Properties

Label 105.3.t.b.86.2
Level 105
Weight 3
Character 105.86
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 86.2
Character \(\chi\) \(=\) 105.86
Dual form 105.3.t.b.11.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.61597 - 1.51033i) q^{2} +(-0.469377 + 2.96305i) q^{3} +(2.56220 + 4.43785i) q^{4} +(1.93649 + 1.11803i) q^{5} +(5.70307 - 7.04234i) q^{6} +(-4.99419 - 4.90490i) q^{7} -3.39641i q^{8} +(-8.55937 - 2.78158i) q^{9} +O(q^{10})\) \(q+(-2.61597 - 1.51033i) q^{2} +(-0.469377 + 2.96305i) 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} +(-8.55937 - 2.78158i) q^{9} +(-3.37720 - 5.84948i) q^{10} +(1.06414 - 0.614380i) q^{11} +(-14.3522 + 5.50889i) 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} +(18.1899 + 20.2040i) q^{18} +(-10.0788 + 17.4570i) q^{19} +11.4585i q^{20} +(16.8776 - 12.4958i) q^{21} -3.71167 q^{22} +(-16.4001 - 9.46858i) q^{23} +(10.0637 + 1.59420i) 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} +(18.9175 - 7.26121i) q^{30} +(-14.6778 - 25.4227i) q^{31} +(-38.5482 + 22.2558i) q^{32} +(1.32096 + 3.44147i) 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} +(8.83354 - 55.7637i) q^{39} +(3.79730 - 6.57711i) q^{40} +58.4356i q^{41} +(-63.0242 + 7.19783i) q^{42} +57.9352 q^{43} +(5.45306 + 3.14833i) q^{44} +(-13.4652 - 14.9562i) 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} +(-20.5875 - 53.6363i) q^{51} +(-48.2197 - 83.5190i) q^{52} +(-3.20503 + 1.85042i) q^{53} +(-68.4035 + 44.4145i) 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} +(-33.9521 - 5.37835i) q^{60} +(-41.8961 + 72.5661i) q^{61} +88.6733i q^{62} +(29.1038 + 55.8746i) q^{63} +93.5020 q^{64} +(-36.4442 - 21.0411i) q^{65} +(1.74217 - 10.9979i) 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} +(-9.44738 + 29.0711i) q^{72} +(4.35332 + 7.54017i) q^{73} +(52.1866 - 30.1299i) q^{74} +(-14.0038 + 5.37517i) 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} +(65.5256 + 47.6171i) q^{81} +(88.2571 - 152.866i) q^{82} -75.5527i q^{83} +(98.6984 + 42.8838i) q^{84} -42.8220 q^{85} +(-151.557 - 87.5014i) q^{86} +(94.7045 + 15.0021i) 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} +(82.2182 - 31.5583i) q^{93} +(-71.7769 - 124.321i) q^{94} +(-39.0351 + 22.5369i) q^{95} +(-47.8516 - 124.667i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 \(-0.605777\pi\)
−0.981760 + 0.190127i \(0.939110\pi\)
\(3\) −0.469377 + 2.96305i −0.156459 + 0.987684i
\(4\) 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
\(9\) −8.55937 2.78158i −0.951041 0.309064i
\(10\) −3.37720 5.84948i −0.337720 0.584948i
\(11\) 1.06414 0.614380i 0.0967398 0.0558528i −0.450850 0.892600i \(-0.648879\pi\)
0.547589 + 0.836747i \(0.315546\pi\)
\(12\) −14.3522 + 5.50889i −1.19602 + 0.459075i
\(13\) −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 \(-0.857117\pi\)
−0.0746481 + 0.997210i \(0.523783\pi\)
\(18\) 18.1899 + 20.2040i 1.01055 + 1.12244i
\(19\) −10.0788 + 17.4570i −0.530464 + 0.918791i 0.468904 + 0.883249i \(0.344649\pi\)
−0.999368 + 0.0355421i \(0.988684\pi\)
\(20\) 11.4585i 0.572924i
\(21\) 16.8776 12.4958i 0.803697 0.595038i
\(22\) −3.71167 −0.168712
\(23\) −16.4001 9.46858i −0.713046 0.411677i 0.0991417 0.995073i \(-0.468390\pi\)
−0.812188 + 0.583396i \(0.801724\pi\)
\(24\) 10.0637 + 1.59420i 0.419322 + 0.0664248i
\(25\) 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 \(-0.185779\pi\)
\(30\) 18.9175 7.26121i 0.630584 0.242040i
\(31\) −14.6778 25.4227i −0.473477 0.820087i 0.526062 0.850446i \(-0.323668\pi\)
−0.999539 + 0.0303595i \(0.990335\pi\)
\(32\) −38.5482 + 22.2558i −1.20463 + 0.695495i
\(33\) 1.32096 + 3.44147i 0.0400291 + 0.104287i
\(34\) 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 −0.968754 0.248022i \(-0.920220\pi\)
0.699170 + 0.714955i \(0.253553\pi\)
\(38\) 52.7318 30.4447i 1.38768 0.801177i
\(39\) 8.83354 55.7637i 0.226501 1.42984i
\(40\) 3.79730 6.57711i 0.0949324 0.164428i
\(41\) 58.4356i 1.42526i 0.701541 + 0.712629i \(0.252496\pi\)
−0.701541 + 0.712629i \(0.747504\pi\)
\(42\) −63.0242 + 7.19783i −1.50058 + 0.171377i
\(43\) 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
\(45\) −13.4652 14.9562i −0.299228 0.332359i
\(46\) 28.6014 + 49.5390i 0.621769 + 1.07694i
