Properties

Label 507.2.j.i.316.1
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
Defining polynomial: \(x^{12} - 5 x^{10} + 19 x^{8} - 28 x^{6} + 31 x^{4} - 6 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.1
Root \(1.56052 - 0.900969i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.i.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.33136 - 1.34601i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.62349 + 4.54402i) q^{4} -1.04892i q^{5} +(-2.33136 + 1.34601i) q^{6} +(-0.480608 + 0.277479i) q^{7} -8.74094i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-2.33136 - 1.34601i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.62349 + 4.54402i) q^{4} -1.04892i q^{5} +(-2.33136 + 1.34601i) q^{6} +(-0.480608 + 0.277479i) q^{7} -8.74094i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.41185 + 2.44540i) q^{10} +(2.52174 + 1.45593i) q^{11} +5.24698 q^{12} +1.49396 q^{14} +(-0.908389 - 0.524459i) q^{15} +(-6.51842 + 11.2902i) q^{16} +(-2.42543 - 4.20096i) q^{17} +2.69202i q^{18} +(-0.652135 + 0.376510i) q^{19} +(4.76630 - 2.75182i) q^{20} +0.554958i q^{21} +(-3.91939 - 6.78858i) q^{22} +(2.88135 - 4.99065i) q^{23} +(-7.56988 - 4.37047i) q^{24} +3.89977 q^{25} -1.00000 q^{27} +(-2.52174 - 1.45593i) q^{28} +(0.955927 - 1.65571i) q^{29} +(1.41185 + 2.44540i) q^{30} -9.51573i q^{31} +(15.2538 - 8.80678i) q^{32} +(2.52174 - 1.45593i) q^{33} +13.0586i q^{34} +(0.291053 + 0.504118i) q^{35} +(2.62349 - 4.54402i) q^{36} +(4.98226 + 2.87651i) q^{37} +2.02715 q^{38} -9.16852 q^{40} +(-4.25379 - 2.45593i) q^{41} +(0.746980 - 1.29381i) q^{42} +(-5.54892 - 9.61101i) q^{43} +15.2784i q^{44} +(-0.908389 + 0.524459i) q^{45} +(-13.4349 + 7.75667i) q^{46} -0.753020i q^{47} +(6.51842 + 11.2902i) q^{48} +(-3.34601 + 5.79546i) q^{49} +(-9.09177 - 5.24914i) q^{50} -4.85086 q^{51} -7.58211 q^{53} +(2.33136 + 1.34601i) q^{54} +(1.52715 - 2.64510i) q^{55} +(2.42543 + 4.20096i) q^{56} +0.753020i q^{57} +(-4.45722 + 2.57338i) q^{58} +(-3.54883 + 2.04892i) q^{59} -5.50365i q^{60} +(1.71164 + 2.96464i) q^{61} +(-12.8083 + 22.1846i) q^{62} +(0.480608 + 0.277479i) q^{63} -21.3424 q^{64} -7.83877 q^{66} +(1.62174 + 0.936313i) q^{67} +(12.7262 - 22.0424i) q^{68} +(-2.88135 - 4.99065i) q^{69} -1.56704i q^{70} +(-9.09643 + 5.25182i) q^{71} +(-7.56988 + 4.37047i) q^{72} -10.4765i q^{73} +(-7.74363 - 13.4124i) q^{74} +(1.94989 - 3.37730i) q^{75} +(-3.42174 - 1.97554i) q^{76} -1.61596 q^{77} +1.33513 q^{79} +(11.8425 + 6.83728i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.61141 + 11.4513i) q^{82} +2.64310i q^{83} +(-2.52174 + 1.45593i) q^{84} +(-4.40646 + 2.54407i) q^{85} +29.8756i q^{86} +(-0.955927 - 1.65571i) q^{87} +(12.7262 - 22.0424i) q^{88} +(8.59696 + 4.96346i) q^{89} +2.82371 q^{90} +30.2368 q^{92} +(-8.24086 - 4.75786i) q^{93} +(-1.01357 + 1.75556i) q^{94} +(0.394928 + 0.684035i) q^{95} -17.6136i q^{96} +(14.7862 - 8.53684i) q^{97} +(15.6015 - 9.00753i) q^{98} -2.91185i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} + 22q^{4} - 6q^{9} + O(q^{10}) \) \( 12q + 6q^{3} + 22q^{4} - 6q^{9} - 2q^{10} + 44q^{12} - 20q^{14} - 22q^{16} - 2q^{17} + 18q^{22} - 44q^{25} - 12q^{27} + 4q^{29} + 2q^{30} - 8q^{35} + 22q^{36} + 12q^{40} - 10q^{42} - 30q^{43} + 22q^{48} - 30q^{49} - 4q^{51} - 68q^{53} - 6q^{55} + 2q^{56} + 26q^{61} - 4q^{62} + 36q^{66} + 26q^{68} - 30q^{74} - 22q^{75} - 60q^{77} + 12q^{79} - 6q^{81} - 6q^{82} - 4q^{87} + 26q^{88} + 4q^{90} + 28q^{92} - 42q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33136 1.34601i −1.64852 0.951773i −0.977661 0.210188i \(-0.932592\pi\)
−0.670859 0.741585i \(-0.734074\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 2.62349 + 4.54402i 1.31174 + 2.27201i
\(5\) 1.04892i 0.469090i −0.972105 0.234545i \(-0.924640\pi\)
0.972105 0.234545i \(-0.0753600\pi\)
\(6\) −2.33136 + 1.34601i −0.951773 + 0.549507i
\(7\) −0.480608 + 0.277479i −0.181653 + 0.104877i −0.588069 0.808811i \(-0.700112\pi\)
0.406416 + 0.913688i \(0.366778\pi\)
\(8\) 8.74094i 3.09039i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.41185 + 2.44540i −0.446467 + 0.773304i
\(11\) 2.52174 + 1.45593i 0.760333 + 0.438979i 0.829415 0.558632i \(-0.188674\pi\)
−0.0690822 + 0.997611i \(0.522007\pi\)
\(12\) 5.24698 1.51467
\(13\) 0 0
\(14\) 1.49396 0.399277
\(15\) −0.908389 0.524459i −0.234545 0.135415i
\(16\) −6.51842 + 11.2902i −1.62960 + 2.82256i
\(17\) −2.42543 4.20096i −0.588253 1.01888i −0.994461 0.105103i \(-0.966483\pi\)
0.406209 0.913780i \(-0.366851\pi\)
\(18\) 2.69202i 0.634516i
\(19\) −0.652135 + 0.376510i −0.149610 + 0.0863774i −0.572936 0.819600i \(-0.694196\pi\)
0.423326 + 0.905977i \(0.360862\pi\)
\(20\) 4.76630 2.75182i 1.06578 0.615327i
\(21\) 0.554958i 0.121102i
\(22\) −3.91939 6.78858i −0.835616 1.44733i
\(23\) 2.88135 4.99065i 0.600804 1.04062i −0.391896 0.920010i \(-0.628181\pi\)
0.992700 0.120613i \(-0.0384861\pi\)
\(24\) −7.56988 4.37047i −1.54519 0.892118i
\(25\) 3.89977 0.779954
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −2.52174 1.45593i −0.476564 0.275144i
\(29\) 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
\(31\) 9.51573i 1.70908i −0.519389 0.854538i \(-0.673841\pi\)
