Properties

Label 60.7.c.a.31.18
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.18
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.17

$q$-expansion

\(f(q)\) \(=\) \(q+(5.21792 + 6.06410i) q^{2} +15.5885i q^{3} +(-9.54653 + 63.2840i) q^{4} +55.9017 q^{5} +(-94.5299 + 81.3394i) q^{6} +234.050i q^{7} +(-433.573 + 272.320i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(5.21792 + 6.06410i) q^{2} +15.5885i q^{3} +(-9.54653 + 63.2840i) q^{4} +55.9017 q^{5} +(-94.5299 + 81.3394i) q^{6} +234.050i q^{7} +(-433.573 + 272.320i) q^{8} -243.000 q^{9} +(291.691 + 338.993i) q^{10} +611.126i q^{11} +(-986.500 - 148.816i) q^{12} +446.025 q^{13} +(-1419.30 + 1221.26i) q^{14} +871.421i q^{15} +(-3913.73 - 1208.29i) q^{16} -4753.29 q^{17} +(-1267.96 - 1473.58i) q^{18} -4220.36i q^{19} +(-533.667 + 3537.68i) q^{20} -3648.49 q^{21} +(-3705.93 + 3188.81i) q^{22} +3897.71i q^{23} +(-4245.05 - 6758.74i) q^{24} +3125.00 q^{25} +(2327.33 + 2704.74i) q^{26} -3788.00i q^{27} +(-14811.6 - 2234.37i) q^{28} +15226.1 q^{29} +(-5284.38 + 4547.01i) q^{30} +25735.3i q^{31} +(-13094.4 - 30038.0i) q^{32} -9526.51 q^{33} +(-24802.3 - 28824.4i) q^{34} +13083.8i q^{35} +(2319.81 - 15378.0i) q^{36} -12963.9 q^{37} +(25592.7 - 22021.5i) q^{38} +6952.85i q^{39} +(-24237.5 + 15223.2i) q^{40} +71144.7 q^{41} +(-19037.5 - 22124.8i) q^{42} +101623. i q^{43} +(-38674.5 - 5834.13i) q^{44} -13584.1 q^{45} +(-23636.1 + 20338.0i) q^{46} +132654. i q^{47} +(18835.3 - 61009.0i) q^{48} +62869.4 q^{49} +(16306.0 + 18950.3i) q^{50} -74096.4i q^{51} +(-4257.99 + 28226.3i) q^{52} +283151. q^{53} +(22970.8 - 19765.5i) q^{54} +34163.0i q^{55} +(-63736.6 - 101478. i) q^{56} +65788.9 q^{57} +(79448.8 + 92332.7i) q^{58} -176836. i q^{59} +(-55147.0 - 8319.05i) q^{60} +219488. q^{61} +(-156061. + 134285. i) q^{62} -56874.3i q^{63} +(113828. - 236141. i) q^{64} +24933.6 q^{65} +(-49708.6 - 57769.7i) q^{66} +420905. i q^{67} +(45377.4 - 300807. i) q^{68} -60759.3 q^{69} +(-79341.5 + 68270.4i) q^{70} -427721. i q^{71} +(105358. - 66173.8i) q^{72} +276028. q^{73} +(-67644.4 - 78614.1i) q^{74} +48713.9i q^{75} +(267081. + 40289.8i) q^{76} -143034. q^{77} +(-42162.7 + 36279.4i) q^{78} +616843. i q^{79} +(-218784. - 67545.2i) q^{80} +59049.0 q^{81} +(371228. + 431429. i) q^{82} -632235. i q^{83} +(34830.4 - 230891. i) q^{84} -265717. q^{85} +(-616250. + 530260. i) q^{86} +237352. i q^{87} +(-166422. - 264968. i) q^{88} -1.04325e6 q^{89} +(-70880.9 - 82375.4i) q^{90} +104392. i q^{91} +(-246663. - 37209.6i) q^{92} -401174. q^{93} +(-804429. + 692181. i) q^{94} -235925. i q^{95} +(468245. - 204121. i) q^{96} -1.31029e6 q^{97} +(328048. + 381246. i) q^{98} -148504. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} + O(q^{10}) \) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} - 750q^{10} + 5040q^{13} - 2596q^{14} + 4194q^{16} - 4860q^{18} + 7000q^{20} + 19440q^{21} + 45780q^{22} + 24786q^{24} + 75000q^{25} + 75852q^{26} + 54300q^{28} + 132800q^{29} - 10700q^{32} - 173484q^{34} + 59778q^{36} - 69840q^{37} + 215800q^{38} - 14250q^{40} - 70448q^{41} - 189540q^{42} - 395668q^{44} - 158760q^{46} + 252720q^{48} - 642984q^{49} + 62500q^{50} - 210240q^{52} - 644320q^{53} - 39366q^{54} - 917708q^{56} + 408240q^{57} - 1345020q^{58} + 222750q^{60} - 222864q^{61} + 1948520q^{62} + 935922q^{64} + 266000q^{65} - 640548q^{66} + 572680q^{68} - 541728q^{69} + 220500q^{70} + 82620q^{72} + 771120q^{73} - 589164q^{74} - 191544q^{76} + 1383840q^{77} - 693360q^{78} - 946000q^{80} + 1417176q^{81} + 2672520q^{82} + 1256796q^{84} - 372000q^{85} + 1781528q^{86} + 956940q^{88} - 1566224q^{89} + 182250q^{90} - 3040560q^{92} + 1496880q^{93} - 3788352q^{94} - 413262q^{96} - 1666800q^{97} - 2709660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.21792 + 6.06410i 0.652241 + 0.758012i
\(3\) 15.5885i 0.577350i
\(4\) −9.54653 + 63.2840i −0.149165 + 0.988812i
\(5\) 55.9017 0.447214
\(6\) −94.5299 + 81.3394i −0.437638 + 0.376571i
\(7\) 234.050i 0.682363i 0.939997 + 0.341181i \(0.110827\pi\)
−0.939997 + 0.341181i \(0.889173\pi\)
\(8\) −433.573 + 272.320i −0.846823 + 0.531875i
\(9\) −243.000 −0.333333
\(10\) 291.691 + 338.993i 0.291691 + 0.338993i
\(11\) 611.126i 0.459148i 0.973291 + 0.229574i \(0.0737333\pi\)
−0.973291 + 0.229574i \(0.926267\pi\)
\(12\) −986.500 148.816i −0.570891 0.0861202i
\(13\) 446.025 0.203016 0.101508 0.994835i \(-0.467633\pi\)
0.101508 + 0.994835i \(0.467633\pi\)
\(14\) −1419.30 + 1221.26i −0.517239 + 0.445065i
\(15\) 871.421i 0.258199i
\(16\) −3913.73 1208.29i −0.955500 0.294991i
\(17\) −4753.29 −0.967491 −0.483746 0.875209i \(-0.660724\pi\)
−0.483746 + 0.875209i \(0.660724\pi\)
\(18\) −1267.96 1473.58i −0.217414 0.252671i
\(19\) 4220.36i 0.615302i −0.951499 0.307651i \(-0.900457\pi\)
0.951499 0.307651i \(-0.0995430\pi\)
\(20\) −533.667 + 3537.68i −0.0667084 + 0.442210i
\(21\) −3648.49 −0.393962
\(22\) −3705.93 + 3188.81i −0.348040 + 0.299475i
\(23\) 3897.71i 0.320351i 0.987089 + 0.160176i \(0.0512061\pi\)
−0.987089 + 0.160176i \(0.948794\pi\)
\(24\) −4245.05 6758.74i −0.307078 0.488913i
\(25\) 3125.00 0.200000
\(26\) 2327.33 + 2704.74i 0.132415 + 0.153888i
\(27\) 3788.00i 0.192450i
\(28\) −14811.6 2234.37i −0.674729 0.101784i
\(29\) 15226.1 0.624303 0.312152 0.950032i \(-0.398950\pi\)
0.312152 + 0.950032i \(0.398950\pi\)
\(30\) −5284.38 + 4547.01i −0.195718 + 0.168408i
\(31\) 25735.3i 0.863862i 0.901907 + 0.431931i \(0.142168\pi\)
−0.901907 + 0.431931i \(0.857832\pi\)
\(32\) −13094.4 30038.0i −0.399609 0.916686i
\(33\) −9526.51 −0.265089
