Properties

Label 43.2.c.b.6.2
Level 43
Weight 2
Character 43.6
Analytic conductor 0.343
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.343356728692\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.2
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 43.6
Dual form 43.2.c.b.36.2

$q$-expansion

\(f(q)\) \(=\) \(q-0.381966 q^{2} +(1.30902 - 2.26728i) q^{3} -1.85410 q^{4} +(-0.618034 + 1.07047i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.11803 + 3.66854i) q^{7} +1.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\) \(q-0.381966 q^{2} +(1.30902 - 2.26728i) q^{3} -1.85410 q^{4} +(-0.618034 + 1.07047i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.11803 + 3.66854i) q^{7} +1.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(0.236068 - 0.408882i) q^{10} -3.61803 q^{11} +(-2.42705 + 4.20378i) q^{12} +(-0.690983 - 1.19682i) q^{13} +(-0.809017 - 1.40126i) q^{14} +(1.61803 + 2.80252i) q^{15} +3.14590 q^{16} +(-3.04508 - 5.27424i) q^{17} +(0.736068 + 1.27491i) q^{18} +(0.618034 - 1.07047i) q^{19} +(1.14590 - 1.98475i) q^{20} +11.0902 q^{21} +1.38197 q^{22} +(-2.19098 + 3.79489i) q^{23} +(1.92705 - 3.33775i) q^{24} +(1.73607 + 3.00696i) q^{25} +(0.263932 + 0.457144i) q^{26} -2.23607 q^{27} +(-3.92705 - 6.80185i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-0.618034 - 1.07047i) q^{30} -4.14590 q^{32} +(-4.73607 + 8.20311i) q^{33} +(1.16312 + 2.01458i) q^{34} -5.23607 q^{35} +(3.57295 + 6.18853i) q^{36} +(2.42705 - 4.20378i) q^{37} +(-0.236068 + 0.408882i) q^{38} -3.61803 q^{39} +(-0.909830 + 1.57587i) q^{40} +9.47214 q^{41} -4.23607 q^{42} +(-6.50000 + 0.866025i) q^{43} +6.70820 q^{44} +4.76393 q^{45} +(0.836881 - 1.44952i) q^{46} +1.14590 q^{47} +(4.11803 - 7.13264i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-0.663119 - 1.14856i) q^{50} -15.9443 q^{51} +(1.28115 + 2.21902i) q^{52} +(0.690983 - 1.19682i) q^{53} +0.854102 q^{54} +(2.23607 - 3.87298i) q^{55} +(3.11803 + 5.40059i) q^{56} +(-1.61803 - 2.80252i) q^{57} +(0.572949 + 0.992377i) q^{58} +5.09017 q^{59} +(-3.00000 - 5.19615i) q^{60} +(-1.42705 - 2.47172i) q^{61} +(8.16312 - 14.1389i) q^{63} -4.70820 q^{64} +1.70820 q^{65} +(1.80902 - 3.13331i) q^{66} +(1.92705 - 3.33775i) q^{67} +(5.64590 + 9.77898i) q^{68} +(5.73607 + 9.93516i) q^{69} +2.00000 q^{70} +(5.39919 + 9.35167i) q^{71} +(-2.83688 - 4.91362i) q^{72} +(-0.927051 - 1.60570i) q^{73} +(-0.927051 + 1.60570i) q^{74} +9.09017 q^{75} +(-1.14590 + 1.98475i) q^{76} +(-7.66312 - 13.2729i) q^{77} +1.38197 q^{78} +(0.690983 + 1.19682i) q^{79} +(-1.94427 + 3.36758i) q^{80} +(2.85410 - 4.94345i) q^{81} -3.61803 q^{82} +(-8.01722 + 13.8862i) q^{83} -20.5623 q^{84} +7.52786 q^{85} +(2.48278 - 0.330792i) q^{86} -7.85410 q^{87} -5.32624 q^{88} +(0.927051 - 1.60570i) q^{89} -1.81966 q^{90} +(2.92705 - 5.06980i) q^{91} +(4.06231 - 7.03612i) q^{92} -0.437694 q^{94} +(0.763932 + 1.32317i) q^{95} +(-5.42705 + 9.39993i) q^{96} -9.23607 q^{97} +(2.09017 - 3.62028i) q^{98} +(6.97214 + 12.0761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 6q^{2} + 3q^{3} + 6q^{4} + 2q^{5} - 2q^{6} + 4q^{7} - 12q^{8} - q^{9} + O(q^{10}) \) \( 4q - 6q^{2} + 3q^{3} + 6q^{4} + 2q^{5} - 2q^{6} + 4q^{7} - 12q^{8} - q^{9} - 8q^{10} - 10q^{11} - 3q^{12} - 5q^{13} - q^{14} + 2q^{15} + 26q^{16} - q^{17} - 6q^{18} - 2q^{19} + 18q^{20} + 22q^{21} + 10q^{22} - 11q^{23} + q^{24} - 2q^{25} + 10q^{26} - 9q^{28} - 6q^{29} + 2q^{30} - 30q^{32} - 10q^{33} - 11q^{34} - 12q^{35} + 21q^{36} + 3q^{37} + 8q^{38} - 10q^{39} - 26q^{40} + 20q^{41} - 8q^{42} - 26q^{43} + 28q^{45} + 19q^{46} + 18q^{47} + 12q^{48} - 4q^{49} + 13q^{50} - 28q^{51} - 15q^{52} + 5q^{53} - 10q^{54} + 8q^{56} - 2q^{57} + 9q^{58} - 2q^{59} - 12q^{60} + q^{61} + 17q^{63} + 8q^{64} - 20q^{65} + 5q^{66} + q^{67} + 36q^{68} + 14q^{69} + 8q^{70} - 3q^{71} - 27q^{72} + 3q^{73} + 3q^{74} + 14q^{75} - 18q^{76} - 15q^{77} + 10q^{78} + 5q^{79} + 28q^{80} - 2q^{81} - 10q^{82} - 3q^{83} - 42q^{84} + 48q^{85} + 39q^{86} - 18q^{87} + 10q^{88} - 3q^{89} - 52q^{90} + 5q^{91} - 24q^{92} - 42q^{94} + 12q^{95} - 15q^{96} - 28q^{97} - 14q^{98} + 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.381966 −0.270091 −0.135045 0.990839i \(-0.543118\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(3\) 1.30902 2.26728i 0.755761 1.30902i −0.189234 0.981932i \(-0.560600\pi\)
0.944995 0.327085i \(-0.106066\pi\)
\(4\) −1.85410 −0.927051
\(5\) −0.618034 + 1.07047i −0.276393 + 0.478727i −0.970486 0.241159i \(-0.922473\pi\)
0.694092 + 0.719886i \(0.255806\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 2.11803 + 3.66854i 0.800542 + 1.38658i 0.919260 + 0.393651i \(0.128788\pi\)
−0.118718 + 0.992928i \(0.537879\pi\)
\(8\) 1.47214 0.520479
\(9\) −1.92705 3.33775i −0.642350 1.11258i
\(10\) 0.236068 0.408882i 0.0746512 0.129300i
\(11\) −3.61803 −1.09088 −0.545439 0.838150i \(-0.683637\pi\)
−0.545439 + 0.838150i \(0.683637\pi\)
\(12\) −2.42705 + 4.20378i −0.700629 + 1.21353i
\(13\) −0.690983 1.19682i −0.191644 0.331937i 0.754151 0.656701i \(-0.228049\pi\)
−0.945795 + 0.324763i \(0.894715\pi\)
\(14\) −0.809017 1.40126i −0.216219 0.374502i
\(15\) 1.61803 + 2.80252i 0.417775 + 0.723607i
\(16\) 3.14590 0.786475
\(17\) −3.04508 5.27424i −0.738542 1.27919i −0.953152 0.302492i \(-0.902182\pi\)
0.214610 0.976700i \(-0.431152\pi\)
\(18\) 0.736068 + 1.27491i 0.173493 + 0.300498i
\(19\) 0.618034 1.07047i 0.141787 0.245582i −0.786383 0.617740i \(-0.788049\pi\)
0.928170 + 0.372158i \(0.121382\pi\)
\(20\) 1.14590 1.98475i 0.256231 0.443804i
\(21\) 11.0902 2.42007
\(22\) 1.38197 0.294636
\(23\) −2.19098 + 3.79489i −0.456852 + 0.791290i −0.998793 0.0491264i \(-0.984356\pi\)
