Properties

Label 690.3.k.b.277.11
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.11
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.94131 - 0.763816i) q^{5} +2.44949 q^{6} +(8.62845 + 8.62845i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.94131 - 0.763816i) q^{5} +2.44949 q^{6} +(8.62845 + 8.62845i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(4.17750 + 5.70513i) q^{10} -9.96233 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-1.36926 + 1.36926i) q^{13} -17.2569i q^{14} +(6.98733 - 5.11637i) q^{15} -4.00000 q^{16} +(12.8665 + 12.8665i) q^{17} +(-3.00000 + 3.00000i) q^{18} +21.6135i q^{19} +(1.52763 - 9.88263i) q^{20} -21.1353 q^{21} +(9.96233 + 9.96233i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(23.8332 + 7.54851i) q^{25} +2.73852 q^{26} +(3.67423 + 3.67423i) q^{27} +(-17.2569 + 17.2569i) q^{28} -41.0639i q^{29} +(-12.1037 - 1.87096i) q^{30} +39.6561 q^{31} +(4.00000 + 4.00000i) q^{32} +(12.2013 - 12.2013i) q^{33} -25.7330i q^{34} +(-36.0453 - 49.2264i) q^{35} +6.00000 q^{36} +(-47.8886 - 47.8886i) q^{37} +(21.6135 - 21.6135i) q^{38} -3.35399i q^{39} +(-11.4103 + 8.35500i) q^{40} -46.0597 q^{41} +(21.1353 + 21.1353i) q^{42} +(-42.5076 + 42.5076i) q^{43} -19.9247i q^{44} +(-2.29145 + 14.8239i) q^{45} -6.78233 q^{46} +(4.44905 + 4.44905i) q^{47} +(4.89898 - 4.89898i) q^{48} +99.9003i q^{49} +(-16.2847 - 31.3817i) q^{50} -31.5164 q^{51} +(-2.73852 - 2.73852i) q^{52} +(-10.1671 + 10.1671i) q^{53} -7.34847i q^{54} +(49.2270 + 7.60939i) q^{55} +34.5138 q^{56} +(-26.4710 - 26.4710i) q^{57} +(-41.0639 + 41.0639i) q^{58} +83.8782i q^{59} +(10.2327 + 13.9747i) q^{60} -94.9681 q^{61} +(-39.6561 - 39.6561i) q^{62} +(25.8853 - 25.8853i) q^{63} -8.00000i q^{64} +(7.81181 - 5.72008i) q^{65} -24.4026 q^{66} +(-24.0838 - 24.0838i) q^{67} +(-25.7330 + 25.7330i) q^{68} +8.30662i q^{69} +(-13.1811 + 85.2718i) q^{70} -127.966 q^{71} +(-6.00000 - 6.00000i) q^{72} +(59.6158 - 59.6158i) q^{73} +95.7772i q^{74} +(-38.4346 + 19.9446i) q^{75} -43.2269 q^{76} +(-85.9595 - 85.9595i) q^{77} +(-3.35399 + 3.35399i) q^{78} +27.1346i q^{79} +(19.7653 + 3.05526i) q^{80} -9.00000 q^{81} +(46.0597 + 46.0597i) q^{82} +(-61.0630 + 61.0630i) q^{83} -42.2706i q^{84} +(-53.7498 - 73.4051i) q^{85} +85.0153 q^{86} +(50.2928 + 50.2928i) q^{87} +(-19.9247 + 19.9247i) q^{88} +84.3721i q^{89} +(17.1154 - 12.5325i) q^{90} -23.6292 q^{91} +(6.78233 + 6.78233i) q^{92} +(-48.5686 + 48.5686i) q^{93} -8.89810i q^{94} +(16.5087 - 106.799i) q^{95} -9.79796 q^{96} +(-111.709 - 111.709i) q^{97} +(99.9003 - 99.9003i) q^{98} +29.8870i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.94131 0.763816i −0.988263 0.152763i
\(6\) 2.44949 0.408248
\(7\) 8.62845 + 8.62845i 1.23264 + 1.23264i 0.962948 + 0.269688i \(0.0869205\pi\)
0.269688 + 0.962948i \(0.413080\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 4.17750 + 5.70513i 0.417750 + 0.570513i
\(11\) −9.96233 −0.905667 −0.452833 0.891595i \(-0.649587\pi\)
−0.452833 + 0.891595i \(0.649587\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −1.36926 + 1.36926i −0.105328 + 0.105328i −0.757807 0.652479i \(-0.773729\pi\)
0.652479 + 0.757807i \(0.273729\pi\)
\(14\) 17.2569i 1.23264i
\(15\) 6.98733 5.11637i 0.465822 0.341091i
\(16\) −4.00000 −0.250000
\(17\) 12.8665 + 12.8665i 0.756853 + 0.756853i 0.975748 0.218895i \(-0.0702452\pi\)
−0.218895 + 0.975748i \(0.570245\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 21.6135i 1.13755i 0.822493 + 0.568776i \(0.192583\pi\)
−0.822493 + 0.568776i \(0.807417\pi\)
\(20\) 1.52763 9.88263i 0.0763816 0.494131i
\(21\) −21.1353 −1.00644
\(22\) 9.96233 + 9.96233i 0.452833 + 0.452833i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 23.8332 + 7.54851i 0.953327 + 0.301940i
\(26\) 2.73852 0.105328
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −17.2569 + 17.2569i −0.616318 + 0.616318i
\(29\) 41.0639i 1.41600i −0.706214 0.707998i \(-0.749598\pi\)
0.706214 0.707998i \(-0.250402\pi\)
