Properties

Label 245.4.e.p.226.3
Level $245$
Weight $4$
Character 245.226
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 226.3
Root \(-1.02943 - 1.78303i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.p.116.3

$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.322324 + 0.558282i −0.113959 + 0.197382i −0.917363 0.398052i \(-0.869687\pi\)
0.803404 + 0.595434i \(0.203020\pi\)
\(3\) 2.09344 + 3.62594i 0.402882 + 0.697812i 0.994072 0.108720i \(-0.0346751\pi\)
−0.591190 + 0.806532i \(0.701342\pi\)
\(4\) 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 0.982206 + 0.187808i \(0.0601383\pi\)
−0.328456 + 0.944519i \(0.606528\pi\)
\(12\) −15.8775 + 27.5007i −0.381954 + 0.661564i
\(13\) 57.2256 1.22089 0.610443 0.792060i \(-0.290991\pi\)
0.610443 + 0.792060i \(0.290991\pi\)
\(14\) 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 \(-0.0817199\pi\)
−0.703514 + 0.710682i \(0.748387\pi\)
\(18\) 3.05244 + 5.28697i 0.0399703 + 0.0692306i
\(19\) −15.3830 + 26.6441i −0.185742 + 0.321714i −0.943826 0.330442i \(-0.892802\pi\)
0.758084 + 0.652156i \(0.226135\pi\)
\(20\) 37.9221 0.423982
\(21\) 0 0
\(22\) −30.7506 −0.298002
\(23\) −26.5641 + 46.0104i −0.240826 + 0.417123i −0.960950 0.276723i \(-0.910752\pi\)
0.720124 + 0.693846i \(0.244085\pi\)
\(24\) −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 −0.949248 0.314529i \(-0.898154\pi\)
0.202234 0.979337i \(-0.435180\pi\)
\(32\) −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 0.168155 + 0.985761i \(0.446219\pi\)
−0.937771 + 0.347254i \(0.887114\pi\)
\(38\) −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 \(-0.330159\pi\)
0.508611 + 0.860996i \(0.330159\pi\)
\(42\) 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 \(-0.672690\pi\)
0.999821 + 0.0189211i \(0.00602314\pi\)
\(48\) −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 0.985891 + 0.167391i \(0.0535343\pi\)
−0.347980 + 0.937502i \(0.613132\pi\)
\(54\) −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 \(-0.201421\pi\)
−0.915352 + 0.402654i \(0.868088\pi\)
\(60\) 79.3876 + 137.503i 0.170815 + 0.295860i
\(61\) −41.0841 + 71.1597i −0.0862340 + 0.149362i −0.905916 0.423457i \(-0.860817\pi\)
0.819682 + 0.572818i \(0.194150\pi\)
\(62\) 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 −0.993280 0.115734i \(-0.963078\pi\)
0.396411 0.918073i \(-0.370255\pi\)
\(68\) −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 0.979256 + 0.202628i \(0.0649481\pi\)
−0.314147 + 0.949374i \(0.601719\pi\)
\(74\) −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 −0.450525 0.892764i \(-0.648763\pi\)
0.998419 0.0562159i \(-0.0179035\pi\)
\(80\) 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 \(-0.367108\pi\)
0.405469 + 0.914109i \(0.367108\pi\)
\(84\) 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 \(-0.745469\pi\)
0.969512 + 0.245043i \(0.0788022\pi\)
\(90\) 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 \(-0.764732\pi\)
−0.739063 + 0.673636i \(0.764732\pi\)
\(98\) 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 −0.829558 0.558421i \(-0.811407\pi\)
−0.0688279 0.997629i \(-0.521926\pi\)
\(102\) −49.8902 86.4124i −0.0484301 0.0838833i
\(103\) −203.887 + 353.143i −0.195045 + 0.337828i −0.946915 0.321483i \(-0.895819\pi\)
0.751870 + 0.659311i \(0.229152\pi\)
\(104\) −574.915 −0.542068
\(105\) 0 0
\(106\) −317.341 −0.290782
\(107\) 185.054 320.524i 0.167195 0.289591i −0.770237 0.637757i \(-0.779862\pi\)
0.937433 + 0.348167i \(0.113196\pi\)
\(108\) 579.055 + 1002.95i 0.515922 + 0.893603i
\(109\) −487.785 844.869i −0.428636 0.742420i 0.568116 0.822948i \(-0.307672\pi\)
−0.996752 + 0.0805287i \(0.974339\pi\)
\(110\) −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 −0.401291 0.915951i \(-0.631438\pi\)
0.993882 0.110447i \(-0.0352282\pi\)
\(132\) −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 0.989935 + 0.141526i \(0.0452009\pi\)
−0.372402 + 0.928071i \(0.621466\pi\)
\(138\) 71.6981 124.185i 0.0442271 0.0766037i
