Properties

Label 114.2.h.e.65.1
Level $114$
Weight $2$
Character 114.65
Analytic conductor $0.910$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 114.65
Dual form 114.2.h.e.107.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(0.724745 + 1.57313i) q^{6} +4.44949 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(0.724745 + 1.57313i) q^{6} +4.44949 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +(1.22474 - 0.707107i) q^{10} -0.317837i q^{11} +(-1.72474 - 0.158919i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(-2.22474 + 3.85337i) q^{14} +(-2.22474 + 1.02494i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.44949 + 3.14626i) q^{17} +(2.94949 + 0.548188i) q^{18} +(-4.17423 + 1.25529i) q^{19} +1.41421i q^{20} +(4.44949 - 6.29253i) q^{21} +(0.275255 + 0.158919i) q^{22} +(-6.12372 + 3.53553i) q^{23} +(1.00000 - 1.41421i) q^{24} +(-1.50000 - 2.59808i) q^{25} -3.46410i q^{26} +(-5.00000 - 1.41421i) q^{27} +(-2.22474 - 3.85337i) q^{28} +(1.22474 + 2.12132i) q^{29} +(0.224745 - 2.43916i) q^{30} +4.24264i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.449490 - 0.317837i) q^{33} +(-5.44949 + 3.14626i) q^{34} +(-5.44949 - 3.14626i) q^{35} +(-1.94949 + 2.28024i) q^{36} -0.778539i q^{37} +(1.00000 - 4.24264i) q^{38} +(-0.550510 + 5.97469i) q^{39} +(-1.22474 - 0.707107i) q^{40} +(1.50000 - 2.59808i) q^{41} +(3.22474 + 6.99964i) q^{42} +(-0.449490 + 0.778539i) q^{43} +(-0.275255 + 0.158919i) q^{44} +(-0.775255 + 4.17121i) q^{45} -7.07107i q^{46} +(5.57321 - 3.21770i) q^{47} +(0.724745 + 1.57313i) q^{48} +12.7980 q^{49} +3.00000 q^{50} +(9.89898 - 4.56048i) q^{51} +(3.00000 + 1.73205i) q^{52} +(0.550510 + 0.953512i) q^{53} +(3.72474 - 3.62302i) q^{54} +(-0.224745 + 0.389270i) q^{55} +4.44949 q^{56} +(-2.39898 + 7.15855i) q^{57} -2.44949 q^{58} +(-3.27526 + 5.67291i) q^{59} +(2.00000 + 1.41421i) q^{60} +(3.22474 + 5.58542i) q^{61} +(-3.67423 - 2.12132i) q^{62} +(-4.44949 - 12.5851i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(0.500000 - 0.230351i) q^{66} +(-5.17423 + 2.98735i) q^{67} -6.29253i q^{68} +(-1.12372 + 12.1958i) q^{69} +(5.44949 - 3.14626i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(-1.00000 - 2.82843i) q^{72} +(5.39898 - 9.35131i) q^{73} +(0.674235 + 0.389270i) q^{74} +(-5.17423 - 0.476756i) q^{75} +(3.17423 + 2.98735i) q^{76} -1.41421i q^{77} +(-4.89898 - 3.46410i) q^{78} +(7.34847 + 4.24264i) q^{79} +(1.22474 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(1.50000 + 2.59808i) q^{82} -14.1742i q^{83} +(-7.67423 - 0.707107i) q^{84} +(-4.44949 - 7.70674i) q^{85} +(-0.449490 - 0.778539i) q^{86} +(4.22474 + 0.389270i) q^{87} -0.317837i q^{88} +(-8.44949 - 14.6349i) q^{89} +(-3.22474 - 2.75699i) q^{90} +(-13.3485 + 7.70674i) q^{91} +(6.12372 + 3.53553i) q^{92} +(6.00000 + 4.24264i) q^{93} +6.43539i q^{94} +(6.00000 + 1.41421i) q^{95} +(-1.72474 - 0.158919i) q^{96} +(-11.8485 - 6.84072i) q^{97} +(-6.39898 + 11.0834i) q^{98} +(-0.898979 + 0.317837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} - 2 q^{12} - 12 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 12 q^{17} + 2 q^{18} - 2 q^{19} + 8 q^{21} + 6 q^{22} + 4 q^{24} - 6 q^{25} - 20 q^{27} - 4 q^{28} - 4 q^{30} - 2 q^{32} + 8 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{38} - 12 q^{39} + 6 q^{41} + 8 q^{42} + 8 q^{43} - 6 q^{44} - 8 q^{45} - 12 q^{47} - 2 q^{48} + 12 q^{49} + 12 q^{50} + 20 q^{51} + 12 q^{52} + 12 q^{53} + 10 q^{54} + 4 q^{55} + 8 q^{56} + 10 q^{57} - 18 q^{59} + 8 q^{60} + 8 q^{61} - 8 q^{63} + 4 q^{64} + 2 q^{66} - 6 q^{67} + 20 q^{69} + 12 q^{70} - 12 q^{71} - 4 q^{72} + 2 q^{73} - 12 q^{74} - 6 q^{75} - 2 q^{76} - 28 q^{81} + 6 q^{82} - 16 q^{84} - 8 q^{85} + 8 q^{86} + 12 q^{87} - 24 q^{89} - 8 q^{90} - 24 q^{91} + 24 q^{93} + 24 q^{95} - 2 q^{96} - 18 q^{97} - 6 q^{98} + 16 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.22474 0.707107i −0.547723 0.316228i 0.200480 0.979698i \(-0.435750\pi\)
−0.748203 + 0.663470i \(0.769083\pi\)
\(6\) 0.724745 + 1.57313i 0.295876 + 0.642229i
\(7\) 4.44949 1.68175 0.840875 0.541230i \(-0.182041\pi\)
0.840875 + 0.541230i \(0.182041\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.22474 0.707107i 0.387298 0.223607i
\(11\) 0.317837i 0.0958315i −0.998851 0.0479158i \(-0.984742\pi\)
0.998851 0.0479158i \(-0.0152579\pi\)
\(12\) −1.72474 0.158919i −0.497891 0.0458759i
\(13\) −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i \(-0.826170\pi\)
0.0225039 + 0.999747i \(0.492836\pi\)
\(14\) −2.22474 + 3.85337i −0.594588 + 1.02986i
\(15\) −2.22474 + 1.02494i −0.574427 + 0.264639i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 5.44949 + 3.14626i 1.32170 + 0.763081i 0.983999 0.178174i \(-0.0570190\pi\)
0.337696 + 0.941255i \(0.390352\pi\)
\(18\) 2.94949 + 0.548188i 0.695201 + 0.129209i
\(19\) −4.17423 + 1.25529i −0.957635 + 0.287984i
\(20\) 1.41421i 0.316228i
\(21\) 4.44949 6.29253i 0.970958 1.37314i
\(22\) 0.275255 + 0.158919i 0.0586846 + 0.0338816i
\(23\) −6.12372 + 3.53553i −1.27688 + 0.737210i −0.976274 0.216537i \(-0.930524\pi\)
−0.300610 + 0.953747i \(0.597190\pi\)
\(24\) 1.00000 1.41421i 0.204124 0.288675i
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 3.46410i 0.679366i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) −2.22474 3.85337i −0.420437 0.728219i
\(29\) 1.22474 + 2.12132i 0.227429 + 0.393919i 0.957046 0.289938i \(-0.0936346\pi\)
−0.729616 + 0.683857i \(0.760301\pi\)
\(30\) 0.224745 2.43916i 0.0410326 0.445327i
\(31\) 4.24264i 0.762001i 0.924575 + 0.381000i \(0.124420\pi\)
−0.924575 + 0.381000i \(0.875580\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.449490 0.317837i −0.0782461 0.0553284i
\(34\) −5.44949 + 3.14626i −0.934580 + 0.539580i
\(35\) −5.44949 3.14626i −0.921132 0.531816i
\(36\) −1.94949 + 2.28024i −0.324915 + 0.380040i
