Properties

Label 144.2.k.b.37.2
Level $144$
Weight $2$
Character 144.37
Analytic conductor $1.150$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.2
Root \(0.500000 + 0.691860i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.2.k.b.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.635665 - 1.26330i) q^{2} +(-1.19186 + 1.60607i) q^{4} +(2.68554 + 2.68554i) q^{5} +2.15894i q^{7} +(2.78658 + 0.484753i) q^{8} +O(q^{10})\) \(q+(-0.635665 - 1.26330i) q^{2} +(-1.19186 + 1.60607i) q^{4} +(2.68554 + 2.68554i) q^{5} +2.15894i q^{7} +(2.78658 + 0.484753i) q^{8} +(1.68554 - 5.09976i) q^{10} +(-1.79793 - 1.79793i) q^{11} +(1.38372 - 1.38372i) q^{13} +(2.72739 - 1.37236i) q^{14} +(-1.15894 - 3.82843i) q^{16} +0.224777 q^{17} +(0.158942 - 0.158942i) q^{19} +(-7.51397 + 1.11239i) q^{20} +(-1.12845 + 3.41421i) q^{22} -2.82843i q^{23} +9.42429i q^{25} +(-2.62764 - 0.868472i) q^{26} +(-3.46742 - 2.57316i) q^{28} +(1.85712 - 1.85712i) q^{29} +1.84106 q^{31} +(-4.09976 + 3.89769i) q^{32} +(-0.142883 - 0.283962i) q^{34} +(-5.79793 + 5.79793i) q^{35} +(-3.66949 - 3.66949i) q^{37} +(-0.301825 - 0.0997575i) q^{38} +(6.18165 + 8.78530i) q^{40} +5.88163i q^{41} +(-7.75481 - 7.75481i) q^{43} +(5.03049 - 0.744728i) q^{44} +(-3.57316 + 1.79793i) q^{46} +2.82843 q^{47} +2.33897 q^{49} +(11.9057 - 5.99069i) q^{50} +(0.573155 + 3.87155i) q^{52} +(-7.51397 - 7.51397i) q^{53} -9.65685i q^{55} +(-1.04655 + 6.01606i) q^{56} +(-3.52660 - 1.16559i) q^{58} +(-4.00000 - 4.00000i) q^{59} +(5.98737 - 5.98737i) q^{61} +(-1.17030 - 2.32581i) q^{62} +(7.53003 + 2.70160i) q^{64} +7.43208 q^{65} +(-10.4243 + 10.4243i) q^{67} +(-0.267903 + 0.361009i) q^{68} +(11.0101 + 3.63899i) q^{70} +4.31788i q^{71} -5.97474i q^{73} +(-2.30310 + 6.96823i) q^{74} +(0.0658358 + 0.444708i) q^{76} +(3.88163 - 3.88163i) q^{77} +15.0075 q^{79} +(7.16902 - 13.3938i) q^{80} +(7.43027 - 3.73875i) q^{82} +(10.1158 - 10.1158i) q^{83} +(0.603650 + 0.603650i) q^{85} +(-4.86720 + 14.7261i) q^{86} +(-4.13853 - 5.88163i) q^{88} +1.42847i q^{89} +(2.98737 + 2.98737i) q^{91} +(4.54266 + 3.37109i) q^{92} +(-1.79793 - 3.57316i) q^{94} +0.853690 q^{95} -16.3990 q^{97} +(-1.48680 - 2.95482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + 12q^{8} + O(q^{10}) \) \( 8q - 4q^{4} + 12q^{8} - 8q^{10} + 8q^{11} - 12q^{14} - 8q^{19} - 16q^{20} - 20q^{26} + 8q^{28} + 16q^{29} + 24q^{31} - 24q^{35} - 16q^{37} + 8q^{38} + 16q^{40} - 8q^{43} + 40q^{44} - 8q^{46} - 8q^{49} + 36q^{50} - 16q^{52} - 16q^{53} - 16q^{58} - 32q^{59} + 16q^{61} + 12q^{62} + 8q^{64} + 16q^{65} - 16q^{67} - 32q^{68} + 32q^{70} - 52q^{74} + 8q^{76} - 16q^{77} - 24q^{79} - 8q^{80} + 40q^{82} + 40q^{83} - 16q^{85} + 16q^{86} + 32q^{88} - 8q^{91} + 16q^{92} + 8q^{94} + 48q^{95} + 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.635665 1.26330i −0.449483 0.893289i
\(3\) 0 0
\(4\) −1.19186 + 1.60607i −0.595930 + 0.803037i
\(5\) 2.68554 + 2.68554i 1.20101 + 1.20101i 0.973859 + 0.227153i \(0.0729416\pi\)
0.227153 + 0.973859i \(0.427058\pi\)
\(6\) 0 0
\(7\) 2.15894i 0.816003i 0.912981 + 0.408002i \(0.133774\pi\)
−0.912981 + 0.408002i \(0.866226\pi\)
\(8\) 2.78658 + 0.484753i 0.985204 + 0.171386i
\(9\) 0 0
\(10\) 1.68554 5.09976i 0.533016 1.61268i
\(11\) −1.79793 1.79793i −0.542097 0.542097i 0.382046 0.924143i \(-0.375220\pi\)
−0.924143 + 0.382046i \(0.875220\pi\)
\(12\) 0 0
\(13\) 1.38372 1.38372i 0.383775 0.383775i −0.488685 0.872460i \(-0.662523\pi\)
0.872460 + 0.488685i \(0.162523\pi\)
\(14\) 2.72739 1.37236i 0.728927 0.366780i
\(15\) 0 0
\(16\) −1.15894 3.82843i −0.289735 0.957107i
\(17\) 0.224777 0.0545165 0.0272583 0.999628i \(-0.491322\pi\)
0.0272583 + 0.999628i \(0.491322\pi\)
\(18\) 0 0
\(19\) 0.158942 0.158942i 0.0364637 0.0364637i −0.688640 0.725104i \(-0.741792\pi\)
0.725104 + 0.688640i \(0.241792\pi\)
\(20\) −7.51397 + 1.11239i −1.68018 + 0.248738i
\(21\) 0 0
\(22\) −1.12845 + 3.41421i −0.240586 + 0.727913i
\(23\) 2.82843i 0.589768i −0.955533 0.294884i \(-0.904719\pi\)
0.955533 0.294884i \(-0.0952810\pi\)
\(24\) 0 0
\(25\) 9.42429i 1.88486i
\(26\) −2.62764 0.868472i −0.515322 0.170321i
\(27\) 0 0
\(28\) −3.46742 2.57316i −0.655280 0.486281i
\(29\) 1.85712 1.85712i 0.344858 0.344858i −0.513332 0.858190i \(-0.671589\pi\)
0.858190 + 0.513332i \(0.171589\pi\)
\(30\) 0 0
\(31\) 1.84106 0.330664 0.165332 0.986238i \(-0.447130\pi\)
0.165332 + 0.986238i \(0.447130\pi\)
\(32\) −4.09976 + 3.89769i −0.724742 + 0.689021i
\(33\) 0 0
\(34\) −0.142883 0.283962i −0.0245043 0.0486990i
\(35\) −5.79793 + 5.79793i −0.980029 + 0.980029i
\(36\) 0 0
\(37\) −3.66949 3.66949i −0.603260 0.603260i 0.337916 0.941176i \(-0.390278\pi\)
−0.941176 + 0.337916i \(0.890278\pi\)
\(38\) −0.301825 0.0997575i −0.0489625 0.0161828i
\(39\) 0 0
\(40\) 6.18165 + 8.78530i 0.977405 + 1.38908i
