Properties

Label 245.4.e.q.116.3
Level $245$
Weight $4$
Character 245.116
Analytic conductor $14.455$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.3
Root \(-1.02943 + 1.78303i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.4.e.q.226.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.322324 - 0.558282i) q^{2} +(-2.09344 + 3.62594i) q^{3} +(3.79221 - 6.56831i) q^{4} +(-2.50000 - 4.33013i) q^{5} +2.69906 q^{6} -10.0465 q^{8} +(4.73504 + 8.20133i) q^{9} +O(q^{10})\) \(q+(-0.322324 - 0.558282i) q^{2} +(-2.09344 + 3.62594i) q^{3} +(3.79221 - 6.56831i) q^{4} +(-2.50000 - 4.33013i) q^{5} +2.69906 q^{6} -10.0465 q^{8} +(4.73504 + 8.20133i) q^{9} +(-1.61162 + 2.79141i) q^{10} +(23.8507 - 41.3106i) q^{11} +(15.8775 + 27.5007i) q^{12} -57.2256 q^{13} +20.9344 q^{15} +(-27.0995 - 46.9377i) q^{16} +(-18.4843 + 32.0157i) q^{17} +(3.05244 - 5.28697i) q^{18} +(15.3830 + 26.6441i) q^{19} -37.9221 q^{20} -30.7506 q^{22} +(-26.5641 - 46.0104i) q^{23} +(21.0317 - 36.4279i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(18.4452 + 31.9480i) q^{26} -152.696 q^{27} -195.663 q^{29} +(-6.74765 - 11.6873i) q^{30} +(128.935 - 223.322i) q^{31} +(-57.6555 + 99.8623i) q^{32} +(99.8597 + 172.962i) q^{33} +23.8317 q^{34} +71.8252 q^{36} +(-173.212 - 300.011i) q^{37} +(9.91660 - 17.1760i) q^{38} +(119.798 - 207.497i) q^{39} +(25.1162 + 43.5025i) q^{40} -267.050 q^{41} -176.859 q^{43} +(-180.894 - 313.317i) q^{44} +(23.6752 - 41.0067i) q^{45} +(-17.1245 + 29.6605i) q^{46} +(-155.799 - 269.852i) q^{47} +226.924 q^{48} +16.1162 q^{50} +(-77.3914 - 134.046i) q^{51} +(-217.012 + 375.875i) q^{52} +(246.135 - 426.318i) q^{53} +(49.2175 + 85.2472i) q^{54} -238.507 q^{55} -128.813 q^{57} +(63.0668 + 109.235i) q^{58} +(49.3827 - 85.5333i) q^{59} +(79.3876 - 137.503i) q^{60} +(41.0841 + 71.1597i) q^{61} -166.235 q^{62} -359.257 q^{64} +(143.064 + 247.794i) q^{65} +(64.3744 - 111.500i) q^{66} +(-327.334 + 566.959i) q^{67} +(140.193 + 242.821i) q^{68} +222.441 q^{69} +779.658 q^{71} +(-47.5705 - 82.3945i) q^{72} +(-414.836 + 718.518i) q^{73} +(-111.660 + 193.402i) q^{74} +(-52.3359 - 90.6485i) q^{75} +233.342 q^{76} -154.455 q^{78} +(384.713 + 666.343i) q^{79} +(-135.497 + 234.689i) q^{80} +(191.813 - 332.229i) q^{81} +(86.0765 + 149.089i) q^{82} -613.203 q^{83} +184.843 q^{85} +(57.0059 + 98.7372i) q^{86} +(409.608 - 709.461i) q^{87} +(-239.615 + 415.025i) q^{88} +(-228.833 - 396.350i) q^{89} -30.5244 q^{90} -402.947 q^{92} +(539.835 + 935.022i) q^{93} +(-100.436 + 173.960i) q^{94} +(76.9148 - 133.220i) q^{95} +(-241.396 - 418.111i) q^{96} +1412.11 q^{97} +451.736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.322324 0.558282i −0.113959 0.197382i 0.803404 0.595434i \(-0.203020\pi\)
−0.917363 + 0.398052i \(0.869687\pi\)
\(3\) −2.09344 + 3.62594i −0.402882 + 0.697812i −0.994072 0.108720i \(-0.965325\pi\)
0.591190 + 0.806532i \(0.298658\pi\)
\(4\) 3.79221 6.56831i 0.474027 0.821039i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 2.69906 0.183648
\(7\) 0 0
\(8\) −10.0465 −0.443995
\(9\) 4.73504 + 8.20133i 0.175372 + 0.303753i
\(10\) −1.61162 + 2.79141i −0.0509639 + 0.0882721i
\(11\) 23.8507 41.3106i 0.653750 1.13233i −0.328456 0.944519i \(-0.606528\pi\)
0.982206 0.187808i \(-0.0601383\pi\)
\(12\) 15.8775 + 27.5007i 0.381954 + 0.661564i
\(13\) −57.2256 −1.22089 −0.610443 0.792060i \(-0.709009\pi\)
−0.610443 + 0.792060i \(0.709009\pi\)
\(14\) 0 0
\(15\) 20.9344 0.360349
\(16\) −27.0995 46.9377i −0.423430 0.733402i
\(17\) −18.4843 + 32.0157i −0.263712 + 0.456762i −0.967225 0.253920i \(-0.918280\pi\)
0.703514 + 0.710682i \(0.251613\pi\)
\(18\) 3.05244 5.28697i 0.0399703 0.0692306i
\(19\) 15.3830 + 26.6441i 0.185742 + 0.321714i 0.943826 0.330442i \(-0.107198\pi\)
−0.758084 + 0.652156i \(0.773865\pi\)
\(20\) −37.9221 −0.423982
\(21\) 0 0
\(22\) −30.7506 −0.298002
\(23\) −26.5641 46.0104i −0.240826 0.417123i 0.720124 0.693846i \(-0.244085\pi\)
−0.960950 + 0.276723i \(0.910752\pi\)
\(24\) 21.0317 36.4279i 0.178878 0.309826i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 18.4452 + 31.9480i 0.139131 + 0.240981i
\(27\) −152.696 −1.08838
\(28\) 0 0
\(29\) −195.663 −1.25288 −0.626442 0.779468i \(-0.715490\pi\)
−0.626442 + 0.779468i \(0.715490\pi\)
\(30\) −6.74765 11.6873i −0.0410649 0.0711265i
\(31\) 128.935 223.322i 0.747014 1.29387i −0.202234 0.979337i \(-0.564820\pi\)
0.949248 0.314529i \(-0.101846\pi\)
\(32\) −57.6555 + 99.8623i −0.318505 + 0.551666i
\(33\) 99.8597 + 172.962i 0.526768 + 0.912389i
\(34\) 23.8317 0.120209
\(35\) 0 0
\(36\) 71.8252 0.332524
\(37\) −173.212 300.011i −0.769616 1.33301i −0.937771 0.347254i \(-0.887114\pi\)
0.168155 0.985761i \(-0.446219\pi\)
\(38\) 9.91660 17.1760i 0.0423338 0.0733243i
\(39\) 119.798 207.497i 0.491873 0.851950i
\(40\) 25.1162 + 43.5025i 0.0992804 + 0.171959i
\(41\) −267.050 −1.01722 −0.508611 0.860996i \(-0.669841\pi\)
−0.508611 + 0.860996i \(0.669841\pi\)
\(42\) 0 0
\(43\) −176.859 −0.627227 −0.313614 0.949551i \(-0.601540\pi\)
−0.313614 + 0.949551i \(0.601540\pi\)
\(44\) −180.894 313.317i −0.619790 1.07351i
\(45\) 23.6752 41.0067i 0.0784287 0.135843i
