Properties

Label 1110.2.u.f.401.10
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
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 401.10
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.55108 - 0.770820i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.64183 - 0.551724i) q^{6} +4.38167 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.81167 + 2.39120i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.55108 - 0.770820i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.64183 - 0.551724i) q^{6} +4.38167 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.81167 + 2.39120i) q^{9} -1.00000 q^{10} +4.49999 q^{11} +(-0.770820 + 1.55108i) q^{12} +(1.45588 - 1.45588i) q^{13} +(-3.09831 + 3.09831i) q^{14} +(-0.551724 - 1.64183i) q^{15} -1.00000 q^{16} +(1.09123 + 1.09123i) q^{17} +(-2.97188 - 0.409787i) q^{18} +(-0.737671 + 0.737671i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-6.79630 - 3.37748i) q^{21} +(-3.18197 + 3.18197i) q^{22} +(-1.56045 - 1.56045i) q^{23} +(-0.551724 - 1.64183i) q^{24} +1.00000i q^{25} +2.05893i q^{26} +(-0.966859 - 5.10541i) q^{27} -4.38167i q^{28} +(-3.68128 + 3.68128i) q^{29} +(1.55108 + 0.770820i) q^{30} +(-0.303265 - 0.303265i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.97982 - 3.46868i) q^{33} -1.54323 q^{34} +(3.09831 + 3.09831i) q^{35} +(2.39120 - 1.81167i) q^{36} +(0.167677 + 6.08045i) q^{37} -1.04322i q^{38} +(-3.38041 + 1.13596i) q^{39} +1.00000i q^{40} -1.99260 q^{41} +(7.19395 - 2.41747i) q^{42} +(0.568955 - 0.568955i) q^{43} -4.49999i q^{44} +(-0.409787 + 2.97188i) q^{45} +2.20681 q^{46} -8.83045i q^{47} +(1.55108 + 0.770820i) q^{48} +12.1990 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-0.851438 - 2.53372i) q^{51} +(-1.45588 - 1.45588i) q^{52} -8.07611i q^{53} +(4.29374 + 2.92640i) q^{54} +(3.18197 + 3.18197i) q^{55} +(3.09831 + 3.09831i) q^{56} +(1.71280 - 0.575573i) q^{57} -5.20612i q^{58} +(9.81764 + 9.81764i) q^{59} +(-1.64183 + 0.551724i) q^{60} +(0.496818 + 0.496818i) q^{61} +0.428882 q^{62} +(7.93815 + 10.4774i) q^{63} +1.00000i q^{64} +2.05893 q^{65} +(7.38821 - 2.48275i) q^{66} +7.31837i q^{67} +(1.09123 - 1.09123i) q^{68} +(1.21755 + 3.62320i) q^{69} -4.38167 q^{70} +13.3890i q^{71} +(-0.409787 + 2.97188i) q^{72} -12.3051i q^{73} +(-4.41809 - 4.18096i) q^{74} +(0.770820 - 1.55108i) q^{75} +(0.737671 + 0.737671i) q^{76} +19.7174 q^{77} +(1.58706 - 3.19355i) q^{78} +(-2.04760 + 2.04760i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-2.43568 + 8.66415i) q^{81} +(1.40898 - 1.40898i) q^{82} -10.2732i q^{83} +(-3.37748 + 6.79630i) q^{84} +1.54323i q^{85} +0.804623i q^{86} +(8.54756 - 2.87234i) q^{87} +(3.18197 + 3.18197i) q^{88} +(11.8187 - 11.8187i) q^{89} +(-1.81167 - 2.39120i) q^{90} +(6.37919 - 6.37919i) q^{91} +(-1.56045 + 1.56045i) q^{92} +(0.236625 + 0.704150i) q^{93} +(6.24407 + 6.24407i) q^{94} -1.04322 q^{95} +(-1.64183 + 0.551724i) q^{96} +(-0.766039 + 0.766039i) q^{97} +(-8.62600 + 8.62600i) q^{98} +(8.15251 + 10.7604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q + 24q^{7} - 8q^{9} - 40q^{10} + 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 16q^{22} - 8q^{31} + 24q^{33} + 24q^{34} + 32q^{37} + 16q^{39} + 12q^{42} + 32q^{43} + 8q^{45} - 56q^{46} - 32q^{49} - 44q^{51} - 16q^{52} - 24q^{54} + 16q^{55} + 8q^{57} - 72q^{61} + 24q^{63} - 28q^{66} + 16q^{69} - 24q^{70} + 8q^{72} - 16q^{76} - 48q^{79} + 120q^{81} - 24q^{82} - 24q^{84} + 20q^{87} + 16q^{88} + 8q^{90} - 92q^{93} - 8q^{94} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.55108 0.770820i −0.895514 0.445033i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) 1.64183 0.551724i 0.670274 0.225241i
\(7\) 4.38167 1.65611 0.828057 0.560643i \(-0.189446\pi\)
0.828057 + 0.560643i \(0.189446\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.81167 + 2.39120i 0.603891 + 0.797067i
\(10\) −1.00000 −0.316228
\(11\) 4.49999 1.35680 0.678399 0.734694i \(-0.262674\pi\)
0.678399 + 0.734694i \(0.262674\pi\)
\(12\) −0.770820 + 1.55108i −0.222517 + 0.447757i
\(13\) 1.45588 1.45588i 0.403789 0.403789i −0.475777 0.879566i \(-0.657833\pi\)
0.879566 + 0.475777i \(0.157833\pi\)
\(14\) −3.09831 + 3.09831i −0.828057 + 0.828057i
\(15\) −0.551724 1.64183i −0.142455 0.423918i
\(16\) −1.00000 −0.250000
\(17\) 1.09123 + 1.09123i 0.264662 + 0.264662i 0.826945 0.562283i \(-0.190077\pi\)
−0.562283 + 0.826945i \(0.690077\pi\)
\(18\) −2.97188 0.409787i −0.700479 0.0965878i
\(19\) −0.737671 + 0.737671i −0.169233 + 0.169233i −0.786642 0.617409i \(-0.788182\pi\)
0.617409 + 0.786642i \(0.288182\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) −6.79630 3.37748i −1.48307 0.737026i
\(22\) −3.18197 + 3.18197i −0.678399 + 0.678399i
\(23\) −1.56045 1.56045i −0.325376 0.325376i 0.525449 0.850825i \(-0.323897\pi\)
−0.850825 + 0.525449i \(0.823897\pi\)
\(24\) −0.551724 1.64183i −0.112620 0.335137i
\(25\) 1.00000i 0.200000i
\(26\) 2.05893i 0.403789i
\(27\) −0.966859 5.10541i −0.186072 0.982536i
\(28\) 4.38167i 0.828057i
\(29\) −3.68128 + 3.68128i −0.683597 + 0.683597i −0.960809 0.277212i \(-0.910590\pi\)
0.277212 + 0.960809i \(0.410590\pi\)
\(30\) 1.55108 + 0.770820i 0.283186 + 0.140732i
\(31\) −0.303265 0.303265i −0.0544680 0.0544680i 0.679348 0.733816i \(-0.262263\pi\)
−0.733816 + 0.679348i \(0.762263\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −6.97982 3.46868i −1.21503 0.603820i
\(34\) −1.54323 −0.264662
\(35\) 3.09831 + 3.09831i 0.523709 + 0.523709i
\(36\) 2.39120 1.81167i 0.398533 0.301946i
\(37\) 0.167677 + 6.08045i 0.0275659 + 0.999620i
\(38\) 1.04322i 0.169233i
\(39\) −3.38041 + 1.13596i −0.541298 + 0.181899i
\(40\) 1.00000i 0.158114i
