Properties

Label 105.3.n.a.61.1
Level 105
Weight 3
Character 105.61
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 61.1
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 \(\chi\) \(=\) 105.61
Dual form 105.3.n.a.31.1

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.357423 + 0.933943i \(0.383656\pi\)
−0.987529 + 0.157434i \(0.949678\pi\)
\(3\) −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 0.993278 0.115750i \(-0.0369273\pi\)
−0.596882 + 0.802329i \(0.703594\pi\)
\(12\) 3.52883 + 2.03737i 0.294069 + 0.169781i
\(13\) 21.5286i 1.65605i −0.560693 0.828024i \(-0.689465\pi\)
0.560693 0.828024i \(-0.310535\pi\)
\(14\) 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 −0.937548 0.347855i \(-0.886910\pi\)
−0.167523 + 0.985868i \(0.553577\pi\)
\(18\) 3.78064 + 6.54826i 0.210036 + 0.363792i
\(19\) −2.71590 1.56803i −0.142942 0.0825276i 0.426823 0.904335i \(-0.359633\pi\)
−0.569765 + 0.821807i \(0.692966\pi\)
\(20\) 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 −0.907221 0.420654i \(-0.861801\pi\)
0.817908 + 0.575349i \(0.195134\pi\)
\(24\) 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 −0.934701 0.355434i \(-0.884333\pi\)
−0.159536 + 0.987192i \(0.551000\pi\)
\(32\) 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 0.246625 + 0.969111i \(0.420678\pi\)
−0.962587 + 0.270972i \(0.912655\pi\)
\(38\) 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 \(-0.851806\pi\)
0.893568 0.448929i \(-0.148194\pi\)
\(42\) −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 0.462325 0.886711i \(-0.347015\pi\)
−0.536751 + 0.843740i \(0.680349\pi\)
\(48\) 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 0.844262 0.535931i \(-0.180039\pi\)
−0.886261 + 0.463187i \(0.846706\pi\)
\(54\) −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 0.389084 0.921202i \(-0.372792\pi\)
0.992327 + 0.123644i \(0.0394582\pi\)
\(60\) −4.55570 7.89071i −0.0759284 0.131512i
\(61\) −63.3781 36.5913i −1.03898 0.599858i −0.119439 0.992842i \(-0.538110\pi\)
−0.919546 + 0.392984i \(0.871443\pi\)
\(62\) 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 0.947706 + 0.319145i \(0.103396\pi\)
−0.197465 + 0.980310i \(0.563271\pi\)
\(68\) 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 0.0145299 0.999894i \(-0.495375\pi\)
0.873199 + 0.487364i \(0.162041\pi\)
\(74\) −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 −0.943044 0.332669i \(-0.892051\pi\)
0.759622 + 0.650365i \(0.225384\pi\)
\(80\) −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 \(-0.959408\pi\)
0.991880 0.127179i \(-0.0405921\pi\)
\(84\) −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 0.810714 0.585442i \(-0.199079\pi\)
−0.101651 + 0.994820i \(0.532412\pi\)
\(90\) 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 \(-0.875785\pi\)
0.924820 0.380405i \(-0.124215\pi\)
\(98\) −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 −0.882701 0.469936i \(-0.844277\pi\)
−0.0343741 + 0.999409i \(0.510944\pi\)
\(102\) 47.3493 + 82.0114i 0.464209 + 0.804033i
\(103\) 18.6535 + 10.7696i 0.181102 + 0.104559i 0.587810 0.808999i \(-0.299990\pi\)
−0.406708 + 0.913558i \(0.633323\pi\)
\(104\) 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 −0.995825 0.0912785i \(-0.970905\pi\)
0.576962 + 0.816771i \(0.304238\pi\)
\(108\) 10.5865 6.11212i 0.0980232 0.0565937i
\(109\) −13.6751 23.6859i −0.125459 0.217302i 0.796453 0.604700i \(-0.206707\pi\)
−0.921912 + 0.387398i \(0.873374\pi\)
\(110\) 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 0.681641 0.731687i \(-0.261267\pi\)
−0.292839 + 0.956162i \(0.594600\pi\)
\(132\) 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 −0.991968 0.126488i \(-0.959629\pi\)
0.386442 0.922314i \(-0.373704\pi\)
\(138\) 15.5324 + 8.96766i 0.112554 + 0.0649831i
\(139\) 139.625i 1.00449i 0.864724 + 0.502247i \(0.167493\pi\)
−0.864724 + 0.502247i \(0.832507\pi\)
\(140\) 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 −0.840967 0.541087i \(-0.818013\pi\)
