Properties

Label 225.2.k.b.49.2
Level $225$
Weight $2$
Character 225.49
Analytic conductor $1.797$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(2.17840 + 0.583700i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.2.k.b.124.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.80664 + 1.04307i) q^{2} +(-1.38276 + 1.04307i) q^{3} +(1.17597 - 2.03684i) q^{4} +(1.41016 - 3.32675i) q^{6} +(3.53869 - 2.04307i) q^{7} +0.734191i q^{8} +(0.824030 - 2.88461i) q^{9} +O(q^{10})\) \(q+(-1.80664 + 1.04307i) q^{2} +(-1.38276 + 1.04307i) q^{3} +(1.17597 - 2.03684i) q^{4} +(1.41016 - 3.32675i) q^{6} +(3.53869 - 2.04307i) q^{7} +0.734191i q^{8} +(0.824030 - 2.88461i) q^{9} +(0.675970 + 1.17081i) q^{11} +(0.498476 + 4.04307i) q^{12} +(0.561237 + 0.324030i) q^{13} +(-4.26210 + 7.38217i) q^{14} +(1.58613 + 2.74726i) q^{16} -1.35194i q^{17} +(1.52011 + 6.07097i) q^{18} -0.648061 q^{19} +(-2.76210 + 6.51615i) q^{21} +(-2.44247 - 1.41016i) q^{22} +(4.14827 + 2.39500i) q^{23} +(-0.765809 - 1.01521i) q^{24} -1.35194 q^{26} +(1.86940 + 4.84823i) q^{27} -9.61033i q^{28} +(1.93807 + 3.35683i) q^{29} +(3.84823 - 6.66533i) q^{31} +(-7.00279 - 4.04307i) q^{32} +(-2.15594 - 0.913870i) q^{33} +(1.41016 + 2.44247i) q^{34} +(-4.90645 - 5.07063i) q^{36} +7.52420i q^{37} +(1.17081 - 0.675970i) q^{38} +(-1.11404 + 0.137352i) q^{39} +(0.0898394 - 0.155606i) q^{41} +(-1.80664 - 14.6534i) q^{42} +(0.710419 - 0.410161i) q^{43} +3.17968 q^{44} -9.99258 q^{46} +(9.44526 - 5.45323i) q^{47} +(-5.05880 - 2.14435i) q^{48} +(4.84823 - 8.39738i) q^{49} +(1.41016 + 1.86940i) q^{51} +(1.32000 - 0.762100i) q^{52} -4.17226i q^{53} +(-8.43436 - 6.80911i) q^{54} +(1.50000 + 2.59808i) q^{56} +(0.896110 - 0.675970i) q^{57} +(-7.00279 - 4.04307i) q^{58} +(2.08613 - 3.61328i) q^{59} +(1.91016 + 3.30850i) q^{61} +16.0558i q^{62} +(-2.97746 - 11.8913i) q^{63} +10.5242 q^{64} +(4.84823 - 0.597746i) q^{66} +(-7.05113 - 4.07097i) q^{67} +(-2.75368 - 1.58984i) q^{68} +(-8.23419 + 1.01521i) q^{69} -6.11644 q^{71} +(2.11785 + 0.604996i) q^{72} +12.3445i q^{73} +(-7.84823 - 13.5935i) q^{74} +(-0.762100 + 1.32000i) q^{76} +(4.78410 + 2.76210i) q^{77} +(1.86940 - 1.41016i) q^{78} +(5.17226 + 8.95862i) q^{79} +(-7.64195 - 4.75401i) q^{81} +0.374833i q^{82} +(10.6161 - 6.12920i) q^{83} +(10.0242 + 13.2887i) q^{84} +(-0.855648 + 1.48203i) q^{86} +(-6.18127 - 2.62015i) q^{87} +(-0.859601 + 0.496291i) q^{88} +3.00000 q^{89} +2.64806 q^{91} +(9.75648 - 5.63290i) q^{92} +(1.63121 + 13.2305i) q^{93} +(-11.3761 + 19.7041i) q^{94} +(13.9003 - 1.71380i) q^{96} +(-11.7606 + 6.79001i) q^{97} +20.2281i q^{98} +(3.93436 - 0.985122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80664 + 1.04307i −1.27749 + 0.737558i −0.976386 0.216033i \(-0.930688\pi\)
−0.301103 + 0.953592i \(0.597355\pi\)
\(3\) −1.38276 + 1.04307i −0.798335 + 0.602214i
\(4\) 1.17597 2.03684i 0.587985 1.01842i
\(5\) 0 0
\(6\) 1.41016 3.32675i 0.575696 1.35814i
\(7\) 3.53869 2.04307i 1.33750 0.772206i 0.351064 0.936351i \(-0.385820\pi\)
0.986436 + 0.164145i \(0.0524866\pi\)
\(8\) 0.734191i 0.259576i
\(9\) 0.824030 2.88461i 0.274677 0.961537i
\(10\) 0 0
\(11\) 0.675970 + 1.17081i 0.203813 + 0.353014i 0.949754 0.312998i \(-0.101333\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(12\) 0.498476 + 4.04307i 0.143898 + 1.16713i
\(13\) 0.561237 + 0.324030i 0.155659 + 0.0898699i 0.575806 0.817586i \(-0.304688\pi\)
−0.420147 + 0.907456i \(0.638022\pi\)
\(14\) −4.26210 + 7.38217i −1.13909 + 1.97297i
\(15\) 0 0
\(16\) 1.58613 + 2.74726i 0.396533 + 0.686815i
\(17\) 1.35194i 0.327893i −0.986469 0.163947i \(-0.947577\pi\)
0.986469 0.163947i \(-0.0524225\pi\)
\(18\) 1.52011 + 6.07097i 0.358293 + 1.43094i
\(19\) −0.648061 −0.148675 −0.0743377 0.997233i \(-0.523684\pi\)
−0.0743377 + 0.997233i \(0.523684\pi\)
\(20\) 0 0
\(21\) −2.76210 + 6.51615i −0.602740 + 1.42194i
\(22\) −2.44247 1.41016i −0.520736 0.300647i
\(23\) 4.14827 + 2.39500i 0.864974 + 0.499393i 0.865675 0.500607i \(-0.166890\pi\)
−0.000700856 1.00000i \(0.500223\pi\)
\(24\) −0.765809 1.01521i −0.156320 0.207228i
\(25\) 0 0
\(26\) −1.35194 −0.265137
\(27\) 1.86940 + 4.84823i 0.359767 + 0.933042i
\(28\) 9.61033i 1.81618i
\(29\) 1.93807 + 3.35683i 0.359890 + 0.623349i 0.987942 0.154823i \(-0.0494807\pi\)
−0.628052 + 0.778172i \(0.716147\pi\)
\(30\) 0 0
\(31\) 3.84823 6.66533i 0.691163 1.19713i −0.280295 0.959914i \(-0.590432\pi\)
0.971457 0.237215i \(-0.0762345\pi\)
\(32\) −7.00279 4.04307i −1.23793 0.714720i
\(33\) −2.15594 0.913870i −0.375300 0.159084i
\(34\) 1.41016 + 2.44247i 0.241841 + 0.418880i
\(35\) 0 0
\(36\) −4.90645 5.07063i −0.817742 0.845105i
\(37\) 7.52420i 1.23697i 0.785796 + 0.618485i \(0.212253\pi\)
−0.785796 + 0.618485i \(0.787747\pi\)
\(38\) 1.17081 0.675970i 0.189931 0.109657i
\(39\) −1.11404 + 0.137352i −0.178389 + 0.0219939i
\(40\) 0 0
\(41\) 0.0898394 0.155606i 0.0140306 0.0243016i −0.858925 0.512102i \(-0.828867\pi\)
0.872955 + 0.487800i \(0.162200\pi\)
\(42\) −1.80664 14.6534i −0.278771 2.26107i
\(43\) 0.710419 0.410161i 0.108338 0.0625489i −0.444852 0.895604i \(-0.646744\pi\)
0.553190 + 0.833055i \(0.313410\pi\)
\(44\) 3.17968 0.479355
