Properties

Label 1110.2.bb.d.1099.11
Level $1110$
Weight $2$
Character 1110.1099
Analytic conductor $8.863$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1099.11
Character \(\chi\) \(=\) 1110.1099
Dual form 1110.2.bb.d.1009.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.529198 + 2.17254i) q^{5} +1.00000 q^{6} +(-2.93485 - 1.69443i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.529198 + 2.17254i) q^{5} +1.00000 q^{6} +(-2.93485 - 1.69443i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.54457 + 1.61688i) q^{10} +4.29568 q^{11} +(0.866025 - 0.500000i) q^{12} +(1.80925 + 1.04457i) q^{13} -3.38887 q^{14} +(-0.627973 + 2.14608i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.53292 - 3.19443i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-1.07231 + 1.85729i) q^{19} +(2.14608 + 0.627973i) q^{20} +(-1.69443 - 2.93485i) q^{21} +(3.72017 - 2.14784i) q^{22} +4.17381i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.43990 + 2.29941i) q^{25} +2.08914 q^{26} +1.00000i q^{27} +(-2.93485 + 1.69443i) q^{28} +2.38887 q^{29} +(0.529198 + 2.17254i) q^{30} +8.38482 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.72017 + 2.14784i) q^{33} +(3.19443 - 5.53292i) q^{34} +(2.12812 - 7.27277i) q^{35} +1.00000 q^{36} +(0.158737 + 6.08069i) q^{37} +2.14462i q^{38} +(1.04457 + 1.80925i) q^{39} +(2.17254 - 0.529198i) q^{40} +(-5.28456 + 9.15313i) q^{41} +(-2.93485 - 1.69443i) q^{42} -2.54477i q^{43} +(2.14784 - 3.72017i) q^{44} +(-1.61688 + 1.54457i) q^{45} +(2.08690 + 3.61462i) q^{46} -10.9276i q^{47} -1.00000i q^{48} +(2.24221 + 3.88362i) q^{49} +(-2.69536 + 4.21130i) q^{50} +6.38887 q^{51} +(1.80925 - 1.04457i) q^{52} +(9.69231 - 5.59586i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.27327 + 9.33256i) q^{55} +(-1.69443 + 2.93485i) q^{56} +(-1.85729 + 1.07231i) q^{57} +(2.06882 - 1.19443i) q^{58} +(-1.78454 - 3.09092i) q^{59} +(1.54457 + 1.61688i) q^{60} +(-1.89207 + 3.27717i) q^{61} +(7.26147 - 4.19241i) q^{62} -3.38887i q^{63} -1.00000 q^{64} +(-1.31193 + 4.48346i) q^{65} +4.29568 q^{66} +(-12.4237 - 7.17284i) q^{67} -6.38887i q^{68} +(-2.08690 + 3.61462i) q^{69} +(-1.79338 - 7.36246i) q^{70} +(-4.72539 + 8.18462i) q^{71} +(0.866025 - 0.500000i) q^{72} -7.65823i q^{73} +(3.17782 + 5.18666i) q^{74} +(-4.99477 - 0.228600i) q^{75} +(1.07231 + 1.85729i) q^{76} +(-12.6072 - 7.27874i) q^{77} +(1.80925 + 1.04457i) q^{78} +(-3.37250 + 5.84135i) q^{79} +(1.61688 - 1.54457i) q^{80} +(-0.500000 + 0.866025i) q^{81} +10.5691i q^{82} +(-10.0539 + 5.80463i) q^{83} -3.38887 q^{84} +(9.86806 + 10.3300i) q^{85} +(-1.27238 - 2.20383i) q^{86} +(2.06882 + 1.19443i) q^{87} -4.29568i q^{88} +(-0.462359 - 0.800829i) q^{89} +(-0.627973 + 2.14608i) q^{90} +(-3.53991 - 6.13131i) q^{91} +(3.61462 + 2.08690i) q^{92} +(7.26147 + 4.19241i) q^{93} +(-5.46381 - 9.46360i) q^{94} +(-4.60251 - 1.34676i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.99803i q^{97} +(3.88362 + 2.24221i) q^{98} +(2.14784 + 3.72017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + O(q^{10}) \) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + 4q^{10} - 12q^{11} + 8q^{14} + 2q^{15} - 14q^{16} - 20q^{19} - 2q^{20} + 4q^{21} + 14q^{24} - 8q^{25} - 20q^{26} - 36q^{29} + 2q^{30} + 24q^{31} + 38q^{34} - 2q^{35} + 28q^{36} - 10q^{39} + 2q^{40} - 6q^{44} + 4q^{45} + 8q^{46} + 50q^{49} - 4q^{50} + 76q^{51} + 14q^{54} - 28q^{55} + 4q^{56} - 26q^{59} + 4q^{60} - 28q^{61} - 28q^{64} + 60q^{65} - 12q^{66} - 8q^{69} - 10q^{70} - 64q^{71} + 24q^{74} - 8q^{75} + 20q^{76} + 32q^{79} - 4q^{80} - 14q^{81} + 8q^{84} + 16q^{85} - 8q^{86} + 76q^{89} + 2q^{90} - 8q^{91} - 38q^{94} - 70q^{95} - 14q^{96} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.529198 + 2.17254i 0.236665 + 0.971591i
\(6\) 1.00000 0.408248
\(7\) −2.93485 1.69443i −1.10927 0.640436i −0.170628 0.985336i \(-0.554580\pi\)
−0.938639 + 0.344900i \(0.887913\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.54457 + 1.61688i 0.488436 + 0.511302i
\(11\) 4.29568 1.29520 0.647598 0.761982i \(-0.275774\pi\)
0.647598 + 0.761982i \(0.275774\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 1.80925 + 1.04457i 0.501796 + 0.289712i 0.729455 0.684029i \(-0.239774\pi\)
−0.227659 + 0.973741i \(0.573107\pi\)
\(14\) −3.38887 −0.905713
\(15\) −0.627973 + 2.14608i −0.162142 + 0.554115i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 5.53292 3.19443i 1.34193 0.774764i 0.354840 0.934927i \(-0.384535\pi\)
0.987091 + 0.160163i \(0.0512020\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) −1.07231 + 1.85729i −0.246004 + 0.426092i −0.962414 0.271588i \(-0.912451\pi\)
0.716409 + 0.697680i \(0.245784\pi\)
\(20\) 2.14608 + 0.627973i 0.479878 + 0.140419i
\(21\) −1.69443 2.93485i −0.369756 0.640436i
\(22\) 3.72017 2.14784i 0.793142 0.457921i
\(23\) 4.17381i 0.870299i 0.900358 + 0.435149i \(0.143304\pi\)
−0.900358 + 0.435149i \(0.856696\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −4.43990 + 2.29941i −0.887980 + 0.459883i
\(26\) 2.08914 0.409715
\(27\) 1.00000i 0.192450i
\(28\) −2.93485 + 1.69443i −0.554634 + 0.320218i
\(29\) 2.38887 0.443602 0.221801 0.975092i \(-0.428807\pi\)
0.221801 + 0.975092i \(0.428807\pi\)
\(30\) 0.529198 + 2.17254i 0.0966179 + 0.396651i
\(31\) 8.38482 1.50596 0.752979 0.658044i \(-0.228616\pi\)
0.752979 + 0.658044i \(0.228616\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 3.72017 + 2.14784i 0.647598 + 0.373891i
\(34\) 3.19443 5.53292i 0.547841 0.948888i
\(35\) 2.12812 7.27277i 0.359718 1.22932i
\(36\) 1.00000 0.166667
\(37\) 0.158737 + 6.08069i 0.0260962 + 0.999659i
\(38\) 2.14462i 0.347903i
\(39\) 1.04457 + 1.80925i 0.167265 + 0.289712i
\(40\) 2.17254 0.529198i 0.343509 0.0836736i
\(41\) −5.28456 + 9.15313i −0.825310 + 1.42948i 0.0763728 + 0.997079i \(0.475666\pi\)
