Properties

Label 210.3.l.b.127.2
Level 210
Weight 3
Character 210.127
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.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.2
Root \(-3.99135 - 3.99135i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.b.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.16484 - 2.76660i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.16484 - 2.76660i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(1.39824 + 6.93144i) q^{10} +17.6826 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-12.3956 + 12.3956i) q^{13} +3.74166i q^{14} +(8.48925 - 1.71249i) q^{15} -4.00000 q^{16} +(18.7246 + 18.7246i) q^{17} +(-3.00000 + 3.00000i) q^{18} +25.5476i q^{19} +(5.53321 - 8.32968i) q^{20} +4.58258 q^{21} +(-17.6826 - 17.6826i) q^{22} +(-5.90052 + 5.90052i) q^{23} +4.89898i q^{24} +(9.69181 + 23.0449i) q^{25} +24.7912 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -15.3647i q^{29} +(-10.2017 - 6.77677i) q^{30} +11.3491 q^{31} +(4.00000 + 4.00000i) q^{32} +(-21.6567 + 21.6567i) q^{33} -37.4492i q^{34} +(2.61586 + 12.9675i) q^{35} +6.00000 q^{36} +(25.5981 + 25.5981i) q^{37} +(25.5476 - 25.5476i) q^{38} -30.3629i q^{39} +(-13.8629 + 2.79648i) q^{40} +58.8283 q^{41} +(-4.58258 - 4.58258i) q^{42} +(0.282745 - 0.282745i) q^{43} +35.3653i q^{44} +(-8.29981 + 12.4945i) q^{45} +11.8010 q^{46} +(-48.6505 - 48.6505i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(13.3531 - 32.7367i) q^{50} -45.8657 q^{51} +(-24.7912 - 24.7912i) q^{52} +(3.93909 - 3.93909i) q^{53} -7.34847i q^{54} +(-73.6454 - 48.9209i) q^{55} -7.48331 q^{56} +(-31.2893 - 31.2893i) q^{57} +(-15.3647 + 15.3647i) q^{58} +86.2636i q^{59} +(3.42497 + 16.9785i) q^{60} +29.2079 q^{61} +(-11.3491 - 11.3491i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(85.9194 - 17.3320i) q^{65} +43.3135 q^{66} +(-65.7277 - 65.7277i) q^{67} +(-37.4492 + 37.4492i) q^{68} -14.4533i q^{69} +(10.3517 - 15.5834i) q^{70} +1.19194 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-87.0749 + 87.0749i) q^{73} -51.1963i q^{74} +(-40.0942 - 16.3542i) q^{75} -51.0953 q^{76} +(-33.0812 - 33.0812i) q^{77} +(-30.3629 + 30.3629i) q^{78} +55.0959i q^{79} +(16.6594 + 11.0664i) q^{80} -9.00000 q^{81} +(-58.8283 - 58.8283i) q^{82} +(-91.8012 + 91.8012i) q^{83} +9.16515i q^{84} +(-26.1814 - 129.788i) q^{85} -0.565490 q^{86} +(18.8178 + 18.8178i) q^{87} +(35.3653 - 35.3653i) q^{88} -103.966i q^{89} +(20.7943 - 4.19472i) q^{90} +46.3801 q^{91} +(-11.8010 - 11.8010i) q^{92} +(-13.8998 + 13.8998i) q^{93} +97.3010i q^{94} +(70.6802 - 106.402i) q^{95} -9.79796 q^{96} +(87.4734 + 87.4734i) q^{97} +(7.00000 - 7.00000i) q^{98} -53.0479i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.16484 2.76660i −0.832968 0.553321i
\(6\) 2.44949 0.408248
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 1.39824 + 6.93144i 0.139824 + 0.693144i
\(11\) 17.6826 1.60751 0.803757 0.594958i \(-0.202831\pi\)
0.803757 + 0.594958i \(0.202831\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −12.3956 + 12.3956i −0.953508 + 0.953508i −0.998966 0.0454585i \(-0.985525\pi\)
0.0454585 + 0.998966i \(0.485525\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 8.48925 1.71249i 0.565950 0.114166i
\(16\) −4.00000 −0.250000
\(17\) 18.7246 + 18.7246i 1.10145 + 1.10145i 0.994236 + 0.107210i \(0.0341918\pi\)
0.107210 + 0.994236i \(0.465808\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 25.5476i 1.34461i 0.740273 + 0.672306i \(0.234696\pi\)
−0.740273 + 0.672306i \(0.765304\pi\)
\(20\) 5.53321 8.32968i 0.276660 0.416484i
\(21\) 4.58258 0.218218
\(22\) −17.6826 17.6826i −0.803757 0.803757i
\(23\) −5.90052 + 5.90052i −0.256545 + 0.256545i −0.823647 0.567103i \(-0.808064\pi\)
0.567103 + 0.823647i \(0.308064\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 9.69181 + 23.0449i 0.387673 + 0.921797i
\(26\) 24.7912 0.953508
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 3.74166 3.74166i 0.133631 0.133631i
\(29\) 15.3647i 0.529816i −0.964274 0.264908i \(-0.914658\pi\)
0.964274 0.264908i \(-0.0853416\pi\)
\(30\) −10.2017 6.77677i −0.340058 0.225892i
\(31\) 11.3491 0.366102 0.183051 0.983103i \(-0.441403\pi\)
0.183051 + 0.983103i \(0.441403\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −21.6567 + 21.6567i −0.656265 + 0.656265i
\(34\) 37.4492i 1.10145i
\(35\) 2.61586 + 12.9675i 0.0747390 + 0.370501i
\(36\) 6.00000 0.166667
\(37\) 25.5981 + 25.5981i 0.691842 + 0.691842i 0.962637 0.270795i \(-0.0872866\pi\)
−0.270795 + 0.962637i \(0.587287\pi\)
\(38\) 25.5476 25.5476i 0.672306 0.672306i
\(39\) 30.3629i 0.778536i
\(40\) −13.8629 + 2.79648i −0.346572 + 0.0699119i
\(41\) 58.8283 1.43484 0.717418 0.696643i \(-0.245324\pi\)
0.717418 + 0.696643i \(0.245324\pi\)
\(42\) −4.58258 4.58258i −0.109109 0.109109i
\(43\) 0.282745 0.282745i 0.00657546 0.00657546i −0.703811 0.710387i \(-0.748520\pi\)
0.710387 + 0.703811i \(0.248520\pi\)
\(44\) 35.3653i 0.803757i
\(45\) −8.29981 + 12.4945i −0.184440 + 0.277656i
\(46\) 11.8010 0.256545
\(47\) −48.6505 48.6505i −1.03512 1.03512i −0.999361 0.0357569i \(-0.988616\pi\)
−0.0357569 0.999361i \(-0.511384\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) 13.3531 32.7367i 0.267062 0.654735i
\(51\) −45.8657 −0.899327
\(52\) −24.7912 24.7912i −0.476754 0.476754i
\(53\) 3.93909 3.93909i 0.0743224 0.0743224i −0.668968 0.743291i \(-0.733264\pi\)