\(30\) −12.1037 1.87096i −0.403457 0.0623653i
\(31\) 39.6561 1.27923 0.639614 0.768696i \(-0.279094\pi\)
0.639614 + 0.768696i \(0.279094\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 12.2013 12.2013i 0.369737 0.369737i
\(34\) 25.7330i 0.756853i
\(35\) −36.0453 49.2264i −1.02987 1.40647i
\(36\) 6.00000 0.166667
\(37\) −47.8886 47.8886i −1.29429 1.29429i −0.932109 0.362178i \(-0.882033\pi\)
−0.362178 0.932109i \(-0.617967\pi\)
\(38\) 21.6135 21.6135i 0.568776 0.568776i
\(39\) 3.35399i 0.0859997i
\(40\) −11.4103 + 8.35500i −0.285257 + 0.208875i
\(41\) −46.0597 −1.12341 −0.561704 0.827338i \(-0.689854\pi\)
−0.561704 + 0.827338i \(0.689854\pi\)
\(42\) 21.1353 + 21.1353i 0.503221 + 0.503221i
\(43\) −42.5076 + 42.5076i −0.988550 + 0.988550i −0.999935 0.0113855i \(-0.996376\pi\)
0.0113855 + 0.999935i \(0.496376\pi\)
\(44\) 19.9247i 0.452833i
\(45\) −2.29145 + 14.8239i −0.0509211 + 0.329421i
\(46\) −6.78233 −0.147442
\(47\) 4.44905 + 4.44905i 0.0946607 + 0.0946607i 0.752851 0.658191i \(-0.228678\pi\)
−0.658191 + 0.752851i \(0.728678\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 99.9003i 2.03878i
\(50\) −16.2847 31.3817i −0.325693 0.627634i
\(51\) −31.5164 −0.617968
\(52\) −2.73852 2.73852i −0.0526638 0.0526638i
\(53\) −10.1671 + 10.1671i −0.191832 + 0.191832i −0.796487 0.604655i \(-0.793311\pi\)
0.604655 + 0.796487i \(0.293311\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 49.2270 + 7.60939i 0.895037 + 0.138353i
\(56\) 34.5138 0.616318
\(57\) −26.4710 26.4710i −0.464403 0.464403i
\(58\) −41.0639 + 41.0639i −0.707998 + 0.707998i
\(59\) 83.8782i 1.42166i 0.703362 + 0.710832i \(0.251681\pi\)
−0.703362 + 0.710832i \(0.748319\pi\)
\(60\) 10.2327 + 13.9747i 0.170546 + 0.232911i
\(61\) −94.9681 −1.55685 −0.778427 0.627735i \(-0.783982\pi\)
−0.778427 + 0.627735i \(0.783982\pi\)
\(62\) −39.6561 39.6561i −0.639614 0.639614i
\(63\) 25.8853 25.8853i 0.410879 0.410879i
\(64\) 8.00000i 0.125000i
\(65\) 7.81181 5.72008i 0.120182 0.0880013i
\(66\) −24.4026 −0.369737
\(67\) −24.0838 24.0838i −0.359460 0.359460i 0.504154 0.863614i \(-0.331804\pi\)
−0.863614 + 0.504154i \(0.831804\pi\)
\(68\) −25.7330 + 25.7330i −0.378427 + 0.378427i
\(69\) 8.30662i 0.120386i
\(70\) −13.1811 + 85.2718i −0.188301 + 1.21817i
\(71\) −127.966 −1.80234 −0.901171 0.433464i \(-0.857291\pi\)
−0.901171 + 0.433464i \(0.857291\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 59.6158 59.6158i 0.816655 0.816655i −0.168967 0.985622i \(-0.554043\pi\)
0.985622 + 0.168967i \(0.0540432\pi\)
\(74\) 95.7772i 1.29429i
\(75\) −38.4346 + 19.9446i −0.512461 + 0.265927i
\(76\) −43.2269 −0.568776
\(77\) −85.9595 85.9595i −1.11636 1.11636i
\(78\) −3.35399 + 3.35399i −0.0429999 + 0.0429999i
\(79\) 27.1346i 0.343476i 0.985143 + 0.171738i \(0.0549383\pi\)
−0.985143 + 0.171738i \(0.945062\pi\)
\(80\) 19.7653 + 3.05526i 0.247066 + 0.0381908i
\(81\) −9.00000 −0.111111
\(82\) 46.0597 + 46.0597i 0.561704 + 0.561704i
\(83\) −61.0630 + 61.0630i −0.735698 + 0.735698i −0.971742 0.236044i \(-0.924149\pi\)
0.236044 + 0.971742i \(0.424149\pi\)
\(84\) 42.2706i 0.503221i
\(85\) −53.7498 73.4051i −0.632351 0.863589i
\(86\) 85.0153 0.988550
\(87\) 50.2928 + 50.2928i 0.578078 + 0.578078i
\(88\) −19.9247 + 19.9247i −0.226417 + 0.226417i
\(89\) 84.3721i 0.948001i 0.880524 + 0.474001i \(0.157191\pi\)
−0.880524 + 0.474001i \(0.842809\pi\)
\(90\) 17.1154 12.5325i 0.190171 0.139250i
\(91\) −23.6292 −0.259661
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −48.5686 + 48.5686i −0.522243 + 0.522243i
\(94\) 8.89810i 0.0946607i
\(95\) 16.5087 106.799i 0.173776 1.12420i
\(96\) −9.79796 −0.102062
\(97\) −111.709 111.709i −1.15164 1.15164i −0.986223 0.165418i \(-0.947103\pi\)
−0.165418 0.986223i \(-0.552897\pi\)
\(98\) 99.9003 99.9003i 1.01939 1.01939i
\(99\) 29.8870i 0.301889i
\(100\) −15.0970 + 47.6663i −0.150970 + 0.476663i
\(101\) 77.7181 0.769486 0.384743 0.923024i \(-0.374290\pi\)
0.384743 + 0.923024i \(0.374290\pi\)
