Properties

Label 74.2.e.a.27.2
Level $74$
Weight $2$
Character 74.27
Analytic conductor $0.591$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 27.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 74.27
Dual form 74.2.e.a.11.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} -1.73205 q^{10} +4.73205 q^{11} +(-0.366025 + 0.633975i) q^{12} +(-5.19615 + 3.00000i) q^{13} -4.00000i q^{14} +(-1.09808 - 0.633975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(2.13397 - 1.23205i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(1.46410 - 2.53590i) q^{21} +(4.09808 + 2.36603i) q^{22} -1.26795i q^{23} +(-0.633975 + 0.366025i) q^{24} +(-1.00000 + 1.73205i) q^{25} -6.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +4.26795i q^{29} +(-0.633975 - 1.09808i) q^{30} +1.26795i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 3.00000i) q^{33} +(-0.866025 - 1.50000i) q^{34} +(6.00000 + 3.46410i) q^{35} +2.46410 q^{36} +(-0.500000 + 6.06218i) q^{37} -1.26795 q^{38} +(-3.80385 - 2.19615i) q^{39} +(-0.866025 - 1.50000i) q^{40} +(-0.232051 - 0.401924i) q^{41} +(2.53590 - 1.46410i) q^{42} -9.46410i q^{43} +(2.36603 + 4.09808i) q^{44} +4.26795i q^{45} +(0.633975 - 1.09808i) q^{46} +11.6603 q^{47} -0.732051 q^{48} +(-4.50000 + 7.79423i) q^{49} +(-1.73205 + 1.00000i) q^{50} -1.26795i q^{51} +(-5.19615 - 3.00000i) q^{52} +(1.26795 - 2.19615i) q^{53} +(3.46410 + 2.00000i) q^{54} +(-7.09808 + 4.09808i) q^{55} +(3.46410 - 2.00000i) q^{56} +(-0.803848 - 0.464102i) q^{57} +(-2.13397 + 3.69615i) q^{58} +(-2.19615 - 1.26795i) q^{59} -1.26795i q^{60} +(12.6962 - 7.33013i) q^{61} +(-0.633975 + 1.09808i) q^{62} -9.85641 q^{63} -1.00000 q^{64} +(5.19615 - 9.00000i) q^{65} +3.46410i q^{66} +(-3.09808 - 5.36603i) q^{67} -1.73205i q^{68} +(0.803848 - 0.464102i) q^{69} +(3.46410 + 6.00000i) q^{70} +(-1.26795 - 2.19615i) q^{71} +(2.13397 + 1.23205i) q^{72} -12.3923 q^{73} +(-3.46410 + 5.00000i) q^{74} -1.46410 q^{75} +(-1.09808 - 0.633975i) q^{76} +(-9.46410 - 16.3923i) q^{77} +(-2.19615 - 3.80385i) q^{78} +(-7.09808 + 4.09808i) q^{79} -1.73205i q^{80} +(-2.23205 - 3.86603i) q^{81} -0.464102i q^{82} +(-5.83013 + 10.0981i) q^{83} +2.92820 q^{84} +3.00000 q^{85} +(4.73205 - 8.19615i) q^{86} +(-2.70577 + 1.56218i) q^{87} +4.73205i q^{88} +(4.50000 + 2.59808i) q^{89} +(-2.13397 + 3.69615i) q^{90} +(20.7846 + 12.0000i) q^{91} +(1.09808 - 0.633975i) q^{92} +(-0.803848 + 0.464102i) q^{93} +(10.0981 + 5.83013i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.633975 - 0.366025i) q^{96} -5.19615i q^{97} +(-7.79423 + 4.50000i) q^{98} +(5.83013 - 10.0981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9} + 12 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{18} + 6 q^{19} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 6 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{27} + 8 q^{28} - 6 q^{30} + 24 q^{35} - 4 q^{36} - 2 q^{37} - 12 q^{38} - 36 q^{39} + 6 q^{41} + 24 q^{42} + 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} - 18 q^{49} + 12 q^{53} - 18 q^{55} - 24 q^{57} - 12 q^{58} + 12 q^{59} + 30 q^{61} - 6 q^{62} + 16 q^{63} - 4 q^{64} - 2 q^{67} + 24 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} + 8 q^{75} + 6 q^{76} - 24 q^{77} + 12 q^{78} - 18 q^{79} - 2 q^{81} - 6 q^{83} - 16 q^{84} + 12 q^{85} + 12 q^{86} - 42 q^{87} + 18 q^{89} - 12 q^{90} - 6 q^{92} - 24 q^{93} + 30 q^{94} - 6 q^{95} - 6 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 0.366025 + 0.633975i 0.211325 + 0.366025i 0.952129 0.305695i \(-0.0988889\pi\)
−0.740805 + 0.671721i \(0.765556\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 0.732051i 0.298858i
\(7\) −2.00000 3.46410i −0.755929 1.30931i −0.944911 0.327327i \(-0.893852\pi\)
0.188982 0.981981i \(-0.439481\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.23205 2.13397i 0.410684 0.711325i
\(10\) −1.73205 −0.547723
\(11\) 4.73205 1.42677 0.713384 0.700774i \(-0.247162\pi\)
0.713384 + 0.700774i \(0.247162\pi\)
\(12\) −0.366025 + 0.633975i −0.105662 + 0.183013i
\(13\) −5.19615 + 3.00000i −1.44115 + 0.832050i −0.997927 0.0643593i \(-0.979500\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) 4.00000i 1.06904i
\(15\) −1.09808 0.633975i −0.283522 0.163692i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 0.866025i −0.363803 0.210042i 0.306944 0.951727i \(-0.400693\pi\)
−0.670748 + 0.741685i \(0.734027\pi\)
\(18\) 2.13397 1.23205i 0.502983 0.290397i
\(19\) −1.09808 + 0.633975i −0.251916 + 0.145444i −0.620641 0.784095i \(-0.713128\pi\)
0.368725 + 0.929538i \(0.379794\pi\)
\(20\) −1.50000 0.866025i −0.335410 0.193649i
\(21\) 1.46410 2.53590i 0.319493 0.553378i
\(22\) 4.09808 + 2.36603i 0.873713 + 0.504438i
\(23\) 1.26795i 0.264386i −0.991224 0.132193i \(-0.957798\pi\)
0.991224 0.132193i \(-0.0422018\pi\)
\(24\) −0.633975 + 0.366025i −0.129410 + 0.0747146i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −6.00000 −1.17670
\(27\) 4.00000 0.769800
\(28\) 2.00000 3.46410i 0.377964 0.654654i
\(29\) 4.26795i 0.792538i 0.918134 + 0.396269i \(0.129695\pi\)
−0.918134 + 0.396269i \(0.870305\pi\)
\(30\) −0.633975 1.09808i −0.115747 0.200480i
\(31\) 1.26795i 0.227730i 0.993496 + 0.113865i \(0.0363232\pi\)
−0.993496 + 0.113865i \(0.963677\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 1.73205 + 3.00000i 0.301511 + 0.522233i
\(34\) −0.866025 1.50000i −0.148522 0.257248i
\(35\) 6.00000 + 3.46410i 1.01419 + 0.585540i
\(36\) 2.46410 0.410684
\(37\) −0.500000 + 6.06218i −0.0821995 + 0.996616i
\(38\) −1.26795 −0.205689
\(39\) −3.80385 2.19615i −0.609103 0.351666i
\(40\) −0.866025 1.50000i −0.136931 0.237171i
