Properties

Label 507.2.e.i.22.1
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.i.484.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34601 + 2.33136i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.62349 - 4.54402i) q^{4} -1.04892 q^{5} +(1.34601 + 2.33136i) q^{6} +(-0.277479 - 0.480608i) q^{7} +8.74094 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.34601 + 2.33136i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.62349 - 4.54402i) q^{4} -1.04892 q^{5} +(1.34601 + 2.33136i) q^{6} +(-0.277479 - 0.480608i) q^{7} +8.74094 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.41185 - 2.44540i) q^{10} +(-1.45593 + 2.52174i) q^{11} -5.24698 q^{12} +1.49396 q^{14} +(-0.524459 + 0.908389i) q^{15} +(-6.51842 + 11.2902i) q^{16} +(2.42543 + 4.20096i) q^{17} +2.69202 q^{18} +(0.376510 + 0.652135i) q^{19} +(2.75182 + 4.76630i) q^{20} -0.554958 q^{21} +(-3.91939 - 6.78858i) q^{22} +(-2.88135 + 4.99065i) q^{23} +(4.37047 - 7.56988i) q^{24} -3.89977 q^{25} -1.00000 q^{27} +(-1.45593 + 2.52174i) q^{28} +(0.955927 - 1.65571i) q^{29} +(-1.41185 - 2.44540i) q^{30} -9.51573 q^{31} +(-8.80678 - 15.2538i) q^{32} +(1.45593 + 2.52174i) q^{33} -13.0586 q^{34} +(0.291053 + 0.504118i) q^{35} +(-2.62349 + 4.54402i) q^{36} +(-2.87651 + 4.98226i) q^{37} -2.02715 q^{38} -9.16852 q^{40} +(-2.45593 + 4.25379i) q^{41} +(0.746980 - 1.29381i) q^{42} +(5.54892 + 9.61101i) q^{43} +15.2784 q^{44} +(0.524459 + 0.908389i) q^{45} +(-7.75667 - 13.4349i) q^{46} +0.753020 q^{47} +(6.51842 + 11.2902i) q^{48} +(3.34601 - 5.79546i) q^{49} +(5.24914 - 9.09177i) q^{50} +4.85086 q^{51} -7.58211 q^{53} +(1.34601 - 2.33136i) q^{54} +(1.52715 - 2.64510i) q^{55} +(-2.42543 - 4.20096i) q^{56} +0.753020 q^{57} +(2.57338 + 4.45722i) q^{58} +(-2.04892 - 3.54883i) q^{59} +5.50365 q^{60} +(1.71164 + 2.96464i) q^{61} +(12.8083 - 22.1846i) q^{62} +(-0.277479 + 0.480608i) q^{63} +21.3424 q^{64} -7.83877 q^{66} +(0.936313 - 1.62174i) q^{67} +(12.7262 - 22.0424i) q^{68} +(2.88135 + 4.99065i) q^{69} -1.56704 q^{70} +(5.25182 + 9.09643i) q^{71} +(-4.37047 - 7.56988i) q^{72} +10.4765 q^{73} +(-7.74363 - 13.4124i) q^{74} +(-1.94989 + 3.37730i) q^{75} +(1.97554 - 3.42174i) q^{76} +1.61596 q^{77} +1.33513 q^{79} +(6.83728 - 11.8425i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.61141 - 11.4513i) q^{82} +2.64310 q^{83} +(1.45593 + 2.52174i) q^{84} +(-2.54407 - 4.40646i) q^{85} -29.8756 q^{86} +(-0.955927 - 1.65571i) q^{87} +(-12.7262 + 22.0424i) q^{88} +(-4.96346 + 8.59696i) q^{89} -2.82371 q^{90} +30.2368 q^{92} +(-4.75786 + 8.24086i) q^{93} +(-1.01357 + 1.75556i) q^{94} +(-0.394928 - 0.684035i) q^{95} -17.6136 q^{96} +(-8.53684 - 14.7862i) q^{97} +(9.00753 + 15.6015i) q^{98} +2.91185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} + 3q^{3} - 11q^{4} + 12q^{5} + 3q^{6} - 2q^{7} + 24q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} + 3q^{3} - 11q^{4} + 12q^{5} + 3q^{6} - 2q^{7} + 24q^{8} - 3q^{9} + q^{10} - 5q^{11} - 22q^{12} - 10q^{14} + 6q^{15} - 11q^{16} + q^{17} + 6q^{18} + 7q^{19} - 15q^{20} - 4q^{21} + 9q^{22} + 12q^{24} + 22q^{25} - 6q^{27} - 5q^{28} + 2q^{29} - q^{30} - 32q^{31} - 22q^{32} + 5q^{33} - 16q^{34} - 4q^{35} - 11q^{36} - 22q^{37} + 6q^{40} - 11q^{41} - 5q^{42} + 15q^{43} + 32q^{44} - 6q^{45} + 7q^{46} + 14q^{47} + 11q^{48} + 15q^{49} + 3q^{50} + 2q^{51} - 34q^{53} + 3q^{54} - 3q^{55} - q^{56} + 14q^{57} - 12q^{58} + 6q^{59} - 30q^{60} + 13q^{61} + 2q^{62} - 2q^{63} + 18q^{66} - 11q^{67} + 13q^{68} - 48q^{70} - 12q^{72} + 12q^{73} - 15q^{74} + 11q^{75} + 21q^{76} + 30q^{77} + 6q^{79} + 20q^{80} - 3q^{81} + 3q^{82} + 24q^{83} + 5q^{84} - 19q^{85} - 58q^{86} - 2q^{87} - 13q^{88} - q^{89} - 2q^{90} + 14q^{92} - 16q^{93} + 21q^{95} - 44q^{96} + 5q^{97} + 29q^{98} + 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34601 + 2.33136i −0.951773 + 1.64852i −0.210188 + 0.977661i \(0.567408\pi\)
−0.741585 + 0.670859i \(0.765926\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −2.62349 4.54402i −1.31174 2.27201i
\(5\) −1.04892 −0.469090 −0.234545 0.972105i \(-0.575360\pi\)
−0.234545 + 0.972105i \(0.575360\pi\)
\(6\) 1.34601 + 2.33136i 0.549507 + 0.951773i
\(7\) −0.277479 0.480608i −0.104877 0.181653i 0.808811 0.588069i \(-0.200112\pi\)
−0.913688 + 0.406416i \(0.866778\pi\)
\(8\) 8.74094 3.09039
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.41185 2.44540i 0.446467 0.773304i
\(11\) −1.45593 + 2.52174i −0.438979 + 0.760333i −0.997611 0.0690822i \(-0.977993\pi\)
0.558632 + 0.829415i \(0.311326\pi\)
\(12\) −5.24698 −1.51467
\(13\) 0 0
\(14\) 1.49396 0.399277
\(15\) −0.524459 + 0.908389i −0.135415 + 0.234545i
\(16\) −6.51842 + 11.2902i −1.62960 + 2.82256i
\(17\) 2.42543 + 4.20096i 0.588253 + 1.01888i 0.994461 + 0.105103i \(0.0335172\pi\)
−0.406209 + 0.913780i \(0.633149\pi\)
\(18\) 2.69202 0.634516
\(19\) 0.376510 + 0.652135i 0.0863774 + 0.149610i 0.905977 0.423326i \(-0.139138\pi\)
−0.819600 + 0.572936i \(0.805804\pi\)
\(20\) 2.75182 + 4.76630i 0.615327 + 1.06578i
\(21\) −0.554958 −0.121102
\(22\) −3.91939 6.78858i −0.835616 1.44733i
\(23\) −2.88135 + 4.99065i −0.600804 + 1.04062i 0.391896 + 0.920010i \(0.371819\pi\)
−0.992700 + 0.120613i \(0.961514\pi\)
\(24\) 4.37047 7.56988i 0.892118 1.54519i
\(25\) −3.89977 −0.779954
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.45593 + 2.52174i −0.275144 + 0.476564i
\(29\) 0.955927 1.65571i 0.177511 0.307458i −0.763516 0.645789i \(-0.776529\pi\)
