Properties

Label 210.3.o.b.31.1
Level 210
Weight 3
Character 210.31
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 31.1
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 \(\chi\) \(=\) 210.31
Dual form 210.3.o.b.61.1

$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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 −0.999281 0.0379228i \(-0.987926\pi\)
0.532482 + 0.846441i \(0.321259\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 7.02340i 0.540261i 0.962824 + 0.270131i \(0.0870669\pi\)
−0.962824 + 0.270131i \(0.912933\pi\)
\(14\) −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 0.987606 + 0.156951i \(0.0501666\pi\)
0.629727 + 0.776816i \(0.283167\pi\)
\(18\) 2.12132 3.67423i 0.117851 0.204124i
\(19\) −26.9408 + 15.5543i −1.41794 + 0.818648i −0.996118 0.0880311i \(-0.971943\pi\)
−0.421822 + 0.906679i \(0.638609\pi\)
\(20\) 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 0.999849 + 0.0173632i \(0.00552716\pi\)
−0.484888 + 0.874576i \(0.661140\pi\)
\(24\) −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 0.754325 0.656502i \(-0.227965\pi\)
−0.191385 + 0.981515i \(0.561298\pi\)
\(32\) −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 −0.982911 0.184081i \(-0.941069\pi\)
0.332037 0.943266i \(-0.392264\pi\)
\(38\) 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 \(0.292098\pi\)
−0.607685 + 0.794178i \(0.707902\pi\)
\(42\) 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 −0.946784 0.321869i \(-0.895689\pi\)
−0.194645 + 0.980874i \(0.562356\pi\)
\(48\) 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 −0.872468 0.488671i \(-0.837482\pi\)
0.859435 + 0.511244i \(0.170815\pi\)
\(54\) −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 −0.988912 0.148500i \(-0.952555\pi\)
−0.623061 0.782173i \(-0.714111\pi\)
\(60\) −3.87298 + 6.70820i −0.0645497 + 0.111803i
\(61\) −34.3741 + 19.8459i −0.563510 + 0.325343i −0.754553 0.656239i \(-0.772146\pi\)
0.191043 + 0.981582i \(0.438813\pi\)
\(62\) 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 −0.919292 0.393576i \(-0.871238\pi\)
0.800493 + 0.599342i \(0.204571\pi\)
\(68\) −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 0.863567 0.504234i \(-0.168225\pi\)
−0.00489557 + 0.999988i \(0.501558\pi\)
\(74\) −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 −0.976845 0.213948i \(-0.931368\pi\)
0.303138 0.952947i \(-0.401966\pi\)
\(80\) 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 \(-0.903757\pi\)
0.954638 0.297770i \(-0.0962429\pi\)
\(84\) −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 −0.614022 + 0.789289i \(0.710449\pi\)
−0.990555 + 0.137114i \(0.956217\pi\)
\(90\) 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 \(-0.917908\pi\)
0.966928 0.255051i \(-0.0820922\pi\)
\(98\) 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 0.950455 0.310863i \(-0.100618\pi\)
0.206012 + 0.978549i \(0.433951\pi\)
\(102\) −38.8833 + 67.3479i −0.381209 + 0.660274i
\(103\) −32.3911 + 18.7010i −0.314477 + 0.181563i −0.648928 0.760850i \(-0.724782\pi\)
0.334451 + 0.942413i \(0.391449\pi\)
\(104\) 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 0.918127 0.396287i \(-0.129701\pi\)
−0.802258 + 0.596978i \(0.796368\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) 28.1448 48.7483i 0.258209 0.447232i −0.707553 0.706660i \(-0.750201\pi\)
0.965762 + 0.259429i \(0.0835342\pi\)
\(110\) −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 −0.229243 0.973369i \(-0.573625\pi\)
0.728341 + 0.685215i \(0.240292\pi\)
\(132\) 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 −0.992765 0.120073i \(-0.961687\pi\)
0.600369 + 0.799723i \(0.295020\pi\)
\(138\) −50.2503 + 29.0120i −0.364133 + 0.210232i
\(139\) 272.004i 1.95686i 0.206576 + 0.978431i \(0.433768\pi\)
−0.206576 + 0.978431i \(0.566232\pi\)
\(140\) −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 0.971374 0.237557i \(-0.0763467\pi\)
