Properties

Label 300.3.c.e.151.1
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4069419264.1
Defining polynomial: \(x^{8} - 7 x^{6} + 50 x^{4} - 84 x^{3} + 55 x^{2} - 12 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.1
Root \(1.65359 - 0.954702i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.e.151.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.97650 - 0.305673i) q^{2} -1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} +0.329898i q^{7} +(-7.16731 - 3.55383i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.97650 - 0.305673i) q^{2} -1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} +0.329898i q^{7} +(-7.16731 - 3.55383i) q^{8} -3.00000 q^{9} +20.4920i q^{11} +(2.09288 - 6.60453i) q^{12} -0.416712 q^{13} +(0.100841 - 0.652044i) q^{14} +(13.0799 + 9.21501i) q^{16} -18.5884 q^{17} +(5.92951 + 0.917019i) q^{18} -12.4503i q^{19} +0.571400 q^{21} +(6.26384 - 40.5024i) q^{22} +23.2304i q^{23} +(-6.15542 + 12.4141i) q^{24} +(0.823633 + 0.127378i) q^{26} +5.19615i q^{27} +(-0.398624 + 1.25794i) q^{28} -23.9166 q^{29} +42.0148i q^{31} +(-23.0357 - 22.2117i) q^{32} +35.4931 q^{33} +(36.7400 + 5.68197i) q^{34} +(-11.4394 - 3.62498i) q^{36} +50.9523 q^{37} +(-3.80573 + 24.6081i) q^{38} +0.721767i q^{39} +46.7073 q^{41} +(-1.12937 - 0.174661i) q^{42} +55.5866i q^{43} +(-24.7610 + 78.1385i) q^{44} +(7.10090 - 45.9149i) q^{46} +81.7616i q^{47} +(15.9609 - 22.6550i) q^{48} +48.8912 q^{49} +32.1960i q^{51} +(-1.58898 - 0.503524i) q^{52} -29.9744 q^{53} +(1.58832 - 10.2702i) q^{54} +(1.17240 - 2.36448i) q^{56} -21.5646 q^{57} +(47.2713 + 7.31067i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(12.8428 - 83.0424i) q^{62} -0.989693i q^{63} +(38.7406 + 50.9428i) q^{64} +(-70.1523 - 10.8493i) q^{66} +72.8008i q^{67} +(-70.8799 - 22.4608i) q^{68} +40.2362 q^{69} -39.2803i q^{71} +(21.5019 + 10.6615i) q^{72} -46.5814 q^{73} +(-100.707 - 15.5747i) q^{74} +(15.0441 - 47.4747i) q^{76} -6.76026 q^{77} +(0.220625 - 1.42657i) q^{78} -101.920i q^{79} +9.00000 q^{81} +(-92.3170 - 14.2771i) q^{82} +5.88913i q^{83} +(2.17882 + 0.690438i) q^{84} +(16.9913 - 109.867i) q^{86} +41.4248i q^{87} +(72.8250 - 146.872i) q^{88} -61.0100 q^{89} -0.137472i q^{91} +(-28.0699 + 88.5804i) q^{92} +72.7718 q^{93} +(24.9923 - 161.602i) q^{94} +(-38.4717 + 39.8989i) q^{96} +95.5437 q^{97} +(-96.6335 - 14.9447i) q^{98} -61.4759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} - 8q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 8q^{4} - 6q^{6} - 20q^{8} - 24q^{9} - 8q^{13} + 22q^{14} + 40q^{16} + 6q^{18} + 24q^{21} - 4q^{22} - 36q^{24} - 66q^{26} - 104q^{28} - 32q^{29} - 112q^{32} + 124q^{34} + 24q^{36} + 176q^{37} + 170q^{38} - 16q^{41} - 54q^{42} + 40q^{44} - 76q^{46} - 24q^{48} + 16q^{49} - 56q^{52} + 304q^{53} + 18q^{54} - 172q^{56} - 72q^{57} + 12q^{58} + 136q^{61} + 238q^{62} + 16q^{64} - 108q^{66} - 88q^{68} - 96q^{69} + 60q^{72} - 240q^{73} - 108q^{74} + 120q^{76} + 384q^{77} - 150q^{78} + 72q^{81} - 320q^{82} - 144q^{84} + 214q^{86} + 200q^{88} + 128q^{89} - 312q^{92} - 72q^{93} + 12q^{94} + 96q^{96} - 216q^{97} - 60q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97650 0.305673i −0.988251 0.152836i
\(3\) 1.73205i 0.577350i
\(4\) 3.81313 + 1.20833i 0.953282 + 0.302082i
\(5\) 0 0
\(6\) −0.529441 + 3.42340i −0.0882402 + 0.570567i
\(7\) 0.329898i 0.0471283i 0.999722 + 0.0235641i \(0.00750139\pi\)
−0.999722 + 0.0235641i \(0.992499\pi\)
\(8\) −7.16731 3.55383i −0.895913 0.444229i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 20.4920i 1.86291i 0.363861 + 0.931453i \(0.381458\pi\)
−0.363861 + 0.931453i \(0.618542\pi\)
\(12\) 2.09288 6.60453i 0.174407 0.550378i
\(13\) −0.416712 −0.0320548 −0.0160274 0.999872i \(-0.505102\pi\)
−0.0160274 + 0.999872i \(0.505102\pi\)
\(14\) 0.100841 0.652044i 0.00720292 0.0465746i
\(15\) 0 0
\(16\) 13.0799 + 9.21501i 0.817493 + 0.575938i
\(17\) −18.5884 −1.09343 −0.546717 0.837317i \(-0.684123\pi\)
−0.546717 + 0.837317i \(0.684123\pi\)
\(18\) 5.92951 + 0.917019i 0.329417 + 0.0509455i
\(19\) 12.4503i 0.655281i −0.944803 0.327640i \(-0.893747\pi\)
0.944803 0.327640i \(-0.106253\pi\)
\(20\) 0 0
\(21\) 0.571400 0.0272095
\(22\) 6.26384 40.5024i 0.284720 1.84102i
\(23\) 23.2304i 1.01002i 0.863114 + 0.505008i \(0.168511\pi\)
−0.863114 + 0.505008i \(0.831489\pi\)
\(24\) −6.15542 + 12.4141i −0.256476 + 0.517256i
\(25\) 0 0
\(26\) 0.823633 + 0.127378i 0.0316782 + 0.00489914i
\(27\) 5.19615i 0.192450i
\(28\) −0.398624 + 1.25794i −0.0142366 + 0.0449265i
\(29\) −23.9166 −0.824712 −0.412356 0.911023i \(-0.635294\pi\)
−0.412356 + 0.911023i \(0.635294\pi\)
\(30\) 0 0
\(31\) 42.0148i 1.35532i 0.735377 + 0.677658i \(0.237005\pi\)
−0.735377 + 0.677658i \(0.762995\pi\)
\(32\) −23.0357 22.2117i −0.719865 0.694115i
\(33\) 35.4931 1.07555
\(34\) 36.7400 + 5.68197i 1.08059 + 0.167117i