\(41\) 5.88163i 0.918557i 0.888292 + 0.459278i \(0.151892\pi\)
−0.888292 + 0.459278i \(0.848108\pi\)
\(42\) 0 0
\(43\) −7.75481 7.75481i −1.18260 1.18260i −0.979069 0.203528i \(-0.934759\pi\)
−0.203528 0.979069i \(-0.565241\pi\)
\(44\) 5.03049 0.744728i 0.758376 0.112272i
\(45\) 0 0
\(46\) −3.57316 + 1.79793i −0.526833 + 0.265091i
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) 0 0
\(49\) 2.33897 0.334139
\(50\) 11.9057 5.99069i 1.68372 0.847212i
\(51\) 0 0
\(52\) 0.573155 + 3.87155i 0.0794823 + 0.536888i
\(53\) −7.51397 7.51397i −1.03212 1.03212i −0.999467 0.0326567i \(-0.989603\pi\)
−0.0326567 0.999467i \(-0.510397\pi\)
\(54\) 0 0
\(55\) 9.65685i 1.30213i
\(56\) −1.04655 + 6.01606i −0.139852 + 0.803930i
\(57\) 0 0
\(58\) −3.52660 1.16559i −0.463066 0.153050i
\(59\) −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) 5.98737 5.98737i 0.766604 0.766604i −0.210903 0.977507i \(-0.567640\pi\)
0.977507 + 0.210903i \(0.0676404\pi\)
\(62\) −1.17030 2.32581i −0.148628 0.295378i
\(63\) 0 0
\(64\) 7.53003 + 2.70160i 0.941254 + 0.337700i
\(65\) 7.43208 0.921836
\(66\) 0 0
\(67\) −10.4243 + 10.4243i −1.27353 + 1.27353i −0.329307 + 0.944223i \(0.606815\pi\)
−0.944223 + 0.329307i \(0.893185\pi\)
\(68\) −0.267903 + 0.361009i −0.0324880 + 0.0437788i
\(69\) 0 0
\(70\) 11.0101 + 3.63899i 1.31596 + 0.434943i
\(71\) 4.31788i 0.512438i 0.966619 + 0.256219i \(0.0824769\pi\)
−0.966619 + 0.256219i \(0.917523\pi\)
\(72\) 0 0
\(73\) 5.97474i 0.699290i −0.936882 0.349645i \(-0.886302\pi\)
0.936882 0.349645i \(-0.113698\pi\)
\(74\) −2.30310 + 6.96823i −0.267730 + 0.810040i
\(75\) 0 0
\(76\) 0.0658358 + 0.444708i 0.00755188 + 0.0510115i
\(77\) 3.88163 3.88163i 0.442353 0.442353i
\(78\) 0 0
\(79\) 15.0075 1.68848 0.844239 0.535966i \(-0.180053\pi\)
0.844239 + 0.535966i \(0.180053\pi\)
\(80\) 7.16902 13.3938i 0.801521 1.49747i
\(81\) 0 0
\(82\) 7.43027 3.73875i 0.820536 0.412876i
\(83\) 10.1158 10.1158i 1.11036 1.11036i 0.117253 0.993102i \(-0.462591\pi\)
0.993102 0.117253i \(-0.0374088\pi\)
\(84\) 0 0
\(85\) 0.603650 + 0.603650i 0.0654750 + 0.0654750i
\(86\) −4.86720 + 14.7261i −0.524843 + 1.58796i
\(87\) 0 0
\(88\) −4.13853 5.88163i −0.441168 0.626984i
\(89\) 1.42847i 0.151417i 0.997130 + 0.0757086i \(0.0241219\pi\)
−0.997130 + 0.0757086i \(0.975878\pi\)
\(90\) 0 0
\(91\) 2.98737 + 2.98737i 0.313161 + 0.313161i
\(92\) 4.54266 + 3.37109i 0.473605 + 0.351460i
\(93\) 0 0
\(94\) −1.79793 3.57316i −0.185443 0.368543i
\(95\) 0.853690 0.0875867
\(96\) 0 0
\(97\) −16.3990 −1.66507 −0.832535 0.553973i \(-0.813111\pi\)
−0.832535 + 0.553973i \(0.813111\pi\)
\(98\) −1.48680 2.95482i −0.150190 0.298482i
\(99\) 0 0
\(100\) −15.1361 11.2324i −1.51361 1.12324i
\(101\) −0.0818942 0.0818942i −0.00814878 0.00814878i 0.703021 0.711169i \(-0.251834\pi\)
−0.711169 + 0.703021i \(0.751834\pi\)
\(102\) 0 0
\(103\) 13.3507i 1.31548i 0.753245 + 0.657740i \(0.228488\pi\)
−0.753245 + 0.657740i \(0.771512\pi\)
\(104\) 4.52660 3.18508i 0.443870 0.312323i
\(105\) 0 0
\(106\) −4.71604 + 14.2688i −0.458062 + 1.38591i
\(107\) 7.27798 + 7.27798i 0.703589 + 0.703589i 0.965179 0.261590i \(-0.0842468\pi\)
−0.261590 + 0.965179i \(0.584247\pi\)
\(108\) 0 0
\(109\) −7.04057 + 7.04057i −0.674365 + 0.674365i −0.958719 0.284355i \(-0.908221\pi\)
0.284355 + 0.958719i \(0.408221\pi\)
\(110\) −12.1995 + 6.13853i −1.16318 + 0.585285i
\(111\) 0 0
\(112\) 8.26535 2.50209i 0.781002 0.236425i
\(113\) −18.8486 −1.77313 −0.886563 0.462608i \(-0.846914\pi\)
−0.886563 + 0.462608i \(0.846914\pi\)
\(114\) 0 0
\(115\) 7.59587 7.59587i 0.708318 0.708318i
\(116\) 0.769243 + 5.19609i 0.0714224 + 0.482445i
\(117\) 0 0
\(118\) −2.51054 + 7.59587i −0.231114 + 0.699256i
\(119\) 0.485281i 0.0444857i
\(120\) 0 0
\(121\) 4.53488i 0.412261i
\(122\) −11.3698 3.75789i −1.02937 0.340223i
\(123\) 0 0
\(124\) −2.19428 + 2.95687i −0.197052 + 0.265535i
\(125\) −11.8816 + 11.8816i −1.06273 + 1.06273i
\(126\) 0 0
\(127\) −3.81580 −0.338597 −0.169299 0.985565i \(-0.554150\pi\)
−0.169299 + 0.985565i \(0.554150\pi\)
\(128\) −1.37364 11.2300i −0.121414 0.992602i
\(129\) 0 0
\(130\) −4.72431 9.38895i −0.414350 0.823465i
\(131\) 0.767438 0.767438i 0.0670514 0.0670514i −0.672786 0.739837i \(-0.734902\pi\)
0.739837 + 0.672786i \(0.234902\pi\)
\(132\) 0 0
\(133\) 0.343146 + 0.343146i 0.0297545 + 0.0297545i
\(134\) 19.7954 + 6.54266i 1.71006 + 0.565200i
\(135\) 0 0
\(136\) 0.626360 + 0.108961i 0.0537099 + 0.00934337i
\(137\) 5.31010i 0.453672i −0.973933 0.226836i \(-0.927162\pi\)
0.973933 0.226836i \(-0.0728382\pi\)
\(138\) 0 0
\(139\) 8.76744 + 8.76744i 0.743644 + 0.743644i 0.973277 0.229633i \(-0.0737526\pi\)
−0.229633 + 0.973277i \(0.573753\pi\)
\(140\) −2.40158 16.2222i −0.202971 1.37103i
\(141\) 0 0
\(142\) 5.45479 2.74473i 0.457756 0.230332i
