Properties

Label 570.2.k.a.77.9
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 77.9
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.65263 + 0.518471i) q^{3} -1.00000i q^{4} +(2.11139 - 0.736229i) q^{5} +(-1.53520 + 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.46238 + 1.71368i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.65263 + 0.518471i) 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} +(0.518471 - 1.65263i) q^{12} +(0.933851 - 0.933851i) q^{13} +3.45230 q^{14} +(3.87106 - 0.122020i) q^{15} -1.00000 q^{16} +(-0.0532613 + 0.0532613i) q^{17} +(-2.95292 + 0.529408i) 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} +(3.18091 + 4.10875i) q^{27} +(-2.44114 + 2.44114i) q^{28} +6.56484 q^{29} +(-2.65097 + 2.82353i) q^{30} -5.11218 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.91441 - 9.28973i) 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} +(5.70537 + 1.78991i) q^{42} +(-7.57828 + 7.57828i) q^{43} -5.62118 q^{44} +(6.46070 + 1.80538i) q^{45} -1.19033 q^{46} +(-2.64154 + 2.64154i) q^{47} +(-1.65263 - 0.518471i) 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} +(-0.518471 + 1.65263i) q^{57} +(-4.64204 + 4.64204i) q^{58} +11.0697 q^{59} +(-0.122020 - 3.87106i) q^{60} +9.82484 q^{61} +(3.61486 - 3.61486i) q^{62} +(-1.82767 - 10.1943i) 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} +(0.529408 + 2.95292i) q^{72} +(-7.35442 + 7.35442i) q^{73} +8.32453 q^{74} +(8.08348 - 3.10762i) q^{75} +1.00000 q^{76} +(-13.7221 + 13.7221i) q^{77} +(-0.684726 + 2.18257i) 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} +(10.8493 + 3.40368i) q^{87} +(3.97477 - 3.97477i) q^{88} -4.69409 q^{89} +(-5.84500 + 3.29181i) q^{90} -4.55933 q^{91} +(0.841693 - 0.841693i) q^{92} +(-8.44855 - 2.65052i) 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
\(3\) 1.65263 + 0.518471i 0.954147 + 0.299339i
\(4\) 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 \(-0.678152\pi\)
0.530916 0.847424i \(-0.321848\pi\)
\(12\) 0.518471 1.65263i 0.149670 0.477073i
\(13\) 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
\(15\) 3.87106 0.122020i 0.999504 0.0315055i
\(16\) −1.00000 −0.250000
\(17\) −0.0532613 + 0.0532613i −0.0129178 + 0.0129178i −0.713536 0.700618i \(-0.752908\pi\)
0.700618 + 0.713536i \(0.252908\pi\)
\(18\) −2.95292 + 0.529408i −0.696010 + 0.124783i
\(19\) 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 0.789393 0.613888i \(-0.210395\pi\)
−0.613888 + 0.789393i \(0.710395\pi\)
\(24\) 0.801972 + 1.53520i 0.163702 + 0.313371i
\(25\) 3.91593 3.10893i 0.783187 0.621786i
\(26\) 1.32067i 0.259004i
\(27\) 3.18091 + 4.10875i 0.612166 + 0.790730i
\(28\) −2.44114 + 2.44114i −0.461332 + 0.461332i
\(29\) 6.56484 1.21906 0.609530 0.792763i \(-0.291358\pi\)
0.609530 + 0.792763i \(0.291358\pi\)
\(30\) −2.65097 + 2.82353i −0.483999 + 0.515505i
\(31\) −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
\(33\) 2.91441 9.28973i 0.507335 1.61713i
\(34\) 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 \(0.148474\pi\)
−0.893173 + 0.449713i \(0.851526\pi\)
\(42\) 5.70537 + 1.78991i 0.880358 + 0.276190i
\(43\) −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
\(45\) 6.46070 + 1.80538i 0.963104 + 0.269130i
\(46\) −1.19033 −0.175505
\(47\) −2.64154 + 2.64154i −0.385308 + 0.385308i −0.873010 0.487702i \(-0.837835\pi\)
