Properties

Label 126.2.f.c.85.2
Level $126$
Weight $2$
Character 126.85
Analytic conductor $1.006$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00611506547\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
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: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 85.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 126.85
Dual form 126.2.f.c.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 + 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.72474 + 2.98735i) q^{5} +(0.724745 - 1.57313i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 + 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.72474 + 2.98735i) q^{5} +(0.724745 - 1.57313i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +3.44949 q^{10} +(-1.00000 - 1.73205i) q^{11} +(-1.72474 + 0.158919i) q^{12} +(2.44949 - 4.24264i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-5.94949 + 0.548188i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(2.94949 - 0.548188i) q^{18} +7.44949 q^{19} +(-1.72474 - 2.98735i) q^{20} +(-0.724745 + 1.57313i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.00000 + 1.41421i) q^{24} +(-3.44949 - 5.97469i) q^{25} -4.89898 q^{26} +(-5.00000 + 1.41421i) q^{27} -1.00000 q^{28} +(-1.44949 - 2.51059i) q^{29} +(3.44949 + 4.87832i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.44949 - 3.14626i) q^{33} +(-1.00000 - 1.73205i) q^{34} -3.44949 q^{35} +(-1.94949 - 2.28024i) q^{36} -7.79796 q^{37} +(-3.72474 - 6.45145i) q^{38} +(8.44949 - 0.778539i) q^{39} +(-1.72474 + 2.98735i) q^{40} +(4.89898 - 8.48528i) q^{41} +(1.72474 - 0.158919i) q^{42} +(1.44949 + 2.51059i) q^{43} +2.00000 q^{44} +(-6.72474 - 7.86566i) q^{45} -1.00000 q^{46} +(4.89898 + 8.48528i) q^{47} +(0.724745 - 1.57313i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-3.44949 + 5.97469i) q^{50} +(2.00000 + 2.82843i) q^{51} +(2.44949 + 4.24264i) q^{52} -1.10102 q^{53} +(3.72474 + 3.62302i) q^{54} +6.89898 q^{55} +(0.500000 + 0.866025i) q^{56} +(7.44949 + 10.5352i) q^{57} +(-1.44949 + 2.51059i) q^{58} +(1.00000 - 1.73205i) q^{59} +(2.50000 - 5.42650i) q^{60} +(-5.72474 - 9.91555i) q^{61} +6.00000 q^{62} +(-2.94949 + 0.548188i) q^{63} +1.00000 q^{64} +(8.44949 + 14.6349i) q^{65} +(-3.44949 + 0.317837i) q^{66} +(1.55051 - 2.68556i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(1.72474 - 0.158919i) q^{69} +(1.72474 + 2.98735i) q^{70} +9.89898 q^{71} +(-1.00000 + 2.82843i) q^{72} +2.89898 q^{73} +(3.89898 + 6.75323i) q^{74} +(5.00000 - 10.8530i) q^{75} +(-3.72474 + 6.45145i) q^{76} +(1.00000 - 1.73205i) q^{77} +(-4.89898 - 6.92820i) q^{78} +(-3.94949 - 6.84072i) q^{79} +3.44949 q^{80} +(-7.00000 - 5.65685i) q^{81} -9.79796 q^{82} +(-1.00000 - 1.73205i) q^{83} +(-1.00000 - 1.41421i) q^{84} +(-3.44949 + 5.97469i) q^{85} +(1.44949 - 2.51059i) q^{86} +(2.10102 - 4.56048i) q^{87} +(-1.00000 - 1.73205i) q^{88} -7.10102 q^{89} +(-3.44949 + 9.75663i) q^{90} +4.89898 q^{91} +(0.500000 + 0.866025i) q^{92} +(-10.3485 + 0.953512i) q^{93} +(4.89898 - 8.48528i) q^{94} +(-12.8485 + 22.2542i) q^{95} +(-1.72474 + 0.158919i) q^{96} +(3.44949 + 5.97469i) q^{97} +1.00000 q^{98} +(5.89898 - 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 4q^{3} - 2q^{4} - 2q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 4q^{3} - 2q^{4} - 2q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 4q^{9} + 4q^{10} - 4q^{11} - 2q^{12} + 2q^{14} - 14q^{15} - 2q^{16} + 8q^{17} + 2q^{18} + 20q^{19} - 2q^{20} + 2q^{21} - 4q^{22} + 2q^{23} + 4q^{24} - 4q^{25} - 20q^{27} - 4q^{28} + 4q^{29} + 4q^{30} - 12q^{31} - 2q^{32} - 4q^{33} - 4q^{34} - 4q^{35} + 2q^{36} + 8q^{37} - 10q^{38} + 24q^{39} - 2q^{40} + 2q^{42} - 4q^{43} + 8q^{44} - 22q^{45} - 4q^{46} - 2q^{48} - 2q^{49} - 4q^{50} + 8q^{51} - 24q^{53} + 10q^{54} + 8q^{55} + 2q^{56} + 20q^{57} + 4q^{58} + 4q^{59} + 10q^{60} - 18q^{61} + 24q^{62} - 2q^{63} + 4q^{64} + 24q^{65} - 4q^{66} + 16q^{67} - 4q^{68} + 2q^{69} + 2q^{70} + 20q^{71} - 4q^{72} - 8q^{73} - 4q^{74} + 20q^{75} - 10q^{76} + 4q^{77} - 6q^{79} + 4q^{80} - 28q^{81} - 4q^{83} - 4q^{84} - 4q^{85} - 4q^{86} + 28q^{87} - 4q^{88} - 48q^{89} - 4q^{90} + 2q^{92} - 12q^{93} - 22q^{95} - 2q^{96} + 4q^{97} + 4q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 1.00000 + 1.41421i 0.577350 + 0.816497i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.72474 + 2.98735i −0.771329 + 1.33598i 0.165505 + 0.986209i \(0.447075\pi\)
−0.936835 + 0.349773i \(0.886259\pi\)
\(6\) 0.724745 1.57313i 0.295876 0.642229i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 3.44949 1.09082
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −1.72474 + 0.158919i −0.497891 + 0.0458759i
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) −5.94949 + 0.548188i −1.53615 + 0.141542i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 2.94949 0.548188i 0.695201 0.129209i
\(19\) 7.44949 1.70903 0.854515 0.519427i \(-0.173854\pi\)
0.854515 + 0.519427i \(0.173854\pi\)
\(20\) −1.72474 2.98735i −0.385665 0.667991i
\(21\) −0.724745 + 1.57313i −0.158152 + 0.343286i
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 1.00000 + 1.41421i 0.204124 + 0.288675i
\(25\) −3.44949 5.97469i −0.689898 1.19494i
\(26\) −4.89898 −0.960769
\(27\) −5.00000 + 1.41421i −0.962250 + 0.272166i
\(28\) −1.00000 −0.188982
\(29\) −1.44949 2.51059i −0.269163 0.466205i 0.699483 0.714650i \(-0.253414\pi\)
−0.968646 + 0.248445i \(0.920081\pi\)
\(30\) 3.44949 + 4.87832i 0.629788 + 0.890654i
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 1.44949 3.14626i 0.252324 0.547694i
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) −3.44949 −0.583070
\(36\) −1.94949 2.28024i −0.324915 0.380040i
\(37\) −7.79796 −1.28198 −0.640988 0.767551i \(-0.721475\pi\)