\(143\) −4.97567 −0.416086
\(144\) 0 0
\(145\) 9.97474 0.828357
\(146\) −7.54789 + 3.79793i −0.624668 + 0.314319i
\(147\) 0 0
\(148\) 10.2670 1.51995i 0.843940 0.124939i
\(149\) 1.02869 + 1.02869i 0.0842735 + 0.0842735i 0.747987 0.663713i \(-0.231021\pi\)
−0.663713 + 0.747987i \(0.731021\pi\)
\(150\) 0 0
\(151\) 2.03696i 0.165766i −0.996559 0.0828829i \(-0.973587\pi\)
0.996559 0.0828829i \(-0.0264127\pi\)
\(152\) 0.519951 0.365856i 0.0421736 0.0296748i
\(153\) 0 0
\(154\) −7.37109 2.43625i −0.593979 0.196319i
\(155\) 4.94424 + 4.94424i 0.397131 + 0.397131i
\(156\) 0 0
\(157\) 6.09378 6.09378i 0.486336 0.486336i −0.420812 0.907148i \(-0.638255\pi\)
0.907148 + 0.420812i \(0.138255\pi\)
\(158\) −9.53976 18.9590i −0.758943 1.50830i
\(159\) 0 0
\(160\) −21.4775 0.542661i −1.69795 0.0429011i
\(161\) 6.10641 0.481252
\(162\) 0 0
\(163\) 3.43692 3.43692i 0.269201 0.269201i −0.559577 0.828778i \(-0.689037\pi\)
0.828778 + 0.559577i \(0.189037\pi\)
\(164\) −9.44633 7.01008i −0.737634 0.547395i
\(165\) 0 0
\(166\) −19.2096 6.34905i −1.49095 0.492782i
\(167\) 21.7023i 1.67937i 0.543072 + 0.839686i \(0.317261\pi\)
−0.543072 + 0.839686i \(0.682739\pi\)
\(168\) 0 0
\(169\) 9.17064i 0.705434i
\(170\) 0.378872 1.14631i 0.0290582 0.0879180i
\(171\) 0 0
\(172\) 21.6974 3.21215i 1.65441 0.244924i
\(173\) 8.74653 8.74653i 0.664987 0.664987i −0.291565 0.956551i \(-0.594176\pi\)
0.956551 + 0.291565i \(0.0941758\pi\)
\(174\) 0 0
\(175\) −20.3465 −1.53805
\(176\) −4.79956 + 8.96695i −0.361780 + 0.675910i
\(177\) 0 0
\(178\) 1.80458 0.908027i 0.135259 0.0680595i
\(179\) −8.23163 + 8.23163i −0.615261 + 0.615261i −0.944312 0.329051i \(-0.893271\pi\)
0.329051 + 0.944312i \(0.393271\pi\)
\(180\) 0 0
\(181\) 6.72269 + 6.72269i 0.499694 + 0.499694i 0.911343 0.411649i \(-0.135047\pi\)
−0.411649 + 0.911343i \(0.635047\pi\)
\(182\) 1.87498 5.67291i 0.138983 0.420504i
\(183\) 0 0
\(184\) 1.37109 7.88163i 0.101078 0.581042i
\(185\) 19.7091i 1.44904i
\(186\) 0 0
\(187\) −0.404135 0.404135i −0.0295533 0.0295533i
\(188\) −3.37109 + 4.54266i −0.245862 + 0.331308i
\(189\) 0 0
\(190\) −0.542661 1.07847i −0.0393687 0.0782402i
\(191\) 20.8032 1.50526 0.752632 0.658441i \(-0.228784\pi\)
0.752632 + 0.658441i \(0.228784\pi\)
\(192\) 0 0
\(193\) 14.1454 1.01821 0.509103 0.860705i \(-0.329977\pi\)
0.509103 + 0.860705i \(0.329977\pi\)
\(194\) 10.4243 + 20.7169i 0.748421 + 1.48739i
\(195\) 0 0
\(196\) −2.78772 + 3.75656i −0.199123 + 0.268326i
\(197\) 2.42865 + 2.42865i 0.173034 + 0.173034i 0.788311 0.615277i \(-0.210956\pi\)
−0.615277 + 0.788311i \(0.710956\pi\)
\(198\) 0 0
\(199\) 0.306182i 0.0217047i 0.999941 + 0.0108523i \(0.00345447\pi\)
−0.999941 + 0.0108523i \(0.996546\pi\)
\(200\) −4.56845 + 26.2615i −0.323038 + 1.85697i
\(201\) 0 0
\(202\) −0.0513998 + 0.155514i −0.00361648 + 0.0109420i
\(203\) 4.00941 + 4.00941i 0.281405 + 0.281405i
\(204\) 0 0
\(205\) −15.7954 + 15.7954i −1.10320 + 1.10320i
\(206\) 16.8659 8.48656i 1.17510 0.591286i
\(207\) 0 0
\(208\) −6.90112 3.69382i −0.478506 0.256120i
\(209\) −0.571533 −0.0395337
\(210\) 0 0
\(211\) 7.23256 7.23256i 0.497910 0.497910i −0.412877 0.910787i \(-0.635476\pi\)
0.910787 + 0.412877i \(0.135476\pi\)
\(212\) 21.0236 3.11239i 1.44391 0.213760i
\(213\) 0 0
\(214\) 4.56792 13.8206i 0.312257 0.944760i
\(215\) 41.6517i 2.84063i
\(216\) 0 0
\(217\) 3.97474i 0.269823i
\(218\) 13.3698 + 4.41892i 0.905518 + 0.299287i
\(219\) 0 0
\(220\) 15.5096 + 11.5096i 1.04566 + 0.775978i
\(221\) 0.311029 0.311029i 0.0209221 0.0209221i
\(222\) 0 0
\(223\) −1.71908 −0.115118 −0.0575591 0.998342i \(-0.518332\pi\)
−0.0575591 + 0.998342i \(0.518332\pi\)
\(224\) −8.41489 8.85114i −0.562243 0.591391i
\(225\) 0 0
\(226\) 11.9814 + 23.8114i 0.796990 + 1.58391i
\(227\) −10.1158 + 10.1158i −0.671410 + 0.671410i −0.958041 0.286631i \(-0.907465\pi\)
0.286631 + 0.958041i \(0.407465\pi\)
\(228\) 0 0
\(229\) −12.0195 12.0195i −0.794270 0.794270i 0.187915 0.982185i \(-0.439827\pi\)
−0.982185 + 0.187915i \(0.939827\pi\)
\(230\) −14.4243 4.76744i −0.951110 0.314356i
\(231\) 0 0
\(232\) 6.07524 4.27476i 0.398859 0.280652i
\(233\) 13.3779i 0.876418i 0.898873 + 0.438209i \(0.144387\pi\)
−0.898873 + 0.438209i \(0.855613\pi\)
\(234\) 0 0
\(235\) 7.59587 + 7.59587i 0.495500 + 0.495500i
\(236\) 11.1917 1.65685i 0.728520 0.107852i
\(237\) 0 0
\(238\) 0.613057 0.308476i 0.0397386 0.0199956i
\(239\) −13.3675 −0.864670 −0.432335 0.901713i \(-0.642310\pi\)
−0.432335 + 0.901713i \(0.642310\pi\)
\(240\) 0 0
\(241\) 0.211474 0.0136222 0.00681112 0.999977i \(-0.497832\pi\)
0.00681112 + 0.999977i \(0.497832\pi\)
\(242\) −5.72891 + 2.88266i −0.368269 + 0.185305i
\(243\) 0 0
\(244\) 2.48005 + 16.7523i 0.158769 + 1.07245i
\(245\) 6.28141 + 6.28141i 0.401305 + 0.401305i
\(246\) 0 0
\(247\) 0.439861i 0.0279877i
