Properties

Label 105.3.t.b.11.6
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 11.6
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50527 + 0.869067i) q^{2} +(-1.65926 + 2.49937i) q^{3} +(-0.489445 + 0.847743i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(0.325501 - 5.20423i) q^{6} +(2.93407 + 6.35541i) q^{7} -8.65398i q^{8} +(-3.49374 - 8.29420i) q^{9} +O(q^{10})\) \(q+(-1.50527 + 0.869067i) q^{2} +(-1.65926 + 2.49937i) 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} +(-3.49374 - 8.29420i) q^{9} +(1.94329 - 3.36588i) q^{10} +(-11.0674 - 6.38976i) q^{11} +(-1.30671 - 2.62993i) 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} +(12.4672 + 9.44870i) q^{18} +(-13.8399 - 23.9714i) q^{19} -2.18886i q^{20} +(-20.7529 - 3.21191i) q^{21} +22.2125 q^{22} +(-37.3582 + 21.5687i) q^{23} +(21.6295 + 14.3592i) 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} +(5.18818 + 10.4419i) q^{30} +(-8.94214 + 15.4882i) q^{31} +(13.2303 + 7.63853i) q^{32} +(34.3340 - 17.0593i) 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} +(-1.14519 + 1.72503i) q^{39} +(9.67544 + 16.7584i) q^{40} -15.0963i q^{41} +(34.0301 - 13.2009i) q^{42} -23.1680 q^{43} +(10.8337 - 6.25487i) q^{44} +(16.0388 + 12.1555i) 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} +(-38.7958 + 19.2762i) q^{51} +(-0.337807 + 0.585099i) q^{52} +(-78.5866 - 45.3720i) q^{53} +(-44.3022 + 15.4825i) 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} +(5.47079 + 3.63188i) q^{60} +(-33.0900 - 57.3136i) q^{61} -31.0853i q^{62} +(42.4622 - 46.5399i) q^{63} -71.0584 q^{64} +(-1.33654 + 0.771649i) q^{65} +(-36.8562 + 55.5174i) 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} +(-71.7778 + 30.2348i) q^{72} +(24.7119 - 42.8023i) q^{73} +(-52.9234 - 30.5554i) q^{74} +(6.67447 + 13.4332i) 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} +(-56.5875 + 57.9556i) q^{81} +(13.1197 + 22.7239i) q^{82} +20.0443i q^{83} +(12.8803 - 16.0211i) q^{84} -32.2894 q^{85} +(34.8741 - 20.1346i) q^{86} +(-66.6373 - 44.2384i) 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} +(-23.8736 - 48.0487i) q^{93} +(38.2848 - 66.3112i) q^{94} +(53.6016 + 30.9469i) q^{95} +(-41.0440 + 20.3932i) 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 −0.826645 0.562724i \(-0.809753\pi\)
0.0740107 + 0.997257i \(0.476420\pi\)
\(3\) −1.65926 + 2.49937i −0.553085 + 0.833125i
\(4\) −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
\(9\) −3.49374 8.29420i −0.388194 0.921578i
\(10\) 1.94329 3.36588i 0.194329 0.336588i
\(11\) −11.0674 6.38976i −1.00613 0.580887i −0.0960710 0.995374i \(-0.530628\pi\)
−0.910055 + 0.414487i \(0.863961\pi\)
\(12\) −1.30671 2.62993i −0.108893 0.219161i
\(13\) 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 0.820476 0.571681i \(-0.193708\pi\)
−0.0848518 + 0.996394i \(0.527042\pi\)
\(18\) 12.4672 + 9.44870i 0.692624 + 0.524928i
\(19\) −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
\(21\) −20.7529 3.21191i −0.988234 0.152948i
\(22\) 22.2125 1.00966
\(23\) −37.3582 + 21.5687i −1.62427 + 0.937771i −0.638507 + 0.769616i \(0.720448\pi\)
−0.985760 + 0.168156i \(0.946219\pi\)
\(24\) 21.6295 + 14.3592i 0.901230 + 0.598298i
\(25\) 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 \(0.152037\pi\)
−0.888083 + 0.459683i \(0.847963\pi\)
\(30\) 5.18818 + 10.4419i 0.172939 + 0.348063i
\(31\) −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
\(33\) 34.3340 17.0593i 1.04042 0.516949i
\(34\) −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
\(39\) −1.14519 + 1.72503i −0.0293639 + 0.0442315i
\(40\) 9.67544 + 16.7584i 0.241886 + 0.418959i
\(41\) 15.0963i 0.368202i −0.982907 0.184101i \(-0.941063\pi\)
0.982907 0.184101i \(-0.0589373\pi\)
\(42\) 34.0301 13.2009i 0.810240 0.314307i
