Properties

Label 65.2.l.a.49.1
Level $65$
Weight $2$
Character 65.49
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.49787136.1
Defining polynomial: \(x^{8} + 3 x^{6} + 5 x^{4} + 12 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(-1.09445 - 0.895644i\) of defining polynomial
Character \(\chi\) \(=\) 65.49
Dual form 65.2.l.a.4.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.09445 - 1.89564i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.39564 + 2.41733i) q^{4} +(0.456850 - 2.18890i) q^{5} +(-1.89564 - 1.09445i) q^{6} +(-0.866025 + 1.50000i) q^{7} +1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.09445 - 1.89564i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.39564 + 2.41733i) q^{4} +(0.456850 - 2.18890i) q^{5} +(-1.89564 - 1.09445i) q^{6} +(-0.866025 + 1.50000i) q^{7} +1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-4.64938 + 1.52962i) q^{10} +(2.29129 - 1.32288i) q^{11} +2.79129i q^{12} +(3.46410 - 1.00000i) q^{13} +3.79129 q^{14} +(-0.698807 - 2.12407i) q^{15} +(0.895644 + 1.55130i) q^{16} +(3.96863 + 2.29129i) q^{17} +4.37780 q^{18} +(-1.50000 - 0.866025i) q^{19} +(4.65369 + 4.15928i) q^{20} +1.73205i q^{21} +(-5.01540 - 2.89564i) q^{22} +(-3.96863 + 2.29129i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-4.58258 - 2.00000i) q^{25} +(-5.68693 - 5.47225i) q^{26} +5.00000i q^{27} +(-2.41733 - 4.18693i) q^{28} +(-2.29129 - 3.96863i) q^{29} +(-3.26167 + 3.64938i) q^{30} +9.66930i q^{31} +(3.69253 - 6.39564i) q^{32} +(1.32288 - 2.29129i) q^{33} -10.0308i q^{34} +(2.88771 + 2.58092i) q^{35} +(-2.79129 - 4.83465i) q^{36} +(-3.96863 - 6.87386i) q^{37} +3.79129i q^{38} +(2.50000 - 2.59808i) q^{39} +(0.791288 - 3.79129i) q^{40} +(-2.29129 + 1.32288i) q^{41} +(3.28335 - 1.89564i) q^{42} +(-1.22753 - 0.708712i) q^{43} +7.38505i q^{44} +(3.33444 + 2.98019i) q^{45} +(8.68693 + 5.01540i) q^{46} -8.75560 q^{47} +(1.55130 + 0.895644i) q^{48} +(2.00000 + 3.46410i) q^{49} +(1.22411 + 10.8758i) q^{50} +4.58258 q^{51} +(-2.41733 + 9.76951i) q^{52} -1.58258i q^{53} +(9.47822 - 5.47225i) q^{54} +(-1.84887 - 5.61976i) q^{55} +(-1.50000 + 2.59808i) q^{56} -1.73205 q^{57} +(-5.01540 + 8.68693i) q^{58} +(-2.91742 - 1.68438i) q^{59} +(6.10985 + 1.27520i) q^{60} +(5.29129 - 9.16478i) q^{61} +(18.3296 - 10.5826i) q^{62} +(-1.73205 - 3.00000i) q^{63} -12.5826 q^{64} +(-0.606325 - 8.03943i) q^{65} -5.79129 q^{66} +(7.43273 + 12.8739i) q^{67} +(-11.0776 + 6.39564i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(1.73205 - 8.29875i) q^{70} +(-3.08258 - 1.77973i) q^{71} +(-1.73205 + 3.00000i) q^{72} +(-8.68693 + 15.0462i) q^{74} +(-4.96863 + 0.559237i) q^{75} +(4.18693 - 2.41733i) q^{76} +4.58258i q^{77} +(-7.66115 - 1.89564i) q^{78} +6.00000 q^{79} +(3.80482 - 1.25176i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.01540 + 2.89564i) q^{82} -11.3060 q^{83} +(-4.18693 - 2.41733i) q^{84} +(6.82847 - 7.64016i) q^{85} +3.10260i q^{86} +(-3.96863 - 2.29129i) q^{87} +(3.96863 - 2.29129i) q^{88} +(3.70871 - 2.14123i) q^{89} +(2.00000 - 9.58258i) q^{90} +(-1.50000 + 6.06218i) q^{91} -12.7913i q^{92} +(4.83465 + 8.37386i) q^{93} +(9.58258 + 16.5975i) q^{94} +(-2.58092 + 2.88771i) q^{95} -7.38505i q^{96} +(2.23658 - 3.87386i) q^{97} +(4.37780 - 7.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} - 6q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 2q^{4} - 6q^{6} - 8q^{9} - 4q^{10} + 12q^{14} - 6q^{15} - 2q^{16} - 12q^{19} + 24q^{20} + 12q^{24} - 18q^{26} - 10q^{30} + 6q^{35} - 4q^{36} + 20q^{39} - 12q^{40} + 12q^{45} + 42q^{46} + 16q^{49} - 12q^{50} + 30q^{54} - 14q^{55} - 12q^{56} - 60q^{59} + 24q^{61} - 64q^{64} - 24q^{65} - 28q^{66} + 12q^{71} - 42q^{74} - 8q^{75} + 6q^{76} + 48q^{79} + 18q^{80} - 4q^{81} - 6q^{84} + 42q^{85} + 48q^{89} + 16q^{90} - 12q^{91} + 40q^{94} - 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09445 1.89564i −0.773893 1.34042i −0.935414 0.353553i \(-0.884973\pi\)
0.161521 0.986869i \(-0.448360\pi\)
\(3\) 0.866025 0.500000i 0.500000 0.288675i −0.228714 0.973494i \(-0.573452\pi\)
0.728714 + 0.684819i \(0.240119\pi\)
\(4\) −1.39564 + 2.41733i −0.697822 + 1.20866i
\(5\) 0.456850 2.18890i 0.204310 0.978906i
\(6\) −1.89564 1.09445i −0.773893 0.446808i
\(7\) −0.866025 + 1.50000i −0.327327 + 0.566947i −0.981981 0.188982i \(-0.939481\pi\)
0.654654 + 0.755929i \(0.272814\pi\)
\(8\) 1.73205 0.612372
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) −4.64938 + 1.52962i −1.47026 + 0.483708i
\(11\) 2.29129 1.32288i 0.690849 0.398862i −0.113081 0.993586i \(-0.536072\pi\)
0.803930 + 0.594724i \(0.202739\pi\)
\(12\) 2.79129i 0.805775i
\(13\) 3.46410 1.00000i 0.960769 0.277350i
\(14\) 3.79129 1.01326
\(15\) −0.698807 2.12407i −0.180431 0.548432i
\(16\) 0.895644 + 1.55130i 0.223911 + 0.387825i
\(17\) 3.96863 + 2.29129i 0.962533 + 0.555719i 0.896952 0.442128i \(-0.145776\pi\)
0.0655816 + 0.997847i \(0.479110\pi\)
\(18\) 4.37780 1.03186
\(19\) −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i \(-0.396999\pi\)
−0.662094 + 0.749421i \(0.730332\pi\)
\(20\) 4.65369 + 4.15928i 1.04060 + 0.930044i
\(21\) 1.73205i 0.377964i
\(22\) −5.01540 2.89564i −1.06929 0.617353i
\(23\) −3.96863 + 2.29129i −0.827516 + 0.477767i −0.853001 0.521909i \(-0.825220\pi\)
0.0254855 + 0.999675i \(0.491887\pi\)
\(24\) 1.50000 0.866025i 0.306186 0.176777i
\(25\) −4.58258 2.00000i −0.916515 0.400000i
\(26\) −5.68693 5.47225i −1.11530 1.07320i
\(27\) 5.00000i 0.962250i
\(28\) −2.41733 4.18693i −0.456832 0.791256i
\(29\) −2.29129 3.96863i −0.425481 0.736956i 0.570984 0.820961i \(-0.306562\pi\)
−0.996465 + 0.0840058i \(0.973229\pi\)
\(30\) −3.26167 + 3.64938i −0.595497 + 0.666282i
\(31\) 9.66930i 1.73666i 0.495988 + 0.868329i \(0.334806\pi\)
−0.495988 + 0.868329i \(0.665194\pi\)
