Properties

Label 210.3.o.b.61.1
Level 210
Weight 3
Character 210.61
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.1
Root \(-3.67087 + 6.35814i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.b.31.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-2.59373 + 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-2.59373 + 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(-5.13478 - 8.89370i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.02340i q^{13} +(-6.12892 - 7.77408i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(27.4947 - 15.8741i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-26.9408 - 15.5543i) q^{19} +4.47214i q^{20} +(-1.74007 - 11.9988i) q^{21} +14.5234 q^{22} +(11.8441 - 20.5146i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(8.60187 + 4.96629i) q^{26} +5.19615i q^{27} +(13.8551 - 2.00927i) q^{28} +9.19673 q^{29} +(-2.73861 + 4.74342i) q^{30} +(17.4511 - 10.0754i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(15.4043 + 8.89370i) q^{33} +44.8986i q^{34} +(12.2919 - 9.69068i) q^{35} -6.00000 q^{36} +(-24.0823 + 41.7118i) q^{37} +(38.1001 - 21.9971i) q^{38} +(6.08244 + 10.5351i) q^{39} +(-5.47723 - 3.16228i) q^{40} -65.1226i q^{41} +(15.9259 + 6.35331i) q^{42} -3.03497 q^{43} +(-10.2696 + 17.7874i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(16.7501 + 29.0120i) q^{46} +(-53.6472 - 30.9732i) q^{47} -6.92820i q^{48} +(-35.5451 - 33.7275i) q^{49} -7.07107 q^{50} +(-27.4947 + 47.6222i) q^{51} +(-12.1649 + 7.02340i) q^{52} +(-0.690751 - 1.19642i) q^{53} +(-6.36396 - 3.67423i) q^{54} +22.9634i q^{55} +(-7.33617 + 18.3897i) q^{56} +53.8817 q^{57} +(-6.50307 + 11.2636i) q^{58} +(-95.1064 + 54.9097i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(-34.3741 - 19.8459i) q^{61} +28.4976i q^{62} +(13.0014 + 16.4913i) q^{63} +8.00000 q^{64} +(-7.85240 + 13.6008i) q^{65} +(-21.7850 + 12.5776i) q^{66} +(-7.95952 - 13.7863i) q^{67} +(-54.9893 - 31.7481i) q^{68} +41.0292i q^{69} +(3.17693 + 21.9068i) q^{70} +53.3489 q^{71} +(4.24264 - 7.34847i) q^{72} +(62.6830 - 36.1901i) q^{73} +(-34.0576 - 58.9894i) q^{74} +(-7.50000 - 4.33013i) q^{75} +62.2172i q^{76} +(71.1427 - 10.3171i) q^{77} -17.2037 q^{78} +(-53.2229 + 92.1847i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(79.7586 + 46.0486i) q^{82} +49.4298i q^{83} +(-19.0425 + 15.0127i) q^{84} -70.9909 q^{85} +(2.14605 - 3.71707i) q^{86} +(-13.7951 + 7.96460i) q^{87} +(-14.5234 - 25.1552i) q^{88} +(-142.807 - 82.4499i) q^{89} -9.48683i q^{90} +(45.6643 + 18.2168i) q^{91} -47.3765 q^{92} +(-17.4511 + 30.2262i) q^{93} +(75.8686 - 43.8027i) q^{94} +(34.7805 + 60.2416i) q^{95} +(8.48528 + 4.89898i) q^{96} +49.4799i q^{97} +(66.4418 - 19.6848i) q^{98} -30.8087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 1.22474i −0.353553 + 0.612372i
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −1.93649 1.11803i −0.387298 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) −2.59373 + 6.50174i −0.370533 + 0.928819i
\(8\) 2.82843 0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 2.73861 1.58114i 0.273861 0.158114i
\(11\) −5.13478 8.89370i −0.466798 0.808518i 0.532482 0.846441i \(-0.321259\pi\)
−0.999281 + 0.0379228i \(0.987926\pi\)
\(12\) 3.00000 + 1.73205i 0.250000 + 0.144338i
\(13\) 7.02340i 0.540261i −0.962824 0.270131i \(-0.912933\pi\)
0.962824 0.270131i \(-0.0870669\pi\)
\(14\) −6.12892 7.77408i −0.437780 0.555291i
\(15\) 3.87298 0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 27.4947 15.8741i 1.61733 0.933768i 0.629727 0.776816i \(-0.283167\pi\)
0.987606 0.156951i \(-0.0501666\pi\)
\(18\) 2.12132 + 3.67423i 0.117851 + 0.204124i
\(19\) −26.9408 15.5543i −1.41794 0.818648i −0.421822 0.906679i \(-0.638609\pi\)
−0.996118 + 0.0880311i \(0.971943\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −1.74007 11.9988i −0.0828607 0.571373i
\(22\) 14.5234 0.660152
\(23\) 11.8441 20.5146i 0.514962 0.891940i −0.484888 0.874576i \(-0.661140\pi\)
0.999849 0.0173632i \(-0.00552716\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 8.60187 + 4.96629i 0.330841 + 0.191011i
\(27\) 5.19615i 0.192450i
\(28\) 13.8551 2.00927i 0.494824 0.0717595i
\(29\) 9.19673 0.317129 0.158564 0.987349i \(-0.449313\pi\)
0.158564 + 0.987349i \(0.449313\pi\)
\(30\) −2.73861 + 4.74342i −0.0912871 + 0.158114i
\(31\) 17.4511 10.0754i 0.562940 0.325013i −0.191385 0.981515i \(-0.561298\pi\)
0.754325 + 0.656502i \(0.227965\pi\)
\(32\) −2.82843 4.89898i −0.0883883 0.153093i
\(33\) 15.4043 + 8.89370i 0.466798 + 0.269506i
\(34\) 44.8986i 1.32055i
\(35\) 12.2919 9.69068i 0.351197 0.276877i
\(36\) −6.00000 −0.166667
\(37\) −24.0823 + 41.7118i −0.650874 + 1.12735i 0.332037 + 0.943266i \(0.392264\pi\)
−0.982911 + 0.184081i \(0.941069\pi\)
\(38\) 38.1001 21.9971i 1.00263 0.578871i
\(39\) 6.08244 + 10.5351i 0.155960 + 0.270131i
\(40\) −5.47723 3.16228i −0.136931 0.0790569i
\(41\) 65.1226i 1.58836i −0.607685 0.794178i \(-0.707902\pi\)
0.607685 0.794178i \(-0.292098\pi\)
\(42\) 15.9259 + 6.35331i 0.379189 + 0.151269i
\(43\) −3.03497 −0.0705807 −0.0352904 0.999377i \(-0.511236\pi\)
−0.0352904 + 0.999377i \(0.511236\pi\)
\(44\) −10.2696 + 17.7874i −0.233399 + 0.404259i
\(45\) −5.80948 + 3.35410i −0.129099 + 0.0745356i
\(46\) 16.7501 + 29.0120i 0.364133 + 0.630697i
\(47\) −53.6472 30.9732i −1.14143 0.659005i −0.194645 0.980874i \(-0.562356\pi\)
−0.946784 + 0.321869i \(0.895689\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −35.5451 33.7275i −0.725411 0.688316i
\(50\) −7.07107 −0.141421
\(51\) −27.4947 + 47.6222i −0.539111 + 0.933768i
\(52\) −12.1649 + 7.02340i −0.233940 + 0.135065i