\(41\) −0.232051 0.401924i −0.0362402 0.0627700i 0.847336 0.531057i \(-0.178205\pi\)
−0.883577 + 0.468287i \(0.844871\pi\)
\(42\) 2.53590 1.46410i 0.391298 0.225916i
\(43\) 9.46410i 1.44326i −0.692278 0.721631i \(-0.743393\pi\)
0.692278 0.721631i \(-0.256607\pi\)
\(44\) 2.36603 + 4.09808i 0.356692 + 0.617808i
\(45\) 4.26795i 0.636228i
\(46\) 0.633975 1.09808i 0.0934745 0.161903i
\(47\) 11.6603 1.70082 0.850411 0.526118i \(-0.176353\pi\)
0.850411 + 0.526118i \(0.176353\pi\)
\(48\) −0.732051 −0.105662
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) −1.73205 + 1.00000i −0.244949 + 0.141421i
\(51\) 1.26795i 0.177548i
\(52\) −5.19615 3.00000i −0.720577 0.416025i
\(53\) 1.26795 2.19615i 0.174166 0.301665i −0.765706 0.643191i \(-0.777610\pi\)
0.939872 + 0.341526i \(0.110944\pi\)
\(54\) 3.46410 + 2.00000i 0.471405 + 0.272166i
\(55\) −7.09808 + 4.09808i −0.957104 + 0.552584i
\(56\) 3.46410 2.00000i 0.462910 0.267261i
\(57\) −0.803848 0.464102i −0.106472 0.0614718i
\(58\) −2.13397 + 3.69615i −0.280205 + 0.485329i
\(59\) −2.19615 1.26795i −0.285915 0.165073i 0.350183 0.936681i \(-0.386119\pi\)
−0.636098 + 0.771608i \(0.719453\pi\)
\(60\) 1.26795i 0.163692i
\(61\) 12.6962 7.33013i 1.62558 0.938527i 0.640184 0.768221i \(-0.278858\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) −0.633975 + 1.09808i −0.0805149 + 0.139456i
\(63\) −9.85641 −1.24179
\(64\) −1.00000 −0.125000
\(65\) 5.19615 9.00000i 0.644503 1.11631i
\(66\) 3.46410i 0.426401i
\(67\) −3.09808 5.36603i −0.378490 0.655564i 0.612353 0.790585i \(-0.290223\pi\)
−0.990843 + 0.135020i \(0.956890\pi\)
\(68\) 1.73205i 0.210042i
\(69\) 0.803848 0.464102i 0.0967719 0.0558713i
\(70\) 3.46410 + 6.00000i 0.414039 + 0.717137i
\(71\) −1.26795 2.19615i −0.150478 0.260635i 0.780925 0.624624i \(-0.214748\pi\)
−0.931403 + 0.363989i \(0.881415\pi\)
\(72\) 2.13397 + 1.23205i 0.251491 + 0.145199i
\(73\) −12.3923 −1.45041 −0.725205 0.688533i \(-0.758255\pi\)
−0.725205 + 0.688533i \(0.758255\pi\)
\(74\) −3.46410 + 5.00000i −0.402694 + 0.581238i
\(75\) −1.46410 −0.169060
\(76\) −1.09808 0.633975i −0.125958 0.0727219i
\(77\) −9.46410 16.3923i −1.07853 1.86808i
\(78\) −2.19615 3.80385i −0.248665 0.430701i
\(79\) −7.09808 + 4.09808i −0.798596 + 0.461070i −0.842980 0.537945i \(-0.819201\pi\)
0.0443840 + 0.999015i \(0.485867\pi\)
\(80\) 1.73205i 0.193649i
\(81\) −2.23205 3.86603i −0.248006 0.429558i
\(82\) 0.464102i 0.0512514i
\(83\) −5.83013 + 10.0981i −0.639940 + 1.10841i 0.345506 + 0.938417i \(0.387707\pi\)
−0.985446 + 0.169991i \(0.945626\pi\)
\(84\) 2.92820 0.319493
\(85\) 3.00000 0.325396
\(86\) 4.73205 8.19615i 0.510270 0.883814i
\(87\) −2.70577 + 1.56218i −0.290089 + 0.167483i
\(88\) 4.73205i 0.504438i
\(89\) 4.50000 + 2.59808i 0.476999 + 0.275396i 0.719165 0.694839i \(-0.244525\pi\)
−0.242166 + 0.970235i \(0.577858\pi\)
\(90\) −2.13397 + 3.69615i −0.224941 + 0.389609i
\(91\) 20.7846 + 12.0000i 2.17882 + 1.25794i
\(92\) 1.09808 0.633975i 0.114482 0.0660964i
\(93\) −0.803848 + 0.464102i −0.0833551 + 0.0481251i
\(94\) 10.0981 + 5.83013i 1.04154 + 0.601332i
\(95\) 1.09808 1.90192i 0.112660 0.195133i
\(96\) −0.633975 0.366025i −0.0647048 0.0373573i
\(97\) 5.19615i 0.527589i −0.964579 0.263795i \(-0.915026\pi\)
0.964579 0.263795i \(-0.0849741\pi\)
\(98\) −7.79423 + 4.50000i −0.787336 + 0.454569i
\(99\) 5.83013 10.0981i 0.585950 1.01489i
\(100\) −2.00000 −0.200000
\(101\) −0.464102 −0.0461798 −0.0230899 0.999733i \(-0.507350\pi\)
−0.0230899 + 0.999733i \(0.507350\pi\)
\(102\) 0.633975 1.09808i 0.0627728 0.108726i
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 5.07180i 0.494957i
\(106\) 2.19615 1.26795i 0.213309 0.123154i
\(107\) 8.19615 + 14.1962i 0.792352 + 1.37239i 0.924507 + 0.381165i \(0.124477\pi\)
−0.132155 + 0.991229i \(0.542190\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) −6.69615 3.86603i −0.641375 0.370298i 0.143769 0.989611i \(-0.454078\pi\)
−0.785144 + 0.619313i \(0.787411\pi\)
\(110\) −8.19615 −0.781472
\(111\) −4.02628 + 1.90192i −0.382158 + 0.180523i
\(112\) 4.00000 0.377964
\(113\) 17.1962 + 9.92820i 1.61768 + 0.933967i 0.987519 + 0.157501i \(0.0503437\pi\)
0.630159 + 0.776466i \(0.282990\pi\)
\(114\) −0.464102 0.803848i −0.0434671 0.0752872i
\(115\) 1.09808 + 1.90192i 0.102396 + 0.177355i
\(116\) −3.69615 + 2.13397i −0.343179 + 0.198135i
\(117\) 14.7846i 1.36684i
\(118\) −1.26795 2.19615i −0.116724 0.202172i
\(119\) 6.92820i 0.635107i
\(120\) 0.633975 1.09808i 0.0578737 0.100240i
\(121\) 11.3923 1.03566
\(122\) 14.6603 1.32728
\(123\) 0.169873 0.294229i 0.0153169 0.0265297i
\(124\) −1.09808 + 0.633975i −0.0986102 + 0.0569326i
\(125\) 12.1244i 1.08444i
\(126\) −8.53590 4.92820i −0.760438 0.439039i
\(127\) 5.29423 9.16987i 0.469787 0.813695i −0.529616 0.848237i \(-0.677664\pi\)
0.999403 + 0.0345426i \(0.0109974\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 6.00000 3.46410i 0.528271 0.304997i
\(130\) 9.00000 5.19615i 0.789352 0.455733i
\(131\) −7.09808 4.09808i −0.620162 0.358051i 0.156770 0.987635i \(-0.449892\pi\)
−0.776932 + 0.629585i \(0.783225\pi\)
\(132\) −1.73205 + 3.00000i −0.150756 + 0.261116i
\(133\) 4.39230 + 2.53590i 0.380861 + 0.219890i
\(134\) 6.19615i 0.535266i
\(135\) −6.00000 + 3.46410i −0.516398 + 0.298142i
\(136\) 0.866025 1.50000i 0.0742611 0.128624i
\(137\) −13.3923 −1.14418 −0.572091 0.820190i \(-0.693868\pi\)
−0.572091 + 0.820190i \(0.693868\pi\)
\(138\) 0.928203 0.0790139
\(139\) −0.901924 + 1.56218i −0.0765002 + 0.132502i −0.901738 0.432284i \(-0.857708\pi\)
0.825237 + 0.564786i \(0.191041\pi\)
\(140\) 6.92820i 0.585540i
