Properties

Label 1050.2.bc.e.943.2
Level $1050$
Weight $2$
Character 1050.943
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 943.2
Root \(3.11681 - 1.79949i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.e.157.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(0.258819 + 2.63306i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(0.258819 + 2.63306i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.54487 - 4.40784i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.02443 - 2.02443i) q^{13} +(2.47635 - 0.931486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.79949 + 6.71580i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.79751 - 3.11338i) q^{19} +(0.431486 - 2.61033i) q^{21} +(-3.59899 + 3.59899i) q^{22} +(-6.71580 + 1.79949i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.47941 - 1.43149i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.54067 - 2.15089i) q^{28} +8.81568i q^{29} +(1.61338 - 0.931486i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.31732 + 4.91631i) q^{33} +6.95271 q^{34} -1.00000 q^{36} +(2.01219 + 7.50959i) q^{37} +(-3.47253 - 0.930461i) q^{38} +(-2.47941 + 1.43149i) q^{39} +4.13703i q^{41} +(-2.63306 + 0.258819i) q^{42} +(7.84163 + 7.84163i) q^{43} +(4.40784 + 2.54487i) q^{44} +(3.47635 + 6.02122i) q^{46} +(-1.79949 + 0.482173i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-6.86603 + 1.36297i) q^{49} +(3.47635 - 6.02122i) q^{51} +(-0.740992 + 2.76542i) q^{52} +(0.235593 - 0.879247i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.67884 + 2.04487i) q^{56} +(-2.54207 + 2.54207i) q^{57} +(8.51530 - 2.28167i) q^{58} +(2.08974 + 3.61953i) q^{59} +(-5.08277 - 2.93454i) q^{61} +(-1.31732 - 1.31732i) q^{62} +(-1.09239 + 2.40971i) q^{63} +1.00000i q^{64} +(4.40784 - 2.54487i) q^{66} +(2.84620 + 0.762637i) q^{67} +(-1.79949 - 6.71580i) q^{68} +6.95271 q^{69} +7.86297 q^{71} +(0.258819 + 0.965926i) q^{72} +(-13.0683 - 3.50165i) q^{73} +(6.73291 - 3.88725i) q^{74} +3.59502i q^{76} +(10.9475 - 7.84163i) q^{77} +(2.02443 + 2.02443i) q^{78} +(10.4700 + 6.04487i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.99606 - 1.07074i) q^{82} +(-1.99099 + 1.99099i) q^{83} +(0.931486 + 2.47635i) q^{84} +(5.54487 - 9.60399i) q^{86} +(2.28167 - 8.51530i) q^{87} +(1.31732 - 4.91631i) q^{88} +(-3.82507 + 6.62522i) q^{89} +(5.85440 + 4.80648i) q^{91} +(4.91631 - 4.91631i) q^{92} +(-1.79949 + 0.482173i) q^{93} +(0.931486 + 1.61338i) q^{94} +(0.866025 + 0.500000i) q^{96} +(13.4951 + 13.4951i) q^{97} +(3.09359 + 6.27931i) 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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 0.258819 + 2.63306i 0.0978244 + 0.995204i
\(8\) 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 \(-0.445070\pi\)
\(12\) 0.965926 0.258819i 0.278839 0.0747146i
\(13\) 2.02443 2.02443i 0.561475 0.561475i −0.368251 0.929726i \(-0.620043\pi\)
0.929726 + 0.368251i \(0.120043\pi\)
\(14\) 2.47635 0.931486i 0.661834 0.248950i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.79949 + 6.71580i −0.436441 + 1.62882i 0.301152 + 0.953576i \(0.402629\pi\)
−0.737593 + 0.675245i \(0.764038\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) 1.79751 3.11338i 0.412378 0.714259i −0.582772 0.812636i \(-0.698032\pi\)
0.995149 + 0.0983771i \(0.0313651\pi\)
\(20\) 0 0
\(21\) 0.431486 2.61033i 0.0941581 0.569621i
\(22\) −3.59899 + 3.59899i −0.767307 + 0.767307i
\(23\) −6.71580 + 1.79949i −1.40034 + 0.375220i −0.878467 0.477802i \(-0.841434\pi\)
−0.521874 + 0.853023i \(0.674767\pi\)
\(24\) −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
\(28\) −1.54067 2.15089i −0.291160 0.406480i
\(29\) 8.81568i 1.63703i 0.574484 + 0.818516i \(0.305203\pi\)
−0.574484 + 0.818516i \(0.694797\pi\)
\(30\) 0 0
\(31\) 1.61338 0.931486i 0.289772 0.167300i −0.348067 0.937470i \(-0.613162\pi\)
0.637839 + 0.770170i \(0.279829\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 1.31732 + 4.91631i 0.229316 + 0.855819i
\(34\) 6.95271 1.19238
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 2.01219 + 7.50959i 0.330802 + 1.23457i 0.908350 + 0.418212i \(0.137343\pi\)
−0.577548 + 0.816357i \(0.695990\pi\)
\(38\) −3.47253 0.930461i −0.563318 0.150941i
\(39\) −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 \(0.895293\pi\)
\(42\) −2.63306 + 0.258819i −0.406290 + 0.0399366i
\(43\) 7.84163 + 7.84163i 1.19584 + 1.19584i 0.975402 + 0.220436i \(0.0707479\pi\)
