Properties

Label 300.3.f.c.199.8
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} - 20 x^{7} + 72 x^{6} - 208 x^{5} + 368 x^{4} - 448 x^{3} + 512 x^{2} - 512 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.8
Root \(-0.152947 + 1.40592i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.c.199.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.305673 + 1.97650i) q^{2} +1.73205 q^{3} +(-3.81313 - 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} +0.329898 q^{7} +(3.55383 - 7.16731i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-0.305673 + 1.97650i) q^{2} +1.73205 q^{3} +(-3.81313 - 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} +0.329898 q^{7} +(3.55383 - 7.16731i) q^{8} +3.00000 q^{9} +20.4920i q^{11} +(-6.60453 - 2.09288i) q^{12} -0.416712i q^{13} +(-0.100841 + 0.652044i) q^{14} +(13.0799 + 9.21501i) q^{16} +18.5884i q^{17} +(-0.917019 + 5.92951i) q^{18} +12.4503i q^{19} +0.571400 q^{21} +(-40.5024 - 6.26384i) q^{22} -23.2304 q^{23} +(6.15542 - 12.4141i) q^{24} +(0.823633 + 0.127378i) q^{26} +5.19615 q^{27} +(-1.25794 - 0.398624i) q^{28} +23.9166 q^{29} +42.0148i q^{31} +(-22.2117 + 23.0357i) q^{32} +35.4931i q^{33} +(-36.7400 - 5.68197i) q^{34} +(-11.4394 - 3.62498i) q^{36} -50.9523i q^{37} +(-24.6081 - 3.80573i) q^{38} -0.721767i q^{39} +46.7073 q^{41} +(-0.174661 + 1.12937i) q^{42} -55.5866 q^{43} +(24.7610 - 78.1385i) q^{44} +(7.10090 - 45.9149i) q^{46} +81.7616 q^{47} +(22.6550 + 15.9609i) q^{48} -48.8912 q^{49} +32.1960i q^{51} +(-0.503524 + 1.58898i) q^{52} -29.9744i q^{53} +(-1.58832 + 10.2702i) q^{54} +(1.17240 - 2.36448i) q^{56} +21.5646i q^{57} +(-7.31067 + 47.2713i) q^{58} +24.3311i q^{59} -74.8416 q^{61} +(-83.0424 - 12.8428i) q^{62} +0.989693 q^{63} +(-38.7406 - 50.9428i) q^{64} +(-70.1523 - 10.8493i) q^{66} +72.8008 q^{67} +(22.4608 - 70.8799i) q^{68} -40.2362 q^{69} -39.2803i q^{71} +(10.6615 - 21.5019i) q^{72} -46.5814i q^{73} +(100.707 + 15.5747i) q^{74} +(15.0441 - 47.4747i) q^{76} +6.76026i q^{77} +(1.42657 + 0.220625i) q^{78} +101.920i q^{79} +9.00000 q^{81} +(-14.2771 + 92.3170i) q^{82} -5.88913 q^{83} +(-2.17882 - 0.690438i) q^{84} +(16.9913 - 109.867i) q^{86} +41.4248 q^{87} +(146.872 + 72.8250i) q^{88} +61.0100 q^{89} -0.137472i q^{91} +(88.5804 + 28.0699i) q^{92} +72.7718i q^{93} +(-24.9923 + 161.602i) q^{94} +(-38.4717 + 39.8989i) q^{96} -95.5437i q^{97} +(14.9447 - 96.6335i) q^{98} +61.4759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} - 44q^{14} + 80q^{16} + 48q^{21} + 72q^{24} - 132q^{26} + 64q^{29} - 248q^{34} + 48q^{36} - 32q^{41} - 80q^{44} - 152q^{46} - 32q^{49} - 36q^{54} - 344q^{56} + 272q^{61} - 32q^{64} - 216q^{66} + 192q^{69} + 216q^{74} + 240q^{76} + 144q^{81} + 288q^{84} + 428q^{86} - 256q^{89} - 24q^{94} + 192q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.305673 + 1.97650i −0.152836 + 0.988251i
\(3\) 1.73205 0.577350
\(4\) −3.81313 1.20833i −0.953282 0.302082i
\(5\) 0 0
\(6\) −0.529441 + 3.42340i −0.0882402 + 0.570567i
\(7\) 0.329898 0.0471283 0.0235641 0.999722i \(-0.492499\pi\)
0.0235641 + 0.999722i \(0.492499\pi\)
\(8\) 3.55383 7.16731i 0.444229 0.895913i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 20.4920i 1.86291i 0.363861 + 0.931453i \(0.381458\pi\)
−0.363861 + 0.931453i \(0.618542\pi\)
\(12\) −6.60453 2.09288i −0.550378 0.174407i
\(13\) 0.416712i 0.0320548i −0.999872 0.0160274i \(-0.994898\pi\)
0.999872 0.0160274i \(-0.00510189\pi\)
\(14\) −0.100841 + 0.652044i −0.00720292 + 0.0465746i
\(15\) 0 0
\(16\) 13.0799 + 9.21501i 0.817493 + 0.575938i
\(17\) 18.5884i 1.09343i 0.837317 + 0.546717i \(0.184123\pi\)
−0.837317 + 0.546717i \(0.815877\pi\)
\(18\) −0.917019 + 5.92951i −0.0509455 + 0.329417i
\(19\) 12.4503i 0.655281i 0.944803 + 0.327640i \(0.106253\pi\)
−0.944803 + 0.327640i \(0.893747\pi\)
\(20\) 0 0
\(21\) 0.571400 0.0272095
\(22\) −40.5024 6.26384i −1.84102 0.284720i
\(23\) −23.2304 −1.01002 −0.505008 0.863114i \(-0.668511\pi\)
−0.505008 + 0.863114i \(0.668511\pi\)
\(24\) 6.15542 12.4141i 0.256476 0.517256i
\(25\) 0 0
\(26\) 0.823633 + 0.127378i 0.0316782 + 0.00489914i
\(27\) 5.19615 0.192450
\(28\) −1.25794 0.398624i −0.0449265 0.0142366i
\(29\) 23.9166 0.824712 0.412356 0.911023i \(-0.364706\pi\)
0.412356 + 0.911023i \(0.364706\pi\)
\(30\) 0 0
\(31\) 42.0148i 1.35532i 0.735377 + 0.677658i \(0.237005\pi\)
−0.735377 + 0.677658i \(0.762995\pi\)
\(32\) −22.2117 + 23.0357i −0.694115 + 0.719865i
\(33\) 35.4931i 1.07555i
\(34\) −36.7400 5.68197i −1.08059 0.167117i
\(35\) 0 0
\(36\) −11.4394 3.62498i −0.317761 0.100694i
\(37\) 50.9523i 1.37709i −0.725194 0.688545i \(-0.758250\pi\)
0.725194 0.688545i \(-0.241750\pi\)
\(38\) −24.6081 3.80573i −0.647582 0.100151i
\(39\) 0.721767i 0.0185068i
\(40\) 0 0
\(41\) 46.7073 1.13920 0.569601 0.821921i \(-0.307098\pi\)