\(35\) 0 0
\(36\) −11.4394 3.62498i −0.317761 0.100694i
\(37\) 50.9523 1.37709 0.688545 0.725194i \(-0.258250\pi\)
0.688545 + 0.725194i \(0.258250\pi\)
\(38\) −3.80573 + 24.6081i −0.100151 + 0.647582i
\(39\) 0.721767i 0.0185068i
\(40\) 0 0
\(41\) 46.7073 1.13920 0.569601 0.821921i \(-0.307098\pi\)
0.569601 + 0.821921i \(0.307098\pi\)
\(42\) −1.12937 0.174661i −0.0268898 0.00415861i
\(43\) 55.5866i 1.29271i 0.763036 + 0.646356i \(0.223708\pi\)
−0.763036 + 0.646356i \(0.776292\pi\)
\(44\) −24.7610 + 78.1385i −0.562750 + 1.77588i
\(45\) 0 0
\(46\) 7.10090 45.9149i 0.154367 0.998151i
\(47\) 81.7616i 1.73961i 0.493397 + 0.869804i \(0.335755\pi\)
−0.493397 + 0.869804i \(0.664245\pi\)
\(48\) 15.9609 22.6550i 0.332518 0.471980i
\(49\) 48.8912 0.997779
\(50\) 0 0
\(51\) 32.1960i 0.631295i
\(52\) −1.58898 0.503524i −0.0305572 0.00968316i
\(53\) −29.9744 −0.565554 −0.282777 0.959186i \(-0.591256\pi\)
−0.282777 + 0.959186i \(0.591256\pi\)
\(54\) 1.58832 10.2702i 0.0294134 0.190189i
\(55\) 0 0
\(56\) 1.17240 2.36448i 0.0209357 0.0422228i
\(57\) −21.5646 −0.378326
\(58\) 47.2713 + 7.31067i 0.815023 + 0.126046i
\(59\) 24.3311i 0.412391i −0.978511 0.206196i \(-0.933892\pi\)
0.978511 0.206196i \(-0.0661083\pi\)
\(60\) 0 0
\(61\) −74.8416 −1.22691 −0.613456 0.789729i \(-0.710221\pi\)
−0.613456 + 0.789729i \(0.710221\pi\)
\(62\) 12.8428 83.0424i 0.207142 1.33939i
\(63\) 0.989693i 0.0157094i
\(64\) 38.7406 + 50.9428i 0.605321 + 0.795981i
\(65\) 0 0
\(66\) −70.1523 10.8493i −1.06291 0.164383i
\(67\) 72.8008i 1.08658i 0.839545 + 0.543290i \(0.182822\pi\)
−0.839545 + 0.543290i \(0.817178\pi\)
\(68\) −70.8799 22.4608i −1.04235 0.330307i
\(69\) 40.2362 0.583133
\(70\) 0 0
\(71\) 39.2803i 0.553244i −0.960979 0.276622i \(-0.910785\pi\)
0.960979 0.276622i \(-0.0892150\pi\)
\(72\) 21.5019 + 10.6615i 0.298638 + 0.148076i
\(73\) −46.5814 −0.638101 −0.319051 0.947738i \(-0.603364\pi\)
−0.319051 + 0.947738i \(0.603364\pi\)
\(74\) −100.707 15.5747i −1.36091 0.210469i
\(75\) 0 0
\(76\) 15.0441 47.4747i 0.197948 0.624667i
\(77\) −6.76026 −0.0877955
\(78\) 0.220625 1.42657i 0.00282852 0.0182894i
\(79\) 101.920i 1.29012i −0.764131 0.645062i \(-0.776832\pi\)
0.764131 0.645062i \(-0.223168\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −92.3170 14.2771i −1.12582 0.174112i
\(83\) 5.88913i 0.0709534i 0.999371 + 0.0354767i \(0.0112950\pi\)
−0.999371 + 0.0354767i \(0.988705\pi\)
\(84\) 2.17882 + 0.690438i 0.0259383 + 0.00821950i
\(85\) 0 0
\(86\) 16.9913 109.867i 0.197574 1.27752i
\(87\) 41.4248i 0.476148i
\(88\) 72.8250 146.872i 0.827557 1.66900i
\(89\) −61.0100 −0.685506 −0.342753 0.939426i \(-0.611359\pi\)
−0.342753 + 0.939426i \(0.611359\pi\)
\(90\) 0 0
\(91\) 0.137472i 0.00151069i
\(92\) −28.0699 + 88.5804i −0.305108 + 0.962831i
\(93\) 72.7718 0.782492
\(94\) 24.9923 161.602i 0.265876 1.71917i
\(95\) 0 0
\(96\) −38.4717 + 39.8989i −0.400747 + 0.415614i
\(97\) 95.5437 0.984987 0.492494 0.870316i \(-0.336086\pi\)
0.492494 + 0.870316i \(0.336086\pi\)
\(98\) −96.6335 14.9447i −0.986057 0.152497i
\(99\) 61.4759i 0.620969i
\(100\) 0 0
\(101\) 162.675 1.61064 0.805322 0.592838i \(-0.201992\pi\)
0.805322 + 0.592838i \(0.201992\pi\)
\(102\) 9.84145 63.6355i 0.0964848 0.623878i
\(103\) 158.196i 1.53588i −0.640521 0.767941i \(-0.721282\pi\)
0.640521 0.767941i \(-0.278718\pi\)
\(104\) 2.98670 + 1.48092i 0.0287183 + 0.0142397i
\(105\) 0 0
\(106\) 59.2445 + 9.16236i 0.558910 + 0.0864373i
\(107\) 18.1827i 0.169932i −0.996384 0.0849660i \(-0.972922\pi\)
0.996384 0.0849660i \(-0.0270782\pi\)
\(108\) −6.27865 + 19.8136i −0.0581357 + 0.183459i
\(109\) −156.842 −1.43891 −0.719457 0.694537i \(-0.755609\pi\)
−0.719457 + 0.694537i \(0.755609\pi\)
\(110\) 0 0
\(111\) 88.2520i 0.795063i
\(112\) −3.04001 + 4.31503i −0.0271430 + 0.0385270i
\(113\) −98.7245 −0.873668 −0.436834 0.899542i \(-0.643900\pi\)
−0.436834 + 0.899542i \(0.643900\pi\)
\(114\) 42.6225 + 6.59172i 0.373882 + 0.0578221i
\(115\) 0 0
\(116\) −91.1972 28.8991i −0.786183 0.249130i
\(117\) 1.25014 0.0106849
\(118\) −7.43735 + 48.0904i −0.0630284 + 0.407546i
\(119\) 6.13227i 0.0515317i
\(120\) 0 0
\(121\) −298.921 −2.47042
\(122\) 147.925 + 22.8770i 1.21250 + 0.187517i
\(123\) 80.8994i 0.657718i
\(124\) −50.7676 + 160.208i −0.409416 + 1.29200i
\(125\) 0 0
\(126\) −0.302523 + 1.95613i −0.00240097 + 0.0155249i
\(127\) 27.0938i 0.213337i −0.994295 0.106669i \(-0.965982\pi\)
0.994295 0.106669i \(-0.0340184\pi\)
\(128\) −60.9990 112.531i −0.476555 0.879145i
\(129\) 96.2789 0.746348
\(130\) 0 0
\(131\) 4.45811i 0.0340314i 0.999855 + 0.0170157i \(0.00541653\pi\)
−0.999855 + 0.0170157i \(0.994583\pi\)
\(132\) 135.340 + 42.8873i 1.02530 + 0.324904i
\(133\) 4.10734 0.0308822
\(134\) 22.2533 143.891i 0.166069 1.07381i
\(135\) 0 0
\(136\) 133.229 + 66.0600i 0.979622 + 0.485735i