\(43\) −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
\(45\) 16.0388 + 12.1555i 0.356418 + 0.270123i
\(46\) 37.4894 64.9335i 0.814986 1.41160i
\(47\) −38.1508 + 22.0264i −0.811719 + 0.468646i −0.847552 0.530712i \(-0.821925\pi\)
0.0358338 + 0.999358i \(0.488591\pi\)
\(48\) −33.3136 2.08361i −0.694032 0.0434085i
\(49\) −31.7825 + 37.2944i −0.648622 + 0.761111i
\(50\) 8.69067i 0.173813i
\(51\) −38.7958 + 19.2762i −0.760702 + 0.377965i
\(52\) −0.337807 + 0.585099i −0.00649628 + 0.0112519i
\(53\) −78.5866 45.3720i −1.48277 0.856075i −0.482957 0.875644i \(-0.660437\pi\)
−0.999809 + 0.0195689i \(0.993771\pi\)
\(54\) −44.3022 + 15.4825i −0.820411 + 0.286713i
\(55\) 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 0.669859 0.742489i \(-0.266355\pi\)
−0.308085 + 0.951359i \(0.599688\pi\)
\(60\) 5.47079 + 3.63188i 0.0911798 + 0.0605314i
\(61\) −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
\(63\) 42.4622 46.5399i 0.674002 0.738729i
\(64\) −71.0584 −1.11029
\(65\) −1.33654 + 0.771649i −0.0205621 + 0.0118715i
\(66\) −36.8562 + 55.5174i −0.558428 + 0.841173i
\(67\) −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 \(0.181164\pi\)
−0.842362 + 0.538912i \(0.818836\pi\)
\(72\) −71.7778 + 30.2348i −0.996914 + 0.419927i
\(73\) 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
\(75\) 6.67447 + 13.4332i 0.0889929 + 0.179110i
\(76\) 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
\(81\) −56.5875 + 57.9556i −0.698611 + 0.715501i
\(82\) 13.1197 + 22.7239i 0.159996 + 0.277121i
\(83\) 20.0443i 0.241498i 0.992683 + 0.120749i \(0.0385296\pi\)
−0.992683 + 0.120749i \(0.961470\pi\)
\(84\) 12.8803 16.0211i 0.153337 0.190727i
\(85\) −32.2894 −0.379875
\(86\) 34.8741 20.1346i 0.405512 0.234123i
\(87\) −66.6373 44.2384i −0.765946 0.508488i
\(88\) −55.2968 + 95.7769i −0.628373 + 1.08837i
\(89\) 62.7886 36.2510i 0.705489 0.407315i −0.103899 0.994588i \(-0.533132\pi\)
0.809389 + 0.587273i \(0.199799\pi\)
\(90\) −34.7067 4.35853i −0.385630 0.0484281i
\(91\) 2.02505 + 4.38640i 0.0222533 + 0.0482022i
\(92\) 42.2268i 0.458987i
\(93\) −23.8736 48.0487i −0.256706 0.516653i
\(94\) 38.2848 66.3112i 0.407285 0.705438i
\(95\) 53.6016 + 30.9469i 0.564228 + 0.325757i
\(96\) −41.0440 + 20.3932i −0.427542 + 0.212430i
\(97\) 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 0.968203 0.250166i \(-0.0804853\pi\)
0.267451 + 0.963571i \(0.413819\pi\)
\(102\) 41.6458 62.7320i 0.408292 0.615020i
\(103\) 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
\(105\) 43.7789 16.9826i 0.416942 0.161739i
\(106\) 157.725 1.48797
\(107\) 35.8969 20.7251i 0.335485 0.193692i −0.322789 0.946471i \(-0.604620\pi\)
0.658274 + 0.752779i \(0.271287\pi\)
\(108\) −17.2478 + 20.0264i −0.159702 + 0.185430i
\(109\) −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 \(0.212678\pi\)
−0.784971 + 0.619533i \(0.787322\pi\)
\(114\) −129.258 + 64.2233i −1.13384 + 0.563362i
\(115\) 48.2292 83.5354i 0.419384 0.726395i
\(116\) −22.6022 13.0494i −0.194847 0.112495i
\(117\) −2.41133 5.72452i −0.0206096 0.0489275i
\(118\) −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
\(123\) 37.7312 + 25.0486i 0.306758 + 0.203647i
\(124\) −8.75337 15.1613i −0.0705917 0.122268i
\(125\) 11.1803i 0.0894427i
\(126\) −23.4706 + 106.958i −0.186275 + 0.848869i
\(127\) −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
\(129\) 38.4416 57.9055i 0.297997 0.448880i
\(130\) 1.34123 2.32308i 0.0103171 0.0178698i
\(131\) 67.6099 39.0346i 0.516106 0.297974i −0.219234 0.975672i \(-0.570356\pi\)
0.735340 + 0.677698i \(0.237022\pi\)
\(132\) −2.34270 + 37.4560i −0.0177477 + 0.283758i
\(133\) 111.741 158.292i 0.840156 1.19016i
\(134\) 47.3338i 0.353238i
\(135\) −56.9937 + 19.9178i −0.422175 + 0.147540i
\(136\) 62.4828 108.223i 0.459432 0.795760i
\(137\) 123.931 + 71.5516i 0.904606 + 0.522274i 0.878692 0.477390i \(-0.158417\pi\)