0.541941 + 0.840417i \(0.317690\pi\)
\(24\) 1.92705 3.33775i 0.393358 0.681315i
\(25\) 1.73607 + 3.00696i 0.347214 + 0.601392i
\(26\) 0.263932 + 0.457144i 0.0517613 + 0.0896533i
\(27\) −2.23607 −0.430331
\(28\) −3.92705 6.80185i −0.742143 1.28543i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) −0.618034 1.07047i −0.112837 0.195440i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −4.14590 −0.732898
\(33\) −4.73607 + 8.20311i −0.824444 + 1.42798i
\(34\) 1.16312 + 2.01458i 0.199473 + 0.345498i
\(35\) −5.23607 −0.885057
\(36\) 3.57295 + 6.18853i 0.595492 + 1.03142i
\(37\) 2.42705 4.20378i 0.399005 0.691096i −0.594599 0.804023i \(-0.702689\pi\)
0.993603 + 0.112926i \(0.0360224\pi\)
\(38\) −0.236068 + 0.408882i −0.0382953 + 0.0663294i
\(39\) −3.61803 −0.579349
\(40\) −0.909830 + 1.57587i −0.143857 + 0.249167i
\(41\) 9.47214 1.47930 0.739650 0.672992i \(-0.234991\pi\)
0.739650 + 0.672992i \(0.234991\pi\)
\(42\) −4.23607 −0.653639
\(43\) −6.50000 + 0.866025i −0.991241 + 0.132068i
\(44\) 6.70820 1.01130
\(45\) 4.76393 0.710165
\(46\) 0.836881 1.44952i 0.123391 0.213720i
\(47\) 1.14590 0.167146 0.0835732 0.996502i \(-0.473367\pi\)
0.0835732 + 0.996502i \(0.473367\pi\)
\(48\) 4.11803 7.13264i 0.594387 1.02951i
\(49\) −5.47214 + 9.47802i −0.781734 + 1.35400i
\(50\) −0.663119 1.14856i −0.0937792 0.162430i
\(51\) −15.9443 −2.23264
\(52\) 1.28115 + 2.21902i 0.177664 + 0.307723i
\(53\) 0.690983 1.19682i 0.0949138 0.164396i −0.814659 0.579941i \(-0.803076\pi\)
0.909573 + 0.415545i \(0.136409\pi\)
\(54\) 0.854102 0.116229
\(55\) 2.23607 3.87298i 0.301511 0.522233i
\(56\) 3.11803 + 5.40059i 0.416665 + 0.721685i
\(57\) −1.61803 2.80252i −0.214314 0.371202i
\(58\) 0.572949 + 0.992377i 0.0752319 + 0.130305i
\(59\) 5.09017 0.662684 0.331342 0.943511i \(-0.392499\pi\)
0.331342 + 0.943511i \(0.392499\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) −1.42705 2.47172i −0.182715 0.316472i 0.760089 0.649819i \(-0.225155\pi\)
−0.942804 + 0.333347i \(0.891822\pi\)
\(62\) 0 0
\(63\) 8.16312 14.1389i 1.02846 1.78134i
\(64\) −4.70820 −0.588525
\(65\) 1.70820 0.211877
\(66\) 1.80902 3.13331i 0.222675 0.385684i
\(67\) 1.92705 3.33775i 0.235427 0.407771i −0.723970 0.689832i \(-0.757685\pi\)
0.959397 + 0.282061i \(0.0910179\pi\)
\(68\) 5.64590 + 9.77898i 0.684666 + 1.18588i
\(69\) 5.73607 + 9.93516i 0.690541 + 1.19605i
\(70\) 2.00000 0.239046
\(71\) 5.39919 + 9.35167i 0.640766 + 1.10984i 0.985262 + 0.171051i \(0.0547163\pi\)
−0.344497 + 0.938788i \(0.611950\pi\)
\(72\) −2.83688 4.91362i −0.334330 0.579076i
\(73\) −0.927051 1.60570i −0.108503 0.187933i 0.806661 0.591015i \(-0.201272\pi\)
−0.915164 + 0.403082i \(0.867939\pi\)
\(74\) −0.927051 + 1.60570i −0.107767 + 0.186659i
\(75\) 9.09017 1.04964
\(76\) −1.14590 + 1.98475i −0.131444 + 0.227667i
\(77\) −7.66312 13.2729i −0.873293 1.51259i
\(78\) 1.38197 0.156477
\(79\) 0.690983 + 1.19682i 0.0777417 + 0.134653i 0.902275 0.431161i \(-0.141896\pi\)
−0.824534 + 0.565813i \(0.808562\pi\)
\(80\) −1.94427 + 3.36758i −0.217376 + 0.376507i
\(81\) 2.85410 4.94345i 0.317122 0.549272i
\(82\) −3.61803 −0.399545
\(83\) −8.01722 + 13.8862i −0.880004 + 1.52421i −0.0286698 + 0.999589i \(0.509127\pi\)
−0.851335 + 0.524623i \(0.824206\pi\)
\(84\) −20.5623 −2.24353
\(85\) 7.52786 0.816511
\(86\) 2.48278 0.330792i 0.267725 0.0356702i
\(87\) −7.85410 −0.842048
\(88\) −5.32624 −0.567779
\(89\) 0.927051 1.60570i 0.0982672 0.170204i −0.812700 0.582682i \(-0.802003\pi\)
0.910968 + 0.412478i \(0.135337\pi\)
\(90\) −1.81966 −0.191809
\(91\) 2.92705 5.06980i 0.306838 0.531460i
\(92\) 4.06231 7.03612i 0.423525 0.733566i
\(93\) 0 0
\(94\) −0.437694 −0.0451447
\(95\) 0.763932 + 1.32317i 0.0783778 + 0.135754i
\(96\) −5.42705 + 9.39993i −0.553896 + 0.959376i
\(97\) −9.23607 −0.937781 −0.468890 0.883256i \(-0.655346\pi\)
−0.468890 + 0.883256i \(0.655346\pi\)
\(98\) 2.09017 3.62028i 0.211139 0.365704i
\(99\) 6.97214 + 12.0761i 0.700726 + 1.21369i
\(100\) −3.21885 5.57521i −0.321885 0.557521i
\(101\) −1.88197 3.25966i −0.187263 0.324348i 0.757074 0.653329i \(-0.226628\pi\)
−0.944337 + 0.328981i \(0.893295\pi\)
\(102\) 6.09017 0.603017
\(103\) 8.20820 + 14.2170i 0.808778 + 1.40085i 0.913710 + 0.406366i \(0.133204\pi\)
−0.104932 + 0.994479i \(0.533463\pi\)
\(104\) −1.01722 1.76188i −0.0997467 0.172766i
\(105\) −6.85410 + 11.8717i −0.668892 + 1.15855i
\(106\) −0.263932 + 0.457144i −0.0256353 + 0.0444017i
\(107\) 7.52786 0.727746 0.363873 0.931449i \(-0.381454\pi\)
0.363873 + 0.931449i \(0.381454\pi\)
\(108\) 4.14590 0.398939
\(109\) 6.92705 11.9980i 0.663491 1.14920i −0.316201 0.948692i \(-0.602407\pi\)
0.979692 0.200508i \(-0.0642593\pi\)
\(110\) −0.854102 + 1.47935i −0.0814354 + 0.141050i
\(111\) −6.35410 11.0056i −0.603105 1.04461i
\(112\) 6.66312 + 11.5409i 0.629606 + 1.09051i
\(113\) −15.6180 −1.46922 −0.734611 0.678489i \(-0.762635\pi\)
−0.734611 + 0.678489i \(0.762635\pi\)
\(114\) 0.618034 + 1.07047i 0.0578842 + 0.100258i
\(115\) −2.70820 4.69075i −0.252541 0.437414i
\(116\) 2.78115 + 4.81710i 0.258224 + 0.447256i
\(117\) −2.66312 + 4.61266i −0.246205 + 0.426440i
\(118\) −1.94427 −0.178985
\(119\) 12.8992 22.3420i 1.18247 2.04809i
\(120\) 2.38197 + 4.12569i 0.217443 + 0.376622i
\(121\) 2.09017 0.190015
\(122\) 0.545085 + 0.944115i 0.0493497 + 0.0854761i
\(123\) 12.3992 21.4760i 1.11800 1.93643i
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) −3.11803 + 5.40059i −0.277777 + 0.481123i
\(127\) −14.6525 −1.30020 −0.650098 0.759850i \(-0.725272\pi\)
−0.650098 + 0.759850i \(0.725272\pi\)
\(128\) 10.0902 0.891853
\(129\) −6.54508 + 15.8710i −0.576263 + 1.39736i
