Properties

Label 95.2.e.c.11.1
Level $95$
Weight $2$
Character 95.11
Analytic conductor $0.759$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.1
Root \(-0.245959 + 0.426014i\) of defining polynomial
Character \(\chi\) \(=\) 95.11
Dual form 95.2.e.c.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.37901 + 2.38851i) q^{2} +(-0.745959 + 1.29204i) q^{3} +(-2.80333 - 4.85550i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.05737 - 3.56347i) q^{6} -2.84864 q^{7} +9.94721 q^{8} +(0.387090 + 0.670459i) q^{9} +O(q^{10})\) \(q+(-1.37901 + 2.38851i) q^{2} +(-0.745959 + 1.29204i) q^{3} +(-2.80333 - 4.85550i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.05737 - 3.56347i) q^{6} -2.84864 q^{7} +9.94721 q^{8} +(0.387090 + 0.670459i) q^{9} +(-1.37901 - 2.38851i) q^{10} -0.864801 q^{11} +8.36467 q^{12} +(-0.321640 - 0.557098i) q^{13} +(3.92829 - 6.80401i) q^{14} +(-0.745959 - 1.29204i) q^{15} +(-8.11063 + 14.0480i) q^{16} +(-1.87093 + 3.24054i) q^{17} -2.13520 q^{18} +(-3.36069 + 2.77592i) q^{19} +5.60665 q^{20} +(2.12497 - 3.68055i) q^{21} +(1.19257 - 2.06559i) q^{22} +(-0.208730 - 0.361531i) q^{23} +(-7.42021 + 12.8522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.77418 q^{26} -5.63077 q^{27} +(7.98566 + 13.8316i) q^{28} +(4.85261 + 8.40497i) q^{29} +4.11474 q^{30} +4.93349 q^{31} +(-12.4220 - 21.5156i) q^{32} +(0.645106 - 1.11736i) q^{33} +(-5.16005 - 8.93746i) q^{34} +(1.42432 - 2.46699i) q^{35} +(2.17028 - 3.75903i) q^{36} +6.36467 q^{37} +(-1.99589 - 11.8551i) q^{38} +0.959723 q^{39} +(-4.97360 + 8.61454i) q^{40} +(2.00686 - 3.47598i) q^{41} +(5.86069 + 10.1510i) q^{42} +(1.02915 - 1.78254i) q^{43} +(2.42432 + 4.19904i) q^{44} -0.774179 q^{45} +1.15136 q^{46} +(1.97698 + 3.42423i) q^{47} +(-12.1004 - 20.9585i) q^{48} +1.11474 q^{49} +2.75802 q^{50} +(-2.79127 - 4.83462i) q^{51} +(-1.80333 + 3.12345i) q^{52} +(5.49374 + 9.51544i) q^{53} +(7.76487 - 13.4492i) q^{54} +(0.432400 - 0.748939i) q^{55} -28.3360 q^{56} +(-1.07966 - 6.41287i) q^{57} -26.7672 q^{58} +(-1.22980 + 2.13007i) q^{59} +(-4.18233 + 7.24402i) q^{60} +(-3.16740 - 5.48609i) q^{61} +(-6.80333 + 11.7837i) q^{62} +(-1.10268 - 1.90989i) q^{63} +36.0778 q^{64} +0.643281 q^{65} +(1.77921 + 3.08169i) q^{66} +(1.26610 + 2.19295i) q^{67} +20.9793 q^{68} +0.622817 q^{69} +(3.92829 + 6.80401i) q^{70} +(0.891065 - 1.54337i) q^{71} +(3.85046 + 6.66920i) q^{72} +(3.56545 - 6.17554i) q^{73} +(-8.77693 + 15.2021i) q^{74} +1.49192 q^{75} +(22.8996 + 8.53606i) q^{76} +2.46350 q^{77} +(-1.32347 + 2.29231i) q^{78} +(-0.912262 + 1.58008i) q^{79} +(-8.11063 - 14.0480i) q^{80} +(3.03905 - 5.26380i) q^{81} +(5.53495 + 9.58681i) q^{82} -7.43913 q^{83} -23.8279 q^{84} +(-1.87093 - 3.24054i) q^{85} +(2.83841 + 4.91626i) q^{86} -14.4794 q^{87} -8.60235 q^{88} +(-2.22294 - 3.85024i) q^{89} +(1.06760 - 1.84914i) q^{90} +(0.916237 + 1.58697i) q^{91} +(-1.17028 + 2.02698i) q^{92} +(-3.68018 + 6.37427i) q^{93} -10.9051 q^{94} +(-0.723670 - 4.29841i) q^{95} +37.0653 q^{96} +(5.42707 - 9.39996i) q^{97} +(-1.53723 + 2.66256i) q^{98} +(-0.334755 - 0.579813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9} - q^{10} - 4 q^{11} + 12 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} - 7 q^{16} + q^{17} - 20 q^{18} + 5 q^{19} + 10 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} - 23 q^{24} - 4 q^{25} + 6 q^{26} + 24 q^{27} + 19 q^{28} + q^{29} + 4 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} + 4 q^{35} + 7 q^{36} - 4 q^{37} + 13 q^{38} + 30 q^{39} - 12 q^{40} + 8 q^{41} + 15 q^{42} - q^{43} + 12 q^{44} + 2 q^{45} + 24 q^{46} + 12 q^{47} - 23 q^{48} - 20 q^{49} + 2 q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} + 34 q^{54} + 2 q^{55} - 82 q^{56} + 7 q^{57} - 54 q^{58} + 5 q^{59} - 6 q^{60} - 37 q^{62} + 3 q^{63} + 112 q^{64} + 14 q^{65} + 31 q^{66} - 4 q^{67} + 32 q^{68} - 18 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} + 20 q^{73} - 25 q^{74} + 6 q^{75} + 63 q^{76} + 28 q^{77} + 18 q^{78} - 17 q^{79} - 7 q^{80} - 12 q^{81} - 21 q^{82} + 2 q^{83} - 40 q^{84} + q^{85} - 8 q^{86} - 32 q^{87} - 14 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} + q^{92} + 8 q^{93} - 62 q^{94} - 4 q^{95} + 42 q^{96} - q^{97} - 9 q^{98} - 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37901 + 2.38851i −0.975106 + 1.68893i −0.295521 + 0.955336i \(0.595493\pi\)
−0.679585 + 0.733597i \(0.737840\pi\)
\(3\) −0.745959 + 1.29204i −0.430680 + 0.745959i −0.996932 0.0782728i \(-0.975059\pi\)
0.566252 + 0.824232i \(0.308393\pi\)
\(4\) −2.80333 4.85550i −1.40166 2.42775i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −2.05737 3.56347i −0.839917 1.45478i
\(7\) −2.84864 −1.07668 −0.538342 0.842727i \(-0.680949\pi\)
−0.538342 + 0.842727i \(0.680949\pi\)
\(8\) 9.94721 3.51687
\(9\) 0.387090 + 0.670459i 0.129030 + 0.223486i
\(10\) −1.37901 2.38851i −0.436081 0.755314i
\(11\) −0.864801 −0.260747 −0.130374 0.991465i \(-0.541618\pi\)
−0.130374 + 0.991465i \(0.541618\pi\)
\(12\) 8.36467 2.41467
\(13\) −0.321640 0.557098i −0.0892070 0.154511i 0.817969 0.575262i \(-0.195100\pi\)
−0.907176 + 0.420751i \(0.861767\pi\)
\(14\) 3.92829 6.80401i 1.04988 1.81845i
\(15\) −0.745959 1.29204i −0.192606 0.333603i
\(16\) −8.11063 + 14.0480i −2.02766 + 3.51201i
\(17\) −1.87093 + 3.24054i −0.453766 + 0.785946i −0.998616 0.0525872i \(-0.983253\pi\)
0.544850 + 0.838534i \(0.316587\pi\)
\(18\) −2.13520 −0.503271
\(19\) −3.36069 + 2.77592i −0.770996 + 0.636840i
\(20\) 5.60665 1.25369
\(21\) 2.12497 3.68055i 0.463706 0.803162i
\(22\) 1.19257 2.06559i 0.254256 0.440385i
\(23\) −0.208730 0.361531i −0.0435233 0.0753845i 0.843443 0.537218i \(-0.180525\pi\)
−0.886966 + 0.461834i \(0.847192\pi\)
