Properties

Label 1110.2.o.a.253.17
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.17
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.17

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(2.05225 + 0.887844i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.84414 + 1.84414i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(2.05225 + 0.887844i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.84414 + 1.84414i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-2.05225 - 0.887844i) q^{10} +2.12202i q^{11} +(0.707107 - 0.707107i) q^{12} -5.07258 q^{13} +(1.84414 - 1.84414i) q^{14} +(2.07896 - 0.823360i) q^{15} +1.00000 q^{16} +2.93495i q^{17} +1.00000i q^{18} +(2.28458 + 2.28458i) q^{19} +(2.05225 + 0.887844i) q^{20} +2.60801i q^{21} -2.12202i q^{22} -5.76461 q^{23} +(-0.707107 + 0.707107i) q^{24} +(3.42347 + 3.64416i) q^{25} +5.07258 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.84414 + 1.84414i) q^{28} +(-5.76649 + 5.76649i) q^{29} +(-2.07896 + 0.823360i) q^{30} +(1.38171 + 1.38171i) q^{31} -1.00000 q^{32} +(1.50049 + 1.50049i) q^{33} -2.93495i q^{34} +(-5.42195 + 2.14733i) q^{35} -1.00000i q^{36} +(-2.66745 + 5.46669i) q^{37} +(-2.28458 - 2.28458i) q^{38} +(-3.58685 + 3.58685i) q^{39} +(-2.05225 - 0.887844i) q^{40} -6.92685i q^{41} -2.60801i q^{42} -2.00391 q^{43} +2.12202i q^{44} +(0.887844 - 2.05225i) q^{45} +5.76461 q^{46} +(7.27515 - 7.27515i) q^{47} +(0.707107 - 0.707107i) q^{48} +0.198289i q^{49} +(-3.42347 - 3.64416i) q^{50} +(2.07533 + 2.07533i) q^{51} -5.07258 q^{52} +(-0.286733 - 0.286733i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-1.88402 + 4.35492i) q^{55} +(1.84414 - 1.84414i) q^{56} +3.23088 q^{57} +(5.76649 - 5.76649i) q^{58} +(-8.25437 - 8.25437i) q^{59} +(2.07896 - 0.823360i) q^{60} +(2.44633 + 2.44633i) q^{61} +(-1.38171 - 1.38171i) q^{62} +(1.84414 + 1.84414i) q^{63} +1.00000 q^{64} +(-10.4102 - 4.50366i) q^{65} +(-1.50049 - 1.50049i) q^{66} +(9.89884 + 9.89884i) q^{67} +2.93495i q^{68} +(-4.07619 + 4.07619i) q^{69} +(5.42195 - 2.14733i) q^{70} +1.69758 q^{71} +1.00000i q^{72} +(-5.92047 + 5.92047i) q^{73} +(2.66745 - 5.46669i) q^{74} +(4.99756 + 0.156051i) q^{75} +(2.28458 + 2.28458i) q^{76} +(-3.91330 - 3.91330i) q^{77} +(3.58685 - 3.58685i) q^{78} +(5.73733 + 5.73733i) q^{79} +(2.05225 + 0.887844i) q^{80} -1.00000 q^{81} +6.92685i q^{82} +(-7.41007 - 7.41007i) q^{83} +2.60801i q^{84} +(-2.60578 + 6.02326i) q^{85} +2.00391 q^{86} +8.15506i q^{87} -2.12202i q^{88} +(11.9236 - 11.9236i) q^{89} +(-0.887844 + 2.05225i) q^{90} +(9.35455 - 9.35455i) q^{91} -5.76461 q^{92} +1.95403 q^{93} +(-7.27515 + 7.27515i) q^{94} +(2.66018 + 6.71688i) q^{95} +(-0.707107 + 0.707107i) q^{96} +7.94678i q^{97} -0.198289i q^{98} +2.12202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) 2.05225 + 0.887844i 0.917794 + 0.397056i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −1.84414 + 1.84414i −0.697020 + 0.697020i −0.963767 0.266747i \(-0.914051\pi\)
0.266747 + 0.963767i \(0.414051\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −2.05225 0.887844i −0.648979 0.280761i
\(11\) 2.12202i 0.639813i 0.947449 + 0.319906i \(0.103651\pi\)
−0.947449 + 0.319906i \(0.896349\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −5.07258 −1.40688 −0.703440 0.710755i \(-0.748354\pi\)
−0.703440 + 0.710755i \(0.748354\pi\)
\(14\) 1.84414 1.84414i 0.492867 0.492867i
\(15\) 2.07896 0.823360i 0.536785 0.212591i
\(16\) 1.00000 0.250000
\(17\) 2.93495i 0.711831i 0.934518 + 0.355916i \(0.115831\pi\)
−0.934518 + 0.355916i \(0.884169\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.28458 + 2.28458i 0.524118 + 0.524118i 0.918813 0.394694i \(-0.129149\pi\)
−0.394694 + 0.918813i \(0.629149\pi\)
\(20\) 2.05225 + 0.887844i 0.458897 + 0.198528i
\(21\) 2.60801i 0.569114i
\(22\) 2.12202i 0.452416i
\(23\) −5.76461 −1.20200 −0.601002 0.799248i \(-0.705232\pi\)
−0.601002 + 0.799248i \(0.705232\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 3.42347 + 3.64416i 0.684693 + 0.728831i
\(26\) 5.07258 0.994814
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −1.84414 + 1.84414i −0.348510 + 0.348510i
\(29\) −5.76649 + 5.76649i −1.07081 + 1.07081i −0.0735173 + 0.997294i \(0.523422\pi\)
−0.997294 + 0.0735173i \(0.976578\pi\)
\(30\) −2.07896 + 0.823360i −0.379565 + 0.150324i
\(31\) 1.38171 + 1.38171i 0.248163 + 0.248163i 0.820216 0.572054i \(-0.193853\pi\)
−0.572054 + 0.820216i \(0.693853\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.50049 + 1.50049i 0.261203 + 0.261203i
\(34\) 2.93495i 0.503341i
\(35\) −5.42195 + 2.14733i −0.916477 + 0.362965i
\(36\) 1.00000i 0.166667i
\(37\) −2.66745 + 5.46669i −0.438526 + 0.898719i
\(38\) −2.28458 2.28458i −0.370608 0.370608i
\(39\) −3.58685 + 3.58685i −0.574356 + 0.574356i
\(40\) −2.05225 0.887844i −0.324489 0.140380i
\(41\) 6.92685i 1.08179i −0.841089 0.540896i \(-0.818085\pi\)
0.841089 0.540896i \(-0.181915\pi\)
\(42\) 2.60801i 0.402425i
\(43\) −2.00391 −0.305593 −0.152797 0.988258i \(-0.548828\pi\)
−0.152797 + 0.988258i \(0.548828\pi\)
\(44\) 2.12202i 0.319906i
\(45\) 0.887844 2.05225i 0.132352 0.305931i
\(46\) 5.76461 0.849945
\(47\) 7.27515 7.27515i 1.06119 1.06119i 0.0631877 0.998002i \(-0.479873\pi\)
0.998002 0.0631877i \(-0.0201267\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 0.198289i 0.0283271i
\(50\) −3.42347 3.64416i −0.484151 0.515362i
\(51\) 2.07533 + 2.07533i 0.290604 + 0.290604i
\(52\) −5.07258 −0.703440