−0.640988 + 0.767551i \(0.721475\pi\)
\(38\) −3.72474 6.45145i −0.604233 1.04656i
\(39\) 8.44949 0.778539i 1.35300 0.124666i
\(40\) −1.72474 + 2.98735i −0.272706 + 0.472341i
\(41\) 4.89898 8.48528i 0.765092 1.32518i −0.175106 0.984550i \(-0.556027\pi\)
0.940198 0.340629i \(-0.110640\pi\)
\(42\) 1.72474 0.158919i 0.266134 0.0245217i
\(43\) 1.44949 + 2.51059i 0.221045 + 0.382861i 0.955126 0.296201i \(-0.0957199\pi\)
−0.734080 + 0.679062i \(0.762387\pi\)
\(44\) 2.00000 0.301511
\(45\) −6.72474 7.86566i −1.00247 1.17254i
\(46\) −1.00000 −0.147442
\(47\) 4.89898 + 8.48528i 0.714590 + 1.23771i 0.963118 + 0.269081i \(0.0867199\pi\)
−0.248528 + 0.968625i \(0.579947\pi\)
\(48\) 0.724745 1.57313i 0.104608 0.227062i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −3.44949 + 5.97469i −0.487832 + 0.844949i
\(51\) 2.00000 + 2.82843i 0.280056 + 0.396059i
\(52\) 2.44949 + 4.24264i 0.339683 + 0.588348i
\(53\) −1.10102 −0.151237 −0.0756184 0.997137i \(-0.524093\pi\)
−0.0756184 + 0.997137i \(0.524093\pi\)
\(54\) 3.72474 + 3.62302i 0.506874 + 0.493031i
\(55\) 6.89898 0.930258
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 7.44949 + 10.5352i 0.986709 + 1.39542i
\(58\) −1.44949 + 2.51059i −0.190327 + 0.329657i
\(59\) 1.00000 1.73205i 0.130189 0.225494i −0.793560 0.608492i \(-0.791775\pi\)
0.923749 + 0.382998i \(0.125108\pi\)
\(60\) 2.50000 5.42650i 0.322749 0.700559i
\(61\) −5.72474 9.91555i −0.732978 1.26956i −0.955605 0.294652i \(-0.904796\pi\)
0.222626 0.974904i \(-0.428537\pi\)
\(62\) 6.00000 0.762001
\(63\) −2.94949 + 0.548188i −0.371601 + 0.0690652i
\(64\) 1.00000 0.125000
\(65\) 8.44949 + 14.6349i 1.04803 + 1.81524i
\(66\) −3.44949 + 0.317837i −0.424603 + 0.0391231i
\(67\) 1.55051 2.68556i 0.189425 0.328094i −0.755634 0.654994i \(-0.772671\pi\)
0.945059 + 0.326901i \(0.106004\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 1.72474 0.158919i 0.207635 0.0191316i
\(70\) 1.72474 + 2.98735i 0.206146 + 0.357056i
\(71\) 9.89898 1.17479 0.587396 0.809299i \(-0.300153\pi\)
0.587396 + 0.809299i \(0.300153\pi\)
\(72\) −1.00000 + 2.82843i −0.117851 + 0.333333i
\(73\) 2.89898 0.339300 0.169650 0.985504i \(-0.445736\pi\)
0.169650 + 0.985504i \(0.445736\pi\)
\(74\) 3.89898 + 6.75323i 0.453247 + 0.785047i
\(75\) 5.00000 10.8530i 0.577350 1.25320i
\(76\) −3.72474 + 6.45145i −0.427258 + 0.740032i
\(77\) 1.00000 1.73205i 0.113961 0.197386i
\(78\) −4.89898 6.92820i −0.554700 0.784465i
\(79\) −3.94949 6.84072i −0.444352 0.769641i 0.553655 0.832746i \(-0.313233\pi\)
−0.998007 + 0.0631057i \(0.979899\pi\)
\(80\) 3.44949 0.385665
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) −9.79796 −1.08200
\(83\) −1.00000 1.73205i −0.109764 0.190117i 0.805910 0.592037i \(-0.201676\pi\)
−0.915675 + 0.401920i \(0.868343\pi\)
\(84\) −1.00000 1.41421i −0.109109 0.154303i
\(85\) −3.44949 + 5.97469i −0.374150 + 0.648046i
\(86\) 1.44949 2.51059i 0.156302 0.270724i
\(87\) 2.10102 4.56048i 0.225253 0.488935i
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) −7.10102 −0.752707 −0.376353 0.926476i \(-0.622822\pi\)
−0.376353 + 0.926476i \(0.622822\pi\)
\(90\) −3.44949 + 9.75663i −0.363608 + 1.02844i
\(91\) 4.89898 0.513553
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) −10.3485 + 0.953512i −1.07309 + 0.0988746i
\(94\) 4.89898 8.48528i 0.505291 0.875190i
\(95\) −12.8485 + 22.2542i −1.31823 + 2.28323i
\(96\) −1.72474 + 0.158919i −0.176031 + 0.0162196i
\(97\) 3.44949 + 5.97469i 0.350243 + 0.606638i 0.986292 0.165011i \(-0.0527658\pi\)
−0.636049 + 0.771649i \(0.719432\pi\)
\(98\) 1.00000 0.101015
\(99\) 5.89898 1.09638i 0.592870 0.110190i
\(100\) 6.89898 0.689898
\(101\) −3.62372 6.27647i −0.360574 0.624533i 0.627481 0.778632i \(-0.284086\pi\)
−0.988055 + 0.154099i \(0.950753\pi\)
\(102\) 1.44949 3.14626i 0.143521 0.311527i
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) 2.44949 4.24264i 0.240192 0.416025i
\(105\) −3.44949 4.87832i −0.336636 0.476075i
\(106\) 0.550510 + 0.953512i 0.0534703 + 0.0926132i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 1.27526 5.03723i 0.122711 0.484708i
\(109\) −16.6969 −1.59928 −0.799638 0.600482i \(-0.794975\pi\)
−0.799638 + 0.600482i \(0.794975\pi\)
\(110\) −3.44949 5.97469i −0.328896 0.569664i
\(111\) −7.79796 11.0280i −0.740150 1.04673i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 7.94949 13.7689i 0.747825 1.29527i −0.201038 0.979583i \(-0.564431\pi\)
0.948863 0.315688i \(-0.102235\pi\)
\(114\) 5.39898 11.7190i 0.505661 1.09759i
\(115\) 1.72474 + 2.98735i 0.160833 + 0.278571i
\(116\) 2.89898 0.269163
\(117\) 9.55051 + 11.1708i 0.882945 + 1.03274i
\(118\) −2.00000 −0.184115
\(119\) 1.00000 + 1.73205i 0.0916698 + 0.158777i
\(120\) −5.94949 + 0.548188i −0.543112 + 0.0500425i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −5.72474 + 9.91555i −0.518294 + 0.897712i
\(123\) 16.8990 1.55708i 1.52373 0.140397i
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) 6.55051 0.585895
\(126\) 1.94949 + 2.28024i 0.173674 + 0.203140i
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.10102 + 4.56048i −0.184985 + 0.401528i
\(130\) 8.44949 14.6349i 0.741069 1.28357i
\(131\) 6.72474 11.6476i 0.587544 1.01766i −0.407009 0.913424i \(-0.633428\pi\)
0.994553 0.104232i \(-0.0332383\pi\)
\(132\) 2.00000 + 2.82843i 0.174078 + 0.246183i
\(133\) 3.72474 + 6.45145i 0.322976 + 0.559411i
\(134\) −3.10102 −0.267887
\(135\) 4.39898 17.3759i 0.378604 1.49548i
\(136\) 2.00000 0.171499
\(137\) 5.89898 + 10.2173i 0.503984 + 0.872926i 0.999989 + 0.00460626i \(0.00146622\pi\)
−0.496006 + 0.868319i \(0.665200\pi\)
\(138\) −1.00000 1.41421i −0.0851257 0.120386i
\(139\) −4.72474 + 8.18350i −0.400748 + 0.694115i −0.993816 0.111037i \(-0.964583\pi\)