\(53\) −0.690751 1.19642i −0.0130330 0.0225739i 0.859435 0.511244i \(-0.170815\pi\)
−0.872468 + 0.488671i \(0.837482\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 22.9634i 0.417517i
\(56\) −7.33617 + 18.3897i −0.131003 + 0.328387i
\(57\) 53.8817 0.945293
\(58\) −6.50307 + 11.2636i −0.112122 + 0.194201i
\(59\) −95.1064 + 54.9097i −1.61197 + 0.930673i −0.623061 + 0.782173i \(0.714111\pi\)
−0.988912 + 0.148500i \(0.952555\pi\)
\(60\) −3.87298 6.70820i −0.0645497 0.111803i
\(61\) −34.3741 19.8459i −0.563510 0.325343i 0.191043 0.981582i \(-0.438813\pi\)
−0.754553 + 0.656239i \(0.772146\pi\)
\(62\) 28.4976i 0.459638i
\(63\) 13.0014 + 16.4913i 0.206372 + 0.261767i
\(64\) 8.00000 0.125000
\(65\) −7.85240 + 13.6008i −0.120806 + 0.209242i
\(66\) −21.7850 + 12.5776i −0.330076 + 0.190570i
\(67\) −7.95952 13.7863i −0.118799 0.205765i 0.800493 0.599342i \(-0.204571\pi\)
−0.919292 + 0.393576i \(0.871238\pi\)
\(68\) −54.9893 31.7481i −0.808667 0.466884i
\(69\) 41.0292i 0.594626i
\(70\) 3.17693 + 21.9068i 0.0453847 + 0.312954i
\(71\) 53.3489 0.751393 0.375696 0.926743i \(-0.377404\pi\)
0.375696 + 0.926743i \(0.377404\pi\)
\(72\) 4.24264 7.34847i 0.0589256 0.102062i
\(73\) 62.6830 36.1901i 0.858672 0.495754i −0.00489557 0.999988i \(-0.501558\pi\)
0.863567 + 0.504234i \(0.168225\pi\)
\(74\) −34.0576 58.9894i −0.460237 0.797155i
\(75\) −7.50000 4.33013i −0.100000 0.0577350i
\(76\) 62.2172i 0.818648i
\(77\) 71.1427 10.3171i 0.923931 0.133989i
\(78\) −17.2037 −0.220561
\(79\) −53.2229 + 92.1847i −0.673707 + 1.16690i 0.303138 + 0.952947i \(0.401966\pi\)
−0.976845 + 0.213948i \(0.931368\pi\)
\(80\) 7.74597 4.47214i 0.0968246 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 79.7586 + 46.0486i 0.972666 + 0.561569i
\(83\) 49.4298i 0.595540i 0.954638 + 0.297770i \(0.0962429\pi\)
−0.954638 + 0.297770i \(0.903757\pi\)
\(84\) −19.0425 + 15.0127i −0.226697 + 0.178723i
\(85\) −70.9909 −0.835187
\(86\) 2.14605 3.71707i 0.0249541 0.0432217i
\(87\) −13.7951 + 7.96460i −0.158564 + 0.0915472i
\(88\) −14.5234 25.1552i −0.165038 0.285854i
\(89\) −142.807 82.4499i −1.60458 0.926403i −0.990555 0.137114i \(-0.956217\pi\)
−0.614022 0.789289i \(-0.710449\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 45.6643 + 18.2168i 0.501805 + 0.200185i
\(92\) −47.3765 −0.514962
\(93\) −17.4511 + 30.2262i −0.187647 + 0.325013i
\(94\) 75.8686 43.8027i 0.807113 0.465987i
\(95\) 34.7805 + 60.2416i 0.366110 + 0.634122i
\(96\) 8.48528 + 4.89898i 0.0883883 + 0.0510310i
\(97\) 49.4799i 0.510102i 0.966928 + 0.255051i \(0.0820922\pi\)
−0.966928 + 0.255051i \(0.917908\pi\)
\(98\) 66.4418 19.6848i 0.677977 0.200865i
\(99\) −30.8087 −0.311199
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) 116.803 67.4364i 1.15647 0.667687i 0.206012 0.978549i \(-0.433951\pi\)
0.950455 + 0.310863i \(0.100618\pi\)
\(102\) −38.8833 67.3479i −0.381209 0.660274i
\(103\) −32.3911 18.7010i −0.314477 0.181563i 0.334451 0.942413i \(-0.391449\pi\)
−0.648928 + 0.760850i \(0.724782\pi\)
\(104\) 19.8652i 0.191011i
\(105\) −10.0455 + 25.1811i −0.0956711 + 0.239820i
\(106\) 1.95374 0.0184315
\(107\) 12.3980 21.4739i 0.115869 0.200691i −0.802258 0.596978i \(-0.796368\pi\)
0.918127 + 0.396287i \(0.129701\pi\)
\(108\) 9.00000 5.19615i 0.0833333 0.0481125i
\(109\) 28.1448 + 48.7483i 0.258209 + 0.447232i 0.965762 0.259429i \(-0.0835342\pi\)
−0.707553 + 0.706660i \(0.750201\pi\)
\(110\) −28.1243 16.2376i −0.255676 0.147615i
\(111\) 83.4237i 0.751565i
\(112\) −17.3352 21.9884i −0.154779 0.196325i
\(113\) 74.9910 0.663637 0.331818 0.943343i \(-0.392338\pi\)
0.331818 + 0.943343i \(0.392338\pi\)
\(114\) −38.1001 + 65.9913i −0.334212 + 0.578871i
\(115\) −45.8721 + 26.4843i −0.398888 + 0.230298i
\(116\) −9.19673 15.9292i −0.0792822 0.137321i
\(117\) −18.2473 10.5351i −0.155960 0.0900436i
\(118\) 155.308i 1.31617i
\(119\) 31.8952 + 219.936i 0.268027 + 1.84820i
\(120\) 10.9545 0.0912871
\(121\) 7.76807 13.4547i 0.0641989 0.111196i
\(122\) 48.6124 28.0664i 0.398462 0.230052i
\(123\) 56.3978 + 97.6839i 0.458519 + 0.794178i
\(124\) −34.9023 20.1508i −0.281470 0.162507i
\(125\) 11.1803i 0.0894427i
\(126\) −29.3910 + 4.26229i −0.233262 + 0.0338277i
\(127\) 128.504 1.01184 0.505921 0.862580i \(-0.331153\pi\)
0.505921 + 0.862580i \(0.331153\pi\)
\(128\) −5.65685 + 9.79796i −0.0441942 + 0.0765466i
\(129\) 4.55246 2.62836i 0.0352904 0.0203749i
\(130\) −11.1050 19.2344i −0.0854228 0.147957i
\(131\) 65.3818 + 37.7482i 0.499098 + 0.288154i 0.728341 0.685215i \(-0.240292\pi\)
−0.229243 + 0.973369i \(0.573625\pi\)
\(132\) 35.5748i 0.269506i
\(133\) 171.007 134.819i 1.28577 1.01367i
\(134\) 22.5129 0.168007
\(135\) 5.80948 10.0623i 0.0430331 0.0745356i
\(136\) 77.7667 44.8986i 0.571814 0.330137i
\(137\) −53.7583 93.1121i −0.392396 0.679650i 0.600369 0.799723i \(-0.295020\pi\)
−0.992765 + 0.120073i \(0.961687\pi\)
\(138\) −50.2503 29.0120i −0.364133 0.210232i
\(139\) 272.004i 1.95686i −0.206576 0.978431i \(-0.566232\pi\)
0.206576 0.978431i \(-0.433768\pi\)
\(140\) −29.0766 11.5995i −0.207690 0.0828536i
\(141\) 107.294 0.760953
\(142\) −37.7234 + 65.3388i −0.265658 + 0.460132i
\(143\) −62.4640 + 36.0636i −0.436811 + 0.252193i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) −17.8094 10.2823i −0.122823 0.0709121i
\(146\) 102.361i 0.701102i
\(147\) 82.5266 + 19.8082i 0.561405 + 0.134750i
\(148\) 96.3294 0.650874
\(149\) 41.7135 72.2498i 0.279956 0.484898i −0.691417 0.722456i \(-0.743013\pi\)
0.971374 + 0.237557i \(0.0763467\pi\)
\(150\) 10.6066 6.12372i 0.0707107 0.0408248i
\(151\) −63.3973 109.807i −0.419850 0.727201i 0.576074 0.817397i \(-0.304584\pi\)
