Properties

Label 1110.2.o.a.253.3
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.3
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(0.0687789 - 2.23501i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.13605 - 2.13605i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(0.0687789 - 2.23501i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.13605 - 2.13605i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.0687789 + 2.23501i) q^{10} -2.07347i q^{11} +(-0.707107 + 0.707107i) q^{12} +4.31443 q^{13} +(-2.13605 + 2.13605i) q^{14} +(1.53176 + 1.62902i) q^{15} +1.00000 q^{16} -2.62056i q^{17} +1.00000i q^{18} +(1.48007 + 1.48007i) q^{19} +(0.0687789 - 2.23501i) q^{20} +3.02083i q^{21} +2.07347i q^{22} -3.49438 q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.99054 - 0.307443i) q^{25} -4.31443 q^{26} +(0.707107 + 0.707107i) q^{27} +(2.13605 - 2.13605i) q^{28} +(0.364989 - 0.364989i) q^{29} +(-1.53176 - 1.62902i) q^{30} +(0.391381 + 0.391381i) q^{31} -1.00000 q^{32} +(1.46616 + 1.46616i) q^{33} +2.62056i q^{34} +(-4.62718 - 4.92101i) q^{35} -1.00000i q^{36} +(-2.65855 - 5.47103i) q^{37} +(-1.48007 - 1.48007i) q^{38} +(-3.05076 + 3.05076i) q^{39} +(-0.0687789 + 2.23501i) q^{40} +3.80013i q^{41} -3.02083i q^{42} -6.28607 q^{43} -2.07347i q^{44} +(-2.23501 - 0.0687789i) q^{45} +3.49438 q^{46} +(3.37898 - 3.37898i) q^{47} +(-0.707107 + 0.707107i) q^{48} -2.12544i q^{49} +(4.99054 + 0.307443i) q^{50} +(1.85302 + 1.85302i) q^{51} +4.31443 q^{52} +(-1.87850 - 1.87850i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-4.63422 - 0.142611i) q^{55} +(-2.13605 + 2.13605i) q^{56} -2.09313 q^{57} +(-0.364989 + 0.364989i) q^{58} +(-0.917356 - 0.917356i) q^{59} +(1.53176 + 1.62902i) q^{60} +(5.87589 + 5.87589i) q^{61} +(-0.391381 - 0.391381i) q^{62} +(-2.13605 - 2.13605i) q^{63} +1.00000 q^{64} +(0.296742 - 9.64280i) q^{65} +(-1.46616 - 1.46616i) q^{66} +(-3.05783 - 3.05783i) q^{67} -2.62056i q^{68} +(2.47090 - 2.47090i) q^{69} +(4.62718 + 4.92101i) q^{70} -9.16581 q^{71} +1.00000i q^{72} +(8.50139 - 8.50139i) q^{73} +(2.65855 + 5.47103i) q^{74} +(3.74624 - 3.31145i) q^{75} +(1.48007 + 1.48007i) q^{76} +(-4.42903 - 4.42903i) q^{77} +(3.05076 - 3.05076i) q^{78} +(9.01137 + 9.01137i) q^{79} +(0.0687789 - 2.23501i) q^{80} -1.00000 q^{81} -3.80013i q^{82} +(-0.381394 - 0.381394i) q^{83} +3.02083i q^{84} +(-5.85698 - 0.180239i) q^{85} +6.28607 q^{86} +0.516172i q^{87} +2.07347i q^{88} +(3.68659 - 3.68659i) q^{89} +(2.23501 + 0.0687789i) q^{90} +(9.21585 - 9.21585i) q^{91} -3.49438 q^{92} -0.553497 q^{93} +(-3.37898 + 3.37898i) q^{94} +(3.40977 - 3.20617i) q^{95} +(0.707107 - 0.707107i) q^{96} -14.1415i q^{97} +2.12544i q^{98} -2.07347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) 0.0687789 2.23501i 0.0307589 0.999527i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 2.13605 2.13605i 0.807352 0.807352i −0.176880 0.984232i \(-0.556601\pi\)
0.984232 + 0.176880i \(0.0566006\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −0.0687789 + 2.23501i −0.0217498 + 0.706772i
\(11\) 2.07347i 0.625174i −0.949889 0.312587i \(-0.898804\pi\)
0.949889 0.312587i \(-0.101196\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 4.31443 1.19661 0.598304 0.801269i \(-0.295842\pi\)
0.598304 + 0.801269i \(0.295842\pi\)
\(14\) −2.13605 + 2.13605i −0.570884 + 0.570884i
\(15\) 1.53176 + 1.62902i 0.395498 + 0.420612i
\(16\) 1.00000 0.250000
\(17\) 2.62056i 0.635579i −0.948161 0.317790i \(-0.897059\pi\)
0.948161 0.317790i \(-0.102941\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.48007 + 1.48007i 0.339551 + 0.339551i 0.856198 0.516647i \(-0.172820\pi\)
−0.516647 + 0.856198i \(0.672820\pi\)
\(20\) 0.0687789 2.23501i 0.0153794 0.499763i
\(21\) 3.02083i 0.659200i
\(22\) 2.07347i 0.442065i
\(23\) −3.49438 −0.728628 −0.364314 0.931276i \(-0.618697\pi\)
−0.364314 + 0.931276i \(0.618697\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) −4.99054 0.307443i −0.998108 0.0614886i
\(26\) −4.31443 −0.846129
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 2.13605 2.13605i 0.403676 0.403676i
\(29\) 0.364989 0.364989i 0.0677767 0.0677767i −0.672406 0.740183i \(-0.734739\pi\)
0.740183 + 0.672406i \(0.234739\pi\)
\(30\) −1.53176 1.62902i −0.279659 0.297418i
\(31\) 0.391381 + 0.391381i 0.0702942 + 0.0702942i 0.741380 0.671086i \(-0.234172\pi\)
−0.671086 + 0.741380i \(0.734172\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.46616 + 1.46616i 0.255226 + 0.255226i
\(34\) 2.62056i 0.449422i
\(35\) −4.62718 4.92101i −0.782137 0.831803i
\(36\) 1.00000i 0.166667i
\(37\) −2.65855 5.47103i −0.437062 0.899431i
\(38\) −1.48007 1.48007i −0.240099 0.240099i
\(39\) −3.05076 + 3.05076i −0.488513 + 0.488513i
\(40\) −0.0687789 + 2.23501i −0.0108749 + 0.353386i
\(41\) 3.80013i 0.593481i 0.954958 + 0.296740i \(0.0958996\pi\)
−0.954958 + 0.296740i \(0.904100\pi\)
\(42\) 3.02083i 0.466125i
\(43\) −6.28607 −0.958617 −0.479308 0.877647i \(-0.659112\pi\)
−0.479308 + 0.877647i \(0.659112\pi\)
\(44\) 2.07347i 0.312587i
\(45\) −2.23501 0.0687789i −0.333176 0.0102530i
\(46\) 3.49438 0.515218
\(47\) 3.37898 3.37898i 0.492876 0.492876i −0.416336 0.909211i \(-0.636686\pi\)
0.909211 + 0.416336i \(0.136686\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 2.12544i 0.303634i
\(50\) 4.99054 + 0.307443i 0.705769 + 0.0434790i
\(51\) 1.85302 + 1.85302i 0.259474 + 0.259474i
\(52\) 4.31443 0.598304
\(53\) −1.87850 1.87850i −0.258031 0.258031i 0.566222 0.824253i \(-0.308405\pi\)