\(141\) 4.26795 + 7.39230i 0.359426 + 0.622544i
\(142\) 2.53590i 0.212808i
\(143\) −24.5885 + 14.1962i −2.05619 + 1.18714i
\(144\) 1.23205 + 2.13397i 0.102671 + 0.177831i
\(145\) −3.69615 6.40192i −0.306949 0.531651i
\(146\) −10.7321 6.19615i −0.888191 0.512797i
\(147\) −6.58846 −0.543407
\(148\) −5.50000 + 2.59808i −0.452097 + 0.213561i
\(149\) 3.92820 0.321811 0.160905 0.986970i \(-0.448559\pi\)
0.160905 + 0.986970i \(0.448559\pi\)
\(150\) −1.26795 0.732051i −0.103528 0.0597717i
\(151\) 0.901924 + 1.56218i 0.0733975 + 0.127128i 0.900388 0.435087i \(-0.143282\pi\)
−0.826991 + 0.562215i \(0.809949\pi\)
\(152\) −0.633975 1.09808i −0.0514221 0.0890657i
\(153\) −3.69615 + 2.13397i −0.298816 + 0.172522i
\(154\) 18.9282i 1.52528i
\(155\) −1.09808 1.90192i −0.0881996 0.152766i
\(156\) 4.39230i 0.351666i
\(157\) 4.69615 8.13397i 0.374794 0.649162i −0.615502 0.788135i \(-0.711047\pi\)
0.990296 + 0.138973i \(0.0443802\pi\)
\(158\) −8.19615 −0.652051
\(159\) 1.85641 0.147223
\(160\) 0.866025 1.50000i 0.0684653 0.118585i
\(161\) −4.39230 + 2.53590i −0.346162 + 0.199857i
\(162\) 4.46410i 0.350733i
\(163\) −2.19615 1.26795i −0.172016 0.0993134i 0.411520 0.911401i \(-0.364998\pi\)
−0.583536 + 0.812087i \(0.698331\pi\)
\(164\) 0.232051 0.401924i 0.0181201 0.0313850i
\(165\) −5.19615 3.00000i −0.404520 0.233550i
\(166\) −10.0981 + 5.83013i −0.783763 + 0.452506i
\(167\) −6.00000 + 3.46410i −0.464294 + 0.268060i −0.713848 0.700301i \(-0.753049\pi\)
0.249554 + 0.968361i \(0.419716\pi\)
\(168\) 2.53590 + 1.46410i 0.195649 + 0.112958i
\(169\) 11.5000 19.9186i 0.884615 1.53220i
\(170\) 2.59808 + 1.50000i 0.199263 + 0.115045i
\(171\) 3.12436i 0.238925i
\(172\) 8.19615 4.73205i 0.624951 0.360815i
\(173\) 4.96410 8.59808i 0.377414 0.653700i −0.613271 0.789872i \(-0.710147\pi\)
0.990685 + 0.136173i \(0.0434802\pi\)
\(174\) −3.12436 −0.236857
\(175\) 8.00000 0.604743
\(176\) −2.36603 + 4.09808i −0.178346 + 0.308904i
\(177\) 1.85641i 0.139536i
\(178\) 2.59808 + 4.50000i 0.194734 + 0.337289i
\(179\) 11.3205i 0.846135i 0.906098 + 0.423067i \(0.139047\pi\)
−0.906098 + 0.423067i \(0.860953\pi\)
\(180\) −3.69615 + 2.13397i −0.275495 + 0.159057i
\(181\) 7.69615 + 13.3301i 0.572051 + 0.990821i 0.996355 + 0.0853011i \(0.0271852\pi\)
−0.424305 + 0.905519i \(0.639481\pi\)
\(182\) 12.0000 + 20.7846i 0.889499 + 1.54066i
\(183\) 9.29423 + 5.36603i 0.687049 + 0.396668i
\(184\) 1.26795 0.0934745
\(185\) −4.50000 9.52628i −0.330847 0.700386i
\(186\) −0.928203 −0.0680592
\(187\) −7.09808 4.09808i −0.519063 0.299681i
\(188\) 5.83013 + 10.0981i 0.425206 + 0.736478i
\(189\) −8.00000 13.8564i −0.581914 1.00791i
\(190\) 1.90192 1.09808i 0.137980 0.0796628i
\(191\) 24.5885i 1.77916i −0.456781 0.889579i \(-0.650998\pi\)
0.456781 0.889579i \(-0.349002\pi\)
\(192\) −0.366025 0.633975i −0.0264156 0.0457532i
\(193\) 12.1244i 0.872730i 0.899770 + 0.436365i \(0.143734\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 2.59808 4.50000i 0.186531 0.323081i
\(195\) 7.60770 0.544798
\(196\) −9.00000 −0.642857
\(197\) −13.1603 + 22.7942i −0.937629 + 1.62402i −0.167752 + 0.985829i \(0.553651\pi\)
−0.769877 + 0.638192i \(0.779682\pi\)
\(198\) 10.0981 5.83013i 0.717639 0.414329i
\(199\) 5.07180i 0.359530i 0.983710 + 0.179765i \(0.0575338\pi\)
−0.983710 + 0.179765i \(0.942466\pi\)
\(200\) −1.73205 1.00000i −0.122474 0.0707107i
\(201\) 2.26795 3.92820i 0.159969 0.277074i
\(202\) −0.401924 0.232051i −0.0282793 0.0163270i
\(203\) 14.7846 8.53590i 1.03768 0.599103i
\(204\) 1.09808 0.633975i 0.0768807 0.0443871i
\(205\) 0.696152 + 0.401924i 0.0486214 + 0.0280716i
\(206\) 3.46410 6.00000i 0.241355 0.418040i
\(207\) −2.70577 1.56218i −0.188064 0.108579i
\(208\) 6.00000i 0.416025i
\(209\) −5.19615 + 3.00000i −0.359425 + 0.207514i
\(210\) −2.53590 + 4.39230i −0.174994 + 0.303098i
\(211\) 12.3923 0.853121 0.426561 0.904459i \(-0.359725\pi\)
0.426561 + 0.904459i \(0.359725\pi\)
\(212\) 2.53590 0.174166
\(213\) 0.928203 1.60770i 0.0635994 0.110157i
\(214\) 16.3923i 1.12055i
\(215\) 8.19615 + 14.1962i 0.558973 + 0.968170i
\(216\) 4.00000i 0.272166i
\(217\) 4.39230 2.53590i 0.298169 0.172148i
\(218\) −3.86603 6.69615i −0.261840 0.453521i
\(219\) −4.53590 7.85641i −0.306508 0.530887i
\(220\) −7.09808 4.09808i −0.478552 0.276292i
\(221\) 10.3923 0.699062
\(222\) −4.43782 0.366025i −0.297847 0.0245660i
\(223\) −22.5885 −1.51263 −0.756317 0.654205i \(-0.773003\pi\)
−0.756317 + 0.654205i \(0.773003\pi\)
\(224\) 3.46410 + 2.00000i 0.231455 + 0.133631i
\(225\) 2.46410 + 4.26795i 0.164273 + 0.284530i
\(226\) 9.92820 + 17.1962i 0.660414 + 1.14387i
\(227\) −1.09808 + 0.633975i −0.0728819 + 0.0420784i −0.535998 0.844219i \(-0.680065\pi\)
0.463116 + 0.886298i \(0.346731\pi\)
\(228\) 0.928203i 0.0614718i
\(229\) 9.50000 + 16.4545i 0.627778 + 1.08734i 0.987997 + 0.154475i \(0.0493686\pi\)
−0.360219 + 0.932868i \(0.617298\pi\)
\(230\) 2.19615i 0.144810i
\(231\) 6.92820 12.0000i 0.455842 0.789542i
\(232\) −4.26795 −0.280205
\(233\) −4.60770 −0.301860 −0.150930 0.988544i \(-0.548227\pi\)
−0.150930 + 0.988544i \(0.548227\pi\)
\(234\) −7.39230 + 12.8038i −0.483250 + 0.837014i
\(235\) −17.4904 + 10.0981i −1.14095 + 0.658726i
\(236\) 2.53590i 0.165073i
\(237\) −5.19615 3.00000i −0.337526 0.194871i
\(238\) −3.46410 + 6.00000i −0.224544 + 0.388922i
\(239\) −4.39230 2.53590i −0.284115 0.164034i 0.351170 0.936312i \(-0.385784\pi\)
−0.635285 + 0.772278i \(0.719117\pi\)
\(240\) 1.09808 0.633975i 0.0708805 0.0409229i
\(241\) −15.5885 + 9.00000i −1.00414 + 0.579741i −0.909471 0.415768i \(-0.863513\pi\)
−0.0946700 + 0.995509i \(0.530180\pi\)