−0.995924 + 0.0901962i \(0.971251\pi\)
\(152\) −76.2002 43.9942i −0.501317 0.289436i
\(153\) 95.2443i 0.622512i
\(154\) −37.6696 + 94.4270i −0.244608 + 0.613162i
\(155\) −45.0586 −0.290701
\(156\) 12.1649 21.0702i 0.0779800 0.135065i
\(157\) −85.9416 + 49.6184i −0.547399 + 0.316041i −0.748072 0.663617i \(-0.769020\pi\)
0.200673 + 0.979658i \(0.435687\pi\)
\(158\) −75.2685 130.369i −0.476383 0.825120i
\(159\) 2.07225 + 1.19642i 0.0130330 + 0.00752463i
\(160\) 12.6491i 0.0790569i
\(161\) 102.660 + 130.217i 0.637641 + 0.808799i
\(162\) 12.7279 0.0785674
\(163\) −139.490 + 241.603i −0.855765 + 1.48223i 0.0201678 + 0.999797i \(0.493580\pi\)
−0.875933 + 0.482433i \(0.839753\pi\)
\(164\) −112.796 + 65.1226i −0.687779 + 0.397089i
\(165\) −19.8869 34.4452i −0.120527 0.208759i
\(166\) −60.5389 34.9522i −0.364692 0.210555i
\(167\) 29.9435i 0.179302i −0.995973 0.0896511i \(-0.971425\pi\)
0.995973 0.0896511i \(-0.0285752\pi\)
\(168\) −4.92167 33.9378i −0.0292957 0.202011i
\(169\) 119.672 0.708118
\(170\) 50.1982 86.9458i 0.295283 0.511446i
\(171\) −80.8225 + 46.6629i −0.472646 + 0.272883i
\(172\) 3.03497 + 5.25673i 0.0176452 + 0.0305624i
\(173\) 92.2369 + 53.2530i 0.533161 + 0.307821i 0.742303 0.670065i \(-0.233734\pi\)
−0.209142 + 0.977885i \(0.567067\pi\)
\(174\) 22.5273i 0.129467i
\(175\) −34.6377 + 5.02316i −0.197930 + 0.0287038i
\(176\) 41.0782 0.233399
\(177\) 95.1064 164.729i 0.537324 0.930673i
\(178\) 201.960 116.602i 1.13461 0.655066i
\(179\) 119.986 + 207.822i 0.670315 + 1.16102i 0.977815 + 0.209471i \(0.0671743\pi\)
−0.307500 + 0.951548i \(0.599492\pi\)
\(180\) 11.6190 + 6.70820i 0.0645497 + 0.0372678i
\(181\) 309.322i 1.70896i −0.519482 0.854482i \(-0.673875\pi\)
0.519482 0.854482i \(-0.326125\pi\)
\(182\) −54.6004 + 43.0459i −0.300002 + 0.236516i
\(183\) 68.7483 0.375674
\(184\) 33.5002 58.0241i 0.182066 0.315348i
\(185\) 93.2705 53.8497i 0.504165 0.291080i
\(186\) −24.6796 42.7464i −0.132686 0.229819i
\(187\) −282.358 163.020i −1.50994 0.871762i
\(188\) 123.893i 0.659005i
\(189\) −33.7840 13.4774i −0.178751 0.0713091i
\(190\) −98.3741 −0.517758
\(191\) −1.54480 + 2.67567i −0.00808796 + 0.0140088i −0.870041 0.492979i \(-0.835908\pi\)
0.861953 + 0.506988i \(0.169241\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) 119.349 + 206.718i 0.618387 + 1.07108i 0.989780 + 0.142602i \(0.0455469\pi\)
−0.371393 + 0.928476i \(0.621120\pi\)
\(194\) −60.6002 34.9875i −0.312372 0.180348i
\(195\) 27.2015i 0.139495i
\(196\) −22.8726 + 95.2935i −0.116697 + 0.486191i
\(197\) −291.539 −1.47989 −0.739946 0.672666i \(-0.765149\pi\)
−0.739946 + 0.672666i \(0.765149\pi\)
\(198\) 21.7850 37.7328i 0.110025 0.190570i
\(199\) 209.224 120.796i 1.05138 0.607013i 0.128342 0.991730i \(-0.459034\pi\)
0.923034 + 0.384717i \(0.125701\pi\)
\(200\) 7.07107 + 12.2474i 0.0353553 + 0.0612372i
\(201\) 23.8785 + 13.7863i 0.118799 + 0.0685885i
\(202\) 190.739i 0.944252i
\(203\) −23.8538 + 59.7947i −0.117507 + 0.294555i
\(204\) 109.979 0.539111
\(205\) −72.8093 + 126.109i −0.355167 + 0.615168i
\(206\) 45.8080 26.4473i 0.222369 0.128385i
\(207\) −35.5324 61.5438i −0.171654 0.297313i
\(208\) 24.3298 + 14.0468i 0.116970 + 0.0675327i
\(209\) 319.472i 1.52857i
\(210\) −23.7372 30.1089i −0.113034 0.143376i
\(211\) −263.018 −1.24653 −0.623266 0.782010i \(-0.714195\pi\)
−0.623266 + 0.782010i \(0.714195\pi\)
\(212\) −1.38150 + 2.39283i −0.00651652 + 0.0112869i
\(213\) −80.0234 + 46.2015i −0.375696 + 0.216908i
\(214\) 17.5334 + 30.3688i 0.0819318 + 0.141910i
\(215\) 5.87720 + 3.39320i 0.0273358 + 0.0157823i
\(216\) 14.6969i 0.0680414i
\(217\) 20.2442 + 139.596i 0.0932911 + 0.643297i
\(218\) −79.6056 −0.365163
\(219\) −62.6830 + 108.570i −0.286224 + 0.495754i
\(220\) 39.7738 22.9634i 0.180790 0.104379i
\(221\) −111.490 193.106i −0.504479 0.873783i
\(222\) 102.173 + 58.9894i 0.460237 + 0.265718i
\(223\) 112.658i 0.505193i −0.967572 0.252597i \(-0.918715\pi\)
0.967572 0.252597i \(-0.0812845\pi\)
\(224\) 39.1880 5.68306i 0.174947 0.0253708i
\(225\) 15.0000 0.0666667
\(226\) −53.0266 + 91.8448i −0.234631 + 0.406393i
\(227\) 42.4529 24.5102i 0.187017 0.107974i −0.403568 0.914950i \(-0.632230\pi\)
0.590585 + 0.806975i \(0.298897\pi\)
\(228\) −53.8817 93.3258i −0.236323 0.409324i
\(229\) 24.3476 + 14.0571i 0.106321 + 0.0613846i 0.552218 0.833700i \(-0.313782\pi\)
−0.445896 + 0.895085i \(0.647115\pi\)
\(230\) 74.9088i 0.325690i
\(231\) −97.7792 + 77.0871i −0.423286 + 0.333710i
\(232\) 26.0123 0.112122
\(233\) −88.1014 + 152.596i −0.378117 + 0.654919i −0.990788 0.135420i \(-0.956762\pi\)
0.612671 + 0.790338i \(0.290095\pi\)
\(234\) 25.8056 14.8989i 0.110280 0.0636704i
\(235\) 69.2582 + 119.959i 0.294716 + 0.510463i
\(236\) 190.213 + 109.819i 0.805987 + 0.465337i
\(237\) 184.369i 0.777930i
\(238\) −291.919 116.455i −1.22655 0.489306i
\(239\) 34.7150 0.145251 0.0726255 0.997359i \(-0.476862\pi\)
0.0726255 + 0.997359i \(0.476862\pi\)
\(240\) −7.74597 + 13.4164i −0.0322749 + 0.0559017i
\(241\) −229.871 + 132.716i −0.953823 + 0.550690i −0.894266 0.447535i \(-0.852302\pi\)
−0.0595563 + 0.998225i \(0.518969\pi\)
\(242\) 10.9857 + 19.0278i 0.0453955 + 0.0786273i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 79.3837i 0.325343i
\(245\) 31.1244 + 105.054i 0.127038 + 0.428790i
\(246\) −159.517 −0.648444
\(247\) −109.244 + 189.216i −0.442284 + 0.766058i
\(248\) 49.3592 28.4976i 0.199029 0.114910i
\(249\) −42.8075 74.1447i −0.171918 0.297770i
\(250\) 13.6931 + 7.90569i 0.0547723 + 0.0316228i
\(251\) 24.1723i 0.0963040i −0.998840 0.0481520i \(-0.984667\pi\)