\(47\) 41.1569 + 23.7620i 0.875680 + 0.505574i 0.869232 0.494405i \(-0.164614\pi\)
0.00644823 + 0.999979i \(0.497947\pi\)
\(48\) 23.8692 + 19.3299i 0.497275 + 0.402706i
\(49\) 0.883910 + 48.9920i 0.0180390 + 0.999837i
\(50\) 15.1033i 0.302066i
\(51\) −20.5875 53.6363i −0.403677 1.05169i
\(52\) −48.2197 83.5190i −0.927302 1.60614i
\(53\) −3.20503 + 1.85042i −0.0604722 + 0.0349137i −0.529931 0.848041i \(-0.677782\pi\)
0.469459 + 0.882954i \(0.344449\pi\)
\(54\) −68.4035 + 44.4145i −1.26673 + 0.822490i
\(55\) 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 \(-0.596424\pi\)
0.677437 + 0.735581i \(0.263091\pi\)
\(60\) −33.9521 5.37835i −0.565869 0.0896392i
\(61\) −41.8961 + 72.5661i −0.686821 + 1.18961i 0.286040 + 0.958218i \(0.407661\pi\)
−0.972861 + 0.231391i \(0.925672\pi\)
\(62\) 88.6733i 1.43021i
\(63\) 29.1038 + 55.8746i 0.461965 + 0.886898i
\(64\) 93.5020 1.46097
\(65\) −36.4442 21.0411i −0.560680 0.323708i
\(66\) 1.74217 10.9979i 0.0263966 0.166634i
\(67\) −21.3926 37.0531i −0.319293 0.553032i 0.661048 0.750344i \(-0.270112\pi\)
−0.980341 + 0.197312i \(0.936779\pi\)
\(68\) −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 \(0.998253\pi\)
\(72\) −9.44738 + 29.0711i −0.131214 + 0.403765i
\(73\) 4.35332 + 7.54017i 0.0596345 + 0.103290i 0.894301 0.447465i \(-0.147673\pi\)
−0.834667 + 0.550755i \(0.814340\pi\)
\(74\) 52.1866 30.1299i 0.705224 0.407161i
\(75\) −14.0038 + 5.37517i −0.186718 + 0.0716689i
\(76\) −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 −0.993218 0.116270i \(-0.962906\pi\)
0.597301 + 0.802017i \(0.296240\pi\)
\(80\) 19.8261 11.4466i 0.247827 0.143083i
\(81\) 65.5256 + 47.6171i 0.808958 + 0.587866i
\(82\) 88.2571 152.866i 1.07631 1.86422i
\(83\) 75.5527i 0.910274i −0.890421 0.455137i \(-0.849590\pi\)
0.890421 0.455137i \(-0.150410\pi\)
\(84\) 98.6984 + 42.8838i 1.17498 + 0.510521i
\(85\) −42.8220 −0.503788
\(86\) −151.557 87.5014i −1.76229 1.01746i
\(87\) 94.7045 + 15.0021i 1.08856 + 0.172438i
\(88\) −2.08668 3.61424i −0.0237123 0.0410710i
\(89\) −73.5337 42.4547i −0.826221 0.477019i 0.0263360 0.999653i \(-0.491616\pi\)
−0.852557 + 0.522634i \(0.824949\pi\)
\(90\) 12.6359 + 59.4619i 0.140399 + 0.660687i
\(91\) 93.9891 + 92.3087i 1.03285 + 1.01438i
\(92\) 97.0414i 1.05480i
\(93\) 82.2182 31.5583i 0.884067 0.339336i
\(94\) −71.7769 124.321i −0.763584 1.32257i
\(95\) −39.0351 + 22.5369i −0.410896 + 0.237231i
\(96\) −47.8516 124.667i −0.498454 1.29861i
\(97\) 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 \(-0.843400\pi\)
−0.0316200 + 0.999500i \(0.510067\pi\)
\(102\) −27.1523 + 171.405i −0.266199 + 1.68044i
\(103\) 32.8210 56.8476i 0.318650 0.551918i −0.661556 0.749895i \(-0.730104\pi\)
0.980207 + 0.197977i \(0.0634372\pi\)
\(104\) 63.9193i 0.614609i
\(105\) 46.6542 5.32825i 0.444325 0.0507453i
\(106\) 11.1790 0.105462
\(107\) 43.2760 + 24.9854i 0.404449 + 0.233509i 0.688402 0.725330i \(-0.258313\pi\)
−0.283953 + 0.958838i \(0.591646\pi\)
\(108\) 138.170 7.23078i 1.27935 0.0669517i
\(109\) −102.244 177.093i −0.938022 1.62470i −0.769154 0.639064i \(-0.779322\pi\)
−0.168868 0.985639i \(-0.554011\pi\)
\(110\) −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 \(0.809795\pi\)
\(114\) 65.4582 + 170.537i 0.574195 + 1.49594i
\(115\) −21.1724 36.6717i −0.184108 0.318884i
\(116\) 141.842 81.8924i 1.22277 0.705969i
\(117\) 161.085 + 52.3485i 1.37679 + 0.447423i
\(118\) −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
\(123\) −173.148 27.4284i −1.40771 0.222995i
\(124\) 75.2148 130.276i 0.606571 1.05061i
\(125\) 11.1803i 0.0894427i
\(126\) 8.25456 190.123i 0.0655124 1.50891i
\(127\) −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
\(129\) −27.1935 + 171.665i −0.210802 + 1.33074i
\(130\) 63.5579 + 110.085i 0.488907 + 0.846811i
\(131\) 151.267 + 87.3343i 1.15471 + 0.666674i 0.950031 0.312155i \(-0.101051\pi\)
0.204682 + 0.978829i \(0.434384\pi\)
\(132\) −11.8882 + 14.6800i −0.0900621 + 0.111212i
\(133\) 135.961 37.7482i 1.02226 0.283821i
\(134\) 129.240i 0.964476i
\(135\) 50.6362 32.8782i 0.375083 0.243542i
\(136\) 32.5216 + 56.3290i 0.239129 + 0.414184i
\(137\) −224.197 + 129.440i −1.63648 + 0.944820i −0.654444 + 0.756111i \(0.727097\pi\)
−0.982033 + 0.188709i \(0.939570\pi\)
\(138\) −160.212 + 61.4949i −1.16095 + 0.445615i
