Properties

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

$q$-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 \(-0.882762\pi\)
0.932936 0.360043i \(-0.117238\pi\)
\(8\) 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 \(0.00519787\pi\)
−0.999867 + 0.0163289i \(0.994802\pi\)
\(12\) −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 \(-0.702372\pi\)
0.593798 0.804614i \(-0.297628\pi\)
\(20\) 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 \(-0.852691\pi\)
0.894812 0.446443i \(-0.147309\pi\)
\(24\) −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 \(0.00551298\pi\)
−0.999850 + 0.0173187i \(0.994487\pi\)
\(32\) 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 \(-0.742555\pi\)
0.690377 0.723450i \(-0.257445\pi\)
\(44\) 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 \(0.230326\pi\)
−0.749434 + 0.662079i \(0.769674\pi\)
\(48\) −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 \(-0.832986\pi\)
0.865479 0.500945i \(-0.167014\pi\)
\(60\) 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 \(0.314206\pi\)
−0.551107 + 0.834435i \(0.685794\pi\)
\(68\) 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 \(-0.848477\pi\)
0.888824 0.458248i \(-0.151523\pi\)
\(72\) −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 \(-0.817932\pi\)
0.840829 0.541300i \(-0.182068\pi\)
\(80\) 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 \(0.114802\pi\)
−0.935664 + 0.352893i \(0.885198\pi\)
\(84\) −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 \(0.159449\pi\)
−0.877140 + 0.480235i \(0.840551\pi\)
\(104\) 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 \(0.394374\pi\)
−0.325777 + 0.945446i \(0.605626\pi\)
\(108\) 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 \(0.212525\pi\)
−0.785269 + 0.619155i \(0.787475\pi\)
\(128\) 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 \(0.353145\pi\)
−0.445164 + 0.895449i \(0.646855\pi\)
\(132\) 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 \(-0.961779\pi\)
0.992800 0.119787i \(-0.0382211\pi\)
\(140\) 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 \(0.360788\pi\)
−0.423539 + 0.905878i \(0.639212\pi\)
\(152\) −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 \(0.0909020\pi\)
−0.959499 + 0.281711i \(0.909098\pi\)
\(164\) 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 \(-0.927996\pi\)
0.974524 0.224282i \(-0.0720037\pi\)
\(168\) −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 \(-0.844981\pi\)
0.883737 0.467984i \(-0.155019\pi\)
\(180\) 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 \(0.190095\pi\)
−0.826914 + 0.562329i \(0.809905\pi\)
\(192\) −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 \(-0.972956\pi\)
0.996393 0.0848587i \(-0.0270439\pi\)
\(200\) 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 \(0.0304389\pi\)
−0.995431 + 0.0954808i \(0.969561\pi\)
\(212\) 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 \(0.0938022\pi\)
−0.956893 + 0.290442i \(0.906198\pi\)
\(224\) −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 \(0.0548233\pi\)
−0.985205 + 0.171382i \(0.945177\pi\)
\(228\) −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 \(0.210666\pi\)
−0.788870 + 0.614560i \(0.789334\pi\)
\(240\) 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 \(-0.805070\pi\)
0.818276 0.574825i \(-0.194930\pi\)
\(252\) 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 \(0.00625142\pi\)
−0.999807 + 0.0196382i \(0.993749\pi\)
\(264\) 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 \(-0.856589\pi\)
0.900212 0.435451i \(-0.143411\pi\)
\(272\) 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 \(-0.787384\pi\)
0.785092 0.619379i \(-0.212616\pi\)
\(284\) −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 \(-0.956271\pi\)
0.990579 0.136946i \(-0.0437286\pi\)
\(308\) 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 \(-0.813924\pi\)
0.833947 0.551844i \(-0.186076\pi\)
\(312\) −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 \(-0.834143\pi\)
0.867295 0.497795i \(-0.165857\pi\)
\(332\) 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 \(-0.752945\pi\)
0.713618 0.700535i \(-0.247055\pi\)