0.519389 0.854538i \(-0.326159\pi\)
\(32\) 15.2538 8.80678i 2.69652 1.55683i
\(33\) 2.52174 1.45593i 0.438979 0.253444i
\(34\) 13.0586i 2.23953i
\(35\) 0.291053 + 0.504118i 0.0491969 + 0.0852115i
\(36\) 2.62349 4.54402i 0.437248 0.757336i
\(37\) 4.98226 + 2.87651i 0.819079 + 0.472895i 0.850099 0.526623i \(-0.176542\pi\)
−0.0310199 + 0.999519i \(0.509876\pi\)
\(38\) 2.02715 0.328847
\(39\) 0 0
\(40\) −9.16852 −1.44967
\(41\) −4.25379 2.45593i −0.664330 0.383551i 0.129595 0.991567i \(-0.458632\pi\)
−0.793925 + 0.608016i \(0.791966\pi\)
\(42\) 0.746980 1.29381i 0.115261 0.199639i
\(43\) −5.54892 9.61101i −0.846202 1.46566i −0.884573 0.466401i \(-0.845550\pi\)
0.0383713 0.999264i \(-0.487783\pi\)
\(44\) 15.2784i 2.30331i
\(45\) −0.908389 + 0.524459i −0.135415 + 0.0781817i
\(46\) −13.4349 + 7.75667i −1.98087 + 1.14366i
\(47\) 0.753020i 0.109839i −0.998491 0.0549197i \(-0.982510\pi\)
0.998491 0.0549197i \(-0.0174903\pi\)
\(48\) 6.51842 + 11.2902i 0.940853 + 1.62960i
\(49\) −3.34601 + 5.79546i −0.478002 + 0.827923i
\(50\) −9.09177 5.24914i −1.28577 0.742340i
\(51\) −4.85086 −0.679256
\(52\) 0 0
\(53\) −7.58211 −1.04148 −0.520741 0.853715i \(-0.674344\pi\)
−0.520741 + 0.853715i \(0.674344\pi\)
\(54\) 2.33136 + 1.34601i 0.317258 + 0.183169i
\(55\) 1.52715 2.64510i 0.205920 0.356665i
\(56\) 2.42543 + 4.20096i 0.324111 + 0.561377i
\(57\) 0.753020i 0.0997400i
\(58\) −4.45722 + 2.57338i −0.585261 + 0.337901i
\(59\) −3.54883 + 2.04892i −0.462018 + 0.266746i −0.712892 0.701273i \(-0.752615\pi\)
0.250874 + 0.968020i \(0.419282\pi\)
\(60\) 5.50365i 0.710518i
\(61\) 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
\(63\) 0.480608 + 0.277479i 0.0605509 + 0.0349591i
\(64\) −21.3424 −2.66780
\(65\) 0 0
\(66\) −7.83877 −0.964886
\(67\) 1.62174 + 0.936313i 0.198127 + 0.114389i 0.595782 0.803146i \(-0.296842\pi\)
−0.397654 + 0.917535i \(0.630176\pi\)
\(68\) 12.7262 22.0424i 1.54327 2.67303i
\(69\) −2.88135 4.99065i −0.346874 0.600804i
\(70\) 1.56704i 0.187297i
\(71\) −9.09643 + 5.25182i −1.07955 + 0.623277i −0.930774 0.365595i \(-0.880866\pi\)
−0.148773 + 0.988871i \(0.547532\pi\)
\(72\) −7.56988 + 4.37047i −0.892118 + 0.515065i
\(73\) 10.4765i 1.22618i −0.790012 0.613091i \(-0.789926\pi\)
0.790012 0.613091i \(-0.210074\pi\)
\(74\) −7.74363 13.4124i −0.900178 1.55915i
\(75\) 1.94989 3.37730i 0.225153 0.389977i
\(76\) −3.42174 1.97554i −0.392500 0.226610i
\(77\) −1.61596 −0.184155
\(78\) 0 0
\(79\) 1.33513 0.150213 0.0751067 0.997176i \(-0.476070\pi\)
0.0751067 + 0.997176i \(0.476070\pi\)
\(80\) 11.8425 + 6.83728i 1.32403 + 0.764431i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 6.61141 + 11.4513i 0.730108 + 1.26458i
\(83\) 2.64310i 0.290118i 0.989423 + 0.145059i \(0.0463373\pi\)
−0.989423 + 0.145059i \(0.953663\pi\)
\(84\) −2.52174 + 1.45593i −0.275144 + 0.158855i
\(85\) −4.40646 + 2.54407i −0.477948 + 0.275943i
\(86\) 29.8756i 3.22157i
\(87\) −0.955927 1.65571i −0.102486 0.177511i
\(88\) 12.7262 22.0424i 1.35661 2.34972i
\(89\) 8.59696 + 4.96346i 0.911276 + 0.526126i 0.880842 0.473411i \(-0.156977\pi\)
0.0304348 + 0.999537i \(0.490311\pi\)
\(90\) 2.82371 0.297645
\(91\) 0 0
\(92\) 30.2368 3.15241
\(93\) −8.24086 4.75786i −0.854538 0.493368i
\(94\) −1.01357 + 1.75556i −0.104542 + 0.181072i
\(95\) 0.394928 + 0.684035i 0.0405188 + 0.0701806i
\(96\) 17.6136i 1.79768i
\(97\) 14.7862 8.53684i 1.50131 0.866784i 0.501316 0.865264i \(-0.332850\pi\)
0.999999 0.00151988i \(-0.000483794\pi\)
\(98\) 15.6015 9.00753i 1.57599 0.909898i
\(99\) 2.91185i 0.292652i
\(100\) 10.2310 + 17.7206i 1.02310 + 1.77206i
\(101\) 3.66152 6.34194i 0.364335 0.631047i −0.624334 0.781157i \(-0.714630\pi\)
0.988669 + 0.150111i \(0.0479630\pi\)
\(102\) 11.3091 + 6.52930i 1.11977 + 0.646497i
\(103\) 4.21983 0.415792 0.207896 0.978151i \(-0.433338\pi\)
0.207896 + 0.978151i \(0.433338\pi\)
\(104\) 0 0
\(105\) 0.582105 0.0568077
\(106\) 17.6766 + 10.2056i 1.71690 + 0.991255i
\(107\) −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
\(109\) 3.46011i 0.331418i −0.986175 0.165709i \(-0.947009\pi\)
0.986175 0.165709i \(-0.0529913\pi\)
\(110\) −7.12066 + 4.11111i −0.678928 + 0.391979i
\(111\) 4.98226 2.87651i 0.472895 0.273026i
\(112\) 7.23490i 0.683634i
\(113\) −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
\(115\) −5.23478 3.02230i −0.488146 0.281831i
\(116\) 10.0315 0.931398
\(117\) 0 0
\(118\) 11.0315 1.01553
\(119\) 2.33136 + 1.34601i 0.213715 + 0.123389i
\(120\) −4.58426 + 7.94017i −0.418484 + 0.724835i
\(121\) −1.26055 2.18334i −0.114596 0.198486i
\(122\) 9.21552i 0.834334i
\(123\) −4.25379 + 2.45593i −0.383551 + 0.221443i
\(124\) 43.2396 24.9644i 3.88303 2.24187i
\(125\) 9.33513i 0.834959i
\(126\) −0.746980 1.29381i −0.0665462 0.115261i
\(127\) −2.24094 + 3.88142i −0.198851 + 0.344420i −0.948156 0.317805i \(-0.897054\pi\)
0.749305 + 0.662225i \(0.230388\pi\)
\(128\) 19.2493 + 11.1136i 1.70141 + 0.982310i
\(129\) −11.0978 −0.977110
\(130\) 0 0
\(131\) −9.21744 −0.805331 −0.402666 0.915347i \(-0.631916\pi\)
−0.402666 + 0.915347i \(0.631916\pi\)
\(132\) 13.2315 + 7.63922i 1.15166 + 0.664909i
\(133\) 0.208947 0.361908i 0.0181180 0.0313814i
