Properties

Label 1050.2.bc.f.607.2
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 28 x^{14} + 519 x^{12} - 5404 x^{10} + 40705 x^{8} - 194544 x^{6} + 672624 x^{4} - 1306368 x^{2} + 1679616\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.2
Root \(-3.11681 - 1.79949i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.f.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63306 - 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63306 - 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.54487 - 4.40784i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(2.02443 + 2.02443i) q^{13} +(-2.47635 + 0.931486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.71580 + 1.79949i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-1.79751 + 3.11338i) q^{19} +(0.431486 - 2.61033i) q^{21} +(3.59899 + 3.59899i) q^{22} +(-1.79949 - 6.71580i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.47941 - 1.43149i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.15089 - 1.54067i) q^{28} -8.81568i q^{29} +(1.61338 - 0.931486i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-4.91631 + 1.31732i) q^{33} -6.95271 q^{34} -1.00000 q^{36} +(7.50959 - 2.01219i) q^{37} +(0.930461 - 3.47253i) q^{38} +(2.47941 - 1.43149i) q^{39} +4.13703i q^{41} +(0.258819 + 2.63306i) q^{42} +(-7.84163 + 7.84163i) q^{43} +(-4.40784 - 2.54487i) q^{44} +(3.47635 + 6.02122i) q^{46} +(0.482173 + 1.79949i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.86603 - 1.36297i) q^{49} +(3.47635 - 6.02122i) q^{51} +(2.76542 + 0.740992i) q^{52} +(0.879247 + 0.235593i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.67884 + 2.04487i) q^{56} +(2.54207 + 2.54207i) q^{57} +(2.28167 + 8.51530i) q^{58} +(-2.08974 - 3.61953i) q^{59} +(-5.08277 - 2.93454i) q^{61} +(-1.31732 + 1.31732i) q^{62} +(-2.40971 - 1.09239i) q^{63} -1.00000i q^{64} +(4.40784 - 2.54487i) q^{66} +(0.762637 - 2.84620i) q^{67} +(6.71580 - 1.79949i) q^{68} -6.95271 q^{69} +7.86297 q^{71} +(0.965926 - 0.258819i) q^{72} +(3.50165 - 13.0683i) q^{73} +(-6.73291 + 3.88725i) q^{74} +3.59502i q^{76} +(-7.84163 - 10.9475i) q^{77} +(-2.02443 + 2.02443i) q^{78} +(-10.4700 - 6.04487i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-1.07074 - 3.99606i) q^{82} +(-1.99099 - 1.99099i) q^{83} +(-0.931486 - 2.47635i) q^{84} +(5.54487 - 9.60399i) q^{86} +(-8.51530 - 2.28167i) q^{87} +(4.91631 + 1.31732i) q^{88} +(3.82507 - 6.62522i) q^{89} +(5.85440 + 4.80648i) q^{91} +(-4.91631 - 4.91631i) q^{92} +(-0.482173 - 1.79949i) q^{93} +(-0.931486 - 1.61338i) q^{94} +(0.866025 + 0.500000i) q^{96} +(13.4951 - 13.4951i) q^{97} +(-6.27931 + 3.09359i) q^{98} +5.08974i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 4q^{11} + 8q^{14} + 8q^{16} - 4q^{19} - 4q^{21} + 8q^{24} - 16q^{34} - 16q^{36} - 12q^{44} + 8q^{46} + 96q^{49} + 8q^{51} + 8q^{54} - 4q^{56} + 40q^{59} - 24q^{61} + 12q^{66} - 16q^{69} + 104q^{71} - 48q^{74} - 12q^{79} + 8q^{81} - 4q^{84} + 52q^{86} + 60q^{89} - 52q^{91} - 4q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.63306 0.258819i 0.995204 0.0978244i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −2.54487 4.40784i −0.767307 1.32901i −0.939018 0.343867i \(-0.888263\pi\)
0.171712 0.985147i \(-0.445070\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) 2.02443 + 2.02443i 0.561475 + 0.561475i 0.929726 0.368251i \(-0.120043\pi\)
−0.368251 + 0.929726i \(0.620043\pi\)
\(14\) −2.47635 + 0.931486i −0.661834 + 0.248950i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 6.71580 + 1.79949i 1.62882 + 0.436441i 0.953576 0.301152i \(-0.0973712\pi\)
0.675245 + 0.737593i \(0.264038\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) −1.79751 + 3.11338i −0.412378 + 0.714259i −0.995149 0.0983771i \(-0.968635\pi\)
0.582772 + 0.812636i \(0.301968\pi\)
\(20\) 0 0
\(21\) 0.431486 2.61033i 0.0941581 0.569621i
\(22\) 3.59899 + 3.59899i 0.767307 + 0.767307i
\(23\) −1.79949 6.71580i −0.375220 1.40034i −0.853023 0.521874i \(-0.825233\pi\)
0.477802 0.878467i \(-0.341434\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −2.47941 1.43149i −0.486252 0.280738i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 2.15089 1.54067i 0.406480 0.291160i
\(29\) 8.81568i 1.63703i −0.574484 0.818516i \(-0.694797\pi\)
0.574484 0.818516i \(-0.305203\pi\)
\(30\) 0 0
\(31\) 1.61338 0.931486i 0.289772 0.167300i −0.348067 0.937470i \(-0.613162\pi\)
0.637839 + 0.770170i \(0.279829\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −4.91631 + 1.31732i −0.855819 + 0.229316i
\(34\) −6.95271 −1.19238
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 7.50959 2.01219i 1.23457 0.330802i 0.418212 0.908350i \(-0.362657\pi\)
0.816357 + 0.577548i \(0.195990\pi\)
\(38\) 0.930461 3.47253i 0.150941 0.563318i
\(39\) 2.47941 1.43149i 0.397023 0.229221i
\(40\) 0 0
\(41\) 4.13703i 0.646095i 0.946383 + 0.323048i \(0.104707\pi\)
−0.946383 + 0.323048i \(0.895293\pi\)
\(42\) 0.258819 + 2.63306i 0.0399366 + 0.406290i
\(43\) −7.84163 + 7.84163i −1.19584 + 1.19584i −0.220436 + 0.975402i \(0.570748\pi\)
−0.975402 + 0.220436i \(0.929252\pi\)
\(44\) −4.40784 2.54487i −0.664507 0.383653i
\(45\) 0 0
\(46\) 3.47635 + 6.02122i 0.512561 + 0.887781i
\(47\) 0.482173 + 1.79949i 0.0703321 + 0.262483i 0.992134 0.125177i \(-0.0399500\pi\)
