Properties

Label 105.3.t.b.11.12
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.12
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.987174 - 0.569945i) q^{2} +(2.69338 - 1.32124i) q^{3} +(-1.35032 + 2.33883i) q^{4} +(1.93649 - 1.11803i) q^{5} +(1.90581 - 2.83938i) q^{6} +(2.61061 - 6.49498i) q^{7} +7.63801i q^{8} +(5.50864 - 7.11722i) q^{9} +O(q^{10})\) \(q+(0.987174 - 0.569945i) q^{2} +(2.69338 - 1.32124i) q^{3} +(-1.35032 + 2.33883i) q^{4} +(1.93649 - 1.11803i) q^{5} +(1.90581 - 2.83938i) q^{6} +(2.61061 - 6.49498i) q^{7} +7.63801i q^{8} +(5.50864 - 7.11722i) q^{9} +(1.27444 - 2.20739i) q^{10} +(12.8353 + 7.41045i) q^{11} +(-0.546784 + 8.08347i) q^{12} -23.9894 q^{13} +(-1.12465 - 7.89958i) q^{14} +(3.73852 - 5.56987i) q^{15} +(-1.04805 - 1.81528i) q^{16} +(-5.54599 - 3.20198i) q^{17} +(1.38156 - 10.1656i) q^{18} +(3.55819 + 6.16296i) q^{19} +6.03883i q^{20} +(-1.55005 - 20.9427i) q^{21} +16.8942 q^{22} +(-28.8602 + 16.6624i) q^{23} +(10.0917 + 20.5721i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-23.6818 + 13.6727i) q^{26} +(5.43333 - 26.4477i) q^{27} +(11.6655 + 14.8761i) q^{28} +32.6179i q^{29} +(0.516055 - 7.62919i) q^{30} +(-1.00299 + 1.73724i) q^{31} +(-28.5281 - 16.4707i) q^{32} +(44.3613 + 3.00070i) q^{33} -7.29982 q^{34} +(-2.20618 - 15.4962i) q^{35} +(9.20752 + 22.4943i) q^{36} +(9.06147 + 15.6949i) q^{37} +(7.02511 + 4.05595i) q^{38} +(-64.6128 + 31.6958i) q^{39} +(8.53955 + 14.7909i) q^{40} -40.8628i q^{41} +(-13.4664 - 19.7907i) q^{42} -29.7063 q^{43} +(-34.6636 + 20.0130i) q^{44} +(2.71015 - 19.9413i) q^{45} +(-18.9933 + 32.8974i) q^{46} +(-6.22822 + 3.59586i) q^{47} +(-5.22122 - 3.50451i) q^{48} +(-35.3694 - 33.9117i) q^{49} -5.69945i q^{50} +(-19.1681 - 1.29657i) q^{51} +(32.3935 - 56.1072i) q^{52} +(34.1430 + 19.7125i) q^{53} +(-9.71008 - 29.2052i) q^{54} +33.1406 q^{55} +(49.6087 + 19.9399i) q^{56} +(17.7263 + 11.8980i) q^{57} +(18.5904 + 32.1996i) q^{58} +(66.6011 + 38.4521i) q^{59} +(7.97876 + 16.2649i) q^{60} +(13.9524 + 24.1662i) q^{61} +2.28661i q^{62} +(-31.8453 - 54.3588i) q^{63} -29.1652 q^{64} +(-46.4554 + 26.8210i) q^{65} +(45.5026 - 22.3213i) q^{66} +(50.9881 - 88.3139i) q^{67} +(14.9778 - 8.64743i) q^{68} +(-55.7164 + 83.0095i) q^{69} +(-11.0099 - 14.0401i) q^{70} -65.1176i q^{71} +(54.3614 + 42.0751i) q^{72} +(58.9896 - 102.173i) q^{73} +(17.8905 + 10.3291i) q^{74} +(1.01232 - 14.9658i) q^{75} -19.2188 q^{76} +(81.6386 - 64.0190i) q^{77} +(-45.7192 + 68.1151i) q^{78} +(17.0304 + 29.4975i) q^{79} +(-4.05908 - 2.34351i) q^{80} +(-20.3097 - 78.4125i) q^{81} +(-23.2896 - 40.3387i) q^{82} -34.5698i q^{83} +(51.0745 + 24.6542i) q^{84} -14.3197 q^{85} +(-29.3253 + 16.9310i) q^{86} +(43.0962 + 87.8527i) q^{87} +(-56.6011 + 98.0360i) q^{88} +(28.7047 - 16.5727i) q^{89} +(-8.69006 - 21.2302i) q^{90} +(-62.6271 + 155.811i) q^{91} -89.9987i q^{92} +(-0.406140 + 6.00424i) q^{93} +(-4.09889 + 7.09949i) q^{94} +(13.7808 + 7.95635i) q^{95} +(-98.5988 - 6.66944i) q^{96} -5.32173 q^{97} +(-54.2436 - 13.3181i) q^{98} +(123.447 - 50.5300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.987174 0.569945i 0.493587 0.284973i −0.232474 0.972603i \(-0.574682\pi\)
0.726061 + 0.687630i \(0.241349\pi\)
\(3\) 2.69338 1.32124i 0.897795 0.440414i
\(4\) −1.35032 + 2.33883i −0.337581 + 0.584708i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) 1.90581 2.83938i 0.317634 0.473230i
\(7\) 2.61061 6.49498i 0.372944 0.927854i
\(8\) 7.63801i 0.954751i
\(9\) 5.50864 7.11722i 0.612071 0.790802i
\(10\) 1.27444 2.20739i 0.127444 0.220739i
\(11\) 12.8353 + 7.41045i 1.16684 + 0.673678i 0.952935 0.303176i \(-0.0980470\pi\)
0.213909 + 0.976854i \(0.431380\pi\)
\(12\) −0.546784 + 8.08347i −0.0455653 + 0.673623i
\(13\) −23.9894 −1.84534 −0.922671 0.385589i \(-0.873998\pi\)
−0.922671 + 0.385589i \(0.873998\pi\)
\(14\) −1.12465 7.89958i −0.0803324 0.564256i
\(15\) 3.73852 5.56987i 0.249235 0.371325i
\(16\) −1.04805 1.81528i −0.0655031 0.113455i
\(17\) −5.54599 3.20198i −0.326235 0.188352i 0.327933 0.944701i \(-0.393648\pi\)
−0.654168 + 0.756349i \(0.726981\pi\)
\(18\) 1.38156 10.1656i 0.0767535 0.564754i
\(19\) 3.55819 + 6.16296i 0.187273 + 0.324367i 0.944340 0.328971i \(-0.106702\pi\)
−0.757067 + 0.653337i \(0.773368\pi\)
\(20\) 6.03883i 0.301942i
\(21\) −1.55005 20.9427i −0.0738119 0.997272i
\(22\) 16.8942 0.767919
\(23\) −28.8602 + 16.6624i −1.25479 + 0.724453i −0.972057 0.234746i \(-0.924574\pi\)
−0.282733 + 0.959199i \(0.591241\pi\)
\(24\) 10.0917 + 20.5721i 0.420485 + 0.857171i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −23.6818 + 13.6727i −0.910837 + 0.525872i
\(27\) 5.43333 26.4477i 0.201234 0.979543i
\(28\) 11.6655 + 14.8761i 0.416624 + 0.531289i
\(29\) 32.6179i 1.12476i 0.826880 + 0.562378i \(0.190113\pi\)
−0.826880 + 0.562378i \(0.809887\pi\)
\(30\) 0.516055 7.62919i 0.0172018 0.254306i
\(31\) −1.00299 + 1.73724i −0.0323546 + 0.0560398i −0.881749 0.471718i \(-0.843634\pi\)
0.849395 + 0.527758i \(0.176967\pi\)
\(32\) −28.5281 16.4707i −0.891502 0.514709i
\(33\) 44.3613 + 3.00070i 1.34428 + 0.0909303i
\(34\) −7.29982 −0.214701
\(35\) −2.20618 15.4962i −0.0630337 0.442749i
\(36\) 9.20752 + 22.4943i 0.255764 + 0.624843i
\(37\) 9.06147 + 15.6949i 0.244904 + 0.424187i 0.962105 0.272680i \(-0.0879101\pi\)
−0.717200 + 0.696867i \(0.754577\pi\)
\(38\) 7.02511 + 4.05595i 0.184871 + 0.106735i
\(39\) −64.6128 + 31.6958i −1.65674 + 0.812714i
\(40\) 8.53955 + 14.7909i 0.213489 + 0.369773i
\(41\) 40.8628i 0.996654i −0.866989 0.498327i \(-0.833948\pi\)
0.866989 0.498327i \(-0.166052\pi\)
\(42\) −13.4664 19.7907i −0.320628 0.471206i
\(43\) −29.7063 −0.690844 −0.345422 0.938448i \(-0.612264\pi\)
−0.345422 + 0.938448i \(0.612264\pi\)
\(44\) −34.6636 + 20.0130i −0.787809 + 0.454842i
\(45\) 2.71015 19.9413i 0.0602255 0.443140i
