Properties

Label 507.2.j.i.361.6
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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 361.6
Root \(-1.56052 - 0.900969i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.i.316.6

$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.33136 1.34601i 1.64852 0.951773i 0.670859 0.741585i \(-0.265926\pi\)
0.977661 0.210188i \(-0.0674077\pi\)
\(3\) 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 \(-0.299888\pi\)
−0.406416 + 0.913688i \(0.633222\pi\)
\(8\) 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 \(-0.811326\pi\)
0.0690822 + 0.997611i \(0.477993\pi\)
\(12\) 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 0.406209 + 0.913780i \(0.366851\pi\)
−0.994461 + 0.105103i \(0.966483\pi\)
\(18\) 2.69202i 0.634516i
\(19\) 0.652135 + 0.376510i 0.149610 + 0.0863774i 0.572936 0.819600i \(-0.305804\pi\)
−0.423326 + 0.905977i \(0.639138\pi\)
\(20\) −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 0.992700 + 0.120613i \(0.0384861\pi\)
−0.391896 + 0.920010i \(0.628181\pi\)
\(24\) 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 0.941027 0.338330i \(-0.109862\pi\)
−0.763516 + 0.645789i \(0.776529\pi\)
\(30\) 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 \(-0.823458\pi\)
0.0310199 + 0.999519i \(0.490124\pi\)
\(38\) 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 \(-0.541368\pi\)
0.793925 + 0.608016i \(0.208034\pi\)
\(42\) 0.746980 + 1.29381i 0.115261 + 0.199639i
\(43\) −5.54892 + 9.61101i −0.846202 + 1.46566i 0.0383713 + 0.999264i \(0.487783\pi\)
−0.884573 + 0.466401i \(0.845550\pi\)
\(44\) 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 \(-0.247385\pi\)
−0.250874 + 0.968020i \(0.580718\pi\)
\(60\) 5.50365i 0.710518i
\(61\) 1.71164 2.96464i 0.219153 0.379583i −0.735397 0.677637i \(-0.763004\pi\)
0.954549 + 0.298054i \(0.0963374\pi\)
\(62\) −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 \(-0.703158\pi\)
0.397654 + 0.917535i \(0.369824\pi\)
\(68\) 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 \(-0.119134\pi\)
0.148773 + 0.988871i \(0.452468\pi\)
\(72\) 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 \(-0.843023\pi\)
−0.0304348 + 0.999537i \(0.509689\pi\)
\(90\) 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 −0.999999 0.00151988i \(-0.999516\pi\)
−0.501316 0.865264i \(-0.667150\pi\)
\(98\) −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 0.988669 0.150111i \(-0.0479630\pi\)
−0.624334 + 0.781157i \(0.714630\pi\)
\(102\) −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 0.669103 0.743170i \(-0.266679\pi\)
−0.978155 + 0.207875i \(0.933345\pi\)
\(108\) −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 −0.997697 0.0678240i \(-0.978394\pi\)
0.557586 + 0.830119i \(0.311728\pi\)
\(114\) 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 0.749305 0.662225i \(-0.230388\pi\)
−0.948156 + 0.317805i \(0.897054\pi\)
\(128\) −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 \(-0.436712\pi\)
−0.750205 + 0.661205i \(0.770045\pi\)
\(138\) 15.5133i 1.32058i
\(139\) 8.99880 15.5864i 0.763269 1.32202i −0.177889 0.984051i \(-0.556927\pi\)
0.941157 0.337969i \(-0.109740\pi\)
\(140\) −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 \(-0.549521\pi\)
−0.933041 + 0.359771i \(0.882855\pi\)
\(150\) 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 \(-0.122434\pi\)
0.138514 + 0.990360i \(0.455767\pi\)
\(164\) 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 \(-0.733617\pi\)
0.308170 + 0.951331i \(0.400283\pi\)
\(168\) 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 0.0962694 0.995355i \(-0.469309\pi\)
0.813868 0.581049i \(-0.197358\pi\)
\(174\) 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 0.972494 + 0.232929i \(0.0748309\pi\)
−0.284525 + 0.958669i \(0.591836\pi\)
\(180\) 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 −0.173409 0.984850i \(-0.555478\pi\)
0.939609 0.342249i \(-0.111189\pi\)
\(192\) −10.6712 18.4831i −0.770128 1.33390i
\(193\) 15.2517 8.80559i 1.09784 0.633840i 0.162189 0.986760i \(-0.448144\pi\)
0.935654 + 0.352920i \(0.114811\pi\)
\(194\) −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 \(-0.719782\pi\)
0.349213 + 0.937043i \(0.386449\pi\)
