Properties

Label 120.2.d.a.109.2
Level $120$
Weight $2$
Character 120.109
Analytic conductor $0.958$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.839056.1
Defining polynomial: \( x^{6} + 6x^{4} + 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.2
Root \(1.32132i\) of defining polynomial
Character \(\chi\) \(=\) 120.109
Dual form 120.2.d.a.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34067 + 0.450129i) q^{2} +1.00000 q^{3} +(1.59477 - 1.20695i) q^{4} +(-0.254102 - 2.22158i) q^{5} +(-1.34067 + 0.450129i) q^{6} -2.64265i q^{7} +(-1.59477 + 2.33596i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.34067 + 0.450129i) q^{2} +1.00000 q^{3} +(1.59477 - 1.20695i) q^{4} +(-0.254102 - 2.22158i) q^{5} +(-1.34067 + 0.450129i) q^{6} -2.64265i q^{7} +(-1.59477 + 2.33596i) q^{8} +1.00000 q^{9} +(1.34067 + 2.86402i) q^{10} +1.51363i q^{11} +(1.59477 - 1.20695i) q^{12} +3.87086 q^{13} +(1.18953 + 3.54291i) q^{14} +(-0.254102 - 2.22158i) q^{15} +(1.08656 - 3.84959i) q^{16} -3.31415i q^{17} +(-1.34067 + 0.450129i) q^{18} +7.08582i q^{19} +(-3.08656 - 3.23622i) q^{20} -2.64265i q^{21} +(-0.681331 - 2.02927i) q^{22} +4.82778i q^{23} +(-1.59477 + 2.33596i) q^{24} +(-4.87086 + 1.12902i) q^{25} +(-5.18953 + 1.74239i) q^{26} +1.00000 q^{27} +(-3.18953 - 4.21441i) q^{28} -2.18513i q^{29} +(1.34067 + 2.86402i) q^{30} -7.36266 q^{31} +(0.276098 + 5.65011i) q^{32} +1.51363i q^{33} +(1.49180 + 4.44317i) q^{34} +(-5.87086 + 0.671502i) q^{35} +(1.59477 - 1.20695i) q^{36} -7.87086 q^{37} +(-3.18953 - 9.49971i) q^{38} +3.87086 q^{39} +(5.59477 + 2.94934i) q^{40} +8.72532 q^{41} +(1.18953 + 3.54291i) q^{42} +1.01641 q^{43} +(1.82687 + 2.41389i) q^{44} +(-0.254102 - 2.22158i) q^{45} +(-2.17313 - 6.47244i) q^{46} +7.08582i q^{47} +(1.08656 - 3.84959i) q^{48} +0.0164068 q^{49} +(6.02200 - 3.70615i) q^{50} -3.31415i q^{51} +(6.17313 - 4.67192i) q^{52} +4.50820 q^{53} +(-1.34067 + 0.450129i) q^{54} +(3.36266 - 0.384617i) q^{55} +(6.17313 + 4.21441i) q^{56} +7.08582i q^{57} +(0.983593 + 2.92953i) q^{58} -6.79893i q^{59} +(-3.08656 - 3.23622i) q^{60} +3.60104i q^{61} +(9.87086 - 3.31415i) q^{62} -2.64265i q^{63} +(-2.91344 - 7.45063i) q^{64} +(-0.983593 - 8.59945i) q^{65} +(-0.681331 - 2.02927i) q^{66} -1.01641 q^{67} +(-4.00000 - 5.28530i) q^{68} +4.82778i q^{69} +(7.56860 - 3.54291i) q^{70} -6.72532 q^{71} +(-1.59477 + 2.33596i) q^{72} +15.5146i q^{73} +(10.5522 - 3.54291i) q^{74} +(-4.87086 + 1.12902i) q^{75} +(8.55220 + 11.3002i) q^{76} +4.00000 q^{77} +(-5.18953 + 1.74239i) q^{78} +7.36266 q^{79} +(-8.82829 - 1.43570i) q^{80} +1.00000 q^{81} +(-11.6977 + 3.92752i) q^{82} +7.74173 q^{83} +(-3.18953 - 4.21441i) q^{84} +(-7.36266 + 0.842131i) q^{85} +(-1.36266 + 0.457515i) q^{86} -2.18513i q^{87} +(-3.53579 - 2.41389i) q^{88} -14.7581 q^{89} +(1.34067 + 2.86402i) q^{90} -10.2293i q^{91} +(5.82687 + 7.69919i) q^{92} -7.36266 q^{93} +(-3.18953 - 9.49971i) q^{94} +(15.7417 - 1.80052i) q^{95} +(0.276098 + 5.65011i) q^{96} -11.1444i q^{97} +(-0.0219960 + 0.00738516i) q^{98} +1.51363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} + 6 q^{3} + q^{4} - q^{6} - q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} + 6 q^{3} + q^{4} - q^{6} - q^{8} + 6 q^{9} + q^{10} + q^{12} - 8 q^{13} - 10 q^{14} + q^{16} - q^{18} - 13 q^{20} + 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} + 6 q^{27} - 2 q^{28} + q^{30} - 16 q^{31} - 21 q^{32} + 12 q^{34} - 4 q^{35} + q^{36} - 16 q^{37} - 2 q^{38} - 8 q^{39} + 25 q^{40} - 4 q^{41} - 10 q^{42} + 22 q^{44} - 2 q^{46} + q^{48} - 6 q^{49} + 15 q^{50} + 26 q^{52} + 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} + 12 q^{58} - 13 q^{60} + 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} - 24 q^{68} - 6 q^{70} + 16 q^{71} - q^{72} + 18 q^{74} + 2 q^{75} + 6 q^{76} + 24 q^{77} - 14 q^{78} + 16 q^{79} + 15 q^{80} + 6 q^{81} - 50 q^{82} - 16 q^{83} - 2 q^{84} - 16 q^{85} + 20 q^{86} + 18 q^{88} - 20 q^{89} + q^{90} + 46 q^{92} - 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34067 + 0.450129i −0.947994 + 0.318290i
\(3\) 1.00000 0.577350
\(4\) 1.59477 1.20695i 0.797384 0.603473i
\(5\) −0.254102 2.22158i −0.113638 0.993522i
\(6\) −1.34067 + 0.450129i −0.547324 + 0.183765i
\(7\) 2.64265i 0.998827i −0.866364 0.499414i \(-0.833549\pi\)
0.866364 0.499414i \(-0.166451\pi\)
\(8\) −1.59477 + 2.33596i −0.563835 + 0.825887i
\(9\) 1.00000 0.333333
\(10\) 1.34067 + 2.86402i 0.423956 + 0.905683i
\(11\) 1.51363i 0.456377i 0.973617 + 0.228189i \(0.0732803\pi\)
−0.973617 + 0.228189i \(0.926720\pi\)
\(12\) 1.59477 1.20695i 0.460370 0.348415i
\(13\) 3.87086 1.07358 0.536792 0.843714i \(-0.319636\pi\)
0.536792 + 0.843714i \(0.319636\pi\)
\(14\) 1.18953 + 3.54291i 0.317916 + 0.946882i
\(15\) −0.254102 2.22158i −0.0656088 0.573610i
\(16\) 1.08656 3.84959i 0.271641 0.962399i
\(17\) 3.31415i 0.803800i −0.915684 0.401900i \(-0.868350\pi\)
0.915684 0.401900i \(-0.131650\pi\)
\(18\) −1.34067 + 0.450129i −0.315998 + 0.106097i
\(19\) 7.08582i 1.62560i 0.582545 + 0.812799i \(0.302057\pi\)
−0.582545 + 0.812799i \(0.697943\pi\)
\(20\) −3.08656 3.23622i −0.690177 0.723641i
\(21\) 2.64265i 0.576673i
\(22\) −0.681331 2.02927i −0.145260 0.432643i
\(23\) 4.82778i 1.00666i 0.864094 + 0.503331i \(0.167892\pi\)
−0.864094 + 0.503331i \(0.832108\pi\)
\(24\) −1.59477 + 2.33596i −0.325530 + 0.476826i
\(25\) −4.87086 + 1.12902i −0.974173 + 0.225803i
\(26\) −5.18953 + 1.74239i −1.01775 + 0.341711i
\(27\) 1.00000 0.192450
\(28\) −3.18953 4.21441i −0.602765 0.796448i
\(29\) 2.18513i 0.405769i −0.979203 0.202885i \(-0.934968\pi\)
