Properties

Label 95.2.e.c.26.4
Level $95$
Weight $2$
Character 95.26
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 26.4
Root \(1.07988 + 1.87040i\) of defining polynomial
Character \(\chi\) \(=\) 95.26
Dual form 95.2.e.c.11.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.832272 + 1.44154i) q^{2} +(0.579878 + 1.00438i) q^{3} +(-0.385355 + 0.667454i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.965233 + 1.67183i) q^{6} -2.43525 q^{7} +2.04621 q^{8} +(0.827483 - 1.43324i) q^{9} +O(q^{10})\) \(q+(0.832272 + 1.44154i) q^{2} +(0.579878 + 1.00438i) q^{3} +(-0.385355 + 0.667454i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.965233 + 1.67183i) q^{6} -2.43525 q^{7} +2.04621 q^{8} +(0.827483 - 1.43324i) q^{9} +(0.832272 - 1.44154i) q^{10} -5.75477 q^{11} -0.893835 q^{12} +(0.797505 - 1.38132i) q^{13} +(-2.02680 - 3.51051i) q^{14} +(0.579878 - 1.00438i) q^{15} +(2.47371 + 4.28460i) q^{16} +(2.99203 + 5.18234i) q^{17} +2.75477 q^{18} +(0.149412 - 4.35634i) q^{19} +0.770710 q^{20} +(-1.41215 - 2.44592i) q^{21} +(-4.78953 - 8.29572i) q^{22} +(0.470022 - 0.814102i) q^{23} +(1.18655 + 2.05517i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.65497 q^{26} +5.39862 q^{27} +(0.938437 - 1.62542i) q^{28} +(-1.30917 + 2.26755i) q^{29} +1.93047 q^{30} -5.26913 q^{31} +(-2.07140 + 3.58777i) q^{32} +(-3.33706 - 5.77996i) q^{33} +(-4.98037 + 8.62625i) q^{34} +(1.21763 + 2.10899i) q^{35} +(0.637749 + 1.10461i) q^{36} -2.89384 q^{37} +(6.40418 - 3.41028i) q^{38} +1.84982 q^{39} +(-1.02310 - 1.77207i) q^{40} +(3.15767 + 5.46925i) q^{41} +(2.35059 - 4.07134i) q^{42} +(-2.26961 - 3.93108i) q^{43} +(2.21763 - 3.84104i) q^{44} -1.65497 q^{45} +1.56475 q^{46} +(-4.47718 + 7.75471i) q^{47} +(-2.86890 + 4.96909i) q^{48} -1.06953 q^{49} -1.66454 q^{50} +(-3.47002 + 6.01025i) q^{51} +(0.614645 + 1.06460i) q^{52} +(1.09819 - 1.90213i) q^{53} +(4.49313 + 7.78232i) q^{54} +(2.87738 + 4.98377i) q^{55} -4.98304 q^{56} +(4.46205 - 2.37608i) q^{57} -4.35834 q^{58} +(5.39939 + 9.35202i) q^{59} +(0.446918 + 0.774084i) q^{60} +(5.26434 - 9.11811i) q^{61} +(-4.38535 - 7.59566i) q^{62} +(-2.01513 + 3.49031i) q^{63} +2.99898 q^{64} -1.59501 q^{65} +(5.55469 - 9.62100i) q^{66} +(-0.504789 + 0.874320i) q^{67} -4.61197 q^{68} +1.09022 q^{69} +(-2.02680 + 3.51051i) q^{70} +(-4.41694 - 7.65036i) q^{71} +(1.69320 - 2.93271i) q^{72} +(5.12499 + 8.87674i) q^{73} +(-2.40846 - 4.17157i) q^{74} -1.15976 q^{75} +(2.85008 + 1.77846i) q^{76} +14.0143 q^{77} +(1.53956 + 2.66659i) q^{78} +(-3.80229 - 6.58577i) q^{79} +(2.47371 - 4.28460i) q^{80} +(0.648093 + 1.12253i) q^{81} +(-5.25609 + 9.10381i) q^{82} +3.11355 q^{83} +2.17672 q^{84} +(2.99203 - 5.18234i) q^{85} +(3.77787 - 6.54346i) q^{86} -3.03663 q^{87} -11.7755 q^{88} +(5.55706 - 9.62511i) q^{89} +(-1.37738 - 2.38570i) q^{90} +(-1.94213 + 3.36387i) q^{91} +(0.362251 + 0.627436i) q^{92} +(-3.05545 - 5.29220i) q^{93} -14.9049 q^{94} +(-3.84741 + 2.04877i) q^{95} -4.80463 q^{96} +(-2.02888 - 3.51412i) q^{97} +(-0.890144 - 1.54177i) q^{98} +(-4.76197 + 8.24798i) 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 \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.832272 + 1.44154i 0.588506 + 1.01932i 0.994428 + 0.105414i \(0.0336168\pi\)
−0.405923 + 0.913907i \(0.633050\pi\)
\(3\) 0.579878 + 1.00438i 0.334793 + 0.579878i 0.983445 0.181207i \(-0.0580004\pi\)
−0.648652 + 0.761085i \(0.724667\pi\)
\(4\) −0.385355 + 0.667454i −0.192677 + 0.333727i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −0.965233 + 1.67183i −0.394055 + 0.682523i
\(7\) −2.43525 −0.920440 −0.460220 0.887805i \(-0.652229\pi\)
−0.460220 + 0.887805i \(0.652229\pi\)
\(8\) 2.04621 0.723444
\(9\) 0.827483 1.43324i 0.275828 0.477748i
\(10\) 0.832272 1.44154i 0.263188 0.455854i
\(11\) −5.75477 −1.73513 −0.867564 0.497326i \(-0.834315\pi\)
−0.867564 + 0.497326i \(0.834315\pi\)
\(12\) −0.893835 −0.258028
\(13\) 0.797505 1.38132i 0.221188 0.383109i −0.733981 0.679170i \(-0.762340\pi\)
0.955169 + 0.296061i \(0.0956732\pi\)
\(14\) −2.02680 3.51051i −0.541684 0.938224i
\(15\) 0.579878 1.00438i 0.149724 0.259329i
\(16\) 2.47371 + 4.28460i 0.618428 + 1.07115i
\(17\) 2.99203 + 5.18234i 0.725673 + 1.25690i 0.958696 + 0.284432i \(0.0918050\pi\)
−0.233023 + 0.972471i \(0.574862\pi\)
\(18\) 2.75477 0.649305
\(19\) 0.149412 4.35634i 0.0342775 0.999412i
\(20\) 0.770710 0.172336
\(21\) −1.41215 2.44592i −0.308156 0.533743i
\(22\) −4.78953 8.29572i −1.02113 1.76865i
\(23\) 0.470022 0.814102i 0.0980064 0.169752i −0.812853 0.582469i \(-0.802087\pi\)
0.910859 + 0.412717i \(0.135420\pi\)
\(24\) 1.18655 + 2.05517i 0.242204 + 0.419509i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.65497 0.520682
\(27\) 5.39862 1.03897
\(28\) 0.938437 1.62542i 0.177348 0.307176i
\(29\) −1.30917 + 2.26755i −0.243106 + 0.421073i −0.961598 0.274463i \(-0.911500\pi\)
0.718491 + 0.695536i \(0.244833\pi\)
\(30\) 1.93047 0.352453
\(31\) −5.26913 −0.946364 −0.473182 0.880965i \(-0.656895\pi\)
−0.473182 + 0.880965i \(0.656895\pi\)
\(32\) −2.07140 + 3.58777i −0.366175 + 0.634233i
\(33\) −3.33706 5.77996i −0.580908 1.00616i
\(34\) −4.98037 + 8.62625i −0.854126 + 1.47939i
\(35\) 1.21763 + 2.10899i 0.205817 + 0.356485i
\(36\) 0.637749 + 1.10461i 0.106292 + 0.184102i
\(37\) −2.89384 −0.475744 −0.237872 0.971297i \(-0.576450\pi\)
−0.237872 + 0.971297i \(0.576450\pi\)
\(38\) 6.40418 3.41028i 1.03889 0.553220i
\(39\) 1.84982 0.296209
\(40\) −1.02310 1.77207i −0.161767 0.280189i
\(41\) 3.15767 + 5.46925i 0.493145 + 0.854153i 0.999969 0.00789701i \(-0.00251372\pi\)
−0.506823 + 0.862050i \(0.669180\pi\)