\(53\) −0.286733 0.286733i −0.0393858 0.0393858i 0.687140 0.726525i \(-0.258866\pi\)
−0.726525 + 0.687140i \(0.758866\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −1.88402 + 4.35492i −0.254041 + 0.587217i
\(56\) 1.84414 1.84414i 0.246434 0.246434i
\(57\) 3.23088 0.427941
\(58\) 5.76649 5.76649i 0.757178 0.757178i
\(59\) −8.25437 8.25437i −1.07463 1.07463i −0.996981 0.0776460i \(-0.975260\pi\)
−0.0776460 0.996981i \(-0.524740\pi\)
\(60\) 2.07896 0.823360i 0.268393 0.106295i
\(61\) 2.44633 + 2.44633i 0.313221 + 0.313221i 0.846156 0.532935i \(-0.178911\pi\)
−0.532935 + 0.846156i \(0.678911\pi\)
\(62\) −1.38171 1.38171i −0.175478 0.175478i
\(63\) 1.84414 + 1.84414i 0.232340 + 0.232340i
\(64\) 1.00000 0.125000
\(65\) −10.4102 4.50366i −1.29123 0.558610i
\(66\) −1.50049 1.50049i −0.184698 0.184698i
\(67\) 9.89884 + 9.89884i 1.20934 + 1.20934i 0.971242 + 0.238093i \(0.0765222\pi\)
0.238093 + 0.971242i \(0.423478\pi\)
\(68\) 2.93495i 0.355916i
\(69\) −4.07619 + 4.07619i −0.490716 + 0.490716i
\(70\) 5.42195 2.14733i 0.648047 0.256655i
\(71\) 1.69758 0.201465 0.100733 0.994914i \(-0.467881\pi\)
0.100733 + 0.994914i \(0.467881\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −5.92047 + 5.92047i −0.692939 + 0.692939i −0.962877 0.269939i \(-0.912997\pi\)
0.269939 + 0.962877i \(0.412997\pi\)
\(74\) 2.66745 5.46669i 0.310085 0.635490i
\(75\) 4.99756 + 0.156051i 0.577069 + 0.0180192i
\(76\) 2.28458 + 2.28458i 0.262059 + 0.262059i
\(77\) −3.91330 3.91330i −0.445962 0.445962i
\(78\) 3.58685 3.58685i 0.406131 0.406131i
\(79\) 5.73733 + 5.73733i 0.645500 + 0.645500i 0.951902 0.306402i \(-0.0991253\pi\)
−0.306402 + 0.951902i \(0.599125\pi\)
\(80\) 2.05225 + 0.887844i 0.229449 + 0.0992640i
\(81\) −1.00000 −0.111111
\(82\) 6.92685i 0.764943i
\(83\) −7.41007 7.41007i −0.813360 0.813360i 0.171776 0.985136i \(-0.445050\pi\)
−0.985136 + 0.171776i \(0.945050\pi\)
\(84\) 2.60801i 0.284557i
\(85\) −2.60578 + 6.02326i −0.282637 + 0.653315i
\(86\) 2.00391 0.216087
\(87\) 8.15506i 0.874314i
\(88\) 2.12202i 0.226208i
\(89\) 11.9236 11.9236i 1.26390 1.26390i 0.314714 0.949187i \(-0.398092\pi\)
0.949187 0.314714i \(-0.101908\pi\)
\(90\) −0.887844 + 2.05225i −0.0935870 + 0.216326i
\(91\) 9.35455 9.35455i 0.980623 0.980623i
\(92\) −5.76461 −0.601002
\(93\) 1.95403 0.202624
\(94\) −7.27515 + 7.27515i −0.750374 + 0.750374i
\(95\) 2.66018 + 6.71688i 0.272929 + 0.689137i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 7.94678i 0.806874i 0.915008 + 0.403437i \(0.132184\pi\)
−0.915008 + 0.403437i \(0.867816\pi\)
\(98\) 0.198289i 0.0200303i
\(99\) 2.12202 0.213271
\(100\) 3.42347 + 3.64416i 0.342347 + 0.364416i
\(101\) 15.2228i 1.51472i 0.652997 + 0.757360i \(0.273511\pi\)
−0.652997 + 0.757360i \(0.726489\pi\)
\(102\) −2.07533 2.07533i −0.205488 0.205488i
\(103\) 13.4988i 1.33008i −0.746810 0.665038i \(-0.768415\pi\)
0.746810 0.665038i \(-0.231585\pi\)
\(104\) 5.07258 0.497407
\(105\) −2.31550 + 5.35229i −0.225970 + 0.522330i
\(106\) 0.286733 + 0.286733i 0.0278500 + 0.0278500i
\(107\) 2.32171 2.32171i 0.224448 0.224448i −0.585920 0.810369i \(-0.699267\pi\)
0.810369 + 0.585920i \(0.199267\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 5.20603 + 5.20603i 0.498647 + 0.498647i 0.911017 0.412369i \(-0.135299\pi\)
−0.412369 + 0.911017i \(0.635299\pi\)
\(110\) 1.88402 4.35492i 0.179634 0.415225i
\(111\) 1.97936 + 5.75171i 0.187873 + 0.545928i
\(112\) −1.84414 + 1.84414i −0.174255 + 0.174255i
\(113\) 16.6356i 1.56494i 0.622687 + 0.782471i \(0.286041\pi\)
−0.622687 + 0.782471i \(0.713959\pi\)
\(114\) −3.23088 −0.302600
\(115\) −11.8304 5.11807i −1.10319 0.477262i
\(116\) −5.76649 + 5.76649i −0.535406 + 0.535406i
\(117\) 5.07258i 0.468960i
\(118\) 8.25437 + 8.25437i 0.759876 + 0.759876i
\(119\) −5.41247 5.41247i −0.496160 0.496160i
\(120\) −2.07896 + 0.823360i −0.189782 + 0.0751621i
\(121\) 6.49703 0.590639
\(122\) −2.44633 2.44633i −0.221481 0.221481i
\(123\) −4.89802 4.89802i −0.441640 0.441640i
\(124\) 1.38171 + 1.38171i 0.124081 + 0.124081i
\(125\) 3.79037 + 10.5182i 0.339021 + 0.940779i
\(126\) −1.84414 1.84414i −0.164289 0.164289i
\(127\) −6.57279 + 6.57279i −0.583241 + 0.583241i −0.935792 0.352552i \(-0.885314\pi\)
0.352552 + 0.935792i \(0.385314\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.41698 + 1.41698i −0.124758 + 0.124758i
\(130\) 10.4102 + 4.50366i 0.913035 + 0.394997i
\(131\) −2.67417 2.67417i −0.233643 0.233643i 0.580568 0.814212i \(-0.302830\pi\)
−0.814212 + 0.580568i \(0.802830\pi\)
\(132\) 1.50049 + 1.50049i 0.130601 + 0.130601i
\(133\) −8.42617 −0.730642
\(134\) −9.89884 9.89884i −0.855129 0.855129i
\(135\) −0.823360 2.07896i −0.0708636 0.178928i
\(136\) 2.93495i 0.251670i
\(137\) 0.925340 0.925340i 0.0790571 0.0790571i −0.666472 0.745530i \(-0.732197\pi\)
0.745530 + 0.666472i \(0.232197\pi\)
\(138\) 4.07619 4.07619i 0.346988 0.346988i
\(139\) 5.44352 0.461713 0.230857 0.972988i \(-0.425847\pi\)
0.230857 + 0.972988i \(0.425847\pi\)
\(140\) −5.42195 + 2.14733i −0.458238 + 0.181483i
\(141\) 10.2886i 0.866457i
\(142\) −1.69758 −0.142457
\(143\) 10.7641i 0.900140i
\(144\) 1.00000i 0.0833333i
\(145\) −16.9540 + 6.71455i −1.40796 + 0.557613i
\(146\) 5.92047 5.92047i 0.489982 0.489982i
\(147\) 0.140212 + 0.140212i 0.0115645 + 0.0115645i
\(148\) −2.66745 + 5.46669i −0.219263 + 0.449359i
\(149\) 16.9497i 1.38858i 0.719698 + 0.694288i \(0.244280\pi\)
−0.719698 + 0.694288i \(0.755720\pi\)
