Properties

Label 105.3.n.a.31.1
Level 105
Weight 3
Character 105.31
Analytic conductor 2.861
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.523596960000.16
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(-1.26021 - 2.18275i\) of \(x^{8} - 2 x^{7} + 13 x^{6} - 2 x^{5} + 91 x^{4} - 50 x^{3} + 190 x^{2} + 100 x + 100\)
Character \(\chi\) \(=\) 105.31
Dual form 105.3.n.a.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26021 - 2.18275i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.17628 + 2.03737i) q^{4} +(-1.93649 + 1.11803i) q^{5} +4.36551i q^{6} +(-6.18050 + 3.28656i) q^{7} -4.15226 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.26021 - 2.18275i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.17628 + 2.03737i) q^{4} +(-1.93649 + 1.11803i) q^{5} +4.36551i q^{6} +(-6.18050 + 3.28656i) q^{7} -4.15226 q^{8} +(1.50000 + 2.59808i) q^{9} +(4.88079 + 2.81792i) q^{10} +(4.36036 - 7.55236i) q^{11} +(3.52883 - 2.03737i) q^{12} +21.5286i q^{13} +(14.9625 + 9.34874i) q^{14} +3.87298 q^{15} +(9.93785 + 17.2129i) q^{16} +(-18.7862 - 10.8462i) q^{17} +(3.78064 - 6.54826i) q^{18} +(-2.71590 + 1.56803i) q^{19} -5.26047i q^{20} +(12.1170 + 0.422628i) q^{21} -21.9799 q^{22} +(-2.05421 - 3.55799i) q^{23} +(6.22840 + 3.59597i) q^{24} +(2.50000 - 4.33013i) q^{25} +(46.9917 - 27.1307i) q^{26} -5.19615i q^{27} +(0.574033 - 16.4579i) q^{28} -50.8583 q^{29} +(-4.88079 - 8.45377i) q^{30} +(-33.9213 - 19.5845i) q^{31} +(16.7431 - 28.9999i) q^{32} +(-13.0811 + 7.55236i) q^{33} +54.6743i q^{34} +(8.29399 - 13.2744i) q^{35} -7.05767 q^{36} +(-26.4906 - 45.8831i) q^{37} +(6.84523 + 3.95209i) q^{38} +(18.6443 - 32.2929i) q^{39} +(8.04083 - 4.64237i) q^{40} +36.8122i q^{41} +(-14.3475 - 26.9810i) q^{42} +17.6504 q^{43} +(10.2580 + 17.7674i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-5.17748 + 8.96766i) q^{46} +(-3.49804 + 2.01959i) q^{47} -34.4257i q^{48} +(27.3971 - 40.6251i) q^{49} -12.6021 q^{50} +(18.7862 + 32.5387i) q^{51} +(-43.8618 - 25.3236i) q^{52} +(-2.22593 + 3.85542i) q^{53} +(-11.3419 + 6.54826i) q^{54} +19.5001i q^{55} +(25.6631 - 13.6467i) q^{56} +5.43180 q^{57} +(64.0923 + 111.011i) q^{58} +(81.5032 + 47.0559i) q^{59} +(-4.55570 + 7.89071i) q^{60} +(-63.3781 + 36.5913i) q^{61} +98.7226i q^{62} +(-17.8095 - 11.1276i) q^{63} -4.89677 q^{64} +(-24.0697 - 41.6900i) q^{65} +(32.9699 + 19.0352i) q^{66} +(50.2661 - 87.0635i) q^{67} +(44.1956 - 25.5164i) q^{68} +7.11598i q^{69} +(-39.4270 - 1.37517i) q^{70} -56.6975 q^{71} +(-6.22840 - 10.7879i) q^{72} +(64.8042 + 37.4147i) q^{73} +(-66.7676 + 115.645i) q^{74} +(-7.50000 + 4.33013i) q^{75} -7.37773i q^{76} +(-2.12789 + 61.0079i) q^{77} -93.9833 q^{78} +(-14.4903 - 25.0980i) q^{79} +(-38.4891 - 22.2217i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(80.3519 - 46.3912i) q^{82} +21.1116i q^{83} +(-15.1140 + 24.1897i) q^{84} +48.5058 q^{85} +(-22.2433 - 38.5266i) q^{86} +(76.2875 + 44.0446i) q^{87} +(-18.1054 + 31.3594i) q^{88} +(63.1066 - 36.4346i) q^{89} +16.9075i q^{90} +(-70.7551 - 133.057i) q^{91} +9.66528 q^{92} +(33.9213 + 58.7535i) q^{93} +(8.81655 + 5.09024i) q^{94} +(3.50621 - 6.07294i) q^{95} +(-50.2293 + 28.9999i) q^{96} +73.7985i q^{97} +(-123.201 - 8.60469i) q^{98} +26.1622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + 20q^{11} + 18q^{12} - 16q^{14} - 2q^{16} - 18q^{17} - 6q^{18} + 48q^{21} - 16q^{22} + 62q^{23} + 48q^{24} + 20q^{25} + 120q^{26} - 120q^{28} - 100q^{29} - 126q^{31} + 36q^{32} - 60q^{33} - 36q^{36} - 80q^{37} + 114q^{38} - 12q^{39} + 90q^{40} + 90q^{42} + 352q^{43} - 18q^{44} - 82q^{46} - 72q^{47} + 38q^{49} + 20q^{50} + 18q^{51} - 48q^{52} - 76q^{53} + 18q^{54} + 196q^{56} - 40q^{58} - 54q^{59} - 60q^{60} - 396q^{61} - 96q^{63} - 4q^{64} - 60q^{65} + 24q^{66} + 184q^{67} - 312q^{68} + 164q^{71} - 48q^{72} + 348q^{73} - 140q^{74} - 60q^{75} + 152q^{77} - 240q^{78} - 206q^{79} - 36q^{81} + 204q^{82} + 132q^{84} - 60q^{85} + 178q^{86} + 150q^{87} + 124q^{88} + 282q^{89} - 114q^{91} - 288q^{92} + 126q^{93} + 30q^{94} - 120q^{95} - 108q^{96} - 592q^{98} + 120q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26021 2.18275i −0.630107 1.09138i −0.987529 0.157434i \(-0.949678\pi\)
0.357423 0.933943i \(-0.383656\pi\)
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −1.17628 + 2.03737i −0.294069 + 0.509343i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 4.36551i 0.727585i
\(7\) −6.18050 + 3.28656i −0.882928 + 0.469508i
\(8\) −4.15226 −0.519033
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 4.88079 + 2.81792i 0.488079 + 0.281792i
\(11\) 4.36036 7.55236i 0.396396 0.686579i −0.596882 0.802329i \(-0.703594\pi\)
0.993278 + 0.115750i \(0.0369273\pi\)
\(12\) 3.52883 2.03737i 0.294069 0.169781i
\(13\) 21.5286i 1.65605i 0.560693 + 0.828024i \(0.310535\pi\)
−0.560693 + 0.828024i \(0.689465\pi\)
\(14\) 14.9625 + 9.34874i 1.06875 + 0.667767i
\(15\) 3.87298 0.258199
\(16\) 9.93785 + 17.2129i 0.621116 + 1.07580i
\(17\) −18.7862 10.8462i −1.10507 0.638013i −0.167523 0.985868i \(-0.553577\pi\)
−0.937548 + 0.347855i \(0.886910\pi\)
\(18\) 3.78064 6.54826i 0.210036 0.363792i
\(19\) −2.71590 + 1.56803i −0.142942 + 0.0825276i −0.569765 0.821807i \(-0.692966\pi\)
0.426823 + 0.904335i \(0.359633\pi\)
\(20\) 5.26047i 0.263024i
\(21\) 12.1170 + 0.422628i 0.576999 + 0.0201251i
\(22\) −21.9799 −0.999088
\(23\) −2.05421 3.55799i −0.0893134 0.154695i 0.817908 0.575349i \(-0.195134\pi\)
−0.907221 + 0.420654i \(0.861801\pi\)
\(24\) 6.22840 + 3.59597i 0.259517 + 0.149832i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 46.9917 27.1307i 1.80737 1.04349i
\(27\) 5.19615i 0.192450i
\(28\) 0.574033 16.4579i 0.0205012 0.587781i
\(29\) −50.8583 −1.75373 −0.876867 0.480732i \(-0.840371\pi\)
−0.876867 + 0.480732i \(0.840371\pi\)
