Properties

Label 300.5.c.c.151.6
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.6
Root \(2.11879 - 3.39275i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.87881 + 3.53130i) q^{2} -5.19615i q^{3} +(-8.94016 - 13.2693i) q^{4} +(18.3492 + 9.76257i) q^{6} +7.86734i q^{7} +(63.6546 - 6.63999i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-1.87881 + 3.53130i) q^{2} -5.19615i q^{3} +(-8.94016 - 13.2693i) q^{4} +(18.3492 + 9.76257i) q^{6} +7.86734i q^{7} +(63.6546 - 6.63999i) q^{8} -27.0000 q^{9} +61.8527i q^{11} +(-68.9491 + 46.4544i) q^{12} +47.0192 q^{13} +(-27.7819 - 14.7812i) q^{14} +(-96.1470 + 237.259i) q^{16} -239.844 q^{17} +(50.7278 - 95.3451i) q^{18} +18.5518i q^{19} +40.8799 q^{21} +(-218.420 - 116.209i) q^{22} -580.792i q^{23} +(-34.5024 - 330.759i) q^{24} +(-88.3401 + 166.039i) q^{26} +140.296i q^{27} +(104.394 - 70.3353i) q^{28} +254.128 q^{29} +1368.88i q^{31} +(-657.190 - 785.288i) q^{32} +321.396 q^{33} +(450.620 - 846.960i) q^{34} +(241.384 + 358.270i) q^{36} +1089.51 q^{37} +(-65.5120 - 34.8553i) q^{38} -244.319i q^{39} +2011.08 q^{41} +(-76.8055 + 144.359i) q^{42} -716.042i q^{43} +(820.740 - 552.973i) q^{44} +(2050.95 + 1091.20i) q^{46} -2546.81i q^{47} +(1232.83 + 499.594i) q^{48} +2339.10 q^{49} +1246.26i q^{51} +(-420.359 - 623.911i) q^{52} +1958.55 q^{53} +(-495.428 - 263.589i) q^{54} +(52.2391 + 500.793i) q^{56} +96.3981 q^{57} +(-477.459 + 897.404i) q^{58} +5125.74i q^{59} +7401.65 q^{61} +(-4833.91 - 2571.85i) q^{62} -212.418i q^{63} +(4007.82 - 845.332i) q^{64} +(-603.841 + 1134.95i) q^{66} -2556.85i q^{67} +(2144.24 + 3182.55i) q^{68} -3017.88 q^{69} -2346.78i q^{71} +(-1718.67 + 179.280i) q^{72} +3540.66 q^{73} +(-2046.97 + 3847.37i) q^{74} +(246.169 - 165.856i) q^{76} -486.616 q^{77} +(862.764 + 459.028i) q^{78} +4948.38i q^{79} +729.000 q^{81} +(-3778.42 + 7101.71i) q^{82} +8824.75i q^{83} +(-365.473 - 542.447i) q^{84} +(2528.56 + 1345.30i) q^{86} -1320.49i q^{87} +(410.701 + 3937.21i) q^{88} -12929.7 q^{89} +369.916i q^{91} +(-7706.68 + 5192.37i) q^{92} +7112.89 q^{93} +(8993.54 + 4784.96i) q^{94} +(-4080.47 + 3414.86i) q^{96} +13176.9 q^{97} +(-4394.73 + 8260.08i) q^{98} -1670.02i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87881 + 3.53130i −0.469702 + 0.882825i
\(3\) 5.19615i 0.577350i
\(4\) −8.94016 13.2693i −0.558760 0.829329i
\(5\) 0 0
\(6\) 18.3492 + 9.76257i 0.509699 + 0.271183i
\(7\) 7.86734i 0.160558i 0.996772 + 0.0802790i \(0.0255811\pi\)
−0.996772 + 0.0802790i \(0.974419\pi\)
\(8\) 63.6546 6.63999i 0.994603 0.103750i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 61.8527i 0.511179i 0.966785 + 0.255590i \(0.0822696\pi\)
−0.966785 + 0.255590i \(0.917730\pi\)
\(12\) −68.9491 + 46.4544i −0.478813 + 0.322600i
\(13\) 47.0192 0.278220 0.139110 0.990277i \(-0.455576\pi\)
0.139110 + 0.990277i \(0.455576\pi\)
\(14\) −27.7819 14.7812i −0.141745 0.0754144i
\(15\) 0 0
\(16\) −96.1470 + 237.259i −0.375574 + 0.926792i
\(17\) −239.844 −0.829909 −0.414955 0.909842i \(-0.636203\pi\)
−0.414955 + 0.909842i \(0.636203\pi\)
\(18\) 50.7278 95.3451i 0.156567 0.294275i
\(19\) 18.5518i 0.0513901i 0.999670 + 0.0256950i \(0.00817988\pi\)
−0.999670 + 0.0256950i \(0.991820\pi\)
\(20\) 0 0
\(21\) 40.8799 0.0926982
\(22\) −218.420 116.209i −0.451282 0.240102i
\(23\) 580.792i 1.09791i −0.835853 0.548953i \(-0.815027\pi\)
0.835853 0.548953i \(-0.184973\pi\)
\(24\) −34.5024 330.759i −0.0599000 0.574235i
\(25\) 0 0
\(26\) −88.3401 + 166.039i −0.130681 + 0.245620i
\(27\) 140.296i 0.192450i
\(28\) 104.394 70.3353i 0.133155 0.0897134i
\(29\) 254.128 0.302174 0.151087 0.988520i \(-0.451723\pi\)
0.151087 + 0.988520i \(0.451723\pi\)
\(30\) 0 0
\(31\) 1368.88i 1.42443i 0.701962 + 0.712214i \(0.252308\pi\)
−0.701962 + 0.712214i \(0.747692\pi\)
\(32\) −657.190 785.288i −0.641788 0.766882i
\(33\) 321.396 0.295129
\(34\) 450.620 846.960i 0.389810 0.732665i
\(35\) 0 0
\(36\) 241.384 + 358.270i 0.186253 + 0.276443i
\(37\) 1089.51 0.795840 0.397920 0.917420i \(-0.369732\pi\)
0.397920 + 0.917420i \(0.369732\pi\)
\(38\) −65.5120 34.8553i −0.0453684 0.0241380i
\(39\) 244.319i 0.160631i
\(40\) 0 0
\(41\) 2011.08 1.19636 0.598178 0.801363i \(-0.295891\pi\)
0.598178 + 0.801363i \(0.295891\pi\)
\(42\) −76.8055 + 144.359i −0.0435405 + 0.0818363i
\(43\) 716.042i 0.387259i −0.981075 0.193629i \(-0.937974\pi\)
0.981075 0.193629i \(-0.0620259\pi\)
\(44\) 820.740 552.973i 0.423936 0.285626i
\(45\) 0 0
\(46\) 2050.95 + 1091.20i 0.969258 + 0.515688i
\(47\) 2546.81i 1.15292i −0.817124 0.576461i \(-0.804433\pi\)
0.817124 0.576461i \(-0.195567\pi\)
\(48\) 1232.83 + 499.594i 0.535084 + 0.216838i
\(49\) 2339.10 0.974221
\(50\) 0 0
\(51\) 1246.26i 0.479148i
