1014.00 1756.30i −0.187591 0.324917i
\(309\) −6496.00 + 11251.4i −1.19594 + 2.07142i
\(310\) −1745.91 + 3024.00i −0.319874 + 0.554038i
\(311\) −6192.00 −1.12899 −0.564495 0.825436i \(-0.690929\pi\)
−0.564495 + 0.825436i \(0.690929\pi\)
\(312\) 0 0
\(313\) −770.000 −0.139051 −0.0695255 0.997580i \(-0.522149\pi\)
−0.0695255 + 0.997580i \(0.522149\pi\)
\(314\) −2656.97 + 4602.00i −0.477520 + 0.827089i
\(315\) 3432.00 5944.40i 0.613877 1.06327i
\(316\) 2488.00 + 4309.34i 0.442914 + 0.767150i
\(317\) −8057.50 −1.42762 −0.713808 0.700341i \(-0.753031\pi\)
−0.713808 + 0.700341i \(0.753031\pi\)
\(318\) −5164.98 8946.00i −0.910810 1.57757i
\(319\) 776.825 + 1345.50i 0.136344 + 0.236155i
\(320\) −886.810 −0.154919
\(321\) −892.500 1545.86i −0.155185 0.268789i
\(322\) −2223.00 + 3850.35i −0.384730 + 0.666371i
\(323\) 1192.52 2065.50i 0.205429 0.355813i
\(324\) −3356.00 −0.575446
\(325\) 0 0
\(326\) 5658.00 0.961250
\(327\) 2133.89 3696.00i 0.360869 0.625044i
\(328\) 2724.00 4718.11i 0.458560 0.794250i
\(329\) 3861.00 + 6687.45i 0.647002 + 1.12064i
\(330\) −7565.60 −1.26204
\(331\) −2638.78 4570.50i −0.438189 0.758965i 0.559361 0.828924i \(-0.311046\pi\)
−0.997550 + 0.0699590i \(0.977713\pi\)
\(332\) −852.169 1476.00i −0.140870 0.243994i
\(333\) 876.418 0.144226
\(334\) −2817.00 4879.19i −0.461495 0.799333i
\(335\) 1140.00 1974.54i 0.185925 0.322031i
\(336\) −6304.66 + 10920.0i −1.02365 + 1.77302i
\(337\) −8278.00 −1.33808 −0.669038 0.743228i \(-0.733294\pi\)
−0.669038 + 0.743228i \(0.733294\pi\)
\(338\) 0 0
\(339\) −2877.00 −0.460936
\(340\) −748.246 + 1296.00i −0.119351 + 0.206722i
\(341\) −819.000 + 1418.55i −0.130063 + 0.225275i
\(342\) 3366.00 + 5830.08i 0.532200 + 0.921798i
\(343\) −4030.48 −0.634477
\(344\) −588.897 1020.00i −0.0923000 0.159868i
\(345\) 2764.35 + 4788.00i 0.431385 + 0.747180i
\(346\) −3024.16 −0.469884
\(347\) −3433.50 5947.00i −0.531181 0.920033i −0.999338 0.0363875i \(-0.988415\pi\)
0.468156 0.883646i \(-0.344918\pi\)
\(348\) −966.000 + 1673.16i −0.148802 + 0.257732i
\(349\) 6076.90 10525.5i 0.932060 1.61438i 0.152266 0.988340i \(-0.451343\pi\)
0.779794 0.626036i \(-0.215324\pi\)
\(350\) −5226.00 −0.798118
\(351\) 0 0
\(352\) 3744.00 0.566920
\(353\) −2903.78 + 5029.50i −0.437827 + 0.758338i −0.997522 0.0703608i \(-0.977585\pi\)
0.559695 + 0.828699i \(0.310918\pi\)
\(354\) 231.000 400.104i 0.0346822 0.0600714i
\(355\) −4044.00 7004.41i −0.604601 1.04720i
\(356\) −1226.29 −0.182566
\(357\) −2127.82 3685.50i −0.315452 0.546379i
\(358\) 2229.15 + 3861.00i 0.329090 + 0.570001i
\(359\) 1340.61 0.197088 0.0985439 0.995133i \(-0.468581\pi\)
0.0985439 + 0.995133i \(0.468581\pi\)
\(360\) 2112.00 + 3658.09i 0.309200 + 0.535551i
\(361\) −472.000 + 817.528i −0.0688147 + 0.119191i
\(362\) −3.46410 + 6.00000i −0.000502953 + 0.000871141i
\(363\) 5768.00 0.833999
\(364\) 0 0
\(365\) −13920.0 −1.99618
\(366\) 206.114 357.000i 0.0294365 0.0509855i