\(30\) −4.88079 8.45377i −0.162693 0.281792i
\(31\) −33.9213 19.5845i −1.09424 0.631758i −0.159536 0.987192i \(-0.551000\pi\)
−0.934701 + 0.355434i \(0.884333\pi\)
\(32\) 16.7431 28.9999i 0.523222 0.906247i
\(33\) −13.0811 + 7.55236i −0.396396 + 0.228860i
\(34\) 54.6743i 1.60807i
\(35\) 8.29399 13.2744i 0.236971 0.379269i
\(36\) −7.05767 −0.196046
\(37\) −26.4906 45.8831i −0.715962 1.24008i −0.962587 0.270972i \(-0.912655\pi\)
0.246625 0.969111i \(-0.420678\pi\)
\(38\) 6.84523 + 3.95209i 0.180138 + 0.104002i
\(39\) 18.6443 32.2929i 0.478060 0.828024i
\(40\) 8.04083 4.64237i 0.201021 0.116059i
\(41\) 36.8122i 0.897857i 0.893568 + 0.448929i \(0.148194\pi\)
−0.893568 + 0.448929i \(0.851806\pi\)
\(42\) −14.3475 26.9810i −0.341607 0.642405i
\(43\) 17.6504 0.410475 0.205238 0.978712i \(-0.434203\pi\)
0.205238 + 0.978712i \(0.434203\pi\)
\(44\) 10.2580 + 17.7674i 0.233136 + 0.403804i
\(45\) −5.80948 3.35410i −0.129099 0.0745356i
\(46\) −5.17748 + 8.96766i −0.112554 + 0.194949i
\(47\) −3.49804 + 2.01959i −0.0744263 + 0.0429701i −0.536751 0.843740i \(-0.680349\pi\)
0.462325 + 0.886711i \(0.347015\pi\)
\(48\) 34.4257i 0.717203i
\(49\) 27.3971 40.6251i 0.559124 0.829084i
\(50\) −12.6021 −0.252043
\(51\) 18.7862 + 32.5387i 0.368357 + 0.638013i
\(52\) −43.8618 25.3236i −0.843496 0.486993i
\(53\) −2.22593 + 3.85542i −0.0419986 + 0.0727438i −0.886261 0.463187i \(-0.846706\pi\)
0.844262 + 0.535931i \(0.180039\pi\)
\(54\) −11.3419 + 6.54826i −0.210036 + 0.121264i
\(55\) 19.5001i 0.354548i
\(56\) 25.6631 13.6467i 0.458269 0.243690i
\(57\) 5.43180 0.0952947
\(58\) 64.0923 + 111.011i 1.10504 + 1.91399i
\(59\) 81.5032 + 47.0559i 1.38141 + 0.797558i 0.992327 0.123644i \(-0.0394582\pi\)
0.389084 + 0.921202i \(0.372792\pi\)
\(60\) −4.55570 + 7.89071i −0.0759284 + 0.131512i
\(61\) −63.3781 + 36.5913i −1.03898 + 0.599858i −0.919546 0.392984i \(-0.871443\pi\)
−0.119439 + 0.992842i \(0.538110\pi\)
\(62\) 98.7226i 1.59230i
\(63\) −17.8095 11.1276i −0.282690 0.176628i
\(64\) −4.89677 −0.0765121
\(65\) −24.0697 41.6900i −0.370303 0.641384i
\(66\) 32.9699 + 19.0352i 0.499544 + 0.288412i
\(67\) 50.2661 87.0635i 0.750241 1.29946i −0.197465 0.980310i \(-0.563271\pi\)
0.947706 0.319145i \(-0.103396\pi\)
\(68\) 44.1956 25.5164i 0.649936 0.375241i
\(69\) 7.11598i 0.103130i
\(70\) −39.4270 1.37517i −0.563242 0.0196453i
\(71\) −56.6975 −0.798557 −0.399278 0.916830i \(-0.630739\pi\)
−0.399278 + 0.916830i \(0.630739\pi\)
\(72\) −6.22840 10.7879i −0.0865055 0.149832i
\(73\) 64.8042 + 37.4147i 0.887729 + 0.512531i 0.873199 0.487364i \(-0.162041\pi\)
0.0145299 + 0.999894i \(0.495375\pi\)
\(74\) −66.7676 + 115.645i −0.902266 + 1.56277i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 7.37773i 0.0970754i
\(77\) −2.12789 + 61.0079i −0.0276350 + 0.792311i
\(78\) −93.9833 −1.20491
\(79\) −14.4903 25.0980i −0.183422 0.317696i 0.759622 0.650365i \(-0.225384\pi\)
−0.943044 + 0.332669i \(0.892051\pi\)
\(80\) −38.4891 22.2217i −0.481114 0.277771i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 80.3519 46.3912i 0.979901 0.565746i
\(83\) 21.1116i 0.254357i 0.991880 + 0.127179i \(0.0405921\pi\)
−0.991880 + 0.127179i \(0.959408\pi\)
\(84\) −15.1140 + 24.1897i −0.179928 + 0.287973i
\(85\) 48.5058 0.570657
\(86\) −22.2433 38.5266i −0.258643 0.447983i
\(87\) 76.2875 + 44.0446i 0.876867 + 0.506260i
\(88\) −18.1054 + 31.3594i −0.205743 + 0.356357i
\(89\) 63.1066 36.4346i 0.709063 0.409378i −0.101651 0.994820i \(-0.532412\pi\)
0.810714 + 0.585442i \(0.199079\pi\)
\(90\) 16.9075i 0.187862i
\(91\) −70.7551 133.057i −0.777528 1.46217i
\(92\) 9.66528 0.105057
\(93\) 33.9213 + 58.7535i 0.364746 + 0.631758i
\(94\) 8.81655 + 5.09024i 0.0937931 + 0.0541515i
\(95\) 3.50621 6.07294i 0.0369075 0.0639256i
\(96\) −50.2293 + 28.9999i −0.523222 + 0.302082i
\(97\) 73.7985i 0.760809i 0.924820 + 0.380405i \(0.124215\pi\)
−0.924820 + 0.380405i \(0.875785\pi\)
\(98\) −123.201 8.60469i −1.25715 0.0878030i
\(99\) 26.1622 0.264264
\(100\) 5.88139 + 10.1869i 0.0588139 + 0.101869i
\(101\) −92.6245 53.4768i −0.917075 0.529473i −0.0343741 0.999409i \(-0.510944\pi\)
−0.882701 + 0.469936i \(0.844277\pi\)
\(102\) 47.3493 82.0114i 0.464209 0.804033i
\(103\) 18.6535 10.7696i 0.181102 0.104559i −0.406708 0.913558i \(-0.633323\pi\)
0.587810 + 0.808999i \(0.299990\pi\)
\(104\) 89.3925i 0.859543i
\(105\) −23.9370 + 12.7288i −0.227971 + 0.121227i
\(106\) 11.2206 0.105855
\(107\) −44.8184 77.6277i −0.418863 0.725492i 0.576962 0.816771i \(-0.304238\pi\)
−0.995825 + 0.0912785i \(0.970905\pi\)
\(108\) 10.5865 + 6.11212i 0.0980232 + 0.0565937i
\(109\) −13.6751 + 23.6859i −0.125459 + 0.217302i −0.921912 0.387398i \(-0.873374\pi\)
0.796453 + 0.604700i \(0.206707\pi\)
\(110\) 42.5640 24.5743i 0.386945 0.223403i
\(111\) 91.7661i 0.826722i
\(112\) −117.992 73.7227i −1.05350 0.658238i
\(113\) −92.3372 −0.817144 −0.408572 0.912726i \(-0.633973\pi\)
−0.408572 + 0.912726i \(0.633973\pi\)
\(114\) −6.84523 11.8563i −0.0600459 0.104002i
\(115\) 7.95591 + 4.59335i 0.0691818 + 0.0399422i
\(116\) 59.8235 103.617i 0.515720 0.893253i
\(117\) −55.9330 + 32.2929i −0.478060 + 0.276008i
\(118\) 237.202i 2.01019i
\(119\) 151.755 + 5.29305i 1.27525 + 0.0444794i
\(120\) −16.0817 −0.134014
\(121\) 22.4745 + 38.9270i 0.185740 + 0.321711i
\(122\) 159.740 + 92.2258i 1.30934 + 0.755949i
\(123\) 31.8803 55.2182i 0.259189 0.448929i
\(124\) 79.8019 46.0736i 0.643563 0.371562i
\(125\) 11.1803i 0.0894427i
\(126\) −1.84498 + 52.8968i −0.0146427 + 0.419816i
\(127\) 191.591 1.50859 0.754297 0.656534i \(-0.227978\pi\)
0.754297 + 0.656534i \(0.227978\pi\)
\(128\) −60.8015 105.311i −0.475011 0.822744i
\(129\) −26.4757 15.2857i −0.205238 0.118494i
\(130\) −60.6660 + 105.077i −0.466661 + 0.808281i
\(131\) 50.9329 29.4062i 0.388801 0.224474i −0.292839 0.956162i \(-0.594600\pi\)
