Properties

Label 105.3.t.b.11.17
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.17
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.17

$q$-expansion

\(f(q)\) \(=\) \(q+(2.61597 - 1.51033i) q^{2} +(2.80077 - 1.07503i) q^{3} +(2.56220 - 4.43785i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.70307 - 7.04234i) q^{6} +(-4.99419 + 4.90490i) q^{7} -3.39641i q^{8} +(6.68860 - 6.02184i) q^{9} +O(q^{10})\) \(q+(2.61597 - 1.51033i) q^{2} +(2.80077 - 1.07503i) q^{3} +(2.56220 - 4.43785i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.70307 - 7.04234i) q^{6} +(-4.99419 + 4.90490i) q^{7} -3.39641i q^{8} +(6.68860 - 6.02184i) q^{9} +(-3.37720 + 5.84948i) q^{10} +(-1.06414 - 0.614380i) q^{11} +(2.40527 - 15.1838i) q^{12} -18.8197 q^{13} +(-5.65663 + 20.3739i) q^{14} +(-4.22174 + 5.21315i) q^{15} +(5.11909 + 8.86652i) q^{16} +(16.5849 + 9.57529i) q^{17} +(8.40221 - 25.8550i) q^{18} +(-10.0788 - 17.4570i) q^{19} +11.4585i q^{20} +(-8.71464 + 19.1064i) q^{21} -3.71167 q^{22} +(16.4001 - 9.46858i) q^{23} +(-3.65125 - 9.51255i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-49.2317 + 28.4239i) q^{26} +(12.2595 - 24.0563i) q^{27} +(8.97113 + 34.7308i) q^{28} -31.9618i q^{29} +(-3.17036 + 20.0137i) q^{30} +(-14.6778 + 25.4227i) q^{31} +(38.5482 + 22.2558i) q^{32} +(-3.64088 - 0.576752i) q^{33} +57.8474 q^{34} +(4.18737 - 15.0820i) q^{35} +(-9.58654 - 45.1122i) q^{36} +(-9.97462 - 17.2765i) q^{37} +(-52.7318 - 30.4447i) q^{38} +(-52.7096 + 20.2318i) q^{39} +(3.79730 + 6.57711i) q^{40} +58.4356i q^{41} +(6.05977 + 63.1438i) q^{42} +57.9352 q^{43} +(-5.45306 + 3.14833i) q^{44} +(-6.21980 + 19.1393i) q^{45} +(28.6014 - 49.5390i) q^{46} +(-41.1569 + 23.7620i) q^{47} +(23.8692 + 19.3299i) q^{48} +(0.883910 - 48.9920i) q^{49} -15.1033i q^{50} +(56.7442 + 8.98884i) q^{51} +(-48.2197 + 83.5190i) q^{52} +(3.20503 + 1.85042i) q^{53} +(-4.26231 - 81.4464i) q^{54} +2.74759 q^{55} +(16.6590 + 16.9623i) q^{56} +(-46.9954 - 38.0580i) q^{57} +(-48.2729 - 83.6111i) q^{58} +(-22.3683 - 12.9144i) q^{59} +(12.3183 + 32.0926i) q^{60} +(-41.8961 - 72.5661i) q^{61} +88.6733i q^{62} +(-3.86764 + 62.8812i) q^{63} +93.5020 q^{64} +(36.4442 - 21.0411i) q^{65} +(-10.3955 + 3.99017i) q^{66} +(-21.3926 + 37.0531i) q^{67} +(84.9874 - 49.0675i) q^{68} +(35.7537 - 44.1499i) q^{69} +(-11.8247 - 45.7783i) q^{70} +0.779222i q^{71} +(-20.4526 - 22.7172i) q^{72} +(4.35332 - 7.54017i) q^{73} +(-52.1866 - 30.1299i) q^{74} +(2.34689 - 14.8153i) q^{75} -103.296 q^{76} +(8.32798 - 2.15116i) q^{77} +(-107.330 + 132.535i) q^{78} +(-31.2774 - 54.1740i) q^{79} +(-19.8261 - 11.4466i) q^{80} +(8.47485 - 80.5554i) q^{81} +(88.2571 + 152.866i) q^{82} -75.5527i q^{83} +(62.4628 + 87.6287i) q^{84} -42.8220 q^{85} +(151.557 - 87.5014i) q^{86} +(-34.3600 - 89.5176i) q^{87} +(-2.08668 + 3.61424i) q^{88} +(73.5337 - 42.4547i) q^{89} +(12.6359 + 59.4619i) q^{90} +(93.9891 - 92.3087i) q^{91} -97.0414i q^{92} +(-13.7789 + 86.9822i) q^{93} +(-71.7769 + 124.321i) q^{94} +(39.0351 + 22.5369i) q^{95} +(131.890 + 20.8928i) q^{96} +133.904 q^{97} +(-71.6819 - 129.497i) q^{98} +(-10.8173 + 2.29872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61597 1.51033i 1.30798 0.755165i 0.326225 0.945292i \(-0.394223\pi\)
0.981760 + 0.190127i \(0.0608900\pi\)
\(3\) 2.80077 1.07503i 0.933589 0.358345i
\(4\) 2.56220 4.43785i 0.640549 1.10946i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 5.70307 7.04234i 0.950511 1.17372i
\(7\) −4.99419 + 4.90490i −0.713456 + 0.700700i
\(8\) 3.39641i 0.424551i
\(9\) 6.68860 6.02184i 0.743178 0.669094i
\(10\) −3.37720 + 5.84948i −0.337720 + 0.584948i
\(11\) −1.06414 0.614380i −0.0967398 0.0558528i 0.450850 0.892600i \(-0.351121\pi\)
−0.547589 + 0.836747i \(0.684454\pi\)
\(12\) 2.40527 15.1838i 0.200439 1.26532i
\(13\) −18.8197 −1.44767 −0.723834 0.689974i \(-0.757622\pi\)
−0.723834 + 0.689974i \(0.757622\pi\)
\(14\) −5.65663 + 20.3739i −0.404045 + 1.45528i
\(15\) −4.22174 + 5.21315i −0.281449 + 0.347543i
\(16\) 5.11909 + 8.86652i 0.319943 + 0.554158i
\(17\) 16.5849 + 9.57529i 0.975581 + 0.563252i 0.900933 0.433958i \(-0.142883\pi\)
0.0746481 + 0.997210i \(0.476217\pi\)
\(18\) 8.40221 25.8550i 0.466789 1.43639i
\(19\) −10.0788 17.4570i −0.530464 0.918791i −0.999368 0.0355421i \(-0.988684\pi\)
0.468904 0.883249i \(-0.344649\pi\)
\(20\) 11.4585i 0.572924i
\(21\) −8.71464 + 19.1064i −0.414983 + 0.909829i
\(22\) −3.71167 −0.168712
\(23\) 16.4001 9.46858i 0.713046 0.411677i −0.0991417 0.995073i \(-0.531610\pi\)
0.812188 + 0.583396i \(0.198276\pi\)
\(24\) −3.65125 9.51255i −0.152135 0.396356i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −49.2317 + 28.4239i −1.89353 + 1.09323i
\(27\) 12.2595 24.0563i 0.454057 0.890973i
\(28\) 8.97113 + 34.7308i 0.320397 + 1.24039i
\(29\) 31.9618i 1.10213i −0.834462 0.551066i \(-0.814221\pi\)
0.834462 0.551066i \(-0.185779\pi\)
\(30\) −3.17036 + 20.0137i −0.105679 + 0.667122i
\(31\) −14.6778 + 25.4227i −0.473477 + 0.820087i −0.999539 0.0303595i \(-0.990335\pi\)
0.526062 + 0.850446i \(0.323668\pi\)
\(32\) 38.5482 + 22.2558i 1.20463 + 0.695495i
\(33\) −3.64088 0.576752i −0.110330 0.0174773i
\(34\) 57.8474 1.70139
\(35\) 4.18737 15.0820i 0.119639 0.430914i
\(36\) −9.58654 45.1122i −0.266293 1.25312i
\(37\) −9.97462 17.2765i −0.269584 0.466934i 0.699170 0.714955i \(-0.253553\pi\)
−0.968754 + 0.248022i \(0.920220\pi\)
\(38\) −52.7318 30.4447i −1.38768 0.801177i
\(39\) −52.7096 + 20.2318i −1.35153 + 0.518764i
\(40\) 3.79730 + 6.57711i 0.0949324 + 0.164428i
\(41\) 58.4356i 1.42526i 0.701541 + 0.712629i \(0.252496\pi\)
−0.701541 + 0.712629i \(0.747504\pi\)
\(42\) 6.05977 + 63.1438i 0.144280 + 1.50342i
\(43\) 57.9352 1.34733 0.673666 0.739036i \(-0.264719\pi\)
0.673666 + 0.739036i \(0.264719\pi\)