\(42\) 2.35059 4.07134i 0.362704 0.628221i
\(43\) −2.26961 3.93108i −0.346113 0.599485i 0.639443 0.768839i \(-0.279165\pi\)
−0.985555 + 0.169354i \(0.945832\pi\)
\(44\) 2.21763 3.84104i 0.334320 0.579059i
\(45\) −1.65497 −0.246708
\(46\) 1.56475 0.230709
\(47\) −4.47718 + 7.75471i −0.653064 + 1.13114i 0.329311 + 0.944221i \(0.393184\pi\)
−0.982375 + 0.186919i \(0.940150\pi\)
\(48\) −2.86890 + 4.96909i −0.414090 + 0.717226i
\(49\) −1.06953 −0.152791
\(50\) −1.66454 −0.235402
\(51\) −3.47002 + 6.01025i −0.485900 + 0.841604i
\(52\) 0.614645 + 1.06460i 0.0852359 + 0.147633i
\(53\) 1.09819 1.90213i 0.150848 0.261277i −0.780691 0.624917i \(-0.785133\pi\)
0.931540 + 0.363640i \(0.118466\pi\)
\(54\) 4.49313 + 7.78232i 0.611437 + 1.05904i
\(55\) 2.87738 + 4.98377i 0.387986 + 0.672012i
\(56\) −4.98304 −0.665887
\(57\) 4.46205 2.37608i 0.591013 0.314719i
\(58\) −4.35834 −0.572278
\(59\) 5.39939 + 9.35202i 0.702941 + 1.21753i 0.967430 + 0.253140i \(0.0814634\pi\)
−0.264489 + 0.964389i \(0.585203\pi\)
\(60\) 0.446918 + 0.774084i 0.0576968 + 0.0999338i
\(61\) 5.26434 9.11811i 0.674030 1.16745i −0.302721 0.953079i \(-0.597895\pi\)
0.976751 0.214375i \(-0.0687716\pi\)
\(62\) −4.38535 7.59566i −0.556941 0.964649i
\(63\) −2.01513 + 3.49031i −0.253883 + 0.439738i
\(64\) 2.99898 0.374873
\(65\) −1.59501 −0.197837
\(66\) 5.55469 9.62100i 0.683735 1.18426i
\(67\) −0.504789 + 0.874320i −0.0616698 + 0.106815i −0.895212 0.445641i \(-0.852976\pi\)
0.833542 + 0.552456i \(0.186309\pi\)
\(68\) −4.61197 −0.559284
\(69\) 1.09022 0.131247
\(70\) −2.02680 + 3.51051i −0.242248 + 0.419587i
\(71\) −4.41694 7.65036i −0.524194 0.907931i −0.999603 0.0281662i \(-0.991033\pi\)
0.475409 0.879765i \(-0.342300\pi\)
\(72\) 1.69320 2.93271i 0.199546 0.345624i
\(73\) 5.12499 + 8.87674i 0.599835 + 1.03894i 0.992845 + 0.119410i \(0.0381003\pi\)
−0.393011 + 0.919534i \(0.628566\pi\)
\(74\) −2.40846 4.17157i −0.279978 0.484936i
\(75\) −1.15976 −0.133917
\(76\) 2.85008 + 1.77846i 0.326927 + 0.204004i
\(77\) 14.0143 1.59708
\(78\) 1.53956 + 2.66659i 0.174320 + 0.301932i
\(79\) −3.80229 6.58577i −0.427792 0.740957i 0.568885 0.822417i \(-0.307375\pi\)
−0.996677 + 0.0814604i \(0.974042\pi\)
\(80\) 2.47371 4.28460i 0.276570 0.479032i
\(81\) 0.648093 + 1.12253i 0.0720103 + 0.124726i
\(82\) −5.25609 + 9.10381i −0.580438 + 1.00535i
\(83\) 3.11355 0.341756 0.170878 0.985292i \(-0.445340\pi\)
0.170878 + 0.985292i \(0.445340\pi\)
\(84\) 2.17672 0.237499
\(85\) 2.99203 5.18234i 0.324531 0.562104i
\(86\) 3.77787 6.54346i 0.407378 0.705600i
\(87\) −3.03663 −0.325561
\(88\) −11.7755 −1.25527
\(89\) 5.55706 9.62511i 0.589047 1.02026i −0.405310 0.914179i \(-0.632837\pi\)
0.994358 0.106081i \(-0.0338302\pi\)
\(90\) −1.37738 2.38570i −0.145189 0.251475i
\(91\) −1.94213 + 3.36387i −0.203590 + 0.352629i
\(92\) 0.362251 + 0.627436i 0.0377672 + 0.0654148i
\(93\) −3.05545 5.29220i −0.316836 0.548776i
\(94\) −14.9049 −1.53733
\(95\) −3.84741 + 2.04877i −0.394735 + 0.210200i
\(96\) −4.80463 −0.490371
\(97\) −2.02888 3.51412i −0.206002 0.356805i 0.744450 0.667678i \(-0.232712\pi\)
−0.950451 + 0.310873i \(0.899379\pi\)
\(98\) −0.890144 1.54177i −0.0899181 0.155743i
\(99\) −4.76197 + 8.24798i −0.478596 + 0.828953i
\(100\) −0.385355 0.667454i −0.0385355 0.0667454i
\(101\) 5.56503 9.63892i 0.553741 0.959108i −0.444259 0.895898i \(-0.646533\pi\)
0.998000 0.0632098i \(-0.0201337\pi\)
\(102\) −11.5520 −1.14382
\(103\) 11.5791 1.14092 0.570460 0.821326i \(-0.306765\pi\)
0.570460 + 0.821326i \(0.306765\pi\)
\(104\) 1.63186 2.82647i 0.160017 0.277158i
\(105\) −1.41215 + 2.44592i −0.137812 + 0.238697i
\(106\) 3.65598 0.355101
\(107\) 17.9177 1.73217 0.866086 0.499894i \(-0.166628\pi\)
0.866086 + 0.499894i \(0.166628\pi\)
\(108\) −2.08039 + 3.60333i −0.200185 + 0.346731i
\(109\) −2.81235 4.87113i −0.269374 0.466570i 0.699326 0.714803i \(-0.253484\pi\)
−0.968700 + 0.248233i \(0.920150\pi\)
\(110\) −4.78953 + 8.29572i −0.456664 + 0.790965i
\(111\) −1.67807 2.90650i −0.159275 0.275873i
\(112\) −6.02412 10.4341i −0.569226 0.985928i
\(113\) −15.6789 −1.47494 −0.737472 0.675378i \(-0.763981\pi\)
−0.737472 + 0.675378i \(0.763981\pi\)
\(114\) 7.13885 + 4.45467i 0.668614 + 0.417218i
\(115\) −0.940044 −0.0876595
\(116\) −1.00899 1.74762i −0.0936822 0.162262i
\(117\) −1.31984 2.28604i −0.122020 0.211344i
\(118\) −8.98753 + 15.5669i −0.827369 + 1.43304i
\(119\) −7.28635 12.6203i −0.667939 1.15690i
\(120\) 1.18655 2.05517i 0.108317 0.187610i
\(121\) 22.1173 2.01067
\(122\) 17.5255 1.58668
\(123\) −3.66213 + 6.34299i −0.330203 + 0.571928i
\(124\) 2.03049 3.51691i 0.182343 0.315827i
\(125\) 1.00000 0.0894427
\(126\) −6.70856 −0.597646
\(127\) −3.05996 + 5.30000i −0.271527 + 0.470299i −0.969253 0.246066i \(-0.920862\pi\)
0.697726 + 0.716365i \(0.254195\pi\)
\(128\) 6.63877 + 11.4987i 0.586790 + 1.01635i
\(129\) 2.63220 4.55910i 0.231752 0.401406i
\(130\) −1.32748 2.29927i −0.116428 0.201659i
\(131\) 7.44055 + 12.8874i 0.650084 + 1.12598i 0.983102 + 0.183058i \(0.0585997\pi\)
−0.333018 + 0.942920i \(0.608067\pi\)
\(132\) 5.14381 0.447711
\(133\) −0.363857 + 10.6088i −0.0315504 + 0.919899i
\(134\) −1.68049 −0.145172
\(135\) −2.69931 4.67535i −0.232320 0.402390i
\(136\) 6.12231 + 10.6042i 0.524984 + 0.909299i
\(137\) −8.67518 + 15.0258i −0.741170 + 1.28374i 0.210793 + 0.977531i \(0.432396\pi\)
−0.951963 + 0.306214i \(0.900938\pi\)
\(138\) 0.907361 + 1.57160i 0.0772397 + 0.133783i
\(139\) 3.35267 5.80700i 0.284370 0.492543i −0.688086 0.725629i \(-0.741549\pi\)
0.972456 + 0.233086i \(0.0748823\pi\)
\(140\) −1.87687 −0.158625
\(141\) −10.3849 −0.874564
\(142\) 7.35219 12.7344i 0.616982 1.06864i