0.743291 + 0.668968i \(0.233264\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −73.6454 48.9209i −1.33901 0.889470i
\(56\) −7.48331 −0.133631
\(57\) −31.2893 31.2893i −0.548936 0.548936i
\(58\) −15.3647 + 15.3647i −0.264908 + 0.264908i
\(59\) 86.2636i 1.46210i 0.682326 + 0.731048i \(0.260968\pi\)
−0.682326 + 0.731048i \(0.739032\pi\)
\(60\) 3.42497 + 16.9785i 0.0570828 + 0.282975i
\(61\) 29.2079 0.478818 0.239409 0.970919i \(-0.423046\pi\)
0.239409 + 0.970919i \(0.423046\pi\)
\(62\) −11.3491 11.3491i −0.183051 0.183051i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 85.9194 17.3320i 1.32184 0.266646i
\(66\) 43.3135 0.656265
\(67\) −65.7277 65.7277i −0.981010 0.981010i 0.0188133 0.999823i \(-0.494011\pi\)
−0.999823 + 0.0188133i \(0.994011\pi\)
\(68\) −37.4492 + 37.4492i −0.550723 + 0.550723i
\(69\) 14.4533i 0.209468i
\(70\) 10.3517 15.5834i 0.147881 0.222620i
\(71\) 1.19194 0.0167879 0.00839397 0.999965i \(-0.497328\pi\)
0.00839397 + 0.999965i \(0.497328\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −87.0749 + 87.0749i −1.19281 + 1.19281i −0.216531 + 0.976276i \(0.569474\pi\)
−0.976276 + 0.216531i \(0.930526\pi\)
\(74\) 51.1963i 0.691842i
\(75\) −40.0942 16.3542i −0.534589 0.218055i
\(76\) −51.0953 −0.672306
\(77\) −33.0812 33.0812i −0.429626 0.429626i
\(78\) −30.3629 + 30.3629i −0.389268 + 0.389268i
\(79\) 55.0959i 0.697417i 0.937231 + 0.348708i \(0.113380\pi\)
−0.937231 + 0.348708i \(0.886620\pi\)
\(80\) 16.6594 + 11.0664i 0.208242 + 0.138330i
\(81\) −9.00000 −0.111111
\(82\) −58.8283 58.8283i −0.717418 0.717418i
\(83\) −91.8012 + 91.8012i −1.10604 + 1.10604i −0.112372 + 0.993666i \(0.535845\pi\)
−0.993666 + 0.112372i \(0.964155\pi\)
\(84\) 9.16515i 0.109109i
\(85\) −26.1814 129.788i −0.308017 1.52692i
\(86\) −0.565490 −0.00657546
\(87\) 18.8178 + 18.8178i 0.216296 + 0.216296i
\(88\) 35.3653 35.3653i 0.401878 0.401878i
\(89\) 103.966i 1.16815i −0.811699 0.584076i \(-0.801457\pi\)
0.811699 0.584076i \(-0.198543\pi\)
\(90\) 20.7943 4.19472i 0.231048 0.0466079i
\(91\) 46.3801 0.509671
\(92\) −11.8010 11.8010i −0.128272 0.128272i
\(93\) −13.8998 + 13.8998i −0.149460 + 0.149460i
\(94\) 97.3010i 1.03512i
\(95\) 70.6802 106.402i 0.744002 1.12002i
\(96\) −9.79796 −0.102062
\(97\) 87.4734 + 87.4734i 0.901788 + 0.901788i 0.995591 0.0938032i \(-0.0299024\pi\)
−0.0938032 + 0.995591i \(0.529902\pi\)
\(98\) 7.00000 7.00000i 0.0714286 0.0714286i
\(99\) 53.0479i 0.535838i
\(100\) −46.0899 + 19.3836i −0.460899 + 0.193836i
\(101\) 5.82092 0.0576329 0.0288164 0.999585i \(-0.490826\pi\)
0.0288164 + 0.999585i \(0.490826\pi\)
\(102\) 45.8657 + 45.8657i 0.449664 + 0.449664i
\(103\) 60.7804 60.7804i 0.590101 0.590101i −0.347558 0.937659i \(-0.612989\pi\)
0.937659 + 0.347558i \(0.112989\pi\)
\(104\) 49.5824i 0.476754i
\(105\) −19.0857 12.6782i −0.181769 0.120744i
\(106\) −7.87818 −0.0743224
\(107\) 80.6808 + 80.6808i 0.754026 + 0.754026i 0.975228 0.221202i \(-0.0709981\pi\)
−0.221202 + 0.975228i \(0.570998\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 64.4450i 0.591238i 0.955306 + 0.295619i \(0.0955259\pi\)
−0.955306 + 0.295619i \(0.904474\pi\)
\(110\) 24.7246 + 122.566i 0.224769 + 1.11424i
\(111\) −62.7024 −0.564887
\(112\) 7.48331 + 7.48331i 0.0668153 + 0.0668153i
\(113\) 80.8773 80.8773i 0.715729 0.715729i −0.251999 0.967728i \(-0.581088\pi\)
0.967728 + 0.251999i \(0.0810880\pi\)
\(114\) 62.5787i 0.548936i
\(115\) 40.8992 8.25034i 0.355645 0.0717421i
\(116\) 30.7293 0.264908
\(117\) 37.1868 + 37.1868i 0.317836 + 0.317836i
\(118\) 86.2636 86.2636i 0.731048 0.731048i
\(119\) 70.0610i 0.588748i
\(120\) 13.5535 20.4035i 0.112946 0.170029i
\(121\) 191.676 1.58410
\(122\) −29.2079 29.2079i −0.239409 0.239409i
\(123\) −72.0496 + 72.0496i −0.585769 + 0.585769i
\(124\) 22.6983i 0.183051i
\(125\) 23.3913 122.792i 0.187130 0.982335i
\(126\) 11.2250 0.0890871
\(127\) 55.3737 + 55.3737i 0.436014 + 0.436014i 0.890668 0.454654i \(-0.150237\pi\)
−0.454654 + 0.890668i \(0.650237\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 0.692581i 0.00536884i
\(130\) −103.251 68.5874i −0.794242 0.527596i
\(131\) −69.2950 −0.528969 −0.264485 0.964390i \(-0.585202\pi\)
−0.264485 + 0.964390i \(0.585202\pi\)
\(132\) −43.3135 43.3135i −0.328132 0.328132i
\(133\) 47.7953 47.7953i 0.359363 0.359363i
\(134\) 131.455i 0.981010i
\(135\) −5.13746 25.4678i −0.0380552 0.188650i
\(136\) 74.8984 0.550723
\(137\) −29.0370 29.0370i −0.211949 0.211949i 0.593146 0.805095i \(-0.297886\pi\)
−0.805095 + 0.593146i \(0.797886\pi\)
\(138\) −14.4533 + 14.4533i −0.104734 + 0.104734i
\(139\) 80.1068i 0.576308i −0.957584 0.288154i \(-0.906958\pi\)
0.957584 0.288154i \(-0.0930415\pi\)
\(140\) −25.9351 + 5.23173i −0.185251 + 0.0373695i
\(141\) 119.169 0.845170
\(142\) −1.19194 1.19194i −0.00839397 0.00839397i
\(143\) −219.187 + 219.187i −1.53278 + 1.53278i
\(144\) 12.0000i 0.0833333i
\(145\) −42.5079 + 63.9914i −0.293158 + 0.441320i
\(146\) 174.150 1.19281
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) −51.1963 + 51.1963i −0.345921 + 0.345921i
\(149\) 216.650i 1.45403i 0.686624 + 0.727013i \(0.259092\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(150\) 23.7400 + 56.4483i 0.158267 + 0.376322i
\(151\) −170.036 −1.12607 −0.563033 0.826434i \(-0.690366\pi\)
−0.563033 + 0.826434i \(0.690366\pi\)
