Properties

Label 300.5.c.c.151.16
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 151.16
Root \(1.95664 - 3.48878i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.15

$q$-expansion

\(f(q)\) \(=\) \(q+(3.99969 + 0.0498899i) q^{2} +5.19615i q^{3} +(15.9950 + 0.399088i) q^{4} +(-0.259236 + 20.7830i) q^{6} +35.2842i q^{7} +(63.9552 + 2.39422i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(3.99969 + 0.0498899i) q^{2} +5.19615i q^{3} +(15.9950 + 0.399088i) q^{4} +(-0.259236 + 20.7830i) q^{6} +35.2842i q^{7} +(63.9552 + 2.39422i) q^{8} -27.0000 q^{9} -3.95158i q^{11} +(-2.07372 + 83.1126i) q^{12} +41.0572 q^{13} +(-1.76033 + 141.126i) q^{14} +(255.681 + 12.7668i) q^{16} +186.761 q^{17} +(-107.992 - 1.34703i) q^{18} +580.932i q^{19} -183.342 q^{21} +(0.197144 - 15.8051i) q^{22} +472.336i q^{23} +(-12.4407 + 332.321i) q^{24} +(164.216 + 2.04834i) q^{26} -140.296i q^{27} +(-14.0815 + 564.372i) q^{28} -979.409 q^{29} -33.2865i q^{31} +(1022.01 + 63.8193i) q^{32} +20.5330 q^{33} +(746.987 + 9.31750i) q^{34} +(-431.866 - 10.7754i) q^{36} -623.253 q^{37} +(-28.9826 + 2323.55i) q^{38} +213.340i q^{39} +154.478 q^{41} +(-733.312 - 9.14693i) q^{42} +2675.32i q^{43} +(1.57703 - 63.2057i) q^{44} +(-23.5648 + 1889.20i) q^{46} -2925.06i q^{47} +(-66.3385 + 1328.56i) q^{48} +1156.02 q^{49} +970.440i q^{51} +(656.711 + 16.3855i) q^{52} +3782.10 q^{53} +(6.99936 - 561.141i) q^{54} +(-84.4782 + 2256.61i) q^{56} -3018.61 q^{57} +(-3917.33 - 48.8626i) q^{58} +3487.58i q^{59} -488.539 q^{61} +(1.66066 - 133.135i) q^{62} -952.674i q^{63} +(4084.54 + 306.245i) q^{64} +(82.1257 + 1.02439i) q^{66} -7491.56i q^{67} +(2987.25 + 74.5342i) q^{68} -2454.33 q^{69} +4620.06i q^{71} +(-1726.79 - 64.6439i) q^{72} -6959.14 q^{73} +(-2492.82 - 31.0940i) q^{74} +(-231.843 + 9292.01i) q^{76} +139.429 q^{77} +(-10.6435 + 853.292i) q^{78} +6756.51i q^{79} +729.000 q^{81} +(617.865 + 7.70690i) q^{82} -4862.15i q^{83} +(-2932.56 - 73.1697i) q^{84} +(-133.471 + 10700.4i) q^{86} -5089.16i q^{87} +(9.46096 - 252.724i) q^{88} +513.707 q^{89} +1448.67i q^{91} +(-188.504 + 7555.03i) q^{92} +172.962 q^{93} +(145.931 - 11699.3i) q^{94} +(-331.615 + 5310.52i) q^{96} +12119.3 q^{97} +(4623.73 + 57.6739i) q^{98} +106.693i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.99969 + 0.0498899i 0.999922 + 0.0124725i
\(3\) 5.19615i 0.577350i
\(4\) 15.9950 + 0.399088i 0.999689 + 0.0249430i
\(5\) 0 0
\(6\) −0.259236 + 20.7830i −0.00720099 + 0.577305i
\(7\) 35.2842i 0.720086i 0.932936 + 0.360043i \(0.117238\pi\)
−0.932936 + 0.360043i \(0.882762\pi\)
\(8\) 63.9552 + 2.39422i 0.999300 + 0.0374097i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 3.95158i 0.0326577i −0.999867 0.0163289i \(-0.994802\pi\)
0.999867 0.0163289i \(-0.00519787\pi\)
\(12\) −2.07372 + 83.1126i −0.0144009 + 0.577171i
\(13\) 41.0572 0.242942 0.121471 0.992595i \(-0.461239\pi\)
0.121471 + 0.992595i \(0.461239\pi\)
\(14\) −1.76033 + 141.126i −0.00898126 + 0.720030i
\(15\) 0 0
\(16\) 255.681 + 12.7668i 0.998756 + 0.0498705i
\(17\) 186.761 0.646233 0.323116 0.946359i \(-0.395269\pi\)
0.323116 + 0.946359i \(0.395269\pi\)
\(18\) −107.992 1.34703i −0.333307 0.00415749i
\(19\) 580.932i 1.60923i 0.593798 + 0.804614i \(0.297628\pi\)
−0.593798 + 0.804614i \(0.702372\pi\)
\(20\) 0 0
\(21\) −183.342 −0.415742
\(22\) 0.197144 15.8051i 0.000407323 0.0326552i
\(23\) 472.336i 0.892885i 0.894812 + 0.446443i \(0.147309\pi\)
−0.894812 + 0.446443i \(0.852691\pi\)
\(24\) −12.4407 + 332.321i −0.0215985 + 0.576946i
\(25\) 0 0
\(26\) 164.216 + 2.04834i 0.242923 + 0.00303009i
\(27\) 140.296i 0.192450i
\(28\) −14.0815 + 564.372i −0.0179611 + 0.719862i
\(29\) −979.409 −1.16458 −0.582288 0.812982i \(-0.697843\pi\)
−0.582288 + 0.812982i \(0.697843\pi\)
\(30\) 0 0
\(31\) 33.2865i 0.0346373i −0.999850 0.0173187i \(-0.994487\pi\)
0.999850 0.0173187i \(-0.00551298\pi\)
\(32\) 1022.01 + 63.8193i 0.998056 + 0.0623236i
\(33\) 20.5330 0.0188549
\(34\) 746.987 + 9.31750i 0.646183 + 0.00806012i
\(35\) 0 0
\(36\) −431.866 10.7754i −0.333230 0.00831434i
\(37\) −623.253 −0.455262 −0.227631 0.973748i \(-0.573098\pi\)
−0.227631 + 0.973748i \(0.573098\pi\)
\(38\) −28.9826 + 2323.55i −0.0200711 + 1.60910i
\(39\) 213.340i 0.140263i
\(40\) 0 0
\(41\) 154.478 0.0918966 0.0459483 0.998944i \(-0.485369\pi\)
0.0459483 + 0.998944i \(0.485369\pi\)
\(42\) −733.312 9.14693i −0.415710 0.00518533i
\(43\) 2675.32i 1.44690i 0.690377 + 0.723450i \(0.257445\pi\)
−0.690377 + 0.723450i \(0.742555\pi\)
\(44\) 1.57703 63.2057i 0.000814582 0.0326476i
\(45\) 0 0
\(46\) −23.5648 + 1889.20i −0.0111365 + 0.892816i
\(47\) 2925.06i 1.32416i −0.749434 0.662079i \(-0.769674\pi\)
0.749434 0.662079i \(-0.230326\pi\)
\(48\) −66.3385 + 1328.56i −0.0287927 + 0.576632i