\(52\) −420.359 623.911i −0.155458 0.230736i
\(53\) 1958.55 0.697242 0.348621 0.937264i \(-0.386650\pi\)
0.348621 + 0.937264i \(0.386650\pi\)
\(54\) −495.428 263.589i −0.169900 0.0903942i
\(55\) 0 0
\(56\) 52.2391 + 500.793i 0.0166579 + 0.159692i
\(57\) 96.3981 0.0296701
\(58\) −477.459 + 897.404i −0.141932 + 0.266767i
\(59\) 5125.74i 1.47249i 0.676715 + 0.736245i \(0.263403\pi\)
−0.676715 + 0.736245i \(0.736597\pi\)
\(60\) 0 0
\(61\) 7401.65 1.98915 0.994577 0.103998i \(-0.0331637\pi\)
0.994577 + 0.103998i \(0.0331637\pi\)
\(62\) −4833.91 2571.85i −1.25752 0.669057i
\(63\) 212.418i 0.0535193i
\(64\) 4007.82 845.332i 0.978472 0.206380i
\(65\) 0 0
\(66\) −603.841 + 1134.95i −0.138623 + 0.260548i
\(67\) 2556.85i 0.569582i −0.958590 0.284791i \(-0.908076\pi\)
0.958590 0.284791i \(-0.0919242\pi\)
\(68\) 2144.24 + 3182.55i 0.463720 + 0.688268i
\(69\) −3017.88 −0.633876
\(70\) 0 0
\(71\) 2346.78i 0.465539i −0.972532 0.232770i \(-0.925221\pi\)
0.972532 0.232770i \(-0.0747788\pi\)
\(72\) −1718.67 + 179.280i −0.331534 + 0.0345833i
\(73\) 3540.66 0.664414 0.332207 0.943207i \(-0.392207\pi\)
0.332207 + 0.943207i \(0.392207\pi\)
\(74\) −2046.97 + 3847.37i −0.373808 + 0.702588i
\(75\) 0 0
\(76\) 246.169 165.856i 0.0426193 0.0287147i
\(77\) −486.616 −0.0820739
\(78\) 862.764 + 459.028i 0.141809 + 0.0754485i
\(79\) 4948.38i 0.792882i 0.918060 + 0.396441i \(0.129755\pi\)
−0.918060 + 0.396441i \(0.870245\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) −3778.42 + 7101.71i −0.561931 + 1.05617i
\(83\) 8824.75i 1.28099i 0.767962 + 0.640496i \(0.221271\pi\)
−0.767962 + 0.640496i \(0.778729\pi\)
\(84\) −365.473 542.447i −0.0517961 0.0768773i
\(85\) 0 0
\(86\) 2528.56 + 1345.30i 0.341882 + 0.181896i
\(87\) 1320.49i 0.174460i
\(88\) 410.701 + 3937.21i 0.0530348 + 0.508420i
\(89\) −12929.7 −1.63233 −0.816166 0.577818i \(-0.803904\pi\)
−0.816166 + 0.577818i \(0.803904\pi\)
\(90\) 0 0
\(91\) 369.916i 0.0446705i
\(92\) −7706.68 + 5192.37i −0.910525 + 0.613466i
\(93\) 7112.89 0.822394
\(94\) 8993.54 + 4784.96i 1.01783 + 0.541530i
\(95\) 0 0
\(96\) −4080.47 + 3414.86i −0.442760 + 0.370536i
\(97\) 13176.9 1.40045 0.700227 0.713921i \(-0.253082\pi\)
0.700227 + 0.713921i \(0.253082\pi\)
\(98\) −4394.73 + 8260.08i −0.457594 + 0.860067i
\(99\) 1670.02i 0.170393i
\(100\) 0 0
\(101\) 10201.8 1.00008 0.500040 0.866002i \(-0.333319\pi\)
0.500040 + 0.866002i \(0.333319\pi\)
\(102\) −4400.93 2341.49i −0.423004 0.225057i
\(103\) 4197.87i 0.395689i 0.980233 + 0.197845i \(0.0633941\pi\)
−0.980233 + 0.197845i \(0.936606\pi\)
\(104\) 2992.99 312.207i 0.276719 0.0288653i
\(105\) 0 0
\(106\) −3679.74 + 6916.24i −0.327496 + 0.615543i
\(107\) 581.398i 0.0507816i 0.999678 + 0.0253908i \(0.00808301\pi\)
−0.999678 + 0.0253908i \(0.991917\pi\)
\(108\) 1861.63 1254.27i 0.159604 0.107533i
\(109\) 7223.44 0.607982 0.303991 0.952675i \(-0.401681\pi\)
0.303991 + 0.952675i \(0.401681\pi\)
\(110\) 0 0
\(111\) 5661.23i 0.459478i
\(112\) −1866.60 756.421i −0.148804 0.0603014i
\(113\) 2422.25 0.189698 0.0948488 0.995492i \(-0.469763\pi\)
0.0948488 + 0.995492i \(0.469763\pi\)
\(114\) −181.113 + 340.410i −0.0139361 + 0.0261935i
\(115\) 0 0
\(116\) −2271.95 3372.10i −0.168843 0.250602i
\(117\) −1269.52 −0.0927401
\(118\) −18100.5 9630.28i −1.29995 0.691632i
\(119\) 1886.93i 0.133249i
\(120\) 0 0
\(121\) 10815.2 0.738696
\(122\) −13906.3 + 26137.4i −0.934310 + 1.75608i
\(123\) 10449.9i 0.690717i
\(124\) 18164.0 12238.0i 1.18132 0.795914i
\(125\) 0 0
\(126\) 750.113 + 399.093i 0.0472482 + 0.0251381i
\(127\) 25636.4i 1.58946i −0.606964 0.794729i \(-0.707613\pi\)
0.606964 0.794729i \(-0.292387\pi\)
\(128\) −4544.80 + 15741.0i −0.277393 + 0.960757i
\(129\) −3720.66 −0.223584
\(130\) 0 0
\(131\) 19837.6i 1.15597i −0.816048 0.577984i \(-0.803840\pi\)
0.816048 0.577984i \(-0.196160\pi\)
\(132\) −2873.33 4264.69i −0.164907 0.244759i
\(133\) −145.953 −0.00825109
\(134\) 9029.02 + 4803.84i 0.502841 + 0.267534i
\(135\) 0 0
\(136\) −15267.2 + 1592.56i −0.825430 + 0.0861030i
\(137\) 29095.2 1.55017 0.775086 0.631856i \(-0.217707\pi\)
0.775086 + 0.631856i \(0.217707\pi\)
\(138\) 5670.02 10657.1i 0.297733 0.559602i
\(139\) 3878.60i 0.200745i −0.994950 0.100373i \(-0.967997\pi\)
0.994950 0.100373i \(-0.0320035\pi\)
\(140\) 0 0
\(141\) −13233.6 −0.665640
\(142\) 8287.20 + 4409.15i 0.410990 + 0.218665i
\(143\) 2908.26i 0.142220i
\(144\) 2595.97 6405.99i 0.125191 0.308931i
\(145\) 0 0
\(146\) −6652.22 + 12503.1i −0.312076 + 0.586561i
\(147\) 12154.3i 0.562467i
\(148\) −9740.35 14456.9i −0.444684 0.660014i
\(149\) −35799.3 −1.61251 −0.806254 0.591570i \(-0.798508\pi\)
−0.806254 + 0.591570i \(0.798508\pi\)
\(150\) 0 0