0.220436 + 0.975402i \(0.429252\pi\)
\(44\) 4.40784 + 2.54487i 0.664507 + 0.383653i
\(45\) 0 0
\(46\) 3.47635 + 6.02122i 0.512561 + 0.887781i
\(47\) −1.79949 + 0.482173i −0.262483 + 0.0703321i −0.387660 0.921802i \(-0.626717\pi\)
0.125177 + 0.992134i \(0.460050\pi\)
\(48\) −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
\(52\) −0.740992 + 2.76542i −0.102757 + 0.383495i
\(53\) 0.235593 0.879247i 0.0323613 0.120774i −0.947856 0.318700i \(-0.896754\pi\)
0.980217 + 0.197926i \(0.0634205\pi\)
\(54\) −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
\(58\) 8.51530 2.28167i 1.11811 0.299597i
\(59\) 2.08974 + 3.61953i 0.272061 + 0.471223i 0.969389 0.245529i \(-0.0789616\pi\)
−0.697329 + 0.716751i \(0.745628\pi\)
\(60\) 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
\(63\) −1.09239 + 2.40971i −0.137628 + 0.303595i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 4.40784 2.54487i 0.542568 0.313252i
\(67\) 2.84620 + 0.762637i 0.347719 + 0.0931710i 0.428451 0.903565i \(-0.359059\pi\)
−0.0807326 + 0.996736i \(0.525726\pi\)
\(68\) −1.79949 6.71580i −0.218221 0.814411i
\(69\) 6.95271 0.837008
\(70\) 0 0
\(71\) 7.86297 0.933163 0.466582 0.884478i \(-0.345485\pi\)
0.466582 + 0.884478i \(0.345485\pi\)
\(72\) 0.258819 + 0.965926i 0.0305021 + 0.113835i
\(73\) −13.0683 3.50165i −1.52953 0.409837i −0.606666 0.794957i \(-0.707493\pi\)
−0.922867 + 0.385120i \(0.874160\pi\)
\(74\) 6.73291 3.88725i 0.782685 0.451883i
\(75\) 0 0
\(76\) 3.59502i 0.412378i
\(77\) 10.9475 7.84163i 1.24758 0.893636i
\(78\) 2.02443 + 2.02443i 0.229221 + 0.229221i
\(79\) 10.4700 + 6.04487i 1.17797 + 0.680101i 0.955544 0.294849i \(-0.0952693\pi\)
0.222425 + 0.974950i \(0.428603\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 3.99606 1.07074i 0.441291 0.118244i
\(83\) −1.99099 + 1.99099i −0.218539 + 0.218539i −0.807883 0.589343i \(-0.799387\pi\)
0.589343 + 0.807883i \(0.299387\pi\)
\(84\) 0.931486 + 2.47635i 0.101634 + 0.270192i
\(85\) 0 0
\(86\) 5.54487 9.60399i 0.597919 1.03563i
\(87\) 2.28167 8.51530i 0.244620 0.912935i
\(88\) 1.31732 4.91631i 0.140427 0.524080i
\(89\) −3.82507 + 6.62522i −0.405457 + 0.702272i −0.994375 0.105921i \(-0.966221\pi\)
0.588918 + 0.808193i \(0.299554\pi\)
\(90\) 0 0
\(91\) 5.85440 + 4.80648i 0.613708 + 0.503856i
\(92\) 4.91631 4.91631i 0.512561 0.512561i
\(93\) −1.79949 + 0.482173i −0.186599 + 0.0499990i
\(94\) 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 0.860115 + 0.510101i \(0.170392\pi\)
0.510101 + 0.860115i \(0.329608\pi\)
\(98\) 3.09359 + 6.27931i 0.312500 + 0.634306i
\(99\) 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 \(0.311719\pi\)
\(102\) −6.71580 1.79949i −0.664963 0.178176i
\(103\) −0.0941560 0.351395i −0.00927747 0.0346240i 0.961132 0.276089i \(-0.0890386\pi\)
−0.970409 + 0.241465i \(0.922372\pi\)
\(104\) 2.86297 0.280738
\(105\) 0 0
\(106\) −0.910263 −0.0884126
\(107\) 0.0550849 + 0.205579i 0.00532525 + 0.0198741i 0.968537 0.248868i \(-0.0800586\pi\)
−0.963212 + 0.268742i \(0.913392\pi\)
\(108\) 0.965926 + 0.258819i 0.0929463 + 0.0249049i
\(109\) −1.35135 + 0.780202i −0.129436 + 0.0747298i −0.563320 0.826239i \(-0.690476\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(110\) 0 0
\(111\) 7.77450i 0.737923i
\(112\) 2.40971 + 1.09239i 0.227696 + 0.103221i
\(113\) −0.0300140 0.0300140i −0.00282348 0.00282348i 0.705694 0.708517i \(-0.250636\pi\)
−0.708517 + 0.705694i \(0.750636\pi\)
\(114\) 3.11338 + 1.79751i 0.291595 + 0.168352i
\(115\) 0 0
\(116\) −4.40784 7.63460i −0.409258 0.708855i
\(117\) 2.76542 0.740992i 0.255663 0.0685047i
\(118\) 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
\(122\) −1.51903 + 5.66909i −0.137526 + 0.513256i
\(123\) 1.07074 3.99606i 0.0965455 0.360313i
\(124\) −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 \(-0.721456\pi\)
0.767589 + 0.640943i \(0.221456\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −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
\(133\) 8.66296 + 3.92716i 0.751174 + 0.340528i
\(134\) 2.94660i 0.254548i
\(135\) 0 0
\(136\) −6.02122 + 3.47635i −0.516316 + 0.298095i
\(137\) −21.2322 5.68916i −1.81399 0.486058i −0.817978 0.575250i \(-0.804905\pi\)
−0.996014 + 0.0891925i \(0.971571\pi\)
\(138\) −1.79949 6.71580i −0.153183 0.571687i
\(139\) −16.5902 −1.40716 −0.703580 0.710616i \(-0.748416\pi\)
−0.703580 + 0.710616i \(0.748416\pi\)
\(140\) 0 0
\(141\) 1.86297 0.156891
