Properties

Label 95.2.e.c.11.3
Level $95$
Weight $2$
Character 95.11
Analytic conductor $0.759$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 11.3
Root \(-1.02359 + 1.77290i\) of defining polynomial
Character \(\chi\) \(=\) 95.11
Dual form 95.2.e.c.26.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.595455 - 1.03136i) q^{2} +(-1.52359 + 2.63893i) q^{3} +(0.290867 + 0.503797i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.81445 + 3.14272i) q^{6} -0.609175 q^{7} +3.07461 q^{8} +(-3.14263 - 5.44319i) q^{9} +O(q^{10})\) \(q+(0.595455 - 1.03136i) q^{2} +(-1.52359 + 2.63893i) q^{3} +(0.290867 + 0.503797i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.81445 + 3.14272i) q^{6} -0.609175 q^{7} +3.07461 q^{8} +(-3.14263 - 5.44319i) q^{9} +(0.595455 + 1.03136i) q^{10} +4.48517 q^{11} -1.77264 q^{12} +(-2.21900 - 3.84342i) q^{13} +(-0.362736 + 0.628278i) q^{14} +(-1.52359 - 2.63893i) q^{15} +(1.24906 - 2.16343i) q^{16} +(-1.45172 + 2.51445i) q^{17} -7.48517 q^{18} +(3.60532 - 2.44983i) q^{19} -0.581734 q^{20} +(0.928131 - 1.60757i) q^{21} +(2.67071 - 4.62581i) q^{22} +(1.42363 + 2.46580i) q^{23} +(-4.68443 + 8.11368i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.28525 q^{26} +10.0107 q^{27} +(-0.177189 - 0.306901i) q^{28} +(-0.558149 - 0.966742i) q^{29} -3.62891 q^{30} -6.22908 q^{31} +(1.58710 + 2.74893i) q^{32} +(-6.83354 + 11.8360i) q^{33} +(1.72886 + 2.99448i) q^{34} +(0.304588 - 0.527561i) q^{35} +(1.82817 - 3.16649i) q^{36} -3.77264 q^{37} +(-0.379847 - 5.17714i) q^{38} +13.5233 q^{39} +(-1.53731 + 2.66269i) q^{40} +(4.15184 - 7.19120i) q^{41} +(-1.10532 - 1.91447i) q^{42} +(4.99438 - 8.65053i) q^{43} +(1.30459 + 2.25961i) q^{44} +6.28525 q^{45} +3.39082 q^{46} +(2.94250 + 5.09656i) q^{47} +(3.80609 + 6.59235i) q^{48} -6.62891 q^{49} -1.19091 q^{50} +(-4.42363 - 7.66195i) q^{51} +(1.29087 - 2.23585i) q^{52} +(-4.22436 - 7.31681i) q^{53} +(5.96093 - 10.3246i) q^{54} +(-2.24258 + 3.88427i) q^{55} -1.87298 q^{56} +(0.971912 + 13.2467i) q^{57} -1.32941 q^{58} +(-5.11793 + 8.86451i) q^{59} +(0.886322 - 1.53515i) q^{60} +(2.49099 + 4.31453i) q^{61} +(-3.70913 + 6.42441i) q^{62} +(1.91441 + 3.31586i) q^{63} +8.77641 q^{64} +4.43800 q^{65} +(8.13812 + 14.0956i) q^{66} +(-4.23808 - 7.34057i) q^{67} -1.68903 q^{68} -8.67608 q^{69} +(-0.362736 - 0.628278i) q^{70} +(-5.80995 + 10.0631i) q^{71} +(-9.66236 - 16.7357i) q^{72} +(-1.86162 + 3.22443i) q^{73} +(-2.24644 + 3.89095i) q^{74} +3.04717 q^{75} +(2.28289 + 1.10377i) q^{76} -2.73225 q^{77} +(8.05253 - 13.9474i) q^{78} +(-4.51908 + 7.82728i) q^{79} +(1.24906 + 2.16343i) q^{80} +(-5.82432 + 10.0880i) q^{81} +(-4.94447 - 8.56407i) q^{82} -2.12178 q^{83} +1.07985 q^{84} +(-1.45172 - 2.51445i) q^{85} +(-5.94786 - 10.3020i) q^{86} +3.40155 q^{87} +13.7901 q^{88} +(-3.96608 - 6.86946i) q^{89} +(3.74258 - 6.48234i) q^{90} +(1.35176 + 2.34131i) q^{91} +(-0.828173 + 1.43444i) q^{92} +(9.49053 - 16.4381i) q^{93} +7.00850 q^{94} +(0.318955 + 4.34721i) q^{95} -9.67231 q^{96} +(4.83628 - 8.37668i) q^{97} +(-3.94721 + 6.83677i) q^{98} +(-14.0952 - 24.4136i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.595455 1.03136i 0.421050 0.729280i −0.574992 0.818159i \(-0.694995\pi\)
0.996042 + 0.0888786i \(0.0283283\pi\)
\(3\) −1.52359 + 2.63893i −0.879643 + 1.52359i −0.0279089 + 0.999610i \(0.508885\pi\)
−0.851734 + 0.523975i \(0.824448\pi\)
\(4\) 0.290867 + 0.503797i 0.145434 + 0.251898i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 1.81445 + 3.14272i 0.740747 + 1.28301i
\(7\) −0.609175 −0.230247 −0.115123 0.993351i \(-0.536726\pi\)
−0.115123 + 0.993351i \(0.536726\pi\)
\(8\) 3.07461 1.08704
\(9\) −3.14263 5.44319i −1.04754 1.81440i
\(10\) 0.595455 + 1.03136i 0.188299 + 0.326144i
\(11\) 4.48517 1.35233 0.676164 0.736751i \(-0.263641\pi\)
0.676164 + 0.736751i \(0.263641\pi\)
\(12\) −1.77264 −0.511718
\(13\) −2.21900 3.84342i −0.615439 1.06597i −0.990307 0.138894i \(-0.955645\pi\)
0.374868 0.927078i \(-0.377688\pi\)
\(14\) −0.362736 + 0.628278i −0.0969454 + 0.167914i
\(15\) −1.52359 2.63893i −0.393388 0.681368i
\(16\) 1.24906 2.16343i 0.312265 0.540858i
\(17\) −1.45172 + 2.51445i −0.352093 + 0.609843i −0.986616 0.163061i \(-0.947863\pi\)
0.634523 + 0.772904i \(0.281197\pi\)
\(18\) −7.48517 −1.76427
\(19\) 3.60532 2.44983i 0.827117 0.562030i
\(20\) −0.581734 −0.130080
\(21\) 0.928131 1.60757i 0.202535 0.350800i
\(22\) 2.67071 4.62581i 0.569398 0.986227i
\(23\) 1.42363 + 2.46580i 0.296847 + 0.514154i 0.975413 0.220386i \(-0.0707315\pi\)
−0.678566 + 0.734540i \(0.737398\pi\)
\(24\) −4.68443 + 8.11368i −0.956206 + 1.65620i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −5.28525 −1.03652
\(27\) 10.0107 1.92656
\(28\) −0.177189 0.306901i −0.0334856 0.0579987i
\(29\) −0.558149 0.966742i −0.103646 0.179519i 0.809538 0.587067i \(-0.199717\pi\)
−0.913184 + 0.407547i \(0.866384\pi\)
\(30\) −3.62891 −0.662544
\(31\) −6.22908 −1.11877 −0.559387 0.828906i \(-0.688964\pi\)
−0.559387 + 0.828906i \(0.688964\pi\)
\(32\) 1.58710 + 2.74893i 0.280562 + 0.485947i
\(33\) −6.83354 + 11.8360i −1.18957 + 2.06039i
\(34\) 1.72886 + 2.99448i 0.296498 + 0.513549i
\(35\) 0.304588 0.527561i 0.0514847 0.0891741i
\(36\) 1.82817 3.16649i 0.304696 0.527748i
\(37\) −3.77264 −0.620219 −0.310109 0.950701i \(-0.600366\pi\)
−0.310109 + 0.950701i \(0.600366\pi\)
\(38\) −0.379847 5.17714i −0.0616193 0.839843i
\(39\) 13.5233 2.16547
\(40\) −1.53731 + 2.66269i −0.243069 + 0.421009i
\(41\) 4.15184 7.19120i 0.648409 1.12308i −0.335094 0.942185i \(-0.608768\pi\)
0.983503 0.180893i \(-0.0578987\pi\)
\(42\) −1.10532 1.91447i −0.170555 0.295409i