0.487702 + 0.873010i \(0.337835\pi\)
\(48\) −1.65263 0.518471i −0.238537 0.0748348i
\(49\) 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 \(0.138876\pi\)
0.422583 + 0.906324i \(0.361124\pi\)
\(54\) −5.15457 0.656086i −0.701448 0.0892821i
\(55\) −4.13847 11.8685i −0.558031 1.60035i
\(56\) 3.45230i 0.461332i
\(57\) −0.518471 + 1.65263i −0.0686731 + 0.218896i
\(58\) −4.64204 + 4.64204i −0.609530 + 0.609530i
\(59\) 11.0697 1.44116 0.720579 0.693373i \(-0.243876\pi\)
0.720579 + 0.693373i \(0.243876\pi\)
\(60\) −0.122020 3.87106i −0.0157528 0.499752i
\(61\) 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
\(63\) −1.82767 10.1943i −0.230265 1.28437i
\(64\) 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 \(-0.956554\pi\)
0.990700 0.136066i \(-0.0434458\pi\)
\(72\) 0.529408 + 2.95292i 0.0623913 + 0.348005i
\(73\) −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
\(75\) 8.08348 3.10762i 0.933400 0.358837i
\(76\) 1.00000 0.114708
\(77\) −13.7221 + 13.7221i −1.56378 + 1.56378i
\(78\) −0.684726 + 2.18257i −0.0775300 + 0.247128i
\(79\) 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 0.389318 0.921103i \(-0.372711\pi\)
−0.921103 + 0.389318i \(0.872711\pi\)
\(84\) −5.29997 + 2.76865i −0.578274 + 0.302084i
\(85\) −0.0732429 + 0.151668i −0.00794431 + 0.0164507i
\(86\) 10.7173i 1.15568i
\(87\) 10.8493 + 3.40368i 1.16316 + 0.364912i
\(88\) 3.97477 3.97477i 0.423712 0.423712i
\(89\) −4.69409 −0.497572 −0.248786 0.968558i \(-0.580032\pi\)
−0.248786 + 0.968558i \(0.580032\pi\)
\(90\) −5.84500 + 3.29181i −0.616117 + 0.346987i
\(91\) −4.55933 −0.477947
\(92\) 0.841693 0.841693i 0.0877526 0.0877526i
\(93\) −8.44855 2.65052i −0.876073 0.274846i
\(94\) 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 \(0.0133902\pi\)
−0.999115 + 0.0420543i \(0.986610\pi\)
\(102\) 0.0390527 0.124481i 0.00386679 0.0123254i
\(103\) 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
\(105\) −9.74768 9.15194i −0.951276 0.893138i
\(106\) −13.6819 −1.32891
\(107\) −6.17999 + 6.17999i −0.597442 + 0.597442i −0.939631 0.342189i \(-0.888832\pi\)
0.342189 + 0.939631i \(0.388832\pi\)
\(108\) 4.10875 3.18091i 0.395365 0.306083i
\(109\) 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 \(0.109045\pi\)
0.335915 + 0.941892i \(0.390955\pi\)
\(114\) −0.801972 1.53520i −0.0751116 0.143785i
\(115\) 2.39682 + 1.15746i 0.223505 + 0.107934i
\(116\) 6.56484i 0.609530i
\(117\) 3.89982 0.699170i 0.360538 0.0646383i
\(118\) −7.82749 + 7.82749i −0.720579 + 0.720579i
\(119\) 0.260037 0.0238375
\(120\) 2.82353 + 2.65097i 0.257752 + 0.242000i
\(121\) −20.5976 −1.87251
\(122\) −6.94721 + 6.94721i −0.628971 + 0.628971i
\(123\) −2.98594 + 9.51772i −0.269233 + 0.858184i
\(124\) 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 \(-0.998151\pi\)
0.999983 0.00580880i \(-0.00184901\pi\)
\(132\) −9.28973 2.91441i −0.808567 0.253667i
\(133\) 2.44114 2.44114i 0.211674 0.211674i
\(134\) −8.87605 −0.766774
\(135\) 9.74111 + 6.33330i 0.838381 + 0.545084i
\(136\) −0.0753229 −0.00645888
\(137\) −11.8447 + 11.8447i −1.01196 + 1.01196i −0.0120322 + 0.999928i \(0.503830\pi\)
−0.999928 + 0.0120322i \(0.996170\pi\)
\(138\) −1.96718 0.617153i −0.167458 0.0525356i
\(139\) 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
\(147\) −2.55002 + 8.12820i −0.210322 + 0.670403i
