Properties

Label 630.2.bk.a.101.2
Level 630
Weight 2
Character 630.101
Analytic conductor 5.031
Analytic rank 1
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bk (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 630.101
Dual form 630.2.bk.a.131.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(1.09808 - 0.633975i) q^{11} +(0.866025 - 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(-0.866025 - 2.50000i) q^{14} +(-0.866025 - 1.50000i) q^{15} +1.00000 q^{16} +(2.59808 - 1.50000i) q^{18} +(4.09808 - 2.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.866025 - 4.50000i) q^{21} +(0.633975 + 1.09808i) q^{22} +(-8.19615 - 4.73205i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-0.401924 - 0.232051i) q^{29} +(1.50000 - 0.866025i) q^{30} -2.19615i q^{31} +1.00000i q^{32} +2.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(2.09808 + 3.63397i) q^{37} +(2.36603 + 4.09808i) q^{38} -6.00000i q^{39} +(0.866025 + 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(3.59808 - 6.23205i) q^{43} +(-1.09808 + 0.633975i) q^{44} +3.00000 q^{45} +(4.73205 - 8.19615i) q^{46} -9.00000 q^{47} +(-0.866025 + 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(-9.29423 - 5.36603i) q^{53} +5.19615i q^{54} +1.26795i q^{55} +(0.866025 + 2.50000i) q^{56} +8.19615i q^{57} +(0.232051 - 0.401924i) q^{58} -8.19615 q^{59} +(0.866025 + 1.50000i) q^{60} -0.928203i q^{61} +2.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} -2.19615 q^{66} -4.00000 q^{67} +(14.1962 - 8.19615i) q^{69} +(2.59808 + 0.500000i) q^{70} -1.26795i q^{71} +(-2.59808 + 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-3.63397 + 2.09808i) q^{74} +1.73205 q^{75} +(-4.09808 + 2.36603i) q^{76} +(-2.19615 + 2.53590i) q^{77} +6.00000 q^{78} -16.5885 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.79423 + 4.50000i) q^{82} +(-0.401924 + 0.696152i) q^{83} +(-0.866025 + 4.50000i) q^{84} +(6.23205 + 3.59808i) q^{86} +(0.696152 - 0.401924i) q^{87} +(-0.633975 - 1.09808i) q^{88} +(-8.19615 - 14.1962i) q^{89} +3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(8.19615 + 4.73205i) q^{92} +(3.29423 + 1.90192i) q^{93} -9.00000i q^{94} +4.73205i q^{95} +(-1.50000 - 0.866025i) q^{96} +(13.3923 + 7.73205i) q^{97} +(4.33013 + 5.50000i) q^{98} +(-3.29423 - 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} - 2q^{5} - 6q^{6} - 10q^{7} - 6q^{9} + O(q^{10}) \) \( 4q - 4q^{4} - 2q^{5} - 6q^{6} - 10q^{7} - 6q^{9} - 6q^{11} - 12q^{13} + 4q^{16} + 6q^{19} + 2q^{20} + 6q^{22} - 12q^{23} + 6q^{24} - 2q^{25} + 10q^{28} - 12q^{29} + 6q^{30} + 2q^{35} + 6q^{36} - 2q^{37} + 6q^{38} + 18q^{41} + 18q^{42} + 4q^{43} + 6q^{44} + 12q^{45} + 12q^{46} - 36q^{47} + 22q^{49} + 12q^{52} - 6q^{53} - 6q^{58} - 12q^{59} - 12q^{62} + 24q^{63} - 4q^{64} + 12q^{66} - 16q^{67} + 36q^{69} + 24q^{73} - 18q^{74} - 6q^{76} + 12q^{77} + 24q^{78} - 4q^{79} - 2q^{80} - 18q^{81} - 12q^{83} + 18q^{86} - 18q^{87} - 6q^{88} - 12q^{89} + 24q^{91} + 12q^{92} - 18q^{93} - 6q^{96} + 12q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i
\(4\) −1.00000 −0.500000
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) 1.09808 0.633975i 0.331082 0.191151i −0.325239 0.945632i \(-0.605445\pi\)
0.656322 + 0.754481i \(0.272111\pi\)
\(12\) 0.866025 1.50000i 0.250000 0.433013i
\(13\) −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i \(-0.826170\pi\)
0.0225039 + 0.999747i \(0.492836\pi\)
\(14\) −0.866025 2.50000i −0.231455 0.668153i
\(15\) −0.866025 1.50000i −0.223607 0.387298i
\(16\) 1.00000 0.250000
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 2.59808 1.50000i 0.612372 0.353553i
\(19\) 4.09808 2.36603i 0.940163 0.542803i 0.0501517 0.998742i \(-0.484030\pi\)
0.890011 + 0.455938i \(0.150696\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0.866025 4.50000i 0.188982 0.981981i
\(22\) 0.633975 + 1.09808i 0.135164 + 0.234111i
\(23\) −8.19615 4.73205i −1.70902 0.986701i −0.935781 0.352581i \(-0.885304\pi\)
−0.773234 0.634120i \(-0.781362\pi\)
\(24\) 1.50000 + 0.866025i 0.306186 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.73205 3.00000i −0.339683 0.588348i
\(27\) 5.19615 1.00000
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −0.401924 0.232051i −0.0746354 0.0430908i 0.462218 0.886766i \(-0.347054\pi\)
−0.536853 + 0.843676i \(0.680387\pi\)
\(30\) 1.50000 0.866025i 0.273861 0.158114i
\(31\) 2.19615i 0.394441i −0.980359 0.197220i \(-0.936809\pi\)
0.980359 0.197220i \(-0.0631914\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.19615i 0.382301i
\(34\) 0 0
\(35\) 0.500000 2.59808i 0.0845154 0.439155i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 2.09808 + 3.63397i 0.344922 + 0.597422i 0.985340 0.170605i \(-0.0545722\pi\)
−0.640418 + 0.768027i \(0.721239\pi\)
\(38\) 2.36603 + 4.09808i 0.383820 + 0.664796i
\(39\) 6.00000i 0.960769i
\(40\) 0.866025 + 0.500000i 0.136931 + 0.0790569i
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 4.50000 + 0.866025i 0.694365 + 0.133631i
\(43\) 3.59808 6.23205i 0.548701 0.950379i −0.449662 0.893199i \(-0.648456\pi\)
0.998364 0.0571802i \(-0.0182110\pi\)
\(44\) −1.09808 + 0.633975i −0.165541 + 0.0955753i
\(45\) 3.00000 0.447214
\(46\) 4.73205 8.19615i 0.697703 1.20846i
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) −0.866025 + 1.50000i −0.125000 + 0.216506i
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 0 0
\(52\) 3.00000 1.73205i 0.416025 0.240192i
\(53\) −9.29423 5.36603i −1.27666 0.737080i −0.300428 0.953805i \(-0.597129\pi\)
