Properties

Label 441.2.g.f.67.1
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(-1.02682 + 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.f.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.02682 + 1.77851i) q^{2} +(-1.09995 - 1.33795i) q^{3} +(-1.10873 - 1.92038i) q^{4} +0.146246 q^{5} +(3.50901 - 0.582422i) q^{6} +0.446582 q^{8} +(-0.580240 + 2.94335i) q^{9} +O(q^{10})\) \(q+(-1.02682 + 1.77851i) q^{2} +(-1.09995 - 1.33795i) q^{3} +(-1.10873 - 1.92038i) q^{4} +0.146246 q^{5} +(3.50901 - 0.582422i) q^{6} +0.446582 q^{8} +(-0.580240 + 2.94335i) q^{9} +(-0.150168 + 0.260099i) q^{10} +1.66404 q^{11} +(-1.34983 + 3.59574i) q^{12} +(-0.0999454 + 0.173111i) q^{13} +(-0.160862 - 0.195670i) q^{15} +(1.75890 - 3.04650i) q^{16} +(-3.13555 + 5.43093i) q^{17} +(-4.63897 - 4.05426i) q^{18} +(-3.45879 - 5.99080i) q^{19} +(-0.162147 - 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} -6.18184 q^{23} +(-0.491216 - 0.597507i) q^{24} -4.97861 q^{25} +(-0.205252 - 0.355508i) q^{26} +(4.57630 - 2.46119i) q^{27} +(-2.46757 - 4.27396i) q^{29} +(0.513178 - 0.0851766i) q^{30} +(-1.25890 - 2.18047i) q^{31} +(4.05873 + 7.02993i) q^{32} +(-1.83035 - 2.22641i) q^{33} +(-6.43931 - 11.1532i) q^{34} +(6.29567 - 2.14910i) q^{36} +(-3.50023 - 6.06257i) q^{37} +14.2062 q^{38} +(0.341548 - 0.0566898i) q^{39} +0.0653107 q^{40} +(-1.15895 + 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(-1.84497 - 3.19558i) q^{44} +(-0.0848576 + 0.430452i) q^{45} +(6.34765 - 10.9944i) q^{46} +(-0.905887 + 1.56904i) q^{47} +(-6.01077 + 0.997660i) q^{48} +(5.11215 - 8.85451i) q^{50} +(10.7153 - 1.77851i) q^{51} +0.443250 q^{52} +(-2.67307 + 4.62989i) q^{53} +(-0.321798 + 10.6662i) q^{54} +0.243359 q^{55} +(-4.21093 + 11.2172i) q^{57} +10.1350 q^{58} +(-2.28549 - 3.95859i) q^{59} +(-0.197407 + 0.525861i) q^{60} +(-0.339138 + 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(-0.0146166 + 0.0253167i) q^{65} +(5.83914 - 0.969173i) q^{66} +(3.09342 + 5.35796i) q^{67} +13.9059 q^{68} +(6.79968 + 8.27101i) q^{69} +1.27749 q^{71} +(-0.259125 + 1.31445i) q^{72} +(0.778603 - 1.34858i) q^{73} +14.3765 q^{74} +(5.47620 + 6.66115i) q^{75} +(-7.66972 + 13.2843i) q^{76} +(-0.249886 + 0.665657i) q^{78} +(-6.39787 + 11.0814i) q^{79} +(0.257231 - 0.445537i) q^{80} +(-8.32664 - 3.41570i) q^{81} +(-2.38008 - 4.12241i) q^{82} +(-3.75687 - 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} +3.86493 q^{86} +(-3.00417 + 8.00262i) q^{87} +0.743131 q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.678430 - 0.592918i) q^{90} +(6.85398 + 11.8714i) q^{92} +(-1.53266 + 4.08275i) q^{93} +(-1.86037 - 3.22226i) q^{94} +(-0.505833 - 0.876128i) q^{95} +(4.94134 - 13.1629i) q^{96} +(3.98514 + 6.90246i) q^{97} +(-0.965543 + 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + 7q^{10} - 8q^{11} - 22q^{12} + 8q^{13} - 19q^{15} + 2q^{16} - 12q^{17} - 2q^{18} - q^{19} - 5q^{20} - q^{22} - 6q^{23} - 3q^{24} + 2q^{25} - 11q^{26} + 7q^{27} + 7q^{29} - 26q^{30} + 3q^{31} - 2q^{32} + q^{33} - 3q^{34} + 34q^{36} + 40q^{38} + 20q^{39} - 6q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + q^{45} + 3q^{46} - 27q^{47} + 5q^{48} + 19q^{50} + 24q^{51} - 20q^{52} - 21q^{53} + 53q^{54} - 4q^{55} - 4q^{57} + 20q^{58} - 30q^{59} - 41q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} + 41q^{66} - 2q^{67} + 54q^{68} - 15q^{69} - 6q^{71} + 48q^{72} - 15q^{73} + 72q^{74} - 31q^{75} - 5q^{76} - 20q^{78} - 4q^{79} - 20q^{80} + 8q^{81} + 5q^{82} - 9q^{83} - 6q^{85} + 16q^{86} - 32q^{87} + 36q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 12q^{93} + 3q^{94} - 14q^{95} + q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02682 + 1.77851i −0.726073 + 1.25760i 0.232458 + 0.972607i \(0.425323\pi\)
−0.958531 + 0.284989i \(0.908010\pi\)
\(3\) −1.09995 1.33795i −0.635054 0.772468i
\(4\) −1.10873 1.92038i −0.554365 0.960188i
\(5\) 0.146246 0.0654030 0.0327015 0.999465i \(-0.489589\pi\)
0.0327015 + 0.999465i \(0.489589\pi\)
\(6\) 3.50901 0.582422i 1.43255 0.237773i
\(7\) 0 0
\(8\) 0.446582 0.157891
\(9\) −0.580240 + 2.94335i −0.193413 + 0.981117i
\(10\) −0.150168 + 0.260099i −0.0474874 + 0.0822506i
\(11\) 1.66404 0.501727 0.250864 0.968022i \(-0.419285\pi\)
0.250864 + 0.968022i \(0.419285\pi\)
\(12\) −1.34983 + 3.59574i −0.389663 + 1.03800i
\(13\) −0.0999454 + 0.173111i −0.0277199 + 0.0480122i −0.879553 0.475802i \(-0.842158\pi\)
0.851833 + 0.523814i \(0.175491\pi\)
\(14\) 0 0
\(15\) −0.160862 0.195670i −0.0415345 0.0505218i
\(16\) 1.75890 3.04650i 0.439724 0.761625i
\(17\) −3.13555 + 5.43093i −0.760483 + 1.31720i 0.182119 + 0.983277i \(0.441704\pi\)
−0.942602 + 0.333919i \(0.891629\pi\)
\(18\) −4.63897 4.05426i −1.09342 0.955599i
\(19\) −3.45879 5.99080i −0.793500 1.37438i −0.923787 0.382907i \(-0.874923\pi\)
0.130287 0.991476i \(-0.458410\pi\)
\(20\) −0.162147 0.280847i −0.0362571 0.0627992i
\(21\) 0 0
\(22\) −1.70867 + 2.95951i −0.364291 + 0.630970i
\(23\) −6.18184 −1.28900 −0.644501 0.764604i \(-0.722935\pi\)
−0.644501 + 0.764604i \(0.722935\pi\)
\(24\) −0.491216 0.597507i −0.100269 0.121966i
\(25\) −4.97861 −0.995722
\(26\) −0.205252 0.355508i −0.0402533 0.0697208i
\(27\) 4.57630 2.46119i 0.880710 0.473657i
\(28\) 0 0
\(29\) −2.46757 4.27396i −0.458217 0.793655i 0.540650 0.841248i \(-0.318178\pi\)
−0.998867 + 0.0475930i \(0.984845\pi\)
\(30\) 0.513178 0.0851766i 0.0936930 0.0155511i
\(31\) −1.25890 2.18047i −0.226105 0.391625i 0.730546 0.682864i \(-0.239266\pi\)
−0.956650 + 0.291239i \(0.905932\pi\)
