Properties

Label 570.2.k.a.77.13
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.13
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.518471 - 1.65263i) q^{3} -1.00000i q^{4} +(-2.11139 + 0.736229i) q^{5} +(-1.53520 - 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46238 + 1.71368i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.518471 - 1.65263i) q^{3} -1.00000i q^{4} +(-2.11139 + 0.736229i) q^{5} +(-1.53520 - 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46238 + 1.71368i) q^{9} +(-0.972386 + 2.01357i) q^{10} +5.62118i q^{11} +(-1.65263 + 0.518471i) q^{12} +(0.933851 - 0.933851i) q^{13} -3.45230 q^{14} +(2.31141 + 3.10763i) q^{15} -1.00000 q^{16} +(0.0532613 - 0.0532613i) q^{17} +(-0.529408 + 2.95292i) q^{18} +1.00000i q^{19} +(0.736229 + 2.11139i) q^{20} +(-2.76865 + 5.29997i) q^{21} +(3.97477 + 3.97477i) q^{22} +(-0.841693 - 0.841693i) q^{23} +(-0.801972 + 1.53520i) q^{24} +(3.91593 - 3.10893i) q^{25} -1.32067i q^{26} +(4.10875 + 3.18091i) q^{27} +(-2.44114 + 2.44114i) q^{28} -6.56484 q^{29} +(3.83184 + 0.563017i) q^{30} -5.11218 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.28973 - 2.91441i) q^{33} -0.0753229i q^{34} +(6.95144 + 3.35696i) q^{35} +(1.71368 + 2.46238i) q^{36} +(-5.88633 - 5.88633i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-2.02749 - 1.05914i) q^{39} +(2.01357 + 0.972386i) q^{40} -5.75913i q^{41} +(1.78991 + 5.70537i) q^{42} +(-7.57828 + 7.57828i) q^{43} +5.62118 q^{44} +(3.93738 - 5.43112i) q^{45} -1.19033 q^{46} +(2.64154 - 2.64154i) q^{47} +(0.518471 + 1.65263i) q^{48} +4.91834i q^{49} +(0.570637 - 4.96733i) q^{50} +(-0.115636 - 0.0604069i) q^{51} +(-0.933851 - 0.933851i) q^{52} +(-9.67459 - 9.67459i) q^{53} +(5.15457 - 0.656086i) q^{54} +(-4.13847 - 11.8685i) q^{55} +3.45230i q^{56} +(1.65263 - 0.518471i) q^{57} +(-4.64204 + 4.64204i) q^{58} -11.0697 q^{59} +(3.10763 - 2.31141i) q^{60} +9.82484 q^{61} +(-3.61486 + 3.61486i) q^{62} +(10.1943 + 1.82767i) q^{63} +1.00000i q^{64} +(-1.28420 + 2.65925i) q^{65} +(4.50803 - 8.62963i) q^{66} +(6.27631 + 6.27631i) q^{67} +(-0.0532613 - 0.0532613i) q^{68} +(-0.954615 + 1.82740i) q^{69} +(7.28914 - 2.54168i) q^{70} +2.29302i q^{71} +(2.95292 + 0.529408i) q^{72} +(-7.35442 + 7.35442i) q^{73} -8.32453 q^{74} +(-7.16821 - 4.85970i) q^{75} +1.00000 q^{76} +(13.7221 - 13.7221i) q^{77} +(-2.18257 + 0.684726i) q^{78} +3.41806i q^{79} +(2.11139 - 0.736229i) q^{80} +(3.12659 - 8.43946i) q^{81} +(-4.07232 - 4.07232i) q^{82} +(4.84479 + 4.84479i) q^{83} +(5.29997 + 2.76865i) q^{84} +(-0.0732429 + 0.151668i) q^{85} +10.7173i q^{86} +(3.40368 + 10.8493i) q^{87} +(3.97477 - 3.97477i) q^{88} +4.69409 q^{89} +(-1.05624 - 6.62453i) q^{90} -4.55933 q^{91} +(-0.841693 + 0.841693i) q^{92} +(2.65052 + 8.44855i) q^{93} -3.73570i q^{94} +(-0.736229 - 2.11139i) q^{95} +(1.53520 + 0.801972i) q^{96} +(-4.18214 - 4.18214i) q^{97} +(3.47779 + 3.47779i) q^{98} +(-9.63290 - 13.8415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.518471 1.65263i −0.299339 0.954147i
\(4\) 1.00000i 0.500000i
\(5\) −2.11139 + 0.736229i −0.944242 + 0.329251i
\(6\) −1.53520 0.801972i −0.626743 0.327404i
\(7\) −2.44114 2.44114i −0.922665 0.922665i 0.0745524 0.997217i \(-0.476247\pi\)
−0.997217 + 0.0745524i \(0.976247\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.46238 + 1.71368i −0.820792 + 0.571227i
\(10\) −0.972386 + 2.01357i −0.307495 + 0.636747i
\(11\) 5.62118i 1.69485i 0.530916 + 0.847424i \(0.321848\pi\)
−0.530916 + 0.847424i \(0.678152\pi\)
\(12\) −1.65263 + 0.518471i −0.477073 + 0.149670i
\(13\) 0.933851 0.933851i 0.259004 0.259004i −0.565645 0.824649i \(-0.691373\pi\)
0.824649 + 0.565645i \(0.191373\pi\)
\(14\) −3.45230 −0.922665
\(15\) 2.31141 + 3.10763i 0.596803 + 0.802388i
\(16\) −1.00000 −0.250000
\(17\) 0.0532613 0.0532613i 0.0129178 0.0129178i −0.700618 0.713536i \(-0.747092\pi\)
0.713536 + 0.700618i \(0.247092\pi\)
\(18\) −0.529408 + 2.95292i −0.124783 + 0.696010i
\(19\) 1.00000i 0.229416i
\(20\) 0.736229 + 2.11139i 0.164626 + 0.472121i
\(21\) −2.76865 + 5.29997i −0.604168 + 1.15655i
\(22\) 3.97477 + 3.97477i 0.847424 + 0.847424i
\(23\) −0.841693 0.841693i −0.175505 0.175505i 0.613888 0.789393i \(-0.289605\pi\)
−0.789393 + 0.613888i \(0.789605\pi\)
\(24\) −0.801972 + 1.53520i −0.163702 + 0.313371i
\(25\) 3.91593 3.10893i 0.783187 0.621786i
\(26\) 1.32067i 0.259004i
\(27\) 4.10875 + 3.18091i 0.790730 + 0.612166i
\(28\) −2.44114 + 2.44114i −0.461332 + 0.461332i
\(29\) −6.56484 −1.21906 −0.609530 0.792763i \(-0.708642\pi\)
−0.609530 + 0.792763i \(0.708642\pi\)
\(30\) 3.83184 + 0.563017i 0.699595 + 0.102792i
\(31\) −5.11218 −0.918175 −0.459087 0.888391i \(-0.651824\pi\)
−0.459087 + 0.888391i \(0.651824\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 9.28973 2.91441i 1.61713 0.507335i
\(34\) 0.0753229i 0.0129178i
\(35\) 6.95144 + 3.35696i 1.17501 + 0.567430i
\(36\) 1.71368 + 2.46238i 0.285614 + 0.410396i
\(37\) −5.88633 5.88633i −0.967707 0.967707i 0.0317880 0.999495i \(-0.489880\pi\)
−0.999495 + 0.0317880i \(0.989880\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) −2.02749 1.05914i −0.324658 0.169598i
\(40\) 2.01357 + 0.972386i 0.318373 + 0.153748i
\(41\) 5.75913i 0.899426i −0.893173 0.449713i \(-0.851526\pi\)
0.893173 0.449713i \(-0.148474\pi\)
\(42\) 1.78991 + 5.70537i 0.276190 + 0.880358i
\(43\) −7.57828 + 7.57828i −1.15568 + 1.15568i −0.170282 + 0.985395i \(0.554468\pi\)
−0.985395 + 0.170282i \(0.945532\pi\)
\(44\) 5.62118 0.847424
\(45\) 3.93738 5.43112i 0.586949 0.809624i
\(46\) −1.19033 −0.175505
\(47\) 2.64154 2.64154i 0.385308 0.385308i −0.487702 0.873010i \(-0.662165\pi\)
0.873010 + 0.487702i \(0.162165\pi\)
\(48\) 0.518471 + 1.65263i 0.0748348 + 0.238537i
