Properties

Label 210.3.o.b.31.6
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 31.6
Root \(2.81422 + 4.87437i\) 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.61.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(6.99242 - 0.325616i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(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} +(6.99242 - 0.325616i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-6.09582 + 10.5583i) q^{11} +(3.00000 - 1.73205i) q^{12} +25.3938i q^{13} +(5.34319 + 8.33369i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-24.9196 - 14.3873i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-13.9147 + 8.03365i) q^{19} -4.47214i q^{20} +(-10.7706 - 5.56719i) q^{21} -17.2416 q^{22} +(11.8709 + 20.5610i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-31.1010 + 17.9562i) q^{26} -5.19615i q^{27} +(-6.42844 + 12.4368i) q^{28} +27.9121 q^{29} +(2.73861 + 4.74342i) q^{30} +(20.0480 + 11.5747i) q^{31} +(2.82843 - 4.89898i) q^{32} +(18.2875 - 10.5583i) q^{33} -40.6936i q^{34} +(-13.1767 + 8.44832i) q^{35} -6.00000 q^{36} +(14.5321 + 25.1703i) q^{37} +(-19.6783 - 11.3613i) q^{38} +(21.9917 - 38.0908i) q^{39} +(5.47723 - 3.16228i) q^{40} -56.9065i q^{41} +(-0.797593 - 17.1279i) q^{42} +7.83839 q^{43} +(-12.1916 - 21.1165i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-16.7880 + 29.0777i) q^{46} +(-19.7390 + 11.3963i) q^{47} +6.92820i q^{48} +(48.7879 - 4.55369i) q^{49} +7.07107 q^{50} +(24.9196 + 43.1620i) q^{51} +(-43.9834 - 25.3938i) q^{52} +(-24.2781 + 42.0510i) q^{53} +(6.36396 - 3.67423i) q^{54} -27.2613i q^{55} +(-19.7776 + 0.920981i) q^{56} +27.8294 q^{57} +(19.7368 + 34.1852i) q^{58} +(-62.3779 - 36.0139i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(99.2512 - 57.3027i) q^{61} +32.7382i q^{62} +(11.3346 + 17.6784i) q^{63} +8.00000 q^{64} +(-28.3912 - 49.1750i) q^{65} +(25.8624 + 14.9316i) q^{66} +(35.2674 - 61.0850i) q^{67} +(49.8392 - 28.7747i) q^{68} -41.1221i q^{69} +(-19.6644 - 10.1643i) q^{70} +6.41501 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-34.2569 - 19.7782i) q^{73} +(-20.5514 + 35.5961i) q^{74} +(-7.50000 + 4.33013i) q^{75} -32.1346i q^{76} +(-39.1866 + 75.8127i) q^{77} +62.2019 q^{78} +(27.3985 + 47.4555i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(69.6960 - 40.2390i) q^{82} +135.934i q^{83} +(20.4133 - 13.0881i) q^{84} +64.3422 q^{85} +(5.54258 + 9.60002i) q^{86} +(-41.8682 - 24.1726i) q^{87} +(17.2416 - 29.8633i) q^{88} +(124.905 - 72.1140i) q^{89} -9.48683i q^{90} +(8.26863 + 177.564i) q^{91} -47.4837 q^{92} +(-20.0480 - 34.7241i) q^{93} +(-27.9152 - 16.1168i) q^{94} +(17.9638 - 31.1142i) q^{95} +(-8.48528 + 4.89898i) q^{96} -78.9980i q^{97} +(40.0754 + 56.5328i) q^{98} -36.5749 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
\(7\) 6.99242 0.325616i 0.998918 0.0465165i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −2.73861 1.58114i −0.273861 0.158114i
\(11\) −6.09582 + 10.5583i −0.554165 + 0.959842i 0.443803 + 0.896125i \(0.353629\pi\)
−0.997968 + 0.0637178i \(0.979704\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 25.3938i 1.95337i 0.214672 + 0.976686i \(0.431132\pi\)
−0.214672 + 0.976686i \(0.568868\pi\)
\(14\) 5.34319 + 8.33369i 0.381656 + 0.595263i
\(15\) 3.87298 0.258199
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −24.9196 14.3873i −1.46586 0.846315i −0.466588 0.884475i \(-0.654517\pi\)
−0.999272 + 0.0381599i \(0.987850\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) −13.9147 + 8.03365i −0.732352 + 0.422824i −0.819282 0.573391i \(-0.805628\pi\)
0.0869298 + 0.996214i \(0.472294\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −10.7706 5.56719i −0.512887 0.265104i
\(22\) −17.2416 −0.783708
\(23\) 11.8709 + 20.5610i 0.516127 + 0.893958i 0.999825 + 0.0187231i \(0.00596009\pi\)
−0.483698 + 0.875235i \(0.660707\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −31.1010 + 17.9562i −1.19619 + 0.690621i
\(27\) 5.19615i 0.192450i
\(28\) −6.42844 + 12.4368i −0.229587 + 0.444173i
\(29\) 27.9121 0.962486 0.481243 0.876587i \(-0.340185\pi\)
0.481243 + 0.876587i \(0.340185\pi\)
\(30\) 2.73861 + 4.74342i 0.0912871 + 0.158114i
\(31\) 20.0480 + 11.5747i 0.646709 + 0.373378i 0.787194 0.616705i \(-0.211533\pi\)
−0.140485 + 0.990083i \(0.544866\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) 18.2875 10.5583i 0.554165 0.319947i
\(34\) 40.6936i 1.19687i
\(35\) −13.1767 + 8.44832i −0.376478 + 0.241381i
\(36\) −6.00000 −0.166667
\(37\) 14.5321 + 25.1703i 0.392758 + 0.680277i 0.992812 0.119682i \(-0.0381876\pi\)
−0.600054 + 0.799960i \(0.704854\pi\)
\(38\) −19.6783 11.3613i −0.517851 0.298982i
\(39\) 21.9917 38.0908i 0.563890 0.976686i
\(40\) 5.47723 3.16228i 0.136931 0.0790569i
\(41\) 56.9065i 1.38796i −0.719992 0.693982i \(-0.755855\pi\)
0.719992 0.693982i \(-0.244145\pi\)
\(42\) −0.797593 17.1279i −0.0189903 0.407806i
\(43\) 7.83839 0.182288 0.0911440 0.995838i \(-0.470948\pi\)
0.0911440 + 0.995838i \(0.470948\pi\)
\(44\) −12.1916 21.1165i −0.277083 0.479921i
\(45\) −5.80948 3.35410i −0.129099 0.0745356i
\(46\) −16.7880 + 29.0777i −0.364957 + 0.632124i
\(47\) −19.7390 + 11.3963i −0.419979 + 0.242475i −0.695068 0.718944i \(-0.744626\pi\)
0.275089 + 0.961419i \(0.411293\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 48.7879 4.55369i 0.995672 0.0929324i
\(50\) 7.07107 0.141421
\(51\) 24.9196 + 43.1620i 0.488620 + 0.846315i
\(52\) −43.9834 25.3938i −0.845835 0.488343i
\(53\) −24.2781 + 42.0510i −0.458078 + 0.793414i −0.998859 0.0477489i \(-0.984795\pi\)