−0.921802 + 0.387660i \(0.873283\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.86603 1.36297i 0.980861 0.194710i
\(50\) 0 0
\(51\) 3.47635 6.02122i 0.486787 0.843140i
\(52\) 2.76542 + 0.740992i 0.383495 + 0.102757i
\(53\) 0.879247 + 0.235593i 0.120774 + 0.0323613i 0.318700 0.947856i \(-0.396754\pi\)
−0.197926 + 0.980217i \(0.563421\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −1.67884 + 2.04487i −0.224345 + 0.273257i
\(57\) 2.54207 + 2.54207i 0.336705 + 0.336705i
\(58\) 2.28167 + 8.51530i 0.299597 + 1.11811i
\(59\) −2.08974 3.61953i −0.272061 0.471223i 0.697329 0.716751i \(-0.254372\pi\)
−0.969389 + 0.245529i \(0.921038\pi\)
\(60\) 0 0
\(61\) −5.08277 2.93454i −0.650782 0.375729i 0.137974 0.990436i \(-0.455941\pi\)
−0.788756 + 0.614707i \(0.789274\pi\)
\(62\) −1.31732 + 1.31732i −0.167300 + 0.167300i
\(63\) −2.40971 1.09239i −0.303595 0.137628i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 4.40784 2.54487i 0.542568 0.313252i
\(67\) 0.762637 2.84620i 0.0931710 0.347719i −0.903565 0.428451i \(-0.859059\pi\)
0.996736 + 0.0807326i \(0.0257260\pi\)
\(68\) 6.71580 1.79949i 0.814411 0.218221i
\(69\) −6.95271 −0.837008
\(70\) 0 0
\(71\) 7.86297 0.933163 0.466582 0.884478i \(-0.345485\pi\)
0.466582 + 0.884478i \(0.345485\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) 3.50165 13.0683i 0.409837 1.52953i −0.385120 0.922867i \(-0.625840\pi\)
0.794957 0.606666i \(-0.207493\pi\)
\(74\) −6.73291 + 3.88725i −0.782685 + 0.451883i
\(75\) 0 0
\(76\) 3.59502i 0.412378i
\(77\) −7.84163 10.9475i −0.893636 1.24758i
\(78\) −2.02443 + 2.02443i −0.229221 + 0.229221i
\(79\) −10.4700 6.04487i −1.17797 0.680101i −0.222425 0.974950i \(-0.571397\pi\)
−0.955544 + 0.294849i \(0.904731\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −1.07074 3.99606i −0.118244 0.441291i
\(83\) −1.99099 1.99099i −0.218539 0.218539i 0.589343 0.807883i \(-0.299387\pi\)
−0.807883 + 0.589343i \(0.799387\pi\)
\(84\) −0.931486 2.47635i −0.101634 0.270192i
\(85\) 0 0
\(86\) 5.54487 9.60399i 0.597919 1.03563i
\(87\) −8.51530 2.28167i −0.912935 0.244620i
\(88\) 4.91631 + 1.31732i 0.524080 + 0.140427i
\(89\) 3.82507 6.62522i 0.405457 0.702272i −0.588918 0.808193i \(-0.700446\pi\)
0.994375 + 0.105921i \(0.0337792\pi\)
\(90\) 0 0
\(91\) 5.85440 + 4.80648i 0.613708 + 0.503856i
\(92\) −4.91631 4.91631i −0.512561 0.512561i
\(93\) −0.482173 1.79949i −0.0499990 0.186599i
\(94\) −0.931486 1.61338i −0.0960755 0.166408i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 13.4951 13.4951i 1.37022 1.37022i 0.510101 0.860115i \(-0.329608\pi\)
0.860115 0.510101i \(-0.170392\pi\)
\(98\) −6.27931 + 3.09359i −0.634306 + 0.312500i
\(99\) 5.08974i 0.511538i
\(100\) 0 0
\(101\) 1.18108 0.681895i 0.117522 0.0678511i −0.440087 0.897955i \(-0.645052\pi\)
0.557609 + 0.830104i \(0.311719\pi\)
\(102\) −1.79949 + 6.71580i −0.178176 + 0.664963i
\(103\) 0.351395 0.0941560i 0.0346240 0.00927747i −0.241465 0.970409i \(-0.577628\pi\)
0.276089 + 0.961132i \(0.410961\pi\)
\(104\) −2.86297 −0.280738
\(105\) 0 0
\(106\) −0.910263 −0.0884126
\(107\) 0.205579 0.0550849i 0.0198741 0.00532525i −0.248868 0.968537i \(-0.580059\pi\)
0.268742 + 0.963212i \(0.413392\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) 1.35135 0.780202i 0.129436 0.0747298i −0.433884 0.900969i \(-0.642857\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(110\) 0 0
\(111\) 7.77450i 0.737923i
\(112\) 1.09239 2.40971i 0.103221 0.227696i
\(113\) 0.0300140 0.0300140i 0.00282348 0.00282348i −0.705694 0.708517i \(-0.749364\pi\)
0.708517 + 0.705694i \(0.249364\pi\)
\(114\) −3.11338 1.79751i −0.291595 0.168352i
\(115\) 0 0
\(116\) −4.40784 7.63460i −0.409258 0.708855i
\(117\) −0.740992 2.76542i −0.0685047 0.255663i
\(118\) 2.95533 + 2.95533i 0.272061 + 0.272061i
\(119\) 18.1489 + 3.00000i 1.66370 + 0.275010i
\(120\) 0 0
\(121\) −7.45271 + 12.9085i −0.677519 + 1.17350i
\(122\) 5.66909 + 1.51903i 0.513256 + 0.137526i
\(123\) 3.99606 + 1.07074i 0.360313 + 0.0965455i
\(124\) 0.931486 1.61338i 0.0836500 0.144886i
\(125\) 0 0
\(126\) 2.61033 + 0.431486i 0.232547 + 0.0384399i
\(127\) −1.42723 1.42723i −0.126646 0.126646i 0.640943 0.767589i \(-0.278544\pi\)
−0.767589 + 0.640943i \(0.778544\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) 5.54487 + 9.60399i 0.488198 + 0.845584i
\(130\) 0 0
\(131\) −4.59216 2.65128i −0.401219 0.231644i 0.285791 0.958292i \(-0.407744\pi\)
−0.687010 + 0.726648i \(0.741077\pi\)
\(132\) −3.59899 + 3.59899i −0.313252 + 0.313252i
\(133\) −3.92716 + 8.66296i −0.340528 + 0.751174i
\(134\) 2.94660i 0.254548i
\(135\) 0 0
\(136\) −6.02122 + 3.47635i −0.516316 + 0.298095i
\(137\) −5.68916 + 21.2322i −0.486058 + 1.81399i 0.0891925 + 0.996014i \(0.471571\pi\)
−0.575250 + 0.817978i \(0.695095\pi\)
\(138\) 6.71580 1.79949i 0.571687 0.153183i
\(139\) 16.5902 1.40716 0.703580 0.710616i \(-0.251584\pi\)
0.703580 + 0.710616i \(0.251584\pi\)
\(140\) 0 0
\(141\) 1.86297 0.156891
\(142\) −7.59505 + 2.03509i −0.637362 + 0.170781i
\(143\) 3.77145 14.0753i 0.315385 1.17703i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 13.5293i 1.11970i
\(147\) 0.460527 6.98483i 0.0379837 0.576099i
\(148\) 5.49740 5.49740i 0.451883 0.451883i
\(149\) −8.60723 4.96939i −0.705132 0.407108i 0.104124 0.994564i \(-0.466796\pi\)
−0.809256 + 0.587456i \(0.800129\pi\)
\(150\) 0 0