\(151\) 8733.91i 0.383049i 0.981488 + 0.191525i \(0.0613432\pi\)
−0.981488 + 0.191525i \(0.938657\pi\)
\(152\) 123.184 + 1180.91i 0.00533171 + 0.0511127i
\(153\) 6475.78 0.276636
\(154\) 914.258 1718.39i 0.0385503 0.0724569i
\(155\) 0 0
\(156\) −3241.93 + 2184.25i −0.133216 + 0.0897539i
\(157\) 34333.1 1.39288 0.696439 0.717616i \(-0.254767\pi\)
0.696439 + 0.717616i \(0.254767\pi\)
\(158\) −17474.2 9297.05i −0.699976 0.372418i
\(159\) 10176.9i 0.402553i
\(160\) 0 0
\(161\) 4569.29 0.176278
\(162\) −1369.65 + 2574.32i −0.0521891 + 0.0980917i
\(163\) 41996.1i 1.58064i −0.612692 0.790322i \(-0.709913\pi\)
0.612692 0.790322i \(-0.290087\pi\)
\(164\) −17979.3 26685.5i −0.668477 0.992174i
\(165\) 0 0
\(166\) −31162.8 16580.0i −1.13089 0.601684i
\(167\) 15039.8i 0.539275i 0.962962 + 0.269637i \(0.0869039\pi\)
−0.962962 + 0.269637i \(0.913096\pi\)
\(168\) 2602.20 271.442i 0.0921980 0.00961743i
\(169\) −26350.2 −0.922594
\(170\) 0 0
\(171\) 500.899i 0.0171300i
\(172\) −9501.35 + 6401.53i −0.321165 + 0.216385i
\(173\) −22917.0 −0.765711 −0.382855 0.923808i \(-0.625059\pi\)
−0.382855 + 0.923808i \(0.625059\pi\)
\(174\) 4663.05 + 2480.95i 0.154018 + 0.0819444i
\(175\) 0 0
\(176\) −14675.1 5946.95i −0.473757 0.191986i
\(177\) 26634.1 0.850143
\(178\) 24292.4 45658.6i 0.766709 1.44106i
\(179\) 21591.7i 0.673879i 0.941526 + 0.336939i \(0.109392\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(180\) 0 0
\(181\) −7885.60 −0.240701 −0.120350 0.992731i \(-0.538402\pi\)
−0.120350 + 0.992731i \(0.538402\pi\)
\(182\) −1306.29 695.002i −0.0394362 0.0209818i
\(183\) 38460.1i 1.14844i
\(184\) −3856.45 36970.1i −0.113908 1.09198i
\(185\) 0 0
\(186\) −13363.7 + 25117.7i −0.386280 + 0.726030i
\(187\) 14835.0i 0.424232i
\(188\) −33794.3 + 22768.9i −0.956153 + 0.644207i
\(189\) −1103.76 −0.0308994
\(190\) 0 0
\(191\) 53547.3i 1.46781i −0.679250 0.733907i \(-0.737695\pi\)
0.679250 0.733907i \(-0.262305\pi\)
\(192\) −4392.48 20825.2i −0.119154 0.564921i
\(193\) 33661.0 0.903676 0.451838 0.892100i \(-0.350769\pi\)
0.451838 + 0.892100i \(0.350769\pi\)
\(194\) −24756.8 + 46531.5i −0.657796 + 1.23636i
\(195\) 0 0
\(196\) −20912.0 31038.2i −0.544356 0.807950i
\(197\) 9889.39 0.254822 0.127411 0.991850i \(-0.459333\pi\)
0.127411 + 0.991850i \(0.459333\pi\)
\(198\) 5897.35 + 3137.65i 0.150427 + 0.0800339i
\(199\) 10733.5i 0.271042i 0.990774 + 0.135521i \(0.0432708\pi\)
−0.990774 + 0.135521i \(0.956729\pi\)
\(200\) 0 0
\(201\) −13285.8 −0.328848
\(202\) −19167.3 + 36025.7i −0.469740 + 0.882896i
\(203\) 1999.32i 0.0485165i
\(204\) 16537.0 11141.8i 0.397372 0.267729i
\(205\) 0 0
\(206\) −14823.9 7886.98i −0.349324 0.185856i
\(207\) 15681.4i 0.365968i
\(208\) −4520.76 + 11155.7i −0.104492 + 0.257852i
\(209\) −1147.48 −0.0262695
\(210\) 0 0
\(211\) 31245.2i 0.701808i 0.936411 + 0.350904i \(0.114126\pi\)
−0.936411 + 0.350904i \(0.885874\pi\)
\(212\) −17509.8 25988.6i −0.389591 0.578243i
\(213\) −12194.2 −0.268779
\(214\) −2053.09 1092.34i −0.0448312 0.0238522i
\(215\) 0 0
\(216\) 931.565 + 8930.50i 0.0199667 + 0.191412i
\(217\) −10769.4 −0.228703
\(218\) −13571.5 + 25508.1i −0.285571 + 0.536742i
\(219\) 18397.8i 0.383599i
\(220\) 0 0
\(221\) −11277.3 −0.230897
\(222\) 19991.5 + 10636.4i 0.405639 + 0.215818i
\(223\) 31962.3i 0.642730i 0.946955 + 0.321365i \(0.104142\pi\)
−0.946955 + 0.321365i \(0.895858\pi\)
\(224\) 6178.13 5170.34i 0.123129 0.103044i
\(225\) 0 0
\(226\) −4550.94 + 8553.69i −0.0891013 + 0.167470i
\(227\) 31878.7i 0.618656i 0.950955 + 0.309328i \(0.100104\pi\)
−0.950955 + 0.309328i \(0.899896\pi\)
\(228\) −861.814 1279.13i −0.0165785 0.0246063i
\(229\) 21252.3 0.405260 0.202630 0.979255i \(-0.435051\pi\)
0.202630 + 0.979255i \(0.435051\pi\)
\(230\) 0 0
\(231\) 2528.53i 0.0473854i
\(232\) 16176.5 1687.41i 0.300543 0.0313505i
\(233\) −77716.9 −1.43154 −0.715770 0.698336i \(-0.753924\pi\)
−0.715770 + 0.698336i \(0.753924\pi\)
\(234\) 2385.18 4483.05i 0.0435602 0.0818733i
\(235\) 0 0
\(236\) 68014.8 45824.9i 1.22118 0.822769i
\(237\) 25712.5 0.457771
\(238\) 6663.33 + 3545.18i 0.117635 + 0.0625871i
\(239\) 56167.8i 0.983313i 0.870789 + 0.491657i \(0.163608\pi\)
−0.870789 + 0.491657i \(0.836392\pi\)
\(240\) 0 0
\(241\) 11285.3 0.194302 0.0971510 0.995270i \(-0.469027\pi\)
0.0971510 + 0.995270i \(0.469027\pi\)
\(242\) −20319.8 + 38191.9i −0.346967 + 0.652139i
\(243\) 3788.00i 0.0641500i
\(244\) −66171.9 98214.4i −1.11146 1.64966i
\(245\) 0 0
\(246\) 36901.6 + 19633.3i 0.609782 + 0.324431i
\(247\) 872.292i 0.0142978i
\(248\) 9089.32 + 87135.3i 0.147784 + 1.41674i
\(249\) 45854.7 0.739581
\(250\) 0 0
\(251\) 74138.0i 1.17677i −0.808579 0.588387i \(-0.799763\pi\)
0.808579 0.588387i \(-0.200237\pi\)