\(242\) 9.86603 + 5.69615i 0.634212 + 0.366163i
\(243\) 7.63397 13.2224i 0.489720 0.848219i
\(244\) 12.6962 + 7.33013i 0.812788 + 0.469263i
\(245\) 15.5885i 0.995910i
\(246\) 0.294229 0.169873i 0.0187593 0.0108307i
\(247\) 3.80385 6.58846i 0.242033 0.419213i
\(248\) −1.26795 −0.0805149
\(249\) −8.53590 −0.540941
\(250\) 6.06218 10.5000i 0.383406 0.664078i
\(251\) 5.07180i 0.320129i 0.987107 + 0.160064i \(0.0511702\pi\)
−0.987107 + 0.160064i \(0.948830\pi\)
\(252\) −4.92820 8.53590i −0.310448 0.537711i
\(253\) 6.00000i 0.377217i
\(254\) 9.16987 5.29423i 0.575369 0.332189i
\(255\) 1.09808 + 1.90192i 0.0687642 + 0.119103i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.69615 + 5.59808i 0.604829 + 0.349198i 0.770939 0.636909i \(-0.219787\pi\)
−0.166110 + 0.986107i \(0.553121\pi\)
\(258\) 6.92820 0.431331
\(259\) 22.0000 10.3923i 1.36701 0.645746i
\(260\) 10.3923 0.644503
\(261\) 9.10770 + 5.25833i 0.563752 + 0.325482i
\(262\) −4.09808 7.09808i −0.253180 0.438521i
\(263\) −11.6603 20.1962i −0.719002 1.24535i −0.961396 0.275170i \(-0.911266\pi\)
0.242393 0.970178i \(-0.422068\pi\)
\(264\) −3.00000 + 1.73205i −0.184637 + 0.106600i
\(265\) 4.39230i 0.269817i
\(266\) 2.53590 + 4.39230i 0.155486 + 0.269309i
\(267\) 3.80385i 0.232792i
\(268\) 3.09808 5.36603i 0.189245 0.327782i
\(269\) −7.60770 −0.463849 −0.231925 0.972734i \(-0.574502\pi\)
−0.231925 + 0.972734i \(0.574502\pi\)
\(270\) −6.92820 −0.421637
\(271\) 7.29423 12.6340i 0.443093 0.767459i −0.554824 0.831968i \(-0.687215\pi\)
0.997917 + 0.0645082i \(0.0205479\pi\)
\(272\) 1.50000 0.866025i 0.0909509 0.0525105i
\(273\) 17.5692i 1.06334i
\(274\) −11.5981 6.69615i −0.700665 0.404529i
\(275\) −4.73205 + 8.19615i −0.285353 + 0.494247i
\(276\) 0.803848 + 0.464102i 0.0483859 + 0.0279356i
\(277\) −5.89230 + 3.40192i −0.354034 + 0.204402i −0.666461 0.745540i \(-0.732192\pi\)
0.312426 + 0.949942i \(0.398858\pi\)
\(278\) −1.56218 + 0.901924i −0.0936932 + 0.0540938i
\(279\) 2.70577 + 1.56218i 0.161990 + 0.0935251i
\(280\) −3.46410 + 6.00000i −0.207020 + 0.358569i
\(281\) −9.69615 5.59808i −0.578424 0.333953i 0.182083 0.983283i \(-0.441716\pi\)
−0.760507 + 0.649330i \(0.775049\pi\)
\(282\) 8.53590i 0.508305i
\(283\) 2.19615 1.26795i 0.130548 0.0753718i −0.433304 0.901248i \(-0.642652\pi\)
0.563852 + 0.825876i \(0.309319\pi\)
\(284\) 1.26795 2.19615i 0.0752389 0.130318i
\(285\) 1.60770 0.0952316
\(286\) −28.3923 −1.67887
\(287\) −0.928203 + 1.60770i −0.0547901 + 0.0948992i
\(288\) 2.46410i 0.145199i
\(289\) −7.00000 12.1244i −0.411765 0.713197i
\(290\) 7.39230i 0.434091i
\(291\) 3.29423 1.90192i 0.193111 0.111493i
\(292\) −6.19615 10.7321i −0.362602 0.628046i
\(293\) −12.6962 21.9904i −0.741717 1.28469i −0.951713 0.306989i \(-0.900678\pi\)
0.209996 0.977702i \(-0.432655\pi\)
\(294\) −5.70577 3.29423i −0.332767 0.192123i
\(295\) 4.39230 0.255730
\(296\) −6.06218 0.500000i −0.352357 0.0290619i
\(297\) 18.9282 1.09833
\(298\) 3.40192 + 1.96410i 0.197068 + 0.113777i
\(299\) 3.80385 + 6.58846i 0.219982 + 0.381020i
\(300\) −0.732051 1.26795i −0.0422650 0.0732051i
\(301\) −32.7846 + 18.9282i −1.88967 + 1.09100i
\(302\) 1.80385i 0.103800i
\(303\) −0.169873 0.294229i −0.00975895 0.0169030i
\(304\) 1.26795i 0.0727219i
\(305\) −12.6962 + 21.9904i −0.726980 + 1.25917i
\(306\) −4.26795 −0.243982
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 9.46410 16.3923i 0.539267 0.934038i
\(309\) 4.39230 2.53590i 0.249869 0.144262i
\(310\) 2.19615i 0.124733i
\(311\) 14.1962 + 8.19615i 0.804990 + 0.464761i 0.845213 0.534430i \(-0.179474\pi\)
−0.0402231 + 0.999191i \(0.512807\pi\)
\(312\) 2.19615 3.80385i 0.124333 0.215350i
\(313\) 18.6962 + 10.7942i 1.05677 + 0.610126i 0.924537 0.381093i \(-0.124452\pi\)
0.132232 + 0.991219i \(0.457786\pi\)
\(314\) 8.13397 4.69615i 0.459027 0.265019i
\(315\) 14.7846 8.53590i 0.833018 0.480943i
\(316\) −7.09808 4.09808i −0.399298 0.230535i
\(317\) −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i \(-0.914667\pi\)
0.711535 + 0.702650i \(0.248000\pi\)
\(318\) 1.60770 + 0.928203i 0.0901551 + 0.0520511i
\(319\) 20.1962i 1.13077i
\(320\) 1.50000 0.866025i 0.0838525 0.0484123i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) −5.07180 −0.282640
\(323\) 2.19615 0.122197
\(324\) 2.23205 3.86603i 0.124003 0.214779i
\(325\) 12.0000i 0.665640i
\(326\) −1.26795 2.19615i −0.0702252 0.121634i
\(327\) 5.66025i 0.313013i
\(328\) 0.401924 0.232051i 0.0221925 0.0128129i
\(329\) −23.3205 40.3923i −1.28570 2.22690i
\(330\) −3.00000 5.19615i −0.165145 0.286039i
\(331\) −26.7846 15.4641i −1.47222 0.849984i −0.472703 0.881222i \(-0.656722\pi\)
−0.999512 + 0.0312377i \(0.990055\pi\)
\(332\) −11.6603 −0.639940
\(333\) 12.3205 + 8.53590i 0.675160 + 0.467764i
\(334\) −6.92820 −0.379094
\(335\) 9.29423 + 5.36603i 0.507798 + 0.293177i
\(336\) 1.46410 + 2.53590i 0.0798733 + 0.138345i
\(337\) 3.50000 + 6.06218i 0.190657 + 0.330228i 0.945468 0.325714i \(-0.105605\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(338\) 19.9186 11.5000i 1.08343 0.625518i
\(339\) 14.5359i 0.789482i
\(340\) 1.50000 + 2.59808i 0.0813489 + 0.140900i
\(341\) 6.00000i 0.324918i
\(342\) −1.56218 + 2.70577i −0.0844729 + 0.146311i
\(343\) 8.00000 0.431959
\(344\) 9.46410 0.510270
\(345\) −0.803848 + 1.39230i −0.0432777 + 0.0749592i
\(346\) 8.59808 4.96410i 0.462235 0.266872i
\(347\) 10.0526i 0.539650i −0.962909 0.269825i \(-0.913034\pi\)
0.962909 0.269825i \(-0.0869658\pi\)
\(348\) −2.70577 1.56218i −0.145045 0.0837415i
\(349\) 3.30385 5.72243i 0.176851 0.306315i −0.763949 0.645276i \(-0.776742\pi\)
0.940800 + 0.338961i \(0.110076\pi\)
