Properties

Label 1050.2.bc.f.607.3
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 607.3
Root \(3.11681 + 1.79949i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.f.493.3

$q$-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 0.368251 0.929726i \(-0.379957\pi\)
−0.929726 + 0.368251i \(0.879957\pi\)
\(14\) −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 −0.675245 0.737593i \(-0.735962\pi\)
−0.953576 + 0.301152i \(0.902629\pi\)
\(18\) −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 \(0.174767\pi\)
−0.477802 + 0.878467i \(0.658566\pi\)
\(24\) 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 −0.816357 0.577548i \(-0.804010\pi\)
−0.418212 + 0.908350i \(0.637343\pi\)
\(38\) −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 \(-0.429252\pi\)
0.975402 0.220436i \(-0.0707479\pi\)
\(44\) −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 0.921802 0.387660i \(-0.126717\pi\)
−0.992134 + 0.125177i \(0.960050\pi\)
\(48\) 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 0.197926 0.980217i \(-0.436579\pi\)
−0.318700 + 0.947856i \(0.603246\pi\)
\(54\) 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 −0.996736 0.0807326i \(-0.974274\pi\)
0.903565 + 0.428451i \(0.140941\pi\)
\(68\) −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 \(0.374160\pi\)
−0.794957 + 0.606666i \(0.792507\pi\)
\(74\) −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 0.807883 0.589343i \(-0.200613\pi\)
−0.589343 + 0.807883i \(0.700613\pi\)
\(84\) −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 \(0.670392\pi\)
−0.860115 + 0.510101i \(0.829608\pi\)
\(98\) 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 −0.276089 0.961132i \(-0.589039\pi\)
0.241465 + 0.970409i \(0.422372\pi\)
\(104\) −2.86297 −0.280738
\(105\) 0 0
\(106\) −0.910263 −0.0884126
\(107\) −0.205579 + 0.0550849i −0.0198741 + 0.00532525i −0.268742 0.963212i \(-0.586608\pi\)
0.248868 + 0.968537i \(0.419941\pi\)
\(108\) 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 −0.708517 0.705694i \(-0.750636\pi\)
0.705694 + 0.708517i \(0.250636\pi\)
\(114\) −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 0.767589 0.640943i \(-0.221456\pi\)
−0.640943 + 0.767589i \(0.721456\pi\)
\(128\) −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 \(-0.528429\pi\)
0.575250 0.817978i \(-0.304905\pi\)
\(138\) −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 −0.433824 0.900998i \(-0.642836\pi\)
−0.826201 + 0.563375i \(0.809503\pi\)
\(158\) −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 \(-0.988508\pi\)
0.847413 0.530933i \(-0.178159\pi\)
\(164\) 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 −0.0103848 0.999946i \(-0.503306\pi\)
0.999946 + 0.0103848i \(0.00330564\pi\)
\(168\) −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 0.390018 0.920807i \(-0.372469\pi\)
0.798169 + 0.602433i \(0.205802\pi\)
\(174\) 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 −0.221319 0.975202i \(-0.571036\pi\)
−0.679268 + 0.733890i \(0.737703\pi\)
\(194\) −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 0.675206 0.737629i \(-0.264055\pi\)
−0.737629 + 0.675206i \(0.764055\pi\)
\(198\) 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 0.791651 0.610973i \(-0.209222\pi\)
−0.610973 + 0.791651i \(0.709222\pi\)
\(224\) −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 0.827155 0.561973i \(-0.189958\pi\)
0.435351 + 0.900261i \(0.356624\pi\)
\(228\) −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 \(-0.940555\pi\)
0.758134 0.652099i \(-0.226111\pi\)
\(234\) 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 \(-0.909724\pi\)
0.691517 0.722361i \(-0.256943\pi\)
\(258\) 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 −0.0856532 0.996325i \(-0.527298\pi\)
−0.572340 + 0.820016i \(0.693964\pi\)
\(264\) 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 \(-0.818840\pi\)
0.998964 0.0455149i \(-0.0144928\pi\)
\(278\) 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 \(0.228650\pi\)
−0.981101 + 0.193498i \(0.938017\pi\)
\(284\) 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 \(-0.968993\pi\)
−0.0972583 0.995259i \(-0.531007\pi\)
\(294\) 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 \(-0.387783\pi\)
0.938499 0.345282i \(-0.112217\pi\)
\(308\) 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 −0.349801 0.936824i \(-0.613751\pi\)
0.165476 + 0.986214i \(0.447084\pi\)
\(314\) −16.3450 −0.922403
\(315\) 0 0
\(316\) −12.0897 −0.680101
\(317\) −13.3465 + 3.57619i −0.749614 + 0.200859i −0.613347 0.789814i \(-0.710177\pi\)
−0.136267 + 0.990672i \(0.543511\pi\)