\(37\) 0.778539i 0.127991i −0.997950 0.0639955i \(-0.979616\pi\)
0.997950 0.0639955i \(-0.0203843\pi\)
\(38\) 1.00000 4.24264i 0.162221 0.688247i
\(39\) −0.550510 + 5.97469i −0.0881522 + 0.956716i
\(40\) −1.22474 0.707107i −0.193649 0.111803i
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 3.22474 + 6.99964i 0.497589 + 1.08007i
\(43\) −0.449490 + 0.778539i −0.0685465 + 0.118726i −0.898262 0.439461i \(-0.855169\pi\)
0.829715 + 0.558187i \(0.188503\pi\)
\(44\) −0.275255 + 0.158919i −0.0414963 + 0.0239579i
\(45\) −0.775255 + 4.17121i −0.115568 + 0.621807i
\(46\) 7.07107i 1.04257i
\(47\) 5.57321 3.21770i 0.812937 0.469349i −0.0350379 0.999386i \(-0.511155\pi\)
0.847975 + 0.530037i \(0.177822\pi\)
\(48\) 0.724745 + 1.57313i 0.104608 + 0.227062i
\(49\) 12.7980 1.82828
\(50\) 3.00000 0.424264
\(51\) 9.89898 4.56048i 1.38613 0.638595i
\(52\) 3.00000 + 1.73205i 0.416025 + 0.240192i
\(53\) 0.550510 + 0.953512i 0.0756184 + 0.130975i 0.901355 0.433081i \(-0.142574\pi\)
−0.825737 + 0.564056i \(0.809240\pi\)
\(54\) 3.72474 3.62302i 0.506874 0.493031i
\(55\) −0.224745 + 0.389270i −0.0303046 + 0.0524891i
\(56\) 4.44949 0.594588
\(57\) −2.39898 + 7.15855i −0.317753 + 0.948174i
\(58\) −2.44949 −0.321634
\(59\) −3.27526 + 5.67291i −0.426402 + 0.738550i −0.996550 0.0829920i \(-0.973552\pi\)
0.570148 + 0.821542i \(0.306886\pi\)
\(60\) 2.00000 + 1.41421i 0.258199 + 0.182574i
\(61\) 3.22474 + 5.58542i 0.412886 + 0.715140i 0.995204 0.0978213i \(-0.0311874\pi\)
−0.582318 + 0.812961i \(0.697854\pi\)
\(62\) −3.67423 2.12132i −0.466628 0.269408i
\(63\) −4.44949 12.5851i −0.560583 1.58557i
\(64\) 1.00000 0.125000
\(65\) 4.89898 0.607644
\(66\) 0.500000 0.230351i 0.0615457 0.0283542i
\(67\) −5.17423 + 2.98735i −0.632133 + 0.364962i −0.781578 0.623808i \(-0.785585\pi\)
0.149444 + 0.988770i \(0.452251\pi\)
\(68\) 6.29253i 0.763081i
\(69\) −1.12372 + 12.1958i −0.135281 + 1.46820i
\(70\) 5.44949 3.14626i 0.651339 0.376051i
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −1.00000 2.82843i −0.117851 0.333333i
\(73\) 5.39898 9.35131i 0.631903 1.09449i −0.355260 0.934768i \(-0.615608\pi\)
0.987162 0.159720i \(-0.0510591\pi\)
\(74\) 0.674235 + 0.389270i 0.0783782 + 0.0452517i
\(75\) −5.17423 0.476756i −0.597469 0.0550510i
\(76\) 3.17423 + 2.98735i 0.364110 + 0.342672i
\(77\) 1.41421i 0.161165i
\(78\) −4.89898 3.46410i −0.554700 0.392232i
\(79\) 7.34847 + 4.24264i 0.826767 + 0.477334i 0.852745 0.522328i \(-0.174936\pi\)
−0.0259772 + 0.999663i \(0.508270\pi\)
\(80\) 1.22474 0.707107i 0.136931 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 14.1742i 1.55583i −0.628372 0.777913i \(-0.716279\pi\)
0.628372 0.777913i \(-0.283721\pi\)
\(84\) −7.67423 0.707107i −0.837328 0.0771517i
\(85\) −4.44949 7.70674i −0.482615 0.835914i
\(86\) −0.449490 0.778539i −0.0484697 0.0839520i
\(87\) 4.22474 + 0.389270i 0.452940 + 0.0417341i
\(88\) 0.317837i 0.0338816i
\(89\) −8.44949 14.6349i −0.895644 1.55130i −0.833005 0.553265i \(-0.813382\pi\)
−0.0626387 0.998036i \(-0.519952\pi\)
\(90\) −3.22474 2.75699i −0.339918 0.290613i
\(91\) −13.3485 + 7.70674i −1.39930 + 0.807886i
\(92\) 6.12372 + 3.53553i 0.638442 + 0.368605i
\(93\) 6.00000 + 4.24264i 0.622171 + 0.439941i
\(94\) 6.43539i 0.663760i
\(95\) 6.00000 + 1.41421i 0.615587 + 0.145095i
\(96\) −1.72474 0.158919i −0.176031 0.0162196i
\(97\) −11.8485 6.84072i −1.20303 0.694570i −0.241802 0.970326i \(-0.577738\pi\)
−0.961228 + 0.275756i \(0.911072\pi\)
\(98\) −6.39898 + 11.0834i −0.646395 + 1.11959i
\(99\) −0.898979 + 0.317837i −0.0903508 + 0.0319438i
\(100\) −1.50000 + 2.59808i −0.150000 + 0.259808i
\(101\) 8.57321 4.94975i 0.853067 0.492518i −0.00861771 0.999963i \(-0.502743\pi\)
0.861684 + 0.507445i \(0.169410\pi\)
\(102\) −1.00000 + 10.8530i −0.0990148 + 1.07461i
\(103\) 11.9494i 1.17741i −0.808349 0.588704i \(-0.799638\pi\)
0.808349 0.588704i \(-0.200362\pi\)
\(104\) −3.00000 + 1.73205i −0.294174 + 0.169842i
\(105\) −9.89898 + 4.56048i −0.966041 + 0.445057i
\(106\) −1.10102 −0.106941
\(107\) −4.89898 −0.473602 −0.236801 0.971558i \(-0.576099\pi\)
−0.236801 + 0.971558i \(0.576099\pi\)
\(108\) 1.27526 + 5.03723i 0.122711 + 0.484708i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) −0.224745 0.389270i −0.0214286 0.0371154i
\(111\) −1.10102 0.778539i −0.104504 0.0738957i
\(112\) −2.22474 + 3.85337i −0.210219 + 0.364109i
\(113\) −0.797959 −0.0750657 −0.0375328 0.999295i \(-0.511950\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) −5.00000 5.65685i −0.468293 0.529813i
\(115\) 10.0000 0.932505
\(116\) 1.22474 2.12132i 0.113715 0.196960i
\(117\) 7.89898 + 6.75323i 0.730261 + 0.624336i
\(118\) −3.27526 5.67291i −0.301512 0.522234i
\(119\) 24.2474 + 13.9993i 2.22276 + 1.28331i
\(120\) −2.22474 + 1.02494i −0.203090 + 0.0935642i
\(121\) 10.8990 0.990816
\(122\) −6.44949 −0.583909
\(123\) −2.17423 4.71940i −0.196044 0.425534i
\(124\) 3.67423 2.12132i 0.329956 0.190500i
\(125\) 11.3137i 1.01193i
\(126\) 13.1237 + 2.43916i 1.16915 + 0.217297i
\(127\) −9.00000 + 5.19615i −0.798621 + 0.461084i −0.842989 0.537931i \(-0.819206\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0.651531 + 1.41421i 0.0573641 + 0.124515i
\(130\) −2.44949 + 4.24264i −0.214834 + 0.372104i
\(131\) −19.0732 11.0119i −1.66643 0.962116i −0.969537 0.244946i \(-0.921230\pi\)
−0.696898 0.717171i \(-0.745437\pi\)
\(132\) −0.0505103 + 0.548188i −0.00439635 + 0.0477137i
\(133\) −18.5732 + 5.58542i −1.61050 + 0.484318i
\(134\) 5.97469i 0.516135i
\(135\) 5.12372 + 5.26758i 0.440980 + 0.453362i
\(136\) 5.44949 + 3.14626i 0.467290 + 0.269790i
\(137\) 6.39898 3.69445i 0.546702 0.315638i −0.201089 0.979573i \(-0.564448\pi\)
0.747791 + 0.663935i \(0.231115\pi\)
\(138\) −10.0000 7.07107i −0.851257 0.601929i