\(134\) −2.52057 4.36576i −0.217744 0.377144i
\(135\) 1.04892i 0.0902764i
\(136\) −36.7204 + 21.2005i −3.14875 + 1.81793i
\(137\) 6.46903 3.73490i 0.552687 0.319094i −0.197518 0.980299i \(-0.563288\pi\)
0.750205 + 0.661205i \(0.229955\pi\)
\(138\) 15.5133i 1.32058i
\(139\) 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
\(141\) −0.652135 0.376510i −0.0549197 0.0317079i
\(142\) 28.2760 2.37287
\(143\) 0 0
\(144\) 13.0368 1.08640
\(145\) −1.73671 1.00269i −0.144226 0.0832687i
\(146\) −14.1015 + 24.4245i −1.16705 + 2.02138i
\(147\) 3.34601 + 5.79546i 0.275974 + 0.478002i
\(148\) 30.1860i 2.48127i
\(149\) 13.2806 7.66756i 1.08799 0.628151i 0.154949 0.987922i \(-0.450479\pi\)
0.933041 + 0.359771i \(0.117145\pi\)
\(150\) −9.09177 + 5.24914i −0.742340 + 0.428590i
\(151\) 2.53079i 0.205953i −0.994684 0.102977i \(-0.967163\pi\)
0.994684 0.102977i \(-0.0328367\pi\)
\(152\) 3.29105 + 5.70027i 0.266940 + 0.462353i
\(153\) −2.42543 + 4.20096i −0.196084 + 0.339628i
\(154\) 3.76738 + 2.17510i 0.303584 + 0.175274i
\(155\) −9.98121 −0.801710
\(156\) 0 0
\(157\) 17.2392 1.37584 0.687919 0.725787i \(-0.258524\pi\)
0.687919 + 0.725787i \(0.258524\pi\)
\(158\) −3.11266 1.79709i −0.247630 0.142969i
\(159\) −3.79105 + 6.56630i −0.300650 + 0.520741i
\(160\) −9.23759 16.0000i −0.730295 1.26491i
\(161\) 3.19806i 0.252043i
\(162\) 2.33136 1.34601i 0.183169 0.105753i
\(163\) −13.6027 + 7.85354i −1.06545 + 0.615137i −0.926934 0.375223i \(-0.877566\pi\)
−0.138514 + 0.990360i \(0.544233\pi\)
\(164\) 25.7724i 2.01249i
\(165\) −1.52715 2.64510i −0.118888 0.205920i
\(166\) 3.55765 6.16202i 0.276127 0.478266i
\(167\) 4.67318 + 2.69806i 0.361622 + 0.208782i 0.669792 0.742549i \(-0.266383\pi\)
−0.308170 + 0.951331i \(0.599717\pi\)
\(168\) 4.85086 0.374252
\(169\) 0 0
\(170\) 13.6974 1.05054
\(171\) 0.652135 + 0.376510i 0.0498700 + 0.0287925i
\(172\) 29.1151 50.4288i 2.22000 3.84516i
\(173\) 11.9710 + 20.7344i 0.910138 + 1.57640i 0.813868 + 0.581049i \(0.197358\pi\)
0.0962694 + 0.995355i \(0.469309\pi\)
\(174\) 5.14675i 0.390174i
\(175\) −1.87426 + 1.08211i −0.141681 + 0.0817995i
\(176\) −32.8755 + 18.9807i −2.47808 + 1.43072i
\(177\) 4.09783i 0.308012i
\(178\) −13.3617 23.1432i −1.00150 1.73466i
\(179\) 9.20440 15.9425i 0.687969 1.19160i −0.284525 0.958669i \(-0.591836\pi\)
0.972494 0.232929i \(-0.0748309\pi\)
\(180\) −4.76630 2.75182i −0.355259 0.205109i
\(181\) 3.63342 0.270070 0.135035 0.990841i \(-0.456885\pi\)
0.135035 + 0.990841i \(0.456885\pi\)
\(182\) 0 0
\(183\) 3.42327 0.253056
\(184\) −43.6230 25.1857i −3.21593 1.85672i
\(185\) 3.01722 5.22598i 0.221831 0.384222i
\(186\) 12.8083 + 22.1846i 0.939148 + 1.62665i
\(187\) 14.1250i 1.03292i
\(188\) 3.42174 1.97554i 0.249556 0.144081i
\(189\) 0.480608 0.277479i 0.0349591 0.0201836i
\(190\) 2.12631i 0.154259i
\(191\) 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
\(193\) −15.2517 8.80559i −1.09784 0.633840i −0.162189 0.986760i \(-0.551856\pi\)
−0.935654 + 0.352920i \(0.885189\pi\)
\(194\) −45.9627 −3.29993
\(195\) 0 0
\(196\) −35.1129 −2.50806
\(197\) 4.03783 + 2.33124i 0.287683 + 0.166094i 0.636897 0.770949i \(-0.280218\pi\)
−0.349213 + 0.937043i \(0.613551\pi\)
\(198\) −3.91939 + 6.78858i −0.278539 + 0.482443i
\(199\) 7.51842 + 13.0223i 0.532967 + 0.923125i 0.999259 + 0.0384944i \(0.0122562\pi\)
−0.466292 + 0.884631i \(0.654410\pi\)
\(200\) 34.0877i 2.41036i
\(201\) 1.62174 0.936313i 0.114389 0.0660424i
\(202\) −17.0726 + 9.85690i −1.20123 + 0.693529i
\(203\) 1.06100i 0.0744675i
\(204\) −12.7262 22.0424i −0.891010 1.54327i
\(205\) −2.57606 + 4.46187i −0.179920 + 0.311631i
\(206\) −9.83794 5.67994i −0.685442 0.395740i
\(207\) −5.76271 −0.400536
\(208\) 0 0
\(209\) −2.19269 −0.151671
\(210\) −1.35710 0.783520i −0.0936485 0.0540680i
\(211\) 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
\(213\) 10.5036i 0.719698i
\(214\) 14.9061 8.60603i 1.01896 0.588296i
\(215\) −10.0812 + 5.82036i −0.687529 + 0.396945i
\(216\) 8.74094i 0.594746i
\(217\) 2.64042 + 4.57333i 0.179243 + 0.310458i
\(218\) −4.65734 + 8.06675i −0.315435 + 0.546349i
\(219\) −9.07292 5.23825i −0.613091 0.353968i
\(220\) 16.0258 1.08046
\(221\) 0 0
\(222\) −15.4873 −1.03944
\(223\) 14.1597 + 8.17510i 0.948202 + 0.547445i 0.892522 0.451004i \(-0.148934\pi\)
0.0556803 + 0.998449i \(0.482267\pi\)
\(224\) −4.88740 + 8.46522i −0.326553 + 0.565606i
\(225\) −1.94989 3.37730i −0.129992 0.225153i
\(226\) 25.1890i 1.67555i
\(227\) 5.68142 3.28017i 0.377089 0.217712i −0.299462 0.954108i \(-0.596807\pi\)
0.676551 + 0.736396i \(0.263474\pi\)
\(228\) −3.42174 + 1.97554i −0.226610 + 0.130833i
\(229\) 3.95539i 0.261380i 0.991423 + 0.130690i \(0.0417192\pi\)
−0.991423 + 0.130690i \(0.958281\pi\)
\(230\) 8.13610 + 14.0921i 0.536479 + 0.929209i
\(231\) −0.807979 + 1.39946i −0.0531611 + 0.0920777i
\(232\) −14.4725 8.35570i −0.950166 0.548579i
\(233\) −8.35690 −0.547478 −0.273739 0.961804i \(-0.588261\pi\)
−0.273739 + 0.961804i \(0.588261\pi\)
\(234\) 0 0
\(235\) −0.789856 −0.0515245
\(236\) −18.6206 10.7506i −1.21210 0.699806i
\(237\) 0.667563 1.15625i 0.0433629 0.0751067i
\(238\) −3.62349 6.27607i −0.234876 0.406817i