\(32\) 4.05873 + 7.02993i 0.717490 + 1.24273i
\(33\) −1.83035 2.22641i −0.318624 0.387568i
\(34\) −6.43931 11.1532i −1.10433 1.91276i
\(35\) 0 0
\(36\) 6.29567 2.14910i 1.04928 0.358184i
\(37\) −3.50023 6.06257i −0.575434 0.996681i −0.995994 0.0894162i \(-0.971500\pi\)
0.420560 0.907264i \(-0.361833\pi\)
\(38\) 14.2062 2.30456
\(39\) 0.341548 0.0566898i 0.0546915 0.00907763i
\(40\) 0.0653107 0.0103265
\(41\) −1.15895 + 2.00736i −0.180998 + 0.313498i −0.942221 0.334993i \(-0.891266\pi\)
0.761223 + 0.648491i \(0.224599\pi\)
\(42\) 0 0
\(43\) −0.940993 1.62985i −0.143500 0.248550i 0.785312 0.619100i \(-0.212502\pi\)
−0.928812 + 0.370550i \(0.879169\pi\)
\(44\) −1.84497 3.19558i −0.278140 0.481752i
\(45\) −0.0848576 + 0.430452i −0.0126498 + 0.0641681i
\(46\) 6.34765 10.9944i 0.935910 1.62104i
\(47\) −0.905887 + 1.56904i −0.132137 + 0.228868i −0.924500 0.381181i \(-0.875517\pi\)
0.792363 + 0.610050i \(0.208851\pi\)
\(48\) −6.01077 + 0.997660i −0.867579 + 0.144000i
\(49\) 0 0
\(50\) 5.11215 8.85451i 0.722967 1.25222i
\(51\) 10.7153 1.77851i 1.50044 0.249041i
\(52\) 0.443250 0.0614677
\(53\) −2.67307 + 4.62989i −0.367174 + 0.635964i −0.989123 0.147094i \(-0.953008\pi\)
0.621948 + 0.783058i \(0.286341\pi\)
\(54\) −0.321798 + 10.6662i −0.0437911 + 1.45149i
\(55\) 0.243359 0.0328145
\(56\) 0 0
\(57\) −4.21093 + 11.2172i −0.557751 + 1.48576i
\(58\) 10.1350 1.33080
\(59\) −2.28549 3.95859i −0.297546 0.515364i 0.678028 0.735036i \(-0.262835\pi\)
−0.975574 + 0.219672i \(0.929501\pi\)
\(60\) −0.197407 + 0.525861i −0.0254851 + 0.0678883i
\(61\) −0.339138 + 0.587404i −0.0434221 + 0.0752094i −0.886920 0.461924i \(-0.847159\pi\)
0.843498 + 0.537133i \(0.180493\pi\)
\(62\) 5.17066 0.656674
\(63\) 0 0
\(64\) −9.63481 −1.20435
\(65\) −0.0146166 + 0.0253167i −0.00181296 + 0.00314015i
\(66\) 5.83914 0.969173i 0.718748 0.119297i
\(67\) 3.09342 + 5.35796i 0.377921 + 0.654579i 0.990760 0.135630i \(-0.0433057\pi\)
−0.612838 + 0.790208i \(0.709972\pi\)
\(68\) 13.9059 1.68634
\(69\) 6.79968 + 8.27101i 0.818586 + 0.995713i
\(70\) 0 0
\(71\) 1.27749 0.151611 0.0758053 0.997123i \(-0.475847\pi\)
0.0758053 + 0.997123i \(0.475847\pi\)
\(72\) −0.259125 + 1.31445i −0.0305382 + 0.154909i
\(73\) 0.778603 1.34858i 0.0911286 0.157839i −0.816858 0.576839i \(-0.804286\pi\)
0.907986 + 0.419000i \(0.137619\pi\)
\(74\) 14.3765 1.67123
\(75\) 5.47620 + 6.66115i 0.632337 + 0.769164i
\(76\) −7.66972 + 13.2843i −0.879777 + 1.52382i
\(77\) 0 0
\(78\) −0.249886 + 0.665657i −0.0282940 + 0.0753708i
\(79\) −6.39787 + 11.0814i −0.719817 + 1.24676i 0.241255 + 0.970462i \(0.422441\pi\)
−0.961072 + 0.276298i \(0.910892\pi\)
\(80\) 0.257231 0.445537i 0.0287593 0.0498126i
\(81\) −8.32664 3.41570i −0.925183 0.379522i
\(82\) −2.38008 4.12241i −0.262835 0.455244i
\(83\) −3.75687 6.50709i −0.412370 0.714246i 0.582778 0.812631i \(-0.301966\pi\)
−0.995148 + 0.0983854i \(0.968632\pi\)
\(84\) 0 0
\(85\) −0.458561 + 0.794251i −0.0497379 + 0.0861486i
\(86\) 3.86493 0.416766
\(87\) −3.00417 + 8.00262i −0.322080 + 0.857971i
\(88\) 0.743131 0.0792181
\(89\) −4.53394 7.85301i −0.480597 0.832418i 0.519155 0.854680i \(-0.326247\pi\)
−0.999752 + 0.0222619i \(0.992913\pi\)
\(90\) −0.678430 0.592918i −0.0715128 0.0624991i
\(91\) 0 0
\(92\) 6.85398 + 11.8714i 0.714577 + 1.23768i
\(93\) −1.53266 + 4.08275i −0.158929 + 0.423361i
\(94\) −1.86037 3.22226i −0.191883 0.332350i
\(95\) −0.505833 0.876128i −0.0518973 0.0898888i
\(96\) 4.94134 13.1629i 0.504323 1.34344i
\(97\) 3.98514 + 6.90246i 0.404630 + 0.700839i 0.994278 0.106821i \(-0.0340671\pi\)
−0.589649 + 0.807660i \(0.700734\pi\)
\(98\) 0 0
\(99\) −0.965543 + 4.89786i −0.0970408 + 0.492253i
\(100\) 5.51993 + 9.56080i 0.551993 + 0.956080i
\(101\) −14.8430 −1.47693 −0.738467 0.674290i \(-0.764450\pi\)
−0.738467 + 0.674290i \(0.764450\pi\)
\(102\) −7.83959 + 20.8834i −0.776235 + 2.06777i
\(103\) 0.203948 0.0200956 0.0100478 0.999950i \(-0.496802\pi\)
0.0100478 + 0.999950i \(0.496802\pi\)
\(104\) −0.0446339 + 0.0773081i −0.00437671 + 0.00758068i
\(105\) 0 0
\(106\) −5.48953 9.50815i −0.533191 0.923513i
\(107\) 3.48444 + 6.03524i 0.336854 + 0.583448i 0.983839 0.179054i \(-0.0573038\pi\)
−0.646985 + 0.762503i \(0.723970\pi\)
\(108\) −9.80029 6.05942i −0.943033 0.583068i
\(109\) 3.33058 5.76874i 0.319012 0.552545i −0.661270 0.750148i \(-0.729982\pi\)
0.980282 + 0.197603i \(0.0633157\pi\)
\(110\) −0.249886 + 0.432816i −0.0238257 + 0.0412674i
\(111\) −4.26138 + 11.3516i −0.404472 + 1.07745i
\(112\) 0 0
\(113\) −0.0193234 + 0.0334691i −0.00181779 + 0.00314851i −0.866933 0.498425i \(-0.833912\pi\)
0.865115 + 0.501573i \(0.167245\pi\)
\(114\) −15.6261 19.0073i −1.46352 1.78020i
\(115\) −0.904067 −0.0843047
\(116\) −5.47174 + 9.47733i −0.508038 + 0.879948i
\(117\) −0.451533 0.394620i −0.0417442 0.0364826i
\(118\) 9.38718 0.864160
\(119\) 0 0
\(120\) −0.0718382 0.0873827i −0.00655790 0.00797692i
\(121\) −8.23097 −0.748270
\(122\) −0.696469 1.20632i −0.0630553 0.109215i
\(123\) 3.96054 0.657366i 0.357110 0.0592727i
\(124\) −2.79155 + 4.83511i −0.250689 + 0.434206i
\(125\) −1.45933 −0.130526
\(126\) 0 0
\(127\) 13.4788 1.19605 0.598027 0.801476i \(-0.295952\pi\)
0.598027 + 0.801476i \(0.295952\pi\)
\(128\) 1.77577 3.07572i 0.156957 0.271858i
\(129\) −1.14562 + 3.05175i −0.100866 + 0.268692i
\(130\) −0.0300173 0.0519914i −0.00263269 0.00455995i
\(131\) 19.8333 1.73284 0.866422 0.499312i \(-0.166414\pi\)
0.866422 + 0.499312i \(0.166414\pi\)
\(132\) −2.24617 + 5.98345i −0.195504 + 0.520793i
\(133\) 0 0
\(134\) −12.7056 −1.09759