\(137\) −181.700 −1.32628 −0.663139 0.748496i \(-0.730776\pi\)
−0.663139 + 0.748496i \(0.730776\pi\)
\(138\) −79.5270 12.2991i −0.576282 0.0891241i
\(139\) 223.419i 1.60733i 0.595083 + 0.803664i \(0.297119\pi\)
−0.595083 + 0.803664i \(0.702881\pi\)
\(140\) 0 0
\(141\) 141.615 1.00436
\(142\) −12.0069 + 77.6377i −0.0845559 + 0.546744i
\(143\) 8.53925i 0.0597151i
\(144\) −39.2397 27.6450i −0.272498 0.191979i
\(145\) 0 0
\(146\) 92.0683 + 14.2387i 0.630604 + 0.0975251i
\(147\) 84.6820i 0.576068i
\(148\) 194.288 + 61.5670i 1.31275 + 0.415994i
\(149\) 123.867 0.831324 0.415662 0.909519i \(-0.363550\pi\)
0.415662 + 0.909519i \(0.363550\pi\)
\(150\) 0 0
\(151\) 76.0961i 0.503948i −0.967734 0.251974i \(-0.918920\pi\)
0.967734 0.251974i \(-0.0810797\pi\)
\(152\) −44.2464 + 89.2353i −0.291095 + 0.587075i
\(153\) 55.7651 0.364478
\(154\) 13.3617 + 2.06643i 0.0867641 + 0.0134184i
\(155\) 0 0
\(156\) −0.872130 + 2.75219i −0.00559058 + 0.0176422i
\(157\) 34.2940 0.218433 0.109217 0.994018i \(-0.465166\pi\)
0.109217 + 0.994018i \(0.465166\pi\)
\(158\) −31.1541 + 201.445i −0.197178 + 1.27497i
\(159\) 51.9172i 0.326523i
\(160\) 0 0
\(161\) −7.66365 −0.0476003
\(162\) −17.7885 2.75106i −0.109806 0.0169818i
\(163\) 165.538i 1.01557i 0.861483 + 0.507786i \(0.169536\pi\)
−0.861483 + 0.507786i \(0.830464\pi\)
\(164\) 178.101 + 56.4377i 1.08598 + 0.344132i
\(165\) 0 0
\(166\) 1.80015 11.6399i 0.0108443 0.0701198i
\(167\) 83.6064i 0.500637i −0.968164 0.250319i \(-0.919465\pi\)
0.968164 0.250319i \(-0.0805353\pi\)
\(168\) −4.09540 2.03066i −0.0243774 0.0120873i
\(169\) −168.826 −0.998972
\(170\) 0 0
\(171\) 37.3510i 0.218427i
\(172\) −67.1668 + 211.959i −0.390505 + 1.23232i
\(173\) 192.900 1.11503 0.557513 0.830168i \(-0.311756\pi\)
0.557513 + 0.830168i \(0.311756\pi\)
\(174\) 12.6625 81.8763i 0.0727727 0.470554i
\(175\) 0 0
\(176\) −188.834 + 268.033i −1.07292 + 1.52291i
\(177\) −42.1427 −0.238094
\(178\) 120.587 + 18.6491i 0.677452 + 0.104770i
\(179\) 120.939i 0.675637i 0.941211 + 0.337819i \(0.109689\pi\)
−0.941211 + 0.337819i \(0.890311\pi\)
\(180\) 0 0
\(181\) −107.583 −0.594381 −0.297191 0.954818i \(-0.596050\pi\)
−0.297191 + 0.954818i \(0.596050\pi\)
\(182\) −0.0420216 + 0.271715i −0.000230888 + 0.00149294i
\(183\) 129.629i 0.708357i
\(184\) 82.5569 166.499i 0.448679 0.904887i
\(185\) 0 0
\(186\) −143.834 22.2444i −0.773299 0.119593i
\(187\) 380.913i 2.03697i
\(188\) −98.7947 + 311.767i −0.525504 + 1.65834i
\(189\) −1.71420 −0.00906984
\(190\) 0 0
\(191\) 279.706i 1.46443i −0.681075 0.732214i \(-0.738487\pi\)
0.681075 0.732214i \(-0.261513\pi\)
\(192\) 88.2355 67.1006i 0.459560 0.349482i
\(193\) −102.534 −0.531263 −0.265632 0.964075i \(-0.585580\pi\)
−0.265632 + 0.964075i \(0.585580\pi\)
\(194\) −188.842 29.2051i −0.973415 0.150542i
\(195\) 0 0
\(196\) 186.428 + 59.0765i 0.951165 + 0.301411i
\(197\) 38.9632 0.197783 0.0988913 0.995098i \(-0.468470\pi\)
0.0988913 + 0.995098i \(0.468470\pi\)
\(198\) −18.7915 + 121.507i −0.0949067 + 0.613673i
\(199\) 147.646i 0.741940i 0.928645 + 0.370970i \(0.120975\pi\)
−0.928645 + 0.370970i \(0.879025\pi\)
\(200\) 0 0
\(201\) 126.095 0.627337
\(202\) −321.528 49.7254i −1.59172 0.246165i
\(203\) 7.89005i 0.0388672i
\(204\) −38.9033 + 122.768i −0.190703 + 0.601802i
\(205\) 0 0
\(206\) −48.3562 + 312.674i −0.234739 + 1.51784i
\(207\) 69.6912i 0.336672i
\(208\) −5.45055 3.84001i −0.0262046 0.0184616i
\(209\) 255.132 1.22073
\(210\) 0 0
\(211\) 233.336i 1.10586i 0.833229 + 0.552928i \(0.186490\pi\)
−0.833229 + 0.552928i \(0.813510\pi\)
\(212\) −114.296 36.2189i −0.539133 0.170844i
\(213\) −68.0355 −0.319416
\(214\) −5.55797 + 35.9382i −0.0259718 + 0.167936i
\(215\) 0 0
\(216\) 18.4663 37.2424i 0.0854919 0.172419i
\(217\) −13.8606 −0.0638737
\(218\) 309.998 + 47.9422i 1.42201 + 0.219918i
\(219\) 80.6813i 0.368408i
\(220\) 0 0
\(221\) 7.74600 0.0350498
\(222\) −26.9762 + 174.430i −0.121515 + 0.785722i
\(223\) 82.7105i 0.370899i −0.982654 0.185450i \(-0.940626\pi\)
0.982654 0.185450i \(-0.0593741\pi\)
\(224\) 7.32758 7.59941i 0.0327124 0.0339260i
\(225\) 0 0
\(226\) 195.129 + 30.1774i 0.863403 + 0.133528i
\(227\) 361.534i 1.59266i −0.604862 0.796330i \(-0.706772\pi\)
0.604862 0.796330i \(-0.293228\pi\)
\(228\) −82.2286 26.0571i −0.360652 0.114286i
\(229\) 121.818 0.531955 0.265977 0.963979i \(-0.414305\pi\)
0.265977 + 0.963979i \(0.414305\pi\)
\(230\) 0 0
\(231\) 11.7091i 0.0506888i
\(232\) 171.418 + 84.9957i 0.738870 + 0.366361i
\(233\) 136.615 0.586329 0.293164 0.956062i \(-0.405292\pi\)
0.293164 + 0.956062i \(0.405292\pi\)
\(234\) −2.47090 0.382133i −0.0105594 0.00163305i
\(235\) 0 0
\(236\) 29.3999 92.7775i 0.124576 0.393125i
\(237\) −176.530 −0.744853
\(238\) −1.87447 + 12.1204i −0.00787592 + 0.0509262i
\(239\) 56.4632i 0.236248i 0.992999 + 0.118124i \(0.0376880\pi\)
−0.992999 + 0.118124i \(0.962312\pi\)