−0.901682 + 0.432399i \(0.857667\pi\)
\(42\) −2.93485 1.69443i −0.452856 0.261457i
\(43\) 2.54477i 0.388074i −0.980994 0.194037i \(-0.937842\pi\)
0.980994 0.194037i \(-0.0621581\pi\)
\(44\) 2.14784 3.72017i 0.323799 0.560836i
\(45\) −1.61688 + 1.54457i −0.241030 + 0.230251i
\(46\) 2.08690 + 3.61462i 0.307697 + 0.532947i
\(47\) 10.9276i 1.59396i −0.604007 0.796979i \(-0.706430\pi\)
0.604007 0.796979i \(-0.293570\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 2.24221 + 3.88362i 0.320316 + 0.554803i
\(50\) −2.69536 + 4.21130i −0.381181 + 0.595568i
\(51\) 6.38887 0.894620
\(52\) 1.80925 1.04457i 0.250898 0.144856i
\(53\) 9.69231 5.59586i 1.33134 0.768650i 0.345836 0.938295i \(-0.387595\pi\)
0.985505 + 0.169645i \(0.0542621\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 2.27327 + 9.33256i 0.306527 + 1.25840i
\(56\) −1.69443 + 2.93485i −0.226428 + 0.392185i
\(57\) −1.85729 + 1.07231i −0.246004 + 0.142031i
\(58\) 2.06882 1.19443i 0.271649 0.156837i
\(59\) −1.78454 3.09092i −0.232328 0.402403i 0.726165 0.687521i \(-0.241301\pi\)
−0.958493 + 0.285117i \(0.907968\pi\)
\(60\) 1.54457 + 1.61688i 0.199403 + 0.208738i
\(61\) −1.89207 + 3.27717i −0.242255 + 0.419598i −0.961356 0.275307i \(-0.911220\pi\)
0.719101 + 0.694905i \(0.244554\pi\)
\(62\) 7.26147 4.19241i 0.922207 0.532437i
\(63\) 3.38887i 0.426957i
\(64\) −1.00000 −0.125000
\(65\) −1.31193 + 4.48346i −0.162724 + 0.556105i
\(66\) 4.29568 0.528762
\(67\) −12.4237 7.17284i −1.51780 0.876302i −0.999781 0.0209325i \(-0.993336\pi\)
−0.518019 0.855369i \(-0.673330\pi\)
\(68\) 6.38887i 0.774764i
\(69\) −2.08690 + 3.61462i −0.251234 + 0.435149i
\(70\) −1.79338 7.36246i −0.214350 0.879983i
\(71\) −4.72539 + 8.18462i −0.560801 + 0.971336i 0.436626 + 0.899643i \(0.356173\pi\)
−0.997427 + 0.0716927i \(0.977160\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 7.65823i 0.896328i −0.893951 0.448164i \(-0.852078\pi\)
0.893951 0.448164i \(-0.147922\pi\)
\(74\) 3.17782 + 5.18666i 0.369414 + 0.602937i
\(75\) −4.99477 0.228600i −0.576747 0.0263964i
\(76\) 1.07231 + 1.85729i 0.123002 + 0.213046i
\(77\) −12.6072 7.27874i −1.43672 0.829490i
\(78\) 1.80925 + 1.04457i 0.204857 + 0.118274i
\(79\) −3.37250 + 5.84135i −0.379436 + 0.657203i −0.990980 0.134008i \(-0.957215\pi\)
0.611544 + 0.791210i \(0.290549\pi\)
\(80\) 1.61688 1.54457i 0.180773 0.172688i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 10.5691i 1.16716i
\(83\) −10.0539 + 5.80463i −1.10356 + 0.637141i −0.937154 0.348916i \(-0.886550\pi\)
−0.166407 + 0.986057i \(0.553217\pi\)
\(84\) −3.38887 −0.369756
\(85\) 9.86806 + 10.3300i 1.07034 + 1.12045i
\(86\) −1.27238 2.20383i −0.137205 0.237646i
\(87\) 2.06882 + 1.19443i 0.221801 + 0.128057i
\(88\) 4.29568i 0.457921i
\(89\) −0.462359 0.800829i −0.0490100 0.0848878i 0.840480 0.541843i \(-0.182273\pi\)
−0.889490 + 0.456955i \(0.848940\pi\)
\(90\) −0.627973 + 2.14608i −0.0661942 + 0.226216i
\(91\) −3.53991 6.13131i −0.371084 0.642736i
\(92\) 3.61462 + 2.08690i 0.376851 + 0.217575i
\(93\) 7.26147 + 4.19241i 0.752979 + 0.434733i
\(94\) −5.46381 9.46360i −0.563549 0.976096i
\(95\) −4.60251 1.34676i −0.472208 0.138175i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 4.99803i 0.507473i −0.967273 0.253737i \(-0.918340\pi\)
0.967273 0.253737i \(-0.0816596\pi\)
\(98\) 3.88362 + 2.24221i 0.392305 + 0.226497i
\(99\) 2.14784 + 3.72017i 0.215866 + 0.373891i
\(100\) −0.228600 + 4.99477i −0.0228600 + 0.499477i
\(101\) −5.80689 −0.577807 −0.288904 0.957358i \(-0.593291\pi\)
−0.288904 + 0.957358i \(0.593291\pi\)
\(102\) 5.53292 3.19443i 0.547841 0.316296i
\(103\) 11.8029i 1.16297i −0.813556 0.581486i \(-0.802471\pi\)
0.813556 0.581486i \(-0.197529\pi\)
\(104\) 1.04457 1.80925i 0.102429 0.177412i
\(105\) 5.47939 5.23435i 0.534734 0.510820i
\(106\) 5.59586 9.69231i 0.543518 0.941400i
\(107\) −10.7144 6.18598i −1.03580 0.598021i −0.117162 0.993113i \(-0.537380\pi\)
−0.918642 + 0.395091i \(0.870713\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 6.61466 + 11.4569i 0.633569 + 1.09737i 0.986816 + 0.161844i \(0.0517442\pi\)
−0.353247 + 0.935530i \(0.614922\pi\)
\(110\) 6.63498 + 6.94560i 0.632621 + 0.662237i
\(111\) −2.90288 + 5.34540i −0.275529 + 0.507363i
\(112\) 3.38887i 0.320218i
\(113\) −6.05799 + 3.49758i −0.569888 + 0.329025i −0.757104 0.653294i \(-0.773387\pi\)
0.187217 + 0.982319i \(0.440053\pi\)
\(114\) −1.07231 + 1.85729i −0.100431 + 0.173951i
\(115\) −9.06778 + 2.20877i −0.845575 + 0.205969i
\(116\) 1.19443 2.06882i 0.110900 0.192085i
\(117\) 2.08914i 0.193141i
\(118\) −3.09092 1.78454i −0.284542 0.164281i
\(119\) −21.6510 −1.98475
\(120\) 2.14608 + 0.627973i 0.195909 + 0.0573259i
\(121\) 7.45286 0.677533
\(122\) 3.78415i 0.342601i
\(123\) −9.15313 + 5.28456i −0.825310 + 0.476493i
\(124\) 4.19241 7.26147i 0.376490 0.652099i
\(125\) −7.34516 8.42903i −0.656971 0.753916i
\(126\) −1.69443 2.93485i −0.150952 0.261457i
\(127\) 17.7444 10.2448i 1.57456 0.909075i 0.578965 0.815352i \(-0.303457\pi\)
0.995598 0.0937225i \(-0.0298766\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 1.27238 2.20383i 0.112027 0.194037i
\(130\) 1.10557 + 4.53875i 0.0969649 + 0.398075i
\(131\) −8.09647 14.0235i −0.707392 1.22524i −0.965821 0.259208i \(-0.916538\pi\)
0.258430 0.966030i \(-0.416795\pi\)
\(132\) 3.72017 2.14784i 0.323799 0.186945i
\(133\) 6.29412 3.63391i 0.545769 0.315100i
\(134\) −14.3457 −1.23928
\(135\) −2.17254 + 0.529198i −0.186983 + 0.0455461i
\(136\) −3.19443 5.53292i −0.273920 0.474444i
\(137\) 19.4802i 1.66431i −0.554544 0.832155i \(-0.687107\pi\)
0.554544 0.832155i \(-0.312893\pi\)
\(138\) 4.17381i 0.355298i
\(139\) −0.0996490 0.172597i −0.00845212 0.0146395i 0.861768 0.507302i \(-0.169357\pi\)
−0.870221 + 0.492662i \(0.836024\pi\)