\(46\) −18.9933 + 32.8974i −0.412899 + 0.715162i
\(47\) −6.22822 + 3.59586i −0.132515 + 0.0765077i −0.564792 0.825233i \(-0.691044\pi\)
0.432277 + 0.901741i \(0.357710\pi\)
\(48\) −5.22122 3.50451i −0.108775 0.0730106i
\(49\) −35.3694 33.9117i −0.721825 0.692076i
\(50\) 5.69945i 0.113989i
\(51\) −19.1681 1.29657i −0.375845 0.0254230i
\(52\) 32.3935 56.1072i 0.622952 1.07899i
\(53\) 34.1430 + 19.7125i 0.644207 + 0.371933i 0.786233 0.617930i \(-0.212028\pi\)
−0.142026 + 0.989863i \(0.545362\pi\)
\(54\) −9.71008 29.2052i −0.179816 0.540836i
\(55\) 33.1406 0.602556
\(56\) 49.6087 + 19.9399i 0.885869 + 0.356069i
\(57\) 17.7263 + 11.8980i 0.310988 + 0.208737i
\(58\) 18.5904 + 32.1996i 0.320525 + 0.555165i
\(59\) 66.6011 + 38.4521i 1.12883 + 0.651731i 0.943641 0.330971i \(-0.107376\pi\)
0.185191 + 0.982703i \(0.440710\pi\)
\(60\) 7.97876 + 16.2649i 0.132979 + 0.271082i
\(61\) 13.9524 + 24.1662i 0.228727 + 0.396167i 0.957431 0.288662i \(-0.0932103\pi\)
−0.728704 + 0.684829i \(0.759877\pi\)
\(62\) 2.28661i 0.0368807i
\(63\) −31.8453 54.3588i −0.505480 0.862838i
\(64\) −29.1652 −0.455706
\(65\) −46.4554 + 26.8210i −0.714698 + 0.412631i
\(66\) 45.5026 22.3213i 0.689434 0.338202i
\(67\) 50.9881 88.3139i 0.761016 1.31812i −0.181311 0.983426i \(-0.558034\pi\)
0.942327 0.334693i \(-0.108632\pi\)
\(68\) 14.9778 8.64743i 0.220262 0.127168i
\(69\) −55.7164 + 83.0095i −0.807485 + 1.20304i
\(70\) −11.0099 14.0401i −0.157284 0.200572i
\(71\) 65.1176i 0.917149i −0.888656 0.458575i \(-0.848360\pi\)
0.888656 0.458575i \(-0.151640\pi\)
\(72\) 54.3614 + 42.0751i 0.755019 + 0.584376i
\(73\) 58.9896 102.173i 0.808077 1.39963i −0.106117 0.994354i \(-0.533842\pi\)
0.914194 0.405276i \(-0.132825\pi\)
\(74\) 17.8905 + 10.3291i 0.241763 + 0.139582i
\(75\) 1.01232 14.9658i 0.0134976 0.199544i
\(76\) −19.2188 −0.252879
\(77\) 81.6386 64.0190i 1.06024 0.831416i
\(78\) −45.7192 + 68.1151i −0.586144 + 0.873270i
\(79\) 17.0304 + 29.4975i 0.215574 + 0.373386i 0.953450 0.301551i \(-0.0975043\pi\)
−0.737876 + 0.674937i \(0.764171\pi\)
\(80\) −4.05908 2.34351i −0.0507385 0.0292939i
\(81\) −20.3097 78.4125i −0.250737 0.968055i
\(82\) −23.2896 40.3387i −0.284019 0.491936i
\(83\) 34.5698i 0.416504i −0.978075 0.208252i \(-0.933223\pi\)
0.978075 0.208252i \(-0.0667774\pi\)
\(84\) 51.0745 + 24.6542i 0.608030 + 0.293502i
\(85\) −14.3197 −0.168467
\(86\) −29.3253 + 16.9310i −0.340992 + 0.196872i
\(87\) 43.0962 + 87.8527i 0.495358 + 1.00980i
\(88\) −56.6011 + 98.0360i −0.643194 + 1.11405i
\(89\) 28.7047 16.5727i 0.322525 0.186210i −0.329993 0.943983i \(-0.607046\pi\)
0.652517 + 0.757774i \(0.273713\pi\)
\(90\) −8.69006 21.2302i −0.0965562 0.235891i
\(91\) −62.6271 + 155.811i −0.688210 + 1.71221i
\(92\) 89.9987i 0.978247i
\(93\) −0.406140 + 6.00424i −0.00436709 + 0.0645617i
\(94\) −4.09889 + 7.09949i −0.0436052 + 0.0755264i
\(95\) 13.7808 + 7.95635i 0.145061 + 0.0837511i
\(96\) −98.5988 6.66944i −1.02707 0.0694733i
\(97\) −5.32173 −0.0548632 −0.0274316 0.999624i \(-0.508733\pi\)
−0.0274316 + 0.999624i \(0.508733\pi\)
\(98\) −54.2436 13.3181i −0.553506 0.135899i
\(99\) 123.447 50.5300i 1.24694 0.510404i
\(100\) 6.75162 + 11.6942i 0.0675162 + 0.116942i
\(101\) 54.4292 + 31.4247i 0.538903 + 0.311136i 0.744634 0.667473i \(-0.232624\pi\)
−0.205731 + 0.978608i \(0.565957\pi\)
\(102\) −19.6612 + 9.64482i −0.192757 + 0.0945571i
\(103\) −53.9650 93.4701i −0.523932 0.907477i −0.999612 0.0278586i \(-0.991131\pi\)
0.475680 0.879619i \(-0.342202\pi\)
\(104\) 183.232i 1.76184i
\(105\) −26.4163 38.8224i −0.251584 0.369737i
\(106\) 44.9401 0.423963
\(107\) −70.6904 + 40.8131i −0.660658 + 0.381431i −0.792528 0.609836i \(-0.791235\pi\)
0.131870 + 0.991267i \(0.457902\pi\)
\(108\) 54.5198 + 48.4206i 0.504813 + 0.448339i
\(109\) 30.5961 52.9940i 0.280698 0.486184i −0.690859 0.722990i \(-0.742767\pi\)
0.971557 + 0.236806i \(0.0761006\pi\)
\(110\) 32.7155 18.8883i 0.297414 0.171712i
\(111\) 45.1428 + 30.3001i 0.406692 + 0.272974i
\(112\) −14.5262 + 2.06808i −0.129698 + 0.0184650i
\(113\) 206.567i 1.82803i 0.405684 + 0.914013i \(0.367033\pi\)
−0.405684 + 0.914013i \(0.632967\pi\)
\(114\) 24.2802 + 1.64237i 0.212984 + 0.0144067i
\(115\) −37.2583 + 64.5333i −0.323985 + 0.561159i
\(116\) −76.2878 44.0448i −0.657654 0.379697i
\(117\) −132.149 + 170.738i −1.12948 + 1.45930i
\(118\) 87.6625 0.742902
\(119\) −35.2752 + 27.6620i −0.296430 + 0.232454i
\(120\) 42.5427 + 28.5549i 0.354523 + 0.237957i
\(121\) 49.3296 + 85.4414i 0.407683 + 0.706128i
\(122\) 27.5468 + 15.9042i 0.225794 + 0.130362i
\(123\) −53.9896 110.059i −0.438940 0.894791i
\(124\) −2.70873 4.69166i −0.0218446 0.0378360i
\(125\) 11.1803i 0.0894427i
\(126\) −62.4184 35.5116i −0.495384 0.281838i
\(127\) −98.3201 −0.774174 −0.387087 0.922043i \(-0.626519\pi\)
−0.387087 + 0.922043i \(0.626519\pi\)
\(128\) 85.3211 49.2602i 0.666571 0.384845i
\(129\) −80.0104 + 39.2492i −0.620236 + 0.304257i
\(130\) −30.5730 + 52.9540i −0.235177 + 0.407339i
\(131\) 5.29133 3.05495i 0.0403918 0.0233202i −0.479668 0.877450i \(-0.659243\pi\)
0.520060 + 0.854130i \(0.325910\pi\)
\(132\) −66.9203 + 99.7018i −0.506972 + 0.755316i
\(133\) 49.3174 7.02125i 0.370807 0.0527914i
\(134\) 116.242i 0.867475i
\(135\) −19.0478 57.2903i −0.141095 0.424373i
\(136\) 24.4568 42.3603i 0.179829 0.311473i
\(137\) 158.164 + 91.3161i 1.15448 + 0.666541i 0.949976 0.312324i \(-0.101108\pi\)
0.204507 + 0.978865i \(0.434441\pi\)
\(138\) −7.69093 + 113.700i −0.0557314 + 0.823915i
\(139\) −81.2651 −0.584641 −0.292321 0.956320i \(-0.594427\pi\)
−0.292321 + 0.956320i \(0.594427\pi\)
\(140\) 39.2221 + 15.7650i 0.280158 + 0.112607i
\(141\) −12.0240 + 17.9140i −0.0852765 + 0.127050i
\(142\) −37.1135 64.2824i −0.261362 0.452693i
\(143\) −307.911 177.773i −2.15323 1.24317i
\(144\) −18.6931 2.54050i −0.129813 0.0176424i