\(367\) −1832.50 + 3173.98i −0.260642 + 0.451446i −0.966413 0.256995i \(-0.917268\pi\)
0.705770 + 0.708441i \(0.250601\pi\)
\(368\) −2280.00 3949.08i −0.322971 0.559402i
\(369\) −8649.86 −1.22031
\(370\) −956.092 1656.00i −0.134337 0.232679i
\(371\) −4796.05 8307.00i −0.671155 1.16247i
\(372\) −2036.89 −0.283892
\(373\) −2685.50 4651.42i −0.372788 0.645688i 0.617205 0.786802i \(-0.288265\pi\)
−0.989993 + 0.141114i \(0.954931\pi\)
\(374\) −1053.00 + 1823.85i −0.145586 + 0.252163i
\(375\) 2812.85 4872.00i 0.387347 0.670904i
\(376\) −4752.00 −0.651770
\(377\) 0 0
\(378\) −2730.00 −0.371471
\(379\) 5754.74 9967.50i 0.779950 1.35091i −0.152020 0.988377i \(-0.548578\pi\)
0.931970 0.362536i \(-0.118089\pi\)
\(380\) 2448.00 4240.06i 0.330473 0.572396i
\(381\) 7850.50 + 13597.5i 1.05563 + 1.82840i
\(382\) 9841.51 1.31816
\(383\) 1209.84 + 2095.50i 0.161409 + 0.279569i 0.935374 0.353659i \(-0.115063\pi\)
−0.773965 + 0.633228i \(0.781729\pi\)
\(384\) −5431.71 9408.00i −0.721838 1.25026i
\(385\) −7025.20 −0.929967
\(386\) 7353.00 + 12735.8i 0.969580 + 1.67936i
\(387\) −935.000 + 1619.47i −0.122813 + 0.212719i
\(388\) 2469.90 4278.00i 0.323171 0.559749i
\(389\) 9858.00 1.28489 0.642443 0.766334i \(-0.277921\pi\)
0.642443 + 0.766334i \(0.277921\pi\)
\(390\) 0 0
\(391\) 1539.00 0.199055
\(392\) −1136.23 + 1968.00i −0.146398 + 0.253569i
\(393\) −1302.00 + 2255.13i −0.167118 + 0.289456i
\(394\) 4767.00 + 8256.69i 0.609538 + 1.05575i
\(395\) 17237.4 2.19571
\(396\) −990.733 1716.00i −0.125723 0.217758i
\(397\) 4360.44 + 7552.50i 0.551245 + 0.954784i 0.998185 + 0.0602200i \(0.0191802\pi\)
−0.446941 + 0.894564i \(0.647486\pi\)
\(398\) −5837.01 −0.735133
\(399\) 6961.50 + 12057.7i 0.873461 + 1.51288i
\(400\) 2680.00 4641.90i 0.335000 0.580237i
\(401\) −3792.33 + 6568.50i −0.472269 + 0.817993i −0.999496 0.0317308i \(-0.989898\pi\)
0.527228 + 0.849724i \(0.323231\pi\)
\(402\) 3990.00 0.495033
\(403\) 0 0
\(404\) −7836.00 −0.964989
\(405\) −5812.76 + 10068.0i −0.713181 + 1.23527i
\(406\) −2691.00 + 4660.95i −0.328946 + 0.569751i
\(407\) −448.500 776.825i −0.0546224 0.0946088i
\(408\) 2618.86 0.317777
\(409\) 2152.07 + 3727.50i 0.260179 + 0.450643i 0.966289 0.257459i \(-0.0828851\pi\)
−0.706110 + 0.708102i \(0.749552\pi\)
\(410\) 9436.21 + 16344.0i 1.13664 + 1.96871i
\(411\) 8329.43 0.999661
\(412\) 3712.00 + 6429.37i 0.443876 + 0.768817i
\(413\) 214.500 371.525i 0.0255565 0.0442652i
\(414\) −2171.99 + 3762.00i −0.257844 + 0.446600i
\(415\) −5904.00 −0.698352
\(416\) 0 0
\(417\) 17815.0 2.09210
\(418\) 3445.05 5967.00i 0.403117 0.698219i
\(419\) −2698.50 + 4673.94i −0.314631 + 0.544957i −0.979359 0.202129i \(-0.935214\pi\)
0.664728 + 0.747085i \(0.268547\pi\)
\(420\) −4368.00 7565.60i −0.507468 0.878960i
\(421\) −7260.76 −0.840541 −0.420270 0.907399i \(-0.638065\pi\)
−0.420270 + 0.907399i \(0.638065\pi\)
\(422\) 2911.58 + 5043.00i 0.335861 + 0.581728i