\(135\) 0.669264 0.359939i 0.0576011 0.0309786i
\(136\) −1.40028 + 2.42536i −0.120073 + 0.207973i
\(137\) −6.44509 −0.550642 −0.275321 0.961352i \(-0.588784\pi\)
−0.275321 + 0.961352i \(0.588784\pi\)
\(138\) −21.6921 + 3.60043i −1.84656 + 0.306489i
\(139\) −6.26527 + 10.8518i −0.531413 + 0.920435i 0.467914 + 0.883774i \(0.345006\pi\)
−0.999328 + 0.0366611i \(0.988328\pi\)
\(140\) 0 0
\(141\) 3.09573 0.513826i 0.260708 0.0432720i
\(142\) −1.31176 + 2.27203i −0.110080 + 0.190665i
\(143\) −0.166313 + 0.288063i −0.0139078 + 0.0240890i
\(144\) 7.94634 + 6.94476i 0.662195 + 0.578730i
\(145\) −0.360872 0.625048i −0.0299688 0.0519074i
\(146\) 1.59897 + 2.76950i 0.132332 + 0.229206i
\(147\) 0 0
\(148\) −7.76161 + 13.4435i −0.638000 + 1.10505i
\(149\) 17.7673 1.45555 0.727776 0.685815i \(-0.240554\pi\)
0.727776 + 0.685815i \(0.240554\pi\)
\(150\) −17.4700 + 2.89965i −1.42642 + 0.236756i
\(151\) 8.46599 0.688953 0.344476 0.938795i \(-0.388056\pi\)
0.344476 + 0.938795i \(0.388056\pi\)
\(152\) −1.54463 2.67538i −0.125286 0.217002i
\(153\) −14.1658 12.3803i −1.14524 1.00089i
\(154\) 0 0
\(155\) −0.184108 0.318885i −0.0147879 0.0256135i
\(156\) −0.487550 0.593047i −0.0390353 0.0474818i
\(157\) 2.84968 + 4.93579i 0.227429 + 0.393919i 0.957045 0.289938i \(-0.0936347\pi\)
−0.729616 + 0.683857i \(0.760301\pi\)
\(158\) −13.1390 22.7573i −1.04528 1.81048i
\(159\) 9.13481 1.51618i 0.724437 0.120241i
\(160\) 0.593572 + 1.02810i 0.0469260 + 0.0812782i
\(161\) 0 0
\(162\) 14.6248 11.3017i 1.14904 0.887944i
\(163\) −1.06267 1.84060i −0.0832349 0.144167i 0.821403 0.570349i \(-0.193192\pi\)
−0.904638 + 0.426181i \(0.859859\pi\)
\(164\) 5.13986 0.401355
\(165\) −0.267681 0.325603i −0.0208390 0.0253481i
\(166\) 15.4306 1.19764
\(167\) 5.78723 10.0238i 0.447829 0.775663i −0.550415 0.834891i \(-0.685530\pi\)
0.998244 + 0.0592278i \(0.0188638\pi\)
\(168\) 0 0
\(169\) 6.48002 + 11.2237i 0.498463 + 0.863364i
\(170\) −0.941721 1.63111i −0.0722267 0.125100i
\(171\) 19.6400 6.70433i 1.50190 0.512693i
\(172\) −2.08661 + 3.61412i −0.159103 + 0.275574i
\(173\) −7.95546 + 13.7793i −0.604842 + 1.04762i 0.387234 + 0.921981i \(0.373430\pi\)
−0.992076 + 0.125636i \(0.959903\pi\)
\(174\) −11.1480 13.5602i −0.845127 1.02800i
\(175\) 0 0
\(176\) 2.92688 5.06950i 0.220622 0.382128i
\(177\) −2.78249 + 7.41212i −0.209145 + 0.557129i
\(178\) 18.6222 1.39579
\(179\) 3.87665 6.71456i 0.289755 0.501870i −0.683996 0.729485i \(-0.739760\pi\)
0.973751 + 0.227615i \(0.0730929\pi\)
\(180\) 0.920714 0.314297i 0.0686260 0.0234263i
\(181\) 12.1618 0.903982 0.451991 0.892022i \(-0.350714\pi\)
0.451991 + 0.892022i \(0.350714\pi\)
\(182\) 0 0
\(183\) 1.15895 0.192362i 0.0856722 0.0142198i
\(184\) −2.76070 −0.203521
\(185\) −0.511893 0.886625i −0.0376351 0.0651860i
\(186\) −5.68744 6.91810i −0.417023 0.507260i
\(187\) −5.21769 + 9.03730i −0.381555 + 0.660873i
\(188\) 4.01754 0.293009
\(189\) 0 0
\(190\) 2.07760 0.150725
\(191\) 2.48383 4.30211i 0.179723 0.311290i −0.762062 0.647504i \(-0.775813\pi\)
0.941786 + 0.336214i \(0.109146\pi\)
\(192\) 10.5978 + 12.8909i 0.764828 + 0.930322i
\(193\) 7.45221 + 12.9076i 0.536422 + 0.929110i 0.999093 + 0.0425800i \(0.0135577\pi\)
−0.462671 + 0.886530i \(0.653109\pi\)
\(194\) −16.3681 −1.17516
\(195\) 0.0499500 0.00829064i 0.00357699 0.000593705i
\(196\) 0 0
\(197\) −21.2608 −1.51477 −0.757386 0.652968i \(-0.773524\pi\)
−0.757386 + 0.652968i \(0.773524\pi\)
\(198\) −7.71944 6.74646i −0.548597 0.479450i
\(199\) 9.97208 17.2722i 0.706902 1.22439i −0.259098 0.965851i \(-0.583425\pi\)
0.966001 0.258540i \(-0.0832413\pi\)
\(200\) −2.22336 −0.157215
\(201\) 3.76611 10.0323i 0.265641 0.707625i
\(202\) 15.2411 26.3984i 1.07236 1.85739i
\(203\) 0 0
\(204\) −15.2957 18.6055i −1.07092 1.30264i
\(205\) −0.169492 + 0.293568i −0.0118378 + 0.0205037i
\(206\) −0.209419 + 0.362724i −0.0145909 + 0.0252722i
\(207\) 3.58695 18.1953i 0.249310 1.26466i
\(208\) 0.351587 + 0.608967i 0.0243782 + 0.0422243i
\(209\) −5.75556 9.96893i −0.398121 0.689565i
\(210\) 0 0
\(211\) 11.7569 20.3636i 0.809381 1.40189i −0.103912 0.994587i \(-0.533136\pi\)
0.913293 0.407303i \(-0.133531\pi\)
\(212\) 11.8548 0.814193
\(213\) −1.40517 1.70923i −0.0962808 0.117114i
\(214\) −14.3116 −0.978323
\(215\) −0.137616 0.238358i −0.00938535 0.0162559i
\(216\) 2.04370 1.09912i 0.139056 0.0747860i
\(217\) 0 0
\(218\) 6.83983 + 11.8469i 0.463252 + 0.802376i
\(219\) −2.66076 + 0.441629i −0.179797 + 0.0298425i
\(220\) −0.269819 0.467340i −0.0181912 0.0315081i
\(221\) −0.626768 1.08559i −0.0421610 0.0730250i
\(222\) −15.8133 19.2350i −1.06132 1.29097i
\(223\) −2.03052 3.51696i −0.135974 0.235513i 0.789995 0.613113i \(-0.210083\pi\)
−0.925969 + 0.377600i \(0.876750\pi\)
\(224\) 0 0
\(225\) 2.88879 14.6538i 0.192586 0.976921i
\(226\) −0.0396834 0.0687336i −0.00263970 0.00457209i
\(227\) 3.85285 0.255723 0.127861 0.991792i \(-0.459189\pi\)
0.127861 + 0.991792i \(0.459189\pi\)
\(228\) 26.2101 4.35032i 1.73581 0.288107i
\(229\) −13.1162 −0.866746 −0.433373 0.901215i \(-0.642677\pi\)
−0.433373 + 0.901215i \(0.642677\pi\)
\(230\) 0.928316 1.60789i 0.0612113 0.106021i
\(231\) 0 0
\(232\) −1.10197 1.90868i −0.0723481 0.125311i
\(233\) −8.75115 15.1574i −0.573307 0.992997i −0.996223 0.0868284i \(-0.972327\pi\)
0.422916 0.906169i \(-0.361007\pi\)
\(234\) 1.16548 0.397850i 0.0761898 0.0260083i
\(235\) −0.132482 + 0.229466i −0.00864218 + 0.0149687i
\(236\) −5.06798 + 8.77801i −0.329898 + 0.571400i
\(237\) 21.8638 3.62892i 1.42020 0.235724i
\(238\) 0 0