0.681641 + 0.731687i \(0.261267\pi\)
\(132\) 35.5347i 0.269202i
\(133\) 11.6322 18.6171i 0.0874601 0.139978i
\(134\) −253.384 −1.89093
\(135\) 5.80948 + 10.0623i 0.0430331 + 0.0745356i
\(136\) 78.0054 + 45.0364i 0.573569 + 0.331150i
\(137\) −82.9571 + 143.686i −0.605526 + 1.04880i 0.386442 + 0.922314i \(0.373704\pi\)
−0.991968 + 0.126488i \(0.959629\pi\)
\(138\) 15.5324 8.96766i 0.112554 0.0649831i
\(139\) 139.625i 1.00449i −0.864724 0.502247i \(-0.832507\pi\)
0.864724 0.502247i \(-0.167493\pi\)
\(140\) 17.2889 + 32.5123i 0.123492 + 0.232231i
\(141\) 6.99607 0.0496176
\(142\) 71.4510 + 123.757i 0.503176 + 0.871527i
\(143\) 162.592 + 93.8725i 1.13701 + 0.656451i
\(144\) −29.8136 + 51.6386i −0.207039 + 0.358601i
\(145\) 98.4867 56.8613i 0.679219 0.392147i
\(146\) 188.602i 1.29180i
\(147\) −76.2780 + 37.2111i −0.518898 + 0.253137i
\(148\) 124.641 0.842171
\(149\) 7.16861 + 12.4164i 0.0481115 + 0.0833315i 0.889078 0.457755i \(-0.151346\pi\)
−0.840967 + 0.541087i \(0.818013\pi\)
\(150\) 18.9032 + 10.9138i 0.126021 + 0.0727585i
\(151\) −106.187 + 183.922i −0.703226 + 1.21802i 0.264102 + 0.964495i \(0.414925\pi\)
−0.967328 + 0.253529i \(0.918409\pi\)
\(152\) 11.2771 6.51085i 0.0741917 0.0428346i
\(153\) 65.0774i 0.425342i
\(154\) 135.847 72.2384i 0.882123 0.469080i
\(155\) 87.5845 0.565062
\(156\) 43.8618 + 75.9709i 0.281165 + 0.486993i
\(157\) −210.373 121.459i −1.33996 0.773624i −0.353156 0.935565i \(-0.614891\pi\)
−0.986801 + 0.161941i \(0.948225\pi\)
\(158\) −36.5218 + 63.2577i −0.231151 + 0.400365i
\(159\) 6.67778 3.85542i 0.0419986 0.0242479i
\(160\) 74.8775i 0.467984i
\(161\) 24.3896 + 15.2389i 0.151488 + 0.0946514i
\(162\) 22.6838 0.140024
\(163\) −6.61728 11.4615i −0.0405968 0.0703157i 0.845013 0.534746i \(-0.179593\pi\)
−0.885610 + 0.464430i \(0.846259\pi\)
\(164\) −75.0001 43.3013i −0.457318 0.264032i
\(165\) 16.8876 29.2502i 0.102349 0.177274i
\(166\) 46.0815 26.6052i 0.277600 0.160272i
\(167\) 212.616i 1.27315i 0.771216 + 0.636574i \(0.219649\pi\)
−0.771216 + 0.636574i \(0.780351\pi\)
\(168\) −50.3129 1.75486i −0.299482 0.0104456i
\(169\) −294.481 −1.74249
\(170\) −61.1277 105.876i −0.359575 0.622802i
\(171\) −8.14770 4.70408i −0.0476474 0.0275092i
\(172\) −20.7618 + 35.9605i −0.120708 + 0.209073i
\(173\) −215.456 + 124.393i −1.24541 + 0.719037i −0.970190 0.242345i \(-0.922084\pi\)
−0.275219 + 0.961382i \(0.588750\pi\)
\(174\) 222.022i 1.27599i
\(175\) −1.22002 + 34.9787i −0.00697155 + 0.199878i
\(176\) 173.330 0.984832
\(177\) −81.5032 141.168i −0.460470 0.797558i
\(178\) −159.056 91.8308i −0.893571 0.515903i
\(179\) −27.6352 + 47.8655i −0.154386 + 0.267405i −0.932835 0.360303i \(-0.882673\pi\)
0.778449 + 0.627708i \(0.216007\pi\)
\(180\) 13.6671 7.89071i 0.0759284 0.0438373i
\(181\) 46.9001i 0.259117i 0.991572 + 0.129558i \(0.0413559\pi\)
−0.991572 + 0.129558i \(0.958644\pi\)
\(182\) −201.265 + 322.122i −1.10585 + 1.76990i
\(183\) 126.756 0.692656
\(184\) 8.52961 + 14.7737i 0.0463566 + 0.0802920i
\(185\) 102.598 + 59.2348i 0.554582 + 0.320188i
\(186\) 85.4963 148.084i 0.459658 0.796150i
\(187\) −163.829 + 94.5869i −0.876093 + 0.505812i
\(188\) 9.50241i 0.0505447i
\(189\) 17.0775 + 32.1148i 0.0903569 + 0.169920i
\(190\) −17.6743 −0.0930226
\(191\) 10.0561 + 17.4177i 0.0526499 + 0.0911923i 0.891149 0.453710i \(-0.149900\pi\)
−0.838499 + 0.544903i \(0.816567\pi\)
\(192\) 7.34516 + 4.24073i 0.0382560 + 0.0220871i
\(193\) −14.3516 + 24.8578i −0.0743609 + 0.128797i −0.900808 0.434217i \(-0.857025\pi\)
0.826447 + 0.563014i \(0.190358\pi\)
\(194\) 161.084 93.0019i 0.830330 0.479391i
\(195\) 83.3800i 0.427589i
\(196\) 50.5420 + 103.604i 0.257867 + 0.528594i
\(197\) 224.436 1.13927 0.569636 0.821897i \(-0.307084\pi\)
0.569636 + 0.821897i \(0.307084\pi\)
\(198\) −32.9699 57.1056i −0.166515 0.288412i
\(199\) −275.447 159.030i −1.38416 0.799144i −0.391509 0.920174i \(-0.628047\pi\)
−0.992649 + 0.121030i \(0.961380\pi\)
\(200\) −10.3807 + 17.9798i −0.0519033 + 0.0898992i
\(201\) −150.798 + 87.0635i −0.750241 + 0.433152i
\(202\) 269.569i 1.33450i
\(203\) 314.330 167.149i 1.54842 0.823393i
\(204\) −88.3913 −0.433290
\(205\) −41.1572 71.2864i −0.200767 0.347739i
\(206\) −47.0148 27.1440i −0.228227 0.131767i
\(207\) 6.16262 10.6740i 0.0297711 0.0515651i
\(208\) −370.569 + 213.948i −1.78158 + 1.02860i
\(209\) 27.3486i 0.130855i
\(210\) 57.9495 + 36.2075i 0.275950 + 0.172417i
\(211\) 285.317 1.35221 0.676107 0.736804i \(-0.263666\pi\)
0.676107 + 0.736804i \(0.263666\pi\)
\(212\) −5.23662 9.07009i −0.0247010 0.0427835i
\(213\) 85.0463 + 49.1015i 0.399278 + 0.230523i
\(214\) −112.961 + 195.655i −0.527857 + 0.914276i
\(215\) −34.1799 + 19.7338i −0.158976 + 0.0917851i
\(216\) 21.5758i 0.0998880i
\(217\) 274.016 + 9.55740i 1.26275 + 0.0440433i
\(218\) 68.9341 0.316211
\(219\) −64.8042 112.244i −0.295910 0.512531i
\(220\) −39.7290 22.9376i −0.180586 0.104262i
\(221\) 233.504 404.441i 1.05658 1.83005i
\(222\) 200.303 115.645i 0.902266 0.520923i
\(223\) 57.0977i 0.256044i 0.991771 + 0.128022i \(0.0408627\pi\)
−0.991771 + 0.128022i \(0.959137\pi\)
\(224\) −8.17078 + 234.261i −0.0364767 + 1.04581i
\(225\) 15.0000 0.0666667
\(226\) 116.365 + 201.549i 0.514888 + 0.891812i
\(227\) −158.185 91.3279i −0.696848 0.402325i 0.109324 0.994006i \(-0.465131\pi\)
−0.806172 + 0.591681i \(0.798465\pi\)
\(228\) −6.38930 + 11.0666i −0.0280233 + 0.0485377i
\(229\) −14.5347 + 8.39159i −0.0634702 + 0.0366445i −0.531399 0.847121i \(-0.678334\pi\)
0.467929 + 0.883766i \(0.345000\pi\)
\(230\) 23.1544i 0.100671i
\(231\) 56.0263 89.6691i 0.242538 0.388178i
\(232\) 211.177 0.910246
\(233\) 133.203 + 230.715i 0.571688 + 0.990193i 0.996393 + 0.0848612i \(0.0270447\pi\)
−0.424704 + 0.905332i \(0.639622\pi\)
\(234\) 140.975 + 81.3920i 0.602457 + 0.347829i
\(235\) 4.51595 7.82185i 0.0192168 0.0332845i