\(45\) 0 0
\(46\) −9.99258 −1.47333
\(47\) 9.44526 5.45323i 1.37773 0.795435i 0.385847 0.922563i \(-0.373909\pi\)
0.991886 + 0.127128i \(0.0405759\pi\)
\(48\) −5.05880 2.14435i −0.730175 0.309510i
\(49\) 4.84823 8.39738i 0.692604 1.19963i
\(50\) 0 0
\(51\) 1.41016 + 1.86940i 0.197462 + 0.261769i
\(52\) 1.32000 0.762100i 0.183050 0.105684i
\(53\) 4.17226i 0.573104i −0.958065 0.286552i \(-0.907491\pi\)
0.958065 0.286552i \(-0.0925091\pi\)
\(54\) −8.43436 6.80911i −1.14777 0.926602i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 0.896110 0.675970i 0.118693 0.0895344i
\(58\) −7.00279 4.04307i −0.919512 0.530880i
\(59\) 2.08613 3.61328i 0.271591 0.470409i −0.697678 0.716411i \(-0.745784\pi\)
0.969269 + 0.246002i \(0.0791169\pi\)
\(60\) 0 0
\(61\) 1.91016 + 3.30850i 0.244571 + 0.423609i 0.962011 0.273011i \(-0.0880195\pi\)
−0.717440 + 0.696620i \(0.754686\pi\)
\(62\) 16.0558i 2.03909i
\(63\) −2.97746 11.8913i −0.375124 1.49816i
\(64\) 10.5242 1.31552
\(65\) 0 0
\(66\) 4.84823 0.597746i 0.596776 0.0735775i
\(67\) −7.05113 4.07097i −0.861433 0.497349i 0.00305885 0.999995i \(-0.499026\pi\)
−0.864492 + 0.502647i \(0.832360\pi\)
\(68\) −2.75368 1.58984i −0.333933 0.192796i
\(69\) −8.23419 + 1.01521i −0.991280 + 0.122217i
\(70\) 0 0
\(71\) −6.11644 −0.725888 −0.362944 0.931811i \(-0.618228\pi\)
−0.362944 + 0.931811i \(0.618228\pi\)
\(72\) 2.11785 + 0.604996i 0.249592 + 0.0712994i
\(73\) 12.3445i 1.44482i 0.691467 + 0.722408i \(0.256965\pi\)
−0.691467 + 0.722408i \(0.743035\pi\)
\(74\) −7.84823 13.5935i −0.912338 1.58022i
\(75\) 0 0
\(76\) −0.762100 + 1.32000i −0.0874188 + 0.151414i
\(77\) 4.78410 + 2.76210i 0.545198 + 0.314770i
\(78\) 1.86940 1.41016i 0.211668 0.159669i
\(79\) 5.17226 + 8.95862i 0.581925 + 1.00792i 0.995251 + 0.0973403i \(0.0310335\pi\)
−0.413326 + 0.910583i \(0.635633\pi\)
\(80\) 0 0
\(81\) −7.64195 4.75401i −0.849105 0.528224i
\(82\) 0.374833i 0.0413934i
\(83\) 10.6161 6.12920i 1.16527 0.672767i 0.212706 0.977116i \(-0.431772\pi\)
0.952560 + 0.304350i \(0.0984392\pi\)
\(84\) 10.0242 + 13.2887i 1.09373 + 1.44992i
\(85\) 0 0
\(86\) −0.855648 + 1.48203i −0.0922669 + 0.159811i
\(87\) −6.18127 2.62015i −0.662702 0.280910i
\(88\) −0.859601 + 0.496291i −0.0916338 + 0.0529048i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 2.64806 0.277592
\(92\) 9.75648 5.63290i 1.01718 0.587271i
\(93\) 1.63121 + 13.2305i 0.169148 + 1.37194i
\(94\) −11.3761 + 19.7041i −1.17336 + 2.03232i
\(95\) 0 0
\(96\) 13.9003 1.71380i 1.41870 0.174914i
\(97\) −11.7606 + 6.79001i −1.19411 + 0.689421i −0.959237 0.282605i \(-0.908802\pi\)
−0.234876 + 0.972025i \(0.575468\pi\)
\(98\) 20.2281i 2.04334i
\(99\) 3.93436 0.985122i 0.395418 0.0990085i
\(100\) 0 0
\(101\) 0.734191 + 1.27166i 0.0730547 + 0.126535i 0.900239 0.435397i \(-0.143392\pi\)
−0.827184 + 0.561931i \(0.810059\pi\)
\(102\) −4.49756 1.90645i −0.445325 0.188767i
\(103\) 6.51615 + 3.76210i 0.642055 + 0.370691i 0.785406 0.618981i \(-0.212454\pi\)
−0.143351 + 0.989672i \(0.545788\pi\)
\(104\) −0.237900 + 0.412055i −0.0233280 + 0.0404053i
\(105\) 0 0
\(106\) 4.35194 + 7.53778i 0.422698 + 0.732134i
\(107\) 1.20999i 0.116974i 0.998288 + 0.0584871i \(0.0186277\pi\)
−0.998288 + 0.0584871i \(0.981372\pi\)
\(108\) 12.0734 + 1.89370i 1.16177 + 0.182221i
\(109\) −14.1042 −1.35094 −0.675469 0.737388i \(-0.736059\pi\)
−0.675469 + 0.737388i \(0.736059\pi\)
\(110\) 0 0
\(111\) −7.84823 10.4041i −0.744921 0.987517i
\(112\) 11.2257 + 6.48113i 1.06072 + 0.612410i
\(113\) −10.3270 5.96227i −0.971478 0.560883i −0.0717915 0.997420i \(-0.522872\pi\)
−0.899687 + 0.436537i \(0.856205\pi\)
\(114\) −0.913870 + 2.15594i −0.0855917 + 0.201922i
\(115\) 0 0
\(116\) 9.11644 0.846440
\(117\) 1.39718 1.35194i 0.129169 0.124987i
\(118\) 8.70388i 0.801257i
\(119\) −2.76210 4.78410i −0.253201 0.438557i
\(120\) 0 0
\(121\) 4.58613 7.94341i 0.416921 0.722128i
\(122\) −6.90195 3.98484i −0.624873 0.360771i
\(123\) 0.0380816 + 0.308874i 0.00343370 + 0.0278502i
\(124\) −9.05080 15.6765i −0.812786 1.40779i
\(125\) 0 0
\(126\) 17.7826 + 18.3776i 1.58420 + 1.63721i
\(127\) 7.07871i 0.628134i −0.949401 0.314067i \(-0.898308\pi\)
0.949401 0.314067i \(-0.101692\pi\)
\(128\) −5.00787 + 2.89130i −0.442637 + 0.255557i
\(129\) −0.554512 + 1.30817i −0.0488221 + 0.115178i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) −4.39672 + 3.31661i −0.382685 + 0.288674i
\(133\) −2.29329 + 1.32403i −0.198853 + 0.114808i
\(134\) 16.9852 1.46729
\(135\) 0 0
\(136\) 0.992582 0.0851132
\(137\) −6.46781 + 3.73419i −0.552582 + 0.319033i −0.750163 0.661253i \(-0.770025\pi\)
0.197581 + 0.980287i \(0.436692\pi\)
\(138\) 13.8173 10.4229i 1.17621 0.887257i
\(139\) 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i \(-0.723151\pi\)
0.984297 + 0.176522i \(0.0564848\pi\)
\(140\) 0 0
\(141\) −7.37243 + 17.3925i −0.620871 + 1.46471i
\(142\) 11.0502 6.37985i 0.927314 0.535385i
\(143\) 0.876139i 0.0732664i
\(144\) 9.23179 2.31154i 0.769316 0.192629i
\(145\) 0 0
\(146\) −12.8761 22.3021i −1.06564 1.84574i
\(147\) 2.05509 + 16.6686i 0.169501 + 1.37480i
\(148\) 15.3256 + 8.84823i 1.25976 + 0.727320i