\(423\) 3772.41 + 6534.00i 0.433619 + 0.751050i
\(424\) 5902.83 0.676101
\(425\) 904.500 + 1566.64i 0.103235 + 0.178808i
\(426\) 7077.00 12257.7i 0.804887 1.39410i
\(427\) 191.392 331.500i 0.0216911 0.0375700i
\(428\) −1020.00 −0.115195
\(429\) 0 0
\(430\) 4080.00 0.457570
\(431\) 243.353 421.500i 0.0271970 0.0471066i −0.852107 0.523368i \(-0.824675\pi\)
0.879304 + 0.476262i \(0.158009\pi\)
\(432\) 1400.00 2424.87i 0.155920 0.270062i
\(433\) 6069.50 + 10512.7i 0.673629 + 1.16676i 0.976867 + 0.213846i \(0.0685989\pi\)
−0.303238 + 0.952915i \(0.598068\pi\)
\(434\) −5674.20 −0.627581
\(435\) 3346.32 + 5796.00i 0.368836 + 0.638844i
\(436\) −1219.36 2112.00i −0.133938 0.231987i
\(437\) −5035.07 −0.551167
\(438\) −12180.0 21096.4i −1.32873 2.30142i
\(439\) 230.500 399.238i 0.0250596 0.0434045i −0.853224 0.521545i \(-0.825356\pi\)
0.878283 + 0.478141i \(0.158689\pi\)
\(440\) 2161.60 3744.00i 0.234205 0.405655i
\(441\) 3608.00 0.389591
\(442\) 0 0
\(443\) 12156.0 1.30372 0.651861 0.758338i \(-0.273988\pi\)
0.651861 + 0.758338i \(0.273988\pi\)
\(444\) 557.720 966.000i 0.0596131 0.103253i
\(445\) −2124.00 + 3678.88i −0.226263 + 0.391900i
\(446\) −7095.00 12288.9i −0.753269 1.30470i
\(447\) 9129.64 0.966034
\(448\) −720.533 1248.00i −0.0759866 0.131613i
\(449\) 148.090 + 256.500i 0.0155653 + 0.0269599i 0.873703 0.486459i \(-0.161712\pi\)
−0.858138 + 0.513419i \(0.828379\pi\)
\(450\) −5106.09 −0.534896
\(451\) 4426.50 + 7666.92i 0.462164 + 0.800491i
\(452\) −822.000 + 1423.75i −0.0855390 + 0.148158i
\(453\) −303.109 + 525.000i −0.0314377 + 0.0544518i
\(454\) 1518.00 0.156924
\(455\) 0 0
\(456\) −8568.00 −0.879898
\(457\) −305.707 + 529.500i −0.0312918 + 0.0541990i −0.881247 0.472656i \(-0.843295\pi\)
0.849955 + 0.526855i \(0.176629\pi\)
\(458\) 312.000 540.400i 0.0318314 0.0551337i
\(459\) 472.500 + 818.394i 0.0480488 + 0.0832230i
\(460\) 3159.26 0.320220
\(461\) −6563.61 11368.5i −0.663119 1.14855i −0.979792 0.200020i \(-0.935899\pi\)
0.316673 0.948535i \(-0.397434\pi\)
\(462\) −6147.05 10647.0i −0.619019 1.07217i
\(463\) −834.848 −0.0837985 −0.0418992 0.999122i \(-0.513341\pi\)
−0.0418992 + 0.999122i \(0.513341\pi\)
\(464\) −2760.00 4780.46i −0.276142 0.478292i
\(465\) −3528.00 + 6110.68i −0.351843 + 0.609410i
\(466\) 10007.8 17334.0i 0.994854 1.72314i
\(467\) −14496.0 −1.43639 −0.718196 0.695841i \(-0.755032\pi\)
−0.718196 + 0.695841i \(0.755032\pi\)
\(468\) 0 0
\(469\) 3705.00 0.364778
\(470\) 8230.71 14256.0i 0.807775 1.39911i
\(471\) −5369.00 + 9299.38i −0.525245 + 0.909751i
\(472\) 132.000 + 228.631i 0.0128724 + 0.0222957i
\(473\) 1913.92 0.186051
\(474\) 15082.7 + 26124.0i 1.46154 + 2.53147i
\(475\) −2959.21 5125.50i −0.285848 0.495103i
\(476\) −2431.80 −0.234162
\(477\) −4686.00 8116.39i −0.449805 0.779086i
\(478\) 3222.00 5580.67i 0.308307 0.534004i
\(479\) −4448.77 + 7705.50i −0.424362 + 0.735017i −0.996361 0.0852376i \(-0.972835\pi\)
0.571998 + 0.820255i \(0.306168\pi\)