\(24\) −7.42021 + 12.8522i −1.51464 + 2.62344i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.77418 0.347945
\(27\) −5.63077 −1.08364
\(28\) 7.98566 + 13.8316i 1.50915 + 2.61392i
\(29\) 4.85261 + 8.40497i 0.901108 + 1.56076i 0.826059 + 0.563584i \(0.190578\pi\)
0.0750490 + 0.997180i \(0.476089\pi\)
\(30\) 4.11474 0.751244
\(31\) 4.93349 0.886081 0.443041 0.896501i \(-0.353900\pi\)
0.443041 + 0.896501i \(0.353900\pi\)
\(32\) −12.4220 21.5156i −2.19593 3.80346i
\(33\) 0.645106 1.11736i 0.112299 0.194507i
\(34\) −5.16005 8.93746i −0.884941 1.53276i
\(35\) 1.42432 2.46699i 0.240754 0.416998i
\(36\) 2.17028 3.75903i 0.361713 0.626505i
\(37\) 6.36467 1.04635 0.523173 0.852227i \(-0.324748\pi\)
0.523173 + 0.852227i \(0.324748\pi\)
\(38\) −1.99589 11.8551i −0.323777 1.92315i
\(39\) 0.959723 0.153679
\(40\) −4.97360 + 8.61454i −0.786396 + 1.36208i
\(41\) 2.00686 3.47598i 0.313419 0.542857i −0.665681 0.746236i \(-0.731859\pi\)
0.979100 + 0.203379i \(0.0651924\pi\)
\(42\) 5.86069 + 10.1510i 0.904325 + 1.56634i
\(43\) 1.02915 1.78254i 0.156944 0.271834i −0.776821 0.629721i \(-0.783169\pi\)
0.933765 + 0.357887i \(0.116503\pi\)
\(44\) 2.42432 + 4.19904i 0.365480 + 0.633030i
\(45\) −0.774179 −0.115408
\(46\) 1.15136 0.169759
\(47\) 1.97698 + 3.42423i 0.288372 + 0.499475i 0.973421 0.229022i \(-0.0735527\pi\)
−0.685049 + 0.728497i \(0.740219\pi\)
\(48\) −12.1004 20.9585i −1.74654 3.02510i
\(49\) 1.11474 0.159248
\(50\) 2.75802 0.390042
\(51\) −2.79127 4.83462i −0.390856 0.676982i
\(52\) −1.80333 + 3.12345i −0.250076 + 0.433145i
\(53\) 5.49374 + 9.51544i 0.754624 + 1.30705i 0.945561 + 0.325444i \(0.105514\pi\)
−0.190937 + 0.981602i \(0.561153\pi\)
\(54\) 7.76487 13.4492i 1.05667 1.83020i
\(55\) 0.432400 0.748939i 0.0583048 0.100987i
\(56\) −28.3360 −3.78656
\(57\) −1.07966 6.41287i −0.143004 0.849406i
\(58\) −26.7672 −3.51470
\(59\) −1.22980 + 2.13007i −0.160106 + 0.277311i −0.934906 0.354894i \(-0.884517\pi\)
0.774801 + 0.632206i \(0.217850\pi\)
\(60\) −4.18233 + 7.24402i −0.539937 + 0.935199i
\(61\) −3.16740 5.48609i −0.405543 0.702422i 0.588841 0.808249i \(-0.299584\pi\)
−0.994385 + 0.105827i \(0.966251\pi\)
\(62\) −6.80333 + 11.7837i −0.864023 + 1.49653i
\(63\) −1.10268 1.90989i −0.138924 0.240624i
\(64\) 36.0778 4.50973
\(65\) 0.643281 0.0797892
\(66\) 1.77921 + 3.08169i 0.219006 + 0.379329i
\(67\) 1.26610 + 2.19295i 0.154678 + 0.267911i 0.932942 0.360027i \(-0.117233\pi\)
−0.778263 + 0.627938i \(0.783899\pi\)
\(68\) 20.9793 2.54411
\(69\) 0.622817 0.0749783
\(70\) 3.92829 + 6.80401i 0.469521 + 0.813234i
\(71\) 0.891065 1.54337i 0.105750 0.183164i −0.808294 0.588779i \(-0.799609\pi\)
0.914044 + 0.405614i \(0.132942\pi\)
\(72\) 3.85046 + 6.66920i 0.453781 + 0.785972i
\(73\) 3.56545 6.17554i 0.417304 0.722792i −0.578363 0.815780i \(-0.696308\pi\)
0.995667 + 0.0929873i \(0.0296416\pi\)
\(74\) −8.77693 + 15.2021i −1.02030 + 1.76721i
\(75\) 1.49192 0.172272
\(76\) 22.8996 + 8.53606i 2.62677 + 0.979153i
\(77\) 2.46350 0.280742
\(78\) −1.32347 + 2.29231i −0.149853 + 0.259553i
\(79\) −0.912262 + 1.58008i −0.102637 + 0.177773i −0.912771 0.408473i \(-0.866061\pi\)
0.810133 + 0.586246i \(0.199395\pi\)
\(80\) −8.11063 14.0480i −0.906796 1.57062i
\(81\) 3.03905 5.26380i 0.337673 0.584866i
\(82\) 5.53495 + 9.58681i 0.611233 + 1.05869i
\(83\) −7.43913 −0.816550 −0.408275 0.912859i \(-0.633870\pi\)
−0.408275 + 0.912859i \(0.633870\pi\)
\(84\) −23.8279 −2.59984
\(85\) −1.87093 3.24054i −0.202930 0.351486i
\(86\) 2.83841 + 4.91626i 0.306073 + 0.530134i
\(87\) −14.4794 −1.55236
\(88\) −8.60235 −0.917014
\(89\) −2.22294 3.85024i −0.235631 0.408125i 0.723825 0.689984i \(-0.242382\pi\)
−0.959456 + 0.281859i \(0.909049\pi\)
\(90\) 1.06760 1.84914i 0.112535 0.194916i
\(91\) 0.916237 + 1.58697i 0.0960478 + 0.166360i
\(92\) −1.17028 + 2.02698i −0.122010 + 0.211327i
\(93\) −3.68018 + 6.37427i −0.381617 + 0.660981i
\(94\) −10.9051 −1.12477
\(95\) −0.723670 4.29841i −0.0742470 0.441007i
\(96\) 37.0653 3.78296
\(97\) 5.42707 9.39996i 0.551036 0.954422i −0.447165 0.894452i \(-0.647566\pi\)
0.998200 0.0599699i \(-0.0191005\pi\)
\(98\) −1.53723 + 2.66256i −0.155284 + 0.268959i
\(99\) −0.334755 0.579813i −0.0336442 0.0582734i
\(100\) −2.80333 + 4.85550i −0.280333 + 0.485550i
\(101\) 2.64799 + 4.58645i 0.263485 + 0.456369i 0.967166 0.254147i \(-0.0817948\pi\)
−0.703681 + 0.710516i \(0.748461\pi\)
\(102\) 15.3967 1.52450
\(103\) −0.385134 −0.0379484 −0.0189742 0.999820i \(-0.506040\pi\)
−0.0189742 + 0.999820i \(0.506040\pi\)
\(104\) −3.19943 5.54157i −0.313729 0.543395i
\(105\) 2.12497 + 3.68055i 0.207376 + 0.359185i
\(106\) −30.3037 −2.94335
\(107\) −6.43336 −0.621937 −0.310968 0.950420i \(-0.600653\pi\)
−0.310968 + 0.950420i \(0.600653\pi\)
\(108\) 15.7849 + 27.3402i 1.51890 + 2.63081i
\(109\) −3.28441 + 5.68877i −0.314590 + 0.544885i −0.979350 0.202171i \(-0.935200\pi\)
0.664761 + 0.747056i \(0.268534\pi\)
\(110\) 1.19257 + 2.06559i 0.113707 + 0.196946i
\(111\) −4.74778 + 8.22340i −0.450640 + 0.780531i
\(112\) 23.1042 40.0177i 2.18315 3.78132i
\(113\) 0.294513 0.0277054 0.0138527 0.999904i \(-0.495590\pi\)
0.0138527 + 0.999904i \(0.495590\pi\)
\(114\) 16.8061 + 6.26463i 1.57403 + 0.586736i
\(115\) 0.417460 0.0389284
\(116\) 27.2069 47.1238i 2.52610 4.37533i
\(117\) 0.249007 0.431294i 0.0230207 0.0398731i
\(118\) −3.39180 5.87477i −0.312240 0.540816i
\(119\) 5.32959 9.23112i 0.488563 0.846216i
\(120\) −7.42021 12.8522i −0.677370 1.17324i
\(121\) −10.2521 −0.932011
\(122\) 17.4715 1.58179
\(123\) 2.99407 + 5.18588i 0.269966 + 0.467595i
\(124\) −13.8302 23.9546i −1.24199 2.15119i
\(125\) 1.00000 0.0894427
\(126\) 6.08241 0.541864
\(127\) −4.41746 7.65127i −0.391986 0.678940i 0.600725 0.799456i \(-0.294879\pi\)
−0.992711 + 0.120516i \(0.961545\pi\)
