Properties

Label 210.3.l.a.127.4
Level 210
Weight 3
Character 210.127
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.12745506816.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.4
Root \(-1.54779 - 1.54779i\) of \(x^{8} + 23 x^{4} + 1\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.a.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(1.80341 + 6.83723i) q^{10} +2.92322 q^{11} +(2.44949 + 2.44949i) q^{12} +(-1.13309 + 1.13309i) q^{13} +3.74166i q^{14} +(8.37386 - 2.20871i) q^{15} -4.00000 q^{16} +(1.54506 + 1.54506i) q^{17} +(3.00000 - 3.00000i) q^{18} +3.35199i q^{19} +(-5.03383 + 8.64064i) q^{20} +4.58258 q^{21} +(2.92322 + 2.92322i) q^{22} +(7.90681 - 7.90681i) q^{23} +4.89898i q^{24} +(12.3303 + 21.7477i) q^{25} -2.26617 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -13.5474i q^{29} +(10.5826 + 6.16515i) q^{30} +15.7936 q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.58019 - 3.58019i) q^{33} +3.09013i q^{34} +(3.37386 + 12.7913i) q^{35} +6.00000 q^{36} +(-16.8305 - 16.8305i) q^{37} +(-3.35199 + 3.35199i) q^{38} +2.77548i q^{39} +(-13.6745 + 3.60681i) q^{40} -72.6227 q^{41} +(4.58258 + 4.58258i) q^{42} +(20.3749 - 20.3749i) q^{43} +5.84643i q^{44} +(7.55074 - 12.9610i) q^{45} +15.8136 q^{46} +(-52.3194 - 52.3194i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-9.41742 + 34.0780i) q^{50} +3.78462 q^{51} +(-2.26617 - 2.26617i) q^{52} +(-40.5379 + 40.5379i) q^{53} -7.34847i q^{54} +(12.6292 + 7.35748i) q^{55} -7.48331 q^{56} +(4.10533 + 4.10533i) q^{57} +(13.5474 - 13.5474i) q^{58} -117.165i q^{59} +(4.41742 + 16.7477i) q^{60} -45.4373 q^{61} +(15.7936 + 15.7936i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-7.74717 + 2.04341i) q^{65} +7.16039 q^{66} +(57.7773 + 57.7773i) q^{67} +(-3.09013 + 3.09013i) q^{68} -19.3676i q^{69} +(-9.41742 + 16.1652i) q^{70} -51.7217 q^{71} +(6.00000 + 6.00000i) q^{72} +(72.3851 - 72.3851i) q^{73} -33.6610i q^{74} +(41.7369 + 11.5339i) q^{75} -6.70398 q^{76} +(5.46884 + 5.46884i) q^{77} +(-2.77548 + 2.77548i) q^{78} -37.1850i q^{79} +(-17.2813 - 10.0677i) q^{80} -9.00000 q^{81} +(-72.6227 - 72.6227i) q^{82} +(-21.3331 + 21.3331i) q^{83} +9.16515i q^{84} +(2.78638 + 10.5640i) q^{85} +40.7498 q^{86} +(-16.5922 - 16.5922i) q^{87} +(-5.84643 + 5.84643i) q^{88} -100.951i q^{89} +(20.5117 - 5.41022i) q^{90} -4.23962 q^{91} +(15.8136 + 15.8136i) q^{92} +(19.3432 - 19.3432i) q^{93} -104.639i q^{94} +(-8.43666 + 14.4817i) q^{95} -9.79796 q^{96} +(52.5887 + 52.5887i) q^{97} +(-7.00000 + 7.00000i) q^{98} -8.76965i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 16q^{8} + O(q^{10}) \) \( 8q + 8q^{2} - 16q^{8} - 8q^{11} + 8q^{13} + 12q^{15} - 32q^{16} - 32q^{17} + 24q^{18} - 8q^{22} - 40q^{23} - 48q^{25} + 16q^{26} + 48q^{30} + 144q^{31} - 32q^{32} + 120q^{33} - 28q^{35} + 48q^{36} + 160q^{37} - 320q^{41} - 32q^{43} - 80q^{46} - 144q^{47} - 112q^{50} + 72q^{51} + 16q^{52} - 200q^{53} + 184q^{55} - 24q^{57} - 64q^{58} + 72q^{60} + 288q^{61} + 144q^{62} + 24q^{65} + 240q^{66} + 80q^{67} + 64q^{68} - 112q^{70} - 280q^{71} + 48q^{72} + 312q^{73} - 56q^{77} + 48q^{78} - 72q^{81} - 320q^{82} - 320q^{83} + 80q^{85} - 64q^{86} - 48q^{87} + 16q^{88} - 80q^{92} + 48q^{93} - 472q^{95} - 24q^{97} - 56q^{98} + O(q^{100}) \)

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
\(5\) 4.32032 + 2.51691i 0.864064 + 0.503383i
\(6\) 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
\(10\) 1.80341 + 6.83723i 0.180341 + 0.683723i
\(11\) 2.92322 0.265747 0.132873 0.991133i \(-0.457580\pi\)
0.132873 + 0.991133i \(0.457580\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −1.13309 + 1.13309i −0.0871605 + 0.0871605i −0.749343 0.662182i \(-0.769630\pi\)
0.662182 + 0.749343i \(0.269630\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 8.37386 2.20871i 0.558258 0.147247i
\(16\) −4.00000 −0.250000
\(17\) 1.54506 + 1.54506i 0.0908861 + 0.0908861i 0.751088 0.660202i \(-0.229529\pi\)
−0.660202 + 0.751088i \(0.729529\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 3.35199i 0.176420i 0.996102 + 0.0882102i \(0.0281147\pi\)
−0.996102 + 0.0882102i \(0.971885\pi\)
\(20\) −5.03383 + 8.64064i −0.251691 + 0.432032i
\(21\) 4.58258 0.218218
\(22\) 2.92322 + 2.92322i 0.132873 + 0.132873i
\(23\) 7.90681 7.90681i 0.343774 0.343774i −0.514010 0.857784i \(-0.671841\pi\)
0.857784 + 0.514010i \(0.171841\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 12.3303 + 21.7477i 0.493212 + 0.869909i
\(26\) −2.26617 −0.0871605
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −3.74166 + 3.74166i −0.133631 + 0.133631i
\(29\) 13.5474i 0.467153i −0.972338 0.233577i \(-0.924957\pi\)
0.972338 0.233577i \(-0.0750430\pi\)
\(30\) 10.5826 + 6.16515i 0.352753 + 0.205505i
\(31\) 15.7936 0.509473 0.254736 0.967011i \(-0.418011\pi\)
0.254736 + 0.967011i \(0.418011\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 3.58019 3.58019i 0.108491 0.108491i
\(34\) 3.09013i 0.0908861i
\(35\) 3.37386 + 12.7913i 0.0963961 + 0.365465i
\(36\) 6.00000 0.166667
\(37\) −16.8305 16.8305i −0.454878 0.454878i 0.442092 0.896970i \(-0.354236\pi\)
−0.896970 + 0.442092i \(0.854236\pi\)
\(38\) −3.35199 + 3.35199i −0.0882102 + 0.0882102i
\(39\) 2.77548i 0.0711662i
\(40\) −13.6745 + 3.60681i −0.341862 + 0.0901703i
\(41\) −72.6227 −1.77129 −0.885643 0.464367i \(-0.846282\pi\)
−0.885643 + 0.464367i \(0.846282\pi\)
\(42\) 4.58258 + 4.58258i 0.109109 + 0.109109i
\(43\) 20.3749 20.3749i 0.473835 0.473835i −0.429318 0.903153i \(-0.641246\pi\)