\(41\) −1.99260 −0.311192 −0.155596 0.987821i \(-0.549730\pi\)
−0.155596 + 0.987821i \(0.549730\pi\)
\(42\) 7.19395 2.41747i 1.11005 0.373024i
\(43\) 0.568955 0.568955i 0.0867648 0.0867648i −0.662392 0.749157i \(-0.730459\pi\)
0.749157 + 0.662392i \(0.230459\pi\)
\(44\) 4.49999i 0.678399i
\(45\) −0.409787 + 2.97188i −0.0610875 + 0.443022i
\(46\) 2.20681 0.325376
\(47\) 8.83045i 1.28805i −0.765003 0.644027i \(-0.777262\pi\)
0.765003 0.644027i \(-0.222738\pi\)
\(48\) 1.55108 + 0.770820i 0.223879 + 0.111258i
\(49\) 12.1990 1.74272
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) −0.851438 2.53372i −0.119225 0.354791i
\(52\) −1.45588 1.45588i −0.201894 0.201894i
\(53\) 8.07611i 1.10934i −0.832071 0.554670i \(-0.812845\pi\)
0.832071 0.554670i \(-0.187155\pi\)
\(54\) 4.29374 + 2.92640i 0.584304 + 0.398232i
\(55\) 3.18197 + 3.18197i 0.429057 + 0.429057i
\(56\) 3.09831 + 3.09831i 0.414029 + 0.414029i
\(57\) 1.71280 0.575573i 0.226865 0.0762365i
\(58\) 5.20612i 0.683597i
\(59\) 9.81764 + 9.81764i 1.27815 + 1.27815i 0.941703 + 0.336445i \(0.109224\pi\)
0.336445 + 0.941703i \(0.390776\pi\)
\(60\) −1.64183 + 0.551724i −0.211959 + 0.0712273i
\(61\) 0.496818 + 0.496818i 0.0636110 + 0.0636110i 0.738197 0.674586i \(-0.235678\pi\)
−0.674586 + 0.738197i \(0.735678\pi\)
\(62\) 0.428882 0.0544680
\(63\) 7.93815 + 10.4774i 1.00011 + 1.32003i
\(64\) 1.00000i 0.125000i
\(65\) 2.05893 0.255378
\(66\) 7.38821 2.48275i 0.909425 0.305606i
\(67\) 7.31837i 0.894081i 0.894514 + 0.447040i \(0.147522\pi\)
−0.894514 + 0.447040i \(0.852478\pi\)
\(68\) 1.09123 1.09123i 0.132331 0.132331i
\(69\) 1.21755 + 3.62320i 0.146576 + 0.436182i
\(70\) −4.38167 −0.523709
\(71\) 13.3890i 1.58898i 0.607280 + 0.794488i \(0.292261\pi\)
−0.607280 + 0.794488i \(0.707739\pi\)
\(72\) −0.409787 + 2.97188i −0.0482939 + 0.350239i
\(73\) 12.3051i 1.44021i −0.693867 0.720104i \(-0.744094\pi\)
0.693867 0.720104i \(-0.255906\pi\)
\(74\) −4.41809 4.18096i −0.513593 0.486027i
\(75\) 0.770820 1.55108i 0.0890066 0.179103i
\(76\) 0.737671 + 0.737671i 0.0846167 + 0.0846167i
\(77\) 19.7174 2.24701
\(78\) 1.58706 3.19355i 0.179699 0.361599i
\(79\) −2.04760 + 2.04760i −0.230373 + 0.230373i −0.812848 0.582475i \(-0.802084\pi\)
0.582475 + 0.812848i \(0.302084\pi\)
\(80\) −0.707107 0.707107i −0.0790569 0.0790569i
\(81\) −2.43568 + 8.66415i −0.270631 + 0.962683i
\(82\) 1.40898 1.40898i 0.155596 0.155596i
\(83\) 10.2732i 1.12763i −0.825903 0.563813i \(-0.809334\pi\)
0.825903 0.563813i \(-0.190666\pi\)
\(84\) −3.37748 + 6.79630i −0.368513 + 0.741537i
\(85\) 1.54323i 0.167387i
\(86\) 0.804623i 0.0867648i
\(87\) 8.54756 2.87234i 0.916394 0.307948i
\(88\) 3.18197 + 3.18197i 0.339199 + 0.339199i
\(89\) 11.8187 11.8187i 1.25278 1.25278i 0.298316 0.954467i \(-0.403575\pi\)
0.954467 0.298316i \(-0.0964250\pi\)
\(90\) −1.81167 2.39120i −0.190967 0.252055i
\(91\) 6.37919 6.37919i 0.668721 0.668721i
\(92\) −1.56045 + 1.56045i −0.162688 + 0.162688i
\(93\) 0.236625 + 0.704150i 0.0245368 + 0.0730170i
\(94\) 6.24407 + 6.24407i 0.644027 + 0.644027i
\(95\) −1.04322 −0.107033
\(96\) −1.64183 + 0.551724i −0.167568 + 0.0563101i
\(97\) −0.766039 + 0.766039i −0.0777795 + 0.0777795i −0.744926 0.667147i \(-0.767515\pi\)
0.667147 + 0.744926i \(0.267515\pi\)
\(98\) −8.62600 + 8.62600i −0.871358 + 0.871358i
\(99\) 8.15251 + 10.7604i 0.819358 + 1.08146i
\(100\) 1.00000 0.100000
\(101\) −12.5125 −1.24504 −0.622519 0.782604i \(-0.713891\pi\)
−0.622519 + 0.782604i \(0.713891\pi\)
\(102\) 2.39367 + 1.18955i 0.237008 + 0.117783i
\(103\) 6.46547 + 6.46547i 0.637062 + 0.637062i 0.949830 0.312768i \(-0.101256\pi\)
−0.312768 + 0.949830i \(0.601256\pi\)
\(104\) 2.05893 0.201894
\(105\) −2.41747 7.19395i −0.235921 0.702057i
\(106\) 5.71067 + 5.71067i 0.554670 + 0.554670i
\(107\) 0.550155i 0.0531855i 0.999646 + 0.0265928i \(0.00846573\pi\)
−0.999646 + 0.0265928i \(0.991534\pi\)
\(108\) −5.10541 + 0.966859i −0.491268 + 0.0930361i
\(109\) −6.68407 + 6.68407i −0.640217 + 0.640217i −0.950609 0.310391i \(-0.899540\pi\)
0.310391 + 0.950609i \(0.399540\pi\)
\(110\) −4.49999 −0.429057
\(111\) 4.42685 9.56049i 0.420178 0.907442i
\(112\) −4.38167 −0.414029
\(113\) −6.11267 + 6.11267i −0.575032 + 0.575032i −0.933530 0.358499i \(-0.883289\pi\)
0.358499 + 0.933530i \(0.383289\pi\)
\(114\) −0.804138 + 1.61812i −0.0753145 + 0.151551i
\(115\) 2.20681i 0.205786i
\(116\) 3.68128 + 3.68128i 0.341799 + 0.341799i
\(117\) 6.11889 + 0.843722i 0.565691 + 0.0780021i
\(118\) −13.8842 −1.27815
\(119\) 4.78140 + 4.78140i 0.438310 + 0.438310i
\(120\) 0.770820 1.55108i 0.0703659 0.141593i
\(121\) 9.24988 0.840898
\(122\) −0.702607 −0.0636110
\(123\) 3.09068 + 1.53594i 0.278677 + 0.138491i
\(124\) −0.303265 + 0.303265i −0.0272340 + 0.0272340i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) −13.0218 1.79555i −1.16007 0.159960i
\(127\) 18.8279 1.67070 0.835352 0.549716i \(-0.185264\pi\)
0.835352 + 0.549716i \(0.185264\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −1.32105 + 0.443930i −0.116312 + 0.0390859i
\(130\) −1.45588 + 1.45588i −0.127689 + 0.127689i
\(131\) −6.50740 + 6.50740i −0.568554 + 0.568554i −0.931723 0.363169i \(-0.881695\pi\)
0.363169 + 0.931723i \(0.381695\pi\)
\(132\) −3.46868 + 6.97982i −0.301910 + 0.607516i
\(133\) −3.23223 + 3.23223i −0.280270 + 0.280270i
\(134\) −5.17487 5.17487i −0.447040 0.447040i
\(135\) 2.92640 4.29374i 0.251864 0.369546i
\(136\) 1.54323i 0.132331i
\(137\) 19.5068i 1.66658i −0.552838 0.833289i \(-0.686455\pi\)
0.552838 0.833289i \(-0.313545\pi\)
\(138\) −3.42293 1.70105i −0.291379 0.144803i
\(139\) 17.7979i 1.50960i 0.655954 + 0.754801i \(0.272266\pi\)
−0.655954 + 0.754801i \(0.727734\pi\)