\(239\) 20.1008i 1.30021i 0.759843 + 0.650107i \(0.225276\pi\)
−0.759843 + 0.650107i \(0.774724\pi\)
\(240\) 11.8425 6.83728i 0.764431 0.441345i
\(241\) 16.4655 9.50634i 1.06063 0.612357i 0.135026 0.990842i \(-0.456888\pi\)
0.925607 + 0.378485i \(0.123555\pi\)
\(242\) 6.78687i 0.436277i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −8.98092 + 15.5554i −0.574944 + 0.995833i
\(245\) 6.07896 + 3.50969i 0.388370 + 0.224226i
\(246\) 13.2228 0.843056
\(247\) 0 0
\(248\) −83.1764 −5.28171
\(249\) 2.28900 + 1.32155i 0.145059 + 0.0837500i
\(250\) −12.5652 + 21.7635i −0.794692 + 1.37645i
\(251\) −0.381887 0.661448i −0.0241045 0.0417502i 0.853722 0.520730i \(-0.174340\pi\)
−0.877826 + 0.478980i \(0.841007\pi\)
\(252\) 2.91185i 0.183430i
\(253\) 14.5321 8.39008i 0.913622 0.527480i
\(254\) 10.4489 6.03266i 0.655620 0.378522i
\(255\) 5.08815i 0.318632i
\(256\) −8.57553 14.8533i −0.535971 0.928329i
\(257\) −6.54556 + 11.3373i −0.408301 + 0.707198i −0.994700 0.102825i \(-0.967212\pi\)
0.586398 + 0.810023i \(0.300545\pi\)
\(258\) 25.8730 + 14.9378i 1.61078 + 0.929987i
\(259\) −3.19269 −0.198384
\(260\) 0 0
\(261\) −1.91185 −0.118341
\(262\) 21.4892 + 12.4068i 1.32760 + 0.766493i
\(263\) −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
\(265\) 7.95300i 0.488549i
\(266\) −0.974263 + 0.562491i −0.0597359 + 0.0344885i
\(267\) 8.59696 4.96346i 0.526126 0.303759i
\(268\) 9.82563i 0.600196i
\(269\) −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
\(271\) −17.1066 9.87651i −1.03915 0.599955i −0.119560 0.992827i \(-0.538148\pi\)
−0.919593 + 0.392872i \(0.871482\pi\)
\(272\) 63.2398 3.83448
\(273\) 0 0
\(274\) −20.1089 −1.21482
\(275\) 9.83421 + 5.67778i 0.593025 + 0.342383i
\(276\) 15.1184 26.1859i 0.910021 1.57620i
\(277\) 0.888887 + 1.53960i 0.0534081 + 0.0925055i 0.891493 0.453034i \(-0.149658\pi\)
−0.838085 + 0.545539i \(0.816325\pi\)
\(278\) 48.4499i 2.90583i
\(279\) −8.24086 + 4.75786i −0.493368 + 0.284846i
\(280\) 4.40646 2.54407i 0.263337 0.152037i
\(281\) 1.62133i 0.0967207i −0.998830 0.0483603i \(-0.984600\pi\)
0.998830 0.0483603i \(-0.0153996\pi\)
\(282\) 1.01357 + 1.75556i 0.0603574 + 0.104542i
\(283\) 2.49180 4.31593i 0.148122 0.256555i −0.782411 0.622762i \(-0.786010\pi\)
0.930533 + 0.366207i \(0.119344\pi\)
\(284\) −47.7288 27.5562i −2.83218 1.63516i
\(285\) 0.789856 0.0467870
\(286\) 0 0
\(287\) 2.72587 0.160903
\(288\) −15.2538 8.80678i −0.898838 0.518945i
\(289\) −3.26540 + 5.65583i −0.192082 + 0.332696i
\(290\) 2.69926 + 4.67525i 0.158506 + 0.274540i
\(291\) 17.0737i 1.00088i
\(292\) 47.6054 27.4850i 2.78590 1.60844i
\(293\) 0.0621395 0.0358763i 0.00363023 0.00209591i −0.498184 0.867071i \(-0.666000\pi\)
0.501814 + 0.864976i \(0.332666\pi\)
\(294\) 18.0151i 1.05066i
\(295\) 2.14914 + 3.72243i 0.125128 + 0.216728i
\(296\) 25.1434 43.5496i 1.46143 2.53127i
\(297\) −2.52174 1.45593i −0.146326 0.0844815i
\(298\) −41.2825 −2.39143
\(299\) 0 0
\(300\) 20.4620 1.18138
\(301\) 5.33371 + 3.07942i 0.307430 + 0.177495i
\(302\) −3.40648 + 5.90019i −0.196021 + 0.339518i
\(303\) −3.66152 6.34194i −0.210349 0.364335i
\(304\) 9.81700i 0.563044i
\(305\) 3.10966 1.79536i 0.178059 0.102802i
\(306\) 11.3091 6.52930i 0.646497 0.373255i
\(307\) 5.19806i 0.296669i 0.988937 + 0.148335i \(0.0473912\pi\)
−0.988937 + 0.148335i \(0.952609\pi\)
\(308\) −4.23945 7.34294i −0.241565 0.418403i
\(309\) 2.10992 3.65448i 0.120029 0.207896i
\(310\) 23.2698 + 13.4348i 1.32164 + 0.763047i
\(311\) 22.5429 1.27829 0.639145 0.769087i \(-0.279289\pi\)
0.639145 + 0.769087i \(0.279289\pi\)
\(312\) 0 0
\(313\) 22.6612 1.28088 0.640442 0.768006i \(-0.278751\pi\)
0.640442 + 0.768006i \(0.278751\pi\)
\(314\) −40.1908 23.2042i −2.26810 1.30949i
\(315\) 0.291053 0.504118i 0.0163990 0.0284038i
\(316\) 3.50269 + 6.06683i 0.197042 + 0.341286i
\(317\) 26.3424i 1.47954i 0.672861 + 0.739769i \(0.265065\pi\)
−0.672861 + 0.739769i \(0.734935\pi\)
\(318\) 17.6766 10.2056i 0.991255 0.572301i
\(319\) 4.82120 2.78352i 0.269935 0.155847i
\(320\) 22.3864i 1.25144i
\(321\) 3.19687 + 5.53713i 0.178432 + 0.309053i
\(322\) 4.30463 7.45583i 0.239887 0.415497i
\(323\) 3.16341 + 1.82640i 0.176017 + 0.101623i
\(324\) −5.24698 −0.291499
\(325\) 0 0
\(326\) 42.2838 2.34188
\(327\) −2.99654 1.73005i −0.165709 0.0956722i
\(328\) −21.4671 + 37.1821i −1.18532 + 2.05304i
\(329\) 0.208947 + 0.361908i 0.0115196 + 0.0199526i
\(330\) 8.22223i 0.452619i
\(331\) −9.72505 + 5.61476i −0.534537 + 0.308615i −0.742862 0.669445i \(-0.766532\pi\)
0.208325 + 0.978060i \(0.433199\pi\)
\(332\) −12.0103 + 6.93416i −0.659151 + 0.380561i
\(333\) 5.75302i 0.315264i
\(334\) −7.26324 12.5803i −0.397427 0.688364i
\(335\) 0.982115 1.70107i 0.0536587 0.0929395i
\(336\) −6.26561 3.61745i −0.341817 0.197348i
\(337\) −2.30798 −0.125724 −0.0628618 0.998022i \(-0.520023\pi\)
−0.0628618 + 0.998022i \(0.520023\pi\)
\(338\) 0 0
\(339\) −9.35690 −0.508197
\(340\) −23.1206 13.3487i −1.25389 0.723935i
\(341\) 13.8542 23.9962i 0.750247 1.29947i
\(342\) −1.01357 1.75556i −0.0548078 0.0949299i
\(343\) 7.59850i 0.410280i
\(344\) −84.0092 + 48.5027i −4.52947 + 2.61509i
\(345\) −5.23478 + 3.02230i −0.281831 + 0.162715i