\(142\) −2.03509 7.59505i −0.170781 0.637362i
\(143\) −14.0753 3.77145i −1.17703 0.315385i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 13.5293i 1.11970i
\(147\) 6.98483 + 0.460527i 0.576099 + 0.0379837i
\(148\) −5.49740 5.49740i −0.451883 0.451883i
\(149\) 8.60723 + 4.96939i 0.705132 + 0.407108i 0.809256 0.587456i \(-0.199871\pi\)
−0.104124 + 0.994564i \(0.533204\pi\)
\(150\) 0 0
\(151\) 7.65825 + 13.2645i 0.623220 + 1.07945i 0.988882 + 0.148701i \(0.0475090\pi\)
−0.365663 + 0.930747i \(0.619158\pi\)
\(152\) 3.47253 0.930461i 0.281659 0.0754703i
\(153\) −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
\(157\) −4.23040 + 15.7881i −0.337623 + 1.26003i 0.563375 + 0.826201i \(0.309503\pi\)
−0.900998 + 0.433824i \(0.857164\pi\)
\(158\) 3.12905 11.6778i 0.248934 0.929035i
\(159\) −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
\(163\) 7.23934 1.93977i 0.567029 0.151935i 0.0360951 0.999348i \(-0.488508\pi\)
0.530933 + 0.847413i \(0.321841\pi\)
\(164\) −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 \(-0.496694\pi\)
−0.999946 + 0.0103848i \(0.996694\pi\)
\(168\) 2.15089 1.54067i 0.165945 0.118866i
\(169\) 4.80339i 0.369491i
\(170\) 0 0
\(171\) 3.11338 1.79751i 0.238086 0.137459i
\(172\) −10.7119 2.87024i −0.816772 0.218853i
\(173\) 4.18756 + 15.6282i 0.318374 + 1.18819i 0.920807 + 0.390018i \(0.127531\pi\)
−0.602433 + 0.798169i \(0.705802\pi\)
\(174\) −8.81568 −0.668315
\(175\) 0 0
\(176\) −5.08974 −0.383653
\(177\) −1.08173 4.03706i −0.0813076 0.303444i
\(178\) 7.38947 + 1.98000i 0.553864 + 0.148407i
\(179\) 8.60723 4.96939i 0.643335 0.371430i −0.142563 0.989786i \(-0.545534\pi\)
0.785898 + 0.618356i \(0.212201\pi\)
\(180\) 0 0
\(181\) 2.60285i 0.193468i 0.995310 + 0.0967342i \(0.0308397\pi\)
−0.995310 + 0.0967342i \(0.969160\pi\)
\(182\) 3.12747 6.89893i 0.231824 0.511383i
\(183\) 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
\(187\) 34.1817 9.15895i 2.49961 0.669769i
\(188\) 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 \(0.214489\pi\)
\(192\) 0.258819 0.965926i 0.0186787 0.0697097i
\(193\) 3.35241 12.5114i 0.241312 0.900587i −0.733890 0.679268i \(-0.762297\pi\)
0.975202 0.221319i \(-0.0710361\pi\)
\(194\) 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 \(-0.764055\pi\)
0.675206 + 0.737629i \(0.264055\pi\)
\(198\) −4.91631 + 1.31732i −0.349387 + 0.0936179i
\(199\) −8.63155 14.9503i −0.611875 1.05980i −0.990924 0.134421i \(-0.957082\pi\)
0.379050 0.925376i \(-0.376251\pi\)
\(200\) 0 0
\(201\) −2.55183 1.47330i −0.179993 0.103919i
\(202\) −0.964346 0.964346i −0.0678511 0.0678511i
\(203\) −23.2122 + 2.28167i −1.62918 + 0.160142i
\(204\) 6.95271i 0.486787i
\(205\) 0 0
\(206\) −0.315052 + 0.181895i −0.0219507 + 0.0126733i
\(207\) −6.71580 1.79949i −0.466780 0.125073i
\(208\) −0.740992 2.76542i −0.0513785 0.191747i
\(209\) −18.2977 −1.26568
\(210\) 0 0
\(211\) −7.40460 −0.509754 −0.254877 0.966974i \(-0.582035\pi\)
−0.254877 + 0.966974i \(0.582035\pi\)
\(212\) 0.235593 + 0.879247i 0.0161806 + 0.0603869i
\(213\) −7.59505 2.03509i −0.520404 0.139442i
\(214\) 0.184318 0.106416i 0.0125997 0.00727443i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 2.87024 + 4.00705i 0.194844 + 0.272016i
\(218\) 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
\(222\) −7.50959 + 2.01219i −0.504011 + 0.135049i
\(223\) −2.69809 + 2.69809i −0.180678 + 0.180678i −0.791651 0.610973i \(-0.790778\pi\)
0.610973 + 0.791651i \(0.290778\pi\)
\(224\) 0.431486 2.61033i 0.0288299 0.174410i
\(225\) 0 0
\(226\) −0.0212231 + 0.0367595i −0.00141174 + 0.00244520i
\(227\) 5.09682 19.0216i 0.338288 1.26251i −0.561973 0.827155i \(-0.689958\pi\)
0.900261 0.435351i \(-0.143376\pi\)
\(228\) 0.930461 3.47253i 0.0616213 0.229974i
\(229\) 11.4884 19.8985i 0.759173 1.31493i −0.184099 0.982908i \(-0.558937\pi\)
0.943273 0.332019i \(-0.107730\pi\)
\(230\) 0 0
\(231\) −12.6040 + 4.74102i −0.829282 + 0.311936i
\(232\) −6.23363 + 6.23363i −0.409258 + 0.409258i
\(233\) 12.7880 3.42652i 0.837766 0.224479i 0.185667 0.982613i \(-0.440555\pi\)
0.652099 + 0.758134i \(0.273889\pi\)
\(234\) −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
\(238\) 1.79949 + 18.3069i 0.116644 + 1.18666i
\(239\) 1.65014i 0.106739i −0.998575 0.0533694i \(-0.983004\pi\)
0.998575 0.0533694i \(-0.0169961\pi\)
\(240\) 0 0
\(241\) −10.9564 + 6.32570i −0.705766 + 0.407474i −0.809491 0.587132i \(-0.800257\pi\)
0.103725 + 0.994606i \(0.466924\pi\)