\(151\) 7.65825 + 13.2645i 0.623220 + 1.07945i 0.988882 + 0.148701i \(0.0475090\pi\)
−0.365663 + 0.930747i \(0.619158\pi\)
\(152\) −0.930461 3.47253i −0.0754703 0.281659i
\(153\) −4.91631 4.91631i −0.397460 0.397460i
\(154\) 10.4078 + 8.54487i 0.838688 + 0.688565i
\(155\) 0 0
\(156\) 1.43149 2.47941i 0.114611 0.198511i
\(157\) 15.7881 + 4.23040i 1.26003 + 0.337623i 0.826201 0.563375i \(-0.190497\pi\)
0.433824 + 0.900998i \(0.357164\pi\)
\(158\) 11.6778 + 3.12905i 0.929035 + 0.248934i
\(159\) 0.455132 0.788311i 0.0360943 0.0625171i
\(160\) 0 0
\(161\) −6.47635 17.2174i −0.510408 1.35692i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 1.93977 + 7.23934i 0.151935 + 0.567029i 0.999348 + 0.0360951i \(0.0114919\pi\)
−0.847413 + 0.530933i \(0.821841\pi\)
\(164\) 2.06851 + 3.58277i 0.161524 + 0.279767i
\(165\) 0 0
\(166\) 2.43845 + 1.40784i 0.189261 + 0.109270i
\(167\) −12.7880 + 12.7880i −0.989561 + 0.989561i −0.999946 0.0103848i \(-0.996694\pi\)
0.0103848 + 0.999946i \(0.496694\pi\)
\(168\) 1.54067 + 2.15089i 0.118866 + 0.165945i
\(169\) 4.80339i 0.369491i
\(170\) 0 0
\(171\) 3.11338 1.79751i 0.238086 0.137459i
\(172\) −2.87024 + 10.7119i −0.218853 + 0.816772i
\(173\) −15.6282 + 4.18756i −1.18819 + 0.318374i −0.798169 0.602433i \(-0.794198\pi\)
−0.390018 + 0.920807i \(0.627531\pi\)
\(174\) 8.81568 0.668315
\(175\) 0 0
\(176\) −5.08974 −0.383653
\(177\) −4.03706 + 1.08173i −0.303444 + 0.0813076i
\(178\) −1.98000 + 7.38947i −0.148407 + 0.553864i
\(179\) −8.60723 + 4.96939i −0.643335 + 0.371430i −0.785898 0.618356i \(-0.787799\pi\)
0.142563 + 0.989786i \(0.454466\pi\)
\(180\) 0 0
\(181\) 2.60285i 0.193468i 0.995310 + 0.0967342i \(0.0308397\pi\)
−0.995310 + 0.0967342i \(0.969160\pi\)
\(182\) −6.89893 3.12747i −0.511383 0.231824i
\(183\) −4.15006 + 4.15006i −0.306782 + 0.306782i
\(184\) 6.02122 + 3.47635i 0.443890 + 0.256280i
\(185\) 0 0
\(186\) 0.931486 + 1.61338i 0.0682999 + 0.118299i
\(187\) −9.15895 34.1817i −0.669769 2.49961i
\(188\) 1.31732 + 1.31732i 0.0960755 + 0.0960755i
\(189\) −1.67884 + 2.04487i −0.122118 + 0.148742i
\(190\) 0 0
\(191\) −2.06851 + 3.58277i −0.149672 + 0.259240i −0.931106 0.364748i \(-0.881155\pi\)
0.781434 + 0.623988i \(0.214489\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) 12.5114 + 3.35241i 0.900587 + 0.241312i 0.679268 0.733890i \(-0.262297\pi\)
0.221319 + 0.975202i \(0.428964\pi\)
\(194\) −9.54245 + 16.5280i −0.685108 + 1.18664i
\(195\) 0 0
\(196\) 5.26467 4.61338i 0.376048 0.329527i
\(197\) 0.876148 + 0.876148i 0.0624229 + 0.0624229i 0.737629 0.675206i \(-0.235945\pi\)
−0.675206 + 0.737629i \(0.735945\pi\)
\(198\) −1.31732 4.91631i −0.0936179 0.349387i
\(199\) 8.63155 + 14.9503i 0.611875 + 1.05980i 0.990924 + 0.134421i \(0.0429176\pi\)
−0.379050 + 0.925376i \(0.623749\pi\)
\(200\) 0 0
\(201\) −2.55183 1.47330i −0.179993 0.103919i
\(202\) −0.964346 + 0.964346i −0.0678511 + 0.0678511i
\(203\) −2.28167 23.2122i −0.160142 1.62918i
\(204\) 6.95271i 0.486787i
\(205\) 0 0
\(206\) −0.315052 + 0.181895i −0.0219507 + 0.0126733i
\(207\) −1.79949 + 6.71580i −0.125073 + 0.466780i
\(208\) 2.76542 0.740992i 0.191747 0.0513785i
\(209\) 18.2977 1.26568
\(210\) 0 0
\(211\) −7.40460 −0.509754 −0.254877 0.966974i \(-0.582035\pi\)
−0.254877 + 0.966974i \(0.582035\pi\)
\(212\) 0.879247 0.235593i 0.0603869 0.0161806i
\(213\) 2.03509 7.59505i 0.139442 0.520404i
\(214\) −0.184318 + 0.106416i −0.0125997 + 0.00727443i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 4.00705 2.87024i 0.272016 0.194844i
\(218\) −1.10337 + 1.10337i −0.0747298 + 0.0747298i
\(219\) −11.7167 6.76467i −0.791744 0.457114i
\(220\) 0 0
\(221\) 9.95271 + 17.2386i 0.669492 + 1.15959i
\(222\) 2.01219 + 7.50959i 0.135049 + 0.504011i
\(223\) −2.69809 2.69809i −0.180678 0.180678i 0.610973 0.791651i \(-0.290778\pi\)
−0.791651 + 0.610973i \(0.790778\pi\)
\(224\) −0.431486 + 2.61033i −0.0288299 + 0.174410i
\(225\) 0 0
\(226\) −0.0212231 + 0.0367595i −0.00141174 + 0.00244520i
\(227\) −19.0216 5.09682i −1.26251 0.338288i −0.435351 0.900261i \(-0.643376\pi\)
−0.827155 + 0.561973i \(0.810042\pi\)
\(228\) 3.47253 + 0.930461i 0.229974 + 0.0616213i
\(229\) −11.4884 + 19.8985i −0.759173 + 1.31493i 0.184099 + 0.982908i \(0.441063\pi\)
−0.943273 + 0.332019i \(0.892270\pi\)
\(230\) 0 0
\(231\) −12.6040 + 4.74102i −0.829282 + 0.311936i
\(232\) 6.23363 + 6.23363i 0.409258 + 0.409258i
\(233\) 3.42652 + 12.7880i 0.224479 + 0.837766i 0.982613 + 0.185667i \(0.0594447\pi\)
−0.758134 + 0.652099i \(0.773889\pi\)
\(234\) 1.43149 + 2.47941i 0.0935792 + 0.162084i
\(235\) 0 0
\(236\) −3.61953 2.08974i −0.235611 0.136030i
\(237\) −8.54873 + 8.54873i −0.555300 + 0.555300i
\(238\) −18.3069 + 1.79949i −1.18666 + 0.116644i
\(239\) 1.65014i 0.106739i 0.998575 + 0.0533694i \(0.0169961\pi\)
−0.998575 + 0.0533694i \(0.983004\pi\)
\(240\) 0 0
\(241\) −10.9564 + 6.32570i −0.705766 + 0.407474i −0.809491 0.587132i \(-0.800257\pi\)
0.103725 + 0.994606i \(0.466924\pi\)
\(242\) 3.85781 14.3975i 0.247989 0.925508i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) −5.86908 −0.375729
\(245\) 0 0
\(246\) −4.13703 −0.263767
\(247\) −9.94175 + 2.66388i −0.632578 + 0.169499i
\(248\) −0.482173 + 1.79949i −0.0306180 + 0.114268i
\(249\) −2.43845 + 1.40784i −0.154531 + 0.0892183i
\(250\) 0 0
\(251\) 7.45189i 0.470359i 0.971952 + 0.235180i \(0.0755678\pi\)
−0.971952 + 0.235180i \(0.924432\pi\)