\(148\) −5.88633 + 5.88633i −0.483853 + 0.483853i
\(149\) −21.7749 −1.78387 −0.891934 0.452165i \(-0.850652\pi\)
−0.891934 + 0.452165i \(0.850652\pi\)
\(150\) −3.51847 + 7.91330i −0.287282 + 0.646119i
\(151\) −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
\(153\) −0.222422 + 0.0398765i −0.0179818 + 0.00322382i
\(154\) 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
\(162\) −8.17843 3.75676i −0.642558 0.295159i
\(163\) 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
\(165\) −0.685899 21.7599i −0.0533971 1.69401i
\(166\) 6.85157 0.531785
\(167\) −11.3116 + 11.3116i −0.875319 + 0.875319i −0.993046 0.117727i \(-0.962439\pi\)
0.117727 + 0.993046i \(0.462439\pi\)
\(168\) 1.78991 5.70537i 0.138095 0.440179i
\(169\) 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 \(-0.900425\pi\)
−0.307746 0.951468i \(-0.599575\pi\)
\(174\) −10.0783 + 5.26482i −0.764037 + 0.399125i
\(175\) −17.1487 1.97001i −1.29632 0.148919i
\(176\) 5.62118i 0.423712i
\(177\) 18.2942 + 5.73934i 1.37508 + 0.431395i
\(178\) 3.31922 3.31922i 0.248786 0.248786i
\(179\) 13.4740 1.00710 0.503549 0.863967i \(-0.332027\pi\)
0.503549 + 0.863967i \(0.332027\pi\)
\(180\) 1.80538 6.46070i 0.134565 0.481552i
\(181\) 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
\(183\) 16.2368 + 5.09389i 1.20026 + 0.376551i
\(184\) 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 \(-0.800004\pi\)
0.809024 0.587775i \(-0.199996\pi\)
\(192\) −0.518471 + 1.65263i −0.0374174 + 0.119268i
\(193\) −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
\(195\) 3.50105 3.72894i 0.250715 0.267035i
\(196\) 4.91834 0.351310
\(197\) 5.51445 5.51445i 0.392889 0.392889i −0.482827 0.875716i \(-0.660390\pi\)
0.875716 + 0.482827i \(0.160390\pi\)
\(198\) 2.97589 + 16.5989i 0.211488 + 1.17963i
\(199\) 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
\(207\) 0.630172 + 3.51496i 0.0438000 + 0.244307i
\(208\) −0.933851 + 0.933851i −0.0647509 + 0.0647509i
\(209\) 5.62118 0.388825
\(210\) 13.3640 0.421251i 0.922207 0.0290691i
\(211\) −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
\(213\) 1.18886 3.78951i 0.0814595 0.259653i
\(214\) 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
\(222\) 13.7574 + 4.31602i 0.923334 + 0.289673i
\(223\) −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
\(225\) 14.9702 0.944697i 0.998015 0.0629798i
\(226\) −19.2097 −1.27781
\(227\) 12.5348 12.5348i 0.831965 0.831965i −0.155820 0.987785i \(-0.549802\pi\)
0.987785 + 0.155820i \(0.0498021\pi\)
\(228\) 1.65263 + 0.518471i 0.109448 + 0.0343366i
\(229\) 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 0.995689 0.0927575i \(-0.0295681\pi\)
−0.0927575 + 0.995689i \(0.529568\pi\)
\(234\) −2.26320 + 3.25198i −0.147950 + 0.212588i
\(235\) −3.63254 + 7.52210i −0.236961 + 0.490688i
\(236\) 11.0697i 0.720579i
\(237\) −1.77216 + 5.64879i −0.115114 + 0.366928i
\(238\) −0.183874 + 0.183874i −0.0119188 + 0.0119188i
\(239\) 0.604284 0.0390879 0.0195439 0.999809i \(-0.493779\pi\)
0.0195439 + 0.999809i \(0.493779\pi\)
\(240\) −3.87106 + 0.122020i −0.249876 + 0.00787639i
\(241\) −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
\(243\) 0.791496 + 15.5684i 0.0507745 + 0.998710i
\(244\) 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 \(0.00804226\pi\)
−0.999681 + 0.0252628i \(0.991958\pi\)