\(248\) 5.13025 + 0.892458i 0.325771 + 0.0566711i
\(249\) 0 0
\(250\) 22.5628 + 7.45734i 1.42700 + 0.471644i
\(251\) −10.4337 10.4337i −0.658569 0.658569i 0.296472 0.955041i \(-0.404190\pi\)
−0.955041 + 0.296472i \(0.904190\pi\)
\(252\) 0 0
\(253\) −5.08532 + 5.08532i −0.319711 + 0.319711i
\(254\) 2.42557 + 4.82050i 0.152194 + 0.302465i
\(255\) 0 0
\(256\) −13.3137 + 8.87385i −0.832107 + 0.554615i
\(257\) 0.742176 0.0462957 0.0231478 0.999732i \(-0.492631\pi\)
0.0231478 + 0.999732i \(0.492631\pi\)
\(258\) 0 0
\(259\) 7.92221 7.92221i 0.492262 0.492262i
\(260\) −8.85799 + 11.9365i −0.549349 + 0.740268i
\(261\) 0 0
\(262\) −1.45734 0.481672i −0.0900347 0.0297578i
\(263\) 5.48435i 0.338180i −0.985601 0.169090i \(-0.945917\pi\)
0.985601 0.169090i \(-0.0540828\pi\)
\(264\) 0 0
\(265\) 40.3582i 2.47918i
\(266\) 0.215371 0.651622i 0.0132052 0.0399535i
\(267\) 0 0
\(268\) −4.31788 29.1665i −0.263757 1.78163i
\(269\) −14.4741 + 14.4741i −0.882500 + 0.882500i −0.993788 0.111289i \(-0.964502\pi\)
0.111289 + 0.993788i \(0.464502\pi\)
\(270\) 0 0
\(271\) −14.0370 −0.852685 −0.426342 0.904562i \(-0.640198\pi\)
−0.426342 + 0.904562i \(0.640198\pi\)
\(272\) −0.260504 0.860544i −0.0157954 0.0521781i
\(273\) 0 0
\(274\) −6.70825 + 3.37545i −0.405260 + 0.203918i
\(275\) 16.9442 16.9442i 1.02178 1.02178i
\(276\) 0 0
\(277\) 9.49013 + 9.49013i 0.570207 + 0.570207i 0.932186 0.361980i \(-0.117899\pi\)
−0.361980 + 0.932186i \(0.617899\pi\)
\(278\) 5.50276 16.6491i 0.330034 0.998545i
\(279\) 0 0
\(280\) −18.9670 + 13.3458i −1.13349 + 0.797566i
\(281\) 3.89359i 0.232272i −0.993233 0.116136i \(-0.962949\pi\)
0.993233 0.116136i \(-0.0370509\pi\)
\(282\) 0 0
\(283\) −12.4853 12.4853i −0.742173 0.742173i 0.230823 0.972996i \(-0.425858\pi\)
−0.972996 + 0.230823i \(0.925858\pi\)
\(284\) −6.93484 5.14631i −0.411507 0.305377i
\(285\) 0 0
\(286\) 3.16286 + 6.28577i 0.187024 + 0.371685i
\(287\) −12.6981 −0.749545
\(288\) 0 0
\(289\) −16.9495 −0.997028
\(290\) −6.34059 12.6011i −0.372332 0.739962i
\(291\) 0 0
\(292\) 9.59587 + 7.12105i 0.561556 + 0.416728i
\(293\) 11.1553 + 11.1553i 0.651697 + 0.651697i 0.953402 0.301704i \(-0.0975556\pi\)
−0.301704 + 0.953402i \(0.597556\pi\)
\(294\) 0 0
\(295\) 21.4844i 1.25087i
\(296\) −8.44651 12.0041i −0.490944 0.697724i
\(297\) 0 0
\(298\) 0.645643 1.95345i 0.0374011 0.113160i
\(299\) −3.91375 3.91375i −0.226338 0.226338i
\(300\) 0 0
\(301\) 16.7422 16.7422i 0.965003 0.965003i
\(302\) −2.57330 + 1.29483i −0.148077 + 0.0745089i
\(303\) 0 0
\(304\) −0.792701 0.424292i −0.0454645 0.0243348i
\(305\) 32.1587 1.84140
\(306\) 0 0
\(307\) −5.40320 + 5.40320i −0.308377 + 0.308377i −0.844280 0.535903i \(-0.819971\pi\)
0.535903 + 0.844280i \(0.319971\pi\)
\(308\) 1.60782 + 10.8605i 0.0916143 + 0.618837i
\(309\) 0 0
\(310\) 3.10318 9.38895i 0.176249 0.533257i
\(311\) 24.1623i 1.37012i 0.728488 + 0.685059i \(0.240224\pi\)
−0.728488 + 0.685059i \(0.759776\pi\)
\(312\) 0 0
\(313\) 16.6105i 0.938881i −0.882964 0.469441i \(-0.844456\pi\)
0.882964 0.469441i \(-0.155544\pi\)
\(314\) −11.5719 3.82467i −0.653039 0.215839i
\(315\) 0 0
\(316\) −17.8869 + 24.1032i −1.00621 + 1.35591i
\(317\) −1.81170 + 1.81170i −0.101755 + 0.101755i −0.756152 0.654397i \(-0.772923\pi\)
0.654397 + 0.756152i \(0.272923\pi\)
\(318\) 0 0
\(319\) −6.67794 −0.373893
\(320\) 12.9670 + 27.4775i 0.724875 + 1.53604i
\(321\) 0 0
\(322\) −3.88163 7.71423i −0.216315 0.429897i
\(323\) 0.0357265 0.0357265i 0.00198788 0.00198788i
\(324\) 0 0
\(325\) 13.0406 + 13.0406i 0.723361 + 0.723361i
\(326\) −6.52660 2.15714i −0.361475 0.119473i
\(327\) 0 0
\(328\) −2.85114 + 16.3896i −0.157428 + 0.904966i
\(329\) 6.10641i 0.336657i
\(330\) 0 0
\(331\) 13.5252 + 13.5252i 0.743411 + 0.743411i 0.973233 0.229822i \(-0.0738142\pi\)
−0.229822 + 0.973233i \(0.573814\pi\)
\(332\) 4.19011 + 28.3034i 0.229962 + 1.55335i
\(333\) 0 0
\(334\) 27.4165 13.7954i 1.50016 0.754850i
\(335\) −55.9898 −3.05905
\(336\) 0 0
\(337\) −1.12615 −0.0613454 −0.0306727 0.999529i \(-0.509765\pi\)
−0.0306727 + 0.999529i \(0.509765\pi\)
\(338\) 11.5853 5.82946i 0.630156 0.317081i
\(339\) 0 0
\(340\) −1.68897 + 0.250040i −0.0915973 + 0.0135603i
\(341\) −3.31010 3.31010i −0.179252 0.179252i
\(342\) 0 0
\(343\) 20.1623i 1.08866i
\(344\) −17.8502 25.3685i −0.962419 1.36778i
\(345\) 0 0
\(346\) −16.6094 5.48964i −0.892925 0.295125i
\(347\) −20.7938 20.7938i −1.11627 1.11627i −0.992284 0.123983i \(-0.960433\pi\)
−0.123983 0.992284i \(-0.539567\pi\)
\(348\) 0 0
\(349\) −19.2855 + 19.2855i −1.03233 + 1.03233i −0.0328700 + 0.999460i \(0.510465\pi\)
−0.999460 + 0.0328700i \(0.989535\pi\)
\(350\) 12.9336 + 25.7038i 0.691328 + 1.37392i
\(351\) 0 0
\(352\) 14.3789 + 0.363303i 0.766396 + 0.0193641i
\(353\) −25.5908 −1.36206 −0.681029 0.732256i \(-0.738467\pi\)