\(128\) −24.9076 + 43.1412i −2.20154 + 3.81318i
\(129\) 1.53540 + 2.65940i 0.135185 + 0.234147i
\(130\) −0.887090 + 1.53648i −0.0778029 + 0.134759i
\(131\) −10.4564 + 18.1110i −0.913578 + 1.58236i −0.104609 + 0.994513i \(0.533359\pi\)
−0.808969 + 0.587851i \(0.799974\pi\)
\(132\) −7.23377 −0.629619
\(133\) 9.57340 7.90759i 0.830119 0.685675i
\(134\) −6.98384 −0.603312
\(135\) 2.81538 4.87639i 0.242310 0.419693i
\(136\) −18.6105 + 32.2343i −1.59584 + 2.76407i
\(137\) −2.60739 4.51613i −0.222764 0.385839i 0.732882 0.680356i \(-0.238175\pi\)
−0.955646 + 0.294517i \(0.904841\pi\)
\(138\) −0.858870 + 1.48761i −0.0731118 + 0.126633i
\(139\) 5.36192 + 9.28711i 0.454792 + 0.787723i 0.998676 0.0514375i \(-0.0163803\pi\)
−0.543884 + 0.839160i \(0.683047\pi\)
\(140\) −15.9713 −1.34982
\(141\) −5.89898 −0.496784
\(142\) 2.45757 + 4.25664i 0.206235 + 0.357209i
\(143\) 0.278155 + 0.481778i 0.0232605 + 0.0402883i
\(144\) −12.5582 −1.04651
\(145\) −9.70523 −0.805975
\(146\) 9.83357 + 17.0322i 0.813832 + 1.40960i
\(147\) −0.831547 + 1.44028i −0.0685848 + 0.118792i
\(148\) −17.8423 30.9037i −1.46662 2.54027i
\(149\) 7.45578 12.9138i 0.610801 1.05794i −0.380304 0.924861i \(-0.624181\pi\)
0.991106 0.133078i \(-0.0424860\pi\)
\(150\) −2.05737 + 3.56347i −0.167983 + 0.290956i
\(151\) 21.4589 1.74630 0.873152 0.487448i \(-0.162072\pi\)
0.873152 + 0.487448i \(0.162072\pi\)
\(152\) −33.4295 + 27.6127i −2.71149 + 2.23968i
\(153\) −2.89687 −0.234198
\(154\) −3.39719 + 5.88411i −0.273753 + 0.474155i
\(155\) −2.46675 + 4.27253i −0.198134 + 0.343178i
\(156\) −2.69042 4.65994i −0.215406 0.373094i
\(157\) 1.21559 2.10546i 0.0970145 0.168034i −0.813433 0.581659i \(-0.802404\pi\)
0.910448 + 0.413624i \(0.135737\pi\)
\(158\) −2.51603 4.35790i −0.200165 0.346696i
\(159\) −16.3924 −1.30000
\(160\) 24.8441 1.96410
\(161\) 0.594597 + 1.02987i 0.0468608 + 0.0811653i
\(162\) 8.38176 + 14.5176i 0.658533 + 1.14061i
\(163\) 17.8175 1.39558 0.697788 0.716305i \(-0.254168\pi\)
0.697788 + 0.716305i \(0.254168\pi\)
\(164\) −22.5035 −1.75723
\(165\) 0.645106 + 1.11736i 0.0502214 + 0.0869861i
\(166\) 10.2586 17.7684i 0.796223 1.37910i
\(167\) 0.202799 + 0.351258i 0.0156931 + 0.0271812i 0.873765 0.486348i \(-0.161671\pi\)
−0.858072 + 0.513529i \(0.828338\pi\)
\(168\) 21.1375 36.6112i 1.63079 2.82462i
\(169\) 6.29309 10.9000i 0.484084 0.838458i
\(170\) 10.3201 0.791515
\(171\) −3.16203 1.17868i −0.241807 0.0901358i
\(172\) −11.5401 −0.879928
\(173\) −9.01051 + 15.6067i −0.685056 + 1.18655i 0.288363 + 0.957521i \(0.406889\pi\)
−0.973419 + 0.229031i \(0.926444\pi\)
\(174\) 19.9672 34.5842i 1.51371 2.62182i
\(175\) 1.42432 + 2.46699i 0.107668 + 0.186487i
\(176\) 7.01408 12.1487i 0.528706 0.915746i
\(177\) −1.83476 3.17789i −0.137909 0.238865i
\(178\) 12.2618 0.919061
\(179\) 20.1523 1.50625 0.753127 0.657875i \(-0.228545\pi\)
0.753127 + 0.657875i \(0.228545\pi\)
\(180\) 2.17028 + 3.75903i 0.161763 + 0.280182i
\(181\) 8.55541 + 14.8184i 0.635919 + 1.10144i 0.986320 + 0.164844i \(0.0527120\pi\)
−0.350401 + 0.936600i \(0.613955\pi\)
\(182\) −5.05399 −0.374627
\(183\) 9.45099 0.698637
\(184\) −2.07628 3.59623i −0.153066 0.265117i
\(185\) −3.18233 + 5.51197i −0.233970 + 0.405248i
\(186\) −10.1500 17.5803i −0.744235 1.28905i
\(187\) 1.61798 2.80242i 0.118318 0.204933i
\(188\) 11.0842 19.1985i 0.808401 1.40019i
\(189\) 16.0400 1.16674
\(190\) 11.2647 + 4.19904i 0.817230 + 0.304631i
\(191\) 5.28080 0.382105 0.191053 0.981580i \(-0.438810\pi\)
0.191053 + 0.981580i \(0.438810\pi\)
\(192\) −26.9126 + 46.6140i −1.94225 + 3.36408i
\(193\) −9.00182 + 15.5916i −0.647966 + 1.12231i 0.335642 + 0.941989i \(0.391047\pi\)
−0.983608 + 0.180320i \(0.942287\pi\)
\(194\) 14.9679 + 25.9252i 1.07464 + 1.86132i
\(195\) −0.479861 + 0.831144i −0.0343636 + 0.0595195i
\(196\) −3.12497 5.41260i −0.223212 0.386614i
\(197\) 8.07785 0.575523 0.287761 0.957702i \(-0.407089\pi\)
0.287761 + 0.957702i \(0.407089\pi\)
\(198\) 1.84652 0.131227
\(199\) −0.701872 1.21568i −0.0497544 0.0861771i 0.840076 0.542469i \(-0.182511\pi\)
−0.889830 + 0.456292i \(0.849177\pi\)
\(200\) −4.97360 8.61454i −0.351687 0.609140i
\(201\) −3.77783 −0.266468
\(202\) −14.6064 −1.02770
\(203\) −13.8233 23.9427i −0.970208 1.68045i
\(204\) −15.6497 + 27.1060i −1.09570 + 1.89780i
\(205\) 2.00686 + 3.47598i 0.140165 + 0.242773i
\(206\) 0.531103 0.919897i 0.0370037 0.0640923i
\(207\) 0.161595 0.279890i 0.0112316 0.0194537i
\(208\) 10.4348 0.723525
\(209\) 2.90633 2.40062i 0.201035 0.166054i
\(210\) −11.7214 −0.808853
\(211\) −9.45817 + 16.3820i −0.651128 + 1.12779i 0.331722 + 0.943377i \(0.392370\pi\)
−0.982850 + 0.184409i \(0.940963\pi\)
\(212\) 30.8015 53.3498i 2.11546 3.66408i
\(213\) 1.32940 + 2.30258i 0.0910888 + 0.157770i
\(214\) 8.87166 15.3662i 0.606454 1.05041i
\(215\) 1.02915 + 1.78254i 0.0701873 + 0.121568i
\(216\) −56.0104 −3.81103
\(217\) −14.0537 −0.954030
\(218\) −9.05846 15.6897i −0.613516 1.06264i
\(219\) 5.31936 + 9.21340i 0.359449 + 0.622584i
\(220\) −4.84864 −0.326895
\(221\) 2.40706 0.161917
\(222\) −13.0945 22.6803i −0.878843 1.52220i
\(223\) 8.07400 13.9846i 0.540675 0.936477i −0.458190 0.888854i \(-0.651502\pi\)
0.998865 0.0476227i \(-0.0151645\pi\)
\(224\) 35.3859 + 61.2901i 2.36432 + 4.09512i
\(225\) 0.387090 0.670459i 0.0258060 0.0446973i
\(226\) −0.406136 + 0.703448i −0.0270157 + 0.0467926i
\(227\) 26.3186 1.74683 0.873414 0.486978i \(-0.161901\pi\)
0.873414 + 0.486978i \(0.161901\pi\)
\(228\) −28.1111 + 23.2197i −1.86170 + 1.53776i
\(229\) −13.3323 −0.881026 −0.440513 0.897746i \(-0.645203\pi\)
−0.440513 + 0.897746i \(0.645203\pi\)
\(230\) −0.575681 + 0.997109i −0.0379593 + 0.0657474i
\(231\) −1.83767 + 3.18294i −0.120910 + 0.209422i
\(232\) 48.2700 + 83.6060i 3.16908 + 5.48900i