0.998840 0.0481520i \(-0.0153332\pi\)
\(252\) 15.5624 39.0104i 0.0617555 0.154803i
\(253\) −243.268 −0.961533
\(254\) −90.8659 + 157.384i −0.357740 + 0.619624i
\(255\) 106.486 61.4799i 0.417594 0.241098i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −8.25969 4.76874i −0.0321389 0.0185554i 0.483844 0.875154i \(-0.339240\pi\)
−0.515983 + 0.856599i \(0.672573\pi\)
\(258\) 7.43413i 0.0288145i
\(259\) −208.736 264.766i −0.805932 1.02226i
\(260\) 31.4096 0.120806
\(261\) 13.7951 23.8938i 0.0528548 0.0915472i
\(262\) −92.4639 + 53.3840i −0.352916 + 0.203756i
\(263\) 65.9316 + 114.197i 0.250691 + 0.434209i 0.963716 0.266929i \(-0.0860090\pi\)
−0.713026 + 0.701138i \(0.752676\pi\)
\(264\) 43.5701 + 25.1552i 0.165038 + 0.0952848i
\(265\) 3.08913i 0.0116571i
\(266\) 44.1980 + 304.771i 0.166158 + 1.14576i
\(267\) 285.615 1.06972
\(268\) −15.9190 + 27.5726i −0.0593994 + 0.102883i
\(269\) −32.8041 + 18.9395i −0.121949 + 0.0704070i −0.559733 0.828673i \(-0.689096\pi\)
0.437785 + 0.899080i \(0.355763\pi\)
\(270\) 8.21584 + 14.2302i 0.0304290 + 0.0527046i
\(271\) 313.801 + 181.173i 1.15794 + 0.668535i 0.950809 0.309779i \(-0.100255\pi\)
0.207128 + 0.978314i \(0.433588\pi\)
\(272\) 126.992i 0.466884i
\(273\) −84.2726 + 12.2212i −0.308691 + 0.0447664i
\(274\) 152.051 0.554932
\(275\) 25.6739 44.4685i 0.0933596 0.161704i
\(276\) 71.0647 41.0292i 0.257481 0.148657i
\(277\) 56.6495 + 98.1197i 0.204511 + 0.354223i 0.949977 0.312321i \(-0.101106\pi\)
−0.745466 + 0.666544i \(0.767773\pi\)
\(278\) 333.135 + 192.336i 1.19833 + 0.691855i
\(279\) 60.4525i 0.216676i
\(280\) 34.7667 27.4094i 0.124167 0.0978907i
\(281\) −178.735 −0.636069 −0.318034 0.948079i \(-0.603023\pi\)
−0.318034 + 0.948079i \(0.603023\pi\)
\(282\) −75.8686 + 131.408i −0.269038 + 0.465987i
\(283\) 37.3850 21.5843i 0.132103 0.0762695i −0.432492 0.901638i \(-0.642366\pi\)
0.564595 + 0.825368i \(0.309032\pi\)
\(284\) −53.3489 92.4030i −0.187848 0.325363i
\(285\) −104.341 60.2416i −0.366110 0.211374i
\(286\) 102.003i 0.356655i
\(287\) 423.410 + 168.910i 1.47530 + 0.588538i
\(288\) −16.9706 −0.0589256
\(289\) 359.471 622.622i 1.24384 2.15440i
\(290\) 25.1863 14.5413i 0.0868493 0.0501424i
\(291\) −42.8508 74.2198i −0.147254 0.255051i
\(292\) −125.366 72.3801i −0.429336 0.247877i
\(293\) 15.4426i 0.0527050i −0.999653 0.0263525i \(-0.991611\pi\)
0.999653 0.0263525i \(-0.00838923\pi\)
\(294\) −82.6151 + 87.0675i −0.281004 + 0.296148i
\(295\) 245.564 0.832420
\(296\) −68.1151 + 117.979i −0.230119 + 0.398577i
\(297\) 46.2130 26.6811i 0.155599 0.0898354i
\(298\) 58.9917 + 102.177i 0.197959 + 0.342875i
\(299\) −144.082 83.1859i −0.481881 0.278214i
\(300\) 17.3205i 0.0577350i
\(301\) 7.87189 19.7326i 0.0261525 0.0655568i
\(302\) 179.315 0.593757
\(303\) −116.803 + 202.309i −0.385489 + 0.667687i
\(304\) 107.763 62.2172i 0.354485 0.204662i
\(305\) 44.3768 + 76.8629i 0.145498 + 0.252009i
\(306\) 116.650 + 67.3479i 0.381209 + 0.220091i
\(307\) 234.648i 0.764327i 0.924095 + 0.382163i \(0.124821\pi\)
−0.924095 + 0.382163i \(0.875179\pi\)
\(308\) −89.0125 112.906i −0.289002 0.366577i
\(309\) 64.7823 0.209651
\(310\) 31.8613 55.1853i 0.102778 0.178017i
\(311\) −345.352 + 199.389i −1.11045 + 0.641121i −0.938947 0.344061i \(-0.888197\pi\)
−0.171508 + 0.985183i \(0.554864\pi\)
\(312\) 17.2037 + 29.7978i 0.0551402 + 0.0955056i
\(313\) 111.891 + 64.6002i 0.357479 + 0.206390i 0.667974 0.744184i \(-0.267162\pi\)
−0.310495 + 0.950575i \(0.600495\pi\)
\(314\) 140.342i 0.446949i
\(315\) −6.73928 46.4713i −0.0213945 0.147528i
\(316\) 212.892 0.673707
\(317\) 201.283 348.632i 0.634961 1.09979i −0.351562 0.936165i \(-0.614349\pi\)
0.986523 0.163621i \(-0.0523173\pi\)
\(318\) −2.93061 + 1.69199i −0.00921575 + 0.00532072i
\(319\) −47.2232 81.7930i −0.148035 0.256404i
\(320\) −15.4919 8.94427i −0.0484123 0.0279508i
\(321\) 42.9479i 0.133794i
\(322\) −232.074 + 33.6554i −0.720726 + 0.104520i
\(323\) −987.640 −3.05771
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) 30.4122 17.5585i 0.0935760 0.0540261i
\(326\) −197.268 341.679i −0.605118 1.04809i
\(327\) −84.4345 48.7483i −0.258209 0.149077i
\(328\) 184.195i 0.561569i
\(329\) 340.526 268.464i 1.03503 0.815999i
\(330\) 56.2487 0.170451
\(331\) 83.4463 144.533i 0.252104 0.436656i −0.712001 0.702178i \(-0.752211\pi\)
0.964105 + 0.265522i \(0.0855443\pi\)
\(332\) 85.6150 49.4298i 0.257876 0.148885i
\(333\) 72.2470 + 125.136i 0.216958 + 0.375782i
\(334\) 36.6731 + 21.1732i 0.109800 + 0.0633929i
\(335\) 35.5960i 0.106257i
\(336\) 45.0453 + 17.9699i 0.134064 + 0.0534818i
\(337\) −541.392 −1.60651 −0.803253 0.595638i \(-0.796899\pi\)
−0.803253 + 0.595638i \(0.796899\pi\)
\(338\) −84.6208 + 146.568i −0.250357 + 0.433632i
\(339\) −112.486 + 64.9441i −0.331818 + 0.191575i
\(340\) 70.9909 + 122.960i 0.208797 + 0.361647i
\(341\) −179.215 103.470i −0.525558 0.303431i
\(342\) 131.983i 0.385914i
\(343\) 311.482 143.625i 0.908110 0.418732i
\(344\) −8.58420 −0.0249541
\(345\) 45.8721 79.4528i 0.132963 0.230298i
\(346\) −130.443 + 75.3111i −0.377002 + 0.217662i
\(347\) −214.342 371.251i −0.617700 1.06989i −0.989904 0.141737i \(-0.954731\pi\)
0.372204 0.928151i \(-0.378602\pi\)
\(348\) 27.5902 + 15.9292i 0.0792822 + 0.0457736i
\(349\) 74.6851i 0.213998i −0.994259 0.106999i \(-0.965876\pi\)
0.994259 0.106999i \(-0.0341241\pi\)
\(350\) 18.3404 45.9742i 0.0524012 0.131355i
\(351\) 36.4946 0.103973
\(352\) −29.0467 + 50.3104i −0.0825190 + 0.142927i
\(353\) 316.890 182.956i 0.897705 0.518290i 0.0212499 0.999774i \(-0.493235\pi\)
0.876455 + 0.481484i \(0.159902\pi\)
\(354\) 134.501 + 232.962i 0.379946 + 0.658085i