\(152\) 51.0953 + 51.0953i 0.336153 + 0.336153i
\(153\) 56.1738 56.1738i 0.367149 0.367149i
\(154\) 66.1624i 0.429626i
\(155\) −47.2674 31.3986i −0.304951 0.202572i
\(156\) 60.7258 0.389268
\(157\) 164.649 + 164.649i 1.04872 + 1.04872i 0.998751 + 0.0499682i \(0.0159120\pi\)
0.0499682 + 0.998751i \(0.484088\pi\)
\(158\) 55.0959 55.0959i 0.348708 0.348708i
\(159\) 9.64876i 0.0606840i
\(160\) −5.59295 27.7258i −0.0349560 0.173286i
\(161\) 22.0777 0.137129
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 104.632 104.632i 0.641912 0.641912i −0.309113 0.951025i \(-0.600032\pi\)
0.951025 + 0.309113i \(0.100032\pi\)
\(164\) 117.657i 0.717418i
\(165\) 150.112 30.2813i 0.909772 0.183523i
\(166\) 183.602 1.10604
\(167\) −215.324 215.324i −1.28937 1.28937i −0.935171 0.354196i \(-0.884754\pi\)
−0.354196 0.935171i \(-0.615246\pi\)
\(168\) 9.16515 9.16515i 0.0545545 0.0545545i
\(169\) 138.302i 0.818354i
\(170\) −103.607 + 155.970i −0.609453 + 0.917470i
\(171\) 76.6429 0.448204
\(172\) 0.565490 + 0.565490i 0.00328773 + 0.00328773i
\(173\) −50.4009 + 50.4009i −0.291334 + 0.291334i −0.837607 0.546273i \(-0.816046\pi\)
0.546273 + 0.837607i \(0.316046\pi\)
\(174\) 37.6356i 0.216296i
\(175\) 24.9814 61.2448i 0.142751 0.349970i
\(176\) −70.7306 −0.401878
\(177\) −105.651 105.651i −0.596898 0.596898i
\(178\) −103.966 + 103.966i −0.584076 + 0.584076i
\(179\) 21.2898i 0.118937i −0.998230 0.0594687i \(-0.981059\pi\)
0.998230 0.0594687i \(-0.0189406\pi\)
\(180\) −24.9891 16.5996i −0.138828 0.0922201i
\(181\) −22.7581 −0.125736 −0.0628678 0.998022i \(-0.520025\pi\)
−0.0628678 + 0.998022i \(0.520025\pi\)
\(182\) −46.3801 46.3801i −0.254836 0.254836i
\(183\) −35.7722 + 35.7722i −0.195476 + 0.195476i
\(184\) 23.6021i 0.128272i
\(185\) −35.7923 177.432i −0.193472 0.959093i
\(186\) 27.7996 0.149460
\(187\) 331.100 + 331.100i 1.77059 + 1.77059i
\(188\) 97.3010 97.3010i 0.517559 0.517559i
\(189\) 13.7477i 0.0727393i
\(190\) −177.082 + 35.7217i −0.932011 + 0.188009i
\(191\) −113.711 −0.595344 −0.297672 0.954668i \(-0.596210\pi\)
−0.297672 + 0.954668i \(0.596210\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 109.936 109.936i 0.569616 0.569616i −0.362405 0.932021i \(-0.618044\pi\)
0.932021 + 0.362405i \(0.118044\pi\)
\(194\) 174.947i 0.901788i
\(195\) −84.0021 + 126.457i −0.430780 + 0.648496i
\(196\) −14.0000 −0.0714286
\(197\) 82.2107 + 82.2107i 0.417313 + 0.417313i 0.884277 0.466963i \(-0.154652\pi\)
−0.466963 + 0.884277i \(0.654652\pi\)
\(198\) −53.0479 + 53.0479i −0.267919 + 0.267919i
\(199\) 232.689i 1.16929i 0.811289 + 0.584646i \(0.198766\pi\)
−0.811289 + 0.584646i \(0.801234\pi\)
\(200\) 65.4735 + 26.7062i 0.327367 + 0.133531i
\(201\) 160.999 0.800991
\(202\) −5.82092 5.82092i −0.0288164 0.0288164i
\(203\) −28.7447 + 28.7447i −0.141599 + 0.141599i
\(204\) 91.7314i 0.449664i
\(205\) −245.011 162.755i −1.19517 0.793925i
\(206\) −121.561 −0.590101
\(207\) 17.7016 + 17.7016i 0.0855148 + 0.0855148i
\(208\) 49.5824 49.5824i 0.238377 0.238377i
\(209\) 451.750i 2.16148i
\(210\) 6.40753 + 31.7639i 0.0305121 + 0.151257i
\(211\) −341.021 −1.61621 −0.808107 0.589035i \(-0.799508\pi\)
−0.808107 + 0.589035i \(0.799508\pi\)
\(212\) 7.87818 + 7.87818i 0.0371612 + 0.0371612i
\(213\) −1.45983 + 1.45983i −0.00685365 + 0.00685365i
\(214\) 161.362i 0.754026i
\(215\) −1.95983 + 0.395345i −0.00911549 + 0.00183881i
\(216\) 14.6969 0.0680414
\(217\) −21.2323 21.2323i −0.0978447 0.0978447i
\(218\) 64.4450 64.4450i 0.295619 0.295619i
\(219\) 213.289i 0.973923i
\(220\) 97.8417 147.291i 0.444735 0.669504i
\(221\) −464.205 −2.10048
\(222\) 62.7024 + 62.7024i 0.282443 + 0.282443i
\(223\) 118.521 118.521i 0.531482 0.531482i −0.389531 0.921013i \(-0.627363\pi\)
0.921013 + 0.389531i \(0.127363\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 69.1348 29.0754i 0.307266 0.129224i
\(226\) −161.755 −0.715729
\(227\) −1.59958 1.59958i −0.00704662 0.00704662i 0.703575 0.710621i \(-0.251586\pi\)
−0.710621 + 0.703575i \(0.751586\pi\)
\(228\) 62.5787 62.5787i 0.274468 0.274468i
\(229\) 59.2261i 0.258629i 0.991604 + 0.129315i \(0.0412777\pi\)
−0.991604 + 0.129315i \(0.958722\pi\)
\(230\) −49.1495 32.6488i −0.213693 0.141951i
\(231\) 81.0321 0.350788
\(232\) −30.7293 30.7293i −0.132454 0.132454i
\(233\) 266.052 266.052i 1.14185 1.14185i 0.153743 0.988111i \(-0.450867\pi\)
0.988111 0.153743i \(-0.0491327\pi\)
\(234\) 74.3736i 0.317836i
\(235\) 68.0250 + 337.218i 0.289468 + 1.43497i
\(236\) −172.527 −0.731048
\(237\) −67.4784 67.4784i −0.284719 0.284719i
\(238\) −70.0610 + 70.0610i −0.294374 + 0.294374i
\(239\) 420.919i 1.76117i −0.473890 0.880584i \(-0.657151\pi\)
0.473890 0.880584i \(-0.342849\pi\)
\(240\) −33.9570 + 6.84994i −0.141488 + 0.0285414i
\(241\) −347.574 −1.44222 −0.721108 0.692823i \(-0.756367\pi\)
−0.721108 + 0.692823i \(0.756367\pi\)
\(242\) −191.676 191.676i −0.792049 0.792049i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 58.4157i 0.239409i
\(245\) 19.3662 29.1539i 0.0790458 0.118995i
\(246\) 144.099 0.585769
\(247\) −316.678 316.678i −1.28210 1.28210i
\(248\) 22.6983 22.6983i 0.0915254 0.0915254i
\(249\) 224.866i 0.903076i
\(250\) −146.183 + 99.4006i −0.584733 + 0.397602i
\(251\) 175.106 0.697632 0.348816 0.937191i \(-0.386584\pi\)
0.348816 + 0.937191i \(0.386584\pi\)
\(252\) −11.2250 11.2250i −0.0445435 0.0445435i