\(346\) 64.4523i 3.46498i
\(347\) 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
\(349\) 20.7637 + 11.9879i 1.11145 + 0.641699i 0.939206 0.343355i \(-0.111563\pi\)
0.172249 + 0.985053i \(0.444897\pi\)
\(350\) 5.82610 0.311418
\(351\) 0 0
\(352\) 51.2881 2.73367
\(353\) 23.4900 + 13.5620i 1.25025 + 0.721830i 0.971158 0.238435i \(-0.0766345\pi\)
0.279088 + 0.960265i \(0.409968\pi\)
\(354\) 5.51573 9.55352i 0.293158 0.507764i
\(355\) 5.50873 + 9.54140i 0.292373 + 0.506405i
\(356\) 52.0863i 2.76057i
\(357\) 2.33136 1.34601i 0.123389 0.0712384i
\(358\) −42.9175 + 24.7784i −2.26826 + 1.30958i
\(359\) 26.0790i 1.37640i 0.725521 + 0.688200i \(0.241599\pi\)
−0.725521 + 0.688200i \(0.758401\pi\)
\(360\) 4.58426 + 7.94017i 0.241612 + 0.418484i
\(361\) −9.21648 + 15.9634i −0.485078 + 0.840180i
\(362\) −8.47080 4.89062i −0.445215 0.257045i
\(363\) −2.52111 −0.132324
\(364\) 0 0
\(365\) −10.9890 −0.575190
\(366\) −7.98088 4.60776i −0.417167 0.240851i
\(367\) −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
\(369\) 4.91185i 0.255701i
\(370\) −14.0685 + 8.12242i −0.731384 + 0.422265i
\(371\) 3.64402 2.10388i 0.189188 0.109228i
\(372\) 49.9288i 2.58869i
\(373\) −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
\(375\) −8.08446 4.66756i −0.417480 0.241032i
\(376\) −6.58211 −0.339446
\(377\) 0 0
\(378\) −1.49396 −0.0768410
\(379\) −13.8967 8.02326i −0.713825 0.412127i 0.0986504 0.995122i \(-0.468547\pi\)
−0.812476 + 0.582995i \(0.801881\pi\)
\(380\) −2.07218 + 3.58912i −0.106301 + 0.184118i
\(381\) 2.24094 + 3.88142i 0.114807 + 0.198851i
\(382\) 57.0122i 2.91700i
\(383\) −21.3186 + 12.3083i −1.08933 + 0.628923i −0.933397 0.358845i \(-0.883171\pi\)
−0.155930 + 0.987768i \(0.549837\pi\)
\(384\) 19.2493 11.1136i 0.982310 0.567137i
\(385\) 1.69501i 0.0863855i
\(386\) 23.7048 + 41.0580i 1.20654 + 2.08980i
\(387\) −5.54892 + 9.61101i −0.282067 + 0.488555i
\(388\) 77.5831 + 44.7926i 3.93868 + 2.27400i
\(389\) 17.2198 0.873080 0.436540 0.899685i \(-0.356204\pi\)
0.436540 + 0.899685i \(0.356204\pi\)
\(390\) 0 0
\(391\) −27.9541 −1.41370
\(392\) 50.6578 + 29.2473i 2.55860 + 1.47721i
\(393\) −4.60872 + 7.98254i −0.232479 + 0.402666i
\(394\) −6.27575 10.8699i −0.316168 0.547619i
\(395\) 1.40044i 0.0704636i
\(396\) 13.2315 7.63922i 0.664909 0.383885i
\(397\) 1.76602 1.01961i 0.0886342 0.0511730i −0.455028 0.890477i \(-0.650371\pi\)
0.543662 + 0.839304i \(0.317037\pi\)
\(398\) 40.4795i 2.02905i
\(399\) −0.208947 0.361908i −0.0104605 0.0181180i
\(400\) −25.4203 + 44.0293i −1.27102 + 2.20147i
\(401\) −1.26564 0.730718i −0.0632031 0.0364903i 0.468065 0.883694i \(-0.344951\pi\)
−0.531269 + 0.847203i \(0.678284\pi\)
\(402\) −5.04115 −0.251430
\(403\) 0 0
\(404\) 38.4239 1.91166
\(405\) 0.908389 + 0.524459i 0.0451382 + 0.0260606i
\(406\) 1.42812 2.47357i 0.0708762 0.122761i
\(407\) 8.37598 + 14.5076i 0.415182 + 0.719116i
\(408\) 42.4010i 2.09916i
\(409\) −25.9279 + 14.9695i −1.28205 + 0.740194i −0.977224 0.212213i \(-0.931933\pi\)
−0.304830 + 0.952407i \(0.598600\pi\)
\(410\) 12.0115 6.93482i 0.593204 0.342486i
\(411\) 7.46980i 0.368458i
\(412\) 11.0707 + 19.1750i 0.545414 + 0.944684i
\(413\) 1.13706 1.96945i 0.0559512 0.0969104i
\(414\) 13.4349 + 7.75667i 0.660291 + 0.381219i
\(415\) 2.77240 0.136092
\(416\) 0 0
\(417\) 17.9976 0.881347
\(418\) 5.11194 + 2.95138i 0.250033 + 0.144357i
\(419\) −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
\(421\) 13.5646i 0.661100i 0.943788 + 0.330550i \(0.107234\pi\)
−0.943788 + 0.330550i \(0.892766\pi\)
\(422\) −1.07268 + 0.619309i −0.0522170 + 0.0301475i
\(423\) −0.652135 + 0.376510i −0.0317079 + 0.0183066i
\(424\) 66.2747i 3.21858i
\(425\) −9.45862 16.3828i −0.458810 0.794683i
\(426\) 14.1380 24.4878i 0.684989 1.18644i
\(427\) −1.64525 0.949886i −0.0796193 0.0459682i
\(428\) −33.5478 −1.62159
\(429\) 0 0
\(430\) 31.3370 1.51121
\(431\) −31.1304 17.9731i −1.49950 0.865736i −0.499499 0.866314i \(-0.666483\pi\)
−1.00000 0.000578325i \(0.999816\pi\)
\(432\) 6.51842 11.2902i 0.313618 0.543201i
\(433\) −16.2371 28.1234i −0.780303 1.35152i −0.931765 0.363061i \(-0.881732\pi\)
0.151462 0.988463i \(-0.451602\pi\)
\(434\) 14.2161i 0.682395i
\(435\) −1.73671 + 1.00269i −0.0832687 + 0.0480752i
\(436\) 15.7228 9.07756i 0.752985 0.434736i
\(437\) 4.33944i 0.207583i
\(438\) 14.1015 + 24.4245i 0.673795 + 1.16705i
\(439\) 6.41603 11.1129i 0.306221 0.530390i −0.671312 0.741175i \(-0.734269\pi\)
0.977532 + 0.210785i \(0.0676021\pi\)
\(440\) −23.1206 13.3487i −1.10223 0.636374i
\(441\) 6.69202 0.318668
\(442\) 0 0
\(443\) 11.9608 0.568273 0.284137 0.958784i \(-0.408293\pi\)
0.284137 + 0.958784i \(0.408293\pi\)
\(444\) 26.1418 + 15.0930i 1.24064 + 0.716282i
\(445\) 5.20626 9.01751i 0.246800 0.427471i
\(446\) −22.0075 38.1182i −1.04209 1.80495i
\(447\) 15.3351i 0.725327i
\(448\) 10.2573 5.92208i 0.484614 0.279792i
\(449\) 10.8070 6.23945i 0.510016 0.294458i −0.222824 0.974859i \(-0.571528\pi\)
0.732840 + 0.680401i \(0.238194\pi\)
\(450\) 10.4983i 0.494893i
\(451\) −7.15130 12.3864i −0.336742 0.583254i
\(452\) 24.5477 42.5179i 1.15463 1.99987i
\(453\) −2.19173 1.26540i −0.102977 0.0594536i
\(454\) −17.6606 −0.828851
