Properties

Label 210.3.l.a.43.1
Level 210
Weight 3
Character 210.43
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.12745506816.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(1.54779 - 1.54779i\) of \(x^{8} + 23 x^{4} + 1\)
Character \(\chi\) \(=\) 210.43
Dual form 210.3.l.a.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.32032 + 2.51691i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.32032 + 2.51691i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-1.80341 + 6.83723i) q^{10} -14.0884 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-6.03207 - 6.03207i) q^{13} +3.74166i q^{14} +(8.37386 + 2.20871i) q^{15} -4.00000 q^{16} +(-9.54506 + 9.54506i) q^{17} +(3.00000 + 3.00000i) q^{18} +21.6823i q^{19} +(5.03383 + 8.64064i) q^{20} +4.58258 q^{21} +(-14.0884 + 14.0884i) q^{22} +(0.423494 + 0.423494i) q^{23} +4.89898i q^{24} +(12.3303 - 21.7477i) q^{25} -12.0641 q^{26} +(3.67423 - 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} -11.2171i q^{29} +(10.5826 - 6.16515i) q^{30} -16.4543 q^{31} +(-4.00000 + 4.00000i) q^{32} +(17.2547 + 17.2547i) q^{33} +19.0901i q^{34} +(3.37386 - 12.7913i) q^{35} +6.00000 q^{36} +(47.6653 - 47.6653i) q^{37} +(21.6823 + 21.6823i) q^{38} +14.7755i q^{39} +(13.6745 + 3.60681i) q^{40} -44.0379 q^{41} +(4.58258 - 4.58258i) q^{42} +(-46.7052 - 46.7052i) q^{43} +28.1767i q^{44} +(-7.55074 - 12.9610i) q^{45} +0.846988 q^{46} +(-20.3412 + 20.3412i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +(-9.41742 - 34.0780i) q^{50} +23.3805 q^{51} +(-12.0641 + 12.0641i) q^{52} +(-18.6273 - 18.6273i) q^{53} -7.34847i q^{54} +(60.8662 - 35.4592i) q^{55} +7.48331 q^{56} +(26.5553 - 26.5553i) q^{57} +(-11.2171 - 11.2171i) q^{58} +13.4774i q^{59} +(4.41742 - 16.7477i) q^{60} -10.8748 q^{61} +(-16.4543 + 16.4543i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +(41.2426 + 10.8783i) q^{65} +34.5093 q^{66} +(72.2045 - 72.2045i) q^{67} +(19.0901 + 19.0901i) q^{68} -1.03734i q^{69} +(-9.41742 - 16.1652i) q^{70} -64.1040 q^{71} +(6.00000 - 6.00000i) q^{72} +(51.4407 + 51.4407i) q^{73} -95.3307i q^{74} +(-41.7369 + 11.5339i) q^{75} +43.3646 q^{76} +(26.3569 - 26.3569i) q^{77} +(14.7755 + 14.7755i) q^{78} +157.457i q^{79} +(17.2813 - 10.0677i) q^{80} -9.00000 q^{81} +(-44.0379 + 44.0379i) q^{82} +(-76.9972 - 76.9972i) q^{83} -9.16515i q^{84} +(17.2136 - 65.2618i) q^{85} -93.4104 q^{86} +(-13.7381 + 13.7381i) q^{87} +(28.1767 + 28.1767i) q^{88} +37.6912i q^{89} +(-20.5117 - 5.41022i) q^{90} +22.5699 q^{91} +(0.846988 - 0.846988i) q^{92} +(20.1523 + 20.1523i) q^{93} +40.6824i q^{94} +(-54.5724 - 93.6744i) q^{95} +9.79796 q^{96} +(97.2189 - 97.2189i) q^{97} +(-7.00000 - 7.00000i) q^{98} -42.2651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 16q^{8} + O(q^{10}) \) \( 8q + 8q^{2} - 16q^{8} - 8q^{11} + 8q^{13} + 12q^{15} - 32q^{16} - 32q^{17} + 24q^{18} - 8q^{22} - 40q^{23} - 48q^{25} + 16q^{26} + 48q^{30} + 144q^{31} - 32q^{32} + 120q^{33} - 28q^{35} + 48q^{36} + 160q^{37} - 320q^{41} - 32q^{43} - 80q^{46} - 144q^{47} - 112q^{50} + 72q^{51} + 16q^{52} - 200q^{53} + 184q^{55} - 24q^{57} - 64q^{58} + 72q^{60} + 288q^{61} + 144q^{62} + 24q^{65} + 240q^{66} + 80q^{67} + 64q^{68} - 112q^{70} - 280q^{71} + 48q^{72} + 312q^{73} - 56q^{77} + 48q^{78} - 72q^{81} - 320q^{82} - 320q^{83} + 80q^{85} - 64q^{86} - 48q^{87} + 16q^{88} - 80q^{92} + 48q^{93} - 472q^{95} - 24q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.32032 + 2.51691i −0.864064 + 0.503383i
\(6\) −2.44949 −0.408248
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −1.80341 + 6.83723i −0.180341 + 0.683723i
\(11\) −14.0884 −1.28076 −0.640380 0.768058i \(-0.721223\pi\)
−0.640380 + 0.768058i \(0.721223\pi\)
\(12\) −2.44949 + 2.44949i −0.204124 + 0.204124i
\(13\) −6.03207 6.03207i −0.464005 0.464005i 0.435961 0.899966i \(-0.356409\pi\)
−0.899966 + 0.435961i \(0.856409\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 8.37386 + 2.20871i 0.558258 + 0.147247i
\(16\) −4.00000 −0.250000
\(17\) −9.54506 + 9.54506i −0.561474 + 0.561474i −0.929726 0.368252i \(-0.879956\pi\)
0.368252 + 0.929726i \(0.379956\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 21.6823i 1.14117i 0.821237 + 0.570587i \(0.193284\pi\)
−0.821237 + 0.570587i \(0.806716\pi\)
\(20\) 5.03383 + 8.64064i 0.251691 + 0.432032i
\(21\) 4.58258 0.218218
\(22\) −14.0884 + 14.0884i −0.640380 + 0.640380i
\(23\) 0.423494 + 0.423494i 0.0184128 + 0.0184128i 0.716253 0.697840i \(-0.245856\pi\)
−0.697840 + 0.716253i \(0.745856\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 12.3303 21.7477i 0.493212 0.869909i
\(26\) −12.0641 −0.464005
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 3.74166 + 3.74166i 0.133631 + 0.133631i
\(29\) 11.2171i 0.386798i −0.981120 0.193399i \(-0.938049\pi\)
0.981120 0.193399i \(-0.0619512\pi\)
\(30\) 10.5826 6.16515i 0.352753 0.205505i
\(31\) −16.4543 −0.530782 −0.265391 0.964141i \(-0.585501\pi\)
−0.265391 + 0.964141i \(0.585501\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 17.2547 + 17.2547i 0.522868 + 0.522868i
\(34\) 19.0901i 0.561474i
\(35\) 3.37386 12.7913i 0.0963961 0.365465i
\(36\) 6.00000 0.166667
\(37\) 47.6653 47.6653i 1.28825 1.28825i 0.352404 0.935848i \(-0.385364\pi\)
0.935848 0.352404i \(-0.114636\pi\)
\(38\) 21.6823 + 21.6823i 0.570587 + 0.570587i
\(39\) 14.7755i 0.378859i
\(40\) 13.6745 + 3.60681i 0.341862 + 0.0901703i
\(41\) −44.0379 −1.07410 −0.537048 0.843552i \(-0.680460\pi\)
−0.537048 + 0.843552i \(0.680460\pi\)