\(198\) −3.91939 6.78858i −0.278539 0.482443i
\(199\) 7.51842 13.0223i 0.532967 0.923125i −0.466292 0.884631i \(-0.654410\pi\)
0.999259 0.0384944i \(-0.0122562\pi\)
\(200\) 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 0.873836 0.486222i \(-0.161625\pi\)
−0.857998 + 0.513653i \(0.828292\pi\)
\(212\) −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 \(-0.851066\pi\)
−0.0556803 + 0.998449i \(0.517733\pi\)
\(224\) −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 \(-0.403193\pi\)
−0.676551 + 0.736396i \(0.736526\pi\)
\(228\) 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 \(-0.543112\pi\)
−0.925607 + 0.378485i \(0.876445\pi\)
\(242\) 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 −0.877826 0.478980i \(-0.841007\pi\)
0.853722 + 0.520730i \(0.174340\pi\)
\(252\) 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 0.586398 0.810023i \(-0.300545\pi\)
−0.994700 + 0.102825i \(0.967212\pi\)
\(258\) −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 −0.996899 0.0786906i \(-0.974926\pi\)
0.430301 0.902685i \(-0.358407\pi\)
\(264\) −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 0.239090 + 0.970997i \(0.423151\pi\)
−0.960453 + 0.278441i \(0.910182\pi\)
\(270\) 1.41185 + 2.44540i 0.0859227 + 0.148822i
\(271\) 17.1066 9.87651i 1.03915 0.599955i 0.119560 0.992827i \(-0.461852\pi\)
0.919593 + 0.392872i \(0.128518\pi\)
\(272\) 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 −0.838085 0.545539i \(-0.816325\pi\)
0.891493 + 0.453034i \(0.149658\pi\)
\(278\) 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 0.930533 0.366207i \(-0.119344\pi\)
−0.782411 + 0.622762i \(0.786010\pi\)
\(284\) 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 \(-0.334000\pi\)
−0.501814 + 0.864976i \(0.667334\pi\)
\(294\) 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 \(-0.233468\pi\)
−0.208325 + 0.978060i \(0.566801\pi\)
\(332\) 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 −0.716951 0.697124i \(-0.754463\pi\)
0.962202 + 0.272336i \(0.0877961\pi\)
\(348\) 5.01573 + 8.68750i 0.268871 + 0.465699i
\(349\) −20.7637 + 11.9879i −1.11145 + 0.641699i −0.939206 0.343355i \(-0.888437\pi\)
−0.172249 + 0.985053i \(0.555103\pi\)
\(350\) 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 \(-0.923366\pi\)
−0.279088 + 0.960265i \(0.590032\pi\)
\(354\) 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 0.713606 0.700547i \(-0.247061\pi\)
−0.963495 + 0.267728i \(0.913727\pi\)
\(368\) 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 0.228635 + 0.973512i \(0.426574\pi\)
−0.957404 + 0.288753i \(0.906759\pi\)
\(374\) −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 \(-0.531453\pi\)
0.812476 + 0.582995i \(0.198119\pi\)
\(380\) −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 \(-0.116829\pi\)
0.155930 + 0.987768i \(0.450163\pi\)
\(384\) −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 \(-0.349629\pi\)
−0.543662 + 0.839304i \(0.682963\pi\)
\(398\) 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 \(-0.655049\pi\)
0.531269 + 0.847203i \(0.321716\pi\)
\(402\) −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 \(-0.0680669\pi\)
0.304830 + 0.952407i \(0.401400\pi\)
\(410\) −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 0.773346 0.633984i \(-0.218582\pi\)
−0.935720 + 0.352745i \(0.885248\pi\)
\(420\) 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 \(-0.333517\pi\)
1.00000 0.000578325i \(0.000184086\pi\)
\(432\) 6.51842 + 11.2902i 0.313618 + 0.543201i
\(433\) −16.2371 + 28.1234i −0.780303 + 1.35152i 0.151462 + 0.988463i \(0.451602\pi\)
−0.931765 + 0.363061i \(0.881732\pi\)
\(434\) 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 0.977532 0.210785i \(-0.0676021\pi\)
−0.671312 + 0.741175i \(0.734269\pi\)
\(440\) 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 \(-0.428472\pi\)
−0.732840 + 0.680401i \(0.761806\pi\)
\(450\) 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 \(-0.392341\pi\)
0.982867 + 0.184319i \(0.0590078\pi\)
\(458\) 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 \(-0.525728\pi\)
−0.903568 + 0.428445i \(0.859062\pi\)
\(462\) −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 \(-0.605610\pi\)
0.655931 + 0.754821i \(0.272276\pi\)