\(139\) −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
\(144\) −68.4791 + 61.6527i −0.475549 + 0.428144i
\(145\) 35.7344 61.8938i 0.246444 0.426854i
\(146\) 26.2998i 0.180136i
\(147\) −145.581 20.3767i −0.990346 0.138617i
\(148\) −102.228 −0.690728
\(149\) −111.858 64.5815i −0.750727 0.433433i 0.0752293 0.997166i \(-0.476031\pi\)
−0.825957 + 0.563734i \(0.809364\pi\)
\(150\) 44.7519 + 7.08915i 0.298346 + 0.0472610i
\(151\) −79.3906 137.509i −0.525766 0.910653i −0.999550 0.0300119i \(-0.990445\pi\)
0.473784 0.880641i \(-0.342888\pi\)
\(152\) 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
\(156\) 270.105 103.676i 1.73144 0.664588i
\(157\) 20.1933 + 34.9759i 0.128620 + 0.222776i 0.923142 0.384459i \(-0.125612\pi\)
−0.794522 + 0.607235i \(0.792279\pi\)
\(158\) 163.641 94.4784i 1.03570 0.597964i
\(159\) −3.97854 10.3652i −0.0250223 0.0651901i
\(160\) −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 −0.376335 0.926484i \(-0.622816\pi\)
0.990526 0.137326i \(-0.0438509\pi\)
\(164\) −259.329 + 149.723i −1.58127 + 0.912948i
\(165\) −1.28966 + 8.14126i −0.00781611 + 0.0493410i
\(166\) −114.110 + 197.644i −0.687407 + 1.19062i
\(167\) 44.2191i 0.264785i −0.991197 0.132393i \(-0.957734\pi\)
0.991197 0.132393i \(-0.0422659\pi\)
\(168\) −42.4408 57.3233i −0.252624 0.341210i
\(169\) 185.181 1.09574
\(170\) 112.021 + 64.6753i 0.658947 + 0.380443i
\(171\) 134.827 121.386i 0.788459 0.709861i
\(172\) 148.441 + 257.108i 0.863032 + 1.49481i
\(173\) −118.309 68.3058i −0.683868 0.394831i 0.117443 0.993080i \(-0.462530\pi\)
−0.801311 + 0.598248i \(0.795864\pi\)
\(174\) −225.086 182.280i −1.29360 1.04759i
\(175\) 8.75336 33.8877i 0.0500192 0.193644i
\(176\) 12.5803i 0.0714788i
\(177\) 27.7668 + 72.3403i 0.156874 + 0.408702i
\(178\) 128.241 + 222.120i 0.720456 + 1.24787i
\(179\) 154.564 89.2377i 0.863488 0.498535i −0.00169111 0.999999i \(-0.500538\pi\)
0.865179 + 0.501464i \(0.167205\pi\)
\(180\) 31.8727 98.0774i 0.177071 0.544875i
\(181\) 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
\(186\) −262.744 41.6212i −1.41260 0.223770i
\(187\) −11.7657 + 20.3788i −0.0629184 + 0.108978i
\(188\) 243.531i 1.29538i
\(189\) −179.220 + 60.0097i −0.948254 + 0.317512i
\(190\) 136.153 0.716594
\(191\) −45.5863 26.3192i −0.238672 0.137797i 0.375894 0.926662i \(-0.377336\pi\)
−0.614566 + 0.788865i \(0.710669\pi\)
\(192\) −43.8877 + 277.051i −0.228582 + 1.44298i
\(193\) −34.7721 60.2270i −0.180166 0.312057i 0.761771 0.647847i \(-0.224330\pi\)
−0.941937 + 0.335790i \(0.890997\pi\)
\(194\) −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 \(0.957140\pi\)
\(198\) 31.7695 + 10.3243i 0.160452 + 0.0521430i
\(199\) 27.7463 + 48.0580i 0.139429 + 0.241497i 0.927280 0.374367i \(-0.122140\pi\)
−0.787852 + 0.615865i \(0.788807\pi\)
\(200\) 14.7069 8.49101i 0.0735343 0.0424551i
\(201\) 119.832 45.9956i 0.596177 0.228834i
\(202\) 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
\(207\) 114.037 + 126.663i 0.550901 + 0.611899i
\(208\) −96.3396 + 166.865i −0.463171 + 0.802236i
\(209\) 24.7689i 0.118512i
\(210\) −130.093 56.5246i −0.619492 0.269165i
\(211\) −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
\(213\) −2.30888 0.365749i −0.0108398 0.00171713i
\(214\) −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
\(219\) −24.3853 + 9.35993i −0.111348 + 0.0427394i
\(220\) 7.03987 + 12.1934i 0.0319994 + 0.0554246i
\(221\) 312.122 180.204i 1.41232 0.815402i
\(222\) 64.7814 + 168.774i 0.291808 + 0.760243i
\(223\) −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 \(-0.896943\pi\)
−0.198509 + 0.980099i \(0.563610\pi\)
\(228\) 48.4847 306.071i 0.212652 1.34242i
\(229\) −51.8598 + 89.8238i −0.226462 + 0.392244i −0.956757 0.290888i \(-0.906049\pi\)
0.730295 + 0.683132i \(0.239383\pi\)
\(230\) 127.909i 0.556127i
\(231\) 10.2830 23.6666i 0.0445150 0.102453i
\(232\) −108.555 −0.467911
\(233\) 74.8292 + 43.2027i 0.321155 + 0.185419i 0.651907 0.758299i \(-0.273969\pi\)
−0.330752 + 0.943718i \(0.607302\pi\)
\(234\) −342.329 380.233i −1.46294 1.62493i
\(235\) 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 \(-0.0114564\pi\)
\(240\) 24.6110 + 64.1187i 0.102546 + 0.267161i
\(241\) 70.3979 + 121.933i 0.292107 + 0.505945i 0.974308 0.225220i \(-0.0723102\pi\)
−0.682200 + 0.731165i \(0.738977\pi\)