\(42\) 4.58258 4.58258i 0.109109 0.109109i
\(43\) −46.7052 46.7052i −1.08617 1.08617i −0.995919 0.0902487i \(-0.971234\pi\)
−0.0902487 0.995919i \(-0.528766\pi\)
\(44\) 28.1767i 0.640380i
\(45\) −7.55074 12.9610i −0.167794 0.288021i
\(46\) 0.846988 0.0184128
\(47\) −20.3412 + 20.3412i −0.432791 + 0.432791i −0.889577 0.456785i \(-0.849001\pi\)
0.456785 + 0.889577i \(0.349001\pi\)
\(48\) 4.89898 + 4.89898i 0.102062 + 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −9.41742 34.0780i −0.188348 0.681561i
\(51\) 23.3805 0.458442
\(52\) −12.0641 + 12.0641i −0.232003 + 0.232003i
\(53\) −18.6273 18.6273i −0.351458 0.351458i 0.509194 0.860652i \(-0.329944\pi\)
−0.860652 + 0.509194i \(0.829944\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 60.8662 35.4592i 1.10666 0.644712i
\(56\) 7.48331 0.133631
\(57\) 26.5553 26.5553i 0.465882 0.465882i
\(58\) −11.2171 11.2171i −0.193399 0.193399i
\(59\) 13.4774i 0.228430i 0.993456 + 0.114215i \(0.0364353\pi\)
−0.993456 + 0.114215i \(0.963565\pi\)
\(60\) 4.41742 16.7477i 0.0736237 0.279129i
\(61\) −10.8748 −0.178275 −0.0891376 0.996019i \(-0.528411\pi\)
−0.0891376 + 0.996019i \(0.528411\pi\)
\(62\) −16.4543 + 16.4543i −0.265391 + 0.265391i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 41.2426 + 10.8783i 0.634502 + 0.167358i
\(66\) 34.5093 0.522868
\(67\) 72.2045 72.2045i 1.07768 1.07768i 0.0809624 0.996717i \(-0.474201\pi\)
0.996717 0.0809624i \(-0.0257994\pi\)
\(68\) 19.0901 + 19.0901i 0.280737 + 0.280737i
\(69\) 1.03734i 0.0150340i
\(70\) −9.41742 16.1652i −0.134535 0.230931i
\(71\) −64.1040 −0.902874 −0.451437 0.892303i \(-0.649088\pi\)
−0.451437 + 0.892303i \(0.649088\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) 51.4407 + 51.4407i 0.704667 + 0.704667i 0.965409 0.260742i \(-0.0839671\pi\)
−0.260742 + 0.965409i \(0.583967\pi\)
\(74\) 95.3307i 1.28825i
\(75\) −41.7369 + 11.5339i −0.556492 + 0.153786i
\(76\) 43.3646 0.570587
\(77\) 26.3569 26.3569i 0.342298 0.342298i
\(78\) 14.7755 + 14.7755i 0.189429 + 0.189429i
\(79\) 157.457i 1.99313i 0.0828028 + 0.996566i \(0.473613\pi\)
−0.0828028 + 0.996566i \(0.526387\pi\)
\(80\) 17.2813 10.0677i 0.216016 0.125846i
\(81\) −9.00000 −0.111111
\(82\) −44.0379 + 44.0379i −0.537048 + 0.537048i
\(83\) −76.9972 76.9972i −0.927677 0.927677i 0.0698788 0.997555i \(-0.477739\pi\)
−0.997555 + 0.0698788i \(0.977739\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 17.2136 65.2618i 0.202513 0.767786i
\(86\) −93.4104 −1.08617
\(87\) −13.7381 + 13.7381i −0.157910 + 0.157910i
\(88\) 28.1767 + 28.1767i 0.320190 + 0.320190i
\(89\) 37.6912i 0.423497i 0.977324 + 0.211749i \(0.0679158\pi\)
−0.977324 + 0.211749i \(0.932084\pi\)
\(90\) −20.5117 5.41022i −0.227908 0.0601135i
\(91\) 22.5699 0.248021
\(92\) 0.846988 0.846988i 0.00920639 0.00920639i
\(93\) 20.1523 + 20.1523i 0.216691 + 0.216691i
\(94\) 40.6824i 0.432791i
\(95\) −54.5724 93.6744i −0.574447 0.986046i
\(96\) 9.79796 0.102062
\(97\) 97.2189 97.2189i 1.00226 1.00226i 0.00225910 0.999997i \(-0.499281\pi\)
0.999997 0.00225910i \(-0.000719096\pi\)
\(98\) −7.00000 7.00000i −0.0714286 0.0714286i
\(99\) 42.2651i 0.426920i
\(100\) −43.4955 24.6606i −0.434955 0.246606i
\(101\) 26.1142 0.258557 0.129278 0.991608i \(-0.458734\pi\)
0.129278 + 0.991608i \(0.458734\pi\)
\(102\) 23.3805 23.3805i 0.229221 0.229221i
\(103\) 52.9553 + 52.9553i 0.514129 + 0.514129i 0.915789 0.401660i \(-0.131567\pi\)
−0.401660 + 0.915789i \(0.631567\pi\)
\(104\) 24.1283i 0.232003i
\(105\) −19.7982 + 11.5339i −0.188554 + 0.109847i
\(106\) −37.2546 −0.351458
\(107\) −81.7515 + 81.7515i −0.764033 + 0.764033i −0.977049 0.213016i \(-0.931671\pi\)
0.213016 + 0.977049i \(0.431671\pi\)
\(108\) −7.34847 7.34847i −0.0680414 0.0680414i
\(109\) 59.2958i 0.543998i 0.962297 + 0.271999i \(0.0876848\pi\)
−0.962297 + 0.271999i \(0.912315\pi\)
\(110\) 25.4070 96.3254i 0.230973 0.875686i
\(111\) −116.756 −1.05185
\(112\) 7.48331 7.48331i 0.0668153 0.0668153i
\(113\) 142.193 + 142.193i 1.25834 + 1.25834i 0.951884 + 0.306458i \(0.0991440\pi\)
0.306458 + 0.951884i \(0.400856\pi\)
\(114\) 53.1105i 0.465882i
\(115\) −2.89553 0.763732i −0.0251785 0.00664114i
\(116\) −22.4343 −0.193399
\(117\) 18.0962 18.0962i 0.154668 0.154668i
\(118\) 13.4774 + 13.4774i 0.114215 + 0.114215i
\(119\) 35.7144i 0.300121i
\(120\) −12.3303 21.1652i −0.102753 0.176376i
\(121\) 77.4821 0.640348
\(122\) −10.8748 + 10.8748i −0.0891376 + 0.0891376i
\(123\) 53.9352 + 53.9352i 0.438498 + 0.438498i
\(124\) 32.9085i 0.265391i
\(125\) 1.46629 + 124.991i 0.0117303 + 0.999931i
\(126\) −11.2250 −0.0890871
\(127\) −95.3116 + 95.3116i −0.750485 + 0.750485i −0.974570 0.224085i \(-0.928061\pi\)
0.224085 + 0.974570i \(0.428061\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 114.404i 0.886852i
\(130\) 52.1209 30.3644i 0.400930 0.233572i
\(131\) −191.866 −1.46463 −0.732313 0.680968i \(-0.761559\pi\)
−0.732313 + 0.680968i \(0.761559\pi\)
\(132\) 34.5093 34.5093i 0.261434 0.261434i
\(133\) −40.5639 40.5639i −0.304991 0.304991i
\(134\) 144.409i 1.07768i
\(135\) −6.62614 + 25.1216i −0.0490825 + 0.186086i
\(136\) 38.1803 0.280737
\(137\) 134.702 134.702i 0.983228 0.983228i −0.0166339 0.999862i \(-0.505295\pi\)
0.999862 + 0.0166339i \(0.00529498\pi\)
\(138\) −1.03734 1.03734i −0.00751699 0.00751699i
\(139\) 49.6297i 0.357048i −0.983936 0.178524i \(-0.942868\pi\)
0.983936 0.178524i \(-0.0571323\pi\)
\(140\) −25.5826 6.74773i −0.182733 0.0481981i
\(141\) 49.8256 0.353373
\(142\) −64.1040 + 64.1040i −0.451437 + 0.451437i