\(32\) 3.69253 6.39564i 0.652753 1.13060i
\(33\) 1.32288 2.29129i 0.230283 0.398862i
\(34\) 10.0308i 1.72027i
\(35\) 2.88771 + 2.58092i 0.488112 + 0.436255i
\(36\) −2.79129 4.83465i −0.465215 0.805775i
\(37\) −3.96863 6.87386i −0.652438 1.13006i −0.982529 0.186107i \(-0.940413\pi\)
0.330091 0.943949i \(-0.392920\pi\)
\(38\) 3.79129i 0.615028i
\(39\) 2.50000 2.59808i 0.400320 0.416025i
\(40\) 0.791288 3.79129i 0.125114 0.599455i
\(41\) −2.29129 + 1.32288i −0.357839 + 0.206598i −0.668132 0.744042i \(-0.732906\pi\)
0.310293 + 0.950641i \(0.399573\pi\)
\(42\) 3.28335 1.89564i 0.506632 0.292504i
\(43\) −1.22753 0.708712i −0.187196 0.108078i 0.403473 0.914991i \(-0.367803\pi\)
−0.590669 + 0.806914i \(0.701136\pi\)
\(44\) 7.38505i 1.11334i
\(45\) 3.33444 + 2.98019i 0.497069 + 0.444260i
\(46\) 8.68693 + 5.01540i 1.28082 + 0.739481i
\(47\) −8.75560 −1.27714 −0.638568 0.769565i \(-0.720473\pi\)
−0.638568 + 0.769565i \(0.720473\pi\)
\(48\) 1.55130 + 0.895644i 0.223911 + 0.129275i
\(49\) 2.00000 + 3.46410i 0.285714 + 0.494872i
\(50\) 1.22411 + 10.8758i 0.173116 + 1.53808i
\(51\) 4.58258 0.641689
\(52\) −2.41733 + 9.76951i −0.335223 + 1.35479i
\(53\) 1.58258i 0.217383i −0.994076 0.108692i \(-0.965334\pi\)
0.994076 0.108692i \(-0.0346661\pi\)
\(54\) 9.47822 5.47225i 1.28982 0.744679i
\(55\) −1.84887 5.61976i −0.249301 0.757768i
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) −1.73205 −0.229416
\(58\) −5.01540 + 8.68693i −0.658555 + 1.14065i
\(59\) −2.91742 1.68438i −0.379816 0.219287i 0.297922 0.954590i \(-0.403706\pi\)
−0.677738 + 0.735303i \(0.737040\pi\)
\(60\) 6.10985 + 1.27520i 0.788779 + 0.164628i
\(61\) 5.29129 9.16478i 0.677480 1.17343i −0.298257 0.954485i \(-0.596405\pi\)
0.975737 0.218944i \(-0.0702613\pi\)
\(62\) 18.3296 10.5826i 2.32786 1.34399i
\(63\) −1.73205 3.00000i −0.218218 0.377964i
\(64\) −12.5826 −1.57282
\(65\) −0.606325 8.03943i −0.0752054 0.997168i
\(66\) −5.79129 −0.712858
\(67\) 7.43273 + 12.8739i 0.908052 + 1.57279i 0.816767 + 0.576968i \(0.195764\pi\)
0.0912856 + 0.995825i \(0.470902\pi\)
\(68\) −11.0776 + 6.39564i −1.34335 + 0.775586i
\(69\) −2.29129 + 3.96863i −0.275839 + 0.477767i
\(70\) 1.73205 8.29875i 0.207020 0.991891i
\(71\) −3.08258 1.77973i −0.365834 0.211215i 0.305803 0.952095i \(-0.401075\pi\)
−0.671637 + 0.740880i \(0.734409\pi\)
\(72\) −1.73205 + 3.00000i −0.204124 + 0.353553i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −8.68693 + 15.0462i −1.00984 + 1.74909i
\(75\) −4.96863 + 0.559237i −0.573728 + 0.0645751i
\(76\) 4.18693 2.41733i 0.480274 0.277286i
\(77\) 4.58258i 0.522233i
\(78\) −7.66115 1.89564i −0.867455 0.214639i
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) 3.80482 1.25176i 0.425392 0.139951i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.01540 + 2.89564i 0.553859 + 0.319770i
\(83\) −11.3060 −1.24100 −0.620498 0.784208i \(-0.713069\pi\)
−0.620498 + 0.784208i \(0.713069\pi\)
\(84\) −4.18693 2.41733i −0.456832 0.263752i
\(85\) 6.82847 7.64016i 0.740652 0.828691i
\(86\) 3.10260i 0.334562i
\(87\) −3.96863 2.29129i −0.425481 0.245652i
\(88\) 3.96863 2.29129i 0.423057 0.244252i
\(89\) 3.70871 2.14123i 0.393123 0.226969i −0.290390 0.956909i \(-0.593785\pi\)
0.683512 + 0.729939i \(0.260452\pi\)
\(90\) 2.00000 9.58258i 0.210819 1.01009i
\(91\) −1.50000 + 6.06218i −0.157243 + 0.635489i
\(92\) 12.7913i 1.33358i
\(93\) 4.83465 + 8.37386i 0.501330 + 0.868329i
\(94\) 9.58258 + 16.5975i 0.988367 + 1.71190i
\(95\) −2.58092 + 2.88771i −0.264797 + 0.296273i
\(96\) 7.38505i 0.753734i
\(97\) 2.23658 3.87386i 0.227090 0.393331i −0.729854 0.683603i \(-0.760412\pi\)
0.956944 + 0.290271i \(0.0937455\pi\)
\(98\) 4.37780 7.58258i 0.442225 0.765956i
\(99\) 5.29150i 0.531816i
\(100\) 11.2303 8.28629i 1.12303 0.828629i
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) −5.01540 8.68693i −0.496599 0.860134i
\(103\) 15.1652i 1.49427i −0.664674 0.747133i \(-0.731430\pi\)
0.664674 0.747133i \(-0.268570\pi\)
\(104\) 6.00000 1.73205i 0.588348 0.169842i
\(105\) 3.79129 + 0.791288i 0.369992 + 0.0772218i
\(106\) −3.00000 + 1.73205i −0.291386 + 0.168232i
\(107\) 1.22753 0.708712i 0.118669 0.0685138i −0.439490 0.898247i \(-0.644841\pi\)
0.558160 + 0.829733i \(0.311508\pi\)
\(108\) −12.0866 6.97822i −1.16304 0.671479i
\(109\) 2.74110i 0.262550i −0.991346 0.131275i \(-0.958093\pi\)
0.991346 0.131275i \(-0.0419071\pi\)
\(110\) −8.62957 + 9.65534i −0.822797 + 0.920601i
\(111\) −6.87386 3.96863i −0.652438 0.376685i
\(112\) −3.10260 −0.293168
\(113\) 14.3609 + 8.29129i 1.35096 + 0.779979i 0.988384 0.151975i \(-0.0485632\pi\)
0.362578 + 0.931953i \(0.381897\pi\)
\(114\) 1.89564 + 3.28335i 0.177543 + 0.307514i
\(115\) 3.20233 + 9.73371i 0.298619 + 0.907673i
\(116\) 12.7913 1.18764
\(117\) −1.73205 + 7.00000i −0.160128 + 0.647150i
\(118\) 7.37386i 0.678819i
\(119\) −6.87386 + 3.96863i −0.630126 + 0.363803i
\(120\) −1.21037 3.67900i −0.110491 0.335845i
\(121\) −2.00000 + 3.46410i −0.181818 + 0.314918i
\(122\) −23.1642 −2.09719
\(123\) −1.32288 + 2.29129i −0.119280 + 0.206598i
\(124\) −23.3739 13.4949i −2.09903 1.21188i
\(125\) −6.47135 + 9.11710i −0.578815 + 0.815459i
\(126\) −3.79129 + 6.56670i −0.337755 + 0.585008i
\(127\) 8.44178 4.87386i 0.749087 0.432485i −0.0762771 0.997087i \(-0.524303\pi\)
0.825364 + 0.564601i \(0.190970\pi\)
\(128\) 6.38595 + 11.0608i 0.564444 + 0.977645i
\(129\) −1.41742 −0.124797
\(130\) −14.5763 + 9.94813i −1.27843 + 0.872509i
\(131\) 1.58258 0.138270 0.0691351 0.997607i \(-0.477976\pi\)
0.0691351 + 0.997607i \(0.477976\pi\)
\(132\) 3.69253 + 6.39564i 0.321393 + 0.556669i
\(133\) 2.59808 1.50000i 0.225282 0.130066i
\(134\) 16.2695 28.1796i 1.40547 2.43435i
\(135\) 10.9445 + 2.28425i 0.941953 + 0.196597i