\(139\) −0.174235 0.301783i −0.0147784 0.0255969i 0.858542 0.512744i \(-0.171371\pi\)
−0.873320 + 0.487147i \(0.838038\pi\)
\(140\) 6.29253i 0.531816i
\(141\) 1.02270 11.0994i 0.0861272 0.934739i
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) 0.550510 + 0.953512i 0.0460360 + 0.0797367i
\(144\) 2.94949 + 0.548188i 0.245791 + 0.0456823i
\(145\) 3.46410i 0.287678i
\(146\) 5.39898 + 9.35131i 0.446823 + 0.773920i
\(147\) 12.7980 18.0990i 1.05556 1.49278i
\(148\) −0.674235 + 0.389270i −0.0554217 + 0.0319978i
\(149\) −4.22474 2.43916i −0.346105 0.199824i 0.316864 0.948471i \(-0.397370\pi\)
−0.662968 + 0.748648i \(0.730704\pi\)
\(150\) 3.00000 4.24264i 0.244949 0.346410i
\(151\) 18.0990i 1.47288i 0.676503 + 0.736440i \(0.263495\pi\)
−0.676503 + 0.736440i \(0.736505\pi\)
\(152\) −4.17423 + 1.25529i −0.338575 + 0.101818i
\(153\) 3.44949 18.5597i 0.278875 1.50047i
\(154\) 1.22474 + 0.707107i 0.0986928 + 0.0569803i
\(155\) 3.00000 5.19615i 0.240966 0.417365i
\(156\) 5.44949 2.51059i 0.436308 0.201008i
\(157\) 9.34847 16.1920i 0.746089 1.29226i −0.203595 0.979055i \(-0.565263\pi\)
0.949684 0.313209i \(-0.101404\pi\)
\(158\) −7.34847 + 4.24264i −0.584613 + 0.337526i
\(159\) 1.89898 + 0.174973i 0.150599 + 0.0138762i
\(160\) 1.41421i 0.111803i
\(161\) −27.2474 + 15.7313i −2.14740 + 1.23980i
\(162\) −1.39898 8.89060i −0.109914 0.698512i
\(163\) 3.65153 0.286010 0.143005 0.989722i \(-0.454324\pi\)
0.143005 + 0.989722i \(0.454324\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0.325765 + 0.707107i 0.0253608 + 0.0550482i
\(166\) 12.2753 + 7.08712i 0.952745 + 0.550067i
\(167\) −2.44949 4.24264i −0.189547 0.328305i 0.755552 0.655089i \(-0.227369\pi\)
−0.945099 + 0.326783i \(0.894035\pi\)
\(168\) 4.44949 6.29253i 0.343286 0.485479i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 8.89898 0.682521
\(171\) 7.72474 + 10.5512i 0.590726 + 0.806872i
\(172\) 0.898979 0.0685465
\(173\) −5.44949 + 9.43879i −0.414317 + 0.717618i −0.995356 0.0962572i \(-0.969313\pi\)
0.581039 + 0.813875i \(0.302646\pi\)
\(174\) −2.44949 + 3.46410i −0.185695 + 0.262613i
\(175\) −6.67423 11.5601i −0.504525 0.873862i
\(176\) 0.275255 + 0.158919i 0.0207481 + 0.0119789i
\(177\) 4.74745 + 10.3048i 0.356840 + 0.774558i
\(178\) 16.8990 1.26663
\(179\) 22.3485 1.67040 0.835202 0.549944i \(-0.185351\pi\)
0.835202 + 0.549944i \(0.185351\pi\)
\(180\) 4.00000 1.41421i 0.298142 0.105409i
\(181\) 11.3258 6.53893i 0.841838 0.486035i −0.0160509 0.999871i \(-0.505109\pi\)
0.857888 + 0.513836i \(0.171776\pi\)
\(182\) 15.4135i 1.14252i
\(183\) 11.1237 + 1.02494i 0.822289 + 0.0757660i
\(184\) −6.12372 + 3.53553i −0.451447 + 0.260643i
\(185\) −0.550510 + 0.953512i −0.0404743 + 0.0701036i
\(186\) −6.67423 + 3.07483i −0.489379 + 0.225458i
\(187\) 1.00000 1.73205i 0.0731272 0.126660i
\(188\) −5.57321 3.21770i −0.406468 0.234675i
\(189\) −22.2474 6.29253i −1.61826 0.457714i
\(190\) −4.22474 + 4.48905i −0.306495 + 0.325670i
\(191\) 19.5133i 1.41193i 0.708247 + 0.705965i \(0.249486\pi\)
−0.708247 + 0.705965i \(0.750514\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) −7.65153 4.41761i −0.550769 0.317987i 0.198663 0.980068i \(-0.436340\pi\)
−0.749432 + 0.662081i \(0.769673\pi\)
\(194\) 11.8485 6.84072i 0.850671 0.491135i
\(195\) 4.89898 6.92820i 0.350823 0.496139i
\(196\) −6.39898 11.0834i −0.457070 0.791668i
\(197\) 0.492810i 0.0351113i −0.999846 0.0175556i \(-0.994412\pi\)
0.999846 0.0175556i \(-0.00558842\pi\)
\(198\) 0.174235 0.937458i 0.0123823 0.0666222i
\(199\) −3.44949 5.97469i −0.244528 0.423535i 0.717471 0.696588i \(-0.245300\pi\)
−0.961999 + 0.273054i \(0.911966\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) −0.949490 + 10.3048i −0.0669718 + 0.726846i
\(202\) 9.89949i 0.696526i
\(203\) 5.44949 + 9.43879i 0.382479 + 0.662473i
\(204\) −8.89898 6.29253i −0.623053 0.440565i
\(205\) −3.67423 + 2.12132i −0.256620 + 0.148159i
\(206\) 10.3485 + 5.97469i 0.721012 + 0.416276i
\(207\) 16.1237 + 13.7850i 1.12068 + 0.958122i
\(208\) 3.46410i 0.240192i
\(209\) 0.398979 + 1.32673i 0.0275980 + 0.0917716i
\(210\) 1.00000 10.8530i 0.0690066 0.748929i
\(211\) 13.3485 + 7.70674i 0.918947 + 0.530554i 0.883299 0.468810i \(-0.155317\pi\)
0.0356477 + 0.999364i \(0.488651\pi\)
\(212\) 0.550510 0.953512i 0.0378092 0.0654875i
\(213\) 4.34847 + 9.43879i 0.297952 + 0.646735i
\(214\) 2.44949 4.24264i 0.167444 0.290021i
\(215\) 1.10102 0.635674i 0.0750890 0.0433526i
\(216\) −5.00000 1.41421i −0.340207 0.0962250i
\(217\) 18.8776i 1.28149i
\(218\) 0 0
\(219\) −7.82577 16.9866i −0.528816 1.14785i
\(220\) 0.449490 0.0303046
\(221\) −21.7980 −1.46629
\(222\) 1.22474 0.564242i 0.0821995 0.0378695i
\(223\) −8.32577 4.80688i −0.557534 0.321893i 0.194621 0.980879i \(-0.437652\pi\)
−0.752155 + 0.658986i \(0.770986\pi\)
\(224\) −2.22474 3.85337i −0.148647 0.257464i
\(225\) −5.84847 + 6.84072i −0.389898 + 0.456048i
\(226\) 0.398979 0.691053i 0.0265397 0.0459681i
\(227\) −5.44949 −0.361695 −0.180848 0.983511i \(-0.557884\pi\)
−0.180848 + 0.983511i \(0.557884\pi\)
\(228\) 7.39898 1.50170i 0.490009 0.0994525i
\(229\) −8.89898 −0.588061 −0.294031 0.955796i \(-0.594997\pi\)
−0.294031 + 0.955796i \(0.594997\pi\)
\(230\) −5.00000 + 8.66025i −0.329690 + 0.571040i
\(231\) −2.00000 1.41421i −0.131590 0.0930484i
\(232\) 1.22474 + 2.12132i 0.0804084 + 0.139272i
\(233\) 5.60102 + 3.23375i 0.366935 + 0.211850i 0.672119 0.740443i \(-0.265384\pi\)
−0.305184 + 0.952294i \(0.598718\pi\)
\(234\) −9.79796 + 3.46410i −0.640513 + 0.226455i
\(235\) −9.10102 −0.593685
\(236\) 6.55051 0.426402
\(237\) 13.3485 6.14966i 0.867076 0.399464i
\(238\) −24.2474 + 13.9993i −1.57173 + 0.907438i
\(239\) 7.21393i 0.466630i 0.972401 + 0.233315i \(0.0749574\pi\)
−0.972401 + 0.233315i \(0.925043\pi\)
\(240\) 0.224745 2.43916i 0.0145072 0.157447i