−0.824253 + 0.566222i \(0.808405\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −4.63422 0.142611i −0.624878 0.0192296i
\(56\) −2.13605 + 2.13605i −0.285442 + 0.285442i
\(57\) −2.09313 −0.277242
\(58\) −0.364989 + 0.364989i −0.0479254 + 0.0479254i
\(59\) −0.917356 0.917356i −0.119430 0.119430i 0.644866 0.764296i \(-0.276913\pi\)
−0.764296 + 0.644866i \(0.776913\pi\)
\(60\) 1.53176 + 1.62902i 0.197749 + 0.210306i
\(61\) 5.87589 + 5.87589i 0.752331 + 0.752331i 0.974914 0.222583i \(-0.0714489\pi\)
−0.222583 + 0.974914i \(0.571449\pi\)
\(62\) −0.391381 0.391381i −0.0497055 0.0497055i
\(63\) −2.13605 2.13605i −0.269117 0.269117i
\(64\) 1.00000 0.125000
\(65\) 0.296742 9.64280i 0.0368063 1.19604i
\(66\) −1.46616 1.46616i −0.180472 0.180472i
\(67\) −3.05783 3.05783i −0.373573 0.373573i 0.495204 0.868777i \(-0.335093\pi\)
−0.868777 + 0.495204i \(0.835093\pi\)
\(68\) 2.62056i 0.317790i
\(69\) 2.47090 2.47090i 0.297461 0.297461i
\(70\) 4.62718 + 4.92101i 0.553054 + 0.588174i
\(71\) −9.16581 −1.08778 −0.543891 0.839156i \(-0.683049\pi\)
−0.543891 + 0.839156i \(0.683049\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 8.50139 8.50139i 0.995012 0.995012i −0.00497545 0.999988i \(-0.501584\pi\)
0.999988 + 0.00497545i \(0.00158374\pi\)
\(74\) 2.65855 + 5.47103i 0.309050 + 0.635994i
\(75\) 3.74624 3.31145i 0.432578 0.382373i
\(76\) 1.48007 + 1.48007i 0.169776 + 0.169776i
\(77\) −4.42903 4.42903i −0.504735 0.504735i
\(78\) 3.05076 3.05076i 0.345431 0.345431i
\(79\) 9.01137 + 9.01137i 1.01386 + 1.01386i 0.999903 + 0.0139555i \(0.00444231\pi\)
0.0139555 + 0.999903i \(0.495558\pi\)
\(80\) 0.0687789 2.23501i 0.00768972 0.249882i
\(81\) −1.00000 −0.111111
\(82\) 3.80013i 0.419654i
\(83\) −0.381394 0.381394i −0.0418634 0.0418634i 0.685865 0.727729i \(-0.259424\pi\)
−0.727729 + 0.685865i \(0.759424\pi\)
\(84\) 3.02083i 0.329600i
\(85\) −5.85698 0.180239i −0.635278 0.0195497i
\(86\) 6.28607 0.677844
\(87\) 0.516172i 0.0553395i
\(88\) 2.07347i 0.221032i
\(89\) 3.68659 3.68659i 0.390778 0.390778i −0.484187 0.874965i \(-0.660884\pi\)
0.874965 + 0.484187i \(0.160884\pi\)
\(90\) 2.23501 + 0.0687789i 0.235591 + 0.00724994i
\(91\) 9.21585 9.21585i 0.966084 0.966084i
\(92\) −3.49438 −0.364314
\(93\) −0.553497 −0.0573950
\(94\) −3.37898 + 3.37898i −0.348516 + 0.348516i
\(95\) 3.40977 3.20617i 0.349835 0.328946i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 14.1415i 1.43586i −0.696117 0.717928i \(-0.745091\pi\)
0.696117 0.717928i \(-0.254909\pi\)
\(98\) 2.12544i 0.214702i
\(99\) −2.07347 −0.208391
\(100\) −4.99054 0.307443i −0.499054 0.0307443i
\(101\) 7.64384i 0.760591i −0.924865 0.380295i \(-0.875822\pi\)
0.924865 0.380295i \(-0.124178\pi\)
\(102\) −1.85302 1.85302i −0.183476 0.183476i
\(103\) 9.85885i 0.971422i −0.874120 0.485711i \(-0.838561\pi\)
0.874120 0.485711i \(-0.161439\pi\)
\(104\) −4.31443 −0.423065
\(105\) 6.75159 + 0.207770i 0.658888 + 0.0202763i
\(106\) 1.87850 + 1.87850i 0.182456 + 0.182456i
\(107\) 4.17096 4.17096i 0.403222 0.403222i −0.476145 0.879367i \(-0.657966\pi\)
0.879367 + 0.476145i \(0.157966\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −0.461041 0.461041i −0.0441597 0.0441597i 0.684682 0.728842i \(-0.259941\pi\)
−0.728842 + 0.684682i \(0.759941\pi\)
\(110\) 4.63422 + 0.142611i 0.441856 + 0.0135974i
\(111\) 5.74848 + 1.98872i 0.545621 + 0.188761i
\(112\) 2.13605 2.13605i 0.201838 0.201838i
\(113\) 17.3203i 1.62936i −0.579913 0.814678i \(-0.696914\pi\)
0.579913 0.814678i \(-0.303086\pi\)
\(114\) 2.09313 0.196040
\(115\) −0.240340 + 7.80997i −0.0224118 + 0.728284i
\(116\) 0.364989 0.364989i 0.0338884 0.0338884i
\(117\) 4.31443i 0.398869i
\(118\) 0.917356 + 0.917356i 0.0844495 + 0.0844495i
\(119\) −5.59765 5.59765i −0.513136 0.513136i
\(120\) −1.53176 1.62902i −0.139830 0.148709i
\(121\) 6.70073 0.609158
\(122\) −5.87589 5.87589i −0.531978 0.531978i
\(123\) −2.68710 2.68710i −0.242287 0.242287i
\(124\) 0.391381 + 0.391381i 0.0351471 + 0.0351471i
\(125\) −1.03038 + 11.1328i −0.0921602 + 0.995744i
\(126\) 2.13605 + 2.13605i 0.190295 + 0.190295i
\(127\) −6.18161 + 6.18161i −0.548529 + 0.548529i −0.926015 0.377486i \(-0.876789\pi\)
0.377486 + 0.926015i \(0.376789\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.44492 4.44492i 0.391354 0.391354i
\(130\) −0.296742 + 9.64280i −0.0260260 + 0.845729i
\(131\) 1.03836 + 1.03836i 0.0907217 + 0.0907217i 0.751011 0.660289i \(-0.229566\pi\)
−0.660289 + 0.751011i \(0.729566\pi\)
\(132\) 1.46616 + 1.46616i 0.127613 + 0.127613i
\(133\) 6.32301 0.548275
\(134\) 3.05783 + 3.05783i 0.264156 + 0.264156i
\(135\) 1.62902 1.53176i 0.140204 0.131833i
\(136\) 2.62056i 0.224711i
\(137\) −13.3475 + 13.3475i −1.14035 + 1.14035i −0.151966 + 0.988386i \(0.548560\pi\)
−0.988386 + 0.151966i \(0.951440\pi\)
\(138\) −2.47090 + 2.47090i −0.210337 + 0.210337i
\(139\) −12.1026 −1.02653 −0.513267 0.858229i \(-0.671565\pi\)
−0.513267 + 0.858229i \(0.671565\pi\)
\(140\) −4.62718 4.92101i −0.391068 0.415902i
\(141\) 4.77861i 0.402431i
\(142\) 9.16581 0.769177
\(143\) 8.94583i 0.748088i
\(144\) 1.00000i 0.0833333i
\(145\) −0.790650 0.840857i −0.0656599 0.0698294i
\(146\) −8.50139 + 8.50139i −0.703580 + 0.703580i
\(147\) 1.50291 + 1.50291i 0.123958 + 0.123958i
\(148\) −2.65855 5.47103i −0.218531 0.449716i
\(149\) 1.78006i 0.145828i −0.997338 0.0729141i \(-0.976770\pi\)
0.997338 0.0729141i \(-0.0232299\pi\)
\(150\) −3.74624 + 3.31145i −0.305879 + 0.270379i