\(252\) −10.1943 + 1.82767i −0.642183 + 0.115132i
\(253\) 4.73131 4.73131i 0.297455 0.297455i
\(254\) 6.84738 0.429643
\(255\) −0.199679 + 0.212677i −0.0125044 + 0.0133183i
\(256\) 1.00000 0.0625000
\(257\) −0.187825 + 0.187825i −0.0117162 + 0.0117162i −0.712941 0.701224i \(-0.752637\pi\)
0.701224 + 0.712941i \(0.252637\pi\)
\(258\) 5.55661 17.7118i 0.345940 1.10269i
\(259\) 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 0.704080 0.710121i \(-0.251360\pi\)
−0.710121 + 0.704080i \(0.751360\pi\)
\(264\) 8.62963 4.50803i 0.531117 0.277450i
\(265\) 27.5495 + 13.3041i 1.69235 + 0.817266i
\(266\) 3.45230i 0.211674i
\(267\) −7.75759 2.43375i −0.474757 0.148943i
\(268\) 6.27631 6.27631i 0.383387 0.383387i
\(269\) 15.3546 0.936185 0.468093 0.883679i \(-0.344941\pi\)
0.468093 + 0.883679i \(0.344941\pi\)
\(270\) −11.3663 + 2.40969i −0.691733 + 0.146649i
\(271\) 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
\(273\) −7.53488 2.36388i −0.456032 0.143068i
\(274\) 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 \(0.0102260\pi\)
−0.999484 + 0.0321205i \(0.989774\pi\)
\(282\) 1.93685 6.17374i 0.115338 0.367641i
\(283\) −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
\(285\) 0.122020 + 3.87106i 0.00722787 + 0.229302i
\(286\) 7.42369 0.438972
\(287\) 14.0589 14.0589i 0.829868 0.829868i
\(288\) 2.95292 0.529408i 0.174002 0.0311956i
\(289\) 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 0.734390 0.678728i \(-0.237468\pi\)
−0.678728 + 0.734390i \(0.737468\pi\)
\(294\) −3.94437 7.55064i −0.230041 0.440362i
\(295\) 23.3726 8.14987i 1.36080 0.474503i
\(296\) 8.32453i 0.483853i
\(297\) 23.0960 17.8804i 1.34017 1.03753i
\(298\) 15.3972 15.3972i 0.891934 0.891934i
\(299\) 1.57203 0.0909130
\(300\) −3.10762 8.08348i −0.179418 0.466700i
\(301\) 36.9993 2.13261
\(302\) 9.18387 9.18387i 0.528472 0.528472i
\(303\) −0.438253 + 1.39694i −0.0251770 + 0.0802519i
\(304\) 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 \(0.0563604\pi\)
−0.984366 + 0.176138i \(0.943640\pi\)
\(312\) 2.18257 + 0.684726i 0.123564 + 0.0387650i
\(313\) −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
\(315\) −11.3643 20.1787i −0.640306 1.13694i
\(316\) 3.41806 0.192281
\(317\) 6.17490 6.17490i 0.346817 0.346817i −0.512106 0.858922i \(-0.671134\pi\)
0.858922 + 0.512106i \(0.171134\pi\)
\(318\) −22.6112 7.09368i −1.26797 0.397794i
\(319\) 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
\(327\) 7.13594 22.7459i 0.394618 1.25785i
\(328\) −4.07232 + 4.07232i −0.224856 + 0.224856i
\(329\) 12.8967 0.711021
\(330\) 15.8716 + 14.9016i 0.873702 + 0.820305i
\(331\) 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
\(333\) −4.40707 24.5817i −0.241506 1.34707i
\(334\) 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
\(342\) −0.529408 2.95292i −0.0286271 0.159676i
\(343\) −5.08162 + 5.08162i −0.274382 + 0.274382i
\(344\) −10.7173 −0.577839
\(345\) 3.36095 + 3.15554i 0.180947 + 0.169889i
\(346\) 23.4227 1.25921
\(347\) −7.59916 + 7.59916i −0.407944 + 0.407944i −0.881021 0.473077i \(-0.843143\pi\)
0.473077 + 0.881021i \(0.343143\pi\)
\(348\) 3.40368 10.8493i 0.182456 0.581581i
\(349\) 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 0.753433 0.657524i \(-0.228396\pi\)
−0.657524 + 0.753433i \(0.728396\pi\)
\(354\) −16.9943 + 8.87763i −0.903236 + 0.471841i