\(241\) 8.84847 5.10867i 0.569980 0.329078i −0.187161 0.982329i \(-0.559929\pi\)
0.757141 + 0.653251i \(0.226595\pi\)
\(242\) −5.44949 + 9.43879i −0.350306 + 0.606749i
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 3.22474 5.58542i 0.206443 0.357570i
\(245\) −15.6742 9.04952i −1.00139 0.578153i
\(246\) 5.17423 + 0.476756i 0.329897 + 0.0303968i
\(247\) 10.3485 10.9959i 0.658457 0.699651i
\(248\) 4.24264i 0.269408i
\(249\) −20.0454 14.1742i −1.27033 0.898256i
\(250\) −9.79796 5.65685i −0.619677 0.357771i
\(251\) 5.72474 3.30518i 0.361343 0.208621i −0.308327 0.951280i \(-0.599769\pi\)
0.669670 + 0.742659i \(0.266436\pi\)
\(252\) −8.67423 + 10.1459i −0.546425 + 0.639132i
\(253\) 1.12372 + 1.94635i 0.0706479 + 0.122366i
\(254\) 10.3923i 0.652071i
\(255\) −15.3485 1.41421i −0.961158 0.0885615i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) −1.55051 0.142865i −0.0965306 0.00889436i
\(259\) 3.46410i 0.215249i
\(260\) −2.44949 4.24264i −0.151911 0.263117i
\(261\) 4.77526 5.58542i 0.295581 0.345729i
\(262\) 19.0732 11.0119i 1.17835 0.680319i
\(263\) −10.2247 5.90326i −0.630485 0.364011i 0.150455 0.988617i \(-0.451926\pi\)
−0.780940 + 0.624606i \(0.785259\pi\)
\(264\) −0.449490 0.317837i −0.0276642 0.0195615i
\(265\) 1.55708i 0.0956506i
\(266\) 4.44949 18.8776i 0.272816 1.15746i
\(267\) −29.1464 2.68556i −1.78373 0.164354i
\(268\) 5.17423 + 2.98735i 0.316067 + 0.182481i
\(269\) 12.2474 21.2132i 0.746740 1.29339i −0.202637 0.979254i \(-0.564951\pi\)
0.949377 0.314138i \(-0.101715\pi\)
\(270\) −7.12372 + 1.80348i −0.433536 + 0.109756i
\(271\) −12.0227 + 20.8239i −0.730327 + 1.26496i 0.226416 + 0.974031i \(0.427299\pi\)
−0.956743 + 0.290933i \(0.906034\pi\)
\(272\) −5.44949 + 3.14626i −0.330424 + 0.190770i
\(273\) −2.44949 + 26.5843i −0.148250 + 1.60896i
\(274\) 7.38891i 0.446380i
\(275\) −0.825765 + 0.476756i −0.0497955 + 0.0287495i
\(276\) 11.1237 5.12472i 0.669570 0.308472i
\(277\) −4.24745 −0.255204 −0.127602 0.991825i \(-0.540728\pi\)
−0.127602 + 0.991825i \(0.540728\pi\)
\(278\) 0.348469 0.0208998
\(279\) 12.0000 4.24264i 0.718421 0.254000i
\(280\) −5.44949 3.14626i −0.325669 0.188025i
\(281\) 8.29796 + 14.3725i 0.495015 + 0.857391i 0.999983 0.00574696i \(-0.00182932\pi\)
−0.504969 + 0.863138i \(0.668496\pi\)
\(282\) 9.10102 + 6.43539i 0.541958 + 0.383222i
\(283\) 2.27526 3.94086i 0.135250 0.234260i −0.790443 0.612536i \(-0.790150\pi\)
0.925693 + 0.378276i \(0.123483\pi\)
\(284\) 6.00000 0.356034
\(285\) 8.00000 7.07107i 0.473879 0.418854i
\(286\) −1.10102 −0.0651047
\(287\) 6.67423 11.5601i 0.393968 0.682372i
\(288\) −1.94949 + 2.28024i −0.114875 + 0.134364i
\(289\) 11.2980 + 19.5686i 0.664586 + 1.15110i
\(290\) 3.00000 + 1.73205i 0.176166 + 0.101710i
\(291\) −21.5227 + 9.91555i −1.26168 + 0.581260i
\(292\) −10.7980 −0.631903
\(293\) 4.65153 0.271745 0.135873 0.990726i \(-0.456616\pi\)
0.135873 + 0.990726i \(0.456616\pi\)
\(294\) 9.27526 + 20.1329i 0.540944 + 1.17417i
\(295\) 8.02270 4.63191i 0.467100 0.269680i
\(296\) 0.778539i 0.0452517i
\(297\) −0.449490 + 1.58919i −0.0260820 + 0.0922139i
\(298\) 4.22474 2.43916i 0.244733 0.141297i
\(299\) 12.2474 21.2132i 0.708288 1.22679i
\(300\) 2.17423 + 4.71940i 0.125529 + 0.272474i
\(301\) −2.00000 + 3.46410i −0.115278 + 0.199667i
\(302\) −15.6742 9.04952i −0.901951 0.520742i
\(303\) 1.57321 17.0741i 0.0903788 0.980882i
\(304\) 1.00000 4.24264i 0.0573539 0.243332i
\(305\) 9.12096i 0.522264i
\(306\) 14.3485 + 12.2672i 0.820247 + 0.701270i
\(307\) −3.52270 2.03383i −0.201051 0.116077i 0.396094 0.918210i \(-0.370365\pi\)
−0.597146 + 0.802133i \(0.703699\pi\)
\(308\) −1.22474 + 0.707107i −0.0697863 + 0.0402911i
\(309\) −16.8990 11.9494i −0.961349 0.679777i
\(310\) 3.00000 + 5.19615i 0.170389 + 0.295122i
\(311\) 15.5563i 0.882120i −0.897478 0.441060i \(-0.854603\pi\)
0.897478 0.441060i \(-0.145397\pi\)
\(312\) −0.550510 + 5.97469i −0.0311665 + 0.338250i
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) 9.34847 + 16.1920i 0.527565 + 0.913769i
\(315\) −3.44949 + 18.5597i −0.194357 + 1.04572i
\(316\) 8.48528i 0.477334i
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) −1.10102 + 1.55708i −0.0617422 + 0.0873166i
\(319\) 0.674235 0.389270i 0.0377499 0.0217949i
\(320\) −1.22474 0.707107i −0.0684653 0.0395285i
\(321\) −4.89898 + 6.92820i −0.273434 + 0.386695i
\(322\) 31.4626i 1.75334i
\(323\) −26.6969 6.29253i −1.48546 0.350126i
\(324\) 8.39898 + 3.23375i 0.466610 + 0.179653i
\(325\) 9.00000 + 5.19615i 0.499230 + 0.288231i
\(326\) −1.82577 + 3.16232i −0.101120 + 0.175145i
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 24.7980 14.3171i 1.36716 0.789328i
\(330\) −0.775255 0.0714323i −0.0426764 0.00393222i
\(331\) 14.8099i 0.814027i −0.913422 0.407013i \(-0.866570\pi\)
0.913422 0.407013i \(-0.133430\pi\)
\(332\) −12.2753 + 7.08712i −0.673692 + 0.388956i
\(333\) −2.20204 + 0.778539i −0.120671 + 0.0426637i
\(334\) 4.89898 0.268060
\(335\) 8.44949 0.461645
\(336\) 3.22474 + 6.99964i 0.175924 + 0.381861i
\(337\) −3.15153 1.81954i −0.171675 0.0991165i 0.411701 0.911319i \(-0.364935\pi\)
−0.583375 + 0.812203i \(0.698268\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) −0.797959 + 1.12848i −0.0433392 + 0.0612909i
\(340\) −4.44949 + 7.70674i −0.241307 + 0.417957i
\(341\) 1.34847 0.0730237
\(342\) −13.0000 + 1.41421i −0.702959 + 0.0764719i
\(343\) 25.7980 1.39296
\(344\) −0.449490 + 0.778539i −0.0242349 + 0.0419760i
\(345\) 10.0000 14.1421i 0.538382 0.761387i
\(346\) −5.44949 9.43879i −0.292966 0.507433i
\(347\) −5.72474 3.30518i −0.307320 0.177432i 0.338406 0.941000i \(-0.390112\pi\)
−0.645727 + 0.763569i \(0.723445\pi\)
\(348\) −1.77526 3.85337i −0.0951637 0.206562i
\(349\) −16.4949 −0.882952 −0.441476 0.897273i \(-0.645545\pi\)
−0.441476 + 0.897273i \(0.645545\pi\)
\(350\) 13.3485 0.713506
\(351\) 17.4495 4.41761i 0.931385 0.235795i