\(34\) −24802.3 28824.4i −0.631037 0.733370i
\(35\) 13083.8i 0.305162i
\(36\) 2319.81 15378.0i 0.0497215 0.329604i
\(37\) −12963.9 −0.255935 −0.127967 0.991778i \(-0.540845\pi\)
−0.127967 + 0.991778i \(0.540845\pi\)
\(38\) 25592.7 22021.5i 0.466407 0.401325i
\(39\) 6952.85i 0.117211i
\(40\) −24237.5 + 15223.2i −0.378711 + 0.237862i
\(41\) 71144.7 1.03227 0.516133 0.856509i \(-0.327371\pi\)
0.516133 + 0.856509i \(0.327371\pi\)
\(42\) −19037.5 22124.8i −0.256958 0.298628i
\(43\) 101623.i 1.27816i 0.769140 + 0.639080i \(0.220685\pi\)
−0.769140 + 0.639080i \(0.779315\pi\)
\(44\) −38674.5 5834.13i −0.454011 0.0684886i
\(45\) −13584.1 −0.149071
\(46\) −23636.1 + 20338.0i −0.242830 + 0.208946i
\(47\) 132654.i 1.27770i 0.769332 + 0.638849i \(0.220589\pi\)
−0.769332 + 0.638849i \(0.779411\pi\)
\(48\) 18835.3 61009.0i 0.170313 0.551658i
\(49\) 62869.4 0.534381
\(50\) 16306.0 + 18950.3i 0.130448 + 0.151602i
\(51\) 74096.4i 0.558581i
\(52\) −4257.99 + 28226.3i −0.0302827 + 0.200744i
\(53\) 283151. 1.90192 0.950958 0.309321i \(-0.100102\pi\)
0.950958 + 0.309321i \(0.100102\pi\)
\(54\) 22970.8 19765.5i 0.145879 0.125524i
\(55\) 34163.0i 0.205337i
\(56\) −63736.6 101478.i −0.362932 0.577840i
\(57\) 65788.9 0.355245
\(58\) 79448.8 + 92332.7i 0.407196 + 0.473229i
\(59\) 176836.i 0.861022i −0.902585 0.430511i \(-0.858333\pi\)
0.902585 0.430511i \(-0.141667\pi\)
\(60\) −55147.0 8319.05i −0.255310 0.0385141i
\(61\) 219488. 0.966986 0.483493 0.875348i \(-0.339368\pi\)
0.483493 + 0.875348i \(0.339368\pi\)
\(62\) −156061. + 134285.i −0.654817 + 0.563446i
\(63\) 56874.3i 0.227454i
\(64\) 113828. 236141.i 0.434218 0.900808i
\(65\) 24933.6 0.0907913
\(66\) −49708.6 57769.7i −0.172902 0.200941i
\(67\) 420905.i 1.39946i 0.714408 + 0.699729i \(0.246696\pi\)
−0.714408 + 0.699729i \(0.753304\pi\)
\(68\) 45377.4 300807.i 0.144315 0.956668i
\(69\) −60759.3 −0.184955
\(70\) −79341.5 + 68270.4i −0.231316 + 0.199039i
\(71\) 427721.i 1.19505i −0.801851 0.597524i \(-0.796151\pi\)
0.801851 0.597524i \(-0.203849\pi\)
\(72\) 105358. 66173.8i 0.282274 0.177292i
\(73\) 276028. 0.709553 0.354777 0.934951i \(-0.384557\pi\)
0.354777 + 0.934951i \(0.384557\pi\)
\(74\) −67644.4 78614.1i −0.166931 0.194002i
\(75\) 48713.9i 0.115470i
\(76\) 267081. + 40289.8i 0.608419 + 0.0917813i
\(77\) −143034. −0.313305
\(78\) −42162.7 + 36279.4i −0.0888474 + 0.0764498i
\(79\) 616843.i 1.25110i 0.780182 + 0.625552i \(0.215126\pi\)
−0.780182 + 0.625552i \(0.784874\pi\)
\(80\) −218784. 67545.2i −0.427313 0.131924i
\(81\) 59049.0 0.111111
\(82\) 371228. + 431429.i 0.673285 + 0.782469i
\(83\) 632235.i 1.10572i −0.833275 0.552859i \(-0.813537\pi\)
0.833275 0.552859i \(-0.186463\pi\)
\(84\) 34830.4 230891.i 0.0587652 0.389555i
\(85\) −265717. −0.432675
\(86\) −616250. + 530260.i −0.968861 + 0.833668i
\(87\) 237352.i 0.360442i
\(88\) −166422. 264968.i −0.244209 0.388817i
\(89\) −1.04325e6 −1.47985 −0.739926 0.672689i \(-0.765139\pi\)
−0.739926 + 0.672689i \(0.765139\pi\)
\(90\) −70880.9 82375.4i −0.0972303 0.112998i
\(91\) 104392.i 0.138530i
\(92\) −246663. 37209.6i −0.316767 0.0477850i
\(93\) −401174. −0.498751
\(94\) −804429. + 692181.i −0.968510 + 0.833366i
\(95\) 235925.i 0.275172i
\(96\) 468245. 204121.i 0.529249 0.230714i
\(97\) −1.31029e6 −1.43566 −0.717832 0.696216i \(-0.754866\pi\)
−0.717832 + 0.696216i \(0.754866\pi\)
\(98\) 328048. + 381246.i 0.348545 + 0.405067i
\(99\) 148504.i 0.153049i
\(100\) −29832.9 + 197762.i −0.0298329 + 0.197762i
\(101\) −591531. −0.574134 −0.287067 0.957911i \(-0.592680\pi\)
−0.287067 + 0.957911i \(0.592680\pi\)
\(102\) 449328. 386629.i 0.423411 0.364329i
\(103\) 369642.i 0.338275i 0.985592 + 0.169138i \(0.0540982\pi\)
−0.985592 + 0.169138i \(0.945902\pi\)
\(104\) −193385. + 121462.i −0.171918 + 0.107979i
\(105\) −203957. −0.176185
\(106\) 1.47746e6 + 1.71706e6i 1.24051 + 1.44167i
\(107\) 829937.i 0.677476i −0.940881 0.338738i \(-0.890000\pi\)
0.940881 0.338738i \(-0.110000\pi\)
\(108\) 239719. + 36162.2i 0.190297 + 0.0287067i
\(109\) −2.19532e6 −1.69519 −0.847594 0.530646i \(-0.821949\pi\)
−0.847594 + 0.530646i \(0.821949\pi\)
\(110\) −207168. + 178260.i −0.155648 + 0.133929i
\(111\) 202087.i 0.147764i
\(112\) 282800. 916010.i 0.201291 0.651998i
\(113\) 2.57865e6 1.78713 0.893565 0.448933i \(-0.148196\pi\)
0.893565 + 0.448933i \(0.148196\pi\)
\(114\) 343281. + 398950.i 0.231705 + 0.269280i
\(115\) 217889.i 0.143265i
\(116\) −145357. + 963571.i −0.0931239 + 0.617319i
\(117\) −108384. −0.0676719
\(118\) 1.07235e6 922716.i 0.652665 0.561593i
\(119\) 1.11251e6i 0.660180i
\(120\) −237305. 377825.i −0.137330 0.218649i
\(121\) 1.39809e6 0.789183
\(122\) 1.14527e6 + 1.33099e6i 0.630708 + 0.732987i
\(123\) 1.10904e6i 0.595979i
\(124\) −1.62863e6 245683.i −0.854197 0.128858i
\(125\) 174693. 0.0894427
\(126\) 344891. 296766.i 0.172413 0.148355i
\(127\) 3.88504e6i 1.89664i −0.317320 0.948319i \(-0.602783\pi\)
0.317320 0.948319i \(-0.397217\pi\)
\(128\) 2.02593e6 541906.i 0.966038 0.258401i
\(129\) −1.58414e6 −0.737946
\(130\) 130101. + 151200.i 0.0592178 + 0.0688209i
\(131\) 2.17769e6i 0.968685i −0.874878 0.484343i \(-0.839059\pi\)
0.874878 0.484343i \(-0.160941\pi\)
\(132\) 90945.1 602876.i 0.0395419 0.262123i
\(133\) 987777. 0.419859
\(134\) −2.55241e6 + 2.19625e6i −1.06081 + 0.912784i
\(135\) 211755.i 0.0860663i
\(136\) 2.06090e6 1.29441e6i 0.819294 0.514585i
\(137\) 4.01481e6 1.56136 0.780681 0.624929i \(-0.214872\pi\)
0.780681 + 0.624929i \(0.214872\pi\)
\(138\) −317038. 368451.i −0.120635 0.140198i