−0.976233 + 0.216724i \(0.930463\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 1.26795i 0.170970i
\(56\) 0.866025 + 2.50000i 0.115728 + 0.334077i
\(57\) 8.19615i 1.08561i
\(58\) 0.232051 0.401924i 0.0304698 0.0527752i
\(59\) −8.19615 −1.06705 −0.533524 0.845785i \(-0.679133\pi\)
−0.533524 + 0.845785i \(0.679133\pi\)
\(60\) 0.866025 + 1.50000i 0.111803 + 0.193649i
\(61\) 0.928203i 0.118844i −0.998233 0.0594221i \(-0.981074\pi\)
0.998233 0.0594221i \(-0.0189258\pi\)
\(62\) 2.19615 0.278912
\(63\) 6.00000 + 5.19615i 0.755929 + 0.654654i
\(64\) −1.00000 −0.125000
\(65\) 3.46410i 0.429669i
\(66\) −2.19615 −0.270328
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 14.1962 8.19615i 1.70902 0.986701i
\(70\) 2.59808 + 0.500000i 0.310530 + 0.0597614i
\(71\) 1.26795i 0.150478i −0.997166 0.0752389i \(-0.976028\pi\)
0.997166 0.0752389i \(-0.0239720\pi\)
\(72\) −2.59808 + 1.50000i −0.306186 + 0.176777i
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) −3.63397 + 2.09808i −0.422441 + 0.243896i
\(75\) 1.73205 0.200000
\(76\) −4.09808 + 2.36603i −0.470082 + 0.271402i
\(77\) −2.19615 + 2.53590i −0.250275 + 0.288992i
\(78\) 6.00000 0.679366
\(79\) −16.5885 −1.86635 −0.933174 0.359426i \(-0.882973\pi\)
−0.933174 + 0.359426i \(0.882973\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −7.79423 + 4.50000i −0.860729 + 0.496942i
\(83\) −0.401924 + 0.696152i −0.0441169 + 0.0764127i −0.887241 0.461307i \(-0.847381\pi\)
0.843124 + 0.537720i \(0.180714\pi\)
\(84\) −0.866025 + 4.50000i −0.0944911 + 0.490990i
\(85\) 0 0
\(86\) 6.23205 + 3.59808i 0.672019 + 0.387991i
\(87\) 0.696152 0.401924i 0.0746354 0.0430908i
\(88\) −0.633975 1.09808i −0.0675819 0.117055i
\(89\) −8.19615 14.1962i −0.868790 1.50479i −0.863234 0.504805i \(-0.831565\pi\)
−0.00555677 0.999985i \(-0.501769\pi\)
\(90\) 3.00000i 0.316228i
\(91\) 6.00000 6.92820i 0.628971 0.726273i
\(92\) 8.19615 + 4.73205i 0.854508 + 0.493350i
\(93\) 3.29423 + 1.90192i 0.341596 + 0.197220i
\(94\) 9.00000i 0.928279i
\(95\) 4.73205i 0.485498i
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) 13.3923 + 7.73205i 1.35978 + 0.785071i 0.989594 0.143886i \(-0.0459598\pi\)
0.370188 + 0.928957i \(0.379293\pi\)
\(98\) 4.33013 + 5.50000i 0.437409 + 0.555584i
\(99\) −3.29423 1.90192i −0.331082 0.191151i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −0.401924 0.696152i −0.0399929 0.0692698i 0.845336 0.534235i \(-0.179400\pi\)
−0.885329 + 0.464965i \(0.846067\pi\)
\(102\) 0 0
\(103\) −10.5000 6.06218i −1.03460 0.597324i −0.116298 0.993214i \(-0.537103\pi\)
−0.918298 + 0.395890i \(0.870436\pi\)
\(104\) 1.73205 + 3.00000i 0.169842 + 0.294174i
\(105\) 3.46410 + 3.00000i 0.338062 + 0.292770i
\(106\) 5.36603 9.29423i 0.521194 0.902735i
\(107\) 1.79423 1.03590i 0.173455 0.100144i −0.410759 0.911744i \(-0.634736\pi\)
0.584214 + 0.811600i \(0.301403\pi\)
\(108\) −5.19615 −0.500000
\(109\) −1.59808 + 2.76795i −0.153068 + 0.265121i −0.932354 0.361547i \(-0.882249\pi\)
0.779286 + 0.626669i \(0.215582\pi\)
\(110\) −1.26795 −0.120894
\(111\) −7.26795 −0.689843
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) −16.0981 + 9.29423i −1.51438 + 0.874327i −0.514522 + 0.857477i \(0.672030\pi\)
−0.999858 + 0.0168501i \(0.994636\pi\)
\(114\) −8.19615 −0.767640
\(115\) 8.19615 4.73205i 0.764295 0.441266i
\(116\) 0.401924 + 0.232051i 0.0373177 + 0.0215454i
\(117\) 9.00000 + 5.19615i 0.832050 + 0.480384i
\(118\) 8.19615i 0.754517i
\(119\) 0 0
\(120\) −1.50000 + 0.866025i −0.136931 + 0.0790569i
\(121\) −4.69615 + 8.13397i −0.426923 + 0.739452i
\(122\) 0.928203 0.0840356
\(123\) −15.5885 −1.40556
\(124\) 2.19615i 0.197220i
\(125\) 1.00000 0.0894427
\(126\) −5.19615 + 6.00000i −0.462910 + 0.534522i
\(127\) 9.39230 0.833432 0.416716 0.909037i \(-0.363181\pi\)
0.416716 + 0.909037i \(0.363181\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 6.23205 + 10.7942i 0.548701 + 0.950379i
\(130\) 3.46410 0.303822
\(131\) −8.19615 + 14.1962i −0.716101 + 1.24032i 0.246432 + 0.969160i \(0.420742\pi\)
−0.962533 + 0.271164i \(0.912592\pi\)
\(132\) 2.19615i 0.191151i
\(133\) −8.19615 + 9.46410i −0.710697 + 0.820642i
\(134\) 4.00000i 0.345547i
\(135\) −2.59808 + 4.50000i −0.223607 + 0.387298i
\(136\) 0 0
\(137\) −9.29423 + 5.36603i −0.794060 + 0.458450i −0.841390 0.540429i \(-0.818262\pi\)
0.0473302 + 0.998879i \(0.484929\pi\)
\(138\) 8.19615 + 14.1962i 0.697703 + 1.20846i
\(139\) −13.9019 + 8.02628i −1.17915 + 0.680780i −0.955817 0.293963i \(-0.905026\pi\)
−0.223329 + 0.974743i \(0.571692\pi\)
\(140\) −0.500000 + 2.59808i −0.0422577 + 0.219578i
\(141\) 7.79423 13.5000i 0.656392 1.13691i
\(142\) 1.26795 0.106404
\(143\) −2.19615 + 3.80385i −0.183651 + 0.318094i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) 0.401924 0.232051i 0.0333780 0.0192708i
\(146\) −3.46410 + 6.00000i −0.286691 + 0.496564i
\(147\) 1.73205 + 12.0000i 0.142857 + 0.989743i
\(148\) −2.09808 3.63397i −0.172461 0.298711i
\(149\) −10.3923 6.00000i −0.851371 0.491539i 0.00974235 0.999953i \(-0.496899\pi\)
−0.861113 + 0.508413i \(0.830232\pi\)
\(150\) 1.73205i 0.141421i
\(151\) −3.09808 5.36603i −0.252118 0.436681i 0.711991 0.702189i \(-0.247794\pi\)
−0.964109 + 0.265508i \(0.914460\pi\)
\(152\) −2.36603 4.09808i −0.191910 0.332398i
\(153\) 0 0
\(154\) −2.53590 2.19615i −0.204349 0.176971i
\(155\) 1.90192 + 1.09808i 0.152766 + 0.0881996i
\(156\) 6.00000i 0.480384i