\(252\) −2.63306 + 0.258819i −0.165867 + 0.0163041i
\(253\) −25.0227 + 25.0227i −1.57316 + 1.57316i
\(254\) 1.74799 + 1.00920i 0.109678 + 0.0633229i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.30494 + 16.0662i 0.268535 + 1.00218i 0.960051 + 0.279824i \(0.0902762\pi\)
−0.691517 + 0.722361i \(0.743057\pi\)
\(258\) −7.84163 7.84163i −0.488198 0.488198i
\(259\) 19.2524 7.24184i 1.19629 0.449986i
\(260\) 0 0
\(261\) −4.40784 + 7.63460i −0.272839 + 0.472570i
\(262\) 5.12189 + 1.37241i 0.316431 + 0.0847875i
\(263\) 10.6709 + 2.85925i 0.657994 + 0.176309i 0.572340 0.820016i \(-0.306036\pi\)
0.0856532 + 0.996325i \(0.472702\pi\)
\(264\) 2.54487 4.40784i 0.156626 0.271284i
\(265\) 0 0
\(266\) 1.55120 9.38420i 0.0951104 0.575382i
\(267\) −5.40947 5.40947i −0.331054 0.331054i
\(268\) −0.762637 2.84620i −0.0465855 0.173859i
\(269\) 13.3014 + 23.0387i 0.811002 + 1.40470i 0.912163 + 0.409827i \(0.134411\pi\)
−0.101161 + 0.994870i \(0.532256\pi\)
\(270\) 0 0
\(271\) −17.5946 10.1583i −1.06880 0.617070i −0.140944 0.990018i \(-0.545014\pi\)
−0.927852 + 0.372948i \(0.878347\pi\)
\(272\) 4.91631 4.91631i 0.298095 0.298095i
\(273\) 6.15794 4.41091i 0.372695 0.266960i
\(274\) 21.9812i 1.32793i
\(275\) 0 0
\(276\) −6.02122 + 3.47635i −0.362435 + 0.209252i
\(277\) −2.60623 + 9.72658i −0.156593 + 0.584414i 0.842370 + 0.538899i \(0.181160\pi\)
−0.998964 + 0.0455149i \(0.985507\pi\)
\(278\) −16.0249 + 4.29385i −0.961109 + 0.257528i
\(279\) −1.86297 −0.111533
\(280\) 0 0
\(281\) 15.2268 0.908353 0.454176 0.890912i \(-0.349934\pi\)
0.454176 + 0.890912i \(0.349934\pi\)
\(282\) −1.79949 + 0.482173i −0.107158 + 0.0287130i
\(283\) 3.83878 14.3265i 0.228192 0.851623i −0.752909 0.658125i \(-0.771350\pi\)
0.981101 0.193498i \(-0.0619834\pi\)
\(284\) 6.80953 3.93149i 0.404072 0.233291i
\(285\) 0 0
\(286\) 14.5718i 0.861647i
\(287\) 1.07074 + 10.8930i 0.0632039 + 0.642996i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 27.1414 + 15.6701i 1.59655 + 0.921770i
\(290\) 0 0
\(291\) −9.54245 16.5280i −0.559388 0.968889i
\(292\) −3.50165 13.0683i −0.204918 0.764766i
\(293\) 18.7009 + 18.7009i 1.09252 + 1.09252i 0.995259 + 0.0972583i \(0.0310073\pi\)
0.0972583 + 0.995259i \(0.468993\pi\)
\(294\) 1.36297 + 6.86603i 0.0794902 + 0.400435i
\(295\) 0 0
\(296\) −3.88725 + 6.73291i −0.225942 + 0.391343i
\(297\) 4.91631 + 1.31732i 0.285273 + 0.0764387i
\(298\) 9.60012 + 2.57234i 0.556120 + 0.149012i
\(299\) 9.95271 17.2386i 0.575580 0.996934i
\(300\) 0 0
\(301\) −18.6179 + 22.6771i −1.07312 + 1.30708i
\(302\) −10.8304 10.8304i −0.623220 0.623220i
\(303\) −0.352975 1.31732i −0.0202779 0.0756781i
\(304\) 1.79751 + 3.11338i 0.103094 + 0.178565i
\(305\) 0 0
\(306\) 6.02122 + 3.47635i 0.344210 + 0.198730i
\(307\) −22.4937 + 22.4937i −1.28378 + 1.28378i −0.345282 + 0.938499i \(0.612217\pi\)
−0.938499 + 0.345282i \(0.887783\pi\)
\(308\) −12.2648 5.55996i −0.698851 0.316808i
\(309\) 0.363791i 0.0206953i
\(310\) 0 0
\(311\) 14.2598 8.23291i 0.808600 0.466846i −0.0378693 0.999283i \(-0.512057\pi\)
0.846470 + 0.532437i \(0.178724\pi\)
\(312\) −0.740992 + 2.76542i −0.0419504 + 0.156561i
\(313\) 3.26105 0.873796i 0.184325 0.0493899i −0.165476 0.986214i \(-0.552916\pi\)
0.349801 + 0.936824i \(0.386249\pi\)
\(314\) −16.3450 −0.922403
\(315\) 0 0
\(316\) −12.0897 −0.680101
\(317\) 13.3465 3.57619i 0.749614 0.200859i 0.136267 0.990672i \(-0.456489\pi\)
0.613347 + 0.789814i \(0.289823\pi\)
\(318\) −0.235593 + 0.879247i −0.0132114 + 0.0493057i
\(319\) −38.8581 + 22.4348i −2.17564 + 1.25610i
\(320\) 0 0
\(321\) 0.212832i 0.0118791i
\(322\) 10.7119 + 14.9545i 0.596949 + 0.833382i
\(323\) −17.6742 + 17.6742i −0.983421 + 0.983421i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) −3.74736 6.49061i −0.207547 0.359482i
\(327\) −0.403862 1.50724i −0.0223336 0.0833503i
\(328\) −2.92532 2.92532i −0.161524 0.161524i
\(329\) 1.73533 + 4.61338i 0.0956721 + 0.254344i
\(330\) 0 0
\(331\) 2.41481 4.18257i 0.132730 0.229895i −0.791998 0.610524i \(-0.790959\pi\)
0.924728 + 0.380629i \(0.124292\pi\)
\(332\) −2.71974 0.728752i −0.149265 0.0399955i
\(333\) −7.50959 2.01219i −0.411523 0.110267i
\(334\) 9.04245 15.6620i 0.494781 0.856985i
\(335\) 0 0
\(336\) −2.04487 1.67884i −0.111557 0.0915884i
\(337\) −6.52431 6.52431i −0.355402 0.355402i 0.506713 0.862115i \(-0.330860\pi\)
−0.862115 + 0.506713i \(0.830860\pi\)
\(338\) 1.24321 + 4.63971i 0.0676216 + 0.252367i
\(339\) −0.0212231 0.0367595i −0.00115268 0.00199650i
\(340\) 0 0
\(341\) −8.21169 4.74102i −0.444688 0.256741i
\(342\) −2.54207 + 2.54207i −0.137459 + 0.137459i
\(343\) 17.7259 5.36585i 0.957109 0.289729i
\(344\) 11.0897i 0.597919i
\(345\) 0 0
\(346\) 14.0118 8.08974i 0.753281 0.434907i
\(347\) −8.13952 + 30.3771i −0.436952 + 1.63073i 0.299399 + 0.954128i \(0.403214\pi\)
−0.736351 + 0.676600i \(0.763453\pi\)
\(348\) −8.51530 + 2.28167i −0.456468 + 0.122310i
\(349\) −28.5083 −1.52601 −0.763006 0.646391i \(-0.776278\pi\)
−0.763006 + 0.646391i \(0.776278\pi\)
\(350\) 0 0
\(351\) −2.86297 −0.152814
\(352\) 4.91631 1.31732i 0.262040 0.0702134i
\(353\) −6.04935 + 22.5765i −0.321974 + 1.20162i 0.595345 + 0.803471i \(0.297016\pi\)
−0.917319 + 0.398154i \(0.869651\pi\)
\(354\) 3.61953 2.08974i 0.192376 0.111068i
\(355\) 0 0
\(356\) 7.65014i 0.405457i
\(357\) 7.59505 16.7540i 0.401973 0.886716i