\(49\) 1156.02 0.481476
\(50\) 0 0
\(51\) 970.440i 0.373103i
\(52\) 656.711 + 16.3855i 0.242867 + 0.00605971i
\(53\) 3782.10 1.34642 0.673212 0.739450i \(-0.264914\pi\)
0.673212 + 0.739450i \(0.264914\pi\)
\(54\) 6.99936 561.141i 0.00240033 0.192435i
\(55\) 0 0
\(56\) −84.4782 + 2256.61i −0.0269382 + 0.719582i
\(57\) −3018.61 −0.929089
\(58\) −3917.33 48.8626i −1.16449 0.0145252i
\(59\) 3487.58i 1.00189i 0.865479 + 0.500945i \(0.167014\pi\)
−0.865479 + 0.500945i \(0.832986\pi\)
\(60\) 0 0
\(61\) −488.539 −0.131292 −0.0656462 0.997843i \(-0.520911\pi\)
−0.0656462 + 0.997843i \(0.520911\pi\)
\(62\) 1.66066 133.135i 0.000432013 0.0346346i
\(63\) 952.674i 0.240029i
\(64\) 4084.54 + 306.245i 0.997201 + 0.0747670i
\(65\) 0 0
\(66\) 82.1257 + 1.02439i 0.0188535 + 0.000235168i
\(67\) 7491.56i 1.66887i −0.551107 0.834435i \(-0.685794\pi\)
0.551107 0.834435i \(-0.314206\pi\)
\(68\) 2987.25 + 74.5342i 0.646032 + 0.0161190i
\(69\) −2454.33 −0.515507
\(70\) 0 0
\(71\) 4620.06i 0.916496i 0.888824 + 0.458248i \(0.151523\pi\)
−0.888824 + 0.458248i \(0.848477\pi\)
\(72\) −1726.79 64.6439i −0.333100 0.0124699i
\(73\) −6959.14 −1.30590 −0.652950 0.757401i \(-0.726469\pi\)
−0.652950 + 0.757401i \(0.726469\pi\)
\(74\) −2492.82 31.0940i −0.455226 0.00567824i
\(75\) 0 0
\(76\) −231.843 + 9292.01i −0.0401390 + 1.60873i
\(77\) 139.429 0.0235164
\(78\) −10.6435 + 853.292i −0.00174942 + 0.140252i
\(79\) 6756.51i 1.08260i 0.840829 + 0.541300i \(0.182068\pi\)
−0.840829 + 0.541300i \(0.817932\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) 617.865 + 7.70690i 0.0918895 + 0.00114618i
\(83\) 4862.15i 0.705785i −0.935664 0.352893i \(-0.885198\pi\)
0.935664 0.352893i \(-0.114802\pi\)
\(84\) −2932.56 73.1697i −0.415613 0.0103699i
\(85\) 0 0
\(86\) −133.471 + 10700.4i −0.0180464 + 1.44679i
\(87\) 5089.16i 0.672369i
\(88\) 9.46096 252.724i 0.00122171 0.0326349i
\(89\) 513.707 0.0648538 0.0324269 0.999474i \(-0.489676\pi\)
0.0324269 + 0.999474i \(0.489676\pi\)
\(90\) 0 0
\(91\) 1448.67i 0.174939i
\(92\) −188.504 + 7555.03i −0.0222712 + 0.892607i
\(93\) 172.962 0.0199979
\(94\) 145.931 11699.3i 0.0165155 1.32405i
\(95\) 0 0
\(96\) −331.615 + 5310.52i −0.0359825 + 0.576228i
\(97\) 12119.3 1.28805 0.644026 0.765004i \(-0.277263\pi\)
0.644026 + 0.765004i \(0.277263\pi\)
\(98\) 4623.73 + 57.6739i 0.481438 + 0.00600519i
\(99\) 106.693i 0.0108859i
\(100\) 0 0
\(101\) −7191.20 −0.704951 −0.352475 0.935821i \(-0.614660\pi\)
−0.352475 + 0.935821i \(0.614660\pi\)
\(102\) −48.4152 + 3881.46i −0.00465351 + 0.373074i
\(103\) 10189.6i 0.960470i −0.877140 0.480235i \(-0.840551\pi\)
0.877140 0.480235i \(-0.159449\pi\)
\(104\) 2625.82 + 98.3000i 0.242772 + 0.00908839i
\(105\) 0 0
\(106\) 15127.2 + 188.689i 1.34632 + 0.0167932i
\(107\) 21648.8i 1.89089i −0.325777 0.945446i \(-0.605626\pi\)
0.325777 0.945446i \(-0.394374\pi\)
\(108\) 55.9905 2244.04i 0.00480028 0.192390i
\(109\) 10655.6 0.896859 0.448430 0.893818i \(-0.351983\pi\)
0.448430 + 0.893818i \(0.351983\pi\)
\(110\) 0 0
\(111\) 3238.52i 0.262845i
\(112\) −450.468 + 9021.52i −0.0359111 + 0.719190i
\(113\) 9876.07 0.773441 0.386721 0.922197i \(-0.373608\pi\)
0.386721 + 0.922197i \(0.373608\pi\)
\(114\) −12073.5 150.598i −0.929017 0.0115880i
\(115\) 0 0
\(116\) −15665.7 390.871i −1.16421 0.0290480i
\(117\) −1108.55 −0.0809807
\(118\) −173.995 + 13949.2i −0.0124961 + 1.00181i
\(119\) 6589.73i 0.465343i
\(120\) 0 0
\(121\) 14625.4 0.998933
\(122\) −1954.00 24.3732i −0.131282 0.00163754i
\(123\) 802.692i 0.0530565i
\(124\) 13.2842 532.418i 0.000863959 0.0346265i
\(125\) 0 0
\(126\) 47.5288 3810.40i 0.00299375 0.240010i
\(127\) 19972.7i 1.23831i −0.785269 0.619155i \(-0.787475\pi\)
0.785269 0.619155i \(-0.212525\pi\)
\(128\) 16321.6 + 1428.66i 0.996191 + 0.0871987i
\(129\) −13901.4 −0.835368
\(130\) 0 0
\(131\) 30733.6i 1.79090i −0.445164 0.895449i \(-0.646855\pi\)
0.445164 0.895449i \(-0.353145\pi\)
\(132\) 328.426 + 8.19449i 0.0188491 + 0.000470299i
\(133\) −20497.7 −1.15878
\(134\) 373.753 29963.9i 0.0208149 1.66874i
\(135\) 0 0
\(136\) 11944.4 + 447.147i 0.645780 + 0.0241754i
\(137\) −7177.05 −0.382388 −0.191194 0.981552i \(-0.561236\pi\)
−0.191194 + 0.981552i \(0.561236\pi\)
\(138\) −9816.56 122.446i −0.515467 0.00642965i
\(139\) 4628.80i 0.239574i 0.992800 + 0.119787i \(0.0382211\pi\)
−0.992800 + 0.119787i \(0.961779\pi\)
\(140\) 0 0
\(141\) 15199.1 0.764503
\(142\) −230.494 + 18478.8i −0.0114310 + 0.916425i
\(143\) 162.241i 0.00793394i
\(144\) −6903.40 344.705i −0.332919 0.0166235i
\(145\) 0 0
\(146\) −27834.4 347.191i −1.30580 0.0162878i
\(147\) 6006.87i 0.277980i
\(148\) −9968.95 248.733i −0.455120 0.0113556i
\(149\) 35128.8 1.58231 0.791154 0.611617i \(-0.209481\pi\)
0.791154 + 0.611617i \(0.209481\pi\)