0.569601 + 0.821921i \(0.307098\pi\)
\(42\) −0.174661 + 1.12937i −0.00415861 + 0.0268898i
\(43\) −55.5866 −1.29271 −0.646356 0.763036i \(-0.723708\pi\)
−0.646356 + 0.763036i \(0.723708\pi\)
\(44\) 24.7610 78.1385i 0.562750 1.77588i
\(45\) 0 0
\(46\) 7.10090 45.9149i 0.154367 0.998151i
\(47\) 81.7616 1.73961 0.869804 0.493397i \(-0.164245\pi\)
0.869804 + 0.493397i \(0.164245\pi\)
\(48\) 22.6550 + 15.9609i 0.471980 + 0.332518i
\(49\) −48.8912 −0.997779
\(50\) 0 0
\(51\) 32.1960i 0.631295i
\(52\) −0.503524 + 1.58898i −0.00968316 + 0.0305572i
\(53\) 29.9744i 0.565554i −0.959186 0.282777i \(-0.908744\pi\)
0.959186 0.282777i \(-0.0912557\pi\)
\(54\) −1.58832 + 10.2702i −0.0294134 + 0.190189i
\(55\) 0 0
\(56\) 1.17240 2.36448i 0.0209357 0.0422228i
\(57\) 21.5646i 0.378326i
\(58\) −7.31067 + 47.2713i −0.126046 + 0.815023i
\(59\) 24.3311i 0.412391i 0.978511 + 0.206196i \(0.0661083\pi\)
−0.978511 + 0.206196i \(0.933892\pi\)
\(60\) 0 0
\(61\) −74.8416 −1.22691 −0.613456 0.789729i \(-0.710221\pi\)
−0.613456 + 0.789729i \(0.710221\pi\)
\(62\) −83.0424 12.8428i −1.33939 0.207142i
\(63\) 0.989693 0.0157094
\(64\) −38.7406 50.9428i −0.605321 0.795981i
\(65\) 0 0
\(66\) −70.1523 10.8493i −1.06291 0.164383i
\(67\) 72.8008 1.08658 0.543290 0.839545i \(-0.317178\pi\)
0.543290 + 0.839545i \(0.317178\pi\)
\(68\) 22.4608 70.8799i 0.330307 1.04235i
\(69\) −40.2362 −0.583133
\(70\) 0 0
\(71\) 39.2803i 0.553244i −0.960979 0.276622i \(-0.910785\pi\)
0.960979 0.276622i \(-0.0892150\pi\)
\(72\) 10.6615 21.5019i 0.148076 0.298638i
\(73\) 46.5814i 0.638101i −0.947738 0.319051i \(-0.896636\pi\)
0.947738 0.319051i \(-0.103364\pi\)
\(74\) 100.707 + 15.5747i 1.36091 + 0.210469i
\(75\) 0 0
\(76\) 15.0441 47.4747i 0.197948 0.624667i
\(77\) 6.76026i 0.0877955i
\(78\) 1.42657 + 0.220625i 0.0182894 + 0.00282852i
\(79\) 101.920i 1.29012i 0.764131 + 0.645062i \(0.223168\pi\)
−0.764131 + 0.645062i \(0.776832\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −14.2771 + 92.3170i −0.174112 + 1.12582i
\(83\) −5.88913 −0.0709534 −0.0354767 0.999371i \(-0.511295\pi\)
−0.0354767 + 0.999371i \(0.511295\pi\)
\(84\) −2.17882 0.690438i −0.0259383 0.00821950i
\(85\) 0 0
\(86\) 16.9913 109.867i 0.197574 1.27752i
\(87\) 41.4248 0.476148
\(88\) 146.872 + 72.8250i 1.66900 + 0.827557i
\(89\) 61.0100 0.685506 0.342753 0.939426i \(-0.388641\pi\)
0.342753 + 0.939426i \(0.388641\pi\)
\(90\) 0 0
\(91\) 0.137472i 0.00151069i
\(92\) 88.5804 + 28.0699i 0.962831 + 0.305108i
\(93\) 72.7718i 0.782492i
\(94\) −24.9923 + 161.602i −0.265876 + 1.71917i
\(95\) 0 0
\(96\) −38.4717 + 39.8989i −0.400747 + 0.415614i
\(97\) 95.5437i 0.984987i −0.870316 0.492494i \(-0.836086\pi\)
0.870316 0.492494i \(-0.163914\pi\)
\(98\) 14.9447 96.6335i 0.152497 0.986057i
\(99\) 61.4759i 0.620969i
\(100\) 0 0
\(101\) 162.675 1.61064 0.805322 0.592838i \(-0.201992\pi\)
0.805322 + 0.592838i \(0.201992\pi\)
\(102\) −63.6355 9.84145i −0.623878 0.0964848i
\(103\) 158.196 1.53588 0.767941 0.640521i \(-0.221282\pi\)
0.767941 + 0.640521i \(0.221282\pi\)
\(104\) −2.98670 1.48092i −0.0287183 0.0142397i
\(105\) 0 0
\(106\) 59.2445 + 9.16236i 0.558910 + 0.0864373i
\(107\) −18.1827 −0.169932 −0.0849660 0.996384i \(-0.527078\pi\)
−0.0849660 + 0.996384i \(0.527078\pi\)
\(108\) −19.8136 6.27865i −0.183459 0.0581357i
\(109\) 156.842 1.43891 0.719457 0.694537i \(-0.244391\pi\)
0.719457 + 0.694537i \(0.244391\pi\)
\(110\) 0 0
\(111\) 88.2520i 0.795063i
\(112\) 4.31503 + 3.04001i 0.0385270 + 0.0271430i
\(113\) 98.7245i 0.873668i −0.899542 0.436834i \(-0.856100\pi\)
0.899542 0.436834i \(-0.143900\pi\)
\(114\) −42.6225 6.59172i −0.373882 0.0578221i
\(115\) 0 0
\(116\) −91.1972 28.8991i −0.786183 0.249130i
\(117\) 1.25014i 0.0106849i
\(118\) −48.0904 7.43735i −0.407546 0.0630284i
\(119\) 6.13227i 0.0515317i
\(120\) 0 0
\(121\) −298.921 −2.47042
\(122\) 22.8770 147.925i 0.187517 1.21250i
\(123\) 80.8994 0.657718
\(124\) 50.7676 160.208i 0.409416 1.29200i
\(125\) 0 0
\(126\) −0.302523 + 1.95613i −0.00240097 + 0.0155249i
\(127\) −27.0938 −0.213337 −0.106669 0.994295i \(-0.534018\pi\)
−0.106669 + 0.994295i \(0.534018\pi\)
\(128\) 112.531 60.9990i 0.879145 0.476555i
\(129\) −96.2789 −0.746348
\(130\) 0 0
\(131\) 4.45811i 0.0340314i 0.999855 + 0.0170157i \(0.00541653\pi\)
−0.999855 + 0.0170157i \(0.994583\pi\)
\(132\) 42.8873 135.340i 0.324904 1.02530i
\(133\) 4.10734i 0.0308822i
\(134\) −22.2533 + 143.891i −0.166069 + 1.07381i
\(135\) 0 0
\(136\) 133.229 + 66.0600i 0.979622 + 0.485735i
\(137\) 181.700i 1.32628i 0.748496 + 0.663139i \(0.230776\pi\)
−0.748496 + 0.663139i \(0.769224\pi\)
\(138\) 12.2991 79.5270i 0.0891241 0.576282i
\(139\) 223.419i 1.60733i −0.595083 0.803664i \(-0.702881\pi\)
0.595083 0.803664i \(-0.297119\pi\)
\(140\) 0 0
\(141\) 141.615 1.00436