\(157\) 0.339746i 0.0271147i 0.999908 + 0.0135573i \(0.00431557\pi\)
−0.999908 + 0.0135573i \(0.995684\pi\)
\(158\) 16.5885i 1.31971i
\(159\) 16.0981 9.29423i 1.27666 0.737080i
\(160\) −0.866025 0.500000i −0.0684653 0.0395285i
\(161\) 24.5885 + 4.73205i 1.93784 + 0.372938i
\(162\) −7.79423 4.50000i −0.612372 0.353553i
\(163\) −6.19615 10.7321i −0.485320 0.840599i 0.514538 0.857468i \(-0.327964\pi\)
−0.999858 + 0.0168687i \(0.994630\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) −1.90192 1.09808i −0.148065 0.0854851i
\(166\) −0.696152 0.401924i −0.0540319 0.0311953i
\(167\) 5.19615 + 9.00000i 0.402090 + 0.696441i 0.993978 0.109580i \(-0.0349504\pi\)
−0.591888 + 0.806020i \(0.701617\pi\)
\(168\) −4.50000 0.866025i −0.347183 0.0668153i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 0 0
\(171\) −12.2942 7.09808i −0.940163 0.542803i
\(172\) −3.59808 + 6.23205i −0.274351 + 0.475189i
\(173\) −2.19615 −0.166970 −0.0834852 0.996509i \(-0.526605\pi\)
−0.0834852 + 0.996509i \(0.526605\pi\)
\(174\) 0.401924 + 0.696152i 0.0304698 + 0.0527752i
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) 1.09808 0.633975i 0.0827706 0.0477876i
\(177\) 7.09808 12.2942i 0.533524 0.924091i
\(178\) 14.1962 8.19615i 1.06405 0.614328i
\(179\) −5.70577 3.29423i −0.426469 0.246222i 0.271372 0.962475i \(-0.412523\pi\)
−0.697841 + 0.716252i \(0.745856\pi\)
\(180\) −3.00000 −0.223607
\(181\) 7.39230i 0.549466i −0.961521 0.274733i \(-0.911411\pi\)
0.961521 0.274733i \(-0.0885894\pi\)
\(182\) 6.92820 + 6.00000i 0.513553 + 0.444750i
\(183\) 1.39230 + 0.803848i 0.102922 + 0.0594221i
\(184\) −4.73205 + 8.19615i −0.348851 + 0.604228i
\(185\) −4.19615 −0.308507
\(186\) −1.90192 + 3.29423i −0.139456 + 0.241545i
\(187\) 0 0
\(188\) 9.00000 0.656392
\(189\) −12.9904 + 4.50000i −0.944911 + 0.327327i
\(190\) −4.73205 −0.343299
\(191\) 3.46410i 0.250654i 0.992116 + 0.125327i \(0.0399979\pi\)
−0.992116 + 0.125327i \(0.960002\pi\)
\(192\) 0.866025 1.50000i 0.0625000 0.108253i
\(193\) 24.1962 1.74168 0.870839 0.491569i \(-0.163576\pi\)
0.870839 + 0.491569i \(0.163576\pi\)
\(194\) −7.73205 + 13.3923i −0.555129 + 0.961511i
\(195\) 5.19615 + 3.00000i 0.372104 + 0.214834i
\(196\) −5.50000 + 4.33013i −0.392857 + 0.309295i
\(197\) 6.33975i 0.451688i −0.974163 0.225844i \(-0.927486\pi\)
0.974163 0.225844i \(-0.0725140\pi\)
\(198\) 1.90192 3.29423i 0.135164 0.234111i
\(199\) 6.00000 + 3.46410i 0.425329 + 0.245564i 0.697355 0.716726i \(-0.254360\pi\)
−0.272026 + 0.962290i \(0.587694\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 3.46410 6.00000i 0.244339 0.423207i
\(202\) 0.696152 0.401924i 0.0489811 0.0282793i
\(203\) 1.20577 + 0.232051i 0.0846286 + 0.0162868i
\(204\) 0 0
\(205\) −9.00000 −0.628587
\(206\) 6.06218 10.5000i 0.422372 0.731570i
\(207\) 28.3923i 1.97340i
\(208\) −3.00000 + 1.73205i −0.208013 + 0.120096i
\(209\) 3.00000 5.19615i 0.207514 0.359425i
\(210\) −3.00000 + 3.46410i −0.207020 + 0.239046i
\(211\) −5.29423 9.16987i −0.364470 0.631280i 0.624221 0.781248i \(-0.285416\pi\)
−0.988691 + 0.149968i \(0.952083\pi\)
\(212\) 9.29423 + 5.36603i 0.638330 + 0.368540i
\(213\) 1.90192 + 1.09808i 0.130318 + 0.0752389i
\(214\) 1.03590 + 1.79423i 0.0708126 + 0.122651i
\(215\) 3.59808 + 6.23205i 0.245387 + 0.425022i
\(216\) 5.19615i 0.353553i
\(217\) 1.90192 + 5.49038i 0.129111 + 0.372711i
\(218\) −2.76795 1.59808i −0.187469 0.108235i
\(219\) −10.3923 + 6.00000i −0.702247 + 0.405442i
\(220\) 1.26795i 0.0854851i
\(221\) 0 0
\(222\) 7.26795i 0.487793i
\(223\) 8.89230 + 5.13397i 0.595473 + 0.343796i 0.767259 0.641338i \(-0.221620\pi\)
−0.171786 + 0.985134i \(0.554954\pi\)
\(224\) −0.866025 2.50000i −0.0578638 0.167038i
\(225\) −1.50000 + 2.59808i −0.100000 + 0.173205i
\(226\) −9.29423 16.0981i −0.618243 1.07083i
\(227\) 2.19615 + 3.80385i 0.145764 + 0.252470i 0.929658 0.368425i \(-0.120103\pi\)
−0.783894 + 0.620895i \(0.786769\pi\)
\(228\) 8.19615i 0.542803i
\(229\) 24.1865 + 13.9641i 1.59829 + 0.922774i 0.991817 + 0.127671i \(0.0407501\pi\)
0.606475 + 0.795103i \(0.292583\pi\)
\(230\) 4.73205 + 8.19615i 0.312022 + 0.540438i
\(231\) −1.90192 5.49038i −0.125137 0.361241i
\(232\) −0.232051 + 0.401924i −0.0152349 + 0.0263876i
\(233\) 4.09808 2.36603i 0.268474 0.155003i −0.359720 0.933060i \(-0.617128\pi\)
0.628194 + 0.778057i \(0.283794\pi\)
\(234\) −5.19615 + 9.00000i −0.339683 + 0.588348i
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) 8.19615 0.533524
\(237\) 14.3660 24.8827i 0.933174 1.61630i
\(238\) 0 0
\(239\) 18.2942 10.5622i 1.18336 0.683210i 0.226567 0.973996i \(-0.427250\pi\)
0.956788 + 0.290785i \(0.0939165\pi\)
\(240\) −0.866025 1.50000i −0.0559017 0.0968246i
\(241\) −17.8923 + 10.3301i −1.15254 + 0.665422i −0.949506 0.313749i \(-0.898415\pi\)
−0.203039 + 0.979171i \(0.565082\pi\)
\(242\) −8.13397 4.69615i −0.522872 0.301880i
\(243\) −7.79423 13.5000i −0.500000 0.866025i
\(244\) 0.928203i 0.0594221i
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 15.5885i 0.993884i
\(247\) −8.19615 + 14.1962i −0.521509 + 0.903280i
\(248\) −2.19615 −0.139456
\(249\) −0.696152 1.20577i −0.0441169 0.0764127i
\(250\) 1.00000i 0.0632456i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) −12.0000 −0.754434
\(254\) 9.39230i 0.589326i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.80385 6.58846i 0.237277 0.410977i −0.722655 0.691209i \(-0.757078\pi\)
0.959932 + 0.280233i \(0.0904116\pi\)
\(258\) −10.7942 + 6.23205i −0.672019 + 0.387991i