−0.681029 + 0.732256i \(0.738467\pi\)
\(354\) 0 0
\(355\) −11.5959 + 11.5959i −0.615445 + 0.615445i
\(356\) −2.29422 1.70253i −0.121594 0.0902340i
\(357\) 0 0
\(358\) 15.6316 + 5.16647i 0.826155 + 0.273056i
\(359\) 3.77296i 0.199129i −0.995031 0.0995645i \(-0.968255\pi\)
0.995031 0.0995645i \(-0.0317450\pi\)
\(360\) 0 0
\(361\) 18.9495i 0.997341i
\(362\) 4.21940 12.7662i 0.221767 0.670975i
\(363\) 0 0
\(364\) −8.35846 + 1.23741i −0.438102 + 0.0648578i
\(365\) 16.0454 16.0454i 0.839856 0.839856i
\(366\) 0 0
\(367\) −27.4474 −1.43274 −0.716371 0.697720i \(-0.754198\pi\)
−0.716371 + 0.697720i \(0.754198\pi\)
\(368\) −10.8284 + 3.27798i −0.564471 + 0.170877i
\(369\) 0 0
\(370\) −24.8986 + 12.5284i −1.29441 + 0.651321i
\(371\) 16.2222 16.2222i 0.842216 0.842216i
\(372\) 0 0
\(373\) 12.6231 + 12.6231i 0.653601 + 0.653601i 0.953858 0.300257i \(-0.0970725\pi\)
−0.300257 + 0.953858i \(0.597072\pi\)
\(374\) −0.253649 + 0.767438i −0.0131159 + 0.0396833i
\(375\) 0 0
\(376\) 7.88163 + 1.37109i 0.406464 + 0.0707085i
\(377\) 5.13946i 0.264695i
\(378\) 0 0
\(379\) −11.6686 11.6686i −0.599373 0.599373i 0.340772 0.940146i \(-0.389311\pi\)
−0.940146 + 0.340772i \(0.889311\pi\)
\(380\) −1.01748 + 1.37109i −0.0521955 + 0.0703353i
\(381\) 0 0
\(382\) −13.2238 26.2807i −0.676591 1.34464i
\(383\) 17.1885 0.878291 0.439145 0.898416i \(-0.355281\pi\)
0.439145 + 0.898416i \(0.355281\pi\)
\(384\) 0 0
\(385\) 20.8486 1.06254
\(386\) −8.99173 17.8699i −0.457667 0.909553i
\(387\) 0 0
\(388\) 19.5453 26.3380i 0.992264 1.33711i
\(389\) 1.88238 + 1.88238i 0.0954404 + 0.0954404i 0.753215 0.657774i \(-0.228502\pi\)
−0.657774 + 0.753215i \(0.728502\pi\)
\(390\) 0 0
\(391\) 0.635767i 0.0321521i
\(392\) 6.51772 + 1.13382i 0.329195 + 0.0572667i
\(393\) 0 0
\(394\) 1.52431 4.61192i 0.0767935 0.232345i
\(395\) 40.3034 + 40.3034i 2.02788 + 2.02788i
\(396\) 0 0
\(397\) 8.41166 8.41166i 0.422169 0.422169i −0.463781 0.885950i \(-0.653507\pi\)
0.885950 + 0.463781i \(0.153507\pi\)
\(398\) 0.386800 0.194629i 0.0193885 0.00975588i
\(399\) 0 0
\(400\) 36.0802 10.9222i 1.80401 0.546110i
\(401\) −1.12389 −0.0561242 −0.0280621 0.999606i \(-0.508934\pi\)
−0.0280621 + 0.999606i \(0.508934\pi\)
\(402\) 0 0
\(403\) 2.54751 2.54751i 0.126900 0.126900i
\(404\) 0.229135 0.0339217i 0.0113999 0.00168767i
\(405\) 0 0
\(406\) 2.51645 7.61373i 0.124889 0.377863i
\(407\) 13.1950i 0.654051i
\(408\) 0 0
\(409\) 13.7211i 0.678464i 0.940703 + 0.339232i \(0.110167\pi\)
−0.940703 + 0.339232i \(0.889833\pi\)
\(410\) 29.9949 + 9.91375i 1.48134 + 0.489605i
\(411\) 0 0
\(412\) −21.4422 15.9121i −1.05638 0.783934i
\(413\) 8.63577 8.63577i 0.424938 0.424938i
\(414\) 0 0
\(415\) 54.3329 2.66710
\(416\) −0.279604 + 11.0662i −0.0137087 + 0.542566i
\(417\) 0 0
\(418\) 0.363303 + 0.722018i 0.0177698 + 0.0353151i
\(419\) 9.30755 9.30755i 0.454703 0.454703i −0.442209 0.896912i \(-0.645805\pi\)
0.896912 + 0.442209i \(0.145805\pi\)
\(420\) 0 0
\(421\) 8.44378 + 8.44378i 0.411525 + 0.411525i 0.882269 0.470745i \(-0.156015\pi\)
−0.470745 + 0.882269i \(0.656015\pi\)
\(422\) −13.7344 4.53942i −0.668580 0.220975i
\(423\) 0 0
\(424\) −17.2958 24.5807i −0.839960 1.19374i
\(425\) 2.11837i 0.102756i
\(426\) 0 0
\(427\) 12.9264 + 12.9264i 0.625551 + 0.625551i
\(428\) −20.3633 + 3.01464i −0.984297 + 0.145718i
\(429\) 0 0
\(430\) −52.6187 + 26.4766i −2.53750 + 1.27681i
\(431\) 30.6054 1.47421 0.737105 0.675778i \(-0.236192\pi\)
0.737105 + 0.675778i \(0.236192\pi\)
\(432\) 0 0
\(433\) −15.3137 −0.735930 −0.367965 0.929840i \(-0.619945\pi\)
−0.367965 + 0.929840i \(0.619945\pi\)
\(434\) 5.02129 2.52660i 0.241030 0.121281i
\(435\) 0 0
\(436\) −2.91630 19.6991i −0.139665 0.943413i
\(437\) −0.449555 0.449555i −0.0215051 0.0215051i
\(438\) 0 0
\(439\) 33.3676i 1.59255i −0.604936 0.796274i \(-0.706801\pi\)
0.604936 0.796274i \(-0.293199\pi\)
\(440\) 4.68119 26.9096i 0.223167 1.28286i
\(441\) 0 0
\(442\) −0.590633 0.195213i −0.0280936 0.00928533i
\(443\) −2.28832 2.28832i −0.108721 0.108721i 0.650653 0.759375i \(-0.274495\pi\)
−0.759375 + 0.650653i \(0.774495\pi\)
\(444\) 0 0
\(445\) −3.83621 + 3.83621i −0.181854 + 0.181854i
\(446\) 1.09276 + 2.17172i 0.0517437 + 0.102834i
\(447\) 0 0
\(448\) −5.83260 + 16.2569i −0.275565 + 0.768066i
\(449\) 27.4165 1.29387 0.646933 0.762547i \(-0.276052\pi\)
0.646933 + 0.762547i \(0.276052\pi\)
\(450\) 0 0
\(451\) 10.5748 10.5748i 0.497947 0.497947i
\(452\) 22.4649 30.2722i 1.05666 1.42388i
\(453\) 0 0
\(454\) 19.2096 + 6.34905i 0.901551 + 0.297976i
\(455\) 16.0454i 0.752221i
\(456\) 0 0
\(457\) 10.9147i 0.510567i 0.966866 + 0.255284i \(0.0821688\pi\)
−0.966866 + 0.255284i \(0.917831\pi\)
\(458\) −7.54386 + 22.8246i −0.352501 + 1.06652i
\(459\) 0 0
\(460\) 3.14631 + 21.2527i 0.146697 + 0.990913i