\(242\) 14.3975 + 3.85781i 0.925508 + 0.247989i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 5.86908 0.375729
\(245\) 0 0
\(246\) −4.13703 −0.263767
\(247\) −2.66388 9.94175i −0.169499 0.632578i
\(248\) 1.79949 + 0.482173i 0.114268 + 0.0306180i
\(249\) 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 \(0.924432\pi\)
\(252\) −0.258819 2.63306i −0.0163041 0.165867i
\(253\) 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
\(257\) −16.0662 + 4.30494i −1.00218 + 0.268535i −0.722361 0.691517i \(-0.756943\pi\)
−0.279824 + 0.960051i \(0.590276\pi\)
\(258\) −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
\(262\) −1.37241 + 5.12189i −0.0847875 + 0.316431i
\(263\) 2.85925 10.6709i 0.176309 0.657994i −0.820016 0.572340i \(-0.806036\pi\)
0.996325 0.0856532i \(-0.0272977\pi\)
\(264\) −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
\(268\) −2.84620 + 0.762637i −0.173859 + 0.0465855i
\(269\) −13.3014 23.0387i −0.811002 1.40470i −0.912163 0.409827i \(-0.865589\pi\)
0.101161 0.994870i \(-0.467744\pi\)
\(270\) 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
\(273\) −4.41091 6.15794i −0.266960 0.372695i
\(274\) 21.9812i 1.32793i
\(275\) 0 0
\(276\) −6.02122 + 3.47635i −0.362435 + 0.209252i
\(277\) −9.72658 2.60623i −0.584414 0.156593i −0.0455149 0.998964i \(-0.514493\pi\)
−0.538899 + 0.842370i \(0.681160\pi\)
\(278\) 4.29385 + 16.0249i 0.257528 + 0.961109i
\(279\) 1.86297 0.111533
\(280\) 0 0
\(281\) 15.2268 0.908353 0.454176 0.890912i \(-0.349934\pi\)
0.454176 + 0.890912i \(0.349934\pi\)
\(282\) −0.482173 1.79949i −0.0287130 0.107158i
\(283\) −14.3265 3.83878i −0.851623 0.228192i −0.193498 0.981101i \(-0.561983\pi\)
−0.658125 + 0.752909i \(0.728650\pi\)
\(284\) −6.80953 + 3.93149i −0.404072 + 0.233291i
\(285\) 0 0
\(286\) 14.5718i 0.861647i
\(287\) −10.8930 + 1.07074i −0.642996 + 0.0632039i
\(288\) −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
\(292\) 13.0683 3.50165i 0.764766 0.204918i
\(293\) 18.7009 18.7009i 1.09252 1.09252i 0.0972583 0.995259i \(-0.468993\pi\)
0.995259 0.0972583i \(-0.0310073\pi\)
\(294\) −1.36297 6.86603i −0.0794902 0.400435i
\(295\) 0 0
\(296\) −3.88725 + 6.73291i −0.225942 + 0.391343i
\(297\) −1.31732 + 4.91631i −0.0764387 + 0.285273i
\(298\) 2.57234 9.60012i 0.149012 0.556120i
\(299\) −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
\(303\) −1.31732 + 0.352975i −0.0756781 + 0.0202779i
\(304\) −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 −0.938499 0.345282i \(-0.887783\pi\)
−0.345282 0.938499i \(-0.612217\pi\)
\(308\) −5.55996 + 12.2648i −0.316808 + 0.698851i
\(309\) 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 \(0.178724\pi\)
\(312\) −2.76542 0.740992i −0.156561 0.0419504i
\(313\) −0.873796 3.26105i −0.0493899 0.184325i 0.936824 0.349801i \(-0.113751\pi\)
−0.986214 + 0.165476i \(0.947084\pi\)
\(314\) 16.3450 0.922403
\(315\) 0 0
\(316\) −12.0897 −0.680101
\(317\) 3.57619 + 13.3465i 0.200859 + 0.749614i 0.990672 + 0.136267i \(0.0435106\pi\)
−0.789814 + 0.613347i \(0.789823\pi\)
\(318\) 0.879247 + 0.235593i 0.0493057 + 0.0132114i
\(319\) 38.8581 22.4348i 2.17564 1.25610i
\(320\) 0 0
\(321\) 0.212832i 0.0118791i
\(322\) −14.9545 + 10.7119i −0.833382 + 0.596949i
\(323\) 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
\(327\) 1.50724 0.403862i 0.0833503 0.0223336i
\(328\) −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 \(0.124292\pi\)
\(332\) 0.728752 2.71974i 0.0399955 0.149265i
\(333\) −2.01219 + 7.50959i −0.110267 + 0.411523i
\(334\) −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 \(-0.669140\pi\)
0.862115 + 0.506713i \(0.169140\pi\)
\(338\) 4.63971 1.24321i 0.252367 0.0676216i
\(339\) 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
\(343\) −5.36585 17.7259i −0.289729 0.957109i
\(344\) 11.0897i 0.597919i
\(345\) 0 0
\(346\) 14.0118 8.08974i 0.753281 0.434907i
\(347\) −30.3771 8.13952i −1.63073 0.436952i −0.676600 0.736351i \(-0.736547\pi\)
−0.954128 + 0.299399i \(0.903214\pi\)
\(348\) 2.28167 + 8.51530i 0.122310 + 0.456468i
\(349\) 28.5083 1.52601 0.763006 0.646391i \(-0.223722\pi\)
0.763006 + 0.646391i \(0.223722\pi\)
\(350\) 0 0
\(351\) −2.86297 −0.152814
\(352\) 1.31732 + 4.91631i 0.0702134 + 0.262040i
\(353\) 22.5765 + 6.04935i 1.20162 + 0.321974i 0.803471 0.595345i \(-0.202984\pi\)
0.398154 + 0.917319i \(0.369651\pi\)
\(354\) −3.61953 + 2.08974i −0.192376 + 0.111068i
\(355\) 0 0