0.979203 0.202885i \(-0.0650316\pi\)
\(30\) 1.34067 + 2.86402i 0.244771 + 0.522896i
\(31\) −7.36266 −1.32237 −0.661187 0.750222i \(-0.729947\pi\)
−0.661187 + 0.750222i \(0.729947\pi\)
\(32\) 0.276098 + 5.65011i 0.0488076 + 0.998808i
\(33\) 1.51363i 0.263490i
\(34\) 1.49180 + 4.44317i 0.255841 + 0.761997i
\(35\) −5.87086 + 0.671502i −0.992357 + 0.113504i
\(36\) 1.59477 1.20695i 0.265795 0.201158i
\(37\) −7.87086 −1.29396 −0.646981 0.762506i \(-0.723969\pi\)
−0.646981 + 0.762506i \(0.723969\pi\)
\(38\) −3.18953 9.49971i −0.517411 1.54106i
\(39\) 3.87086 0.619834
\(40\) 5.59477 + 2.94934i 0.884610 + 0.466331i
\(41\) 8.72532 1.36267 0.681333 0.731973i \(-0.261400\pi\)
0.681333 + 0.731973i \(0.261400\pi\)
\(42\) 1.18953 + 3.54291i 0.183549 + 0.546683i
\(43\) 1.01641 0.155001 0.0775003 0.996992i \(-0.475306\pi\)
0.0775003 + 0.996992i \(0.475306\pi\)
\(44\) 1.82687 + 2.41389i 0.275411 + 0.363908i
\(45\) −0.254102 2.22158i −0.0378792 0.331174i
\(46\) −2.17313 6.47244i −0.320410 0.954309i
\(47\) 7.08582i 1.03357i 0.856114 + 0.516786i \(0.172872\pi\)
−0.856114 + 0.516786i \(0.827128\pi\)
\(48\) 1.08656 3.84959i 0.156832 0.555641i
\(49\) 0.0164068 0.00234382
\(50\) 6.02200 3.70615i 0.851639 0.524129i
\(51\) 3.31415i 0.464074i
\(52\) 6.17313 4.67192i 0.856059 0.647879i
\(53\) 4.50820 0.619249 0.309625 0.950859i \(-0.399797\pi\)
0.309625 + 0.950859i \(0.399797\pi\)
\(54\) −1.34067 + 0.450129i −0.182441 + 0.0612549i
\(55\) 3.36266 0.384617i 0.453421 0.0518617i
\(56\) 6.17313 + 4.21441i 0.824919 + 0.563174i
\(57\) 7.08582i 0.938539i
\(58\) 0.983593 + 2.92953i 0.129152 + 0.384667i
\(59\) 6.79893i 0.885145i −0.896733 0.442573i \(-0.854066\pi\)
0.896733 0.442573i \(-0.145934\pi\)
\(60\) −3.08656 3.23622i −0.398474 0.417794i
\(61\) 3.60104i 0.461065i 0.973065 + 0.230533i \(0.0740469\pi\)
−0.973065 + 0.230533i \(0.925953\pi\)
\(62\) 9.87086 3.31415i 1.25360 0.420898i
\(63\) 2.64265i 0.332942i
\(64\) −2.91344 7.45063i −0.364180 0.931329i
\(65\) −0.983593 8.59945i −0.122000 1.06663i
\(66\) −0.681331 2.02927i −0.0838660 0.249786i
\(67\) −1.01641 −0.124174 −0.0620869 0.998071i \(-0.519776\pi\)
−0.0620869 + 0.998071i \(0.519776\pi\)
\(68\) −4.00000 5.28530i −0.485071 0.640937i
\(69\) 4.82778i 0.581197i
\(70\) 7.56860 3.54291i 0.904621 0.423458i
\(71\) −6.72532 −0.798149 −0.399074 0.916919i \(-0.630669\pi\)
−0.399074 + 0.916919i \(0.630669\pi\)
\(72\) −1.59477 + 2.33596i −0.187945 + 0.275296i
\(73\) 15.5146i 1.81585i 0.419132 + 0.907925i \(0.362334\pi\)
−0.419132 + 0.907925i \(0.637666\pi\)
\(74\) 10.5522 3.54291i 1.22667 0.411855i
\(75\) −4.87086 + 1.12902i −0.562439 + 0.130368i
\(76\) 8.55220 + 11.3002i 0.981004 + 1.29622i
\(77\) 4.00000 0.455842
\(78\) −5.18953 + 1.74239i −0.587599 + 0.197287i
\(79\) 7.36266 0.828364 0.414182 0.910194i \(-0.364068\pi\)
0.414182 + 0.910194i \(0.364068\pi\)
\(80\) −8.82829 1.43570i −0.987033 0.160516i
\(81\) 1.00000 0.111111
\(82\) −11.6977 + 3.92752i −1.29180 + 0.433723i
\(83\) 7.74173 0.849765 0.424883 0.905248i \(-0.360315\pi\)
0.424883 + 0.905248i \(0.360315\pi\)
\(84\) −3.18953 4.21441i −0.348007 0.459830i
\(85\) −7.36266 + 0.842131i −0.798593 + 0.0913420i
\(86\) −1.36266 + 0.457515i −0.146940 + 0.0493351i
\(87\) 2.18513i 0.234271i
\(88\) −3.53579 2.41389i −0.376916 0.257322i
\(89\) −14.7581 −1.56436 −0.782180 0.623053i \(-0.785892\pi\)
−0.782180 + 0.623053i \(0.785892\pi\)
\(90\) 1.34067 + 2.86402i 0.141319 + 0.301894i
\(91\) 10.2293i 1.07233i
\(92\) 5.82687 + 7.69919i 0.607493 + 0.802696i
\(93\) −7.36266 −0.763472
\(94\) −3.18953 9.49971i −0.328975 0.979820i
\(95\) 15.7417 1.80052i 1.61507 0.184729i
\(96\) 0.276098 + 5.65011i 0.0281791 + 0.576662i
\(97\) 11.1444i 1.13154i −0.824563 0.565769i \(-0.808579\pi\)
0.824563 0.565769i \(-0.191421\pi\)
\(98\) −0.0219960 + 0.00738516i −0.00222193 + 0.000746014i
\(99\) 1.51363i 0.152126i
\(100\) −6.40523 + 7.67939i −0.640523 + 0.767939i
\(101\) 13.3295i 1.32633i 0.748471 + 0.663167i \(0.230788\pi\)
−0.748471 + 0.663167i \(0.769212\pi\)
\(102\) 1.49180 + 4.44317i 0.147710 + 0.439939i
\(103\) 0.958386i 0.0944326i −0.998885 0.0472163i \(-0.984965\pi\)
0.998885 0.0472163i \(-0.0150350\pi\)
\(104\) −6.17313 + 9.04219i −0.605325 + 0.886660i
\(105\) −5.87086 + 0.671502i −0.572938 + 0.0655318i
\(106\) −6.04399 + 2.02927i −0.587044 + 0.197101i
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 1.59477 1.20695i 0.153457 0.116138i
\(109\) 0.769233i 0.0736792i 0.999321 + 0.0368396i \(0.0117291\pi\)
−0.999321 + 0.0368396i \(0.988271\pi\)
\(110\) −4.33508 + 2.02927i −0.413333 + 0.193484i
\(111\) −7.87086 −0.747069
\(112\) −10.1731 2.87141i −0.961270 0.271322i
\(113\) 14.4585i 1.36014i −0.733146 0.680071i \(-0.761949\pi\)
0.733146 0.680071i \(-0.238051\pi\)
\(114\) −3.18953 9.49971i −0.298727 0.889729i
\(115\) 10.7253 1.22675i 1.00014 0.114395i
\(116\) −2.63734 3.48478i −0.244871 0.323554i
\(117\) 3.87086 0.357862
\(118\) 3.06040 + 9.11509i 0.281733 + 0.839112i
\(119\) −8.75814 −0.802857
\(120\) 5.59477 + 2.94934i 0.510730 + 0.269236i
\(121\) 8.70892 0.791720
\(122\) −1.62093 4.82778i −0.146752 0.437087i
\(123\) 8.72532 0.786736
\(124\) −11.7417 + 8.88633i −1.05444 + 0.798016i
\(125\) 3.74590 + 10.5341i 0.335043 + 0.942203i
\(126\) 1.18953 + 3.54291i 0.105972 + 0.315627i
\(127\) 11.5290i 1.02303i −0.859274 0.511516i \(-0.829084\pi\)
0.859274 0.511516i \(-0.170916\pi\)
\(128\) 7.25969 + 8.67738i 0.641672 + 0.766979i
\(129\) 1.01641 0.0894896
\(130\) 5.18953 + 11.0862i 0.455152 + 0.972327i
\(131\) 7.37270i 0.644156i −0.946713 0.322078i \(-0.895619\pi\)
