Properties

Label 225.4.h.a.136.5
Level $225$
Weight $4$
Character 225.136
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
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.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.5
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.a.91.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.08389 - 0.787491i) q^{2} +(-1.91746 + 5.90135i) q^{4} +(3.83217 + 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 + 18.0999i) q^{8} +O(q^{10})\) \(q+(1.08389 - 0.787491i) q^{2} +(-1.91746 + 5.90135i) q^{4} +(3.83217 + 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 + 18.0999i) q^{8} +(12.4247 + 8.36635i) q^{10} +(-2.00821 + 1.45905i) q^{11} +(-69.2682 - 50.3263i) q^{13} +(-13.2344 + 9.61535i) q^{14} +(-19.5320 - 14.1909i) q^{16} +(1.71458 + 5.27694i) q^{17} +(-7.45887 - 22.9561i) q^{19} +(-69.3303 + 2.47571i) q^{20} +(-1.02769 + 3.16290i) q^{22} +(-83.6143 + 60.7493i) q^{23} +(-95.6289 + 80.4991i) q^{25} -114.710 q^{26} +(23.4124 - 72.0561i) q^{28} +(35.3035 - 108.653i) q^{29} +(47.5487 + 146.340i) q^{31} -184.596 q^{32} +(6.01395 + 4.36939i) q^{34} +(-46.7912 - 128.244i) q^{35} +(277.229 + 201.419i) q^{37} +(-26.1623 - 19.0080i) q^{38} +(-167.567 + 131.130i) q^{40} +(28.0530 + 20.3817i) q^{41} -154.740 q^{43} +(-4.75970 - 14.6489i) q^{44} +(-42.7890 + 131.691i) q^{46} +(-104.613 + 321.965i) q^{47} -193.913 q^{49} +(-40.2588 + 162.559i) q^{50} +(429.812 - 312.277i) q^{52} +(-199.512 + 614.036i) q^{53} +(-23.0204 - 15.5011i) q^{55} +(-71.8077 - 221.001i) q^{56} +(-47.2982 - 145.569i) q^{58} +(536.260 + 389.616i) q^{59} +(289.370 - 210.239i) q^{61} +(166.779 + 121.172i) q^{62} +(-43.8256 + 31.8411i) q^{64} +(263.133 - 920.387i) q^{65} +(-164.205 - 505.370i) q^{67} -34.4287 q^{68} +(-151.707 - 102.154i) q^{70} +(196.164 - 603.732i) q^{71} +(-779.001 + 565.977i) q^{73} +459.101 q^{74} +149.774 q^{76} +(24.5205 - 17.8152i) q^{77} +(175.752 - 540.908i) q^{79} +(74.1975 - 259.528i) q^{80} +46.4568 q^{82} +(98.8352 + 304.184i) q^{83} +(-48.8535 + 38.2305i) q^{85} +(-167.721 + 121.856i) q^{86} +(-38.2190 - 27.7677i) q^{88} +(-1079.81 + 784.525i) q^{89} +(845.772 + 614.489i) q^{91} +(-198.176 - 609.922i) q^{92} +(140.156 + 431.355i) q^{94} +(212.525 - 166.313i) q^{95} +(123.390 - 379.754i) q^{97} +(-210.180 + 152.705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + O(q^{10}) \) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08389 0.787491i 0.383212 0.278420i −0.379456 0.925210i \(-0.623889\pi\)
0.762668 + 0.646790i \(0.223889\pi\)
\(3\) 0 0
\(4\) −1.91746 + 5.90135i −0.239683 + 0.737669i
\(5\) 3.83217 + 10.5031i 0.342760 + 0.939423i
\(6\) 0 0
\(7\) −12.2101 −0.659284 −0.329642 0.944106i \(-0.606928\pi\)
−0.329642 + 0.944106i \(0.606928\pi\)
\(8\) 5.88101 + 18.0999i 0.259906 + 0.799909i
\(9\) 0 0
\(10\) 12.4247 + 8.36635i 0.392904 + 0.264567i
\(11\) −2.00821 + 1.45905i −0.0550454 + 0.0399928i −0.614968 0.788552i \(-0.710831\pi\)
0.559922 + 0.828545i \(0.310831\pi\)
\(12\) 0 0
\(13\) −69.2682 50.3263i −1.47781 1.07369i −0.978254 0.207411i \(-0.933496\pi\)
−0.499557 0.866281i \(-0.666504\pi\)
\(14\) −13.2344 + 9.61535i −0.252646 + 0.183558i
\(15\) 0 0
\(16\) −19.5320 14.1909i −0.305188 0.221732i
\(17\) 1.71458 + 5.27694i 0.0244616 + 0.0752850i 0.962542 0.271132i \(-0.0873981\pi\)
−0.938080 + 0.346417i \(0.887398\pi\)
\(18\) 0 0
\(19\) −7.45887 22.9561i −0.0900623 0.277183i 0.895873 0.444310i \(-0.146551\pi\)
−0.985935 + 0.167127i \(0.946551\pi\)
\(20\) −69.3303 + 2.47571i −0.775137 + 0.0276793i
\(21\) 0 0
\(22\) −1.02769 + 3.16290i −0.00995927 + 0.0306515i
\(23\) −83.6143 + 60.7493i −0.758034 + 0.550744i −0.898307 0.439369i \(-0.855202\pi\)
0.140273 + 0.990113i \(0.455202\pi\)
\(24\) 0 0
\(25\) −95.6289 + 80.4991i −0.765031 + 0.643993i
\(26\) −114.710 −0.865253
\(27\) 0 0
\(28\) 23.4124 72.0561i 0.158019 0.486333i
\(29\) 35.3035 108.653i 0.226059 0.695737i −0.772124 0.635472i \(-0.780806\pi\)
0.998182 0.0602646i \(-0.0191945\pi\)
\(30\) 0 0
\(31\) 47.5487 + 146.340i 0.275484 + 0.847852i 0.989091 + 0.147306i \(0.0470602\pi\)
−0.713607 + 0.700546i \(0.752940\pi\)
\(32\) −184.596 −1.01976
\(33\) 0 0
\(34\) 6.01395 + 4.36939i 0.0303348 + 0.0220395i
\(35\) −46.7912 128.244i −0.225976 0.619346i
\(36\) 0 0
\(37\) 277.229 + 201.419i 1.23179 + 0.894948i 0.997023 0.0771043i \(-0.0245674\pi\)
0.234767 + 0.972052i \(0.424567\pi\)
\(38\) −26.1623 19.0080i −0.111686 0.0811449i
\(39\) 0 0
\(40\) −167.567 + 131.130i −0.662368 + 0.518339i
\(41\) 28.0530 + 20.3817i 0.106857 + 0.0776363i 0.639931 0.768433i \(-0.278963\pi\)
−0.533073 + 0.846069i \(0.678963\pi\)
\(42\) 0 0
\(43\) −154.740 −0.548783 −0.274391 0.961618i \(-0.588476\pi\)
−0.274391 + 0.961618i \(0.588476\pi\)
\(44\) −4.75970 14.6489i −0.0163080 0.0501908i
\(45\) 0 0
\(46\) −42.7890 + 131.691i −0.137150 + 0.422104i