\(480\) 16128.0 1.53362
\(481\) 0 0
\(482\) −7134.00 −0.674159
\(483\) −4492.07 + 7780.50i −0.423181 + 0.732971i
\(484\) 1648.00 2854.42i 0.154771 0.268071i
\(485\) −8556.00 14819.4i −0.801047 1.38745i
\(486\) −17071.1 −1.59333
\(487\) 2377.24 + 4117.50i 0.221197 + 0.383125i 0.955172 0.296052i \(-0.0956702\pi\)
−0.733975 + 0.679177i \(0.762337\pi\)
\(488\) 117.779 + 204.000i 0.0109255 + 0.0189235i
\(489\) 11433.3 1.05732
\(490\) −3936.00 6817.35i −0.362878 0.628524i
\(491\) −817.500 + 1415.95i −0.0751390 + 0.130145i −0.901147 0.433514i \(-0.857273\pi\)
0.826008 + 0.563659i \(0.190607\pi\)
\(492\) −5504.46 + 9534.00i −0.504390 + 0.873630i
\(493\) 1863.00 0.170193
\(494\) 0 0
\(495\) −6864.00 −0.623260
\(496\) 2909.85 5040.00i 0.263419 0.456255i
\(497\) 6571.50 11382.2i 0.593103 1.02728i
\(498\) −5166.00 8947.77i −0.464847 0.805139i
\(499\) 14434.9 1.29498 0.647490 0.762074i \(-0.275819\pi\)
0.647490 + 0.762074i \(0.275819\pi\)
\(500\) −1607.34 2784.00i −0.143765 0.249009i
\(501\) −5692.38 9859.50i −0.507619 0.879222i
\(502\) 15557.3 1.38318
\(503\) −6343.50 10987.3i −0.562312 0.973952i −0.997294 0.0735133i \(-0.976579\pi\)
0.434983 0.900439i \(-0.356754\pi\)
\(504\) −3432.00 + 5944.40i −0.303320 + 0.525366i
\(505\) −13572.4 + 23508.0i −1.19596 + 2.07147i
\(506\) 4446.00 0.390610
\(507\) 0 0
\(508\) 8972.00 0.783599
\(509\) 2874.34 4978.50i 0.250300 0.433533i −0.713308 0.700850i \(-0.752804\pi\)
0.963608 + 0.267318i \(0.0861373\pi\)
\(510\) −4536.00 + 7856.58i −0.393838 + 0.682148i
\(511\) −11310.0 19589.5i −0.979109 1.69587i
\(512\) −4434.05 −0.382733
\(513\) −1545.86 2677.50i −0.133043 0.230438i
\(514\) −9441.41 16353.0i −0.810200 1.40331i
\(515\) 25717.5 2.20048
\(516\) 1190.00 + 2061.14i 0.101525 + 0.175846i
\(517\) 3861.00 6687.45i 0.328446 0.568885i
\(518\) 1553.65 2691.00i 0.131783 0.228254i
\(519\) −6111.00 −0.516846
\(520\) 0 0
\(521\) 6054.00 0.509080 0.254540 0.967062i \(-0.418076\pi\)
0.254540 + 0.967062i \(0.418076\pi\)
\(522\) −2629.25 + 4554.00i −0.220458 + 0.381845i
\(523\) 7401.50 12819.8i 0.618824 1.07183i −0.370877 0.928682i \(-0.620943\pi\)
0.989701 0.143153i \(-0.0457240\pi\)
\(524\) 744.000 + 1288.65i 0.0620263 + 0.107433i
\(525\) −10560.3 −0.877885
\(526\) −1356.20 2349.00i −0.112420 0.194717i
\(527\) 982.073 + 1701.00i 0.0811760 + 0.140601i
\(528\) 12609.3 1.03930
\(529\) 4459.00 + 7723.21i 0.366483 + 0.634767i
\(530\) −10224.0 + 17708.5i −0.837929 + 1.45133i
\(531\) 209.578 363.000i 0.0171279 0.0296664i
\(532\) 7956.00 0.648377
\(533\) 0 0
\(534\) −7434.00 −0.602436
\(535\) −1766.69 + 3060.00i −0.142768 + 0.247281i
\(536\) −1140.00 + 1974.54i −0.0918666 + 0.159118i
\(537\) 4504.50 + 7802.02i 0.361980 + 0.626969i
\(538\) 17615.0 1.41159
\(539\) −1846.37 3198.00i −0.147548 0.255561i
\(540\) 969.948 + 1680.00i 0.0772962 + 0.133881i
\(541\) −21470.5 −1.70626 −0.853132 0.521695i \(-0.825300\pi\)
−0.853132 + 0.521695i \(0.825300\pi\)