0.946713 0.322078i \(-0.104381\pi\)
\(132\) 1.82687 + 2.41389i 0.159009 + 0.210102i
\(133\) 18.7253 1.62369
\(134\) 1.36266 0.457515i 0.117716 0.0395232i
\(135\) −0.254102 2.22158i −0.0218696 0.191203i
\(136\) 7.74173 + 5.28530i 0.663848 + 0.453211i
\(137\) 3.88792i 0.332167i 0.986112 + 0.166084i \(0.0531122\pi\)
−0.986112 + 0.166084i \(0.946888\pi\)
\(138\) −2.17313 6.47244i −0.184989 0.550971i
\(139\) 14.6291i 1.24083i −0.784275 0.620414i \(-0.786965\pi\)
0.784275 0.620414i \(-0.213035\pi\)
\(140\) −8.55220 + 8.15670i −0.722792 + 0.689367i
\(141\) 7.08582i 0.596733i
\(142\) 9.01641 3.02727i 0.756640 0.254042i
\(143\) 5.85907i 0.489960i
\(144\) 1.08656 3.84959i 0.0905470 0.320800i
\(145\) −4.85446 + 0.555246i −0.403141 + 0.0461107i
\(146\) −6.98359 20.7999i −0.577966 1.72141i
\(147\) 0.0164068 0.00135321
\(148\) −12.5522 + 9.49971i −1.03178 + 0.780871i
\(149\) 11.0715i 0.907010i −0.891254 0.453505i \(-0.850173\pi\)
0.891254 0.453505i \(-0.149827\pi\)
\(150\) 6.02200 3.70615i 0.491694 0.302606i
\(151\) 0.637339 0.0518659 0.0259329 0.999664i \(-0.491744\pi\)
0.0259329 + 0.999664i \(0.491744\pi\)
\(152\) −16.5522 11.3002i −1.34256 0.916569i
\(153\) 3.31415i 0.267933i
\(154\) −5.36266 + 1.80052i −0.432136 + 0.145090i
\(155\) 1.87086 + 16.3568i 0.150271 + 1.31381i
\(156\) 6.17313 4.67192i 0.494246 0.374053i
\(157\) 0.129135 0.0103061 0.00515306 0.999987i \(-0.498360\pi\)
0.00515306 + 0.999987i \(0.498360\pi\)
\(158\) −9.87086 + 3.31415i −0.785284 + 0.263660i
\(159\) 4.50820 0.357524
\(160\) 12.4820 2.04908i 0.986792 0.161994i
\(161\) 12.7581 1.00548
\(162\) −1.34067 + 0.450129i −0.105333 + 0.0353655i
\(163\) −19.4835 −1.52606 −0.763031 0.646362i \(-0.776290\pi\)
−0.763031 + 0.646362i \(0.776290\pi\)
\(164\) 13.9149 10.5310i 1.08657 0.822332i
\(165\) 3.36266 0.384617i 0.261783 0.0299424i
\(166\) −10.3791 + 3.48478i −0.805572 + 0.270471i
\(167\) 1.80052i 0.139328i −0.997571 0.0696641i \(-0.977807\pi\)
0.997571 0.0696641i \(-0.0221928\pi\)
\(168\) 6.17313 + 4.21441i 0.476267 + 0.325149i
\(169\) 1.98359 0.152584
\(170\) 9.49180 4.44317i 0.727988 0.340775i
\(171\) 7.08582i 0.541866i
\(172\) 1.62093 1.22675i 0.123595 0.0935386i
\(173\) −23.2335 −1.76641 −0.883206 0.468985i \(-0.844620\pi\)
−0.883206 + 0.468985i \(0.844620\pi\)
\(174\) 0.983593 + 2.92953i 0.0745660 + 0.222087i
\(175\) 2.98359 + 12.8720i 0.225538 + 0.973031i
\(176\) 5.82687 + 1.64466i 0.439217 + 0.123971i
\(177\) 6.79893i 0.511039i
\(178\) 19.7857 6.64307i 1.48300 0.497919i
\(179\) 2.85664i 0.213515i −0.994285 0.106757i \(-0.965953\pi\)
0.994285 0.106757i \(-0.0340468\pi\)
\(180\) −3.08656 3.23622i −0.230059 0.241214i
\(181\) 5.28530i 0.392853i −0.980519 0.196427i \(-0.937066\pi\)
0.980519 0.196427i \(-0.0629337\pi\)
\(182\) 4.60453 + 13.7141i 0.341310 + 1.01656i
\(183\) 3.60104i 0.266196i
\(184\) −11.2775 7.69919i −0.831390 0.567592i
\(185\) 2.00000 + 17.4858i 0.147043 + 1.28558i
\(186\) 9.87086 3.31415i 0.723767 0.243005i
\(187\) 5.01641 0.366836
\(188\) 8.55220 + 11.3002i 0.623733 + 0.824154i
\(189\) 2.64265i 0.192224i
\(190\) −20.2939 + 9.49971i −1.47228 + 0.689181i
\(191\) −5.96719 −0.431770 −0.215885 0.976419i \(-0.569264\pi\)
−0.215885 + 0.976419i \(0.569264\pi\)
\(192\) −2.91344 7.45063i −0.210259 0.537703i
\(193\) 14.9409i 1.07547i −0.843115 0.537733i \(-0.819281\pi\)
0.843115 0.537733i \(-0.180719\pi\)
\(194\) 5.01641 + 14.9409i 0.360157 + 1.07269i
\(195\) −0.983593 8.59945i −0.0704366 0.615819i
\(196\) 0.0261649 0.0198021i 0.00186892 0.00141443i
\(197\) 3.23353 0.230379 0.115190 0.993344i \(-0.463252\pi\)
0.115190 + 0.993344i \(0.463252\pi\)
\(198\) −0.681331 2.02927i −0.0484201 0.144214i
\(199\) 8.12080 0.575668 0.287834 0.957680i \(-0.407065\pi\)
0.287834 + 0.957680i \(0.407065\pi\)
\(200\) 5.13056 13.1787i 0.362785 0.931873i
\(201\) −1.01641 −0.0716918
\(202\) −6.00000 17.8704i −0.422159 1.25736i
\(203\) −5.77454 −0.405293
\(204\) −4.00000 5.28530i −0.280056 0.370045i
\(205\) −2.21712 19.3840i −0.154850 1.35384i
\(206\) 0.431398 + 1.28488i 0.0300569 + 0.0895215i
\(207\) 4.82778i 0.335554i
\(208\) 4.20594 14.9013i 0.291630 1.03322i
\(209\) −10.7253 −0.741886
\(210\) 7.56860 3.54291i 0.522283 0.244484i
\(211\) 13.7141i 0.944119i 0.881567 + 0.472059i \(0.156489\pi\)
−0.881567 + 0.472059i \(0.843511\pi\)
\(212\) 7.18953 5.44116i 0.493779 0.373700i
\(213\) −6.72532 −0.460812
\(214\) 5.36266 1.80052i 0.366584 0.123081i
\(215\) −0.258271 2.25803i −0.0176139 0.153997i
\(216\) −1.59477 + 2.33596i −0.108510 + 0.158942i
\(217\) 19.4569i 1.32082i
\(218\) −0.346255 1.03128i −0.0234513 0.0698474i
\(219\) 15.5146i 1.04838i
\(220\) 4.89845 4.67192i 0.330253 0.314981i
\(221\) 12.8286i 0.862947i
\(222\) 10.5522 3.54291i 0.708217 0.237784i
\(223\) 9.84472i 0.659251i −0.944112 0.329626i \(-0.893077\pi\)
0.944112 0.329626i \(-0.106923\pi\)
\(224\) 14.9313 0.729629i 0.997637 0.0487504i
\(225\) −4.87086 + 1.12902i −0.324724 + 0.0752677i
\(226\) 6.50820 + 19.3840i 0.432919 + 1.28941i
\(227\) −5.70892 −0.378914 −0.189457 0.981889i \(-0.560673\pi\)
−0.189457 + 0.981889i \(0.560673\pi\)
\(228\) 8.55220 + 11.3002i 0.566383 + 0.748376i
\(229\) 0.769233i 0.0508324i −0.999677 0.0254162i \(-0.991909\pi\)
0.999677 0.0254162i \(-0.00809109\pi\)
\(230\) −13.8269 + 6.47244i −0.911717 + 0.426780i
\(231\) 4.00000 0.263181
\(232\) 5.10439 + 3.48478i 0.335120 + 0.228787i
\(233\) 18.4008i 1.20548i 0.797939 + 0.602739i \(0.205924\pi\)
−0.797939 + 0.602739i \(0.794076\pi\)
\(234\) −5.18953 + 1.74239i −0.339250 + 0.113904i
\(235\) 15.7417 1.80052i 1.02688 0.117453i
