Properties

Label 120.2.d.b.109.5
Level $120$
Weight $2$
Character 120.109
Analytic conductor $0.958$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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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 109.5
Root \(-1.32132i\) of defining polynomial
Character \(\chi\) \(=\) 120.109
Dual form 120.2.d.b.109.6

$q$-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} +(-0.659335 - 3.09278i) 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} +(-2.27610 - 3.84959i) 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} +(0.659335 + 3.09278i) 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} +(-4.78430 - 4.13648i) 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} +(-7.03840 + 0.678887i) 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} +(2.27610 + 3.84959i) 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} +(8.17313 - 1.74239i) 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} +(-8.27610 - 3.39208i) 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} +(-0.659335 - 3.09278i) 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 \( 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9} - 11 q^{10} - q^{12} + 8 q^{13} - 10 q^{14} + q^{16} + q^{18} + 9 q^{20} - 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} - 6 q^{27} + 2 q^{28} + 11 q^{30} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} + q^{36} + 16 q^{37} + 2 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 10 q^{42} + 22 q^{44} - 2 q^{46} - q^{48} - 6 q^{49} - 15 q^{50} - 26 q^{52} - 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} - 12 q^{58} - 9 q^{60} - 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} + 24 q^{68} + 38 q^{70} + 16 q^{71} + q^{72} + 18 q^{74} - 2 q^{75} + 6 q^{76} - 24 q^{77} + 14 q^{78} + 16 q^{79} - 27 q^{80} + 6 q^{81} + 50 q^{82} + 16 q^{83} - 2 q^{84} + 16 q^{85} + 20 q^{86} - 18 q^{88} - 20 q^{89} - 11 q^{90} - 46 q^{92} + 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} - 21 q^{98}+O(q^{100}) \) 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 \(0.166451\pi\)
−0.866364 + 0.499414i \(0.833549\pi\)
\(8\) 1.59477 2.33596i 0.563835 0.825887i
\(9\) 1.00000 0.333333
\(10\) −0.659335 3.09278i −0.208500 0.978022i
\(11\) 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 \(-0.680364\pi\)
−0.536792 + 0.843714i \(0.680364\pi\)
\(14\) 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 \(0.131650\pi\)
−0.915684 + 0.401900i \(0.868350\pi\)
\(18\) 1.34067 0.450129i 0.315998 0.106097i
\(19\) 7.08582i 1.62560i 0.582545 + 0.812799i \(0.302057\pi\)
−0.582545 + 0.812799i \(0.697943\pi\)
\(20\) −2.27610 3.84959i −0.508951 0.860796i
\(21\) 2.64265i 0.576673i
\(22\) 0.681331 + 2.02927i 0.145260 + 0.432643i
\(23\) 4.82778i 1.00666i −0.864094 0.503331i \(-0.832108\pi\)
0.864094 0.503331i \(-0.167892\pi\)
\(24\) −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 \(-0.0650316\pi\)
\(30\) 0.659335 + 3.09278i 0.120377 + 0.564661i
\(31\) −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 \(-0.276031\pi\)
0.646981 + 0.762506i \(0.276031\pi\)
\(38\) 3.18953 + 9.49971i 0.517411 + 1.54106i
\(39\) 3.87086 0.619834
\(40\) −4.78430 4.13648i −0.756464 0.654035i
\(41\) 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 \(-0.524694\pi\)
−0.0775003 + 0.996992i \(0.524694\pi\)
\(44\) 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 \(-0.827128\pi\)
0.856114 0.516786i \(-0.172872\pi\)
\(48\) −1.08656 + 3.84959i −0.156832 + 0.555641i
\(49\) 0.0164068 0.00234382
\(50\) −7.03840 + 0.678887i −0.995380 + 0.0960091i