\(151\) 14.7620i 1.20132i 0.799506 + 0.600658i \(0.205095\pi\)
−0.799506 + 0.600658i \(0.794905\pi\)
\(152\) −1.48007 1.48007i −0.120049 0.120049i
\(153\) −2.62056 −0.211860
\(154\) 4.42903 + 4.42903i 0.356902 + 0.356902i
\(155\) 0.901660 0.847823i 0.0724231 0.0680988i
\(156\) −3.05076 + 3.05076i −0.244257 + 0.244257i
\(157\) 3.02964 3.02964i 0.241792 0.241792i −0.575799 0.817591i \(-0.695309\pi\)
0.817591 + 0.575799i \(0.195309\pi\)
\(158\) −9.01137 9.01137i −0.716906 0.716906i
\(159\) 2.65660 0.210682
\(160\) −0.0687789 + 2.23501i −0.00543745 + 0.176693i
\(161\) −7.46418 + 7.46418i −0.588260 + 0.588260i
\(162\) 1.00000 0.0785674
\(163\) 6.39530i 0.500918i 0.968127 + 0.250459i \(0.0805816\pi\)
−0.968127 + 0.250459i \(0.919418\pi\)
\(164\) 3.80013i 0.296740i
\(165\) 3.37773 3.17605i 0.262956 0.247255i
\(166\) 0.381394 + 0.381394i 0.0296019 + 0.0296019i
\(167\) 7.40255i 0.572826i 0.958106 + 0.286413i \(0.0924630\pi\)
−0.958106 + 0.286413i \(0.907537\pi\)
\(168\) 3.02083i 0.233062i
\(169\) 5.61431 0.431870
\(170\) 5.85698 + 0.180239i 0.449210 + 0.0138237i
\(171\) 1.48007 1.48007i 0.113184 0.113184i
\(172\) −6.28607 −0.479308
\(173\) 16.3983 16.3983i 1.24674 1.24674i 0.289586 0.957152i \(-0.406483\pi\)
0.957152 0.289586i \(-0.0935175\pi\)
\(174\) 0.516172i 0.0391309i
\(175\) −11.3168 + 10.0033i −0.855467 + 0.756181i
\(176\) 2.07347i 0.156293i
\(177\) 1.29734 0.0975139
\(178\) −3.68659 + 3.68659i −0.276322 + 0.276322i
\(179\) 16.2448 16.2448i 1.21419 1.21419i 0.244559 0.969634i \(-0.421357\pi\)
0.969634 0.244559i \(-0.0786432\pi\)
\(180\) −2.23501 0.0687789i −0.166588 0.00512648i
\(181\) −5.45708 −0.405621 −0.202811 0.979218i \(-0.565008\pi\)
−0.202811 + 0.979218i \(0.565008\pi\)
\(182\) −9.21585 + 9.21585i −0.683124 + 0.683124i
\(183\) −8.30976 −0.614275
\(184\) 3.49438 0.257609
\(185\) −12.4107 + 5.56559i −0.912449 + 0.409190i
\(186\) 0.553497 0.0405844
\(187\) −5.43364 −0.397347
\(188\) 3.37898 3.37898i 0.246438 0.246438i
\(189\) 3.02083 0.219733
\(190\) −3.40977 + 3.20617i −0.247370 + 0.232600i
\(191\) −8.47691 + 8.47691i −0.613367 + 0.613367i −0.943822 0.330455i \(-0.892798\pi\)
0.330455 + 0.943822i \(0.392798\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −0.815237 −0.0586820 −0.0293410 0.999569i \(-0.509341\pi\)
−0.0293410 + 0.999569i \(0.509341\pi\)
\(194\) 14.1415i 1.01530i
\(195\) 6.60866 + 7.02831i 0.473256 + 0.503308i
\(196\) 2.12544i 0.151817i
\(197\) −12.1517 + 12.1517i −0.865772 + 0.865772i −0.992001 0.126229i \(-0.959713\pi\)
0.126229 + 0.992001i \(0.459713\pi\)
\(198\) 2.07347 0.147355
\(199\) −6.43148 + 6.43148i −0.455915 + 0.455915i −0.897312 0.441397i \(-0.854483\pi\)
0.441397 + 0.897312i \(0.354483\pi\)
\(200\) 4.99054 + 0.307443i 0.352884 + 0.0217395i
\(201\) 4.32442 0.305021
\(202\) 7.64384i 0.537819i
\(203\) 1.55927i 0.109439i
\(204\) 1.85302 + 1.85302i 0.129737 + 0.129737i
\(205\) 8.49333 + 0.261369i 0.593200 + 0.0182548i
\(206\) 9.85885i 0.686899i
\(207\) 3.49438i 0.242876i
\(208\) 4.31443 0.299152
\(209\) 3.06887 3.06887i 0.212279 0.212279i
\(210\) −6.75159 0.207770i −0.465904 0.0143375i
\(211\) −1.84896 −0.127287 −0.0636437 0.997973i \(-0.520272\pi\)
−0.0636437 + 0.997973i \(0.520272\pi\)
\(212\) −1.87850 1.87850i −0.129016 0.129016i
\(213\) 6.48120 6.48120i 0.444085 0.444085i
\(214\) −4.17096 + 4.17096i −0.285121 + 0.285121i
\(215\) −0.432349 + 14.0494i −0.0294860 + 0.958163i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 1.67202 0.113504
\(218\) 0.461041 + 0.461041i 0.0312256 + 0.0312256i
\(219\) 12.0228i 0.812424i
\(220\) −4.63422 0.142611i −0.312439 0.00961482i
\(221\) 11.3062i 0.760539i
\(222\) −5.74848 1.98872i −0.385812 0.133474i
\(223\) 4.85478 + 4.85478i 0.325100 + 0.325100i 0.850720 0.525620i \(-0.176166\pi\)
−0.525620 + 0.850720i \(0.676166\pi\)
\(224\) −2.13605 + 2.13605i −0.142721 + 0.142721i
\(225\) −0.307443 + 4.99054i −0.0204962 + 0.332703i
\(226\) 17.3203i 1.15213i
\(227\) 19.5601i 1.29825i 0.760683 + 0.649123i \(0.224864\pi\)
−0.760683 + 0.649123i \(0.775136\pi\)
\(228\) −2.09313 −0.138621
\(229\) 5.52626i 0.365186i −0.983189 0.182593i \(-0.941551\pi\)
0.983189 0.182593i \(-0.0584490\pi\)
\(230\) 0.240340 7.80997i 0.0158475 0.514974i
\(231\) 6.26360 0.412115
\(232\) −0.364989 + 0.364989i −0.0239627 + 0.0239627i
\(233\) 8.07622 8.07622i 0.529091 0.529091i −0.391210 0.920301i \(-0.627944\pi\)
0.920301 + 0.391210i \(0.127944\pi\)
\(234\) 4.31443i 0.282043i
\(235\) −7.31966 7.78447i −0.477482 0.507803i
\(236\) −0.917356 0.917356i −0.0597148 0.0597148i
\(237\) −12.7440 −0.827812
\(238\) 5.59765 + 5.59765i 0.362842 + 0.362842i
\(239\) −1.04218 1.04218i −0.0674129 0.0674129i 0.672597 0.740009i \(-0.265179\pi\)
−0.740009 + 0.672597i \(0.765179\pi\)
\(240\) 1.53176 + 1.62902i 0.0988745 + 0.105153i
\(241\) 2.39676 2.39676i 0.154389 0.154389i −0.625686 0.780075i \(-0.715181\pi\)
0.780075 + 0.625686i \(0.215181\pi\)
\(242\) −6.70073 −0.430739
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 5.87589 + 5.87589i 0.376165 + 0.376165i
\(245\) −4.75038 0.146186i −0.303491 0.00933945i
\(246\) 2.68710 + 2.68710i 0.171323 + 0.171323i
\(247\) 6.38566 + 6.38566i 0.406310 + 0.406310i
\(248\) −0.391381 0.391381i −0.0248527 0.0248527i
\(249\) 0.539372 0.0341813
\(250\) 1.03038 11.1328i 0.0651671 0.704097i
\(251\) 14.2994 + 14.2994i 0.902571 + 0.902571i 0.995658 0.0930871i \(-0.0296735\pi\)
−0.0930871 + 0.995658i \(0.529674\pi\)