0.941027 + 0.338330i \(0.109862\pi\)
\(30\) −1.41185 2.44540i −0.257768 0.446467i
\(31\) −9.51573 −1.70908 −0.854538 0.519389i \(-0.826159\pi\)
−0.854538 + 0.519389i \(0.826159\pi\)
\(32\) −8.80678 15.2538i −1.55683 2.69652i
\(33\) 1.45593 + 2.52174i 0.253444 + 0.438979i
\(34\) −13.0586 −2.23953
\(35\) 0.291053 + 0.504118i 0.0491969 + 0.0852115i
\(36\) −2.62349 + 4.54402i −0.437248 + 0.757336i
\(37\) −2.87651 + 4.98226i −0.472895 + 0.819079i −0.999519 0.0310199i \(-0.990124\pi\)
0.526623 + 0.850099i \(0.323458\pi\)
\(38\) −2.02715 −0.328847
\(39\) 0 0
\(40\) −9.16852 −1.44967
\(41\) −2.45593 + 4.25379i −0.383551 + 0.664330i −0.991567 0.129595i \(-0.958632\pi\)
0.608016 + 0.793925i \(0.291966\pi\)
\(42\) 0.746980 1.29381i 0.115261 0.199639i
\(43\) 5.54892 + 9.61101i 0.846202 + 1.46566i 0.884573 + 0.466401i \(0.154450\pi\)
−0.0383713 + 0.999264i \(0.512217\pi\)
\(44\) 15.2784 2.30331
\(45\) 0.524459 + 0.908389i 0.0781817 + 0.135415i
\(46\) −7.75667 13.4349i −1.14366 1.98087i
\(47\) 0.753020 0.109839 0.0549197 0.998491i \(-0.482510\pi\)
0.0549197 + 0.998491i \(0.482510\pi\)
\(48\) 6.51842 + 11.2902i 0.940853 + 1.62960i
\(49\) 3.34601 5.79546i 0.478002 0.827923i
\(50\) 5.24914 9.09177i 0.742340 1.28577i
\(51\) 4.85086 0.679256
\(52\) 0 0
\(53\) −7.58211 −1.04148 −0.520741 0.853715i \(-0.674344\pi\)
−0.520741 + 0.853715i \(0.674344\pi\)
\(54\) 1.34601 2.33136i 0.183169 0.317258i
\(55\) 1.52715 2.64510i 0.205920 0.356665i
\(56\) −2.42543 4.20096i −0.324111 0.561377i
\(57\) 0.753020 0.0997400
\(58\) 2.57338 + 4.45722i 0.337901 + 0.585261i
\(59\) −2.04892 3.54883i −0.266746 0.462018i 0.701273 0.712892i \(-0.252615\pi\)
−0.968020 + 0.250874i \(0.919282\pi\)
\(60\) 5.50365 0.710518
\(61\) 1.71164 + 2.96464i 0.219153 + 0.379583i 0.954549 0.298054i \(-0.0963374\pi\)
−0.735397 + 0.677637i \(0.763004\pi\)
\(62\) 12.8083 22.1846i 1.62665 2.81744i
\(63\) −0.277479 + 0.480608i −0.0349591 + 0.0605509i
\(64\) 21.3424 2.66780
\(65\) 0 0
\(66\) −7.83877 −0.964886
\(67\) 0.936313 1.62174i 0.114389 0.198127i −0.803146 0.595782i \(-0.796842\pi\)
0.917535 + 0.397654i \(0.130176\pi\)
\(68\) 12.7262 22.0424i 1.54327 2.67303i
\(69\) 2.88135 + 4.99065i 0.346874 + 0.600804i
\(70\) −1.56704 −0.187297
\(71\) 5.25182 + 9.09643i 0.623277 + 1.07955i 0.988871 + 0.148773i \(0.0475324\pi\)
−0.365595 + 0.930774i \(0.619134\pi\)
\(72\) −4.37047 7.56988i −0.515065 0.892118i
\(73\) 10.4765 1.22618 0.613091 0.790012i \(-0.289926\pi\)
0.613091 + 0.790012i \(0.289926\pi\)
\(74\) −7.74363 13.4124i −0.900178 1.55915i
\(75\) −1.94989 + 3.37730i −0.225153 + 0.389977i
\(76\) 1.97554 3.42174i 0.226610 0.392500i
\(77\) 1.61596 0.184155
\(78\) 0 0
\(79\) 1.33513 0.150213 0.0751067 0.997176i \(-0.476070\pi\)
0.0751067 + 0.997176i \(0.476070\pi\)
\(80\) 6.83728 11.8425i 0.764431 1.32403i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.61141 11.4513i −0.730108 1.26458i
\(83\) 2.64310 0.290118 0.145059 0.989423i \(-0.453663\pi\)
0.145059 + 0.989423i \(0.453663\pi\)
\(84\) 1.45593 + 2.52174i 0.158855 + 0.275144i
\(85\) −2.54407 4.40646i −0.275943 0.477948i
\(86\) −29.8756 −3.22157
\(87\) −0.955927 1.65571i −0.102486 0.177511i
\(88\) −12.7262 + 22.0424i −1.35661 + 2.34972i
\(89\) −4.96346 + 8.59696i −0.526126 + 0.911276i 0.473411 + 0.880842i \(0.343023\pi\)
−0.999537 + 0.0304348i \(0.990311\pi\)
\(90\) −2.82371 −0.297645
\(91\) 0 0
\(92\) 30.2368 3.15241
\(93\) −4.75786 + 8.24086i −0.493368 + 0.854538i
\(94\) −1.01357 + 1.75556i −0.104542 + 0.181072i
\(95\) −0.394928 0.684035i −0.0405188 0.0701806i
\(96\) −17.6136 −1.79768
\(97\) −8.53684 14.7862i −0.866784 1.50131i −0.865264 0.501316i \(-0.832850\pi\)
−0.00151988 0.999999i \(-0.500484\pi\)
\(98\) 9.00753 + 15.6015i 0.909898 + 1.57599i
\(99\) 2.91185 0.292652
\(100\) 10.2310 + 17.7206i 1.02310 + 1.77206i
\(101\) −3.66152 + 6.34194i −0.364335 + 0.631047i −0.988669 0.150111i \(-0.952037\pi\)
0.624334 + 0.781157i \(0.285370\pi\)
\(102\) −6.52930 + 11.3091i −0.646497 + 1.11977i
\(103\) −4.21983 −0.415792 −0.207896 0.978151i \(-0.566662\pi\)
−0.207896 + 0.978151i \(0.566662\pi\)
\(104\) 0 0
\(105\) 0.582105 0.0568077
\(106\) 10.2056 17.6766i 0.991255 1.71690i
\(107\) −3.19687 + 5.53713i −0.309053 + 0.535295i −0.978155 0.207875i \(-0.933345\pi\)
0.669103 + 0.743170i \(0.266679\pi\)
\(108\) 2.62349 + 4.54402i 0.252445 + 0.437248i
\(109\) −3.46011 −0.331418 −0.165709 0.986175i \(-0.552991\pi\)
−0.165709 + 0.986175i \(0.552991\pi\)
\(110\) 4.11111 + 7.12066i 0.391979 + 0.678928i
\(111\) 2.87651 + 4.98226i 0.273026 + 0.472895i
\(112\) 7.23490 0.683634
\(113\) −4.67845 8.10331i −0.440111 0.762295i 0.557586 0.830119i \(-0.311728\pi\)
−0.997697 + 0.0678240i \(0.978394\pi\)
\(114\) −1.01357 + 1.75556i −0.0949299 + 0.164423i
\(115\) 3.02230 5.23478i 0.281831 0.488146i
\(116\) −10.0315 −0.931398
\(117\) 0 0
\(118\) 11.0315 1.01553
\(119\) 1.34601 2.33136i 0.123389 0.213715i
\(120\) −4.58426 + 7.94017i −0.418484 + 0.724835i
\(121\) 1.26055 + 2.18334i 0.114596 + 0.198486i
\(122\) −9.21552 −0.834334
\(123\) 2.45593 + 4.25379i 0.221443 + 0.383551i
\(124\) 24.9644 + 43.2396i 2.24187 + 3.88303i
\(125\) 9.33513 0.834959
\(126\) −0.746980 1.29381i −0.0665462 0.115261i
\(127\) 2.24094 3.88142i 0.198851 0.344420i −0.749305 0.662225i \(-0.769612\pi\)
0.948156 + 0.317805i \(0.102946\pi\)
\(128\) −11.1136 + 19.2493i −0.982310 + 1.70141i
\(129\) 11.0978 0.977110
\(130\) 0 0
\(131\) −9.21744 −0.805331 −0.402666 0.915347i \(-0.631916\pi\)