\(253\) −104.337 + 104.337i −0.412399 + 0.412399i
\(254\) 110.747i 0.436014i
\(255\) 191.023 + 126.892i 0.749111 + 0.497616i
\(256\) 16.0000 0.0625000
\(257\) −227.773 227.773i −0.886275 0.886275i 0.107888 0.994163i \(-0.465591\pi\)
−0.994163 + 0.107888i \(0.965591\pi\)
\(258\) 0.692581 0.692581i 0.00268442 0.00268442i
\(259\) 95.7795i 0.369805i
\(260\) 34.6640 + 171.839i 0.133323 + 0.660919i
\(261\) −46.0940 −0.176605
\(262\) 69.2950 + 69.2950i 0.264485 + 0.264485i
\(263\) −37.9825 + 37.9825i −0.144420 + 0.144420i −0.775620 0.631200i \(-0.782563\pi\)
0.631200 + 0.775620i \(0.282563\pi\)
\(264\) 86.6269i 0.328132i
\(265\) −27.3036 + 5.50778i −0.103032 + 0.0207841i
\(266\) −95.5905 −0.359363
\(267\) 127.331 + 127.331i 0.476896 + 0.476896i
\(268\) 131.455 131.455i 0.490505 0.490505i
\(269\) 236.114i 0.877748i −0.898549 0.438874i \(-0.855377\pi\)
0.898549 0.438874i \(-0.144623\pi\)
\(270\) −20.3303 + 30.6052i −0.0752974 + 0.113353i
\(271\) 167.587 0.618404 0.309202 0.950996i \(-0.399938\pi\)
0.309202 + 0.950996i \(0.399938\pi\)
\(272\) −74.8984 74.8984i −0.275362 0.275362i
\(273\) −56.8038 + 56.8038i −0.208072 + 0.208072i
\(274\) 58.0741i 0.211949i
\(275\) 171.377 + 407.495i 0.623189 + 1.48180i
\(276\) 28.9065 0.104734
\(277\) 354.986 + 354.986i 1.28154 + 1.28154i 0.939793 + 0.341743i \(0.111017\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(278\) −80.1068 + 80.1068i −0.288154 + 0.288154i
\(279\) 34.0474i 0.122034i
\(280\) 31.1668 + 20.7034i 0.111310 + 0.0739406i
\(281\) 396.987 1.41277 0.706383 0.707829i \(-0.250326\pi\)
0.706383 + 0.707829i \(0.250326\pi\)
\(282\) −119.169 119.169i −0.422585 0.422585i
\(283\) 204.927 204.927i 0.724124 0.724124i −0.245319 0.969442i \(-0.578893\pi\)
0.969442 + 0.245319i \(0.0788926\pi\)
\(284\) 2.38389i 0.00839397i
\(285\) 43.7500 + 216.880i 0.153509 + 0.760984i
\(286\) 438.374 1.53278
\(287\) −110.058 110.058i −0.383476 0.383476i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 412.221i 1.42637i
\(290\) 106.499 21.4835i 0.367239 0.0740809i
\(291\) −214.265 −0.736306
\(292\) −174.150 174.150i −0.596404 0.596404i
\(293\) −320.724 + 320.724i −1.09462 + 1.09462i −0.0995946 + 0.995028i \(0.531755\pi\)
−0.995028 + 0.0995946i \(0.968245\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 238.657 359.274i 0.809008 1.21788i
\(296\) 102.393 0.345921
\(297\) 64.9702 + 64.9702i 0.218755 + 0.218755i
\(298\) 216.650 216.650i 0.727013 0.727013i
\(299\) 146.281i 0.489234i
\(300\) 32.7083 80.1883i 0.109028 0.267294i
\(301\) −1.05793 −0.00351473
\(302\) 170.036 + 170.036i 0.563033 + 0.563033i
\(303\) −7.12914 + 7.12914i −0.0235285 + 0.0235285i
\(304\) 102.191i 0.336153i
\(305\) −121.646 80.8066i −0.398840 0.264940i
\(306\) −112.348 −0.367149
\(307\) 33.1738 + 33.1738i 0.108058 + 0.108058i 0.759069 0.651011i \(-0.225655\pi\)
−0.651011 + 0.759069i \(0.725655\pi\)
\(308\) 66.1624 66.1624i 0.214813 0.214813i
\(309\) 148.881i 0.481815i
\(310\) 15.8688 + 78.6660i 0.0511897 + 0.253761i
\(311\) −31.4965 −0.101275 −0.0506375 0.998717i \(-0.516125\pi\)
−0.0506375 + 0.998717i \(0.516125\pi\)
\(312\) −60.7258 60.7258i −0.194634 0.194634i
\(313\) 117.156 117.156i 0.374299 0.374299i −0.494741 0.869040i \(-0.664737\pi\)
0.869040 + 0.494741i \(0.164737\pi\)
\(314\) 329.298i 1.04872i
\(315\) 38.9026 7.84759i 0.123500 0.0249130i
\(316\) −110.192 −0.348708
\(317\) 256.649 + 256.649i 0.809619 + 0.809619i 0.984576 0.174957i \(-0.0559788\pi\)
−0.174957 + 0.984576i \(0.555979\pi\)
\(318\) 9.64876 9.64876i 0.0303420 0.0303420i
\(319\) 271.688i 0.851686i
\(320\) −22.1328 + 33.3187i −0.0691651 + 0.104121i
\(321\) −197.627 −0.615659
\(322\) −22.0777 22.0777i −0.0685644 0.0685644i
\(323\) −478.369 + 478.369i −1.48102 + 1.48102i
\(324\) 18.0000i 0.0555556i
\(325\) −405.792 165.520i −1.24859 0.509292i
\(326\) −209.263 −0.641912
\(327\) −78.9287 78.9287i −0.241372 0.241372i
\(328\) 117.657 117.657i 0.358709 0.358709i
\(329\) 182.034i 0.553294i
\(330\) −180.394 119.831i −0.546648 0.363125i
\(331\) −536.093 −1.61962 −0.809809 0.586694i \(-0.800429\pi\)
−0.809809 + 0.586694i \(0.800429\pi\)
\(332\) −183.602 183.602i −0.553019 0.553019i
\(333\) 76.7944 76.7944i 0.230614 0.230614i
\(334\) 430.649i 1.28937i
\(335\) 91.9029 + 455.588i 0.274337 + 1.35996i
\(336\) −18.3303 −0.0545545
\(337\) 147.571 + 147.571i 0.437896 + 0.437896i 0.891304 0.453407i \(-0.149792\pi\)
−0.453407 + 0.891304i \(0.649792\pi\)
\(338\) −138.302 + 138.302i −0.409177 + 0.409177i
\(339\) 198.108i 0.584390i
\(340\) 259.577 52.3629i 0.763462 0.154008i
\(341\) 200.683 0.588513
\(342\) −76.6429 76.6429i −0.224102 0.224102i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 1.13098i 0.00328773i
\(345\) −39.9865 + 60.1956i −0.115903 + 0.174480i
\(346\) 100.802 0.291334
\(347\) 53.7981 + 53.7981i 0.155038 + 0.155038i 0.780364 0.625326i \(-0.215034\pi\)
−0.625326 + 0.780364i \(0.715034\pi\)
\(348\) −37.6356 + 37.6356i −0.108148 + 0.108148i
\(349\) 71.8031i 0.205740i 0.994695 + 0.102870i \(0.0328025\pi\)
−0.994695 + 0.102870i \(0.967197\pi\)
\(350\) −86.2262 + 36.2634i −0.246361 + 0.103610i
\(351\) −91.0887 −0.259512
\(352\) 70.7306 + 70.7306i 0.200939 + 0.200939i
\(353\) 114.588 114.588i 0.324612 0.324612i −0.525921 0.850533i \(-0.676279\pi\)
0.850533 + 0.525921i \(0.176279\pi\)
\(354\) 211.302i 0.596898i
\(355\) −4.96426 3.29764i −0.0139838 0.00928912i