\(252\) −2818.63 + 1899.05i −0.0443852 + 0.0299045i
\(253\) 35923.5 0.561226
\(254\) 90529.7 + 48165.8i 1.40321 + 0.746572i
\(255\) 0 0
\(256\) −47047.5 45623.4i −0.717888 0.696159i
\(257\) −391.260 −0.00592379 −0.00296189 0.999996i \(-0.500943\pi\)
−0.00296189 + 0.999996i \(0.500943\pi\)
\(258\) 6990.41 13138.8i 0.105018 0.197386i
\(259\) 8571.51i 0.127779i
\(260\) 0 0
\(261\) −6861.47 −0.100725
\(262\) 70052.4 + 37271.0i 1.02052 + 0.542960i
\(263\) 62550.4i 0.904313i 0.891939 + 0.452157i \(0.149345\pi\)
−0.891939 + 0.452157i \(0.850655\pi\)
\(264\) 20458.3 2134.07i 0.293537 0.0306196i
\(265\) 0 0
\(266\) 274.219 515.406i 0.00387555 0.00728427i
\(267\) 67184.7i 0.942427i
\(268\) −33927.6 + 22858.7i −0.472371 + 0.318260i
\(269\) 47440.2 0.655604 0.327802 0.944746i \(-0.393692\pi\)
0.327802 + 0.944746i \(0.393692\pi\)
\(270\) 0 0
\(271\) 139480.i 1.89921i 0.313453 + 0.949604i \(0.398514\pi\)
−0.313453 + 0.949604i \(0.601486\pi\)
\(272\) 23060.3 56905.0i 0.311692 0.769153i
\(273\) 1922.14 0.0257905
\(274\) −54664.2 + 102744.i −0.728118 + 1.36853i
\(275\) 0 0
\(276\) 26980.4 + 40045.1i 0.354185 + 0.525692i
\(277\) −147171. −1.91806 −0.959029 0.283307i \(-0.908568\pi\)
−0.959029 + 0.283307i \(0.908568\pi\)
\(278\) 13696.5 + 7287.13i 0.177223 + 0.0942903i
\(279\) 36959.6i 0.474810i
\(280\) 0 0
\(281\) 31803.9 0.402780 0.201390 0.979511i \(-0.435454\pi\)
0.201390 + 0.979511i \(0.435454\pi\)
\(282\) 24863.4 46731.8i 0.312653 0.587644i
\(283\) 116313.i 1.45229i 0.687541 + 0.726146i \(0.258690\pi\)
−0.687541 + 0.726146i \(0.741310\pi\)
\(284\) −31140.1 + 20980.6i −0.386085 + 0.260125i
\(285\) 0 0
\(286\) −10270.0 5464.07i −0.125556 0.0668012i
\(287\) 15821.8i 0.192085i
\(288\) 17744.1 + 21202.8i 0.213929 + 0.255627i
\(289\) −25996.0 −0.311251
\(290\) 0 0
\(291\) 68469.0i 0.808552i
\(292\) −31654.1 46982.0i −0.371248 0.551018i
\(293\) −50816.7 −0.591931 −0.295965 0.955199i \(-0.595641\pi\)
−0.295965 + 0.955199i \(0.595641\pi\)
\(294\) 42920.6 + 22835.7i 0.496560 + 0.264192i
\(295\) 0 0
\(296\) 69352.0 7234.30i 0.791545 0.0825683i
\(297\) −8677.69 −0.0983765
\(298\) 67260.0 126418.i 0.757398 1.42356i
\(299\) 27308.4i 0.305459i
\(300\) 0 0
\(301\) 5633.34 0.0621775
\(302\) −30842.1 16409.3i −0.338166 0.179919i
\(303\) 53010.2i 0.577397i
\(304\) −4401.58 1783.70i −0.0476279 0.0193008i
\(305\) 0 0
\(306\) −12166.7 + 22867.9i −0.129937 + 0.244222i
\(307\) 104571.i 1.10952i −0.832011 0.554760i \(-0.812810\pi\)
0.832011 0.554760i \(-0.187190\pi\)
\(308\) 4350.43 + 6457.04i 0.0458596 + 0.0680663i
\(309\) 21812.7 0.228451
\(310\) 0 0
\(311\) 42105.4i 0.435329i 0.976024 + 0.217664i \(0.0698438\pi\)
−0.976024 + 0.217664i \(0.930156\pi\)
\(312\) −1622.28 15552.0i −0.0166654 0.159764i
\(313\) 137890. 1.40749 0.703745 0.710453i \(-0.251510\pi\)
0.703745 + 0.710453i \(0.251510\pi\)
\(314\) −64505.2 + 121240.i −0.654238 + 1.22967i
\(315\) 0 0
\(316\) 65661.4 44239.3i 0.657561 0.443031i
\(317\) −162907. −1.62114 −0.810569 0.585643i \(-0.800842\pi\)
−0.810569 + 0.585643i \(0.800842\pi\)
\(318\) 35937.8 + 19120.5i 0.355384 + 0.189080i
\(319\) 15718.5i 0.154465i
\(320\) 0 0
\(321\) 3021.03 0.0293187
\(322\) −8584.82 + 16135.5i −0.0827979 + 0.155622i
\(323\) 4449.54i 0.0426491i
\(324\) −6517.38 9673.30i −0.0620845 0.0921477i
\(325\) 0 0
\(326\) 148301. + 78902.6i 1.39543 + 0.742431i
\(327\) 37534.1i 0.351019i
\(328\) 128014. 13353.5i 1.18990 0.124122i
\(329\) 20036.6 0.185111
\(330\) 0 0
\(331\) 171369.i 1.56414i 0.623192 + 0.782069i \(0.285836\pi\)
−0.623192 + 0.782069i \(0.714164\pi\)
\(332\) 117098. 78894.7i 1.06236 0.715767i
\(333\) −29416.6 −0.265280
\(334\) −53110.2 28257.0i −0.476085 0.253298i
\(335\) 0 0
\(336\) −3930.48 + 9699.12i −0.0348151 + 0.0859120i
\(337\) −150057. −1.32129 −0.660643 0.750700i \(-0.729716\pi\)
−0.660643 + 0.750700i \(0.729716\pi\)
\(338\) 49506.9 93050.4i 0.433344 0.814489i
\(339\) 12586.4i 0.109522i
\(340\) 0 0
\(341\) −84668.6 −0.728138
\(342\) 1768.82 + 941.093i 0.0151228 + 0.00804601i
\(343\) 37292.0i 0.316977i
\(344\) −4754.51 45579.4i −0.0401781 0.385169i
\(345\) 0 0
\(346\) 43056.6 80926.7i 0.359656 0.675989i
\(347\) 105689.i 0.877754i 0.898547 + 0.438877i \(0.144624\pi\)
−0.898547 + 0.438877i \(0.855376\pi\)
\(348\) −17521.9 + 11805.4i −0.144685 + 0.0974815i
\(349\) 101691. 0.834897 0.417448 0.908701i \(-0.362924\pi\)
0.417448 + 0.908701i \(0.362924\pi\)
\(350\) 0 0
\(351\) 6596.61i 0.0535435i
\(352\) 48572.1 40649.0i 0.392014 0.328068i
\(353\) 75384.5 0.604969 0.302484 0.953154i \(-0.402184\pi\)
0.302484 + 0.953154i \(0.402184\pi\)
\(354\) −50040.4 + 94053.1i −0.399314 + 0.750527i
\(355\) 0 0
\(356\) 115594. + 171568.i 0.912082 + 1.35374i