−0.402666 + 0.915347i \(0.631916\pi\)
\(132\) 7.63922 13.2315i 0.664909 1.15166i
\(133\) 0.208947 0.361908i 0.0181180 0.0313814i
\(134\) 2.52057 + 4.36576i 0.217744 + 0.377144i
\(135\) 1.04892 0.0902764
\(136\) 21.2005 + 36.7204i 1.81793 + 3.14875i
\(137\) 3.73490 + 6.46903i 0.319094 + 0.552687i 0.980299 0.197518i \(-0.0632881\pi\)
−0.661205 + 0.750205i \(0.729955\pi\)
\(138\) −15.5133 −1.32058
\(139\) 8.99880 + 15.5864i 0.763269 + 1.32202i 0.941157 + 0.337969i \(0.109740\pi\)
−0.177889 + 0.984051i \(0.556927\pi\)
\(140\) 1.52715 2.64510i 0.129067 0.223551i
\(141\) 0.376510 0.652135i 0.0317079 0.0549197i
\(142\) −28.2760 −2.37287
\(143\) 0 0
\(144\) 13.0368 1.08640
\(145\) −1.00269 + 1.73671i −0.0832687 + 0.144226i
\(146\) −14.1015 + 24.4245i −1.16705 + 2.02138i
\(147\) −3.34601 5.79546i −0.275974 0.478002i
\(148\) 30.1860 2.48127
\(149\) −7.66756 13.2806i −0.628151 1.08799i −0.987922 0.154949i \(-0.950479\pi\)
0.359771 0.933041i \(-0.382855\pi\)
\(150\) −5.24914 9.09177i −0.428590 0.742340i
\(151\) 2.53079 0.205953 0.102977 0.994684i \(-0.467163\pi\)
0.102977 + 0.994684i \(0.467163\pi\)
\(152\) 3.29105 + 5.70027i 0.266940 + 0.462353i
\(153\) 2.42543 4.20096i 0.196084 0.339628i
\(154\) −2.17510 + 3.76738i −0.175274 + 0.303584i
\(155\) 9.98121 0.801710
\(156\) 0 0
\(157\) 17.2392 1.37584 0.687919 0.725787i \(-0.258524\pi\)
0.687919 + 0.725787i \(0.258524\pi\)
\(158\) −1.79709 + 3.11266i −0.142969 + 0.247630i
\(159\) −3.79105 + 6.56630i −0.300650 + 0.520741i
\(160\) 9.23759 + 16.0000i 0.730295 + 1.26491i
\(161\) 3.19806 0.252043
\(162\) −1.34601 2.33136i −0.105753 0.183169i
\(163\) −7.85354 13.6027i −0.615137 1.06545i −0.990360 0.138514i \(-0.955767\pi\)
0.375223 0.926934i \(-0.377566\pi\)
\(164\) 25.7724 2.01249
\(165\) −1.52715 2.64510i −0.118888 0.205920i
\(166\) −3.55765 + 6.16202i −0.276127 + 0.478266i
\(167\) −2.69806 + 4.67318i −0.208782 + 0.361622i −0.951331 0.308170i \(-0.900283\pi\)
0.742549 + 0.669792i \(0.233617\pi\)
\(168\) −4.85086 −0.374252
\(169\) 0 0
\(170\) 13.6974 1.05054
\(171\) 0.376510 0.652135i 0.0287925 0.0498700i
\(172\) 29.1151 50.4288i 2.22000 3.84516i
\(173\) −11.9710 20.7344i −0.910138 1.57640i −0.813868 0.581049i \(-0.802642\pi\)
−0.0962694 0.995355i \(-0.530691\pi\)
\(174\) 5.14675 0.390174
\(175\) 1.08211 + 1.87426i 0.0817995 + 0.141681i
\(176\) −18.9807 32.8755i −1.43072 2.47808i
\(177\) −4.09783 −0.308012
\(178\) −13.3617 23.1432i −1.00150 1.73466i
\(179\) −9.20440 + 15.9425i −0.687969 + 1.19160i 0.284525 + 0.958669i \(0.408164\pi\)
−0.972494 + 0.232929i \(0.925169\pi\)
\(180\) 2.75182 4.76630i 0.205109 0.355259i
\(181\) −3.63342 −0.270070 −0.135035 0.990841i \(-0.543115\pi\)
−0.135035 + 0.990841i \(0.543115\pi\)
\(182\) 0 0
\(183\) 3.42327 0.253056
\(184\) −25.1857 + 43.6230i −1.85672 + 3.21593i
\(185\) 3.01722 5.22598i 0.221831 0.384222i
\(186\) −12.8083 22.1846i −0.939148 1.62665i
\(187\) −14.1250 −1.03292
\(188\) −1.97554 3.42174i −0.144081 0.249556i
\(189\) 0.277479 + 0.480608i 0.0201836 + 0.0349591i
\(190\) 2.12631 0.154259
\(191\) 10.5891 + 18.3409i 0.766201 + 1.32710i 0.939609 + 0.342249i \(0.111189\pi\)
−0.173409 + 0.984850i \(0.555478\pi\)
\(192\) 10.6712 18.4831i 0.770128 1.33390i
\(193\) 8.80559 15.2517i 0.633840 1.09784i −0.352920 0.935654i \(-0.614811\pi\)
0.986760 0.162189i \(-0.0518555\pi\)
\(194\) 45.9627 3.29993
\(195\) 0 0
\(196\) −35.1129 −2.50806
\(197\) 2.33124 4.03783i 0.166094 0.287683i −0.770949 0.636897i \(-0.780218\pi\)
0.937043 + 0.349213i \(0.113551\pi\)
\(198\) −3.91939 + 6.78858i −0.278539 + 0.482443i
\(199\) −7.51842 13.0223i −0.532967 0.923125i −0.999259 0.0384944i \(-0.987744\pi\)
0.466292 0.884631i \(-0.345590\pi\)
\(200\) −34.0877 −2.41036
\(201\) −0.936313 1.62174i −0.0660424 0.114389i
\(202\) −9.85690 17.0726i −0.693529 1.20123i
\(203\) −1.06100 −0.0744675
\(204\) −12.7262 22.0424i −0.891010 1.54327i
\(205\) 2.57606 4.46187i 0.179920 0.311631i
\(206\) 5.67994 9.83794i 0.395740 0.685442i
\(207\) 5.76271 0.400536
\(208\) 0 0
\(209\) −2.19269 −0.151671
\(210\) −0.783520 + 1.35710i −0.0540680 + 0.0936485i
\(211\) 0.230054 0.398465i 0.0158375 0.0274314i −0.857998 0.513653i \(-0.828292\pi\)
0.873836 + 0.486222i \(0.161625\pi\)
\(212\) 19.8916 + 34.4532i 1.36616 + 2.36626i
\(213\) 10.5036 0.719698
\(214\) −8.60603 14.9061i −0.588296 1.01896i
\(215\) −5.82036 10.0812i −0.396945 0.687529i
\(216\) −8.74094 −0.594746
\(217\) 2.64042 + 4.57333i 0.179243 + 0.310458i
\(218\) 4.65734 8.06675i 0.315435 0.546349i
\(219\) 5.23825 9.07292i 0.353968 0.613091i
\(220\) −16.0258 −1.08046
\(221\) 0 0
\(222\) −15.4873 −1.03944
\(223\) 8.17510 14.1597i 0.547445 0.948202i −0.451004 0.892522i \(-0.648934\pi\)
0.998449 0.0556803i \(-0.0177328\pi\)
\(224\) −4.88740 + 8.46522i −0.326553 + 0.565606i
\(225\) 1.94989 + 3.37730i 0.129992 + 0.225153i
\(226\) 25.1890 1.67555
\(227\) −3.28017 5.68142i −0.217712 0.377089i 0.736396 0.676551i \(-0.236526\pi\)
−0.954108 + 0.299462i \(0.903193\pi\)
\(228\) −1.97554 3.42174i −0.130833 0.226610i
\(229\) −3.95539 −0.261380 −0.130690 0.991423i \(-0.541719\pi\)
−0.130690 + 0.991423i \(0.541719\pi\)
\(230\) 8.13610 + 14.0921i 0.536479 + 0.929209i
\(231\) 0.807979 1.39946i 0.0531611 0.0920777i
\(232\) 8.35570 14.4725i 0.548579 0.950166i
\(233\) 8.35690 0.547478 0.273739 0.961804i \(-0.411739\pi\)
0.273739 + 0.961804i \(0.411739\pi\)
\(234\) 0 0
\(235\) −0.789856 −0.0515245
\(236\) −10.7506 + 18.6206i −0.699806 + 1.21210i