0.540781 + 0.841163i \(0.318129\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 27.2613i 0.495660i
\(56\) −19.7776 + 0.920981i −0.353171 + 0.0164461i
\(57\) 27.8294 0.488235
\(58\) 19.7368 + 34.1852i 0.340290 + 0.589400i
\(59\) −62.3779 36.0139i −1.05725 0.610405i −0.132581 0.991172i \(-0.542327\pi\)
−0.924671 + 0.380767i \(0.875660\pi\)
\(60\) −3.87298 + 6.70820i −0.0645497 + 0.111803i
\(61\) 99.2512 57.3027i 1.62707 0.939388i 0.642107 0.766615i \(-0.278060\pi\)
0.984962 0.172773i \(-0.0552729\pi\)
\(62\) 32.7382i 0.528036i
\(63\) 11.3346 + 17.6784i 0.179914 + 0.280610i
\(64\) 8.00000 0.125000
\(65\) −28.3912 49.1750i −0.436787 0.756538i
\(66\) 25.8624 + 14.9316i 0.391854 + 0.226237i
\(67\) 35.2674 61.0850i 0.526380 0.911716i −0.473148 0.880983i \(-0.656882\pi\)
0.999528 0.0307332i \(-0.00978424\pi\)
\(68\) 49.8392 28.7747i 0.732930 0.423157i
\(69\) 41.1221i 0.595972i
\(70\) −19.6644 10.1643i −0.280920 0.145204i
\(71\) 6.41501 0.0903522 0.0451761 0.998979i \(-0.485615\pi\)
0.0451761 + 0.998979i \(0.485615\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) −34.2569 19.7782i −0.469272 0.270934i 0.246663 0.969101i \(-0.420666\pi\)
−0.715935 + 0.698167i \(0.753999\pi\)
\(74\) −20.5514 + 35.5961i −0.277722 + 0.481029i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 32.1346i 0.422824i
\(77\) −39.1866 + 75.8127i −0.508917 + 0.984581i
\(78\) 62.2019 0.797461
\(79\) 27.3985 + 47.4555i 0.346816 + 0.600703i 0.985682 0.168615i \(-0.0539295\pi\)
−0.638866 + 0.769318i \(0.720596\pi\)
\(80\) 7.74597 + 4.47214i 0.0968246 + 0.0559017i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 69.6960 40.2390i 0.849951 0.490719i
\(83\) 135.934i 1.63775i 0.573969 + 0.818877i \(0.305403\pi\)
−0.573969 + 0.818877i \(0.694597\pi\)
\(84\) 20.4133 13.0881i 0.243015 0.155810i
\(85\) 64.3422 0.756967
\(86\) 5.54258 + 9.60002i 0.0644486 + 0.111628i
\(87\) −41.8682 24.1726i −0.481243 0.277846i
\(88\) 17.2416 29.8633i 0.195927 0.339356i
\(89\) 124.905 72.1140i 1.40343 0.810270i 0.408686 0.912675i \(-0.365987\pi\)
0.994743 + 0.102405i \(0.0326537\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 8.26863 + 177.564i 0.0908641 + 1.95126i
\(92\) −47.4837 −0.516127
\(93\) −20.0480 34.7241i −0.215570 0.373378i
\(94\) −27.9152 16.1168i −0.296970 0.171456i
\(95\) 17.9638 31.1142i 0.189093 0.327518i
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 78.9980i 0.814412i −0.913336 0.407206i \(-0.866503\pi\)
0.913336 0.407206i \(-0.133497\pi\)
\(98\) 40.0754 + 56.5328i 0.408933 + 0.576866i
\(99\) −36.5749 −0.369443
\(100\) 5.00000 + 8.66025i 0.0500000 + 0.0866025i
\(101\) −40.4728 23.3670i −0.400721 0.231356i 0.286074 0.958208i \(-0.407650\pi\)
−0.686795 + 0.726851i \(0.740983\pi\)
\(102\) −35.2417 + 61.0404i −0.345507 + 0.598435i
\(103\) −144.022 + 83.1514i −1.39828 + 0.807295i −0.994212 0.107435i \(-0.965736\pi\)
−0.404064 + 0.914731i \(0.632403\pi\)
\(104\) 71.8246i 0.690621i
\(105\) 27.0815 1.26110i 0.257919 0.0120105i
\(106\) −68.6689 −0.647820
\(107\) 16.4908 + 28.5629i 0.154120 + 0.266943i 0.932738 0.360554i \(-0.117413\pi\)
−0.778618 + 0.627498i \(0.784079\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) 75.8575 131.389i 0.695940 1.20540i −0.273923 0.961752i \(-0.588321\pi\)
0.969863 0.243652i \(-0.0783454\pi\)
\(110\) 33.3882 19.2767i 0.303529 0.175242i
\(111\) 50.3405i 0.453518i
\(112\) −15.1128 23.5712i −0.134936 0.210457i
\(113\) −42.1910 −0.373372 −0.186686 0.982420i \(-0.559775\pi\)
−0.186686 + 0.982420i \(0.559775\pi\)
\(114\) 19.6783 + 34.0839i 0.172617 + 0.298982i
\(115\) −45.9759 26.5442i −0.399790 0.230819i
\(116\) −27.9121 + 48.3452i −0.240622 + 0.416769i
\(117\) −65.9751 + 38.0908i −0.563890 + 0.325562i
\(118\) 101.863i 0.863243i
\(119\) −178.933 92.4882i −1.50364 0.777212i
\(120\) −10.9545 −0.0912871
\(121\) −13.8180 23.9334i −0.114198 0.197797i
\(122\) 140.362 + 81.0383i 1.15051 + 0.664248i
\(123\) −49.2825 + 85.3598i −0.400671 + 0.693982i
\(124\) −40.0960 + 23.1494i −0.323354 + 0.186689i
\(125\) 11.1803i 0.0894427i
\(126\) −13.6368 + 26.3825i −0.108228 + 0.209385i
\(127\) 49.3159 0.388314 0.194157 0.980970i \(-0.437803\pi\)
0.194157 + 0.980970i \(0.437803\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) −11.7576 6.78824i −0.0911440 0.0526220i
\(130\) 40.1512 69.5439i 0.308855 0.534953i
\(131\) −12.6892 + 7.32612i −0.0968642 + 0.0559246i −0.547650 0.836708i \(-0.684477\pi\)
0.450785 + 0.892632i \(0.351144\pi\)
\(132\) 42.2331i 0.319947i
\(133\) −94.6815 + 60.7055i −0.711891 + 0.456433i
\(134\) 99.7514 0.744413
\(135\) 5.80948 + 10.0623i 0.0430331 + 0.0745356i
\(136\) 70.4833 + 40.6936i 0.518260 + 0.299217i
\(137\) 8.61062 14.9140i 0.0628512 0.108862i −0.832888 0.553442i \(-0.813314\pi\)
0.895739 + 0.444581i \(0.146647\pi\)
\(138\) 50.3641 29.0777i 0.364957 0.210708i
\(139\) 31.2612i 0.224901i −0.993657 0.112450i \(-0.964130\pi\)
0.993657 0.112450i \(-0.0358699\pi\)
\(140\) −1.45620 31.2711i −0.0104014 0.223365i
\(141\) 39.4780 0.279986
\(142\) 4.53610 + 7.85675i 0.0319443 + 0.0553292i
\(143\) −268.115 154.796i −1.87493 1.08249i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) −54.0516 + 31.2067i −0.372769 + 0.215218i
\(146\) 55.9412i 0.383159i
\(147\) −77.1255 35.4211i −0.524663 0.240960i
\(148\) −58.1282 −0.392758
\(149\) 71.5886 + 123.995i 0.480460 + 0.832182i 0.999749 0.0224175i \(-0.00713631\pi\)
−0.519288 + 0.854599i \(0.673803\pi\)
\(150\) −10.6066 6.12372i −0.0707107 0.0408248i
\(151\) −23.1788 + 40.1468i −0.153502 + 0.265873i −0.932512 0.361138i \(-0.882388\pi\)
0.779011 + 0.627011i \(0.215722\pi\)