\(352\) −0.275255 + 0.158919i −0.0146711 + 0.00847039i
\(353\) 14.6028i 0.777231i −0.921400 0.388615i \(-0.872954\pi\)
0.921400 0.388615i \(-0.127046\pi\)
\(354\) −11.2980 1.04100i −0.600480 0.0553284i
\(355\) 7.34847 4.24264i 0.390016 0.225176i
\(356\) −8.44949 + 14.6349i −0.447822 + 0.775651i
\(357\) 44.0454 20.2918i 2.33113 1.07396i
\(358\) −11.1742 + 19.3543i −0.590577 + 1.02291i
\(359\) 20.8207 + 12.0208i 1.09887 + 0.634434i 0.935925 0.352200i \(-0.114566\pi\)
0.162948 + 0.986635i \(0.447900\pi\)
\(360\) −0.775255 + 4.17121i −0.0408595 + 0.219842i
\(361\) 15.8485 10.4798i 0.834130 0.551568i
\(362\) 13.0779i 0.687357i
\(363\) 10.8990 15.4135i 0.572048 0.808998i
\(364\) 13.3485 + 7.70674i 0.699650 + 0.403943i
\(365\) −13.2247 + 7.63531i −0.692215 + 0.399650i
\(366\) −6.44949 + 9.12096i −0.337120 + 0.476760i
\(367\) 11.6742 + 20.2204i 0.609390 + 1.05549i 0.991341 + 0.131312i \(0.0419190\pi\)
−0.381951 + 0.924183i \(0.624748\pi\)
\(368\) 7.07107i 0.368605i
\(369\) −8.84847 1.64456i −0.460633 0.0856126i
\(370\) −0.550510 0.953512i −0.0286197 0.0495707i
\(371\) 2.44949 + 4.24264i 0.127171 + 0.220267i
\(372\) 0.674235 7.31747i 0.0349574 0.379393i
\(373\) 25.4558i 1.31805i −0.752119 0.659027i \(-0.770968\pi\)
0.752119 0.659027i \(-0.229032\pi\)
\(374\) 1.00000 + 1.73205i 0.0517088 + 0.0895622i
\(375\) 16.0000 + 11.3137i 0.826236 + 0.584237i
\(376\) 5.57321 3.21770i 0.287417 0.165940i
\(377\) −7.34847 4.24264i −0.378465 0.218507i
\(378\) 16.5732 16.1206i 0.852434 0.829154i
\(379\) 15.4135i 0.791738i 0.918307 + 0.395869i \(0.129556\pi\)
−0.918307 + 0.395869i \(0.870444\pi\)
\(380\) −1.77526 5.90326i −0.0910687 0.302831i
\(381\) −1.65153 + 17.9241i −0.0846105 + 0.918278i
\(382\) −16.8990 9.75663i −0.864627 0.499193i
\(383\) −7.77526 + 13.4671i −0.397297 + 0.688139i −0.993391 0.114776i \(-0.963385\pi\)
0.596094 + 0.802914i \(0.296718\pi\)
\(384\) 0.724745 + 1.57313i 0.0369845 + 0.0802786i
\(385\) −1.00000 + 1.73205i −0.0509647 + 0.0882735i
\(386\) 7.65153 4.41761i 0.389453 0.224851i
\(387\) 2.65153 + 0.492810i 0.134785 + 0.0250509i
\(388\) 13.6814i 0.694570i
\(389\) 22.8990 13.2207i 1.16102 0.670318i 0.209475 0.977814i \(-0.432824\pi\)
0.951549 + 0.307496i \(0.0994912\pi\)
\(390\) 3.55051 + 7.70674i 0.179787 + 0.390246i
\(391\) −44.4949 −2.25020
\(392\) 12.7980 0.646395
\(393\) −34.6464 + 15.9617i −1.74768 + 0.805160i
\(394\) 0.426786 + 0.246405i 0.0215012 + 0.0124137i
\(395\) −6.00000 10.3923i −0.301893 0.522894i
\(396\) 0.724745 + 0.619620i 0.0364198 + 0.0311371i
\(397\) −4.67423 + 8.09601i −0.234593 + 0.406327i −0.959154 0.282883i \(-0.908709\pi\)
0.724561 + 0.689210i \(0.242042\pi\)
\(398\) 6.89898 0.345815
\(399\) −10.6742 + 31.8519i −0.534380 + 1.59459i
\(400\) 3.00000 0.150000
\(401\) −6.39898 + 11.0834i −0.319550 + 0.553476i −0.980394 0.197047i \(-0.936865\pi\)
0.660844 + 0.750523i \(0.270198\pi\)
\(402\) −8.44949 5.97469i −0.421422 0.297991i
\(403\) −7.34847 12.7279i −0.366053 0.634023i
\(404\) −8.57321 4.94975i −0.426533 0.246259i
\(405\) 12.5732 1.97846i 0.624768 0.0983103i
\(406\) −10.8990 −0.540907
\(407\) −0.247449 −0.0122656
\(408\) 9.89898 4.56048i 0.490073 0.225777i
\(409\) 17.8485 10.3048i 0.882550 0.509540i 0.0110517 0.999939i \(-0.496482\pi\)
0.871498 + 0.490398i \(0.163149\pi\)
\(410\) 4.24264i 0.209529i
\(411\) 1.17423 12.7440i 0.0579207 0.628614i
\(412\) −10.3485 + 5.97469i −0.509832 + 0.294352i
\(413\) −14.5732 + 25.2415i −0.717101 + 1.24206i
\(414\) −20.0000 + 7.07107i −0.982946 + 0.347524i
\(415\) −10.0227 + 17.3598i −0.491995 + 0.852161i
\(416\) 3.00000 + 1.73205i 0.147087 + 0.0849208i
\(417\) −0.601021 0.0553782i −0.0294321 0.00271188i
\(418\) −1.34847 0.317837i −0.0659558 0.0155459i
\(419\) 3.74983i 0.183191i 0.995796 + 0.0915956i \(0.0291967\pi\)
−0.995796 + 0.0915956i \(0.970803\pi\)
\(420\) 8.89898 + 6.29253i 0.434226 + 0.307044i
\(421\) −26.0227 15.0242i −1.26827 0.732235i −0.293609 0.955926i \(-0.594856\pi\)
−0.974660 + 0.223690i \(0.928190\pi\)
\(422\) −13.3485 + 7.70674i −0.649793 + 0.375158i
\(423\) −14.6742 12.5457i −0.713486 0.609994i
\(424\) 0.550510 + 0.953512i 0.0267351 + 0.0463066i
\(425\) 18.8776i 0.915697i
\(426\) −10.3485 0.953512i −0.501385 0.0461978i
\(427\) 14.3485 + 24.8523i 0.694371 + 1.20269i
\(428\) 2.44949 + 4.24264i 0.118401 + 0.205076i
\(429\) 1.89898 + 0.174973i 0.0916836 + 0.00844776i
\(430\) 1.27135i 0.0613099i
\(431\) −16.3485 28.3164i −0.787478 1.36395i −0.927507 0.373805i \(-0.878053\pi\)
0.140029 0.990147i \(-0.455280\pi\)
\(432\) 3.72474 3.62302i 0.179207 0.174313i
\(433\) 11.6969 6.75323i 0.562119 0.324540i −0.191877 0.981419i \(-0.561457\pi\)
0.753996 + 0.656880i \(0.228124\pi\)
\(434\) −16.3485 9.43879i −0.784752 0.453077i
\(435\) −4.89898 3.46410i −0.234888 0.166091i
\(436\) 0 0
\(437\) 21.1237 22.4452i 1.01048 1.07370i
\(438\) 18.6237 + 1.71600i 0.889876 + 0.0819935i
\(439\) −2.32577 1.34278i −0.111003 0.0640875i 0.443471 0.896289i \(-0.353747\pi\)
−0.554474 + 0.832201i \(0.687080\pi\)
\(440\) −0.224745 + 0.389270i −0.0107143 + 0.0185577i
\(441\) −12.7980 36.1981i −0.609427 1.72372i
\(442\) 10.8990 18.8776i 0.518412 0.897915i
\(443\) −25.3207 + 14.6189i −1.20302 + 0.694564i −0.961226 0.275763i \(-0.911070\pi\)
−0.241795 + 0.970327i \(0.577736\pi\)
\(444\) −0.123724 + 1.34278i −0.00587170 + 0.0637256i
\(445\) 23.8988i 1.13291i
\(446\) 8.32577 4.80688i 0.394236 0.227613i
\(447\) −7.67423 + 3.53553i −0.362979 + 0.167225i
\(448\) 4.44949 0.210219
\(449\) −11.2020 −0.528657 −0.264329 0.964433i \(-0.585150\pi\)
−0.264329 + 0.964433i \(0.585150\pi\)
\(450\) −3.00000 8.48528i −0.141421 0.400000i
\(451\) −0.825765 0.476756i −0.0388838 0.0224496i
\(452\) 0.398979 + 0.691053i 0.0187664 + 0.0325044i
\(453\) 25.5959 + 18.0990i 1.20260 + 0.850367i