0.903153 + 0.429318i \(0.141246\pi\)
\(44\) 5.84643i 0.132873i
\(45\) 7.55074 12.9610i 0.167794 0.288021i
\(46\) 15.8136 0.343774
\(47\) −52.3194 52.3194i −1.11318 1.11318i −0.992718 0.120461i \(-0.961563\pi\)
−0.120461 0.992718i \(-0.538437\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −9.41742 + 34.0780i −0.188348 + 0.681561i
\(51\) 3.78462 0.0742082
\(52\) −2.26617 2.26617i −0.0435802 0.0435802i
\(53\) −40.5379 + 40.5379i −0.764865 + 0.764865i −0.977198 0.212332i \(-0.931894\pi\)
0.212332 + 0.977198i \(0.431894\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 12.6292 + 7.35748i 0.229622 + 0.133772i
\(56\) −7.48331 −0.133631
\(57\) 4.10533 + 4.10533i 0.0720233 + 0.0720233i
\(58\) 13.5474 13.5474i 0.233577 0.233577i
\(59\) 117.165i 1.98585i −0.118752 0.992924i \(-0.537889\pi\)
0.118752 0.992924i \(-0.462111\pi\)
\(60\) 4.41742 + 16.7477i 0.0736237 + 0.279129i
\(61\) −45.4373 −0.744874 −0.372437 0.928057i \(-0.621478\pi\)
−0.372437 + 0.928057i \(0.621478\pi\)
\(62\) 15.7936 + 15.7936i 0.254736 + 0.254736i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −7.74717 + 2.04341i −0.119187 + 0.0314371i
\(66\) 7.16039 0.108491
\(67\) 57.7773 + 57.7773i 0.862348 + 0.862348i 0.991610 0.129263i \(-0.0412611\pi\)
−0.129263 + 0.991610i \(0.541261\pi\)
\(68\) −3.09013 + 3.09013i −0.0454430 + 0.0454430i
\(69\) 19.3676i 0.280691i
\(70\) −9.41742 + 16.1652i −0.134535 + 0.230931i
\(71\) −51.7217 −0.728475 −0.364238 0.931306i \(-0.618670\pi\)
−0.364238 + 0.931306i \(0.618670\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 72.3851 72.3851i 0.991576 0.991576i −0.00838858 0.999965i \(-0.502670\pi\)
0.999965 + 0.00838858i \(0.00267020\pi\)
\(74\) 33.6610i 0.454878i
\(75\) 41.7369 + 11.5339i 0.556492 + 0.153786i
\(76\) −6.70398 −0.0882102
\(77\) 5.46884 + 5.46884i 0.0710238 + 0.0710238i
\(78\) −2.77548 + 2.77548i −0.0355831 + 0.0355831i
\(79\) 37.1850i 0.470696i −0.971911 0.235348i \(-0.924377\pi\)
0.971911 0.235348i \(-0.0756230\pi\)
\(80\) −17.2813 10.0677i −0.216016 0.125846i
\(81\) −9.00000 −0.111111
\(82\) −72.6227 72.6227i −0.885643 0.885643i
\(83\) −21.3331 + 21.3331i −0.257026 + 0.257026i −0.823843 0.566818i \(-0.808174\pi\)
0.566818 + 0.823843i \(0.308174\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 2.78638 + 10.5640i 0.0327809 + 0.124282i
\(86\) 40.7498 0.473835
\(87\) −16.5922 16.5922i −0.190715 0.190715i
\(88\) −5.84643 + 5.84643i −0.0664367 + 0.0664367i
\(89\) 100.951i 1.13428i −0.823620 0.567141i \(-0.808049\pi\)
0.823620 0.567141i \(-0.191951\pi\)
\(90\) 20.5117 5.41022i 0.227908 0.0601135i
\(91\) −4.23962 −0.0465892
\(92\) 15.8136 + 15.8136i 0.171887 + 0.171887i
\(93\) 19.3432 19.3432i 0.207991 0.207991i
\(94\) 104.639i 1.11318i
\(95\) −8.43666 + 14.4817i −0.0888070 + 0.152438i
\(96\) −9.79796 −0.102062
\(97\) 52.5887 + 52.5887i 0.542151 + 0.542151i 0.924159 0.382008i \(-0.124767\pi\)
−0.382008 + 0.924159i \(0.624767\pi\)
\(98\) −7.00000 + 7.00000i −0.0714286 + 0.0714286i
\(99\) 8.76965i 0.0885823i
\(100\) −43.4955 + 24.6606i −0.434955 + 0.246606i
\(101\) −129.417 −1.28136 −0.640679 0.767808i \(-0.721347\pi\)
−0.640679 + 0.767808i \(0.721347\pi\)
\(102\) 3.78462 + 3.78462i 0.0371041 + 0.0371041i
\(103\) 31.0447 31.0447i 0.301405 0.301405i −0.540158 0.841563i \(-0.681636\pi\)
0.841563 + 0.540158i \(0.181636\pi\)
\(104\) 4.53234i 0.0435802i
\(105\) 19.7982 + 11.5339i 0.188554 + 0.109847i
\(106\) −81.0757 −0.764865
\(107\) 109.421 + 109.421i 1.02263 + 1.02263i 0.999738 + 0.0228904i \(0.00728688\pi\)
0.0228904 + 0.999738i \(0.492713\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 68.6170i 0.629514i 0.949172 + 0.314757i \(0.101923\pi\)
−0.949172 + 0.314757i \(0.898077\pi\)
\(110\) 5.27174 + 19.9867i 0.0479249 + 0.181697i
\(111\) −41.2261 −0.371406
\(112\) −7.48331 7.48331i −0.0668153 0.0668153i
\(113\) −68.0366 + 68.0366i −0.602094 + 0.602094i −0.940868 0.338774i \(-0.889988\pi\)
0.338774 + 0.940868i \(0.389988\pi\)
\(114\) 8.21066i 0.0720233i
\(115\) 54.0607 14.2592i 0.470093 0.123993i
\(116\) 27.0949 0.233577
\(117\) 3.39926 + 3.39926i 0.0290535 + 0.0290535i
\(118\) 117.165 117.165i 0.992924 0.992924i
\(119\) 5.78110i 0.0485807i
\(120\) −12.3303 + 21.1652i −0.102753 + 0.176376i
\(121\) −112.455 −0.929379
\(122\) −45.4373 45.4373i −0.372437 0.372437i
\(123\) −88.9443 + 88.9443i −0.723124 + 0.723124i
\(124\) 31.5873i 0.254736i
\(125\) −1.46629 + 124.991i −0.0117303 + 0.999931i
\(126\) 11.2250 0.0890871
\(127\) 142.963 + 142.963i 1.12569 + 1.12569i 0.990870 + 0.134824i \(0.0430470\pi\)
0.134824 + 0.990870i \(0.456953\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 49.9082i 0.386885i
\(130\) −9.79058 5.70376i −0.0753122 0.0438750i
\(131\) 3.55384 0.0271285 0.0135643 0.999908i \(-0.495682\pi\)
0.0135643 + 0.999908i \(0.495682\pi\)
\(132\) 7.16039 + 7.16039i 0.0542454 + 0.0542454i
\(133\) −6.27100 + 6.27100i −0.0471503 + 0.0471503i
\(134\) 115.555i 0.862348i
\(135\) −6.62614 25.1216i −0.0490825 0.186086i
\(136\) −6.18025 −0.0454430
\(137\) 75.1054 + 75.1054i 0.548214 + 0.548214i 0.925924 0.377710i \(-0.123288\pi\)
−0.377710 + 0.925924i \(0.623288\pi\)
\(138\) 19.3676 19.3676i 0.140345 0.140345i
\(139\) 192.352i 1.38383i 0.721980 + 0.691914i \(0.243232\pi\)
−0.721980 + 0.691914i \(0.756768\pi\)
\(140\) −25.5826 + 6.74773i −0.182733 + 0.0481981i
\(141\) −128.156 −0.908907
\(142\) −51.7217 51.7217i −0.364238 0.364238i
\(143\) −3.31225 + 3.31225i −0.0231626 + 0.0231626i
\(144\) 12.0000i 0.0833333i