\(239\) 3.65857 6.33683i 0.236653 0.409895i −0.723099 0.690745i \(-0.757283\pi\)
0.959752 + 0.280849i \(0.0906161\pi\)
\(240\) −0.879049 + 0.145903i −0.0567423 + 0.00941803i
\(241\) −6.23107 −0.401378 −0.200689 0.979655i \(-0.564318\pi\)
−0.200689 + 0.979655i \(0.564318\pi\)
\(242\) 8.45174 14.6389i 0.543299 0.941021i
\(243\) 4.58880 + 14.8977i 0.294372 + 0.955691i
\(244\) 1.50405 0.0962868
\(245\) 0 0
\(246\) −2.89764 + 7.71886i −0.184747 + 0.492137i
\(247\) 1.38276 0.0879829
\(248\) −0.562201 0.973761i −0.0356998 0.0618339i
\(249\) −4.57383 + 12.1840i −0.289855 + 0.772127i
\(250\) 1.49847 2.59543i 0.0947717 0.164149i
\(251\) −5.65283 −0.356803 −0.178402 0.983958i \(-0.557093\pi\)
−0.178402 + 0.983958i \(0.557093\pi\)
\(252\) 0 0
\(253\) −10.2868 −0.646727
\(254\) −13.8404 + 23.9722i −0.868422 + 1.50415i
\(255\) 1.56706 0.260099i 0.0981333 0.0162880i
\(256\) −5.98801 10.3715i −0.374250 0.648221i
\(257\) −11.8016 −0.736166 −0.368083 0.929793i \(-0.619986\pi\)
−0.368083 + 0.929793i \(0.619986\pi\)
\(258\) −4.25121 5.17110i −0.264669 0.321939i
\(259\) 0 0
\(260\) 0.0648233 0.00402017
\(261\) 14.0116 4.78301i 0.867293 0.296061i
\(262\) −20.3653 + 35.2737i −1.25817 + 2.17922i
\(263\) −22.2401 −1.37138 −0.685691 0.727893i \(-0.740500\pi\)
−0.685691 + 0.727893i \(0.740500\pi\)
\(264\) −0.817404 0.994275i −0.0503077 0.0611934i
\(265\) −0.390925 + 0.677101i −0.0240143 + 0.0415940i
\(266\) 0 0
\(267\) −5.51988 + 14.7041i −0.337811 + 0.899876i
\(268\) 6.85953 11.8810i 0.419012 0.725750i
\(269\) 1.19442 2.06880i 0.0728251 0.126137i −0.827313 0.561741i \(-0.810132\pi\)
0.900138 + 0.435604i \(0.143465\pi\)
\(270\) −0.0470615 + 1.55989i −0.00286407 + 0.0949316i
\(271\) 11.6129 + 20.1142i 0.705435 + 1.22185i 0.966534 + 0.256537i \(0.0825815\pi\)
−0.261100 + 0.965312i \(0.584085\pi\)
\(272\) 11.0302 + 19.1049i 0.668806 + 1.15841i
\(273\) 0 0
\(274\) 6.61797 11.4627i 0.399806 0.692484i
\(275\) −8.28461 −0.499581
\(276\) 8.34444 22.2283i 0.502276 1.33798i
\(277\) −4.61800 −0.277469 −0.138734 0.990330i \(-0.544303\pi\)
−0.138734 + 0.990330i \(0.544303\pi\)
\(278\) −12.8666 22.2857i −0.771690 1.33661i
\(279\) 7.14837 2.44018i 0.427962 0.146090i
\(280\) 0 0
\(281\) 5.90841 + 10.2337i 0.352466 + 0.610489i 0.986681 0.162668i \(-0.0520098\pi\)
−0.634215 + 0.773157i \(0.718676\pi\)
\(282\) −2.26492 + 6.03340i −0.134874 + 0.359284i
\(283\) 7.92483 + 13.7262i 0.471082 + 0.815939i 0.999453 0.0330753i \(-0.0105301\pi\)
−0.528370 + 0.849014i \(0.677197\pi\)
\(284\) −1.41639 2.45327i −0.0840475 0.145575i
\(285\) −0.615830 + 1.64047i −0.0364786 + 0.0971733i
\(286\) −0.341548 0.591579i −0.0201962 0.0349808i
\(287\) 0 0
\(288\) −23.0466 + 7.86723i −1.35803 + 0.463581i
\(289\) −11.1634 19.3355i −0.656669 1.13738i
\(290\) 1.48220 0.0870381
\(291\) 4.85174 12.9243i 0.284414 0.757634i
\(292\) −3.45304 −0.202074
\(293\) −7.04804 + 12.2076i −0.411751 + 0.713173i −0.995081 0.0990615i \(-0.968416\pi\)
0.583330 + 0.812235i \(0.301749\pi\)
\(294\) 0 0
\(295\) −0.334243 0.578927i −0.0194604 0.0337064i
\(296\) −1.56314 2.70744i −0.0908557 0.157367i
\(297\) 7.61515 4.09552i 0.441876 0.237646i
\(298\) −18.2438 + 31.5993i −1.05684 + 1.83050i
\(299\) 0.617846 1.07014i 0.0357310 0.0618878i
\(300\) 6.72029 17.9018i 0.387996 1.03356i
\(301\) 0 0
\(302\) −8.69307 + 15.0568i −0.500230 + 0.866424i
\(303\) 16.3265 + 19.8592i 0.937932 + 1.14088i
\(304\) −24.3346 −1.39569
\(305\) −0.0495974 + 0.0859053i −0.00283994 + 0.00491892i
\(306\) 36.5642 12.4816i 2.09024 0.713526i
\(307\) −27.3916 −1.56332 −0.781660 0.623704i \(-0.785627\pi\)
−0.781660 + 0.623704i \(0.785627\pi\)
\(308\) 0 0
\(309\) −0.224332 0.272873i −0.0127618 0.0155232i
\(310\) 0.756186 0.0429485
\(311\) −7.02785 12.1726i −0.398513 0.690244i 0.595030 0.803704i \(-0.297140\pi\)
−0.993543 + 0.113459i \(0.963807\pi\)
\(312\) 0.152529 0.0253167i 0.00863528 0.00143327i
\(313\) 10.8723 18.8314i 0.614540 1.06441i −0.375925 0.926650i \(-0.622675\pi\)
0.990465 0.137764i \(-0.0439916\pi\)
\(314\) −11.7045 −0.660520
\(315\) 0 0
\(316\) 28.3740 1.59616
\(317\) −4.28148 + 7.41575i −0.240472 + 0.416510i −0.960849 0.277073i \(-0.910636\pi\)
0.720377 + 0.693583i \(0.243969\pi\)
\(318\) −6.68328 + 17.8032i −0.374780 + 0.998353i
\(319\) −4.10614 7.11204i −0.229900 0.398198i
\(320\) −1.40905 −0.0787682
\(321\) 4.24217 11.3005i 0.236775 0.630730i
\(322\) 0 0
\(323\) 43.3808 2.41377
\(324\) 2.67256 + 19.7774i 0.148476 + 1.09874i
\(325\) 0.497589 0.861850i 0.0276013 0.0478068i
\(326\) 4.36471 0.241739
\(327\) −11.3818 + 1.88913i −0.629413 + 0.104469i
\(328\) −0.517568 + 0.896453i −0.0285779 + 0.0494984i
\(329\) 0 0
\(330\) 0.853949 0.141737i 0.0470083 0.00780239i
\(331\) −5.42360 + 9.39396i −0.298108 + 0.516339i −0.975703 0.219097i \(-0.929689\pi\)
0.677595 + 0.735435i \(0.263022\pi\)
\(332\) −8.33070 + 14.4292i −0.457207 + 0.791905i
\(333\) 19.8753 6.78465i 1.08916 0.371797i
\(334\) 11.8849 + 20.5853i 0.650314 + 1.12638i
\(335\) 0.452399 + 0.783578i 0.0247172 + 0.0428114i
\(336\) 0 0
\(337\) 1.67411 2.89964i 0.0911945 0.157954i −0.816819 0.576893i \(-0.804265\pi\)
0.908014 + 0.418940i \(0.137598\pi\)
\(338\) −26.6153 −1.44768
\(339\) 0.0660347 0.0109604i 0.00358651 0.000595285i
\(340\) 2.03368 0.110292
\(341\) −2.09486 3.62840i −0.113443 0.196489i
\(342\) −8.24304 + 41.8140i −0.445732 + 2.26104i
\(343\) 0 0
\(344\) −0.420231 0.727861i −0.0226573 0.0392437i
\(345\) 0.994424 + 1.20960i 0.0535380 + 0.0651226i
\(346\) −16.3377 28.2977i −0.878319 1.52129i