\(140\) −5.23435 5.47939i −0.442383 0.463093i
\(141\) 5.46381 9.46360i 0.460136 0.796979i
\(142\) 9.45079i 0.793092i
\(143\) 7.77196 + 4.48714i 0.649924 + 0.375234i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 1.26418 + 5.18992i 0.104985 + 0.430999i
\(146\) −3.82911 6.63222i −0.316900 0.548886i
\(147\) 4.48442i 0.369869i
\(148\) 5.34540 + 2.90288i 0.439389 + 0.238615i
\(149\) 16.8868 1.38342 0.691708 0.722177i \(-0.256858\pi\)
0.691708 + 0.722177i \(0.256858\pi\)
\(150\) −4.43990 + 2.29941i −0.362516 + 0.187746i
\(151\) 10.9847 19.0261i 0.893926 1.54832i 0.0587967 0.998270i \(-0.481274\pi\)
0.835129 0.550054i \(-0.185393\pi\)
\(152\) 1.85729 + 1.07231i 0.150646 + 0.0869757i
\(153\) 5.53292 + 3.19443i 0.447310 + 0.258255i
\(154\) −14.5575 −1.17308
\(155\) 4.43723 + 18.2164i 0.356407 + 1.46318i
\(156\) 2.08914 0.167265
\(157\) −6.75998 + 3.90288i −0.539505 + 0.311483i −0.744878 0.667200i \(-0.767492\pi\)
0.205373 + 0.978684i \(0.434159\pi\)
\(158\) 6.74500i 0.536604i
\(159\) 11.1917 0.887561
\(160\) 0.627973 2.14608i 0.0496456 0.169662i
\(161\) 7.07224 12.2495i 0.557371 0.965394i
\(162\) 1.00000i 0.0785674i
\(163\) 9.14720 5.28114i 0.716464 0.413651i −0.0969857 0.995286i \(-0.530920\pi\)
0.813450 + 0.581635i \(0.197587\pi\)
\(164\) 5.28456 + 9.15313i 0.412655 + 0.714739i
\(165\) −2.69757 + 9.21886i −0.210006 + 0.717687i
\(166\) −5.80463 + 10.0539i −0.450527 + 0.780335i
\(167\) 11.3039 + 6.52632i 0.874723 + 0.505022i 0.868915 0.494961i \(-0.164818\pi\)
0.00580833 + 0.999983i \(0.498151\pi\)
\(168\) −2.93485 + 1.69443i −0.226428 + 0.130728i
\(169\) −4.31774 7.47855i −0.332134 0.575273i
\(170\) 13.7110 + 4.01204i 1.05159 + 0.307709i
\(171\) −2.14462 −0.164003
\(172\) −2.20383 1.27238i −0.168041 0.0970184i
\(173\) −14.2230 + 8.21166i −1.08136 + 0.624321i −0.931262 0.364350i \(-0.881291\pi\)
−0.150094 + 0.988672i \(0.547958\pi\)
\(174\) 2.38887 0.181100
\(175\) 16.9266 + 0.774694i 1.27953 + 0.0585614i
\(176\) −2.14784 3.72017i −0.161900 0.280418i
\(177\) 3.56909i 0.268269i
\(178\) −0.800829 0.462359i −0.0600247 0.0346553i
\(179\) −19.2317 −1.43745 −0.718723 0.695297i \(-0.755273\pi\)
−0.718723 + 0.695297i \(0.755273\pi\)
\(180\) 0.529198 + 2.17254i 0.0394441 + 0.161932i
\(181\) −3.66105 + 6.34113i −0.272124 + 0.471333i −0.969406 0.245465i \(-0.921059\pi\)
0.697282 + 0.716797i \(0.254393\pi\)
\(182\) −6.13131 3.53991i −0.454483 0.262396i
\(183\) −3.27717 + 1.89207i −0.242255 + 0.139866i
\(184\) 4.17381 0.307697
\(185\) −13.1266 + 3.56275i −0.965084 + 0.261939i
\(186\) 8.38482 0.614805
\(187\) 23.7677 13.7223i 1.73806 1.00347i
\(188\) −9.46360 5.46381i −0.690204 0.398489i
\(189\) 1.69443 2.93485i 0.123252 0.213479i
\(190\) −4.65928 + 1.13493i −0.338019 + 0.0823363i
\(191\) 4.38596 0.317357 0.158679 0.987330i \(-0.449277\pi\)
0.158679 + 0.987330i \(0.449277\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 12.6079i 0.907538i 0.891119 + 0.453769i \(0.149921\pi\)
−0.891119 + 0.453769i \(0.850079\pi\)
\(194\) −2.49902 4.32842i −0.179419 0.310763i
\(195\) −3.37789 + 3.22683i −0.241896 + 0.231078i
\(196\) 4.48442 0.320316
\(197\) −22.8097 + 13.1692i −1.62512 + 0.938264i −0.639601 + 0.768707i \(0.720900\pi\)
−0.985520 + 0.169557i \(0.945766\pi\)
\(198\) 3.72017 + 2.14784i 0.264381 + 0.152640i
\(199\) 3.41609 0.242160 0.121080 0.992643i \(-0.461364\pi\)
0.121080 + 0.992643i \(0.461364\pi\)
\(200\) 2.29941 + 4.43990i 0.162593 + 0.313948i
\(201\) −7.17284 12.4237i −0.505933 0.876302i
\(202\) −5.02892 + 2.90345i −0.353833 + 0.204286i
\(203\) −7.01096 4.04778i −0.492073 0.284098i
\(204\) 3.19443 5.53292i 0.223655 0.387382i
\(205\) −22.6822 6.63713i −1.58419 0.463557i
\(206\) −5.90144 10.2216i −0.411173 0.712172i
\(207\) −3.61462 + 2.08690i −0.251234 + 0.145050i
\(208\) 2.08914i 0.144856i
\(209\) −4.60629 + 7.97834i −0.318624 + 0.551873i
\(210\) 2.12812 7.27277i 0.146854 0.501869i
\(211\) −24.2031 −1.66621 −0.833105 0.553115i \(-0.813439\pi\)
−0.833105 + 0.553115i \(0.813439\pi\)
\(212\) 11.1917i 0.768650i
\(213\) −8.18462 + 4.72539i −0.560801 + 0.323779i
\(214\) −12.3720 −0.845730
\(215\) 5.52862 1.34669i 0.377049 0.0918433i
\(216\) 1.00000 0.0680414
\(217\) −24.6082 14.2075i −1.67051 0.964470i
\(218\) 11.4569 + 6.61466i 0.775961 + 0.448001i
\(219\) 3.82911 6.63222i 0.258748 0.448164i
\(220\) 9.21886 + 2.69757i 0.621536 + 0.181870i
\(221\) 13.3473 0.897833
\(222\) 0.158737 + 6.08069i 0.0106537 + 0.408109i
\(223\) 19.7702i 1.32391i 0.749543 + 0.661956i \(0.230273\pi\)
−0.749543 + 0.661956i \(0.769727\pi\)
\(224\) 1.69443 + 2.93485i 0.113214 + 0.196093i
\(225\) −4.21130 2.69536i −0.280753 0.179691i
\(226\) −3.49758 + 6.05799i −0.232656 + 0.402971i
\(227\) −11.9969 6.92642i −0.796263 0.459723i 0.0458996 0.998946i \(-0.485385\pi\)
−0.842163 + 0.539223i \(0.818718\pi\)
\(228\) 2.14462i 0.142031i
\(229\) −6.33284 + 10.9688i −0.418486 + 0.724839i −0.995787 0.0916924i \(-0.970772\pi\)
0.577302 + 0.816531i \(0.304106\pi\)
\(230\) −6.74854 + 6.44674i −0.444986 + 0.425086i
\(231\) −7.27874 12.6072i −0.478906 0.829490i
\(232\) 2.38887i 0.156837i
\(233\) 2.09559i 0.137286i 0.997641 + 0.0686432i \(0.0218670\pi\)
−0.997641 + 0.0686432i \(0.978133\pi\)
\(234\) 1.04457 + 1.80925i 0.0682858 + 0.118274i
\(235\) 23.7407 5.78288i 1.54868 0.377233i
\(236\) −3.56909 −0.232328
\(237\) −5.84135 + 3.37250i −0.379436 + 0.219068i
\(238\) −18.7503 + 10.8255i −1.21540 + 0.701714i
\(239\) 7.83955 + 13.5785i 0.507098 + 0.878320i 0.999966 + 0.00821610i \(0.00261529\pi\)
−0.492868 + 0.870104i \(0.664051\pi\)
\(240\) 2.17254 0.529198i 0.140237 0.0341596i
\(241\) −7.74941 + 13.4224i −0.499183 + 0.864611i −1.00000 0.000942704i \(-0.999700\pi\)
0.500816 + 0.865554i \(0.333033\pi\)
\(242\) 6.45437 3.72643i 0.414903 0.239544i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 1.89207 + 3.27717i 0.121128 + 0.209799i