\(461\) −17.8319 + 17.8319i −0.830512 + 0.830512i −0.987587 0.157075i \(-0.949794\pi\)
0.157075 + 0.987587i \(0.449794\pi\)
\(462\) 0 0
\(463\) 22.4937 1.04537 0.522686 0.852525i \(-0.324930\pi\)
0.522686 + 0.852525i \(0.324930\pi\)
\(464\) −9.26213 4.95755i −0.429983 0.230148i
\(465\) 0 0
\(466\) 16.9004 8.50389i 0.782895 0.393935i
\(467\) −24.2171 + 24.2171i −1.12063 + 1.12063i −0.128989 + 0.991646i \(0.541173\pi\)
−0.991646 + 0.128989i \(0.958827\pi\)
\(468\) 0 0
\(469\) −22.5054 22.5054i −1.03920 1.03920i
\(470\) 4.76744 14.4243i 0.219906 0.665343i
\(471\) 0 0
\(472\) −9.20730 13.0853i −0.423800 0.602301i
\(473\) 27.8852i 1.28216i
\(474\) 0 0
\(475\) 1.49791 + 1.49791i 0.0687289 + 0.0687289i
\(476\) −0.779397 0.578387i −0.0357236 0.0265103i
\(477\) 0 0
\(478\) 8.49724 + 16.8872i 0.388655 + 0.772400i
\(479\) 36.2362 1.65568 0.827838 0.560968i \(-0.189571\pi\)
0.827838 + 0.560968i \(0.189571\pi\)
\(480\) 0 0
\(481\) −10.1551 −0.463032
\(482\) −0.134427 0.267156i −0.00612297 0.0121686i
\(483\) 0 0
\(484\) 7.28334 + 5.40494i 0.331061 + 0.245679i
\(485\) −44.0403 44.0403i −1.99977 1.99977i
\(486\) 0 0
\(487\) 16.8200i 0.762186i 0.924537 + 0.381093i \(0.124452\pi\)
−0.924537 + 0.381093i \(0.875548\pi\)
\(488\) 19.5867 13.7819i 0.886646 0.623876i
\(489\) 0 0
\(490\) 3.94244 11.9282i 0.178101 0.538860i
\(491\) −6.10641 6.10641i −0.275578 0.275578i 0.555763 0.831341i \(-0.312426\pi\)
−0.831341 + 0.555763i \(0.812426\pi\)
\(492\) 0 0
\(493\) 0.417438 0.417438i 0.0188005 0.0188005i
\(494\) −0.555677 + 0.279604i −0.0250011 + 0.0125800i
\(495\) 0 0
\(496\) −2.13368 7.04836i −0.0958050 0.316481i
\(497\) −9.32206 −0.418151
\(498\) 0 0
\(499\) −19.6770 + 19.6770i −0.880864 + 0.880864i −0.993622 0.112758i \(-0.964031\pi\)
0.112758 + 0.993622i \(0.464031\pi\)
\(500\) −4.92153 33.2440i −0.220098 1.48672i
\(501\) 0 0
\(502\) −6.54856 + 19.8132i −0.292277 + 0.884308i
\(503\) 25.7308i 1.14728i −0.819108 0.573639i \(-0.805531\pi\)
0.819108 0.573639i \(-0.194469\pi\)
\(504\) 0 0
\(505\) 0.439861i 0.0195736i
\(506\) 9.65685 + 3.19173i 0.429300 + 0.141890i
\(507\) 0 0
\(508\) 4.54789 6.12845i 0.201780 0.271906i
\(509\) −1.73514 + 1.73514i −0.0769087 + 0.0769087i −0.744515 0.667606i \(-0.767319\pi\)
0.667606 + 0.744515i \(0.267319\pi\)
\(510\) 0 0
\(511\) 12.8991 0.570623
\(512\) 19.6734 + 11.1784i 0.869450 + 0.494021i
\(513\) 0 0
\(514\) −0.471775 0.937591i −0.0208091 0.0413554i
\(515\) −35.8538 + 35.8538i −1.57991 + 1.57991i
\(516\) 0 0
\(517\) −5.08532 5.08532i −0.223652 0.223652i
\(518\) −15.0440 4.97226i −0.660995 0.218469i
\(519\) 0 0
\(520\) 20.7101 + 3.60272i 0.908196 + 0.157990i
\(521\) 33.5944i 1.47180i −0.677092 0.735898i \(-0.736760\pi\)
0.677092 0.735898i \(-0.263240\pi\)
\(522\) 0 0
\(523\) −21.8158 21.8158i −0.953938 0.953938i 0.0450467 0.998985i \(-0.485656\pi\)
−0.998985 + 0.0450467i \(0.985656\pi\)
\(524\) 0.317883 + 2.14724i 0.0138868 + 0.0938026i
\(525\) 0 0
\(526\) −6.92839 + 3.48621i −0.302092 + 0.152006i
\(527\) 0.413828 0.0180266
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) −50.9846 + 25.6543i −2.21463 + 1.11435i
\(531\) 0 0
\(532\) −0.960099 + 0.142136i −0.0416256 + 0.00616236i
\(533\) 8.13853 + 8.13853i 0.352519 + 0.352519i
\(534\) 0 0
\(535\) 39.0907i 1.69004i
\(536\) −34.1013 + 23.9949i −1.47295 + 1.03642i
\(537\) 0 0
\(538\) 27.4858 + 9.08445i 1.18500 + 0.391658i
\(539\) −4.20531 4.20531i −0.181136 0.181136i
\(540\) 0 0
\(541\) 27.2112 27.2112i 1.16990 1.16990i 0.187669 0.982232i \(-0.439907\pi\)
0.982232 0.187669i \(-0.0600933\pi\)
\(542\) 8.92281 + 17.7329i 0.383267 + 0.761694i
\(543\) 0 0
\(544\) −0.921533 + 0.876113i −0.0395104 + 0.0375630i
\(545\) −37.8155 −1.61984
\(546\) 0 0
\(547\) −6.80116 + 6.80116i −0.290796 + 0.290796i −0.837395 0.546598i \(-0.815922\pi\)
0.546598 + 0.837395i \(0.315922\pi\)
\(548\) 8.52841 + 6.32889i 0.364315 + 0.270357i
\(549\) 0 0
\(550\) −32.1765 10.6348i −1.37201 0.453470i
\(551\) 0.590346i 0.0251496i
\(552\) 0 0
\(553\) 32.4004i 1.37780i
\(554\) 5.95635 18.0214i 0.253061 0.765657i
\(555\) 0 0
\(556\) −24.5307 + 3.63159i −1.04033 + 0.154014i
\(557\) 4.29337 4.29337i 0.181916 0.181916i −0.610274 0.792190i \(-0.708941\pi\)
0.792190 + 0.610274i \(0.208941\pi\)
\(558\) 0 0
\(559\) −21.4609 −0.907701
\(560\) 28.9164 + 15.4775i 1.22194 + 0.654044i
\(561\) 0 0
\(562\) −4.91878 + 2.47502i −0.207486 + 0.104402i
\(563\) 10.0801 10.0801i 0.424825 0.424825i −0.462036 0.886861i \(-0.652881\pi\)
0.886861 + 0.462036i \(0.152881\pi\)
\(564\) 0 0
\(565\) −50.6187 50.6187i −2.12954 2.12954i
\(566\) −7.83621 + 23.7091i −0.329381 + 0.996569i
\(567\) 0 0
\(568\) −2.09311 + 12.0321i −0.0878248 + 0.504856i
\(569\) 32.5018i 1.36255i 0.732029 + 0.681274i \(0.238574\pi\)
−0.732029 + 0.681274i \(0.761426\pi\)
\(570\) 0 0