\(44\) −5.45306 + 3.14833i −0.123933 + 0.0715528i
\(45\) −6.21980 + 19.1393i −0.138218 + 0.425319i
\(46\) 28.6014 49.5390i 0.621769 1.07694i
\(47\) −41.1569 + 23.7620i −0.875680 + 0.505574i −0.869232 0.494405i \(-0.835386\pi\)
−0.00644823 + 0.999979i \(0.502053\pi\)
\(48\) 23.8692 + 19.3299i 0.497275 + 0.402706i
\(49\) 0.883910 48.9920i 0.0180390 0.999837i
\(50\) 15.1033i 0.302066i
\(51\) 56.7442 + 8.98884i 1.11263 + 0.176252i
\(52\) −48.2197 + 83.5190i −0.927302 + 1.60614i
\(53\) 3.20503 + 1.85042i 0.0604722 + 0.0349137i 0.529931 0.848041i \(-0.322218\pi\)
−0.469459 + 0.882954i \(0.655551\pi\)
\(54\) −4.26231 81.4464i −0.0789316 1.50827i
\(55\) 2.74759 0.0499562
\(56\) 16.6590 + 16.9623i 0.297483 + 0.302898i
\(57\) −46.9954 38.0580i −0.824480 0.667685i
\(58\) −48.2729 83.6111i −0.832291 1.44157i
\(59\) −22.3683 12.9144i −0.379124 0.218888i 0.298313 0.954468i \(-0.403576\pi\)
−0.677437 + 0.735581i \(0.736909\pi\)
\(60\) 12.3183 + 32.0926i 0.205304 + 0.534876i
\(61\) −41.8961 72.5661i −0.686821 1.18961i −0.972861 0.231391i \(-0.925672\pi\)
0.286040 0.958218i \(-0.407661\pi\)
\(62\) 88.6733i 1.43021i
\(63\) −3.86764 + 62.8812i −0.0613912 + 0.998114i
\(64\) 93.5020 1.46097
\(65\) 36.4442 21.0411i 0.560680 0.323708i
\(66\) −10.3955 + 3.99017i −0.157508 + 0.0604571i
\(67\) −21.3926 + 37.0531i −0.319293 + 0.553032i −0.980341 0.197312i \(-0.936779\pi\)
0.661048 + 0.750344i \(0.270112\pi\)
\(68\) 84.9874 49.0675i 1.24982 0.721581i
\(69\) 35.7537 44.1499i 0.518170 0.639854i
\(70\) −11.8247 45.7783i −0.168925 0.653976i
\(71\) 0.779222i 0.0109750i 0.999985 + 0.00548748i \(0.00174673\pi\)
−0.999985 + 0.00548748i \(0.998253\pi\)
\(72\) −20.4526 22.7172i −0.284064 0.315517i
\(73\) 4.35332 7.54017i 0.0596345 0.103290i −0.834667 0.550755i \(-0.814340\pi\)
0.894301 + 0.447465i \(0.147673\pi\)
\(74\) −52.1866 30.1299i −0.705224 0.407161i
\(75\) 2.34689 14.8153i 0.0312918 0.197537i
\(76\) −103.296 −1.35915
\(77\) 8.32798 2.15116i 0.108156 0.0279371i
\(78\) −107.330 + 132.535i −1.37602 + 1.69916i
\(79\) −31.2774 54.1740i −0.395916 0.685747i 0.597301 0.802017i \(-0.296240\pi\)
−0.993218 + 0.116270i \(0.962906\pi\)
\(80\) −19.8261 11.4466i −0.247827 0.143083i
\(81\) 8.47485 80.5554i 0.104628 0.994511i
\(82\) 88.2571 + 152.866i 1.07631 + 1.86422i
\(83\) 75.5527i 0.910274i −0.890421 0.455137i \(-0.849590\pi\)
0.890421 0.455137i \(-0.150410\pi\)
\(84\) 62.4628 + 87.6287i 0.743605 + 1.04320i
\(85\) −42.8220 −0.503788
\(86\) 151.557 87.5014i 1.76229 1.01746i
\(87\) −34.3600 89.5176i −0.394943 1.02894i
\(88\) −2.08668 + 3.61424i −0.0237123 + 0.0410710i
\(89\) 73.5337 42.4547i 0.826221 0.477019i −0.0263360 0.999653i \(-0.508384\pi\)
0.852557 + 0.522634i \(0.175051\pi\)
\(90\) 12.6359 + 59.4619i 0.140399 + 0.660687i
\(91\) 93.9891 92.3087i 1.03285 1.01438i
\(92\) 97.0414i 1.05480i
\(93\) −13.7789 + 86.9822i −0.148160 + 0.935293i
\(94\) −71.7769 + 124.321i −0.763584 + 1.32257i
\(95\) 39.0351 + 22.5369i 0.410896 + 0.237231i
\(96\) 131.890 + 20.8928i 1.37386 + 0.217633i
\(97\) 133.904 1.38045 0.690226 0.723594i \(-0.257511\pi\)
0.690226 + 0.723594i \(0.257511\pi\)
\(98\) −71.6819 129.497i −0.731448 1.32139i
\(99\) −10.8173 + 2.29872i −0.109266 + 0.0232194i
\(100\) −12.8110 22.1893i −0.128110 0.221893i
\(101\) 92.2153 + 53.2405i 0.913022 + 0.527134i 0.881402 0.472366i \(-0.156600\pi\)
0.0316200 + 0.999500i \(0.489933\pi\)
\(102\) 162.017 62.1879i 1.58840 0.609685i
\(103\) 32.8210 + 56.8476i 0.318650 + 0.551918i 0.980207 0.197977i \(-0.0634372\pi\)
−0.661556 + 0.749895i \(0.730104\pi\)
\(104\) 63.9193i 0.614609i
\(105\) −4.48579 46.7427i −0.0427218 0.445168i
\(106\) 11.1790 0.105462
\(107\) −43.2760 + 24.9854i −0.404449 + 0.233509i −0.688402 0.725330i \(-0.741687\pi\)
0.283953 + 0.958838i \(0.408354\pi\)
\(108\) −75.3468 116.043i −0.697655 1.07447i
\(109\) −102.244 + 177.093i −0.938022 + 1.62470i −0.168868 + 0.985639i \(0.554011\pi\)
−0.769154 + 0.639064i \(0.779322\pi\)
\(110\) 7.18762 4.14977i 0.0653420 0.0377252i
\(111\) −46.5095 37.6645i −0.419004 0.339320i
\(112\) −69.0551 19.1725i −0.616563 0.171183i
\(113\) 127.151i 1.12523i 0.826719 + 0.562616i \(0.190205\pi\)
−0.826719 + 0.562616i \(0.809795\pi\)
\(114\) −180.419 28.5801i −1.58262 0.250703i
\(115\) −21.1724 + 36.6717i −0.184108 + 0.318884i
\(116\) −141.842 81.8924i −1.22277 0.705969i
\(117\) −125.877 + 113.329i −1.07588 + 0.968626i
\(118\) −78.0199 −0.661185
\(119\) −129.794 + 33.5264i −1.09071 + 0.281734i
\(120\) 17.7060 + 14.3387i 0.147550 + 0.119490i
\(121\) −59.7451 103.482i −0.493761 0.855219i
\(122\) −219.198 126.554i −1.79670 1.03733i
\(123\) 62.8203 + 163.665i 0.510734 + 1.33061i
\(124\) 75.2148 + 130.276i 0.606571 + 1.05061i
\(125\) 11.1803i 0.0894427i
\(126\) 84.8537 + 170.337i 0.673442 + 1.35188i
\(127\) −36.8150 −0.289882 −0.144941 0.989440i \(-0.546299\pi\)
−0.144941 + 0.989440i \(0.546299\pi\)
\(128\) 90.4053 52.1955i 0.706292 0.407778i
\(129\) 162.263 62.2824i 1.25785 0.482809i
\(130\) 63.5579 110.085i 0.488907 0.846811i
\(131\) −151.267 + 87.3343i −1.15471 + 0.666674i −0.950031 0.312155i \(-0.898949\pi\)
−0.204682 + 0.978829i \(0.565616\pi\)
\(132\) −11.8882 + 14.6800i −0.0900621 + 0.111212i
\(133\) 135.961 + 37.7482i 1.02226 + 0.283821i
\(134\) 129.240i 0.964476i
\(135\) 3.15521 + 60.2913i 0.0233719 + 0.446602i
\(136\) 32.5216 56.3290i 0.239129 0.414184i
\(137\) 224.197 + 129.440i 1.63648 + 0.944820i 0.982033 + 0.188709i \(0.0604304\pi\)
0.654444 + 0.756111i \(0.272903\pi\)
\(138\) 26.8497 169.495i 0.194563 1.22822i
\(139\) −214.685 −1.54449 −0.772247 0.635323i \(-0.780867\pi\)
−0.772247 + 0.635323i \(0.780867\pi\)
\(140\) −56.2027 57.2259i −0.401448 0.408756i
\(141\) −89.7261 + 110.797i −0.636356 + 0.785794i
\(142\) 1.17688 + 2.03842i 0.00828791 + 0.0143551i