\(252\) −2.13605 2.13605i −0.134559 0.134559i
\(253\) 7.24548i 0.455519i
\(254\) 6.18161 6.18161i 0.387869 0.387869i
\(255\) 4.26896 4.01406i 0.267332 0.251370i
\(256\) 1.00000 0.0625000
\(257\) 22.9481i 1.43146i 0.698376 + 0.715731i \(0.253906\pi\)
−0.698376 + 0.715731i \(0.746094\pi\)
\(258\) −4.44492 + 4.44492i −0.276729 + 0.276729i
\(259\) −17.3652 6.00760i −1.07902 0.373294i
\(260\) 0.296742 9.64280i 0.0184032 0.598021i
\(261\) −0.364989 0.364989i −0.0225922 0.0225922i
\(262\) −1.03836 1.03836i −0.0641499 0.0641499i
\(263\) 0.797307 0.797307i 0.0491641 0.0491641i −0.682097 0.731261i \(-0.738932\pi\)
0.731261 + 0.682097i \(0.238932\pi\)
\(264\) −1.46616 1.46616i −0.0902361 0.0902361i
\(265\) −4.32766 + 4.06926i −0.265846 + 0.249973i
\(266\) −6.32301 −0.387689
\(267\) 5.21363i 0.319069i
\(268\) −3.05783 3.05783i −0.186787 0.186787i
\(269\) 17.8697i 1.08954i −0.838587 0.544768i \(-0.816618\pi\)
0.838587 0.544768i \(-0.183382\pi\)
\(270\) −1.62902 + 1.53176i −0.0991393 + 0.0932197i
\(271\) −20.7623 −1.26122 −0.630610 0.776100i \(-0.717195\pi\)
−0.630610 + 0.776100i \(0.717195\pi\)
\(272\) 2.62056i 0.158895i
\(273\) 13.0332i 0.788804i
\(274\) 13.3475 13.3475i 0.806350 0.806350i
\(275\) −0.637473 + 10.3477i −0.0384411 + 0.623991i
\(276\) 2.47090 2.47090i 0.148731 0.148731i
\(277\) 17.8467 1.07230 0.536152 0.844122i \(-0.319878\pi\)
0.536152 + 0.844122i \(0.319878\pi\)
\(278\) 12.1026 0.725869
\(279\) 0.391381 0.391381i 0.0234314 0.0234314i
\(280\) 4.62718 + 4.92101i 0.276527 + 0.294087i
\(281\) −10.2645 + 10.2645i −0.612330 + 0.612330i −0.943553 0.331223i \(-0.892539\pi\)
0.331223 + 0.943553i \(0.392539\pi\)
\(282\) 4.77861i 0.284562i
\(283\) 9.49377i 0.564346i −0.959364 0.282173i \(-0.908945\pi\)
0.959364 0.282173i \(-0.0910552\pi\)
\(284\) −9.16581 −0.543891
\(285\) −0.143963 + 4.67818i −0.00852766 + 0.277111i
\(286\) 8.94583i 0.528978i
\(287\) 8.11728 + 8.11728i 0.479148 + 0.479148i
\(288\) 1.00000i 0.0589256i
\(289\) 10.1327 0.596039
\(290\) 0.790650 + 0.840857i 0.0464286 + 0.0493768i
\(291\) 9.99958 + 9.99958i 0.586186 + 0.586186i
\(292\) 8.50139 8.50139i 0.497506 0.497506i
\(293\) −1.37161 1.37161i −0.0801303 0.0801303i 0.665906 0.746036i \(-0.268045\pi\)
−0.746036 + 0.665906i \(0.768045\pi\)
\(294\) −1.50291 1.50291i −0.0876517 0.0876517i
\(295\) −2.11340 + 1.98721i −0.123047 + 0.115700i
\(296\) 2.65855 + 5.47103i 0.154525 + 0.317997i
\(297\) 1.46616 1.46616i 0.0850754 0.0850754i
\(298\) 1.78006i 0.103116i
\(299\) −15.0763 −0.871882
\(300\) 3.74624 3.31145i 0.216289 0.191187i
\(301\) −13.4274 + 13.4274i −0.773941 + 0.773941i
\(302\) 14.7620i 0.849459i
\(303\) 5.40501 + 5.40501i 0.310510 + 0.310510i
\(304\) 1.48007 + 1.48007i 0.0848878 + 0.0848878i
\(305\) 13.5368 12.7285i 0.775115 0.728834i
\(306\) 2.62056 0.149807
\(307\) 12.9742 + 12.9742i 0.740476 + 0.740476i 0.972670 0.232194i \(-0.0745903\pi\)
−0.232194 + 0.972670i \(0.574590\pi\)
\(308\) −4.42903 4.42903i −0.252368 0.252368i
\(309\) 6.97126 + 6.97126i 0.396581 + 0.396581i
\(310\) −0.901660 + 0.847823i −0.0512109 + 0.0481531i
\(311\) 21.1073 + 21.1073i 1.19689 + 1.19689i 0.975094 + 0.221794i \(0.0711911\pi\)
0.221794 + 0.975094i \(0.428809\pi\)
\(312\) 3.05076 3.05076i 0.172715 0.172715i
\(313\) 27.9746 1.58122 0.790608 0.612323i \(-0.209765\pi\)
0.790608 + 0.612323i \(0.209765\pi\)
\(314\) −3.02964 + 3.02964i −0.170973 + 0.170973i
\(315\) −4.92101 + 4.62718i −0.277268 + 0.260712i
\(316\) 9.01137 + 9.01137i 0.506929 + 0.506929i
\(317\) 4.72175 + 4.72175i 0.265200 + 0.265200i 0.827163 0.561963i \(-0.189954\pi\)
−0.561963 + 0.827163i \(0.689954\pi\)
\(318\) −2.65660 −0.148975
\(319\) −0.756793 0.756793i −0.0423722 0.0423722i
\(320\) 0.0687789 2.23501i 0.00384486 0.124941i
\(321\) 5.89863i 0.329229i
\(322\) 7.46418 7.46418i 0.415962 0.415962i
\(323\) 3.87861 3.87861i 0.215812 0.215812i
\(324\) −1.00000 −0.0555556
\(325\) −21.5313 1.32644i −1.19434 0.0735778i
\(326\) 6.39530i 0.354203i
\(327\) 0.652011 0.0360563
\(328\) 3.80013i 0.209827i
\(329\) 14.4354i 0.795848i
\(330\) −3.37773 + 3.17605i −0.185938 + 0.174836i
\(331\) 5.59691 5.59691i 0.307634 0.307634i −0.536357 0.843991i \(-0.680200\pi\)
0.843991 + 0.536357i \(0.180200\pi\)
\(332\) −0.381394 0.381394i −0.0209317 0.0209317i
\(333\) −5.47103 + 2.65855i −0.299810 + 0.145687i
\(334\) 7.40255i 0.405049i
\(335\) −7.04459 + 6.62397i −0.384887 + 0.361906i
\(336\) 3.02083i 0.164800i
\(337\) −15.5752 15.5752i −0.848433 0.848433i 0.141505 0.989938i \(-0.454806\pi\)
−0.989938 + 0.141505i \(0.954806\pi\)
\(338\) −5.61431 −0.305378
\(339\) 12.2473 + 12.2473i 0.665182 + 0.665182i
\(340\) −5.85698 0.180239i −0.317639 0.00977485i
\(341\) 0.811517 0.811517i 0.0439461 0.0439461i
\(342\) −1.48007 + 1.48007i −0.0800330 + 0.0800330i
\(343\) 10.4123 + 10.4123i 0.562212 + 0.562212i
\(344\) 6.28607 0.338922
\(345\) −5.35254 5.69243i −0.288171 0.306470i
\(346\) −16.3983 + 16.3983i −0.881577 + 0.881577i
\(347\) 7.34661 0.394386 0.197193 0.980365i \(-0.436817\pi\)
0.197193 + 0.980365i \(0.436817\pi\)
\(348\) 0.516172i 0.0276697i
\(349\) 5.62756i 0.301236i 0.988592 + 0.150618i \(0.0481264\pi\)
−0.988592 + 0.150618i \(0.951874\pi\)
\(350\) 11.3168 10.0033i 0.604907 0.534701i
\(351\) 3.05076 + 3.05076i 0.162838 + 0.162838i
\(352\) 2.07347i 0.110516i
\(353\) 25.6724i 1.36640i 0.730231 + 0.683201i \(0.239413\pi\)
−0.730231 + 0.683201i \(0.760587\pi\)
\(354\) −1.29734 −0.0689527
\(355\) −0.630414 + 20.4857i −0.0334589 + 1.08727i