\(143\) −4.58946 + 7.94917i −0.383790 + 0.664743i
\(144\) 8.18782 0.682319
\(145\) 2.61834 0.217441
\(146\) −8.53077 + 14.7757i −0.706012 + 1.22285i
\(147\) −0.620199 1.07422i −0.0511532 0.0885999i
\(148\) 1.11515 1.93150i 0.0916651 0.158769i
\(149\) −7.19642 12.4646i −0.589553 1.02114i −0.994291 0.106704i \(-0.965970\pi\)
0.404737 0.914433i \(-0.367363\pi\)
\(150\) −0.965233 1.67183i −0.0788109 0.136505i
\(151\) 12.7219 1.03529 0.517645 0.855595i \(-0.326809\pi\)
0.517645 + 0.855595i \(0.326809\pi\)
\(152\) 0.305729 8.91398i 0.0247979 0.723019i
\(153\) 9.90341 0.800644
\(154\) 11.6637 + 20.2022i 0.939890 + 1.62794i
\(155\) 2.63457 + 4.56320i 0.211614 + 0.366525i
\(156\) −0.712838 + 1.23467i −0.0570727 + 0.0988529i
\(157\) 1.68765 + 2.92309i 0.134689 + 0.233288i 0.925479 0.378800i \(-0.123663\pi\)
−0.790790 + 0.612088i \(0.790330\pi\)
\(158\) 6.32909 10.9623i 0.503515 0.872114i
\(159\) 2.54727 0.202012
\(160\) 4.14280 0.327517
\(161\) −1.14462 + 1.98255i −0.0902089 + 0.156246i
\(162\) −1.07878 + 1.86850i −0.0847569 + 0.146803i
\(163\) 0.307960 0.0241213 0.0120607 0.999927i \(-0.496161\pi\)
0.0120607 + 0.999927i \(0.496161\pi\)
\(164\) −4.86730 −0.380072
\(165\) −3.33706 + 5.77996i −0.259790 + 0.449969i
\(166\) 2.59132 + 4.48830i 0.201125 + 0.348359i
\(167\) −7.13215 + 12.3532i −0.551902 + 0.955923i 0.446235 + 0.894916i \(0.352765\pi\)
−0.998137 + 0.0610070i \(0.980569\pi\)
\(168\) −2.88955 5.00486i −0.222934 0.386133i
\(169\) 5.22797 + 9.05511i 0.402152 + 0.696547i
\(170\) 9.96073 0.763953
\(171\) −6.12005 3.81894i −0.468012 0.292042i
\(172\) 3.49842 0.266752
\(173\) −6.67357 11.5590i −0.507382 0.878811i −0.999963 0.00854514i \(-0.997280\pi\)
0.492581 0.870266i \(-0.336053\pi\)
\(174\) −2.52730 4.37742i −0.191594 0.331851i
\(175\) 1.21763 2.10899i 0.0920440 0.159425i
\(176\) −14.2356 24.6569i −1.07305 1.85858i
\(177\) −6.26197 + 10.8461i −0.470679 + 0.815239i
\(178\) 18.5000 1.38663
\(179\) −14.2207 −1.06291 −0.531454 0.847087i \(-0.678354\pi\)
−0.531454 + 0.847087i \(0.678354\pi\)
\(180\) 0.637749 1.10461i 0.0475350 0.0823331i
\(181\) −4.94132 + 8.55861i −0.367285 + 0.636157i −0.989140 0.146976i \(-0.953046\pi\)
0.621855 + 0.783133i \(0.286379\pi\)
\(182\) −6.46552 −0.479256
\(183\) 12.2107 0.902641
\(184\) 0.961763 1.66582i 0.0709021 0.122806i
\(185\) 1.44692 + 2.50613i 0.106379 + 0.184255i
\(186\) 5.08594 8.80911i 0.372919 0.645915i
\(187\) −17.2184 29.8232i −1.25914 2.18089i
\(188\) −3.45061 5.97663i −0.251661 0.435891i
\(189\) −13.1470 −0.956305
\(190\) −6.15548 3.84104i −0.446565 0.278659i
\(191\) −12.9942 −0.940228 −0.470114 0.882606i \(-0.655787\pi\)
−0.470114 + 0.882606i \(0.655787\pi\)
\(192\) 1.73904 + 3.01211i 0.125505 + 0.217380i
\(193\) −7.25795 12.5711i −0.522439 0.904890i −0.999659 0.0261066i \(-0.991689\pi\)
0.477221 0.878784i \(-0.341644\pi\)
\(194\) 3.37716 5.84942i 0.242466 0.419964i
\(195\) −0.924911 1.60199i −0.0662343 0.114721i
\(196\) 0.412150 0.713865i 0.0294393 0.0509904i
\(197\) −25.0010 −1.78125 −0.890624 0.454740i \(-0.849732\pi\)
−0.890624 + 0.454740i \(0.849732\pi\)
\(198\) −15.8530 −1.12663
\(199\) 1.12769 1.95322i 0.0799401 0.138460i −0.823284 0.567630i \(-0.807860\pi\)
0.903224 + 0.429170i \(0.141194\pi\)
\(200\) −1.02310 + 1.77207i −0.0723444 + 0.125304i
\(201\) −1.17086 −0.0825864
\(202\) 18.5265 1.30352
\(203\) 3.18816 5.52205i 0.223765 0.387572i
\(204\) −2.67438 4.63216i −0.187244 0.324316i
\(205\) 3.15767 5.46925i 0.220541 0.381989i
\(206\) 9.63694 + 16.6917i 0.671437 + 1.16296i
\(207\) −0.777871 1.34731i −0.0540657 0.0936446i
\(208\) 7.89120 0.547156
\(209\) −0.859833 + 25.0697i −0.0594759 + 1.73411i
\(210\) −4.70118 −0.324412
\(211\) −11.1081 19.2397i −0.764710 1.32452i −0.940400 0.340071i \(-0.889549\pi\)
0.175689 0.984446i \(-0.443785\pi\)
\(212\) 0.846388 + 1.46599i 0.0581302 + 0.100684i
\(213\) 5.12257 8.87255i 0.350993 0.607937i
\(214\) 14.9124 + 25.8291i 1.01939 + 1.76564i
\(215\) −2.26961 + 3.93108i −0.154786 + 0.268098i
\(216\) 11.0467 0.751634
\(217\) 12.8317 0.871071
\(218\) 4.68128 8.10822i 0.317057 0.549158i
\(219\) −5.94373 + 10.2949i −0.401640 + 0.695662i
\(220\) −4.43525 −0.299025
\(221\) 9.54463 0.642041
\(222\) 2.79322 4.83801i 0.187469 0.324706i
\(223\) −5.10799 8.84730i −0.342056 0.592459i 0.642758 0.766069i \(-0.277790\pi\)
−0.984814 + 0.173610i \(0.944457\pi\)
\(224\) 5.04438 8.73712i 0.337042 0.583774i
\(225\) 0.827483 + 1.43324i 0.0551656 + 0.0955495i
\(226\) −13.0491 22.6017i −0.868012 1.50344i
\(227\) 4.15180 0.275565 0.137782 0.990463i \(-0.456003\pi\)
0.137782 + 0.990463i \(0.456003\pi\)
\(228\) −0.133550 + 3.89385i −0.00884456 + 0.257876i
\(229\) 6.53286 0.431703 0.215852 0.976426i \(-0.430747\pi\)
0.215852 + 0.976426i \(0.430747\pi\)
\(230\) −0.782373 1.35511i −0.0515881 0.0893533i
\(231\) 8.12660 + 14.0757i 0.534691 + 0.926111i
\(232\) −2.67883 + 4.63987i −0.175874 + 0.304623i
\(233\) −2.57410 4.45848i −0.168635 0.292084i 0.769305 0.638882i \(-0.220603\pi\)
−0.937940 + 0.346797i \(0.887269\pi\)
\(234\) 2.19694 3.80521i 0.143618 0.248755i
\(235\) 8.95437 0.584118
\(236\) −8.32272 −0.541763
\(237\) 4.40973 7.63788i 0.286443 0.496134i
\(238\) 12.1285 21.0071i 0.786171 1.36169i
\(239\) 13.9962 0.905338 0.452669 0.891679i \(-0.350472\pi\)
0.452669 + 0.891679i \(0.350472\pi\)
\(240\) 5.73781 0.370374
\(241\) −7.61285 + 13.1858i −0.490387 + 0.849375i −0.999939 0.0110652i \(-0.996478\pi\)
0.509552 + 0.860440i \(0.329811\pi\)
\(242\) 18.4076 + 31.8830i 1.18329 + 2.04952i
\(243\) 7.34631 12.7242i 0.471266 0.816256i
\(244\) 4.05728 + 7.02742i 0.259741 + 0.449884i