\(152\) 39.3567 22.7226i 0.258926 0.149491i
\(153\) 86.3241i 0.564210i
\(154\) −120.560 + 5.61413i −0.782860 + 0.0364554i
\(155\) −51.7637 −0.333959
\(156\) 43.9834 + 76.1815i 0.281945 + 0.488343i
\(157\) 71.4553 + 41.2548i 0.455130 + 0.262769i 0.709994 0.704208i \(-0.248698\pi\)
−0.254865 + 0.966977i \(0.582031\pi\)
\(158\) −38.7473 + 67.1122i −0.245236 + 0.424761i
\(159\) 72.8344 42.0510i 0.458078 0.264471i
\(160\) 12.6491i 0.0790569i
\(161\) 89.7015 + 139.906i 0.557152 + 0.868982i
\(162\) −12.7279 −0.0785674
\(163\) 123.208 + 213.403i 0.755879 + 1.30922i 0.944936 + 0.327254i \(0.106123\pi\)
−0.189058 + 0.981966i \(0.560543\pi\)
\(164\) 98.5650 + 56.9065i 0.601006 + 0.346991i
\(165\) −23.6090 + 40.8920i −0.143085 + 0.247830i
\(166\) −166.484 + 96.1195i −1.00292 + 0.579033i
\(167\) 287.387i 1.72088i 0.509549 + 0.860441i \(0.329812\pi\)
−0.509549 + 0.860441i \(0.670188\pi\)
\(168\) 30.4639 + 15.7464i 0.181333 + 0.0937286i
\(169\) −475.847 −2.81566
\(170\) 45.4968 + 78.8028i 0.267628 + 0.463546i
\(171\) −41.7441 24.1010i −0.244117 0.140941i
\(172\) −7.83839 + 13.5765i −0.0455720 + 0.0789330i
\(173\) 236.901 136.775i 1.36937 0.790605i 0.378521 0.925593i \(-0.376433\pi\)
0.990847 + 0.134988i \(0.0430995\pi\)
\(174\) 68.3704i 0.392933i
\(175\) 16.0711 31.0921i 0.0918349 0.177669i
\(176\) 48.7665 0.277083
\(177\) 62.3779 + 108.042i 0.352417 + 0.610405i
\(178\) 176.643 + 101.985i 0.992374 + 0.572948i
\(179\) 50.3990 87.2936i 0.281558 0.487674i −0.690210 0.723609i \(-0.742482\pi\)
0.971769 + 0.235935i \(0.0758153\pi\)
\(180\) 11.6190 6.70820i 0.0645497 0.0372678i
\(181\) 135.147i 0.746667i 0.927697 + 0.373333i \(0.121785\pi\)
−0.927697 + 0.373333i \(0.878215\pi\)
\(182\) −211.624 + 135.684i −1.16277 + 0.745516i
\(183\) −198.502 −1.08471
\(184\) −33.5760 58.1554i −0.182478 0.316062i
\(185\) −56.2824 32.4947i −0.304229 0.175647i
\(186\) 28.3521 49.1073i 0.152431 0.264018i
\(187\) 303.811 175.405i 1.62466 0.937996i
\(188\) 45.5853i 0.242475i
\(189\) −1.69195 36.3337i −0.00895211 0.192242i
\(190\) 50.8093 0.267417
\(191\) −89.0902 154.309i −0.466441 0.807900i 0.532824 0.846226i \(-0.321131\pi\)
−0.999265 + 0.0383263i \(0.987797\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) −67.5577 + 117.013i −0.350040 + 0.606287i −0.986256 0.165224i \(-0.947165\pi\)
0.636216 + 0.771511i \(0.280499\pi\)
\(194\) 96.7523 55.8600i 0.498723 0.287938i
\(195\) 98.3499i 0.504359i
\(196\) −40.9007 + 89.0569i −0.208677 + 0.454372i
\(197\) 64.7529 0.328695 0.164347 0.986403i \(-0.447448\pi\)
0.164347 + 0.986403i \(0.447448\pi\)
\(198\) −25.8624 44.7949i −0.130618 0.226237i
\(199\) 116.757 + 67.4097i 0.586719 + 0.338742i 0.763799 0.645454i \(-0.223332\pi\)
−0.177080 + 0.984196i \(0.556665\pi\)
\(200\) −7.07107 + 12.2474i −0.0353553 + 0.0612372i
\(201\) −105.802 + 61.0850i −0.526380 + 0.303905i
\(202\) 66.0918i 0.327187i
\(203\) 195.173 9.08862i 0.961444 0.0447715i
\(204\) −99.6785 −0.488620
\(205\) 63.6234 + 110.199i 0.310358 + 0.537556i
\(206\) −203.679 117.594i −0.988731 0.570844i
\(207\) −35.6128 + 61.6831i −0.172042 + 0.297986i
\(208\) 87.9668 50.7877i 0.422917 0.244172i
\(209\) 195.887i 0.937257i
\(210\) 20.6941 + 32.2762i 0.0985432 + 0.153696i
\(211\) −116.352 −0.551432 −0.275716 0.961239i \(-0.588915\pi\)
−0.275716 + 0.961239i \(0.588915\pi\)
\(212\) −48.5563 84.1019i −0.229039 0.396707i
\(213\) −9.62251 5.55556i −0.0451761 0.0260824i
\(214\) −23.3215 + 40.3941i −0.108979 + 0.188757i
\(215\) −15.1790 + 8.76358i −0.0705999 + 0.0407608i
\(216\) 14.6969i 0.0680414i
\(217\) 143.953 + 74.4073i 0.663377 + 0.342891i
\(218\) 214.557 0.984208
\(219\) 34.2569 + 59.3346i 0.156424 + 0.270934i
\(220\) 47.2180 + 27.2613i 0.214627 + 0.123915i
\(221\) 365.350 632.805i 1.65317 2.86337i
\(222\) 61.6543 35.5961i 0.277722 0.160343i
\(223\) 30.0511i 0.134758i 0.997727 + 0.0673791i \(0.0214637\pi\)
−0.997727 + 0.0673791i \(0.978536\pi\)
\(224\) 18.1824 35.1767i 0.0811713 0.157039i
\(225\) 15.0000 0.0666667
\(226\) −29.8335 51.6732i −0.132007 0.228642i
\(227\) 122.698 + 70.8400i 0.540522 + 0.312070i 0.745290 0.666740i \(-0.232311\pi\)
−0.204769 + 0.978810i \(0.565644\pi\)
\(228\) −27.8294 + 48.2019i −0.122059 + 0.211412i
\(229\) −188.648 + 108.916i −0.823792 + 0.475617i −0.851722 0.523993i \(-0.824442\pi\)
0.0279303 + 0.999610i \(0.491108\pi\)
\(230\) 75.0783i 0.326427i
\(231\) 124.436 79.7825i 0.538683 0.345379i
\(232\) −78.9473 −0.340290
\(233\) 2.12597 + 3.68229i 0.00912435 + 0.0158038i 0.870552 0.492077i \(-0.163762\pi\)
−0.861427 + 0.507881i \(0.830429\pi\)
\(234\) −93.3029 53.8685i −0.398730 0.230207i
\(235\) 25.4830 44.1378i 0.108438 0.187820i
\(236\) 124.756 72.0278i 0.528626 0.305202i
\(237\) 94.9110i 0.400468i
\(238\) −13.2505 284.547i −0.0556742 1.19557i
\(239\) 261.513 1.09419 0.547097 0.837069i \(-0.315733\pi\)
0.547097 + 0.837069i \(0.315733\pi\)
\(240\) −7.74597 13.4164i −0.0322749 0.0559017i
\(241\) −86.5156 49.9498i −0.358986 0.207261i 0.309650 0.950851i \(-0.399788\pi\)
−0.668636 + 0.743590i \(0.733121\pi\)
\(242\) 19.5416 33.8470i 0.0807503 0.139864i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 229.211i 0.939388i
\(245\) −89.3863 + 63.3648i −0.364842 + 0.258632i
\(246\) −139.392 −0.566634
\(247\) −204.005 353.347i −0.825932 1.43056i
\(248\) −56.7042 32.7382i −0.228646 0.132009i
\(249\) 117.722 203.900i 0.472779 0.818877i
\(250\) −13.6931 + 7.90569i −0.0547723 + 0.0316228i
\(251\) 250.563i 0.998258i 0.866528 + 0.499129i \(0.166347\pi\)
−0.866528 + 0.499129i \(0.833653\pi\)
\(252\) −41.9545 + 1.95369i −0.166486 + 0.00775276i
\(253\) −289.452 −1.14408