\(236\) −8.20594 10.8427i −0.534161 0.705800i
\(237\) 7.36266 0.478256
\(238\) 11.7417 3.94229i 0.761103 0.255541i
\(239\) −10.0328 −0.648969 −0.324484 0.945891i \(-0.605191\pi\)
−0.324484 + 0.945891i \(0.605191\pi\)
\(240\) −8.82829 1.43570i −0.569864 0.0926742i
\(241\) 10.7581 0.692992 0.346496 0.938051i \(-0.387371\pi\)
0.346496 + 0.938051i \(0.387371\pi\)
\(242\) −11.6757 + 3.92014i −0.750545 + 0.251996i
\(243\) 1.00000 0.0641500
\(244\) 4.34625 + 5.74281i 0.278240 + 0.367646i
\(245\) −0.00416898 0.0364490i −0.000266347 0.00232864i
\(246\) −11.6977 + 3.92752i −0.745820 + 0.250410i
\(247\) 27.4282i 1.74522i
\(248\) 11.7417 17.1989i 0.745601 1.09213i
\(249\) 7.74173 0.490612
\(250\) −9.76373 12.4366i −0.617512 0.786561i
\(251\) 12.6580i 0.798966i 0.916741 + 0.399483i \(0.130810\pi\)
−0.916741 + 0.399483i \(0.869190\pi\)
\(252\) −3.18953 4.21441i −0.200922 0.265483i
\(253\) −7.30749 −0.459418
\(254\) 5.18953 + 15.4565i 0.325620 + 0.969827i
\(255\) −7.36266 + 0.842131i −0.461068 + 0.0527363i
\(256\) −13.6388 8.36566i −0.852422 0.522854i
\(257\) 13.3110i 0.830316i 0.909749 + 0.415158i \(0.136274\pi\)
−0.909749 + 0.415158i \(0.863726\pi\)
\(258\) −1.36266 + 0.457515i −0.0848356 + 0.0284836i
\(259\) 20.7999i 1.29244i
\(260\) −11.9477 12.5270i −0.740963 0.776890i
\(261\) 2.18513i 0.135256i
\(262\) 3.31867 + 9.88432i 0.205028 + 0.610656i
\(263\) 18.4256i 1.13617i −0.822969 0.568087i \(-0.807684\pi\)
0.822969 0.568087i \(-0.192316\pi\)
\(264\) −3.53579 2.41389i −0.217613 0.148565i
\(265\) −1.14554 10.0153i −0.0703701 0.615238i
\(266\) −25.1044 + 8.42882i −1.53925 + 0.516804i
\(267\) −14.7581 −0.903183
\(268\) −1.62093 + 1.22675i −0.0990142 + 0.0749356i
\(269\) 3.86940i 0.235921i −0.993018 0.117961i \(-0.962364\pi\)
0.993018 0.117961i \(-0.0376357\pi\)
\(270\) 1.34067 + 2.86402i 0.0815903 + 0.174299i
\(271\) −17.3955 −1.05670 −0.528350 0.849027i \(-0.677189\pi\)
−0.528350 + 0.849027i \(0.677189\pi\)
\(272\) −12.7581 3.60104i −0.773576 0.218345i
\(273\) 10.2293i 0.619108i
\(274\) −1.75007 5.21240i −0.105725 0.314893i
\(275\) −1.70892 7.37270i −0.103052 0.444591i
\(276\) 5.82687 + 7.69919i 0.350737 + 0.463437i
\(277\) 0.887271 0.0533110 0.0266555 0.999645i \(-0.491514\pi\)
0.0266555 + 0.999645i \(0.491514\pi\)
\(278\) 6.58501 + 19.6128i 0.394943 + 1.17630i
\(279\) −7.36266 −0.440791
\(280\) 7.79406 14.7850i 0.465784 0.883573i
\(281\) −13.4835 −0.804356 −0.402178 0.915562i \(-0.631747\pi\)
−0.402178 + 0.915562i \(0.631747\pi\)
\(282\) −3.18953 9.49971i −0.189934 0.565699i
\(283\) −28.4342 −1.69024 −0.845120 0.534577i \(-0.820471\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(284\) −10.7253 + 8.11710i −0.636431 + 0.481661i
\(285\) 15.7417 1.80052i 0.932460 0.106653i
\(286\) −2.63734 7.85505i −0.155949 0.464479i
\(287\) 23.0580i 1.36107i
\(288\) 0.276098 + 5.65011i 0.0162692 + 0.332936i
\(289\) 6.01641 0.353906
\(290\) 6.25827 2.92953i 0.367498 0.172028i
\(291\) 11.1444i 0.653294i
\(292\) 18.7253 + 24.7422i 1.09582 + 1.44793i
\(293\) −7.99166 −0.466878 −0.233439 0.972371i \(-0.574998\pi\)
−0.233439 + 0.972371i \(0.574998\pi\)
\(294\) −0.0219960 + 0.00738516i −0.00128283 + 0.000430711i
\(295\) −15.1044 + 1.72762i −0.879412 + 0.100586i
\(296\) 12.5522 18.3860i 0.729582 1.06867i
\(297\) 1.51363i 0.0878299i
\(298\) 4.98359 + 14.8431i 0.288692 + 0.859840i
\(299\) 18.6877i 1.08074i
\(300\) −6.40523 + 7.67939i −0.369806 + 0.443370i
\(301\) 2.68601i 0.154819i
\(302\) −0.854458 + 0.286885i −0.0491685 + 0.0165084i
\(303\) 13.3295i 0.765760i
\(304\) 27.2775 + 7.69919i 1.56447 + 0.441579i
\(305\) 8.00000 0.915029i 0.458079 0.0523944i
\(306\) 1.49180 + 4.44317i 0.0852803 + 0.253999i
\(307\) 17.4506 0.995961 0.497980 0.867188i \(-0.334075\pi\)
0.497980 + 0.867188i \(0.334075\pi\)
\(308\) 6.37907 4.82778i 0.363481 0.275088i
\(309\) 0.958386i 0.0545207i
\(310\) −9.87086 21.0868i −0.560627 1.19765i
\(311\) 21.4506 1.21635 0.608177 0.793801i \(-0.291901\pi\)
0.608177 + 0.793801i \(0.291901\pi\)
\(312\) −6.17313 + 9.04219i −0.349485 + 0.511913i
\(313\) 7.73879i 0.437422i −0.975790 0.218711i \(-0.929815\pi\)
0.975790 0.218711i \(-0.0701853\pi\)
\(314\) −0.173127 + 0.0581276i −0.00977014 + 0.00328033i
\(315\) −5.87086 + 0.671502i −0.330786 + 0.0378348i
\(316\) 11.7417 8.88633i 0.660524 0.499895i
\(317\) 11.2335 0.630938 0.315469 0.948936i \(-0.397838\pi\)
0.315469 + 0.948936i \(0.397838\pi\)
\(318\) −6.04399 + 2.02927i −0.338930 + 0.113796i
\(319\) 3.30749 0.185184
\(320\) −15.8119 + 8.36566i −0.883911 + 0.467655i
\(321\) −4.00000 −0.223258
\(322\) −17.1044 + 5.74281i −0.953190 + 0.320034i
\(323\) 23.4835 1.30665
\(324\) 1.59477 1.20695i 0.0885982 0.0670525i
\(325\) −18.8545 + 4.37027i −1.04586 + 0.242419i
\(326\) 26.1208 8.77008i 1.44670 0.485730i
\(327\) 0.769233i 0.0425387i
\(328\) −13.9149 + 20.3820i −0.768319 + 1.12541i
\(329\) 18.7253 1.03236
\(330\) −4.33508 + 2.02927i −0.238638 + 0.111708i
\(331\) 8.00084i 0.439766i −0.975526 0.219883i \(-0.929432\pi\)
0.975526 0.219883i \(-0.0705676\pi\)
\(332\) 12.3463 9.34385i 0.677589 0.512810i
\(333\) −7.87086 −0.431321
\(334\) 0.810466 + 2.41389i 0.0443467 + 0.132082i
\(335\) 0.258271 + 2.25803i 0.0141108 + 0.123369i
\(336\) −10.1731 2.87141i −0.554990 0.156648i
\(337\) 21.5692i 1.17495i −0.809243 0.587474i \(-0.800123\pi\)
0.809243 0.587474i \(-0.199877\pi\)
\(338\) −2.65933 + 0.892874i −0.144649 + 0.0485659i
\(339\) 14.4585i 0.785279i
\(340\) −10.7253 + 10.2293i −0.581662 + 0.554764i
\(341\) 11.1444i 0.603501i
\(342\) −3.18953 9.49971i −0.172470 0.513685i
\(343\) 18.5419i 1.00117i
