Properties

Label 95.2.e.c.26.3
Level $95$
Weight $2$
Character 95.26
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 26.3
Root \(-1.02359 - 1.77290i\) of defining polynomial
Character \(\chi\) \(=\) 95.26
Dual form 95.2.e.c.11.3

$q$-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 \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.595455 + 1.03136i 0.421050 + 0.729280i 0.996042 0.0888786i \(-0.0283283\pi\)
−0.574992 + 0.818159i \(0.694995\pi\)
\(3\) −1.52359 2.63893i −0.879643 1.52359i −0.851734 0.523975i \(-0.824448\pi\)
−0.0279089 0.999610i \(-0.508885\pi\)
\(4\) 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 0.374868 + 0.927078i \(0.377688\pi\)
−0.990307 + 0.138894i \(0.955645\pi\)
\(14\) −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 0.634523 0.772904i \(-0.281197\pi\)
−0.986616 + 0.163061i \(0.947863\pi\)
\(18\) −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 −0.678566 0.734540i \(-0.737398\pi\)
0.975413 + 0.220386i \(0.0707315\pi\)
\(24\) −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 −0.913184 0.407547i \(-0.866384\pi\)
0.809538 + 0.587067i \(0.199717\pi\)
\(30\) −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 0.983503 + 0.180893i \(0.0578987\pi\)
−0.335094 + 0.942185i \(0.608768\pi\)
\(42\) −1.10532 + 1.91447i −0.170555 + 0.295409i
\(43\) 4.99438 + 8.65053i 0.761637 + 1.31919i 0.942007 + 0.335594i \(0.108937\pi\)
−0.180370 + 0.983599i \(0.557730\pi\)
\(44\) 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 −0.567595 0.823308i \(-0.692126\pi\)
0.996803 + 0.0798983i \(0.0254596\pi\)
\(48\) 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 0.415188 + 0.909736i \(0.363716\pi\)
−0.995448 + 0.0953049i \(0.969617\pi\)
\(54\) 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 −0.978932 0.204187i \(-0.934545\pi\)
0.312634 0.949874i \(-0.398789\pi\)
\(60\) 0.886322 + 1.53515i 0.114424 + 0.198188i
\(61\) 2.49099 4.31453i 0.318939 0.552419i −0.661328 0.750097i \(-0.730007\pi\)
0.980267 + 0.197678i \(0.0633401\pi\)
\(62\) −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 0.482023 + 0.876159i \(0.339902\pi\)
−0.999787 + 0.0206350i \(0.993431\pi\)
\(68\) −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 −0.971995 0.235001i \(-0.924491\pi\)
0.282481 0.959273i \(-0.408843\pi\)
\(72\) −9.66236 + 16.7357i −1.13872 + 1.97232i
\(73\) −1.86162 3.22443i −0.217887 0.377391i 0.736275 0.676682i \(-0.236583\pi\)
−0.954162 + 0.299292i \(0.903250\pi\)
\(74\) −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 −0.999952 0.00976923i \(-0.996890\pi\)
0.491516 0.870869i \(-0.336443\pi\)
\(80\) 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 −0.995979 0.0895879i \(-0.971445\pi\)
0.575575 + 0.817749i \(0.304778\pi\)
\(90\) 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 0.999947 0.0103043i \(-0.00328001\pi\)
−0.508897 + 0.860827i \(0.669947\pi\)
\(98\) −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 −0.840853 0.541264i \(-0.817946\pi\)
0.889175 + 0.457568i \(0.151279\pi\)
\(102\) −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 0.702203 0.711977i \(-0.252200\pi\)
−0.967692 + 0.252137i \(0.918867\pi\)
\(110\) 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 −0.912628 0.408792i \(-0.865950\pi\)
0.810338 + 0.585963i \(0.199283\pi\)
\(128\) 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 0.997112 + 0.0759493i \(0.0241987\pi\)
−0.432782 + 0.901499i \(0.642468\pi\)
\(132\) −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 −0.454722 0.890633i \(-0.650261\pi\)
0.998672 0.0515159i \(-0.0164053\pi\)
\(138\) −5.16621 8.94814i −0.439777 0.761716i
\(139\) −5.30433 + 9.18738i −0.449908 + 0.779263i −0.998380 0.0569059i \(-0.981876\pi\)
0.548472 + 0.836169i \(0.315210\pi\)
\(140\) 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 0.778344 0.627837i \(-0.216060\pi\)
−0.932895 + 0.360147i \(0.882726\pi\)
\(150\) 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 0.926712 0.375773i \(-0.122623\pi\)
−0.788785 + 0.614669i \(0.789290\pi\)
\(158\) 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 −0.349474 0.936946i \(-0.613640\pi\)
0.986156 0.165820i \(-0.0530271\pi\)
\(168\) 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 0.865992 + 0.500057i \(0.166688\pi\)
6.58713e−5 1.00000i \(0.499979\pi\)