\(145\) 34.0977 58.5293i 0.235157 0.403650i
\(146\) 144.770 0.991576
\(147\) 8.57321 + 8.57321i 0.0583212 + 0.0583212i
\(148\) 33.6610 33.6610i 0.227439 0.227439i
\(149\) 77.5005i 0.520138i −0.965590 0.260069i \(-0.916255\pi\)
0.965590 0.260069i \(-0.0837453\pi\)
\(150\) 30.2030 + 53.2708i 0.201353 + 0.355139i
\(151\) 36.8195 0.243837 0.121919 0.992540i \(-0.461095\pi\)
0.121919 + 0.992540i \(0.461095\pi\)
\(152\) −6.70398 6.70398i −0.0441051 0.0441051i
\(153\) 4.63519 4.63519i 0.0302954 0.0302954i
\(154\) 10.9377i 0.0710238i
\(155\) 68.2336 + 39.7512i 0.440217 + 0.256460i
\(156\) −5.55096 −0.0355831
\(157\) 75.7654 + 75.7654i 0.482582 + 0.482582i 0.905955 0.423373i \(-0.139154\pi\)
−0.423373 + 0.905955i \(0.639154\pi\)
\(158\) 37.1850 37.1850i 0.235348 0.235348i
\(159\) 99.2971i 0.624510i
\(160\) −7.21362 27.3489i −0.0450851 0.170931i
\(161\) 29.5846 0.183755
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 174.453 174.453i 1.07026 1.07026i 0.0729236 0.997338i \(-0.476767\pi\)
0.997338 0.0729236i \(-0.0232329\pi\)
\(164\) 145.245i 0.885643i
\(165\) 24.4786 6.45654i 0.148355 0.0391306i
\(166\) −42.6663 −0.257026
\(167\) 119.275 + 119.275i 0.714222 + 0.714222i 0.967416 0.253194i \(-0.0814810\pi\)
−0.253194 + 0.967416i \(0.581481\pi\)
\(168\) −9.16515 + 9.16515i −0.0545545 + 0.0545545i
\(169\) 166.432i 0.984806i
\(170\) −7.77758 + 13.3503i −0.0457505 + 0.0785314i
\(171\) 10.0560 0.0588068
\(172\) 40.7498 + 40.7498i 0.236918 + 0.236918i
\(173\) 110.021 110.021i 0.635957 0.635957i −0.313599 0.949556i \(-0.601535\pi\)
0.949556 + 0.313599i \(0.101535\pi\)
\(174\) 33.1843i 0.190715i
\(175\) −17.6184 + 63.7542i −0.100677 + 0.364309i
\(176\) −11.6929 −0.0664367
\(177\) −143.497 143.497i −0.810719 0.810719i
\(178\) 100.951 100.951i 0.567141 0.567141i
\(179\) 49.0357i 0.273943i −0.990575 0.136971i \(-0.956263\pi\)
0.990575 0.136971i \(-0.0437368\pi\)
\(180\) 25.9219 + 15.1015i 0.144011 + 0.0838971i
\(181\) −327.143 −1.80742 −0.903709 0.428148i \(-0.859166\pi\)
−0.903709 + 0.428148i \(0.859166\pi\)
\(182\) −4.23962 4.23962i −0.0232946 0.0232946i
\(183\) −55.6491 + 55.6491i −0.304094 + 0.304094i
\(184\) 31.6272i 0.171887i
\(185\) −30.3522 115.074i −0.164066 0.622021i
\(186\) 38.6864 0.207991
\(187\) 4.51655 + 4.51655i 0.0241527 + 0.0241527i
\(188\) 104.639 104.639i 0.556589 0.556589i
\(189\) 13.7477i 0.0727393i
\(190\) −22.9183 + 6.04500i −0.120623 + 0.0318158i
\(191\) 289.078 1.51350 0.756749 0.653705i \(-0.226786\pi\)
0.756749 + 0.653705i \(0.226786\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −131.213 + 131.213i −0.679858 + 0.679858i −0.959968 0.280110i \(-0.909629\pi\)
0.280110 + 0.959968i \(0.409629\pi\)
\(194\) 105.177i 0.542151i
\(195\) −6.98565 + 11.9910i −0.0358238 + 0.0614921i
\(196\) −14.0000 −0.0714286
\(197\) 111.798 + 111.798i 0.567504 + 0.567504i 0.931429 0.363924i \(-0.118563\pi\)
−0.363924 + 0.931429i \(0.618563\pi\)
\(198\) 8.76965 8.76965i 0.0442911 0.0442911i
\(199\) 58.3715i 0.293324i −0.989187 0.146662i \(-0.953147\pi\)
0.989187 0.146662i \(-0.0468530\pi\)
\(200\) −68.1561 18.8348i −0.340780 0.0941742i
\(201\) 141.525 0.704104
\(202\) −129.417 129.417i −0.640679 0.640679i
\(203\) 25.3450 25.3450i 0.124852 0.124852i
\(204\) 7.56923i 0.0371041i
\(205\) −313.753 182.785i −1.53050 0.891634i
\(206\) 62.0894 0.301405
\(207\) −23.7204 23.7204i −0.114591 0.114591i
\(208\) 4.53234 4.53234i 0.0217901 0.0217901i
\(209\) 9.79858i 0.0468832i
\(210\) 8.26424 + 31.3321i 0.0393535 + 0.149201i
\(211\) 55.0602 0.260949 0.130474 0.991452i \(-0.458350\pi\)
0.130474 + 0.991452i \(0.458350\pi\)
\(212\) −81.0757 81.0757i −0.382433 0.382433i
\(213\) −63.3459 + 63.3459i −0.297399 + 0.297399i
\(214\) 218.842i 1.02263i
\(215\) 139.308 36.7443i 0.647944 0.170903i
\(216\) 14.6969 0.0680414
\(217\) 29.5472 + 29.5472i 0.136162 + 0.136162i
\(218\) −68.6170 + 68.6170i −0.314757 + 0.314757i
\(219\) 177.306i 0.809619i
\(220\) −14.7150 + 25.2584i −0.0668862 + 0.114811i
\(221\) −3.50138 −0.0158433
\(222\) −41.2261 41.2261i −0.185703 0.185703i
\(223\) −101.768 + 101.768i −0.456360 + 0.456360i −0.897459 0.441099i \(-0.854589\pi\)
0.441099 + 0.897459i \(0.354589\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 65.2432 36.9909i 0.289970 0.164404i
\(226\) −136.073 −0.602094
\(227\) −25.0589 25.0589i −0.110392 0.110392i 0.649753 0.760145i \(-0.274872\pi\)
−0.760145 + 0.649753i \(0.774872\pi\)
\(228\) −8.21066 + 8.21066i −0.0360117 + 0.0360117i
\(229\) 283.497i 1.23798i 0.785399 + 0.618990i \(0.212458\pi\)
−0.785399 + 0.618990i \(0.787542\pi\)
\(230\) 68.3199 + 39.8015i 0.297043 + 0.173050i
\(231\) 13.3959 0.0579907
\(232\) 27.0949 + 27.0949i 0.116788 + 0.116788i
\(233\) 139.119 139.119i 0.597077 0.597077i −0.342457 0.939534i \(-0.611259\pi\)
0.939534 + 0.342457i \(0.111259\pi\)
\(234\) 6.79852i 0.0290535i
\(235\) −94.3531 357.720i −0.401503 1.52221i
\(236\) 234.330 0.992924
\(237\) −45.5421 45.5421i −0.192161 0.192161i
\(238\) −5.78110 + 5.78110i −0.0242903 + 0.0242903i
\(239\) 183.280i 0.766864i −0.923569 0.383432i \(-0.874742\pi\)
0.923569 0.383432i \(-0.125258\pi\)
\(240\) −33.4955 + 8.83485i −0.139564 + 0.0368119i
\(241\) −280.094 −1.16222 −0.581108 0.813827i \(-0.697380\pi\)
−0.581108 + 0.813827i \(0.697380\pi\)
\(242\) −112.455 112.455i −0.464689 0.464689i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 90.8747i 0.372437i
\(245\) −17.6184 + 30.2422i −0.0719118 + 0.123438i
\(246\) −177.889 −0.723124
\(247\) −3.79809 3.79809i −0.0153769 0.0153769i