\(233\) −12.6547 + 21.9186i −0.829038 + 1.43594i 0.0697556 + 0.997564i \(0.477778\pi\)
−0.898794 + 0.438372i \(0.855555\pi\)
\(234\) 0.686767 + 1.18951i 0.0448953 + 0.0777610i
\(235\) −3.95396 −0.257928
\(236\) 13.7901 0.897658
\(237\) −1.36102 2.35736i −0.0884077 0.153127i
\(238\) 14.6991 + 25.4596i 0.952801 + 1.65030i
\(239\) −23.5500 −1.52332 −0.761660 0.647977i \(-0.775615\pi\)
−0.761660 + 0.647977i \(0.775615\pi\)
\(240\) 24.2008 1.56215
\(241\) −4.19208 7.26089i −0.270035 0.467715i 0.698835 0.715283i \(-0.253702\pi\)
−0.968871 + 0.247568i \(0.920369\pi\)
\(242\) 14.1378 24.4873i 0.908809 1.57410i
\(243\) −3.91213 6.77601i −0.250963 0.434681i
\(244\) −17.7585 + 30.7586i −1.13687 + 1.96912i
\(245\) −0.557368 + 0.965389i −0.0356089 + 0.0616764i
\(246\) −16.5154 −1.05298
\(247\) 2.62739 + 0.979387i 0.167177 + 0.0623169i
\(248\) 49.0745 3.11623
\(249\) 5.54929 9.61165i 0.351672 0.609113i
\(250\) −1.37901 + 2.38851i −0.0872161 + 0.151063i
\(251\) −9.12391 15.8031i −0.575896 0.997481i −0.995944 0.0899792i \(-0.971320\pi\)
0.420048 0.907502i \(-0.362013\pi\)
\(252\) −6.18233 + 10.7081i −0.389450 + 0.674548i
\(253\) 0.180510 + 0.312652i 0.0113486 + 0.0196563i
\(254\) 24.3669 1.52891
\(255\) 5.58254 0.349592
\(256\) −32.6176 56.4954i −2.03860 3.53096i
\(257\) −7.04989 12.2108i −0.439760 0.761687i 0.557911 0.829901i \(-0.311603\pi\)
−0.997671 + 0.0682144i \(0.978270\pi\)
\(258\) −8.46934 −0.527278
\(259\) −18.1306 −1.12658
\(260\) −1.80333 3.12345i −0.111838 0.193708i
\(261\) −3.75679 + 6.50696i −0.232540 + 0.402770i
\(262\) −28.8389 49.9504i −1.78167 3.08595i
\(263\) 3.20536 5.55184i 0.197651 0.342341i −0.750116 0.661307i \(-0.770002\pi\)
0.947766 + 0.318966i \(0.103335\pi\)
\(264\) 6.41700 11.1146i 0.394939 0.684055i
\(265\) −10.9875 −0.674956
\(266\) 5.68558 + 33.7708i 0.348605 + 2.07062i
\(267\) 6.63288 0.405926
\(268\) 7.09857 12.2951i 0.433614 0.751042i
\(269\) −8.99557 + 15.5808i −0.548469 + 0.949977i 0.449910 + 0.893074i \(0.351456\pi\)
−0.998380 + 0.0569032i \(0.981877\pi\)
\(270\) 7.76487 + 13.4492i 0.472555 + 0.818490i
\(271\) −5.94095 + 10.2900i −0.360887 + 0.625075i −0.988107 0.153767i \(-0.950859\pi\)
0.627220 + 0.778842i \(0.284193\pi\)
\(272\) −30.3488 52.5656i −1.84017 3.18726i
\(273\) −2.73390 −0.165463
\(274\) 14.3824 0.868874
\(275\) 0.432400 + 0.748939i 0.0260747 + 0.0451627i
\(276\) −1.74596 3.02409i −0.105094 0.182029i
\(277\) 23.6240 1.41943 0.709715 0.704489i \(-0.248824\pi\)
0.709715 + 0.704489i \(0.248824\pi\)
\(278\) −29.5765 −1.77388
\(279\) 1.90970 + 3.30770i 0.114331 + 0.198027i
\(280\) 14.1680 24.5397i 0.846700 1.46653i
\(281\) −6.90465 11.9592i −0.411897 0.713426i 0.583200 0.812328i \(-0.301800\pi\)
−0.995097 + 0.0989020i \(0.968467\pi\)
\(282\) 8.13474 14.0898i 0.484417 0.839035i
\(283\) 5.87868 10.1822i 0.349451 0.605268i −0.636701 0.771111i \(-0.719701\pi\)
0.986152 + 0.165843i \(0.0530346\pi\)
\(284\) −9.99179 −0.592904
\(285\) 6.09354 + 2.27143i 0.360950 + 0.134548i
\(286\) −1.53431 −0.0907257
\(287\) −5.71681 + 9.90181i −0.337453 + 0.584485i
\(288\) 9.61689 16.6569i 0.566680 0.981519i
\(289\) 1.49927 + 2.59681i 0.0881922 + 0.152753i
\(290\) 13.3836 23.1810i 0.785911 1.36124i
\(291\) 8.09675 + 14.0240i 0.474640 + 0.822100i
\(292\) −39.9805 −2.33968
\(293\) −27.0576 −1.58072 −0.790362 0.612640i \(-0.790108\pi\)
−0.790362 + 0.612640i \(0.790108\pi\)
\(294\) −2.29342 3.97232i −0.133755 0.231670i
\(295\) −1.22980 2.13007i −0.0716015 0.124017i
\(296\) 63.3107 3.67986
\(297\) 4.86949 0.282557
\(298\) 20.5632 + 35.6165i 1.19119 + 2.06321i
\(299\) −0.134272 + 0.232566i −0.00776516 + 0.0134497i
\(300\) −4.18233 7.24402i −0.241467 0.418233i
\(301\) −2.93167 + 5.07780i −0.168979 + 0.292679i
\(302\) −29.5921 + 51.2549i −1.70283 + 2.94939i
\(303\) −7.90117 −0.453910
\(304\) −11.7388 69.7256i −0.673269 3.99904i
\(305\) 6.33479 0.362729
\(306\) 3.99480 6.91920i 0.228368 0.395544i
\(307\) −4.41912 + 7.65414i −0.252212 + 0.436845i −0.964135 0.265414i \(-0.914492\pi\)
0.711922 + 0.702258i \(0.247825\pi\)
\(308\) −6.90601 11.9616i −0.393506 0.681573i
\(309\) 0.287294 0.497608i 0.0163436 0.0283080i
\(310\) −6.80333 11.7837i −0.386403 0.669270i
\(311\) −0.651493 −0.0369428 −0.0184714 0.999829i \(-0.505880\pi\)
−0.0184714 + 0.999829i \(0.505880\pi\)
\(312\) 9.54656 0.540468
\(313\) 1.48278 + 2.56825i 0.0838116 + 0.145166i 0.904884 0.425658i \(-0.139957\pi\)
−0.821073 + 0.570824i \(0.806624\pi\)
\(314\) 3.35261 + 5.80690i 0.189199 + 0.327702i
\(315\) 2.20536 0.124258
\(316\) 10.2295 0.575453
\(317\) 5.18993 + 8.98921i 0.291495 + 0.504885i 0.974164 0.225844i \(-0.0725139\pi\)
−0.682668 + 0.730728i \(0.739181\pi\)
\(318\) 22.6053 39.1535i 1.26764 2.19562i
\(319\) −4.19654 7.26862i −0.234961 0.406965i
\(320\) −18.0389 + 31.2443i −1.00841 + 1.74661i
\(321\) 4.79903 8.31216i 0.267856 0.463939i
\(322\) −3.27981 −0.182777
\(323\) −2.70787 16.0840i −0.150670 0.894938i
\(324\) −34.0778 −1.89321
\(325\) −0.321640 + 0.557098i −0.0178414 + 0.0309022i
\(326\) −24.5705 + 42.5574i −1.36083 + 2.35703i
\(327\) −4.90007 8.48718i −0.270975 0.469342i
\(328\) 19.9626 34.5763i 1.10225 1.90916i
\(329\) −5.63170 9.75438i −0.310485 0.537776i
\(330\) −3.55843 −0.195885
\(331\) 15.0922 0.829543 0.414772 0.909926i \(-0.363861\pi\)
0.414772 + 0.909926i \(0.363861\pi\)
\(332\) 20.8543 + 36.1207i 1.14453 + 1.98238i
\(333\) 2.46370 + 4.26725i 0.135010 + 0.233844i
\(334\) −1.11865 −0.0612096
\(335\) −2.53220 −0.138349
\(336\) 34.4696 + 59.7032i 1.88047 + 3.25708i
\(337\) −7.89872 + 13.6810i −0.430271 + 0.745251i −0.996896 0.0787246i \(-0.974915\pi\)
0.566626 + 0.823975i \(0.308249\pi\)
\(338\) 17.3565 + 30.0623i 0.944067 + 1.63517i
\(339\) −0.219695 + 0.380522i −0.0119322 + 0.0206671i