\(150\) −4.99756 0.156051i −0.408049 0.0127415i
\(151\) 1.25999i 0.102536i −0.998685 0.0512681i \(-0.983674\pi\)
0.998685 0.0512681i \(-0.0163263\pi\)
\(152\) −2.28458 2.28458i −0.185304 0.185304i
\(153\) 2.93495 0.237277
\(154\) 3.91330 + 3.91330i 0.315343 + 0.315343i
\(155\) 1.60887 + 4.06236i 0.129228 + 0.326297i
\(156\) −3.58685 + 3.58685i −0.287178 + 0.287178i
\(157\) 4.05205 4.05205i 0.323389 0.323389i −0.526677 0.850066i \(-0.676562\pi\)
0.850066 + 0.526677i \(0.176562\pi\)
\(158\) −5.73733 5.73733i −0.456437 0.456437i
\(159\) −0.405502 −0.0321584
\(160\) −2.05225 0.887844i −0.162245 0.0701902i
\(161\) 10.6307 10.6307i 0.837820 0.837820i
\(162\) 1.00000 0.0785674
\(163\) 0.200876i 0.0157338i 0.999969 + 0.00786690i \(0.00250414\pi\)
−0.999969 + 0.00786690i \(0.997496\pi\)
\(164\) 6.92685i 0.540896i
\(165\) 1.74719 + 4.41160i 0.136018 + 0.343442i
\(166\) 7.41007 + 7.41007i 0.575133 + 0.575133i
\(167\) 7.20812i 0.557781i 0.960323 + 0.278891i \(0.0899667\pi\)
−0.960323 + 0.278891i \(0.910033\pi\)
\(168\) 2.60801i 0.201212i
\(169\) 12.7311 0.979312
\(170\) 2.60578 6.02326i 0.199854 0.461963i
\(171\) 2.28458 2.28458i 0.174706 0.174706i
\(172\) −2.00391 −0.152797
\(173\) 1.14427 1.14427i 0.0869969 0.0869969i −0.662269 0.749266i \(-0.730406\pi\)
0.749266 + 0.662269i \(0.230406\pi\)
\(174\) 8.15506i 0.618233i
\(175\) −13.0337 0.406983i −0.985255 0.0307650i
\(176\) 2.12202i 0.159953i
\(177\) −11.6734 −0.877429
\(178\) −11.9236 + 11.9236i −0.893712 + 0.893712i
\(179\) 9.71351 9.71351i 0.726022 0.726022i −0.243803 0.969825i \(-0.578395\pi\)
0.969825 + 0.243803i \(0.0783950\pi\)
\(180\) 0.887844 2.05225i 0.0661760 0.152966i
\(181\) −1.59280 −0.118392 −0.0591961 0.998246i \(-0.518854\pi\)
−0.0591961 + 0.998246i \(0.518854\pi\)
\(182\) −9.35455 + 9.35455i −0.693405 + 0.693405i
\(183\) 3.45964 0.255744
\(184\) 5.76461 0.424972
\(185\) −10.3278 + 8.85074i −0.759318 + 0.650720i
\(186\) −1.95403 −0.143277
\(187\) −6.22803 −0.455439
\(188\) 7.27515 7.27515i 0.530595 0.530595i
\(189\) 2.60801 0.189705
\(190\) −2.66018 6.71688i −0.192990 0.487294i
\(191\) −14.2911 + 14.2911i −1.03407 + 1.03407i −0.0346716 + 0.999399i \(0.511039\pi\)
−0.999399 + 0.0346716i \(0.988961\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 11.4610 0.824978 0.412489 0.910963i \(-0.364660\pi\)
0.412489 + 0.910963i \(0.364660\pi\)
\(194\) 7.94678i 0.570546i
\(195\) −10.5457 + 4.17656i −0.755193 + 0.299090i
\(196\) 0.198289i 0.0141635i
\(197\) 3.61811 3.61811i 0.257780 0.257780i −0.566371 0.824151i \(-0.691653\pi\)
0.824151 + 0.566371i \(0.191653\pi\)
\(198\) −2.12202 −0.150805
\(199\) 14.1563 14.1563i 1.00351 1.00351i 0.00351772 0.999994i \(-0.498880\pi\)
0.999994 0.00351772i \(-0.00111973\pi\)
\(200\) −3.42347 3.64416i −0.242076 0.257681i
\(201\) 13.9991 0.987418
\(202\) 15.2228i 1.07107i
\(203\) 21.2685i 1.49275i
\(204\) 2.07533 + 2.07533i 0.145302 + 0.145302i
\(205\) 6.14996 14.2156i 0.429532 0.992863i
\(206\) 13.4988i 0.940505i
\(207\) 5.76461i 0.400668i
\(208\) −5.07258 −0.351720
\(209\) −4.84792 + 4.84792i −0.335338 + 0.335338i
\(210\) 2.31550 5.35229i 0.159785 0.369343i
\(211\) 8.13385 0.559957 0.279979 0.960006i \(-0.409673\pi\)
0.279979 + 0.960006i \(0.409673\pi\)
\(212\) −0.286733 0.286733i −0.0196929 0.0196929i
\(213\) 1.20037 1.20037i 0.0822478 0.0822478i
\(214\) −2.32171 + 2.32171i −0.158709 + 0.158709i
\(215\) −4.11252 1.77916i −0.280472 0.121338i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) −5.09614 −0.345949
\(218\) −5.20603 5.20603i −0.352597 0.352597i
\(219\) 8.37281i 0.565782i
\(220\) −1.88402 + 4.35492i −0.127021 + 0.293608i
\(221\) 14.8878i 1.00146i
\(222\) −1.97936 5.75171i −0.132846 0.386029i
\(223\) −18.5142 18.5142i −1.23980 1.23980i −0.960081 0.279721i \(-0.909758\pi\)
−0.279721 0.960081i \(-0.590242\pi\)
\(224\) 1.84414 1.84414i 0.123217 0.123217i
\(225\) 3.64416 3.42347i 0.242944 0.228231i
\(226\) 16.6356i 1.10658i
\(227\) 8.71126i 0.578187i −0.957301 0.289093i \(-0.906646\pi\)
0.957301 0.289093i \(-0.0933538\pi\)
\(228\) 3.23088 0.213970
\(229\) 18.0323i 1.19160i 0.803131 + 0.595802i \(0.203166\pi\)
−0.803131 + 0.595802i \(0.796834\pi\)
\(230\) 11.8304 + 5.11807i 0.780075 + 0.337476i
\(231\) −5.53425 −0.364127
\(232\) 5.76649 5.76649i 0.378589 0.378589i
\(233\) 15.7454 15.7454i 1.03151 1.03151i 0.0320280 0.999487i \(-0.489803\pi\)
0.999487 0.0320280i \(-0.0101966\pi\)
\(234\) 5.07258i 0.331605i
\(235\) 21.3896 8.47123i 1.39531 0.552602i
\(236\) −8.25437 8.25437i −0.537314 0.537314i
\(237\) 8.11381 0.527048
\(238\) 5.41247 + 5.41247i 0.350838 + 0.350838i
\(239\) −10.3297 10.3297i −0.668170 0.668170i 0.289122 0.957292i \(-0.406637\pi\)
−0.957292 + 0.289122i \(0.906637\pi\)
\(240\) 2.07896 0.823360i 0.134196 0.0531477i
\(241\) −6.49380 + 6.49380i −0.418303 + 0.418303i −0.884618 0.466316i \(-0.845581\pi\)
0.466316 + 0.884618i \(0.345581\pi\)
\(242\) −6.49703 −0.417645
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 2.44633 + 2.44633i 0.156610 + 0.156610i
\(245\) −0.176050 + 0.406940i −0.0112474 + 0.0259984i
\(246\) 4.89802 + 4.89802i 0.312287 + 0.312287i
\(247\) −11.5887 11.5887i −0.737372 0.737372i
\(248\) −1.38171 1.38171i −0.0877388 0.0877388i
\(249\) −10.4794 −0.664106
\(250\) −3.79037 10.5182i −0.239724 0.665231i
\(251\) −2.81874 2.81874i −0.177917 0.177917i 0.612530 0.790447i \(-0.290152\pi\)
−0.790447 + 0.612530i \(0.790152\pi\)
\(252\) 1.84414 + 1.84414i 0.116170 + 0.116170i