\(356\) 207.931 0.584076
\(357\) 85.8069 + 85.8069i 0.240355 + 0.240355i
\(358\) −21.2898 + 21.2898i −0.0594687 + 0.0594687i
\(359\) 60.5664i 0.168709i 0.996436 + 0.0843543i \(0.0268828\pi\)
−0.996436 + 0.0843543i \(0.973117\pi\)
\(360\) 8.38943 + 41.5887i 0.0233040 + 0.115524i
\(361\) −291.682 −0.807983
\(362\) 22.7581 + 22.7581i 0.0628678 + 0.0628678i
\(363\) −234.754 + 234.754i −0.646706 + 0.646706i
\(364\) 92.7602i 0.254836i
\(365\) 603.555 121.751i 1.65358 0.333566i
\(366\) 71.5444 0.195476
\(367\) −18.4536 18.4536i −0.0502824 0.0502824i 0.681519 0.731801i \(-0.261320\pi\)
−0.731801 + 0.681519i \(0.761320\pi\)
\(368\) 23.6021 23.6021i 0.0641361 0.0641361i
\(369\) 176.485i 0.478279i
\(370\) −141.640 + 213.224i −0.382810 + 0.576282i
\(371\) −14.7387 −0.0397270
\(372\) −27.7996 27.7996i −0.0747302 0.0747302i
\(373\) 269.454 269.454i 0.722397 0.722397i −0.246696 0.969093i \(-0.579345\pi\)
0.969093 + 0.246696i \(0.0793448\pi\)
\(374\) 662.201i 1.77059i
\(375\) 121.740 + 179.037i 0.324641 + 0.477432i
\(376\) −194.602 −0.517559
\(377\) 190.454 + 190.454i 0.505184 + 0.505184i
\(378\) −13.7477 + 13.7477i −0.0363696 + 0.0363696i
\(379\) 10.4860i 0.0276676i 0.999904 + 0.0138338i \(0.00440357\pi\)
−0.999904 + 0.0138338i \(0.995596\pi\)
\(380\) 212.804 + 141.360i 0.560010 + 0.372001i
\(381\) −135.637 −0.356004
\(382\) 113.711 + 113.711i 0.297672 + 0.297672i
\(383\) 93.8346 93.8346i 0.244999 0.244999i −0.573916 0.818915i \(-0.694576\pi\)
0.818915 + 0.573916i \(0.194576\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 46.2554 + 229.301i 0.120144 + 0.595586i
\(386\) −219.872 −0.569616
\(387\) −0.848235 0.848235i −0.00219182 0.00219182i
\(388\) −174.947 + 174.947i −0.450894 + 0.450894i
\(389\) 130.485i 0.335437i −0.985835 0.167718i \(-0.946360\pi\)
0.985835 0.167718i \(-0.0536399\pi\)
\(390\) 210.459 42.4546i 0.539638 0.108858i
\(391\) −220.970 −0.565140
\(392\) 14.0000 + 14.0000i 0.0357143 + 0.0357143i
\(393\) 84.8686 84.8686i 0.215951 0.215951i
\(394\) 164.421i 0.417313i
\(395\) 152.429 229.466i 0.385895 0.580926i
\(396\) 106.096 0.267919
\(397\) 44.8845 + 44.8845i 0.113059 + 0.113059i 0.761373 0.648314i \(-0.224526\pi\)
−0.648314 + 0.761373i \(0.724526\pi\)
\(398\) 232.689 232.689i 0.584646 0.584646i
\(399\) 117.074i 0.293419i
\(400\) −38.7673 92.1797i −0.0969181 0.230449i
\(401\) 329.486 0.821660 0.410830 0.911712i \(-0.365239\pi\)
0.410830 + 0.911712i \(0.365239\pi\)
\(402\) −160.999 160.999i −0.400496 0.400496i
\(403\) −140.679 + 140.679i −0.349081 + 0.349081i
\(404\) 11.6418i 0.0288164i
\(405\) 37.4836 + 24.8994i 0.0925520 + 0.0614801i
\(406\) 57.4893 0.141599
\(407\) 452.643 + 452.643i 1.11214 + 1.11214i
\(408\) −91.7314 + 91.7314i −0.224832 + 0.224832i
\(409\) 388.439i 0.949730i −0.880059 0.474865i \(-0.842497\pi\)
0.880059 0.474865i \(-0.157503\pi\)
\(410\) 82.2560 + 407.765i 0.200624 + 0.994549i
\(411\) 71.1259 0.173056
\(412\) 121.561 + 121.561i 0.295051 + 0.295051i
\(413\) 161.384 161.384i 0.390761 0.390761i
\(414\) 35.4031i 0.0855148i
\(415\) 636.315 128.360i 1.53329 0.309301i
\(416\) −99.1648 −0.238377
\(417\) 98.1104 + 98.1104i 0.235277 + 0.235277i
\(418\) 451.750 451.750i 1.08074 1.08074i
\(419\) 268.553i 0.640937i 0.947259 + 0.320469i \(0.103840\pi\)
−0.947259 + 0.320469i \(0.896160\pi\)
\(420\) 25.3563 38.1714i 0.0603722 0.0908843i
\(421\) −680.092 −1.61542 −0.807710 0.589580i \(-0.799293\pi\)
−0.807710 + 0.589580i \(0.799293\pi\)
\(422\) 341.021 + 341.021i 0.808107 + 0.808107i
\(423\) −145.952 + 145.952i −0.345039 + 0.345039i
\(424\) 15.7564i 0.0371612i
\(425\) −250.032 + 612.982i −0.588310 + 1.44231i
\(426\) 2.91965 0.00685365
\(427\) −54.6429 54.6429i −0.127969 0.127969i
\(428\) −161.362 + 161.362i −0.377013 + 0.377013i
\(429\) 536.896i 1.25151i
\(430\) 2.35518 + 1.56449i 0.00547715 + 0.00363834i
\(431\) 451.123 1.04669 0.523344 0.852121i \(-0.324684\pi\)
0.523344 + 0.852121i \(0.324684\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −223.798 + 223.798i −0.516855 + 0.516855i −0.916618 0.399763i \(-0.869092\pi\)
0.399763 + 0.916618i \(0.369092\pi\)
\(434\) 42.4646i 0.0978447i
\(435\) −26.3118 130.435i −0.0604868 0.299849i
\(436\) −128.890 −0.295619
\(437\) −150.744 150.744i −0.344953 0.344953i
\(438\) −213.289 + 213.289i −0.486961 + 0.486961i
\(439\) 599.647i 1.36594i −0.730447 0.682969i \(-0.760688\pi\)
0.730447 0.682969i \(-0.239312\pi\)
\(440\) −245.133 + 49.4491i −0.557119 + 0.112384i
\(441\) 21.0000 0.0476190
\(442\) 464.205 + 464.205i 1.05024 + 1.05024i
\(443\) 212.227 212.227i 0.479068 0.479068i −0.425765 0.904834i \(-0.639995\pi\)
0.904834 + 0.425765i \(0.139995\pi\)
\(444\) 125.405i 0.282443i
\(445\) −287.631 + 433.000i −0.646362 + 0.973033i
\(446\) −237.041 −0.531482
\(447\) −265.341 265.341i −0.593604 0.593604i
\(448\) −14.9666 + 14.9666i −0.0334077 + 0.0334077i
\(449\) 69.3409i 0.154434i −0.997014 0.0772170i \(-0.975397\pi\)
0.997014 0.0772170i \(-0.0246034\pi\)
\(450\) −98.2102 40.0594i −0.218245 0.0890208i
\(451\) 1040.24 2.30652
\(452\) 161.755 + 161.755i 0.357864 + 0.357864i
\(453\) 208.251 208.251i 0.459715 0.459715i
\(454\) 3.19917i 0.00704662i
\(455\) −193.166 128.315i −0.424540 0.282012i
\(456\) −125.157 −0.274468
\(457\) −399.145 399.145i −0.873404 0.873404i 0.119438 0.992842i \(-0.461891\pi\)
−0.992842 + 0.119438i \(0.961891\pi\)