\(236\) −191.741 + 110.702i −0.812461 + 0.469075i
\(237\) 50.1960i 0.211797i
\(238\) −179.690 337.914i −0.755001 1.41981i
\(239\) −39.7012 −0.166114 −0.0830568 0.996545i \(-0.526468\pi\)
−0.0830568 + 0.996545i \(0.526468\pi\)
\(240\) 38.4891 + 66.6651i 0.160371 + 0.277771i
\(241\) 72.1896 + 41.6787i 0.299542 + 0.172941i 0.642237 0.766506i \(-0.278006\pi\)
−0.342695 + 0.939447i \(0.611340\pi\)
\(242\) 56.6454 98.1128i 0.234072 0.405425i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 172.166i 0.705600i
\(245\) −7.63390 + 109.301i −0.0311588 + 0.446127i
\(246\) −160.704 −0.653267
\(247\) −33.7574 58.4695i −0.136670 0.236719i
\(248\) 140.850 + 81.3200i 0.567945 + 0.327903i
\(249\) 18.2832 31.6675i 0.0734266 0.127179i
\(250\) 24.4039 14.0896i 0.0976157 0.0563585i
\(251\) 111.464i 0.444079i −0.975038 0.222039i \(-0.928729\pi\)
0.975038 0.222039i \(-0.0712713\pi\)
\(252\) 43.6199 23.1954i 0.173095 0.0920454i
\(253\) −35.8283 −0.141614
\(254\) −241.446 418.197i −0.950575 1.64644i
\(255\) −72.7587 42.0073i −0.285328 0.164734i
\(256\) −163.039 + 282.392i −0.636872 + 1.10309i
\(257\) −193.043 + 111.454i −0.751141 + 0.433672i −0.826106 0.563515i \(-0.809449\pi\)
0.0749649 + 0.997186i \(0.476116\pi\)
\(258\) 77.0531i 0.298656i
\(259\) 314.522 + 196.517i 1.21437 + 0.758754i
\(260\) 113.251 0.435580
\(261\) −76.2875 132.134i −0.292289 0.506260i
\(262\) −128.373 74.1161i −0.489973 0.282886i
\(263\) 213.250 369.360i 0.810837 1.40441i −0.101442 0.994841i \(-0.532346\pi\)
0.912279 0.409569i \(-0.134321\pi\)
\(264\) 54.3161 31.3594i 0.205743 0.118786i
\(265\) 9.95465i 0.0375647i
\(266\) −55.2957 1.92865i −0.207879 0.00725058i
\(267\) −126.213 −0.472709
\(268\) 118.254 + 204.822i 0.441246 + 0.764260i
\(269\) −51.5210 29.7457i −0.191528 0.110579i 0.401170 0.916004i \(-0.368604\pi\)
−0.592698 + 0.805425i \(0.701937\pi\)
\(270\) 14.6424 25.3613i 0.0542310 0.0939308i
\(271\) −47.1819 + 27.2405i −0.174103 + 0.100518i −0.584519 0.811380i \(-0.698717\pi\)
0.410416 + 0.911898i \(0.365383\pi\)
\(272\) 431.153i 1.58512i
\(273\) −9.09858 + 260.862i −0.0333281 + 0.955538i
\(274\) 418.175 1.52618
\(275\) −21.8018 37.7618i −0.0792793 0.137316i
\(276\) −14.4979 8.37037i −0.0525287 0.0303274i
\(277\) 236.189 409.092i 0.852669 1.47687i −0.0261222 0.999659i \(-0.508316\pi\)
0.878791 0.477207i \(-0.158351\pi\)
\(278\) −304.766 + 175.957i −1.09628 + 0.632939i
\(279\) 117.507i 0.421172i
\(280\) −34.4389 + 55.1188i −0.122996 + 0.196853i
\(281\) −534.544 −1.90229 −0.951146 0.308743i \(-0.900092\pi\)
−0.951146 + 0.308743i \(0.900092\pi\)
\(282\) −8.81655 15.2707i −0.0312644 0.0541515i
\(283\) −387.352 223.638i −1.36873 0.790239i −0.377967 0.925819i \(-0.623377\pi\)
−0.990766 + 0.135580i \(0.956710\pi\)
\(284\) 66.6921 115.514i 0.234831 0.406740i
\(285\) −10.5186 + 6.07294i −0.0369075 + 0.0213085i
\(286\) 473.198i 1.65454i
\(287\) −120.985 227.517i −0.421552 0.792743i
\(288\) 100.459 0.348815
\(289\) 90.7814 + 157.238i 0.314122 + 0.544076i
\(290\) −248.229 143.315i −0.855961 0.494189i
\(291\) 63.9114 110.698i 0.219627 0.380405i
\(292\) −152.456 + 88.0202i −0.522108 + 0.301439i
\(293\) 504.200i 1.72082i −0.509604 0.860409i \(-0.670208\pi\)
0.509604 0.860409i \(-0.329792\pi\)
\(294\) 177.349 + 119.602i 0.603229 + 0.406810i
\(295\) −210.440 −0.713357
\(296\) 109.996 + 190.519i 0.371608 + 0.643644i
\(297\) −39.2432 22.6571i −0.132132 0.0762865i
\(298\) 18.0680 31.2946i 0.0606308 0.105016i
\(299\) 76.5986 44.2242i 0.256183 0.147907i
\(300\) 20.3737i 0.0679124i
\(301\) −109.088 + 58.0092i −0.362420 + 0.192722i
\(302\) 535.274 1.77243
\(303\) 92.6245 + 160.430i 0.305692 + 0.529473i
\(304\) −53.9804 31.1656i −0.177567 0.102518i
\(305\) 81.8207 141.718i 0.268265 0.464648i
\(306\) −142.048 + 82.0114i −0.464209 + 0.268011i
\(307\) 398.792i 1.29900i 0.760363 + 0.649499i \(0.225021\pi\)
−0.760363 + 0.649499i \(0.774979\pi\)
\(308\) −121.793 76.0976i −0.395432 0.247070i
\(309\) −37.3070 −0.120735
\(310\) −110.375 191.176i −0.356049 0.616695i
\(311\) −207.085 119.561i −0.665869 0.384440i 0.128640 0.991691i \(-0.458939\pi\)
−0.794510 + 0.607252i \(0.792272\pi\)
\(312\) −77.4162 + 134.089i −0.248129 + 0.429772i
\(313\) 193.296 111.599i 0.617559 0.356548i −0.158359 0.987382i \(-0.550620\pi\)
0.775918 + 0.630834i \(0.217287\pi\)
\(314\) 612.257i 1.94986i
\(315\) 46.9289 + 1.63683i 0.148981 + 0.00519628i
\(316\) 68.1786 0.215755
\(317\) 143.007 + 247.695i 0.451126 + 0.781373i 0.998456 0.0555434i \(-0.0176891\pi\)
−0.547330 + 0.836917i \(0.684356\pi\)
\(318\) −16.8309 9.71731i −0.0529273 0.0305576i
\(319\) −221.761 + 384.100i −0.695174 + 1.20408i
\(320\) 9.48256 5.47476i 0.0296330 0.0171086i
\(321\) 155.255i 0.483662i
\(322\) 2.52665 72.4407i 0.00784675 0.224971i
\(323\) 68.0286 0.210615
\(324\) −10.5865 18.3364i −0.0326744 0.0565937i
\(325\) 93.2216 + 53.8215i 0.286836 + 0.165605i
\(326\) −16.6784 + 28.8878i −0.0511607 + 0.0886129i
\(327\) 41.0252 23.6859i 0.125459 0.0724340i
\(328\) 152.854i 0.466018i
\(329\) 14.9821 23.9786i 0.0455383 0.0728833i
\(330\) −85.1279 −0.257963
\(331\) −269.512 466.809i −0.814236 1.41030i −0.909875 0.414882i \(-0.863823\pi\)
0.0956391 0.995416i \(-0.469511\pi\)
\(332\) −43.0123 24.8332i −0.129555 0.0747987i
\(333\) 79.4718 137.649i 0.238654 0.413361i
\(334\) 464.088 267.941i 1.38948 0.802219i
\(335\) 224.797i 0.671036i
\(336\) 113.142 + 212.768i 0.336733 + 0.633238i
\(337\) 68.2484 0.202518 0.101259 0.994860i \(-0.467713\pi\)
0.101259 + 0.994860i \(0.467713\pi\)
\(338\) 371.109 + 642.780i 1.09796 + 1.90172i
\(339\) 138.506 + 79.9664i 0.408572 + 0.235889i
\(340\) −57.0563 + 98.8244i −0.167813 + 0.290660i
\(341\) −295.819 + 170.791i −0.867503 + 0.500853i
\(342\) 23.7126i 0.0693350i
\(343\) −35.8105 + 341.126i −0.104404 + 0.994535i
\(344\) −73.2893 −0.213050
