Properties

Label 690.3.k.a.277.13
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.13
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.72431 - 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 + 6.04624i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.72431 - 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 + 6.04624i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(7.06040 + 0.388220i) q^{10} +6.03072 q^{11} +(2.44949 + 2.44949i) q^{12} +(-0.224734 + 0.224734i) q^{13} +12.0925i q^{14} +(0.475470 - 8.64719i) q^{15} -4.00000 q^{16} +(3.58233 + 3.58233i) q^{17} +(3.00000 - 3.00000i) q^{18} +25.3766i q^{19} +(6.67218 + 7.44862i) q^{20} +14.8102 q^{21} +(6.03072 + 6.03072i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(2.74099 - 24.8493i) q^{25} -0.449468 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-12.0925 + 12.0925i) q^{28} -37.7718i q^{29} +(9.12266 - 8.17172i) q^{30} +11.5048 q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.38610 - 7.38610i) q^{33} +7.16467i q^{34} +(42.6889 + 2.34727i) q^{35} +6.00000 q^{36} +(20.7844 + 20.7844i) q^{37} +(-25.3766 + 25.3766i) q^{38} +0.550483i q^{39} +(-0.776439 + 14.1208i) q^{40} -24.7818 q^{41} +(14.8102 + 14.8102i) q^{42} +(-19.3473 + 19.3473i) q^{43} +12.0614i q^{44} +(-10.0083 - 11.1729i) q^{45} +6.78233 q^{46} +(5.86417 + 5.86417i) q^{47} +(-4.89898 + 4.89898i) q^{48} +24.1140i q^{49} +(27.5903 - 22.1083i) q^{50} +8.77489 q^{51} +(-0.449468 - 0.449468i) q^{52} +(33.5894 - 33.5894i) q^{53} -7.34847i q^{54} +(22.4603 - 20.1190i) q^{55} -24.1849 q^{56} +(31.0798 + 31.0798i) q^{57} +(37.7718 - 37.7718i) q^{58} -20.0519i q^{59} +(17.2944 + 0.950940i) q^{60} +10.4754 q^{61} +(11.5048 + 11.5048i) q^{62} +(18.1387 - 18.1387i) q^{63} -8.00000i q^{64} +(-0.0872461 + 1.58671i) q^{65} +14.7722 q^{66} +(22.9516 + 22.9516i) q^{67} +(-7.16467 + 7.16467i) q^{68} -8.30662i q^{69} +(40.3416 + 45.0361i) q^{70} +21.4134 q^{71} +(6.00000 + 6.00000i) q^{72} +(25.3312 - 25.3312i) q^{73} +41.5687i q^{74} +(-27.0770 - 33.7910i) q^{75} -50.7531 q^{76} +(36.4632 + 36.4632i) q^{77} +(-0.550483 + 0.550483i) q^{78} -8.78027i q^{79} +(-14.8972 + 13.3444i) q^{80} -9.00000 q^{81} +(-24.7818 - 24.7818i) q^{82} +(-47.9297 + 47.9297i) q^{83} +29.6204i q^{84} +(25.2927 + 1.39073i) q^{85} -38.6945 q^{86} +(-46.2608 - 46.2608i) q^{87} +(-12.0614 + 12.0614i) q^{88} +10.7360i q^{89} +(1.16466 - 21.1812i) q^{90} -2.71759 q^{91} +(6.78233 + 6.78233i) q^{92} +(14.0904 - 14.0904i) q^{93} +11.7283i q^{94} +(84.6586 + 94.5102i) q^{95} -9.79796 q^{96} +(-63.2192 - 63.2192i) q^{97} +(-24.1140 + 24.1140i) q^{98} -18.0922i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 3.72431 3.33609i 0.744862 0.667218i
\(6\) 2.44949 0.408248
\(7\) 6.04624 + 6.04624i 0.863748 + 0.863748i 0.991771 0.128023i \(-0.0408632\pi\)
−0.128023 + 0.991771i \(0.540863\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 7.06040 + 0.388220i 0.706040 + 0.0388220i
\(11\) 6.03072 0.548247 0.274124 0.961694i \(-0.411612\pi\)
0.274124 + 0.961694i \(0.411612\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −0.224734 + 0.224734i −0.0172872 + 0.0172872i −0.715698 0.698410i \(-0.753891\pi\)
0.698410 + 0.715698i \(0.253891\pi\)
\(14\) 12.0925i 0.863748i
\(15\) 0.475470 8.64719i 0.0316980 0.576479i
\(16\) −4.00000 −0.250000
\(17\) 3.58233 + 3.58233i 0.210725 + 0.210725i 0.804576 0.593850i \(-0.202393\pi\)
−0.593850 + 0.804576i \(0.702393\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 25.3766i 1.33561i 0.744337 + 0.667804i \(0.232766\pi\)
−0.744337 + 0.667804i \(0.767234\pi\)
\(20\) 6.67218 + 7.44862i 0.333609 + 0.372431i
\(21\) 14.8102 0.705247
\(22\) 6.03072 + 6.03072i 0.274124 + 0.274124i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 2.74099 24.8493i 0.109639 0.993971i
\(26\) −0.449468 −0.0172872
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −12.0925 + 12.0925i −0.431874 + 0.431874i
\(29\) 37.7718i 1.30248i −0.758874 0.651238i \(-0.774250\pi\)
0.758874 0.651238i \(-0.225750\pi\)
\(30\) 9.12266 8.17172i 0.304089 0.272391i
\(31\) 11.5048 0.371122 0.185561 0.982633i \(-0.440590\pi\)
0.185561 + 0.982633i \(0.440590\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 7.38610 7.38610i 0.223821 0.223821i
\(34\) 7.16467i 0.210725i
\(35\) 42.6889 + 2.34727i 1.21968 + 0.0670648i
\(36\) 6.00000 0.166667
\(37\) 20.7844 + 20.7844i 0.561739 + 0.561739i 0.929801 0.368062i \(-0.119979\pi\)
−0.368062 + 0.929801i \(0.619979\pi\)
\(38\) −25.3766 + 25.3766i −0.667804 + 0.667804i
\(39\) 0.550483i 0.0141150i
\(40\) −0.776439 + 14.1208i −0.0194110 + 0.353020i
\(41\) −24.7818 −0.604434 −0.302217 0.953239i \(-0.597727\pi\)
−0.302217 + 0.953239i \(0.597727\pi\)
\(42\) 14.8102 + 14.8102i 0.352624 + 0.352624i
\(43\) −19.3473 + 19.3473i −0.449937 + 0.449937i −0.895333 0.445397i \(-0.853063\pi\)
0.445397 + 0.895333i \(0.353063\pi\)
\(44\) 12.0614i 0.274124i
\(45\) −10.0083 11.1729i −0.222406 0.248287i
\(46\) 6.78233 0.147442
\(47\) 5.86417 + 5.86417i 0.124770 + 0.124770i 0.766734 0.641965i \(-0.221880\pi\)
−0.641965 + 0.766734i \(0.721880\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 24.1140i 0.492122i
\(50\) 27.5903 22.1083i 0.551805 0.442166i
\(51\) 8.77489 0.172057
\(52\) −0.449468 0.449468i −0.00864361 0.00864361i
\(53\) 33.5894 33.5894i 0.633763 0.633763i −0.315247 0.949010i \(-0.602087\pi\)