\(253\) 12.2326i 0.769057i
\(254\) 6.57279 6.57279i 0.412413 0.412413i
\(255\) 2.41652 + 6.10166i 0.151329 + 0.382101i
\(256\) 1.00000 0.0625000
\(257\) 11.1961i 0.698394i 0.937049 + 0.349197i \(0.113546\pi\)
−0.937049 + 0.349197i \(0.886454\pi\)
\(258\) 1.41698 1.41698i 0.0882172 0.0882172i
\(259\) −5.16220 15.0005i −0.320763 0.932086i
\(260\) −10.4102 4.50366i −0.645613 0.279305i
\(261\) 5.76649 + 5.76649i 0.356937 + 0.356937i
\(262\) 2.67417 + 2.67417i 0.165211 + 0.165211i
\(263\) −2.56637 + 2.56637i −0.158249 + 0.158249i −0.781790 0.623541i \(-0.785693\pi\)
0.623541 + 0.781790i \(0.285693\pi\)
\(264\) −1.50049 1.50049i −0.0923490 0.0923490i
\(265\) −0.333874 0.843022i −0.0205097 0.0517864i
\(266\) 8.42617 0.516642
\(267\) 16.8625i 1.03197i
\(268\) 9.89884 + 9.89884i 0.604668 + 0.604668i
\(269\) 32.1166i 1.95819i −0.203414 0.979093i \(-0.565204\pi\)
0.203414 0.979093i \(-0.434796\pi\)
\(270\) 0.823360 + 2.07896i 0.0501081 + 0.126522i
\(271\) 15.5594 0.945166 0.472583 0.881286i \(-0.343322\pi\)
0.472583 + 0.881286i \(0.343322\pi\)
\(272\) 2.93495i 0.177958i
\(273\) 13.2293i 0.800675i
\(274\) −0.925340 + 0.925340i −0.0559018 + 0.0559018i
\(275\) −7.73297 + 7.26466i −0.466316 + 0.438076i
\(276\) −4.07619 + 4.07619i −0.245358 + 0.245358i
\(277\) 14.4437 0.867838 0.433919 0.900952i \(-0.357130\pi\)
0.433919 + 0.900952i \(0.357130\pi\)
\(278\) −5.44352 −0.326481
\(279\) 1.38171 1.38171i 0.0827209 0.0827209i
\(280\) 5.42195 2.14733i 0.324023 0.128328i
\(281\) 10.1736 10.1736i 0.606908 0.606908i −0.335229 0.942137i \(-0.608814\pi\)
0.942137 + 0.335229i \(0.108814\pi\)
\(282\) 10.2886i 0.612678i
\(283\) 11.7533i 0.698659i −0.937000 0.349330i \(-0.886409\pi\)
0.937000 0.349330i \(-0.113591\pi\)
\(284\) 1.69758 0.100733
\(285\) 6.63058 + 2.86852i 0.392762 + 0.169916i
\(286\) 10.7641i 0.636495i
\(287\) 12.7741 + 12.7741i 0.754031 + 0.754031i
\(288\) 1.00000i 0.0589256i
\(289\) 8.38604 0.493296
\(290\) 16.9540 6.71455i 0.995576 0.394292i
\(291\) 5.61922 + 5.61922i 0.329405 + 0.329405i
\(292\) −5.92047 + 5.92047i −0.346469 + 0.346469i
\(293\) −14.2767 14.2767i −0.834051 0.834051i 0.154017 0.988068i \(-0.450779\pi\)
−0.988068 + 0.154017i \(0.950779\pi\)
\(294\) −0.140212 0.140212i −0.00817732 0.00817732i
\(295\) −9.61144 24.2686i −0.559600 1.41297i
\(296\) 2.66745 5.46669i 0.155042 0.317745i
\(297\) 1.50049 1.50049i 0.0870675 0.0870675i
\(298\) 16.9497i 0.981871i
\(299\) 29.2414 1.69107
\(300\) 4.99756 + 0.156051i 0.288535 + 0.00900961i
\(301\) 3.69549 3.69549i 0.213005 0.213005i
\(302\) 1.25999i 0.0725041i
\(303\) 10.7641 + 10.7641i 0.618382 + 0.618382i
\(304\) 2.28458 + 2.28458i 0.131030 + 0.131030i
\(305\) 2.84853 + 7.19245i 0.163106 + 0.411839i
\(306\) −2.93495 −0.167780
\(307\) 16.2628 + 16.2628i 0.928166 + 0.928166i 0.997587 0.0694214i \(-0.0221153\pi\)
−0.0694214 + 0.997587i \(0.522115\pi\)
\(308\) −3.91330 3.91330i −0.222981 0.222981i
\(309\) −9.54509 9.54509i −0.543001 0.543001i
\(310\) −1.60887 4.06236i −0.0913779 0.230727i
\(311\) 11.0741 + 11.0741i 0.627952 + 0.627952i 0.947552 0.319600i \(-0.103549\pi\)
−0.319600 + 0.947552i \(0.603549\pi\)
\(312\) 3.58685 3.58685i 0.203066 0.203066i
\(313\) 4.41462 0.249529 0.124764 0.992186i \(-0.460182\pi\)
0.124764 + 0.992186i \(0.460182\pi\)
\(314\) −4.05205 + 4.05205i −0.228671 + 0.228671i
\(315\) 2.14733 + 5.42195i 0.120988 + 0.305492i
\(316\) 5.73733 + 5.73733i 0.322750 + 0.322750i
\(317\) 1.75051 + 1.75051i 0.0983187 + 0.0983187i 0.754555 0.656237i \(-0.227853\pi\)
−0.656237 + 0.754555i \(0.727853\pi\)
\(318\) 0.405502 0.0227394
\(319\) −12.2366 12.2366i −0.685119 0.685119i
\(320\) 2.05225 + 0.887844i 0.114724 + 0.0496320i
\(321\) 3.28340i 0.183261i
\(322\) −10.6307 + 10.6307i −0.592428 + 0.592428i
\(323\) −6.70514 + 6.70514i −0.373084 + 0.373084i
\(324\) −1.00000 −0.0555556
\(325\) −17.3658 18.4853i −0.963281 1.02538i
\(326\) 0.200876i 0.0111255i
\(327\) 7.36244 0.407144
\(328\) 6.92685i 0.382471i
\(329\) 26.8328i 1.47934i
\(330\) −1.74719 4.41160i −0.0961794 0.242850i
\(331\) −17.0019 + 17.0019i −0.934511 + 0.934511i −0.997984 0.0634724i \(-0.979783\pi\)
0.0634724 + 0.997984i \(0.479783\pi\)
\(332\) −7.41007 7.41007i −0.406680 0.406680i
\(333\) 5.46669 + 2.66745i 0.299573 + 0.146175i
\(334\) 7.20812i 0.394411i
\(335\) 11.5263 + 29.1035i 0.629748 + 1.59009i
\(336\) 2.60801i 0.142279i
\(337\) −16.7264 16.7264i −0.911145 0.911145i 0.0852173 0.996362i \(-0.472842\pi\)
−0.996362 + 0.0852173i \(0.972842\pi\)
\(338\) −12.7311 −0.692478
\(339\) 11.7631 + 11.7631i 0.638885 + 0.638885i
\(340\) −2.60578 + 6.02326i −0.141318 + 0.326657i
\(341\) −2.93202 + 2.93202i −0.158778 + 0.158778i
\(342\) −2.28458 + 2.28458i −0.123536 + 0.123536i
\(343\) −13.2747 13.2747i −0.716764 0.716764i
\(344\) 2.00391 0.108044
\(345\) −11.9844 + 4.74635i −0.645218 + 0.255535i
\(346\) −1.14427 + 1.14427i −0.0615161 + 0.0615161i
\(347\) −27.1062 −1.45514 −0.727568 0.686036i \(-0.759349\pi\)
−0.727568 + 0.686036i \(0.759349\pi\)
\(348\) 8.15506i 0.437157i
\(349\) 1.86734i 0.0999566i −0.998750 0.0499783i \(-0.984085\pi\)
0.998750 0.0499783i \(-0.0159152\pi\)
\(350\) 13.0337 + 0.406983i 0.696680 + 0.0217541i
\(351\) 3.58685 + 3.58685i 0.191452 + 0.191452i
\(352\) 2.12202i 0.113104i
\(353\) 15.2302i 0.810619i 0.914179 + 0.405310i \(0.132836\pi\)
−0.914179 + 0.405310i \(0.867164\pi\)
\(354\) 11.6734 0.620436
\(355\) 3.48385 + 1.50718i 0.184904 + 0.0799929i
\(356\) 11.9236 11.9236i 0.631950 0.631950i