\(47\) −104.613 + 321.965i −0.324666 + 0.999221i 0.646924 + 0.762554i \(0.276055\pi\)
−0.971591 + 0.236667i \(0.923945\pi\)
\(48\) 0 0
\(49\) −193.913 −0.565345
\(50\) −40.2588 + 162.559i −0.113869 + 0.459786i
\(51\) 0 0
\(52\) 429.812 312.277i 1.14624 0.832789i
\(53\) −199.512 + 614.036i −0.517078 + 1.59140i 0.262390 + 0.964962i \(0.415489\pi\)
−0.779469 + 0.626441i \(0.784511\pi\)
\(54\) 0 0
\(55\) −23.0204 15.5011i −0.0564375 0.0380030i
\(56\) −71.8077 221.001i −0.171352 0.527367i
\(57\) 0 0
\(58\) −47.2982 145.569i −0.107079 0.329554i
\(59\) 536.260 + 389.616i 1.18331 + 0.859724i 0.992541 0.121912i \(-0.0389025\pi\)
0.190767 + 0.981635i \(0.438903\pi\)
\(60\) 0 0
\(61\) 289.370 210.239i 0.607377 0.441285i −0.241113 0.970497i \(-0.577512\pi\)
0.848490 + 0.529212i \(0.177512\pi\)
\(62\) 166.779 + 121.172i 0.341628 + 0.248207i
\(63\) 0 0
\(64\) −43.8256 + 31.8411i −0.0855968 + 0.0621897i
\(65\) 263.133 920.387i 0.502117 1.75631i
\(66\) 0 0
\(67\) −164.205 505.370i −0.299415 0.921504i −0.981703 0.190420i \(-0.939015\pi\)
0.682288 0.731083i \(-0.260985\pi\)
\(68\) −34.4287 −0.0613984
\(69\) 0 0
\(70\) −151.707 102.154i −0.259035 0.174425i
\(71\) 196.164 603.732i 0.327893 1.00915i −0.642224 0.766517i \(-0.721988\pi\)
0.970118 0.242635i \(-0.0780118\pi\)
\(72\) 0 0
\(73\) −779.001 + 565.977i −1.24897 + 0.907433i −0.998162 0.0606028i \(-0.980698\pi\)
−0.250812 + 0.968036i \(0.580698\pi\)
\(74\) 459.101 0.721208
\(75\) 0 0
\(76\) 149.774 0.226056
\(77\) 24.5205 17.8152i 0.0362905 0.0263666i
\(78\) 0 0
\(79\) 175.752 540.908i 0.250299 0.770340i −0.744421 0.667711i \(-0.767274\pi\)
0.994720 0.102630i \(-0.0327257\pi\)
\(80\) 74.1975 259.528i 0.103694 0.362702i
\(81\) 0 0
\(82\) 46.4568 0.0625645
\(83\) 98.8352 + 304.184i 0.130706 + 0.402271i 0.994897 0.100892i \(-0.0321696\pi\)
−0.864192 + 0.503163i \(0.832170\pi\)
\(84\) 0 0
\(85\) −48.8535 + 38.2305i −0.0623400 + 0.0487844i
\(86\) −167.721 + 121.856i −0.210300 + 0.152792i
\(87\) 0 0
\(88\) −38.2190 27.7677i −0.0462973 0.0336369i
\(89\) −1079.81 + 784.525i −1.28606 + 0.934376i −0.999718 0.0237515i \(-0.992439\pi\)
−0.286341 + 0.958128i \(0.592439\pi\)
\(90\) 0 0
\(91\) 845.772 + 614.489i 0.974296 + 0.707868i
\(92\) −198.176 609.922i −0.224579 0.691182i
\(93\) 0 0
\(94\) 140.156 + 431.355i 0.153787 + 0.473307i
\(95\) 212.525 166.313i 0.229523 0.179614i
\(96\) 0 0
\(97\) 123.390 379.754i 0.129158 0.397507i −0.865478 0.500947i \(-0.832985\pi\)
0.994636 + 0.103440i \(0.0329850\pi\)
\(98\) −210.180 + 152.705i −0.216647 + 0.157403i
\(99\) 0 0
\(100\) −291.688 718.694i −0.291688 0.718694i
\(101\) 131.408 0.129461 0.0647307 0.997903i \(-0.479381\pi\)
0.0647307 + 0.997903i \(0.479381\pi\)
\(102\) 0 0
\(103\) 5.82218 17.9188i 0.00556967 0.0171417i −0.948233 0.317575i \(-0.897131\pi\)
0.953803 + 0.300434i \(0.0971314\pi\)
\(104\) 503.533 1549.72i 0.474764 1.46117i
\(105\) 0 0
\(106\) 267.299 + 822.661i 0.244928 + 0.753810i
\(107\) 1832.09 1.65528 0.827640 0.561259i \(-0.189683\pi\)
0.827640 + 0.561259i \(0.189683\pi\)
\(108\) 0 0
\(109\) 1082.18 + 786.250i 0.950954 + 0.690909i 0.951032 0.309091i \(-0.100025\pi\)
−7.79623e−5 1.00000i \(0.500025\pi\)
\(110\) −37.1584 + 1.32689i −0.0322083 + 0.00115013i
\(111\) 0 0
\(112\) 238.488 + 173.272i 0.201206 + 0.146184i
\(113\) 29.3061 + 21.2921i 0.0243972 + 0.0177256i 0.599917 0.800062i \(-0.295200\pi\)
−0.575520 + 0.817788i \(0.695200\pi\)
\(114\) 0 0
\(115\) −958.478 645.405i −0.777205 0.523342i
\(116\) 573.506 + 416.677i 0.459041 + 0.333513i
\(117\) 0 0
\(118\) 888.065 0.692822
\(119\) −20.9352 64.4319i −0.0161271 0.0496342i
\(120\) 0 0
\(121\) −409.398 + 1260.00i −0.307586 + 0.946654i
\(122\) 148.083 455.752i 0.109892 0.338212i
\(123\) 0 0
\(124\) −954.776 −0.691463
\(125\) −1211.95 695.911i −0.867204 0.497953i
\(126\) 0 0
\(127\) 1130.69 821.496i 0.790021 0.573984i −0.117949 0.993020i \(-0.537632\pi\)
0.907970 + 0.419036i \(0.137632\pi\)
\(128\) 433.920 1335.47i 0.299637 0.922187i
\(129\) 0 0
\(130\) −439.590 1204.81i −0.296574 0.812838i
\(131\) 877.005 + 2699.14i 0.584918 + 1.80019i 0.599598 + 0.800301i \(0.295327\pi\)
−0.0146799 + 0.999892i \(0.504673\pi\)
\(132\) 0 0
\(133\) 91.0736 + 280.296i 0.0593766 + 0.182742i
\(134\) −575.953 418.455i −0.371304 0.269768i
\(135\) 0 0
\(136\) −85.4284 + 62.0674i −0.0538634 + 0.0391341i
\(137\) −655.541 476.279i −0.408808 0.297016i 0.364311 0.931277i \(-0.381304\pi\)
−0.773119 + 0.634261i \(0.781304\pi\)
\(138\) 0 0
\(139\) 2540.67 1845.91i 1.55034 1.12639i 0.606927 0.794758i \(-0.292402\pi\)
0.943410 0.331628i \(-0.107598\pi\)
\(140\) 846.530 30.2287i 0.511035 0.0182485i
\(141\) 0 0
\(142\) −262.813 808.855i −0.155315 0.478012i
\(143\) 212.534 0.124287
\(144\) 0 0
\(145\) 1276.48 45.5818i 0.731075 0.0261059i
\(146\) −398.648 + 1226.91i −0.225975 + 0.695479i
\(147\) 0 0
\(148\) −1720.22 + 1249.81i −0.955414 + 0.694149i