\(150\) 0 0
\(151\) 41309.8i 1.81176i −0.423539 0.905878i \(-0.639212\pi\)
0.423539 0.905878i \(-0.360788\pi\)
\(152\) −1390.88 + 37153.6i −0.0602007 + 1.60810i
\(153\) −5042.55 −0.215411
\(154\) 557.671 + 6.95608i 0.0235146 + 0.000293307i
\(155\) 0 0
\(156\) −85.1413 + 3412.37i −0.00349857 + 0.140219i
\(157\) 3581.96 0.145319 0.0726594 0.997357i \(-0.476851\pi\)
0.0726594 + 0.997357i \(0.476851\pi\)
\(158\) −337.082 + 27023.9i −0.0135027 + 1.08252i
\(159\) 19652.4i 0.777358i
\(160\) 0 0
\(161\) −16666.0 −0.642954
\(162\) 2915.77 + 36.3697i 0.111102 + 0.00138583i
\(163\) 14969.6i 0.563422i −0.959499 0.281711i \(-0.909098\pi\)
0.959499 0.281711i \(-0.0909020\pi\)
\(164\) 2470.88 + 61.6504i 0.0918680 + 0.00229218i
\(165\) 0 0
\(166\) 242.572 19447.1i 0.00880289 0.705730i
\(167\) 12510.0i 0.448564i 0.974524 + 0.224282i \(0.0720037\pi\)
−0.974524 + 0.224282i \(0.927996\pi\)
\(168\) −11725.7 438.961i −0.415451 0.0155528i
\(169\) −26875.3 −0.940979
\(170\) 0 0
\(171\) 15685.2i 0.536410i
\(172\) −1067.69 + 42791.8i −0.0360901 + 1.44645i
\(173\) 51365.9 1.71626 0.858129 0.513434i \(-0.171627\pi\)
0.858129 + 0.513434i \(0.171627\pi\)
\(174\) 253.898 20355.0i 0.00838610 0.672316i
\(175\) 0 0
\(176\) 50.4493 1010.35i 0.00162866 0.0326171i
\(177\) −18122.0 −0.578442
\(178\) 2054.67 + 25.6288i 0.0648487 + 0.000808887i
\(179\) 29989.3i 0.935967i 0.883737 + 0.467984i \(0.155019\pi\)
−0.883737 + 0.467984i \(0.844981\pi\)
\(180\) 0 0
\(181\) −47416.2 −1.44734 −0.723668 0.690149i \(-0.757545\pi\)
−0.723668 + 0.690149i \(0.757545\pi\)
\(182\) −72.2741 + 5794.24i −0.00218193 + 0.174926i
\(183\) 2538.52i 0.0758017i
\(184\) −1130.88 + 30208.4i −0.0334025 + 0.892260i
\(185\) 0 0
\(186\) 691.792 + 8.62903i 0.0199963 + 0.000249423i
\(187\) 738.003i 0.0211045i
\(188\) 1167.36 46786.5i 0.0330285 1.32375i
\(189\) 4950.24 0.138581
\(190\) 0 0
\(191\) 41028.6i 1.12466i −0.826914 0.562329i \(-0.809905\pi\)
0.826914 0.562329i \(-0.190095\pi\)
\(192\) −1591.30 + 21223.9i −0.0431667 + 0.575734i
\(193\) −44180.6 −1.18609 −0.593044 0.805170i \(-0.702074\pi\)
−0.593044 + 0.805170i \(0.702074\pi\)
\(194\) 48473.3 + 604.629i 1.28795 + 0.0160652i
\(195\) 0 0
\(196\) 18490.6 + 461.355i 0.481326 + 0.0120094i
\(197\) 8724.29 0.224801 0.112400 0.993663i \(-0.464146\pi\)
0.112400 + 0.993663i \(0.464146\pi\)
\(198\) −5.32289 + 426.738i −0.000135774 + 0.0108851i
\(199\) 6720.98i 0.169717i 0.996393 + 0.0848587i \(0.0270439\pi\)
−0.996393 + 0.0848587i \(0.972956\pi\)
\(200\) 0 0
\(201\) 38927.3 0.963522
\(202\) −28762.6 358.768i −0.704896 0.00879248i
\(203\) 34557.7i 0.838596i
\(204\) −387.291 + 15522.2i −0.00930630 + 0.372987i
\(205\) 0 0
\(206\) 508.359 40755.3i 0.0119794 0.960395i
\(207\) 12753.1i 0.297628i
\(208\) 10497.6 + 524.171i 0.242640 + 0.0121156i
\(209\) 2295.60 0.0525537
\(210\) 0 0
\(211\) 8501.81i 0.190962i −0.995431 0.0954808i \(-0.969561\pi\)
0.995431 0.0954808i \(-0.0304389\pi\)
\(212\) 60494.8 + 1509.39i 1.34600 + 0.0335839i
\(213\) −24006.5 −0.529139
\(214\) 1080.06 86588.6i 0.0235841 1.89075i
\(215\) 0 0
\(216\) 335.900 8972.67i 0.00719949 0.192315i
\(217\) 1174.49 0.0249419
\(218\) 42619.0 + 531.606i 0.896790 + 0.0111861i
\(219\) 36160.7i 0.753961i
\(220\) 0 0
\(221\) 7667.90 0.156997
\(222\) 161.569 12953.1i 0.00327833 0.262825i
\(223\) 28886.8i 0.580883i −0.956893 0.290442i \(-0.906198\pi\)
0.956893 0.290442i \(-0.0938022\pi\)
\(224\) −2251.82 + 36060.8i −0.0448784 + 0.718687i
\(225\) 0 0
\(226\) 39501.2 + 492.716i 0.773381 + 0.00964672i
\(227\) 17662.3i 0.342764i −0.985205 0.171382i \(-0.945177\pi\)
0.985205 0.171382i \(-0.0548233\pi\)
\(228\) −48282.7 1204.69i −0.928800 0.0231743i
\(229\) −99665.8 −1.90053 −0.950266 0.311439i \(-0.899189\pi\)
−0.950266 + 0.311439i \(0.899189\pi\)
\(230\) 0 0
\(231\) 724.492i 0.0135772i
\(232\) −62638.3 2344.92i −1.16376 0.0435664i
\(233\) 72559.0 1.33653 0.668266 0.743922i \(-0.267037\pi\)
0.668266 + 0.743922i \(0.267037\pi\)
\(234\) −4433.84 55.3052i −0.0809744 0.00101003i
\(235\) 0 0
\(236\) −1391.85 + 55783.9i −0.0249902 + 1.00158i
\(237\) −35107.9 −0.625040
\(238\) −328.761 + 26356.9i −0.00580399 + 0.465307i
\(239\) 70208.6i 1.22912i −0.788870 0.614560i \(-0.789334\pi\)
0.788870 0.614560i \(-0.210666\pi\)
\(240\) 0 0
\(241\) −51440.5 −0.885668 −0.442834 0.896604i \(-0.646027\pi\)
−0.442834 + 0.896604i \(0.646027\pi\)
\(242\) 58497.0 + 729.659i 0.998856 + 0.0124592i
\(243\) 3788.00i 0.0641500i
\(244\) −7814.19 194.970i −0.131252 0.00327483i
\(245\) 0 0
\(246\) −40.0462 + 3210.52i −0.000661746 + 0.0530524i
\(247\) 23851.4i 0.390950i
\(248\) 79.6951 2128.84i 0.00129577 0.0346131i
\(249\) 25264.5 0.407485
\(250\) 0 0
\(251\) 72429.1i 1.14965i 0.818276 + 0.574825i \(0.194930\pi\)
