Properties

Label 507.2.e.l.22.3
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 22.3
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.l.484.3

$q$-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 \(-0.432592\pi\)
0.741585 0.670859i \(-0.234074\pi\)
\(3\) 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 \(-0.424640\pi\)
0.234545 + 0.972105i \(0.424640\pi\)
\(6\) −1.34601 2.33136i −0.549507 0.951773i
\(7\) 0.277479 + 0.480608i 0.104877 + 0.181653i 0.913688 0.406416i \(-0.133222\pi\)
−0.808811 + 0.588069i \(0.799888\pi\)
\(8\) −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 −0.558632 0.829415i \(-0.688674\pi\)
0.997611 + 0.0690822i \(0.0220071\pi\)
\(12\) −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 0.819600 0.572936i \(-0.194196\pi\)
−0.905977 + 0.423326i \(0.860862\pi\)
\(20\) −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 \(-0.173841\pi\)
0.854538 + 0.519389i \(0.173841\pi\)
\(32\) 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 −0.526623 0.850099i \(-0.676542\pi\)
0.999519 + 0.0310199i \(0.00987552\pi\)
\(38\) −2.02715 −0.328847
\(39\) 0 0
\(40\) −9.16852 −1.44967
\(41\) 2.45593 4.25379i 0.383551 0.664330i −0.608016 0.793925i \(-0.708034\pi\)
0.991567 + 0.129595i \(0.0413676\pi\)
\(42\) 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 \(-0.517490\pi\)
−0.0549197 + 0.998491i \(0.517490\pi\)
\(48\) 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 0.968020 0.250874i \(-0.0807181\pi\)
−0.701273 + 0.712892i \(0.747385\pi\)
\(60\) −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 −0.917535 0.397654i \(-0.869824\pi\)
0.803146 + 0.595782i \(0.203158\pi\)
\(68\) 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 \(-0.952468\pi\)
0.365595 0.930774i \(-0.380866\pi\)
\(72\) 4.37047 + 7.56988i 0.515065 + 0.892118i
\(73\) −10.4765 −1.22618 −0.613091 0.790012i \(-0.710074\pi\)
−0.613091 + 0.790012i \(0.710074\pi\)
\(74\) −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 \(-0.546337\pi\)
−0.145059 + 0.989423i \(0.546337\pi\)
\(84\) −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 \(-0.656977\pi\)
0.999537 0.0304348i \(-0.00968919\pi\)
\(90\) −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 \(0.167150\pi\)
0.00151988 + 0.999999i \(0.499516\pi\)
\(98\) −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 \(-0.447009\pi\)
0.165709 + 0.986175i \(0.447009\pi\)
\(110\) −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 0.661205 0.750205i \(-0.270045\pi\)
−0.980299 + 0.197518i \(0.936712\pi\)
\(138\) 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 \(0.0495214\pi\)
−0.359771 + 0.933041i \(0.617145\pi\)
\(150\) 5.24914 + 9.09177i 0.428590 + 0.742340i
\(151\) −2.53079 −0.205953 −0.102977 0.994684i \(-0.532837\pi\)
−0.102977 + 0.994684i \(0.532837\pi\)
\(152\) 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 \(0.0442326\pi\)
−0.375223 + 0.926934i \(0.622434\pi\)
\(164\) −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 −0.742549 0.669792i \(-0.766383\pi\)
0.951331 + 0.308170i \(0.0997166\pi\)
\(168\) −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 \(0.385189\pi\)
−0.986760 + 0.162189i \(0.948144\pi\)
\(194\) 45.9627 3.29993
\(195\) 0 0
\(196\) −35.1129 −2.50806
\(197\) −2.33124 + 4.03783i −0.166094 + 0.287683i −0.937043 0.349213i \(-0.886449\pi\)
0.770949 + 0.636897i \(0.219782\pi\)
\(198\) −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 \(0.351066\pi\)
−0.998449 + 0.0556803i \(0.982267\pi\)
\(224\) −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 0.954108 0.299462i \(-0.0968072\pi\)
−0.736396 + 0.676551i \(0.763474\pi\)
\(228\) 1.97554 + 3.42174i 0.130833 + 0.226610i
\(229\) 3.95539 0.261380 0.130690 0.991423i \(-0.458281\pi\)
0.130690 + 0.991423i \(0.458281\pi\)
\(230\) 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 \(-0.725276\pi\)
−0.650107 + 0.759843i \(0.725276\pi\)
\(240\) 6.83728 + 11.8425i 0.441345 + 0.764431i
\(241\) −9.50634 16.4655i −0.612357 1.06063i −0.990842 0.135026i \(-0.956888\pi\)
0.378485 0.925607i \(-0.376445\pi\)
\(242\) 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 \(0.371482\pi\)
−0.992827 + 0.119560i \(0.961852\pi\)
\(272\) −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 \(-0.515400\pi\)
−0.0483603 + 0.998830i \(0.515400\pi\)
\(282\) 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 0.864976 0.501814i \(-0.167334\pi\)
−0.867071 + 0.498184i \(0.834000\pi\)
\(294\) −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 \(-0.452609\pi\)
0.148335 + 0.988937i \(0.452609\pi\)
\(308\) −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 \(-0.765065\pi\)
−0.739769 + 0.672861i \(0.765065\pi\)
\(318\) 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 0.669445 0.742862i \(-0.266532\pi\)
−0.978060 + 0.208325i \(0.933199\pi\)
\(332\) 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 \(-0.611563\pi\)