\(46\) −17.1245 + 29.6605i −0.0548884 + 0.0950696i
\(47\) −155.799 269.852i −0.483524 0.837489i 0.516297 0.856410i \(-0.327310\pi\)
−0.999821 + 0.0189211i \(0.993977\pi\)
\(48\) 226.924 0.682369
\(49\) 0 0
\(50\) 16.1162 0.0455835
\(51\) −77.3914 134.046i −0.212489 0.368042i
\(52\) −217.012 + 375.875i −0.578733 + 1.00240i
\(53\) 246.135 426.318i 0.637910 1.10489i −0.347980 0.937502i \(-0.613132\pi\)
0.985891 0.167391i \(-0.0535343\pi\)
\(54\) 49.2175 + 85.2472i 0.124031 + 0.214827i
\(55\) −238.507 −0.584731
\(56\) 0 0
\(57\) −128.813 −0.299328
\(58\) 63.0668 + 109.235i 0.142777 + 0.247297i
\(59\) 49.3827 85.5333i 0.108967 0.188737i −0.806385 0.591391i \(-0.798579\pi\)
0.915352 + 0.402654i \(0.131912\pi\)
\(60\) 79.3876 137.503i 0.170815 0.295860i
\(61\) 41.0841 + 71.1597i 0.0862340 + 0.149362i 0.905916 0.423457i \(-0.139183\pi\)
−0.819682 + 0.572818i \(0.805850\pi\)
\(62\) −166.235 −0.340515
\(63\) 0 0
\(64\) −359.257 −0.701674
\(65\) 143.064 + 247.794i 0.272999 + 0.472847i
\(66\) 64.3744 111.500i 0.120060 0.207949i
\(67\) −327.334 + 566.959i −0.596869 + 1.03381i 0.396411 + 0.918073i \(0.370255\pi\)
−0.993280 + 0.115734i \(0.963078\pi\)
\(68\) 140.193 + 242.821i 0.250013 + 0.433035i
\(69\) 222.441 0.388098
\(70\) 0 0
\(71\) 779.658 1.30322 0.651608 0.758556i \(-0.274095\pi\)
0.651608 + 0.758556i \(0.274095\pi\)
\(72\) −47.5705 82.3945i −0.0778643 0.134865i
\(73\) −414.836 + 718.518i −0.665109 + 1.15200i 0.314147 + 0.949374i \(0.398281\pi\)
−0.979256 + 0.202628i \(0.935052\pi\)
\(74\) −111.660 + 193.402i −0.175409 + 0.303817i
\(75\) −52.3359 90.6485i −0.0805764 0.139562i
\(76\) 233.342 0.352186
\(77\) 0 0
\(78\) −154.455 −0.224213
\(79\) 384.713 + 666.343i 0.547894 + 0.948980i 0.998419 + 0.0562159i \(0.0179035\pi\)
−0.450525 + 0.892764i \(0.648763\pi\)
\(80\) −135.497 + 234.689i −0.189363 + 0.327987i
\(81\) 191.813 332.229i 0.263117 0.455733i
\(82\) 86.0765 + 149.089i 0.115921 + 0.200782i
\(83\) −613.203 −0.810937 −0.405469 0.914109i \(-0.632892\pi\)
−0.405469 + 0.914109i \(0.632892\pi\)
\(84\) 0 0
\(85\) 184.843 0.235871
\(86\) 57.0059 + 98.7372i 0.0714780 + 0.123804i
\(87\) 409.608 709.461i 0.504765 0.874278i
\(88\) −239.615 + 415.025i −0.290262 + 0.502748i
\(89\) −228.833 396.350i −0.272542 0.472057i 0.696970 0.717100i \(-0.254531\pi\)
−0.969512 + 0.245043i \(0.921198\pi\)
\(90\) −30.5244 −0.0357506
\(91\) 0 0
\(92\) −402.947 −0.456632
\(93\) 539.835 + 935.022i 0.601917 + 1.04255i
\(94\) −100.436 + 173.960i −0.110204 + 0.190878i
\(95\) 76.9148 133.220i 0.0830662 0.143875i
\(96\) −241.396 418.111i −0.256640 0.444513i
\(97\) 1412.11 1.47813 0.739063 0.673636i \(-0.235268\pi\)
0.739063 + 0.673636i \(0.235268\pi\)
\(98\) 0 0
\(99\) 451.736 0.458597
\(100\) 94.8054 + 164.208i 0.0948054 + 0.164208i
\(101\) 911.895 1579.45i 0.898386 1.55605i 0.0688279 0.997629i \(-0.478074\pi\)
0.829558 0.558421i \(-0.188593\pi\)
\(102\) −49.8902 + 86.4124i −0.0484301 + 0.0838833i
\(103\) 203.887 + 353.143i 0.195045 + 0.337828i 0.946915 0.321483i \(-0.104181\pi\)
−0.751870 + 0.659311i \(0.770848\pi\)
\(104\) 574.915 0.542068
\(105\) 0 0
\(106\) −317.341 −0.290782
\(107\) 185.054 + 320.524i 0.167195 + 0.289591i 0.937433 0.348167i \(-0.113196\pi\)
−0.770237 + 0.637757i \(0.779862\pi\)
\(108\) −579.055 + 1002.95i −0.515922 + 0.893603i
\(109\) −487.785 + 844.869i −0.428636 + 0.742420i −0.996752 0.0805287i \(-0.974339\pi\)
0.568116 + 0.822948i \(0.307672\pi\)
\(110\) 76.8764 + 133.154i 0.0666352 + 0.115416i
\(111\) 1450.43 1.24026
\(112\) 0 0
\(113\) 1978.85 1.64739 0.823693 0.567036i \(-0.191910\pi\)
0.823693 + 0.567036i \(0.191910\pi\)
\(114\) 41.5195 + 71.9139i 0.0341111 + 0.0590821i
\(115\) −132.820 + 230.052i −0.107701 + 0.186543i
\(116\) −741.995 + 1285.17i −0.593901 + 1.02867i
\(117\) −270.966 469.326i −0.214109 0.370848i
\(118\) −63.6689 −0.0496711
\(119\) 0 0
\(120\) −210.317 −0.159993
\(121\) −472.208 817.888i −0.354777 0.614492i
\(122\) 26.4848 45.8730i 0.0196542 0.0340422i
\(123\) 559.052 968.306i 0.409821 0.709831i
\(124\) −977.899 1693.77i −0.708209 1.22665i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1392.38 0.972867 0.486433 0.873718i \(-0.338298\pi\)
0.486433 + 0.873718i \(0.338298\pi\)
\(128\) 577.041 + 999.465i 0.398467 + 0.690164i
\(129\) 370.243 641.280i 0.252699 0.437687i
\(130\) 92.2259 159.740i 0.0622211 0.107770i
\(131\) −888.509 1538.94i −0.592591 1.02640i −0.993882 0.110447i \(-0.964772\pi\)
0.401291 0.915951i \(-0.368562\pi\)
\(132\) 1514.76 0.998809
\(133\) 0 0
\(134\) 422.031 0.272074
\(135\) 381.739 + 661.192i 0.243369 + 0.421528i
\(136\) 185.702 321.645i 0.117087 0.202800i
\(137\) 990.240 1715.15i 0.617532 1.06960i −0.372402 0.928071i \(-0.621466\pi\)
0.989935 0.141526i \(-0.0452009\pi\)
\(138\) −71.6981 124.185i −0.0442271 0.0766037i
\(139\) −2182.09 −1.33153 −0.665763 0.746163i \(-0.731894\pi\)
−0.665763 + 0.746163i \(0.731894\pi\)
\(140\) 0 0
\(141\) 1304.62 0.779213
\(142\) −251.302 435.268i −0.148513 0.257232i
\(143\) −1364.87 + 2364.02i −0.798154 + 1.38244i
\(144\) 256.635 444.504i 0.148515 0.257236i
\(145\) 489.157 + 847.244i 0.280153 + 0.485240i
\(146\) 534.847 0.303180