\(355\) −1.68819 4.84145i −0.0895996 0.256958i
\(356\) 4.69409i 0.248786i
\(357\) 0.429745 + 0.134821i 0.0227445 + 0.00713551i
\(358\) −9.52759 + 9.52759i −0.503549 + 0.503549i
\(359\) 16.7534 0.884209 0.442104 0.896964i \(-0.354232\pi\)
0.442104 + 0.896964i \(0.354232\pi\)
\(360\) 3.29181 + 5.84500i 0.173494 + 0.308058i
\(361\) −1.00000 −0.0526316
\(362\) −7.42232 + 7.42232i −0.390108 + 0.390108i
\(363\) −34.0403 10.6793i −1.78665 0.560516i
\(364\) 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
\(372\) −2.65052 + 8.44855i −0.137423 + 0.438037i
\(373\) 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
\(375\) 14.7795 12.5127i 0.763208 0.646152i
\(376\) −3.73570 −0.192654
\(377\) 6.13059 6.13059i 0.315741 0.315741i
\(378\) 10.9814 + 14.1846i 0.564824 + 0.729578i
\(379\) 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 0.471921 0.881641i \(-0.343561\pi\)
−0.881641 + 0.471921i \(0.843561\pi\)
\(384\) −0.801972 1.53520i −0.0409255 0.0783429i
\(385\) −18.8701 + 39.0753i −0.961708 + 1.99146i
\(386\) 3.16174i 0.160928i
\(387\) −31.6473 + 5.67383i −1.60873 + 0.288417i
\(388\) −4.18214 + 4.18214i −0.212316 + 0.212316i
\(389\) 23.1601 1.17426 0.587131 0.809492i \(-0.300257\pi\)
0.587131 + 0.809492i \(0.300257\pi\)
\(390\) 0.161148 + 5.11238i 0.00816006 + 0.258875i
\(391\) −0.0896594 −0.00453427
\(392\) −3.47779 + 3.47779i −0.175655 + 0.175655i
\(393\) 0.0689408 0.219749i 0.00347760 0.0110849i
\(394\) 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 \(0.322081\pi\)
−0.530295 + 0.847813i \(0.677919\pi\)
\(402\) −14.6688 4.60197i −0.731614 0.229525i
\(403\) −4.77402 + 4.77402i −0.237811 + 0.237811i
\(404\) 0.845280 0.0420543
\(405\) 12.8148 + 15.5171i 0.636774 + 0.771050i
\(406\) 22.6638 1.12478
\(407\) −33.0881 + 33.0881i −1.64012 + 1.64012i
\(408\) −0.124481 0.0390527i −0.00616272 0.00193340i
\(409\) 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
\(417\) 5.93532 18.9189i 0.290654 0.926463i
\(418\) −3.97477 + 3.97477i −0.194412 + 0.194412i
\(419\) 1.26502 0.0618005 0.0309003 0.999522i \(-0.490163\pi\)
0.0309003 + 0.999522i \(0.490163\pi\)
\(420\) −9.15194 + 9.74768i −0.446569 + 0.475638i
\(421\) −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
\(423\) −11.0312 + 1.97771i −0.536356 + 0.0961595i
\(424\) 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 \(-0.896469\pi\)
0.947571 0.319546i \(-0.103531\pi\)
\(432\) −3.18091 4.10875i −0.153041 0.197682i
\(433\) 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
\(435\) 25.4129 0.801045i 1.21845 0.0384072i
\(436\) −13.7634 −0.659149
\(437\) −0.841693 + 0.841693i −0.0402636 + 0.0402636i
\(438\) 5.39247 17.1886i 0.257662 0.821301i
\(439\) 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 0.0607845 0.998151i \(-0.480640\pi\)
−0.998151 + 0.0607845i \(0.980640\pi\)
\(444\) −12.7798 + 6.67604i −0.606503 + 0.316831i
\(445\) −9.91105 + 3.45592i −0.469829 + 0.163826i
\(446\) 8.58534i 0.406527i
\(447\) −35.9859 11.2896i −1.70207 0.533982i
\(448\) 2.44114 2.44114i 0.115333 0.115333i
\(449\) −18.2109 −0.859426 −0.429713 0.902966i \(-0.641385\pi\)
−0.429713 + 0.902966i \(0.641385\pi\)
\(450\) −9.91754 + 11.2535i −0.467517 + 0.530497i
\(451\) 32.3731 1.52439
\(452\) 13.5833 13.5833i 0.638904 0.638904i
\(453\) −21.4643 6.73387i −1.00848 0.316385i
\(454\) 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 \(-0.890430\pi\)