\(102\) 31.5164 + 31.5164i 0.308984 + 0.308984i
\(103\) 42.3360 42.3360i 0.411029 0.411029i −0.471068 0.882097i \(-0.656131\pi\)
0.882097 + 0.471068i \(0.156131\pi\)
\(104\) 5.47704i 0.0526638i
\(105\) 104.436 + 16.1435i 0.994630 + 0.153747i
\(106\) 20.3342 0.191832
\(107\) −106.967 106.967i −0.999693 0.999693i 0.000307102 1.00000i \(-0.499902\pi\)
−1.00000 0.000307102i \(0.999902\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 36.5144i 0.334994i 0.985873 + 0.167497i \(0.0535685\pi\)
−0.985873 + 0.167497i \(0.946432\pi\)
\(110\) −41.6176 56.8364i −0.378342 0.516695i
\(111\) 117.303 1.05678
\(112\) −34.5138 34.5138i −0.308159 0.308159i
\(113\) −10.6656 + 10.6656i −0.0943859 + 0.0943859i −0.752723 0.658337i \(-0.771260\pi\)
0.658337 + 0.752723i \(0.271260\pi\)
\(114\) 52.9420i 0.464403i
\(115\) −19.3470 + 14.1666i −0.168235 + 0.123188i
\(116\) 82.1278 0.707998
\(117\) 4.10778 + 4.10778i 0.0351092 + 0.0351092i
\(118\) 83.8782 83.8782i 0.710832 0.710832i
\(119\) 222.036i 1.86585i
\(120\) 3.74192 24.2074i 0.0311827 0.201728i
\(121\) −21.7519 −0.179768
\(122\) 94.9681 + 94.9681i 0.778427 + 0.778427i
\(123\) 56.4114 56.4114i 0.458629 0.458629i
\(124\) 79.3121i 0.639614i
\(125\) −112.002 55.5037i −0.896012 0.444030i
\(126\) −51.7707 −0.410879
\(127\) 121.366 + 121.366i 0.955634 + 0.955634i 0.999057 0.0434223i \(-0.0138261\pi\)
−0.0434223 + 0.999057i \(0.513826\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 104.122i 0.807147i
\(130\) −13.5319 2.09173i −0.104091 0.0160902i
\(131\) 188.546 1.43928 0.719642 0.694345i \(-0.244306\pi\)
0.719642 + 0.694345i \(0.244306\pi\)
\(132\) 24.4026 + 24.4026i 0.184868 + 0.184868i
\(133\) −186.491 + 186.491i −1.40219 + 1.40219i
\(134\) 48.1676i 0.359460i
\(135\) −15.3491 20.9620i −0.113697 0.155274i
\(136\) 51.4660 0.378427
\(137\) −86.1083 86.1083i −0.628528 0.628528i 0.319170 0.947698i \(-0.396596\pi\)
−0.947698 + 0.319170i \(0.896596\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 145.443i 1.04636i 0.852224 + 0.523178i \(0.175254\pi\)
−0.852224 + 0.523178i \(0.824746\pi\)
\(140\) 98.4528 72.0907i 0.703235 0.514933i
\(141\) −10.8979 −0.0772901
\(142\) 127.966 + 127.966i 0.901171 + 0.901171i
\(143\) 13.6410 13.6410i 0.0953918 0.0953918i
\(144\) 12.0000i 0.0833333i
\(145\) −31.3653 + 202.910i −0.216312 + 1.39938i
\(146\) −119.232 −0.816655
\(147\) −122.352 122.352i −0.832329 0.832329i
\(148\) 95.7772 95.7772i 0.647144 0.647144i
\(149\) 135.574i 0.909889i −0.890520 0.454945i \(-0.849659\pi\)
0.890520 0.454945i \(-0.150341\pi\)
\(150\) 58.3791 + 18.4900i 0.389194 + 0.123267i
\(151\) −222.424 −1.47300 −0.736502 0.676435i \(-0.763524\pi\)
−0.736502 + 0.676435i \(0.763524\pi\)
\(152\) 43.2269 + 43.2269i 0.284388 + 0.284388i
\(153\) 38.5995 38.5995i 0.252284 0.252284i
\(154\) 171.919i 1.11636i
\(155\) −195.953 30.2899i −1.26421 0.195419i
\(156\) 6.70798 0.0429999
\(157\) −164.277 164.277i −1.04635 1.04635i −0.998872 0.0474752i \(-0.984882\pi\)
−0.0474752 0.998872i \(-0.515118\pi\)
\(158\) 27.1346 27.1346i 0.171738 0.171738i
\(159\) 24.9042i 0.156630i
\(160\) −16.7100 22.8205i −0.104437 0.142628i
\(161\) 58.5210 0.363484
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 50.5955 50.5955i 0.310402 0.310402i −0.534663 0.845065i \(-0.679562\pi\)
0.845065 + 0.534663i \(0.179562\pi\)
\(164\) 92.1194i 0.561704i
\(165\) −69.6101 + 50.9710i −0.421879 + 0.308915i
\(166\) 122.126 0.735698
\(167\) −129.032 129.032i −0.772645 0.772645i 0.205923 0.978568i \(-0.433980\pi\)
−0.978568 + 0.205923i \(0.933980\pi\)
\(168\) −42.2706 + 42.2706i −0.251611 + 0.251611i
\(169\) 165.250i 0.977812i
\(170\) −19.6553 + 127.155i −0.115619 + 0.747970i
\(171\) 64.8404 0.379184
\(172\) −85.0153 85.0153i −0.494275 0.494275i
\(173\) 31.0922 31.0922i 0.179724 0.179724i −0.611512 0.791235i \(-0.709438\pi\)
0.791235 + 0.611512i \(0.209438\pi\)
\(174\) 100.586i 0.578078i
\(175\) 140.511 + 270.775i 0.802922 + 1.54729i
\(176\) 39.8493 0.226417
\(177\) −102.729 102.729i −0.580392 0.580392i