\(340\) −10.4896 + 18.1686i −0.568880 + 0.985330i
\(341\) −4.26649 −0.231043
\(342\) 7.17575 5.92714i 0.388020 0.320503i
\(343\) 16.7650 0.905224
\(344\) 10.2371 17.7313i 0.551950 0.956005i
\(345\) −0.311408 + 0.539375i −0.0167657 + 0.0290390i
\(346\) −24.8511 43.0434i −1.33600 2.31403i
\(347\) 10.6761 18.4915i 0.573122 0.992676i −0.423121 0.906073i \(-0.639065\pi\)
0.996243 0.0866031i \(-0.0276012\pi\)
\(348\) 40.5905 + 70.3048i 2.17588 + 3.76873i
\(349\) −32.3897 −1.73378 −0.866891 0.498497i \(-0.833885\pi\)
−0.866891 + 0.498497i \(0.833885\pi\)
\(350\) −7.85659 −0.419952
\(351\) 1.81108 + 3.13689i 0.0966685 + 0.167435i
\(352\) 10.7426 + 18.6067i 0.572582 + 0.991741i
\(353\) 0.730583 0.0388850 0.0194425 0.999811i \(-0.493811\pi\)
0.0194425 + 0.999811i \(0.493811\pi\)
\(354\) 10.1206 0.537902
\(355\) 0.891065 + 1.54337i 0.0472928 + 0.0819136i
\(356\) −12.4632 + 21.5870i −0.660551 + 1.14411i
\(357\) 7.95132 + 13.7721i 0.420828 + 0.728896i
\(358\) −27.7902 + 48.1340i −1.46876 + 2.54396i
\(359\) 13.4248 23.2524i 0.708533 1.22722i −0.256868 0.966447i \(-0.582691\pi\)
0.965401 0.260769i \(-0.0839761\pi\)
\(360\) −7.70092 −0.405874
\(361\) 3.58853 18.6580i 0.188870 0.982002i
\(362\) −47.1919 −2.48035
\(363\) 7.64766 13.2461i 0.401398 0.695242i
\(364\) 5.13702 8.89759i 0.269253 0.466360i
\(365\) 3.56545 + 6.17554i 0.186624 + 0.323242i
\(366\) −13.0330 + 22.5738i −0.681245 + 1.17995i
\(367\) 11.4822 + 19.8877i 0.599364 + 1.03813i 0.992915 + 0.118826i \(0.0379130\pi\)
−0.393551 + 0.919303i \(0.628754\pi\)
\(368\) 6.77173 0.353001
\(369\) 3.10734 0.161761
\(370\) −8.77693 15.2021i −0.456291 0.790319i
\(371\) −15.6497 27.1060i −0.812491 1.40728i
\(372\) 41.2670 2.13960
\(373\) 29.5305 1.52903 0.764515 0.644606i \(-0.222979\pi\)
0.764515 + 0.644606i \(0.222979\pi\)
\(374\) 4.46241 + 7.72912i 0.230746 + 0.399663i
\(375\) −0.745959 + 1.29204i −0.0385212 + 0.0667206i
\(376\) 19.6654 + 34.0615i 1.01417 + 1.75659i
\(377\) 3.12159 5.40676i 0.160770 0.278462i
\(378\) −22.1193 + 38.3118i −1.13769 + 1.97054i
\(379\) 17.5117 0.899517 0.449759 0.893150i \(-0.351510\pi\)
0.449759 + 0.893150i \(0.351510\pi\)
\(380\) −18.8423 + 15.5636i −0.966587 + 0.798397i
\(381\) 13.1810 0.675282
\(382\) −7.28226 + 12.6132i −0.372593 + 0.645350i
\(383\) −4.05326 + 7.02045i −0.207112 + 0.358728i −0.950804 0.309794i \(-0.899740\pi\)
0.743692 + 0.668523i \(0.233073\pi\)
\(384\) −37.1601 64.3631i −1.89632 3.28452i
\(385\) −1.23175 + 2.13346i −0.0627759 + 0.108731i
\(386\) −24.8272 43.0019i −1.26367 2.18874i
\(387\) 1.59349 0.0810016
\(388\) −60.8554 −3.08947
\(389\) −8.65392 14.9890i −0.438771 0.759974i 0.558824 0.829286i \(-0.311253\pi\)
−0.997595 + 0.0693125i \(0.977919\pi\)
\(390\) −1.32347 2.29231i −0.0670163 0.116076i
\(391\) 1.56208 0.0789976
\(392\) 11.0885 0.560054
\(393\) −15.6001 27.0201i −0.786920 1.36298i
\(394\) −11.1394 + 19.2940i −0.561196 + 0.972019i
\(395\) −0.912262 1.58008i −0.0459009 0.0795026i
\(396\) −1.87686 + 3.25081i −0.0943156 + 0.163359i
\(397\) 5.69472 9.86354i 0.285810 0.495037i −0.686996 0.726662i \(-0.741071\pi\)
0.972805 + 0.231625i \(0.0744041\pi\)
\(398\) 3.87155 0.194063
\(399\) 3.07555 + 18.2679i 0.153970 + 0.914541i
\(400\) 16.2213 0.811063
\(401\) 4.46930 7.74106i 0.223186 0.386570i −0.732587 0.680673i \(-0.761687\pi\)
0.955774 + 0.294103i \(0.0950208\pi\)
\(402\) 5.20966 9.02339i 0.259834 0.450046i
\(403\) −1.58681 2.74844i −0.0790447 0.136909i
\(404\) 14.8464 25.7146i 0.738634 1.27935i
\(405\) 3.03905 + 5.26380i 0.151012 + 0.261560i
\(406\) 76.2500 3.78422
\(407\) −5.50417 −0.272832
\(408\) −27.7653 48.0910i −1.37459 2.38086i
\(409\) 3.27235 + 5.66788i 0.161808 + 0.280259i 0.935517 0.353282i \(-0.114934\pi\)
−0.773709 + 0.633541i \(0.781601\pi\)
\(410\) −11.0699 −0.546703
\(411\) 7.78001 0.383760
\(412\) 1.07966 + 1.87002i 0.0531909 + 0.0921293i
\(413\) 3.50324 6.06780i 0.172383 0.298577i
\(414\) 0.445681 + 0.771941i 0.0219040 + 0.0379389i
\(415\) 3.71956 6.44247i 0.182586 0.316249i
\(416\) −7.99086 + 13.8406i −0.391784 + 0.678590i
\(417\) −15.9991 −0.783479
\(418\) 1.72605 + 10.2523i 0.0844239 + 0.501455i
\(419\) 21.8441 1.06715 0.533576 0.845752i \(-0.320848\pi\)
0.533576 + 0.845752i \(0.320848\pi\)
\(420\) 11.9140 20.6356i 0.581342 1.00691i
\(421\) 14.6717 25.4121i 0.715054 1.23851i −0.247885 0.968789i \(-0.579736\pi\)
0.962939 0.269720i \(-0.0869311\pi\)
\(422\) −26.0858 45.1819i −1.26984 2.19942i
\(423\) −1.53054 + 2.65097i −0.0744172 + 0.128894i
\(424\) 54.6474 + 94.6521i 2.65391 + 4.59671i
\(425\) 3.74185 0.181507
\(426\) −7.33299 −0.355285
\(427\) 9.02276 + 15.6279i 0.436642 + 0.756286i
\(428\) 18.0348 + 31.2372i 0.871746 + 1.50991i
\(429\) −0.829969 −0.0400713
\(430\) −5.67681 −0.273760
\(431\) 6.44336 + 11.1602i 0.310366 + 0.537570i 0.978442 0.206524i \(-0.0662151\pi\)
−0.668076 + 0.744093i \(0.732882\pi\)
\(432\) 45.6691 79.1011i 2.19725 3.80576i
\(433\) 6.92144 + 11.9883i 0.332623 + 0.576120i 0.983025 0.183470i \(-0.0587330\pi\)
−0.650402 + 0.759590i \(0.725400\pi\)
\(434\) 19.3802 33.5675i 0.930280 1.61129i
\(435\) 7.23970 12.5395i 0.347117 0.601225i
\(436\) 36.8291 1.76379
\(437\) 1.70506 + 0.635578i 0.0815641 + 0.0304038i
\(438\) −29.3418 −1.40200
\(439\) 0.0354040 0.0613216i 0.00168974 0.00292672i −0.865179 0.501463i \(-0.832795\pi\)
0.866869 + 0.498536i \(0.166129\pi\)
\(440\) 4.30118 7.44986i 0.205051 0.355158i
\(441\) 0.431503 + 0.747384i 0.0205477 + 0.0355897i
\(442\) −3.31936 + 5.74930i −0.157886 + 0.273466i
\(443\) 1.89457 + 3.28149i 0.0900137 + 0.155908i 0.907517 0.420016i \(-0.137976\pi\)
−0.817503 + 0.575924i \(0.804642\pi\)
\(444\) 53.2384 2.52658
\(445\) 4.44588 0.210755
\(446\) 22.2682 + 38.5697i 1.05443 + 1.82633i