\(254\) 34.8716 + 60.3993i 0.137290 + 0.237793i
\(255\) −96.5133 55.7220i −0.378483 0.218518i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 151.261 87.3305i 0.588563 0.339807i −0.175966 0.984396i \(-0.556305\pi\)
0.764529 + 0.644589i \(0.222971\pi\)
\(258\) 19.2000i 0.0744188i
\(259\) 109.810 + 171.269i 0.423977 + 0.661271i
\(260\) 113.565 0.436787
\(261\) 41.8682 + 72.5178i 0.160414 + 0.277846i
\(262\) −17.9452 10.3607i −0.0684933 0.0395446i
\(263\) −10.4417 + 18.0856i −0.0397023 + 0.0687664i −0.885194 0.465223i \(-0.845974\pi\)
0.845491 + 0.533989i \(0.179308\pi\)
\(264\) −51.7247 + 29.8633i −0.195927 + 0.113119i
\(265\) 108.575i 0.409717i
\(266\) −141.299 73.0354i −0.531198 0.274569i
\(267\) −249.810 −0.935619
\(268\) 70.5349 + 122.170i 0.263190 + 0.455858i
\(269\) 0.255741 + 0.147652i 0.000950712 + 0.000548894i 0.500475 0.865751i \(-0.333159\pi\)
−0.499525 + 0.866300i \(0.666492\pi\)
\(270\) −8.21584 + 14.2302i −0.0304290 + 0.0527046i
\(271\) 284.141 164.049i 1.04849 0.605346i 0.126264 0.991997i \(-0.459702\pi\)
0.922226 + 0.386651i \(0.126368\pi\)
\(272\) 115.099i 0.423157i
\(273\) 141.372 273.508i 0.517848 1.00186i
\(274\) 24.3545 0.0888851
\(275\) 30.4791 + 52.7913i 0.110833 + 0.191968i
\(276\) 71.2255 + 41.1221i 0.258064 + 0.148993i
\(277\) 251.485 435.585i 0.907888 1.57251i 0.0908951 0.995860i \(-0.471027\pi\)
0.816993 0.576648i \(-0.195639\pi\)
\(278\) 38.2870 22.1050i 0.137723 0.0795144i
\(279\) 69.4482i 0.248918i
\(280\) 37.2694 23.8955i 0.133105 0.0853409i
\(281\) 264.481 0.941213 0.470607 0.882343i \(-0.344035\pi\)
0.470607 + 0.882343i \(0.344035\pi\)
\(282\) 27.9152 + 48.3505i 0.0989900 + 0.171456i
\(283\) −399.801 230.825i −1.41272 0.815636i −0.417079 0.908870i \(-0.636946\pi\)
−0.995644 + 0.0932336i \(0.970280\pi\)
\(284\) −6.41501 + 11.1111i −0.0225881 + 0.0391237i
\(285\) −53.8914 + 31.1142i −0.189093 + 0.109173i
\(286\) 437.830i 1.53087i
\(287\) −18.5297 397.914i −0.0645633 1.38646i
\(288\) 16.9706 0.0589256
\(289\) 269.492 + 466.773i 0.932497 + 1.61513i
\(290\) −76.4404 44.1329i −0.263588 0.152182i
\(291\) −68.4142 + 118.497i −0.235100 + 0.407206i
\(292\) 68.5137 39.5564i 0.234636 0.135467i
\(293\) 134.788i 0.460027i 0.973187 + 0.230014i \(0.0738771\pi\)
−0.973187 + 0.230014i \(0.926123\pi\)
\(294\) −11.1542 119.506i −0.0379395 0.406482i
\(295\) 161.059 0.545963
\(296\) −41.1029 71.1922i −0.138861 0.240514i
\(297\) 54.8624 + 31.6748i 0.184722 + 0.106649i
\(298\) −101.242 + 175.355i −0.339737 + 0.588441i
\(299\) −522.124 + 301.448i −1.74623 + 1.00819i
\(300\) 17.3205i 0.0577350i
\(301\) 54.8093 2.55230i 0.182091 0.00847941i
\(302\) −65.5595 −0.217084
\(303\) 40.4728 + 70.1010i 0.133574 + 0.231356i
\(304\) 55.6588 + 32.1346i 0.183088 + 0.105706i
\(305\) −128.133 + 221.932i −0.420107 + 0.727647i
\(306\) 105.725 61.0404i 0.345507 0.199478i
\(307\) 23.7237i 0.0772760i 0.999253 + 0.0386380i \(0.0123019\pi\)
−0.999253 + 0.0386380i \(0.987698\pi\)
\(308\) −92.1249 143.686i −0.299107 0.466513i
\(309\) 288.045 0.932184
\(310\) −36.6024 63.3973i −0.118072 0.204507i
\(311\) 245.097 + 141.507i 0.788092 + 0.455005i 0.839290 0.543683i \(-0.182971\pi\)
−0.0511984 + 0.998689i \(0.516304\pi\)
\(312\) −62.2019 + 107.737i −0.199365 + 0.345311i
\(313\) 367.522 212.189i 1.17419 0.677920i 0.219528 0.975606i \(-0.429548\pi\)
0.954664 + 0.297687i \(0.0962150\pi\)
\(314\) 116.686i 0.371612i
\(315\) −41.7145 21.5616i −0.132427 0.0684497i
\(316\) −109.594 −0.346816
\(317\) 14.0641 + 24.3597i 0.0443661 + 0.0768444i 0.887356 0.461085i \(-0.152540\pi\)
−0.842990 + 0.537930i \(0.819207\pi\)
\(318\) 103.003 + 59.4690i 0.323910 + 0.187010i
\(319\) −170.147 + 294.703i −0.533376 + 0.923835i
\(320\) −15.4919 + 8.94427i −0.0484123 + 0.0279508i
\(321\) 57.1258i 0.177962i
\(322\) −107.921 + 208.790i −0.335158 + 0.648416i
\(323\) 462.332 1.43137
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 109.959 + 63.4846i 0.338334 + 0.195337i
\(326\) −174.243 + 301.797i −0.534487 + 0.925758i
\(327\) −227.572 + 131.389i −0.695940 + 0.401801i
\(328\) 160.956i 0.490719i
\(329\) −134.313 + 86.1153i −0.408245 + 0.261749i
\(330\) −66.7763 −0.202353
\(331\) −130.940 226.795i −0.395590 0.685182i 0.597586 0.801805i \(-0.296127\pi\)
−0.993176 + 0.116623i \(0.962793\pi\)
\(332\) −235.444 135.934i −0.709168 0.409438i
\(333\) −43.5962 + 75.5108i −0.130919 + 0.226759i
\(334\) −351.976 + 203.214i −1.05382 + 0.608424i
\(335\) 157.721i 0.470808i
\(336\) 2.25593 + 48.4449i 0.00671408 + 0.144181i
\(337\) −539.998 −1.60237 −0.801185 0.598417i \(-0.795796\pi\)
−0.801185 + 0.598417i \(0.795796\pi\)
\(338\) −336.475 582.791i −0.995487 1.72423i
\(339\) 63.2865 + 36.5385i 0.186686 + 0.107783i
\(340\) −64.3422 + 111.444i −0.189242 + 0.327776i
\(341\) −244.418 + 141.115i −0.716767 + 0.413826i
\(342\) 68.1678i 0.199321i
\(343\) 339.663 47.7274i 0.990272 0.139147i
\(344\) −22.1703 −0.0644486
\(345\) 45.9759 + 79.6326i 0.133263 + 0.230819i
\(346\) 335.028 + 193.429i 0.968289 + 0.559042i
\(347\) 19.9273 34.5150i 0.0574273 0.0994670i −0.835883 0.548908i \(-0.815044\pi\)
0.893310 + 0.449441i \(0.148377\pi\)
\(348\) 83.7363 48.3452i 0.240622 0.138923i
\(349\) 326.000i 0.934099i 0.884231 + 0.467049i \(0.154683\pi\)
−0.884231 + 0.467049i \(0.845317\pi\)
\(350\) 49.4439 2.30245i 0.141268 0.00657843i
\(351\) 131.950 0.375927
\(352\) 34.4832 + 59.7266i 0.0979635 + 0.169678i
\(353\) −126.505 73.0374i −0.358370 0.206905i 0.309996 0.950738i \(-0.399672\pi\)
−0.668365 + 0.743833i \(0.733006\pi\)
\(354\) −88.2156 + 152.794i −0.249197 + 0.431621i