\(145\) 36.4680 + 63.1644i 0.251503 + 0.435616i
\(146\) 134.483i 0.921119i
\(147\) −140.069 44.6057i −0.952850 0.303440i
\(148\) −48.9437 −0.330701
\(149\) −108.076 + 62.3975i −0.725340 + 0.418775i −0.816715 0.577041i \(-0.804207\pi\)
0.0913747 + 0.995817i \(0.470874\pi\)
\(150\) −7.53035 15.3508i −0.0502024 0.102339i
\(151\) −34.8705 + 60.3975i −0.230930 + 0.399983i −0.958082 0.286493i \(-0.907510\pi\)
0.727152 + 0.686477i \(0.240844\pi\)
\(152\) −47.0728 + 27.1775i −0.309689 + 0.178799i
\(153\) −53.3401 + 21.8335i −0.348628 + 0.142703i
\(154\) 44.1042 109.728i 0.286391 0.712516i
\(155\) 4.48552i 0.0289388i
\(156\) 13.1170 193.918i 0.0840836 1.24306i
\(157\) −75.8353 + 131.351i −0.483028 + 0.836628i −0.999810 0.0194883i \(-0.993796\pi\)
0.516782 + 0.856117i \(0.327130\pi\)
\(158\) 33.6239 + 19.4128i 0.212810 + 0.122866i
\(159\) 118.005 + 7.98212i 0.742170 + 0.0502020i
\(160\) −73.6591 −0.460369
\(161\) 32.8794 + 230.945i 0.204220 + 1.43444i
\(162\) −64.7400 65.8314i −0.399630 0.406366i
\(163\) 20.6594 + 35.7831i 0.126745 + 0.219528i 0.922414 0.386204i \(-0.126214\pi\)
−0.795669 + 0.605732i \(0.792880\pi\)
\(164\) 95.5712 + 55.1781i 0.582751 + 0.336452i
\(165\) 89.2603 43.7867i 0.540971 0.265374i
\(166\) −19.7029 34.1264i −0.118692 0.205581i
\(167\) 65.7703i 0.393834i 0.980420 + 0.196917i \(0.0630929\pi\)
−0.980420 + 0.196917i \(0.936907\pi\)
\(168\) 159.961 11.8393i 0.952147 0.0704720i
\(169\) 406.493 2.40529
\(170\) −14.1360 + 8.16144i −0.0831532 + 0.0480085i
\(171\) 63.4640 + 8.62515i 0.371134 + 0.0504395i
\(172\) 40.1131 69.4779i 0.233216 0.403941i
\(173\) 204.420 118.022i 1.18162 0.682209i 0.225232 0.974305i \(-0.427686\pi\)
0.956389 + 0.292096i \(0.0943527\pi\)
\(174\) 92.6146 + 62.1634i 0.532268 + 0.357261i
\(175\) −21.5975 27.5417i −0.123415 0.157381i
\(176\) 31.0661i 0.176512i
\(177\) 230.187 + 15.5703i 1.30049 + 0.0879680i
\(178\) 18.8910 32.7202i 0.106129 0.183821i
\(179\) −98.3428 56.7782i −0.549401 0.317197i 0.199479 0.979902i \(-0.436075\pi\)
−0.748880 + 0.662705i \(0.769408\pi\)
\(180\) 42.9797 + 33.2658i 0.238776 + 0.184810i
\(181\) 94.3627 0.521341 0.260671 0.965428i \(-0.416056\pi\)
0.260671 + 0.965428i \(0.416056\pi\)
\(182\) 26.9798 + 189.507i 0.148241 + 1.04124i
\(183\) 69.5085 + 46.6544i 0.379828 + 0.254942i
\(184\) −127.268 220.434i −0.691672 1.19801i
\(185\) 35.0949 + 20.2621i 0.189702 + 0.109525i
\(186\) 3.02116 + 6.15871i 0.0162428 + 0.0331113i
\(187\) −47.4563 82.1967i −0.253777 0.439554i
\(188\) 19.4223i 0.103310i
\(189\) −157.593 104.334i −0.833823 0.552031i
\(190\) 18.1387 0.0954671
\(191\) 96.4070 55.6606i 0.504748 0.291417i −0.225924 0.974145i \(-0.572540\pi\)
0.730672 + 0.682728i \(0.239207\pi\)
\(192\) −78.5530 + 38.5342i −0.409130 + 0.200699i
\(193\) 77.5358 134.296i 0.401740 0.695834i −0.592196 0.805794i \(-0.701739\pi\)
0.993936 + 0.109960i \(0.0350722\pi\)
\(194\) −5.25347 + 3.03309i −0.0270798 + 0.0156345i
\(195\) −89.6851 + 133.618i −0.459924 + 0.685221i
\(196\) 127.074 36.9313i 0.648336 0.188425i
\(197\) 67.7367i 0.343841i 0.985111 + 0.171921i \(0.0549973\pi\)
−0.985111 + 0.171921i \(0.945003\pi\)
\(198\) 93.0642 120.240i 0.470021 0.607272i
\(199\) −20.2389 + 35.0548i −0.101703 + 0.176155i −0.912386 0.409330i \(-0.865762\pi\)
0.810683 + 0.585485i \(0.199096\pi\)
\(200\) 33.0735 + 19.0950i 0.165368 + 0.0954751i
\(201\) 20.6465 305.231i 0.102719 1.51856i
\(202\) 71.6414 0.354661
\(203\) 211.853 + 85.1527i 1.04361 + 0.419472i
\(204\) 28.9156 43.0801i 0.141743 0.211177i
\(205\) −45.6860 79.1305i −0.222859 0.386002i
\(206\) −106.546 61.5142i −0.517212 0.298613i
\(207\) −40.3902 + 297.191i −0.195122 + 1.43571i
\(208\) 25.1421 + 43.5474i 0.120876 + 0.209363i
\(209\) 105.471i 0.504647i
\(210\) −48.2042 23.2686i −0.229544 0.110803i
\(211\) −225.238 −1.06748 −0.533738 0.845650i \(-0.679213\pi\)
−0.533738 + 0.845650i \(0.679213\pi\)
\(212\) −92.2082 + 53.2364i −0.434944 + 0.251115i
\(213\) −86.0360 175.387i −0.403925 0.823412i
\(214\) −46.5225 + 80.5793i −0.217395 + 0.376539i
\(215\) −57.5260 + 33.2126i −0.267563 + 0.154477i
\(216\) 202.007 + 41.4998i 0.935220 + 0.192129i
\(217\) 8.66488 + 11.0497i 0.0399303 + 0.0509201i
\(218\) 69.7525i 0.319965i
\(219\) 23.8865 353.131i 0.109071 1.61247i
\(220\) −44.7505 + 77.5101i −0.203411 + 0.352319i
\(221\) 133.045 + 76.8137i 0.602015 + 0.347573i
\(222\) 61.8332 + 4.18253i 0.278528 + 0.0188402i
\(223\) 190.035 0.852174 0.426087 0.904682i \(-0.359892\pi\)
0.426087 + 0.904682i \(0.359892\pi\)
\(224\) −181.452 + 142.290i −0.810055 + 0.635225i
\(225\) −17.0469 41.6462i −0.0757639 0.185094i
\(226\) 117.732 + 203.918i 0.520938 + 0.902291i
\(227\) −336.012 193.996i −1.48023 0.854610i −0.480479 0.877006i \(-0.659537\pi\)
−0.999749 + 0.0223962i \(0.992870\pi\)
\(228\) −51.7637 + 25.3927i −0.227034 + 0.111372i
\(229\) 25.2334 + 43.7055i 0.110189 + 0.190854i 0.915847 0.401529i \(-0.131521\pi\)
−0.805657 + 0.592382i \(0.798188\pi\)
\(230\) 84.9408i 0.369308i
\(231\) 135.300 280.292i 0.585713 1.21339i
\(232\) −249.136 −1.07386
\(233\) −175.684 + 101.431i −0.754008 + 0.435327i −0.827140 0.561995i \(-0.810034\pi\)
0.0731321 + 0.997322i \(0.476701\pi\)
\(234\) −33.1429 + 243.866i −0.141636 + 1.04216i
\(235\) −8.04059 + 13.9267i −0.0342153 + 0.0592626i
\(236\) −179.866 + 103.846i −0.762144 + 0.440024i
\(237\) 84.8427 + 56.9468i 0.357986 + 0.240282i
\(238\) −19.0570 + 47.4121i −0.0800714 + 0.199211i
\(239\) 54.4765i 0.227935i −0.993484 0.113968i \(-0.963644\pi\)
0.993484 0.113968i \(-0.0363560\pi\)
\(240\) −14.0290 0.948953i −0.0584542 0.00395397i
\(241\) −120.038 + 207.911i −0.498082 + 0.862703i −0.999998 0.00221369i \(-0.999295\pi\)
0.501916 + 0.864916i \(0.332629\pi\)
\(242\) 97.3939 + 56.2304i 0.402454 + 0.232357i
\(243\) −158.304 184.361i −0.651455 0.758687i