\(356\) 7.65014i 0.405457i
\(357\) 16.7540 + 7.59505i 0.886716 + 0.401973i
\(358\) −7.02778 7.02778i −0.371430 0.371430i
\(359\) 14.5889 + 8.42292i 0.769974 + 0.444545i 0.832865 0.553476i \(-0.186699\pi\)
−0.0628915 + 0.998020i \(0.520032\pi\)
\(360\) 0 0
\(361\) 3.03790 + 5.26180i 0.159890 + 0.276937i
\(362\) 2.51416 0.673667i 0.132141 0.0354072i
\(363\) 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
\(367\) −6.97882 + 26.0453i −0.364291 + 1.35955i 0.504088 + 0.863653i \(0.331829\pi\)
−0.868379 + 0.495901i \(0.834838\pi\)
\(368\) −1.79949 + 6.71580i −0.0938051 + 0.350085i
\(369\) −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
\(373\) 9.94175 2.66388i 0.514764 0.137931i 0.00792053 0.999969i \(-0.497479\pi\)
0.506844 + 0.862038i \(0.330812\pi\)
\(374\) −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
\(378\) −2.40971 1.09239i −0.123942 0.0561863i
\(379\) 24.4633i 1.25659i 0.777974 + 0.628297i \(0.216248\pi\)
−0.777974 + 0.628297i \(0.783752\pi\)
\(380\) 0 0
\(381\) −1.74799 + 1.00920i −0.0895521 + 0.0517029i
\(382\) 3.99606 + 1.07074i 0.204456 + 0.0547839i
\(383\) 1.59701 + 5.96013i 0.0816036 + 0.304549i 0.994649 0.103308i \(-0.0329429\pi\)
−0.913046 + 0.407857i \(0.866276\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −12.9527 −0.659276
\(387\) 2.87024 + 10.7119i 0.145902 + 0.544515i
\(388\) −18.4346 4.93953i −0.935875 0.250767i
\(389\) −11.9344 + 6.89034i −0.605099 + 0.349354i −0.771045 0.636781i \(-0.780266\pi\)
0.165946 + 0.986135i \(0.446932\pi\)
\(390\) 0 0
\(391\) 48.3402i 2.44467i
\(392\) −5.81878 3.89125i −0.293893 0.196538i
\(393\) 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
\(397\) 1.11395 0.298482i 0.0559075 0.0149804i −0.230757 0.973011i \(-0.574120\pi\)
0.286664 + 0.958031i \(0.407454\pi\)
\(398\) −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 \(0.232904\pi\)
\(402\) −0.762637 + 2.84620i −0.0380369 + 0.141956i
\(403\) 1.38045 5.15190i 0.0687650 0.256634i
\(404\) −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
\(408\) 6.71580 1.79949i 0.332482 0.0890882i
\(409\) 18.2355 + 31.5849i 0.901690 + 1.56177i 0.825300 + 0.564694i \(0.191006\pi\)
0.0763896 + 0.997078i \(0.475661\pi\)
\(410\) 0 0
\(411\) 19.0363 + 10.9906i 0.938991 + 0.542127i
\(412\) 0.257239 + 0.257239i 0.0126733 + 0.0126733i
\(413\) −8.98958 + 6.43921i −0.442348 + 0.316853i
\(414\) 6.95271i 0.341707i
\(415\) 0 0
\(416\) −2.47941 + 1.43149i −0.121563 + 0.0701844i
\(417\) 16.0249 + 4.29385i 0.784742 + 0.210271i
\(418\) 4.73580 + 17.6742i 0.231636 + 0.864476i
\(419\) 9.05638 0.442433 0.221217 0.975225i \(-0.428997\pi\)
0.221217 + 0.975225i \(0.428997\pi\)
\(420\) 0 0
\(421\) 10.3149 0.502716 0.251358 0.967894i \(-0.419123\pi\)
0.251358 + 0.967894i \(0.419123\pi\)
\(422\) 1.91645 + 7.15230i 0.0932914 + 0.348168i
\(423\) −1.79949 0.482173i −0.0874944 0.0234440i
\(424\) 0.788311 0.455132i 0.0382838 0.0221031i
\(425\) 0 0
\(426\) 7.86297i 0.380962i
\(427\) 6.41130 14.1428i 0.310265 0.684416i
\(428\) −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 \(0.647486\pi\)
\(432\) −0.965926 + 0.258819i −0.0464731 + 0.0124524i
\(433\) 17.2780 17.2780i 0.830327 0.830327i −0.157235 0.987561i \(-0.550258\pi\)
0.987561 + 0.157235i \(0.0502579\pi\)
\(434\) 3.12764 3.80953i 0.150131 0.182863i
\(435\) 0 0
\(436\) 0.780202 1.35135i 0.0373649 0.0647179i
\(437\) −6.46922 + 24.1435i −0.309465 + 1.15494i
\(438\) 3.50165 13.0683i 0.167315 0.624429i
\(439\) 2.48269 4.30015i 0.118492 0.205235i −0.800678 0.599095i \(-0.795527\pi\)
0.919170 + 0.393860i \(0.128861\pi\)
\(440\) 0 0
\(441\) −6.62764 2.25264i −0.315602 0.107269i
\(442\) 14.0753 14.0753i 0.669492 0.669492i
\(443\) −12.5524 + 3.36339i −0.596380 + 0.159800i −0.544368 0.838847i \(-0.683230\pi\)
−0.0520128 + 0.998646i \(0.516564\pi\)
\(444\) 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
\(448\) −2.63306 + 0.258819i −0.124400 + 0.0122281i
\(449\) 15.0710i 0.711243i 0.934630 + 0.355621i \(0.115731\pi\)
−0.934630 + 0.355621i \(0.884269\pi\)
\(450\) 0 0
\(451\) 18.2354 10.5282i 0.858669 0.495753i
\(452\) 0.0409999 + 0.0109859i 0.00192847 + 0.000516733i
\(453\) −3.96420 14.7946i −0.186254 0.695111i
\(454\) −19.6926 −0.924219
\(455\) 0 0
\(456\) −3.59502 −0.168352
\(457\) −6.70321 25.0167i −0.313563 1.17023i −0.925320 0.379187i \(-0.876204\pi\)
0.611757 0.791046i \(-0.290463\pi\)
\(458\) −22.1938 5.94682i −1.03705 0.277877i