\(248\) −31.5873 + 31.5873i −0.127368 + 0.127368i
\(249\) 52.2553i 0.209861i
\(250\) −126.458 + 123.525i −0.505831 + 0.494100i
\(251\) 148.745 0.592611 0.296305 0.955093i \(-0.404245\pi\)
0.296305 + 0.955093i \(0.404245\pi\)
\(252\) 11.2250 + 11.2250i 0.0445435 + 0.0445435i
\(253\) 23.1133 23.1133i 0.0913569 0.0913569i
\(254\) 285.926i 1.12569i
\(255\) 16.3507 + 9.52555i 0.0641206 + 0.0373551i
\(256\) 16.0000 0.0625000
\(257\) −241.684 241.684i −0.940404 0.940404i 0.0579178 0.998321i \(-0.481554\pi\)
−0.998321 + 0.0579178i \(0.981554\pi\)
\(258\) 49.9082 49.9082i 0.193442 0.193442i
\(259\) 62.9739i 0.243142i
\(260\) −4.08683 15.4943i −0.0157186 0.0595936i
\(261\) −40.6423 −0.155718
\(262\) 3.55384 + 3.55384i 0.0135643 + 0.0135643i
\(263\) −234.607 + 234.607i −0.892042 + 0.892042i −0.994715 0.102673i \(-0.967260\pi\)
0.102673 + 0.994715i \(0.467260\pi\)
\(264\) 14.3208i 0.0542454i
\(265\) −277.167 + 73.1062i −1.04591 + 0.275872i
\(266\) −12.5420 −0.0471503
\(267\) −123.639 123.639i −0.463069 0.463069i
\(268\) −115.555 + 115.555i −0.431174 + 0.431174i
\(269\) 357.902i 1.33049i −0.746625 0.665245i \(-0.768327\pi\)
0.746625 0.665245i \(-0.231673\pi\)
\(270\) 18.4955 31.7477i 0.0685017 0.117584i
\(271\) 178.869 0.660035 0.330017 0.943975i \(-0.392945\pi\)
0.330017 + 0.943975i \(0.392945\pi\)
\(272\) −6.18025 6.18025i −0.0227215 0.0227215i
\(273\) −5.19245 + 5.19245i −0.0190200 + 0.0190200i
\(274\) 150.211i 0.548214i
\(275\) 36.0441 + 63.5733i 0.131070 + 0.231176i
\(276\) 38.7353 0.140345
\(277\) −119.355 119.355i −0.430883 0.430883i 0.458045 0.888929i \(-0.348550\pi\)
−0.888929 + 0.458045i \(0.848550\pi\)
\(278\) −192.352 + 192.352i −0.691914 + 0.691914i
\(279\) 47.3809i 0.169824i
\(280\) −32.3303 18.8348i −0.115465 0.0672673i
\(281\) −42.3632 −0.150759 −0.0753793 0.997155i \(-0.524017\pi\)
−0.0753793 + 0.997155i \(0.524017\pi\)
\(282\) −128.156 128.156i −0.454453 0.454453i
\(283\) 3.43964 3.43964i 0.0121542 0.0121542i −0.701004 0.713158i \(-0.747264\pi\)
0.713158 + 0.701004i \(0.247264\pi\)
\(284\) 103.443i 0.364238i
\(285\) 7.40358 + 28.0691i 0.0259775 + 0.0984880i
\(286\) −6.62451 −0.0231626
\(287\) −135.865 135.865i −0.473396 0.473396i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 284.226i 0.983479i
\(290\) 92.6270 24.4315i 0.319403 0.0842467i
\(291\) 128.815 0.442665
\(292\) 144.770 + 144.770i 0.495788 + 0.495788i
\(293\) −25.3982 + 25.3982i −0.0866834 + 0.0866834i −0.749119 0.662436i \(-0.769523\pi\)
0.662436 + 0.749119i \(0.269523\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 294.894 506.190i 0.999641 1.71590i
\(296\) 67.3219 0.227439
\(297\) −10.7406 10.7406i −0.0361636 0.0361636i
\(298\) 77.5005 77.5005i 0.260069 0.260069i
\(299\) 17.9182i 0.0599270i
\(300\) −23.0679 + 83.4738i −0.0768929 + 0.278246i
\(301\) 76.2360 0.253276
\(302\) 36.8195 + 36.8195i 0.121919 + 0.121919i
\(303\) −158.503 + 158.503i −0.523113 + 0.523113i
\(304\) 13.4080i 0.0441051i
\(305\) −196.304 114.362i −0.643619 0.374957i
\(306\) 9.27038 0.0302954
\(307\) −323.839 323.839i −1.05485 1.05485i −0.998406 0.0564445i \(-0.982024\pi\)
−0.0564445 0.998406i \(-0.517976\pi\)
\(308\) −10.9377 + 10.9377i −0.0355119 + 0.0355119i
\(309\) 76.0437i 0.246096i
\(310\) 28.4824 + 107.985i 0.0918786 + 0.348338i
\(311\) −284.428 −0.914561 −0.457280 0.889323i \(-0.651176\pi\)
−0.457280 + 0.889323i \(0.651176\pi\)
\(312\) −5.55096 5.55096i −0.0177916 0.0177916i
\(313\) 178.964 178.964i 0.571771 0.571771i −0.360852 0.932623i \(-0.617514\pi\)
0.932623 + 0.360852i \(0.117514\pi\)
\(314\) 151.531i 0.482582i
\(315\) 38.3739 10.1216i 0.121822 0.0321320i
\(316\) 74.3700 0.235348
\(317\) 335.800 + 335.800i 1.05931 + 1.05931i 0.998127 + 0.0611787i \(0.0194860\pi\)
0.0611787 + 0.998127i \(0.480514\pi\)
\(318\) −99.2971 + 99.2971i −0.312255 + 0.312255i
\(319\) 39.6021i 0.124145i
\(320\) 20.1353 34.5625i 0.0629228 0.108008i
\(321\) 268.026 0.834973
\(322\) 29.5846 + 29.5846i 0.0918775 + 0.0918775i
\(323\) −5.17903 + 5.17903i −0.0160342 + 0.0160342i
\(324\) 18.0000i 0.0555556i
\(325\) −38.6133 10.6708i −0.118810 0.0328331i
\(326\) 348.905 1.07026
\(327\) 84.0384 + 84.0384i 0.256998 + 0.256998i
\(328\) 145.245 145.245i 0.442821 0.442821i
\(329\) 195.761i 0.595019i
\(330\) 30.9352 + 18.0221i 0.0937429 + 0.0546123i
\(331\) 444.301 1.34230 0.671150 0.741322i \(-0.265801\pi\)
0.671150 + 0.741322i \(0.265801\pi\)
\(332\) −42.6663 42.6663i −0.128513 0.128513i
\(333\) −50.4914 + 50.4914i −0.151626 + 0.151626i
\(334\) 238.550i 0.714222i
\(335\) 104.196 + 395.037i 0.311033 + 1.17921i
\(336\) −18.3303 −0.0545545
\(337\) 431.469 + 431.469i 1.28032 + 1.28032i 0.940483 + 0.339842i \(0.110374\pi\)
0.339842 + 0.940483i \(0.389626\pi\)
\(338\) −166.432 + 166.432i −0.492403 + 0.492403i
\(339\) 166.655i 0.491608i
\(340\) −21.1279 + 5.57275i −0.0621409 + 0.0163904i
\(341\) 46.1682 0.135391
\(342\) 10.0560 + 10.0560i 0.0294034 + 0.0294034i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 81.4997i 0.236918i
\(345\) 48.7467 83.6744i 0.141295 0.242534i
\(346\) 220.041 0.635957
\(347\) −227.893 227.893i −0.656751 0.656751i 0.297859 0.954610i \(-0.403728\pi\)
−0.954610 + 0.297859i \(0.903728\pi\)
\(348\) 33.1843 33.1843i 0.0953573 0.0953573i
\(349\) 280.016i 0.802337i 0.916004 + 0.401168i \(0.131396\pi\)
−0.916004 + 0.401168i \(0.868604\pi\)
\(350\) −81.3725 + 46.1358i −0.232493 + 0.131816i
\(351\) 8.32645 0.0237221
\(352\) −11.6929 11.6929i −0.0332184 0.0332184i
\(353\) −114.469 + 114.469i −0.324276 + 0.324276i −0.850405 0.526129i \(-0.823643\pi\)