\(147\) 0 0
\(148\) −2627.42 −1.45928
\(149\) −335.077 580.370i −0.184232 0.319099i 0.759085 0.650991i \(-0.225646\pi\)
−0.943317 + 0.331892i \(0.892313\pi\)
\(150\) −33.7383 + 58.4364i −0.0183648 + 0.0318087i
\(151\) −1674.42 + 2900.18i −0.902401 + 1.56300i −0.0780315 + 0.996951i \(0.524863\pi\)
−0.824369 + 0.566053i \(0.808470\pi\)
\(152\) −154.544 267.679i −0.0824685 0.142840i
\(153\) −350.096 −0.184990
\(154\) 0 0
\(155\) −1289.35 −0.668149
\(156\) −908.601 1573.74i −0.466322 0.807694i
\(157\) 1204.20 2085.74i 0.612140 1.06026i −0.378739 0.925504i \(-0.623642\pi\)
0.990879 0.134754i \(-0.0430245\pi\)
\(158\) 248.005 429.556i 0.124875 0.216289i
\(159\) 1030.54 + 1784.94i 0.514005 + 0.890284i
\(160\) 576.555 0.284879
\(161\) 0 0
\(162\) −247.303 −0.119938
\(163\) 1905.52 + 3300.45i 0.915654 + 1.58596i 0.805942 + 0.591995i \(0.201659\pi\)
0.109712 + 0.993963i \(0.465007\pi\)
\(164\) −1012.71 + 1754.06i −0.482191 + 0.835179i
\(165\) 499.299 864.810i 0.235578 0.408033i
\(166\) 197.650 + 342.340i 0.0924134 + 0.160065i
\(167\) −1207.15 −0.559354 −0.279677 0.960094i \(-0.590227\pi\)
−0.279677 + 0.960094i \(0.590227\pi\)
\(168\) 0 0
\(169\) 1077.77 0.490564
\(170\) −59.5793 103.194i −0.0268795 0.0465567i
\(171\) −145.678 + 252.322i −0.0651478 + 0.112839i
\(172\) −670.688 + 1161.67i −0.297322 + 0.514978i
\(173\) 1621.64 + 2808.76i 0.712665 + 1.23437i 0.963853 + 0.266434i \(0.0858454\pi\)
−0.251188 + 0.967938i \(0.580821\pi\)
\(174\) −528.105 −0.230089
\(175\) 0 0
\(176\) −2585.36 −1.10727
\(177\) 206.759 + 358.117i 0.0878020 + 0.152078i
\(178\) −147.517 + 255.507i −0.0621171 + 0.107590i
\(179\) −429.864 + 744.546i −0.179495 + 0.310894i −0.941708 0.336433i \(-0.890780\pi\)
0.762213 + 0.647326i \(0.224113\pi\)
\(180\) −179.563 311.012i −0.0743546 0.128786i
\(181\) 290.504 0.119298 0.0596491 0.998219i \(-0.481002\pi\)
0.0596491 + 0.998219i \(0.481002\pi\)
\(182\) 0 0
\(183\) −344.028 −0.138969
\(184\) 266.875 + 462.242i 0.106926 + 0.185201i
\(185\) −866.058 + 1500.06i −0.344183 + 0.596142i
\(186\) 348.004 602.760i 0.137187 0.237616i
\(187\) 881.725 + 1527.19i 0.344803 + 0.597216i
\(188\) −2363.30 −0.916814
\(189\) 0 0
\(190\) −99.1660 −0.0378645
\(191\) −2447.81 4239.73i −0.927315 1.60616i −0.787795 0.615937i \(-0.788778\pi\)
−0.139519 0.990219i \(-0.544556\pi\)
\(192\) 752.082 1302.64i 0.282692 0.489637i
\(193\) 1774.36 3073.29i 0.661770 1.14622i −0.318381 0.947963i \(-0.603139\pi\)
0.980150 0.198256i \(-0.0635276\pi\)
\(194\) −455.158 788.356i −0.168445 0.291756i
\(195\) −1197.98 −0.439945
\(196\) 0 0
\(197\) −650.107 −0.235118 −0.117559 0.993066i \(-0.537507\pi\)
−0.117559 + 0.993066i \(0.537507\pi\)
\(198\) −145.605 252.196i −0.0522612 0.0905190i
\(199\) 2027.55 3511.81i 0.722256 1.25098i −0.237838 0.971305i \(-0.576439\pi\)
0.960094 0.279679i \(-0.0902279\pi\)
\(200\) 125.581 217.512i 0.0443995 0.0769023i
\(201\) −1370.51 2373.79i −0.480936 0.833005i
\(202\) −1175.70 −0.409516
\(203\) 0 0
\(204\) −1173.94 −0.402903
\(205\) 667.624 + 1156.36i 0.227458 + 0.393969i
\(206\) 131.436 227.653i 0.0444541 0.0769968i
\(207\) 251.564 435.722i 0.0844682 0.146303i
\(208\) 1550.79 + 2686.04i 0.516960 + 0.895400i
\(209\) 1467.58 0.485714
\(210\) 0 0
\(211\) −1569.67 −0.512134 −0.256067 0.966659i \(-0.582427\pi\)
−0.256067 + 0.966659i \(0.582427\pi\)
\(212\) −1866.79 3233.38i −0.604773 1.04750i
\(213\) −1632.16 + 2826.99i −0.525042 + 0.909400i
\(214\) 119.295 206.625i 0.0381067 0.0660027i
\(215\) 442.148 + 765.822i 0.140252 + 0.242924i
\(216\) 1534.05 0.483236
\(217\) 0 0
\(218\) 628.900 0.195387
\(219\) −1736.87 3008.34i −0.535921 0.928242i
\(220\) −904.468 + 1566.58i −0.277178 + 0.480087i
\(221\) 1057.77 1832.12i 0.321962 0.557655i
\(222\) −467.508 809.748i −0.141338 0.244805i
\(223\) −4723.86 −1.41853 −0.709267 0.704940i \(-0.750974\pi\)
−0.709267 + 0.704940i \(0.750974\pi\)
\(224\) 0 0
\(225\) −236.752 −0.0701488
\(226\) −637.831 1104.76i −0.187734 0.325165i
\(227\) 1842.51 3191.32i 0.538730 0.933108i −0.460243 0.887793i \(-0.652238\pi\)
0.998973 0.0453145i \(-0.0144290\pi\)
\(228\) −488.487 + 846.084i −0.141890 + 0.245760i
\(229\) 1678.39 + 2907.05i 0.484328 + 0.838880i 0.999838 0.0180032i \(-0.00573089\pi\)
−0.515510 + 0.856883i \(0.672398\pi\)
\(230\) 171.245 0.0490937
\(231\) 0 0
\(232\) 1965.72 0.556275
\(233\) −1157.01 2004.00i −0.325314 0.563460i 0.656262 0.754533i \(-0.272137\pi\)
−0.981576 + 0.191073i \(0.938803\pi\)
\(234\) −174.677 + 302.550i −0.0487992 + 0.0845228i
\(235\) −778.996 + 1349.26i −0.216239 + 0.374536i
\(236\) −374.539 648.721i −0.103307 0.178933i
\(237\) −3221.49 −0.882946
\(238\) 0 0
\(239\) 941.179 0.254727 0.127364 0.991856i \(-0.459348\pi\)
0.127364 + 0.991856i \(0.459348\pi\)
\(240\) −567.311 982.611i −0.152582 0.264280i
\(241\) 2819.12 4882.86i 0.753509 1.30512i −0.192604 0.981277i \(-0.561693\pi\)
0.946112 0.323838i \(-0.104973\pi\)
\(242\) −304.408 + 527.250i −0.0808599 + 0.140053i
\(243\) −1258.30 2179.43i −0.332180 0.575353i
\(244\) 623.199 0.163509
\(245\) 0 0
\(246\) −720.783 −0.186811
\(247\) −880.299 1524.72i −0.226770 0.392777i
\(248\) −1295.34 + 2243.60i −0.331671 + 0.574471i