\(345\) −7.95591 13.7800i −0.0230606 0.0399422i
\(346\) 543.041 + 313.525i 1.56948 + 0.906141i
\(347\) −190.947 + 330.731i −0.550281 + 0.953114i 0.447973 + 0.894047i \(0.352146\pi\)
−0.998254 + 0.0590672i \(0.981187\pi\)
\(348\) −179.470 + 103.617i −0.515720 + 0.297751i
\(349\) 301.869i 0.864953i 0.901645 + 0.432477i \(0.142360\pi\)
−0.901645 + 0.432477i \(0.857640\pi\)
\(350\) 77.8875 41.4177i 0.222536 0.118336i
\(351\) 111.866 0.318706
\(352\) −146.012 252.900i −0.414807 0.718466i
\(353\) 110.891 + 64.0227i 0.314138 + 0.181367i 0.648776 0.760979i \(-0.275281\pi\)
−0.334639 + 0.942346i \(0.608614\pi\)
\(354\) −205.423 + 355.803i −0.580291 + 1.00509i
\(355\) 109.794 63.3898i 0.309280 0.178563i
\(356\) 171.429i 0.481542i
\(357\) −223.048 139.363i −0.624786 0.390373i
\(358\) 139.305 0.389120
\(359\) 262.113 + 453.993i 0.730119 + 1.26460i 0.956832 + 0.290642i \(0.0938688\pi\)
−0.226713 + 0.973962i \(0.572798\pi\)
\(360\) 24.1225 + 13.9271i 0.0670069 + 0.0386864i
\(361\) −175.583 + 304.118i −0.486378 + 0.842432i
\(362\) 102.371 59.1041i 0.282794 0.163271i
\(363\) 77.8541i 0.214474i
\(364\) 354.315 + 12.3581i 0.973394 + 0.0339509i
\(365\) −167.324 −0.458421
\(366\) −159.740 276.677i −0.436448 0.755949i
\(367\) 30.8202 + 17.7941i 0.0839789 + 0.0484852i 0.541401 0.840764i \(-0.317894\pi\)
−0.457423 + 0.889249i \(0.651227\pi\)
\(368\) 40.8288 70.7176i 0.110948 0.192167i
\(369\) −95.6408 + 55.2182i −0.259189 + 0.149643i
\(370\) 298.594i 0.807011i
\(371\) 1.08627 31.1441i 0.00292796 0.0839462i
\(372\) −159.604 −0.429042
\(373\) 133.546 + 231.308i 0.358031 + 0.620128i 0.987632 0.156791i \(-0.0501148\pi\)
−0.629601 + 0.776919i \(0.716781\pi\)
\(374\) 412.920 + 238.399i 1.10406 + 0.637432i
\(375\) 9.68246 16.7705i 0.0258199 0.0447214i
\(376\) 14.5248 8.38588i 0.0386297 0.0223029i
\(377\) 1094.91i 2.90427i
\(378\) 48.5775 77.7474i 0.128512 0.205681i
\(379\) −125.687 −0.331627 −0.165813 0.986157i \(-0.553025\pi\)
−0.165813 + 0.986157i \(0.553025\pi\)
\(380\) 8.24856 + 14.2869i 0.0217067 + 0.0375972i
\(381\) −287.387 165.923i −0.754297 0.435493i
\(382\) 25.3457 43.9001i 0.0663501 0.114922i
\(383\) −308.755 + 178.260i −0.806149 + 0.465430i −0.845617 0.533790i \(-0.820767\pi\)
0.0394677 + 0.999221i \(0.487434\pi\)
\(384\) 210.622i 0.548496i
\(385\) −64.0883 120.520i −0.166463 0.313040i
\(386\) 72.3446 0.187421
\(387\) 26.4757 + 45.8572i 0.0684126 + 0.118494i
\(388\) −150.355 86.8076i −0.387513 0.223731i
\(389\) −223.316 + 386.795i −0.574078 + 0.994332i 0.422064 + 0.906566i \(0.361306\pi\)
−0.996141 + 0.0877654i \(0.972027\pi\)
\(390\) 181.998 105.077i 0.466661 0.269427i
\(391\) 89.1216i 0.227933i
\(392\) −113.760 + 168.686i −0.290204 + 0.430322i
\(393\) −101.866 −0.259201
\(394\) −282.838 489.890i −0.717863 1.24337i
\(395\) 56.1208 + 32.4014i 0.142078 + 0.0820288i
\(396\) −30.7740 + 53.3021i −0.0777120 + 0.134601i
\(397\) 525.089 303.160i 1.32264 0.763627i 0.338492 0.940969i \(-0.390083\pi\)
0.984149 + 0.177342i \(0.0567499\pi\)
\(398\) 801.645i 2.01418i
\(399\) −33.5712 + 17.8519i −0.0841384 + 0.0447417i
\(400\) 99.3785 0.248446
\(401\) 364.402 + 631.163i 0.908734 + 1.57397i 0.815826 + 0.578298i \(0.196283\pi\)
0.0929080 + 0.995675i \(0.470384\pi\)
\(402\) 380.076 + 219.437i 0.945464 + 0.545864i
\(403\) 421.627 730.280i 1.04622 1.81211i
\(404\) 217.904 125.807i 0.539367 0.311404i
\(405\) 20.1246i 0.0496904i
\(406\) −760.967 475.461i −1.87430 1.17109i
\(407\) −462.034 −1.13522
\(408\) −78.0054 135.109i −0.191190 0.331150i
\(409\) −459.563 265.329i −1.12363 0.648725i −0.181301 0.983428i \(-0.558031\pi\)
−0.942324 + 0.334702i \(0.891364\pi\)
\(410\) −103.734 + 179.672i −0.253009 + 0.438225i
\(411\) 248.871 143.686i 0.605526 0.349601i
\(412\) 50.6722i 0.122991i
\(413\) −658.382 22.9637i −1.59415 0.0556021i
\(414\) −31.0649 −0.0750360
\(415\) −23.6035 40.8825i −0.0568760 0.0985121i
\(416\) 624.328 + 360.456i 1.50079 + 0.866481i
\(417\) −120.919 + 209.437i −0.289973 + 0.502247i
\(418\) 59.6953 34.4651i 0.142812 0.0824524i
\(419\) 282.637i 0.674552i −0.941406 0.337276i \(-0.890494\pi\)
0.941406 0.337276i \(-0.109506\pi\)
\(420\) 2.22322 63.7411i 0.00529338 0.151765i
\(421\) 440.590 1.04653 0.523267 0.852169i \(-0.324713\pi\)
0.523267 + 0.852169i \(0.324713\pi\)
\(422\) −359.560 622.777i −0.852039 1.47577i
\(423\) −10.4941 6.05878i −0.0248088 0.0143234i
\(424\) 9.24264 16.0087i 0.0217987 0.0377564i
\(425\) −93.9311 + 54.2311i −0.221014 + 0.127603i
\(426\) 247.514i 0.581018i
\(427\) 271.448 434.448i 0.635710 1.01744i
\(428\) 210.875 0.492700
\(429\) −162.592 281.617i −0.379002 0.656451i
\(430\) 86.1480 + 49.7376i 0.200344 + 0.115669i
\(431\) 63.7174 110.362i 0.147836 0.256060i −0.782591 0.622536i \(-0.786103\pi\)
0.930427 + 0.366476i \(0.119436\pi\)
\(432\) 89.4407 51.6386i 0.207039 0.119534i
\(433\) 433.284i 1.00066i 0.865836 + 0.500328i \(0.166787\pi\)
−0.865836 + 0.500328i \(0.833213\pi\)
\(434\) −324.458 610.155i −0.747599 1.40589i
\(435\) −196.973 −0.452812
\(436\) −32.1714 55.7225i −0.0737876 0.127804i
\(437\) 11.1580 + 6.44210i 0.0255333 + 0.0147416i
\(438\) −163.334 + 282.903i −0.372909 + 0.645898i
\(439\) −54.7578 + 31.6144i −0.124733 + 0.0720146i −0.561068 0.827770i \(-0.689609\pi\)
0.436335 + 0.899784i \(0.356276\pi\)
\(440\) 80.9697i 0.184022i
\(441\) 146.643 + 10.2419i 0.332523 + 0.0232244i
\(442\) −1177.06 −2.66303
\(443\) −219.190 379.648i −0.494785 0.856992i 0.505197 0.863004i \(-0.331420\pi\)
−0.999982 + 0.00601155i \(0.998086\pi\)
\(444\) −186.962 107.942i −0.421085 0.243114i
\(445\) −81.4703 + 141.111i −0.183079 + 0.317103i
\(446\) 124.630 71.9553i 0.279440 0.161335i
\(447\) 24.8328i 0.0555544i
\(448\) 30.2645 16.0935i 0.0675547 0.0359231i
\(449\) 214.986 0.478810 0.239405 0.970920i \(-0.423048\pi\)
0.239405 + 0.970920i \(0.423048\pi\)