\(357\) −9804.79 −0.0769311
\(358\) −76246.9 40566.7i −0.594917 0.316522i
\(359\) 157519.i 1.22220i −0.791553 0.611101i \(-0.790727\pi\)
0.791553 0.611101i \(-0.209273\pi\)
\(360\) 0 0
\(361\) 129977. 0.997359
\(362\) 14815.5 27846.4i 0.113058 0.212497i
\(363\) 56197.7i 0.426486i
\(364\) 4908.52 3307.11i 0.0370465 0.0249601i
\(365\) 0 0
\(366\) 135814. + 72259.1i 1.01387 + 0.539424i
\(367\) 105819.i 0.785653i −0.919613 0.392827i \(-0.871497\pi\)
0.919613 0.392827i \(-0.128503\pi\)
\(368\) 137798. + 55841.4i 1.01753 + 0.412345i
\(369\) −54299.0 −0.398786
\(370\) 0 0
\(371\) 15408.6i 0.111948i
\(372\) −63590.4 94382.8i −0.459521 0.682036i
\(373\) −12801.2 −0.0920098 −0.0460049 0.998941i \(-0.514649\pi\)
−0.0460049 + 0.998941i \(0.514649\pi\)
\(374\) 52386.7 + 27872.1i 0.374523 + 0.199263i
\(375\) 0 0
\(376\) −16910.8 162116.i −0.119616 1.14670i
\(377\) 11948.9 0.0840710
\(378\) 2073.75 3897.70i 0.0145135 0.0272788i
\(379\) 83667.5i 0.582476i −0.956651 0.291238i \(-0.905933\pi\)
0.956651 0.291238i \(-0.0940672\pi\)
\(380\) 0 0
\(381\) −133210. −0.917674
\(382\) 189092. + 100605.i 1.29582 + 0.689435i
\(383\) 53274.8i 0.363182i −0.983374 0.181591i \(-0.941875\pi\)
0.983374 0.181591i \(-0.0581247\pi\)
\(384\) 81792.8 + 23615.5i 0.554693 + 0.160153i
\(385\) 0 0
\(386\) −63242.6 + 118867.i −0.424458 + 0.797788i
\(387\) 19333.1i 0.129086i
\(388\) −117803. 174847.i −0.782518 1.16144i
\(389\) 130363. 0.861497 0.430749 0.902472i \(-0.358250\pi\)
0.430749 + 0.902472i \(0.358250\pi\)
\(390\) 0 0
\(391\) 139299.i 0.911162i
\(392\) 148895. 15531.6i 0.968964 0.101075i
\(393\) −103079. −0.667398
\(394\) −18580.3 + 34922.4i −0.119690 + 0.224963i
\(395\) 0 0
\(396\) −22160.0 + 14930.3i −0.141312 + 0.0952088i
\(397\) −213615. −1.35535 −0.677674 0.735362i \(-0.737012\pi\)
−0.677674 + 0.735362i \(0.737012\pi\)
\(398\) −37903.3 20166.2i −0.239283 0.127309i
\(399\) 758.397i 0.00476377i
\(400\) 0 0
\(401\) −99636.7 −0.619627 −0.309814 0.950797i \(-0.600267\pi\)
−0.309814 + 0.950797i \(0.600267\pi\)
\(402\) 24961.5 46916.2i 0.154461 0.290316i
\(403\) 64363.5i 0.396305i
\(404\) −91205.9 135371.i −0.558805 0.829396i
\(405\) 0 0
\(406\) −7060.18 3756.33i −0.0428316 0.0227883i
\(407\) 67388.8i 0.406817i
\(408\) 8275.19 + 79330.5i 0.0497116 + 0.476563i
\(409\) 235531. 1.40800 0.703999 0.710201i \(-0.251396\pi\)
0.703999 + 0.710201i \(0.251396\pi\)
\(410\) 0 0
\(411\) 151183.i 0.894992i
\(412\) 55702.6 37529.6i 0.328157 0.221095i
\(413\) −40325.9 −0.236420
\(414\) −55375.7 29462.3i −0.323086 0.171896i
\(415\) 0 0
\(416\) −30900.6 36923.6i −0.178558 0.213362i
\(417\) −20153.8 −0.115900
\(418\) 2155.89 4052.09i 0.0123388 0.0231914i
\(419\) 201684.i 1.14880i −0.818575 0.574399i \(-0.805236\pi\)
0.818575 0.574399i \(-0.194764\pi\)
\(420\) 0 0
\(421\) −12875.0 −0.0726412 −0.0363206 0.999340i \(-0.511564\pi\)
−0.0363206 + 0.999340i \(0.511564\pi\)
\(422\) −110336. 58703.7i −0.619574 0.329641i
\(423\) 68763.8i 0.384308i
\(424\) 124671. 13004.8i 0.693479 0.0723388i
\(425\) 0 0
\(426\) 22910.6 43061.5i 0.126246 0.237285i
\(427\) 58231.3i 0.319375i
\(428\) 7714.73 5197.79i 0.0421146 0.0283747i
\(429\) 15111.8 0.0821110
\(430\) 0 0
\(431\) 99240.2i 0.534236i 0.963664 + 0.267118i \(0.0860713\pi\)
−0.963664 + 0.267118i \(0.913929\pi\)
\(432\) −33286.5 13489.0i −0.178361 0.0722793i
\(433\) −269220. −1.43592 −0.717962 0.696082i \(-0.754925\pi\)
−0.717962 + 0.696082i \(0.754925\pi\)
\(434\) 20233.7 38030.0i 0.107422 0.201905i
\(435\) 0 0
\(436\) −64578.7 95849.8i −0.339716 0.504218i
\(437\) 10774.7 0.0564214
\(438\) 64968.2 + 34565.9i 0.338651 + 0.180177i
\(439\) 277426.i 1.43952i 0.694221 + 0.719762i \(0.255749\pi\)
−0.694221 + 0.719762i \(0.744251\pi\)
\(440\) 0 0
\(441\) −63155.8 −0.324740
\(442\) 21187.8 39823.4i 0.108453 0.203842i
\(443\) 241969.i 1.23297i −0.787366 0.616485i \(-0.788556\pi\)
0.787366 0.616485i \(-0.211444\pi\)
\(444\) −75120.4 + 50612.4i −0.381059 + 0.256738i
\(445\) 0 0
\(446\) −112869. 60051.1i −0.567418 0.301892i
\(447\) 186018.i 0.930981i
\(448\) 6650.52 + 31530.9i 0.0331360 + 0.157102i
\(449\) −150123. −0.744653 −0.372326 0.928102i \(-0.621440\pi\)
−0.372326 + 0.928102i \(0.621440\pi\)
\(450\) 0 0
\(451\) 124390.i 0.611553i
\(452\) −21655.3 32141.5i −0.105995 0.157322i
\(453\) 45382.7 0.221154
\(454\) −112573. 59894.0i −0.546165 0.290584i
\(455\) 0 0
\(456\) 6136.18 640.082i 0.0295100 0.00307827i
\(457\) 199480. 0.955141 0.477571 0.878593i \(-0.341517\pi\)
0.477571 + 0.878593i \(0.341517\pi\)
\(458\) −39928.9 + 75048.1i −0.190352 + 0.357774i
\(459\) 33649.1i 0.159716i
\(460\) 0 0
\(461\) −123874. −0.582879 −0.291440 0.956589i \(-0.594134\pi\)
−0.291440 + 0.956589i \(0.594134\pi\)