\(237\) 0.667563 1.15625i 0.0433629 0.0751067i
\(238\) 3.62349 + 6.27607i 0.234876 + 0.406817i
\(239\) 20.1008 1.30021 0.650107 0.759843i \(-0.274724\pi\)
0.650107 + 0.759843i \(0.274724\pi\)
\(240\) −6.83728 11.8425i −0.441345 0.764431i
\(241\) 9.50634 + 16.4655i 0.612357 + 1.06063i 0.990842 + 0.135026i \(0.0431118\pi\)
−0.378485 + 0.925607i \(0.623555\pi\)
\(242\) −6.78687 −0.436277
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 8.98092 15.5554i 0.574944 0.995833i
\(245\) −3.50969 + 6.07896i −0.224226 + 0.388370i
\(246\) −13.2228 −0.843056
\(247\) 0 0
\(248\) −83.1764 −5.28171
\(249\) 1.32155 2.28900i 0.0837500 0.145059i
\(250\) −12.5652 + 21.7635i −0.794692 + 1.37645i
\(251\) 0.381887 + 0.661448i 0.0241045 + 0.0417502i 0.877826 0.478980i \(-0.158993\pi\)
−0.853722 + 0.520730i \(0.825660\pi\)
\(252\) 2.91185 0.183430
\(253\) −8.39008 14.5321i −0.527480 0.913622i
\(254\) 6.03266 + 10.4489i 0.378522 + 0.655620i
\(255\) −5.08815 −0.318632
\(256\) −8.57553 14.8533i −0.535971 0.928329i
\(257\) 6.54556 11.3373i 0.408301 0.707198i −0.586398 0.810023i \(-0.699455\pi\)
0.994700 + 0.102825i \(0.0327880\pi\)
\(258\) −14.9378 + 25.8730i −0.929987 + 1.61078i
\(259\) 3.19269 0.198384
\(260\) 0 0
\(261\) −1.91185 −0.118341
\(262\) 12.4068 21.4892i 0.766493 1.32760i
\(263\) −9.18867 + 15.9152i −0.566598 + 0.981376i 0.430301 + 0.902685i \(0.358407\pi\)
−0.996899 + 0.0786906i \(0.974926\pi\)
\(264\) 12.7262 + 22.0424i 0.783242 + 1.35661i
\(265\) 7.95300 0.488549
\(266\) 0.562491 + 0.974263i 0.0344885 + 0.0597359i
\(267\) 4.96346 + 8.59696i 0.303759 + 0.526126i
\(268\) −9.82563 −0.600196
\(269\) −11.8312 20.4923i −0.721363 1.24944i −0.960453 0.278441i \(-0.910182\pi\)
0.239090 0.970997i \(-0.423151\pi\)
\(270\) −1.41185 + 2.44540i −0.0859227 + 0.148822i
\(271\) 9.87651 17.1066i 0.599955 1.03915i −0.392872 0.919593i \(-0.628518\pi\)
0.992827 0.119560i \(-0.0381483\pi\)
\(272\) −63.2398 −3.83448
\(273\) 0 0
\(274\) −20.1089 −1.21482
\(275\) 5.67778 9.83421i 0.342383 0.593025i
\(276\) 15.1184 26.1859i 0.910021 1.57620i
\(277\) −0.888887 1.53960i −0.0534081 0.0925055i 0.838085 0.545539i \(-0.183675\pi\)
−0.891493 + 0.453034i \(0.850342\pi\)
\(278\) −48.4499 −2.90583
\(279\) 4.75786 + 8.24086i 0.284846 + 0.493368i
\(280\) 2.54407 + 4.40646i 0.152037 + 0.263337i
\(281\) 1.62133 0.0967207 0.0483603 0.998830i \(-0.484600\pi\)
0.0483603 + 0.998830i \(0.484600\pi\)
\(282\) 1.01357 + 1.75556i 0.0603574 + 0.104542i
\(283\) −2.49180 + 4.31593i −0.148122 + 0.256555i −0.930533 0.366207i \(-0.880656\pi\)
0.782411 + 0.622762i \(0.213990\pi\)
\(284\) 27.5562 47.7288i 1.63516 2.83218i
\(285\) −0.789856 −0.0467870
\(286\) 0 0
\(287\) 2.72587 0.160903
\(288\) −8.80678 + 15.2538i −0.518945 + 0.898838i
\(289\) −3.26540 + 5.65583i −0.192082 + 0.332696i
\(290\) −2.69926 4.67525i −0.158506 0.274540i
\(291\) −17.0737 −1.00088
\(292\) −27.4850 47.6054i −1.60844 2.78590i
\(293\) 0.0358763 + 0.0621395i 0.00209591 + 0.00363023i 0.867071 0.498184i \(-0.166000\pi\)
−0.864976 + 0.501814i \(0.832666\pi\)
\(294\) 18.0151 1.05066
\(295\) 2.14914 + 3.72243i 0.125128 + 0.216728i
\(296\) −25.1434 + 43.5496i −1.46143 + 2.53127i
\(297\) 1.45593 2.52174i 0.0844815 0.146326i
\(298\) 41.2825 2.39143
\(299\) 0 0
\(300\) 20.4620 1.18138
\(301\) 3.07942 5.33371i 0.177495 0.307430i
\(302\) −3.40648 + 5.90019i −0.196021 + 0.339518i
\(303\) 3.66152 + 6.34194i 0.210349 + 0.364335i
\(304\) −9.81700 −0.563044
\(305\) −1.79536 3.10966i −0.102802 0.178059i
\(306\) 6.52930 + 11.3091i 0.373255 + 0.646497i
\(307\) −5.19806 −0.296669 −0.148335 0.988937i \(-0.547391\pi\)
−0.148335 + 0.988937i \(0.547391\pi\)
\(308\) −4.23945 7.34294i −0.241565 0.418403i
\(309\) −2.10992 + 3.65448i −0.120029 + 0.207896i
\(310\) −13.4348 + 23.2698i −0.763047 + 1.32164i
\(311\) −22.5429 −1.27829 −0.639145 0.769087i \(-0.720711\pi\)
−0.639145 + 0.769087i \(0.720711\pi\)
\(312\) 0 0
\(313\) 22.6612 1.28088 0.640442 0.768006i \(-0.278751\pi\)
0.640442 + 0.768006i \(0.278751\pi\)
\(314\) −23.2042 + 40.1908i −1.30949 + 2.26810i
\(315\) 0.291053 0.504118i 0.0163990 0.0284038i
\(316\) −3.50269 6.06683i −0.197042 0.341286i
\(317\) 26.3424 1.47954 0.739769 0.672861i \(-0.234935\pi\)
0.739769 + 0.672861i \(0.234935\pi\)
\(318\) −10.2056 17.6766i −0.572301 0.991255i
\(319\) 2.78352 + 4.82120i 0.155847 + 0.269935i
\(320\) −22.3864 −1.25144
\(321\) 3.19687 + 5.53713i 0.178432 + 0.309053i
\(322\) −4.30463 + 7.45583i −0.239887 + 0.415497i
\(323\) −1.82640 + 3.16341i −0.101623 + 0.176017i
\(324\) 5.24698 0.291499
\(325\) 0 0
\(326\) 42.2838 2.34188
\(327\) −1.73005 + 2.99654i −0.0956722 + 0.165709i
\(328\) −21.4671 + 37.1821i −1.18532 + 2.05304i
\(329\) −0.208947 0.361908i −0.0115196 0.0199526i
\(330\) 8.22223 0.452619
\(331\) 5.61476 + 9.72505i 0.308615 + 0.534537i 0.978060 0.208325i \(-0.0668011\pi\)
−0.669445 + 0.742862i \(0.733468\pi\)
\(332\) −6.93416 12.0103i −0.380561 0.659151i
\(333\) 5.75302 0.315264
\(334\) −7.26324 12.5803i −0.397427 0.688364i
\(335\) −0.982115 + 1.70107i −0.0536587 + 0.0929395i
\(336\) 3.61745 6.26561i 0.197348 0.341817i
\(337\) 2.30798 0.125724 0.0628618 0.998022i \(-0.479977\pi\)
0.0628618 + 0.998022i \(0.479977\pi\)
\(338\) 0 0
\(339\) −9.35690 −0.508197
\(340\) −13.3487 + 23.1206i −0.723935 + 1.25389i
\(341\) 13.8542 23.9962i 0.750247 1.29947i
\(342\) 1.01357 + 1.75556i 0.0548078 + 0.0949299i
\(343\) −7.59850 −0.410280
\(344\) 48.5027 + 84.0092i 2.61509 + 4.52947i