\(350\) 6.92820 + 4.00000i 0.370328 + 0.213809i
\(351\) −20.7846 + 12.0000i −1.10940 + 0.640513i
\(352\) −4.09808 + 2.36603i −0.218428 + 0.126110i
\(353\) 26.0885 + 15.0622i 1.38855 + 0.801679i 0.993152 0.116832i \(-0.0372738\pi\)
0.395397 + 0.918510i \(0.370607\pi\)
\(354\) 0.928203 1.60770i 0.0493334 0.0854480i
\(355\) 3.80385 + 2.19615i 0.201887 + 0.116560i
\(356\) 5.19615i 0.275396i
\(357\) −4.39230 + 2.53590i −0.232465 + 0.134214i
\(358\) −5.66025 + 9.80385i −0.299154 + 0.518149i
\(359\) 33.4641 1.76617 0.883084 0.469215i \(-0.155463\pi\)
0.883084 + 0.469215i \(0.155463\pi\)
\(360\) −4.26795 −0.224941
\(361\) −8.69615 + 15.0622i −0.457692 + 0.792746i
\(362\) 15.3923i 0.809002i
\(363\) 4.16987 + 7.22243i 0.218862 + 0.379079i
\(364\) 24.0000i 1.25794i
\(365\) 18.5885 10.7321i 0.972964 0.561741i
\(366\) 5.36603 + 9.29423i 0.280487 + 0.485817i
\(367\) −0.196152 0.339746i −0.0102391 0.0177346i 0.860860 0.508841i \(-0.169926\pi\)
−0.871100 + 0.491106i \(0.836593\pi\)
\(368\) 1.09808 + 0.633975i 0.0572412 + 0.0330482i
\(369\) −1.14359 −0.0595331
\(370\) 0.866025 10.5000i 0.0450225 0.545869i
\(371\) −10.1436 −0.526629
\(372\) −0.803848 0.464102i −0.0416776 0.0240625i
\(373\) 9.89230 + 17.1340i 0.512204 + 0.887164i 0.999900 + 0.0141499i \(0.00450421\pi\)
−0.487696 + 0.873014i \(0.662162\pi\)
\(374\) −4.09808 7.09808i −0.211906 0.367033i
\(375\) 7.68653 4.43782i 0.396931 0.229168i
\(376\) 11.6603i 0.601332i
\(377\) −12.8038 22.1769i −0.659432 1.14217i
\(378\) 16.0000i 0.822951i
\(379\) −12.3923 + 21.4641i −0.636550 + 1.10254i 0.349635 + 0.936886i \(0.386306\pi\)
−0.986184 + 0.165651i \(0.947028\pi\)
\(380\) 2.19615 0.112660
\(381\) 7.75129 0.397111
\(382\) 12.2942 21.2942i 0.629027 1.08951i
\(383\) 22.3923 12.9282i 1.14419 0.660600i 0.196728 0.980458i \(-0.436968\pi\)
0.947466 + 0.319858i \(0.103635\pi\)
\(384\) 0.732051i 0.0373573i
\(385\) 28.3923 + 16.3923i 1.44701 + 0.835429i
\(386\) −6.06218 + 10.5000i −0.308557 + 0.534436i
\(387\) −20.1962 11.6603i −1.02663 0.592724i
\(388\) 4.50000 2.59808i 0.228453 0.131897i
\(389\) 0.696152 0.401924i 0.0352963 0.0203783i −0.482248 0.876035i \(-0.660180\pi\)
0.517544 + 0.855656i \(0.326846\pi\)
\(390\) 6.58846 + 3.80385i 0.333620 + 0.192615i
\(391\) −1.09808 + 1.90192i −0.0555321 + 0.0961844i
\(392\) −7.79423 4.50000i −0.393668 0.227284i
\(393\) 6.00000i 0.302660i
\(394\) −22.7942 + 13.1603i −1.14836 + 0.663004i
\(395\) 7.09808 12.2942i 0.357143 0.618590i
\(396\) 11.6603 0.585950
\(397\) −5.00000 −0.250943 −0.125471 0.992097i \(-0.540044\pi\)
−0.125471 + 0.992097i \(0.540044\pi\)
\(398\) −2.53590 + 4.39230i −0.127113 + 0.220166i
\(399\) 3.71281i 0.185873i
\(400\) −1.00000 1.73205i −0.0500000 0.0866025i
\(401\) 14.7846i 0.738308i 0.929368 + 0.369154i \(0.120353\pi\)
−0.929368 + 0.369154i \(0.879647\pi\)
\(402\) 3.92820 2.26795i 0.195921 0.113115i
\(403\) −3.80385 6.58846i −0.189483 0.328194i
\(404\) −0.232051 0.401924i −0.0115450 0.0199965i
\(405\) 6.69615 + 3.86603i 0.332734 + 0.192104i
\(406\) 17.0718 0.847259
\(407\) −2.36603 + 28.6865i −0.117280 + 1.42194i
\(408\) 1.26795 0.0627728
\(409\) −29.0885 16.7942i −1.43833 0.830421i −0.440598 0.897705i \(-0.645233\pi\)
−0.997734 + 0.0672835i \(0.978567\pi\)
\(410\) 0.401924 + 0.696152i 0.0198496 + 0.0343805i
\(411\) −4.90192 8.49038i −0.241794 0.418800i
\(412\) 6.00000 3.46410i 0.295599 0.170664i
\(413\) 10.1436i 0.499134i
\(414\) −1.56218 2.70577i −0.0767769 0.132981i
\(415\) 20.1962i 0.991390i
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) −1.32051 −0.0646656
\(418\) −6.00000 −0.293470
\(419\) −5.07180 + 8.78461i −0.247773 + 0.429156i −0.962908 0.269831i \(-0.913032\pi\)
0.715134 + 0.698987i \(0.246366\pi\)
\(420\) −4.39230 + 2.53590i −0.214323 + 0.123739i
\(421\) 3.33975i 0.162769i −0.996683 0.0813846i \(-0.974066\pi\)
0.996683 0.0813846i \(-0.0259342\pi\)
\(422\) 10.7321 + 6.19615i 0.522428 + 0.301624i
\(423\) 14.3660 24.8827i 0.698500 1.20984i
\(424\) 2.19615 + 1.26795i 0.106655 + 0.0615771i
\(425\) 3.00000 1.73205i 0.145521 0.0840168i
\(426\) 1.60770 0.928203i 0.0778931 0.0449716i
\(427\) −50.7846 29.3205i −2.45764 1.41892i
\(428\) −8.19615 + 14.1962i −0.396176 + 0.686197i
\(429\) −18.0000 10.3923i −0.869048 0.501745i
\(430\) 16.3923i 0.790507i
\(431\) 19.0981 11.0263i 0.919922 0.531117i 0.0363118 0.999341i \(-0.488439\pi\)
0.883610 + 0.468223i \(0.155106\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) −12.6077 −0.605887 −0.302944 0.953008i \(-0.597969\pi\)
−0.302944 + 0.953008i \(0.597969\pi\)
\(434\) 5.07180 0.243454
\(435\) 2.70577 4.68653i 0.129732 0.224702i
\(436\) 7.73205i 0.370298i
\(437\) 0.803848 + 1.39230i 0.0384532 + 0.0666030i
\(438\) 9.07180i 0.433467i
\(439\) 2.19615 1.26795i 0.104817 0.0605159i −0.446675 0.894696i \(-0.647392\pi\)
0.551492 + 0.834180i \(0.314059\pi\)
\(440\) −4.09808 7.09808i −0.195368 0.338388i
\(441\) 11.0885 + 19.2058i 0.528022 + 0.914561i
\(442\) 9.00000 + 5.19615i 0.428086 + 0.247156i
\(443\) −9.46410 −0.449653 −0.224827 0.974399i \(-0.572182\pi\)
−0.224827 + 0.974399i \(0.572182\pi\)
\(444\) −3.66025 2.53590i −0.173708 0.120348i
\(445\) −9.00000 −0.426641
\(446\) −19.5622 11.2942i −0.926296 0.534797i
\(447\) 1.43782 + 2.49038i 0.0680067 + 0.117791i
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) 9.58846 5.53590i 0.452507 0.261255i −0.256381 0.966576i \(-0.582530\pi\)
0.708889 + 0.705321i \(0.249197\pi\)
\(450\) 4.92820i 0.232318i
\(451\) −1.09808 1.90192i −0.0517064 0.0895581i
\(452\) 19.8564i 0.933967i
\(453\) −0.660254 + 1.14359i −0.0310214 + 0.0537307i
\(454\) −1.26795 −0.0595078
\(455\) −41.5692 −1.94880