\(142\) 77.6377 + 12.0069i 0.546744 + 0.0845559i
\(143\) 8.53925 0.0597151
\(144\) 39.2397 + 27.6450i 0.272498 + 0.191979i
\(145\) 0 0
\(146\) 92.0683 + 14.2387i 0.630604 + 0.0975251i
\(147\) −84.6820 −0.576068
\(148\) −61.5670 + 194.288i −0.415994 + 1.31275i
\(149\) −123.867 −0.831324 −0.415662 0.909519i \(-0.636450\pi\)
−0.415662 + 0.909519i \(0.636450\pi\)
\(150\) 0 0
\(151\) 76.0961i 0.503948i −0.967734 0.251974i \(-0.918920\pi\)
0.967734 0.251974i \(-0.0810797\pi\)
\(152\) 89.2353 + 44.2464i 0.587075 + 0.291095i
\(153\) 55.7651i 0.364478i
\(154\) −13.3617 2.06643i −0.0867641 0.0134184i
\(155\) 0 0
\(156\) −0.872130 + 2.75219i −0.00559058 + 0.0176422i
\(157\) 34.2940i 0.218433i −0.994018 0.109217i \(-0.965166\pi\)
0.994018 0.109217i \(-0.0348342\pi\)
\(158\) −201.445 31.1541i −1.27497 0.197178i
\(159\) 51.9172i 0.326523i
\(160\) 0 0
\(161\) −7.66365 −0.0476003
\(162\) −2.75106 + 17.7885i −0.0169818 + 0.109806i
\(163\) −165.538 −1.01557 −0.507786 0.861483i \(-0.669536\pi\)
−0.507786 + 0.861483i \(0.669536\pi\)
\(164\) −178.101 56.4377i −1.08598 0.344132i
\(165\) 0 0
\(166\) 1.80015 11.6399i 0.0108443 0.0701198i
\(167\) −83.6064 −0.500637 −0.250319 0.968164i \(-0.580535\pi\)
−0.250319 + 0.968164i \(0.580535\pi\)
\(168\) 2.03066 4.09540i 0.0120873 0.0243774i
\(169\) 168.826 0.998972
\(170\) 0 0
\(171\) 37.3510i 0.218427i
\(172\) 211.959 + 67.1668i 1.23232 + 0.390505i
\(173\) 192.900i 1.11503i 0.830168 + 0.557513i \(0.188244\pi\)
−0.830168 + 0.557513i \(0.811756\pi\)
\(174\) −12.6625 + 81.8763i −0.0727727 + 0.470554i
\(175\) 0 0
\(176\) −188.834 + 268.033i −1.07292 + 1.52291i
\(177\) 42.1427i 0.238094i
\(178\) −18.6491 + 120.587i −0.104770 + 0.677452i
\(179\) 120.939i 0.675637i −0.941211 0.337819i \(-0.890311\pi\)
0.941211 0.337819i \(-0.109689\pi\)
\(180\) 0 0
\(181\) −107.583 −0.594381 −0.297191 0.954818i \(-0.596050\pi\)
−0.297191 + 0.954818i \(0.596050\pi\)
\(182\) 0.271715 + 0.0420216i 0.00149294 + 0.000230888i
\(183\) −129.629 −0.708357
\(184\) −82.5569 + 166.499i −0.448679 + 0.904887i
\(185\) 0 0
\(186\) −143.834 22.2444i −0.773299 0.119593i
\(187\) −380.913 −2.03697
\(188\) −311.767 98.7947i −1.65834 0.525504i
\(189\) 1.71420 0.00906984
\(190\) 0 0
\(191\) 279.706i 1.46443i −0.681075 0.732214i \(-0.738487\pi\)
0.681075 0.732214i \(-0.261513\pi\)
\(192\) −67.1006 88.2355i −0.349482 0.459560i
\(193\) 102.534i 0.531263i −0.964075 0.265632i \(-0.914420\pi\)
0.964075 0.265632i \(-0.0855805\pi\)
\(194\) 188.842 + 29.2051i 0.973415 + 0.150542i
\(195\) 0 0
\(196\) 186.428 + 59.0765i 0.951165 + 0.301411i
\(197\) 38.9632i 0.197783i −0.995098 0.0988913i \(-0.968470\pi\)
0.995098 0.0988913i \(-0.0315296\pi\)
\(198\) −121.507 18.7915i −0.613673 0.0949067i
\(199\) 147.646i 0.741940i −0.928645 0.370970i \(-0.879025\pi\)
0.928645 0.370970i \(-0.120975\pi\)
\(200\) 0 0
\(201\) 126.095 0.627337
\(202\) −49.7254 + 321.528i −0.246165 + 1.59172i
\(203\) 7.89005 0.0388672
\(204\) 38.9033 122.768i 0.190703 0.601802i
\(205\) 0 0
\(206\) −48.3562 + 312.674i −0.234739 + 1.51784i
\(207\) −69.6912 −0.336672
\(208\) 3.84001 5.45055i 0.0184616 0.0262046i
\(209\) −255.132 −1.22073
\(210\) 0 0
\(211\) 233.336i 1.10586i 0.833229 + 0.552928i \(0.186490\pi\)
−0.833229 + 0.552928i \(0.813510\pi\)
\(212\) −36.2189 + 114.296i −0.170844 + 0.539133i
\(213\) 68.0355i 0.319416i
\(214\) 5.55797 35.9382i 0.0259718 0.167936i
\(215\) 0 0
\(216\) 18.4663 37.2424i 0.0854919 0.172419i
\(217\) 13.8606i 0.0638737i
\(218\) −47.9422 + 309.998i −0.219918 + 1.42201i
\(219\) 80.6813i 0.368408i
\(220\) 0 0
\(221\) 7.74600 0.0350498
\(222\) 174.430 + 26.9762i 0.785722 + 0.121515i
\(223\) 82.7105 0.370899 0.185450 0.982654i \(-0.440626\pi\)
0.185450 + 0.982654i \(0.440626\pi\)
\(224\) −7.32758 + 7.59941i −0.0327124 + 0.0339260i
\(225\) 0 0
\(226\) 195.129 + 30.1774i 0.863403 + 0.133528i
\(227\) −361.534 −1.59266 −0.796330 0.604862i \(-0.793228\pi\)
−0.796330 + 0.604862i \(0.793228\pi\)
\(228\) 26.0571 82.2286i 0.114286 0.360652i
\(229\) −121.818 −0.531955 −0.265977 0.963979i \(-0.585695\pi\)
−0.265977 + 0.963979i \(0.585695\pi\)
\(230\) 0 0
\(231\) 11.7091i 0.0506888i
\(232\) 84.9957 171.418i 0.366361 0.738870i
\(233\) 136.615i 0.586329i 0.956062 + 0.293164i \(0.0947083\pi\)
−0.956062 + 0.293164i \(0.905292\pi\)
\(234\) 2.47090 + 0.382133i 0.0105594 + 0.00163305i
\(235\) 0 0
\(236\) 29.3999 92.7775i 0.124576 0.393125i
\(237\) 176.530i 0.744853i
\(238\) −12.1204 1.87447i −0.0509262 0.00787592i
\(239\) 56.4632i 0.236248i −0.992999 0.118124i \(-0.962312\pi\)
0.992999 0.118124i \(-0.0376880\pi\)
\(240\) 0 0
\(241\) −2.24158 −0.00930117 −0.00465059 0.999989i \(-0.501480\pi\)
−0.00465059 + 0.999989i \(0.501480\pi\)
\(242\) 91.3720 590.818i 0.377570 2.44140i
\(243\) 15.5885 0.0641500
\(244\) 285.381 + 90.4331i 1.16959 + 0.370627i