\(149\) −5.29241 + 9.16673i −0.433571 + 0.750968i −0.997178 0.0750759i \(-0.976080\pi\)
0.563607 + 0.826043i \(0.309413\pi\)
\(150\) 0 0
\(151\) −8.84823 15.3256i −0.720059 1.24718i −0.960976 0.276633i \(-0.910781\pi\)
0.240917 0.970546i \(-0.422552\pi\)
\(152\) 0.475800i 0.0385925i
\(153\) −3.89982 1.11404i −0.315282 0.0900647i
\(154\) −11.5242 −0.928646
\(155\) 0 0
\(156\) −1.03031 + 2.43064i −0.0824910 + 0.194607i
\(157\) 2.19245 + 1.26581i 0.174976 + 0.101023i 0.584930 0.811084i \(-0.301122\pi\)
−0.409954 + 0.912106i \(0.634455\pi\)
\(158\) −18.6888 10.7900i −1.48680 0.858407i
\(159\) 4.35194 + 5.76922i 0.345131 + 0.457529i
\(160\) 0 0
\(161\) 19.5726 1.54254
\(162\) 18.7650 + 0.617748i 1.47432 + 0.0485349i
\(163\) 8.47580i 0.663876i −0.943301 0.331938i \(-0.892298\pi\)
0.943301 0.331938i \(-0.107702\pi\)
\(164\) −0.211297 0.365977i −0.0164995 0.0285780i
\(165\) 0 0
\(166\) −12.7863 + 22.1465i −0.992409 + 1.71890i
\(167\) −11.0281 6.36710i −0.853383 0.492701i 0.00840816 0.999965i \(-0.497324\pi\)
−0.861791 + 0.507264i \(0.830657\pi\)
\(168\) −4.78410 2.02791i −0.369101 0.156457i
\(169\) −6.29001 10.8946i −0.483847 0.838047i
\(170\) 0 0
\(171\) −0.534022 + 1.86940i −0.0408377 + 0.142957i
\(172\) 1.92935i 0.147111i
\(173\) −19.9605 + 11.5242i −1.51757 + 0.876169i −0.517782 + 0.855513i \(0.673242\pi\)
−0.999787 + 0.0206561i \(0.993424\pi\)
\(174\) 13.9003 1.71380i 1.05378 0.129923i
\(175\) 0 0
\(176\) −2.14435 + 3.71413i −0.161637 + 0.279963i
\(177\) 0.884280 + 7.17226i 0.0664666 + 0.539100i
\(178\) −5.41993 + 3.12920i −0.406241 + 0.234543i
\(179\) −2.22808 −0.166534 −0.0832672 0.996527i \(-0.526535\pi\)
−0.0832672 + 0.996527i \(0.526535\pi\)
\(180\) 0 0
\(181\) 0.468382 0.0348146 0.0174073 0.999848i \(-0.494459\pi\)
0.0174073 + 0.999848i \(0.494459\pi\)
\(182\) −4.78410 + 2.76210i −0.354621 + 0.204740i
\(183\) −6.09226 2.58242i −0.450353 0.190898i
\(184\) −1.75839 + 3.04562i −0.129630 + 0.224526i
\(185\) 0 0
\(186\) −16.7473 22.2013i −1.22797 1.62788i
\(187\) 1.58287 0.913870i 0.115751 0.0668288i
\(188\) 25.6513i 1.87081i
\(189\) 16.5205 + 13.3371i 1.20169 + 0.970130i
\(190\) 0 0
\(191\) 10.1140 + 17.5180i 0.731826 + 1.26756i 0.956102 + 0.293034i \(0.0946650\pi\)
−0.224276 + 0.974526i \(0.572002\pi\)
\(192\) −14.5524 + 10.9774i −1.05023 + 0.792227i
\(193\) −17.2593 9.96467i −1.24235 0.717273i −0.272780 0.962076i \(-0.587943\pi\)
−0.969573 + 0.244804i \(0.921277\pi\)
\(194\) 14.1648 24.5342i 1.01698 1.76145i
\(195\) 0 0
\(196\) −11.4027 19.7501i −0.814482 1.41072i
\(197\) 15.5800i 1.11003i −0.831840 0.555015i \(-0.812712\pi\)
0.831840 0.555015i \(-0.187288\pi\)
\(198\) −6.08043 + 5.88356i −0.432118 + 0.418126i
\(199\) −3.58482 −0.254121 −0.127061 0.991895i \(-0.540554\pi\)
−0.127061 + 0.991895i \(0.540554\pi\)
\(200\) 0 0
\(201\) 13.9963 1.72563i 0.987222 0.121716i
\(202\) −2.65284 1.53162i −0.186653 0.107764i
\(203\) 13.7165 + 7.91920i 0.962707 + 0.555819i
\(204\) 5.46598 0.673910i 0.382695 0.0471831i
\(205\) 0 0
\(206\) −15.6965 −1.09362
\(207\) 10.3270 9.99258i 0.717773 0.694532i
\(208\) 2.05582i 0.142545i
\(209\) −0.438069 0.758758i −0.0303019 0.0524844i
\(210\) 0 0
\(211\) −7.49629 + 12.9840i −0.516066 + 0.893852i 0.483760 + 0.875201i \(0.339271\pi\)
−0.999826 + 0.0186518i \(0.994063\pi\)
\(212\) −8.49822 4.90645i −0.583660 0.336976i
\(213\) 8.45755 6.37985i 0.579502 0.437140i
\(214\) −1.26210 2.18602i −0.0862754 0.149433i
\(215\) 0 0
\(216\) −3.55953 + 1.37250i −0.242195 + 0.0933867i
\(217\) 31.4487i 2.13488i
\(218\) 25.4813 14.7116i 1.72581 0.996396i
\(219\) −12.8761 17.0695i −0.870089 1.15345i
\(220\) 0 0
\(221\) 0.438069 0.758758i 0.0294677 0.0510396i
\(222\) 25.0311 + 10.6103i 1.67998 + 0.712119i
\(223\) 23.2363 13.4155i 1.55602 0.898368i 0.558388 0.829580i \(-0.311420\pi\)
0.997631 0.0687878i \(-0.0219131\pi\)
\(224\) −33.0410 −2.20764
\(225\) 0 0
\(226\) 24.8761 1.65474
\(227\) 1.17081 0.675970i 0.0777096 0.0448657i −0.460642 0.887586i \(-0.652381\pi\)
0.538351 + 0.842721i \(0.319047\pi\)
\(228\) −0.323043 2.62015i −0.0213940 0.173524i
\(229\) −4.11775 + 7.13215i −0.272108 + 0.471306i −0.969402 0.245480i \(-0.921054\pi\)
0.697293 + 0.716786i \(0.254388\pi\)
\(230\) 0 0
\(231\) −9.49629 + 1.17081i −0.624810 + 0.0770339i
\(232\) −2.46456 + 1.42291i −0.161806 + 0.0934188i
\(233\) 8.58744i 0.562582i −0.959623 0.281291i \(-0.909237\pi\)
0.959623 0.281291i \(-0.0907626\pi\)
\(234\) −1.11404 + 3.89982i −0.0728270 + 0.254939i
\(235\) 0 0
\(236\) −4.90645 8.49822i −0.319383 0.553187i
\(237\) −16.4964 6.99258i −1.07156 0.454217i
\(238\) 9.98025 + 5.76210i 0.646923 + 0.373501i
\(239\) −11.9623 + 20.7193i −0.773775 + 1.34022i 0.161706 + 0.986839i \(0.448300\pi\)
−0.935480 + 0.353378i \(0.885033\pi\)
\(240\) 0 0
\(241\) 3.12015 + 5.40426i 0.200987 + 0.348119i 0.948847 0.315737i \(-0.102252\pi\)
−0.747860 + 0.663857i \(0.768919\pi\)
\(242\) 19.1345i 1.23001i
\(243\) 15.5257 1.39741i 0.995974 0.0896438i
\(244\) 8.98516 0.575216
\(245\) 0 0
\(246\) −0.390976 0.518303i −0.0249277 0.0330458i
\(247\) −0.363716 0.209991i −0.0231427 0.0133614i
\(248\) 4.89363 + 2.82534i 0.310746 + 0.179409i
\(249\) −8.28630 + 19.5484i −0.525123 + 1.23883i