\(130\) −0.652476 −0.0572259
\(131\) 9.94427 0.868835 0.434418 0.900712i \(-0.356954\pi\)
0.434418 + 0.900712i \(0.356954\pi\)
\(132\) 8.78115 15.2094i 0.764301 1.32381i
\(133\) 5.23607 0.454025
\(134\) −0.736068 + 1.27491i −0.0635866 + 0.110135i
\(135\) 1.38197 2.39364i 0.118941 0.206011i
\(136\) −4.48278 7.76440i −0.384395 0.665792i
\(137\) 3.70820 0.316813 0.158407 0.987374i \(-0.449364\pi\)
0.158407 + 0.987374i \(0.449364\pi\)
\(138\) −2.19098 3.79489i −0.186509 0.323043i
\(139\) 2.64590 4.58283i 0.224422 0.388711i −0.731724 0.681601i \(-0.761284\pi\)
0.956146 + 0.292891i \(0.0946172\pi\)
\(140\) 9.70820 0.820493
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) −2.06231 3.57202i −0.173065 0.299757i
\(143\) 2.50000 + 4.33013i 0.209061 + 0.362103i
\(144\) −6.06231 10.5002i −0.505192 0.875018i
\(145\) 3.70820 0.307950
\(146\) 0.354102 + 0.613323i 0.0293057 + 0.0507589i
\(147\) 14.3262 + 24.8138i 1.18161 + 2.04661i
\(148\) −4.50000 + 7.79423i −0.369898 + 0.640682i
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) −3.47214 −0.283499
\(151\) −8.85410 −0.720537 −0.360268 0.932849i \(-0.617315\pi\)
−0.360268 + 0.932849i \(0.617315\pi\)
\(152\) 0.909830 1.57587i 0.0737970 0.127820i
\(153\) −11.7361 + 20.3275i −0.948805 + 1.64338i
\(154\) 2.92705 + 5.06980i 0.235868 + 0.408536i
\(155\) 0 0
\(156\) 6.70820 0.537086
\(157\) 2.57295 + 4.45648i 0.205344 + 0.355666i 0.950242 0.311512i \(-0.100835\pi\)
−0.744898 + 0.667178i \(0.767502\pi\)
\(158\) −0.263932 0.457144i −0.0209973 0.0363684i
\(159\) −1.80902 3.13331i −0.143464 0.248488i
\(160\) 2.56231 4.43804i 0.202568 0.350858i
\(161\) −18.5623 −1.46291
\(162\) −1.09017 + 1.88823i −0.0856518 + 0.148353i
\(163\) −7.00000 12.1244i −0.548282 0.949653i −0.998392 0.0566798i \(-0.981949\pi\)
0.450110 0.892973i \(-0.351385\pi\)
\(164\) −17.5623 −1.37139
\(165\) −5.85410 10.1396i −0.455741 0.789367i
\(166\) 3.06231 5.30407i 0.237681 0.411676i
\(167\) −7.11803 + 12.3288i −0.550810 + 0.954031i 0.447406 + 0.894331i \(0.352348\pi\)
−0.998216 + 0.0597001i \(0.980986\pi\)
\(168\) 16.3262 1.25960
\(169\) 5.54508 9.60437i 0.426545 0.738798i
\(170\) −2.87539 −0.220532
\(171\) −4.76393 −0.364307
\(172\) 12.0517 1.60570i 0.918931 0.122433i
\(173\) −3.76393 −0.286166 −0.143083 0.989711i \(-0.545702\pi\)
−0.143083 + 0.989711i \(0.545702\pi\)
\(174\) 3.00000 0.227429
\(175\) −7.35410 + 12.7377i −0.555918 + 0.962878i
\(176\) −11.3820 −0.857948
\(177\) 6.66312 11.5409i 0.500831 0.867464i
\(178\) −0.354102 + 0.613323i −0.0265411 + 0.0459705i
\(179\) −4.82624 8.35929i −0.360730 0.624803i 0.627351 0.778736i \(-0.284139\pi\)
−0.988081 + 0.153934i \(0.950806\pi\)
\(180\) −8.83282 −0.658359
\(181\) 9.69098 + 16.7853i 0.720325 + 1.24764i 0.960869 + 0.277002i \(0.0893407\pi\)
−0.240544 + 0.970638i \(0.577326\pi\)
\(182\) −1.11803 + 1.93649i −0.0828742 + 0.143542i
\(183\) −7.47214 −0.552356
\(184\) −3.22542 + 5.58660i −0.237781 + 0.411850i
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 11.0172 + 19.0824i 0.805659 + 1.39544i
\(188\) −2.12461 −0.154953
\(189\) −4.73607 8.20311i −0.344498 0.596688i
\(190\) −0.291796 0.505406i −0.0211691 0.0366660i
\(191\) 7.26393 12.5815i 0.525600 0.910365i −0.473956 0.880549i \(-0.657174\pi\)
0.999555 0.0298167i \(-0.00949234\pi\)
\(192\) −6.16312 + 10.6748i −0.444785 + 0.770390i
\(193\) 2.70820 0.194941 0.0974704 0.995238i \(-0.468925\pi\)
0.0974704 + 0.995238i \(0.468925\pi\)
\(194\) 3.52786 0.253286
\(195\) 2.23607 3.87298i 0.160128 0.277350i
\(196\) 10.1459 17.5732i 0.724707 1.25523i
\(197\) 1.47214 + 2.54981i 0.104885 + 0.181667i 0.913691 0.406409i \(-0.133219\pi\)
−0.808806 + 0.588076i \(0.799886\pi\)
\(198\) −2.66312 4.61266i −0.189260 0.327807i
\(199\) 1.94427 0.137826 0.0689129 0.997623i \(-0.478047\pi\)
0.0689129 + 0.997623i \(0.478047\pi\)
\(200\) 2.55573 + 4.42665i 0.180717 + 0.313011i
\(201\) −5.04508 8.73834i −0.355853 0.616355i
\(202\) 0.718847 + 1.24508i 0.0505779 + 0.0876035i
\(203\) 6.35410 11.0056i 0.445971 0.772444i
\(204\) 29.5623 2.06978
\(205\) −5.85410 + 10.1396i −0.408868 + 0.708181i
\(206\) −3.13525 5.43042i −0.218444 0.378355i
\(207\) 16.8885 1.17383
\(208\) −2.17376 3.76507i −0.150723 0.261060i
\(209\) −2.23607 + 3.87298i −0.154672 + 0.267900i
\(210\) 2.61803 4.53457i 0.180662 0.312915i
\(211\) −9.23607 −0.635837 −0.317919 0.948118i \(-0.602984\pi\)
−0.317919 + 0.948118i \(0.602984\pi\)
\(212\) −1.28115 + 2.21902i −0.0879899 + 0.152403i
\(213\) 28.2705 1.93706
\(214\) −2.87539 −0.196557
\(215\) 3.09017 7.49326i 0.210748 0.511036i
\(216\) −3.29180 −0.223978
\(217\) 0 0
\(218\) −2.64590 + 4.58283i −0.179203 + 0.310388i
\(219\) −4.85410 −0.328010
\(220\) −4.14590 + 7.18091i −0.279516 + 0.484137i
\(221\) −4.20820 + 7.28882i −0.283074 + 0.490299i
\(222\) 2.42705 + 4.20378i 0.162893 + 0.282139i
\(223\) 2.76393 0.185087 0.0925433 0.995709i \(-0.470500\pi\)
0.0925433 + 0.995709i \(0.470500\pi\)
\(224\) −8.78115 15.2094i −0.586715 1.01622i
\(225\) 6.69098 11.5891i 0.446066 0.772608i
\(226\) 5.96556 0.396823
\(227\) 0.736068 1.27491i 0.0488545 0.0846186i −0.840564 0.541712i \(-0.817776\pi\)
0.889419 + 0.457094i \(0.151110\pi\)
\(228\) 3.00000 + 5.19615i 0.198680 + 0.344124i
\(229\) 1.14590 + 1.98475i 0.0757231 + 0.131156i 0.901400 0.432986i \(-0.142540\pi\)
−0.825677 + 0.564143i \(0.809207\pi\)
\(230\) 1.03444 + 1.79171i 0.0682091 + 0.118142i
\(231\) −40.1246 −2.64001
\(232\) −2.20820 3.82472i −0.144976 0.251105i
\(233\) −9.01722 15.6183i −0.590738 1.02319i −0.994133 0.108162i \(-0.965503\pi\)
0.403395 0.915026i \(-0.367830\pi\)
\(234\) 1.01722 1.76188i 0.0664978 0.115178i
\(235\) −0.708204 + 1.22665i −0.0461981 + 0.0800175i