−0.691417 + 0.722456i \(0.743013\pi\)
\(150\) 10.6066 + 6.12372i 0.0707107 + 0.0408248i
\(151\) −63.3973 + 109.807i −0.419850 + 0.727201i −0.995924 0.0901962i \(-0.971251\pi\)
0.576074 + 0.817397i \(0.304584\pi\)
\(152\) −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 0.200673 0.979658i \(-0.435687\pi\)
−0.748072 + 0.663617i \(0.769020\pi\)
\(158\) −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 −0.875933 0.482433i \(-0.839753\pi\)
0.0201678 0.999797i \(-0.493580\pi\)
\(164\) −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 \(0.0285752\pi\)
−0.995973 + 0.0896511i \(0.971425\pi\)
\(168\) −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 −0.209142 0.977885i \(-0.567067\pi\)
0.742303 + 0.670065i \(0.233734\pi\)
\(174\) 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 −0.307500 0.951548i \(-0.599492\pi\)
0.977815 0.209471i \(-0.0671743\pi\)
\(180\) 11.6190 6.70820i 0.0645497 0.0372678i
\(181\) 309.322i 1.70896i 0.519482 + 0.854482i \(0.326125\pi\)
−0.519482 + 0.854482i \(0.673875\pi\)
\(182\) −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 0.861953 0.506988i \(-0.169241\pi\)
−0.870041 + 0.492979i \(0.835908\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) 119.349 206.718i 0.618387 1.07108i −0.371393 0.928476i \(-0.621120\pi\)
0.989780 0.142602i \(-0.0455469\pi\)
\(194\) −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 0.923034 0.384717i \(-0.125701\pi\)
0.128342 + 0.991730i \(0.459034\pi\)
\(200\) 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 \(0.0812845\pi\)
−0.967572 + 0.252597i \(0.918715\pi\)
\(224\) 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 0.590585 0.806975i \(-0.298897\pi\)
−0.403568 + 0.914950i \(0.632230\pi\)
\(228\) −53.8817 + 93.3258i −0.236323 + 0.409324i
\(229\) 24.3476 14.0571i 0.106321 0.0613846i −0.445896 0.895085i \(-0.647115\pi\)
0.552218 + 0.833700i \(0.313782\pi\)
\(230\) 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 0.612671 0.790338i \(-0.290095\pi\)
−0.990788 + 0.135420i \(0.956762\pi\)
\(234\) 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 −0.0595563 0.998225i \(-0.518969\pi\)
−0.894266 + 0.447535i \(0.852302\pi\)
\(242\) 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 \(0.0153332\pi\)
−0.998840 + 0.0481520i \(0.984667\pi\)
\(252\) 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 −0.515983 0.856599i \(-0.672573\pi\)
0.483844 + 0.875154i \(0.339240\pi\)
\(258\) 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 −0.713026 0.701138i \(-0.752676\pi\)
0.963716 + 0.266929i \(0.0860090\pi\)
\(264\) 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 0.437785 0.899080i \(-0.355763\pi\)
−0.559733 + 0.828673i \(0.689096\pi\)
\(270\) 8.21584 14.2302i 0.0304290 0.0527046i
\(271\) 313.801 181.173i 1.15794 0.668535i 0.207128 0.978314i \(-0.433588\pi\)
0.950809 + 0.309779i \(0.100255\pi\)
\(272\) 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 −0.745466 0.666544i \(-0.767773\pi\)
0.949977 + 0.312321i \(0.101106\pi\)
\(278\) 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 0.564595 0.825368i \(-0.309032\pi\)
−0.432492 + 0.901638i \(0.642366\pi\)
\(284\) −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 \(0.00838923\pi\)
−0.999653 + 0.0263525i \(0.991611\pi\)
\(294\) −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 \(-0.875179\pi\)
0.924095 0.382163i \(-0.124821\pi\)
\(308\) −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 −0.171508 0.985183i \(-0.554864\pi\)
−0.938947 + 0.344061i \(0.888197\pi\)
\(312\) 17.2037 29.7978i 0.0551402 0.0955056i
\(313\) 111.891 64.6002i 0.357479 0.206390i −0.310495 0.950575i \(-0.600495\pi\)
0.667974 + 0.744184i \(0.267162\pi\)
\(314\) 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 0.986523 + 0.163621i \(0.0523173\pi\)
−0.351562 + 0.936165i \(0.614349\pi\)
