Properties

Label 105.3.t.b.11.13
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 11.13
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50527 - 0.869067i) q^{2} +(-1.33489 + 2.68664i) q^{3} +(-0.489445 + 0.847743i) q^{4} +(1.93649 - 1.11803i) q^{5} +(0.325501 + 5.20423i) q^{6} +(2.93407 + 6.35541i) q^{7} +8.65398i q^{8} +(-5.43612 - 7.17277i) q^{9} +O(q^{10})\) \(q+(1.50527 - 0.869067i) q^{2} +(-1.33489 + 2.68664i) q^{3} +(-0.489445 + 0.847743i) q^{4} +(1.93649 - 1.11803i) q^{5} +(0.325501 + 5.20423i) q^{6} +(2.93407 + 6.35541i) q^{7} +8.65398i q^{8} +(-5.43612 - 7.17277i) q^{9} +(1.94329 - 3.36588i) q^{10} +(11.0674 + 6.38976i) q^{11} +(-1.62423 - 2.44661i) q^{12} +0.690184 q^{13} +(9.93984 + 7.01669i) q^{14} +(0.418749 + 6.69512i) q^{15} +(5.56311 + 9.63559i) q^{16} +(-12.5056 - 7.22012i) q^{17} +(-14.4164 - 6.07260i) q^{18} +(-13.8399 - 23.9714i) q^{19} +2.18886i q^{20} +(-20.9914 - 0.600994i) q^{21} +22.2125 q^{22} +(37.3582 - 21.5687i) q^{23} +(-23.2502 - 11.5521i) q^{24} +(2.50000 - 4.33013i) q^{25} +(1.03891 - 0.599816i) q^{26} +(26.5273 - 5.03002i) q^{27} +(-6.82382 - 0.623284i) q^{28} -26.6616i q^{29} +(6.44884 + 9.71403i) q^{30} +(-8.94214 + 15.4882i) q^{31} +(-13.2303 - 7.63853i) q^{32} +(-31.9408 + 21.2045i) q^{33} -25.0991 q^{34} +(12.7874 + 9.02681i) q^{35} +(8.74134 - 1.09776i) q^{36} +(17.5794 + 30.4484i) q^{37} +(-41.6655 - 24.0556i) q^{38} +(-0.921322 + 1.85428i) q^{39} +(9.67544 + 16.7584i) q^{40} +15.0963i q^{41} +(-32.1200 + 17.3383i) q^{42} -23.1680 q^{43} +(-10.8337 + 6.25487i) q^{44} +(-18.5464 - 7.81225i) q^{45} +(37.4894 - 64.9335i) q^{46} +(38.1508 - 22.0264i) q^{47} +(-33.3136 + 2.08361i) q^{48} +(-31.7825 + 37.2944i) q^{49} -8.69067i q^{50} +(36.0916 - 23.9600i) q^{51} +(-0.337807 + 0.585099i) q^{52} +(78.5866 + 45.3720i) q^{53} +(35.5593 - 30.6256i) q^{54} +28.5759 q^{55} +(-54.9996 + 25.3914i) q^{56} +(82.8774 - 5.18359i) q^{57} +(-23.1707 - 40.1329i) q^{58} +(-21.3447 - 12.3233i) q^{59} +(-5.88070 - 2.92190i) q^{60} +(-33.0900 - 57.3136i) q^{61} +31.0853i q^{62} +(29.6359 - 55.5942i) q^{63} -71.0584 q^{64} +(1.33654 - 0.771649i) q^{65} +(-29.6514 + 59.6771i) q^{66} +(-13.6163 + 23.5841i) q^{67} +(12.2416 - 7.06770i) q^{68} +(8.07836 + 129.160i) q^{69} +(27.0933 + 2.47469i) q^{70} -76.5254i q^{71} +(62.0730 - 47.0440i) q^{72} +(24.7119 - 42.8023i) q^{73} +(52.9234 + 30.5554i) q^{74} +(8.29628 + 12.4969i) q^{75} +27.0954 q^{76} +(-8.13704 + 89.0858i) q^{77} +(0.224655 + 3.59188i) q^{78} +(18.5245 + 32.0854i) q^{79} +(21.5458 + 12.4395i) q^{80} +(-21.8973 + 77.9840i) q^{81} +(13.1197 + 22.7239i) q^{82} -20.0443i q^{83} +(10.7836 - 17.5012i) q^{84} -32.2894 q^{85} +(-34.8741 + 20.1346i) q^{86} +(71.6303 + 35.5904i) q^{87} +(-55.2968 + 95.7769i) q^{88} +(-62.7886 + 36.2510i) q^{89} +(-34.7067 + 4.35853i) q^{90} +(2.02505 + 4.38640i) q^{91} +42.2268i q^{92} +(-29.6746 - 44.6995i) q^{93} +(38.2848 - 66.3112i) q^{94} +(-53.6016 - 30.9469i) q^{95} +(38.1831 - 25.3485i) q^{96} +23.2629 q^{97} +(-15.4298 + 83.7592i) q^{98} +(-14.3313 - 114.119i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50527 0.869067i 0.752634 0.434534i −0.0740107 0.997257i \(-0.523580\pi\)
0.826645 + 0.562724i \(0.190247\pi\)
\(3\) −1.33489 + 2.68664i −0.444965 + 0.895548i
\(4\) −0.489445 + 0.847743i −0.122361 + 0.211936i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) 0.325501 + 5.20423i 0.0542501 + 0.867372i
\(7\) 2.93407 + 6.35541i 0.419153 + 0.907916i
\(8\) 8.65398i 1.08175i
\(9\) −5.43612 7.17277i −0.604013 0.796975i
\(10\) 1.94329 3.36588i 0.194329 0.336588i
\(11\) 11.0674 + 6.38976i 1.00613 + 0.580887i 0.910055 0.414487i \(-0.136039\pi\)
0.0960710 + 0.995374i \(0.469372\pi\)
\(12\) −1.62423 2.44661i −0.135352 0.203884i
\(13\) 0.690184 0.0530911 0.0265455 0.999648i \(-0.491549\pi\)
0.0265455 + 0.999648i \(0.491549\pi\)
\(14\) 9.93984 + 7.01669i 0.709989 + 0.501192i
\(15\) 0.418749 + 6.69512i 0.0279166 + 0.446341i
\(16\) 5.56311 + 9.63559i 0.347694 + 0.602224i
\(17\) −12.5056 7.22012i −0.735625 0.424713i 0.0848518 0.996394i \(-0.472958\pi\)
−0.820476 + 0.571681i \(0.806292\pi\)
\(18\) −14.4164 6.07260i −0.800913 0.337366i
\(19\) −13.8399 23.9714i −0.728415 1.26165i −0.957553 0.288258i \(-0.906924\pi\)
0.229138 0.973394i \(-0.426409\pi\)
\(20\) 2.18886i 0.109443i
\(21\) −20.9914 0.600994i −0.999590 0.0286188i
\(22\) 22.2125 1.00966
\(23\) 37.3582 21.5687i 1.62427 0.937771i 0.638507 0.769616i \(-0.279552\pi\)
0.985760 0.168156i \(-0.0537811\pi\)
\(24\) −23.2502 11.5521i −0.968757 0.481339i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 1.03891 0.599816i 0.0399581 0.0230698i
\(27\) 26.5273 5.03002i 0.982493 0.186297i
\(28\) −6.82382 0.623284i −0.243708 0.0222601i
\(29\) 26.6616i 0.919366i −0.888083 0.459683i \(-0.847963\pi\)
0.888083 0.459683i \(-0.152037\pi\)
\(30\) 6.44884 + 9.71403i 0.214961 + 0.323801i
\(31\) −8.94214 + 15.4882i −0.288456 + 0.499621i −0.973441 0.228936i \(-0.926475\pi\)
0.684985 + 0.728557i \(0.259809\pi\)
\(32\) −13.2303 7.63853i −0.413447 0.238704i
\(33\) −31.9408 + 21.2045i −0.967903 + 0.642560i
\(34\) −25.0991 −0.738208
\(35\) 12.7874 + 9.02681i 0.365353 + 0.257909i
\(36\) 8.74134 1.09776i 0.242815 0.0304932i
\(37\) 17.5794 + 30.4484i 0.475119 + 0.822930i 0.999594 0.0284956i \(-0.00907164\pi\)
−0.524475 + 0.851426i \(0.675738\pi\)
\(38\) −41.6655 24.0556i −1.09646 0.633041i
\(39\) −0.921322 + 1.85428i −0.0236236 + 0.0475456i
\(40\) 9.67544 + 16.7584i 0.241886 + 0.418959i
\(41\) 15.0963i 0.368202i 0.982907 + 0.184101i \(0.0589373\pi\)
−0.982907 + 0.184101i \(0.941063\pi\)
\(42\) −32.1200 + 17.3383i −0.764762 + 0.412816i
\(43\) −23.1680 −0.538791 −0.269395 0.963030i \(-0.586824\pi\)
−0.269395 + 0.963030i \(0.586824\pi\)
\(44\) −10.8337 + 6.25487i −0.246222 + 0.142156i