\(456\) 0.464102 0.803848i 0.0217335 0.0376436i
\(457\) 27.6962 15.9904i 1.29557 0.747998i 0.315935 0.948781i \(-0.397682\pi\)
0.979636 + 0.200782i \(0.0643484\pi\)
\(458\) 19.0000i 0.887812i
\(459\) −6.00000 3.46410i −0.280056 0.161690i
\(460\) −1.09808 + 1.90192i −0.0511981 + 0.0886777i
\(461\) −18.8038 10.8564i −0.875782 0.505633i −0.00651699 0.999979i \(-0.502074\pi\)
−0.869266 + 0.494346i \(0.835408\pi\)
\(462\) 12.0000 6.92820i 0.558291 0.322329i
\(463\) 18.5885 10.7321i 0.863879 0.498761i −0.00143043 0.999999i \(-0.500455\pi\)
0.865309 + 0.501238i \(0.167122\pi\)
\(464\) −3.69615 2.13397i −0.171590 0.0990673i
\(465\) 0.803848 1.39230i 0.0372775 0.0645666i
\(466\) −3.99038 2.30385i −0.184851 0.106724i
\(467\) 18.2487i 0.844450i 0.906491 + 0.422225i \(0.138751\pi\)
−0.906491 + 0.422225i \(0.861249\pi\)
\(468\) −12.8038 + 7.39230i −0.591858 + 0.341709i
\(469\) −12.3923 + 21.4641i −0.572223 + 0.991120i
\(470\) −20.1962 −0.931579
\(471\) 6.87564 0.316813
\(472\) 1.26795 2.19615i 0.0583621 0.101086i
\(473\) 44.7846i 2.05920i
\(474\) −3.00000 5.19615i −0.137795 0.238667i
\(475\) 2.53590i 0.116355i
\(476\) −6.00000 + 3.46410i −0.275010 + 0.158777i
\(477\) −3.12436 5.41154i −0.143054 0.247778i
\(478\) −2.53590 4.39230i −0.115989 0.200899i
\(479\) 2.19615 + 1.26795i 0.100345 + 0.0579341i 0.549333 0.835604i \(-0.314882\pi\)
−0.448988 + 0.893538i \(0.648215\pi\)
\(480\) 1.26795 0.0578737
\(481\) −15.5885 33.0000i −0.710772 1.50467i
\(482\) −18.0000 −0.819878
\(483\) −3.21539 1.85641i −0.146305 0.0844694i
\(484\) 5.69615 + 9.86603i 0.258916 + 0.448456i
\(485\) 4.50000 + 7.79423i 0.204334 + 0.353918i
\(486\) 13.2224 7.63397i 0.599782 0.346284i
\(487\) 10.0526i 0.455525i 0.973717 + 0.227762i \(0.0731410\pi\)
−0.973717 + 0.227762i \(0.926859\pi\)
\(488\) 7.33013 + 12.6962i 0.331819 + 0.574728i
\(489\) 1.85641i 0.0839496i
\(490\) 7.79423 13.5000i 0.352107 0.609868i
\(491\) −22.9808 −1.03711 −0.518554 0.855045i \(-0.673529\pi\)
−0.518554 + 0.855045i \(0.673529\pi\)
\(492\) 0.339746 0.0153169
\(493\) 3.69615 6.40192i 0.166466 0.288328i
\(494\) 6.58846 3.80385i 0.296429 0.171143i
\(495\) 20.1962i 0.907750i
\(496\) −1.09808 0.633975i −0.0493051 0.0284663i
\(497\) −5.07180 + 8.78461i −0.227501 + 0.394044i
\(498\) −7.39230 4.26795i −0.331257 0.191251i
\(499\) 7.09808 4.09808i 0.317754 0.183455i −0.332637 0.943055i \(-0.607938\pi\)
0.650391 + 0.759600i \(0.274605\pi\)
\(500\) 10.5000 6.06218i 0.469574 0.271109i
\(501\) −4.39230 2.53590i −0.196234 0.113296i
\(502\) −2.53590 + 4.39230i −0.113183 + 0.196038i
\(503\) 10.9019 + 6.29423i 0.486093 + 0.280646i 0.722952 0.690898i \(-0.242785\pi\)
−0.236859 + 0.971544i \(0.576118\pi\)
\(504\) 9.85641i 0.439039i
\(505\) 0.696152 0.401924i 0.0309784 0.0178854i
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 16.8372 0.747765
\(508\) 10.5885 0.469787
\(509\) −15.8205 + 27.4019i −0.701232 + 1.21457i 0.266803 + 0.963751i \(0.414033\pi\)
−0.968034 + 0.250818i \(0.919301\pi\)
\(510\) 2.19615i 0.0972473i
\(511\) 24.7846 + 42.9282i 1.09641 + 1.89903i
\(512\) 1.00000i 0.0441942i
\(513\) −4.39230 + 2.53590i −0.193925 + 0.111963i
\(514\) 5.59808 + 9.69615i 0.246921 + 0.427679i
\(515\) 6.00000 + 10.3923i 0.264392 + 0.457940i
\(516\) 6.00000 + 3.46410i 0.264135 + 0.152499i
\(517\) 55.1769 2.42668
\(518\) 24.2487 + 2.00000i 1.06543 + 0.0878750i
\(519\) 7.26795 0.319028
\(520\) 9.00000 + 5.19615i 0.394676 + 0.227866i
\(521\) −13.2679 22.9808i −0.581279 1.00681i −0.995328 0.0965507i \(-0.969219\pi\)
0.414049 0.910255i \(-0.364114\pi\)
\(522\) 5.25833 + 9.10770i 0.230151 + 0.398633i
\(523\) 10.9019 6.29423i 0.476708 0.275227i −0.242336 0.970192i \(-0.577914\pi\)
0.719043 + 0.694965i \(0.244580\pi\)
\(524\) 8.19615i 0.358051i
\(525\) 2.92820 + 5.07180i 0.127797 + 0.221351i
\(526\) 23.3205i 1.01682i
\(527\) 1.09808 1.90192i 0.0478330 0.0828491i
\(528\) −3.46410 −0.150756
\(529\) 21.3923 0.930100
\(530\) −2.19615 + 3.80385i −0.0953948 + 0.165229i
\(531\) −5.41154 + 3.12436i −0.234841 + 0.135585i
\(532\) 5.07180i 0.219890i
\(533\) 2.41154 + 1.39230i 0.104456 + 0.0603074i
\(534\) −1.90192 + 3.29423i −0.0823043 + 0.142555i
\(535\) −24.5885 14.1962i −1.06305 0.613753i
\(536\) 5.36603 3.09808i 0.231777 0.133817i
\(537\) −7.17691 + 4.14359i −0.309707 + 0.178809i
\(538\) −6.58846 3.80385i −0.284049 0.163996i
\(539\) −21.2942 + 36.8827i −0.917207 + 1.58865i
\(540\) −6.00000 3.46410i −0.258199 0.149071i
\(541\) 3.58846i 0.154280i −0.997020 0.0771399i \(-0.975421\pi\)
0.997020 0.0771399i \(-0.0245788\pi\)
\(542\) 12.6340 7.29423i 0.542676 0.313314i
\(543\) −5.63397 + 9.75833i −0.241777 + 0.418770i
\(544\) 1.73205 0.0742611
\(545\) 13.3923 0.573663
\(546\) −8.78461 + 15.2154i −0.375947 + 0.651159i
\(547\) 12.5885i 0.538244i 0.963106 + 0.269122i \(0.0867334\pi\)
−0.963106 + 0.269122i \(0.913267\pi\)
\(548\) −6.69615 11.5981i −0.286045 0.495445i
\(549\) 36.1244i 1.54175i
\(550\) −8.19615 + 4.73205i −0.349485 + 0.201775i
\(551\) −2.70577 4.68653i −0.115270 0.199653i
\(552\) 0.464102 + 0.803848i 0.0197535 + 0.0342140i
\(553\) 28.3923 + 16.3923i 1.20736 + 0.697072i
\(554\) −6.80385 −0.289068
\(555\) 4.39230 6.33975i 0.186443 0.269107i
\(556\) −1.80385 −0.0765002
\(557\) 9.10770 + 5.25833i 0.385905 + 0.222803i 0.680385 0.732855i \(-0.261813\pi\)
−0.294479 + 0.955658i \(0.595146\pi\)
\(558\) 1.56218 + 2.70577i 0.0661323 + 0.114544i
\(559\) 28.3923 + 49.1769i 1.20087 + 2.07996i
\(560\) −6.00000 + 3.46410i −0.253546 + 0.146385i
\(561\) 6.00000i 0.253320i
\(562\) −5.59808 9.69615i −0.236141 0.409008i
\(563\) 11.4115i 0.480939i −0.970657 0.240470i \(-0.922699\pi\)