\(49\) 4.91834i 0.702620i
\(50\) 0.570637 4.96733i 0.0807003 0.702487i
\(51\) −0.115636 0.0604069i −0.0161922 0.00845865i
\(52\) −0.933851 0.933851i −0.129502 0.129502i
\(53\) −9.67459 9.67459i −1.32891 1.32891i −0.906324 0.422583i \(-0.861124\pi\)
−0.422583 0.906324i \(-0.638876\pi\)
\(54\) 5.15457 0.656086i 0.701448 0.0892821i
\(55\) −4.13847 11.8685i −0.558031 1.60035i
\(56\) 3.45230i 0.461332i
\(57\) 1.65263 0.518471i 0.218896 0.0686731i
\(58\) −4.64204 + 4.64204i −0.609530 + 0.609530i
\(59\) −11.0697 −1.44116 −0.720579 0.693373i \(-0.756124\pi\)
−0.720579 + 0.693373i \(0.756124\pi\)
\(60\) 3.10763 2.31141i 0.401194 0.298401i
\(61\) 9.82484 1.25794 0.628971 0.777429i \(-0.283476\pi\)
0.628971 + 0.777429i \(0.283476\pi\)
\(62\) −3.61486 + 3.61486i −0.459087 + 0.459087i
\(63\) 10.1943 + 1.82767i 1.28437 + 0.230265i
\(64\) 1.00000i 0.125000i
\(65\) −1.28420 + 2.65925i −0.159285 + 0.329840i
\(66\) 4.50803 8.62963i 0.554900 1.06223i
\(67\) 6.27631 + 6.27631i 0.766774 + 0.766774i 0.977537 0.210764i \(-0.0675950\pi\)
−0.210764 + 0.977537i \(0.567595\pi\)
\(68\) −0.0532613 0.0532613i −0.00645888 0.00645888i
\(69\) −0.954615 + 1.82740i −0.114922 + 0.219993i
\(70\) 7.28914 2.54168i 0.871219 0.303789i
\(71\) 2.29302i 0.272131i 0.990700 + 0.136066i \(0.0434458\pi\)
−0.990700 + 0.136066i \(0.956554\pi\)
\(72\) 2.95292 + 0.529408i 0.348005 + 0.0623913i
\(73\) −7.35442 + 7.35442i −0.860770 + 0.860770i −0.991428 0.130658i \(-0.958291\pi\)
0.130658 + 0.991428i \(0.458291\pi\)
\(74\) −8.32453 −0.967707
\(75\) −7.16821 4.85970i −0.827714 0.561150i
\(76\) 1.00000 0.114708
\(77\) 13.7221 13.7221i 1.56378 1.56378i
\(78\) −2.18257 + 0.684726i −0.247128 + 0.0775300i
\(79\) 3.41806i 0.384561i 0.981340 + 0.192281i \(0.0615884\pi\)
−0.981340 + 0.192281i \(0.938412\pi\)
\(80\) 2.11139 0.736229i 0.236061 0.0823129i
\(81\) 3.12659 8.43946i 0.347399 0.937717i
\(82\) −4.07232 4.07232i −0.449713 0.449713i
\(83\) 4.84479 + 4.84479i 0.531785 + 0.531785i 0.921103 0.389318i \(-0.127289\pi\)
−0.389318 + 0.921103i \(0.627289\pi\)
\(84\) 5.29997 + 2.76865i 0.578274 + 0.302084i
\(85\) −0.0732429 + 0.151668i −0.00794431 + 0.0164507i
\(86\) 10.7173i 1.15568i
\(87\) 3.40368 + 10.8493i 0.364912 + 1.16316i
\(88\) 3.97477 3.97477i 0.423712 0.423712i
\(89\) 4.69409 0.497572 0.248786 0.968558i \(-0.419968\pi\)
0.248786 + 0.968558i \(0.419968\pi\)
\(90\) −1.05624 6.62453i −0.111337 0.698286i
\(91\) −4.55933 −0.477947
\(92\) −0.841693 + 0.841693i −0.0877526 + 0.0877526i
\(93\) 2.65052 + 8.44855i 0.274846 + 0.876073i
\(94\) 3.73570i 0.385308i
\(95\) −0.736229 2.11139i −0.0755355 0.216624i
\(96\) 1.53520 + 0.801972i 0.156686 + 0.0818509i
\(97\) −4.18214 4.18214i −0.424632 0.424632i 0.462163 0.886795i \(-0.347073\pi\)
−0.886795 + 0.462163i \(0.847073\pi\)
\(98\) 3.47779 + 3.47779i 0.351310 + 0.351310i
\(99\) −9.63290 13.8415i −0.968143 1.39112i
\(100\) −3.10893 3.91593i −0.310893 0.391593i
\(101\) 0.845280i 0.0841085i −0.999115 0.0420543i \(-0.986610\pi\)
0.999115 0.0420543i \(-0.0133902\pi\)
\(102\) −0.124481 + 0.0390527i −0.0123254 + 0.00386679i
\(103\) 1.72028 1.72028i 0.169505 0.169505i −0.617257 0.786762i \(-0.711756\pi\)
0.786762 + 0.617257i \(0.211756\pi\)
\(104\) −1.32067 −0.129502
\(105\) 1.94370 13.2286i 0.189686 1.29098i
\(106\) −13.6819 −1.32891
\(107\) 6.17999 6.17999i 0.597442 0.597442i −0.342189 0.939631i \(-0.611168\pi\)
0.939631 + 0.342189i \(0.111168\pi\)
\(108\) 3.18091 4.10875i 0.306083 0.395365i
\(109\) 13.7634i 1.31830i −0.752012 0.659149i \(-0.770917\pi\)
0.752012 0.659149i \(-0.229083\pi\)
\(110\) −11.3186 5.46595i −1.07919 0.521158i
\(111\) −6.67604 + 12.7798i −0.633662 + 1.21301i
\(112\) 2.44114 + 2.44114i 0.230666 + 0.230666i
\(113\) −13.5833 13.5833i −1.27781 1.27781i −0.941892 0.335915i \(-0.890955\pi\)
−0.335915 0.941892i \(-0.609045\pi\)
\(114\) 0.801972 1.53520i 0.0751116 0.143785i
\(115\) 2.39682 + 1.15746i 0.223505 + 0.107934i
\(116\) 6.56484i 0.609530i
\(117\) −0.699170 + 3.89982i −0.0646383 + 0.360538i
\(118\) −7.82749 + 7.82749i −0.720579 + 0.720579i
\(119\) −0.260037 −0.0238375
\(120\) 0.563017 3.83184i 0.0513962 0.349798i
\(121\) −20.5976 −1.87251
\(122\) 6.94721 6.94721i 0.628971 0.628971i
\(123\) −9.51772 + 2.98594i −0.858184 + 0.269233i
\(124\) 5.11218i 0.459087i
\(125\) −5.97918 + 9.44719i −0.534794 + 0.844982i
\(126\) 8.50085 5.91613i 0.757316 0.527051i
\(127\) −4.84183 4.84183i −0.429643 0.429643i 0.458864 0.888507i \(-0.348257\pi\)
−0.888507 + 0.458864i \(0.848257\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 16.4532 + 8.59499i 1.44863 + 0.756746i
\(130\) 0.972312 + 2.78844i 0.0852774 + 0.244562i
\(131\) 0.132969i 0.0116176i 0.999983 + 0.00580880i \(0.00184901\pi\)
−0.999983 + 0.00580880i \(0.998151\pi\)
\(132\) −2.91441 9.28973i −0.253667 0.808567i
\(133\) 2.44114 2.44114i 0.211674 0.211674i
\(134\) 8.87605 0.766774
\(135\) −11.0171 3.69115i −0.948197 0.317684i
\(136\) −0.0753229 −0.00645888
\(137\) 11.8447 11.8447i 1.01196 1.01196i 0.0120322 0.999928i \(-0.496170\pi\)
0.999928 0.0120322i \(-0.00383006\pi\)
\(138\) 0.617153 + 1.96718i 0.0525356 + 0.167458i
\(139\) 11.4478i 0.970986i −0.874241 0.485493i \(-0.838640\pi\)
0.874241 0.485493i \(-0.161360\pi\)
\(140\) 3.35696 6.95144i 0.283715 0.587504i
\(141\) −5.73505 2.99593i −0.482978 0.252303i
\(142\) 1.62141 + 1.62141i 0.136066 + 0.136066i
\(143\) 5.24934 + 5.24934i 0.438972 + 0.438972i
\(144\) 2.46238 1.71368i 0.205198 0.142807i
\(145\) 13.8609 4.83322i 1.15109 0.401377i
\(146\) 10.4007i 0.860770i
\(147\) 8.12820 2.55002i 0.670403 0.210322i
\(148\) −5.88633 + 5.88633i −0.483853 + 0.483853i
\(149\) 21.7749 1.78387 0.891934 0.452165i \(-0.149348\pi\)
0.891934 + 0.452165i \(0.149348\pi\)