\(347\) 5.76652 + 9.98790i 0.309563 + 0.536178i 0.978267 0.207350i \(-0.0664840\pi\)
−0.668704 + 0.743529i \(0.733151\pi\)
\(348\) 18.6988 3.10361i 1.00236 0.166371i
\(349\) 4.44917 + 7.70619i 0.238159 + 0.412503i 0.960186 0.279362i \(-0.0901228\pi\)
−0.722027 + 0.691865i \(0.756789\pi\)
\(350\) 0 0
\(351\) −0.0313221 + 1.03819i −0.00167185 + 0.0554145i
\(352\) 6.75390 + 11.6981i 0.359984 + 0.623511i
\(353\) 2.64699 0.140885 0.0704424 0.997516i \(-0.477559\pi\)
0.0704424 + 0.997516i \(0.477559\pi\)
\(354\) −10.3254 12.5596i −0.548788 0.667536i
\(355\) 0.186828 0.00991579
\(356\) −10.0538 + 17.4137i −0.532852 + 0.922926i
\(357\) 0 0
\(358\) 7.96127 + 13.7893i 0.420766 + 0.728789i
\(359\) −12.9835 22.4882i −0.685245 1.18688i −0.973360 0.229284i \(-0.926362\pi\)
0.288114 0.957596i \(-0.406972\pi\)
\(360\) −0.0378959 + 0.192232i −0.00199729 + 0.0101315i
\(361\) −14.4264 + 24.9873i −0.759286 + 1.31512i
\(362\) −12.4880 + 21.6299i −0.656357 + 1.13684i
\(363\) 9.05362 + 11.0127i 0.475192 + 0.578014i
\(364\) 0 0
\(365\) 0.113867 0.197224i 0.00596009 0.0103232i
\(366\) −0.847922 + 2.25873i −0.0443216 + 0.118066i
\(367\) −17.5874 −0.918056 −0.459028 0.888422i \(-0.651802\pi\)
−0.459028 + 0.888422i \(0.651802\pi\)
\(368\) −10.8732 + 18.8330i −0.566806 + 0.981736i
\(369\) −5.23591 4.57596i −0.272570 0.238215i
\(370\) 2.10249 0.109303
\(371\) 0 0
\(372\) 9.53971 1.58339i 0.494611 0.0820950i
\(373\) 0.815075 0.0422030 0.0211015 0.999777i \(-0.493283\pi\)
0.0211015 + 0.999777i \(0.493283\pi\)
\(374\) −10.7153 18.5594i −0.554074 0.959684i
\(375\) 1.60518 + 1.95251i 0.0828912 + 0.100827i
\(376\) −0.404553 + 0.700707i −0.0208632 + 0.0361362i
\(377\) 0.986490 0.0508068
\(378\) 0 0
\(379\) −20.4312 −1.04948 −0.524741 0.851262i \(-0.675838\pi\)
−0.524741 + 0.851262i \(0.675838\pi\)
\(380\) −1.12166 + 1.94278i −0.0575401 + 0.0996624i
\(381\) −14.8260 18.0341i −0.759558 0.923913i
\(382\) 5.10090 + 8.83501i 0.260985 + 0.452039i
\(383\) −17.8928 −0.914278 −0.457139 0.889395i \(-0.651126\pi\)
−0.457139 + 0.889395i \(0.651126\pi\)
\(384\) −6.06843 + 1.00723i −0.309678 + 0.0514000i
\(385\) 0 0
\(386\) −30.6084 −1.55793
\(387\) 5.34322 1.82397i 0.271611 0.0927177i
\(388\) 8.83688 15.3059i 0.448625 0.777041i
\(389\) 15.6278 0.792363 0.396181 0.918172i \(-0.370335\pi\)
0.396181 + 0.918172i \(0.370335\pi\)
\(390\) −0.0365448 + 0.0973495i −0.00185052 + 0.00492948i
\(391\) 19.3835 33.5731i 0.980264 1.69787i
\(392\) 0 0
\(393\) −21.8156 26.5360i −1.10045 1.33857i
\(394\) 21.8311 37.8126i 1.09984 1.90497i
\(395\) −0.935661 + 1.62061i −0.0470782 + 0.0815419i
\(396\) 10.4763 3.57619i 0.526451 0.179710i
\(397\) −9.63064 16.6808i −0.483348 0.837183i 0.516469 0.856306i \(-0.327246\pi\)
−0.999817 + 0.0191225i \(0.993913\pi\)
\(398\) 20.4791 + 35.4709i 1.02653 + 1.77799i
\(399\) 0 0
\(400\) −8.75687 + 15.1673i −0.437843 + 0.758367i
\(401\) 14.3013 0.714172 0.357086 0.934072i \(-0.383770\pi\)
0.357086 + 0.934072i \(0.383770\pi\)
\(402\) 13.9754 + 16.9995i 0.697031 + 0.847856i
\(403\) 0.503284 0.0250704
\(404\) 16.4569 + 28.5041i 0.818760 + 1.41813i
\(405\) −1.21774 0.499532i −0.0605098 0.0248219i
\(406\) 0 0
\(407\) −5.82452 10.0884i −0.288711 0.500062i
\(408\) 4.78525 0.794251i 0.236905 0.0393213i
\(409\) 15.9305 + 27.5924i 0.787712 + 1.36436i 0.927366 + 0.374156i \(0.122068\pi\)
−0.139654 + 0.990200i \(0.544599\pi\)
\(410\) −0.348076 0.602885i −0.0171902 0.0297744i
\(411\) 7.08925 + 8.62324i 0.349687 + 0.425353i
\(412\) −0.226124 0.391657i −0.0111403 0.0192956i
\(413\) 0 0
\(414\) 28.6774 + 25.0628i 1.40942 + 1.23177i
\(415\) −0.549426 0.951633i −0.0269702 0.0467138i
\(416\) −1.62261 −0.0795549
\(417\) 21.4106 3.55371i 1.04848 0.174026i
\(418\) 23.6398 1.15626
\(419\) −11.9480 + 20.6945i −0.583697 + 1.01099i 0.411339 + 0.911482i \(0.365061\pi\)
−0.995036 + 0.0995110i \(0.968272\pi\)
\(420\) 0 0
\(421\) −1.22251 2.11744i −0.0595813 0.103198i 0.834696 0.550711i \(-0.185643\pi\)
−0.894278 + 0.447513i \(0.852310\pi\)
\(422\) 24.1446 + 41.8197i 1.17534 + 2.03575i
\(423\) −4.09261 3.57677i −0.198990 0.173908i
\(424\) −1.19375 + 2.06763i −0.0579734 + 0.100413i
\(425\) 15.6107 27.0385i 0.757230 1.31156i
\(426\) 4.48274 0.744039i 0.217189 0.0360488i
\(427\) 0 0
\(428\) 7.72661 13.3829i 0.373480 0.646886i
\(429\) 0.568350 0.0943341i 0.0274402 0.00455449i
\(430\) 0.565230 0.0272578
\(431\) 2.46382 4.26746i 0.118678 0.205556i −0.800566 0.599244i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(432\) 0.551224 18.2707i 0.0265208 0.879049i
\(433\) −30.8539 −1.48274 −0.741371 0.671095i \(-0.765824\pi\)
−0.741371 + 0.671095i \(0.765824\pi\)
\(434\) 0 0
\(435\) −0.439346 + 1.17035i −0.0210650 + 0.0561139i
\(436\) −14.7709 −0.707395
\(437\) 21.3817 + 37.0341i 1.02282 + 1.77158i
\(438\) 1.94668 5.18566i 0.0930162 0.247780i
\(439\) 1.22411 2.12022i 0.0584235 0.101192i −0.835334 0.549742i \(-0.814726\pi\)
0.893758 + 0.448550i \(0.148059\pi\)
\(440\) 0.108680 0.00518110
\(441\) 0 0
\(442\) 2.57432 0.122448
\(443\) 13.1475 22.7722i 0.624657 1.08194i −0.363950 0.931419i \(-0.618572\pi\)
0.988607 0.150520i \(-0.0480946\pi\)
\(444\) 26.5241 4.40244i 1.25878 0.208931i
\(445\) −0.663069 1.14847i −0.0314325 0.0544427i
\(446\) 8.33993 0.394907
\(447\) −19.5430 23.7718i −0.924354 1.12437i
\(448\) 0 0
\(449\) −38.7077 −1.82673 −0.913365 0.407141i \(-0.866526\pi\)
−0.913365 + 0.407141i \(0.866526\pi\)
\(450\) 23.0957 + 20.1846i 1.08874 + 0.951511i
\(451\) −1.92854 + 3.34034i −0.0908116 + 0.157290i
\(452\) 0.0856976 0.00403087
\(453\) −9.31213 11.3271i −0.437522 0.532194i
