Properties

Label 390.2.bb.c.121.4
Level $390$
Weight $2$
Character 390.121
Analytic conductor $3.114$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 121.4
Root \(-1.70006 + 1.70006i\) of defining polynomial
Character \(\chi\) \(=\) 390.121
Dual form 390.2.bb.c.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(4.02239 - 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(4.02239 - 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.81062 + 2.20006i) q^{11} -1.00000 q^{12} +(-3.35432 - 1.32233i) q^{13} +4.64466 q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-6.96699 + 4.02239i) q^{19} +(-0.866025 + 0.500000i) q^{20} +4.64466i q^{21} +(2.20006 + 3.81062i) q^{22} +(-0.488292 + 0.845746i) q^{23} +(-0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(-2.24376 - 2.82233i) q^{26} +1.00000 q^{27} +(4.02239 + 2.32233i) q^{28} +(2.15637 - 3.73494i) q^{29} +(-0.500000 - 0.866025i) q^{30} -6.44069i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.81062 + 2.20006i) q^{33} +4.00000i q^{34} +(2.32233 + 4.02239i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.28745 + 1.89801i) q^{37} -8.04479 q^{38} +(2.82233 - 2.24376i) q^{39} -1.00000 q^{40} +(-6.31274 - 3.64466i) q^{41} +(-2.32233 + 4.02239i) q^{42} +(0.358228 + 0.620469i) q^{43} +4.40013i q^{44} +(0.866025 - 0.500000i) q^{45} +(-0.845746 + 0.488292i) q^{46} -9.75342i q^{47} +(-0.500000 - 0.866025i) q^{48} +(7.28643 - 12.6205i) q^{49} +(-0.866025 - 0.500000i) q^{50} -4.00000 q^{51} +(-0.531987 - 3.56609i) q^{52} +13.5089 q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.20006 + 3.81062i) q^{55} +(2.32233 + 4.02239i) q^{56} -8.04479i q^{57} +(3.73494 - 2.15637i) q^{58} +(-1.88842 + 1.09028i) q^{59} -1.00000i q^{60} +(-3.73205 - 6.46410i) q^{61} +(3.22034 - 5.57780i) q^{62} +(-4.02239 - 2.32233i) q^{63} -1.00000 q^{64} +(1.32233 - 3.35432i) q^{65} -4.40013 q^{66} +(-1.58068 - 0.912609i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-0.488292 - 0.845746i) q^{69} +4.64466i q^{70} +(-6.88764 + 3.97658i) q^{71} +(0.866025 - 0.500000i) q^{72} +4.36112i q^{73} +(1.89801 + 3.28745i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-6.96699 - 4.02239i) q^{76} +20.4371 q^{77} +(3.56609 - 0.531987i) q^{78} -14.9340 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.64466 - 6.31274i) q^{82} -3.51093i q^{83} +(-4.02239 + 2.32233i) q^{84} +(-3.46410 + 2.00000i) q^{85} +0.716456i q^{86} +(2.15637 + 3.73494i) q^{87} +(-2.20006 + 3.81062i) q^{88} +(7.07780 + 4.08637i) q^{89} +1.00000 q^{90} +(-16.5633 + 2.47090i) q^{91} -0.976584 q^{92} +(5.57780 + 3.22034i) q^{93} +(4.87671 - 8.44671i) q^{94} +(-4.02239 - 6.96699i) q^{95} -1.00000i q^{96} +(11.9730 - 6.91261i) q^{97} +(12.6205 - 7.28643i) q^{98} -4.40013i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} - 4q^{10} + 6q^{11} - 8q^{12} - 12q^{13} + 4q^{14} - 4q^{16} + 16q^{17} - 6q^{19} + 2q^{22} + 4q^{23} - 8q^{25} - 12q^{26} + 8q^{27} - 8q^{29} - 4q^{30} - 6q^{33} + 2q^{35} + 4q^{36} + 30q^{37} + 6q^{39} - 8q^{40} - 2q^{42} + 14q^{43} - 6q^{46} - 4q^{48} + 14q^{49} - 32q^{51} - 6q^{52} + 16q^{53} - 2q^{55} + 2q^{56} - 6q^{58} + 24q^{59} - 16q^{61} + 4q^{62} - 8q^{64} - 6q^{65} - 4q^{66} + 24q^{67} - 16q^{68} + 4q^{69} - 12q^{71} + 10q^{74} + 4q^{75} - 6q^{76} + 16q^{77} + 6q^{78} - 20q^{79} - 4q^{81} + 4q^{82} - 8q^{87} - 2q^{88} + 42q^{89} + 8q^{90} - 10q^{91} + 8q^{92} + 30q^{93} - 8q^{94} - 24q^{97} + 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 4.02239 2.32233i 1.52032 0.877758i 0.520609 0.853795i \(-0.325705\pi\)
0.999713 0.0239629i \(-0.00762835\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 3.81062 + 2.20006i 1.14895 + 0.663344i 0.948630 0.316387i \(-0.102470\pi\)
0.200316 + 0.979731i \(0.435803\pi\)
\(12\) −1.00000 −0.288675
\(13\) −3.35432 1.32233i −0.930320 0.366748i
\(14\) 4.64466 1.24134
\(15\) −0.866025 0.500000i −0.223607 0.129099i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.96699 + 4.02239i −1.59834 + 0.922800i −0.606529 + 0.795061i \(0.707439\pi\)
−0.991808 + 0.127739i \(0.959228\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) 4.64466i 1.01355i
\(22\) 2.20006 + 3.81062i 0.469055 + 0.812427i
\(23\) −0.488292 + 0.845746i −0.101816 + 0.176350i −0.912433 0.409226i \(-0.865799\pi\)
0.810617 + 0.585577i \(0.199132\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) −1.00000 −0.200000
\(26\) −2.24376 2.82233i −0.440037 0.553504i
\(27\) 1.00000 0.192450
\(28\) 4.02239 + 2.32233i 0.760161 + 0.438879i
\(29\) 2.15637 3.73494i 0.400427 0.693561i −0.593350 0.804945i \(-0.702195\pi\)
0.993777 + 0.111384i \(0.0355283\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 6.44069i 1.15678i −0.815760 0.578391i \(-0.803681\pi\)
0.815760 0.578391i \(-0.196319\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −3.81062 + 2.20006i −0.663344 + 0.382982i
\(34\) 4.00000i 0.685994i
\(35\) 2.32233 + 4.02239i 0.392545 + 0.679909i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 3.28745 + 1.89801i 0.540454 + 0.312031i 0.745263 0.666771i \(-0.232324\pi\)
−0.204809 + 0.978802i \(0.565657\pi\)
\(38\) −8.04479 −1.30504
\(39\) 2.82233 2.24376i 0.451934 0.359289i
\(40\) −1.00000 −0.158114
\(41\) −6.31274 3.64466i −0.985884 0.569200i −0.0818424 0.996645i \(-0.526080\pi\)
−0.904041 + 0.427445i \(0.859414\pi\)
\(42\) −2.32233 + 4.02239i −0.358343 + 0.620669i
\(43\) 0.358228 + 0.620469i 0.0546293 + 0.0946207i 0.892047 0.451943i \(-0.149269\pi\)
−0.837418 + 0.546564i \(0.815936\pi\)
\(44\) 4.40013i 0.663344i
\(45\) 0.866025 0.500000i 0.129099 0.0745356i
\(46\) −0.845746 + 0.488292i −0.124698 + 0.0719947i
