Properties

Label 177.2.d.c.176.1
Level $177$
Weight $2$
Character 177.176
Analytic conductor $1.413$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.19298288.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + 9 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.1
Root \(1.34067 + 1.09664i\) of defining polynomial
Character \(\chi\) \(=\) 177.176
Dual form 177.2.d.c.176.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.93543 q^{2} +(-1.34067 - 1.09664i) q^{3} +1.74590 q^{4} -3.21911i q^{5} +(2.59477 + 2.12247i) q^{6} +0.254102 q^{7} +0.491797 q^{8} +(0.594767 + 2.94045i) q^{9} +O(q^{10})\) \(q-1.93543 q^{2} +(-1.34067 - 1.09664i) q^{3} +1.74590 q^{4} -3.21911i q^{5} +(2.59477 + 2.12247i) q^{6} +0.254102 q^{7} +0.491797 q^{8} +(0.594767 + 2.94045i) q^{9} +6.23037i q^{10} -5.68133 q^{11} +(-2.34067 - 1.91462i) q^{12} -2.66179i q^{13} -0.491797 q^{14} +(-3.53020 + 4.31575i) q^{15} -4.44364 q^{16} +4.03709i q^{17} +(-1.15113 - 5.69104i) q^{18} -2.44364 q^{19} -5.62024i q^{20} +(-0.340665 - 0.278658i) q^{21} +10.9958 q^{22} -3.25410 q^{23} +(-0.659335 - 0.539323i) q^{24} -5.36266 q^{25} +5.15172i q^{26} +(2.42723 - 4.59441i) q^{27} +0.443636 q^{28} +3.56857i q^{29} +(6.83246 - 8.35284i) q^{30} +7.81351i q^{31} +7.61676 q^{32} +(7.61676 + 6.23037i) q^{33} -7.81351i q^{34} -0.817981i q^{35} +(1.03840 + 5.13373i) q^{36} -5.15172i q^{37} +4.72949 q^{38} +(-2.91903 + 3.56857i) q^{39} -1.58315i q^{40} -7.25620i q^{41} +(0.659335 + 0.539323i) q^{42} -9.79894i q^{43} -9.91903 q^{44} +(9.46563 - 1.91462i) q^{45} +6.29809 q^{46} +5.06457 q^{47} +(5.95743 + 4.87306i) q^{48} -6.93543 q^{49} +10.3791 q^{50} +(4.42723 - 5.41239i) q^{51} -4.64722i q^{52} +1.16745i q^{53} +(-4.69774 + 8.89216i) q^{54} +18.2888i q^{55} +0.124966 q^{56} +(3.27610 + 2.67979i) q^{57} -6.90673i q^{58} +(-7.12497 + 2.86964i) q^{59} +(-6.16337 + 7.53486i) q^{60} +0.676366i q^{61} -15.1225i q^{62} +(0.151131 + 0.747174i) q^{63} -5.85446 q^{64} -8.56860 q^{65} +(-14.7417 - 12.0585i) q^{66} +2.66179i q^{67} +7.04835i q^{68} +(4.36266 + 3.56857i) q^{69} +1.58315i q^{70} -16.2372i q^{71} +(0.292504 + 1.44610i) q^{72} -13.1371i q^{73} +9.97081i q^{74} +(7.18953 + 5.88090i) q^{75} -4.26634 q^{76} -1.44364 q^{77} +(5.64958 - 6.90673i) q^{78} -11.7253 q^{79} +14.3045i q^{80} +(-8.29250 + 3.49777i) q^{81} +14.0439i q^{82} -9.91903 q^{83} +(-0.594767 - 0.486508i) q^{84} +12.9958 q^{85} +18.9652i q^{86} +(3.91344 - 4.78426i) q^{87} -2.79406 q^{88} +7.95184 q^{89} +(-18.3201 + 3.70562i) q^{90} -0.676366i q^{91} -5.68133 q^{92} +(8.56860 - 10.4753i) q^{93} -9.80213 q^{94} +7.86633i q^{95} +(-10.2115 - 8.35284i) q^{96} -4.47535i q^{97} +13.4231 q^{98} +(-3.37907 - 16.7057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{2} - q^{3} + 12q^{4} + 7q^{6} + 6q^{8} - 5q^{9} + O(q^{10}) \) \( 6q + 4q^{2} - q^{3} + 12q^{4} + 7q^{6} + 6q^{8} - 5q^{9} - 20q^{11} - 7q^{12} - 6q^{14} + 3q^{15} - 8q^{16} - 17q^{18} + 4q^{19} + 5q^{21} + 2q^{22} - 18q^{23} - 11q^{24} - 4q^{25} + 2q^{27} - 16q^{28} + 37q^{30} + 16q^{32} + 16q^{33} - 21q^{36} + 36q^{38} - 8q^{39} + 11q^{42} - 50q^{44} + 17q^{45} - 6q^{46} + 46q^{47} - q^{48} - 26q^{49} + 28q^{50} + 14q^{51} - 8q^{54} - 32q^{56} - 3q^{57} - 10q^{59} + 23q^{60} + 11q^{63} - 10q^{64} - 26q^{66} - 2q^{69} - 27q^{72} + 26q^{75} + 46q^{76} + 10q^{77} - 8q^{78} - 14q^{79} - 21q^{81} - 50q^{83} + 5q^{84} + 14q^{85} + 29q^{87} - 40q^{88} + 26q^{89} - 45q^{90} - 20q^{92} + 52q^{94} - 23q^{96} + 4q^{98} + 14q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93543 −1.36856 −0.684279 0.729221i \(-0.739883\pi\)
−0.684279 + 0.729221i \(0.739883\pi\)
\(3\) −1.34067 1.09664i −0.774033 0.633145i
\(4\) 1.74590 0.872949
\(5\) 3.21911i 1.43963i −0.694166 0.719815i \(-0.744227\pi\)
0.694166 0.719815i \(-0.255773\pi\)
\(6\) 2.59477 + 2.12247i 1.05931 + 0.866495i
\(7\) 0.254102 0.0960414 0.0480207 0.998846i \(-0.484709\pi\)
0.0480207 + 0.998846i \(0.484709\pi\)
\(8\) 0.491797 0.173876
\(9\) 0.594767 + 2.94045i 0.198256 + 0.980150i
\(10\) 6.23037i 1.97022i
\(11\) −5.68133 −1.71299 −0.856493 0.516159i \(-0.827361\pi\)
−0.856493 + 0.516159i \(0.827361\pi\)
\(12\) −2.34067 1.91462i −0.675692 0.552703i
\(13\) 2.66179i 0.738249i −0.929380 0.369124i \(-0.879658\pi\)
0.929380 0.369124i \(-0.120342\pi\)
\(14\) −0.491797 −0.131438
\(15\) −3.53020 + 4.31575i −0.911494 + 1.11432i
\(16\) −4.44364 −1.11091
\(17\) 4.03709i 0.979138i 0.871965 + 0.489569i \(0.162846\pi\)
−0.871965 + 0.489569i \(0.837154\pi\)
\(18\) −1.15113 5.69104i −0.271324 1.34139i
\(19\) −2.44364 −0.560608 −0.280304 0.959911i \(-0.590435\pi\)
−0.280304 + 0.959911i \(0.590435\pi\)
\(20\) 5.62024i 1.25672i
\(21\) −0.340665 0.278658i −0.0743393 0.0608081i
\(22\) 10.9958 2.34432
\(23\) −3.25410 −0.678527 −0.339264 0.940691i \(-0.610178\pi\)
−0.339264 + 0.940691i \(0.610178\pi\)
\(24\) −0.659335 0.539323i −0.134586 0.110089i
\(25\) −5.36266 −1.07253
\(26\) 5.15172i 1.01034i
\(27\) 2.42723 4.59441i 0.467120 0.884194i
\(28\) 0.443636 0.0838393