\(140\) 3.09831 3.09831i 0.261855 0.261855i
\(141\) −6.80669 + 13.6967i −0.573227 + 1.15347i
\(142\) −9.46742 9.46742i −0.794488 0.794488i
\(143\) 6.55145 6.55145i 0.547860 0.547860i
\(144\) −1.81167 2.39120i −0.150973 0.199267i
\(145\) −5.20612 −0.432345
\(146\) 8.70104 + 8.70104i 0.720104 + 0.720104i
\(147\) −18.9216 9.40324i −1.56063 0.775566i
\(148\) 6.08045 0.167677i 0.499810 0.0137830i
\(149\) 19.3712i 1.58695i −0.608602 0.793476i \(-0.708269\pi\)
0.608602 0.793476i \(-0.291731\pi\)
\(150\) 0.551724 + 1.64183i 0.0450481 + 0.134055i
\(151\) 12.1984i 0.992693i −0.868124 0.496347i \(-0.834675\pi\)
0.868124 0.496347i \(-0.165325\pi\)
\(152\) −1.04322 −0.0846167
\(153\) −0.632396 + 4.58629i −0.0511262 + 0.370780i
\(154\) −13.9423 + 13.9423i −1.12351 + 1.12351i
\(155\) 0.428882i 0.0344486i
\(156\) 1.13596 + 3.38041i 0.0909496 + 0.270649i
\(157\) −7.11091 −0.567512 −0.283756 0.958896i \(-0.591581\pi\)
−0.283756 + 0.958896i \(0.591581\pi\)
\(158\) 2.89575i 0.230373i
\(159\) −6.22523 + 12.5267i −0.493692 + 0.993429i
\(160\) 1.00000 0.0790569
\(161\) −6.83737 6.83737i −0.538860 0.538860i
\(162\) −4.40419 7.84876i −0.346026 0.616657i
\(163\) −3.95330 3.95330i −0.309646 0.309646i 0.535126 0.844772i \(-0.320264\pi\)
−0.844772 + 0.535126i \(0.820264\pi\)
\(164\) 1.99260i 0.155596i
\(165\) −2.48275 7.38821i −0.193282 0.575171i
\(166\) 7.26422 + 7.26422i 0.563813 + 0.563813i
\(167\) −1.00757 1.00757i −0.0779683 0.0779683i 0.667047 0.745015i \(-0.267558\pi\)
−0.745015 + 0.667047i \(0.767558\pi\)
\(168\) −2.41747 7.19395i −0.186512 0.555025i
\(169\) 8.76082i 0.673909i
\(170\) −1.09123 1.09123i −0.0836934 0.0836934i
\(171\) −3.10034 0.427500i −0.237089 0.0326918i
\(172\) −0.568955 0.568955i −0.0433824 0.0433824i
\(173\) −1.51433 −0.115132 −0.0575660 0.998342i \(-0.518334\pi\)
−0.0575660 + 0.998342i \(0.518334\pi\)
\(174\) −4.01298 + 8.07509i −0.304223 + 0.612171i
\(175\) 4.38167i 0.331223i
\(176\) −4.49999 −0.339199
\(177\) −7.66027 22.7955i −0.575782 1.71342i
\(178\) 16.7142i 1.25278i
\(179\) 2.61668 2.61668i 0.195580 0.195580i −0.602522 0.798102i \(-0.705838\pi\)
0.798102 + 0.602522i \(0.205838\pi\)
\(180\) 2.97188 + 0.409787i 0.221511 + 0.0305437i
\(181\) −8.02378 −0.596403 −0.298201 0.954503i \(-0.596387\pi\)
−0.298201 + 0.954503i \(0.596387\pi\)
\(182\) 9.02154i 0.668721i
\(183\) −0.387645 1.15356i −0.0286556 0.0852736i
\(184\) 2.20681i 0.162688i
\(185\) −4.18096 + 4.41809i −0.307390 + 0.324825i
\(186\) −0.665228 0.330591i −0.0487769 0.0242401i
\(187\) 4.91051 + 4.91051i 0.359092 + 0.359092i
\(188\) −8.83045 −0.644027
\(189\) −4.23646 22.3702i −0.308157 1.62719i
\(190\) 0.737671 0.737671i 0.0535163 0.0535163i
\(191\) −3.71929 3.71929i −0.269118 0.269118i 0.559627 0.828745i \(-0.310945\pi\)
−0.828745 + 0.559627i \(0.810945\pi\)
\(192\) 0.770820 1.55108i 0.0556291 0.111939i
\(193\) 11.4367 11.4367i 0.823235 0.823235i −0.163336 0.986571i \(-0.552225\pi\)
0.986571 + 0.163336i \(0.0522253\pi\)
\(194\) 1.08334i 0.0777795i
\(195\) −3.19355 1.58706i −0.228695 0.113652i
\(196\) 12.1990i 0.871358i
\(197\) 12.8748i 0.917293i 0.888619 + 0.458646i \(0.151666\pi\)
−0.888619 + 0.458646i \(0.848334\pi\)
\(198\) −13.3734 1.84404i −0.950408 0.131050i
\(199\) 16.5646 + 16.5646i 1.17423 + 1.17423i 0.981190 + 0.193044i \(0.0618359\pi\)
0.193044 + 0.981190i \(0.438164\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 5.64114 11.3513i 0.397895 0.800662i
\(202\) 8.84766 8.84766i 0.622519 0.622519i
\(203\) −16.1302 + 16.1302i −1.13212 + 1.13212i
\(204\) −2.53372 + 0.851438i −0.177396 + 0.0596126i
\(205\) −1.40898 1.40898i −0.0984076 0.0984076i
\(206\) −9.14355 −0.637062
\(207\) 0.904321 6.55837i 0.0628547 0.455838i
\(208\) −1.45588 + 1.45588i −0.100947 + 0.100947i
\(209\) −3.31951 + 3.31951i −0.229615 + 0.229615i
\(210\) 6.79630 + 3.37748i 0.468989 + 0.233068i
\(211\) −9.22945 −0.635382 −0.317691 0.948194i \(-0.602907\pi\)
−0.317691 + 0.948194i \(0.602907\pi\)
\(212\) −8.07611 −0.554670
\(213\) 10.3205 20.7673i 0.707147 1.42295i
\(214\) −0.389018 0.389018i −0.0265928 0.0265928i
\(215\) 0.804623 0.0548749
\(216\) 2.92640 4.29374i 0.199116 0.292152i
\(217\) −1.32881 1.32881i −0.0902053 0.0902053i
\(218\) 9.45270i 0.640217i
\(219\) −9.48504 + 19.0862i −0.640940 + 1.28973i
\(220\) 3.18197 3.18197i 0.214528 0.214528i
\(221\) 3.17740 0.213735
\(222\) 3.63003 + 9.89054i 0.243632 + 0.663810i
\(223\) −21.7378 −1.45567 −0.727837 0.685750i \(-0.759474\pi\)
−0.727837 + 0.685750i \(0.759474\pi\)
\(224\) 3.09831 3.09831i 0.207014 0.207014i
\(225\) −2.39120 + 1.81167i −0.159413 + 0.120778i
\(226\) 8.64462i 0.575032i
\(227\) 11.6318 + 11.6318i 0.772032 + 0.772032i 0.978462 0.206429i \(-0.0661843\pi\)
−0.206429 + 0.978462i \(0.566184\pi\)
\(228\) −0.575573 1.71280i −0.0381182 0.113433i
\(229\) 10.0261 0.662545 0.331272 0.943535i \(-0.392522\pi\)
0.331272 + 0.943535i \(0.392522\pi\)
\(230\) 1.56045 + 1.56045i 0.102893 + 0.102893i
\(231\) −30.5833 15.1986i −2.01223 0.999994i
\(232\) −5.20612 −0.341799
\(233\) −14.0316 −0.919243 −0.459622 0.888115i \(-0.652015\pi\)
−0.459622 + 0.888115i \(0.652015\pi\)
\(234\) −4.92331 + 3.73010i −0.321847 + 0.243845i
\(235\) 6.24407 6.24407i 0.407318 0.407318i
\(236\) 9.81764 9.81764i 0.639074 0.639074i
\(237\) 4.75432 1.59765i 0.308826 0.103779i
\(238\) −6.76192 −0.438310
\(239\) −1.89394 1.89394i −0.122509 0.122509i 0.643194 0.765703i \(-0.277609\pi\)
−0.765703 + 0.643194i \(0.777609\pi\)
\(240\) 0.551724 + 1.64183i 0.0356137 + 0.105980i
\(241\) 11.7784 11.7784i 0.758715 0.758715i −0.217373 0.976089i \(-0.569749\pi\)
0.976089 + 0.217373i \(0.0697489\pi\)
\(242\) −6.54065 + 6.54065i −0.420449 + 0.420449i
\(243\) 10.4564 11.5613i 0.670780 0.741657i