\(259\) −8.39230 7.26795i −0.521472 0.451608i
\(260\) 3.46410i 0.214834i
\(261\) 1.39230i 0.0861815i
\(262\) −14.1962 8.19615i −0.877041 0.506360i
\(263\) 8.89230 5.13397i 0.548323 0.316574i −0.200122 0.979771i \(-0.564134\pi\)
0.748445 + 0.663196i \(0.230801\pi\)
\(264\) 2.19615 0.135164
\(265\) 9.29423 5.36603i 0.570940 0.329632i
\(266\) −9.46410 8.19615i −0.580281 0.502538i
\(267\) 28.3923 1.73758
\(268\) 4.00000 0.244339
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −4.50000 2.59808i −0.273861 0.158114i
\(271\) 21.2942 12.2942i 1.29353 0.746821i 0.314254 0.949339i \(-0.398246\pi\)
0.979279 + 0.202518i \(0.0649124\pi\)
\(272\) 0 0
\(273\) 5.19615 + 15.0000i 0.314485 + 0.907841i
\(274\) −5.36603 9.29423i −0.324173 0.561485i
\(275\) −1.09808 0.633975i −0.0662165 0.0382301i
\(276\) −14.1962 + 8.19615i −0.854508 + 0.493350i
\(277\) 6.90192 + 11.9545i 0.414696 + 0.718275i 0.995397 0.0958423i \(-0.0305544\pi\)
−0.580700 + 0.814118i \(0.697221\pi\)
\(278\) −8.02628 13.9019i −0.481384 0.833782i
\(279\) −5.70577 + 3.29423i −0.341596 + 0.197220i
\(280\) −2.59808 0.500000i −0.155265 0.0298807i
\(281\) 2.30385 + 1.33013i 0.137436 + 0.0793487i 0.567141 0.823620i \(-0.308049\pi\)
−0.429705 + 0.902969i \(0.641383\pi\)
\(282\) 13.5000 + 7.79423i 0.803913 + 0.464140i
\(283\) 10.8564i 0.645346i −0.946510 0.322673i \(-0.895419\pi\)
0.946510 0.322673i \(-0.104581\pi\)
\(284\) 1.26795i 0.0752389i
\(285\) −7.09808 4.09808i −0.420454 0.242749i
\(286\) −3.80385 2.19615i −0.224926 0.129861i
\(287\) −18.0000 15.5885i −1.06251 0.920158i
\(288\) 2.59808 1.50000i 0.153093 0.0883883i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0.232051 + 0.401924i 0.0136265 + 0.0236018i
\(291\) −23.1962 + 13.3923i −1.35978 + 0.785071i
\(292\) −6.00000 3.46410i −0.351123 0.202721i
\(293\) −2.19615 3.80385i −0.128301 0.222223i 0.794718 0.606979i \(-0.207619\pi\)
−0.923018 + 0.384756i \(0.874286\pi\)
\(294\) −12.0000 + 1.73205i −0.699854 + 0.101015i
\(295\) 4.09808 7.09808i 0.238599 0.413266i
\(296\) 3.63397 2.09808i 0.211220 0.121948i
\(297\) 5.70577 3.29423i 0.331082 0.191151i
\(298\) 6.00000 10.3923i 0.347571 0.602010i
\(299\) 32.7846 1.89598
\(300\) −1.73205 −0.100000
\(301\) −3.59808 + 18.6962i −0.207390 + 1.07763i
\(302\) 5.36603 3.09808i 0.308780 0.178274i
\(303\) 1.39230 0.0799858
\(304\) 4.09808 2.36603i 0.235041 0.135701i
\(305\) 0.803848 + 0.464102i 0.0460282 + 0.0265744i
\(306\) 0 0
\(307\) 17.7846i 1.01502i 0.861645 + 0.507511i \(0.169434\pi\)
−0.861645 + 0.507511i \(0.830566\pi\)
\(308\) 2.19615 2.53590i 0.125137 0.144496i
\(309\) 18.1865 10.5000i 1.03460 0.597324i
\(310\) −1.09808 + 1.90192i −0.0623665 + 0.108022i
\(311\) −26.1962 −1.48545 −0.742724 0.669598i \(-0.766466\pi\)
−0.742724 + 0.669598i \(0.766466\pi\)
\(312\) −6.00000 −0.339683
\(313\) 9.80385i 0.554146i −0.960849 0.277073i \(-0.910636\pi\)
0.960849 0.277073i \(-0.0893644\pi\)
\(314\) −0.339746 −0.0191730
\(315\) −7.50000 + 2.59808i −0.422577 + 0.146385i
\(316\) 16.5885 0.933174
\(317\) 27.4641i 1.54254i −0.636510 0.771269i \(-0.719622\pi\)
0.636510 0.771269i \(-0.280378\pi\)
\(318\) 9.29423 + 16.0981i 0.521194 + 0.902735i
\(319\) −0.588457 −0.0329473
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 3.58846i 0.200288i
\(322\) −4.73205 + 24.5885i −0.263707 + 1.37026i
\(323\) 0 0
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 3.00000 + 1.73205i 0.166410 + 0.0960769i
\(326\) 10.7321 6.19615i 0.594393 0.343173i
\(327\) −2.76795 4.79423i −0.153068 0.265121i
\(328\) 7.79423 4.50000i 0.430364 0.248471i
\(329\) 22.5000 7.79423i 1.24047 0.429710i
\(330\) 1.09808 1.90192i 0.0604471 0.104697i
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0.401924 0.696152i 0.0220584 0.0382063i
\(333\) 6.29423 10.9019i 0.344922 0.597422i
\(334\) −9.00000 + 5.19615i −0.492458 + 0.284321i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) 0.866025 4.50000i 0.0472456 0.245495i
\(337\) −5.00000 8.66025i −0.272367 0.471754i 0.697100 0.716974i \(-0.254473\pi\)
−0.969468 + 0.245220i \(0.921140\pi\)
\(338\) −0.866025 0.500000i −0.0471056 0.0271964i
\(339\) 32.1962i 1.74865i
\(340\) 0 0
\(341\) −1.39230 2.41154i −0.0753975 0.130592i
\(342\) 7.09808 12.2942i 0.383820 0.664796i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −6.23205 3.59808i −0.336010 0.193995i
\(345\) 16.3923i 0.882532i
\(346\) 2.19615i 0.118066i
\(347\) 27.2487i 1.46279i −0.681955 0.731394i \(-0.738870\pi\)
0.681955 0.731394i \(-0.261130\pi\)
\(348\) −0.696152 + 0.401924i −0.0373177 + 0.0215454i
\(349\) −3.80385 2.19615i −0.203615 0.117557i 0.394725 0.918799i \(-0.370840\pi\)
−0.598341 + 0.801242i \(0.704173\pi\)
\(350\) −1.73205 + 2.00000i −0.0925820 + 0.106904i
\(351\) −15.5885 + 9.00000i −0.832050 + 0.480384i
\(352\) 0.633975 + 1.09808i 0.0337910 + 0.0585277i
\(353\) 15.2942 + 26.4904i 0.814030 + 1.40994i 0.910023 + 0.414559i \(0.136064\pi\)
−0.0959929 + 0.995382i \(0.530603\pi\)
\(354\) 12.2942 + 7.09808i 0.653431 + 0.377258i
\(355\) 1.09808 + 0.633975i 0.0582798 + 0.0336479i
\(356\) 8.19615 + 14.1962i 0.434395 + 0.752395i
\(357\) 0 0
\(358\) 3.29423 5.70577i 0.174105 0.301559i
\(359\) −22.6865 + 13.0981i −1.19735 + 0.691290i −0.959963 0.280125i \(-0.909624\pi\)
−0.237386 + 0.971415i \(0.576291\pi\)
\(360\) 3.00000i 0.158114i
\(361\) 1.69615 2.93782i 0.0892712 0.154622i
\(362\) 7.39230 0.388531
\(363\) −8.13397 14.0885i −0.426923 0.739452i
\(364\) −6.00000 + 6.92820i −0.314485 + 0.363137i