0.970657 0.240470i \(-0.0773014\pi\)
\(564\) −4.26795 + 7.39230i −0.179713 + 0.311272i
\(565\) −34.3923 −1.44690
\(566\) 2.53590 0.106592
\(567\) −8.92820 + 15.4641i −0.374949 + 0.649431i
\(568\) 2.19615 1.26795i 0.0921485 0.0532020i
\(569\) 28.5167i 1.19548i 0.801690 + 0.597740i \(0.203935\pi\)
−0.801690 + 0.597740i \(0.796065\pi\)
\(570\) 1.39230 + 0.803848i 0.0583172 + 0.0336695i
\(571\) −7.49038 + 12.9737i −0.313463 + 0.542933i −0.979110 0.203334i \(-0.934822\pi\)
0.665647 + 0.746267i \(0.268156\pi\)
\(572\) −24.5885 14.1962i −1.02810 0.593571i
\(573\) 15.5885 9.00000i 0.651217 0.375980i
\(574\) −1.60770 + 0.928203i −0.0671039 + 0.0387425i
\(575\) 2.19615 + 1.26795i 0.0915859 + 0.0528771i
\(576\) −1.23205 + 2.13397i −0.0513355 + 0.0889156i
\(577\) 3.58846 + 2.07180i 0.149389 + 0.0862500i 0.572831 0.819673i \(-0.305845\pi\)
−0.423442 + 0.905923i \(0.639178\pi\)
\(578\) 14.0000i 0.582323i
\(579\) −7.68653 + 4.43782i −0.319441 + 0.184430i
\(580\) 3.69615 6.40192i 0.153474 0.265825i
\(581\) 46.6410 1.93500
\(582\) 3.80385 0.157675
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 12.3923i 0.512797i
\(585\) −12.8038 22.1769i −0.529374 0.916903i
\(586\) 25.3923i 1.04895i
\(587\) 19.0981 11.0263i 0.788262 0.455103i −0.0510884 0.998694i \(-0.516269\pi\)
0.839350 + 0.543591i \(0.182936\pi\)
\(588\) −3.29423 5.70577i −0.135852 0.235302i
\(589\) −0.803848 1.39230i −0.0331220 0.0573689i
\(590\) 3.80385 + 2.19615i 0.156602 + 0.0904142i
\(591\) −19.2679 −0.792578
\(592\) −5.00000 3.46410i −0.205499 0.142374i
\(593\) 23.5359 0.966504 0.483252 0.875481i \(-0.339456\pi\)
0.483252 + 0.875481i \(0.339456\pi\)
\(594\) 16.3923 + 9.46410i 0.672584 + 0.388317i
\(595\) −6.00000 10.3923i −0.245976 0.426043i
\(596\) 1.96410 + 3.40192i 0.0804527 + 0.139348i
\(597\) −3.21539 + 1.85641i −0.131597 + 0.0759777i
\(598\) 7.60770i 0.311102i
\(599\) −2.36603 4.09808i −0.0966732 0.167443i 0.813633 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413937i \(0.864153\pi\)
\(600\) 1.46410i 0.0597717i
\(601\) 12.8923 22.3301i 0.525888 0.910865i −0.473657 0.880709i \(-0.657066\pi\)
0.999545 0.0301556i \(-0.00960027\pi\)
\(602\) −37.8564 −1.54291
\(603\) −15.2679 −0.621759
\(604\) −0.901924 + 1.56218i −0.0366988 + 0.0635641i
\(605\) −17.0885 + 9.86603i −0.694745 + 0.401111i
\(606\) 0.339746i 0.0138012i
\(607\) 1.68653 + 0.973721i 0.0684543 + 0.0395221i 0.533836 0.845588i \(-0.320750\pi\)
−0.465382 + 0.885110i \(0.654083\pi\)
\(608\) 0.633975 1.09808i 0.0257111 0.0445329i
\(609\) 10.8231 + 6.24871i 0.438574 + 0.253211i
\(610\) −21.9904 + 12.6962i −0.890365 + 0.514052i
\(611\) −60.5885 + 34.9808i −2.45115 + 1.41517i
\(612\) −3.69615 2.13397i −0.149408 0.0862608i
\(613\) −6.30385 + 10.9186i −0.254610 + 0.440997i −0.964790 0.263023i \(-0.915280\pi\)
0.710180 + 0.704021i \(0.248614\pi\)
\(614\) −3.46410 2.00000i −0.139800 0.0807134i
\(615\) 0.588457i 0.0237289i
\(616\) 16.3923 9.46410i 0.660465 0.381320i
\(617\) −11.6603 + 20.1962i −0.469424 + 0.813066i −0.999389 0.0349532i \(-0.988872\pi\)
0.529965 + 0.848020i \(0.322205\pi\)
\(618\) 5.07180 0.204018
\(619\) 21.1769 0.851172 0.425586 0.904918i \(-0.360068\pi\)
0.425586 + 0.904918i \(0.360068\pi\)
\(620\) 1.09808 1.90192i 0.0440998 0.0763831i
\(621\) 5.07180i 0.203524i
\(622\) 8.19615 + 14.1962i 0.328636 + 0.569214i
\(623\) 20.7846i 0.832718i
\(624\) 3.80385 2.19615i 0.152276 0.0879165i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 10.7942 + 18.6962i 0.431424 + 0.747249i
\(627\) −3.80385 2.19615i −0.151911 0.0877059i
\(628\) 9.39230 0.374794
\(629\) 6.00000 8.66025i 0.239236 0.345307i
\(630\) 17.0718 0.680157
\(631\) −25.6865 14.8301i −1.02256 0.590378i −0.107719 0.994181i \(-0.534355\pi\)
−0.914846 + 0.403803i \(0.867688\pi\)
\(632\) −4.09808 7.09808i −0.163013 0.282346i
\(633\) 4.53590 + 7.85641i 0.180286 + 0.312264i
\(634\) −7.79423 + 4.50000i −0.309548 + 0.178718i
\(635\) 18.3397i 0.727791i
\(636\) 0.928203 + 1.60770i 0.0368057 + 0.0637493i
\(637\) 54.0000i 2.13956i
\(638\) −10.0981 + 17.4904i −0.399787 + 0.692451i
\(639\) −6.24871 −0.247195
\(640\) 1.73205 0.0684653
\(641\) 9.57180 16.5788i 0.378063 0.654825i −0.612717 0.790302i \(-0.709924\pi\)
0.990780 + 0.135478i \(0.0432569\pi\)
\(642\) −10.3923 + 6.00000i −0.410152 + 0.236801i
\(643\) 15.1244i 0.596446i −0.954496 0.298223i \(-0.903606\pi\)
0.954496 0.298223i \(-0.0963940\pi\)
\(644\) −4.39230 2.53590i −0.173081 0.0999284i
\(645\) −6.00000 + 10.3923i −0.236250 + 0.409197i
\(646\) 1.90192 + 1.09808i 0.0748302 + 0.0432032i
\(647\) 2.19615 1.26795i 0.0863397 0.0498482i −0.456209 0.889873i \(-0.650793\pi\)
0.542548 + 0.840025i \(0.317460\pi\)
\(648\) 3.86603 2.23205i 0.151872 0.0876832i
\(649\) −10.3923 6.00000i −0.407934 0.235521i
\(650\) 6.00000 10.3923i 0.235339 0.407620i
\(651\) 3.21539 + 1.85641i 0.126021 + 0.0727583i
\(652\) 2.53590i 0.0993134i
\(653\) −14.8923 + 8.59808i −0.582781 + 0.336469i −0.762238 0.647297i \(-0.775899\pi\)
0.179457 + 0.983766i \(0.442566\pi\)
\(654\) 2.83013 4.90192i 0.110667 0.191680i
\(655\) 14.1962 0.554690
\(656\) 0.464102 0.0181201
\(657\) −15.2679 + 26.4449i −0.595659 + 1.03171i
\(658\) 46.6410i 1.81826i
\(659\) −10.7321 18.5885i −0.418061 0.724103i 0.577683 0.816261i \(-0.303957\pi\)
−0.995744 + 0.0921577i \(0.970624\pi\)
\(660\) 6.00000i 0.233550i
\(661\) −16.2846 + 9.40192i −0.633398 + 0.365692i −0.782067 0.623195i \(-0.785834\pi\)
0.148669 + 0.988887i \(0.452501\pi\)
\(662\) −15.4641 26.7846i −0.601029 1.04101i
\(663\) 3.80385 + 6.58846i 0.147729 + 0.255874i
\(664\) −10.0981 5.83013i −0.391881 0.226253i