\(450\) −18.9032 32.7413i −0.0420071 0.0727585i
\(451\) 278.019 + 160.514i 0.616450 + 0.355907i
\(452\) 108.614 188.125i 0.240297 0.416207i
\(453\) 318.561 183.922i 0.703226 0.406008i
\(454\) 460.371i 1.01403i
\(455\) 285.779 + 178.558i 0.628087 + 0.392436i
\(456\) −22.5543 −0.0494611
\(457\) 120.600 + 208.885i 0.263894 + 0.457078i 0.967273 0.253737i \(-0.0816597\pi\)
−0.703379 + 0.710815i \(0.748326\pi\)
\(458\) 36.6336 + 21.1504i 0.0799860 + 0.0461799i
\(459\) −56.3587 + 97.6161i −0.122786 + 0.212671i
\(460\) −18.7167 + 10.8061i −0.0406885 + 0.0234915i
\(461\) 343.383i 0.744865i 0.928059 + 0.372432i \(0.121476\pi\)
−0.928059 + 0.372432i \(0.878524\pi\)
\(462\) −266.331 9.28933i −0.576473 0.0201068i
\(463\) 74.7714 0.161493 0.0807467 0.996735i \(-0.474270\pi\)
0.0807467 + 0.996735i \(0.474270\pi\)
\(464\) −505.422 875.417i −1.08927 1.88667i
\(465\) −131.377 75.8504i −0.282531 0.163119i
\(466\) 335.730 581.501i 0.720450 1.24786i
\(467\) −308.470 + 178.095i −0.660535 + 0.381360i −0.792481 0.609897i \(-0.791211\pi\)
0.131946 + 0.991257i \(0.457878\pi\)
\(468\) 151.942i 0.324662i
\(469\) −24.5303 + 703.298i −0.0523034 + 1.49957i
\(470\) −22.7642 −0.0484345
\(471\) 210.373 + 364.377i 0.446652 + 0.773624i
\(472\) −338.423 195.389i −0.716998 0.413959i
\(473\) 76.9623 133.303i 0.162711 0.281824i
\(474\) 109.565 63.2577i 0.231151 0.133455i
\(475\) 15.6803i 0.0330111i
\(476\) −189.290 + 302.955i −0.397668 + 0.636461i
\(477\) −13.3556 −0.0279991
\(478\) 50.0319 + 86.6579i 0.104669 + 0.181293i
\(479\) 323.678 + 186.876i 0.675737 + 0.390137i 0.798247 0.602330i \(-0.205761\pi\)
−0.122510 + 0.992467i \(0.539094\pi\)
\(480\) 64.8458 112.316i 0.135095 0.233992i
\(481\) 987.799 570.306i 2.05364 1.18567i
\(482\) 210.096i 0.435884i
\(483\) −23.3871 43.9803i −0.0484205 0.0910565i
\(484\) −105.745 −0.218482
\(485\) −82.5093 142.910i −0.170122 0.294660i
\(486\) −34.0258 19.6448i −0.0700119 0.0404214i
\(487\) −388.781 + 673.389i −0.798319 + 1.38273i 0.122391 + 0.992482i \(0.460944\pi\)
−0.920710 + 0.390247i \(0.872390\pi\)
\(488\) 263.162 151.937i 0.539267 0.311346i
\(489\) 22.9229i 0.0468772i
\(490\) 248.198 121.080i 0.506526 0.247102i
\(491\) 458.794 0.934407 0.467203 0.884150i \(-0.345262\pi\)
0.467203 + 0.884150i \(0.345262\pi\)
\(492\) 75.0001 + 129.904i 0.152439 + 0.264032i
\(493\) 955.435 + 551.621i 1.93800 + 1.11891i
\(494\) −85.0831 + 147.368i −0.172233 + 0.298316i
\(495\) −50.6628 + 29.2502i −0.102349 + 0.0590913i
\(496\) 778.511i 1.56958i
\(497\) 350.419 186.340i 0.705068 0.374929i
\(498\) −92.1631 −0.185066
\(499\) −317.772 550.396i −0.636817 1.10300i −0.986127 0.165992i \(-0.946917\pi\)
0.349310 0.937007i \(-0.386416\pi\)
\(500\) −22.7785 13.1512i −0.0455570 0.0263024i
\(501\) 184.131 318.924i 0.367526 0.636574i
\(502\) −243.298 + 140.468i −0.484657 + 0.279817i
\(503\) 10.6561i 0.0211852i −0.999944 0.0105926i \(-0.996628\pi\)
0.999944 0.0105926i \(-0.00337179\pi\)
\(504\) 73.9496 + 46.2046i 0.146725 + 0.0916757i
\(505\) 239.156 0.473575
\(506\) 45.1514 + 78.2045i 0.0892319 + 0.154554i
\(507\) 441.722 + 255.028i 0.871246 + 0.503014i
\(508\) −225.365 + 390.343i −0.443631 + 0.768392i
\(509\) 706.084 407.658i 1.38720 0.800899i 0.394200 0.919025i \(-0.371022\pi\)
0.992999 + 0.118126i \(0.0376885\pi\)
\(510\) 211.753i 0.415201i
\(511\) −523.488 18.2587i −1.02444 0.0357313i
\(512\) 335.445 0.655167
\(513\) 8.14770 + 14.1122i 0.0158825 + 0.0275092i
\(514\) 486.552 + 280.911i 0.946599 + 0.546519i
\(515\) −24.0816 + 41.7105i −0.0467604 + 0.0809913i
\(516\) 62.2855 35.9605i 0.120708 0.0696909i
\(517\) 35.2246i 0.0681327i
\(518\) 32.5832 934.179i 0.0629019 1.80343i
\(519\) 430.911 0.830273
\(520\) 99.9438 + 173.108i 0.192200 + 0.332900i
\(521\) −383.930 221.662i −0.736911 0.425456i 0.0840344 0.996463i \(-0.473219\pi\)
−0.820945 + 0.571007i \(0.806553\pi\)
\(522\) −192.277 + 333.034i −0.368347 + 0.637995i
\(523\) −549.148 + 317.051i −1.05000 + 0.606216i −0.922648 0.385642i \(-0.873980\pi\)
−0.127348 + 0.991858i \(0.540646\pi\)
\(524\) 138.359i 0.264044i
\(525\) 32.1225 51.4115i 0.0611857 0.0979267i
\(526\) −1074.96 −2.04366
\(527\) 424.836 + 735.837i 0.806140 + 1.39628i
\(528\) −259.996 150.109i −0.492416 0.284297i
\(529\) 256.060 443.510i 0.484046 0.838393i
\(530\) −21.7286 + 12.5450i −0.0409973 + 0.0236698i
\(531\) 282.335i 0.531705i
\(532\) 24.2474 + 45.5980i 0.0455777 + 0.0857106i
\(533\) −792.515 −1.48689
\(534\) 159.056 + 275.492i 0.297857 + 0.515903i
\(535\) 173.581 + 100.217i 0.324450 + 0.187321i
\(536\) −208.718 + 361.511i −0.389400 + 0.674460i
\(537\) 82.9055 47.8655i 0.154386 0.0891351i
\(538\) 149.944i 0.278706i
\(539\) −187.355 384.053i −0.347597 0.712528i
\(540\) −27.3342 −0.0506189
\(541\) 87.5750 + 151.684i 0.161876 + 0.280378i 0.935542 0.353217i \(-0.114912\pi\)
−0.773665 + 0.633594i \(0.781579\pi\)
\(542\) 118.919 + 68.6577i 0.219407 + 0.126675i
\(543\) 40.6167 70.3501i 0.0748005 0.129558i
\(544\) −629.079 + 363.199i −1.15640 + 0.667646i
\(545\) 61.1568i 0.112214i
\(546\) 580.864 308.882i 1.06385 0.565718i
\(547\) −773.543 −1.41416 −0.707078 0.707136i \(-0.749987\pi\)
−0.707078 + 0.707136i \(0.749987\pi\)
\(548\) −195.161 338.029i −0.356133 0.616841i
\(549\) −190.134 109.774i −0.346328 0.199953i
\(550\) −54.9499 + 95.1759i −0.0999088 + 0.173047i
\(551\) 138.126 79.7471i 0.250682 0.144732i
\(552\) 29.5474i 0.0535280i
\(553\) 172.043 + 107.495i 0.311109 + 0.194385i
\(554\) −1190.60 −2.14909
\(555\) −102.598 177.704i −0.184861 0.320188i
\(556\) 284.468 + 164.237i 0.511632 + 0.295391i
\(557\) 378.264 655.173i 0.679110 1.17625i −0.296140 0.955145i \(-0.595699\pi\)
0.975249 0.221108i \(-0.0709673\pi\)
\(558\) −256.489 + 148.084i −0.459658 + 0.265383i
\(559\) 379.989i 0.679766i
\(560\) 310.915 + 10.8444i 0.555205 + 0.0193650i
\(561\) 327.659 0.584062