0.889078 + 0.457755i \(0.151346\pi\)
\(150\) 18.9032 10.9138i 0.126021 0.0727585i
\(151\) −106.187 183.922i −0.703226 1.21802i −0.967328 0.253529i \(-0.918409\pi\)
0.264102 0.964495i \(-0.414925\pi\)
\(152\) 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 −0.986801 0.161941i \(-0.948225\pi\)
−0.353156 + 0.935565i \(0.614891\pi\)
\(158\) −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 −0.885610 0.464430i \(-0.846259\pi\)
0.845013 + 0.534746i \(0.179593\pi\)
\(164\) −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 \(-0.780351\pi\)
0.771216 0.636574i \(-0.219649\pi\)
\(168\) −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 −0.275219 0.961382i \(-0.588750\pi\)
−0.970190 + 0.242345i \(0.922084\pi\)
\(174\) 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 0.778449 0.627708i \(-0.216007\pi\)
−0.932835 + 0.360303i \(0.882673\pi\)
\(180\) 13.6671 + 7.89071i 0.0759284 + 0.0438373i
\(181\) 46.9001i 0.259117i −0.991572 0.129558i \(-0.958644\pi\)
0.991572 0.129558i \(-0.0413559\pi\)
\(182\) −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 −0.838499 0.544903i \(-0.816567\pi\)
0.891149 + 0.453710i \(0.149900\pi\)
\(192\) 7.34516 4.24073i 0.0382560 0.0220871i
\(193\) −14.3516 24.8578i −0.0743609 0.128797i 0.826447 0.563014i \(-0.190358\pi\)
−0.900808 + 0.434217i \(0.857025\pi\)
\(194\) 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 −0.992649 0.121030i \(-0.961380\pi\)
−0.391509 + 0.920174i \(0.628047\pi\)
\(200\) −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 \(-0.959137\pi\)
0.991771 0.128022i \(-0.0408627\pi\)
\(224\) −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 −0.806172 0.591681i \(-0.798465\pi\)
0.109324 + 0.994006i \(0.465131\pi\)
\(228\) −6.38930 11.0666i −0.0280233 0.0485377i
\(229\) −14.5347 8.39159i −0.0634702 0.0366445i 0.467929 0.883766i \(-0.345000\pi\)
−0.531399 + 0.847121i \(0.678334\pi\)
\(230\) 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 −0.424704 0.905332i \(-0.639622\pi\)
0.996393 0.0848612i \(-0.0270447\pi\)
\(234\) 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 −0.342695 0.939447i \(-0.611340\pi\)
0.642237 + 0.766506i \(0.278006\pi\)
\(242\) 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 \(0.0712713\pi\)
−0.975038 + 0.222039i \(0.928729\pi\)
\(252\) 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 0.0749649 0.997186i \(-0.476116\pi\)
−0.826106 + 0.563515i \(0.809449\pi\)
\(258\) 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 0.912279 + 0.409569i \(0.134321\pi\)
−0.101442 + 0.994841i \(0.532346\pi\)
\(264\) 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 −0.592698 0.805425i \(-0.701937\pi\)
0.401170 + 0.916004i \(0.368604\pi\)
\(270\) 14.6424 + 25.3613i 0.0542310 + 0.0939308i
\(271\) −47.1819 27.2405i −0.174103 0.100518i 0.410416 0.911898i \(-0.365383\pi\)
−0.584519 + 0.811380i \(0.698717\pi\)
\(272\) 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 0.878791 + 0.477207i \(0.158351\pi\)
−0.0261222 + 0.999659i \(0.508316\pi\)
\(278\) −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 −0.990766 0.135580i \(-0.956710\pi\)
−0.377967 + 0.925819i \(0.623377\pi\)
\(284\) 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 \(0.329792\pi\)
−0.509604 + 0.860409i \(0.670208\pi\)
\(294\) 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 \(-0.774979\pi\)
0.760363 0.649499i \(-0.225021\pi\)
\(308\) −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 −0.794510 0.607252i \(-0.792272\pi\)
0.128640 + 0.991691i \(0.458939\pi\)
\(312\) −77.4162 134.089i −0.248129 0.429772i
\(313\) 193.296 + 111.599i 0.617559 + 0.356548i 0.775918 0.630834i \(-0.217287\pi\)
−0.158359 + 0.987382i \(0.550620\pi\)
\(314\) 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 −0.547330 0.836917i \(-0.684356\pi\)
0.998456 + 0.0555434i \(0.0176891\pi\)
\(318\) −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 0.0956391 + 0.995416i \(0.469511\pi\)