\(365\) −6.00000 + 3.46410i −0.314054 + 0.181319i
\(366\) −0.803848 + 1.39230i −0.0420178 + 0.0727769i
\(367\) 16.2846 9.40192i 0.850050 0.490776i −0.0106179 0.999944i \(-0.503380\pi\)
0.860668 + 0.509167i \(0.170047\pi\)
\(368\) −8.19615 4.73205i −0.427254 0.246675i
\(369\) 13.5000 23.3827i 0.702782 1.21725i
\(370\) 4.19615i 0.218148i
\(371\) 27.8827 + 5.36603i 1.44760 + 0.278590i
\(372\) −3.29423 1.90192i −0.170798 0.0986102i
\(373\) 0.0980762 0.169873i 0.00507819 0.00879569i −0.863475 0.504391i \(-0.831717\pi\)
0.868553 + 0.495596i \(0.165050\pi\)
\(374\) 0 0
\(375\) −0.866025 + 1.50000i −0.0447214 + 0.0774597i
\(376\) 9.00000i 0.464140i
\(377\) 1.60770 0.0828005
\(378\) −4.50000 12.9904i −0.231455 0.668153i
\(379\) −30.3923 −1.56115 −0.780574 0.625063i \(-0.785073\pi\)
−0.780574 + 0.625063i \(0.785073\pi\)
\(380\) 4.73205i 0.242749i
\(381\) −8.13397 + 14.0885i −0.416716 + 0.721774i
\(382\) −3.46410 −0.177239
\(383\) −0.696152 + 1.20577i −0.0355717 + 0.0616120i −0.883263 0.468878i \(-0.844659\pi\)
0.847691 + 0.530490i \(0.177992\pi\)
\(384\) 1.50000 + 0.866025i 0.0765466 + 0.0441942i
\(385\) −1.09808 3.16987i −0.0559631 0.161552i
\(386\) 24.1962i 1.23155i
\(387\) −21.5885 −1.09740
\(388\) −13.3923 7.73205i −0.679891 0.392535i
\(389\) 26.5981 15.3564i 1.34858 0.778601i 0.360528 0.932748i \(-0.382596\pi\)
0.988048 + 0.154148i \(0.0492631\pi\)
\(390\) −3.00000 + 5.19615i −0.151911 + 0.263117i
\(391\) 0 0
\(392\) −4.33013 5.50000i −0.218704 0.277792i
\(393\) −14.1962 24.5885i −0.716101 1.24032i
\(394\) 6.33975 0.319392
\(395\) 8.29423 14.3660i 0.417328 0.722833i
\(396\) 3.29423 + 1.90192i 0.165541 + 0.0955753i
\(397\) −0.509619 + 0.294229i −0.0255770 + 0.0147669i −0.512734 0.858548i \(-0.671367\pi\)
0.487157 + 0.873314i \(0.338034\pi\)
\(398\) −3.46410 + 6.00000i −0.173640 + 0.300753i
\(399\) −7.09808 20.4904i −0.355348 1.02580i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 23.8923 + 13.7942i 1.19312 + 0.688851i 0.959014 0.283359i \(-0.0914488\pi\)
0.234111 + 0.972210i \(0.424782\pi\)
\(402\) 6.00000 + 3.46410i 0.299253 + 0.172774i
\(403\) 3.80385 + 6.58846i 0.189483 + 0.328194i
\(404\) 0.401924 + 0.696152i 0.0199965 + 0.0346349i
\(405\) −4.50000 7.79423i −0.223607 0.387298i
\(406\) −0.232051 + 1.20577i −0.0115165 + 0.0598414i
\(407\) 4.60770 + 2.66025i 0.228395 + 0.131864i
\(408\) 0 0
\(409\) 34.5167i 1.70674i −0.521307 0.853370i \(-0.674555\pi\)
0.521307 0.853370i \(-0.325445\pi\)
\(410\) 9.00000i 0.444478i
\(411\) 18.5885i 0.916901i
\(412\) 10.5000 + 6.06218i 0.517298 + 0.298662i
\(413\) 20.4904 7.09808i 1.00827 0.349273i
\(414\) −28.3923 −1.39541
\(415\) −0.401924 0.696152i −0.0197297 0.0341728i
\(416\) −1.73205 3.00000i −0.0849208 0.147087i
\(417\) 27.8038i 1.36156i
\(418\) 5.19615 + 3.00000i 0.254152 + 0.146735i
\(419\) 5.19615 + 9.00000i 0.253849 + 0.439679i 0.964582 0.263783i \(-0.0849701\pi\)
−0.710734 + 0.703461i \(0.751637\pi\)
\(420\) −3.46410 3.00000i −0.169031 0.146385i
\(421\) −10.9904 + 19.0359i −0.535638 + 0.927753i 0.463494 + 0.886100i \(0.346596\pi\)
−0.999132 + 0.0416527i \(0.986738\pi\)
\(422\) 9.16987 5.29423i 0.446382 0.257719i
\(423\) 13.5000 + 23.3827i 0.656392 + 1.13691i
\(424\) −5.36603 + 9.29423i −0.260597 + 0.451368i
\(425\) 0 0
\(426\) −1.09808 + 1.90192i −0.0532020 + 0.0921485i
\(427\) 0.803848 + 2.32051i 0.0389009 + 0.112297i
\(428\) −1.79423 + 1.03590i −0.0867273 + 0.0500720i
\(429\) −3.80385 6.58846i −0.183651 0.318094i
\(430\) −6.23205 + 3.59808i −0.300536 + 0.173515i
\(431\) 2.41154 + 1.39230i 0.116160 + 0.0670650i 0.556954 0.830543i \(-0.311970\pi\)
−0.440794 + 0.897608i \(0.645303\pi\)
\(432\) 5.19615 0.250000
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) −5.49038 + 1.90192i −0.263547 + 0.0912953i
\(435\) 0.803848i 0.0385415i
\(436\) 1.59808 2.76795i 0.0765340 0.132561i
\(437\) −44.7846 −2.14234
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) 12.3397i 0.588944i 0.955660 + 0.294472i \(0.0951438\pi\)
−0.955660 + 0.294472i \(0.904856\pi\)
\(440\) 1.26795 0.0604471
\(441\) −19.5000 7.79423i −0.928571 0.371154i
\(442\) 0 0
\(443\) 9.00000i 0.427603i −0.976877 0.213801i \(-0.931415\pi\)
0.976877 0.213801i \(-0.0685846\pi\)
\(444\) 7.26795 0.344922
\(445\) 16.3923 0.777070
\(446\) −5.13397 + 8.89230i −0.243101 + 0.421063i
\(447\) 18.0000 10.3923i 0.851371 0.491539i
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) 21.5885i 1.01882i −0.860523 0.509411i \(-0.829863\pi\)
0.860523 0.509411i \(-0.170137\pi\)
\(450\) −2.59808 1.50000i −0.122474 0.0707107i
\(451\) 9.88269 + 5.70577i 0.465358 + 0.268674i
\(452\) 16.0981 9.29423i 0.757190 0.437164i
\(453\) 10.7321 0.504236
\(454\) −3.80385 + 2.19615i −0.178523 + 0.103071i
\(455\) 3.00000 + 8.66025i 0.140642 + 0.405999i
\(456\) 8.19615 0.383820
\(457\) −18.3923 −0.860356 −0.430178 0.902744i \(-0.641549\pi\)
−0.430178 + 0.902744i \(0.641549\pi\)
\(458\) −13.9641 + 24.1865i −0.652500 + 1.13016i
\(459\) 0 0
\(460\) −8.19615 + 4.73205i −0.382148 + 0.220633i
\(461\) −2.59808 + 4.50000i −0.121004 + 0.209586i −0.920164 0.391533i \(-0.871945\pi\)
0.799160 + 0.601119i \(0.205278\pi\)
\(462\) 5.49038 1.90192i 0.255436 0.0884855i
\(463\) 11.6962 + 20.2583i 0.543566 + 0.941484i 0.998696 + 0.0510591i \(0.0162597\pi\)
−0.455129 + 0.890425i \(0.650407\pi\)
\(464\) −0.401924 0.232051i −0.0186588 0.0107727i
\(465\) −3.29423 + 1.90192i −0.152766 + 0.0881996i
\(466\) 2.36603 + 4.09808i 0.109604 + 0.189840i