\(454\) 2.72474 4.71940i 0.127879 0.221492i
\(455\) 21.7980 1.02190
\(456\) −2.39898 + 7.15855i −0.112343 + 0.335230i
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 4.44949 7.70674i 0.207911 0.360112i
\(459\) −22.7980 23.4381i −1.06412 1.09400i
\(460\) −5.00000 8.66025i −0.233126 0.403786i
\(461\) 8.75255 + 5.05329i 0.407647 + 0.235355i 0.689778 0.724021i \(-0.257708\pi\)
−0.282131 + 0.959376i \(0.591041\pi\)
\(462\) 2.22474 1.02494i 0.103504 0.0476847i
\(463\) −0.202041 −0.00938964 −0.00469482 0.999989i \(-0.501494\pi\)
−0.00469482 + 0.999989i \(0.501494\pi\)
\(464\) −2.44949 −0.113715
\(465\) −4.34847 9.43879i −0.201655 0.437714i
\(466\) −5.60102 + 3.23375i −0.259462 + 0.149801i
\(467\) 32.4162i 1.50004i 0.661415 + 0.750020i \(0.269956\pi\)
−0.661415 + 0.750020i \(0.730044\pi\)
\(468\) 1.89898 10.2173i 0.0877804 0.472296i
\(469\) −23.0227 + 13.2922i −1.06309 + 0.613775i
\(470\) 4.55051 7.88171i 0.209899 0.363556i
\(471\) −13.5505 29.4128i −0.624375 1.35527i
\(472\) −3.27526 + 5.67291i −0.150756 + 0.261117i
\(473\) 0.247449 + 0.142865i 0.0113777 + 0.00656892i
\(474\) −1.34847 + 14.6349i −0.0619372 + 0.672205i
\(475\) 9.52270 + 8.96204i 0.436932 + 0.411206i
\(476\) 27.9985i 1.28331i
\(477\) 2.14643 2.51059i 0.0982782 0.114952i
\(478\) −6.24745 3.60697i −0.285752 0.164979i
\(479\) −35.1464 + 20.2918i −1.60588 + 0.927156i −0.615603 + 0.788057i \(0.711087\pi\)
−0.990278 + 0.139099i \(0.955579\pi\)
\(480\) 2.00000 + 1.41421i 0.0912871 + 0.0645497i
\(481\) 1.34847 + 2.33562i 0.0614849 + 0.106495i
\(482\) 10.2173i 0.465387i
\(483\) −5.00000 + 54.2650i −0.227508 + 2.46914i
\(484\) −5.44949 9.43879i −0.247704 0.429036i
\(485\) 9.67423 + 16.7563i 0.439284 + 0.760863i
\(486\) −13.9722 6.91215i −0.633792 0.313541i
\(487\) 16.5420i 0.749588i −0.927108 0.374794i \(-0.877713\pi\)
0.927108 0.374794i \(-0.122287\pi\)
\(488\) 3.22474 + 5.58542i 0.145977 + 0.252840i
\(489\) 3.65153 5.16404i 0.165128 0.233526i
\(490\) 15.6742 9.04952i 0.708090 0.408816i
\(491\) 4.10102 + 2.36773i 0.185076 + 0.106854i 0.589676 0.807640i \(-0.299256\pi\)
−0.404599 + 0.914494i \(0.632589\pi\)
\(492\) −3.00000 + 4.24264i −0.135250 + 0.191273i
\(493\) 15.4135i 0.694188i
\(494\) 4.34847 + 14.4600i 0.195647 + 0.650585i
\(495\) 1.32577 + 0.246405i 0.0595887 + 0.0110751i
\(496\) −3.67423 2.12132i −0.164978 0.0952501i
\(497\) −13.3485 + 23.1202i −0.598761 + 1.03708i
\(498\) 22.2980 10.2727i 0.999195 0.460331i
\(499\) −1.27526 + 2.20881i −0.0570883 + 0.0988798i −0.893157 0.449745i \(-0.851515\pi\)
0.836069 + 0.548624i \(0.184848\pi\)
\(500\) 9.79796 5.65685i 0.438178 0.252982i
\(501\) −8.44949 0.778539i −0.377495 0.0347826i
\(502\) 6.61037i 0.295035i
\(503\) −13.4722 + 7.77817i −0.600695 + 0.346812i −0.769315 0.638870i \(-0.779402\pi\)
0.168620 + 0.985681i \(0.446069\pi\)
\(504\) −4.44949 12.5851i −0.198196 0.560583i
\(505\) −14.0000 −0.622992
\(506\) −2.24745 −0.0999113
\(507\) 0.724745 + 1.57313i 0.0321870 + 0.0698653i
\(508\) 9.00000 + 5.19615i 0.399310 + 0.230542i
\(509\) 20.6969 + 35.8481i 0.917376 + 1.58894i 0.803385 + 0.595459i \(0.203030\pi\)
0.113990 + 0.993482i \(0.463637\pi\)
\(510\) 8.89898 12.5851i 0.394053 0.557276i
\(511\) 24.0227 41.6085i 1.06270 1.84065i
\(512\) 1.00000 0.0441942
\(513\) 22.6464 0.373215i 0.999864 0.0164779i
\(514\) −15.0000 −0.661622
\(515\) −8.44949 + 14.6349i −0.372329 + 0.644893i
\(516\) 0.898979 1.27135i 0.0395754 0.0559680i
\(517\) −1.02270 1.77138i −0.0449785 0.0779050i
\(518\) 3.00000 + 1.73205i 0.131812 + 0.0761019i
\(519\) 7.89898 + 17.1455i 0.346727 + 0.752605i
\(520\) 4.89898 0.214834
\(521\) 16.1010 0.705399 0.352699 0.935737i \(-0.385264\pi\)
0.352699 + 0.935737i \(0.385264\pi\)
\(522\) 2.44949 + 6.92820i 0.107211 + 0.303239i
\(523\) 23.6969 13.6814i 1.03619 0.598247i 0.117442 0.993080i \(-0.462531\pi\)
0.918753 + 0.394832i \(0.129197\pi\)
\(524\) 22.0239i 0.962116i
\(525\) −23.0227 2.12132i −1.00479 0.0925820i
\(526\) 10.2247 5.90326i 0.445820 0.257394i
\(527\) −13.3485 + 23.1202i −0.581468 + 1.00713i
\(528\) 0.500000 0.230351i 0.0217597 0.0100247i
\(529\) 13.5000 23.3827i 0.586957 1.01664i
\(530\) 1.34847 + 0.778539i 0.0585738 + 0.0338176i
\(531\) 19.3207 + 3.59091i 0.838445 + 0.155832i
\(532\) 14.1237 + 13.2922i 0.612341 + 0.576288i
\(533\) 10.3923i 0.450141i
\(534\) 16.8990 23.8988i 0.731290 1.03420i
\(535\) 6.00000 + 3.46410i 0.259403 + 0.149766i
\(536\) −5.17423 + 2.98735i −0.223493 + 0.129034i
\(537\) 22.3485 31.6055i 0.964408 1.36388i
\(538\) 12.2474 + 21.2132i 0.528025 + 0.914566i
\(539\) 4.06767i 0.175207i
\(540\) 2.00000 7.07107i 0.0860663 0.304290i
\(541\) 9.34847 + 16.1920i 0.401922 + 0.696149i 0.993958 0.109762i \(-0.0350089\pi\)
−0.592036 + 0.805912i \(0.701676\pi\)
\(542\) −12.0227 20.8239i −0.516419 0.894465i
\(543\) 2.07832 22.5560i 0.0891891 0.967970i
\(544\) 6.29253i 0.269790i
\(545\) 0 0
\(546\) −21.7980 15.4135i −0.932867 0.659636i
\(547\) 26.3939 15.2385i 1.12852 0.651552i 0.184958 0.982746i \(-0.440785\pi\)
0.943562 + 0.331195i \(0.107452\pi\)
\(548\) −6.39898 3.69445i −0.273351 0.157819i
\(549\) 12.5732 14.7064i 0.536612 0.627653i
\(550\) 0.953512i 0.0406579i
\(551\) −7.77526 7.31747i −0.331237 0.311735i
\(552\) −1.12372 + 12.1958i −0.0478289 + 0.519087i
\(553\) 32.6969 + 18.8776i 1.39042 + 0.802757i
\(554\) 2.12372 3.67840i 0.0902284 0.156280i
\(555\) 0.797959 + 1.73205i 0.0338715 + 0.0735215i
\(556\) −0.174235 + 0.301783i −0.00738919 + 0.0127985i
\(557\) 24.2474 13.9993i 1.02740 0.593168i 0.111159 0.993803i \(-0.464544\pi\)
0.916238 + 0.400634i \(0.131210\pi\)
\(558\) −2.32577 + 12.5136i −0.0984575 + 0.529744i
\(559\) 3.11416i 0.131715i
\(560\) 5.44949 3.14626i 0.230283 0.132954i
\(561\) −1.44949 3.14626i −0.0611975 0.132835i
\(562\) −16.5959 −0.700057
\(563\) 22.8434 0.962733 0.481367 0.876519i \(-0.340141\pi\)