0.0259142 + 0.999664i \(0.491750\pi\)
\(138\) 100.089 + 201.441i 0.725280 + 1.45972i
\(139\) 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
\(144\) 60.4834 79.8058i 0.420024 0.554207i
\(145\) −29.8086 51.6300i −0.205576 0.356069i
\(146\) 85.9054i 0.588393i
\(147\) −40.4775 141.317i −0.275357 0.961342i
\(148\) −34.4166 −0.232545
\(149\) 124.082 71.6388i 0.832765 0.480797i −0.0220332 0.999757i \(-0.507014\pi\)
0.854799 + 0.518960i \(0.173681\pi\)
\(150\) −21.7212 14.4200i −0.144808 0.0961336i
\(151\) 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
\(156\) −0.901872 1.81513i −0.00578123 0.0116355i
\(157\) −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
\(159\) 243.797 121.134i 1.53331 0.761846i
\(160\) −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
\(165\) −47.4147 + 71.4218i −0.287362 + 0.432859i
\(166\) −17.4199 30.1721i −0.104939 0.181760i
\(167\) 196.020i 1.17378i 0.809668 + 0.586888i \(0.199647\pi\)
−0.809668 + 0.586888i \(0.800353\pi\)
\(168\) −27.7958 + 179.595i −0.165451 + 1.06902i
\(169\) −168.524 −0.997181
\(170\) 48.6042 28.0616i 0.285907 0.165068i
\(171\) −150.470 + 198.541i −0.879944 + 1.16106i
\(172\) 11.3395 19.6405i 0.0659271 0.114189i
\(173\) 89.9489 51.9320i 0.519936 0.300185i −0.216972 0.976178i \(-0.569618\pi\)
0.736909 + 0.675992i \(0.236285\pi\)
\(174\) 138.753 + 8.67837i 0.797432 + 0.0498757i
\(175\) 34.8549 + 3.18363i 0.199171 + 0.0181922i
\(176\) 142.188i 0.807885i
\(177\) −66.2169 + 32.9007i −0.374107 + 0.185880i
\(178\) −63.0091 + 109.135i −0.353984 + 0.613118i
\(179\) −243.418 140.537i −1.35988 0.785124i −0.370269 0.928925i \(-0.620734\pi\)
−0.989607 + 0.143800i \(0.954068\pi\)
\(180\) −18.1549 + 7.64733i −0.100860 + 0.0424851i
\(181\) 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
\(186\) 77.6937 + 51.5784i 0.417708 + 0.277303i
\(187\) −92.2697 159.816i −0.493421 0.854630i
\(188\) 43.1227i 0.229376i
\(189\) 45.8652 + 183.350i 0.242673 + 0.970108i
\(190\) −107.580 −0.566209
\(191\) −91.5701 + 52.8680i −0.479424 + 0.276796i −0.720177 0.693791i \(-0.755939\pi\)
0.240752 + 0.970587i \(0.422606\pi\)
\(192\) 117.904 177.602i 0.614084 0.925009i
\(193\) 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 \(-0.834637\pi\)
0.868066 0.496448i \(-0.165363\pi\)
\(198\) −77.6048 184.235i −0.391944 0.930480i
\(199\) 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
\(201\) −36.3526 73.1642i −0.180859 0.364001i
\(202\) −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
\(207\) 309.415 + 234.500i 1.49476 + 1.13285i
\(208\) 3.83957 + 6.65033i 0.0184595 + 0.0319727i
\(209\) 353.734i 1.69251i
\(210\) −51.1399 + 63.6102i −0.243523 + 0.302906i
\(211\) 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
\(213\) −191.266 126.975i −0.897961 0.596128i
\(214\) −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
\(219\) 65.9757 + 132.784i 0.301259 + 0.606322i
\(220\) −13.9863 + 24.2250i −0.0635741 + 0.110114i
\(221\) 8.63117 + 4.98321i 0.0390551 + 0.0225485i
\(222\) 164.183 81.5764i 0.739562 0.367461i
\(223\) −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 −0.219824 0.975539i \(-0.570548\pi\)
−0.954754 + 0.297396i \(0.903882\pi\)
\(228\) −44.9582 + 67.7216i −0.197185 + 0.297025i
\(229\) −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
\(231\) 209.157 + 168.154i 0.905443 + 0.727938i
\(232\) 230.729 0.994522
\(233\) 176.629 101.977i 0.758062 0.437668i −0.0705372 0.997509i \(-0.522471\pi\)
0.828600 + 0.559842i \(0.189138\pi\)
\(234\) 8.60469 + 6.52134i 0.0367722 + 0.0278690i
\(235\) 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 \(0.0562106\pi\)
−0.984448 + 0.175674i \(0.943789\pi\)
\(240\) 66.8410 33.2108i 0.278504 0.138378i
\(241\) −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