\(47\) 9.75342i 1.42268i −0.702847 0.711341i \(-0.748088\pi\)
0.702847 0.711341i \(-0.251912\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 7.28643 12.6205i 1.04092 1.80292i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) −4.00000 −0.560112
\(52\) −0.531987 3.56609i −0.0737734 0.494528i
\(53\) 13.5089 1.85559 0.927794 0.373092i \(-0.121703\pi\)
0.927794 + 0.373092i \(0.121703\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) −2.20006 + 3.81062i −0.296656 + 0.513824i
\(56\) 2.32233 + 4.02239i 0.310334 + 0.537515i
\(57\) 8.04479i 1.06556i
\(58\) 3.73494 2.15637i 0.490421 0.283145i
\(59\) −1.88842 + 1.09028i −0.245851 + 0.141942i −0.617863 0.786286i \(-0.712001\pi\)
0.372012 + 0.928228i \(0.378668\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −3.73205 6.46410i −0.477840 0.827643i 0.521837 0.853045i \(-0.325247\pi\)
−0.999677 + 0.0254017i \(0.991914\pi\)
\(62\) 3.22034 5.57780i 0.408984 0.708381i
\(63\) −4.02239 2.32233i −0.506774 0.292586i
\(64\) −1.00000 −0.125000
\(65\) 1.32233 3.35432i 0.164015 0.416052i
\(66\) −4.40013 −0.541618
\(67\) −1.58068 0.912609i −0.193111 0.111493i 0.400327 0.916372i \(-0.368897\pi\)
−0.593438 + 0.804879i \(0.702230\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) −0.488292 0.845746i −0.0587834 0.101816i
\(70\) 4.64466i 0.555143i
\(71\) −6.88764 + 3.97658i −0.817413 + 0.471934i −0.849524 0.527551i \(-0.823110\pi\)
0.0321105 + 0.999484i \(0.489777\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 4.36112i 0.510430i 0.966884 + 0.255215i \(0.0821463\pi\)
−0.966884 + 0.255215i \(0.917854\pi\)
\(74\) 1.89801 + 3.28745i 0.220640 + 0.382159i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) −6.96699 4.02239i −0.799168 0.461400i
\(77\) 20.4371 2.32902
\(78\) 3.56609 0.531987i 0.403780 0.0602357i
\(79\) −14.9340 −1.68020 −0.840102 0.542429i \(-0.817505\pi\)
−0.840102 + 0.542429i \(0.817505\pi\)
\(80\) −0.866025 0.500000i −0.0968246 0.0559017i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.64466 6.31274i −0.402485 0.697125i
\(83\) 3.51093i 0.385375i −0.981260 0.192688i \(-0.938280\pi\)
0.981260 0.192688i \(-0.0617204\pi\)
\(84\) −4.02239 + 2.32233i −0.438879 + 0.253387i
\(85\) −3.46410 + 2.00000i −0.375735 + 0.216930i
\(86\) 0.716456i 0.0772575i
\(87\) 2.15637 + 3.73494i 0.231187 + 0.400427i
\(88\) −2.20006 + 3.81062i −0.234528 + 0.406214i
\(89\) 7.07780 + 4.08637i 0.750245 + 0.433154i 0.825782 0.563989i \(-0.190734\pi\)
−0.0755374 + 0.997143i \(0.524067\pi\)
\(90\) 1.00000 0.105409
\(91\) −16.5633 + 2.47090i −1.73630 + 0.259021i
\(92\) −0.976584 −0.101816
\(93\) 5.57780 + 3.22034i 0.578391 + 0.333934i
\(94\) 4.87671 8.44671i 0.502994 0.871212i
\(95\) −4.02239 6.96699i −0.412689 0.714798i
\(96\) 1.00000i 0.102062i
\(97\) 11.9730 6.91261i 1.21567 0.701869i 0.251683 0.967810i \(-0.419016\pi\)
0.963989 + 0.265941i \(0.0856825\pi\)
\(98\) 12.6205 7.28643i 1.27486 0.736041i
\(99\) 4.40013i 0.442229i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.40013 + 5.88919i −0.338325 + 0.585997i −0.984118 0.177516i \(-0.943194\pi\)
0.645793 + 0.763513i \(0.276527\pi\)
\(102\) −3.46410 2.00000i −0.342997 0.198030i
\(103\) −5.29137 −0.521374 −0.260687 0.965423i \(-0.583949\pi\)
−0.260687 + 0.965423i \(0.583949\pi\)
\(104\) 1.32233 3.35432i 0.129665 0.328918i
\(105\) −4.64466 −0.453272
\(106\) 11.6990 + 6.75444i 1.13631 + 0.656050i
\(107\) −8.46410 + 14.6603i −0.818256 + 1.41726i 0.0887109 + 0.996057i \(0.471725\pi\)
−0.906966 + 0.421203i \(0.861608\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 12.8003i 1.22604i −0.790067 0.613021i \(-0.789954\pi\)
0.790067 0.613021i \(-0.210046\pi\)
\(110\) −3.81062 + 2.20006i −0.363329 + 0.209768i
\(111\) −3.28745 + 1.89801i −0.312031 + 0.180151i
\(112\) 4.64466i 0.438879i
\(113\) −6.53308 11.3156i −0.614580 1.06448i −0.990458 0.137815i \(-0.955992\pi\)
0.375878 0.926669i \(-0.377341\pi\)
\(114\) 4.02239 6.96699i 0.376732 0.652518i
\(115\) −0.845746 0.488292i −0.0788662 0.0455334i
\(116\) 4.31274 0.400427
\(117\) 0.531987 + 3.56609i 0.0491823 + 0.329685i
\(118\) −2.18056 −0.200737
\(119\) 16.0896 + 9.28932i 1.47493 + 0.851550i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) 4.18056 + 7.24094i 0.380051 + 0.658267i
\(122\) 7.46410i 0.675768i
\(123\) 6.31274 3.64466i 0.569200 0.328628i
\(124\) 5.57780 3.22034i 0.500901 0.289195i
\(125\) 1.00000i 0.0894427i
\(126\) −2.32233 4.02239i −0.206890 0.358343i
\(127\) 6.10978 10.5825i 0.542156 0.939041i −0.456624 0.889660i \(-0.650942\pi\)
0.998780 0.0493816i \(-0.0157250\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −0.716456 −0.0630805
\(130\) 2.82233 2.24376i 0.247535 0.196791i
\(131\) −0.378757 −0.0330921 −0.0165461 0.999863i \(-0.505267\pi\)
−0.0165461 + 0.999863i \(0.505267\pi\)
\(132\) −3.81062 2.20006i −0.331672 0.191491i
\(133\) −18.6826 + 32.3593i −1.61999 + 2.80591i
\(134\) −0.912609 1.58068i −0.0788374 0.136550i
\(135\) 1.00000i 0.0860663i
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) −1.08457 + 0.626177i −0.0926612 + 0.0534979i −0.545615 0.838036i \(-0.683704\pi\)
0.452953 + 0.891534i \(0.350370\pi\)
\(138\) 0.976584i 0.0831323i
\(139\) −1.67767 2.90581i −0.142298 0.246468i 0.786064 0.618146i \(-0.212116\pi\)
−0.928362 + 0.371678i \(0.878783\pi\)
\(140\) −2.32233 + 4.02239i −0.196273 + 0.339954i
\(141\) 8.44671 + 4.87671i 0.711341 + 0.410693i
\(142\) −7.95317 −0.667415
\(143\) −9.87282 12.4186i −0.825607 1.03850i
\(144\) 1.00000 0.0833333
\(145\) 3.73494 + 2.15637i 0.310170 + 0.179077i
\(146\) −2.18056 + 3.77684i −0.180464 + 0.312573i
\(147\) 7.28643 + 12.6205i 0.600975 + 1.04092i
\(148\) 3.79603i 0.312031i