\(455\) 0 0
\(456\) 6.58211 0.308235
\(457\) −28.1045 16.2262i −1.31468 0.759028i −0.331809 0.943347i \(-0.607659\pi\)
−0.982867 + 0.184319i \(0.940992\pi\)
\(458\) 5.32400 9.22144i 0.248774 0.430890i
\(459\) 2.42543 + 4.20096i 0.113209 + 0.196084i
\(460\) 31.7159i 1.47876i
\(461\) 21.1340 12.2017i 0.984308 0.568290i 0.0807398 0.996735i \(-0.474272\pi\)
0.903568 + 0.428445i \(0.140938\pi\)
\(462\) 3.76738 2.17510i 0.175274 0.101195i
\(463\) 33.1836i 1.54217i 0.636731 + 0.771086i \(0.280286\pi\)
−0.636731 + 0.771086i \(0.719714\pi\)
\(464\) 12.4623 + 21.5853i 0.578546 + 1.00207i
\(465\) −4.99061 + 8.64398i −0.231434 + 0.400855i
\(466\) 19.4829 + 11.2485i 0.902529 + 0.521075i
\(467\) 38.5206 1.78252 0.891261 0.453490i \(-0.149821\pi\)
0.891261 + 0.453490i \(0.149821\pi\)
\(468\) 0 0
\(469\) −1.03923 −0.0479871
\(470\) 1.84144 + 1.06315i 0.0849392 + 0.0490397i
\(471\) 8.61960 14.9296i 0.397170 0.687919i
\(472\) 17.9095 + 31.0201i 0.824350 + 1.42782i
\(473\) 32.3153i 1.48586i
\(474\) −3.11266 + 1.79709i −0.142969 + 0.0825432i
\(475\) −2.54318 + 1.46830i −0.116689 + 0.0673704i
\(476\) 14.1250i 0.647417i
\(477\) 3.79105 + 6.56630i 0.173580 + 0.300650i
\(478\) 27.0559 46.8622i 1.23751 2.14343i
\(479\) −7.22682 4.17241i −0.330202 0.190642i 0.325729 0.945463i \(-0.394390\pi\)
−0.655931 + 0.754821i \(0.727724\pi\)
\(480\) −18.4752 −0.843272
\(481\) 0 0
\(482\) −51.1825 −2.33130
\(483\) 2.76960 + 1.59903i 0.126021 + 0.0727584i
\(484\) 6.61410 11.4560i 0.300641 0.520725i
\(485\) −8.95444 15.5095i −0.406600 0.704252i
\(486\) 2.69202i 0.122113i
\(487\) −12.8679 + 7.42931i −0.583102 + 0.336654i −0.762365 0.647147i \(-0.775962\pi\)
0.179263 + 0.983801i \(0.442629\pi\)
\(488\) 25.9137 14.9613i 1.17306 0.677266i
\(489\) 15.7071i 0.710299i
\(490\) −9.44816 16.3647i −0.426824 0.739281i
\(491\) 2.49947 4.32920i 0.112799 0.195374i −0.804099 0.594496i \(-0.797352\pi\)
0.916898 + 0.399122i \(0.130685\pi\)
\(492\) −22.3196 12.8862i −1.00624 0.580955i
\(493\) −9.27413 −0.417686
\(494\) 0 0
\(495\) −3.05429 −0.137280
\(496\) 107.435 + 62.0275i 4.82396 + 2.78512i
\(497\) 2.91454 5.04814i 0.130735 0.226440i
\(498\) −3.55765 6.16202i −0.159422 0.276127i
\(499\) 0.385371i 0.0172516i −0.999963 0.00862579i \(-0.997254\pi\)
0.999963 0.00862579i \(-0.00274571\pi\)
\(500\) 42.4190 24.4906i 1.89703 1.09525i
\(501\) 4.67318 2.69806i 0.208782 0.120541i
\(502\) 2.05610i 0.0917681i
\(503\) −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
\(505\) −6.65217 3.84063i −0.296018 0.170906i
\(506\) −45.1726 −2.00817
\(507\) 0 0
\(508\) −23.5163 −1.04337
\(509\) 10.0493 + 5.80194i 0.445425 + 0.257166i 0.705896 0.708315i \(-0.250544\pi\)
−0.260471 + 0.965482i \(0.583878\pi\)
\(510\) 6.84870 11.8623i 0.303265 0.525271i
\(511\) 2.90701 + 5.03509i 0.128599 + 0.222739i
\(512\) 1.71678i 0.0758715i
\(513\) 0.652135 0.376510i 0.0287925 0.0166233i
\(514\) 30.5201 17.6208i 1.34618 0.777220i
\(515\) 4.42626i 0.195044i
\(516\) −29.1151 50.4288i −1.28172 2.22000i
\(517\) 1.09634 1.89892i 0.0482171 0.0835145i
\(518\) 7.44330 + 4.29739i 0.327040 + 0.188816i
\(519\) 23.9420 1.05094
\(520\) 0 0
\(521\) −1.62671 −0.0712675 −0.0356337 0.999365i \(-0.511345\pi\)
−0.0356337 + 0.999365i \(0.511345\pi\)
\(522\) 4.45722 + 2.57338i 0.195087 + 0.112634i
\(523\) −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
\(525\) 2.16421i 0.0944539i
\(526\) 42.8442 24.7361i 1.86809 1.07854i
\(527\) −39.9752 + 23.0797i −1.74135 + 1.00537i
\(528\) 37.9614i 1.65206i
\(529\) −5.10441 8.84109i −0.221931 0.384395i
\(530\) 10.7048 18.5413i 0.464988 0.805383i
\(531\) 3.54883 + 2.04892i 0.154006 + 0.0889154i
\(532\) 2.19269 0.0950650
\(533\) 0 0
\(534\) −26.7235 −1.15644
\(535\) 5.80800 + 3.35325i 0.251102 + 0.144974i
\(536\) 8.18425 14.1755i 0.353506 0.612290i
\(537\) −9.20440 15.9425i −0.397199 0.687969i
\(538\) 63.6999i 2.74630i
\(539\) −16.8755 + 9.74309i −0.726881 + 0.419665i
\(540\) −4.76630 + 2.75182i −0.205109 + 0.118420i
\(541\) 20.4674i 0.879962i 0.898007 + 0.439981i \(0.145015\pi\)
−0.898007 + 0.439981i \(0.854985\pi\)
\(542\) 26.5878 + 46.0514i 1.14204 + 1.97808i
\(543\) 1.81671 3.14663i 0.0779624 0.135035i
\(544\) −73.9939 42.7204i −3.17246 1.83162i
\(545\) −3.62937 −0.155465
\(546\) 0 0
\(547\) −27.5478 −1.17786 −0.588929 0.808185i \(-0.700450\pi\)
−0.588929 + 0.808185i \(0.700450\pi\)
\(548\) 33.9429 + 19.5969i 1.44997 + 0.837140i
\(549\) 1.71164 2.96464i 0.0730508 0.126528i
\(550\) −15.2847 26.4739i −0.651742 1.12885i
\(551\) 1.43967i 0.0613318i
\(552\) −43.6230 + 25.1857i −1.85672 + 1.07198i
\(553\) −0.641672 + 0.370469i −0.0272867 + 0.0157540i
\(554\) 4.78581i 0.203329i
\(555\) −3.01722 5.22598i −0.128074 0.221831i
\(556\) −47.2165 + 81.7814i −2.00243 + 3.46831i
\(557\) 32.8964 + 18.9928i 1.39387 + 0.804749i 0.993741 0.111711i \(-0.0356331\pi\)
0.400126 + 0.916460i \(0.368966\pi\)
\(558\) 25.6165 1.08443
\(559\) 0 0
\(560\) −7.58881 −0.320686
\(561\) −12.2326 7.06249i −0.516460 0.298179i
\(562\) −2.18233 + 3.77991i −0.0920562 + 0.159446i
\(563\) −14.8862 25.7837i −0.627378 1.08665i −0.988076 0.153968i \(-0.950795\pi\)
0.360697 0.932683i \(-0.382539\pi\)
\(564\) 3.95108i 0.166371i