\(136\) 6.87386 + 3.96863i 0.589429 + 0.340307i
\(137\) −0.0476751 + 0.0825757i −0.00407316 + 0.00705492i −0.868055 0.496468i \(-0.834630\pi\)
0.863982 + 0.503523i \(0.167963\pi\)
\(138\) 10.0308 0.853879
\(139\) 2.87386 4.97768i 0.243758 0.422201i −0.718024 0.696019i \(-0.754953\pi\)
0.961782 + 0.273817i \(0.0882864\pi\)
\(140\) −10.2691 + 3.37849i −0.867900 + 0.285534i
\(141\) −7.58258 + 4.37780i −0.638568 + 0.368677i
\(142\) 7.79129i 0.653830i
\(143\) 6.61438 6.87386i 0.553122 0.574821i
\(144\) −3.58258 −0.298548
\(145\) −9.73371 + 3.20233i −0.808340 + 0.265939i
\(146\) 0 0
\(147\) 3.46410 + 2.00000i 0.285714 + 0.164957i
\(148\) 22.1552 1.82114
\(149\) 8.45644 + 4.88233i 0.692778 + 0.399976i 0.804652 0.593747i \(-0.202352\pi\)
−0.111874 + 0.993722i \(0.535685\pi\)
\(150\) 6.49803 + 8.80669i 0.530562 + 0.719063i
\(151\) 6.20520i 0.504972i −0.967601 0.252486i \(-0.918752\pi\)
0.967601 0.252486i \(-0.0812482\pi\)
\(152\) −2.59808 1.50000i −0.210732 0.121666i
\(153\) −7.93725 + 4.58258i −0.641689 + 0.370479i
\(154\) 8.68693 5.01540i 0.700013 0.404153i
\(155\) 21.1652 + 4.41742i 1.70003 + 0.354816i
\(156\) 2.79129 + 9.66930i 0.223482 + 0.774164i
\(157\) 9.16515i 0.731459i 0.930721 + 0.365729i \(0.119180\pi\)
−0.930721 + 0.365729i \(0.880820\pi\)
\(158\) −6.56670 11.3739i −0.522419 0.904856i
\(159\) −0.791288 1.37055i −0.0627532 0.108692i
\(160\) −12.3125 11.0044i −0.973389 0.869976i
\(161\) 7.93725i 0.625543i
\(162\) −1.09445 + 1.89564i −0.0859882 + 0.148936i
\(163\) −5.33918 + 9.24773i −0.418197 + 0.724338i −0.995758 0.0920093i \(-0.970671\pi\)
0.577561 + 0.816347i \(0.304004\pi\)
\(164\) 7.38505i 0.576676i
\(165\) −4.41105 3.94242i −0.343399 0.306917i
\(166\) 12.3739 + 21.4322i 0.960398 + 1.66346i
\(167\) −2.14123 3.70871i −0.165693 0.286989i 0.771208 0.636583i \(-0.219653\pi\)
−0.936901 + 0.349594i \(0.886319\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) −21.9564 4.58258i −1.68398 0.351468i
\(171\) 3.00000 1.73205i 0.229416 0.132453i
\(172\) 3.42638 1.97822i 0.261259 0.150838i
\(173\) 6.42368 + 3.70871i 0.488383 + 0.281968i 0.723903 0.689901i \(-0.242346\pi\)
−0.235520 + 0.971869i \(0.575679\pi\)
\(174\) 10.0308i 0.760433i
\(175\) 6.96863 5.14181i 0.526779 0.388685i
\(176\) 4.10436 + 2.36965i 0.309377 + 0.178619i
\(177\) −3.36875 −0.253211
\(178\) −8.11800 4.68693i −0.608470 0.351300i
\(179\) −0.0825757 0.143025i −0.00617200 0.0106902i 0.862923 0.505336i \(-0.168631\pi\)
−0.869095 + 0.494645i \(0.835298\pi\)
\(180\) −11.8578 + 3.90114i −0.883826 + 0.290774i
\(181\) −18.7477 −1.39351 −0.696754 0.717310i \(-0.745373\pi\)
−0.696754 + 0.717310i \(0.745373\pi\)
\(182\) 13.1334 3.79129i 0.973513 0.281029i
\(183\) 10.5826i 0.782287i
\(184\) −6.87386 + 3.96863i −0.506748 + 0.292571i
\(185\) −16.8593 + 5.54661i −1.23952 + 0.407795i
\(186\) 10.5826 18.3296i 0.775952 1.34399i
\(187\) 12.1244 0.886621
\(188\) 12.2197 21.1652i 0.891214 1.54363i
\(189\) −7.50000 4.33013i −0.545545 0.314970i
\(190\) 8.29875 + 1.73205i 0.602055 + 0.125656i
\(191\) 3.70871 6.42368i 0.268353 0.464801i −0.700084 0.714061i \(-0.746854\pi\)
0.968437 + 0.249260i \(0.0801873\pi\)
\(192\) −10.8968 + 6.29129i −0.786411 + 0.454035i
\(193\) −0.504525 0.873864i −0.0363165 0.0629021i 0.847296 0.531121i \(-0.178229\pi\)
−0.883612 + 0.468219i \(0.844896\pi\)
\(194\) −9.79129 −0.702973
\(195\) −4.54481 6.65918i −0.325460 0.476874i
\(196\) −11.1652 −0.797511
\(197\) −9.98313 17.2913i −0.711269 1.23195i −0.964381 0.264516i \(-0.914788\pi\)
0.253113 0.967437i \(-0.418546\pi\)
\(198\) 10.0308 5.79129i 0.712858 0.411569i
\(199\) 0.708712 1.22753i 0.0502393 0.0870170i −0.839812 0.542877i \(-0.817335\pi\)
0.890051 + 0.455860i \(0.150668\pi\)
\(200\) −7.93725 3.46410i −0.561249 0.244949i
\(201\) 12.8739 + 7.43273i 0.908052 + 0.524264i
\(202\) −9.85005 + 17.0608i −0.693047 + 1.20039i
\(203\) 7.93725 0.557086
\(204\) −6.39564 + 11.0776i −0.447785 + 0.775586i
\(205\) 1.84887 + 5.61976i 0.129131 + 0.392501i
\(206\) −28.7477 + 16.5975i −2.00295 + 1.15640i
\(207\) 9.16515i 0.637022i
\(208\) 4.65390 + 4.47822i 0.322690 + 0.310509i
\(209\) −4.58258 −0.316983
\(210\) −2.64938 8.05296i −0.182824 0.555707i
\(211\) −9.08258 15.7315i −0.625270 1.08300i −0.988489 0.151296i \(-0.951655\pi\)
0.363218 0.931704i \(-0.381678\pi\)
\(212\) 3.82560 + 2.20871i 0.262743 + 0.151695i
\(213\) −3.55945 −0.243890
\(214\) −2.68693 1.55130i −0.183675 0.106045i
\(215\) −2.11210 + 2.36316i −0.144044 + 0.161166i
\(216\) 8.66025i 0.589256i
\(217\) −14.5040 8.37386i −0.984593 0.568455i
\(218\) −5.19615 + 3.00000i −0.351928 + 0.203186i
\(219\) 0 0
\(220\) 16.1652 + 3.37386i 1.08985 + 0.227466i
\(221\) 16.0390 + 3.96863i 1.07890 + 0.266959i
\(222\) 17.3739i 1.16606i
\(223\) −4.33013 7.50000i −0.289967 0.502237i 0.683835 0.729637i \(-0.260311\pi\)
−0.973801 + 0.227400i \(0.926978\pi\)
\(224\) 6.39564 + 11.0776i 0.427327 + 0.740152i
\(225\) 8.04668 5.93725i 0.536445 0.395817i
\(226\) 36.2976i 2.41448i
\(227\) 3.05493 5.29129i 0.202763 0.351195i −0.746655 0.665212i \(-0.768341\pi\)
0.949418 + 0.314016i \(0.101675\pi\)
\(228\) 2.41733 4.18693i 0.160091 0.277286i
\(229\) 5.48220i 0.362274i 0.983458 + 0.181137i \(0.0579778\pi\)
−0.983458 + 0.181137i \(0.942022\pi\)
\(230\) 14.9468 16.7235i 0.985566 1.10272i
\(231\) 2.29129 + 3.96863i 0.150756 + 0.261116i
\(232\) −3.96863 6.87386i −0.260553 0.451291i
\(233\) 21.1652i 1.38658i 0.720661 + 0.693288i \(0.243838\pi\)
−0.720661 + 0.693288i \(0.756162\pi\)
\(234\) 15.1652 4.37780i 0.991377 0.286186i
\(235\) −4.00000 + 19.1652i −0.260931 + 1.25020i
\(236\) 8.14337 4.70158i 0.530088 0.306047i
\(237\) 5.19615 3.00000i 0.337526 0.194871i
\(238\) 15.0462 + 8.68693i 0.975301 + 0.563090i
\(239\) 20.9753i 1.35678i 0.734702 + 0.678390i \(0.237322\pi\)