\(250\) 0 0
\(251\) −28.5726 −1.80349 −0.901743 0.432272i \(-0.857712\pi\)
−0.901743 + 0.432272i \(0.857712\pi\)
\(252\) −27.7221 7.91920i −1.74633 0.498863i
\(253\) 6.47580i 0.407130i
\(254\) 7.38356 + 12.7887i 0.463286 + 0.802434i
\(255\) 0 0
\(256\) −4.49258 + 7.78138i −0.280786 + 0.486336i
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) −0.362697 2.94178i −0.0225805 0.183147i
\(259\) 15.3724 + 26.6258i 0.955196 + 1.65445i
\(260\) 0 0
\(261\) 11.2802 2.82444i 0.698226 0.174828i
\(262\) 12.5168i 0.773289i
\(263\) −27.5991 + 15.9344i −1.70183 + 0.982555i −0.757931 + 0.652335i \(0.773789\pi\)
−0.943904 + 0.330220i \(0.892877\pi\)
\(264\) 0.670955 1.58287i 0.0412944 0.0974188i
\(265\) 0 0
\(266\) 2.76210 4.78410i 0.169355 0.293332i
\(267\) −4.14827 + 3.12920i −0.253870 + 0.191504i
\(268\) −16.5838 + 9.57468i −1.01302 + 0.584867i
\(269\) 31.4971 1.92041 0.960207 0.279289i \(-0.0900987\pi\)
0.960207 + 0.279289i \(0.0900987\pi\)
\(270\) 0 0
\(271\) −3.24030 −0.196834 −0.0984172 0.995145i \(-0.531378\pi\)
−0.0984172 + 0.995145i \(0.531378\pi\)
\(272\) 3.71413 2.14435i 0.225202 0.130020i
\(273\) −3.66162 + 2.76210i −0.221612 + 0.167170i
\(274\) 7.79001 13.4927i 0.470612 0.815123i
\(275\) 0 0
\(276\) −7.61534 + 17.9656i −0.458390 + 1.08140i
\(277\) −4.83660 + 2.79241i −0.290603 + 0.167780i −0.638214 0.769859i \(-0.720326\pi\)
0.347611 + 0.937639i \(0.386993\pi\)
\(278\) 16.6890i 1.00094i
\(279\) −16.0558 16.5931i −0.961237 0.993402i
\(280\) 0 0
\(281\) 12.0521 + 20.8749i 0.718969 + 1.24529i 0.961409 + 0.275124i \(0.0887188\pi\)
−0.242440 + 0.970166i \(0.577948\pi\)
\(282\) −4.82218 39.1120i −0.287157 2.32908i
\(283\) −9.12989 5.27114i −0.542715 0.313337i 0.203463 0.979083i \(-0.434780\pi\)
−0.746179 + 0.665746i \(0.768114\pi\)
\(284\) −7.19275 + 12.4582i −0.426811 + 0.739259i
\(285\) 0 0
\(286\) −0.913870 1.58287i −0.0540383 0.0935970i
\(287\) 0.734191i 0.0433379i
\(288\) −17.4332 + 16.8687i −1.02726 + 0.993999i
\(289\) 15.1723 0.892486
\(290\) 0 0
\(291\) 9.17968 21.6560i 0.538122 1.26950i
\(292\) 25.1438 + 14.5168i 1.47143 + 0.849530i
\(293\) 16.4481 + 9.49629i 0.960906 + 0.554779i 0.896452 0.443141i \(-0.146136\pi\)
0.0644541 + 0.997921i \(0.479469\pi\)
\(294\) −21.0992 27.9705i −1.23053 1.63127i
\(295\) 0 0
\(296\) −5.52420 −0.321088
\(297\) −4.41271 + 5.46598i −0.256052 + 0.317168i
\(298\) 22.0813i 1.27914i
\(299\) 1.55211 + 2.68833i 0.0897607 + 0.155470i
\(300\) 0 0
\(301\) 1.67597 2.90286i 0.0966013 0.167318i
\(302\) 31.9712 + 18.4586i 1.83973 + 1.06217i
\(303\) −2.34163 0.992582i −0.134523 0.0570223i
\(304\) −1.02791 1.78039i −0.0589546 0.102112i
\(305\) 0 0
\(306\) 8.20759 2.05509i 0.469197 0.117482i
\(307\) 29.4791i 1.68246i 0.540679 + 0.841229i \(0.318167\pi\)
−0.540679 + 0.841229i \(0.681833\pi\)
\(308\) 11.2519 6.49629i 0.641137 0.370161i
\(309\) −12.9344 + 1.59470i −0.735810 + 0.0907193i
\(310\) 0 0
\(311\) 4.70628 8.15152i 0.266869 0.462230i −0.701183 0.712982i \(-0.747344\pi\)
0.968052 + 0.250751i \(0.0806776\pi\)
\(312\) −0.100842 0.817917i −0.00570908 0.0463055i
\(313\) −10.0641 + 5.81050i −0.568855 + 0.328429i −0.756692 0.653771i \(-0.773186\pi\)
0.187837 + 0.982200i \(0.439852\pi\)
\(314\) −5.28128 −0.298040
\(315\) 0 0
\(316\) 24.3297 1.36865
\(317\) −7.94984 + 4.58984i −0.446507 + 0.257791i −0.706354 0.707859i \(-0.749661\pi\)
0.259847 + 0.965650i \(0.416328\pi\)
\(318\) −13.8801 5.88356i −0.778355 0.329934i
\(319\) −2.62015 + 4.53824i −0.146700 + 0.254092i
\(320\) 0 0
\(321\) −1.26210 1.67312i −0.0704435 0.0933846i
\(322\) −35.3607 + 20.4155i −1.97057 + 1.13771i
\(323\) 0.876139i 0.0487497i
\(324\) −18.6699 + 9.97484i −1.03721 + 0.554158i
\(325\) 0 0
\(326\) 8.84081 + 15.3127i 0.489647 + 0.848094i
\(327\) 19.5027 14.7116i 1.07850 0.813554i
\(328\) 0.114245 + 0.0659593i 0.00630812 + 0.00364199i
\(329\) 22.2826 38.5946i 1.22848 2.12779i
\(330\) 0 0
\(331\) 3.61033 + 6.25327i 0.198442 + 0.343711i 0.948023 0.318201i \(-0.103079\pi\)
−0.749582 + 0.661912i \(0.769745\pi\)
\(332\) 28.8310i 1.58231i
\(333\) 21.7044 + 6.20017i 1.18939 + 0.339767i
\(334\) 26.5652 1.45358
\(335\) 0 0
\(336\) −22.2826 + 2.74726i −1.21561 + 0.149875i
\(337\) −1.97791 1.14195i −0.107744 0.0622059i 0.445160 0.895451i \(-0.353147\pi\)
−0.552904 + 0.833245i \(0.686480\pi\)
\(338\) 22.7276 + 13.1218i 1.23622 + 0.713731i
\(339\) 20.4987 2.52732i 1.11334 0.137265i
\(340\) 0 0
\(341\) 10.4051 0.563470
\(342\) −0.985122 3.93436i −0.0532693 0.212746i
\(343\) 11.0181i 0.594921i
\(344\) 0.301136 + 0.521583i 0.0162362 + 0.0281219i
\(345\) 0 0
\(346\) 24.0410 41.6402i 1.29245 2.23859i
\(347\) 0.613740 + 0.354343i 0.0329473 + 0.0190221i 0.516383 0.856358i \(-0.327278\pi\)
−0.483436 + 0.875380i \(0.660611\pi\)
\(348\) −12.6058 + 9.50904i −0.675743 + 0.509738i
\(349\) −10.6723 18.4849i −0.571273 0.989474i −0.996436 0.0843569i \(-0.973116\pi\)
0.425163 0.905117i \(-0.360217\pi\)
\(350\) 0 0
\(351\) −0.521796 + 3.32675i −0.0278514 + 0.177569i
\(352\) 10.9320i 0.582675i
\(353\) 8.74408 5.04840i 0.465401 0.268699i −0.248912 0.968526i \(-0.580073\pi\)
0.714312 + 0.699827i \(0.246740\pi\)