\(174\) 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 −0.0676258 0.997711i \(-0.521542\pi\)
0.897856 0.440290i \(-0.145124\pi\)
\(182\) 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 0.936125 0.351669i \(-0.114386\pi\)
−0.772616 + 0.634873i \(0.781052\pi\)
\(194\) −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 −0.736186 0.676779i \(-0.763375\pi\)
0.954201 + 0.299167i \(0.0967087\pi\)
\(200\) −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 0.560531 0.828133i \(-0.310597\pi\)
−0.997450 + 0.0713679i \(0.977264\pi\)
\(212\) 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 −0.945566 0.325430i \(-0.894491\pi\)
0.190952 0.981599i \(-0.438842\pi\)
\(224\) −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 −0.999863 0.0165573i \(-0.994729\pi\)
0.485592 0.874185i \(-0.338604\pi\)
\(234\) 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 −0.996341 0.0854634i \(-0.972763\pi\)
0.572184 + 0.820125i \(0.306096\pi\)
\(242\) 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 −0.451716 0.892162i \(-0.649188\pi\)
0.998493 0.0548830i \(-0.0174786\pi\)
\(252\) −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 −0.763759 0.645502i \(-0.776648\pi\)
0.940900 + 0.338683i \(0.109982\pi\)
\(258\) 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 0.765532 0.643398i \(-0.222476\pi\)
−0.939965 + 0.341272i \(0.889142\pi\)
\(264\) −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 0.956284 + 0.292440i \(0.0944672\pi\)
−0.224881 + 0.974386i \(0.572199\pi\)
\(270\) 5.96093 10.3246i 0.362771 0.628338i
\(271\) 10.6497 + 18.4459i 0.646926 + 1.12051i 0.983853 + 0.178978i \(0.0572791\pi\)
−0.336927 + 0.941531i \(0.609388\pi\)
\(272\) 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 −0.857131 0.515099i \(-0.827755\pi\)
0.874654 + 0.484748i \(0.161089\pi\)
\(282\) −10.6780 18.4949i −0.635869 1.10136i
\(283\) −15.4712 26.7969i −0.919667 1.59291i −0.799921 0.600105i \(-0.795125\pi\)
−0.119746 0.992805i \(-0.538208\pi\)
\(284\) −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 −0.995422 0.0955798i \(-0.969529\pi\)
0.414936 0.909850i \(-0.363804\pi\)
\(308\) −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 0.297486 + 0.954726i \(0.403852\pi\)
−0.975560 + 0.219733i \(0.929481\pi\)
\(314\) −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 −0.880246 0.474517i \(-0.842623\pi\)
0.851067 + 0.525057i \(0.175956\pi\)
\(318\) 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 −0.997122 0.0758124i \(-0.975845\pi\)
0.432906 0.901439i \(-0.357488\pi\)
\(338\) 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 0.734340 0.678782i \(-0.237492\pi\)
−0.955013 + 0.296566i \(0.904159\pi\)
\(348\) 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 0.864560 0.502530i \(-0.167597\pi\)
−0.867484 + 0.497465i \(0.834264\pi\)
\(360\) 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 −0.977573 0.210597i \(-0.932459\pi\)
0.671169 + 0.741305i \(0.265793\pi\)
\(368\) 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 0.900348 0.435171i \(-0.143312\pi\)
−0.827043 + 0.562139i \(0.809979\pi\)
\(384\) 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 −0.774542 0.632523i \(-0.782020\pi\)
0.935052 + 0.354512i \(0.115353\pi\)
\(390\) 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 0.939382 + 0.342871i \(0.111399\pi\)
−0.172756 + 0.984965i \(0.555267\pi\)
\(398\) 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 −0.944067 0.329754i \(-0.893034\pi\)
0.186458 0.982463i \(-0.440299\pi\)
\(402\) 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 −0.619419 0.785060i \(-0.712632\pi\)
0.989592 + 0.143903i \(0.0459652\pi\)
\(410\) 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 0.977571 + 0.210608i \(0.0675443\pi\)
−0.306394 + 0.951905i \(0.599122\pi\)
\(422\) 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 −0.625722 0.780046i \(-0.715195\pi\)
0.988401 + 0.151868i \(0.0485288\pi\)
\(432\) 12.5040 + 21.6575i 0.601598 + 1.04200i
\(433\) 0.485420 0.840772i 0.0233278 0.0404049i −0.854126 0.520066i \(-0.825907\pi\)
0.877454 + 0.479661i \(0.159241\pi\)
\(434\) 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 0.981954 + 0.189120i \(0.0605636\pi\)
−0.327194 + 0.944957i \(0.606103\pi\)
\(440\) −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 −0.742928 0.669372i \(-0.766563\pi\)
