Properties

Label 91.2.f.a.22.1
Level $91$
Weight $2$
Character 91.22
Analytic conductor $0.727$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 91.22
Dual form 91.2.f.a.29.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30902 + 2.26728i) q^{2} +(1.30902 - 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} +2.61803 q^{5} +(3.42705 + 5.93583i) q^{6} +(-0.500000 - 0.866025i) q^{7} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\) \(q+(-1.30902 + 2.26728i) q^{2} +(1.30902 - 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} +2.61803 q^{5} +(3.42705 + 5.93583i) q^{6} +(-0.500000 - 0.866025i) q^{7} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-3.42705 + 5.93583i) q^{10} +(-0.927051 + 1.60570i) q^{11} -12.7082 q^{12} +(-2.50000 + 2.59808i) q^{13} +2.61803 q^{14} +(3.42705 - 5.93583i) q^{15} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +10.0902 q^{18} +(0.927051 + 1.60570i) q^{19} +(-6.35410 - 11.0056i) q^{20} -2.61803 q^{21} +(-2.42705 - 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} +(9.78115 - 16.9415i) q^{24} +1.85410 q^{25} +(-2.61803 - 9.06914i) q^{26} -2.23607 q^{27} +(-2.42705 + 4.20378i) q^{28} +(-3.54508 + 6.14027i) q^{29} +(8.97214 + 15.5402i) q^{30} -4.70820 q^{31} +(-5.42705 - 9.39993i) q^{32} +(2.42705 + 4.20378i) q^{33} -3.85410 q^{34} +(-1.30902 - 2.26728i) q^{35} +(-9.35410 + 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} -4.85410 q^{38} +(2.61803 + 9.06914i) q^{39} +19.5623 q^{40} +(-0.381966 + 0.661585i) q^{41} +(3.42705 - 5.93583i) q^{42} +(-6.28115 - 10.8793i) q^{43} +9.00000 q^{44} +(-5.04508 - 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} -2.23607 q^{47} +(12.8992 + 22.3420i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.42705 + 4.20378i) q^{50} +3.85410 q^{51} +(16.9894 + 4.20378i) q^{52} +3.76393 q^{53} +(2.92705 - 5.06980i) q^{54} +(-2.42705 + 4.20378i) q^{55} +(-3.73607 - 6.47106i) q^{56} +4.85410 q^{57} +(-9.28115 - 16.0754i) q^{58} +(1.11803 + 1.93649i) q^{59} -33.2705 q^{60} +(3.00000 + 5.19615i) q^{61} +(6.16312 - 10.6748i) q^{62} +(-1.92705 + 3.33775i) q^{63} +8.70820 q^{64} +(-6.54508 + 6.80185i) q^{65} -12.7082 q^{66} +(6.35410 - 11.0056i) q^{67} +(3.57295 - 6.18853i) q^{68} +(-5.85410 - 10.1396i) q^{69} +6.85410 q^{70} +(7.09017 + 12.2805i) q^{71} +(-14.3992 - 24.9401i) q^{72} -2.00000 q^{73} +(-5.23607 - 9.06914i) q^{74} +(2.42705 - 4.20378i) q^{75} +(4.50000 - 7.79423i) q^{76} +1.85410 q^{77} +(-23.9894 - 5.93583i) q^{78} +4.00000 q^{79} +(-12.8992 + 22.3420i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(6.35410 + 11.0056i) q^{84} +(1.92705 + 3.33775i) q^{85} +32.8885 q^{86} +(9.28115 + 16.0754i) q^{87} +(-6.92705 + 11.9980i) q^{88} +(-2.45492 + 4.25204i) q^{89} +26.4164 q^{90} +(3.50000 + 0.866025i) q^{91} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} +(2.92705 - 5.06980i) q^{94} +(2.42705 + 4.20378i) q^{95} -28.4164 q^{96} +(-9.42705 - 16.3281i) q^{97} +(-1.30902 - 2.26728i) q^{98} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} + 3q^{3} - 3q^{4} + 6q^{5} + 7q^{6} - 2q^{7} + 12q^{8} - q^{9} + O(q^{10}) \) \( 4q - 3q^{2} + 3q^{3} - 3q^{4} + 6q^{5} + 7q^{6} - 2q^{7} + 12q^{8} - q^{9} - 7q^{10} + 3q^{11} - 24q^{12} - 10q^{13} + 6q^{14} + 7q^{15} - 13q^{16} - 6q^{17} + 18q^{18} - 3q^{19} - 12q^{20} - 6q^{21} - 3q^{22} + 19q^{24} - 6q^{25} - 6q^{26} - 3q^{28} - 3q^{29} + 18q^{30} + 8q^{31} - 15q^{32} + 3q^{33} - 2q^{34} - 3q^{35} - 24q^{36} - 8q^{37} - 6q^{38} + 6q^{39} + 38q^{40} - 6q^{41} + 7q^{42} - 5q^{43} + 36q^{44} - 9q^{45} + 10q^{46} + 27q^{48} - 2q^{49} - 3q^{50} + 2q^{51} + 21q^{52} + 24q^{53} + 5q^{54} - 3q^{55} - 6q^{56} + 6q^{57} - 17q^{58} - 66q^{60} + 12q^{61} + 9q^{62} - q^{63} + 8q^{64} - 15q^{65} - 24q^{66} + 12q^{67} + 21q^{68} - 10q^{69} + 14q^{70} + 6q^{71} - 33q^{72} - 8q^{73} - 12q^{74} + 3q^{75} + 18q^{76} - 6q^{77} - 49q^{78} + 16q^{79} - 27q^{80} - 2q^{81} - 4q^{82} + 12q^{84} + q^{85} + 60q^{86} + 17q^{87} - 21q^{88} - 21q^{89} + 52q^{90} + 14q^{91} - 60q^{92} - 9q^{93} + 5q^{94} + 3q^{95} - 60q^{96} - 31q^{97} - 3q^{98} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30902 + 2.26728i −0.925615 + 1.60321i −0.135045 + 0.990839i \(0.543118\pi\)
−0.790569 + 0.612372i \(0.790215\pi\)
\(3\) 1.30902 2.26728i 0.755761 1.30902i −0.189234 0.981932i \(-0.560600\pi\)
0.944995 0.327085i \(-0.106066\pi\)
\(4\) −2.42705 4.20378i −1.21353 2.10189i
\(5\) 2.61803 1.17082 0.585410 0.810737i \(-0.300933\pi\)
0.585410 + 0.810737i \(0.300933\pi\)
\(6\) 3.42705 + 5.93583i 1.39909 + 2.42329i
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 7.47214 2.64180
\(9\) −1.92705 3.33775i −0.642350 1.11258i
\(10\) −3.42705 + 5.93583i −1.08373 + 1.87707i
\(11\) −0.927051 + 1.60570i −0.279516 + 0.484137i −0.971265 0.238002i \(-0.923507\pi\)
0.691748 + 0.722139i \(0.256841\pi\)
\(12\) −12.7082 −3.66854
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 2.61803 0.699699
\(15\) 3.42705 5.93583i 0.884861 1.53262i
\(16\) −4.92705 + 8.53390i −1.23176 + 2.13348i
\(17\) 0.736068 + 1.27491i 0.178523 + 0.309210i 0.941375 0.337363i \(-0.109535\pi\)
−0.762852 + 0.646573i \(0.776202\pi\)
\(18\) 10.0902 2.37828
\(19\) 0.927051 + 1.60570i 0.212680 + 0.368373i 0.952552 0.304375i \(-0.0984475\pi\)
−0.739872 + 0.672747i \(0.765114\pi\)
\(20\) −6.35410 11.0056i −1.42082 2.46093i
\(21\) −2.61803 −0.571302
\(22\) −2.42705 4.20378i −0.517449 0.896248i
\(23\) 2.23607 3.87298i 0.466252 0.807573i −0.533005 0.846112i \(-0.678937\pi\)
0.999257 + 0.0385394i \(0.0122705\pi\)
\(24\) 9.78115 16.9415i 1.99657 3.45816i
\(25\) 1.85410 0.370820
\(26\) −2.61803 9.06914i −0.513439 1.77860i