0.949010 + 0.315247i \(0.102087\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 22.4603 20.1190i 0.408369 0.365801i
\(56\) −24.1849 −0.431874
\(57\) 31.0798 + 31.0798i 0.545260 + 0.545260i
\(58\) 37.7718 37.7718i 0.651238 0.651238i
\(59\) 20.0519i 0.339863i −0.985456 0.169931i \(-0.945645\pi\)
0.985456 0.169931i \(-0.0543546\pi\)
\(60\) 17.2944 + 0.950940i 0.288240 + 0.0158490i
\(61\) 10.4754 0.171727 0.0858637 0.996307i \(-0.472635\pi\)
0.0858637 + 0.996307i \(0.472635\pi\)
\(62\) 11.5048 + 11.5048i 0.185561 + 0.185561i
\(63\) 18.1387 18.1387i 0.287916 0.287916i
\(64\) 8.00000i 0.125000i
\(65\) −0.0872461 + 1.58671i −0.00134225 + 0.0244109i
\(66\) 14.7722 0.223821
\(67\) 22.9516 + 22.9516i 0.342561 + 0.342561i 0.857329 0.514769i \(-0.172122\pi\)
−0.514769 + 0.857329i \(0.672122\pi\)
\(68\) −7.16467 + 7.16467i −0.105363 + 0.105363i
\(69\) 8.30662i 0.120386i
\(70\) 40.3416 + 45.0361i 0.576309 + 0.643373i
\(71\) 21.4134 0.301597 0.150799 0.988565i \(-0.451815\pi\)
0.150799 + 0.988565i \(0.451815\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 25.3312 25.3312i 0.347002 0.347002i −0.511989 0.858992i \(-0.671091\pi\)
0.858992 + 0.511989i \(0.171091\pi\)
\(74\) 41.5687i 0.561739i
\(75\) −27.0770 33.7910i −0.361027 0.450547i
\(76\) −50.7531 −0.667804
\(77\) 36.4632 + 36.4632i 0.473548 + 0.473548i
\(78\) −0.550483 + 0.550483i −0.00705748 + 0.00705748i
\(79\) 8.78027i 0.111143i −0.998455 0.0555713i \(-0.982302\pi\)
0.998455 0.0555713i \(-0.0176980\pi\)
\(80\) −14.8972 + 13.3444i −0.186216 + 0.166805i
\(81\) −9.00000 −0.111111
\(82\) −24.7818 24.7818i −0.302217 0.302217i
\(83\) −47.9297 + 47.9297i −0.577467 + 0.577467i −0.934204 0.356738i \(-0.883889\pi\)
0.356738 + 0.934204i \(0.383889\pi\)
\(84\) 29.6204i 0.352624i
\(85\) 25.2927 + 1.39073i 0.297561 + 0.0163615i
\(86\) −38.6945 −0.449937
\(87\) −46.2608 46.2608i −0.531733 0.531733i
\(88\) −12.0614 + 12.0614i −0.137062 + 0.137062i
\(89\) 10.7360i 0.120629i 0.998179 + 0.0603145i \(0.0192104\pi\)
−0.998179 + 0.0603145i \(0.980790\pi\)
\(90\) 1.16466 21.1812i 0.0129407 0.235347i
\(91\) −2.71759 −0.0298636
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 14.0904 14.0904i 0.151510 0.151510i
\(94\) 11.7283i 0.124770i
\(95\) 84.6586 + 94.5102i 0.891143 + 0.994845i
\(96\) −9.79796 −0.102062
\(97\) −63.2192 63.2192i −0.651745 0.651745i 0.301668 0.953413i \(-0.402456\pi\)
−0.953413 + 0.301668i \(0.902456\pi\)
\(98\) −24.1140 + 24.1140i −0.246061 + 0.246061i
\(99\) 18.0922i 0.182749i
\(100\) 49.6986 + 5.48197i 0.496986 + 0.0548197i
\(101\) −6.89640 −0.0682812 −0.0341406 0.999417i \(-0.510869\pi\)
−0.0341406 + 0.999417i \(0.510869\pi\)
\(102\) 8.77489 + 8.77489i 0.0860283 + 0.0860283i
\(103\) −88.5287 + 88.5287i −0.859502 + 0.859502i −0.991279 0.131777i \(-0.957932\pi\)
0.131777 + 0.991279i \(0.457932\pi\)
\(104\) 0.898935i 0.00864361i
\(105\) 55.1578 49.4082i 0.525312 0.470554i
\(106\) 67.1788 0.633763
\(107\) 87.3608 + 87.3608i 0.816456 + 0.816456i 0.985593 0.169137i \(-0.0540980\pi\)
−0.169137 + 0.985593i \(0.554098\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 8.33514i 0.0764692i −0.999269 0.0382346i \(-0.987827\pi\)
0.999269 0.0382346i \(-0.0121734\pi\)
\(110\) 42.5793 + 2.34124i 0.387085 + 0.0212840i
\(111\) 50.9111 0.458658
\(112\) −24.1849 24.1849i −0.215937 0.215937i
\(113\) −50.5727 + 50.5727i −0.447546 + 0.447546i −0.894538 0.446992i \(-0.852495\pi\)
0.446992 + 0.894538i \(0.352495\pi\)
\(114\) 62.1596i 0.545260i
\(115\) 1.31652 23.9430i 0.0114480 0.208200i
\(116\) 75.5436 0.651238
\(117\) 0.674201 + 0.674201i 0.00576240 + 0.00576240i
\(118\) 20.0519 20.0519i 0.169931 0.169931i
\(119\) 43.3193i 0.364027i
\(120\) 16.3434 + 18.2453i 0.136195 + 0.152044i
\(121\) −84.6304 −0.699425
\(122\) 10.4754 + 10.4754i 0.0858637 + 0.0858637i
\(123\) −30.3514 + 30.3514i −0.246759 + 0.246759i
\(124\) 23.0095i 0.185561i
\(125\) −72.6912 101.691i −0.581530 0.813525i
\(126\) 36.2774 0.287916
\(127\) −171.315 171.315i −1.34893 1.34893i −0.886822 0.462111i \(-0.847092\pi\)
−0.462111 0.886822i \(-0.652908\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 47.3910i 0.367372i
\(130\) −1.67396 + 1.49946i −0.0128766 + 0.0115343i
\(131\) −9.31847 −0.0711333 −0.0355667 0.999367i \(-0.511324\pi\)
−0.0355667 + 0.999367i \(0.511324\pi\)
\(132\) 14.7722 + 14.7722i 0.111911 + 0.111911i
\(133\) −153.433 + 153.433i −1.15363 + 1.15363i
\(134\) 45.9031i 0.342561i
\(135\) −25.9416 1.42641i −0.192160 0.0105660i
\(136\) −14.3293 −0.105363
\(137\) −108.397 108.397i −0.791218 0.791218i 0.190474 0.981692i \(-0.438997\pi\)
−0.981692 + 0.190474i \(0.938997\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 126.720i 0.911653i −0.890069 0.455827i \(-0.849344\pi\)
0.890069 0.455827i \(-0.150656\pi\)
\(140\) −4.69454 + 85.3777i −0.0335324 + 0.609841i
\(141\) 14.3642 0.101874
\(142\) 21.4134 + 21.4134i 0.150799 + 0.150799i
\(143\) −1.35531 + 1.35531i −0.00947767 + 0.00947767i
\(144\) 12.0000i 0.0833333i
\(145\) −126.010 140.674i −0.869035 0.970165i
\(146\) 50.6624 0.347002
\(147\) 29.5334 + 29.5334i 0.200908 + 0.200908i
\(148\) −41.5687 + 41.5687i −0.280870 + 0.280870i
\(149\) 61.5397i 0.413018i 0.978445 + 0.206509i \(0.0662103\pi\)
−0.978445 + 0.206509i \(0.933790\pi\)
\(150\) 6.71402 60.8681i 0.0447601 0.405787i
\(151\) −100.953 −0.668560 −0.334280 0.942474i \(-0.608493\pi\)
−0.334280 + 0.942474i \(0.608493\pi\)
\(152\) −50.7531 50.7531i −0.333902 0.333902i