\(43\) 4.99438 8.65053i 0.761637 1.31919i −0.180370 0.983599i \(-0.557730\pi\)
0.942007 0.335594i \(-0.108937\pi\)
\(44\) 1.30459 + 2.25961i 0.196674 + 0.340649i
\(45\) 6.28525 0.936950
\(46\) 3.39082 0.499950
\(47\) 2.94250 + 5.09656i 0.429208 + 0.743409i 0.996803 0.0798983i \(-0.0254596\pi\)
−0.567595 + 0.823308i \(0.692126\pi\)
\(48\) 3.80609 + 6.59235i 0.549362 + 0.951524i
\(49\) −6.62891 −0.946986
\(50\) −1.19091 −0.168420
\(51\) −4.42363 7.66195i −0.619432 1.07289i
\(52\) 1.29087 2.23585i 0.179011 0.310056i
\(53\) −4.22436 7.31681i −0.580261 1.00504i −0.995448 0.0953049i \(-0.969617\pi\)
0.415188 0.909736i \(-0.363716\pi\)
\(54\) 5.96093 10.3246i 0.811180 1.40501i
\(55\) −2.24258 + 3.88427i −0.302390 + 0.523755i
\(56\) −1.87298 −0.250287
\(57\) 0.971912 + 13.2467i 0.128733 + 1.75457i
\(58\) −1.32941 −0.174560
\(59\) −5.11793 + 8.86451i −0.666297 + 1.15406i 0.312634 + 0.949874i \(0.398789\pi\)
−0.978932 + 0.204187i \(0.934545\pi\)
\(60\) 0.886322 1.53515i 0.114424 0.198188i
\(61\) 2.49099 + 4.31453i 0.318939 + 0.552419i 0.980267 0.197678i \(-0.0633401\pi\)
−0.661328 + 0.750097i \(0.730007\pi\)
\(62\) −3.70913 + 6.42441i −0.471060 + 0.815900i
\(63\) 1.91441 + 3.31586i 0.241193 + 0.417759i
\(64\) 8.77641 1.09705
\(65\) 4.43800 0.550466
\(66\) 8.13812 + 14.0956i 1.00173 + 1.73505i
\(67\) −4.23808 7.34057i −0.517764 0.896794i −0.999787 0.0206350i \(-0.993431\pi\)
0.482023 0.876159i \(-0.339902\pi\)
\(68\) −1.68903 −0.204825
\(69\) −8.67608 −1.04448
\(70\) −0.362736 0.628278i −0.0433553 0.0750936i
\(71\) −5.80995 + 10.0631i −0.689514 + 1.19427i 0.282481 + 0.959273i \(0.408843\pi\)
−0.971995 + 0.235001i \(0.924491\pi\)
\(72\) −9.66236 16.7357i −1.13872 1.97232i
\(73\) −1.86162 + 3.22443i −0.217887 + 0.377391i −0.954162 0.299292i \(-0.903250\pi\)
0.736275 + 0.676682i \(0.236583\pi\)
\(74\) −2.24644 + 3.89095i −0.261143 + 0.452313i
\(75\) 3.04717 0.351857
\(76\) 2.28289 + 1.10377i 0.261865 + 0.126611i
\(77\) −2.73225 −0.311369
\(78\) 8.05253 13.9474i 0.911770 1.57923i
\(79\) −4.51908 + 7.82728i −0.508437 + 0.880638i 0.491516 + 0.870869i \(0.336443\pi\)
−0.999952 + 0.00976923i \(0.996890\pi\)
\(80\) 1.24906 + 2.16343i 0.139649 + 0.241879i
\(81\) −5.82432 + 10.0880i −0.647146 + 1.12089i
\(82\) −4.94447 8.56407i −0.546025 0.945744i
\(83\) −2.12178 −0.232896 −0.116448 0.993197i \(-0.537151\pi\)
−0.116448 + 0.993197i \(0.537151\pi\)
\(84\) 1.07985 0.117821
\(85\) −1.45172 2.51445i −0.157461 0.272730i
\(86\) −5.94786 10.3020i −0.641374 1.11089i
\(87\) 3.40155 0.364684
\(88\) 13.7901 1.47003
\(89\) −3.96608 6.86946i −0.420404 0.728161i 0.575575 0.817749i \(-0.304778\pi\)
−0.995979 + 0.0895879i \(0.971445\pi\)
\(90\) 3.74258 6.48234i 0.394503 0.683299i
\(91\) 1.35176 + 2.34131i 0.141703 + 0.245436i
\(92\) −0.828173 + 1.43444i −0.0863430 + 0.149551i
\(93\) 9.49053 16.4381i 0.984122 1.70455i
\(94\) 7.00850 0.722872
\(95\) 0.318955 + 4.34721i 0.0327241 + 0.446015i
\(96\) −9.67231 −0.987176
\(97\) 4.83628 8.37668i 0.491050 0.850523i −0.508897 0.860827i \(-0.669947\pi\)
0.999947 + 0.0103043i \(0.00328001\pi\)
\(98\) −3.94721 + 6.83677i −0.398729 + 0.690619i
\(99\) −14.0952 24.4136i −1.41662 2.45366i
\(100\) 0.290867 0.503797i 0.0290867 0.0503797i
\(101\) 0.485632 + 0.841140i 0.0483222 + 0.0836965i 0.889175 0.457568i \(-0.151279\pi\)
−0.840853 + 0.541264i \(0.817946\pi\)
\(102\) −10.5363 −1.04325
\(103\) −3.34143 −0.329241 −0.164620 0.986357i \(-0.552640\pi\)
−0.164620 + 0.986357i \(0.552640\pi\)
\(104\) −6.82256 11.8170i −0.669007 1.15875i
\(105\) 0.928131 + 1.60757i 0.0905763 + 0.156883i
\(106\) −10.0617 −0.977275
\(107\) 9.51655 0.920000 0.460000 0.887919i \(-0.347849\pi\)
0.460000 + 0.887919i \(0.347849\pi\)
\(108\) 2.91179 + 5.04337i 0.280187 + 0.485298i
\(109\) −2.77178 + 4.80087i −0.265489 + 0.459840i −0.967692 0.252137i \(-0.918867\pi\)
0.702203 + 0.711977i \(0.252200\pi\)
\(110\) 2.67071 + 4.62581i 0.254643 + 0.441054i
\(111\) 5.74795 9.95573i 0.545571 0.944956i
\(112\) −0.760896 + 1.31791i −0.0718979 + 0.124531i
\(113\) 1.54134 0.144997 0.0724987 0.997369i \(-0.476903\pi\)
0.0724987 + 0.997369i \(0.476903\pi\)
\(114\) 14.2408 + 6.88542i 1.33378 + 0.644879i
\(115\) −2.84726 −0.265508
\(116\) 0.324694 0.562387i 0.0301471 0.0522163i
\(117\) −13.9470 + 24.1568i −1.28940 + 2.23330i
\(118\) 6.09499 + 10.5568i 0.561089 + 0.971835i
\(119\) 0.884350 1.53174i 0.0810682 0.140414i
\(120\) −4.68443 8.11368i −0.427628 0.740674i
\(121\) 9.11672 0.828793
\(122\) 5.93310 0.537158
\(123\) 12.6514 + 21.9128i 1.14074 + 1.97581i
\(124\) −1.81183 3.13819i −0.162707 0.281818i
\(125\) 1.00000 0.0894427
\(126\) 4.55978 0.406217
\(127\) −1.15274 1.99661i −0.102289 0.177171i 0.810338 0.585963i \(-0.199283\pi\)
−0.912628 + 0.408792i \(0.865950\pi\)
\(128\) 2.05176 3.55376i 0.181352 0.314111i
\(129\) 15.2187 + 26.3596i 1.33994 + 2.32084i
\(130\) 2.64263 4.57716i 0.231774 0.401444i
\(131\) 6.45905 11.1874i 0.564330 0.977448i −0.432782 0.901499i \(-0.642468\pi\)
0.997112 0.0759493i \(-0.0241987\pi\)
\(132\) −7.95060 −0.692011
\(133\) −2.19627 + 1.49238i −0.190441 + 0.129405i
\(134\) −10.0943 −0.872018
\(135\) −5.00536 + 8.66954i −0.430793 + 0.746155i
\(136\) −4.46346 + 7.73095i −0.382739 + 0.662923i
\(137\) 6.36677 + 11.0276i 0.543950 + 0.942149i 0.998672 + 0.0515159i \(0.0164053\pi\)
−0.454722 + 0.890633i \(0.650261\pi\)
\(138\) −5.16621 + 8.94814i −0.439777 + 0.761716i
\(139\) −5.30433 9.18738i −0.449908 0.779263i 0.548472 0.836169i \(-0.315210\pi\)
−0.998380 + 0.0569059i \(0.981876\pi\)
\(140\) 0.354378 0.0299504
\(141\) −17.9326 −1.51020