\(143\) 84.9820 + 84.9820i 0.594279 + 0.594279i
\(144\) 12.0000i 0.0833333i
\(145\) 28.2326 + 48.4616i 0.194707 + 0.334218i
\(146\) 102.881 0.704667
\(147\) −8.57321 + 8.57321i −0.0583212 + 0.0583212i
\(148\) −95.3307 95.3307i −0.644126 0.644126i
\(149\) 137.142i 0.920415i 0.887811 + 0.460208i \(0.152225\pi\)
−0.887811 + 0.460208i \(0.847775\pi\)
\(150\) −30.2030 + 53.2708i −0.201353 + 0.355139i
\(151\) −197.792 −1.30988 −0.654941 0.755680i \(-0.727307\pi\)
−0.654941 + 0.755680i \(0.727307\pi\)
\(152\) 43.3646 43.3646i 0.285293 0.285293i
\(153\) −28.6352 28.6352i −0.187158 0.187158i
\(154\) 52.7138i 0.342298i
\(155\) 71.0876 41.4139i 0.458630 0.267187i
\(156\) 29.5510 0.189429
\(157\) −179.903 + 179.903i −1.14588 + 1.14588i −0.158526 + 0.987355i \(0.550674\pi\)
−0.987355 + 0.158526i \(0.949326\pi\)
\(158\) 157.457 + 157.457i 0.996566 + 0.996566i
\(159\) 45.6274i 0.286965i
\(160\) 7.21362 27.3489i 0.0450851 0.170931i
\(161\) −1.58457 −0.00984205
\(162\) −9.00000 + 9.00000i −0.0555556 + 0.0555556i
\(163\) −19.4617 19.4617i −0.119397 0.119397i 0.644884 0.764281i \(-0.276906\pi\)
−0.764281 + 0.644884i \(0.776906\pi\)
\(164\) 88.0758i 0.537048i
\(165\) −117.974 31.1171i −0.714994 0.188589i
\(166\) −153.994 −0.927677
\(167\) −78.3023 + 78.3023i −0.468876 + 0.468876i −0.901550 0.432674i \(-0.857570\pi\)
0.432674 + 0.901550i \(0.357570\pi\)
\(168\) −9.16515 9.16515i −0.0545545 0.0545545i
\(169\) 96.2284i 0.569399i
\(170\) −48.0482 82.4754i −0.282636 0.485150i
\(171\) −65.0469 −0.380391
\(172\) −93.4104 + 93.4104i −0.543084 + 0.543084i
\(173\) 66.9522 + 66.9522i 0.387007 + 0.387007i 0.873618 0.486612i \(-0.161767\pi\)
−0.486612 + 0.873618i \(0.661767\pi\)
\(174\) 27.4763i 0.157910i
\(175\) 17.6184 + 63.7542i 0.100677 + 0.364309i
\(176\) 56.3535 0.320190
\(177\) 16.5064 16.5064i 0.0932563 0.0932563i
\(178\) 37.6912 + 37.6912i 0.211749 + 0.211749i
\(179\) 66.4948i 0.371479i −0.982599 0.185740i \(-0.940532\pi\)
0.982599 0.185740i \(-0.0594681\pi\)
\(180\) −25.9219 + 15.1015i −0.144011 + 0.0838971i
\(181\) −33.5180 −0.185183 −0.0925913 0.995704i \(-0.529515\pi\)
−0.0925913 + 0.995704i \(0.529515\pi\)
\(182\) 22.5699 22.5699i 0.124011 0.124011i
\(183\) 13.3188 + 13.3188i 0.0727805 + 0.0727805i
\(184\) 1.69398i 0.00920639i
\(185\) −85.9599 + 325.899i −0.464648 + 1.76162i
\(186\) 40.3045 0.216691
\(187\) 134.474 134.474i 0.719114 0.719114i
\(188\) 40.6824 + 40.6824i 0.216396 + 0.216396i
\(189\) 13.7477i 0.0727393i
\(190\) −148.247 39.1020i −0.780246 0.205800i
\(191\) −209.877 −1.09883 −0.549415 0.835549i \(-0.685150\pi\)
−0.549415 + 0.835549i \(0.685150\pi\)
\(192\) 9.79796 9.79796i 0.0510310 0.0510310i
\(193\) −247.934 247.934i −1.28463 1.28463i −0.938001 0.346634i \(-0.887325\pi\)
−0.346634 0.938001i \(-0.612675\pi\)
\(194\) 194.438i 1.00226i
\(195\) −37.1886 63.8348i −0.190711 0.327358i
\(196\) −14.0000 −0.0714286
\(197\) −14.3392 + 14.3392i −0.0727881 + 0.0727881i −0.742564 0.669776i \(-0.766390\pi\)
0.669776 + 0.742564i \(0.266390\pi\)
\(198\) −42.2651 42.2651i −0.213460 0.213460i
\(199\) 282.601i 1.42011i 0.704148 + 0.710053i \(0.251329\pi\)
−0.704148 + 0.710053i \(0.748671\pi\)
\(200\) −68.1561 + 18.8348i −0.340780 + 0.0941742i
\(201\) −176.864 −0.879922
\(202\) 26.1142 26.1142i 0.129278 0.129278i
\(203\) 20.9854 + 20.9854i 0.103376 + 0.103376i
\(204\) 46.7611i 0.229221i
\(205\) 190.258 110.840i 0.928087 0.540681i
\(206\) 105.911 0.514129
\(207\) −1.27048 + 1.27048i −0.00613759 + 0.00613759i
\(208\) 24.1283 + 24.1283i 0.116001 + 0.116001i
\(209\) 305.468i 1.46157i
\(210\) −8.26424 + 31.3321i −0.0393535 + 0.149201i
\(211\) 208.591 0.988584 0.494292 0.869296i \(-0.335427\pi\)
0.494292 + 0.869296i \(0.335427\pi\)
\(212\) −37.2546 + 37.2546i −0.175729 + 0.175729i
\(213\) 78.5111 + 78.5111i 0.368597 + 0.368597i
\(214\) 163.503i 0.764033i
\(215\) 319.334 + 84.2285i 1.48528 + 0.391760i
\(216\) −14.6969 −0.0680414
\(217\) 30.7831 30.7831i 0.141858 0.141858i
\(218\) 59.2958 + 59.2958i 0.271999 + 0.271999i
\(219\) 126.003i 0.575358i
\(220\) −70.9184 121.732i −0.322356 0.553329i
\(221\) 115.153 0.521054
\(222\) −116.756 + 116.756i −0.525927 + 0.525927i
\(223\) −205.186 205.186i −0.920118 0.920118i 0.0769196 0.997037i \(-0.475492\pi\)
−0.997037 + 0.0769196i \(0.975492\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 65.2432 + 36.9909i 0.289970 + 0.164404i
\(226\) 284.385 1.25834
\(227\) 316.050 316.050i 1.39229 1.39229i 0.572120 0.820170i \(-0.306121\pi\)
0.820170 0.572120i \(-0.193879\pi\)
\(228\) −53.1105 53.1105i −0.232941 0.232941i
\(229\) 123.494i 0.539274i −0.962962 0.269637i \(-0.913096\pi\)
0.962962 0.269637i \(-0.0869036\pi\)
\(230\) −3.65926 + 2.13179i −0.0159098 + 0.00926867i
\(231\) −64.5610 −0.279485
\(232\) −22.4343 + 22.4343i −0.0966995 + 0.0966995i
\(233\) 209.367 + 209.367i 0.898572 + 0.898572i 0.995310 0.0967375i \(-0.0308407\pi\)
−0.0967375 + 0.995310i \(0.530841\pi\)
\(234\) 36.1924i 0.154668i
\(235\) 36.6834 139.077i 0.156100 0.591819i
\(236\) 26.9548 0.114215
\(237\) 192.845 192.845i 0.813693 0.813693i
\(238\) −35.7144 35.7144i −0.150060 0.150060i
\(239\) 147.491i 0.617117i −0.951205 0.308559i \(-0.900153\pi\)
0.951205 0.308559i \(-0.0998466\pi\)
\(240\) −33.4955 8.83485i −0.139564 0.0368119i
\(241\) −180.182 −0.747643 −0.373821 0.927501i \(-0.621953\pi\)
−0.373821 + 0.927501i \(0.621953\pi\)
\(242\) 77.4821 77.4821i 0.320174 0.320174i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 21.7496i 0.0891376i
\(245\) 17.6184 + 30.2422i 0.0719118 + 0.123438i