\(454\) −3.95620 + 6.85233i −0.185673 + 0.321596i
\(455\) 0 0
\(456\) −1.88053 + 5.00943i −0.0880638 + 0.234588i
\(457\) 4.57756 7.92856i 0.214129 0.370882i −0.738874 0.673844i \(-0.764642\pi\)
0.953003 + 0.302961i \(0.0979754\pi\)
\(458\) 13.4681 23.3274i 0.629321 1.09002i
\(459\) −0.982656 + 32.5708i −0.0458665 + 1.52027i
\(460\) 1.00237 + 1.73615i 0.0467355 + 0.0809483i
\(461\) −14.6152 25.3143i −0.680698 1.17900i −0.974768 0.223220i \(-0.928343\pi\)
0.294070 0.955784i \(-0.404990\pi\)
\(462\) 0 0
\(463\) −8.21031 + 14.2207i −0.381565 + 0.660891i −0.991286 0.131726i \(-0.957948\pi\)
0.609721 + 0.792616i \(0.291282\pi\)
\(464\) −17.3608 −0.805956
\(465\) −0.224144 + 0.597084i −0.0103944 + 0.0276891i
\(466\) 35.9435 1.66505
\(467\) −7.68632 13.3131i −0.355680 0.616057i 0.631554 0.775332i \(-0.282418\pi\)
−0.987234 + 0.159276i \(0.949084\pi\)
\(468\) −0.257191 + 1.30464i −0.0118887 + 0.0603070i
\(469\) 0 0
\(470\) −0.272071 0.471241i −0.0125497 0.0217367i
\(471\) 3.46936 9.24183i 0.159860 0.425841i
\(472\) −1.02066 1.76784i −0.0469797 0.0813713i
\(473\) −1.56585 2.71213i −0.0719979 0.124704i
\(474\) −15.9961 + 42.6112i −0.734727 + 1.95720i
\(475\) 17.2200 + 29.8259i 0.790106 + 1.36850i
\(476\) 0 0
\(477\) −12.0764 10.5542i −0.552939 0.483245i
\(478\) 7.51341 + 13.0136i 0.343655 + 0.595228i
\(479\) 37.9291 1.73303 0.866513 0.499155i \(-0.166356\pi\)
0.866513 + 0.499155i \(0.166356\pi\)
\(480\) 0.722649 1.92502i 0.0329843 0.0878649i
\(481\) 1.39933 0.0638038
\(482\) 6.39820 11.0820i 0.291430 0.504772i
\(483\) 0 0
\(484\) 9.12591 + 15.8065i 0.414814 + 0.718479i
\(485\) 0.582809 + 1.00946i 0.0264640 + 0.0458370i
\(486\) −31.2077 7.13612i −1.41561 0.323701i
\(487\) 2.30247 3.98800i 0.104335 0.180714i −0.809131 0.587628i \(-0.800062\pi\)
0.913466 + 0.406914i \(0.133395\pi\)
\(488\) −0.151453 + 0.262324i −0.00685595 + 0.0118749i
\(489\) −1.29376 + 3.44637i −0.0585058 + 0.155850i
\(490\) 0 0
\(491\) −15.1876 + 26.3056i −0.685405 + 1.18716i 0.287904 + 0.957659i \(0.407042\pi\)
−0.973309 + 0.229497i \(0.926292\pi\)
\(492\) −5.65356 6.87689i −0.254882 0.310034i
\(493\) 30.9488 1.39386
\(494\) −1.41985 + 2.45925i −0.0638820 + 0.110647i
\(495\) −0.141207 + 0.716290i −0.00634676 + 0.0321949i
\(496\) −8.85709 −0.397695
\(497\) 0 0
\(498\) −16.9728 20.6454i −0.760568 0.925141i
\(499\) 9.26871 0.414925 0.207462 0.978243i \(-0.433480\pi\)
0.207462 + 0.978243i \(0.433480\pi\)
\(500\) 1.61800 + 2.80246i 0.0723592 + 0.125330i
\(501\) −19.7770 + 3.28256i −0.883571 + 0.146654i
\(502\) 5.80445 10.0536i 0.259065 0.448715i
\(503\) 22.4230 0.999791 0.499896 0.866086i \(-0.333372\pi\)
0.499896 + 0.866086i \(0.333372\pi\)
\(504\) 0 0
\(505\) −2.17072 −0.0965960
\(506\) 10.5627 18.2952i 0.469571 0.813321i
\(507\) 7.88916 21.0155i 0.350370 0.933329i
\(508\) −14.9444 25.8844i −0.663050 1.14844i
\(509\) 37.6414 1.66843 0.834213 0.551443i \(-0.185923\pi\)
0.834213 + 0.551443i \(0.185923\pi\)
\(510\) −1.14651 + 3.05411i −0.0507682 + 0.135238i
\(511\) 0 0
\(512\) 31.6976 1.40085
\(513\) −30.5730 18.9030i −1.34983 0.834586i
\(514\) 12.1182 20.9893i 0.534511 0.925800i
\(515\) 0.0298266 0.00131432
\(516\) 7.13069 1.18354i 0.313911 0.0521026i
\(517\) −1.50743 + 2.61095i −0.0662969 + 0.114830i
\(518\) 0 0
\(519\) 27.1866 4.51240i 1.19336 0.198072i
\(520\) −0.00652751 + 0.0113060i −0.000286250 + 0.000495800i
\(521\) −17.4641 + 30.2488i −0.765117 + 1.32522i 0.175067 + 0.984556i \(0.443986\pi\)
−0.940185 + 0.340666i \(0.889348\pi\)
\(522\) −5.88075 + 29.8310i −0.257394 + 1.30567i
\(523\) 11.8735 + 20.5656i 0.519194 + 0.899270i 0.999751 + 0.0223069i \(0.00710109\pi\)
−0.480557 + 0.876963i \(0.659566\pi\)
\(524\) −21.9898 38.0874i −0.960628 1.66386i
\(525\) 0 0
\(526\) 22.8366 39.5542i 0.995723 1.72464i
\(527\) 15.7894 0.687795
\(528\) −10.0022 + 1.66015i −0.435288 + 0.0722486i
\(529\) 15.2151 0.661526
\(530\) −0.802820 1.39053i −0.0348723 0.0604006i
\(531\) 12.9777 4.43008i 0.563182 0.192249i
\(532\) 0 0
\(533\) −0.231664 0.401254i −0.0100345 0.0173802i
\(534\) −20.4834 24.9157i −0.886404 1.07821i
\(535\) 0.509585 + 0.882627i 0.0220313 + 0.0381593i
\(536\) 1.38147 + 2.39277i 0.0596702 + 0.103352i
\(537\) −13.2479 + 2.19887i −0.571688 + 0.0948882i
\(538\) 2.45292 + 4.24857i 0.105753 + 0.183169i
\(539\) 0 0
\(540\) −1.43325 0.886164i −0.0616773 0.0381344i
\(541\) 8.58542 + 14.8704i 0.369116 + 0.639328i 0.989428 0.145028i \(-0.0463271\pi\)
−0.620311 + 0.784356i \(0.712994\pi\)
\(542\) −47.6976 −2.04879
\(543\) −13.3774 16.2720i −0.574077 0.698297i
\(544\) −50.9055 −2.18255
\(545\) 0.487083 0.843653i 0.0208643 0.0361381i
\(546\) 0 0
\(547\) −10.0046 17.3284i −0.427765 0.740910i 0.568910 0.822400i \(-0.307365\pi\)
−0.996674 + 0.0814901i \(0.974032\pi\)
\(548\) 7.14586 + 12.3770i 0.305256 + 0.528719i
\(549\) −1.53215 1.33904i −0.0653908 0.0571487i
\(550\) 8.50683 14.7343i 0.362732 0.628271i
\(551\) −17.0696 + 29.5654i −0.727190 + 1.25953i
\(552\) 3.03662 + 3.69369i 0.129247 + 0.157214i
\(553\) 0 0
\(554\) 4.74187 8.21316i 0.201463 0.348944i
\(555\) −0.623209 + 1.66013i −0.0264537 + 0.0704685i
\(556\) 27.7860 1.17839
\(557\) −0.122740 + 0.212593i −0.00520068 + 0.00900784i −0.868614 0.495489i \(-0.834989\pi\)
0.863413 + 0.504497i \(0.168322\pi\)
\(558\) −3.00022 + 15.2191i −0.127010 + 0.644274i
\(559\) 0.376192 0.0159112
\(560\) 0 0
\(561\) 17.8307 2.95951i 0.752811 0.124951i
\(562\) −24.2676 −1.02367
\(563\) −22.1255 38.3224i −0.932477 1.61510i −0.779073 0.626934i \(-0.784310\pi\)
−0.153404 0.988164i \(-0.549024\pi\)