\(357\) −7.65439 −0.405113
\(358\) −9.71351 + 9.71351i −0.513375 + 0.513375i
\(359\) 18.9718i 1.00129i −0.865651 0.500647i \(-0.833095\pi\)
0.865651 0.500647i \(-0.166905\pi\)
\(360\) −0.887844 + 2.05225i −0.0467935 + 0.108163i
\(361\) 8.56139i 0.450600i
\(362\) 1.59280 0.0837159
\(363\) 4.59410 4.59410i 0.241128 0.241128i
\(364\) 9.35455 9.35455i 0.490312 0.490312i
\(365\) −17.4067 + 6.89384i −0.911111 + 0.360840i
\(366\) −3.45964 −0.180838
\(367\) −23.8239 + 23.8239i −1.24360 + 1.24360i −0.285103 + 0.958497i \(0.592028\pi\)
−0.958497 + 0.285103i \(0.907972\pi\)
\(368\) −5.76461 −0.300501
\(369\) −6.92685 −0.360598
\(370\) 10.3278 8.85074i 0.536919 0.460128i
\(371\) 1.05755 0.0549054
\(372\) 1.95403 0.101312
\(373\) 2.47846 2.47846i 0.128330 0.128330i −0.640025 0.768354i \(-0.721076\pi\)
0.768354 + 0.640025i \(0.221076\pi\)
\(374\) 6.22803 0.322044
\(375\) 10.1177 + 4.75731i 0.522476 + 0.245667i
\(376\) −7.27515 + 7.27515i −0.375187 + 0.375187i
\(377\) 29.2510 29.2510i 1.50650 1.50650i
\(378\) −2.60801 −0.134142
\(379\) 31.6861i 1.62761i −0.581139 0.813804i \(-0.697393\pi\)
0.581139 0.813804i \(-0.302607\pi\)
\(380\) 2.66018 + 6.71688i 0.136464 + 0.344569i
\(381\) 9.29533i 0.476214i
\(382\) 14.2911 14.2911i 0.731198 0.731198i
\(383\) 12.7864 0.653357 0.326678 0.945136i \(-0.394071\pi\)
0.326678 + 0.945136i \(0.394071\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −4.55668 11.5055i −0.232230 0.586374i
\(386\) −11.4610 −0.583347
\(387\) 2.00391i 0.101864i
\(388\) 7.94678i 0.403437i
\(389\) −15.4731 15.4731i −0.784518 0.784518i 0.196071 0.980590i \(-0.437182\pi\)
−0.980590 + 0.196071i \(0.937182\pi\)
\(390\) 10.5457 4.17656i 0.534002 0.211488i
\(391\) 16.9189i 0.855623i
\(392\) 0.198289i 0.0100151i
\(393\) −3.78185 −0.190769
\(394\) −3.61811 + 3.61811i −0.182278 + 0.182278i
\(395\) 6.68059 + 16.8683i 0.336137 + 0.848736i
\(396\) 2.12202 0.106635
\(397\) 11.7358 + 11.7358i 0.589002 + 0.589002i 0.937361 0.348359i \(-0.113261\pi\)
−0.348359 + 0.937361i \(0.613261\pi\)
\(398\) −14.1563 + 14.1563i −0.709590 + 0.709590i
\(399\) −5.95820 + 5.95820i −0.298283 + 0.298283i
\(400\) 3.42347 + 3.64416i 0.171173 + 0.182208i
\(401\) −11.6604 11.6604i −0.582291 0.582291i 0.353241 0.935532i \(-0.385079\pi\)
−0.935532 + 0.353241i \(0.885079\pi\)
\(402\) −13.9991 −0.698210
\(403\) −7.00884 7.00884i −0.349135 0.349135i
\(404\) 15.2228i 0.757360i
\(405\) −2.05225 0.887844i −0.101977 0.0441173i
\(406\) 21.2685i 1.05554i
\(407\) −11.6004 5.66038i −0.575012 0.280575i
\(408\) −2.07533 2.07533i −0.102744 0.102744i
\(409\) −22.9972 + 22.9972i −1.13714 + 1.13714i −0.148176 + 0.988961i \(0.547340\pi\)
−0.988961 + 0.148176i \(0.952660\pi\)
\(410\) −6.14996 + 14.2156i −0.303725 + 0.702060i
\(411\) 1.30863i 0.0645499i
\(412\) 13.4988i 0.665038i
\(413\) 30.4444 1.49807
\(414\) 5.76461i 0.283315i
\(415\) −8.62833 21.7863i −0.423548 1.06945i
\(416\) 5.07258 0.248704
\(417\) 3.84915 3.84915i 0.188494 0.188494i
\(418\) 4.84792 4.84792i 0.237120 0.237120i
\(419\) 24.2039i 1.18244i 0.806512 + 0.591218i \(0.201353\pi\)
−0.806512 + 0.591218i \(0.798647\pi\)
\(420\) −2.31550 + 5.35229i −0.112985 + 0.261165i
\(421\) −9.91998 9.91998i −0.483470 0.483470i 0.422768 0.906238i \(-0.361059\pi\)
−0.906238 + 0.422768i \(0.861059\pi\)
\(422\) −8.13385 −0.395949
\(423\) −7.27515 7.27515i −0.353730 0.353730i
\(424\) 0.286733 + 0.286733i 0.0139250 + 0.0139250i
\(425\) −10.6954 + 10.0477i −0.518805 + 0.487386i
\(426\) −1.20037 + 1.20037i −0.0581580 + 0.0581580i
\(427\) −9.02276 −0.436642
\(428\) 2.32171 2.32171i 0.112224 0.112224i
\(429\) −7.61138 7.61138i −0.367481 0.367481i
\(430\) 4.11252 + 1.77916i 0.198324 + 0.0857986i
\(431\) 18.4635 + 18.4635i 0.889356 + 0.889356i 0.994461 0.105105i \(-0.0335180\pi\)
−0.105105 + 0.994461i \(0.533518\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 20.6095 + 20.6095i 0.990427 + 0.990427i 0.999955 0.00952737i \(-0.00303270\pi\)
−0.00952737 + 0.999955i \(0.503033\pi\)
\(434\) 5.09614 0.244623
\(435\) −7.24042 + 16.7362i −0.347151 + 0.802440i
\(436\) 5.20603 + 5.20603i 0.249324 + 0.249324i
\(437\) −13.1697 13.1697i −0.629992 0.629992i
\(438\) 8.37281i 0.400068i
\(439\) −6.00049 + 6.00049i −0.286388 + 0.286388i −0.835650 0.549262i \(-0.814909\pi\)
0.549262 + 0.835650i \(0.314909\pi\)
\(440\) 1.88402 4.35492i 0.0898172 0.207612i
\(441\) 0.198289 0.00944235
\(442\) 14.8878i 0.708140i
\(443\) 19.3252 19.3252i 0.918168 0.918168i −0.0787279 0.996896i \(-0.525086\pi\)
0.996896 + 0.0787279i \(0.0250858\pi\)
\(444\) 1.97936 + 5.75171i 0.0939364 + 0.272964i
\(445\) 35.0565 13.8839i 1.66184 0.658162i
\(446\) 18.5142 + 18.5142i 0.876673 + 0.876673i
\(447\) 11.9853 + 11.9853i 0.566884 + 0.566884i
\(448\) −1.84414 + 1.84414i −0.0871275 + 0.0871275i
\(449\) 23.5893 + 23.5893i 1.11325 + 1.11325i 0.992709 + 0.120538i \(0.0384620\pi\)
0.120538 + 0.992709i \(0.461538\pi\)
\(450\) −3.64416 + 3.42347i −0.171787 + 0.161384i
\(451\) 14.6989 0.692145
\(452\) 16.6356i 0.782471i
\(453\) −0.890945 0.890945i −0.0418603 0.0418603i
\(454\) 8.71126i 0.408840i
\(455\) 27.5033 10.8925i 1.28937 0.510648i
\(456\) −3.23088 −0.151300
\(457\) 10.5479i 0.493409i 0.969091 + 0.246704i \(0.0793476\pi\)
−0.969091 + 0.246704i \(0.920652\pi\)
\(458\) 18.0323i 0.842592i
\(459\) 2.07533 2.07533i 0.0968679 0.0968679i
\(460\) −11.8304 5.11807i −0.551596 0.238631i
\(461\) −26.9418 + 26.9418i −1.25481 + 1.25481i −0.301265 + 0.953541i \(0.597409\pi\)