\(244\) −75.3609 −0.308856
\(245\) −106.407 26.1255i −0.434314 0.106635i
\(246\) −116.025 77.8766i −0.471646 0.316571i
\(247\) −85.3590 147.846i −0.345583 0.598567i
\(248\) −13.2690 7.66087i −0.0535041 0.0308906i
\(249\) −45.6751 93.1098i −0.183434 0.373935i
\(250\) −6.37218 11.0369i −0.0254887 0.0441478i
\(251\) 159.670i 0.636136i 0.948068 + 0.318068i \(0.103034\pi\)
−0.948068 + 0.318068i \(0.896966\pi\)
\(252\) 170.137 1.07866i 0.675149 0.00428038i
\(253\) −493.904 −1.95219
\(254\) −97.0591 + 56.0371i −0.382123 + 0.220619i
\(255\) −38.5684 + 18.9198i −0.151249 + 0.0741952i
\(256\) 114.482 198.288i 0.447193 0.774562i
\(257\) 143.851 83.0525i 0.559732 0.323161i −0.193306 0.981139i \(-0.561921\pi\)
0.753038 + 0.657977i \(0.228588\pi\)
\(258\) −56.6144 + 84.3473i −0.219436 + 0.326928i
\(259\) 125.594 17.8807i 0.484919 0.0690374i
\(260\) 144.868i 0.557186i
\(261\) 232.149 + 179.681i 0.889460 + 0.688431i
\(262\) 3.48231 6.03154i 0.0132913 0.0230211i
\(263\) −78.7862 45.4872i −0.299567 0.172955i 0.342681 0.939452i \(-0.388665\pi\)
−0.642249 + 0.766496i \(0.721998\pi\)
\(264\) −22.9194 + 338.832i −0.0868158 + 1.28346i
\(265\) 88.1568 0.332667
\(266\) 44.6831 35.0394i 0.167982 0.131727i
\(267\) 55.4163 82.5624i 0.207552 0.309222i
\(268\) 137.701 + 238.505i 0.513809 + 0.889944i
\(269\) −89.8384 51.8682i −0.333972 0.192819i 0.323631 0.946183i \(-0.395096\pi\)
−0.657603 + 0.753365i \(0.728430\pi\)
\(270\) −51.4559 45.6993i −0.190577 0.169257i
\(271\) 120.306 + 208.376i 0.443933 + 0.768915i 0.997977 0.0635727i \(-0.0202495\pi\)
−0.554044 + 0.832487i \(0.686916\pi\)
\(272\) 13.4233i 0.0493505i
\(273\) 37.1849 + 502.404i 0.136208 + 1.84031i
\(274\) 208.181 0.759784
\(275\) 64.1764 37.0523i 0.233369 0.134736i
\(276\) −118.910 242.401i −0.430833 0.878265i
\(277\) 58.5235 101.366i 0.211276 0.365941i −0.740838 0.671684i \(-0.765571\pi\)
0.952114 + 0.305743i \(0.0989047\pi\)
\(278\) −80.2229 + 46.3167i −0.288571 + 0.166607i
\(279\) 6.83916 + 16.7083i 0.0245131 + 0.0598865i
\(280\) 118.360 16.8508i 0.422715 0.0601814i
\(281\) 182.734i 0.650299i 0.945663 + 0.325150i \(0.105415\pi\)
−0.945663 + 0.325150i \(0.894585\pi\)
\(282\) −1.65975 + 24.5373i −0.00588565 + 0.0870116i
\(283\) 90.4474 156.659i 0.319602 0.553567i −0.660803 0.750559i \(-0.729784\pi\)
0.980405 + 0.196992i \(0.0631174\pi\)
\(284\) 152.299 + 87.9299i 0.536264 + 0.309612i
\(285\) 47.6293 + 3.22175i 0.167120 + 0.0113044i
\(286\) −405.283 −1.41707
\(287\) −265.403 106.677i −0.924749 0.371697i
\(288\) −274.376 + 112.309i −0.952696 + 0.389963i
\(289\) −123.995 214.765i −0.429047 0.743132i
\(290\) 72.0005 + 41.5695i 0.248278 + 0.143343i
\(291\) −14.3335 + 7.03129i −0.0492559 + 0.0241625i
\(292\) 159.310 + 275.933i 0.545583 + 0.944977i
\(293\) 283.962i 0.969155i −0.874748 0.484578i \(-0.838973\pi\)
0.874748 0.484578i \(-0.161027\pi\)
\(294\) −163.695 + 35.7981i −0.556787 + 0.121762i
\(295\) 171.963 0.582926
\(296\) −119.878 + 69.2116i −0.404993 + 0.233823i
\(297\) 265.727 299.200i 0.894705 1.00741i
\(298\) −71.1264 + 123.195i −0.238679 + 0.413404i
\(299\) 692.339 399.722i 2.31552 1.33686i
\(300\) 33.6355 + 22.5763i 0.112118 + 0.0752544i
\(301\) −77.5515 + 192.942i −0.257646 + 0.641002i
\(302\) 79.4971i 0.263236i
\(303\) 188.118 + 12.7247i 0.620852 + 0.0419958i
\(304\) 7.45832 12.9182i 0.0245339 0.0424940i
\(305\) 54.0373 + 31.1984i 0.177171 + 0.102290i
\(306\) −40.2121 + 51.9544i −0.131412 + 0.169786i
\(307\) 166.816 0.543375 0.271688 0.962385i \(-0.412418\pi\)
0.271688 + 0.962385i \(0.412418\pi\)
\(308\) 39.4910 + 277.385i 0.128218 + 0.900602i
\(309\) −268.845 180.450i −0.870049 0.583981i
\(310\) 2.55650 + 4.42799i 0.00824678 + 0.0142838i
\(311\) −433.784 250.445i −1.39480 0.805290i −0.400962 0.916095i \(-0.631324\pi\)
−0.993842 + 0.110804i \(0.964657\pi\)
\(312\) −242.093 493.513i −0.775939 1.58177i
\(313\) −200.841 347.866i −0.641664 1.11139i −0.985061 0.172204i \(-0.944911\pi\)
0.343398 0.939190i \(-0.388422\pi\)
\(314\) 172.888i 0.550599i
\(315\) −122.443 69.6613i −0.388708 0.221147i
\(316\) −91.9862 −0.291095
\(317\) 137.569 79.4256i 0.433972 0.250554i −0.267065 0.963678i \(-0.586054\pi\)
0.701037 + 0.713125i \(0.252721\pi\)
\(318\) 121.041 59.3767i 0.380632 0.186719i
\(319\) −241.714 + 418.660i −0.757723 + 1.31242i
\(320\) −56.4781 + 32.6076i −0.176494 + 0.101899i
\(321\) −136.472 + 203.325i −0.425148 + 0.633410i
\(322\) 164.084 + 209.244i 0.509577 + 0.649825i
\(323\) 45.5730i 0.141093i
\(324\) 210.818 + 58.3813i 0.650673 + 0.180189i
\(325\) −59.9736 + 103.877i −0.184534 + 0.319623i
\(326\) 40.7889 + 23.5495i 0.125119 + 0.0722376i
\(327\) 12.3892 183.158i 0.0378875 0.560117i
\(328\) 312.111 0.951557
\(329\) 7.09559 + 49.8395i 0.0215671 + 0.151488i
\(330\) 63.1594 94.0986i 0.191392 0.285147i
\(331\) −205.917 356.658i −0.622105 1.07752i −0.989093 0.147292i \(-0.952944\pi\)
0.366988 0.930226i \(-0.380389\pi\)
\(332\) 80.8530 + 46.6805i 0.243533 + 0.140604i
\(333\) 161.621 + 21.9652i 0.485347 + 0.0659617i
\(334\) 37.4855 + 64.9267i 0.112232 + 0.194391i
\(335\) 228.026i 0.680673i
\(336\) −36.3923 + 24.7628i −0.108310 + 0.0736987i
\(337\) 363.035 1.07725 0.538627 0.842544i \(-0.318943\pi\)
0.538627 + 0.842544i \(0.318943\pi\)
\(338\) 401.280 231.679i 1.18722 0.685441i
\(339\) 272.925 + 556.364i 0.805088 + 1.64119i
\(340\) 19.3362 33.4913i 0.0568713 0.0985039i
\(341\) −25.7474 + 14.8653i −0.0755056 + 0.0435932i
\(342\) 67.5659 27.6565i 0.197561 0.0808669i
\(343\) −312.592 + 141.193i −0.911346 + 0.411642i
\(344\) 226.897i 0.659584i
\(345\) −15.0869 + 223.040i −0.0437302 + 0.646493i
\(346\) 134.532 233.017i 0.388822 0.673459i
\(347\) 304.373 + 175.730i 0.877155 + 0.506426i 0.869719 0.493547i \(-0.164300\pi\)
0.00743572 + 0.999972i \(0.497633\pi\)
\(348\) −263.666 17.8350i −0.757662 0.0512499i