\(344\) −1.62093 + 2.37429i −0.0873948 + 0.128013i
\(345\) 10.7253 1.22675i 0.577432 0.0660459i
\(346\) 31.1484 10.4581i 1.67455 0.562231i
\(347\) 21.7089 1.16540 0.582698 0.812689i \(-0.301997\pi\)
0.582698 + 0.812689i \(0.301997\pi\)
\(348\) −2.63734 3.48478i −0.141376 0.186804i
\(349\) 24.7422i 1.32442i 0.749318 + 0.662211i \(0.230382\pi\)
−0.749318 + 0.662211i \(0.769618\pi\)
\(350\) −9.79406 15.9140i −0.523514 0.850640i
\(351\) 3.87086 0.206611
\(352\) −8.55220 + 0.417910i −0.455834 + 0.0222747i
\(353\) 3.31415i 0.176394i −0.996103 0.0881972i \(-0.971889\pi\)
0.996103 0.0881972i \(-0.0281106\pi\)
\(354\) 3.06040 + 9.11509i 0.162658 + 0.484462i
\(355\) 1.70892 + 14.9409i 0.0906998 + 0.792979i
\(356\) −23.5358 + 17.8123i −1.24739 + 0.944048i
\(357\) −8.75814 −0.463530
\(358\) 1.28586 + 3.82979i 0.0679596 + 0.202411i
\(359\) 16.7581 0.884461 0.442230 0.896902i \(-0.354187\pi\)
0.442230 + 0.896902i \(0.354187\pi\)
\(360\) 5.59477 + 2.94934i 0.294870 + 0.155444i
\(361\) −31.2088 −1.64257
\(362\) 2.37907 + 7.08582i 0.125041 + 0.372422i
\(363\) 8.70892 0.457100
\(364\) −12.3463 16.3134i −0.647120 0.855055i
\(365\) 34.4671 3.94229i 1.80409 0.206349i
\(366\) −1.62093 4.82778i −0.0847275 0.252352i
\(367\) 28.5324i 1.48938i 0.667411 + 0.744690i \(0.267403\pi\)
−0.667411 + 0.744690i \(0.732597\pi\)
\(368\) 18.5850 + 5.24569i 0.968811 + 0.273451i
\(369\) 8.72532 0.454222
\(370\) −10.5522 22.5423i −0.548583 1.17192i
\(371\) 11.9136i 0.618523i
\(372\) −11.7417 + 8.88633i −0.608780 + 0.460735i
\(373\) 37.5798 1.94581 0.972904 0.231211i \(-0.0742688\pi\)
0.972904 + 0.231211i \(0.0742688\pi\)
\(374\) −6.72532 + 2.25803i −0.347758 + 0.116760i
\(375\) 3.74590 + 10.5341i 0.193437 + 0.543981i
\(376\) −16.5522 11.3002i −0.853614 0.582765i
\(377\) 8.45836i 0.435628i
\(378\) 1.18953 + 3.54291i 0.0611830 + 0.182228i
\(379\) 6.74456i 0.346445i −0.984883 0.173222i \(-0.944582\pi\)
0.984883 0.173222i \(-0.0554179\pi\)
\(380\) 22.9313 21.8708i 1.17635 1.12195i
\(381\) 11.5290i 0.590648i
\(382\) 8.00000 2.68601i 0.409316 0.137428i
\(383\) 21.8312i 1.11552i −0.830001 0.557762i \(-0.811660\pi\)
0.830001 0.557762i \(-0.188340\pi\)
\(384\) 7.25969 + 8.67738i 0.370470 + 0.442816i
\(385\) −1.01641 8.88633i −0.0518009 0.452889i
\(386\) 6.72532 + 20.0307i 0.342310 + 1.01954i
\(387\) 1.01641 0.0516669
\(388\) −13.4506 17.7727i −0.682853 0.902270i
\(389\) 8.81344i 0.446859i 0.974720 + 0.223429i \(0.0717252\pi\)
−0.974720 + 0.223429i \(0.928275\pi\)
\(390\) 5.18953 + 11.0862i 0.262782 + 0.561373i
\(391\) 16.0000 0.809155
\(392\) −0.0261649 + 0.0383256i −0.00132153 + 0.00193573i
\(393\) 7.37270i 0.371904i
\(394\) −4.33508 + 1.45551i −0.218398 + 0.0733273i
\(395\) −1.87086 16.3568i −0.0941334 0.822998i
\(396\) 1.82687 + 2.41389i 0.0918038 + 0.121303i
\(397\) −0.821644 −0.0412372 −0.0206186 0.999787i \(-0.506564\pi\)
−0.0206186 + 0.999787i \(0.506564\pi\)
\(398\) −10.8873 + 3.65541i −0.545730 + 0.183229i
\(399\) 18.7253 0.937439
\(400\) −0.946250 + 19.9776i −0.0473125 + 0.998880i
\(401\) −12.7253 −0.635472 −0.317736 0.948179i \(-0.602923\pi\)
−0.317736 + 0.948179i \(0.602923\pi\)
\(402\) 1.36266 0.457515i 0.0679634 0.0228188i
\(403\) −28.4999 −1.41968
\(404\) 16.0880 + 21.2574i 0.800407 + 1.05760i
\(405\) −0.254102 2.22158i −0.0126264 0.110391i
\(406\) 7.74173 2.59929i 0.384216 0.129001i
\(407\) 11.9136i 0.590535i
\(408\) 7.74173 + 5.28530i 0.383273 + 0.261661i
\(409\) −2.25827 −0.111664 −0.0558321 0.998440i \(-0.517781\pi\)
−0.0558321 + 0.998440i \(0.517781\pi\)
\(410\) 11.6977 + 24.9895i 0.577710 + 1.23414i
\(411\) 3.88792i 0.191777i
\(412\) −1.15672 1.52840i −0.0569875 0.0752990i
\(413\) −17.9672 −0.884107
\(414\) −2.17313 6.47244i −0.106803 0.318103i
\(415\) −1.96719 17.1989i −0.0965654 0.844261i
\(416\) 1.06874 + 21.8708i 0.0523991 + 1.07231i
\(417\) 14.6291i 0.716392i
\(418\) 14.3791 4.82778i 0.703303 0.236135i
\(419\) 33.4579i 1.63453i −0.576264 0.817263i \(-0.695490\pi\)
0.576264 0.817263i \(-0.304510\pi\)
\(420\) −8.55220 + 8.15670i −0.417304 + 0.398006i
\(421\) 11.3398i 0.552669i 0.961061 + 0.276335i \(0.0891198\pi\)
−0.961061 + 0.276335i \(0.910880\pi\)
\(422\) −6.17313 18.3860i −0.300503 0.895018i
\(423\) 7.08582i 0.344524i
\(424\) −7.18953 + 10.5310i −0.349155 + 0.511430i
\(425\) 3.74173 + 16.1428i 0.181501 + 0.783040i
\(426\) 9.01641 3.02727i 0.436846 0.146671i
\(427\) 9.51627 0.460525
\(428\) −6.37907 + 4.82778i −0.308344 + 0.233360i
\(429\) 5.85907i 0.282878i
\(430\) 1.36266 + 2.91101i 0.0657134 + 0.140381i
\(431\) 10.6597 0.513459 0.256730 0.966483i \(-0.417355\pi\)
0.256730 + 0.966483i \(0.417355\pi\)
\(432\) 1.08656 3.84959i 0.0522773 0.185214i
\(433\) 26.5132i 1.27414i 0.770805 + 0.637072i \(0.219854\pi\)
−0.770805 + 0.637072i \(0.780146\pi\)
\(434\) −8.75814 26.0852i −0.420404 1.25213i
\(435\) −4.85446 + 0.555246i −0.232753 + 0.0266220i
\(436\) 0.928423 + 1.22675i 0.0444634 + 0.0587506i
\(437\) −34.2088 −1.63643
\(438\) −6.98359 20.7999i −0.333689 0.993859i
\(439\) −32.8789 −1.56923 −0.784613 0.619986i \(-0.787138\pi\)
−0.784613 + 0.619986i \(0.787138\pi\)
\(440\) −4.46421 + 8.46842i −0.212823 + 0.403716i
\(441\) 0.0164068 0.000781274
\(442\) 5.77454 + 17.1989i 0.274667 + 0.818068i
\(443\) 5.70892 0.271239 0.135619 0.990761i \(-0.456698\pi\)
0.135619 + 0.990761i \(0.456698\pi\)
\(444\) −12.5522 + 9.49971i −0.595701 + 0.450836i
\(445\) 3.75007 + 32.7864i 0.177770 + 1.55423i
\(446\) 4.43140 + 13.1985i 0.209833 + 0.624966i
\(447\) 11.0715i 0.523662i
\(448\) −19.6894 + 7.69919i −0.930237 + 0.363753i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 6.02200 3.70615i 0.283880 0.174710i