\(149\) −4.00077 + 2.30985i −0.327756 + 0.189230i −0.654844 0.755764i \(-0.727266\pi\)
0.327088 + 0.944994i \(0.393933\pi\)
\(150\) 0.866025 0.500000i 0.0707107 0.0408248i
\(151\) 11.2425i 0.914901i −0.889235 0.457450i \(-0.848763\pi\)
0.889235 0.457450i \(-0.151237\pi\)
\(152\) −4.02239 6.96699i −0.326259 0.565097i
\(153\) 2.00000 3.46410i 0.161690 0.280056i
\(154\) 17.6990 + 10.2185i 1.42623 + 0.823434i
\(155\) 6.44069 0.517328
\(156\) 3.35432 + 1.32233i 0.268560 + 0.105871i
\(157\) −1.50311 −0.119961 −0.0599807 0.998200i \(-0.519104\pi\)
−0.0599807 + 0.998200i \(0.519104\pi\)
\(158\) −12.9332 7.46699i −1.02891 0.594042i
\(159\) −6.75444 + 11.6990i −0.535662 + 0.927794i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 4.53590i 0.357479i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −0.152706 + 0.0881650i −0.0119609 + 0.00690561i −0.505969 0.862552i \(-0.668865\pi\)
0.494008 + 0.869458i \(0.335531\pi\)
\(164\) 7.28932i 0.569200i
\(165\) −2.20006 3.81062i −0.171275 0.296656i
\(166\) 1.75547 3.04056i 0.136251 0.235993i
\(167\) 7.51851 + 4.34081i 0.581800 + 0.335902i 0.761848 0.647756i \(-0.224292\pi\)
−0.180049 + 0.983658i \(0.557626\pi\)
\(168\) −4.64466 −0.358343
\(169\) 9.50289 + 8.87103i 0.730991 + 0.682387i
\(170\) −4.00000 −0.306786
\(171\) 6.96699 + 4.02239i 0.532779 + 0.307600i
\(172\) −0.358228 + 0.620469i −0.0273146 + 0.0473103i
\(173\) 0.890216 + 1.54190i 0.0676818 + 0.117228i 0.897880 0.440239i \(-0.145106\pi\)
−0.830199 + 0.557468i \(0.811773\pi\)
\(174\) 4.31274i 0.326948i
\(175\) −4.02239 + 2.32233i −0.304064 + 0.175552i
\(176\) −3.81062 + 2.20006i −0.287236 + 0.165836i
\(177\) 2.18056i 0.163901i
\(178\) 4.08637 + 7.07780i 0.306286 + 0.530503i
\(179\) −8.70786 + 15.0825i −0.650856 + 1.12732i 0.332059 + 0.943258i \(0.392257\pi\)
−0.982916 + 0.184057i \(0.941077\pi\)
\(180\) 0.866025 + 0.500000i 0.0645497 + 0.0372678i
\(181\) −10.3611 −0.770136 −0.385068 0.922888i \(-0.625822\pi\)
−0.385068 + 0.922888i \(0.625822\pi\)
\(182\) −15.5797 6.14177i −1.15484 0.455258i
\(183\) 7.46410 0.551762
\(184\) −0.845746 0.488292i −0.0623492 0.0359973i
\(185\) −1.89801 + 3.28745i −0.139545 + 0.241698i
\(186\) 3.22034 + 5.57780i 0.236127 + 0.408984i
\(187\) 17.6005i 1.28708i
\(188\) 8.44671 4.87671i 0.616040 0.355671i
\(189\) 4.02239 2.32233i 0.292586 0.168925i
\(190\) 8.04479i 0.583630i
\(191\) 0.448507 + 0.776837i 0.0324528 + 0.0562100i 0.881796 0.471632i \(-0.156335\pi\)
−0.849343 + 0.527842i \(0.823001\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 17.5494 + 10.1322i 1.26324 + 0.729330i 0.973699 0.227837i \(-0.0731652\pi\)
0.289537 + 0.957167i \(0.406499\pi\)
\(194\) 13.8252 0.992593
\(195\) 2.24376 + 2.82233i 0.160679 + 0.202111i
\(196\) 14.5729 1.04092
\(197\) 7.95060 + 4.59028i 0.566457 + 0.327044i 0.755733 0.654880i \(-0.227281\pi\)
−0.189276 + 0.981924i \(0.560614\pi\)
\(198\) 2.20006 3.81062i 0.156352 0.270809i
\(199\) −8.10876 14.0448i −0.574815 0.995609i −0.996062 0.0886625i \(-0.971741\pi\)
0.421247 0.906946i \(-0.361593\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 1.58068 0.912609i 0.111493 0.0643705i
\(202\) −5.88919 + 3.40013i −0.414362 + 0.239232i
\(203\) 20.0312i 1.40591i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 3.64466 6.31274i 0.254554 0.440901i
\(206\) −4.58246 2.64568i −0.319275 0.184333i
\(207\) 0.976584 0.0678773
\(208\) 2.82233 2.24376i 0.195693 0.155577i
\(209\) −35.3981 −2.44854
\(210\) −4.02239 2.32233i −0.277572 0.160256i
\(211\) 0.809848 1.40270i 0.0557522 0.0965657i −0.836802 0.547505i \(-0.815578\pi\)
0.892555 + 0.450939i \(0.148911\pi\)
\(212\) 6.75444 + 11.6990i 0.463897 + 0.803493i
\(213\) 7.95317i 0.544942i
\(214\) −14.6603 + 8.46410i −1.00215 + 0.578594i
\(215\) −0.620469 + 0.358228i −0.0423157 + 0.0244310i
\(216\) 1.00000i 0.0680414i
\(217\) −14.9574 25.9070i −1.01537 1.75868i
\(218\) 6.40013 11.0853i 0.433471 0.750794i
\(219\) −3.77684 2.18056i −0.255215 0.147348i
\(220\) −4.40013 −0.296656
\(221\) −2.12795 14.2644i −0.143141 0.959524i
\(222\) −3.79603 −0.254773
\(223\) 1.93705 + 1.11836i 0.129714 + 0.0748906i 0.563453 0.826148i \(-0.309473\pi\)
−0.433739 + 0.901039i \(0.642806\pi\)
\(224\) −2.32233 + 4.02239i −0.155167 + 0.268757i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 13.0662i 0.869148i
\(227\) −13.2679 + 7.66025i −0.880625 + 0.508429i −0.870864 0.491523i \(-0.836440\pi\)
−0.00976038 + 0.999952i \(0.503107\pi\)
\(228\) 6.96699 4.02239i 0.461400 0.266389i
\(229\) 10.1279i 0.669274i 0.942347 + 0.334637i \(0.108614\pi\)
−0.942347 + 0.334637i \(0.891386\pi\)
\(230\) −0.488292 0.845746i −0.0321970 0.0557669i
\(231\) −10.2185 + 17.6990i −0.672331 + 1.16451i
\(232\) 3.73494 + 2.15637i 0.245211 + 0.141572i
\(233\) 20.7519 1.35950 0.679750 0.733444i \(-0.262088\pi\)
0.679750 + 0.733444i \(0.262088\pi\)
\(234\) −1.32233 + 3.35432i −0.0864434 + 0.219279i
\(235\) 9.75342 0.636243
\(236\) −1.88842 1.09028i −0.122926 0.0709711i
\(237\) 7.46699 12.9332i 0.485033 0.840102i
\(238\) 9.28932 + 16.0896i 0.602137 + 1.04293i
\(239\) 24.3539i 1.57532i 0.616107 + 0.787662i \(0.288709\pi\)
−0.616107 + 0.787662i \(0.711291\pi\)
\(240\) 0.866025 0.500000i 0.0559017 0.0322749i
\(241\) −17.2066 + 9.93423i −1.10837 + 0.639920i −0.938408 0.345530i \(-0.887699\pi\)
−0.169966 + 0.985450i \(0.554366\pi\)
\(242\) 8.36112i 0.537473i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 3.73205 6.46410i 0.238920 0.413822i
\(245\) 12.6205 + 7.28643i 0.806292 + 0.465513i
\(246\) 7.28932 0.464750
\(247\) 28.6884 4.27973i 1.82540 0.272312i
\(248\) 6.44069 0.408984