\(45\) −18.5464 7.81225i −0.412142 0.173606i
\(46\) 37.4894 64.9335i 0.814986 1.41160i
\(47\) 38.1508 22.0264i 0.811719 0.468646i −0.0358338 0.999358i \(-0.511409\pi\)
0.847552 + 0.530712i \(0.178075\pi\)
\(48\) −33.3136 + 2.08361i −0.694032 + 0.0434085i
\(49\) −31.7825 + 37.2944i −0.648622 + 0.761111i
\(50\) 8.69067i 0.173813i
\(51\) 36.0916 23.9600i 0.707678 0.469805i
\(52\) −0.337807 + 0.585099i −0.00649628 + 0.0112519i
\(53\) 78.5866 + 45.3720i 1.48277 + 0.856075i 0.999809 0.0195689i \(-0.00622937\pi\)
0.482957 + 0.875644i \(0.339563\pi\)
\(54\) 35.5593 30.6256i 0.658506 0.567140i
\(55\) 28.5759 0.519561
\(56\) −54.9996 + 25.3914i −0.982135 + 0.453417i
\(57\) 82.8774 5.18359i 1.45399 0.0909402i
\(58\) −23.1707 40.1329i −0.399495 0.691946i
\(59\) −21.3447 12.3233i −0.361774 0.208870i 0.308085 0.951359i \(-0.400312\pi\)
−0.669859 + 0.742489i \(0.733645\pi\)
\(60\) −5.88070 2.92190i −0.0980116 0.0486983i
\(61\) −33.0900 57.3136i −0.542460 0.939568i −0.998762 0.0497429i \(-0.984160\pi\)
0.456302 0.889825i \(-0.349174\pi\)
\(62\) 31.0853i 0.501375i
\(63\) 29.6359 55.5942i 0.470412 0.882447i
\(64\) −71.0584 −1.11029
\(65\) 1.33654 0.771649i 0.0205621 0.0118715i
\(66\) −29.6514 + 59.6771i −0.449263 + 0.904199i
\(67\) −13.6163 + 23.5841i −0.203228 + 0.352001i −0.949567 0.313565i \(-0.898477\pi\)
0.746339 + 0.665566i \(0.231810\pi\)
\(68\) 12.2416 7.06770i 0.180024 0.103937i
\(69\) 8.07836 + 129.160i 0.117078 + 1.87188i
\(70\) 27.0933 + 2.47469i 0.387047 + 0.0353527i
\(71\) 76.5254i 1.07782i −0.842362 0.538912i \(-0.818836\pi\)
0.842362 0.538912i \(-0.181164\pi\)
\(72\) 62.0730 47.0440i 0.862125 0.653389i
\(73\) 24.7119 42.8023i 0.338520 0.586333i −0.645635 0.763646i \(-0.723407\pi\)
0.984155 + 0.177313i \(0.0567405\pi\)
\(74\) 52.9234 + 30.5554i 0.715182 + 0.412910i
\(75\) 8.29628 + 12.4969i 0.110617 + 0.166625i
\(76\) 27.0954 0.356519
\(77\) −8.13704 + 89.0858i −0.105676 + 1.15696i
\(78\) 0.224655 + 3.59188i 0.00288020 + 0.0460497i
\(79\) 18.5245 + 32.0854i 0.234487 + 0.406144i 0.959124 0.282988i \(-0.0913255\pi\)
−0.724636 + 0.689132i \(0.757992\pi\)
\(80\) 21.5458 + 12.4395i 0.269323 + 0.155494i
\(81\) −21.8973 + 77.9840i −0.270337 + 0.962766i
\(82\) 13.1197 + 22.7239i 0.159996 + 0.277121i
\(83\) 20.0443i 0.241498i −0.992683 0.120749i \(-0.961470\pi\)
0.992683 0.120749i \(-0.0385296\pi\)
\(84\) 10.7836 17.5012i 0.128376 0.208347i
\(85\) −32.2894 −0.379875
\(86\) −34.8741 + 20.1346i −0.405512 + 0.234123i
\(87\) 71.6303 + 35.5904i 0.823336 + 0.409085i
\(88\) −55.2968 + 95.7769i −0.628373 + 1.08837i
\(89\) −62.7886 + 36.2510i −0.705489 + 0.407315i −0.809389 0.587273i \(-0.800201\pi\)
0.103899 + 0.994588i \(0.466868\pi\)
\(90\) −34.7067 + 4.35853i −0.385630 + 0.0484281i
\(91\) 2.02505 + 4.38640i 0.0222533 + 0.0482022i
\(92\) 42.2268i 0.458987i
\(93\) −29.6746 44.6995i −0.319082 0.480640i
\(94\) 38.2848 66.3112i 0.407285 0.705438i
\(95\) −53.6016 30.9469i −0.564228 0.325757i
\(96\) 38.1831 25.3485i 0.397740 0.264047i
\(97\) 23.2629 0.239823 0.119912 0.992785i \(-0.461739\pi\)
0.119912 + 0.992785i \(0.461739\pi\)
\(98\) −15.4298 + 83.7592i −0.157447 + 0.854686i
\(99\) −14.3313 114.119i −0.144761 1.15272i
\(100\) 2.44722 + 4.23872i 0.0244722 + 0.0423872i
\(101\) −124.801 72.0539i −1.23565 0.713405i −0.267451 0.963571i \(-0.586181\pi\)
−0.968203 + 0.250166i \(0.919515\pi\)
\(102\) 33.5046 67.4323i 0.328477 0.661101i
\(103\) 75.7306 + 131.169i 0.735249 + 1.27349i 0.954614 + 0.297846i \(0.0962681\pi\)
−0.219365 + 0.975643i \(0.570399\pi\)
\(104\) 5.97284i 0.0574311i
\(105\) −41.3216 + 22.3053i −0.393539 + 0.212431i
\(106\) 157.725 1.48797
\(107\) −35.8969 + 20.7251i −0.335485 + 0.193692i −0.658274 0.752779i \(-0.728713\pi\)
0.322789 + 0.946471i \(0.395380\pi\)
\(108\) −8.71949 + 24.9503i −0.0807360 + 0.231021i
\(109\) −1.31599 + 2.27937i −0.0120733 + 0.0209116i −0.871999 0.489508i \(-0.837176\pi\)
0.859926 + 0.510419i \(0.170510\pi\)
\(110\) 43.0144 24.8343i 0.391040 0.225767i
\(111\) −105.271 + 6.58420i −0.948385 + 0.0593171i
\(112\) −44.9156 + 63.6273i −0.401032 + 0.568101i
\(113\) 140.014i 1.23907i −0.784971 0.619533i \(-0.787322\pi\)
0.784971 0.619533i \(-0.212678\pi\)
\(114\) 120.248 79.8287i 1.05481 0.700252i
\(115\) 48.2292 83.5354i 0.419384 0.726395i
\(116\) 22.6022 + 13.0494i 0.194847 + 0.112495i
\(117\) −3.75192 4.95053i −0.0320677 0.0423122i
\(118\) −42.8393 −0.363045
\(119\) 9.19447 100.663i 0.0772645 0.845905i
\(120\) −57.9394 + 3.62384i −0.482829 + 0.0301987i
\(121\) 21.1580 + 36.6468i 0.174860 + 0.302866i
\(122\) −99.6188 57.5149i −0.816547 0.471434i
\(123\) −40.5583 20.1519i −0.329742 0.163837i
\(124\) −8.75337 15.1613i −0.0705917 0.122268i
\(125\) 11.1803i 0.0894427i
\(126\) −3.70500 109.440i −0.0294048 0.868570i
\(127\) −235.143 −1.85152 −0.925758 0.378117i \(-0.876572\pi\)
−0.925758 + 0.378117i \(0.876572\pi\)
\(128\) −54.0408 + 31.2004i −0.422193 + 0.243754i
\(129\) 30.9268 62.2442i 0.239743 0.482513i
\(130\) 1.34123 2.32308i 0.0103171 0.0178698i
\(131\) −67.6099 + 39.0346i −0.516106 + 0.297974i −0.735340 0.677698i \(-0.762978\pi\)
0.219234 + 0.975672i \(0.429644\pi\)
\(132\) −2.34270 37.4560i −0.0177477 0.283758i
\(133\) 111.741 158.292i 0.840156 1.19016i
\(134\) 47.3338i 0.353238i
\(135\) 45.7462 39.3990i 0.338861 0.291845i
\(136\) 62.4828 108.223i 0.459432 0.795760i
\(137\) −123.931 71.5516i −0.904606 0.522274i −0.0259142 0.999664i \(-0.508250\pi\)
−0.878692 + 0.477390i \(0.841583\pi\)
\(138\) 124.409 + 187.400i 0.901514 + 1.35797i
\(139\) 119.427 0.859185 0.429593 0.903023i \(-0.358657\pi\)
0.429593 + 0.903023i \(0.358657\pi\)
\(140\) −13.9111 + 6.42228i −0.0993652 + 0.0458734i
\(141\) 8.24976 + 131.900i 0.0585089 + 0.935464i
\(142\) −66.5057 115.191i −0.468350 0.811206i
\(143\) 7.63853 + 4.41011i 0.0534163 + 0.0308399i