−0.818276 + 0.574825i \(0.805070\pi\)
\(252\) 380.201 15238.0i 0.00598704 0.239954i
\(253\) 1866.48 0.0291596
\(254\) 996.436 79884.6i 0.0154448 1.23821i
\(255\) 0 0
\(256\) 65210.0 + 6528.49i 0.995026 + 0.0996169i
\(257\) 77711.9 1.17658 0.588290 0.808650i \(-0.299801\pi\)
0.588290 + 0.808650i \(0.299801\pi\)
\(258\) −55601.1 693.538i −0.835303 0.0104191i
\(259\) 21991.0i 0.327828i
\(260\) 0 0
\(261\) 26444.0 0.388192
\(262\) 1533.30 122925.i 0.0223369 1.79076i
\(263\) 2716.70i 0.0392763i −0.999807 0.0196382i \(-0.993749\pi\)
0.999807 0.0196382i \(-0.00625142\pi\)
\(264\) 1313.19 + 49.1606i 0.0188417 + 0.000705357i
\(265\) 0 0
\(266\) −81984.5 1022.63i −1.15869 0.0144529i
\(267\) 2669.30i 0.0374434i
\(268\) 2989.79 119828.i 0.0416266 1.66835i
\(269\) 66666.6 0.921306 0.460653 0.887580i \(-0.347615\pi\)
0.460653 + 0.887580i \(0.347615\pi\)
\(270\) 0 0
\(271\) 63959.9i 0.870902i 0.900212 + 0.435451i \(0.143411\pi\)
−0.900212 + 0.435451i \(0.856589\pi\)
\(272\) 47751.4 + 2384.35i 0.645429 + 0.0322280i
\(273\) −7527.53 −0.101001
\(274\) −28706.0 358.062i −0.382359 0.00476933i
\(275\) 0 0
\(276\) −39257.1 979.494i −0.515347 0.0128583i
\(277\) −36446.7 −0.475005 −0.237502 0.971387i \(-0.576329\pi\)
−0.237502 + 0.971387i \(0.576329\pi\)
\(278\) −230.930 + 18513.8i −0.00298808 + 0.239555i
\(279\) 898.734i 0.0115458i
\(280\) 0 0
\(281\) 83688.9 1.05988 0.529938 0.848036i \(-0.322215\pi\)
0.529938 + 0.848036i \(0.322215\pi\)
\(282\) 60791.6 + 758.281i 0.764443 + 0.00953524i
\(283\) 99210.9i 1.23876i 0.785092 + 0.619379i \(0.212616\pi\)
−0.785092 + 0.619379i \(0.787384\pi\)
\(284\) −1843.81 + 73897.9i −0.0228602 + 0.916211i
\(285\) 0 0
\(286\) 8.09419 648.914i 9.89558e−5 0.00793332i
\(287\) 5450.65i 0.0661735i
\(288\) −27594.3 1723.12i −0.332685 0.0207745i
\(289\) −48641.2 −0.582383
\(290\) 0 0
\(291\) 62973.6i 0.743657i
\(292\) −111312. 2777.31i −1.30549 0.0325731i
\(293\) 5554.90 0.0647054 0.0323527 0.999477i \(-0.489700\pi\)
0.0323527 + 0.999477i \(0.489700\pi\)
\(294\) −299.682 + 24025.6i −0.00346710 + 0.277958i
\(295\) 0 0
\(296\) −39860.3 1492.20i −0.454943 0.0170312i
\(297\) −554.392 −0.00628498
\(298\) 140504. + 1752.57i 1.58219 + 0.0197353i
\(299\) 19392.8i 0.216919i
\(300\) 0 0
\(301\) −94396.6 −1.04189
\(302\) 2060.94 165226.i 0.0225971 1.81161i
\(303\) 37366.6i 0.407004i
\(304\) −7416.67 + 148533.i −0.0802531 + 1.60723i
\(305\) 0 0
\(306\) −20168.6 251.573i −0.215394 0.00268671i
\(307\) 25814.0i 0.273891i 0.990579 + 0.136946i \(0.0437286\pi\)
−0.990579 + 0.136946i \(0.956271\pi\)
\(308\) 2230.16 + 55.6443i 0.0235091 + 0.000586569i
\(309\) 52946.8 0.554527
\(310\) 0 0
\(311\) 106750.i 1.10369i 0.833947 + 0.551844i \(0.186076\pi\)
−0.833947 + 0.551844i \(0.813924\pi\)
\(312\) −510.782 + 13644.2i −0.00524718 + 0.140165i
\(313\) −76334.9 −0.779174 −0.389587 0.920990i \(-0.627382\pi\)
−0.389587 + 0.920990i \(0.627382\pi\)
\(314\) 14326.7 + 178.704i 0.145307 + 0.00181248i
\(315\) 0 0
\(316\) −2696.44 + 108071.i −0.0270033 + 1.08226i
\(317\) −108286. −1.07759 −0.538794 0.842437i \(-0.681120\pi\)
−0.538794 + 0.842437i \(0.681120\pi\)
\(318\) −980.456 + 78603.4i −0.00969558 + 0.777298i
\(319\) 3870.22i 0.0380324i
\(320\) 0 0
\(321\) 112491. 1.09171
\(322\) −66658.9 831.466i −0.642904 0.00801923i
\(323\) 108496.i 1.03994i
\(324\) 11660.4 + 290.935i 0.111077 + 0.00277145i
\(325\) 0 0
\(326\) 746.830 59873.6i 0.00702727 0.563378i
\(327\) 55368.1i 0.517802i
\(328\) 9879.69 + 369.855i 0.0918323 + 0.00343782i
\(329\) 103209. 0.953508
\(330\) 0 0
\(331\) 109078.i 0.995590i 0.867295 + 0.497795i \(0.165857\pi\)
−0.867295 + 0.497795i \(0.834143\pi\)
\(332\) 1940.43 77770.3i 0.0176044 0.705565i
\(333\) 16827.8 0.151754
\(334\) −624.123 + 50036.1i −0.00559471 + 0.448529i
\(335\) 0 0
\(336\) −46877.2 2340.70i −0.415225 0.0207333i
\(337\) 152574. 1.34345 0.671725 0.740801i \(-0.265554\pi\)
0.671725 + 0.740801i \(0.265554\pi\)
\(338\) −107493. 1340.81i −0.940906 0.0117363i
\(339\) 51317.6i 0.446546i
\(340\) 0 0
\(341\) −131.534 −0.00113118
\(342\) 782.531 62735.7i 0.00669036 0.536368i
\(343\) 125507.i 1.06679i
\(344\) −6405.30 + 171101.i −0.0541281 + 1.44589i
\(345\) 0 0
\(346\) 205448. + 2562.64i 1.71612 + 0.0214060i
\(347\) 168701.i 1.40107i 0.713618 + 0.700535i \(0.247055\pi\)
−0.713618 + 0.700535i \(0.752945\pi\)
\(348\) 2031.02 81401.2i 0.0167709 0.672159i
\(349\) −19680.8 −0.161582 −0.0807910 0.996731i \(-0.525745\pi\)
−0.0807910 + 0.996731i \(0.525745\pi\)
\(350\) 0 0
\(351\) 5760.17i 0.0467542i
\(352\) 252.187 4038.56i 0.00203535 0.0325942i
\(353\) 55058.2 0.441848 0.220924 0.975291i \(-0.429093\pi\)
0.220924 + 0.975291i \(0.429093\pi\)
\(354\) −72482.4 904.105i −0.578397 0.00721460i
\(355\) 0 0
\(356\) 8216.75 + 205.014i 0.0648336 + 0.00161765i