\(358\) 7.02778 7.02778i 0.371430 0.371430i
\(359\) −14.5889 8.42292i −0.769974 0.444545i 0.0628915 0.998020i \(-0.479968\pi\)
−0.832865 + 0.553476i \(0.813301\pi\)
\(360\) 0 0
\(361\) 3.03790 + 5.26180i 0.159890 + 0.276937i
\(362\) −0.673667 2.51416i −0.0354072 0.132141i
\(363\) 10.5397 + 10.5397i 0.553192 + 0.553192i
\(364\) 7.47330 + 1.23533i 0.391707 + 0.0647491i
\(365\) 0 0
\(366\) 2.93454 5.08277i 0.153391 0.265681i
\(367\) 26.0453 + 6.97882i 1.35955 + 0.364291i 0.863653 0.504088i \(-0.168171\pi\)
0.495901 + 0.868379i \(0.334838\pi\)
\(368\) −6.71580 1.79949i −0.350085 0.0938051i
\(369\) 2.06851 3.58277i 0.107683 0.186512i
\(370\) 0 0
\(371\) 2.37609 + 0.392766i 0.123360 + 0.0203914i
\(372\) −1.31732 1.31732i −0.0682999 0.0682999i
\(373\) 2.66388 + 9.94175i 0.137931 + 0.514764i 0.999969 + 0.00792053i \(0.00252121\pi\)
−0.862038 + 0.506844i \(0.830812\pi\)
\(374\) 17.6937 + 30.6464i 0.914921 + 1.58469i
\(375\) 0 0
\(376\) −1.61338 0.931486i −0.0832038 0.0480377i
\(377\) 17.8467 17.8467i 0.919152 0.919152i
\(378\) 1.09239 2.40971i 0.0561863 0.123942i
\(379\) 24.4633i 1.25659i −0.777974 0.628297i \(-0.783752\pi\)
0.777974 0.628297i \(-0.216248\pi\)
\(380\) 0 0
\(381\) −1.74799 + 1.00920i −0.0895521 + 0.0517029i
\(382\) 1.07074 3.99606i 0.0547839 0.204456i
\(383\) −5.96013 + 1.59701i −0.304549 + 0.0816036i −0.407857 0.913046i \(-0.633724\pi\)
0.103308 + 0.994649i \(0.467057\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −12.9527 −0.659276
\(387\) 10.7119 2.87024i 0.544515 0.145902i
\(388\) 4.93953 18.4346i 0.250767 0.935875i
\(389\) 11.9344 6.89034i 0.605099 0.349354i −0.165946 0.986135i \(-0.553068\pi\)
0.771045 + 0.636781i \(0.219734\pi\)
\(390\) 0 0
\(391\) 48.3402i 2.44467i
\(392\) −3.89125 + 5.81878i −0.196538 + 0.293893i
\(393\) −3.74948 + 3.74948i −0.189136 + 0.189136i
\(394\) −1.07306 0.619530i −0.0540599 0.0312115i
\(395\) 0 0
\(396\) 2.54487 + 4.40784i 0.127884 + 0.221502i
\(397\) −0.298482 1.11395i −0.0149804 0.0559075i 0.958031 0.286664i \(-0.0925465\pi\)
−0.973011 + 0.230757i \(0.925880\pi\)
\(398\) −12.2069 12.2069i −0.611875 0.611875i
\(399\) 7.35135 + 6.03548i 0.368028 + 0.302152i
\(400\) 0 0
\(401\) −4.13703 + 7.16554i −0.206593 + 0.357830i −0.950639 0.310298i \(-0.899571\pi\)
0.744046 + 0.668128i \(0.232904\pi\)
\(402\) 2.84620 + 0.762637i 0.141956 + 0.0380369i
\(403\) 5.15190 + 1.38045i 0.256634 + 0.0687650i
\(404\) 0.681895 1.18108i 0.0339256 0.0587608i
\(405\) 0 0
\(406\) 8.21169 + 21.8308i 0.407539 + 1.08344i
\(407\) −27.9803 27.9803i −1.38693 1.38693i
\(408\) 1.79949 + 6.71580i 0.0890882 + 0.332482i
\(409\) −18.2355 31.5849i −0.901690 1.56177i −0.825300 0.564694i \(-0.808994\pi\)
−0.0763896 0.997078i \(-0.524339\pi\)
\(410\) 0 0
\(411\) 19.0363 + 10.9906i 0.938991 + 0.542127i
\(412\) 0.257239 0.257239i 0.0126733 0.0126733i
\(413\) −6.43921 8.98958i −0.316853 0.442348i
\(414\) 6.95271i 0.341707i
\(415\) 0 0
\(416\) −2.47941 + 1.43149i −0.121563 + 0.0701844i
\(417\) 4.29385 16.0249i 0.210271 0.784742i
\(418\) −17.6742 + 4.73580i −0.864476 + 0.231636i
\(419\) −9.05638 −0.442433 −0.221217 0.975225i \(-0.571003\pi\)
−0.221217 + 0.975225i \(0.571003\pi\)
\(420\) 0 0
\(421\) 10.3149 0.502716 0.251358 0.967894i \(-0.419123\pi\)
0.251358 + 0.967894i \(0.419123\pi\)
\(422\) 7.15230 1.91645i 0.348168 0.0932914i
\(423\) 0.482173 1.79949i 0.0234440 0.0874944i
\(424\) −0.788311 + 0.455132i −0.0382838 + 0.0221031i
\(425\) 0 0
\(426\) 7.86297i 0.380962i
\(427\) −14.1428 6.41130i −0.684416 0.310265i
\(428\) 0.150495 0.150495i 0.00727443 0.00727443i
\(429\) −12.6195 7.28589i −0.609277 0.351766i
\(430\) 0 0
\(431\) 11.4441 + 19.8218i 0.551245 + 0.954784i 0.998185 + 0.0602202i \(0.0191803\pi\)
−0.446940 + 0.894564i \(0.647486\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) 17.2780 + 17.2780i 0.830327 + 0.830327i 0.987561 0.157235i \(-0.0502579\pi\)
−0.157235 + 0.987561i \(0.550258\pi\)
\(434\) −3.12764 + 3.80953i −0.150131 + 0.182863i
\(435\) 0 0
\(436\) 0.780202 1.35135i 0.0373649 0.0647179i
\(437\) 24.1435 + 6.46922i 1.15494 + 0.309465i
\(438\) 13.0683 + 3.50165i 0.624429 + 0.167315i
\(439\) −2.48269 + 4.30015i −0.118492 + 0.205235i −0.919170 0.393860i \(-0.871139\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(440\) 0 0
\(441\) −6.62764 2.25264i −0.315602 0.107269i
\(442\) −14.0753 14.0753i −0.669492 0.669492i
\(443\) −3.36339 12.5524i −0.159800 0.596380i −0.998646 0.0520128i \(-0.983436\pi\)
0.838847 0.544368i \(-0.183230\pi\)
\(444\) −3.88725 6.73291i −0.184481 0.319530i
\(445\) 0 0
\(446\) 3.30448 + 1.90784i 0.156472 + 0.0903389i
\(447\) −7.02778 + 7.02778i −0.332402 + 0.332402i
\(448\) −0.258819 2.63306i −0.0122281 0.124400i
\(449\) 15.0710i 0.711243i −0.934630 0.355621i \(-0.884269\pi\)
0.934630 0.355621i \(-0.115731\pi\)
\(450\) 0 0
\(451\) 18.2354 10.5282i 0.858669 0.495753i
\(452\) 0.0109859 0.0409999i 0.000516733 0.00192847i
\(453\) 14.7946 3.96420i 0.695111 0.186254i
\(454\) 19.6926 0.924219
\(455\) 0 0
\(456\) −3.59502 −0.168352
\(457\) −25.0167 + 6.70321i −1.17023 + 0.313563i −0.791046 0.611757i \(-0.790463\pi\)
−0.379187 + 0.925320i \(0.623796\pi\)
\(458\) 5.94682 22.1938i 0.277877 1.03705i
\(459\) −6.02122 + 3.47635i −0.281047 + 0.162262i
\(460\) 0 0
\(461\) 19.9054i 0.927088i −0.886074 0.463544i \(-0.846578\pi\)