\(139\) 278268.i 0.103614i 0.998657 + 0.0518070i \(0.0164981\pi\)
−0.998657 + 0.0518070i \(0.983502\pi\)
\(140\) −827996. 124905.i −0.301748 0.0455193i
\(141\) −2.06788e6 −0.737679
\(142\) 2.59374e6 2.23181e6i 0.905861 0.779459i
\(143\) 272578.i 0.0932142i
\(144\) 951036. + 293613.i 0.318500 + 0.0983305i
\(145\) 851167. 0.279197
\(146\) 1.44030e6 + 1.67386e6i 0.462800 + 0.537850i
\(147\) 980037.i 0.308525i
\(148\) 123760. 820405.i 0.0381764 0.253071i
\(149\) 991141. 0.299624 0.149812 0.988715i \(-0.452133\pi\)
0.149812 + 0.988715i \(0.452133\pi\)
\(150\) −295406. + 254186.i −0.0875277 + 0.0753143i
\(151\) 29572.7i 0.00858936i 0.999991 + 0.00429468i \(0.00136704\pi\)
−0.999991 + 0.00429468i \(0.998633\pi\)
\(152\) 1.14929e6 + 1.82984e6i 0.327264 + 0.521052i
\(153\) 1.15505e6 0.322497
\(154\) −746342. 867374.i −0.204351 0.237489i
\(155\) 1.43865e6i 0.386331i
\(156\) −440004. 66375.5i −0.115900 0.0174837i
\(157\) −2.86209e6 −0.739580 −0.369790 0.929115i \(-0.620570\pi\)
−0.369790 + 0.929115i \(0.620570\pi\)
\(158\) −3.74060e6 + 3.21864e6i −0.948352 + 0.816021i
\(159\) 4.41389e6i 1.09807i
\(160\) −731998. 1.67917e6i −0.178710 0.409954i
\(161\) −912262. −0.218596
\(162\) 308113. + 358079.i 0.0724712 + 0.0842236i
\(163\) 5.86822e6i 1.35501i 0.735517 + 0.677506i \(0.236939\pi\)
−0.735517 + 0.677506i \(0.763061\pi\)
\(164\) −679185. + 4.50232e6i −0.153977 + 1.02072i
\(165\) −532548. −0.118551
\(166\) 3.83393e6 3.29895e6i 0.838147 0.721194i
\(167\) 635821.i 0.136517i 0.997668 + 0.0682583i \(0.0217442\pi\)
−0.997668 + 0.0682583i \(0.978256\pi\)
\(168\) 1.58189e6 993556.i 0.333616 0.209539i
\(169\) −4.62787e6 −0.958785
\(170\) −1.38649e6 1.61133e6i −0.282208 0.327973i
\(171\) 1.02555e6i 0.205101i
\(172\) −6.43109e6 970144.i −1.26386 0.190656i
\(173\) 7.53757e6 1.45577 0.727886 0.685698i \(-0.240503\pi\)
0.727886 + 0.685698i \(0.240503\pi\)
\(174\) −1.43932e6 + 1.23848e6i −0.273219 + 0.235095i
\(175\) 731408.i 0.136473i
\(176\) 738414. 2.39178e6i 0.135445 0.438716i
\(177\) 2.75660e6 0.497111
\(178\) −5.44360e6 6.32636e6i −0.965219 1.12175i
\(179\) 878241.i 0.153128i 0.997065 + 0.0765640i \(0.0243949\pi\)
−0.997065 + 0.0765640i \(0.975605\pi\)
\(180\) 129681. 859657.i 0.0222361 0.147403i
\(181\) −4.23487e6 −0.714174 −0.357087 0.934071i \(-0.616230\pi\)
−0.357087 + 0.934071i \(0.616230\pi\)
\(182\) −633046. + 544712.i −0.105008 + 0.0903551i
\(183\) 3.42147e6i 0.558290i
\(184\) −1.06143e6 1.68994e6i −0.170387 0.271281i
\(185\) −724702. −0.114457
\(186\) −2.09329e6 2.43276e6i −0.325305 0.378059i
\(187\) 2.90486e6i 0.444222i
\(188\) −8.39490e6 1.26639e6i −1.26340 0.190587i
\(189\) 886582. 0.131321
\(190\) 1.43067e6 1.23104e6i 0.208583 0.179478i
\(191\) 8.58674e6i 1.23233i −0.787616 0.616167i \(-0.788685\pi\)
0.787616 0.616167i \(-0.211315\pi\)
\(192\) 3.68108e6 + 1.77440e6i 0.520082 + 0.250696i
\(193\) 9.47926e6 1.31857 0.659284 0.751894i \(-0.270859\pi\)
0.659284 + 0.751894i \(0.270859\pi\)
\(194\) −6.83701e6 7.94574e6i −0.936399 1.08825i
\(195\) 388676.i 0.0524184i
\(196\) −600185. + 3.97863e6i −0.0797107 + 0.528403i
\(197\) −152893. −0.0199981 −0.00999903 0.999950i \(-0.503183\pi\)
−0.00999903 + 0.999950i \(0.503183\pi\)
\(198\) 900540. 774880.i 0.116013 0.0998250i
\(199\) 4.24007e6i 0.538038i −0.963135 0.269019i \(-0.913300\pi\)
0.963135 0.269019i \(-0.0866995\pi\)
\(200\) −1.35492e6 + 851000.i −0.169365 + 0.106375i
\(201\) −6.56126e6 −0.807978
\(202\) −3.08656e6 3.58710e6i −0.374473 0.435200i
\(203\) 3.56368e6i 0.426001i
\(204\) 4.68912e6 + 707363.i 0.552332 + 0.0833205i
\(205\) 3.97711e6 0.461643
\(206\) −2.24155e6 + 1.92877e6i −0.256417 + 0.220637i
\(207\) 947144.i 0.106784i
\(208\) −1.74562e6 538926.i −0.193981 0.0598879i
\(209\) 2.57917e6 0.282515
\(210\) −1.06423e6 1.23681e6i −0.114915 0.133551i
\(211\) 7.09394e6i 0.755162i 0.925977 + 0.377581i \(0.123244\pi\)
−0.925977 + 0.377581i \(0.876756\pi\)
\(212\) −2.70311e6 + 1.79190e7i −0.283698 + 1.88064i
\(213\) 6.66751e6 0.689961
\(214\) 5.03282e6 4.33055e6i 0.513535 0.441877i
\(215\) 5.68088e6i 0.571611i
\(216\) 1.03155e6 + 1.64237e6i 0.102359 + 0.162971i
\(217\) −6.02336e6 −0.589467
\(218\) −1.14550e7 1.33126e7i −1.10567 1.28497i
\(219\) 4.30286e6i 0.409661i
\(220\) −2.16197e6 326138.i −0.203040 0.0306290i
\(221\) −2.12009e6 −0.196416
\(222\) 1.22547e6 1.05447e6i 0.112007 0.0963776i
\(223\) 1.19865e6i 0.108088i −0.998539 0.0540442i \(-0.982789\pi\)
0.998539 0.0540442i \(-0.0172112\pi\)
\(224\) 7.03040e6 3.06474e6i 0.625512 0.272678i
\(225\) −759375. −0.0666667
\(226\) 1.34552e7 + 1.56372e7i 1.16564 + 1.35467i
\(227\) 5.84907e6i 0.500045i 0.968240 + 0.250023i \(0.0804380\pi\)
−0.968240 + 0.250023i \(0.919562\pi\)
\(228\) −628056. + 4.16338e6i −0.0529900 + 0.351271i
\(229\) 1.27570e7 1.06228 0.531142 0.847283i \(-0.321763\pi\)
0.531142 + 0.847283i \(0.321763\pi\)
\(230\) −1.32130e6 + 1.13693e6i −0.108597 + 0.0934435i
\(231\) 2.22968e6i 0.180887i
\(232\) −6.60164e6 + 4.14638e6i −0.528674 + 0.332051i
\(233\) −6.04654e6 −0.478012 −0.239006 0.971018i \(-0.576822\pi\)
−0.239006 + 0.971018i \(0.576822\pi\)
\(234\) −565540. 657252.i −0.0441383 0.0512961i
\(235\) 7.41561e6i 0.571404i
\(236\) 1.11909e7 + 1.68817e6i 0.851389 + 0.128434i
\(237\) −9.61564e6 −0.722326
\(238\) 6.74636e6 5.80499e6i 0.500425 0.430596i
\(239\) 2.45629e7i 1.79923i −0.436685 0.899614i \(-0.643848\pi\)
0.436685 0.899614i \(-0.356152\pi\)
\(240\) 1.05293e6 3.41051e6i 0.0761665 0.246709i
\(241\) −5.34775e6 −0.382050 −0.191025 0.981585i \(-0.561181\pi\)
−0.191025 + 0.981585i \(0.561181\pi\)