\(150\) −8.50502 + 1.63236i −0.694432 + 0.133282i
\(151\) −12.9880 −1.05694 −0.528472 0.848951i \(-0.677235\pi\)
−0.528472 + 0.848951i \(0.677235\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) −0.0398765 + 0.222422i −0.00322382 + 0.0179818i
\(154\) 19.4060i 1.56378i
\(155\) 10.7938 3.76373i 0.866979 0.302310i
\(156\) −1.05914 + 2.02749i −0.0847988 + 0.162329i
\(157\) 10.2762 + 10.2762i 0.820131 + 0.820131i 0.986127 0.165995i \(-0.0530837\pi\)
−0.165995 + 0.986127i \(0.553084\pi\)
\(158\) 2.41693 + 2.41693i 0.192281 + 0.192281i
\(159\) −10.9725 + 21.0045i −0.870178 + 1.66577i
\(160\) 0.972386 2.01357i 0.0768738 0.159187i
\(161\) 4.10938i 0.323865i
\(162\) −3.75676 8.17843i −0.295159 0.642558i
\(163\) 4.97451 4.97451i 0.389634 0.389634i −0.484923 0.874557i \(-0.661152\pi\)
0.874557 + 0.484923i \(0.161152\pi\)
\(164\) −5.75913 −0.449713
\(165\) −17.4686 + 12.9928i −1.35993 + 1.01149i
\(166\) 6.85157 0.531785
\(167\) 11.3116 11.3116i 0.875319 0.875319i −0.117727 0.993046i \(-0.537561\pi\)
0.993046 + 0.117727i \(0.0375607\pi\)
\(168\) 5.70537 1.78991i 0.440179 0.138095i
\(169\) 11.2558i 0.865834i
\(170\) 0.0554549 + 0.159036i 0.00425319 + 0.0121975i
\(171\) −1.71368 2.46238i −0.131048 0.188303i
\(172\) 7.57828 + 7.57828i 0.577839 + 0.577839i
\(173\) 16.5624 + 16.5624i 1.25921 + 1.25921i 0.951468 + 0.307746i \(0.0995748\pi\)
0.307746 + 0.951468i \(0.400425\pi\)
\(174\) 10.0783 + 5.26482i 0.764037 + 0.399125i
\(175\) −17.1487 1.97001i −1.29632 0.148919i
\(176\) 5.62118i 0.423712i
\(177\) 5.73934 + 18.2942i 0.431395 + 1.37508i
\(178\) 3.31922 3.31922i 0.248786 0.248786i
\(179\) −13.4740 −1.00710 −0.503549 0.863967i \(-0.667973\pi\)
−0.503549 + 0.863967i \(0.667973\pi\)
\(180\) −5.43112 3.93738i −0.404812 0.293475i
\(181\) 10.4967 0.780217 0.390108 0.920769i \(-0.372438\pi\)
0.390108 + 0.920769i \(0.372438\pi\)
\(182\) −3.22393 + 3.22393i −0.238974 + 0.238974i
\(183\) −5.09389 16.2368i −0.376551 1.20026i
\(184\) 1.19033i 0.0877526i
\(185\) 16.7620 + 8.09465i 1.23237 + 0.595131i
\(186\) 7.84822 + 4.09983i 0.575460 + 0.300614i
\(187\) 0.299391 + 0.299391i 0.0218937 + 0.0218937i
\(188\) −2.64154 2.64154i −0.192654 0.192654i
\(189\) −2.26500 17.7951i −0.164755 1.29440i
\(190\) −2.01357 0.972386i −0.146080 0.0705443i
\(191\) 16.2464i 1.17555i 0.809024 + 0.587775i \(0.199996\pi\)
−0.809024 + 0.587775i \(0.800004\pi\)
\(192\) 1.65263 0.518471i 0.119268 0.0374174i
\(193\) −2.23569 + 2.23569i −0.160928 + 0.160928i −0.782978 0.622049i \(-0.786300\pi\)
0.622049 + 0.782978i \(0.286300\pi\)
\(194\) −5.91443 −0.424632
\(195\) 5.06058 + 0.743558i 0.362396 + 0.0532473i
\(196\) 4.91834 0.351310
\(197\) −5.51445 + 5.51445i −0.392889 + 0.392889i −0.875716 0.482827i \(-0.839610\pi\)
0.482827 + 0.875716i \(0.339610\pi\)
\(198\) −16.5989 2.97589i −1.17963 0.211488i
\(199\) 22.3312i 1.58302i −0.611159 0.791508i \(-0.709297\pi\)
0.611159 0.791508i \(-0.290703\pi\)
\(200\) −4.96733 0.570637i −0.351243 0.0403501i
\(201\) 7.11834 13.6265i 0.502089 0.961140i
\(202\) −0.597703 0.597703i −0.0420543 0.0420543i
\(203\) 16.0257 + 16.0257i 1.12478 + 1.12478i
\(204\) −0.0604069 + 0.115636i −0.00422933 + 0.00809612i
\(205\) 4.24004 + 12.1598i 0.296137 + 0.849276i
\(206\) 2.43285i 0.169505i
\(207\) 3.51496 + 0.630172i 0.244307 + 0.0438000i
\(208\) −0.933851 + 0.933851i −0.0647509 + 0.0647509i
\(209\) −5.62118 −0.388825
\(210\) −7.97966 10.7285i −0.550649 0.740335i
\(211\) −4.91417 −0.338305 −0.169153 0.985590i \(-0.554103\pi\)
−0.169153 + 0.985590i \(0.554103\pi\)
\(212\) −9.67459 + 9.67459i −0.664454 + 0.664454i
\(213\) 3.78951 1.18886i 0.259653 0.0814595i
\(214\) 8.73982i 0.597442i
\(215\) 10.4214 21.5801i 0.710731 1.47175i
\(216\) −0.656086 5.15457i −0.0446410 0.350724i
\(217\) 12.4796 + 12.4796i 0.847167 + 0.847167i
\(218\) −9.73222 9.73222i −0.659149 0.659149i
\(219\) 15.9672 + 8.34109i 1.07896 + 0.563639i
\(220\) −11.8685 + 4.13847i −0.800174 + 0.279016i
\(221\) 0.0994763i 0.00669150i
\(222\) 4.31602 + 13.7574i 0.289673 + 0.923334i
\(223\) −6.07075 + 6.07075i −0.406527 + 0.406527i −0.880526 0.473998i \(-0.842810\pi\)
0.473998 + 0.880526i \(0.342810\pi\)
\(224\) 3.45230 0.230666
\(225\) −4.31479 + 14.3660i −0.287652 + 0.957735i
\(226\) −19.2097 −1.27781
\(227\) −12.5348 + 12.5348i −0.831965 + 0.831965i −0.987785 0.155820i \(-0.950198\pi\)
0.155820 + 0.987785i \(0.450198\pi\)
\(228\) −0.518471 1.65263i −0.0343366 0.109448i
\(229\) 4.03489i 0.266633i 0.991073 + 0.133317i \(0.0425627\pi\)
−0.991073 + 0.133317i \(0.957437\pi\)
\(230\) 2.51326 0.876358i 0.165719 0.0577853i
\(231\) −29.7920 15.5630i −1.96017 1.02397i
\(232\) 4.64204 + 4.64204i 0.304765 + 0.304765i
\(233\) −13.7826 13.7826i −0.902931 0.902931i 0.0927575 0.995689i \(-0.470432\pi\)
−0.995689 + 0.0927575i \(0.970432\pi\)
\(234\) 2.26320 + 3.25198i 0.147950 + 0.212588i
\(235\) −3.63254 + 7.52210i −0.236961 + 0.490688i
\(236\) 11.0697i 0.720579i
\(237\) 5.64879 1.77216i 0.366928 0.115114i
\(238\) −0.183874 + 0.183874i −0.0119188 + 0.0119188i
\(239\) −0.604284 −0.0390879 −0.0195439 0.999809i \(-0.506221\pi\)
−0.0195439 + 0.999809i \(0.506221\pi\)
\(240\) −2.31141 3.10763i −0.149201 0.200597i
\(241\) −1.64307 −0.105839 −0.0529196 0.998599i \(-0.516853\pi\)
−0.0529196 + 0.998599i \(0.516853\pi\)
\(242\) −14.5647 + 14.5647i −0.936255 + 0.936255i
\(243\) −15.5684 0.791496i −0.998710 0.0507745i
\(244\) 9.82484i 0.628971i
\(245\) −3.62103 10.3845i −0.231339 0.663444i
\(246\) −4.61867 + 8.84143i −0.294475 + 0.563709i
\(247\) 0.933851 + 0.933851i 0.0594195 + 0.0594195i
\(248\) 3.61486 + 3.61486i 0.229544 + 0.229544i
\(249\) 5.49477 10.5185i 0.348217 0.666585i
\(250\) 2.45225 + 10.9081i 0.155094 + 0.689888i
\(251\) 0.800477i 0.0505256i −0.999681 0.0252628i \(-0.991958\pi\)