\(245\) −7.25077 + 6.92651i −0.463235 + 0.442518i
\(246\) −5.28456 + 9.15313i −0.336931 + 0.583582i
\(247\) −3.88015 + 2.24021i −0.246888 + 0.142541i
\(248\) 8.38482i 0.532437i
\(249\) −11.6093 −0.735707
\(250\) −10.5756 3.62718i −0.668861 0.229403i
\(251\) −4.21275 −0.265906 −0.132953 0.991122i \(-0.542446\pi\)
−0.132953 + 0.991122i \(0.542446\pi\)
\(252\) −2.93485 1.69443i −0.184878 0.106739i
\(253\) 17.9293i 1.12721i
\(254\) 10.2448 17.7444i 0.642813 1.11338i
\(255\) 3.38098 + 13.8801i 0.211725 + 0.869205i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.32051 4.80385i 0.519019 0.299656i −0.217514 0.976057i \(-0.569795\pi\)
0.736533 + 0.676401i \(0.236462\pi\)
\(258\) 2.54477i 0.158430i
\(259\) 9.83746 18.1149i 0.611270 1.12560i
\(260\) 3.22683 + 3.37789i 0.200119 + 0.209488i
\(261\) 1.19443 + 2.06882i 0.0739336 + 0.128057i
\(262\) −14.0235 8.09647i −0.866375 0.500202i
\(263\) −3.97236 2.29344i −0.244946 0.141420i 0.372502 0.928031i \(-0.378500\pi\)
−0.617448 + 0.786612i \(0.711833\pi\)
\(264\) 2.14784 3.72017i 0.132190 0.228960i
\(265\) 17.2864 + 18.0957i 1.06189 + 1.11161i
\(266\) 3.63391 6.29412i 0.222809 0.385917i
\(267\) 0.924718i 0.0565918i
\(268\) −12.4237 + 7.17284i −0.758900 + 0.438151i
\(269\) 4.20182 0.256190 0.128095 0.991762i \(-0.459114\pi\)
0.128095 + 0.991762i \(0.459114\pi\)
\(270\) −1.61688 + 1.54457i −0.0984002 + 0.0939996i
\(271\) 5.94377 + 10.2949i 0.361058 + 0.625372i 0.988135 0.153586i \(-0.0490821\pi\)
−0.627077 + 0.778957i \(0.715749\pi\)
\(272\) −5.53292 3.19443i −0.335483 0.193691i
\(273\) 7.07983i 0.428491i
\(274\) −9.74012 16.8704i −0.588422 1.01918i
\(275\) −19.0724 + 9.87754i −1.15011 + 0.595638i
\(276\) 2.08690 + 3.61462i 0.125617 + 0.217575i
\(277\) 0.789513 + 0.455826i 0.0474372 + 0.0273879i 0.523531 0.852007i \(-0.324614\pi\)
−0.476094 + 0.879394i \(0.657948\pi\)
\(278\) −0.172597 0.0996490i −0.0103517 0.00597655i
\(279\) 4.19241 + 7.26147i 0.250993 + 0.434733i
\(280\) −7.27277 2.12812i −0.434631 0.127179i
\(281\) −1.60452 2.77912i −0.0957178 0.165788i 0.814190 0.580598i \(-0.197181\pi\)
−0.909908 + 0.414810i \(0.863848\pi\)
\(282\) 10.9276i 0.650730i
\(283\) 11.6307 + 6.71497i 0.691372 + 0.399164i 0.804126 0.594459i \(-0.202634\pi\)
−0.112754 + 0.993623i \(0.535967\pi\)
\(284\) 4.72539 + 8.18462i 0.280401 + 0.485668i
\(285\) −3.31251 3.46759i −0.196216 0.205402i
\(286\) 8.97429 0.530661
\(287\) 31.0187 17.9087i 1.83098 1.05712i
\(288\) 1.00000i 0.0589256i
\(289\) 11.9088 20.6267i 0.700518 1.21333i
\(290\) 3.68978 + 3.86251i 0.216671 + 0.226814i
\(291\) 2.49902 4.32842i 0.146495 0.253737i
\(292\) −6.63222 3.82911i −0.388121 0.224082i
\(293\) 4.45789 + 2.57376i 0.260432 + 0.150361i 0.624532 0.780999i \(-0.285290\pi\)
−0.364099 + 0.931360i \(0.618623\pi\)
\(294\) 2.24221 + 3.88362i 0.130768 + 0.226497i
\(295\) 5.77078 5.51271i 0.335988 0.320962i
\(296\) 6.08069 0.158737i 0.353433 0.00922641i
\(297\) 4.29568i 0.249261i
\(298\) 14.6244 8.44338i 0.847166 0.489112i
\(299\) −4.35984 + 7.55146i −0.252136 + 0.436712i
\(300\) −2.69536 + 4.21130i −0.155617 + 0.243139i
\(301\) −4.31194 + 7.46850i −0.248536 + 0.430477i
\(302\) 21.9695i 1.26420i
\(303\) −5.02892 2.90345i −0.288904 0.166799i
\(304\) 2.14462 0.123002
\(305\) −8.12107 2.37634i −0.465011 0.136069i
\(306\) 6.38887 0.365227
\(307\) 3.44266i 0.196483i −0.995163 0.0982416i \(-0.968678\pi\)
0.995163 0.0982416i \(-0.0313218\pi\)
\(308\) −12.6072 + 7.27874i −0.718359 + 0.414745i
\(309\) 5.90144 10.2216i 0.335721 0.581486i
\(310\) 12.9510 + 13.5572i 0.735565 + 0.770000i
\(311\) −14.3862 24.9177i −0.815768 1.41295i −0.908775 0.417286i \(-0.862982\pi\)
0.0930079 0.995665i \(-0.470352\pi\)
\(312\) 1.80925 1.04457i 0.102429 0.0591372i
\(313\) −5.98765 + 3.45697i −0.338442 + 0.195399i −0.659583 0.751632i \(-0.729267\pi\)
0.321141 + 0.947031i \(0.395934\pi\)
\(314\) −3.90288 + 6.75998i −0.220252 + 0.381488i
\(315\) 7.36246 1.79338i 0.414828 0.101046i
\(316\) 3.37250 + 5.84135i 0.189718 + 0.328601i
\(317\) −1.33689 + 0.771852i −0.0750871 + 0.0433515i −0.537073 0.843535i \(-0.680470\pi\)
0.461986 + 0.886887i \(0.347137\pi\)
\(318\) 9.69231 5.59586i 0.543518 0.313800i
\(319\) 10.2618 0.574551
\(320\) −0.529198 2.17254i −0.0295831 0.121449i
\(321\) −6.18598 10.7144i −0.345268 0.598021i
\(322\) 14.1445i 0.788241i
\(323\) 13.7017i 0.762382i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) −10.4348 0.477577i −0.578818 0.0264912i
\(326\) 5.28114 9.14720i 0.292495 0.506617i
\(327\) 13.2293i 0.731583i
\(328\) 9.15313 + 5.28456i 0.505397 + 0.291791i
\(329\) −18.5161 + 32.0709i −1.02083 + 1.76812i
\(330\) 2.27327 + 9.33256i 0.125139 + 0.513740i
\(331\) 2.95680 + 5.12132i 0.162520 + 0.281493i 0.935772 0.352606i \(-0.114704\pi\)
−0.773252 + 0.634099i \(0.781371\pi\)
\(332\) 11.6093i 0.637141i
\(333\) −5.18666 + 3.17782i −0.284227 + 0.174143i
\(334\) 13.0526 0.714209
\(335\) 9.00870 30.7869i 0.492198 1.68207i
\(336\) −1.69443 + 2.93485i −0.0924389 + 0.160109i
\(337\) 15.7431 + 9.08928i 0.857581 + 0.495125i 0.863201 0.504860i \(-0.168456\pi\)
−0.00562055 + 0.999984i \(0.501789\pi\)
\(338\) −7.47855 4.31774i −0.406779 0.234854i
\(339\) −6.99516 −0.379925
\(340\) 13.8801 3.38098i 0.752754 0.183359i
\(341\) 36.0185 1.95051
\(342\) −1.85729 + 1.07231i −0.100431 + 0.0579838i
\(343\) 8.52496i 0.460305i
\(344\) −2.54477 −0.137205
\(345\) −8.95731 2.62104i −0.482246 0.141112i
\(346\) −8.21166 + 14.2230i −0.441462 + 0.764634i
\(347\) 12.9131i 0.693211i −0.938011 0.346605i \(-0.887334\pi\)
0.938011 0.346605i \(-0.112666\pi\)
\(348\) 2.06882 1.19443i 0.110900 0.0640284i
\(349\) −0.845677 1.46476i −0.0452681 0.0784066i 0.842504 0.538691i \(-0.181081\pi\)
−0.887772 + 0.460284i \(0.847748\pi\)