\(565\) −8.49970 + 4.90731i −0.357585 + 0.206452i
\(566\) −11.6186 + 6.70799i −0.488365 + 0.281958i
\(567\) 0.554958i 0.0233061i
\(568\) 45.9059 + 79.5113i 1.92617 + 3.33622i
\(569\) −10.9770 + 19.0128i −0.460181 + 0.797057i −0.998970 0.0453839i \(-0.985549\pi\)
0.538788 + 0.842441i \(0.318882\pi\)
\(570\) −1.84144 1.06315i −0.0771294 0.0445307i
\(571\) −2.46575 −0.103188 −0.0515942 0.998668i \(-0.516430\pi\)
−0.0515942 + 0.998668i \(0.516430\pi\)
\(572\) 0 0
\(573\) 21.1782 0.884732
\(574\) −6.35499 3.66905i −0.265252 0.153143i
\(575\) 11.2366 19.4624i 0.468600 0.811639i
\(576\) 10.6712 + 18.4831i 0.444634 + 0.770128i
\(577\) 17.4547i 0.726650i 0.931662 + 0.363325i \(0.118359\pi\)
−0.931662 + 0.363325i \(0.881641\pi\)
\(578\) 15.2256 8.79052i 0.633303 0.365637i
\(579\) −15.2517 + 8.80559i −0.633840 + 0.365948i
\(580\) 10.5222i 0.436909i
\(581\) −0.733406 1.27030i −0.0304268 0.0527008i
\(582\) −22.9813 + 39.8049i −0.952607 + 1.64996i
\(583\) −19.1201 11.0390i −0.791873 0.457188i
\(584\) −91.5745 −3.78938
\(585\) 0 0
\(586\) −0.193159 −0.00797934
\(587\) −5.42424 3.13169i −0.223882 0.129259i 0.383864 0.923390i \(-0.374593\pi\)
−0.607747 + 0.794131i \(0.707926\pi\)
\(588\) −17.5565 + 30.4087i −0.724016 + 1.25403i
\(589\) 3.58277 + 6.20554i 0.147625 + 0.255695i
\(590\) 11.5711i 0.476374i
\(591\) 4.03783 2.33124i 0.166094 0.0958944i
\(592\) −64.9529 + 37.5006i −2.66955 + 1.54126i
\(593\) 22.8745i 0.939345i −0.882841 0.469672i \(-0.844372\pi\)
0.882841 0.469672i \(-0.155628\pi\)
\(594\) 3.91939 + 6.78858i 0.160814 + 0.278539i
\(595\) 1.41185 2.44540i 0.0578804 0.100252i
\(596\) 69.6831 + 40.2315i 2.85433 + 1.64795i
\(597\) 15.0368 0.615417
\(598\) 0 0
\(599\) −1.05621 −0.0431557 −0.0215778 0.999767i \(-0.506869\pi\)
−0.0215778 + 0.999767i \(0.506869\pi\)
\(600\) −29.5208 17.0438i −1.20518 0.695812i
\(601\) 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
\(603\) 1.87263i 0.0762592i
\(604\) 11.5000 6.63951i 0.467927 0.270158i
\(605\) −2.29015 + 1.32222i −0.0931076 + 0.0537557i
\(606\) 19.7138i 0.800818i
\(607\) −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
\(609\) 0.918852 + 0.530499i 0.0372338 + 0.0214969i
\(610\) −9.66632 −0.391378
\(611\) 0 0
\(612\) −25.4523 −1.02885
\(613\) −9.56772 5.52393i −0.386437 0.223109i 0.294178 0.955751i \(-0.404954\pi\)
−0.680615 + 0.732641i \(0.738287\pi\)
\(614\) 6.99665 12.1185i 0.282362 0.489065i
\(615\) 2.57606 + 4.46187i 0.103877 + 0.179920i
\(616\) 14.1250i 0.569112i
\(617\) −4.03524 + 2.32975i −0.162453 + 0.0937922i −0.579022 0.815312i \(-0.696566\pi\)
0.416570 + 0.909104i \(0.363232\pi\)
\(618\) −9.83794 + 5.67994i −0.395740 + 0.228481i
\(619\) 31.9259i 1.28321i −0.767036 0.641604i \(-0.778269\pi\)
0.767036 0.641604i \(-0.221731\pi\)
\(620\) −26.1856 45.3548i −1.05164 1.82149i
\(621\) −2.88135 + 4.99065i −0.115625 + 0.200268i
\(622\) −52.5555 30.3430i −2.10729 1.21664i
\(623\) −5.50902 −0.220714
\(624\) 0 0
\(625\) 9.70709 0.388283
\(626\) −52.8313 30.5022i −2.11156 1.21911i
\(627\) −1.09634 + 1.89892i −0.0437837 + 0.0758356i
\(628\) 45.2269 + 78.3353i 1.80475 + 3.12592i
\(629\) 27.9071i 1.11273i
\(630\) −1.35710 + 0.783520i −0.0540680 + 0.0312162i
\(631\) 34.1572 19.7207i 1.35978 0.785067i 0.370183 0.928959i \(-0.379295\pi\)
0.989593 + 0.143892i \(0.0459618\pi\)
\(632\) 11.6703i 0.464218i
\(633\) −0.230054 0.398465i −0.00914381 0.0158375i
\(634\) 35.4572 61.4136i 1.40818 2.43905i
\(635\) 4.07129 + 2.35056i 0.161564 + 0.0932791i
\(636\) −39.7832 −1.57750
\(637\) 0 0
\(638\) −14.9866 −0.593325
\(639\) 9.09643 + 5.25182i 0.359849 + 0.207759i
\(640\) 11.6572 20.1909i 0.460792 0.798115i
\(641\) 22.7255 + 39.3617i 0.897603 + 1.55469i 0.830549 + 0.556946i \(0.188027\pi\)
0.0670544 + 0.997749i \(0.478640\pi\)
\(642\) 17.2121i 0.679306i
\(643\) −25.7616 + 14.8735i −1.01594 + 0.586552i −0.912925 0.408128i \(-0.866182\pi\)
−0.103013 + 0.994680i \(0.532848\pi\)
\(644\) −14.5321 + 8.39008i −0.572643 + 0.330616i
\(645\) 11.6407i 0.458353i
\(646\) −4.91670 8.51597i −0.193445 0.335056i
\(647\) −8.46562 + 14.6629i −0.332818 + 0.576457i −0.983063 0.183267i \(-0.941333\pi\)
0.650245 + 0.759724i \(0.274666\pi\)
\(648\) 7.56988 + 4.37047i 0.297373 + 0.171688i
\(649\) −11.9323 −0.468384
\(650\) 0 0
\(651\) 5.28083 0.206972
\(652\) −71.3733 41.2074i −2.79519 1.61381i
\(653\) 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
\(655\) 9.66833i 0.377773i
\(656\) 55.4560 32.0175i 2.16519 1.25007i
\(657\) −9.07292 + 5.23825i −0.353968 + 0.204364i
\(658\) 1.12498i 0.0438564i
\(659\) 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
\(661\) 33.5067 + 19.3451i 1.30326 + 0.752438i 0.980962 0.194201i \(-0.0622113\pi\)
0.322298 + 0.946638i \(0.395545\pi\)
\(662\) 30.2301 1.17493
\(663\) 0 0
\(664\) 23.1032 0.896578
\(665\) −0.379611 0.219169i −0.0147207 0.00849899i
\(666\) −7.74363 + 13.4124i −0.300059 + 0.519718i
\(667\) −5.50873 9.54140i −0.213299 0.369444i
\(668\) 28.3134i 1.09548i
\(669\) 14.1597 8.17510i 0.547445 0.316067i
\(670\) −4.57932 + 2.64387i −0.176915 + 0.102142i
\(671\) 9.96807i 0.384813i
\(672\) 4.88740 + 8.46522i 0.188535 + 0.326553i