0.999681 0.0252628i \(-0.00804226\pi\)
\(252\) 1.82767 10.1943i 0.115132 0.642183i
\(253\) 4.73131 4.73131i 0.297455 0.297455i
\(254\) −6.84738 −0.429643
\(255\) 0.288625 + 0.0424081i 0.0180744 + 0.00265570i
\(256\) 1.00000 0.0625000
\(257\) 0.187825 0.187825i 0.0117162 0.0117162i −0.701224 0.712941i \(-0.747363\pi\)
0.712941 + 0.701224i \(0.247363\pi\)
\(258\) 17.7118 5.55661i 1.10269 0.345940i
\(259\) 28.7387i 1.78574i
\(260\) 2.65925 + 1.28420i 0.164920 + 0.0796425i
\(261\) 16.1651 11.2500i 1.00059 0.696360i
\(262\) 0.0940236 + 0.0940236i 0.00580880 + 0.00580880i
\(263\) 0.0979650 + 0.0979650i 0.00604078 + 0.00604078i 0.710121 0.704080i \(-0.248640\pi\)
−0.704080 + 0.710121i \(0.748640\pi\)
\(264\) −8.62963 4.50803i −0.531117 0.277450i
\(265\) 27.5495 + 13.3041i 1.69235 + 0.817266i
\(266\) 3.45230i 0.211674i
\(267\) −2.43375 7.75759i −0.148943 0.474757i
\(268\) 6.27631 6.27631i 0.383387 0.383387i
\(269\) −15.3546 −0.936185 −0.468093 0.883679i \(-0.655059\pi\)
−0.468093 + 0.883679i \(0.655059\pi\)
\(270\) −10.4003 + 5.18019i −0.632940 + 0.315257i
\(271\) 8.91573 0.541592 0.270796 0.962637i \(-0.412713\pi\)
0.270796 + 0.962637i \(0.412713\pi\)
\(272\) −0.0532613 + 0.0532613i −0.00322944 + 0.00322944i
\(273\) 2.36388 + 7.53488i 0.143068 + 0.456032i
\(274\) 16.7509i 1.01196i
\(275\) 17.4759 + 22.0122i 1.05383 + 1.32738i
\(276\) 1.82740 + 0.954615i 0.109997 + 0.0574611i
\(277\) −5.23704 5.23704i −0.314663 0.314663i 0.532050 0.846713i \(-0.321422\pi\)
−0.846713 + 0.532050i \(0.821422\pi\)
\(278\) −8.09478 8.09478i −0.485493 0.485493i
\(279\) 12.5881 8.76065i 0.753631 0.524486i
\(280\) −2.54168 7.28914i −0.151894 0.435610i
\(281\) 1.07688i 0.0642410i −0.999484 0.0321205i \(-0.989774\pi\)
0.999484 0.0321205i \(-0.0102260\pi\)
\(282\) −6.17374 + 1.93685i −0.367641 + 0.115338i
\(283\) −13.3657 + 13.3657i −0.794508 + 0.794508i −0.982223 0.187715i \(-0.939892\pi\)
0.187715 + 0.982223i \(0.439892\pi\)
\(284\) 2.29302 0.136066
\(285\) −3.10763 + 2.31141i −0.184080 + 0.136916i
\(286\) 7.42369 0.438972
\(287\) −14.0589 + 14.0589i −0.829868 + 0.829868i
\(288\) 0.529408 2.95292i 0.0311956 0.174002i
\(289\) 16.9943i 0.999666i
\(290\) 6.38356 13.2188i 0.374855 0.776233i
\(291\) −4.74321 + 9.07984i −0.278052 + 0.532270i
\(292\) 7.35442 + 7.35442i 0.430385 + 0.430385i
\(293\) −0.952778 0.952778i −0.0556619 0.0556619i 0.678728 0.734390i \(-0.262532\pi\)
−0.734390 + 0.678728i \(0.762532\pi\)
\(294\) 3.94437 7.55064i 0.230041 0.440362i
\(295\) 23.3726 8.14987i 1.36080 0.474503i
\(296\) 8.32453i 0.483853i
\(297\) −17.8804 + 23.0960i −1.03753 + 1.34017i
\(298\) 15.3972 15.3972i 0.891934 0.891934i
\(299\) −1.57203 −0.0909130
\(300\) −4.85970 + 7.16821i −0.280575 + 0.413857i
\(301\) 36.9993 2.13261
\(302\) −9.18387 + 9.18387i −0.528472 + 0.528472i
\(303\) −1.39694 + 0.438253i −0.0802519 + 0.0251770i
\(304\) 1.00000i 0.0573539i
\(305\) −20.7441 + 7.23333i −1.18780 + 0.414179i
\(306\) 0.129079 + 0.185473i 0.00737898 + 0.0106028i
\(307\) 12.7740 + 12.7740i 0.729052 + 0.729052i 0.970431 0.241379i \(-0.0775997\pi\)
−0.241379 + 0.970431i \(0.577600\pi\)
\(308\) −13.7221 13.7221i −0.781888 0.781888i
\(309\) −3.73491 1.95108i −0.212472 0.110993i
\(310\) 4.97101 10.2937i 0.282334 0.584645i
\(311\) 6.21244i 0.352275i −0.984366 0.176138i \(-0.943640\pi\)
0.984366 0.176138i \(-0.0563604\pi\)
\(312\) 0.684726 + 2.18257i 0.0387650 + 0.123564i
\(313\) −1.38773 + 1.38773i −0.0784393 + 0.0784393i −0.745238 0.666799i \(-0.767664\pi\)
0.666799 + 0.745238i \(0.267664\pi\)
\(314\) 14.5328 0.820131
\(315\) −22.8698 + 3.64644i −1.28857 + 0.205454i
\(316\) 3.41806 0.192281
\(317\) −6.17490 + 6.17490i −0.346817 + 0.346817i −0.858922 0.512106i \(-0.828866\pi\)
0.512106 + 0.858922i \(0.328866\pi\)
\(318\) 7.09368 + 22.6112i 0.397794 + 1.26797i
\(319\) 36.9021i 2.06612i
\(320\) −0.736229 2.11139i −0.0411564 0.118030i
\(321\) −13.4174 7.00910i −0.748885 0.391210i
\(322\) 2.90577 + 2.90577i 0.161932 + 0.161932i
\(323\) 0.0532613 + 0.0532613i 0.00296354 + 0.00296354i
\(324\) −8.43946 3.12659i −0.468859 0.173700i
\(325\) 0.753621 6.56018i 0.0418034 0.363893i
\(326\) 7.03502i 0.389634i
\(327\) −22.7459 + 7.13594i −1.25785 + 0.394618i
\(328\) −4.07232 + 4.07232i −0.224856 + 0.224856i
\(329\) −12.8967 −0.711021
\(330\) −3.16482 + 21.5395i −0.174218 + 1.18571i
\(331\) 9.52357 0.523463 0.261731 0.965141i \(-0.415707\pi\)
0.261731 + 0.965141i \(0.415707\pi\)
\(332\) 4.84479 4.84479i 0.265892 0.265892i
\(333\) 24.5817 + 4.40707i 1.34707 + 0.241506i
\(334\) 15.9970i 0.875319i
\(335\) −17.8725 8.63094i −0.976481 0.471559i
\(336\) 2.76865 5.29997i 0.151042 0.289137i
\(337\) −16.6674 16.6674i −0.907932 0.907932i 0.0881729 0.996105i \(-0.471897\pi\)
−0.996105 + 0.0881729i \(0.971897\pi\)
\(338\) 7.95908 + 7.95908i 0.432917 + 0.432917i
\(339\) −15.4056 + 29.4907i −0.836718 + 1.60171i
\(340\) 0.151668 + 0.0732429i 0.00822535 + 0.00397215i
\(341\) 28.7365i 1.55617i
\(342\) −2.95292 0.529408i −0.159676 0.0286271i
\(343\) −5.08162 + 5.08162i −0.274382 + 0.274382i
\(344\) 10.7173 0.577839
\(345\) 0.670179 4.56117i 0.0360812 0.245565i
\(346\) 23.4227 1.25921
\(347\) 7.59916 7.59916i 0.407944 0.407944i −0.473077 0.881021i \(-0.656857\pi\)
0.881021 + 0.473077i \(0.156857\pi\)
\(348\) 10.8493 3.40368i 0.581581 0.182456i
\(349\) 9.65125i 0.516619i 0.966062 + 0.258310i \(0.0831655\pi\)
−0.966062 + 0.258310i \(0.916835\pi\)
\(350\) −13.5190 + 10.7330i −0.722619 + 0.573700i
\(351\) 6.80746 0.866471i 0.363355 0.0462488i
\(352\) −3.97477 3.97477i −0.211856 0.211856i
\(353\) −1.80197 1.80197i −0.0959090 0.0959090i 0.657524 0.753433i \(-0.271604\pi\)
−0.753433 + 0.657524i \(0.771604\pi\)
\(354\) 16.9943 + 8.87763i 0.903236 + 0.471841i