\(178\) 84.3721 84.3721i 0.474001 0.474001i
\(179\) 66.4446i 0.371199i −0.982625 0.185599i \(-0.940577\pi\)
0.982625 0.185599i \(-0.0594227\pi\)
\(180\) −29.6479 4.58290i −0.164710 0.0254605i
\(181\) 57.8597 0.319667 0.159833 0.987144i \(-0.448904\pi\)
0.159833 + 0.987144i \(0.448904\pi\)
\(182\) 23.6292 + 23.6292i 0.129831 + 0.129831i
\(183\) 116.312 116.312i 0.635583 0.635583i
\(184\) 13.5647i 0.0737210i
\(185\) 200.055 + 273.211i 1.08138 + 1.47682i
\(186\) 97.1371 0.522243
\(187\) −128.180 128.180i −0.685457 0.685457i
\(188\) −8.89810 + 8.89810i −0.0473303 + 0.0473303i
\(189\) 63.4059i 0.335481i
\(190\) −123.308 + 90.2903i −0.648988 + 0.475212i
\(191\) 5.50354 0.0288143 0.0144072 0.999896i \(-0.495414\pi\)
0.0144072 + 0.999896i \(0.495414\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 179.960 179.960i 0.932434 0.932434i −0.0654238 0.997858i \(-0.520840\pi\)
0.997858 + 0.0654238i \(0.0208399\pi\)
\(194\) 223.419i 1.15164i
\(195\) −2.56183 + 16.5731i −0.0131376 + 0.0849903i
\(196\) −199.801 −1.01939
\(197\) 145.865 + 145.865i 0.740432 + 0.740432i 0.972661 0.232229i \(-0.0746019\pi\)
−0.232229 + 0.972661i \(0.574602\pi\)
\(198\) 29.8870 29.8870i 0.150944 0.150944i
\(199\) 94.1556i 0.473144i −0.971614 0.236572i \(-0.923976\pi\)
0.971614 0.236572i \(-0.0760239\pi\)
\(200\) 62.7634 32.5693i 0.313817 0.162847i
\(201\) 58.9930 0.293498
\(202\) −77.7181 77.7181i −0.384743 0.384743i
\(203\) 354.318 354.318i 1.74541 1.74541i
\(204\) 63.0328i 0.308984i
\(205\) 227.596 + 35.1811i 1.11022 + 0.171615i
\(206\) −84.6721 −0.411029
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 5.47704 5.47704i 0.0263319 0.0263319i
\(209\) 215.321i 1.03024i
\(210\) −88.2927 120.580i −0.420441 0.574189i
\(211\) −36.0474 −0.170841 −0.0854204 0.996345i \(-0.527223\pi\)
−0.0854204 + 0.996345i \(0.527223\pi\)
\(212\) −20.3342 20.3342i −0.0959159 0.0959159i
\(213\) 156.726 156.726i 0.735803 0.735803i
\(214\) 213.934i 0.999693i
\(215\) 242.512 177.576i 1.12796 0.825933i
\(216\) 14.6969 0.0680414
\(217\) 342.170 + 342.170i 1.57682 + 1.57682i
\(218\) 36.5144 36.5144i 0.167497 0.167497i
\(219\) 146.028i 0.666796i
\(220\) −15.2188 + 98.4540i −0.0691763 + 0.447518i
\(221\) −35.2352 −0.159435
\(222\) −117.303 117.303i −0.528391 0.528391i
\(223\) 68.4373 68.4373i 0.306894 0.306894i −0.536810 0.843703i \(-0.680371\pi\)
0.843703 + 0.536810i \(0.180371\pi\)
\(224\) 69.0276i 0.308159i
\(225\) 22.6455 71.4995i 0.100647 0.317776i
\(226\) 21.3312 0.0943859
\(227\) −157.931 157.931i −0.695732 0.695732i 0.267755 0.963487i \(-0.413718\pi\)
−0.963487 + 0.267755i \(0.913718\pi\)
\(228\) 52.9420 52.9420i 0.232202 0.232202i
\(229\) 278.744i 1.21722i 0.793468 + 0.608612i \(0.208274\pi\)
−0.793468 + 0.608612i \(0.791726\pi\)
\(230\) 33.5136 + 5.18045i 0.145711 + 0.0225237i
\(231\) 210.557 0.911502
\(232\) −82.1278 82.1278i −0.353999 0.353999i
\(233\) −263.213 + 263.213i −1.12967 + 1.12967i −0.139438 + 0.990231i \(0.544530\pi\)
−0.990231 + 0.139438i \(0.955470\pi\)
\(234\) 8.21556i 0.0351092i
\(235\) −18.5859 25.3824i −0.0790889 0.108010i
\(236\) −167.756 −0.710832
\(237\) −33.2330 33.2330i −0.140224 0.140224i
\(238\) 222.036 222.036i 0.932924 0.932924i
\(239\) 47.8510i 0.200214i −0.994977 0.100107i \(-0.968082\pi\)
0.994977 0.100107i \(-0.0319184\pi\)
\(240\) −27.9493 + 20.4655i −0.116455 + 0.0852728i
\(241\) −91.5567 −0.379903 −0.189952 0.981793i \(-0.560833\pi\)
−0.189952 + 0.981793i \(0.560833\pi\)
\(242\) 21.7519 + 21.7519i 0.0898839 + 0.0898839i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 189.936i 0.778427i
\(245\) 76.3054 493.639i 0.311451 2.01485i
\(246\) −112.823 −0.458629
\(247\) −29.5945 29.5945i −0.119816 0.119816i
\(248\) 79.3121 79.3121i 0.319807 0.319807i
\(249\) 149.573i 0.600695i
\(250\) 56.4978 + 167.505i 0.225991 + 0.670021i
\(251\) 358.473 1.42818 0.714090 0.700054i \(-0.246841\pi\)
0.714090 + 0.700054i \(0.246841\pi\)
\(252\) 51.7707 + 51.7707i 0.205439 + 0.205439i