\(29\) 3.56857i 0.662668i 0.943514 + 0.331334i \(0.107499\pi\)
−0.943514 + 0.331334i \(0.892501\pi\)
\(30\) 6.83246 8.35284i 1.24743 1.52501i
\(31\) 7.81351i 1.40335i 0.712498 + 0.701674i \(0.247564\pi\)
−0.712498 + 0.701674i \(0.752436\pi\)
\(32\) 7.61676 1.34647
\(33\) 7.61676 + 6.23037i 1.32591 + 1.08457i
\(34\) 7.81351i 1.34001i
\(35\) 0.817981i 0.138264i
\(36\) 1.03840 + 5.13373i 0.173067 + 0.855621i
\(37\) 5.15172i 0.846938i −0.905911 0.423469i \(-0.860812\pi\)
0.905911 0.423469i \(-0.139188\pi\)
\(38\) 4.72949 0.767225
\(39\) −2.91903 + 3.56857i −0.467418 + 0.571429i
\(40\) 1.58315i 0.250317i
\(41\) 7.25620i 1.13323i −0.823983 0.566614i \(-0.808253\pi\)
0.823983 0.566614i \(-0.191747\pi\)
\(42\) 0.659335 + 0.539323i 0.101738 + 0.0832194i
\(43\) 9.79894i 1.49432i −0.664642 0.747162i \(-0.731416\pi\)
0.664642 0.747162i \(-0.268584\pi\)
\(44\) −9.91903 −1.49535
\(45\) 9.46563 1.91462i 1.41105 0.285415i
\(46\) 6.29809 0.928603
\(47\) 5.06457 0.738743 0.369372 0.929282i \(-0.379573\pi\)
0.369372 + 0.929282i \(0.379573\pi\)
\(48\) 5.95743 + 4.87306i 0.859881 + 0.703366i
\(49\) −6.93543 −0.990776
\(50\) 10.3791 1.46782
\(51\) 4.42723 5.41239i 0.619936 0.757886i
\(52\) 4.64722i 0.644454i
\(53\) 1.16745i 0.160361i 0.996780 + 0.0801805i \(0.0255497\pi\)
−0.996780 + 0.0801805i \(0.974450\pi\)
\(54\) −4.69774 + 8.89216i −0.639281 + 1.21007i
\(55\) 18.2888i 2.46606i
\(56\) 0.124966 0.0166993
\(57\) 3.27610 + 2.67979i 0.433930 + 0.354946i
\(58\) 6.90673i 0.906899i
\(59\) −7.12497 + 2.86964i −0.927592 + 0.373596i
\(60\) −6.16337 + 7.53486i −0.795688 + 0.972746i
\(61\) 0.676366i 0.0865998i 0.999062 + 0.0432999i \(0.0137871\pi\)
−0.999062 + 0.0432999i \(0.986213\pi\)
\(62\) 15.1225i 1.92056i
\(63\) 0.151131 + 0.747174i 0.0190408 + 0.0941350i
\(64\) −5.85446 −0.731807
\(65\) −8.56860 −1.06280
\(66\) −14.7417 12.0585i −1.81458 1.48429i
\(67\) 2.66179i 0.325190i 0.986693 + 0.162595i \(0.0519864\pi\)
−0.986693 + 0.162595i \(0.948014\pi\)
\(68\) 7.04835i 0.854738i
\(69\) 4.36266 + 3.56857i 0.525203 + 0.429606i
\(70\) 1.58315i 0.189222i
\(71\) 16.2372i 1.92700i −0.267715 0.963498i \(-0.586269\pi\)
0.267715 0.963498i \(-0.413731\pi\)
\(72\) 0.292504 + 1.44610i 0.0344720 + 0.170425i
\(73\) 13.1371i 1.53758i −0.639501 0.768791i \(-0.720859\pi\)
0.639501 0.768791i \(-0.279141\pi\)
\(74\) 9.97081i 1.15908i
\(75\) 7.18953 + 5.88090i 0.830176 + 0.679068i
\(76\) −4.26634 −0.489383
\(77\) −1.44364 −0.164518
\(78\) 5.64958 6.90673i 0.639689 0.782034i
\(79\) −11.7253 −1.31920 −0.659601 0.751616i \(-0.729275\pi\)
−0.659601 + 0.751616i \(0.729275\pi\)
\(80\) 14.3045i 1.59930i
\(81\) −8.29250 + 3.49777i −0.921389 + 0.388641i
\(82\) 14.0439i 1.55089i
\(83\) −9.91903 −1.08875 −0.544377 0.838841i \(-0.683234\pi\)
−0.544377 + 0.838841i \(0.683234\pi\)
\(84\) −0.594767 0.486508i −0.0648944 0.0530824i
\(85\) 12.9958 1.40960
\(86\) 18.9652i 2.04507i
\(87\) 3.91344 4.78426i 0.419564 0.512927i
\(88\) −2.79406 −0.297848
\(89\) 7.95184 0.842893 0.421447 0.906853i \(-0.361522\pi\)
0.421447 + 0.906853i \(0.361522\pi\)
\(90\) −18.3201 + 3.70562i −1.93111 + 0.390606i
\(91\) 0.676366i 0.0709024i
\(92\) −5.68133 −0.592320
\(93\) 8.56860 10.4753i 0.888523 1.08624i
\(94\) −9.80213 −1.01101
\(95\) 7.86633i 0.807068i
\(96\) −10.2115 8.35284i −1.04221 0.852508i
\(97\) 4.47535i 0.454403i −0.973848 0.227202i \(-0.927042\pi\)
0.973848 0.227202i \(-0.0729577\pi\)
\(98\) 13.4231 1.35593
\(99\) −3.37907 16.7057i −0.339609 1.67898i
\(100\) −9.36266 −0.936266
\(101\) 4.85446 0.483037 0.241518 0.970396i \(-0.422355\pi\)
0.241518 + 0.970396i \(0.422355\pi\)
\(102\) −8.56860 + 10.4753i −0.848418 + 1.03721i
\(103\) 12.4607i 1.22779i 0.789387 + 0.613896i \(0.210399\pi\)
−0.789387 + 0.613896i \(0.789601\pi\)
\(104\) 1.30906i 0.128364i
\(105\) −0.897030 + 1.09664i −0.0875411 + 0.107021i
\(106\) 2.25951i 0.219463i
\(107\) 9.91799i 0.958808i −0.877594 0.479404i \(-0.840853\pi\)
0.877594 0.479404i \(-0.159147\pi\)
\(108\) 4.23769 8.02136i 0.407772 0.771856i
\(109\) 3.33816i 0.319738i −0.987138 0.159869i \(-0.948893\pi\)
0.987138 0.159869i \(-0.0511071\pi\)
\(110\) 35.3968i 3.37495i
\(111\) −5.64958 + 6.90673i −0.536234 + 0.655558i
\(112\) −1.12914 −0.106693
\(113\) 4.69774 0.441926 0.220963 0.975282i \(-0.429080\pi\)
0.220963 + 0.975282i \(0.429080\pi\)
\(114\) −6.34067 5.18654i −0.593858 0.485764i
\(115\) 10.4753i 0.976827i
\(116\) 6.23037i 0.578475i
\(117\) 7.82687 1.58315i 0.723595 0.146362i
\(118\) 13.7899 5.55400i 1.26946 0.511287i
\(119\) 1.02583i 0.0940378i
\(120\) −1.73614 + 2.12247i −0.158487 + 0.193754i
\(121\) 21.2775 1.93432
\(122\) 1.30906i 0.118517i
\(123\) −7.95743 + 9.72813i −0.717497 + 0.877156i
\(124\) 13.6416i 1.22505i
\(125\) 1.16745i 0.104420i
\(126\) −0.292504 1.44610i −0.0260584 0.128829i
\(127\) 2.62093 0.232570 0.116285 0.993216i \(-0.462901\pi\)
0.116285 + 0.993216i \(0.462901\pi\)
\(128\) −3.90262 −0.344946
\(129\) −10.7459 + 13.1371i −0.946124 + 1.15666i
\(130\) 16.5839 1.45451