\(564\) −4.41907 5.37528i −0.186076 0.226340i
\(565\) −0.00282596 + 0.00489471i −0.000118889 + 0.000205922i
\(566\) −32.5496 −1.36816
\(567\) 0 0
\(568\) 0.570506 0.0239379
\(569\) 2.76767 4.79374i 0.116027 0.200964i −0.802163 0.597105i \(-0.796318\pi\)
0.918190 + 0.396141i \(0.129651\pi\)
\(570\) −2.28525 2.77974i −0.0957185 0.116430i
\(571\) 2.05191 + 3.55400i 0.0858696 + 0.148730i 0.905761 0.423788i \(-0.139300\pi\)
−0.819892 + 0.572518i \(0.805966\pi\)
\(572\) 0.737585 0.0308400
\(573\) −8.48810 + 1.40884i −0.354595 + 0.0588553i
\(574\) 0 0
\(575\) 30.7770 1.28349
\(576\) 5.59050 28.3586i 0.232938 1.18161i
\(577\) 2.82275 4.88915i 0.117513 0.203538i −0.801269 0.598305i \(-0.795841\pi\)
0.918781 + 0.394767i \(0.129175\pi\)
\(578\) 45.8512 1.90716
\(579\) 9.07276 24.1684i 0.377051 1.00440i
\(580\) −0.800218 + 1.38602i −0.0332272 + 0.0575513i
\(581\) 0 0
\(582\) 18.0040 + 21.8998i 0.746292 + 0.907776i
\(583\) −4.44809 + 7.70433i −0.184221 + 0.319081i
\(584\) 0.347710 0.602252i 0.0143884 0.0249214i
\(585\) −0.0660347 0.0577115i −0.00273020 0.00238608i
\(586\) −14.4742 25.0700i −0.597923 1.03563i
\(587\) −9.36644 16.2232i −0.386595 0.669601i 0.605394 0.795926i \(-0.293015\pi\)
−0.991989 + 0.126324i \(0.959682\pi\)
\(588\) 0 0
\(589\) −8.70852 + 15.0836i −0.358828 + 0.621509i
\(590\) 1.37283 0.0565187
\(591\) 23.3858 + 28.4460i 0.961962 + 1.17011i
\(592\) −24.6262 −1.01213
\(593\) 9.43516 + 16.3422i 0.387456 + 0.671093i 0.992107 0.125398i \(-0.0400207\pi\)
−0.604651 + 0.796491i \(0.706687\pi\)
\(594\) −0.535484 + 17.7490i −0.0219712 + 0.728250i
\(595\) 0 0
\(596\) −19.6991 34.1198i −0.806906 1.39760i
\(597\) −34.0781 + 5.65624i −1.39472 + 0.231495i
\(598\) 1.26884 + 2.19769i 0.0518866 + 0.0898702i
\(599\) −1.33726 2.31620i −0.0546388 0.0946372i 0.837412 0.546572i \(-0.184067\pi\)
−0.892051 + 0.451934i \(0.850734\pi\)
\(600\) 2.44558 + 2.97475i 0.0998402 + 0.121444i
\(601\) 6.60716 + 11.4439i 0.269511 + 0.466808i 0.968736 0.248095i \(-0.0798044\pi\)
−0.699224 + 0.714902i \(0.746471\pi\)
\(602\) 0 0
\(603\) −17.5653 + 5.99612i −0.715313 + 0.244181i
\(604\) −9.38650 16.2579i −0.381931 0.661524i
\(605\) −1.20374 −0.0489391
\(606\) −52.0843 + 8.64488i −2.11578 + 0.351174i
\(607\) −25.8052 −1.04740 −0.523701 0.851902i \(-0.675449\pi\)
−0.523701 + 0.851902i \(0.675449\pi\)
\(608\) 28.0766 48.6301i 1.13866 1.97221i
\(609\) 0 0
\(610\) −0.101856 0.176419i −0.00412401 0.00714299i
\(611\) −0.181079 0.313637i −0.00732565 0.0126884i
\(612\) −8.06877 + 40.9300i −0.326161 + 1.65450i
\(613\) 13.4766 23.3422i 0.544316 0.942784i −0.454333 0.890832i \(-0.650122\pi\)
0.998650 0.0519519i \(-0.0165443\pi\)
\(614\) 28.1263 48.7162i 1.13509 1.96603i
\(615\) 0.579212 0.0961370i 0.0233561 0.00387662i
\(616\) 0 0
\(617\) −4.76588 + 8.25474i −0.191867 + 0.332323i −0.945869 0.324549i \(-0.894788\pi\)
0.754002 + 0.656872i \(0.228121\pi\)
\(618\) 0.715657 0.118784i 0.0287880 0.00477819i
\(619\) −34.7071 −1.39500 −0.697499 0.716586i \(-0.745704\pi\)
−0.697499 + 0.716586i \(0.745704\pi\)
\(620\) −0.408253 + 0.707114i −0.0163958 + 0.0283984i
\(621\) −28.2899 + 15.2147i −1.13524 + 0.610544i
\(622\) 28.8654 1.15740
\(623\) 0 0
\(624\) 0.428043 1.14024i 0.0171354 0.0456461i
\(625\) 24.6796 0.987186
\(626\) 22.3279 + 38.6730i 0.892402 + 1.54568i
\(627\) −7.00716 + 18.6660i −0.279839 + 0.745447i
\(628\) 6.31904 10.9449i 0.252157 0.436749i
\(629\) 43.9006 1.75043
\(630\) 0 0
\(631\) −36.7963 −1.46484 −0.732419 0.680854i \(-0.761609\pi\)
−0.732419 + 0.680854i \(0.761609\pi\)
\(632\) −2.85718 + 4.94877i −0.113652 + 0.196852i
\(633\) −40.1776 + 6.66863i −1.59692 + 0.265054i
\(634\) −8.79265 15.2293i −0.349201 0.604833i
\(635\) 1.97122 0.0782256
\(636\) −13.0397 15.8612i −0.517057 0.628938i
\(637\) 0 0
\(638\) 16.8651 0.667696
\(639\) −0.741253 + 3.76011i −0.0293235 + 0.148748i
\(640\) 0.259699 0.449811i 0.0102655 0.0177804i
\(641\) −44.1844 −1.74518 −0.872590 0.488454i \(-0.837561\pi\)
−0.872590 + 0.488454i \(0.837561\pi\)
\(642\) 15.7420 + 19.1483i 0.621288 + 0.755723i
\(643\) −7.24065 + 12.5412i −0.285543 + 0.494575i −0.972741 0.231895i \(-0.925507\pi\)
0.687197 + 0.726471i \(0.258841\pi\)
\(644\) 0 0
\(645\) −0.167542 + 0.446305i −0.00659696 + 0.0175732i
\(646\) −44.5444 + 77.1532i −1.75258 + 3.03555i
\(647\) 16.6536 28.8448i 0.654719 1.13401i −0.327245 0.944940i \(-0.606120\pi\)
0.981964 0.189068i \(-0.0605465\pi\)
\(648\) −3.71853 1.52539i −0.146078 0.0599231i
\(649\) −3.80315 6.58725i −0.149287 0.258572i
\(650\) 1.02187 + 1.76993i 0.0400811 + 0.0694225i
\(651\) 0 0
\(652\) −2.35643 + 4.08146i −0.0922850 + 0.159842i
\(653\) −9.06643 −0.354797 −0.177398 0.984139i \(-0.556768\pi\)
−0.177398 + 0.984139i \(0.556768\pi\)
\(654\) 8.32721 22.1824i 0.325620 0.867399i
\(655\) 2.90054 0.113333
\(656\) 4.07696 + 7.06150i 0.159178 + 0.275705i
\(657\) 3.51757 + 3.07420i 0.137233 + 0.119936i
\(658\) 0 0
\(659\) 16.1806 + 28.0256i 0.630305 + 1.09172i 0.987489 + 0.157686i \(0.0504035\pi\)
−0.357184 + 0.934034i \(0.616263\pi\)
\(660\) −0.328493 + 0.875054i −0.0127866 + 0.0340614i
\(661\) −4.32958 7.49905i −0.168401 0.291679i 0.769457 0.638699i \(-0.220527\pi\)
−0.937858 + 0.347020i \(0.887194\pi\)
\(662\) −11.1382 19.2919i −0.432897 0.749799i
\(663\) −0.763064 + 2.03268i −0.0296349 + 0.0789428i
\(664\) −1.67775 2.90595i −0.0651094 0.112773i
\(665\) 0 0
\(666\) −8.34179 + 42.3150i −0.323238 + 1.63967i
\(667\) 15.2541 + 26.4209i 0.590642 + 1.02302i
\(668\) −25.6659 −0.993043
\(669\) −2.47207 + 6.58520i −0.0955758 + 0.254599i