\(249\) 1283.70 2223.44i 0.326712 0.565882i
\(250\) −40.2905 69.7852i −0.0101928 0.0176544i
\(251\) −365.822 −0.0919940 −0.0459970 0.998942i \(-0.514646\pi\)
−0.0459970 + 0.998942i \(0.514646\pi\)
\(252\) 0 0
\(253\) −2534.28 −0.629759
\(254\) −448.799 777.342i −0.110867 0.192027i
\(255\) −386.957 + 670.229i −0.0950282 + 0.164594i
\(256\) −1065.04 + 1844.70i −0.260019 + 0.450367i
\(257\) −3138.23 5435.57i −0.761702 1.31931i −0.941973 0.335689i \(-0.891031\pi\)
0.180271 0.983617i \(-0.442303\pi\)
\(258\) −477.353 −0.115189
\(259\) 0 0
\(260\) 2170.12 0.517635
\(261\) −926.471 1604.69i −0.219721 0.380568i
\(262\) −572.776 + 992.076i −0.135062 + 0.233934i
\(263\) 2112.99 3659.80i 0.495408 0.858072i −0.504578 0.863366i \(-0.668352\pi\)
0.999986 + 0.00529397i \(0.00168513\pi\)
\(264\) −1003.24 1737.66i −0.233883 0.405097i
\(265\) −2461.35 −0.570564
\(266\) 0 0
\(267\) 1916.19 0.439210
\(268\) 2482.64 + 4300.06i 0.565864 + 0.980105i
\(269\) 490.796 850.083i 0.111243 0.192678i −0.805029 0.593236i \(-0.797850\pi\)
0.916272 + 0.400557i \(0.131184\pi\)
\(270\) 246.087 426.236i 0.0554681 0.0960737i
\(271\) 1942.21 + 3364.01i 0.435354 + 0.754055i 0.997324 0.0731021i \(-0.0232899\pi\)
−0.561971 + 0.827157i \(0.689957\pi\)
\(272\) 2003.66 0.446653
\(273\) 0 0
\(274\) −1276.71 −0.281493
\(275\) 596.267 + 1032.76i 0.130750 + 0.226465i
\(276\) 843.544 1461.06i 0.183969 0.318643i
\(277\) −1807.46 + 3130.62i −0.392058 + 0.679064i −0.992721 0.120438i \(-0.961570\pi\)
0.600663 + 0.799502i \(0.294903\pi\)
\(278\) 703.339 + 1218.22i 0.151739 + 0.262820i
\(279\) 2442.05 0.524021
\(280\) 0 0
\(281\) 72.6835 0.0154304 0.00771518 0.999970i \(-0.497544\pi\)
0.00771518 + 0.999970i \(0.497544\pi\)
\(282\) −420.511 728.347i −0.0887982 0.153803i
\(283\) 871.522 1509.52i 0.183062 0.317073i −0.759860 0.650087i \(-0.774732\pi\)
0.942922 + 0.333014i \(0.108066\pi\)
\(284\) 2956.63 5121.03i 0.617759 1.06999i
\(285\) 322.033 + 557.777i 0.0669318 + 0.115929i
\(286\) 1759.72 0.363827
\(287\) 0 0
\(288\) −1092.01 −0.223427
\(289\) 1773.16 + 3071.21i 0.360912 + 0.625119i
\(290\) 315.334 546.174i 0.0638519 0.110595i
\(291\) −2956.17 + 5120.23i −0.595511 + 1.03145i
\(292\) 3146.30 + 5449.55i 0.630559 + 1.09216i
\(293\) 4989.29 0.994804 0.497402 0.867520i \(-0.334287\pi\)
0.497402 + 0.867520i \(0.334287\pi\)
\(294\) 0 0
\(295\) −493.827 −0.0974634
\(296\) 1740.17 + 3014.05i 0.341706 + 0.591853i
\(297\) −3641.89 + 6307.94i −0.711529 + 1.23240i
\(298\) −216.007 + 374.135i −0.0419897 + 0.0727283i
\(299\) 1520.15 + 2632.97i 0.294021 + 0.509260i
\(300\) −793.876 −0.152782
\(301\) 0 0
\(302\) 2158.82 0.411346
\(303\) 3817.99 + 6612.95i 0.723887 + 1.25381i
\(304\) 833.741 1444.08i 0.157297 0.272447i
\(305\) 205.420 355.799i 0.0385650 0.0667966i
\(306\) 112.844 + 195.452i 0.0210813 + 0.0365139i
\(307\) −1664.61 −0.309461 −0.154731 0.987957i \(-0.549451\pi\)
−0.154731 + 0.987957i \(0.549451\pi\)
\(308\) 0 0
\(309\) −1707.30 −0.314320
\(310\) 415.589 + 719.821i 0.0761415 + 0.131881i
\(311\) 272.812 472.524i 0.0497419 0.0861555i −0.840082 0.542459i \(-0.817493\pi\)
0.889824 + 0.456303i \(0.150827\pi\)
\(312\) −1203.55 + 2084.61i −0.218390 + 0.378262i
\(313\) 106.782 + 184.952i 0.0192833 + 0.0333997i 0.875506 0.483207i \(-0.160528\pi\)
−0.856223 + 0.516607i \(0.827195\pi\)
\(314\) −1552.58 −0.279035
\(315\) 0 0
\(316\) 5835.66 1.03887
\(317\) 1341.97 + 2324.35i 0.237767 + 0.411825i 0.960073 0.279748i \(-0.0902511\pi\)
−0.722306 + 0.691574i \(0.756918\pi\)
\(318\) 664.333 1150.66i 0.117151 0.202911i
\(319\) −4666.68 + 8082.93i −0.819073 + 1.41868i
\(320\) 898.142 + 1555.63i 0.156899 + 0.271757i
\(321\) −1549.60 −0.269440
\(322\) 0 0
\(323\) −1137.37 −0.195929
\(324\) −1454.79 2519.77i −0.249449 0.432059i
\(325\) 715.320 1238.97i 0.122089 0.211464i
\(326\) 1228.39 2127.63i 0.208693 0.361468i
\(327\) −2042.30 3537.36i −0.345380 0.598215i
\(328\) 2682.91 0.451642
\(329\) 0 0
\(330\) −643.744 −0.107385
\(331\) 2533.76 + 4388.61i 0.420750 + 0.728760i 0.996013 0.0892084i \(-0.0284337\pi\)
−0.575263 + 0.817968i \(0.695100\pi\)
\(332\) −2325.40 + 4027.71i −0.384406 + 0.665811i
\(333\) 1640.33 2841.13i 0.269938 0.467547i
\(334\) 389.093 + 673.930i 0.0637433 + 0.110407i
\(335\) 3273.34 0.533856
\(336\) 0 0
\(337\) −9353.21 −1.51187 −0.755937 0.654644i \(-0.772818\pi\)
−0.755937 + 0.654644i \(0.772818\pi\)
\(338\) −347.391 601.699i −0.0559041 0.0968287i
\(339\) −4142.60 + 7175.19i −0.663703 + 1.14957i
\(340\) 700.964 1214.10i 0.111809 0.193659i
\(341\) −6150.37 10652.8i −0.976720 1.69173i
\(342\) 187.822 0.0296966
\(343\) 0 0
\(344\) 1776.81 0.278486
\(345\) −556.103 963.198i −0.0867813 0.150310i
\(346\) 1045.39 1810.66i 0.162429 0.281335i
\(347\) −1174.67 + 2034.59i −0.181728 + 0.314762i −0.942469 0.334293i \(-0.891502\pi\)
0.760741 + 0.649055i \(0.224836\pi\)
\(348\) −3106.64 5380.86i −0.478544 0.828863i
\(349\) 10472.6 1.60626 0.803128 0.595806i \(-0.203167\pi\)
0.803128 + 0.595806i \(0.203167\pi\)
\(350\) 0 0
\(351\) 8738.10 1.32879
\(352\) 2750.24 + 4763.56i 0.416445 + 0.721303i
\(353\) −3587.31 + 6213.41i −0.540888 + 0.936845i 0.457966 + 0.888970i \(0.348578\pi\)