−0.734702 + 0.678390i \(0.762678\pi\)
\(240\) 2.66919 2.98647i 0.172295 0.192776i
\(241\) −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 8.75560 0.562832
\(243\) −13.8564 8.00000i −0.888889 0.513200i
\(244\) 14.7695 + 25.5815i 0.945521 + 1.63769i
\(245\) 8.49628 2.79523i 0.542807 0.178580i
\(246\) 5.79129 0.369239
\(247\) −6.06218 1.50000i −0.385727 0.0954427i
\(248\) 16.7477i 1.06348i
\(249\) −9.79129 + 5.65300i −0.620498 + 0.358244i
\(250\) 24.3654 + 2.28916i 1.54100 + 0.144779i
\(251\) −9.08258 + 15.7315i −0.573287 + 0.992962i 0.422938 + 0.906158i \(0.360999\pi\)
−0.996225 + 0.0868039i \(0.972335\pi\)
\(252\) 9.66930 0.609109
\(253\) −6.06218 + 10.5000i −0.381126 + 0.660129i
\(254\) −18.4782 10.6684i −1.15943 0.669395i
\(255\) 2.09355 10.0308i 0.131103 0.628153i
\(256\) 1.39564 2.41733i 0.0872277 0.151083i
\(257\) −0.143025 + 0.0825757i −0.00892167 + 0.00515093i −0.504454 0.863438i \(-0.668306\pi\)
0.495533 + 0.868589i \(0.334973\pi\)
\(258\) 1.55130 + 2.68693i 0.0965798 + 0.167281i
\(259\) 13.7477 0.854242
\(260\) 20.2801 + 9.75449i 1.25772 + 0.604948i
\(261\) 9.16515 0.567309
\(262\) −1.73205 3.00000i −0.107006 0.185341i
\(263\) 7.79423 4.50000i 0.480613 0.277482i −0.240059 0.970758i \(-0.577167\pi\)
0.720672 + 0.693276i \(0.243833\pi\)
\(264\) 2.29129 3.96863i 0.141019 0.244252i
\(265\) −3.46410 0.723000i −0.212798 0.0444135i
\(266\) −5.68693 3.28335i −0.348688 0.201315i
\(267\) 2.14123 3.70871i 0.131041 0.226969i
\(268\) −41.4938 −2.53464
\(269\) −7.50000 + 12.9904i −0.457283 + 0.792038i −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) −7.64809 23.2469i −0.465448 1.41476i
\(271\) 7.50000 4.33013i 0.455593 0.263036i −0.254597 0.967047i \(-0.581943\pi\)
0.710189 + 0.704011i \(0.248609\pi\)
\(272\) 8.20871i 0.497726i
\(273\) 1.73205 + 6.00000i 0.104828 + 0.363137i
\(274\) 0.208712 0.0126088
\(275\) −13.1458 + 1.47960i −0.792719 + 0.0892234i
\(276\) −6.39564 11.0776i −0.384973 0.666792i
\(277\) −14.3609 8.29129i −0.862865 0.498175i 0.00210581 0.999998i \(-0.499330\pi\)
−0.864971 + 0.501823i \(0.832663\pi\)
\(278\) −12.5812 −0.754571
\(279\) −16.7477 9.66930i −1.00266 0.578886i
\(280\) 5.00166 + 4.47028i 0.298906 + 0.267151i
\(281\) 17.5112i 1.04463i 0.852752 + 0.522316i \(0.174932\pi\)
−0.852752 + 0.522316i \(0.825068\pi\)
\(282\) 16.5975 + 9.58258i 0.988367 + 0.570634i
\(283\) −0.218475 + 0.126136i −0.0129870 + 0.00749803i −0.506479 0.862252i \(-0.669053\pi\)
0.493492 + 0.869750i \(0.335720\pi\)
\(284\) 8.60436 4.96773i 0.510575 0.294780i
\(285\) −0.791288 + 3.79129i −0.0468718 + 0.224577i
\(286\) −20.2695 5.01540i −1.19856 0.296567i
\(287\) 4.58258i 0.270501i
\(288\) 7.38505 + 12.7913i 0.435168 + 0.753734i
\(289\) 2.00000 + 3.46410i 0.117647 + 0.203771i
\(290\) 16.7235 + 14.9468i 0.982040 + 0.877709i
\(291\) 4.47315i 0.262221i
\(292\) 0 0
\(293\) −11.7152 + 20.2913i −0.684408 + 1.18543i 0.289214 + 0.957264i \(0.406606\pi\)
−0.973622 + 0.228165i \(0.926727\pi\)
\(294\) 8.75560i 0.510637i
\(295\) −5.01976 + 5.61645i −0.292262 + 0.327002i
\(296\) −6.87386 11.9059i −0.399535 0.692015i
\(297\) 6.61438 + 11.4564i 0.383805 + 0.664770i
\(298\) 21.3739i 1.23815i
\(299\) −11.4564 + 11.9059i −0.662543 + 0.688535i
\(300\) 5.58258 12.7913i 0.322310 0.738505i
\(301\) 2.12614 1.22753i 0.122548 0.0707534i
\(302\) −11.7629 + 6.79129i −0.676876 + 0.390795i
\(303\) −7.79423 4.50000i −0.447767 0.258518i
\(304\) 3.10260i 0.177946i
\(305\) −17.6435 15.7690i −1.01026 0.902932i
\(306\) 17.3739 + 10.0308i 0.993198 + 0.573423i
\(307\) 24.2487 1.38395 0.691974 0.721923i \(-0.256741\pi\)
0.691974 + 0.721923i \(0.256741\pi\)
\(308\) −11.0776 6.39564i −0.631204 0.364426i
\(309\) −7.58258 13.1334i −0.431358 0.747133i
\(310\) −14.7903 44.9562i −0.840035 2.55334i
\(311\) −1.58258 −0.0897396 −0.0448698 0.998993i \(-0.514287\pi\)
−0.0448698 + 0.998993i \(0.514287\pi\)
\(312\) 4.33013 4.50000i 0.245145 0.254762i
\(313\) 30.7477i 1.73796i −0.494843 0.868982i \(-0.664775\pi\)
0.494843 0.868982i \(-0.335225\pi\)
\(314\) 17.3739 10.0308i 0.980464 0.566071i
\(315\) −7.35799 + 2.42074i −0.414576 + 0.136393i
\(316\) −8.37386 + 14.5040i −0.471067 + 0.815911i
\(317\) 20.9753 1.17809 0.589045 0.808100i \(-0.299504\pi\)
0.589045 + 0.808100i \(0.299504\pi\)
\(318\) −1.73205 + 3.00000i −0.0971286 + 0.168232i
\(319\) −10.5000 6.06218i −0.587887 0.339417i
\(320\) −5.74835 + 27.5420i −0.321343 + 1.53965i
\(321\) 0.708712 1.22753i 0.0395565 0.0685138i
\(322\) −15.0462 + 8.68693i −0.838492 + 0.484104i
\(323\) −3.96863 6.87386i −0.220820 0.382472i
\(324\) 2.79129 0.155072
\(325\) −17.8745 2.34563i −0.991499 0.130112i
\(326\) 23.3739 1.29456
\(327\) −1.37055 2.37386i −0.0757916 0.131275i
\(328\) −3.96863 + 2.29129i −0.219131 + 0.126515i
\(329\) 7.58258 13.1334i 0.418041 0.724068i
\(330\) −2.64575 + 12.6766i −0.145644 + 0.697821i
\(331\) 9.87386 + 5.70068i 0.542717 + 0.313338i 0.746179 0.665745i \(-0.231886\pi\)
−0.203463 + 0.979083i \(0.565220\pi\)
\(332\) 15.7792 27.3303i 0.865994 1.49995i
\(333\) 15.8745 0.869918
\(334\) −4.68693 + 8.11800i −0.256457 + 0.444197i
\(335\) 31.5753 10.3881i 1.72514 0.567561i
\(336\) −2.68693 + 1.55130i −0.146584 + 0.0846304i
\(337\) 3.25227i 0.177163i −0.996069 0.0885813i \(-0.971767\pi\)
0.996069 0.0885813i \(-0.0282333\pi\)
\(338\) −25.1724 13.2695i −1.36920 0.721766i
\(339\) 16.5826 0.900642
\(340\) 8.93864 + 27.1696i 0.484766 + 1.47348i
\(341\) 12.7913 + 22.1552i 0.692687 + 1.19977i
\(342\) −6.56670 3.79129i −0.355087 0.205009i
\(343\) −19.0526 −1.02874
\(344\) −2.12614 1.22753i −0.114634 0.0661837i
\(345\) 7.64016 + 6.82847i 0.411332 + 0.367633i
\(346\) 16.2360i 0.872853i
\(347\) 13.2764 + 7.66515i 0.712716 + 0.411487i 0.812066 0.583566i \(-0.198343\pi\)
−0.0993497 + 0.995053i \(0.531676\pi\)