0.941337 0.337467i \(-0.109570\pi\)
\(462\) 10.0614 32.0709i 0.468100 1.49207i
\(463\) −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
\(465\) −19.7896 + 0.623791i −0.917719 + 0.0289276i
\(466\) −19.4916 −0.902931
\(467\) 1.06586 1.06586i 0.0493219 0.0493219i −0.682016 0.731338i \(-0.738896\pi\)
0.731338 + 0.682016i \(0.238896\pi\)
\(468\) −0.699170 3.89982i −0.0323192 0.180269i
\(469\) 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
\(477\) 7.24332 + 40.4016i 0.331649 + 1.84986i
\(478\) −0.427293 + 0.427293i −0.0195439 + 0.0195439i
\(479\) 10.1543 0.463962 0.231981 0.972720i \(-0.425479\pi\)
0.231981 + 0.972720i \(0.425479\pi\)
\(480\) 2.65097 2.82353i 0.121000 0.128876i
\(481\) −10.9939 −0.501279
\(482\) 1.16182 1.16182i 0.0529196 0.0529196i
\(483\) 2.13059 6.79129i 0.0969454 0.309015i
\(484\) 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 \(0.00769487\pi\)
−0.999708 + 0.0241718i \(0.992305\pi\)
\(492\) 9.51772 + 2.98594i 0.429092 + 0.134617i
\(493\) −0.349652 + 0.349652i −0.0157475 + 0.0157475i
\(494\) −1.32067 −0.0594195
\(495\) 10.1483 36.3167i 0.456134 1.63232i
\(496\) 5.11218 0.229544
\(497\) −5.59758 + 5.59758i −0.251086 + 0.251086i
\(498\) 11.3231 + 3.55234i 0.507401 + 0.159184i
\(499\) 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 \(0.00299252\pi\)
0.00940114 + 0.999956i \(0.497007\pi\)
\(504\) 5.91613 8.50085i 0.263526 0.378658i
\(505\) 0.622320 + 1.78472i 0.0276929 + 0.0794188i
\(506\) 6.69108i 0.297455i
\(507\) −5.83582 + 18.6018i −0.259178 + 0.826133i
\(508\) −4.84183 + 4.84183i −0.214822 + 0.214822i
\(509\) −13.7670 −0.610210 −0.305105 0.952319i \(-0.598692\pi\)
−0.305105 + 0.952319i \(0.598692\pi\)
\(510\) −0.00919093 0.291579i −0.000406981 0.0129114i
\(511\) 35.9064 1.58840
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.10875 + 3.18091i −0.181406 + 0.140440i
\(514\) 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 \(-0.987629\pi\)
0.999245 0.0388537i \(-0.0123706\pi\)
\(522\) −19.3854 + 3.47548i −0.848478 + 0.152117i
\(523\) 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
\(525\) −27.3191 12.1468i −1.19230 0.530129i
\(526\) 0.138543 0.00604078
\(527\) 0.272282 0.272282i 0.0118608 0.0118608i
\(528\) −2.91441 + 9.28973i −0.126834 + 0.404284i
\(529\) 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
\(537\) 22.2676 + 6.98590i 0.960919 + 0.301464i
\(538\) −10.8573 + 10.8573i −0.468093 + 0.468093i
\(539\) 27.6469 1.19084
\(540\) 6.33330 9.74111i 0.272542 0.419191i
\(541\) 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
\(543\) 17.3472 + 5.44225i 0.744441 + 0.233549i
\(544\) 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
\(552\) −0.617153 + 1.96718i −0.0262678 + 0.0837288i
\(553\) 8.34396 8.34396i 0.354821 0.354821i
\(554\) 7.40629 0.314663
\(555\) −23.5046 22.0681i −0.997714 0.936738i
\(556\) −11.4478 −0.485493
\(557\) −8.91400 + 8.91400i −0.377698 + 0.377698i −0.870271 0.492573i \(-0.836057\pi\)
0.492573 + 0.870271i \(0.336057\pi\)
\(558\) 15.0959 2.70643i 0.639058 0.114572i
\(559\) 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 0.971755 0.235993i \(-0.0758344\pi\)
−0.235993 + 0.971755i \(0.575834\pi\)
\(564\) 2.99593 + 5.73505i 0.126151 + 0.241489i
\(565\) 38.6800 + 18.6792i 1.62728 + 0.785840i
\(566\) 18.9019i 0.794508i