\(153\) 10.7470 10.7470i 0.0702418 0.0702418i
\(154\) 72.9263i 0.473548i
\(155\) 42.8473 38.3810i 0.276434 0.247619i
\(156\) −1.10097 −0.00705748
\(157\) −63.0830 63.0830i −0.401803 0.401803i 0.477065 0.878868i \(-0.341701\pi\)
−0.878868 + 0.477065i \(0.841701\pi\)
\(158\) 8.78027 8.78027i 0.0555713 0.0555713i
\(159\) 82.2769i 0.517465i
\(160\) −28.2416 1.55288i −0.176510 0.00970549i
\(161\) 41.0076 0.254705
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −35.1517 + 35.1517i −0.215655 + 0.215655i −0.806664 0.591010i \(-0.798729\pi\)
0.591010 + 0.806664i \(0.298729\pi\)
\(164\) 49.5636i 0.302217i
\(165\) 2.86743 52.1488i 0.0173783 0.316053i
\(166\) −95.8594 −0.577467
\(167\) 65.9932 + 65.9932i 0.395169 + 0.395169i 0.876525 0.481356i \(-0.159856\pi\)
−0.481356 + 0.876525i \(0.659856\pi\)
\(168\) −29.6204 + 29.6204i −0.176312 + 0.176312i
\(169\) 168.899i 0.999402i
\(170\) 23.9020 + 26.6834i 0.140600 + 0.156961i
\(171\) 76.1297 0.445203
\(172\) −38.6945 38.6945i −0.224968 0.224968i
\(173\) 153.430 153.430i 0.886880 0.886880i −0.107343 0.994222i \(-0.534234\pi\)
0.994222 + 0.107343i \(0.0342341\pi\)
\(174\) 92.5216i 0.531733i
\(175\) 166.817 133.672i 0.953242 0.763840i
\(176\) −24.1229 −0.137062
\(177\) −24.5585 24.5585i −0.138748 0.138748i
\(178\) −10.7360 + 10.7360i −0.0603145 + 0.0603145i
\(179\) 17.5087i 0.0978139i −0.998803 0.0489069i \(-0.984426\pi\)
0.998803 0.0489069i \(-0.0155738\pi\)
\(180\) 22.3459 20.0165i 0.124144 0.111203i
\(181\) −345.567 −1.90921 −0.954606 0.297871i \(-0.903723\pi\)
−0.954606 + 0.297871i \(0.903723\pi\)
\(182\) −2.71759 2.71759i −0.0149318 0.0149318i
\(183\) 12.8297 12.8297i 0.0701074 0.0701074i
\(184\) 13.5647i 0.0737210i
\(185\) 146.746 + 8.06889i 0.793221 + 0.0436156i
\(186\) 28.1808 0.151510
\(187\) 21.6041 + 21.6041i 0.115530 + 0.115530i
\(188\) −11.7283 + 11.7283i −0.0623848 + 0.0623848i
\(189\) 44.4306i 0.235082i
\(190\) −9.85168 + 179.169i −0.0518510 + 0.942994i
\(191\) 109.218 0.571822 0.285911 0.958256i \(-0.407704\pi\)
0.285911 + 0.958256i \(0.407704\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 24.0047 24.0047i 0.124377 0.124377i −0.642178 0.766555i \(-0.721969\pi\)
0.766555 + 0.642178i \(0.221969\pi\)
\(194\) 126.438i 0.651745i
\(195\) 1.83646 + 2.05017i 0.00941775 + 0.0105137i
\(196\) −48.2279 −0.246061
\(197\) −141.884 141.884i −0.720223 0.720223i 0.248428 0.968650i \(-0.420086\pi\)
−0.968650 + 0.248428i \(0.920086\pi\)
\(198\) 18.0922 18.0922i 0.0913746 0.0913746i
\(199\) 176.579i 0.887330i −0.896193 0.443665i \(-0.853678\pi\)
0.896193 0.443665i \(-0.146322\pi\)
\(200\) 44.2166 + 55.1805i 0.221083 + 0.275903i
\(201\) 56.2196 0.279700
\(202\) −6.89640 6.89640i −0.0341406 0.0341406i
\(203\) 228.377 228.377i 1.12501 1.12501i
\(204\) 17.5498i 0.0860283i
\(205\) −92.2950 + 82.6743i −0.450220 + 0.403289i
\(206\) −177.057 −0.859502
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 0.898935 0.898935i 0.00432180 0.00432180i
\(209\) 153.039i 0.732244i
\(210\) 104.566 + 5.74961i 0.497933 + 0.0273791i
\(211\) −126.385 −0.598980 −0.299490 0.954099i \(-0.596817\pi\)
−0.299490 + 0.954099i \(0.596817\pi\)
\(212\) 67.1788 + 67.1788i 0.316881 + 0.316881i
\(213\) 26.2260 26.2260i 0.123127 0.123127i
\(214\) 174.722i 0.816456i
\(215\) −7.51099 + 136.600i −0.0349348 + 0.635347i
\(216\) 14.6969 0.0680414
\(217\) 69.5605 + 69.5605i 0.320555 + 0.320555i
\(218\) 8.33514 8.33514i 0.0382346 0.0382346i
\(219\) 62.0485i 0.283326i
\(220\) 40.2381 + 44.9206i 0.182900 + 0.204184i
\(221\) −1.61014 −0.00728571
\(222\) 50.9111 + 50.9111i 0.229329 + 0.229329i
\(223\) 100.240 100.240i 0.449507 0.449507i −0.445683 0.895191i \(-0.647039\pi\)
0.895191 + 0.445683i \(0.147039\pi\)
\(224\) 48.3699i 0.215937i
\(225\) −74.5479 8.22296i −0.331324 0.0365465i
\(226\) −101.145 −0.447546
\(227\) −260.102 260.102i −1.14582 1.14582i −0.987366 0.158457i \(-0.949348\pi\)
−0.158457 0.987366i \(-0.550652\pi\)
\(228\) −62.1596 + 62.1596i −0.272630 + 0.272630i
\(229\) 328.074i 1.43264i 0.697773 + 0.716319i \(0.254174\pi\)
−0.697773 + 0.716319i \(0.745826\pi\)
\(230\) 25.2595 22.6265i 0.109824 0.0983760i
\(231\) 89.3162 0.386650
\(232\) 75.5436 + 75.5436i 0.325619 + 0.325619i
\(233\) −133.968 + 133.968i −0.574970 + 0.574970i −0.933513 0.358543i \(-0.883274\pi\)
0.358543 + 0.933513i \(0.383274\pi\)
\(234\) 1.34840i 0.00576240i
\(235\) 41.4034 + 2.27659i 0.176185 + 0.00968760i
\(236\) 40.1038 0.169931
\(237\) −10.7536 10.7536i −0.0453738 0.0453738i
\(238\) −43.3193 + 43.3193i −0.182014 + 0.182014i
\(239\) 28.2933i 0.118382i 0.998247 + 0.0591910i \(0.0188521\pi\)
−0.998247 + 0.0591910i \(0.981148\pi\)
\(240\) −1.90188 + 34.5888i −0.00792450 + 0.144120i
\(241\) −298.141 −1.23710 −0.618550 0.785746i \(-0.712279\pi\)
−0.618550 + 0.785746i \(0.712279\pi\)
\(242\) −84.6304 84.6304i −0.349712 0.349712i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 20.9508i 0.0858637i
\(245\) 80.4464 + 89.8079i 0.328352 + 0.366563i
\(246\) −60.7027 −0.246759
\(247\) −5.70297 5.70297i −0.0230890 0.0230890i
\(248\) −23.0095 + 23.0095i −0.0927804 + 0.0927804i
\(249\) 117.403i 0.471499i
\(250\) 28.9994 174.382i 0.115998 0.697527i
\(251\) −338.924 −1.35030 −0.675148 0.737682i \(-0.735920\pi\)
−0.675148 + 0.737682i \(0.735920\pi\)
\(252\) 36.2774 + 36.2774i 0.143958 + 0.143958i
\(253\) 20.4512 20.4512i 0.0808347 0.0808347i
\(254\) 342.629i 1.34893i
\(255\) 32.6804 29.2738i 0.128158 0.114799i