\(240\) 0 0
\(241\) −2.24158 −0.00930117 −0.00465059 0.999989i \(-0.501480\pi\)
−0.00465059 + 0.999989i \(0.501480\pi\)
\(242\) 590.818 + 91.3720i 2.44140 + 0.377570i
\(243\) 15.5885i 0.0641500i
\(244\) −285.381 90.4331i −1.16959 0.370627i
\(245\) 0 0
\(246\) −24.7287 + 159.898i −0.100523 + 0.649991i
\(247\) 5.18820i 0.0210049i
\(248\) 149.314 301.133i 0.602071 1.21425i
\(249\) 10.2003 0.0409650
\(250\) 0 0
\(251\) 395.809i 1.57693i 0.615081 + 0.788464i \(0.289123\pi\)
−0.615081 + 0.788464i \(0.710877\pi\)
\(252\) 1.19587 3.77383i 0.00474553 0.0149755i
\(253\) −476.036 −1.88157
\(254\) −8.28184 + 53.5510i −0.0326057 + 0.210831i
\(255\) 0 0
\(256\) 86.1671 + 241.063i 0.336590 + 0.941651i
\(257\) 109.778 0.427151 0.213576 0.976927i \(-0.431489\pi\)
0.213576 + 0.976927i \(0.431489\pi\)
\(258\) −190.295 29.4298i −0.737579 0.114069i
\(259\) 16.8091i 0.0648998i
\(260\) 0 0
\(261\) 71.7499 0.274904
\(262\) 1.36272 8.81147i 0.00520124 0.0336316i
\(263\) 327.702i 1.24601i −0.782216 0.623007i \(-0.785911\pi\)
0.782216 0.623007i \(-0.214089\pi\)
\(264\) −254.390 126.137i −0.963599 0.477790i
\(265\) 0 0
\(266\) −8.11816 1.25550i −0.0305194 0.00471993i
\(267\) 105.673i 0.395777i
\(268\) −87.9672 + 277.599i −0.328236 + 1.03582i
\(269\) −130.032 −0.483392 −0.241696 0.970352i \(-0.577704\pi\)
−0.241696 + 0.970352i \(0.577704\pi\)
\(270\) 0 0
\(271\) 329.669i 1.21649i −0.793750 0.608245i \(-0.791874\pi\)
0.793750 0.608245i \(-0.208126\pi\)
\(272\) −243.134 171.292i −0.893875 0.629751i
\(273\) −0.238109 −0.000872195
\(274\) 359.131 + 55.5408i 1.31070 + 0.202704i
\(275\) 0 0
\(276\) 153.426 + 48.6185i 0.555891 + 0.176154i
\(277\) 304.124 1.09792 0.548960 0.835849i \(-0.315024\pi\)
0.548960 + 0.835849i \(0.315024\pi\)
\(278\) 68.2930 441.588i 0.245658 1.58844i
\(279\) 126.044i 0.451772i
\(280\) 0 0
\(281\) 240.099 0.854446 0.427223 0.904146i \(-0.359492\pi\)
0.427223 + 0.904146i \(0.359492\pi\)
\(282\) −279.903 43.2879i −0.992563 0.153503i
\(283\) 86.6730i 0.306265i 0.988206 + 0.153133i \(0.0489362\pi\)
−0.988206 + 0.153133i \(0.951064\pi\)
\(284\) 47.4635 149.781i 0.167125 0.527398i
\(285\) 0 0
\(286\) −2.61022 + 16.8779i −0.00912664 + 0.0590135i
\(287\) 15.4086i 0.0536886i
\(288\) 69.1070 + 66.6350i 0.239955 + 0.231372i
\(289\) 56.5280 0.195599
\(290\) 0 0
\(291\) 165.487i 0.568683i
\(292\) −177.621 56.2856i −0.608290 0.192759i
\(293\) 390.339 1.33222 0.666108 0.745855i \(-0.267959\pi\)
0.666108 + 0.745855i \(0.267959\pi\)
\(294\) −25.8850 + 167.374i −0.0880442 + 0.569300i
\(295\) 0 0
\(296\) −365.191 181.076i −1.23375 0.611743i
\(297\) −106.479 −0.358517
\(298\) −244.824 37.8629i −0.821557 0.127057i
\(299\) 9.68038i 0.0323759i
\(300\) 0 0
\(301\) −18.3379 −0.0609233
\(302\) −23.2605 + 150.404i −0.0770216 + 0.498027i
\(303\) 281.761i 0.929906i
\(304\) 114.730 162.849i 0.377401 0.535687i
\(305\) 0 0
\(306\) −110.220 17.0459i −0.360196 0.0557056i
\(307\) 60.2318i 0.196195i 0.995177 + 0.0980973i \(0.0312757\pi\)
−0.995177 + 0.0980973i \(0.968724\pi\)
\(308\) −25.7777 8.16860i −0.0836939 0.0265214i
\(309\) −274.003 −0.886741
\(310\) 0 0
\(311\) 106.594i 0.342747i −0.985206 0.171373i \(-0.945180\pi\)
0.985206 0.171373i \(-0.0548205\pi\)
\(312\) 2.56504 5.17312i 0.00822127 0.0165805i
\(313\) −46.2243 −0.147682 −0.0738408 0.997270i \(-0.523526\pi\)
−0.0738408 + 0.997270i \(0.523526\pi\)
\(314\) −67.7823 10.4828i −0.215867 0.0333846i
\(315\) 0 0
\(316\) 123.152 388.633i 0.389723 1.22985i
\(317\) −8.36780 −0.0263969 −0.0131984 0.999913i \(-0.504201\pi\)
−0.0131984 + 0.999913i \(0.504201\pi\)
\(318\) 15.8697 102.614i 0.0499046 0.322687i
\(319\) 490.099i 1.53636i
\(320\) 0 0
\(321\) −31.4934 −0.0981103
\(322\) 15.1472 + 2.34257i 0.0470411 + 0.00727507i
\(323\) 231.432i 0.716506i
\(324\) 34.3182 + 10.8749i 0.105920 + 0.0335646i
\(325\) 0 0
\(326\) 50.6006 327.187i 0.155217 1.00364i
\(327\) 271.658i 0.830757i
\(328\) −334.765 165.990i −1.02063 0.506066i
\(329\) −26.9730 −0.0819847
\(330\) 0 0
\(331\) 111.072i 0.335564i 0.985824 + 0.167782i \(0.0536605\pi\)
−0.985824 + 0.167782i \(0.946339\pi\)
\(332\) −7.11600 + 22.4560i −0.0214337 + 0.0676386i
\(333\) −152.857 −0.459030
\(334\) −25.5562 + 165.248i −0.0765156 + 0.494755i
\(335\) 0 0
\(336\) 7.47385 + 5.26546i 0.0222436 + 0.0156710i
\(337\) −231.853 −0.687990 −0.343995 0.938972i \(-0.611780\pi\)
−0.343995 + 0.938972i \(0.611780\pi\)
\(338\) 333.686 + 51.6057i 0.987236 + 0.152679i
\(339\) 170.996i 0.504412i
\(340\) 0 0
\(341\) −860.966 −2.52483
\(342\) 11.4172 73.8244i 0.0333836 0.215861i
\(343\) 32.2941i 0.0941518i
\(344\) 197.546 398.406i 0.574260 1.15816i
\(345\) 0 0
\(346\) −381.266 58.9642i −1.10193 0.170417i
\(347\) 402.088i 1.15875i 0.815059 + 0.579377i \(0.196704\pi\)
−0.815059 + 0.579377i \(0.803296\pi\)
\(348\) −50.0548 + 157.958i −0.143835 + 0.453903i