\(350\) 15.0462 7.79240i 0.804255 0.416522i
\(351\) −1.04457 + 1.80925i −0.0557551 + 0.0965706i
\(352\) −3.72017 2.14784i −0.198286 0.114480i
\(353\) 4.80463 2.77396i 0.255725 0.147643i −0.366658 0.930356i \(-0.619498\pi\)
0.622383 + 0.782713i \(0.286165\pi\)
\(354\) −1.78454 3.09092i −0.0948474 0.164281i
\(355\) −20.2821 5.93484i −1.07646 0.314989i
\(356\) −0.924718 −0.0490100
\(357\) −18.7503 10.8255i −0.992373 0.572947i
\(358\) −16.6552 + 9.61586i −0.880252 + 0.508214i
\(359\) 20.3437 1.07370 0.536851 0.843677i \(-0.319614\pi\)
0.536851 + 0.843677i \(0.319614\pi\)
\(360\) 1.54457 + 1.61688i 0.0814060 + 0.0852170i
\(361\) 7.20031 + 12.4713i 0.378964 + 0.656384i
\(362\) 7.32211i 0.384841i
\(363\) 6.45437 + 3.72643i 0.338767 + 0.195587i
\(364\) −7.07983 −0.371084
\(365\) 16.6378 4.05272i 0.870864 0.212129i
\(366\) −1.89207 + 3.27717i −0.0989003 + 0.171300i
\(367\) 0.369651 + 0.213418i 0.0192956 + 0.0111403i 0.509617 0.860401i \(-0.329787\pi\)
−0.490321 + 0.871542i \(0.663121\pi\)
\(368\) 3.61462 2.08690i 0.188425 0.108787i
\(369\) −10.5691 −0.550206
\(370\) −9.58656 + 9.64872i −0.498382 + 0.501613i
\(371\) −37.9272 −1.96908
\(372\) 7.26147 4.19241i 0.376490 0.217366i
\(373\) −22.9294 13.2383i −1.18724 0.685454i −0.229563 0.973294i \(-0.573730\pi\)
−0.957679 + 0.287839i \(0.907063\pi\)
\(374\) 13.7223 23.7677i 0.709561 1.22900i
\(375\) −2.14658 10.9723i −0.110849 0.566609i
\(376\) −10.9276 −0.563549
\(377\) 4.32206 + 2.49534i 0.222597 + 0.128517i
\(378\) 3.38887i 0.174305i
\(379\) −1.48389 2.57017i −0.0762222 0.132021i 0.825395 0.564556i \(-0.190952\pi\)
−0.901617 + 0.432535i \(0.857619\pi\)
\(380\) −3.46759 + 3.31251i −0.177883 + 0.169928i
\(381\) 20.4895 1.04971
\(382\) 3.79836 2.19298i 0.194341 0.112203i
\(383\) −30.4946 17.6061i −1.55820 0.899628i −0.997429 0.0716589i \(-0.977171\pi\)
−0.560773 0.827970i \(-0.689496\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 9.14171 31.2415i 0.465905 1.59221i
\(386\) 6.30396 + 10.9188i 0.320863 + 0.555751i
\(387\) 2.20383 1.27238i 0.112027 0.0646789i
\(388\) −4.32842 2.49902i −0.219742 0.126868i
\(389\) 13.8150 23.9283i 0.700450 1.21322i −0.267858 0.963458i \(-0.586316\pi\)
0.968309 0.249757i \(-0.0803508\pi\)
\(390\) −1.31193 + 4.48346i −0.0664319 + 0.227029i
\(391\) 13.3330 + 23.0933i 0.674276 + 1.16788i
\(392\) 3.88362 2.24221i 0.196153 0.113249i
\(393\) 16.1929i 0.816826i
\(394\) −13.1692 + 22.8097i −0.663453 + 1.14913i
\(395\) −14.4753 4.23568i −0.728332 0.213120i
\(396\) 4.29568 0.215866
\(397\) 31.9573i 1.60389i 0.597397 + 0.801946i \(0.296202\pi\)
−0.597397 + 0.801946i \(0.703798\pi\)
\(398\) 2.95842 1.70804i 0.148292 0.0856165i
\(399\) 7.26782 0.363846
\(400\) 4.21130 + 2.69536i 0.210565 + 0.134768i
\(401\) 8.53388 0.426162 0.213081 0.977035i \(-0.431650\pi\)
0.213081 + 0.977035i \(0.431650\pi\)
\(402\) −12.4237 7.17284i −0.619639 0.357749i
\(403\) 15.1702 + 8.75854i 0.755684 + 0.436294i
\(404\) −2.90345 + 5.02892i −0.144452 + 0.250198i
\(405\) −2.14608 0.627973i −0.106639 0.0312042i
\(406\) −8.09555 −0.401776
\(407\) 0.681884 + 26.1207i 0.0337997 + 1.29476i
\(408\) 6.38887i 0.316296i
\(409\) 15.5232 + 26.8870i 0.767573 + 1.32948i 0.938875 + 0.344257i \(0.111869\pi\)
−0.171302 + 0.985219i \(0.554797\pi\)
\(410\) −22.9619 + 5.59316i −1.13401 + 0.276226i
\(411\) 9.74012 16.8704i 0.480445 0.832155i
\(412\) −10.2216 5.90144i −0.503582 0.290743i
\(413\) 12.0952i 0.595164i
\(414\) −2.08690 + 3.61462i −0.102566 + 0.177649i
\(415\) −17.9313 18.7708i −0.880215 0.921422i
\(416\) −1.04457 1.80925i −0.0512143 0.0887058i
\(417\) 0.199298i 0.00975967i
\(418\) 9.21259i 0.450602i
\(419\) −6.27177 10.8630i −0.306396 0.530693i 0.671175 0.741299i \(-0.265790\pi\)
−0.977571 + 0.210605i \(0.932456\pi\)
\(420\) −1.79338 7.36246i −0.0875081 0.359251i
\(421\) −24.0695 −1.17308 −0.586538 0.809922i \(-0.699510\pi\)
−0.586538 + 0.809922i \(0.699510\pi\)
\(422\) −20.9605 + 12.1015i −1.02034 + 0.589094i
\(423\) 9.46360 5.46381i 0.460136 0.265660i
\(424\) −5.59586 9.69231i −0.271759 0.470700i
\(425\) −17.2203 + 26.9054i −0.835307 + 1.30511i
\(426\) −4.72539 + 8.18462i −0.228946 + 0.396546i
\(427\) 11.1059 6.41199i 0.537451 0.310298i
\(428\) −10.7144 + 6.18598i −0.517902 + 0.299011i
\(429\) 4.48714 + 7.77196i 0.216641 + 0.375234i
\(430\) 4.11459 3.93058i 0.198423 0.189549i
\(431\) 10.1880 17.6460i 0.490736 0.849980i −0.509207 0.860644i \(-0.670061\pi\)
0.999943 + 0.0106640i \(0.00339451\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 15.6081i 0.750079i −0.927009 0.375039i \(-0.877629\pi\)
0.927009 0.375039i \(-0.122371\pi\)
\(434\) −28.4150 −1.36397
\(435\) −1.50014 + 5.12669i −0.0719264 + 0.245806i
\(436\) 13.2293 0.633569
\(437\) −7.75198 4.47561i −0.370828 0.214097i
\(438\) 7.65823i 0.365924i
\(439\) −7.26387 + 12.5814i −0.346686 + 0.600477i −0.985659 0.168752i \(-0.946026\pi\)
0.638973 + 0.769229i \(0.279360\pi\)
\(440\) 9.33256 2.27327i 0.444912 0.108374i
\(441\) −2.24221 + 3.88362i −0.106772 + 0.184934i
\(442\) 11.5591 6.67363i 0.549808 0.317432i
\(443\) 23.3745i 1.11055i 0.831665 + 0.555277i \(0.187388\pi\)
−0.831665 + 0.555277i \(0.812612\pi\)
\(444\) 3.17782 + 5.18666i 0.150812 + 0.246148i
\(445\) 1.49516 1.42829i 0.0708773 0.0677076i
\(446\) 9.88511 + 17.1215i 0.468073 + 0.810727i
\(447\) 14.6244 + 8.44338i 0.691708 + 0.399358i
\(448\) 2.93485 + 1.69443i 0.138658 + 0.0800545i
\(449\) 8.00485 13.8648i 0.377772 0.654321i −0.612965 0.790110i \(-0.710024\pi\)
0.990738 + 0.135789i \(0.0433568\pi\)
\(450\) −4.99477 0.228600i −0.235456 0.0107763i
\(451\) −22.7008 + 39.3189i −1.06894 + 1.85145i
\(452\) 6.99516i 0.329025i
\(453\) 19.0261 10.9847i 0.893926 0.516108i
\(454\) −13.8528 −0.650146
\(455\) 11.4472 10.9353i 0.536654 0.512655i
\(456\) 1.07231 + 1.85729i 0.0502154 + 0.0869757i