\(131\) 16.8873 1.47545 0.737724 0.675103i \(-0.235901\pi\)
0.737724 + 0.675103i \(0.235901\pi\)
\(132\) 13.2981 + 10.8776i 1.15745 + 0.946772i
\(133\) −0.620932 −0.0538416
\(134\) 5.15172i 0.445041i
\(135\) −14.7899 7.81351i −1.27291 0.672480i
\(136\) 1.98543i 0.170249i
\(137\) 0.646115i 0.0552013i 0.999619 + 0.0276007i \(0.00878668\pi\)
−0.999619 + 0.0276007i \(0.991213\pi\)
\(138\) −8.44364 6.90673i −0.718770 0.587940i
\(139\) −12.5358 −1.06327 −0.531636 0.846973i \(-0.678422\pi\)
−0.531636 + 0.846973i \(0.678422\pi\)
\(140\) 1.42811i 0.120697i
\(141\) −6.78989 5.55400i −0.571812 0.467731i
\(142\) 31.4259i 2.63720i
\(143\) 15.1225i 1.26461i
\(144\) −2.64293 13.0663i −0.220244 1.08886i
\(145\) 11.4876 0.953996
\(146\) 25.4260i 2.10427i
\(147\) 9.29809 + 7.60566i 0.766894 + 0.627305i
\(148\) 8.99438i 0.739334i
\(149\) 6.45481 0.528799 0.264399 0.964413i \(-0.414826\pi\)
0.264399 + 0.964413i \(0.414826\pi\)
\(150\) −13.9149 11.3821i −1.13614 0.929344i
\(151\) 13.1371i 1.06908i −0.845143 0.534541i \(-0.820484\pi\)
0.845143 0.534541i \(-0.179516\pi\)
\(152\) −1.20177 −0.0974766
\(153\) −11.8709 + 2.40113i −0.959703 + 0.194120i
\(154\) 2.79406 0.225152
\(155\) 25.1526 2.02030
\(156\) −5.09632 + 6.23037i −0.408032 + 0.498829i
\(157\) 11.1517i 0.890000i −0.895530 0.445000i \(-0.853204\pi\)
0.895530 0.445000i \(-0.146796\pi\)
\(158\) 22.6936 1.80540
\(159\) 1.28027 1.56515i 0.101532 0.124125i
\(160\) 24.5192i 1.93841i
\(161\) −0.826873 −0.0651667
\(162\) 16.0496 6.76969i 1.26097 0.531877i
\(163\) 7.66075 0.600037 0.300018 0.953933i \(-0.403007\pi\)
0.300018 + 0.953933i \(0.403007\pi\)
\(164\) 12.6686i 0.989250i
\(165\) 20.0562 24.5192i 1.56138 1.90882i
\(166\) 19.1976 1.49002
\(167\) 12.5798i 0.973453i 0.873554 + 0.486726i \(0.161809\pi\)
−0.873554 + 0.486726i \(0.838191\pi\)
\(168\) −0.167538 0.137043i −0.0129258 0.0105731i
\(169\) 5.91486 0.454989
\(170\) −25.1526 −1.92911
\(171\) −1.45339 7.18539i −0.111144 0.549481i
\(172\) 17.1080i 1.30447i
\(173\) −23.1854 −1.76275 −0.881375 0.472417i \(-0.843382\pi\)
−0.881375 + 0.472417i \(0.843382\pi\)
\(174\) −7.57419 + 9.25962i −0.574198 + 0.701970i
\(175\) −1.36266 −0.103008
\(176\) 25.2458 1.90297
\(177\) 12.6992 + 3.96628i 0.954527 + 0.298124i
\(178\) −15.3902 −1.15355
\(179\) −14.8269 −1.10821 −0.554106 0.832446i \(-0.686940\pi\)
−0.554106 + 0.832446i \(0.686940\pi\)
\(180\) 16.5260 3.34273i 1.23178 0.249152i
\(181\) −2.76231 −0.205321 −0.102660 0.994716i \(-0.532735\pi\)
−0.102660 + 0.994716i \(0.532735\pi\)
\(182\) 1.30906i 0.0970341i
\(183\) 0.741729 0.906781i 0.0548302 0.0670312i
\(184\) −1.60036 −0.117980
\(185\) −16.5839 −1.21928
\(186\) −16.5839 + 20.2742i −1.21599 + 1.48658i
\(187\) 22.9360i 1.67725i
\(188\) 8.84222 0.644885
\(189\) 0.616763 1.16745i 0.0448629 0.0849192i
\(190\) 15.2247i 1.10452i
\(191\) 4.69774 0.339916 0.169958 0.985451i \(-0.445637\pi\)
0.169958 + 0.985451i \(0.445637\pi\)
\(192\) 7.84887 + 6.42023i 0.566443 + 0.463340i
\(193\) −13.5686 −0.976689 −0.488345 0.872651i \(-0.662399\pi\)
−0.488345 + 0.872651i \(0.662399\pi\)
\(194\) 8.66175i 0.621877i
\(195\) 11.4876 + 9.39666i 0.822646 + 0.672909i
\(196\) −12.1086 −0.864897
\(197\) 4.62466i 0.329493i −0.986336 0.164747i \(-0.947319\pi\)
0.986336 0.164747i \(-0.0526806\pi\)
\(198\) 6.53996 + 32.3327i 0.464775 + 2.29779i
\(199\) 10.2541 0.726894 0.363447 0.931615i \(-0.381600\pi\)
0.363447 + 0.931615i \(0.381600\pi\)
\(200\) −2.63734 −0.186488
\(201\) 2.91903 3.56857i 0.205892 0.251708i
\(202\) −9.39547 −0.661063
\(203\) 0.906781i 0.0636435i
\(204\) 7.72949 9.44948i 0.541173 0.661596i
\(205\) −23.3585 −1.63143
\(206\) 24.1169i 1.68030i
\(207\) −1.93543 9.56853i −0.134522 0.665059i
\(208\) 11.8280i 0.820127i
\(209\) 13.8831 0.960314
\(210\) 1.73614 2.12247i 0.119805 0.146464i
\(211\) 9.12257i 0.628024i 0.949419 + 0.314012i \(0.101673\pi\)
−0.949419 + 0.314012i \(0.898327\pi\)
\(212\) 2.03824i 0.139987i
\(213\) −17.8063 + 21.7686i −1.22007 + 1.49156i
\(214\) 19.1956i 1.31218i
\(215\) −31.5439 −2.15127
\(216\) 1.19370 2.25951i 0.0812212 0.153740i
\(217\) 1.98543i 0.134780i
\(218\) 6.46078i 0.437579i
\(219\) −14.4067 + 17.6125i −0.973511 + 1.19014i
\(220\) 31.9304i 2.15275i
\(221\) 10.7459 0.722847
\(222\) 10.9344 13.3675i 0.733867 0.897169i
\(223\) −11.2663 −0.754450 −0.377225 0.926122i \(-0.623122\pi\)
−0.377225 + 0.926122i \(0.623122\pi\)
\(224\) 1.93543 0.129317
\(225\) −3.18953 15.7686i −0.212636 1.05124i
\(226\) −9.09215 −0.604801
\(227\) 1.28692 0.0854156 0.0427078 0.999088i \(-0.486402\pi\)
0.0427078 + 0.999088i \(0.486402\pi\)
\(228\) 5.71973 + 4.67863i 0.378799 + 0.309850i
\(229\) 26.9506i 1.78094i 0.455038 + 0.890472i \(0.349626\pi\)
−0.455038 + 0.890472i \(0.650374\pi\)
\(230\) 20.2742i 1.33684i
\(231\) 1.93543 + 1.58315i 0.127342 + 0.104163i
\(232\) 1.75501i 0.115222i
\(233\) −5.52461 −0.361929 −0.180965 0.983490i \(-0.557922\pi\)
−0.180965 + 0.983490i \(0.557922\pi\)
\(234\) −15.1484 + 3.06407i −0.990281 + 0.200305i
\(235\) 16.3034i 1.06352i