\(51\) 3.31415i 0.464074i
\(52\) −6.17313 + 4.67192i −0.856059 + 0.647879i
\(53\) −4.50820 −0.619249 −0.309625 0.950859i \(-0.600203\pi\)
−0.309625 + 0.950859i \(0.600203\pi\)
\(54\) −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 \(-0.145934\pi\)
\(60\) 2.27610 + 3.84959i 0.293843 + 0.496981i
\(61\) 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 \(-0.480224\pi\)
0.0620869 + 0.998071i \(0.480224\pi\)
\(68\) 4.00000 + 5.28530i 0.485071 + 0.640937i
\(69\) 4.82778i 0.581197i
\(70\) 8.17313 1.74239i 0.976876 0.208255i
\(71\) −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 \(-0.637666\pi\)
0.419132 0.907925i \(-0.362334\pi\)
\(74\) 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 \(0.364068\pi\)
\(80\) −8.27610 3.39208i −0.925296 0.379246i
\(81\) 1.00000 0.111111
\(82\) 11.6977 3.92752i 1.29180 0.433723i
\(83\) −7.74173 −0.849765 −0.424883 0.905248i \(-0.639685\pi\)
−0.424883 + 0.905248i \(0.639685\pi\)
\(84\) −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 \(0.785892\pi\)
\(90\) −0.659335 3.09278i −0.0695000 0.326007i
\(91\) 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 \(0.191421\pi\)
−0.824563 + 0.565769i \(0.808579\pi\)
\(98\) 0.0219960 0.00738516i 0.00222193 0.000746014i
\(99\) 1.51363i 0.152126i
\(100\) −9.13056 + 4.07835i −0.913056 + 0.407835i
\(101\) 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 \(0.0150350\pi\)
−0.998885 + 0.0472163i \(0.984965\pi\)
\(104\) −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 \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) −1.59477 + 1.20695i −0.153457 + 0.116138i
\(109\) 0.769233i 0.0736792i 0.999321 + 0.0368396i \(0.0117291\pi\)
−0.999321 + 0.0368396i \(0.988271\pi\)
\(110\) 4.68133 0.997991i 0.446347 0.0951547i
\(111\) −7.87086 −0.747069
\(112\) 10.1731 + 2.87141i 0.961270 + 0.271322i
\(113\) 14.4585i 1.36014i 0.733146 + 0.680071i \(0.238051\pi\)
−0.733146 + 0.680071i \(0.761949\pi\)
\(114\) −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
\(120\) 4.78430 + 4.13648i 0.436745 + 0.377607i
\(121\) 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 \(0.170916\pi\)
−0.859274 + 0.511516i \(0.829084\pi\)
\(128\) −7.25969 8.67738i −0.641672 0.766979i
\(129\) 1.01641 0.0894896
\(130\) 2.55220 + 11.9717i 0.223842 + 1.04999i
\(131\) 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 \(-0.946888\pi\)
0.986112 0.166084i \(-0.0531122\pi\)
\(138\) 2.17313 + 6.47244i 0.184989 + 0.550971i
\(139\) 14.6291i 1.24083i −0.784275 0.620414i \(-0.786965\pi\)
0.784275 0.620414i \(-0.213035\pi\)
\(140\) 10.1731 6.01493i 0.859786 0.508354i
\(141\) 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 \(-0.149827\pi\)
\(150\) 7.03840 0.678887i 0.574683 0.0554309i
\(151\) 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 \(-0.501640\pi\)
−0.00515306 + 0.999987i \(0.501640\pi\)
\(158\) 9.87086 3.31415i 0.785284 0.263660i
\(159\) 4.50820 0.357524
\(160\) −12.6224 0.822329i −0.997885 0.0650108i
\(161\) 12.7581 1.00548
\(162\) 1.34067 0.450129i 0.105333 0.0353655i
\(163\) 19.4835 1.52606 0.763031 0.646362i \(-0.223710\pi\)
0.763031 + 0.646362i \(0.223710\pi\)
\(164\) 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 \(0.0221928\pi\)
−0.997571 + 0.0696641i \(0.977807\pi\)
\(168\) −6.17313 4.21441i −0.476267 0.325149i
\(169\) 1.98359 0.152584
\(170\) 10.2499 2.18513i 0.786134 0.167592i
\(171\) 7.08582i 0.541866i
\(172\) −1.62093 + 1.22675i −0.123595 + 0.0935386i
\(173\) 23.2335 1.76641 0.883206 0.468985i \(-0.155380\pi\)
0.883206 + 0.468985i \(0.155380\pi\)