\(355\) −103.310 59.6459i −0.291013 0.168017i
\(356\) 329.799i 0.926403i
\(357\) −238.313 302.282i −0.667543 0.846728i
\(358\) −339.373 −0.947968
\(359\) 248.793 430.922i 0.693017 1.20034i −0.277828 0.960631i \(-0.589614\pi\)
0.970845 0.239710i \(-0.0770522\pi\)
\(360\) −16.4317 + 9.48683i −0.0456435 + 0.0263523i
\(361\) 303.373 + 525.457i 0.840368 + 1.45556i
\(362\) 378.841 + 218.724i 1.04652 + 0.604210i
\(363\) 26.9094i 0.0741305i
\(364\) −14.1119 97.3096i −0.0387689 0.267334i
\(365\) −161.847 −0.443416
\(366\) −48.6124 + 84.1991i −0.132821 + 0.230052i
\(367\) 120.700 69.6861i 0.328882 0.189880i −0.326462 0.945210i \(-0.605857\pi\)
0.655345 + 0.755330i \(0.272523\pi\)
\(368\) 47.3765 + 82.0584i 0.128740 + 0.222985i
\(369\) −169.194 97.6839i −0.458519 0.264726i
\(370\) 152.310i 0.411649i
\(371\) 9.57040 1.38790i 0.0257962 0.00374098i
\(372\) 69.8045 0.187647
\(373\) −173.760 + 300.961i −0.465844 + 0.806865i −0.999239 0.0390009i \(-0.987582\pi\)
0.533395 + 0.845866i \(0.320916\pi\)
\(374\) 399.315 230.544i 1.06769 0.616429i
\(375\) 9.68246 + 16.7705i 0.0258199 + 0.0447214i
\(376\) −151.737 87.6055i −0.403556 0.232993i
\(377\) 64.5923i 0.171332i
\(378\) 40.3953 31.8468i 0.106866 0.0842509i
\(379\) 307.387 0.811048 0.405524 0.914084i \(-0.367089\pi\)
0.405524 + 0.914084i \(0.367089\pi\)
\(380\) 69.5610 120.483i 0.183055 0.317061i
\(381\) −192.756 + 111.288i −0.505921 + 0.292093i
\(382\) −2.18468 3.78397i −0.00571905 0.00990569i
\(383\) −440.572 254.364i −1.15032 0.664136i −0.201353 0.979519i \(-0.564534\pi\)
−0.948965 + 0.315382i \(0.897867\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −149.302 59.5609i −0.387798 0.154704i
\(386\) −337.569 −0.874531
\(387\) −4.55246 + 7.88509i −0.0117635 + 0.0203749i
\(388\) 85.7016 49.4799i 0.220880 0.127525i
\(389\) 85.4840 + 148.063i 0.219753 + 0.380624i 0.954732 0.297466i \(-0.0961414\pi\)
−0.734979 + 0.678090i \(0.762808\pi\)
\(390\) 33.3149 + 19.2344i 0.0854228 + 0.0493189i
\(391\) 752.057i 1.92342i
\(392\) −100.537 95.3957i −0.256472 0.243356i
\(393\) −130.764 −0.332732
\(394\) 206.149 357.061i 0.523221 0.906245i
\(395\) 206.131 119.010i 0.521851 0.301291i
\(396\) 30.8087 + 53.3622i 0.0777997 + 0.134753i
\(397\) 551.223 + 318.249i 1.38847 + 0.801634i 0.993143 0.116906i \(-0.0372975\pi\)
0.395328 + 0.918540i \(0.370631\pi\)
\(398\) 341.661i 0.858446i
\(399\) −139.755 + 350.325i −0.350262 + 0.878006i
\(400\) −20.0000 −0.0500000
\(401\) 296.110 512.878i 0.738429 1.27900i −0.214773 0.976664i \(-0.568901\pi\)
0.953202 0.302333i \(-0.0977654\pi\)
\(402\) −33.7694 + 19.4968i −0.0840034 + 0.0484994i
\(403\) −70.7636 122.566i −0.175592 0.304135i
\(404\) −233.606 134.873i −0.578234 0.333843i
\(405\) 20.1246i 0.0496904i
\(406\) −56.3661 71.4961i −0.138833 0.176099i
\(407\) 494.630 1.21531
\(408\) −77.7667 + 134.696i −0.190605 + 0.330137i
\(409\) −245.717 + 141.865i −0.600776 + 0.346858i −0.769347 0.638831i \(-0.779418\pi\)
0.168571 + 0.985690i \(0.446085\pi\)
\(410\) −102.968 178.346i −0.251141 0.434989i
\(411\) 161.275 + 93.1121i 0.392396 + 0.226550i
\(412\) 74.8041i 0.181563i
\(413\) −110.328 760.778i −0.267138 1.84208i
\(414\) 100.501 0.242755
\(415\) 55.2642 95.7204i 0.133167 0.230652i
\(416\) −34.4075 + 19.8652i −0.0827103 + 0.0477528i
\(417\) 235.562 + 408.006i 0.564897 + 0.978431i
\(418\) −391.271 225.901i −0.936056 0.540432i
\(419\) 482.511i 1.15158i 0.817599 + 0.575789i \(0.195305\pi\)
−0.817599 + 0.575789i \(0.804695\pi\)
\(420\) 53.6604 7.78185i 0.127763 0.0185282i
\(421\) 762.080 1.81017 0.905083 0.425234i \(-0.139808\pi\)
0.905083 + 0.425234i \(0.139808\pi\)
\(422\) 185.982 322.130i 0.440716 0.763342i
\(423\) −160.942 + 92.9197i −0.380476 + 0.219668i
\(424\) −1.95374 3.38397i −0.00460787 0.00798107i
\(425\) 137.473 + 79.3703i 0.323467 + 0.186754i
\(426\) 130.678i 0.306755i
\(427\) 218.190 172.017i 0.510984 0.402849i
\(428\) −49.5920 −0.115869
\(429\) 62.4640 108.191i 0.145604 0.252193i
\(430\) −8.31161 + 4.79871i −0.0193293 + 0.0111598i
\(431\) −128.008 221.717i −0.297003 0.514424i 0.678446 0.734650i \(-0.262654\pi\)
−0.975449 + 0.220226i \(0.929320\pi\)
\(432\) −18.0000 10.3923i −0.0416667 0.0240563i
\(433\) 646.579i 1.49325i 0.665243 + 0.746627i \(0.268328\pi\)
−0.665243 + 0.746627i \(0.731672\pi\)
\(434\) −185.284 73.9150i −0.426921 0.170311i
\(435\) 35.6188 0.0818823
\(436\) 56.2897 97.4966i 0.129105 0.223616i
\(437\) −638.181 + 368.454i −1.46037 + 0.843144i
\(438\) −88.6472 153.541i −0.202391 0.350551i
\(439\) 290.352 + 167.635i 0.661394 + 0.381856i 0.792808 0.609472i \(-0.208618\pi\)
−0.131414 + 0.991328i \(0.541952\pi\)
\(440\) 64.9504i 0.147615i
\(441\) −140.944 + 41.7578i −0.319602 + 0.0946888i
\(442\) 315.341 0.713441
\(443\) 140.527 243.400i 0.317216 0.549435i −0.662690 0.748894i \(-0.730585\pi\)
0.979906 + 0.199459i \(0.0639185\pi\)
\(444\) −144.494 + 83.4237i −0.325437 + 0.187891i
\(445\) 184.363 + 319.327i 0.414300 + 0.717589i
\(446\) 137.977 + 79.6613i 0.309366 + 0.178613i
\(447\) 144.500i 0.323265i
\(448\) −20.7498 + 52.0139i −0.0463166 + 0.116102i
\(449\) 47.2320 0.105194 0.0525969 0.998616i \(-0.483250\pi\)
0.0525969 + 0.998616i \(0.483250\pi\)
\(450\) −10.6066 + 18.3712i −0.0235702 + 0.0408248i
\(451\) −579.181 + 334.390i −1.28422 + 0.741442i
\(452\) −74.9910 129.888i −0.165909 0.287363i
\(453\) 190.192 + 109.807i 0.419850 + 0.242400i
\(454\) 69.3253i 0.152699i
\(455\) −68.0615 86.3309i −0.149586 0.189738i
\(456\) 152.400 0.334212
\(457\) −294.396 + 509.909i −0.644193 + 1.11578i 0.340294 + 0.940319i \(0.389473\pi\)
−0.984487 + 0.175456i \(0.943860\pi\)