\(149\) 1008.26 0.554362 0.277181 0.960818i \(-0.410600\pi\)
0.277181 + 0.960818i \(0.410600\pi\)
\(150\) 0 0
\(151\) −2162.97 −1.16570 −0.582848 0.812581i \(-0.698062\pi\)
−0.582848 + 0.812581i \(0.698062\pi\)
\(152\) 371.636 270.009i 0.198314 0.144083i
\(153\) 0 0
\(154\) 12.5482 38.6193i 0.00656598 0.0202080i
\(155\) −1354.80 + 1060.21i −0.702067 + 0.549406i
\(156\) 0 0
\(157\) −2618.64 −1.33115 −0.665575 0.746331i \(-0.731814\pi\)
−0.665575 + 0.746331i \(0.731814\pi\)
\(158\) −235.465 724.686i −0.118561 0.364892i
\(159\) 0 0
\(160\) −707.405 1938.83i −0.349533 0.957987i
\(161\) 1020.94 741.756i 0.499759 0.363096i
\(162\) 0 0
\(163\) 261.518 + 190.004i 0.125667 + 0.0913022i 0.648843 0.760922i \(-0.275253\pi\)
−0.523176 + 0.852224i \(0.675253\pi\)
\(164\) −174.070 + 126.469i −0.0828818 + 0.0602171i
\(165\) 0 0
\(166\) 346.668 + 251.869i 0.162088 + 0.117764i
\(167\) −49.1296 151.205i −0.0227650 0.0700636i 0.939029 0.343839i \(-0.111727\pi\)
−0.961794 + 0.273775i \(0.911727\pi\)
\(168\) 0 0
\(169\) 1586.44 + 4882.55i 0.722092 + 2.22237i
\(170\) −22.8455 + 79.9092i −0.0103069 + 0.0360515i
\(171\) 0 0
\(172\) 296.709 913.176i 0.131534 0.404820i
\(173\) −2663.82 + 1935.38i −1.17067 + 0.850545i −0.991089 0.133198i \(-0.957475\pi\)
−0.179585 + 0.983743i \(0.557475\pi\)
\(174\) 0 0
\(175\) 1167.64 982.903i 0.504373 0.424574i
\(176\) 59.9297 0.0256669
\(177\) 0 0
\(178\) −552.583 + 1700.67i −0.232684 + 0.716129i
\(179\) −871.102 + 2680.98i −0.363739 + 1.11947i 0.587028 + 0.809566i \(0.300298\pi\)
−0.950767 + 0.309906i \(0.899702\pi\)
\(180\) 0 0
\(181\) 129.046 + 397.161i 0.0529938 + 0.163098i 0.974051 0.226330i \(-0.0726727\pi\)
−0.921057 + 0.389428i \(0.872673\pi\)
\(182\) 1400.63 0.570447
\(183\) 0 0
\(184\) −1591.29 1156.14i −0.637563 0.463217i
\(185\) −1053.13 + 3683.63i −0.418526 + 1.46392i
\(186\) 0 0
\(187\) −11.1426 8.09555i −0.00435736 0.00316580i
\(188\) −1699.43 1234.71i −0.659277 0.478992i
\(189\) 0 0
\(190\) 99.3841 347.626i 0.0379478 0.132734i
\(191\) 421.982 + 306.588i 0.159861 + 0.116146i 0.664840 0.746986i \(-0.268500\pi\)
−0.504979 + 0.863132i \(0.668500\pi\)
\(192\) 0 0
\(193\) −4528.65 −1.68901 −0.844506 0.535547i \(-0.820106\pi\)
−0.844506 + 0.535547i \(0.820106\pi\)
\(194\) −165.312 508.779i −0.0611791 0.188290i
\(195\) 0 0
\(196\) 371.822 1144.35i 0.135504 0.417037i
\(197\) 859.280 2644.59i 0.310767 0.956444i −0.666694 0.745331i \(-0.732291\pi\)
0.977462 0.211112i \(-0.0677086\pi\)
\(198\) 0 0
\(199\) 4988.03 1.77685 0.888423 0.459026i \(-0.151801\pi\)
0.888423 + 0.459026i \(0.151801\pi\)
\(200\) −2019.42 1257.46i −0.713972 0.444578i
\(201\) 0 0
\(202\) 142.432 103.483i 0.0496112 0.0360446i
\(203\) −431.060 + 1326.67i −0.149037 + 0.458688i
\(204\) 0 0
\(205\) −106.567 + 372.749i −0.0363070 + 0.126995i
\(206\) −7.80032 24.0069i −0.00263822 0.00811961i
\(207\) 0 0
\(208\) 638.776 + 1965.95i 0.212938 + 0.655356i
\(209\) 48.4731 + 35.2178i 0.0160428 + 0.0116558i
\(210\) 0 0
\(211\) −3035.52 + 2205.44i −0.990398 + 0.719566i −0.960008 0.279972i \(-0.909675\pi\)
−0.0303898 + 0.999538i \(0.509675\pi\)
\(212\) −3241.08 2354.79i −1.04999 0.762865i
\(213\) 0 0
\(214\) 1985.78 1442.76i 0.634324 0.460863i
\(215\) −592.991 1625.25i −0.188101 0.515539i
\(216\) 0 0
\(217\) −580.575 1786.83i −0.181622 0.558975i
\(218\) 1792.13 0.556780
\(219\) 0 0
\(220\) 135.618 106.128i 0.0415607 0.0325235i
\(221\) 146.803 451.812i 0.0446833 0.137521i
\(222\) 0 0
\(223\) −1324.82 + 962.540i −0.397833 + 0.289042i −0.768658 0.639660i \(-0.779075\pi\)
0.370825 + 0.928703i \(0.379075\pi\)
\(224\) 2253.94 0.672312
\(225\) 0 0
\(226\) 48.5319 0.0142845
\(227\) −3068.69 + 2229.54i −0.897252 + 0.651892i −0.937759 0.347287i \(-0.887103\pi\)
0.0405064 + 0.999179i \(0.487103\pi\)
\(228\) 0 0
\(229\) 27.8795 85.8041i 0.00804509 0.0247603i −0.946953 0.321371i \(-0.895856\pi\)
0.954998 + 0.296611i \(0.0958564\pi\)
\(230\) −1547.13 + 55.2465i −0.443543 + 0.0158385i
\(231\) 0 0
\(232\) 2174.23 0.615280
\(233\) −1118.15 3441.31i −0.314388 0.967587i −0.976006 0.217746i \(-0.930130\pi\)
0.661617 0.749842i \(-0.269870\pi\)
\(234\) 0 0
\(235\) −3782.51 + 135.070i −1.04997 + 0.0374935i
\(236\) −3327.52 + 2417.59i −0.917810 + 0.666828i
\(237\) 0 0
\(238\) −73.4310 53.3507i −0.0199993 0.0145303i
\(239\) −1189.87 + 864.489i −0.322034 + 0.233971i −0.737043 0.675846i \(-0.763778\pi\)
0.415009 + 0.909817i \(0.363778\pi\)
\(240\) 0 0
\(241\) 3192.76 + 2319.68i 0.853377 + 0.620014i 0.926075 0.377340i \(-0.123161\pi\)
−0.0726983 + 0.997354i \(0.523161\pi\)
\(242\) 548.494 + 1688.09i 0.145696 + 0.448408i
\(243\) 0 0
\(244\) 685.840 + 2110.80i 0.179944 + 0.553811i
\(245\) −743.109 2036.69i −0.193778 0.531098i
\(246\) 0 0
\(247\) −638.630 + 1965.50i −0.164514 + 0.506323i
\(248\) −2369.10 + 1721.25i −0.606605 + 0.440724i
\(249\) 0 0
\(250\) −1861.65 + 200.113i −0.470963 + 0.0506251i