\(143\) 20.0267 + 11.5624i 0.140047 + 0.0808563i
\(144\) 87.6323 + 28.4783i 0.608558 + 0.197766i
\(145\) 35.7344 + 61.8938i 0.246444 + 0.426854i
\(146\) 26.2998i 0.180136i
\(147\) −50.1925 138.166i −0.341445 0.939902i
\(148\) −102.228 −0.690728
\(149\) 111.858 64.5815i 0.750727 0.433433i −0.0752293 0.997166i \(-0.523969\pi\)
0.825957 + 0.563734i \(0.190636\pi\)
\(150\) −16.2366 42.3009i −0.108244 0.282006i
\(151\) −79.3906 + 137.509i −0.525766 + 0.910653i 0.473784 + 0.880641i \(0.342888\pi\)
−0.999550 + 0.0300119i \(0.990445\pi\)
\(152\) −59.2912 + 34.2318i −0.390074 + 0.225209i
\(153\) 168.591 35.8262i 1.10190 0.234158i
\(154\) 18.5368 18.2054i 0.120369 0.118217i
\(155\) 65.6411i 0.423491i
\(156\) −45.2665 + 285.755i −0.290170 + 1.83176i
\(157\) 20.1933 34.9759i 0.128620 0.222776i −0.794522 0.607235i \(-0.792279\pi\)
0.923142 + 0.384459i \(0.125612\pi\)
\(158\) −163.641 94.4784i −1.03570 0.597964i
\(159\) 10.9658 + 1.73709i 0.0689674 + 0.0109251i
\(160\) −99.5311 −0.622070
\(161\) −35.4626 + 127.729i −0.220265 + 0.793345i
\(162\) −99.4954 223.530i −0.614169 1.37982i
\(163\) 100.113 + 173.401i 0.614191 + 1.06381i 0.990526 + 0.137326i \(0.0438509\pi\)
−0.376335 + 0.926484i \(0.622816\pi\)
\(164\) 259.329 + 149.723i 1.58127 + 0.912948i
\(165\) 7.69537 2.95375i 0.0466386 0.0179015i
\(166\) −114.110 197.644i −0.687407 1.19062i
\(167\) 44.2191i 0.264785i −0.991197 0.132393i \(-0.957734\pi\)
0.991197 0.132393i \(-0.0422659\pi\)
\(168\) 64.8931 + 29.5985i 0.386269 + 0.176181i
\(169\) 185.181 1.09574
\(170\) −112.021 + 64.6753i −0.658947 + 0.380443i
\(171\) −172.537 56.0701i −1.00899 0.327895i
\(172\) 148.441 257.108i 0.863032 1.49481i
\(173\) 118.309 68.3058i 0.683868 0.394831i −0.117443 0.993080i \(-0.537470\pi\)
0.801311 + 0.598248i \(0.204136\pi\)
\(174\) −225.086 182.280i −1.29360 1.04759i
\(175\) 8.75336 + 33.8877i 0.0500192 + 0.193644i
\(176\) 12.5803i 0.0714788i
\(177\) −76.5319 12.1234i −0.432384 0.0684939i
\(178\) 128.241 222.120i 0.720456 1.24787i
\(179\) −154.564 89.2377i −0.863488 0.498535i 0.00169111 0.999999i \(-0.499462\pi\)
−0.865179 + 0.501464i \(0.832795\pi\)
\(180\) 69.0012 + 76.6413i 0.383340 + 0.425785i
\(181\) 359.028 1.98358 0.991791 0.127869i \(-0.0408138\pi\)
0.991791 + 0.127869i \(0.0408138\pi\)
\(182\) 106.456 383.431i 0.584923 2.10677i
\(183\) −195.352 158.201i −1.06750 0.864488i
\(184\) −32.1591 55.7013i −0.174778 0.302724i
\(185\) 38.6315 + 22.3039i 0.208819 + 0.120562i
\(186\) 95.3268 + 248.353i 0.512510 + 1.33523i
\(187\) −11.7657 20.3788i −0.0629184 0.108978i
\(188\) 243.531i 1.29538i
\(189\) 56.7670 + 180.273i 0.300355 + 0.953828i
\(190\) 136.153 0.716594
\(191\) 45.5863 26.3192i 0.238672 0.137797i −0.375894 0.926662i \(-0.622664\pi\)
0.614566 + 0.788865i \(0.289331\pi\)
\(192\) 261.877 100.518i 1.36394 0.523530i
\(193\) −34.7721 + 60.2270i −0.180166 + 0.312057i −0.941937 0.335790i \(-0.890997\pi\)
0.761771 + 0.647847i \(0.224330\pi\)
\(194\) 350.288 202.239i 1.80561 1.04247i
\(195\) 79.4518 98.1098i 0.407445 0.503127i
\(196\) −215.155 129.450i −1.09773 0.660458i
\(197\) 52.8910i 0.268482i 0.990949 + 0.134241i \(0.0428596\pi\)
−0.990949 + 0.134241i \(0.957140\pi\)
\(198\) −24.8259 + 22.3511i −0.125383 + 0.112884i
\(199\) 27.7463 48.0580i 0.139429 0.241497i −0.787852 0.615865i \(-0.788807\pi\)
0.927280 + 0.374367i \(0.122140\pi\)
\(200\) −14.7069 8.49101i −0.0735343 0.0424551i
\(201\) −20.0824 + 126.775i −0.0999127 + 0.630722i
\(202\) 321.643 1.59229
\(203\) 156.769 + 159.623i 0.772263 + 0.786322i
\(204\) 185.281 228.791i 0.908239 1.12152i
\(205\) −65.3330 113.160i −0.318698 0.552000i
\(206\) 171.717 + 99.1410i 0.833579 + 0.481267i
\(207\) 52.6752 162.090i 0.254470 0.783044i
\(208\) −96.3396 166.865i −0.463171 0.802236i
\(209\) 24.7689i 0.118512i
\(210\) −82.3316 115.502i −0.392055 0.550011i
\(211\) −174.983 −0.829302 −0.414651 0.909980i \(-0.636096\pi\)
−0.414651 + 0.909980i \(0.636096\pi\)
\(212\) 16.4238 9.48230i 0.0774709 0.0447278i
\(213\) 0.837690 + 2.18242i 0.00393282 + 0.0102461i
\(214\) −75.4725 + 130.722i −0.352675 + 0.610851i
\(215\) −112.191 + 64.7736i −0.521819 + 0.301272i
\(216\) −81.7048 41.6384i −0.378263 0.192770i
\(217\) −51.3920 198.959i −0.236830 0.916862i
\(218\) 617.691i 2.83345i
\(219\) 4.08670 25.7982i 0.0186607 0.117800i
\(220\) 7.03987 12.1934i 0.0319994 0.0554246i
\(221\) −312.122 180.204i −1.41232 0.815402i
\(222\) −178.553 28.2846i −0.804294 0.127408i
\(223\) −193.145 −0.866121 −0.433061 0.901365i \(-0.642566\pi\)
−0.433061 + 0.901365i \(0.642566\pi\)
\(224\) −301.680 + 77.9254i −1.34679 + 0.347881i
\(225\) −9.35383 44.0171i −0.0415726 0.195632i
\(226\) 192.040 + 332.623i 0.849736 + 1.47179i
\(227\) 260.268 + 150.266i 1.14655 + 0.661964i 0.948045 0.318135i \(-0.103057\pi\)
0.198509 + 0.980099i \(0.436390\pi\)
\(228\) −289.307 + 111.046i −1.26889 + 0.487046i
\(229\) −51.8598 89.8238i −0.226462 0.392244i 0.730295 0.683132i \(-0.239383\pi\)
−0.956757 + 0.290888i \(0.906049\pi\)
\(230\) 127.909i 0.556127i
\(231\) 21.0122 14.9778i 0.0909618 0.0648388i
\(232\) −108.555 −0.467911
\(233\) −74.8292 + 43.2027i −0.321155 + 0.185419i −0.651907 0.758299i \(-0.726031\pi\)
0.330752 + 0.943718i \(0.392698\pi\)
\(234\) −158.127 + 486.582i −0.675756 + 2.07941i
\(235\) 53.1334 92.0297i 0.226100 0.391616i
\(236\) −114.624 + 66.1783i −0.485696 + 0.280416i
\(237\) −145.840 118.105i −0.615357 0.498332i
\(238\) −288.901 + 283.736i −1.21387 + 1.19217i
\(239\) 17.2002i 0.0719672i −0.999352 0.0359836i \(-0.988544\pi\)
0.999352 0.0359836i \(-0.0114564\pi\)
\(240\) −67.8339 10.7456i −0.282641 0.0447732i
\(241\) 70.3979 121.933i 0.292107 0.505945i −0.682200 0.731165i \(-0.738977\pi\)
0.974308 + 0.225220i \(0.0723102\pi\)
\(242\) −312.583 180.470i −1.29166 0.745742i
\(243\) −62.8637 234.728i −0.258698 0.965958i