\(27\) −2.23607 −0.430331
\(28\) −2.42705 + 4.20378i −0.458670 + 0.794439i
\(29\) −3.54508 + 6.14027i −0.658306 + 1.14022i 0.322748 + 0.946485i \(0.395393\pi\)
−0.981054 + 0.193734i \(0.937940\pi\)
\(30\) 8.97214 + 15.5402i 1.63808 + 2.83724i
\(31\) −4.70820 −0.845618 −0.422809 0.906219i \(-0.638956\pi\)
−0.422809 + 0.906219i \(0.638956\pi\)
\(32\) −5.42705 9.39993i −0.959376 1.66169i
\(33\) 2.42705 + 4.20378i 0.422495 + 0.731783i
\(34\) −3.85410 −0.660973
\(35\) −1.30902 2.26728i −0.221264 0.383241i
\(36\) −9.35410 + 16.2018i −1.55902 + 2.70030i
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −4.85410 −0.787439
\(39\) 2.61803 + 9.06914i 0.419221 + 1.45222i
\(40\) 19.5623 3.09307
\(41\) −0.381966 + 0.661585i −0.0596531 + 0.103322i −0.894310 0.447449i \(-0.852333\pi\)
0.834657 + 0.550771i \(0.185666\pi\)
\(42\) 3.42705 5.93583i 0.528805 0.915918i
\(43\) −6.28115 10.8793i −0.957867 1.65907i −0.727667 0.685931i \(-0.759395\pi\)
−0.230200 0.973143i \(-0.573938\pi\)
\(44\) 9.00000 1.35680
\(45\) −5.04508 8.73834i −0.752077 1.30264i
\(46\) 5.85410 + 10.1396i 0.863140 + 1.49500i
\(47\) −2.23607 −0.326164 −0.163082 0.986613i \(-0.552144\pi\)
−0.163082 + 0.986613i \(0.552144\pi\)
\(48\) 12.8992 + 22.3420i 1.86184 + 3.22480i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −2.42705 + 4.20378i −0.343237 + 0.594504i
\(51\) 3.85410 0.539682
\(52\) 16.9894 + 4.20378i 2.35600 + 0.582959i
\(53\) 3.76393 0.517016 0.258508 0.966009i \(-0.416769\pi\)
0.258508 + 0.966009i \(0.416769\pi\)
\(54\) 2.92705 5.06980i 0.398321 0.689913i
\(55\) −2.42705 + 4.20378i −0.327263 + 0.566837i
\(56\) −3.73607 6.47106i −0.499253 0.864732i
\(57\) 4.85410 0.642942
\(58\) −9.28115 16.0754i −1.21868 2.11081i
\(59\) 1.11803 + 1.93649i 0.145556 + 0.252110i 0.929580 0.368620i \(-0.120170\pi\)
−0.784024 + 0.620730i \(0.786836\pi\)
\(60\) −33.2705 −4.29520
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) 6.16312 10.6748i 0.782717 1.35571i
\(63\) −1.92705 + 3.33775i −0.242786 + 0.420517i
\(64\) 8.70820 1.08853
\(65\) −6.54508 + 6.80185i −0.811818 + 0.843666i
\(66\) −12.7082 −1.56427
\(67\) 6.35410 11.0056i 0.776277 1.34455i −0.157797 0.987472i \(-0.550439\pi\)
0.934074 0.357080i \(-0.116228\pi\)
\(68\) 3.57295 6.18853i 0.433284 0.750469i
\(69\) −5.85410 10.1396i −0.704751 1.22066i
\(70\) 6.85410 0.819222
\(71\) 7.09017 + 12.2805i 0.841448 + 1.45743i 0.888670 + 0.458547i \(0.151630\pi\)
−0.0472218 + 0.998884i \(0.515037\pi\)
\(72\) −14.3992 24.9401i −1.69696 2.93922i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −5.23607 9.06914i −0.608681 1.05427i
\(75\) 2.42705 4.20378i 0.280252 0.485410i
\(76\) 4.50000 7.79423i 0.516185 0.894059i
\(77\) 1.85410 0.211295
\(78\) −23.9894 5.93583i −2.71626 0.672100i
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −12.8992 + 22.3420i −1.44217 + 2.49792i
\(81\) 2.85410 4.94345i 0.317122 0.549272i
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) 6.70820 0.736321 0.368161 0.929762i \(-0.379988\pi\)
0.368161 + 0.929762i \(0.379988\pi\)
\(84\) 6.35410 + 11.0056i 0.693289 + 1.20081i
\(85\) 1.92705 + 3.33775i 0.209018 + 0.362030i
\(86\) 32.8885 3.54646
\(87\) 9.28115 + 16.0754i 0.995044 + 1.72347i
\(88\) −6.92705 + 11.9980i −0.738426 + 1.27899i
\(89\) −2.45492 + 4.25204i −0.260220 + 0.450715i −0.966300 0.257417i \(-0.917129\pi\)
0.706080 + 0.708132i \(0.250462\pi\)
\(90\) 26.4164 2.78453
\(91\) 3.50000 + 0.866025i 0.366900 + 0.0907841i
\(92\) −21.7082 −2.26324
\(93\) −6.16312 + 10.6748i −0.639086 + 1.10693i
\(94\) 2.92705 5.06980i 0.301902 0.522910i
\(95\) 2.42705 + 4.20378i 0.249010 + 0.431298i
\(96\) −28.4164 −2.90024
\(97\) −9.42705 16.3281i −0.957172 1.65787i −0.729318 0.684175i \(-0.760162\pi\)
−0.227854 0.973695i \(-0.573171\pi\)
\(98\) −1.30902 2.26728i −0.132231 0.229030i
\(99\) 7.14590 0.718190
\(100\) −4.50000 7.79423i −0.450000 0.779423i
\(101\) 5.78115 10.0133i 0.575246 0.996356i −0.420769 0.907168i \(-0.638240\pi\)
0.996015 0.0891877i \(-0.0284271\pi\)
\(102\) −5.04508 + 8.73834i −0.499538 + 0.865225i
\(103\) −8.70820 −0.858045 −0.429022 0.903294i \(-0.641142\pi\)
−0.429022 + 0.903294i \(0.641142\pi\)
\(104\) −18.6803 + 19.4132i −1.83176 + 1.90362i
\(105\) −6.85410 −0.668892
\(106\) −4.92705 + 8.53390i −0.478557 + 0.828886i
\(107\) 1.69098 2.92887i 0.163473 0.283144i −0.772639 0.634846i \(-0.781064\pi\)
0.936112 + 0.351702i \(0.114397\pi\)
\(108\) 5.42705 + 9.39993i 0.522218 + 0.904508i
\(109\) −2.70820 −0.259399 −0.129699 0.991553i \(-0.541401\pi\)
−0.129699 + 0.991553i \(0.541401\pi\)
\(110\) −6.35410 11.0056i −0.605840 1.04935i
\(111\) 5.23607 + 9.06914i 0.496986 + 0.860804i
\(112\) 9.85410 0.931125
\(113\) −0.736068 1.27491i −0.0692435 0.119933i 0.829325 0.558766i \(-0.188725\pi\)
−0.898568 + 0.438833i \(0.855392\pi\)
\(114\) −6.35410 + 11.0056i −0.595116 + 1.03077i
\(115\) 5.85410 10.1396i 0.545898 0.945523i
\(116\) 34.4164 3.19548
\(117\) 13.4894 + 3.33775i 1.24709 + 0.308575i
\(118\) −5.85410 −0.538914
\(119\) 0.736068 1.27491i 0.0674752 0.116871i
\(120\) 25.6074 44.3533i 2.33762 4.04888i
\(121\) 3.78115 + 6.54915i 0.343741 + 0.595377i
\(122\) −15.7082 −1.42215
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 11.4271 + 19.7922i 1.02618 + 1.77739i
\(125\) −8.23607 −0.736656
\(126\) −5.04508 8.73834i −0.449452 0.778474i
\(127\) 10.4271 18.0602i 0.925251 1.60258i 0.134094 0.990969i \(-0.457187\pi\)
0.791157 0.611613i \(-0.209479\pi\)
\(128\) −0.545085 + 0.944115i −0.0481792 + 0.0834488i
\(129\) −32.8885 −2.89567
\(130\) −6.85410 23.7433i −0.601145 2.08243i
\(131\) −15.3262 −1.33906 −0.669530 0.742785i \(-0.733504\pi\)