\(348\) 11.0776 6.39564i 0.593821 0.342843i
\(349\) 15.8739 9.16478i 0.849708 0.490579i −0.0108440 0.999941i \(-0.503452\pi\)
0.860552 + 0.509362i \(0.170118\pi\)
\(350\) −17.3739 7.58258i −0.928672 0.405306i
\(351\) 5.00000 + 17.3205i 0.266880 + 0.924500i
\(352\) 19.5390i 1.04143i
\(353\) 8.70793 + 15.0826i 0.463476 + 0.802765i 0.999131 0.0416724i \(-0.0132686\pi\)
−0.535655 + 0.844437i \(0.679935\pi\)
\(354\) 3.68693 + 6.38595i 0.195958 + 0.339410i
\(355\) −5.30392 + 5.93438i −0.281503 + 0.314964i
\(356\) 11.9536i 0.633537i
\(357\) −3.96863 + 6.87386i −0.210042 + 0.363803i
\(358\) −0.180750 + 0.313068i −0.00955294 + 0.0165462i
\(359\) 33.3857i 1.76203i −0.473088 0.881015i \(-0.656861\pi\)
0.473088 0.881015i \(-0.343139\pi\)
\(360\) 5.77542 + 5.16184i 0.304391 + 0.272053i
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) 20.5185 + 35.5390i 1.07843 + 1.86789i
\(363\) 4.00000i 0.209946i
\(364\) −12.5608 12.0866i −0.658365 0.633512i
\(365\) 0 0
\(366\) −20.0608 + 11.5821i −1.04859 + 0.605406i
\(367\) −22.2982 + 12.8739i −1.16396 + 0.672010i −0.952249 0.305323i \(-0.901236\pi\)
−0.211707 + 0.977333i \(0.567902\pi\)
\(368\) −7.10895 4.10436i −0.370580 0.213954i
\(369\) 5.29150i 0.275465i
\(370\) 28.9660 + 25.8887i 1.50587 + 1.34589i
\(371\) 2.37386 + 1.37055i 0.123245 + 0.0711554i
\(372\) −26.9898 −1.39936
\(373\) 11.2583 + 6.50000i 0.582934 + 0.336557i 0.762299 0.647225i \(-0.224071\pi\)
−0.179364 + 0.983783i \(0.557404\pi\)
\(374\) −13.2695 22.9835i −0.686150 1.18845i
\(375\) −1.04580 + 11.1313i −0.0540051 + 0.574819i
\(376\) −15.1652 −0.782083
\(377\) −11.9059 11.4564i −0.613184 0.590037i
\(378\) 18.9564i 0.975014i
\(379\) 18.2477 10.5353i 0.937323 0.541164i 0.0482027 0.998838i \(-0.484651\pi\)
0.889120 + 0.457674i \(0.151317\pi\)
\(380\) −3.37849 10.2691i −0.173313 0.526796i
\(381\) 4.87386 8.44178i 0.249696 0.432485i
\(382\) −16.2360 −0.830706
\(383\) −1.41823 + 2.45644i −0.0724680 + 0.125518i −0.899982 0.435926i \(-0.856421\pi\)
0.827514 + 0.561444i \(0.189754\pi\)
\(384\) 11.0608 + 6.38595i 0.564444 + 0.325882i
\(385\) 10.0308 + 2.09355i 0.511217 + 0.106697i
\(386\) −1.10436 + 1.91280i −0.0562102 + 0.0973590i
\(387\) 2.45505 1.41742i 0.124797 0.0720517i
\(388\) 6.24293 + 10.8131i 0.316937 + 0.548950i
\(389\) −15.1652 −0.768904 −0.384452 0.923145i \(-0.625610\pi\)
−0.384452 + 0.923145i \(0.625610\pi\)
\(390\) −7.64938 + 15.9035i −0.387341 + 0.805304i
\(391\) −21.0000 −1.06202
\(392\) 3.46410 + 6.00000i 0.174964 + 0.303046i
\(393\) 1.37055 0.791288i 0.0691351 0.0399152i
\(394\) −21.8521 + 37.8489i −1.10089 + 1.90680i
\(395\) 2.74110 13.1334i 0.137920 0.660813i
\(396\) −12.7913 7.38505i −0.642786 0.371113i
\(397\) 13.6379 23.6216i 0.684468 1.18553i −0.289135 0.957288i \(-0.593368\pi\)
0.973604 0.228245i \(-0.0732989\pi\)
\(398\) −3.10260 −0.155519
\(399\) 1.50000 2.59808i 0.0750939 0.130066i
\(400\) −1.00175 8.90024i −0.0500877 0.445012i
\(401\) 10.8303 6.25288i 0.540840 0.312254i −0.204580 0.978850i \(-0.565583\pi\)
0.745419 + 0.666596i \(0.232249\pi\)
\(402\) 32.5390i 1.62290i
\(403\) 9.66930 + 33.4955i 0.481662 + 1.66853i
\(404\) 25.1216 1.24985
\(405\) −2.12407 + 0.698807i −0.105546 + 0.0347240i
\(406\) −8.68693 15.0462i −0.431125 0.746731i
\(407\) −18.1865 10.5000i −0.901473 0.520466i
\(408\) 7.93725 0.392953
\(409\) 7.50000 + 4.33013i 0.370851 + 0.214111i 0.673830 0.738886i \(-0.264648\pi\)
−0.302979 + 0.952997i \(0.597981\pi\)
\(410\) 8.62957 9.65534i 0.426184 0.476843i
\(411\) 0.0953502i 0.00470328i
\(412\) 36.6591 + 21.1652i 1.80607 + 1.04273i
\(413\) 5.05313 2.91742i 0.248648 0.143557i
\(414\) −17.3739 + 10.0308i −0.853879 + 0.492987i
\(415\) −5.16515 + 24.7477i −0.253547 + 1.21482i
\(416\) 6.39564 25.8477i 0.313572 1.26729i
\(417\) 5.74773i 0.281467i
\(418\) 5.01540 + 8.68693i 0.245311 + 0.424892i
\(419\) −12.0826 20.9276i −0.590272 1.02238i −0.994195 0.107589i \(-0.965687\pi\)
0.403923 0.914793i \(-0.367646\pi\)
\(420\) −7.20409 + 8.06042i −0.351524 + 0.393308i
\(421\) 26.2668i 1.28017i 0.768306 + 0.640083i \(0.221100\pi\)
−0.768306 + 0.640083i \(0.778900\pi\)
\(422\) −19.8809 + 34.4347i −0.967785 + 1.67625i
\(423\) 8.75560 15.1652i 0.425712 0.737355i
\(424\) 2.74110i 0.133120i
\(425\) −13.6040 18.4373i −0.659889 0.894338i
\(426\) 3.89564 + 6.74745i 0.188745 + 0.326915i
\(427\) 9.16478 + 15.8739i 0.443515 + 0.768190i
\(428\) 3.95644i 0.191242i
\(429\) 2.29129 9.26013i 0.110624 0.447083i
\(430\) 6.79129 + 1.41742i 0.327505 + 0.0683543i
\(431\) 25.6652 14.8178i 1.23625 0.713747i 0.267922 0.963441i \(-0.413663\pi\)
0.968325 + 0.249693i \(0.0803298\pi\)
\(432\) −7.75650 + 4.47822i −0.373185 + 0.215458i
\(433\) 15.3700 + 8.87386i 0.738634 + 0.426451i 0.821573 0.570104i \(-0.193097\pi\)
−0.0829383 + 0.996555i \(0.526430\pi\)
\(434\) 36.6591i 1.75969i
\(435\) −6.82847 + 7.64016i −0.327400 + 0.366317i
\(436\) 6.62614 + 3.82560i 0.317334 + 0.183213i
\(437\) 7.93725 0.379690
\(438\) 0 0
\(439\) 20.2477 + 35.0701i 0.966371 + 1.67380i 0.705885 + 0.708327i \(0.250550\pi\)
0.260487 + 0.965477i \(0.416117\pi\)
\(440\) −3.20233 9.73371i −0.152665 0.464036i
\(441\) −8.00000 −0.380952
\(442\) −10.0308 34.7477i −0.477117 1.65278i
\(443\) 25.9129i 1.23116i −0.788075 0.615579i \(-0.788922\pi\)
0.788075 0.615579i \(-0.211078\pi\)
\(444\) 19.1869 11.0776i 0.910571 0.525719i
\(445\) −2.99261 9.09622i −0.141863 0.431202i
\(446\) −9.47822 + 16.4168i −0.448807 + 0.777356i
\(447\) 9.76465 0.461852
\(448\) 10.8968 18.8739i 0.514827 0.891706i
\(449\) 32.4564 + 18.7387i 1.53171 + 0.884336i 0.999283 + 0.0378622i \(0.0120548\pi\)
0.532431 + 0.846473i \(0.321279\pi\)
\(450\) −20.0616 8.75560i −0.945713 0.412743i
\(451\) −3.50000 + 6.06218i −0.164809 + 0.285457i
\(452\) −40.0855 + 23.1434i −1.88546 + 1.08857i