\(242\) 312.583 180.470i 1.29166 0.745742i
\(243\) −171.848 + 171.805i −0.707195 + 0.707019i
\(244\) −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
\(249\) 223.867 + 35.4627i 0.899063 + 0.142421i
\(250\) 16.8860 29.2474i 0.0675440 0.116990i
\(251\) 201.133i 0.801329i −0.916225 0.400664i \(-0.868779\pi\)
0.916225 0.400664i \(-0.131221\pi\)
\(252\) −173.394 + 272.320i −0.688070 + 1.08063i
\(253\) −23.2692 −0.0919733
\(254\) 96.3069 + 55.6028i 0.379161 + 0.218909i
\(255\) 20.0997 126.884i 0.0788222 0.497584i
\(256\) −29.3390 50.8166i −0.114605 0.198502i
\(257\) 240.370 + 138.777i 0.935290 + 0.539990i 0.888481 0.458914i \(-0.151761\pi\)
0.0468093 + 0.998904i \(0.485095\pi\)
\(258\) 330.409 408.000i 1.28065 1.58139i
\(259\) 134.555 37.3579i 0.519517 0.144239i
\(260\) 215.645i 0.829405i
\(261\) −88.9043 + 273.573i −0.340630 + 1.04817i
\(262\) −263.807 456.927i −1.00690 1.74400i
\(263\) 118.944 68.6721i 0.452257 0.261111i −0.256526 0.966537i \(-0.582578\pi\)
0.708783 + 0.705427i \(0.249245\pi\)
\(264\) 11.6886 4.48651i 0.0442752 0.0169944i
\(265\) −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 \(-0.775872\pi\)
0.179541 + 0.983750i \(0.442539\pi\)
\(270\) −182.120 + 9.53081i −0.674517 + 0.0352993i
\(271\) −11.5380 + 19.9844i −0.0425757 + 0.0737433i −0.886528 0.462675i \(-0.846890\pi\)
0.843952 + 0.536418i \(0.180223\pi\)
\(272\) 196.067i 0.720834i
\(273\) −317.632 + 235.167i −1.16349 + 0.861418i
\(274\) 781.991 2.85398
\(275\) 5.32069 + 3.07190i 0.0193480 + 0.0111706i
\(276\) 287.539 + 45.5491i 1.04181 + 0.165033i
\(277\) −58.5237 101.366i −0.211277 0.365942i 0.740838 0.671684i \(-0.234429\pi\)
−0.952114 + 0.305742i \(0.901095\pi\)
\(278\) 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 \(-0.422607\pi\)
\(282\) 402.061 154.325i 1.42575 0.547252i
\(283\) 16.3060 + 28.2428i 0.0576182 + 0.0997977i 0.893396 0.449270i \(-0.148316\pi\)
−0.835778 + 0.549068i \(0.814983\pi\)
\(284\) −3.45807 + 1.99652i −0.0121763 + 0.00703000i
\(285\) −48.4559 126.241i −0.170021 0.442953i
\(286\) 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
\(291\) −62.8514 + 396.764i −0.215984 + 1.36345i
\(292\) −22.3081 + 38.6388i −0.0763976 + 0.132325i
\(293\) 180.379i 0.615628i −0.951447 0.307814i \(-0.900403\pi\)
0.951447 0.307814i \(-0.0995974\pi\)
\(294\) 350.060 + 273.180i 1.19068 + 0.929184i
\(295\) 57.7548 0.195779
\(296\) 58.6781 + 33.8778i 0.198237 + 0.114452i
\(297\) −1.73384 33.1312i −0.00583786 0.111553i
\(298\) 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
\(303\) −114.471 298.229i −0.377791 0.984253i
\(304\) 103.189 + 178.728i 0.339437 + 0.587922i
\(305\) −162.263 + 93.6825i −0.532009 + 0.307156i
\(306\) −495.137 160.907i −1.61810 0.525840i
\(307\) −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 \(-0.733669\pi\)
0.308014 + 0.951382i \(0.400336\pi\)
\(312\) −189.396 30.0023i −0.607039 0.0961611i
\(313\) 105.619 182.938i 0.337441 0.584466i −0.646509 0.762906i \(-0.723772\pi\)
0.983951 + 0.178440i \(0.0571052\pi\)
\(314\) 121.995i 0.388518i
\(315\) −6.11051 + 140.740i −0.0193984 + 0.446793i
\(316\) −320.555 −1.01442
\(317\) −402.217 232.220i −1.26882 0.732556i −0.294059 0.955787i \(-0.595006\pi\)
−0.974766 + 0.223231i \(0.928340\pi\)
\(318\) −5.24717 + 33.1240i −0.0165005 + 0.104164i
\(319\) −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
\(324\) −43.4284 + 412.798i −0.134038 + 1.27407i
\(325\) −47.0492 81.4916i −0.144767 0.250744i
\(326\) −523.786 + 302.408i −1.60670 + 0.927631i
\(327\) 572.726 219.832i 1.75146 0.672271i
\(328\) 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 −0.00413794 + 0.999991i \(0.501317\pi\)
−0.863949 + 0.503579i \(0.832016\pi\)
\(332\) 335.292 193.581i 1.00992 0.583075i
\(333\) 133.433 120.131i 0.400698 0.360754i
\(334\) −66.7855 + 115.676i −0.199956 + 0.346335i
\(335\) 95.6708i 0.285585i
\(336\) −24.3962 213.613i −0.0726078 0.635753i
\(337\) −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
\(339\) −376.756 59.6819i −1.11137 0.176053i
\(340\) −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
\(345\) 118.598 45.5221i 0.343762 0.131948i
\(346\) 206.329 + 357.372i 0.596326 + 1.03287i
\(347\) −262.342 + 151.463i −0.756029 + 0.436494i −0.827868 0.560922i \(-0.810447\pi\)
0.0718390 + 0.997416i \(0.477113\pi\)