\(462\) −8929.00 4750.62i −0.0418330 0.0222570i
\(463\) 426435.i 1.98926i 0.103503 + 0.994629i \(0.466995\pi\)
−0.103503 + 0.994629i \(0.533005\pi\)
\(464\) −24433.7 + 60294.2i −0.113489 + 0.280053i
\(465\) 0 0
\(466\) 146015. 274442.i 0.672397 1.26380i
\(467\) 229937.i 1.05433i 0.849763 + 0.527164i \(0.176745\pi\)
−0.849763 + 0.527164i \(0.823255\pi\)
\(468\) 11349.7 + 16845.6i 0.0518195 + 0.0769121i
\(469\) 20115.7 0.0914510
\(470\) 0 0
\(471\) 178400.i 0.804179i
\(472\) 34034.9 + 326277.i 0.152771 + 1.46454i
\(473\) 44289.1 0.197959
\(474\) −48308.9 + 90798.7i −0.215016 + 0.404132i
\(475\) 0 0
\(476\) −25038.2 + 16869.5i −0.110507 + 0.0744540i
\(477\) −52880.9 −0.232414
\(478\) −198345. 105529.i −0.868093 0.461864i
\(479\) 27874.0i 0.121486i 0.998153 + 0.0607432i \(0.0193471\pi\)
−0.998153 + 0.0607432i \(0.980653\pi\)
\(480\) 0 0
\(481\) 51227.7 0.221419
\(482\) −21202.8 + 39851.6i −0.0912640 + 0.171535i
\(483\) 23742.7i 0.101774i
\(484\) −96690.1 143510.i −0.412754 0.612622i
\(485\) 0 0
\(486\) 13376.5 + 7116.91i 0.0566333 + 0.0301314i
\(487\) 20395.8i 0.0859968i −0.999075 0.0429984i \(-0.986309\pi\)
0.999075 0.0429984i \(-0.0136910\pi\)
\(488\) 471149. 49146.9i 1.97842 0.206375i
\(489\) −218218. −0.912585
\(490\) 0 0
\(491\) 373834.i 1.55066i −0.631557 0.775330i \(-0.717584\pi\)
0.631557 0.775330i \(-0.282416\pi\)
\(492\) −138662. + 93423.4i −0.572832 + 0.385945i
\(493\) −60951.1 −0.250777
\(494\) −3080.32 1638.87i −0.0126224 0.00671568i
\(495\) 0 0
\(496\) −324778. 131613.i −1.32015 0.534979i
\(497\) 18462.9 0.0747461
\(498\) −86152.2 + 161927.i −0.347382 + 0.652920i
\(499\) 277828.i 1.11577i 0.829919 + 0.557884i \(0.188387\pi\)
−0.829919 + 0.557884i \(0.811613\pi\)
\(500\) 0 0
\(501\) 78149.3 0.311351
\(502\) 261803. + 139291.i 1.03889 + 0.552733i
\(503\) 250329.i 0.989409i −0.869061 0.494704i \(-0.835276\pi\)
0.869061 0.494704i \(-0.164724\pi\)
\(504\) −1410.46 13521.4i −0.00555262 0.0532305i
\(505\) 0 0
\(506\) −67493.4 + 126857.i −0.263609 + 0.495465i
\(507\) 136920.i 0.532660i
\(508\) −340176. + 229193.i −1.31818 + 0.888126i
\(509\) −41577.1 −0.160479 −0.0802396 0.996776i \(-0.525569\pi\)
−0.0802396 + 0.996776i \(0.525569\pi\)
\(510\) 0 0
\(511\) 27855.6i 0.106677i
\(512\) 249503. 80421.2i 0.951780 0.306783i
\(513\) −2602.75 −0.00989002
\(514\) 735.103 1381.66i 0.00278241 0.00522967i
\(515\) 0 0
\(516\) 33263.3 + 49370.5i 0.124930 + 0.185425i
\(517\) 157527. 0.589350
\(518\) −30268.6 16104.2i −0.112806 0.0600178i
\(519\) 119080.i 0.442083i
\(520\) 0 0
\(521\) −476195. −1.75432 −0.877161 0.480196i \(-0.840565\pi\)
−0.877161 + 0.480196i \(0.840565\pi\)
\(522\) 12891.4 24229.9i 0.0473106 0.0889223i
\(523\) 105663.i 0.386294i −0.981170 0.193147i \(-0.938131\pi\)
0.981170 0.193147i \(-0.0618694\pi\)
\(524\) −263230. + 177351.i −0.958678 + 0.645909i
\(525\) 0 0
\(526\) −220884. 117520.i −0.798350 0.424758i
\(527\) 328316.i 1.18215i
\(528\) −30901.2 + 76254.0i −0.110843 + 0.273524i
\(529\) −57478.3 −0.205396
\(530\) 0 0
\(531\) 138395.i 0.490830i
\(532\) 1304.85 + 1936.70i 0.00461038 + 0.00684287i
\(533\) 94559.2 0.332851
\(534\) −237249. 126227.i −0.831998 0.442660i
\(535\) 0 0
\(536\) −16977.5 162756.i −0.0590941 0.566508i
\(537\) 112194. 0.389064
\(538\) −89131.0 + 167526.i −0.307939 + 0.578784i
\(539\) 144680.i 0.498001i
\(540\) 0 0
\(541\) 258293. 0.882507 0.441254 0.897382i \(-0.354534\pi\)
0.441254 + 0.897382i \(0.354534\pi\)
\(542\) −492545. 262055.i −1.67667 0.892061i
\(543\) 40974.8i 0.138969i
\(544\) 157623. + 188346.i 0.532625 + 0.636443i
\(545\) 0 0
\(546\) −3611.33 + 6787.66i −0.0121139 + 0.0227685i
\(547\) 40859.8i 0.136559i 0.997666 + 0.0682796i \(0.0217510\pi\)
−0.997666 + 0.0682796i \(0.978249\pi\)
\(548\) −260115. 386072.i −0.866174 1.28560i
\(549\) −199844. −0.663052
\(550\) 0 0
\(551\) 4714.54i 0.0155288i
\(552\) −192102. + 20038.7i −0.630455 + 0.0657645i
\(553\) −38930.6 −0.127304
\(554\) 276505. 519704.i 0.900916 1.69331i
\(555\) 0 0
\(556\) −51466.1 + 34675.3i −0.166484 + 0.112168i
\(557\) 445511. 1.43598 0.717989 0.696055i \(-0.245063\pi\)
0.717989 + 0.696055i \(0.245063\pi\)
\(558\) 130516. + 69440.1i 0.419174 + 0.223019i
\(559\) 33667.7i 0.107743i
\(560\) 0 0
\(561\) −77084.8 −0.244931
\(562\) −59753.5 + 112309.i −0.189187 + 0.355585i
\(563\) 320372.i 1.01074i −0.862904 0.505368i \(-0.831357\pi\)
0.862904 0.505368i \(-0.168643\pi\)
\(564\) 118310. + 175600.i 0.371933 + 0.552035i
\(565\) 0 0
\(566\) −410735. 218529.i −1.28212 0.682144i
\(567\) 5735.29i 0.0178398i
\(568\) −15582.6 149384.i −0.0482996 0.463027i
\(569\) 26018.1 0.0803619 0.0401810 0.999192i \(-0.487207\pi\)
0.0401810 + 0.999192i \(0.487207\pi\)