\(246\) 107.870 0.438498
\(247\) 130.789 130.789i 0.529510 0.529510i
\(248\) 32.9085 + 32.9085i 0.132696 + 0.132696i
\(249\) 188.604i 0.757445i
\(250\) 126.458 + 123.525i 0.505831 + 0.494100i
\(251\) 25.2366 0.100544 0.0502720 0.998736i \(-0.483991\pi\)
0.0502720 + 0.998736i \(0.483991\pi\)
\(252\) −11.2250 + 11.2250i −0.0445435 + 0.0445435i
\(253\) −5.96634 5.96634i −0.0235824 0.0235824i
\(254\) 190.623i 0.750485i
\(255\) −101.011 + 58.8468i −0.396123 + 0.230772i
\(256\) 16.0000 0.0625000
\(257\) 228.675 228.675i 0.889784 0.889784i −0.104718 0.994502i \(-0.533394\pi\)
0.994502 + 0.104718i \(0.0333938\pi\)
\(258\) 114.404 + 114.404i 0.443426 + 0.443426i
\(259\) 178.347i 0.688600i
\(260\) 21.7565 82.4852i 0.0836789 0.317251i
\(261\) 33.6514 0.128933
\(262\) −191.866 + 191.866i −0.732313 + 0.732313i
\(263\) −17.1641 17.1641i −0.0652629 0.0652629i 0.673722 0.738985i \(-0.264695\pi\)
−0.738985 + 0.673722i \(0.764695\pi\)
\(264\) 69.0186i 0.261434i
\(265\) 127.359 + 33.5926i 0.480600 + 0.126764i
\(266\) −81.1277 −0.304991
\(267\) 46.1622 46.1622i 0.172892 0.172892i
\(268\) −144.409 144.409i −0.538840 0.538840i
\(269\) 503.847i 1.87304i −0.350617 0.936519i \(-0.614028\pi\)
0.350617 0.936519i \(-0.385972\pi\)
\(270\) 18.4955 + 31.7477i 0.0685017 + 0.117584i
\(271\) 147.700 0.545019 0.272510 0.962153i \(-0.412146\pi\)
0.272510 + 0.962153i \(0.412146\pi\)
\(272\) 38.1803 38.1803i 0.140369 0.140369i
\(273\) −27.6424 27.6424i −0.101254 0.101254i
\(274\) 269.404i 0.983228i
\(275\) −173.714 + 306.390i −0.631687 + 1.11415i
\(276\) −2.07469 −0.00751699
\(277\) 2.85013 2.85013i 0.0102893 0.0102893i −0.701943 0.712233i \(-0.747684\pi\)
0.712233 + 0.701943i \(0.247684\pi\)
\(278\) −49.6297 49.6297i −0.178524 0.178524i
\(279\) 49.3628i 0.176927i
\(280\) −32.3303 + 18.8348i −0.115465 + 0.0672673i
\(281\) 384.657 1.36889 0.684443 0.729066i \(-0.260045\pi\)
0.684443 + 0.729066i \(0.260045\pi\)
\(282\) 49.8256 49.8256i 0.176686 0.176686i
\(283\) −201.734 201.734i −0.712839 0.712839i 0.254289 0.967128i \(-0.418159\pi\)
−0.967128 + 0.254289i \(0.918159\pi\)
\(284\) 128.208i 0.451437i
\(285\) −47.8899 + 181.565i −0.168035 + 0.637069i
\(286\) 169.964 0.594279
\(287\) 82.3874 82.3874i 0.287064 0.287064i
\(288\) −12.0000 12.0000i −0.0416667 0.0416667i
\(289\) 106.784i 0.369493i
\(290\) 76.6942 + 20.2291i 0.264463 + 0.0697554i
\(291\) −238.137 −0.818339
\(292\) 102.881 102.881i 0.352334 0.352334i
\(293\) −366.878 366.878i −1.25214 1.25214i −0.954758 0.297384i \(-0.903886\pi\)
−0.297384 0.954758i \(-0.596114\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) −33.9214 58.2266i −0.114988 0.197378i
\(296\) −190.661 −0.644126
\(297\) −51.7640 + 51.7640i −0.174289 + 0.174289i
\(298\) 137.142 + 137.142i 0.460208 + 0.460208i
\(299\) 5.10909i 0.0170872i
\(300\) 23.0679 + 83.4738i 0.0768929 + 0.278246i
\(301\) 174.755 0.580581
\(302\) −197.792 + 197.792i −0.654941 + 0.654941i
\(303\) −31.9833 31.9833i −0.105555 0.105555i
\(304\) 86.7292i 0.285293i
\(305\) 46.9825 27.3709i 0.154041 0.0897406i
\(306\) −57.2704 −0.187158
\(307\) −412.785 + 412.785i −1.34458 + 1.34458i −0.453136 + 0.891442i \(0.649695\pi\)
−0.891442 + 0.453136i \(0.850305\pi\)
\(308\) −52.7138 52.7138i −0.171149 0.171149i
\(309\) 129.713i 0.419785i
\(310\) 29.6737 112.502i 0.0957216 0.362908i
\(311\) 512.668 1.64845 0.824225 0.566263i \(-0.191611\pi\)
0.824225 + 0.566263i \(0.191611\pi\)
\(312\) 29.5510 29.5510i 0.0947146 0.0947146i
\(313\) −101.469 101.469i −0.324182 0.324182i 0.526187 0.850369i \(-0.323621\pi\)
−0.850369 + 0.526187i \(0.823621\pi\)
\(314\) 359.806i 1.14588i
\(315\) 38.3739 + 10.1216i 0.121822 + 0.0321320i
\(316\) 314.915 0.996566
\(317\) −202.617 + 202.617i −0.639169 + 0.639169i −0.950350 0.311182i \(-0.899275\pi\)
0.311182 + 0.950350i \(0.399275\pi\)
\(318\) 45.6274 + 45.6274i 0.143482 + 0.143482i
\(319\) 158.031i 0.495396i
\(320\) −20.1353 34.5625i −0.0629228 0.108008i
\(321\) 200.250 0.623830
\(322\) −1.58457 + 1.58457i −0.00492102 + 0.00492102i
\(323\) −206.959 206.959i −0.640739 0.640739i
\(324\) 18.0000i 0.0555556i
\(325\) −205.561 + 56.8065i −0.632495 + 0.174789i
\(326\) −38.9233 −0.119397
\(327\) 72.6223 72.6223i 0.222086 0.222086i
\(328\) 88.0758 + 88.0758i 0.268524 + 0.268524i
\(329\) 76.1098i 0.231337i
\(330\) −149.091 + 86.8569i −0.451792 + 0.263203i
\(331\) 65.9564 0.199264 0.0996321 0.995024i \(-0.468233\pi\)
0.0996321 + 0.995024i \(0.468233\pi\)
\(332\) −153.994 + 153.994i −0.463838 + 0.463838i
\(333\) 142.996 + 142.996i 0.429417 + 0.429417i
\(334\) 156.605i 0.468876i
\(335\) −130.214 + 493.679i −0.388699 + 1.47367i
\(336\) −18.3303 −0.0545545
\(337\) −360.772 + 360.772i −1.07054 + 1.07054i −0.0732257 + 0.997315i \(0.523329\pi\)
−0.997315 + 0.0732257i \(0.976671\pi\)
\(338\) −96.2284 96.2284i −0.284699 0.284699i
\(339\) 348.300i 1.02743i
\(340\) −130.524 34.4272i −0.383893 0.101257i
\(341\) 231.814 0.679805
\(342\) −65.0469 + 65.0469i −0.190196 + 0.190196i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 186.821i 0.543084i
\(345\) 2.61090 + 4.48166i 0.00756784 + 0.0129903i
\(346\) 133.904 0.387007
\(347\) −195.218 + 195.218i −0.562588 + 0.562588i −0.930042 0.367454i \(-0.880230\pi\)
0.367454 + 0.930042i \(0.380230\pi\)
\(348\) 27.4763 + 27.4763i 0.0789548 + 0.0789548i
\(349\) 204.957i 0.587270i −0.955918 0.293635i \(-0.905135\pi\)
0.955918 0.293635i \(-0.0948650\pi\)
\(350\) 81.3725 + 46.1358i 0.232493 + 0.131816i
\(351\) −44.3264 −0.126286