\(467\) −8.59808 14.8923i −0.397872 0.689134i 0.595592 0.803287i \(-0.296918\pi\)
−0.993463 + 0.114154i \(0.963584\pi\)
\(468\) −9.00000 5.19615i −0.416025 0.240192i
\(469\) 10.0000 3.46410i 0.461757 0.159957i
\(470\) 7.79423 + 4.50000i 0.359521 + 0.207570i
\(471\) −0.509619 0.294229i −0.0234820 0.0135573i
\(472\) 8.19615i 0.377258i
\(473\) 9.12436i 0.419538i
\(474\) 24.8827 + 14.3660i 1.14290 + 0.659853i
\(475\) −4.09808 2.36603i −0.188033 0.108561i
\(476\) 0 0
\(477\) 32.1962i 1.47416i
\(478\) 10.5622 + 18.2942i 0.483103 + 0.836759i
\(479\) 5.19615 + 9.00000i 0.237418 + 0.411220i 0.959973 0.280094i \(-0.0903655\pi\)
−0.722554 + 0.691314i \(0.757032\pi\)
\(480\) 1.50000 0.866025i 0.0684653 0.0395285i
\(481\) −12.5885 7.26795i −0.573984 0.331390i
\(482\) −10.3301 17.8923i −0.470524 0.814972i
\(483\) −28.3923 + 32.7846i −1.29189 + 1.49175i
\(484\) 4.69615 8.13397i 0.213461 0.369726i
\(485\) −13.3923 + 7.73205i −0.608113 + 0.351094i
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) −17.0000 + 29.4449i −0.770344 + 1.33427i 0.167031 + 0.985952i \(0.446582\pi\)
−0.937375 + 0.348323i \(0.886751\pi\)
\(488\) −0.928203 −0.0420178
\(489\) 21.4641 0.970640
\(490\) −6.92820 + 1.00000i −0.312984 + 0.0451754i
\(491\) 2.49038 1.43782i 0.112389 0.0648880i −0.442752 0.896644i \(-0.645998\pi\)
0.555141 + 0.831756i \(0.312664\pi\)
\(492\) 15.5885 0.702782
\(493\) 0 0
\(494\) −14.1962 8.19615i −0.638715 0.368762i
\(495\) 3.29423 1.90192i 0.148065 0.0854851i
\(496\) 2.19615i 0.0986102i
\(497\) 1.09808 + 3.16987i 0.0492554 + 0.142188i
\(498\) 1.20577 0.696152i 0.0540319 0.0311953i
\(499\) 2.90192 5.02628i 0.129908 0.225007i −0.793733 0.608267i \(-0.791865\pi\)
0.923641 + 0.383259i \(0.125198\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −18.0000 −0.804181
\(502\) 18.0000i 0.803379i
\(503\) −13.3923 −0.597133 −0.298567 0.954389i \(-0.596509\pi\)
−0.298567 + 0.954389i \(0.596509\pi\)
\(504\) 5.19615 6.00000i 0.231455 0.267261i
\(505\) 0.803848 0.0357707
\(506\) 12.0000i 0.533465i
\(507\) −0.866025 1.50000i −0.0384615 0.0666173i
\(508\) −9.39230 −0.416716
\(509\) −10.7942 + 18.6962i −0.478446 + 0.828692i −0.999695 0.0247124i \(-0.992133\pi\)
0.521249 + 0.853405i \(0.325466\pi\)
\(510\) 0 0
\(511\) −18.0000 3.46410i −0.796273 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 21.2942 12.2942i 0.940163 0.542803i
\(514\) 6.58846 + 3.80385i 0.290604 + 0.167781i
\(515\) 10.5000 6.06218i 0.462685 0.267131i
\(516\) −6.23205 10.7942i −0.274351 0.475189i
\(517\) −9.88269 + 5.70577i −0.434640 + 0.250940i
\(518\) 7.26795 8.39230i 0.319335 0.368737i
\(519\) 1.90192 3.29423i 0.0834852 0.144601i
\(520\) −3.46410 −0.151911
\(521\) −10.5000 + 18.1865i −0.460013 + 0.796766i −0.998961 0.0455727i \(-0.985489\pi\)
0.538948 + 0.842339i \(0.318822\pi\)
\(522\) −1.39230 −0.0609395
\(523\) −28.5788 + 16.5000i −1.24967 + 0.721495i −0.971043 0.238906i \(-0.923211\pi\)
−0.278623 + 0.960401i \(0.589878\pi\)
\(524\) 8.19615 14.1962i 0.358051 0.620162i
\(525\) −4.33013 + 1.50000i −0.188982 + 0.0654654i
\(526\) 5.13397 + 8.89230i 0.223852 + 0.387723i
\(527\) 0 0
\(528\) 2.19615i 0.0955753i
\(529\) 33.2846 + 57.6506i 1.44716 + 2.50655i
\(530\) 5.36603 + 9.29423i 0.233085 + 0.403715i
\(531\) 12.2942 + 21.2942i 0.533524 + 0.924091i
\(532\) 8.19615 9.46410i 0.355348 0.410321i
\(533\) −27.0000 15.5885i −1.16950 0.675211i
\(534\) 28.3923i 1.22866i
\(535\) 2.07180i 0.0895716i
\(536\) 4.00000i 0.172774i
\(537\) 9.88269 5.70577i 0.426469 0.246222i
\(538\) −15.5885 9.00000i −0.672066 0.388018i
\(539\) 3.29423 8.24167i 0.141892 0.354994i
\(540\) 2.59808 4.50000i 0.111803 0.193649i
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 12.2942 + 21.2942i 0.528082 + 0.914665i
\(543\) 11.0885 + 6.40192i 0.475851 + 0.274733i
\(544\) 0 0
\(545\) −1.59808 2.76795i −0.0684541 0.118566i
\(546\) −15.0000 + 5.19615i −0.641941 + 0.222375i
\(547\) 12.7942 22.1603i 0.547042 0.947504i −0.451434 0.892305i \(-0.649087\pi\)
0.998475 0.0551993i \(-0.0175794\pi\)
\(548\) 9.29423 5.36603i 0.397030 0.229225i
\(549\) −2.41154 + 1.39230i −0.102922 + 0.0594221i
\(550\) 0.633975 1.09808i 0.0270328 0.0468221i
\(551\) −2.19615 −0.0935592
\(552\) −8.19615 14.1962i −0.348851 0.604228i
\(553\) 41.4711 14.3660i 1.76353 0.610906i
\(554\) −11.9545 + 6.90192i −0.507897 + 0.293235i
\(555\) 3.63397 6.29423i 0.154254 0.267175i
\(556\) 13.9019 8.02628i 0.589573 0.340390i
\(557\) −7.60770 4.39230i −0.322348 0.186108i 0.330090 0.943949i \(-0.392921\pi\)
−0.652439 + 0.757841i \(0.726254\pi\)
\(558\) −3.29423 5.70577i −0.139456 0.241545i
\(559\) 24.9282i 1.05435i
\(560\) 0.500000 2.59808i 0.0211289 0.109789i
\(561\) 0 0
\(562\) −1.33013 + 2.30385i −0.0561080 + 0.0971819i
\(563\) −34.3923 −1.44946 −0.724731 0.689031i \(-0.758036\pi\)
−0.724731 + 0.689031i \(0.758036\pi\)
\(564\) −7.79423 + 13.5000i −0.328196 + 0.568453i
\(565\) 18.5885i 0.782022i
\(566\) 10.8564 0.456329
\(567\) 4.50000 23.3827i 0.188982 0.981981i
\(568\) −1.26795 −0.0532020
\(569\) 6.00000i 0.251533i 0.992060 + 0.125767i \(0.0401390\pi\)
−0.992060 + 0.125767i \(0.959861\pi\)
\(570\) 4.09808 7.09808i 0.171650 0.297306i
\(571\) 42.3923 1.77406 0.887031 0.461709i \(-0.152764\pi\)
0.887031 + 0.461709i \(0.152764\pi\)
\(572\) 2.19615 3.80385i 0.0918257 0.159047i
\(573\) −5.19615 3.00000i −0.217072 0.125327i
\(574\) 15.5885 18.0000i 0.650650 0.751305i
\(575\) 9.46410i 0.394680i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −20.7846 12.0000i −0.865275 0.499567i 0.000500448 1.00000i \(-0.499841\pi\)