\(256\) 16.0000 0.0625000
\(257\) 166.864 + 166.864i 0.649277 + 0.649277i 0.952818 0.303541i \(-0.0981690\pi\)
−0.303541 + 0.952818i \(0.598169\pi\)
\(258\) −47.3910 + 47.3910i −0.183686 + 0.183686i
\(259\) 251.334i 0.970403i
\(260\) −3.17342 0.174492i −0.0122055 0.000671124i
\(261\) −113.315 −0.434158
\(262\) −9.31847 9.31847i −0.0355667 0.0355667i
\(263\) 302.953 302.953i 1.15191 1.15191i 0.165744 0.986169i \(-0.446998\pi\)
0.986169 0.165744i \(-0.0530024\pi\)
\(264\) 29.5444i 0.111911i
\(265\) 13.0401 237.155i 0.0492078 0.894924i
\(266\) −306.865 −1.15363
\(267\) 13.1488 + 13.1488i 0.0492466 + 0.0492466i
\(268\) −45.9031 + 45.9031i −0.171280 + 0.171280i
\(269\) 259.411i 0.964354i 0.876074 + 0.482177i \(0.160154\pi\)
−0.876074 + 0.482177i \(0.839846\pi\)
\(270\) −24.5152 27.3680i −0.0907969 0.101363i
\(271\) −430.196 −1.58744 −0.793719 0.608284i \(-0.791858\pi\)
−0.793719 + 0.608284i \(0.791858\pi\)
\(272\) −14.3293 14.3293i −0.0526814 0.0526814i
\(273\) −3.32835 + 3.32835i −0.0121918 + 0.0121918i
\(274\) 216.794i 0.791218i
\(275\) 16.5301 149.859i 0.0601096 0.544942i
\(276\) 16.6132 0.0601929
\(277\) −171.893 171.893i −0.620553 0.620553i 0.325120 0.945673i \(-0.394595\pi\)
−0.945673 + 0.325120i \(0.894595\pi\)
\(278\) 126.720 126.720i 0.455827 0.455827i
\(279\) 34.5143i 0.123707i
\(280\) −90.0723 + 80.6832i −0.321687 + 0.288154i
\(281\) 349.790 1.24481 0.622403 0.782697i \(-0.286157\pi\)
0.622403 + 0.782697i \(0.286157\pi\)
\(282\) 14.3642 + 14.3642i 0.0509370 + 0.0509370i
\(283\) 370.808 370.808i 1.31028 1.31028i 0.389065 0.921210i \(-0.372798\pi\)
0.921210 0.389065i \(-0.127202\pi\)
\(284\) 42.8268i 0.150799i
\(285\) 219.436 + 12.0658i 0.769951 + 0.0423361i
\(286\) −2.71061 −0.00947767
\(287\) −149.836 149.836i −0.522078 0.522078i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 263.334i 0.911190i
\(290\) 14.6637 266.684i 0.0505646 0.919600i
\(291\) −154.855 −0.532147
\(292\) 50.6624 + 50.6624i 0.173501 + 0.173501i
\(293\) −50.6461 + 50.6461i −0.172854 + 0.172854i −0.788232 0.615378i \(-0.789003\pi\)
0.615378 + 0.788232i \(0.289003\pi\)
\(294\) 59.0669i 0.200908i
\(295\) −66.8950 74.6795i −0.226763 0.253151i
\(296\) −83.1374 −0.280870
\(297\) −22.1583 22.1583i −0.0746070 0.0746070i
\(298\) −61.5397 + 61.5397i −0.206509 + 0.206509i
\(299\) 1.52422i 0.00509772i
\(300\) 67.5821 54.1541i 0.225274 0.180514i
\(301\) −233.956 −0.777264
\(302\) −100.953 100.953i −0.334280 0.334280i
\(303\) −8.44633 + 8.44633i −0.0278757 + 0.0278757i
\(304\) 101.506i 0.333902i
\(305\) 39.0136 34.9468i 0.127913 0.114580i
\(306\) 21.4940 0.0702418
\(307\) 218.758 + 218.758i 0.712568 + 0.712568i 0.967072 0.254504i \(-0.0819121\pi\)
−0.254504 + 0.967072i \(0.581912\pi\)
\(308\) −72.9263 + 72.9263i −0.236774 + 0.236774i
\(309\) 216.850i 0.701781i
\(310\) 81.2283 + 4.46638i 0.262027 + 0.0144077i
\(311\) 162.318 0.521924 0.260962 0.965349i \(-0.415960\pi\)
0.260962 + 0.965349i \(0.415960\pi\)
\(312\) −1.10097 1.10097i −0.00352874 0.00352874i
\(313\) 64.2791 64.2791i 0.205365 0.205365i −0.596929 0.802294i \(-0.703613\pi\)
0.802294 + 0.596929i \(0.203613\pi\)
\(314\) 126.166i 0.401803i
\(315\) 7.04180 128.067i 0.0223549 0.406561i
\(316\) 17.5605 0.0555713
\(317\) −340.744 340.744i −1.07490 1.07490i −0.996958 0.0779433i \(-0.975165\pi\)
−0.0779433 0.996958i \(-0.524835\pi\)
\(318\) 82.2769 82.2769i 0.258732 0.258732i
\(319\) 227.791i 0.714079i
\(320\) −26.6887 29.7945i −0.0834023 0.0931078i
\(321\) 213.989 0.666633
\(322\) 41.0076 + 41.0076i 0.127353 + 0.127353i
\(323\) −90.9073 + 90.9073i −0.281447 + 0.281447i
\(324\) 18.0000i 0.0555556i
\(325\) 4.96848 + 6.20047i 0.0152876 + 0.0190784i
\(326\) −70.3034 −0.215655
\(327\) −10.2084 10.2084i −0.0312184 0.0312184i
\(328\) 49.5636 49.5636i 0.151108 0.151108i
\(329\) 70.9123i 0.215539i
\(330\) 55.0162 49.2814i 0.166716 0.149338i
\(331\) −482.017 −1.45624 −0.728122 0.685447i \(-0.759607\pi\)
−0.728122 + 0.685447i \(0.759607\pi\)
\(332\) −95.8594 95.8594i −0.288733 0.288733i
\(333\) 62.3531 62.3531i 0.187246 0.187246i
\(334\) 131.986i 0.395169i
\(335\) 162.047 + 8.91025i 0.483723 + 0.0265978i
\(336\) −59.2408 −0.176312
\(337\) 299.309 + 299.309i 0.888158 + 0.888158i 0.994346 0.106188i \(-0.0338646\pi\)
−0.106188 + 0.994346i \(0.533865\pi\)
\(338\) −168.899 + 168.899i −0.499701 + 0.499701i
\(339\) 123.877i 0.365420i
\(340\) −2.78146 + 50.5854i −0.00818077 + 0.148781i
\(341\) 69.3821 0.203466
\(342\) 76.1297 + 76.1297i 0.222601 + 0.222601i
\(343\) 150.467 150.467i 0.438679 0.438679i
\(344\) 77.3891i 0.224968i
\(345\) −27.7117 30.9365i −0.0803236 0.0896709i
\(346\) 306.860 0.886880
\(347\) −34.8305 34.8305i −0.100376 0.100376i 0.655135 0.755512i \(-0.272612\pi\)
−0.755512 + 0.655135i \(0.772612\pi\)
\(348\) 92.5216 92.5216i 0.265867 0.265867i
\(349\) 455.518i 1.30521i 0.757699 + 0.652604i \(0.226324\pi\)
−0.757699 + 0.652604i \(0.773676\pi\)
\(350\) 300.489 + 33.1453i 0.858541 + 0.0947009i
\(351\) 1.65145 0.00470498
\(352\) −24.1229 24.1229i −0.0685309 0.0685309i
\(353\) 31.7609 31.7609i 0.0899741 0.0899741i −0.660687 0.750661i \(-0.729735\pi\)
0.750661 + 0.660687i \(0.229735\pi\)
\(354\) 49.1169i 0.138748i
\(355\) 79.7502 71.4371i 0.224648 0.201231i
\(356\) −21.4720 −0.0603145
\(357\) 53.0550 + 53.0550i 0.148614 + 0.148614i
\(358\) 17.5087 17.5087i 0.0489069 0.0489069i
\(359\) 39.3142i 0.109510i −0.998500 0.0547551i \(-0.982562\pi\)