\(174\) 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 \(-0.0340468\pi\)
\(180\) −2.27610 3.84959i −0.169650 0.286932i
\(181\) 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
\(190\) 21.9149 4.67192i 1.58987 0.338937i
\(191\) −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 \(0.180719\pi\)
−0.843115 + 0.537733i \(0.819281\pi\)
\(194\) 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 \(-0.536748\pi\)
−0.115190 + 0.993344i \(0.536748\pi\)
\(198\) 0.681331 + 2.02927i 0.0484201 + 0.144214i
\(199\) 8.12080 0.575668 0.287834 0.957680i \(-0.407065\pi\)
0.287834 + 0.957680i \(0.407065\pi\)
\(200\) −10.4052 + 9.57764i −0.735761 + 0.677241i
\(201\) −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
\(210\) −8.17313 + 1.74239i −0.563999 + 0.120236i
\(211\) 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
\(220\) 5.82687 3.44518i 0.392848 0.232274i
\(221\) 12.8286i 0.862947i
\(222\) −10.5522 + 3.54291i −0.708217 + 0.237784i
\(223\) 9.84472i 0.659251i 0.944112 + 0.329626i \(0.106923\pi\)
−0.944112 + 0.329626i \(0.893077\pi\)
\(224\) 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 \(-0.439327\pi\)
0.189457 + 0.981889i \(0.439327\pi\)
\(228\) −8.55220 11.3002i −0.566383 0.748376i
\(229\) 0.769233i 0.0508324i −0.999677 0.0254162i \(-0.991909\pi\)
0.999677 0.0254162i \(-0.00809109\pi\)
\(230\) −14.9313 + 3.18312i −0.984538 + 0.209889i
\(231\) 4.00000 0.263181
\(232\) −5.10439 3.48478i −0.335120 0.228787i
\(233\) 18.4008i 1.20548i −0.797939 0.602739i \(-0.794076\pi\)
0.797939 0.602739i \(-0.205924\pi\)
\(234\) −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 \(0.605191\pi\)
\(240\) 8.27610 + 3.39208i 0.534220 + 0.218958i
\(241\) 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
\(250\) −0.280267 + 15.8089i −0.0177256 + 0.999843i
\(251\) 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 \(-0.863726\pi\)
0.909749 0.415158i \(-0.136274\pi\)
\(258\) 1.36266 0.457515i 0.0848356 0.0284836i
\(259\) 20.7999i 1.29244i
\(260\) 8.81047 + 14.9013i 0.546402 + 0.924137i
\(261\) 2.18513i 0.135256i
\(262\) −3.31867 9.88432i −0.205028 0.610656i
\(263\) 18.4256i 1.13617i 0.822969 + 0.568087i \(0.192316\pi\)
−0.822969 + 0.568087i \(0.807684\pi\)
\(264\) −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 \(-0.0376357\pi\)
\(270\) 0.659335 + 3.09278i 0.0401258 + 0.188220i
\(271\) −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 \(-0.508486\pi\)
−0.0266555 + 0.999645i \(0.508486\pi\)
\(278\) −6.58501 19.6128i −0.394943 1.17630i
\(279\) −7.36266 −0.440791
\(280\) 10.9313 12.6432i 0.653268 0.755577i
\(281\) −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 \(-0.179529\pi\)
0.845120 + 0.534577i \(0.179529\pi\)
\(284\) −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
\(290\) −6.75814 + 1.44073i −0.396851 + 0.0846029i
\(291\) 11.1444i 0.653294i
\(292\) −18.7253 24.7422i −1.09582 1.44793i
\(293\) 7.99166 0.466878 0.233439 0.972371i \(-0.425002\pi\)
0.233439 + 0.972371i \(0.425002\pi\)
\(294\) −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
\(300\) 9.13056 4.07835i 0.527153 0.235464i
\(301\) 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 \(-0.665925\pi\)
−0.497980 + 0.867188i \(0.665925\pi\)
\(308\) −6.37907 + 4.82778i −0.363481 + 0.275088i
\(309\) 0.958386i 0.0545207i
\(310\) 4.85446 + 22.7711i 0.275715 + 1.29331i
\(311\) 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 \(0.0701853\pi\)
−0.975790 + 0.218711i \(0.929815\pi\)
\(314\) −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 \(-0.602162\pi\)
−0.315469 + 0.948936i \(0.602162\pi\)