\(348\) 176.074 + 458.723i 0.505960 + 1.31817i
\(349\) 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 \(-0.564895\pi\)
0.746858 + 0.664984i \(0.231561\pi\)
\(354\) 36.6208 231.177i 0.103448 0.653042i
\(355\) −0.871197 + 1.50896i −0.00245408 + 0.00425058i
\(356\) 435.109i 1.22222i
\(357\) −160.263 + 368.850i −0.448915 + 1.03319i
\(358\) −539.114 −1.50590
\(359\) 479.747 + 276.982i 1.33634 + 0.771538i 0.986263 0.165183i \(-0.0528213\pi\)
0.350079 + 0.936720i \(0.386155\pi\)
\(360\) −50.7972 + 45.7334i −0.141103 + 0.127037i
\(361\) −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
\(366\) 272.099 + 708.896i 0.743441 + 1.93687i
\(367\) 213.410 + 369.637i 0.581499 + 1.00719i 0.995302 + 0.0968195i \(0.0308669\pi\)
−0.413803 + 0.910367i \(0.635800\pi\)
\(368\) −167.907 + 96.9410i −0.456268 + 0.263427i
\(369\) 162.543 500.172i 0.440497 1.35548i
\(370\) 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 −0.842259 0.539073i \(-0.818775\pi\)
0.887980 + 0.459881i \(0.152108\pi\)
\(374\) 61.5576 35.5403i 0.164592 0.0950275i
\(375\) −33.1279 5.24780i −0.0883412 0.0139941i
\(376\) 80.7053 139.786i 0.214642 0.371770i
\(377\) 601.511i 1.59552i
\(378\) 559.469 + 113.698i 1.48008 + 0.300788i
\(379\) −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
\(381\) 17.2801 109.085i 0.0453547 0.286312i
\(382\) 79.5015 + 137.701i 0.208119 + 0.360473i
\(383\) −27.1258 15.6611i −0.0708245 0.0408905i 0.464170 0.885746i \(-0.346353\pi\)
−0.534994 + 0.844856i \(0.679686\pi\)
\(384\) 197.092 243.376i 0.513261 0.633793i
\(385\) −13.7220 13.4767i −0.0356416 0.0350043i
\(386\) 210.069i 0.544221i
\(387\) −495.889 161.152i −1.28137 0.416412i
\(388\) 343.088 + 594.245i 0.884247 + 1.53156i
\(389\) 96.1676 55.5224i 0.247218 0.142731i −0.371272 0.928524i \(-0.621078\pi\)
0.618490 + 0.785793i \(0.287745\pi\)
\(390\) −356.022 + 136.654i −0.912876 + 0.350394i
\(391\) 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
\(396\) −37.9174 42.1158i −0.0957511 0.106353i
\(397\) −192.946 + 334.192i −0.486009 + 0.841792i −0.999871 0.0160808i \(-0.994881\pi\)
0.513862 + 0.857873i \(0.328214\pi\)
\(398\) 167.624i 0.421167i
\(399\) 48.0330 + 420.577i 0.120383 + 1.05408i
\(400\) 51.1909 0.127977
\(401\) −316.717 182.857i −0.789817 0.456001i 0.0500808 0.998745i \(-0.484052\pi\)
−0.839898 + 0.542744i \(0.817385\pi\)
\(402\) −382.945 60.6623i −0.952598 0.150901i
\(403\) 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
\(408\) −182.171 + 69.9236i −0.446497 + 0.171381i
\(409\) 37.9388 + 65.7119i 0.0927599 + 0.160665i 0.908671 0.417512i \(-0.137098\pi\)
−0.815912 + 0.578177i \(0.803764\pi\)
\(410\) 341.818 197.349i 0.833703 0.481339i
\(411\) −278.306 725.065i −0.677143 1.76415i
\(412\) 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
\(417\) 100.768 636.122i 0.241650 1.52547i
\(418\) 37.4093 64.7947i 0.0894958 0.155011i
\(419\) 394.222i 0.940864i 0.882436 + 0.470432i \(0.155902\pi\)
−0.882436 + 0.470432i \(0.844098\pi\)
\(420\) 143.183 + 193.392i 0.340912 + 0.460458i
\(421\) 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
\(423\) −286.182 317.869i −0.676552 0.751463i
\(424\) 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
\(429\) −24.8600 64.7675i −0.0579488 0.150973i
\(430\) −195.659 338.891i −0.455021 0.788119i
\(431\) 452.693 261.362i 1.05033 0.606409i 0.127589 0.991827i \(-0.459276\pi\)
0.922742 + 0.385418i \(0.125943\pi\)
\(432\) −150.538 231.846i −0.348467 0.536680i
\(433\) −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
\(438\) 77.9277 + 12.3445i 0.177917 + 0.0281839i
\(439\) 24.8300 43.0069i 0.0565605 0.0979656i −0.836359 0.548182i \(-0.815320\pi\)
0.892919 + 0.450217i \(0.148653\pi\)
\(440\) 9.33194i 0.0212090i
\(441\) 128.710 421.800i 0.291858 0.956462i
\(442\) −1088.67 −2.46305
\(443\) 394.066 + 227.514i 0.889541 + 0.513576i 0.873792 0.486300i \(-0.161654\pi\)
0.0157484 + 0.999876i \(0.494987\pi\)
\(444\) 47.9834 302.906i 0.108071 0.682221i
\(445\) −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 \(-0.272432\pi\)
\(450\) −42.0111 + 129.275i −0.0933579 + 0.287277i
\(451\) 35.9017 + 62.1835i 0.0796046 + 0.137879i
\(452\) −564.278 + 325.786i −1.24840 + 0.720766i
\(453\) 444.710 170.695i 0.981699 0.376811i