\(458\) 59.2261 59.2261i 0.129315 0.129315i
\(459\) 137.597i 0.299776i
\(460\) 16.5007 + 81.7983i 0.0358710 + 0.177822i
\(461\) 357.157 0.774743 0.387372 0.921924i \(-0.373383\pi\)
0.387372 + 0.921924i \(0.373383\pi\)
\(462\) −81.0321 81.0321i −0.175394 0.175394i
\(463\) 139.822 139.822i 0.301991 0.301991i −0.539801 0.841793i \(-0.681501\pi\)
0.841793 + 0.539801i \(0.181501\pi\)
\(464\) 61.4587i 0.132454i
\(465\) 96.3458 19.4352i 0.207195 0.0417962i
\(466\) −532.104 −1.14185
\(467\) −429.131 429.131i −0.918909 0.918909i 0.0780407 0.996950i \(-0.475134\pi\)
−0.996950 + 0.0780407i \(0.975134\pi\)
\(468\) −74.3736 + 74.3736i −0.158918 + 0.158918i
\(469\) 245.930i 0.524372i
\(470\) 269.193 405.243i 0.572752 0.862220i
\(471\) −403.306 −0.856276
\(472\) 172.527 + 172.527i 0.365524 + 0.365524i
\(473\) 4.99968 4.99968i 0.0105701 0.0105701i
\(474\) 134.957i 0.284719i
\(475\) −588.743 + 247.603i −1.23946 + 0.521269i
\(476\) 140.122 0.294374
\(477\) −11.8173 11.8173i −0.0247741 0.0247741i
\(478\) −420.919 + 420.919i −0.880584 + 0.880584i
\(479\) 524.078i 1.09411i −0.837097 0.547054i \(-0.815749\pi\)
0.837097 0.547054i \(-0.184251\pi\)
\(480\) 40.8069 + 27.1071i 0.0850145 + 0.0564731i
\(481\) −634.609 −1.31935
\(482\) 347.574 + 347.574i 0.721108 + 0.721108i
\(483\) −27.0396 + 27.0396i −0.0559826 + 0.0559826i
\(484\) 383.352i 0.792049i
\(485\) −122.309 606.317i −0.252183 1.25014i
\(486\) −22.0454 −0.0453609
\(487\) 234.249 + 234.249i 0.481005 + 0.481005i 0.905453 0.424447i \(-0.139532\pi\)
−0.424447 + 0.905453i \(0.639532\pi\)
\(488\) 58.4157 58.4157i 0.119704 0.119704i
\(489\) 256.294i 0.524119i
\(490\) −48.5201 + 9.78767i −0.0990206 + 0.0199748i
\(491\) 171.731 0.349758 0.174879 0.984590i \(-0.444046\pi\)
0.174879 + 0.984590i \(0.444046\pi\)
\(492\) −144.099 144.099i −0.292885 0.292885i
\(493\) 287.697 287.697i 0.583564 0.583564i
\(494\) 633.357i 1.28210i
\(495\) −146.763 + 220.936i −0.296490 + 0.446336i
\(496\) −45.3966 −0.0915254
\(497\) −2.22992 2.22992i −0.00448677 0.00448677i
\(498\) −224.866 + 224.866i −0.451538 + 0.451538i
\(499\) 507.901i 1.01784i −0.860814 0.508919i \(-0.830045\pi\)
0.860814 0.508919i \(-0.169955\pi\)
\(500\) 245.584 + 46.7826i 0.491168 + 0.0935652i
\(501\) 527.435 1.05276
\(502\) −175.106 175.106i −0.348816 0.348816i
\(503\) 409.302 409.302i 0.813722 0.813722i −0.171468 0.985190i \(-0.554851\pi\)
0.985190 + 0.171468i \(0.0548510\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −24.2432 16.1042i −0.0480064 0.0318895i
\(506\) 208.674 0.412399
\(507\) 169.384 + 169.384i 0.334092 + 0.334092i
\(508\) −110.747 + 110.747i −0.218007 + 0.218007i
\(509\) 762.148i 1.49734i −0.662941 0.748671i \(-0.730692\pi\)
0.662941 0.748671i \(-0.269308\pi\)
\(510\) −64.1312 317.916i −0.125747 0.623364i
\(511\) 325.805 0.637582
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −93.8680 + 93.8680i −0.182979 + 0.182979i
\(514\) 455.545i 0.886275i
\(515\) −421.296 + 84.9855i −0.818051 + 0.165020i
\(516\) −1.38516 −0.00268442
\(517\) −860.270 860.270i −1.66396 1.66396i
\(518\) −95.7795 + 95.7795i −0.184903 + 0.184903i
\(519\) 123.456i 0.237874i
\(520\) 137.175 206.503i 0.263798 0.397121i
\(521\) −870.243 −1.67033 −0.835166 0.549999i \(-0.814628\pi\)
−0.835166 + 0.549999i \(0.814628\pi\)
\(522\) 46.0940 + 46.0940i 0.0883027 + 0.0883027i
\(523\) 94.5185 94.5185i 0.180724 0.180724i −0.610947 0.791671i \(-0.709211\pi\)
0.791671 + 0.610947i \(0.209211\pi\)
\(524\) 138.590i 0.264485i
\(525\) 44.4135 + 105.605i 0.0845971 + 0.201153i
\(526\) 75.9650 0.144420
\(527\) 212.508 + 212.508i 0.403241 + 0.403241i
\(528\) 86.6269 86.6269i 0.164066 0.164066i
\(529\) 459.368i 0.868370i
\(530\) 32.8114 + 21.7958i 0.0619082 + 0.0411241i
\(531\) 258.791 0.487365
\(532\) 95.5905 + 95.5905i 0.179681 + 0.179681i
\(533\) −729.212 + 729.212i −1.36813 + 1.36813i
\(534\) 254.662i 0.476896i
\(535\) −112.811 559.234i −0.210862 1.04530i
\(536\) −262.911 −0.490505
\(537\) 26.0746 + 26.0746i 0.0485560 + 0.0485560i
\(538\) −236.114 + 236.114i −0.438874 + 0.438874i
\(539\) 123.779i 0.229645i
\(540\) 50.9355 10.2749i 0.0943250 0.0190276i
\(541\) −211.503 −0.390948 −0.195474 0.980709i \(-0.562624\pi\)
−0.195474 + 0.980709i \(0.562624\pi\)
\(542\) −167.587 167.587i −0.309202 0.309202i
\(543\) 27.8729 27.8729i 0.0513313 0.0513313i
\(544\) 149.797i 0.275362i
\(545\) 178.294 268.403i 0.327144 0.492483i
\(546\) 113.608 0.208072
\(547\) 76.5236 + 76.5236i 0.139897 + 0.139897i 0.773587 0.633690i \(-0.218461\pi\)
−0.633690 + 0.773587i \(0.718461\pi\)
\(548\) 58.0741 58.0741i 0.105975 0.105975i
\(549\) 87.6236i 0.159606i
\(550\) 236.118 578.872i 0.429306 1.05249i
\(551\) 392.531 0.712397
\(552\) −28.9065 28.9065i −0.0523669 0.0523669i
\(553\) 103.075 103.075i 0.186392 0.186392i
\(554\) 709.971i 1.28154i
\(555\) 261.146 + 173.473i 0.470533 + 0.312563i
\(556\) 160.214 0.288154
\(557\) 251.466 + 251.466i 0.451465 + 0.451465i 0.895841 0.444376i \(-0.146574\pi\)
−0.444376 + 0.895841i \(0.646574\pi\)
\(558\) −34.0474 + 34.0474i −0.0610169 + 0.0610169i
\(559\) 7.00959i 0.0125395i
\(560\) −10.4635 51.8702i −0.0186847 0.0926253i
\(561\) −811.027 −1.44568
\(562\) −396.987 396.987i −0.706383 0.706383i
\(563\) −89.8908 + 89.8908i −0.159664 + 0.159664i −0.782418 0.622754i \(-0.786014\pi\)
0.622754 + 0.782418i \(0.286014\pi\)
\(564\) 238.338i 0.422585i