\(357\) −34241.2 −0.268666
\(358\) −1496.16 + 119948.i −0.0116738 + 0.935894i
\(359\) 73206.8i 0.568019i −0.958822 0.284009i \(-0.908335\pi\)
0.958822 0.284009i \(-0.0916647\pi\)
\(360\) 0 0
\(361\) −207161. −1.58962
\(362\) −189650. 2365.59i −1.44722 0.0180519i
\(363\) 75995.7i 0.576735i
\(364\) −578.148 + 23171.6i −0.00436351 + 0.174885i
\(365\) 0 0
\(366\) 126.647 10153.3i 0.000945435 0.0757958i
\(367\) 156333.i 1.16069i 0.814370 + 0.580346i \(0.197083\pi\)
−0.814370 + 0.580346i \(0.802917\pi\)
\(368\) −6030.24 + 120768.i −0.0445286 + 0.891774i
\(369\) −4170.91 −0.0306322
\(370\) 0 0
\(371\) 133449.i 0.969542i
\(372\) 2766.52 + 69.0269i 0.0199916 + 0.000498807i
\(373\) −233763. −1.68019 −0.840096 0.542438i \(-0.817501\pi\)
−0.840096 + 0.542438i \(0.817501\pi\)
\(374\) 36.8189 2951.78i 0.000263225 0.0211028i
\(375\) 0 0
\(376\) 7003.24 187073.i 0.0495363 1.32323i
\(377\) −40211.8 −0.282925
\(378\) 19799.4 + 246.967i 0.138570 + 0.00172844i
\(379\) 25001.6i 0.174056i −0.996206 0.0870282i \(-0.972263\pi\)
0.996206 0.0870282i \(-0.0277370\pi\)
\(380\) 0 0
\(381\) 103781. 0.714938
\(382\) 2046.92 164102.i 0.0140273 1.12457i
\(383\) 165132.i 1.12573i 0.826549 + 0.562864i \(0.190301\pi\)
−0.826549 + 0.562864i \(0.809699\pi\)
\(384\) −7423.55 + 84809.5i −0.0503442 + 0.575151i
\(385\) 0 0
\(386\) −176709. 2204.17i −1.18600 0.0147935i
\(387\) 72233.6i 0.482300i
\(388\) 193848. + 4836.66i 1.28765 + 0.0321279i
\(389\) 46311.3 0.306047 0.153023 0.988223i \(-0.451099\pi\)
0.153023 + 0.988223i \(0.451099\pi\)
\(390\) 0 0
\(391\) 88214.1i 0.577012i
\(392\) 73933.7 + 2767.77i 0.481138 + 0.0180118i
\(393\) 159696. 1.03398
\(394\) 34894.4 + 435.254i 0.224783 + 0.00280382i
\(395\) 0 0
\(396\) −42.5798 + 1706.55i −0.000271527 + 0.0108825i
\(397\) 244029. 1.54832 0.774161 0.632989i \(-0.218172\pi\)
0.774161 + 0.632989i \(0.218172\pi\)
\(398\) −335.309 + 26881.8i −0.00211680 + 0.169704i
\(399\) 106509.i 0.669024i
\(400\) 0 0
\(401\) 102342. 0.636451 0.318225 0.948015i \(-0.396913\pi\)
0.318225 + 0.948015i \(0.396913\pi\)
\(402\) 155697. + 1942.08i 0.963447 + 0.0120175i
\(403\) 1366.65i 0.00841487i
\(404\) −115023. 2869.92i −0.704732 0.0175836i
\(405\) 0 0
\(406\) 1724.08 138220.i 0.0104594 0.838531i
\(407\) 2462.84i 0.0148678i
\(408\) −2323.45 + 62064.7i −0.0139576 + 0.372842i
\(409\) −110640. −0.661405 −0.330702 0.943735i \(-0.607286\pi\)
−0.330702 + 0.943735i \(0.607286\pi\)
\(410\) 0 0
\(411\) 37293.0i 0.220772i
\(412\) 4066.56 162983.i 0.0239570 0.960171i
\(413\) −123057. −0.721448
\(414\) 636.250 51008.3i 0.00371216 0.297605i
\(415\) 0 0
\(416\) 41960.9 + 2620.25i 0.242470 + 0.0151410i
\(417\) −24052.0 −0.138318
\(418\) 9181.69 + 114.527i 0.0525497 + 0.000655475i
\(419\) 2345.08i 0.0133576i 0.999978 + 0.00667882i \(0.00212595\pi\)
−0.999978 + 0.00667882i \(0.997874\pi\)
\(420\) 0 0
\(421\) −158819. −0.896062 −0.448031 0.894018i \(-0.647875\pi\)
−0.448031 + 0.894018i \(0.647875\pi\)
\(422\) 424.154 34004.6i 0.00238176 0.190947i
\(423\) 78976.7i 0.441386i
\(424\) 241885. + 9055.18i 1.34548 + 0.0503693i
\(425\) 0 0
\(426\) −96018.6 1197.68i −0.529098 0.00659968i
\(427\) 17237.7i 0.0945419i
\(428\) 8639.79 346274.i 0.0471646 1.89030i
\(429\) 843.029 0.00458066
\(430\) 0 0
\(431\) 269669.i 1.45170i −0.687853 0.725850i \(-0.741447\pi\)
0.687853 0.725850i \(-0.258553\pi\)
\(432\) 1791.14 35871.1i 0.00959758 0.192211i
\(433\) 161609. 0.861967 0.430983 0.902360i \(-0.358167\pi\)
0.430983 + 0.902360i \(0.358167\pi\)
\(434\) 4697.58 + 58.5951i 0.0249399 + 0.000311087i
\(435\) 0 0
\(436\) 170436. + 4252.52i 0.896580 + 0.0223704i
\(437\) −274395. −1.43686
\(438\) 1804.06 144632.i 0.00940376 0.753903i
\(439\) 171500.i 0.889885i −0.895559 0.444943i \(-0.853224\pi\)
0.895559 0.444943i \(-0.146776\pi\)
\(440\) 0 0
\(441\) −31212.6 −0.160492
\(442\) 30669.2 + 382.551i 0.156985 + 0.00195814i
\(443\) 78491.9i 0.399961i −0.979800 0.199980i \(-0.935912\pi\)
0.979800 0.199980i \(-0.0640878\pi\)
\(444\) 1292.45 51800.2i 0.00655616 0.262764i
\(445\) 0 0
\(446\) 1441.16 115538.i 0.00724505 0.580838i
\(447\) 182535.i 0.913546i
\(448\) −10805.6 + 144120.i −0.0538387 + 0.718071i
\(449\) −256874. −1.27417 −0.637085 0.770794i \(-0.719860\pi\)
−0.637085 + 0.770794i \(0.719860\pi\)
\(450\) 0 0
\(451\) 610.434i 0.00300113i
\(452\) 157968. + 3941.42i 0.773200 + 0.0192919i
\(453\) 214652. 1.04602
\(454\) 881.170 70643.7i 0.00427512 0.342738i
\(455\) 0 0
\(456\) −193056. 7227.21i −0.928438 0.0347569i
\(457\) 182963. 0.876053 0.438027 0.898962i \(-0.355678\pi\)
0.438027 + 0.898962i \(0.355678\pi\)
\(458\) −398632. 4972.32i −1.90038 0.0237043i
\(459\) 26201.9i 0.124368i
\(460\) 0 0
\(461\) 328023. 1.54348 0.771742 0.635936i \(-0.219386\pi\)