\(356\) 3.68659 3.68659i 0.195389 0.195389i
\(357\) 7.91628 0.418974
\(358\) −16.2448 + 16.2448i −0.858564 + 0.858564i
\(359\) 29.6458i 1.56465i 0.622872 + 0.782324i \(0.285966\pi\)
−0.622872 + 0.782324i \(0.714034\pi\)
\(360\) 2.23501 + 0.0687789i 0.117795 + 0.00362497i
\(361\) 14.6188i 0.769410i
\(362\) 5.45708 0.286818
\(363\) −4.73813 + 4.73813i −0.248688 + 0.248688i
\(364\) 9.21585 9.21585i 0.483042 0.483042i
\(365\) −18.4160 19.5854i −0.963936 1.02515i
\(366\) 8.30976 0.434358
\(367\) −22.3758 + 22.3758i −1.16801 + 1.16801i −0.185329 + 0.982677i \(0.559335\pi\)
−0.982677 + 0.185329i \(0.940665\pi\)
\(368\) −3.49438 −0.182157
\(369\) 3.80013 0.197827
\(370\) 12.4107 5.56559i 0.645199 0.289341i
\(371\) −8.02514 −0.416644
\(372\) −0.553497 −0.0286975
\(373\) 2.58745 2.58745i 0.133973 0.133973i −0.636940 0.770913i \(-0.719800\pi\)
0.770913 + 0.636940i \(0.219800\pi\)
\(374\) 5.43364 0.280967
\(375\) −7.14346 8.60064i −0.368887 0.444135i
\(376\) −3.37898 + 3.37898i −0.174258 + 0.174258i
\(377\) 1.57472 1.57472i 0.0811022 0.0811022i
\(378\) −3.02083 −0.155375
\(379\) 30.1390i 1.54814i −0.633102 0.774069i \(-0.718219\pi\)
0.633102 0.774069i \(-0.281781\pi\)
\(380\) 3.40977 3.20617i 0.174917 0.164473i
\(381\) 8.74212i 0.447872i
\(382\) 8.47691 8.47691i 0.433716 0.433716i
\(383\) −27.3379 −1.39690 −0.698451 0.715658i \(-0.746127\pi\)
−0.698451 + 0.715658i \(0.746127\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) −10.2036 + 9.59431i −0.520022 + 0.488971i
\(386\) 0.815237 0.0414945
\(387\) 6.28607i 0.319539i
\(388\) 14.1415i 0.717928i
\(389\) −7.29908 7.29908i −0.370078 0.370078i 0.497428 0.867506i \(-0.334278\pi\)
−0.867506 + 0.497428i \(0.834278\pi\)
\(390\) −6.60866 7.02831i −0.334642 0.355893i
\(391\) 9.15723i 0.463101i
\(392\) 2.12544i 0.107351i
\(393\) −1.46846 −0.0740739
\(394\) 12.1517 12.1517i 0.612194 0.612194i
\(395\) 20.7603 19.5207i 1.04456 0.982193i
\(396\) −2.07347 −0.104196
\(397\) −23.8828 23.8828i −1.19864 1.19864i −0.974573 0.224069i \(-0.928066\pi\)
−0.224069 0.974573i \(-0.571934\pi\)
\(398\) 6.43148 6.43148i 0.322381 0.322381i
\(399\) −4.47104 + 4.47104i −0.223832 + 0.223832i
\(400\) −4.99054 0.307443i −0.249527 0.0153722i
\(401\) 9.30160 + 9.30160i 0.464500 + 0.464500i 0.900127 0.435627i \(-0.143473\pi\)
−0.435627 + 0.900127i \(0.643473\pi\)
\(402\) −4.32442 −0.215683
\(403\) 1.68859 + 1.68859i 0.0841146 + 0.0841146i
\(404\) 7.64384i 0.380295i
\(405\) −0.0687789 + 2.23501i −0.00341765 + 0.111059i
\(406\) 1.55927i 0.0773853i
\(407\) −11.3440 + 5.51241i −0.562301 + 0.273240i
\(408\) −1.85302 1.85302i −0.0917379 0.0917379i
\(409\) 24.5847 24.5847i 1.21563 1.21563i 0.246487 0.969146i \(-0.420724\pi\)
0.969146 0.246487i \(-0.0792763\pi\)
\(410\) −8.49333 0.261369i −0.419456 0.0129081i
\(411\) 18.8762i 0.931093i
\(412\) 9.85885i 0.485711i
\(413\) −3.91904 −0.192844
\(414\) 3.49438i 0.171739i
\(415\) −0.878651 + 0.826187i −0.0431313 + 0.0405559i
\(416\) −4.31443 −0.211532
\(417\) 8.55786 8.55786i 0.419080 0.419080i
\(418\) −3.06887 + 3.06887i −0.150104 + 0.150104i
\(419\) 23.6748i 1.15659i 0.815829 + 0.578294i \(0.196281\pi\)
−0.815829 + 0.578294i \(0.803719\pi\)
\(420\) 6.75159 + 0.207770i 0.329444 + 0.0101381i
\(421\) −26.6921 26.6921i −1.30089 1.30089i −0.927790 0.373102i \(-0.878294\pi\)
−0.373102 0.927790i \(-0.621706\pi\)
\(422\) 1.84896 0.0900058
\(423\) −3.37898 3.37898i −0.164292 0.164292i
\(424\) 1.87850 + 1.87850i 0.0912279 + 0.0912279i
\(425\) −0.805673 + 13.0780i −0.0390809 + 0.634376i
\(426\) −6.48120 + 6.48120i −0.314015 + 0.314015i
\(427\) 25.1024 1.21479
\(428\) 4.17096 4.17096i 0.201611 0.201611i
\(429\) 6.32566 + 6.32566i 0.305406 + 0.305406i
\(430\) 0.432349 14.0494i 0.0208497 0.677524i
\(431\) 25.8053 + 25.8053i 1.24300 + 1.24300i 0.958752 + 0.284245i \(0.0917428\pi\)
0.284245 + 0.958752i \(0.408257\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −2.62555 2.62555i −0.126176 0.126176i 0.641199 0.767375i \(-0.278437\pi\)
−0.767375 + 0.641199i \(0.778437\pi\)
\(434\) −1.67202 −0.0802597
\(435\) 1.15365 + 0.0355018i 0.0553133 + 0.00170218i
\(436\) −0.461041 0.461041i −0.0220799 0.0220799i
\(437\) −5.17192 5.17192i −0.247407 0.247407i
\(438\) 12.0228i 0.574471i
\(439\) −4.04448 + 4.04448i −0.193033 + 0.193033i −0.797005 0.603973i \(-0.793584\pi\)
0.603973 + 0.797005i \(0.293584\pi\)
\(440\) 4.63422 + 0.142611i 0.220928 + 0.00679871i
\(441\) −2.12544 −0.101211
\(442\) 11.3062i 0.537782i
\(443\) −0.534873 + 0.534873i −0.0254126 + 0.0254126i −0.719699 0.694286i \(-0.755720\pi\)
0.694286 + 0.719699i \(0.255720\pi\)
\(444\) 5.74848 + 1.98872i 0.272811 + 0.0943806i
\(445\) −7.98601 8.49313i −0.378573 0.402613i
\(446\) −4.85478 4.85478i −0.229881 0.229881i
\(447\) 1.25869 + 1.25869i 0.0595341 + 0.0595341i
\(448\) 2.13605 2.13605i 0.100919 0.100919i
\(449\) 15.2168 + 15.2168i 0.718124 + 0.718124i 0.968221 0.250097i \(-0.0804625\pi\)
−0.250097 + 0.968221i \(0.580462\pi\)
\(450\) 0.307443 4.99054i 0.0144930 0.235256i
\(451\) 7.87944 0.371029
\(452\) 17.3203i 0.814678i
\(453\) −10.4383 10.4383i −0.490435 0.490435i
\(454\) 19.5601i 0.917999i
\(455\) −19.9637 21.2314i −0.935911 0.995342i
\(456\) 2.09313 0.0980200
\(457\) 26.8366i 1.25536i 0.778470 + 0.627682i \(0.215996\pi\)
−0.778470 + 0.627682i \(0.784004\pi\)
\(458\) 5.52626i 0.258225i
\(459\) 1.85302 1.85302i 0.0864914 0.0864914i
\(460\) −0.240340 + 7.80997i −0.0112059 + 0.364142i
\(461\) 9.31792 9.31792i 0.433979 0.433979i −0.456001 0.889980i \(-0.650718\pi\)