\(249\) 3.04056 + 1.75547i 0.192688 + 0.111248i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 6.78566 + 11.7531i 0.428307 + 0.741849i 0.996723 0.0808920i \(-0.0257769\pi\)
−0.568416 + 0.822741i \(0.692444\pi\)
\(252\) 4.64466i 0.292586i
\(253\) −3.72139 + 2.14855i −0.233962 + 0.135078i
\(254\) 10.5825 6.10978i 0.664002 0.383362i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.331150 0.573569i 0.0206566 0.0357783i −0.855512 0.517782i \(-0.826758\pi\)
0.876169 + 0.482004i \(0.160091\pi\)
\(258\) −0.620469 0.358228i −0.0386287 0.0223023i
\(259\) 17.6312 1.09555
\(260\) 3.56609 0.531987i 0.221159 0.0329925i
\(261\) −4.31274 −0.266952
\(262\) −0.328013 0.189378i −0.0202647 0.0116998i
\(263\) −15.3749 + 26.6301i −0.948058 + 1.64208i −0.198548 + 0.980091i \(0.563623\pi\)
−0.749510 + 0.661993i \(0.769711\pi\)
\(264\) −2.20006 3.81062i −0.135405 0.234528i
\(265\) 13.5089i 0.829844i
\(266\) −32.3593 + 18.6826i −1.98408 + 1.14551i
\(267\) −7.07780 + 4.08637i −0.433154 + 0.250082i
\(268\) 1.82522i 0.111493i
\(269\) 1.87205 + 3.24249i 0.114141 + 0.197698i 0.917436 0.397883i \(-0.130255\pi\)
−0.803295 + 0.595581i \(0.796922\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 24.0419 + 13.8806i 1.46044 + 0.843186i 0.999031 0.0440009i \(-0.0140104\pi\)
0.461410 + 0.887187i \(0.347344\pi\)
\(272\) −4.00000 −0.242536
\(273\) 6.14177 15.5797i 0.371717 0.942924i
\(274\) −1.25235 −0.0756575
\(275\) −3.81062 2.20006i −0.229789 0.132669i
\(276\) 0.488292 0.845746i 0.0293917 0.0509079i
\(277\) 5.99609 + 10.3855i 0.360270 + 0.624006i 0.988005 0.154421i \(-0.0493512\pi\)
−0.627735 + 0.778427i \(0.716018\pi\)
\(278\) 3.35534i 0.201240i
\(279\) −5.57780 + 3.22034i −0.333934 + 0.192797i
\(280\) −4.02239 + 2.32233i −0.240384 + 0.138786i
\(281\) 3.63888i 0.217078i −0.994092 0.108539i \(-0.965383\pi\)
0.994092 0.108539i \(-0.0346172\pi\)
\(282\) 4.87671 + 8.44671i 0.290404 + 0.502994i
\(283\) 2.42220 4.19538i 0.143985 0.249389i −0.785009 0.619485i \(-0.787342\pi\)
0.928994 + 0.370095i \(0.120675\pi\)
\(284\) −6.88764 3.97658i −0.408707 0.235967i
\(285\) 8.04479 0.476532
\(286\) −2.34081 15.6912i −0.138415 0.927843i
\(287\) −33.8564 −1.99848
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 2.15637 + 3.73494i 0.126626 + 0.219323i
\(291\) 13.8252i 0.810449i
\(292\) −3.77684 + 2.18056i −0.221023 + 0.127608i
\(293\) 3.20500 1.85041i 0.187238 0.108102i −0.403451 0.915001i \(-0.632189\pi\)
0.590689 + 0.806899i \(0.298856\pi\)
\(294\) 14.5729i 0.849907i
\(295\) −1.09028 1.88842i −0.0634785 0.109948i
\(296\) −1.89801 + 3.28745i −0.110320 + 0.191079i
\(297\) 3.81062 + 2.20006i 0.221115 + 0.127661i
\(298\) −4.61970 −0.267612
\(299\) 2.75624 2.19122i 0.159398 0.126721i
\(300\) 1.00000 0.0577350
\(301\) 2.88187 + 1.66385i 0.166108 + 0.0959026i
\(302\) 5.62124 9.73628i 0.323466 0.560260i
\(303\) −3.40013 5.88919i −0.195332 0.338325i
\(304\) 8.04479i 0.461400i
\(305\) 6.46410 3.73205i 0.370133 0.213697i
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 7.11454i 0.406048i 0.979174 + 0.203024i \(0.0650770\pi\)
−0.979174 + 0.203024i \(0.934923\pi\)
\(308\) 10.2185 + 17.6990i 0.582256 + 1.00850i
\(309\) 2.64568 4.58246i 0.150508 0.260687i
\(310\) 5.57780 + 3.22034i 0.316798 + 0.182903i
\(311\) −19.9148 −1.12926 −0.564632 0.825343i \(-0.690982\pi\)
−0.564632 + 0.825343i \(0.690982\pi\)
\(312\) 2.24376 + 2.82233i 0.127028 + 0.159783i
\(313\) 6.13950 0.347025 0.173513 0.984832i \(-0.444488\pi\)
0.173513 + 0.984832i \(0.444488\pi\)
\(314\) −1.30173 0.751556i −0.0734611 0.0424128i
\(315\) 2.32233 4.02239i 0.130848 0.226636i
\(316\) −7.46699 12.9332i −0.420051 0.727550i
\(317\) 7.85286i 0.441061i −0.975380 0.220530i \(-0.929221\pi\)
0.975380 0.220530i \(-0.0707788\pi\)
\(318\) −11.6990 + 6.75444i −0.656050 + 0.378770i
\(319\) 16.4342 9.48829i 0.920139 0.531242i
\(320\) 1.00000i 0.0559017i
\(321\) −8.46410 14.6603i −0.472420 0.818256i
\(322\) −2.26795 + 3.92820i −0.126388 + 0.218910i
\(323\) −27.8680 16.0896i −1.55061 0.895248i
\(324\) −1.00000 −0.0555556
\(325\) 3.35432 + 1.32233i 0.186064 + 0.0733497i
\(326\) −0.176330 −0.00976601
\(327\) 11.0853 + 6.40013i 0.613021 + 0.353928i
\(328\) 3.64466 6.31274i 0.201243 0.348563i
\(329\) −22.6507 39.2321i −1.24877 2.16294i
\(330\) 4.40013i 0.242219i
\(331\) 27.7093 15.9980i 1.52304 0.879327i 0.523410 0.852081i \(-0.324659\pi\)
0.999629 0.0272463i \(-0.00867385\pi\)
\(332\) 3.04056 1.75547i 0.166872 0.0963438i
\(333\) 3.79603i 0.208021i
\(334\) 4.34081 + 7.51851i 0.237519 + 0.411394i
\(335\) 0.912609 1.58068i 0.0498611 0.0863620i
\(336\) −4.02239 2.32233i −0.219440 0.126693i
\(337\) −35.6432 −1.94161 −0.970806 0.239867i \(-0.922896\pi\)
−0.970806 + 0.239867i \(0.922896\pi\)
\(338\) 3.79423 + 12.4340i 0.206379 + 0.676319i
\(339\) 13.0662 0.709656
\(340\) −3.46410 2.00000i −0.187867 0.108465i
\(341\) 14.1699 24.5430i 0.767344 1.32908i
\(342\) 4.02239 + 6.96699i 0.217506 + 0.376732i
\(343\) 35.1734i 1.89918i
\(344\) −0.620469 + 0.358228i −0.0334535 + 0.0193144i
\(345\) 0.845746 0.488292i 0.0455334 0.0262887i
\(346\) 1.78043i 0.0957166i
\(347\) 3.44851 + 5.97299i 0.185126 + 0.320647i 0.943619 0.331034i \(-0.107397\pi\)
−0.758493 + 0.651681i \(0.774064\pi\)
\(348\) −2.15637 + 3.73494i −0.115593 + 0.200214i
\(349\) 16.7321 + 9.66025i 0.895646 + 0.517102i 0.875785 0.482701i \(-0.160344\pi\)
0.0198610 + 0.999803i \(0.493678\pi\)
\(350\) −4.64466 −0.248267
\(351\) −3.35432 1.32233i −0.179040 0.0705807i
\(352\) −4.40013 −0.234528
\(353\) −23.7441 13.7086i −1.26377 0.729637i −0.289967 0.957037i \(-0.593644\pi\)
−0.973802 + 0.227400i \(0.926978\pi\)
\(354\) 1.09028 1.88842i 0.0579477 0.100368i