0.526129 + 0.850405i \(0.323643\pi\)
\(354\) 286.995i 0.810719i
\(355\) −223.454 130.179i −0.629449 0.366702i
\(356\) 201.902 0.567141
\(357\) 7.08037 + 7.08037i 0.0198330 + 0.0198330i
\(358\) 49.0357 49.0357i 0.136971 0.136971i
\(359\) 700.748i 1.95195i 0.217893 + 0.975973i \(0.430082\pi\)
−0.217893 + 0.975973i \(0.569918\pi\)
\(360\) 10.8204 + 41.0234i 0.0300568 + 0.113954i
\(361\) 349.764 0.968876
\(362\) −327.143 327.143i −0.903709 0.903709i
\(363\) −137.728 + 137.728i −0.379417 + 0.379417i
\(364\) 8.47924i 0.0232946i
\(365\) 494.913 130.540i 1.35593 0.357643i
\(366\) −111.298 −0.304094
\(367\) 412.257 + 412.257i 1.12332 + 1.12332i 0.991240 + 0.132075i \(0.0421641\pi\)
0.132075 + 0.991240i \(0.457836\pi\)
\(368\) −31.6272 + 31.6272i −0.0859436 + 0.0859436i
\(369\) 217.868i 0.590428i
\(370\) 84.7217 145.426i 0.228978 0.393043i
\(371\) −151.679 −0.408838
\(372\) 38.6864 + 38.6864i 0.103996 + 0.103996i
\(373\) −121.669 + 121.669i −0.326191 + 0.326191i −0.851136 0.524945i \(-0.824086\pi\)
0.524945 + 0.851136i \(0.324086\pi\)
\(374\) 9.03311i 0.0241527i
\(375\) 151.287 + 154.878i 0.403431 + 0.413009i
\(376\) 209.278 0.556589
\(377\) 15.3504 + 15.3504i 0.0407173 + 0.0407173i
\(378\) 13.7477 13.7477i 0.0363696 0.0363696i
\(379\) 709.113i 1.87101i −0.353312 0.935506i \(-0.614945\pi\)
0.353312 0.935506i \(-0.385055\pi\)
\(380\) −28.9633 16.8733i −0.0762192 0.0444035i
\(381\) 350.187 0.919125
\(382\) 289.078 + 289.078i 0.756749 + 0.756749i
\(383\) −476.611 + 476.611i −1.24441 + 1.24441i −0.286264 + 0.958151i \(0.592413\pi\)
−0.958151 + 0.286264i \(0.907587\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 9.86253 + 37.3917i 0.0256170 + 0.0971213i
\(386\) −262.425 −0.679858
\(387\) −61.1248 61.1248i −0.157945 0.157945i
\(388\) −105.177 + 105.177i −0.271076 + 0.271076i
\(389\) 270.210i 0.694627i 0.937749 + 0.347313i \(0.112906\pi\)
−0.937749 + 0.347313i \(0.887094\pi\)
\(390\) −18.9766 + 5.00532i −0.0486580 + 0.0128342i
\(391\) 24.4330 0.0624886
\(392\) −14.0000 14.0000i −0.0357143 0.0357143i
\(393\) 4.35255 4.35255i 0.0110752 0.0110752i
\(394\) 223.597i 0.567504i
\(395\) 93.5914 160.651i 0.236940 0.406712i
\(396\) 17.5393 0.0442911
\(397\) −169.270 169.270i −0.426374 0.426374i 0.461017 0.887391i \(-0.347485\pi\)
−0.887391 + 0.461017i \(0.847485\pi\)
\(398\) 58.3715 58.3715i 0.146662 0.146662i
\(399\) 15.3607i 0.0384981i
\(400\) −49.3212 86.9909i −0.123303 0.217477i
\(401\) 397.414 0.991058 0.495529 0.868592i \(-0.334974\pi\)
0.495529 + 0.868592i \(0.334974\pi\)
\(402\) 141.525 + 141.525i 0.352052 + 0.352052i
\(403\) −17.8956 + 17.8956i −0.0444059 + 0.0444059i
\(404\) 258.834i 0.640679i
\(405\) −38.8829 22.6522i −0.0960071 0.0559314i
\(406\) 50.6899 0.124852
\(407\) −49.1991 49.1991i −0.120882 0.120882i
\(408\) −7.56923 + 7.56923i −0.0185520 + 0.0185520i
\(409\) 787.478i 1.92537i 0.270616 + 0.962687i \(0.412773\pi\)
−0.270616 + 0.962687i \(0.587227\pi\)
\(410\) −130.968 496.538i −0.319435 1.21107i
\(411\) 183.970 0.447615
\(412\) 62.0894 + 62.0894i 0.150703 + 0.150703i
\(413\) 219.196 219.196i 0.530740 0.530740i
\(414\) 47.4409i 0.114591i
\(415\) −145.860 + 38.4723i −0.351469 + 0.0927043i
\(416\) 9.06469 0.0217901
\(417\) 235.582 + 235.582i 0.564945 + 0.564945i
\(418\) −9.79858 + 9.79858i −0.0234416 + 0.0234416i
\(419\) 293.606i 0.700730i −0.936613 0.350365i \(-0.886058\pi\)
0.936613 0.350365i \(-0.113942\pi\)
\(420\) −23.0679 + 39.5964i −0.0549235 + 0.0942771i
\(421\) −294.797 −0.700230 −0.350115 0.936707i \(-0.613857\pi\)
−0.350115 + 0.936707i \(0.613857\pi\)
\(422\) 55.0602 + 55.0602i 0.130474 + 0.130474i
\(423\) −156.958 + 156.958i −0.371060 + 0.371060i
\(424\) 162.151i 0.382433i
\(425\) −14.5505 + 52.6527i −0.0342365 + 0.123889i
\(426\) −126.692 −0.297399
\(427\) −85.0055 85.0055i −0.199076 0.199076i
\(428\) −218.842 + 218.842i −0.511314 + 0.511314i
\(429\) 8.11333i 0.0189122i
\(430\) 176.052 + 102.564i 0.409424 + 0.238520i
\(431\) −314.916 −0.730663 −0.365332 0.930877i \(-0.619044\pi\)
−0.365332 + 0.930877i \(0.619044\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 236.366 236.366i 0.545880 0.545880i −0.379367 0.925246i \(-0.623858\pi\)
0.925246 + 0.379367i \(0.123858\pi\)
\(434\) 59.0944i 0.136162i
\(435\) −29.9224 113.444i −0.0687871 0.260792i
\(436\) −137.234 −0.314757
\(437\) 26.5035 + 26.5035i 0.0606488 + 0.0606488i
\(438\) 177.306 177.306i 0.404809 0.404809i
\(439\) 254.993i 0.580850i 0.956898 + 0.290425i \(0.0937967\pi\)
−0.956898 + 0.290425i \(0.906203\pi\)
\(440\) −39.9734 + 10.5435i −0.0908486 + 0.0239625i
\(441\) 21.0000 0.0476190
\(442\) −3.50138 3.50138i −0.00792167 0.00792167i
\(443\) −292.628 + 292.628i −0.660559 + 0.660559i −0.955512 0.294953i \(-0.904696\pi\)
0.294953 + 0.955512i \(0.404696\pi\)
\(444\) 82.4522i 0.185703i
\(445\) 254.085 436.141i 0.570978 0.980093i
\(446\) −203.537 −0.456360
\(447\) −94.9184 94.9184i −0.212345 0.212345i
\(448\) 14.9666 14.9666i 0.0334077 0.0334077i
\(449\) 400.989i 0.893072i −0.894766 0.446536i \(-0.852657\pi\)
0.894766 0.446536i \(-0.147343\pi\)
\(450\) 102.234 + 28.2523i 0.227187 + 0.0627828i
\(451\) −212.292 −0.470714
\(452\) −136.073 136.073i −0.301047 0.301047i
\(453\) 45.0944 45.0944i 0.0995462 0.0995462i
\(454\) 50.1179i 0.110392i
\(455\) −18.3165 10.6708i −0.0402561 0.0234522i
\(456\) −16.4213 −0.0360117
\(457\) −172.040 172.040i −0.376454 0.376454i 0.493367 0.869821i \(-0.335766\pi\)
−0.869821 + 0.493367i \(0.835766\pi\)