−0.865775 + 0.500433i \(0.833174\pi\)
\(578\) −14.7224 + 8.50000i −0.612372 + 0.353553i
\(579\) −20.9545 + 36.2942i −0.870839 + 1.50834i
\(580\) −0.401924 + 0.232051i −0.0166890 + 0.00963539i
\(581\) 0.401924 2.08846i 0.0166746 0.0866438i
\(582\) −13.3923 23.1962i −0.555129 0.961511i
\(583\) −13.6077 −0.563573
\(584\) 3.46410 6.00000i 0.143346 0.248282i
\(585\) −9.00000 + 5.19615i −0.372104 + 0.214834i
\(586\) 3.80385 2.19615i 0.157135 0.0907222i
\(587\) −20.5981 + 35.6769i −0.850174 + 1.47254i 0.0308777 + 0.999523i \(0.490170\pi\)
−0.881051 + 0.473021i \(0.843164\pi\)
\(588\) −1.73205 12.0000i −0.0714286 0.494872i
\(589\) −5.19615 9.00000i −0.214104 0.370839i
\(590\) 7.09808 + 4.09808i 0.292223 + 0.168715i
\(591\) 9.50962 + 5.49038i 0.391173 + 0.225844i
\(592\) 2.09808 + 3.63397i 0.0862304 + 0.149355i
\(593\) −7.39230 12.8038i −0.303566 0.525791i 0.673375 0.739301i \(-0.264844\pi\)
−0.976941 + 0.213510i \(0.931510\pi\)
\(594\) 3.29423 + 5.70577i 0.135164 + 0.234111i
\(595\) 0 0
\(596\) 10.3923 + 6.00000i 0.425685 + 0.245770i
\(597\) −10.3923 + 6.00000i −0.425329 + 0.245564i
\(598\) 32.7846i 1.34066i
\(599\) 16.3923i 0.669771i −0.942259 0.334886i \(-0.891302\pi\)
0.942259 0.334886i \(-0.108698\pi\)
\(600\) 1.73205i 0.0707107i
\(601\) 3.58846 + 2.07180i 0.146376 + 0.0845104i 0.571399 0.820672i \(-0.306401\pi\)
−0.425023 + 0.905182i \(0.639734\pi\)
\(602\) −18.6962 3.59808i −0.761998 0.146647i
\(603\) 6.00000 + 10.3923i 0.244339 + 0.423207i
\(604\) 3.09808 + 5.36603i 0.126059 + 0.218340i
\(605\) −4.69615 8.13397i −0.190926 0.330693i
\(606\) 1.39230i 0.0565585i
\(607\) −15.6962 9.06218i −0.637087 0.367822i 0.146404 0.989225i \(-0.453230\pi\)
−0.783492 + 0.621402i \(0.786563\pi\)
\(608\) 2.36603 + 4.09808i 0.0959550 + 0.166199i
\(609\) −1.39230 + 1.60770i −0.0564190 + 0.0651471i
\(610\) −0.464102 + 0.803848i −0.0187909 + 0.0325468i
\(611\) 27.0000 15.5885i 1.09230 0.630641i
\(612\) 0 0
\(613\) −17.3923 + 30.1244i −0.702469 + 1.21671i 0.265129 + 0.964213i \(0.414586\pi\)
−0.967597 + 0.252498i \(0.918748\pi\)
\(614\) −17.7846 −0.717728
\(615\) 7.79423 13.5000i 0.314294 0.544373i
\(616\) 2.53590 + 2.19615i 0.102174 + 0.0884855i
\(617\) 26.1962 15.1244i 1.05462 0.608884i 0.130679 0.991425i \(-0.458284\pi\)
0.923938 + 0.382541i \(0.124951\pi\)
\(618\) 10.5000 + 18.1865i 0.422372 + 0.731570i
\(619\) 3.80385 2.19615i 0.152890 0.0882708i −0.421603 0.906780i \(-0.638533\pi\)
0.574493 + 0.818509i \(0.305199\pi\)
\(620\) −1.90192 1.09808i −0.0763831 0.0440998i
\(621\) −42.5885 24.5885i −1.70902 0.986701i
\(622\) 26.1962i 1.05037i
\(623\) 32.7846 + 28.3923i 1.31349 + 1.13751i
\(624\) 6.00000i 0.240192i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 9.80385 0.391841
\(627\) 5.19615 + 9.00000i 0.207514 + 0.359425i
\(628\) 0.339746i 0.0135573i
\(629\) 0 0
\(630\) −2.59808 7.50000i −0.103510 0.298807i
\(631\) −8.39230 −0.334092 −0.167046 0.985949i \(-0.553423\pi\)
−0.167046 + 0.985949i \(0.553423\pi\)
\(632\) 16.5885i 0.659853i
\(633\) 18.3397 0.728939
\(634\) 27.4641 1.09074
\(635\) −4.69615 + 8.13397i −0.186361 + 0.322787i
\(636\) −16.0981 + 9.29423i −0.638330 + 0.368540i
\(637\) −9.00000 + 22.5167i −0.356593 + 0.892143i
\(638\) 0.588457i 0.0232972i
\(639\) −3.29423 + 1.90192i −0.130318 + 0.0752389i
\(640\) 0.866025 + 0.500000i 0.0342327 + 0.0197642i
\(641\) −38.7846 + 22.3923i −1.53190 + 0.884443i −0.532626 + 0.846351i \(0.678795\pi\)
−0.999274 + 0.0380920i \(0.987872\pi\)
\(642\) −3.58846 −0.141625
\(643\) −31.7942 + 18.3564i −1.25384 + 0.723906i −0.971870 0.235517i \(-0.924322\pi\)
−0.281972 + 0.959423i \(0.590988\pi\)
\(644\) −24.5885 4.73205i −0.968921 0.186469i
\(645\) −12.4641 −0.490774
\(646\) 0 0
\(647\) −12.6962 + 21.9904i −0.499137 + 0.864531i −1.00000 0.000995924i \(-0.999683\pi\)
0.500862 + 0.865527i \(0.333016\pi\)
\(648\) 7.79423 + 4.50000i 0.306186 + 0.176777i
\(649\) −9.00000 + 5.19615i −0.353281 + 0.203967i
\(650\) −1.73205 + 3.00000i −0.0679366 + 0.117670i
\(651\) −9.88269 1.90192i −0.387333 0.0745423i
\(652\) 6.19615 + 10.7321i 0.242660 + 0.420300i
\(653\) 19.1769 + 11.0718i 0.750451 + 0.433273i 0.825857 0.563880i \(-0.190692\pi\)
−0.0754061 + 0.997153i \(0.524025\pi\)
\(654\) 4.79423 2.76795i 0.187469 0.108235i
\(655\) −8.19615 14.1962i −0.320250 0.554690i
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) 20.7846i 0.810885i
\(658\) 7.79423 + 22.5000i 0.303851 + 0.877141i
\(659\) −17.7058 10.2224i −0.689719 0.398209i 0.113788 0.993505i \(-0.463702\pi\)
−0.803507 + 0.595296i \(0.797035\pi\)
\(660\) 1.90192 + 1.09808i 0.0740323 + 0.0427426i
\(661\) 40.8564i 1.58913i −0.607179 0.794565i \(-0.707699\pi\)
0.607179 0.794565i \(-0.292301\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 0 0
\(664\) 0.696152 + 0.401924i 0.0270160 + 0.0155977i
\(665\) −4.09808 11.8301i −0.158917 0.458753i
\(666\) 10.9019 + 6.29423i 0.422441 + 0.243896i
\(667\) 2.19615 + 3.80385i 0.0850354 + 0.147286i
\(668\) −5.19615 9.00000i −0.201045 0.348220i
\(669\) −15.4019 + 8.89230i −0.595473 + 0.343796i
\(670\) 3.46410 + 2.00000i 0.133830 + 0.0772667i
\(671\) −0.588457 1.01924i −0.0227171 0.0393472i
\(672\) 4.50000 + 0.866025i 0.173591 + 0.0334077i
\(673\) −13.4904 + 23.3660i −0.520016 + 0.900694i 0.479713 + 0.877425i \(0.340741\pi\)
−0.999729 + 0.0232688i \(0.992593\pi\)
\(674\) 8.66025 5.00000i 0.333581 0.192593i
\(675\) −2.59808 4.50000i −0.100000 0.173205i