\(244\) −429.384 −1.75977
\(245\) 53.0631 + 95.8609i 0.216584 + 0.391269i
\(246\) 411.523 + 333.262i 1.67286 + 1.35472i
\(247\) 189.680 + 328.536i 0.767937 + 1.33011i
\(248\) 86.3458 + 49.8518i 0.348169 + 0.201015i
\(249\) −81.2218 211.606i −0.326192 0.849822i
\(250\) 16.8860 + 29.2474i 0.0675440 + 0.116990i
\(251\) 201.133i 0.801329i −0.916225 0.400664i \(-0.868779\pi\)
0.916225 0.400664i \(-0.131221\pi\)
\(252\) 269.148 + 178.278i 1.06805 + 0.707452i
\(253\) −23.2692 −0.0919733
\(254\) −96.3069 + 55.6028i −0.379161 + 0.218909i
\(255\) −119.934 + 46.0351i −0.470331 + 0.180530i
\(256\) −29.3390 + 50.8166i −0.114605 + 0.198502i
\(257\) −240.370 + 138.777i −0.935290 + 0.539990i −0.888481 0.458914i \(-0.848239\pi\)
−0.0468093 + 0.998904i \(0.514905\pi\)
\(258\) 330.409 408.000i 1.28065 1.58139i
\(259\) 134.555 + 37.3579i 0.519517 + 0.144239i
\(260\) 215.645i 0.829405i
\(261\) −192.469 213.780i −0.737429 0.819080i
\(262\) −263.807 + 456.927i −1.00690 + 1.74400i
\(263\) −118.944 68.6721i −0.452257 0.261111i 0.256526 0.966537i \(-0.417422\pi\)
−0.708783 + 0.705427i \(0.750755\pi\)
\(264\) −1.95889 + 12.3659i −0.00742002 + 0.0468406i
\(265\) −8.27535 −0.0312277
\(266\) 412.681 106.597i 1.55143 0.400742i
\(267\) 160.311 197.957i 0.600414 0.741412i
\(268\) 109.624 + 189.875i 0.409046 + 0.708488i
\(269\) 156.731 + 90.4884i 0.582641 + 0.336388i 0.762182 0.647362i \(-0.224128\pi\)
−0.179541 + 0.983750i \(0.557461\pi\)
\(270\) 99.3138 + 152.955i 0.367829 + 0.566499i
\(271\) −11.5380 19.9844i −0.0425757 0.0737433i 0.843952 0.536418i \(-0.180223\pi\)
−0.886528 + 0.462675i \(0.846890\pi\)
\(272\) 196.067i 0.720834i
\(273\) 164.007 359.577i 0.600758 1.31713i
\(274\) 781.991 2.85398
\(275\) −5.32069 + 3.07190i −0.0193480 + 0.0111706i
\(276\) −104.323 271.791i −0.377981 0.984748i
\(277\) −58.5237 + 101.366i −0.211277 + 0.365942i −0.952114 0.305742i \(-0.901095\pi\)
0.740838 + 0.671684i \(0.234429\pi\)
\(278\) −561.608 + 324.245i −2.02017 + 1.16635i
\(279\) 54.9175 + 258.430i 0.196837 + 0.926271i
\(280\) −51.2245 14.2220i −0.182945 0.0507928i
\(281\) 545.470i 1.94117i −0.240750 0.970587i \(-0.577393\pi\)
0.240750 0.970587i \(-0.422607\pi\)
\(282\) −67.3809 + 425.357i −0.238939 + 1.50836i
\(283\) 16.3060 28.2428i 0.0576182 0.0997977i −0.835778 0.549068i \(-0.814983\pi\)
0.893396 + 0.449270i \(0.148316\pi\)
\(284\) 3.45807 + 1.99652i 0.0121763 + 0.00703000i
\(285\) 133.556 + 21.1567i 0.468619 + 0.0742339i
\(286\) 69.8525 0.244239
\(287\) −286.621 291.839i −0.998679 1.01686i
\(288\) 391.855 83.2709i 1.36061 0.289135i
\(289\) 38.8722 + 67.3286i 0.134506 + 0.232971i
\(290\) 186.960 + 107.941i 0.644690 + 0.372212i
\(291\) 375.033 143.951i 1.28877 0.494677i
\(292\) −22.3081 38.6388i −0.0763976 0.132325i
\(293\) 180.379i 0.615628i −0.951447 0.307814i \(-0.900403\pi\)
0.951447 0.307814i \(-0.0995974\pi\)
\(294\) −339.978 285.630i −1.15639 0.971529i
\(295\) 57.7548 0.195779
\(296\) −58.6781 + 33.8778i −0.198237 + 0.114452i
\(297\) −27.8255 + 18.0672i −0.0936887 + 0.0608322i
\(298\) 195.079 337.886i 0.654627 1.13385i
\(299\) −308.644 + 178.196i −1.03225 + 0.595972i
\(300\) −59.7348 48.3748i −0.199116 0.161249i
\(301\) −289.340 + 284.167i −0.961262 + 0.944075i
\(302\) 479.624i 1.58816i
\(303\) 315.509 + 49.9798i 1.04128 + 0.164950i
\(304\) 103.189 178.728i 0.339437 0.587922i
\(305\) 162.263 + 93.6825i 0.532009 + 0.307156i
\(306\) 386.918 348.348i 1.26444 1.13839i
\(307\) −396.005 −1.28992 −0.644960 0.764217i \(-0.723126\pi\)
−0.644960 + 0.764217i \(0.723126\pi\)
\(308\) 11.7914 42.4701i 0.0382838 0.137890i
\(309\) 153.037 + 123.933i 0.495265 + 0.401078i
\(310\) −99.1398 171.715i −0.319806 0.553920i
\(311\) 112.551 + 64.9812i 0.361899 + 0.208943i 0.669914 0.742439i \(-0.266331\pi\)
−0.308014 + 0.951382i \(0.599664\pi\)
\(312\) 68.7154 + 179.023i 0.220242 + 0.573792i
\(313\) 105.619 + 182.938i 0.337441 + 0.584466i 0.983951 0.178440i \(-0.0571052\pi\)
−0.646509 + 0.762906i \(0.723772\pi\)
\(314\) 121.995i 0.388518i
\(315\) −62.8136 126.093i −0.199408 0.400295i
\(316\) −320.555 −1.01442
\(317\) 402.217 232.220i 1.26882 0.732556i 0.294059 0.955787i \(-0.404994\pi\)
0.974766 + 0.223231i \(0.0716604\pi\)
\(318\) 31.3098 12.0178i 0.0984585 0.0377919i
\(319\) −19.6367 + 34.0118i −0.0615571 + 0.106620i
\(320\) −181.066 + 104.538i −0.565831 + 0.326683i
\(321\) −94.3459 + 116.502i −0.293913 + 0.362933i
\(322\) 100.143 + 387.694i 0.311004 + 1.20402i
\(323\) 386.031i 1.19514i
\(324\) −335.779 244.009i −1.03635 0.753114i
\(325\) −47.0492 + 81.4916i −0.144767 + 0.250744i
\(326\) 523.786 + 302.408i 1.60670 + 0.927631i
\(327\) −95.9824 + 605.911i −0.293524 + 1.85294i
\(328\) 198.471 0.605095
\(329\) 88.9956 320.543i 0.270503 0.974294i
\(330\) 15.6697 19.3495i 0.0474839 0.0586348i
\(331\) −287.337 497.682i −0.868087 1.50357i −0.863949 0.503579i \(-0.832016\pi\)
−0.00413794 0.999991i \(-0.501317\pi\)
\(332\) −335.292 193.581i −1.00992 0.583075i
\(333\) −170.753 55.4904i −0.512771 0.166638i
\(334\) −66.7855 115.676i −0.199956 0.346335i
\(335\) 95.6708i 0.285585i
\(336\) −214.018 + 20.5389i −0.636960 + 0.0611276i
\(337\) −243.217 −0.721711 −0.360856 0.932622i \(-0.617515\pi\)
−0.360856 + 0.932622i \(0.617515\pi\)
\(338\) 484.427 279.684i 1.43322 0.827468i
\(339\) 136.692 + 356.121i 0.403221 + 1.05050i
\(340\) −109.718 + 190.038i −0.322701 + 0.558934i
\(341\) 31.2384 18.0355i 0.0916082 0.0528900i
\(342\) −536.035 + 113.910i −1.56735 + 0.333070i
\(343\) 235.887 + 249.011i 0.687716 + 0.725980i
\(344\) 196.772i 0.572011i
\(345\) −19.8757 + 125.470i −0.0576107 + 0.363681i
\(346\) 206.329 357.372i 0.596326 1.03287i
\(347\) 262.342 + 151.463i 0.756029 + 0.436494i 0.827868 0.560922i \(-0.189553\pi\)
−0.0718390 + 0.997416i \(0.522887\pi\)
\(348\) −485.303 76.8769i −1.39455 0.220911i