\(245\) 0.534767 + 0.926244i 0.0341650 + 0.0591756i
\(246\) −12.1916 −0.777305
\(247\) −5.89834 3.68059i −0.375302 0.234190i
\(248\) −10.7817 −0.684642
\(249\) 1.80548 + 3.12718i 0.114417 + 0.198177i
\(250\) 0.832272 + 1.44154i 0.0526375 + 0.0911709i
\(251\) 3.05630 5.29366i 0.192912 0.334133i −0.753302 0.657674i \(-0.771540\pi\)
0.946214 + 0.323542i \(0.104874\pi\)
\(252\) −1.55308 2.69002i −0.0978350 0.169455i
\(253\) −2.70487 + 4.68497i −0.170053 + 0.294541i
\(254\) −10.1869 −0.639181
\(255\) 6.94004 0.434602
\(256\) −8.05154 + 13.9457i −0.503221 + 0.871605i
\(257\) −0.0613414 + 0.106246i −0.00382637 + 0.00662747i −0.867932 0.496683i \(-0.834551\pi\)
0.864106 + 0.503310i \(0.167885\pi\)
\(258\) 8.76281 0.545549
\(259\) 7.04723 0.437893
\(260\) 0.614645 1.06460i 0.0381187 0.0660235i
\(261\) 2.16663 + 3.75271i 0.134111 + 0.232287i
\(262\) −12.3851 + 21.4517i −0.765156 + 1.32529i
\(263\) 5.03027 + 8.71267i 0.310179 + 0.537247i 0.978401 0.206716i \(-0.0662775\pi\)
−0.668222 + 0.743962i \(0.732944\pi\)
\(264\) −6.82832 11.8270i −0.420254 0.727902i
\(265\) −2.19639 −0.134923
\(266\) −15.5958 + 8.30489i −0.956240 + 0.509206i
\(267\) 12.8897 0.788835
\(268\) −0.389046 0.673847i −0.0237648 0.0411618i
\(269\) −2.85614 4.94698i −0.174142 0.301623i 0.765722 0.643172i \(-0.222382\pi\)
−0.939864 + 0.341549i \(0.889049\pi\)
\(270\) 4.49313 7.78232i 0.273443 0.473617i
\(271\) 6.35560 + 11.0082i 0.386075 + 0.668702i 0.991918 0.126883i \(-0.0404972\pi\)
−0.605843 + 0.795585i \(0.707164\pi\)
\(272\) −14.8028 + 25.6393i −0.897554 + 1.55461i
\(273\) −4.50479 −0.272642
\(274\) −28.8804 −1.74473
\(275\) 2.87738 4.98377i 0.173513 0.300533i
\(276\) −0.420122 + 0.727673i −0.0252884 + 0.0438008i
\(277\) 17.6019 1.05760 0.528799 0.848747i \(-0.322642\pi\)
0.528799 + 0.848747i \(0.322642\pi\)
\(278\) 11.1613 0.669413
\(279\) −4.36012 + 7.55195i −0.261034 + 0.452123i
\(280\) 2.49152 + 4.31544i 0.148897 + 0.257897i
\(281\) 10.2502 17.7539i 0.611476 1.05911i −0.379516 0.925185i \(-0.623910\pi\)
0.990992 0.133922i \(-0.0427571\pi\)
\(282\) −8.64305 14.9702i −0.514686 0.891462i
\(283\) 5.92805 + 10.2677i 0.352386 + 0.610350i 0.986667 0.162752i \(-0.0520371\pi\)
−0.634281 + 0.773103i \(0.718704\pi\)
\(284\) 6.80836 0.404002
\(285\) −4.28877 2.67621i −0.254045 0.158525i
\(286\) −15.2787 −0.903449
\(287\) −7.68973 13.3190i −0.453911 0.786196i
\(288\) 3.42809 + 5.93763i 0.202002 + 0.349878i
\(289\) −9.40447 + 16.2890i −0.553204 + 0.958177i
\(290\) 2.17917 + 3.77443i 0.127965 + 0.221642i
\(291\) 2.35301 4.07552i 0.137936 0.238911i
\(292\) −7.89976 −0.462298
\(293\) −24.9814 −1.45943 −0.729715 0.683751i \(-0.760347\pi\)
−0.729715 + 0.683751i \(0.760347\pi\)
\(294\) 1.03235 1.78808i 0.0602079 0.104283i
\(295\) 5.39939 9.35202i 0.314365 0.544495i
\(296\) −5.92139 −0.344174
\(297\) −31.0678 −1.80274
\(298\) 11.9788 20.7478i 0.693911 1.20189i
\(299\) −0.749690 1.29850i −0.0433557 0.0750943i
\(300\) 0.446918 0.774084i 0.0258028 0.0446918i
\(301\) 5.52708 + 9.57319i 0.318576 + 0.551789i
\(302\) 10.5881 + 18.3391i 0.609274 + 1.05529i
\(303\) 12.9082 0.741554
\(304\) 19.0348 10.1362i 1.09172 0.581348i
\(305\) −10.5287 −0.602871
\(306\) 8.24234 + 14.2761i 0.471183 + 0.816113i
\(307\) −8.45997 14.6531i −0.482836 0.836296i 0.516970 0.856003i \(-0.327060\pi\)
−0.999806 + 0.0197074i \(0.993727\pi\)
\(308\) −5.40049 + 9.35392i −0.307721 + 0.532989i
\(309\) 6.71444 + 11.6298i 0.381971 + 0.661594i
\(310\) −4.38535 + 7.59566i −0.249071 + 0.431404i
\(311\) −15.2133 −0.862670 −0.431335 0.902192i \(-0.641957\pi\)
−0.431335 + 0.902192i \(0.641957\pi\)
\(312\) 3.78512 0.214290
\(313\) −12.4637 + 21.5877i −0.704488 + 1.22021i 0.262389 + 0.964962i \(0.415490\pi\)
−0.966876 + 0.255246i \(0.917844\pi\)
\(314\) −2.80917 + 4.86562i −0.158531 + 0.274583i
\(315\) 4.03027 0.227080
\(316\) 5.86093 0.329703
\(317\) 12.6152 21.8502i 0.708541 1.22723i −0.256857 0.966449i \(-0.582687\pi\)
0.965398 0.260780i \(-0.0839798\pi\)
\(318\) 2.12002 + 3.67199i 0.118885 + 0.205915i
\(319\) 7.53396 13.0492i 0.421821 0.730615i
\(320\) −1.49949 2.59720i −0.0838241 0.145188i
\(321\) 10.3901 + 17.9962i 0.579919 + 1.00445i
\(322\) −3.81055 −0.212354
\(323\) 23.0231 12.2600i 1.28104 0.682163i
\(324\) −0.998983 −0.0554991
\(325\) 0.797505 + 1.38132i 0.0442376 + 0.0766218i
\(326\) 0.256307 + 0.443937i 0.0141955 + 0.0245874i
\(327\) 3.26164 5.64933i 0.180369 0.312408i
\(328\) 6.46125 + 11.1912i 0.356763 + 0.617932i
\(329\) 10.9031 18.8847i 0.601106 1.04115i
\(330\) −11.1094 −0.611551
\(331\) −20.2063 −1.11064 −0.555320 0.831637i \(-0.687404\pi\)
−0.555320 + 0.831637i \(0.687404\pi\)
\(332\) −1.19982 + 2.07815i −0.0658487 + 0.114053i
\(333\) −2.39460 + 4.14757i −0.131223 + 0.227285i
\(334\) −23.7436 −1.29919
\(335\) 1.00958 0.0551592
\(336\) 6.98651 12.1010i 0.381145 0.660163i
\(337\) 15.9123 + 27.5610i 0.866800 + 1.50134i 0.865249 + 0.501342i \(0.167160\pi\)
0.00155051 + 0.999999i \(0.499506\pi\)
\(338\) −8.70219 + 15.0726i −0.473337 + 0.819843i
\(339\) −9.09183 15.7475i −0.493800 0.855287i
\(340\) 2.30599 + 3.99408i 0.125060 + 0.216610i
\(341\) 30.3226 1.64206
\(342\) 0.411596 12.0007i 0.0222566 0.648923i
\(343\) 19.6514 1.06107
\(344\) −4.64410 8.04382i −0.250393 0.433693i
\(345\) −0.545111 0.944159i −0.0293478 0.0508318i
\(346\) 11.1085 19.2404i 0.597194 1.03437i
\(347\) 1.65128 + 2.86009i 0.0886451 + 0.153538i 0.906939 0.421263i \(-0.138413\pi\)
−0.818294 + 0.574801i \(0.805080\pi\)
\(348\) 1.17018 2.02681i 0.0627283 0.108649i
\(349\) 17.8486 0.955416 0.477708 0.878519i \(-0.341468\pi\)
0.477708 + 0.878519i \(0.341468\pi\)
\(350\) 4.05359 0.216674