\(352\) 56.3535 56.3535i 0.160095 0.160095i
\(353\) −233.494 233.494i −0.661457 0.661457i 0.294267 0.955723i \(-0.404925\pi\)
−0.955723 + 0.294267i \(0.904925\pi\)
\(354\) 33.0127i 0.0932563i
\(355\) 276.950 161.344i 0.780140 0.454491i
\(356\) 75.3825 0.211749
\(357\) −43.7410 + 43.7410i −0.122524 + 0.122524i
\(358\) −66.4948 66.4948i −0.185740 0.185740i
\(359\) 263.565i 0.734164i 0.930189 + 0.367082i \(0.119643\pi\)
−0.930189 + 0.367082i \(0.880357\pi\)
\(360\) −10.8204 + 41.0234i −0.0300568 + 0.113954i
\(361\) −109.122 −0.302276
\(362\) −33.5180 + 33.5180i −0.0925913 + 0.0925913i
\(363\) −94.8958 94.8958i −0.261421 0.261421i
\(364\) 45.1398i 0.124011i
\(365\) −351.712 92.7684i −0.963594 0.254160i
\(366\) 26.6377 0.0727805
\(367\) 22.0009 22.0009i 0.0599481 0.0599481i −0.676497 0.736445i \(-0.736503\pi\)
0.736445 + 0.676497i \(0.236503\pi\)
\(368\) −1.69398 1.69398i −0.00460320 0.00460320i
\(369\) 132.114i 0.358032i
\(370\) 239.939 + 411.859i 0.648484 + 1.11313i
\(371\) 69.6970 0.187862
\(372\) 40.3045 40.3045i 0.108346 0.108346i
\(373\) −170.973 170.973i −0.458373 0.458373i 0.439748 0.898121i \(-0.355068\pi\)
−0.898121 + 0.439748i \(0.855068\pi\)
\(374\) 268.949i 0.719114i
\(375\) 151.287 154.878i 0.403431 0.413009i
\(376\) 81.3648 0.216396
\(377\) −67.6625 + 67.6625i −0.179476 + 0.179476i
\(378\) 13.7477 + 13.7477i 0.0363696 + 0.0363696i
\(379\) 272.520i 0.719050i 0.933135 + 0.359525i \(0.117061\pi\)
−0.933135 + 0.359525i \(0.882939\pi\)
\(380\) −187.349 + 109.145i −0.493023 + 0.287223i
\(381\) 233.465 0.612769
\(382\) −209.877 + 209.877i −0.549415 + 0.549415i
\(383\) −283.977 283.977i −0.741454 0.741454i 0.231403 0.972858i \(-0.425668\pi\)
−0.972858 + 0.231403i \(0.925668\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −47.5322 + 180.208i −0.123460 + 0.468074i
\(386\) −495.869 −1.28463
\(387\) 140.116 140.116i 0.362056 0.362056i
\(388\) −194.438 194.438i −0.501128 0.501128i
\(389\) 12.8522i 0.0330392i 0.999864 + 0.0165196i \(0.00525859\pi\)
−0.999864 + 0.0165196i \(0.994741\pi\)
\(390\) −101.023 26.6462i −0.259034 0.0683236i
\(391\) −8.08455 −0.0206766
\(392\) −14.0000 + 14.0000i −0.0357143 + 0.0357143i
\(393\) 234.987 + 234.987i 0.597931 + 0.597931i
\(394\) 28.6785i 0.0727881i
\(395\) −396.307 680.266i −1.00331 1.72219i
\(396\) −84.5302 −0.213460
\(397\) −242.868 + 242.868i −0.611757 + 0.611757i −0.943404 0.331647i \(-0.892396\pi\)
0.331647 + 0.943404i \(0.392396\pi\)
\(398\) 282.601 + 282.601i 0.710053 + 0.710053i
\(399\) 99.3607i 0.249024i
\(400\) −49.3212 + 86.9909i −0.123303 + 0.217477i
\(401\) −523.505 −1.30550 −0.652749 0.757574i \(-0.726385\pi\)
−0.652749 + 0.757574i \(0.726385\pi\)
\(402\) −176.864 + 176.864i −0.439961 + 0.439961i
\(403\) 99.2531 + 99.2531i 0.246286 + 0.246286i
\(404\) 52.2284i 0.129278i
\(405\) 38.8829 22.6522i 0.0960071 0.0559314i
\(406\) 41.9707 0.103376
\(407\) −671.527 + 671.527i −1.64994 + 1.64994i
\(408\) −46.7611 46.7611i −0.114610 0.114610i
\(409\) 39.5511i 0.0967019i 0.998830 + 0.0483509i \(0.0153966\pi\)
−0.998830 + 0.0483509i \(0.984603\pi\)
\(410\) 79.4182 301.097i 0.193703 0.734384i
\(411\) −329.952 −0.802802
\(412\) 105.911 105.911i 0.257064 0.257064i
\(413\) −25.2139 25.2139i −0.0610506 0.0610506i
\(414\) 2.54096i 0.00613759i
\(415\) 526.447 + 138.857i 1.26855 + 0.334596i
\(416\) 48.2565 0.116001
\(417\) −60.7838 + 60.7838i −0.145764 + 0.145764i
\(418\) −305.468 305.468i −0.730785 0.730785i
\(419\) 171.715i 0.409822i 0.978781 + 0.204911i \(0.0656905\pi\)
−0.978781 + 0.204911i \(0.934310\pi\)
\(420\) 23.0679 + 39.5964i 0.0549235 + 0.0942771i
\(421\) 361.127 0.857784 0.428892 0.903356i \(-0.358904\pi\)
0.428892 + 0.903356i \(0.358904\pi\)
\(422\) 208.591 208.591i 0.494292 0.494292i
\(423\) −61.0236 61.0236i −0.144264 0.144264i
\(424\) 74.5092i 0.175729i
\(425\) 89.8899 + 325.277i 0.211506 + 0.765358i
\(426\) 157.022 0.368597
\(427\) 20.3449 20.3449i 0.0476460 0.0476460i
\(428\) 163.503 + 163.503i 0.382017 + 0.382017i
\(429\) 208.162i 0.485227i
\(430\) 403.563 235.106i 0.938518 0.546758i
\(431\) 323.054 0.749545 0.374772 0.927117i \(-0.377721\pi\)
0.374772 + 0.927117i \(0.377721\pi\)
\(432\) −14.6969 + 14.6969i −0.0340207 + 0.0340207i
\(433\) 76.7446 + 76.7446i 0.177239 + 0.177239i 0.790151 0.612912i \(-0.210002\pi\)
−0.612912 + 0.790151i \(0.710002\pi\)
\(434\) 61.5662i 0.141858i
\(435\) 24.7754 93.9308i 0.0569550 0.215933i
\(436\) 118.592 0.271999
\(437\) −9.18232 + 9.18232i −0.0210122 + 0.0210122i
\(438\) −126.003 126.003i −0.287679 0.287679i
\(439\) 864.627i 1.96954i 0.173872 + 0.984768i \(0.444372\pi\)
−0.173872 + 0.984768i \(0.555628\pi\)
\(440\) −192.651 50.8141i −0.437843 0.115487i
\(441\) 21.0000 0.0476190
\(442\) 115.153 115.153i 0.260527 0.260527i
\(443\) −326.831 326.831i −0.737768 0.737768i 0.234377 0.972146i \(-0.424695\pi\)
−0.972146 + 0.234377i \(0.924695\pi\)
\(444\) 233.511i 0.525927i
\(445\) −94.8656 162.838i −0.213181 0.365929i
\(446\) −410.372 −0.920118
\(447\) 167.964 167.964i 0.375758 0.375758i
\(448\) −14.9666 14.9666i −0.0334077 0.0334077i
\(449\) 331.011i 0.737217i 0.929585 + 0.368609i \(0.120166\pi\)
−0.929585 + 0.368609i \(0.879834\pi\)
\(450\) 102.234 28.2523i 0.227187 0.0627828i
\(451\) 620.422 1.37566
\(452\) 284.385 284.385i 0.629171 0.629171i
\(453\) 242.245 + 242.245i 0.534757 + 0.534757i
\(454\) 632.100i 1.39229i
\(455\) −97.5093 + 56.8065i −0.214306 + 0.124849i
\(456\) −106.221 −0.232941
\(457\) 485.728 485.728i 1.06286 1.06286i 0.0649742 0.997887i \(-0.479304\pi\)