\(349\) −466.577 −1.33690 −0.668448 0.743758i \(-0.733041\pi\)
−0.668448 + 0.743758i \(0.733041\pi\)
\(350\) −37.0178 14.8791i −0.105765 0.0425116i
\(351\) −130.343 + 634.465i −0.371346 + 1.80759i
\(352\) −244.110 422.812i −0.693495 1.20117i
\(353\) 263.206 + 151.962i 0.745625 + 0.430487i 0.824111 0.566429i \(-0.191675\pi\)
−0.0784861 + 0.996915i \(0.525009\pi\)
\(354\) 236.109 115.823i 0.666974 0.327184i
\(355\) −72.8037 126.100i −0.205081 0.355210i
\(356\) 89.5139i 0.251444i
\(357\) −58.4616 + 121.111i −0.163758 + 0.339248i
\(358\) −129.442 −0.361570
\(359\) −358.252 + 206.837i −0.997917 + 0.576148i −0.907631 0.419768i \(-0.862111\pi\)
−0.0902857 + 0.995916i \(0.528778\pi\)
\(360\) 152.312 + 20.7001i 0.423088 + 0.0575003i
\(361\) 155.179 268.777i 0.429858 0.744535i
\(362\) 93.1525 53.7816i 0.257327 0.148568i
\(363\) 245.752 + 164.950i 0.677004 + 0.454409i
\(364\) −279.848 356.869i −0.768814 0.980410i
\(365\) 263.810i 0.722766i
\(366\) 95.2075 + 6.44004i 0.260130 + 0.0175957i
\(367\) 14.7313 25.5153i 0.0401397 0.0695240i −0.845258 0.534359i \(-0.820553\pi\)
0.885397 + 0.464835i \(0.153886\pi\)
\(368\) 60.4938 + 34.9261i 0.164385 + 0.0949079i
\(369\) −290.830 225.099i −0.788156 0.610024i
\(370\) 46.1931 0.124846
\(371\) 217.166 170.296i 0.585353 0.459020i
\(372\) −13.4945 9.05756i −0.0362755 0.0243483i
\(373\) 160.449 + 277.905i 0.430157 + 0.745054i 0.996886 0.0788499i \(-0.0251248\pi\)
−0.566729 + 0.823904i \(0.691791\pi\)
\(374\) −93.6952 54.0950i −0.250522 0.144639i
\(375\) −14.7719 30.1130i −0.0393918 0.0803012i
\(376\) −27.4652 47.5712i −0.0730458 0.126519i
\(377\) 782.486i 2.07556i
\(378\) −215.036 13.1765i −0.568878 0.0348586i
\(379\) 635.564 1.67695 0.838475 0.544941i \(-0.183448\pi\)
0.838475 + 0.544941i \(0.183448\pi\)
\(380\) −37.2171 + 21.4873i −0.0979398 + 0.0565456i
\(381\) −264.814 + 129.905i −0.695050 + 0.340957i
\(382\) 63.4470 109.893i 0.166092 0.287679i
\(383\) −605.811 + 349.765i −1.58175 + 0.913225i −0.587147 + 0.809480i \(0.699749\pi\)
−0.994604 + 0.103744i \(0.966918\pi\)
\(384\) 164.718 245.406i 0.428953 0.639079i
\(385\) 86.5171 215.247i 0.224720 0.559083i
\(386\) 176.765i 0.457940i
\(387\) −163.641 + 211.426i −0.422846 + 0.546321i
\(388\) 7.18606 12.4466i 0.0185208 0.0320789i
\(389\) 345.371 + 199.400i 0.887843 + 0.512596i 0.873236 0.487297i \(-0.162017\pi\)
0.0146067 + 0.999893i \(0.495350\pi\)
\(390\) −12.3799 + 183.020i −0.0317433 + 0.469282i
\(391\) 213.411 0.545808
\(392\) 259.018 270.152i 0.660760 0.689163i
\(393\) 10.2153 15.2193i 0.0259930 0.0387259i
\(394\) 38.6062 + 66.8680i 0.0979854 + 0.169716i
\(395\) 65.9584 + 38.0811i 0.166983 + 0.0964078i
\(396\) −48.5121 + 356.953i −0.122505 + 0.901397i
\(397\) −44.1635 76.4934i −0.111243 0.192678i 0.805029 0.593236i \(-0.202150\pi\)
−0.916272 + 0.400557i \(0.868817\pi\)
\(398\) 46.1402i 0.115930i
\(399\) 123.554 84.0711i 0.309659 0.210704i
\(400\) −10.4805 −0.0262012
\(401\) 344.542 198.921i 0.859206 0.496063i −0.00454048 0.999990i \(-0.501445\pi\)
0.863746 + 0.503927i \(0.168112\pi\)
\(402\) −153.583 313.084i −0.382048 0.778815i
\(403\) 24.0612 41.6753i 0.0597053 0.103413i
\(404\) −146.994 + 84.8671i −0.363847 + 0.210067i
\(405\) −126.997 129.138i −0.313574 0.318860i
\(406\) 257.668 36.6839i 0.634650 0.0903544i
\(407\) 268.598i 0.659947i
\(408\) 9.90322 146.406i 0.0242726 0.358838i
\(409\) −333.799 + 578.156i −0.816134 + 1.41358i 0.0923773 + 0.995724i \(0.470553\pi\)
−0.908511 + 0.417861i \(0.862780\pi\)
\(410\) −90.2001 52.0771i −0.220000 0.127017i
\(411\) 546.647 + 36.9764i 1.33004 + 0.0899670i
\(412\) 291.481 0.707478
\(413\) 423.615 332.189i 1.02570 0.804331i
\(414\) 129.511 + 316.400i 0.312828 + 0.764251i
\(415\) −38.6502 66.9442i −0.0931331 0.161311i
\(416\) 684.372 + 395.122i 1.64513 + 0.949813i
\(417\) −218.878 + 107.371i −0.524888 + 0.257484i
\(418\) 60.1128 + 104.118i 0.143811 + 0.249087i
\(419\) 416.317i 0.993596i 0.867866 + 0.496798i \(0.165491\pi\)
−0.867866 + 0.496798i \(0.834509\pi\)
\(420\) 126.470 9.36050i 0.301118 0.0222869i
\(421\) 207.519 0.492920 0.246460 0.969153i \(-0.420733\pi\)
0.246460 + 0.969153i \(0.420733\pi\)
\(422\) −222.349 + 128.373i −0.526893 + 0.304202i
\(423\) −8.71647 + 64.1359i −0.0206063 + 0.151622i
\(424\) −150.564 + 260.784i −0.355104 + 0.615058i
\(425\) −27.7300 + 16.0099i −0.0652470 + 0.0376704i
\(426\) −184.893 124.101i −0.434022 0.291318i
\(427\) 193.383 27.5317i 0.452888 0.0644771i
\(428\) 220.444i 0.515056i
\(429\) −1064.20 71.9851i −2.48066 0.167797i
\(430\) −37.8588 + 65.5733i −0.0880436 + 0.152496i
\(431\) −572.655 330.623i −1.32867 0.767106i −0.343573 0.939126i \(-0.611637\pi\)
−0.985093 + 0.172020i \(0.944971\pi\)
\(432\) −53.7042 + 17.8555i −0.124315 + 0.0413321i
\(433\) −505.711 −1.16792 −0.583962 0.811781i \(-0.698498\pi\)
−0.583962 + 0.811781i \(0.698498\pi\)
\(434\) 14.8514 + 5.96944i 0.0342199 + 0.0137545i
\(435\) 181.678 + 121.943i 0.417650 + 0.280329i
\(436\) 82.6294 + 143.118i 0.189517 + 0.328253i
\(437\) −205.380 118.576i −0.469977 0.271341i
\(438\) −177.685 362.216i −0.405674 0.826976i
\(439\) 214.372 + 371.303i 0.488319 + 0.845793i 0.999910 0.0134360i \(-0.00427695\pi\)
−0.511591 + 0.859229i \(0.670944\pi\)
\(440\) 253.128i 0.575291i
\(441\) −436.195 + 64.9245i −0.989104 + 0.147221i
\(442\) 175.119 0.396196
\(443\) −4.51372 + 2.60600i −0.0101890 + 0.00588261i −0.505086 0.863069i \(-0.668539\pi\)
0.494897 + 0.868952i \(0.335206\pi\)
\(444\) −131.824 + 64.6664i −0.296901 + 0.145645i
\(445\) 37.0576 64.1856i 0.0832755 0.144237i
\(446\) 187.597 108.309i 0.420622 0.242846i
\(447\) −208.647 + 310.855i −0.466772 + 0.695424i
\(448\) −76.1389 + 189.427i −0.169953 + 0.422828i
\(449\) 249.987i 0.556765i −0.960470 0.278383i \(-0.910202\pi\)
0.960470 0.278383i \(-0.0897983\pi\)
\(450\) −40.5643 31.3963i −0.0901428 0.0697695i