\(139\) 2182.09 1.33153 0.665763 0.746163i \(-0.268106\pi\)
0.665763 + 0.746163i \(0.268106\pi\)
\(140\) 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 −0.943317 0.331892i \(-0.892313\pi\)
0.759085 + 0.650991i \(0.225646\pi\)
\(150\) 33.7383 + 58.4364i 0.0183648 + 0.0318087i
\(151\) −1674.42 2900.18i −0.902401 1.56300i −0.824369 0.566053i \(-0.808470\pi\)
−0.0780315 0.996951i \(-0.524863\pi\)
\(152\) 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 −0.990879 0.134754i \(-0.956975\pi\)
0.378739 0.925504i \(-0.376358\pi\)
\(158\) 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 0.109712 0.993963i \(-0.465007\pi\)
0.805942 0.591995i \(-0.201659\pi\)
\(164\) 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 \(-0.409773\pi\)
0.279677 + 0.960094i \(0.409773\pi\)
\(168\) 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 0.251188 + 0.967938i \(0.419179\pi\)
−0.963853 + 0.266434i \(0.914155\pi\)
\(174\) 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 0.762213 0.647326i \(-0.224113\pi\)
−0.941708 + 0.336433i \(0.890780\pi\)
\(180\) 179.563 311.012i 0.0743546 0.128786i
\(181\) −290.504 −0.119298 −0.0596491 0.998219i \(-0.518998\pi\)
−0.0596491 + 0.998219i \(0.518998\pi\)
\(182\) 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 −0.139519 + 0.990219i \(0.544556\pi\)
−0.787795 + 0.615937i \(0.788778\pi\)
\(192\) −752.082 1302.64i −0.282692 0.489637i
\(193\) 1774.36 + 3073.29i 0.661770 + 1.14622i 0.980150 + 0.198256i \(0.0635276\pi\)
−0.318381 + 0.947963i \(0.603139\pi\)
\(194\) 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 −0.960094 0.279679i \(-0.909772\pi\)
0.237838 0.971305i \(-0.423561\pi\)
\(200\) 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 \(-0.249026\pi\)
0.709267 + 0.704940i \(0.249026\pi\)
\(224\) 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 −0.998973 0.0453145i \(-0.985571\pi\)
0.460243 0.887793i \(-0.347762\pi\)
\(228\) −488.487 846.084i −0.141890 0.245760i
\(229\) −1678.39 + 2907.05i −0.484328 + 0.838880i −0.999838 0.0180032i \(-0.994269\pi\)
0.515510 + 0.856883i \(0.327602\pi\)
\(230\) −171.245 −0.0490937
\(231\) 0 0
\(232\) 1965.72 0.556275
\(233\) −1157.01 + 2004.00i −0.325314 + 0.563460i −0.981576 0.191073i \(-0.938803\pi\)
0.656262 + 0.754533i \(0.272137\pi\)
\(234\) 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 −0.946112 0.323838i \(-0.895027\pi\)
0.192604 0.981277i \(-0.438307\pi\)
\(242\) −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 \(-0.485354\pi\)
0.0459970 + 0.998942i \(0.485354\pi\)
\(252\) 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 −0.180271 0.983617i \(-0.557697\pi\)
0.941973 0.335689i \(-0.108969\pi\)
\(258\) 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 0.999986 0.00529397i \(-0.00168513\pi\)
−0.504578 + 0.863366i \(0.668352\pi\)
\(264\) 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 \(-0.202150\pi\)
−0.916272 + 0.400557i \(0.868816\pi\)
\(270\) 246.087 + 426.236i 0.0554681 + 0.0960737i
\(271\) −1942.21 + 3364.01i −0.435354 + 0.754055i −0.997324 0.0731021i \(-0.976710\pi\)
0.561971 + 0.827157i \(0.310043\pi\)
\(272\) −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 0.600663 0.799502i \(-0.294903\pi\)
−0.992721 + 0.120438i \(0.961570\pi\)
\(278\) −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 \(-0.225268\pi\)
−0.942922 + 0.333014i \(0.891934\pi\)
\(284\) 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 \(-0.665713\pi\)
−0.497402 + 0.867520i \(0.665713\pi\)
\(294\) 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 \(-0.450549\pi\)
0.154731 + 0.987957i \(0.450549\pi\)
\(308\) 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 \(-0.182507\pi\)
−0.889824 + 0.456303i \(0.849173\pi\)
\(312\) −1203.55 2084.61i −0.218390 0.378262i
\(313\) −106.782 + 184.952i −0.0192833 + 0.0333997i −0.875506 0.483207i \(-0.839472\pi\)
0.856223 + 0.516607i \(0.172805\pi\)
\(314\) 1552.58 0.279035
\(315\) 0 0