\(243\) −50.9596 237.597i −0.209710 0.977764i
\(244\) 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
\(249\) −50.0983 33.2587i −0.201198 0.133569i
\(250\) −9.71647 16.8294i −0.0388659 0.0673176i
\(251\) 130.419i 0.519597i 0.965663 + 0.259799i \(0.0836562\pi\)
−0.965663 + 0.259799i \(0.916344\pi\)
\(252\) 18.6710 + 58.7757i 0.0740914 + 0.233237i
\(253\) 551.276 2.17896
\(254\) 353.953 204.355i 1.39351 0.804546i
\(255\) 53.5763 80.7032i 0.210103 0.316483i
\(256\) 87.8863 152.224i 0.343306 0.594623i
\(257\) −139.531 + 80.5581i −0.542921 + 0.313456i −0.746262 0.665652i \(-0.768153\pi\)
0.203341 + 0.979108i \(0.434820\pi\)
\(258\) −7.54120 + 120.572i −0.0292295 + 0.467332i
\(259\) −141.933 + 201.062i −0.548004 + 0.776302i
\(260\) 1.51072i 0.00581045i
\(261\) 221.137 93.1488i 0.847267 0.356892i
\(262\) −67.8474 + 117.515i −0.258959 + 0.448531i
\(263\) 237.621 + 137.191i 0.903503 + 0.521638i 0.878335 0.478046i \(-0.158655\pi\)
0.0251677 + 0.999683i \(0.491988\pi\)
\(264\) −147.631 297.126i −0.559208 1.12548i
\(265\) 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 0.187311 0.982301i \(-0.440023\pi\)
−0.757042 + 0.653366i \(0.773356\pi\)
\(270\) 68.4808 79.5130i 0.253633 0.294493i
\(271\) 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
\(273\) −14.3233 2.21681i −0.0524664 0.00812017i
\(274\) −248.733 −0.907783
\(275\) −55.3369 + 31.9488i −0.201225 + 0.116177i
\(276\) 105.541 + 70.0651i 0.382394 + 0.253859i
\(277\) −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 \(0.260561\pi\)
−0.683261 + 0.730174i \(0.739439\pi\)
\(282\) 102.212 + 205.715i 0.362455 + 0.729486i
\(283\) −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
\(285\) −166.287 + 82.6217i −0.583462 + 0.289901i
\(286\) 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
\(291\) −38.5990 + 58.1426i −0.132643 + 0.199803i
\(292\) 24.1903 + 41.8988i 0.0828434 + 0.143489i
\(293\) 22.0605i 0.0752917i 0.999291 + 0.0376458i \(0.0119859\pi\)
−0.999291 + 0.0376458i \(0.988014\pi\)
\(294\) 183.744 + 177.543i 0.624979 + 0.603887i
\(295\) −55.1117 −0.186819
\(296\) 263.500 152.132i 0.890203 0.513959i
\(297\) −261.448 225.172i −0.880295 0.758156i
\(298\) −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
\(303\) −387.166 + 192.369i −1.27778 + 0.634880i
\(304\) 153.986 266.711i 0.506531 0.877338i
\(305\) 128.157 + 73.9916i 0.420187 + 0.242595i
\(306\) 87.6897 + 208.177i 0.286568 + 0.680316i
\(307\) 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 0.222823 0.974859i \(-0.428473\pi\)
−0.732841 + 0.680400i \(0.761806\pi\)
\(312\) 14.9284 + 9.91046i 0.0478473 + 0.0317643i
\(313\) 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
\(315\) −30.1944 + 137.598i −0.0958551 + 0.436820i
\(316\) −36.2669 −0.114769
\(317\) 264.854 152.913i 0.835501 0.482377i −0.0202312 0.999795i \(-0.506440\pi\)
0.855733 + 0.517418i \(0.173107\pi\)
\(318\) −261.706 + 394.214i −0.822976 + 1.23967i
\(319\) 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
\(324\) −21.4350 76.3377i −0.0661574 0.235610i
\(325\) 1.72546 2.98858i 0.00530911 0.00919564i
\(326\) 13.9265 + 8.04046i 0.0427193 + 0.0246640i
\(327\) −3.51342 7.07121i −0.0107444 0.0216245i
\(328\) −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
\(333\) 191.127 252.186i 0.573956 0.757316i
\(334\) −170.355 295.063i −0.510045 0.883423i
\(335\) 60.8939i 0.181773i
\(336\) −84.5021 217.835i −0.251494 0.648318i
\(337\) 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
\(339\) −349.948 232.320i −1.03230 0.685309i
\(340\) 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
\(345\) 128.762 + 259.149i 0.373222 + 0.751157i
\(346\) −90.2649 + 156.343i −0.260881 + 0.451859i
\(347\) −304.200 175.630i −0.876658 0.506139i −0.00710329 0.999975i \(-0.502261\pi\)
−0.869555 + 0.493836i \(0.835594\pi\)