\(349\) −163.284 −0.467864 −0.233932 0.972253i \(-0.575159\pi\)
−0.233932 + 0.972253i \(0.575159\pi\)
\(350\) 0 0
\(351\) 2.16530i 0.00616894i
\(352\) 455.161 472.046i 1.29307 1.34104i
\(353\) 175.851 0.498161 0.249081 0.968483i \(-0.419872\pi\)
0.249081 + 0.968483i \(0.419872\pi\)
\(354\) 83.2951 + 12.8819i 0.235297 + 0.0363895i
\(355\) 0 0
\(356\) −232.639 73.7201i −0.653481 0.207079i
\(357\) −10.6214 −0.0297518
\(358\) 36.9678 239.037i 0.103262 0.667700i
\(359\) 345.628i 0.962753i −0.876514 0.481377i \(-0.840137\pi\)
0.876514 0.481377i \(-0.159863\pi\)
\(360\) 0 0
\(361\) 205.989 0.570607
\(362\) 212.638 + 32.8852i 0.587398 + 0.0908431i
\(363\) 517.746i 1.42630i
\(364\) 0.166112 0.524200i 0.000456351 0.00144011i
\(365\) 0 0
\(366\) 39.6242 256.213i 0.108263 0.700035i
\(367\) 728.998i 1.98637i 0.116546 + 0.993185i \(0.462818\pi\)
−0.116546 + 0.993185i \(0.537182\pi\)
\(368\) −214.068 + 303.851i −0.581707 + 0.825682i
\(369\) −140.122 −0.379734
\(370\) 0 0
\(371\) 9.88848i 0.0266536i
\(372\) 277.488 + 87.9321i 0.745936 + 0.236377i
\(373\) −46.6749 −0.125134 −0.0625668 0.998041i \(-0.519929\pi\)
−0.0625668 + 0.998041i \(0.519929\pi\)
\(374\) −116.435 + 752.875i −0.311323 + 2.01303i
\(375\) 0 0
\(376\) 290.567 586.010i 0.772784 1.55854i
\(377\) 9.96635 0.0264360
\(378\) 3.38812 + 0.523984i 0.00896328 + 0.00138620i
\(379\) 117.629i 0.310368i −0.987886 0.155184i \(-0.950403\pi\)
0.987886 0.155184i \(-0.0495970\pi\)
\(380\) 0 0
\(381\) −46.9278 −0.123170
\(382\) −85.4985 + 552.839i −0.223818 + 1.44722i
\(383\) 251.669i 0.657100i −0.944487 0.328550i \(-0.893440\pi\)
0.944487 0.328550i \(-0.106560\pi\)
\(384\) −194.909 + 105.653i −0.507575 + 0.275139i
\(385\) 0 0
\(386\) 202.658 + 31.3418i 0.525022 + 0.0811964i
\(387\) 166.760i 0.430904i
\(388\) 364.321 + 115.448i 0.938970 + 0.297547i
\(389\) 356.890 0.917454 0.458727 0.888577i \(-0.348306\pi\)
0.458727 + 0.888577i \(0.348306\pi\)
\(390\) 0 0
\(391\) 431.815i 1.10439i
\(392\) −350.418 173.751i −0.893923 0.443242i
\(393\) 7.72168 0.0196480
\(394\) −77.0108 11.9100i −0.195459 0.0302284i
\(395\) 0 0
\(396\) 74.2830 234.416i 0.187583 0.591958i
\(397\) −103.819 −0.261508 −0.130754 0.991415i \(-0.541740\pi\)
−0.130754 + 0.991415i \(0.541740\pi\)
\(398\) 45.1314 291.823i 0.113396 0.733224i
\(399\) 7.11412i 0.0178299i
\(400\) 0 0
\(401\) −121.598 −0.303237 −0.151618 0.988439i \(-0.548449\pi\)
−0.151618 + 0.988439i \(0.548449\pi\)
\(402\) −249.227 38.5438i −0.619967 0.0958800i
\(403\) 17.5081i 0.0434444i
\(404\) 620.301 + 196.565i 1.53540 + 0.486546i
\(405\) 0 0
\(406\) −2.41177 + 15.5947i −0.00594033 + 0.0384106i
\(407\) 1044.11i 2.56539i
\(408\) 114.419 230.759i 0.280439 0.565585i
\(409\) 182.788 0.446915 0.223457 0.974714i \(-0.428266\pi\)
0.223457 + 0.974714i \(0.428266\pi\)
\(410\) 0 0
\(411\) 314.714i 0.765727i
\(412\) 191.152 603.221i 0.463962 1.46413i
\(413\) 8.02677 0.0194353
\(414\) −21.3027 + 137.745i −0.0514558 + 0.332717i
\(415\) 0 0
\(416\) 9.59924 + 9.25587i 0.0230751 + 0.0222497i
\(417\) 386.972 0.927991
\(418\) −504.269 77.9869i −1.20638 0.186572i
\(419\) 168.020i 0.401003i −0.979693 0.200502i \(-0.935743\pi\)
0.979693 0.200502i \(-0.0642572\pi\)
\(420\) 0 0
\(421\) 625.291 1.48525 0.742626 0.669706i \(-0.233580\pi\)
0.742626 + 0.669706i \(0.233580\pi\)
\(422\) 71.3244 461.189i 0.169015 1.09286i
\(423\) 245.285i 0.579869i
\(424\) 214.836 + 106.524i 0.506688 + 0.251236i
\(425\) 0 0
\(426\) 134.472 + 20.7966i 0.315663 + 0.0488184i
\(427\) 24.6901i 0.0578222i
\(428\) 21.9707 69.3331i 0.0513334 0.161993i
\(429\) −14.7904 −0.0344765
\(430\) 0 0
\(431\) 133.413i 0.309544i −0.987950 0.154772i \(-0.950536\pi\)
0.987950 0.154772i \(-0.0494643\pi\)
\(432\) −47.8826 + 67.9651i −0.110839 + 0.157327i
\(433\) 706.716 1.63214 0.816069 0.577954i \(-0.196149\pi\)
0.816069 + 0.577954i \(0.196149\pi\)
\(434\) 27.3955 + 4.23681i 0.0631233 + 0.00976223i
\(435\) 0 0
\(436\) −598.057 189.516i −1.37169 0.434670i
\(437\) 289.226 0.661844
\(438\) 24.6621 159.467i 0.0563062 0.364080i
\(439\) 507.488i 1.15601i 0.816033 + 0.578005i \(0.196169\pi\)
−0.816033 + 0.578005i \(0.803831\pi\)
\(440\) 0 0
\(441\) −146.674 −0.332593
\(442\) −15.3100 2.36774i −0.0346380 0.00535689i
\(443\) 412.172i 0.930410i 0.885203 + 0.465205i \(0.154019\pi\)
−0.885203 + 0.465205i \(0.845981\pi\)
\(444\) 106.637 336.516i 0.240174 0.757919i
\(445\) 0 0
\(446\) −25.2824 + 163.478i −0.0566869 + 0.366542i
\(447\) 214.544i 0.479965i
\(448\) −16.8059 + 12.7804i −0.0375132 + 0.0285277i
\(449\) −808.617 −1.80093 −0.900465 0.434929i \(-0.856773\pi\)
−0.900465 + 0.434929i \(0.856773\pi\)
\(450\) 0 0
\(451\) 957.124i 2.12223i
\(452\) −376.449 119.291i −0.832852 0.263919i
\(453\) −131.802 −0.290955
\(454\) −110.511 + 714.573i −0.243417 + 1.57395i
\(455\) 0 0
\(456\) 154.560 + 76.6370i 0.338948 + 0.168064i