\(451\) 13.2069i 0.621890i
\(452\) −17.4506 23.0580i −0.820809 1.08456i
\(453\) 0.637339 0.0299448
\(454\) 7.65375 2.56975i 0.359208 0.120604i
\(455\) −22.7253 + 2.59929i −1.06538 + 0.121857i
\(456\) −16.5522 11.3002i −0.775128 0.529182i
\(457\) 3.94229i 0.184413i 0.995740 + 0.0922064i \(0.0293920\pi\)
−0.995740 + 0.0922064i \(0.970608\pi\)
\(458\) 0.346255 + 1.03128i 0.0161794 + 0.0481888i
\(459\) 3.31415i 0.154691i
\(460\) 15.6238 14.9013i 0.728462 0.694775i
\(461\) 33.8969i 1.57874i 0.613920 + 0.789369i \(0.289592\pi\)
−0.613920 + 0.789369i \(0.710408\pi\)
\(462\) −5.36266 + 1.80052i −0.249494 + 0.0837677i
\(463\) 22.8688i 1.06280i 0.847120 + 0.531402i \(0.178335\pi\)
−0.847120 + 0.531402i \(0.821665\pi\)
\(464\) −8.41188 2.37429i −0.390512 0.110224i
\(465\) 1.87086 + 16.3568i 0.0867593 + 0.758527i
\(466\) −8.28275 24.6693i −0.383691 1.14278i
\(467\) −15.7417 −0.728440 −0.364220 0.931313i \(-0.618664\pi\)
−0.364220 + 0.931313i \(0.618664\pi\)
\(468\) 6.17313 4.67192i 0.285353 0.215960i
\(469\) 2.68601i 0.124028i
\(470\) −20.2939 + 9.49971i −0.936089 + 0.438189i
\(471\) 0.129135 0.00595024
\(472\) 15.8820 + 10.8427i 0.731030 + 0.499076i
\(473\) 1.53847i 0.0707388i
\(474\) −9.87086 + 3.31415i −0.453384 + 0.152224i
\(475\) −8.00000 34.5140i −0.367065 1.58361i
\(476\) −13.9672 + 10.5706i −0.640185 + 0.484502i
\(477\) 4.50820 0.206416
\(478\) 13.4506 4.51606i 0.615218 0.206560i
\(479\) −20.6925 −0.945465 −0.472732 0.881206i \(-0.656732\pi\)
−0.472732 + 0.881206i \(0.656732\pi\)
\(480\) 12.4820 2.04908i 0.569725 0.0935271i
\(481\) −30.4671 −1.38918
\(482\) −14.4231 + 4.84255i −0.656952 + 0.220572i
\(483\) 12.7581 0.580515
\(484\) 13.8887 10.5112i 0.631304 0.477781i
\(485\) −24.7581 + 2.83180i −1.12421 + 0.128586i
\(486\) −1.34067 + 0.450129i −0.0608138 + 0.0204183i
\(487\) 30.8401i 1.39750i −0.715366 0.698750i \(-0.753740\pi\)
0.715366 0.698750i \(-0.246260\pi\)
\(488\) −8.41188 5.74281i −0.380788 0.259965i
\(489\) −19.4835 −0.881072
\(490\) 0.0219960 + 0.0469893i 0.000993676 + 0.00212276i
\(491\) 10.9737i 0.495238i 0.968858 + 0.247619i \(0.0796481\pi\)
−0.968858 + 0.247619i \(0.920352\pi\)
\(492\) 13.9149 10.5310i 0.627330 0.474774i
\(493\) −7.24186 −0.326157
\(494\) −12.3463 36.7721i −0.555484 1.65445i
\(495\) 3.36266 0.384617i 0.151140 0.0172872i
\(496\) −8.00000 + 28.3433i −0.359211 + 1.27265i
\(497\) 17.7727i 0.797213i
\(498\) −10.3791 + 3.48478i −0.465097 + 0.156157i
\(499\) 3.71729i 0.166409i 0.996533 + 0.0832044i \(0.0265154\pi\)
−0.996533 + 0.0832044i \(0.973485\pi\)
\(500\) 18.6880 + 12.2784i 0.835752 + 0.549107i
\(501\) 1.80052i 0.0804412i
\(502\) −5.69774 16.9701i −0.254302 0.757414i
\(503\) 39.9451i 1.78107i 0.454919 + 0.890533i \(0.349668\pi\)
−0.454919 + 0.890533i \(0.650332\pi\)
\(504\) 6.17313 + 4.21441i 0.274973 + 0.187725i
\(505\) 29.6126 3.38705i 1.31774 0.150722i
\(506\) 9.79690 3.28932i 0.435525 0.146228i
\(507\) 1.98359 0.0880945
\(508\) −13.9149 18.3860i −0.617372 0.815749i
\(509\) 0.0728979i 0.00323114i −0.999999 0.00161557i \(-0.999486\pi\)
0.999999 0.00161557i \(-0.000514253\pi\)
\(510\) 9.49180 4.44317i 0.420304 0.196747i
\(511\) 40.9997 1.81372
\(512\) 22.0506 + 5.07634i 0.974510 + 0.224345i
\(513\) 7.08582i 0.312846i
\(514\) −5.99166 17.8456i −0.264281 0.787134i
\(515\) −2.12914 + 0.243528i −0.0938209 + 0.0107311i
\(516\) 1.62093 1.22675i 0.0713576 0.0540046i
\(517\) −10.7253 −0.471699
\(518\) −9.36266 27.8857i −0.411372 1.22523i
\(519\) −23.2335 −1.01984
\(520\) 21.6566 + 11.4165i 0.949704 + 0.500646i
\(521\) −11.9672 −0.524292 −0.262146 0.965028i \(-0.584430\pi\)
−0.262146 + 0.965028i \(0.584430\pi\)
\(522\) 0.983593 + 2.92953i 0.0430507 + 0.128222i
\(523\) 16.0656 0.702501 0.351250 0.936282i \(-0.385757\pi\)
0.351250 + 0.936282i \(0.385757\pi\)
\(524\) −8.89845 11.7577i −0.388731 0.513639i
\(525\) 2.98359 + 12.8720i 0.130215 + 0.561779i
\(526\) 8.29392 + 24.7026i 0.361632 + 1.07709i
\(527\) 24.4010i 1.06292i
\(528\) 5.82687 + 1.64466i 0.253582 + 0.0715746i
\(529\) −0.307491 −0.0133692
\(530\) 6.04399 + 12.9116i 0.262534 + 0.560844i
\(531\) 6.79893i 0.295048i
\(532\) 29.8625 22.6004i 1.29470 0.979854i
\(533\) 33.7745 1.46294
\(534\) 19.7857 6.64307i 0.856212 0.287474i
\(535\) 1.01641 + 8.88633i 0.0439431 + 0.384190i
\(536\) 1.62093 2.37429i 0.0700136 0.102554i
\(537\) 2.85664i 0.123273i
\(538\) 1.74173 + 5.18757i 0.0750913 + 0.223652i
\(539\) 0.0248338i 0.00106967i
\(540\) −3.08656 3.23622i −0.132825 0.139265i
\(541\) 15.8559i 0.681698i −0.940118 0.340849i \(-0.889285\pi\)
0.940118 0.340849i \(-0.110715\pi\)
\(542\) 23.3215 7.83021i 1.00174 0.336337i
\(543\) 5.28530i 0.226814i
\(544\) 18.7253 0.915029i 0.802842 0.0392316i
\(545\) 1.70892 0.195463i 0.0732019 0.00837274i
\(546\) 4.60453 + 13.7141i 0.197055 + 0.586910i
\(547\) 4.95078 0.211680 0.105840 0.994383i \(-0.466247\pi\)
0.105840 + 0.994383i \(0.466247\pi\)
\(548\) 4.69251 + 6.20033i 0.200454 + 0.264865i
\(549\) 3.60104i 0.153688i
\(550\) 5.60975 + 9.11509i 0.239201 + 0.388669i
\(551\) 15.4835 0.659618
\(552\) −11.2775 7.69919i −0.480003 0.327699i
\(553\) 19.4569i 0.827393i
\(554\) −1.18953 + 0.399387i −0.0505385 + 0.0169683i
\(555\) 2.00000 + 17.4858i 0.0848953 + 0.742230i
\(556\) −17.6566 23.3301i −0.748806 0.989416i
\(557\) −1.26634 −0.0536565 −0.0268283 0.999640i \(-0.508541\pi\)
−0.0268283 + 0.999640i \(0.508541\pi\)
\(558\) 9.87086 3.31415i 0.417867 0.140299i
\(559\) 3.93437 0.166406
\(560\) −3.79406 + 23.3301i −0.160328 + 0.985876i
\(561\) 5.01641 0.211793