\(142\) 6.91913 + 11.9843i 0.580640 + 1.00570i
\(143\) −9.95258 17.2384i −0.832276 1.44154i
\(144\) −15.7013 −1.30844
\(145\) 1.11630 0.0927035
\(146\) 2.21703 + 3.84000i 0.183482 + 0.317801i
\(147\) 10.0997 17.4932i 0.833010 1.44281i
\(148\) −1.09734 1.90065i −0.0902006 0.156232i
\(149\) −1.88653 + 3.26757i −0.154551 + 0.267690i −0.932895 0.360147i \(-0.882726\pi\)
0.778344 + 0.627837i \(0.216060\pi\)
\(150\) 1.81445 3.14272i 0.148149 0.256602i
\(151\) −9.51562 −0.774370 −0.387185 0.922002i \(-0.626553\pi\)
−0.387185 + 0.922002i \(0.626553\pi\)
\(152\) 11.0850 7.53228i 0.899109 0.610948i
\(153\) 18.2488 1.47533
\(154\) −1.62693 + 2.81793i −0.131102 + 0.227075i
\(155\) 3.11454 5.39454i 0.250166 0.433300i
\(156\) 3.93349 + 6.81301i 0.314931 + 0.545477i
\(157\) 1.72822 2.99336i 0.137927 0.238896i −0.788785 0.614669i \(-0.789290\pi\)
0.926712 + 0.375773i \(0.122623\pi\)
\(158\) 5.38182 + 9.32158i 0.428155 + 0.741585i
\(159\) 25.7447 2.04169
\(160\) −3.17419 −0.250942
\(161\) −0.867239 1.50210i −0.0683480 0.118382i
\(162\) 6.93624 + 12.0139i 0.544962 + 0.943902i
\(163\) 6.65283 0.521090 0.260545 0.965462i \(-0.416098\pi\)
0.260545 + 0.965462i \(0.416098\pi\)
\(164\) 4.83054 0.377202
\(165\) −6.83354 11.8360i −0.531990 0.921434i
\(166\) −1.26343 + 2.18832i −0.0980609 + 0.169846i
\(167\) 8.22775 + 14.2509i 0.636682 + 1.10277i 0.986156 + 0.165820i \(0.0530271\pi\)
−0.349474 + 0.936946i \(0.613640\pi\)
\(168\) 2.85364 4.94265i 0.220163 0.381334i
\(169\) −3.34790 + 5.79874i −0.257531 + 0.446057i
\(170\) −3.45773 −0.265195
\(171\) −24.6651 11.9255i −1.88618 0.911968i
\(172\) 5.81081 0.443070
\(173\) 11.3912 19.7302i 0.866058 1.50006i 6.58713e−5 1.00000i \(-0.499979\pi\)
0.865992 0.500057i \(-0.166688\pi\)
\(174\) 2.02547 3.50822i 0.153550 0.265957i
\(175\) 0.304588 + 0.527561i 0.0230247 + 0.0398799i
\(176\) 5.60224 9.70336i 0.422284 0.731418i
\(177\) −15.5952 27.0117i −1.17221 2.03032i
\(178\) −9.44650 −0.708045
\(179\) −2.32916 −0.174090 −0.0870449 0.996204i \(-0.527742\pi\)
−0.0870449 + 0.996204i \(0.527742\pi\)
\(180\) 1.82817 + 3.16649i 0.136264 + 0.236016i
\(181\) 11.1696 + 19.3463i 0.830230 + 1.43800i 0.897856 + 0.440290i \(0.145124\pi\)
−0.0676258 + 0.997711i \(0.521542\pi\)
\(182\) 3.21965 0.238656
\(183\) −15.1810 −1.12221
\(184\) 4.37710 + 7.58137i 0.322684 + 0.558906i
\(185\) 1.88632 3.26721i 0.138685 0.240210i
\(186\) −11.3024 19.5763i −0.828729 1.43540i
\(187\) −6.51119 + 11.2777i −0.476145 + 0.824708i
\(188\) −1.71175 + 2.96484i −0.124842 + 0.216233i
\(189\) −6.09829 −0.443585
\(190\) 4.67346 + 2.25961i 0.339048 + 0.163929i
\(191\) 2.23766 0.161911 0.0809556 0.996718i \(-0.474203\pi\)
0.0809556 + 0.996718i \(0.474203\pi\)
\(192\) −13.3716 + 23.1603i −0.965013 + 1.67145i
\(193\) 2.27153 3.93441i 0.163508 0.283205i −0.772616 0.634873i \(-0.781052\pi\)
0.936125 + 0.351669i \(0.114386\pi\)
\(194\) −5.75957 9.97587i −0.413513 0.716226i
\(195\) −6.76167 + 11.7115i −0.484213 + 0.838681i
\(196\) −1.92813 3.33962i −0.137724 0.238544i
\(197\) −19.2236 −1.36962 −0.684812 0.728720i \(-0.740116\pi\)
−0.684812 + 0.728720i \(0.740116\pi\)
\(198\) −33.5722 −2.38587
\(199\) 3.07547 + 5.32687i 0.218014 + 0.377612i 0.954201 0.299167i \(-0.0967087\pi\)
−0.736186 + 0.676779i \(0.763375\pi\)
\(200\) −1.53731 2.66269i −0.108704 0.188281i
\(201\) 25.8283 1.82179
\(202\) 1.15669 0.0813843
\(203\) 0.340010 + 0.588915i 0.0238641 + 0.0413338i
\(204\) 2.57338 4.45722i 0.180172 0.312068i
\(205\) 4.15184 + 7.19120i 0.289977 + 0.502255i
\(206\) −1.98967 + 3.44621i −0.138627 + 0.240109i
\(207\) 8.94786 15.4981i 0.621919 1.07720i
\(208\) −11.0866 −0.768720
\(209\) 16.1705 10.9879i 1.11853 0.760049i
\(210\) 2.21064 0.152549
\(211\) −6.34661 + 10.9926i −0.436919 + 0.756765i −0.997450 0.0713679i \(-0.977264\pi\)
0.560531 + 0.828133i \(0.310597\pi\)
\(212\) 2.45746 4.25644i 0.168779 0.292333i
\(213\) −17.7039 30.6641i −1.21305 2.10107i
\(214\) 5.66668 9.81497i 0.387366 0.670938i
\(215\) 4.99438 + 8.65053i 0.340614 + 0.589961i
\(216\) 30.7791 2.09425
\(217\) 3.79460 0.257594
\(218\) 3.30094 + 5.71740i 0.223568 + 0.387231i
\(219\) −5.67269 9.82538i −0.383325 0.663938i
\(220\) −2.60918 −0.175911
\(221\) 12.8854 0.866767
\(222\) −6.84528 11.8564i −0.459425 0.795748i
\(223\) −11.2688 + 19.5181i −0.754614 + 1.30703i 0.190952 + 0.981599i \(0.438842\pi\)
−0.945566 + 0.325430i \(0.894491\pi\)
\(224\) −0.966820 1.67458i −0.0645984 0.111888i
\(225\) −3.14263 + 5.44319i −0.209508 + 0.362879i
\(226\) 0.917800 1.58968i 0.0610512 0.105744i
\(227\) 18.1124 1.20216 0.601080 0.799189i \(-0.294737\pi\)
0.601080 + 0.799189i \(0.294737\pi\)
\(228\) −6.39095 + 4.34268i −0.423251 + 0.287601i
\(229\) −9.41604 −0.622229 −0.311115 0.950372i \(-0.600702\pi\)
−0.311115 + 0.950372i \(0.600702\pi\)
\(230\) −1.69541 + 2.93654i −0.111792 + 0.193630i
\(231\) 4.16282 7.21022i 0.273894 0.474398i
\(232\) −1.71609 2.97236i −0.112667 0.195145i
\(233\) −7.85000 + 13.5966i −0.514271 + 0.890743i 0.485592 + 0.874185i \(0.338604\pi\)
−0.999863 + 0.0165573i \(0.994729\pi\)
\(234\) 16.6096 + 28.7686i 1.08580 + 1.88066i
\(235\) −5.88500 −0.383895
\(236\) −5.95455 −0.387608
\(237\) −13.7704 23.8511i −0.894485 1.54929i
\(238\) −1.05318 1.82416i −0.0682676 0.118243i
\(239\) −23.4610 −1.51757 −0.758783 0.651344i \(-0.774205\pi\)
−0.758783 + 0.651344i \(0.774205\pi\)
\(240\) −7.61219 −0.491365
\(241\) −6.58469 11.4050i −0.424157 0.734662i 0.572184 0.820125i \(-0.306096\pi\)
−0.996341 + 0.0854634i \(0.972763\pi\)
\(242\) 5.42860 9.40260i 0.348963 0.604422i
\(243\) −2.73161 4.73128i −0.175233 0.303512i
\(244\) −1.44910 + 2.50991i −0.0927689 + 0.160680i