\(355\) −12.4226 + 7.17220i −0.0349933 + 0.0202034i
\(356\) 288.456i 0.810270i
\(357\) 188.303 + 293.693i 0.527459 + 0.822670i
\(358\) 142.550 0.398184
\(359\) −10.7785 18.6689i −0.0300237 0.0520026i 0.850623 0.525776i \(-0.176225\pi\)
−0.880647 + 0.473773i \(0.842892\pi\)
\(360\) 16.4317 + 9.48683i 0.0456435 + 0.0263523i
\(361\) −51.4209 + 89.0636i −0.142440 + 0.246714i
\(362\) −165.520 + 95.5632i −0.457238 + 0.263987i
\(363\) 47.8669i 0.131865i
\(364\) −315.819 163.243i −0.867635 0.448469i
\(365\) 88.4508 0.242331
\(366\) −140.362 243.115i −0.383504 0.664248i
\(367\) 176.974 + 102.176i 0.482217 + 0.278408i 0.721340 0.692581i \(-0.243527\pi\)
−0.239123 + 0.970989i \(0.576860\pi\)
\(368\) 47.4837 82.2442i 0.129032 0.223490i
\(369\) 147.847 85.3598i 0.400671 0.231327i
\(370\) 91.9088i 0.248402i
\(371\) −156.070 + 301.943i −0.420675 + 0.813864i
\(372\) 80.1919 0.215570
\(373\) −281.632 487.800i −0.755045 1.30778i −0.945352 0.326051i \(-0.894282\pi\)
0.190308 0.981724i \(-0.439051\pi\)
\(374\) 429.654 + 248.061i 1.14881 + 0.663264i
\(375\) 9.68246 16.7705i 0.0258199 0.0447214i
\(376\) 55.8304 32.2337i 0.148485 0.0857279i
\(377\) 708.795i 1.88009i
\(378\) 43.3031 27.7640i 0.114559 0.0734498i
\(379\) 300.642 0.793250 0.396625 0.917981i \(-0.370181\pi\)
0.396625 + 0.917981i \(0.370181\pi\)
\(380\) 35.9276 + 62.2284i 0.0945463 + 0.163759i
\(381\) −73.9738 42.7088i −0.194157 0.112097i
\(382\) 125.993 218.226i 0.329824 0.571271i
\(383\) −9.34543 + 5.39559i −0.0244006 + 0.0140877i −0.512151 0.858896i \(-0.671151\pi\)
0.487750 + 0.872983i \(0.337818\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −8.87672 190.623i −0.0230564 0.495124i
\(386\) −191.082 −0.495031
\(387\) 11.7576 + 20.3647i 0.0303813 + 0.0526220i
\(388\) 136.828 + 78.9980i 0.352651 + 0.203603i
\(389\) 65.7124 113.817i 0.168927 0.292589i −0.769116 0.639109i \(-0.779303\pi\)
0.938043 + 0.346520i \(0.112637\pi\)
\(390\) −120.454 + 69.5439i −0.308855 + 0.178318i
\(391\) 683.164i 1.74722i
\(392\) −137.993 + 12.8798i −0.352023 + 0.0328566i
\(393\) 25.3784 0.0645761
\(394\) 45.7872 + 79.3058i 0.116211 + 0.201284i
\(395\) −106.114 61.2648i −0.268642 0.155101i
\(396\) 36.5749 63.3496i 0.0923609 0.159974i
\(397\) −485.778 + 280.464i −1.22362 + 0.706459i −0.965689 0.259703i \(-0.916375\pi\)
−0.257935 + 0.966162i \(0.583042\pi\)
\(398\) 190.664i 0.479054i
\(399\) 194.595 9.06169i 0.487706 0.0227110i
\(400\) −20.0000 −0.0500000
\(401\) −170.877 295.967i −0.426126 0.738072i 0.570399 0.821368i \(-0.306789\pi\)
−0.996525 + 0.0832958i \(0.973455\pi\)
\(402\) −149.627 86.3872i −0.372207 0.214894i
\(403\) −293.926 + 509.095i −0.729345 + 1.26326i
\(404\) 80.9456 46.7340i 0.200360 0.115678i
\(405\) 20.1246i 0.0496904i
\(406\) 149.140 + 232.611i 0.367339 + 0.572933i
\(407\) −354.339 −0.870612
\(408\) −70.4833 122.081i −0.172753 0.299217i
\(409\) 19.6793 + 11.3619i 0.0481157 + 0.0277796i 0.523865 0.851801i \(-0.324490\pi\)
−0.475749 + 0.879581i \(0.657823\pi\)
\(410\) −89.9771 + 155.845i −0.219456 + 0.380110i
\(411\) −25.8319 + 14.9140i −0.0628512 + 0.0362872i
\(412\) 332.606i 0.807295i
\(413\) −447.899 231.513i −1.08450 0.560564i
\(414\) −100.728 −0.243305
\(415\) −151.978 263.234i −0.366213 0.634299i
\(416\) 124.404 + 71.8246i 0.299048 + 0.172655i
\(417\) −27.0730 + 46.8918i −0.0649232 + 0.112450i
\(418\) 239.911 138.513i 0.573950 0.331370i
\(419\) 347.375i 0.829057i 0.910036 + 0.414529i \(0.136054\pi\)
−0.910036 + 0.414529i \(0.863946\pi\)
\(420\) −24.8972 + 48.1677i −0.0592791 + 0.114685i
\(421\) −340.381 −0.808507 −0.404253 0.914647i \(-0.632469\pi\)
−0.404253 + 0.914647i \(0.632469\pi\)
\(422\) −82.2734 142.502i −0.194961 0.337682i
\(423\) −59.2170 34.1890i −0.139993 0.0808250i
\(424\) 68.6689 118.938i 0.161955 0.280514i
\(425\) −124.598 + 71.9367i −0.293172 + 0.169263i
\(426\) 15.7135i 0.0368861i
\(427\) 675.348 433.002i 1.58161 1.01406i
\(428\) −65.9632 −0.154120
\(429\) 268.115 + 464.389i 0.624976 + 1.08249i
\(430\) −21.4663 12.3936i −0.0499216 0.0288223i
\(431\) 21.7871 37.7363i 0.0505500 0.0875552i −0.839643 0.543138i \(-0.817236\pi\)
0.890193 + 0.455583i \(0.150569\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 304.620i 0.703509i −0.936092 0.351755i \(-0.885585\pi\)
0.936092 0.351755i \(-0.114415\pi\)
\(434\) 10.6601 + 228.919i 0.0245624 + 0.527464i
\(435\) 108.103 0.248513
\(436\) 151.715 + 262.778i 0.347970 + 0.602702i
\(437\) −330.360 190.734i −0.755974 0.436462i
\(438\) −48.4465 + 83.9118i −0.110608 + 0.191579i
\(439\) −539.136 + 311.270i −1.22810 + 0.709044i −0.966632 0.256168i \(-0.917540\pi\)
−0.261468 + 0.965212i \(0.584207\pi\)
\(440\) 77.1067i 0.175242i
\(441\) 85.0127 + 119.924i 0.192773 + 0.271937i
\(442\) 1033.37 2.33793
\(443\) 42.8024 + 74.1360i 0.0966195 + 0.167350i 0.910283 0.413986i \(-0.135864\pi\)
−0.813664 + 0.581336i \(0.802530\pi\)
\(444\) 87.1923 + 50.3405i 0.196379 + 0.113380i
\(445\) −161.252 + 279.297i −0.362364 + 0.627633i
\(446\) −36.8049 + 21.2493i −0.0825222 + 0.0476442i
\(447\) 247.990i 0.554788i
\(448\) 55.9394 2.60493i 0.124865 0.00581457i
\(449\) −143.625 −0.319876 −0.159938 0.987127i \(-0.551129\pi\)
−0.159938 + 0.987127i \(0.551129\pi\)
\(450\) 10.6066 + 18.3712i 0.0235702 + 0.0408248i
\(451\) 600.834 + 346.892i 1.33223 + 0.769161i
\(452\) 42.1910 73.0769i 0.0933429 0.161675i
\(453\) 69.5363 40.1468i 0.153502 0.0886243i
\(454\) 200.366i 0.441334i
\(455\) −214.535 334.607i −0.471506 0.735401i
\(456\) −78.7134 −0.172617
\(457\) 11.7226 + 20.3041i 0.0256512 + 0.0444292i 0.878566 0.477621i \(-0.158501\pi\)
−0.852915 + 0.522050i \(0.825167\pi\)