\(458\) −283.497 + 283.497i −0.618990 + 0.618990i
\(459\) 11.3539i 0.0247361i
\(460\) 28.5184 + 108.121i 0.0619965 + 0.235046i
\(461\) 153.918 0.333878 0.166939 0.985967i \(-0.446612\pi\)
0.166939 + 0.985967i \(0.446612\pi\)
\(462\) 13.3959 + 13.3959i 0.0289954 + 0.0289954i
\(463\) −291.763 + 291.763i −0.630158 + 0.630158i −0.948108 0.317949i \(-0.897006\pi\)
0.317949 + 0.948108i \(0.397006\pi\)
\(464\) 54.1898i 0.116788i
\(465\) 132.254 34.8836i 0.284417 0.0750185i
\(466\) 278.238 0.597077
\(467\) −503.234 503.234i −1.07759 1.07759i −0.996725 0.0808645i \(-0.974232\pi\)
−0.0808645 0.996725i \(-0.525768\pi\)
\(468\) −6.79852 + 6.79852i −0.0145267 + 0.0145267i
\(469\) 216.183i 0.460944i
\(470\) 263.367 452.073i 0.560355 0.961857i
\(471\) 185.586 0.394026
\(472\) 234.330 + 234.330i 0.496462 + 0.496462i
\(473\) 59.5603 59.5603i 0.125920 0.125920i
\(474\) 91.0843i 0.192161i
\(475\) −72.8981 + 41.3310i −0.153470 + 0.0870127i
\(476\) −11.5622 −0.0242903
\(477\) 121.614 + 121.614i 0.254955 + 0.254955i
\(478\) 183.280 183.280i 0.383432 0.383432i
\(479\) 670.857i 1.40054i 0.713880 + 0.700268i \(0.246936\pi\)
−0.713880 + 0.700268i \(0.753064\pi\)
\(480\) −42.3303 24.6606i −0.0881881 0.0513763i
\(481\) 38.1408 0.0792947
\(482\) −280.094 280.094i −0.581108 0.581108i
\(483\) 36.2335 36.2335i 0.0750177 0.0750177i
\(484\) 224.910i 0.464689i
\(485\) 94.8388 + 359.561i 0.195544 + 0.741363i
\(486\) −22.0454 −0.0453609
\(487\) −431.350 431.350i −0.885729 0.885729i 0.108380 0.994110i \(-0.465434\pi\)
−0.994110 + 0.108380i \(0.965434\pi\)
\(488\) 90.8747 90.8747i 0.186219 0.186219i
\(489\) 427.320i 0.873865i
\(490\) −47.8606 + 12.6238i −0.0976747 + 0.0257629i
\(491\) −643.019 −1.30961 −0.654806 0.755797i \(-0.727250\pi\)
−0.654806 + 0.755797i \(0.727250\pi\)
\(492\) −177.889 177.889i −0.361562 0.361562i
\(493\) 20.9317 20.9317i 0.0424577 0.0424577i
\(494\) 7.59618i 0.0153769i
\(495\) 22.0724 37.8877i 0.0445908 0.0765407i
\(496\) −63.1746 −0.127368
\(497\) −96.7625 96.7625i −0.194693 0.194693i
\(498\) −52.2553 + 52.2553i −0.104930 + 0.104930i
\(499\) 350.058i 0.701520i −0.936465 0.350760i \(-0.885923\pi\)
0.936465 0.350760i \(-0.114077\pi\)
\(500\) −249.983 2.93258i −0.499966 0.00586517i
\(501\) 292.163 0.583160
\(502\) 148.745 + 148.745i 0.296305 + 0.296305i
\(503\) 160.423 160.423i 0.318932 0.318932i −0.529425 0.848357i \(-0.677592\pi\)
0.848357 + 0.529425i \(0.177592\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −559.124 325.732i −1.10718 0.645014i
\(506\) 46.2266 0.0913569
\(507\) 203.837 + 203.837i 0.402045 + 0.402045i
\(508\) −285.926 + 285.926i −0.562847 + 0.562847i
\(509\) 402.935i 0.791620i 0.918332 + 0.395810i \(0.129536\pi\)
−0.918332 + 0.395810i \(0.870464\pi\)
\(510\) 6.82520 + 25.8763i 0.0133827 + 0.0507378i
\(511\) 270.840 0.530020
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 12.3160 12.3160i 0.0240078 0.0240078i
\(514\) 483.367i 0.940404i
\(515\) 212.260 55.9862i 0.412155 0.108711i
\(516\) 99.8163 0.193442
\(517\) −152.941 152.941i −0.295824 0.295824i
\(518\) 62.9739 62.9739i 0.121571 0.121571i
\(519\) 269.494i 0.519257i
\(520\) 11.4075 19.5812i 0.0219375 0.0376561i
\(521\) −725.448 −1.39241 −0.696207 0.717841i \(-0.745131\pi\)
−0.696207 + 0.717841i \(0.745131\pi\)
\(522\) −40.6423 40.6423i −0.0778589 0.0778589i
\(523\) 454.490 454.490i 0.869005 0.869005i −0.123357 0.992362i \(-0.539366\pi\)
0.992362 + 0.123357i \(0.0393661\pi\)
\(524\) 7.10768i 0.0135643i
\(525\) 56.5045 + 99.6606i 0.107628 + 0.189830i
\(526\) −469.214 −0.892042
\(527\) 24.4022 + 24.4022i 0.0463040 + 0.0463040i
\(528\) −14.3208 + 14.3208i −0.0271227 + 0.0271227i
\(529\) 403.965i 0.763638i
\(530\) −350.273 204.060i −0.660892 0.385020i
\(531\) −351.495 −0.661949
\(532\) −12.5420 12.5420i −0.0235752 0.0235752i
\(533\) 82.2878 82.2878i 0.154386 0.154386i
\(534\) 247.279i 0.463069i
\(535\) 197.331 + 748.138i 0.368843 + 1.39839i
\(536\) −231.109 −0.431174
\(537\) −60.0563 60.0563i −0.111837 0.111837i
\(538\) 357.902 357.902i 0.665245 0.665245i
\(539\) 20.4625i 0.0379638i
\(540\) 50.2432 13.2523i 0.0930429 0.0245412i
\(541\) −173.852 −0.321354 −0.160677 0.987007i \(-0.551368\pi\)
−0.160677 + 0.987007i \(0.551368\pi\)
\(542\) 178.869 + 178.869i 0.330017 + 0.330017i
\(543\) −400.666 + 400.666i −0.737875 + 0.737875i
\(544\) 12.3605i 0.0227215i
\(545\) −172.703 + 296.447i −0.316886 + 0.543940i
\(546\) −10.3849 −0.0190200
\(547\) −293.440 293.440i −0.536453 0.536453i 0.386032 0.922485i \(-0.373845\pi\)
−0.922485 + 0.386032i \(0.873845\pi\)
\(548\) −150.211 + 150.211i −0.274107 + 0.274107i
\(549\) 136.312i 0.248291i
\(550\) −27.5292 + 99.6174i −0.0500530 + 0.181123i
\(551\) 45.4109 0.0824154
\(552\) 38.7353 + 38.7353i 0.0701726 + 0.0701726i
\(553\) 69.5668 69.5668i 0.125799 0.125799i
\(554\) 238.709i 0.430883i
\(555\) −178.110 103.762i −0.320919 0.186959i
\(556\) −384.704 −0.691914
\(557\) 234.581 + 234.581i 0.421151 + 0.421151i 0.885600 0.464449i \(-0.153747\pi\)
−0.464449 + 0.885600i \(0.653747\pi\)
\(558\) 47.3809 47.3809i 0.0849121 0.0849121i
\(559\) 46.1731i 0.0825994i
\(560\) −13.4955 51.1652i −0.0240990 0.0913663i
\(561\) 11.0633 0.0197206
\(562\) −42.3632 42.3632i −0.0753793 0.0753793i
\(563\) 177.541 177.541i 0.315348 0.315348i −0.531629 0.846977i \(-0.678420\pi\)
0.846977 + 0.531629i \(0.178420\pi\)
\(564\) 256.312i 0.454453i
\(565\) −465.182 + 122.698i −0.823331 + 0.217164i
\(566\) 6.87928 0.0121542
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 103.443 103.443i 0.182119 0.182119i