\(251\) −3410.52 −0.857649 −0.428825 0.903388i \(-0.641072\pi\)
−0.428825 + 0.903388i \(0.641072\pi\)
\(252\) 0 0
\(253\) 79.2789 243.995i 0.0197005 0.0606318i
\(254\) 578.623 1780.82i 0.142937 0.439915i
\(255\) 0 0
\(256\) −715.268 2201.37i −0.174626 0.537443i
\(257\) 6919.87 1.67957 0.839785 0.542918i \(-0.182681\pi\)
0.839785 + 0.542918i \(0.182681\pi\)
\(258\) 0 0
\(259\) −3385.00 2459.35i −0.812099 0.590024i
\(260\) 4926.98 + 3317.65i 1.17522 + 0.791353i
\(261\) 0 0
\(262\) 3076.13 + 2234.94i 0.725358 + 0.527003i
\(263\) 3081.19 + 2238.62i 0.722413 + 0.524863i 0.887154 0.461473i \(-0.152679\pi\)
−0.164742 + 0.986337i \(0.552679\pi\)
\(264\) 0 0
\(265\) −7213.83 + 257.598i −1.67223 + 0.0597138i
\(266\) 319.444 + 232.090i 0.0736330 + 0.0534975i
\(267\) 0 0
\(268\) 3297.22 0.751529
\(269\) −799.222 2459.75i −0.181150 0.557523i 0.818711 0.574206i \(-0.194689\pi\)
−0.999861 + 0.0166834i \(0.994689\pi\)
\(270\) 0 0
\(271\) 329.230 1013.27i 0.0737981 0.227127i −0.907353 0.420370i \(-0.861900\pi\)
0.981151 + 0.193242i \(0.0619004\pi\)
\(272\) 41.3950 127.401i 0.00922772 0.0284000i
\(273\) 0 0
\(274\) −1085.60 −0.239356
\(275\) 74.5909 301.187i 0.0163564 0.0660446i
\(276\) 0 0
\(277\) 1996.88 1450.82i 0.433144 0.314698i −0.349761 0.936839i \(-0.613737\pi\)
0.782905 + 0.622141i \(0.213737\pi\)
\(278\) 1300.17 4001.51i 0.280500 0.863290i
\(279\) 0 0
\(280\) 2046.01 1601.12i 0.436688 0.341732i
\(281\) −960.683 2956.68i −0.203948 0.627689i −0.999755 0.0221378i \(-0.992953\pi\)
0.795806 0.605551i \(-0.207047\pi\)
\(282\) 0 0
\(283\) −1994.41 6138.15i −0.418923 1.28931i −0.908695 0.417461i \(-0.862920\pi\)
0.489772 0.871851i \(-0.337080\pi\)
\(284\) 3186.69 + 2315.27i 0.665829 + 0.483753i
\(285\) 0 0
\(286\) 230.363 167.369i 0.0476282 0.0346039i
\(287\) −342.530 248.863i −0.0704493 0.0511844i
\(288\) 0 0
\(289\) 3949.79 2869.69i 0.803948 0.584102i
\(290\) 1347.67 1054.62i 0.272888 0.213550i
\(291\) 0 0
\(292\) −1846.32 5682.39i −0.370027 1.13883i
\(293\) −835.063 −0.166501 −0.0832507 0.996529i \(-0.526530\pi\)
−0.0832507 + 0.996529i \(0.526530\pi\)
\(294\) 0 0
\(295\) −2037.12 + 7125.46i −0.402054 + 1.40631i
\(296\) −2015.27 + 6202.36i −0.395727 + 1.21792i
\(297\) 0 0
\(298\) 1092.84 793.996i 0.212438 0.154346i
\(299\) 8849.10 1.71156
\(300\) 0 0
\(301\) 1889.39 0.361803
\(302\) −2344.42 + 1703.32i −0.446709 + 0.324553i
\(303\) 0 0
\(304\) −180.079 + 554.227i −0.0339745 + 0.104563i
\(305\) 3317.07 + 2233.60i 0.622738 + 0.419329i
\(306\) 0 0
\(307\) 2681.88 0.498577 0.249289 0.968429i \(-0.419803\pi\)
0.249289 + 0.968429i \(0.419803\pi\)
\(308\) 58.1164 + 178.864i 0.0107516 + 0.0330900i
\(309\) 0 0
\(310\) −633.552 + 2216.04i −0.116075 + 0.406009i
\(311\) 6580.24 4780.83i 1.19978 0.871691i 0.205516 0.978654i \(-0.434113\pi\)
0.994263 + 0.106963i \(0.0341126\pi\)
\(312\) 0 0
\(313\) −6248.59 4539.87i −1.12841 0.819835i −0.142944 0.989731i \(-0.545657\pi\)
−0.985462 + 0.169895i \(0.945657\pi\)
\(314\) −2838.32 + 2062.16i −0.510113 + 0.370619i
\(315\) 0 0
\(316\) 2855.09 + 2074.34i 0.508263 + 0.369275i
\(317\) −995.186 3062.87i −0.176326 0.542674i 0.823366 0.567511i \(-0.192093\pi\)
−0.999692 + 0.0248365i \(0.992093\pi\)
\(318\) 0 0
\(319\) 87.6335 + 269.708i 0.0153810 + 0.0473378i
\(320\) −502.377 338.282i −0.0877616 0.0590955i
\(321\) 0 0
\(322\) 522.458 1607.96i 0.0904206 0.278286i
\(323\) 108.349 78.7200i 0.0186647 0.0135607i
\(324\) 0 0
\(325\) 10675.3 763.379i 1.82202 0.130291i
\(326\) 433.083 0.0735774
\(327\) 0 0
\(328\) −203.927 + 627.622i −0.0343292 + 0.105654i
\(329\) 1277.33 3931.22i 0.214047 0.658770i
\(330\) 0 0
\(331\) 1297.25 + 3992.52i 0.215417 + 0.662987i 0.999124 + 0.0418550i \(0.0133268\pi\)
−0.783706 + 0.621132i \(0.786673\pi\)
\(332\) −1984.61 −0.328071
\(333\) 0 0
\(334\) −172.324 125.201i −0.0282309 0.0205110i
\(335\) 4678.67 3661.31i 0.763054 0.597131i
\(336\) 0 0
\(337\) −1039.69 755.378i −0.168058 0.122101i 0.500577 0.865692i \(-0.333121\pi\)
−0.668635 + 0.743591i \(0.733121\pi\)
\(338\) 5564.48 + 4042.83i 0.895467 + 0.650595i
\(339\) 0 0
\(340\) −131.937 361.607i −0.0210449 0.0576791i
\(341\) −309.006 224.506i −0.0490721 0.0356530i
\(342\) 0 0
\(343\) 6555.77 1.03201
\(344\) −910.028 2800.78i −0.142632 0.438976i
\(345\) 0 0
\(346\) −1363.19 + 4195.47i −0.211808 + 0.651878i
\(347\) 96.1696 295.980i 0.0148780 0.0457897i −0.943342 0.331822i \(-0.892337\pi\)
0.958220 + 0.286033i \(0.0923366\pi\)
\(348\) 0 0
\(349\) −3853.76 −0.591081 −0.295540 0.955330i \(-0.595500\pi\)
−0.295540 + 0.955330i \(0.595500\pi\)
\(350\) 491.564 1984.86i 0.0750719 0.303129i
\(351\) 0 0
\(352\) 370.709 269.336i 0.0561331 0.0407831i
\(353\) −371.671 + 1143.89i −0.0560398 + 0.172473i −0.975159 0.221508i \(-0.928902\pi\)
0.919119 + 0.393980i \(0.128902\pi\)
\(354\) 0 0
\(355\) 7092.77 253.276i 1.06041 0.0378661i
\(356\) −2559.27 7876.61i −0.381014 1.17264i