\(354\) −9.07871 12.0353i −0.482528 0.639671i
\(355\) 0 0
\(356\) 3.52791 6.11052i 0.186979 0.323857i
\(357\) 8.80944 + 3.73419i 0.466245 + 0.197634i
\(358\) 4.02534 2.32403i 0.212746 0.122829i
\(359\) −30.5578 −1.61278 −0.806388 0.591386i \(-0.798581\pi\)
−0.806388 + 0.591386i \(0.798581\pi\)
\(360\) 0 0
\(361\) −18.5800 −0.977896
\(362\) −0.846198 + 0.488553i −0.0444752 + 0.0256778i
\(363\) 1.94399 + 15.7674i 0.102033 + 0.827576i
\(364\) 3.11404 5.39367i 0.163220 0.282705i
\(365\) 0 0
\(366\) 13.7002 1.68912i 0.716119 0.0882916i
\(367\) −6.21778 + 3.58984i −0.324566 + 0.187388i −0.653426 0.756991i \(-0.726669\pi\)
0.328860 + 0.944379i \(0.393336\pi\)
\(368\) 15.1952i 0.792102i
\(369\) −0.374833 0.387376i −0.0195130 0.0201660i
\(370\) 0 0
\(371\) −8.52420 14.7643i −0.442554 0.766527i
\(372\) 28.8666 + 12.2361i 1.49666 + 0.634414i
\(373\) −18.9872 10.9623i −0.983120 0.567605i −0.0799096 0.996802i \(-0.525463\pi\)
−0.903211 + 0.429197i \(0.858796\pi\)
\(374\) −1.90645 + 3.30207i −0.0985803 + 0.170746i
\(375\) 0 0
\(376\) 4.00371 + 6.93463i 0.206476 + 0.357626i
\(377\) 2.51197i 0.129373i
\(378\) −43.7581 6.86339i −2.25067 0.353014i
\(379\) 17.3929 0.893414 0.446707 0.894680i \(-0.352597\pi\)
0.446707 + 0.894680i \(0.352597\pi\)
\(380\) 0 0
\(381\) 7.38356 + 9.78813i 0.378271 + 0.501461i
\(382\) −36.5449 21.0992i −1.86980 1.07953i
\(383\) 0.412055 + 0.237900i 0.0210550 + 0.0121561i 0.510491 0.859883i \(-0.329464\pi\)
−0.489436 + 0.872039i \(0.662797\pi\)
\(384\) 3.90886 9.22149i 0.199473 0.470582i
\(385\) 0 0
\(386\) 41.5752 2.11612
\(387\) −0.597746 2.38727i −0.0303852 0.121352i
\(388\) 31.9394i 1.62148i
\(389\) −2.79372 4.83886i −0.141647 0.245340i 0.786470 0.617629i \(-0.211906\pi\)
−0.928117 + 0.372289i \(0.878573\pi\)
\(390\) 0 0
\(391\) 3.23790 5.60821i 0.163748 0.283619i
\(392\) 6.16528 + 3.55953i 0.311394 + 0.179783i
\(393\) 1.27166 + 10.3142i 0.0641466 + 0.520283i
\(394\) 16.2510 + 28.1475i 0.818712 + 1.41805i
\(395\) 0 0
\(396\) 2.62015 9.17213i 0.131668 0.460917i
\(397\) 3.75228i 0.188321i 0.995557 + 0.0941607i \(0.0300168\pi\)
−0.995557 + 0.0941607i \(0.969983\pi\)
\(398\) 6.47649 3.73921i 0.324637 0.187429i
\(399\) 1.79001 4.22286i 0.0896125 0.211407i
\(400\) 0 0
\(401\) −11.7826 + 20.4080i −0.588394 + 1.01913i 0.406048 + 0.913852i \(0.366906\pi\)
−0.994443 + 0.105278i \(0.966427\pi\)
\(402\) −23.4863 + 17.7166i −1.17139 + 0.883625i
\(403\) 4.31954 2.49389i 0.215172 0.124229i
\(404\) 3.45355 0.171820
\(405\) 0 0
\(406\) −33.0410 −1.63980
\(407\) −8.80944 + 5.08613i −0.436668 + 0.252110i
\(408\) −1.37250 + 1.03533i −0.0679488 + 0.0512563i
\(409\) 0.524200 0.907940i 0.0259200 0.0448948i −0.852774 0.522279i \(-0.825082\pi\)
0.878694 + 0.477385i \(0.158415\pi\)
\(410\) 0 0
\(411\) 5.04840 11.9098i 0.249019 0.587468i
\(412\) 15.3256 8.84823i 0.755037 0.435921i
\(413\) 17.0484i 0.838897i
\(414\) −8.23419 + 28.8247i −0.404688 + 1.41666i
\(415\) 0 0
\(416\) −2.62015 4.53824i −0.128464 0.222505i
\(417\) 1.69554 + 13.7523i 0.0830310 + 0.673452i
\(418\) 1.58287 + 0.913870i 0.0774207 + 0.0446988i
\(419\) −12.9599 + 22.4471i −0.633131 + 1.09661i 0.353777 + 0.935330i \(0.384897\pi\)
−0.986908 + 0.161285i \(0.948436\pi\)
\(420\) 0 0
\(421\) −3.82032 6.61699i −0.186191 0.322492i 0.757786 0.652503i \(-0.226281\pi\)
−0.943977 + 0.330011i \(0.892948\pi\)
\(422\) 31.2765i 1.52252i
\(423\) −7.94724 31.7395i −0.386408 1.54323i
\(424\) 3.06324 0.148764
\(425\) 0 0
\(426\) −8.62517 + 20.3479i −0.417891 + 0.985858i
\(427\) 13.5189 + 7.80516i 0.654227 + 0.377718i
\(428\) 2.46456 + 1.42291i 0.119129 + 0.0687791i
\(429\) −0.913870 1.21149i −0.0441220 0.0584911i
\(430\) 0 0
\(431\) 7.98516 0.384632 0.192316 0.981333i \(-0.438400\pi\)
0.192316 + 0.981333i \(0.438400\pi\)
\(432\) −10.3542 + 12.8257i −0.498168 + 0.617075i
\(433\) 12.5120i 0.601287i 0.953737 + 0.300644i \(0.0972014\pi\)
−0.953737 + 0.300644i \(0.902799\pi\)
\(434\) 32.8031 + 56.8166i 1.57460 + 2.72728i
\(435\) 0 0
\(436\) −16.5861 + 28.7280i −0.794332 + 1.37582i
\(437\) −2.68833 1.55211i −0.128600 0.0742474i
\(438\) 41.0671 + 17.4078i 1.96226 + 0.831775i
\(439\) −4.38225 7.59028i −0.209153 0.362264i 0.742295 0.670074i \(-0.233737\pi\)
−0.951448 + 0.307809i \(0.900404\pi\)
\(440\) 0 0
\(441\) −20.2281 20.9049i −0.963242 0.995474i
\(442\) 1.82774i 0.0869367i
\(443\) −3.17914 + 1.83548i −0.151046 + 0.0872062i −0.573618 0.819123i \(-0.694461\pi\)
0.422572 + 0.906329i \(0.361127\pi\)
\(444\) −30.4208 + 3.75064i −1.44371 + 0.177997i
\(445\) 0 0
\(446\) −27.9865 + 48.4740i −1.32520 + 2.29531i
\(447\) −2.24338 18.1957i −0.106108 0.860626i
\(448\) 37.2419 21.5016i 1.75951 1.01586i
\(449\) −28.1723 −1.32953 −0.664766 0.747052i \(-0.731469\pi\)
−0.664766 + 0.747052i \(0.731469\pi\)
\(450\) 0 0
\(451\) 0.242915 0.0114384
\(452\) −24.2884 + 14.0229i −1.14243 + 0.659581i
\(453\) 28.2205 + 11.9623i 1.32592 + 0.562036i
\(454\) −1.41016 + 2.44247i −0.0661821 + 0.114631i
\(455\) 0 0
\(456\) 0.496291 + 0.657916i 0.0232409 + 0.0308097i
\(457\) 30.5375 17.6308i 1.42848 0.824735i 0.431482 0.902122i \(-0.357991\pi\)
0.997001 + 0.0773867i \(0.0246576\pi\)
\(458\) 17.1803i 0.802784i