\(355\) −3.97658 6.88764i −0.211055 0.365558i
\(356\) 8.17274i 0.433154i
\(357\) −16.0896 + 9.28932i −0.851550 + 0.491643i
\(358\) −15.0825 + 8.70786i −0.797133 + 0.460225i
\(359\) 14.3611i 0.757951i −0.925407 0.378975i \(-0.876277\pi\)
0.925407 0.378975i \(-0.123723\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 22.8593 39.5935i 1.20312 2.08387i
\(362\) −8.97299 5.18056i −0.471610 0.272284i
\(363\) −8.36112 −0.438845
\(364\) −10.4215 13.1088i −0.546235 0.687086i
\(365\) −4.36112 −0.228271
\(366\) 6.46410 + 3.73205i 0.337884 + 0.195077i
\(367\) 6.88764 11.9298i 0.359532 0.622728i −0.628351 0.777930i \(-0.716270\pi\)
0.987883 + 0.155202i \(0.0496030\pi\)
\(368\) −0.488292 0.845746i −0.0254540 0.0440876i
\(369\) 7.28932i 0.379467i
\(370\) −3.28745 + 1.89801i −0.170907 + 0.0986730i
\(371\) 54.3381 31.3721i 2.82109 1.62876i
\(372\) 6.44069i 0.333934i
\(373\) 16.7313 + 28.9795i 0.866316 + 1.50050i 0.865734 + 0.500504i \(0.166852\pi\)
0.000581860 1.00000i \(0.499815\pi\)
\(374\) −8.80025 + 15.2425i −0.455050 + 0.788170i
\(375\) 0.866025 + 0.500000i 0.0447214 + 0.0258199i
\(376\) 9.75342 0.502994
\(377\) −12.1720 + 9.67674i −0.626888 + 0.498377i
\(378\) 4.64466 0.238896
\(379\) −28.9052 16.6884i −1.48476 0.857227i −0.484910 0.874564i \(-0.661148\pi\)
−0.999850 + 0.0173371i \(0.994481\pi\)
\(380\) 4.02239 6.96699i 0.206344 0.357399i
\(381\) 6.10978 + 10.5825i 0.313014 + 0.542156i
\(382\) 0.897014i 0.0458952i
\(383\) 6.34829 3.66519i 0.324383 0.187282i −0.328962 0.944343i \(-0.606699\pi\)
0.653344 + 0.757061i \(0.273365\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 20.4371i 1.04157i
\(386\) 10.1322 + 17.5494i 0.515714 + 0.893243i
\(387\) 0.358228 0.620469i 0.0182098 0.0315402i
\(388\) 11.9730 + 6.91261i 0.607836 + 0.350935i
\(389\) −32.6198 −1.65389 −0.826946 0.562282i \(-0.809924\pi\)
−0.826946 + 0.562282i \(0.809924\pi\)
\(390\) 0.531987 + 3.56609i 0.0269382 + 0.180576i
\(391\) −3.90633 −0.197552
\(392\) 12.6205 + 7.28643i 0.637430 + 0.368020i
\(393\) 0.189378 0.328013i 0.00955288 0.0165461i
\(394\) 4.59028 + 7.95060i 0.231255 + 0.400545i
\(395\) 14.9340i 0.751410i
\(396\) 3.81062 2.20006i 0.191491 0.110557i
\(397\) 12.5299 7.23416i 0.628860 0.363072i −0.151451 0.988465i \(-0.548394\pi\)
0.780310 + 0.625392i \(0.215061\pi\)
\(398\) 16.2175i 0.812911i
\(399\) −18.6826 32.3593i −0.935302 1.61999i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −6.31096 3.64364i −0.315154 0.181955i 0.334076 0.942546i \(-0.391576\pi\)
−0.649231 + 0.760592i \(0.724909\pi\)
\(402\) 1.82522 0.0910336
\(403\) −8.51671 + 21.6041i −0.424248 + 1.07618i
\(404\) −6.80025 −0.338325
\(405\) −0.866025 0.500000i −0.0430331 0.0248452i
\(406\) 10.0156 17.3475i 0.497066 0.860943i
\(407\) 8.35150 + 14.4652i 0.413968 + 0.717014i
\(408\) 4.00000i 0.198030i
\(409\) −21.2840 + 12.2883i −1.05242 + 0.607617i −0.923327 0.384015i \(-0.874541\pi\)
−0.129097 + 0.991632i \(0.541208\pi\)
\(410\) 6.31274 3.64466i 0.311764 0.179997i
\(411\) 1.25235i 0.0617741i
\(412\) −2.64568 4.58246i −0.130343 0.225761i
\(413\) −5.06397 + 8.77106i −0.249182 + 0.431596i
\(414\) 0.845746 + 0.488292i 0.0415662 + 0.0239982i
\(415\) 3.51093 0.172345
\(416\) 3.56609 0.531987i 0.174842 0.0260828i
\(417\) 3.35534 0.164312
\(418\) −30.6556 17.6990i −1.49942 0.865688i
\(419\) −7.77684 + 13.4699i −0.379923 + 0.658047i −0.991051 0.133486i \(-0.957383\pi\)
0.611127 + 0.791532i \(0.290716\pi\)
\(420\) −2.32233 4.02239i −0.113318 0.196273i
\(421\) 22.3143i 1.08753i 0.839237 + 0.543766i \(0.183002\pi\)
−0.839237 + 0.543766i \(0.816998\pi\)
\(422\) 1.40270 0.809848i 0.0682822 0.0394228i
\(423\) −8.44671 + 4.87671i −0.410693 + 0.237114i
\(424\) 13.5089i 0.656050i
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) 3.97658 6.88764i 0.192666 0.333707i
\(427\) −30.0236 17.3341i −1.45294 0.838856i
\(428\) −16.9282 −0.818256
\(429\) 15.6912 2.34081i 0.757580 0.113015i
\(430\) −0.716456 −0.0345506
\(431\) 21.0135 + 12.1322i 1.01219 + 0.584386i 0.911831 0.410565i \(-0.134669\pi\)
0.100356 + 0.994952i \(0.468002\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −11.5494 20.0042i −0.555031 0.961342i −0.997901 0.0647561i \(-0.979373\pi\)
0.442870 0.896586i \(-0.353960\pi\)
\(434\) 29.9148i 1.43596i
\(435\) −3.73494 + 2.15637i −0.179077 + 0.103390i
\(436\) 11.0853 6.40013i 0.530892 0.306510i
\(437\) 7.85641i 0.375823i
\(438\) −2.18056 3.77684i −0.104191 0.180464i
\(439\) −19.9980 + 34.6375i −0.954450 + 1.65316i −0.218829 + 0.975763i \(0.570224\pi\)
−0.735621 + 0.677393i \(0.763110\pi\)
\(440\) −3.81062 2.20006i −0.181664 0.104884i
\(441\) −14.5729 −0.693946
\(442\) 5.28932 13.4173i 0.251587 0.638194i
\(443\) −15.6036 −0.741350 −0.370675 0.928763i \(-0.620874\pi\)
−0.370675 + 0.928763i \(0.620874\pi\)
\(444\) −3.28745 1.89801i −0.156016 0.0900757i
\(445\) −4.08637 + 7.07780i −0.193712 + 0.335520i
\(446\) 1.11836 + 1.93705i 0.0529557 + 0.0917219i
\(447\) 4.61970i 0.218504i
\(448\) −4.02239 + 2.32233i −0.190040 + 0.109720i
\(449\) 23.3863 13.5021i 1.10367 0.637203i 0.166486 0.986044i \(-0.446758\pi\)
0.937182 + 0.348841i \(0.113425\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −16.0370 27.7768i −0.755151 1.30796i
\(452\) 6.53308 11.3156i 0.307290 0.532242i
\(453\) 9.73628 + 5.62124i 0.457450 + 0.264109i
\(454\) −15.3205 −0.719027
\(455\) −2.47090 16.5633i −0.115838 0.776498i
\(456\) 8.04479 0.376732
\(457\) 15.4039 + 8.89342i 0.720562 + 0.416017i 0.814959 0.579518i \(-0.196759\pi\)
−0.0943975 + 0.995535i \(0.530092\pi\)
\(458\) −5.06397 + 8.77106i −0.236624 + 0.409845i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0.976584i 0.0455334i