\(357\) 0 0
\(358\) 1167.07 + 3591.86i 0.172295 + 0.530268i
\(359\) 8830.61 + 6415.81i 1.29822 + 0.943213i 0.999937 0.0112636i \(-0.00358538\pi\)
0.298285 + 0.954477i \(0.403585\pi\)
\(360\) 0 0
\(361\) 5077.70 3689.17i 0.740298 0.537858i
\(362\) 452.632 + 328.856i 0.0657177 + 0.0477467i
\(363\) 0 0
\(364\) −5248.05 + 3812.93i −0.755694 + 0.549044i
\(365\) −8929.76 6012.98i −1.28056 0.862284i
\(366\) 0 0
\(367\) −44.8963 138.177i −0.00638575 0.0196533i 0.947813 0.318827i \(-0.103289\pi\)
−0.954199 + 0.299174i \(0.903289\pi\)
\(368\) 2495.24 0.353461
\(369\) 0 0
\(370\) 1759.35 + 4821.97i 0.247201 + 0.677520i
\(371\) 2436.07 7497.45i 0.340901 1.04919i
\(372\) 0 0
\(373\) 2847.26 2068.66i 0.395243 0.287161i −0.372358 0.928089i \(-0.621451\pi\)
0.767601 + 0.640929i \(0.221451\pi\)
\(374\) −18.4525 −0.00255122
\(375\) 0 0
\(376\) −6442.75 −0.883669
\(377\) −7913.51 + 5749.50i −1.08108 + 0.785450i
\(378\) 0 0
\(379\) −124.955 + 384.571i −0.0169354 + 0.0521217i −0.959167 0.282840i \(-0.908723\pi\)
0.942232 + 0.334962i \(0.108723\pi\)
\(380\) 573.959 + 1573.08i 0.0774828 + 0.212362i
\(381\) 0 0
\(382\) 698.816 0.0935982
\(383\) 1292.81 + 3978.86i 0.172479 + 0.530836i 0.999509 0.0313212i \(-0.00997146\pi\)
−0.827030 + 0.562158i \(0.809971\pi\)
\(384\) 0 0
\(385\) 281.081 + 189.270i 0.0372083 + 0.0250547i
\(386\) −4908.55 + 3566.27i −0.647250 + 0.470255i
\(387\) 0 0
\(388\) 2004.47 + 1456.33i 0.262272 + 0.190551i
\(389\) −8299.40 + 6029.87i −1.08174 + 0.785929i −0.977985 0.208674i \(-0.933085\pi\)
−0.103754 + 0.994603i \(0.533085\pi\)
\(390\) 0 0
\(391\) −463.934 337.067i −0.0600054 0.0435965i
\(392\) −1140.41 3509.81i −0.146937 0.452225i
\(393\) 0 0
\(394\) −1151.23 3543.12i −0.147203 0.453045i
\(395\) 6354.70 226.920i 0.809468 0.0289053i
\(396\) 0 0
\(397\) −3149.37 + 9692.75i −0.398142 + 1.22535i 0.528346 + 0.849029i \(0.322812\pi\)
−0.926488 + 0.376325i \(0.877188\pi\)
\(398\) 5406.47 3928.03i 0.680909 0.494710i
\(399\) 0 0
\(400\) 3010.18 215.255i 0.376273 0.0269069i
\(401\) −5912.32 −0.736277 −0.368139 0.929771i \(-0.620005\pi\)
−0.368139 + 0.929771i \(0.620005\pi\)
\(402\) 0 0
\(403\) 4071.13 12529.6i 0.503219 1.54875i
\(404\) −251.970 + 775.485i −0.0310297 + 0.0954996i
\(405\) 0 0
\(406\) 577.516 + 1777.41i 0.0705952 + 0.217270i
\(407\) −850.616 −0.103596
\(408\) 0 0
\(409\) −4576.30 3324.88i −0.553260 0.401967i 0.275726 0.961236i \(-0.411082\pi\)
−0.828986 + 0.559269i \(0.811082\pi\)
\(410\) 178.030 + 487.939i 0.0214446 + 0.0587746i
\(411\) 0 0
\(412\) 94.5814 + 68.7174i 0.0113099 + 0.00821714i
\(413\) −6547.80 4757.25i −0.780136 0.566802i
\(414\) 0 0
\(415\) −2816.11 + 2203.76i −0.333102 + 0.260670i
\(416\) 12786.7 + 9290.05i 1.50701 + 1.09491i
\(417\) 0 0
\(418\) 80.2731 0.00939303
\(419\) −4234.75 13033.2i −0.493749 1.51960i −0.818897 0.573940i \(-0.805414\pi\)
0.325148 0.945663i \(-0.394586\pi\)
\(420\) 0 0
\(421\) 2847.48 8763.66i 0.329639 1.01452i −0.639664 0.768654i \(-0.720927\pi\)
0.969303 0.245869i \(-0.0790734\pi\)
\(422\) −1553.41 + 4780.89i −0.179191 + 0.551493i
\(423\) 0 0
\(424\) −12287.3 −1.40737
\(425\) −588.752 366.606i −0.0671969 0.0418423i
\(426\) 0 0
\(427\) −3533.23 + 2567.04i −0.400434 + 0.290932i
\(428\) −3512.97 + 10811.8i −0.396743 + 1.22105i
\(429\) 0 0
\(430\) −1922.60 1294.61i −0.215619 0.145190i
\(431\) −2337.94 7195.44i −0.261287 0.804158i −0.992526 0.122036i \(-0.961058\pi\)
0.731239 0.682121i \(-0.238942\pi\)
\(432\) 0 0
\(433\) 1250.50 + 3848.63i 0.138788 + 0.427144i 0.996160 0.0875525i \(-0.0279046\pi\)
−0.857372 + 0.514697i \(0.827905\pi\)
\(434\) −2036.39 1479.52i −0.225230 0.163639i
\(435\) 0 0
\(436\) −6714.97 + 4878.71i −0.737589 + 0.535890i
\(437\) 2018.23 + 1466.33i 0.220927 + 0.160513i
\(438\) 0 0
\(439\) −3157.92 + 2294.36i −0.343324 + 0.249440i −0.746063 0.665875i \(-0.768058\pi\)
0.402739 + 0.915315i \(0.368058\pi\)
\(440\) 145.185 507.828i 0.0157305 0.0550221i
\(441\) 0 0
\(442\) −196.680 605.320i −0.0211654 0.0651405i
\(443\) −2288.91 −0.245484 −0.122742 0.992439i \(-0.539169\pi\)
−0.122742 + 0.992439i \(0.539169\pi\)
\(444\) 0 0
\(445\) −12377.9 8334.84i −1.31858 0.887887i
\(446\) −677.968 + 2086.57i −0.0719792 + 0.221529i
\(447\) 0 0
\(448\) 535.115 388.784i 0.0564326 0.0410007i
\(449\) −10025.3 −1.05373 −0.526863 0.849950i \(-0.676632\pi\)
−0.526863 + 0.849950i \(0.676632\pi\)
\(450\) 0 0
\(451\) −86.0745 −0.00898690
\(452\) −181.846 + 132.119i −0.0189232 + 0.0137485i
\(453\) 0 0
\(454\) −1570.38 + 4833.13i −0.162338 + 0.499626i
\(455\) −3212.88 + 11238.0i −0.331038 + 1.15791i
\(456\) 0 0
\(457\) −3293.06 −0.337075 −0.168537 0.985695i \(-0.553904\pi\)
−0.168537 + 0.985695i \(0.553904\pi\)
\(458\) −37.3518 114.957i −0.00381077 0.0117283i
\(459\) 0 0
\(460\) 5646.61 4418.77i 0.572336 0.447884i
\(461\) −672.561 + 488.644i −0.0679486 + 0.0493676i −0.621241 0.783620i \(-0.713371\pi\)