\(459\) 6.55451 2.52732i 0.305938 0.117965i
\(460\) 0 0
\(461\) −17.3384 30.0310i −0.807530 1.39868i −0.914570 0.404428i \(-0.867470\pi\)
0.107039 0.994255i \(-0.465863\pi\)
\(462\) 15.9352 12.0205i 0.741371 0.559244i
\(463\) 6.45080 + 3.72437i 0.299794 + 0.173086i 0.642350 0.766411i \(-0.277959\pi\)
−0.342556 + 0.939497i \(0.611293\pi\)
\(464\) −6.14806 + 10.6488i −0.285417 + 0.494356i
\(465\) 0 0
\(466\) 8.95725 + 15.5144i 0.414937 + 0.718692i
\(467\) 29.9655i 1.38664i 0.720630 + 0.693319i \(0.243852\pi\)
−0.720630 + 0.693319i \(0.756148\pi\)
\(468\) −1.11064 4.43567i −0.0513395 0.205039i
\(469\) −33.2691 −1.53622
\(470\) 0 0
\(471\) −4.35194 + 0.536558i −0.200527 + 0.0247233i
\(472\) 2.65284 + 1.53162i 0.122107 + 0.0704984i
\(473\) 0.960443 + 0.554512i 0.0441612 + 0.0254965i
\(474\) 37.0968 4.57373i 1.70391 0.210078i
\(475\) 0 0
\(476\) −12.9926 −0.595514
\(477\) −12.0353 3.43807i −0.551061 0.157418i
\(478\) 49.9097i 2.28282i
\(479\) −3.99258 6.91535i −0.182426 0.315971i 0.760280 0.649595i \(-0.225062\pi\)
−0.942706 + 0.333625i \(0.891728\pi\)
\(480\) 0 0
\(481\) −2.43807 + 4.22286i −0.111166 + 0.192546i
\(482\) −11.2740 6.50904i −0.513516 0.296479i
\(483\) −27.0641 + 20.4155i −1.23146 + 0.928937i
\(484\) −10.7863 18.6824i −0.490286 0.849201i
\(485\) 0 0
\(486\) −26.5918 + 18.7189i −1.20623 + 0.849108i
\(487\) 11.9442i 0.541243i −0.962686 0.270621i \(-0.912771\pi\)
0.962686 0.270621i \(-0.0872291\pi\)
\(488\) −2.42907 + 1.40242i −0.109959 + 0.0634847i
\(489\) 8.84081 + 11.7200i 0.399795 + 0.529995i
\(490\) 0 0
\(491\) 4.61033 7.98533i 0.208061 0.360373i −0.743042 0.669244i \(-0.766618\pi\)
0.951104 + 0.308872i \(0.0999513\pi\)
\(492\) 0.673910 + 0.285660i 0.0303822 + 0.0128786i
\(493\) 4.53824 2.62015i 0.204392 0.118006i
\(494\) 0.876139 0.0394193
\(495\) 0 0
\(496\) 24.4152 1.09627
\(497\) −21.6442 + 12.4963i −0.970876 + 0.560535i
\(498\) −5.41993 43.9602i −0.242873 1.96990i
\(499\) 15.0861 26.1299i 0.675348 1.16974i −0.301019 0.953618i \(-0.597327\pi\)
0.976367 0.216119i \(-0.0693399\pi\)
\(500\) 0 0
\(501\) 21.8905 2.69892i 0.977996 0.120579i
\(502\) 51.6204 29.8031i 2.30393 1.33018i
\(503\) 10.5981i 0.472546i 0.971687 + 0.236273i \(0.0759260\pi\)
−0.971687 + 0.236273i \(0.924074\pi\)
\(504\) 8.73048 2.18602i 0.388887 0.0973731i
\(505\) 0 0
\(506\) −6.75468 11.6995i −0.300282 0.520104i
\(507\) 20.0613 + 8.50371i 0.890955 + 0.377663i
\(508\) −14.4182 8.32435i −0.639704 0.369333i
\(509\) 14.3761 24.9002i 0.637211 1.10368i −0.348831 0.937186i \(-0.613421\pi\)
0.986042 0.166496i \(-0.0532454\pi\)
\(510\) 0 0
\(511\) 25.2207 + 43.6835i 1.11570 + 1.93244i
\(512\) 30.3094i 1.33950i
\(513\) −1.21149 3.14195i −0.0534884 0.138720i
\(514\) −37.5503 −1.65627
\(515\) 0 0
\(516\) 2.01243 + 2.66781i 0.0885924 + 0.117444i
\(517\) 12.7694 + 7.37243i 0.561599 + 0.324239i
\(518\) −55.5449 32.0689i −2.44050 1.40903i
\(519\) 15.5800 36.7553i 0.683887 1.61338i
\(520\) 0 0
\(521\) −36.0942 −1.58132 −0.790658 0.612259i \(-0.790261\pi\)
−0.790658 + 0.612259i \(0.790261\pi\)
\(522\) −17.4332 + 16.8687i −0.763030 + 0.738324i
\(523\) 11.1297i 0.486669i −0.969942 0.243334i \(-0.921759\pi\)
0.969942 0.243334i \(-0.0782412\pi\)
\(524\) −7.05582 12.2210i −0.308235 0.533878i
\(525\) 0 0
\(526\) 33.2411 57.5754i 1.44938 2.51041i
\(527\) −9.01112 5.20257i −0.392531 0.226628i
\(528\) −0.908959 7.37243i −0.0395574 0.320844i
\(529\) −0.0279088 0.0483395i −0.00121343 0.00210172i
\(530\) 0 0
\(531\) −8.70388 8.99513i −0.377716 0.390355i
\(532\) 6.22808i 0.270021i
\(533\) 0.100842 0.0582214i 0.00436797 0.00252185i
\(534\) 4.23048 9.98025i 0.183071 0.431888i
\(535\) 0 0
\(536\) 2.98887 5.17688i 0.129100 0.223607i
\(537\) 3.08089 2.32403i 0.132950 0.100289i
\(538\) −56.9040 + 32.8536i −2.45331 + 1.41642i
\(539\) 13.1090 0.564646
\(540\) 0 0
\(541\) −34.7374 −1.49348 −0.746740 0.665116i \(-0.768382\pi\)
−0.746740 + 0.665116i \(0.768382\pi\)
\(542\) 5.85407 3.37985i 0.251454 0.145177i
\(543\) −0.647658 + 0.488553i −0.0277937 + 0.0209658i
\(544\) −5.46598 + 9.46735i −0.234352 + 0.405909i
\(545\) 0 0
\(546\) 3.73419 8.80944i 0.159809 0.377009i
\(547\) −2.35087 + 1.35727i −0.100516 + 0.0580328i −0.549415 0.835549i \(-0.685149\pi\)
0.448899 + 0.893582i \(0.351816\pi\)
\(548\) 17.5652i 0.750347i
\(549\) 11.1177 2.78377i 0.474494 0.118808i
\(550\) 0 0
\(551\) −1.25599 2.17543i −0.0535068 0.0926766i
\(552\) −0.745356 6.04547i −0.0317245 0.257312i
\(553\) 36.6061 + 21.1345i 1.55665 + 0.898732i
\(554\) 5.82534 10.0898i 0.247495 0.428674i
\(555\) 0 0
\(556\) −9.40776 16.2947i −0.398978 0.691050i
\(557\) 8.93676i 0.378663i −0.981913 0.189331i \(-0.939368\pi\)
0.981913 0.189331i \(-0.0606321\pi\)
\(558\) 46.3148 + 13.2305i 1.96066 + 0.560091i
\(559\) 0.531618 0.0224850
\(560\) 0 0
\(561\) −1.23550 + 2.91469i −0.0521627 + 0.123059i
\(562\) −43.5477 25.1423i −1.83695 1.06056i
\(563\) −8.10826 4.68130i −0.341722 0.197293i 0.319311 0.947650i \(-0.396549\pi\)
−0.661033 + 0.750357i \(0.729882\pi\)
\(564\) 26.7560 + 35.4695i 1.12663 + 1.49354i
\(565\) 0 0
\(566\) 21.9926 0.924417
\(567\) −36.7553 1.20999i −1.54358 0.0508149i
\(568\) 4.49064i 0.188423i