\(244\) 0.496818 0.496818i 0.0318055 0.0318055i
\(245\) 8.62600 + 8.62600i 0.551095 + 0.551095i
\(246\) −3.27151 + 1.09937i −0.208584 + 0.0700931i
\(247\) 2.14792i 0.136669i
\(248\) 0.428882i 0.0272340i
\(249\) −7.91876 + 15.9345i −0.501831 + 1.00980i
\(250\) 1.00000i 0.0632456i
\(251\) 10.9133 10.9133i 0.688839 0.688839i −0.273136 0.961975i \(-0.588061\pi\)
0.961975 + 0.273136i \(0.0880610\pi\)
\(252\) 10.4774 7.93815i 0.660017 0.500057i
\(253\) −7.02200 7.02200i −0.441469 0.441469i
\(254\) −13.3133 + 13.3133i −0.835352 + 0.835352i
\(255\) 1.18955 2.39367i 0.0744926 0.149897i
\(256\) 1.00000 0.0625000
\(257\) −16.7640 16.7640i −1.04571 1.04571i −0.998904 0.0468078i \(-0.985095\pi\)
−0.0468078 0.998904i \(-0.514905\pi\)
\(258\) 0.620220 1.24803i 0.0386132 0.0776991i
\(259\) 0.734705 + 26.6425i 0.0456524 + 1.65549i
\(260\) 2.05893i 0.127689i
\(261\) −15.4720 2.13340i −0.957691 0.132054i
\(262\) 9.20286i 0.568554i
\(263\) 16.2544 1.00229 0.501145 0.865363i \(-0.332912\pi\)
0.501145 + 0.865363i \(0.332912\pi\)
\(264\) −2.48275 7.38821i −0.152803 0.454713i
\(265\) 5.71067 5.71067i 0.350804 0.350804i
\(266\) 4.57106i 0.280270i
\(267\) −27.4419 + 9.22164i −1.67942 + 0.564355i
\(268\) 7.31837 0.447040
\(269\) 14.2889i 0.871212i 0.900137 + 0.435606i \(0.143466\pi\)
−0.900137 + 0.435606i \(0.856534\pi\)
\(270\) 0.966859 + 5.10541i 0.0588412 + 0.310705i
\(271\) 20.3803 1.23802 0.619008 0.785385i \(-0.287535\pi\)
0.619008 + 0.785385i \(0.287535\pi\)
\(272\) −1.09123 1.09123i −0.0661654 0.0661654i
\(273\) −14.8118 + 4.97740i −0.896452 + 0.301246i
\(274\) 13.7934 + 13.7934i 0.833289 + 0.833289i
\(275\) 4.49999i 0.271359i
\(276\) 3.62320 1.21755i 0.218091 0.0732879i
\(277\) −17.5786 17.5786i −1.05619 1.05619i −0.998324 0.0578693i \(-0.981569\pi\)
−0.0578693 0.998324i \(-0.518431\pi\)
\(278\) −12.5850 12.5850i −0.754801 0.754801i
\(279\) 0.175750 1.27459i 0.0105219 0.0763074i
\(280\) 4.38167i 0.261855i
\(281\) 1.34583 + 1.34583i 0.0802855 + 0.0802855i 0.746109 0.665824i \(-0.231920\pi\)
−0.665824 + 0.746109i \(0.731920\pi\)
\(282\) −4.87198 14.4981i −0.290122 0.863349i
\(283\) 0.275222 + 0.275222i 0.0163602 + 0.0163602i 0.715240 0.698879i \(-0.246318\pi\)
−0.698879 + 0.715240i \(0.746318\pi\)
\(284\) 13.3890 0.794488
\(285\) 1.61812 + 0.804138i 0.0958492 + 0.0476330i
\(286\) 9.26515i 0.547860i
\(287\) −8.73092 −0.515370
\(288\) 2.97188 + 0.409787i 0.175120 + 0.0241469i
\(289\) 14.6184i 0.859908i
\(290\) 3.68128 3.68128i 0.216172 0.216172i
\(291\) 1.77866 0.597707i 0.104267 0.0350382i
\(292\) −12.3051 −0.720104
\(293\) 3.04158i 0.177691i 0.996045 + 0.0888455i \(0.0283178\pi\)
−0.996045 + 0.0888455i \(0.971682\pi\)
\(294\) 20.0287 6.73049i 1.16810 0.392530i
\(295\) 13.8842i 0.808372i
\(296\) −4.18096 + 4.41809i −0.243014 + 0.256796i
\(297\) −4.35085 22.9743i −0.252462 1.33310i
\(298\) 13.6975 + 13.6975i 0.793476 + 0.793476i
\(299\) −4.54366 −0.262766
\(300\) −1.55108 0.770820i −0.0895514 0.0445033i
\(301\) 2.49297 2.49297i 0.143692 0.143692i
\(302\) 8.62559 + 8.62559i 0.496347 + 0.496347i
\(303\) 19.4078 + 9.64487i 1.11495 + 0.554083i
\(304\) 0.737671 0.737671i 0.0423084 0.0423084i
\(305\) 0.702607i 0.0402311i
\(306\) −2.79583 3.69017i −0.159827 0.210953i
\(307\) 13.1974i 0.753217i 0.926373 + 0.376608i \(0.122910\pi\)
−0.926373 + 0.376608i \(0.877090\pi\)
\(308\) 19.7174i 1.12351i
\(309\) −5.04472 15.0121i −0.286984 0.854011i
\(310\) 0.303265 + 0.303265i 0.0172243 + 0.0172243i
\(311\) 16.5296 16.5296i 0.937307 0.937307i −0.0608406 0.998147i \(-0.519378\pi\)
0.998147 + 0.0608406i \(0.0193781\pi\)
\(312\) −3.19355 1.58706i −0.180799 0.0898497i
\(313\) 4.43787 4.43787i 0.250843 0.250843i −0.570473 0.821316i \(-0.693240\pi\)
0.821316 + 0.570473i \(0.193240\pi\)
\(314\) 5.02817 5.02817i 0.283756 0.283756i
\(315\) −1.79555 + 13.0218i −0.101168 + 0.733695i
\(316\) 2.04760 + 2.04760i 0.115187 + 0.115187i
\(317\) −3.18702 −0.179001 −0.0895003 0.995987i \(-0.528527\pi\)
−0.0895003 + 0.995987i \(0.528527\pi\)
\(318\) −4.45579 13.2596i −0.249868 0.743561i
\(319\) −16.5657 + 16.5657i −0.927503 + 0.927503i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) 0.424070 0.853332i 0.0236693 0.0476284i
\(322\) 9.66950 0.538860
\(323\) −1.60994 −0.0895792
\(324\) 8.66415 + 2.43568i 0.481342 + 0.135315i
\(325\) 1.45588 + 1.45588i 0.0807578 + 0.0807578i
\(326\) 5.59081 0.309646
\(327\) 15.5197 5.21528i 0.858242 0.288406i
\(328\) −1.40898 1.40898i −0.0777981 0.0777981i
\(329\) 38.6921i 2.13317i
\(330\) 6.97982 + 3.46868i 0.384227 + 0.190944i
\(331\) −13.9140 + 13.9140i −0.764780 + 0.764780i −0.977182 0.212402i \(-0.931871\pi\)
0.212402 + 0.977182i \(0.431871\pi\)
\(332\) −10.2732 −0.563813
\(333\) −14.2358 + 11.4167i −0.780117 + 0.625634i
\(334\) 1.42492 0.0779683
\(335\) −5.17487 + 5.17487i −0.282733 + 0.282733i
\(336\) 6.79630 + 3.37748i 0.370769 + 0.184256i
\(337\) 22.2998i 1.21475i 0.794416 + 0.607374i \(0.207777\pi\)
−0.794416 + 0.607374i \(0.792223\pi\)
\(338\) −6.19483 6.19483i −0.336955 0.336955i
\(339\) 14.1930 4.76945i 0.770857 0.259041i
\(340\) 1.54323 0.0836934
\(341\) −1.36469 1.36469i −0.0739021 0.0739021i
\(342\) 2.49456 1.88998i 0.134890 0.102199i
\(343\) 22.7803 1.23002
\(344\) 0.804623 0.0433824
\(345\) −1.70105 + 3.42293i −0.0915815 + 0.184284i
\(346\) 1.07079 1.07079i 0.0575660 0.0575660i
\(347\) −8.92530 + 8.92530i −0.479135 + 0.479135i −0.904855 0.425720i \(-0.860021\pi\)
0.425720 + 0.904855i \(0.360021\pi\)
\(348\) −2.87234 8.54756i −0.153974 0.458197i
\(349\) −7.54456 −0.403851 −0.201926 0.979401i \(-0.564720\pi\)
−0.201926 + 0.979401i \(0.564720\pi\)
\(350\) −3.09831 3.09831i −0.165611 0.165611i