\(565\) −560.597 + 113.086i −0.992207 + 0.200152i
\(566\) −409.854 −0.724124
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) 2.38389 2.38389i 0.00419699 0.00419699i
\(569\) 404.950i 0.711687i 0.934545 + 0.355844i \(0.115806\pi\)
−0.934545 + 0.355844i \(0.884194\pi\)
\(570\) 173.130 260.630i 0.303737 0.457246i
\(571\) 186.774 0.327099 0.163550 0.986535i \(-0.447706\pi\)
0.163550 + 0.986535i \(0.447706\pi\)
\(572\) −438.374 438.374i −0.766388 0.766388i
\(573\) 139.267 139.267i 0.243048 0.243048i
\(574\) 220.115i 0.383476i
\(575\) −193.164 78.7904i −0.335937 0.137027i
\(576\) −24.0000 −0.0416667
\(577\) −428.779 428.779i −0.743117 0.743117i 0.230059 0.973177i \(-0.426108\pi\)
−0.973177 + 0.230059i \(0.926108\pi\)
\(578\) 412.221 412.221i 0.713184 0.713184i
\(579\) 269.287i 0.465090i
\(580\) −127.983 85.0159i −0.220660 0.146579i
\(581\) 343.489 0.591202
\(582\) 214.265 + 214.265i 0.368153 + 0.368153i
\(583\) 69.6535 69.6535i 0.119474 0.119474i
\(584\) 348.300i 0.596404i
\(585\) −51.9960 257.758i −0.0888821 0.440612i
\(586\) 641.449 1.09462
\(587\) −278.861 278.861i −0.475061 0.475061i 0.428487 0.903548i \(-0.359047\pi\)
−0.903548 + 0.428487i \(0.859047\pi\)
\(588\) 17.1464 17.1464i 0.0291606 0.0291606i
\(589\) 289.944i 0.492265i
\(590\) −597.932 + 120.617i −1.01344 + 0.204436i
\(591\) −201.374 −0.340735
\(592\) −102.393 102.393i −0.172960 0.172960i
\(593\) 439.594 439.594i 0.741306 0.741306i −0.231523 0.972829i \(-0.574371\pi\)
0.972829 + 0.231523i \(0.0743710\pi\)
\(594\) 129.940i 0.218755i
\(595\) −193.831 + 291.793i −0.325766 + 0.490408i
\(596\) −433.300 −0.727013
\(597\) −284.985 284.985i −0.477361 0.477361i
\(598\) −146.281 + 146.281i −0.244617 + 0.244617i
\(599\) 782.181i 1.30581i −0.757439 0.652906i \(-0.773550\pi\)
0.757439 0.652906i \(-0.226450\pi\)
\(600\) −112.897 + 47.4800i −0.188161 + 0.0791333i
\(601\) 589.687 0.981177 0.490589 0.871391i \(-0.336782\pi\)
0.490589 + 0.871391i \(0.336782\pi\)
\(602\) 1.05793 + 1.05793i 0.00175737 + 0.00175737i
\(603\) −197.183 + 197.183i −0.327003 + 0.327003i
\(604\) 340.072i 0.563033i
\(605\) −798.300 530.291i −1.31950 0.876514i
\(606\) 14.2583 0.0235285
\(607\) −167.200 167.200i −0.275453 0.275453i 0.555838 0.831291i \(-0.312398\pi\)
−0.831291 + 0.555838i \(0.812398\pi\)
\(608\) −102.191 + 102.191i −0.168077 + 0.168077i
\(609\) 70.4097i 0.115615i
\(610\) 40.8396 + 202.453i 0.0669501 + 0.331890i
\(611\) 1206.10 1.97398
\(612\) 112.348 + 112.348i 0.183574 + 0.183574i
\(613\) −334.599 + 334.599i −0.545838 + 0.545838i −0.925234 0.379396i \(-0.876132\pi\)
0.379396 + 0.925234i \(0.376132\pi\)
\(614\) 66.3477i 0.108058i
\(615\) 499.408 100.743i 0.812046 0.163809i
\(616\) −132.325 −0.214813
\(617\) −79.8866 79.8866i −0.129476 0.129476i 0.639399 0.768875i \(-0.279183\pi\)
−0.768875 + 0.639399i \(0.779183\pi\)
\(618\) 148.881 148.881i 0.240908 0.240908i
\(619\) 415.380i 0.671050i 0.942031 + 0.335525i \(0.108914\pi\)
−0.942031 + 0.335525i \(0.891086\pi\)
\(620\) 62.7972 94.5348i 0.101286 0.152475i
\(621\) −43.3598 −0.0698226
\(622\) 31.4965 + 31.4965i 0.0506375 + 0.0506375i
\(623\) −194.502 + 194.502i −0.312202 + 0.312202i
\(624\) 121.452i 0.194634i
\(625\) −437.138 + 446.694i −0.699420 + 0.714711i
\(626\) −234.311 −0.374299
\(627\) −553.278 553.278i −0.882421 0.882421i
\(628\) −329.298 + 329.298i −0.524360 + 0.524360i
\(629\) 958.630i 1.52405i
\(630\) −46.7502 31.0550i −0.0742067 0.0492937i
\(631\) −452.429 −0.717002 −0.358501 0.933529i \(-0.616712\pi\)
−0.358501 + 0.933529i \(0.616712\pi\)
\(632\) 110.192 + 110.192i 0.174354 + 0.174354i
\(633\) 417.664 417.664i 0.659817 0.659817i
\(634\) 513.298i 0.809619i
\(635\) −77.4257 383.820i −0.121930 0.604441i
\(636\) −19.2975 −0.0303420
\(637\) −86.7692 86.7692i −0.136215 0.136215i
\(638\) −271.688 + 271.688i −0.425843 + 0.425843i
\(639\) 3.57583i 0.00559598i
\(640\) 55.4516 11.1859i 0.0866431 0.0174780i
\(641\) −333.271 −0.519924 −0.259962 0.965619i \(-0.583710\pi\)
−0.259962 + 0.965619i \(0.583710\pi\)
\(642\) 197.627 + 197.627i 0.307830 + 0.307830i
\(643\) 614.442 614.442i 0.955587 0.955587i −0.0434678 0.999055i \(-0.513841\pi\)
0.999055 + 0.0434678i \(0.0138406\pi\)
\(644\) 44.1555i 0.0685644i
\(645\) 1.91610 2.88449i 0.00297069 0.00447208i
\(646\) 956.738 1.48102
\(647\) 800.292 + 800.292i 1.23693 + 1.23693i 0.961250 + 0.275678i \(0.0889024\pi\)
0.275678 + 0.961250i \(0.411098\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 1525.37i 2.35034i
\(650\) 240.272 + 571.311i 0.369649 + 0.878941i
\(651\) 52.0083 0.0798899
\(652\) 209.263 + 209.263i 0.320956 + 0.320956i
\(653\) −327.250 + 327.250i −0.501148 + 0.501148i −0.911795 0.410647i \(-0.865303\pi\)
0.410647 + 0.911795i \(0.365303\pi\)
\(654\) 157.857i 0.241372i
\(655\) 288.603 + 191.712i 0.440615 + 0.292690i
\(656\) −235.313 −0.358709
\(657\) 261.225 + 261.225i 0.397602 + 0.397602i
\(658\) 182.034 182.034i 0.276647 0.276647i
\(659\) 1113.68i 1.68995i 0.534802 + 0.844977i \(0.320386\pi\)
−0.534802 + 0.844977i \(0.679614\pi\)
\(660\) 60.5625 + 300.225i 0.0917614 + 0.454886i
\(661\) −58.5883 −0.0886359 −0.0443179 0.999017i \(-0.514111\pi\)
−0.0443179 + 0.999017i \(0.514111\pi\)
\(662\) 536.093 + 536.093i 0.809809 + 0.809809i
\(663\) 568.533 568.533i 0.857516 0.857516i
\(664\) 367.205i 0.553019i
\(665\) −331.290 + 66.8292i −0.498181 + 0.100495i