\(253\) −33.7839 + 33.7839i −0.133533 + 0.133533i
\(254\) 242.731i 0.955634i
\(255\) 155.732 + 24.0727i 0.610715 + 0.0944028i
\(256\) 16.0000 0.0625000
\(257\) 45.2189 + 45.2189i 0.175949 + 0.175949i 0.789587 0.613638i \(-0.210295\pi\)
−0.613638 + 0.789587i \(0.710295\pi\)
\(258\) −104.122 + 104.122i −0.403574 + 0.403574i
\(259\) 826.409i 3.19077i
\(260\) 11.4402 + 15.6236i 0.0440006 + 0.0600908i
\(261\) −123.192 −0.471999
\(262\) −188.546 188.546i −0.719642 0.719642i
\(263\) 7.35905 7.35905i 0.0279812 0.0279812i −0.692978 0.720959i \(-0.743702\pi\)
0.720959 + 0.692978i \(0.243702\pi\)
\(264\) 48.8053i 0.184868i
\(265\) 58.0046 42.4730i 0.218885 0.160275i
\(266\) 372.982 1.40219
\(267\) −103.334 103.334i −0.387020 0.387020i
\(268\) 48.1676 48.1676i 0.179730 0.179730i
\(269\) 159.878i 0.594341i 0.954824 + 0.297171i \(0.0960430\pi\)
−0.954824 + 0.297171i \(0.903957\pi\)
\(270\) −5.61288 + 36.3111i −0.0207884 + 0.134486i
\(271\) 211.259 0.779554 0.389777 0.920909i \(-0.372552\pi\)
0.389777 + 0.920909i \(0.372552\pi\)
\(272\) −51.4660 51.4660i −0.189213 0.189213i
\(273\) 28.9397 28.9397i 0.106006 0.106006i
\(274\) 172.217i 0.628528i
\(275\) −237.434 75.2008i −0.863396 0.273457i
\(276\) −16.6132 −0.0601929
\(277\) 219.374 + 219.374i 0.791962 + 0.791962i 0.981813 0.189851i \(-0.0608004\pi\)
−0.189851 + 0.981813i \(0.560800\pi\)
\(278\) 145.443 145.443i 0.523178 0.523178i
\(279\) 118.968i 0.426409i
\(280\) −170.544 26.3622i −0.609084 0.0941507i
\(281\) 168.520 0.599714 0.299857 0.953984i \(-0.403061\pi\)
0.299857 + 0.953984i \(0.403061\pi\)
\(282\) 10.8979 + 10.8979i 0.0386450 + 0.0386450i
\(283\) 154.756 154.756i 0.546843 0.546843i −0.378684 0.925526i \(-0.623623\pi\)
0.925526 + 0.378684i \(0.123623\pi\)
\(284\) 255.933i 0.901171i
\(285\) 110.583 + 151.020i 0.388009 + 0.529896i
\(286\) −27.2821 −0.0953918
\(287\) −397.424 397.424i −1.38475 1.38475i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 42.0941i 0.145654i
\(290\) 234.275 171.544i 0.807844 0.591532i
\(291\) 273.631 0.940312
\(292\) 119.232 + 119.232i 0.408327 + 0.408327i
\(293\) −312.900 + 312.900i −1.06792 + 1.06792i −0.0703988 + 0.997519i \(0.522427\pi\)
−0.997519 + 0.0703988i \(0.977573\pi\)
\(294\) 244.705i 0.832329i
\(295\) 64.0675 414.469i 0.217178 1.40498i
\(296\) −191.554 −0.647144
\(297\) −36.6040 36.6040i −0.123246 0.123246i
\(298\) −135.574 + 135.574i −0.454945 + 0.454945i
\(299\) 9.28677i 0.0310594i
\(300\) −39.8891 76.8691i −0.132964 0.256230i
\(301\) −733.550 −2.43704
\(302\) 222.424 + 222.424i 0.736502 + 0.736502i
\(303\) −95.1848 + 95.1848i −0.314141 + 0.314141i
\(304\) 86.4539i 0.284388i
\(305\) 469.267 + 72.5381i 1.53858 + 0.237830i
\(306\) −77.1991 −0.252284
\(307\) 66.0310 + 66.0310i 0.215085 + 0.215085i 0.806423 0.591339i \(-0.201400\pi\)
−0.591339 + 0.806423i \(0.701400\pi\)
\(308\) 171.919 171.919i 0.558179 0.558179i
\(309\) 103.702i 0.335604i
\(310\) 165.663 + 226.243i 0.534397 + 0.729816i
\(311\) −47.7193 −0.153438 −0.0767191 0.997053i \(-0.524444\pi\)
−0.0767191 + 0.997053i \(0.524444\pi\)
\(312\) −6.70798 6.70798i −0.0214999 0.0214999i
\(313\) −342.502 + 342.502i −1.09425 + 1.09425i −0.0991860 + 0.995069i \(0.531624\pi\)
−0.995069 + 0.0991860i \(0.968376\pi\)
\(314\) 328.553i 1.04635i
\(315\) −147.679 + 108.136i −0.468823 + 0.343289i
\(316\) −54.2693 −0.171738
\(317\) 265.894 + 265.894i 0.838783 + 0.838783i 0.988699 0.149916i \(-0.0479002\pi\)
−0.149916 + 0.988699i \(0.547900\pi\)
\(318\) −24.9042 + 24.9042i −0.0783150 + 0.0783150i
\(319\) 409.092i 1.28242i
\(320\) −6.11053 + 39.5305i −0.0190954 + 0.123533i
\(321\) 262.015 0.816246
\(322\) −58.5210 58.5210i −0.181742 0.181742i
\(323\) −278.090 + 278.090i −0.860960 + 0.860960i
\(324\) 18.0000i 0.0555556i
\(325\) −42.9697 + 22.2979i −0.132214 + 0.0686090i
\(326\) −101.191 −0.310402
\(327\) −44.7208 44.7208i −0.136761 0.136761i
\(328\) −92.1194 + 92.1194i −0.280852 + 0.280852i
\(329\) 76.7768i 0.233364i
\(330\) 120.581 + 18.6391i 0.365397 + 0.0564822i