\(351\) −8.84050 6.02524i −0.471871 0.321603i
\(352\) 3.18197 3.18197i 0.169600 0.169600i
\(353\) −4.41933 + 4.41933i −0.235217 + 0.235217i −0.814866 0.579649i \(-0.803190\pi\)
0.579649 + 0.814866i \(0.303190\pi\)
\(354\) 21.5355 + 10.7022i 1.14460 + 0.568818i
\(355\) −9.46742 + 9.46742i −0.502478 + 0.502478i
\(356\) −11.8187 11.8187i −0.626392 0.626392i
\(357\) −3.73072 11.1019i −0.197450 0.587575i
\(358\) 3.70055i 0.195580i
\(359\) 24.0431i 1.26895i −0.772944 0.634474i \(-0.781217\pi\)
0.772944 0.634474i \(-0.218783\pi\)
\(360\) −2.39120 + 1.81167i −0.126027 + 0.0954836i
\(361\) 17.9117i 0.942720i
\(362\) 5.67367 5.67367i 0.298201 0.298201i
\(363\) −14.3473 7.12999i −0.753036 0.374228i
\(364\) −6.37919 6.37919i −0.334360 0.334360i
\(365\) 8.70104 8.70104i 0.455433 0.455433i
\(366\) 1.08980 + 0.541583i 0.0569646 + 0.0283090i
\(367\) −23.6025 −1.23204 −0.616020 0.787730i \(-0.711256\pi\)
−0.616020 + 0.787730i \(0.711256\pi\)
\(368\) 1.56045 + 1.56045i 0.0813440 + 0.0813440i
\(369\) −3.60995 4.76471i −0.187926 0.248041i
\(370\) −0.167677 6.08045i −0.00871712 0.316108i
\(371\) 35.3868i 1.83719i
\(372\) 0.704150 0.236625i 0.0365085 0.0122684i
\(373\) 36.5693i 1.89349i −0.321991 0.946743i \(-0.604352\pi\)
0.321991 0.946743i \(-0.395648\pi\)
\(374\) −6.94451 −0.359092
\(375\) 1.64183 0.551724i 0.0847836 0.0284909i
\(376\) 6.24407 6.24407i 0.322014 0.322014i
\(377\) 10.7190i 0.552058i
\(378\) 18.8137 + 12.8225i 0.967675 + 0.659518i
\(379\) −36.7825 −1.88939 −0.944695 0.327950i \(-0.893642\pi\)
−0.944695 + 0.327950i \(0.893642\pi\)
\(380\) 1.04322i 0.0535163i
\(381\) −29.2035 14.5129i −1.49614 0.743518i
\(382\) 5.25987 0.269118
\(383\) 7.74910 + 7.74910i 0.395960 + 0.395960i 0.876806 0.480845i \(-0.159670\pi\)
−0.480845 + 0.876806i \(0.659670\pi\)
\(384\) 0.551724 + 1.64183i 0.0281551 + 0.0837842i
\(385\) 13.9423 + 13.9423i 0.710567 + 0.710567i
\(386\) 16.1740i 0.823235i
\(387\) 2.39124 + 0.329724i 0.121554 + 0.0167608i
\(388\) 0.766039 + 0.766039i 0.0388897 + 0.0388897i
\(389\) 16.8656 + 16.8656i 0.855119 + 0.855119i 0.990758 0.135640i \(-0.0433089\pi\)
−0.135640 + 0.990758i \(0.543309\pi\)
\(390\) 3.38041 1.13596i 0.171173 0.0575216i
\(391\) 3.40561i 0.172229i
\(392\) 8.62600 + 8.62600i 0.435679 + 0.435679i
\(393\) 15.1095 5.07744i 0.762174 0.256123i
\(394\) −9.10387 9.10387i −0.458646 0.458646i
\(395\) −2.89575 −0.145701
\(396\) 10.7604 8.15251i 0.540729 0.409679i
\(397\) 2.62029i 0.131509i −0.997836 0.0657543i \(-0.979055\pi\)
0.997836 0.0657543i \(-0.0209453\pi\)
\(398\) −23.4259 −1.17423
\(399\) 7.50490 2.52197i 0.375715 0.126256i
\(400\) 1.00000i 0.0500000i
\(401\) −23.7337 + 23.7337i −1.18521 + 1.18521i −0.206830 + 0.978377i \(0.566315\pi\)
−0.978377 + 0.206830i \(0.933685\pi\)
\(402\) 4.03772 + 12.0155i 0.201383 + 0.599279i
\(403\) −0.883036 −0.0439872
\(404\) 12.5125i 0.622519i
\(405\) −7.84876 + 4.40419i −0.390008 + 0.218846i
\(406\) 22.8115i 1.13212i
\(407\) 0.754545 + 27.3619i 0.0374014 + 1.35628i
\(408\) 1.18955 2.39367i 0.0588916 0.118504i
\(409\) −8.35272 8.35272i −0.413015 0.413015i 0.469772 0.882788i \(-0.344336\pi\)
−0.882788 + 0.469772i \(0.844336\pi\)
\(410\) 1.99260 0.0984076
\(411\) −15.0362 + 30.2565i −0.741682 + 1.49244i
\(412\) 6.46547 6.46547i 0.318531 0.318531i
\(413\) 43.0176 + 43.0176i 2.11676 + 2.11676i
\(414\) 3.99801 + 5.27692i 0.196492 + 0.259346i
\(415\) 7.26422 7.26422i 0.356587 0.356587i
\(416\) 2.05893i 0.100947i
\(417\) 13.7190 27.6060i 0.671823 1.35187i
\(418\) 4.69450i 0.229615i
\(419\) 21.3828i 1.04462i −0.852757 0.522309i \(-0.825071\pi\)
0.852757 0.522309i \(-0.174929\pi\)
\(420\) −7.19395 + 2.41747i −0.351029 + 0.117961i
\(421\) −24.9099 24.9099i −1.21404 1.21404i −0.969688 0.244348i \(-0.921426\pi\)
−0.244348 0.969688i \(-0.578574\pi\)
\(422\) 6.52621 6.52621i 0.317691 0.317691i
\(423\) 21.1154 15.9979i 1.02667 0.777845i
\(424\) 5.71067 5.71067i 0.277335 0.277335i
\(425\) −1.09123 + 1.09123i −0.0529323 + 0.0529323i
\(426\) 7.38701 + 21.9824i 0.357902 + 1.06505i
\(427\) 2.17689 + 2.17689i 0.105347 + 0.105347i
\(428\) 0.550155 0.0265928
\(429\) −15.2118 + 5.11181i −0.734432 + 0.246800i
\(430\) −0.568955 + 0.568955i −0.0274374 + 0.0274374i
\(431\) −13.1558 + 13.1558i −0.633692 + 0.633692i −0.948992 0.315300i \(-0.897895\pi\)
0.315300 + 0.948992i \(0.397895\pi\)
\(432\) 0.966859 + 5.10541i 0.0465180 + 0.245634i
\(433\) 40.5145 1.94700 0.973502 0.228679i \(-0.0734405\pi\)
0.973502 + 0.228679i \(0.0734405\pi\)
\(434\) 1.87922 0.0902053
\(435\) 8.07509 + 4.01298i 0.387171 + 0.192408i
\(436\) 6.68407 + 6.68407i 0.320109 + 0.320109i
\(437\) 2.30220 0.110129
\(438\) −6.78904 20.2029i −0.324393 0.965333i
\(439\) −16.5074 16.5074i −0.787857 0.787857i 0.193285 0.981143i \(-0.438086\pi\)
−0.981143 + 0.193285i \(0.938086\pi\)
\(440\) 4.49999i 0.214528i
\(441\) 22.1006 + 29.1703i 1.05241 + 1.38906i
\(442\) −2.24676 + 2.24676i −0.106867 + 0.106867i
\(443\) −17.2944 −0.821681 −0.410841 0.911707i \(-0.634765\pi\)
−0.410841 + 0.911707i \(0.634765\pi\)
\(444\) −9.56049 4.42685i −0.453721 0.210089i
\(445\) 16.7142 0.792330
\(446\) 15.3710 15.3710i 0.727837 0.727837i
\(447\) −14.9317 + 30.0462i −0.706246 + 1.42114i
\(448\) 4.38167i 0.207014i
\(449\) 5.59586 + 5.59586i 0.264085 + 0.264085i 0.826711 0.562626i \(-0.190209\pi\)
−0.562626 + 0.826711i \(0.690209\pi\)
\(450\) 0.409787 2.97188i 0.0193176 0.140096i
\(451\) −8.96669 −0.422225
\(452\) 6.11267 + 6.11267i 0.287516 + 0.287516i
\(453\) −9.40278 + 18.9207i −0.441781 + 0.888971i
\(454\) −16.4499 −0.772032
\(455\) 9.02154 0.422936
\(456\) 1.61812 + 0.804138i 0.0757755 + 0.0376572i
\(457\) −21.3020 + 21.3020i −0.996467 + 0.996467i −0.999994 0.00352675i \(-0.998877\pi\)