0.771742 + 0.635936i \(0.219386\pi\)
\(462\) −36.1449 + 2897.74i −0.000169341 + 0.0135761i
\(463\) 288300.i 1.34488i −0.740153 0.672439i \(-0.765247\pi\)
0.740153 0.672439i \(-0.234753\pi\)
\(464\) −250417. 12504.0i −1.16313 0.0580780i
\(465\) 0 0
\(466\) 290213. + 3619.96i 1.33643 + 0.0166699i
\(467\) 187893.i 0.861542i 0.902461 + 0.430771i \(0.141758\pi\)
−0.902461 + 0.430771i \(0.858242\pi\)
\(468\) −17731.2 442.407i −0.0809555 0.00201990i
\(469\) 264334. 1.20173
\(470\) 0 0
\(471\) 18612.4i 0.0838998i
\(472\) −8350.03 + 223049.i −0.0374804 + 1.00119i
\(473\) 10571.7 0.0472525
\(474\) −140420. 1751.53i −0.624991 0.00779579i
\(475\) 0 0
\(476\) −2629.88 + 105403.i −0.0116071 + 0.465199i
\(477\) −102117. −0.448808
\(478\) 3502.70 280812.i 0.0153302 1.22902i
\(479\) 42484.8i 0.185167i −0.995705 0.0925833i \(-0.970488\pi\)
0.995705 0.0925833i \(-0.0295125\pi\)
\(480\) 0 0
\(481\) −25589.1 −0.110602
\(482\) −205746. 2566.36i −0.885599 0.0110465i
\(483\) 86599.2i 0.371210i
\(484\) 233933. + 5836.82i 0.998623 + 0.0249164i
\(485\) 0 0
\(486\) −188.983 + 15150.8i −0.000800110 + 0.0641450i
\(487\) 115941.i 0.488854i 0.969668 + 0.244427i \(0.0785998\pi\)
−0.969668 + 0.244427i \(0.921400\pi\)
\(488\) −31244.6 1169.67i −0.131200 0.00491160i
\(489\) 77784.1 0.325292
\(490\) 0 0
\(491\) 254668.i 1.05636i 0.849133 + 0.528179i \(0.177125\pi\)
−0.849133 + 0.528179i \(0.822875\pi\)
\(492\) −320.345 + 12839.1i −0.00132339 + 0.0530400i
\(493\) −182916. −0.752588
\(494\) −1189.95 + 95398.3i −0.00487611 + 0.390919i
\(495\) 0 0
\(496\) 424.963 8510.73i 0.00172738 0.0345942i
\(497\) −163015. −0.659956
\(498\) 101050. + 1260.44i 0.407454 + 0.00508235i
\(499\) 139763.i 0.561296i −0.959811 0.280648i \(-0.909451\pi\)
0.959811 0.280648i \(-0.0905494\pi\)
\(500\) 0 0
\(501\) −65003.9 −0.258979
\(502\) −3613.48 + 289694.i −0.0143390 + 1.14956i
\(503\) 416958.i 1.64800i −0.566592 0.823998i \(-0.691739\pi\)
0.566592 0.823998i \(-0.308261\pi\)
\(504\) 2280.91 60928.5i 0.00897940 0.239861i
\(505\) 0 0
\(506\) 7465.32 + 93.1183i 0.0291573 + 0.000363692i
\(507\) 139648.i 0.543275i
\(508\) 7970.87 319464.i 0.0308872 1.23792i
\(509\) −414530. −1.60000 −0.800000 0.600000i \(-0.795167\pi\)
−0.800000 + 0.600000i \(0.795167\pi\)
\(510\) 0 0
\(511\) 245548.i 0.940360i
\(512\) 260494. + 29365.3i 0.993706 + 0.112020i
\(513\) 81502.5 0.309696
\(514\) 310823. + 3877.04i 1.17649 + 0.0146749i
\(515\) 0 0
\(516\) −222353. 5547.87i −0.835108 0.0208366i
\(517\) −11558.6 −0.0432440
\(518\) 1097.13 87957.2i 0.00408882 0.327802i
\(519\) 266905.i 0.990882i
\(520\) 0 0
\(521\) 7651.52 0.0281885 0.0140943 0.999901i \(-0.495514\pi\)
0.0140943 + 0.999901i \(0.495514\pi\)
\(522\) 105768. + 1319.29i 0.388162 + 0.00484172i
\(523\) 120269.i 0.439692i −0.975535 0.219846i \(-0.929444\pi\)
0.975535 0.219846i \(-0.0705555\pi\)
\(524\) 12265.4 491585.i 0.0446704 1.79034i
\(525\) 0 0
\(526\) 135.536 10866.0i 0.000489873 0.0392732i
\(527\) 6216.62i 0.0223838i
\(528\) 5249.92 + 262.142i 0.0188315 + 0.000940305i
\(529\) 56739.5 0.202756
\(530\) 0 0
\(531\) 94164.7i 0.333964i
\(532\) −327862. 8180.40i −1.15842 0.0289036i
\(533\) 6342.45 0.0223256
\(534\) −133.171 + 10676.4i −0.000467011 + 0.0374404i
\(535\) 0 0
\(536\) 17936.4 479124.i 0.0624319 1.66770i
\(537\) −155829. −0.540381
\(538\) 266646. + 3325.99i 0.921234 + 0.0114910i
\(539\) 4568.12i 0.0157239i
\(540\) 0 0
\(541\) −479201. −1.63728 −0.818640 0.574307i \(-0.805272\pi\)
−0.818640 + 0.574307i \(0.805272\pi\)
\(542\) −3190.95 + 255820.i −0.0108623 + 0.870834i
\(543\) 246382.i 0.835619i
\(544\) 190872. + 11919.0i 0.644977 + 0.0402755i
\(545\) 0 0
\(546\) −30107.8 375.547i −0.100993 0.00125974i
\(547\) 327802.i 1.09556i −0.836622 0.547781i \(-0.815473\pi\)
0.836622 0.547781i \(-0.184527\pi\)
\(548\) −114797. 2864.28i −0.382269 0.00953792i
\(549\) 13190.6 0.0437641
\(550\) 0 0
\(551\) 568970.i 1.87407i
\(552\) −156967. 5876.20i −0.515147 0.0192850i
\(553\) −238398. −0.779566
\(554\) −145775. 1818.32i −0.474968 0.00592449i
\(555\) 0 0
\(556\) −1847.30 + 74037.8i −0.00597569 + 0.239499i
\(557\) 131341. 0.423342 0.211671 0.977341i \(-0.432109\pi\)
0.211671 + 0.977341i \(0.432109\pi\)
\(558\) −44.8378 + 3594.66i −0.000144004 + 0.0115449i
\(559\) 109841.i 0.351513i
\(560\) 0 0
\(561\) 3834.78 0.0121847
\(562\) 334730. + 4175.23i 1.05979 + 0.0132193i
\(563\) 137401.i 0.433485i 0.976229 + 0.216742i \(0.0695432\pi\)
−0.976229 + 0.216742i \(0.930457\pi\)
\(564\) 243110. + 6065.77i 0.764265 + 0.0190690i
\(565\) 0 0
\(566\) −4949.62 + 396813.i −0.0154504 + 1.23866i
\(567\) 25722.2i 0.0800096i
\(568\) −11061.4 + 295477.i −0.0342858 + 0.915855i
\(569\) 152095. 0.469775 0.234887 0.972023i \(-0.424528\pi\)
0.234887 + 0.972023i \(0.424528\pi\)
\(570\) 0 0