\(458\) −266.789 154.031i −0.582509 0.336312i
\(459\) −74.7589 + 129.486i −0.162873 + 0.282105i
\(460\) 91.9518 53.0884i 0.199895 0.115410i
\(461\) 170.444i 0.369728i 0.982764 + 0.184864i \(0.0591844\pi\)
−0.982764 + 0.184864i \(0.940816\pi\)
\(462\) 185.703 + 95.9872i 0.401954 + 0.207764i
\(463\) 475.871 1.02780 0.513899 0.857850i \(-0.328200\pi\)
0.513899 + 0.857850i \(0.328200\pi\)
\(464\) −55.8242 96.6904i −0.120311 0.208384i
\(465\) 77.6455 + 44.8286i 0.166980 + 0.0964057i
\(466\) −3.00658 + 5.20755i −0.00645189 + 0.0111750i
\(467\) −188.847 + 109.031i −0.404384 + 0.233471i −0.688374 0.725356i \(-0.741675\pi\)
0.283990 + 0.958827i \(0.408342\pi\)
\(468\) 152.363i 0.325562i
\(469\) 226.715 438.616i 0.483400 0.935215i
\(470\) 72.0767 0.153355
\(471\) −71.4553 123.764i −0.151710 0.262769i
\(472\) 176.431 + 101.863i 0.373795 + 0.215811i
\(473\) −47.7814 + 82.7598i −0.101018 + 0.174968i
\(474\) 116.242 67.1122i 0.245236 0.141587i
\(475\) 80.3365i 0.169130i
\(476\) 339.128 217.433i 0.712453 0.456793i
\(477\) −145.669 −0.305385
\(478\) 184.917 + 320.286i 0.386856 + 0.670055i
\(479\) −482.916 278.812i −1.00817 0.582070i −0.0975181 0.995234i \(-0.531090\pi\)
−0.910657 + 0.413164i \(0.864424\pi\)
\(480\) 10.9545 18.9737i 0.0228218 0.0395285i
\(481\) −639.170 + 369.025i −1.32883 + 0.767203i
\(482\) 141.279i 0.293111i
\(483\) −13.3900 287.543i −0.0277226 0.595327i
\(484\) 55.2719 0.114198
\(485\) 88.3224 + 152.979i 0.182108 + 0.315420i
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) 258.122 447.080i 0.530024 0.918029i −0.469362 0.883006i \(-0.655516\pi\)
0.999386 0.0350234i \(-0.0111506\pi\)
\(488\) −280.725 + 162.077i −0.575256 + 0.332124i
\(489\) 426.806i 0.872813i
\(490\) −140.811 64.6697i −0.287370 0.131979i
\(491\) 122.586 0.249666 0.124833 0.992178i \(-0.460161\pi\)
0.124833 + 0.992178i \(0.460161\pi\)
\(492\) −98.5650 170.720i −0.200335 0.346991i
\(493\) −695.559 401.581i −1.41087 0.814566i
\(494\) 288.507 499.709i 0.584022 1.01156i
\(495\) 70.8270 40.8920i 0.143085 0.0826101i
\(496\) 92.5976i 0.186689i
\(497\) 44.8565 2.08883i 0.0902544 0.00420287i
\(498\) 332.968 0.668610
\(499\) −187.525 324.802i −0.375801 0.650906i 0.614646 0.788803i \(-0.289299\pi\)
−0.990447 + 0.137897i \(0.955966\pi\)
\(500\) −19.3649 11.1803i −0.0387298 0.0223607i
\(501\) 248.885 431.081i 0.496776 0.860441i
\(502\) −306.875 + 177.175i −0.611306 + 0.352938i
\(503\) 303.836i 0.604048i −0.953300 0.302024i \(-0.902338\pi\)
0.953300 0.302024i \(-0.0976622\pi\)
\(504\) −32.0591 50.0021i −0.0636094 0.0992106i
\(505\) 104.500 0.206931
\(506\) −204.673 354.505i −0.404493 0.700602i
\(507\) 713.771 + 412.096i 1.40783 + 0.812812i
\(508\) −49.3159 + 85.4176i −0.0970784 + 0.168145i
\(509\) −161.864 + 93.4522i −0.318004 + 0.183600i −0.650503 0.759504i \(-0.725442\pi\)
0.332499 + 0.943104i \(0.392108\pi\)
\(510\) 157.606i 0.309030i
\(511\) −245.978 127.143i −0.481367 0.248812i
\(512\) −22.6274 −0.0441942
\(513\) 41.7441 + 72.3029i 0.0813725 + 0.140941i
\(514\) 213.915 + 123.504i 0.416177 + 0.240280i
\(515\) 185.932 322.044i 0.361033 0.625328i
\(516\) 23.5152 13.5765i 0.0455720 0.0263110i
\(517\) 277.880i 0.537485i
\(518\) −132.114 + 255.595i −0.255046 + 0.493427i
\(519\) −473.801 −0.912912
\(520\) 80.3024 + 139.088i 0.154428 + 0.267477i
\(521\) 518.758 + 299.505i 0.995697 + 0.574866i 0.906972 0.421190i \(-0.138388\pi\)
0.0887246 + 0.996056i \(0.471721\pi\)
\(522\) −59.2105 + 102.556i −0.113430 + 0.196467i
\(523\) 132.497 76.4975i 0.253341 0.146267i −0.367952 0.929845i \(-0.619941\pi\)
0.621293 + 0.783578i \(0.286608\pi\)
\(524\) 29.3045i 0.0559246i
\(525\) −51.0332 + 32.7202i −0.0972061 + 0.0623242i
\(526\) −29.5336 −0.0561475
\(527\) −333.059 576.875i −0.631990 1.09464i
\(528\) −73.1498 42.2331i −0.138541 0.0799869i
\(529\) −17.3376 + 30.0295i −0.0327742 + 0.0567666i
\(530\) 132.977 76.7742i 0.250900 0.144857i
\(531\) 216.083i 0.406937i
\(532\) −10.4635 224.699i −0.0196683 0.422366i
\(533\) 1445.07 2.71121
\(534\) −176.643 305.954i −0.330791 0.572948i
\(535\) −63.8686 36.8746i −0.119381 0.0689244i
\(536\) −99.7514 + 172.774i −0.186103 + 0.322340i
\(537\) −151.197 + 87.2936i −0.281558 + 0.162558i
\(538\) 0.417624i 0.000776253i
\(539\) −249.323 + 542.875i −0.462567 + 1.00719i
\(540\) −23.2379 −0.0430331
\(541\) −71.7086 124.203i −0.132548 0.229580i 0.792110 0.610378i \(-0.208983\pi\)
−0.924658 + 0.380798i \(0.875649\pi\)
\(542\) 401.836 + 232.000i 0.741394 + 0.428044i
\(543\) 117.040 202.720i 0.215544 0.373333i
\(544\) −140.967 + 81.3871i −0.259130 + 0.149609i
\(545\) 339.245i 0.622468i
\(546\) 434.942 20.2539i 0.796598 0.0370951i
\(547\) −103.778 −0.189721 −0.0948607 0.995491i \(-0.530241\pi\)
−0.0948607 + 0.995491i \(0.530241\pi\)
\(548\) 17.2212 + 29.8281i 0.0314256 + 0.0544308i
\(549\) 297.754 + 171.908i 0.542356 + 0.313129i
\(550\) −43.1039 + 74.6582i −0.0783708 + 0.135742i
\(551\) −388.388 + 224.236i −0.704879 + 0.406962i
\(552\) 116.311i 0.210708i
\(553\) 207.034 + 322.908i 0.374383 + 0.583920i
\(554\) 711.307 1.28395
\(555\) 56.2824 + 97.4840i 0.101410 + 0.175647i
\(556\) 54.1460 + 31.2612i 0.0973848 + 0.0562251i
\(557\) −412.613 + 714.666i −0.740777 + 1.28306i 0.211366 + 0.977407i \(0.432209\pi\)
−0.952142 + 0.305656i \(0.901124\pi\)
\(558\) −85.0564 + 49.1073i −0.152431 + 0.0880059i
\(559\) 199.047i 0.356076i
\(560\) 55.6193 + 28.7489i 0.0993201 + 0.0513372i
\(561\) −607.622 −1.08310
\(562\) 187.016 + 323.922i 0.332769 + 0.576373i
\(563\) 331.959 + 191.657i 0.589626 + 0.340421i 0.764949 0.644090i \(-0.222764\pi\)
−0.175324 + 0.984511i \(0.556097\pi\)