\(355\) −1.68819 4.84145i −0.0895996 0.256958i
\(356\) 4.69409i 0.248786i
\(357\) 0.134821 + 0.429745i 0.00713551 + 0.0227445i
\(358\) −9.52759 + 9.52759i −0.503549 + 0.503549i
\(359\) −16.7534 −0.884209 −0.442104 0.896964i \(-0.645768\pi\)
−0.442104 + 0.896964i \(0.645768\pi\)
\(360\) −6.62453 + 1.05624i −0.349143 + 0.0556686i
\(361\) −1.00000 −0.0526316
\(362\) 7.42232 7.42232i 0.390108 0.390108i
\(363\) 10.6793 + 34.0403i 0.560516 + 1.78665i
\(364\) 4.55933i 0.238974i
\(365\) 10.1135 20.9426i 0.529366 1.09619i
\(366\) −15.0831 7.87925i −0.788406 0.411855i
\(367\) 7.97950 + 7.97950i 0.416526 + 0.416526i 0.884005 0.467478i \(-0.154837\pi\)
−0.467478 + 0.884005i \(0.654837\pi\)
\(368\) 0.841693 + 0.841693i 0.0438763 + 0.0438763i
\(369\) 9.86932 + 14.1812i 0.513776 + 0.738241i
\(370\) 17.5763 6.12876i 0.913750 0.318619i
\(371\) 47.2341i 2.45227i
\(372\) 8.44855 2.65052i 0.438037 0.137423i
\(373\) 13.0474 13.0474i 0.675570 0.675570i −0.283424 0.958995i \(-0.591470\pi\)
0.958995 + 0.283424i \(0.0914704\pi\)
\(374\) 0.423403 0.0218937
\(375\) 18.7127 + 4.98329i 0.966322 + 0.257336i
\(376\) −3.73570 −0.192654
\(377\) −6.13059 + 6.13059i −0.315741 + 0.315741i
\(378\) −14.1846 10.9814i −0.729578 0.564824i
\(379\) 29.4531i 1.51290i 0.654050 + 0.756451i \(0.273069\pi\)
−0.654050 + 0.756451i \(0.726931\pi\)
\(380\) −2.11139 + 0.736229i −0.108312 + 0.0377677i
\(381\) −5.49141 + 10.5121i −0.281334 + 0.538551i
\(382\) 11.4880 + 11.4880i 0.587775 + 0.587775i
\(383\) 8.01839 + 8.01839i 0.409721 + 0.409721i 0.881641 0.471921i \(-0.156439\pi\)
−0.471921 + 0.881641i \(0.656439\pi\)
\(384\) 0.801972 1.53520i 0.0409255 0.0783429i
\(385\) −18.8701 + 39.0753i −0.961708 + 1.99146i
\(386\) 3.16174i 0.160928i
\(387\) 5.67383 31.6473i 0.288417 1.60873i
\(388\) −4.18214 + 4.18214i −0.212316 + 0.212316i
\(389\) −23.1601 −1.17426 −0.587131 0.809492i \(-0.699743\pi\)
−0.587131 + 0.809492i \(0.699743\pi\)
\(390\) 4.10415 3.05260i 0.207821 0.154574i
\(391\) −0.0896594 −0.00453427
\(392\) 3.47779 3.47779i 0.175655 0.175655i
\(393\) 0.219749 0.0689408i 0.0110849 0.00347760i
\(394\) 7.79862i 0.392889i
\(395\) −2.51647 7.21685i −0.126617 0.363119i
\(396\) −13.8415 + 9.63290i −0.695559 + 0.484072i
\(397\) −16.3811 16.3811i −0.822143 0.822143i 0.164272 0.986415i \(-0.447472\pi\)
−0.986415 + 0.164272i \(0.947472\pi\)
\(398\) −15.7905 15.7905i −0.791508 0.791508i
\(399\) −5.29997 2.76865i −0.265330 0.138606i
\(400\) −3.91593 + 3.10893i −0.195797 + 0.155447i
\(401\) 33.9549i 1.69563i −0.530295 0.847813i \(-0.677919\pi\)
0.530295 0.847813i \(-0.322081\pi\)
\(402\) −4.60197 14.6688i −0.229525 0.731614i
\(403\) −4.77402 + 4.77402i −0.237811 + 0.237811i
\(404\) −0.845280 −0.0420543
\(405\) −0.388091 + 20.1209i −0.0192844 + 0.999814i
\(406\) 22.6638 1.12478
\(407\) 33.0881 33.0881i 1.64012 1.64012i
\(408\) 0.0390527 + 0.124481i 0.00193340 + 0.00616272i
\(409\) 33.7198i 1.66734i 0.552266 + 0.833668i \(0.313763\pi\)
−0.552266 + 0.833668i \(0.686237\pi\)
\(410\) 11.5964 + 5.60010i 0.572706 + 0.276569i
\(411\) −25.7160 13.4338i −1.26848 0.662639i
\(412\) −1.72028 1.72028i −0.0847523 0.0847523i
\(413\) 27.0228 + 27.0228i 1.32971 + 1.32971i
\(414\) 2.93105 2.03985i 0.144053 0.100253i
\(415\) −13.7961 6.66237i −0.677225 0.327043i
\(416\) 1.32067i 0.0647509i
\(417\) −18.9189 + 5.93532i −0.926463 + 0.290654i
\(418\) −3.97477 + 3.97477i −0.194412 + 0.194412i
\(419\) −1.26502 −0.0618005 −0.0309003 0.999522i \(-0.509837\pi\)
−0.0309003 + 0.999522i \(0.509837\pi\)
\(420\) −13.2286 1.94370i −0.645492 0.0948430i
\(421\) −4.67210 −0.227704 −0.113852 0.993498i \(-0.536319\pi\)
−0.113852 + 0.993498i \(0.536319\pi\)
\(422\) −3.47484 + 3.47484i −0.169153 + 0.169153i
\(423\) −1.97771 + 11.0312i −0.0961595 + 0.536356i
\(424\) 13.6819i 0.664454i
\(425\) 0.0429820 0.374154i 0.00208494 0.0181491i
\(426\) 1.83894 3.52024i 0.0890967 0.170556i
\(427\) −23.9838 23.9838i −1.16066 1.16066i
\(428\) −6.17999 6.17999i −0.298721 0.298721i
\(429\) 5.95360 11.3969i 0.287442 0.550245i
\(430\) −7.89039 22.6284i −0.380509 1.09124i
\(431\) 13.2679i 0.639093i 0.947571 + 0.319546i \(0.103531\pi\)
−0.947571 + 0.319546i \(0.896469\pi\)
\(432\) −4.10875 3.18091i −0.197682 0.153041i
\(433\) 27.9513 27.9513i 1.34326 1.34326i 0.450459 0.892797i \(-0.351260\pi\)
0.892797 0.450459i \(-0.148740\pi\)
\(434\) 17.6488 0.847167
\(435\) −15.1740 20.4011i −0.727539 0.978159i
\(436\) −13.7634 −0.659149
\(437\) 0.841693 0.841693i 0.0402636 0.0402636i
\(438\) 17.1886 5.39247i 0.821301 0.257662i
\(439\) 6.40984i 0.305925i −0.988232 0.152962i \(-0.951119\pi\)
0.988232 0.152962i \(-0.0488813\pi\)
\(440\) −5.46595 + 11.3186i −0.260579 + 0.539595i
\(441\) −8.42847 12.1108i −0.401356 0.576705i
\(442\) −0.0703404 0.0703404i −0.00334575 0.00334575i
\(443\) 19.7293 + 19.7293i 0.937366 + 0.937366i 0.998151 0.0607845i \(-0.0193602\pi\)
−0.0607845 + 0.998151i \(0.519360\pi\)
\(444\) 12.7798 + 6.67604i 0.606503 + 0.316831i
\(445\) −9.91105 + 3.45592i −0.469829 + 0.163826i
\(446\) 8.58534i 0.406527i
\(447\) −11.2896 35.9859i −0.533982 1.70207i
\(448\) 2.44114 2.44114i 0.115333 0.115333i
\(449\) 18.2109 0.859426 0.429713 0.902966i \(-0.358615\pi\)
0.429713 + 0.902966i \(0.358615\pi\)
\(450\) 7.10730 + 13.2093i 0.335041 + 0.622694i
\(451\) 32.3731 1.52439
\(452\) −13.5833 + 13.5833i −0.638904 + 0.638904i
\(453\) 6.73387 + 21.4643i 0.316385 + 1.00848i
\(454\) 17.7269i 0.831965i
\(455\) 9.62652 3.35671i 0.451298 0.157365i
\(456\) −1.53520 0.801972i −0.0718923 0.0375558i
\(457\) −6.89858 6.89858i −0.322702 0.322702i 0.527101 0.849803i \(-0.323279\pi\)
−0.849803 + 0.527101i \(0.823279\pi\)
\(458\) 2.85310 + 2.85310i 0.133317 + 0.133317i
\(459\) 0.388257 0.0494183i 0.0181223 0.00230665i