\(569\) 17.9368 + 31.0674i 0.751948 + 1.30241i 0.946877 + 0.321595i \(0.104219\pi\)
−0.194929 + 0.980817i \(0.562448\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 1.78455 + 1.03031i 0.0746159 + 0.0430795i
\(573\) −32.2577 13.6736i −1.34758 0.571221i
\(574\) 0.765809 + 1.32642i 0.0319643 + 0.0553637i
\(575\) 0 0
\(576\) 8.67226 30.3582i 0.361344 1.26493i
\(577\) 1.35675i 0.0564821i 0.999601 + 0.0282411i \(0.00899060\pi\)
−0.999601 + 0.0282411i \(0.991009\pi\)
\(578\) −27.4108 + 15.8257i −1.14014 + 0.658260i
\(579\) 34.2592 4.22388i 1.42377 0.175538i
\(580\) 0 0
\(581\) 25.0447 43.3787i 1.03903 1.79965i
\(582\) 6.00427 + 48.6997i 0.248885 + 2.01867i
\(583\) 4.88494 2.82032i 0.202314 0.116806i
\(584\) −9.06324 −0.375039
\(585\) 0 0
\(586\) −39.6210 −1.63673
\(587\) 24.9329 14.3950i 1.02909 0.594145i 0.112366 0.993667i \(-0.464157\pi\)
0.916724 + 0.399521i \(0.130824\pi\)
\(588\) 36.3679 + 15.4158i 1.49979 + 0.635737i
\(589\) −2.49389 + 4.31954i −0.102759 + 0.177984i
\(590\) 0 0
\(591\) 16.2510 + 21.5434i 0.668476 + 0.886176i
\(592\) −20.6709 + 11.9344i −0.849570 + 0.490499i
\(593\) 30.9171i 1.26961i −0.772671 0.634807i \(-0.781080\pi\)
0.772671 0.634807i \(-0.218920\pi\)
\(594\) 2.27082 14.4778i 0.0931730 0.594032i
\(595\) 0 0
\(596\) 12.4474 + 21.5596i 0.509867 + 0.883115i
\(597\) 4.95694 3.73921i 0.202874 0.153035i
\(598\) −5.60821 3.23790i −0.229337 0.132408i
\(599\) 0.696460 1.20630i 0.0284566 0.0492882i −0.851446 0.524442i \(-0.824274\pi\)
0.879903 + 0.475153i \(0.157607\pi\)
\(600\) 0 0
\(601\) −4.41256 7.64279i −0.179992 0.311756i 0.761885 0.647712i \(-0.224274\pi\)
−0.941878 + 0.335956i \(0.890941\pi\)
\(602\) 6.99258i 0.284996i
\(603\) −17.5535 + 16.9852i −0.714835 + 0.691689i
\(604\) −41.6210 −1.69353
\(605\) 0 0
\(606\) 5.26581 0.649230i 0.213909 0.0263732i
\(607\) 1.86783 + 1.07839i 0.0758129 + 0.0437706i 0.537427 0.843310i \(-0.319396\pi\)
−0.461614 + 0.887081i \(0.652730\pi\)
\(608\) 4.53824 + 2.62015i 0.184050 + 0.106261i
\(609\) −27.2268 + 3.35683i −1.10328 + 0.136026i
\(610\) 0 0
\(611\) 7.06804 0.285942
\(612\) −6.85518 + 6.63322i −0.277104 + 0.268132i
\(613\) 9.57521i 0.386739i 0.981126 + 0.193370i \(0.0619416\pi\)
−0.981126 + 0.193370i \(0.938058\pi\)
\(614\) −30.7486 53.2581i −1.24091 2.14932i
\(615\) 0 0
\(616\) −2.02791 + 3.51244i −0.0817068 + 0.141520i
\(617\) 32.6291 + 18.8384i 1.31360 + 0.758406i 0.982690 0.185258i \(-0.0593119\pi\)
0.330907 + 0.943663i \(0.392645\pi\)
\(618\) 21.7044 16.3724i 0.873078 0.658596i
\(619\) 8.55211 + 14.8127i 0.343738 + 0.595372i 0.985124 0.171847i \(-0.0549734\pi\)
−0.641385 + 0.767219i \(0.721640\pi\)
\(620\) 0 0
\(621\) −3.85675 + 24.5890i −0.154766 + 0.986722i
\(622\) 19.6358i 0.787325i
\(623\) 10.6161 6.12920i 0.425324 0.245561i
\(624\) −2.14435 2.84269i −0.0858428 0.113799i
\(625\) 0 0
\(626\) 12.1215 20.9950i 0.484471 0.839128i
\(627\) 1.39718 + 0.592243i 0.0557979 + 0.0236519i
\(628\) 5.15650 2.97711i 0.205767 0.118799i
\(629\) 10.1723 0.405595
\(630\) 0 0
\(631\) 33.1090 1.31805 0.659025 0.752121i \(-0.270969\pi\)
0.659025 + 0.752121i \(0.270969\pi\)
\(632\) −6.57734 + 3.79743i −0.261632 + 0.151054i
\(633\) −3.17757 25.7728i −0.126297 1.02438i
\(634\) 9.57500 16.5844i 0.380272 0.658650i
\(635\) 0 0
\(636\) 16.8687 2.07977i 0.668888 0.0824684i
\(637\) 5.44201 3.14195i 0.215620 0.124489i
\(638\) 10.9320i 0.432800i
\(639\) −5.04013 + 17.6436i −0.199385 + 0.697968i
\(640\) 0 0
\(641\) 11.5763 + 20.0508i 0.457237 + 0.791957i 0.998814 0.0486939i \(-0.0155059\pi\)
−0.541577 + 0.840651i \(0.682173\pi\)
\(642\) 4.02534 + 1.70628i 0.158867 + 0.0673416i
\(643\) 37.2944 + 21.5319i 1.47075 + 0.849137i 0.999461 0.0328430i \(-0.0104561\pi\)
0.471287 + 0.881980i \(0.343789\pi\)
\(644\) 23.0168 39.8662i 0.906988 1.57095i
\(645\) 0 0
\(646\) −0.913870 1.58287i −0.0359557 0.0622771i
\(647\) 20.6439i 0.811595i −0.913963 0.405798i \(-0.866994\pi\)
0.913963 0.405798i \(-0.133006\pi\)
\(648\) 3.49035 5.61065i 0.137114 0.220407i
\(649\) 5.64064 0.221415
\(650\) 0 0
\(651\) 32.8031 + 43.4859i 1.28565 + 1.70435i
\(652\) −17.2638 9.96728i −0.676104 0.390349i
\(653\) 5.91942 + 3.41758i 0.231645 + 0.133740i 0.611331 0.791375i \(-0.290635\pi\)
−0.379686 + 0.925116i \(0.623968\pi\)
\(654\) −19.8892 + 46.9212i −0.777730 + 1.83476i
\(655\) 0 0
\(656\) 0.569988 0.0222543
\(657\) 35.6091 + 10.1723i 1.38924 + 0.396858i
\(658\) 92.9688i 3.62430i
\(659\) −13.4307 23.2626i −0.523184 0.906181i −0.999636 0.0269806i \(-0.991411\pi\)
0.476452 0.879200i \(-0.341923\pi\)
\(660\) 0 0
\(661\) 1.06063 1.83706i 0.0412535 0.0714532i −0.844661 0.535301i \(-0.820198\pi\)
0.885915 + 0.463848i \(0.153532\pi\)
\(662\) −13.0451 7.53162i −0.507014 0.292725i
\(663\) 0.185691 + 1.50611i 0.00721165 + 0.0584926i
\(664\) 4.50000 + 7.79423i 0.174634 + 0.302475i
\(665\) 0 0
\(666\) −45.6792 + 11.4376i −1.77003 + 0.443198i
\(667\) 18.5667i 0.718907i
\(668\) −25.9375 + 14.9750i −1.00355 + 0.579401i
\(669\) −18.1369 + 42.7874i −0.701214 + 1.65425i
\(670\) 0 0
\(671\) −2.58242 + 4.47288i −0.0996933 + 0.172674i
\(672\) 45.6876 34.4639i 1.76244 1.32947i
\(673\) −30.1553 + 17.4102i −1.16240 + 0.671112i −0.951878 0.306477i \(-0.900850\pi\)