0.889980 + 0.456001i \(0.150718\pi\)
\(462\) −6.26360 −0.291409
\(463\) 31.8446 1.47995 0.739973 0.672637i \(-0.234838\pi\)
0.739973 + 0.672637i \(0.234838\pi\)
\(464\) 0.364989 0.364989i 0.0169442 0.0169442i
\(465\) −0.0380689 + 1.23707i −0.00176540 + 0.0573678i
\(466\) −8.07622 + 8.07622i −0.374124 + 0.374124i
\(467\) 24.6295i 1.13972i −0.821743 0.569859i \(-0.806998\pi\)
0.821743 0.569859i \(-0.193002\pi\)
\(468\) 4.31443i 0.199435i
\(469\) −13.0634 −0.603210
\(470\) 7.31966 + 7.78447i 0.337631 + 0.359071i
\(471\) 4.28456i 0.197422i
\(472\) 0.917356 + 0.917356i 0.0422248 + 0.0422248i
\(473\) 13.0340i 0.599302i
\(474\) 12.7440 0.585351
\(475\) −6.93131 7.84138i −0.318030 0.359787i
\(476\) −5.59765 5.59765i −0.256568 0.256568i
\(477\) −1.87850 + 1.87850i −0.0860105 + 0.0860105i
\(478\) 1.04218 + 1.04218i 0.0476681 + 0.0476681i
\(479\) 3.98964 + 3.98964i 0.182291 + 0.182291i 0.792353 0.610062i \(-0.208856\pi\)
−0.610062 + 0.792353i \(0.708856\pi\)
\(480\) −1.53176 1.62902i −0.0699148 0.0743545i
\(481\) −11.4701 23.6044i −0.522992 1.07627i
\(482\) −2.39676 + 2.39676i −0.109169 + 0.109169i
\(483\) 10.5559i 0.480312i
\(484\) 6.70073 0.304579
\(485\) −31.6065 0.972640i −1.43518 0.0441653i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 33.5571i 1.52062i −0.649561 0.760309i \(-0.725047\pi\)
0.649561 0.760309i \(-0.274953\pi\)
\(488\) −5.87589 5.87589i −0.265989 0.265989i
\(489\) −4.52216 4.52216i −0.204499 0.204499i
\(490\) 4.75038 + 0.146186i 0.214600 + 0.00660399i
\(491\) 31.9342 1.44117 0.720585 0.693366i \(-0.243873\pi\)
0.720585 + 0.693366i \(0.243873\pi\)
\(492\) −2.68710 2.68710i −0.121144 0.121144i
\(493\) −0.956475 0.956475i −0.0430775 0.0430775i
\(494\) −6.38566 6.38566i −0.287304 0.287304i
\(495\) −0.142611 + 4.63422i −0.00640988 + 0.208293i
\(496\) 0.391381 + 0.391381i 0.0175735 + 0.0175735i
\(497\) −19.5786 + 19.5786i −0.878222 + 0.878222i
\(498\) −0.539372 −0.0241698
\(499\) 25.1910 25.1910i 1.12770 1.12770i 0.137154 0.990550i \(-0.456204\pi\)
0.990550 0.137154i \(-0.0437956\pi\)
\(500\) −1.03038 + 11.1328i −0.0460801 + 0.497872i
\(501\) −5.23439 5.23439i −0.233855 0.233855i
\(502\) −14.2994 14.2994i −0.638214 0.638214i
\(503\) 6.19986 0.276438 0.138219 0.990402i \(-0.455862\pi\)
0.138219 + 0.990402i \(0.455862\pi\)
\(504\) 2.13605 + 2.13605i 0.0951473 + 0.0951473i
\(505\) −17.0841 0.525735i −0.760231 0.0233949i
\(506\) 7.24548i 0.322101i
\(507\) −3.96992 + 3.96992i −0.176310 + 0.176310i
\(508\) −6.18161 + 6.18161i −0.274265 + 0.274265i
\(509\) 2.76652 0.122624 0.0613120 0.998119i \(-0.480472\pi\)
0.0613120 + 0.998119i \(0.480472\pi\)
\(510\) −4.26896 + 4.01406i −0.189033 + 0.177746i
\(511\) 36.3188i 1.60665i
\(512\) −1.00000 −0.0441942
\(513\) 2.09313i 0.0924141i
\(514\) 22.9481i 1.01220i
\(515\) −22.0346 0.678081i −0.970962 0.0298798i
\(516\) 4.44492 4.44492i 0.195677 0.195677i
\(517\) −7.00621 7.00621i −0.308133 0.308133i
\(518\) 17.3652 + 6.00760i 0.762983 + 0.263959i
\(519\) 23.1907i 1.01796i
\(520\) −0.296742 + 9.64280i −0.0130130 + 0.422865i
\(521\) 9.79854i 0.429282i −0.976693 0.214641i \(-0.931142\pi\)
0.976693 0.214641i \(-0.0688581\pi\)
\(522\) 0.364989 + 0.364989i 0.0159751 + 0.0159751i
\(523\) −10.5951 −0.463289 −0.231645 0.972800i \(-0.574411\pi\)
−0.231645 + 0.972800i \(0.574411\pi\)
\(524\) 1.03836 + 1.03836i 0.0453608 + 0.0453608i
\(525\) 0.928735 15.0756i 0.0405333 0.657953i
\(526\) −0.797307 + 0.797307i −0.0347642 + 0.0347642i
\(527\) 1.02564 1.02564i 0.0446775 0.0446775i
\(528\) 1.46616 + 1.46616i 0.0638065 + 0.0638065i
\(529\) −10.7893 −0.469101
\(530\) 4.32766 4.06926i 0.187982 0.176757i
\(531\) −0.917356 + 0.917356i −0.0398099 + 0.0398099i
\(532\) 6.32301 0.274137
\(533\) 16.3954i 0.710163i
\(534\) 5.21363i 0.225616i
\(535\) −9.03526 9.60901i −0.390629 0.415434i
\(536\) 3.05783 + 3.05783i 0.132078 + 0.132078i
\(537\) 22.9736i 0.991385i
\(538\) 17.8697i 0.770418i
\(539\) −4.40703 −0.189824
\(540\) 1.62902 1.53176i 0.0701021 0.0659163i
\(541\) 23.3766 23.3766i 1.00504 1.00504i 0.00505037 0.999987i \(-0.498392\pi\)
0.999987 0.00505037i \(-0.00160759\pi\)
\(542\) 20.7623 0.891818
\(543\) 3.85874 3.85874i 0.165594 0.165594i
\(544\) 2.62056i 0.112356i
\(545\) −1.06214 + 0.998722i −0.0454971 + 0.0427805i
\(546\) 13.0332i 0.557769i
\(547\) −17.2554 −0.737787 −0.368894 0.929472i \(-0.620263\pi\)
−0.368894 + 0.929472i \(0.620263\pi\)
\(548\) −13.3475 + 13.3475i −0.570176 + 0.570176i
\(549\) 5.87589 5.87589i 0.250777 0.250777i
\(550\) 0.637473 10.3477i 0.0271820 0.441228i
\(551\) 1.08042 0.0460273
\(552\) −2.47090 + 2.47090i −0.105168 + 0.105168i
\(553\) 38.4975 1.63708
\(554\) −17.8467 −0.758233
\(555\) 4.84019 12.7111i 0.205455 0.539557i
\(556\) −12.1026 −0.513267
\(557\) 17.6010 0.745779 0.372889 0.927876i \(-0.378367\pi\)
0.372889 + 0.927876i \(0.378367\pi\)
\(558\) −0.391381 + 0.391381i −0.0165685 + 0.0165685i
\(559\) −27.1208 −1.14709
\(560\) −4.62718 4.92101i −0.195534 0.207951i
\(561\) 3.84217 3.84217i 0.162216 0.162216i
\(562\) 10.2645 10.2645i 0.432983 0.432983i
\(563\) 24.3413 1.02586 0.512932 0.858429i \(-0.328559\pi\)
0.512932 + 0.858429i \(0.328559\pi\)
\(564\) 4.77861i 0.201216i
\(565\) −38.7110 1.19127i −1.62859 0.0501172i
\(566\) 9.49377i 0.399053i
\(567\) −2.13605 + 2.13605i −0.0897058 + 0.0897058i
\(568\) 9.16581 0.384589
\(569\) 3.96188 3.96188i 0.166090 0.166090i −0.619168 0.785259i \(-0.712530\pi\)