\(331\) −49.2824 −0.148889 −0.0744447 0.997225i \(-0.523718\pi\)
−0.0744447 + 0.997225i \(0.523718\pi\)
\(332\) −122.126 122.126i −0.367849 0.367849i
\(333\) −143.666 + 143.666i −0.431429 + 0.431429i
\(334\) 258.064i 0.772645i
\(335\) 100.610 + 137.401i 0.300328 + 0.410153i
\(336\) 84.5412 0.251611
\(337\) 196.678 + 196.678i 0.583614 + 0.583614i 0.935894 0.352281i \(-0.114594\pi\)
−0.352281 + 0.935894i \(0.614594\pi\)
\(338\) 165.250 165.250i 0.488906 0.488906i
\(339\) 26.1253i 0.0770658i
\(340\) 146.810 107.500i 0.431795 0.316175i
\(341\) −395.067 −1.15855
\(342\) −64.8404 64.8404i −0.189592 0.189592i
\(343\) −439.190 + 439.190i −1.28044 + 1.28044i
\(344\) 170.031i 0.494275i
\(345\) 6.34473 41.0456i 0.0183905 0.118973i
\(346\) −62.1844 −0.179724
\(347\) 161.562 + 161.562i 0.465596 + 0.465596i 0.900484 0.434888i \(-0.143212\pi\)
−0.434888 + 0.900484i \(0.643212\pi\)
\(348\) −100.586 + 100.586i −0.289039 + 0.289039i
\(349\) 69.2537i 0.198435i 0.995066 + 0.0992173i \(0.0316339\pi\)
−0.995066 + 0.0992173i \(0.968366\pi\)
\(350\) 130.264 411.287i 0.372182 1.17510i
\(351\) −10.0620 −0.0286666
\(352\) −39.8493 39.8493i −0.113208 0.113208i
\(353\) 187.924 187.924i 0.532363 0.532363i −0.388912 0.921275i \(-0.627149\pi\)
0.921275 + 0.388912i \(0.127149\pi\)
\(354\) 205.459i 0.580392i
\(355\) 632.322 + 97.7427i 1.78119 + 0.275331i
\(356\) −168.744 −0.474001
\(357\) −271.937 271.937i −0.761730 0.761730i
\(358\) −66.4446 + 66.4446i −0.185599 + 0.185599i
\(359\) 327.086i 0.911103i 0.890209 + 0.455551i \(0.150558\pi\)
−0.890209 + 0.455551i \(0.849442\pi\)
\(360\) 25.0650 + 34.2308i 0.0696250 + 0.0950855i
\(361\) −106.142 −0.294023
\(362\) −57.8597 57.8597i −0.159833 0.159833i
\(363\) 26.6405 26.6405i 0.0733899 0.0733899i
\(364\) 47.2584i 0.129831i
\(365\) −340.116 + 249.045i −0.931824 + 0.682315i
\(366\) −232.623 −0.635583
\(367\) −490.806 490.806i −1.33735 1.33735i −0.898622 0.438724i \(-0.855431\pi\)
−0.438724 0.898622i \(-0.644569\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 138.179i 0.374469i
\(370\) 73.1562 473.265i 0.197719 1.27910i
\(371\) −175.452 −0.472917
\(372\) −97.1371 97.1371i −0.261121 0.261121i
\(373\) −21.0158 + 21.0158i −0.0563427 + 0.0563427i −0.734717 0.678374i \(-0.762685\pi\)
0.678374 + 0.734717i \(0.262685\pi\)
\(374\) 256.361i 0.685457i
\(375\) 205.151 69.1954i 0.547070 0.184521i
\(376\) 17.7962 0.0473303
\(377\) 56.2272 + 56.2272i 0.149144 + 0.149144i
\(378\) 63.4059 63.4059i 0.167740 0.167740i
\(379\) 310.295i 0.818720i −0.912373 0.409360i \(-0.865752\pi\)
0.912373 0.409360i \(-0.134248\pi\)
\(380\) 213.598 + 33.0174i 0.562100 + 0.0868880i
\(381\) −297.284 −0.780272
\(382\) −5.50354 5.50354i −0.0144072 0.0144072i
\(383\) 246.947 246.947i 0.644769 0.644769i −0.306955 0.951724i \(-0.599310\pi\)
0.951724 + 0.306955i \(0.0993101\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 359.096 + 490.410i 0.932716 + 1.27379i
\(386\) −359.919 −0.932434
\(387\) 127.523 + 127.523i 0.329517 + 0.329517i
\(388\) 223.419 223.419i 0.575821 0.575821i
\(389\) 467.057i 1.20066i 0.799752 + 0.600330i \(0.204964\pi\)
−0.799752 + 0.600330i \(0.795036\pi\)
\(390\) 19.1349 14.0113i 0.0490639 0.0359264i
\(391\) 87.2649 0.223184
\(392\) 199.801 + 199.801i 0.509695 + 0.509695i
\(393\) −230.921 + 230.921i −0.587586 + 0.587586i
\(394\) 291.730i 0.740432i
\(395\) 20.7259 134.081i 0.0524705 0.339445i
\(396\) −59.7740 −0.150944
\(397\) 387.028 + 387.028i 0.974882 + 0.974882i 0.999692 0.0248106i \(-0.00789828\pi\)
−0.0248106 + 0.999692i \(0.507898\pi\)
\(398\) −94.1556 + 94.1556i −0.236572 + 0.236572i
\(399\) 456.807i 1.14488i
\(400\) −95.3327 30.1940i −0.238332 0.0754851i
\(401\) −448.866 −1.11937 −0.559684 0.828706i \(-0.689077\pi\)
−0.559684 + 0.828706i \(0.689077\pi\)
\(402\) −58.9930 58.9930i −0.146749 0.146749i
\(403\) −54.2995 + 54.2995i −0.134738 + 0.134738i
\(404\) 155.436i 0.384743i
\(405\) 44.4718 + 6.87434i 0.109807 + 0.0169737i
\(406\) −708.635 −1.74541