\(569\) 253.619i 0.445727i 0.974850 + 0.222864i \(0.0715405\pi\)
−0.974850 + 0.222864i \(0.928460\pi\)
\(570\) −20.6655 + 35.4727i −0.0362553 + 0.0622328i
\(571\) 219.857 0.385038 0.192519 0.981293i \(-0.438334\pi\)
0.192519 + 0.981293i \(0.438334\pi\)
\(572\) −6.62451 6.62451i −0.0115813 0.0115813i
\(573\) 354.047 354.047i 0.617883 0.617883i
\(574\) 271.729i 0.473396i
\(575\) 269.448 + 74.4618i 0.468606 + 0.129499i
\(576\) −24.0000 −0.0416667
\(577\) 419.350 + 419.350i 0.726776 + 0.726776i 0.969976 0.243200i \(-0.0781972\pi\)
−0.243200 + 0.969976i \(0.578197\pi\)
\(578\) 284.226 284.226i 0.491740 0.491740i
\(579\) 321.404i 0.555101i
\(580\) 117.059 + 68.1955i 0.201825 + 0.117578i
\(581\) −79.8213 −0.137386
\(582\) 128.815 + 128.815i 0.221332 + 0.221332i
\(583\) −118.501 + 118.501i −0.203261 + 0.203261i
\(584\) 289.540i 0.495788i
\(585\) 6.13024 + 23.2415i 0.0104790 + 0.0397291i
\(586\) −50.7965 −0.0866834
\(587\) −493.116 493.116i −0.840061 0.840061i 0.148805 0.988867i \(-0.452457\pi\)
−0.988867 + 0.148805i \(0.952457\pi\)
\(588\) −17.1464 + 17.1464i −0.0291606 + 0.0291606i
\(589\) 52.9401i 0.0898814i
\(590\) 801.084 211.296i 1.35777 0.358129i
\(591\) 273.849 0.463365
\(592\) 67.3219 + 67.3219i 0.113719 + 0.113719i
\(593\) 528.205 528.205i 0.890733 0.890733i −0.103859 0.994592i \(-0.533119\pi\)
0.994592 + 0.103859i \(0.0331191\pi\)
\(594\) 21.4812i 0.0361636i
\(595\) −14.5505 + 24.9762i −0.0244546 + 0.0419768i
\(596\) 155.001 0.260069
\(597\) −71.4902 71.4902i −0.119749 0.119749i
\(598\) −17.9182 + 17.9182i −0.0299635 + 0.0299635i
\(599\) 436.395i 0.728540i −0.931293 0.364270i \(-0.881319\pi\)
0.931293 0.364270i \(-0.118681\pi\)
\(600\) −106.542 + 60.4059i −0.177569 + 0.100677i
\(601\) 907.900 1.51065 0.755324 0.655351i \(-0.227479\pi\)
0.755324 + 0.655351i \(0.227479\pi\)
\(602\) 76.2360 + 76.2360i 0.126638 + 0.126638i
\(603\) 173.332 173.332i 0.287449 0.287449i
\(604\) 73.6389i 0.121919i
\(605\) −485.841 283.039i −0.803042 0.467833i
\(606\) −317.006 −0.523113
\(607\) −46.6746 46.6746i −0.0768939 0.0768939i 0.667614 0.744508i \(-0.267316\pi\)
−0.744508 + 0.667614i \(0.767316\pi\)
\(608\) 13.4080 13.4080i 0.0220526 0.0220526i
\(609\) 62.0822i 0.101941i
\(610\) −81.9420 310.666i −0.134331 0.509288i
\(611\) 118.565 0.194050
\(612\) 9.27038 + 9.27038i 0.0151477 + 0.0151477i
\(613\) 404.981 404.981i 0.660653 0.660653i −0.294881 0.955534i \(-0.595280\pi\)
0.955534 + 0.294881i \(0.0952799\pi\)
\(614\) 647.678i 1.05485i
\(615\) −608.133 + 160.403i −0.988834 + 0.260817i
\(616\) −21.8753 −0.0355119
\(617\) 821.889 + 821.889i 1.33207 + 1.33207i 0.903514 + 0.428558i \(0.140978\pi\)
0.428558 + 0.903514i \(0.359022\pi\)
\(618\) 76.0437 76.0437i 0.123048 0.123048i
\(619\) 355.855i 0.574886i 0.957798 + 0.287443i \(0.0928052\pi\)
−0.957798 + 0.287443i \(0.907195\pi\)
\(620\) −79.5025 + 136.467i −0.128230 + 0.220108i
\(621\) −58.1029 −0.0935635
\(622\) −284.428 284.428i −0.457280 0.457280i
\(623\) 188.862 188.862i 0.303150 0.303150i
\(624\) 11.1019i 0.0177916i
\(625\) −320.927 + 536.312i −0.513484 + 0.858099i
\(626\) 357.929 0.571771
\(627\) 12.0008 + 12.0008i 0.0191400 + 0.0191400i
\(628\) −151.531 + 151.531i −0.241291 + 0.241291i
\(629\) 52.0083i 0.0826841i
\(630\) 48.4955 + 28.2523i 0.0769769 + 0.0448449i
\(631\) −588.910 −0.933297 −0.466648 0.884443i \(-0.654539\pi\)
−0.466648 + 0.884443i \(0.654539\pi\)
\(632\) 74.3700 + 74.3700i 0.117674 + 0.117674i
\(633\) 67.4347 67.4347i 0.106532 0.106532i
\(634\) 671.600i 1.05931i
\(635\) 257.821 + 977.472i 0.406017 + 1.53933i
\(636\) −198.594 −0.312255
\(637\) −7.93160 7.93160i −0.0124515 0.0124515i
\(638\) 39.6021 39.6021i 0.0620723 0.0620723i
\(639\) 155.165i 0.242825i
\(640\) 54.6978 14.4272i 0.0854654 0.0225426i
\(641\) −703.566 −1.09761 −0.548804 0.835951i \(-0.684917\pi\)
−0.548804 + 0.835951i \(0.684917\pi\)
\(642\) 268.026 + 268.026i 0.417486 + 0.417486i
\(643\) 75.8005 75.8005i 0.117886 0.117886i −0.645703 0.763589i \(-0.723436\pi\)
0.763589 + 0.645703i \(0.223436\pi\)
\(644\) 59.1691i 0.0918775i
\(645\) 125.614 215.619i 0.194751 0.334293i
\(646\) −10.3581 −0.0160342
\(647\) 362.070 + 362.070i 0.559613 + 0.559613i 0.929197 0.369584i \(-0.120500\pi\)
−0.369584 + 0.929197i \(0.620500\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 342.499i 0.527733i
\(650\) −27.9426 49.2841i −0.0429886 0.0758217i
\(651\) 72.3756 0.111176
\(652\) 348.905 + 348.905i 0.535131 + 0.535131i
\(653\) 804.153 804.153i 1.23147 1.23147i 0.268077 0.963397i \(-0.413612\pi\)
0.963397 0.268077i \(-0.0863882\pi\)
\(654\) 168.077i 0.256998i
\(655\) 15.3537 + 8.94470i 0.0234408 + 0.0136560i
\(656\) 290.491 0.442821
\(657\) −217.155 217.155i −0.330525 0.330525i
\(658\) 195.761 195.761i 0.297510 0.297510i
\(659\) 803.984i 1.22001i −0.792399 0.610003i \(-0.791168\pi\)
0.792399 0.610003i \(-0.208832\pi\)
\(660\) 12.9131 + 48.9572i 0.0195653 + 0.0741776i
\(661\) −923.281 −1.39679 −0.698397 0.715710i \(-0.746103\pi\)
−0.698397 + 0.715710i \(0.746103\pi\)
\(662\) 444.301 + 444.301i 0.671150 + 0.671150i
\(663\) −4.28830 + 4.28830i −0.00646802 + 0.00646802i
\(664\) 85.3325i 0.128513i
\(665\) −42.8762 + 11.3092i −0.0644756 + 0.0170062i
\(666\) −100.983 −0.151626
\(667\) −107.117 107.117i −0.160595 0.160595i
\(668\) −238.550 + 238.550i −0.357111 + 0.357111i
\(669\) 249.280i 0.372616i
\(670\) −290.841 + 499.233i −0.434091 + 0.745123i
\(671\) −132.823 −0.197948
\(672\) −18.3303 18.3303i −0.0272772 0.0272772i