−0.953541 + 0.301265i \(0.902591\pi\)
\(462\) 5.53425 0.257476
\(463\) −16.5851 −0.770773 −0.385387 0.922755i \(-0.625932\pi\)
−0.385387 + 0.922755i \(0.625932\pi\)
\(464\) −5.76649 + 5.76649i −0.267703 + 0.267703i
\(465\) 4.01017 + 1.73488i 0.185967 + 0.0804530i
\(466\) −15.7454 + 15.7454i −0.729391 + 0.729391i
\(467\) 34.4641i 1.59481i −0.603447 0.797403i \(-0.706207\pi\)
0.603447 0.797403i \(-0.293793\pi\)
\(468\) 5.07258i 0.234480i
\(469\) −36.5097 −1.68586
\(470\) −21.3896 + 8.47123i −0.986630 + 0.390749i
\(471\) 5.73047i 0.264046i
\(472\) 8.25437 + 8.25437i 0.379938 + 0.379938i
\(473\) 4.25233i 0.195523i
\(474\) −8.11381 −0.372680
\(475\) −0.504183 + 16.1465i −0.0231335 + 0.740854i
\(476\) −5.41247 5.41247i −0.248080 0.248080i
\(477\) −0.286733 + 0.286733i −0.0131286 + 0.0131286i
\(478\) 10.3297 + 10.3297i 0.472467 + 0.472467i
\(479\) −15.9403 15.9403i −0.728333 0.728333i 0.241954 0.970288i \(-0.422212\pi\)
−0.970288 + 0.241954i \(0.922212\pi\)
\(480\) −2.07896 + 0.823360i −0.0948911 + 0.0375811i
\(481\) 13.5308 27.7302i 0.616953 1.26439i
\(482\) 6.49380 6.49380i 0.295785 0.295785i
\(483\) 15.0341i 0.684077i
\(484\) 6.49703 0.295320
\(485\) −7.05550 + 16.3088i −0.320374 + 0.740544i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 5.52466i 0.250346i −0.992135 0.125173i \(-0.960051\pi\)
0.992135 0.125173i \(-0.0399486\pi\)
\(488\) −2.44633 2.44633i −0.110740 0.110740i
\(489\) 0.142041 + 0.142041i 0.00642329 + 0.00642329i
\(490\) 0.176050 0.406940i 0.00795313 0.0183837i
\(491\) 30.9165 1.39524 0.697621 0.716467i \(-0.254242\pi\)
0.697621 + 0.716467i \(0.254242\pi\)
\(492\) −4.89802 4.89802i −0.220820 0.220820i
\(493\) −16.9244 16.9244i −0.762237 0.762237i
\(494\) 11.5887 + 11.5887i 0.521401 + 0.521401i
\(495\) 4.35492 + 1.88402i 0.195739 + 0.0846805i
\(496\) 1.38171 + 1.38171i 0.0620407 + 0.0620407i
\(497\) −3.13057 + 3.13057i −0.140425 + 0.140425i
\(498\) 10.4794 0.469594
\(499\) −15.3419 + 15.3419i −0.686798 + 0.686798i −0.961523 0.274725i \(-0.911413\pi\)
0.274725 + 0.961523i \(0.411413\pi\)
\(500\) 3.79037 + 10.5182i 0.169511 + 0.470389i
\(501\) 5.09691 + 5.09691i 0.227713 + 0.227713i
\(502\) 2.81874 + 2.81874i 0.125806 + 0.125806i
\(503\) 6.97745 0.311109 0.155555 0.987827i \(-0.450284\pi\)
0.155555 + 0.987827i \(0.450284\pi\)
\(504\) −1.84414 1.84414i −0.0821446 0.0821446i
\(505\) −13.5154 + 31.2409i −0.601429 + 1.39020i
\(506\) 12.2326i 0.543806i
\(507\) 9.00221 9.00221i 0.399802 0.399802i
\(508\) −6.57279 + 6.57279i −0.291620 + 0.291620i
\(509\) 15.9733 0.708002 0.354001 0.935245i \(-0.384821\pi\)
0.354001 + 0.935245i \(0.384821\pi\)
\(510\) −2.41652 6.10166i −0.107006 0.270186i
\(511\) 21.8364i 0.965984i
\(512\) −1.00000 −0.0441942
\(513\) 3.23088i 0.142647i
\(514\) 11.1961i 0.493839i
\(515\) 11.9848 27.7029i 0.528114 1.22074i
\(516\) −1.41698 + 1.41698i −0.0623790 + 0.0623790i
\(517\) 15.4380 + 15.4380i 0.678963 + 0.678963i
\(518\) 5.16220 + 15.0005i 0.226814 + 0.659084i
\(519\) 1.61824i 0.0710327i
\(520\) 10.4102 + 4.50366i 0.456518 + 0.197498i
\(521\) 38.5368i 1.68833i −0.536084 0.844165i \(-0.680097\pi\)
0.536084 0.844165i \(-0.319903\pi\)
\(522\) −5.76649 5.76649i −0.252393 0.252393i
\(523\) −14.7060 −0.643047 −0.321523 0.946902i \(-0.604195\pi\)
−0.321523 + 0.946902i \(0.604195\pi\)
\(524\) −2.67417 2.67417i −0.116822 0.116822i
\(525\) −9.50399 + 8.92843i −0.414788 + 0.389669i
\(526\) 2.56637 2.56637i 0.111899 0.111899i
\(527\) −4.05526 + 4.05526i −0.176650 + 0.176650i
\(528\) 1.50049 + 1.50049i 0.0653006 + 0.0653006i
\(529\) 10.2307 0.444812
\(530\) 0.333874 + 0.843022i 0.0145026 + 0.0366185i
\(531\) −8.25437 + 8.25437i −0.358209 + 0.358209i
\(532\) −8.42617 −0.365321
\(533\) 35.1370i 1.52195i
\(534\) 16.8625i 0.729713i
\(535\) 6.82606 2.70342i 0.295116 0.116879i
\(536\) −9.89884 9.89884i −0.427565 0.427565i
\(537\) 13.7370i 0.592794i
\(538\) 32.1166i 1.38465i
\(539\) −0.420774 −0.0181240
\(540\) −0.823360 2.07896i −0.0354318 0.0894642i
\(541\) −24.9509 + 24.9509i −1.07272 + 1.07272i −0.0755841 + 0.997139i \(0.524082\pi\)
−0.997139 + 0.0755841i \(0.975918\pi\)
\(542\) −15.5594 −0.668333
\(543\) −1.12628 + 1.12628i −0.0483334 + 0.0483334i
\(544\) 2.93495i 0.125835i
\(545\) 6.06194 + 15.3062i 0.259665 + 0.655646i
\(546\) 13.2293i 0.566163i
\(547\) 36.4914 1.56026 0.780131 0.625617i \(-0.215153\pi\)
0.780131 + 0.625617i \(0.215153\pi\)
\(548\) 0.925340 0.925340i 0.0395286 0.0395286i
\(549\) 2.44633 2.44633i 0.104407 0.104407i
\(550\) 7.73297 7.26466i 0.329735 0.309766i
\(551\) −26.3480 −1.12246
\(552\) 4.07619 4.07619i 0.173494 0.173494i
\(553\) −21.1609 −0.899852
\(554\) −14.4437 −0.613654
\(555\) −1.04447 + 13.5613i −0.0443351 + 0.575645i
\(556\) 5.44352 0.230857
\(557\) −32.6303 −1.38259 −0.691296 0.722572i \(-0.742960\pi\)
−0.691296 + 0.722572i \(0.742960\pi\)
\(558\) −1.38171 + 1.38171i −0.0584925 + 0.0584925i
\(559\) 10.1650 0.429933
\(560\) −5.42195 + 2.14733i −0.229119 + 0.0907413i
\(561\) −4.40388 + 4.40388i −0.185932 + 0.185932i
\(562\) −10.1736 + 10.1736i −0.429149 + 0.429149i
\(563\) 20.4470 0.861738 0.430869 0.902415i \(-0.358207\pi\)
0.430869 + 0.902415i \(0.358207\pi\)
\(564\) 10.2886i 0.433229i
\(565\) −14.7698 + 34.1404i −0.621369 + 1.43630i
\(566\) 11.7533i 0.494027i
\(567\) 1.84414 1.84414i 0.0774466 0.0774466i
\(568\) −1.69758 −0.0712287
\(569\) −11.2342 + 11.2342i −0.470964 + 0.470964i −0.902226 0.431263i \(-0.858068\pi\)