0.481367 + 0.876519i \(0.340141\pi\)
\(564\) −10.1237 + 4.66402i −0.426286 + 0.196391i
\(565\) 0.977296 + 0.564242i 0.0411152 + 0.0237378i
\(566\) 2.27526 + 3.94086i 0.0956361 + 0.165647i
\(567\) −31.1464 + 25.1701i −1.30803 + 1.05705i
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) −34.2929 −1.43763 −0.718816 0.695201i \(-0.755315\pi\)
−0.718816 + 0.695201i \(0.755315\pi\)
\(570\) 2.12372 + 10.4637i 0.0889530 + 0.438278i
\(571\) −11.0454 −0.462236 −0.231118 0.972926i \(-0.574238\pi\)
−0.231118 + 0.972926i \(0.574238\pi\)
\(572\) 0.550510 0.953512i 0.0230180 0.0398683i
\(573\) 27.5959 + 19.5133i 1.15284 + 0.815178i
\(574\) 6.67423 + 11.5601i 0.278577 + 0.482510i
\(575\) 18.3712 + 10.6066i 0.766131 + 0.442326i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) −20.5959 −0.857419 −0.428710 0.903442i \(-0.641032\pi\)
−0.428710 + 0.903442i \(0.641032\pi\)
\(578\) −22.5959 −0.939866
\(579\) −13.8990 + 6.40329i −0.577622 + 0.266111i
\(580\) −3.00000 + 1.73205i −0.124568 + 0.0719195i
\(581\) 63.0682i 2.61651i
\(582\) 2.17423 23.5970i 0.0901249 0.978126i
\(583\) 0.303062 0.174973i 0.0125515 0.00724663i
\(584\) 5.39898 9.35131i 0.223411 0.386960i
\(585\) −4.89898 13.8564i −0.202548 0.572892i
\(586\) −2.32577 + 4.02834i −0.0960765 + 0.166409i
\(587\) 4.10102 + 2.36773i 0.169267 + 0.0977265i 0.582240 0.813017i \(-0.302176\pi\)
−0.412973 + 0.910743i \(0.635510\pi\)
\(588\) −22.0732 2.03383i −0.910284 0.0838739i
\(589\) −5.32577 17.7098i −0.219444 0.729719i
\(590\) 9.26382i 0.381385i
\(591\) −0.696938 0.492810i −0.0286682 0.0202715i
\(592\) 0.674235 + 0.389270i 0.0277109 + 0.0159989i
\(593\) 24.0959 13.9118i 0.989501 0.571289i 0.0843757 0.996434i \(-0.473110\pi\)
0.905125 + 0.425145i \(0.139777\pi\)
\(594\) −1.15153 1.18386i −0.0472479 0.0485745i
\(595\) −19.7980 34.2911i −0.811637 1.40580i
\(596\) 4.87832i 0.199824i
\(597\) −11.8990 1.09638i −0.486993 0.0448717i
\(598\) 12.2474 + 21.2132i 0.500835 + 0.867472i
\(599\) −14.5732 25.2415i −0.595445 1.03134i −0.993484 0.113973i \(-0.963642\pi\)
0.398038 0.917369i \(-0.369691\pi\)
\(600\) −5.17423 0.476756i −0.211237 0.0194635i
\(601\) 31.0019i 1.26460i 0.774725 + 0.632298i \(0.217888\pi\)
−0.774725 + 0.632298i \(0.782112\pi\)
\(602\) −2.00000 3.46410i −0.0815139 0.141186i
\(603\) 13.6237 + 11.6476i 0.554801 + 0.474327i
\(604\) 15.6742 9.04952i 0.637776 0.368220i
\(605\) −13.3485 7.70674i −0.542692 0.313324i
\(606\) 14.0000 + 9.89949i 0.568711 + 0.402139i
\(607\) 36.9766i 1.50084i −0.660964 0.750418i \(-0.729852\pi\)
0.660964 0.750418i \(-0.270148\pi\)
\(608\) 3.17423 + 2.98735i 0.128732 + 0.121153i
\(609\) 18.7980 + 1.73205i 0.761732 + 0.0701862i
\(610\) 7.89898 + 4.56048i 0.319820 + 0.184648i
\(611\) −11.1464 + 19.3062i −0.450936 + 0.781044i
\(612\) −17.7980 + 6.29253i −0.719440 + 0.254360i
\(613\) −14.1010 + 24.4237i −0.569535 + 0.986463i 0.427077 + 0.904215i \(0.359543\pi\)
−0.996612 + 0.0822481i \(0.973790\pi\)
\(614\) 3.52270 2.03383i 0.142165 0.0820789i
\(615\) −0.674235 + 7.31747i −0.0271878 + 0.295069i
\(616\) 1.41421i 0.0569803i
\(617\) −12.9495 + 7.47639i −0.521327 + 0.300988i −0.737477 0.675372i \(-0.763983\pi\)
0.216151 + 0.976360i \(0.430650\pi\)
\(618\) 18.7980 8.66025i 0.756165 0.348367i
\(619\) −1.30306 −0.0523745 −0.0261872 0.999657i \(-0.508337\pi\)
−0.0261872 + 0.999657i \(0.508337\pi\)
\(620\) −6.00000 −0.240966
\(621\) 35.6186 9.01742i 1.42933 0.361856i
\(622\) 13.4722 + 7.77817i 0.540186 + 0.311876i
\(623\) −37.5959 65.1180i −1.50625 2.60890i
\(624\) −4.89898 3.46410i −0.196116 0.138675i
\(625\) 0.500000 0.866025i 0.0200000 0.0346410i
\(626\) −19.0000 −0.759393
\(627\) 2.27526 + 0.762485i 0.0908649 + 0.0304507i
\(628\) −18.6969 −0.746089
\(629\) 2.44949 4.24264i 0.0976676 0.169165i
\(630\) −14.3485 12.2672i −0.571657 0.488738i
\(631\) 4.87628 + 8.44596i 0.194121 + 0.336228i 0.946612 0.322375i \(-0.104481\pi\)
−0.752491 + 0.658603i \(0.771148\pi\)
\(632\) 7.34847 + 4.24264i 0.292306 + 0.168763i
\(633\) 24.2474 11.1708i 0.963750 0.444001i
\(634\) −6.00000 −0.238290
\(635\) 14.6969 0.583230
\(636\) −0.797959 1.73205i −0.0316411 0.0686803i
\(637\) −38.3939 + 22.1667i −1.52122 + 0.878277i
\(638\) 0.778539i 0.0308227i
\(639\) 17.6969 + 3.28913i 0.700080 + 0.130116i
\(640\) 1.22474 0.707107i 0.0484123 0.0279508i
\(641\) −16.1969 + 28.0539i −0.639741 + 1.10806i 0.345749 + 0.938327i \(0.387625\pi\)
−0.985490 + 0.169736i \(0.945708\pi\)
\(642\) −3.55051 7.70674i −0.140127 0.304161i
\(643\) 12.0732 20.9114i 0.476121 0.824666i −0.523505 0.852023i \(-0.675376\pi\)
0.999626 + 0.0273569i \(0.00870906\pi\)
\(644\) 27.2474 + 15.7313i 1.07370 + 0.619901i
\(645\) 0.202041 2.19275i 0.00795536 0.0863396i
\(646\) 18.7980 19.9740i 0.739596 0.785865i
\(647\) 7.84961i 0.308600i −0.988024 0.154300i \(-0.950688\pi\)
0.988024 0.154300i \(-0.0493122\pi\)
\(648\) −7.00000 + 5.65685i −0.274986 + 0.222222i
\(649\) 1.80306 + 1.04100i 0.0707764 + 0.0408627i
\(650\) −9.00000 + 5.19615i −0.353009 + 0.203810i
\(651\) 26.6969 + 18.8776i 1.04634 + 0.739871i
\(652\) −1.82577 3.16232i −0.0715025 0.123846i
\(653\) 19.5133i 0.763613i 0.924242 + 0.381806i \(0.124698\pi\)
−0.924242 + 0.381806i \(0.875302\pi\)
\(654\) 0 0
\(655\) 15.5732 + 26.9736i 0.608496 + 1.05395i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) −31.8485 5.91931i −1.24253 0.230934i
\(658\) 28.6342i 1.11628i
\(659\) 12.0000 + 20.7846i 0.467454 + 0.809653i 0.999309 0.0371821i \(-0.0118382\pi\)
−0.531855 + 0.846836i \(0.678505\pi\)
\(660\) 0.449490 0.635674i 0.0174964 0.0247436i
\(661\) −25.7196 + 14.8492i −1.00038 + 0.577569i −0.908360 0.418189i \(-0.862665\pi\)
−0.0920180 + 0.995757i \(0.529332\pi\)
\(662\) 12.8258 + 7.40496i 0.498488 + 0.287802i
\(663\) −21.7980 + 30.8270i −0.846563 + 1.19722i
\(664\) 14.1742i 0.550067i