\(245\) 3.31445 5.74080i 0.211753 0.366766i
\(246\) 30.1333 1.92123
\(247\) −17.4159 8.42058i −1.10815 0.535789i
\(248\) −19.1520 −1.21615
\(249\) 3.23272 5.59923i 0.204865 0.354837i
\(250\) 0.595455 1.03136i 0.0376599 0.0652288i
\(251\) 8.66257 + 15.0040i 0.546776 + 0.947045i 0.998493 + 0.0548830i \(0.0174786\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(252\) −1.11368 + 1.92895i −0.0701551 + 0.121512i
\(253\) 6.38521 + 11.0595i 0.401435 + 0.695305i
\(254\) −2.74563 −0.172276
\(255\) 8.84726 0.554037
\(256\) 6.33295 + 10.9690i 0.395809 + 0.685562i
\(257\) 2.83980 + 4.91867i 0.177142 + 0.306818i 0.940900 0.338683i \(-0.109982\pi\)
−0.763759 + 0.645502i \(0.776648\pi\)
\(258\) 36.2483 2.25672
\(259\) 2.29820 0.142803
\(260\) 1.29087 + 2.23585i 0.0800562 + 0.138661i
\(261\) −3.50811 + 6.07622i −0.217146 + 0.376108i
\(262\) −7.69215 13.3232i −0.475222 0.823109i
\(263\) −2.82882 + 4.89966i −0.174433 + 0.302126i −0.939965 0.341272i \(-0.889142\pi\)
0.765532 + 0.643398i \(0.222476\pi\)
\(264\) −21.0105 + 36.3912i −1.29311 + 2.23972i
\(265\) 8.44872 0.519001
\(266\) 0.231393 + 3.15379i 0.0141876 + 0.193371i
\(267\) 24.1707 1.47922
\(268\) 2.46544 4.27026i 0.150601 0.260848i
\(269\) 11.9959 20.7775i 0.731402 1.26683i −0.224881 0.974386i \(-0.572199\pi\)
0.956284 0.292440i \(-0.0944672\pi\)
\(270\) 5.96093 + 10.3246i 0.362771 + 0.628338i
\(271\) 10.6497 18.4459i 0.646926 1.12051i −0.336927 0.941531i \(-0.609388\pi\)
0.983853 0.178978i \(-0.0572791\pi\)
\(272\) 3.62656 + 6.28138i 0.219892 + 0.380865i
\(273\) −8.23808 −0.498591
\(274\) 15.1645 0.916121
\(275\) −2.24258 3.88427i −0.135233 0.234230i
\(276\) −2.52359 4.37098i −0.151902 0.263102i
\(277\) −0.821109 −0.0493357 −0.0246678 0.999696i \(-0.507853\pi\)
−0.0246678 + 0.999696i \(0.507853\pi\)
\(278\) −12.6340 −0.757735
\(279\) 19.5757 + 33.9060i 1.17196 + 2.02990i
\(280\) 0.936489 1.62205i 0.0559659 0.0969358i
\(281\) 0.293739 + 0.508772i 0.0175230 + 0.0303508i 0.874654 0.484748i \(-0.161089\pi\)
−0.857131 + 0.515099i \(0.827755\pi\)
\(282\) −10.6780 + 18.4949i −0.635869 + 1.10136i
\(283\) −15.4712 + 26.7969i −0.919667 + 1.59291i −0.119746 + 0.992805i \(0.538208\pi\)
−0.799921 + 0.600105i \(0.795125\pi\)
\(284\) −6.75969 −0.401114
\(285\) −11.9579 5.78165i −0.708327 0.342475i
\(286\) −23.7052 −1.40172
\(287\) −2.52920 + 4.38070i −0.149294 + 0.258585i
\(288\) 9.97530 17.2777i 0.587800 1.01810i
\(289\) 4.28504 + 7.42191i 0.252061 + 0.436583i
\(290\) 0.664705 1.15130i 0.0390328 0.0676068i
\(291\) 14.7370 + 25.5252i 0.863896 + 1.49631i
\(292\) −2.16594 −0.126752
\(293\) 3.76271 0.219820 0.109910 0.993942i \(-0.464944\pi\)
0.109910 + 0.993942i \(0.464944\pi\)
\(294\) −12.0278 20.8328i −0.701478 1.21499i
\(295\) −5.11793 8.86451i −0.297977 0.516112i
\(296\) −11.5994 −0.674202
\(297\) 44.8998 2.60535
\(298\) 2.24669 + 3.89138i 0.130147 + 0.225422i
\(299\) 6.31806 10.9432i 0.365383 0.632861i
\(300\) 0.886322 + 1.53515i 0.0511718 + 0.0886322i
\(301\) −3.04246 + 5.26969i −0.175364 + 0.303740i
\(302\) −5.66612 + 9.81401i −0.326049 + 0.564733i
\(303\) −2.95961 −0.170025
\(304\) −0.796788 10.8598i −0.0456989 0.622855i
\(305\) −4.98199 −0.285268
\(306\) 10.8663 18.8211i 0.621187 1.07593i
\(307\) −10.1709 + 17.6166i −0.580485 + 1.00543i 0.414936 + 0.909850i \(0.363804\pi\)
−0.995422 + 0.0955798i \(0.969529\pi\)
\(308\) −0.794723 1.37650i −0.0452835 0.0784334i
\(309\) 5.09095 8.81779i 0.289614 0.501626i
\(310\) −3.70913 6.42441i −0.210665 0.364882i
\(311\) −7.67830 −0.435397 −0.217698 0.976016i \(-0.569855\pi\)
−0.217698 + 0.976016i \(0.569855\pi\)
\(312\) 41.5790 2.35395
\(313\) −11.9964 20.7783i −0.678074 1.17446i −0.975560 0.219733i \(-0.929481\pi\)
0.297486 0.954726i \(-0.403852\pi\)
\(314\) −2.05815 3.56482i −0.116148 0.201174i
\(315\) −3.82882 −0.215730
\(316\) −5.25781 −0.295775
\(317\) −0.519518 0.899831i −0.0291790 0.0505395i 0.851067 0.525057i \(-0.175956\pi\)
−0.880246 + 0.474517i \(0.842623\pi\)
\(318\) 15.3298 26.5520i 0.859653 1.48896i
\(319\) −2.50339 4.33600i −0.140163 0.242769i
\(320\) −4.38821 + 7.60059i −0.245308 + 0.424886i
\(321\) −14.4993 + 25.1135i −0.809271 + 1.40170i
\(322\) −2.06561 −0.115112
\(323\) 0.926066 + 12.6218i 0.0515277 + 0.702298i
\(324\) −6.77641 −0.376467
\(325\) −2.21900 + 3.84342i −0.123088 + 0.213194i
\(326\) 3.96146 6.86145i 0.219405 0.380020i
\(327\) −8.44610 14.6291i −0.467070 0.808990i
\(328\) 12.7653 22.1102i 0.704846 1.22083i
\(329\) −1.79250 3.10470i −0.0988236 0.171167i
\(330\) −16.2762 −0.895978
\(331\) 30.8316 1.69466 0.847328 0.531069i \(-0.178210\pi\)
0.847328 + 0.531069i \(0.178210\pi\)
\(332\) −0.617157 1.06895i −0.0338709 0.0586661i
\(333\) 11.8560 + 20.5352i 0.649705 + 1.12532i
\(334\) 19.5970 1.07230
\(335\) 8.47616 0.463102
\(336\) −2.31858 4.01590i −0.126489 0.219085i
\(337\) −10.3576 + 17.9400i −0.564217 + 0.977252i 0.432906 + 0.901439i \(0.357488\pi\)
−0.997122 + 0.0758124i \(0.975845\pi\)
\(338\) 3.98705 + 6.90577i 0.216867 + 0.375625i
\(339\) −2.34837 + 4.06749i −0.127546 + 0.220916i
\(340\) 0.844513 1.46274i 0.0458002 0.0793282i
\(341\) −27.9384 −1.51295
\(342\) −26.9864 + 18.3374i −1.45926 + 0.991572i
\(343\) 8.30239 0.448287
\(344\) 15.3558 26.5970i 0.827929 1.43402i
\(345\) 4.33804 7.51370i 0.233552 0.404524i
\(346\) −13.5659 23.4968i −0.729308 1.26320i
\(347\) −4.11068 + 7.11991i −0.220673 + 0.382217i −0.955013 0.296566i \(-0.904159\pi\)
0.734340 + 0.678782i \(0.237492\pi\)
\(348\) 0.989399 + 1.71369i 0.0530373 + 0.0918634i
\(349\) 11.9216 0.638150 0.319075 0.947730i \(-0.396628\pi\)
0.319075 + 0.947730i \(0.396628\pi\)