\(542\) 2295.00 + 3975.06i 0.181880 + 0.315025i
\(543\) −7.00000 + 12.1244i −0.000553221 + 0.000958206i
\(544\) 2244.74 3888.00i 0.176916 0.306428i
\(545\) −8448.00 −0.663986
\(546\) 0 0
\(547\) −13516.0 −1.05649 −0.528247 0.849091i \(-0.677151\pi\)
−0.528247 + 0.849091i \(0.677151\pi\)
\(548\) 2379.84 4122.00i 0.185514 0.321320i
\(549\) 187.000 323.894i 0.0145373 0.0251793i
\(550\) 2613.00 + 4525.85i 0.202579 + 0.350878i
\(551\) −6095.09 −0.471251
\(552\) −2764.35 4788.00i −0.213150 0.369186i
\(553\) 14005.4 + 24258.0i 1.07698 + 1.86538i
\(554\) −11850.7 −0.908822
\(555\) −1932.00 3346.32i −0.147764 0.255934i
\(556\) 5090.00 8816.14i 0.388245 0.672460i
\(557\) 1445.40 2503.50i 0.109952 0.190443i −0.805798 0.592190i \(-0.798264\pi\)
0.915751 + 0.401747i \(0.131597\pi\)
\(558\) −5544.00 −0.420603
\(559\) 0 0
\(560\) 24960.0 1.88349
\(561\) −2127.82 + 3685.50i −0.160137 + 0.277365i
\(562\) 1404.00 2431.80i 0.105381 0.182525i
\(563\) 5791.50 + 10031.2i 0.433539 + 0.750912i 0.997175 0.0751113i \(-0.0239312\pi\)
−0.563636 + 0.826023i \(0.690598\pi\)
\(564\) 9602.49 0.716911
\(565\) 2847.49 + 4932.00i 0.212026 + 0.367240i
\(566\) −12430.9 21531.0i −0.923164 1.59897i
\(567\) −18891.5 −1.39924
\(568\) 4044.00 + 7004.41i 0.298737 + 0.517427i
\(569\) 6439.50 11153.5i 0.474443 0.821759i −0.525129 0.851023i \(-0.675983\pi\)
0.999572 + 0.0292638i \(0.00931628\pi\)
\(570\) 14840.2 25704.0i 1.09051 1.88881i
\(571\) 11636.0 0.852805 0.426402 0.904534i \(-0.359781\pi\)
0.426402 + 0.904534i \(0.359781\pi\)
\(572\) 0 0
\(573\) 19887.0 1.44990
\(574\) −15333.8 + 26559.0i −1.11502 + 1.93127i
\(575\) 1909.50 3307.35i 0.138490 0.239871i
\(576\) −704.000 1219.36i −0.0509259 0.0882063i
\(577\) −12311.4 −0.888269 −0.444134 0.895960i \(-0.646489\pi\)
−0.444134 + 0.895960i \(0.646489\pi\)
\(578\) −7246.90 12552.0i −0.521507 0.903277i
\(579\) 14858.4 + 25735.5i 1.06648 + 1.84720i
\(580\) 3824.37 0.273790
\(581\) −4797.00 8308.65i −0.342535 0.593289i
\(582\) 14973.0 25934.0i 1.06641 1.84708i
\(583\) −4796.05 + 8307.00i −0.340707 + 0.590121i
\(584\) 13920.0 0.986325
\(585\) 0 0
\(586\) −32262.0 −2.27428
\(587\) 7822.81 13549.5i 0.550054 0.952722i −0.448216 0.893925i \(-0.647940\pi\)
0.998270 0.0587964i \(-0.0187263\pi\)
\(588\) 2296.00 3976.79i 0.161030 0.278912i
\(589\) −3213.00 5565.08i −0.224770 0.389313i
\(590\) −914.523 −0.0638141
\(591\) 9632.80 + 16684.5i 0.670458 + 1.16127i
\(592\) 1593.49 + 2760.00i 0.110628 + 0.191614i
\(593\) 25821.4 1.78813 0.894063 0.447942i \(-0.147843\pi\)
0.894063 + 0.447942i \(0.147843\pi\)
\(594\) 1365.00 + 2364.25i 0.0942873 + 0.163310i
\(595\) −4212.00 + 7295.40i −0.290210 + 0.502659i
\(596\) 2608.47 4518.00i 0.179274 0.310511i
\(597\) −11795.0 −0.808605
\(598\) 0 0
\(599\) 1668.00 0.113777 0.0568887 0.998381i \(-0.481882\pi\)
0.0568887 + 0.998381i \(0.481882\pi\)
\(600\) 3249.33 5628.00i 0.221089 0.382937i