\(665\) 26.6969 + 6.29253i 1.03526 + 0.244014i
\(666\) 0.426786 2.29629i 0.0165376 0.0889795i
\(667\) −15.0000 8.66025i −0.580802 0.335326i
\(668\) −2.44949 + 4.24264i −0.0947736 + 0.164153i
\(669\) −15.1237 + 6.96753i −0.584717 + 0.269380i
\(670\) −4.22474 + 7.31747i −0.163216 + 0.282699i
\(671\) 1.77526 1.02494i 0.0685330 0.0395675i
\(672\) −7.67423 0.707107i −0.296040 0.0272772i
\(673\) 3.46410i 0.133531i −0.997769 0.0667657i \(-0.978732\pi\)
0.997769 0.0667657i \(-0.0212680\pi\)
\(674\) 3.15153 1.81954i 0.121392 0.0700860i
\(675\) 3.82577 + 15.1117i 0.147254 + 0.581650i
\(676\) 1.00000 0.0384615
\(677\) 3.30306 0.126947 0.0634735 0.997984i \(-0.479782\pi\)
0.0634735 + 0.997984i \(0.479782\pi\)
\(678\) −0.578317 1.25529i −0.0222101 0.0482093i
\(679\) −52.7196 30.4377i −2.02319 1.16809i
\(680\) −4.44949 7.70674i −0.170630 0.295540i
\(681\) −5.44949 + 7.70674i −0.208825 + 0.295323i
\(682\) −0.674235 + 1.16781i −0.0258178 + 0.0447177i
\(683\) 41.3939 1.58389 0.791946 0.610591i \(-0.209068\pi\)
0.791946 + 0.610591i \(0.209068\pi\)
\(684\) 5.27526 11.9654i 0.201704 0.457510i
\(685\) −10.4495 −0.399254
\(686\) −12.8990 + 22.3417i −0.492485 + 0.853010i
\(687\) −8.89898 + 12.5851i −0.339517 + 0.480150i
\(688\) −0.449490 0.778539i −0.0171366 0.0296815i
\(689\) −3.30306 1.90702i −0.125837 0.0726518i
\(690\) 7.24745 + 15.7313i 0.275906 + 0.598881i
\(691\) −40.0000 −1.52167 −0.760836 0.648944i \(-0.775211\pi\)
−0.760836 + 0.648944i \(0.775211\pi\)
\(692\) 10.8990 0.414317
\(693\) −4.00000 + 1.41421i −0.151947 + 0.0537215i
\(694\) 5.72474 3.30518i 0.217308 0.125463i
\(695\) 0.492810i 0.0186933i
\(696\) 4.22474 + 0.389270i 0.160139 + 0.0147552i
\(697\) 16.3485 9.43879i 0.619242 0.357520i
\(698\) 8.24745 14.2850i 0.312171 0.540695i
\(699\) 10.1742 4.68729i 0.384825 0.177290i
\(700\) −6.67423 + 11.5601i −0.252262 + 0.436931i
\(701\) −8.57321 4.94975i −0.323806 0.186949i 0.329282 0.944232i \(-0.393193\pi\)
−0.653088 + 0.757282i \(0.726527\pi\)
\(702\) −4.89898 + 17.3205i −0.184900 + 0.653720i
\(703\) 0.977296 + 3.24980i 0.0368594 + 0.122569i
\(704\) 0.317837i 0.0119789i
\(705\) −9.10102 + 12.8708i −0.342764 + 0.484742i
\(706\) 12.6464 + 7.30142i 0.475955 + 0.274793i
\(707\) 38.1464 22.0239i 1.43464 0.828292i
\(708\) 6.55051 9.26382i 0.246183 0.348156i
\(709\) 1.32577 + 2.29629i 0.0497902 + 0.0862391i 0.889846 0.456260i \(-0.150811\pi\)
−0.840056 + 0.542499i \(0.817478\pi\)
\(710\) 8.48528i 0.318447i
\(711\) 4.65153 25.0273i 0.174446 0.938595i
\(712\) −8.44949 14.6349i −0.316658 0.548468i
\(713\) −15.0000 25.9808i −0.561754 0.972987i
\(714\) −4.44949 + 48.2903i −0.166518 + 1.80722i
\(715\) 1.55708i 0.0582314i
\(716\) −11.1742 19.3543i −0.417601 0.723306i
\(717\) 10.2020 + 7.21393i 0.381002 + 0.269409i
\(718\) −20.8207 + 12.0208i −0.777020 + 0.448613i
\(719\) 8.14643 + 4.70334i 0.303811 + 0.175405i 0.644153 0.764896i \(-0.277210\pi\)
−0.340343 + 0.940301i \(0.610543\pi\)
\(720\) −3.22474 2.75699i −0.120179 0.102747i
\(721\) 53.1687i 1.98010i
\(722\) 1.15153 + 18.9651i 0.0428555 + 0.705807i
\(723\) 1.62372 17.6223i 0.0603870 0.655380i
\(724\) −11.3258 6.53893i −0.420919 0.243018i
\(725\) 3.67423 6.36396i 0.136458 0.236352i
\(726\) 7.89898 + 17.1455i 0.293159 + 0.636331i
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) −13.3485 + 7.70674i −0.494727 + 0.285631i
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 15.2706i 0.565191i
\(731\) −4.89898 + 2.82843i −0.181195 + 0.104613i
\(732\) −4.67423 10.1459i −0.172765 0.375003i
\(733\) 24.0454 0.888137 0.444069 0.895993i \(-0.353535\pi\)
0.444069 + 0.895993i \(0.353535\pi\)
\(734\) −23.3485 −0.861808
\(735\) −28.4722 + 13.1172i −1.05021 + 0.483835i
\(736\) 6.12372 + 3.53553i 0.225723 + 0.130322i
\(737\) 0.949490 + 1.64456i 0.0349749 + 0.0605783i
\(738\) 5.84847 6.84072i 0.215285 0.251810i
\(739\) −4.82577 + 8.35847i −0.177519 + 0.307471i −0.941030 0.338323i \(-0.890140\pi\)
0.763511 + 0.645794i \(0.223474\pi\)
\(740\) 1.10102 0.0404743
\(741\) −5.20204 25.6308i −0.191102 0.941572i
\(742\) −4.89898 −0.179847
\(743\) 9.67423 16.7563i 0.354913 0.614728i −0.632190 0.774814i \(-0.717844\pi\)
0.987103 + 0.160086i \(0.0511771\pi\)
\(744\) 6.00000 + 4.24264i 0.219971 + 0.155543i
\(745\) 3.44949 + 5.97469i 0.126380 + 0.218896i
\(746\) 22.0454 + 12.7279i 0.807140 + 0.466002i
\(747\) −40.0908 + 14.1742i −1.46685 + 0.518608i
\(748\) −2.00000 −0.0731272
\(749\) −21.7980 −0.796480
\(750\) −17.7980 + 8.19955i −0.649890 + 0.299405i
\(751\) −11.6969 + 6.75323i −0.426827 + 0.246429i −0.697994 0.716103i \(-0.745924\pi\)
0.271167 + 0.962532i \(0.412591\pi\)
\(752\) 6.43539i 0.234675i
\(753\) 1.05051 11.4012i 0.0382827 0.415483i
\(754\) 7.34847 4.24264i 0.267615 0.154508i
\(755\) 12.7980 22.1667i 0.465765 0.806729i
\(756\) 5.67423 + 22.4131i 0.206370 + 0.815157i
\(757\) −9.69694 + 16.7956i −0.352441 + 0.610446i −0.986677 0.162694i \(-0.947982\pi\)
0.634235 + 0.773140i \(0.281315\pi\)
\(758\) −13.3485 7.70674i −0.484838 0.279921i
\(759\) 3.87628 + 0.357161i 0.140700 + 0.0129641i
\(760\) 6.00000 + 1.41421i 0.217643 + 0.0512989i
\(761\) 41.9657i 1.52126i −0.649188 0.760628i \(-0.724891\pi\)
0.649188 0.760628i \(-0.275109\pi\)
\(762\) −14.6969 10.3923i −0.532414 0.376473i
\(763\) 0 0
\(764\) 16.8990 9.75663i 0.611384 0.352982i
\(765\) −17.3485 + 20.2918i −0.627235 + 0.733652i
\(766\) −7.77526 13.4671i −0.280931 0.486587i
\(767\) 22.6916i 0.819347i
\(768\) −1.72474 0.158919i −0.0622364 0.00573448i
\(769\) 17.7980 + 30.8270i 0.641811 + 1.11165i 0.985028 + 0.172393i \(0.0551499\pi\)
−0.343217 + 0.939256i \(0.611517\pi\)
\(770\) −1.00000 1.73205i −0.0360375 0.0624188i
\(771\) 25.8712 + 2.38378i 0.931728 + 0.0858497i
\(772\) 8.83523i 0.317987i
\(773\) −1.22474 2.12132i −0.0440510 0.0762986i 0.843159 0.537664i \(-0.180693\pi\)