\(236\) −9.43769 −0.614342
\(237\) 3.61803 0.235017
\(238\) −4.92705 + 8.53390i −0.319373 + 0.553171i
\(239\) 4.14590 7.18091i 0.268176 0.464494i −0.700215 0.713932i \(-0.746913\pi\)
0.968391 + 0.249438i \(0.0802458\pi\)
\(240\) 5.09017 + 8.81643i 0.328569 + 0.569098i
\(241\) −2.13525 3.69837i −0.137544 0.238233i 0.789022 0.614364i \(-0.210587\pi\)
−0.926566 + 0.376131i \(0.877254\pi\)
\(242\) −0.798374 −0.0513214
\(243\) −10.8262 18.7516i −0.694503 1.20292i
\(244\) 2.64590 + 4.58283i 0.169386 + 0.293386i
\(245\) −6.76393 11.7155i −0.432132 0.748474i
\(246\) −4.73607 + 8.20311i −0.301961 + 0.523011i
\(247\) −1.70820 −0.108690
\(248\) 0 0
\(249\) 20.9894 + 36.3546i 1.33015 + 2.30388i
\(250\) 4.00000 0.252982
\(251\) 14.5902 + 25.2709i 0.920923 + 1.59509i 0.797990 + 0.602671i \(0.205897\pi\)
0.122934 + 0.992415i \(0.460770\pi\)
\(252\) −15.1353 + 26.2150i −0.953431 + 1.65139i
\(253\) 7.92705 13.7301i 0.498369 0.863201i
\(254\) 5.59675 0.351171
\(255\) 9.85410 17.0678i 0.617088 1.06883i
\(256\) 5.56231 0.347644
\(257\) 3.43769 0.214437 0.107219 0.994235i \(-0.465805\pi\)
0.107219 + 0.994235i \(0.465805\pi\)
\(258\) 2.50000 6.06218i 0.155643 0.377415i
\(259\) 20.5623 1.27768
\(260\) −3.16718 −0.196420
\(261\) −5.78115 + 10.0133i −0.357844 + 0.619805i
\(262\) −3.79837 −0.234664
\(263\) −13.7533 + 23.8214i −0.848064 + 1.46889i 0.0348693 + 0.999392i \(0.488899\pi\)
−0.882933 + 0.469498i \(0.844435\pi\)
\(264\) −6.97214 + 12.0761i −0.429105 + 0.743232i
\(265\) 0.854102 + 1.47935i 0.0524671 + 0.0908756i
\(266\) −2.00000 −0.122628
\(267\) −2.42705 4.20378i −0.148533 0.257267i
\(268\) −3.57295 + 6.18853i −0.218253 + 0.378025i
\(269\) 11.5623 0.704966 0.352483 0.935818i \(-0.385337\pi\)
0.352483 + 0.935818i \(0.385337\pi\)
\(270\) −0.527864 + 0.914287i −0.0321248 + 0.0556418i
\(271\) −6.92705 11.9980i −0.420788 0.728827i 0.575228 0.817993i \(-0.304913\pi\)
−0.996017 + 0.0891660i \(0.971580\pi\)
\(272\) −9.57953 16.5922i −0.580844 1.00605i
\(273\) −7.66312 13.2729i −0.463793 0.803313i
\(274\) −1.41641 −0.0855683
\(275\) −6.28115 10.8793i −0.378768 0.656045i
\(276\) −10.6353 18.4208i −0.640167 1.10880i
\(277\) 6.23607 10.8012i 0.374689 0.648980i −0.615591 0.788065i \(-0.711083\pi\)
0.990280 + 0.139085i \(0.0444161\pi\)
\(278\) −1.01064 + 1.75049i −0.0606143 + 0.104987i
\(279\) 0 0
\(280\) −7.70820 −0.460653
\(281\) −3.73607 + 6.47106i −0.222875 + 0.386031i −0.955680 0.294408i \(-0.904878\pi\)
0.732805 + 0.680439i \(0.238211\pi\)
\(282\) −0.572949 + 0.992377i −0.0341186 + 0.0590952i
\(283\) −5.38197 9.32184i −0.319925 0.554126i 0.660547 0.750784i \(-0.270324\pi\)
−0.980472 + 0.196659i \(0.936991\pi\)
\(284\) −10.0106 17.3389i −0.594022 1.02888i
\(285\) 4.00000 0.236940
\(286\) −0.954915 1.65396i −0.0564653 0.0978008i
\(287\) 20.0623 + 34.7489i 1.18424 + 2.05116i
\(288\) 7.98936 + 13.8380i 0.470777 + 0.815410i
\(289\) −10.0451 + 17.3986i −0.590887 + 1.02345i
\(290\) −1.41641 −0.0831743
\(291\) −12.0902 + 20.9408i −0.708738 + 1.22757i
\(292\) 1.71885 + 2.97713i 0.100588 + 0.174223i
\(293\) −12.0902 −0.706315 −0.353158 0.935564i \(-0.614892\pi\)
−0.353158 + 0.935564i \(0.614892\pi\)
\(294\) −5.47214 9.47802i −0.319141 0.552769i
\(295\) −3.14590 + 5.44886i −0.183161 + 0.317245i
\(296\) 3.57295 6.18853i 0.207673 0.359701i
\(297\) 8.09017 0.469439
\(298\) 1.71885 2.97713i 0.0995701 0.172461i
\(299\) 6.05573 0.350212
\(300\) −16.8541 −0.973072
\(301\) −16.9443 22.0113i −0.976652 1.26871i
\(302\) 3.38197 0.194610
\(303\) −9.85410 −0.566103
\(304\) 1.94427 3.36758i 0.111512 0.193144i
\(305\) 3.52786 0.202005
\(306\) 4.48278 7.76440i 0.256263 0.443861i
\(307\) 11.6074 20.1046i 0.662469 1.14743i −0.317496 0.948260i \(-0.602842\pi\)
0.979965 0.199170i \(-0.0638246\pi\)
\(308\) 14.2082 + 24.6093i 0.809588 + 1.40225i
\(309\) 42.9787 2.44497
\(310\) 0 0
\(311\) 14.9164 25.8360i 0.845832 1.46502i −0.0390649 0.999237i \(-0.512438\pi\)
0.884897 0.465787i \(-0.154229\pi\)
\(312\) −5.32624 −0.301539
\(313\) −6.56231 + 11.3662i −0.370923 + 0.642458i −0.989708 0.143103i \(-0.954292\pi\)
0.618784 + 0.785561i \(0.287625\pi\)
\(314\) −0.982779 1.70222i −0.0554614 0.0960620i
\(315\) 10.0902 + 17.4767i 0.568517 + 0.984700i
\(316\) −1.28115 2.21902i −0.0720705 0.124830i
\(317\) 33.3050 1.87059 0.935296 0.353866i \(-0.115133\pi\)
0.935296 + 0.353866i \(0.115133\pi\)
\(318\) 0.690983 + 1.19682i 0.0387484 + 0.0671142i
\(319\) 5.42705 + 9.39993i 0.303857 + 0.526295i
\(320\) 2.90983 5.03997i 0.162664 0.281743i
\(321\) 9.85410 17.0678i 0.550002 0.952632i
\(322\) 7.09017 0.395120
\(323\) −7.52786 −0.418862
\(324\) −5.29180 + 9.16566i −0.293989 + 0.509203i
\(325\) 2.39919 4.15551i 0.133083 0.230506i
\(326\) 2.67376 + 4.63109i 0.148086 + 0.256492i
\(327\) −18.1353 31.4112i −1.00288 1.73704i
\(328\) 13.9443 0.769944
\(329\) 2.42705 + 4.20378i 0.133808 + 0.231762i
\(330\) 2.23607 + 3.87298i 0.123091 + 0.213201i
\(331\) 2.73607 + 4.73901i 0.150388 + 0.260479i 0.931370 0.364074i \(-0.118614\pi\)
−0.780982 + 0.624553i \(0.785281\pi\)
\(332\) 14.8647 25.7465i 0.815809 1.41302i
\(333\) −18.7082 −1.02520
\(334\) 2.71885 4.70918i 0.148769 0.257675i
\(335\) 2.38197 + 4.12569i 0.130141 + 0.225410i
\(336\) 34.8885 1.90333
\(337\) −14.0000 24.2487i −0.762629 1.32091i −0.941491 0.337037i \(-0.890575\pi\)
0.178863 0.983874i \(-0.442758\pi\)
\(338\) −2.11803 + 3.66854i −0.115206 + 0.199542i
\(339\) −20.4443 + 35.4105i −1.11038 + 1.92324i
\(340\) −13.9574 −0.756948
\(341\) 0 0
\(342\) 1.81966 0.0983959
\(343\) −16.7082 −0.902158
\(344\) −9.56888 + 1.27491i −0.515920 + 0.0687384i
\(345\) −14.1803 −0.763444