0.431263 + 0.902226i \(0.358068\pi\)
\(570\) −6.63058 2.86852i −0.277725 0.120149i
\(571\) 26.4113 1.10528 0.552639 0.833421i \(-0.313621\pi\)
0.552639 + 0.833421i \(0.313621\pi\)
\(572\) 10.7641i 0.450070i
\(573\) 20.2107i 0.844315i
\(574\) −12.7741 12.7741i −0.533180 0.533180i
\(575\) −19.7349 21.0071i −0.823004 0.876058i
\(576\) 1.00000i 0.0416667i
\(577\) 7.95386i 0.331123i 0.986199 + 0.165562i \(0.0529437\pi\)
−0.986199 + 0.165562i \(0.947056\pi\)
\(578\) −8.38604 −0.348813
\(579\) 8.10412 8.10412i 0.336796 0.336796i
\(580\) −16.9540 + 6.71455i −0.703978 + 0.278806i
\(581\) 27.3304 1.13386
\(582\) −5.61922 5.61922i −0.232924 0.232924i
\(583\) 0.608453 0.608453i 0.0251995 0.0251995i
\(584\) 5.92047 5.92047i 0.244991 0.244991i
\(585\) −4.50366 + 10.4102i −0.186203 + 0.430409i
\(586\) 14.2767 + 14.2767i 0.589763 + 0.589763i
\(587\) −12.8759 −0.531445 −0.265723 0.964050i \(-0.585611\pi\)
−0.265723 + 0.964050i \(0.585611\pi\)
\(588\) 0.140212 + 0.140212i 0.00578224 + 0.00578224i
\(589\) 6.31326i 0.260133i
\(590\) 9.61144 + 24.2686i 0.395697 + 0.999123i
\(591\) 5.11678i 0.210476i
\(592\) −2.66745 + 5.46669i −0.109631 + 0.224680i
\(593\) 17.6097 + 17.6097i 0.723143 + 0.723143i 0.969244 0.246102i \(-0.0791497\pi\)
−0.246102 + 0.969244i \(0.579150\pi\)
\(594\) −1.50049 + 1.50049i −0.0615660 + 0.0615660i
\(595\) −6.30232 15.9132i −0.258370 0.652377i
\(596\) 16.9497i 0.694288i
\(597\) 20.0200i 0.819364i
\(598\) −29.2414 −1.19577
\(599\) 28.1341i 1.14953i 0.818320 + 0.574763i \(0.194906\pi\)
−0.818320 + 0.574763i \(0.805094\pi\)
\(600\) −4.99756 0.156051i −0.204025 0.00637076i
\(601\) −14.8826 −0.607072 −0.303536 0.952820i \(-0.598167\pi\)
−0.303536 + 0.952820i \(0.598167\pi\)
\(602\) −3.69549 + 3.69549i −0.150617 + 0.150617i
\(603\) 9.89884 9.89884i 0.403112 0.403112i
\(604\) 1.25999i 0.0512681i
\(605\) 13.3335 + 5.76835i 0.542086 + 0.234517i
\(606\) −10.7641 10.7641i −0.437262 0.437262i
\(607\) 5.21022 0.211476 0.105738 0.994394i \(-0.466279\pi\)
0.105738 + 0.994394i \(0.466279\pi\)
\(608\) −2.28458 2.28458i −0.0926519 0.0926519i
\(609\) −15.0391 15.0391i −0.609414 0.609414i
\(610\) −2.84853 7.19245i −0.115333 0.291214i
\(611\) −36.9038 + 36.9038i −1.49297 + 1.49297i
\(612\) 2.93495 0.118639
\(613\) −15.0091 + 15.0091i −0.606211 + 0.606211i −0.941954 0.335743i \(-0.891013\pi\)
0.335743 + 0.941954i \(0.391013\pi\)
\(614\) −16.2628 16.2628i −0.656312 0.656312i
\(615\) −5.70329 14.4007i −0.229979 0.580690i
\(616\) 3.91330 + 3.91330i 0.157671 + 0.157671i
\(617\) 6.06777 + 6.06777i 0.244279 + 0.244279i 0.818618 0.574339i \(-0.194741\pi\)
−0.574339 + 0.818618i \(0.694741\pi\)
\(618\) 9.54509 + 9.54509i 0.383960 + 0.383960i
\(619\) 20.1898 0.811495 0.405747 0.913985i \(-0.367011\pi\)
0.405747 + 0.913985i \(0.367011\pi\)
\(620\) 1.60887 + 4.06236i 0.0646139 + 0.163148i
\(621\) 4.07619 + 4.07619i 0.163572 + 0.163572i
\(622\) −11.0741 11.0741i −0.444029 0.444029i
\(623\) 43.9776i 1.76193i
\(624\) −3.58685 + 3.58685i −0.143589 + 0.143589i
\(625\) −1.55975 + 24.9513i −0.0623900 + 0.998052i
\(626\) −4.41462 −0.176444
\(627\) 6.85600i 0.273802i
\(628\) 4.05205 4.05205i 0.161695 0.161695i
\(629\) −16.0445 7.82884i −0.639736 0.312156i
\(630\) −2.14733 5.42195i −0.0855517 0.216016i
\(631\) 1.59016 + 1.59016i 0.0633034 + 0.0633034i 0.738050 0.674746i \(-0.235747\pi\)
−0.674746 + 0.738050i \(0.735747\pi\)
\(632\) −5.73733 5.73733i −0.228219 0.228219i
\(633\) 5.75150 5.75150i 0.228602 0.228602i
\(634\) −1.75051 1.75051i −0.0695218 0.0695218i
\(635\) −19.3246 + 7.65340i −0.766874 + 0.303716i
\(636\) −0.405502 −0.0160792
\(637\) 1.00584i 0.0398528i
\(638\) 12.2366 + 12.2366i 0.484452 + 0.484452i
\(639\) 1.69758i 0.0671550i
\(640\) −2.05225 0.887844i −0.0811223 0.0350951i
\(641\) −27.0270 −1.06750 −0.533752 0.845641i \(-0.679218\pi\)
−0.533752 + 0.845641i \(0.679218\pi\)
\(642\) 3.28340i 0.129585i
\(643\) 18.0452i 0.711635i 0.934556 + 0.355817i \(0.115797\pi\)
−0.934556 + 0.355817i \(0.884203\pi\)
\(644\) 10.6307 10.6307i 0.418910 0.418910i
\(645\) −4.16605 + 1.64994i −0.164038 + 0.0649663i
\(646\) 6.70514 6.70514i 0.263810 0.263810i
\(647\) −2.13093 −0.0837754 −0.0418877 0.999122i \(-0.513337\pi\)
−0.0418877 + 0.999122i \(0.513337\pi\)
\(648\) 1.00000 0.0392837
\(649\) 17.5159 17.5159i 0.687560 0.687560i
\(650\) 17.3658 + 18.4853i 0.681143 + 0.725052i
\(651\) −3.60352 + 3.60352i −0.141233 + 0.141233i
\(652\) 0.200876i 0.00786690i
\(653\) 12.1928i 0.477142i 0.971125 + 0.238571i \(0.0766790\pi\)
−0.971125 + 0.238571i \(0.923321\pi\)
\(654\) −7.36244 −0.287894
\(655\) −3.11382 7.86231i −0.121667 0.307206i
\(656\) 6.92685i 0.270448i
\(657\) 5.92047 + 5.92047i 0.230980 + 0.230980i
\(658\) 26.8328i 1.04605i
\(659\) 19.4303 0.756898 0.378449 0.925622i \(-0.376457\pi\)
0.378449 + 0.925622i \(0.376457\pi\)
\(660\) 1.74719 + 4.41160i 0.0680091 + 0.171721i
\(661\) 25.0660 + 25.0660i 0.974956 + 0.974956i 0.999694 0.0247380i \(-0.00787514\pi\)
−0.0247380 + 0.999694i \(0.507875\pi\)
\(662\) 17.0019 17.0019i 0.660799 0.660799i
\(663\) −10.5273 10.5273i −0.408845 0.408845i
\(664\) 7.41007 + 7.41007i 0.287566 + 0.287566i
\(665\) −17.2926 7.48113i −0.670579 0.290106i
\(666\) −5.46669 2.66745i −0.211830 0.103362i
\(667\) 33.2416 33.2416i 1.28712 1.28712i
\(668\) 7.20812i 0.278891i
\(669\) −26.1830 −1.01229
\(670\) −11.5263 29.1035i −0.445299 1.12437i
\(671\) −5.19117 + 5.19117i −0.200403 + 0.200403i
\(672\) 2.60801i 0.100606i