0.00352675 + 0.999994i \(0.498877\pi\)
\(458\) −7.08954 + 7.08954i −0.331272 + 0.331272i
\(459\) 4.51610 6.62623i 0.210794 0.309286i
\(460\) −2.20681 −0.102893
\(461\) 15.6647 + 15.6647i 0.729576 + 0.729576i 0.970535 0.240959i \(-0.0774620\pi\)
−0.240959 + 0.970535i \(0.577462\pi\)
\(462\) 32.3727 10.8786i 1.50611 0.506118i
\(463\) 12.1234 12.1234i 0.563420 0.563420i −0.366857 0.930277i \(-0.619566\pi\)
0.930277 + 0.366857i \(0.119566\pi\)
\(464\) 3.68128 3.68128i 0.170899 0.170899i
\(465\) −0.330591 + 0.665228i −0.0153308 + 0.0308492i
\(466\) 9.92187 9.92187i 0.459622 0.459622i
\(467\) 12.9695 + 12.9695i 0.600158 + 0.600158i 0.940355 0.340196i \(-0.110493\pi\)
−0.340196 + 0.940355i \(0.610493\pi\)
\(468\) 0.843722 6.11889i 0.0390011 0.282846i
\(469\) 32.0667i 1.48070i
\(470\) 8.83045i 0.407318i
\(471\) 11.0296 + 5.48123i 0.508215 + 0.252562i
\(472\) 13.8842i 0.639074i
\(473\) 2.56029 2.56029i 0.117722 0.117722i
\(474\) −2.23210 + 4.49152i −0.102524 + 0.206303i
\(475\) −0.737671 0.737671i −0.0338467 0.0338467i
\(476\) 4.78140 4.78140i 0.219155 0.219155i
\(477\) 19.3116 14.6313i 0.884217 0.669920i
\(478\) 2.67843 0.122509
\(479\) 20.6435 + 20.6435i 0.943226 + 0.943226i 0.998473 0.0552467i \(-0.0175945\pi\)
−0.0552467 + 0.998473i \(0.517595\pi\)
\(480\) −1.55108 0.770820i −0.0707966 0.0351829i
\(481\) 9.09653 + 8.60830i 0.414766 + 0.392505i
\(482\) 16.6572i 0.758715i
\(483\) 5.33490 + 15.8757i 0.242746 + 0.722367i
\(484\) 9.24988i 0.420449i
\(485\) −1.08334 −0.0491921
\(486\) 0.781259 + 15.5689i 0.0354386 + 0.706218i
\(487\) −20.1438 + 20.1438i −0.912801 + 0.912801i −0.996492 0.0836904i \(-0.973329\pi\)
0.0836904 + 0.996492i \(0.473329\pi\)
\(488\) 0.702607i 0.0318055i
\(489\) 3.08458 + 9.17914i 0.139490 + 0.415095i
\(490\) −12.1990 −0.551095
\(491\) 35.5626i 1.60492i −0.596707 0.802460i \(-0.703524\pi\)
0.596707 0.802460i \(-0.296476\pi\)
\(492\) 1.53594 3.09068i 0.0692454 0.139339i
\(493\) −8.03424 −0.361844
\(494\) −1.51881 1.51881i −0.0683346 0.0683346i
\(495\) −1.84404 + 13.3734i −0.0828833 + 0.601091i
\(496\) 0.303265 + 0.303265i 0.0136170 + 0.0136170i
\(497\) 58.6659i 2.63153i
\(498\) −5.66795 16.8668i −0.253987 0.755818i
\(499\) −5.43817 5.43817i −0.243446 0.243446i 0.574828 0.818274i \(-0.305069\pi\)
−0.818274 + 0.574828i \(0.805069\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) 0.786165 + 2.33948i 0.0351233 + 0.104520i
\(502\) 15.4337i 0.688839i
\(503\) 18.5290 + 18.5290i 0.826166 + 0.826166i 0.986984 0.160818i \(-0.0514133\pi\)
−0.160818 + 0.986984i \(0.551413\pi\)
\(504\) −1.79555 + 13.0218i −0.0799802 + 0.580037i
\(505\) −8.84766 8.84766i −0.393716 0.393716i
\(506\) 9.93060 0.441469
\(507\) 6.75301 13.5887i 0.299912 0.603495i
\(508\) 18.8279i 0.835352i
\(509\) −29.5711 −1.31072 −0.655358 0.755318i \(-0.727482\pi\)
−0.655358 + 0.755318i \(0.727482\pi\)
\(510\) 0.851438 + 2.53372i 0.0377023 + 0.112195i
\(511\) 53.9170i 2.38515i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 4.47934 + 3.05289i 0.197768 + 0.134788i
\(514\) 23.7079 1.04571
\(515\) 9.14355i 0.402913i
\(516\) 0.443930 + 1.32105i 0.0195429 + 0.0581561i
\(517\) 39.7369i 1.74763i
\(518\) −19.3586 18.3196i −0.850569 0.804917i
\(519\) 2.34883 + 1.16727i 0.103102 + 0.0512376i
\(520\) 1.45588 + 1.45588i 0.0638446 + 0.0638446i
\(521\) 3.80161 0.166552 0.0832759 0.996527i \(-0.473462\pi\)
0.0832759 + 0.996527i \(0.473462\pi\)
\(522\) 12.4489 9.43179i 0.544873 0.412818i
\(523\) −18.5143 + 18.5143i −0.809573 + 0.809573i −0.984569 0.174996i \(-0.944009\pi\)
0.174996 + 0.984569i \(0.444009\pi\)
\(524\) 6.50740 + 6.50740i 0.284277 + 0.284277i
\(525\) 3.37748 6.79630i 0.147405 0.296615i
\(526\) −11.4936 + 11.4936i −0.501145 + 0.501145i
\(527\) 0.661863i 0.0288312i
\(528\) 6.97982 + 3.46868i 0.303758 + 0.150955i
\(529\) 18.1300i 0.788261i
\(530\) 8.07611i 0.350804i
\(531\) −5.68958 + 41.2623i −0.246907 + 1.79063i
\(532\) 3.23223 + 3.23223i 0.140135 + 0.140135i
\(533\) −2.90099 + 2.90099i −0.125656 + 0.125656i
\(534\) 12.8836 25.9250i 0.557530 1.12189i
\(535\) −0.389018 + 0.389018i −0.0168187 + 0.0168187i
\(536\) −5.17487 + 5.17487i −0.223520 + 0.223520i
\(537\) −6.07566 + 2.04168i −0.262184 + 0.0881051i
\(538\) −10.1038 10.1038i −0.435606 0.435606i
\(539\) 54.8954 2.36451
\(540\) −4.29374 2.92640i −0.184773 0.125932i
\(541\) −26.4175 + 26.4175i −1.13578 + 1.13578i −0.146576 + 0.989199i \(0.546825\pi\)
−0.989199 + 0.146576i \(0.953175\pi\)
\(542\) −14.4111 + 14.4111i −0.619008 + 0.619008i
\(543\) 12.4455 + 6.18489i 0.534087 + 0.265419i
\(544\) 1.54323 0.0661654
\(545\) −9.45270 −0.404909
\(546\) 6.95398 13.9931i 0.297603 0.598849i
\(547\) 13.2147 + 13.2147i 0.565018 + 0.565018i 0.930729 0.365710i \(-0.119174\pi\)
−0.365710 + 0.930729i \(0.619174\pi\)
\(548\) −19.5068 −0.833289
\(549\) −0.287919 + 2.08806i −0.0122881 + 0.0891164i
\(550\) −3.18197 3.18197i −0.135680 0.135680i
\(551\) 5.43115i 0.231375i
\(552\) −1.70105 + 3.42293i −0.0724015 + 0.145689i
\(553\) −8.97191 + 8.97191i −0.381525 + 0.381525i
\(554\) 24.8598 1.05619
\(555\) 9.89054 3.63003i 0.419830 0.154086i
\(556\) 17.7979 0.754801
\(557\) −17.3259 + 17.3259i −0.734123 + 0.734123i −0.971434 0.237311i \(-0.923734\pi\)
0.237311 + 0.971434i \(0.423734\pi\)
\(558\) 0.776994 + 1.02554i 0.0328928 + 0.0434147i
\(559\) 1.65666i 0.0700693i
\(560\) −3.09831 3.09831i −0.130927 0.130927i
\(561\) −3.83146 11.4017i −0.161764 0.481380i
\(562\) −1.90329 −0.0802855
\(563\) 12.6771 + 12.6771i 0.534276 + 0.534276i 0.921842 0.387566i \(-0.126684\pi\)
−0.387566 + 0.921842i \(0.626684\pi\)
\(564\) 13.6967 + 6.80669i 0.576735 + 0.286613i
\(565\) −8.64462 −0.363682