\(571\) 150818.i 0.462573i −0.972886 0.231286i \(-0.925707\pi\)
0.972886 0.231286i \(-0.0742935\pi\)
\(572\) 64.7485 2595.05i 0.000197896 0.00793147i
\(573\) 213191. 0.649322
\(574\) −271.932 + 21800.9i −0.000825348 + 0.0661684i
\(575\) 0 0
\(576\) −110282. 8268.63i −0.332400 0.0249223i
\(577\) 258173. 0.775461 0.387730 0.921773i \(-0.373259\pi\)
0.387730 + 0.921773i \(0.373259\pi\)
\(578\) −194550. 2426.71i −0.582338 0.00726376i
\(579\) 229569.i 0.684788i
\(580\) 0 0
\(581\) 171557. 0.508226
\(582\) −3141.75 + 251875.i −0.00927524 + 0.743599i
\(583\) 14945.3i 0.0439711i
\(584\) −445073. 16661.7i −1.30499 0.0488533i
\(585\) 0 0
\(586\) 22217.9 + 277.133i 0.0647004 + 0.000807037i
\(587\) 574134.i 1.66624i −0.553095 0.833118i \(-0.686553\pi\)
0.553095 0.833118i \(-0.313447\pi\)
\(588\) −2397.27 + 96080.0i −0.00693366 + 0.277894i
\(589\) 19337.2 0.0557394
\(590\) 0 0
\(591\) 45332.7i 0.129789i
\(592\) −159354. 7956.98i −0.454695 0.0227041i
\(593\) −275339. −0.782995 −0.391497 0.920179i \(-0.628043\pi\)
−0.391497 + 0.920179i \(0.628043\pi\)
\(594\) −2217.39 27.6586i −0.00628449 7.83893e-5i
\(595\) 0 0
\(596\) 561886. + 14019.5i 1.58182 + 0.0394675i
\(597\) −34923.2 −0.0979864
\(598\) −967.506 + 77565.2i −0.00270552 + 0.216903i
\(599\) 86528.9i 0.241161i −0.992704 0.120581i \(-0.961524\pi\)
0.992704 0.120581i \(-0.0384756\pi\)
\(600\) 0 0
\(601\) −391085. −1.08273 −0.541367 0.840786i \(-0.682093\pi\)
−0.541367 + 0.840786i \(0.682093\pi\)
\(602\) −377557. 4709.44i −1.04181 0.0129950i
\(603\) 202272.i 0.556290i
\(604\) 16486.3 660752.i 0.0451906 1.81119i
\(605\) 0 0
\(606\) 1864.22 149455.i 0.00507634 0.406972i
\(607\) 86135.8i 0.233779i 0.993145 + 0.116890i \(0.0372924\pi\)
−0.993145 + 0.116890i \(0.962708\pi\)
\(608\) −37074.7 + 593718.i −0.100293 + 1.60610i
\(609\) 179567. 0.484164
\(610\) 0 0
\(611\) 120095.i 0.321694i
\(612\) −80655.8 2012.42i −0.215344 0.00537300i
\(613\) 161510. 0.429811 0.214906 0.976635i \(-0.431056\pi\)
0.214906 + 0.976635i \(0.431056\pi\)
\(614\) −1287.86 + 103248.i −0.00341610 + 0.273870i
\(615\) 0 0
\(616\) 8917.19 + 333.823i 0.0234999 + 0.000879740i
\(617\) −3300.03 −0.00866857 −0.00433428 0.999991i \(-0.501380\pi\)
−0.00433428 + 0.999991i \(0.501380\pi\)
\(618\) 211771. + 2641.51i 0.554484 + 0.00691633i
\(619\) 670945.i 1.75108i 0.483147 + 0.875539i \(0.339494\pi\)
−0.483147 + 0.875539i \(0.660506\pi\)
\(620\) 0 0
\(621\) 66266.9 0.171836
\(622\) −5325.74 + 426966.i −0.0137657 + 1.10360i
\(623\) 18125.8i 0.0467003i
\(624\) −2723.67 + 54547.0i −0.00699497 + 0.140088i
\(625\) 0 0
\(626\) −305316. 3808.34i −0.779113 0.00971822i
\(627\) 11928.3i 0.0303419i
\(628\) 57293.6 + 1429.52i 0.145274 + 0.00362469i
\(629\) −116400. −0.294205
\(630\) 0 0
\(631\) 563090.i 1.41423i −0.707100 0.707113i \(-0.749997\pi\)
0.707100 0.707113i \(-0.250003\pi\)
\(632\) −16176.6 + 432114.i −0.0404997 + 1.08184i
\(633\) 44176.7 0.110252
\(634\) −433110. 5402.37i −1.07750 0.0134402i
\(635\) 0 0
\(636\) −7843.04 + 314340.i −0.0193897 + 0.777116i
\(637\) 47463.1 0.116971
\(638\) −193.085 + 15479.7i −0.000474358 + 0.0380295i
\(639\) 124742.i 0.305499i
\(640\) 0 0
\(641\) 758985. 1.84721 0.923607 0.383341i \(-0.125226\pi\)
0.923607 + 0.383341i \(0.125226\pi\)
\(642\) 449928. + 5612.15i 1.09162 + 0.0136163i
\(643\) 572545.i 1.38480i 0.721513 + 0.692401i \(0.243447\pi\)
−0.721513 + 0.692401i \(0.756553\pi\)
\(644\) −266573. 6651.21i −0.642754 0.0160372i
\(645\) 0 0
\(646\) −5412.83 + 433948.i −0.0129706 + 1.03986i
\(647\) 263241.i 0.628847i −0.949283 0.314423i \(-0.898189\pi\)
0.949283 0.314423i \(-0.101811\pi\)
\(648\) 46623.3 + 1745.39i 0.111033 + 0.00415663i
\(649\) 13781.5 0.0327195
\(650\) 0 0
\(651\) 6102.82i 0.0144002i
\(652\) 5974.18 239439.i 0.0140534 0.563247i
\(653\) −224745. −0.527065 −0.263532 0.964651i \(-0.584888\pi\)
−0.263532 + 0.964651i \(0.584888\pi\)
\(654\) −2762.31 + 221455.i −0.00645827 + 0.517762i
\(655\) 0 0
\(656\) 39497.2 + 1972.20i 0.0917823 + 0.00458293i
\(657\) 187897. 0.435300
\(658\) 412803. + 5149.07i 0.953434 + 0.0118926i
\(659\) 778617.i 1.79289i 0.443158 + 0.896444i \(0.353858\pi\)
−0.443158 + 0.896444i \(0.646142\pi\)
\(660\) 0 0
\(661\) 339420. 0.776844 0.388422 0.921482i \(-0.373020\pi\)
0.388422 + 0.921482i \(0.373020\pi\)
\(662\) −5441.88 + 436277.i −0.0124175 + 0.995512i
\(663\) 39843.6i 0.0906424i
\(664\) 11641.1 310960.i 0.0264032 0.705291i
\(665\) 0 0
\(666\) 67306.1 + 839.539i 0.151742 + 0.00189275i
\(667\) 462610.i 1.03983i
\(668\) −4992.60 + 200098.i −0.0111885 + 0.448425i
\(669\) 150100. 0.335373
\(670\) 0 0
\(671\) 1930.50i 0.00428771i
\(672\) −187378. 11700.8i −0.414934 0.0259105i
\(673\) −20796.2 −0.0459149 −0.0229574 0.999736i \(-0.507308\pi\)
−0.0229574 + 0.999736i \(0.507308\pi\)