0.997887 0.0649742i \(-0.0206965\pi\)
\(458\) −123.494 123.494i −0.269637 0.269637i
\(459\) 70.1416i 0.152814i
\(460\) −1.52746 + 5.79105i −0.00332057 + 0.0125892i
\(461\) −560.524 −1.21589 −0.607944 0.793980i \(-0.708005\pi\)
−0.607944 + 0.793980i \(0.708005\pi\)
\(462\) −64.5610 + 64.5610i −0.139742 + 0.139742i
\(463\) 279.103 + 279.103i 0.602814 + 0.602814i 0.941058 0.338245i \(-0.109833\pi\)
−0.338245 + 0.941058i \(0.609833\pi\)
\(464\) 44.8686i 0.0966995i
\(465\) −137.786 36.3427i −0.296313 0.0781564i
\(466\) 418.735 0.898572
\(467\) 201.253 201.253i 0.430948 0.430948i −0.458003 0.888951i \(-0.651435\pi\)
0.888951 + 0.458003i \(0.151435\pi\)
\(468\) −36.1924 36.1924i −0.0773342 0.0773342i
\(469\) 270.165i 0.576044i
\(470\) −102.394 175.761i −0.217860 0.373959i
\(471\) 440.671 0.935607
\(472\) 26.9548 26.9548i 0.0571076 0.0571076i
\(473\) 658.000 + 658.000i 1.39112 + 1.39112i
\(474\) 385.690i 0.813693i
\(475\) 471.541 + 267.349i 0.992717 + 0.562840i
\(476\) −71.4287 −0.150060
\(477\) 55.8819 55.8819i 0.117153 0.117153i
\(478\) −147.491 147.491i −0.308559 0.308559i
\(479\) 705.419i 1.47269i −0.676606 0.736346i \(-0.736550\pi\)
0.676606 0.736346i \(-0.263450\pi\)
\(480\) −42.3303 + 24.6606i −0.0881881 + 0.0513763i
\(481\) −575.041 −1.19551
\(482\) −180.182 + 180.182i −0.373821 + 0.373821i
\(483\) 1.94069 + 1.94069i 0.00401800 + 0.00401800i
\(484\) 154.964i 0.320174i
\(485\) −175.325 + 664.708i −0.361495 + 1.37053i
\(486\) 22.0454 0.0453609
\(487\) −457.935 + 457.935i −0.940317 + 0.940317i −0.998317 0.0579991i \(-0.981528\pi\)
0.0579991 + 0.998317i \(0.481528\pi\)
\(488\) 21.7496 + 21.7496i 0.0445688 + 0.0445688i
\(489\) 47.6711i 0.0974870i
\(490\) 47.8606 + 12.6238i 0.0976747 + 0.0257629i
\(491\) 714.606 1.45541 0.727704 0.685891i \(-0.240587\pi\)
0.727704 + 0.685891i \(0.240587\pi\)
\(492\) 107.870 107.870i 0.219249 0.219249i
\(493\) 107.068 + 107.068i 0.217177 + 0.217177i
\(494\) 261.578i 0.529510i
\(495\) 106.378 + 182.599i 0.214904 + 0.368886i
\(496\) 65.8170 0.132696
\(497\) 119.928 119.928i 0.241303 0.241303i
\(498\) 188.604 + 188.604i 0.378722 + 0.378722i
\(499\) 746.370i 1.49573i −0.663850 0.747866i \(-0.731078\pi\)
0.663850 0.747866i \(-0.268922\pi\)
\(500\) 249.983 2.93258i 0.499966 0.00586517i
\(501\) 191.801 0.382836
\(502\) 25.2366 25.2366i 0.0502720 0.0502720i
\(503\) 10.5315 + 10.5315i 0.0209375 + 0.0209375i 0.717498 0.696561i \(-0.245287\pi\)
−0.696561 + 0.717498i \(0.745287\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −112.822 + 65.7272i −0.223409 + 0.130153i
\(506\) −11.9327 −0.0235824
\(507\) −117.855 + 117.855i −0.232456 + 0.232456i
\(508\) 190.623 + 190.623i 0.375243 + 0.375243i
\(509\) 137.581i 0.270296i −0.990825 0.135148i \(-0.956849\pi\)
0.990825 0.135148i \(-0.0431510\pi\)
\(510\) −42.1646 + 159.858i −0.0826757 + 0.313447i
\(511\) −192.473 −0.376660
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 79.6658 + 79.6658i 0.155294 + 0.155294i
\(514\) 457.349i 0.889784i
\(515\) −362.067 95.4999i −0.703044 0.185437i
\(516\) 228.808 0.443426
\(517\) 286.574 286.574i 0.554302 0.554302i
\(518\) 178.347 + 178.347i 0.344300 + 0.344300i
\(519\) 163.999i 0.315990i
\(520\) −60.7287 104.242i −0.116786 0.200465i
\(521\) 397.521 0.762995 0.381498 0.924370i \(-0.375408\pi\)
0.381498 + 0.924370i \(0.375408\pi\)
\(522\) 33.6514 33.6514i 0.0644663 0.0644663i
\(523\) 59.4921 + 59.4921i 0.113752 + 0.113752i 0.761692 0.647940i \(-0.224369\pi\)
−0.647940 + 0.761692i \(0.724369\pi\)
\(524\) 383.732i 0.732313i
\(525\) 56.5045 99.6606i 0.107628 0.189830i
\(526\) −34.3283 −0.0652629
\(527\) 157.057 157.057i 0.298021 0.298021i
\(528\) −69.0186 69.0186i −0.130717 0.130717i
\(529\) 528.641i 0.999322i
\(530\) 160.952 93.7665i 0.303682 0.176918i
\(531\) −40.4322 −0.0761434
\(532\) −81.1277 + 81.1277i −0.152496 + 0.152496i
\(533\) 265.640 + 265.640i 0.498386 + 0.498386i
\(534\) 92.3243i 0.172892i
\(535\) 147.431 558.954i 0.275572 1.04477i
\(536\) −288.818 −0.538840
\(537\) −81.4392 + 81.4392i −0.151656 + 0.151656i
\(538\) −503.847 503.847i −0.936519 0.936519i
\(539\) 98.6186i 0.182966i
\(540\) 50.2432 + 13.2523i 0.0930429 + 0.0245412i
\(541\) −964.790 −1.78335 −0.891673 0.452680i \(-0.850468\pi\)
−0.891673 + 0.452680i \(0.850468\pi\)
\(542\) 147.700 147.700i 0.272510 0.272510i
\(543\) 41.0510 + 41.0510i 0.0756004 + 0.0756004i
\(544\) 76.3605i 0.140369i
\(545\) −149.242 256.177i −0.273839 0.470049i
\(546\) −55.2848 −0.101254
\(547\) −397.442 + 397.442i −0.726585 + 0.726585i −0.969938 0.243353i \(-0.921753\pi\)
0.243353 + 0.969938i \(0.421753\pi\)
\(548\) −269.404 269.404i −0.491614 0.491614i
\(549\) 32.6244i 0.0594251i
\(550\) 132.676 + 480.104i 0.241229 + 0.872916i
\(551\) 243.213 0.441404
\(552\) −2.07469 + 2.07469i −0.00375849 + 0.00375849i
\(553\) −294.576 294.576i −0.532687 0.532687i
\(554\) 5.70025i 0.0102893i
\(555\) 504.422 293.864i 0.908868 0.529485i
\(556\) −99.2595 −0.178524
\(557\) 236.896 236.896i 0.425307 0.425307i −0.461719 0.887026i \(-0.652767\pi\)
0.887026 + 0.461719i \(0.152767\pi\)
\(558\) −49.3628 49.3628i −0.0884637 0.0884637i
\(559\) 563.458i 1.00797i
\(560\) −13.4955 + 51.1652i −0.0240990 + 0.0913663i
\(561\) −329.394 −0.587154
\(562\) 384.657 384.657i 0.684443 0.684443i
\(563\) −113.926 113.926i −0.202355 0.202355i 0.598653 0.801008i \(-0.295703\pi\)
−0.801008 + 0.598653i \(0.795703\pi\)
\(564\) 99.6511i 0.176686i
\(565\) −972.204 256.431i −1.72072 0.453860i
\(566\) −403.467 −0.712839