\(461\) 21.6205 12.4826i 1.00697 0.581372i 0.0966638 0.995317i \(-0.469183\pi\)
0.910302 + 0.413945i \(0.135849\pi\)
\(462\) −17.6990 + 10.2185i −0.823434 + 0.475410i
\(463\) 15.6389i 0.726801i −0.931633 0.363400i \(-0.881616\pi\)
0.931633 0.363400i \(-0.118384\pi\)
\(464\) 2.15637 + 3.73494i 0.100107 + 0.173390i
\(465\) −3.22034 + 5.57780i −0.149340 + 0.258664i
\(466\) 17.9716 + 10.3759i 0.832521 + 0.480656i
\(467\) −2.43914 −0.112870 −0.0564349 0.998406i \(-0.517973\pi\)
−0.0564349 + 0.998406i \(0.517973\pi\)
\(468\) −2.82233 + 2.24376i −0.130462 + 0.103718i
\(469\) −8.47751 −0.391455
\(470\) 8.44671 + 4.87671i 0.389618 + 0.224946i
\(471\) 0.751556 1.30173i 0.0346299 0.0599807i
\(472\) −1.09028 1.88842i −0.0501842 0.0869215i
\(473\) 3.15250i 0.144952i
\(474\) 12.9332 7.46699i 0.594042 0.342970i
\(475\) 6.96699 4.02239i 0.319667 0.184560i
\(476\) 18.5786i 0.851550i
\(477\) −6.75444 11.6990i −0.309265 0.535662i
\(478\) −12.1770 + 21.0911i −0.556961 + 0.964685i
\(479\) 12.2857 + 7.09317i 0.561349 + 0.324095i 0.753687 0.657234i \(-0.228274\pi\)
−0.192338 + 0.981329i \(0.561607\pi\)
\(480\) 1.00000 0.0456435
\(481\) −8.51737 10.7136i −0.388358 0.488500i
\(482\) −19.8685 −0.904983
\(483\) −3.92820 2.26795i −0.178739 0.103195i
\(484\) −4.18056 + 7.24094i −0.190025 + 0.329134i
\(485\) 6.91261 + 11.9730i 0.313885 + 0.543665i
\(486\) 1.00000i 0.0453609i
\(487\) 4.99115 2.88164i 0.226171 0.130580i −0.382633 0.923900i \(-0.624983\pi\)
0.608804 + 0.793320i \(0.291649\pi\)
\(488\) 6.46410 3.73205i 0.292616 0.168942i
\(489\) 0.176330i 0.00797392i
\(490\) 7.28643 + 12.6205i 0.329167 + 0.570135i
\(491\) −0.537671 + 0.931273i −0.0242647 + 0.0420278i −0.877903 0.478839i \(-0.841058\pi\)
0.853638 + 0.520867i \(0.174391\pi\)
\(492\) 6.31274 + 3.64466i 0.284600 + 0.164314i
\(493\) 17.2509 0.776943
\(494\) 26.9848 + 10.6379i 1.21410 + 0.478620i
\(495\) 4.40013 0.197771
\(496\) 5.57780 + 3.22034i 0.250450 + 0.144598i
\(497\) −18.4699 + 31.9908i −0.828487 + 1.43498i
\(498\) 1.75547 + 3.04056i 0.0786644 + 0.136251i
\(499\) 14.7534i 0.660454i −0.943902 0.330227i \(-0.892875\pi\)
0.943902 0.330227i \(-0.107125\pi\)
\(500\) 0.866025 0.500000i 0.0387298 0.0223607i
\(501\) −7.51851 + 4.34081i −0.335902 + 0.193933i
\(502\) 13.5713i 0.605717i
\(503\) 13.3309 + 23.0898i 0.594395 + 1.02952i 0.993632 + 0.112675i \(0.0359419\pi\)
−0.399236 + 0.916848i \(0.630725\pi\)
\(504\) 2.32233 4.02239i 0.103445 0.179172i
\(505\) −5.88919 3.40013i −0.262066 0.151304i
\(506\) −4.29709 −0.191029
\(507\) −12.4340 + 3.79423i −0.552212 + 0.168508i
\(508\) 12.2196 0.542156
\(509\) 12.2807 + 7.09028i 0.544333 + 0.314271i 0.746833 0.665011i \(-0.231573\pi\)
−0.202500 + 0.979282i \(0.564907\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) 10.1279 + 17.5421i 0.448034 + 0.776018i
\(512\) 1.00000i 0.0441942i
\(513\) −6.96699 + 4.02239i −0.307600 + 0.177593i
\(514\) 0.573569 0.331150i 0.0252990 0.0146064i
\(515\) 5.29137i 0.233165i
\(516\) −0.358228 0.620469i −0.0157701 0.0273146i
\(517\) 21.4581 37.1666i 0.943728 1.63459i
\(518\) 15.2691 + 8.81562i 0.670886 + 0.387336i
\(519\) −1.78043 −0.0781523
\(520\) 3.35432 + 1.32233i 0.147097 + 0.0579880i
\(521\) 23.7476 1.04040 0.520202 0.854043i \(-0.325857\pi\)
0.520202 + 0.854043i \(0.325857\pi\)
\(522\) −3.73494 2.15637i −0.163474 0.0943817i
\(523\) −6.92532 + 11.9950i −0.302823 + 0.524505i −0.976774 0.214271i \(-0.931262\pi\)
0.673951 + 0.738776i \(0.264596\pi\)
\(524\) −0.189378 0.328013i −0.00827303 0.0143293i
\(525\) 4.64466i 0.202710i
\(526\) −26.6301 + 15.3749i −1.16113 + 0.670378i
\(527\) 22.3112 12.8814i 0.971891 0.561121i
\(528\) 4.40013i 0.191491i
\(529\) 11.0231 + 19.0926i 0.479267 + 0.830115i
\(530\) −6.75444 + 11.6990i −0.293394 + 0.508174i
\(531\) 1.88842 + 1.09028i 0.0819504 + 0.0473141i
\(532\) −37.3653 −1.61999
\(533\) 16.3555 + 20.5729i 0.708434 + 0.891110i
\(534\) −8.17274 −0.353669
\(535\) −14.6603 8.46410i −0.633818 0.365935i
\(536\) 0.912609 1.58068i 0.0394187 0.0682752i
\(537\) −8.70786 15.0825i −0.375772 0.650856i
\(538\) 3.74410i 0.161420i
\(539\) 55.5317 32.0612i 2.39192 1.38097i
\(540\) −0.866025 + 0.500000i −0.0372678 + 0.0215166i
\(541\) 14.8898i 0.640164i −0.947390 0.320082i \(-0.896290\pi\)
0.947390 0.320082i \(-0.103710\pi\)
\(542\) 13.8806 + 24.0419i 0.596223 + 1.03269i
\(543\) 5.18056 8.97299i 0.222319 0.385068i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 12.8003 0.548303
\(546\) 13.1088 10.4215i 0.561003 0.445999i
\(547\) −22.2019 −0.949284 −0.474642 0.880179i \(-0.657422\pi\)
−0.474642 + 0.880179i \(0.657422\pi\)
\(548\) −1.08457 0.626177i −0.0463306 0.0267490i
\(549\) −3.73205 + 6.46410i −0.159280 + 0.275881i
\(550\) −2.20006 3.81062i −0.0938110 0.162485i
\(551\) 34.6950i 1.47806i
\(552\) 0.845746 0.488292i 0.0359973 0.0207831i
\(553\) −60.0703 + 34.6816i −2.55445 + 1.47481i
\(554\) 11.9922i 0.509499i
\(555\) −1.89801 3.28745i −0.0805662 0.139545i
\(556\) 1.67767 2.90581i 0.0711491 0.123234i
\(557\) 1.64518 + 0.949847i 0.0697087 + 0.0402463i 0.534449 0.845201i \(-0.320519\pi\)
−0.464741 + 0.885447i \(0.653852\pi\)
\(558\) −6.44069 −0.272656
\(559\) −0.381146 2.55495i −0.0161207 0.108063i
\(560\) −4.64466 −0.196273
\(561\) −15.2425 8.80025i −0.643538 0.371547i
\(562\) 1.81944 3.15137i 0.0767485 0.132932i
\(563\) −0.860000 1.48956i −0.0362447 0.0627777i 0.847334 0.531060i \(-0.178206\pi\)
−0.883579 + 0.468283i \(0.844873\pi\)
\(564\) 9.75342i 0.410693i
\(565\) 11.3156 6.53308i 0.476052 0.274849i
\(566\) 4.19538 2.42220i 0.176345 0.101813i
\(567\) 4.64466i 0.195057i