\(144\) 38.8722 92.2831i 0.269945 0.640855i
\(145\) −29.8086 51.6300i −0.205576 0.356069i
\(146\) 85.9054i 0.588393i
\(147\) −57.7707 135.172i −0.392998 0.919539i
\(148\) −34.4166 −0.232545
\(149\) −124.082 + 71.6388i −0.832765 + 0.480797i −0.854799 0.518960i \(-0.826319\pi\)
0.0220332 + 0.999757i \(0.492986\pi\)
\(150\) 23.3487 + 11.6011i 0.155658 + 0.0773408i
\(151\) 1.71655 2.97316i 0.0113679 0.0196898i −0.860285 0.509813i \(-0.829715\pi\)
0.871653 + 0.490123i \(0.163048\pi\)
\(152\) 207.448 119.770i 1.36479 0.787961i
\(153\) 16.1937 + 128.949i 0.105841 + 0.842806i
\(154\) 65.1731 + 141.170i 0.423202 + 0.916686i
\(155\) 39.9905i 0.258003i
\(156\) −1.12102 1.68861i −0.00718600 0.0108244i
\(157\) −121.784 + 210.937i −0.775697 + 1.34355i 0.158705 + 0.987326i \(0.449268\pi\)
−0.934402 + 0.356221i \(0.884065\pi\)
\(158\) 55.7687 + 32.1981i 0.352966 + 0.203785i
\(159\) −226.803 + 150.567i −1.42643 + 0.946965i
\(160\) −34.1605 −0.213503
\(161\) 246.690 + 174.142i 1.53223 + 1.08163i
\(162\) 34.8121 + 136.417i 0.214889 + 0.842081i
\(163\) −4.62591 8.01232i −0.0283798 0.0491553i 0.851487 0.524376i \(-0.175701\pi\)
−0.879866 + 0.475221i \(0.842368\pi\)
\(164\) −12.7978 7.38879i −0.0780351 0.0450536i
\(165\) −38.1458 + 76.7732i −0.231186 + 0.465292i
\(166\) −17.4199 30.1721i −0.104939 0.181760i
\(167\) 196.020i 1.17378i −0.809668 0.586888i \(-0.800353\pi\)
0.809668 0.586888i \(-0.199647\pi\)
\(168\) 5.20099 181.659i 0.0309583 1.08130i
\(169\) −168.524 −0.997181
\(170\) −48.6042 + 28.0616i −0.285907 + 0.165068i
\(171\) −96.7060 + 229.582i −0.565532 + 1.34258i
\(172\) 11.3395 19.6405i 0.0659271 0.114189i
\(173\) −89.9489 + 51.9320i −0.519936 + 0.300185i −0.736909 0.675992i \(-0.763715\pi\)
0.216972 + 0.976178i \(0.430382\pi\)
\(174\) 138.753 8.67837i 0.797432 0.0498757i
\(175\) 34.8549 + 3.18363i 0.199171 + 0.0181922i
\(176\) 142.188i 0.807885i
\(177\) 61.6013 40.8952i 0.348030 0.231046i
\(178\) −63.0091 + 109.135i −0.353984 + 0.613118i
\(179\) 243.418 + 140.537i 1.35988 + 0.785124i 0.989607 0.143800i \(-0.0459323\pi\)
0.370269 + 0.928925i \(0.379266\pi\)
\(180\) 15.7002 11.8989i 0.0872234 0.0661051i
\(181\) 53.4762 0.295448 0.147724 0.989029i \(-0.452805\pi\)
0.147724 + 0.989029i \(0.452805\pi\)
\(182\) 6.86032 + 4.84281i 0.0376940 + 0.0266088i
\(183\) 198.153 12.3936i 1.08280 0.0677243i
\(184\) 186.655 + 323.297i 1.01443 + 1.75705i
\(185\) 68.0847 + 39.3087i 0.368026 + 0.212480i
\(186\) −83.5151 41.4956i −0.449006 0.223094i
\(187\) −92.2697 159.816i −0.493421 0.854630i
\(188\) 43.1227i 0.229376i
\(189\) 109.801 + 153.834i 0.580957 + 0.813934i
\(190\) −107.580 −0.566209
\(191\) 91.5701 52.8680i 0.479424 0.276796i −0.240752 0.970587i \(-0.577394\pi\)
0.720177 + 0.693791i \(0.244061\pi\)
\(192\) 94.8555 190.909i 0.494039 0.994316i
\(193\) 45.0633 78.0519i 0.233489 0.404414i −0.725344 0.688387i \(-0.758319\pi\)
0.958832 + 0.283973i \(0.0916525\pi\)
\(194\) 35.0169 20.2170i 0.180499 0.104211i
\(195\) 0.289014 + 4.62086i 0.00148212 + 0.0236967i
\(196\) −16.0603 45.1969i −0.0819405 0.230597i
\(197\) 195.601i 0.992897i 0.868066 + 0.496448i \(0.165363\pi\)
−0.868066 + 0.496448i \(0.834637\pi\)
\(198\) −120.750 159.325i −0.609848 0.804673i
\(199\) 116.030 200.970i 0.583067 1.00990i −0.412046 0.911163i \(-0.635186\pi\)
0.995113 0.0987388i \(-0.0314808\pi\)
\(200\) 37.4728 + 21.6349i 0.187364 + 0.108175i
\(201\) −45.1858 68.0644i −0.224805 0.338629i
\(202\) −250.479 −1.23999
\(203\) 169.445 78.2270i 0.834707 0.385355i
\(204\) 2.64714 + 42.3235i 0.0129762 + 0.207468i
\(205\) 16.8781 + 29.2338i 0.0823324 + 0.142604i
\(206\) 227.990 + 131.630i 1.10675 + 0.638981i
\(207\) −357.791 150.711i −1.72846 0.728074i
\(208\) 3.83957 + 6.65033i 0.0184595 + 0.0319727i
\(209\) 353.734i 1.69251i
\(210\) −42.8153 + 69.4867i −0.203882 + 0.330889i
\(211\) 210.912 0.999585 0.499793 0.866145i \(-0.333410\pi\)
0.499793 + 0.866145i \(0.333410\pi\)
\(212\) −76.9276 + 44.4142i −0.362866 + 0.209501i
\(213\) 205.597 + 102.153i 0.965242 + 0.479593i
\(214\) −36.0230 + 62.3936i −0.168332 + 0.291559i
\(215\) −44.8647 + 25.9026i −0.208673 + 0.120477i
\(216\) 43.5297 + 229.567i 0.201526 + 1.06281i
\(217\) −124.671 11.3874i −0.574521 0.0524764i
\(218\) 4.57475i 0.0209851i
\(219\) 82.0069 + 123.529i 0.374461 + 0.564058i
\(220\) −13.9863 + 24.2250i −0.0635741 + 0.110114i
\(221\) −8.63117 4.98321i −0.0390551 0.0225485i
\(222\) −152.739 + 101.398i −0.688012 + 0.456749i
\(223\) −99.6553 −0.446885 −0.223442 0.974717i \(-0.571729\pi\)
−0.223442 + 0.974717i \(0.571729\pi\)
\(224\) 9.72729 106.496i 0.0434254 0.475429i
\(225\) −44.6493 + 5.60715i −0.198441 + 0.0249207i
\(226\) −121.682 210.759i −0.538415 0.932563i
\(227\) 266.629 + 153.939i 1.17458 + 0.678143i 0.954754 0.297396i \(-0.0961182\pi\)
0.219824 + 0.975539i \(0.429452\pi\)
\(228\) −36.1695 + 72.7958i −0.158638 + 0.319280i
\(229\) −27.9040 48.3312i −0.121852 0.211053i 0.798646 0.601801i \(-0.205550\pi\)
−0.920498 + 0.390748i \(0.872217\pi\)
\(230\) 167.658i 0.728946i
\(231\) −228.480 140.781i −0.989090 0.609443i
\(232\) 230.729 0.994522
\(233\) −176.629 + 101.977i −0.758062 + 0.437668i −0.828600 0.559842i \(-0.810862\pi\)
0.0705372 + 0.997509i \(0.477529\pi\)
\(234\) −9.94999 4.19121i −0.0425213 0.0179111i
\(235\) 49.2524 85.3077i 0.209585 0.363012i
\(236\) 20.8941 12.0632i 0.0885342 0.0511152i
\(237\) −110.930 + 6.93817i −0.468060 + 0.0292750i
\(238\) −73.6425 159.515i −0.309422 0.670231i
\(239\) 83.9724i 0.351349i −0.984448 0.175674i \(-0.943789\pi\)
0.984448 0.175674i \(-0.0562106\pi\)
\(240\) −62.1819 + 41.2806i −0.259091 + 0.172002i
\(241\) −68.2986 + 118.297i −0.283397 + 0.490858i −0.972219 0.234072i \(-0.924795\pi\)
0.688822 + 0.724930i \(0.258128\pi\)
\(242\) 63.6971 + 36.7755i 0.263211 + 0.151965i
\(243\) −180.285 162.931i −0.741913 0.670496i