\(245\) 0 0
\(246\) −24.7287 + 159.898i −0.100523 + 0.649991i
\(247\) 5.18820 0.0210049
\(248\) 301.133 + 149.314i 1.21425 + 0.602071i
\(249\) −10.2003 −0.0409650
\(250\) 0 0
\(251\) 395.809i 1.57693i 0.615081 + 0.788464i \(0.289123\pi\)
−0.615081 + 0.788464i \(0.710877\pi\)
\(252\) −3.77383 1.19587i −0.0149755 0.00474553i
\(253\) 476.036i 1.88157i
\(254\) 8.28184 53.5510i 0.0326057 0.210831i
\(255\) 0 0
\(256\) 86.1671 + 241.063i 0.336590 + 0.941651i
\(257\) 109.778i 0.427151i −0.976927 0.213576i \(-0.931489\pi\)
0.976927 0.213576i \(-0.0685110\pi\)
\(258\) 29.4298 190.295i 0.114069 0.737579i
\(259\) 16.8091i 0.0648998i
\(260\) 0 0
\(261\) 71.7499 0.274904
\(262\) −8.81147 1.36272i −0.0336316 0.00520124i
\(263\) 327.702 1.24601 0.623007 0.782216i \(-0.285911\pi\)
0.623007 + 0.782216i \(0.285911\pi\)
\(264\) 254.390 + 126.137i 0.963599 + 0.477790i
\(265\) 0 0
\(266\) −8.11816 1.25550i −0.0305194 0.00471993i
\(267\) 105.673 0.395777
\(268\) −277.599 87.9672i −1.03582 0.328236i
\(269\) 130.032 0.483392 0.241696 0.970352i \(-0.422296\pi\)
0.241696 + 0.970352i \(0.422296\pi\)
\(270\) 0 0
\(271\) 329.669i 1.21649i −0.793750 0.608245i \(-0.791874\pi\)
0.793750 0.608245i \(-0.208126\pi\)
\(272\) −171.292 + 243.134i −0.629751 + 0.893875i
\(273\) 0.238109i 0.000872195i
\(274\) −359.131 55.5408i −1.31070 0.202704i
\(275\) 0 0
\(276\) 153.426 + 48.6185i 0.555891 + 0.176154i
\(277\) 304.124i 1.09792i −0.835849 0.548960i \(-0.815024\pi\)
0.835849 0.548960i \(-0.184976\pi\)
\(278\) 441.588 + 68.2930i 1.58844 + 0.245658i
\(279\) 126.044i 0.451772i
\(280\) 0 0
\(281\) 240.099 0.854446 0.427223 0.904146i \(-0.359492\pi\)
0.427223 + 0.904146i \(0.359492\pi\)
\(282\) −43.2879 + 279.903i −0.153503 + 0.992563i
\(283\) −86.6730 −0.306265 −0.153133 0.988206i \(-0.548936\pi\)
−0.153133 + 0.988206i \(0.548936\pi\)
\(284\) −47.4635 + 149.781i −0.167125 + 0.527398i
\(285\) 0 0
\(286\) −2.61022 + 16.8779i −0.00912664 + 0.0590135i
\(287\) 15.4086 0.0536886
\(288\) −66.6350 + 69.1070i −0.231372 + 0.239955i
\(289\) −56.5280 −0.195599
\(290\) 0 0
\(291\) 165.487i 0.568683i
\(292\) −56.2856 + 177.621i −0.192759 + 0.608290i
\(293\) 390.339i 1.33222i 0.745855 + 0.666108i \(0.232041\pi\)
−0.745855 + 0.666108i \(0.767959\pi\)
\(294\) 25.8850 167.374i 0.0880442 0.569300i
\(295\) 0 0
\(296\) −365.191 181.076i −1.23375 0.611743i
\(297\) 106.479i 0.358517i
\(298\) 37.8629 244.824i 0.127057 0.821557i
\(299\) 9.68038i 0.0323759i
\(300\) 0 0
\(301\) −18.3379 −0.0609233
\(302\) 150.404 + 23.2605i 0.498027 + 0.0770216i
\(303\) 281.761 0.929906
\(304\) −114.730 + 162.849i −0.377401 + 0.535687i
\(305\) 0 0
\(306\) −110.220 17.0459i −0.360196 0.0557056i
\(307\) 60.2318 0.196195 0.0980973 0.995177i \(-0.468724\pi\)
0.0980973 + 0.995177i \(0.468724\pi\)
\(308\) 8.16860 25.7777i 0.0265214 0.0836939i
\(309\) 274.003 0.886741
\(310\) 0 0
\(311\) 106.594i 0.342747i −0.985206 0.171373i \(-0.945180\pi\)
0.985206 0.171373i \(-0.0548205\pi\)
\(312\) −5.17312 2.56504i −0.0165805 0.00822127i
\(313\) 46.2243i 0.147682i −0.997270 0.0738408i \(-0.976474\pi\)
0.997270 0.0738408i \(-0.0235257\pi\)
\(314\) 67.7823 + 10.4828i 0.215867 + 0.0333846i
\(315\) 0 0
\(316\) 123.152 388.633i 0.389723 1.22985i
\(317\) 8.36780i 0.0263969i 0.999913 + 0.0131984i \(0.00420131\pi\)
−0.999913 + 0.0131984i \(0.995799\pi\)
\(318\) 102.614 + 15.8697i 0.322687 + 0.0499046i
\(319\) 490.099i 1.53636i
\(320\) 0 0
\(321\) −31.4934 −0.0981103
\(322\) 2.34257 15.1472i 0.00727507 0.0470411i
\(323\) −231.432 −0.716506
\(324\) −34.3182 10.8749i −0.105920 0.0335646i
\(325\) 0 0
\(326\) 50.6006 327.187i 0.155217 1.00364i
\(327\) 271.658 0.830757
\(328\) 165.990 334.765i 0.506066 1.02063i
\(329\) 26.9730 0.0819847
\(330\) 0 0
\(331\) 111.072i 0.335564i 0.985824 + 0.167782i \(0.0536605\pi\)
−0.985824 + 0.167782i \(0.946339\pi\)
\(332\) 22.4560 + 7.11600i 0.0676386 + 0.0214337i
\(333\) 152.857i 0.459030i
\(334\) 25.5562 165.248i 0.0765156 0.494755i
\(335\) 0 0
\(336\) 7.47385 + 5.26546i 0.0222436 + 0.0156710i
\(337\) 231.853i 0.687990i 0.938972 + 0.343995i \(0.111780\pi\)
−0.938972 + 0.343995i \(0.888220\pi\)
\(338\) −51.6057 + 333.686i −0.152679 + 0.987236i
\(339\) 170.996i 0.504412i
\(340\) 0 0
\(341\) −860.966 −2.52483
\(342\) −73.8244 11.4172i −0.215861 0.0333836i
\(343\) −32.2941 −0.0941518
\(344\) −197.546 + 398.406i −0.574260 + 1.15816i
\(345\) 0 0
\(346\) −381.266 58.9642i −1.10193 0.170417i
\(347\) 402.088 1.15875 0.579377 0.815059i \(-0.303296\pi\)
0.579377 + 0.815059i \(0.303296\pi\)
\(348\) −157.958 50.0548i −0.453903 0.143835i
\(349\) 163.284 0.467864 0.233932 0.972253i \(-0.424841\pi\)
0.233932 + 0.972253i \(0.424841\pi\)
\(350\) 0 0
\(351\) 2.16530i 0.00616894i
\(352\) −472.046 455.161i −1.34104 1.29307i