−0.998853 + 0.0478752i \(0.984755\pi\)
\(354\) 133.287 230.859i 0.0200116 0.0346611i
\(355\) −1949.14 3376.02i −0.291408 0.504733i
\(356\) −3471.14 −0.516769
\(357\) 0 0
\(358\) 554.222 0.0818199
\(359\) 3767.06 + 6524.74i 0.553811 + 0.959228i 0.997995 + 0.0632926i \(0.0201601\pi\)
−0.444185 + 0.895935i \(0.646507\pi\)
\(360\) −237.852 + 411.972i −0.0348220 + 0.0603135i
\(361\) 2956.23 5120.34i 0.431000 0.746514i
\(362\) −93.6364 162.183i −0.0135951 0.0235474i
\(363\) 3954.15 0.571733
\(364\) 0 0
\(365\) 4148.36 0.594891
\(366\) 110.888 + 192.064i 0.0158367 + 0.0274300i
\(367\) 2726.53 4722.49i 0.387803 0.671694i −0.604351 0.796718i \(-0.706567\pi\)
0.992154 + 0.125024i \(0.0399008\pi\)
\(368\) −1439.75 + 2493.71i −0.203946 + 0.353244i
\(369\) −1264.49 2190.16i −0.178392 0.308985i
\(370\) 1116.60 0.156891
\(371\) 0 0
\(372\) 8188.68 1.14130
\(373\) −4115.65 7128.51i −0.571314 0.989545i −0.996431 0.0844067i \(-0.973101\pi\)
0.425117 0.905138i \(-0.360233\pi\)
\(374\) 568.402 984.501i 0.0785866 0.136116i
\(375\) −261.680 + 453.242i −0.0360349 + 0.0624142i
\(376\) 1565.23 + 2711.06i 0.214683 + 0.371841i
\(377\) 11196.9 1.52963
\(378\) 0 0
\(379\) 1670.06 0.226346 0.113173 0.993575i \(-0.463898\pi\)
0.113173 + 0.993575i \(0.463898\pi\)
\(380\) −583.355 1010.40i −0.0787512 0.136401i
\(381\) −2914.87 + 5048.70i −0.391951 + 0.678879i
\(382\) −1577.97 + 2733.13i −0.211351 + 0.366071i
\(383\) 1610.07 + 2788.72i 0.214806 + 0.372055i 0.953213 0.302301i \(-0.0977548\pi\)
−0.738407 + 0.674356i \(0.764421\pi\)
\(384\) −4832.00 −0.642140
\(385\) 0 0
\(386\) −2287.68 −0.301658
\(387\) −837.435 1450.48i −0.109998 0.190522i
\(388\) 5355.03 9275.19i 0.700672 1.21360i
\(389\) −1761.11 + 3050.34i −0.229543 + 0.397579i −0.957673 0.287860i \(-0.907056\pi\)
0.728130 + 0.685439i \(0.240390\pi\)
\(390\) 386.138 + 668.811i 0.0501356 + 0.0868374i
\(391\) 1964.07 0.254034
\(392\) 0 0
\(393\) 7440.15 0.954977
\(394\) 209.545 + 362.943i 0.0267937 + 0.0464081i
\(395\) 1923.57 3331.71i 0.245026 0.424397i
\(396\) 1713.08 2967.14i 0.217387 0.376526i
\(397\) −2727.58 4724.31i −0.344819 0.597245i 0.640502 0.767957i \(-0.278726\pi\)
−0.985321 + 0.170712i \(0.945393\pi\)
\(398\) −2614.11 −0.329229
\(399\) 0 0
\(400\) 1354.97 0.169372
\(401\) 580.899 + 1006.15i 0.0723409 + 0.125298i 0.899927 0.436041i \(-0.143620\pi\)
−0.827586 + 0.561339i \(0.810286\pi\)
\(402\) −883.494 + 1530.26i −0.109614 + 0.189856i
\(403\) −7378.39 + 12779.7i −0.912019 + 1.57966i
\(404\) −6916.20 11979.2i −0.851718 1.47522i
\(405\) −1918.13 −0.235339
\(406\) 0 0
\(407\) −16524.8 −2.01255
\(408\) 777.510 + 1346.69i 0.0943443 + 0.163409i
\(409\) −3699.32 + 6407.42i −0.447237 + 0.774637i −0.998205 0.0598896i \(-0.980925\pi\)
0.550968 + 0.834526i \(0.314258\pi\)
\(410\) 430.382 745.444i 0.0518416 0.0897924i
\(411\) 4146.01 + 7181.10i 0.497586 + 0.861843i
\(412\) 3092.74 0.369826
\(413\) 0 0
\(414\) −324.341 −0.0385036
\(415\) 1533.01 + 2655.25i 0.181331 + 0.314075i
\(416\) 3299.37 5714.68i 0.388858 0.673522i
\(417\) 4568.06 7912.11i 0.536448 0.929155i
\(418\) −473.035 819.320i −0.0553514 0.0958714i
\(419\) −2134.46 −0.248867 −0.124433 0.992228i \(-0.539711\pi\)
−0.124433 + 0.992228i \(0.539711\pi\)
\(420\) 0 0
\(421\) −3902.36 −0.451756 −0.225878 0.974156i \(-0.572525\pi\)
−0.225878 + 0.974156i \(0.572525\pi\)
\(422\) 505.941 + 876.316i 0.0583621 + 0.101086i
\(423\) 1475.43 2555.52i 0.169593 0.293744i
\(424\) −2472.79 + 4283.00i −0.283229 + 0.490568i
\(425\) −462.107 800.393i −0.0527423 0.0913524i
\(426\) 2104.34 0.239333
\(427\) 0 0
\(428\) 2807.06 0.317020
\(429\) −5714.53 9897.86i −0.643124 1.11392i
\(430\) 285.030 493.686i 0.0319659 0.0553666i
\(431\) 1809.07 3133.39i 0.202180 0.350186i −0.747050 0.664767i \(-0.768531\pi\)
0.949231 + 0.314581i \(0.101864\pi\)
\(432\) 4137.98 + 7167.18i 0.460853 + 0.798221i
\(433\) −4222.37 −0.468624 −0.234312 0.972161i \(-0.575284\pi\)
−0.234312 + 0.972161i \(0.575284\pi\)
\(434\) 0 0
\(435\) −4096.08 −0.451475
\(436\) 3699.57 + 6407.85i 0.406370 + 0.703854i
\(437\) 817.269 1415.55i 0.0894629 0.154954i
\(438\) −1119.67 + 1939.32i −0.122146 + 0.211563i
\(439\) 6758.98 + 11706.9i 0.734826 + 1.27276i 0.954800 + 0.297250i \(0.0960693\pi\)
−0.219974 + 0.975506i \(0.570597\pi\)
\(440\) 2396.15 0.259618
\(441\) 0 0
\(442\) −1363.78 −0.146762
\(443\) −8295.58 14368.4i −0.889695 1.54100i −0.840236 0.542222i \(-0.817583\pi\)
−0.0494599 0.998776i \(-0.515750\pi\)
\(444\) 5500.34 9526.87i 0.587916 1.01830i
\(445\) −1144.17 + 1981.75i −0.121885 + 0.211110i
\(446\) 1522.61 + 2637.24i 0.161654 + 0.279993i
\(447\) 2805.85 0.296895
\(448\) 0 0
\(449\) 8354.32 0.878095 0.439048 0.898464i \(-0.355316\pi\)
0.439048 + 0.898464i \(0.355316\pi\)
\(450\) 76.3109 + 132.174i 0.00799407 + 0.0138461i
\(451\) −6369.31 + 11032.0i −0.665009 + 1.15183i
\(452\) 7504.23 12997.7i 0.780905 1.35257i
\(453\) −7010.59 12142.7i −0.727122 1.25941i
\(454\) −2375.54 −0.245572
\(455\) 0 0
\(456\) 1294.12 0.132900
\(457\) 640.168 + 1108.80i 0.0655269 + 0.113496i 0.896928 0.442177i \(-0.145794\pi\)
−0.831401 + 0.555673i \(0.812461\pi\)