\(350\) 0.725473 0.0387782
\(351\) −22.2138 38.4754i −1.18568 2.05366i
\(352\) 7.11839 + 12.3294i 0.379412 + 0.657160i
\(353\) −11.7983 −0.627959 −0.313980 0.949430i \(-0.601662\pi\)
−0.313980 + 0.949430i \(0.601662\pi\)
\(354\) −37.1450 −1.97423
\(355\) −5.80995 10.0631i −0.308360 0.534095i
\(356\) 2.30721 3.99620i 0.122282 0.211798i
\(357\) 2.69477 + 4.66747i 0.142622 + 0.247029i
\(358\) −1.38691 + 2.40220i −0.0733005 + 0.126960i
\(359\) −0.0554058 + 0.0959656i −0.00292420 + 0.00506487i −0.867484 0.497465i \(-0.834264\pi\)
0.864560 + 0.502530i \(0.167597\pi\)
\(360\) 19.3247 1.01850
\(361\) 6.99666 17.6648i 0.368245 0.929729i
\(362\) 26.6040 1.39827
\(363\) −13.8901 + 24.0584i −0.729042 + 1.26274i
\(364\) −0.786364 + 1.36202i −0.0412167 + 0.0713894i
\(365\) −1.86162 3.22443i −0.0974418 0.168774i
\(366\) −9.03958 + 15.6570i −0.472507 + 0.818405i
\(367\) −5.86986 10.1669i −0.306404 0.530708i 0.671169 0.741305i \(-0.265793\pi\)
−0.977573 + 0.210597i \(0.932459\pi\)
\(368\) 7.11278 0.370779
\(369\) −52.1908 −2.71694
\(370\) −2.24644 3.89095i −0.116787 0.202281i
\(371\) 2.57338 + 4.45722i 0.133603 + 0.231407i
\(372\) 11.0419 0.572498
\(373\) 14.5190 0.751763 0.375882 0.926668i \(-0.377340\pi\)
0.375882 + 0.926668i \(0.377340\pi\)
\(374\) 7.75424 + 13.4307i 0.400962 + 0.694487i
\(375\) −1.52359 + 2.63893i −0.0786776 + 0.136274i
\(376\) 9.04704 + 15.6699i 0.466566 + 0.808115i
\(377\) −2.47706 + 4.29040i −0.127575 + 0.220967i
\(378\) −3.63125 + 6.28952i −0.186772 + 0.323498i
\(379\) −6.59023 −0.338518 −0.169259 0.985572i \(-0.554137\pi\)
−0.169259 + 0.985572i \(0.554137\pi\)
\(380\) −2.09734 + 1.42515i −0.107591 + 0.0731087i
\(381\) 7.02522 0.359913
\(382\) 1.33242 2.30782i 0.0681727 0.118079i
\(383\) 1.43461 2.48481i 0.0733049 0.126968i −0.827043 0.562139i \(-0.809979\pi\)
0.900348 + 0.435171i \(0.143312\pi\)
\(384\) 6.25207 + 10.8289i 0.319050 + 0.552610i
\(385\) 1.36613 2.36620i 0.0696243 0.120593i
\(386\) −2.70519 4.68552i −0.137690 0.238487i
\(387\) −62.7819 −3.19138
\(388\) 5.62686 0.285660
\(389\) 3.16575 + 5.48323i 0.160510 + 0.278011i 0.935052 0.354512i \(-0.115353\pi\)
−0.774542 + 0.632523i \(0.782020\pi\)
\(390\) 8.05253 + 13.9474i 0.407756 + 0.706254i
\(391\) −8.26682 −0.418071
\(392\) −20.3813 −1.02941
\(393\) 19.6818 + 34.0899i 0.992817 + 1.71961i
\(394\) −11.4468 + 19.8264i −0.576680 + 0.998840i
\(395\) −4.51908 7.82728i −0.227380 0.393833i
\(396\) 8.19966 14.2022i 0.412049 0.713689i
\(397\) 15.2749 26.4569i 0.766626 1.32784i −0.172756 0.984965i \(-0.555267\pi\)
0.939382 0.342871i \(-0.111399\pi\)
\(398\) 7.32522 0.367180
\(399\) −0.592065 8.06957i −0.0296403 0.403984i
\(400\) −2.49812 −0.124906
\(401\) −15.1711 + 26.2771i −0.757609 + 1.31222i 0.186458 + 0.982463i \(0.440299\pi\)
−0.944067 + 0.329754i \(0.893034\pi\)
\(402\) 15.3796 26.6382i 0.767064 1.32859i
\(403\) 13.8223 + 23.9409i 0.688538 + 1.19258i
\(404\) −0.282509 + 0.489320i −0.0140553 + 0.0243446i
\(405\) −5.82432 10.0880i −0.289413 0.501277i
\(406\) 0.809843 0.0401919
\(407\) −16.9209 −0.838740
\(408\) −13.6009 23.5575i −0.673347 1.16627i
\(409\) 7.48628 + 12.9666i 0.370173 + 0.641158i 0.989592 0.143903i \(-0.0459652\pi\)
−0.619419 + 0.785060i \(0.712632\pi\)
\(410\) 9.88894 0.488380
\(411\) −38.8013 −1.91393
\(412\) −0.971912 1.68340i −0.0478827 0.0829352i
\(413\) 3.11772 5.40004i 0.153413 0.265719i
\(414\) −10.6561 18.4569i −0.523718 0.907107i
\(415\) 1.06089 1.83752i 0.0520771 0.0902002i
\(416\) 7.04353 12.1997i 0.345337 0.598142i
\(417\) 32.3264 1.58303
\(418\) −1.70368 23.2203i −0.0833296 1.13574i
\(419\) −6.17419 −0.301629 −0.150815 0.988562i \(-0.548190\pi\)
−0.150815 + 0.988562i \(0.548190\pi\)
\(420\) −0.539925 + 0.935178i −0.0263457 + 0.0456320i
\(421\) 13.7714 23.8528i 0.671177 1.16251i −0.306394 0.951905i \(-0.599122\pi\)
0.977571 0.210608i \(-0.0675443\pi\)
\(422\) 7.55824 + 13.0913i 0.367929 + 0.637272i
\(423\) 18.4943 32.0331i 0.899226 1.55750i
\(424\) −12.9883 22.4963i −0.630766 1.09252i
\(425\) 2.90343 0.140837
\(426\) −42.1675 −2.04302
\(427\) −1.51745 2.62830i −0.0734347 0.127193i
\(428\) 2.76805 + 4.79441i 0.133799 + 0.231746i
\(429\) 60.6544 2.92842
\(430\) 11.8957 0.573663
\(431\) 7.52941 + 13.0413i 0.362679 + 0.628179i 0.988401 0.151868i \(-0.0485288\pi\)
−0.625722 + 0.780046i \(0.715195\pi\)
\(432\) 12.5040 21.6575i 0.601598 1.04200i
\(433\) 0.485420 + 0.840772i 0.0233278 + 0.0404049i 0.877454 0.479661i \(-0.159241\pi\)
−0.854126 + 0.520066i \(0.825907\pi\)
\(434\) 2.25951 3.91359i 0.108460 0.187858i
\(435\) −1.70077 + 2.94583i −0.0815459 + 0.141242i
\(436\) −3.22488 −0.154444
\(437\) 11.1734 + 5.40234i 0.534497 + 0.258429i
\(438\) −13.5113 −0.645596
\(439\) 13.7187 23.7616i 0.654760 1.13408i −0.327194 0.944957i \(-0.606103\pi\)
0.981954 0.189120i \(-0.0605636\pi\)
\(440\) −6.89507 + 11.9426i −0.328710 + 0.569342i
\(441\) 20.8322 + 36.0824i 0.992008 + 1.71821i
\(442\) 7.67269 13.2895i 0.364952 0.632116i
\(443\) 4.38272 + 7.59109i 0.208229 + 0.360664i 0.951157 0.308708i \(-0.0998966\pi\)
−0.742928 + 0.669372i \(0.766563\pi\)
\(444\) 6.68755 0.317377
\(445\) 7.93217 0.376021
\(446\) 13.4201 + 23.2443i 0.635461 + 1.10065i
\(447\) −5.74859 9.95686i −0.271899 0.470943i
\(448\) −5.34637 −0.252592
\(449\) −9.63397 −0.454655 −0.227327 0.973818i \(-0.572999\pi\)
−0.227327 + 0.973818i \(0.572999\pi\)
\(450\) 3.74258 + 6.48234i 0.176427 + 0.305581i
\(451\) 18.6217 32.2538i 0.876862 1.51877i
\(452\) 0.448326 + 0.776524i 0.0210875 + 0.0365246i
\(453\) 14.4979 25.1110i 0.681169 1.17982i
\(454\) 10.7851 18.6803i 0.506169 0.876711i
\(455\) −2.70352 −0.126743