\(351\) 4.30543 7.45723i 0.229807 0.398037i
\(352\) 11.9204 20.6468i 0.635360 1.10048i
\(353\) −8.29523 −0.441511 −0.220755 0.975329i \(-0.570852\pi\)
−0.220755 + 0.975329i \(0.570852\pi\)
\(354\) −20.8467 −1.10799
\(355\) −4.41694 + 7.65036i −0.234427 + 0.406039i
\(356\) 4.28288 + 7.41817i 0.226992 + 0.393162i
\(357\) 8.45039 14.6365i 0.447242 0.774646i
\(358\) −11.8355 20.4997i −0.625527 1.08344i
\(359\) −4.17511 7.23150i −0.220354 0.381664i 0.734562 0.678542i \(-0.237388\pi\)
−0.954915 + 0.296878i \(0.904055\pi\)
\(360\) −3.38641 −0.178479
\(361\) −18.9554 1.30178i −0.997650 0.0685148i
\(362\) −16.4501 −0.864598
\(363\) 12.8254 + 22.2142i 0.673156 + 1.16594i
\(364\) −1.49682 2.59256i −0.0784545 0.135887i
\(365\) 5.12499 8.87674i 0.268254 0.464630i
\(366\) 10.1626 + 17.6022i 0.531209 + 0.920082i
\(367\) −7.20988 + 12.4879i −0.376353 + 0.651862i −0.990528 0.137307i \(-0.956155\pi\)
0.614176 + 0.789169i \(0.289489\pi\)
\(368\) 4.65080 0.242440
\(369\) 10.4517 0.544093
\(370\) −2.40846 + 4.17157i −0.125210 + 0.216870i
\(371\) −2.67438 + 4.63216i −0.138847 + 0.240490i
\(372\) 4.70974 0.244188
\(373\) −24.1157 −1.24866 −0.624332 0.781159i \(-0.714629\pi\)
−0.624332 + 0.781159i \(0.714629\pi\)
\(374\) 28.6608 49.6420i 1.48202 2.56693i
\(375\) 0.579878 + 1.00438i 0.0299448 + 0.0518659i
\(376\) −9.16125 + 15.8678i −0.472455 + 0.818317i
\(377\) 2.08814 + 3.61676i 0.107545 + 0.186273i
\(378\) −10.9419 18.9519i −0.562791 0.974783i
\(379\) 16.6757 0.856571 0.428285 0.903644i \(-0.359118\pi\)
0.428285 + 0.903644i \(0.359118\pi\)
\(380\) 0.115154 3.35747i 0.00590725 0.172235i
\(381\) −7.09760 −0.363621
\(382\) −10.8147 18.7316i −0.553329 0.958395i
\(383\) 5.43895 + 9.42053i 0.277917 + 0.481367i 0.970867 0.239619i \(-0.0770226\pi\)
−0.692950 + 0.720986i \(0.743689\pi\)
\(384\) −7.69935 + 13.3357i −0.392906 + 0.680533i
\(385\) −7.00716 12.1368i −0.357118 0.618546i
\(386\) 12.0812 20.9252i 0.614916 1.06507i
\(387\) −7.51226 −0.381870
\(388\) 3.12736 0.158767
\(389\) −18.2272 + 31.5704i −0.924154 + 1.60068i −0.131237 + 0.991351i \(0.541895\pi\)
−0.792917 + 0.609330i \(0.791438\pi\)
\(390\) 1.53956 2.66659i 0.0779585 0.135028i
\(391\) 5.62528 0.284482
\(392\) −2.18849 −0.110535
\(393\) −8.62922 + 14.9463i −0.435287 + 0.753939i
\(394\) −20.8077 36.0399i −1.04827 1.81566i
\(395\) −3.80229 + 6.58577i −0.191314 + 0.331366i
\(396\) −3.67010 6.35680i −0.184429 0.319441i
\(397\) −4.29191 7.43380i −0.215405 0.373092i 0.737993 0.674808i \(-0.235774\pi\)
−0.953398 + 0.301717i \(0.902440\pi\)
\(398\) 3.75419 0.188181
\(399\) −10.8662 + 5.78635i −0.543992 + 0.289680i
\(400\) −4.94743 −0.247371
\(401\) 8.52785 + 14.7707i 0.425860 + 0.737612i 0.996500 0.0835885i \(-0.0266381\pi\)
−0.570640 + 0.821200i \(0.693305\pi\)
\(402\) −0.974478 1.68785i −0.0486026 0.0841821i
\(403\) −4.20216 + 7.27836i −0.209325 + 0.362561i
\(404\) 4.28903 + 7.42881i 0.213387 + 0.369597i
\(405\) 0.648093 1.12253i 0.0322040 0.0557790i
\(406\) 10.6137 0.526747
\(407\) 16.6533 0.825476
\(408\) −7.10039 + 12.2982i −0.351522 + 0.608853i
\(409\) 5.89702 10.2139i 0.291589 0.505047i −0.682597 0.730795i \(-0.739149\pi\)
0.974186 + 0.225749i \(0.0724828\pi\)
\(410\) 10.5122 0.519159
\(411\) −20.1222 −0.992553
\(412\) −4.46205 + 7.72850i −0.219829 + 0.380756i
\(413\) −13.1489 22.7745i −0.647015 1.12066i
\(414\) 1.29480 2.24266i 0.0636360 0.110221i
\(415\) −1.55677 2.69641i −0.0764190 0.132362i
\(416\) 3.30390 + 5.72252i 0.161987 + 0.280570i
\(417\) 7.77656 0.380820
\(418\) −36.8546 + 19.6253i −1.80261 + 0.959907i
\(419\) 1.14280 0.0558292 0.0279146 0.999610i \(-0.491113\pi\)
0.0279146 + 0.999610i \(0.491113\pi\)
\(420\) −1.08836 1.88509i −0.0531064 0.0919830i
\(421\) −9.75944 16.9039i −0.475646 0.823843i 0.523965 0.851740i \(-0.324452\pi\)
−0.999611 + 0.0278967i \(0.991119\pi\)
\(422\) 18.4899 32.0254i 0.900072 1.55897i
\(423\) 7.40959 + 12.8338i 0.360266 + 0.624000i
\(424\) 2.24713 3.89215i 0.109130 0.189019i
\(425\) −5.98406 −0.290269
\(426\) 17.0535 0.826245
\(427\) −12.8200 + 22.2049i −0.620404 + 1.07457i
\(428\) −6.90469 + 11.9593i −0.333751 + 0.578073i
\(429\) −10.6453 −0.513960
\(430\) −7.55574 −0.364370
\(431\) 18.4392 31.9377i 0.888187 1.53838i 0.0461694 0.998934i \(-0.485299\pi\)
0.842017 0.539451i \(-0.181368\pi\)
\(432\) 13.3546 + 23.1309i 0.642526 + 1.11289i
\(433\) −0.184467 + 0.319506i −0.00886490 + 0.0153545i −0.870424 0.492303i \(-0.836155\pi\)
0.861559 + 0.507658i \(0.169488\pi\)
\(434\) 10.6795 + 18.4974i 0.512630 + 0.887902i
\(435\) 1.51832 + 2.62980i 0.0727976 + 0.126089i
\(436\) 4.33501 0.207609
\(437\) −3.47628 2.16921i −0.166293 0.103767i
\(438\) −19.7872 −0.945470
\(439\) 1.13220 + 1.96102i 0.0540367 + 0.0935944i 0.891778 0.452472i \(-0.149458\pi\)
−0.837742 + 0.546067i \(0.816125\pi\)
\(440\) 5.88773 + 10.1978i 0.280686 + 0.486163i
\(441\) −0.885022 + 1.53290i −0.0421439 + 0.0729954i
\(442\) 7.94373 + 13.7590i 0.377845 + 0.654447i
\(443\) 8.23137 14.2572i 0.391084 0.677378i −0.601508 0.798866i \(-0.705433\pi\)
0.992593 + 0.121488i \(0.0387667\pi\)
\(444\) 2.58661 0.122755
\(445\) −11.1141 −0.526860
\(446\) 8.50248 14.7267i 0.402604 0.697331i
\(447\) 8.34609 14.4558i 0.394756 0.683738i
\(448\) −7.30329 −0.345048
\(449\) 14.1613 0.668315 0.334158 0.942517i \(-0.391548\pi\)
0.334158 + 0.942517i \(0.391548\pi\)
\(450\) −1.37738 + 2.38570i −0.0649305 + 0.112463i
\(451\) −18.1717 31.4742i −0.855670 1.48206i
\(452\) 6.04193 10.4649i 0.284188 0.492229i
\(453\) 7.37713 + 12.7776i 0.346608 + 0.600342i
\(454\) 3.45543 + 5.98498i 0.162171 + 0.280889i
\(455\) 3.88426 0.182097
\(456\) 9.13029 4.86195i 0.427565 0.227682i