\(454\) 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 0.493383 + 0.869812i \(0.335760\pi\)
−0.999971 + 0.00762394i \(0.997573\pi\)
\(458\) 271.327 156.651i 0.592418 0.342033i
\(459\) 27.0224 + 516.359i 0.0588724 + 1.12496i
\(460\) 108.496 187.920i 0.235860 0.408522i
\(461\) 766.505i 1.66270i 0.555749 + 0.831350i \(0.312432\pi\)
−0.555749 + 0.831350i \(0.687568\pi\)
\(462\) −62.6442 + 46.3803i −0.135594 + 0.100390i
\(463\) 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
\(465\) 194.498 + 30.8105i 0.418276 + 0.0662590i
\(466\) −130.501 226.034i −0.280044 0.485051i
\(467\) −563.725 325.467i −1.20712 0.696931i −0.244990 0.969526i \(-0.578785\pi\)
−0.962129 + 0.272595i \(0.912118\pi\)
\(468\) 180.416 + 848.997i 0.385503 + 1.81410i
\(469\) −74.9030 + 289.979i −0.159708 + 0.618293i
\(470\) 320.996i 0.682970i
\(471\) −113.114 + 43.4171i −0.240157 + 0.0921806i
\(472\) −43.8624 75.9720i −0.0929289 0.160958i
\(473\) 61.6511 35.5943i 0.130341 0.0752522i
\(474\) 203.135 + 529.224i 0.428555 + 1.11651i
\(475\) −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 \(-0.551691\pi\)
0.773792 + 0.633440i \(0.218358\pi\)
\(480\) 46.7177 294.916i 0.0973285 0.614409i
\(481\) 187.719 325.139i 0.390269 0.675965i
\(482\) 425.296i 0.882357i
\(483\) −395.112 + 45.1247i −0.818037 + 0.0934260i
\(484\) −612.314 −1.26511
\(485\) 259.304 + 149.709i 0.534646 + 0.308678i
\(486\) 709.033 189.890i 1.45892 0.390720i
\(487\) −108.262 187.515i −0.222304 0.385042i 0.733203 0.680010i \(-0.238024\pi\)
−0.955507 + 0.294968i \(0.904691\pi\)
\(488\) 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 \(0.768168\pi\)
\(492\) −321.916 838.682i −0.654300 1.70464i
\(493\) 306.043 + 530.083i 0.620778 + 1.07522i
\(494\) −992.396 + 572.960i −2.00890 + 1.15984i
\(495\) −23.5177 7.64265i −0.0475104 0.0154397i
\(496\) −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 −0.995576 0.0939646i \(-0.970046\pi\)
0.579164 + 0.815211i \(0.303379\pi\)
\(500\) −49.6167 + 28.6462i −0.0992334 + 0.0572924i
\(501\) 131.024 + 20.7554i 0.261524 + 0.0414280i
\(502\) −303.778 + 526.159i −0.605135 + 1.04813i
\(503\) 319.315i 0.634820i 0.948288 + 0.317410i \(0.102813\pi\)
−0.948288 + 0.317410i \(0.897187\pi\)
\(504\) 189.773 98.8482i 0.376533 0.196127i
\(505\) −238.099 −0.471483
\(506\) 60.8716 + 35.1442i 0.120300 + 0.0694550i
\(507\) −86.9196 + 548.700i −0.171439 + 1.08225i
\(508\) −94.3273 163.380i −0.185684 0.321613i
\(509\) −384.362 221.911i −0.755131 0.435975i 0.0724140 0.997375i \(-0.476930\pi\)
−0.827545 + 0.561400i \(0.810263\pi\)
\(510\) −244.217 + 301.567i −0.478856 + 0.591308i
\(511\) 15.2425 59.0097i 0.0298287 0.115479i
\(512\) 594.810i 1.16174i
\(513\) 296.389 + 456.474i 0.577757 + 0.889813i
\(514\) −419.200 726.075i −0.815563 1.41260i
\(515\) 127.115 73.3899i 0.246825 0.142505i
\(516\) −831.500 + 319.159i −1.61143 + 0.618526i
\(517\) 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 \(-0.812074\pi\)
0.0667394 + 0.997770i \(0.478740\pi\)
\(522\) 645.756 581.383i 1.23708 1.11376i
\(523\) −152.912 + 264.851i −0.292375 + 0.506408i −0.974371 0.224948i \(-0.927779\pi\)
0.681996 + 0.731356i \(0.261112\pi\)
\(524\) 895.070i 1.70815i
\(525\) 96.3025 + 41.8428i 0.183433 + 0.0797006i
\(526\) −414.870 −0.788727
\(527\) 486.859 + 281.088i 0.923831 + 0.533374i
\(528\) 37.2760 + 5.90489i 0.0705985 + 0.0111835i
\(529\) −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
\(534\) −718.348 + 275.727i −1.34522 + 0.516343i
\(535\) 55.8691 + 96.7681i 0.104428 + 0.180875i
\(536\) −125.848 + 72.6581i −0.234790 + 0.135556i
\(537\) 191.867 + 499.868i 0.357295 + 0.930853i
\(538\) 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 −0.292094 0.956390i \(-0.594352\pi\)
0.974305 0.225234i \(-0.0723147\pi\)
\(542\) 60.3662 34.8524i 0.111377 0.0643034i
\(543\) −168.520 + 1063.82i −0.310350 + 1.95915i
\(544\) 426.212 738.221i 0.783478 1.35702i
\(545\) 457.251i 0.838993i
\(546\) 1186.10 135.461i 2.17234 0.248097i
\(547\) 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
\(549\) 560.453 504.583i 1.02086 0.919095i
\(550\) −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
\(555\) −47.9549 124.936i −0.0864053 0.225110i
\(556\) −550.064 952.739i −0.989324 1.71356i
\(557\) 295.072 170.360i 0.529753 0.305853i −0.211163 0.977451i \(-0.567725\pi\)