−0.669530 + 0.742785i \(0.733504\pi\)
\(132\) 11.7812 20.4056i 1.02542 1.77608i
\(133\) 0.927051 1.60570i 0.0803855 0.139232i
\(134\) 16.6353 + 28.8131i 1.43707 + 2.48907i
\(135\) −5.85410 −0.503841
\(136\) 5.50000 + 9.52628i 0.471621 + 0.816872i
\(137\) 1.30902 + 2.26728i 0.111837 + 0.193707i 0.916511 0.400010i \(-0.130993\pi\)
−0.804674 + 0.593717i \(0.797660\pi\)
\(138\) 30.6525 2.60931
\(139\) −2.28115 3.95107i −0.193485 0.335126i 0.752918 0.658114i \(-0.228646\pi\)
−0.946403 + 0.322989i \(0.895312\pi\)
\(140\) −6.35410 + 11.0056i −0.537020 + 0.930145i
\(141\) −2.92705 + 5.06980i −0.246502 + 0.426954i
\(142\) −37.1246 −3.11543
\(143\) −1.85410 6.42280i −0.155048 0.537101i
\(144\) 37.9787 3.16489
\(145\) −9.28115 + 16.0754i −0.770758 + 1.33499i
\(146\) 2.61803 4.53457i 0.216670 0.375284i
\(147\) 1.30902 + 2.26728i 0.107966 + 0.187002i
\(148\) 19.4164 1.59602
\(149\) −0.927051 1.60570i −0.0759470 0.131544i 0.825551 0.564328i \(-0.190865\pi\)
−0.901498 + 0.432784i \(0.857531\pi\)
\(150\) 6.35410 + 11.0056i 0.518810 + 0.898606i
\(151\) −1.29180 −0.105125 −0.0525624 0.998618i \(-0.516739\pi\)
−0.0525624 + 0.998618i \(0.516739\pi\)
\(152\) 6.92705 + 11.9980i 0.561858 + 0.973167i
\(153\) 2.83688 4.91362i 0.229348 0.397243i
\(154\) −2.42705 + 4.20378i −0.195577 + 0.338750i
\(155\) −12.3262 −0.990067
\(156\) 31.7705 33.0169i 2.54368 2.64347i
\(157\) 14.8541 1.18549 0.592743 0.805392i \(-0.298045\pi\)
0.592743 + 0.805392i \(0.298045\pi\)
\(158\) −5.23607 + 9.06914i −0.416559 + 0.721502i
\(159\) 4.92705 8.53390i 0.390741 0.676783i
\(160\) −14.2082 24.6093i −1.12326 1.94554i
\(161\) −4.47214 −0.352454
\(162\) 7.47214 + 12.9421i 0.587066 + 1.01683i
\(163\) 1.85410 + 3.21140i 0.145224 + 0.251536i 0.929457 0.368931i \(-0.120276\pi\)
−0.784232 + 0.620467i \(0.786943\pi\)
\(164\) 3.70820 0.289562
\(165\) 6.35410 + 11.0056i 0.494666 + 0.856787i
\(166\) −8.78115 + 15.2094i −0.681550 + 1.18048i
\(167\) −7.11803 + 12.3288i −0.550810 + 0.954031i 0.447406 + 0.894331i \(0.352348\pi\)
−0.998216 + 0.0597001i \(0.980986\pi\)
\(168\) −19.5623 −1.50926
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) −10.0902 −0.773881
\(171\) 3.57295 6.18853i 0.273230 0.473249i
\(172\) −30.4894 + 52.8091i −2.32479 + 4.02666i
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) −48.5967 −3.68411
\(175\) −0.927051 1.60570i −0.0700785 0.121379i
\(176\) −9.13525 15.8227i −0.688596 1.19268i
\(177\) 5.85410 0.440021
\(178\) −6.42705 11.1320i −0.481728 0.834377i
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) −24.4894 + 42.4168i −1.82533 + 3.16156i
\(181\) 9.70820 0.721605 0.360803 0.932642i \(-0.382503\pi\)
0.360803 + 0.932642i \(0.382503\pi\)
\(182\) −6.54508 + 6.80185i −0.485154 + 0.504187i
\(183\) 15.7082 1.16118
\(184\) 16.7082 28.9395i 1.23175 2.13345i
\(185\) −5.23607 + 9.06914i −0.384963 + 0.666776i
\(186\) −16.1353 27.9471i −1.18309 2.04918i
\(187\) −2.72949 −0.199600
\(188\) 5.42705 + 9.39993i 0.395808 + 0.685560i
\(189\) 1.11803 + 1.93649i 0.0813250 + 0.140859i
\(190\) −12.7082 −0.921950
\(191\) −10.6910 18.5173i −0.773572 1.33987i −0.935593 0.353079i \(-0.885135\pi\)
0.162021 0.986787i \(-0.448199\pi\)
\(192\) 11.3992 19.7440i 0.822665 1.42490i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) 49.3607 3.54389
\(195\) 6.85410 + 23.7433i 0.490832 + 1.70029i
\(196\) 4.85410 0.346722
\(197\) 8.39919 14.5478i 0.598417 1.03649i −0.394638 0.918837i \(-0.629130\pi\)
0.993055 0.117652i \(-0.0375368\pi\)
\(198\) −9.35410 + 16.2018i −0.664767 + 1.15141i
\(199\) 12.2082 + 21.1452i 0.865417 + 1.49895i 0.866633 + 0.498946i \(0.166280\pi\)
−0.00121626 + 0.999999i \(0.500387\pi\)
\(200\) 13.8541 0.979633
\(201\) −16.6353 28.8131i −1.17336 2.03232i
\(202\) 15.1353 + 26.2150i 1.06491 + 1.84448i
\(203\) 7.09017 0.497632
\(204\) −9.35410 16.2018i −0.654918 1.13435i
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) 11.3992 19.7440i 0.794219 1.37563i
\(207\) −17.2361 −1.19799
\(208\) −9.85410 34.1356i −0.683259 2.36688i
\(209\) −3.43769 −0.237790
\(210\) 8.97214 15.5402i 0.619136 1.07238i
\(211\) −2.35410 + 4.07742i −0.162063 + 0.280701i −0.935608 0.353039i \(-0.885148\pi\)
0.773545 + 0.633741i \(0.218481\pi\)
\(212\) −9.13525 15.8227i −0.627412 1.08671i
\(213\) 37.1246 2.54374
\(214\) 4.42705 + 7.66788i 0.302627 + 0.524165i
\(215\) −16.4443 28.4823i −1.12149 1.94248i
\(216\) −16.7082 −1.13685
\(217\) 2.35410 + 4.07742i 0.159807 + 0.276794i
\(218\) 3.54508 6.14027i 0.240103 0.415871i
\(219\) −2.61803 + 4.53457i −0.176910 + 0.306418i
\(220\) 23.5623 1.58857
\(221\) −5.15248 1.27491i −0.346593 0.0857595i
\(222\) −27.4164 −1.84007
\(223\) −10.1353 + 17.5548i −0.678707 + 1.17555i 0.296664 + 0.954982i \(0.404126\pi\)
−0.975371 + 0.220573i \(0.929207\pi\)
\(224\) −5.42705 + 9.39993i −0.362610 + 0.628059i
\(225\) −3.57295 6.18853i −0.238197 0.412569i
\(226\) 3.85410 0.256371
\(227\) −0.736068 1.27491i −0.0488545 0.0846186i 0.840564 0.541712i \(-0.182224\pi\)
−0.889419 + 0.457094i \(0.848890\pi\)
\(228\) −11.7812 20.4056i −0.780226 1.35139i
\(229\) −13.1246 −0.867299 −0.433649 0.901082i \(-0.642774\pi\)
−0.433649 + 0.901082i \(0.642774\pi\)
\(230\) 15.3262 + 26.5458i 1.01058 + 1.75038i
\(231\) 2.42705 4.20378i 0.159688 0.276588i
\(232\) −26.4894 + 45.8809i −1.73911 + 3.01223i
\(233\) 2.61803 0.171513 0.0857566 0.996316i \(-0.472669\pi\)
0.0857566 + 0.996316i \(0.472669\pi\)
\(234\) −25.2254 + 26.2150i −1.64904 + 1.71373i
\(235\) −5.85410 −0.381880
\(236\) 5.42705 9.39993i 0.353271 0.611883i
\(237\) 5.23607 9.06914i 0.340119 0.589104i
\(238\) 1.92705 + 3.33775i 0.124912 + 0.216354i
\(239\) −24.7082 −1.59824 −0.799120 0.601171i \(-0.794701\pi\)