0.553292 + 0.832987i \(0.313371\pi\)
\(462\) 0 0
\(463\) 7302.69 + 5305.71i 0.733012 + 0.532565i 0.890515 0.454954i \(-0.150344\pi\)
−0.157503 + 0.987519i \(0.550344\pi\)
\(464\) −2231.43 + 1621.23i −0.223258 + 0.162206i
\(465\) 0 0
\(466\) −3921.95 2849.46i −0.389873 0.283259i
\(467\) −406.581 1251.33i −0.0402876 0.123992i 0.928890 0.370356i \(-0.120764\pi\)
−0.969177 + 0.246364i \(0.920764\pi\)
\(468\) 0 0
\(469\) 2004.95 + 6170.62i 0.197399 + 0.607532i
\(470\) −3993.45 + 3125.09i −0.391924 + 0.306702i
\(471\) 0 0
\(472\) −3898.25 + 11997.6i −0.380152 + 1.16999i
\(473\) 310.751 225.774i 0.0302080 0.0219474i
\(474\) 0 0
\(475\) 2561.23 + 1594.83i 0.247404 + 0.154054i
\(476\) 420.378 0.0404790
\(477\) 0 0
\(478\) −608.906 + 1874.02i −0.0582651 + 0.179321i
\(479\) −2883.48 + 8874.45i −0.275052 + 0.846522i 0.714154 + 0.699989i \(0.246812\pi\)
−0.989206 + 0.146533i \(0.953188\pi\)
\(480\) 0 0
\(481\) −9066.51 27903.8i −0.859454 2.64513i
\(482\) 5287.32 0.499649
\(483\) 0 0
\(484\) −6650.67 4831.99i −0.624593 0.453794i
\(485\) 4461.43 159.313i 0.417698 0.0149155i
\(486\) 0 0
\(487\) 1662.91 + 1208.18i 0.154731 + 0.112418i 0.662457 0.749100i \(-0.269514\pi\)
−0.507726 + 0.861519i \(0.669514\pi\)
\(488\) 5507.09 + 4001.14i 0.510849 + 0.371154i
\(489\) 0 0
\(490\) −2409.32 1622.35i −0.222126 0.149572i
\(491\) 2888.29 + 2098.47i 0.265472 + 0.192877i 0.712556 0.701615i \(-0.247537\pi\)
−0.447084 + 0.894492i \(0.647537\pi\)
\(492\) 0 0
\(493\) 633.886 0.0579083
\(494\) 855.611 + 2633.30i 0.0779266 + 0.239833i
\(495\) 0 0
\(496\) 1147.97 3533.07i 0.103922 0.319838i
\(497\) −2395.19 + 7371.63i −0.216175 + 0.665317i
\(498\) 0 0
\(499\) −316.957 −0.0284347 −0.0142174 0.999899i \(-0.504526\pi\)
−0.0142174 + 0.999899i \(0.504526\pi\)
\(500\) 6430.69 5817.78i 0.575179 0.520358i
\(501\) 0 0
\(502\) −3696.62 + 2685.75i −0.328662 + 0.238787i
\(503\) 3270.63 10066.0i 0.289921 0.892285i −0.694959 0.719049i \(-0.744578\pi\)
0.984880 0.173236i \(-0.0554223\pi\)
\(504\) 0 0
\(505\) 503.578 + 1380.19i 0.0443741 + 0.121619i
\(506\) −106.215 326.895i −0.00933165 0.0287199i
\(507\) 0 0
\(508\) 2679.87 + 8247.79i 0.234055 + 0.720348i
\(509\) −11989.3 8710.74i −1.04404 0.758540i −0.0729705 0.997334i \(-0.523248\pi\)
−0.971070 + 0.238794i \(0.923248\pi\)
\(510\) 0 0
\(511\) 9511.68 6910.64i 0.823428 0.598256i
\(512\) 6579.32 + 4780.15i 0.567905 + 0.412607i
\(513\) 0 0
\(514\) 7500.37 5449.34i 0.643632 0.467626i
\(515\) 210.514 7.51724i 0.0180124 0.000643202i
\(516\) 0 0
\(517\) −259.679 799.209i −0.0220903 0.0679868i
\(518\) −5605.67 −0.475481
\(519\) 0 0
\(520\) 18206.4 650.131i 1.53539 0.0548272i
\(521\) −1266.26 + 3897.16i −0.106480 + 0.327711i −0.990075 0.140541i \(-0.955116\pi\)
0.883595 + 0.468252i \(0.155116\pi\)
\(522\) 0 0
\(523\) −4884.26 + 3548.62i −0.408363 + 0.296693i −0.772939 0.634481i \(-0.781214\pi\)
0.364576 + 0.931174i \(0.381214\pi\)
\(524\) −17610.2 −1.46814
\(525\) 0 0
\(526\) 5102.56 0.422970
\(527\) −690.700 + 501.823i −0.0570918 + 0.0414796i
\(528\) 0 0
\(529\) −458.945 + 1412.49i −0.0377204 + 0.116092i
\(530\) −7616.13 + 5960.03i −0.624195 + 0.488467i
\(531\) 0 0
\(532\) −1828.75 −0.149035
\(533\) −917.446 2823.61i −0.0745573 0.229464i
\(534\) 0 0
\(535\) 7020.89 + 19242.6i 0.567364 + 1.55501i
\(536\) 8181.44 5944.17i 0.659300 0.479009i
\(537\) 0 0
\(538\) −2803.30 2036.72i −0.224645 0.163214i
\(539\) 389.419 282.930i 0.0311196 0.0226097i
\(540\) 0 0
\(541\) −3971.18 2885.23i −0.315590 0.229290i 0.418701 0.908124i \(-0.362485\pi\)
−0.734291 + 0.678834i \(0.762485\pi\)
\(542\) −441.089 1357.53i −0.0349564 0.107585i
\(543\) 0 0
\(544\) −316.505 974.104i −0.0249450 0.0767727i
\(545\) −4110.94 + 14379.3i −0.323107 + 1.13016i
\(546\) 0 0
\(547\) −5430.58 + 16713.6i −0.424488 + 1.30644i 0.478995 + 0.877817i \(0.341001\pi\)
−0.903484 + 0.428623i \(0.858999\pi\)
\(548\) 4067.66 2955.33i 0.317084 0.230375i
\(549\) 0 0
\(550\) −156.334 385.193i −0.0121202 0.0298630i
\(551\) −2757.57 −0.213206
\(552\) 0 0
\(553\) −2145.95 + 6604.54i −0.165018 + 0.507873i
\(554\) 1021.89 3145.05i 0.0783680 0.241192i
\(555\) 0 0
\(556\) 6021.68 + 18532.8i 0.459310 + 1.41361i
\(557\) 23625.5 1.79721 0.898603 0.438764i \(-0.144583\pi\)
0.898603 + 0.438764i \(0.144583\pi\)
\(558\) 0 0
\(559\) 10718.6 + 7787.50i 0.810997 + 0.589224i
\(560\) −905.959 + 3168.87i −0.0683638 + 0.239123i
\(561\) 0 0
\(562\) −3369.63 2448.18i −0.252917 0.183755i
\(563\) −18736.1 13612.6i −1.40254 1.01901i −0.994355 0.106109i \(-0.966161\pi\)
−0.408188 0.912898i \(-0.633839\pi\)
\(564\) 0 0
\(565\) −111.327 + 389.399i −0.00828947 + 0.0289950i
\(566\) −6995.45 5082.49i −0.519507 0.377444i
\(567\) 0 0
\(568\) 12081.1 0.892452
\(569\) 2625.00 + 8078.93i 0.193402 + 0.595231i 0.999992 + 0.00411844i \(0.00131094\pi\)
−0.806589 + 0.591112i \(0.798689\pi\)
\(570\) 0 0