0.998500 0.0547551i \(-0.0174378\pi\)
\(360\) 42.3624 + 2.32932i 0.117673 + 0.00647033i
\(361\) −282.970 −0.783851
\(362\) −345.567 345.567i −0.954606 0.954606i
\(363\) −103.651 + 103.651i −0.285539 + 0.285539i
\(364\) 5.43517i 0.0149318i
\(365\) 9.83406 178.848i 0.0269426 0.489995i
\(366\) 25.6593 0.0701074
\(367\) 421.823 + 421.823i 1.14938 + 1.14938i 0.986674 + 0.162708i \(0.0520227\pi\)
0.162708 + 0.986674i \(0.447977\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 74.3453i 0.201478i
\(370\) 138.677 + 154.815i 0.374803 + 0.418418i
\(371\) 406.179 1.09482
\(372\) 28.1808 + 28.1808i 0.0757549 + 0.0757549i
\(373\) −324.873 + 324.873i −0.870973 + 0.870973i −0.992579 0.121605i \(-0.961196\pi\)
0.121605 + 0.992579i \(0.461196\pi\)
\(374\) 43.2081i 0.115530i
\(375\) −213.573 35.5169i −0.569529 0.0947118i
\(376\) −23.4567 −0.0623848
\(377\) 8.48860 + 8.48860i 0.0225162 + 0.0225162i
\(378\) 44.4306 44.4306i 0.117541 0.117541i
\(379\) 188.177i 0.496509i 0.968695 + 0.248255i \(0.0798570\pi\)
−0.968695 + 0.248255i \(0.920143\pi\)
\(380\) −189.020 + 169.317i −0.497422 + 0.445571i
\(381\) −419.633 −1.10140
\(382\) 109.218 + 109.218i 0.285911 + 0.285911i
\(383\) 231.954 231.954i 0.605624 0.605624i −0.336175 0.941799i \(-0.609133\pi\)
0.941799 + 0.336175i \(0.109133\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 257.445 + 14.1557i 0.668687 + 0.0367681i
\(386\) 48.0095 0.124377
\(387\) 58.0418 + 58.0418i 0.149979 + 0.149979i
\(388\) 126.438 126.438i 0.325872 0.325872i
\(389\) 645.912i 1.66044i 0.557435 + 0.830220i \(0.311786\pi\)
−0.557435 + 0.830220i \(0.688214\pi\)
\(390\) −0.213708 + 3.88663i −0.000547970 + 0.00996572i
\(391\) 24.2966 0.0621395
\(392\) −48.2279 48.2279i −0.123030 0.123030i
\(393\) −11.4127 + 11.4127i −0.0290401 + 0.0290401i
\(394\) 283.768i 0.720223i
\(395\) −29.2918 32.7005i −0.0741564 0.0827860i
\(396\) 36.1843 0.0913746
\(397\) −192.099 192.099i −0.483877 0.483877i 0.422491 0.906367i \(-0.361156\pi\)
−0.906367 + 0.422491i \(0.861156\pi\)
\(398\) 176.579 176.579i 0.443665 0.443665i
\(399\) 375.832i 0.941935i
\(400\) −10.9639 + 99.3971i −0.0274099 + 0.248493i
\(401\) 143.800 0.358602 0.179301 0.983794i \(-0.442616\pi\)
0.179301 + 0.983794i \(0.442616\pi\)
\(402\) 56.2196 + 56.2196i 0.139850 + 0.139850i
\(403\) −2.58551 + 2.58551i −0.00641566 + 0.00641566i
\(404\) 13.7928i 0.0341406i
\(405\) −33.5188 + 30.0248i −0.0827625 + 0.0741354i
\(406\) 456.754 1.12501
\(407\) 125.345 + 125.345i 0.307972 + 0.307972i
\(408\) −17.5498 + 17.5498i −0.0430142 + 0.0430142i
\(409\) 174.989i 0.427846i −0.976851 0.213923i \(-0.931376\pi\)
0.976851 0.213923i \(-0.0686241\pi\)
\(410\) −174.969 9.62077i −0.426754 0.0234653i
\(411\) −265.517 −0.646027
\(412\) −177.057 177.057i −0.429751 0.429751i
\(413\) 121.239 121.239i 0.293556 0.293556i
\(414\) 20.3470i 0.0491473i
\(415\) −18.6073 + 338.403i −0.0448368 + 0.815429i
\(416\) 1.79787 0.00432180
\(417\) −155.199 155.199i −0.372181 0.372181i
\(418\) −153.039 + 153.039i −0.366122 + 0.366122i
\(419\) 677.602i 1.61719i 0.588366 + 0.808595i \(0.299771\pi\)
−0.588366 + 0.808595i \(0.700229\pi\)
\(420\) 98.8163 + 110.316i 0.235277 + 0.262656i
\(421\) −647.109 −1.53708 −0.768538 0.639805i \(-0.779015\pi\)
−0.768538 + 0.639805i \(0.779015\pi\)
\(422\) −126.385 126.385i −0.299490 0.299490i
\(423\) 17.5925 17.5925i 0.0415899 0.0415899i
\(424\) 134.358i 0.316881i
\(425\) 98.8375 79.1993i 0.232559 0.186351i
\(426\) 52.4519 0.123127
\(427\) 63.3366 + 63.3366i 0.148329 + 0.148329i
\(428\) −174.722 + 174.722i −0.408228 + 0.408228i
\(429\) 3.31981i 0.00773849i
\(430\) −144.111 + 129.089i −0.335141 + 0.300206i
\(431\) 79.7599 0.185058 0.0925289 0.995710i \(-0.470505\pi\)
0.0925289 + 0.995710i \(0.470505\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −32.7197 + 32.7197i −0.0755652 + 0.0755652i −0.743879 0.668314i \(-0.767016\pi\)
0.668314 + 0.743879i \(0.267016\pi\)
\(434\) 139.121i 0.320555i
\(435\) −326.620 17.9594i −0.750850 0.0412859i
\(436\) 16.6703 0.0382346
\(437\) 86.0561 + 86.0561i 0.196925 + 0.196925i
\(438\) 62.0485 62.0485i 0.141663 0.141663i
\(439\) 701.466i 1.59787i 0.601416 + 0.798936i \(0.294603\pi\)
−0.601416 + 0.798936i \(0.705397\pi\)
\(440\) −4.68249 + 85.1587i −0.0106420 + 0.193542i
\(441\) 72.3419 0.164041
\(442\) −1.61014 1.61014i −0.00364286 0.00364286i
\(443\) 150.926 150.926i 0.340691 0.340691i −0.515936 0.856627i \(-0.672556\pi\)
0.856627 + 0.515936i \(0.172556\pi\)
\(444\) 101.822i 0.229329i
\(445\) 35.8162 + 39.9841i 0.0804858 + 0.0898519i
\(446\) 200.480 0.449507
\(447\) 75.3704 + 75.3704i 0.168614 + 0.168614i
\(448\) 48.3699 48.3699i 0.107969 0.107969i
\(449\) 233.234i 0.519451i 0.965682 + 0.259726i \(0.0836321\pi\)
−0.965682 + 0.259726i \(0.916368\pi\)
\(450\) −66.3249 82.7708i −0.147389 0.183935i
\(451\) −149.452 −0.331379
\(452\) −101.145 101.145i −0.223773 0.223773i
\(453\) −123.641 + 123.641i −0.272938 + 0.272938i
\(454\) 520.204i 1.14582i
\(455\) −10.1211 + 9.06612i −0.0222443 + 0.0199255i
\(456\) −124.319 −0.272630
\(457\) 323.809 + 323.809i 0.708554 + 0.708554i 0.966231 0.257677i \(-0.0829570\pi\)
−0.257677 + 0.966231i \(0.582957\pi\)
\(458\) −328.074 + 328.074i −0.716319 + 0.716319i
\(459\) 26.3247i 0.0573522i
\(460\) 47.8860 + 2.63303i 0.104100 + 0.00572399i
\(461\) 461.068 1.00015 0.500074 0.865983i \(-0.333306\pi\)
0.500074 + 0.865983i \(0.333306\pi\)