\(459\) 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 \(-0.153422\pi\)
\(462\) 7.84163 + 10.9475i 0.364826 + 0.509322i
\(463\) −29.0870 29.0870i −1.35179 1.35179i −0.883664 0.468121i \(-0.844931\pi\)
−0.468121 0.883664i \(-0.655069\pi\)
\(464\) 7.63460 + 4.40784i 0.354428 + 0.204629i
\(465\) 0 0
\(466\) −6.61953 11.4654i −0.306644 0.531123i
\(467\) −27.5100 + 7.37127i −1.27301 + 0.341102i −0.831183 0.555999i \(-0.812336\pi\)
−0.441826 + 0.897101i \(0.645669\pi\)
\(468\) −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
\(472\) −1.08173 + 4.03706i −0.0497905 + 0.185821i
\(473\) 14.6087 54.5206i 0.671711 2.50686i
\(474\) −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
\(478\) −1.59391 + 0.427088i −0.0729039 + 0.0195346i
\(479\) −4.79770 8.30986i −0.219212 0.379687i 0.735355 0.677682i \(-0.237015\pi\)
−0.954567 + 0.297995i \(0.903682\pi\)
\(480\) 0 0
\(481\) 19.2761 + 11.1291i 0.878917 + 0.507443i
\(482\) 8.94589 + 8.94589i 0.407474 + 0.407474i
\(483\) 1.79949 + 18.3069i 0.0818798 + 0.832993i
\(484\) 14.9054i 0.677519i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 12.0433 + 3.22698i 0.545733 + 0.146229i 0.521144 0.853469i \(-0.325506\pi\)
0.0245890 + 0.999698i \(0.492172\pi\)
\(488\) −1.51903 5.66909i −0.0687632 0.256628i
\(489\) −7.49471 −0.338923
\(490\) 0 0
\(491\) 36.3288 1.63950 0.819748 0.572725i \(-0.194114\pi\)
0.819748 + 0.572725i \(0.194114\pi\)
\(492\) 1.07074 + 3.99606i 0.0482728 + 0.180156i
\(493\) −59.2044 15.8638i −2.66643 0.714468i
\(494\) −8.91353 + 5.14623i −0.401039 + 0.231540i
\(495\) 0 0
\(496\) 1.86297i 0.0836500i
\(497\) 2.03509 + 20.7037i 0.0912861 + 0.928687i
\(498\) −1.99099 1.99099i −0.0892183 0.0892183i
\(499\) 2.42441 + 1.39973i 0.108531 + 0.0626606i 0.553283 0.832993i \(-0.313375\pi\)
−0.444752 + 0.895654i \(0.646708\pi\)
\(500\) 0 0
\(501\) 9.04245 + 15.6620i 0.403987 + 0.699725i
\(502\) 7.19797 1.92869i 0.321261 0.0860817i
\(503\) 12.1725 12.1725i 0.542743 0.542743i −0.381589 0.924332i \(-0.624623\pi\)
0.924332 + 0.381589i \(0.124623\pi\)
\(504\) −2.47635 + 0.931486i −0.110306 + 0.0414917i
\(505\) 0 0
\(506\) 17.6937 30.6464i 0.786582 1.36240i
\(507\) 1.24321 4.63971i 0.0552128 0.206057i
\(508\) −0.522401 + 1.94963i −0.0231778 + 0.0865007i
\(509\) 10.4503 18.1004i 0.463201 0.802287i −0.535917 0.844270i \(-0.680034\pi\)
0.999118 + 0.0419830i \(0.0133675\pi\)
\(510\) 0 0
\(511\) 5.83772 35.3160i 0.258246 1.56229i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −3.47253 + 0.930461i −0.153316 + 0.0410808i
\(514\) 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
\(518\) 11.9780 + 16.7221i 0.526282 + 0.734726i
\(519\) 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 \(0.515384\pi\)
\(522\) 8.51530 + 2.28167i 0.372704 + 0.0998658i
\(523\) 7.79435 + 29.0889i 0.340823 + 1.27197i 0.897417 + 0.441184i \(0.145441\pi\)
−0.556594 + 0.830785i \(0.687892\pi\)
\(524\) 5.30257 0.231644
\(525\) 0 0
\(526\) −11.0473 −0.481685
\(527\) 3.35241 + 12.5114i 0.146033 + 0.545003i
\(528\) 4.91631 + 1.31732i 0.213955 + 0.0573290i
\(529\) 21.9452 12.6701i 0.954140 0.550873i
\(530\) 0 0
\(531\) 4.17947i 0.181374i
\(532\) −9.46592 + 0.930461i −0.410400 + 0.0403406i
\(533\) 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
\(537\) −9.60012 + 2.57234i −0.414276 + 0.111005i
\(538\) −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 \(0.835853\pi\)
\(542\) −5.25830 + 19.6242i −0.225863 + 0.842933i
\(543\) 0.673667 2.51416i 0.0289098 0.107893i
\(544\) 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 −0.144420 + 0.989516i \(0.546132\pi\)
−0.989516 + 0.144420i \(0.953868\pi\)
\(548\) 21.2322 5.68916i 0.906996 0.243029i
\(549\) −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
\(553\) −13.2067 + 29.1327i −0.561605 + 1.23885i
\(554\) 10.0697i 0.427821i
\(555\) 0 0
\(556\) 14.3675 8.29509i 0.609318 0.351790i
\(557\) −5.03679 1.34960i −0.213416 0.0571845i 0.150527 0.988606i \(-0.451903\pi\)
−0.363943 + 0.931421i \(0.618570\pi\)
\(558\) −0.482173 1.79949i −0.0204120 0.0761786i
\(559\) 31.7496 1.34287
\(560\) 0 0
\(561\) −35.3875 −1.49406
\(562\) −3.94098 14.7079i −0.166240 0.620416i
\(563\) −14.9814 4.01426i −0.631392 0.169181i −0.0710904 0.997470i \(-0.522648\pi\)
−0.560301 + 0.828289i \(0.689315\pi\)
\(564\) −1.61338 + 0.931486i −0.0679356 + 0.0392227i
\(565\) 0 0
\(566\) 14.8319i 0.623431i
\(567\) −2.15089 + 1.54067i −0.0903288 + 0.0647023i