−0.799120 + 0.601171i \(0.794701\pi\)
\(240\) 33.7705 + 58.4922i 2.17988 + 3.77566i
\(241\) −12.2812 21.2716i −0.791099 1.37022i −0.925287 0.379267i \(-0.876176\pi\)
0.134189 0.990956i \(-0.457157\pi\)
\(242\) −19.7984 −1.27269
\(243\) −10.8262 18.7516i −0.694503 1.20292i
\(244\) 14.5623 25.2227i 0.932256 1.61471i
\(245\) −1.30902 + 2.26728i −0.0836300 + 0.144851i
\(246\) −5.23607 −0.333840
\(247\) −6.48936 1.60570i −0.412908 0.102168i
\(248\) −35.1803 −2.23395
\(249\) 8.78115 15.2094i 0.556483 0.963857i
\(250\) 10.7812 18.6735i 0.681860 1.18102i
\(251\) −0.381966 0.661585i −0.0241095 0.0417588i 0.853719 0.520734i \(-0.174342\pi\)
−0.877828 + 0.478975i \(0.841008\pi\)
\(252\) 18.7082 1.17851
\(253\) 4.14590 + 7.18091i 0.260650 + 0.451460i
\(254\) 27.2984 + 47.2822i 1.71285 + 2.96675i
\(255\) 10.0902 0.631871
\(256\) 7.28115 + 12.6113i 0.455072 + 0.788208i
\(257\) −8.37132 + 14.4996i −0.522189 + 0.904457i 0.477478 + 0.878644i \(0.341551\pi\)
−0.999667 + 0.0258138i \(0.991782\pi\)
\(258\) 43.0517 74.5677i 2.68028 4.64238i
\(259\) 4.00000 0.248548
\(260\) 44.4787 + 11.0056i 2.75845 + 0.682540i
\(261\) 27.3262 1.69145
\(262\) 20.0623 34.7489i 1.23945 2.14680i
\(263\) −4.50000 + 7.79423i −0.277482 + 0.480613i −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 18.1353 + 31.4112i 1.11615 + 1.93322i
\(265\) 9.85410 0.605333
\(266\) 2.42705 + 4.20378i 0.148812 + 0.257750i
\(267\) 6.42705 + 11.1320i 0.393329 + 0.681266i
\(268\) −61.6869 −3.76813
\(269\) 14.3713 + 24.8919i 0.876235 + 1.51768i 0.855441 + 0.517900i \(0.173286\pi\)
0.0207937 + 0.999784i \(0.493381\pi\)
\(270\) 7.66312 13.2729i 0.466363 0.807764i
\(271\) 4.20820 7.28882i 0.255630 0.442764i −0.709436 0.704770i \(-0.751050\pi\)
0.965066 + 0.262005i \(0.0843837\pi\)
\(272\) −14.5066 −0.879590
\(273\) 6.54508 6.80185i 0.396127 0.411667i
\(274\) −6.85410 −0.414071
\(275\) −1.71885 + 2.97713i −0.103650 + 0.179528i
\(276\) −28.4164 + 49.2187i −1.71047 + 2.96262i
\(277\) 2.50000 + 4.33013i 0.150210 + 0.260172i 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 11.9443 0.716370
\(279\) 9.07295 + 15.7148i 0.543183 + 0.940821i
\(280\) −9.78115 16.9415i −0.584536 1.01245i
\(281\) 20.1803 1.20386 0.601929 0.798550i \(-0.294399\pi\)
0.601929 + 0.798550i \(0.294399\pi\)
\(282\) −7.66312 13.2729i −0.456332 0.790390i
\(283\) −6.70820 + 11.6190i −0.398761 + 0.690675i −0.993573 0.113190i \(-0.963893\pi\)
0.594812 + 0.803865i \(0.297226\pi\)
\(284\) 34.4164 59.6110i 2.04224 3.53726i
\(285\) 12.7082 0.752769
\(286\) 16.9894 + 4.20378i 1.00460 + 0.248574i
\(287\) 0.763932 0.0450935
\(288\) −20.9164 + 36.2283i −1.23251 + 2.13477i
\(289\) 7.41641 12.8456i 0.436259 0.755623i
\(290\) −24.2984 42.0860i −1.42685 2.47138i
\(291\) −49.3607 −2.89357
\(292\) 4.85410 + 8.40755i 0.284065 + 0.492015i
\(293\) 3.38197 + 5.85774i 0.197577 + 0.342213i 0.947742 0.319037i \(-0.103360\pi\)
−0.750166 + 0.661250i \(0.770026\pi\)
\(294\) −6.85410 −0.399739
\(295\) 2.92705 + 5.06980i 0.170419 + 0.295175i
\(296\) −14.9443 + 25.8842i −0.868618 + 1.50449i
\(297\) 2.07295 3.59045i 0.120285 0.208339i
\(298\) 4.85410 0.281191
\(299\) 4.47214 + 15.4919i 0.258630 + 0.895922i
\(300\) −23.5623 −1.36037
\(301\) −6.28115 + 10.8793i −0.362040 + 0.627071i
\(302\) 1.69098 2.92887i 0.0973051 0.168537i
\(303\) −15.1353 26.2150i −0.869498 1.50601i
\(304\) −18.2705 −1.04789
\(305\) 7.85410 + 13.6037i 0.449725 + 0.778946i
\(306\) 7.42705 + 12.8640i 0.424576 + 0.735388i
\(307\) −4.85410 −0.277038 −0.138519 0.990360i \(-0.544234\pi\)
−0.138519 + 0.990360i \(0.544234\pi\)
\(308\) −4.50000 7.79423i −0.256411 0.444117i
\(309\) −11.3992 + 19.7440i −0.648477 + 1.12320i
\(310\) 16.1353 27.9471i 0.916421 1.58729i
\(311\) 3.32624 0.188614 0.0943068 0.995543i \(-0.469937\pi\)
0.0943068 + 0.995543i \(0.469937\pi\)
\(312\) 19.5623 + 67.7658i 1.10750 + 3.83648i
\(313\) 25.1246 1.42013 0.710064 0.704138i \(-0.248666\pi\)
0.710064 + 0.704138i \(0.248666\pi\)
\(314\) −19.4443 + 33.6785i −1.09730 + 1.90059i
\(315\) −5.04508 + 8.73834i −0.284258 + 0.492350i
\(316\) −9.70820 16.8151i −0.546129 0.945923i
\(317\) 26.2361 1.47356 0.736782 0.676130i \(-0.236344\pi\)
0.736782 + 0.676130i \(0.236344\pi\)
\(318\) 12.8992 + 22.3420i 0.723350 + 1.25288i
\(319\) −6.57295 11.3847i −0.368014 0.637420i
\(320\) 22.7984 1.27447
\(321\) −4.42705 7.66788i −0.247094 0.427979i
\(322\) 5.85410 10.1396i 0.326236 0.565058i
\(323\) −1.36475 + 2.36381i −0.0759364 + 0.131526i
\(324\) −27.7082 −1.53934
\(325\) −4.63525 + 4.81710i −0.257118 + 0.267205i
\(326\) −9.70820 −0.537688
\(327\) −3.54508 + 6.14027i −0.196044 + 0.339558i
\(328\) −2.85410 + 4.94345i −0.157591 + 0.272956i
\(329\) 1.11803 + 1.93649i 0.0616392 + 0.106762i
\(330\) −33.2705 −1.83148
\(331\) 5.07295 + 8.78661i 0.278834 + 0.482956i 0.971095 0.238692i \(-0.0767186\pi\)
−0.692261 + 0.721647i \(0.743385\pi\)
\(332\) −16.2812 28.1998i −0.893544 1.54766i
\(333\) 15.4164 0.844814
\(334\) −18.6353 32.2772i −1.01968 1.76613i
\(335\) 16.6353 28.8131i 0.908881 1.57423i
\(336\) 12.8992 22.3420i 0.703708 1.21886i
\(337\) −11.5623 −0.629839 −0.314919 0.949118i \(-0.601978\pi\)
−0.314919 + 0.949118i \(0.601978\pi\)
\(338\) 30.1074 + 15.8710i 1.63763 + 0.863268i
\(339\) −3.85410 −0.209326
\(340\) 9.35410 16.2018i 0.507297 0.878665i
\(341\) 4.36475 7.55996i 0.236364 0.409395i
\(342\) 9.35410 + 16.2018i 0.505812 + 0.876092i
\(343\) 1.00000 0.0539949
\(344\) −46.9336 81.2914i −2.53049 4.38294i
\(345\) −15.3262 26.5458i −0.825137 1.42918i
\(346\) −23.5623 −1.26672
\(347\) −15.3820 26.6423i −0.825747 1.43024i −0.901347 0.433098i \(-0.857420\pi\)