\(456\) 2.98825 + 40.7285i 0.139938 + 1.90729i
\(457\) −10.6708 −0.499161 −0.249580 0.968354i \(-0.580293\pi\)
−0.249580 + 0.968354i \(0.580293\pi\)
\(458\) −5.60683 + 9.71131i −0.261990 + 0.453780i
\(459\) −14.5327 + 25.1714i −0.678330 + 1.17490i
\(460\) −0.828173 1.43444i −0.0386138 0.0668810i
\(461\) −2.84340 + 4.92491i −0.132430 + 0.229376i −0.924613 0.380908i \(-0.875611\pi\)
0.792183 + 0.610284i \(0.208945\pi\)
\(462\) −4.95754 8.58672i −0.230646 0.399490i
\(463\) 35.3550 1.64309 0.821543 0.570147i \(-0.193114\pi\)
0.821543 + 0.570147i \(0.193114\pi\)
\(464\) −2.78864 −0.129459
\(465\) 9.49053 + 16.4381i 0.440113 + 0.762298i
\(466\) 9.34864 + 16.1923i 0.433067 + 0.750095i
\(467\) −32.9071 −1.52276 −0.761380 0.648306i \(-0.775478\pi\)
−0.761380 + 0.648306i \(0.775478\pi\)
\(468\) −16.2269 −0.750086
\(469\) 2.58173 + 4.47169i 0.119213 + 0.206484i
\(470\) −3.50425 + 6.06954i −0.161639 + 0.279967i
\(471\) 5.26617 + 9.12127i 0.242652 + 0.420286i
\(472\) −15.7356 + 27.2549i −0.724292 + 1.25451i
\(473\) 22.4006 38.7991i 1.02998 1.78398i
\(474\) −32.7986 −1.50649
\(475\) −3.92428 1.89738i −0.180058 0.0870579i
\(476\) 1.02891 0.0471602
\(477\) −26.5512 + 45.9880i −1.21569 + 2.10564i
\(478\) −13.9700 + 24.1967i −0.638971 + 1.10673i
\(479\) 4.52861 + 7.84378i 0.206917 + 0.358391i 0.950742 0.309984i \(-0.100324\pi\)
−0.743825 + 0.668375i \(0.766990\pi\)
\(480\) 4.83615 8.37647i 0.220739 0.382332i
\(481\) 8.37149 + 14.4998i 0.381707 + 0.661136i
\(482\) −15.6835 −0.714366
\(483\) 5.28525 0.240487
\(484\) 2.65175 + 4.59297i 0.120534 + 0.208772i
\(485\) 4.83628 + 8.37668i 0.219604 + 0.380365i
\(486\) −6.50619 −0.295127
\(487\) −16.5206 −0.748620 −0.374310 0.927304i \(-0.622120\pi\)
−0.374310 + 0.927304i \(0.622120\pi\)
\(488\) 7.65884 + 13.2655i 0.346700 + 0.600501i
\(489\) −10.1362 + 17.5563i −0.458373 + 0.793925i
\(490\) −3.94721 6.83677i −0.178317 0.308854i
\(491\) 0.695625 1.20486i 0.0313931 0.0543745i −0.849902 0.526941i \(-0.823339\pi\)
0.881295 + 0.472566i \(0.156672\pi\)
\(492\) −7.35974 + 12.7474i −0.331803 + 0.574699i
\(493\) 3.24109 0.145972
\(494\) −19.0550 + 12.9480i −0.857326 + 0.582557i
\(495\) 28.1904 1.26706
\(496\) −7.78048 + 13.4762i −0.349354 + 0.605099i
\(497\) 3.53928 6.13021i 0.158758 0.274977i
\(498\) −3.84988 6.66818i −0.172517 0.298808i
\(499\) 8.33255 14.4324i 0.373016 0.646083i −0.617012 0.786954i \(-0.711657\pi\)
0.990028 + 0.140871i \(0.0449902\pi\)
\(500\) 0.290867 + 0.503797i 0.0130080 + 0.0225305i
\(501\) −50.1427 −2.24021
\(502\) 20.6327 0.920881
\(503\) −7.81956 13.5439i −0.348657 0.603892i 0.637354 0.770571i \(-0.280029\pi\)
−0.986011 + 0.166679i \(0.946696\pi\)
\(504\) 5.88607 + 10.1950i 0.262186 + 0.454120i
\(505\) −0.971265 −0.0432207
\(506\) 15.2084 0.676096
\(507\) −10.2016 17.6697i −0.453070 0.784741i
\(508\) 0.670591 1.16150i 0.0297526 0.0515331i
\(509\) 9.57702 + 16.5879i 0.424494 + 0.735245i 0.996373 0.0850929i \(-0.0271187\pi\)
−0.571879 + 0.820338i \(0.693785\pi\)
\(510\) 5.26814 9.12469i 0.233277 0.404048i
\(511\) 1.13406 1.96424i 0.0501677 0.0868929i
\(512\) 23.2910 1.02933
\(513\) 36.0919 24.5246i 1.59349 1.08279i
\(514\) 6.76389 0.298342
\(515\) 1.67071 2.89376i 0.0736205 0.127514i
\(516\) −8.85327 + 15.3343i −0.389743 + 0.675055i
\(517\) 13.1976 + 22.8589i 0.580430 + 1.00533i
\(518\) 1.36848 2.37027i 0.0601273 0.104144i
\(519\) 34.7110 + 60.1212i 1.52364 + 2.63903i
\(520\) 13.6451 0.598378
\(521\) −19.2394 −0.842892 −0.421446 0.906853i \(-0.638477\pi\)
−0.421446 + 0.906853i \(0.638477\pi\)
\(522\) 4.17784 + 7.23622i 0.182859 + 0.316721i
\(523\) −3.31973 5.74993i −0.145161 0.251427i 0.784272 0.620418i \(-0.213037\pi\)
−0.929433 + 0.368990i \(0.879704\pi\)
\(524\) 7.51490 0.328290
\(525\) −1.85626 −0.0810139
\(526\) 3.36887 + 5.83505i 0.146890 + 0.254420i
\(527\) 9.04285 15.6627i 0.393913 0.682277i
\(528\) 17.0710 + 29.5678i 0.742919 + 1.28677i
\(529\) 7.44657 12.8978i 0.323764 0.560775i
\(530\) 5.03083 8.71366i 0.218525 0.378497i
\(531\) 64.3349 2.79190
\(532\) −1.39068 0.672391i −0.0602935 0.0291519i
\(533\) −36.8517 −1.59623
\(534\) 14.3925 24.9286i 0.622826 1.07877i
\(535\) −4.75828 + 8.24158i −0.205718 + 0.356314i
\(536\) −13.0305 22.5694i −0.562830 0.974850i
\(537\) 3.54868 6.14649i 0.153137 0.265241i
\(538\) −14.2860 24.7441i −0.615914 1.06679i
\(539\) −29.7317 −1.28064
\(540\) −5.82358 −0.250607
\(541\) −20.8756 36.1575i −0.897510 1.55453i −0.830667 0.556770i \(-0.812040\pi\)
−0.0668435 0.997763i \(-0.521293\pi\)
\(542\) −12.6829 21.9674i −0.544777 0.943581i
\(543\) −68.0714 −2.92122
\(544\) −9.21606 −0.395135
\(545\) −2.77178 4.80087i −0.118730 0.205647i
\(546\) −4.90540 + 8.49641i −0.209932 + 0.363613i
\(547\) −6.10258 10.5700i −0.260927 0.451939i 0.705561 0.708649i \(-0.250695\pi\)
−0.966489 + 0.256710i \(0.917362\pi\)
\(548\) −3.70377 + 6.41512i −0.158217 + 0.274040i
\(549\) 15.6565 27.1179i 0.668204 1.15736i
\(550\) −5.34143 −0.227759
\(551\) −4.38066 2.11804i −0.186622 0.0902317i
\(552\) −26.6756 −1.13539
\(553\) 2.75291 4.76819i 0.117066 0.202764i
\(554\) −0.488934 + 0.846858i −0.0207728 + 0.0359795i
\(555\) 5.74795 + 9.95573i 0.243987 + 0.422597i
\(556\) 3.08571 5.34461i 0.130863 0.226662i
\(557\) −17.5774 30.4450i −0.744779 1.28999i −0.950298 0.311342i \(-0.899222\pi\)
0.205519 0.978653i \(-0.434112\pi\)
\(558\) 46.6257 1.97382
\(559\) −44.3301 −1.87496
\(560\) −0.760896 1.31791i −0.0321537 0.0556919i
\(561\) −19.8407 34.3651i −0.837675 1.45090i
\(562\) 0.699634 0.0295123
\(563\) 17.8406 0.751891 0.375945 0.926642i \(-0.377318\pi\)
0.375945 + 0.926642i \(0.377318\pi\)
\(564\) −5.21600 9.03438i −0.219633 0.380416i