\(353\) 175.851i 0.498161i 0.968483 + 0.249081i \(0.0801285\pi\)
−0.968483 + 0.249081i \(0.919872\pi\)
\(354\) −83.2951 12.8819i −0.235297 0.0363895i
\(355\) 0 0
\(356\) −232.639 73.7201i −0.653481 0.207079i
\(357\) 10.6214i 0.0297518i
\(358\) 239.037 + 36.9678i 0.667700 + 0.103262i
\(359\) 345.628i 0.962753i 0.876514 + 0.481377i \(0.159863\pi\)
−0.876514 + 0.481377i \(0.840137\pi\)
\(360\) 0 0
\(361\) 205.989 0.570607
\(362\) 32.8852 212.638i 0.0908431 0.587398i
\(363\) −517.746 −1.42630
\(364\) −0.166112 + 0.524200i −0.000456351 + 0.00144011i
\(365\) 0 0
\(366\) 39.6242 256.213i 0.108263 0.700035i
\(367\) 728.998 1.98637 0.993185 0.116546i \(-0.0371823\pi\)
0.993185 + 0.116546i \(0.0371823\pi\)
\(368\) −303.851 214.068i −0.825682 0.581707i
\(369\) 140.122 0.379734
\(370\) 0 0
\(371\) 9.88848i 0.0266536i
\(372\) 87.9321 277.488i 0.236377 0.745936i
\(373\) 46.6749i 0.125134i −0.998041 0.0625668i \(-0.980071\pi\)
0.998041 0.0625668i \(-0.0199287\pi\)
\(374\) 116.435 752.875i 0.311323 2.01303i
\(375\) 0 0
\(376\) 290.567 586.010i 0.772784 1.55854i
\(377\) 9.96635i 0.0264360i
\(378\) −0.523984 + 3.38812i −0.00138620 + 0.00896328i
\(379\) 117.629i 0.310368i 0.987886 + 0.155184i \(0.0495970\pi\)
−0.987886 + 0.155184i \(0.950403\pi\)
\(380\) 0 0
\(381\) −46.9278 −0.123170
\(382\) 552.839 + 85.4985i 1.44722 + 0.223818i
\(383\) 251.669 0.657100 0.328550 0.944487i \(-0.393440\pi\)
0.328550 + 0.944487i \(0.393440\pi\)
\(384\) 194.909 105.653i 0.507575 0.275139i
\(385\) 0 0
\(386\) 202.658 + 31.3418i 0.525022 + 0.0811964i
\(387\) −166.760 −0.430904
\(388\) −115.448 + 364.321i −0.297547 + 0.938970i
\(389\) −356.890 −0.917454 −0.458727 0.888577i \(-0.651694\pi\)
−0.458727 + 0.888577i \(0.651694\pi\)
\(390\) 0 0
\(391\) 431.815i 1.10439i
\(392\) −173.751 + 350.418i −0.443242 + 0.893923i
\(393\) 7.72168i 0.0196480i
\(394\) 77.0108 + 11.9100i 0.195459 + 0.0302284i
\(395\) 0 0
\(396\) 74.2830 234.416i 0.187583 0.591958i
\(397\) 103.819i 0.261508i 0.991415 + 0.130754i \(0.0417398\pi\)
−0.991415 + 0.130754i \(0.958260\pi\)
\(398\) 291.823 + 45.1314i 0.733224 + 0.113396i
\(399\) 7.11412i 0.0178299i
\(400\) 0 0
\(401\) −121.598 −0.303237 −0.151618 0.988439i \(-0.548449\pi\)
−0.151618 + 0.988439i \(0.548449\pi\)
\(402\) −38.5438 + 249.227i −0.0958800 + 0.619967i
\(403\) 17.5081 0.0434444
\(404\) −620.301 196.565i −1.53540 0.486546i
\(405\) 0 0
\(406\) −2.41177 + 15.5947i −0.00594033 + 0.0384106i
\(407\) 1044.11 2.56539
\(408\) 230.759 + 114.419i 0.565585 + 0.280439i
\(409\) −182.788 −0.446915 −0.223457 0.974714i \(-0.571734\pi\)
−0.223457 + 0.974714i \(0.571734\pi\)
\(410\) 0 0
\(411\) 314.714i 0.765727i
\(412\) −603.221 191.152i −1.46413 0.463962i
\(413\) 8.02677i 0.0194353i
\(414\) 21.3027 137.745i 0.0514558 0.332717i
\(415\) 0 0
\(416\) 9.59924 + 9.25587i 0.0230751 + 0.0222497i
\(417\) 386.972i 0.927991i
\(418\) 77.9869 504.269i 0.186572 1.20638i
\(419\) 168.020i 0.401003i 0.979693 + 0.200502i \(0.0642572\pi\)
−0.979693 + 0.200502i \(0.935743\pi\)
\(420\) 0 0
\(421\) 625.291 1.48525 0.742626 0.669706i \(-0.233580\pi\)
0.742626 + 0.669706i \(0.233580\pi\)
\(422\) −461.189 71.3244i −1.09286 0.169015i
\(423\) 245.285 0.579869
\(424\) −214.836 106.524i −0.506688 0.251236i
\(425\) 0 0
\(426\) 134.472 + 20.7966i 0.315663 + 0.0488184i
\(427\) −24.6901 −0.0578222
\(428\) 69.3331 + 21.9707i 0.161993 + 0.0513334i
\(429\) 14.7904 0.0344765
\(430\) 0 0
\(431\) 133.413i 0.309544i −0.987950 0.154772i \(-0.950536\pi\)
0.987950 0.154772i \(-0.0494643\pi\)
\(432\) 67.9651 + 47.8826i 0.157327 + 0.110839i
\(433\) 706.716i 1.63214i 0.577954 + 0.816069i \(0.303851\pi\)
−0.577954 + 0.816069i \(0.696149\pi\)
\(434\) −27.3955 4.23681i −0.0631233 0.00976223i
\(435\) 0 0
\(436\) −598.057 189.516i −1.37169 0.434670i
\(437\) 289.226i 0.661844i
\(438\) 159.467 + 24.6621i 0.364080 + 0.0563062i
\(439\) 507.488i 1.15601i −0.816033 0.578005i \(-0.803831\pi\)
0.816033 0.578005i \(-0.196169\pi\)
\(440\) 0 0
\(441\) −146.674 −0.332593
\(442\) −2.36774 + 15.3100i −0.00535689 + 0.0346380i
\(443\) −412.172 −0.930410 −0.465205 0.885203i \(-0.654019\pi\)
−0.465205 + 0.885203i \(0.654019\pi\)
\(444\) −106.637 + 336.516i −0.240174 + 0.757919i
\(445\) 0 0
\(446\) −25.2824 + 163.478i −0.0566869 + 0.366542i
\(447\) −214.544 −0.479965
\(448\) −12.7804 16.8059i −0.0285277 0.0375132i
\(449\) 808.617 1.80093 0.900465 0.434929i \(-0.143227\pi\)
0.900465 + 0.434929i \(0.143227\pi\)
\(450\) 0 0
\(451\) 957.124i 2.12223i
\(452\) −119.291 + 376.449i −0.263919 + 0.832852i
\(453\) 131.802i 0.290955i
\(454\) 110.511 714.573i 0.243417 1.57395i
\(455\) 0 0
\(456\) 154.560 + 76.6370i 0.338948 + 0.168064i
\(457\) 472.873i 1.03473i −0.855764 0.517367i \(-0.826912\pi\)
0.855764 0.517367i \(-0.173088\pi\)
\(458\) 37.2364 240.773i 0.0813021 0.525705i