\(457\) 1.22073 0.0571033 0.0285516 0.999592i \(-0.490910\pi\)
0.0285516 + 0.999592i \(0.490910\pi\)
\(458\) 5.43712 + 9.41736i 0.254060 + 0.440045i
\(459\) 16.1528 + 27.9775i 0.753950 + 1.30588i
\(460\) 0.362251 0.627436i 0.0168900 0.0292544i
\(461\) 4.34580 + 7.52714i 0.202404 + 0.350574i 0.949303 0.314364i \(-0.101791\pi\)
−0.746898 + 0.664938i \(0.768458\pi\)
\(462\) −13.5271 + 23.4296i −0.629337 + 1.09004i
\(463\) −19.7149 −0.916229 −0.458114 0.888893i \(-0.651475\pi\)
−0.458114 + 0.888893i \(0.651475\pi\)
\(464\) −12.9540 −0.601375
\(465\) −3.05545 + 5.29220i −0.141693 + 0.245420i
\(466\) 4.28471 7.42133i 0.198485 0.343787i
\(467\) −11.4795 −0.531207 −0.265604 0.964082i \(-0.585571\pi\)
−0.265604 + 0.964082i \(0.585571\pi\)
\(468\) 2.03443 0.0940418
\(469\) 1.22929 2.12919i 0.0567633 0.0983170i
\(470\) 7.45247 + 12.9081i 0.343757 + 0.595404i
\(471\) −1.95726 + 3.39008i −0.0901858 + 0.156206i
\(472\) 11.0483 + 19.1362i 0.508538 + 0.880814i
\(473\) 13.0611 + 22.6225i 0.600549 + 1.04018i
\(474\) 14.6804 0.674293
\(475\) 3.69799 + 2.30756i 0.169676 + 0.105878i
\(476\) 11.2313 0.514787
\(477\) −1.81747 3.14796i −0.0832164 0.144135i
\(478\) 11.6486 + 20.1760i 0.532796 + 0.922830i
\(479\) −19.6316 + 34.0029i −0.896989 + 1.55363i −0.0656652 + 0.997842i \(0.520917\pi\)
−0.831324 + 0.555789i \(0.812416\pi\)
\(480\) 2.40232 + 4.16093i 0.109650 + 0.189920i
\(481\) −2.30785 + 3.99731i −0.105229 + 0.182262i
\(482\) −25.3439 −1.15438
\(483\) −2.65497 −0.120805
\(484\) −8.52302 + 14.7623i −0.387410 + 0.671014i
\(485\) −2.02888 + 3.51412i −0.0921267 + 0.159568i
\(486\) 24.4565 1.10937
\(487\) 31.5943 1.43168 0.715838 0.698266i \(-0.246045\pi\)
0.715838 + 0.698266i \(0.246045\pi\)
\(488\) 10.7719 18.6576i 0.487623 0.844588i
\(489\) 0.178579 + 0.309309i 0.00807564 + 0.0139874i
\(490\) −0.890144 + 1.54177i −0.0402126 + 0.0696503i
\(491\) 5.53187 + 9.58148i 0.249650 + 0.432406i 0.963429 0.267965i \(-0.0863511\pi\)
−0.713779 + 0.700371i \(0.753018\pi\)
\(492\) −2.82244 4.88861i −0.127245 0.220395i
\(493\) −15.6683 −0.705663
\(494\) 0.396685 11.5659i 0.0178477 0.520376i
\(495\) 9.52395 0.428070
\(496\) −13.0343 22.5761i −0.585258 1.01370i
\(497\) 10.7564 + 18.6306i 0.482489 + 0.835696i
\(498\) −3.00530 + 5.20533i −0.134671 + 0.233256i
\(499\) 10.1868 + 17.6440i 0.456023 + 0.789854i 0.998746 0.0500570i \(-0.0159403\pi\)
−0.542724 + 0.839911i \(0.682607\pi\)
\(500\) −0.385355 + 0.667454i −0.0172336 + 0.0298495i
\(501\) −16.5431 −0.739091
\(502\) 10.1747 0.454118
\(503\) 6.83622 11.8407i 0.304812 0.527950i −0.672407 0.740181i \(-0.734740\pi\)
0.977219 + 0.212231i \(0.0680730\pi\)
\(504\) −4.12338 + 7.14191i −0.183670 + 0.318126i
\(505\) −11.1301 −0.495281
\(506\) −9.00474 −0.400310
\(507\) −6.06317 + 10.5017i −0.269275 + 0.466398i
\(508\) −2.35834 4.08476i −0.104634 0.181232i
\(509\) 3.86196 6.68912i 0.171179 0.296490i −0.767654 0.640865i \(-0.778576\pi\)
0.938832 + 0.344375i \(0.111909\pi\)
\(510\) 5.77601 + 10.0043i 0.255766 + 0.443000i
\(511\) −12.4807 21.6171i −0.552112 0.956285i
\(512\) −0.249240 −0.0110150
\(513\) 0.806621 23.5182i 0.0356132 1.03836i
\(514\) −0.204211 −0.00900736
\(515\) −5.78953 10.0278i −0.255117 0.441876i
\(516\) 2.02866 + 3.51374i 0.0893067 + 0.154684i
\(517\) 25.7651 44.6265i 1.13315 1.96267i
\(518\) 5.86521 + 10.1588i 0.257703 + 0.446354i
\(519\) 7.73971 13.4056i 0.339736 0.588439i
\(520\) −3.26372 −0.143124
\(521\) −2.16876 −0.0950151 −0.0475075 0.998871i \(-0.515128\pi\)
−0.0475075 + 0.998871i \(0.515128\pi\)
\(522\) −3.60645 + 6.24656i −0.157850 + 0.273404i
\(523\) 11.9466 20.6921i 0.522389 0.904804i −0.477272 0.878756i \(-0.658374\pi\)
0.999661 0.0260485i \(-0.00829243\pi\)
\(524\) −11.4690 −0.501026
\(525\) 2.82430 0.123263
\(526\) −8.37310 + 14.5026i −0.365085 + 0.632345i
\(527\) −15.7654 27.3065i −0.686751 1.18949i
\(528\) 16.5099 28.5959i 0.718500 1.24448i
\(529\) 11.0582 + 19.1533i 0.480790 + 0.832752i
\(530\) −1.82799 3.16617i −0.0794029 0.137530i
\(531\) 17.8716 0.775562
\(532\) −6.94067 4.33101i −0.300916 0.187773i
\(533\) 10.0730 0.436312
\(534\) 10.7277 + 18.5809i 0.464234 + 0.804076i
\(535\) −8.95887 15.5172i −0.387326 0.670868i
\(536\) −1.03290 + 1.78904i −0.0446147 + 0.0772749i
\(537\) −8.24629 14.2830i −0.355854 0.616356i
\(538\) 4.75418 8.23448i 0.204967 0.355013i
\(539\) 6.15492 0.265111
\(540\) 4.16077 0.179051
\(541\) −21.2275 + 36.7671i −0.912641 + 1.58074i −0.102323 + 0.994751i \(0.532627\pi\)
−0.810319 + 0.585990i \(0.800706\pi\)
\(542\) −10.5792 + 18.3237i −0.454415 + 0.787069i
\(543\) −11.4614 −0.491858
\(544\) −24.7907 −1.06289
\(545\) −2.81235 + 4.87113i −0.120468 + 0.208656i
\(546\) −3.74921 6.49383i −0.160451 0.277910i
\(547\) −6.01535 + 10.4189i −0.257198 + 0.445480i −0.965490 0.260439i \(-0.916133\pi\)
0.708292 + 0.705919i \(0.249466\pi\)
\(548\) −6.68604 11.5806i −0.285614 0.494697i
\(549\) −8.71231 15.0902i −0.371833 0.644033i
\(550\) 9.57907 0.408453
\(551\) 9.68259 + 6.04198i 0.412492 + 0.257397i
\(552\) 2.23082 0.0949500
\(553\) 9.25956 + 16.0380i 0.393756 + 0.682006i
\(554\) 14.6496 + 25.3739i 0.622403 + 1.07803i
\(555\) −1.67807 + 2.90650i −0.0712301 + 0.123374i
\(556\) 2.58394 + 4.47551i 0.109583 + 0.189804i
\(557\) 4.37635 7.58006i 0.185432 0.321178i −0.758290 0.651917i \(-0.773965\pi\)
0.943722 + 0.330740i \(0.107298\pi\)
\(558\) −14.5152 −0.614479
\(559\) −7.24011 −0.306224
\(560\) −6.02412 + 10.4341i −0.254566 + 0.440921i
\(561\) 19.9692 34.5876i 0.843099 1.46029i
\(562\) 34.1238 1.43943
\(563\) −35.9707 −1.51598 −0.757991 0.652265i \(-0.773819\pi\)
−0.757991 + 0.652265i \(0.773819\pi\)