\(345\) −3.02230 5.23478i −0.162715 0.281831i
\(346\) 64.4523 3.46498
\(347\) 4.56853 + 7.91293i 0.245252 + 0.424788i 0.962202 0.272336i \(-0.0877961\pi\)
−0.716951 + 0.697124i \(0.754463\pi\)
\(348\) −5.01573 + 8.68750i −0.268871 + 0.465699i
\(349\) −11.9879 + 20.7637i −0.641699 + 1.11145i 0.343355 + 0.939206i \(0.388437\pi\)
−0.985053 + 0.172249i \(0.944897\pi\)
\(350\) −5.82610 −0.311418
\(351\) 0 0
\(352\) 51.2881 2.73367
\(353\) 13.5620 23.4900i 0.721830 1.25025i −0.238435 0.971158i \(-0.576634\pi\)
0.960265 0.279088i \(-0.0900322\pi\)
\(354\) 5.51573 9.55352i 0.293158 0.507764i
\(355\) −5.50873 9.54140i −0.292373 0.506405i
\(356\) 52.0863 2.76057
\(357\) −1.34601 2.33136i −0.0712384 0.123389i
\(358\) −24.7784 42.9175i −1.30958 2.26826i
\(359\) −26.0790 −1.37640 −0.688200 0.725521i \(-0.741599\pi\)
−0.688200 + 0.725521i \(0.741599\pi\)
\(360\) 4.58426 + 7.94017i 0.241612 + 0.418484i
\(361\) 9.21648 15.9634i 0.485078 0.840180i
\(362\) 4.89062 8.47080i 0.257045 0.445215i
\(363\) 2.52111 0.132324
\(364\) 0 0
\(365\) −10.9890 −0.575190
\(366\) −4.60776 + 7.98088i −0.240851 + 0.417167i
\(367\) −4.78717 + 8.29162i −0.249888 + 0.432819i −0.963495 0.267728i \(-0.913727\pi\)
0.713606 + 0.700547i \(0.247061\pi\)
\(368\) −37.5637 65.0623i −1.95815 3.39161i
\(369\) 4.91185 0.255701
\(370\) 8.12242 + 14.0685i 0.422265 + 0.731384i
\(371\) 2.10388 + 3.64402i 0.109228 + 0.189188i
\(372\) 49.9288 2.58869
\(373\) −14.0749 24.3784i −0.728769 1.26227i −0.957404 0.288753i \(-0.906759\pi\)
0.228635 0.973512i \(-0.426574\pi\)
\(374\) 19.0124 32.9304i 0.983107 1.70279i
\(375\) 4.66756 8.08446i 0.241032 0.417480i
\(376\) 6.58211 0.339446
\(377\) 0 0
\(378\) −1.49396 −0.0768410
\(379\) −8.02326 + 13.8967i −0.412127 + 0.713825i −0.995122 0.0986504i \(-0.968547\pi\)
0.582995 + 0.812476i \(0.301881\pi\)
\(380\) −2.07218 + 3.58912i −0.106301 + 0.184118i
\(381\) −2.24094 3.88142i −0.114807 0.198851i
\(382\) −57.0122 −2.91700
\(383\) 12.3083 + 21.3186i 0.628923 + 1.08933i 0.987768 + 0.155930i \(0.0498374\pi\)
−0.358845 + 0.933397i \(0.616829\pi\)
\(384\) 11.1136 + 19.2493i 0.567137 + 0.982310i
\(385\) −1.69501 −0.0863855
\(386\) 23.7048 + 41.0580i 1.20654 + 2.08980i
\(387\) 5.54892 9.61101i 0.282067 0.488555i
\(388\) −44.7926 + 77.5831i −2.27400 + 3.93868i
\(389\) −17.2198 −0.873080 −0.436540 0.899685i \(-0.643796\pi\)
−0.436540 + 0.899685i \(0.643796\pi\)
\(390\) 0 0
\(391\) −27.9541 −1.41370
\(392\) 29.2473 50.6578i 1.47721 2.55860i
\(393\) −4.60872 + 7.98254i −0.232479 + 0.402666i
\(394\) 6.27575 + 10.8699i 0.316168 + 0.547619i
\(395\) −1.40044 −0.0704636
\(396\) −7.63922 13.2315i −0.383885 0.664909i
\(397\) 1.01961 + 1.76602i 0.0511730 + 0.0886342i 0.890477 0.455028i \(-0.150371\pi\)
−0.839304 + 0.543662i \(0.817037\pi\)
\(398\) 40.4795 2.02905
\(399\) −0.208947 0.361908i −0.0104605 0.0181180i
\(400\) 25.4203 44.0293i 1.27102 2.20147i
\(401\) 0.730718 1.26564i 0.0364903 0.0632031i −0.847203 0.531269i \(-0.821716\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(402\) 5.04115 0.251430
\(403\) 0 0
\(404\) 38.4239 1.91166
\(405\) 0.524459 0.908389i 0.0260606 0.0451382i
\(406\) 1.42812 2.47357i 0.0708762 0.122761i
\(407\) −8.37598 14.5076i −0.415182 0.719116i
\(408\) 42.4010 2.09916
\(409\) 14.9695 + 25.9279i 0.740194 + 1.28205i 0.952407 + 0.304830i \(0.0985998\pi\)
−0.212213 + 0.977224i \(0.568067\pi\)
\(410\) 6.93482 + 12.0115i 0.342486 + 0.593204i
\(411\) 7.46980 0.368458
\(412\) 11.0707 + 19.1750i 0.545414 + 0.944684i
\(413\) −1.13706 + 1.96945i −0.0559512 + 0.0969104i
\(414\) −7.75667 + 13.4349i −0.381219 + 0.660291i
\(415\) −2.77240 −0.136092
\(416\) 0 0
\(417\) 17.9976 0.881347
\(418\) 2.95138 5.11194i 0.144357 0.250033i
\(419\) −3.32371 + 5.75683i −0.162374 + 0.281240i −0.935720 0.352745i \(-0.885248\pi\)
0.773346 + 0.633984i \(0.218582\pi\)
\(420\) −1.52715 2.64510i −0.0745171 0.129067i
\(421\) 13.5646 0.661100 0.330550 0.943788i \(-0.392766\pi\)
0.330550 + 0.943788i \(0.392766\pi\)
\(422\) 0.619309 + 1.07268i 0.0301475 + 0.0522170i
\(423\) −0.376510 0.652135i −0.0183066 0.0317079i
\(424\) −66.2747 −3.21858
\(425\) −9.45862 16.3828i −0.458810 0.794683i
\(426\) −14.1380 + 24.4878i −0.684989 + 1.18644i
\(427\) 0.949886 1.64525i 0.0459682 0.0796193i
\(428\) 33.5478 1.62159
\(429\) 0 0
\(430\) 31.3370 1.51121
\(431\) −17.9731 + 31.1304i −0.865736 + 1.49950i 0.000578325 1.00000i \(0.499816\pi\)
−0.866314 + 0.499499i \(0.833517\pi\)
\(432\) 6.51842 11.2902i 0.313618 0.543201i
\(433\) 16.2371 + 28.1234i 0.780303 + 1.35152i 0.931765 + 0.363061i \(0.118268\pi\)
−0.151462 + 0.988463i \(0.548398\pi\)
\(434\) −14.2161 −0.682395
\(435\) 1.00269 + 1.73671i 0.0480752 + 0.0832687i
\(436\) 9.07756 + 15.7228i 0.434736 + 0.752985i
\(437\) −4.33944 −0.207583
\(438\) 14.1015 + 24.4245i 0.673795 + 1.16705i
\(439\) −6.41603 + 11.1129i −0.306221 + 0.530390i −0.977532 0.210785i \(-0.932398\pi\)
0.671312 + 0.741175i \(0.265731\pi\)
\(440\) 13.3487 23.1206i 0.636374 1.10223i
\(441\) −6.69202 −0.318668
\(442\) 0 0
\(443\) 11.9608 0.568273 0.284137 0.958784i \(-0.408293\pi\)
0.284137 + 0.958784i \(0.408293\pi\)
\(444\) 15.0930 26.1418i 0.716282 1.24064i
\(445\) 5.20626 9.01751i 0.246800 0.427471i
\(446\) 22.0075 + 38.1182i 1.04209 + 1.80495i
\(447\) −15.3351 −0.725327
\(448\) −5.92208 10.2573i −0.279792 0.484614i
\(449\) 6.23945 + 10.8070i 0.294458 + 0.510016i 0.974859 0.222824i \(-0.0715277\pi\)
−0.680401 + 0.732840i \(0.738194\pi\)
\(450\) −10.4983 −0.494893