\(236\) −12.4395 + 5.01011i −0.809740 + 0.326130i
\(237\) 15.7197 + 12.8584i 1.02111 + 0.835246i
\(238\) 1.98543i 0.128696i
\(239\) 14.7428i 0.953633i −0.879003 0.476817i \(-0.841791\pi\)
0.879003 0.476817i \(-0.158209\pi\)
\(240\) 15.6869 19.1776i 1.01259 1.23791i
\(241\) 0.777652 0.0500930 0.0250465 0.999686i \(-0.492027\pi\)
0.0250465 + 0.999686i \(0.492027\pi\)
\(242\) −41.1812 −2.64723
\(243\) 14.9533 + 4.40455i 0.959252 + 0.282552i
\(244\) 1.18087i 0.0755972i
\(245\) 22.3259i 1.42635i
\(246\) 15.4011 18.8281i 0.981936 1.20044i
\(247\) 6.50445i 0.413868i
\(248\) 3.84266i 0.244009i
\(249\) 13.2981 + 10.8776i 0.842732 + 0.689339i
\(250\) 2.25951i 0.142904i
\(251\) 13.5226i 0.853536i 0.904361 + 0.426768i \(0.140348\pi\)
−0.904361 + 0.426768i \(0.859652\pi\)
\(252\) 0.263860 + 1.30449i 0.0166216 + 0.0821751i
\(253\) 18.4876 1.16231
\(254\) −5.07264 −0.318286
\(255\) −17.4231 14.2517i −1.09107 0.892478i
\(256\) 19.2622 1.20389
\(257\) 17.1214i 1.06800i −0.845484 0.534001i \(-0.820688\pi\)
0.845484 0.534001i \(-0.179312\pi\)
\(258\) 20.7980 25.4260i 1.29482 1.58295i
\(259\) 1.30906i 0.0813411i
\(260\) −14.9599 −0.927774
\(261\) −10.4932 + 2.12247i −0.649514 + 0.131378i
\(262\) −32.6842 −2.01923
\(263\) 26.3327i 1.62375i −0.583833 0.811873i \(-0.698448\pi\)
0.583833 0.811873i \(-0.301552\pi\)
\(264\) 3.74590 + 3.06407i 0.230544 + 0.188581i
\(265\) 3.75814 0.230860
\(266\) 1.20177 0.0736854
\(267\) −10.6608 8.72029i −0.652428 0.533673i
\(268\) 4.64722i 0.283874i
\(269\) −15.6402 −0.953599 −0.476799 0.879012i \(-0.658203\pi\)
−0.476799 + 0.879012i \(0.658203\pi\)
\(270\) 28.6248 + 15.1225i 1.74205 + 0.920328i
\(271\) 26.2663 1.59557 0.797783 0.602944i \(-0.206006\pi\)
0.797783 + 0.602944i \(0.206006\pi\)
\(272\) 17.9394i 1.08773i
\(273\) −0.741729 + 0.906781i −0.0448915 + 0.0548809i
\(274\) 1.25051i 0.0755462i
\(275\) 30.4671 1.83723
\(276\) 7.61676 + 6.23037i 0.458475 + 0.375024i
\(277\) −19.0552 −1.14491 −0.572457 0.819935i \(-0.694010\pi\)
−0.572457 + 0.819935i \(0.694010\pi\)
\(278\) 24.2622 1.45515
\(279\) −22.9753 + 4.64722i −1.37549 + 0.278222i
\(280\) 0.402280i 0.0240408i
\(281\) 13.4338i 0.801390i 0.916211 + 0.400695i \(0.131231\pi\)
−0.916211 + 0.400695i \(0.868769\pi\)
\(282\) 13.1414 + 10.7494i 0.782557 + 0.640117i
\(283\) 18.9652i 1.12736i −0.825992 0.563682i \(-0.809384\pi\)
0.825992 0.563682i \(-0.190616\pi\)
\(284\) 28.3484i 1.68217i
\(285\) 8.62652 10.5461i 0.510991 0.624698i
\(286\) 29.2686i 1.73069i
\(287\) 1.84381i 0.108837i
\(288\) 4.53020 + 22.3967i 0.266945 + 1.31974i
\(289\) 0.701906 0.0412886
\(290\) −22.2335 −1.30560
\(291\) −4.90785 + 5.99995i −0.287703 + 0.351723i
\(292\) 22.9360i 1.34223i
\(293\) 6.40797i 0.374357i 0.982326 + 0.187179i \(0.0599343\pi\)
−0.982326 + 0.187179i \(0.940066\pi\)
\(294\) −17.9958 14.7202i −1.04954 0.858502i
\(295\) 9.23769 + 22.9360i 0.537839 + 1.33539i
\(296\) 2.53360i 0.147262i
\(297\) −13.7899 + 26.1023i −0.800171 + 1.51461i
\(298\) −12.4929 −0.723692
\(299\) 8.66175i 0.500922i
\(300\) 12.5522 + 10.2675i 0.724701 + 0.592792i
\(301\) 2.48993i 0.143517i
\(302\) 25.4260i 1.46310i
\(303\) −6.50820 5.32359i −0.373887 0.305832i
\(304\) 10.8586 0.622785
\(305\) 2.17730 0.124672
\(306\) 22.9753 4.64722i 1.31341 0.265664i
\(307\) 13.9149 0.794163 0.397081 0.917783i \(-0.370023\pi\)
0.397081 + 0.917783i \(0.370023\pi\)
\(308\) −2.52044 −0.143615
\(309\) 13.6649 16.7057i 0.777370 0.950353i
\(310\) −48.6811 −2.76490
\(311\) 1.60571i 0.0910515i −0.998963 0.0455258i \(-0.985504\pi\)
0.998963 0.0455258i \(-0.0144963\pi\)
\(312\) −1.43557 + 1.75501i −0.0812730 + 0.0993580i
\(313\) 26.1023i 1.47539i 0.675133 + 0.737696i \(0.264086\pi\)
−0.675133 + 0.737696i \(0.735914\pi\)
\(314\) 21.5833i 1.21802i
\(315\) 2.40523 0.486508i 0.135520 0.0274116i
\(316\) −20.4712 −1.15160
\(317\) 9.27761i 0.521083i −0.965463 0.260541i \(-0.916099\pi\)
0.965463 0.260541i \(-0.0839010\pi\)
\(318\) −2.47787 + 3.02925i −0.138952 + 0.169872i
\(319\) 20.2742i 1.13514i
\(320\) 18.8461i 1.05353i
\(321\) −10.8765 + 13.2967i −0.607064 + 0.742150i
\(322\) 1.60036 0.0891844
\(323\) 9.86518i 0.548913i
\(324\) −14.4779 + 6.10674i −0.804326 + 0.339264i
\(325\) 14.2743i 0.791795i
\(326\) −14.8269 −0.821185
\(327\) −3.66075 + 4.47535i −0.202440 + 0.247488i
\(328\) 3.56857i 0.197042i
\(329\) 1.28692 0.0709499
\(330\) −38.8175 + 47.4552i −2.13683 + 2.61232i
\(331\) 25.0932 1.37925 0.689624 0.724168i \(-0.257776\pi\)
0.689624 + 0.724168i \(0.257776\pi\)
\(332\) −17.3176 −0.950427
\(333\) 15.1484 3.06407i 0.830126 0.167910i
\(334\) 24.3473i 1.33223i
\(335\) 8.56860 0.468153
\(336\) 1.51379 + 1.23825i 0.0825842 + 0.0675523i
\(337\) 20.7787i 1.13189i 0.824443 + 0.565945i \(0.191489\pi\)
−0.824443 + 0.565945i \(0.808511\pi\)
\(338\) −11.4478 −0.622678
\(339\) −6.29809 5.15172i −0.342065 0.279803i
\(340\) 22.6894 1.23051
\(341\) 44.3912i 2.40392i
\(342\) 2.81295 + 13.9068i 0.152107 + 0.751996i
\(343\) −3.54102 −0.191197
\(344\) 4.81909i 0.259828i