\(566\) −0.389222 −0.0163602
\(567\) −10.6723 + 37.9634i −0.448196 + 1.59431i
\(568\) −9.46742 + 9.46742i −0.397244 + 0.397244i
\(569\) −19.4272 + 19.4272i −0.814430 + 0.814430i −0.985295 0.170864i \(-0.945344\pi\)
0.170864 + 0.985295i \(0.445344\pi\)
\(570\) −1.71280 + 0.575573i −0.0717411 + 0.0241081i
\(571\) 18.7824 0.786020 0.393010 0.919534i \(-0.371434\pi\)
0.393010 + 0.919534i \(0.371434\pi\)
\(572\) −6.55145 6.55145i −0.273930 0.273930i
\(573\) 2.90200 + 8.63580i 0.121233 + 0.360766i
\(574\) 6.17369 6.17369i 0.257685 0.257685i
\(575\) 1.56045 1.56045i 0.0650752 0.0650752i
\(576\) −2.39120 + 1.81167i −0.0996333 + 0.0754864i
\(577\) 15.0730 15.0730i 0.627496 0.627496i −0.319941 0.947437i \(-0.603663\pi\)
0.947437 + 0.319941i \(0.103663\pi\)
\(578\) 10.3368 + 10.3368i 0.429954 + 0.429954i
\(579\) −26.5549 + 8.92359i −1.10359 + 0.370852i
\(580\) 5.20612i 0.216172i
\(581\) 45.0136i 1.86748i
\(582\) −0.835062 + 1.68035i −0.0346144 + 0.0696526i
\(583\) 36.3424i 1.50515i
\(584\) 8.70104 8.70104i 0.360052 0.360052i
\(585\) 3.73010 + 4.92331i 0.154221 + 0.203554i
\(586\) −2.15072 2.15072i −0.0888455 0.0888455i
\(587\) −28.6854 + 28.6854i −1.18397 + 1.18397i −0.205266 + 0.978706i \(0.565806\pi\)
−0.978706 + 0.205266i \(0.934194\pi\)
\(588\) −9.40324 + 18.9216i −0.387783 + 0.780313i
\(589\) 0.447420 0.0184356
\(590\) −9.81764 9.81764i −0.404186 0.404186i
\(591\) 9.92416 19.9698i 0.408226 0.821449i
\(592\) −0.167677 6.08045i −0.00689149 0.249905i
\(593\) 19.5396i 0.802396i 0.915991 + 0.401198i \(0.131406\pi\)
−0.915991 + 0.401198i \(0.868594\pi\)
\(594\) 19.3218 + 13.1687i 0.792782 + 0.540320i
\(595\) 6.76192i 0.277212i
\(596\) −19.3712 −0.793476
\(597\) −12.9246 38.4613i −0.528970 1.57412i
\(598\) 3.21285 3.21285i 0.131383 0.131383i
\(599\) 19.5959i 0.800668i −0.916369 0.400334i \(-0.868894\pi\)
0.916369 0.400334i \(-0.131106\pi\)
\(600\) 1.64183 0.551724i 0.0670274 0.0225241i
\(601\) −21.1149 −0.861294 −0.430647 0.902520i \(-0.641715\pi\)
−0.430647 + 0.902520i \(0.641715\pi\)
\(602\) 3.52559i 0.143692i
\(603\) −17.4997 + 13.2585i −0.712642 + 0.539928i
\(604\) −12.1984 −0.496347
\(605\) 6.54065 + 6.54065i 0.265915 + 0.265915i
\(606\) −20.5433 + 6.90344i −0.834516 + 0.280433i
\(607\) −26.0839 26.0839i −1.05871 1.05871i −0.998165 0.0605486i \(-0.980715\pi\)
−0.0605486 0.998165i \(-0.519285\pi\)
\(608\) 1.04322i 0.0423084i
\(609\) 37.4526 12.5857i 1.51765 0.509997i
\(610\) −0.496818 0.496818i −0.0201156 0.0201156i
\(611\) −12.8561 12.8561i −0.520102 0.520102i
\(612\) 4.58629 + 0.632396i 0.185390 + 0.0255631i
\(613\) 8.19734i 0.331087i −0.986202 0.165544i \(-0.947062\pi\)
0.986202 0.165544i \(-0.0529379\pi\)
\(614\) −9.33199 9.33199i −0.376608 0.376608i
\(615\) 1.09937 + 3.27151i 0.0443308 + 0.131920i
\(616\) 13.9423 + 13.9423i 0.561753 + 0.561753i
\(617\) 25.5042 1.02676 0.513379 0.858162i \(-0.328393\pi\)
0.513379 + 0.858162i \(0.328393\pi\)
\(618\) 14.1823 + 7.04803i 0.570498 + 0.283513i
\(619\) 29.5707i 1.18855i −0.804262 0.594274i \(-0.797439\pi\)
0.804262 0.594274i \(-0.202561\pi\)
\(620\) −0.428882 −0.0172243
\(621\) −6.45799 + 9.47546i −0.259150 + 0.380237i
\(622\) 23.3764i 0.937307i
\(623\) 51.7858 51.7858i 2.07475 2.07475i
\(624\) 3.38041 1.13596i 0.135325 0.0454748i
\(625\) −1.00000 −0.0400000
\(626\) 6.27610i 0.250843i
\(627\) 7.70756 2.59007i 0.307810 0.103437i
\(628\) 7.11091i 0.283756i
\(629\) −6.45219 + 6.81813i −0.257265 + 0.271857i
\(630\) −7.93815 10.4774i −0.316264 0.417431i
\(631\) −2.03316 2.03316i −0.0809387 0.0809387i 0.665478 0.746417i \(-0.268228\pi\)
−0.746417 + 0.665478i \(0.768228\pi\)
\(632\) −2.89575 −0.115187
\(633\) 14.3156 + 7.11424i 0.568993 + 0.282766i
\(634\) 2.25356 2.25356i 0.0895003 0.0895003i
\(635\) 13.3133 + 13.3133i 0.528323 + 0.528323i
\(636\) 12.5267 + 6.22523i 0.496714 + 0.246846i
\(637\) 17.7603 17.7603i 0.703689 0.703689i
\(638\) 23.4275i 0.927503i
\(639\) −32.0157 + 24.2564i −1.26652 + 0.959569i
\(640\) 1.00000i 0.0395285i
\(641\) 6.05439i 0.239134i 0.992826 + 0.119567i \(0.0381507\pi\)
−0.992826 + 0.119567i \(0.961849\pi\)
\(642\) 0.303534 + 0.903260i 0.0119795 + 0.0356488i
\(643\) −13.8840 13.8840i −0.547530 0.547530i 0.378196 0.925726i \(-0.376545\pi\)
−0.925726 + 0.378196i \(0.876545\pi\)
\(644\) −6.83737 + 6.83737i −0.269430 + 0.269430i
\(645\) −1.24803 0.620220i −0.0491412 0.0244211i
\(646\) 1.13840 1.13840i 0.0447896 0.0447896i
\(647\) 15.4482 15.4482i 0.607330 0.607330i −0.334917 0.942248i \(-0.608708\pi\)
0.942248 + 0.334917i \(0.108708\pi\)
\(648\) −7.84876 + 4.40419i −0.308329 + 0.173013i
\(649\) 44.1793 + 44.1793i 1.73419 + 1.73419i
\(650\) −2.05893 −0.0807578
\(651\) 1.03681 + 3.08535i 0.0406358 + 0.120924i
\(652\) −3.95330 + 3.95330i −0.154823 + 0.154823i
\(653\) 14.5821 14.5821i 0.570642 0.570642i −0.361666 0.932308i \(-0.617792\pi\)
0.932308 + 0.361666i \(0.117792\pi\)
\(654\) −7.28633 + 14.6619i −0.284918 + 0.573324i
\(655\) −9.20286 −0.359585
\(656\) 1.99260 0.0777981
\(657\) 29.4240 22.2929i 1.14794 0.869728i
\(658\) 27.3595 + 27.3595i 1.06658 + 1.06658i
\(659\) 14.6678 0.571375 0.285688 0.958323i \(-0.407778\pi\)
0.285688 + 0.958323i \(0.407778\pi\)
\(660\) −7.38821 + 2.48275i −0.287586 + 0.0966410i
\(661\) −32.3272 32.3272i −1.25738 1.25738i −0.952338 0.305044i \(-0.901329\pi\)
−0.305044 0.952338i \(-0.598671\pi\)
\(662\) 19.6773i 0.764780i
\(663\) −4.92839 2.44920i −0.191403 0.0951191i
\(664\) 7.26422 7.26422i 0.281906 0.281906i
\(665\) −4.57106 −0.177258
\(666\) 1.99337 18.1391i 0.0772417 0.702875i
\(667\) 11.4889 0.444852
\(668\) −1.00757 + 1.00757i −0.0389842 + 0.0389842i
\(669\) 33.7171 + 16.7560i 1.30358 + 0.647823i
\(670\) 7.31837i 0.282733i