\(447\) 11.1234 + 19.2663i 0.526120 + 0.911266i
\(448\) −102.773 −4.85555
\(449\) −26.5765 −1.25422 −0.627112 0.778929i \(-0.715763\pi\)
−0.627112 + 0.778929i \(0.715763\pi\)
\(450\) 1.06760 + 1.84914i 0.0503271 + 0.0871692i
\(451\) −1.73553 + 3.00603i −0.0817230 + 0.141548i
\(452\) −0.825616 1.43001i −0.0388337 0.0672620i
\(453\) −16.0075 + 27.7258i −0.752098 + 1.30267i
\(454\) −36.2936 + 62.8624i −1.70334 + 2.95028i
\(455\) −1.83247 −0.0859077
\(456\) −10.7396 63.7902i −0.502927 2.98725i
\(457\) −33.1523 −1.55080 −0.775400 0.631471i \(-0.782452\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(458\) 18.3854 31.8445i 0.859094 1.48799i
\(459\) 10.5348 18.2467i 0.491720 0.851684i
\(460\) −1.17028 2.02698i −0.0545645 0.0945085i
\(461\) 9.62679 16.6741i 0.448364 0.776590i −0.549915 0.835220i \(-0.685340\pi\)
0.998280 + 0.0586304i \(0.0186734\pi\)
\(462\) −5.06833 8.77861i −0.235800 0.408418i
\(463\) 39.1713 1.82044 0.910222 0.414120i \(-0.135911\pi\)
0.910222 + 0.414120i \(0.135911\pi\)
\(464\) −157.431 −7.30855
\(465\) −3.68018 6.37427i −0.170664 0.295600i
\(466\) −34.9019 60.4519i −1.61680 2.80038i
\(467\) −39.0650 −1.80771 −0.903856 0.427836i \(-0.859276\pi\)
−0.903856 + 0.427836i \(0.859276\pi\)
\(468\) −2.79220 −0.129069
\(469\) −3.60665 6.24691i −0.166540 0.288455i
\(470\) 5.45254 9.44407i 0.251507 0.435623i
\(471\) 1.81356 + 3.14118i 0.0835644 + 0.144738i
\(472\) −12.2330 + 21.1882i −0.563071 + 0.975268i
\(473\) −0.890007 + 1.54154i −0.0409226 + 0.0708800i
\(474\) 7.50743 0.344828
\(475\) 4.08436 + 1.52249i 0.187404 + 0.0698565i
\(476\) −59.7623 −2.73920
\(477\) −4.25314 + 7.36666i −0.194738 + 0.337296i
\(478\) 32.4756 56.2493i 1.48540 2.57279i
\(479\) 12.3775 + 21.4385i 0.565543 + 0.979550i 0.996999 + 0.0774158i \(0.0246669\pi\)
−0.431455 + 0.902134i \(0.642000\pi\)
\(480\) −18.5327 + 32.0995i −0.845897 + 1.46514i
\(481\) −2.04714 3.54574i −0.0933413 0.161672i
\(482\) 23.1236 1.05325
\(483\) −1.77418 −0.0807280
\(484\) 28.7400 + 49.7792i 1.30637 + 2.26269i
\(485\) 5.42707 + 9.39996i 0.246431 + 0.426830i
\(486\) 21.5794 0.978863
\(487\) 21.8871 0.991797 0.495899 0.868380i \(-0.334839\pi\)
0.495899 + 0.868380i \(0.334839\pi\)
\(488\) −31.5067 54.5713i −1.42624 2.47033i
\(489\) −13.2911 + 23.0209i −0.601046 + 1.04104i
\(490\) −1.53723 2.66256i −0.0694449 0.120282i
\(491\) −4.69777 + 8.13677i −0.212007 + 0.367207i −0.952343 0.305030i \(-0.901333\pi\)
0.740335 + 0.672238i \(0.234667\pi\)
\(492\) 16.7867 29.0754i 0.756803 1.31082i
\(493\) −36.3155 −1.63557
\(494\) −5.96247 + 4.92498i −0.268264 + 0.221585i
\(495\) 0.669511 0.0300923
\(496\) −40.0137 + 69.3058i −1.79667 + 3.11192i
\(497\) −2.53832 + 4.39650i −0.113859 + 0.197210i
\(498\) 15.3050 + 26.5091i 0.685834 + 1.18790i
\(499\) −12.4558 + 21.5740i −0.557596 + 0.965785i 0.440100 + 0.897949i \(0.354943\pi\)
−0.997696 + 0.0678367i \(0.978390\pi\)
\(500\) −2.80333 4.85550i −0.125369 0.217145i
\(501\) −0.605119 −0.0270347
\(502\) 50.3278 2.24624
\(503\) 15.6590 + 27.1222i 0.698200 + 1.20932i 0.969090 + 0.246707i \(0.0793486\pi\)
−0.270890 + 0.962610i \(0.587318\pi\)
\(504\) −10.9686 18.9981i −0.488579 0.846244i
\(505\) −5.29598 −0.235668
\(506\) −0.995699 −0.0442642
\(507\) 9.38878 + 16.2619i 0.416971 + 0.722214i
\(508\) −24.7672 + 42.8980i −1.09887 + 1.90329i
\(509\) 4.83310 + 8.37117i 0.214223 + 0.371045i 0.953032 0.302870i \(-0.0979447\pi\)
−0.738809 + 0.673915i \(0.764611\pi\)
\(510\) −7.69837 + 13.3340i −0.340889 + 0.590438i
\(511\) −10.1567 + 17.5919i −0.449305 + 0.778219i
\(512\) 80.2896 3.54833
\(513\) 18.9233 15.6306i 0.835484 0.690106i
\(514\) 38.8874 1.71525
\(515\) 0.192567 0.333536i 0.00848552 0.0146973i
\(516\) 8.60848 14.9103i 0.378967 0.656390i
\(517\) −1.70969 2.96127i −0.0751922 0.130237i
\(518\) 25.0023 43.3052i 1.09854 1.90272i
\(519\) −13.4429 23.2839i −0.590080 1.02205i
\(520\) 6.39885 0.280608
\(521\) −0.982633 −0.0430499 −0.0215250 0.999768i \(-0.506852\pi\)
−0.0215250 + 0.999768i \(0.506852\pi\)
\(522\) −10.3613 17.9463i −0.453502 0.785488i
\(523\) −19.8604 34.3993i −0.868436 1.50418i −0.863594 0.504187i \(-0.831792\pi\)
−0.00484172 0.999988i \(-0.501541\pi\)
\(524\) 117.251 5.12212
\(525\) −4.24993 −0.185482
\(526\) 8.84043 + 15.3121i 0.385461 + 0.667638i
\(527\) −9.23020 + 15.9872i −0.402074 + 0.696413i
\(528\) 10.4644 + 18.1249i 0.455406 + 0.788786i
\(529\) 11.4129 19.7677i 0.496211 0.859463i
\(530\) 15.1518 26.2437i 0.658154 1.13996i
\(531\) −1.90417 −0.0826337
\(532\) −65.2327 24.3161i −2.82820 1.05424i
\(533\) −2.58195 −0.111837
\(534\) −9.14680 + 15.8427i −0.395821 + 0.685582i
\(535\) 3.21668 5.57146i 0.139069 0.240875i
\(536\) 12.5941 + 21.8137i 0.543984 + 0.942208i
\(537\) −15.0328 + 26.0376i −0.648713 + 1.12360i
\(538\) −24.8099 42.9720i −1.06963 1.85266i
\(539\) −0.964024 −0.0415234
\(540\) −31.5698 −1.35855
\(541\) −15.3887 26.6541i −0.661614 1.14595i −0.980191 0.198052i \(-0.936538\pi\)
0.318577 0.947897i \(-0.396795\pi\)
\(542\) −16.3852 28.3801i −0.703807 1.21903i
\(543\) −25.5280 −1.09551
\(544\) 92.9629 3.98575
\(545\) −3.28441 5.68877i −0.140689 0.243680i
\(546\) 3.77007 6.52996i 0.161344 0.279456i
\(547\) 8.93287 + 15.4722i 0.381942 + 0.661543i 0.991340 0.131322i \(-0.0419221\pi\)
−0.609398 + 0.792865i \(0.708589\pi\)
\(548\) −14.6187 + 25.3203i −0.624480 + 1.08163i
\(549\) 2.45213 4.24722i 0.104654 0.181267i
\(550\) −2.38513 −0.101702
\(551\) −39.6397 14.7761i −1.68871 0.629482i
\(552\) 6.19529 0.263689
\(553\) 2.59870 4.50109i 0.110508 0.191406i
\(554\) −32.5777 + 56.4263i −1.38409 + 2.39732i
\(555\) −4.74778 8.22340i −0.201532 0.349064i
\(556\) 30.0624 52.0696i 1.27493 2.20824i
\(557\) 5.32878 + 9.22971i 0.225787 + 0.391075i 0.956555 0.291551i \(-0.0941712\pi\)
−0.730768 + 0.682626i \(0.760838\pi\)