\(451\) −7.15130 12.3864i −0.336742 0.583254i
\(452\) −24.5477 + 42.5179i −1.15463 + 1.99987i
\(453\) 1.26540 2.19173i 0.0594536 0.102977i
\(454\) 17.6606 0.828851
\(455\) 0 0
\(456\) 6.58211 0.308235
\(457\) −16.2262 + 28.1045i −0.759028 + 1.31468i 0.184319 + 0.982867i \(0.440992\pi\)
−0.943347 + 0.331809i \(0.892341\pi\)
\(458\) 5.32400 9.22144i 0.248774 0.430890i
\(459\) −2.42543 4.20096i −0.113209 0.196084i
\(460\) −31.7159 −1.47876
\(461\) −12.2017 21.1340i −0.568290 0.984308i −0.996735 0.0807398i \(-0.974272\pi\)
0.428445 0.903568i \(-0.359062\pi\)
\(462\) 2.17510 + 3.76738i 0.101195 + 0.175274i
\(463\) −33.1836 −1.54217 −0.771086 0.636731i \(-0.780286\pi\)
−0.771086 + 0.636731i \(0.780286\pi\)
\(464\) 12.4623 + 21.5853i 0.578546 + 1.00207i
\(465\) 4.99061 8.64398i 0.231434 0.400855i
\(466\) −11.2485 + 19.4829i −0.521075 + 0.902529i
\(467\) −38.5206 −1.78252 −0.891261 0.453490i \(-0.850179\pi\)
−0.891261 + 0.453490i \(0.850179\pi\)
\(468\) 0 0
\(469\) −1.03923 −0.0479871
\(470\) 1.06315 1.84144i 0.0490397 0.0849392i
\(471\) 8.61960 14.9296i 0.397170 0.687919i
\(472\) −17.9095 31.0201i −0.824350 1.42782i
\(473\) −32.3153 −1.48586
\(474\) 1.79709 + 3.11266i 0.0825432 + 0.142969i
\(475\) −1.46830 2.54318i −0.0673704 0.116689i
\(476\) −14.1250 −0.647417
\(477\) 3.79105 + 6.56630i 0.173580 + 0.300650i
\(478\) −27.0559 + 46.8622i −1.23751 + 2.14343i
\(479\) 4.17241 7.22682i 0.190642 0.330202i −0.754821 0.655931i \(-0.772276\pi\)
0.945463 + 0.325729i \(0.105610\pi\)
\(480\) 18.4752 0.843272
\(481\) 0 0
\(482\) −51.1825 −2.33130
\(483\) 1.59903 2.76960i 0.0727584 0.126021i
\(484\) 6.61410 11.4560i 0.300641 0.520725i
\(485\) 8.95444 + 15.5095i 0.406600 + 0.704252i
\(486\) −2.69202 −0.122113
\(487\) 7.42931 + 12.8679i 0.336654 + 0.583102i 0.983801 0.179263i \(-0.0573713\pi\)
−0.647147 + 0.762365i \(0.724038\pi\)
\(488\) 14.9613 + 25.9137i 0.677266 + 1.17306i
\(489\) −15.7071 −0.710299
\(490\) −9.44816 16.3647i −0.426824 0.739281i
\(491\) −2.49947 + 4.32920i −0.112799 + 0.195374i −0.916898 0.399122i \(-0.869315\pi\)
0.804099 + 0.594496i \(0.202648\pi\)
\(492\) 12.8862 22.3196i 0.580955 1.00624i
\(493\) 9.27413 0.417686
\(494\) 0 0
\(495\) −3.05429 −0.137280
\(496\) 62.0275 107.435i 2.78512 4.82396i
\(497\) 2.91454 5.04814i 0.130735 0.226440i
\(498\) 3.55765 + 6.16202i 0.159422 + 0.276127i
\(499\) −0.385371 −0.0172516 −0.00862579 0.999963i \(-0.502746\pi\)
−0.00862579 + 0.999963i \(0.502746\pi\)
\(500\) −24.4906 42.4190i −1.09525 1.89703i
\(501\) 2.69806 + 4.67318i 0.120541 + 0.208782i
\(502\) −2.05610 −0.0917681
\(503\) −11.3089 19.5877i −0.504241 0.873370i −0.999988 0.00490359i \(-0.998439\pi\)
0.495747 0.868467i \(-0.334894\pi\)
\(504\) −2.42543 + 4.20096i −0.108037 + 0.187126i
\(505\) 3.84063 6.65217i 0.170906 0.296018i
\(506\) 45.1726 2.00817
\(507\) 0 0
\(508\) −23.5163 −1.04337
\(509\) 5.80194 10.0493i 0.257166 0.445425i −0.708315 0.705896i \(-0.750544\pi\)
0.965482 + 0.260471i \(0.0838778\pi\)
\(510\) 6.84870 11.8623i 0.303265 0.525271i
\(511\) −2.90701 5.03509i −0.128599 0.222739i
\(512\) 1.71678 0.0758715
\(513\) −0.376510 0.652135i −0.0166233 0.0287925i
\(514\) 17.6208 + 30.5201i 0.777220 + 1.34618i
\(515\) 4.42626 0.195044
\(516\) −29.1151 50.4288i −1.28172 2.22000i
\(517\) −1.09634 + 1.89892i −0.0482171 + 0.0835145i
\(518\) −4.29739 + 7.44330i −0.188816 + 0.327040i
\(519\) −23.9420 −1.05094
\(520\) 0 0
\(521\) −1.62671 −0.0712675 −0.0356337 0.999365i \(-0.511345\pi\)
−0.0356337 + 0.999365i \(0.511345\pi\)
\(522\) 2.57338 4.45722i 0.112634 0.195087i
\(523\) −5.03588 + 8.72239i −0.220203 + 0.381404i −0.954870 0.297025i \(-0.904005\pi\)
0.734666 + 0.678429i \(0.237339\pi\)
\(524\) 24.1819 + 41.8842i 1.05639 + 1.82972i
\(525\) 2.16421 0.0944539
\(526\) −24.7361 42.8442i −1.07854 1.86809i
\(527\) −23.0797 39.9752i −1.00537 1.74135i
\(528\) −37.9614 −1.65206
\(529\) −5.10441 8.84109i −0.221931 0.384395i
\(530\) −10.7048 + 18.5413i −0.464988 + 0.805383i
\(531\) −2.04892 + 3.54883i −0.0889154 + 0.154006i
\(532\) −2.19269 −0.0950650
\(533\) 0 0
\(534\) −26.7235 −1.15644
\(535\) 3.35325 5.80800i 0.144974 0.251102i
\(536\) 8.18425 14.1755i 0.353506 0.612290i
\(537\) 9.20440 + 15.9425i 0.397199 + 0.687969i
\(538\) 63.6999 2.74630
\(539\) 9.74309 + 16.8755i 0.419665 + 0.726881i
\(540\) −2.75182 4.76630i −0.118420 0.205109i
\(541\) −20.4674 −0.879962 −0.439981 0.898007i \(-0.645015\pi\)
−0.439981 + 0.898007i \(0.645015\pi\)
\(542\) 26.5878 + 46.0514i 1.14204 + 1.97808i
\(543\) −1.81671 + 3.14663i −0.0779624 + 0.135035i
\(544\) 42.7204 73.9939i 1.83162 3.17246i
\(545\) 3.62937 0.155465
\(546\) 0 0
\(547\) −27.5478 −1.17786 −0.588929 0.808185i \(-0.700450\pi\)
−0.588929 + 0.808185i \(0.700450\pi\)
\(548\) 19.5969 33.9429i 0.837140 1.44997i
\(549\) 1.71164 2.96464i 0.0730508 0.126528i
\(550\) 15.2847 + 26.4739i 0.651742 + 1.12885i
\(551\) 1.43967 0.0613318
\(552\) 25.1857 + 43.6230i 1.07198 + 1.85672i
\(553\) −0.370469 0.641672i −0.0157540 0.0272867i
\(554\) 4.78581 0.203329
\(555\) −3.01722 5.22598i −0.128074 0.221831i
\(556\) 47.2165 81.7814i 2.00243 3.46831i
\(557\) −18.9928 + 32.8964i −0.804749 + 1.39387i 0.111711 + 0.993741i \(0.464367\pi\)
−0.916460 + 0.400126i \(0.868966\pi\)
\(558\) −25.6165 −1.08443
\(559\) 0 0
\(560\) −7.58881 −0.320686
\(561\) −7.06249 + 12.2326i −0.298179 + 0.516460i
\(562\) −2.18233 + 3.77991i −0.0920562 + 0.159446i
\(563\) 14.8862 + 25.7837i 0.627378 + 1.08665i 0.988076 + 0.153968i \(0.0492054\pi\)