\(345\) 11.4876 14.0439i 0.618473 0.756097i
\(346\) 44.8737 2.41243
\(347\) 1.75708 0.0943248 0.0471624 0.998887i \(-0.484982\pi\)
0.0471624 + 0.998887i \(0.484982\pi\)
\(348\) 6.83246 8.35284i 0.366258 0.447759i
\(349\) 9.79894i 0.524525i 0.964997 + 0.262263i \(0.0844687\pi\)
−0.964997 + 0.262263i \(0.915531\pi\)
\(350\) 2.63734 0.140972
\(351\) −12.2294 6.46078i −0.652755 0.344851i
\(352\) −43.2733 −2.30648
\(353\) 27.2130 1.44840 0.724200 0.689590i \(-0.242209\pi\)
0.724200 + 0.689590i \(0.242209\pi\)
\(354\) −24.5784 7.67647i −1.30633 0.408000i
\(355\) −52.2692 −2.77416
\(356\) 13.8831 0.735803
\(357\) 1.12497 1.37530i 0.0595395 0.0727884i
\(358\) 28.6964 1.51665
\(359\) 4.24494i 0.224039i 0.993706 + 0.112020i \(0.0357320\pi\)
−0.993706 + 0.112020i \(0.964268\pi\)
\(360\) 4.65517 0.941604i 0.245349 0.0496269i
\(361\) −13.0286 −0.685718
\(362\) 5.34625 0.280993
\(363\) −28.5260 23.3338i −1.49723 1.22470i
\(364\) 1.18087i 0.0618942i
\(365\) −42.2898 −2.21355
\(366\) −1.43557 + 1.75501i −0.0750383 + 0.0917360i
\(367\) 23.6124i 1.23256i −0.787528 0.616279i \(-0.788639\pi\)
0.787528 0.616279i \(-0.211361\pi\)
\(368\) 14.4600 0.753782
\(369\) 21.3365 4.31575i 1.11073 0.224669i
\(370\) 32.0971 1.66865
\(371\) 0.296650i 0.0154013i
\(372\) 14.9599 18.2888i 0.775635 0.948231i
\(373\) 21.5040 1.11344 0.556718 0.830701i \(-0.312060\pi\)
0.556718 + 0.830701i \(0.312060\pi\)
\(374\) 44.3912i 2.29541i
\(375\) 1.28027 1.56515i 0.0661127 0.0808242i
\(376\) 2.49074 0.128450
\(377\) 9.49881 0.489213
\(378\) −1.19370 + 2.25951i −0.0613975 + 0.116217i
\(379\) 14.9588 0.768384 0.384192 0.923253i \(-0.374480\pi\)
0.384192 + 0.923253i \(0.374480\pi\)
\(380\) 13.7338i 0.704530i
\(381\) −3.51379 2.87422i −0.180017 0.147251i
\(382\) −9.09215 −0.465195
\(383\) 9.38324i 0.479461i −0.970839 0.239731i \(-0.922941\pi\)
0.970839 0.239731i \(-0.0770591\pi\)
\(384\) 5.23211 + 4.27976i 0.267000 + 0.218401i
\(385\) 4.64722i 0.236844i
\(386\) 26.2611 1.33666
\(387\) 28.8133 5.82809i 1.46466 0.296258i
\(388\) 7.81351i 0.396671i
\(389\) 1.39786i 0.0708743i 0.999372 + 0.0354372i \(0.0112824\pi\)
−0.999372 + 0.0354372i \(0.988718\pi\)
\(390\) −22.2335 18.1866i −1.12584 0.920914i
\(391\) 13.1371i 0.664372i
\(392\) −3.41082 −0.172273
\(393\) −22.6402 18.5192i −1.14205 0.934172i
\(394\) 8.95071i 0.450930i
\(395\) 37.7451i 1.89916i
\(396\) −5.89951 29.1664i −0.296461 1.46567i
\(397\) 12.9652i 0.650706i −0.945593 0.325353i \(-0.894517\pi\)
0.945593 0.325353i \(-0.105483\pi\)
\(398\) −19.8461 −0.994796
\(399\) 0.832462 + 0.680938i 0.0416752 + 0.0340895i
\(400\) 23.8297 1.19149
\(401\) −19.9711 −0.997308 −0.498654 0.866801i \(-0.666172\pi\)
−0.498654 + 0.866801i \(0.666172\pi\)
\(402\) −5.64958 + 6.90673i −0.281775 + 0.344477i
\(403\) 20.7980 1.03602
\(404\) 8.47539 0.421666
\(405\) 11.2597 + 26.6945i 0.559499 + 1.32646i
\(406\) 1.75501i 0.0870998i
\(407\) 29.2686i 1.45079i
\(408\) 2.17730 2.66179i 0.107792 0.131778i
\(409\) 11.1080i 0.549255i −0.961551 0.274628i \(-0.911445\pi\)
0.961551 0.274628i \(-0.0885546\pi\)
\(410\) 45.2088 2.23270
\(411\) 0.708555 0.866224i 0.0349504 0.0427277i
\(412\) 21.7552i 1.07180i
\(413\) −1.81047 + 0.729181i −0.0890872 + 0.0358807i
\(414\) 3.74590 + 18.5192i 0.184101 + 0.910171i
\(415\) 31.9304i 1.56740i
\(416\) 20.2742i 0.994027i
\(417\) 16.8063 + 13.7472i 0.823008 + 0.673205i
\(418\) −26.8698 −1.31425
\(419\) 7.91202 0.386527 0.193264 0.981147i \(-0.438093\pi\)
0.193264 + 0.981147i \(0.438093\pi\)
\(420\) −1.56612 + 1.91462i −0.0764190 + 0.0934239i
\(421\) 29.3968i 1.43271i 0.697734 + 0.716357i \(0.254192\pi\)
−0.697734 + 0.716357i \(0.745808\pi\)
\(422\) 17.6561i 0.859487i
\(423\) 3.01224 + 14.8921i 0.146460 + 0.724079i
\(424\) 0.574146i 0.0278830i
\(425\) 21.6495i 1.05016i
\(426\) 34.4629 42.1316i 1.66973 2.04128i
\(427\) 0.171866i 0.00831717i
\(428\) 17.3158i 0.836991i
\(429\) 16.5839 20.2742i 0.800681 0.978850i
\(430\) 61.0510 2.94414
\(431\) −23.4988 −1.13190 −0.565949 0.824440i \(-0.691490\pi\)
−0.565949 + 0.824440i \(0.691490\pi\)
\(432\) −10.7857 + 20.4159i −0.518928 + 0.982259i
\(433\) −5.16896 −0.248404 −0.124202 0.992257i \(-0.539637\pi\)
−0.124202 + 0.992257i \(0.539637\pi\)
\(434\) 3.84266i 0.184454i
\(435\) −15.4011 12.5978i −0.738424 0.604017i
\(436\) 5.82809i 0.279115i
\(437\) 7.95184 0.380388
\(438\) 27.8831 34.0877i 1.33231 1.62877i
\(439\) −22.6084 −1.07904 −0.539521 0.841972i \(-0.681395\pi\)
−0.539521 + 0.841972i \(0.681395\pi\)
\(440\) 8.99438i 0.428790i
\(441\) −4.12497 20.3933i −0.196427 0.971109i
\(442\) −20.7980 −0.989258
\(443\) 29.1166 1.38337 0.691686 0.722198i \(-0.256868\pi\)
0.691686 + 0.722198i \(0.256868\pi\)
\(444\) −9.86359 + 12.0585i −0.468105 + 0.572269i
\(445\) 25.5978i 1.21345i
\(446\) 21.8052 1.03251
\(447\) −8.65375 7.07860i −0.409308 0.334806i
\(448\) −1.48763 −0.0702838
\(449\) 20.0664i 0.946992i −0.880796 0.473496i \(-0.842992\pi\)
0.880796 0.473496i \(-0.157008\pi\)
\(450\) 6.17313 + 30.5191i 0.291004 + 1.43869i
\(451\) 41.2249i 1.94120i