\(562\) 673.639 + 1166.78i 1.19865 + 2.07612i
\(563\) −451.185 260.492i −0.801394 0.462685i 0.0425646 0.999094i \(-0.486447\pi\)
−0.843958 + 0.536409i \(0.819781\pi\)
\(564\) −8.22933 + 14.2536i −0.0145910 + 0.0252724i
\(565\) 178.810 103.236i 0.316478 0.182719i
\(566\) 1127.32i 1.99174i
\(567\) 2.19604 62.9617i 0.00387308 0.111044i
\(568\) 235.423 0.414477
\(569\) 91.5332 + 158.540i 0.160867 + 0.278629i 0.935180 0.354173i \(-0.115238\pi\)
−0.774313 + 0.632803i \(0.781904\pi\)
\(570\) 26.5115 + 15.3064i 0.0465113 + 0.0268533i
\(571\) −498.800 + 863.947i −0.873555 + 1.51304i −0.0152618 + 0.999884i \(0.504858\pi\)
−0.858294 + 0.513159i \(0.828475\pi\)
\(572\) −382.507 + 220.840i −0.668718 + 0.386084i
\(573\) 34.8355i 0.0607949i
\(574\) −344.147 + 550.802i −0.599560 + 0.959585i
\(575\) −20.5421 −0.0357254
\(576\) −7.34516 12.7222i −0.0127520 0.0220871i
\(577\) 279.135 + 161.158i 0.483769 + 0.279304i 0.721986 0.691908i \(-0.243230\pi\)
−0.238217 + 0.971212i \(0.576563\pi\)
\(578\) 228.808 396.307i 0.395861 0.685652i
\(579\) 43.0549 24.8578i 0.0743609 0.0429323i
\(580\) 267.539i 0.461274i
\(581\) −69.3847 130.480i −0.119423 0.224579i
\(582\) −322.168 −0.553553
\(583\) 19.4117 + 33.6220i 0.0332962 + 0.0576707i
\(584\) −269.084 155.356i −0.460761 0.266020i
\(585\) 72.2092 125.070i 0.123434 0.213795i
\(586\) −1100.54 + 635.400i −1.87806 + 1.08430i
\(587\) 406.391i 0.692318i −0.938176 0.346159i \(-0.887486\pi\)
0.938176 0.346159i \(-0.112514\pi\)
\(588\) 13.9111 199.177i 0.0236583 0.338737i
\(589\) 122.836 0.208550
\(590\) 265.200 + 459.340i 0.449491 + 0.778542i
\(591\) −336.655 194.368i −0.569636 0.328879i
\(592\) 526.519 911.958i 0.889391 1.54047i
\(593\) 333.688 192.655i 0.562711 0.324881i −0.191522 0.981488i \(-0.561342\pi\)
0.754233 + 0.656607i \(0.228009\pi\)
\(594\) 114.211i 0.192275i
\(595\) −299.790 + 159.417i −0.503849 + 0.267928i
\(596\) −33.7291 −0.0565925
\(597\) 275.447 + 477.089i 0.461386 + 0.799144i
\(598\) −193.061 111.464i −0.322845 0.186395i
\(599\) 448.272 776.430i 0.748367 1.29621i −0.200238 0.979747i \(-0.564171\pi\)
0.948605 0.316463i \(-0.102495\pi\)
\(600\) 31.1420 17.9798i 0.0519033 0.0299664i
\(601\) 599.296i 0.997166i −0.866842 0.498583i \(-0.833854\pi\)
0.866842 0.498583i \(-0.166146\pi\)
\(602\) 264.095 + 165.009i 0.438695 + 0.274102i
\(603\) 301.597 0.500161
\(604\) −249.811 432.686i −0.413595 0.716367i
\(605\) −87.0435 50.2546i −0.143874 0.0830654i
\(606\) 233.453 404.353i 0.385237 0.667250i
\(607\) −426.925 + 246.485i −0.703336 + 0.406071i −0.808589 0.588374i \(-0.799768\pi\)
0.105253 + 0.994445i \(0.466435\pi\)
\(608\) 105.014i 0.172721i
\(609\) −616.249 21.4941i −1.01190 0.0352941i
\(610\) −412.446 −0.676142
\(611\) −43.4790 75.3079i −0.0711604 0.123253i
\(612\) 132.587 + 76.5491i 0.216645 + 0.125080i
\(613\) 70.4822 122.079i 0.114979 0.199150i −0.802792 0.596259i \(-0.796653\pi\)
0.917771 + 0.397109i \(0.129987\pi\)
\(614\) 870.465 502.563i 1.41770 0.818507i
\(615\) 142.573i 0.231826i
\(616\) 8.83557 253.321i 0.0143435 0.411236i
\(617\) 61.9853 0.100462 0.0502312 0.998738i \(-0.484004\pi\)
0.0502312 + 0.998738i \(0.484004\pi\)
\(618\) 47.0148 + 81.4321i 0.0760758 + 0.131767i
\(619\) −549.456 317.228i −0.887651 0.512485i −0.0144774 0.999895i \(-0.504608\pi\)
−0.873173 + 0.487410i \(0.837942\pi\)
\(620\) −103.024 + 178.442i −0.166167 + 0.287810i
\(621\) −18.4879 + 10.6740i −0.0297711 + 0.0171884i
\(622\) 602.689i 0.968953i
\(623\) −270.286 + 432.588i −0.433845 + 0.694362i
\(624\) 741.138 1.18772
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −487.188 281.278i −0.778256 0.449326i
\(627\) 23.6846 41.0229i 0.0377745 0.0654273i
\(628\) 494.914 285.739i 0.788080 0.454998i
\(629\) 1149.29i 1.82717i
\(630\) −55.5676 104.497i −0.0882026 0.165868i
\(631\) 93.3216 0.147895 0.0739474 0.997262i \(-0.476440\pi\)
0.0739474 + 0.997262i \(0.476440\pi\)
\(632\) 60.1677 + 104.213i 0.0952020 + 0.164895i
\(633\) −427.976 247.092i −0.676107 0.390350i
\(634\) 360.439 624.298i 0.568515 0.984698i
\(635\) −371.015 + 214.206i −0.584276 + 0.337332i
\(636\) 18.1402i 0.0285223i
\(637\) 874.603 + 589.821i 1.37300 + 0.925935i
\(638\) 1117.86 1.75214
\(639\) −85.0463 147.305i −0.133093 0.230523i
\(640\) 235.483 + 135.956i 0.367942 + 0.212432i
\(641\) −153.961 + 266.668i −0.240188 + 0.416018i −0.960768 0.277354i \(-0.910543\pi\)
0.720579 + 0.693372i \(0.243876\pi\)
\(642\) 338.884 195.655i 0.527857 0.304759i
\(643\) 296.519i 0.461150i 0.973055 + 0.230575i \(0.0740607\pi\)
−0.973055 + 0.230575i \(0.925939\pi\)
\(644\) −59.7362 + 31.7655i −0.0927581 + 0.0493253i
\(645\) 68.3599 0.105984
\(646\) −85.7306 148.490i −0.132710 0.229860i
\(647\) 203.727 + 117.622i 0.314880 + 0.181796i 0.649108 0.760696i \(-0.275142\pi\)
−0.334228 + 0.942492i \(0.608476\pi\)
\(648\) 18.6852 32.3637i 0.0288352 0.0499440i
\(649\) 710.767 410.361i 1.09517 0.632298i
\(650\) 271.307i 0.417395i
\(651\) −402.748 251.641i −0.618660 0.386546i
\(652\) 31.1350 0.0477531
\(653\) −148.823 257.769i −0.227906 0.394746i 0.729281 0.684214i \(-0.239855\pi\)
−0.957187 + 0.289469i \(0.906521\pi\)
\(654\) −103.401 59.6987i −0.158106 0.0912823i
\(655\) −65.7542 + 113.890i −0.100388 + 0.173877i
\(656\) −633.643 + 365.834i −0.965919 + 0.557673i
\(657\) 224.488i 0.341687i
\(658\) −71.2200 2.48408i −0.108237 0.00377519i
\(659\) −127.740 −0.193839 −0.0969197 0.995292i \(-0.530899\pi\)
−0.0969197 + 0.995292i \(0.530899\pi\)
\(660\) 39.7290 + 68.8127i 0.0601955 + 0.104262i
\(661\) −823.610 475.512i −1.24601 0.719382i −0.275696 0.961245i \(-0.588908\pi\)
−0.970311 + 0.241863i \(0.922242\pi\)
\(662\) −679.286 + 1176.56i −1.02611 + 1.77728i
\(663\) −700.513 + 404.441i −1.05658 + 0.610017i
\(664\) 87.6611i 0.132020i
\(665\) −1.71106 + 49.0571i −0.00257302 + 0.0737701i
\(666\) −400.606 −0.601510