\(564\) −39.4780 + 68.3780i −0.0699965 + 0.121238i
\(565\) 81.7025 47.1710i 0.144606 0.0834884i
\(566\) 652.872i 1.15348i
\(567\) −28.9280 + 55.9658i −0.0510194 + 0.0987051i
\(568\) −18.1444 −0.0319443
\(569\) −377.462 653.783i −0.663377 1.14900i −0.979723 0.200359i \(-0.935789\pi\)
0.316345 0.948644i \(-0.397544\pi\)
\(570\) −76.2139 44.0021i −0.133709 0.0771967i
\(571\) 345.652 598.687i 0.605346 1.04849i −0.386651 0.922226i \(-0.626368\pi\)
0.991997 0.126263i \(-0.0402984\pi\)
\(572\) 536.230 309.592i 0.937465 0.541245i
\(573\) 308.618i 0.538600i
\(574\) 474.241 304.062i 0.826204 0.529725i
\(575\) 118.709 0.206451
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 338.973 + 195.706i 0.587476 + 0.339179i 0.764099 0.645099i \(-0.223184\pi\)
−0.176623 + 0.984279i \(0.556517\pi\)
\(578\) −381.119 + 660.117i −0.659375 + 1.14207i
\(579\) 202.673 117.013i 0.350040 0.202096i
\(580\) 124.827i 0.215218i
\(581\) 44.2621 + 950.505i 0.0761826 + 1.63598i
\(582\) −193.505 −0.332482
\(583\) −295.990 512.670i −0.507702 0.879365i
\(584\) 96.8930 + 55.9412i 0.165913 + 0.0957897i
\(585\) 85.1735 147.525i 0.145596 0.252179i
\(586\) −165.081 + 95.3095i −0.281708 + 0.162644i
\(587\) 1027.13i 1.74979i −0.484312 0.874896i \(-0.660930\pi\)
0.484312 0.874896i \(-0.339070\pi\)
\(588\) 138.477 98.1643i 0.235504 0.166946i
\(589\) −371.949 −0.631492
\(590\) 113.886 + 197.256i 0.193027 + 0.334332i
\(591\) −97.1294 56.0777i −0.164347 0.0948861i
\(592\) 58.1282 100.681i 0.0981896 0.170069i
\(593\) 116.894 67.4886i 0.197123 0.113809i −0.398190 0.917303i \(-0.630362\pi\)
0.595313 + 0.803494i \(0.297028\pi\)
\(594\) 89.5899i 0.150825i
\(595\) 449.908 20.9508i 0.756147 0.0352115i
\(596\) −286.354 −0.480460
\(597\) −116.757 202.229i −0.195573 0.338742i
\(598\) −738.394 426.312i −1.23477 0.712897i
\(599\) 380.159 658.455i 0.634656 1.09926i −0.351932 0.936026i \(-0.614475\pi\)
0.986588 0.163231i \(-0.0521917\pi\)
\(600\) 21.2132 12.2474i 0.0353553 0.0204124i
\(601\) 604.796i 1.00632i 0.864194 + 0.503158i \(0.167829\pi\)
−0.864194 + 0.503158i \(0.832171\pi\)
\(602\) 41.8820 + 65.3227i 0.0695714 + 0.108509i
\(603\) 211.605 0.350920
\(604\) −46.3575 80.2936i −0.0767509 0.132936i
\(605\) 53.5168 + 30.8979i 0.0884575 + 0.0510710i
\(606\) −57.2372 + 99.1377i −0.0944508 + 0.163594i
\(607\) 11.2280 6.48250i 0.0184976 0.0106796i −0.490723 0.871316i \(-0.663267\pi\)
0.509220 + 0.860636i \(0.329934\pi\)
\(608\) 90.8904i 0.149491i
\(609\) −300.631 155.392i −0.493647 0.255159i
\(610\) −362.414 −0.594121
\(611\) −289.396 501.249i −0.473644 0.820375i
\(612\) 149.518 + 86.3241i 0.244310 + 0.141052i
\(613\) −566.514 + 981.231i −0.924167 + 1.60070i −0.131271 + 0.991347i \(0.541906\pi\)
−0.792896 + 0.609357i \(0.791428\pi\)
\(614\) −29.0555 + 16.7752i −0.0473217 + 0.0273212i
\(615\) 220.398i 0.358371i
\(616\) 110.836 214.431i 0.179929 0.348102i
\(617\) 19.5534 0.0316910 0.0158455 0.999874i \(-0.494956\pi\)
0.0158455 + 0.999874i \(0.494956\pi\)
\(618\) 203.679 + 352.782i 0.329577 + 0.570844i
\(619\) 574.387 + 331.623i 0.927928 + 0.535739i 0.886156 0.463388i \(-0.153366\pi\)
0.0417724 + 0.999127i \(0.486700\pi\)
\(620\) 51.7637 89.6573i 0.0834898 0.144609i
\(621\) 106.838 61.6831i 0.172042 0.0993287i
\(622\) 400.241i 0.643474i
\(623\) 849.908 544.923i 1.36422 0.874676i
\(624\) −175.934 −0.281945
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 519.754 + 300.080i 0.830279 + 0.479362i
\(627\) −169.643 + 293.830i −0.270563 + 0.468628i
\(628\) −142.911 + 82.5095i −0.227565 + 0.131385i
\(629\) 836.311i 1.32959i
\(630\) −3.08906 66.3359i −0.00490327 0.105295i
\(631\) −303.828 −0.481503 −0.240752 0.970587i \(-0.577394\pi\)
−0.240752 + 0.970587i \(0.577394\pi\)
\(632\) −77.4945 134.224i −0.122618 0.212380i
\(633\) 174.528 + 100.764i 0.275716 + 0.159185i
\(634\) −19.8896 + 34.4498i −0.0313716 + 0.0543372i
\(635\) −95.4997 + 55.1368i −0.150393 + 0.0868296i
\(636\) 168.204i 0.264471i
\(637\) 115.636 + 1238.91i 0.181532 + 1.94492i
\(638\) −481.249 −0.754308
\(639\) 9.62251 + 16.6667i 0.0150587 + 0.0260824i
\(640\) −21.9089 12.6491i −0.0342327 0.0197642i
\(641\) 470.134 814.296i 0.733439 1.27035i −0.221967 0.975054i \(-0.571248\pi\)
0.955405 0.295298i \(-0.0954191\pi\)
\(642\) 69.9646 40.3941i 0.108979 0.0629191i
\(643\) 1143.40i 1.77823i 0.457681 + 0.889116i \(0.348680\pi\)
−0.457681 + 0.889116i \(0.651320\pi\)
\(644\) −332.026 + 15.4614i −0.515568 + 0.0240084i
\(645\) 30.3579 0.0470666
\(646\) 326.918 + 566.239i 0.506065 + 0.876530i
\(647\) 790.146 + 456.191i 1.22125 + 0.705087i 0.965184 0.261573i \(-0.0842413\pi\)
0.256063 + 0.966660i \(0.417575\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) 760.488 439.068i 1.17178 0.676530i
\(650\) 179.562i 0.276249i
\(651\) −151.491 236.278i −0.232705 0.362946i
\(652\) −492.833 −0.755879
\(653\) −109.628 189.881i −0.167884 0.290783i 0.769792 0.638295i \(-0.220360\pi\)
−0.937676 + 0.347512i \(0.887027\pi\)
\(654\) −321.836 185.812i −0.492104 0.284116i
\(655\) 16.3817 28.3739i 0.0250102 0.0433190i
\(656\) −197.130 + 113.813i −0.300503 + 0.173495i
\(657\) 118.669i 0.180623i
\(658\) −200.443 103.606i −0.304624 0.157456i
\(659\) 661.525 1.00383 0.501916 0.864916i \(-0.332629\pi\)
0.501916 + 0.864916i \(0.332629\pi\)
\(660\) −47.2180 81.7840i −0.0715424 0.123915i
\(661\) −481.878 278.212i −0.729013 0.420896i 0.0890478 0.996027i \(-0.471618\pi\)
−0.818061 + 0.575131i \(0.804951\pi\)
\(662\) 185.178 320.737i 0.279724 0.484497i
\(663\) −1096.05 + 632.805i −1.65317 + 0.954457i
\(664\) 384.478i 0.579033i