\(242\) 7.29511e6 + 8.47813e6i 0.514737 + 0.598210i
\(243\) 920483.i 0.0641500i
\(244\) −2.09534e6 + 1.38900e7i −0.144240 + 0.956168i
\(245\) 3.51451e6 0.238982
\(246\) −6.72531e6 + 5.78687e6i −0.451759 + 0.388721i
\(247\) 1.88239e6i 0.124916i
\(248\) −7.00824e6 1.11581e7i −0.459466 0.731538i
\(249\) 9.85557e6 0.638386
\(250\) 911534. + 1.05935e6i 0.0583382 + 0.0677987i
\(251\) 1.62600e6i 0.102825i −0.998677 0.0514126i \(-0.983628\pi\)
0.998677 0.0514126i \(-0.0163724\pi\)
\(252\) 3.59923e6 + 542952.i 0.224910 + 0.0339281i
\(253\) −2.38199e6 −0.147089
\(254\) 2.35593e7 2.02718e7i 1.43767 1.23706i
\(255\) 4.14211e6i 0.249805i
\(256\) 1.38573e7 + 9.45780e6i 0.825960 + 0.563729i
\(257\) −5.96301e6 −0.351290 −0.175645 0.984454i \(-0.556201\pi\)
−0.175645 + 0.984454i \(0.556201\pi\)
\(258\) −8.26593e6 9.60639e6i −0.481319 0.559372i
\(259\) 3.03420e6i 0.174640i
\(260\) −238029. + 1.57790e6i −0.0135428 + 0.0897756i
\(261\) −3.69995e6 −0.208101
\(262\) 1.32057e7 1.13630e7i 0.734275 0.631816i
\(263\) 5.56063e6i 0.305673i 0.988252 + 0.152836i \(0.0488407\pi\)
−0.988252 + 0.152836i \(0.951159\pi\)
\(264\) 4.13044e6 2.59426e6i 0.224484 0.140994i
\(265\) 1.58286e7 0.850562
\(266\) 5.15415e6 + 5.98997e6i 0.273849 + 0.318259i
\(267\) 1.62626e7i 0.854393i
\(268\) −2.66366e7 4.01818e6i −1.38380 0.208750i
\(269\) 8.71314e6 0.447629 0.223814 0.974632i \(-0.428149\pi\)
0.223814 + 0.974632i \(0.428149\pi\)
\(270\) 1.28410e6 1.10492e6i 0.0652393 0.0561359i
\(271\) 2.16067e7i 1.08563i −0.839853 0.542815i \(-0.817359\pi\)
0.839853 0.542815i \(-0.182641\pi\)
\(272\) 1.86031e7 + 5.74332e6i 0.924438 + 0.285402i
\(273\) −1.62732e6 −0.0799805
\(274\) 2.09490e7 + 2.43462e7i 1.01838 + 1.18353i
\(275\) 1.90977e6i 0.0918296i
\(276\) 580041. 3.84509e6i 0.0275887 0.182886i
\(277\) −1.96628e7 −0.925138 −0.462569 0.886583i \(-0.653072\pi\)
−0.462569 + 0.886583i \(0.653072\pi\)
\(278\) −1.68744e6 + 1.45198e6i −0.0785407 + 0.0675813i
\(279\) 6.25368e6i 0.287954i
\(280\) −3.56299e6 5.67279e6i −0.162308 0.258418i
\(281\) −4.23673e7 −1.90946 −0.954732 0.297467i \(-0.903858\pi\)
−0.954732 + 0.297467i \(0.903858\pi\)
\(282\) −1.07900e7 1.25398e7i −0.481144 0.559170i
\(283\) 3.51305e7i 1.54998i 0.631975 + 0.774989i \(0.282245\pi\)
−0.631975 + 0.774989i \(0.717755\pi\)
\(284\) 2.70679e7 + 4.08325e6i 1.18168 + 0.178259i
\(285\) 3.67771e6 0.158870
\(286\) −1.65294e6 + 1.42229e6i −0.0706575 + 0.0607981i
\(287\) 1.66515e7i 0.704379i
\(288\) 3.18193e6 + 7.29922e6i 0.133203 + 0.305562i
\(289\) −1.54385e6 −0.0639603
\(290\) 4.44132e6 + 5.16156e6i 0.182104 + 0.211635i
\(291\) 2.04254e7i 0.828882i
\(292\) −2.63511e6 + 1.74682e7i −0.105840 + 0.701615i
\(293\) 1.11354e7 0.442695 0.221348 0.975195i \(-0.428954\pi\)
0.221348 + 0.975195i \(0.428954\pi\)
\(294\) −5.94304e6 + 5.11376e6i −0.233866 + 0.201233i
\(295\) 9.88542e6i 0.385061i
\(296\) 5.62078e6 3.53032e6i 0.216731 0.136125i
\(297\) 2.31494e6 0.0883631
\(298\) 5.17170e6 + 6.01037e6i 0.195427 + 0.227119i
\(299\) 1.73848e6i 0.0650363i
\(300\) −3.08281e6 465049.i −0.114178 0.0172240i
\(301\) −2.37848e7 −0.872169
\(302\) −179332. + 154308.i −0.00651084 + 0.00560233i
\(303\) 9.22105e6i 0.331476i
\(304\) −5.09940e6 + 1.65173e7i −0.181509 + 0.587921i
\(305\) 1.22697e7 0.432450
\(306\) 6.02696e6 + 7.00432e6i 0.210346 + 0.244457i
\(307\) 1.40533e7i 0.485695i −0.970064 0.242847i \(-0.921919\pi\)
0.970064 0.242847i \(-0.0780814\pi\)
\(308\) 1.36548e6 9.05178e6i 0.0467341 0.309800i
\(309\) −5.76215e6 −0.195303
\(310\) −8.72409e6 + 7.50675e6i −0.292843 + 0.251981i
\(311\) 4.02124e7i 1.33684i −0.743785 0.668419i \(-0.766971\pi\)
0.743785 0.668419i \(-0.233029\pi\)
\(312\) −1.89340e6 3.01457e6i −0.0623417 0.0992570i
\(313\) −2.19464e7 −0.715699 −0.357850 0.933779i \(-0.616490\pi\)
−0.357850 + 0.933779i \(0.616490\pi\)
\(314\) −1.49342e7 1.73560e7i −0.482384 0.560610i
\(315\) 3.17937e6i 0.101721i
\(316\) −3.90363e7 5.88871e6i −1.23711 0.186620i
\(317\) −2.87330e7 −0.901992 −0.450996 0.892526i \(-0.648931\pi\)
−0.450996 + 0.892526i \(0.648931\pi\)
\(318\) −2.67663e7 + 2.30314e7i −0.832351 + 0.716207i
\(319\) 9.30508e6i 0.286648i
\(320\) 6.36316e6 1.32007e7i 0.194188 0.402854i
\(321\) 1.29374e7 0.391141
\(322\) −4.76011e6 5.53204e6i −0.142577 0.165698i
\(323\) 2.00606e7i 0.595300i
\(324\) −563713. + 3.73686e6i −0.0165738 + 0.109868i
\(325\) 1.39383e6 0.0406031
\(326\) −3.55854e7 + 3.06199e7i −1.02712 + 0.883794i
\(327\) 3.42216e7i 0.978717i
\(328\) −3.08465e7 + 1.93741e7i −0.874146 + 0.549036i
\(329\) −3.10478e7 −0.871853
\(330\) −2.77880e6 3.22942e6i −0.0773241 0.0898635i
\(331\) 6.61370e6i 0.182373i −0.995834 0.0911865i \(-0.970934\pi\)
0.995834 0.0911865i \(-0.0290660\pi\)
\(332\) 4.00104e7 + 6.03565e6i 1.09335 + 0.164934i
\(333\) 3.15022e6 0.0853116
\(334\) −3.85568e6 + 3.31767e6i −0.103481 + 0.0890417i
\(335\) 2.35293e7i 0.625857i
\(336\) 1.42792e7 + 4.40841e6i 0.376431 + 0.116216i
\(337\) 2.36992e7 0.619219 0.309610 0.950864i \(-0.399802\pi\)
0.309610 + 0.950864i \(0.399802\pi\)
\(338\) −2.41479e7 2.80639e7i −0.625358 0.726770i
\(339\) 4.01971e7i 1.03180i
\(340\) 2.53667e6 1.68156e7i 0.0645398 0.427835i
\(341\) −1.57275e7 −0.396640
\(342\) −6.21902e6 + 5.35123e6i −0.155469 + 0.133775i
\(343\) 4.22504e7i 1.04700i
\(344\) −2.76739e7 4.40609e7i −0.679822 1.08238i
\(345\) −3.39655e6 −0.0827143
\(346\) 3.93305e7 + 4.57086e7i 0.949513 + 1.10349i
\(347\) 7.87037e7i 1.88368i 0.336065 + 0.941839i \(0.390904\pi\)
−0.336065 + 0.941839i \(0.609096\pi\)
\(348\) −1.50206e7 2.26589e6i −0.356409 0.0537651i