\(457\) 13.7823 + 7.95720i 0.644708 + 0.372222i 0.786426 0.617685i \(-0.211929\pi\)
−0.141718 + 0.989907i \(0.545263\pi\)
\(458\) 12.6657i 0.591828i
\(459\) 3.19443 + 5.53292i 0.149103 + 0.258255i
\(460\) −2.62104 + 8.95731i −0.122207 + 0.417637i
\(461\) −15.1275 26.2017i −0.704559 1.22033i −0.966850 0.255344i \(-0.917811\pi\)
0.262291 0.964989i \(-0.415522\pi\)
\(462\) −12.6072 7.27874i −0.586538 0.338638i
\(463\) 4.63056 + 2.67345i 0.215200 + 0.124246i 0.603726 0.797192i \(-0.293682\pi\)
−0.388526 + 0.921438i \(0.627016\pi\)
\(464\) −1.19443 2.06882i −0.0554502 0.0960425i
\(465\) −5.26544 + 17.9945i −0.244179 + 0.834474i
\(466\) 1.04779 + 1.81483i 0.0485381 + 0.0840704i
\(467\) 23.4925i 1.08710i −0.839376 0.543551i \(-0.817080\pi\)
0.839376 0.543551i \(-0.182920\pi\)
\(468\) 1.80925 + 1.04457i 0.0836326 + 0.0482853i
\(469\) 24.3078 + 42.1024i 1.12243 + 1.94411i
\(470\) 17.6687 16.8785i 0.814994 0.778547i
\(471\) −7.80575 −0.359670
\(472\) −3.09092 + 1.78454i −0.142271 + 0.0821403i
\(473\) 10.9315i 0.502631i
\(474\) −3.37250 + 5.84135i −0.154904 + 0.268302i
\(475\) 0.490259 10.7119i 0.0224946 0.491494i
\(476\) −10.8255 + 18.7503i −0.496187 + 0.859420i
\(477\) 9.69231 + 5.59586i 0.443780 + 0.256217i
\(478\) 13.5785 + 7.83955i 0.621066 + 0.358573i
\(479\) 16.8406 + 29.1687i 0.769465 + 1.33275i 0.937853 + 0.347032i \(0.112811\pi\)
−0.168388 + 0.985721i \(0.553856\pi\)
\(480\) 1.61688 1.54457i 0.0738001 0.0704997i
\(481\) −6.06452 + 11.1673i −0.276518 + 0.509185i
\(482\) 15.4988i 0.705952i
\(483\) 12.2495 7.07224i 0.557371 0.321798i
\(484\) 3.72643 6.45437i 0.169383 0.293380i
\(485\) 10.8584 2.64495i 0.493057 0.120101i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 26.1574i 1.18530i −0.805459 0.592652i \(-0.798081\pi\)
0.805459 0.592652i \(-0.201919\pi\)
\(488\) 3.27717 + 1.89207i 0.148350 + 0.0856501i
\(489\) 10.5623 0.477643
\(490\) −2.81610 + 9.62392i −0.127218 + 0.434764i
\(491\) 12.3778 0.558604 0.279302 0.960203i \(-0.409897\pi\)
0.279302 + 0.960203i \(0.409897\pi\)
\(492\) 10.5691i 0.476493i
\(493\) 13.2174 7.63108i 0.595282 0.343686i
\(494\) −2.24021 + 3.88015i −0.100792 + 0.174576i
\(495\) −6.94560 + 6.63498i −0.312181 + 0.298220i
\(496\) −4.19241 7.26147i −0.188245 0.326050i
\(497\) 27.7366 16.0137i 1.24416 0.718314i
\(498\) −10.0539 + 5.80463i −0.450527 + 0.260112i
\(499\) 12.5681 21.7686i 0.562625 0.974494i −0.434642 0.900603i \(-0.643125\pi\)
0.997266 0.0738909i \(-0.0235417\pi\)
\(500\) −10.9723 + 2.14658i −0.490698 + 0.0959980i
\(501\) 6.52632 + 11.3039i 0.291574 + 0.505022i
\(502\) −3.64835 + 2.10637i −0.162834 + 0.0940120i
\(503\) 4.83312 2.79040i 0.215498 0.124418i −0.388366 0.921505i \(-0.626960\pi\)
0.603864 + 0.797087i \(0.293627\pi\)
\(504\) −3.38887 −0.150952
\(505\) −3.07300 12.6157i −0.136746 0.561393i
\(506\) 8.96467 + 15.5273i 0.398528 + 0.690271i
\(507\) 8.63548i 0.383515i
\(508\) 20.4895i 0.909075i
\(509\) −4.88714 8.46478i −0.216619 0.375195i 0.737153 0.675726i \(-0.236170\pi\)
−0.953772 + 0.300531i \(0.902836\pi\)
\(510\) 9.86806 + 10.3300i 0.436965 + 0.457421i
\(511\) −12.9764 + 22.4757i −0.574040 + 0.994267i
\(512\) 1.00000i 0.0441942i
\(513\) −1.85729 1.07231i −0.0820015 0.0473436i
\(514\) 4.80385 8.32051i 0.211889 0.367002i
\(515\) 25.6423 6.24606i 1.12993 0.275234i
\(516\) −1.27238 2.20383i −0.0560136 0.0970184i
\(517\) 46.9416i 2.06449i
\(518\) −0.537939 20.6067i −0.0236357 0.905404i
\(519\) −16.4233 −0.720904
\(520\) 4.48346 + 1.31193i 0.196613 + 0.0575317i
\(521\) −8.56513 + 14.8352i −0.375245 + 0.649943i −0.990364 0.138491i \(-0.955775\pi\)
0.615119 + 0.788435i \(0.289108\pi\)
\(522\) 2.06882 + 1.19443i 0.0905498 + 0.0522789i
\(523\) 4.79471 + 2.76822i 0.209658 + 0.121046i 0.601152 0.799134i \(-0.294708\pi\)
−0.391495 + 0.920180i \(0.628042\pi\)
\(524\) −16.1929 −0.707392
\(525\) 14.2715 + 9.13421i 0.622861 + 0.398650i
\(526\) −4.58688 −0.199998
\(527\) 46.3926 26.7848i 2.02089 1.16676i
\(528\) 4.29568i 0.186945i
\(529\) 5.57933 0.242580
\(530\) 24.0183 + 7.02810i 1.04329 + 0.305281i
\(531\) 1.78454 3.09092i 0.0774426 0.134134i
\(532\) 7.26782i 0.315100i
\(533\) −19.1222 + 11.0402i −0.828274 + 0.478204i
\(534\) −0.462359 0.800829i −0.0200082 0.0346553i
\(535\) 7.76926 26.5512i 0.335895 1.14791i
\(536\) −7.17284 + 12.4237i −0.309820 + 0.536623i
\(537\) −16.6552 9.61586i −0.718723 0.414955i
\(538\) 3.63889 2.10091i 0.156883 0.0905767i
\(539\) 9.63182 + 16.6828i 0.414872 + 0.718579i
\(540\) −0.627973 + 2.14608i −0.0270237 + 0.0923525i
\(541\) 8.03851 0.345602 0.172801 0.984957i \(-0.444718\pi\)
0.172801 + 0.984957i \(0.444718\pi\)
\(542\) 10.2949 + 5.94377i 0.442204 + 0.255307i
\(543\) −6.34113 + 3.66105i −0.272124 + 0.157111i
\(544\) −6.38887 −0.273920
\(545\) −21.3902 + 20.4336i −0.916256 + 0.875280i
\(546\) −3.53991 6.13131i −0.151494 0.262396i
\(547\) 8.07970i 0.345463i −0.984969 0.172732i \(-0.944741\pi\)
0.984969 0.172732i \(-0.0552593\pi\)
\(548\) −16.8704 9.74012i −0.720667 0.416077i
\(549\) −3.78415 −0.161503
\(550\) −11.5784 + 18.0904i −0.493705 + 0.771377i
\(551\) −2.56160 + 4.43683i −0.109128 + 0.189015i
\(552\) 3.61462 + 2.08690i 0.153849 + 0.0888245i
\(553\) 19.7955 11.4290i 0.841792 0.486009i
\(554\) 0.911651 0.0387324
\(555\) −13.1493 3.47785i −0.558157 0.147626i
\(556\) −0.199298 −0.00845212
\(557\) −36.2741 + 20.9429i −1.53698 + 0.887377i −0.537969 + 0.842964i \(0.680808\pi\)
−0.999013 + 0.0444128i \(0.985858\pi\)
\(558\) 7.26147 + 4.19241i 0.307402 + 0.177479i
\(559\) 2.65819 4.60412i 0.112430 0.194734i
\(560\) −7.36246 + 1.79338i −0.311121 + 0.0757842i
\(561\) 27.4445 1.15871
\(562\) −2.77912 1.60452i −0.117230 0.0676827i
\(563\) 42.3364i 1.78427i 0.451771 + 0.892134i \(0.350792\pi\)
−0.451771 + 0.892134i \(0.649208\pi\)