−0.909875 + 0.414882i \(0.863823\pi\)
\(332\) −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 −0.998254 0.0590672i \(-0.981187\pi\)
0.447973 0.894047i \(-0.352146\pi\)
\(348\) −179.470 103.617i −0.515720 0.297751i
\(349\) 301.869i 0.864953i −0.901645 0.432477i \(-0.857640\pi\)
0.901645 0.432477i \(-0.142360\pi\)
\(350\) 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 −0.334639 0.942346i \(-0.608614\pi\)
0.648776 + 0.760979i \(0.275281\pi\)
\(354\) −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 −0.226713 0.973962i \(-0.572798\pi\)
0.956832 0.290642i \(-0.0938688\pi\)
\(360\) 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 −0.457423 0.889249i \(-0.651227\pi\)
0.541401 + 0.840764i \(0.317894\pi\)
\(368\) 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 −0.629601 0.776919i \(-0.716781\pi\)
0.987632 + 0.156791i \(0.0501148\pi\)
\(374\) 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 0.0394677 0.999221i \(-0.487434\pi\)
−0.845617 + 0.533790i \(0.820767\pi\)
\(384\) 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 −0.996141 0.0877654i \(-0.972027\pi\)
0.422064 0.906566i \(-0.361306\pi\)
\(390\) 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 0.984149 0.177342i \(-0.0567499\pi\)
0.338492 + 0.940969i \(0.390083\pi\)
\(398\) 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 0.0929080 0.995675i \(-0.470384\pi\)
0.815826 0.578298i \(-0.196283\pi\)
\(402\) 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 −0.942324 0.334702i \(-0.891364\pi\)
−0.181301 + 0.983428i \(0.558031\pi\)
\(410\) −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 \(0.109506\pi\)
−0.941406 + 0.337276i \(0.890494\pi\)
\(420\) 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 0.930427 0.366476i \(-0.119436\pi\)
−0.782591 + 0.622536i \(0.786103\pi\)
\(432\) 89.4407 + 51.6386i 0.207039 + 0.119534i
\(433\) 433.284i 1.00066i −0.865836 0.500328i \(-0.833213\pi\)
0.865836 0.500328i \(-0.166787\pi\)
\(434\) −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 0.436335 0.899784i \(-0.356276\pi\)
−0.561068 + 0.827770i \(0.689609\pi\)
\(440\) 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 −0.999982 0.00601155i \(-0.998086\pi\)
0.505197 + 0.863004i \(0.331420\pi\)
\(444\) −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 −0.703379 0.710815i \(-0.748326\pi\)
0.967273 + 0.253737i \(0.0816597\pi\)
\(458\) 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 \(-0.878524\pi\)
0.928059 0.372432i \(-0.121476\pi\)
\(462\) −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 0.131946 0.991257i \(-0.457878\pi\)
−0.792481 + 0.609897i \(0.791211\pi\)
\(468\) 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 −0.122510 0.992467i \(-0.539094\pi\)
0.798247 + 0.602330i \(0.205761\pi\)
\(480\) 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 −0.920710 0.390247i \(-0.872390\pi\)
0.122391 0.992482i \(-0.460944\pi\)
\(488\) 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 0.349310 + 0.937007i \(0.386416\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(500\) −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 \(0.00337179\pi\)
−0.999944 + 0.0105926i \(0.996628\pi\)
\(504\) 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 0.992999 0.118126i \(-0.0376885\pi\)
0.394200 + 0.919025i \(0.371022\pi\)
\(510\) 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 −0.820945 0.571007i \(-0.806553\pi\)
0.0840344 + 0.996463i \(0.473219\pi\)
\(522\) −192.277 333.034i −0.368347 0.637995i
\(523\) −549.148 317.051i −1.05000 0.606216i −0.127348 0.991858i \(-0.540646\pi\)
−0.922648 + 0.385642i \(0.873980\pi\)
\(524\) 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 −0.773665 0.633594i \(-0.781579\pi\)
0.935542 + 0.353217i \(0.114912\pi\)
\(542\) 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 0.975249 + 0.221108i \(0.0709673\pi\)
−0.296140 + 0.955145i \(0.595699\pi\)