\(349\) 91.0108 0.260776 0.130388 0.991463i \(-0.458378\pi\)
0.130388 + 0.991463i \(0.458378\pi\)
\(350\) 74.0802 + 75.4288i 0.211658 + 0.215511i
\(351\) −230.721 + 452.731i −0.657324 + 1.28983i
\(352\) −27.3471 47.3666i −0.0776906 0.134564i
\(353\) −192.171 110.950i −0.544394 0.314306i 0.202464 0.979290i \(-0.435105\pi\)
−0.746858 + 0.664984i \(0.768439\pi\)
\(354\) −218.516 + 83.8740i −0.617276 + 0.236932i
\(355\) −0.871197 1.50896i −0.00245408 0.00425058i
\(356\) 435.109i 1.22222i
\(357\) −327.481 + 233.432i −0.917313 + 0.653872i
\(358\) −539.114 −1.50590
\(359\) −479.747 + 276.982i −1.33634 + 0.771538i −0.986263 0.165183i \(-0.947179\pi\)
−0.350079 + 0.936720i \(0.613845\pi\)
\(360\) 65.0049 + 21.1250i 0.180569 + 0.0586805i
\(361\) −22.6654 + 39.2577i −0.0627851 + 0.108747i
\(362\) 939.207 542.251i 2.59449 1.49793i
\(363\) −278.578 225.600i −0.767433 0.621487i
\(364\) −168.834 653.623i −0.463829 1.79567i
\(365\) 19.4686i 0.0533387i
\(366\) −749.972 118.803i −2.04910 0.324598i
\(367\) 213.410 369.637i 0.581499 1.00719i −0.413803 0.910367i \(-0.635800\pi\)
0.995302 0.0968195i \(-0.0308669\pi\)
\(368\) 167.907 + 96.9410i 0.456268 + 0.263427i
\(369\) 351.890 + 390.853i 0.953631 + 1.05922i
\(370\) 134.745 0.364176
\(371\) −25.0827 + 6.47897i −0.0676083 + 0.0174635i
\(372\) 350.710 + 284.014i 0.942769 + 0.763479i
\(373\) 17.0540 + 29.5384i 0.0457211 + 0.0791913i 0.887980 0.459881i \(-0.152108\pi\)
−0.842259 + 0.539073i \(0.818775\pi\)
\(374\) −61.5576 35.5403i −0.164592 0.0950275i
\(375\) 12.0192 + 31.3135i 0.0320513 + 0.0835028i
\(376\) 80.7053 + 139.786i 0.214642 + 0.371770i
\(377\) 601.511i 1.59552i
\(378\) 420.773 + 385.853i 1.11316 + 1.02077i
\(379\) −366.427 −0.966826 −0.483413 0.875392i \(-0.660603\pi\)
−0.483413 + 0.875392i \(0.660603\pi\)
\(380\) 200.031 115.488i 0.526398 0.303916i
\(381\) −103.110 + 39.5774i −0.270631 + 0.103878i
\(382\) 79.5015 137.701i 0.208119 0.360473i
\(383\) 27.1258 15.6611i 0.0708245 0.0408905i −0.464170 0.885746i \(-0.653647\pi\)
0.534994 + 0.844856i \(0.320314\pi\)
\(384\) 197.092 243.376i 0.513261 0.633793i
\(385\) −13.7220 + 13.4767i −0.0356416 + 0.0350043i
\(386\) 210.069i 0.544221i
\(387\) 387.506 348.877i 1.00131 0.901491i
\(388\) 343.088 594.245i 0.884247 1.53156i
\(389\) −96.1676 55.5224i −0.247218 0.142731i 0.371272 0.928524i \(-0.378922\pi\)
−0.618490 + 0.785793i \(0.712255\pi\)
\(390\) 59.6653 376.651i 0.152988 0.965771i
\(391\) 362.657 0.927513
\(392\) −166.397 3.00212i −0.424482 0.00765846i
\(393\) −329.778 + 407.221i −0.839129 + 1.03618i
\(394\) 79.8828 + 138.361i 0.202748 + 0.351170i
\(395\) 121.137 + 69.9384i 0.306675 + 0.177059i
\(396\) −17.5146 + 53.8954i −0.0442289 + 0.136099i
\(397\) −192.946 334.192i −0.486009 0.841792i 0.513862 0.857873i \(-0.328214\pi\)
−0.999871 + 0.0160808i \(0.994881\pi\)
\(398\) 167.624i 0.421167i
\(399\) 421.375 40.4384i 1.05608 0.101349i
\(400\) 51.1909 0.127977
\(401\) 316.717 182.857i 0.789817 0.456001i −0.0500808 0.998745i \(-0.515948\pi\)
0.839898 + 0.542744i \(0.182615\pi\)
\(402\) 138.937 + 361.971i 0.345615 + 0.900425i
\(403\) 276.232 478.447i 0.685438 1.18721i
\(404\) 472.547 272.825i 1.16967 0.675310i
\(405\) 73.6522 + 165.470i 0.181857 + 0.408568i
\(406\) 651.188 + 180.796i 1.60391 + 0.445311i
\(407\) 24.5128i 0.0602281i
\(408\) 30.5298 192.726i 0.0748279 0.472368i
\(409\) 37.9388 65.7119i 0.0927599 0.160665i −0.815912 0.578177i \(-0.803764\pi\)
0.908671 + 0.417512i \(0.137098\pi\)
\(410\) −341.818 197.349i −0.833703 0.481339i
\(411\) 767.077 + 121.513i 1.86637 + 0.295651i
\(412\) 336.375 0.816444
\(413\) 175.055 45.2176i 0.423863 0.109486i
\(414\) −107.013 503.580i −0.258485 1.21638i
\(415\) 84.4705 + 146.307i 0.203543 + 0.352548i
\(416\) −725.466 418.848i −1.74391 1.00685i
\(417\) −601.282 + 230.793i −1.44192 + 0.553461i
\(418\) 37.4093 + 64.7947i 0.0894958 + 0.155011i
\(419\) 394.222i 0.940864i 0.882436 + 0.470432i \(0.155902\pi\)
−0.882436 + 0.470432i \(0.844098\pi\)
\(420\) −218.931 99.8566i −0.521263 0.237754i
\(421\) 50.8766 0.120847 0.0604235 0.998173i \(-0.480755\pi\)
0.0604235 + 0.998173i \(0.480755\pi\)
\(422\) −457.750 + 264.282i −1.08471 + 0.626260i
\(423\) −132.192 + 406.775i −0.312510 + 0.961643i
\(424\) 6.28479 10.8856i 0.0148226 0.0256735i
\(425\) 82.9244 47.8764i 0.195116 0.112650i
\(426\) 5.48755 + 4.44396i 0.0128816 + 0.0104318i
\(427\) 565.167 + 156.913i 1.32358 + 0.367478i
\(428\) 256.070i 0.598295i
\(429\) 68.5203 + 10.8543i 0.159721 + 0.0253014i
\(430\) −195.659 + 338.891i −0.455021 + 0.788119i
\(431\) −452.693 261.362i −1.05033 0.606409i −0.127589 0.991827i \(-0.540724\pi\)
−0.922742 + 0.385418i \(0.874057\pi\)
\(432\) 276.053 14.4466i 0.639012 0.0334412i
\(433\) −458.230 −1.05827 −0.529134 0.848538i \(-0.677483\pi\)
−0.529134 + 0.848538i \(0.677483\pi\)
\(434\) −434.934 442.852i −1.00215 1.02040i
\(435\) 166.622 + 134.934i 0.383038 + 0.310194i
\(436\) 523.940 + 907.492i 1.20170 + 2.08140i
\(437\) −330.587 190.864i −0.756491 0.436761i
\(438\) −28.2732 73.6596i −0.0645506 0.168173i
\(439\) 24.8300 + 43.0069i 0.0565605 + 0.0979656i 0.892919 0.450217i \(-0.148653\pi\)
−0.836359 + 0.548182i \(0.815320\pi\)
\(440\) 9.33194i 0.0212090i
\(441\) −289.110 333.011i −0.655578 0.755127i
\(442\) −1088.67 −2.46305
\(443\) −394.066 + 227.514i −0.889541 + 0.513576i −0.873792 0.486300i \(-0.838346\pi\)
−0.0157484 + 0.999876i \(0.505013\pi\)
\(444\) −286.316 + 109.898i −0.644856 + 0.247519i
\(445\) −94.9316 + 164.426i −0.213329 + 0.369497i
\(446\) −505.262 + 291.713i −1.13287 + 0.654065i
\(447\) 243.862 301.129i 0.545553 0.673667i
\(448\) −466.967 + 458.618i −1.04234 + 1.02370i
\(449\) 678.117i 1.51028i −0.655562 0.755141i \(-0.727568\pi\)
0.655562 0.755141i \(-0.272432\pi\)