\(458\) 1081.97 1874.03i 0.110387 0.191195i
\(459\) 2822.47 4888.66i 0.287019 0.497131i
\(460\) 1007.37 + 1744.81i 0.102106 + 0.176853i
\(461\) −6986.72 −0.705865 −0.352932 0.935649i \(-0.614815\pi\)
−0.352932 + 0.935649i \(0.614815\pi\)
\(462\) 0 0
\(463\) −5587.32 −0.560831 −0.280416 0.959879i \(-0.590472\pi\)
−0.280416 + 0.959879i \(0.590472\pi\)
\(464\) 5302.36 + 9183.96i 0.530508 + 0.918867i
\(465\) 2699.18 4675.11i 0.269185 0.466243i
\(466\) −745.863 + 1291.87i −0.0741447 + 0.128422i
\(467\) 4966.92 + 8602.95i 0.492166 + 0.852456i 0.999959 0.00902263i \(-0.00287203\pi\)
−0.507793 + 0.861479i \(0.669539\pi\)
\(468\) −4110.24 −0.405974
\(469\) 0 0
\(470\) 1004.36 0.0985691
\(471\) 5041.85 + 8732.75i 0.493241 + 0.854318i
\(472\) −496.121 + 859.308i −0.0483810 + 0.0837984i
\(473\) −4218.21 + 7306.15i −0.410049 + 0.710226i
\(474\) 1038.36 + 1798.50i 0.100619 + 0.174278i
\(475\) −769.148 −0.0742967
\(476\) 0 0
\(477\) 4661.84 0.447486
\(478\) −303.365 525.443i −0.0290284 0.0502787i
\(479\) −2534.31 + 4389.55i −0.241744 + 0.418714i −0.961211 0.275813i \(-0.911053\pi\)
0.719467 + 0.694527i \(0.244386\pi\)
\(480\) −1206.98 + 2090.55i −0.114773 + 0.198792i
\(481\) 9912.14 + 17168.3i 0.939614 + 1.62746i
\(482\) −3634.68 −0.343476
\(483\) 0 0
\(484\) −7162.86 −0.672695
\(485\) −3530.28 6114.62i −0.330519 0.572476i
\(486\) −811.158 + 1404.97i −0.0757096 + 0.131133i
\(487\) −132.177 + 228.937i −0.0122988 + 0.0213021i −0.872109 0.489311i \(-0.837248\pi\)
0.859811 + 0.510613i \(0.170582\pi\)
\(488\) −412.750 714.904i −0.0382875 0.0663159i
\(489\) −15956.3 −1.47560
\(490\) 0 0
\(491\) −7459.47 −0.685623 −0.342812 0.939404i \(-0.611379\pi\)
−0.342812 + 0.939404i \(0.611379\pi\)
\(492\) −4240.09 7344.05i −0.388532 0.672958i
\(493\) 3616.68 6264.28i 0.330400 0.572270i
\(494\) −567.483 + 982.910i −0.0516848 + 0.0895206i
\(495\) −1129.34 1956.07i −0.102545 0.177614i
\(496\) −13976.3 −1.26523
\(497\) 0 0
\(498\) −1655.07 −0.148927
\(499\) −3603.34 6241.16i −0.323261 0.559905i 0.657897 0.753108i \(-0.271446\pi\)
−0.981159 + 0.193202i \(0.938113\pi\)
\(500\) 474.027 821.039i 0.0423982 0.0734359i
\(501\) 2527.09 4377.05i 0.225354 0.390324i
\(502\) 117.913 + 204.232i 0.0104835 + 0.0181580i
\(503\) 10886.7 0.965037 0.482519 0.875886i \(-0.339722\pi\)
0.482519 + 0.875886i \(0.339722\pi\)
\(504\) 0 0
\(505\) −9118.95 −0.803541
\(506\) 816.861 + 1414.84i 0.0717666 + 0.124303i
\(507\) −2256.24 + 3907.93i −0.197640 + 0.342322i
\(508\) 5280.22 9145.61i 0.461165 0.798761i
\(509\) −3752.48 6499.49i −0.326770 0.565982i 0.655099 0.755543i \(-0.272627\pi\)
−0.981869 + 0.189561i \(0.939294\pi\)
\(510\) 498.902 0.0433172
\(511\) 0 0
\(512\) 10605.8 0.915459
\(513\) −2348.91 4068.43i −0.202158 0.350148i
\(514\) −2023.05 + 3504.03i −0.173605 + 0.300693i
\(515\) 1019.44 1765.72i 0.0872267 0.151081i
\(516\) −2808.09 4863.75i −0.239572 0.414951i
\(517\) −14863.7 −1.26442
\(518\) 0 0
\(519\) −13579.2 −1.14848
\(520\) −1437.29 2489.46i −0.121210 0.209942i
\(521\) −11132.4 + 19281.8i −0.936120 + 1.62141i −0.163495 + 0.986544i \(0.552277\pi\)
−0.772625 + 0.634863i \(0.781056\pi\)
\(522\) −597.248 + 1034.46i −0.0500782 + 0.0867380i
\(523\) 5643.33 + 9774.54i 0.471828 + 0.817229i 0.999480 0.0322308i \(-0.0102612\pi\)
−0.527653 + 0.849460i \(0.676928\pi\)
\(524\) −13477.7 −1.12362
\(525\) 0 0
\(526\) −2724.27 −0.225824
\(527\) 4766.55 + 8255.90i 0.393992 + 0.682415i
\(528\) 5412.30 9374.37i 0.446098 0.772665i
\(529\) 4672.20 8092.48i 0.384006 0.665118i
\(530\) 793.352 + 1374.13i 0.0650208 + 0.112619i
\(531\) 935.316 0.0764393
\(532\) 0 0
\(533\) 15282.1 1.24191
\(534\) −617.634 1069.77i −0.0500518 0.0866922i
\(535\) 925.272 1602.62i 0.0747720 0.129509i
\(536\) 3288.55 5695.94i 0.265007 0.459006i
\(537\) −1799.79 3117.32i −0.144630 0.250507i
\(538\) −632.781 −0.0507084
\(539\) 0 0
\(540\) 5790.55 0.461455
\(541\) −8203.38 14208.7i −0.651924 1.12917i −0.982655 0.185440i \(-0.940629\pi\)
0.330732 0.943725i \(-0.392705\pi\)
\(542\) 1252.04 2168.60i 0.0992248 0.171862i
\(543\) −608.152 + 1053.35i −0.0480631 + 0.0832478i
\(544\) −2131.44 3691.77i −0.167987 0.290962i
\(545\) 4877.85 0.383384
\(546\) 0 0
\(547\) −8692.48 −0.679458 −0.339729 0.940523i \(-0.610335\pi\)
−0.339729 + 0.940523i \(0.610335\pi\)
\(548\) −7510.41 13008.4i −0.585454 1.01404i
\(549\) −389.070 + 673.888i −0.0302461 + 0.0523877i
\(550\) 384.382 665.769i 0.0298002 0.0516154i
\(551\) −3009.87 5213.25i −0.232713 0.403071i
\(552\) −2234.75 −0.172314
\(553\) 0 0
\(554\) 2330.36 0.178714
\(555\) −3626.08 6280.55i −0.277330 0.480350i
\(556\) −8274.94 + 14332.6i −0.631179 + 1.09323i
\(557\) 6967.85 12068.7i 0.530049 0.918071i −0.469337 0.883019i \(-0.655507\pi\)
0.999385 0.0350521i \(-0.0111597\pi\)
\(558\) −787.132 1363.35i −0.0597168 0.103432i
\(559\) 10120.9 0.765773
\(560\) 0 0
\(561\) −7383.34 −0.555659
\(562\) −23.4276 40.5778i −0.00175843 0.00304568i
\(563\) 11131.8 19280.9i 0.833304 1.44332i −0.0621002 0.998070i \(-0.519780\pi\)
0.895404 0.445255i \(-0.146887\pi\)
\(564\) 4947.41 8569.17i 0.369368 0.639764i
\(565\) −4947.13 8568.68i −0.368367 0.638030i