\(673\) −750.322 + 750.322i −1.11489 + 1.11489i −0.122413 + 0.992479i \(0.539063\pi\)
−0.992479 + 0.122413i \(0.960937\pi\)
\(674\) 862.939i 1.28032i
\(675\) 34.6018 125.211i 0.0512620 0.185497i
\(676\) −332.864 −0.492403
\(677\) −405.042 405.042i −0.598290 0.598290i 0.341567 0.939857i \(-0.389042\pi\)
−0.939857 + 0.341567i \(0.889042\pi\)
\(678\) −166.655 + 166.655i −0.245804 + 0.245804i
\(679\) 196.769i 0.289792i
\(680\) −26.7007 15.5552i −0.0392657 0.0228752i
\(681\) −61.3816 −0.0901345
\(682\) 46.1682 + 46.1682i 0.0676954 + 0.0676954i
\(683\) 666.271 666.271i 0.975506 0.975506i −0.0242009 0.999707i \(-0.507704\pi\)
0.999707 + 0.0242009i \(0.00770413\pi\)
\(684\) 20.1119i 0.0294034i
\(685\) 135.445 + 513.513i 0.197731 + 0.749654i
\(686\) −26.1916 −0.0381802
\(687\) 347.212 + 347.212i 0.505403 + 0.505403i
\(688\) −81.4997 + 81.4997i −0.118459 + 0.118459i
\(689\) 91.8658i 0.133332i
\(690\) 132.421 34.9277i 0.191915 0.0506199i
\(691\) 521.895 0.755275 0.377637 0.925954i \(-0.376737\pi\)
0.377637 + 0.925954i \(0.376737\pi\)
\(692\) 220.041 + 220.041i 0.317978 + 0.317978i
\(693\) 16.4065 16.4065i 0.0236746 0.0236746i
\(694\) 455.785i 0.656751i
\(695\) −484.133 + 831.022i −0.696595 + 1.19572i
\(696\) 66.3687 0.0953573
\(697\) −112.207 112.207i −0.160985 0.160985i
\(698\) −280.016 + 280.016i −0.401168 + 0.401168i
\(699\) 340.771i 0.487511i
\(700\) −127.508 35.2368i −0.182155 0.0503383i
\(701\) 525.400 0.749501 0.374750 0.927126i \(-0.377728\pi\)
0.374750 + 0.927126i \(0.377728\pi\)
\(702\) 8.32645 + 8.32645i 0.0118610 + 0.0118610i
\(703\) 56.4156 56.4156i 0.0802497 0.0802497i
\(704\) 23.3857i 0.0332184i
\(705\) −553.674 322.557i −0.785353 0.457528i
\(706\) −228.939 −0.324276
\(707\) −242.117 242.117i −0.342458 0.342458i
\(708\) 286.995 286.995i 0.405360 0.405360i
\(709\) 269.858i 0.380618i −0.981724 0.190309i \(-0.939051\pi\)
0.981724 0.190309i \(-0.0609489\pi\)
\(710\) −93.2753 353.633i −0.131374 0.498075i
\(711\) −111.555 −0.156899
\(712\) 201.902 + 201.902i 0.283571 + 0.283571i
\(713\) 124.877 124.877i 0.175144 0.175144i
\(714\) 14.1607i 0.0198330i
\(715\) −22.6466 + 5.97334i −0.0316736 + 0.00835432i
\(716\) 98.0715 0.136971
\(717\) −224.472 224.472i −0.313071 0.313071i
\(718\) −700.748 + 700.748i −0.975973 + 0.975973i
\(719\) 42.9232i 0.0596985i −0.999554 0.0298493i \(-0.990497\pi\)
0.999554 0.0298493i \(-0.00950273\pi\)
\(720\) −30.2030 + 51.8438i −0.0419485 + 0.0720053i
\(721\) 116.159 0.161108
\(722\) 349.764 + 349.764i 0.484438 + 0.484438i
\(723\) −343.044 + 343.044i −0.474472 + 0.474472i
\(724\) 654.285i 0.903709i
\(725\) 294.626 167.044i 0.406381 0.230406i
\(726\) −275.457 −0.379417
\(727\) 109.192 + 109.192i 0.150195 + 0.150195i 0.778205 0.628010i \(-0.216130\pi\)
−0.628010 + 0.778205i \(0.716130\pi\)
\(728\) 8.47924 8.47924i 0.0116473 0.0116473i
\(729\) 27.0000i 0.0370370i
\(730\) 625.453 + 364.374i 0.856785 + 0.499142i
\(731\) 62.9611 0.0861301
\(732\) −111.298 111.298i −0.152047 0.152047i
\(733\) 414.682 414.682i 0.565733 0.565733i −0.365197 0.930930i \(-0.618999\pi\)
0.930930 + 0.365197i \(0.118999\pi\)
\(734\) 824.513i 1.12332i
\(735\) 15.4610 + 58.6170i 0.0210354 + 0.0797511i
\(736\) −63.2545 −0.0859436
\(737\) 168.895 + 168.895i 0.229166 + 0.229166i
\(738\) −217.868 + 217.868i −0.295214 + 0.295214i
\(739\) 1042.54i 1.41074i −0.708838 0.705372i \(-0.750780\pi\)
0.708838 0.705372i \(-0.249220\pi\)
\(740\) 230.148 60.7044i 0.311010 0.0820329i
\(741\) −9.30338 −0.0125552
\(742\) −151.679 151.679i −0.204419 0.204419i
\(743\) −403.117 + 403.117i −0.542553 + 0.542553i −0.924277 0.381724i \(-0.875331\pi\)
0.381724 + 0.924277i \(0.375331\pi\)
\(744\) 77.3728i 0.103996i
\(745\) 195.062 334.827i 0.261828 0.449432i
\(746\) −243.338 −0.326191
\(747\) 63.9994 + 63.9994i 0.0856752 + 0.0856752i
\(748\) −9.03311 + 9.03311i −0.0120763 + 0.0120763i
\(749\) 409.417i 0.546618i
\(750\) −3.59167 + 306.165i −0.00478889 + 0.408220i
\(751\) 346.283 0.461096 0.230548 0.973061i \(-0.425948\pi\)
0.230548 + 0.973061i \(0.425948\pi\)
\(752\) 209.278 + 209.278i 0.278295 + 0.278295i
\(753\) 182.175 182.175i 0.241932 0.241932i
\(754\) 30.7008i 0.0407173i
\(755\) 159.072 + 92.6713i 0.210691 + 0.122744i
\(756\) 27.4955 0.0363696
\(757\) 284.836 + 284.836i 0.376270 + 0.376270i 0.869754 0.493485i \(-0.164277\pi\)
−0.493485 + 0.869754i \(0.664277\pi\)
\(758\) 709.113 709.113i 0.935506 0.935506i
\(759\) 56.6158i 0.0745926i
\(760\) −12.0900 45.8366i −0.0159079 0.0603114i
\(761\) 321.609 0.422614 0.211307 0.977420i \(-0.432228\pi\)
0.211307 + 0.977420i \(0.432228\pi\)
\(762\) 350.187 + 350.187i 0.459563 + 0.459563i
\(763\) −128.371 + 128.371i −0.168245 + 0.168245i
\(764\) 578.156i 0.756749i
\(765\) 31.6919 8.35913i 0.0414273 0.0109270i
\(766\) −953.222 −1.24441
\(767\) 132.758 + 132.758i 0.173087 + 0.173087i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 634.413i 0.824984i 0.910961 + 0.412492i \(0.135342\pi\)
−0.910961 + 0.412492i \(0.864658\pi\)
\(770\) −27.5292 + 47.2542i −0.0357522 + 0.0613691i
\(771\) −592.002 −0.767836
\(772\) −262.425 262.425i −0.339929 0.339929i
\(773\) 793.682 793.682i 1.02676 1.02676i 0.0271240 0.999632i \(-0.491365\pi\)
0.999632 0.0271240i \(-0.00863490\pi\)
\(774\) 122.250i 0.157945i
\(775\) 194.740 + 343.476i 0.251278 + 0.443195i
\(776\) −210.355 −0.271076
\(777\) −77.1269 77.1269i −0.0992625 0.0992625i
\(778\) −270.210 + 270.210i −0.347313 + 0.347313i
\(779\) 243.430i 0.312491i
\(780\) −23.9819 13.9713i −0.0307461 0.0179119i
\(781\) −151.194 −0.193590