\(667\) 104.474 + 180.953i 0.156632 + 0.271295i
\(668\) −433.178 250.095i −0.648469 0.374394i
\(669\) 49.4481 85.6466i 0.0739134 0.128022i
\(670\) 490.677 283.292i 0.732353 0.422824i
\(671\) 638.206i 0.951126i
\(672\) 215.132 344.316i 0.320137 0.512374i
\(673\) −1003.39 −1.49092 −0.745460 0.666550i \(-0.767770\pi\)
−0.745460 + 0.666550i \(0.767770\pi\)
\(674\) −86.0076 148.970i −0.127608 0.221023i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) 346.392 599.968i 0.512414 0.887526i
\(677\) 408.603 235.907i 0.603550 0.348460i −0.166887 0.985976i \(-0.553371\pi\)
0.770437 + 0.637516i \(0.220038\pi\)
\(678\) 403.099i 0.594541i
\(679\) −242.543 456.111i −0.357206 0.671740i
\(680\) −201.409 −0.296190
\(681\) 158.185 + 273.984i 0.232283 + 0.402325i
\(682\) 745.589 + 430.466i 1.09324 + 0.631182i
\(683\) −208.614 + 361.330i −0.305438 + 0.529034i −0.977359 0.211589i \(-0.932136\pi\)
0.671921 + 0.740623i \(0.265470\pi\)
\(684\) 19.1679 11.0666i 0.0280233 0.0161792i
\(685\) 370.995i 0.541599i
\(686\) 789.722 351.726i 1.15120 0.512719i
\(687\) 29.0693 0.0423134
\(688\) 175.407 + 303.815i 0.254953 + 0.441591i
\(689\) −83.0019 47.9211i −0.120467 0.0695517i
\(690\) −20.0523 + 34.7316i −0.0290613 + 0.0503357i
\(691\) 160.907 92.8995i 0.232860 0.134442i −0.379030 0.925384i \(-0.623742\pi\)
0.611891 + 0.790942i \(0.290409\pi\)
\(692\) 585.285i 0.845787i
\(693\) −161.695 + 85.9835i −0.233326 + 0.124074i
\(694\) 962.538 1.38694
\(695\) 156.105 + 270.382i 0.224612 + 0.389039i
\(696\) −316.766 182.885i −0.455123 0.262765i
\(697\) 399.273 691.561i 0.572845 0.992197i
\(698\) 658.905 380.419i 0.943990 0.545013i
\(699\) 461.430i 0.660129i
\(700\) −69.8296 43.6303i −0.0997566 0.0623291i
\(701\) 1034.80 1.47618 0.738089 0.674704i \(-0.235729\pi\)
0.738089 + 0.674704i \(0.235729\pi\)
\(702\) −140.975 244.176i −0.200819 0.347829i
\(703\) 143.892 + 83.0759i 0.204682 + 0.118173i
\(704\) −21.3517 + 36.9822i −0.0303291 + 0.0525316i
\(705\) −13.5478 + 7.82185i −0.0192168 + 0.0110948i
\(706\) 322.729i 0.457123i
\(707\) 748.220 + 26.0971i 1.05830 + 0.0369125i
\(708\) 383.482 0.541641
\(709\) 108.321 + 187.618i 0.152780 + 0.264623i 0.932248 0.361819i \(-0.117844\pi\)
−0.779468 + 0.626442i \(0.784511\pi\)
\(710\) −276.729 159.769i −0.389759 0.225027i
\(711\) 43.4710 75.2940i 0.0611406 0.105899i
\(712\) −262.035 + 151.286i −0.368027 + 0.212481i
\(713\) 160.923i 0.225698i
\(714\) −23.1069 + 662.487i −0.0323625 + 0.927854i
\(715\) −419.811 −0.587148
\(716\) −65.0133 112.606i −0.0908007 0.157271i
\(717\) 59.5517 + 34.3822i 0.0830568 + 0.0479529i
\(718\) 660.636 1144.26i 0.920106 1.59367i
\(719\) 0.325449 0.187898i 0.000452641 0.000261332i −0.499774 0.866156i \(-0.666583\pi\)
0.500226 + 0.865895i \(0.333250\pi\)
\(720\) 133.330i 0.185181i
\(721\) −79.8930 + 127.867i −0.110809 + 0.177347i
\(722\) 885.086 1.22588
\(723\) −72.1896 125.036i −0.0998473 0.172941i
\(724\) −95.5530 55.1675i −0.131979 0.0761983i
\(725\) −127.146 + 220.223i −0.175373 + 0.303756i
\(726\) −169.936 + 98.1128i −0.234072 + 0.135142i
\(727\) 174.857i 0.240518i −0.992743 0.120259i \(-0.961627\pi\)
0.992743 0.120259i \(-0.0383726\pi\)
\(728\) 293.794 + 552.490i 0.403563 + 0.758915i
\(729\) −27.0000 −0.0370370
\(730\) 210.864 + 365.227i 0.288854 + 0.500310i
\(731\) −331.585 191.441i −0.453605 0.261889i
\(732\) −149.100 + 258.249i −0.203689 + 0.352800i
\(733\) −738.210 + 426.206i −1.00711 + 0.581454i −0.910344 0.413853i \(-0.864183\pi\)
−0.0967645 + 0.995307i \(0.530849\pi\)
\(734\) 89.6973i 0.122203i
\(735\) 106.108 157.340i 0.144365 0.214069i
\(736\) −137.575 −0.186923
\(737\) −438.357 759.256i −0.594785 1.03020i
\(738\) 241.056 + 139.174i 0.326634 + 0.188582i
\(739\) 584.126 1011.74i 0.790428 1.36906i −0.135275 0.990808i \(-0.543192\pi\)
0.925702 0.378253i \(-0.123475\pi\)
\(740\) −241.367 + 139.353i −0.326171 + 0.188315i
\(741\) 116.939i 0.157813i
\(742\) −69.3488 + 36.8771i −0.0934619 + 0.0496996i
\(743\) −558.877 −0.752190 −0.376095 0.926581i \(-0.622733\pi\)
−0.376095 + 0.926581i \(0.622733\pi\)
\(744\) −140.850 243.960i −0.189315 0.327903i
\(745\) −27.7639 16.0295i −0.0372670 0.0215161i
\(746\) 336.592 582.995i 0.451196 0.781494i
\(747\) −54.8497 + 31.6675i −0.0734266 + 0.0423929i
\(748\) 445.042i 0.594976i
\(749\) 532.128 + 332.479i 0.710451 + 0.443898i
\(750\) −48.8079 −0.0650772
\(751\) −630.654 1092.32i −0.839752 1.45449i −0.890102 0.455762i \(-0.849367\pi\)
0.0503493 0.998732i \(-0.483967\pi\)
\(752\) −69.5260 40.1408i −0.0924547 0.0533788i
\(753\) −96.5304 + 167.196i −0.128194 + 0.222039i
\(754\) −2389.92 + 1379.82i −3.16965 + 1.83000i
\(755\) 474.883i 0.628985i
\(756\) −85.5177 2.98276i −0.113119 0.00394546i
\(757\) −1269.13 −1.67652 −0.838262 0.545268i \(-0.816428\pi\)
−0.838262 + 0.545268i \(0.816428\pi\)
\(758\) 158.392 + 274.343i 0.208960 + 0.361930i
\(759\) 53.7425 + 31.0282i 0.0708070 + 0.0408804i
\(760\) −14.5587 + 25.2164i −0.0191562 + 0.0331795i
\(761\) −157.718 + 91.0585i −0.207251 + 0.119656i −0.600033 0.799975i \(-0.704846\pi\)
0.392782 + 0.919632i \(0.371513\pi\)
\(762\) 836.394i 1.09763i
\(763\) 6.67355 191.335i 0.00874646 0.250766i
\(764\) −47.3152 −0.0619309
\(765\) 72.7587 + 126.022i 0.0951094 + 0.164734i
\(766\) 778.195 + 449.291i 1.01592 + 0.586542i
\(767\) −1013.05 + 1754.65i −1.32079 + 2.28768i
\(768\) 489.118 282.392i 0.636872 0.367698i
\(769\) 810.237i 1.05362i −0.849982 0.526812i \(-0.823387\pi\)
0.849982 0.526812i \(-0.176613\pi\)
\(770\) −182.301 + 291.771i −0.236755 + 0.378923i
\(771\) 386.087 0.500761
\(772\) −33.7630 58.4793i −0.0437345 0.0757504i
\(773\) 212.492 + 122.682i 0.274893 + 0.158709i 0.631109 0.775694i \(-0.282600\pi\)
−0.356216 + 0.934404i \(0.615933\pi\)
\(774\) 66.7300 115.580i 0.0862144 0.149328i
\(775\) −169.607 + 97.9225i −0.218847 + 0.126352i
\(776\)