\(665\) 115.479 223.413i 0.173653 0.335959i
\(666\) −123.309 −0.185148
\(667\) 331.342 + 573.902i 0.496765 + 0.860423i
\(668\) −497.770 287.387i −0.745164 0.430221i
\(669\) 26.0250 45.0766i 0.0389014 0.0673791i
\(670\) −193.168 + 111.525i −0.288310 + 0.166456i
\(671\) 1397.23i 2.08231i
\(672\) −57.7375 + 37.0187i −0.0859189 + 0.0550873i
\(673\) −153.903 −0.228682 −0.114341 0.993442i \(-0.536476\pi\)
−0.114341 + 0.993442i \(0.536476\pi\)
\(674\) −381.837 661.360i −0.566523 0.981247i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) 475.847 824.191i 0.703916 1.21922i
\(677\) −362.794 + 209.459i −0.535886 + 0.309394i −0.743410 0.668836i \(-0.766793\pi\)
0.207524 + 0.978230i \(0.433459\pi\)
\(678\) 103.346i 0.152428i
\(679\) −25.7230 552.387i −0.0378836 0.813530i
\(680\) −181.987 −0.267628
\(681\) −122.698 212.520i −0.180174 0.312070i
\(682\) −345.659 199.566i −0.506831 0.292619i
\(683\) −614.628 + 1064.57i −0.899895 + 1.55866i −0.0722678 + 0.997385i \(0.523024\pi\)
−0.827627 + 0.561278i \(0.810310\pi\)
\(684\) 83.4882 48.2019i 0.122059 0.0704706i
\(685\) 38.5079i 0.0562158i
\(686\) 298.632 + 382.252i 0.435324 + 0.557219i
\(687\) 377.297 0.549195
\(688\) −15.6768 27.1530i −0.0227860 0.0394665i
\(689\) −1067.84 616.515i −1.54983 0.894797i
\(690\) −65.0197 + 112.617i −0.0942315 + 0.163214i
\(691\) 314.293 181.457i 0.454838 0.262601i −0.255033 0.966932i \(-0.582086\pi\)
0.709871 + 0.704331i \(0.248753\pi\)
\(692\) 547.099i 0.790605i
\(693\) −255.747 + 11.9094i −0.369044 + 0.0171852i
\(694\) 56.3628 0.0812144
\(695\) 34.9511 + 60.5370i 0.0502893 + 0.0871036i
\(696\) 118.421 + 68.3704i 0.170145 + 0.0982333i
\(697\) −818.734 + 1418.09i −1.17465 + 2.03456i
\(698\) −399.267 + 230.517i −0.572016 + 0.330254i
\(699\) 7.36459i 0.0105359i
\(700\) 37.7820 + 58.9281i 0.0539743 + 0.0841830i
\(701\) −319.012 −0.455081 −0.227541 0.973769i \(-0.573068\pi\)
−0.227541 + 0.973769i \(0.573068\pi\)
\(702\) 93.3029 + 161.605i 0.132910 + 0.230207i
\(703\) −404.418 233.491i −0.575275 0.332135i
\(704\) −48.7665 + 84.4661i −0.0692707 + 0.119980i
\(705\) −76.4489 + 44.1378i −0.108438 + 0.0626068i
\(706\) 206.581i 0.292608i
\(707\) −290.612 150.213i −0.411049 0.212466i
\(708\) −249.512 −0.352417
\(709\) −565.639 979.716i −0.797799 1.38183i −0.921047 0.389452i \(-0.872664\pi\)
0.123248 0.992376i \(-0.460669\pi\)
\(710\) −17.5682 10.1430i −0.0247440 0.0142859i
\(711\) −82.1954 + 142.367i −0.115605 + 0.200234i
\(712\) −353.285 + 203.969i −0.496187 + 0.286474i
\(713\) 549.610i 0.770841i
\(714\) −226.549 + 438.295i −0.317295 + 0.613859i
\(715\) 692.270 0.968209
\(716\) 100.798 + 174.587i 0.140779 + 0.243837i
\(717\) −392.269 226.477i −0.547097 0.315867i
\(718\) 15.2431 26.4018i 0.0212300 0.0367714i
\(719\) −243.094 + 140.350i −0.338100 + 0.195202i −0.659431 0.751765i \(-0.729203\pi\)
0.321332 + 0.946967i \(0.395870\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −979.991 + 628.326i −1.35921 + 0.871464i
\(722\) −145.440 −0.201441
\(723\) 86.5156 + 149.849i 0.119662 + 0.207261i
\(724\) −234.081 135.147i −0.323316 0.186667i
\(725\) 69.7803 120.863i 0.0962486 0.166708i
\(726\) −58.6247 + 33.8470i −0.0807503 + 0.0466212i
\(727\) 737.233i 1.01408i −0.861924 0.507038i \(-0.830740\pi\)
0.861924 0.507038i \(-0.169260\pi\)
\(728\) −23.3872 502.228i −0.0321253 0.689874i
\(729\) −27.0000 −0.0370370
\(730\) 62.5442 + 108.330i 0.0856769 + 0.148397i
\(731\) −195.330 112.774i −0.267209 0.154273i
\(732\) 198.502 343.816i 0.271178 0.469694i
\(733\) 1172.96 677.208i 1.60022 0.923886i 0.608775 0.793343i \(-0.291661\pi\)
0.991443 0.130543i \(-0.0416719\pi\)
\(734\) 288.997i 0.393728i
\(735\) 188.955 17.6364i 0.257082 0.0239950i
\(736\) 134.304 0.182478
\(737\) 429.968 + 744.726i 0.583403 + 1.01048i
\(738\) 209.088 + 120.717i 0.283317 + 0.163573i
\(739\) −2.66286 + 4.61222i −0.00360333 + 0.00624116i −0.867821 0.496876i \(-0.834480\pi\)
0.864218 + 0.503117i \(0.167814\pi\)
\(740\) 112.565 64.9893i 0.152115 0.0878234i
\(741\) 706.695i 0.953704i
\(742\) −480.162 + 22.3597i −0.647119 + 0.0301343i
\(743\) 58.3655 0.0785539 0.0392769 0.999228i \(-0.487495\pi\)
0.0392769 + 0.999228i \(0.487495\pi\)
\(744\) 56.7042 + 98.2146i 0.0762154 + 0.132009i
\(745\) −277.261 160.077i −0.372163 0.214868i
\(746\) 398.287 689.854i 0.533897 0.924737i
\(747\) −353.166 + 203.900i −0.472779 + 0.272959i
\(748\) 701.621i 0.937996i
\(749\) 124.611 + 194.354i 0.166370 + 0.259485i
\(750\) 27.3861 0.0365148
\(751\) −139.145 241.006i −0.185279 0.320913i 0.758391 0.651800i \(-0.225986\pi\)
−0.943671 + 0.330886i \(0.892652\pi\)
\(752\) 78.9561 + 45.5853i 0.104995 + 0.0606188i
\(753\) 216.994 375.844i 0.288172 0.499129i
\(754\) −868.094 + 501.194i −1.15132 + 0.664714i
\(755\) 103.659i 0.137296i
\(756\) 64.6238 + 33.4032i 0.0854812 + 0.0441841i
\(757\) −59.2916 −0.0783244 −0.0391622 0.999233i \(-0.512469\pi\)
−0.0391622 + 0.999233i \(0.512469\pi\)
\(758\) 212.586 + 368.209i 0.280456 + 0.485764i
\(759\) 434.178 + 250.673i 0.572039 + 0.330267i
\(760\) −50.8093 + 88.0042i −0.0668543 + 0.115795i
\(761\) 788.790 455.408i 1.03652 0.598434i 0.117673 0.993052i \(-0.462457\pi\)
0.918845 + 0.394619i \(0.129123\pi\)
\(762\) 120.799i 0.158528i
\(763\) 487.645 943.428i 0.639115 1.23647i
\(764\) 356.361 0.466441
\(765\) 96.5133 + 167.166i 0.126161 + 0.218518i
\(766\) −13.2164 7.63051i −0.0172538 0.00996150i
\(767\) 914.531 1584.01i 1.19235 2.06521i
\(768\) 24.0000 13.8564i 0.0312500 0.0180422i
\(769\) 660.381i 0.858753i −0.903126 0.429376i \(-0.858733\pi\)
0.903126 0.429376i \(-0.141267\pi\)
\(770\) 227.187 145.662i 0.295049 0.189172i