\(346\) 1.43769 0.0772909
\(347\) −5.04508 + 8.73834i −0.270834 + 0.469099i −0.969076 0.246764i \(-0.920633\pi\)
0.698241 + 0.715862i \(0.253966\pi\)
\(348\) 14.5623 0.780622
\(349\) −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i \(0.353659\pi\)
−0.997962 + 0.0638103i \(0.979675\pi\)
\(350\) 2.80902 4.86536i 0.150148 0.260064i
\(351\) 1.54508 + 2.67617i 0.0824705 + 0.142843i
\(352\) 15.0000 0.799503
\(353\) 8.61803 + 14.9269i 0.458692 + 0.794477i 0.998892 0.0470591i \(-0.0149849\pi\)
−0.540200 + 0.841536i \(0.681652\pi\)
\(354\) −2.54508 + 4.40822i −0.135270 + 0.234294i
\(355\) −13.3475 −0.708413
\(356\) −1.71885 + 2.97713i −0.0910987 + 0.157788i
\(357\) −33.7705 58.4922i −1.78732 3.09574i
\(358\) 1.84346 + 3.19296i 0.0974298 + 0.168753i
\(359\) 2.67376 + 4.63109i 0.141116 + 0.244420i 0.927917 0.372787i \(-0.121598\pi\)
−0.786801 + 0.617206i \(0.788264\pi\)
\(360\) 7.01316 0.369626
\(361\) 8.73607 + 15.1313i 0.459793 + 0.796385i
\(362\) −3.70163 6.41140i −0.194553 0.336976i
\(363\) 2.73607 4.73901i 0.143606 0.248733i
\(364\) −5.42705 + 9.39993i −0.284455 + 0.492690i
\(365\) 2.29180 0.119958
\(366\) 2.85410 0.149186
\(367\) −9.59017 + 16.6107i −0.500603 + 0.867069i 0.499397 + 0.866373i \(0.333555\pi\)
−1.00000 0.000696189i \(0.999778\pi\)
\(368\) −6.89261 + 11.9383i −0.359302 + 0.622329i
\(369\) −18.2533 31.6156i −0.950228 1.64584i
\(370\) −1.14590 1.98475i −0.0595724 0.103182i
\(371\) 5.85410 0.303930
\(372\) 0 0
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) −4.20820 7.28882i −0.217601 0.376896i
\(375\) −13.7082 + 23.7433i −0.707889 + 1.22610i
\(376\) 1.68692 0.0869961
\(377\) −2.07295 + 3.59045i −0.106762 + 0.184918i
\(378\) 1.80902 + 3.13331i 0.0930458 + 0.161160i
\(379\) −27.3607 −1.40542 −0.702712 0.711475i \(-0.748028\pi\)
−0.702712 + 0.711475i \(0.748028\pi\)
\(380\) −1.41641 2.45329i −0.0726602 0.125851i
\(381\) −19.1803 + 33.2213i −0.982639 + 1.70198i
\(382\) −2.77458 + 4.80571i −0.141960 + 0.245881i
\(383\) 38.1246 1.94808 0.974038 0.226383i \(-0.0726901\pi\)
0.974038 + 0.226383i \(0.0726901\pi\)
\(384\) 13.2082 22.8773i 0.674028 1.16745i
\(385\) 18.9443 0.965489
\(386\) −1.03444 −0.0526517
\(387\) 15.4164 + 20.0265i 0.783660 + 1.01800i
\(388\) 17.1246 0.869370
\(389\) −35.0689 −1.77806 −0.889031 0.457846i \(-0.848621\pi\)
−0.889031 + 0.457846i \(0.848621\pi\)
\(390\) −0.854102 + 1.47935i −0.0432491 + 0.0749097i
\(391\) 26.6869 1.34962
\(392\) −8.05573 + 13.9529i −0.406876 + 0.704729i
\(393\) 13.0172 22.5465i 0.656632 1.13732i
\(394\) −0.562306 0.973942i −0.0283286 0.0490665i
\(395\) −1.70820 −0.0859491
\(396\) −12.9271 22.3903i −0.649609 1.12516i
\(397\) −16.2082 + 28.0734i −0.813466 + 1.40897i 0.0969574 + 0.995289i \(0.469089\pi\)
−0.910424 + 0.413677i \(0.864244\pi\)
\(398\) −0.742646 −0.0372255
\(399\) 6.85410 11.8717i 0.343134 0.594326i
\(400\) 5.46149 + 9.45958i 0.273075 + 0.472979i
\(401\) 12.7082 + 22.0113i 0.634617 + 1.09919i 0.986596 + 0.163182i \(0.0521756\pi\)
−0.351979 + 0.936008i \(0.614491\pi\)
\(402\) 1.92705 + 3.33775i 0.0961126 + 0.166472i
\(403\) 0 0
\(404\) 3.48936 + 6.04374i 0.173602 + 0.300687i
\(405\) 3.52786 + 6.11044i 0.175301 + 0.303630i
\(406\) −2.42705 + 4.20378i −0.120453 + 0.208630i
\(407\) −8.78115 + 15.2094i −0.435266 + 0.753902i
\(408\) −23.4721 −1.16204
\(409\) 8.90983 0.440563 0.220281 0.975436i \(-0.429302\pi\)
0.220281 + 0.975436i \(0.429302\pi\)
\(410\) 2.23607 3.87298i 0.110432 0.191273i
\(411\) 4.85410 8.40755i 0.239435 0.414714i
\(412\) −15.2188 26.3598i −0.749779 1.29865i
\(413\) 10.7812 + 18.6735i 0.530506 + 0.918863i
\(414\) −6.45085 −0.317042
\(415\) −9.90983 17.1643i −0.486454 0.842564i
\(416\) 2.86475 + 4.96188i 0.140456 + 0.243276i
\(417\) −6.92705 11.9980i −0.339219 0.587545i
\(418\) 0.854102 1.47935i 0.0417755 0.0723573i
\(419\) −10.2361 −0.500065 −0.250032 0.968237i \(-0.580441\pi\)
−0.250032 + 0.968237i \(0.580441\pi\)
\(420\) 12.7082 22.0113i 0.620097 1.07404i
\(421\) 3.82624 + 6.62724i 0.186479 + 0.322992i 0.944074 0.329734i \(-0.106959\pi\)
−0.757595 + 0.652725i \(0.773626\pi\)
\(422\) 3.52786 0.171734
\(423\) −2.20820 3.82472i −0.107367 0.185964i
\(424\) 1.01722 1.76188i 0.0494006 0.0855644i
\(425\) 10.5729 18.3129i 0.512863 0.888305i
\(426\) −10.7984 −0.523183
\(427\) 6.04508 10.4704i 0.292542 0.506698i
\(428\) −13.9574 −0.674658
\(429\) 13.0902 0.631999
\(430\) −1.18034 + 2.86217i −0.0569210 + 0.138026i
\(431\) −24.7984 −1.19450 −0.597248 0.802057i \(-0.703739\pi\)
−0.597248 + 0.802057i \(0.703739\pi\)
\(432\) −7.03444 −0.338445
\(433\) 17.3541 30.0582i 0.833985 1.44450i −0.0608693 0.998146i \(-0.519387\pi\)
0.894854 0.446359i \(-0.147279\pi\)
\(434\) 0 0
\(435\) 4.85410 8.40755i 0.232736 0.403111i
\(436\) −12.8435 + 22.2455i −0.615090 + 1.06537i
\(437\) 2.70820 + 4.69075i 0.129551 + 0.224389i
\(438\) 1.85410 0.0885924
\(439\) −0.572949 0.992377i −0.0273454 0.0473636i 0.852029 0.523495i \(-0.175372\pi\)
−0.879374 + 0.476131i \(0.842039\pi\)
\(440\) 3.29180 5.70156i 0.156930 0.271811i
\(441\) 42.1803 2.00859
\(442\) 1.60739 2.78408i 0.0764558 0.132425i
\(443\) −1.23607 2.14093i −0.0587274 0.101719i 0.835167 0.549996i \(-0.185371\pi\)
−0.893894 + 0.448278i \(0.852038\pi\)
\(444\) 11.7812 + 20.4056i 0.559109 + 0.968405i
\(445\) 1.14590 + 1.98475i 0.0543208 + 0.0940863i
\(446\) −1.05573 −0.0499902
\(447\) 11.7812 + 20.4056i 0.557229 + 0.965150i
\(448\) −9.97214 17.2722i −0.471139 0.816037i
\(449\) 16.4164 28.4341i 0.774738 1.34189i −0.160203 0.987084i \(-0.551215\pi\)
0.934942 0.354802i \(-0.115452\pi\)
\(450\) −2.55573 + 4.42665i −0.120478 + 0.208674i
\(451\) −34.2705 −1.61374
\(452\) 28.9574 1.36204