\(601\) −6849.50 + 11863.7i −0.464887 + 0.805207i −0.999196 0.0400813i \(-0.987238\pi\)
0.534310 + 0.845289i \(0.320572\pi\)
\(602\) 3315.00 + 5741.75i 0.224434 + 0.388731i
\(603\) 3619.99 0.244473
\(604\) 173.205 + 300.000i 0.0116682 + 0.0202100i
\(605\) −5708.84 9888.00i −0.383632 0.664470i
\(606\) −47503.2 −3.18430
\(607\) 11586.5 + 20068.4i 0.774764 + 1.34193i 0.934927 + 0.354839i \(0.115464\pi\)
−0.160164 + 0.987090i \(0.551202\pi\)
\(608\) −7344.00 + 12720.2i −0.489866 + 0.848473i
\(609\) −5437.77 + 9418.50i −0.361822 + 0.626694i
\(610\) −816.000 −0.0541621
\(611\) 0 0
\(612\) −2376.00 −0.156935
\(613\) −8307.78 + 14389.5i −0.547387 + 0.948102i 0.451066 + 0.892491i \(0.351044\pi\)
−0.998453 + 0.0556111i \(0.982289\pi\)
\(614\) −8274.00 + 14331.0i −0.543830 + 0.941941i
\(615\) 19068.0 + 33026.7i 1.25024 + 2.16547i
\(616\) 7025.20 0.459502
\(617\) 14196.8 + 24589.5i 0.926321 + 1.60443i 0.789423 + 0.613849i \(0.210380\pi\)
0.136897 + 0.990585i \(0.456287\pi\)
\(618\) 22502.8 + 38976.0i 1.46472 + 2.53697i
\(619\) −6245.78 −0.405556 −0.202778 0.979225i \(-0.564997\pi\)
−0.202778 + 0.979225i \(0.564997\pi\)
\(620\) 2016.00 + 3491.81i 0.130588 + 0.226185i
\(621\) 997.500 1727.72i 0.0644578 0.111644i
\(622\) −10724.9 + 18576.0i −0.691363 + 1.19748i
\(623\) −6903.00 −0.443921
\(624\) 0 0
\(625\) −19511.0 −1.24870
\(626\) −1333.68 + 2310.00i −0.0851510 + 0.147486i
\(627\) 6961.50 12057.7i 0.443406 0.768002i
\(628\) 3068.00 + 5313.93i 0.194947 + 0.337658i
\(629\) −1075.60 −0.0681830
\(630\) −11888.8 20592.0i −0.751843 1.30223i
\(631\) −11189.9 19381.5i −0.705964 1.22277i −0.966342 0.257259i \(-0.917181\pi\)
0.260378 0.965507i \(-0.416153\pi\)
\(632\) −17237.4 −1.08491
\(633\) 5883.50 + 10190.5i 0.369428 + 0.639869i
\(634\) −13956.0 + 24172.5i −0.874233 + 1.51422i
\(635\) 15540.0 26916.0i 0.971157 1.68209i
\(636\) −11928.0 −0.743673
\(637\) 0 0
\(638\) 5382.00 0.333974
\(639\) 6420.71 11121.0i 0.397495 0.688482i
\(640\) −10752.0 + 18623.0i −0.664078 + 1.15022i
\(641\) 9913.50 + 17170.7i 0.610858 + 1.05804i 0.991096 + 0.133148i \(0.0425085\pi\)
−0.380239 + 0.924888i \(0.624158\pi\)
\(642\) −6183.42 −0.380125
\(643\) −4225.34 7318.50i −0.259146 0.448855i 0.706867 0.707346i \(-0.250108\pi\)
−0.966013 + 0.258492i \(0.916775\pi\)
\(644\) 2566.90 + 4446.00i 0.157065 + 0.272045i
\(645\) 8244.56 0.503301
\(646\) −4131.00 7155.10i −0.251598 0.435780i
\(647\) 1474.50 2553.91i 0.0895959 0.155185i −0.817744 0.575581i \(-0.804776\pi\)
0.907340 + 0.420397i \(0.138109\pi\)
\(648\) 5812.76 10068.0i 0.352387 0.610352i
\(649\) −429.000 −0.0259472
\(650\) 0 0
\(651\) −11466.0 −0.690304
\(652\) 3266.65 5658.00i 0.196214 0.339853i
\(653\) −6019.50 + 10426.1i −0.360737 + 0.624815i −0.988082 0.153926i \(-0.950808\pi\)
0.627345 + 0.778741i \(0.284141\pi\)
\(654\) −7392.00 12803.3i −0.441973 0.765519i
\(655\) 5154.58 0.307490
\(656\) −15727.0 27240.0i −0.936032 1.62126i
\(657\) −11050.5 19140.0i −0.656196 1.13656i