\(244\) 64.7830 0.265504
\(245\) −19.8500 + 107.754i −0.0810205 + 0.439813i
\(246\) −78.5645 + 4.91385i −0.319368 + 0.0199750i
\(247\) −9.55206 16.5447i −0.0386723 0.0669824i
\(248\) −134.035 77.3851i −0.540463 0.312037i
\(249\) 53.8520 + 26.7571i 0.216273 + 0.107458i
\(250\) −9.71647 16.8294i −0.0388659 0.0673176i
\(251\) 130.419i 0.519597i −0.965663 0.259799i \(-0.916344\pi\)
0.965663 0.259799i \(-0.0836562\pi\)
\(252\) 32.6244 + 52.3339i 0.129462 + 0.207674i
\(253\) 551.276 2.17896
\(254\) −353.953 + 204.355i −1.39351 + 0.804546i
\(255\) 43.1029 86.7500i 0.169031 0.340196i
\(256\) 87.8863 152.224i 0.343306 0.594623i
\(257\) 139.531 80.5581i 0.542921 0.313456i −0.203341 0.979108i \(-0.565180\pi\)
0.746262 + 0.665652i \(0.231847\pi\)
\(258\) −7.54120 120.572i −0.0292295 0.467332i
\(259\) −141.933 + 201.062i −0.548004 + 0.776302i
\(260\) 1.51072i 0.00581045i
\(261\) −191.238 + 144.936i −0.732711 + 0.555309i
\(262\) −67.8474 + 117.515i −0.258959 + 0.448531i
\(263\) −237.621 137.191i −0.903503 0.521638i −0.0251677 0.999683i \(-0.508012\pi\)
−0.878335 + 0.478046i \(0.841345\pi\)
\(264\) −183.503 276.415i −0.695088 1.04703i
\(265\) 202.910 0.765697
\(266\) 30.6336 335.382i 0.115164 1.26083i
\(267\) −13.5775 217.082i −0.0508519 0.813040i
\(268\) −13.3288 23.0862i −0.0497344 0.0861426i
\(269\) 153.258 + 88.4834i 0.569732 + 0.328935i 0.757042 0.653366i \(-0.226644\pi\)
−0.187311 + 0.982301i \(0.559977\pi\)
\(270\) 34.6199 99.0627i 0.128222 0.366899i
\(271\) 142.395 + 246.636i 0.525444 + 0.910096i 0.999561 + 0.0296340i \(0.00943416\pi\)
−0.474117 + 0.880462i \(0.657233\pi\)
\(272\) 160.665i 0.590681i
\(273\) −14.4879 0.414797i −0.0530693 0.00151940i
\(274\) −248.733 −0.907783
\(275\) 55.3369 31.9488i 0.201225 0.116177i
\(276\) −113.448 56.3683i −0.411045 0.204233i
\(277\) −35.1794 + 60.9325i −0.127001 + 0.219973i −0.922514 0.385965i \(-0.873869\pi\)
0.795512 + 0.605938i \(0.207202\pi\)
\(278\) 179.769 103.790i 0.646652 0.373345i
\(279\) 159.704 20.0560i 0.572416 0.0718852i
\(280\) −78.1178 + 110.662i −0.278992 + 0.395220i
\(281\) 410.358i 1.46035i −0.683261 0.730174i \(-0.739439\pi\)
0.683261 0.730174i \(-0.260561\pi\)
\(282\) 127.048 + 191.376i 0.450526 + 0.678638i
\(283\) −209.909 + 363.573i −0.741727 + 1.28471i 0.209981 + 0.977705i \(0.432660\pi\)
−0.951708 + 0.307004i \(0.900674\pi\)
\(284\) 64.8739 + 37.4550i 0.228429 + 0.131884i
\(285\) 154.696 102.698i 0.542793 0.360343i
\(286\) 15.3307 0.0536039
\(287\) −95.9430 + 44.2935i −0.334296 + 0.154333i
\(288\) 17.1321 + 136.422i 0.0594866 + 0.473687i
\(289\) −40.2397 69.6972i −0.139238 0.241167i
\(290\) −89.7398 51.8113i −0.309448 0.178660i
\(291\) −31.0535 + 62.4991i −0.106713 + 0.214773i
\(292\) 24.1903 + 41.8988i 0.0828434 + 0.143489i
\(293\) 22.0605i 0.0752917i −0.999291 0.0376458i \(-0.988014\pi\)
0.999291 0.0376458i \(-0.0119859\pi\)
\(294\) −204.434 153.264i −0.695354 0.521306i
\(295\) −55.1117 −0.186819
\(296\) −263.500 + 152.132i −0.890203 + 0.513959i
\(297\) 325.729 + 113.834i 1.09673 + 0.383279i
\(298\) −124.518 + 215.671i −0.417845 + 0.723729i
\(299\) 25.7840 14.8864i 0.0862341 0.0497873i
\(300\) −14.6547 + 0.916584i −0.0488490 + 0.00305528i
\(301\) −67.9766 147.242i −0.225836 0.489177i
\(302\) 5.96720i 0.0197589i
\(303\) 360.179 239.112i 1.18871 0.789147i
\(304\) 153.986 266.711i 0.506531 0.877338i
\(305\) −128.157 73.9916i −0.420187 0.242595i
\(306\) 136.442 + 180.030i 0.445887 + 0.588333i
\(307\) 477.487 1.55533 0.777666 0.628678i \(-0.216404\pi\)
0.777666 + 0.628678i \(0.216404\pi\)
\(308\) −71.5392 50.5007i −0.232270 0.163963i
\(309\) −453.498 + 28.3642i −1.46763 + 0.0917934i
\(310\) 34.7544 + 60.1964i 0.112111 + 0.194182i
\(311\) 158.616 + 91.5767i 0.510018 + 0.294459i 0.732841 0.680400i \(-0.238194\pi\)
−0.222823 + 0.974859i \(0.571527\pi\)
\(312\) −16.0469 7.97310i −0.0514323 0.0255548i
\(313\) 50.2014 + 86.9514i 0.160388 + 0.277800i 0.935008 0.354627i \(-0.115392\pi\)
−0.774620 + 0.632427i \(0.782059\pi\)
\(314\) 423.356i 1.34827i
\(315\) −4.76639 140.792i −0.0151314 0.446958i
\(316\) −36.2669 −0.114769
\(317\) −264.854 + 152.913i −0.835501 + 0.482377i −0.855733 0.517418i \(-0.826893\pi\)
0.0202312 + 0.999795i \(0.493560\pi\)
\(318\) −210.546 + 423.751i −0.662096 + 1.33255i
\(319\) 170.361 295.074i 0.534048 0.924998i
\(320\) −137.604 + 79.4458i −0.430013 + 0.248268i
\(321\) −7.76237 124.108i −0.0241819 0.386629i
\(322\) 522.675 + 47.7409i 1.62322 + 0.148264i
\(323\) 399.703i 1.23747i
\(324\) −55.3929 56.7321i −0.170966 0.175099i
\(325\) 1.72546 2.98858i 0.00530911 0.00919564i
\(326\) −13.9265 8.04046i −0.0427193 0.0246640i
\(327\) −4.36714 6.57832i −0.0133552 0.0201172i
\(328\) −130.643 −0.398301
\(329\) 251.924 + 177.837i 0.765725 + 0.540538i
\(330\) 9.30146 + 148.716i 0.0281863 + 0.450653i
\(331\) −91.0722 157.742i −0.275143 0.476561i 0.695028 0.718982i \(-0.255392\pi\)
−0.970171 + 0.242421i \(0.922058\pi\)
\(332\) 16.9925 + 9.81060i 0.0511821 + 0.0295500i
\(333\) 122.836 291.614i 0.368876 0.875718i
\(334\) −170.355 295.063i −0.510045 0.883423i
\(335\) 60.8939i 0.181773i
\(336\) −110.987 205.608i −0.330317 0.611928i
\(337\) 127.130 0.377241 0.188621 0.982050i \(-0.439598\pi\)
0.188621 + 0.982050i \(0.439598\pi\)
\(338\) −253.673 + 146.458i −0.750513 + 0.433309i
\(339\) 376.169 + 186.904i 1.10964 + 0.551340i
\(340\) 15.8039 27.3731i 0.0464819 0.0805091i
\(341\) −197.932 + 114.276i −0.580447 + 0.335121i
\(342\) 53.9533 + 429.626i 0.157758 + 1.25622i
\(343\) −330.273 92.5661i −0.962896 0.269872i
\(344\) 200.495i 0.582836i
\(345\) 160.049 + 241.086i 0.463910 + 0.698799i
\(346\) −90.2649 + 156.343i −0.260881 + 0.451859i
\(347\) 304.200 + 175.630i 0.876658 + 0.506139i 0.869555 0.493836i \(-0.164406\pi\)
0.00710329 + 0.999975i \(0.497739\pi\)