0.593069 + 0.805152i \(0.297916\pi\)
\(140\) 1.72474 2.98735i 0.145768 0.252477i
\(141\) −7.10102 + 15.4135i −0.598014 + 1.29805i
\(142\) −4.94949 8.57277i −0.415352 0.719411i
\(143\) −9.79796 −0.819346
\(144\) 2.94949 0.548188i 0.245791 0.0456823i
\(145\) 10.0000 0.830455
\(146\) −1.44949 2.51059i −0.119961 0.207778i
\(147\) −1.72474 + 0.158919i −0.142255 + 0.0131074i
\(148\) 3.89898 6.75323i 0.320494 0.555112i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) −11.8990 + 1.09638i −0.971548 + 0.0895188i
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) 7.44949 0.604233
\(153\) −2.00000 + 5.65685i −0.161690 + 0.457330i
\(154\) −2.00000 −0.161165
\(155\) −10.3485 17.9241i −0.831209 1.43970i
\(156\) −3.55051 + 7.70674i −0.284268 + 0.617033i
\(157\) −3.17423 + 5.49794i −0.253332 + 0.438783i −0.964441 0.264298i \(-0.914860\pi\)
0.711109 + 0.703081i \(0.248193\pi\)
\(158\) −3.94949 + 6.84072i −0.314205 + 0.544218i
\(159\) −1.10102 1.55708i −0.0873166 0.123484i
\(160\) −1.72474 2.98735i −0.136353 0.236170i
\(161\) 1.00000 0.0788110
\(162\) −1.39898 + 8.89060i −0.109914 + 0.698512i
\(163\) −0.202041 −0.0158251 −0.00791254 0.999969i \(-0.502519\pi\)
−0.00791254 + 0.999969i \(0.502519\pi\)
\(164\) 4.89898 + 8.48528i 0.382546 + 0.662589i
\(165\) 6.89898 + 9.75663i 0.537085 + 0.759553i
\(166\) −1.00000 + 1.73205i −0.0776151 + 0.134433i
\(167\) −9.34847 + 16.1920i −0.723406 + 1.25298i 0.236220 + 0.971700i \(0.424091\pi\)
−0.959627 + 0.281277i \(0.909242\pi\)
\(168\) −0.724745 + 1.57313i −0.0559153 + 0.121370i
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) 6.89898 0.529128
\(171\) −7.44949 + 21.0703i −0.569677 + 1.61129i
\(172\) −2.89898 −0.221045
\(173\) 6.44949 + 11.1708i 0.490346 + 0.849304i 0.999938 0.0111123i \(-0.00353722\pi\)
−0.509593 + 0.860416i \(0.670204\pi\)
\(174\) −5.00000 + 0.460702i −0.379049 + 0.0349257i
\(175\) 3.44949 5.97469i 0.260757 0.451644i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 3.44949 0.317837i 0.259280 0.0238901i
\(178\) 3.55051 + 6.14966i 0.266122 + 0.460937i
\(179\) −8.69694 −0.650040 −0.325020 0.945707i \(-0.605371\pi\)
−0.325020 + 0.945707i \(0.605371\pi\)
\(180\) 10.1742 1.89097i 0.758343 0.140945i
\(181\) 4.34847 0.323219 0.161610 0.986855i \(-0.448331\pi\)
0.161610 + 0.986855i \(0.448331\pi\)
\(182\) −2.44949 4.24264i −0.181568 0.314485i
\(183\) 8.29796 18.0116i 0.613403 1.33145i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) 13.4495 23.2952i 0.988826 1.71270i
\(186\) 6.00000 + 8.48528i 0.439941 + 0.622171i
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) −9.79796 −0.714590
\(189\) −3.72474 3.62302i −0.270935 0.263536i
\(190\) 25.6969 1.86425
\(191\) −6.94949 12.0369i −0.502847 0.870957i −0.999995 0.00329106i \(-0.998952\pi\)
0.497147 0.867666i \(-0.334381\pi\)
\(192\) 1.00000 + 1.41421i 0.0721688 + 0.102062i
\(193\) 4.05051 7.01569i 0.291562 0.505000i −0.682617 0.730776i \(-0.739158\pi\)
0.974179 + 0.225776i \(0.0724917\pi\)
\(194\) 3.44949 5.97469i 0.247659 0.428958i
\(195\) −12.2474 + 26.5843i −0.877058 + 1.90374i
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) −12.6969 −0.904619 −0.452310 0.891861i \(-0.649400\pi\)
−0.452310 + 0.891861i \(0.649400\pi\)
\(198\) −3.89898 4.56048i −0.277088 0.324099i
\(199\) 6.89898 0.489056 0.244528 0.969642i \(-0.421367\pi\)
0.244528 + 0.969642i \(0.421367\pi\)
\(200\) −3.44949 5.97469i −0.243916 0.422474i
\(201\) 5.34847 0.492810i 0.377252 0.0347601i
\(202\) −3.62372 + 6.27647i −0.254964 + 0.441611i
\(203\) 1.44949 2.51059i 0.101734 0.176209i
\(204\) −3.44949 + 0.317837i −0.241513 + 0.0222531i
\(205\) 16.8990 + 29.2699i 1.18028 + 2.04430i
\(206\) 14.0000 0.975426
\(207\) 1.94949 + 2.28024i 0.135499 + 0.158488i
\(208\) −4.89898 −0.339683
\(209\) −7.44949 12.9029i −0.515292 0.892512i
\(210\) −2.50000 + 5.42650i −0.172516 + 0.374464i
\(211\) −1.55051 + 2.68556i −0.106742 + 0.184882i −0.914448 0.404703i \(-0.867375\pi\)
0.807707 + 0.589584i \(0.200708\pi\)
\(212\) 0.550510 0.953512i 0.0378092 0.0654875i
\(213\) 9.89898 + 13.9993i 0.678267 + 0.959214i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −10.0000 −0.681994
\(216\) −5.00000 + 1.41421i −0.340207 + 0.0962250i
\(217\) −6.00000 −0.407307
\(218\) 8.34847 + 14.4600i 0.565430 + 0.979353i
\(219\) 2.89898 + 4.09978i 0.195895 + 0.277037i
\(220\) −3.44949 + 5.97469i −0.232565 + 0.402814i
\(221\) 4.89898 8.48528i 0.329541 0.570782i
\(222\) −5.65153 + 12.2672i −0.379306 + 0.823322i
\(223\) 10.4495 + 18.0990i 0.699750 + 1.21200i 0.968553 + 0.248807i \(0.0800384\pi\)
−0.268804 + 0.963195i \(0.586628\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 20.3485 3.78194i 1.35656 0.252129i
\(226\) −15.8990 −1.05758
\(227\) 0.275255 + 0.476756i 0.0182693 + 0.0316434i 0.875016 0.484095i \(-0.160851\pi\)
−0.856746 + 0.515738i \(0.827518\pi\)
\(228\) −12.8485 + 1.18386i −0.850911 + 0.0784032i
\(229\) 11.6237 20.1329i 0.768117 1.33042i −0.170465 0.985364i \(-0.554527\pi\)
0.938583 0.345055i \(-0.112140\pi\)
\(230\) 1.72474 2.98735i 0.113726 0.196980i
\(231\) 3.44949 0.317837i 0.226960 0.0209122i
\(232\) −1.44949 2.51059i −0.0951637 0.164828i
\(233\) −7.00000 −0.458585 −0.229293 0.973358i \(-0.573641\pi\)
−0.229293 + 0.973358i \(0.573641\pi\)
\(234\) 4.89898 13.8564i 0.320256 0.905822i
\(235\) −33.7980 −2.20474
\(236\) 1.00000 + 1.73205i 0.0650945 + 0.112747i
\(237\) 5.72474 12.4261i 0.371862 0.807164i
\(238\) 1.00000 1.73205i 0.0648204 0.112272i
\(239\) 6.39898 11.0834i 0.413916 0.716923i −0.581398 0.813619i \(-0.697494\pi\)
0.995314 + 0.0966962i \(0.0308275\pi\)
\(240\) 3.44949 + 4.87832i 0.222664 + 0.314894i
\(241\) 4.44949 + 7.70674i 0.286617 + 0.496435i 0.973000 0.230805i \(-0.0741360\pi\)
−0.686383 + 0.727240i \(0.740803\pi\)