\(565\) −0.770672 + 1.33484i −0.0324224 + 0.0561572i
\(566\) 18.4248 + 31.9127i 0.774452 + 1.34139i
\(567\) 3.54803 6.14537i 0.149003 0.258081i
\(568\) −17.8633 + 30.9402i −0.749529 + 1.29822i
\(569\) 31.6042 1.32492 0.662459 0.749098i \(-0.269513\pi\)
0.662459 + 0.749098i \(0.269513\pi\)
\(570\) −13.0834 + 8.89020i −0.548002 + 0.372370i
\(571\) −4.73053 −0.197967 −0.0989833 0.995089i \(-0.531559\pi\)
−0.0989833 + 0.995089i \(0.531559\pi\)
\(572\) 5.78975 10.0281i 0.242082 0.419298i
\(573\) −3.40926 + 5.90501i −0.142424 + 0.246685i
\(574\) 3.01205 + 5.21702i 0.125721 + 0.217754i
\(575\) 1.42363 2.46580i 0.0593694 0.102831i
\(576\) −27.5810 47.7717i −1.14921 1.99049i
\(577\) 24.4074 1.01609 0.508047 0.861330i \(-0.330368\pi\)
0.508047 + 0.861330i \(0.330368\pi\)
\(578\) 10.2062 0.424522
\(579\) 6.92174 + 11.9888i 0.287658 + 0.498238i
\(580\) 0.324694 + 0.562387i 0.0134822 + 0.0233518i
\(581\) 1.29254 0.0536235
\(582\) 35.1008 1.45497
\(583\) −18.9470 32.8171i −0.784703 1.35915i
\(584\) −5.72377 + 9.91386i −0.236851 + 0.410239i
\(585\) −13.9470 24.1568i −0.576636 0.998763i
\(586\) 2.24052 3.88070i 0.0925551 0.160310i
\(587\) 14.3077 24.7817i 0.590543 1.02285i −0.403616 0.914928i \(-0.632247\pi\)
0.994159 0.107922i \(-0.0344197\pi\)
\(588\) 11.7507 0.484590
\(589\) −22.4578 + 15.2602i −0.925358 + 0.628785i
\(590\) −12.1900 −0.501853
\(591\) 29.2888 50.7297i 1.20478 2.08674i
\(592\) −4.71225 + 8.16186i −0.193672 + 0.335450i
\(593\) −1.85756 3.21738i −0.0762807 0.132122i 0.825362 0.564604i \(-0.190971\pi\)
−0.901642 + 0.432482i \(0.857638\pi\)
\(594\) 26.7358 46.3077i 1.09698 1.90003i
\(595\) 0.884350 + 1.53174i 0.0362548 + 0.0627952i
\(596\) −2.19492 −0.0899076
\(597\) −18.7430 −0.767099
\(598\) −7.52423 13.0324i −0.307689 0.532933i
\(599\) −3.54970 6.14826i −0.145037 0.251211i 0.784350 0.620319i \(-0.212997\pi\)
−0.929387 + 0.369108i \(0.879663\pi\)
\(600\) 9.36887 0.382482
\(601\) −11.0596 −0.451131 −0.225566 0.974228i \(-0.572423\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(602\) 3.62329 + 6.27572i 0.147674 + 0.255779i
\(603\) −26.6374 + 46.1373i −1.08476 + 1.87886i
\(604\) −2.76778 4.79394i −0.112619 0.195063i
\(605\) −4.55836 + 7.89531i −0.185324 + 0.320990i
\(606\) −1.76231 + 3.05242i −0.0715891 + 0.123996i
\(607\) 27.1193 1.10074 0.550369 0.834921i \(-0.314487\pi\)
0.550369 + 0.834921i \(0.314487\pi\)
\(608\) 12.4564 + 6.02266i 0.505174 + 0.244251i
\(609\) −2.07214 −0.0839673
\(610\) −2.96655 + 5.13821i −0.120112 + 0.208040i
\(611\) 13.0588 22.6185i 0.528302 0.915046i
\(612\) 5.30798 + 9.19369i 0.214562 + 0.371633i
\(613\) −20.9156 + 36.2268i −0.844772 + 1.46319i 0.0410468 + 0.999157i \(0.486931\pi\)
−0.885819 + 0.464031i \(0.846403\pi\)
\(614\) 12.1127 + 20.9797i 0.488827 + 0.846673i
\(615\) −25.3028 −1.02031
\(616\) −8.40062 −0.338471
\(617\) 8.85262 + 15.3332i 0.356393 + 0.617291i 0.987355 0.158523i \(-0.0506731\pi\)
−0.630962 + 0.775813i \(0.717340\pi\)
\(618\) −6.06286 10.5012i −0.243884 0.422420i
\(619\) −39.8064 −1.59995 −0.799976 0.600032i \(-0.795155\pi\)
−0.799976 + 0.600032i \(0.795155\pi\)
\(620\) 3.62367 0.145530
\(621\) 14.2515 + 24.6844i 0.571895 + 0.990551i
\(622\) −4.57208 + 7.91908i −0.183324 + 0.317526i
\(623\) 2.41604 + 4.18471i 0.0967966 + 0.167657i
\(624\) 16.8914 29.2568i 0.676198 1.17121i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −28.5732 −1.14201
\(627\) 4.35919 + 59.4137i 0.174089 + 2.37275i
\(628\) 2.01072 0.0802366
\(629\) 5.47681 9.48611i 0.218375 0.378236i
\(630\) −2.27989 + 3.94888i −0.0908330 + 0.157327i
\(631\) −23.0990 40.0087i −0.919557 1.59272i −0.800088 0.599882i \(-0.795214\pi\)
−0.119469 0.992838i \(-0.538119\pi\)
\(632\) −13.8944 + 24.0659i −0.552691 + 0.957288i
\(633\) −19.3392 33.4965i −0.768664 1.33137i
\(634\) −1.23740 −0.0491433
\(635\) 2.30549 0.0914905
\(636\) 7.48829 + 12.9701i 0.296930 + 0.514298i
\(637\) 14.7095 + 25.4776i 0.582813 + 1.00946i
\(638\) −5.96262 −0.236062
\(639\) 73.0340 2.88918
\(640\) 2.05176 + 3.55376i 0.0811030 + 0.140475i
\(641\) −3.30674 + 5.72744i −0.130608 + 0.226220i −0.923911 0.382607i \(-0.875026\pi\)
0.793303 + 0.608827i \(0.208360\pi\)
\(642\) 17.2673 + 29.9079i 0.681487 + 1.18037i
\(643\) 15.3076 26.5135i 0.603673 1.04559i −0.388587 0.921412i \(-0.627037\pi\)
0.992260 0.124180i \(-0.0396300\pi\)
\(644\) 0.504503 0.873824i 0.0198802 0.0344335i
\(645\) −30.4375 −1.19847
\(646\) 13.5691 + 6.56063i 0.533868 + 0.258125i
\(647\) −11.8979 −0.467753 −0.233877 0.972266i \(-0.575141\pi\)
−0.233877 + 0.972266i \(0.575141\pi\)
\(648\) −17.9075 + 31.0167i −0.703474 + 1.21845i
\(649\) −22.9548 + 39.7588i −0.901053 + 1.56067i
\(650\) 2.64263 + 4.57716i 0.103652 + 0.179531i
\(651\) −5.78140 + 10.0137i −0.226591 + 0.392467i
\(652\) 1.93509 + 3.35167i 0.0757839 + 0.131262i
\(653\) −1.42899 −0.0559207 −0.0279604 0.999609i \(-0.508901\pi\)
−0.0279604 + 0.999609i \(0.508901\pi\)
\(654\) −20.1171 −0.786640
\(655\) 6.45905 + 11.1874i 0.252376 + 0.437128i
\(656\) −10.3718 17.9645i −0.404950 0.701395i
\(657\) 23.4015 0.912981
\(658\) −4.26941 −0.166439
\(659\) 12.2485 + 21.2150i 0.477134 + 0.826420i 0.999657 0.0262051i \(-0.00834231\pi\)
−0.522523 + 0.852625i \(0.675009\pi\)
\(660\) 3.97530 6.88542i 0.154738 0.268015i
\(661\) 1.61303 + 2.79385i 0.0627396 + 0.108668i 0.895689 0.444681i \(-0.146683\pi\)
−0.832949 + 0.553349i \(0.813350\pi\)
\(662\) 18.3588 31.7984i 0.713535 1.23588i
\(663\) −19.6320 + 34.0037i −0.762445 + 1.32059i
\(664\) −6.52366 −0.253167
\(665\) −0.194300 2.64822i −0.00753462 0.102693i
\(666\) 28.2389 1.09423
\(667\) 1.58919 2.75256i 0.0615338 0.106580i