\(673\) 25.0421 + 25.0421i 0.965303 + 0.965303i 0.999418 0.0341149i \(-0.0108612\pi\)
−0.0341149 + 0.999418i \(0.510861\pi\)
\(674\) 16.7264 + 16.7264i 0.644277 + 0.644277i
\(675\) 0.156051 4.99756i 0.00600641 0.192356i
\(676\) 12.7311 0.489656
\(677\) 4.04562 + 4.04562i 0.155486 + 0.155486i 0.780563 0.625077i \(-0.214932\pi\)
−0.625077 + 0.780563i \(0.714932\pi\)
\(678\) −11.7631 11.7631i −0.451760 0.451760i
\(679\) −14.6550 14.6550i −0.562407 0.562407i
\(680\) 2.60578 6.02326i 0.0999272 0.230982i
\(681\) −6.15979 6.15979i −0.236044 0.236044i
\(682\) 2.93202 2.93202i 0.112273 0.112273i
\(683\) 49.4497 1.89214 0.946070 0.323961i \(-0.105015\pi\)
0.946070 + 0.323961i \(0.105015\pi\)
\(684\) 2.28458 2.28458i 0.0873531 0.0873531i
\(685\) 2.72059 1.07747i 0.103948 0.0411681i
\(686\) 13.2747 + 13.2747i 0.506829 + 0.506829i
\(687\) 12.7507 + 12.7507i 0.486471 + 0.486471i
\(688\) −2.00391 −0.0763983
\(689\) 1.45448 + 1.45448i 0.0554111 + 0.0554111i
\(690\) 11.9844 4.74635i 0.456238 0.180690i
\(691\) 9.04475i 0.344078i −0.985090 0.172039i \(-0.944964\pi\)
0.985090 0.172039i \(-0.0550356\pi\)
\(692\) 1.14427 1.14427i 0.0434985 0.0434985i
\(693\) −3.91330 + 3.91330i −0.148654 + 0.148654i
\(694\) 27.1062 1.02894
\(695\) 11.1715 + 4.83299i 0.423758 + 0.183326i
\(696\) 8.15506i 0.309117i
\(697\) 20.3300 0.770054
\(698\) 1.86734i 0.0706800i
\(699\) 22.2673i 0.842228i
\(700\) −13.0337 0.406983i −0.492627 0.0153825i
\(701\) −6.79801 + 6.79801i −0.256757 + 0.256757i −0.823734 0.566977i \(-0.808113\pi\)
0.566977 + 0.823734i \(0.308113\pi\)
\(702\) −3.58685 3.58685i −0.135377 0.135377i
\(703\) −18.5831 + 6.39509i −0.700875 + 0.241195i
\(704\) 2.12202i 0.0799766i
\(705\) 9.13468 21.1148i 0.344032 0.795230i
\(706\) 15.2302i 0.573194i
\(707\) −28.0729 28.0729i −1.05579 1.05579i
\(708\) −11.6734 −0.438715
\(709\) −12.7014 12.7014i −0.477012 0.477012i 0.427163 0.904175i \(-0.359513\pi\)
−0.904175 + 0.427163i \(0.859513\pi\)
\(710\) −3.48385 1.50718i −0.130747 0.0565635i
\(711\) 5.73733 5.73733i 0.215167 0.215167i
\(712\) −11.9236 + 11.9236i −0.446856 + 0.446856i
\(713\) −7.96502 7.96502i −0.298292 0.298292i
\(714\) 7.65439 0.286458
\(715\) 9.55685 22.0907i 0.357406 0.826144i
\(716\) 9.71351 9.71351i 0.363011 0.363011i
\(717\) −14.6083 −0.545558
\(718\) 18.9718i 0.708022i
\(719\) 25.0596i 0.934567i 0.884108 + 0.467283i \(0.154767\pi\)
−0.884108 + 0.467283i \(0.845233\pi\)
\(720\) 0.887844 2.05225i 0.0330880 0.0764829i
\(721\) 24.8937 + 24.8937i 0.927089 + 0.927089i
\(722\) 8.56139i 0.318622i
\(723\) 9.18363i 0.341543i
\(724\) −1.59280 −0.0591961
\(725\) −40.7554 1.27261i −1.51362 0.0472634i
\(726\) −4.59410 + 4.59410i −0.170503 + 0.170503i
\(727\) 28.9528 1.07380 0.536899 0.843646i \(-0.319596\pi\)
0.536899 + 0.843646i \(0.319596\pi\)
\(728\) −9.35455 + 9.35455i −0.346703 + 0.346703i
\(729\) 1.00000i 0.0370370i
\(730\) 17.4067 6.89384i 0.644253 0.255152i
\(731\) 5.88138i 0.217531i
\(732\) 3.45964 0.127872
\(733\) −12.6845 + 12.6845i −0.468513 + 0.468513i −0.901433 0.432920i \(-0.857483\pi\)
0.432920 + 0.901433i \(0.357483\pi\)
\(734\) 23.8239 23.8239i 0.879358 0.879358i
\(735\) 0.163264 + 0.412236i 0.00602207 + 0.0152055i
\(736\) 5.76461 0.212486
\(737\) −21.0055 + 21.0055i −0.773748 + 0.773748i
\(738\) 6.92685 0.254981
\(739\) 5.09966 0.187594 0.0937970 0.995591i \(-0.470100\pi\)
0.0937970 + 0.995591i \(0.470100\pi\)
\(740\) −10.3278 + 8.85074i −0.379659 + 0.325360i
\(741\) −16.3889 −0.602062
\(742\) −1.05755 −0.0388240
\(743\) 5.46112 5.46112i 0.200349 0.200349i −0.599801 0.800150i \(-0.704753\pi\)
0.800150 + 0.599801i \(0.204753\pi\)
\(744\) −1.95403 −0.0716384
\(745\) −15.0487 + 34.7851i −0.551342 + 1.27443i
\(746\) −2.47846 + 2.47846i −0.0907429 + 0.0907429i
\(747\) −7.41007 + 7.41007i −0.271120 + 0.271120i
\(748\) −6.22803 −0.227719
\(749\) 8.56313i 0.312890i
\(750\) −10.1177 4.75731i −0.369446 0.173712i
\(751\) 50.1472i 1.82990i −0.403569 0.914949i \(-0.632230\pi\)
0.403569 0.914949i \(-0.367770\pi\)
\(752\) 7.27515 7.27515i 0.265297 0.265297i
\(753\) −3.98630 −0.145269
\(754\) −29.2510 + 29.2510i −1.06526 + 1.06526i
\(755\) 1.11867 2.58581i 0.0407126 0.0941072i
\(756\) 2.60801 0.0948524
\(757\) 38.6619i 1.40519i 0.711589 + 0.702596i \(0.247976\pi\)
−0.711589 + 0.702596i \(0.752024\pi\)
\(758\) 31.6861i 1.15089i
\(759\) −8.64976 8.64976i −0.313966 0.313966i
\(760\) −2.66018 6.71688i −0.0964949 0.243647i
\(761\) 2.58952i 0.0938702i 0.998898 + 0.0469351i \(0.0149454\pi\)
−0.998898 + 0.0469351i \(0.985055\pi\)
\(762\) 9.29533i 0.336734i
\(763\) −19.2013 −0.695134
\(764\) −14.2911 + 14.2911i −0.517035 + 0.517035i
\(765\) 6.02326 + 2.60578i 0.217772 + 0.0942122i
\(766\) −12.7864 −0.461993
\(767\) 41.8709 + 41.8709i 1.51187 + 1.51187i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −0.970999 + 0.970999i −0.0350151 + 0.0350151i −0.724398 0.689382i \(-0.757882\pi\)
0.689382 + 0.724398i \(0.257882\pi\)
\(770\) 4.55668 + 11.5055i 0.164211 + 0.414629i
\(771\) 7.91684 + 7.91684i 0.285118 + 0.285118i
\(772\) 11.4610 0.412489
\(773\) 33.8554 + 33.8554i 1.21769 + 1.21769i 0.968438 + 0.249255i \(0.0801859\pi\)
0.249255 + 0.968438i \(0.419814\pi\)
\(774\) 2.00391i 0.0720290i
\(775\) −0.304929 + 9.76541i −0.0109534 + 0.350784i
\(776\) 7.94678i 0.285273i
\(777\) −14.2572 6.95673i −0.511473 0.249571i
\(778\) 15.4731 + 15.4731i 0.554738 + 0.554738i
\(779\) 15.8249 15.8249i 0.566988 0.566988i
\(780\) −10.5457 + 4.17656i