\(566\) −1123.65 −0.0834462
\(567\) 0 0
\(568\) −7832.81 −0.578622
\(569\) −4762.83 8249.47i −0.350911 0.607795i 0.635498 0.772102i \(-0.280795\pi\)
−0.986409 + 0.164307i \(0.947461\pi\)
\(570\) 207.598 359.570i 0.0152549 0.0264223i
\(571\) −3835.00 + 6642.41i −0.281068 + 0.486823i −0.971648 0.236432i \(-0.924022\pi\)
0.690580 + 0.723256i \(0.257355\pi\)
\(572\) 10351.7 + 17929.8i 0.756693 + 1.31063i
\(573\) 20497.3 1.49439
\(574\) 0 0
\(575\) 1328.20 0.0963304
\(576\) −1701.10 2946.39i −0.123054 0.213136i
\(577\) −1953.57 + 3383.69i −0.140950 + 0.244133i −0.927855 0.372942i \(-0.878349\pi\)
0.786904 + 0.617075i \(0.211682\pi\)
\(578\) 1143.07 1979.85i 0.0822582 0.142475i
\(579\) 7429.04 + 12867.5i 0.533230 + 0.923582i
\(580\) 7419.95 0.531201
\(581\) 0 0
\(582\) 3811.38 0.271455
\(583\) −11741.0 20336.0i −0.834067 1.44465i
\(584\) 4167.64 7218.57i 0.295305 0.511484i
\(585\) −1354.83 + 2346.63i −0.0957526 + 0.165848i
\(586\) −1608.17 2785.43i −0.113367 0.196357i
\(587\) −19891.6 −1.39866 −0.699331 0.714798i \(-0.746519\pi\)
−0.699331 + 0.714798i \(0.746519\pi\)
\(588\) 0 0
\(589\) 7933.61 0.555007
\(590\) 159.172 + 275.694i 0.0111068 + 0.0192375i
\(591\) 1360.96 2357.25i 0.0947248 0.164068i
\(592\) −9387.89 + 16260.3i −0.651757 + 1.12888i
\(593\) −2390.18 4139.91i −0.165519 0.286688i 0.771320 0.636447i \(-0.219597\pi\)
−0.936840 + 0.349759i \(0.886263\pi\)
\(594\) 4695.48 0.324340
\(595\) 0 0
\(596\) −5082.74 −0.349324
\(597\) 8489.08 + 14703.5i 0.581968 + 1.00800i
\(598\) 979.959 1697.34i 0.0670126 0.116069i
\(599\) −5542.80 + 9600.42i −0.378085 + 0.654862i −0.990784 0.135454i \(-0.956751\pi\)
0.612699 + 0.790317i \(0.290084\pi\)
\(600\) 525.791 + 910.697i 0.0357756 + 0.0619651i
\(601\) −1573.44 −0.106792 −0.0533958 0.998573i \(-0.517005\pi\)
−0.0533958 + 0.998573i \(0.517005\pi\)
\(602\) 0 0
\(603\) −6199.76 −0.418696
\(604\) 12699.5 + 21996.2i 0.855524 + 1.48181i
\(605\) −2361.04 + 4089.44i −0.158661 + 0.274809i
\(606\) 2461.26 4263.03i 0.164987 0.285765i
\(607\) −4271.36 7398.22i −0.285617 0.494702i 0.687142 0.726523i \(-0.258865\pi\)
−0.972759 + 0.231821i \(0.925532\pi\)
\(608\) −3547.65 −0.236639
\(609\) 0 0
\(610\) −264.848 −0.0175793
\(611\) 8915.70 + 15442.4i 0.590328 + 1.02248i
\(612\) −1327.64 + 2299.54i −0.0876904 + 0.151884i
\(613\) −7534.08 + 13049.4i −0.496409 + 0.859805i −0.999991 0.00414209i \(-0.998682\pi\)
0.503583 + 0.863947i \(0.332015\pi\)
\(614\) 536.545 + 929.323i 0.0352658 + 0.0610822i
\(615\) −5590.52 −0.366555
\(616\) 0 0
\(617\) 2524.58 0.164725 0.0823627 0.996602i \(-0.473753\pi\)
0.0823627 + 0.996602i \(0.473753\pi\)
\(618\) 550.304 + 953.155i 0.0358196 + 0.0620413i
\(619\) 10619.5 18393.4i 0.689551 1.19434i −0.282433 0.959287i \(-0.591141\pi\)
0.971983 0.235050i \(-0.0755253\pi\)
\(620\) −4889.50 + 8468.85i −0.316721 + 0.548576i
\(621\) 4056.22 + 7025.58i 0.262110 + 0.453988i
\(622\) −351.735 −0.0226741
\(623\) 0 0
\(624\) −12985.9 −0.833095
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 68.8369 119.229i 0.00439501 0.00761238i
\(627\) −3072.28 + 5321.34i −0.195686 + 0.338937i
\(628\) −9133.21 15819.2i −0.580342 1.00518i
\(629\) 12806.8 0.811827
\(630\) 0 0
\(631\) −8885.83 −0.560601 −0.280300 0.959912i \(-0.590434\pi\)
−0.280300 + 0.959912i \(0.590434\pi\)
\(632\) −3865.01 6694.39i −0.243262 0.421343i
\(633\) 3286.00 5691.51i 0.206330 0.357373i
\(634\) 865.095 1498.39i 0.0541914 0.0938622i
\(635\) −3480.96 6029.20i −0.217540 0.376790i
\(636\) 15632.1 0.974609
\(637\) 0 0
\(638\) 6016.74 0.373362
\(639\) 3691.71 + 6394.23i 0.228547 + 0.395856i
\(640\) 2885.21 4997.32i 0.178200 0.308651i
\(641\) −1827.82 + 3165.87i −0.112628 + 0.195077i −0.916829 0.399280i \(-0.869260\pi\)
0.804201 + 0.594357i \(0.202593\pi\)
\(642\) 499.473 + 865.112i 0.0307050 + 0.0531827i
\(643\) 4221.22 0.258894 0.129447 0.991586i \(-0.458680\pi\)
0.129447 + 0.991586i \(0.458680\pi\)
\(644\) 0 0
\(645\) −3702.43 −0.226020
\(646\) 366.602 + 634.974i 0.0223278 + 0.0386729i
\(647\) −51.8393 + 89.7884i −0.00314995 + 0.00545587i −0.867596 0.497270i \(-0.834336\pi\)
0.864446 + 0.502725i \(0.167669\pi\)
\(648\) −1927.04 + 3337.73i −0.116823 + 0.202343i
\(649\) −2355.62 4080.05i −0.142475 0.246773i
\(650\) −922.259 −0.0556523
\(651\) 0 0
\(652\) 28904.5 1.73618
\(653\) −2238.05 3876.42i −0.134122 0.232307i 0.791140 0.611636i \(-0.209488\pi\)
−0.925262 + 0.379329i \(0.876155\pi\)
\(654\) −1316.56 + 2280.35i −0.0787181 + 0.136344i
\(655\) −4442.55 + 7694.71i −0.265015 + 0.459019i
\(656\) 7236.91 + 12534.7i 0.430722 + 0.746033i
\(657\) −7857.07 −0.466566
\(658\) 0 0
\(659\) 12022.0 0.710641 0.355321 0.934745i \(-0.384372\pi\)
0.355321 + 0.934745i \(0.384372\pi\)
\(660\) −3786.89 6559.09i −0.223340 0.386837i
\(661\) −6725.51 + 11648.9i −0.395752 + 0.685462i −0.993197 0.116448i \(-0.962849\pi\)
0.597445 + 0.801910i \(0.296183\pi\)
\(662\) 1633.38 2829.11i 0.0958962 0.166097i
\(663\) 4428.77 + 7670.85i 0.259426 + 0.449338i
\(664\) 6160.53 0.360053
\(665\) 0 0
\(666\) −2114.87 −0.123047
\(667\) 5197.60 + 9002.51i 0.301727 + 0.522606i
\(668\) −4577.77 + 7928.93i −0.265149 + 0.459251i