\(571\) −9.17157 9.17157i −0.383818 0.383818i 0.488657 0.872476i \(-0.337487\pi\)
−0.872476 + 0.488657i \(0.837487\pi\)
\(572\) 5.93030 7.99129i 0.247958 0.334132i
\(573\) 0 0
\(574\) 8.07174 + 16.0415i 0.336908 + 0.669560i
\(575\) 26.6559 1.11163
\(576\) 0 0
\(577\) 11.7536 0.489308 0.244654 0.969611i \(-0.421326\pi\)
0.244654 + 0.969611i \(0.421326\pi\)
\(578\) 10.7742 + 21.4123i 0.448147 + 0.890634i
\(579\) 0 0
\(580\) −11.8885 + 16.0202i −0.493643 + 0.665201i
\(581\) 21.8395 + 21.8395i 0.906053 + 0.906053i
\(582\) 0 0
\(583\) 27.0192i 1.11902i
\(584\) 2.89627 16.6491i 0.119849 0.688943i
\(585\) 0 0
\(586\) 7.00144 21.1835i 0.289227 0.875081i
\(587\) −6.46002 6.46002i −0.266634 0.266634i 0.561109 0.827742i \(-0.310375\pi\)
−0.827742 + 0.561109i \(0.810375\pi\)
\(588\) 0 0
\(589\) 0.292621 0.292621i 0.0120572 0.0120572i
\(590\) −27.1412 + 13.6569i −1.11739 + 0.562244i
\(591\) 0 0
\(592\) −9.79564 + 18.3011i −0.402598 + 0.752170i
\(593\) −5.49270 −0.225558 −0.112779 0.993620i \(-0.535975\pi\)
−0.112779 + 0.993620i \(0.535975\pi\)
\(594\) 0 0
\(595\) −1.30324 + 1.30324i −0.0534278 + 0.0534278i
\(596\) −2.87820 + 0.426097i −0.117896 + 0.0174536i
\(597\) 0 0
\(598\) −2.45641 + 7.43208i −0.100450 + 0.303920i
\(599\) 36.4348i 1.48868i −0.667799 0.744342i \(-0.732763\pi\)
0.667799 0.744342i \(-0.267237\pi\)
\(600\) 0 0
\(601\) 9.97474i 0.406878i −0.979088 0.203439i \(-0.934788\pi\)
0.979088 0.203439i \(-0.0652119\pi\)
\(602\) −31.7928 10.5080i −1.29578 0.428274i
\(603\) 0 0
\(604\) 3.27151 + 2.42777i 0.133116 + 0.0987848i
\(605\) 12.1786 12.1786i 0.495131 0.495131i
\(606\) 0 0
\(607\) 4.51900 0.183421 0.0917103 0.995786i \(-0.470767\pi\)
0.0917103 + 0.995786i \(0.470767\pi\)
\(608\) −0.0321169 + 1.27113i −0.00130251 + 0.0515510i
\(609\) 0 0
\(610\) −20.4422 40.6261i −0.827679 1.64490i
\(611\) 3.91375 3.91375i 0.158333 0.158333i
\(612\) 0 0
\(613\) −8.43692 8.43692i −0.340764 0.340764i 0.515890 0.856655i \(-0.327461\pi\)
−0.856655 + 0.515890i \(0.827461\pi\)
\(614\) 10.2605 + 3.39125i 0.414080 + 0.136860i
\(615\) 0 0
\(616\) 12.6981 8.93484i 0.511621 0.359995i
\(617\) 32.1201i 1.29311i −0.762869 0.646554i \(-0.776210\pi\)
0.762869 0.646554i \(-0.223790\pi\)
\(618\) 0 0
\(619\) 15.0412 + 15.0412i 0.604559 + 0.604559i 0.941519 0.336960i \(-0.109399\pi\)
−0.336960 + 0.941519i \(0.609399\pi\)
\(620\) −13.8337 + 2.04797i −0.555573 + 0.0822486i
\(621\) 0 0
\(622\) 30.5243 15.3591i 1.22391 0.615845i
\(623\) −3.08398 −0.123557
\(624\) 0 0
\(625\) −16.6958 −0.667833
\(626\) −20.9841 + 10.5587i −0.838692 + 0.422011i
\(627\) 0 0
\(628\) 2.52413 + 17.0500i 0.100724 + 0.680368i
\(629\) −0.824818 0.824818i −0.0328876 0.0328876i
\(630\) 0 0
\(631\) 36.4685i 1.45179i −0.687807 0.725894i \(-0.741426\pi\)
0.687807 0.725894i \(-0.258574\pi\)
\(632\) 41.8196 + 7.27494i 1.66350 + 0.289382i
\(633\) 0 0
\(634\) 3.44035 + 1.13709i 0.136634 + 0.0451595i
\(635\) −10.2475 10.2475i −0.406659 0.406659i
\(636\) 0 0
\(637\) 3.23648 3.23648i 0.128234 0.128234i
\(638\) 4.24494 + 8.43625i 0.168059 + 0.333994i
\(639\) 0 0
\(640\) 26.4697 33.8477i 1.04631 1.33795i
\(641\) −14.0036 −0.553109 −0.276555 0.960998i \(-0.589193\pi\)
−0.276555 + 0.960998i \(0.589193\pi\)
\(642\) 0 0
\(643\) 16.6034 16.6034i 0.654774 0.654774i −0.299365 0.954139i \(-0.596775\pi\)
0.954139 + 0.299365i \(0.0967748\pi\)
\(644\) −7.27798 + 9.80734i −0.286793 + 0.386463i
\(645\) 0 0
\(646\) −0.0678434 0.0224232i −0.00266926 0.000882230i
\(647\) 12.1908i 0.479270i 0.970863 + 0.239635i \(0.0770277\pi\)
−0.970863 + 0.239635i \(0.922972\pi\)
\(648\) 0 0
\(649\) 14.3835i 0.564600i
\(650\) 8.18473 24.7636i 0.321032 0.971309i
\(651\) 0 0
\(652\) 1.42362 + 9.61628i 0.0557533 + 0.376603i
\(653\) −0.983270 + 0.983270i −0.0384783 + 0.0384783i −0.726084 0.687606i \(-0.758662\pi\)
0.687606 + 0.726084i \(0.258662\pi\)
\(654\) 0 0
\(655\) 4.12198 0.161059
\(656\) 22.5174 6.81647i 0.879157 0.266138i
\(657\) 0 0
\(658\) 7.71423 3.88163i 0.300732 0.151322i
\(659\) 18.0559 18.0559i 0.703357 0.703357i −0.261772 0.965130i \(-0.584307\pi\)
0.965130 + 0.261772i \(0.0843069\pi\)
\(660\) 0 0
\(661\) −4.55890 4.55890i −0.177321 0.177321i 0.612866 0.790187i \(-0.290017\pi\)
−0.790187 + 0.612866i \(0.790017\pi\)
\(662\) 8.48889 25.6839i 0.329930 0.998232i
\(663\) 0 0
\(664\) 33.0922 23.2848i 1.28423 0.903627i
\(665\) 1.84307i 0.0714710i
\(666\) 0 0
\(667\) −5.25272 5.25272i −0.203386 0.203386i
\(668\) −34.8554 25.8661i −1.34860 1.00079i
\(669\) 0 0
\(670\) 35.5908 + 70.7320i 1.37499 + 2.73261i
\(671\) −21.5298 −0.831148
\(672\) 0 0
\(673\) −10.8569 −0.418504 −0.209252 0.977862i \(-0.567103\pi\)
−0.209252 + 0.977862i \(0.567103\pi\)
\(674\) 0.715856 + 1.42267i 0.0275737 + 0.0547992i
\(675\) 0 0
\(676\) −14.7287 10.9301i −0.566489 0.420389i
\(677\) −23.7066 23.7066i −0.911120 0.911120i 0.0852405 0.996360i \(-0.472834\pi\)