\(348\) 70.1181 34.8391i 0.201489 0.100112i
\(349\) −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 0.563023 0.826441i \(-0.309638\pi\)
−0.434208 + 0.900813i \(0.642972\pi\)
\(354\) 71.0813 107.071i 0.200795 0.302461i
\(355\) −85.5580 148.191i −0.241009 0.417439i
\(356\) 70.9714i 0.199358i
\(357\) −236.338 190.005i −0.662010 0.532228i
\(358\) 488.545 1.36465
\(359\) −366.445 + 211.567i −1.02074 + 0.589323i −0.914318 0.404998i \(-0.867272\pi\)
−0.106420 + 0.994321i \(0.533939\pi\)
\(360\) 105.194 138.799i 0.292205 0.385554i
\(361\) −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
\(366\) −309.044 + 153.553i −0.844383 + 0.419543i
\(367\) −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
\(369\) −125.211 + 52.7425i −0.339327 + 0.142934i
\(370\) 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
\(375\) −27.9439 18.5510i −0.0745169 0.0494694i
\(376\) 190.616 + 330.156i 0.506956 + 0.878074i
\(377\) 18.4014i 0.0488101i
\(378\) −228.383 236.132i −0.604188 0.624687i
\(379\) −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
\(381\) 390.161 587.709i 1.02405 1.54254i
\(382\) 91.8917 159.161i 0.240554 0.416652i
\(383\) 322.534 186.215i 0.842125 0.486201i −0.0158611 0.999874i \(-0.505049\pi\)
0.857986 + 0.513673i \(0.171716\pi\)
\(384\) −11.6858 + 186.838i −0.0304318 + 0.486556i
\(385\) 83.8436 + 181.611i 0.217776 + 0.471718i
\(386\) 156.652i 0.405835i
\(387\) 80.9431 + 192.160i 0.209155 + 0.496538i
\(388\) −11.3859 + 19.7209i −0.0293451 + 0.0508272i
\(389\) 550.051 + 317.572i 1.41401 + 0.816381i 0.995764 0.0919506i \(-0.0293102\pi\)
0.418250 + 0.908332i \(0.362644\pi\)
\(390\) 3.58080 + 7.20681i 0.00918153 + 0.0184790i
\(391\) −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
\(396\) −89.7295 68.0044i −0.226590 0.171728i
\(397\) 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
\(399\) 210.224 + 541.929i 0.526877 + 1.35822i
\(400\) 55.6311 0.139078
\(401\) 16.9155 9.76619i 0.0421834 0.0243546i −0.478760 0.877946i \(-0.658914\pi\)
0.520943 + 0.853591i \(0.325580\pi\)
\(402\) 118.305 + 78.5389i 0.294291 + 0.195370i
\(403\) −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
\(408\) 166.816 + 335.738i 0.408862 + 0.822887i
\(409\) 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
\(411\) −384.467 + 191.028i −0.935444 + 0.464787i
\(412\) −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
\(417\) −198.159 + 298.492i −0.475202 + 0.715808i
\(418\) −307.419 532.465i −0.735451 1.27384i
\(419\) 476.423i 1.13705i −0.822667 0.568523i \(-0.807515\pi\)
0.822667 0.568523i \(-0.192485\pi\)
\(420\) −7.03043 + 45.4253i −0.0167391 + 0.108155i
\(421\) −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
\(423\) 315.980 + 239.476i 0.746998 + 0.566136i
\(424\) −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
\(429\) 23.6968 11.7741i 0.0552373 0.0274453i
\(430\) −45.0222 + 77.9808i −0.104703 + 0.181351i
\(431\) 93.3104 + 53.8728i 0.216498 + 0.124995i 0.604327 0.796736i \(-0.293442\pi\)
−0.387830 + 0.921731i \(0.626775\pi\)
\(432\) 99.1072 + 283.589i 0.229415 + 0.656456i
\(433\) −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
\(438\) −214.710 142.539i −0.490205 0.325431i
\(439\) 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
\(441\) 420.367 + 133.313i 0.953214 + 0.302297i
\(442\) −17.3230 −0.0391923
\(443\) −381.536 + 220.280i −0.861256 + 0.497246i −0.864433 0.502749i \(-0.832322\pi\)
0.00317679 + 0.999995i \(0.498989\pi\)
\(444\) 57.1059 86.0199i 0.128617 0.193739i
\(445\) −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 \(-0.926121\pi\)
0.973186 0.230021i \(-0.0738795\pi\)
\(450\) 72.0822 30.3630i 0.160183 0.0674733i
\(451\) −96.4615 + 167.076i −0.213884 + 0.370457i
\(452\) −118.696 68.5293i −0.262602 0.151613i
\(453\) 4.58283 + 9.22354i 0.0101166 + 0.0203610i