\(462\) 89.3162 + 89.3162i 0.193325 + 0.193325i
\(463\) 168.651 168.651i 0.364258 0.364258i −0.501120 0.865378i \(-0.667079\pi\)
0.865378 + 0.501120i \(0.167079\pi\)
\(464\) 151.087i 0.325619i
\(465\) 5.47017 99.4839i 0.0117638 0.213944i
\(466\) −267.936 −0.574970
\(467\) 616.116 + 616.116i 1.31931 + 1.31931i 0.914325 + 0.404980i \(0.132722\pi\)
0.404980 + 0.914325i \(0.367278\pi\)
\(468\) −1.34840 + 1.34840i −0.00288120 + 0.00288120i
\(469\) 277.541i 0.591772i
\(470\) 39.1268 + 43.6800i 0.0832486 + 0.0929362i
\(471\) −154.521 −0.328070
\(472\) 40.1038 + 40.1038i 0.0849657 + 0.0849657i
\(473\) −116.678 + 116.678i −0.246677 + 0.246677i
\(474\) 21.5072i 0.0453738i
\(475\) 630.590 + 69.5568i 1.32756 + 0.146435i
\(476\) −86.6385 −0.182014
\(477\) −100.768 100.768i −0.211254 0.211254i
\(478\) −28.2933 + 28.2933i −0.0591910 + 0.0591910i
\(479\) 465.174i 0.971136i 0.874199 + 0.485568i \(0.161387\pi\)
−0.874199 + 0.485568i \(0.838613\pi\)
\(480\) −36.4906 + 32.6869i −0.0760222 + 0.0680977i
\(481\) −9.34189 −0.0194218
\(482\) −298.141 298.141i −0.618550 0.618550i
\(483\) 50.2238 50.2238i 0.103983 0.103983i
\(484\) 169.261i 0.349712i
\(485\) −446.353 24.5429i −0.920316 0.0506040i
\(486\) −22.0454 −0.0453609
\(487\) −326.491 326.491i −0.670412 0.670412i 0.287399 0.957811i \(-0.407209\pi\)
−0.957811 + 0.287399i \(0.907209\pi\)
\(488\) −20.9508 + 20.9508i −0.0429319 + 0.0429319i
\(489\) 86.1038i 0.176081i
\(490\) −9.36151 + 170.254i −0.0191051 + 0.347458i
\(491\) 520.742 1.06057 0.530287 0.847818i \(-0.322084\pi\)
0.530287 + 0.847818i \(0.322084\pi\)
\(492\) −60.7027 60.7027i −0.123379 0.123379i
\(493\) 135.311 135.311i 0.274465 0.274465i
\(494\) 11.4059i 0.0230890i
\(495\) −60.3571 67.3809i −0.121934 0.136123i
\(496\) −46.0191 −0.0927804
\(497\) 129.471 + 129.471i 0.260504 + 0.260504i
\(498\) −117.403 + 117.403i −0.235750 + 0.235750i
\(499\) 153.945i 0.308506i −0.988031 0.154253i \(-0.950703\pi\)
0.988031 0.154253i \(-0.0492971\pi\)
\(500\) 203.381 145.382i 0.406763 0.290765i
\(501\) 161.650 0.322654
\(502\) −338.924 338.924i −0.675148 0.675148i
\(503\) 413.457 413.457i 0.821982 0.821982i −0.164410 0.986392i \(-0.552572\pi\)
0.986392 + 0.164410i \(0.0525721\pi\)
\(504\) 72.5548i 0.143958i
\(505\) −25.6843 + 23.0070i −0.0508601 + 0.0455585i
\(506\) 40.9023 0.0808347
\(507\) 206.858 + 206.858i 0.408004 + 0.408004i
\(508\) 342.629 342.629i 0.674467 0.674467i
\(509\) 528.261i 1.03784i 0.854823 + 0.518920i \(0.173666\pi\)
−0.854823 + 0.518920i \(0.826334\pi\)
\(510\) 61.9542 + 3.40658i 0.121479 + 0.00667957i
\(511\) 306.317 0.599445
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 93.2395 93.2395i 0.181753 0.181753i
\(514\) 333.729i 0.649277i
\(515\) −34.3686 + 625.048i −0.0667351 + 1.21369i
\(516\) −94.7819 −0.183686
\(517\) 35.3652 + 35.3652i 0.0684046 + 0.0684046i
\(518\) −251.334 + 251.334i −0.485201 + 0.485201i
\(519\) 375.826i 0.724134i
\(520\) −2.99893 3.34791i −0.00576717 0.00643830i
\(521\) 630.082 1.20937 0.604685 0.796464i \(-0.293299\pi\)
0.604685 + 0.796464i \(0.293299\pi\)
\(522\) −113.315 113.315i −0.217079 0.217079i
\(523\) 325.068 325.068i 0.621545 0.621545i −0.324381 0.945927i \(-0.605156\pi\)
0.945927 + 0.324381i \(0.105156\pi\)
\(524\) 18.6369i 0.0355667i
\(525\) 40.5945 368.023i 0.0773229 0.700996i
\(526\) 605.906 1.15191
\(527\) 41.2139 + 41.2139i 0.0782047 + 0.0782047i
\(528\) −29.5444 + 29.5444i −0.0559553 + 0.0559553i
\(529\) 23.0000i 0.0434783i
\(530\) 250.195 224.115i 0.472066 0.422858i
\(531\) −60.1557 −0.113288
\(532\) −306.865 306.865i −0.576815 0.576815i
\(533\) 5.56930 5.56930i 0.0104490 0.0104490i
\(534\) 26.2977i 0.0492466i
\(535\) 616.802 + 33.9152i 1.15290 + 0.0633928i
\(536\) −91.8063 −0.171280
\(537\) −21.4437 21.4437i −0.0399323 0.0399323i
\(538\) −259.411 + 259.411i −0.482177 + 0.482177i
\(539\) 145.425i 0.269804i
\(540\) 2.85282 51.8832i 0.00528300 0.0960799i
\(541\) 242.869 0.448926 0.224463 0.974483i \(-0.427937\pi\)
0.224463 + 0.974483i \(0.427937\pi\)
\(542\) −430.196 430.196i −0.793719 0.793719i
\(543\) −423.232 + 423.232i −0.779433 + 0.779433i
\(544\) 28.6587i 0.0526814i
\(545\) −27.8068 31.0426i −0.0510216 0.0569590i
\(546\) −6.65670 −0.0121918
\(547\) 139.082 + 139.082i 0.254263 + 0.254263i 0.822716 0.568453i \(-0.192458\pi\)
−0.568453 + 0.822716i \(0.692458\pi\)
\(548\) 216.794 216.794i 0.395609 0.395609i
\(549\) 31.4261i 0.0572425i
\(550\) 166.389 133.329i 0.302526 0.242416i
\(551\) 958.518 1.73960
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 53.0876 53.0876i 0.0959992 0.0959992i
\(554\) 343.787i 0.620553i
\(555\) 189.609 169.844i 0.341637 0.306025i
\(556\) 253.440 0.455827
\(557\) −501.877 501.877i −0.901036 0.901036i 0.0944902 0.995526i \(-0.469878\pi\)
−0.995526 + 0.0944902i \(0.969878\pi\)
\(558\) 34.5143 34.5143i 0.0618536 0.0618536i
\(559\) 8.69597i 0.0155563i
\(560\) −170.755 9.38907i −0.304920 0.0167662i
\(561\) 52.9189 0.0943296
\(562\) 349.790 + 349.790i 0.622403 + 0.622403i
\(563\) 592.906 592.906i 1.05312 1.05312i 0.0546116 0.998508i \(-0.482608\pi\)
0.998508 0.0546116i \(-0.0173921\pi\)
\(564\) 28.7285i 0.0509370i
\(565\) −19.6333 + 357.064i −0.0347492 + 0.631971i
\(566\) 741.616 1.31028
\(567\) −54.4161 54.4161i −0.0959720 0.0959720i
\(568\) −42.8268 + 42.8268i −0.0753993 + 0.0753993i
\(569\) 204.295i 0.359043i 0.983754 + 0.179521i \(0.0574549\pi\)
−0.983754 + 0.179521i \(0.942545\pi\)