\(460\) 1.15746 2.39682i 0.0539670 0.111752i
\(461\) 14.4915i 0.674935i 0.941337 + 0.337467i \(0.109570\pi\)
−0.941337 + 0.337467i \(0.890430\pi\)
\(462\) −32.0709 + 10.0614i −1.49207 + 0.468100i
\(463\) −19.3659 + 19.3659i −0.900009 + 0.900009i −0.995436 0.0954276i \(-0.969578\pi\)
0.0954276 + 0.995436i \(0.469578\pi\)
\(464\) 6.56484 0.304765
\(465\) −11.8163 15.8868i −0.547969 0.736732i
\(466\) −19.4916 −0.902931
\(467\) −1.06586 + 1.06586i −0.0493219 + 0.0493219i −0.731338 0.682016i \(-0.761104\pi\)
0.682016 + 0.731338i \(0.261104\pi\)
\(468\) 3.89982 + 0.699170i 0.180269 + 0.0323192i
\(469\) 30.6427i 1.41495i
\(470\) 2.75033 + 7.88752i 0.126863 + 0.363824i
\(471\) 11.6549 22.3107i 0.537028 1.02802i
\(472\) 7.82749 + 7.82749i 0.360290 + 0.360290i
\(473\) −42.5989 42.5989i −1.95870 1.95870i
\(474\) 2.74119 5.24740i 0.125907 0.241021i
\(475\) 3.10893 + 3.91593i 0.142648 + 0.179675i
\(476\) 0.260037i 0.0119188i
\(477\) 40.4016 + 7.24332i 1.84986 + 0.331649i
\(478\) −0.427293 + 0.427293i −0.0195439 + 0.0195439i
\(479\) −10.1543 −0.463962 −0.231981 0.972720i \(-0.574521\pi\)
−0.231981 + 0.972720i \(0.574521\pi\)
\(480\) −3.83184 0.563017i −0.174899 0.0256981i
\(481\) −10.9939 −0.501279
\(482\) −1.16182 + 1.16182i −0.0529196 + 0.0529196i
\(483\) 6.79129 2.13059i 0.309015 0.0969454i
\(484\) 20.5976i 0.936255i
\(485\) 11.9091 + 5.75111i 0.540766 + 0.261144i
\(486\) −11.5682 + 10.4488i −0.524742 + 0.473968i
\(487\) −20.9045 20.9045i −0.947275 0.947275i 0.0514027 0.998678i \(-0.483631\pi\)
−0.998678 + 0.0514027i \(0.983631\pi\)
\(488\) −6.94721 6.94721i −0.314485 0.314485i
\(489\) −10.8002 5.64189i −0.488400 0.255135i
\(490\) −9.90343 4.78253i −0.447391 0.216053i
\(491\) 1.07122i 0.0483436i −0.999708 0.0241718i \(-0.992305\pi\)
0.999708 0.0241718i \(-0.00769487\pi\)
\(492\) 2.98594 + 9.51772i 0.134617 + 0.429092i
\(493\) −0.349652 + 0.349652i −0.0157475 + 0.0157475i
\(494\) 1.32067 0.0594195
\(495\) 30.5293 + 22.1327i 1.37219 + 0.994790i
\(496\) 5.11218 0.229544
\(497\) 5.59758 5.59758i 0.251086 0.251086i
\(498\) −3.55234 11.3231i −0.159184 0.507401i
\(499\) 2.97605i 0.133226i −0.997779 0.0666132i \(-0.978781\pi\)
0.997779 0.0666132i \(-0.0212193\pi\)
\(500\) 9.44719 + 5.97918i 0.422491 + 0.267397i
\(501\) −24.5587 12.8292i −1.09720 0.573166i
\(502\) −0.566023 0.566023i −0.0252628 0.0252628i
\(503\) −22.6375 22.6375i −1.00936 1.00936i −0.999956 0.00940114i \(-0.997007\pi\)
−0.00940114 0.999956i \(-0.502993\pi\)
\(504\) −5.91613 8.50085i −0.263526 0.378658i
\(505\) 0.622320 + 1.78472i 0.0276929 + 0.0794188i
\(506\) 6.69108i 0.297455i
\(507\) 18.6018 5.83582i 0.826133 0.259178i
\(508\) −4.84183 + 4.84183i −0.214822 + 0.214822i
\(509\) 13.7670 0.610210 0.305105 0.952319i \(-0.401308\pi\)
0.305105 + 0.952319i \(0.401308\pi\)
\(510\) 0.234076 0.174102i 0.0103651 0.00770936i
\(511\) 35.9064 1.58840
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −3.18091 + 4.10875i −0.140440 + 0.181406i
\(514\) 0.265624i 0.0117162i
\(515\) −2.36567 + 4.89871i −0.104244 + 0.215863i
\(516\) 8.59499 16.4532i 0.378373 0.724313i
\(517\) 14.8486 + 14.8486i 0.653039 + 0.653039i
\(518\) 20.3213 + 20.3213i 0.892869 + 0.892869i
\(519\) 18.7844 35.9586i 0.824543 1.57841i
\(520\) 2.78844 0.972312i 0.122281 0.0426387i
\(521\) 1.77371i 0.0777075i 0.999245 + 0.0388537i \(0.0123706\pi\)
−0.999245 + 0.0388537i \(0.987629\pi\)
\(522\) 3.47548 19.3854i 0.152117 0.848478i
\(523\) 15.4539 15.4539i 0.675753 0.675753i −0.283283 0.959036i \(-0.591424\pi\)
0.959036 + 0.283283i \(0.0914237\pi\)
\(524\) 0.132969 0.00580880
\(525\) 5.63540 + 29.3618i 0.245949 + 1.28146i
\(526\) 0.138543 0.00604078
\(527\) −0.272282 + 0.272282i −0.0118608 + 0.0118608i
\(528\) −9.28973 + 2.91441i −0.404284 + 0.126834i
\(529\) 21.5831i 0.938396i
\(530\) 28.8879 10.0730i 1.25481 0.437545i
\(531\) 27.2579 18.9700i 1.18289 0.823228i
\(532\) −2.44114 2.44114i −0.105837 0.105837i
\(533\) −5.37818 5.37818i −0.232955 0.232955i
\(534\) −7.20637 3.76453i −0.311850 0.162907i
\(535\) −8.49848 + 17.5983i −0.367421 + 0.760839i
\(536\) 8.87605i 0.383387i
\(537\) 6.98590 + 22.2676i 0.301464 + 0.960919i
\(538\) −10.8573 + 10.8573i −0.468093 + 0.468093i
\(539\) −27.6469 −1.19084
\(540\) −3.69115 + 11.0171i −0.158842 + 0.474098i
\(541\) 11.0282 0.474141 0.237070 0.971492i \(-0.423813\pi\)
0.237070 + 0.971492i \(0.423813\pi\)
\(542\) 6.30438 6.30438i 0.270796 0.270796i
\(543\) −5.44225 17.3472i −0.233549 0.744441i
\(544\) 0.0753229i 0.00322944i
\(545\) 10.1330 + 29.0600i 0.434052 + 1.24479i
\(546\) 6.99948 + 3.65645i 0.299550 + 0.156482i
\(547\) −8.33939 8.33939i −0.356567 0.356567i 0.505979 0.862546i \(-0.331131\pi\)
−0.862546 + 0.505979i \(0.831131\pi\)
\(548\) −11.8447 11.8447i −0.505980 0.505980i
\(549\) −24.1925 + 16.8366i −1.03251 + 0.718570i
\(550\) 27.9222 + 3.20765i 1.19061 + 0.136775i
\(551\) 6.56484i 0.279672i
\(552\) 1.96718 0.617153i 0.0837288 0.0262678i
\(553\) 8.34396 8.34396i 0.354821 0.354821i
\(554\) −7.40629 −0.314663
\(555\) 4.68685 31.8983i 0.198946 1.35401i
\(556\) −11.4478 −0.485493
\(557\) 8.91400 8.91400i 0.377698 0.377698i −0.492573 0.870271i \(-0.663943\pi\)
0.870271 + 0.492573i \(0.163943\pi\)
\(558\) 2.70643 15.0959i 0.114572 0.639058i
\(559\) 14.1540i 0.598650i
\(560\) −6.95144 3.35696i −0.293752 0.141858i
\(561\) 0.339558 0.650009i 0.0143361 0.0274434i
\(562\) −0.761466 0.761466i −0.0321205 0.0321205i
\(563\) −17.4579 17.4579i −0.735761 0.735761i 0.235993 0.971755i \(-0.424166\pi\)
−0.971755 + 0.235993i \(0.924166\pi\)
\(564\) −2.99593 + 5.73505i −0.126151 + 0.241489i
\(565\) 38.6800 + 18.6792i 1.62728 + 0.785840i
\(566\) 18.9019i 0.794508i
\(567\) −28.2344 + 12.9694i −1.18573 + 0.544665i