\(318\) 6.04399 2.02927i 0.338930 0.113796i
\(319\) 3.30749 0.185184
\(320\) −17.2925 + 4.57922i −0.966680 + 0.255986i
\(321\) −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
\(330\) −4.68133 + 0.997991i −0.257699 + 0.0549376i
\(331\) 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 \(0.199877\pi\)
−0.809243 + 0.587474i \(0.800123\pi\)
\(338\) 2.65933 0.892874i 0.144649 0.0485659i
\(339\) 14.4585i 0.785279i
\(340\) 12.7581 7.54333i 0.691907 0.409095i
\(341\) 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 \(-0.698003\pi\)
−0.582698 + 0.812689i \(0.698003\pi\)
\(348\) 2.63734 + 3.48478i 0.141376 + 0.186804i
\(349\) 24.7422i 1.32442i 0.749318 + 0.662211i \(0.230382\pi\)
−0.749318 + 0.662211i \(0.769618\pi\)
\(350\) −1.79406 18.6000i −0.0958965 0.994213i
\(351\) 3.87086 0.206611
\(352\) 8.55220 0.417910i 0.455834 0.0222747i
\(353\) 3.31415i 0.176394i 0.996103 + 0.0881972i \(0.0281106\pi\)
−0.996103 + 0.0881972i \(0.971889\pi\)
\(354\) 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 \(0.354187\pi\)
\(360\) −4.78430 4.13648i −0.252155 0.218012i
\(361\) −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 \(-0.732597\pi\)
0.667411 0.744690i \(-0.267403\pi\)
\(368\) −18.5850 5.24569i −0.968811 0.273451i
\(369\) 8.72532 0.454222
\(370\) −5.18953 24.3428i −0.269791 1.26552i
\(371\) 11.9136i 0.618523i
\(372\) 11.7417 8.88633i 0.608780 0.460735i
\(373\) −37.5798 −1.94581 −0.972904 0.231211i \(-0.925731\pi\)
−0.972904 + 0.231211i \(0.925731\pi\)
\(374\) −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 \(-0.0554179\pi\)
\(380\) 27.2775 16.1280i 1.39931 0.827349i
\(381\) 11.5290i 0.590648i
\(382\) −8.00000 + 2.68601i −0.409316 + 0.137428i
\(383\) 21.8312i 1.11552i 0.830001 + 0.557762i \(0.188340\pi\)
−0.830001 + 0.557762i \(0.811660\pi\)
\(384\) 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 \(0.928275\pi\)
\(390\) −2.55220 11.9717i −0.129235 0.606212i
\(391\) 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 \(-0.493436\pi\)
0.0206186 + 0.999787i \(0.493436\pi\)
\(398\) 10.8873 3.65541i 0.545730 0.183229i
\(399\) 18.7253 0.937439
\(400\) −9.63876 + 17.5241i −0.481938 + 0.876205i
\(401\) −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 \(0.517781\pi\)
\(410\) −5.75291 26.9855i −0.284116 1.33272i
\(411\) 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 \(-0.304510\pi\)
\(420\) −10.1731 + 6.01493i −0.496398 + 0.293498i
\(421\) 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
\(430\) 0.670152 + 3.14352i 0.0323176 + 0.151594i
\(431\) 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 \(-0.780146\pi\)
0.770805 0.637072i \(-0.219854\pi\)
\(434\) −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 \(0.787138\pi\)
\(440\) 6.26111 7.24167i 0.298487 0.345233i
\(441\) 0.0164068 0.000781274
\(442\) −5.77454 17.1989i −0.274667 0.818068i
\(443\) −5.70892 −0.271239 −0.135619 0.990761i \(-0.543302\pi\)
−0.135619 + 0.990761i \(0.543302\pi\)
\(444\) −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 \(0.484972\pi\)
\(450\) −7.03840 + 0.678887i −0.331793 + 0.0320030i
\(451\) 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 \(-0.970608\pi\)
0.995740 0.0922064i \(-0.0293920\pi\)
\(458\) −0.346255 1.03128i −0.0161794 0.0481888i
\(459\) 3.31415i 0.154691i
\(460\) −18.5850 + 10.9885i −0.866531 + 0.512342i
\(461\) 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 \(-0.821665\pi\)
0.847120 0.531402i \(-0.178335\pi\)
\(464\) −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 \(-0.381336\pi\)
0.364220 + 0.931313i \(0.381336\pi\)
\(468\) −6.17313 + 4.67192i −0.285353 + 0.215960i