\(348\) −65.2306 + 43.3045i −0.187444 + 0.124438i
\(349\) −542.999 −1.55587 −0.777936 0.628344i \(-0.783733\pi\)
−0.777936 + 0.628344i \(0.783733\pi\)
\(350\) 55.2328 25.4990i 0.157808 0.0728544i
\(351\) 18.3087 3.47164i 0.0521616 0.00989071i
\(352\) −97.6167 169.077i −0.277320 0.480333i
\(353\) −45.4717 26.2531i −0.128815 0.0743714i 0.434208 0.900813i \(-0.357028\pi\)
−0.563023 + 0.826441i \(0.690362\pi\)
\(354\) 57.1859 115.094i 0.161542 0.325124i
\(355\) −85.5580 148.191i −0.241009 0.417439i
\(356\) 70.9714i 0.199358i
\(357\) 258.171 + 159.076i 0.723168 + 0.445592i
\(358\) 488.545 1.36465
\(359\) 366.445 211.567i 1.02074 0.589323i 0.106420 0.994321i \(-0.466061\pi\)
0.914318 + 0.404998i \(0.132728\pi\)
\(360\) 67.6070 160.500i 0.187797 0.445834i
\(361\) −202.585 + 350.887i −0.561177 + 0.971986i
\(362\) 80.4960 46.4744i 0.222365 0.128382i
\(363\) −126.701 + 7.92454i −0.349038 + 0.0218307i
\(364\) −4.70969 0.430180i −0.0129387 0.00118181i
\(365\) 110.515i 0.302781i
\(366\) 287.503 190.864i 0.785526 0.521486i
\(367\) −25.6698 + 44.4614i −0.0699449 + 0.121148i −0.898877 0.438201i \(-0.855616\pi\)
0.828932 + 0.559350i \(0.188949\pi\)
\(368\) 415.655 + 239.979i 1.12950 + 0.652116i
\(369\) 108.282 82.0651i 0.293447 0.222399i
\(370\) 136.648 0.369318
\(371\) −57.7790 + 632.574i −0.155739 + 1.70505i
\(372\) 52.4178 3.27849i 0.140908 0.00881314i
\(373\) −236.881 410.290i −0.635070 1.09997i −0.986500 0.163760i \(-0.947638\pi\)
0.351430 0.936214i \(-0.385696\pi\)
\(374\) −277.781 160.377i −0.742731 0.428816i
\(375\) 30.0376 + 14.9246i 0.0801003 + 0.0397988i
\(376\) 190.616 + 330.156i 0.506956 + 0.878074i
\(377\) 18.4014i 0.0488101i
\(378\) 298.972 + 136.136i 0.790930 + 0.360149i
\(379\) −359.932 −0.949689 −0.474845 0.880070i \(-0.657496\pi\)
−0.474845 + 0.880070i \(0.657496\pi\)
\(380\) 52.4701 30.2936i 0.138079 0.0797200i
\(381\) 313.890 631.744i 0.823859 1.65812i
\(382\) 91.8917 159.161i 0.240554 0.416652i
\(383\) −322.534 + 186.215i −0.842125 + 0.486201i −0.857986 0.513673i \(-0.828284\pi\)
0.0158611 + 0.999874i \(0.494951\pi\)
\(384\) −11.6858 186.838i −0.0304318 0.486556i
\(385\) 83.8436 + 181.611i 0.217776 + 0.471718i
\(386\) 156.652i 0.405835i
\(387\) 125.944 + 166.179i 0.325437 + 0.429403i
\(388\) −11.3859 + 19.7209i −0.0293451 + 0.0508272i
\(389\) −550.051 317.572i −1.41401 0.816381i −0.418250 0.908332i \(-0.637356\pi\)
−0.995764 + 0.0919506i \(0.970690\pi\)
\(390\) 4.45088 + 6.70447i 0.0114125 + 0.0171909i
\(391\) −622.916 −1.59313
\(392\) −322.745 275.045i −0.823330 0.701645i
\(393\) −14.6200 233.751i −0.0372011 0.594786i
\(394\) 169.990 + 294.432i 0.431447 + 0.747288i
\(395\) 71.7451 + 41.4220i 0.181633 + 0.104866i
\(396\) 103.758 + 43.7058i 0.262016 + 0.110368i
\(397\) 380.530 + 659.097i 0.958514 + 1.66019i 0.726114 + 0.687575i \(0.241325\pi\)
0.232400 + 0.972620i \(0.425342\pi\)
\(398\) 403.353i 1.01345i
\(399\) 276.112 + 511.511i 0.692010 + 1.28198i
\(400\) 55.6311 0.139078
\(401\) −16.9155 + 9.76619i −0.0421834 + 0.0243546i −0.520943 0.853591i \(-0.674420\pi\)
0.478760 + 0.877946i \(0.341086\pi\)
\(402\) −127.169 63.1857i −0.316341 0.157178i
\(403\) −6.17172 + 10.6897i −0.0153144 + 0.0265254i
\(404\) 122.166 70.5328i 0.302392 0.174586i
\(405\) 44.7849 + 175.497i 0.110580 + 0.433327i
\(406\) 187.076 265.012i 0.460779 0.652739i
\(407\) 449.313i 1.10396i
\(408\) 207.350 + 312.336i 0.508210 + 0.765529i
\(409\) 308.387 534.141i 0.754002 1.30597i −0.191868 0.981421i \(-0.561454\pi\)
0.945869 0.324548i \(-0.105212\pi\)
\(410\) 50.8123 + 29.3365i 0.123932 + 0.0715524i
\(411\) 357.668 237.445i 0.870240 0.577724i
\(412\) −148.264 −0.359864
\(413\) 15.6932 171.812i 0.0379980 0.416009i
\(414\) −669.550 + 84.0834i −1.61727 + 0.203100i
\(415\) −22.4103 38.8157i −0.0540006 0.0935318i
\(416\) −9.13135 5.27199i −0.0219504 0.0126730i
\(417\) −159.422 + 320.857i −0.382307 + 0.769442i
\(418\) −307.419 532.465i −0.735451 1.27384i
\(419\) 476.423i 1.13705i 0.822667 + 0.568523i \(0.192485\pi\)
−0.822667 + 0.568523i \(0.807515\pi\)
\(420\) 1.31549 45.9473i 0.00313213 0.109398i
\(421\) −168.350 −0.399881 −0.199941 0.979808i \(-0.564075\pi\)
−0.199941 + 0.979808i \(0.564075\pi\)
\(422\) 317.480 183.297i 0.752322 0.434353i
\(423\) −365.382 153.909i −0.863787 0.363851i
\(424\) −392.648 + 680.087i −0.926057 + 1.60398i
\(425\) −62.5281 + 36.1006i −0.147125 + 0.0849426i
\(426\) 398.256 24.9091i 0.934874 0.0584720i
\(427\) 267.163 378.463i 0.625675 0.886330i
\(428\) 40.5751i 0.0948016i
\(429\) −22.0450 + 14.6350i −0.0513870 + 0.0341142i
\(430\) −45.0222 + 77.9808i −0.104703 + 0.181351i
\(431\) −93.3104 53.8728i −0.216498 0.124995i 0.387830 0.921731i \(-0.373225\pi\)
−0.604327 + 0.796736i \(0.706558\pi\)
\(432\) 196.042 + 227.624i 0.453800 + 0.526907i
\(433\) −49.6338 −0.114628 −0.0573139 0.998356i \(-0.518254\pi\)
−0.0573139 + 0.998356i \(0.518254\pi\)
\(434\) −197.560 + 91.2064i −0.455207 + 0.210153i
\(435\) 178.503 11.1645i 0.410351 0.0256656i
\(436\) −1.28821 2.23125i −0.00295462 0.00511754i
\(437\) −1034.07 597.018i −2.36628 1.36617i
\(438\) 230.797 + 114.675i 0.526934 + 0.261814i
\(439\) 67.1866 + 116.371i 0.153045 + 0.265081i 0.932345 0.361569i \(-0.117759\pi\)
−0.779301 + 0.626650i \(0.784426\pi\)
\(440\) 247.295i 0.562034i
\(441\) 440.278 + 25.2314i 0.998362 + 0.0572141i
\(442\) −17.3230 −0.0391923
\(443\) 381.536 220.280i 0.861256 0.497246i −0.00317679 0.999995i \(-0.501011\pi\)
0.864433 + 0.502749i \(0.167678\pi\)
\(444\) 45.9425 92.4651i 0.103474 0.208255i
\(445\) −81.0597 + 140.400i −0.182157 + 0.315504i
\(446\) −150.008 + 86.6071i −0.336341 + 0.194186i
\(447\) −26.8316 428.995i −0.0600260 0.959719i
\(448\) −208.490 451.605i −0.465380 1.00805i
\(449\) 206.559i 0.460042i 0.973186 + 0.230021i \(0.0738795\pi\)
−0.973186 + 0.230021i \(0.926121\pi\)