−0.210523 + 0.977589i \(0.567517\pi\)
\(674\) 4.76450 0.183522
\(675\) 0 0
\(676\) −29.5874 −1.13798
\(677\) −21.3772 + 12.3421i −0.821592 + 0.474346i −0.850965 0.525222i \(-0.823982\pi\)
0.0293735 + 0.999569i \(0.490649\pi\)
\(678\) −34.3976 + 25.9474i −1.32103 + 0.996505i
\(679\) −27.7449 + 48.0555i −1.06475 + 1.84420i
\(680\) 0 0
\(681\) −0.913870 + 2.15594i −0.0350196 + 0.0826157i
\(682\) −18.7984 + 10.8532i −0.719827 + 0.415592i
\(683\) 38.4610i 1.47167i 0.677162 + 0.735834i \(0.263210\pi\)
−0.677162 + 0.735834i \(0.736790\pi\)
\(684\) 3.17968 + 3.28608i 0.121578 + 0.125646i
\(685\) 0 0
\(686\) 11.4926 + 19.9057i 0.438789 + 0.760005i
\(687\) −1.74545 14.1571i −0.0665932 0.540127i
\(688\) 2.25363 + 1.30114i 0.0859190 + 0.0496054i
\(689\) 1.35194 2.34163i 0.0515048 0.0892089i
\(690\) 0 0
\(691\) −0.240304 0.416219i −0.00914159 0.0158337i 0.861418 0.507896i \(-0.169577\pi\)
−0.870560 + 0.492062i \(0.836243\pi\)
\(692\) 54.2084i 2.06070i
\(693\) 11.9098 11.5242i 0.452417 0.437768i
\(694\) −1.47841 −0.0561197
\(695\) 0 0
\(696\) 1.92369 4.53824i 0.0729174 0.172021i
\(697\) −0.210370 0.121457i −0.00796835 0.00460053i
\(698\) 38.5619 + 22.2637i 1.45959 + 0.842694i
\(699\) 8.95725 + 11.8743i 0.338794 + 0.449128i
\(700\) 0 0
\(701\) −18.1797 −0.686637 −0.343318 0.939219i \(-0.611551\pi\)
−0.343318 + 0.939219i \(0.611551\pi\)
\(702\) −2.52732 6.55451i −0.0953875 0.247384i
\(703\) 4.87614i 0.183907i
\(704\) 7.11404 + 12.3219i 0.268120 + 0.464398i
\(705\) 0 0
\(706\) −10.5316 + 18.2413i −0.396363 + 0.686520i
\(707\) 5.19615 + 3.00000i 0.195421 + 0.112827i
\(708\) 15.6486 + 6.63322i 0.588111 + 0.249292i
\(709\) 3.59355 + 6.22421i 0.134959 + 0.233755i 0.925582 0.378548i \(-0.123577\pi\)
−0.790623 + 0.612303i \(0.790243\pi\)
\(710\) 0 0
\(711\) 30.1042 7.53778i 1.12900 0.282689i
\(712\) 2.20257i 0.0825449i
\(713\) 31.9270 18.4331i 1.19568 0.690323i
\(714\) −19.8105 + 2.44247i −0.741389 + 0.0914071i
\(715\) 0 0
\(716\) −2.62015 + 4.53824i −0.0979197 + 0.169602i
\(717\) −5.07063 41.1271i −0.189366 1.53592i
\(718\) 55.2069 31.8737i 2.06030 1.18952i
\(719\) −12.5168 −0.466797 −0.233399 0.972381i \(-0.574985\pi\)
−0.233399 + 0.972381i \(0.574985\pi\)
\(720\) 0 0
\(721\) 30.7449 1.14500
\(722\) 33.5674 19.3802i 1.24925 0.721255i
\(723\) −9.95141 4.21826i −0.370097 0.156879i
\(724\) 0.550803 0.954019i 0.0204704 0.0354558i
\(725\) 0 0
\(726\) −19.9586 26.4584i −0.740732 0.981963i
\(727\) 7.29699 4.21292i 0.270631 0.156249i −0.358544 0.933513i \(-0.616727\pi\)
0.629174 + 0.777264i \(0.283393\pi\)
\(728\) 1.94418i 0.0720562i
\(729\) −20.0107 + 18.1266i −0.741136 + 0.671355i
\(730\) 0 0
\(731\) −0.554512 0.960443i −0.0205094 0.0355233i
\(732\) −12.4243 + 9.37211i −0.459215 + 0.346403i
\(733\) −19.0526 11.0000i −0.703722 0.406294i 0.105010 0.994471i \(-0.466513\pi\)
−0.808732 + 0.588177i \(0.799846\pi\)
\(734\) 7.48887 12.9711i 0.276419 0.478772i
\(735\) 0 0
\(736\) −19.3663 33.5434i −0.713852 1.23643i
\(737\) 11.0074i 0.405463i
\(738\) 1.08125 + 0.308874i 0.0398013 + 0.0113698i
\(739\) 1.81290 0.0666887 0.0333444 0.999444i \(-0.489384\pi\)
0.0333444 + 0.999444i \(0.489384\pi\)
\(740\) 0 0
\(741\) 0.721965 0.0890123i 0.0265220 0.00326995i
\(742\) 30.8003 + 17.7826i 1.13072 + 0.652819i
\(743\) 17.4393 + 10.0686i 0.639785 + 0.369380i 0.784532 0.620089i \(-0.212903\pi\)
−0.144747 + 0.989469i \(0.546237\pi\)
\(744\) −9.71370 + 1.19762i −0.356122 + 0.0439068i
\(745\) 0 0
\(746\) 45.7374 1.67457
\(747\) −8.93237 35.6739i −0.326818 1.30524i
\(748\) 4.29873i 0.157177i
\(749\) 2.47209 + 4.28179i 0.0903282 + 0.156453i
\(750\) 0 0
\(751\) −6.10662 + 10.5770i −0.222834 + 0.385959i −0.955667 0.294449i \(-0.904864\pi\)
0.732834 + 0.680408i \(0.238197\pi\)
\(752\) 29.9628 + 17.2991i 1.09263 + 0.630832i
\(753\) 39.5089 29.8031i 1.43979 1.08608i
\(754\) −2.62015 4.53824i −0.0954203 0.165273i
\(755\) 0 0
\(756\) 46.5931 17.9656i 1.69457 0.653402i
\(757\) 52.9533i 1.92462i 0.271955 + 0.962310i \(0.412330\pi\)
−0.271955 + 0.962310i \(0.587670\pi\)
\(758\) −31.4228 + 18.1419i −1.14133 + 0.658945i
\(759\) −6.75468 8.95445i −0.245179 0.325026i
\(760\) 0 0
\(761\) 9.22677 15.9812i 0.334470 0.579319i −0.648913 0.760863i \(-0.724776\pi\)
0.983383 + 0.181543i \(0.0581093\pi\)
\(762\) −23.5491 9.98212i −0.853094 0.361614i
\(763\) −49.9105 + 28.8158i −1.80688 + 1.04320i
\(764\) 47.5752 1.72121
\(765\) 0 0
\(766\) −0.992582 −0.0358634
\(767\) 2.34163 1.35194i 0.0845513 0.0488157i
\(768\) −1.90434 15.4458i −0.0687169 0.557353i
\(769\) −2.22677 + 3.85688i −0.0802995 + 0.139083i −0.903379 0.428844i \(-0.858921\pi\)
0.823079 + 0.567927i \(0.192254\pi\)
\(770\) 0 0
\(771\) −30.9426 + 3.81497i −1.11437 + 0.137393i
\(772\) −40.5929 + 23.4363i −1.46097 + 0.843491i
\(773\) 38.9368i 1.40046i −0.713918 0.700229i \(-0.753081\pi\)
0.713918 0.700229i \(-0.246919\pi\)
\(774\) 3.56999 + 3.68945i 0.128321 + 0.132614i
\(775\) 0 0
\(776\) −4.98516 8.63456i −0.178957 0.309962i
\(777\) −49.0288 20.7826i −1.75890 0.745571i
\(778\) 10.0945 + 5.82806i 0.361905 + 0.208946i
\(779\) −0.0582214 + 0.100842i −0.00208600 + 0.00361305i
\(780\)