\(349\) 5.84311e7 1.37457 0.687286 0.726387i \(-0.258802\pi\)
0.687286 + 0.726387i \(0.258802\pi\)
\(350\) −4.43533e6 + 3.81643e6i −0.103448 + 0.0890129i
\(351\) 1.68954e6i 0.0390704i
\(352\) 1.83570e7 8.00231e6i 0.420894 0.183479i
\(353\) 2.20704e6 0.0501749 0.0250875 0.999685i \(-0.492014\pi\)
0.0250875 + 0.999685i \(0.492014\pi\)
\(354\) 1.43837e7 + 1.67163e7i 0.324236 + 0.376816i
\(355\) 2.39103e7i 0.534442i
\(356\) 9.95941e6 6.60210e7i 0.220741 1.46330i
\(357\) 1.73423e7 0.381155
\(358\) −5.32574e6 + 4.58259e6i −0.116073 + 0.0998763i
\(359\) 1.20278e7i 0.259957i 0.991517 + 0.129979i \(0.0414909\pi\)
−0.991517 + 0.129979i \(0.958509\pi\)
\(360\) 5.88971e6 3.69923e6i 0.126237 0.0792872i
\(361\) 2.92344e7 0.621403
\(362\) −2.20972e7 2.56806e7i −0.465813 0.541352i
\(363\) 2.17940e7i 0.455635i
\(364\) −6.60637e6 996585.i −0.136980 0.0206638i
\(365\) 1.54305e7 0.317322
\(366\) −2.07481e7 + 1.78530e7i −0.423190 + 0.364139i
\(367\) 7.63147e7i 1.54387i −0.635703 0.771934i \(-0.719290\pi\)
0.635703 0.771934i \(-0.280710\pi\)
\(368\) 4.70955e6 1.52546e7i 0.0945009 0.306096i
\(369\) −1.72882e7 −0.344088
\(370\) −3.78144e6 4.39466e6i −0.0746538 0.0867601i
\(371\) 6.62717e7i 1.29780i
\(372\) 3.82982e6 2.53879e7i 0.0743959 0.493171i
\(373\) 5.43943e7 1.04816 0.524079 0.851669i \(-0.324410\pi\)
0.524079 + 0.851669i \(0.324410\pi\)
\(374\) 1.76153e7 1.51573e7i 0.336725 0.289739i
\(375\) 2.72319e6i 0.0516398i
\(376\) −3.61244e7 5.75154e7i −0.679575 1.08198i
\(377\) 6.79124e6 0.126743
\(378\) 4.62612e6 + 5.37632e6i 0.0856527 + 0.0995427i
\(379\) 1.26362e7i 0.232113i 0.993243 + 0.116057i \(0.0370254\pi\)
−0.993243 + 0.116057i \(0.962975\pi\)
\(380\) 1.49303e7 + 2.25227e6i 0.272093 + 0.0410458i
\(381\) 6.05618e7 1.09502
\(382\) 5.20708e7 4.48050e7i 0.934124 0.803778i
\(383\) 6.10284e7i 1.08627i −0.839647 0.543133i \(-0.817238\pi\)
0.839647 0.543133i \(-0.182762\pi\)
\(384\) 8.44748e6 + 3.15811e7i 0.149188 + 0.557742i
\(385\) −7.99586e6 −0.140114
\(386\) 4.94621e7 + 5.74832e7i 0.860024 + 0.999491i
\(387\) 2.46943e7i 0.426054i
\(388\) 1.25087e7 8.29205e7i 0.214150 1.41960i
\(389\) −6.42261e7 −1.09110 −0.545548 0.838080i \(-0.683678\pi\)
−0.545548 + 0.838080i \(0.683678\pi\)
\(390\) −2.35697e6 + 2.02808e6i −0.0397338 + 0.0341894i
\(391\) 1.85269e7i 0.309937i
\(392\) −2.72585e7 + 1.71206e7i −0.452526 + 0.284224i
\(393\) 3.39469e7 0.559271
\(394\) −797782. 927156.i −0.0130435 0.0151588i
\(395\) 3.44826e7i 0.559511i
\(396\) 9.39790e6 + 1.41769e6i 0.151337 + 0.0228295i
\(397\) 5.76615e7 0.921540 0.460770 0.887520i \(-0.347573\pi\)
0.460770 + 0.887520i \(0.347573\pi\)
\(398\) 2.57122e7 2.21243e7i 0.407840 0.350931i
\(399\) 1.53979e7i 0.242406i
\(400\) −1.22304e7 3.77589e6i −0.191100 0.0589983i
\(401\) 6.22427e7 0.965285 0.482643 0.875817i \(-0.339677\pi\)
0.482643 + 0.875817i \(0.339677\pi\)
\(402\) −3.42362e7 3.97881e7i −0.526996 0.612457i
\(403\) 1.14786e7i 0.175377i
\(404\) 5.64706e6 3.74344e7i 0.0856404 0.567711i
\(405\) 3.30094e6 0.0496904
\(406\) −2.16105e7 + 1.85950e7i −0.322914 + 0.277855i
\(407\) 7.92255e6i 0.117512i
\(408\) 2.01779e7 + 3.21262e7i 0.297096 + 0.473020i
\(409\) 6.41818e7 0.938084 0.469042 0.883176i \(-0.344599\pi\)
0.469042 + 0.883176i \(0.344599\pi\)
\(410\) 2.07523e7 + 2.41176e7i 0.301102 + 0.349931i
\(411\) 6.25848e7i 0.901453i
\(412\) −2.33924e7 3.52880e6i −0.334491 0.0504587i
\(413\) 4.13885e7 0.587529
\(414\) 5.74358e6 4.94213e6i 0.0809434 0.0696487i
\(415\) 3.53430e7i 0.494492i
\(416\) −5.84042e6 1.33977e7i −0.0811268 0.186102i
\(417\) −4.33777e6 −0.0598216
\(418\) 1.34579e7 + 1.56403e7i 0.184268 + 0.214150i
\(419\) 7.52734e6i 0.102329i −0.998690 0.0511646i \(-0.983707\pi\)
0.998690 0.0511646i \(-0.0162933\pi\)
\(420\) 1.94708e6 1.29072e7i 0.0262806 0.174214i
\(421\) −9.54679e7 −1.27941 −0.639707 0.768619i \(-0.720944\pi\)
−0.639707 + 0.768619i \(0.720944\pi\)
\(422\) −4.30183e7 + 3.70156e7i −0.572422 + 0.492547i
\(423\) 3.22350e7i 0.425899i
\(424\) −1.22767e8 + 7.71078e7i −1.61059 + 1.01158i
\(425\) −1.48540e7 −0.193498
\(426\) 3.47905e7 + 4.04324e7i 0.450021 + 0.522999i
\(427\) 5.13712e7i 0.659836i
\(428\) 5.25217e7 + 7.92302e6i 0.669897 + 0.101055i
\(429\) −4.24906e6 −0.0538172
\(430\) −3.44494e7 + 2.96424e7i −0.433288 + 0.372828i
\(431\) 6.05446e7i 0.756212i 0.925762 + 0.378106i \(0.123424\pi\)
−0.925762 + 0.378106i \(0.876576\pi\)
\(432\) −4.57698e6 + 1.48252e7i −0.0567711 + 0.183886i
\(433\) −4.68934e7 −0.577628 −0.288814 0.957385i \(-0.593261\pi\)
−0.288814 + 0.957385i \(0.593261\pi\)
\(434\) −3.14294e7 3.65262e7i −0.384474 0.446823i
\(435\) 1.32684e7i 0.161194i
\(436\) 2.09577e7 1.38928e8i 0.252862 1.67622i
\(437\) 1.64498e7 0.197113
\(438\) −2.60929e7 + 2.24520e7i −0.310528 + 0.267197i
\(439\) 7.62674e7i 0.901457i −0.892661 0.450729i \(-0.851164\pi\)
0.892661 0.450729i \(-0.148836\pi\)
\(440\) −9.30326e6 1.48122e7i −0.109214 0.173884i
\(441\) −1.52773e7 −0.178127
\(442\) −1.10624e7 1.28564e7i −0.128110 0.148886i
\(443\) 4.11703e7i 0.473558i −0.971564 0.236779i \(-0.923908\pi\)
0.971564 0.236779i \(-0.0760917\pi\)
\(444\) 1.27888e7 + 1.92923e6i 0.146111 + 0.0220411i
\(445\) −5.83194e7 −0.661810
\(446\) 7.26874e6 6.25448e6i 0.0819322 0.0704996i
\(447\) 1.54504e7i 0.172988i
\(448\) 5.52690e7 + 2.66414e7i 0.614678 + 0.296294i
\(449\) −2.74161e7 −0.302877 −0.151439 0.988467i \(-0.548391\pi\)
−0.151439 + 0.988467i \(0.548391\pi\)
\(450\) −3.96236e6 4.60492e6i −0.0434827 0.0505341i
\(451\) 4.34784e7i 0.473962i
\(452\) −2.46171e7 + 1.63187e8i −0.266577 + 1.76714i