\(450\) −62.3362 + 47.2435i −0.138525 + 0.104986i
\(451\) −96.4615 + 167.076i −0.213884 + 0.370457i
\(452\) 118.696 + 68.5293i 0.262602 + 0.151613i
\(453\) 5.69640 + 8.58062i 0.0125748 + 0.0189418i
\(454\) 535.132 1.17870
\(455\) 8.82563 + 6.23016i 0.0193970 + 0.0136927i
\(456\) 44.8587 + 717.219i 0.0983744 + 1.57285i
\(457\) −14.6514 25.3770i −0.0320600 0.0555295i 0.849550 0.527508i \(-0.176873\pi\)
−0.881610 + 0.471978i \(0.843540\pi\)
\(458\) −84.0061 48.5009i −0.183419 0.105897i
\(459\) −368.058 128.627i −0.801869 0.280233i
\(460\) 47.2110 + 81.7719i 0.102633 + 0.177765i
\(461\) 41.0856i 0.0891228i −0.999007 0.0445614i \(-0.985811\pi\)
0.999007 0.0445614i \(-0.0141890\pi\)
\(462\) −466.272 13.3496i −1.00925 0.0288952i
\(463\) 228.244 0.492968 0.246484 0.969147i \(-0.420725\pi\)
0.246484 + 0.969147i \(0.420725\pi\)
\(464\) 256.900 148.321i 0.553664 0.319658i
\(465\) −107.440 53.3830i −0.231054 0.114802i
\(466\) −177.249 + 307.004i −0.380362 + 0.658807i
\(467\) −508.155 + 293.383i −1.08813 + 0.628230i −0.933077 0.359677i \(-0.882887\pi\)
−0.155049 + 0.987907i \(0.549553\pi\)
\(468\) 6.03313 0.757653i 0.0128913 0.00161892i
\(469\) −189.838 17.3397i −0.404771 0.0369716i
\(470\) 171.215i 0.364287i
\(471\) −404.143 608.770i −0.858053 1.29251i
\(472\) 106.646 184.716i 0.225945 0.391348i
\(473\) −256.409 148.038i −0.542092 0.312977i
\(474\) −160.950 + 106.850i −0.339557 + 0.225421i
\(475\) −138.399 −0.291366
\(476\) 80.8359 + 57.0634i 0.169823 + 0.119881i
\(477\) −101.763 810.331i −0.213340 1.69881i
\(478\) −72.9776 126.401i −0.152673 0.264437i
\(479\) −629.208 363.273i −1.31359 0.758399i −0.330898 0.943666i \(-0.607352\pi\)
−0.982688 + 0.185267i \(0.940685\pi\)
\(480\) 45.6007 91.7772i 0.0950014 0.191202i
\(481\) 12.1330 + 21.0150i 0.0252246 + 0.0436902i
\(482\) 237.424i 0.492582i
\(483\) −797.163 + 430.306i −1.65044 + 0.890903i
\(484\) −41.4228 −0.0855842
\(485\) 45.0484 26.0087i 0.0928832 0.0536262i
\(486\) −412.975 88.5747i −0.849742 0.182252i
\(487\) 317.553 550.018i 0.652060 1.12940i −0.330562 0.943784i \(-0.607238\pi\)
0.982622 0.185617i \(-0.0594284\pi\)
\(488\) 495.991 286.360i 1.01637 0.586804i
\(489\) 27.7014 1.73259i 0.0566490 0.00354313i
\(490\) 63.7660 + 179.450i 0.130135 + 0.366225i
\(491\) 68.0254i 0.138545i 0.997598 + 0.0692723i \(0.0220677\pi\)
−0.997598 + 0.0692723i \(0.977932\pi\)
\(492\) 36.9347 24.5198i 0.0750705 0.0498369i
\(493\) −192.500 + 333.420i −0.390467 + 0.676308i
\(494\) −28.7568 16.6028i −0.0582122 0.0336088i
\(495\) −155.342 204.968i −0.313822 0.414077i
\(496\) −198.984 −0.401178
\(497\) 486.350 224.531i 0.978572 0.451773i
\(498\) 104.315 6.52445i 0.209469 0.0131013i
\(499\) 354.547 + 614.093i 0.710515 + 1.23065i 0.964664 + 0.263483i \(0.0848712\pi\)
−0.254149 + 0.967165i \(0.581795\pi\)
\(500\) 9.47806 + 5.47216i 0.0189561 + 0.0109443i
\(501\) 526.637 + 261.666i 1.05117 + 0.522288i
\(502\) −113.343 196.315i −0.225782 0.391067i
\(503\) 96.8787i 0.192602i 0.995352 + 0.0963009i \(0.0307011\pi\)
−0.995352 + 0.0963009i \(0.969299\pi\)
\(504\) 481.111 + 256.469i 0.954585 + 0.508867i
\(505\) −322.235 −0.638089
\(506\) 829.819 479.096i 1.63996 0.946830i
\(507\) 224.961 452.763i 0.443710 0.893024i
\(508\) 115.089 199.340i 0.226554 0.392402i
\(509\) 550.592 317.884i 1.08171 0.624527i 0.150355 0.988632i \(-0.451958\pi\)
0.931358 + 0.364105i \(0.118625\pi\)
\(510\) −10.5102 168.041i −0.0206083 0.329493i
\(511\) 344.533 + 31.4694i 0.674233 + 0.0615841i
\(512\) 555.120i 1.08422i
\(513\) −487.712 566.282i −0.950705 1.10386i
\(514\) 140.021 242.523i 0.272414 0.471835i
\(515\) 293.303 + 169.339i 0.569521 + 0.328813i
\(516\) 37.6301 + 56.6831i 0.0729266 + 0.109851i
\(517\) 562.972 1.08892
\(518\) −38.9108 + 426.002i −0.0751173 + 0.822397i
\(519\) −19.4506 310.985i −0.0374772 0.599200i
\(520\) 6.67783 + 11.5663i 0.0128420 + 0.0222430i
\(521\) −3.34581 1.93170i −0.00642190 0.00370769i 0.496786 0.867873i \(-0.334514\pi\)
−0.503208 + 0.864166i \(0.667847\pi\)
\(522\) −161.905 + 384.365i −0.310163 + 0.736332i
\(523\) 414.213 + 717.439i 0.791995 + 1.37178i 0.924730 + 0.380624i \(0.124291\pi\)
−0.132735 + 0.991152i \(0.542376\pi\)
\(524\) 76.4211i 0.145842i
\(525\) −55.0809 + 89.3929i −0.104916 + 0.170272i
\(526\) −476.912 −0.906676
\(527\) 223.654 129.127i 0.424391 0.245022i
\(528\) −382.008 189.806i −0.723500 0.359480i
\(529\) 665.921 1153.41i 1.25883 2.18036i
\(530\) 305.434 176.342i 0.576290 0.332721i
\(531\) 27.6395 + 220.092i 0.0520518 + 0.414485i
\(532\) 79.4999 + 172.203i 0.149436 + 0.323689i
\(533\) 10.4192i 0.0195482i
\(534\) −209.096 314.967i −0.391566 0.589825i
\(535\) −46.3427 + 80.2679i −0.0866218 + 0.150033i
\(536\) −204.096 117.835i −0.380776 0.219841i
\(537\) −702.510 + 466.374i −1.30821 + 0.868481i
\(538\) 307.592 0.571733
\(539\) −590.051 + 209.670i −1.09471 + 0.388998i
\(540\) 11.0100 + 58.0647i 0.0203890 + 0.107527i
\(541\) −13.9137 24.0992i −0.0257185 0.0445457i 0.852880 0.522107i \(-0.174854\pi\)
−0.878598 + 0.477562i \(0.841521\pi\)
\(542\) 428.687 + 247.502i 0.790935 + 0.456646i
\(543\) −71.3850 + 143.671i −0.131464 + 0.264588i
\(544\) 110.302 + 191.049i 0.202761 + 0.351193i
\(545\) 5.88530i 0.0107987i
\(546\) −22.1687 + 11.9666i −0.0406020 + 0.0219168i
\(547\) −610.439 −1.11598 −0.557988 0.829849i \(-0.688426\pi\)
−0.557988 + 0.829849i \(0.688426\pi\)
\(548\) 121.315 70.0411i 0.221377 0.127812i
\(549\) −231.216 + 548.911i −0.421159 + 0.999837i
\(550\) 55.5313 96.1830i 0.100966 0.174878i
\(551\) −639.116 + 368.994i −1.15992 + 0.669680i
\(552\) −1117.75 + 69.9100i −2.02491 + 0.126649i
\(553\) −149.564 + 211.872i −0.270458 + 0.383131i
\(554\) 122.293i 0.220746i
\(555\) −196.495 + 130.446i −0.354044 + 0.235039i
\(556\) −58.4528 + 101.243i −0.105131 + 0.182092i
\(557\) 438.946 + 253.425i 0.788053 + 0.454983i 0.839277 0.543704i \(-0.182979\pi\)