\(458\) −34.4327 + 19.8797i −0.0751805 + 0.0434055i
\(459\) 82.4840 + 142.866i 0.179704 + 0.311256i
\(460\) 91.7441 + 52.9685i 0.199444 + 0.115149i
\(461\) 60.5606i 0.131368i 0.997840 + 0.0656839i \(0.0209229\pi\)
−0.997840 + 0.0656839i \(0.979077\pi\)
\(462\) −25.2717 174.263i −0.0547007 0.377193i
\(463\) 88.7592 0.191704 0.0958522 0.995396i \(-0.469442\pi\)
0.0958522 + 0.995396i \(0.469442\pi\)
\(464\) −18.3935 + 31.8584i −0.0396411 + 0.0686604i
\(465\) 67.5879 39.0219i 0.145350 0.0839181i
\(466\) −124.594 215.803i −0.267369 0.463097i
\(467\) 261.733 + 151.112i 0.560457 + 0.323580i 0.753329 0.657644i \(-0.228447\pi\)
−0.192872 + 0.981224i \(0.561780\pi\)
\(468\) 42.1404i 0.0900436i
\(469\) 110.280 15.9928i 0.235138 0.0340997i
\(470\) −195.892 −0.416791
\(471\) 85.9416 148.855i 0.182466 0.316041i
\(472\) −269.002 + 155.308i −0.569919 + 0.329043i
\(473\) 15.5839 + 26.9921i 0.0329470 + 0.0570658i
\(474\) 225.806 + 130.369i 0.476383 + 0.275040i
\(475\) 155.543i 0.327459i
\(476\) 349.045 275.180i 0.733288 0.578110i
\(477\) −4.14451 −0.00868869
\(478\) −24.5472 + 42.5170i −0.0513540 + 0.0889478i
\(479\) 30.4237 17.5651i 0.0635151 0.0366704i −0.467906 0.883778i \(-0.654991\pi\)
0.531421 + 0.847108i \(0.321658\pi\)
\(480\) −10.9545 18.9737i −0.0228218 0.0395285i
\(481\) 292.959 + 169.140i 0.609062 + 0.351642i
\(482\) 375.378i 0.778793i
\(483\) −266.761 106.419i −0.552301 0.220329i
\(484\) −31.0723 −0.0641989
\(485\) 55.3202 95.8173i 0.114062 0.197561i
\(486\) −19.0919 + 11.0227i −0.0392837 + 0.0226805i
\(487\) −32.3167 55.9741i −0.0663586 0.114937i 0.830937 0.556366i \(-0.187805\pi\)
−0.897296 + 0.441430i \(0.854471\pi\)
\(488\) −97.2247 56.1327i −0.199231 0.115026i
\(489\) 483.207i 0.988153i
\(490\) −150.672 36.1647i −0.307494 0.0738056i
\(491\) 241.365 0.491578 0.245789 0.969323i \(-0.420953\pi\)
0.245789 + 0.969323i \(0.420953\pi\)
\(492\) 112.796 195.368i 0.229260 0.397089i
\(493\) 252.861 145.989i 0.512903 0.296125i
\(494\) −154.494 267.592i −0.312742 0.541685i
\(495\) 59.6608 + 34.4452i 0.120527 + 0.0695862i
\(496\) 80.6033i 0.162507i
\(497\) −138.373 + 346.860i −0.278416 + 0.697908i
\(498\) 121.078 0.243128
\(499\) 95.8123 165.952i 0.192009 0.332569i −0.753907 0.656981i \(-0.771833\pi\)
0.945916 + 0.324412i \(0.105166\pi\)
\(500\) −19.3649 + 11.1803i −0.0387298 + 0.0223607i
\(501\) 25.9318 + 44.9152i 0.0517601 + 0.0896511i
\(502\) 29.6049 + 17.0924i 0.0589739 + 0.0340486i
\(503\) 919.711i 1.82845i 0.405205 + 0.914226i \(0.367200\pi\)
−0.405205 + 0.914226i \(0.632800\pi\)
\(504\) 36.7735 + 46.6445i 0.0729634 + 0.0925485i
\(505\) −301.585 −0.597197
\(506\) 172.016 297.941i 0.339953 0.588816i
\(507\) −179.508 + 103.639i −0.354059 + 0.204416i
\(508\) −128.504 222.575i −0.252960 0.438140i
\(509\) 250.976 + 144.901i 0.493076 + 0.284678i 0.725850 0.687853i \(-0.241447\pi\)
−0.232773 + 0.972531i \(0.574780\pi\)
\(510\) 173.892i 0.340964i
\(511\) 72.7154 + 501.416i 0.142300 + 0.981244i
\(512\) 22.6274 0.0441942
\(513\) 80.8225 139.989i 0.157549 0.272883i
\(514\) 11.6810 6.74401i 0.0227256 0.0131206i
\(515\) 41.8168 + 72.4288i 0.0811976 + 0.140638i
\(516\) −9.10492 5.25673i −0.0176452 0.0101875i
\(517\) 636.163i 1.23049i
\(518\) 471.870 68.4307i 0.910946 0.132106i
\(519\) −184.474 −0.355441
\(520\) −22.2099 + 38.4687i −0.0427114 + 0.0739783i
\(521\) −653.176 + 377.112i −1.25370 + 0.723823i −0.971842 0.235634i \(-0.924283\pi\)
−0.281856 + 0.959457i \(0.590950\pi\)
\(522\) 19.5092 + 33.7909i 0.0373740 + 0.0647336i
\(523\) 65.5821 + 37.8638i 0.125396 + 0.0723974i 0.561386 0.827554i \(-0.310268\pi\)
−0.435990 + 0.899952i \(0.643602\pi\)
\(524\) 150.993i 0.288154i
\(525\) 47.6063 37.5318i 0.0906787 0.0714892i
\(526\) −186.483 −0.354530
\(527\) 319.875 554.040i 0.606974 1.05131i
\(528\) −61.6174 + 35.5748i −0.116700 + 0.0673765i
\(529\) −16.0662 27.8275i −0.0303709 0.0526039i
\(530\) −3.78340 2.18435i −0.00713849 0.00412141i
\(531\) 329.458i 0.620449i
\(532\) −404.520 161.375i −0.760376 0.303336i
\(533\) −457.382 −0.858128
\(534\) −201.960 + 349.805i −0.378202 + 0.655066i
\(535\) −48.0172 + 27.7228i −0.0897518 + 0.0518182i
\(536\) −22.5129 38.9935i −0.0420017 0.0727491i
\(537\) −359.959 207.822i −0.670315 0.387007i
\(538\) 53.5689i 0.0995705i
\(539\) −117.446 + 489.311i −0.217895 + 0.907813i
\(540\) −23.2379 −0.0430331
\(541\) −493.177 + 854.207i −0.911602 + 1.57894i −0.0998002 + 0.995007i \(0.531820\pi\)
−0.811802 + 0.583933i \(0.801513\pi\)
\(542\) −443.782 + 256.217i −0.818785 + 0.472726i
\(543\) 267.881 + 463.984i 0.493335 + 0.854482i
\(544\) −155.533 89.7972i −0.285907 0.165068i
\(545\) 125.868i 0.230950i
\(546\) 44.6218 111.854i 0.0817250 0.204861i
\(547\) 346.700 0.633820 0.316910 0.948456i \(-0.397355\pi\)
0.316910 + 0.948456i \(0.397355\pi\)
\(548\) −107.517 + 186.224i −0.196198 + 0.339825i
\(549\) −103.122 + 59.5377i −0.187837 + 0.108448i
\(550\) 36.3084 + 62.8880i 0.0660152 + 0.114342i
\(551\) −247.768 143.049i −0.449669 0.259617i
\(552\) 116.048i 0.210232i
\(553\) −461.315 585.143i −0.834204 1.05813i
\(554\) −160.229 −0.289222
\(555\) −93.2705 + 161.549i −0.168055 + 0.291080i
\(556\) −471.124 + 272.004i −0.847346 + 0.489215i
\(557\) 76.7246 + 132.891i 0.137746 + 0.238583i 0.926643 0.375942i \(-0.122681\pi\)
−0.788897 + 0.614525i \(0.789348\pi\)
\(558\) 74.0389 + 42.7464i 0.132686 + 0.0766064i
\(559\) 21.3158i 0.0381320i
\(560\) 8.98571 + 61.9617i 0.0160459 + 0.110646i
\(561\) 564.716 1.00662
\(562\) 126.385 218.905i 0.224884 0.389511i
\(563\) 150.809 87.0695i 0.267866 0.154653i −0.360051 0.932933i \(-0.617241\pi\)
0.627918 + 0.778280i \(0.283907\pi\)