0.886074 0.463544i \(-0.153422\pi\)
\(462\) 10.9475 7.84163i 0.509322 0.364826i
\(463\) 29.0870 29.0870i 1.35179 1.35179i 0.468121 0.883664i \(-0.344931\pi\)
0.883664 0.468121i \(-0.155069\pi\)
\(464\) −7.63460 4.40784i −0.354428 0.204629i
\(465\) 0 0
\(466\) −6.61953 11.4654i −0.306644 0.531123i
\(467\) 7.37127 + 27.5100i 0.341102 + 1.27301i 0.897101 + 0.441826i \(0.145669\pi\)
−0.555999 + 0.831183i \(0.687664\pi\)
\(468\) −2.02443 2.02443i −0.0935792 0.0935792i
\(469\) 1.27142 7.69161i 0.0587087 0.355165i
\(470\) 0 0
\(471\) 8.17251 14.1552i 0.376569 0.652237i
\(472\) 4.03706 + 1.08173i 0.185821 + 0.0497905i
\(473\) 54.5206 + 14.6087i 2.50686 + 0.671711i
\(474\) 6.04487 10.4700i 0.277650 0.480904i
\(475\) 0 0
\(476\) 17.2174 6.47635i 0.789157 0.296843i
\(477\) −0.643653 0.643653i −0.0294709 0.0294709i
\(478\) −0.427088 1.59391i −0.0195346 0.0729039i
\(479\) 4.79770 + 8.30986i 0.219212 + 0.379687i 0.954567 0.297995i \(-0.0963179\pi\)
−0.735355 + 0.677682i \(0.762985\pi\)
\(480\) 0 0
\(481\) 19.2761 + 11.1291i 0.878917 + 0.507443i
\(482\) 8.94589 8.94589i 0.407474 0.407474i
\(483\) −18.3069 + 1.79949i −0.832993 + 0.0818798i
\(484\) 14.9054i 0.677519i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 3.22698 12.0433i 0.146229 0.545733i −0.853469 0.521144i \(-0.825506\pi\)
0.999698 0.0245890i \(-0.00782772\pi\)
\(488\) 5.66909 1.51903i 0.256628 0.0687632i
\(489\) 7.49471 0.338923
\(490\) 0 0
\(491\) 36.3288 1.63950 0.819748 0.572725i \(-0.194114\pi\)
0.819748 + 0.572725i \(0.194114\pi\)
\(492\) 3.99606 1.07074i 0.180156 0.0482728i
\(493\) 15.8638 59.2044i 0.714468 2.66643i
\(494\) 8.91353 5.14623i 0.401039 0.231540i
\(495\) 0 0
\(496\) 1.86297i 0.0836500i
\(497\) 20.7037 2.03509i 0.928687 0.0912861i
\(498\) 1.99099 1.99099i 0.0892183 0.0892183i
\(499\) −2.42441 1.39973i −0.108531 0.0626606i 0.444752 0.895654i \(-0.353292\pi\)
−0.553283 + 0.832993i \(0.686625\pi\)
\(500\) 0 0
\(501\) 9.04245 + 15.6620i 0.403987 + 0.699725i
\(502\) −1.92869 7.19797i −0.0860817 0.321261i
\(503\) 12.1725 + 12.1725i 0.542743 + 0.542743i 0.924332 0.381589i \(-0.124623\pi\)
−0.381589 + 0.924332i \(0.624623\pi\)
\(504\) 2.47635 0.931486i 0.110306 0.0414917i
\(505\) 0 0
\(506\) 17.6937 30.6464i 0.786582 1.36240i
\(507\) −4.63971 1.24321i −0.206057 0.0552128i
\(508\) −1.94963 0.522401i −0.0865007 0.0231778i
\(509\) −10.4503 + 18.1004i −0.463201 + 0.802287i −0.999118 0.0419830i \(-0.986632\pi\)
0.535917 + 0.844270i \(0.319966\pi\)
\(510\) 0 0
\(511\) 5.83772 35.3160i 0.258246 1.56229i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −0.930461 3.47253i −0.0410808 0.153316i
\(514\) −8.31650 14.4046i −0.366825 0.635360i
\(515\) 0 0
\(516\) 9.60399 + 5.54487i 0.422792 + 0.244099i
\(517\) 6.70482 6.70482i 0.294877 0.294877i
\(518\) −16.7221 + 11.9780i −0.734726 + 0.526282i
\(519\) 16.1795i 0.710200i
\(520\) 0 0
\(521\) −21.3985 + 12.3544i −0.937483 + 0.541256i −0.889170 0.457576i \(-0.848718\pi\)
−0.0483128 + 0.998832i \(0.515384\pi\)
\(522\) 2.28167 8.51530i 0.0998658 0.372704i
\(523\) −29.0889 + 7.79435i −1.27197 + 0.340823i −0.830785 0.556594i \(-0.812108\pi\)
−0.441184 + 0.897417i \(0.645441\pi\)
\(524\) −5.30257 −0.231644
\(525\) 0 0
\(526\) −11.0473 −0.481685
\(527\) 12.5114 3.35241i 0.545003 0.146033i
\(528\) −1.31732 + 4.91631i −0.0573290 + 0.213955i
\(529\) −21.9452 + 12.6701i −0.954140 + 0.550873i
\(530\) 0 0
\(531\) 4.17947i 0.181374i
\(532\) 0.930461 + 9.46592i 0.0403406 + 0.410400i
\(533\) −8.37511 + 8.37511i −0.362766 + 0.362766i
\(534\) 6.62522 + 3.82507i 0.286701 + 0.165527i
\(535\) 0 0
\(536\) 1.47330 + 2.55183i 0.0636370 + 0.110222i
\(537\) 2.57234 + 9.60012i 0.111005 + 0.414276i
\(538\) −18.8111 18.8111i −0.811002 0.811002i
\(539\) −23.4809 26.7958i −1.01139 1.15418i
\(540\) 0 0
\(541\) −20.0506 + 34.7286i −0.862041 + 1.49310i 0.00791517 + 0.999969i \(0.497480\pi\)
−0.869956 + 0.493130i \(0.835853\pi\)
\(542\) 19.6242 + 5.25830i 0.842933 + 0.225863i
\(543\) 2.51416 + 0.673667i 0.107893 + 0.0289098i
\(544\) −3.47635 + 6.02122i −0.149047 + 0.258158i
\(545\) 0 0
\(546\) −4.80648 + 5.85440i −0.205698 + 0.250545i
\(547\) 26.5205 + 26.5205i 1.13394 + 1.13394i 0.989516 + 0.144420i \(0.0461317\pi\)
0.144420 + 0.989516i \(0.453868\pi\)
\(548\) 5.68916 + 21.2322i 0.243029 + 0.906996i
\(549\) 2.93454 + 5.08277i 0.125243 + 0.216927i
\(550\) 0 0
\(551\) 27.4466 + 15.8463i 1.16926 + 0.675075i
\(552\) 4.91631 4.91631i 0.209252 0.209252i
\(553\) −29.1327 13.2067i −1.23885 0.561605i
\(554\) 10.0697i 0.427821i
\(555\) 0 0
\(556\) 14.3675 8.29509i 0.609318 0.351790i
\(557\) −1.34960 + 5.03679i −0.0571845 + 0.213416i −0.988606 0.150527i \(-0.951903\pi\)
0.931421 + 0.363943i \(0.118570\pi\)
\(558\) 1.79949 0.482173i 0.0761786 0.0204120i
\(559\) −31.7496 −1.34287
\(560\) 0 0
\(561\) −35.3875 −1.49406
\(562\) −14.7079 + 3.94098i −0.620416 + 0.166240i
\(563\) 4.01426 14.9814i 0.169181 0.631392i −0.828289 0.560301i \(-0.810685\pi\)
0.997470 0.0710904i \(-0.0226479\pi\)
\(564\) 1.61338 0.931486i 0.0679356 0.0392227i
\(565\) 0 0
\(566\) 14.8319i 0.623431i
\(567\) 1.54067 + 2.15089i 0.0647023 + 0.0903288i
\(568\) −5.55996 + 5.55996i −0.233291 + 0.233291i
\(569\) −23.8369 13.7622i −0.999295 0.576943i −0.0912554 0.995828i \(-0.529088\pi\)
−0.908040 + 0.418884i \(0.862421\pi\)
\(570\) 0 0