\(567\) 12.9694 28.2344i 0.544665 1.18573i
\(568\) 1.62141 1.62141i 0.0680328 0.0680328i
\(569\) −6.84928 −0.287137 −0.143568 0.989640i \(-0.545858\pi\)
−0.143568 + 0.989640i \(0.545858\pi\)
\(570\) −2.82353 2.65097i −0.118265 0.111037i
\(571\) −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
\(573\) 8.42329 26.8493i 0.351888 1.12165i
\(574\) 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
\(582\) 9.77437 + 3.06646i 0.405161 + 0.127109i
\(583\) 54.3826 54.3826i 2.25230 2.25230i
\(584\) −10.4007 −0.430385
\(585\) 7.71929 4.34738i 0.319153 0.179742i
\(586\) −1.34743 −0.0556619
\(587\) −27.2033 + 27.2033i −1.12280 + 1.12280i −0.131481 + 0.991319i \(0.541973\pi\)
−0.991319 + 0.131481i \(0.958027\pi\)
\(588\) 8.12820 + 2.55002i 0.335201 + 0.105161i
\(589\) 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 0.669702 0.742630i \(-0.266422\pi\)
−0.742630 + 0.669702i \(0.766422\pi\)
\(594\) −3.68798 + 28.9747i −0.151320 + 1.18885i
\(595\) 0.549039 0.191447i 0.0225084 0.00784855i
\(596\) 21.7749i 0.891934i
\(597\) 11.5781 36.9052i 0.473858 1.51043i
\(598\) −1.11159 + 1.11159i −0.0454565 + 0.0454565i
\(599\) 4.67096 0.190850 0.0954252 0.995437i \(-0.469579\pi\)
0.0954252 + 0.995437i \(0.469579\pi\)
\(600\) 7.91330 + 3.51847i 0.323059 + 0.143641i
\(601\) −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
\(603\) 4.69905 + 26.2102i 0.191360 + 1.06736i
\(604\) 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
\(612\) 0.0398765 + 0.222422i 0.00161191 + 0.00899089i
\(613\) −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
\(615\) 0.702732 + 22.2940i 0.0283369 + 0.898979i
\(616\) −19.4060 −0.781888
\(617\) 32.7653 32.7653i 1.31908 1.31908i 0.404577 0.914504i \(-0.367419\pi\)
0.914504 0.404577i \(-0.132581\pi\)
\(618\) −1.26136 + 4.02060i −0.0507394 + 0.161732i
\(619\) 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
\(627\) 9.28973 + 2.91441i 0.370996 + 0.116391i
\(628\) 10.2762 10.2762i 0.410066 0.410066i
\(629\) 0.627027 0.0250012
\(630\) 22.3042 + 6.23269i 0.888622 + 0.248316i
\(631\) −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
\(633\) −8.12130 2.54785i −0.322793 0.101268i
\(634\) 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 \(-0.768151\pi\)
0.746256 0.665659i \(-0.231849\pi\)
\(642\) 4.53134 14.4437i 0.178838 0.570047i
\(643\) 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
\(645\) −28.4113 + 30.2607i −1.11869 + 1.19151i
\(646\) 0.0753229 0.00296354
\(647\) 18.8461 18.8461i 0.740918 0.740918i −0.231837 0.972755i \(-0.574474\pi\)
0.972755 + 0.231837i \(0.0744736\pi\)
\(648\) −3.75676 + 8.17843i −0.147579 + 0.321279i
\(649\) 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 \(0.0216894\pi\)
0.0680864 + 0.997679i \(0.478311\pi\)
\(654\) 11.0379 + 21.1296i 0.431616 + 0.826234i
\(655\) −0.0978959 0.280750i −0.00382511 0.0109698i
\(656\) 5.75913i 0.224856i
\(657\) −30.7125 + 5.50622i −1.19821 + 0.214818i
\(658\) −9.11938 + 9.11938i −0.355510 + 0.355510i
\(659\) −25.2158 −0.982269 −0.491135 0.871084i \(-0.663418\pi\)
−0.491135 + 0.871084i \(0.663418\pi\)
\(660\) −21.7599 + 0.685899i −0.847003 + 0.0266986i
\(661\) 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
\(663\) −0.0515756 + 0.164398i −0.00200303 + 0.00638468i
\(664\) 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