\(673\) −1.29709 + 2.24663i −0.0499993 + 0.0866013i −0.889942 0.456074i \(-0.849255\pi\)
0.839943 + 0.542675i \(0.182589\pi\)
\(674\) 5.38073 + 3.10656i 0.207258 + 0.119660i
\(675\) −3.89977 −0.150102
\(676\) 0 0
\(677\) 1.75302 0.0673740 0.0336870 0.999432i \(-0.489275\pi\)
0.0336870 + 0.999432i \(0.489275\pi\)
\(678\) 21.8143 + 12.5945i 0.837773 + 0.483688i
\(679\) −4.73759 + 8.20574i −0.181812 + 0.314907i
\(680\) 22.2376 + 38.5166i 0.852773 + 1.47705i
\(681\) 6.56033i 0.251393i
\(682\) −64.5983 + 37.2958i −2.47360 + 1.42813i
\(683\) −14.1466 + 8.16756i −0.541306 + 0.312523i −0.745608 0.666385i \(-0.767841\pi\)
0.204302 + 0.978908i \(0.434508\pi\)
\(684\) 3.95108i 0.151073i
\(685\) −3.91760 6.78548i −0.149684 0.259260i
\(686\) −10.2277 + 17.7148i −0.390494 + 0.676355i
\(687\) 3.42547 + 1.97770i 0.130690 + 0.0754539i
\(688\) 144.681 5.51590
\(689\) 0 0
\(690\) 16.2722 0.619472
\(691\) −13.7789 7.95526i −0.524175 0.302632i 0.214466 0.976731i \(-0.431199\pi\)
−0.738641 + 0.674099i \(0.764532\pi\)
\(692\) −62.8116 + 108.793i −2.38774 + 4.13568i
\(693\) 0.807979 + 1.39946i 0.0306926 + 0.0531611i
\(694\) 24.5972i 0.933696i
\(695\) 16.3488 9.43900i 0.620146 0.358042i
\(696\) −14.4725 + 8.35570i −0.548579 + 0.316722i
\(697\) 23.8267i 0.902500i
\(698\) −32.2717 55.8963i −1.22150 2.11571i
\(699\) −4.17845 + 7.23728i −0.158043 + 0.273739i
\(700\) −9.83421 5.67778i −0.371698 0.214600i
\(701\) 20.8635 0.788005 0.394002 0.919109i \(-0.371090\pi\)
0.394002 + 0.919109i \(0.371090\pi\)
\(702\) 0 0
\(703\) −4.33214 −0.163390
\(704\) −53.8200 31.0730i −2.02842 1.17111i
\(705\) −0.394928 + 0.684035i −0.0148739 + 0.0257623i
\(706\) −36.5091 63.2356i −1.37404 2.37990i
\(707\) 4.06398i 0.152842i
\(708\) −18.6206 + 10.7506i −0.699806 + 0.404033i
\(709\) −13.5520 + 7.82424i −0.508955 + 0.293846i −0.732404 0.680870i \(-0.761602\pi\)
0.223449 + 0.974716i \(0.428268\pi\)
\(710\) 29.6592i 1.11309i
\(711\) −0.667563 1.15625i −0.0250356 0.0433629i
\(712\) 43.3853 75.1455i 1.62593 2.81620i
\(713\) −47.4897 27.4182i −1.77850 1.02682i
\(714\) −7.24698 −0.271211
\(715\) 0 0
\(716\) 96.5906 3.60976
\(717\) 17.4078 + 10.0504i 0.650107 + 0.375339i
\(718\) 35.1027 60.7996i 1.31002 2.26902i
\(719\) −13.5797 23.5208i −0.506438 0.877176i −0.999972 0.00744977i \(-0.997629\pi\)
0.493534 0.869726i \(-0.335705\pi\)
\(720\) 13.6746i 0.509621i
\(721\) −2.02808 + 1.17092i −0.0755298 + 0.0436072i
\(722\) 42.9738 24.8110i 1.59932 0.923368i
\(723\) 19.0127i 0.707089i
\(724\) 9.53223 + 16.5103i 0.354262 + 0.613601i
\(725\) 3.72790 6.45691i 0.138451 0.239804i
\(726\) 5.87760 + 3.39344i 0.218138 + 0.125942i
\(727\) −31.7784 −1.17859 −0.589297 0.807916i \(-0.700595\pi\)
−0.589297 + 0.807916i \(0.700595\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 25.6193 + 14.7913i 0.948212 + 0.547450i
\(731\) −26.9170 + 46.6216i −0.995561 + 1.72436i
\(732\) 8.98092 + 15.5554i 0.331944 + 0.574944i
\(733\) 46.8907i 1.73195i 0.500090 + 0.865973i \(0.333300\pi\)
−0.500090 + 0.865973i \(0.666700\pi\)
\(734\) 22.3212 12.8872i 0.823891 0.475674i
\(735\) 6.07896 3.50969i 0.224226 0.129457i
\(736\) 101.502i 3.74141i
\(737\) 2.72641 + 4.72227i 0.100428 + 0.173947i
\(738\) 6.61141 11.4513i 0.243369 0.421528i
\(739\) 14.7639 + 8.52393i 0.543098 + 0.313558i 0.746334 0.665572i \(-0.231812\pi\)
−0.203236 + 0.979130i \(0.565146\pi\)
\(740\) 31.6626 1.16394
\(741\) 0 0
\(742\) −11.3274 −0.415840
\(743\) 10.0739 + 5.81618i 0.369576 + 0.213375i 0.673273 0.739394i \(-0.264888\pi\)
−0.303697 + 0.952769i \(0.598221\pi\)
\(744\) −41.5882 + 72.0329i −1.52470 + 2.64085i
\(745\) −8.04264 13.9303i −0.294660 0.510365i
\(746\) 75.7797i 2.77449i
\(747\) 2.28900 1.32155i 0.0837500 0.0483531i
\(748\) 64.1842 37.0567i 2.34681 1.35493i
\(749\) 3.54825i 0.129650i
\(750\) 12.5652 + 21.7635i 0.458815 + 0.794692i
\(751\) −6.51477 + 11.2839i −0.237727 + 0.411756i −0.960062 0.279788i \(-0.909736\pi\)
0.722334 + 0.691544i \(0.243069\pi\)
\(752\) 8.50177 + 4.90850i 0.310028 + 0.178995i
\(753\) −0.763774 −0.0278335
\(754\) 0 0
\(755\) −2.65459 −0.0966106
\(756\) 2.52174 + 1.45593i 0.0917148 + 0.0529516i
\(757\) −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
\(759\) 16.7802i 0.609081i
\(760\) 5.97911 3.45204i 0.216885 0.125219i
\(761\) 33.2055 19.1712i 1.20370 0.694956i 0.242323 0.970196i \(-0.422091\pi\)
0.961376 + 0.275240i \(0.0887572\pi\)
\(762\) 12.0653i 0.437080i
\(763\) 0.960107 + 1.66295i 0.0347582 + 0.0602030i
\(764\) −55.5608 + 96.2342i −2.01012 + 3.48163i
\(765\) 4.40646 + 2.54407i 0.159316 + 0.0919812i
\(766\) 66.2683 2.39437
\(767\) 0 0
\(768\) −17.1511 −0.618886
\(769\) 3.15129 + 1.81940i 0.113638 + 0.0656091i 0.555742 0.831355i \(-0.312434\pi\)
−0.442104 + 0.896964i \(0.645768\pi\)
\(770\) 2.28150 3.95167i 0.0822194 0.142408i
\(771\) 6.54556 + 11.3373i 0.235733 + 0.408301i
\(772\) 92.4055i 3.32575i
\(773\) −34.0715 + 19.6712i −1.22547 + 0.707524i −0.966079 0.258249i \(-0.916855\pi\)
−0.259389 + 0.965773i \(0.583521\pi\)
\(774\) 25.8730 14.9378i 0.929987 0.536928i
\(775\) 37.1092i 1.33300i
\(776\) −74.6200 129.246i −2.67870 4.63965i
\(777\) −1.59634 + 2.76495i −0.0572685 + 0.0991919i
\(778\) −40.1456 23.1781i −1.43929 0.830974i