\(459\) 96.5881i 0.210432i
\(460\) 0 0
\(461\) 433.776 0.940946 0.470473 0.882414i \(-0.344083\pi\)
0.470473 + 0.882414i \(0.344083\pi\)
\(462\) −23.1431 3.57916i −0.0500933 0.00774709i
\(463\) −530.624 −1.14606 −0.573028 0.819536i \(-0.694231\pi\)
−0.573028 + 0.819536i \(0.694231\pi\)
\(464\) 312.827 + 220.392i 0.674196 + 0.474983i
\(465\) 0 0
\(466\) −270.019 41.7594i −0.579440 0.0896124i
\(467\) −355.266 −0.760741 −0.380370 0.924834i \(-0.624203\pi\)
−0.380370 + 0.924834i \(0.624203\pi\)
\(468\) −1.51057 + 4.76693i −0.00322772 + 0.0101857i
\(469\) 24.0168 0.0512086
\(470\) 0 0
\(471\) 59.3990i 0.126113i
\(472\) 174.388 + 86.4686i 0.369467 + 0.183196i
\(473\) 1139.08i 2.40820i
\(474\) −348.912 53.9605i −0.736102 0.113841i
\(475\) 0 0
\(476\) 7.40978 23.3831i 0.0155668 0.0491242i
\(477\) 89.9232i 0.188518i
\(478\) 111.600 + 17.2593i 0.233472 + 0.0361072i
\(479\) 548.640i 1.14539i 0.819770 + 0.572693i \(0.194101\pi\)
−0.819770 + 0.572693i \(0.805899\pi\)
\(480\) 0 0
\(481\) −21.2324 −0.0441423
\(482\) 0.685191 4.43050i 0.00142156 0.00919190i
\(483\) −13.2738 −0.0274821
\(484\) 1139.82 + 361.194i 2.35501 + 0.746269i
\(485\) 0 0
\(486\) −4.76497 + 30.8106i −0.00980446 + 0.0633964i
\(487\) 134.618 0.276422 0.138211 0.990403i \(-0.455865\pi\)
0.138211 + 0.990403i \(0.455865\pi\)
\(488\) −265.974 + 536.412i −0.545029 + 1.09921i
\(489\) −286.721 −0.586341
\(490\) 0 0
\(491\) 756.810i 1.54136i 0.637220 + 0.770682i \(0.280084\pi\)
−0.637220 + 0.770682i \(0.719916\pi\)
\(492\) −308.480 97.7529i −0.626991 0.198685i
\(493\) 444.572i 0.901768i
\(494\) −1.58589 + 10.2545i −0.00321031 + 0.0207581i
\(495\) 0 0
\(496\) −387.167 + 549.549i −0.780579 + 1.10796i
\(497\) 12.9585i 0.0260734i
\(498\) 3.11795 20.1609i 0.00626094 0.0404837i
\(499\) 706.956i 1.41675i 0.705838 + 0.708373i \(0.250570\pi\)
−0.705838 + 0.708373i \(0.749430\pi\)
\(500\) 0 0
\(501\) −144.811 −0.289043
\(502\) −782.318 120.988i −1.55840 0.241012i
\(503\) 100.567 0.199935 0.0999673 0.994991i \(-0.468126\pi\)
0.0999673 + 0.994991i \(0.468126\pi\)
\(504\) 3.51720 7.09344i 0.00697858 0.0140743i
\(505\) 0 0
\(506\) 940.887 + 145.511i 1.85946 + 0.287572i
\(507\) 292.416 0.576757
\(508\) 103.312 + 32.7382i 0.203370 + 0.0644452i
\(509\) −753.185 −1.47973 −0.739867 0.672753i \(-0.765112\pi\)
−0.739867 + 0.672753i \(0.765112\pi\)
\(510\) 0 0
\(511\) 15.3671i 0.0300726i
\(512\) −502.800 + 96.6232i −0.982031 + 0.188717i
\(513\) 64.6938i 0.126109i
\(514\) 216.976 + 33.5561i 0.422133 + 0.0652843i
\(515\) 0 0
\(516\) 367.124 + 116.336i 0.711480 + 0.225458i
\(517\) 1675.46i 3.24073i
\(518\) 33.2231 + 5.13807i 0.0641373 + 0.00991906i
\(519\) 334.112i 0.643761i
\(520\) 0 0
\(521\) 117.708 0.225926 0.112963 0.993599i \(-0.463966\pi\)
0.112963 + 0.993599i \(0.463966\pi\)
\(522\) −21.9320 + 141.814i −0.0420153 + 0.271674i
\(523\) 617.411 1.18052 0.590259 0.807214i \(-0.299026\pi\)
0.590259 + 0.807214i \(0.299026\pi\)
\(524\) 5.38686 16.9994i 0.0102803 0.0324415i
\(525\) 0 0
\(526\) −100.170 + 647.704i −0.190437 + 1.23138i
\(527\) −780.988 −1.48195
\(528\) −327.070 + 464.246i −0.619450 + 0.879254i
\(529\) 10.6508 0.0201338
\(530\) 0 0
\(531\) 72.9932i 0.137464i
\(532\) 4.96301 15.6618i 0.00932896 0.0294395i
\(533\) 19.4635i 0.0365169i
\(534\) −32.3012 + 208.862i −0.0604892 + 0.391127i
\(535\) 0 0
\(536\) 258.722 521.786i 0.482690 0.973481i
\(537\) 209.473i 0.390079i
\(538\) −39.7474 + 257.009i −0.0738799 + 0.477713i
\(539\) 1001.88i 1.85877i
\(540\) 0 0
\(541\) 352.762 0.652056 0.326028 0.945360i \(-0.394290\pi\)
0.326028 + 0.945360i \(0.394290\pi\)
\(542\) 651.591 + 100.771i 1.20220 + 0.185924i
\(543\) −186.339 −0.343166
\(544\) −428.196 412.879i −0.787125 0.758969i
\(545\) 0 0
\(546\) 0.470623 + 0.0727835i 0.000861948 + 0.000133303i
\(547\) −295.110 −0.539507 −0.269753 0.962929i \(-0.586942\pi\)
−0.269753 + 0.962929i \(0.586942\pi\)
\(548\) 219.553 692.846i 0.400644 1.26432i
\(549\) −224.525 −0.408970
\(550\) 0 0
\(551\) 297.770i 0.540418i
\(552\) −142.993 + 288.385i −0.259045 + 0.522437i
\(553\) 33.6231i 0.0608013i
\(554\) 601.102 + 92.9624i 1.08502 + 0.167802i
\(555\) 0 0
\(556\) −269.963 + 851.924i −0.485545 + 1.53224i
\(557\) 31.8538i 0.0571882i −0.999591 0.0285941i \(-0.990897\pi\)
0.999591 0.0285941i \(-0.00910302\pi\)
\(558\) −249.127 38.5284i −0.446465 0.0690473i
\(559\) 23.1636i 0.0414376i
\(560\) 0 0
\(561\) −659.760 −1.17604
\(562\) −73.3919 + 474.557i −0.130591 + 0.844408i
\(563\) −906.668 −1.61042 −0.805211 0.592988i \(-0.797948\pi\)
−0.805211 + 0.592988i \(0.797948\pi\)
\(564\) −539.997 171.117i −0.957441 0.303400i
\(565\) 0 0
\(566\) 26.4936 171.310i 0.0468085 0.302667i
\(567\) 2.96908 0.00523647
\(568\) −281.534 139.596i −0.495659 0.245767i
\(569\) 465.009 0.817239 0.408620 0.912705i \(-0.366010\pi\)