\(451\) 302.812 524.486i 0.671423 1.16294i
\(452\) −483.125 278.932i −1.06886 0.617107i
\(453\) −14.1200 + 208.746i −0.0311701 + 0.460808i
\(454\) −442.270 −0.974162
\(455\) 52.9250 + 371.746i 0.116319 + 0.817023i
\(456\) −90.8771 + 135.394i −0.199292 + 0.296916i
\(457\) 295.560 + 511.926i 0.646741 + 1.12019i 0.983897 + 0.178739i \(0.0572017\pi\)
−0.337156 + 0.941449i \(0.609465\pi\)
\(458\) 49.8195 + 28.7633i 0.108776 + 0.0628019i
\(459\) −114.818 + 129.281i −0.250148 + 0.281658i
\(460\) −100.622 174.282i −0.218743 0.378873i
\(461\) 470.217i 1.01999i −0.860176 0.509997i \(-0.829646\pi\)
0.860176 0.509997i \(-0.170354\pi\)
\(462\) −26.1869 353.811i −0.0566816 0.765824i
\(463\) 371.655 0.802710 0.401355 0.915923i \(-0.368539\pi\)
0.401355 + 0.915923i \(0.368539\pi\)
\(464\) 59.2105 34.1852i 0.127609 0.0736750i
\(465\) 5.92646 + 12.0812i 0.0127451 + 0.0259812i
\(466\) −115.620 + 200.261i −0.248113 + 0.429744i
\(467\) −211.724 + 122.239i −0.453370 + 0.261753i −0.709252 0.704955i \(-0.750967\pi\)
0.255882 + 0.966708i \(0.417634\pi\)
\(468\) −220.883 539.627i −0.471973 1.15305i
\(469\) −440.487 561.720i −0.939204 1.19770i
\(470\) 18.3308i 0.0390017i
\(471\) −30.7078 + 453.975i −0.0651971 + 0.963853i
\(472\) −293.698 + 508.699i −0.622241 + 1.07775i
\(473\) −381.288 220.137i −0.806107 0.465406i
\(474\) 116.211 + 7.86077i 0.245171 + 0.0165839i
\(475\) 35.5819 0.0749093
\(476\) −17.0637 119.855i −0.0358480 0.251797i
\(477\) 328.379 134.414i 0.688427 0.281791i
\(478\) −31.0487 53.7779i −0.0649554 0.112506i
\(479\) 83.3647 + 48.1306i 0.174039 + 0.100481i 0.584489 0.811402i \(-0.301295\pi\)
−0.410450 + 0.911883i \(0.634628\pi\)
\(480\) −198.392 + 97.3215i −0.413317 + 0.202753i
\(481\) −217.380 376.512i −0.451932 0.782770i
\(482\) 273.660i 0.567759i
\(483\) 393.691 + 578.582i 0.815095 + 1.19789i
\(484\) −266.444 −0.550504
\(485\) −10.3055 + 5.94987i −0.0212484 + 0.0122678i
\(486\) −261.349 91.7720i −0.537755 0.188831i
\(487\) −323.308 + 559.986i −0.663877 + 1.14987i 0.315711 + 0.948855i \(0.397757\pi\)
−0.979588 + 0.201014i \(0.935576\pi\)
\(488\) −184.582 + 106.568i −0.378241 + 0.218378i
\(489\) 102.922 + 69.0817i 0.210474 + 0.141271i
\(490\) −119.932 + 34.8558i −0.244760 + 0.0711342i
\(491\) 562.098i 1.14480i 0.819973 + 0.572402i \(0.193988\pi\)
−0.819973 + 0.572402i \(0.806012\pi\)
\(492\) 330.314 + 22.3431i 0.671369 + 0.0454129i
\(493\) 104.442 180.899i 0.211850 0.366935i
\(494\) −168.528 97.2999i −0.341151 0.196963i
\(495\) 182.559 235.869i 0.368807 0.476502i
\(496\) 4.20475 0.00847731
\(497\) −422.937 169.997i −0.850980 0.342046i
\(498\) −98.1568 65.8834i −0.197102 0.132296i
\(499\) 407.282 + 705.433i 0.816197 + 1.41369i 0.908465 + 0.417960i \(0.137255\pi\)
−0.0922688 + 0.995734i \(0.529412\pi\)
\(500\) 26.1489 + 15.0971i 0.0522978 + 0.0301942i
\(501\) 86.8984 + 177.145i 0.173450 + 0.353582i
\(502\) 91.0033 + 157.622i 0.181281 + 0.313989i
\(503\) 146.815i 0.291879i 0.989294 + 0.145939i \(0.0466205\pi\)
−0.989294 + 0.145939i \(0.953380\pi\)
\(504\) 415.193 243.234i 0.823796 0.482608i
\(505\) 140.535 0.278288
\(506\) −487.570 + 281.499i −0.963577 + 0.556321i
\(507\) 1094.84 537.076i 2.15945 1.05932i
\(508\) 132.764 229.954i 0.261347 0.452666i
\(509\) −543.481 + 313.779i −1.06774 + 0.616462i −0.927564 0.373664i \(-0.878101\pi\)
−0.140179 + 0.990126i \(0.544768\pi\)
\(510\) −27.2905 + 40.6590i −0.0535109 + 0.0797236i
\(511\) −509.612 649.870i −0.997284 1.27176i
\(512\) 133.088i 0.259938i
\(513\) 182.329 60.6204i 0.355417 0.118168i
\(514\) 94.6708 163.975i 0.184184 0.319017i
\(515\) −209.006 120.669i −0.405836 0.234310i
\(516\) 16.2429 240.130i 0.0314785 0.465368i
\(517\) −106.588 −0.206166
\(518\) 113.792 89.2331i 0.219676 0.172265i
\(519\) 394.647 587.968i 0.760399 1.13289i
\(520\) −204.859 354.826i −0.393960 0.682358i
\(521\) 328.220 + 189.498i 0.629980 + 0.363719i 0.780744 0.624850i \(-0.214840\pi\)
−0.150764 + 0.988570i \(0.548173\pi\)
\(522\) 331.580 + 45.0637i 0.635210 + 0.0863290i
\(523\) 19.9172 + 34.4977i 0.0380827 + 0.0659611i 0.884439 0.466657i \(-0.154542\pi\)
−0.846356 + 0.532618i \(0.821208\pi\)
\(524\) 16.5007i 0.0314899i
\(525\) −94.5597 45.6449i −0.180114 0.0869426i
\(526\) −103.701 −0.197150
\(527\) 11.1252 6.42313i 0.0211104 0.0121881i
\(528\) −41.0458 83.6730i −0.0777383 0.158472i
\(529\) 290.772 503.633i 0.549664 0.952047i
\(530\) 87.0261 50.2446i 0.164200 0.0948011i
\(531\) 640.554 262.195i 1.20632 0.493777i
\(532\) −50.1729 + 124.826i −0.0943100 + 0.234635i
\(533\) 980.276i 1.83917i
\(534\) 7.64950 113.088i 0.0143249 0.211775i
\(535\) −91.2609 + 158.069i −0.170581 + 0.295455i
\(536\) 674.542 + 389.447i 1.25847 + 0.726581i
\(537\) −339.893 22.9911i −0.632947 0.0428139i
\(538\) −118.248 −0.219792
\(539\) −202.675 697.370i −0.376021 1.29382i
\(540\) 159.713 + 32.8110i 0.295765 + 0.0607611i
\(541\) −55.8982 96.8186i −0.103324 0.178962i 0.809728 0.586805i \(-0.199614\pi\)
−0.913052 + 0.407843i \(0.866281\pi\)
\(542\) 237.526 + 137.136i 0.438239 + 0.253018i
\(543\) 254.155 124.676i 0.468057 0.229606i
\(544\) 105.478 + 182.693i 0.193893 + 0.335832i
\(545\) 136.830i 0.251064i
\(546\) 323.051 + 474.767i 0.591668 + 0.869537i
\(547\) −1064.02 −1.94519 −0.972595 0.232508i \(-0.925307\pi\)
−0.972595 + 0.232508i \(0.925307\pi\)
\(548\) −427.146 + 246.613i −0.779463 + 0.450023i
\(549\) 248.855 + 33.8209i 0.453287 + 0.0616046i
\(550\) 42.2355 73.1541i 0.0767919 0.133007i
\(551\) −201.023 + 116.061i −0.364833 + 0.210637i
\(552\) −634.028 425.563i −1.14860 0.770947i
\(553\) 236.045 33.6055i 0.426845 0.0607694i
\(554\) 133.421i 0.240832i
\(555\) 121.295 + 8.20467i 0.218550 + 0.0147832i
\(556\) 109.734 190.065i 0.197364 0.341844i
\(557\) 179.164 + 103.440i 0.321659 + 0.185710i 0.652132 0.758106i \(-0.273875\pi\)
−0.330473 + 0.943815i \(0.607208\pi\)