\(454\) 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
\(459\) 295.423 + 254.434i 0.643623 + 0.554323i
\(460\) 47.2110 + 81.7719i 0.102633 + 0.177765i
\(461\) 41.0856i 0.0891228i 0.999007 + 0.0445614i \(0.0141890\pi\)
−0.999007 + 0.0445614i \(0.985811\pi\)
\(462\) −460.975 71.3446i −0.997780 0.154425i
\(463\) 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
\(465\) 99.9511 + 66.3544i 0.214949 + 0.142698i
\(466\) −177.249 + 307.004i −0.380362 + 0.658807i
\(467\) 508.155 293.383i 1.08813 0.628230i 0.155049 0.987907i \(-0.450447\pi\)
0.933077 + 0.359677i \(0.117113\pi\)
\(468\) 6.03313 + 0.757653i 0.0128913 + 0.00161892i
\(469\) −189.838 17.3397i −0.404771 0.0369716i
\(470\) 171.215i 0.364287i
\(471\) −325.139 654.383i −0.690316 1.38935i
\(472\) 106.646 184.716i 0.225945 0.391348i
\(473\) 256.409 + 148.038i 0.542092 + 0.312977i
\(474\) 173.010 85.9620i 0.364999 0.181354i
\(475\) −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 0.982688 0.185267i \(-0.0593150\pi\)
0.330898 + 0.943666i \(0.392648\pi\)
\(480\) 56.6810 85.3799i 0.118085 0.177875i
\(481\) 12.1330 + 21.0150i 0.0252246 + 0.0436902i
\(482\) 237.424i 0.492582i
\(483\) 844.568 327.623i 1.74859 0.678309i
\(484\) −41.4228 −0.0855842
\(485\) −45.0484 + 26.0087i −0.0928832 + 0.0536262i
\(486\) 283.195 + 313.359i 0.582706 + 0.644772i
\(487\) 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 \(-0.977932\pi\)
0.997598 0.0692723i \(-0.0220677\pi\)
\(492\) −39.7021 + 19.7265i −0.0806953 + 0.0400945i
\(493\) −192.500 + 333.420i −0.390467 + 0.676308i
\(494\) 28.7568 + 16.6028i 0.0582122 + 0.0336088i
\(495\) −99.8368 237.014i −0.201690 0.478816i
\(496\) −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
\(501\) −489.928 325.248i −0.977901 0.649197i
\(502\) −113.343 196.315i −0.225782 0.391067i
\(503\) 96.8787i 0.192602i −0.995352 0.0963009i \(-0.969299\pi\)
0.995352 0.0963009i \(-0.0307011\pi\)
\(504\) −402.756 367.467i −0.799118 0.729100i
\(505\) −322.235 −0.638089
\(506\) −829.819 + 479.096i −1.63996 + 0.946830i
\(507\) 279.624 421.204i 0.551526 0.830776i
\(508\) 115.089 199.340i 0.226554 0.392402i
\(509\) −550.592 + 317.884i −1.08171 + 0.624527i −0.931358 0.364105i \(-0.881375\pi\)
−0.150355 + 0.988632i \(0.548042\pi\)
\(510\) −10.5102 + 168.041i −0.0206083 + 0.329493i
\(511\) 344.533 + 31.4694i 0.674233 + 0.0615841i
\(512\) 555.120i 1.08422i
\(513\) −246.558 705.512i −0.480621 1.37527i
\(514\) 140.021 242.523i 0.272414 0.471835i
\(515\) −293.303 169.339i −0.569521 0.328813i
\(516\) 30.2739 + 60.9302i 0.0586704 + 0.118082i
\(517\) 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 0.503208 0.864166i \(-0.332153\pi\)
−0.496786 + 0.867873i \(0.665486\pi\)
\(522\) −251.918 + 332.397i −0.482601 + 0.636775i
\(523\) 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
\(525\) −65.7903 + 81.8330i −0.125315 + 0.155872i
\(526\) −476.912 −0.906676
\(527\) −223.654 + 129.127i −0.424391 + 0.245022i
\(528\) 355.380 + 235.926i 0.673069 + 0.446829i
\(529\) 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
\(534\) −168.221 338.566i −0.315020 0.634019i
\(535\) −46.3427 + 80.2679i −0.0866218 + 0.150033i
\(536\) 204.096 + 117.835i 0.380776 + 0.219841i
\(537\) 755.147 375.205i 1.40623 0.698705i
\(538\) 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
\(543\) −88.7306 + 133.657i −0.163408 + 0.246145i
\(544\) 110.302 + 191.049i 0.202761 + 0.351193i
\(545\) 5.88530i 0.0107987i
\(546\) 23.4870 9.11104i 0.0430165 0.0166869i
\(547\) −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
\(549\) −359.763 + 474.694i −0.655305 + 0.864653i
\(550\) 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
\(555\) 211.217 104.946i 0.380572 0.189092i
\(556\) −58.4528 + 101.243i −0.105131 + 0.182092i
\(557\) −438.946 253.425i −0.788053 0.454983i 0.0512234 0.998687i \(-0.483688\pi\)