0.740916 + 0.671598i \(0.234392\pi\)
\(558\) 246.652 758.988i 0.442029 1.36019i
\(559\) −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 \(-0.568464\pi\)
0.739355 + 0.673316i \(0.235131\pi\)
\(564\) −721.596 114.308i −1.27943 0.202674i
\(565\) −142.159 + 246.227i −0.251609 + 0.435800i
\(566\) 98.5096i 0.174045i
\(567\) −93.6902 559.206i −0.165238 0.986254i
\(568\) 2.64656 0.00465943
\(569\) 615.104 + 355.130i 1.08103 + 0.624131i 0.931173 0.364578i \(-0.118787\pi\)
0.149853 + 0.988708i \(0.452120\pi\)
\(570\) −63.9071 + 403.428i −0.112118 + 0.707769i
\(571\) −13.7983 23.8993i −0.0241651 0.0418552i 0.853690 0.520782i \(-0.174359\pi\)
−0.877855 + 0.478926i \(0.841026\pi\)
\(572\) −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
\(576\) −800.318 260.083i −1.38944 0.451533i
\(577\) −144.408 250.122i −0.250274 0.433488i 0.713327 0.700831i \(-0.247187\pi\)
−0.963601 + 0.267344i \(0.913854\pi\)
\(578\) −203.377 + 117.420i −0.351863 + 0.203148i
\(579\) 194.777 74.7623i 0.336402 0.129123i
\(580\) 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
\(585\) 253.412 + 281.471i 0.433182 + 0.481146i
\(586\) −272.432 + 471.866i −0.464901 + 0.805232i
\(587\) 942.812i 1.60615i −0.595876 0.803077i \(-0.703195\pi\)
0.595876 0.803077i \(-0.296805\pi\)
\(588\) −282.578 698.276i −0.480575 1.18754i
\(589\) 591.740 1.00465
\(590\) −151.085 87.2289i −0.256076 0.147846i
\(591\) −156.719 24.8258i −0.265176 0.0420065i
\(592\) 102.122 + 176.880i 0.172503 + 0.298784i
\(593\) −414.204 239.141i −0.698489 0.403273i 0.108295 0.994119i \(-0.465461\pi\)
−0.806784 + 0.590846i \(0.798794\pi\)
\(594\) −45.5034 + 89.2889i −0.0766050 + 0.150318i
\(595\) 213.861 + 210.038i 0.359431 + 0.353004i
\(596\) 661.882i 1.11054i
\(597\) −155.422 + 59.6564i −0.260338 + 0.0999270i
\(598\) −538.269 932.309i −0.900115 1.55905i
\(599\) −745.356 + 430.332i −1.24433 + 0.718417i −0.969974 0.243210i \(-0.921799\pi\)
−0.274360 + 0.961627i \(0.588466\pi\)
\(600\) 18.2563 + 47.5627i 0.0304271 + 0.0792712i
\(601\) 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
\(606\) −150.972 + 953.045i −0.249129 + 1.57268i
\(607\) −27.9096 + 48.3409i −0.0459796 + 0.0796390i −0.888099 0.459652i \(-0.847974\pi\)
0.842120 + 0.539291i \(0.181308\pi\)
\(608\) 897.251i 1.47574i
\(609\) −399.389 539.440i −0.655810 0.885780i
\(610\) 565.966 0.927813
\(611\) −774.561 447.193i −1.26769 0.731903i
\(612\) 590.954 + 656.386i 0.965610 + 1.07253i
\(613\) −53.4478 92.5743i −0.0871906 0.151019i 0.819132 0.573605i \(-0.194456\pi\)
−0.906323 + 0.422587i \(0.861122\pi\)
\(614\) 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 \(0.714092\pi\)
\(618\) −213.160 555.342i −0.344919 0.898612i
\(619\) −16.9218 29.3094i −0.0273373 0.0473496i 0.852033 0.523488i \(-0.175369\pi\)
−0.879370 + 0.476138i \(0.842036\pi\)
\(620\) 291.306 168.185i 0.469848 0.271267i
\(621\) −428.836 + 278.444i −0.690557 + 0.448380i
\(622\) 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
\(627\) −73.3916 11.6260i −0.117052 0.0185422i
\(628\) −103.479 + 179.230i −0.164775 + 0.285398i
\(629\) 382.039i 0.607375i
\(630\) 228.548 358.942i 0.362775 0.569749i
\(631\) 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
\(633\) 82.1330 518.483i 0.129752 0.819089i
\(634\) 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
\(639\) 2.16747 6.66965i 0.00339197 0.0104376i
\(640\) −116.713 202.152i −0.182364 0.315863i
\(641\) 420.859 242.983i 0.656566 0.379068i −0.134401 0.990927i \(-0.542911\pi\)
0.790967 + 0.611858i \(0.209578\pi\)
\(642\) 422.762 162.271i 0.658508 0.252759i
\(643\) −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 \(-0.620807\pi\)
0.619160 + 0.785265i \(0.287473\pi\)
\(648\) 161.727 222.552i 0.249579 0.343444i
\(649\) 15.8687 27.4853i 0.0244510 0.0423503i
\(650\) 284.239i 0.437292i
\(651\) −565.404 245.664i −0.868516 0.377364i
\(652\) 1026.04 1.57368
\(653\) 788.464 + 455.220i 1.20745 + 0.697121i 0.962201 0.272340i \(-0.0877975\pi\)
0.245247 + 0.969461i \(0.421131\pi\)
\(654\) −1830.25 289.930i −2.79855 0.443319i
\(655\) 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 \(0.957618\pi\)
\(660\) −39.4341 + 15.1362i −0.0597486 + 0.0229336i
\(661\) −70.4654 122.050i −0.106604 0.184644i 0.807788 0.589473i \(-0.200664\pi\)