\(407\) 477.082 + 477.082i 1.17219 + 1.17219i
\(408\) −63.0328 + 63.0328i −0.154492 + 0.154492i
\(409\) 335.091i 0.819293i 0.912244 + 0.409647i \(0.134348\pi\)
−0.912244 + 0.409647i \(0.865652\pi\)
\(410\) −192.414 262.777i −0.469303 0.640919i
\(411\) 210.921 0.513191
\(412\) 84.6721 + 84.6721i 0.205515 + 0.205515i
\(413\) −723.739 + 723.739i −1.75239 + 1.75239i
\(414\) 20.3470i 0.0491473i
\(415\) 348.372 255.090i 0.839451 0.614676i
\(416\) −10.9541 −0.0263319
\(417\) −178.131 178.131i −0.427173 0.427173i
\(418\) −215.321 + 215.321i −0.515121 + 0.515121i
\(419\) 235.423i 0.561869i 0.959727 + 0.280934i \(0.0906444\pi\)
−0.959727 + 0.280934i \(0.909356\pi\)
\(420\) −32.2870 + 208.872i −0.0768737 + 0.497315i
\(421\) −326.446 −0.775406 −0.387703 0.921784i \(-0.626731\pi\)
−0.387703 + 0.921784i \(0.626731\pi\)
\(422\) 36.0474 + 36.0474i 0.0854204 + 0.0854204i
\(423\) 13.3472 13.3472i 0.0315536 0.0315536i
\(424\) 40.6683i 0.0959159i
\(425\) 209.527 + 403.773i 0.493004 + 0.950053i
\(426\) −313.452 −0.735803
\(427\) −819.427 819.427i −1.91903 1.91903i
\(428\) 213.934 213.934i 0.499846 0.499846i
\(429\) 33.4136i 0.0778871i
\(430\) −420.087 64.9360i −0.976947 0.151014i
\(431\) −307.959 −0.714523 −0.357262 0.934004i \(-0.616290\pi\)
−0.357262 + 0.934004i \(0.616290\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 393.236 393.236i 0.908166 0.908166i −0.0879578 0.996124i \(-0.528034\pi\)
0.996124 + 0.0879578i \(0.0280341\pi\)
\(434\) 684.341i 1.57682i
\(435\) −210.098 286.927i −0.482984 0.659602i
\(436\) −73.0287 −0.167497
\(437\) 73.2949 + 73.2949i 0.167723 + 0.167723i
\(438\) 146.028 146.028i 0.333398 0.333398i
\(439\) 330.522i 0.752897i −0.926438 0.376448i \(-0.877145\pi\)
0.926438 0.376448i \(-0.122855\pi\)
\(440\) 113.673 83.2353i 0.258347 0.189171i
\(441\) 299.701 0.679594
\(442\) 35.2352 + 35.2352i 0.0797176 + 0.0797176i
\(443\) −116.455 + 116.455i −0.262879 + 0.262879i −0.826223 0.563344i \(-0.809515\pi\)
0.563344 + 0.826223i \(0.309515\pi\)
\(444\) 234.605i 0.528391i
\(445\) 64.4448 416.909i 0.144820 0.936874i
\(446\) −136.875 −0.306894
\(447\) 166.043 + 166.043i 0.371461 + 0.371461i
\(448\) 69.0276 69.0276i 0.154079 0.154079i
\(449\) 149.486i 0.332930i −0.986047 0.166465i \(-0.946765\pi\)
0.986047 0.166465i \(-0.0532354\pi\)
\(450\) −94.1450 + 48.8540i −0.209211 + 0.108564i
\(451\) 458.862 1.01743
\(452\) −21.3312 21.3312i −0.0471929 0.0471929i
\(453\) 272.412 272.412i 0.601351 0.601351i
\(454\) 315.862i 0.695732i
\(455\) 116.759 + 18.0483i 0.256614 + 0.0396667i
\(456\) −105.884 −0.232202
\(457\) 259.178 + 259.178i 0.567130 + 0.567130i 0.931323 0.364193i \(-0.118655\pi\)
−0.364193 + 0.931323i \(0.618655\pi\)
\(458\) 278.744 278.744i 0.608612 0.608612i
\(459\) 94.5491i 0.205989i
\(460\) −28.3332 38.6941i −0.0615939 0.0841176i
\(461\) −804.421 −1.74495 −0.872474 0.488661i \(-0.837486\pi\)
−0.872474 + 0.488661i \(0.837486\pi\)
\(462\) −210.557 210.557i −0.455751 0.455751i
\(463\) 284.414 284.414i 0.614284 0.614284i −0.329775 0.944059i \(-0.606973\pi\)
0.944059 + 0.329775i \(0.106973\pi\)
\(464\) 164.256i 0.353999i
\(465\) 277.090 202.895i 0.595892 0.436333i
\(466\) 526.426 1.12967
\(467\) 542.008 + 542.008i 1.16062 + 1.16062i 0.984341 + 0.176276i \(0.0564050\pi\)
0.176276 + 0.984341i \(0.443595\pi\)
\(468\) −8.21556 + 8.21556i −0.0175546 + 0.0175546i
\(469\) 415.612i 0.886165i
\(470\) −6.79651 + 43.9683i −0.0144607 + 0.0935496i
\(471\) 402.394 0.854339
\(472\) 167.756 + 167.756i 0.355416 + 0.355416i
\(473\) 423.475 423.475i 0.895297 0.895297i
\(474\) 66.4660i 0.140224i
\(475\) −163.149 + 515.118i −0.343473 + 1.08446i
\(476\) −444.072 −0.932924
\(477\) 30.5013 + 30.5013i 0.0639439 + 0.0639439i
\(478\) −47.8510 + 47.8510i −0.100107 + 0.100107i
\(479\) 419.970i 0.876764i 0.898789 + 0.438382i \(0.144448\pi\)
−0.898789 + 0.438382i \(0.855552\pi\)
\(480\) 48.4148 + 7.48384i 0.100864 + 0.0155913i
\(481\) 131.144 0.272649
\(482\) 91.5567 + 91.5567i 0.189952 + 0.189952i