\(568\) 5.55996 + 5.55996i 0.233291 + 0.233291i
\(569\) 23.8369 + 13.7622i 0.999295 + 0.576943i 0.908040 0.418884i \(-0.137579\pi\)
0.0912554 + 0.995828i \(0.470912\pi\)
\(570\) 0 0
\(571\) −1.46210 2.53243i −0.0611869 0.105979i 0.833809 0.552053i \(-0.186155\pi\)
−0.894996 + 0.446074i \(0.852822\pi\)
\(572\) 14.0753 3.77145i 0.588516 0.157692i
\(573\) 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
\(577\) 0.900627 3.36119i 0.0374936 0.139928i −0.944642 0.328103i \(-0.893591\pi\)
0.982135 + 0.188175i \(0.0602573\pi\)
\(578\) −8.11143 + 30.2723i −0.337391 + 1.25916i
\(579\) −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
\(583\) −4.47514 + 1.19911i −0.185341 + 0.0496620i
\(584\) −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 0.971410 + 0.237407i \(0.0762975\pi\)
0.237407 + 0.971410i \(0.423702\pi\)
\(588\) −6.27931 + 3.09359i −0.258954 + 0.127577i
\(589\) 6.69743i 0.275963i
\(590\) 0 0
\(591\) 1.07306 0.619530i 0.0441397 0.0254841i
\(592\) 7.50959 + 2.01219i 0.308642 + 0.0827004i
\(593\) −3.25700 12.1553i −0.133749 0.499158i 0.866251 0.499609i \(-0.166523\pi\)
−1.00000 0.000451399i \(0.999856\pi\)
\(594\) 5.08974 0.208834
\(595\) 0 0
\(596\) −9.93878 −0.407108
\(597\) 4.46802 + 16.6749i 0.182864 + 0.682457i
\(598\) 19.2272 + 5.15190i 0.786257 + 0.210677i
\(599\) 41.1024 23.7305i 1.67940 0.969602i 0.717355 0.696708i \(-0.245353\pi\)
0.962044 0.272894i \(-0.0879807\pi\)
\(600\) 0 0
\(601\) 39.1953i 1.59881i −0.600792 0.799405i \(-0.705148\pi\)
0.600792 0.799405i \(-0.294852\pi\)
\(602\) 26.7230 + 12.1143i 1.08915 + 0.493741i
\(603\) 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
\(607\) −12.9338 + 3.46559i −0.524965 + 0.140664i −0.511562 0.859246i \(-0.670933\pi\)
−0.0134030 + 0.999910i \(0.504266\pi\)
\(608\) −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
\(612\) 1.79949 6.71580i 0.0727402 0.271470i
\(613\) −5.34717 + 19.9559i −0.215970 + 0.806012i 0.769853 + 0.638222i \(0.220330\pi\)
−0.985823 + 0.167790i \(0.946337\pi\)
\(614\) −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 \(-0.720724\pi\)
0.769061 + 0.639175i \(0.220724\pi\)
\(618\) 0.351395 0.0941560i 0.0141352 0.00378751i
\(619\) 2.10527 + 3.64644i 0.0846181 + 0.146563i 0.905228 0.424925i \(-0.139700\pi\)
−0.820610 + 0.571488i \(0.806366\pi\)
\(620\) 0 0
\(621\) 6.02122 + 3.47635i 0.241623 + 0.139501i
\(622\) −11.6431 11.6431i −0.466846 0.466846i
\(623\) −18.4346 8.35691i −0.738567 0.334813i
\(624\) 2.86297i 0.114611i
\(625\) 0 0
\(626\) −2.92378 + 1.68804i −0.116858 + 0.0674678i
\(627\) 17.6742 + 4.73580i 0.705841 + 0.189130i
\(628\) −4.23040 15.7881i −0.168811 0.630013i
\(629\) −54.0538 −2.15527
\(630\) 0 0
\(631\) 35.1730 1.40021 0.700107 0.714038i \(-0.253135\pi\)
0.700107 + 0.714038i \(0.253135\pi\)
\(632\) 3.12905 + 11.6778i 0.124467 + 0.464517i
\(633\) 7.15230 + 1.91645i 0.284278 + 0.0761721i
\(634\) 11.9661 6.90866i 0.475236 0.274378i
\(635\) 0 0
\(636\) 0.910263i 0.0360943i
\(637\) −11.1405 + 16.6590i −0.441404 + 0.660054i
\(638\) −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 \(0.903889\pi\)
\(642\) −0.205579 + 0.0550849i −0.00811358 + 0.00217403i
\(643\) 20.3659 20.3659i 0.803153 0.803153i −0.180434 0.983587i \(-0.557750\pi\)
0.983587 + 0.180434i \(0.0577502\pi\)
\(644\) 14.2174 + 11.6725i 0.560243 + 0.459961i
\(645\) 0 0
\(646\) 12.4976 21.6464i 0.491711 0.851668i
\(647\) 2.95760 11.0379i 0.116275 0.433946i −0.883104 0.469178i \(-0.844550\pi\)
0.999379 + 0.0352321i \(0.0112171\pi\)
\(648\) −0.258819 + 0.965926i −0.0101674 + 0.0379452i
\(649\) 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
\(653\) 13.6641 3.66128i 0.534717 0.143277i 0.0186516 0.999826i \(-0.494063\pi\)
0.516066 + 0.856549i \(0.327396\pi\)
\(654\) −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
\(658\) −4.00705 + 2.87024i −0.156211 + 0.111893i
\(659\) 11.7840i 0.459038i 0.973304 + 0.229519i \(0.0737153\pi\)
−0.973304 + 0.229519i \(0.926285\pi\)
\(660\) 0 0
\(661\) 41.3181 23.8550i 1.60709 0.927853i 0.617072 0.786907i \(-0.288319\pi\)
0.990017 0.140946i \(-0.0450145\pi\)
\(662\) −4.66505 1.25000i −0.181312 0.0485825i
\(663\) −5.15190 19.2272i −0.200083 0.746721i
\(664\) −2.81568 −0.109270
\(665\) 0 0
\(666\) 7.77450 0.301256
\(667\) −15.8638 59.2044i −0.614247 2.29240i
\(668\) 17.4687 + 4.68071i 0.675883 + 0.181102i
\(669\) 3.30448 1.90784i 0.127758 0.0737614i
\(670\) 0 0
\(671\) 29.8721i 1.15320i