−0.914392 + 0.404829i \(0.867331\pi\)
\(662\) 1503.33 867.947i 2.27089 1.31110i
\(663\) 387.451 + 1009.42i 0.584390 + 1.52250i
\(664\) −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
\(669\) 90.6579 572.299i 0.135513 0.855455i
\(670\) −144.495 + 250.272i −0.215663 + 0.373540i
\(671\) 102.961i 0.153443i
\(672\) −372.499 + 857.318i −0.554314 + 1.27577i
\(673\) 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
\(675\) 134.816 7.05526i 0.199727 0.0104522i
\(676\) 474.469 + 821.805i 0.701878 + 1.21569i
\(677\) −579.837 334.769i −0.856481 0.494489i 0.00635162 0.999980i \(-0.497978\pi\)
−0.862832 + 0.505491i \(0.831312\pi\)
\(678\) 895.442 + 725.151i 1.32071 + 1.06954i
\(679\) −668.741 656.785i −0.984891 0.967282i
\(680\) 145.441i 0.213884i
\(681\) −323.082 841.719i −0.474422 1.23600i
\(682\) 54.4791 + 94.3606i 0.0798814 + 0.138359i
\(683\) −441.858 + 255.107i −0.646937 + 0.373509i −0.787282 0.616594i \(-0.788512\pi\)
0.140345 + 0.990103i \(0.455179\pi\)
\(684\) 884.146 + 287.325i 1.29261 + 0.420066i
\(685\) −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
\(690\) −379.002 60.0377i −0.549278 0.0870112i
\(691\) 491.747 851.731i 0.711646 1.23261i −0.252593 0.967573i \(-0.581283\pi\)
0.964239 0.265034i \(-0.0853833\pi\)
\(692\) 700.052i 1.01164i
\(693\) 65.2987 + 41.5775i 0.0942261 + 0.0599964i
\(694\) 915.039 1.31850
\(695\) −415.735 240.025i −0.598180 0.345359i
\(696\) 50.9534 321.655i 0.0732089 0.462148i
\(697\) −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 \(-0.251665\pi\)
\(702\) 1287.33 835.866i 1.83381 1.19069i
\(703\) −201.065 348.254i −0.286010 0.495383i
\(704\) 99.4990 57.4458i 0.141334 0.0815991i
\(705\) −297.629 + 114.240i −0.422168 + 0.162043i
\(706\) −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 −0.999004 0.0446304i \(-0.985789\pi\)
0.538153 + 0.842847i \(0.319122\pi\)
\(710\) 4.55805 2.63159i 0.00641979 0.00370647i
\(711\) 418.404 376.695i 0.588473 0.529810i
\(712\) −144.193 + 249.750i −0.202519 + 0.350773i
\(713\) 555.912i 0.779680i
\(714\) 976.327 722.850i 1.36741 1.01239i
\(715\) −51.7088 −0.0723200
\(716\) 792.048 + 457.289i 1.10621 + 0.638672i
\(717\) 50.9650 + 8.07336i 0.0710809 + 0.0112599i
\(718\) −836.669 1449.15i −1.16528 2.01832i
\(719\) −465.382 268.688i −0.647262 0.373697i 0.140144 0.990131i \(-0.455243\pi\)
−0.787407 + 0.616434i \(0.788577\pi\)
\(720\) −201.539 + 42.8279i −0.279915 + 0.0594832i
\(721\) −442.746 + 122.924i −0.614072 + 0.170491i
\(722\) 136.929i 0.189653i
\(723\) −394.336 + 151.360i −0.545417 + 0.209350i
\(724\) 919.901 + 1593.32i 1.27058 + 2.20071i
\(725\) 138.399 79.9045i 0.190895 0.110213i
\(726\) 388.022 + 1010.91i 0.534465 + 1.39243i
\(727\) 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
\(732\) 201.543 1272.29i 0.275332 1.73810i
\(733\) −351.349 + 608.555i −0.479330 + 0.830224i −0.999719 0.0237050i \(-0.992454\pi\)
0.520389 + 0.853930i \(0.325787\pi\)
\(734\) 1289.28i 1.75651i
\(735\) −259.134 202.224i −0.352564 0.275134i
\(736\) 842.925 1.14528
\(737\) −45.5294 26.2864i −0.0617767 0.0356668i
\(738\) −1180.63 + 1062.94i −1.59977 + 1.44030i
\(739\) 99.5025 + 172.343i 0.134645 + 0.233212i 0.925462 0.378841i \(-0.123677\pi\)
−0.790817 + 0.612053i \(0.790344\pi\)
\(740\) −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 \(0.807381\pi\)
\(744\) −107.185 279.246i −0.144065 0.375331i
\(745\) −144.409 250.123i −0.193837 0.335736i
\(746\) −89.2254 + 51.5143i −0.119605 + 0.0690540i
\(747\) −210.156 + 646.684i −0.281333 + 0.865708i
\(748\) −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 −0.717467 0.696593i \(-0.754698\pi\)
0.962000 + 0.273048i \(0.0880317\pi\)
\(752\) 421.372 243.279i 0.560335 0.323510i
\(753\) 595.969 + 94.4075i 0.791460 + 0.125375i
\(754\) 908.481 1573.53i 1.20488 2.08692i
\(755\) 355.046i 0.470259i
\(756\) −725.511 641.596i −0.959671 0.848672i
\(757\) 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
\(759\) 10.9221 68.9480i 0.0143901 0.0908406i
\(760\) 76.5446 + 132.579i 0.100717 + 0.174446i
\(761\) −401.326 231.706i −0.527367 0.304475i 0.212577 0.977144i \(-0.431814\pi\)
−0.739944 + 0.672669i \(0.765148\pi\)
\(762\) −209.958 + 259.264i −0.275536 + 0.340241i
\(763\) −357.993 + 1385.93i −0.469191 + 1.81643i
\(764\) 269.740i 0.353063i
\(765\) 366.529 + 119.113