\(665\) −8.78461 −0.340653
\(666\) 6.40192 + 13.5526i 0.248070 + 0.525151i
\(667\) 5.41154 0.209536
\(668\) −6.00000 3.46410i −0.232147 0.134030i
\(669\) −8.26795 14.3205i −0.319657 0.553663i
\(670\) 5.36603 + 9.29423i 0.207308 + 0.359067i
\(671\) 60.0788 34.6865i 2.31932 1.33906i
\(672\) 2.92820i 0.112958i
\(673\) −4.19615 7.26795i −0.161750 0.280159i 0.773747 0.633495i \(-0.218380\pi\)
−0.935496 + 0.353336i \(0.885047\pi\)
\(674\) 7.00000i 0.269630i
\(675\) −4.00000 + 6.92820i −0.153960 + 0.266667i
\(676\) 23.0000 0.884615
\(677\) 34.8564 1.33964 0.669820 0.742523i \(-0.266371\pi\)
0.669820 + 0.742523i \(0.266371\pi\)
\(678\) −7.26795 + 12.5885i −0.279124 + 0.483457i
\(679\) −18.0000 + 10.3923i −0.690777 + 0.398820i
\(680\) 3.00000i 0.115045i
\(681\) −0.803848 0.464102i −0.0308035 0.0177844i
\(682\) −3.00000 + 5.19615i −0.114876 + 0.198971i
\(683\) −14.7846 8.53590i −0.565717 0.326617i 0.189720 0.981838i \(-0.439242\pi\)
−0.755437 + 0.655221i \(0.772575\pi\)
\(684\) −2.70577 + 1.56218i −0.103458 + 0.0597314i
\(685\) 20.0885 11.5981i 0.767540 0.443140i
\(686\) 6.92820 + 4.00000i 0.264520 + 0.152721i
\(687\) −6.95448 + 12.0455i −0.265330 + 0.459565i
\(688\) 8.19615 + 4.73205i 0.312475 + 0.180408i
\(689\) 15.2154i 0.579660i
\(690\) −1.39230 + 0.803848i −0.0530041 + 0.0306020i
\(691\) 11.0981 19.2224i 0.422191 0.731256i −0.573963 0.818881i \(-0.694595\pi\)
0.996153 + 0.0876256i \(0.0279279\pi\)
\(692\) 9.92820 0.377414
\(693\) −46.6410 −1.77175
\(694\) 5.02628 8.70577i 0.190795 0.330467i
\(695\) 3.12436i 0.118514i
\(696\) −1.56218 2.70577i −0.0592142 0.102562i
\(697\) 0.803848i 0.0304479i
\(698\) 5.72243 3.30385i 0.216597 0.125052i
\(699\) −1.68653 2.92116i −0.0637906 0.110488i
\(700\) 4.00000 + 6.92820i 0.151186 + 0.261861i
\(701\) 1.60770 + 0.928203i 0.0607218 + 0.0350578i 0.530054 0.847964i \(-0.322172\pi\)
−0.469332 + 0.883022i \(0.655505\pi\)
\(702\) −24.0000 −0.905822
\(703\) −3.29423 6.97372i −0.124244 0.263019i
\(704\) −4.73205 −0.178346
\(705\) −12.8038 7.39230i −0.482221 0.278410i
\(706\) 15.0622 + 26.0885i 0.566873 + 0.981852i
\(707\) 0.928203 + 1.60770i 0.0349087 + 0.0604636i
\(708\) 1.60770 0.928203i 0.0604209 0.0348840i
\(709\) 30.0000i 1.12667i 0.826227 + 0.563337i \(0.190483\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 2.19615 + 3.80385i 0.0824201 + 0.142756i
\(711\) 20.1962i 0.757415i
\(712\) −2.59808 + 4.50000i −0.0973670 + 0.168645i
\(713\) 1.60770 0.0602087
\(714\) −5.07180 −0.189807
\(715\) 24.5885 42.5885i 0.919556 1.59272i
\(716\) −9.80385 + 5.66025i −0.366387 + 0.211534i
\(717\) 3.71281i 0.138658i
\(718\) 28.9808 + 16.7321i 1.08155 + 0.624435i
\(719\) 16.2224 28.0981i 0.604995 1.04788i −0.387058 0.922055i \(-0.626509\pi\)
0.992052 0.125826i \(-0.0401581\pi\)
\(720\) −3.69615 2.13397i −0.137747 0.0795285i
\(721\) −24.0000 + 13.8564i −0.893807 + 0.516040i
\(722\) −15.0622 + 8.69615i −0.560556 + 0.323637i
\(723\) −11.4115 6.58846i −0.424400 0.245027i
\(724\) −7.69615 + 13.3301i −0.286025 + 0.495410i
\(725\) −7.39230 4.26795i −0.274543 0.158508i
\(726\) 8.33975i 0.309517i
\(727\) −1.60770 + 0.928203i −0.0596261 + 0.0344252i −0.529517 0.848300i \(-0.677627\pi\)
0.469891 + 0.882725i \(0.344293\pi\)
\(728\) −12.0000 + 20.7846i −0.444750 + 0.770329i
\(729\) −2.21539 −0.0820515
\(730\) 21.4641 0.794422
\(731\) −8.19615 + 14.1962i −0.303146 + 0.525064i
\(732\) 10.7321i 0.396668i
\(733\) −7.80385 13.5167i −0.288242 0.499249i 0.685148 0.728403i \(-0.259737\pi\)
−0.973390 + 0.229154i \(0.926404\pi\)
\(734\) 0.392305i 0.0144802i
\(735\) 9.88269 5.70577i 0.364528 0.210461i
\(736\) 0.633975 + 1.09808i 0.0233686 + 0.0404756i
\(737\) −14.6603 25.3923i −0.540017 0.935338i
\(738\) −0.990381 0.571797i −0.0364564 0.0210481i
\(739\) 6.98076 0.256791 0.128396 0.991723i \(-0.459017\pi\)
0.128396 + 0.991723i \(0.459017\pi\)
\(740\) 6.00000 8.66025i 0.220564 0.318357i
\(741\) 5.56922 0.204590
\(742\) −8.78461 5.07180i −0.322493 0.186192i
\(743\) 20.9545 + 36.2942i 0.768745 + 1.33151i 0.938244 + 0.345976i \(0.112452\pi\)
−0.169498 + 0.985531i \(0.554215\pi\)
\(744\) −0.464102 0.803848i −0.0170148 0.0294705i
\(745\) −5.89230 + 3.40192i −0.215877 + 0.124637i
\(746\) 19.7846i 0.724366i
\(747\) 14.3660 + 24.8827i 0.525625 + 0.910410i
\(748\) 8.19615i 0.299681i
\(749\) 32.7846 56.7846i 1.19792 2.07486i
\(750\) 8.87564 0.324093
\(751\) −36.3923 −1.32797 −0.663987 0.747744i \(-0.731137\pi\)
−0.663987 + 0.747744i \(0.731137\pi\)
\(752\) −5.83013 + 10.0981i −0.212603 + 0.368239i
\(753\) −3.21539 + 1.85641i −0.117175 + 0.0676512i
\(754\) 25.6077i 0.932577i
\(755\) −2.70577 1.56218i −0.0984731 0.0568535i
\(756\) 8.00000 13.8564i 0.290957 0.503953i
\(757\) 3.69615 + 2.13397i 0.134339 + 0.0775606i 0.565663 0.824636i \(-0.308620\pi\)
−0.431324 + 0.902197i \(0.641954\pi\)
\(758\) −21.4641 + 12.3923i −0.779611 + 0.450109i
\(759\) 3.80385 2.19615i 0.138071 0.0797153i
\(760\) 1.90192 + 1.09808i 0.0689900 + 0.0398314i
\(761\) −16.1603 + 27.9904i −0.585809 + 1.01465i 0.408965 + 0.912550i \(0.365890\pi\)
−0.994774 + 0.102101i \(0.967444\pi\)
\(762\) 6.71281 + 3.87564i 0.243180 + 0.140400i
\(763\) 30.9282i 1.11968i
\(764\) 21.2942 12.2942i 0.770398 0.444790i
\(765\) 3.69615 6.40192i 0.133635 0.231462i
\(766\) 25.8564 0.934230
\(767\) 15.2154 0.549396
\(768\) 0.366025 0.633975i 0.0132078 0.0228766i
\(769\) 21.7128i 0.782984i −0.920181 0.391492i \(-0.871959\pi\)
0.920181 0.391492i \(-0.128041\pi\)
\(770\) 16.3923 + 28.3923i 0.590738 + 1.02319i
\(771\) 8.19615i 0.295177i
\(772\) −10.5000 + 6.06218i −0.377903 + 0.218183i
\(773\) 10.9641 + 18.9904i 0.394351 + 0.683037i