\(457\) 472.873 1.03473 0.517367 0.855764i \(-0.326912\pi\)
0.517367 + 0.855764i \(0.326912\pi\)
\(458\) −240.773 37.2364i −0.525705 0.0813021i
\(459\) 96.5881i 0.210432i
\(460\) 0 0
\(461\) 433.776 0.940946 0.470473 0.882414i \(-0.344083\pi\)
0.470473 + 0.882414i \(0.344083\pi\)
\(462\) 3.57916 23.1431i 0.00774709 0.0500933i
\(463\) 530.624i 1.14606i 0.819536 + 0.573028i \(0.194231\pi\)
−0.819536 + 0.573028i \(0.805769\pi\)
\(464\) −312.827 220.392i −0.674196 0.474983i
\(465\) 0 0
\(466\) −270.019 41.7594i −0.579440 0.0896124i
\(467\) 355.266i 0.760741i −0.924834 0.380370i \(-0.875797\pi\)
0.924834 0.380370i \(-0.124203\pi\)
\(468\) 4.76693 + 1.51057i 0.0101857 + 0.00322772i
\(469\) −24.0168 −0.0512086
\(470\) 0 0
\(471\) 59.3990i 0.126113i
\(472\) −86.4686 + 174.388i −0.183196 + 0.369467i
\(473\) −1139.08 −2.40820
\(474\) 348.912 + 53.9605i 0.736102 + 0.113841i
\(475\) 0 0
\(476\) 7.40978 23.3831i 0.0155668 0.0491242i
\(477\) 89.9232 0.188518
\(478\) 17.2593 111.600i 0.0361072 0.233472i
\(479\) 548.640i 1.14539i −0.819770 0.572693i \(-0.805899\pi\)
0.819770 0.572693i \(-0.194101\pi\)
\(480\) 0 0
\(481\) −21.2324 −0.0441423
\(482\) 4.43050 + 0.685191i 0.00919190 + 0.00142156i
\(483\) 13.2738i 0.0274821i
\(484\) −1139.82 361.194i −2.35501 0.746269i
\(485\) 0 0
\(486\) −4.76497 + 30.8106i −0.00980446 + 0.0633964i
\(487\) 134.618i 0.276422i 0.990403 + 0.138211i \(0.0441352\pi\)
−0.990403 + 0.138211i \(0.955865\pi\)
\(488\) 536.412 + 265.974i 1.09921 + 0.545029i
\(489\) 286.721 0.586341
\(490\) 0 0
\(491\) 756.810i 1.54136i 0.637220 + 0.770682i \(0.280084\pi\)
−0.637220 + 0.770682i \(0.719916\pi\)
\(492\) 97.7529 308.480i 0.198685 0.626991i
\(493\) 444.572 0.901768
\(494\) 1.58589 10.2545i 0.00321031 0.0207581i
\(495\) 0 0
\(496\) −387.167 + 549.549i −0.780579 + 1.10796i
\(497\) 12.9585 0.0260734
\(498\) −20.1609 3.11795i −0.0404837 0.00626094i
\(499\) 706.956i 1.41675i −0.705838 0.708373i \(-0.749430\pi\)
0.705838 0.708373i \(-0.250570\pi\)
\(500\) 0 0
\(501\) −144.811 −0.289043
\(502\) 120.988 782.318i 0.241012 1.55840i
\(503\) 100.567i 0.199935i −0.994991 0.0999673i \(-0.968126\pi\)
0.994991 0.0999673i \(-0.0318738\pi\)
\(504\) −3.51720 + 7.09344i −0.00697858 + 0.0140743i
\(505\) 0 0
\(506\) 940.887 + 145.511i 1.85946 + 0.287572i
\(507\) 292.416i 0.576757i
\(508\) 32.7382 103.312i 0.0644452 0.203370i
\(509\) 753.185 1.47973 0.739867 0.672753i \(-0.234888\pi\)
0.739867 + 0.672753i \(0.234888\pi\)
\(510\) 0 0
\(511\) 15.3671i 0.0300726i
\(512\) −96.6232 502.800i −0.188717 0.982031i
\(513\) 64.6938 0.126109
\(514\) −216.976 33.5561i −0.422133 0.0652843i
\(515\) 0 0
\(516\) 367.124 + 116.336i 0.711480 + 0.225458i
\(517\) −1675.46 −3.24073
\(518\) 5.13807 33.2231i 0.00991906 0.0641373i
\(519\) 334.112i 0.643761i
\(520\) 0 0
\(521\) 117.708 0.225926 0.112963 0.993599i \(-0.463966\pi\)
0.112963 + 0.993599i \(0.463966\pi\)
\(522\) −141.814 21.9320i −0.271674 0.0420153i
\(523\) 617.411i 1.18052i −0.807214 0.590259i \(-0.799026\pi\)
0.807214 0.590259i \(-0.200974\pi\)
\(524\) −5.38686 + 16.9994i −0.0102803 + 0.0324415i
\(525\) 0 0
\(526\) −100.170 + 647.704i −0.190437 + 1.23138i
\(527\) 780.988i 1.48195i
\(528\) 464.246 + 327.070i 0.879254 + 0.619450i
\(529\) −10.6508 −0.0201338
\(530\) 0 0
\(531\) 72.9932i 0.137464i
\(532\) 15.6618 + 4.96301i 0.0294395 + 0.00932896i
\(533\) −19.4635 −0.0365169
\(534\) 32.3012 208.862i 0.0604892 0.391127i
\(535\) 0 0
\(536\) 258.722 521.786i 0.482690 0.973481i
\(537\) 209.473 0.390079
\(538\) 257.009 + 39.7474i 0.477713 + 0.0738799i
\(539\) 1001.88i 1.85877i
\(540\) 0 0
\(541\) 352.762 0.652056 0.326028 0.945360i \(-0.394290\pi\)
0.326028 + 0.945360i \(0.394290\pi\)
\(542\) −100.771 + 651.591i −0.185924 + 1.20220i
\(543\) 186.339i 0.343166i
\(544\) 428.196 + 412.879i 0.787125 + 0.758969i
\(545\) 0 0
\(546\) 0.470623 + 0.0727835i 0.000861948 + 0.000133303i
\(547\) 295.110i 0.539507i −0.962929 0.269753i \(-0.913058\pi\)
0.962929 0.269753i \(-0.0869422\pi\)
\(548\) −692.846 219.553i −1.26432 0.400644i
\(549\) 224.525 0.408970
\(550\) 0 0
\(551\) 297.770i 0.540418i
\(552\) −288.385 142.993i −0.522437 0.259045i
\(553\) 33.6231 0.0608013
\(554\) −601.102 92.9624i −1.08502 0.167802i
\(555\) 0 0
\(556\) −269.963 + 851.924i −0.485545 + 1.53224i
\(557\) 31.8538 0.0571882 0.0285941 0.999591i \(-0.490897\pi\)
0.0285941 + 0.999591i \(0.490897\pi\)
\(558\) −38.5284 + 249.127i −0.0690473 + 0.446465i
\(559\) 23.1636i 0.0414376i
\(560\) 0 0
\(561\) −659.760 −1.17604
\(562\) −474.557 73.3919i −0.844408 0.130591i
\(563\) 906.668i 1.61042i 0.592988 + 0.805211i \(0.297948\pi\)
−0.592988 + 0.805211i \(0.702052\pi\)
\(564\) 539.997 + 171.117i 0.957441 + 0.303400i
\(565\) 0 0
\(566\) 26.4936 171.310i 0.0468085 0.302667i
\(567\) 2.96908i 0.00523647i
\(568\) −139.596 + 281.534i −0.245767 + 0.495659i