\(450\) −90.9497 101.020i −0.202110 0.224489i
\(451\) 35.9017 62.1835i 0.0796046 0.137879i
\(452\) 564.278 + 325.786i 1.24840 + 0.720766i
\(453\) −74.5283 + 470.477i −0.164522 + 1.03858i
\(454\) 907.804 1.99957
\(455\) −78.8049 + 283.838i −0.173198 + 0.623820i
\(456\) −129.261 + 159.615i −0.283466 + 0.350034i
\(457\) −231.511 400.988i −0.506588 0.877436i −0.999971 0.00762394i \(-0.997573\pi\)
0.493383 0.869812i \(-0.335760\pi\)
\(458\) −271.327 156.651i −0.592418 0.342033i
\(459\) 433.669 281.582i 0.944812 0.613467i
\(460\) 108.496 + 187.920i 0.235860 + 0.408522i
\(461\) 766.505i 1.66270i 0.555749 + 0.831350i \(0.312432\pi\)
−0.555749 + 0.831350i \(0.687568\pi\)
\(462\) 32.3459 70.9167i 0.0700127 0.153499i
\(463\) 102.747 0.221915 0.110958 0.993825i \(-0.464608\pi\)
0.110958 + 0.993825i \(0.464608\pi\)
\(464\) 283.390 163.615i 0.610754 0.352619i
\(465\) −70.5664 183.846i −0.151756 0.395367i
\(466\) −130.501 + 226.034i −0.280044 + 0.485051i
\(467\) 563.725 325.467i 1.20712 0.696931i 0.244990 0.969526i \(-0.421215\pi\)
0.962129 + 0.272595i \(0.0878819\pi\)
\(468\) 180.416 + 848.997i 0.385503 + 1.81410i
\(469\) −74.9030 289.979i −0.159708 0.618293i
\(470\) 320.996i 0.682970i
\(471\) 18.9566 119.668i 0.0402476 0.254072i
\(472\) −43.8624 + 75.9720i −0.0929289 + 0.160958i
\(473\) −61.6511 35.5943i −0.130341 0.0752522i
\(474\) −559.889 88.6920i −1.18120 0.187114i
\(475\) −100.788 −0.212186
\(476\) −183.772 + 661.907i −0.386076 + 1.39056i
\(477\) 32.5801 6.92342i 0.0683022 0.0145145i
\(478\) −25.9779 44.9951i −0.0543471 0.0941320i
\(479\) −293.202 169.280i −0.612112 0.353403i 0.161680 0.986843i \(-0.448309\pi\)
−0.773792 + 0.633440i \(0.781642\pi\)
\(480\) −278.764 + 106.999i −0.580758 + 0.222915i
\(481\) 187.719 + 325.139i 0.390269 + 0.675965i
\(482\) 425.296i 0.882357i
\(483\) 37.9900 + 395.862i 0.0786542 + 0.819589i
\(484\) −612.314 −1.26511
\(485\) −259.304 + 149.709i −0.534646 + 0.308678i
\(486\) −518.966 519.096i −1.06783 1.06810i
\(487\) −108.262 + 187.515i −0.222304 + 0.385042i −0.955507 0.294968i \(-0.904691\pi\)
0.733203 + 0.680010i \(0.238024\pi\)
\(488\) −246.464 + 142.296i −0.505049 + 0.291590i
\(489\) 466.806 + 378.031i 0.954613 + 0.773070i
\(490\) 283.593 + 170.626i 0.578761 + 0.348217i
\(491\) 653.638i 1.33124i 0.746292 + 0.665619i \(0.231832\pi\)
−0.746292 + 0.665619i \(0.768168\pi\)
\(492\) 887.277 + 140.554i 1.80341 + 0.285678i
\(493\) 306.043 530.083i 0.620778 1.07522i
\(494\) 992.396 + 572.960i 2.00890 + 1.15984i
\(495\) 18.3776 16.5456i 0.0371264 0.0334254i
\(496\) −300.548 −0.605943
\(497\) −3.82201 3.89159i −0.00769016 0.00783015i
\(498\) −532.068 430.882i −1.06841 0.865225i
\(499\) −207.790 359.902i −0.416412 0.721247i 0.579164 0.815211i \(-0.303379\pi\)
−0.995576 + 0.0939646i \(0.970046\pi\)
\(500\) 49.6167 + 28.6462i 0.0992334 + 0.0572924i
\(501\) −47.5370 123.847i −0.0948843 0.247201i
\(502\) −303.778 526.159i −0.605135 1.04813i
\(503\) 319.315i 0.634820i 0.948288 + 0.317410i \(0.102813\pi\)
−0.948288 + 0.317410i \(0.897187\pi\)
\(504\) 213.570 + 13.1361i 0.423750 + 0.0260637i
\(505\) −238.099 −0.471483
\(506\) −60.8716 + 35.1442i −0.120300 + 0.0694550i
\(507\) 518.648 199.076i 1.02297 0.392654i
\(508\) −94.3273 + 163.380i −0.185684 + 0.321613i
\(509\) 384.362 221.911i 0.755131 0.435975i −0.0724140 0.997375i \(-0.523070\pi\)
0.827545 + 0.561400i \(0.189737\pi\)
\(510\) −244.217 + 301.567i −0.478856 + 0.591308i
\(511\) 15.2425 + 59.0097i 0.0298287 + 0.115479i
\(512\) 594.810i 1.16174i
\(513\) −543.513 + 28.4435i −1.05948 + 0.0554454i
\(514\) −419.200 + 726.075i −0.815563 + 1.41260i
\(515\) −127.115 73.3899i −0.246825 0.142505i
\(516\) 139.350 879.680i 0.270058 1.70481i
\(517\) 58.3956 0.112951
\(518\) 408.414 105.495i 0.788444 0.203659i
\(519\) 257.925 318.495i 0.496966 0.613671i
\(520\) −71.4640 123.779i −0.137431 0.238037i
\(521\) 398.036 + 229.806i 0.763985 + 0.441087i 0.830725 0.556683i \(-0.187926\pi\)
−0.0667394 + 0.997770i \(0.521260\pi\)
\(522\) −826.371 268.550i −1.58309 0.514463i
\(523\) −152.912 264.851i −0.292375 0.506408i 0.681996 0.731356i \(-0.261112\pi\)
−0.974371 + 0.224948i \(0.927779\pi\)
\(524\) 895.070i 1.70815i
\(525\) 60.9466 + 85.5015i 0.116089 + 0.162860i
\(526\) −414.870 −0.788727
\(527\) −486.859 + 281.088i −0.923831 + 0.533374i
\(528\) −13.5242 35.2344i −0.0256140 0.0667318i
\(529\) −85.1919 + 147.557i −0.161043 + 0.278935i
\(530\) −21.6481 + 12.4985i −0.0408454 + 0.0235821i
\(531\) −227.381 + 48.3195i −0.428213 + 0.0909972i
\(532\) 515.879 506.655i 0.969697 0.952359i
\(533\) 1099.74i 2.06330i
\(534\) 120.387 759.971i 0.225444 1.42317i
\(535\) 55.8691 96.7681i 0.104428 0.180875i
\(536\) 125.848 + 72.6581i 0.234790 + 0.135556i
\(537\) −528.832 83.7723i −0.984790 0.156001i
\(538\) 546.670 1.01611
\(539\) −31.0403 + 51.5912i −0.0575888 + 0.0957165i
\(540\) 275.648 + 140.476i 0.510460 + 0.260140i
\(541\) 369.076 + 639.258i 0.682211 + 1.18162i 0.974305 + 0.225234i \(0.0723147\pi\)
−0.292094 + 0.956390i \(0.594352\pi\)
\(542\) −60.3662 34.8524i −0.111377 0.0643034i
\(543\) 1005.56 385.968i 1.85185 0.710806i
\(544\) 426.212 + 738.221i 0.783478 + 1.35702i
\(545\) 457.251i 0.838993i
\(546\) −114.043 1188.35i −0.208870 2.17646i
\(547\) 875.414 1.60039 0.800196 0.599739i \(-0.204729\pi\)
0.800196 + 0.599739i \(0.204729\pi\)
\(548\) 1148.87 663.303i 2.09649 1.21041i
\(549\) −717.208 233.075i −1.30639 0.424544i
\(550\) −9.27917 + 16.0720i −0.0168712 + 0.0292218i
\(551\) −557.958 + 322.137i −1.01263 + 0.584641i
\(552\) −149.951 121.434i −0.271651 0.219989i
\(553\) 421.923 + 117.143i 0.762972 + 0.211832i
\(554\) 353.560i 0.638195i
\(555\) 132.175 + 20.9379i 0.238154 + 0.0377260i
\(556\) −550.064 + 952.739i −0.989324 + 1.71356i
\(557\) −295.072 170.360i −0.529753 0.305853i 0.211163 0.977451i \(-0.432275\pi\)