\(453\) −11.5902 + 20.0748i −0.544554 + 0.943195i
\(454\) −0.281153 + 0.486971i −0.0131952 + 0.0228547i
\(455\) 3.61803 + 6.26662i 0.169616 + 0.293784i
\(456\) −2.38197 4.12569i −0.111546 0.193203i
\(457\) −15.7082 −0.734799 −0.367399 0.930063i \(-0.619752\pi\)
−0.367399 + 0.930063i \(0.619752\pi\)
\(458\) −0.437694 0.758108i −0.0204521 0.0354241i
\(459\) 6.80902 + 11.7936i 0.317818 + 0.550476i
\(460\) 5.02129 + 8.69712i 0.234119 + 0.405505i
\(461\) 15.7984 27.3636i 0.735804 1.27445i −0.218566 0.975822i \(-0.570138\pi\)
0.954370 0.298627i \(-0.0965287\pi\)
\(462\) 15.3262 0.713041
\(463\) 14.9164 25.8360i 0.693224 1.20070i −0.277551 0.960711i \(-0.589523\pi\)
0.970776 0.239989i \(-0.0771438\pi\)
\(464\) −4.71885 8.17328i −0.219067 0.379435i
\(465\) 0 0
\(466\) 3.44427 + 5.96565i 0.159553 + 0.276354i
\(467\) 7.52786 13.0386i 0.348348 0.603356i −0.637608 0.770361i \(-0.720076\pi\)
0.985956 + 0.167004i \(0.0534094\pi\)
\(468\) 4.93769 8.55234i 0.228245 0.395332i
\(469\) 16.3262 0.753876
\(470\) 0.270510 0.468537i 0.0124777 0.0216120i
\(471\) 13.4721 0.620763
\(472\) 7.49342 0.344913
\(473\) 23.5172 3.13331i 1.08132 0.144070i
\(474\) −1.38197 −0.0634758
\(475\) 4.29180 0.196921
\(476\) −23.9164 + 41.4244i −1.09621 + 1.89869i
\(477\) −5.32624 −0.243872
\(478\) −1.58359 + 2.74286i −0.0724318 + 0.125456i
\(479\) 6.90983 11.9682i 0.315718 0.546840i −0.663872 0.747846i \(-0.731088\pi\)
0.979590 + 0.201007i \(0.0644212\pi\)
\(480\) −6.70820 11.6190i −0.306186 0.530330i
\(481\) −6.70820 −0.305868
\(482\) 0.815595 + 1.41265i 0.0371493 + 0.0643445i
\(483\) −24.2984 + 42.0860i −1.10561 + 1.91498i
\(484\) −3.87539 −0.176154
\(485\) 5.70820 9.88690i 0.259196 0.448941i
\(486\) 4.13525 + 7.16247i 0.187579 + 0.324896i
\(487\) −0.663119 1.14856i −0.0300488 0.0520460i 0.850610 0.525797i \(-0.176233\pi\)
−0.880659 + 0.473751i \(0.842900\pi\)
\(488\) −2.10081 3.63871i −0.0950993 0.164717i
\(489\) −36.6525 −1.65748
\(490\) 2.58359 + 4.47491i 0.116715 + 0.202156i
\(491\) −10.8262 18.7516i −0.488581 0.846248i 0.511332 0.859383i \(-0.329152\pi\)
−0.999914 + 0.0131354i \(0.995819\pi\)
\(492\) −22.9894 + 39.8187i −1.03644 + 1.79517i
\(493\) −9.13525 + 15.8227i −0.411431 + 0.712620i
\(494\) 0.652476 0.0293563
\(495\) −17.2361 −0.774704
\(496\) 0 0
\(497\) −22.8713 + 39.6143i −1.02592 + 1.77694i
\(498\) −8.01722 13.8862i −0.359260 0.622257i
\(499\) −6.92705 11.9980i −0.310097 0.537104i 0.668286 0.743905i \(-0.267028\pi\)
−0.978383 + 0.206800i \(0.933695\pi\)
\(500\) 19.4164 0.868328
\(501\) 18.6353 + 32.2772i 0.832562 + 1.44204i
\(502\) −5.57295 9.65263i −0.248733 0.430818i
\(503\) 6.73607 + 11.6672i 0.300346 + 0.520215i 0.976214 0.216807i \(-0.0695644\pi\)
−0.675868 + 0.737023i \(0.736231\pi\)
\(504\) 12.0172 20.8144i 0.535290 0.927149i
\(505\) 4.65248 0.207032
\(506\) −3.02786 + 5.24441i −0.134605 + 0.233143i
\(507\) −14.5172 25.1446i −0.644732 1.11671i
\(508\) 27.1672 1.20535
\(509\) −9.35410 16.2018i −0.414613 0.718131i 0.580774 0.814064i \(-0.302750\pi\)
−0.995388 + 0.0959332i \(0.969416\pi\)
\(510\) −3.76393 + 6.51932i −0.166670 + 0.288680i
\(511\) 3.92705 6.80185i 0.173723 0.300896i
\(512\) −22.3050 −0.985749
\(513\) −1.38197 + 2.39364i −0.0610153 + 0.105682i
\(514\) −1.31308 −0.0579176
\(515\) −20.2918 −0.894163
\(516\) 12.1353 29.4264i 0.534225 1.29543i
\(517\) −4.14590 −0.182336
\(518\) −7.85410 −0.345089
\(519\) −4.92705 + 8.53390i −0.216274 + 0.374597i
\(520\) 2.51471 0.110277
\(521\) 11.0172 19.0824i 0.482673 0.836015i −0.517129 0.855908i \(-0.672999\pi\)
0.999802 + 0.0198930i \(0.00633256\pi\)
\(522\) 2.20820 3.82472i 0.0966505 0.167404i
\(523\) −17.9164 31.0321i −0.783430 1.35694i −0.929933 0.367730i \(-0.880135\pi\)
0.146503 0.989210i \(-0.453198\pi\)
\(524\) −18.4377 −0.805454
\(525\) 19.2533 + 33.3477i 0.840282 + 1.45541i
\(526\) 5.25329 9.09896i 0.229054 0.396734i
\(527\) 0 0
\(528\) −14.8992 + 25.8061i −0.648404 + 1.12307i
\(529\) 1.89919 + 3.28949i 0.0825733 + 0.143021i
\(530\) −0.326238 0.565061i −0.0141709 0.0245447i
\(531\) −9.80902 16.9897i −0.425675 0.737291i
\(532\) −9.70820 −0.420904
\(533\) −6.54508 11.3364i −0.283499 0.491035i
\(534\) 0.927051 + 1.60570i 0.0401174 + 0.0694854i
\(535\) −4.65248 + 8.05832i −0.201144 + 0.348392i
\(536\) 2.83688 4.91362i 0.122535 0.212236i
\(537\) −25.2705 −1.09050
\(538\) −4.41641 −0.190405
\(539\) 19.7984 34.2918i 0.852776 1.47705i
\(540\) −2.56231 + 4.43804i −0.110264 + 0.190983i
\(541\) 18.9721 + 32.8607i 0.815676 + 1.41279i 0.908842 + 0.417141i \(0.136968\pi\)
−0.0931658 + 0.995651i \(0.529699\pi\)
\(542\) 2.64590 + 4.58283i 0.113651 + 0.196849i
\(543\) 50.7426 2.17758
\(544\) 12.6246 + 21.8665i 0.541276 + 0.937517i
\(545\) 8.56231 + 14.8303i 0.366769 + 0.635262i
\(546\) 2.92705 + 5.06980i 0.125266 + 0.216967i
\(547\) −10.5000 + 18.1865i −0.448948 + 0.777600i −0.998318 0.0579790i \(-0.981534\pi\)
0.549370 + 0.835579i \(0.314868\pi\)
\(548\) −6.87539 −0.293702
\(549\) −5.50000 + 9.52628i −0.234734 + 0.406572i
\(550\) 2.39919 + 4.15551i 0.102302 + 0.177192i
\(551\) −3.70820 −0.157975
\(552\) 8.44427 + 14.6259i 0.359412 + 0.622520i
\(553\) −2.92705 + 5.06980i −0.124471 + 0.215590i
\(554\) −2.38197 + 4.12569i −0.101200 + 0.175284i
\(555\) 15.7082 0.666776
\(556\) −4.90576 + 8.49703i −0.208051 + 0.360354i
\(557\) −38.5623 −1.63394 −0.816969 0.576682i \(-0.804347\pi\)
−0.816969 + 0.576682i \(0.804347\pi\)
\(558\) 0 0
\(559\) 5.52786 + 7.18091i 0.233804 + 0.303720i
\(560\) −16.4721 −0.696075
\(561\) 57.6869 2.43554
\(562\) 1.42705 2.47172i 0.0601965 0.104263i
\(563\) −1.32624 −0.0558943 −0.0279471 0.999609i \(-0.508897\pi\)
−0.0279471 + 0.999609i \(0.508897\pi\)