\(318\) −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 0.964105 0.265522i \(-0.0855443\pi\)
−0.712001 + 0.702178i \(0.752211\pi\)
\(332\) 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 0.372204 + 0.928151i \(0.378602\pi\)
−0.989904 + 0.141737i \(0.954731\pi\)
\(348\) 27.5902 15.9292i 0.0792822 0.0457736i
\(349\) 74.6851i 0.213998i 0.994259 + 0.106999i \(0.0341241\pi\)
−0.994259 + 0.106999i \(0.965876\pi\)
\(350\) 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 0.876455 0.481484i \(-0.159902\pi\)
0.0212499 + 0.999774i \(0.493235\pi\)
\(354\) 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 0.970845 + 0.239710i \(0.0770522\pi\)
−0.277828 + 0.960631i \(0.589614\pi\)
\(360\) −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 0.655345 0.755330i \(-0.272523\pi\)
−0.326462 + 0.945210i \(0.605857\pi\)
\(368\) 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 0.533395 0.845866i \(-0.320916\pi\)
−0.999239 + 0.0390009i \(0.987582\pi\)
\(374\) 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 −0.948965 0.315382i \(-0.897867\pi\)
−0.201353 + 0.979519i \(0.564534\pi\)
\(384\) 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 −0.734979 0.678090i \(-0.762808\pi\)
0.954732 + 0.297466i \(0.0961414\pi\)
\(390\) 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 0.395328 0.918540i \(-0.370631\pi\)
0.993143 + 0.116906i \(0.0372975\pi\)
\(398\) 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 0.953202 + 0.302333i \(0.0977654\pi\)
−0.214773 + 0.976664i \(0.568901\pi\)
\(402\) −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 0.168571 0.985690i \(-0.446085\pi\)
−0.769347 + 0.638831i \(0.779418\pi\)
\(410\) −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 \(-0.804695\pi\)
0.817599 0.575789i \(-0.195305\pi\)
\(420\) 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 −0.975449 0.220226i \(-0.929320\pi\)
0.678446 + 0.734650i \(0.262654\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 646.579i 1.49325i −0.665243 0.746627i \(-0.731672\pi\)
0.665243 0.746627i \(-0.268328\pi\)
\(434\) −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 −0.131414 0.991328i \(-0.541952\pi\)
0.792808 + 0.609472i \(0.208618\pi\)
\(440\) 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 0.979906 0.199459i \(-0.0639185\pi\)
−0.662690 + 0.748894i \(0.730585\pi\)
\(444\) −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 −0.984487 0.175456i \(-0.943860\pi\)
0.340294 0.940319i \(-0.389473\pi\)
\(458\) −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 \(-0.979077\pi\)
0.997840 0.0656839i \(-0.0209229\pi\)
\(462\) −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 −0.192872 0.981224i \(-0.561780\pi\)
0.753329 + 0.657644i \(0.228447\pi\)
\(468\) 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 0.531421 0.847108i \(-0.321658\pi\)
−0.467906 + 0.883778i \(0.654991\pi\)
\(480\) −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 −0.897296 0.441430i \(-0.854471\pi\)
0.830937 + 0.556366i \(0.187805\pi\)
\(488\) −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 0.945916 0.324412i \(-0.105166\pi\)
−0.753907 + 0.656981i \(0.771833\pi\)
\(500\) −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 \(-0.632800\pi\)
0.405205 0.914226i \(-0.367200\pi\)
\(504\) 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 −0.232773 0.972531i \(-0.574780\pi\)
0.725850 + 0.687853i \(0.241447\pi\)
\(510\) 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 −0.281856 0.959457i \(-0.590950\pi\)
−0.971842 + 0.235634i \(0.924283\pi\)
\(522\) 19.5092 33.7909i 0.0373740 0.0647336i
\(523\) 65.5821 37.8638i 0.125396 0.0723974i −0.435990 0.899952i \(-0.643602\pi\)
0.561386 + 0.827554i \(0.310268\pi\)
\(524\) 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 −0.811802 0.583933i \(-0.801513\pi\)
−0.0998002 0.995007i \(-0.531820\pi\)
\(542\) −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 −0.788897 0.614525i \(-0.789348\pi\)