\(568\) −3.97658 6.88764i −0.166854 0.288999i
\(569\) −0.300960 + 0.521278i −0.0126169 + 0.0218531i −0.872265 0.489034i \(-0.837350\pi\)
0.859648 + 0.510887i \(0.170683\pi\)
\(570\) 6.96699 + 4.02239i 0.291815 + 0.168480i
\(571\) 11.9808 0.501381 0.250691 0.968067i \(-0.419342\pi\)
0.250691 + 0.968067i \(0.419342\pi\)
\(572\) 5.81842 14.7594i 0.243280 0.617122i
\(573\) −0.897014 −0.0374733
\(574\) −29.3205 16.9282i −1.22381 0.706570i
\(575\) 0.488292 0.845746i 0.0203632 0.0352701i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 43.0293i 1.79133i 0.444725 + 0.895667i \(0.353301\pi\)
−0.444725 + 0.895667i \(0.646699\pi\)
\(578\) 0.866025 0.500000i 0.0360219 0.0207973i
\(579\) −17.5494 + 10.1322i −0.729330 + 0.421079i
\(580\) 4.31274i 0.179077i
\(581\) −8.15355 14.1224i −0.338266 0.585894i
\(582\) −6.91261 + 11.9730i −0.286537 + 0.496296i
\(583\) 51.4773 + 29.7204i 2.13197 + 1.23089i
\(584\) −4.36112 −0.180464
\(585\) −3.56609 + 0.531987i −0.147440 + 0.0219950i
\(586\) 3.70081 0.152879
\(587\) −15.5147 8.95740i −0.640359 0.369711i 0.144394 0.989520i \(-0.453877\pi\)
−0.784753 + 0.619809i \(0.787210\pi\)
\(588\) −7.28643 + 12.6205i −0.300487 + 0.520459i
\(589\) 25.9070 + 44.8722i 1.06748 + 1.84893i
\(590\) 2.18056i 0.0897722i
\(591\) −7.95060 + 4.59028i −0.327044 + 0.188819i
\(592\) −3.28745 + 1.89801i −0.135114 + 0.0780078i
\(593\) 0.669624i 0.0274981i −0.999905 0.0137491i \(-0.995623\pi\)
0.999905 0.0137491i \(-0.00437660\pi\)
\(594\) 2.20006 + 3.81062i 0.0902697 + 0.156352i
\(595\) −9.28932 + 16.0896i −0.380825 + 0.659608i
\(596\) −4.00077 2.30985i −0.163878 0.0946151i
\(597\) 16.2175 0.663739
\(598\) 3.48258 0.519530i 0.142413 0.0212452i
\(599\) 1.29241 0.0528066 0.0264033 0.999651i \(-0.491595\pi\)
0.0264033 + 0.999651i \(0.491595\pi\)
\(600\) 0.866025 + 0.500000i 0.0353553 + 0.0204124i
\(601\) 5.73671 9.93627i 0.234005 0.405309i −0.724978 0.688772i \(-0.758150\pi\)
0.958983 + 0.283463i \(0.0914834\pi\)
\(602\) 1.66385 + 2.88187i 0.0678134 + 0.117456i
\(603\) 1.82522i 0.0743286i
\(604\) 9.73628 5.62124i 0.396164 0.228725i
\(605\) −7.24094 + 4.18056i −0.294386 + 0.169964i
\(606\) 6.80025i 0.276241i
\(607\) 12.0672 + 20.9010i 0.489792 + 0.848344i 0.999931 0.0117477i \(-0.00373949\pi\)
−0.510139 + 0.860092i \(0.670406\pi\)
\(608\) 4.02239 6.96699i 0.163130 0.282549i
\(609\) 17.3475 + 10.0156i 0.702957 + 0.405852i
\(610\) 7.46410 0.302213
\(611\) −12.8972 + 32.7161i −0.521766 + 1.32355i
\(612\) 4.00000 0.161690
\(613\) 25.0716 + 14.4751i 1.01263 + 0.584644i 0.911961 0.410276i \(-0.134568\pi\)
0.100671 + 0.994920i \(0.467901\pi\)
\(614\) −3.55727 + 6.16137i −0.143560 + 0.248653i
\(615\) 3.64466 + 6.31274i 0.146967 + 0.254554i
\(616\) 20.4371i 0.823434i
\(617\) −0.728597 + 0.420655i −0.0293322 + 0.0169349i −0.514594 0.857434i \(-0.672057\pi\)
0.485262 + 0.874369i \(0.338724\pi\)
\(618\) 4.58246 2.64568i 0.184333 0.106425i
\(619\) 6.25076i 0.251239i 0.992078 + 0.125620i \(0.0400919\pi\)
−0.992078 + 0.125620i \(0.959908\pi\)
\(620\) 3.22034 + 5.57780i 0.129332 + 0.224010i
\(621\) −0.488292 + 0.845746i −0.0195945 + 0.0339386i
\(622\) −17.2467 9.95740i −0.691530 0.399255i
\(623\) 37.9596 1.52082
\(624\) 0.531987 + 3.56609i 0.0212965 + 0.142758i
\(625\) 1.00000 0.0400000
\(626\) 5.31696 + 3.06975i 0.212509 + 0.122692i
\(627\) 17.6990 30.6556i 0.706832 1.22427i
\(628\) −0.751556 1.30173i −0.0299904 0.0519448i
\(629\) 15.1841i 0.605430i
\(630\) 4.02239 2.32233i 0.160256 0.0925238i
\(631\) 2.61970 1.51248i 0.104288 0.0602110i −0.446949 0.894560i \(-0.647489\pi\)
0.551237 + 0.834349i \(0.314156\pi\)
\(632\) 14.9340i 0.594042i
\(633\) 0.809848 + 1.40270i 0.0321886 + 0.0557522i
\(634\) 3.92643 6.80078i 0.155938 0.270093i
\(635\) 10.5825 + 6.10978i 0.419952 + 0.242459i
\(636\) −13.5089 −0.535662
\(637\) −41.1294 + 32.6980i −1.62961 + 1.29554i
\(638\) 18.9766 0.751290
\(639\) 6.88764 + 3.97658i 0.272471 + 0.157311i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 0.386305 + 0.669099i 0.0152581 + 0.0264278i 0.873554 0.486728i \(-0.161810\pi\)
−0.858296 + 0.513156i \(0.828476\pi\)
\(642\) 16.9282i 0.668103i
\(643\) 16.7788 9.68726i 0.661693 0.382028i −0.131229 0.991352i \(-0.541892\pi\)
0.792922 + 0.609324i \(0.208559\pi\)
\(644\) −3.92820 + 2.26795i −0.154793 + 0.0893697i
\(645\) 0.716456i 0.0282104i
\(646\) −16.0896 27.8680i −0.633036 1.09645i
\(647\) −13.5953 + 23.5477i −0.534485 + 0.925755i 0.464703 + 0.885466i \(0.346161\pi\)
−0.999188 + 0.0402882i \(0.987172\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −9.59473 −0.376626
\(650\) 2.24376 + 2.82233i 0.0880075 + 0.110701i
\(651\) 29.9148 1.17245
\(652\) −0.152706 0.0881650i −0.00598044 0.00345281i
\(653\) −7.89799 + 13.6797i −0.309072 + 0.535329i −0.978160 0.207855i \(-0.933352\pi\)
0.669088 + 0.743184i \(0.266685\pi\)
\(654\) 6.40013 + 11.0853i 0.250265 + 0.433471i
\(655\) 0.378757i 0.0147993i
\(656\) 6.31274 3.64466i 0.246471 0.142300i
\(657\) 3.77684 2.18056i 0.147348 0.0850717i
\(658\) 45.3013i 1.76603i
\(659\) −15.2381 26.3932i −0.593593 1.02813i −0.993744 0.111684i \(-0.964376\pi\)
0.400151 0.916449i \(-0.368958\pi\)
\(660\) 2.20006 3.81062i 0.0856374 0.148328i
\(661\) −24.1514 13.9438i −0.939379 0.542351i −0.0496136 0.998768i \(-0.515799\pi\)
−0.889766 + 0.456418i \(0.849132\pi\)
\(662\) 31.9959 1.24356
\(663\) 13.4173 + 5.28932i 0.521084 + 0.205420i
\(664\) 3.51093 0.136251
\(665\) −32.3593 18.6826i −1.25484 0.724482i
\(666\) 1.89801 3.28745i 0.0735465 0.127386i
\(667\) 2.10587 + 3.64748i 0.0815397 + 0.141231i
\(668\) 8.68162i 0.335902i
\(669\) −1.93705 + 1.11836i −0.0748906 + 0.0432381i
\(670\) 1.58068 0.912609i 0.0610672 0.0352572i