−0.360697 + 0.932683i \(0.617461\pi\)
\(564\) −3.95108 −0.166371
\(565\) 4.90731 + 8.49970i 0.206452 + 0.357585i
\(566\) −6.70799 11.6186i −0.281958 0.488365i
\(567\) 0.554958 0.0233061
\(568\) 45.9059 + 79.5113i 1.92617 + 3.33622i
\(569\) 10.9770 19.0128i 0.460181 0.797057i −0.538788 0.842441i \(-0.681118\pi\)
0.998970 + 0.0453839i \(0.0144511\pi\)
\(570\) 1.06315 1.84144i 0.0445307 0.0771294i
\(571\) 2.46575 0.103188 0.0515942 0.998668i \(-0.483570\pi\)
0.0515942 + 0.998668i \(0.483570\pi\)
\(572\) 0 0
\(573\) 21.1782 0.884732
\(574\) −3.66905 + 6.35499i −0.153143 + 0.265252i
\(575\) 11.2366 19.4624i 0.468600 0.811639i
\(576\) −10.6712 18.4831i −0.444634 0.770128i
\(577\) 17.4547 0.726650 0.363325 0.931662i \(-0.381641\pi\)
0.363325 + 0.931662i \(0.381641\pi\)
\(578\) −8.79052 15.2256i −0.365637 0.633303i
\(579\) −8.80559 15.2517i −0.365948 0.633840i
\(580\) 10.5222 0.436909
\(581\) −0.733406 1.27030i −0.0304268 0.0527008i
\(582\) 22.9813 39.8049i 0.952607 1.64996i
\(583\) 11.0390 19.1201i 0.457188 0.791873i
\(584\) 91.5745 3.78938
\(585\) 0 0
\(586\) −0.193159 −0.00797934
\(587\) −3.13169 + 5.42424i −0.129259 + 0.223882i −0.923390 0.383864i \(-0.874593\pi\)
0.794131 + 0.607747i \(0.207926\pi\)
\(588\) −17.5565 + 30.4087i −0.724016 + 1.25403i
\(589\) −3.58277 6.20554i −0.147625 0.255695i
\(590\) −11.5711 −0.476374
\(591\) −2.33124 4.03783i −0.0958944 0.166094i
\(592\) −37.5006 64.9529i −1.54126 2.66955i
\(593\) 22.8745 0.939345 0.469672 0.882841i \(-0.344372\pi\)
0.469672 + 0.882841i \(0.344372\pi\)
\(594\) 3.91939 + 6.78858i 0.160814 + 0.278539i
\(595\) −1.41185 + 2.44540i −0.0578804 + 0.100252i
\(596\) −40.2315 + 69.6831i −1.64795 + 2.85433i
\(597\) −15.0368 −0.615417
\(598\) 0 0
\(599\) −1.05621 −0.0431557 −0.0215778 0.999767i \(-0.506869\pi\)
−0.0215778 + 0.999767i \(0.506869\pi\)
\(600\) −17.0438 + 29.5208i −0.695812 + 1.20518i
\(601\) 16.6618 28.8591i 0.679650 1.17719i −0.295437 0.955362i \(-0.595465\pi\)
0.975086 0.221826i \(-0.0712015\pi\)
\(602\) 8.28986 + 14.3585i 0.337869 + 0.585207i
\(603\) −1.87263 −0.0762592
\(604\) −6.63951 11.5000i −0.270158 0.467927i
\(605\) −1.32222 2.29015i −0.0537557 0.0931076i
\(606\) −19.7138 −0.800818
\(607\) −8.12014 14.0645i −0.329586 0.570860i 0.652844 0.757493i \(-0.273576\pi\)
−0.982430 + 0.186633i \(0.940243\pi\)
\(608\) 6.63169 11.4864i 0.268950 0.465836i
\(609\) −0.530499 + 0.918852i −0.0214969 + 0.0372338i
\(610\) 9.66632 0.391378
\(611\) 0 0
\(612\) −25.4523 −1.02885
\(613\) −5.52393 + 9.56772i −0.223109 + 0.386437i −0.955751 0.294178i \(-0.904954\pi\)
0.732641 + 0.680615i \(0.238287\pi\)
\(614\) 6.99665 12.1185i 0.282362 0.489065i
\(615\) −2.57606 4.46187i −0.103877 0.179920i
\(616\) 14.1250 0.569112
\(617\) 2.32975 + 4.03524i 0.0937922 + 0.162453i 0.909104 0.416570i \(-0.136768\pi\)
−0.815312 + 0.579022i \(0.803434\pi\)
\(618\) −5.67994 9.83794i −0.228481 0.395740i
\(619\) 31.9259 1.28321 0.641604 0.767036i \(-0.278269\pi\)
0.641604 + 0.767036i \(0.278269\pi\)
\(620\) −26.1856 45.3548i −1.05164 1.82149i
\(621\) 2.88135 4.99065i 0.115625 0.200268i
\(622\) 30.3430 52.5555i 1.21664 2.10729i
\(623\) 5.50902 0.220714
\(624\) 0 0
\(625\) 9.70709 0.388283
\(626\) −30.5022 + 52.8313i −1.21911 + 2.11156i
\(627\) −1.09634 + 1.89892i −0.0437837 + 0.0758356i
\(628\) −45.2269 78.3353i −1.80475 3.12592i
\(629\) −27.9071 −1.11273
\(630\) 0.783520 + 1.35710i 0.0312162 + 0.0540680i
\(631\) 19.7207 + 34.1572i 0.785067 + 1.35978i 0.928959 + 0.370183i \(0.120705\pi\)
−0.143892 + 0.989593i \(0.545962\pi\)
\(632\) 11.6703 0.464218
\(633\) −0.230054 0.398465i −0.00914381 0.0158375i
\(634\) −35.4572 + 61.4136i −1.40818 + 2.43905i
\(635\) −2.35056 + 4.07129i −0.0932791 + 0.161564i
\(636\) 39.7832 1.57750
\(637\) 0 0
\(638\) −14.9866 −0.593325
\(639\) 5.25182 9.09643i 0.207759 0.359849i
\(640\) 11.6572 20.1909i 0.460792 0.798115i
\(641\) −22.7255 39.3617i −0.897603 1.55469i −0.830549 0.556946i \(-0.811973\pi\)
−0.0670544 0.997749i \(-0.521360\pi\)
\(642\) −17.2121 −0.679306
\(643\) 14.8735 + 25.7616i 0.586552 + 1.01594i 0.994680 + 0.103013i \(0.0328483\pi\)
−0.408128 + 0.912925i \(0.633818\pi\)
\(644\) −8.39008 14.5321i −0.330616 0.572643i
\(645\) −11.6407 −0.458353
\(646\) −4.91670 8.51597i −0.193445 0.335056i
\(647\) 8.46562 14.6629i 0.332818 0.576457i −0.650245 0.759724i \(-0.725334\pi\)
0.983063 + 0.183267i \(0.0586673\pi\)
\(648\) −4.37047 + 7.56988i −0.171688 + 0.297373i
\(649\) 11.9323 0.468384
\(650\) 0 0
\(651\) 5.28083 0.206972
\(652\) −41.2074 + 71.3733i −1.61381 + 2.79519i
\(653\) 16.5988 28.7500i 0.649561 1.12507i −0.333667 0.942691i \(-0.608286\pi\)
0.983228 0.182382i \(-0.0583806\pi\)
\(654\) −4.65734 8.06675i −0.182116 0.315435i
\(655\) 9.66833 0.377773
\(656\) −32.0175 55.4560i −1.25007 2.16519i
\(657\) −5.23825 9.07292i −0.204364 0.353968i
\(658\) 1.12498 0.0438564
\(659\) 21.3286 + 36.9421i 0.830842 + 1.43906i 0.897371 + 0.441277i \(0.145474\pi\)
−0.0665286 + 0.997785i \(0.521192\pi\)
\(660\) −8.01291 + 13.8788i −0.311902 + 0.540230i
\(661\) −19.3451 + 33.5067i −0.752438 + 1.30326i 0.194201 + 0.980962i \(0.437789\pi\)
−0.946638 + 0.322298i \(0.895545\pi\)
\(662\) −30.2301 −1.17493
\(663\) 0 0
\(664\) 23.1032 0.896578
\(665\) −0.219169 + 0.379611i −0.00849899 + 0.0147207i
\(666\) −7.74363 + 13.4124i −0.300059 + 0.519718i
\(667\) 5.50873 + 9.54140i 0.213299 + 0.369444i
\(668\) 28.3134 1.09548
\(669\) −8.17510 14.1597i −0.316067 0.547445i