\(671\) 2.23567 + 2.23567i 0.0863073 + 0.0863073i
\(672\) −7.19395 + 2.41747i −0.277512 + 0.0932561i
\(673\) −11.1901 −0.431345 −0.215673 0.976466i \(-0.569194\pi\)
−0.215673 + 0.976466i \(0.569194\pi\)
\(674\) −15.7683 15.7683i −0.607374 0.607374i
\(675\) 5.10541 0.966859i 0.196507 0.0372144i
\(676\) 8.76082 0.336955
\(677\) 13.6262 0.523699 0.261850 0.965109i \(-0.415668\pi\)
0.261850 + 0.965109i \(0.415668\pi\)
\(678\) −6.66344 + 13.4085i −0.255908 + 0.514949i
\(679\) −3.35653 + 3.35653i −0.128812 + 0.128812i
\(680\) −1.09123 + 1.09123i −0.0418467 + 0.0418467i
\(681\) −9.07582 27.0079i −0.347786 1.03495i
\(682\) 1.92996 0.0739021
\(683\) −19.9135 19.9135i −0.761970 0.761970i 0.214708 0.976678i \(-0.431120\pi\)
−0.976678 + 0.214708i \(0.931120\pi\)
\(684\) −0.427500 + 3.10034i −0.0163459 + 0.118544i
\(685\) 13.7934 13.7934i 0.527018 0.527018i
\(686\) −16.1081 + 16.1081i −0.615012 + 0.615012i
\(687\) −15.5513 7.72833i −0.593318 0.294854i
\(688\) −0.568955 + 0.568955i −0.0216912 + 0.0216912i
\(689\) −11.7579 11.7579i −0.447939 0.447939i
\(690\) −1.21755 3.62320i −0.0463513 0.137933i
\(691\) 18.2283i 0.693436i −0.937969 0.346718i \(-0.887296\pi\)
0.937969 0.346718i \(-0.112704\pi\)
\(692\) 1.51433i 0.0575660i
\(693\) 35.7216 + 47.1484i 1.35695 + 1.79102i
\(694\) 12.6223i 0.479135i
\(695\) −12.5850 + 12.5850i −0.477378 + 0.477378i
\(696\) 8.07509 + 4.01298i 0.306085 + 0.152112i
\(697\) −2.17438 2.17438i −0.0823607 0.0823607i
\(698\) 5.33481 5.33481i 0.201926 0.201926i
\(699\) 21.7641 + 10.8159i 0.823195 + 0.409094i
\(700\) 4.38167 0.165611
\(701\) 17.6579 + 17.6579i 0.666930 + 0.666930i 0.957004 0.290074i \(-0.0936799\pi\)
−0.290074 + 0.957004i \(0.593680\pi\)
\(702\) 10.5117 1.99069i 0.396737 0.0751338i
\(703\) −4.60906 4.36168i −0.173834 0.164504i
\(704\) 4.49999i 0.169600i
\(705\) −14.4981 + 4.87198i −0.546030 + 0.183489i
\(706\) 6.24988i 0.235217i
\(707\) −54.8255 −2.06193
\(708\) −22.7955 + 7.66027i −0.856709 + 0.287891i
\(709\) 8.86406 8.86406i 0.332897 0.332897i −0.520789 0.853686i \(-0.674362\pi\)
0.853686 + 0.520789i \(0.174362\pi\)
\(710\) 13.3890i 0.502478i
\(711\) −8.60581 1.18664i −0.322743 0.0445025i
\(712\) 16.7142 0.626392
\(713\) 0.946460i 0.0354452i
\(714\) 10.4883 + 5.21222i 0.392513 + 0.195062i
\(715\) 9.26515 0.346497
\(716\) −2.61668 2.61668i −0.0977900 0.0977900i
\(717\) 1.47776 + 4.39753i 0.0551879 + 0.164229i
\(718\) 17.0011 + 17.0011i 0.634474 + 0.634474i
\(719\) 36.0585i 1.34476i −0.740208 0.672378i \(-0.765273\pi\)
0.740208 0.672378i \(-0.234727\pi\)
\(720\) 0.409787 2.97188i 0.0152719 0.110755i
\(721\) 28.3295 + 28.3295i 1.05505 + 1.05505i
\(722\) −12.6655 12.6655i −0.471360 0.471360i
\(723\) −27.3483 + 9.19019i −1.01709 + 0.341787i
\(724\) 8.02378i 0.298201i
\(725\) −3.68128 3.68128i −0.136719 0.136719i
\(726\) 15.1867 5.10339i 0.563632 0.189404i
\(727\) −4.79330 4.79330i −0.177774 0.177774i 0.612611 0.790385i \(-0.290119\pi\)
−0.790385 + 0.612611i \(0.790119\pi\)
\(728\) 9.02154 0.334360
\(729\) −25.1304 + 9.87242i −0.930754 + 0.365645i
\(730\) 12.3051i 0.455433i
\(731\) 1.24172 0.0459266
\(732\) −1.15356 + 0.387645i −0.0426368 + 0.0143278i
\(733\) 3.58673i 0.132479i 0.997804 + 0.0662394i \(0.0211001\pi\)
−0.997804 + 0.0662394i \(0.978900\pi\)
\(734\) 16.6895 16.6895i 0.616020 0.616020i
\(735\) −6.73049 20.0287i −0.248258 0.738769i
\(736\) −2.20681 −0.0813440
\(737\) 32.9326i 1.21309i
\(738\) 5.92178 + 0.816543i 0.217984 + 0.0300574i
\(739\) 38.9164i 1.43156i 0.698324 + 0.715781i \(0.253929\pi\)
−0.698324 + 0.715781i \(0.746071\pi\)
\(740\) 4.41809 + 4.18096i 0.162412 + 0.153695i
\(741\) 1.65566 3.33159i 0.0608223 0.122389i
\(742\) 25.0223 + 25.0223i 0.918596 + 0.918596i
\(743\) −25.3462 −0.929863 −0.464931 0.885347i \(-0.653921\pi\)
−0.464931 + 0.885347i \(0.653921\pi\)
\(744\) −0.330591 + 0.665228i −0.0121200 + 0.0243885i
\(745\) 13.6975 13.6975i 0.501838 0.501838i
\(746\) 25.8584 + 25.8584i 0.946743 + 0.946743i
\(747\) 24.5652 18.6116i 0.898793 0.680963i
\(748\) 4.91051 4.91051i 0.179546 0.179546i
\(749\) 2.41060i 0.0880813i
\(750\) −0.770820 + 1.55108i −0.0281464 + 0.0566373i
\(751\) 12.8037i 0.467215i −0.972331 0.233608i \(-0.924947\pi\)
0.972331 0.233608i \(-0.0750531\pi\)
\(752\) 8.83045i 0.322014i
\(753\) −25.3395 + 8.51514i −0.923421 + 0.310309i
\(754\) −7.57950 7.57950i −0.276029 0.276029i
\(755\) 8.62559 8.62559i 0.313917 0.313917i
\(756\) −22.3702 + 4.23646i −0.813596 + 0.154078i
\(757\) 0.841475 0.841475i 0.0305839 0.0305839i −0.691649 0.722233i \(-0.743116\pi\)
0.722233 + 0.691649i \(0.243116\pi\)
\(758\) 26.0092 26.0092i 0.944695 0.944695i
\(759\) 5.47896 + 16.3043i 0.198874 + 0.591810i
\(760\) −0.737671 0.737671i −0.0267582 0.0267582i
\(761\) 45.4549 1.64774 0.823870 0.566779i \(-0.191811\pi\)
0.823870 + 0.566779i \(0.191811\pi\)
\(762\) 30.9121 10.3878i 1.11983 0.376310i
\(763\) −29.2874 + 29.2874i −1.06027 + 1.06027i
\(764\) −3.71929 + 3.71929i −0.134559 + 0.134559i
\(765\) −3.69017 + 2.79583i −0.133418 + 0.101083i
\(766\) −10.9589 −0.395960
\(767\) 28.5866 1.03220
\(768\) −1.55108 0.770820i −0.0559696 0.0278146i
\(769\) −35.9501 35.9501i −1.29639 1.29639i −0.930759 0.365634i \(-0.880852\pi\)
−0.365634 0.930759i \(-0.619148\pi\)
\(770\) −19.7174 −0.710567
\(771\) 13.0802 + 38.9243i 0.471073 + 1.40183i
\(772\) −11.4367 11.4367i −0.411617 0.411617i
\(773\) 3.80731i 0.136939i 0.997653 + 0.0684697i \(0.0218116\pi\)
−0.997653 + 0.0684697i \(0.978188\pi\)
\(774\) −1.92402 + 1.45772i −0.0691573 + 0.0523965i
\(775\) 0.303265 0.303265i 0.0108936 0.0108936i
\(776\) −1.08334 −0.0388897
\(777\) 19.3970 41.8909i 0.695863 1.50283i
\(778\) −23.8515 −0.855119
\(779\) 1.46989 1.46989i