\(570\) 207.370 + 231.502i 0.363807 + 0.406144i
\(571\) 106.932 0.187271 0.0936357 0.995607i \(-0.470151\pi\)
0.0936357 + 0.995607i \(0.470151\pi\)
\(572\) −2.71061 2.71061i −0.00473884 0.00473884i
\(573\) 133.764 133.764i 0.233445 0.233445i
\(574\) 299.673i 0.522078i
\(575\) −74.9729 93.5632i −0.130388 0.162719i
\(576\) −24.0000 −0.0416667
\(577\) −258.933 258.933i −0.448757 0.448757i 0.446184 0.894941i \(-0.352783\pi\)
−0.894941 + 0.446184i \(0.852783\pi\)
\(578\) 263.334 263.334i 0.455595 0.455595i
\(579\) 58.7993i 0.101553i
\(580\) 281.348 252.020i 0.485082 0.434518i
\(581\) −579.589 −0.997571
\(582\) −154.855 154.855i −0.266074 0.266074i
\(583\) 202.568 202.568i 0.347459 0.347459i
\(584\) 101.325i 0.173501i
\(585\) 4.76013 + 0.261738i 0.00813698 + 0.000447416i
\(586\) −101.292 −0.172854
\(587\) −668.767 668.767i −1.13930 1.13930i −0.988577 0.150719i \(-0.951841\pi\)
−0.150719 0.988577i \(-0.548159\pi\)
\(588\) −59.0669 + 59.0669i −0.100454 + 0.100454i
\(589\) 291.952i 0.495673i
\(590\) 7.78454 141.574i 0.0131941 0.239957i
\(591\) −347.543 −0.588059
\(592\) −83.1374 83.1374i −0.140435 0.140435i
\(593\) 31.4468 31.4468i 0.0530300 0.0530300i −0.680094 0.733124i \(-0.738061\pi\)
0.733124 + 0.680094i \(0.238061\pi\)
\(594\) 44.3166i 0.0746070i
\(595\) 144.517 + 161.334i 0.242886 + 0.271150i
\(596\) −123.079 −0.206509
\(597\) −216.264 216.264i −0.362251 0.362251i
\(598\) −1.52422 + 1.52422i −0.00254886 + 0.00254886i
\(599\) 789.984i 1.31884i 0.751776 + 0.659419i \(0.229198\pi\)
−0.751776 + 0.659419i \(0.770802\pi\)
\(600\) 121.736 + 13.4280i 0.202894 + 0.0223801i
\(601\) 490.719 0.816503 0.408252 0.912869i \(-0.366139\pi\)
0.408252 + 0.912869i \(0.366139\pi\)
\(602\) −233.956 233.956i −0.388632 0.388632i
\(603\) 68.8547 68.8547i 0.114187 0.114187i
\(604\) 201.905i 0.334280i
\(605\) −315.190 + 282.335i −0.520975 + 0.466669i
\(606\) −16.8927 −0.0278757
\(607\) 268.721 + 268.721i 0.442703 + 0.442703i 0.892920 0.450216i \(-0.148653\pi\)
−0.450216 + 0.892920i \(0.648653\pi\)
\(608\) 101.506 101.506i 0.166951 0.166951i
\(609\) 559.408i 0.918567i
\(610\) 73.9604 + 4.06675i 0.121247 + 0.00666680i
\(611\) −2.63575 −0.00431384
\(612\) 21.4940 + 21.4940i 0.0351209 + 0.0351209i
\(613\) 754.006 754.006i 1.23003 1.23003i 0.266073 0.963953i \(-0.414274\pi\)
0.963953 0.266073i \(-0.0857261\pi\)
\(614\) 437.517i 0.712568i
\(615\) −11.7830 + 214.293i −0.0191593 + 0.348444i
\(616\) −145.853 −0.236774
\(617\) −577.903 577.903i −0.936634 0.936634i 0.0614748 0.998109i \(-0.480420\pi\)
−0.998109 + 0.0614748i \(0.980420\pi\)
\(618\) −216.850 + 216.850i −0.350890 + 0.350890i
\(619\) 71.5819i 0.115641i 0.998327 + 0.0578206i \(0.0184151\pi\)
−0.998327 + 0.0578206i \(0.981585\pi\)
\(620\) 76.7619 + 85.6947i 0.123810 + 0.138217i
\(621\) −24.9199 −0.0401286
\(622\) 162.318 + 162.318i 0.260962 + 0.260962i
\(623\) −64.9123 + 64.9123i −0.104193 + 0.104193i
\(624\) 2.20193i 0.00352874i
\(625\) −609.974 136.223i −0.975958 0.217957i
\(626\) 128.558 0.205365
\(627\) 187.434 + 187.434i 0.298937 + 0.298937i
\(628\) 126.166 126.166i 0.200901 0.200901i
\(629\) 148.913i 0.236746i
\(630\) 135.108 121.025i 0.214458 0.192103i
\(631\) 568.739 0.901330 0.450665 0.892693i \(-0.351187\pi\)
0.450665 + 0.892693i \(0.351187\pi\)
\(632\) 17.5605 + 17.5605i 0.0277857 + 0.0277857i
\(633\) −154.789 + 154.789i −0.244533 + 0.244533i
\(634\) 681.487i 1.07490i
\(635\) −1209.55 66.5077i −1.90480 0.104736i
\(636\) 164.554 0.258732
\(637\) −5.41922 5.41922i −0.00850741 0.00850741i
\(638\) 227.791 227.791i 0.357039 0.357039i
\(639\) 64.2402i 0.100532i
\(640\) 3.10576 56.4832i 0.00485275 0.0882550i
\(641\) −1051.81 −1.64089 −0.820445 0.571726i \(-0.806274\pi\)
−0.820445 + 0.571726i \(0.806274\pi\)
\(642\) 213.989 + 213.989i 0.333317 + 0.333317i
\(643\) −64.6780 + 64.6780i −0.100588 + 0.100588i −0.755610 0.655022i \(-0.772659\pi\)
0.655022 + 0.755610i \(0.272659\pi\)
\(644\) 82.0151i 0.127353i
\(645\) 158.101 + 176.499i 0.245117 + 0.273641i
\(646\) −181.815 −0.281447
\(647\) 682.188 + 682.188i 1.05439 + 1.05439i 0.998433 + 0.0559524i \(0.0178195\pi\)
0.0559524 + 0.998433i \(0.482181\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 120.927i 0.186329i
\(650\) −1.23198 + 11.1689i −0.00189536 + 0.0171830i
\(651\) 170.388 0.261732
\(652\) −70.3034 70.3034i −0.107827 0.107827i
\(653\) −740.977 + 740.977i −1.13473 + 1.13473i −0.145346 + 0.989381i \(0.546429\pi\)
−0.989381 + 0.145346i \(0.953571\pi\)
\(654\) 20.4168i 0.0312184i
\(655\) −34.7049 + 31.0873i −0.0529845 + 0.0474615i
\(656\) 99.1271 0.151108
\(657\) −75.9935 75.9935i −0.115667 0.115667i
\(658\) −70.9123 + 70.9123i −0.107770 + 0.107770i
\(659\) 985.952i 1.49613i −0.663623 0.748067i \(-0.730982\pi\)
0.663623 0.748067i \(-0.269018\pi\)
\(660\) 104.298 + 5.73485i 0.158027 + 0.00868917i
\(661\) 649.680 0.982875 0.491438 0.870913i \(-0.336472\pi\)
0.491438 + 0.870913i \(0.336472\pi\)
\(662\) −482.017 482.017i −0.728122 0.728122i
\(663\) −1.97201 + 1.97201i −0.00297438 + 0.00297438i
\(664\) 191.719i 0.288733i
\(665\) −59.5656 + 1083.30i −0.0895723 + 1.62902i
\(666\) 124.706 0.187246
\(667\) −128.090 128.090i −0.192040 0.192040i
\(668\) −131.986 + 131.986i −0.197584 + 0.197584i
\(669\) 245.537i 0.367021i
\(670\) 153.137 + 170.958i 0.228563 + 0.255160i
\(671\) 63.1741 0.0941492
\(672\) −59.2408 59.2408i −0.0881559 0.0881559i