−0.839277 + 0.543704i \(0.817021\pi\)
\(558\) −257.828 + 108.604i −0.462057 + 0.194631i
\(559\) −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 \(-0.915347\pi\)
−0.710032 0.704169i \(-0.751320\pi\)
\(564\) 107.780 + 71.5516i 0.191099 + 0.126865i
\(565\) −156.541 271.137i −0.277063 0.479888i
\(566\) 729.699i 1.28922i
\(567\) −534.363 189.591i −0.942440 0.334376i
\(568\) 662.249 1.16593
\(569\) −39.3937 + 22.7440i −0.0692333 + 0.0399718i −0.534217 0.845347i \(-0.679393\pi\)
0.464984 + 0.885319i \(0.346060\pi\)
\(570\) 178.502 268.882i 0.313162 0.471723i
\(571\) −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
\(576\) 248.260 + 589.373i 0.431007 + 1.02322i
\(577\) −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
\(579\) 120.309 + 242.138i 0.207788 + 0.418201i
\(580\) 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
\(585\) 11.0697 + 8.38955i 0.0189226 + 0.0143411i
\(586\) −19.1720 33.2069i −0.0327168 0.0566671i
\(587\) 1139.56i 1.94133i −0.240439 0.970664i \(-0.577291\pi\)
0.240439 0.970664i \(-0.422709\pi\)
\(588\) 139.612 + 34.8524i 0.237436 + 0.0592729i
\(589\) 495.033 0.840463
\(590\) 82.9579 47.8957i 0.140607 0.0811792i
\(591\) 488.879 + 324.551i 0.827207 + 0.549156i
\(592\) −195.592 + 338.776i −0.330392 + 0.572256i
\(593\) −379.938 + 219.358i −0.640706 + 0.369912i −0.784886 0.619640i \(-0.787279\pi\)
0.144181 + 0.989551i \(0.453945\pi\)
\(594\) 589.239 + 111.729i 0.991984 + 0.188097i
\(595\) −94.7393 205.212i −0.159226 0.344894i
\(596\) 140.253i 0.235324i
\(597\) 309.776 + 623.464i 0.518888 + 1.04433i
\(598\) 25.8746 44.8160i 0.0432685 0.0749432i
\(599\) −749.729 432.856i −1.25163 0.722631i −0.280200 0.959942i \(-0.590401\pi\)
−0.971434 + 0.237310i \(0.923734\pi\)
\(600\) 116.251 57.7607i 0.193751 0.0962679i
\(601\) −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
\(606\) 415.608 626.040i 0.685822 1.03307i
\(607\) −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
\(609\) 85.6346 553.306i 0.140615 0.908549i
\(610\) −257.215 −0.421663
\(611\) −26.3310 + 15.2022i −0.0430950 + 0.0248809i
\(612\) 101.390 + 76.8417i 0.165670 + 0.125558i
\(613\) −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 \(0.0647061\pi\)
−0.979410 + 0.201883i \(0.935294\pi\)
\(618\) 707.286 351.424i 1.14448 0.568648i
\(619\) 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
\(621\) −1099.50 + 384.249i −1.77054 + 0.618758i
\(622\) 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
\(627\) −884.114 586.935i −1.41007 0.936101i
\(628\) −119.214 206.484i −0.189830 0.328796i
\(629\) 507.702i 0.807157i
\(630\) −74.1315 233.363i −0.117669 0.370418i
\(631\) 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
\(633\) −349.958 + 527.149i −0.552856 + 0.832779i
\(634\) −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
\(639\) 634.717 267.360i 0.993298 0.418404i
\(640\) −69.7663 + 120.839i −0.109010 + 0.188811i
\(641\) 534.570 + 308.634i 0.833962 + 0.481488i 0.855207 0.518286i \(-0.173430\pi\)
−0.0212454 + 0.999774i \(0.506763\pi\)
\(642\) −96.1737 193.562i −0.149803 0.301498i
\(643\) −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 0.847947 0.530081i \(-0.177838\pi\)
−0.0350901 + 0.999384i \(0.511172\pi\)
\(648\) 501.547 + 489.707i 0.773992 + 0.755721i
\(649\) −157.486 272.774i −0.242660 0.420300i
\(650\) 5.99816i 0.00922794i
\(651\) 235.322 292.705i 0.361478 0.449623i
\(652\) 9.05652 0.0138904
\(653\) −922.762 + 532.757i −1.41311 + 0.815861i −0.995680 0.0928474i \(-0.970403\pi\)
−0.417432 + 0.908708i \(0.637070\pi\)
\(654\) 11.4340 + 7.59067i 0.0174832 + 0.0116065i
\(655\) −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 \(-0.762425\pi\)
0.734162 0.678974i \(-0.237575\pi\)
\(660\) −37.3405 75.1525i −0.0565765 0.113867i