\(453\) −460994. −0.00495907
\(454\) −3.54693e7 + 3.05200e7i −0.379040 + 0.326150i
\(455\) 5.83571e6i 0.0619526i
\(456\) −2.85243e7 + 1.79156e7i −0.300830 + 0.188946i
\(457\) −3.51153e7 −0.367915 −0.183957 0.982934i \(-0.558891\pi\)
−0.183957 + 0.982934i \(0.558891\pi\)
\(458\) 6.65649e7 + 7.73595e7i 0.692865 + 0.805225i
\(459\) 1.80054e7i 0.186194i
\(460\) −1.37889e7 2.08008e6i −0.141663 0.0213701i
\(461\) 7.39800e7 0.755112 0.377556 0.925987i \(-0.376765\pi\)
0.377556 + 0.925987i \(0.376765\pi\)
\(462\) 1.35210e7 1.16343e7i 0.137115 0.117982i
\(463\) 1.00507e8i 1.01263i −0.862348 0.506316i \(-0.831007\pi\)
0.862348 0.506316i \(-0.168993\pi\)
\(464\) −5.95909e7 1.83975e7i −0.596522 0.184164i
\(465\) −2.24263e7 −0.223048
\(466\) −3.15504e7 3.66668e7i −0.311779 0.362339i
\(467\) 1.62350e8i 1.59405i 0.603945 + 0.797026i \(0.293595\pi\)
−0.603945 + 0.797026i \(0.706405\pi\)
\(468\) 1.03469e6 6.85898e6i 0.0100942 0.0669148i
\(469\) −9.85131e7 −0.954938
\(470\) −4.49689e7 + 3.86941e7i −0.433131 + 0.372693i
\(471\) 4.46156e7i 0.426997i
\(472\) 4.81559e7 + 7.66713e7i 0.457956 + 0.729133i
\(473\) −6.21043e7 −0.586865
\(474\) −5.01737e7 5.83102e7i −0.471130 0.547532i
\(475\) 1.31886e7i 0.123060i
\(476\) 7.04040e7 + 1.06206e7i 0.652794 + 0.0984755i
\(477\) −6.88058e7 −0.633972
\(478\) 1.48952e8 1.28167e8i 1.36384 1.17353i
\(479\) 1.59054e8i 1.44723i −0.690202 0.723617i \(-0.742478\pi\)
0.690202 0.723617i \(-0.257522\pi\)
\(480\) 2.61757e7 1.14107e7i 0.236687 0.103179i
\(481\) −5.78221e6 −0.0519587
\(482\) −2.79042e7 3.24293e7i −0.249188 0.289598i
\(483\) 1.42208e7i 0.126206i
\(484\) −1.33469e7 + 8.84765e7i −0.117718 + 0.780354i
\(485\) −7.32476e7 −0.642049
\(486\) −5.58190e6 + 4.80301e6i −0.0486265 + 0.0418413i
\(487\) 1.46667e7i 0.126983i −0.997982 0.0634914i \(-0.979776\pi\)
0.997982 0.0634914i \(-0.0202236\pi\)
\(488\) −9.51639e7 + 5.97709e7i −0.818866 + 0.514316i
\(489\) −9.14765e7 −0.782317
\(490\) 1.83384e7 + 2.13123e7i 0.155874 + 0.181152i
\(491\) 1.18752e8i 1.00322i −0.865094 0.501610i \(-0.832741\pi\)
0.865094 0.501610i \(-0.167259\pi\)
\(492\) −7.01843e7 1.05875e7i −0.589311 0.0888989i
\(493\) −7.23742e7 −0.604008
\(494\) 1.14150e7 9.82215e6i 0.0946878 0.0814753i
\(495\) 8.30160e6i 0.0684457i
\(496\) 3.10956e7 1.00721e8i 0.254832 0.825420i
\(497\) 1.00108e8 0.815456
\(498\) 5.14256e7 + 5.97651e7i 0.416382 + 0.483905i
\(499\) 2.10310e7i 0.169261i −0.996412 0.0846307i \(-0.973029\pi\)
0.996412 0.0846307i \(-0.0269711\pi\)
\(500\) −1.66771e6 + 1.10553e7i −0.0133417 + 0.0884421i
\(501\) −9.91147e6 −0.0788179
\(502\) 9.86023e6 8.48435e6i 0.0779428 0.0670668i
\(503\) 1.30335e8i 1.02414i −0.858944 0.512069i \(-0.828879\pi\)
0.858944 0.512069i \(-0.171121\pi\)
\(504\) 1.54880e7 + 2.46592e7i 0.120977 + 0.192613i
\(505\) −3.30676e7 −0.256760
\(506\) −1.24291e7 1.44446e7i −0.0959372 0.111495i
\(507\) 7.21414e7i 0.553555i
\(508\) 2.45861e8 + 3.70886e7i 1.87542 + 0.282911i
\(509\) −9.12352e7 −0.691846 −0.345923 0.938263i \(-0.612434\pi\)
−0.345923 + 0.938263i \(0.612434\pi\)
\(510\) 2.51182e7 2.16132e7i 0.189355 0.162933i
\(511\) 6.46046e7i 0.484173i
\(512\) 1.49534e7 + 1.33382e8i 0.111412 + 0.993774i
\(513\) −1.59867e7 −0.118415
\(514\) −3.11145e7 3.61603e7i −0.229126 0.266282i
\(515\) 2.06636e7i 0.151281i
\(516\) 1.51231e7 1.00251e8i 0.110075 0.729691i
\(517\) −8.10685e7 −0.586652
\(518\) 1.83997e7 1.58322e7i 0.132379 0.113907i
\(519\) 1.17499e8i 0.840490i
\(520\) −1.08105e7 + 6.78991e6i −0.0768842 + 0.0482896i
\(521\) 1.57984e8 1.11712 0.558560 0.829464i \(-0.311354\pi\)
0.558560 + 0.829464i \(0.311354\pi\)
\(522\) −1.93061e7 2.24369e7i −0.135732 0.157743i
\(523\) 1.17971e8i 0.824653i 0.911036 + 0.412327i \(0.135284\pi\)
−0.911036 + 0.412327i \(0.864716\pi\)
\(524\) 1.37813e8 + 2.07894e7i 0.957848 + 0.144494i
\(525\) −1.14015e7 −0.0787925
\(526\) −3.37202e7 + 2.90149e7i −0.231704 + 0.199372i
\(527\) 1.22327e8i 0.835779i
\(528\) 3.72842e7 + 1.15107e7i 0.253293 + 0.0781990i
\(529\) 1.32844e8 0.897375
\(530\) 8.25927e7 + 9.59864e7i 0.554771 + 0.644736i
\(531\) 4.29711e7i 0.287007i
\(532\) −9.42984e6 + 6.25105e7i −0.0626281 + 0.415162i
\(533\) 3.17324e7 0.209566
\(534\) 9.86183e7 8.48573e7i 0.647640 0.557269i
\(535\) 4.63949e7i 0.302976i
\(536\) −1.14621e8 1.82493e8i −0.744337 1.18509i
\(537\) −1.36904e7 −0.0884085
\(538\) 4.54645e7 + 5.28373e7i 0.291962 + 0.339308i
\(539\) 3.84211e7i 0.245360i
\(540\) 1.34007e7 + 2.02153e6i 0.0851034 + 0.0128380i
\(541\) −2.37184e7 −0.149794 −0.0748969 0.997191i \(-0.523863\pi\)
−0.0748969 + 0.997191i \(0.523863\pi\)
\(542\) 1.31025e8 1.12742e8i 0.822920 0.708091i
\(543\) 6.60150e7i 0.412328i
\(544\) 6.22413e7 + 1.42779e8i 0.386618 + 0.886886i
\(545\) −1.22722e8 −0.758111
\(546\) −8.49121e6 9.86820e6i −0.0521665 0.0606262i
\(547\) 1.30769e8i 0.798992i 0.916735 + 0.399496i \(0.130815\pi\)
−0.916735 + 0.399496i \(0.869185\pi\)
\(548\) −3.83275e7 + 2.54073e8i −0.232900 + 1.54389i
\(549\) −5.33355e7 −0.322329
\(550\) −1.15810e7 + 9.96503e6i −0.0696079 + 0.0598950i
\(551\) 6.42598e7i 0.384135i
\(552\) 2.63436e7 1.65460e7i 0.156624 0.0983729i
\(553\) −1.44372e8 −0.853707
\(554\) −1.02599e8 1.19237e8i −0.603412 0.701266i
\(555\) 1.12970e7i 0.0660821i
\(556\) −1.76099e7 2.65649e6i −0.102455 0.0154555i
\(557\) 8.04273e7 0.465412 0.232706 0.972547i \(-0.425242\pi\)
0.232706 + 0.972547i \(0.425242\pi\)
\(558\) 3.79229e7 3.26312e7i 0.218272 0.187815i
\(559\) 4.53263e7i 0.259487i
\(560\) 1.58090e7 5.12065e7i 0.0900202 0.291582i
\(561\) 4.52822e7 0.256472