\(671\) 32.8430i 1.26789i
\(672\) −2.32233 4.02239i −0.0895858 0.155167i
\(673\) −0.489066 + 0.847086i −0.0188521 + 0.0326528i −0.875298 0.483585i \(-0.839334\pi\)
0.856445 + 0.516238i \(0.172668\pi\)
\(674\) −30.8680 17.8216i −1.18899 0.686463i
\(675\) −1.00000 −0.0384900
\(676\) −2.93109 + 12.6653i −0.112734 + 0.487125i
\(677\) −19.1926 −0.737630 −0.368815 0.929503i \(-0.620236\pi\)
−0.368815 + 0.929503i \(0.620236\pi\)
\(678\) 11.3156 + 6.53308i 0.434574 + 0.250901i
\(679\) 32.1067 55.6105i 1.23214 2.13413i
\(680\) −2.00000 3.46410i −0.0766965 0.132842i
\(681\) 15.3205i 0.587083i
\(682\) 24.5430 14.1699i 0.939801 0.542594i
\(683\) −1.30851 + 0.755467i −0.0500687 + 0.0289071i −0.524825 0.851210i \(-0.675869\pi\)
0.474757 + 0.880117i \(0.342536\pi\)
\(684\) 8.04479i 0.307600i
\(685\) −0.626177 1.08457i −0.0239250 0.0414393i
\(686\) 17.5867 30.4610i 0.671463 1.16301i
\(687\) −8.77106 5.06397i −0.334637 0.193203i
\(688\) −0.716456 −0.0273146
\(689\) −45.3131 17.8632i −1.72629 0.680534i
\(690\) 0.976584 0.0371779
\(691\) 28.6798 + 16.5583i 1.09103 + 0.629907i 0.933851 0.357663i \(-0.116426\pi\)
0.157180 + 0.987570i \(0.449760\pi\)
\(692\) −0.890216 + 1.54190i −0.0338409 + 0.0586142i
\(693\) −10.2185 17.6990i −0.388170 0.672331i
\(694\) 6.89701i 0.261807i
\(695\) 2.90581 1.67767i 0.110224 0.0636377i
\(696\) −3.73494 + 2.15637i −0.141572 + 0.0817369i
\(697\) 29.1573i 1.10441i
\(698\) 9.66025 + 16.7321i 0.365646 + 0.633317i
\(699\) −10.3759 + 17.9716i −0.392454 + 0.679750i
\(700\) −4.02239 2.32233i −0.152032 0.0877758i
\(701\) 27.8695 1.05262 0.526308 0.850294i \(-0.323576\pi\)
0.526308 + 0.850294i \(0.323576\pi\)
\(702\) −2.24376 2.82233i −0.0846852 0.106522i
\(703\) −30.5382 −1.15177
\(704\) −3.81062 2.20006i −0.143618 0.0829180i
\(705\) −4.87671 + 8.44671i −0.183668 + 0.318122i
\(706\) −13.7086 23.7441i −0.515931 0.893619i
\(707\) 31.5849i 1.18787i
\(708\) 1.88842 1.09028i 0.0709711 0.0409752i
\(709\) −9.57491 + 5.52808i −0.359593 + 0.207611i −0.668902 0.743350i \(-0.733236\pi\)
0.309309 + 0.950962i \(0.399902\pi\)
\(710\) 7.95317i 0.298477i
\(711\) 7.46699 + 12.9332i 0.280034 + 0.485033i
\(712\) −4.08637 + 7.07780i −0.153143 + 0.265252i
\(713\) 5.44719 + 3.14493i 0.203999 + 0.117779i
\(714\) −18.5786 −0.695288
\(715\) 12.4186 9.87282i 0.464430 0.369223i
\(716\) −17.4157 −0.650856
\(717\) −21.0911 12.1770i −0.787662 0.454757i
\(718\) 7.18056 12.4371i 0.267976 0.464148i
\(719\) 5.85641 + 10.1436i 0.218407 + 0.378292i 0.954321 0.298783i \(-0.0965806\pi\)
−0.735914 + 0.677075i \(0.763247\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) −21.2840 + 12.2883i −0.792656 + 0.457640i
\(722\) 39.5935 22.8593i 1.47352 0.850735i
\(723\) 19.8685i 0.738916i
\(724\) −5.18056 8.97299i −0.192534 0.333479i
\(725\) −2.15637 + 3.73494i −0.0800855 + 0.138712i
\(726\) −7.24094 4.18056i −0.268736 0.155155i
\(727\) −19.4152 −0.720071 −0.360035 0.932939i \(-0.617235\pi\)
−0.360035 + 0.932939i \(0.617235\pi\)
\(728\) −2.47090 16.5633i −0.0915777 0.613876i
\(729\) 1.00000 0.0370370
\(730\) −3.77684 2.18056i −0.139787 0.0807061i
\(731\) −1.43291 + 2.48188i −0.0529982 + 0.0917956i
\(732\) 3.73205 + 6.46410i 0.137941 + 0.238920i
\(733\) 11.9340i 0.440792i −0.975411 0.220396i \(-0.929265\pi\)
0.975411 0.220396i \(-0.0707349\pi\)
\(734\) 11.9298 6.88764i 0.440335 0.254228i
\(735\) −12.6205 + 7.28643i −0.465513 + 0.268764i
\(736\) 0.976584i 0.0359973i
\(737\) −4.01559 6.95521i −0.147916 0.256199i
\(738\) −3.64466 + 6.31274i −0.134162 + 0.232375i
\(739\) 17.2017 + 9.93141i 0.632775 + 0.365333i 0.781826 0.623497i \(-0.214289\pi\)
−0.149051 + 0.988830i \(0.547622\pi\)
\(740\) −3.79603 −0.139545
\(741\) −10.6379 + 26.9848i −0.390792 + 0.991310i
\(742\) 62.7442 2.30341
\(743\) 14.2787 + 8.24383i 0.523836 + 0.302437i 0.738503 0.674251i \(-0.235533\pi\)
−0.214667 + 0.976687i \(0.568867\pi\)
\(744\) −3.22034 + 5.57780i −0.118063 + 0.204492i
\(745\) −2.30985 4.00077i −0.0846263 0.146577i
\(746\) 33.4627i 1.22516i
\(747\) −3.04056 + 1.75547i −0.111248 + 0.0642292i
\(748\) −15.2425 + 8.80025i −0.557320 + 0.321769i
\(749\) 78.6257i 2.87292i
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) −23.3312 + 40.4109i −0.851368 + 1.47461i 0.0286056 + 0.999591i \(0.490893\pi\)
−0.879974 + 0.475022i \(0.842440\pi\)
\(752\) 8.44671 + 4.87671i 0.308020 + 0.177835i
\(753\) −13.5713 −0.494566
\(754\) −15.3796 + 2.29432i −0.560092 + 0.0835542i
\(755\) 11.2425 0.409156
\(756\) 4.02239 + 2.32233i 0.146293 + 0.0844623i
\(757\) −1.31799 + 2.28282i −0.0479030 + 0.0829705i −0.888983 0.457941i \(-0.848587\pi\)
0.841080 + 0.540911i \(0.181921\pi\)
\(758\) −16.6884 28.9052i −0.606151 1.04988i
\(759\) 4.29709i 0.155975i
\(760\) 6.96699 4.02239i 0.252719 0.145908i
\(761\) 0.0693410 0.0400340i 0.00251361 0.00145123i −0.498743 0.866750i \(-0.666205\pi\)
0.501256 + 0.865299i \(0.332871\pi\)
\(762\) 12.2196i 0.442668i
\(763\) −29.7264 51.4877i −1.07617 1.86398i
\(764\) −0.448507 + 0.776837i −0.0162264 + 0.0281050i
\(765\) 3.46410 + 2.00000i 0.125245 + 0.0723102i
\(766\) 7.33038 0.264857
\(767\) 7.77606 1.16003i 0.280777 0.0418862i
\(768\) 1.00000 0.0360844
\(769\) 4.92177 + 2.84159i 0.177484 + 0.102470i 0.586110 0.810232i \(-0.300659\pi\)
−0.408626 + 0.912702i \(0.633992\pi\)
\(770\) −10.2185 + 17.6990i −0.368251 + 0.637829i
\(771\) 0.331150 + 0.573569i 0.0119261 + 0.0206566i
\(772\) 20.2644i 0.729330i
\(773\) −6.57184 + 3.79425i −0.236373 + 0.136470i −0.613508 0.789688i \(-0.710242\pi\)
0.377136 + 0.926158i \(0.376909\pi\)
\(774\) 0.620469 0.358228i 0.0223023 0.0128762i
\(775\) 6.44069i 0.231356i