−0.996360 + 0.0852405i \(0.972834\pi\)
\(678\) 0 0
\(679\) 35.4045i 1.35870i
\(680\) 1.38950 + 1.97474i 0.0532847 + 0.0757277i
\(681\) 0 0
\(682\) −2.07754 + 6.28577i −0.0795530 + 0.240694i
\(683\) 17.8337 + 17.8337i 0.682386 + 0.682386i 0.960537 0.278151i \(-0.0897217\pi\)
−0.278151 + 0.960537i \(0.589722\pi\)
\(684\) 0 0
\(685\) 14.2605 14.2605i 0.544866 0.544866i
\(686\) 25.4710 12.8165i 0.972489 0.489335i
\(687\) 0 0
\(688\) −20.7013 + 38.6761i −0.789231 + 1.47451i
\(689\) −20.7945 −0.792205
\(690\) 0 0
\(691\) 10.8557 10.8557i 0.412970 0.412970i −0.469802 0.882772i \(-0.655675\pi\)
0.882772 + 0.469802i \(0.155675\pi\)
\(692\) 3.62293 + 24.4722i 0.137723 + 0.930294i
\(693\) 0 0
\(694\) −13.0509 + 39.4866i −0.495406 + 1.49889i
\(695\) 47.0907i 1.78625i
\(696\) 0 0
\(697\) 1.32206i 0.0500765i
\(698\) 36.6225 + 12.1043i 1.38618 + 0.458154i
\(699\) 0 0
\(700\) 24.2502 32.6780i 0.916570 1.23511i
\(701\) 6.08875 6.08875i 0.229969 0.229969i −0.582711 0.812680i \(-0.698008\pi\)
0.812680 + 0.582711i \(0.198008\pi\)
\(702\) 0 0
\(703\) −1.16647 −0.0439942
\(704\) −8.68119 18.3958i −0.327185 0.693317i
\(705\) 0 0
\(706\) 16.2672 + 32.3288i 0.612222 + 1.21671i
\(707\) 0.176805 0.176805i 0.00664943 0.00664943i
\(708\) 0 0
\(709\) 22.8836 + 22.8836i 0.859413 + 0.859413i 0.991269 0.131856i \(-0.0420936\pi\)
−0.131856 + 0.991269i \(0.542094\pi\)
\(710\) 22.0202 + 7.27798i 0.826402 + 0.273138i
\(711\) 0 0
\(712\) −0.692453 + 3.98053i −0.0259508 + 0.149177i
\(713\) 5.20730i 0.195015i
\(714\) 0 0
\(715\) −13.3624 13.3624i −0.499724 0.499724i
\(716\) −3.40965 23.0316i −0.127425 0.860729i
\(717\) 0 0
\(718\) −4.76638 + 2.39834i −0.177880 + 0.0895052i
\(719\) 1.46744 0.0547262 0.0273631 0.999626i \(-0.491289\pi\)
0.0273631 + 0.999626i \(0.491289\pi\)
\(720\) 0 0
\(721\) −28.8233 −1.07344
\(722\) 23.9389 12.0455i 0.890913 0.448288i
\(723\) 0 0
\(724\) −18.8096 + 2.78463i −0.699055 + 0.103490i
\(725\) 17.5020 + 17.5020i 0.650008 + 0.650008i
\(726\) 0 0
\(727\) 15.3928i 0.570889i 0.958395 + 0.285445i \(0.0921412\pi\)
−0.958395 + 0.285445i \(0.907859\pi\)
\(728\) 6.87640 + 9.77267i 0.254856 + 0.362199i
\(729\) 0 0
\(730\) −30.4697 10.0707i −1.12773 0.372733i
\(731\) −1.74311 1.74311i −0.0644711 0.0644711i
\(732\) 0 0
\(733\) −12.4185 + 12.4185i −0.458688 + 0.458688i −0.898225 0.439536i \(-0.855143\pi\)
0.439536 + 0.898225i \(0.355143\pi\)
\(734\) 17.4473 + 34.6743i 0.643993 + 1.27985i
\(735\) 0 0
\(736\) 11.0243 + 11.5959i 0.406362 + 0.427429i
\(737\) 37.4844 1.38075
\(738\) 0 0
\(739\) −14.6559 + 14.6559i −0.539127 + 0.539127i −0.923273 0.384146i \(-0.874496\pi\)
0.384146 + 0.923273i \(0.374496\pi\)
\(740\) 31.6543 + 23.4905i 1.16364 + 0.863528i
\(741\) 0 0
\(742\) −30.8055 10.1817i −1.13090 0.373780i
\(743\) 31.7821i 1.16597i 0.812482 + 0.582986i \(0.198116\pi\)
−0.812482 + 0.582986i \(0.801884\pi\)
\(744\) 0 0
\(745\) 5.52518i 0.202427i
\(746\) 7.92273 23.9709i 0.290072 0.877637i
\(747\) 0 0
\(748\) 1.13074 0.167398i 0.0413440 0.00612068i
\(749\) −15.7127 + 15.7127i −0.574131 + 0.574131i
\(750\) 0 0
\(751\) 29.7594 1.08594 0.542968 0.839753i \(-0.317301\pi\)
0.542968 + 0.839753i \(0.317301\pi\)
\(752\) −3.27798 10.8284i −0.119536 0.394872i
\(753\) 0 0
\(754\) −6.49268 + 3.26697i −0.236449 + 0.118976i
\(755\) 5.47036 5.47036i 0.199087 0.199087i
\(756\) 0 0
\(757\) 15.6355 + 15.6355i 0.568282 + 0.568282i 0.931647 0.363365i \(-0.118372\pi\)
−0.363365 + 0.931647i \(0.618372\pi\)
\(758\) −7.32361 + 22.1582i −0.266005 + 0.804822i
\(759\) 0 0
\(760\) 2.37887 + 0.413828i 0.0862908 + 0.0150111i
\(761\) 4.55957i 0.165284i 0.996579 + 0.0826422i \(0.0263359\pi\)
−0.996579 + 0.0826422i \(0.973664\pi\)
\(762\) 0 0
\(763\) −15.2002 15.2002i −0.550284 0.550284i
\(764\) −24.7945 + 33.4114i −0.897032 + 1.20878i
\(765\) 0 0
\(766\) −10.9261 21.7142i −0.394777 0.784567i
\(767\) −11.0698 −0.399706
\(768\) 0 0
\(769\) 36.5794 1.31909 0.659543 0.751667i \(-0.270750\pi\)
0.659543 + 0.751667i \(0.270750\pi\)
\(770\) −13.2527 26.3380i −0.477595 0.949157i
\(771\) 0 0
\(772\) −16.8593 + 22.7185i −0.606780 + 0.817657i
\(773\) 18.7108 + 18.7108i 0.672981 + 0.672981i 0.958402 0.285421i \(-0.0921335\pi\)
−0.285421 + 0.958402i \(0.592133\pi\)
\(774\) 0 0
\(775\) 17.3507i 0.623255i
\(776\) −45.6972 7.94948i −1.64043 0.285370i
\(777\) 0 0
\(778\) 1.18145 3.57457i 0.0423570 0.128155i
\(779\) 0.934836 + 0.934836i 0.0334940 + 0.0334940i
\(780\) 0 0
\(781\) 7.76326 7.76326i 0.277791 0.277791i
\(782\) −0.803165 + 0.404135i −0.0287211 + 0.0144518i
\(783\) 0 0
\(784\) −2.71073 8.95458i −0.0968118 0.319806i
\(785\) 32.7302 1.16819
\(786\) 0 0
\(787\) 13.3759 13.3759i 0.476801 0.476801i −0.427306 0.904107i \(-0.640537\pi\)
0.904107 + 0.427306i \(0.140537\pi\)
\(788\) −6.79520