\(558\) −10.5340 −0.445939
\(559\) −1.32406 −0.0560019
\(560\) 23.1042 + 40.0177i 0.976332 + 1.69106i
\(561\) 2.41389 + 4.18098i 0.101915 + 0.176521i
\(562\) 38.0863 1.60657
\(563\) 7.75961 0.327029 0.163514 0.986541i \(-0.447717\pi\)
0.163514 + 0.986541i \(0.447717\pi\)
\(564\) 16.5368 + 28.6425i 0.696324 + 1.20607i
\(565\) −0.147256 + 0.255056i −0.00619513 + 0.0107303i
\(566\) 16.2135 + 28.0826i 0.681504 + 1.18040i
\(567\) −8.65716 + 14.9946i −0.363567 + 0.629716i
\(568\) 8.86361 15.3522i 0.371909 0.644165i
\(569\) 5.72754 0.240111 0.120056 0.992767i \(-0.461693\pi\)
0.120056 + 0.992767i \(0.461693\pi\)
\(570\) −13.8284 + 11.4222i −0.579207 + 0.478422i
\(571\) −20.8347 −0.871903 −0.435952 0.899970i \(-0.643588\pi\)
−0.435952 + 0.899970i \(0.643588\pi\)
\(572\) 1.55952 2.70116i 0.0652067 0.112941i
\(573\) −3.93926 + 6.82300i −0.164565 + 0.285035i
\(574\) −15.7671 27.3093i −0.658104 1.13987i
\(575\) −0.208730 + 0.361531i −0.00870465 + 0.0150769i
\(576\) 13.9654 + 24.1887i 0.581890 + 1.00786i
\(577\) −5.11190 −0.212811 −0.106406 0.994323i \(-0.533934\pi\)
−0.106406 + 0.994323i \(0.533934\pi\)
\(578\) −8.27001 −0.343987
\(579\) −13.4300 23.2614i −0.558131 0.966712i
\(580\) 27.2069 + 47.1238i 1.12971 + 1.95671i
\(581\) 21.1914 0.879167
\(582\) −44.6619 −1.85130
\(583\) −4.75099 8.22896i −0.196766 0.340809i
\(584\) 35.4663 61.4294i 1.46760 2.54197i
\(585\) 0.249007 + 0.431294i 0.0102952 + 0.0178318i
\(586\) 37.3127 64.6275i 1.54137 2.66974i
\(587\) 5.33462 9.23984i 0.220184 0.381369i −0.734680 0.678414i \(-0.762668\pi\)
0.954864 + 0.297045i \(0.0960010\pi\)
\(588\) 9.32439 0.384531
\(589\) −16.5800 + 13.6950i −0.683165 + 0.564292i
\(590\) 6.78360 0.279276
\(591\) −6.02574 + 10.4369i −0.247866 + 0.429316i
\(592\) −51.6215 + 89.4110i −2.12163 + 3.67477i
\(593\) 8.50133 + 14.7247i 0.349108 + 0.604673i 0.986091 0.166205i \(-0.0531513\pi\)
−0.636983 + 0.770878i \(0.719818\pi\)
\(594\) −6.71507 + 11.6308i −0.275523 + 0.477219i
\(595\) 5.32959 + 9.23112i 0.218492 + 0.378439i
\(596\) −83.6040 −3.42455
\(597\) 2.09427 0.0857128
\(598\) −0.370325 0.641421i −0.0151437 0.0262297i
\(599\) −14.3375 24.8334i −0.585816 1.01466i −0.994773 0.102110i \(-0.967441\pi\)
0.408957 0.912554i \(-0.365893\pi\)
\(600\) 14.8404 0.605858
\(601\) 27.4370 1.11918 0.559590 0.828770i \(-0.310959\pi\)
0.559590 + 0.828770i \(0.310959\pi\)
\(602\) −8.08559 14.0046i −0.329544 0.570787i
\(603\) −0.980187 + 1.69773i −0.0399163 + 0.0691371i
\(604\) −60.1564 104.194i −2.44773 4.23959i
\(605\) 5.12606 8.87860i 0.208404 0.360966i
\(606\) 10.8958 18.8720i 0.442611 0.766624i
\(607\) −17.7547 −0.720639 −0.360320 0.932829i \(-0.617332\pi\)
−0.360320 + 0.932829i \(0.617332\pi\)
\(608\) 101.472 + 37.8248i 4.11524 + 1.53400i
\(609\) 41.2466 1.67140
\(610\) −8.73573 + 15.1307i −0.353699 + 0.612625i
\(611\) 1.27175 2.20274i 0.0514496 0.0891133i
\(612\) 8.12086 + 14.0657i 0.328266 + 0.568574i
\(613\) −17.3196 + 29.9983i −0.699530 + 1.21162i 0.269099 + 0.963112i \(0.413274\pi\)
−0.968629 + 0.248509i \(0.920059\pi\)
\(614\) −12.1880 21.1102i −0.491868 0.851940i
\(615\) −5.98814 −0.241465
\(616\) 24.5050 0.987334
\(617\) −2.23284 3.86740i −0.0898909 0.155696i 0.817574 0.575824i \(-0.195319\pi\)
−0.907465 + 0.420128i \(0.861985\pi\)
\(618\) 0.792362 + 1.37241i 0.0318735 + 0.0552065i
\(619\) −17.9112 −0.719913 −0.359957 0.932969i \(-0.617209\pi\)
−0.359957 + 0.932969i \(0.617209\pi\)
\(620\) 27.6604 1.11087
\(621\) 1.17531 + 2.03570i 0.0471636 + 0.0816898i
\(622\) 0.898414 1.55610i 0.0360231 0.0623939i
\(623\) 6.33234 + 10.9679i 0.253700 + 0.439421i
\(624\) −7.78396 + 13.4822i −0.311608 + 0.539720i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −8.17906 −0.326901
\(627\) 0.933688 + 5.54586i 0.0372879 + 0.221480i
\(628\) −13.6308 −0.543927
\(629\) −11.9078 + 20.6250i −0.474796 + 0.822371i
\(630\) −3.04120 + 5.26752i −0.121164 + 0.209863i
\(631\) −2.48440 4.30311i −0.0989026 0.171304i 0.812328 0.583201i \(-0.198200\pi\)
−0.911231 + 0.411896i \(0.864867\pi\)
\(632\) −9.07446 + 15.7174i −0.360963 + 0.625205i
\(633\) −14.1108 24.4407i −0.560855 0.971429i
\(634\) −28.6278 −1.13696
\(635\) 8.83492 0.350603
\(636\) 45.9534 + 79.5935i 1.82217 + 3.15609i
\(637\) −0.358544 0.621016i −0.0142060 0.0246056i
\(638\) 23.1483 0.916449
\(639\) 1.37969 0.0545796
\(640\) −24.9076 43.1412i −0.984558 1.70530i
\(641\) 18.9760 32.8675i 0.749508 1.29819i −0.198550 0.980091i \(-0.563623\pi\)
0.948059 0.318096i \(-0.103043\pi\)
\(642\) 13.2358 + 22.9251i 0.522375 + 0.904780i
\(643\) −17.6251 + 30.5276i −0.695067 + 1.20389i 0.275092 + 0.961418i \(0.411292\pi\)
−0.970158 + 0.242473i \(0.922042\pi\)
\(644\) 3.33370 5.77413i 0.131366 0.227533i
\(645\) −3.07081 −0.120913
\(646\) 42.1510 + 15.7122i 1.65841 + 0.618188i
\(647\) 35.5219 1.39651 0.698254 0.715850i \(-0.253960\pi\)
0.698254 + 0.715850i \(0.253960\pi\)
\(648\) 30.2301 52.3601i 1.18755 2.05690i
\(649\) 1.06353 1.84209i 0.0417471 0.0723082i
\(650\) −0.887090 1.53648i −0.0347945 0.0602659i
\(651\) 10.4835 18.1580i 0.410881 0.711667i
\(652\) −49.9483 86.5130i −1.95613 3.38811i
\(653\) 8.02411 0.314008 0.157004 0.987598i \(-0.449816\pi\)
0.157004 + 0.987598i \(0.449816\pi\)
\(654\) 27.0290 1.05692
\(655\) −10.4564 18.1110i −0.408565 0.707655i
\(656\) 32.5538 + 56.3848i 1.27101 + 2.20146i
\(657\) 5.52059 0.215379
\(658\) 31.0646 1.21102
\(659\) 23.6098 + 40.8933i 0.919706 + 1.59298i 0.799861 + 0.600185i \(0.204906\pi\)
0.119844 + 0.992793i \(0.461760\pi\)
\(660\) 3.61689 6.26463i 0.140787 0.243850i
\(661\) 13.0580 + 22.6171i 0.507896 + 0.879702i 0.999958 + 0.00914181i \(0.00290997\pi\)
−0.492062 + 0.870560i \(0.663757\pi\)
\(662\) −20.8123 + 36.0479i −0.808892 + 1.40104i