\(469\) 2.68601i 0.124028i
\(470\) −21.9149 + 4.67192i −1.01086 + 0.215500i
\(471\) 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 \(0.656732\pi\)
\(480\) 12.6224 + 0.822329i 0.576129 + 0.0375340i
\(481\) −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 \(0.246260\pi\)
−0.715366 + 0.698750i \(0.753740\pi\)
\(488\) 8.41188 + 5.74281i 0.380788 + 0.259965i
\(489\) −19.4835 −0.881072
\(490\) −0.0108175 0.0507425i −0.000488687 0.00229231i
\(491\) 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 \(0.973485\pi\)
\(500\) 6.74031 + 21.3206i 0.301436 + 0.953486i
\(501\) 1.80052i 0.0804412i
\(502\) 5.69774 + 16.9701i 0.254302 + 0.757414i
\(503\) 39.9451i 1.78107i −0.454919 0.890533i \(-0.650332\pi\)
0.454919 0.890533i \(-0.349668\pi\)
\(504\) 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 \(-0.000514253\pi\)
\(510\) −10.2499 + 2.18513i −0.453875 + 0.0967594i
\(511\) 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
\(520\) 18.5194 + 16.0118i 0.812129 + 0.702162i
\(521\) −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 \(-0.614243\pi\)
−0.351250 + 0.936282i \(0.614243\pi\)
\(524\) −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
\(530\) 2.97241 + 13.9429i 0.129113 + 0.605640i
\(531\) 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
\(540\) 2.27610 + 3.84959i 0.0979476 + 0.165660i
\(541\) 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 \(-0.533753\pi\)
−0.105840 + 0.994383i \(0.533753\pi\)
\(548\) −4.69251 6.20033i −0.200454 0.264865i
\(549\) 3.60104i 0.153688i
\(550\) −1.02759 10.6536i −0.0438164 0.454269i
\(551\) 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 \(-0.491459\pi\)
0.0268283 + 0.999640i \(0.491459\pi\)
\(558\) −9.87086 + 3.31415i −0.417867 + 0.140299i
\(559\) 3.93437 0.166406
\(560\) 8.96408 21.8708i 0.378801 0.924211i
\(561\) 5.01641 0.211793
\(562\) −18.0768 + 6.06930i −0.762524 + 0.256018i
\(563\) 5.70892 0.240602 0.120301 0.992737i \(-0.461614\pi\)
0.120301 + 0.992737i \(0.461614\pi\)
\(564\) 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 \(0.481587\pi\)
\(570\) −21.9149 + 4.67192i −0.917912 + 0.195685i
\(571\) 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 \(-0.761571\pi\)
0.732338 0.680941i \(-0.238429\pi\)
\(578\) 8.06599 2.70816i 0.335501 0.112645i
\(579\) 14.9409i 0.620921i
\(580\) −8.41188 + 4.97358i −0.349284 + 0.206517i
\(581\) 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 \(-0.145470\pi\)
0.897377 + 0.441264i \(0.145470\pi\)
\(588\) −0.0261649 + 0.0198021i −0.00107902 + 0.000816623i
\(589\) 52.1705i 2.14965i
\(590\) −21.0276 + 4.48277i −0.865692 + 0.184553i
\(591\) 3.23353 0.133009
\(592\) 8.55220 30.2996i 0.351493 1.24531i
\(593\) 7.83021i 0.321548i −0.986991 0.160774i \(-0.948601\pi\)
0.986991 0.160774i \(-0.0513991\pi\)
\(594\) −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 \(0.266624\pi\)
\(600\) 10.4052 9.57764i 0.424792 0.391005i
\(601\) 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 \(-0.977942\pi\)
0.997600 0.0692420i \(-0.0220581\pi\)
\(608\) 40.0357 1.95638i 1.62366 0.0793416i
\(609\) −5.77454 −0.233996
\(610\) 11.1372 2.37429i 0.450932 0.0961321i
\(611\) 27.4282i 1.10963i
\(612\) 4.00000 + 5.28530i 0.161690 + 0.213646i
\(613\) −36.6290 −1.47943 −0.739716 0.672920i \(-0.765040\pi\)
−0.739716 + 0.672920i \(0.765040\pi\)
\(614\) −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 \(0.302266\pi\)
−0.582012 + 0.813180i \(0.697734\pi\)
\(618\) −0.431398 1.28488i −0.0173534 0.0516853i
\(619\) 24.5172i 0.985430i −0.870191 0.492715i \(-0.836004\pi\)