\(571\) −1.46210 2.53243i −0.0611869 0.105979i 0.833809 0.552053i \(-0.186155\pi\)
−0.894996 + 0.446074i \(0.852822\pi\)
\(572\) −3.77145 14.0753i −0.157692 0.588516i
\(573\) 2.92532 + 2.92532i 0.122207 + 0.122207i
\(574\) −3.85358 10.2447i −0.160846 0.427607i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −3.36119 0.900627i −0.139928 0.0374936i 0.188175 0.982135i \(-0.439743\pi\)
−0.328103 + 0.944642i \(0.606409\pi\)
\(578\) −30.2723 8.11143i −1.25916 0.337391i
\(579\) 6.47635 11.2174i 0.269148 0.466178i
\(580\) 0 0
\(581\) −5.75770 4.72709i −0.238870 0.196113i
\(582\) 13.4951 + 13.4951i 0.559388 + 0.559388i
\(583\) −1.19911 4.47514i −0.0496620 0.185341i
\(584\) 6.76467 + 11.7167i 0.279924 + 0.484842i
\(585\) 0 0
\(586\) −22.9038 13.2235i −0.946148 0.546259i
\(587\) 29.2873 29.2873i 1.20882 1.20882i 0.237407 0.971410i \(-0.423702\pi\)
0.971410 0.237407i \(-0.0762975\pi\)
\(588\) −3.09359 6.27931i −0.127577 0.258954i
\(589\) 6.69743i 0.275963i
\(590\) 0 0
\(591\) 1.07306 0.619530i 0.0441397 0.0254841i
\(592\) 2.01219 7.50959i 0.0827004 0.308642i
\(593\) 12.1553 3.25700i 0.499158 0.133749i −0.000451399 1.00000i \(-0.500144\pi\)
0.499609 + 0.866251i \(0.333477\pi\)
\(594\) −5.08974 −0.208834
\(595\) 0 0
\(596\) −9.93878 −0.407108
\(597\) 16.6749 4.46802i 0.682457 0.182864i
\(598\) −5.15190 + 19.2272i −0.210677 + 0.786257i
\(599\) −41.1024 + 23.7305i −1.67940 + 0.969602i −0.717355 + 0.696708i \(0.754647\pi\)
−0.962044 + 0.272894i \(0.912019\pi\)
\(600\) 0 0
\(601\) 39.1953i 1.59881i −0.600792 0.799405i \(-0.705148\pi\)
0.600792 0.799405i \(-0.294852\pi\)
\(602\) 12.1143 26.7230i 0.493741 1.08915i
\(603\) −2.08356 + 2.08356i −0.0848493 + 0.0848493i
\(604\) 13.2645 + 7.65825i 0.539724 + 0.311610i
\(605\) 0 0
\(606\) 0.681895 + 1.18108i 0.0277001 + 0.0479780i
\(607\) 3.46559 + 12.9338i 0.140664 + 0.524965i 0.999910 + 0.0134030i \(0.00426642\pi\)
−0.859246 + 0.511562i \(0.829067\pi\)
\(608\) −2.54207 2.54207i −0.103094 0.103094i
\(609\) −23.0118 3.80385i −0.932487 0.154140i
\(610\) 0 0
\(611\) −2.66682 + 4.61907i −0.107888 + 0.186868i
\(612\) −6.71580 1.79949i −0.271470 0.0727402i
\(613\) −19.9559 5.34717i −0.806012 0.215970i −0.167790 0.985823i \(-0.553663\pi\)
−0.638222 + 0.769853i \(0.720330\pi\)
\(614\) 15.9054 27.5490i 0.641890 1.11179i
\(615\) 0 0
\(616\) 13.2859 + 2.19615i 0.535304 + 0.0884855i
\(617\) −3.22631 3.22631i −0.129886 0.129886i 0.639175 0.769061i \(-0.279276\pi\)
−0.769061 + 0.639175i \(0.779276\pi\)
\(618\) 0.0941560 + 0.351395i 0.00378751 + 0.0141352i
\(619\) −2.10527 3.64644i −0.0846181 0.146563i 0.820610 0.571488i \(-0.193634\pi\)
−0.905228 + 0.424925i \(0.860300\pi\)
\(620\) 0 0
\(621\) 6.02122 + 3.47635i 0.241623 + 0.139501i
\(622\) −11.6431 + 11.6431i −0.466846 + 0.466846i
\(623\) 8.35691 18.4346i 0.334813 0.738567i
\(624\) 2.86297i 0.114611i
\(625\) 0 0
\(626\) −2.92378 + 1.68804i −0.116858 + 0.0674678i
\(627\) 4.73580 17.6742i 0.189130 0.705841i
\(628\) 15.7881 4.23040i 0.630013 0.168811i
\(629\) 54.0538 2.15527
\(630\) 0 0
\(631\) 35.1730 1.40021 0.700107 0.714038i \(-0.253135\pi\)
0.700107 + 0.714038i \(0.253135\pi\)
\(632\) 11.6778 3.12905i 0.464517 0.124467i
\(633\) −1.91645 + 7.15230i −0.0761721 + 0.284278i
\(634\) −11.9661 + 6.90866i −0.475236 + 0.274378i
\(635\) 0 0
\(636\) 0.910263i 0.0360943i
\(637\) 16.6590 + 11.1405i 0.660054 + 0.441404i
\(638\) 31.7275 31.7275i 1.25610 1.25610i
\(639\) −6.80953 3.93149i −0.269381 0.155527i
\(640\) 0 0
\(641\) −5.56609 9.64075i −0.219847 0.380787i 0.734914 0.678161i \(-0.237223\pi\)
−0.954761 + 0.297374i \(0.903889\pi\)
\(642\) 0.0550849 + 0.205579i 0.00217403 + 0.00811358i
\(643\) 20.3659 + 20.3659i 0.803153 + 0.803153i 0.983587 0.180434i \(-0.0577502\pi\)
−0.180434 + 0.983587i \(0.557750\pi\)
\(644\) −14.2174 11.6725i −0.560243 0.459961i
\(645\) 0 0
\(646\) 12.4976 21.6464i 0.491711 0.851668i
\(647\) −11.0379 2.95760i −0.433946 0.116275i 0.0352321 0.999379i \(-0.488783\pi\)
−0.469178 + 0.883104i \(0.655450\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) −10.6362 + 18.4225i −0.417508 + 0.723145i
\(650\) 0 0
\(651\) −1.73533 4.61338i −0.0680131 0.180813i
\(652\) 5.29956 + 5.29956i 0.207547 + 0.207547i
\(653\) 3.66128 + 13.6641i 0.143277 + 0.534717i 0.999826 + 0.0186516i \(0.00593735\pi\)
−0.856549 + 0.516066i \(0.827396\pi\)
\(654\) 0.780202 + 1.35135i 0.0305083 + 0.0528420i
\(655\) 0 0
\(656\) 3.58277 + 2.06851i 0.139884 + 0.0807619i
\(657\) −9.56668 + 9.56668i −0.373232 + 0.373232i
\(658\) −2.87024 4.00705i −0.111893 0.156211i
\(659\) 11.7840i 0.459038i −0.973304 0.229519i \(-0.926285\pi\)
0.973304 0.229519i \(-0.0737153\pi\)
\(660\) 0 0
\(661\) 41.3181 23.8550i 1.60709 0.927853i 0.617072 0.786907i \(-0.288319\pi\)
0.990017 0.140946i \(-0.0450145\pi\)
\(662\) −1.25000 + 4.66505i −0.0485825 + 0.181312i
\(663\) 19.2272 5.15190i 0.746721 0.200083i
\(664\) 2.81568 0.109270
\(665\) 0 0
\(666\) 7.77450 0.301256
\(667\) −59.2044 + 15.8638i −2.29240 + 0.614247i
\(668\) −4.68071 + 17.4687i −0.181102 + 0.675883i
\(669\) −3.30448 + 1.90784i −0.127758 + 0.0737614i
\(670\) 0 0
\(671\) 29.8721i 1.15320i
\(672\) 2.40971 + 1.09239i 0.0929565 + 0.0421397i
\(673\) −23.3048 + 23.3048i −0.898334 + 0.898334i −0.995289 0.0969544i \(-0.969090\pi\)
0.0969544 + 0.995289i \(0.469090\pi\)
\(674\) 7.99061 + 4.61338i 0.307787 + 0.177701i