\(453\) −3.10260 5.37386i −0.145773 0.252486i
\(454\) −13.3739 −0.627667
\(455\) 12.5842 + 6.05286i 0.589958 + 0.283762i
\(456\) −3.00000 −0.140488
\(457\) 0.866025 + 1.50000i 0.0405110 + 0.0701670i 0.885570 0.464506i \(-0.153768\pi\)
−0.845059 + 0.534673i \(0.820435\pi\)
\(458\) 10.3923 6.00000i 0.485601 0.280362i
\(459\) −11.4564 + 19.8431i −0.534741 + 0.926198i
\(460\) −27.9989 5.84370i −1.30545 0.272464i
\(461\) −1.03901 0.599876i −0.0483917 0.0279390i 0.475609 0.879657i \(-0.342228\pi\)
−0.524001 + 0.851718i \(0.675561\pi\)
\(462\) 5.01540 8.68693i 0.233338 0.404153i
\(463\) −8.22330 −0.382169 −0.191085 0.981574i \(-0.561201\pi\)
−0.191085 + 0.981574i \(0.561201\pi\)
\(464\) 4.10436 7.10895i 0.190540 0.330025i
\(465\) 20.5383 6.75697i 0.952440 0.313347i
\(466\) 40.1216 23.1642i 1.85860 1.07306i
\(467\) 12.3303i 0.570578i −0.958441 0.285289i \(-0.907910\pi\)
0.958441 0.285289i \(-0.0920896\pi\)
\(468\) −14.5040 13.9564i −0.670446 0.645137i
\(469\) −25.7477 −1.18892
\(470\) 40.7081 13.3927i 1.87772 0.617761i
\(471\) 4.58258 + 7.93725i 0.211154 + 0.365729i
\(472\) −5.05313 2.91742i −0.232589 0.134285i
\(473\) −3.75015 −0.172432
\(474\) −11.3739 6.56670i −0.522419 0.301619i
\(475\) 5.14181 + 6.96863i 0.235923 + 0.319743i
\(476\) 22.1552i 1.01548i
\(477\) 2.74110 + 1.58258i 0.125506 + 0.0724612i
\(478\) 39.7617 22.9564i 1.81866 1.05000i
\(479\) −28.0390 + 16.1883i −1.28114 + 0.739664i −0.977056 0.212983i \(-0.931682\pi\)
−0.304079 + 0.952647i \(0.598349\pi\)
\(480\) −16.1652 3.37386i −0.737835 0.153995i
\(481\) −20.6216 19.8431i −0.940264 0.904769i
\(482\) 3.79129i 0.172688i
\(483\) −3.96863 6.87386i −0.180579 0.312772i
\(484\) −5.58258 9.66930i −0.253753 0.439514i
\(485\) −7.45772 6.66542i −0.338638 0.302661i
\(486\) 35.0224i 1.58865i
\(487\) −10.5353 + 18.2477i −0.477401 + 0.826883i −0.999665 0.0259009i \(-0.991755\pi\)
0.522263 + 0.852784i \(0.325088\pi\)
\(488\) 9.16478 15.8739i 0.414870 0.718576i
\(489\) 10.6784i 0.482892i
\(490\) −14.5975 13.0467i −0.659448 0.589389i
\(491\) −14.2913 24.7532i −0.644957 1.11710i −0.984311 0.176439i \(-0.943542\pi\)
0.339355 0.940658i \(-0.389791\pi\)
\(492\) −3.69253 6.39564i −0.166472 0.288338i
\(493\) 21.0000i 0.945792i
\(494\) 3.79129 + 13.1334i 0.170578 + 0.590900i
\(495\) 11.5826 + 2.41742i 0.520598 + 0.108655i
\(496\) −15.0000 + 8.66025i −0.673520 + 0.388857i
\(497\) 5.33918 3.08258i 0.239495 0.138272i
\(498\) 21.4322 + 12.3739i 0.960398 + 0.554486i
\(499\) 16.5975i 0.743006i −0.928432 0.371503i \(-0.878842\pi\)
0.928432 0.371503i \(-0.121158\pi\)
\(500\) −13.0073 28.3676i −0.581705 1.26864i
\(501\) −3.70871 2.14123i −0.165693 0.0956629i
\(502\) 39.7617 1.77465
\(503\) 15.7315 + 9.08258i 0.701432 + 0.404972i 0.807881 0.589346i \(-0.200615\pi\)
−0.106448 + 0.994318i \(0.533948\pi\)
\(504\) −3.00000 5.19615i −0.133631 0.231455i
\(505\) −19.1166 + 6.28926i −0.850678 + 0.279868i
\(506\) 26.5390 1.17980
\(507\) 6.06218 11.5000i 0.269231 0.510733i
\(508\) 27.2087i 1.20719i
\(509\) −25.6652 + 14.8178i −1.13759 + 0.656787i −0.945832 0.324656i \(-0.894751\pi\)
−0.191756 + 0.981443i \(0.561418\pi\)
\(510\) −21.3061 + 7.00959i −0.943451 + 0.310390i
\(511\) 0 0
\(512\) 19.4340 0.858868
\(513\) 4.33013 7.50000i 0.191180 0.331133i
\(514\) 0.313068 + 0.180750i 0.0138088 + 0.00797254i
\(515\) −33.1950 6.92820i −1.46275 0.305293i
\(516\) 1.97822 3.42638i 0.0870863 0.150838i
\(517\) −20.0616 + 11.5826i −0.882309 + 0.509401i
\(518\) −15.0462 26.0608i −0.661092 1.14505i
\(519\) 7.41742 0.325589
\(520\) −1.05019 13.9247i −0.0460537 0.610638i
\(521\) −27.4955 −1.20460 −0.602299 0.798271i \(-0.705748\pi\)
−0.602299 + 0.798271i \(0.705748\pi\)
\(522\) −10.0308 17.3739i −0.439036 0.760433i
\(523\) −15.7315 + 9.08258i −0.687890 + 0.397153i −0.802821 0.596220i \(-0.796669\pi\)
0.114931 + 0.993373i \(0.463335\pi\)
\(524\) −2.20871 + 3.82560i −0.0964880 + 0.167122i
\(525\) 3.46410 7.93725i 0.151186 0.346410i
\(526\) −17.0608 9.85005i −0.743886 0.429483i
\(527\) −22.1552 + 38.3739i −0.965094 + 1.67159i
\(528\) 4.73930 0.206252
\(529\) −1.00000 + 1.73205i −0.0434783 + 0.0753066i
\(530\) 2.42074 + 7.35799i 0.105150 + 0.319611i
\(531\) 5.83485 3.36875i 0.253211 0.146191i
\(532\) 8.37386i 0.363053i
\(533\) −6.61438 + 6.87386i −0.286501 + 0.297740i
\(534\) −9.37386 −0.405647
\(535\) −0.990505 3.01071i −0.0428233 0.130164i
\(536\) 12.8739 + 22.2982i 0.556066 + 0.963135i
\(537\) −0.143025 0.0825757i −0.00617200 0.00356340i
\(538\) 32.8335 1.41555
\(539\) 9.16515 + 5.29150i 0.394771 + 0.227921i
\(540\) −20.7964 + 23.2684i −0.894935 + 1.00131i
\(541\) 10.3923i 0.446800i 0.974727 + 0.223400i \(0.0717156\pi\)
−0.974727 + 0.223400i \(0.928284\pi\)
\(542\) −16.4168 9.47822i −0.705160 0.407124i
\(543\) −16.2360 + 9.37386i −0.696754 + 0.402271i
\(544\) 29.3085 16.9213i 1.25659 0.725494i
\(545\) −6.00000 1.25227i −0.257012 0.0536415i
\(546\) 9.47822 9.85005i 0.405630 0.421543i
\(547\) 1.25227i 0.0535433i −0.999642 0.0267717i \(-0.991477\pi\)
0.999642 0.0267717i \(-0.00852270\pi\)
\(548\) −0.133075 0.230493i −0.00568468 0.00984615i
\(549\) 10.5826 + 18.3296i 0.451653 + 0.782287i
\(550\) 17.1922 + 23.3003i 0.733077 + 0.993529i
\(551\) 7.93725i 0.338138i
\(552\) −3.96863 + 6.87386i −0.168916 + 0.292571i
\(553\) −5.19615 + 9.00000i −0.220963 + 0.382719i
\(554\) 36.2976i 1.54214i
\(555\) −11.8273 + 13.2331i −0.502039 + 0.561715i
\(556\) 8.02178 + 13.8941i 0.340199 + 0.589242i
\(557\) 6.51903 + 11.2913i 0.276220 + 0.478427i 0.970442 0.241334i \(-0.0775848\pi\)
−0.694222 + 0.719761i \(0.744251\pi\)
\(558\) 42.3303i 1.79198i
\(559\) −4.96099 1.22753i −0.209827 0.0519188i
\(560\) −1.41742 + 6.79129i −0.0598971 + 0.286984i
\(561\) 10.5000 6.06218i 0.443310 0.255945i
\(562\) 33.1950 19.1652i 1.40025 0.808433i