\(569\) −465.009 −0.817239 −0.408620 0.912705i \(-0.633990\pi\)
−0.408620 + 0.912705i \(0.633990\pi\)
\(570\) 0 0
\(571\) 265.895i 0.465666i 0.972517 + 0.232833i \(0.0747995\pi\)
−0.972517 + 0.232833i \(0.925200\pi\)
\(572\) 10.3182 32.5613i 0.0180388 0.0569253i
\(573\) −484.464 −0.845488
\(574\) 4.71000 30.4552i 0.00820557 0.0530578i
\(575\) 0 0
\(576\) −116.222 152.828i −0.201774 0.265327i
\(577\) 138.097 0.239336 0.119668 0.992814i \(-0.461817\pi\)
0.119668 + 0.992814i \(0.461817\pi\)
\(578\) −111.728 17.2791i −0.193301 0.0298946i
\(579\) 177.594i 0.306725i
\(580\) 0 0
\(581\) −1.94281 −0.00334391
\(582\) −50.5848 + 327.085i −0.0869154 + 0.562001i
\(583\) 614.234i 1.05358i
\(584\) 333.863 + 165.542i 0.571683 + 0.283463i
\(585\) 0 0
\(586\) −771.507 119.316i −1.31656 0.203611i
\(587\) 648.473i 1.10472i −0.833604 0.552362i \(-0.813727\pi\)
0.833604 0.552362i \(-0.186273\pi\)
\(588\) 102.324 322.903i 0.174020 0.549155i
\(589\) 523.098 0.888113
\(590\) 0 0
\(591\) 67.4862i 0.114190i
\(592\) 666.451 + 469.526i 1.12576 + 0.793118i
\(593\) −350.392 −0.590880 −0.295440 0.955361i \(-0.595466\pi\)
−0.295440 + 0.955361i \(0.595466\pi\)
\(594\) 210.457 + 32.5479i 0.354304 + 0.0547944i
\(595\) 0 0
\(596\) 472.322 + 149.672i 0.792486 + 0.251128i
\(597\) 255.731 0.428359
\(598\) −2.95903 + 19.1333i −0.00494821 + 0.0319955i
\(599\) 276.745i 0.462012i 0.972952 + 0.231006i \(0.0742017\pi\)
−0.972952 + 0.231006i \(0.925798\pi\)
\(600\) 0 0
\(601\) 815.487 1.35688 0.678442 0.734654i \(-0.262656\pi\)
0.678442 + 0.734654i \(0.262656\pi\)
\(602\) 36.2449 + 5.60540i 0.0602075 + 0.00931130i
\(603\) 218.403i 0.362193i
\(604\) 91.9490 290.164i 0.152233 0.480405i
\(605\) 0 0
\(606\) −86.1269 + 556.902i −0.142124 + 0.918981i
\(607\) 247.049i 0.407001i 0.979075 + 0.203500i \(0.0652318\pi\)
−0.979075 + 0.203500i \(0.934768\pi\)
\(608\) −276.543 + 286.802i −0.454840 + 0.471713i
\(609\) −13.6660 −0.0224400
\(610\) 0 0
\(611\) 34.0710i 0.0557627i
\(612\) 212.640 + 67.3825i 0.347450 + 0.110102i
\(613\) 1005.15 1.63972 0.819862 0.572561i \(-0.194050\pi\)
0.819862 + 0.572561i \(0.194050\pi\)
\(614\) 18.4112 119.048i 0.0299857 0.193890i
\(615\) 0 0
\(616\) 48.4528 + 24.0248i 0.0786572 + 0.0390013i
\(617\) 533.282 0.864314 0.432157 0.901798i \(-0.357753\pi\)
0.432157 + 0.901798i \(0.357753\pi\)
\(618\) 541.568 + 83.7553i 0.876324 + 0.135526i
\(619\) 1136.85i 1.83659i 0.395900 + 0.918294i \(0.370433\pi\)
−0.395900 + 0.918294i \(0.629567\pi\)
\(620\) 0 0
\(621\) −120.709 −0.194378
\(622\) −32.5830 + 210.684i −0.0523842 + 0.338720i
\(623\) 20.1271i 0.0323067i
\(624\) −6.65109 + 9.44063i −0.0106588 + 0.0151292i
\(625\) 0 0
\(626\) 91.3625 + 14.1295i 0.145946 + 0.0225711i
\(627\) 441.901i 0.704787i
\(628\) 130.768 + 41.4384i 0.208229 + 0.0659847i
\(629\) −947.121 −1.50576
\(630\) 0 0
\(631\) 936.738i 1.48453i −0.670107 0.742265i \(-0.733752\pi\)
0.670107 0.742265i \(-0.266248\pi\)
\(632\) −362.206 + 730.490i −0.573110 + 1.15584i
\(633\) 404.149 0.638466
\(634\) 16.5390 + 2.55781i 0.0260867 + 0.00403440i
\(635\) 0 0
\(636\) −62.7329 + 197.967i −0.0986366 + 0.311269i
\(637\) −20.3735 −0.0319836
\(638\) −149.810 + 968.682i −0.234812 + 1.51831i
\(639\) 117.841i 0.184415i
\(640\) 0 0
\(641\) 214.558 0.334723 0.167362 0.985896i \(-0.446475\pi\)
0.167362 + 0.985896i \(0.446475\pi\)
\(642\) 62.2468 + 9.62669i 0.0969577 + 0.0149948i
\(643\) 786.394i 1.22301i 0.791241 + 0.611504i \(0.209435\pi\)
−0.791241 + 0.611504i \(0.790565\pi\)
\(644\) −29.2225 9.26020i −0.0453765 0.0143792i
\(645\) 0 0
\(646\) 70.7424 457.425i 0.109508 0.708088i
\(647\) 316.550i 0.489258i 0.969617 + 0.244629i \(0.0786661\pi\)
−0.969617 + 0.244629i \(0.921334\pi\)
\(648\) −64.5058 31.9845i −0.0995459 0.0493588i
\(649\) 498.592 0.768246
\(650\) 0 0
\(651\) 24.0073i 0.0368775i
\(652\) −200.024 + 631.219i −0.306786 + 0.968127i
\(653\) −516.391 −0.790797 −0.395399 0.918510i \(-0.629394\pi\)
−0.395399 + 0.918510i \(0.629394\pi\)
\(654\) 83.0384 536.932i 0.126970 0.820997i
\(655\) 0 0
\(656\) 610.926 + 430.408i 0.931290 + 0.656110i
\(657\) 139.744 0.212700
\(658\) 53.3121 + 8.24491i 0.0810215 + 0.0125303i
\(659\) 285.118i 0.432653i 0.976321 + 0.216326i \(0.0694076\pi\)
−0.976321 + 0.216326i \(0.930592\pi\)
\(660\) 0 0
\(661\) −391.847 −0.592809 −0.296405 0.955062i \(-0.595788\pi\)
−0.296405 + 0.955062i \(0.595788\pi\)
\(662\) 33.9516 219.534i 0.0512865 0.331622i
\(663\) 13.4165i 0.0202360i
\(664\) 20.9290 42.2092i 0.0315196 0.0635681i
\(665\) 0 0
\(666\) 302.122 + 46.7242i 0.453637 + 0.0701565i
\(667\) 555.593i 0.832973i
\(668\) 101.024 318.802i 0.151233 0.477248i
\(669\) −143.259 −0.214139
\(670\) 0 0
\(671\) 1533.65i 2.28562i
\(672\) −13.1626 12.6917i −0.0195872 0.0188865i
\(673\) 1213.59 1.80325 0.901626 0.432517i \(-0.142375\pi\)
0.901626 + 0.432517i \(0.142375\pi\)