\(675\) 0 0
\(676\) −2.40169 4.15985i −0.0923728 0.159994i
\(677\) −1.58293 5.90757i −0.0608369 0.227046i 0.928813 0.370548i \(-0.120830\pi\)
−0.989650 + 0.143502i \(0.954164\pi\)
\(678\) 0.0300140 + 0.0300140i 0.00115268 + 0.00115268i
\(679\) 32.0405 39.0261i 1.22960 1.49768i
\(680\) 0 0
\(681\) −9.84629 + 17.0543i −0.377311 + 0.653521i
\(682\) 9.15895 + 2.45413i 0.350714 + 0.0939736i
\(683\) −27.6574 7.41077i −1.05828 0.283565i −0.312610 0.949882i \(-0.601203\pi\)
−0.745669 + 0.666316i \(0.767870\pi\)
\(684\) 1.79751 3.11338i 0.0687296 0.119043i
\(685\) 0 0
\(686\) −15.7331 + 9.77081i −0.600693 + 0.373051i
\(687\) 16.2470 + 16.2470i 0.619862 + 0.619862i
\(688\) 2.87024 + 10.7119i 0.109427 + 0.408386i
\(689\) 1.30303 + 2.25691i 0.0496415 + 0.0859816i
\(690\) 0 0
\(691\) −8.56043 4.94237i −0.325654 0.188016i 0.328256 0.944589i \(-0.393539\pi\)
−0.653910 + 0.756572i \(0.726873\pi\)
\(692\) −11.4406 + 11.4406i −0.434907 + 0.434907i
\(693\) 1.31732 + 13.4016i 0.0500409 + 0.509084i
\(694\) 31.4487i 1.19378i
\(695\) 0 0
\(696\) 7.63460 4.40784i 0.289389 0.167079i
\(697\) −7.44455 + 27.7835i −0.281983 + 1.05237i
\(698\) 27.5369 7.37848i 1.04229 0.279280i
\(699\) 13.2391 0.500747
\(700\) 0 0
\(701\) −22.4772 −0.848952 −0.424476 0.905439i \(-0.639542\pi\)
−0.424476 + 0.905439i \(0.639542\pi\)
\(702\) 2.76542 0.740992i 0.104374 0.0279669i
\(703\) −7.23386 + 26.9971i −0.272830 + 1.01822i
\(704\) −4.40784 + 2.54487i −0.166127 + 0.0959133i
\(705\) 0 0
\(706\) 23.3729i 0.879650i
\(707\) 2.93336 2.10116i 0.110320 0.0790222i
\(708\) −2.95533 + 2.95533i −0.111068 + 0.111068i
\(709\) −6.12307 3.53516i −0.229957 0.132766i 0.380595 0.924742i \(-0.375719\pi\)
−0.610552 + 0.791976i \(0.709052\pi\)
\(710\) 0 0
\(711\) 6.04487 + 10.4700i 0.226700 + 0.392656i
\(712\) 1.98000 + 7.38947i 0.0742037 + 0.276932i
\(713\) −9.15895 9.15895i −0.343005 0.343005i
\(714\) −3.00000 + 18.1489i −0.112272 + 0.679204i
\(715\) 0 0
\(716\) −4.96939 + 8.60723i −0.185715 + 0.321667i
\(717\) 1.59391 + 0.427088i 0.0595258 + 0.0159499i
\(718\) 16.2718 + 4.36002i 0.607259 + 0.162715i
\(719\) 18.1121 31.3711i 0.675467 1.16994i −0.300865 0.953667i \(-0.597275\pi\)
0.976332 0.216277i \(-0.0693914\pi\)
\(720\) 0 0
\(721\) 0.900875 0.338866i 0.0335503 0.0126200i
\(722\) −4.29624 4.29624i −0.159890 0.159890i
\(723\) 3.27442 + 12.2203i 0.121777 + 0.454478i
\(724\) 1.30143 + 2.25414i 0.0483671 + 0.0837743i
\(725\) 0 0
\(726\) −12.9085 7.45271i −0.479078 0.276596i
\(727\) 8.46215 8.46215i 0.313844 0.313844i −0.532553 0.846397i \(-0.678767\pi\)
0.846397 + 0.532553i \(0.178767\pi\)
\(728\) −7.53838 + 0.740992i −0.279391 + 0.0274630i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −66.7738 + 38.5519i −2.46972 + 1.42589i
\(732\) −1.51903 + 5.66909i −0.0561449 + 0.209536i
\(733\) −4.51455 + 1.20967i −0.166749 + 0.0446802i −0.341228 0.939981i \(-0.610843\pi\)
0.174479 + 0.984661i \(0.444176\pi\)
\(734\) −26.9641 −0.995262
\(735\) 0 0
\(736\) 6.95271 0.256280
\(737\) −14.4864 + 3.88162i −0.533614 + 0.142981i
\(738\) −1.07074 + 3.99606i −0.0394145 + 0.147097i
\(739\) 22.4673 12.9715i 0.826474 0.477165i −0.0261702 0.999658i \(-0.508331\pi\)
0.852644 + 0.522493i \(0.174998\pi\)
\(740\) 0 0
\(741\) 10.2925i 0.378103i
\(742\) −2.39678 + 0.235593i −0.0879885 + 0.00864891i
\(743\) 33.8328 33.8328i 1.24121 1.24121i 0.281704 0.959501i \(-0.409101\pi\)
0.959501 0.281704i \(-0.0908995\pi\)
\(744\) 1.61338 + 0.931486i 0.0591494 + 0.0341500i
\(745\) 0 0
\(746\) −5.14623 8.91353i −0.188417 0.326347i
\(747\) 0.728752 + 2.71974i 0.0266637 + 0.0995101i
\(748\) −25.0227 25.0227i −0.914921 0.914921i
\(749\) 0.527046 0.198250i 0.0192579 0.00724389i
\(750\) 0 0
\(751\) −5.00811 + 8.67430i −0.182748 + 0.316530i −0.942816 0.333315i \(-0.891833\pi\)
0.760067 + 0.649845i \(0.225166\pi\)
\(752\) 1.79949 + 0.482173i 0.0656208 + 0.0175830i
\(753\) 7.19797 + 1.92869i 0.262309 + 0.0702854i
\(754\) −12.6195 + 21.8577i −0.459576 + 0.796009i
\(755\) 0 0
\(756\) −0.431486 + 2.61033i −0.0156930 + 0.0949368i
\(757\) 2.56404 + 2.56404i 0.0931915 + 0.0931915i 0.752166 0.658974i \(-0.229009\pi\)
−0.658974 + 0.752166i \(0.729009\pi\)
\(758\) 6.33156 + 23.6297i 0.229973 + 0.858269i
\(759\) 17.6937 + 30.6464i 0.642242 + 1.11240i
\(760\) 0 0
\(761\) 1.98202 + 1.14432i 0.0718481 + 0.0414815i 0.535494 0.844539i \(-0.320126\pi\)
−0.463646 + 0.886021i \(0.653459\pi\)
\(762\) 1.42723 1.42723i 0.0517029 0.0517029i
\(763\) 3.35626 2.40408i 0.121505 0.0870334i
\(764\) 4.13703i 0.149672i
\(765\) 0 0
\(766\) 5.34371 3.08519i 0.193076 0.111473i
\(767\) 3.09696 11.5580i 0.111825 0.417335i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) 8.35895 0.301431 0.150716 0.988577i \(-0.451842\pi\)
0.150716 + 0.988577i \(0.451842\pi\)
\(770\) 0 0
\(771\) 16.6330 0.599023
\(772\) 12.5114 3.35241i 0.450294 0.120656i
\(773\) −2.81515 + 10.5063i −0.101254 + 0.377885i −0.997893 0.0648769i \(-0.979335\pi\)
0.896639 + 0.442762i \(0.146001\pi\)
\(774\) −9.60399 + 5.54487i −0.345208 + 0.199306i
\(775\) 0 0
\(776\) 19.0849i 0.685108i
\(777\) −2.01219 20.4707i −0.0721868 0.734383i
\(778\) −9.74442 + 9.74442i −0.349354 + 0.349354i
\(779\) −12.8801 7.43636i −0.461479 0.266435i
\(780\) 0 0
\(781\) −20.0102 34.6587i −0.716022 1.24019i
\(782\) 12.5114 + 46.6930i 0.447405 + 1.66974i
\(783\)