\(452\) 8.20177 0.385779
\(453\) −14.4067 + 17.6125i −0.676884 + 0.827505i
\(454\) −2.49074 −0.116896
\(455\) −2.17730 −0.102073
\(456\) 1.61117 + 1.31791i 0.0754501 + 0.0617168i
\(457\) 41.2249i 1.92842i −0.265144 0.964209i \(-0.585419\pi\)
0.265144 0.964209i \(-0.414581\pi\)
\(458\) 52.1610i 2.43732i
\(459\) 18.5480 + 9.79894i 0.865748 + 0.457375i
\(460\) 18.2888i 0.852721i
\(461\) 15.7384i 0.733010i −0.930416 0.366505i \(-0.880554\pi\)
0.930416 0.366505i \(-0.119446\pi\)
\(462\) −3.74590 3.06407i −0.174275 0.142554i
\(463\) 15.7989i 0.734237i 0.930174 + 0.367118i \(0.119656\pi\)
−0.930174 + 0.367118i \(0.880344\pi\)
\(464\) 15.8574i 0.736163i
\(465\) −33.7212 27.5833i −1.56378 1.27914i
\(466\) 10.6925 0.495321
\(467\) 16.2171 0.750439 0.375219 0.926936i \(-0.377567\pi\)
0.375219 + 0.926936i \(0.377567\pi\)
\(468\) 13.6649 2.76401i 0.631661 0.127767i
\(469\) 0.676366i 0.0312317i
\(470\) 31.5541i 1.45548i
\(471\) −12.2294 + 14.9507i −0.563499 + 0.688890i
\(472\) −3.50403 + 1.41128i −0.161286 + 0.0649595i
\(473\) 55.6710i 2.55976i
\(474\) −30.4245 24.8866i −1.39744 1.14308i
\(475\) 13.1044 0.601271
\(476\) 1.79100i 0.0820902i
\(477\) −3.43282 + 0.694358i −0.157178 + 0.0317925i
\(478\) 28.5337i 1.30510i
\(479\) 6.37198i 0.291143i −0.989348 0.145572i \(-0.953498\pi\)
0.989348 0.145572i \(-0.0465021\pi\)
\(480\) −26.8887 + 32.8720i −1.22730 + 1.50040i
\(481\) −13.7128 −0.625251
\(482\) −1.50509 −0.0685551
\(483\) 1.10856 + 0.906781i 0.0504412 + 0.0412599i
\(484\) 37.1484 1.68856
\(485\) −14.4067 −0.654172
\(486\) −28.9410 8.52470i −1.31279 0.386688i
\(487\) 29.6688 1.34442 0.672211 0.740359i \(-0.265345\pi\)
0.672211 + 0.740359i \(0.265345\pi\)
\(488\) 0.332635i 0.0150577i
\(489\) −10.2705 8.40108i −0.464448 0.379910i
\(490\) 43.2103i 1.95204i
\(491\) 28.7281i 1.29648i 0.761435 + 0.648241i \(0.224495\pi\)
−0.761435 + 0.648241i \(0.775505\pi\)
\(492\) −13.8929 + 16.9843i −0.626339 + 0.765713i
\(493\) −14.4067 −0.648843
\(494\) 12.5889i 0.566403i
\(495\) −53.7774 + 10.8776i −2.41711 + 0.488911i
\(496\) 34.7204i 1.55899i
\(497\) 4.12589i 0.185071i
\(498\) −25.7376 21.0528i −1.15333 0.943400i
\(499\) −23.0328 −1.03109 −0.515545 0.856862i \(-0.672411\pi\)
−0.515545 + 0.856862i \(0.672411\pi\)
\(500\) 2.03824i 0.0911530i
\(501\) 13.7955 16.8653i 0.616337 0.753485i
\(502\) 26.1720i 1.16811i
\(503\) 22.4517 1.00107 0.500536 0.865716i \(-0.333136\pi\)
0.500536 + 0.865716i \(0.333136\pi\)
\(504\) 0.0743259 + 0.367457i 0.00331074 + 0.0163679i
\(505\) 15.6270i 0.695394i
\(506\) −35.7816 −1.59068
\(507\) −7.92984 6.48646i −0.352177 0.288074i
\(508\) 4.57588 0.203022
\(509\) −3.16089 −0.140104 −0.0700520 0.997543i \(-0.522317\pi\)
−0.0700520 + 0.997543i \(0.522317\pi\)
\(510\) 33.7212 + 27.5833i 1.49320 + 1.22141i
\(511\) 3.33816i 0.147671i
\(512\) −29.4754 −1.30264
\(513\) −5.93126 + 11.2271i −0.261872 + 0.495686i
\(514\) 33.1373i 1.46162i
\(515\) 40.1125 1.76757
\(516\) −18.7612 + 22.9360i −0.825918 + 1.00970i
\(517\) −28.7735 −1.26546
\(518\) 2.53360i 0.111320i
\(519\) 31.0838 + 25.4260i 1.36443 + 1.11608i
\(520\) −4.21401 −0.184797
\(521\) 16.5415i 0.724696i 0.932043 + 0.362348i \(0.118025\pi\)
−0.932043 + 0.362348i \(0.881975\pi\)
\(522\) 20.3089 4.10790i 0.888897 0.179798i
\(523\) −28.0716 −1.22748 −0.613742 0.789507i \(-0.710337\pi\)
−0.613742 + 0.789507i \(0.710337\pi\)
\(524\) 29.4835 1.28799
\(525\) 1.82687 + 1.49435i 0.0797313 + 0.0652187i
\(526\) 50.9653i 2.22219i
\(527\) −31.5439 −1.37407
\(528\) −33.8461 27.6855i −1.47296 1.20486i
\(529\) −12.4108 −0.539601
\(530\) −7.27362 −0.315946
\(531\) −12.6757 19.2438i −0.550080 0.835112i
\(532\) −1.08408 −0.0470010
\(533\) −19.3145 −0.836604
\(534\) 20.6332 + 16.8775i 0.892885 + 0.730363i
\(535\) −31.9271 −1.38033
\(536\) 1.30906i 0.0565428i
\(537\) 19.8779 + 16.2597i 0.857794 + 0.701659i
\(538\) 30.2705 1.30505
\(539\) 39.4025 1.69719
\(540\) −25.8216 13.6416i −1.11119 0.587041i
\(541\) 12.9652i 0.557419i 0.960375 + 0.278709i \(0.0899067\pi\)
−0.960375 + 0.278709i \(0.910093\pi\)
\(542\) −50.8367 −2.18362
\(543\) 3.70333 + 3.02925i 0.158925 + 0.129998i
\(544\) 30.7496i 1.31838i
\(545\) −10.7459 −0.460304
\(546\) 1.43557 1.75501i 0.0614366 0.0751076i
\(547\) 5.30927 0.227008 0.113504 0.993538i \(-0.463793\pi\)
0.113504 + 0.993538i \(0.463793\pi\)
\(548\) 1.12805i 0.0481880i
\(549\) −1.98882 + 0.402280i −0.0848808 + 0.0171689i
\(550\) −58.9669 −2.51436
\(551\) 8.72029i 0.371497i
\(552\) 2.14554 + 1.75501i 0.0913203 + 0.0746983i
\(553\) −2.97942 −0.126698
\(554\) 36.8800 1.56688
\(555\) 22.2335 + 18.1866i 0.943761 + 0.771978i
\(556\) −21.8862 −0.928182
\(557\) 39.0541i 1.65478i 0.561630 + 0.827389i \(0.310175\pi\)
−0.561630 + 0.827389i \(0.689825\pi\)
\(558\) 44.4671 8.99438i 1.88244 0.380762i
\(559\) −26.0828 −1.10318
\(560\) 3.63481i 0.153599i
\(561\) −25.1526 + 30.7496i −1.06194 + 1.29825i
\(562\) 26.0001i 1.09675i
\(563\) 5.26111 0.221729 0.110865 0.993836i \(-0.464638\pi\)
0.110865 + 0.993836i \(0.464638\pi\)