\(242\) −7.00000 −0.449977
\(243\) 1.00000 15.5563i 0.0641500 0.997940i
\(244\) 11.4495 0.732978
\(245\) −1.72474 2.98735i −0.110190 0.190855i
\(246\) −9.79796 13.8564i −0.624695 0.883452i
\(247\) 18.2474 31.6055i 1.16106 2.01101i
\(248\) −3.00000 + 5.19615i −0.190500 + 0.329956i
\(249\) 1.44949 3.14626i 0.0918577 0.199386i
\(250\) −3.27526 5.67291i −0.207145 0.358786i
\(251\) 12.5505 0.792181 0.396091 0.918211i \(-0.370367\pi\)
0.396091 + 0.918211i \(0.370367\pi\)
\(252\) 1.00000 2.82843i 0.0629941 0.178174i
\(253\) −2.00000 −0.125739
\(254\) 1.50000 + 2.59808i 0.0941184 + 0.163018i
\(255\) −11.8990 + 1.09638i −0.745143 + 0.0686577i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.8990 + 24.0737i −0.866995 + 1.50168i −0.00194150 + 0.999998i \(0.500618\pi\)
−0.865053 + 0.501680i \(0.832715\pi\)
\(258\) 5.00000 0.460702i 0.311286 0.0286820i
\(259\) −3.89898 6.75323i −0.242271 0.419625i
\(260\) −16.8990 −1.04803
\(261\) 8.55051 1.58919i 0.529263 0.0983682i
\(262\) −13.4495 −0.830912
\(263\) −8.05051 13.9439i −0.496416 0.859817i 0.503576 0.863951i \(-0.332017\pi\)
−0.999991 + 0.00413383i \(0.998684\pi\)
\(264\) 1.44949 3.14626i 0.0892099 0.193639i
\(265\) 1.89898 3.28913i 0.116653 0.202050i
\(266\) 3.72474 6.45145i 0.228379 0.395564i
\(267\) −7.10102 10.0424i −0.434575 0.614582i
\(268\) 1.55051 + 2.68556i 0.0947125 + 0.164047i
\(269\) −3.65153 −0.222638 −0.111319 0.993785i \(-0.535507\pi\)
−0.111319 + 0.993785i \(0.535507\pi\)
\(270\) −17.2474 + 4.87832i −1.04965 + 0.296885i
\(271\) 16.8990 1.02654 0.513270 0.858227i \(-0.328434\pi\)
0.513270 + 0.858227i \(0.328434\pi\)
\(272\) −1.00000 1.73205i −0.0606339 0.105021i
\(273\) 4.89898 + 6.92820i 0.296500 + 0.419314i
\(274\) 5.89898 10.2173i 0.356370 0.617252i
\(275\) −6.89898 + 11.9494i −0.416024 + 0.720575i
\(276\) −0.724745 + 1.57313i −0.0436245 + 0.0946914i
\(277\) −5.34847 9.26382i −0.321358 0.556609i 0.659410 0.751783i \(-0.270806\pi\)
−0.980769 + 0.195174i \(0.937473\pi\)
\(278\) 9.44949 0.566743
\(279\) −11.6969 13.6814i −0.700277 0.819086i
\(280\) −3.44949 −0.206146
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) 16.8990 1.55708i 1.00632 0.0927227i
\(283\) 10.2753 17.7973i 0.610801 1.05794i −0.380305 0.924861i \(-0.624181\pi\)
0.991106 0.133077i \(-0.0424856\pi\)
\(284\) −4.94949 + 8.57277i −0.293698 + 0.508700i
\(285\) −44.3207 + 4.08372i −2.62533 + 0.241899i
\(286\) 4.89898 + 8.48528i 0.289683 + 0.501745i
\(287\) 9.79796 0.578355
\(288\) −1.94949 2.28024i −0.114875 0.134364i
\(289\) −13.0000 −0.764706
\(290\) −5.00000 8.66025i −0.293610 0.508548i
\(291\) −5.00000 + 10.8530i −0.293105 + 0.636215i
\(292\) −1.44949 + 2.51059i −0.0848250 + 0.146921i
\(293\) −13.6237 + 23.5970i −0.795906 + 1.37855i 0.126356 + 0.991985i \(0.459672\pi\)
−0.922262 + 0.386565i \(0.873661\pi\)
\(294\) 1.00000 + 1.41421i 0.0583212 + 0.0824786i
\(295\) 3.44949 + 5.97469i 0.200837 + 0.347860i
\(296\) −7.79796 −0.453247
\(297\) 7.44949 + 7.24604i 0.432263 + 0.420458i
\(298\) −6.00000 −0.347571
\(299\) −2.44949 4.24264i −0.141658 0.245358i
\(300\) 6.89898 + 9.75663i 0.398313 + 0.563299i
\(301\) −1.44949 + 2.51059i −0.0835472 + 0.144708i
\(302\) 2.50000 4.33013i 0.143859 0.249171i
\(303\) 5.25255 11.4012i 0.301751 0.654982i
\(304\) −3.72474 6.45145i −0.213629 0.370016i
\(305\) 39.4949 2.26147
\(306\) 5.89898 1.09638i 0.337222 0.0626757i
\(307\) 0.752551 0.0429504 0.0214752 0.999769i \(-0.493164\pi\)
0.0214752 + 0.999769i \(0.493164\pi\)
\(308\) 1.00000 + 1.73205i 0.0569803 + 0.0986928i
\(309\) −24.1464 + 2.22486i −1.37364 + 0.126568i
\(310\) −10.3485 + 17.9241i −0.587754 + 1.01802i
\(311\) −0.651531 + 1.12848i −0.0369449 + 0.0639905i −0.883907 0.467663i \(-0.845096\pi\)
0.846962 + 0.531654i \(0.178429\pi\)
\(312\) 8.44949 0.778539i 0.478358 0.0440761i
\(313\) −12.3485 21.3882i −0.697977 1.20893i −0.969167 0.246405i \(-0.920751\pi\)
0.271190 0.962526i \(-0.412583\pi\)
\(314\) 6.34847 0.358265
\(315\) 3.44949 9.75663i 0.194357 0.549724i
\(316\) 7.89898 0.444352
\(317\) 4.34847 + 7.53177i 0.244234 + 0.423026i 0.961916 0.273345i \(-0.0881300\pi\)
−0.717682 + 0.696371i \(0.754797\pi\)
\(318\) −0.797959 + 1.73205i −0.0447473 + 0.0971286i
\(319\) −2.89898 + 5.02118i −0.162312 + 0.281132i
\(320\) −1.72474 + 2.98735i −0.0964162 + 0.166998i
\(321\) −12.0000 16.9706i −0.669775 0.947204i
\(322\) −0.500000 0.866025i −0.0278639 0.0482617i
\(323\) 14.8990 0.829001
\(324\) 8.39898 3.23375i 0.466610 0.179653i
\(325\) −33.7980 −1.87477
\(326\) 0.101021 + 0.174973i 0.00559501 + 0.00969084i
\(327\) −16.6969 23.6130i −0.923343 1.30580i
\(328\) 4.89898 8.48528i 0.270501 0.468521i
\(329\) −4.89898 + 8.48528i −0.270089 + 0.467809i
\(330\) 5.00000 10.8530i 0.275241 0.597438i
\(331\) 12.3485 + 21.3882i 0.678733 + 1.17560i 0.975363 + 0.220608i \(0.0708041\pi\)
−0.296629 + 0.954993i \(0.595863\pi\)
\(332\) 2.00000 0.109764
\(333\) 7.79796 22.0560i 0.427326 1.20866i
\(334\) 18.6969 1.02305
\(335\) 5.34847 + 9.26382i 0.292218 + 0.506137i
\(336\) 1.72474 0.158919i 0.0940925 0.00866972i
\(337\) −17.6969 + 30.6520i −0.964014 + 1.66972i −0.251772 + 0.967787i \(0.581013\pi\)
−0.712242 + 0.701934i \(0.752320\pi\)
\(338\) −5.50000 + 9.52628i −0.299161 + 0.518161i
\(339\) 27.4217 2.52664i 1.48934 0.137228i
\(340\) −3.44949 5.97469i −0.187075 0.324023i
\(341\) 12.0000 0.649836
\(342\) 21.9722 4.08372i 1.18812 0.220822i
\(343\) −1.00000 −0.0539949
\(344\) 1.44949 + 2.51059i 0.0781512 + 0.135362i
\(345\) −2.50000 + 5.42650i −0.134595 + 0.292153i
\(346\) 6.44949 11.1708i 0.346727 0.600548i
\(347\) 9.79796 16.9706i 0.525982 0.911028i −0.473560 0.880762i \(-0.657031\pi\)
0.999542 0.0302659i \(-0.00963541\pi\)
\(348\) 2.89898 + 4.09978i 0.155402 + 0.219771i
\(349\) −10.4495 18.0990i −0.559348 0.968820i −0.997551 0.0699435i \(-0.977718\pi\)