\(564\) −107.294 185.839i −0.190238 0.329502i
\(565\) −145.219 83.8424i −0.257025 0.148394i
\(566\) 61.0495i 0.107861i
\(567\) 62.3478 9.04169i 0.109961 0.0159465i
\(568\) 150.893 0.265658
\(569\) 109.591 189.817i 0.192603 0.333597i −0.753509 0.657437i \(-0.771641\pi\)
0.946112 + 0.323840i \(0.104974\pi\)
\(570\) 147.561 85.1944i 0.258879 0.149464i
\(571\) −478.914 829.504i −0.838729 1.45272i −0.890958 0.454087i \(-0.849966\pi\)
0.0522282 0.998635i \(-0.483368\pi\)
\(572\) 124.928 + 72.1272i 0.218406 + 0.126097i
\(573\) 5.35135i 0.00933917i
\(574\) −506.268 + 399.132i −0.882001 + 0.695351i
\(575\) 118.441 0.205985
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) −898.838 + 518.944i −1.55778 + 0.899384i −0.560309 + 0.828284i \(0.689318\pi\)
−0.997469 + 0.0710997i \(0.977349\pi\)
\(578\) 508.369 + 880.521i 0.879531 + 1.52339i
\(579\) −358.046 206.718i −0.618387 0.357026i
\(580\) 41.1290i 0.0709121i
\(581\) −321.380 128.208i −0.553149 0.220667i
\(582\) 121.200 0.208248
\(583\) −7.09371 + 12.2867i −0.0121676 + 0.0210749i
\(584\) 177.294 102.361i 0.303586 0.175276i
\(585\) 23.5572 + 40.8023i 0.0402687 + 0.0697474i
\(586\) 18.9132 + 10.9195i 0.0322751 + 0.0186340i
\(587\) 819.162i 1.39551i −0.716339 0.697753i \(-0.754183\pi\)
0.716339 0.697753i \(-0.245817\pi\)
\(588\) −48.2177 162.748i −0.0820029 0.276783i
\(589\) −626.864 −1.06429
\(590\) −173.640 + 300.753i −0.294305 + 0.509751i
\(591\) 437.308 252.480i 0.739946 0.427208i
\(592\) −96.3294 166.847i −0.162719 0.281837i
\(593\) 461.919 + 266.689i 0.778953 + 0.449729i 0.836059 0.548639i \(-0.184854\pi\)
−0.0571059 + 0.998368i \(0.518187\pi\)
\(594\) 75.4655i 0.127046i
\(595\) 184.131 461.564i 0.309464 0.775738i
\(596\) −166.854 −0.279956
\(597\) −209.224 + 362.387i −0.350459 + 0.607013i
\(598\) 203.763 117.643i 0.340741 0.196727i
\(599\) 171.452 + 296.963i 0.286230 + 0.495765i 0.972907 0.231198i \(-0.0742646\pi\)
−0.686677 + 0.726963i \(0.740931\pi\)
\(600\) −21.2132 12.2474i −0.0353553 0.0204124i
\(601\) 418.941i 0.697073i 0.937295 + 0.348536i \(0.113321\pi\)
−0.937295 + 0.348536i \(0.886679\pi\)
\(602\) 18.6011 + 23.5941i 0.0308989 + 0.0391929i
\(603\) −47.7571 −0.0791992
\(604\) −126.795 + 219.615i −0.209925 + 0.363601i
\(605\) −30.0856 + 17.3699i −0.0497282 + 0.0287106i
\(606\) −165.185 286.108i −0.272582 0.472126i
\(607\) 122.608 + 70.7875i 0.201989 + 0.116619i 0.597583 0.801807i \(-0.296128\pi\)
−0.395594 + 0.918426i \(0.629461\pi\)
\(608\) 175.977i 0.289436i
\(609\) −16.0030 110.350i −0.0262775 0.181199i
\(610\) −125.517 −0.205765
\(611\) −217.537 + 376.786i −0.356035 + 0.616670i
\(612\) −164.968 + 95.2443i −0.269556 + 0.155628i
\(613\) 148.520 + 257.244i 0.242284 + 0.419647i 0.961364 0.275279i \(-0.0887703\pi\)
−0.719081 + 0.694926i \(0.755437\pi\)
\(614\) −287.384 165.921i −0.468053 0.270230i
\(615\) 252.219i 0.410112i
\(616\) 201.222 29.1813i 0.326659 0.0473722i
\(617\) −674.329 −1.09292 −0.546458 0.837486i \(-0.684024\pi\)
−0.546458 + 0.837486i \(0.684024\pi\)
\(618\) −45.8080 + 79.3418i −0.0741230 + 0.128385i
\(619\) −833.055 + 480.965i −1.34581 + 0.777003i −0.987653 0.156659i \(-0.949928\pi\)
−0.358156 + 0.933662i \(0.616594\pi\)
\(620\) 45.0586 + 78.0438i 0.0726752 + 0.125877i
\(621\) 106.597 + 61.5438i 0.171654 + 0.0991044i
\(622\) 563.957i 0.906683i
\(623\) 906.471 714.643i 1.45501 1.14710i
\(624\) −48.6595 −0.0779800
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) −158.238 + 91.3585i −0.252776 + 0.145940i
\(627\) −276.671 479.208i −0.441261 0.764287i
\(628\) 171.883 + 99.2368i 0.273699 + 0.158020i
\(629\) 1529.14i 2.43106i
\(630\) 61.6809 + 24.6063i 0.0979062 + 0.0390576i
\(631\) 1185.17 1.87824 0.939122 0.343584i \(-0.111641\pi\)
0.939122 + 0.343584i \(0.111641\pi\)
\(632\) −150.537 + 260.738i −0.238191 + 0.412560i
\(633\) 394.527 227.781i 0.623266 0.359843i
\(634\) 284.657 + 493.040i 0.448985 + 0.777666i
\(635\) −248.847 143.672i −0.391884 0.226255i
\(636\) 4.78566i 0.00752463i
\(637\) −236.882 + 249.648i −0.371871 + 0.391912i
\(638\) 133.567 0.209353
\(639\) 80.0234 138.605i 0.125232 0.216908i
\(640\) 21.9089 12.6491i 0.0342327 0.0197642i
\(641\) −203.549 352.557i −0.317549 0.550011i 0.662427 0.749126i \(-0.269526\pi\)
−0.979976 + 0.199115i \(0.936193\pi\)
\(642\) −52.6002 30.3688i −0.0819318 0.0473034i
\(643\) 1077.83i 1.67626i −0.545474 0.838128i \(-0.683650\pi\)
0.545474 0.838128i \(-0.316350\pi\)
\(644\) 122.882 308.029i 0.190810 0.478306i
\(645\) −11.7544 −0.0182239
\(646\) 698.367 1209.61i 1.08106 1.87246i
\(647\) 1019.05 588.349i 1.57504 0.909350i 0.579504 0.814969i \(-0.303246\pi\)
0.995536 0.0943805i \(-0.0300870\pi\)
\(648\) −12.7279 22.0454i −0.0196419 0.0340207i
\(649\) 976.701 + 563.899i 1.50493 + 0.868873i
\(650\) 49.6629i 0.0764045i
\(651\) −151.260 191.861i −0.232349 0.294718i
\(652\) 557.959 0.855765
\(653\) 439.563 761.345i 0.673144 1.16592i −0.303864 0.952715i \(-0.598277\pi\)
0.977008 0.213204i \(-0.0683898\pi\)
\(654\) 119.408 68.9405i 0.182582 0.105414i
\(655\) −84.4076 146.198i −0.128867 0.223203i
\(656\) 225.591 + 130.245i 0.343889 + 0.198545i
\(657\) 217.140i 0.330503i
\(658\) 88.0113 + 606.890i 0.133756 + 0.922325i
\(659\) 65.1550 0.0988696 0.0494348 0.998777i \(-0.484258\pi\)
0.0494348 + 0.998777i \(0.484258\pi\)
\(660\) −39.7738 + 68.8903i −0.0602634 + 0.104379i
\(661\) 22.0376 12.7234i 0.0333397 0.0192487i −0.483237 0.875489i \(-0.660539\pi\)
0.516577 + 0.856241i \(0.327206\pi\)
\(662\) 118.011 + 204.401i 0.178264 + 0.308762i
\(663\) 334.469 + 193.106i 0.504479 + 0.291261i
\(664\) 139.809i 0.210555i