\(670\) −2.64387 4.57932i −0.102142 0.176915i
\(671\) −9.96807 −0.384813
\(672\) 4.88740 + 8.46522i 0.188535 + 0.326553i
\(673\) 1.29709 2.24663i 0.0499993 0.0866013i −0.839943 0.542675i \(-0.817411\pi\)
0.889942 + 0.456074i \(0.150745\pi\)
\(674\) −3.10656 + 5.38073i −0.119660 + 0.207258i
\(675\) 3.89977 0.150102
\(676\) 0 0
\(677\) 1.75302 0.0673740 0.0336870 0.999432i \(-0.489275\pi\)
0.0336870 + 0.999432i \(0.489275\pi\)
\(678\) 12.5945 21.8143i 0.483688 0.837773i
\(679\) −4.73759 + 8.20574i −0.181812 + 0.314907i
\(680\) −22.2376 38.5166i −0.852773 1.47705i
\(681\) −6.56033 −0.251393
\(682\) 37.2958 + 64.5983i 1.42813 + 2.47360i
\(683\) −8.16756 14.1466i −0.312523 0.541306i 0.666385 0.745608i \(-0.267841\pi\)
−0.978908 + 0.204302i \(0.934508\pi\)
\(684\) −3.95108 −0.151073
\(685\) −3.91760 6.78548i −0.149684 0.259260i
\(686\) 10.2277 17.7148i 0.390494 0.676355i
\(687\) −1.97770 + 3.42547i −0.0754539 + 0.130690i
\(688\) −144.681 −5.51590
\(689\) 0 0
\(690\) 16.2722 0.619472
\(691\) −7.95526 + 13.7789i −0.302632 + 0.524175i −0.976731 0.214466i \(-0.931199\pi\)
0.674099 + 0.738641i \(0.264532\pi\)
\(692\) −62.8116 + 108.793i −2.38774 + 4.13568i
\(693\) −0.807979 1.39946i −0.0306926 0.0531611i
\(694\) −24.5972 −0.933696
\(695\) −9.43900 16.3488i −0.358042 0.620146i
\(696\) −8.35570 14.4725i −0.316722 0.548579i
\(697\) −23.8267 −0.902500
\(698\) −32.2717 55.8963i −1.22150 2.11571i
\(699\) 4.17845 7.23728i 0.158043 0.273739i
\(700\) 5.67778 9.83421i 0.214600 0.371698i
\(701\) −20.8635 −0.788005 −0.394002 0.919109i \(-0.628910\pi\)
−0.394002 + 0.919109i \(0.628910\pi\)
\(702\) 0 0
\(703\) −4.33214 −0.163390
\(704\) −31.0730 + 53.8200i −1.17111 + 2.02842i
\(705\) −0.394928 + 0.684035i −0.0148739 + 0.0257623i
\(706\) 36.5091 + 63.2356i 1.37404 + 2.37990i
\(707\) 4.06398 0.152842
\(708\) 10.7506 + 18.6206i 0.404033 + 0.699806i
\(709\) −7.82424 13.5520i −0.293846 0.508955i 0.680870 0.732404i \(-0.261602\pi\)
−0.974716 + 0.223449i \(0.928268\pi\)
\(710\) 29.6592 1.11309
\(711\) −0.667563 1.15625i −0.0250356 0.0433629i
\(712\) −43.3853 + 75.1455i −1.62593 + 2.81620i
\(713\) 27.4182 47.4897i 1.02682 1.77850i
\(714\) 7.24698 0.271211
\(715\) 0 0
\(716\) 96.5906 3.60976
\(717\) 10.0504 17.4078i 0.375339 0.650107i
\(718\) 35.1027 60.7996i 1.31002 2.26902i
\(719\) 13.5797 + 23.5208i 0.506438 + 0.877176i 0.999972 + 0.00744977i \(0.00237136\pi\)
−0.493534 + 0.869726i \(0.664295\pi\)
\(720\) −13.6746 −0.509621
\(721\) 1.17092 + 2.02808i 0.0436072 + 0.0755298i
\(722\) 24.8110 + 42.9738i 0.923368 + 1.59932i
\(723\) 19.0127 0.707089
\(724\) 9.53223 + 16.5103i 0.354262 + 0.613601i
\(725\) −3.72790 + 6.45691i −0.138451 + 0.239804i
\(726\) −3.39344 + 5.87760i −0.125942 + 0.218138i
\(727\) 31.7784 1.17859 0.589297 0.807916i \(-0.299405\pi\)
0.589297 + 0.807916i \(0.299405\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 14.7913 25.6193i 0.547450 0.948212i
\(731\) −26.9170 + 46.6216i −0.995561 + 1.72436i
\(732\) −8.98092 15.5554i −0.331944 0.574944i
\(733\) 46.8907 1.73195 0.865973 0.500090i \(-0.166700\pi\)
0.865973 + 0.500090i \(0.166700\pi\)
\(734\) −12.8872 22.3212i −0.475674 0.823891i
\(735\) 3.50969 + 6.07896i 0.129457 + 0.224226i
\(736\) 101.502 3.74141
\(737\) 2.72641 + 4.72227i 0.100428 + 0.173947i
\(738\) −6.61141 + 11.4513i −0.243369 + 0.421528i
\(739\) −8.52393 + 14.7639i −0.313558 + 0.543098i −0.979130 0.203236i \(-0.934854\pi\)
0.665572 + 0.746334i \(0.268188\pi\)
\(740\) −31.6626 −1.16394
\(741\) 0 0
\(742\) −11.3274 −0.415840
\(743\) 5.81618 10.0739i 0.213375 0.369576i −0.739394 0.673273i \(-0.764888\pi\)
0.952769 + 0.303697i \(0.0982211\pi\)
\(744\) −41.5882 + 72.0329i −1.52470 + 2.64085i
\(745\) 8.04264 + 13.9303i 0.294660 + 0.510365i
\(746\) 75.7797 2.77449
\(747\) −1.32155 2.28900i −0.0483531 0.0837500i
\(748\) 37.0567 + 64.1842i 1.35493 + 2.34681i
\(749\) 3.54825 0.129650
\(750\) 12.5652 + 21.7635i 0.458815 + 0.794692i
\(751\) 6.51477 11.2839i 0.237727 0.411756i −0.722334 0.691544i \(-0.756931\pi\)
0.960062 + 0.279788i \(0.0902642\pi\)
\(752\) −4.90850 + 8.50177i −0.178995 + 0.310028i
\(753\) 0.763774 0.0278335
\(754\) 0 0
\(755\) −2.65459 −0.0966106
\(756\) 1.45593 2.52174i 0.0529516 0.0917148i
\(757\) −11.3949 + 19.7366i −0.414156 + 0.717339i −0.995339 0.0964337i \(-0.969256\pi\)
0.581184 + 0.813772i \(0.302590\pi\)
\(758\) −21.5988 37.4102i −0.784504 1.35880i
\(759\) −16.7802 −0.609081
\(760\) −3.45204 5.97911i −0.125219 0.216885i
\(761\) 19.1712 + 33.2055i 0.694956 + 1.20370i 0.970196 + 0.242323i \(0.0779094\pi\)
−0.275240 + 0.961376i \(0.588757\pi\)
\(762\) 12.0653 0.437080
\(763\) 0.960107 + 1.66295i 0.0347582 + 0.0602030i
\(764\) 55.5608 96.2342i 2.01012 3.48163i
\(765\) −2.54407 + 4.40646i −0.0919812 + 0.159316i
\(766\) −66.2683 −2.39437
\(767\) 0 0
\(768\) −17.1511 −0.618886
\(769\) 1.81940 3.15129i 0.0656091 0.113638i −0.831355 0.555742i \(-0.812434\pi\)
0.896964 + 0.442104i \(0.145768\pi\)
\(770\) 2.28150 3.95167i 0.0822194 0.142408i
\(771\) −6.54556 11.3373i −0.235733 0.408301i
\(772\) −92.4055 −3.32575
\(773\) 19.6712 + 34.0715i 0.707524 + 1.22547i 0.965773 + 0.259389i \(0.0835213\pi\)
−0.258249 + 0.966079i \(0.583145\pi\)
\(774\) 14.9378 + 25.8730i 0.536928 + 0.929987i
\(775\) 37.1092 1.33300
\(776\) −74.6200 129.246i −2.67870 4.63965i
\(777\) 1.59634 2.76495i 0.0572685 0.0991919i
\(778\) 23.1781 40.1456i 0.830974 1.43929i
\(779\) −3.69873 −0.132521
\(780\) 0 0