\(562\) −2.21069e8 2.56919e8i −1.24543 1.44740i
\(563\) 2.79719e8i 1.56746i −0.621101 0.783730i \(-0.713314\pi\)
0.621101 0.783730i \(-0.286686\pi\)
\(564\) 1.97411e7 1.30864e8i 0.110036 0.729426i
\(565\) 1.44151e8 0.799229
\(566\) −2.13035e8 + 1.83308e8i −1.17490 + 1.01096i
\(567\) 1.38204e7i 0.0758181i
\(568\) 1.16477e8 + 1.85448e8i 0.635616 + 1.01199i
\(569\) 8.01186e7 0.434907 0.217454 0.976071i \(-0.430225\pi\)
0.217454 + 0.976071i \(0.430225\pi\)
\(570\) 1.91900e7 + 2.23020e7i 0.103622 + 0.120426i
\(571\) 2.60254e8i 1.39794i 0.715149 + 0.698972i \(0.246359\pi\)
−0.715149 + 0.698972i \(0.753641\pi\)
\(572\) −1.72498e7 2.60217e6i −0.0921713 0.0139042i
\(573\) 1.33854e8 0.711488
\(574\) −1.00976e8 + 8.68861e7i −0.533928 + 0.459425i
\(575\) 1.21804e7i 0.0640703i
\(576\) −2.76601e7 + 5.73824e7i −0.144739 + 0.300269i
\(577\) 2.08528e8 1.08552 0.542760 0.839888i \(-0.317379\pi\)
0.542760 + 0.839888i \(0.317379\pi\)
\(578\) −8.05567e6 9.36203e6i −0.0417175 0.0484827i
\(579\) 1.47767e8i 0.761276i
\(580\) −8.12569e6 + 5.38652e7i −0.0416463 + 0.276073i
\(581\) 1.47975e8 0.754501
\(582\) 1.23862e8 1.06578e8i 0.628302 0.540630i
\(583\) 1.73041e8i 0.873260i
\(584\) −1.19679e8 + 7.51680e7i −0.600866 + 0.377394i
\(585\) −6.05886e6 −0.0302638
\(586\) 5.81039e7 + 6.75264e7i 0.288744 + 0.335568i
\(587\) 2.03436e8i 1.00580i −0.864343 0.502902i \(-0.832266\pi\)
0.864343 0.502902i \(-0.167734\pi\)
\(588\) −6.20206e7 9.35595e6i −0.305073 0.0460210i
\(589\) 1.08612e8 0.531536
\(590\) 5.99461e7 5.15814e7i 0.291881 0.251152i
\(591\) 2.38336e6i 0.0115459i
\(592\) 5.07370e7 + 1.56640e7i 0.244546 + 0.0754985i
\(593\) −2.65879e7 −0.127503 −0.0637513 0.997966i \(-0.520306\pi\)
−0.0637513 + 0.997966i \(0.520306\pi\)
\(594\) 1.20792e7 + 1.40380e7i 0.0576340 + 0.0669803i
\(595\) 6.21911e7i 0.295242i
\(596\) −9.46195e6 + 6.27233e7i −0.0446933 + 0.296272i
\(597\) 6.60961e7 0.310637
\(598\) −1.05423e7 + 9.07125e6i −0.0492983 + 0.0424193i
\(599\) 1.00479e8i 0.467516i 0.972295 + 0.233758i \(0.0751023\pi\)
−0.972295 + 0.233758i \(0.924898\pi\)
\(600\) −1.32658e7 2.11211e7i −0.0614156 0.0977827i
\(601\) 3.21498e8 1.48100 0.740500 0.672056i \(-0.234589\pi\)
0.740500 + 0.672056i \(0.234589\pi\)
\(602\) −1.24108e8 1.44234e8i −0.568864 0.661115i
\(603\) 1.02280e8i 0.466486i
\(604\) −1.87148e6 282317.i −0.00849327 0.00128123i
\(605\) 7.81554e7 0.352933
\(606\) 5.59173e7 4.81147e7i 0.251263 0.216202i
\(607\) 1.80290e8i 0.806130i 0.915171 + 0.403065i \(0.132055\pi\)
−0.915171 + 0.403065i \(0.867945\pi\)
\(608\) −1.26771e8 + 5.52630e7i −0.564039 + 0.245880i
\(609\) −5.55523e7 −0.245952
\(610\) 6.40225e7 + 7.44048e7i 0.282061 + 0.327802i
\(611\) 5.91672e7i 0.259393i
\(612\) −1.10267e7 + 7.30961e7i −0.0481051 + 0.318889i
\(613\) −4.52010e8 −1.96230 −0.981152 0.193237i \(-0.938101\pi\)
−0.981152 + 0.193237i \(0.938101\pi\)
\(614\) 8.52206e7 7.33291e7i 0.368163 0.316790i
\(615\) 6.19970e7i 0.266530i
\(616\) 6.20158e7 3.89511e7i 0.265314 0.166639i
\(617\) 5.84022e6 0.0248641 0.0124321 0.999923i \(-0.496043\pi\)
0.0124321 + 0.999923i \(0.496043\pi\)
\(618\) −3.00665e7 3.49423e7i −0.127385 0.148042i
\(619\) 2.69398e8i 1.13586i −0.823078 0.567928i \(-0.807745\pi\)
0.823078 0.567928i \(-0.192255\pi\)
\(620\) −9.10433e7 1.37341e7i −0.382009 0.0576268i
\(621\) 1.47645e7 0.0616516
\(622\) 2.43852e8 2.09825e8i 1.01334 0.871940i
\(623\) 2.44173e8i 1.00980i
\(624\) 8.40102e6 2.72115e7i 0.0345763 0.111995i
\(625\) 9.76562e6 0.0400000
\(626\) −1.14515e8 1.33085e8i −0.466808 0.542509i
\(627\) 4.02053e7i 0.163110i
\(628\) 2.73231e7 1.81125e8i 0.110319 0.731306i
\(629\) 6.16209e7 0.247615
\(630\) 1.92800e7 1.65897e7i 0.0771055 0.0663463i
\(631\) 2.83825e8i 1.12970i 0.825195 + 0.564848i \(0.191065\pi\)
−0.825195 + 0.564848i \(0.808935\pi\)
\(632\) −1.67979e8 2.67447e8i −0.665431 1.05946i
\(633\) −1.10584e8 −0.435993
\(634\) −1.49926e8 1.74240e8i −0.588316 0.683721i
\(635\) 2.17180e8i 0.848202i
\(636\) −2.79329e8 4.21374e7i −1.08579 0.163793i
\(637\) 2.80413e7 0.108488
\(638\) −5.64269e7 + 4.85532e7i −0.217282 + 0.186963i
\(639\) 1.03936e8i 0.398349i
\(640\) 1.13253e8 3.02935e7i 0.432025 0.115560i
\(641\) 8.05312e7 0.305767 0.152883 0.988244i \(-0.451144\pi\)
0.152883 + 0.988244i \(0.451144\pi\)
\(642\) 6.75066e7 + 7.84539e7i 0.255118 + 0.296490i
\(643\) 1.70629e8i 0.641829i 0.947108 + 0.320915i \(0.103990\pi\)
−0.947108 + 0.320915i \(0.896010\pi\)
\(644\) 8.70893e6 5.77316e7i 0.0326067 0.216150i
\(645\) −8.85562e7 −0.330020
\(646\) −1.21649e8 + 1.04675e8i −0.451244 + 0.388279i
\(647\) 1.72635e8i 0.637404i 0.947855 + 0.318702i \(0.103247\pi\)
−0.947855 + 0.318702i \(0.896753\pi\)
\(648\) −2.56021e7 + 1.60802e7i −0.0940914 + 0.0590972i
\(649\) 1.08069e8 0.395336
\(650\) 7.27289e6 + 8.45231e6i 0.0264830 + 0.0307777i
\(651\) 9.38949e7i 0.340329i
\(652\) −3.71364e8 5.60211e7i −1.33985 0.202120i
\(653\) −9.10476e7 −0.326986 −0.163493 0.986545i \(-0.552276\pi\)
−0.163493 + 0.986545i \(0.552276\pi\)
\(654\) 2.07523e8 1.78566e8i 0.741879 0.638359i
\(655\) 1.21737e8i 0.433209i
\(656\) −2.78441e8 8.59631e7i −0.986329 0.304509i
\(657\) −6.70749e7 −0.236518
\(658\) −1.62005e8 1.88277e8i −0.568658 0.660875i
\(659\) 4.48502e8i 1.56714i 0.621302 + 0.783571i \(0.286604\pi\)
−0.621302 + 0.783571i \(0.713396\pi\)
\(660\) 5.08399e6 3.37018e7i 0.0176837 0.117225i
\(661\) −1.10377e8 −0.382186 −0.191093 0.981572i \(-0.561203\pi\)
−0.191093 + 0.981572i \(0.561203\pi\)
\(662\) 4.01061e7 3.45098e7i 0.138241 0.118951i
\(663\) 3.30489e7i 0.113401i