0.870191 0.492715i \(-0.163996\pi\)
\(620\) 16.7581 + 28.3433i 0.673023 + 1.13829i
\(621\) 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
\(630\) 8.17313 1.74239i 0.325625 0.0694185i
\(631\) 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
\(640\) −21.1222 + 13.9231i −0.834929 + 0.550358i
\(641\) −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 \(-0.611814\pi\)
−0.344093 + 0.938936i \(0.611814\pi\)
\(644\) 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 \(-0.916838\pi\)
0.966065 0.258300i \(-0.0831624\pi\)
\(648\) 1.59477 2.33596i 0.0626484 0.0917653i
\(649\) 10.2911 0.403960
\(650\) 27.2447 2.62788i 1.06863 0.103074i
\(651\) 19.4569i 0.762577i
\(652\) 31.0716 23.5155i 1.21686 0.920937i
\(653\) 14.7993 0.579141 0.289570 0.957157i \(-0.406488\pi\)
0.289570 + 0.957157i \(0.406488\pi\)
\(654\) −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 \(0.950223\pi\)
\(660\) −5.82687 + 3.44518i −0.226811 + 0.134103i
\(661\) 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
\(670\) −0.670152 3.14352i −0.0258902 0.121445i
\(671\) −5.45065 −0.210420
\(672\) −14.9313 + 0.729629i −0.575986 + 0.0281461i
\(673\) 34.3978i 1.32594i −0.748647 0.662969i \(-0.769296\pi\)
0.748647 0.662969i \(-0.230704\pi\)
\(674\) 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 \(-0.780685\pi\)
−0.771884 + 0.635764i \(0.780685\pi\)
\(678\) −6.50820 19.3840i −0.249946 0.744439i
\(679\) −29.4506 −1.13021
\(680\) 13.7089 15.8559i 0.525713 0.608046i
\(681\) −5.70892 −0.218766
\(682\) −5.01641 14.9409i −0.192088 0.572115i
\(683\) −33.2580 −1.27258 −0.636291 0.771449i \(-0.719532\pi\)
−0.636291 + 0.771449i \(0.719532\pi\)
\(684\) 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
\(690\) 14.9313 3.18312i 0.568423 0.121179i
\(691\) 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
\(700\) −10.7777 24.1289i −0.407357 0.911985i
\(701\) 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 \(-0.238851\pi\)
\(710\) 4.43424 + 20.7999i 0.166414 + 0.780608i
\(711\) 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 \(0.694194\pi\)
\(720\) −8.27610 3.39208i −0.308432 0.126415i
\(721\) −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 \(0.0323700\pi\)
−0.994834 + 0.101518i \(0.967630\pi\)
\(728\) −23.8953 16.3134i −0.885620 0.604615i
\(729\) 1.00000 0.0370370
\(730\) −47.9833 + 10.2293i −1.77594 + 0.378605i
\(731\) 3.36852i 0.124589i
\(732\) −4.34625 5.74281i −0.160642 0.212260i
\(733\) 17.1455 0.633285 0.316643 0.948545i \(-0.397444\pi\)
0.316643 + 0.948545i \(0.397444\pi\)
\(734\) −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 \(0.931549\pi\)
\(740\) −17.9149 30.2996i −0.658563 1.11384i
\(741\) 27.4282i 1.00760i
\(742\) −5.36266 15.9721i −0.196869 0.586356i
\(743\) 23.6613i 0.868048i 0.900901 + 0.434024i \(0.142907\pi\)
−0.900901 + 0.434024i \(0.857093\pi\)
\(744\) 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
\(750\) 0.280267 15.8089i 0.0102339 0.577260i
\(751\) −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 \(-0.386683\pi\)
0.348525 + 0.937300i \(0.386683\pi\)
\(758\) −3.03592 9.04219i −0.110270 0.328427i
\(759\) −7.30749 −0.265245
\(760\) 29.3103 33.9007i 1.06320 1.22971i
\(761\) 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 \(0.483057\pi\)
\(770\) 2.63734 + 12.3711i 0.0950431 + 0.445824i
\(771\) 13.3110i 0.479383i
\(772\) 18.0328 + 23.8272i 0.649015 + 0.857560i
\(773\) −45.2663 −1.62812 −0.814059 0.580783i \(-0.802747\pi\)
−0.814059 + 0.580783i \(0.802747\pi\)
\(774\) −1.36266 + 0.457515i −0.0489798 + 0.0164450i
\(775\) 35.8625 + 8.31256i 1.28822 +