\(673\) 634.795 634.795i 0.943232 0.943232i −0.0552411 0.998473i \(-0.517593\pi\)
0.998473 + 0.0552411i \(0.0175927\pi\)
\(674\) 598.618i 0.888158i
\(675\) −101.373 + 81.2311i −0.150182 + 0.120342i
\(676\) −337.798 −0.499701
\(677\) −500.696 500.696i −0.739580 0.739580i 0.232916 0.972497i \(-0.425173\pi\)
−0.972497 + 0.232916i \(0.925173\pi\)
\(678\) −123.877 + 123.877i −0.182710 + 0.182710i
\(679\) 764.477i 1.12589i
\(680\) −53.3669 + 47.8040i −0.0784807 + 0.0702999i
\(681\) −637.117 −0.935560
\(682\) 69.3821 + 69.3821i 0.101733 + 0.101733i
\(683\) −457.846 + 457.846i −0.670345 + 0.670345i −0.957796 0.287450i \(-0.907192\pi\)
0.287450 + 0.957796i \(0.407192\pi\)
\(684\) 152.259i 0.222601i
\(685\) −765.325 42.0818i −1.11726 0.0614333i
\(686\) 300.934 0.438679
\(687\) 401.807 + 401.807i 0.584872 + 0.584872i
\(688\) 77.3891 77.3891i 0.112484 0.112484i
\(689\) 15.0974i 0.0219120i
\(690\) 3.22479 58.6481i 0.00467361 0.0849973i
\(691\) 182.546 0.264176 0.132088 0.991238i \(-0.457832\pi\)
0.132088 + 0.991238i \(0.457832\pi\)
\(692\) 306.860 + 306.860i 0.443440 + 0.443440i
\(693\) 109.390 109.390i 0.157849 0.157849i
\(694\) 69.6610i 0.100376i
\(695\) −422.749 471.944i −0.608272 0.679056i
\(696\) 185.043 0.265867
\(697\) −88.7766 88.7766i −0.127370 0.127370i
\(698\) −455.518 + 455.518i −0.652604 + 0.652604i
\(699\) 328.153i 0.469461i
\(700\) 267.344 + 333.635i 0.381920 + 0.476621i
\(701\) 336.087 0.479440 0.239720 0.970842i \(-0.422944\pi\)
0.239720 + 0.970842i \(0.422944\pi\)
\(702\) 1.65145 + 1.65145i 0.00235249 + 0.00235249i
\(703\) −527.436 + 527.436i −0.750264 + 0.750264i
\(704\) 48.2458i 0.0685309i
\(705\) 53.4969 47.9204i 0.0758821 0.0679722i
\(706\) 63.5217 0.0899741
\(707\) −41.6973 41.6973i −0.0589777 0.0589777i
\(708\) 49.1169 49.1169i 0.0693742 0.0693742i
\(709\) 607.338i 0.856612i −0.903634 0.428306i \(-0.859110\pi\)
0.903634 0.428306i \(-0.140890\pi\)
\(710\) 151.187 + 8.31310i 0.212940 + 0.0117086i
\(711\) −26.3408 −0.0370475
\(712\) −21.4720 21.4720i −0.0301572 0.0301572i
\(713\) 39.0146 39.0146i 0.0547189 0.0547189i
\(714\) 106.110i 0.148614i
\(715\) −0.526157 + 9.56901i −0.000735884 + 0.0133832i
\(716\) 35.0174 0.0489069
\(717\) 34.6521 + 34.6521i 0.0483293 + 0.0483293i
\(718\) 39.3142 39.3142i 0.0547551 0.0547551i
\(719\) 916.546i 1.27475i −0.770553 0.637376i \(-0.780020\pi\)
0.770553 0.637376i \(-0.219980\pi\)
\(720\) 40.0331 + 44.6917i 0.0556015 + 0.0620719i
\(721\) −1070.53 −1.48479
\(722\) −282.970 282.970i −0.391926 0.391926i
\(723\) −365.147 + 365.147i −0.505044 + 0.505044i
\(724\) 691.135i 0.954606i
\(725\) −938.602 103.532i −1.29462 0.142803i
\(726\) −207.301 −0.285539
\(727\) 246.536 + 246.536i 0.339114 + 0.339114i 0.856034 0.516920i \(-0.172922\pi\)
−0.516920 + 0.856034i \(0.672922\pi\)
\(728\) 5.43517 5.43517i 0.00746590 0.00746590i
\(729\) 27.0000i 0.0370370i
\(730\) 188.682 169.014i 0.258469 0.231526i
\(731\) −138.617 −0.189626
\(732\) 25.6593 + 25.6593i 0.0350537 + 0.0350537i
\(733\) 730.190 730.190i 0.996166 0.996166i −0.00382636 0.999993i \(-0.501218\pi\)
0.999993 + 0.00382636i \(0.00121797\pi\)
\(734\) 843.646i 1.14938i
\(735\) 208.518 + 11.4655i 0.283698 + 0.0155993i
\(736\) −27.1293 −0.0368605
\(737\) 138.414 + 138.414i 0.187808 + 0.187808i
\(738\) −74.3453 + 74.3453i −0.100739 + 0.100739i
\(739\) 865.300i 1.17091i −0.810706 0.585453i \(-0.800917\pi\)
0.810706 0.585453i \(-0.199083\pi\)
\(740\) −16.1378 + 293.492i −0.0218078 + 0.396611i
\(741\) −13.9694 −0.0188521
\(742\) 406.179 + 406.179i 0.547411 + 0.547411i
\(743\) 791.656 791.656i 1.06549 1.06549i 0.0677859 0.997700i \(-0.478407\pi\)
0.997700 0.0677859i \(-0.0215935\pi\)
\(744\) 56.3616i 0.0757549i
\(745\) 205.302 + 229.193i 0.275573 + 0.307641i
\(746\) −649.746 −0.870973
\(747\) 143.789 + 143.789i 0.192489 + 0.192489i
\(748\) −43.2081 + 43.2081i −0.0577648 + 0.0577648i
\(749\) 1056.41i 1.41042i
\(750\) −178.056 249.090i −0.237408 0.332120i
\(751\) 1140.21 1.51825 0.759125 0.650944i \(-0.225627\pi\)
0.759125 + 0.650944i \(0.225627\pi\)
\(752\) −23.4567 23.4567i −0.0311924 0.0311924i
\(753\) −415.096 + 415.096i −0.551256 + 0.551256i
\(754\) 16.9772i 0.0225162i
\(755\) −375.979 + 336.787i −0.497985 + 0.446075i
\(756\) 88.8612 0.117541
\(757\) 171.242 + 171.242i 0.226212 + 0.226212i 0.811108 0.584896i \(-0.198865\pi\)
−0.584896 + 0.811108i \(0.698865\pi\)
\(758\) −188.177 + 188.177i −0.248255 + 0.248255i
\(759\) 50.0949i 0.0660012i
\(760\) −358.338 19.7034i −0.471497 0.0259255i
\(761\) 82.4693 0.108370 0.0541848 0.998531i \(-0.482744\pi\)
0.0541848 + 0.998531i \(0.482744\pi\)
\(762\) −419.633 419.633i −0.550700 0.550700i
\(763\) 50.3962 50.3962i 0.0660501 0.0660501i
\(764\) 218.436i 0.285911i
\(765\) 4.17220 75.8781i 0.00545385 0.0991871i
\(766\) 463.908 0.605624
\(767\) 4.50634 + 4.50634i 0.00587528 + 0.00587528i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 643.087i 0.836264i 0.908386 + 0.418132i \(0.137315\pi\)
−0.908386 + 0.418132i \(0.862685\pi\)
\(770\) 243.289 + 271.600i 0.315960 + 0.352728i
\(771\) 408.732 0.530133
\(772\) 48.0095 + 48.0095i 0.0621884 + 0.0621884i
\(773\) −815.269 + 815.269i −1.05468 + 1.05468i −0.0562666 + 0.998416i \(0.517920\pi\)
−0.998416 + 0.0562666i \(0.982080\pi\)
\(774\) 116.084i 0.149979i
\(775\) 31.5344 285.885i 0.0406896 0.368884i
\(776\) 252.877 0.325872
\(777\) 307.820 + 307.820i 0.396165 + 0.396165i
\(778\) −645.912 + 645.912i −0.830220 + 0.830220i
\(779\)