\(562\) 18.0768 6.06930i 0.762524 0.256018i
\(563\) −5.70892 −0.240602 −0.120301 0.992737i \(-0.538386\pi\)
−0.120301 + 0.992737i \(0.538386\pi\)
\(564\) 8.55220 + 11.3002i 0.360112 + 0.475825i
\(565\) −32.1208 + 3.67393i −1.35133 + 0.154564i
\(566\) 38.1208 12.7991i 1.60234 0.537986i
\(567\) 2.64265i 0.110981i
\(568\) 10.7253 15.7101i 0.450025 0.659181i
\(569\) 2.75814 0.115627 0.0578135 0.998327i \(-0.481587\pi\)
0.0578135 + 0.998327i \(0.481587\pi\)
\(570\) −20.2939 + 9.49971i −0.850019 + 0.397899i
\(571\) 25.7735i 1.07859i −0.842118 0.539294i \(-0.818691\pi\)
0.842118 0.539294i \(-0.181309\pi\)
\(572\) 7.07158 + 9.34385i 0.295677 + 0.390686i
\(573\) −5.96719 −0.249283
\(574\) 10.3791 + 30.9130i 0.433214 + 1.29028i
\(575\) −5.45065 23.5155i −0.227308 0.980663i
\(576\) −2.91344 7.45063i −0.121393 0.310443i
\(577\) 32.7135i 1.36188i 0.732338 + 0.680941i \(0.238429\pi\)
−0.732338 + 0.680941i \(0.761571\pi\)
\(578\) −8.06599 + 2.70816i −0.335501 + 0.112645i
\(579\) 14.9409i 0.620921i
\(580\) −7.07158 + 6.74456i −0.293631 + 0.280052i
\(581\) 20.4587i 0.848769i
\(582\) 5.01641 + 14.9409i 0.207937 + 0.619319i
\(583\) 6.82376i 0.282611i
\(584\) −36.2416 24.7422i −1.49969 1.02384i
\(585\) −0.983593 8.59945i −0.0406666 0.355543i
\(586\) 10.7141 3.59728i 0.442597 0.148602i
\(587\) −43.4835 −1.79475 −0.897377 0.441264i \(-0.854530\pi\)
−0.897377 + 0.441264i \(0.854530\pi\)
\(588\) 0.0261649 0.0198021i 0.00107902 0.000816623i
\(589\) 52.1705i 2.14965i
\(590\) 19.4723 9.11509i 0.801661 0.375262i
\(591\) 3.23353 0.133009
\(592\) −8.55220 + 30.2996i −0.351493 + 1.24531i
\(593\) 7.83021i 0.321548i 0.986991 + 0.160774i \(0.0513991\pi\)
−0.986991 + 0.160774i \(0.948601\pi\)
\(594\) −0.681331 2.02927i −0.0279553 0.0832622i
\(595\) 2.22546 + 19.4569i 0.0912348 + 0.797656i
\(596\) −13.3627 17.6564i −0.547356 0.723235i
\(597\) 8.12080 0.332362
\(598\) −8.41188 25.0539i −0.343987 1.02453i
\(599\) 32.7581 1.33846 0.669231 0.743055i \(-0.266624\pi\)
0.669231 + 0.743055i \(0.266624\pi\)
\(600\) 5.13056 13.1787i 0.209454 0.538017i
\(601\) 17.8074 0.726377 0.363189 0.931716i \(-0.381688\pi\)
0.363189 + 0.931716i \(0.381688\pi\)
\(602\) 1.20905 + 3.60104i 0.0492772 + 0.146767i
\(603\) −1.01641 −0.0413913
\(604\) 1.01641 0.769233i 0.0413570 0.0312997i
\(605\) −2.21295 19.3476i −0.0899692 0.786591i
\(606\) −6.00000 17.8704i −0.243733 0.725935i
\(607\) 3.41188i 0.138484i 0.997600 + 0.0692420i \(0.0220581\pi\)
−0.997600 + 0.0692420i \(0.977942\pi\)
\(608\) −40.0357 + 1.95638i −1.62366 + 0.0793416i
\(609\) −5.77454 −0.233996
\(610\) −10.3134 + 4.82778i −0.417579 + 0.195471i
\(611\) 27.4282i 1.10963i
\(612\) −4.00000 5.28530i −0.161690 0.213646i
\(613\) 36.6290 1.47943 0.739716 0.672920i \(-0.234960\pi\)
0.739716 + 0.672920i \(0.234960\pi\)
\(614\) −23.3955 + 7.85505i −0.944165 + 0.317004i
\(615\) −2.21712 19.3840i −0.0894029 0.781640i
\(616\) −6.37907 + 9.34385i −0.257020 + 0.376474i
\(617\) 40.3979i 1.62636i −0.582012 0.813180i \(-0.697734\pi\)
0.582012 0.813180i \(-0.302266\pi\)
\(618\) 0.431398 + 1.28488i 0.0173534 + 0.0516853i
\(619\) 24.5172i 0.985430i −0.870191 0.492715i \(-0.836004\pi\)
0.870191 0.492715i \(-0.163996\pi\)
\(620\) 22.7253 + 23.8272i 0.912671 + 0.956923i
\(621\) 4.82778i 0.193732i
\(622\) −28.7581 + 9.65557i −1.15310 + 0.387153i
\(623\) 39.0006i 1.56252i
\(624\) 4.20594 14.9013i 0.168372 0.596528i
\(625\) 22.4506 10.9986i 0.898026 0.439943i
\(626\) 3.48346 + 10.3751i 0.139227 + 0.414674i
\(627\) −10.7253 −0.428328
\(628\) 0.205941 0.155859i 0.00821793 0.00621947i
\(629\) 26.0852i 1.04009i
\(630\) 7.56860 3.54291i 0.301540 0.141153i
\(631\) 18.7805 0.747640 0.373820 0.927501i \(-0.378048\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(632\) −11.7417 + 17.1989i −0.467061 + 0.684135i
\(633\) 13.7141i 0.545087i
\(634\) −15.0604 + 5.05654i −0.598125 + 0.200821i
\(635\) −25.6126 + 2.92953i −1.01640 + 0.116255i
\(636\) 7.18953 5.44116i 0.285084 0.215756i
\(637\) 0.0635083 0.00251629
\(638\) −4.43424 + 1.48880i −0.175553 + 0.0589421i
\(639\) −6.72532 −0.266050
\(640\) 17.4328 18.3329i 0.689093 0.724673i
\(641\) −15.5163 −0.612856 −0.306428 0.951894i \(-0.599134\pi\)
−0.306428 + 0.951894i \(0.599134\pi\)
\(642\) 5.36266 1.80052i 0.211647 0.0710608i
\(643\) 17.4506 0.688186 0.344093 0.938936i \(-0.388186\pi\)
0.344093 + 0.938936i \(0.388186\pi\)
\(644\) 20.3463 15.3984i 0.801755 0.606781i
\(645\) −0.258271 2.25803i −0.0101694 0.0889099i
\(646\) −31.4835 + 10.5706i −1.23870 + 0.415895i
\(647\) 13.1403i 0.516600i 0.966065 + 0.258300i \(0.0831624\pi\)
−0.966065 + 0.258300i \(0.916838\pi\)
\(648\) −1.59477 + 2.33596i −0.0626484 + 0.0917653i
\(649\) 10.2911 0.403960
\(650\) 23.3103 14.3460i 0.914306 0.562697i
\(651\) 19.4569i 0.762577i
\(652\) −31.0716 + 23.5155i −1.21686 + 0.920937i
\(653\) −14.7993 −0.579141 −0.289570 0.957157i \(-0.593512\pi\)
−0.289570 + 0.957157i \(0.593512\pi\)
\(654\) −0.346255 1.03128i −0.0135396 0.0403264i
\(655\) −16.3791 + 1.87342i −0.639983 + 0.0732004i
\(656\) 9.48062 33.5890i 0.370156 1.31143i
\(657\) 15.5146i 0.605284i
\(658\) −25.1044 + 8.42882i −0.978671 + 0.328590i
\(659\) 7.99614i 0.311485i 0.987798 + 0.155743i \(0.0497771\pi\)
−0.987798 + 0.155743i \(0.950223\pi\)
\(660\) 4.89845 4.67192i 0.190672 0.181854i
\(661\) 0.915029i 0.0355905i 0.999842 + 0.0177953i \(0.00566470\pi\)
−0.999842 + 0.0177953i \(0.994335\pi\)
\(662\) 3.60142 + 10.7265i 0.139973 + 0.416896i
\(663\) 12.8286i 0.498223i
\(664\) −12.3463 + 18.0844i −0.479128 + 0.701810i
\(665\) −4.75814 41.5999i −0.184513 1.61317i
\(666\) 10.5522 3.54291i 0.408889 0.137285i