\(665\) −481.886 + 69.8832i −0.724641 + 0.105088i
\(666\) −204.345 −0.306825
\(667\) 108.927 188.667i 0.163309 0.282860i
\(668\) −51.8636 + 29.9435i −0.0776401 + 0.0448256i
\(669\) 97.5647 + 168.987i 0.145837 + 0.252597i
\(670\) −43.5961 25.1702i −0.0650688 0.0375675i
\(671\) 407.618i 0.607478i
\(672\) −53.8604 + 42.4624i −0.0801494 + 0.0631881i
\(673\) 23.1893 0.0344566 0.0172283 0.999852i \(-0.494516\pi\)
0.0172283 + 0.999852i \(0.494516\pi\)
\(674\) 382.822 663.068i 0.567986 0.983780i
\(675\) −22.5000 + 12.9904i −0.0333333 + 0.0192450i
\(676\) −119.672 207.278i −0.177029 0.306624i
\(677\) −123.090 71.0658i −0.181816 0.104972i 0.406330 0.913727i \(-0.366809\pi\)
−0.588146 + 0.808755i \(0.700142\pi\)
\(678\) 183.690i 0.270929i
\(679\) −321.705 128.337i −0.473792 0.189009i
\(680\) −200.793 −0.295283
\(681\) −42.4529 + 73.5306i −0.0623391 + 0.107974i
\(682\) 253.449 146.329i 0.371626 0.214558i
\(683\) −328.352 568.722i −0.480749 0.832682i 0.519007 0.854770i \(-0.326302\pi\)
−0.999756 + 0.0220879i \(0.992969\pi\)
\(684\) 161.645 + 93.3258i 0.236323 + 0.136441i
\(685\) 240.414i 0.350970i
\(686\) −44.3466 + 483.044i −0.0646452 + 0.704146i
\(687\) −48.6951 −0.0708808
\(688\) 6.06994 10.5135i 0.00882259 0.0152812i
\(689\) −8.40290 + 4.85142i −0.0121958 + 0.00704125i
\(690\) 64.8729 + 112.363i 0.0940187 + 0.162845i
\(691\) 212.350 + 122.600i 0.307308 + 0.177425i 0.645721 0.763573i \(-0.276557\pi\)
−0.338413 + 0.940998i \(0.609890\pi\)
\(692\) 213.012i 0.307821i
\(693\) 79.9094 200.310i 0.115309 0.289047i
\(694\) 606.250 0.873560
\(695\) −304.109 + 526.733i −0.437567 + 0.757889i
\(696\) −39.0184 + 22.5273i −0.0560610 + 0.0323668i
\(697\) −1033.76 1790.52i −1.48316 2.56890i
\(698\) 91.4702 + 52.8104i 0.131046 + 0.0756595i
\(699\) 305.192i 0.436612i
\(700\) 43.3380 + 54.9710i 0.0619115 + 0.0785300i
\(701\) 379.419 0.541254 0.270627 0.962684i \(-0.412769\pi\)
0.270627 + 0.962684i \(0.412769\pi\)
\(702\) −25.8056 + 44.6966i −0.0367601 + 0.0636704i
\(703\) 1297.60 749.168i 1.84580 1.06567i
\(704\) −41.0782 71.1496i −0.0583498 0.101065i
\(705\) −207.775 119.959i −0.294716 0.170154i
\(706\) 517.479i 0.732973i
\(707\) 135.498 + 934.335i 0.191651 + 1.32155i
\(708\) −380.426 −0.537324
\(709\) 442.054 765.661i 0.623490 1.07992i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 0.149042i \(-0.0476191\pi\)
\(710\) 146.102 84.3520i 0.205777 0.118806i
\(711\) 159.669 + 276.554i 0.224569 + 0.388965i
\(712\) −403.920 233.203i −0.567304 0.327533i
\(713\) 477.337i 0.669477i
\(714\) 538.731 78.1269i 0.754525 0.109421i
\(715\) 161.281 0.225568
\(716\) 239.973 415.645i 0.335157 0.580510i
\(717\) −52.0725 + 30.0641i −0.0726255 + 0.0419304i
\(718\) 351.847 + 609.416i 0.490037 + 0.848769i
\(719\) −825.831 476.794i −1.14858 0.663135i −0.200042 0.979787i \(-0.564108\pi\)
−0.948542 + 0.316653i \(0.897441\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 205.603 162.093i 0.285164 0.224817i
\(722\) −858.068 −1.18846
\(723\) 229.871 398.149i 0.317941 0.550690i
\(724\) −535.762 + 309.322i −0.740003 + 0.427241i
\(725\) 22.9918 + 39.8230i 0.0317129 + 0.0549283i
\(726\) −32.9571 19.0278i −0.0453955 0.0262091i
\(727\) 1110.82i 1.52795i −0.645248 0.763974i \(-0.723246\pi\)
0.645248 0.763974i \(-0.276754\pi\)
\(728\) 129.158 + 51.5249i 0.177415 + 0.0707759i
\(729\) −27.0000 −0.0370370
\(730\) 114.443 198.221i 0.156771 0.271536i
\(731\) −83.4455 + 48.1773i −0.114153 + 0.0659060i
\(732\) −68.7483 119.075i −0.0939184 0.162671i
\(733\) 35.2595 + 20.3571i 0.0481029 + 0.0277722i 0.523859 0.851805i \(-0.324492\pi\)
−0.475756 + 0.879577i \(0.657825\pi\)
\(734\) 197.102i 0.268531i
\(735\) −137.666 130.626i −0.187300 0.177722i
\(736\) −134.001 −0.182066
\(737\) −81.7407 + 141.579i −0.110910 + 0.192102i
\(738\) 239.276 138.146i 0.324222 0.187190i
\(739\) −422.735 732.199i −0.572037 0.990797i −0.996357 0.0852847i \(-0.972820\pi\)
0.424320 0.905512i \(-0.360513\pi\)
\(740\) −186.541 107.699i −0.252082 0.145540i
\(741\) 378.433i 0.510705i
\(742\) −5.06747 + 12.7027i −0.00682947 + 0.0171195i
\(743\) 355.319 0.478222 0.239111 0.970992i \(-0.423144\pi\)
0.239111 + 0.970992i \(0.423144\pi\)
\(744\) −49.3592 + 85.4927i −0.0663431 + 0.114910i
\(745\) −161.556 + 93.2741i −0.216853 + 0.125200i
\(746\) −245.733 425.623i −0.329401 0.570540i
\(747\) 128.422 + 74.1447i 0.171918 + 0.0992567i
\(748\) 652.078i 0.871762i
\(749\) 107.461 + 136.306i 0.143473 + 0.181984i
\(750\) −27.3861 −0.0365148
\(751\) −108.768 + 188.392i −0.144831 + 0.250855i −0.929310 0.369300i \(-0.879597\pi\)
0.784479 + 0.620156i \(0.212931\pi\)
\(752\) 214.589 123.893i 0.285357 0.164751i
\(753\) 20.9338 + 36.2584i 0.0278006 + 0.0481520i
\(754\) 79.1091 + 45.6737i 0.104919 + 0.0605751i
\(755\) 283.521i 0.375525i
\(756\) 10.4404 + 71.9930i 0.0138101 + 0.0952289i
\(757\) 1178.25 1.55647 0.778233 0.627975i \(-0.216116\pi\)
0.778233 + 0.627975i \(0.216116\pi\)
\(758\) −217.356 + 376.471i −0.286749 + 0.496663i
\(759\) 364.902 210.676i 0.480766 0.277571i
\(760\) 98.3741 + 170.389i 0.129440 + 0.224196i
\(761\) 711.636 + 410.863i 0.935133 + 0.539899i 0.888431 0.459010i \(-0.151796\pi\)
0.0467017 + 0.998909i \(0.485129\pi\)
\(762\) 314.769i 0.413082i
\(763\) −389.948 + 56.5504i −0.511073 + 0.0741159i
\(764\) 6.17920 0.00808796
\(765\) −106.486 + 184.440i −0.139198 + 0.241098i
\(766\) 623.063 359.725i 0.813398 0.469615i
\(767\) 385.653 + 667.970i 0.502807 + 0.870887i
\(768\) 24.0000 + 13.8564i 0.0312500 + 0.0180422i
\(769\) 230.888i 0.300244i 0.988667 + 0.150122i \(0.0479667\pi\)
−0.988667 + 0.150122i \(0.952033\pi\)
\(770\) 178.520 140.741i 0.231844