\(316\) 5835.66 1.03887
\(317\) 1341.97 2324.35i 0.237767 0.411825i −0.722306 0.691574i \(-0.756918\pi\)
0.960073 + 0.279748i \(0.0902511\pi\)
\(318\) −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 −0.575263 0.817968i \(-0.695100\pi\)
0.996013 + 0.0892084i \(0.0284337\pi\)
\(332\) 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 0.760741 0.649055i \(-0.224836\pi\)
−0.942469 + 0.334293i \(0.891502\pi\)
\(348\) 3106.64 5380.86i 0.478544 0.828863i
\(349\) −10472.6 −1.60626 −0.803128 0.595806i \(-0.796833\pi\)
−0.803128 + 0.595806i \(0.796833\pi\)
\(350\) 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 0.998853 + 0.0478752i \(0.0152450\pi\)
−0.457966 + 0.888970i \(0.651422\pi\)
\(354\) 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 −0.444185 0.895935i \(-0.646507\pi\)
0.997995 0.0632926i \(-0.0201601\pi\)
\(360\) 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 \(-0.293433\pi\)
−0.992154 + 0.125024i \(0.960099\pi\)
\(368\) −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 0.425117 + 0.905138i \(0.360233\pi\)
−0.996431 + 0.0844067i \(0.973101\pi\)
\(374\) −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 \(-0.902245\pi\)
0.738407 + 0.674356i \(0.235579\pi\)
\(384\) 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 0.728130 0.685439i \(-0.240390\pi\)
−0.957673 + 0.287860i \(0.907056\pi\)
\(390\) −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 \(-0.721274\pi\)
0.985321 + 0.170712i \(0.0546068\pi\)
\(398\) 2614.11 0.329229
\(399\) 0 0
\(400\) 1354.97 0.169372
\(401\) 580.899 1006.15i 0.0723409 0.125298i −0.827586 0.561339i \(-0.810286\pi\)
0.899927 + 0.436041i \(0.143620\pi\)
\(402\) 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 \(-0.0190749\pi\)
−0.550968 + 0.834526i \(0.685742\pi\)
\(410\) 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 \(-0.460289\pi\)
0.124433 + 0.992228i \(0.460289\pi\)
\(420\) 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 0.949231 0.314581i \(-0.101864\pi\)
−0.747050 + 0.664767i \(0.768531\pi\)
\(432\) −4137.98 + 7167.18i −0.460853 + 0.798221i
\(433\) 4222.37 0.468624 0.234312 0.972161i \(-0.424716\pi\)
0.234312 + 0.972161i \(0.424716\pi\)
\(434\) 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 0.219974 + 0.975506i \(0.429403\pi\)
−0.954800 + 0.297250i \(0.903931\pi\)
\(440\) −2396.15 −0.259618
\(441\) 0 0
\(442\) −1363.78 −0.146762
\(443\) −8295.58 + 14368.4i −0.889695 + 1.54100i −0.0494599 + 0.998776i \(0.515750\pi\)
−0.840236 + 0.542222i \(0.817583\pi\)
\(444\) −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 −0.831401 0.555673i \(-0.812461\pi\)
0.896928 + 0.442177i \(0.145794\pi\)
\(458\) −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 \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(462\) 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 \(-0.997128\pi\)
0.507793 + 0.861479i \(0.330461\pi\)
\(468\) 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 \(-0.0889471\pi\)
−0.719467 + 0.694527i \(0.755614\pi\)
\(480\) −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 0.859811 0.510613i \(-0.170582\pi\)
−0.872109 + 0.489311i \(0.837248\pi\)
\(488\) 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 −0.981159 0.193202i \(-0.938113\pi\)
0.657897 + 0.753108i \(0.271446\pi\)
\(500\) −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 \(-0.660278\pi\)
−0.482519 + 0.875886i \(0.660278\pi\)
\(504\) 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 \(-0.727373\pi\)
0.981869 + 0.189561i \(0.0607064\pi\)
\(510\) −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 0.772625 + 0.634863i \(0.218944\pi\)
0.163495 + 0.986544i \(0.447723\pi\)
\(522\) −597.248 1034.46i −0.0500782 0.0867380i
\(523\) −5643.33 + 9774.54i −0.471828 + 0.817229i −0.999480 0.0322308i \(-0.989739\pi\)
0.527653 + 0.849460i \(0.323072\pi\)
\(524\) 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 0.330732 + 0.943725i \(0.392705\pi\)
−0.982655 + 0.185440i \(0.940629\pi\)