0.951157 + 0.308708i \(0.0998966\pi\)
\(444\) 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 0.792183 0.610284i \(-0.208945\pi\)
−0.924613 + 0.380908i \(0.875611\pi\)
\(462\) −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 −0.743825 0.668375i \(-0.766990\pi\)
0.950742 + 0.309984i \(0.100324\pi\)
\(480\) 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 0.881295 0.472566i \(-0.156672\pi\)
−0.849902 + 0.526941i \(0.823339\pi\)
\(492\) −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 0.990028 0.140871i \(-0.0449902\pi\)
−0.617012 + 0.786954i \(0.711657\pi\)
\(500\) 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 −0.986011 0.166679i \(-0.946696\pi\)
0.637354 + 0.770571i \(0.280029\pi\)
\(504\) 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 −0.571879 0.820338i \(-0.693785\pi\)
0.996373 + 0.0850929i \(0.0271187\pi\)
\(510\) 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 −0.929433 0.368990i \(-0.879704\pi\)
0.784272 + 0.620418i \(0.213037\pi\)
\(524\) 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 −0.0668435 + 0.997763i \(0.521293\pi\)
−0.830667 + 0.556770i \(0.812040\pi\)
\(542\) −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 −0.966489 0.256710i \(-0.917362\pi\)
0.705561 + 0.708649i \(0.250695\pi\)
\(548\) −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 0.205519 + 0.978653i \(0.434112\pi\)
−0.950298 + 0.311342i \(0.899222\pi\)
\(558\) 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 0.994159 + 0.107922i \(0.0344197\pi\)
−0.403616 + 0.914928i \(0.632247\pi\)
\(588\) 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 −0.901642 0.432482i \(-0.857638\pi\)
0.825362 + 0.564604i \(0.190971\pi\)
\(594\) 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 −0.929387 0.369108i \(-0.879663\pi\)
0.784350 + 0.620319i \(0.212997\pi\)
\(600\) 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 −0.885819 0.464031i \(-0.846403\pi\)
0.0410468 0.999157i \(-0.486931\pi\)
\(614\) 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 −0.630962 0.775813i \(-0.717340\pi\)
0.987355 + 0.158523i \(0.0506731\pi\)
\(618\) −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 −0.119469 + 0.992838i \(0.538119\pi\)
−0.800088 + 0.599882i \(0.795214\pi\)
\(632\) −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 0.793303 0.608827i \(-0.208360\pi\)
−0.923911 + 0.382607i \(0.875026\pi\)
\(642\) 17.2673 29.9079i 0.681487 1.18037i
\(643\) 15.3076 + 26.5135i 0.603673 + 1.04559i 0.992260 + 0.124180i \(0.0396300\pi\)
−0.388587 + 0.921412i \(0.627037\pi\)
\(644\) 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 −0.522523 0.852625i \(-0.675009\pi\)
0.999657 + 0.0262051i \(0.00834231\pi\)
\(660\) 3.97530 + 6.88542i 0.154738 + 0.268015i
\(661\) 1.61303 2.79385i 0.0627396 0.108668i −0.832949 0.553349i \(-0.813350\pi\)
0.895689 + 0.444681i \(0.146683\pi\)
\(662\) 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 0.865818 0.500359i \(-0.166799\pi\)
−0.866233 + 0.499641i \(0.833465\pi\)
\(702\) −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 −0.649067 0.760731i \(-0.724840\pi\)
0.983346 + 0.181743i \(0.0581738\pi\)
\(710\) −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 0.635629 0.771995i \(-0.280741\pi\)
−0.986382 + 0.164473i \(0.947408\pi\)
\(720\) 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 0.815902 0.578190i \(-0.196241\pi\)
−0.908678 + 0.417497i \(0.862907\pi\)
\(728\) 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 0.972615 + 0.232421i \(0.0746646\pi\)
−0.285026 + 0.958520i \(0.592002\pi\)
\(740\) 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 0.754876 0.655868i \(-0.227697\pi\)
−0.945436 + 0.325808i \(0.894364\pi\)
\(744\) 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 −0.425731 0.904850i \(-0.639983\pi\)
0.996488 0.0837314i \(-0.0266838\pi\)
\(752\) 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 0.957635 0.287985i \(-0.0929853\pi\)
−0.728220 + 0.685344i \(0.759652\pi\)
\(758\) −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 −0.514467 0.857510i \(-0.672010\pi\)
0.999859 + 0.0167864i \(0.00534353\pi\)
\(770\) −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 −0.991581 0.129489i \(-0.958666\pi\)
0.607932 + 0.793989i \(0.291999\pi\)
\(774\) −37.3838 64.7506i −1.34373 2.32741i