\(564\) 4.00186 6.93143i 0.168509 0.291866i
\(565\) 7.83943 + 13.5783i 0.329807 + 0.571243i
\(566\) −9.86750 + 17.0910i −0.414762 + 0.718389i
\(567\) −1.57827 2.73365i −0.0662812 0.114802i
\(568\) −9.03798 15.6542i −0.379225 0.656837i
\(569\) −20.3125 −0.851543 −0.425772 0.904831i \(-0.639997\pi\)
−0.425772 + 0.904831i \(0.639997\pi\)
\(570\) 0.288435 8.40976i 0.0120812 0.352246i
\(571\) 10.1773 0.425906 0.212953 0.977062i \(-0.431692\pi\)
0.212953 + 0.977062i \(0.431692\pi\)
\(572\) −3.53714 6.12650i −0.147895 0.256162i
\(573\) −7.53505 13.0511i −0.314781 0.545217i
\(574\) 12.7999 22.1701i 0.534258 0.925362i
\(575\) 0.470022 + 0.814102i 0.0196013 + 0.0339504i
\(576\) 2.48161 4.29827i 0.103400 0.179095i
\(577\) −32.7441 −1.36316 −0.681578 0.731745i \(-0.738706\pi\)
−0.681578 + 0.731745i \(0.738706\pi\)
\(578\) −31.3083 −1.30225
\(579\) 8.41745 14.5794i 0.349817 0.605901i
\(580\) −1.00899 + 1.74762i −0.0418960 + 0.0725660i
\(581\) −7.58228 −0.314566
\(582\) 7.83337 0.324703
\(583\) −6.31984 + 10.9463i −0.261741 + 0.453349i
\(584\) 10.4868 + 18.1637i 0.433947 + 0.751618i
\(585\) −1.31984 + 2.28604i −0.0545689 + 0.0945160i
\(586\) −20.7913 36.0117i −0.858883 1.48763i
\(587\) −4.38663 7.59786i −0.181056 0.313597i 0.761185 0.648535i \(-0.224618\pi\)
−0.942240 + 0.334938i \(0.891285\pi\)
\(588\) 0.955987 0.0394243
\(589\) −0.787274 + 22.9541i −0.0324390 + 0.945808i
\(590\) 17.9751 0.740021
\(591\) −14.4975 25.1105i −0.596349 1.03291i
\(592\) −7.15852 12.3989i −0.294213 0.509592i
\(593\) 16.1603 27.9905i 0.663625 1.14943i −0.316031 0.948749i \(-0.602350\pi\)
0.979656 0.200684i \(-0.0643163\pi\)
\(594\) −25.8569 44.7855i −1.06092 1.83757i
\(595\) −7.28635 + 12.6203i −0.298711 + 0.517383i
\(596\) 11.0927 0.454375
\(597\) 2.61570 0.107053
\(598\) 1.24789 2.16141i 0.0510301 0.0883868i
\(599\) 9.77520 16.9311i 0.399404 0.691787i −0.594249 0.804281i \(-0.702551\pi\)
0.993652 + 0.112494i \(0.0358839\pi\)
\(600\) −2.37310 −0.0968815
\(601\) −0.401837 −0.0163913 −0.00819564 0.999966i \(-0.502609\pi\)
−0.00819564 + 0.999966i \(0.502609\pi\)
\(602\) −9.20008 + 15.9350i −0.374967 + 0.649462i
\(603\) 0.835409 + 1.44697i 0.0340205 + 0.0589252i
\(604\) −4.90243 + 8.49126i −0.199477 + 0.345505i
\(605\) −11.0587 19.1542i −0.449599 0.778728i
\(606\) 10.7431 + 18.6076i 0.436409 + 0.755882i
\(607\) 13.4453 0.545727 0.272863 0.962053i \(-0.412029\pi\)
0.272863 + 0.962053i \(0.412029\pi\)
\(608\) 15.3200 + 9.55976i 0.621309 + 0.387700i
\(609\) 7.39497 0.299659
\(610\) −8.76274 15.1775i −0.354793 0.614519i
\(611\) 7.14115 + 12.3688i 0.288900 + 0.500390i
\(612\) −3.81633 + 6.61008i −0.154266 + 0.267196i
\(613\) 10.3527 + 17.9313i 0.418140 + 0.724239i 0.995752 0.0920716i \(-0.0293489\pi\)
−0.577613 + 0.816311i \(0.696016\pi\)
\(614\) 14.0820 24.3907i 0.568303 0.984330i
\(615\) 7.32425 0.295342
\(616\) 28.6762 1.15540
\(617\) 4.63936 8.03560i 0.186773 0.323501i −0.757399 0.652952i \(-0.773530\pi\)
0.944173 + 0.329451i \(0.106864\pi\)
\(618\) −11.1765 + 19.3583i −0.449585 + 0.778703i
\(619\) −2.89129 −0.116211 −0.0581053 0.998310i \(-0.518506\pi\)
−0.0581053 + 0.998310i \(0.518506\pi\)
\(620\) −4.06097 −0.163093
\(621\) 2.53747 4.39503i 0.101825 0.176366i
\(622\) −12.6616 21.9306i −0.507686 0.879338i
\(623\) −13.5329 + 23.4396i −0.542183 + 0.939088i
\(624\) 4.57593 + 7.92574i 0.183184 + 0.317284i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −41.4926 −1.65838
\(627\) −25.6781 + 13.6738i −1.02548 + 0.546078i
\(628\) −2.60138 −0.103806
\(629\) −8.65844 14.9969i −0.345234 0.597964i
\(630\) 3.35428 + 5.80978i 0.133638 + 0.231467i
\(631\) −15.2270 + 26.3740i −0.606178 + 1.04993i 0.385686 + 0.922630i \(0.373965\pi\)
−0.991864 + 0.127301i \(0.959369\pi\)
\(632\) −7.78029 13.4759i −0.309483 0.536041i
\(633\) 12.8826 22.3134i 0.512039 0.886877i
\(634\) 41.9972 1.66792
\(635\) 6.11991 0.242861
\(636\) −0.981604 + 1.70019i −0.0389231 + 0.0674168i
\(637\) −0.852959 + 1.47737i −0.0337955 + 0.0585355i
\(638\) 25.0812 0.992975
\(639\) −14.6198 −0.578349
\(640\) 6.63877 11.4987i 0.262420 0.454525i
\(641\) 10.0369 + 17.3845i 0.396434 + 0.686645i 0.993283 0.115709i \(-0.0369141\pi\)
−0.596849 + 0.802354i \(0.703581\pi\)
\(642\) −17.2948 + 29.9554i −0.682571 + 1.18225i
\(643\) 1.04457 + 1.80924i 0.0411937 + 0.0713496i 0.885887 0.463901i \(-0.153551\pi\)
−0.844693 + 0.535250i \(0.820217\pi\)
\(644\) −0.882172 1.52797i −0.0347625 0.0602103i
\(645\) −5.26439 −0.207285
\(646\) 36.8347 + 22.9850i 1.44924 + 0.904334i
\(647\) −2.10623 −0.0828043 −0.0414021 0.999143i \(-0.513182\pi\)
−0.0414021 + 0.999143i \(0.513182\pi\)
\(648\) 1.32613 + 2.29693i 0.0520954 + 0.0902319i
\(649\) −31.0722 53.8187i −1.21969 2.11257i
\(650\) −1.32748 + 2.29927i −0.0520682 + 0.0901847i
\(651\) 7.44081 + 12.8879i 0.291628 + 0.505115i
\(652\) −0.118674 + 0.205549i −0.00464763 + 0.00804994i
\(653\) 1.83067 0.0716395 0.0358197 0.999358i \(-0.488596\pi\)
0.0358197 + 0.999358i \(0.488596\pi\)
\(654\) 10.8583 0.424593
\(655\) 7.44055 12.8874i 0.290726 0.503553i
\(656\) −15.6223 + 27.0587i −0.609950 + 1.05646i
\(657\) 16.9634 0.661804
\(658\) 36.2973 1.41502
\(659\) −12.0268 + 20.8310i −0.468497 + 0.811460i −0.999352 0.0360024i \(-0.988538\pi\)
0.530855 + 0.847463i \(0.321871\pi\)
\(660\) −2.57191 4.45467i −0.100111 0.173398i
\(661\) 8.72110 15.1054i 0.339211 0.587531i −0.645073 0.764121i \(-0.723173\pi\)
0.984285 + 0.176589i \(0.0565065\pi\)
\(662\) −16.8172 29.1282i −0.653617 1.13210i
\(663\) 5.53472 + 9.58642i 0.214951 + 0.372306i
\(664\) 6.37097 0.247241
\(665\) 9.36941 4.98929i 0.363330 0.193476i
\(666\) −7.97184 −0.308902