0.408620 + 0.912705i \(0.366010\pi\)
\(570\) 0 0
\(571\) 265.895i 0.465666i 0.972517 + 0.232833i \(0.0747995\pi\)
−0.972517 + 0.232833i \(0.925200\pi\)
\(572\) −32.5613 10.3182i −0.0569253 0.0180388i
\(573\) 484.464i 0.845488i
\(574\) −4.71000 + 30.4552i −0.00820557 + 0.0530578i
\(575\) 0 0
\(576\) −116.222 152.828i −0.201774 0.265327i
\(577\) 138.097i 0.239336i −0.992814 0.119668i \(-0.961817\pi\)
0.992814 0.119668i \(-0.0381830\pi\)
\(578\) 17.2791 111.728i 0.0298946 0.193301i
\(579\) 177.594i 0.306725i
\(580\) 0 0
\(581\) −1.94281 −0.00334391
\(582\) 327.085 + 50.5848i 0.562001 + 0.0869154i
\(583\) 614.234 1.05358
\(584\) −333.863 165.542i −0.571683 0.283463i
\(585\) 0 0
\(586\) −771.507 119.316i −1.31656 0.203611i
\(587\) −648.473 −1.10472 −0.552362 0.833604i \(-0.686273\pi\)
−0.552362 + 0.833604i \(0.686273\pi\)
\(588\) 322.903 + 102.324i 0.549155 + 0.174020i
\(589\) −523.098 −0.888113
\(590\) 0 0
\(591\) 67.4862i 0.114190i
\(592\) 469.526 666.451i 0.793118 1.12576i
\(593\) 350.392i 0.590880i −0.955361 0.295440i \(-0.904534\pi\)
0.955361 0.295440i \(-0.0954662\pi\)
\(594\) −210.457 32.5479i −0.354304 0.0547944i
\(595\) 0 0
\(596\) 472.322 + 149.672i 0.792486 + 0.251128i
\(597\) 255.731i 0.428359i
\(598\) −19.1333 2.95903i −0.0319955 0.00494821i
\(599\) 276.745i 0.462012i −0.972952 0.231006i \(-0.925798\pi\)
0.972952 0.231006i \(-0.0742017\pi\)
\(600\) 0 0
\(601\) 815.487 1.35688 0.678442 0.734654i \(-0.262656\pi\)
0.678442 + 0.734654i \(0.262656\pi\)
\(602\) 5.60540 36.2449i 0.00931130 0.0602075i
\(603\) 218.403 0.362193
\(604\) −91.9490 + 290.164i −0.152233 + 0.480405i
\(605\) 0 0
\(606\) −86.1269 + 556.902i −0.142124 + 0.918981i
\(607\) 247.049 0.407001 0.203500 0.979075i \(-0.434768\pi\)
0.203500 + 0.979075i \(0.434768\pi\)
\(608\) −286.802 276.543i −0.471713 0.454840i
\(609\) 13.6660 0.0224400
\(610\) 0 0
\(611\) 34.0710i 0.0557627i
\(612\) 67.3825 212.640i 0.110102 0.347450i
\(613\) 1005.15i 1.63972i 0.572561 + 0.819862i \(0.305950\pi\)
−0.572561 + 0.819862i \(0.694050\pi\)
\(614\) −18.4112 + 119.048i −0.0299857 + 0.193890i
\(615\) 0 0
\(616\) 48.4528 + 24.0248i 0.0786572 + 0.0390013i
\(617\) 533.282i 0.864314i −0.901798 0.432157i \(-0.857753\pi\)
0.901798 0.432157i \(-0.142247\pi\)
\(618\) −83.7553 + 541.568i −0.135526 + 0.876324i
\(619\) 1136.85i 1.83659i −0.395900 0.918294i \(-0.629567\pi\)
0.395900 0.918294i \(-0.370433\pi\)
\(620\) 0 0
\(621\) −120.709 −0.194378
\(622\) 210.684 + 32.5830i 0.338720 + 0.0523842i
\(623\) 20.1271 0.0323067
\(624\) 6.65109 9.44063i 0.0106588 0.0151292i
\(625\) 0 0
\(626\) 91.3625 + 14.1295i 0.145946 + 0.0225711i
\(627\) −441.901 −0.704787
\(628\) −41.4384 + 130.768i −0.0659847 + 0.208229i
\(629\) 947.121 1.50576
\(630\) 0 0
\(631\) 936.738i 1.48453i −0.670107 0.742265i \(-0.733752\pi\)
0.670107 0.742265i \(-0.266248\pi\)
\(632\) 730.490 + 362.206i 1.15584 + 0.573110i
\(633\) 404.149i 0.638466i
\(634\) −16.5390 2.55781i −0.0260867 0.00403440i
\(635\) 0 0
\(636\) −62.7329 + 197.967i −0.0986366 + 0.311269i
\(637\) 20.3735i 0.0319836i
\(638\) −968.682 149.810i −1.51831 0.234812i
\(639\) 117.841i 0.184415i
\(640\) 0 0
\(641\) 214.558 0.334723 0.167362 0.985896i \(-0.446475\pi\)
0.167362 + 0.985896i \(0.446475\pi\)
\(642\) 9.62669 62.2468i 0.0149948 0.0969577i
\(643\) −786.394 −1.22301 −0.611504 0.791241i \(-0.709435\pi\)
−0.611504 + 0.791241i \(0.709435\pi\)
\(644\) 29.2225 + 9.26020i 0.0453765 + 0.0143792i
\(645\) 0 0
\(646\) 70.7424 457.425i 0.109508 0.708088i
\(647\) 316.550 0.489258 0.244629 0.969617i \(-0.421334\pi\)
0.244629 + 0.969617i \(0.421334\pi\)
\(648\) 31.9845 64.5058i 0.0493588 0.0995459i
\(649\) −498.592 −0.768246
\(650\) 0 0
\(651\) 24.0073i 0.0368775i
\(652\) 631.219 + 200.024i 0.968127 + 0.306786i
\(653\) 516.391i 0.790797i −0.918510 0.395399i \(-0.870606\pi\)
0.918510 0.395399i \(-0.129394\pi\)
\(654\) −83.0384 + 536.932i −0.126970 + 0.820997i
\(655\) 0 0
\(656\) 610.926 + 430.408i 0.931290 + 0.656110i
\(657\) 139.744i 0.212700i
\(658\) −8.24491 + 53.3121i −0.0125303 + 0.0810215i
\(659\) 285.118i 0.432653i −0.976321 0.216326i \(-0.930592\pi\)
0.976321 0.216326i \(-0.0694076\pi\)
\(660\) 0 0
\(661\) −391.847 −0.592809 −0.296405 0.955062i \(-0.595788\pi\)
−0.296405 + 0.955062i \(0.595788\pi\)
\(662\) −219.534 33.9516i −0.331622 0.0512865i
\(663\) 13.4165 0.0202360
\(664\) −20.9290 + 42.2092i −0.0315196 + 0.0635681i
\(665\) 0 0
\(666\) 302.122 + 46.7242i 0.453637 + 0.0701565i
\(667\) −555.593 −0.832973
\(668\) 318.802 + 101.024i 0.477248 + 0.151233i
\(669\) 143.259 0.214139
\(670\) 0 0
\(671\) 1533.65i 2.28562i
\(672\) −12.6917 + 13.1626i −0.0188865 + 0.0195872i
\(673\) 1213.59i 1.80325i 0.432517 + 0.901626i \(0.357625\pi\)
−0.432517 + 0.901626i \(0.642375\pi\)
\(674\) −458.257 70.8711i −0.679907 0.105150i