\(672\) −5.70537 1.78991i −0.220089 0.0690474i
\(673\) 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
\(675\) 25.2300 + 6.20039i 0.971105 + 0.238653i
\(676\) 11.2558 0.432917
\(677\) 4.56460 4.56460i 0.175432 0.175432i −0.613929 0.789361i \(-0.710412\pi\)
0.789361 + 0.613929i \(0.210412\pi\)
\(678\) −31.7465 9.95964i −1.21922 0.382498i
\(679\) 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 0.0916982 0.995787i \(-0.470770\pi\)
−0.995787 + 0.0916982i \(0.970770\pi\)
\(684\) 2.46238 + 1.71368i 0.0941513 + 0.0655242i
\(685\) −16.2884 + 33.7291i −0.622346 + 1.28872i
\(686\) 7.18650i 0.274382i
\(687\) −2.09197 + 6.66819i −0.0798138 + 0.254407i
\(688\) 7.57828 7.57828i 0.288919 0.288919i
\(689\) 18.0693 0.688384
\(690\) −4.60785 + 0.145245i −0.175418 + 0.00552939i
\(691\) 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
\(693\) −57.3042 + 10.2737i −2.17681 + 0.390264i
\(694\) 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 \(0.282883\pi\)
−0.630419 + 0.776255i \(0.717117\pi\)
\(702\) −5.42629 + 4.20091i −0.204802 + 0.158553i
\(703\) 5.88633 5.88633i 0.222007 0.222007i
\(704\) 5.62118 0.211856
\(705\) −9.90324 + 10.5479i −0.372978 + 0.397256i
\(706\) −2.54837 −0.0959090
\(707\) 2.06345 2.06345i 0.0776040 0.0776040i
\(708\) 5.73934 18.2942i 0.215698 0.687538i
\(709\) 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
\(717\) 0.998658 + 0.313304i 0.0372956 + 0.0117005i
\(718\) −11.8464 + 11.8464i −0.442104 + 0.442104i
\(719\) −20.7582 −0.774149 −0.387075 0.922048i \(-0.626514\pi\)
−0.387075 + 0.922048i \(0.626514\pi\)
\(720\) −6.46070 1.80538i −0.240776 0.0672824i
\(721\) −8.39891 −0.312792
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −2.71538 0.851882i −0.100986 0.0316818i
\(724\) 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
\(732\) 5.09389 16.2368i 0.188276 0.600131i
\(733\) 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
\(735\) 0.600138 + 19.0392i 0.0221364 + 0.702272i
\(736\) 1.19033 0.0438763
\(737\) 35.2803 35.2803i 1.29956 1.29956i
\(738\) −3.04893 17.0063i −0.112233 0.626009i
\(739\) 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 \(0.0130403\pi\)
0.0409557 + 0.999161i \(0.486960\pi\)
\(744\) −4.09983 7.84822i −0.150307 0.287730i
\(745\) −45.9753 + 16.0313i −1.68440 + 0.587341i
\(746\) 18.4519i 0.675570i
\(747\) −3.62727 20.2321i −0.132715 0.740255i
\(748\) 0.299391 0.299391i 0.0109468 0.0109468i
\(749\) 30.1725 1.10248
\(750\) −1.60286 + 19.2985i −0.0585280 + 0.704680i
\(751\) 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
\(753\) −0.415024 + 1.32289i −0.0151243 + 0.0482089i
\(754\) 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 \(0.0466327\pi\)
−0.989288 + 0.145977i \(0.953367\pi\)
\(762\) 11.3162 + 3.55017i 0.409943 + 0.128609i
\(763\) −33.5985 + 33.5985i −1.21635 + 1.21635i
\(764\) −16.2464 −0.587775
\(765\) −0.440262 + 0.247949i −0.0159177 + 0.00896460i
\(766\) 11.3397 0.409721
\(767\) 10.3375 10.3375i 0.373265 0.373265i
\(768\) 1.65263 + 0.518471i 0.0596342 + 0.0187087i
\(769\) 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 0.550769 0.834658i \(-0.314334\pi\)
−0.834658 + 0.550769i \(0.814334\pi\)
\(774\) 18.3661 26.3901i 0.660154 0.948571i
\(775\) −20.0190 + 15.8934i −0.719102 + 0.570909i
\(776\) 5.91443i 0.212316i
\(777\) −14.9002 + 47.4945i −0.534541 + 1.70386i
\(778\)