\(563\) 7.79423 + 4.50000i 0.328488 + 0.189652i 0.655169 0.755482i \(-0.272597\pi\)
−0.326682 + 0.945134i \(0.605931\pi\)
\(564\) 24.4394i 1.02908i
\(565\) 24.7096 27.6468i 1.03954 1.16311i
\(566\) 0.478220 + 0.276100i 0.0201011 + 0.0116054i
\(567\) 1.73205 0.0727393
\(568\) −5.33918 3.08258i −0.224027 0.129342i
\(569\) −9.87386 17.1020i −0.413934 0.716955i 0.581382 0.813631i \(-0.302512\pi\)
−0.995316 + 0.0966762i \(0.969179\pi\)
\(570\) 8.05296 2.64938i 0.337301 0.110970i
\(571\) 29.0780 1.21688 0.608439 0.793601i \(-0.291796\pi\)
0.608439 + 0.793601i \(0.291796\pi\)
\(572\) 7.38505 + 25.5826i 0.308785 + 1.06966i
\(573\) 7.41742i 0.309867i
\(574\) −8.68693 + 5.01540i −0.362586 + 0.209339i
\(575\) 22.7691 2.56275i 0.949537 0.106874i
\(576\) 12.5826 21.7937i 0.524274 0.908069i
\(577\) −6.92820 −0.288425 −0.144212 0.989547i \(-0.546065\pi\)
−0.144212 + 0.989547i \(0.546065\pi\)
\(578\) 4.37780 7.58258i 0.182093 0.315394i
\(579\) −0.873864 0.504525i −0.0363165 0.0209674i
\(580\) 5.84370 27.9989i 0.242647 1.16259i
\(581\) 9.79129 16.9590i 0.406211 0.703578i
\(582\) −8.47950 + 4.89564i −0.351487 + 0.202931i
\(583\) −2.09355 3.62614i −0.0867060 0.150179i
\(584\) 0 0
\(585\) 14.5310 + 6.98924i 0.600784 + 0.288969i
\(586\) 51.2867 2.11864
\(587\) −9.35548 16.2042i −0.386142 0.668818i 0.605785 0.795628i \(-0.292859\pi\)
−0.991927 + 0.126811i \(0.959526\pi\)
\(588\) −9.66930 + 5.58258i −0.398755 + 0.230222i
\(589\) 8.37386 14.5040i 0.345039 0.597625i
\(590\) 16.1407 + 3.36875i 0.664500 + 0.138689i
\(591\) −17.2913 9.98313i −0.711269 0.410651i
\(592\) 7.10895 12.3131i 0.292176 0.506064i
\(593\) 21.1660 0.869184 0.434592 0.900627i \(-0.356893\pi\)
0.434592 + 0.900627i \(0.356893\pi\)
\(594\) 14.4782 25.0770i 0.594049 1.02892i
\(595\) 5.54661 + 16.8593i 0.227389 + 0.691163i
\(596\) −23.6044 + 13.6280i −0.966872 + 0.558224i
\(597\) 1.41742i 0.0580113i
\(598\) 35.1078 + 8.68693i 1.43567 + 0.355235i
\(599\) 39.4955 1.61374 0.806870 0.590729i \(-0.201160\pi\)
0.806870 + 0.590729i \(0.201160\pi\)
\(600\) −8.60591 + 0.968627i −0.351335 + 0.0395440i
\(601\) 14.4564 + 25.0393i 0.589690 + 1.02137i 0.994273 + 0.106872i \(0.0340836\pi\)
−0.404582 + 0.914502i \(0.632583\pi\)
\(602\) −4.65390 2.68693i −0.189679 0.109511i
\(603\) −29.7309 −1.21074
\(604\) 15.0000 + 8.66025i 0.610341 + 0.352381i
\(605\) 6.66888 + 5.96038i 0.271128 + 0.242324i
\(606\) 19.7001i 0.800262i
\(607\) −17.1020 9.87386i −0.694150 0.400768i 0.111015 0.993819i \(-0.464590\pi\)
−0.805165 + 0.593051i \(0.797923\pi\)
\(608\) −11.0776 + 6.39564i −0.449255 + 0.259378i
\(609\) 6.87386 3.96863i 0.278543 0.160817i
\(610\) −10.5826 + 50.7042i −0.428476 + 2.05295i
\(611\) −30.3303 + 8.75560i −1.22703 + 0.354214i
\(612\) 25.5826i 1.03411i
\(613\) −10.8968 18.8739i −0.440119 0.762308i 0.557579 0.830124i \(-0.311730\pi\)
−0.997698 + 0.0678157i \(0.978397\pi\)
\(614\) −26.5390 45.9669i −1.07103 1.85507i
\(615\) 4.41105 + 3.94242i 0.177871 + 0.158974i
\(616\) 7.93725i 0.319801i
\(617\) −1.68438 + 2.91742i −0.0678104 + 0.117451i −0.897937 0.440124i \(-0.854935\pi\)
0.830127 + 0.557575i \(0.188268\pi\)
\(618\) −16.5975 + 28.7477i −0.667650 + 1.15640i
\(619\) 2.01810i 0.0811143i −0.999177 0.0405572i \(-0.987087\pi\)
0.999177 0.0405572i \(-0.0129133\pi\)
\(620\) −40.2174 + 44.9979i −1.61517 + 1.80716i
\(621\) −11.4564 19.8431i −0.459731 0.796278i
\(622\) 1.73205 + 3.00000i 0.0694489 + 0.120289i
\(623\) 7.41742i 0.297173i
\(624\) 6.26951 + 1.55130i 0.250981 + 0.0621017i
\(625\) 17.0000 + 18.3303i 0.680000 + 0.733212i
\(626\) −58.2867 + 33.6519i −2.32961 + 1.34500i
\(627\) −3.96863 + 2.29129i −0.158492 + 0.0915052i
\(628\) −22.1552 12.7913i −0.884087 0.510428i
\(629\) 36.3731i 1.45029i
\(630\) 12.6418 + 11.2988i 0.503662 + 0.450153i
\(631\) −18.8739 10.8968i −0.751357 0.433796i 0.0748272 0.997197i \(-0.476159\pi\)
−0.826184 + 0.563401i \(0.809493\pi\)
\(632\) 10.3923 0.413384
\(633\) −15.7315 9.08258i −0.625270 0.361000i
\(634\) −22.9564 39.7617i −0.911717 1.57914i
\(635\) −6.81178 20.7048i −0.270317 0.821647i
\(636\) 4.41742 0.175162
\(637\) 10.3923 + 10.0000i 0.411758 + 0.396214i
\(638\) 26.5390i 1.05069i
\(639\) 6.16515 3.55945i 0.243890 0.140810i
\(640\) 27.1284 8.92509i 1.07234 0.352795i
\(641\) 0.0825757 0.143025i 0.00326154 0.00564916i −0.864390 0.502822i \(-0.832295\pi\)
0.867652 + 0.497173i \(0.165628\pi\)
\(642\) −3.10260 −0.122450
\(643\) −2.95958 + 5.12614i −0.116714 + 0.202155i −0.918464 0.395505i \(-0.870570\pi\)
0.801749 + 0.597660i \(0.203903\pi\)
\(644\) 19.1869 + 11.0776i 0.756071 + 0.436518i
\(645\) −0.647551 + 3.10260i −0.0254973 + 0.122165i
\(646\) −8.68693 + 15.0462i −0.341783 + 0.591985i
\(647\) −23.3827 + 13.5000i −0.919268 + 0.530740i −0.883402 0.468617i \(-0.844753\pi\)
−0.0358667 + 0.999357i \(0.511419\pi\)
\(648\) −0.866025 1.50000i −0.0340207 0.0589256i
\(649\) −8.91288 −0.349861
\(650\) 15.1163 + 36.4509i 0.592910 + 1.42972i
\(651\) −16.7477 −0.656395
\(652\) −14.9032 25.8131i −0.583654 1.01092i
\(653\) 42.2843 24.4129i 1.65471 0.955350i 0.679619 0.733566i \(-0.262145\pi\)
0.975096 0.221784i \(-0.0711880\pi\)
\(654\) −3.00000 + 5.19615i −0.117309 + 0.203186i
\(655\) 0.723000 3.46410i 0.0282500 0.135354i
\(656\) −4.10436 2.36965i −0.160248 0.0925193i
\(657\) 0 0
\(658\) −33.1950 −1.29408
\(659\) −12.2477 + 21.2137i −0.477104 + 0.826368i −0.999656 0.0262396i \(-0.991647\pi\)
0.522552 + 0.852607i \(0.324980\pi\)
\(660\) 15.6864 5.16072i 0.610591 0.200881i
\(661\) 2.12614 1.22753i 0.0826971 0.0477452i −0.458081 0.888910i \(-0.651463\pi\)
0.540778 + 0.841165i \(0.318130\pi\)
\(662\) 24.9564i 0.969960i
\(663\) 15.8745 4.58258i 0.616515 0.177972i
\(664\) −19.5826 −0.759951
\(665\) −2.09642 6.37221i −0.0812957 0.247104i