\(564\) −2.78115 + 4.81710i −0.117108 + 0.202836i
\(565\) 9.65248 16.7186i 0.406083 0.703356i
\(566\) 2.05573 + 3.56063i 0.0864087 + 0.149664i
\(567\) 24.1803 1.01548
\(568\) 7.94834 + 13.7669i 0.333505 + 0.577647i
\(569\) 12.9721 22.4684i 0.543820 0.941924i −0.454860 0.890563i \(-0.650311\pi\)
0.998680 0.0513613i \(-0.0163560\pi\)
\(570\) −1.52786 −0.0639952
\(571\) 21.5902 37.3953i 0.903520 1.56494i 0.0806295 0.996744i \(-0.474307\pi\)
0.822891 0.568199i \(-0.192360\pi\)
\(572\) −4.63525 8.02850i −0.193810 0.335688i
\(573\) −19.0172 32.9388i −0.794456 1.37604i
\(574\) −7.66312 13.2729i −0.319852 0.554001i
\(575\) −15.2148 −0.634500
\(576\) 9.07295 + 15.7148i 0.378040 + 0.654784i
\(577\) 14.1074 + 24.4347i 0.587298 + 1.01723i 0.994585 + 0.103930i \(0.0331418\pi\)
−0.407286 + 0.913301i \(0.633525\pi\)
\(578\) 3.83688 6.64567i 0.159593 0.276424i
\(579\) 3.54508 6.14027i 0.147329 0.255181i
\(580\) −6.87539 −0.285485
\(581\) −67.9230 −2.81792
\(582\) 4.61803 7.99867i 0.191424 0.331556i
\(583\) −2.50000 + 4.33013i −0.103539 + 0.179336i
\(584\) −1.36475 2.36381i −0.0564736 0.0978151i
\(585\) −3.29180 5.70156i −0.136099 0.235730i
\(586\) 4.61803 0.190769
\(587\) −7.87132 13.6335i −0.324884 0.562716i 0.656605 0.754235i \(-0.271992\pi\)
−0.981489 + 0.191519i \(0.938659\pi\)
\(588\) −26.5623 46.0073i −1.09541 1.89731i
\(589\) 0 0
\(590\) 1.20163 2.08128i 0.0494702 0.0856848i
\(591\) 7.70820 0.317073
\(592\) 7.63525 13.2246i 0.313807 0.543530i
\(593\) 15.2361 + 26.3896i 0.625670 + 1.08369i 0.988411 + 0.151803i \(0.0485078\pi\)
−0.362741 + 0.931890i \(0.618159\pi\)
\(594\) −3.09017 −0.126791
\(595\) 15.9443 + 27.6163i 0.653651 + 1.13216i
\(596\) 8.34346 14.4513i 0.341761 0.591948i
\(597\) 2.54508 4.40822i 0.104163 0.180416i
\(598\) −2.31308 −0.0945890
\(599\) −18.1180 + 31.3814i −0.740283 + 1.28221i 0.212084 + 0.977252i \(0.431975\pi\)
−0.952366 + 0.304956i \(0.901358\pi\)
\(600\) 13.3820 0.546316
\(601\) 29.4164 1.19992 0.599960 0.800030i \(-0.295183\pi\)
0.599960 + 0.800030i \(0.295183\pi\)
\(602\) 6.47214 + 8.40755i 0.263785 + 0.342666i
\(603\) −14.8541 −0.604906
\(604\) 16.4164 0.667974
\(605\) −1.29180 + 2.23746i −0.0525190 + 0.0909655i
\(606\) 3.76393 0.152899
\(607\) 11.9271 20.6583i 0.484104 0.838493i −0.515729 0.856752i \(-0.672479\pi\)
0.999833 + 0.0182588i \(0.00581228\pi\)
\(608\) −2.56231 + 4.43804i −0.103915 + 0.179986i
\(609\) −16.6353 28.8131i −0.674095 1.16757i
\(610\) −1.34752 −0.0545597
\(611\) −0.791796 1.37143i −0.0320326 0.0554822i
\(612\) 21.7599 37.6892i 0.879590 1.52350i
\(613\) 5.20163 0.210092 0.105046 0.994467i \(-0.466501\pi\)
0.105046 + 0.994467i \(0.466501\pi\)
\(614\) −4.43363 + 7.67927i −0.178927 + 0.309910i
\(615\) 15.3262 + 26.5458i 0.618014 + 1.07043i
\(616\) −11.2812 19.5395i −0.454531 0.787270i
\(617\) −4.85410 8.40755i −0.195419 0.338475i 0.751619 0.659598i \(-0.229273\pi\)
−0.947038 + 0.321122i \(0.895940\pi\)
\(618\) −16.4164 −0.660365
\(619\) 15.1353 + 26.2150i 0.608337 + 1.05367i 0.991514 + 0.129996i \(0.0414965\pi\)
−0.383177 + 0.923675i \(0.625170\pi\)
\(620\) 0 0
\(621\) 4.89919 8.48564i 0.196598 0.340517i
\(622\) −5.69756 + 9.86846i −0.228451 + 0.395689i
\(623\) 7.85410 0.314668
\(624\) −11.3820 −0.455643
\(625\) −2.20820 + 3.82472i −0.0883282 + 0.152989i
\(626\) 2.50658 4.34152i 0.100183 0.173522i
\(627\) 5.85410 + 10.1396i 0.233790 + 0.404937i
\(628\) −4.77051 8.26277i −0.190364 0.329720i
\(629\) −29.5623 −1.17873
\(630\) −3.85410 6.67550i −0.153551 0.265958i
\(631\) 13.5451 + 23.4608i 0.539221 + 0.933959i 0.998946 + 0.0458973i \(0.0146147\pi\)
−0.459725 + 0.888061i \(0.652052\pi\)
\(632\) 1.01722 + 1.76188i 0.0404629 + 0.0700838i
\(633\) −12.0902 + 20.9408i −0.480541 + 0.832322i
\(634\) −12.7214 −0.505230
\(635\) 9.05573 15.6850i 0.359366 0.622439i
\(636\) 3.35410 + 5.80948i 0.132999 + 0.230361i
\(637\) 15.1246 0.599259
\(638\) −2.07295 3.59045i −0.0820688 0.142147i
\(639\) 20.8090 36.0423i 0.823192 1.42581i
\(640\) −6.23607 + 10.8012i −0.246502 + 0.426954i
\(641\) 10.8197 0.427351 0.213675 0.976905i \(-0.431457\pi\)
0.213675 + 0.976905i \(0.431457\pi\)
\(642\) −3.76393 + 6.51932i −0.148551 + 0.257297i
\(643\) 9.43769 0.372186 0.186093 0.982532i \(-0.440417\pi\)
0.186093 + 0.982532i \(0.440417\pi\)
\(644\) 34.4164 1.35620
\(645\) −12.9443 16.8151i −0.509680 0.662094i
\(646\) 2.87539 0.113131
\(647\) −21.6738 −0.852084 −0.426042 0.904703i \(-0.640092\pi\)
−0.426042 + 0.904703i \(0.640092\pi\)
\(648\) 4.20163 7.27743i 0.165055 0.285884i
\(649\) −18.4164 −0.722907
\(650\) −0.916408 + 1.58726i −0.0359445 + 0.0622577i
\(651\) 0 0
\(652\) 12.9787 + 22.4798i 0.508286 + 0.880377i
\(653\) −32.8885 −1.28703 −0.643514 0.765434i \(-0.722524\pi\)
−0.643514 + 0.765434i \(0.722524\pi\)
\(654\) 6.92705 + 11.9980i 0.270869 + 0.469159i
\(655\) −6.14590 + 10.6450i −0.240140 + 0.415935i
\(656\) 29.7984 1.16343
\(657\) −3.57295 + 6.18853i −0.139394 + 0.241438i
\(658\) −0.927051 1.60570i −0.0361402 0.0625967i
\(659\) 14.6803 + 25.4271i 0.571865 + 0.990499i 0.996375 + 0.0850756i \(0.0271132\pi\)
−0.424510 + 0.905423i \(0.639553\pi\)
\(660\) 10.8541 + 18.7999i 0.422495 + 0.731783i
\(661\) −43.3951 −1.68787 −0.843937 0.536442i \(-0.819768\pi\)
−0.843937 + 0.536442i \(0.819768\pi\)
\(662\) −1.04508 1.81014i −0.0406184 0.0703531i
\(663\) 11.0172 + 19.0824i 0.427873 + 0.741098i
\(664\) −11.8024 + 20.4424i −0.458023 + 0.793320i
\(665\) −3.23607 + 5.60503i −0.125489 + 0.217354i
\(666\) 7.14590 0.276898
\(667\) 13.1459 0.509011
\(668\) 13.1976 22.8588i 0.510629 0.884435i
\(669\) 3.61803 6.26662i 0.139881 0.242281i
\(670\) −0.909830 1.57587i −0.0351498 0.0608812i