\(674\) 458.257 + 70.8711i 0.679907 + 0.105150i
\(675\) 0 0
\(676\) −643.756 203.997i −0.952303 0.301771i
\(677\) −251.863 −0.372028 −0.186014 0.982547i \(-0.559557\pi\)
−0.186014 + 0.982547i \(0.559557\pi\)
\(678\) 52.2688 337.974i 0.0770926 0.498486i
\(679\) 31.5197i 0.0464207i
\(680\) 0 0
\(681\) −626.195 −0.919523
\(682\) 1701.70 + 263.174i 2.49517 + 0.385886i
\(683\) 664.793i 0.973342i −0.873585 0.486671i \(-0.838211\pi\)
0.873585 0.486671i \(-0.161789\pi\)
\(684\) −45.1322 + 142.424i −0.0659828 + 0.208222i
\(685\) 0 0
\(686\) 9.87143 63.8293i 0.0143898 0.0930457i
\(687\) 210.994i 0.307124i
\(688\) −512.231 + 727.067i −0.744522 + 1.05678i
\(689\) 12.4907 0.0181287
\(690\) 0 0
\(691\) 654.347i 0.946957i −0.880805 0.473479i \(-0.842998\pi\)
0.880805 0.473479i \(-0.157002\pi\)
\(692\) 735.551 + 233.086i 1.06293 + 0.336829i
\(693\) 20.2808 0.0292652
\(694\) 122.907 794.728i 0.177100 1.14514i
\(695\) 0 0
\(696\) 147.217 296.904i 0.211519 0.426587i
\(697\) −868.213 −1.24564
\(698\) 322.732 + 49.9117i 0.462367 + 0.0715067i
\(699\) 236.623i 0.338517i
\(700\) 0 0
\(701\) −1266.25 −1.80635 −0.903174 0.429275i \(-0.858769\pi\)
−0.903174 + 0.429275i \(0.858769\pi\)
\(702\) −0.661874 + 4.27972i −0.000942840 + 0.00609647i
\(703\) 634.373i 0.902380i
\(704\) −1043.92 + 793.870i −1.48284 + 1.12766i
\(705\) 0 0
\(706\) −347.570 53.7529i −0.492309 0.0761372i
\(707\) 53.6661i 0.0759068i
\(708\) −160.695 50.9221i −0.226971 0.0719239i
\(709\) −493.220 −0.695656 −0.347828 0.937558i \(-0.613081\pi\)
−0.347828 + 0.937558i \(0.613081\pi\)
\(710\) 0 0
\(711\) 305.759i 0.430041i
\(712\) 437.278 + 216.819i 0.614154 + 0.304522i
\(713\) −976.020 −1.36889
\(714\) 20.9932 + 3.24667i 0.0294023 + 0.00454716i
\(715\) 0 0
\(716\) −146.134 + 461.156i −0.204098 + 0.644073i
\(717\) 97.7971 0.136398
\(718\) −105.649 + 683.135i −0.147144 + 0.951442i
\(719\) 60.3910i 0.0839930i 0.999118 + 0.0419965i \(0.0133718\pi\)
−0.999118 + 0.0419965i \(0.986628\pi\)
\(720\) 0 0
\(721\) 52.1884 0.0723834
\(722\) −407.138 62.9653i −0.563904 0.0872096i
\(723\) 3.88254i 0.00537003i
\(724\) −410.228 129.995i −0.566613 0.179552i
\(725\) 0 0
\(726\) 158.261 1023.33i 0.217990 1.40954i
\(727\) 994.690i 1.36821i −0.729383 0.684106i \(-0.760193\pi\)
0.729383 0.684106i \(-0.239807\pi\)
\(728\) −0.488554 + 0.985307i −0.000671090 + 0.00135344i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 1033.27i 1.41350i
\(732\) −156.635 + 494.294i −0.213982 + 0.675264i
\(733\) −1167.65 −1.59298 −0.796488 0.604654i \(-0.793311\pi\)
−0.796488 + 0.604654i \(0.793311\pi\)
\(734\) 222.835 1440.87i 0.303590 1.96303i
\(735\) 0 0
\(736\) 515.986 535.127i 0.701067 0.727075i
\(737\) −1491.83 −2.02420
\(738\) 276.951 + 42.8314i 0.375273 + 0.0580372i
\(739\) 79.9863i 0.108236i −0.998535 0.0541179i \(-0.982765\pi\)
0.998535 0.0541179i \(-0.0172347\pi\)
\(740\) 0 0
\(741\) 8.98623 0.0121272
\(742\) −3.02264 + 19.5446i −0.00407364 + 0.0263405i
\(743\) 402.122i 0.541214i −0.962690 0.270607i \(-0.912776\pi\)
0.962690 0.270607i \(-0.0872244\pi\)
\(744\) −521.578 258.619i −0.701045 0.347606i
\(745\) 0 0
\(746\) 92.2530 + 14.2672i 0.123664 + 0.0191250i
\(747\) 17.6674i 0.0236511i
\(748\) 460.267 1452.47i 0.615330 1.94180i
\(749\) 5.99844 0.00800860
\(750\) 0 0
\(751\) 58.7486i 0.0782271i −0.999235 0.0391136i \(-0.987547\pi\)
0.999235 0.0391136i \(-0.0124534\pi\)
\(752\) −753.434 + 1069.43i −1.00191 + 1.42212i
\(753\) 685.561 0.910440
\(754\) −19.6985 3.04644i −0.0261254 0.00404038i
\(755\) 0 0
\(756\) −6.53646 2.07131i −0.00864611 0.00273983i
\(757\) 1040.91 1.37504 0.687522 0.726164i \(-0.258699\pi\)
0.687522 + 0.726164i \(0.258699\pi\)
\(758\) −35.9561 + 232.495i −0.0474355 + 0.306721i
\(759\) 824.519i 1.08632i
\(760\) 0 0
\(761\) 750.095 0.985670 0.492835 0.870123i \(-0.335961\pi\)
0.492835 + 0.870123i \(0.335961\pi\)
\(762\) 92.7530 + 14.3446i 0.121723 + 0.0188249i
\(763\) 51.7417i 0.0678135i
\(764\) 337.976 1066.55i 0.442377 1.39601i
\(765\) 0 0
\(766\) −76.9285 + 497.425i −0.100429 + 0.649380i
\(767\) 10.1391i 0.0132191i
\(768\) 417.533 149.246i 0.543663 0.194331i
\(769\) 1065.98 1.38619 0.693094 0.720847i \(-0.256247\pi\)
0.693094 + 0.720847i \(0.256247\pi\)
\(770\) 0 0
\(771\) 190.141i 0.246616i
\(772\) −390.975 123.894i −0.506444 0.160485i
\(773\) 947.271 1.22545 0.612724 0.790297i \(-0.290074\pi\)
0.612724 + 0.790297i \(0.290074\pi\)
\(774\) −50.9740 + 329.601i −0.0658579 + 0.425842i
\(775\) 0 0
\(776\) −684.791 339.546i −0.882463 0.437560i
\(777\) 29.1141 0.0374699
\(778\) −705.393 109.092i −0.906675 0.140220i
\(779\) 581.521i 0.746497i
\(780\) 0 0
\(781\) 804.931 1.03064
\(782\) −131.994 + 853.484i −0.168791 + 1.09141i
\(783\) 124.275i 0.158716i
\(784\) 639.491 + 450.533i 0.815678 + 0.574659i
\(785\) 0 0
\(786\) −15.2619 2.36031i −0.0194172 0.00300294i
\(787\) 11.5874i 0.0147236i