\(571\) 4777.92 14704.9i 0.350174 1.07773i −0.608580 0.793492i \(-0.708261\pi\)
0.958755 0.284234i \(-0.0917393\pi\)
\(572\) −407.526 + 1254.24i −0.0297894 + 0.0916823i
\(573\) 0 0
\(574\) −567.242 −0.0412478
\(575\) 3105.68 12540.3i 0.225245 0.909505i
\(576\) 0 0
\(577\) −21389.0 + 15540.0i −1.54322 + 1.12121i −0.594937 + 0.803772i \(0.702823\pi\)
−0.948278 + 0.317440i \(0.897177\pi\)
\(578\) 2021.28 6220.85i 0.145457 0.447670i
\(579\) 0 0
\(580\) −2178.61 + 7620.35i −0.155969 + 0.545548i
\(581\) −1206.79 3714.11i −0.0861722 0.265211i
\(582\) 0 0
\(583\) −495.248 1524.22i −0.0351819 0.108279i
\(584\) −14825.4 10771.3i −1.05048 0.763219i
\(585\) 0 0
\(586\) −905.115 + 657.605i −0.0638054 + 0.0463573i
\(587\) −4812.71 3496.64i −0.338402 0.245863i 0.405585 0.914057i \(-0.367068\pi\)
−0.743987 + 0.668194i \(0.767068\pi\)
\(588\) 0 0
\(589\) 3004.73 2183.06i 0.210200 0.152719i
\(590\) 3403.22 + 9327.41i 0.237472 + 0.650853i
\(591\) 0 0
\(592\) −2556.55 7868.24i −0.177489 0.546255i
\(593\) 11755.3 0.814054 0.407027 0.913416i \(-0.366566\pi\)
0.407027 + 0.913416i \(0.366566\pi\)
\(594\) 0 0
\(595\) 596.506 466.798i 0.0410998 0.0321628i
\(596\) −1933.30 + 5950.10i −0.132871 + 0.408936i
\(597\) 0 0
\(598\) 9591.43 6968.58i 0.655891 0.476533i
\(599\) 10184.4 0.694698 0.347349 0.937736i \(-0.387082\pi\)
0.347349 + 0.937736i \(0.387082\pi\)
\(600\) 0 0
\(601\) −16384.2 −1.11202 −0.556012 0.831174i \(-0.687669\pi\)
−0.556012 + 0.831174i \(0.687669\pi\)
\(602\) 2047.89 1487.88i 0.138648 0.100733i
\(603\) 0 0
\(604\) 4147.42 12764.4i 0.279398 0.859897i
\(605\) −14802.7 + 528.589i −0.994737 + 0.0355210i
\(606\) 0 0
\(607\) 20161.1 1.34813 0.674066 0.738672i \(-0.264547\pi\)
0.674066 + 0.738672i \(0.264547\pi\)
\(608\) 1376.88 + 4237.61i 0.0918420 + 0.282661i
\(609\) 0 0
\(610\) 5354.27 191.195i 0.355390 0.0126906i
\(611\) 23449.6 17037.1i 1.55265 1.12807i
\(612\) 0 0
\(613\) 2555.01 + 1856.32i 0.168346 + 0.122310i 0.668768 0.743471i \(-0.266822\pi\)
−0.500422 + 0.865781i \(0.666822\pi\)
\(614\) 2906.86 2111.96i 0.191061 0.138814i
\(615\) 0 0
\(616\) 466.658 + 339.047i 0.0305230 + 0.0221763i
\(617\) −2032.29 6254.74i −0.132604 0.408114i 0.862605 0.505877i \(-0.168831\pi\)
−0.995210 + 0.0977634i \(0.968831\pi\)
\(618\) 0 0
\(619\) −6522.15 20073.1i −0.423502 1.30340i −0.904422 0.426639i \(-0.859697\pi\)
0.480920 0.876764i \(-0.340303\pi\)
\(620\) −3658.86 10028.1i −0.237006 0.649576i
\(621\) 0 0
\(622\) 3367.39 10363.8i 0.217074 0.668085i
\(623\) 13184.5 9579.13i 0.847877 0.616019i
\(624\) 0 0
\(625\) 2664.79 15396.1i 0.170546 0.985350i
\(626\) −10347.9 −0.660678
\(627\) 0 0
\(628\) 5021.16 15453.5i 0.319054 0.981947i
\(629\) −587.542 + 1808.27i −0.0372446 + 0.114627i
\(630\) 0 0
\(631\) −8297.74 25537.8i −0.523499 1.61116i −0.767265 0.641331i \(-0.778383\pi\)
0.243765 0.969834i \(-0.421617\pi\)
\(632\) 10824.0 0.681257
\(633\) 0 0
\(634\) −3490.65 2536.11i −0.218662 0.158867i
\(635\) 12961.2 + 8727.62i 0.810001 + 0.545425i
\(636\) 0 0
\(637\) 13432.0 + 9758.94i 0.835473 + 0.607007i
\(638\) 307.378 + 223.323i 0.0190740 + 0.0138581i
\(639\) 0 0
\(640\) 15689.4 560.251i 0.969027 0.0346029i
\(641\) 20566.4 + 14942.4i 1.26728 + 0.920732i 0.999091 0.0426350i \(-0.0135753\pi\)
0.268188 + 0.963367i \(0.413575\pi\)
\(642\) 0 0
\(643\) −10481.7 −0.642856 −0.321428 0.946934i \(-0.604163\pi\)
−0.321428 + 0.946934i \(0.604163\pi\)
\(644\) 2419.74 + 7447.21i 0.148061 + 0.455685i
\(645\) 0 0
\(646\) 55.4467 170.647i 0.00337697 0.0103932i
\(647\) −5847.14 + 17995.7i −0.355294 + 1.09348i 0.600545 + 0.799591i \(0.294950\pi\)
−0.955839 + 0.293891i \(0.905050\pi\)
\(648\) 0 0
\(649\) −1645.40 −0.0995184
\(650\) 10969.6 9234.09i 0.661946 0.557217i
\(651\) 0 0
\(652\) −1622.73 + 1178.98i −0.0974710 + 0.0708168i
\(653\) 3911.37 12037.9i 0.234401 0.721411i −0.762800 0.646635i \(-0.776176\pi\)
0.997200 0.0747761i \(-0.0238242\pi\)
\(654\) 0 0
\(655\) −24988.5 + 19554.8i −1.49066 + 1.16652i
\(656\) −258.699 796.193i −0.0153971 0.0473874i
\(657\) 0 0
\(658\) −1711.32 5266.89i −0.101389 0.312044i
\(659\) 9820.27 + 7134.84i 0.580491 + 0.421751i 0.838901 0.544284i \(-0.183199\pi\)
−0.258410 + 0.966035i \(0.583199\pi\)
\(660\) 0 0
\(661\) −3379.82 + 2455.59i −0.198880 + 0.144495i −0.682768 0.730635i \(-0.739224\pi\)
0.483888 + 0.875130i \(0.339224\pi\)
\(662\) 4550.14 + 3305.87i 0.267139 + 0.194088i
\(663\) 0 0
\(664\) −4924.44 + 3577.81i −0.287809 + 0.209105i
\(665\) −2594.96 + 2030.69i −0.151320 + 0.118416i
\(666\) 0 0
\(667\) 3648.72 + 11229.6i 0.211813 + 0.651892i
\(668\) 986.519 0.0571401
\(669\) 0 0
\(670\) 2187.91 7652.87i 0.126159 0.441278i
\(671\) −274.366 + 844.411i −0.0157851 + 0.0485814i
\(672\) 0 0
\(673\) −6124.43 + 4449.66i −0.350787 + 0.254862i −0.749199 0.662345i \(-0.769561\pi\)
0.398412 + 0.917206i \(0.369561\pi\)
\(674\) −1721.76 −0.0983972
\(675\) 0 0