\(568\) 1.62141 1.62141i 0.0680328 0.0680328i
\(569\) 6.84928 0.287137 0.143568 0.989640i \(-0.454142\pi\)
0.143568 + 0.989640i \(0.454142\pi\)
\(570\) −0.563017 + 3.83184i −0.0235822 + 0.160498i
\(571\) −30.2902 −1.26761 −0.633803 0.773495i \(-0.718507\pi\)
−0.633803 + 0.773495i \(0.718507\pi\)
\(572\) 5.24934 5.24934i 0.219486 0.219486i
\(573\) 26.8493 8.42329i 1.12165 0.351888i
\(574\) 19.8822i 0.829868i
\(575\) −5.91278 0.679249i −0.246580 0.0283266i
\(576\) −1.71368 2.46238i −0.0714034 0.102599i
\(577\) −31.9328 31.9328i −1.32938 1.32938i −0.905910 0.423471i \(-0.860811\pi\)
−0.423471 0.905910i \(-0.639189\pi\)
\(578\) 12.0168 + 12.0168i 0.499833 + 0.499833i
\(579\) 4.85391 + 2.53563i 0.201722 + 0.105377i
\(580\) −4.83322 13.8609i −0.200689 0.575544i
\(581\) 23.6536i 0.981318i
\(582\) 3.06646 + 9.77437i 0.127109 + 0.405161i
\(583\) 54.3826 54.3826i 2.25230 2.25230i
\(584\) 10.4007 0.430385
\(585\) −1.39494 8.74878i −0.0576735 0.361718i
\(586\) −1.34743 −0.0556619
\(587\) 27.2033 27.2033i 1.12280 1.12280i 0.131481 0.991319i \(-0.458027\pi\)
0.991319 0.131481i \(-0.0419732\pi\)
\(588\) −2.55002 8.12820i −0.105161 0.335201i
\(589\) 5.11218i 0.210644i
\(590\) 10.7641 22.2897i 0.443150 0.917653i
\(591\) 11.9724 + 6.25427i 0.492480 + 0.257266i
\(592\) 5.88633 + 5.88633i 0.241927 + 0.241927i
\(593\) 1.77591 + 1.77591i 0.0729280 + 0.0729280i 0.742630 0.669702i \(-0.233578\pi\)
−0.669702 + 0.742630i \(0.733578\pi\)
\(594\) 3.68798 + 28.9747i 0.151320 + 1.18885i
\(595\) 0.549039 0.191447i 0.0225084 0.00784855i
\(596\) 21.7749i 0.891934i
\(597\) −36.9052 + 11.5781i −1.51043 + 0.473858i
\(598\) −1.11159 + 1.11159i −0.0454565 + 0.0454565i
\(599\) −4.67096 −0.190850 −0.0954252 0.995437i \(-0.530421\pi\)
−0.0954252 + 0.995437i \(0.530421\pi\)
\(600\) 1.63236 + 8.50502i 0.0666409 + 0.347216i
\(601\) −46.7693 −1.90776 −0.953880 0.300187i \(-0.902951\pi\)
−0.953880 + 0.300187i \(0.902951\pi\)
\(602\) 26.1625 26.1625i 1.06630 1.06630i
\(603\) −26.2102 4.69905i −1.06736 0.191360i
\(604\) 12.9880i 0.528472i
\(605\) 43.4896 15.1646i 1.76810 0.616527i
\(606\) −0.677891 + 1.29767i −0.0275374 + 0.0527144i
\(607\) −10.3777 10.3777i −0.421219 0.421219i 0.464404 0.885623i \(-0.346268\pi\)
−0.885623 + 0.464404i \(0.846268\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) 18.1757 34.7934i 0.736517 1.40990i
\(610\) −9.55353 + 19.7830i −0.386811 + 0.800990i
\(611\) 4.93361i 0.199593i
\(612\) 0.222422 + 0.0398765i 0.00899089 + 0.00161191i
\(613\) −0.440870 + 0.440870i −0.0178066 + 0.0178066i −0.715954 0.698147i \(-0.754008\pi\)
0.698147 + 0.715954i \(0.254008\pi\)
\(614\) 18.0652 0.729052
\(615\) 17.8973 13.3117i 0.721688 0.536780i
\(616\) −19.4060 −0.781888
\(617\) −32.7653 + 32.7653i −1.31908 + 1.31908i −0.404577 + 0.914504i \(0.632581\pi\)
−0.914504 + 0.404577i \(0.867419\pi\)
\(618\) −4.02060 + 1.26136i −0.161732 + 0.0507394i
\(619\) 48.9217i 1.96633i 0.182725 + 0.983164i \(0.441508\pi\)
−0.182725 + 0.983164i \(0.558492\pi\)
\(620\) −3.76373 10.7938i −0.151155 0.433490i
\(621\) −0.780962 6.13565i −0.0313389 0.246215i
\(622\) −4.39286 4.39286i −0.176138 0.176138i
\(623\) −11.4589 11.4589i −0.459092 0.459092i
\(624\) 2.02749 + 1.05914i 0.0811644 + 0.0423994i
\(625\) 5.66909 24.3487i 0.226763 0.973950i
\(626\) 1.96255i 0.0784393i
\(627\) 2.91441 + 9.28973i 0.116391 + 0.370996i
\(628\) 10.2762 10.2762i 0.410066 0.410066i
\(629\) −0.627027 −0.0250012
\(630\) −13.5930 + 18.7498i −0.541557 + 0.747011i
\(631\) −2.96028 −0.117847 −0.0589235 0.998263i \(-0.518767\pi\)
−0.0589235 + 0.998263i \(0.518767\pi\)
\(632\) 2.41693 2.41693i 0.0961404 0.0961404i
\(633\) 2.54785 + 8.12130i 0.101268 + 0.322793i
\(634\) 8.73263i 0.346817i
\(635\) 13.7877 + 6.65830i 0.547148 + 0.264226i
\(636\) 21.0045 + 10.9725i 0.832883 + 0.435089i
\(637\) 4.59300 + 4.59300i 0.181981 + 0.181981i
\(638\) −26.0937 26.0937i −1.03306 1.03306i
\(639\) −3.92950 5.64627i −0.155449 0.223363i
\(640\) −2.01357 0.972386i −0.0795934 0.0384369i
\(641\) 33.7063i 1.33132i 0.746256 + 0.665659i \(0.231849\pi\)
−0.746256 + 0.665659i \(0.768151\pi\)
\(642\) −14.4437 + 4.53134i −0.570047 + 0.178838i
\(643\) 27.8461 27.8461i 1.09814 1.09814i 0.103516 0.994628i \(-0.466991\pi\)
0.994628 0.103516i \(-0.0330093\pi\)
\(644\) 4.10938 0.161932
\(645\) −41.0670 6.03403i −1.61701 0.237590i
\(646\) 0.0753229 0.00296354
\(647\) −18.8461 + 18.8461i −0.740918 + 0.740918i −0.972755 0.231837i \(-0.925526\pi\)
0.231837 + 0.972755i \(0.425526\pi\)
\(648\) −8.17843 + 3.75676i −0.321279 + 0.147579i
\(649\) 62.2250i 2.44254i
\(650\) −4.10586 5.17164i −0.161045 0.202848i
\(651\) 14.1538 27.0944i 0.554732 1.06191i
\(652\) −4.97451 4.97451i −0.194817 0.194817i
\(653\) −27.2344 27.2344i −1.06577 1.06577i −0.997679 0.0680864i \(-0.978311\pi\)
−0.0680864 0.997679i \(-0.521689\pi\)
\(654\) −11.0379 + 21.1296i −0.431616 + 0.826234i
\(655\) −0.0978959 0.280750i −0.00382511 0.0109698i
\(656\) 5.75913i 0.224856i
\(657\) 5.50622 30.7125i 0.214818 1.19821i
\(658\) −9.11938 + 9.11938i −0.355510 + 0.355510i
\(659\) 25.2158 0.982269 0.491135 0.871084i \(-0.336582\pi\)
0.491135 + 0.871084i \(0.336582\pi\)
\(660\) 12.9928 + 17.4686i 0.505745 + 0.679963i
\(661\) 4.05017 0.157533 0.0787666 0.996893i \(-0.474902\pi\)
0.0787666 + 0.996893i \(0.474902\pi\)
\(662\) 6.73418 6.73418i 0.261731 0.261731i
\(663\) −0.164398 + 0.0515756i −0.00638468 + 0.00200303i
\(664\) 6.85157i 0.265892i
\(665\) −3.35696 + 6.95144i −0.130177 + 0.269565i
\(666\) 20.4981 14.2656i 0.794286 0.552780i
\(667\) 5.52558 + 5.52558i 0.213951 + 0.213951i
\(668\) −11.3116 11.3116i −0.437660 0.437660i
\(669\) 13.1802 + 6.88520i 0.509576 + 0.266197i
\(670\) −18.7408 + 6.53480i −0.724020 + 0.252461i
\(671\) 55.2271i 2.13202i