\(667\) 1.23068 + 2.13159i 0.0476519 + 0.0825356i
\(668\) −5.49682 9.52077i −0.212678 0.368370i
\(669\) 5.92402 10.2607i 0.229036 0.396702i
\(670\) 0.840244 + 1.45535i 0.0324615 + 0.0562249i
\(671\) −30.2951 + 52.4726i −1.16953 + 2.02568i
\(672\) 11.7005 0.451357
\(673\) 47.5187 1.83171 0.915856 0.401506i \(-0.131513\pi\)
0.915856 + 0.401506i \(0.131513\pi\)
\(674\) −26.4868 + 45.8765i −1.02023 + 1.76709i
\(675\) −2.69931 + 4.67535i −0.103897 + 0.179954i
\(676\) −8.05850 −0.309942
\(677\) 14.5531 0.559321 0.279661 0.960099i \(-0.409778\pi\)
0.279661 + 0.960099i \(0.409778\pi\)
\(678\) 15.1338 26.2124i 0.581208 1.00668i
\(679\) 4.94084 + 8.55778i 0.189612 + 0.328418i
\(680\) 6.12231 10.6042i 0.234780 0.406651i
\(681\) 2.40754 + 4.16998i 0.0922570 + 0.159794i
\(682\) 25.2367 + 43.7112i 0.966363 + 1.67379i
\(683\) 3.33714 0.127692 0.0638460 0.997960i \(-0.479663\pi\)
0.0638460 + 0.997960i \(0.479663\pi\)
\(684\) 4.90736 2.61321i 0.187638 0.0999185i
\(685\) 17.3504 0.662923
\(686\) 16.3553 + 28.3282i 0.624448 + 1.08158i
\(687\) 3.78826 + 6.56146i 0.144531 + 0.250335i
\(688\) 11.2287 19.4487i 0.428092 0.741476i
\(689\) −1.75163 3.03391i −0.0667318 0.115583i
\(690\) 0.907361 1.57160i 0.0345426 0.0598296i
\(691\) −19.3318 −0.735415 −0.367708 0.929941i \(-0.619857\pi\)
−0.367708 + 0.929941i \(0.619857\pi\)
\(692\) 10.2868 0.391044
\(693\) 11.5966 20.0859i 0.440519 0.763001i
\(694\) −2.74862 + 4.76075i −0.104336 + 0.180716i
\(695\) −6.70534 −0.254348
\(696\) −6.21358 −0.235525
\(697\) −18.8957 + 32.7283i −0.715725 + 1.23967i
\(698\) 14.8549 + 25.7295i 0.562268 + 0.973876i
\(699\) 2.98533 5.17074i 0.112916 0.195575i
\(700\) 0.938437 + 1.62542i 0.0354696 + 0.0614351i
\(701\) −4.96892 8.60643i −0.187674 0.325060i 0.756801 0.653646i \(-0.226761\pi\)
−0.944474 + 0.328586i \(0.893428\pi\)
\(702\) 14.3332 0.540971
\(703\) −0.432375 + 12.6065i −0.0163073 + 0.475464i
\(704\) −17.2584 −0.650452
\(705\) 5.19244 + 8.99357i 0.195559 + 0.338717i
\(706\) −6.90389 11.9579i −0.259831 0.450041i
\(707\) −13.5523 + 23.4732i −0.509686 + 0.882801i
\(708\) −4.82616 8.35916i −0.181378 0.314157i
\(709\) −18.6059 + 32.2264i −0.698760 + 1.21029i 0.270136 + 0.962822i \(0.412931\pi\)
−0.968897 + 0.247466i \(0.920402\pi\)
\(710\) −14.7044 −0.551846
\(711\) −12.5853 −0.471987
\(712\) 11.3709 19.6950i 0.426143 0.738101i
\(713\) −2.47661 + 4.28961i −0.0927497 + 0.160647i
\(714\) 28.1321 1.05282
\(715\) 9.17891 0.343272
\(716\) 5.48003 9.49169i 0.204798 0.354721i
\(717\) 8.11608 + 14.0575i 0.303100 + 0.524985i
\(718\) 6.94966 12.0372i 0.259359 0.449223i
\(719\) 1.32109 + 2.28819i 0.0492683 + 0.0853351i 0.889608 0.456725i \(-0.150978\pi\)
−0.840340 + 0.542060i \(0.817644\pi\)
\(720\) −4.09391 7.09086i −0.152571 0.264261i
\(721\) −28.1980 −1.05015
\(722\) −13.8995 28.4083i −0.517284 1.05725i
\(723\) −17.6581 −0.656711
\(724\) −3.80832 6.59621i −0.141535 0.245146i
\(725\) −1.30917 2.26755i −0.0486213 0.0842145i
\(726\) −21.3484 + 36.9765i −0.792313 + 1.37233i
\(727\) 5.08653 + 8.81013i 0.188649 + 0.326750i 0.944800 0.327647i \(-0.106256\pi\)
−0.756151 + 0.654397i \(0.772923\pi\)
\(728\) −3.97400 + 6.88317i −0.147286 + 0.255107i
\(729\) 20.9284 0.775126
\(730\) 17.0615 0.631476
\(731\) 13.5815 23.5238i 0.502329 0.870060i
\(732\) −4.70546 + 8.15009i −0.173919 + 0.301236i
\(733\) 14.8222 0.547472 0.273736 0.961805i \(-0.411741\pi\)
0.273736 + 0.961805i \(0.411741\pi\)
\(734\) −24.0023 −0.885942
\(735\) −0.620199 + 1.07422i −0.0228764 + 0.0396231i
\(736\) 1.94720 + 3.37266i 0.0717749 + 0.124318i
\(737\) 2.90494 5.03151i 0.107005 0.185338i
\(738\) 8.69865 + 15.0665i 0.320202 + 0.554605i
\(739\) −17.7433 30.7323i −0.652697 1.13050i −0.982466 0.186443i \(-0.940304\pi\)
0.329769 0.944062i \(-0.393029\pi\)
\(740\) −2.23031 −0.0819877
\(741\) 0.276386 8.05845i 0.0101533 0.296035i
\(742\) −8.90325 −0.326849
\(743\) 4.36941 + 7.56804i 0.160298 + 0.277645i 0.934976 0.354712i \(-0.115421\pi\)
−0.774677 + 0.632357i \(0.782088\pi\)
\(744\) −6.25210 10.8289i −0.229213 0.397009i
\(745\) −7.19642 + 12.4646i −0.263656 + 0.456666i
\(746\) −20.0708 34.7637i −0.734846 1.27279i
\(747\) 2.57641 4.46247i 0.0942658 0.163273i
\(748\) 26.5408 0.970428
\(749\) −43.6342 −1.59436
\(750\) −0.965233 + 1.67183i −0.0352453 + 0.0610467i
\(751\) −6.54957 + 11.3442i −0.238997 + 0.413955i −0.960427 0.278533i \(-0.910152\pi\)
0.721430 + 0.692488i \(0.243485\pi\)
\(752\) −44.3011 −1.61549
\(753\) 7.08911 0.258342
\(754\) −3.47580 + 6.02026i −0.126581 + 0.219245i
\(755\) −6.36093 11.0175i −0.231498 0.400966i
\(756\) 5.06627 8.77504i 0.184258 0.319145i
\(757\) 8.21901 + 14.2357i 0.298725 + 0.517407i 0.975845 0.218466i \(-0.0701053\pi\)
−0.677119 + 0.735873i \(0.736772\pi\)
\(758\) 13.8787 + 24.0386i 0.504097 + 0.873121i
\(759\) −6.27397 −0.227731
\(760\) −7.87259 + 4.19222i −0.285569 + 0.152068i
\(761\) 16.3918 0.594203 0.297101 0.954846i \(-0.403980\pi\)
0.297101 + 0.954846i \(0.403980\pi\)
\(762\) −5.90714 10.2315i −0.213993 0.370647i
\(763\) 6.84879 + 11.8625i 0.247943 + 0.429450i
\(764\) 5.00738 8.67304i 0.181161 0.313780i
\(765\) −4.95171 8.57661i −0.179029 0.310088i
\(766\) −9.05337 + 15.6809i −0.327112 + 0.566574i
\(767\) 17.2242 0.621929
\(768\) −18.6756 −0.673899
\(769\) 25.0210 43.3377i 0.902282 1.56280i 0.0777564 0.996972i \(-0.475224\pi\)
0.824525 0.565825i \(-0.191442\pi\)
\(770\) 11.6637 20.2022i 0.420332 0.728036i
\(771\) −0.142282 −0.00512416
\(772\) 11.1875 0.402649
\(773\) −24.3436 + 42.1644i −0.875580 + 1.51655i −0.0194356 + 0.999811i \(0.506187\pi\)
−0.856144 + 0.516737i \(0.827146\pi\)
\(774\) −6.25225 10.8292i −0.224732 0.389248i