\(564\) −11.8545 9.69672i −0.499163 0.408306i
\(565\) 15.1225i 0.636210i
\(566\) 36.7058i 1.54286i
\(567\) −2.10714 + 0.888788i −0.0884915 + 0.0373256i
\(568\) 7.98538i 0.335059i
\(569\) −9.43530 −0.395548 −0.197774 0.980248i \(-0.563371\pi\)
−0.197774 + 0.980248i \(0.563371\pi\)
\(570\) −16.6960 + 20.4113i −0.699320 + 0.854935i
\(571\) 24.0732i 1.00743i −0.863869 0.503717i \(-0.831966\pi\)
0.863869 0.503717i \(-0.168034\pi\)
\(572\) 26.4024i 1.10394i
\(573\) −6.29809 5.15172i −0.263107 0.215216i
\(574\) 3.56857i 0.148949i
\(575\) 17.4506 0.727742
\(576\) −3.48204 17.2147i −0.145085 0.717281i
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) −1.35849 −0.0565058
\(579\) 18.1910 + 14.8799i 0.755990 + 0.618386i
\(580\) 20.0562 0.832790
\(581\) −2.52044 −0.104566
\(582\) 9.49881 11.6125i 0.393738 0.481354i
\(583\) 6.63265i 0.274696i
\(584\) 6.46078i 0.267349i
\(585\) −5.09632 25.1956i −0.210707 1.04171i
\(586\) 12.4022i 0.512330i
\(587\) 25.2856 1.04365 0.521824 0.853053i \(-0.325252\pi\)
0.521824 + 0.853053i \(0.325252\pi\)
\(588\) 16.2335 + 13.2787i 0.669459 + 0.547605i
\(589\) 19.0934i 0.786729i
\(590\) −17.8789 44.3912i −0.736064 1.82755i
\(591\) −5.07158 + 6.20012i −0.208617 + 0.255039i
\(592\) 22.8924i 0.940871i
\(593\) 40.9056i 1.67979i 0.542746 + 0.839897i \(0.317385\pi\)
−0.542746 + 0.839897i \(0.682615\pi\)
\(594\) 26.6894 50.5193i 1.09508 2.07283i
\(595\) 3.30226 0.135380
\(596\) 11.2694 0.461615
\(597\) −13.7473 11.2450i −0.562640 0.460229i
\(598\) 16.7642i 0.685540i
\(599\) 5.46520i 0.223302i −0.993747 0.111651i \(-0.964386\pi\)
0.993747 0.111651i \(-0.0356139\pi\)
\(600\) 3.53579 + 2.89221i 0.144348 + 0.118074i
\(601\) 13.6416i 0.556453i 0.960516 + 0.278226i \(0.0897465\pi\)
−0.960516 + 0.278226i \(0.910253\pi\)
\(602\) 4.81909i 0.196411i
\(603\) −7.82687 + 1.58315i −0.318735 + 0.0644707i
\(604\) 22.9360i 0.933254i
\(605\) 68.4946i 2.78470i
\(606\) 12.5962 + 10.3034i 0.511685 + 0.418549i
\(607\) 13.7581 0.558426 0.279213 0.960229i \(-0.409927\pi\)
0.279213 + 0.960229i \(0.409927\pi\)
\(608\) −18.6126 −0.754840
\(609\) 0.994411 1.21569i 0.0402956 0.0492622i
\(610\) −4.21401 −0.170620
\(611\) 13.4808i 0.545376i
\(612\) −20.7253 + 4.19212i −0.837772 + 0.169457i
\(613\) 13.8135i 0.557921i 0.960303 + 0.278960i \(0.0899898\pi\)
−0.960303 + 0.278960i \(0.910010\pi\)
\(614\) −26.9313 −1.08686
\(615\) 31.3159 + 25.6158i 1.26278 + 1.03293i
\(616\) −0.709975 −0.0286057
\(617\) 31.3899i 1.26371i −0.775086 0.631856i \(-0.782294\pi\)
0.775086 0.631856i \(-0.217706\pi\)
\(618\) −26.4475 + 32.3327i −1.06388 + 1.30061i
\(619\) 26.4835 1.06446 0.532230 0.846600i \(-0.321354\pi\)
0.532230 + 0.846600i \(0.321354\pi\)
\(620\) 43.9138 1.76362
\(621\) −7.89845 + 14.9507i −0.316954 + 0.599949i
\(622\) 3.10774i 0.124609i
\(623\) 2.02058 0.0809527
\(624\) 12.9711 15.8574i 0.519259 0.634806i
\(625\) −23.0552 −0.922207
\(626\) 50.5193i 2.01916i
\(627\) −18.6126 15.2247i −0.743315 0.608018i
\(628\) 19.4697i 0.776925i
\(629\) 20.7980 0.829269
\(630\) −4.65517 + 0.941604i −0.185466 + 0.0375144i
\(631\) −18.4723 −0.735370 −0.367685 0.929950i \(-0.619850\pi\)
−0.367685 + 0.929950i \(0.619850\pi\)
\(632\) −5.76647 −0.229378
\(633\) 10.0042 12.2303i 0.397630 0.486112i
\(634\) 17.9562i 0.713131i
\(635\) 8.43707i 0.334815i
\(636\) 2.23522 2.73260i 0.0886321 0.108355i
\(637\) 18.4607i 0.731439i
\(638\) 39.2394i 1.55350i
\(639\) 47.7446 9.65733i 1.88875 0.382038i
\(640\) 12.5630i 0.496594i
\(641\) 33.8439i 1.33675i 0.743823 + 0.668376i \(0.233010\pi\)
−0.743823 + 0.668376i \(0.766990\pi\)
\(642\) 21.0506 25.7349i 0.830803 1.01567i
\(643\) 10.2405 0.403847 0.201924 0.979401i \(-0.435281\pi\)
0.201924 + 0.979401i \(0.435281\pi\)
\(644\) −1.44364 −0.0568872
\(645\) 42.2898 + 34.5922i 1.66516 + 1.36207i
\(646\) 19.0934i 0.751219i
\(647\) 14.7865i 0.581317i −0.956827 0.290658i \(-0.906126\pi\)
0.956827 0.290658i \(-0.0938743\pi\)
\(648\) −4.07823 + 1.72019i −0.160208 + 0.0675754i
\(649\) 40.4793 16.3034i 1.58895 0.639964i
\(650\) 27.6269i 1.08362i
\(651\) 2.17730 2.66179i 0.0853350 0.104324i
\(652\) 13.3749 0.523801
\(653\) 18.7348i 0.733148i −0.930389 0.366574i \(-0.880531\pi\)
0.930389 0.366574i \(-0.119469\pi\)
\(654\) 7.08514 8.66175i 0.277051 0.338701i
\(655\) 54.3620i 2.12410i
\(656\) 32.2439i 1.25891i
\(657\) 38.6290 7.81351i 1.50706 0.304834i
\(658\) −2.49074 −0.0970990
\(659\) −25.8091 −1.00538 −0.502691 0.864466i \(-0.667657\pi\)
−0.502691 + 0.864466i \(0.667657\pi\)
\(660\) 35.0161 42.8080i 1.36300 1.66630i
\(661\) 37.9547 1.47627 0.738133 0.674655i \(-0.235708\pi\)
0.738133 + 0.674655i \(0.235708\pi\)
\(662\) −48.5662 −1.88758
\(663\) −14.4067 11.7844i −0.559508 0.457667i
\(664\) −4.87814 −0.189309
\(665\) 1.99885i 0.0775120i
\(666\) −29.3187 + 5.93031i −1.13608 + 0.229795i
\(667\) 11.6125i 0.449638i
\(668\) 21.9630i 0.849775i
\(669\) 15.1044 + 12.3551i 0.583969 + 0.477676i
\(670\) −16.5839 −0.640694
\(671\) 3.84266i 0.148344i
\(672\) −2.59477 2.12247i −0.100095 0.0818761i