\(672\) −1.78991 5.70537i −0.0690474 0.220089i
\(673\) 14.9688 14.9688i 0.577004 0.577004i −0.357073 0.934077i \(-0.616225\pi\)
0.934077 + 0.357073i \(0.116225\pi\)
\(674\) −23.5713 −0.907932
\(675\) 25.9788 0.317611i 0.999925 0.0122249i
\(676\) 11.2558 0.432917
\(677\) −4.56460 + 4.56460i −0.175432 + 0.175432i −0.789361 0.613929i \(-0.789588\pi\)
0.613929 + 0.789361i \(0.289588\pi\)
\(678\) 9.95964 + 31.7465i 0.382498 + 1.21922i
\(679\) 20.4184i 0.783585i
\(680\) 0.159036 0.0554549i 0.00609875 0.00212660i
\(681\) 27.2144 + 14.2165i 1.04286 + 0.544777i
\(682\) −20.3198 20.3198i −0.778083 0.778083i
\(683\) 23.6277 + 23.6277i 0.904089 + 0.904089i 0.995787 0.0916982i \(-0.0292295\pi\)
−0.0916982 + 0.995787i \(0.529230\pi\)
\(684\) −2.46238 + 1.71368i −0.0941513 + 0.0655242i
\(685\) −16.2884 + 33.7291i −0.622346 + 1.28872i
\(686\) 7.18650i 0.274382i
\(687\) 6.66819 2.09197i 0.254407 0.0798138i
\(688\) 7.57828 7.57828i 0.288919 0.288919i
\(689\) −18.0693 −0.688384
\(690\) −2.75135 3.69912i −0.104742 0.140823i
\(691\) 33.5858 1.27766 0.638831 0.769347i \(-0.279418\pi\)
0.638831 + 0.769347i \(0.279418\pi\)
\(692\) 16.5624 16.5624i 0.629607 0.629607i
\(693\) −10.2737 + 57.3042i −0.390264 + 2.17681i
\(694\) 10.7468i 0.407944i
\(695\) 8.42816 + 24.1707i 0.319698 + 0.916846i
\(696\) 5.26482 10.0783i 0.199562 0.382019i
\(697\) −0.306739 0.306739i −0.0116186 0.0116186i
\(698\) 6.82446 + 6.82446i 0.258310 + 0.258310i
\(699\) −15.6317 + 29.9235i −0.591246 + 1.13181i
\(700\) −1.97001 + 17.1487i −0.0744593 + 0.648160i
\(701\) 41.1049i 1.55251i −0.630419 0.776255i \(-0.717117\pi\)
0.630419 0.776255i \(-0.282883\pi\)
\(702\) 4.20091 5.42629i 0.158553 0.204802i
\(703\) 5.88633 5.88633i 0.222007 0.222007i
\(704\) −5.62118 −0.211856
\(705\) 14.3146 + 2.10327i 0.539120 + 0.0792136i
\(706\) −2.54837 −0.0959090
\(707\) −2.06345 + 2.06345i −0.0776040 + 0.0776040i
\(708\) 18.2942 5.73934i 0.687538 0.215698i
\(709\) 12.7911i 0.480378i 0.970726 + 0.240189i \(0.0772095\pi\)
−0.970726 + 0.240189i \(0.922791\pi\)
\(710\) −4.61715 2.22970i −0.173279 0.0836791i
\(711\) −5.85746 8.41654i −0.219672 0.315645i
\(712\) −3.31922 3.31922i −0.124393 0.124393i
\(713\) 4.30289 + 4.30289i 0.161144 + 0.161144i
\(714\) 0.399209 + 0.208542i 0.0149400 + 0.00780450i
\(715\) −14.9481 7.21869i −0.559028 0.269964i
\(716\) 13.4740i 0.503549i
\(717\) 0.313304 + 0.998658i 0.0117005 + 0.0372956i
\(718\) −11.8464 + 11.8464i −0.442104 + 0.442104i
\(719\) 20.7582 0.774149 0.387075 0.922048i \(-0.373486\pi\)
0.387075 + 0.922048i \(0.373486\pi\)
\(720\) −3.93738 + 5.43112i −0.146737 + 0.202406i
\(721\) −8.39891 −0.312792
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) 0.851882 + 2.71538i 0.0316818 + 0.100986i
\(724\) 10.4967i 0.390108i
\(725\) −25.7075 + 20.4096i −0.954752 + 0.757995i
\(726\) 31.6215 + 16.5187i 1.17358 + 0.613067i
\(727\) −7.71093 7.71093i −0.285983 0.285983i 0.549507 0.835489i \(-0.314816\pi\)
−0.835489 + 0.549507i \(0.814816\pi\)
\(728\) 3.22393 + 3.22393i 0.119487 + 0.119487i
\(729\) 6.76368 + 26.1391i 0.250507 + 0.968115i
\(730\) −7.65731 21.9600i −0.283410 0.812775i
\(731\) 0.807259i 0.0298575i
\(732\) −16.2368 + 5.09389i −0.600131 + 0.188276i
\(733\) 21.6850 21.6850i 0.800954 0.800954i −0.182291 0.983245i \(-0.558351\pi\)
0.983245 + 0.182291i \(0.0583512\pi\)
\(734\) 11.2847 0.416526
\(735\) −15.2844 + 11.3683i −0.563774 + 0.419326i
\(736\) 1.19033 0.0438763
\(737\) −35.2803 + 35.2803i −1.29956 + 1.29956i
\(738\) 17.0063 + 3.04893i 0.626009 + 0.112233i
\(739\) 9.14938i 0.336565i 0.985739 + 0.168283i \(0.0538221\pi\)
−0.985739 + 0.168283i \(0.946178\pi\)
\(740\) 8.09465 16.7620i 0.297565 0.616184i
\(741\) 1.05914 2.02749i 0.0389084 0.0744816i
\(742\) 33.3995 + 33.3995i 1.22614 + 1.22614i
\(743\) −28.3515 28.3515i −1.04012 1.04012i −0.999161 0.0409557i \(-0.986960\pi\)
−0.0409557 0.999161i \(-0.513040\pi\)
\(744\) 4.09983 7.84822i 0.150307 0.287730i
\(745\) −45.9753 + 16.0313i −1.68440 + 0.587341i
\(746\) 18.4519i 0.675570i
\(747\) −20.2321 3.62727i −0.740255 0.132715i
\(748\) 0.299391 0.299391i 0.0109468 0.0109468i
\(749\) −30.1725 −1.10248
\(750\) 16.7556 9.70820i 0.611829 0.354493i
\(751\) 19.6549 0.717219 0.358609 0.933488i \(-0.383251\pi\)
0.358609 + 0.933488i \(0.383251\pi\)
\(752\) −2.64154 + 2.64154i −0.0963271 + 0.0963271i
\(753\) −1.32289 + 0.415024i −0.0482089 + 0.0151243i
\(754\) 8.66996i 0.315741i
\(755\) 27.4226 9.56210i 0.998012 0.348001i
\(756\) −17.7951 + 2.26500i −0.647201 + 0.0823774i
\(757\) −7.94564 7.94564i −0.288789 0.288789i 0.547812 0.836601i \(-0.315461\pi\)
−0.836601 + 0.547812i \(0.815461\pi\)
\(758\) 20.8265 + 20.8265i 0.756451 + 0.756451i
\(759\) −10.2721 5.36606i −0.372855 0.194776i
\(760\) −0.972386 + 2.01357i −0.0352721 + 0.0730399i
\(761\) 8.05394i 0.291955i −0.989288 0.145977i \(-0.953367\pi\)
0.989288 0.145977i \(-0.0466327\pi\)
\(762\) 3.55017 + 11.3162i 0.128609 + 0.409943i
\(763\) −33.5985 + 33.5985i −1.21635 + 1.21635i
\(764\) 16.2464 0.587775
\(765\) −0.0795589 0.498979i −0.00287646 0.0180406i
\(766\) 11.3397 0.409721
\(767\) −10.3375 + 10.3375i −0.373265 + 0.373265i
\(768\) −0.518471 1.65263i −0.0187087 0.0596342i
\(769\) 29.3869i 1.05972i 0.848086 + 0.529859i \(0.177755\pi\)
−0.848086 + 0.529859i \(0.822245\pi\)
\(770\) 14.2872 + 40.9735i 0.514876 + 1.47658i
\(771\) −0.407787 0.213023i −0.0146861 0.00767185i
\(772\) 2.23569 + 2.23569i 0.0804642 + 0.0804642i
\(773\) 7.89291 + 7.89291i 0.283888 + 0.283888i 0.834658 0.550769i \(-0.185666\pi\)
−0.550769 + 0.834658i \(0.685666\pi\)
\(774\) −18.3661 26.3901i −0.660154 0.948571i
\(775\) −20.0190 + 15.8934i −0.719102 + 0.570909i
\(776\) 5.91443i 0.212316i
\(777\) 47.4945 14.9002i 1.70386 0.534541i