\(570\) 0 0
\(571\) 321694.i 0.986667i −0.869840 0.493334i \(-0.835778\pi\)
0.869840 0.493334i \(-0.164222\pi\)
\(572\) 38590.5 26000.3i 0.117947 0.0794671i
\(573\) −278240. −0.847443
\(574\) −55871.6 29726.2i −0.169577 0.0902225i
\(575\) 0 0
\(576\) −108211. + 22824.0i −0.326157 + 0.0687933i
\(577\) 259440. 0.779267 0.389633 0.920970i \(-0.372602\pi\)
0.389633 + 0.920970i \(0.372602\pi\)
\(578\) 48841.4 91799.6i 0.146195 0.274780i
\(579\) 174908.i 0.521738i
\(580\) 0 0
\(581\) −69427.3 −0.205673
\(582\) 241785. + 128640.i 0.713810 + 0.379779i
\(583\) 121142.i 0.356415i
\(584\) 225379. 23510.0i 0.660828 0.0689328i
\(585\) 0 0
\(586\) 95474.7 179449.i 0.278031 0.522571i
\(587\) 236459.i 0.686247i −0.939290 0.343123i \(-0.888515\pi\)
0.939290 0.343123i \(-0.111485\pi\)
\(588\) −161279. + 108662.i −0.466470 + 0.314284i
\(589\) −25395.1 −0.0732015
\(590\) 0 0
\(591\) 51386.8i 0.147122i
\(592\) −104753. + 258495.i −0.298897 + 0.737579i
\(593\) 94856.8 0.269748 0.134874 0.990863i \(-0.456937\pi\)
0.134874 + 0.990863i \(0.456937\pi\)
\(594\) 16303.7 30643.5i 0.0462076 0.0868492i
\(595\) 0 0
\(596\) 320051. + 475030.i 0.901005 + 1.33730i
\(597\) 55773.0 0.156486
\(598\) 96434.1 + 51307.2i 0.269667 + 0.143475i
\(599\) 201635.i 0.561969i −0.959712 0.280985i \(-0.909339\pi\)
0.959712 0.280985i \(-0.0906610\pi\)
\(600\) 0 0
\(601\) 371285. 1.02792 0.513959 0.857815i \(-0.328178\pi\)
0.513959 + 0.857815i \(0.328178\pi\)
\(602\) −10584.0 + 19893.0i −0.0292049 + 0.0548919i
\(603\) 69035.1i 0.189861i
\(604\) 115893. 78082.6i 0.317674 0.214033i
\(605\) 0 0
\(606\) 187195. + 99596.0i 0.509740 + 0.271204i
\(607\) 258037.i 0.700332i −0.936688 0.350166i \(-0.886125\pi\)
0.936688 0.350166i \(-0.113875\pi\)
\(608\) 14568.5 12192.1i 0.0394101 0.0329815i
\(609\) 10388.7 0.0280110
\(610\) 0 0
\(611\) 119749.i 0.320766i
\(612\) −57894.5 85928.9i −0.154573 0.229423i
\(613\) 259378. 0.690258 0.345129 0.938555i \(-0.387835\pi\)
0.345129 + 0.938555i \(0.387835\pi\)
\(614\) 369272. + 196469.i 0.979511 + 0.521143i
\(615\) 0 0
\(616\) −30975.4 + 3231.13i −0.0816310 + 0.00851516i
\(617\) 423059. 1.11130 0.555650 0.831417i \(-0.312470\pi\)
0.555650 + 0.831417i \(0.312470\pi\)
\(618\) −40982.0 + 77027.4i −0.107304 + 0.201682i
\(619\) 178609.i 0.466145i −0.972459 0.233073i \(-0.925122\pi\)
0.972459 0.233073i \(-0.0748780\pi\)
\(620\) 0 0
\(621\) 81482.9 0.211292
\(622\) −148687. 79108.0i −0.384319 0.204475i
\(623\) 101722.i 0.262084i
\(624\) 57966.8 + 23490.5i 0.148871 + 0.0603287i
\(625\) 0 0
\(626\) −259069. + 486932.i −0.661101 + 1.24257i
\(627\) 5962.48i 0.0151667i
\(628\) −306943. 455575.i −0.778285 1.15515i
\(629\) −261311. −0.660475
\(630\) 0 0
\(631\) 637150.i 1.60023i 0.599846 + 0.800116i \(0.295229\pi\)
−0.599846 + 0.800116i \(0.704771\pi\)
\(632\) 32857.2 + 314987.i 0.0822614 + 0.788603i
\(633\) 162355. 0.405189
\(634\) 306070. 575272.i 0.761452 1.43118i
\(635\) 0 0
\(636\) −135041. + 90983.5i −0.333849 + 0.224930i
\(637\) 109983. 0.271048
\(638\) −55506.8 29532.1i −0.136366 0.0725526i
\(639\) 63363.1i 0.155180i
\(640\) 0 0
\(641\) 744727. 1.81251 0.906257 0.422727i \(-0.138927\pi\)
0.906257 + 0.422727i \(0.138927\pi\)
\(642\) −5675.94 + 10668.2i −0.0137711 + 0.0258833i
\(643\) 36186.6i 0.0875237i −0.999042 0.0437619i \(-0.986066\pi\)
0.999042 0.0437619i \(-0.0139343\pi\)
\(644\) −40850.2 60631.1i −0.0984968 0.146192i
\(645\) 0 0
\(646\) 15712.7 + 8359.82i 0.0376517 + 0.0200324i
\(647\) 362450.i 0.865845i −0.901431 0.432922i \(-0.857482\pi\)
0.901431 0.432922i \(-0.142518\pi\)
\(648\) 46404.2 4840.55i 0.110511 0.0115278i
\(649\) −317041. −0.752706
\(650\) 0 0
\(651\) 55959.5i 0.132042i
\(652\) −557258. + 375452.i −1.31087 + 0.883200i
\(653\) 190115. 0.445850 0.222925 0.974836i \(-0.428439\pi\)
0.222925 + 0.974836i \(0.428439\pi\)
\(654\) 132544. + 70519.3i 0.309888 + 0.164874i
\(655\) 0 0
\(656\) −193359. + 477145.i −0.449321 + 1.10877i
\(657\) −95597.8 −0.221471
\(658\) −37644.9 + 70755.2i −0.0869470 + 0.163421i
\(659\) 345083.i 0.794608i −0.917687 0.397304i \(-0.869946\pi\)
0.917687 0.397304i \(-0.130054\pi\)
\(660\) 0 0
\(661\) 37084.2 0.0848761 0.0424381 0.999099i \(-0.486487\pi\)
0.0424381 + 0.999099i \(0.486487\pi\)
\(662\) −605154. 321969.i −1.38086 0.734679i
\(663\) 58598.4i 0.133309i
\(664\) 58596.2 + 561736.i 0.132903 + 1.27408i
\(665\) 0 0
\(666\) 55268.2 103879.i 0.124603 0.234196i
\(667\) 147596.i 0.331759i
\(668\) 199568. 134459.i 0.447236 0.301325i
\(669\) 166081. 0.371080
\(670\) 0 0
\(671\) 457812.i 1.01681i
\(672\) −26865.9 32102.5i −0.0594926 0.0710886i
\(673\) 239821. 0.529490 0.264745 0.964319i \(-0.414712\pi\)
0.264745 + 0.964319i \(0.414712\pi\)