\(480\) −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 \(-0.224038\pi\)
−0.179263 + 0.983801i \(0.557371\pi\)
\(488\) −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 0.916898 0.399122i \(-0.130685\pi\)
−0.804099 + 0.594496i \(0.797352\pi\)
\(492\) 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 0.495747 + 0.868467i \(0.334894\pi\)
−0.999988 + 0.00490359i \(0.998439\pi\)
\(504\) 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 \(-0.749456\pi\)
0.260471 + 0.965482i \(0.416122\pi\)
\(510\) 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 0.734666 0.678429i \(-0.237339\pi\)
−0.954870 + 0.297025i \(0.904005\pi\)
\(524\) −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 \(-0.964367\pi\)
−0.400126 + 0.916460i \(0.631034\pi\)
\(558\) 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 0.360697 + 0.932683i \(0.382539\pi\)
−0.988076 + 0.153968i \(0.950795\pi\)
\(564\) 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 0.538788 0.842441i \(-0.318882\pi\)
−0.998970 + 0.0453839i \(0.985549\pi\)
\(570\) 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 \(-0.625407\pi\)
0.607747 + 0.794131i \(0.292074\pi\)
\(588\) −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 0.975086 + 0.221826i \(0.0712015\pi\)
−0.295437 + 0.955362i \(0.595465\pi\)
\(602\) −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 −0.982430 0.186633i \(-0.940243\pi\)
0.652844 + 0.757493i \(0.273576\pi\)
\(608\) −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 \(-0.595046\pi\)
0.680615 + 0.732641i \(0.261713\pi\)
\(614\) 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 \(-0.303434\pi\)
−0.416570 + 0.909104i \(0.636768\pi\)
\(618\) 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 \(-0.620705\pi\)
−0.989593 + 0.143892i \(0.954038\pi\)
\(632\) 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 0.0670544 0.997749i \(-0.478640\pi\)
0.830549 0.556946i \(-0.188027\pi\)
\(642\) 17.2121i 0.679306i
\(643\) 25.7616 + 14.8735i 1.01594 + 0.586552i 0.912925 0.408128i \(-0.133818\pi\)
0.103013 + 0.994680i \(0.467152\pi\)
\(644\) 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 0.650245 0.759724i \(-0.274666\pi\)
−0.983063 + 0.183267i \(0.941333\pi\)
\(648\) −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 0.983228 + 0.182382i \(0.0583806\pi\)
−0.333667 + 0.942691i \(0.608286\pi\)
\(654\) 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 −0.0665286 0.997785i \(-0.521192\pi\)
0.897371 0.441277i \(-0.145474\pi\)
\(660\) 8.01291 + 13.8788i 0.311902 + 0.540230i
\(661\) −33.5067 + 19.3451i −1.30326 + 0.752438i −0.980962 0.194201i \(-0.937789\pi\)
−0.322298 + 0.946638i \(0.604455\pi\)
\(662\) 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 0.839943 0.542675i \(-0.182589\pi\)
−0.889942 + 0.456074i \(0.849255\pi\)
\(674\) −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 \(-0.232159\pi\)
−0.204302 + 0.978908i \(0.565492\pi\)
\(684\) 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 \(-0.568801\pi\)
0.738641 + 0.674099i \(0.235468\pi\)
\(692\) −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 \(-0.238398\pi\)
−0.223449 + 0.974716i \(0.571732\pi\)
\(710\) 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 0.493534 + 0.869726i \(0.335705\pi\)
−0.999972 + 0.00744977i \(0.997629\pi\)
\(720\) 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 \(-0.768188\pi\)
0.203236 + 0.979130i \(0.434854\pi\)
\(740\) 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 \(-0.735112\pi\)
0.303697 + 0.952769i \(0.401779\pi\)
\(744\) −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 0.722334 0.691544i \(-0.243069\pi\)
−0.960062 + 0.279788i \(0.909736\pi\)
\(752\) −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 0.581184 0.813772i \(-0.302590\pi\)
−0.995339 + 0.0964337i \(0.969256\pi\)
\(758\) 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 \(-0.577909\pi\)
−0.961376 + 0.275240i \(0.911243\pi\)
\(762\) 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 \(-0.687566\pi\)
0.442104 + 0.896964i \(0.354232\pi\)
\(770\) 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 \(-0.0831453\pi\)
0.259389 + 0.965773i \(0.416479\pi\)
\(774\) −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
\(779\)