−0.0512234 + 0.998687i \(0.516312\pi\)
\(558\) 222.968 168.983i 0.399583 0.302837i
\(559\) −15.9902 −0.0286050
\(560\) −15.8411 + 173.431i −0.0282876 + 0.309698i
\(561\) 552.538 34.5587i 0.984917 0.0616020i
\(562\) −356.629 617.699i −0.634571 1.09911i
\(563\) 942.956 + 544.416i 1.67488 + 0.966990i 0.964845 + 0.262821i \(0.0846529\pi\)
0.710032 + 0.704169i \(0.248680\pi\)
\(564\) −115.855 57.5643i −0.205417 0.102064i
\(565\) −156.541 271.137i −0.277063 0.479888i
\(566\) 729.699i 1.28922i
\(567\) −559.869 + 89.6445i −0.987423 + 0.158103i
\(568\) 662.249 1.16593
\(569\) 39.3937 22.7440i 0.0692333 0.0399718i −0.464984 0.885319i \(-0.653940\pi\)
0.534217 + 0.845347i \(0.320607\pi\)
\(570\) 143.608 289.029i 0.251943 0.507068i
\(571\) −225.847 + 391.179i −0.395529 + 0.685077i −0.993169 0.116688i \(-0.962772\pi\)
0.597639 + 0.801765i \(0.296105\pi\)
\(572\) −7.47728 + 4.31701i −0.0130722 + 0.00754722i
\(573\) 19.8012 + 316.589i 0.0345571 + 0.552512i
\(574\) −105.926 + 150.055i −0.184540 + 0.261419i
\(575\) 215.687i 0.375109i
\(576\) 386.282 + 509.686i 0.670628 + 0.884871i
\(577\) −322.681 + 558.900i −0.559239 + 0.968630i 0.438321 + 0.898818i \(0.355573\pi\)
−0.997560 + 0.0698117i \(0.977760\pi\)
\(578\) −121.143 69.9420i −0.209590 0.121007i
\(579\) 149.543 + 225.260i 0.258278 + 0.389050i
\(580\) 58.3586 0.100618
\(581\) 127.390 58.8115i 0.219260 0.101225i
\(582\) 7.57208 + 121.065i 0.0130104 + 0.208016i
\(583\) 579.832 + 1004.30i 0.994566 + 1.72264i
\(584\) 370.411 + 213.857i 0.634265 + 0.366193i
\(585\) −12.8004 5.39189i −0.0218811 0.00921690i
\(586\) −19.1720 33.2069i −0.0327168 0.0566671i
\(587\) 1139.56i 1.94133i 0.240439 + 0.970664i \(0.422709\pi\)
−0.240439 + 0.970664i \(0.577291\pi\)
\(588\) 142.867 + 17.1847i 0.242971 + 0.0292256i
\(589\) 495.033 0.840463
\(590\) −82.9579 + 47.8957i −0.140607 + 0.0811792i
\(591\) −525.509 261.106i −0.889187 0.441804i
\(592\) −195.592 + 338.776i −0.330392 + 0.572256i
\(593\) 379.938 219.358i 0.640706 0.369912i −0.144181 0.989551i \(-0.546055\pi\)
0.784886 + 0.619640i \(0.212721\pi\)
\(594\) 589.239 111.729i 0.991984 0.188097i
\(595\) −94.7393 205.212i −0.159226 0.344894i
\(596\) 140.253i 0.235324i
\(597\) 385.048 + 580.006i 0.644971 + 0.971535i
\(598\) 25.8746 44.8160i 0.0432685 0.0749432i
\(599\) 749.729 + 432.856i 1.25163 + 0.722631i 0.971434 0.237310i \(-0.0762658\pi\)
0.280200 + 0.959942i \(0.409599\pi\)
\(600\) −108.148 + 71.7958i −0.180246 + 0.119660i
\(601\) −85.8542 −0.142852 −0.0714261 0.997446i \(-0.522755\pi\)
−0.0714261 + 0.997446i \(0.522755\pi\)
\(602\) −230.286 162.563i −0.382535 0.270038i
\(603\) 243.183 30.5394i 0.403288 0.0506458i
\(604\) 1.68032 + 2.91039i 0.00278198 + 0.00481853i
\(605\) 81.9447 + 47.3108i 0.135446 + 0.0781997i
\(606\) 334.363 672.947i 0.551753 1.11047i
\(607\) −512.102 886.986i −0.843660 1.46126i −0.886780 0.462192i \(-0.847063\pi\)
0.0431202 0.999070i \(-0.486270\pi\)
\(608\) 422.865i 0.695502i
\(609\) −16.0235 + 559.664i −0.0263111 + 0.918989i
\(610\) −257.215 −0.421663
\(611\) 26.3310 15.2022i 0.0430950 0.0248809i
\(612\) −117.242 49.3855i −0.191572 0.0806952i
\(613\) −164.682 + 285.238i −0.268650 + 0.465315i −0.968513 0.248961i \(-0.919911\pi\)
0.699864 + 0.714276i \(0.253244\pi\)
\(614\) 718.746 414.968i 1.17060 0.675844i
\(615\) −101.071 + 6.32155i −0.164344 + 0.0102789i
\(616\) −770.946 70.4178i −1.25154 0.114315i
\(617\) 249.124i 0.403766i −0.979410 0.201883i \(-0.935294\pi\)
0.979410 0.201883i \(-0.0647061\pi\)
\(618\) −657.985 + 436.816i −1.06470 + 0.706821i
\(619\) 286.676 496.537i 0.463128 0.802161i −0.535987 0.844226i \(-0.680060\pi\)
0.999115 + 0.0420654i \(0.0133938\pi\)
\(620\) −33.9016 19.5731i −0.0546801 0.0315696i
\(621\) 882.521 760.073i 1.42113 1.22395i
\(622\) 318.345 0.511809
\(623\) −414.616 292.684i −0.665515 0.469798i
\(624\) −22.9925 + 1.43807i −0.0368469 + 0.00230460i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 151.133 + 87.2568i 0.241427 + 0.139388i
\(627\) 950.358 + 472.197i 1.51572 + 0.753106i
\(628\) −119.214 206.484i −0.189830 0.328796i
\(629\) 507.702i 0.807157i
\(630\) −129.532 207.787i −0.205606 0.329820i
\(631\) 919.331 1.45694 0.728471 0.685076i \(-0.240231\pi\)
0.728471 + 0.685076i \(0.240231\pi\)
\(632\) −277.666 + 160.311i −0.439345 + 0.253656i
\(633\) −281.546 + 566.647i −0.444780 + 0.895177i
\(634\) −265.784 + 460.352i −0.419218 + 0.726107i
\(635\) −455.352 + 262.897i −0.717089 + 0.414012i
\(636\) −16.6349 265.965i −0.0261555 0.418184i
\(637\) −21.9357 + 25.7400i −0.0344360 + 0.0404082i
\(638\) 592.221i 0.928247i
\(639\) −548.899 + 416.001i −0.858998 + 0.651019i
\(640\) −69.7663 + 120.839i −0.109010 + 0.188811i
\(641\) −534.570 308.634i −0.833962 0.481488i 0.0212454 0.999774i \(-0.493237\pi\)
−0.855207 + 0.518286i \(0.826570\pi\)
\(642\) −119.543 180.070i −0.186203 0.280482i
\(643\) −787.857 −1.22528 −0.612642 0.790361i \(-0.709893\pi\)
−0.612642 + 0.790361i \(0.709893\pi\)
\(644\) −268.369 + 123.896i −0.416722 + 0.192386i
\(645\) −9.70158 155.113i −0.0150412 0.240485i
\(646\) 347.368 + 601.660i 0.537722 + 0.931362i
\(647\) −525.918 303.639i −0.812857 0.469303i 0.0350901 0.999384i \(-0.488828\pi\)
−0.847947 + 0.530081i \(0.822162\pi\)
\(648\) −674.872 189.499i −1.04147 0.292436i
\(649\) −157.486 272.774i −0.242660 0.420300i
\(650\) 5.99816i 0.00922794i
\(651\) 197.016 319.746i 0.302637 0.491161i
\(652\) 9.05652 0.0138904
\(653\) 922.762 532.757i 1.41311 0.815861i 0.417432 0.908708i \(-0.362930\pi\)
0.995680 + 0.0928474i \(0.0295969\pi\)
\(654\) −12.2907 6.10680i −0.0187931 0.00933762i
\(655\) −87.2840 + 151.180i −0.133258 + 0.230810i
\(656\) −145.461 + 83.9822i −0.221740 + 0.128022i
\(657\) −441.348 + 55.4254i −0.671763 + 0.0843614i
\(658\) 533.765 + 48.7538i 0.811193 + 0.0740939i