−0.740916 + 0.671598i \(0.765608\pi\)
\(558\) 533.977 + 593.101i 0.956947 + 1.06290i
\(559\) −1090.32 −1.95049
\(560\) 155.160 40.0786i 0.277072 0.0715689i
\(561\) −54.8610 44.4279i −0.0977915 0.0791941i
\(562\) −823.840 1426.93i −1.46591 2.53903i
\(563\) −296.094 170.950i −0.525923 0.303642i 0.213432 0.976958i \(-0.431536\pi\)
−0.739355 + 0.673316i \(0.764869\pi\)
\(564\) 261.804 + 682.075i 0.464192 + 1.20935i
\(565\) −142.159 246.227i −0.251609 0.435800i
\(566\) 98.5096i 0.174045i
\(567\) 352.791 + 443.878i 0.622207 + 0.782853i
\(568\) 2.64656 0.00465943
\(569\) −615.104 + 355.130i −1.08103 + 0.624131i −0.931173 0.364578i \(-0.881213\pi\)
−0.149853 + 0.988708i \(0.547880\pi\)
\(570\) 381.333 146.369i 0.669005 0.256788i
\(571\) −13.7983 + 23.8993i −0.0241651 + 0.0418552i −0.877855 0.478926i \(-0.841026\pi\)
0.853690 + 0.520782i \(0.174359\pi\)
\(572\) 102.625 59.2505i 0.179414 0.103585i
\(573\) 99.3825 122.721i 0.173442 0.214173i
\(574\) −1190.56 330.549i −2.07415 0.575869i
\(575\) 94.6858i 0.164671i
\(576\) 625.398 563.054i 1.08576 0.977525i
\(577\) −144.408 + 250.122i −0.250274 + 0.433488i −0.963601 0.267344i \(-0.913854\pi\)
0.713327 + 0.700831i \(0.247187\pi\)
\(578\) 203.377 + 117.420i 0.351863 + 0.203148i
\(579\) −32.6424 + 206.063i −0.0563773 + 0.355895i
\(580\) 366.234 0.631438
\(581\) 370.579 + 377.325i 0.637829 + 0.649440i
\(582\) 763.662 942.996i 1.31213 1.62027i
\(583\) −2.27373 3.93821i −0.00390005 0.00675508i
\(584\) −25.6095 14.7856i −0.0438518 0.0253179i
\(585\) 117.055 360.196i 0.200094 0.615720i
\(586\) −272.432 471.866i −0.464901 0.805232i
\(587\) 942.812i 1.60615i −0.595876 0.803077i \(-0.703195\pi\)
0.595876 0.803077i \(-0.296805\pi\)
\(588\) −741.761 131.260i −1.26150 0.223232i
\(589\) 591.740 1.00465
\(590\) 151.085 87.2289i 0.256076 0.147846i
\(591\) 56.8596 + 148.135i 0.0962091 + 0.250652i
\(592\) 102.122 176.880i 0.172503 0.298784i
\(593\) 414.204 239.141i 0.698489 0.403273i −0.108295 0.994119i \(-0.534539\pi\)
0.806784 + 0.590846i \(0.201206\pi\)
\(594\) −45.5034 + 89.2889i −0.0766050 + 0.150318i
\(595\) 213.861 210.038i 0.359431 0.353004i
\(596\) 661.882i 1.11054i
\(597\) 26.0470 164.427i 0.0436298 0.275423i
\(598\) −538.269 + 932.309i −0.900115 + 1.55905i
\(599\) 745.356 + 430.332i 1.24433 + 0.718417i 0.969974 0.243210i \(-0.0782005\pi\)
0.274360 + 0.961627i \(0.411534\pi\)
\(600\) −50.3187 7.97098i −0.0838644 0.0132850i
\(601\) 29.3420 0.0488219 0.0244109 0.999702i \(-0.492229\pi\)
0.0244109 + 0.999702i \(0.492229\pi\)
\(602\) −327.718 + 1180.37i −0.544383 + 1.96075i
\(603\) 80.0413 + 376.657i 0.132738 + 0.624638i
\(604\) 406.829 + 704.648i 0.673558 + 1.16664i
\(605\) 231.392 + 133.594i 0.382466 + 0.220817i
\(606\) 900.848 345.777i 1.48655 0.570589i
\(607\) −27.9096 48.3409i −0.0459796 0.0796390i 0.842120 0.539291i \(-0.181308\pi\)
−0.888099 + 0.459652i \(0.847974\pi\)
\(608\) 897.251i 1.47574i
\(609\) 610.675 + 278.536i 1.00275 + 0.457365i
\(610\) 565.966 0.927813
\(611\) 774.561 447.193i 1.26769 0.731903i
\(612\) 272.970 839.974i 0.446030 1.37251i
\(613\) −53.4478 + 92.5743i −0.0871906 + 0.151019i −0.906323 0.422587i \(-0.861122\pi\)
0.819132 + 0.573605i \(0.194456\pi\)
\(614\) −1035.94 + 598.099i −1.68719 + 0.974102i
\(615\) −304.634 246.700i −0.495339 0.401138i
\(616\) −7.30620 28.2852i −0.0118607 0.0459175i
\(617\) 965.247i 1.56442i 0.623015 + 0.782210i \(0.285908\pi\)
−0.623015 + 0.782210i \(0.714092\pi\)
\(618\) 587.520 + 93.0691i 0.950680 + 0.150597i
\(619\) −16.9218 + 29.3094i −0.0273373 + 0.0473496i −0.879370 0.476138i \(-0.842036\pi\)
0.852033 + 0.523488i \(0.175369\pi\)
\(620\) −291.306 168.185i −0.469848 0.271267i
\(621\) −26.7213 510.605i −0.0430295 0.822230i
\(622\) 392.572 0.631145
\(623\) −159.005 + 572.702i −0.255225 + 0.919265i
\(624\) −449.211 363.782i −0.719889 0.582984i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 552.593 + 319.040i 0.882736 + 0.509648i
\(627\) 26.6274 + 69.3720i 0.0424680 + 0.110641i
\(628\) −103.479 179.230i −0.164775 0.285398i
\(629\) 382.039i 0.607375i
\(630\) −354.761 234.986i −0.563112 0.372994i
\(631\) 685.963 1.08710 0.543552 0.839375i \(-0.317079\pi\)
0.543552 + 0.839375i \(0.317079\pi\)
\(632\) −183.997 + 106.231i −0.291134 + 0.168087i
\(633\) −490.086 + 188.112i −0.774228 + 0.297176i
\(634\) 701.459 1214.96i 1.10640 1.91634i
\(635\) 71.2920 41.1604i 0.112271 0.0648196i
\(636\) 35.8055 44.2139i 0.0562980 0.0695187i
\(637\) −16.6349 + 922.015i −0.0261145 + 1.44743i
\(638\) 118.632i 0.185943i
\(639\) 4.69235 + 5.21191i 0.00734328 + 0.00815635i
\(640\) −116.713 + 202.152i −0.182364 + 0.315863i
\(641\) −420.859 242.983i −0.656566 0.379068i 0.134401 0.990927i \(-0.457089\pi\)
−0.790967 + 0.611858i \(0.790422\pi\)
\(642\) −70.8502 + 447.258i −0.110359 + 0.696664i
\(643\) −31.0066 −0.0482217 −0.0241109 0.999709i \(-0.507675\pi\)
−0.0241109 + 0.999709i \(0.507675\pi\)
\(644\) 475.979 + 484.644i 0.739097 + 0.752552i
\(645\) −244.588 + 302.025i −0.379205 + 0.468256i
\(646\) −583.034 1009.84i −0.902529 1.56323i
\(647\) −160.897 92.8937i −0.248681 0.143576i 0.370479 0.928841i \(-0.379193\pi\)
−0.619160 + 0.785265i \(0.712527\pi\)
\(648\) −273.599 28.7840i −0.422221 0.0444198i
\(649\) 15.8687 + 27.4853i 0.0244510 + 0.0423503i
\(650\) 284.239i 0.437292i
\(651\) −357.825 501.990i −0.549654 0.771106i
\(652\) 1026.04 1.57368
\(653\) −788.464 + 455.220i −1.20745 + 0.697121i −0.962201 0.272340i \(-0.912202\pi\)
−0.245247 + 0.969461i \(0.578869\pi\)
\(654\) 664.039 + 1730.01i 1.01535 + 2.64528i
\(655\) 195.285 338.244i 0.298146 0.516403i
\(656\) −518.121 + 299.137i −0.789818 + 0.456002i
\(657\) −16.2881 76.6482i −0.0247916 0.116664i
\(658\) −251.316 972.942i −0.381938 1.47864i
\(659\) 174.971i 0.265509i 0.991149 + 0.132755i \(0.0423822\pi\)