0.985053 0.172249i \(-0.0551033\pi\)
\(350\) −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 \(0.423366\pi\)
−0.960265 + 0.279088i \(0.909968\pi\)
\(354\) 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 \(-0.258401\pi\)
0.688200 + 0.725521i \(0.258401\pi\)
\(360\) 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 −0.582995 0.812476i \(-0.698119\pi\)
0.995122 + 0.0986504i \(0.0314526\pi\)
\(380\) −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 \(-0.950163\pi\)
0.358845 0.933397i \(-0.383171\pi\)
\(384\) −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 0.839304 0.543662i \(-0.182963\pi\)
−0.890477 + 0.455028i \(0.849629\pi\)
\(398\) −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 −0.883694 0.468065i \(-0.844951\pi\)
0.847203 + 0.531269i \(0.178284\pi\)
\(402\) 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 \(-0.901400\pi\)
0.212213 0.977224i \(-0.431933\pi\)
\(410\) −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 \(-0.607234\pi\)
−0.330550 + 0.943788i \(0.607234\pi\)
\(422\) −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 \(-0.500184\pi\)
0.866314 0.499499i \(-0.166483\pi\)
\(432\) 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 0.680401 0.732840i \(-0.261806\pi\)
−0.974859 + 0.222824i \(0.928472\pi\)
\(450\) 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 \(-0.559008\pi\)
0.943347 0.331809i \(-0.107659\pi\)
\(458\) 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 \(0.0257283\pi\)
−0.428445 + 0.903568i \(0.640938\pi\)
\(462\) −2.17510 3.76738i −0.101195 0.175274i
\(463\) 33.1836 1.54217 0.771086 0.636731i \(-0.219714\pi\)
0.771086 + 0.636731i \(0.219714\pi\)
\(464\) 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 −0.945463 0.325729i \(-0.894390\pi\)
0.754821 + 0.655931i \(0.227724\pi\)
\(480\) 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 0.647147 0.762365i \(-0.275962\pi\)
−0.983801 + 0.179263i \(0.942629\pi\)
\(488\) −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 \(-0.497254\pi\)
0.00862579 + 0.999963i \(0.497254\pi\)
\(500\) 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 −0.965482 0.260471i \(-0.916122\pi\)
0.708315 + 0.705896i \(0.249456\pi\)
\(510\) 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 \(-0.354985\pi\)
0.439981 + 0.898007i \(0.354985\pi\)
\(542\) 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 \(-0.535633\pi\)
0.916460 0.400126i \(-0.131034\pi\)
\(558\) −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 \(-0.618359\pi\)
−0.363325 + 0.931662i \(0.618359\pi\)
\(578\) 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 −0.794131 0.607747i \(-0.792074\pi\)
0.923390 + 0.383864i \(0.125407\pi\)
\(588\) −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 \(-0.655628\pi\)
−0.469672 + 0.882841i \(0.655628\pi\)
\(594\) 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 −0.732641 0.680615i \(-0.761713\pi\)
0.955751 + 0.294178i \(0.0950460\pi\)
\(614\) 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 0.815312 0.579022i \(-0.196566\pi\)
−0.909104 + 0.416570i \(0.863232\pi\)
\(618\) 5.67994 + 9.83794i 0.228481 + 0.395740i
\(619\) −31.9259 −1.28321 −0.641604 0.767036i \(-0.721731\pi\)
−0.641604 + 0.767036i \(0.721731\pi\)
\(620\) −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 \(-0.879295\pi\)
0.143892 0.989593i \(-0.454038\pi\)
\(632\) −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 \(-0.967152\pi\)
0.408128 0.912925i \(-0.366182\pi\)
\(644\) 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 \(-0.562211\pi\)
0.946638 0.322298i \(-0.104455\pi\)
\(662\) −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 0.978908 0.204302i \(-0.0654925\pi\)
−0.666385 + 0.745608i \(0.732159\pi\)
\(684\) 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 −0.674099 0.738641i \(-0.735468\pi\)
0.976731 + 0.214466i \(0.0688012\pi\)
\(692\) −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 0.974716 0.223449i \(-0.0717315\pi\)
−0.680870 + 0.732404i \(0.738398\pi\)
\(710\) −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 \(-0.833300\pi\)
−0.865973 + 0.500090i \(0.833300\pi\)
\(734\) 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 −0.665572 0.746334i \(-0.731812\pi\)
0.979130 + 0.203236i \(0.0651457\pi\)
\(740\) −31.6626 −1.16394
\(741\) 0 0
\(742\) −11.3274 −0.415840
\(743\) −5.81618 + 10.0739i −0.213375 + 0.369576i −0.952769 0.303697i \(-0.901779\pi\)
0.739394 + 0.673273i \(0.235112\pi\)
\(744\) −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 \(-0.922091\pi\)
0.275240 0.961376i \(-0.411243\pi\)
\(762\) −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 −0.896964 0.442104i \(-0.854232\pi\)
0.831355 + 0.555742i \(0.187566\pi\)
\(770\) 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 \(-0.916479\pi\)
0.258249 0.966079i \(-0.416855\pi\)
\(774\) −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