\(658\) 26749.8 1.58483
\(659\) −1681.50 2912.44i −0.0993960 0.172159i 0.812039 0.583603i \(-0.198358\pi\)
−0.911435 + 0.411445i \(0.865024\pi\)
\(660\) −4368.00 + 7565.60i −0.257612 + 0.446198i
\(661\) 5079.24 8797.50i 0.298880 0.517675i −0.677000 0.735983i \(-0.736720\pi\)
0.975880 + 0.218308i \(0.0700537\pi\)
\(662\) −18282.0 −1.07334
\(663\) 0 0
\(664\) 5904.00 0.345060
\(665\) 13780.2 23868.0i 0.803569 1.39182i
\(666\) 1518.00 2629.25i 0.0883203 0.152975i
\(667\) −1966.50 3406.08i −0.114158 0.197727i
\(668\) −6505.58 −0.376809
\(669\) −14337.1 24832.5i −0.828554 1.43510i
\(670\) −3949.08 6840.00i −0.227711 0.394406i
\(671\) −382.783 −0.0220226
\(672\) 13104.0 + 22696.8i 0.752229 + 1.30290i
\(673\) −9084.50 + 15734.8i −0.520329 + 0.901237i 0.479391 + 0.877601i \(0.340858\pi\)
−0.999721 + 0.0236358i \(0.992476\pi\)
\(674\) −14337.9 + 24834.0i −0.819400 + 1.41924i
\(675\) 2345.00 0.133717
\(676\) 0 0
\(677\) 9042.00 0.513312 0.256656 0.966503i \(-0.417379\pi\)
0.256656 + 0.966503i \(0.417379\pi\)
\(678\) −4983.11 + 8631.00i −0.282264 + 0.488896i
\(679\) 13903.5 24081.6i 0.785813 1.36107i
\(680\) −2592.00 4489.48i −0.146175 0.253182i
\(681\) 3067.46 0.172607
\(682\) 2837.10 + 4914.00i 0.159293 + 0.275904i
\(683\) 6231.05 + 10792.5i 0.349084 + 0.604632i 0.986087 0.166230i \(-0.0531593\pi\)
−0.637003 + 0.770862i \(0.719826\pi\)
\(684\) 7773.44 0.434540
\(685\) −8244.00 14279.0i −0.459835 0.796458i
\(686\) −6981.00 + 12091.4i −0.388536 + 0.672964i
\(687\) 630.466 1092.00i 0.0350128 0.0606440i
\(688\) −6800.00 −0.376813
\(689\) 0 0
\(690\) 19152.0 1.05667
\(691\) 2159.00 3739.50i 0.118860 0.205872i −0.800456 0.599391i \(-0.795409\pi\)
0.919316 + 0.393520i \(0.128743\pi\)
\(692\) −1746.00 + 3024.16i −0.0959147 + 0.166129i
\(693\) −5577.00 9659.65i −0.305704 0.529494i
\(694\) −23788.0 −1.30112
\(695\) −17632.3 30540.0i −0.962346 1.66683i
\(696\) −3346.32 5796.00i −0.182244 0.315656i
\(697\) 10615.7 0.576901
\(698\) −21051.0 36461.4i −1.14154 1.97720i
\(699\) 20223.0 35027.3i 1.09428 1.89535i
\(700\) −3017.23 + 5226.00i −0.162915 + 0.282177i
\(701\) 18270.0 0.984377 0.492189 0.870489i \(-0.336197\pi\)
0.492189 + 0.870489i \(0.336197\pi\)
\(702\) 0 0
\(703\) 3519.00 0.188793
\(704\) −720.533 + 1248.00i −0.0385740 + 0.0668122i
\(705\) 16632.0 28807.5i 0.888507 1.53894i
\(706\) 10059.0 + 17422.7i 0.536226 + 0.928770i
\(707\) −44110.1 −2.34644
\(708\) −266.736 462.000i −0.0141590 0.0245240i
\(709\) −814.930 1411.50i −0.0431669 0.0747673i 0.843635 0.536918i \(-0.180411\pi\)
−0.886802 + 0.462150i \(0.847078\pi\)
\(710\) −28017.7 −1.48096
\(711\) 13684.0 + 23701.4i 0.721786 + 1.25017i
\(712\) 2124.00 3678.88i 0.111798 0.193640i
\(713\) 2073.26 3591.00i 0.108898 0.188617i
\(714\) −14742.0 −0.772697
\(715\) 0 0
\(716\) 5148.00 0.268701
\(717\) 6510.78 11277.0i 0.339121 0.587374i
\(718\) 2322.00 4021.82i 0.120691 0.209043i