0.0755997 0.997138i \(-0.475913\pi\)
\(348\) 45.0517 78.0318i 2.41502 4.18294i
\(349\) −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i \(0.353659\pi\)
−0.997962 + 0.0638103i \(0.979675\pi\)
\(350\) 4.85410 0.259463
\(351\) 5.59017 5.80948i 0.298381 0.310087i
\(352\) 20.1246 1.07265
\(353\) −11.0729 + 19.1789i −0.589354 + 1.02079i 0.404964 + 0.914333i \(0.367284\pi\)
−0.994317 + 0.106458i \(0.966049\pi\)
\(354\) −7.66312 + 13.2729i −0.407290 + 0.705447i
\(355\) 18.5623 + 32.1509i 0.985185 + 1.70639i
\(356\) 23.8328 1.26314
\(357\) −1.92705 3.33775i −0.101990 0.176652i
\(358\) 11.7812 + 20.4056i 0.622653 + 1.07847i
\(359\) −22.0902 −1.16587 −0.582937 0.812517i \(-0.698097\pi\)
−0.582937 + 0.812517i \(0.698097\pi\)
\(360\) −37.6976 65.2941i −1.98684 3.44130i
\(361\) 7.78115 13.4774i 0.409534 0.709334i
\(362\) −12.7082 + 22.0113i −0.667928 + 1.15689i
\(363\) 19.7984 1.03915
\(364\) −4.85410 16.8151i −0.254424 0.881351i
\(365\) −5.23607 −0.274068
\(366\) −20.5623 + 35.6150i −1.07481 + 1.86162i
\(367\) 0.708204 1.22665i 0.0369679 0.0640304i −0.846949 0.531673i \(-0.821563\pi\)
0.883917 + 0.467643i \(0.154897\pi\)
\(368\) 22.0344 + 38.1648i 1.14862 + 1.98948i
\(369\) 2.94427 0.153273
\(370\) −13.7082 23.7433i −0.712656 1.23436i
\(371\) −1.88197 3.25966i −0.0977068 0.169233i
\(372\) 59.8328 3.10219
\(373\) 10.2812 + 17.8075i 0.532338 + 0.922036i 0.999287 + 0.0377522i \(0.0120198\pi\)
−0.466949 + 0.884284i \(0.654647\pi\)
\(374\) 3.57295 6.18853i 0.184753 0.320001i
\(375\) −10.7812 + 18.6735i −0.556736 + 0.964296i
\(376\) −16.7082 −0.861660
\(377\) −7.09017 24.5611i −0.365162 1.26496i
\(378\) −5.85410 −0.301103
\(379\) 3.07295 5.32250i 0.157847 0.273399i −0.776245 0.630431i \(-0.782878\pi\)
0.934092 + 0.357032i \(0.116211\pi\)
\(380\) 11.7812 20.4056i 0.604360 1.04678i
\(381\) −27.2984 47.2822i −1.39854 2.42234i
\(382\) 55.9787 2.86412
\(383\) 10.9894 + 19.0341i 0.561530 + 0.972598i 0.997363 + 0.0725709i \(0.0231204\pi\)
−0.435833 + 0.900027i \(0.643546\pi\)
\(384\) 1.42705 + 2.47172i 0.0728239 + 0.126135i
\(385\) 4.85410 0.247388
\(386\) 7.85410 + 13.6037i 0.399763 + 0.692410i
\(387\) −24.2082 + 41.9298i −1.23057 + 2.13141i
\(388\) −45.7599 + 79.2584i −2.32311 + 4.02374i
\(389\) −11.8885 −0.602773 −0.301387 0.953502i \(-0.597449\pi\)
−0.301387 + 0.953502i \(0.597449\pi\)
\(390\) −62.8050 15.5402i −3.18025 0.786908i
\(391\) 6.58359 0.332947
\(392\) −3.73607 + 6.47106i −0.188700 + 0.326838i
\(393\) −20.0623 + 34.7489i −1.01201 + 1.75285i
\(394\) 21.9894 + 38.0867i 1.10781 + 1.91878i
\(395\) 10.4721 0.526910
\(396\) −17.3435 30.0398i −0.871542 1.50955i
\(397\) −0.708204 1.22665i −0.0355437 0.0615636i 0.847706 0.530466i \(-0.177983\pi\)
−0.883250 + 0.468902i \(0.844650\pi\)
\(398\) −63.9230 −3.20417
\(399\) −2.42705 4.20378i −0.121505 0.210452i
\(400\) −9.13525 + 15.8227i −0.456763 + 0.791136i
\(401\) −17.7254 + 30.7013i −0.885165 + 1.53315i −0.0396416 + 0.999214i \(0.512622\pi\)
−0.845524 + 0.533938i \(0.820712\pi\)
\(402\) 87.1033 4.34432
\(403\) 11.7705 12.2323i 0.586331 0.609333i
\(404\) −56.1246 −2.79230
\(405\) 7.47214 12.9421i 0.371293 0.643099i
\(406\) −9.28115 + 16.0754i −0.460616 + 0.797810i
\(407\) −3.70820 6.42280i −0.183809 0.318366i
\(408\) 28.7984 1.42573
\(409\) −7.21885 12.5034i −0.356949 0.618254i 0.630500 0.776189i \(-0.282850\pi\)
−0.987450 + 0.157935i \(0.949516\pi\)
\(410\) −2.61803 4.53457i −0.129295 0.223946i
\(411\) 6.85410 0.338088
\(412\) 21.1353 + 36.6073i 1.04126 + 1.80351i
\(413\) 1.11803 1.93649i 0.0550149 0.0952885i
\(414\) 22.5623 39.0791i 1.10888 1.92063i
\(415\) 17.5623 0.862100
\(416\) 37.9894 + 9.39993i 1.86258 + 0.460869i
\(417\) −11.9443 −0.584914
\(418\) 4.50000 7.79423i 0.220102 0.381228i
\(419\) 5.97214 10.3440i 0.291758 0.505340i −0.682468 0.730916i \(-0.739093\pi\)
0.974226 + 0.225576i \(0.0724265\pi\)
\(420\) 16.6353 + 28.8131i 0.811717 + 1.40594i
\(421\) 1.41641 0.0690315 0.0345157 0.999404i \(-0.489011\pi\)
0.0345157 + 0.999404i \(0.489011\pi\)
\(422\) −6.16312 10.6748i −0.300016 0.519643i
\(423\) 4.30902 + 7.46344i 0.209512 + 0.362885i
\(424\) 28.1246 1.36585
\(425\) 1.36475 + 2.36381i 0.0661999 + 0.114662i
\(426\) −48.5967 + 84.1720i −2.35452 + 4.07815i
\(427\) 3.00000 5.19615i 0.145180 0.251459i
\(428\) −16.4164 −0.793517
\(429\) −16.9894 4.20378i −0.820254 0.202960i
\(430\) 86.1033 4.15227
\(431\) −3.89919 + 6.75359i −0.187817 + 0.325309i −0.944522 0.328448i \(-0.893475\pi\)
0.756705 + 0.653756i \(0.226808\pi\)
\(432\) 11.0172 19.0824i 0.530066 0.918102i
\(433\) −0.500000 0.866025i −0.0240285 0.0416185i 0.853761 0.520665i \(-0.174316\pi\)
−0.877790 + 0.479046i \(0.840983\pi\)
\(434\) −12.3262 −0.591678
\(435\) 24.2984 + 42.0860i 1.16502 + 2.01787i
\(436\) 6.57295 + 11.3847i 0.314787 + 0.545227i
\(437\) 8.29180 0.396650
\(438\) −6.85410 11.8717i −0.327502 0.567250i
\(439\) −7.42705 + 12.8640i −0.354474 + 0.613967i −0.987028 0.160550i \(-0.948673\pi\)
0.632554 + 0.774516i \(0.282007\pi\)
\(440\) −18.1353 + 31.4112i −0.864564 + 1.49747i
\(441\) 3.85410 0.183529
\(442\) 9.63525 10.0133i 0.458302 0.476282i
\(443\) −5.23607 −0.248773 −0.124387 0.992234i \(-0.539696\pi\)
−0.124387 + 0.992234i \(0.539696\pi\)
\(444\) 25.4164 44.0225i 1.20621 2.08922i
\(445\) −6.42705 + 11.1320i −0.304671 + 0.527706i
\(446\) −26.5344 45.9590i −1.25644 2.17622i
\(447\) −4.85410 −0.229591
\(448\) −4.35410 7.54153i −0.205712 0.356304i
\(449\) −9.76393 16.9116i −0.460788 0.798109i 0.538212 0.842809i \(-0.319100\pi\)
−0.999000 + 0.0447005i \(0.985767\pi\)
\(450\) 18.7082 0.881913
\(451\) −0.708204 1.22665i −0.0333480 0.0577605i
\(452\) −3.57295 + 6.18853i −0.168057 + 0.291084i