\(674\) 281929. 529897.i 0.620611 1.16646i
\(675\) 0 0
\(676\) 235575. + 349648.i 0.515508 + 0.765134i
\(677\) −294470. −0.642487 −0.321244 0.946997i \(-0.604101\pi\)
−0.321244 + 0.946997i \(0.604101\pi\)
\(678\) 44446.3 + 23647.4i 0.0966887 + 0.0514427i
\(679\) 103667.i 0.224854i
\(680\) 0 0
\(681\) 165647. 0.357181
\(682\) 159076. 298990.i 0.342008 0.642819i
\(683\) 393749.i 0.844070i −0.906579 0.422035i \(-0.861316\pi\)
0.906579 0.422035i \(-0.138684\pi\)
\(684\) −6646.56 + 4478.12i −0.0142064 + 0.00957157i
\(685\) 0 0
\(686\) −131689. 70064.6i −0.279835 0.148885i
\(687\) 110430.i 0.233977i
\(688\) 169887. + 68845.2i 0.358909 + 0.145444i
\(689\) 92089.6 0.193987
\(690\) 0 0
\(691\) 675096.i 1.41387i −0.707279 0.706935i \(-0.750077\pi\)
0.707279 0.706935i \(-0.249923\pi\)
\(692\) 204881. + 304091.i 0.427849 + 0.635027i
\(693\) 13138.6 0.0273580
\(694\) −373221. 198570.i −0.774903 0.412283i
\(695\) 0 0
\(696\) −8768.04 84055.3i −0.0181002 0.173519i
\(697\) −482344. −0.992867
\(698\) −191058. + 359102.i −0.392153 + 0.737068i
\(699\) 403829.i 0.826500i
\(700\) 0 0
\(701\) 110087. 0.224027 0.112013 0.993707i \(-0.464270\pi\)
0.112013 + 0.993707i \(0.464270\pi\)
\(702\) −23294.6 12393.8i −0.0472695 0.0251495i
\(703\) 20212.3i 0.0408983i
\(704\) 52286.1 + 247894.i 0.105497 + 0.500174i
\(705\) 0 0
\(706\) −141633. + 266205.i −0.284155 + 0.534081i
\(707\) 80261.2i 0.160571i
\(708\) −238113. 353415.i −0.475026 0.705048i
\(709\) −539972. −1.07418 −0.537092 0.843524i \(-0.680477\pi\)
−0.537092 + 0.843524i \(0.680477\pi\)
\(710\) 0 0
\(711\) 133606.i 0.264294i
\(712\) −823035. + 85853.1i −1.62352 + 0.169354i
\(713\) 795032. 1.56389
\(714\) 18421.3 34623.7i 0.0361347 0.0679167i
\(715\) 0 0
\(716\) 286507. 193034.i 0.558867 0.376537i
\(717\) 291857. 0.567716
\(718\) 556245. + 295947.i 1.07899 + 0.574070i
\(719\) 206020.i 0.398520i 0.979947 + 0.199260i \(0.0638539\pi\)
−0.979947 + 0.199260i \(0.936146\pi\)
\(720\) 0 0
\(721\) −33026.0 −0.0635310
\(722\) −244201. + 458987.i −0.468461 + 0.880494i
\(723\) 58639.9i 0.112180i
\(724\) 70498.6 + 104636.i 0.134494 + 0.199620i
\(725\) 0 0
\(726\) 198451. + 105585.i 0.376513 + 0.200321i
\(727\) 961559.i 1.81931i −0.415363 0.909656i \(-0.636345\pi\)
0.415363 0.909656i \(-0.363655\pi\)
\(728\) 2456.24 + 23546.9i 0.00463456 + 0.0444294i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 171738.i 0.321390i
\(732\) −510337. + 343839.i −0.952434 + 0.641702i
\(733\) 454366. 0.845665 0.422832 0.906208i \(-0.361036\pi\)
0.422832 + 0.906208i \(0.361036\pi\)
\(734\) 373678. + 198813.i 0.693595 + 0.369023i
\(735\) 0 0
\(736\) −456089. + 381691.i −0.841964 + 0.704622i
\(737\) 158148. 0.291158
\(738\) 102017. 191746.i 0.187310 0.352058i
\(739\) 259643.i 0.475432i 0.971335 + 0.237716i \(0.0763987\pi\)
−0.971335 + 0.237716i \(0.923601\pi\)
\(740\) 0 0
\(741\) 4532.56 0.00825481
\(742\) −54412.4 28949.8i −0.0988303 0.0525821i
\(743\) 834340.i 1.51135i 0.654946 + 0.755676i \(0.272691\pi\)
−0.654946 + 0.755676i \(0.727309\pi\)
\(744\) 452768. 47229.5i 0.817956 0.0853233i
\(745\) 0 0
\(746\) 24051.1 45205.0i 0.0432172 0.0812285i
\(747\) 238268.i 0.426997i
\(748\) −196849. + 132627.i −0.351828 + 0.237044i
\(749\) −4574.06 −0.00815339
\(750\) 0 0
\(751\) 597678.i 1.05971i 0.848088 + 0.529855i \(0.177754\pi\)
−0.848088 + 0.529855i \(0.822246\pi\)
\(752\) 604252. + 244868.i 1.06852 + 0.433008i
\(753\) −385232. −0.679411
\(754\) −22449.7 + 42195.2i −0.0394883 + 0.0742199i
\(755\) 0 0
\(756\) 9867.77 + 14646.1i 0.0172654 + 0.0256258i
\(757\) 266595. 0.465221 0.232611 0.972570i \(-0.425273\pi\)
0.232611 + 0.972570i \(0.425273\pi\)
\(758\) 295455. + 157195.i 0.514225 + 0.273590i
\(759\) 186664.i 0.324024i
\(760\) 0 0
\(761\) 441424. 0.762230 0.381115 0.924528i \(-0.375540\pi\)
0.381115 + 0.924528i \(0.375540\pi\)
\(762\) 250277. 470406.i 0.431033 0.810146i
\(763\) 56829.3i 0.0976165i
\(764\) −710534. + 478722.i −1.21730 + 0.820156i
\(765\) 0 0
\(766\) 188129. + 100093.i 0.320626 + 0.170587i
\(767\) 241008.i 0.409677i
\(768\) −237066. + 244466.i −0.401927 + 0.414473i
\(769\) −292264. −0.494223 −0.247112 0.968987i \(-0.579481\pi\)
−0.247112 + 0.968987i \(0.579481\pi\)
\(770\) 0 0
\(771\) 2033.05i 0.00342010i
\(772\) −300935. 446657.i −0.504938 0.749445i
\(773\) −617969. −1.03421 −0.517104 0.855923i \(-0.672990\pi\)
−0.517104 + 0.855923i \(0.672990\pi\)
\(774\) −68271.1 36323.2i −0.113961 0.0606321i
\(775\) 0 0
\(776\) 838768. 87494.3i 1.39290 0.145297i
\(777\) 44538.9 0.0737730
\(778\) −244926. + 460350.i −0.404647 + 0.760551i
\(779\) 37309.1i 0.0614809i
\(780\) 0 0
\(781\) 145155. 0.237974
\(782\) −491908. 261717.i −0.804396 0.427974i
\(783\) 35653.2i 0.0581534i