\(667\) 10.5494 0.408473
\(668\) −2.17313 2.87141i −0.0840808 0.111098i
\(669\) 9.84472i 0.380619i
\(670\) −1.36266 2.91101i −0.0526442 0.112462i
\(671\) −5.45065 −0.210420
\(672\) 14.9313 0.729629i 0.575986 0.0281461i
\(673\) 34.3978i 1.32594i 0.748647 + 0.662969i \(0.230704\pi\)
−0.748647 + 0.662969i \(0.769296\pi\)
\(674\) 9.70892 + 28.9170i 0.373973 + 1.11384i
\(675\) −4.87086 + 1.12902i −0.187480 + 0.0434559i
\(676\) 3.16337 2.39409i 0.121668 0.0920804i
\(677\) 40.1676 1.54377 0.771884 0.635764i \(-0.219315\pi\)
0.771884 + 0.635764i \(0.219315\pi\)
\(678\) 6.50820 + 19.3840i 0.249946 + 0.744439i
\(679\) −29.4506 −1.13021
\(680\) 9.77454 18.5419i 0.374837 0.711049i
\(681\) −5.70892 −0.218766
\(682\) 5.01641 + 14.9409i 0.192088 + 0.572115i
\(683\) 33.2580 1.27258 0.636291 0.771449i \(-0.280468\pi\)
0.636291 + 0.771449i \(0.280468\pi\)
\(684\) 8.55220 + 11.3002i 0.327001 + 0.432075i
\(685\) 8.63734 0.987927i 0.330016 0.0377468i
\(686\) 8.34625 + 24.8585i 0.318661 + 0.949101i
\(687\) 0.769233i 0.0293481i
\(688\) 1.10439 3.91275i 0.0421045 0.149172i
\(689\) 17.4506 0.664817
\(690\) −13.8269 + 6.47244i −0.526380 + 0.246402i
\(691\) 50.2241i 1.91062i 0.295611 + 0.955308i \(0.404477\pi\)
−0.295611 + 0.955308i \(0.595523\pi\)
\(692\) −37.0521 + 28.0416i −1.40851 + 1.06598i
\(693\) 4.00000 0.151947
\(694\) −29.1044 + 9.77182i −1.10479 + 0.370933i
\(695\) −32.4999 + 3.71729i −1.23279 + 0.141005i
\(696\) 5.10439 + 3.48478i 0.193481 + 0.132090i
\(697\) 28.9170i 1.09531i
\(698\) −11.1372 33.1710i −0.421549 1.25554i
\(699\) 18.4008i 0.695983i
\(700\) 20.2939 + 16.9268i 0.767038 + 0.639772i
\(701\) 23.7543i 0.897188i −0.893736 0.448594i \(-0.851925\pi\)
0.893736 0.448594i \(-0.148075\pi\)
\(702\) −5.18953 + 1.74239i −0.195866 + 0.0657623i
\(703\) 55.7715i 2.10346i
\(704\) 11.2775 4.40987i 0.425037 0.166203i
\(705\) 15.7417 1.80052i 0.592868 0.0678114i
\(706\) 1.49180 + 4.44317i 0.0561445 + 0.167221i
\(707\) 35.2252 1.32478
\(708\) −8.20594 10.8427i −0.308398 0.407494i
\(709\) 36.3146i 1.36382i −0.731435 0.681911i \(-0.761149\pi\)
0.731435 0.681911i \(-0.238851\pi\)
\(710\) −9.01641 19.2615i −0.338380 0.722870i
\(711\) 7.36266 0.276121
\(712\) 23.5358 34.4744i 0.882041 1.29198i
\(713\) 35.5453i 1.33118i
\(714\) 11.7417 3.94229i 0.439423 0.147537i
\(715\) 13.0164 1.48880i 0.486786 0.0556779i
\(716\) −3.44780 4.55567i −0.128851 0.170253i
\(717\) −10.0328 −0.374682
\(718\) −22.4671 + 7.54333i −0.838463 + 0.281515i
\(719\) −30.7253 −1.14586 −0.572931 0.819604i \(-0.694194\pi\)
−0.572931 + 0.819604i \(0.694194\pi\)
\(720\) −8.82829 1.43570i −0.329011 0.0535055i
\(721\) −2.53268 −0.0943219
\(722\) 41.8405 14.0480i 1.55714 0.522812i
\(723\) 10.7581 0.400099
\(724\) −6.37907 8.42882i −0.237076 0.313255i
\(725\) 2.46705 + 10.6435i 0.0916240 + 0.395289i
\(726\) −11.6757 + 3.92014i −0.433327 + 0.145490i
\(727\) 5.47445i 0.203036i −0.994834 0.101518i \(-0.967630\pi\)
0.994834 0.101518i \(-0.0323700\pi\)
\(728\) 23.8953 + 16.3134i 0.885620 + 0.604615i
\(729\) 1.00000 0.0370370
\(730\) −44.4342 + 20.7999i −1.64458 + 0.769840i
\(731\) 3.36852i 0.124589i
\(732\) 4.34625 + 5.74281i 0.160642 + 0.212260i
\(733\) −17.1455 −0.633285 −0.316643 0.948545i \(-0.602556\pi\)
−0.316643 + 0.948545i \(0.602556\pi\)
\(734\) −12.8433 38.2524i −0.474054 1.41192i
\(735\) −0.00416898 0.0364490i −0.000153775 0.00134444i
\(736\) −27.2775 + 1.33294i −1.00546 + 0.0491328i
\(737\) 1.53847i 0.0566701i
\(738\) −11.6977 + 3.92752i −0.430600 + 0.144574i
\(739\) 11.6019i 0.426782i 0.976967 + 0.213391i \(0.0684508\pi\)
−0.976967 + 0.213391i \(0.931549\pi\)
\(740\) 24.2939 + 25.4719i 0.893062 + 0.936364i
\(741\) 27.4282i 1.00760i
\(742\) 5.36266 + 15.9721i 0.196869 + 0.586356i
\(743\) 23.6613i 0.868048i −0.900901 0.434024i \(-0.857093\pi\)
0.900901 0.434024i \(-0.142907\pi\)
\(744\) 11.7417 17.1989i 0.430473 0.630542i
\(745\) −24.5962 + 2.81328i −0.901135 + 0.103071i
\(746\) −50.3819 + 16.9158i −1.84461 + 0.619330i
\(747\) 7.74173 0.283255
\(748\) 8.00000 6.05453i 0.292509 0.221376i
\(749\) 10.5706i 0.386241i
\(750\) −9.76373 12.4366i −0.356521 0.454121i
\(751\) −11.4283 −0.417024 −0.208512 0.978020i \(-0.566862\pi\)
−0.208512 + 0.978020i \(0.566862\pi\)
\(752\) 27.2775 + 7.69919i 0.994709 + 0.280761i
\(753\) 12.6580i 0.461283i
\(754\) 3.80736 + 11.3398i 0.138656 + 0.412972i
\(755\) −0.161949 1.41590i −0.00589392 0.0515299i
\(756\) −3.18953 4.21441i −0.116002 0.153277i
\(757\) −19.1784 −0.697049 −0.348525 0.937300i \(-0.613317\pi\)
−0.348525 + 0.937300i \(0.613317\pi\)
\(758\) 3.03592 + 9.04219i 0.110270 + 0.328427i
\(759\) −7.30749 −0.265245
\(760\) −20.8984 + 39.6435i −0.758066 + 1.43802i
\(761\) 4.03281 0.146189 0.0730947 0.997325i \(-0.476712\pi\)
0.0730947 + 0.997325i \(0.476712\pi\)
\(762\) 5.18953 + 15.4565i 0.187997 + 0.559930i
\(763\) 2.03281 0.0735928
\(764\) −9.51627 + 7.20207i −0.344287 + 0.260562i
\(765\) −7.36266 + 0.842131i −0.266198 + 0.0304473i
\(766\) 9.82687 + 29.2684i 0.355059 + 1.05751i
\(767\) 26.3177i 0.950279i
\(768\) −13.6388 8.36566i −0.492146 0.301870i
\(769\) 2.95078 0.106408 0.0532039 0.998584i \(-0.483057\pi\)
0.0532039 + 0.998584i \(0.483057\pi\)
\(770\) 5.36266 + 11.4561i 0.193257 + 0.412849i
\(771\) 13.3110i 0.479383i
\(772\) −18.0328 23.8272i −0.649015 0.857560i
\(773\) 45.2663 1.62812 0.814059 0.580783i \(-0.197253\pi\)
0.814059 + 0.580783i \(0.197253\pi\)
\(774\) −1.36266 + 0.457515i −0.0489798 + 0.0164450i
\(775\) 35.8625 8.31256i 1.28822 0.298596i
\(776\) 26.0328 + 17.7727i 0.934524 + 0.638002i
\(777\) 20.7999i