\(670\) −1.85813 −0.0717860
\(671\) −0.564339 + 0.977464i −0.0217861 + 0.0377346i
\(672\) 0 0
\(673\) 7.24842 + 12.5546i 0.279406 + 0.483946i 0.971237 0.238114i \(-0.0765291\pi\)
−0.691831 + 0.722059i \(0.743196\pi\)
\(674\) 3.43803 + 5.95484i 0.132428 + 0.229372i
\(675\) −22.7836 + 12.2533i −0.876942 + 0.471631i
\(676\) 14.3692 24.8881i 0.552661 0.957236i
\(677\) 19.1657 33.1960i 0.736600 1.27583i −0.217418 0.976078i \(-0.569764\pi\)
0.954018 0.299749i \(-0.0969030\pi\)
\(678\) −0.0483128 + 0.128698i −0.00185544 + 0.00494260i
\(679\) 0 0
\(680\) −0.204785 + 0.354698i −0.00785315 + 0.0136021i
\(681\) −4.23793 5.15494i −0.162398 0.197538i
\(682\) 8.60418 0.329471
\(683\) −3.31659 + 5.74450i −0.126906 + 0.219807i −0.922476 0.386054i \(-0.873838\pi\)
0.795570 + 0.605861i \(0.207171\pi\)
\(684\) −34.6502 30.2828i −1.32488 1.15789i
\(685\) −0.942567 −0.0360136
\(686\) 0 0
\(687\) 14.4272 + 17.5489i 0.550430 + 0.669534i
\(688\) −6.62044 −0.252402
\(689\) −0.534322 0.925472i −0.0203560 0.0352577i
\(690\) −3.17238 + 0.526548i −0.120770 + 0.0200453i
\(691\) −11.6938 + 20.2542i −0.444852 + 0.770506i −0.998042 0.0625490i \(-0.980077\pi\)
0.553190 + 0.833055i \(0.313410\pi\)
\(692\) 35.2818 1.34121
\(693\) 0 0
\(694\) −23.6848 −0.899061
\(695\) −0.916269 + 1.58702i −0.0347561 + 0.0601992i
\(696\) −1.34161 + 3.57383i −0.0508535 + 0.135466i
\(697\) −7.26791 12.5884i −0.275292 0.476819i
\(698\) −18.2740 −0.691683
\(699\) −10.6542 + 28.3810i −0.402978 + 1.07347i
\(700\) 0 0
\(701\) 9.26736 0.350023 0.175012 0.984566i \(-0.444004\pi\)
0.175012 + 0.984566i \(0.444004\pi\)
\(702\) −1.81427 1.12174i −0.0684752 0.0423375i
\(703\) −24.2131 + 41.9383i −0.913214 + 1.58173i
\(704\) −16.0327 −0.604256
\(705\) 0.452738 0.0751449i 0.0170511 0.00283012i
\(706\) −2.71799 + 4.70769i −0.102293 + 0.177176i
\(707\) 0 0
\(708\) 17.3191 2.87460i 0.650891 0.108034i
\(709\) −7.11775 + 12.3283i −0.267313 + 0.462999i −0.968167 0.250305i \(-0.919469\pi\)
0.700854 + 0.713305i \(0.252802\pi\)
\(710\) −0.191839 + 0.332275i −0.00719959 + 0.0124701i
\(711\) −28.9043 25.2611i −1.08399 0.947365i
\(712\) −2.02478 3.50702i −0.0758817 0.131431i
\(713\) 7.78230 + 13.4793i 0.291449 + 0.504805i
\(714\) 0 0
\(715\) −0.0243226 + 0.0421280i −0.000909613 + 0.00157550i
\(716\) −17.1926 −0.642519
\(717\) −12.5026 + 2.07517i −0.466919 + 0.0774986i
\(718\) 53.3272 1.99015
\(719\) −6.92848 12.0005i −0.258389 0.447542i 0.707422 0.706792i \(-0.249858\pi\)
−0.965810 + 0.259249i \(0.916525\pi\)
\(720\) 1.16212 + 1.01564i 0.0433096 + 0.0378507i
\(721\) 0 0
\(722\) −29.6268 51.3151i −1.10259 1.90975i
\(723\) 6.85383 + 8.33688i 0.254897 + 0.310052i
\(724\) −13.4842 23.3553i −0.501136 0.867993i
\(725\) 12.2851 + 21.2784i 0.456257 + 0.790260i
\(726\) −28.8826 + 4.79389i −1.07193 + 0.177918i
\(727\) −15.7000 27.1932i −0.582280 1.00854i −0.995208 0.0977755i \(-0.968827\pi\)
0.412928 0.910764i \(-0.364506\pi\)
\(728\) 0 0
\(729\) 14.8851 22.5263i 0.551299 0.834308i
\(730\) 0.233843 + 0.405028i 0.00865492 + 0.0149908i
\(731\) 11.8021 0.436518
\(732\) −1.65437 2.01235i −0.0611473 0.0743785i
\(733\) 26.6006 0.982515 0.491257 0.871014i \(-0.336537\pi\)
0.491257 + 0.871014i \(0.336537\pi\)
\(734\) 18.0592 31.2794i 0.666576 1.15454i
\(735\) 0 0
\(736\) −25.0904 43.4579i −0.924845 1.60188i
\(737\) 5.14757 + 8.91586i 0.189613 + 0.328420i
\(738\) 13.5147 4.61341i 0.497484 0.169822i
\(739\) 16.5019 28.5822i 0.607034 1.05141i −0.384693 0.923045i \(-0.625693\pi\)
0.991727 0.128368i \(-0.0409740\pi\)
\(740\) −1.13510 + 1.96605i −0.0417272 + 0.0722736i
\(741\) −1.52096 1.85007i −0.0558739 0.0679640i
\(742\) 0 0
\(743\) 19.3008 33.4299i 0.708076 1.22642i −0.257493 0.966280i \(-0.582897\pi\)
0.965570 0.260144i \(-0.0837701\pi\)
\(744\) −0.684457 + 1.82328i −0.0250934 + 0.0668448i
\(745\) 2.59839 0.0951975
\(746\) −0.836938 + 1.44962i −0.0306425 + 0.0530743i
\(747\) 21.3325 7.28211i 0.780517 0.266439i
\(748\) 23.1400 0.846082
\(749\) 0 0
\(750\) −5.12080 + 0.849945i −0.186985 + 0.0310356i
\(751\) −37.8996 −1.38297 −0.691487 0.722389i \(-0.743044\pi\)
−0.691487 + 0.722389i \(0.743044\pi\)
\(752\) 3.18673 + 5.51957i 0.116208 + 0.201278i
\(753\) 6.21780 + 7.56323i 0.226589 + 0.275619i
\(754\) −1.01295 + 1.75448i −0.0368895 + 0.0638944i
\(755\) 1.23811 0.0450596
\(756\) 0 0
\(757\) 22.5927 0.821147 0.410573 0.911828i \(-0.365329\pi\)
0.410573 + 0.911828i \(0.365329\pi\)
\(758\) 20.9793 36.3371i 0.762001 1.31982i
\(759\) 11.3149 + 13.7633i 0.410707 + 0.499576i
\(760\) −0.225896 0.391263i −0.00819411 0.0141926i
\(761\) −27.7470 −1.00583 −0.502913 0.864337i \(-0.667739\pi\)
−0.502913 + 0.864337i \(0.667739\pi\)
\(762\) 47.2974 7.85037i 1.71340 0.284389i
\(763\) 0 0
\(764\) −11.0156 −0.398529
\(765\) −2.07168 1.81056i −0.0749019 0.0654610i
\(766\) 18.3727 31.8224i 0.663832 1.14979i
\(767\) 0.913698 0.0329917
\(768\) −7.29015 + 19.4198i −0.263061 + 0.700751i
\(769\) 6.07668 10.5251i 0.219131 0.379546i −0.735412 0.677621i \(-0.763011\pi\)
0.954542 + 0.298075i \(0.0963445\pi\)
\(770\) 0 0
\(771\) 12.9812 + 15.7901i 0.467505 + 0.568665i
\(772\) 16.5250 28.6221i 0.594747 1.03013i
\(773\) 20.7795 35.9912i 0.747388 1.29451i −0.201682 0.979451i \(-0.564641\pi\)
0.949071 0.315063i \(-0.102026\pi\)
\(774\) −2.24259 + 11.3759i −0.0806082 + 0.408897i
\(775\) 6.26756 + 10.8557i 0.225137 + 0.389950i
\(776\) 1.77969 + 3.08252i 0.0638873 + 0.110656i
\(777\) 0 0
\(778\) −16.0470 + 27.7942i −0.575313 + 0.996472i
\(779\) 16.0343 0.574488
\(780\) −0.0713021 0.0867306i