0.438203 0.898876i \(-0.355615\pi\)
\(350\) −6.89898 −0.368766
\(351\) −6.24745 + 24.6773i −0.333464 + 1.31718i
\(352\) 2.00000 0.106600
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) −2.00000 2.82843i −0.106299 0.150329i
\(355\) −17.0732 + 29.5717i −0.906152 + 1.56950i
\(356\) 3.55051 6.14966i 0.188177 0.325932i
\(357\) −1.44949 + 3.14626i −0.0767151 + 0.166518i
\(358\) 4.34847 + 7.53177i 0.229824 + 0.398066i
\(359\) 10.7980 0.569894 0.284947 0.958543i \(-0.408024\pi\)
0.284947 + 0.958543i \(0.408024\pi\)
\(360\) −6.72474 7.86566i −0.354425 0.414557i
\(361\) 36.4949 1.92078
\(362\) −2.17423 3.76588i −0.114275 0.197931i
\(363\) 12.0732 1.11243i 0.633679 0.0583875i
\(364\) −2.44949 + 4.24264i −0.128388 + 0.222375i
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) −19.7474 + 1.81954i −1.03222 + 0.0951087i
\(367\) −2.89898 5.02118i −0.151325 0.262103i 0.780389 0.625294i \(-0.215021\pi\)
−0.931715 + 0.363190i \(0.881687\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 19.1010 + 22.3417i 0.994359 + 1.16306i
\(370\) −26.8990 −1.39841
\(371\) −0.550510 0.953512i −0.0285811 0.0495039i
\(372\) 4.34847 9.43879i 0.225458 0.489379i
\(373\) −1.44949 + 2.51059i −0.0750517 + 0.129993i −0.901109 0.433593i \(-0.857246\pi\)
0.826057 + 0.563587i \(0.190579\pi\)
\(374\) −2.00000 + 3.46410i −0.103418 + 0.179124i
\(375\) 6.55051 + 9.26382i 0.338267 + 0.478382i
\(376\) 4.89898 + 8.48528i 0.252646 + 0.437595i
\(377\) −14.2020 −0.731442
\(378\) −1.27526 + 5.03723i −0.0655920 + 0.259087i
\(379\) −26.4949 −1.36095 −0.680476 0.732771i \(-0.738227\pi\)
−0.680476 + 0.732771i \(0.738227\pi\)
\(380\) −12.8485 22.2542i −0.659113 1.14162i
\(381\) −3.00000 4.24264i −0.153695 0.217357i
\(382\) −6.94949 + 12.0369i −0.355567 + 0.615860i
\(383\) −3.44949 + 5.97469i −0.176261 + 0.305292i −0.940597 0.339526i \(-0.889734\pi\)
0.764336 + 0.644818i \(0.223067\pi\)
\(384\) 0.724745 1.57313i 0.0369845 0.0802786i
\(385\) 3.44949 + 5.97469i 0.175802 + 0.304498i
\(386\) −8.10102 −0.412331
\(387\) −8.55051 + 1.58919i −0.434647 + 0.0807829i
\(388\) −6.89898 −0.350243
\(389\) 7.55051 + 13.0779i 0.382826 + 0.663074i 0.991465 0.130373i \(-0.0416175\pi\)
−0.608639 + 0.793447i \(0.708284\pi\)
\(390\) 29.1464 2.68556i 1.47589 0.135989i
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) 23.1969 2.13737i 1.17013 0.107816i
\(394\) 6.34847 + 10.9959i 0.319831 + 0.553964i
\(395\) 27.2474 1.37097
\(396\) −2.00000 + 5.65685i −0.100504 + 0.284268i
\(397\) 9.30306 0.466907 0.233454 0.972368i \(-0.424997\pi\)
0.233454 + 0.972368i \(0.424997\pi\)
\(398\) −3.44949 5.97469i −0.172907 0.299484i
\(399\) −5.39898 + 11.7190i −0.270287 + 0.586685i
\(400\) −3.44949 + 5.97469i −0.172474 + 0.298735i
\(401\) 5.05051 8.74774i 0.252210 0.436841i −0.711924 0.702257i \(-0.752176\pi\)
0.964134 + 0.265416i \(0.0855091\pi\)
\(402\) −3.10102 4.38551i −0.154665 0.218729i
\(403\) 14.6969 + 25.4558i 0.732107 + 1.26805i
\(404\) 7.24745 0.360574
\(405\) 28.9722 11.1548i 1.43964 0.554286i
\(406\) −2.89898 −0.143874
\(407\) 7.79796 + 13.5065i 0.386530 + 0.669490i
\(408\) 2.00000 + 2.82843i 0.0990148 + 0.140028i
\(409\) −2.89898 + 5.02118i −0.143345 + 0.248281i −0.928754 0.370696i \(-0.879119\pi\)
0.785409 + 0.618977i \(0.212453\pi\)
\(410\) 16.8990 29.2699i 0.834581 1.44554i
\(411\) −8.55051 + 18.5597i −0.421766 + 0.915485i
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) 2.00000 0.0984136
\(414\) 1.00000 2.82843i 0.0491473 0.139010i
\(415\) 6.89898 0.338658
\(416\) 2.44949 + 4.24264i 0.120096 + 0.208013i
\(417\) −16.2980 + 1.50170i −0.798114 + 0.0735386i
\(418\) −7.44949 + 12.9029i −0.364366 + 0.631101i
\(419\) −12.2753 + 21.2614i −0.599685 + 1.03869i 0.393182 + 0.919461i \(0.371374\pi\)
−0.992867 + 0.119225i \(0.961959\pi\)
\(420\) 5.94949 0.548188i 0.290305 0.0267488i
\(421\) −6.55051 11.3458i −0.319252 0.552961i 0.661080 0.750316i \(-0.270098\pi\)
−0.980332 + 0.197354i \(0.936765\pi\)
\(422\) 3.10102 0.150955
\(423\) −28.8990 + 5.37113i −1.40512 + 0.261153i
\(424\) −1.10102 −0.0534703
\(425\) −6.89898 11.9494i −0.334650 0.579630i
\(426\) 7.17423 15.5724i 0.347593 0.754485i
\(427\) 5.72474 9.91555i 0.277040 0.479847i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) −9.79796 13.8564i −0.473050 0.668994i
\(430\) 5.00000 + 8.66025i 0.241121 + 0.417635i
\(431\) −7.59592 −0.365882 −0.182941 0.983124i \(-0.558562\pi\)
−0.182941 + 0.983124i \(0.558562\pi\)
\(432\) 3.72474 + 3.62302i 0.179207 + 0.174313i
\(433\) 11.7980 0.566974 0.283487 0.958976i \(-0.408509\pi\)
0.283487 + 0.958976i \(0.408509\pi\)
\(434\) 3.00000 + 5.19615i 0.144005 + 0.249423i
\(435\) 10.0000 + 14.1421i 0.479463 + 0.678064i
\(436\) 8.34847 14.4600i 0.399819 0.692507i
\(437\) 3.72474 6.45145i 0.178179 0.308615i
\(438\) 2.10102 4.56048i 0.100391 0.217908i
\(439\) −10.8990 18.8776i −0.520180 0.900978i −0.999725 0.0234607i \(-0.992532\pi\)
0.479545 0.877517i \(-0.340802\pi\)
\(440\) 6.89898 0.328896
\(441\) −1.94949 2.28024i −0.0928328 0.108583i
\(442\) −9.79796 −0.466041
\(443\) 2.55051 + 4.41761i 0.121178 + 0.209887i 0.920233 0.391372i \(-0.127999\pi\)
−0.799054 + 0.601259i \(0.794666\pi\)
\(444\) 13.4495 1.23924i 0.638285 0.0588118i
\(445\) 12.2474 21.2132i 0.580585 1.00560i
\(446\) 10.4495 18.0990i 0.494798 0.857015i
\(447\) 10.3485 0.953512i 0.489466 0.0450996i
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −18.5959 −0.877596 −0.438798 0.898586i \(-0.644596\pi\)
−0.438798 + 0.898586i \(0.644596\pi\)
\(450\) −13.4495 15.7313i −0.634015 0.741582i
\(451\) −19.5959 −0.922736
\(452\) 7.94949 + 13.7689i 0.373913 + 0.647636i
\(453\) −3.62372 + 7.86566i −0.170257 + 0.369561i
\(454\) 0.275255 0.476756i 0.0129184 0.0223753i