\(348\) 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 \(0.0916647\pi\)
−0.958822 + 0.284009i \(0.908335\pi\)
\(360\) 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 \(-0.802917\pi\)
0.814370 0.580346i \(-0.197083\pi\)
\(368\) −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 \(0.0277370\pi\)
−0.996206 + 0.0870282i \(0.972263\pi\)
\(380\) 0 0
\(381\) 103781. 0.714938
\(382\) 2046.92 + 164102.i 0.0140273 + 1.12457i
\(383\) 165132.i 1.12573i −0.826549 0.562864i \(-0.809699\pi\)
0.826549 0.562864i \(-0.190301\pi\)
\(384\) −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 \(-0.997874\pi\)
0.999978 0.00667882i \(-0.00212595\pi\)
\(420\) 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 \(0.258553\pi\)
−0.687853 + 0.725850i \(0.741447\pi\)
\(432\) 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 \(0.146776\pi\)
−0.895559 + 0.444943i \(0.853224\pi\)
\(440\) 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 \(0.0640878\pi\)
−0.979800 + 0.199980i \(0.935912\pi\)
\(444\) 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 \(0.234753\pi\)
−0.740153 + 0.672439i \(0.765247\pi\)
\(464\) −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 \(-0.858242\pi\)
0.902461 0.430771i \(-0.141758\pi\)
\(468\) −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 \(0.0295125\pi\)
−0.995705 + 0.0925833i \(0.970488\pi\)
\(480\) 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 \(-0.921400\pi\)
0.969668 0.244427i \(-0.0785998\pi\)
\(488\) −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 \(-0.822875\pi\)
0.849133 0.528179i \(-0.177125\pi\)
\(492\) −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 \(0.0905494\pi\)
−0.959811 + 0.280648i \(0.909451\pi\)
\(500\) 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 \(0.308261\pi\)
−0.566592 + 0.823998i \(0.691739\pi\)
\(504\) 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 \(0.0705555\pi\)
−0.975535 + 0.219846i \(0.929444\pi\)
\(524\) 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 \(0.184527\pi\)
−0.836622 + 0.547781i \(0.815473\pi\)
\(548\) −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 \(-0.930457\pi\)
0.976229 0.216742i \(-0.0695432\pi\)
\(564\) 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 \(0.0742935\pi\)
−0.972886 + 0.231286i \(0.925707\pi\)
\(572\) 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 \(0.313447\pi\)
−0.553095 + 0.833118i \(0.686553\pi\)
\(588\) −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 \(0.0384756\pi\)
−0.992704 + 0.120581i \(0.961524\pi\)
\(600\) 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 \(-0.962708\pi\)
0.993145 0.116890i \(-0.0372924\pi\)
\(608\) −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 \(-0.660506\pi\)
0.483147 0.875539i \(-0.339494\pi\)
\(620\) 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 \(0.250003\pi\)
−0.707100 + 0.707113i \(0.749997\pi\)
\(632\) −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 \(-0.756553\pi\)
0.721513 0.692401i \(-0.243447\pi\)
\(644\) −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 \(0.101811\pi\)
−0.949283 + 0.314423i \(0.898189\pi\)
\(648\) 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 \(-0.646142\pi\)
0.443158 0.896444i \(-0.353858\pi\)
\(660\) 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 \(-0.974641\pi\)
0.996828 0.0795821i \(-0.0253586\pi\)
\(684\) 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 \(-0.771562\pi\)
0.753346 0.657624i \(-0.228438\pi\)
\(692\) 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 \(-0.925174\pi\)
0.972497 0.232914i \(-0.0748261\pi\)
\(720\) 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 \(0.139107\pi\)
−0.906018 + 0.423238i \(0.860893\pi\)
\(728\) −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 \(0.0687710\pi\)
−0.976752 + 0.214374i \(0.931229\pi\)
\(740\) 0 0
\(741\) −123936. −0.225715
\(742\) −6657.74 533753.i −0.0120926 0.969466i
\(743\) 242702.i 0.439639i 0.975541 + 0.219819i \(0.0705468\pi\)
−0.975541 + 0.219819i \(0.929453\pi\)
\(744\) 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 \(0.0939428\pi\)
−0.956764 + 0.290864i \(0.906057\pi\)
\(752\) 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
\(783\)