\(673\) 15.1662i 0.584614i −0.956325 0.292307i \(-0.905577\pi\)
0.956325 0.292307i \(-0.0944229\pi\)
\(674\) 40.2159i 1.54906i
\(675\) −13.0164 + 24.6382i −0.501002 + 0.948326i
\(676\) 10.3267 0.397182
\(677\) 36.7552i 1.41262i 0.707903 + 0.706309i \(0.249641\pi\)
−0.707903 + 0.706309i \(0.750359\pi\)
\(678\) 12.1895 + 9.97081i 0.468136 + 0.382927i
\(679\) 1.13720i 0.0436415i
\(680\) 6.39131 0.245095
\(681\) −1.72532 1.41128i −0.0661145 0.0540804i
\(682\) 85.9161i 3.28990i
\(683\) 16.4806 0.630613 0.315307 0.948990i \(-0.397893\pi\)
0.315307 + 0.948990i \(0.397893\pi\)
\(684\) −2.53748 12.5450i −0.0970229 0.479669i
\(685\) 2.07992 0.0794695
\(686\) 6.85340 0.261664
\(687\) 29.5550 36.1317i 1.12759 1.37851i
\(688\) 43.5429i 1.66006i
\(689\) 3.10750 0.118386
\(690\) −22.2335 + 27.1810i −0.846416 + 1.03476i
\(691\) 16.0879i 0.612011i −0.952030 0.306005i \(-0.901007\pi\)
0.952030 0.306005i \(-0.0989926\pi\)
\(692\) −40.4793 −1.53879
\(693\) −0.858627 4.24494i −0.0326165 0.161252i
\(694\) −3.40070 −0.129089
\(695\) 40.3541i 1.53072i
\(696\) 1.92461 2.35288i 0.0729523 0.0891859i
\(697\) 29.2939 1.10959
\(698\) 18.9652i 0.717843i
\(699\) 7.40665 + 6.05850i 0.280145 + 0.229154i
\(700\) −2.37907 −0.0899203
\(701\) −26.3861 −0.996588 −0.498294 0.867008i \(-0.666040\pi\)
−0.498294 + 0.867008i \(0.666040\pi\)
\(702\) 23.6691 + 12.5044i 0.893332 + 0.471948i
\(703\) 12.5889i 0.474800i
\(704\) 33.2611 1.25358
\(705\) −17.8789 + 21.8574i −0.673360 + 0.823197i
\(706\) −52.6688 −1.98222
\(707\) 1.23353 0.0463915
\(708\) 22.1714 + 6.92473i 0.833254 + 0.260247i
\(709\) 32.8901 1.23521 0.617607 0.786487i \(-0.288102\pi\)
0.617607 + 0.786487i \(0.288102\pi\)
\(710\) 101.163 3.79660
\(711\) −6.97384 34.4777i −0.261539 1.29302i
\(712\) 3.91069 0.146559
\(713\) 25.4260i 0.952210i
\(714\) −2.17730 + 2.66179i −0.0814833 + 0.0996151i
\(715\) 48.6811 1.82057
\(716\) −25.8862 −0.967413
\(717\) −16.1675 + 19.7652i −0.603788 + 0.738144i
\(718\) 8.21579i 0.306611i
\(719\) 33.0510 1.23259 0.616297 0.787514i \(-0.288632\pi\)
0.616297 + 0.787514i \(0.288632\pi\)
\(720\) −42.0618 + 8.50787i −1.56755 + 0.317070i
\(721\) 3.16629i 0.117919i
\(722\) 25.2161 0.938445
\(723\) −1.04257 0.852804i −0.0387737 0.0317161i
\(724\) −4.82270 −0.179234
\(725\) 19.1371i 0.710732i
\(726\) 55.2102 + 45.1609i 2.04904 + 1.67608i
\(727\) −47.6043 −1.76554 −0.882772 0.469802i \(-0.844325\pi\)
−0.882772 + 0.469802i \(0.844325\pi\)
\(728\) 0.332635i 0.0123283i
\(729\) −15.2171 22.3033i −0.563597 0.826050i
\(730\) 81.8490 3.02937
\(731\) 39.5592 1.46315
\(732\) 1.29498 1.58315i 0.0478640 0.0585148i
\(733\) −44.3900 −1.63958 −0.819791 0.572663i \(-0.805910\pi\)
−0.819791 + 0.572663i \(0.805910\pi\)
\(734\) 45.7002i 1.68683i
\(735\) 24.4835 29.9316i 0.903086 1.10404i
\(736\) −24.7857 −0.913614
\(737\) 15.1225i 0.557045i
\(738\) −41.2953 + 8.35284i −1.52010 + 0.307472i
\(739\) 27.4551i 1.00995i −0.863134 0.504975i \(-0.831502\pi\)
0.863134 0.504975i \(-0.168498\pi\)
\(740\) −28.9539 −1.06437
\(741\) 7.13304 8.72029i 0.262039 0.320348i
\(742\) 0.574146i 0.0210776i
\(743\) 5.49545i 0.201609i −0.994906 0.100804i \(-0.967858\pi\)
0.994906 0.100804i \(-0.0321416\pi\)
\(744\) 4.21401 5.15172i 0.154493 0.188871i
\(745\) 20.7787i 0.761274i
\(746\) −41.6196 −1.52380
\(747\) −5.89951 29.1664i −0.215852 1.06714i
\(748\) 40.0440i 1.46415i
\(749\) 2.52018i 0.0920853i
\(750\) −2.47787 + 3.02925i −0.0904790 + 0.110613i
\(751\) 2.61812i 0.0955366i 0.998858 + 0.0477683i \(0.0152109\pi\)
−0.998858 + 0.0477683i \(0.984789\pi\)
\(752\) −22.5051 −0.820676
\(753\) 14.8294 18.1292i 0.540412 0.660665i
\(754\) −18.3843 −0.669517
\(755\) −42.2898 −1.53908
\(756\) 1.07681 2.03824i 0.0391630 0.0741302i
\(757\) −1.36372 −0.0495653 −0.0247826 0.999693i \(-0.507889\pi\)
−0.0247826 + 0.999693i \(0.507889\pi\)
\(758\) −28.9518 −1.05158
\(759\) −24.7857 20.2742i −0.899665 0.735909i
\(760\) 3.86863i 0.140330i
\(761\) 9.13600i 0.331180i −0.986195 0.165590i \(-0.947047\pi\)
0.986195 0.165590i \(-0.0529528\pi\)
\(762\) 6.80071 + 5.56285i 0.246364 + 0.201521i
\(763\) 0.848232i 0.0307081i
\(764\) 8.20177 0.296730
\(765\) 7.72949 + 38.2136i 0.279460 + 1.38162i
\(766\) 18.1606i 0.656170i
\(767\) 7.63840 + 18.9652i 0.275807 + 0.684793i
\(768\) −25.8241 21.1236i −0.931848 0.762234i
\(769\) 30.0732i 1.08447i −0.840228 0.542233i \(-0.817579\pi\)
0.840228 0.542233i \(-0.182421\pi\)
\(770\) 8.99438i 0.324135i
\(771\) −18.7760 + 22.9540i −0.676200 + 0.826669i
\(772\) −23.6894 −0.852600
\(773\) −5.41783 −0.194866 −0.0974329 0.995242i \(-0.531063\pi\)
−0.0974329 + 0.995242i \(0.531063\pi\)
\(774\) −55.7662 + 11.2799i −2.00447 + 0.405446i
\(775\) 41.9012i 1.50514i
\(776\) 2.20096i 0.0790100i
\(777\) −1.43557 + 1.75501i −0.0515007 + 0.0629607i
\(778\) 2.70546i 0.0969956i
\(779\) 17.7315i 0.635297i
\(780\) 20.0562 + 16.4056i 0.718128 + 0.587415i
\(781\) 92.2487i 3.30092i
\(782\) 25.4260i 0.909231i
\(783\) 16.3955 + 8.66175i 0.585926 + 0.309546i
\(784\) 30.8185