0.785259 + 0.619168i \(0.212530\pi\)
\(570\) 0.143963 4.67818i 0.00602997 0.195947i
\(571\) −12.7277 −0.532638 −0.266319 0.963885i \(-0.585807\pi\)
−0.266319 + 0.963885i \(0.585807\pi\)
\(572\) 8.94583i 0.374044i
\(573\) 11.9882i 0.500812i
\(574\) −8.11728 8.11728i −0.338809 0.338809i
\(575\) 17.4388 + 1.07432i 0.727250 + 0.0448024i
\(576\) 1.00000i 0.0416667i
\(577\) 30.3340i 1.26282i 0.775449 + 0.631410i \(0.217524\pi\)
−0.775449 + 0.631410i \(0.782476\pi\)
\(578\) −10.1327 −0.421463
\(579\) 0.576459 0.576459i 0.0239568 0.0239568i
\(580\) −0.790650 0.840857i −0.0328300 0.0349147i
\(581\) −1.62935 −0.0675970
\(582\) −9.99958 9.99958i −0.414496 0.414496i
\(583\) −3.89500 + 3.89500i −0.161315 + 0.161315i
\(584\) −8.50139 + 8.50139i −0.351790 + 0.351790i
\(585\) −9.64280 0.296742i −0.398681 0.0122688i
\(586\) 1.37161 + 1.37161i 0.0566606 + 0.0566606i
\(587\) −25.0340 −1.03327 −0.516633 0.856207i \(-0.672815\pi\)
−0.516633 + 0.856207i \(0.672815\pi\)
\(588\) 1.50291 + 1.50291i 0.0619791 + 0.0619791i
\(589\) 1.15854i 0.0477369i
\(590\) 2.11340 1.98721i 0.0870071 0.0818120i
\(591\) 17.1851i 0.706900i
\(592\) −2.65855 5.47103i −0.109266 0.224858i
\(593\) 16.2930 + 16.2930i 0.669073 + 0.669073i 0.957502 0.288428i \(-0.0931327\pi\)
−0.288428 + 0.957502i \(0.593133\pi\)
\(594\) −1.46616 + 1.46616i −0.0601574 + 0.0601574i
\(595\) −12.8958 + 12.1258i −0.528677 + 0.497110i
\(596\) 1.78006i 0.0729141i
\(597\) 9.09548i 0.372253i
\(598\) 15.0763 0.616514
\(599\) 18.7185i 0.764818i −0.923993 0.382409i \(-0.875095\pi\)
0.923993 0.382409i \(-0.124905\pi\)
\(600\) −3.74624 + 3.31145i −0.152940 + 0.135189i
\(601\) −34.1418 −1.39267 −0.696337 0.717715i \(-0.745188\pi\)
−0.696337 + 0.717715i \(0.745188\pi\)
\(602\) 13.4274 13.4274i 0.547259 0.547259i
\(603\) −3.05783 + 3.05783i −0.124524 + 0.124524i
\(604\) 14.7620i 0.600658i
\(605\) 0.460869 14.9762i 0.0187370 0.608869i
\(606\) −5.40501 5.40501i −0.219564 0.219564i
\(607\) 15.4550 0.627298 0.313649 0.949539i \(-0.398449\pi\)
0.313649 + 0.949539i \(0.398449\pi\)
\(608\) −1.48007 1.48007i −0.0600247 0.0600247i
\(609\) 1.10257 + 1.10257i 0.0446784 + 0.0446784i
\(610\) −13.5368 + 12.7285i −0.548089 + 0.515363i
\(611\) 14.5784 14.5784i 0.589779 0.589779i
\(612\) −2.62056 −0.105930
\(613\) −25.2055 + 25.2055i −1.01804 + 1.01804i −0.0182063 + 0.999834i \(0.505796\pi\)
−0.999834 + 0.0182063i \(0.994204\pi\)
\(614\) −12.9742 12.9742i −0.523596 0.523596i
\(615\) −6.19050 + 5.82087i −0.249625 + 0.234720i
\(616\) 4.42903 + 4.42903i 0.178451 + 0.178451i
\(617\) 14.0812 + 14.0812i 0.566887 + 0.566887i 0.931255 0.364368i \(-0.118715\pi\)
−0.364368 + 0.931255i \(0.618715\pi\)
\(618\) −6.97126 6.97126i −0.280425 0.280425i
\(619\) −11.5159 −0.462861 −0.231431 0.972851i \(-0.574341\pi\)
−0.231431 + 0.972851i \(0.574341\pi\)
\(620\) 0.901660 0.847823i 0.0362115 0.0340494i
\(621\) −2.47090 2.47090i −0.0991538 0.0991538i
\(622\) −21.1073 21.1073i −0.846327 0.846327i
\(623\) 15.7495i 0.630991i
\(624\) −3.05076 + 3.05076i −0.122128 + 0.122128i
\(625\) 24.8110 + 3.06861i 0.992438 + 0.122745i
\(626\) −27.9746 −1.11809
\(627\) 4.34004i 0.173325i
\(628\) 3.02964 3.02964i 0.120896 0.120896i
\(629\) −14.3372 + 6.96688i −0.571660 + 0.277788i
\(630\) 4.92101 4.62718i 0.196058 0.184351i
\(631\) 24.9435 + 24.9435i 0.992985 + 0.992985i 0.999976 0.00699059i \(-0.00222519\pi\)
−0.00699059 + 0.999976i \(0.502225\pi\)
\(632\) −9.01137 9.01137i −0.358453 0.358453i
\(633\) 1.30741 1.30741i 0.0519649 0.0519649i
\(634\) −4.72175 4.72175i −0.187525 0.187525i
\(635\) 13.3908 + 14.2411i 0.531398 + 0.565142i
\(636\) 2.65660 0.105341
\(637\) 9.17007i 0.363331i
\(638\) 0.756793 + 0.756793i 0.0299617 + 0.0299617i
\(639\) 9.16581i 0.362594i
\(640\) −0.0687789 + 2.23501i −0.00271873 + 0.0883465i
\(641\) 41.0494 1.62136 0.810678 0.585492i \(-0.199099\pi\)
0.810678 + 0.585492i \(0.199099\pi\)
\(642\) 5.89863i 0.232800i
\(643\) 16.4624i 0.649212i 0.945849 + 0.324606i \(0.105232\pi\)
−0.945849 + 0.324606i \(0.894768\pi\)
\(644\) −7.46418 + 7.46418i −0.294130 + 0.294130i
\(645\) −9.62873 10.2402i −0.379131 0.403206i
\(646\) −3.87861 + 3.87861i −0.152602 + 0.152602i
\(647\) 40.3405 1.58595 0.792974 0.609256i \(-0.208532\pi\)
0.792974 + 0.609256i \(0.208532\pi\)
\(648\) 1.00000 0.0392837
\(649\) −1.90211 + 1.90211i −0.0746643 + 0.0746643i
\(650\) 21.5313 + 1.32644i 0.844528 + 0.0520273i
\(651\) −1.18230 + 1.18230i −0.0463379 + 0.0463379i
\(652\) 6.39530i 0.250459i
\(653\) 34.2938i 1.34202i −0.741449 0.671009i \(-0.765861\pi\)
0.741449 0.671009i \(-0.234139\pi\)
\(654\) −0.652011 −0.0254956
\(655\) 2.39216 2.24932i 0.0934692 0.0878883i
\(656\) 3.80013i 0.148370i
\(657\) −8.50139 8.50139i −0.331671 0.331671i
\(658\) 14.4354i 0.562750i
\(659\) 35.9415 1.40008 0.700040 0.714104i \(-0.253165\pi\)
0.700040 + 0.714104i \(0.253165\pi\)
\(660\) 3.37773 3.17605i 0.131478 0.123627i
\(661\) 15.5165 + 15.5165i 0.603520 + 0.603520i 0.941245 0.337725i \(-0.109657\pi\)
−0.337725 + 0.941245i \(0.609657\pi\)
\(662\) −5.59691 + 5.59691i −0.217530 + 0.217530i
\(663\) 7.99471 + 7.99471i 0.310489 + 0.310489i
\(664\) 0.381394 + 0.381394i 0.0148009 + 0.0148009i
\(665\) 0.434890 14.1320i 0.0168643 0.548015i
\(666\) 5.47103 2.65855i 0.211998 0.103017i
\(667\) −1.27541 + 1.27541i −0.0493841 + 0.0493841i
\(668\) 7.40255i 0.286413i
\(669\) −6.86570 −0.265443
\(670\) 7.04459 6.62397i 0.272156 0.255906i
\(671\) 12.1835 12.1835i 0.470337 0.470337i
\(672\) 3.02083i 0.116531i