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) 128.208 + 128.208i 0.225718 + 0.225718i
\(569\) 932.914i 1.63957i −0.572673 0.819784i \(-0.694093\pi\)
0.572673 0.819784i \(-0.305907\pi\)
\(570\) 133.675 + 229.454i 0.234517 + 0.402552i
\(571\) 384.804 0.673912 0.336956 0.941520i \(-0.390603\pi\)
0.336956 + 0.941520i \(0.390603\pi\)
\(572\) 169.964 169.964i 0.297140 0.297140i
\(573\) 257.045 + 257.045i 0.448596 + 0.448596i
\(574\) 164.775i 0.287064i
\(575\) 14.4318 3.98822i 0.0250989 0.00693604i
\(576\) −24.0000 −0.0416667
\(577\) −207.248 + 207.248i −0.359182 + 0.359182i −0.863512 0.504329i \(-0.831740\pi\)
0.504329 + 0.863512i \(0.331740\pi\)
\(578\) 106.784 + 106.784i 0.184747 + 0.184747i
\(579\) 607.313i 1.04890i
\(580\) 96.9233 56.4651i 0.167109 0.0973537i
\(581\) 288.097 0.495864
\(582\) −238.137 + 238.137i −0.409170 + 0.409170i
\(583\) 262.428 + 262.428i 0.450134 + 0.450134i
\(584\) 205.763i 0.352334i
\(585\) −32.6348 + 123.728i −0.0557860 + 0.211501i
\(586\) −733.755 −1.25214
\(587\) 517.152 517.152i 0.881009 0.881009i −0.112628 0.993637i \(-0.535927\pi\)
0.993637 + 0.112628i \(0.0359268\pi\)
\(588\) 17.1464 + 17.1464i 0.0291606 + 0.0291606i
\(589\) 356.766i 0.605715i
\(590\) −92.1480 24.3052i −0.156183 0.0411953i
\(591\) 35.1238 0.0594312
\(592\) −190.661 + 190.661i −0.322063 + 0.322063i
\(593\) −455.580 455.580i −0.768264 0.768264i 0.209537 0.977801i \(-0.432804\pi\)
−0.977801 + 0.209537i \(0.932804\pi\)
\(594\) 103.528i 0.174289i
\(595\) 89.8899 + 154.297i 0.151075 + 0.259323i
\(596\) 274.284 0.460208
\(597\) 346.114 346.114i 0.579756 0.579756i
\(598\) −5.10909 5.10909i −0.00854362 0.00854362i
\(599\) 812.606i 1.35660i 0.734783 + 0.678302i \(0.237284\pi\)
−0.734783 + 0.678302i \(0.762716\pi\)
\(600\) 106.542 + 60.4059i 0.177569 + 0.100677i
\(601\) −315.588 −0.525105 −0.262552 0.964918i \(-0.584564\pi\)
−0.262552 + 0.964918i \(0.584564\pi\)
\(602\) 174.755 174.755i 0.290291 0.290291i
\(603\) 216.614 + 216.614i 0.359227 + 0.359227i
\(604\) 395.584i 0.654941i
\(605\) −334.747 + 195.016i −0.553301 + 0.322340i
\(606\) −63.9665 −0.105555
\(607\) 523.720 523.720i 0.862801 0.862801i −0.128862 0.991663i \(-0.541132\pi\)
0.991663 + 0.128862i \(0.0411324\pi\)
\(608\) −86.7292 86.7292i −0.142647 0.142647i
\(609\) 51.4034i 0.0844063i
\(610\) 19.6117 74.3534i 0.0321503 0.121891i
\(611\) 245.399 0.401635
\(612\) −57.2704 + 57.2704i −0.0935791 + 0.0935791i
\(613\) −239.438 239.438i −0.390601 0.390601i 0.484301 0.874901i \(-0.339074\pi\)
−0.874901 + 0.484301i \(0.839074\pi\)
\(614\) 825.570i 1.34458i
\(615\) −368.767 97.2670i −0.599622 0.158158i
\(616\) −105.428 −0.171149
\(617\) −508.117 + 508.117i −0.823529 + 0.823529i −0.986612 0.163083i \(-0.947856\pi\)
0.163083 + 0.986612i \(0.447856\pi\)
\(618\) −129.713 129.713i −0.209892 0.209892i
\(619\) 237.357i 0.383453i −0.981448 0.191727i \(-0.938591\pi\)
0.981448 0.191727i \(-0.0614087\pi\)
\(620\) −82.8278 142.175i −0.133593 0.229315i
\(621\) 3.11203 0.00501132
\(622\) 512.668 512.668i 0.824225 0.824225i
\(623\) −70.5139 70.5139i −0.113184 0.113184i
\(624\) 59.1019i 0.0947146i
\(625\) −320.927 536.312i −0.513484 0.858099i
\(626\) −202.938 −0.324182
\(627\) −374.120 + 374.120i −0.596683 + 0.596683i
\(628\) 359.806 + 359.806i 0.572940 + 0.572940i
\(629\) 909.937i 1.44664i
\(630\) 48.4955 28.2523i 0.0769769 0.0448449i
\(631\) 717.680 1.13737 0.568685 0.822556i \(-0.307453\pi\)
0.568685 + 0.822556i \(0.307453\pi\)
\(632\) 314.915 314.915i 0.498283 0.498283i
\(633\) −255.471 255.471i −0.403588 0.403588i
\(634\) 405.233i 0.639169i
\(635\) 171.886 651.667i 0.270686 1.02625i
\(636\) 91.2547 0.143482
\(637\) −42.2245 + 42.2245i −0.0662864 + 0.0662864i
\(638\) 158.031 + 158.031i 0.247698 + 0.247698i
\(639\) 192.312i 0.300958i
\(640\) −54.6978 14.4272i −0.0854654 0.0225426i
\(641\) −894.582 −1.39560 −0.697802 0.716291i \(-0.745838\pi\)
−0.697802 + 0.716291i \(0.745838\pi\)
\(642\) 200.250 200.250i 0.311915 0.311915i
\(643\) 27.5752 + 27.5752i 0.0428853 + 0.0428853i 0.728224 0.685339i \(-0.240346\pi\)
−0.685339 + 0.728224i \(0.740346\pi\)
\(644\) 3.16914i 0.00492102i
\(645\) −287.945 494.262i −0.446426 0.766297i
\(646\) −413.918 −0.640739
\(647\) 76.5361 76.5361i 0.118294 0.118294i −0.645482 0.763776i \(-0.723343\pi\)
0.763776 + 0.645482i \(0.223343\pi\)
\(648\) 18.0000 + 18.0000i 0.0277778 + 0.0277778i
\(649\) 189.874i 0.292565i
\(650\) −148.754 + 262.367i −0.228853 + 0.403642i
\(651\) −75.4029 −0.115826
\(652\) −38.9233 + 38.9233i −0.0596983 + 0.0596983i
\(653\) 873.233 + 873.233i 1.33726 + 1.33726i 0.898700 + 0.438564i \(0.144513\pi\)
0.438564 + 0.898700i \(0.355487\pi\)
\(654\) 145.245i 0.222086i
\(655\) 828.922 482.910i 1.26553 0.737267i
\(656\) 176.152 0.268524
\(657\) −154.322 + 154.322i −0.234889 + 0.234889i
\(658\) −76.1098 76.1098i −0.115668 0.115668i
\(659\) 62.2133i 0.0944055i −0.998885 0.0472028i \(-0.984969\pi\)
0.998885 0.0472028i \(-0.0150307\pi\)
\(660\) −62.2343 + 235.948i −0.0942944 + 0.357497i
\(661\) −1086.21 −1.64328 −0.821639 0.570008i \(-0.806940\pi\)
−0.821639 + 0.570008i \(0.806940\pi\)
\(662\) 65.9564 65.9564i 0.0996321 0.0996321i
\(663\) −141.033 141.033i −0.212719 0.212719i
\(664\) 307.989i 0.463838i
\(665\) 277.344 + 73.1531i 0.417059 + 0.110005i
\(666\) 285.992 0.429417
\(667\) 4.75039 4.75039i 0.00712203 0.00712203i
\(668\) 156.605 + 156.605i 0.234438 + 0.234438i
\(669\) 502.602i 0.751273i
\(670\) 363.465 + 623.893i 0.542485 + 0.931184i
\(671\) 153.208 0.228328
\(672\) −18.3303 + 18.3303i −0.0272772 + 0.0272772i