\(564\) −5.46381 9.46360i −0.230068 0.398489i
\(565\) −10.8045 11.3103i −0.454550 0.475829i
\(566\) 13.4299 0.564503
\(567\) 2.93485 1.69443i 0.123252 0.0711595i
\(568\) 8.18462 + 4.72539i 0.343419 + 0.198273i
\(569\) 3.65368 0.153170 0.0765852 0.997063i \(-0.475598\pi\)
0.0765852 + 0.997063i \(0.475598\pi\)
\(570\) −4.60251 1.34676i −0.192778 0.0564097i
\(571\) 0.382372 + 0.662288i 0.0160018 + 0.0277159i 0.873915 0.486078i \(-0.161573\pi\)
−0.857914 + 0.513794i \(0.828240\pi\)
\(572\) 7.77196 4.48714i 0.324962 0.187617i
\(573\) 3.79836 + 2.19298i 0.158679 + 0.0916131i
\(574\) 17.9087 31.0187i 0.747494 1.29470i
\(575\) −9.59730 18.5313i −0.400235 0.772808i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 1.14731 0.662402i 0.0477633 0.0275761i −0.475928 0.879484i \(-0.657888\pi\)
0.523691 + 0.851908i \(0.324554\pi\)
\(578\) 23.8176i 0.990683i
\(579\) −6.30396 + 10.9188i −0.261984 + 0.453769i
\(580\) 5.12669 + 1.50014i 0.212874 + 0.0622901i
\(581\) 39.3423 1.63219
\(582\) 4.99803i 0.207175i
\(583\) 41.6351 24.0380i 1.72435 0.995553i
\(584\) −7.65823 −0.316900
\(585\) −4.53875 + 1.10557i −0.187654 + 0.0457097i
\(586\) 5.14752 0.212642
\(587\) 7.06825 + 4.08086i 0.291738 + 0.168435i 0.638725 0.769435i \(-0.279462\pi\)
−0.346987 + 0.937870i \(0.612795\pi\)
\(588\) 3.88362 + 2.24221i 0.160158 + 0.0924672i
\(589\) −8.99112 + 15.5731i −0.370472 + 0.641677i
\(590\) 2.24129 7.65954i 0.0922725 0.315338i
\(591\) −26.3383 −1.08341
\(592\) 5.18666 3.17782i 0.213171 0.130607i
\(593\) 3.99327i 0.163984i −0.996633 0.0819919i \(-0.973872\pi\)
0.996633 0.0819919i \(-0.0261282\pi\)
\(594\) 2.14784 + 3.72017i 0.0881269 + 0.152640i
\(595\) −11.4577 47.0378i −0.469719 1.92836i
\(596\) 8.44338 14.6244i 0.345854 0.599037i
\(597\) 2.95842 + 1.70804i 0.121080 + 0.0699056i
\(598\) 8.71968i 0.356574i
\(599\) 15.7398 27.2621i 0.643109 1.11390i −0.341626 0.939836i \(-0.610977\pi\)
0.984735 0.174062i \(-0.0556892\pi\)
\(600\) −0.228600 + 4.99477i −0.00933255 + 0.203911i
\(601\) −5.06605 8.77466i −0.206649 0.357926i 0.744008 0.668171i \(-0.232922\pi\)
−0.950657 + 0.310245i \(0.899589\pi\)
\(602\) 8.62388i 0.351483i
\(603\) 14.3457i 0.584201i
\(604\) −10.9847 19.0261i −0.446963 0.774162i
\(605\) 3.94404 + 16.1917i 0.160348 + 0.658285i
\(606\) −5.80689 −0.235889
\(607\) −27.9541 + 16.1393i −1.13462 + 0.655074i −0.945093 0.326801i \(-0.894029\pi\)
−0.189529 + 0.981875i \(0.560696\pi\)
\(608\) 1.85729 1.07231i 0.0753232 0.0434879i
\(609\) −4.04778 7.01096i −0.164024 0.284098i
\(610\) −8.22123 + 2.00256i −0.332868 + 0.0810814i
\(611\) 11.4147 19.7708i 0.461789 0.799841i
\(612\) 5.53292 3.19443i 0.223655 0.129127i
\(613\) 2.79022 1.61093i 0.112696 0.0650650i −0.442593 0.896723i \(-0.645941\pi\)
0.555288 + 0.831658i \(0.312608\pi\)
\(614\) −1.72133 2.98143i −0.0694673 0.120321i
\(615\) −16.3248 17.0890i −0.658278 0.689095i
\(616\) −7.27874 + 12.6072i −0.293269 + 0.507957i
\(617\) 22.0266 12.7171i 0.886757 0.511970i 0.0138769 0.999904i \(-0.495583\pi\)
0.872880 + 0.487934i \(0.162249\pi\)
\(618\) 11.8029i 0.474781i
\(619\) 20.9639 0.842612 0.421306 0.906919i \(-0.361572\pi\)
0.421306 + 0.906919i \(0.361572\pi\)
\(620\) 17.9945 + 5.26544i 0.722676 + 0.211465i
\(621\) −4.17381 −0.167489
\(622\) −24.9177 14.3862i −0.999107 0.576835i
\(623\) 3.13375i 0.125551i
\(624\) 1.04457 1.80925i 0.0418163 0.0724280i
\(625\) 14.4254 20.4183i 0.577016 0.816733i
\(626\) −3.45697 + 5.98765i −0.138168 + 0.239315i
\(627\) −7.97834 + 4.60629i −0.318624 + 0.183958i
\(628\) 7.80575i 0.311483i
\(629\) 20.3026 + 33.1369i 0.809519 + 1.32126i
\(630\) 5.47939 5.23435i 0.218304 0.208541i
\(631\) −9.21454 15.9600i −0.366825 0.635359i 0.622242 0.782825i \(-0.286222\pi\)
−0.989067 + 0.147465i \(0.952889\pi\)
\(632\) 5.84135 + 3.37250i 0.232356 + 0.134151i
\(633\) −20.9605 12.1015i −0.833105 0.480993i
\(634\) −0.771852 + 1.33689i −0.0306542 + 0.0530946i
\(635\) 31.6475 + 33.1291i 1.25589 + 1.31469i
\(636\) 5.59586 9.69231i 0.221890 0.384325i
\(637\) 9.36859i 0.371197i
\(638\) 8.88699 5.13090i 0.351839 0.203134i
\(639\) −9.45079 −0.373867
\(640\) −1.54457 1.61688i −0.0610545 0.0639128i
\(641\) −5.87842 10.1817i −0.232183 0.402154i 0.726267 0.687413i \(-0.241254\pi\)
−0.958450 + 0.285259i \(0.907920\pi\)
\(642\) −10.7144 6.18598i −0.422865 0.244141i
\(643\) 1.38385i 0.0545738i 0.999628 + 0.0272869i \(0.00868677\pi\)
−0.999628 + 0.0272869i \(0.991313\pi\)
\(644\) −7.07224 12.2495i −0.278685 0.482697i
\(645\) 5.46127 + 1.59805i 0.215037 + 0.0629230i
\(646\) 6.85084 + 11.8660i 0.269543 + 0.466861i
\(647\) −26.9727 15.5727i −1.06041 0.612226i −0.134862 0.990864i \(-0.543059\pi\)
−0.925545 + 0.378638i \(0.876392\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −7.66583 13.2776i −0.300910 0.521191i
\(650\) −9.27558 + 4.80380i −0.363818 + 0.188421i
\(651\) −14.2075 24.6082i −0.556837 0.964470i
\(652\) 10.5623i 0.413651i
\(653\) 36.4720 + 21.0571i 1.42726 + 0.824028i 0.996904 0.0786314i \(-0.0250550\pi\)
0.430355 + 0.902660i \(0.358388\pi\)
\(654\) 6.61466 + 11.4569i 0.258654 + 0.448001i
\(655\) 26.1820 25.0111i 1.02302 0.977266i
\(656\) 10.5691 0.412655
\(657\) 6.63222 3.82911i 0.258748 0.149388i
\(658\) 37.0323i 1.44367i
\(659\) 13.0406 22.5870i 0.507990 0.879864i −0.491968 0.870613i \(-0.663722\pi\)
0.999957 0.00925020i \(-0.00294447\pi\)
\(660\) 6.63498 + 6.94560i 0.258266 + 0.270357i
\(661\) 9.31601 16.1358i 0.362351 0.627610i −0.625996 0.779826i \(-0.715308\pi\)
0.988347 + 0.152216i \(0.0486409\pi\)
\(662\) 5.12132 + 2.95680i 0.199046 + 0.114919i
\(663\) 11.5591 + 6.67363i 0.448917 + 0.259182i
\(664\) 5.80463 + 10.0539i 0.225263 + 0.390168i
\(665\) 11.2257 + 11.7512i 0.435313 + 0.455692i
\(666\) −2.90288 + 5.34540i −0.112484 + 0.207130i
\(667\) 9.97067i 0.386066i