\(558\) −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 −0.843958 0.536409i \(-0.819781\pi\)
0.0425646 + 0.999094i \(0.486447\pi\)
\(564\) −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 −0.774313 0.632803i \(-0.781904\pi\)
0.935180 + 0.354173i \(0.115238\pi\)
\(570\) 26.5115 15.3064i 0.0465113 0.0268533i
\(571\) −498.800 863.947i −0.873555 1.51304i −0.858294 0.513159i \(-0.828475\pi\)
−0.0152618 0.999884i \(-0.504858\pi\)
\(572\) −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 −0.238217 0.971212i \(-0.576563\pi\)
0.721986 + 0.691908i \(0.243230\pi\)
\(578\) 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 \(0.112514\pi\)
−0.938176 + 0.346159i \(0.887486\pi\)
\(588\) 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 0.754233 0.656607i \(-0.228009\pi\)
−0.191522 + 0.981488i \(0.561342\pi\)
\(594\) 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 0.948605 + 0.316463i \(0.102495\pi\)
−0.200238 + 0.979747i \(0.564171\pi\)
\(600\) 31.1420 + 17.9798i 0.0519033 + 0.0299664i
\(601\) 599.296i 0.997166i 0.866842 + 0.498583i \(0.166146\pi\)
−0.866842 + 0.498583i \(0.833854\pi\)
\(602\) 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 0.105253 0.994445i \(-0.466435\pi\)
−0.808589 + 0.588374i \(0.799768\pi\)
\(608\) 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 0.917771 0.397109i \(-0.129987\pi\)
−0.802792 + 0.596259i \(0.796653\pi\)
\(614\) 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 −0.873173 0.487410i \(-0.837942\pi\)
−0.0144774 + 0.999895i \(0.504608\pi\)
\(620\) −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 0.720579 0.693372i \(-0.243876\pi\)
−0.960768 + 0.277354i \(0.910543\pi\)
\(642\) 338.884 + 195.655i 0.527857 + 0.304759i
\(643\) 296.519i 0.461150i −0.973055 0.230575i \(-0.925939\pi\)
0.973055 0.230575i \(-0.0740607\pi\)
\(644\) −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 −0.334228 0.942492i \(-0.608476\pi\)
0.649108 + 0.760696i \(0.275142\pi\)
\(648\) 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 −0.957187 0.289469i \(-0.906521\pi\)
0.729281 + 0.684214i \(0.239855\pi\)
\(654\) −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 −0.970311 0.241863i \(-0.922242\pi\)
−0.275696 + 0.961245i \(0.588908\pi\)
\(662\) −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 0.770437 0.637516i \(-0.220038\pi\)
−0.166887 + 0.985976i \(0.553371\pi\)
\(678\) 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 0.671921 0.740623i \(-0.265470\pi\)
−0.977359 + 0.211589i \(0.932136\pi\)
\(684\) 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 0.611891 0.790942i \(-0.290409\pi\)
−0.379030 + 0.925384i \(0.623742\pi\)
\(692\) 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 −0.779468 0.626442i \(-0.784511\pi\)
0.932248 + 0.361819i \(0.117844\pi\)
\(710\) −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 0.500226 0.865895i \(-0.333250\pi\)
−0.499774 + 0.866156i \(0.666583\pi\)
\(720\) 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 \(0.0383726\pi\)
−0.992743 + 0.120259i \(0.961627\pi\)
\(728\) 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 −0.0967645 0.995307i \(-0.530849\pi\)
−0.910344 + 0.413853i \(0.864183\pi\)
\(734\) 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 0.925702 + 0.378253i \(0.123475\pi\)
−0.135275 + 0.990808i \(0.543192\pi\)
\(740\) −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 0.0503493 + 0.998732i \(0.483967\pi\)
−0.890102 + 0.455762i \(0.849367\pi\)
\(752\) −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 0.392782 0.919632i \(-0.371513\pi\)
−0.600033 + 0.799975i \(0.704846\pi\)
\(762\) 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 \(0.176613\pi\)
−0.849982 + 0.526812i \(0.823387\pi\)
\(770\) −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 −0.356216 0.934404i \(-0.615933\pi\)
0.631109 + 0.775694i \(0.282600\pi\)
\(774\) 66.7300 + 115.580i 0.0862144 + 0.149328i
\(775\) −169.607 97.9225i −0.218847 0.126352i
\(776\)