\(672\) −1.09239 + 2.40971i −0.0421397 + 0.0929565i
\(673\) 23.3048 + 23.3048i 0.898334 + 0.898334i 0.995289 0.0969544i \(-0.0309101\pi\)
−0.0969544 + 0.995289i \(0.530910\pi\)
\(674\) −7.99061 4.61338i −0.307787 0.177701i
\(675\) 0 0
\(676\) −2.40169 4.15985i −0.0923728 0.159994i
\(677\) 5.90757 1.58293i 0.227046 0.0608369i −0.143502 0.989650i \(-0.545836\pi\)
0.370548 + 0.928813i \(0.379170\pi\)
\(678\) 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
\(682\) −2.45413 + 9.15895i −0.0939736 + 0.350714i
\(683\) −7.41077 + 27.6574i −0.283565 + 1.05828i 0.666316 + 0.745669i \(0.267870\pi\)
−0.949882 + 0.312610i \(0.898797\pi\)
\(684\) −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
\(688\) 10.7119 2.87024i 0.408386 0.109427i
\(689\) −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
\(693\) 13.4016 1.31732i 0.509084 0.0500409i
\(694\) 31.4487i 1.19378i
\(695\) 0 0
\(696\) 7.63460 4.40784i 0.289389 0.167079i
\(697\) −27.7835 7.44455i −1.05237 0.281983i
\(698\) −7.37848 27.5369i −0.279280 1.04229i
\(699\) −13.2391 −0.500747
\(700\) 0 0
\(701\) −22.4772 −0.848952 −0.424476 0.905439i \(-0.639542\pi\)
−0.424476 + 0.905439i \(0.639542\pi\)
\(702\) 0.740992 + 2.76542i 0.0279669 + 0.104374i
\(703\) 26.9971 + 7.23386i 1.01822 + 0.272830i
\(704\) 4.40784 2.54487i 0.166127 0.0959133i
\(705\) 0 0
\(706\) 23.3729i 0.879650i
\(707\) 2.10116 + 2.93336i 0.0790222 + 0.110320i
\(708\) 2.95533 + 2.95533i 0.111068 + 0.111068i
\(709\) 6.12307 + 3.53516i 0.229957 + 0.132766i 0.610552 0.791976i \(-0.290948\pi\)
−0.380595 + 0.924742i \(0.624281\pi\)
\(710\) 0 0
\(711\) 6.04487 + 10.4700i 0.226700 + 0.392656i
\(712\) −7.38947 + 1.98000i −0.276932 + 0.0742037i
\(713\) −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
\(717\) −0.427088 + 1.59391i −0.0159499 + 0.0595258i
\(718\) 4.36002 16.2718i 0.162715 0.607259i
\(719\) −18.1121 + 31.3711i −0.675467 + 1.16994i 0.300865 + 0.953667i \(0.402725\pi\)
−0.976332 + 0.216277i \(0.930609\pi\)
\(720\) 0 0
\(721\) 0.900875 0.338866i 0.0335503 0.0126200i
\(722\) 4.29624 4.29624i 0.159890 0.159890i
\(723\) 12.2203 3.27442i 0.454478 0.121777i
\(724\) −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 \(-0.178767\pi\)
−0.532553 + 0.846397i \(0.678767\pi\)
\(728\) 0.740992 + 7.53838i 0.0274630 + 0.279391i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −66.7738 + 38.5519i −2.46972 + 1.42589i
\(732\) −5.66909 1.51903i −0.209536 0.0561449i
\(733\) 1.20967 + 4.51455i 0.0446802 + 0.166749i 0.984661 0.174479i \(-0.0558240\pi\)
−0.939981 + 0.341228i \(0.889157\pi\)
\(734\) 26.9641 0.995262
\(735\) 0 0
\(736\) 6.95271 0.256280
\(737\) −3.88162 14.4864i −0.142981 0.533614i
\(738\) 3.99606 + 1.07074i 0.147097 + 0.0394145i
\(739\) −22.4673 + 12.9715i −0.826474 + 0.477165i −0.852644 0.522493i \(-0.825002\pi\)
0.0261702 + 0.999658i \(0.491669\pi\)
\(740\) 0 0
\(741\) 10.2925i 0.378103i
\(742\) −0.235593 2.39678i −0.00864891 0.0879885i
\(743\) −33.8328 33.8328i −1.24121 1.24121i −0.959501 0.281704i \(-0.909101\pi\)
−0.281704 0.959501i \(-0.590899\pi\)
\(744\) −1.61338 0.931486i −0.0591494 0.0341500i
\(745\) 0 0
\(746\) −5.14623 8.91353i −0.188417 0.326347i
\(747\) −2.71974 + 0.728752i −0.0995101 + 0.0266637i
\(748\) −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 \(0.225166\pi\)
\(752\) −0.482173 + 1.79949i −0.0175830 + 0.0656208i
\(753\) 1.92869 7.19797i 0.0702854 0.262309i
\(754\) 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 \(-0.770991\pi\)
0.658974 + 0.752166i \(0.270991\pi\)
\(758\) 23.6297 6.33156i 0.858269 0.229973i
\(759\) −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
\(763\) −2.40408 3.35626i −0.0870334 0.121505i
\(764\) 4.13703i 0.149672i
\(765\) 0 0
\(766\) 5.34371 3.08519i 0.193076 0.111473i
\(767\) 11.5580 + 3.09696i 0.417335 + 0.111825i
\(768\) 0.258819 + 0.965926i 0.00933933 + 0.0348548i
\(769\) −8.35895 −0.301431 −0.150716 0.988577i \(-0.548158\pi\)
−0.150716 + 0.988577i \(0.548158\pi\)
\(770\) 0 0
\(771\) 16.6330 0.599023
\(772\) 3.35241 + 12.5114i 0.120656 + 0.450294i
\(773\) 10.5063 + 2.81515i 0.377885 + 0.101254i 0.442762 0.896639i \(-0.353999\pi\)
−0.0648769 + 0.997893i \(0.520665\pi\)
\(774\) 9.60399 5.54487i 0.345208 0.199306i
\(775\) 0 0
\(776\) 19.0849i 0.685108i
\(777\) 20.4707 2.01219i 0.734383 0.0721868i
\(778\) 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
\(782\) −46.6930 + 12.5114i −1.66974 + 0.447405i
\(783\) 6.23363