\(659\) 894.888i 1.35795i 0.734162 + 0.678974i \(0.237575\pi\)
−0.734162 + 0.678974i \(0.762425\pi\)
\(660\) −46.4137 69.9140i −0.0703238 0.105930i
\(661\) 241.970 419.105i 0.366067 0.634047i −0.622880 0.782318i \(-0.714037\pi\)
0.988947 + 0.148271i \(0.0473707\pi\)
\(662\) −274.176 158.296i −0.414163 0.239117i
\(663\) 24.9098 16.5368i 0.0375714 0.0249424i
\(664\) 173.463 0.261240
\(665\) 39.4094 431.461i 0.0592622 0.648813i
\(666\) −68.5314 545.710i −0.102900 0.819385i
\(667\) −575.057 996.029i −0.862155 1.49330i
\(668\) 166.175 + 95.9412i 0.248765 + 0.143624i
\(669\) 133.029 267.738i 0.198848 0.400207i
\(670\) 52.9208 + 91.6616i 0.0789863 + 0.136808i
\(671\) 845.749i 1.26043i
\(672\) 273.132 + 168.295i 0.406447 + 0.250439i
\(673\) −466.753 −0.693540 −0.346770 0.937950i \(-0.612722\pi\)
−0.346770 + 0.937950i \(0.612722\pi\)
\(674\) 191.365 110.485i 0.283925 0.163924i
\(675\) 44.5377 127.442i 0.0659817 0.188803i
\(676\) 82.4830 142.865i 0.122016 0.211338i
\(677\) 958.597 553.446i 1.41595 0.817498i 0.420008 0.907520i \(-0.362027\pi\)
0.995940 + 0.0900224i \(0.0286939\pi\)
\(678\) 728.668 45.5748i 1.07473 0.0672194i
\(679\) 68.2549 + 147.845i 0.100523 + 0.217739i
\(680\) 279.431i 0.410929i
\(681\) −769.500 + 510.847i −1.12996 + 0.750142i
\(682\) −198.627 + 344.033i −0.291243 + 0.504447i
\(683\) −222.898 128.690i −0.326351 0.188419i 0.327869 0.944723i \(-0.393670\pi\)
−0.654220 + 0.756305i \(0.727003\pi\)
\(684\) −147.294 194.349i −0.215342 0.284136i
\(685\) −319.988 −0.467136
\(686\) −577.596 + 147.693i −0.841977 + 0.215296i
\(687\) 167.098 10.4512i 0.243228 0.0152128i
\(688\) −128.886 223.237i −0.187335 0.324473i
\(689\) 54.2392 + 31.3150i 0.0787216 + 0.0454499i
\(690\) 450.436 + 223.805i 0.652806 + 0.324355i
\(691\) −237.797 411.877i −0.344135 0.596059i 0.641061 0.767490i \(-0.278494\pi\)
−0.985196 + 0.171431i \(0.945161\pi\)
\(692\) 101.671i 0.146924i
\(693\) 683.226 425.916i 0.985896 0.614597i
\(694\) 610.538 0.879738
\(695\) 231.269 133.523i 0.332761 0.192120i
\(696\) −307.999 + 619.887i −0.442527 + 0.890642i
\(697\) 108.997 188.788i 0.156380 0.270858i
\(698\) −817.359 + 471.903i −1.17100 + 0.676078i
\(699\) −38.1943 610.666i −0.0546414 0.873628i
\(700\) −19.7584 + 27.9898i −0.0282264 + 0.0399854i
\(701\) 310.690i 0.443209i −0.975137 0.221605i \(-0.928871\pi\)
0.975137 0.221605i \(-0.0711294\pi\)
\(702\) 24.5425 21.1373i 0.0349608 0.0301101i
\(703\) 486.594 842.805i 0.692168 1.19887i
\(704\) −786.431 454.046i −1.11709 0.644952i
\(705\) 163.445 + 246.201i 0.231836 + 0.349221i
\(706\) −91.2628 −0.129267
\(707\) 91.7571 1004.57i 0.129784 1.42090i
\(708\) 4.51815 + 72.2380i 0.00638157 + 0.102031i
\(709\) 134.556 + 233.058i 0.189783 + 0.328714i 0.945178 0.326556i \(-0.105888\pi\)
−0.755395 + 0.655270i \(0.772555\pi\)
\(710\) −257.576 148.711i −0.362783 0.209453i
\(711\) 129.440 307.292i 0.182053 0.432197i
\(712\) −313.715 543.371i −0.440611 0.763161i
\(713\) 771.483i 1.08202i
\(714\) 526.865 + 15.0844i 0.737906 + 0.0211266i
\(715\) 19.7226 0.0275841
\(716\) −238.279 + 137.570i −0.332792 + 0.192137i
\(717\) 225.604 + 112.094i 0.314650 + 0.156338i
\(718\) 367.732 636.930i 0.512161 0.887090i
\(719\) −845.804 + 488.325i −1.17636 + 0.679173i −0.955170 0.296057i \(-0.904328\pi\)
−0.221192 + 0.975230i \(0.570995\pi\)
\(720\) −27.9000 222.166i −0.0387500 0.308564i
\(721\) −611.436 + 866.159i −0.848038 + 1.20133i
\(722\) 704.239i 0.975400i
\(723\) −226.650 341.408i −0.313485 0.472210i
\(724\) −26.1736 + 45.3340i −0.0361514 + 0.0626161i
\(725\) −115.448 66.6540i −0.159239 0.0919366i
\(726\) −183.832 + 122.040i −0.253211 + 0.168099i
\(727\) 214.232 0.294680 0.147340 0.989086i \(-0.452929\pi\)
0.147340 + 0.989086i \(0.452929\pi\)
\(728\) −37.9598 + 17.5247i −0.0521426 + 0.0240724i
\(729\) 678.398 266.866i 0.930587 0.366072i
\(730\) −96.0451 166.355i −0.131569 0.227884i
\(731\) 289.730 + 167.276i 0.396348 + 0.228832i
\(732\) −86.4784 + 174.049i −0.118140 + 0.237772i
\(733\) −29.1732 50.5295i −0.0397997 0.0689352i 0.845439 0.534071i \(-0.179339\pi\)
−0.885239 + 0.465136i \(0.846005\pi\)
\(734\) 89.2351i 0.121574i
\(735\) −263.000 197.170i −0.357823 0.268259i
\(736\) −659.014 −0.895399
\(737\) −301.393 + 174.010i −0.408946 + 0.236105i
\(738\) 91.6735 217.634i 0.124219 0.294898i
\(739\) −444.978 + 770.724i −0.602135 + 1.04293i 0.390363 + 0.920661i \(0.372350\pi\)
−0.992497 + 0.122267i \(0.960984\pi\)
\(740\) −66.6474 + 38.4789i −0.0900641 + 0.0519985i
\(741\) 57.2006 3.57763i 0.0771938 0.00482811i
\(742\) 462.777 + 1002.41i 0.623688 + 1.35095i
\(743\) 625.012i 0.841200i 0.907246 + 0.420600i \(0.138180\pi\)
−0.907246 + 0.420600i \(0.861820\pi\)
\(744\) 386.829 256.803i 0.519931 0.345166i
\(745\) −160.189 + 277.456i −0.215019 + 0.372424i
\(746\) −713.140 411.731i −0.955951 0.551919i
\(747\) −143.773 + 108.963i −0.192468 + 0.145868i
\(748\) 180.644 0.241502
\(749\) −237.040 167.331i −0.316476 0.223405i
\(750\) 58.1851 3.63921i 0.0775801 0.00485228i
\(751\) 84.2527 + 145.930i 0.112187 + 0.194314i 0.916652 0.399686i \(-0.130881\pi\)
−0.804465 + 0.594001i \(0.797548\pi\)
\(752\) 424.474 + 245.070i 0.564460 + 0.325891i
\(753\) 350.389 + 174.095i 0.465324 + 0.231202i
\(754\) −15.9921 27.6991i −0.0212096 0.0367362i
\(755\) 7.67666i 0.0101678i
\(756\) −184.153 + 17.7899i −0.243588 + 0.0235316i
\(757\) 226.565 0.299294 0.149647 0.988740i \(-0.452186\pi\)
0.149647 + 0.988740i \(0.452186\pi\)
\(758\) −541.795 + 312.805i −0.714769 + 0.412672i
\(759\) −735.895 + 1481.08i −0.969559 + 1.95136i
\(760\) 267.814 463.867i 0.352387 0.610352i
\(761\) 216.707 125.116i 0.284766 0.164410i −0.350813 0.936446i \(-0.614095\pi\)
0.635579 + 0.772036i \(0.280761\pi\)
\(762\) −76.5390 1223.74i −0.100445 1.60595i
\(763\) −18.3475 1.67585i −0.0240466 0.00219640i
\(764\) 103.504i 0.135476i