\(455\) −8.44949 + 14.6349i −0.396118 + 0.686097i
\(456\) 7.44949 + 10.5352i 0.348854 + 0.493355i
\(457\) −15.7474 27.2754i −0.736635 1.27589i −0.954002 0.299799i \(-0.903080\pi\)
0.217368 0.976090i \(-0.430253\pi\)
\(458\) −23.2474 −1.08628
\(459\) −10.0000 + 2.82843i −0.466760 + 0.132020i
\(460\) −3.44949 −0.160833
\(461\) −10.1742 17.6223i −0.473861 0.820752i 0.525691 0.850676i \(-0.323807\pi\)
−0.999552 + 0.0299238i \(0.990474\pi\)
\(462\) −2.00000 2.82843i −0.0930484 0.131590i
\(463\) 12.8485 22.2542i 0.597119 1.03424i −0.396125 0.918197i \(-0.629645\pi\)
0.993244 0.116044i \(-0.0370213\pi\)
\(464\) −1.44949 + 2.51059i −0.0672909 + 0.116551i
\(465\) 15.0000 32.5590i 0.695608 1.50989i
\(466\) 3.50000 + 6.06218i 0.162134 + 0.280825i
\(467\) 10.0000 0.462745 0.231372 0.972865i \(-0.425678\pi\)
0.231372 + 0.972865i \(0.425678\pi\)
\(468\) −14.4495 + 2.68556i −0.667928 + 0.124140i
\(469\) 3.10102 0.143192
\(470\) 16.8990 + 29.2699i 0.779492 + 1.35012i
\(471\) −10.9495 + 1.00889i −0.504526 + 0.0464872i
\(472\) 1.00000 1.73205i 0.0460287 0.0797241i
\(473\) 2.89898 5.02118i 0.133295 0.230874i
\(474\) −13.6237 + 1.25529i −0.625758 + 0.0576576i
\(475\) −25.6969 44.5084i −1.17906 2.04219i
\(476\) −2.00000 −0.0916698
\(477\) 1.10102 3.11416i 0.0504123 0.142587i
\(478\) −12.7980 −0.585365
\(479\) 14.7980 + 25.6308i 0.676136 + 1.17110i 0.976135 + 0.217163i \(0.0696802\pi\)
−0.299999 + 0.953939i \(0.596987\pi\)
\(480\) 2.50000 5.42650i 0.114109 0.247685i
\(481\) −19.1010 + 33.0839i −0.870932 + 1.50850i
\(482\) 4.44949 7.70674i 0.202669 0.351032i
\(483\) 1.00000 + 1.41421i 0.0455016 + 0.0643489i
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) −23.7980 −1.08061
\(486\) −13.9722 + 6.91215i −0.633792 + 0.313541i
\(487\) 22.3939 1.01476 0.507382 0.861721i \(-0.330613\pi\)
0.507382 + 0.861721i \(0.330613\pi\)
\(488\) −5.72474 9.91555i −0.259147 0.448856i
\(489\) −0.202041 0.285729i −0.00913661 0.0129211i
\(490\) −1.72474 + 2.98735i −0.0779160 + 0.134955i
\(491\) 1.89898 3.28913i 0.0856997 0.148436i −0.819989 0.572379i \(-0.806021\pi\)
0.905689 + 0.423942i \(0.139354\pi\)
\(492\) −7.10102 + 15.4135i −0.320139 + 0.694894i
\(493\) −2.89898 5.02118i −0.130563 0.226143i
\(494\) −36.4949 −1.64198
\(495\) −6.89898 + 19.5133i −0.310086 + 0.877056i
\(496\) 6.00000 0.269408
\(497\) 4.94949 + 8.57277i 0.222015 + 0.384541i
\(498\) −3.44949 + 0.317837i −0.154575 + 0.0142426i
\(499\) −16.6969 + 28.9199i −0.747458 + 1.29463i 0.201580 + 0.979472i \(0.435392\pi\)
−0.949038 + 0.315163i \(0.897941\pi\)
\(500\) −3.27526 + 5.67291i −0.146474 + 0.253700i
\(501\) −32.2474 + 2.97129i −1.44071 + 0.132748i
\(502\) −6.27526 10.8691i −0.280078 0.485110i
\(503\) 24.4949 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(504\) −2.94949 + 0.548188i −0.131381 + 0.0244182i
\(505\) 25.0000 1.11249
\(506\) 1.00000 + 1.73205i 0.0444554 + 0.0769991i
\(507\) 7.97219 17.3045i 0.354058 0.768518i
\(508\) 1.50000 2.59808i 0.0665517 0.115271i
\(509\) 8.44949 14.6349i 0.374517 0.648683i −0.615738 0.787951i \(-0.711142\pi\)
0.990255 + 0.139269i \(0.0444752\pi\)
\(510\) 6.89898 + 9.75663i 0.305492 + 0.432031i
\(511\) 1.44949 + 2.51059i 0.0641217 + 0.111062i
\(512\) 1.00000 0.0441942
\(513\) −37.2474 + 10.5352i −1.64452 + 0.465139i
\(514\) 27.7980 1.22612
\(515\) −24.1464 41.8228i −1.06402 1.84293i
\(516\) −2.89898 4.09978i −0.127620 0.180483i
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) −3.89898 + 6.75323i −0.171311 + 0.296720i
\(519\) −9.34847 + 20.2918i −0.410352 + 0.890711i
\(520\) 8.44949 + 14.6349i 0.370535 + 0.641785i
\(521\) −38.6969 −1.69534 −0.847672 0.530521i \(-0.821996\pi\)
−0.847672 + 0.530521i \(0.821996\pi\)
\(522\) −5.65153 6.61037i −0.247361 0.289328i
\(523\) 0.348469 0.0152375 0.00761875 0.999971i \(-0.497575\pi\)
0.00761875 + 0.999971i \(0.497575\pi\)
\(524\) 6.72474 + 11.6476i 0.293772 + 0.508828i
\(525\) 11.8990 1.09638i 0.519314 0.0478498i
\(526\) −8.05051 + 13.9439i −0.351019 + 0.607983i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) −3.44949 + 0.317837i −0.150120 + 0.0138321i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −3.79796 −0.164973
\(531\) 3.89898 + 4.56048i 0.169201 + 0.197908i
\(532\) −7.44949 −0.322976
\(533\) −24.0000 41.5692i −1.03956 1.80056i
\(534\) −5.14643 + 11.1708i −0.222708 + 0.483410i
\(535\) 20.6969 35.8481i 0.894807 1.54985i
\(536\) 1.55051 2.68556i 0.0669718 0.115999i
\(537\) −8.69694 12.2993i −0.375301 0.530755i
\(538\) 1.82577 + 3.16232i 0.0787143 + 0.136337i
\(539\) 2.00000 0.0861461
\(540\) 12.8485 + 12.4976i 0.552910 + 0.537810i
\(541\) 30.4949 1.31108 0.655539 0.755161i \(-0.272441\pi\)
0.655539 + 0.755161i \(0.272441\pi\)
\(542\) −8.44949 14.6349i −0.362937 0.628625i
\(543\) 4.34847 + 6.14966i 0.186611 + 0.263907i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 28.7980 49.8795i 1.23357 2.13660i
\(546\) 3.55051 7.70674i 0.151948 0.329818i
\(547\) −15.7980 27.3629i −0.675472 1.16995i −0.976331 0.216283i \(-0.930607\pi\)
0.300859 0.953669i \(-0.402727\pi\)
\(548\) −11.7980 −0.503984
\(549\) 33.7702 6.27647i 1.44127 0.267873i
\(550\) 13.7980 0.588347
\(551\) −10.7980 18.7026i −0.460009 0.796758i
\(552\) 1.72474 0.158919i 0.0734100 0.00676403i
\(553\) 3.94949 6.84072i 0.167949 0.290897i
\(554\) −5.34847 + 9.26382i −0.227235 + 0.393582i
\(555\) 46.3939 4.27475i 1.96931 0.181453i
\(556\) −4.72474 8.18350i −0.200374 0.347058i
\(557\) −3.10102 −0.131394 −0.0656972 0.997840i \(-0.520927\pi\)
−0.0656972 + 0.997840i \(0.520927\pi\)
\(558\) −6.00000 + 16.9706i −0.254000 + 0.718421i
\(559\) 14.2020 0.600682
\(560\) 1.72474 + 2.98735i 0.0728838 + 0.126238i
\(561\) 2.89898 6.29253i 0.122395 0.265671i
\(562\) 9.50000 16.4545i 0.400733 0.694090i