−0.991149 + 0.132755i \(0.957618\pi\)
\(660\) 6.60871 41.7190i 0.0100132 0.0632106i
\(661\) −70.4654 + 122.050i −0.106604 + 0.184644i −0.914392 0.404829i \(-0.867331\pi\)
0.807788 + 0.589473i \(0.200664\pi\)
\(662\) −1503.33 867.947i −2.27089 1.31110i
\(663\) −1067.91 169.167i −1.61072 0.255154i
\(664\) −256.608 −0.386457
\(665\) −305.490 + 78.9096i −0.459384 + 0.118661i
\(666\) −530.493 + 112.732i −0.796536 + 0.169267i
\(667\) −302.633 524.176i −0.453723 0.785870i
\(668\) −196.238 113.298i −0.293769 0.169608i
\(669\) −540.955 + 207.638i −0.808602 + 0.310370i
\(670\) −144.495 250.272i −0.215663 0.373540i
\(671\) 102.961i 0.153443i
\(672\) −761.163 + 542.567i −1.13268 + 0.807392i
\(673\) 115.134 0.171076 0.0855382 0.996335i \(-0.472739\pi\)
0.0855382 + 0.996335i \(0.472739\pi\)
\(674\) −636.248 + 367.338i −0.943987 + 0.545011i
\(675\) −73.5178 113.226i −0.108915 0.167742i
\(676\) 474.469 821.805i 0.701878 1.21569i
\(677\) 579.837 334.769i 0.856481 0.494489i −0.00635162 0.999980i \(-0.502022\pi\)
0.862832 + 0.505491i \(0.168688\pi\)
\(678\) 895.442 + 725.151i 1.32071 + 1.06954i
\(679\) −668.741 + 656.785i −0.984891 + 0.967282i
\(680\) 145.441i 0.213884i
\(681\) 890.491 + 141.063i 1.30762 + 0.207140i
\(682\) 54.4791 94.3606i 0.0798814 0.138359i
\(683\) 441.858 + 255.107i 0.646937 + 0.373509i 0.787282 0.616594i \(-0.211488\pi\)
−0.140345 + 0.990103i \(0.544821\pi\)
\(684\) −690.904 + 622.030i −1.01009 + 0.909401i
\(685\) −578.875 −0.845073
\(686\) 993.161 + 295.139i 1.44776 + 0.430231i
\(687\) −241.811 195.825i −0.351981 0.285043i
\(688\) 296.576 + 513.684i 0.431069 + 0.746634i
\(689\) −60.3176 34.8244i −0.0875438 0.0505434i
\(690\) 137.507 + 358.244i 0.199285 + 0.519194i
\(691\) 491.747 + 851.731i 0.711646 + 1.23261i 0.964239 + 0.265034i \(0.0853833\pi\)
−0.252593 + 0.967573i \(0.581283\pi\)
\(692\) 700.052i 1.01164i
\(693\) 42.7487 64.5380i 0.0616864 0.0931285i
\(694\) 915.039 1.31850
\(695\) 415.735 240.025i 0.598180 0.345359i
\(696\) −304.038 + 116.701i −0.436836 + 0.167673i
\(697\) −559.538 + 969.148i −0.802780 + 1.39046i
\(698\) 238.081 137.456i 0.341091 0.196929i
\(699\) −163.135 + 201.445i −0.233383 + 0.288190i
\(700\) 172.817 + 47.9809i 0.246881 + 0.0685441i
\(701\) 996.536i 1.42159i −0.703398 0.710796i \(-0.748335\pi\)
0.703398 0.710796i \(-0.251665\pi\)
\(702\) 80.2153 + 1532.80i 0.114267 + 2.18347i
\(703\) −201.065 + 348.254i −0.286010 + 0.495383i
\(704\) −99.4990 57.4458i −0.141334 0.0815991i
\(705\) 49.8792 314.874i 0.0707507 0.446630i
\(706\) −670.285 −0.949413
\(707\) −721.680 + 186.413i −1.02076 + 0.263668i
\(708\) −249.892 + 308.575i −0.352954 + 0.435840i
\(709\) −326.743 565.936i −0.460851 0.798217i 0.538153 0.842847i \(-0.319122\pi\)
−0.999004 + 0.0446304i \(0.985789\pi\)
\(710\) −4.55805 2.63159i −0.00641979 0.00370647i
\(711\) −535.429 174.001i −0.753065 0.244727i
\(712\) −144.193 249.750i −0.202519 0.350773i
\(713\) 555.912i 0.779680i
\(714\) −504.119 + 1105.26i −0.706049 + 1.54798i
\(715\) −51.7088 −0.0723200
\(716\) −792.048 + 457.289i −1.10621 + 0.638672i
\(717\) −18.4908 48.1737i −0.0257891 0.0671878i
\(718\) −836.669 + 1449.15i −1.16528 + 2.01832i
\(719\) 465.382 268.688i 0.647262 0.373697i −0.140144 0.990131i \(-0.544757\pi\)
0.787407 + 0.616434i \(0.211423\pi\)
\(720\) −201.539 + 42.8279i −0.279915 + 0.0594832i
\(721\) −442.746 122.924i −0.614072 0.170491i
\(722\) 136.929i 0.189653i
\(723\) 66.0863 417.185i 0.0914057 0.577020i
\(724\) 919.901 1593.32i 1.27058 2.20071i
\(725\) −138.399 79.9045i −0.190895 0.110213i
\(726\) −1069.48 169.417i −1.47312 0.233356i
\(727\) 871.976 1.19942 0.599708 0.800219i \(-0.295283\pi\)
0.599708 + 0.800219i \(0.295283\pi\)
\(728\) −313.518 319.225i −0.430656 0.438496i
\(729\) −428.407 589.838i −0.587664 0.809105i
\(730\) 29.4041 + 50.9293i 0.0402795 + 0.0697662i
\(731\) 960.849 + 554.747i 1.31443 + 0.758887i
\(732\) −1202.60 + 461.602i −1.64290 + 0.630604i
\(733\) −351.349 608.555i −0.479330 0.830224i 0.520389 0.853930i \(-0.325787\pi\)
−0.999719 + 0.0237050i \(0.992454\pi\)
\(734\) 1289.28i 1.75651i
\(735\) 251.671 + 211.440i 0.342410 + 0.287673i
\(736\) 842.925 1.14528
\(737\) 45.5294 26.2864i 0.0617767 0.0356668i
\(738\) 1510.85 + 490.988i 2.04722 + 0.665296i
\(739\) 99.5025 172.343i 0.134645 0.233212i −0.790817 0.612053i \(-0.790344\pi\)
0.925462 + 0.378841i \(0.123677\pi\)
\(740\) 197.963 114.294i 0.267518 0.154451i
\(741\) 884.438 + 716.240i 1.19357 + 0.966586i
\(742\) −55.8301 + 54.8319i −0.0752427 + 0.0738975i
\(743\) 845.338i 1.13774i 0.822429 + 0.568868i \(0.192619\pi\)
−0.822429 + 0.568868i \(0.807381\pi\)
\(744\) 295.427 + 46.7986i 0.397079 + 0.0629013i
\(745\) −144.409 + 250.123i −0.193837 + 0.335736i
\(746\) 89.2254 + 51.5143i 0.119605 + 0.0690540i
\(747\) −454.967 505.342i −0.609058 0.676496i
\(748\) −120.584 −0.161209
\(749\) 93.5778 337.047i 0.124937 0.449995i
\(750\) 78.7358 + 63.7622i 0.104981 + 0.0850163i
\(751\) 183.645 + 318.083i 0.244534 + 0.423545i 0.962000 0.273048i \(-0.0880317\pi\)
−0.717467 + 0.696593i \(0.754698\pi\)
\(752\) −421.372 243.279i −0.560335 0.323510i
\(753\) −216.225 563.328i −0.287152 0.748112i
\(754\) 908.481 + 1573.53i 1.20488 + 2.08692i
\(755\) 355.046i 0.470259i
\(756\) 945.475 + 209.972i 1.25063 + 0.277741i
\(757\) 883.400 1.16697 0.583487 0.812122i \(-0.301688\pi\)
0.583487 + 0.812122i \(0.301688\pi\)
\(758\) −958.562 + 553.426i −1.26459 + 0.730113i
\(759\) −65.1717 + 25.0152i −0.0858653 + 0.0329581i
\(760\) 76.5446 132.579i 0.100717 0.174446i
\(761\) 401.326 231.706i 0.527367 0.304475i −0.212577 0.977144i \(-0.568186\pi\)
0.739944 + 0.672669i \(0.234852\pi\)
\(762\) −209.958 + 259.264i −0.275536 + 0.340241i
\(763\) −357.993 1385.93i −0.469191 1.81643i
\(764\) 269.740i 0.353063i
\(765\) −286.419 +