\(558\) 16.2743 + 12.5961i 0.0291654 + 0.0225736i
\(559\) 712.637 1.27484
\(560\) −25.8177 + 20.2456i −0.0461031 + 0.0361529i
\(561\) −236.420 158.686i −0.421425 0.282863i
\(562\) 104.148 + 180.390i 0.185318 + 0.320979i
\(563\) −14.1856 8.19005i −0.0251964 0.0145472i 0.487349 0.873207i \(-0.337964\pi\)
−0.512545 + 0.858660i \(0.671297\pi\)
\(564\) −25.6616 52.3118i −0.0454992 0.0927514i
\(565\) 230.949 + 400.015i 0.408759 + 0.707992i
\(566\) 206.200i 0.364312i
\(567\) −562.308 72.7934i −0.991725 0.128383i
\(568\) 497.369 0.875649
\(569\) 358.446 206.949i 0.629957 0.363706i −0.150778 0.988568i \(-0.548178\pi\)
0.780735 + 0.624862i \(0.214845\pi\)
\(570\) 48.8546 23.9657i 0.0857099 0.0420450i
\(571\) 174.912 302.957i 0.306326 0.530573i −0.671229 0.741250i \(-0.734233\pi\)
0.977556 + 0.210677i \(0.0675668\pi\)
\(572\) 831.560 480.101i 1.45378 0.839338i
\(573\) 186.120 277.292i 0.324817 0.483931i
\(574\) −322.799 + 45.9565i −0.562368 + 0.0800636i
\(575\) 166.624i 0.289781i
\(576\) −160.660 + 207.575i −0.278924 + 0.360373i
\(577\) −390.984 + 677.204i −0.677616 + 1.17366i 0.298081 + 0.954540i \(0.403653\pi\)
−0.975697 + 0.219124i \(0.929680\pi\)
\(578\) −244.809 141.340i −0.423544 0.244533i
\(579\) 31.3964 464.154i 0.0542252 0.801648i
\(580\) −196.974 −0.339611
\(581\) −224.530 90.2484i −0.386455 0.155333i
\(582\) −10.1422 + 15.1104i −0.0174264 + 0.0259629i
\(583\) 292.157 + 506.030i 0.501126 + 0.867976i
\(584\) 780.398 + 450.563i 1.33630 + 0.771512i
\(585\) −65.0149 + 478.380i −0.111137 + 0.817744i
\(586\) −161.843 280.320i −0.276183 0.478363i
\(587\) 720.660i 1.22770i 0.789422 + 0.613850i \(0.210380\pi\)
−0.789422 + 0.613850i \(0.789620\pi\)
\(588\) 293.464 267.365i 0.499088 0.454703i
\(589\) −14.2754 −0.0242366
\(590\) 169.758 98.0096i 0.287725 0.166118i
\(591\) 89.4966 + 182.441i 0.151432 + 0.308699i
\(592\) 18.9937 32.8981i 0.0320840 0.0555711i
\(593\) 141.904 81.9281i 0.239298 0.138159i −0.375556 0.926800i \(-0.622548\pi\)
0.614854 + 0.788641i \(0.289215\pi\)
\(594\) 91.7918 446.813i 0.154532 0.752210i
\(595\) −37.3831 + 93.0061i −0.0628288 + 0.156313i
\(596\) 337.028i 0.565483i
\(597\) −8.19528 + 121.156i −0.0137274 + 0.202942i
\(598\) 455.640 789.191i 0.761939 1.31972i
\(599\) −79.5260 45.9144i −0.132765 0.0766517i 0.432147 0.901803i \(-0.357756\pi\)
−0.564911 + 0.825152i \(0.691090\pi\)
\(600\) 114.309 + 7.73211i 0.190515 + 0.0128868i
\(601\) −45.5540 −0.0757970 −0.0378985 0.999282i \(-0.512066\pi\)
−0.0378985 + 0.999282i \(0.512066\pi\)
\(602\) 33.4093 + 234.667i 0.0554971 + 0.389812i
\(603\) −347.675 849.383i −0.576575 1.40860i
\(604\) −94.1730 163.112i −0.155916 0.270054i
\(605\) 191.053 + 110.304i 0.315790 + 0.182321i
\(606\) 192.958 94.6556i 0.318412 0.156197i
\(607\) −410.405 710.843i −0.676121 1.17108i −0.976140 0.217142i \(-0.930326\pi\)
0.300019 0.953933i \(-0.403007\pi\)
\(608\) 234.423i 0.385564i
\(609\) 683.108 50.5595i 1.12169 0.0830205i
\(610\) 71.1256 0.116599
\(611\) 149.411 86.2627i 0.244536 0.141183i
\(612\) 20.9616 154.236i 0.0342510 0.252019i
\(613\) −217.446 + 376.628i −0.354725 + 0.614401i −0.987071 0.160285i \(-0.948759\pi\)
0.632346 + 0.774686i \(0.282092\pi\)
\(614\) 164.677 95.0762i 0.268203 0.154847i
\(615\) −227.601 152.767i −0.370082 0.248401i
\(616\) 488.978 + 623.557i 0.793795 + 1.01227i
\(617\) 880.290i 1.42673i 0.700795 + 0.713363i \(0.252829\pi\)
−0.700795 + 0.713363i \(0.747171\pi\)
\(618\) −368.244 24.9088i −0.595864 0.0403055i
\(619\) 535.898 928.202i 0.865748 1.49952i −0.000554937 1.00000i \(-0.500177\pi\)
0.866303 0.499519i \(-0.166490\pi\)
\(620\) −10.4909 6.05691i −0.0169208 0.00976921i
\(621\) 283.875 + 853.816i 0.457126 + 1.37491i
\(622\) −570.961 −0.917943
\(623\) −32.7023 229.701i −0.0524916 0.368702i
\(624\) 125.254 + 84.0712i 0.200728 + 0.134730i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −396.530 228.937i −0.633434 0.365713i
\(627\) 139.353 + 284.074i 0.222253 + 0.453069i
\(628\) −204.805 354.732i −0.326122 0.564860i
\(629\) 116.059i 0.184513i
\(630\) −160.576 + 1.01804i −0.254882 + 0.00161593i
\(631\) −561.284 −0.889516 −0.444758 0.895651i \(-0.646710\pi\)
−0.444758 + 0.895651i \(0.646710\pi\)
\(632\) −225.302 + 130.078i −0.356491 + 0.205820i
\(633\) −606.651 + 297.593i −0.958375 + 0.470131i
\(634\) 90.5365 156.814i 0.142802 0.247340i
\(635\) −190.396 + 109.925i −0.299836 + 0.173111i
\(636\) −178.014 + 265.215i −0.279896 + 0.417005i
\(637\) 848.493 + 813.523i 1.33201 + 1.27712i
\(638\) 551.054i 0.863722i
\(639\) −463.456 358.710i −0.725284 0.561361i
\(640\) 110.149 190.784i 0.172108 0.298100i
\(641\) −755.593 436.242i −1.17877 0.680564i −0.223042 0.974809i \(-0.571599\pi\)
−0.955730 + 0.294245i \(0.904932\pi\)
\(642\) −18.8383 + 278.499i −0.0293431 + 0.433798i
\(643\) −15.3320 −0.0238445 −0.0119223 0.999929i \(-0.503795\pi\)
−0.0119223 + 0.999929i \(0.503795\pi\)
\(644\) −584.539 234.952i −0.907670 0.364832i
\(645\) −111.058 + 165.460i −0.172182 + 0.256527i
\(646\) −25.9741 44.9885i −0.0402076 0.0696417i
\(647\) 608.626 + 351.390i 0.940689 + 0.543107i 0.890176 0.455616i \(-0.150581\pi\)
0.0505128 + 0.998723i \(0.483914\pi\)
\(648\) 598.915 155.126i 0.924252 0.239391i
\(649\) 569.896 + 987.088i 0.878113 + 1.52094i
\(650\) 136.727i 0.210349i
\(651\) 37.9371 + 18.3126i 0.0582751 + 0.0281299i
\(652\) −111.588 −0.171147
\(653\) 24.5206 14.1570i 0.0375506 0.0216799i −0.481107 0.876662i \(-0.659765\pi\)
0.518658 + 0.854982i \(0.326432\pi\)
\(654\) −92.1598 187.870i −0.140917 0.287263i
\(655\) 6.83107 11.8318i 0.0104291 0.0180638i
\(656\) −74.1773 + 42.8263i −0.113075 + 0.0652839i
\(657\) −402.235 982.677i −0.612230 1.49570i
\(658\) 35.4104 + 45.1562i 0.0538152 + 0.0686264i
\(659\) 99.8613i 0.151535i 0.997126 + 0.0757673i \(0.0241406\pi\)
−0.997126 + 0.0757673i \(0.975859\pi\)