\(676\) 0.500000 0.866025i 0.0192308 0.0333087i
\(677\) −28.9808 −1.11382 −0.556911 0.830572i \(-0.688013\pi\)
−0.556911 + 0.830572i \(0.688013\pi\)
\(678\) 32.1962 1.23649
\(679\) −40.1769 7.73205i −1.54185 0.296729i
\(680\) 0 0
\(681\) −7.60770 −0.291528
\(682\) 2.41154 1.39230i 0.0923427 0.0533141i
\(683\) 36.7750 + 21.2321i 1.40716 + 0.812422i 0.995113 0.0987426i \(-0.0314820\pi\)
0.412043 + 0.911164i \(0.364815\pi\)
\(684\) 12.2942 + 7.09808i 0.470082 + 0.271402i
\(685\) 10.7321i 0.410051i
\(686\) −15.5885 10.0000i −0.595170 0.381802i
\(687\) −41.8923 + 24.1865i −1.59829 + 0.922774i
\(688\) 3.59808 6.23205i 0.137175 0.237595i
\(689\) 37.1769 1.41633
\(690\) −16.3923 −0.624044
\(691\) 18.9282i 0.720063i −0.932940 0.360031i \(-0.882766\pi\)
0.932940 0.360031i \(-0.117234\pi\)
\(692\) 2.19615 0.0834852
\(693\) 9.88269 + 1.90192i 0.375412 + 0.0722481i
\(694\) 27.2487 1.03435
\(695\) 16.0526i 0.608908i
\(696\) −0.401924 0.696152i −0.0152349 0.0263876i
\(697\) 0 0
\(698\) 2.19615 3.80385i 0.0831256 0.143978i
\(699\) 8.19615i 0.310007i
\(700\) −2.00000 1.73205i −0.0755929 0.0654654i
\(701\) 9.67949i 0.365589i 0.983151 + 0.182795i \(0.0585144\pi\)
−0.983151 + 0.182795i \(0.941486\pi\)
\(702\) −9.00000 15.5885i −0.339683 0.588348i
\(703\) 17.1962 + 9.92820i 0.648565 + 0.374449i
\(704\) −1.09808 + 0.633975i −0.0413853 + 0.0238938i
\(705\) 7.79423 + 13.5000i 0.293548 + 0.508439i
\(706\) −26.4904 + 15.2942i −0.996979 + 0.575606i
\(707\) 1.60770 + 1.39230i 0.0604636 + 0.0523630i
\(708\) −7.09808 + 12.2942i −0.266762 + 0.462045i
\(709\) −5.21539 −0.195868 −0.0979340 0.995193i \(-0.531223\pi\)
−0.0979340 + 0.995193i \(0.531223\pi\)
\(710\) −0.633975 + 1.09808i −0.0237926 + 0.0412101i
\(711\) 24.8827 + 43.0981i 0.933174 + 1.61630i
\(712\) −14.1962 + 8.19615i −0.532023 + 0.307164i
\(713\) −10.3923 + 18.0000i −0.389195 + 0.674105i
\(714\) 0 0
\(715\) −2.19615 3.80385i −0.0821314 0.142256i
\(716\) 5.70577 + 3.29423i 0.213235 + 0.123111i
\(717\) 36.5885i 1.36642i
\(718\) −13.0981 22.6865i −0.488816 0.846654i
\(719\) 20.7846 + 36.0000i 0.775135 + 1.34257i 0.934718 + 0.355389i \(0.115652\pi\)
−0.159583 + 0.987184i \(0.551015\pi\)
\(720\) 3.00000 0.111803
\(721\) 31.5000 + 6.06218i 1.17312 + 0.225767i
\(722\) 2.93782 + 1.69615i 0.109334 + 0.0631243i
\(723\) 35.7846i 1.33084i
\(724\) 7.39230i 0.274733i
\(725\) 0.464102i 0.0172363i
\(726\) 14.0885 8.13397i 0.522872 0.301880i
\(727\) 0.215390 + 0.124356i 0.00798838 + 0.00461210i 0.503989 0.863710i \(-0.331865\pi\)
−0.496000 + 0.868322i \(0.665199\pi\)
\(728\) −6.92820 6.00000i −0.256776 0.222375i
\(729\) 27.0000 1.00000
\(730\) −3.46410 6.00000i −0.128212 0.222070i
\(731\) 0 0
\(732\) −1.39230 0.803848i −0.0514611 0.0297111i
\(733\) −3.50962 2.02628i −0.129631 0.0748423i 0.433782 0.901018i \(-0.357179\pi\)
−0.563413 + 0.826175i \(0.690512\pi\)
\(734\) 9.40192 + 16.2846i 0.347031 + 0.601076i
\(735\) −11.2583 4.50000i −0.415270 0.165985i
\(736\) 4.73205 8.19615i 0.174426 0.302114i
\(737\) −4.39230 + 2.53590i −0.161793 + 0.0934110i
\(738\) 23.3827 + 13.5000i 0.860729 + 0.496942i
\(739\) 14.5885 25.2679i 0.536645 0.929497i −0.462437 0.886652i \(-0.653025\pi\)
0.999082 0.0428442i \(-0.0136419\pi\)
\(740\) 4.19615 0.154254
\(741\) −14.1962 24.5885i −0.521509 0.903280i
\(742\) −5.36603 + 27.8827i −0.196993 + 1.02361i
\(743\) 38.6769 22.3301i 1.41892 0.819213i 0.422714 0.906263i \(-0.361077\pi\)
0.996204 + 0.0870500i \(0.0277440\pi\)
\(744\) 1.90192 3.29423i 0.0697279 0.120772i
\(745\) 10.3923 6.00000i 0.380745 0.219823i
\(746\) 0.169873 + 0.0980762i 0.00621949 + 0.00359083i
\(747\) 2.41154 0.0882337
\(748\) 0 0
\(749\) −3.58846 + 4.14359i −0.131119 + 0.151404i
\(750\) −1.50000 0.866025i −0.0547723 0.0316228i
\(751\) 21.1962 36.7128i 0.773459 1.33967i −0.162198 0.986758i \(-0.551858\pi\)
0.935657 0.352911i \(-0.114808\pi\)
\(752\) −9.00000 −0.328196
\(753\) −15.5885 + 27.0000i −0.568075 + 0.983935i
\(754\) 1.60770i 0.0585488i
\(755\) 6.19615 0.225501
\(756\) 12.9904 4.50000i 0.472456 0.163663i
\(757\) 22.5885 0.820991 0.410496 0.911863i \(-0.365356\pi\)
0.410496 + 0.911863i \(0.365356\pi\)
\(758\) 30.3923i 1.10390i
\(759\) 10.3923 18.0000i 0.377217 0.653359i
\(760\) 4.73205 0.171650
\(761\) −16.5000 + 28.5788i −0.598125 + 1.03598i 0.394973 + 0.918693i \(0.370754\pi\)
−0.993098 + 0.117289i \(0.962579\pi\)
\(762\) −14.0885 8.13397i −0.510371 0.294663i
\(763\) 1.59808 8.30385i 0.0578542 0.300619i
\(764\) 3.46410i 0.125327i
\(765\) 0 0
\(766\) −1.20577 0.696152i −0.0435663 0.0251530i
\(767\) 24.5885 14.1962i 0.887838 0.512593i
\(768\) −0.866025 + 1.50000i −0.0312500 + 0.0541266i
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) 3.16987 1.09808i 0.114234 0.0395719i
\(771\) 6.58846 + 11.4115i 0.237277 + 0.410977i
\(772\) −24.1962 −0.870839
\(773\) 9.00000 15.5885i 0.323708 0.560678i −0.657542 0.753418i \(-0.728404\pi\)
0.981250 + 0.192740i \(0.0617373\pi\)
\(774\) 21.5885i 0.775981i
\(775\) −1.90192 + 1.09808i −0.0683191 + 0.0394441i
\(776\) 7.73205 13.3923i 0.277564 0.480756i
\(777\) 18.1699 6.29423i 0.651841 0.225804i
\(778\) 15.3564 + 26.5981i 0.550554 + 0.953587i
\(779\) 36.8827 + 21.2942i 1.32146 + 0.762945i
\(780\) −5.19615 3.00000i −0.186052 0.107417i
\(781\) −0.803848 1.39230i −0.0287639 0.0498206i
\(782\) 0 0
\(783\) −2.08846 1.20577i −0.0746354 0.0430908i
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) −0.294229 0.169873i −0.0105015