\(674\) 610250. + 7611.92i 1.34335 + 0.0167561i
\(675\) 0 0
\(676\) −429871. 10725.6i −0.940686 0.0234709i
\(677\) −202957. −0.442820 −0.221410 0.975181i \(-0.571066\pi\)
−0.221410 + 0.975181i \(0.571066\pi\)
\(678\) −2560.23 + 205254.i −0.00556954 + 0.446512i
\(679\) 427619.i 0.927508i
\(680\) 0 0
\(681\) 91776.0 0.197895
\(682\) −526.096 6.56223i −0.00113109 1.41086e-5i
\(683\) 74248.4i 0.159164i 0.996828 + 0.0795821i \(0.0253586\pi\)
−0.996828 + 0.0795821i \(0.974641\pi\)
\(684\) 6259.76 250884.i 0.0133797 0.536243i
\(685\) 0 0
\(686\) −6261.52 + 501988.i −0.0133055 + 1.06671i
\(687\) 517879.i 1.09727i
\(688\) −34155.4 + 684029.i −0.0721577 + 1.44510i
\(689\) 155283. 0.327103
\(690\) 0 0
\(691\) 628006.i 1.31525i 0.753346 + 0.657624i \(0.228438\pi\)
−0.753346 + 0.657624i \(0.771562\pi\)
\(692\) 821599. + 20499.5i 1.71572 + 0.0428086i
\(693\) −3764.57 −0.00783879
\(694\) −8416.50 + 674753.i −0.0174748 + 1.40096i
\(695\) 0 0
\(696\) 12184.6 325478.i 0.0251531 0.671898i
\(697\) 28850.6 0.0593866
\(698\) −78717.3 981.876i −0.161569 0.00201533i
\(699\) 377028.i 0.771647i
\(700\) 0 0
\(701\) −508002. −1.03378 −0.516892 0.856051i \(-0.672911\pi\)
−0.516892 + 0.856051i \(0.672911\pi\)
\(702\) 287.374 23038.9i 0.000583141 0.0467506i
\(703\) 362068.i 0.732620i
\(704\) 1210.15 16140.4i 0.00244172 0.0325663i
\(705\) 0 0
\(706\) 220216. + 2746.85i 0.441813 + 0.00551094i
\(707\) 253736.i 0.507626i
\(708\) −289862. 7232.28i −0.578262 0.0144281i
\(709\) −60762.6 −0.120877 −0.0604385 0.998172i \(-0.519250\pi\)
−0.0604385 + 0.998172i \(0.519250\pi\)
\(710\) 0 0
\(711\) 182426.i 0.360867i
\(712\) 32854.2 + 1229.93i 0.0648084 + 0.00242616i
\(713\) 15722.4 0.0309271
\(714\) −136954. 1708.29i −0.268645 0.00335093i
\(715\) 0 0
\(716\) −11968.4 + 479680.i −0.0233458 + 0.935676i
\(717\) 364814. 0.709633
\(718\) 3652.28 292804.i 0.00708460 0.567974i
\(719\) 240815.i 0.465828i 0.972497 + 0.232914i \(0.0748261\pi\)
−0.972497 + 0.232914i \(0.925174\pi\)
\(720\) 0 0
\(721\) 359533. 0.691621
\(722\) −828578. 10335.2i −1.58949 0.0198265i
\(723\) 267292.i 0.511340i
\(724\) −758422. 18923.2i −1.44689 0.0361009i
\(725\) 0 0
\(726\) −3791.42 + 303959.i −0.00719331 + 0.576690i
\(727\) 447387.i 0.846476i −0.906018 0.423238i \(-0.860893\pi\)
0.906018 0.423238i \(-0.139107\pi\)
\(728\) −3468.44 + 92650.2i −0.00654442 + 0.174817i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 499646.i 0.935035i
\(732\) 1013.09 40603.7i 0.00189072 0.0757781i
\(733\) 855174. 1.59165 0.795823 0.605529i \(-0.207039\pi\)
0.795823 + 0.605529i \(0.207039\pi\)
\(734\) −7799.41 + 625282.i −0.0144767 + 1.16060i
\(735\) 0 0
\(736\) −30144.2 + 482732.i −0.0556478 + 0.891149i
\(737\) −29603.5 −0.0545015
\(738\) −16682.4 208.086i −0.0306298 0.000382059i
\(739\) 234148.i 0.428747i −0.976752 0.214374i \(-0.931229\pi\)
0.976752 0.214374i \(-0.0687710\pi\)
\(740\) 0 0
\(741\) −123936. −0.225715
\(742\) −6657.74 + 533753.i −0.0120926 + 0.969466i
\(743\) 242702.i 0.439639i −0.975541 0.219819i \(-0.929453\pi\)
0.975541 0.219819i \(-0.0705468\pi\)
\(744\) 11061.8 + 414.108i 0.0199839 + 0.000748113i
\(745\) 0 0
\(746\) −934981. 11662.4i −1.68006 0.0209562i
\(747\) 131278.i 0.235262i
\(748\) 294.528 11804.4i 0.000526409 0.0210979i
\(749\) 763863. 1.36161
\(750\) 0 0
\(751\) 328095.i 0.581728i −0.956764 0.290864i \(-0.906057\pi\)
0.956764 0.290864i \(-0.0939428\pi\)
\(752\) 37343.9 747885.i 0.0660364 1.32251i
\(753\) −376353. −0.663751
\(754\) −160835. 2006.16i −0.282903 0.00352877i
\(755\) 0 0
\(756\) 79179.2 + 1975.58i 0.138538 + 0.00345662i
\(757\) −270737. −0.472450 −0.236225 0.971698i \(-0.575910\pi\)
−0.236225 + 0.971698i \(0.575910\pi\)
\(758\) 1247.33 99998.8i 0.00217092 0.174043i
\(759\) 9698.49i 0.0168353i
\(760\) 0 0
\(761\) −718672. −1.24097 −0.620485 0.784218i \(-0.713064\pi\)
−0.620485 + 0.784218i \(0.713064\pi\)
\(762\) 415092. + 5177.63i 0.714883 + 0.00891705i
\(763\) 375974.i 0.645816i
\(764\) 16374.0 656254.i 0.0280524 1.12431i
\(765\) 0 0
\(766\) −8238.42 + 660476.i −0.0140406 + 1.12564i
\(767\) 143190.i 0.243401i
\(768\) −33923.0 + 338841.i −0.0575138 + 0.574478i
\(769\) −654646. −1.10702 −0.553508 0.832844i \(-0.686711\pi\)
−0.553508 + 0.832844i \(0.686711\pi\)
\(770\) 0 0
\(771\) 403803.i 0.679298i
\(772\) −706670. 17632.0i −1.18572 0.0295846i
\(773\) −547589. −0.916423 −0.458211 0.888843i \(-0.651510\pi\)
−0.458211 + 0.888843i \(0.651510\pi\)
\(774\) 3603.73 288912.i 0.00601548 0.482263i
\(775\) 0 0
\(776\) 775091. + 29016.2i 1.28715 + 0.0481856i
\(777\) 114269. 0.189271
\(778\) 185231. + 2310.46i 0.306023 + 0.00381716i
\(779\) 89741.3i 0.147883i
\(780\) 0 0
\(781\) 18256.5 0.0299307
\(782\) −4400.99 + 352829.i −0.00719676 + 0.576967i
\(783\) 137407.i