\(719\) 4915.50 + 8513.90i 0.254961 + 0.441606i 0.964885 0.262673i \(-0.0846039\pi\)
−0.709924 + 0.704279i \(0.751271\pi\)
\(720\) 24387.3 1.26231
\(721\) 20895.5 + 36192.0i 1.07932 + 1.86943i
\(722\) 1635.06 + 2832.00i 0.0842804 + 0.145978i
\(723\) −14415.9 −0.741537
\(724\) 4.00000 + 6.92820i 0.000205330 + 0.000355642i
\(725\) 2311.50 4003.64i 0.118410 0.205091i
\(726\) 9990.47 17304.0i 0.510718 0.884589i
\(727\) 15464.0 0.788897 0.394448 0.918918i \(-0.370936\pi\)
0.394448 + 0.918918i \(0.370936\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) −24110.1 + 41760.0i −1.22241 + 2.11727i
\(731\) 1147.50 1987.53i 0.0580599 0.100563i
\(732\) −238.000 412.228i −0.0120174 0.0208147i
\(733\) 12616.3 0.635733 0.317866 0.948136i \(-0.397034\pi\)
0.317866 + 0.948136i \(0.397034\pi\)
\(734\) 6347.97 + 10995.0i 0.319220 + 0.552906i
\(735\) −7953.58 13776.0i −0.399146 0.691341i
\(736\) −9477.78 −0.474668
\(737\) −1852.50 3208.62i −0.0925885 0.160368i
\(738\) −14982.0 + 25949.6i −0.747283 + 1.29433i
\(739\) −8141.50 + 14101.5i −0.405264 + 0.701938i −0.994352 0.106131i \(-0.966154\pi\)
0.589088 + 0.808069i \(0.299487\pi\)
\(740\) −2208.00 −0.109686
\(741\) 0 0
\(742\) −33228.0 −1.64399
\(743\) −5403.13 + 9358.50i −0.266786 + 0.462086i −0.968030 0.250835i \(-0.919295\pi\)
0.701244 + 0.712921i \(0.252628\pi\)
\(744\) 3528.00 6110.68i 0.173848 0.301113i
\(745\) −9036.00 15650.8i −0.444367 0.769666i
\(746\) −18605.7 −0.913140
\(747\) −4686.93 8118.00i −0.229566 0.397620i
\(748\) 1215.90 + 2106.00i 0.0594354 + 0.102945i
\(749\) −5741.75 −0.280105
\(750\) −9744.00 16877.1i −0.474401 0.821686i
\(751\) −6807.50 + 11790.9i −0.330771 + 0.572913i −0.982663 0.185399i \(-0.940642\pi\)
0.651892 + 0.758312i \(0.273976\pi\)
\(752\) −13717.8 + 23760.0i −0.665210 + 1.15218i
\(753\) 31437.0 1.52142
\(754\) 0 0
\(755\) 1200.00 0.0578443
\(756\) −1576.17 + 2730.00i −0.0758262 + 0.131335i
\(757\) −2775.50 + 4807.31i −0.133259 + 0.230812i −0.924931 0.380135i \(-0.875878\pi\)
0.791672 + 0.610947i \(0.209211\pi\)
\(758\) −19935.0 34528.4i −0.955240 1.65452i
\(759\) 8984.15 0.429649
\(760\) 8480.12 + 14688.0i 0.404745 + 0.701039i
\(761\) −5041.13 8731.50i −0.240133 0.415922i 0.720619 0.693331i \(-0.243858\pi\)
−0.960752 + 0.277409i \(0.910524\pi\)
\(762\) 54389.9 2.58574
\(763\) −6864.00 11888.8i −0.325680 0.564093i
\(764\) 5682.00 9841.51i 0.269067 0.466039i
\(765\) −4115.35 + 7128.00i −0.194498 + 0.336880i
\(766\) 8382.00 0.395371
\(767\) 0 0
\(768\) −34048.0 −1.59974
\(769\) −14879.2 + 25771.5i −0.697733 + 1.20851i 0.271517 + 0.962434i \(0.412475\pi\)
−0.969250 + 0.246076i \(0.920859\pi\)
\(770\) −12168.0 + 21075.6i −0.569486 + 0.986379i
\(771\) −19078.5 33044.9i −0.891174 1.54356i
\(772\) 16981.0 0.791659
\(773\) 13867.7 + 24019.5i 0.645259 + 1.11762i 0.984242 + 0.176829i \(0.0565839\pi\)
−0.338983 + 0.940793i \(0.610083\pi\)
\(774\) 3238.94 + 5610.00i 0.150415 + 0.260526i
\(775\) 4873.99 0.225908
\(776\)