0.926643 + 0.375942i \(0.122681\pi\)
\(558\) 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 0.627918 0.778280i \(-0.283907\pi\)
−0.360051 + 0.932933i \(0.617241\pi\)
\(564\) −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 0.946112 0.323840i \(-0.104974\pi\)
−0.753509 + 0.657437i \(0.771641\pi\)
\(570\) 147.561 + 85.1944i 0.258879 + 0.149464i
\(571\) −478.914 + 829.504i −0.838729 + 1.45272i 0.0522282 + 0.998635i \(0.483368\pi\)
−0.890958 + 0.454087i \(0.849966\pi\)
\(572\) 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 −0.997469 0.0710997i \(-0.977349\pi\)
−0.560309 0.828284i \(-0.689318\pi\)
\(578\) 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 \(0.245817\pi\)
−0.716339 + 0.697753i \(0.754183\pi\)
\(588\) −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 −0.0571059 0.998368i \(-0.518187\pi\)
0.836059 + 0.548639i \(0.184854\pi\)
\(594\) 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 −0.686677 0.726963i \(-0.740931\pi\)
0.972907 + 0.231198i \(0.0742646\pi\)
\(600\) −21.2132 + 12.2474i −0.0353553 + 0.0204124i
\(601\) 418.941i 0.697073i −0.937295 0.348536i \(-0.886679\pi\)
0.937295 0.348536i \(-0.113321\pi\)
\(602\) 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 −0.395594 0.918426i \(-0.629461\pi\)
0.597583 + 0.801807i \(0.296128\pi\)
\(608\) 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 −0.719081 0.694926i \(-0.755437\pi\)
0.961364 + 0.275279i \(0.0887703\pi\)
\(614\) −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 −0.358156 0.933662i \(-0.616594\pi\)
−0.987653 + 0.156659i \(0.949928\pi\)
\(620\) 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 −0.979976 0.199115i \(-0.936193\pi\)
0.662427 + 0.749126i \(0.269526\pi\)
\(642\) −52.6002 + 30.3688i −0.0819318 + 0.0473034i
\(643\) 1077.83i 1.67626i 0.545474 + 0.838128i \(0.316350\pi\)
−0.545474 + 0.838128i \(0.683650\pi\)
\(644\) 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 0.995536 + 0.0943805i \(0.0300870\pi\)
0.579504 + 0.814969i \(0.303246\pi\)
\(648\) −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 0.977008 + 0.213204i \(0.0683898\pi\)
−0.303864 + 0.952715i \(0.598277\pi\)
\(654\) 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 0.516577 0.856241i \(-0.327206\pi\)
−0.483237 + 0.875489i \(0.660539\pi\)
\(662\) 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 −0.588146 0.808755i \(-0.700142\pi\)
0.406330 + 0.913727i \(0.366809\pi\)
\(678\) 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 −0.999756 0.0220879i \(-0.992969\pi\)
0.519007 + 0.854770i \(0.326302\pi\)
\(684\) 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 −0.338413 0.940998i \(-0.609890\pi\)
0.645721 + 0.763573i \(0.276557\pi\)
\(692\) 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 0.988831 + 0.149042i \(0.0476191\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(710\) 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 −0.948542 0.316653i \(-0.897441\pi\)
−0.200042 + 0.979787i \(0.564108\pi\)
\(720\) 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 \(0.276754\pi\)
−0.645248 + 0.763974i \(0.723246\pi\)
\(728\) 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 −0.475756 0.879577i \(-0.657825\pi\)
0.523859 + 0.851805i \(0.324492\pi\)
\(734\) 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 0.424320 + 0.905512i \(0.360513\pi\)
−0.996357 + 0.0852847i \(0.972820\pi\)
\(740\) −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 0.784479 0.620156i \(-0.212931\pi\)
−0.929310 + 0.369300i \(0.879597\pi\)
\(752\) 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 0.0467017 0.998909i \(-0.485129\pi\)
0.888431 + 0.459010i \(0.151796\pi\)
\(762\) 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 \(-0.952033\pi\)
0.988667 0.150122i \(-0.0479667\pi\)
\(770\) 178.520 + 140.741i 0.231844 + 0.182781i