\(675\) 0 0
\(676\) −643.756 203.997i −0.952303 0.301771i
\(677\) 251.863i 0.372028i 0.982547 + 0.186014i \(0.0595570\pi\)
−0.982547 + 0.186014i \(0.940443\pi\)
\(678\) 337.974 + 52.2688i 0.498486 + 0.0770926i
\(679\) 31.5197i 0.0464207i
\(680\) 0 0
\(681\) −626.195 −0.919523
\(682\) 263.174 1701.70i 0.385886 2.49517i
\(683\) 664.793 0.973342 0.486671 0.873585i \(-0.338211\pi\)
0.486671 + 0.873585i \(0.338211\pi\)
\(684\) 45.1322 142.424i 0.0659828 0.208222i
\(685\) 0 0
\(686\) 9.87143 63.8293i 0.0143898 0.0930457i
\(687\) −210.994 −0.307124
\(688\) −727.067 512.231i −1.05678 0.744522i
\(689\) −12.4907 −0.0181287
\(690\) 0 0
\(691\) 654.347i 0.946957i −0.880805 0.473479i \(-0.842998\pi\)
0.880805 0.473479i \(-0.157002\pi\)
\(692\) 233.086 735.551i 0.336829 1.06293i
\(693\) 20.2808i 0.0292652i
\(694\) −122.907 + 794.728i −0.177100 + 1.14514i
\(695\) 0 0
\(696\) 147.217 296.904i 0.211519 0.426587i
\(697\) 868.213i 1.24564i
\(698\) −49.9117 + 322.732i −0.0715067 + 0.462367i
\(699\) 236.623i 0.338517i
\(700\) 0 0
\(701\) −1266.25 −1.80635 −0.903174 0.429275i \(-0.858769\pi\)
−0.903174 + 0.429275i \(0.858769\pi\)
\(702\) 4.27972 + 0.661874i 0.00609647 + 0.000942840i
\(703\) 634.373 0.902380
\(704\) 1043.92 793.870i 1.48284 1.12766i
\(705\) 0 0
\(706\) −347.570 53.7529i −0.492309 0.0761372i
\(707\) 53.6661 0.0759068
\(708\) 50.9221 160.695i 0.0719239 0.226971i
\(709\) 493.220 0.695656 0.347828 0.937558i \(-0.386919\pi\)
0.347828 + 0.937558i \(0.386919\pi\)
\(710\) 0 0
\(711\) 305.759i 0.430041i
\(712\) 216.819 437.278i 0.304522 0.614154i
\(713\) 976.020i 1.36889i
\(714\) −20.9932 3.24667i −0.0294023 0.00454716i
\(715\) 0 0
\(716\) −146.134 + 461.156i −0.204098 + 0.644073i
\(717\) 97.7971i 0.136398i
\(718\) −683.135 105.649i −0.951442 0.147144i
\(719\) 60.3910i 0.0839930i −0.999118 0.0419965i \(-0.986628\pi\)
0.999118 0.0419965i \(-0.0133718\pi\)
\(720\) 0 0
\(721\) 52.1884 0.0723834
\(722\) −62.9653 + 407.138i −0.0872096 + 0.563904i
\(723\) −3.88254 −0.00537003
\(724\) 410.228 + 129.995i 0.566613 + 0.179552i
\(725\) 0 0
\(726\) 158.261 1023.33i 0.217990 1.40954i
\(727\) −994.690 −1.36821 −0.684106 0.729383i \(-0.739807\pi\)
−0.684106 + 0.729383i \(0.739807\pi\)
\(728\) −0.985307 0.488554i −0.00135344 0.000671090i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1033.27i 1.41350i
\(732\) 494.294 + 156.635i 0.675264 + 0.213982i
\(733\) 1167.65i 1.59298i −0.604654 0.796488i \(-0.706689\pi\)
0.604654 0.796488i \(-0.293311\pi\)
\(734\) −222.835 + 1440.87i −0.303590 + 1.96303i
\(735\) 0 0
\(736\) 515.986 535.127i 0.701067 0.727075i
\(737\) 1491.83i 2.02420i
\(738\) −42.8314 + 276.951i −0.0580372 + 0.375273i
\(739\) 79.9863i 0.108236i 0.998535 + 0.0541179i \(0.0172347\pi\)
−0.998535 + 0.0541179i \(0.982765\pi\)
\(740\) 0 0
\(741\) 8.98623 0.0121272
\(742\) 19.5446 + 3.02264i 0.0263405 + 0.00407364i
\(743\) 402.122 0.541214 0.270607 0.962690i \(-0.412776\pi\)
0.270607 + 0.962690i \(0.412776\pi\)
\(744\) 521.578 + 258.619i 0.701045 + 0.347606i
\(745\) 0 0
\(746\) 92.2530 + 14.2672i 0.123664 + 0.0191250i
\(747\) −17.6674 −0.0236511
\(748\) 1452.47 + 460.267i 1.94180 + 0.615330i
\(749\) −5.99844 −0.00800860
\(750\) 0 0
\(751\) 58.7486i 0.0782271i −0.999235 0.0391136i \(-0.987547\pi\)
0.999235 0.0391136i \(-0.0124534\pi\)
\(752\) 1069.43 + 753.434i 1.42212 + 1.00191i
\(753\) 685.561i 0.910440i
\(754\) 19.6985 + 3.04644i 0.0261254 + 0.00404038i
\(755\) 0 0
\(756\) −6.53646 2.07131i −0.00864611 0.00273983i
\(757\) 1040.91i 1.37504i −0.726164 0.687522i \(-0.758699\pi\)
0.726164 0.687522i \(-0.241301\pi\)
\(758\) −232.495 35.9561i −0.306721 0.0474355i
\(759\) 824.519i 1.08632i
\(760\) 0 0
\(761\) 750.095 0.985670 0.492835 0.870123i \(-0.335961\pi\)
0.492835 + 0.870123i \(0.335961\pi\)
\(762\) 14.3446 92.7530i 0.0188249 0.121723i
\(763\) 51.7417 0.0678135
\(764\) −337.976 + 1066.55i −0.442377 + 1.39601i
\(765\) 0 0
\(766\) −76.9285 + 497.425i −0.100429 + 0.649380i
\(767\) 10.1391 0.0132191
\(768\) 149.246 + 417.533i 0.194331 + 0.543663i
\(769\) −1065.98 −1.38619 −0.693094 0.720847i \(-0.743753\pi\)
−0.693094 + 0.720847i \(0.743753\pi\)
\(770\) 0 0
\(771\) 190.141i 0.246616i
\(772\) −123.894 + 390.975i −0.160485 + 0.506444i
\(773\) 947.271i 1.22545i 0.790297 + 0.612724i \(0.209926\pi\)
−0.790297 + 0.612724i \(0.790074\pi\)
\(774\) 50.9740 329.601i 0.0658579 0.425842i
\(775\) 0 0
\(776\) −684.791 339.546i −0.882463 0.437560i
\(777\) 29.1141i 0.0374699i
\(778\) 109.092 705.393i 0.140220 0.906675i
\(779\) 581.521i 0.746497i
\(780\) 0 0
\(781\) 804.931 1.03064
\(782\) 853.484 + 131.994i 1.09141 + 0.168791i
\(783\) 124.275 0.158716
\(784\) −639.491 450.533i −0.815678 0.574659i
\(785\) 0 0
\(786\) −15.2619 2.36031i −0.0194172 0.00300294i
\(787\) 11.5874 0.0147236 0.00736178