\(563\) −6.97219 + 12.0762i −0.293843 + 0.508951i −0.974715 0.223451i \(-0.928268\pi\)
0.680872 + 0.732402i \(0.261601\pi\)
\(564\) −9.79796 13.8564i −0.412568 0.583460i
\(565\) 27.4217 + 47.4957i 1.15364 + 1.99816i
\(566\) −20.5505 −0.863802
\(567\) 1.39898 8.89060i 0.0587516 0.373370i
\(568\) 9.89898 0.415352
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 25.6969 + 36.3410i 1.07633 + 1.52216i
\(571\) −7.10102 + 12.2993i −0.297168 + 0.514711i −0.975487 0.220057i \(-0.929376\pi\)
0.678319 + 0.734768i \(0.262709\pi\)
\(572\) 4.89898 8.48528i 0.204837 0.354787i
\(573\) 10.0732 21.8649i 0.420815 0.913421i
\(574\) −4.89898 8.48528i −0.204479 0.354169i
\(575\) −6.89898 −0.287707
\(576\) −1.00000 + 2.82843i −0.0416667 + 0.117851i
\(577\) 23.5959 0.982311 0.491155 0.871072i \(-0.336575\pi\)
0.491155 + 0.871072i \(0.336575\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 13.9722 1.28740i 0.580665 0.0535026i
\(580\) −5.00000 + 8.66025i −0.207614 + 0.359597i
\(581\) 1.00000 1.73205i 0.0414870 0.0718576i
\(582\) 11.8990 1.09638i 0.493229 0.0454463i
\(583\) 1.10102 + 1.90702i 0.0455996 + 0.0789808i
\(584\) 2.89898 0.119961
\(585\) −49.8434 + 9.26382i −2.06077 + 0.383012i
\(586\) 27.2474 1.12558
\(587\) 9.07321 + 15.7153i 0.374492 + 0.648639i 0.990251 0.139296i \(-0.0444839\pi\)
−0.615759 + 0.787934i \(0.711151\pi\)
\(588\) 0.724745 1.57313i 0.0298880 0.0648749i
\(589\) −22.3485 + 38.7087i −0.920853 + 1.59496i
\(590\) 3.44949 5.97469i 0.142013 0.245974i
\(591\) −12.6969 17.9562i −0.522282 0.738619i
\(592\) 3.89898 + 6.75323i 0.160247 + 0.277556i
\(593\) −14.6969 −0.603531 −0.301765 0.953382i \(-0.597576\pi\)
−0.301765 + 0.953382i \(0.597576\pi\)
\(594\) 2.55051 10.0745i 0.104649 0.413360i
\(595\) −6.89898 −0.282831
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 6.89898 + 9.75663i 0.282356 + 0.399312i
\(598\) −2.44949 + 4.24264i −0.100167 + 0.173494i
\(599\) 7.10102 12.2993i 0.290140 0.502537i −0.683703 0.729761i \(-0.739632\pi\)
0.973843 + 0.227224i \(0.0729648\pi\)
\(600\) 5.00000 10.8530i 0.204124 0.443072i
\(601\) 6.34847 + 10.9959i 0.258959 + 0.448531i 0.965963 0.258679i \(-0.0832871\pi\)
−0.707004 + 0.707210i \(0.749954\pi\)
\(602\) 2.89898 0.118154
\(603\) 6.04541 + 7.07107i 0.246188 + 0.287956i
\(604\) −5.00000 −0.203447
\(605\) 12.0732 + 20.9114i 0.490846 + 0.850170i
\(606\) −12.5000 + 1.15175i −0.507778 + 0.0467868i
\(607\) 4.34847 7.53177i 0.176499 0.305705i −0.764180 0.645003i \(-0.776856\pi\)
0.940679 + 0.339298i \(0.110189\pi\)
\(608\) −3.72474 + 6.45145i −0.151058 + 0.261641i
\(609\) 5.00000 0.460702i 0.202610 0.0186686i
\(610\) −19.7474 34.2036i −0.799551 1.38486i
\(611\) 48.0000 1.94187
\(612\) −3.89898 4.56048i −0.157607 0.184346i
\(613\) 14.6969 0.593604 0.296802 0.954939i \(-0.404080\pi\)
0.296802 + 0.954939i \(0.404080\pi\)
\(614\) −0.376276 0.651729i −0.0151852 0.0263016i
\(615\) −24.4949 + 53.1687i −0.987730 + 2.14397i
\(616\) 1.00000 1.73205i 0.0402911 0.0697863i
\(617\) −21.6969 + 37.5802i −0.873486 + 1.51292i −0.0151189 + 0.999886i \(0.504813\pi\)
−0.858367 + 0.513036i \(0.828521\pi\)
\(618\) 14.0000 + 19.7990i 0.563163 + 0.796432i
\(619\) 2.07321 + 3.59091i 0.0833295 + 0.144331i 0.904678 0.426096i \(-0.140111\pi\)
−0.821349 + 0.570426i \(0.806778\pi\)
\(620\) 20.6969 0.831209
\(621\) −1.27526 + 5.03723i −0.0511742 + 0.202137i
\(622\) 1.30306 0.0522480
\(623\) −3.55051 6.14966i −0.142248 0.246381i
\(624\) −4.89898 6.92820i −0.196116 0.277350i
\(625\) 5.94949 10.3048i 0.237980 0.412193i
\(626\) −12.3485 + 21.3882i −0.493544 + 0.854843i
\(627\) 10.7980 23.4381i 0.431229 0.936026i
\(628\) −3.17423 5.49794i −0.126666 0.219392i
\(629\) −15.5959 −0.621850
\(630\) −10.1742 + 1.89097i −0.405351 + 0.0753380i
\(631\) 18.1010 0.720590 0.360295 0.932838i \(-0.382676\pi\)
0.360295 + 0.932838i \(0.382676\pi\)
\(632\) −3.94949 6.84072i −0.157102 0.272109i
\(633\) −5.34847 + 0.492810i −0.212583 + 0.0195874i
\(634\) 4.34847 7.53177i 0.172700 0.299125i
\(635\) 5.17423 8.96204i 0.205333 0.355648i
\(636\) 1.89898 0.174973i 0.0752994 0.00693812i
\(637\) 2.44949 + 4.24264i 0.0970523 + 0.168100i
\(638\) 5.79796 0.229543
\(639\) −9.89898 + 27.9985i −0.391598 + 1.10761i
\(640\) 3.44949 0.136353
\(641\) −20.7474 35.9356i −0.819475 1.41937i −0.906070 0.423129i \(-0.860932\pi\)
0.0865947 0.996244i \(-0.472401\pi\)
\(642\) −8.69694 + 18.8776i −0.343241 + 0.745039i
\(643\) −9.69694 + 16.7956i −0.382410 + 0.662353i −0.991406 0.130820i \(-0.958239\pi\)
0.608996 + 0.793173i \(0.291572\pi\)
\(644\) −0.500000 + 0.866025i −0.0197028 + 0.0341262i
\(645\) −10.0000 14.1421i −0.393750 0.556846i
\(646\) −7.44949 12.9029i −0.293096 0.507658i
\(647\) −21.3031 −0.837510 −0.418755 0.908099i \(-0.637533\pi\)
−0.418755 + 0.908099i \(0.637533\pi\)
\(648\) −7.00000 5.65685i −0.274986 0.222222i
\(649\) −4.00000 −0.157014
\(650\) 16.8990 + 29.2699i 0.662833 + 1.14806i
\(651\) −6.00000 8.48528i −0.235159 0.332564i
\(652\) 0.101021 0.174973i 0.00395627 0.00685246i
\(653\) 4.89898 8.48528i 0.191712 0.332055i −0.754106 0.656753i \(-0.771929\pi\)
0.945818 + 0.324698i \(0.105263\pi\)
\(654\) −12.1010 + 26.2665i −0.473187 + 1.02710i
\(655\) 23.1969 + 40.1783i 0.906379 + 1.56990i
\(656\) −9.79796 −0.382546
\(657\) −2.89898 + 8.19955i −0.113100 + 0.319895i
\(658\) 9.79796 0.381964
\(659\) −2.34847 4.06767i −0.0914834 0.158454i 0.816652 0.577130i \(-0.195828\pi\)
−0.908136 + 0.418676i \(0.862494\pi\)
\(660\) −11.8990 + 1.09638i −0.463167 + 0.0426764i
\(661\) −4.72474 + 8.18350i −0.183771 + 0.318301i −0.943162 0.332334i \(-0.892164\pi\)
0.759391 + 0.650635i \(0.225497\pi\)
\(662\) 12.3485 21.3882i 0.479937 0.831275i
\(663\) 16.8990 1.55708i 0.656302 0.0604719i
\(664\) −1.00000 1.73205i −0.0388075 0.0672166i
\(665\) −25.6969 −0.996485