\(668\) −4.78636 + 8.29023i −0.185190 + 0.320758i
\(669\) −34.3379 59.4750i −1.32758 2.29944i
\(670\) 5.04717 8.74196i 0.194989 0.337731i
\(671\) 11.1725 + 19.3514i 0.431311 + 0.747052i
\(672\) 5.89213 0.227294
\(673\) 37.1424 1.43173 0.715866 0.698237i \(-0.246032\pi\)
0.715866 + 0.698237i \(0.246032\pi\)
\(674\) 12.3350 + 21.3649i 0.475127 + 0.822944i
\(675\) −5.00536 8.66954i −0.192656 0.333691i
\(676\) −3.89518 −0.149815
\(677\) −24.7550 −0.951412 −0.475706 0.879604i \(-0.657807\pi\)
−0.475706 + 0.879604i \(0.657807\pi\)
\(678\) 2.79669 + 4.84402i 0.107406 + 0.186033i
\(679\) −2.94614 + 5.10287i −0.113063 + 0.195830i
\(680\) −4.46346 7.73095i −0.171166 0.296468i
\(681\) −27.5957 + 47.7972i −1.05747 + 1.83159i
\(682\) −16.6361 + 28.8145i −0.637028 + 1.10337i
\(683\) 40.1153 1.53497 0.767484 0.641068i \(-0.221508\pi\)
0.767484 + 0.641068i \(0.221508\pi\)
\(684\) −1.16621 15.8949i −0.0445912 0.607757i
\(685\) −12.7335 −0.486524
\(686\) 4.94370 8.56274i 0.188751 0.326927i
\(687\) 14.3461 24.8482i 0.547340 0.948020i
\(688\) −12.4766 21.6100i −0.475664 0.823875i
\(689\) −18.7477 + 32.4720i −0.714230 + 1.23708i
\(690\) −5.16621 8.94814i −0.196674 0.340650i
\(691\) 39.4963 1.50251 0.751254 0.660013i \(-0.229449\pi\)
0.751254 + 0.660013i \(0.229449\pi\)
\(692\) 13.2533 0.503816
\(693\) 8.58645 + 14.8722i 0.326172 + 0.564947i
\(694\) 4.89545 + 8.47917i 0.185829 + 0.321865i
\(695\) 10.6087 0.402410
\(696\) 10.4584 0.396426
\(697\) 12.0546 + 20.8792i 0.456600 + 0.790855i
\(698\) 7.09879 12.2955i 0.268693 0.465390i
\(699\) −23.9203 41.4312i −0.904748 1.56707i
\(700\) −0.177189 + 0.306901i −0.00669712 + 0.0115997i
\(701\) −0.0109776 + 0.0190137i −0.000414618 + 0.000718139i −0.866233 0.499641i \(-0.833465\pi\)
0.865818 + 0.500359i \(0.166799\pi\)
\(702\) −52.9092 −1.99693
\(703\) −13.6016 + 9.24234i −0.512994 + 0.348581i
\(704\) 39.3637 1.48357
\(705\) 8.96630 15.5301i 0.337690 0.584897i
\(706\) −7.02535 + 12.1683i −0.264402 + 0.457958i
\(707\) −0.295835 0.512402i −0.0111260 0.0192708i
\(708\) 9.07226 15.7136i 0.340957 0.590554i
\(709\) 8.90087 + 15.4168i 0.334279 + 0.578989i 0.983346 0.181743i \(-0.0581738\pi\)
−0.649067 + 0.760731i \(0.724840\pi\)
\(710\) −13.8383 −0.519340
\(711\) 56.8071 2.13043
\(712\) −12.1942 21.1209i −0.456996 0.791540i
\(713\) −8.86789 15.3596i −0.332105 0.575223i
\(714\) 6.41844 0.240204
\(715\) 19.9052 0.744410
\(716\) −0.677477 1.17342i −0.0253185 0.0438529i
\(717\) 35.7448 61.9118i 1.33491 2.31214i
\(718\) 0.0659833 + 0.114286i 0.00246247 + 0.00426513i
\(719\) −9.40515 + 16.2902i −0.350753 + 0.607522i −0.986382 0.164473i \(-0.947408\pi\)
0.635629 + 0.771995i \(0.280741\pi\)
\(720\) 7.85065 13.5977i 0.292576 0.506757i
\(721\) 2.03552 0.0758066
\(722\) −14.0526 17.7347i −0.522983 0.660016i
\(723\) 40.1294 1.49243
\(724\) −6.49774 + 11.2544i −0.241487 + 0.418267i
\(725\) −0.558149 + 0.966742i −0.0207291 + 0.0359039i
\(726\) 16.5419 + 28.6513i 0.613926 + 1.06335i
\(727\) −2.50151 + 4.33274i −0.0927758 + 0.160692i −0.908678 0.417497i \(-0.862907\pi\)
0.815902 + 0.578190i \(0.196241\pi\)
\(728\) 4.15613 + 7.19864i 0.154037 + 0.266799i
\(729\) −18.2986 −0.677725
\(730\) −4.43405 −0.164112
\(731\) 14.5009 + 25.1162i 0.536334 + 0.928957i
\(732\) −4.41565 7.64812i −0.163207 0.282683i
\(733\) −23.5259 −0.868950 −0.434475 0.900684i \(-0.643066\pi\)
−0.434475 + 0.900684i \(0.643066\pi\)
\(734\) −13.9809 −0.516046
\(735\) 10.0997 + 17.4932i 0.372533 + 0.645246i
\(736\) −4.51887 + 7.82691i −0.166568 + 0.288504i
\(737\) −19.0085 32.9237i −0.700187 1.21276i
\(738\) −31.0772 + 53.8274i −1.14397 + 1.98141i
\(739\) 18.6918 32.3752i 0.687590 1.19094i −0.285026 0.958520i \(-0.592002\pi\)
0.972615 0.232421i \(-0.0746646\pi\)
\(740\) 2.19468 0.0806779
\(741\) 48.7559 33.1299i 1.79109 1.21706i
\(742\) 6.12932 0.225014
\(743\) −5.19430 + 8.99679i −0.190560 + 0.330060i −0.945436 0.325808i \(-0.894364\pi\)
0.754876 + 0.655868i \(0.227697\pi\)
\(744\) 29.1797 50.5407i 1.06978 1.85291i
\(745\) −1.88653 3.26757i −0.0691173 0.119715i
\(746\) 8.64539 14.9742i 0.316530 0.548246i
\(747\) 6.66797 + 11.5493i 0.243968 + 0.422566i
\(748\) −7.57556 −0.276990
\(749\) −5.79725 −0.211827
\(750\) 1.81445 + 3.14272i 0.0662544 + 0.114756i
\(751\) 15.6413 + 27.0915i 0.570758 + 0.988581i 0.996488 + 0.0837314i \(0.0266838\pi\)
−0.425731 + 0.904850i \(0.639983\pi\)
\(752\) 14.7014 0.536105
\(753\) −52.7927 −1.92387
\(754\) 2.94996 + 5.10947i 0.107431 + 0.186076i
\(755\) 4.75781 8.24077i 0.173154 0.299912i
\(756\) −1.77379 3.07230i −0.0645122 0.111738i
\(757\) 6.31205 10.9328i 0.229415 0.397359i −0.728220 0.685344i \(-0.759652\pi\)
0.957635 + 0.287985i \(0.0929853\pi\)
\(758\) −3.92419 + 6.79689i −0.142533 + 0.246874i
\(759\) −38.9137 −1.41248
\(760\) 0.980664 + 13.3660i 0.0355724 + 0.484836i
\(761\) 11.5495 0.418668 0.209334 0.977844i \(-0.432870\pi\)
0.209334 + 0.977844i \(0.432870\pi\)
\(762\) 4.18320 7.24551i 0.151541 0.262477i
\(763\) 1.68850 2.92457i 0.0611279 0.105877i
\(764\) 0.650861 + 1.12732i 0.0235473 + 0.0407851i
\(765\) −9.12440 + 15.8039i −0.329893 + 0.571392i
\(766\) −1.70849 2.95918i −0.0617301 0.106920i
\(767\) 45.4267 1.64026
\(768\) −38.5951 −1.39268
\(769\) 13.4603 + 23.3140i 0.485392 + 0.840724i 0.999859 0.0167864i \(-0.00534353\pi\)
−0.514467 + 0.857510i \(0.672010\pi\)
\(770\) −1.62693 2.81793i −0.0586306 0.101551i
\(771\) −17.3067 −0.623286
\(772\) 2.64286 0.0951184
\(773\) −10.6666 18.4750i −0.383649 0.664500i 0.607932 0.793989i \(-0.291999\pi\)
−0.991581 + 0.129489i \(0.958666\pi\)
\(774\) −37.3838 + 64.7506i −1.34373 + 2.32741i