\(453\) −1.69098 + 2.92887i −0.0794493 + 0.137610i
\(454\) 3.85410 0.180882
\(455\) 9.16312 + 2.26728i 0.429574 + 0.106292i
\(456\) 36.2705 1.69852
\(457\) −7.70820 + 13.3510i −0.360575 + 0.624533i −0.988055 0.154098i \(-0.950753\pi\)
0.627481 + 0.778632i \(0.284086\pi\)
\(458\) 17.1803 29.7572i 0.802785 1.39046i
\(459\) −1.64590 2.85078i −0.0768239 0.133063i
\(460\) −56.8328 −2.64984
\(461\) 6.10739 + 10.5783i 0.284450 + 0.492681i 0.972476 0.233005i \(-0.0748558\pi\)
−0.688026 + 0.725686i \(0.741523\pi\)
\(462\) 6.35410 + 11.0056i 0.295620 + 0.512028i
\(463\) 6.70820 0.311757 0.155878 0.987776i \(-0.450179\pi\)
0.155878 + 0.987776i \(0.450179\pi\)
\(464\) −34.9336 60.5068i −1.62175 2.80896i
\(465\) −16.1353 + 27.9471i −0.748255 + 1.29601i
\(466\) −3.42705 + 5.93583i −0.158755 + 0.274972i
\(467\) 2.34752 0.108630 0.0543152 0.998524i \(-0.482702\pi\)
0.0543152 + 0.998524i \(0.482702\pi\)
\(468\) −18.7082 64.8071i −0.864787 2.99571i
\(469\) −12.7082 −0.586810
\(470\) 7.66312 13.2729i 0.353473 0.612234i
\(471\) 19.4443 33.6785i 0.895945 1.55182i
\(472\) 8.35410 + 14.4697i 0.384529 + 0.666023i
\(473\) 23.2918 1.07096
\(474\) 13.7082 + 23.7433i 0.629639 + 1.09057i
\(475\) 1.71885 + 2.97713i 0.0788661 + 0.136600i
\(476\) −7.14590 −0.327532
\(477\) −7.25329 12.5631i −0.332105 0.575223i
\(478\) 32.3435 56.0205i 1.47936 2.56232i
\(479\) −12.4894 + 21.6322i −0.570653 + 0.988400i 0.425846 + 0.904796i \(0.359977\pi\)
−0.996499 + 0.0836047i \(0.973357\pi\)
\(480\) −74.3951 −3.39566
\(481\) −4.00000 13.8564i −0.182384 0.631798i
\(482\) 64.3050 2.92901
\(483\) −5.85410 + 10.1396i −0.266371 + 0.461368i
\(484\) 18.3541 31.7902i 0.834277 1.44501i
\(485\) −24.6803 42.7476i −1.12068 1.94107i
\(486\) 56.6869 2.57137
\(487\) −14.9894 25.9623i −0.679233 1.17647i −0.975212 0.221271i \(-0.928979\pi\)
0.295980 0.955194i \(-0.404354\pi\)
\(488\) 22.4164 + 38.8264i 1.01474 + 1.75759i
\(489\) 9.70820 0.439020
\(490\) −3.42705 5.93583i −0.154818 0.268153i
\(491\) −6.19098 + 10.7231i −0.279395 + 0.483927i −0.971235 0.238125i \(-0.923467\pi\)
0.691839 + 0.722051i \(0.256801\pi\)
\(492\) 4.85410 8.40755i 0.218840 0.379042i
\(493\) −10.4377 −0.470090
\(494\) 12.1353 12.6113i 0.545991 0.567410i
\(495\) 18.7082 0.840871
\(496\) 23.1976 40.1794i 1.04160 1.80411i
\(497\) 7.09017 12.2805i 0.318038 0.550857i
\(498\) 22.9894 + 39.8187i 1.03018 + 1.78432i
\(499\) 14.8541 0.664961 0.332480 0.943110i \(-0.392114\pi\)
0.332480 + 0.943110i \(0.392114\pi\)
\(500\) 19.9894 + 34.6226i 0.893951 + 1.54837i
\(501\) 18.6353 + 32.2772i 0.832562 + 1.44204i
\(502\) 2.00000 0.0892644
\(503\) −13.3090 23.0519i −0.593420 1.02783i −0.993768 0.111470i \(-0.964444\pi\)
0.400348 0.916363i \(-0.368889\pi\)
\(504\) −14.3992 + 24.9401i −0.641391 + 1.11092i
\(505\) 15.1353 26.2150i 0.673510 1.16655i
\(506\) −21.7082 −0.965047
\(507\) −30.1074 15.8710i −1.33712 0.704855i
\(508\) −101.228 −4.49126
\(509\) 9.29837 16.1053i 0.412143 0.713853i −0.582981 0.812486i \(-0.698114\pi\)
0.995124 + 0.0986331i \(0.0314470\pi\)
\(510\) −13.2082 + 22.8773i −0.584869 + 1.01302i
\(511\) 1.00000 + 1.73205i 0.0442374 + 0.0766214i
\(512\) −40.3050 −1.78124
\(513\) −2.07295 3.59045i −0.0915229 0.158522i
\(514\) −21.9164 37.9603i −0.966691 1.67436i
\(515\) −22.7984 −1.00462
\(516\) 79.8222 + 138.256i 3.51398 + 6.08638i
\(517\) 2.07295 3.59045i 0.0911682 0.157908i
\(518\) −5.23607 + 9.06914i −0.230060 + 0.398475i
\(519\) 23.5623 1.03427
\(520\) −48.9058 + 50.8244i −2.14466 + 2.22880i
\(521\) 18.6525 0.817180 0.408590 0.912718i \(-0.366021\pi\)
0.408590 + 0.912718i \(0.366021\pi\)
\(522\) −35.7705 + 61.9563i −1.56563 + 2.71176i
\(523\) −0.562306 + 0.973942i −0.0245879 + 0.0425875i −0.878058 0.478555i \(-0.841161\pi\)
0.853470 + 0.521143i \(0.174494\pi\)
\(524\) 37.1976 + 64.4281i 1.62498 + 2.81455i
\(525\) −4.85410 −0.211850
\(526\) −11.7812 20.4056i −0.513683 0.889724i
\(527\) −3.46556 6.00252i −0.150962 0.261474i
\(528\) −47.8328 −2.08166
\(529\) 1.50000 + 2.59808i 0.0652174 + 0.112960i
\(530\) −12.8992 + 22.3420i −0.560305 + 0.970477i
\(531\) 4.30902 7.46344i 0.186995 0.323886i
\(532\) −9.00000 −0.390199
\(533\) −0.763932 2.64634i −0.0330896 0.114626i
\(534\) −33.6525 −1.45629
\(535\) 4.42705 7.66788i 0.191398 0.331511i
\(536\) 47.4787 82.2355i 2.05077 3.55203i
\(537\) −11.7812 20.4056i −0.508394 0.880565i
\(538\) −75.2492 −3.24422
\(539\) −0.927051 1.60570i −0.0399309 0.0691624i
\(540\) 14.2082 + 24.6093i 0.611424 + 1.05902i
\(541\) 35.2705 1.51640 0.758199 0.652023i \(-0.226080\pi\)
0.758199 + 0.652023i \(0.226080\pi\)
\(542\) 11.0172 + 19.0824i 0.473230 + 0.819659i
\(543\) 12.7082 22.0113i 0.545361 0.944593i
\(544\) 7.98936 13.8380i 0.342541 0.593298i
\(545\) −7.09017 −0.303710
\(546\) 6.85410 + 23.7433i 0.293328 + 1.01612i
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) 6.35410 11.0056i 0.271434 0.470137i
\(549\) 11.5623 20.0265i 0.493467 0.854710i
\(550\) −4.50000 7.79423i −0.191881 0.332347i
\(551\) −13.1459 −0.560034
\(552\) −43.7426 75.7645i −1.86181 3.22475i
\(553\) −2.00000 3.46410i −0.0850487 0.147309i
\(554\) −13.0902 −0.556148
\(555\) 13.7082 + 23.7433i 0.581881 + 1.00785i
\(556\) −11.0729 + 19.1789i −0.469598 + 0.813367i
\(557\) 13.9894 24.2303i 0.592748 1.02667i −0.401112 0.916029i \(-0.631376\pi\)
0.993860 0.110641i \(-0.0352904\pi\)
\(558\) −47.5066 −2.01111
\(559\) 43.9681 + 10.8793i 1.85965 + 0.460144i
\(560\) 25.7984 1.09018
\(561\) −3.57295 + 6.18853i −0.150850 + 0.261280i
\(562\) −26.4164 + 45.7546i −1.11431 + 1.93004i
\(563\) 10.5279 + 18.2348i 0.443697 + 0.768505i 0.997960 0.0638360i \(-0.0203335\pi\)