\(666\) −23.0000 + 4.27475i −0.891232 + 0.165643i
\(667\) −2.89898 −0.112249
\(668\) −9.34847 16.1920i −0.361703 0.626488i
\(669\) −15.1464 + 32.8769i −0.585595 + 1.27109i
\(670\) 5.34847 9.26382i 0.206629 0.357893i
\(671\) −11.4495 + 19.8311i −0.442003 + 0.765571i
\(672\) −1.00000 1.41421i −0.0385758 0.0545545i
\(673\) −15.2980 26.4968i −0.589693 1.02138i −0.994272 0.106875i \(-0.965915\pi\)
0.404579 0.914503i \(-0.367418\pi\)
\(674\) 35.3939 1.36332
\(675\) 25.6969 + 24.9951i 0.989076 + 0.962063i
\(676\) 11.0000 0.423077
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) −15.8990 22.4846i −0.610597 0.863514i
\(679\) −3.44949 + 5.97469i −0.132379 + 0.229288i
\(680\) −3.44949 + 5.97469i −0.132282 + 0.229119i
\(681\) −0.398979 + 0.866025i −0.0152889 + 0.0331862i
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) 32.2020 1.23218 0.616088 0.787677i \(-0.288716\pi\)
0.616088 + 0.787677i \(0.288716\pi\)
\(684\) −14.5227 16.9866i −0.555289 0.649500i
\(685\) −40.6969 −1.55495
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 40.0959 3.69445i 1.52975 0.140952i
\(688\) 1.44949 2.51059i 0.0552613 0.0957153i
\(689\) −2.69694 + 4.67123i −0.102745 + 0.177960i
\(690\) 5.94949 0.548188i 0.226493 0.0208692i
\(691\) −3.47730 6.02285i −0.132283 0.229120i 0.792274 0.610166i \(-0.208897\pi\)
−0.924556 + 0.381046i \(0.875564\pi\)
\(692\) −12.8990 −0.490346
\(693\) 3.89898 + 4.56048i 0.148110 + 0.173238i
\(694\) −19.5959 −0.743851
\(695\) −16.2980 28.2289i −0.618217 1.07078i
\(696\) 2.10102 4.56048i 0.0796390 0.172864i
\(697\) 9.79796 16.9706i 0.371124 0.642806i
\(698\) −10.4495 + 18.0990i −0.395519 + 0.685059i
\(699\) −7.00000 9.89949i −0.264764 0.374433i
\(700\) 3.44949 + 5.97469i 0.130378 + 0.225822i
\(701\) 51.3939 1.94112 0.970560 0.240860i \(-0.0774293\pi\)
0.970560 + 0.240860i \(0.0774293\pi\)
\(702\) 24.4949 6.92820i 0.924500 0.261488i
\(703\) −58.0908 −2.19094
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) −33.7980 47.7975i −1.27290 1.80016i
\(706\) 3.00000 5.19615i 0.112906 0.195560i
\(707\) 3.62372 6.27647i 0.136284 0.236051i
\(708\) −1.44949 + 3.14626i −0.0544752 + 0.118244i
\(709\) 5.79796 + 10.0424i 0.217747 + 0.377149i 0.954119 0.299428i \(-0.0967959\pi\)
−0.736372 + 0.676577i \(0.763463\pi\)
\(710\) 34.1464 1.28149
\(711\) 23.2980 4.33013i 0.873742 0.162392i
\(712\) −7.10102 −0.266122
\(713\) 3.00000 + 5.19615i 0.112351 + 0.194597i
\(714\) 3.44949 0.317837i 0.129094 0.0118948i
\(715\) 16.8990 29.2699i 0.631986 1.09463i
\(716\) 4.34847 7.53177i 0.162510 0.281475i
\(717\) 22.0732 2.03383i 0.824339 0.0759549i
\(718\) −5.39898 9.35131i −0.201488 0.348988i
\(719\) −9.79796 −0.365402 −0.182701 0.983169i \(-0.558484\pi\)
−0.182701 + 0.983169i \(0.558484\pi\)
\(720\) −3.44949 + 9.75663i −0.128555 + 0.363608i
\(721\) −14.0000 −0.521387
\(722\) −18.2474 31.6055i −0.679100 1.17624i
\(723\) −6.44949 + 13.9993i −0.239859 + 0.520638i
\(724\) −2.17423 + 3.76588i −0.0808048 + 0.139958i
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) −7.00000 9.89949i −0.259794 0.367405i
\(727\) −20.2474 35.0696i −0.750936 1.30066i −0.947369 0.320143i \(-0.896269\pi\)
0.196433 0.980517i \(-0.437064\pi\)
\(728\) 4.89898 0.181568
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 10.0000 0.370117
\(731\) 2.89898 + 5.02118i 0.107223 + 0.185715i
\(732\) 11.4495 + 16.1920i 0.423185 + 0.598474i
\(733\) 6.27526 10.8691i 0.231782 0.401458i −0.726551 0.687113i \(-0.758878\pi\)
0.958333 + 0.285655i \(0.0922111\pi\)
\(734\) −2.89898 + 5.02118i −0.107003 + 0.185335i
\(735\) 2.50000 5.42650i 0.0922139 0.200160i
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) −6.20204 −0.228455
\(738\) 9.79796 27.7128i 0.360668 1.02012i
\(739\) −25.5959 −0.941561 −0.470781 0.882250i \(-0.656028\pi\)
−0.470781 + 0.882250i \(0.656028\pi\)
\(740\) 13.4495 + 23.2952i 0.494413 + 0.856349i
\(741\) 62.9444 5.79972i 2.31232 0.213058i
\(742\) −0.550510 + 0.953512i −0.0202099 + 0.0350045i
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) −10.3485 + 0.953512i −0.379393 + 0.0349574i
\(745\) 10.3485 + 17.9241i 0.379139 + 0.656687i
\(746\) 2.89898 0.106139
\(747\) 5.89898 1.09638i 0.215832 0.0401143i
\(748\) 4.00000 0.146254
\(749\) −6.00000 10.3923i −0.219235 0.379727i
\(750\) 4.74745 10.3048i 0.173352 0.376279i
\(751\) −20.2980 + 35.1571i −0.740683 + 1.28290i 0.211502 + 0.977378i \(0.432165\pi\)
−0.952185 + 0.305523i \(0.901169\pi\)
\(752\) 4.89898 8.48528i 0.178647 0.309426i
\(753\) 12.5505 + 17.7491i 0.457366 + 0.646813i
\(754\) 7.10102 + 12.2993i 0.258604 + 0.447915i
\(755\) −17.2474 −0.627699
\(756\) 5.00000 1.41421i 0.181848 0.0514344i
\(757\) 23.3939 0.850265 0.425132 0.905131i \(-0.360228\pi\)
0.425132 + 0.905131i \(0.360228\pi\)
\(758\) 13.2474 + 22.9453i 0.481169 + 0.833409i
\(759\) −2.00000 2.82843i −0.0725954 0.102665i
\(760\) −12.8485 + 22.2542i −0.466063 + 0.807245i
\(761\) −1.00000 + 1.73205i −0.0362500 + 0.0627868i −0.883581 0.468278i \(-0.844875\pi\)
0.847331 + 0.531065i \(0.178208\pi\)
\(762\) −2.17423 + 4.71940i −0.0787642 + 0.170966i
\(763\) −8.34847 14.4600i −0.302235 0.523486i
\(764\) 13.8990 0.502847
\(765\) −13.4495 15.7313i −0.486267 0.568767i
\(766\) 6.89898 0.249270
\(767\) −4.89898 8.48528i −0.176892 0.306386i
\(768\) −1.72474 + 0.158919i −0.0622364 + 0.00573448i
\(769\) −27.0454 + 46.8440i −0.975282 + 1.68924i −0.296282 + 0.955100i \(0.595747\pi\)
−0.679000 + 0.734138i \(0.737586\pi\)
\(770\) 3.44949 5.97469i 0.124311 0.215313i
\(771\) −47.9444 + 4.41761i −1.72667 + 0.159096i
\(772\) 4.05051 + 7.01569i 0.145781 + 0.252500i
\(773\) −19.9444 −0.717350 −0.358675 0.933463i \(-0.616771\pi\)
−0.358675 + 0.933463i \(0.616771\pi\)
\(774\) 5.65153 + 6.61037i 0.203140 + 0.237605i
\(775\) 41.3939