\(666\) −153.589 −0.230614
\(667\) 90.6596 + 90.6596i 0.135921 + 0.135921i
\(668\) 430.649 430.649i 0.644684 0.644684i
\(669\) 290.315i 0.433954i
\(670\) 363.685 547.491i 0.542813 0.817150i
\(671\) 516.472 0.769706
\(672\) 18.3303 + 18.3303i 0.0272772 + 0.0272772i
\(673\) 544.810 544.810i 0.809524 0.809524i −0.175038 0.984562i \(-0.556005\pi\)
0.984562 + 0.175038i \(0.0560048\pi\)
\(674\) 295.142i 0.437896i
\(675\) −49.0625 + 120.282i −0.0726852 + 0.178196i
\(676\) 276.604 0.409177
\(677\) −654.528 654.528i −0.966807 0.966807i 0.0326593 0.999467i \(-0.489602\pi\)
−0.999467 + 0.0326593i \(0.989602\pi\)
\(678\) 198.108 198.108i 0.292195 0.292195i
\(679\) 327.295i 0.482026i
\(680\) −311.940 207.214i −0.458735 0.304727i
\(681\) 3.91816 0.00575354
\(682\) −200.683 200.683i −0.294257 0.294257i
\(683\) −378.585 + 378.585i −0.554298 + 0.554298i −0.927678 0.373381i \(-0.878199\pi\)
0.373381 + 0.927678i \(0.378199\pi\)
\(684\) 153.286i 0.224102i
\(685\) 40.6007 + 201.269i 0.0592711 + 0.293823i
\(686\) −26.1916 −0.0381802
\(687\) −72.5369 72.5369i −0.105585 0.105585i
\(688\) −1.13098 + 1.13098i −0.00164387 + 0.00164387i
\(689\) 97.6547i 0.141734i
\(690\) 100.182 20.2091i 0.145191 0.0292886i
\(691\) 612.032 0.885719 0.442859 0.896591i \(-0.353964\pi\)
0.442859 + 0.896591i \(0.353964\pi\)
\(692\) −100.802 100.802i −0.145667 0.145667i
\(693\) −99.2436 + 99.2436i −0.143209 + 0.143209i
\(694\) 107.596i 0.155038i
\(695\) −221.624 + 333.632i −0.318883 + 0.480046i
\(696\) 75.2712 0.108148
\(697\) 1101.54 + 1101.54i 1.58040 + 1.58040i
\(698\) 71.8031 71.8031i 0.102870 0.102870i
\(699\) 651.691i 0.932320i
\(700\) 122.490 + 49.9628i 0.174985 + 0.0713754i
\(701\) 351.130 0.500899 0.250450 0.968130i \(-0.419422\pi\)
0.250450 + 0.968130i \(0.419422\pi\)
\(702\) 91.0887 + 91.0887i 0.129756 + 0.129756i
\(703\) −653.972 + 653.972i −0.930259 + 0.930259i
\(704\) 141.461i 0.200939i
\(705\) −496.320 329.693i −0.704000 0.467650i
\(706\) −229.176 −0.324612
\(707\) −10.8899 10.8899i −0.0154030 0.0154030i
\(708\) 211.302 211.302i 0.298449 0.298449i
\(709\) 652.326i 0.920065i 0.887902 + 0.460033i \(0.152162\pi\)
−0.887902 + 0.460033i \(0.847838\pi\)
\(710\) 1.66662 + 8.26189i 0.00234735 + 0.0116365i
\(711\) 165.288 0.232472
\(712\) −207.931 207.931i −0.292038 0.292038i
\(713\) −66.9659 + 66.9659i −0.0939213 + 0.0939213i
\(714\) 171.614i 0.240355i
\(715\) 1519.28 306.476i 2.12487 0.428637i
\(716\) 42.5796 0.0594687
\(717\) 515.519 + 515.519i 0.718994 + 0.718994i
\(718\) 60.5664 60.5664i 0.0843543 0.0843543i
\(719\) 823.559i 1.14542i 0.819757 + 0.572711i \(0.194108\pi\)
−0.819757 + 0.572711i \(0.805892\pi\)
\(720\) 33.1992 49.9781i 0.0461101 0.0694140i
\(721\) −227.419 −0.315422
\(722\) 291.682 + 291.682i 0.403991 + 0.403991i
\(723\) 425.689 425.689i 0.588782 0.588782i
\(724\) 45.5163i 0.0628678i
\(725\) 354.078 148.911i 0.488383 0.205395i
\(726\) 469.508 0.646706
\(727\) −724.914 724.914i −0.997131 0.997131i 0.00286477 0.999996i \(-0.499088\pi\)
−0.999996 + 0.00286477i \(0.999088\pi\)
\(728\) 92.7602 92.7602i 0.127418 0.127418i
\(729\) 27.0000i 0.0370370i
\(730\) −725.306 481.804i −0.993571 0.660005i
\(731\) 10.5886 0.0144850
\(732\) −71.5444 71.5444i −0.0977382 0.0977382i
\(733\) 49.2582 49.2582i 0.0672008 0.0672008i −0.672708 0.739908i \(-0.734869\pi\)
0.739908 + 0.672708i \(0.234869\pi\)
\(734\) 36.9073i 0.0502824i
\(735\) 11.9874 + 59.4248i 0.0163094 + 0.0808500i
\(736\) −47.2042 −0.0641361
\(737\) −1162.24 1162.24i −1.57699 1.57699i
\(738\) −176.485 + 176.485i −0.239139 + 0.239139i
\(739\) 417.024i 0.564309i 0.959369 + 0.282154i \(0.0910490\pi\)
−0.959369 + 0.282154i \(0.908951\pi\)
\(740\) 354.864 71.5846i 0.479546 0.0967360i
\(741\) 775.700 1.04683
\(742\) 14.7387 + 14.7387i 0.0198635 + 0.0198635i
\(743\) −736.124 + 736.124i −0.990746 + 0.990746i −0.999958 0.00921142i \(-0.997068\pi\)
0.00921142 + 0.999958i \(0.497068\pi\)
\(744\) 55.5992i 0.0747302i
\(745\) 599.384 902.313i 0.804543 1.21116i
\(746\) −538.908 −0.722397
\(747\) 275.404 + 275.404i 0.368679 + 0.368679i
\(748\) −662.201 + 662.201i −0.885295 + 0.885295i
\(749\) 301.880i 0.403044i
\(750\) 57.2968 300.777i 0.0763957 0.401037i
\(751\) 1083.70 1.44301 0.721506 0.692409i \(-0.243450\pi\)
0.721506 + 0.692409i \(0.243450\pi\)
\(752\) 194.602 + 194.602i 0.258779 + 0.258779i
\(753\) −214.460 + 214.460i −0.284807 + 0.284807i
\(754\) 380.909i 0.505184i
\(755\) 708.173 + 470.422i 0.937978 + 0.623076i
\(756\) 27.4955 0.0363696
\(757\) 1002.25 + 1002.25i 1.32397 + 1.32397i 0.910532 + 0.413439i \(0.135672\pi\)
0.413439 + 0.910532i \(0.364328\pi\)
\(758\) 10.4860 10.4860i 0.0138338 0.0138338i
\(759\) 255.572i 0.336722i
\(760\) −71.4434 354.164i −0.0940044 0.466005i
\(761\) 1104.17 1.45095 0.725474 0.688250i \(-0.241621\pi\)
0.725474 + 0.688250i \(0.241621\pi\)
\(762\) 135.637 + 135.637i 0.178002 + 0.178002i
\(763\) 120.566 120.566i 0.158015 0.158015i
\(764\) 227.421i 0.297672i
\(765\) −389.365 + 78.5443i −0.508974 + 0.102672i
\(766\) −187.669 −0.244999
\(767\) −1069.29 1069.29i −1.39412 1.39412i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 198.908i 0.258658i −0.991602 0.129329i \(-0.958718\pi\)
0.991602 0.129329i \(-0.0412823\pi\)
\(770\) 183.045 275.556i 0.237721 0.357865i
\(771\) 557.927 0.723640
\(772\) 219.872 + 219.872i 0.284808 + 0.284808i
\(773\) 326.316