−0.554264 + 0.832341i \(0.687000\pi\)
\(564\) 28.4164 1.19655
\(565\) −1.92705 3.33775i −0.0810716 0.140420i
\(566\) −17.5623 30.4188i −0.738199 1.27860i
\(567\) −5.70820 −0.239722
\(568\) 52.9787 + 91.7618i 2.22294 + 3.85024i
\(569\) −7.47214 + 12.9421i −0.313248 + 0.542562i −0.979064 0.203555i \(-0.934751\pi\)
0.665815 + 0.746117i \(0.268084\pi\)
\(570\) −16.6353 + 28.8131i −0.696774 + 1.20685i
\(571\) 24.6869 1.03312 0.516558 0.856252i \(-0.327213\pi\)
0.516558 + 0.856252i \(0.327213\pi\)
\(572\) −22.5000 + 23.3827i −0.940772 + 0.977679i
\(573\) −55.9787 −2.33854
\(574\) −1.00000 + 1.73205i −0.0417392 + 0.0722944i
\(575\) 4.14590 7.18091i 0.172896 0.299464i
\(576\) −16.7812 29.0658i −0.699215 1.21108i
\(577\) −43.8328 −1.82478 −0.912392 0.409318i \(-0.865767\pi\)
−0.912392 + 0.409318i \(0.865767\pi\)
\(578\) 19.4164 + 33.6302i 0.807616 + 1.39883i
\(579\) −7.85410 13.6037i −0.326405 0.565351i
\(580\) 90.1033 3.74134
\(581\) −3.35410 5.80948i −0.139152 0.241018i
\(582\) 64.6140 111.915i 2.67834 4.63901i
\(583\) −3.48936 + 6.04374i −0.144514 + 0.250306i
\(584\) −14.9443 −0.618398
\(585\) 35.3156 + 8.73834i 1.46012 + 0.361286i
\(586\) −17.7082 −0.731519
\(587\) 9.95492 17.2424i 0.410883 0.711671i −0.584103 0.811679i \(-0.698554\pi\)
0.994987 + 0.100009i \(0.0318870\pi\)
\(588\) 6.35410 11.0056i 0.262039 0.453864i
\(589\) −4.36475 7.55996i −0.179846 0.311503i
\(590\) −15.3262 −0.630971
\(591\) −21.9894 38.0867i −0.904521 1.56668i
\(592\) −19.7082 34.1356i −0.810002 1.40296i
\(593\) 43.7984 1.79858 0.899292 0.437349i \(-0.144083\pi\)
0.899292 + 0.437349i \(0.144083\pi\)
\(594\) 5.42705 + 9.39993i 0.222675 + 0.385684i
\(595\) 1.92705 3.33775i 0.0790014 0.136834i
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) 63.9230 2.61619
\(598\) −40.9787 10.1396i −1.67574 0.414639i
\(599\) 29.5066 1.20561 0.602803 0.797890i \(-0.294050\pi\)
0.602803 + 0.797890i \(0.294050\pi\)
\(600\) 18.1353 31.4112i 0.740369 1.28236i
\(601\) −20.1976 + 34.9832i −0.823876 + 1.42699i 0.0788998 + 0.996883i \(0.474859\pi\)
−0.902776 + 0.430112i \(0.858474\pi\)
\(602\) −16.4443 28.4823i −0.670218 1.16085i
\(603\) −48.9787 −1.99457
\(604\) 3.13525 + 5.43042i 0.127572 + 0.220961i
\(605\) 9.89919 + 17.1459i 0.402459 + 0.697080i
\(606\) 79.2492 3.21928
\(607\) 11.5000 + 19.9186i 0.466771 + 0.808470i 0.999279 0.0379540i \(-0.0120840\pi\)
−0.532509 + 0.846424i \(0.678751\pi\)
\(608\) 10.0623 17.4284i 0.408080 0.706816i
\(609\) 9.28115 16.0754i 0.376091 0.651409i
\(610\) −41.1246 −1.66509
\(611\) 5.59017 5.80948i 0.226154 0.235026i
\(612\) −27.5410 −1.11328
\(613\) −17.2812 + 29.9318i −0.697979 + 1.20894i 0.271187 + 0.962527i \(0.412584\pi\)
−0.969166 + 0.246409i \(0.920749\pi\)
\(614\) 6.35410 11.0056i 0.256431 0.444151i
\(615\) 2.61803 + 4.53457i 0.105569 + 0.182851i
\(616\) 13.8541 0.558198
\(617\) −0.0278640 0.0482619i −0.00112176 0.00194295i 0.865464 0.500971i \(-0.167024\pi\)
−0.866586 + 0.499028i \(0.833690\pi\)
\(618\) −29.8435 51.6904i −1.20048 2.07929i
\(619\) 9.41641 0.378477 0.189239 0.981931i \(-0.439398\pi\)
0.189239 + 0.981931i \(0.439398\pi\)
\(620\) 29.9164 + 51.8167i 1.20147 + 2.08101i
\(621\) −5.00000 + 8.66025i −0.200643 + 0.347524i
\(622\) −4.35410 + 7.54153i −0.174584 + 0.302388i
\(623\) 4.90983 0.196708
\(624\) −90.2943 22.3420i −3.61467 0.894398i
\(625\) −30.8328 −1.23331
\(626\) −32.8885 + 56.9646i −1.31449 + 2.27676i
\(627\) −4.50000 + 7.79423i −0.179713 + 0.311272i
\(628\) −36.0517 62.4433i −1.43862 2.49176i
\(629\) −5.88854 −0.234792
\(630\) −13.2082 22.8773i −0.526227 0.911453i
\(631\) −17.1976 29.7870i −0.684624 1.18580i −0.973555 0.228454i \(-0.926633\pi\)
0.288931 0.957350i \(-0.406700\pi\)
\(632\) 29.8885 1.18890
\(633\) 6.16312 + 10.6748i 0.244962 + 0.424287i
\(634\) −34.3435 + 59.4846i −1.36395 + 2.36244i
\(635\) 27.2984 47.2822i 1.08330 1.87634i
\(636\) −47.8328 −1.89669
\(637\) −1.00000 3.46410i −0.0396214 0.137253i
\(638\) 34.4164 1.36256
\(639\) 27.3262 47.3304i 1.08101 1.87236i
\(640\) −1.42705 + 2.47172i −0.0564091 + 0.0977035i
\(641\) 23.7533 + 41.1419i 0.938199 + 1.62501i 0.768829 + 0.639455i \(0.220840\pi\)
0.169370 + 0.985553i \(0.445827\pi\)
\(642\) 23.1803 0.914855
\(643\) 3.50000 + 6.06218i 0.138027 + 0.239069i 0.926750 0.375680i \(-0.122591\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 10.8541 + 18.7999i 0.427712 + 0.740818i
\(645\) −86.1033 −3.39032
\(646\) −3.57295 6.18853i −0.140576 0.243484i
\(647\) −12.3820 + 21.4462i −0.486785 + 0.843137i −0.999885 0.0151924i \(-0.995164\pi\)
0.513099 + 0.858329i \(0.328497\pi\)
\(648\) 21.3262 36.9381i 0.837774 1.45107i
\(649\) −4.14590 −0.162741
\(650\) −4.85410 16.8151i −0.190394 0.659543i
\(651\) 12.3262 0.483103
\(652\) 9.00000 15.5885i 0.352467 0.610491i
\(653\) 0.190983 0.330792i 0.00747374 0.0129449i −0.862264 0.506458i \(-0.830954\pi\)
0.869738 + 0.493514i \(0.164288\pi\)
\(654\) −9.28115 16.0754i −0.362922 0.628599i
\(655\) −40.1246 −1.56780
\(656\) −3.76393 6.51932i −0.146957 0.254537i
\(657\) 3.85410 + 6.67550i 0.150363 + 0.260436i
\(658\) −5.85410 −0.228217
\(659\) 11.9443 + 20.6881i 0.465283 + 0.805893i 0.999214 0.0396343i \(-0.0126193\pi\)
−0.533931 + 0.845528i \(0.679286\pi\)
\(660\) 30.8435 53.4224i 1.20058 2.07947i
\(661\) 24.2705 42.0378i 0.944013 1.63508i 0.186299 0.982493i \(-0.440351\pi\)
0.757715 0.652586i \(-0.226316\pi\)
\(662\) −26.5623 −1.03237
\(663\) −9.63525 + 10.0133i −0.374202 + 0.388882i
\(664\) 50.1246 1.94521
\(665\) 2.42705 4.20378i 0.0941170 0.163015i
\(666\) −20.1803 + 34.9534i −0.781972 + 1.35442i
\(667\) 15.8541 + 27.4601i 0.613873 + 1.06326i
\(668\) 69.1033 2.67369