\(664\) 1.72170e8 + 2.74120e8i 0.588104 + 0.936347i
\(665\) 5.52184e7 0.187767
\(666\) 1.64376e7 + 1.91032e7i 0.0556437 + 0.0646672i
\(667\) 5.93471e7i 0.199996i
\(668\) −4.02373e7 6.06989e6i −0.134989 0.0203634i
\(669\) 1.86851e7 0.0624048
\(670\) −1.42684e8 + 1.22774e8i −0.474407 + 0.408209i
\(671\) 1.34135e8i 0.443990i
\(672\) 4.77746e7 + 1.09593e8i 0.157431 + 0.361140i
\(673\) −3.09349e8 −1.01485 −0.507427 0.861695i \(-0.669403\pi\)
−0.507427 + 0.861695i \(0.669403\pi\)
\(674\) 1.23661e8 + 1.43714e8i 0.403880 + 0.469376i
\(675\) 1.18375e7i 0.0384900i
\(676\) 4.41801e7 2.92870e8i 0.143017 0.948058i
\(677\) 1.46692e8 0.472761 0.236381 0.971661i \(-0.424039\pi\)
0.236381 + 0.971661i \(0.424039\pi\)
\(678\) −2.43759e8 + 2.09745e8i −0.782117 + 0.672982i
\(679\) 3.06675e8i 0.979644i
\(680\) 1.15208e8 7.23600e7i 0.366399 0.230129i
\(681\) −9.11780e7 −0.288701
\(682\) −8.20649e7 9.53731e7i −0.258705 0.300658i
\(683\) 4.83173e8i 1.51649i 0.651968 + 0.758247i \(0.273944\pi\)
−0.651968 + 0.758247i \(0.726056\pi\)
\(684\) −6.49007e7 9.79042e6i −0.202806 0.0305938i
\(685\) 2.24435e8 0.698263
\(686\) −2.56211e8 + 2.20459e8i −0.793642 + 0.682899i
\(687\) 1.98861e8i 0.613310i
\(688\) 1.22789e8 3.97724e8i 0.377047 1.22128i
\(689\) 1.26293e8 0.386118
\(690\) −1.77229e7 2.05970e7i −0.0539496 0.0626985i
\(691\) 1.33819e8i 0.405586i 0.979222 + 0.202793i \(0.0650019\pi\)
−0.979222 + 0.202793i \(0.934998\pi\)
\(692\) −7.19577e7 + 4.77008e8i −0.217149 + 1.43948i
\(693\) 3.47573e7 0.104435
\(694\) −4.77267e8 + 4.10670e8i −1.42785 + 1.22861i
\(695\) 1.55556e7i 0.0463376i
\(696\) −6.46357e7 1.02909e8i −0.191710 0.305230i
\(697\) −3.38171e8 −0.998708
\(698\) 3.04889e8 + 3.54332e8i 0.896552 + 1.04194i
\(699\) 9.42562e7i 0.275980i
\(700\) −4.62864e7 6.98240e6i −0.134946 0.0203569i
\(701\) −2.21186e8 −0.642101 −0.321050 0.947062i \(-0.604036\pi\)
−0.321050 + 0.947062i \(0.604036\pi\)
\(702\) 1.02455e7 8.81590e6i 0.0296158 0.0254833i
\(703\) 5.47121e7i 0.157477i
\(704\) 1.44312e8 + 6.95630e7i 0.413604 + 0.199370i
\(705\) −1.15598e8 −0.329900
\(706\) 1.15162e7 + 1.33837e7i 0.0327261 + 0.0380332i
\(707\) 1.38448e8i 0.391768i
\(708\) −2.63159e7 + 1.74448e8i −0.0741513 + 0.491550i
\(709\) 4.32781e8 1.21431 0.607155 0.794583i \(-0.292311\pi\)
0.607155 + 0.794583i \(0.292311\pi\)
\(710\) 1.44994e8 1.24762e8i 0.405113 0.348584i
\(711\) 1.49893e8i 0.417035i
\(712\) 4.52325e8 2.84098e8i 1.25317 0.787096i
\(713\) −1.00309e8 −0.276739
\(714\) 9.04908e7 + 1.05165e8i 0.248605 + 0.288920i
\(715\) 1.52375e7i 0.0416866i
\(716\) −5.55786e7 8.38415e6i −0.151415 0.0228413i
\(717\) 3.82898e8 1.03879
\(718\) −7.29376e7 + 6.27601e7i −0.197051 + 0.169555i
\(719\) 5.42829e8i 1.46042i 0.683225 + 0.730208i \(0.260577\pi\)
−0.683225 + 0.730208i \(0.739423\pi\)
\(720\) 5.31645e7 + 1.64135e7i 0.142438 + 0.0439747i
\(721\) −8.65150e7 −0.230826
\(722\) 1.52543e8 + 1.77280e8i 0.405304 + 0.471031i
\(723\) 8.33632e7i 0.220577i
\(724\) 4.04283e7 2.67999e8i 0.106529 0.706184i
\(725\) 4.75817e7 0.124861
\(726\) −1.32161e8 + 1.13719e8i −0.345377 + 0.297184i
\(727\) 1.71836e8i 0.447210i −0.974680 0.223605i \(-0.928217\pi\)
0.974680 0.223605i \(-0.0717826\pi\)
\(728\) −2.84281e7 4.52618e7i −0.0736808 0.117311i
\(729\) −1.43489e7 −0.0370370
\(730\) 8.05149e7 + 9.35718e7i 0.206970 + 0.240534i
\(731\) 4.83042e8i 1.23661i
\(732\) −2.16524e8 3.26632e7i −0.552044 0.0832770i
\(733\) −3.55710e8 −0.903200 −0.451600 0.892221i \(-0.649147\pi\)
−0.451600 + 0.892221i \(0.649147\pi\)
\(734\) 4.62780e8 3.98204e8i 1.17027 1.00697i
\(735\) 5.47857e7i 0.137977i
\(736\) 1.17079e8 5.10381e7i 0.293661 0.128015i
\(737\) −2.57226e8 −0.642558
\(738\) −9.02084e7 1.04837e8i −0.224428 0.260823i
\(739\) 6.71490e8i 1.66382i −0.554912 0.831909i \(-0.687248\pi\)
0.554912 0.831909i \(-0.312752\pi\)
\(740\) 6.91839e6 4.58620e7i 0.0170730 0.113177i
\(741\) 2.93435e7 0.0721203
\(742\) −4.01878e8 + 3.45801e8i −0.983745 + 0.846475i
\(743\) 2.37075e8i 0.577988i −0.957331 0.288994i \(-0.906679\pi\)
0.957331 0.288994i \(-0.0933208\pi\)
\(744\) 1.73938e8 1.09248e8i 0.422354 0.265273i
\(745\) 5.54064e7 0.133996
\(746\) 2.83825e8 + 3.29852e8i 0.683652 + 0.794517i
\(747\) 1.53633e8i 0.368573i
\(748\) 1.83831e8 + 2.77313e7i 0.439252 + 0.0662621i
\(749\) 1.94247e8 0.462284
\(750\) −1.65137e7 + 1.42094e7i −0.0391436 + 0.0336816i
\(751\) 5.41645e8i 1.27878i −0.768884 0.639389i \(-0.779187\pi\)
0.768884 0.639389i \(-0.220813\pi\)
\(752\) 1.60284e8 5.19173e8i 0.376910 1.22084i
\(753\) 2.53469e7 0.0593662
\(754\) 3.54362e7 + 4.11827e7i 0.0826671 + 0.0960729i
\(755\) 1.65317e6i 0.00384128i
\(756\) −8.46378e6 + 5.61064e7i −0.0195884 + 0.129852i
\(757\) −5.37604e8 −1.23930 −0.619648 0.784880i \(-0.712725\pi\)
−0.619648 + 0.784880i \(0.712725\pi\)
\(758\) −7.66273e7 + 6.59349e7i −0.175945 + 0.151394i
\(759\) 3.71316e7i 0.0849217i
\(760\) 6.42472e7 + 1.02291e8i 0.146357 + 0.233022i
\(761\) −4.02108e8 −0.912407 −0.456204 0.889875i \(-0.650791\pi\)
−0.456204 + 0.889875i \(0.650791\pi\)
\(762\) 3.16007e8 + 3.67252e8i 0.714219 + 0.830041i
\(763\) 5.13815e8i 1.15673i
\(764\) 5.43403e8 + 8.19736e7i 1.21855 + 0.183820i
\(765\) 6.45692e7 0.144225
\(766\) 3.70082e8 3.18442e8i 0.823402 0.708506i
\(767\) 7.88732e7i 0.174801i
\(768\) −1.47432e8 + 2.16014e8i −0.325469 + 0.476868i
\(769\) 7.17215e8 1.57714 0.788570 0.614945i \(-0.210822\pi\)
0.788570 + 0.614945i \(0.210822\pi\)
\(770\) −4.17218e7 4.84877e7i −0.0913883 0.106208i
\(771\) 9.29541e7i 0.202817i
\(772\) −9.04941e7 + 5.99886e8i −0.196684 + 1.30382i
\(773\) 7.16120e8