\(542\) −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 0.999385 + 0.0350521i \(0.0111597\pi\)
−0.469337 + 0.883019i \(0.655507\pi\)
\(558\) 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 −0.895404 0.445255i \(-0.853113\pi\)
0.0621002 0.998070i \(-0.480220\pi\)
\(564\) 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 −0.986409 0.164307i \(-0.947461\pi\)
0.635498 + 0.772102i \(0.280795\pi\)
\(570\) −207.598 359.570i −0.0152549 0.0264223i
\(571\) −3835.00 6642.41i −0.281068 0.486823i 0.690580 0.723256i \(-0.257355\pi\)
−0.971648 + 0.236432i \(0.924022\pi\)
\(572\) −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 \(-0.121651\pi\)
−0.786904 + 0.617075i \(0.788318\pi\)
\(578\) 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 \(-0.253481\pi\)
0.699331 + 0.714798i \(0.253481\pi\)
\(588\) 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 \(-0.780403\pi\)
0.936840 + 0.349759i \(0.113737\pi\)
\(594\) −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 0.612699 0.790317i \(-0.290084\pi\)
−0.990784 + 0.135454i \(0.956751\pi\)
\(600\) −525.791 + 910.697i −0.0357756 + 0.0619651i
\(601\) 1573.44 0.106792 0.0533958 0.998573i \(-0.482995\pi\)
0.0533958 + 0.998573i \(0.482995\pi\)
\(602\) 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 \(-0.741135\pi\)
0.972759 + 0.231821i \(0.0744683\pi\)
\(608\) 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 0.503583 0.863947i \(-0.332015\pi\)
−0.999991 + 0.00414209i \(0.998682\pi\)
\(614\) −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 −0.971983 0.235050i \(-0.924475\pi\)
0.282433 0.959287i \(-0.408859\pi\)
\(620\) −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 0.804201 0.594357i \(-0.202593\pi\)
−0.916829 + 0.399280i \(0.869260\pi\)
\(642\) −499.473 + 865.112i −0.0307050 + 0.0531827i
\(643\) −4221.22 −0.258894 −0.129447 0.991586i \(-0.541320\pi\)
−0.129447 + 0.991586i \(0.541320\pi\)
\(644\) 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 \(-0.165664\pi\)
−0.864446 + 0.502725i \(0.832331\pi\)
\(648\) −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 −0.925262 0.379329i \(-0.876155\pi\)
0.791140 + 0.611636i \(0.209488\pi\)
\(654\) 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 \(-0.0371507\pi\)
−0.597445 + 0.801910i \(0.703817\pi\)
\(662\) 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 −0.298634 0.954368i \(-0.596531\pi\)
0.975824 0.218560i \(-0.0701358\pi\)
\(678\) −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 0.649388 0.760457i \(-0.275025\pi\)
−0.983269 + 0.182158i \(0.941692\pi\)
\(684\) −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 \(-0.905838\pi\)
0.730747 + 0.682648i \(0.239172\pi\)
\(692\) −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 −0.890060 0.455843i \(-0.849338\pi\)
0.839801 + 0.542894i \(0.182671\pi\)
\(710\) 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 \(-0.779462\pi\)
0.937870 + 0.346986i \(0.112795\pi\)
\(720\) 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 \(-0.345308\pi\)
0.467074 + 0.884218i \(0.345308\pi\)
\(728\) 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 −0.464193 0.885734i \(-0.653656\pi\)
0.999165 0.0408640i \(-0.0130111\pi\)
\(734\) 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 0.998402 + 0.0565080i \(0.0179966\pi\)
−0.450264 + 0.892896i \(0.648670\pi\)
\(740\) −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 0.209067 0.977901i \(-0.432957\pi\)
0.742354 0.670008i \(-0.233709\pi\)
\(752\) 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 \(-0.808229\pi\)
0.902726 + 0.430216i \(0.141563\pi\)
\(762\) −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 \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(770\) 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 \(-0.231741\pi\)
−0.949499 + 0.313770i \(0.898408\pi\)
\(774\) −539.851 935.049i −0.0250705 0.0434233i
\(775\) −3223.38 + 5583.05i −0.149403 + 0.258773i
\(776\) 14186.7 0.656281