\(663\) −1.79557 + 3.11002i −0.0697342 + 0.120783i
\(664\) −73.9986 −2.87170
\(665\) 2.06147 + 12.2446i 0.0799405 + 0.474825i
\(666\) −13.5898 −0.526596
\(667\) 2.02577 3.50874i 0.0784383 0.135859i
\(668\) 1.13702 1.96938i 0.0439928 0.0761978i
\(669\) 12.0458 + 20.8639i 0.465716 + 0.806643i
\(670\) 3.49192 6.04818i 0.134905 0.233662i
\(671\) 2.73917 + 4.74437i 0.105744 + 0.183154i
\(672\) −105.586 −4.07306
\(673\) 15.3820 0.592931 0.296466 0.955044i \(-0.404192\pi\)
0.296466 + 0.955044i \(0.404192\pi\)
\(674\) −21.7848 37.7324i −0.839119 1.45340i
\(675\) 2.81538 + 4.87639i 0.108364 + 0.187692i
\(676\) −70.5664 −2.71409
\(677\) 24.4763 0.940701 0.470350 0.882480i \(-0.344128\pi\)
0.470350 + 0.882480i \(0.344128\pi\)
\(678\) −0.605921 1.04949i −0.0232703 0.0403053i
\(679\) −15.4598 + 26.7771i −0.593291 + 1.02761i
\(680\) −18.6105 32.2343i −0.713680 1.23613i
\(681\) −19.6326 + 34.0047i −0.752324 + 1.30306i
\(682\) 5.88352 10.1906i 0.225292 0.390217i
\(683\) −17.8502 −0.683018 −0.341509 0.939879i \(-0.610938\pi\)
−0.341509 + 0.939879i \(0.610938\pi\)
\(684\) 3.14113 + 18.6575i 0.120104 + 0.713386i
\(685\) 5.21477 0.199246
\(686\) −23.1191 + 40.0434i −0.882689 + 1.52886i
\(687\) 9.94538 17.2259i 0.379440 0.657210i
\(688\) 16.6941 + 28.9150i 0.636455 + 1.10237i
\(689\) 3.53402 6.12110i 0.134635 0.233195i
\(690\) −0.858870 1.48761i −0.0326966 0.0566322i
\(691\) −9.27242 −0.352739 −0.176370 0.984324i \(-0.556435\pi\)
−0.176370 + 0.984324i \(0.556435\pi\)
\(692\) 101.038 3.84087
\(693\) 0.953597 + 1.65168i 0.0362241 + 0.0627421i
\(694\) 29.4448 + 50.9999i 1.11771 + 1.93593i
\(695\) −10.7238 −0.406778
\(696\) −144.030 −5.45943
\(697\) 7.50937 + 13.0066i 0.284438 + 0.492660i
\(698\) 44.6657 77.3633i 1.69062 2.92824i
\(699\) −18.8798 32.7008i −0.714100 1.23686i
\(700\) 7.98566 13.8316i 0.301830 0.522784i
\(701\) 3.84453 6.65892i 0.145206 0.251504i −0.784244 0.620453i \(-0.786949\pi\)
0.929450 + 0.368949i \(0.120282\pi\)
\(702\) −9.98999 −0.377048
\(703\) −21.3897 + 17.6678i −0.806728 + 0.666354i
\(704\) −31.2001 −1.17590
\(705\) 2.94949 5.10867i 0.111084 0.192404i
\(706\) −1.00748 + 1.74501i −0.0379170 + 0.0656742i
\(707\) −7.54316 13.0651i −0.283690 0.491365i
\(708\) −10.2868 + 17.8173i −0.386603 + 0.669616i
\(709\) −12.2187 21.1635i −0.458885 0.794812i 0.540018 0.841654i \(-0.318418\pi\)
−0.998902 + 0.0468421i \(0.985084\pi\)
\(710\) −4.91514 −0.184462
\(711\) −1.41251 −0.0529732
\(712\) −22.1120 38.2992i −0.828683 1.43532i
\(713\) −1.02977 1.78361i −0.0385652 0.0667968i
\(714\) −43.8597 −1.64141
\(715\) −0.556310 −0.0208048
\(716\) −56.4935 97.8496i −2.11126 3.65681i
\(717\) 17.5673 30.4275i 0.656063 1.13633i
\(718\) 37.0258 + 64.1305i 1.38179 + 2.39333i
\(719\) 11.0563 19.1501i 0.412331 0.714178i −0.582813 0.812606i \(-0.698048\pi\)
0.995144 + 0.0984282i \(0.0313815\pi\)
\(720\) 6.27908 10.8757i 0.234008 0.405313i
\(721\) 1.09711 0.0408584
\(722\) 39.6163 + 34.3008i 1.47437 + 1.27655i
\(723\) 12.5085 0.465195
\(724\) 47.9672 83.0817i 1.78269 3.08771i
\(725\) 4.85261 8.40497i 0.180222 0.312153i
\(726\) 21.0924 + 36.5331i 0.782812 + 1.35587i
\(727\) 14.5247 25.1575i 0.538692 0.933042i −0.460283 0.887772i \(-0.652252\pi\)
0.998975 0.0452694i \(-0.0144146\pi\)
\(728\) 9.11400 + 15.7859i 0.337787 + 0.585065i
\(729\) 29.9075 1.10768
\(730\) −19.6671 −0.727913
\(731\) 3.85092 + 6.66999i 0.142431 + 0.246698i
\(732\) −26.4942 45.8893i −0.979254 1.69612i
\(733\) 14.5428 0.537151 0.268576 0.963259i \(-0.413447\pi\)
0.268576 + 0.963259i \(0.413447\pi\)
\(734\) −63.3360 −2.33777
\(735\) −0.831547 1.44028i −0.0306721 0.0531256i
\(736\) −5.18571 + 8.98191i −0.191148 + 0.331078i
\(737\) −1.09492 1.89646i −0.0403320 0.0698570i
\(738\) −4.28504 + 7.42191i −0.157735 + 0.273204i
\(739\) 2.37798 4.11878i 0.0874754 0.151512i −0.818968 0.573839i \(-0.805453\pi\)
0.906443 + 0.422327i \(0.138787\pi\)
\(740\) 35.6845 1.31179
\(741\) −3.22533 + 2.66411i −0.118486 + 0.0978687i
\(742\) 86.3242 3.16906
\(743\) −2.93853 + 5.08968i −0.107804 + 0.186722i −0.914880 0.403725i \(-0.867715\pi\)
0.807076 + 0.590447i \(0.201049\pi\)
\(744\) −36.6076 + 63.4062i −1.34210 + 2.32458i
\(745\) 7.45578 + 12.9138i 0.273159 + 0.473125i
\(746\) −40.7228 + 70.5339i −1.49097 + 2.58243i
\(747\) −2.87961 4.98763i −0.105359 0.182488i
\(748\) −18.1429 −0.663370
\(749\) 18.3263 0.669629
\(750\) −2.05737 3.56347i −0.0751244 0.130119i
\(751\) −0.810481 1.40379i −0.0295749 0.0512252i 0.850859 0.525394i \(-0.176082\pi\)
−0.880434 + 0.474169i \(0.842749\pi\)
\(752\) −64.1382 −2.33888
\(753\) 27.2243 0.992107
\(754\) 8.60941 + 14.9119i 0.313536 + 0.543060i
\(755\) −10.7295 + 18.5840i −0.390485 + 0.676341i
\(756\) −44.9654 77.8824i −1.63538 2.83255i
\(757\) 14.0567 24.3470i 0.510901 0.884907i −0.489019 0.872273i \(-0.662645\pi\)
0.999920 0.0126336i \(-0.00402151\pi\)
\(758\) −24.1488 + 41.8270i −0.877125 + 1.51922i
\(759\) −0.538612 −0.0195504
\(760\) −7.19850 42.7572i −0.261117 1.55096i
\(761\) 20.1663 0.731027 0.365514 0.930806i \(-0.380893\pi\)
0.365514 + 0.930806i \(0.380893\pi\)
\(762\) −18.1767 + 31.4829i −0.658472 + 1.14051i
\(763\) 9.35610 16.2052i 0.338713 0.586669i
\(764\) −14.8038 25.6409i −0.535583 0.927656i
\(765\) 1.44843 2.50876i 0.0523682 0.0907044i
\(766\) −11.1790 19.3625i −0.403912 0.699597i
\(767\) 1.58221 0.0571303
\(768\) 97.3257 3.51194
\(769\) −22.6524 39.2350i −0.816865 1.41485i −0.907981 0.419011i \(-0.862377\pi\)
0.0911160 0.995840i \(-0.470957\pi\)
\(770\) −3.39719 5.88411i −0.122426 0.212049i
\(771\) 21.0357 0.757583
\(772\) 100.940 3.63292
\(773\) 10.0881 + 17.4731i 0.362843 + 0.628462i 0.988428 0.151694i \(-0.0484728\pi\)
−0.625585 + 0.780156i \(0.715139\pi\)
\(774\) −2.19744 + 3.80607i −0.0789852 + 0.136806i
\(775\) −2.46675