\(668\) 11.3039 6.52632i 0.437362 0.252511i
\(669\) −9.88511 + 17.1215i −0.382180 + 0.661956i
\(670\) −7.59171 31.1666i −0.293293 1.20407i
\(671\) −8.12774 + 14.0777i −0.313768 + 0.543462i
\(672\) 3.38887i 0.130728i
\(673\) 2.31679 + 1.33760i 0.0893056 + 0.0515606i 0.543988 0.839093i \(-0.316914\pi\)
−0.454682 + 0.890654i \(0.650247\pi\)
\(674\) 18.1786 0.700212
\(675\) −2.29941 4.43990i −0.0885044 0.170892i
\(676\) −8.63548 −0.332134
\(677\) 18.7360i 0.720083i 0.932936 + 0.360041i \(0.117237\pi\)
−0.932936 + 0.360041i \(0.882763\pi\)
\(678\) −6.05799 + 3.49758i −0.232656 + 0.134324i
\(679\) −8.46883 + 14.6684i −0.325004 + 0.562923i
\(680\) 10.3300 9.86806i 0.396139 0.378423i
\(681\) −6.92642 11.9969i −0.265421 0.459723i
\(682\) 31.1929 18.0093i 1.19444 0.689610i
\(683\) 12.7062 7.33593i 0.486189 0.280701i −0.236803 0.971558i \(-0.576100\pi\)
0.722992 + 0.690856i \(0.242766\pi\)
\(684\) −1.07231 + 1.85729i −0.0410007 + 0.0710154i
\(685\) 42.3217 10.3089i 1.61703 0.393883i
\(686\) 4.26248 + 7.38283i 0.162742 + 0.281878i
\(687\) −10.9688 + 6.33284i −0.418486 + 0.241613i
\(688\) −2.20383 + 1.27238i −0.0840204 + 0.0485092i
\(689\) 23.3811 0.890748
\(690\) −9.06778 + 2.20877i −0.345205 + 0.0840865i
\(691\) 7.39577 + 12.8098i 0.281348 + 0.487309i 0.971717 0.236148i \(-0.0758851\pi\)
−0.690369 + 0.723458i \(0.742552\pi\)
\(692\) 16.4233i 0.624321i
\(693\) 14.5575i 0.552993i
\(694\) −6.45654 11.1831i −0.245087 0.424503i
\(695\) 0.322241 0.307830i 0.0122233 0.0116767i
\(696\) 1.19443 2.06882i 0.0452749 0.0784184i
\(697\) 67.5247i 2.55768i
\(698\) −1.46476 0.845677i −0.0554418 0.0320094i
\(699\) −1.04779 + 1.81483i −0.0396312 + 0.0686432i
\(700\) 9.13421 14.2715i 0.345241 0.539413i
\(701\) 13.3246 + 23.0789i 0.503264 + 0.871678i 0.999993 + 0.00377282i \(0.00120093\pi\)
−0.496729 + 0.867906i \(0.665466\pi\)
\(702\) 2.08914i 0.0788496i
\(703\) −11.4638 6.22556i −0.432367 0.234801i
\(704\) −4.29568 −0.161900
\(705\) 23.4515 + 6.86226i 0.883236 + 0.258447i
\(706\) 2.77396 4.80463i 0.104399 0.180825i
\(707\) 17.0423 + 9.83939i 0.640943 + 0.370048i
\(708\) −3.09092 1.78454i −0.116164 0.0670672i
\(709\) −17.9366 −0.673622 −0.336811 0.941572i \(-0.609348\pi\)
−0.336811 + 0.941572i \(0.609348\pi\)
\(710\) −20.5323 + 5.00134i −0.770562 + 0.187697i
\(711\) −6.74500 −0.252957
\(712\) −0.800829 + 0.462359i −0.0300124 + 0.0173276i
\(713\) 34.9966i 1.31063i
\(714\) −21.6510 −0.810269
\(715\) −5.63561 + 19.2595i −0.210760 + 0.720265i
\(716\) −9.61586 + 16.6552i −0.359361 + 0.622432i
\(717\) 15.6791i 0.585547i
\(718\) 17.6182 10.1719i 0.657505 0.379611i
\(719\) −8.52478 14.7654i −0.317921 0.550655i 0.662133 0.749386i \(-0.269651\pi\)
−0.980054 + 0.198731i \(0.936318\pi\)
\(720\) 2.14608 + 0.627973i 0.0799796 + 0.0234032i
\(721\) −19.9992 + 34.6396i −0.744809 + 1.29005i
\(722\) 12.4713 + 7.20031i 0.464134 + 0.267968i
\(723\) −13.4224 + 7.74941i −0.499183 + 0.288204i
\(724\) 3.66105 + 6.34113i 0.136062 + 0.235666i
\(725\) −10.6063 + 5.49299i −0.393909 + 0.204005i
\(726\) 7.45286 0.276602
\(727\) 10.4909 + 6.05695i 0.389087 + 0.224640i 0.681765 0.731572i \(-0.261213\pi\)
−0.292677 + 0.956211i \(0.594546\pi\)
\(728\) −6.13131 + 3.53991i −0.227241 + 0.131198i
\(729\) −1.00000 −0.0370370
\(730\) 12.3824 11.8287i 0.458294 0.437799i
\(731\) −8.12910 14.0800i −0.300665 0.520768i
\(732\) 3.78415i 0.139866i
\(733\) 2.80038 + 1.61680i 0.103434 + 0.0597178i 0.550825 0.834621i \(-0.314313\pi\)
−0.447390 + 0.894339i \(0.647647\pi\)
\(734\) 0.426836 0.0157548
\(735\) −9.74261 + 2.37315i −0.359361 + 0.0875348i
\(736\) 2.08690 3.61462i 0.0769243 0.133237i
\(737\) −53.3683 30.8122i −1.96585 1.13498i
\(738\) −9.15313 + 5.28456i −0.336931 + 0.194527i
\(739\) 31.7088 1.16643 0.583214 0.812318i \(-0.301795\pi\)
0.583214 + 0.812318i \(0.301795\pi\)
\(740\) −3.47785 + 13.1493i −0.127848 + 0.483379i
\(741\) −4.48041 −0.164592
\(742\) −32.8459 + 18.9636i −1.20581 + 0.696176i
\(743\) −15.9225 9.19286i −0.584140 0.337253i 0.178637 0.983915i \(-0.442831\pi\)
−0.762777 + 0.646662i \(0.776165\pi\)
\(744\) 4.19241 7.26147i 0.153701 0.266218i
\(745\) 8.93644 + 36.6872i 0.327406 + 1.34412i
\(746\) −26.4766 −0.969379
\(747\) −10.0539 5.80463i −0.367854 0.212380i
\(748\) 27.4445i 1.00347i
\(749\) 20.9635 + 36.3098i 0.765989 + 1.32673i
\(750\) −7.34516 8.42903i −0.268207 0.307785i
\(751\) 2.77635 0.101310 0.0506552 0.998716i \(-0.483869\pi\)
0.0506552 + 0.998716i \(0.483869\pi\)
\(752\) −9.46360 + 5.46381i −0.345102 + 0.199245i
\(753\) −3.64835 2.10637i −0.132953 0.0767605i
\(754\) 4.99068 0.181750
\(755\) 47.1482 + 13.7962i 1.71590 + 0.502097i
\(756\) −1.69443 2.93485i −0.0616260 0.106739i
\(757\) 16.1194 9.30653i 0.585869 0.338252i −0.177593 0.984104i \(-0.556831\pi\)
0.763462 + 0.645852i \(0.223498\pi\)
\(758\) −2.57017 1.48389i −0.0933527 0.0538972i
\(759\) −8.96467 + 15.5273i −0.325397 + 0.563604i
\(760\) −1.34676 + 4.60251i −0.0488522 + 0.166951i
\(761\) 10.6131 + 18.3824i 0.384724 + 0.666361i 0.991731 0.128335i \(-0.0409634\pi\)
−0.607007 + 0.794696i \(0.707630\pi\)
\(762\) 17.7444 10.2448i 0.642813 0.371128i
\(763\) 44.8324i 1.62304i
\(764\) 2.19298 3.79836i 0.0793393 0.137420i
\(765\) −4.01204 + 13.7110i −0.145056 + 0.495722i
\(766\) −35.2122 −1.27227
\(767\) 7.45633i 0.269232i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) −20.1047 −0.724993 −0.362496 0.931985i \(-0.618075\pi\)
−0.362496 + 0.931985i \(0.618075\pi\)
\(770\) −7.70379 31.6268i −0.277625 1.13975i
\(771\) 9.60769 0.346013
\(772\) 10.9188 + 6.30396i 0.392975 + 0.226884i
\(773\) −36.8790 21.2921i −1.32645 0.765823i −0.341697 0.939810i \(-0.611002\pi\)
−0.984748 + 0.173987i \(0.944335\pi\)
\(774\) 1.27238 2.20383i 0.0457349 0.0792152i
\(775\) −37.2278 + 19.2802i −1.33726 + 0.692564i
\(776\) −4.99803 −0.179419