\(671\) 5.16312 + 8.94278i 0.199320 + 0.345232i
\(672\) −45.9787 −1.77367
\(673\) −6.91641 11.9796i −0.266608 0.461778i 0.701376 0.712792i \(-0.252570\pi\)
−0.967984 + 0.251013i \(0.919236\pi\)
\(674\) 5.34752 + 9.26218i 0.205979 + 0.356766i
\(675\) −3.88197 6.72376i −0.149417 0.258798i
\(676\) −10.2812 + 17.8075i −0.395429 + 0.684903i
\(677\) −31.7639 −1.22079 −0.610394 0.792098i \(-0.708989\pi\)
−0.610394 + 0.792098i \(0.708989\pi\)
\(678\) 7.80902 13.5256i 0.299903 0.519448i
\(679\) −19.5623 33.8829i −0.750732 1.30031i
\(680\) 11.0820 0.424977
\(681\) −1.92705 3.33775i −0.0738448 0.127903i
\(682\) 0 0
\(683\) 5.56231 9.63420i 0.212836 0.368642i −0.739765 0.672865i \(-0.765063\pi\)
0.952601 + 0.304223i \(0.0983968\pi\)
\(684\) 8.83282 0.337731
\(685\) −2.29180 + 3.96951i −0.0875650 + 0.151667i
\(686\) 6.38197 0.243665
\(687\) 6.00000 0.228914
\(688\) −20.4483 + 2.72443i −0.779586 + 0.103868i
\(689\) −1.90983 −0.0727587
\(690\) 5.41641 0.206199
\(691\) −7.86475 + 13.6221i −0.299189 + 0.518211i −0.975951 0.217992i \(-0.930049\pi\)
0.676762 + 0.736202i \(0.263383\pi\)
\(692\) 6.97871 0.265291
\(693\) −29.5344 + 51.1552i −1.12192 + 1.94322i
\(694\) 1.92705 3.33775i 0.0731499 0.126699i
\(695\) 3.27051 + 5.66469i 0.124058 + 0.214874i
\(696\) −11.5623 −0.438268
\(697\) −28.8435 49.9583i −1.09252 1.89231i
\(698\) 3.95492 6.85011i 0.149696 0.259281i
\(699\) −47.2148 −1.78583
\(700\) 13.6353 23.6170i 0.515364 0.892637i
\(701\) 7.25329 + 12.5631i 0.273953 + 0.474500i 0.969870 0.243621i \(-0.0783354\pi\)
−0.695917 + 0.718122i \(0.745002\pi\)
\(702\) −0.590170 1.02220i −0.0222745 0.0385806i
\(703\) −3.00000 5.19615i −0.113147 0.195977i
\(704\) 17.0344 0.642010
\(705\) 1.85410 + 3.21140i 0.0698295 + 0.120948i
\(706\) −3.29180 5.70156i −0.123888 0.214581i
\(707\) 7.97214 13.8081i 0.299823 0.519309i
\(708\) −12.3541 + 21.3979i −0.464296 + 0.804184i
\(709\) 28.8885 1.08493 0.542466 0.840078i \(-0.317491\pi\)
0.542466 + 0.840078i \(0.317491\pi\)
\(710\) 5.09830 0.191336
\(711\) 2.66312 4.61266i 0.0998748 0.172988i
\(712\) 1.36475 2.36381i 0.0511460 0.0885874i
\(713\) 0 0
\(714\) 12.8992 + 22.3420i 0.482740 + 0.836130i
\(715\) −6.18034 −0.231132
\(716\) 8.94834 + 15.4990i 0.334415 + 0.579224i
\(717\) −10.8541 18.7999i −0.405354 0.702093i
\(718\) −1.02129 1.76892i −0.0381141 0.0660155i
\(719\) 5.39919 9.35167i 0.201356 0.348758i −0.747610 0.664138i \(-0.768799\pi\)
0.948965 + 0.315380i \(0.102132\pi\)
\(720\) 14.9868 0.558527
\(721\) −34.7705 + 60.2243i −1.29492 + 2.24287i
\(722\) −3.33688 5.77965i −0.124186 0.215096i
\(723\) −11.1803 −0.415801
\(724\) −17.9681 31.1216i −0.667778 1.15663i
\(725\) 5.20820 9.02087i 0.193428 0.335027i
\(726\) −1.04508 + 1.81014i −0.0387867 + 0.0671806i
\(727\) −17.9787 −0.666794 −0.333397 0.942787i \(-0.608195\pi\)
−0.333397 + 0.942787i \(0.608195\pi\)
\(728\) 4.30902 7.46344i 0.159703 0.276613i
\(729\) −39.5623 −1.46527
\(730\) −0.875388 −0.0323996
\(731\) 24.3607 + 31.6455i 0.901012 + 1.17045i
\(732\) 13.8541 0.512062
\(733\) 24.5410 0.906443 0.453222 0.891398i \(-0.350275\pi\)
0.453222 + 0.891398i \(0.350275\pi\)
\(734\) 3.66312 6.34471i 0.135208 0.234187i
\(735\) −35.4164 −1.30635
\(736\) 9.08359 15.7332i 0.334826 0.579935i
\(737\) −6.97214 + 12.0761i −0.256822 + 0.444829i
\(738\) 6.97214 + 12.0761i 0.256648 + 0.444527i
\(739\) 49.5410 1.82240 0.911198 0.411969i \(-0.135159\pi\)
0.911198 + 0.411969i \(0.135159\pi\)
\(740\) −5.56231 9.63420i −0.204474 0.354160i
\(741\) −2.23607 + 3.87298i −0.0821440 + 0.142278i
\(742\) −2.23607 −0.0820886
\(743\) −16.6803 + 28.8912i −0.611942 + 1.05992i 0.378970 + 0.925409i \(0.376278\pi\)
−0.990913 + 0.134506i \(0.957055\pi\)
\(744\) 0 0
\(745\) −5.56231 9.63420i −0.203787 0.352970i
\(746\) 1.14590 + 1.98475i 0.0419543 + 0.0726670i
\(747\) 61.7984 2.26108
\(748\) −20.4271 35.3807i −0.746887 1.29365i
\(749\) 15.9443 + 27.6163i 0.582591 + 1.00908i
\(750\) 5.23607 9.06914i 0.191194 0.331158i
\(751\) 18.9894 32.8905i 0.692931 1.20019i −0.277942 0.960598i \(-0.589652\pi\)
0.970873 0.239595i \(-0.0770145\pi\)
\(752\) 3.60488 0.131456
\(753\) 76.3951 2.78399
\(754\) 0.791796 1.37143i 0.0288355 0.0499446i
\(755\) 5.47214 9.47802i 0.199151 0.344940i
\(756\) 8.78115 + 15.2094i 0.319367 + 0.553161i
\(757\) 15.4894 + 26.8284i 0.562970 + 0.975093i 0.997235 + 0.0743080i \(0.0236748\pi\)
−0.434265 + 0.900785i \(0.642992\pi\)
\(758\) 10.4508 0.379592
\(759\) −20.7533 35.9458i −0.753297 1.30475i
\(760\) 1.12461 + 1.94788i 0.0407940 + 0.0706572i
\(761\) −0.545085 0.944115i −0.0197593 0.0342241i 0.855977 0.517014i \(-0.172957\pi\)
−0.875736 + 0.482790i \(0.839623\pi\)
\(762\) 7.32624 12.6894i 0.265402 0.459689i
\(763\) 58.6869 2.12461
\(764\) −13.4681 + 23.3274i −0.487258 + 0.843955i
\(765\) −14.5066 25.1261i −0.524486 0.908437i
\(766\) −14.5623 −0.526157
\(767\) −3.51722 6.09201i −0.126999 0.219970i
\(768\) 7.28115 12.6113i 0.262736 0.455072i
\(769\) −9.94427 + 17.2240i −0.358600 + 0.621113i −0.987727 0.156189i \(-0.950079\pi\)
0.629128 + 0.777302i \(0.283412\pi\)
\(770\) −7.23607 −0.260770
\(771\) 4.50000 7.79423i 0.162064 0.280702i
\(772\) −5.02129 −0.180720
\(773\) 15.5967 0.560976 0.280488 0.959858i \(-0.409504\pi\)
0.280488 + 0.959858i \(0.409504\pi\)
\(774\) −5.88854 7.64944i −0.211659 0.274954i
\(775\) 0 0
\(776\) −13.5967 −0.488095
\(777\) 26.9164 46.6206i 0.965621 1.67250i
\(778\) 13.3951 0.480238
\(779\) 5.85410 10.1396i 0.209745 0.363289i
\(780\) −4.14590 + 7.18091i −0.148447 + 0.257118i
\(781\) −19.5344 33.8346i −0.698997 1.21070i
\(782\) −10.1935 −0.364519
\(783\) 3.35410 + 5.80948i 0.119866 + 0.207614i
\(784\) −17.2148 + 29.8169i