\(318\) 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 0.862115 0.506713i \(-0.169140\pi\)
−0.506713 + 0.862115i \(0.669140\pi\)
\(338\) −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 \(-0.596786\pi\)
0.736351 0.676600i \(-0.236547\pi\)
\(348\) 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 \(-0.702984\pi\)
0.917319 0.398154i \(-0.130349\pi\)
\(354\) 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 −0.495901 0.868379i \(-0.665162\pi\)
−0.863653 + 0.504088i \(0.831829\pi\)
\(368\) 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 \(-0.997479\pi\)
0.862038 0.506844i \(-0.169188\pi\)
\(374\) 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 −0.103308 0.994649i \(-0.532943\pi\)
0.407857 + 0.913046i \(0.366276\pi\)
\(384\) 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 0.973011 0.230757i \(-0.0741202\pi\)
−0.958031 + 0.286664i \(0.907454\pi\)
\(398\) 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 0.157235 0.987561i \(-0.449742\pi\)
−0.987561 + 0.157235i \(0.949742\pi\)
\(434\) −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 \(0.0165637\pi\)
−0.838847 + 0.544368i \(0.816770\pi\)
\(444\) −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 0.379187 0.925320i \(-0.376204\pi\)
0.791046 + 0.611757i \(0.209537\pi\)
\(458\) −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 \(0.655069\pi\)
−0.883664 + 0.468121i \(0.844931\pi\)
\(464\) −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 \(-0.854331\pi\)
0.555999 0.831183i \(-0.312336\pi\)
\(468\) 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 \(0.174494\pi\)
−0.999698 + 0.0245890i \(0.992172\pi\)
\(488\) −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 0.381589 0.924332i \(-0.375377\pi\)
−0.924332 + 0.381589i \(0.875377\pi\)
\(504\) 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 0.441184 0.897417i \(-0.354559\pi\)
0.830785 + 0.556594i \(0.187892\pi\)
\(524\) −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 \(-0.953868\pi\)
−0.144420 0.989516i \(-0.546132\pi\)
\(548\) −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 −0.931421 0.363943i \(-0.881430\pi\)
0.988606 + 0.150527i \(0.0480971\pi\)
\(558\) −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 \(0.189315\pi\)
−0.997470 + 0.0710904i \(0.977352\pi\)
\(564\) 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 0.328103 0.944642i \(-0.393591\pi\)
−0.188175 + 0.982135i \(0.560257\pi\)
\(578\) 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 \(0.576298\pi\)
−0.971410 + 0.237407i \(0.923702\pi\)
\(588\) 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 −0.499609 0.866251i \(-0.666523\pi\)
0.000451399 1.00000i \(0.499856\pi\)
\(594\) −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 \(-0.995734\pi\)
0.859246 0.511562i \(-0.170933\pi\)
\(608\) 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 0.638222 0.769853i \(-0.279670\pi\)
0.167790 + 0.985823i \(0.446337\pi\)
\(614\) 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 0.769061 0.639175i \(-0.220724\pi\)
−0.639175 + 0.769061i \(0.720724\pi\)
\(618\) −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 0.180434 0.983587i \(-0.442250\pi\)
−0.983587 + 0.180434i \(0.942250\pi\)
\(644\) −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 0.469178 0.883104i \(-0.344550\pi\)
−0.0352321 + 0.999379i \(0.511217\pi\)
\(648\) 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 \(-0.994063\pi\)
0.856549 0.516066i \(-0.172604\pi\)
\(654\) 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 −0.0969544 0.995289i \(-0.530910\pi\)
0.995289 + 0.0969544i \(0.0309101\pi\)
\(674\) 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 0.989650 0.143502i \(-0.0458364\pi\)
−0.928813 + 0.370548i \(0.879170\pi\)
\(678\) −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 0.745669 0.666316i \(-0.232130\pi\)
0.312610 + 0.949882i \(0.398797\pi\)
\(684\) 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 −0.846397 0.532553i \(-0.821233\pi\)
0.532553 + 0.846397i \(0.321233\pi\)
\(728\) 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 −0.174479 0.984661i \(-0.555824\pi\)
0.341228 + 0.939981i \(0.389157\pi\)
\(734\) −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 \(0.590899\pi\)
−0.959501 + 0.281704i \(0.909101\pi\)
\(744\) 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 0.658974 0.752166i \(-0.270991\pi\)
−0.752166 + 0.658974i \(0.770991\pi\)
\(758\) −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 −0.896639 0.442762i \(-0.853999\pi\)
0.997893 + 0.0648769i \(0.0206655\pi\)
\(774\) −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