\(661\) 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
\(663\) −26.7762 + 13.3041i −0.0403865 + 0.0200665i
\(664\) 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
\(669\) 165.354 249.076i 0.247165 0.372311i
\(670\) 52.9208 + 91.6616i 0.0789863 + 0.136808i
\(671\) 845.749i 1.26043i
\(672\) −250.033 201.016i −0.372074 0.299131i
\(673\) −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
\(675\) 88.0989 102.292i 0.130517 0.151543i
\(676\) 82.4830 142.865i 0.122016 0.211338i
\(677\) −958.597 + 553.446i −1.41595 + 0.817498i −0.995940 0.0900224i \(-0.971306\pi\)
−0.420008 + 0.907520i \(0.637973\pi\)
\(678\) 728.668 + 45.5748i 1.07473 + 0.0672194i
\(679\) 68.2549 + 147.845i 0.100523 + 0.217739i
\(680\) 279.431i 0.410929i
\(681\) 827.156 410.983i 1.21462 0.603500i
\(682\) −198.627 + 344.033i −0.291243 + 0.504447i
\(683\) 222.898 + 128.690i 0.326351 + 0.188419i 0.654220 0.756305i \(-0.272997\pi\)
−0.327869 + 0.944723i \(0.606330\pi\)
\(684\) −94.6645 224.735i −0.138398 0.328560i
\(685\) −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
\(690\) −419.039 278.187i −0.607303 0.403169i
\(691\) −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
\(693\) −767.324 + 243.753i −1.10725 + 0.351735i
\(694\) 610.538 0.879738
\(695\) −231.269 + 133.523i −0.332761 + 0.192120i
\(696\) −382.838 + 576.678i −0.550055 + 0.828560i
\(697\) 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 \(0.0711294\pi\)
−0.975137 + 0.221605i \(0.928871\pi\)
\(702\) −30.5766 + 10.6858i −0.0435565 + 0.0152219i
\(703\) 486.594 842.805i 0.692168 1.19887i
\(704\) 786.431 + 454.046i 1.11709 + 0.644952i
\(705\) 131.494 + 264.648i 0.186516 + 0.375387i
\(706\) −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
\(711\) 201.403 265.744i 0.283267 0.373761i
\(712\) −313.715 543.371i −0.440611 0.763161i
\(713\) 771.483i 1.08202i
\(714\) 520.879 + 80.6159i 0.729523 + 0.112907i
\(715\) 19.7226 0.0275841
\(716\) 238.279 137.570i 0.332792 0.192137i
\(717\) −209.878 139.332i −0.292717 0.194326i
\(718\) 367.732 636.930i 0.512161 0.887090i
\(719\) 845.804 488.325i 1.17636 0.679173i 0.221192 0.975230i \(-0.429005\pi\)
0.955170 + 0.296057i \(0.0956720\pi\)
\(720\) −27.9000 + 222.166i −0.0387500 + 0.308564i
\(721\) −611.436 + 866.159i −0.848038 + 1.20133i
\(722\) 704.239i 0.975400i
\(723\) −182.343 366.988i −0.252203 0.507591i
\(724\) −26.1736 + 45.3340i −0.0361514 + 0.0626161i
\(725\) 115.448 + 66.6540i 0.159239 + 0.0919366i
\(726\) 197.605 98.1828i 0.272184 0.135238i
\(727\) 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
\(732\) −107.491 + 161.917i −0.146846 + 0.221198i
\(733\) −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
\(735\) 236.382 + 228.404i 0.321608 + 0.310754i
\(736\) −659.014 −0.895399
\(737\) 301.393 174.010i 0.408946 0.236105i
\(738\) 142.640 188.209i 0.193279 0.255025i
\(739\) −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 \(-0.861820\pi\)
0.907246 0.420600i \(-0.138180\pi\)
\(744\) −415.812 + 206.602i −0.558888 + 0.277691i
\(745\) −160.189 + 277.456i −0.215019 + 0.372424i
\(746\) 713.140 + 411.731i 0.955951 + 0.551919i
\(747\) 166.252 70.0298i 0.222559 0.0937481i
\(748\) 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
\(753\) −325.966 216.398i −0.432889 0.287382i
\(754\) −15.9921 27.6991i −0.0212096 0.0367362i
\(755\) 7.67666i 0.0101678i
\(756\) −177.883 50.8580i −0.235294 0.0672725i
\(757\) 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
\(759\) −914.708 + 1377.85i −1.20515 + 1.81534i
\(760\) 267.814 463.867i 0.352387 0.610352i
\(761\) −216.707 + 125.116i −0.284766 + 0.164410i −0.635579 0.772036i \(-0.719239\pi\)
0.350813 + 0.936446i \(0.385905\pi\)
\(762\) −76.5390 + 1223.74i −0.100445 + 1.60595i
\(763\) −18.3475 1.67585i −0.0240466 0.00219640i
\(764\) 103.504i 0.135476i
\(765\) 112.811 + 267.814i