\(669\) 9889.10 17128.4i 0.571502 0.989870i
\(670\) −1055.08 1827.45i −0.0608375 0.105374i
\(671\) 3919.53 0.225502
\(672\) 0 0
\(673\) 9774.83 0.559869 0.279935 0.960019i \(-0.409687\pi\)
0.279935 + 0.960019i \(0.409687\pi\)
\(674\) 3014.76 + 5221.72i 0.172291 + 0.298417i
\(675\) 1908.70 3305.96i 0.108838 0.188513i
\(676\) 4087.13 7079.13i 0.232541 0.402772i
\(677\) −11928.7 20661.1i −0.677190 1.17293i −0.975824 0.218560i \(-0.929864\pi\)
0.298634 0.954368i \(-0.403469\pi\)
\(678\) 5341.04 0.302539
\(679\) 0 0
\(680\) −1857.02 −0.104726
\(681\) 7714.36 + 13361.7i 0.434089 + 0.751865i
\(682\) −3964.83 + 6867.28i −0.222612 + 0.385574i
\(683\) −5959.68 + 10322.5i −0.333881 + 0.578299i −0.983269 0.182158i \(-0.941692\pi\)
0.649388 + 0.760457i \(0.275025\pi\)
\(684\) 1104.88 + 1913.72i 0.0617636 + 0.106978i
\(685\) −9902.40 −0.552338
\(686\) 0 0
\(687\) −14054.4 −0.780508
\(688\) 4792.79 + 8301.36i 0.265587 + 0.460009i
\(689\) −14085.2 + 24396.3i −0.778816 + 1.34895i
\(690\) −358.490 + 620.924i −0.0197790 + 0.0342582i
\(691\) 4101.79 + 7104.51i 0.225817 + 0.391126i 0.956564 0.291522i \(-0.0941616\pi\)
−0.730747 + 0.682648i \(0.760828\pi\)
\(692\) 24598.4 1.35129
\(693\) 0 0
\(694\) 1514.50 0.0828380
\(695\) 5455.21 + 9448.71i 0.297738 + 0.515698i
\(696\) −4115.11 + 7127.58i −0.224113 + 0.388176i
\(697\) 4936.22 8549.79i 0.268254 0.464629i
\(698\) −3375.56 5846.64i −0.183047 0.317047i
\(699\) 9688.49 0.524252
\(700\) 0 0
\(701\) 449.084 0.0241964 0.0120982 0.999927i \(-0.496149\pi\)
0.0120982 + 0.999927i \(0.496149\pi\)
\(702\) −2816.50 4878.32i −0.151427 0.262280i
\(703\) 5329.01 9230.12i 0.285900 0.495193i
\(704\) −8568.51 + 14841.1i −0.458719 + 0.794524i
\(705\) −3261.56 5649.18i −0.174237 0.301788i
\(706\) 4625.11 0.246556
\(707\) 0 0
\(708\) 3136.30 0.166482
\(709\) −948.819 1643.40i −0.0502590 0.0870512i 0.839801 0.542894i \(-0.182671\pi\)
−0.890060 + 0.455843i \(0.849338\pi\)
\(710\) −1256.51 + 2176.34i −0.0664170 + 0.115038i
\(711\) −3643.27 + 6310.32i −0.192170 + 0.332849i
\(712\) 2298.96 + 3981.92i 0.121007 + 0.209591i
\(713\) −13700.2 −0.719601
\(714\) 0 0
\(715\) 13648.7 0.713891
\(716\) 3260.27 + 5646.96i 0.170171 + 0.294744i
\(717\) −1970.30 + 3412.66i −0.102625 + 0.177752i
\(718\) 2428.43 4206.16i 0.126223 0.218625i
\(719\) −3247.35 5624.58i −0.168436 0.291740i 0.769434 0.638726i \(-0.220538\pi\)
−0.937870 + 0.346986i \(0.887205\pi\)
\(720\) −2566.35 −0.132836
\(721\) 0 0
\(722\) −3811.45 −0.196465
\(723\) 11803.3 + 20443.9i 0.607150 + 1.05162i
\(724\) 1101.65 1908.12i 0.0565506 0.0979485i
\(725\) 2445.78 4236.22i 0.125288 0.217006i
\(726\) −1274.52 2207.53i −0.0651540 0.112850i
\(727\) −18311.2 −0.934148 −0.467074 0.884218i \(-0.654692\pi\)
−0.467074 + 0.884218i \(0.654692\pi\)
\(728\) 0 0
\(729\) 20894.5 1.06155
\(730\) −1337.12 2315.96i −0.0677931 0.117421i
\(731\) 3269.11 5662.27i 0.165407 0.286493i
\(732\) −1304.63 + 2259.68i −0.0658749 + 0.114099i
\(733\) −10616.6 18388.5i −0.534972 0.926598i −0.999165 0.0408640i \(-0.986989\pi\)
0.464193 0.885734i \(-0.346344\pi\)
\(734\) −3515.30 −0.176774
\(735\) 0 0
\(736\) 6126.27 0.306817
\(737\) 15614.3 + 27044.7i 0.780406 + 1.35170i
\(738\) −815.152 + 1411.88i −0.0406587 + 0.0704230i
\(739\) 11011.8 19072.9i 0.548138 0.949404i −0.450264 0.892896i \(-0.648670\pi\)
0.998402 0.0565080i \(-0.0179966\pi\)
\(740\) 6568.55 + 11377.1i 0.326304 + 0.565175i
\(741\) 7371.40 0.365446
\(742\) 0 0
\(743\) 9436.77 0.465951 0.232975 0.972483i \(-0.425154\pi\)
0.232975 + 0.972483i \(0.425154\pi\)
\(744\) −5423.44 9393.67i −0.267248 0.462888i
\(745\) −1675.38 + 2901.85i −0.0823911 + 0.142706i
\(746\) −2653.14 + 4595.38i −0.130212 + 0.225535i
\(747\) −2903.54 5029.08i −0.142216 0.246325i
\(748\) 13374.8 0.653783
\(749\) 0 0
\(750\) 337.383 0.0164260
\(751\) 19580.9 + 33915.1i 0.951421 + 1.64791i 0.742354 + 0.670008i \(0.233709\pi\)
0.209067 + 0.977901i \(0.432957\pi\)
\(752\) −8444.16 + 14625.7i −0.409477 + 0.709235i
\(753\) 765.826 1326.45i 0.0370627 0.0641946i
\(754\) −3609.03 6251.03i −0.174315 0.301922i
\(755\) 16744.2 0.807132
\(756\) 0 0
\(757\) 20340.6 0.976607 0.488303 0.872674i \(-0.337616\pi\)
0.488303 + 0.872674i \(0.337616\pi\)
\(758\) −538.301 932.365i −0.0257942 0.0446768i
\(759\) 5305.36 9189.16i 0.253719 0.439454i
\(760\) −772.722 + 1338.39i −0.0368810 + 0.0638798i
\(761\) −1653.95 2864.72i −0.0787852 0.136460i 0.823941 0.566676i \(-0.191771\pi\)
−0.902726 + 0.430216i \(0.858437\pi\)
\(762\) 3758.13 0.178665
\(763\) 0 0
\(764\) −37130.4 −1.75829
\(765\) 875.239 + 1515.96i 0.0413651 + 0.0716465i
\(766\) 1037.93 1797.74i 0.0489580 0.0847978i
\(767\) −2825.95 + 4894.69i −0.133037 + 0.230427i
\(768\) −4459.19 7723.54i −0.209514 0.362889i
\(769\) 17234.0 0.808159 0.404079 0.914724i \(-0.367592\pi\)
0.404079 + 0.914724i \(0.367592\pi\)
\(770\) 0 0
\(771\) 26278.7 1.22750
\(772\) −13457.5 23309.1i −0.627393 1.08668i
\(773\) 4363.17 7557.23i 0.203017 0.351636i −0.746482 0.665406i \(-0.768259\pi\)
0.949499 + 0.313770i \(0.101592\pi\)
\(774\) −539.851 + 935.049i −0.0250705 + 0.0434233i
\(775\) 3223.38 + 5583.05i 0.149403 + 0.258773i
\(776\) −14186.7 −0.656281