\(669\) 26.5344 + 45.9590i 1.02588 + 1.77688i
\(670\) 43.5517 + 75.4337i 1.68255 + 2.91426i
\(671\) −11.1246 −0.429461
\(672\) 14.2082 + 24.6093i 0.548093 + 0.949326i
\(673\) 19.6246 33.9908i 0.756473 1.31025i −0.188165 0.982137i \(-0.560254\pi\)
0.944639 0.328113i \(-0.106413\pi\)
\(674\) 15.1353 26.2150i 0.582988 1.00977i
\(675\) −4.14590 −0.159576
\(676\) −53.3951 + 33.6302i −2.05366 + 1.29347i
\(677\) 43.7426 1.68117 0.840583 0.541682i \(-0.182212\pi\)
0.840583 + 0.541682i \(0.182212\pi\)
\(678\) 5.04508 8.73834i 0.193755 0.335594i
\(679\) −9.42705 + 16.3281i −0.361777 + 0.626616i
\(680\) 14.3992 + 24.9401i 0.552184 + 0.956410i
\(681\) −3.85410 −0.147690
\(682\) 11.4271 + 19.7922i 0.437564 + 0.757884i
\(683\) −0.736068 1.27491i −0.0281649 0.0487830i 0.851599 0.524193i \(-0.175633\pi\)
−0.879764 + 0.475410i \(0.842300\pi\)
\(684\) −34.6869 −1.32629
\(685\) 3.42705 + 5.93583i 0.130941 + 0.226796i
\(686\) −1.30902 + 2.26728i −0.0499785 + 0.0865653i
\(687\) −17.1803 + 29.7572i −0.655471 + 1.13531i
\(688\) 123.790 4.71946
\(689\) −9.40983 + 9.77898i −0.358486 + 0.372550i
\(690\) 80.2492 3.05504
\(691\) 2.92705 5.06980i 0.111350 0.192864i −0.804965 0.593323i \(-0.797816\pi\)
0.916315 + 0.400458i \(0.131149\pi\)
\(692\) 21.8435 37.8340i 0.830364 1.43823i
\(693\) −3.57295 6.18853i −0.135725 0.235083i
\(694\) 80.5410 3.05730
\(695\) −5.97214 10.3440i −0.226536 0.392372i
\(696\) 69.3500 + 120.118i 2.62871 + 4.55305i
\(697\) −1.12461 −0.0425977
\(698\) −27.1074 46.9514i −1.02603 1.77714i
\(699\) 3.42705 5.93583i 0.129623 0.224514i
\(700\) −4.50000 + 7.79423i −0.170084 + 0.294594i
\(701\) 11.2361 0.424380 0.212190 0.977228i \(-0.431940\pi\)
0.212190 + 0.977228i \(0.431940\pi\)
\(702\) 5.85410 + 20.2792i 0.220949 + 0.765389i
\(703\) −7.41641 −0.279715
\(704\) −8.07295 + 13.9828i −0.304261 + 0.526995i
\(705\) −7.66312 + 13.2729i −0.288610 + 0.499887i
\(706\) −28.9894 50.2110i −1.09103 1.88972i
\(707\) −11.5623 −0.434845
\(708\) −14.2082 24.6093i −0.533977 0.924875i
\(709\) −11.7812 20.4056i −0.442450 0.766347i 0.555420 0.831570i \(-0.312557\pi\)
−0.997871 + 0.0652231i \(0.979224\pi\)
\(710\) −97.1935 −3.64761
\(711\) −7.70820 13.3510i −0.289080 0.500702i
\(712\) −18.3435 + 31.7718i −0.687450 + 1.19070i
\(713\) −10.5279 + 18.2348i −0.394272 + 0.682898i
\(714\) 10.0902 0.377615
\(715\) −4.85410 16.8151i −0.181533 0.628849i
\(716\) −43.6869 −1.63266
\(717\) −32.3435 + 56.0205i −1.20789 + 2.09212i
\(718\) 28.9164 50.0847i 1.07915 1.86914i
\(719\) −4.06231 7.03612i −0.151498 0.262403i 0.780280 0.625430i \(-0.215077\pi\)
−0.931779 + 0.363027i \(0.881743\pi\)
\(720\) 99.4296 3.70552
\(721\) 4.35410 + 7.54153i 0.162155 + 0.280861i
\(722\) 20.3713 + 35.2842i 0.758142 + 1.31314i
\(723\) −64.3050 −2.39153
\(724\) −23.5623 40.8111i −0.875686 1.51673i
\(725\) −6.57295 + 11.3847i −0.244113 + 0.422816i
\(726\) −25.9164 + 44.8885i −0.961848 + 1.66597i
\(727\) −30.7082 −1.13890 −0.569452 0.822025i \(-0.692845\pi\)
−0.569452 + 0.822025i \(0.692845\pi\)
\(728\) 26.1525 + 6.47106i 0.969275 + 0.239833i
\(729\) −39.5623 −1.46527
\(730\) 6.85410 11.8717i 0.253682 0.439390i
\(731\) 9.24671 16.0158i 0.342002 0.592365i
\(732\) −38.1246 66.0338i −1.40913 2.44068i
\(733\) −32.2705 −1.19194 −0.595969 0.803007i \(-0.703232\pi\)
−0.595969 + 0.803007i \(0.703232\pi\)
\(734\) 1.85410 + 3.21140i 0.0684362 + 0.118535i
\(735\) 3.42705 + 5.93583i 0.126409 + 0.218946i
\(736\) −48.5410 −1.78925
\(737\) 11.7812 + 20.4056i 0.433964 + 0.751648i
\(738\) −3.85410 + 6.67550i −0.141871 + 0.245729i
\(739\) 3.43769 5.95426i 0.126458 0.219031i −0.795844 0.605502i \(-0.792973\pi\)
0.922302 + 0.386470i \(0.126306\pi\)
\(740\) 50.8328 1.86865
\(741\) −12.1353 + 12.6113i −0.445800 + 0.463289i
\(742\) 9.85410 0.361755
\(743\) −19.6631 + 34.0575i −0.721370 + 1.24945i 0.239081 + 0.971000i \(0.423154\pi\)
−0.960451 + 0.278450i \(0.910179\pi\)
\(744\) −46.0517 + 79.7638i −1.68834 + 2.92428i
\(745\) −2.42705 4.20378i −0.0889203 0.154014i
\(746\) −53.8328 −1.97096
\(747\) −12.9271 22.3903i −0.472976 0.819219i
\(748\) 6.62461 + 11.4742i 0.242220 + 0.419537i
\(749\) −3.38197 −0.123574
\(750\) −28.2254 48.8879i −1.03065 1.78513i
\(751\) −11.3541 + 19.6659i −0.414317 + 0.717618i −0.995356 0.0962572i \(-0.969313\pi\)
0.581039 + 0.813875i \(0.302646\pi\)
\(752\) 11.0172 19.0824i 0.401757 0.695863i
\(753\) −2.00000 −0.0728841
\(754\) 64.9681 + 16.0754i 2.36600 + 0.585433i
\(755\) −3.38197 −0.123082
\(756\) 5.42705 9.39993i 0.197380 0.341872i
\(757\) −14.0000 + 24.2487i −0.508839 + 0.881334i 0.491109 + 0.871098i \(0.336592\pi\)
−0.999948 + 0.0102362i \(0.996742\pi\)
\(758\) 8.04508 + 13.9345i 0.292211 + 0.506124i
\(759\) 21.7082 0.787958
\(760\) 18.1353 + 31.4112i 0.657835 + 1.13940i
\(761\) 14.4271 + 24.9884i 0.522980 + 0.905828i 0.999642 + 0.0267417i \(0.00851317\pi\)
−0.476662 + 0.879087i \(0.658154\pi\)
\(762\) 142.936 5.17803
\(763\) 1.35410 + 2.34537i 0.0490218 + 0.0849082i
\(764\) −51.8951 + 89.8850i −1.87750 + 3.25192i
\(765\) 7.42705 12.8640i 0.268526 0.465100i
\(766\) −57.5410 −2.07904
\(767\) −7.82624 1.93649i −0.282589 0.0699227i
\(768\) 38.1246 1.37570
\(769\) 9.20820 15.9491i 0.332056 0.575138i −0.650859 0.759199i \(-0.725591\pi\)
0.982915 + 0.184061i \(0.0589243\pi\)
\(770\) −6.35410 + 11.0056i −0.228986 + 0.396615i
\(771\) 21.9164 + 37.9603i 0.789300 + 1.36711i
\(772\) −29.1246 −1.04822
\(773\) −12.6803 21.9630i −0.456080 0.789954i 0.542669 0.839946i \(-0.317414\pi\)
−0.998750 + 0.0499924i \(0.984080\pi\)
\(774\) −63.3779 109.774i −2.27807 3.94574i
\(775\) −8.72949 −0.313573
\(776\) −70.4402 122.006i −2.52866 4.37976i
\(777\) 5.23607 9.06914i