\(676\) −31855.6 −1.81245
\(677\) −26966.3 + 19592.1i −1.53087 + 1.11224i −0.575114 + 0.818073i \(0.695042\pi\)
−0.955754 + 0.294168i \(0.904958\pi\)
\(678\) 0 0
\(679\) −1506.60 + 4636.84i −0.0851517 + 0.262070i
\(680\) −979.275 659.408i −0.0552257 0.0371870i
\(681\) 0 0
\(682\) −511.724 −0.0287315
\(683\) 10789.5 + 33206.6i 0.604463 + 1.86035i 0.500440 + 0.865771i \(0.333172\pi\)
0.104023 + 0.994575i \(0.466828\pi\)
\(684\) 0 0
\(685\) 2490.24 8710.38i 0.138901 0.485849i
\(686\) 7105.72 5162.61i 0.395478 0.287331i
\(687\) 0 0
\(688\) 3022.39 + 2195.90i 0.167482 + 0.121683i
\(689\) 44722.0 32492.5i 2.47282 1.79661i
\(690\) 0 0
\(691\) 27262.3 + 19807.2i 1.50088 + 1.09045i 0.970031 + 0.242982i \(0.0781257\pi\)
0.530846 + 0.847468i \(0.321874\pi\)
\(692\) −6313.57 19431.2i −0.346829 1.06743i
\(693\) 0 0
\(694\) −128.844 396.542i −0.00704735 0.0216895i
\(695\) 29124.0 + 19611.0i 1.58955 + 1.07034i
\(696\) 0 0
\(697\) −59.4539 + 182.980i −0.00323095 + 0.00994386i
\(698\) −4177.05 + 3034.80i −0.226510 + 0.164569i
\(699\) 0 0
\(700\) 3561.54 + 8775.33i 0.192305 + 0.473823i
\(701\) −23077.6 −1.24341 −0.621704 0.783252i \(-0.713559\pi\)
−0.621704 + 0.783252i \(0.713559\pi\)
\(702\) 0 0
\(703\) 2555.96 7866.45i 0.137127 0.422032i
\(704\) 41.5532 127.888i 0.00222457 0.00684651i
\(705\) 0 0
\(706\) 497.950 + 1532.53i 0.0265447 + 0.0816963i
\(707\) −1604.51 −0.0853518
\(708\) 0 0
\(709\) 15178.3 + 11027.7i 0.803997 + 0.584138i 0.912084 0.410003i \(-0.134472\pi\)
−0.108087 + 0.994141i \(0.534472\pi\)
\(710\) 7488.32 5860.02i 0.395819 0.309750i
\(711\) 0 0
\(712\) −20550.2 14930.6i −1.08167 0.785880i
\(713\) −12865.8 9347.55i −0.675776 0.490980i
\(714\) 0 0
\(715\) 814.467 + 2232.26i 0.0426005 + 0.116758i
\(716\) −14151.1 10281.4i −0.738618 0.536637i
\(717\) 0 0
\(718\) 14623.8 0.760104
\(719\) 4136.61 + 12731.2i 0.214561 + 0.660351i 0.999184 + 0.0403783i \(0.0128563\pi\)
−0.784623 + 0.619973i \(0.787144\pi\)
\(720\) 0 0
\(721\) −71.0894 + 218.791i −0.00367199 + 0.0113012i
\(722\) 2598.48 7997.29i 0.133941 0.412227i
\(723\) 0 0
\(724\) −2591.23 −0.133014
\(725\) 5370.44 + 13232.3i 0.275108 + 0.677841i
\(726\) 0 0
\(727\) 8138.17 5912.73i 0.415169 0.301638i −0.360522 0.932751i \(-0.617401\pi\)
0.775691 + 0.631113i \(0.217401\pi\)
\(728\) −6148.19 + 18922.2i −0.313004 + 0.963328i
\(729\) 0 0
\(730\) −14414.0 + 514.710i −0.730804 + 0.0260963i
\(731\) −265.314 816.554i −0.0134241 0.0413151i
\(732\) 0 0
\(733\) −884.238 2721.40i −0.0445567 0.137131i 0.926303 0.376779i \(-0.122968\pi\)
−0.970860 + 0.239647i \(0.922968\pi\)
\(734\) −157.475 114.413i −0.00791897 0.00575347i
\(735\) 0 0
\(736\) 15434.9 11214.1i 0.773013 0.561627i
\(737\) 1067.12 + 775.307i 0.0533349 + 0.0387501i
\(738\) 0 0
\(739\) −24379.0 + 17712.4i −1.21353 + 0.881680i −0.995546 0.0942726i \(-0.969947\pi\)
−0.217982 + 0.975953i \(0.569947\pi\)
\(740\) −19719.1 13278.1i −0.979577 0.659611i
\(741\) 0 0
\(742\) −3263.75 10044.8i −0.161477 0.496975i
\(743\) −1183.79 −0.0584508 −0.0292254 0.999573i \(-0.509304\pi\)
−0.0292254 + 0.999573i \(0.509304\pi\)
\(744\) 0 0
\(745\) 3863.83 + 10589.8i 0.190013 + 0.520781i
\(746\) 1457.06 4484.38i 0.0715106 0.220087i
\(747\) 0 0
\(748\) 69.1401 50.2333i 0.00337970 0.00245549i
\(749\) −22370.0 −1.09130
\(750\) 0 0
\(751\) 33092.2 1.60793 0.803964 0.594679i \(-0.202721\pi\)
0.803964 + 0.594679i \(0.202721\pi\)
\(752\) 6612.26 4804.08i 0.320644 0.232961i
\(753\) 0 0
\(754\) −4049.68 + 12463.6i −0.195598 + 0.601988i
\(755\) −8288.88 22717.8i −0.399554 1.09508i
\(756\) 0 0
\(757\) 14001.4 0.672246 0.336123 0.941818i \(-0.390884\pi\)
0.336123 + 0.941818i \(0.390884\pi\)
\(758\) 167.409 + 515.233i 0.00802188 + 0.0246888i
\(759\) 0 0
\(760\) 4260.10 + 2868.60i 0.203329 + 0.136914i
\(761\) −13651.0 + 9918.02i −0.650260 + 0.472441i −0.863360 0.504589i \(-0.831644\pi\)
0.213100 + 0.977030i \(0.431644\pi\)
\(762\) 0 0
\(763\) −13213.5 9600.19i −0.626949 0.455505i
\(764\) −2618.41 + 1902.39i −0.123993 + 0.0900864i
\(765\) 0 0
\(766\) 4534.58 + 3294.56i 0.213892 + 0.155401i
\(767\) −17537.9 53976.0i −0.825627 2.54102i
\(768\) 0 0
\(769\) 2146.67 + 6606.78i 0.100665 + 0.309813i 0.988688 0.149984i \(-0.0479221\pi\)
−0.888024 + 0.459797i \(0.847922\pi\)
\(770\) 453.708 16.2015i 0.0212344 0.000758260i
\(771\) 0 0
\(772\) 8683.52 26725.1i 0.404827 1.24593i
\(773\) −6808.98 + 4947.01i −0.316820 + 0.230183i −0.734817 0.678265i \(-0.762732\pi\)
0.417997 + 0.908448i \(0.362732\pi\)
\(774\) 0 0
\(775\) −16327.3 10166.7i −0.756765 0.471224i
\(776\) 7599.16 0.351539
\(777\) 0 0
\(778\) −4247.16 + 13071.4i −0.195717 + 0.602356i
\(779\) 258.640 796.012i 0.0118957 0.0366111i
\(780\) 0 0
\(781\) 486.937 + 1498.64i 0.0223098 + 0.0686625i
\(782\) −768.290 −0.0351330
\(783\) 0 0
\(784\) 3787.52 + 2751.80i 0.172537 + 0.125355i
\(785\) −10035.1 27503.8i −0.456265 1.25051i
\(786\)