\(666\) −17.3739 30.0924i −0.673224 1.16606i
\(667\) 18.1865 + 10.5000i 0.704185 + 0.406562i
\(668\) 11.9536 0.462497
\(669\) −7.50000 4.33013i −0.289967 0.167412i
\(670\) −54.2497 48.4862i −2.09585 1.87319i
\(671\) 27.9989i 1.08088i
\(672\) 11.0776 + 6.39564i 0.427327 + 0.246717i
\(673\) −5.05313 + 2.91742i −0.194784 + 0.112458i −0.594220 0.804302i \(-0.702539\pi\)
0.399436 + 0.916761i \(0.369206\pi\)
\(674\) −6.16515 + 3.55945i −0.237473 + 0.137105i
\(675\) 10.0000 22.9129i 0.384900 0.881917i
\(676\) 1.39564 + 36.2599i 0.0536786 + 1.39461i
\(677\) 21.1652i 0.813443i 0.913552 + 0.406721i \(0.133328\pi\)
−0.913552 + 0.406721i \(0.866672\pi\)
\(678\) −18.1488 31.4347i −0.697001 1.20724i
\(679\) 3.87386 + 6.70973i 0.148665 + 0.257496i
\(680\) 11.8273 13.2331i 0.453555 0.507468i
\(681\) 6.10985i 0.234130i
\(682\) 27.9989 48.4955i 1.07213 1.85699i
\(683\) 5.96683 10.3348i 0.228314 0.395452i −0.728994 0.684520i \(-0.760012\pi\)
0.957309 + 0.289068i \(0.0933453\pi\)
\(684\) 9.66930i 0.369715i
\(685\) 0.158970 + 0.142081i 0.00607392 + 0.00542863i
\(686\) 20.8521 + 36.1169i 0.796136 + 1.37895i
\(687\) 2.74110 + 4.74773i 0.104580 + 0.181137i
\(688\) 2.53901i 0.0967990i
\(689\) −1.58258 5.48220i −0.0602913 0.208855i
\(690\) 4.58258 21.9564i 0.174456 0.835867i
\(691\) 30.8739 17.8250i 1.17450 0.678096i 0.219762 0.975554i \(-0.429472\pi\)
0.954735 + 0.297457i \(0.0961386\pi\)
\(692\) −17.9303 + 10.3521i −0.681609 + 0.393527i
\(693\) −7.93725 4.58258i −0.301511 0.174078i
\(694\) 33.5565i 1.27379i
\(695\) −9.58272 8.56466i −0.363493 0.324876i
\(696\) −6.87386 3.96863i −0.260553 0.150430i
\(697\) −12.1244 −0.459243
\(698\) −34.7463 20.0608i −1.31517 0.759312i
\(699\) 10.5826 + 18.3296i 0.400270 + 0.693288i
\(700\) 2.70372 + 24.0216i 0.102191 + 0.907931i
\(701\) −2.83485 −0.107071 −0.0535354 0.998566i \(-0.517049\pi\)
−0.0535354 + 0.998566i \(0.517049\pi\)
\(702\) 27.3613 28.4347i 1.03268 1.07320i
\(703\) 13.7477i 0.518505i
\(704\) −28.8303 + 16.6452i −1.08658 + 0.627339i
\(705\) 6.11847 + 18.5975i 0.230435 + 0.700423i
\(706\) 19.0608 33.0143i 0.717362 1.24251i
\(707\) 15.5885 0.586264
\(708\) 4.70158 8.14337i 0.176696 0.306047i
\(709\) 31.5000 + 18.1865i 1.18301 + 0.683010i 0.956708 0.291048i \(-0.0940040\pi\)
0.226299 + 0.974058i \(0.427337\pi\)
\(710\) 17.0544 + 3.55945i 0.640039 + 0.133584i
\(711\) −6.00000 + 10.3923i −0.225018 + 0.389742i
\(712\) 6.42368 3.70871i 0.240738 0.138990i
\(713\) −22.1552 38.3739i −0.829717 1.43711i
\(714\) 17.3739 0.650201
\(715\) −12.0244 17.6185i −0.449688 0.658896i
\(716\) 0.460985 0.0172278
\(717\) 10.4877 + 18.1652i 0.391669 + 0.678390i
\(718\) −63.2874 + 36.5390i −2.36187 + 1.36362i
\(719\) 15.2477 26.4098i 0.568644 0.984921i −0.428056 0.903752i \(-0.640801\pi\)
0.996700 0.0811686i \(-0.0258652\pi\)
\(720\) −1.63670 + 7.84190i −0.0609962 + 0.292250i
\(721\) 22.7477 + 13.1334i 0.847170 + 0.489114i
\(722\) −17.5112 + 30.3303i −0.651700 + 1.12878i
\(723\) −1.73205 −0.0644157
\(724\) 26.1652 45.3194i 0.972420 1.68428i
\(725\) 2.56275 + 22.7691i 0.0951780 + 0.845623i
\(726\) 7.58258 4.37780i 0.281416 0.162475i
\(727\) 42.7477i 1.58543i 0.609595 + 0.792713i \(0.291332\pi\)
−0.609595 + 0.792713i \(0.708668\pi\)
\(728\) −2.59808 + 10.5000i −0.0962911 + 0.389156i
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) −3.24773 5.62523i −0.120122 0.208057i
\(732\) 25.5815 + 14.7695i 0.945521 + 0.545897i
\(733\) −8.94630 −0.330439 −0.165220 0.986257i \(-0.552833\pi\)
−0.165220 + 0.986257i \(0.552833\pi\)
\(734\) 48.8085 + 28.1796i 1.80156 + 1.04013i
\(735\) 5.96038 6.66888i 0.219852 0.245985i
\(736\) 33.8426i 1.24745i
\(737\) 34.0610 + 19.6652i 1.25465 + 0.724375i
\(738\) −10.0308 + 5.79129i −0.369239 + 0.213180i
\(739\) −42.2477 + 24.3917i −1.55411 + 0.897265i −0.556307 + 0.830977i \(0.687782\pi\)
−0.997801 + 0.0662878i \(0.978884\pi\)
\(740\) 10.1216 48.4955i 0.372077 1.78273i
\(741\) −6.00000 + 1.73205i −0.220416 + 0.0636285i
\(742\) 6.00000i 0.220267i
\(743\) 21.3845 + 37.0390i 0.784521 + 1.35883i 0.929285 + 0.369364i \(0.120424\pi\)
−0.144764 + 0.989466i \(0.546242\pi\)
\(744\) 8.37386 + 14.5040i 0.307001 + 0.531741i
\(745\) 14.5503 16.2798i 0.533080 0.596446i
\(746\) 28.4557i 1.04184i
\(747\) 11.3060 19.5826i 0.413665 0.716489i
\(748\) −16.9213 + 29.3085i −0.618703 + 1.07163i
\(749\) 2.45505i 0.0897056i
\(750\) 22.2456 10.2002i 0.812294 0.372459i
\(751\) 7.87386 + 13.6379i 0.287321 + 0.497655i 0.973169 0.230090i \(-0.0739019\pi\)
−0.685848 + 0.727745i \(0.740569\pi\)
\(752\) −7.84190 13.5826i −0.285965 0.495306i
\(753\) 18.1652i 0.661975i
\(754\) −8.68693 + 35.1078i −0.316359 + 1.27855i
\(755\) −13.5826 2.83485i −0.494321 0.103171i
\(756\) 20.9347 12.0866i 0.761386 0.439587i
\(757\) 15.3700 8.87386i 0.558632 0.322526i −0.193965 0.981009i \(-0.562135\pi\)
0.752596 + 0.658482i \(0.228801\pi\)
\(758\) −39.9425 23.0608i −1.45078 0.837606i
\(759\) 12.1244i 0.440086i
\(760\) −4.47028 + 5.00166i −0.162154 + 0.181429i
\(761\) −35.2913 20.3754i −1.27931 0.738609i −0.302587 0.953122i \(-0.597850\pi\)
−0.976721 + 0.214513i \(0.931184\pi\)
\(762\) −21.3368 −0.772951
\(763\) 4.11165 + 2.37386i 0.148852 + 0.0859396i
\(764\) 10.3521 + 17.9303i 0.374525 + 0.648697i
\(765\) 6.40467 + 19.4674i 0.231561 + 0.703846i
\(766\) 6.20871 0.224330
\(767\) −11.7906 2.91742i −0.425735 0.105342i
\(768\) 2.79129i 0.100722i
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) −7.00959 21.3061i −0.252608 0.767819i
\(771\) −0.0825757 + 0.143025i −0.00297389 + 0.00515093i
\(772\) 2.81655 0.101370
\(773\) −17.3682 + 30.0826i −0.624690 + 1.08200i 0.363911 + 0.931434i \(0.381441\pi\)
−0.988601 + 0.150561i \(0.951892\pi\)
\(774\) −5.37386 3.10260i −0.193160 0.111521i
\(775\) 19.3386 44.3103i 0.694663 1.59167i