\(673\) 32.7754 + 32.7754i 1.26340 + 1.26340i 0.949434 + 0.313966i \(0.101658\pi\)
0.313966 + 0.949434i \(0.398342\pi\)
\(674\) 15.5752 + 15.5752i 0.599933 + 0.599933i
\(675\) −3.31145 3.74624i −0.127458 0.144193i
\(676\) 5.61431 0.215935
\(677\) −5.04971 5.04971i −0.194076 0.194076i 0.603379 0.797455i \(-0.293821\pi\)
−0.797455 + 0.603379i \(0.793821\pi\)
\(678\) −12.2473 12.2473i −0.470355 0.470355i
\(679\) −30.2071 30.2071i −1.15924 1.15924i
\(680\) 5.85698 + 0.180239i 0.224605 + 0.00691186i
\(681\) −13.8310 13.8310i −0.530007 0.530007i
\(682\) −0.811517 + 0.811517i −0.0310746 + 0.0310746i
\(683\) 35.9730 1.37647 0.688235 0.725488i \(-0.258386\pi\)
0.688235 + 0.725488i \(0.258386\pi\)
\(684\) 1.48007 1.48007i 0.0565919 0.0565919i
\(685\) 28.9137 + 30.7498i 1.10474 + 1.17489i
\(686\) −10.4123 10.4123i −0.397544 0.397544i
\(687\) 3.90766 + 3.90766i 0.149086 + 0.149086i
\(688\) −6.28607 −0.239654
\(689\) −8.10465 8.10465i −0.308762 0.308762i
\(690\) 5.35254 + 5.69243i 0.203768 + 0.216707i
\(691\) 18.4832i 0.703135i 0.936163 + 0.351567i \(0.114351\pi\)
−0.936163 + 0.351567i \(0.885649\pi\)
\(692\) 16.3983 16.3983i 0.623369 0.623369i
\(693\) −4.42903 + 4.42903i −0.168245 + 0.168245i
\(694\) −7.34661 −0.278873
\(695\) −0.832407 + 27.0495i −0.0315750 + 1.02605i
\(696\) 0.516172i 0.0195655i
\(697\) 9.95847 0.377204
\(698\) 5.62756i 0.213006i
\(699\) 11.4215i 0.432001i
\(700\) −11.3168 + 10.0033i −0.427734 + 0.378091i
\(701\) −14.1983 + 14.1983i −0.536264 + 0.536264i −0.922429 0.386166i \(-0.873799\pi\)
0.386166 + 0.922429i \(0.373799\pi\)
\(702\) −3.05076 3.05076i −0.115144 0.115144i
\(703\) 4.16266 12.0323i 0.156998 0.453808i
\(704\) 2.07347i 0.0781467i
\(705\) 10.6802 + 0.328667i 0.402241 + 0.0123783i
\(706\) 25.6724i 0.966192i
\(707\) −16.3276 16.3276i −0.614064 0.614064i
\(708\) 1.29734 0.0487569
\(709\) 19.8820 + 19.8820i 0.746684 + 0.746684i 0.973855 0.227171i \(-0.0729475\pi\)
−0.227171 + 0.973855i \(0.572947\pi\)
\(710\) 0.630414 20.4857i 0.0236590 0.768814i
\(711\) 9.01137 9.01137i 0.337953 0.337953i
\(712\) −3.68659 + 3.68659i −0.138161 + 0.138161i
\(713\) −1.36764 1.36764i −0.0512183 0.0512183i
\(714\) −7.91628 −0.296259
\(715\) −19.9940 0.615285i −0.747734 0.0230103i
\(716\) 16.2448 16.2448i 0.607097 0.607097i
\(717\) 1.47386 0.0550424
\(718\) 29.6458i 1.10637i
\(719\) 5.03356i 0.187720i 0.995585 + 0.0938601i \(0.0299206\pi\)
−0.995585 + 0.0938601i \(0.970079\pi\)
\(720\) −2.23501 0.0687789i −0.0832939 0.00256324i
\(721\) −21.0590 21.0590i −0.784279 0.784279i
\(722\) 14.6188i 0.544055i
\(723\) 3.38953i 0.126058i
\(724\) −5.45708 −0.202811
\(725\) −1.93370 + 1.70928i −0.0718160 + 0.0634810i
\(726\) 4.73813 4.73813i 0.175849 0.175849i
\(727\) −6.59381 −0.244551 −0.122275 0.992496i \(-0.539019\pi\)
−0.122275 + 0.992496i \(0.539019\pi\)
\(728\) −9.21585 + 9.21585i −0.341562 + 0.341562i
\(729\) 1.00000i 0.0370370i
\(730\) 18.4160 + 19.5854i 0.681606 + 0.724888i
\(731\) 16.4730i 0.609277i
\(732\) −8.30976 −0.307138
\(733\) 32.6674 32.6674i 1.20660 1.20660i 0.234474 0.972122i \(-0.424663\pi\)
0.972122 0.234474i \(-0.0753369\pi\)
\(734\) 22.3758 22.3758i 0.825904 0.825904i
\(735\) 3.46240 3.25566i 0.127712 0.120087i
\(736\) 3.49438 0.128805
\(737\) −6.34031 + 6.34031i −0.233548 + 0.233548i
\(738\) −3.80013 −0.139885
\(739\) −2.57619 −0.0947665 −0.0473833 0.998877i \(-0.515088\pi\)
−0.0473833 + 0.998877i \(0.515088\pi\)
\(740\) −12.4107 + 5.56559i −0.456225 + 0.204595i
\(741\) −9.03068 −0.331750
\(742\) 8.02514 0.294612
\(743\) −16.2323 + 16.2323i −0.595504 + 0.595504i −0.939113 0.343609i \(-0.888351\pi\)
0.343609 + 0.939113i \(0.388351\pi\)
\(744\) 0.553497 0.0202922
\(745\) −3.97845 0.122431i −0.145759 0.00448551i
\(746\) −2.58745 + 2.58745i −0.0947334 + 0.0947334i
\(747\) −0.381394 + 0.381394i −0.0139545 + 0.0139545i
\(748\) −5.43364 −0.198674
\(749\) 17.8188i 0.651084i
\(750\) 7.14346 + 8.60064i 0.260842 + 0.314051i
\(751\) 9.18070i 0.335009i 0.985871 + 0.167504i \(0.0535708\pi\)
−0.985871 + 0.167504i \(0.946429\pi\)
\(752\) 3.37898 3.37898i 0.123219 0.123219i
\(753\) −20.2224 −0.736946
\(754\) −1.57472 + 1.57472i −0.0573479 + 0.0573479i
\(755\) 32.9933 + 1.01532i 1.20075 + 0.0369511i
\(756\) 3.02083 0.109867
\(757\) 7.11882i 0.258738i −0.991597 0.129369i \(-0.958705\pi\)
0.991597 0.129369i \(-0.0412951\pi\)
\(758\) 30.1390i 1.09470i
\(759\) −5.12333 5.12333i −0.185965 0.185965i
\(760\) −3.40977 + 3.20617i −0.123685 + 0.116300i
\(761\) 7.70500i 0.279306i −0.990200 0.139653i \(-0.955401\pi\)
0.990200 0.139653i \(-0.0445987\pi\)
\(762\) 8.74212i 0.316694i
\(763\) −1.96962 −0.0713049
\(764\) −8.47691 + 8.47691i −0.306684 + 0.306684i
\(765\) −0.180239 + 5.85698i −0.00651656 + 0.211759i
\(766\) 27.3379 0.987759
\(767\) −3.95787 3.95787i −0.142910 0.142910i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) −30.6954 + 30.6954i −1.10690 + 1.10690i −0.113349 + 0.993555i \(0.536158\pi\)
−0.993555 + 0.113349i \(0.963842\pi\)
\(770\) 10.2036 9.59431i 0.367711 0.345755i
\(771\) −16.2267 16.2267i −0.584392 0.584392i
\(772\) −0.815237 −0.0293410
\(773\) −26.9674 26.9674i −0.969949 0.969949i 0.0296121 0.999561i \(-0.490573\pi\)
−0.999561 + 0.0296121i \(0.990573\pi\)
\(774\) 6.28607i 0.225948i
\(775\) −1.83288 2.07353i −0.0658389 0.0744835i
\(776\) 14.1415i 0.507652i
\(777\) 16.5271 8.03103i 0.592905 0.288112i
\(778\) 7.29908 + 7.29908i 0.261685 + 0.261685i
\(779\) −5.62445 + 5.62445i −0.201517 + 0.201517i