\(660\) −18.1207 + 267.891i −0.0274556 + 0.405895i
\(661\) 569.474 986.358i 0.861534 1.49222i −0.00891369 0.999960i \(-0.502837\pi\)
0.870448 0.492261i \(-0.163829\pi\)
\(662\) −406.551 234.723i −0.614126 0.354566i
\(663\) 459.832 + 31.1040i 0.693562 + 0.0469141i
\(664\) 264.045 0.397658
\(665\) 87.6526 68.7351i 0.131808 0.103361i
\(666\) 172.067 70.4314i 0.258358 0.105753i
\(667\) −543.494 941.359i −0.814833 1.41133i
\(668\) −153.826 88.8112i −0.230278 0.132951i
\(669\) 511.837 251.082i 0.765077 0.375309i
\(670\) −129.962 225.101i −0.193973 0.335972i
\(671\) 413.573i 0.616354i
\(672\) −300.721 + 622.985i −0.447501 + 0.927061i
\(673\) −974.867 −1.44854 −0.724270 0.689517i \(-0.757823\pi\)
−0.724270 + 0.689517i \(0.757823\pi\)
\(674\) 358.379 206.910i 0.531719 0.306988i
\(675\) −100.938 89.6462i −0.149538 0.132809i
\(676\) −548.898 + 950.719i −0.811979 + 1.40639i
\(677\) 271.115 156.528i 0.400465 0.231209i −0.286220 0.958164i \(-0.592399\pi\)
0.686685 + 0.726955i \(0.259065\pi\)
\(678\) 586.522 + 393.676i 0.865076 + 0.580644i
\(679\) −13.8930 + 34.5645i −0.0204609 + 0.0509050i
\(680\) 109.374i 0.160844i
\(681\) −1161.33 78.5546i −1.70532 0.115352i
\(682\) −16.9448 + 29.3492i −0.0248457 + 0.0430341i
\(683\) 755.669 + 436.286i 1.10640 + 0.638779i 0.937894 0.346922i \(-0.112773\pi\)
0.168503 + 0.985701i \(0.446107\pi\)
\(684\) −105.870 + 136.785i −0.154780 + 0.199978i
\(685\) 408.378 0.596172
\(686\) −228.110 + 317.543i −0.332522 + 0.462890i
\(687\) 125.709 + 84.3763i 0.182982 + 0.122818i
\(688\) 31.1337 + 53.9251i 0.0452524 + 0.0783795i
\(689\) −819.071 472.891i −1.18878 0.686344i
\(690\) 112.227 + 228.778i 0.162648 + 0.331563i
\(691\) 136.246 + 235.985i 0.197172 + 0.341512i 0.947610 0.319429i \(-0.103491\pi\)
−0.750438 + 0.660940i \(0.770158\pi\)
\(692\) 637.473i 0.921204i
\(693\) −5.91957 933.698i −0.00854194 1.34733i
\(694\) 400.625 0.577270
\(695\) −157.369 + 90.8572i −0.226431 + 0.130730i
\(696\) −671.019 + 329.169i −0.964108 + 0.472944i
\(697\) −130.842 + 226.625i −0.187722 + 0.325143i
\(698\) −460.593 + 265.923i −0.659875 + 0.380979i
\(699\) −339.169 + 505.314i −0.485221 + 0.722910i
\(700\) 93.5791 13.3227i 0.133684 0.0190325i
\(701\) 916.260i 1.30707i −0.756894 0.653537i \(-0.773284\pi\)
0.756894 0.653537i \(-0.226716\pi\)
\(702\) 232.939 + 700.615i 0.331823 + 0.998028i
\(703\) −64.4848 + 111.691i −0.0917281 + 0.158878i
\(704\) −374.343 216.127i −0.531737 0.306999i
\(705\) −3.25586 + 48.1336i −0.00461824 + 0.0682745i
\(706\) 346.440 0.490708
\(707\) 346.196 271.478i 0.489669 0.383987i
\(708\) −347.243 + 517.343i −0.490457 + 0.730710i
\(709\) 279.280 + 483.727i 0.393907 + 0.682267i 0.992961 0.118442i \(-0.0377899\pi\)
−0.599054 + 0.800709i \(0.704457\pi\)
\(710\) −143.740 82.9882i −0.202450 0.116885i
\(711\) 303.754 + 41.2821i 0.427222 + 0.0580621i
\(712\) 126.582 + 219.247i 0.177784 + 0.307931i
\(713\) 66.8492i 0.0937576i
\(714\) 11.3151 + 152.878i 0.0158475 + 0.214115i
\(715\) −795.023 −1.11192
\(716\) 265.589 153.338i 0.370935 0.214159i
\(717\) −71.9767 146.726i −0.100386 0.204639i
\(718\) −235.772 + 408.368i −0.328373 + 0.568758i
\(719\) −454.362 + 262.326i −0.631937 + 0.364849i −0.781502 0.623903i \(-0.785546\pi\)
0.149565 + 0.988752i \(0.452213\pi\)
\(720\) −39.0393 + 15.9798i −0.0542213 + 0.0221942i
\(721\) −747.968 + 106.487i −1.03740 + 0.147694i
\(722\) 353.773i 0.489991i
\(723\) −48.6066 + 718.584i −0.0672290 + 0.993892i
\(724\) −127.420 + 220.698i −0.175995 + 0.304832i
\(725\) 141.240 + 81.5448i 0.194814 + 0.112476i
\(726\) 336.613 + 22.7693i 0.463655 + 0.0313626i
\(727\) 626.396 0.861618 0.430809 0.902443i \(-0.358228\pi\)
0.430809 + 0.902443i \(0.358228\pi\)
\(728\) −1190.08 478.346i −1.63473 0.657069i
\(729\) −669.958 287.398i −0.919009 0.394236i
\(730\) −150.357 260.426i −0.205969 0.356748i
\(731\) 164.751 + 95.1189i 0.225377 + 0.130122i
\(732\) −202.976 + 99.5699i −0.277289 + 0.136024i
\(733\) 222.455 + 385.303i 0.303485 + 0.525652i 0.976923 0.213592i \(-0.0685163\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(734\) 33.5841i 0.0457548i
\(735\) −321.113 + 70.2233i −0.436889 + 0.0955419i
\(736\) 1097.77 1.49153
\(737\) 1308.89 755.689i 1.77597 1.02536i
\(738\) −415.394 56.4546i −0.562864 0.0764967i
\(739\) 180.910 313.346i 0.244804 0.424013i −0.717272 0.696793i \(-0.754610\pi\)
0.962077 + 0.272780i \(0.0879430\pi\)
\(740\) −94.7790 + 54.7207i −0.128080 + 0.0739469i
\(741\) −425.245 285.427i −0.573880 0.385191i
\(742\) 117.321 291.885i 0.158115 0.393376i
\(743\) 1133.77i 1.52593i −0.646438 0.762967i \(-0.723742\pi\)
0.646438 0.762967i \(-0.276258\pi\)
\(744\) −45.8604 3.10210i −0.0616404 0.00416949i
\(745\) −139.525 + 241.665i −0.187282 + 0.324382i
\(746\) 316.782 + 182.894i 0.424640 + 0.245166i
\(747\) −246.041 190.433i −0.329372 0.254930i
\(748\) 256.325 0.342681
\(749\) 80.5351 + 565.680i 0.107524 + 0.755246i
\(750\) −31.7452 21.3075i −0.0423269 0.0284101i
\(751\) 64.7013 + 112.066i 0.0861536 + 0.149222i 0.905882 0.423530i \(-0.139209\pi\)
−0.819729 + 0.572752i \(0.805876\pi\)
\(752\) 13.0550 + 7.53728i 0.0173603 + 0.0100230i
\(753\) 210.963 + 430.053i 0.280163 + 0.571120i
\(754\) −445.974 772.450i −0.591478 1.02447i
\(755\) 155.946i 0.206550i
\(756\) 456.820 227.698i 0.604260 0.301188i
\(757\) 271.769 0.359008 0.179504 0.983757i \(-0.442551\pi\)
0.179504 + 0.983757i \(0.442551\pi\)
\(758\) 627.412 362.237i 0.827721 0.477885i
\(759\) −1330.27 + 652.567i −1.75267 + 0.859772i
\(760\) −60.7707 + 105.258i −0.0799614 + 0.138497i
\(761\) −853.490 + 492.763i −1.12154 + 0.647520i −0.941793 0.336193i \(-0.890860\pi\)
−0.179745 + 0.983713i \(0.557527\pi\)
\(762\) −187.379 + 279.168i −0.245904 + 0.366362i
\(763\) −264.320 337.068i −0.346422 0.441766i
\(764\) 300.639i 0.393507i
\(765\) −78.8821 + 101.916i