\(673\) 663.103 + 663.103i 0.985294 + 0.985294i 0.999893 0.0145998i \(-0.00464744\pi\)
−0.0145998 + 0.999893i \(0.504647\pi\)
\(674\) 721.545i 1.07054i
\(675\) −34.6018 125.211i −0.0512620 0.185497i
\(676\) −192.457 −0.284699
\(677\) 363.300 363.300i 0.536632 0.536632i −0.385906 0.922538i \(-0.626111\pi\)
0.922538 + 0.385906i \(0.126111\pi\)
\(678\) −348.300 348.300i −0.513716 0.513716i
\(679\) 363.760i 0.535729i
\(680\) −164.951 + 96.0964i −0.242575 + 0.141318i
\(681\) −774.161 −1.13680
\(682\) 231.814 231.814i 0.339903 0.339903i
\(683\) 133.225 + 133.225i 0.195058 + 0.195058i 0.797878 0.602819i \(-0.205956\pi\)
−0.602819 + 0.797878i \(0.705956\pi\)
\(684\) 130.094i 0.190196i
\(685\) −242.923 + 920.990i −0.354632 + 1.34451i
\(686\) 26.1916 0.0381802
\(687\) −151.248 + 151.248i −0.220157 + 0.220157i
\(688\) 186.821 + 186.821i 0.271542 + 0.271542i
\(689\) 224.722i 0.326157i
\(690\) 7.09256 + 1.87075i 0.0102791 + 0.00271124i
\(691\) −1151.29 −1.66612 −0.833060 0.553183i \(-0.813413\pi\)
−0.833060 + 0.553183i \(0.813413\pi\)
\(692\) 133.904 133.904i 0.193503 0.193503i
\(693\) 79.0708 + 79.0708i 0.114099 + 0.114099i
\(694\) 390.436i 0.562588i
\(695\) 124.914 + 214.416i 0.179732 + 0.308513i
\(696\) 54.9526 0.0789548
\(697\) 420.345 420.345i 0.603077 0.603077i
\(698\) −204.957 204.957i −0.293635 0.293635i
\(699\) 512.843i 0.733681i
\(700\) 127.508 35.2368i 0.182155 0.0503383i
\(701\) 181.482 0.258890 0.129445 0.991587i \(-0.458680\pi\)
0.129445 + 0.991587i \(0.458680\pi\)
\(702\) −44.3264 + 44.3264i −0.0631431 + 0.0631431i
\(703\) 1033.49 + 1033.49i 1.47012 + 1.47012i
\(704\) 112.707i 0.160095i
\(705\) −215.262 + 125.407i −0.305337 + 0.177882i
\(706\) −466.988 −0.661457
\(707\) −48.8552 + 48.8552i −0.0691022 + 0.0691022i
\(708\) −33.0127 33.0127i −0.0466281 0.0466281i
\(709\) 436.784i 0.616057i 0.951377 + 0.308029i \(0.0996692\pi\)
−0.951377 + 0.308029i \(0.900331\pi\)
\(710\) 115.606 438.294i 0.162825 0.617316i
\(711\) −472.372 −0.664377
\(712\) 75.3825 75.3825i 0.105874 0.105874i
\(713\) −6.96828 6.96828i −0.00977318 0.00977318i
\(714\) 87.4820i 0.122524i
\(715\) −581.041 153.257i −0.812645 0.214345i
\(716\) −132.990 −0.185740
\(717\) −180.639 + 180.639i −0.251937 + 0.251937i
\(718\) 263.565 + 263.565i 0.367082 + 0.367082i
\(719\) 553.810i 0.770250i 0.922864 + 0.385125i \(0.125842\pi\)
−0.922864 + 0.385125i \(0.874158\pi\)
\(720\) 30.2030 + 51.8438i 0.0419485 + 0.0720053i
\(721\) −198.141 −0.274813
\(722\) −109.122 + 109.122i −0.151138 + 0.151138i
\(723\) 220.677 + 220.677i 0.305224 + 0.305224i
\(724\) 67.0361i 0.0925913i
\(725\) −243.947 138.311i −0.336479 0.190773i
\(726\) −189.792 −0.261421
\(727\) −377.156 + 377.156i −0.518783 + 0.518783i −0.917203 0.398420i \(-0.869559\pi\)
0.398420 + 0.917203i \(0.369559\pi\)
\(728\) −45.1398 45.1398i −0.0620053 0.0620053i
\(729\) 27.0000i 0.0370370i
\(730\) −444.480 + 258.943i −0.608877 + 0.354717i
\(731\) 891.609 1.21971
\(732\) 26.6377 26.6377i 0.0363903 0.0363903i
\(733\) −100.250 100.250i −0.136767 0.136767i 0.635409 0.772176i \(-0.280832\pi\)
−0.772176 + 0.635409i \(0.780832\pi\)
\(734\) 44.0019i 0.0599481i
\(735\) 15.4610 58.6170i 0.0210354 0.0797511i
\(736\) −3.38795 −0.00460320
\(737\) −1017.24 + 1017.24i −1.38025 + 1.38025i
\(738\) −132.114 132.114i −0.179016 0.179016i
\(739\) 606.576i 0.820806i −0.911904 0.410403i \(-0.865388\pi\)
0.911904 0.410403i \(-0.134612\pi\)
\(740\) 651.798 + 171.920i 0.880808 + 0.232324i
\(741\) −320.366 −0.432343
\(742\) 69.6970 69.6970i 0.0939312 0.0939312i
\(743\) −345.903 345.903i −0.465549 0.465549i 0.434920 0.900469i \(-0.356777\pi\)
−0.900469 + 0.434920i \(0.856777\pi\)
\(744\) 80.6091i 0.108346i
\(745\) −345.174 592.497i −0.463321 0.795298i
\(746\) −341.946 −0.458373
\(747\) 230.992 230.992i 0.309226 0.309226i
\(748\) −268.949 268.949i −0.359557 0.359557i
\(749\) 305.886i 0.408393i
\(750\) −3.59167 306.165i −0.00478889 0.408220i
\(751\) −203.256 −0.270647 −0.135324 0.990801i \(-0.543207\pi\)
−0.135324 + 0.990801i \(0.543207\pi\)
\(752\) 81.3648 81.3648i 0.108198 0.108198i
\(753\) −30.9083 30.9083i −0.0410469 0.0410469i
\(754\) 135.325i 0.179476i
\(755\) 854.525 497.826i 1.13182 0.659372i
\(756\) 27.4955 0.0363696
\(757\) −6.94517 + 6.94517i −0.00917460 + 0.00917460i −0.711679 0.702505i \(-0.752065\pi\)
0.702505 + 0.711679i \(0.252065\pi\)
\(758\) 272.520 + 272.520i 0.359525 + 0.359525i
\(759\) 14.6145i 0.0192549i
\(760\) −78.2039 + 296.494i −0.102900 + 0.390123i
\(761\) 977.803 1.28489 0.642446 0.766331i \(-0.277920\pi\)
0.642446 + 0.766331i \(0.277920\pi\)
\(762\) 233.465 233.465i 0.306384 0.306384i
\(763\) −110.932 110.932i −0.145390 0.145390i
\(764\) 419.753i 0.549415i
\(765\) 195.785 + 51.6409i 0.255929 + 0.0675044i
\(766\) −567.954 −0.741454
\(767\) 81.2965 81.2965i 0.105993 0.105993i
\(768\) −19.5959 19.5959i −0.0255155 0.0255155i
\(769\) 821.202i 1.06788i −0.845521 0.533942i \(-0.820710\pi\)
0.845521 0.533942i \(-0.179290\pi\)
\(770\) 132.676 + 227.741i 0.172307 + 0.295767i
\(771\) −560.136 −0.726506
\(772\) −495.869 + 495.869i −0.642317 + 0.642317i
\(773\) 433.236 + 433.236i 0.560460 + 0.560460i 0.929438 0.368978i \(-0.120292\pi\)
−0.368978 + 0.929438i \(0.620292\pi\)
\(774\) 280.231i 0.362056i
\(775\) −202.886 + 357.843i −0.261788 + 0.461732i
\(776\) −388.876 −0.501128
\(777\) 218.430 218.430i 0.281120 0.281120i
\(778\) 12.8522 + 12.8522i 0.0165196 + 0.0165196i
\(779\) 954.843i 1.22573i
\(780\) −127.670 + 74.3772i −0.163679 + 0.0953554i
\(781\) 903.121