\(483\) −71.6733 + 71.6733i −0.148392 + 0.148392i
\(484\) 43.5038i 0.0898839i
\(485\) 466.665 + 637.316i 0.962196 + 1.31405i
\(486\) −22.0454 −0.0453609
\(487\) −463.650 463.650i −0.952054 0.952054i 0.0468485 0.998902i \(-0.485082\pi\)
−0.998902 + 0.0468485i \(0.985082\pi\)
\(488\) −189.936 + 189.936i −0.389213 + 0.389213i
\(489\) 123.933i 0.253442i
\(490\) −569.944 + 417.333i −1.16315 + 0.851700i
\(491\) −81.2134 −0.165404 −0.0827021 0.996574i \(-0.526355\pi\)
−0.0827021 + 0.996574i \(0.526355\pi\)
\(492\) 112.823 + 112.823i 0.229315 + 0.229315i
\(493\) 528.349 528.349i 1.07170 1.07170i
\(494\) 59.1889i 0.119816i
\(495\) 22.8282 147.681i 0.0461175 0.298346i
\(496\) −158.624 −0.319807
\(497\) −1104.15 1104.15i −2.22163 2.22163i
\(498\) −149.573 + 149.573i −0.300348 + 0.300348i
\(499\) 486.389i 0.974727i 0.873199 + 0.487364i \(0.162041\pi\)
−0.873199 + 0.487364i \(0.837959\pi\)
\(500\) 111.007 224.003i 0.222015 0.448006i
\(501\) 316.062 0.630862
\(502\) −358.473 358.473i −0.714090 0.714090i
\(503\) −243.288 + 243.288i −0.483674 + 0.483674i −0.906303 0.422629i \(-0.861107\pi\)
0.422629 + 0.906303i \(0.361107\pi\)
\(504\) 103.541i 0.205439i
\(505\) −384.029 59.3623i −0.760454 0.117549i
\(506\) 67.5678 0.133533
\(507\) −202.389 202.389i −0.399190 0.399190i
\(508\) −242.731 + 242.731i −0.477817 + 0.477817i
\(509\) 224.497i 0.441056i −0.975381 0.220528i \(-0.929222\pi\)
0.975381 0.220528i \(-0.0707780\pi\)
\(510\) −131.660 179.805i −0.258156 0.352559i
\(511\) 1028.78 2.01327
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −79.4130 + 79.4130i −0.154801 + 0.154801i
\(514\) 90.4377i 0.175949i
\(515\) −241.533 + 176.859i −0.468995 + 0.343415i
\(516\) 208.244 0.403574
\(517\) −44.3229 44.3229i −0.0857310 0.0857310i
\(518\) −826.409 + 826.409i −1.59538 + 1.59538i
\(519\) 76.1600i 0.146744i
\(520\) 4.18345 27.0638i 0.00804510 0.0520457i
\(521\) −581.302 −1.11574 −0.557872 0.829927i \(-0.688382\pi\)
−0.557872 + 0.829927i \(0.688382\pi\)
\(522\) 123.192 + 123.192i 0.235999 + 0.235999i
\(523\) −573.621 + 573.621i −1.09679 + 1.09679i −0.102005 + 0.994784i \(0.532526\pi\)
−0.994784 + 0.102005i \(0.967474\pi\)
\(524\) 377.093i 0.719642i
\(525\) −503.721 159.540i −0.959469 0.303886i
\(526\) −14.7181 −0.0279812
\(527\) 510.235 + 510.235i 0.968188 + 0.968188i
\(528\) −48.8053 + 48.8053i −0.0924342 + 0.0924342i
\(529\) 23.0000i 0.0434783i
\(530\) −100.478 15.5316i −0.189580 0.0293048i
\(531\) 251.635 0.473888
\(532\) −372.982 372.982i −0.701093 0.701093i
\(533\) 63.0677 63.0677i 0.118326 0.118326i
\(534\) 206.669i 0.387020i
\(535\) 446.855 + 610.261i 0.835243 + 1.14068i
\(536\) −96.3352 −0.179730
\(537\) 81.3777 + 81.3777i 0.151541 + 0.151541i
\(538\) 159.878 159.878i 0.297171 0.297171i
\(539\) 995.240i 1.84646i
\(540\) 41.9240 30.6982i 0.0776370 0.0568486i
\(541\) 582.198 1.07615 0.538075 0.842897i \(-0.319152\pi\)
0.538075 + 0.842897i \(0.319152\pi\)
\(542\) −211.259 211.259i −0.389777 0.389777i
\(543\) −70.8634 + 70.8634i −0.130503 + 0.130503i
\(544\) 102.932i 0.189213i
\(545\) 27.8902 180.429i 0.0511748 0.331062i
\(546\) −57.8794 −0.106006
\(547\) −242.902 242.902i −0.444063 0.444063i 0.449312 0.893375i \(-0.351669\pi\)
−0.893375 + 0.449312i \(0.851669\pi\)
\(548\) 172.217 172.217i 0.314264 0.314264i
\(549\) 284.904i 0.518951i
\(550\) 162.233 + 312.635i 0.294970 + 0.568427i
\(551\) 887.533 1.61077
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) −234.130 + 234.130i −0.423381 + 0.423381i
\(554\) 438.747i 0.791962i
\(555\) −579.629 89.5977i −1.04438 0.161437i
\(556\) −290.887 −0.523178
\(557\) 269.139 + 269.139i 0.483194 + 0.483194i 0.906150 0.422956i \(-0.139007\pi\)
−0.422956 + 0.906150i \(0.639007\pi\)
\(558\) −118.968 + 118.968i −0.213205 + 0.213205i
\(559\) 116.408i 0.208243i
\(560\) 144.181 + 196.906i 0.257467 + 0.351617i
\(561\) 313.977 0.559673
\(562\) −168.520 168.520i −0.299857 0.299857i
\(563\) −695.370 + 695.370i −1.23511 + 1.23511i −0.273141 + 0.961974i \(0.588062\pi\)
−0.961974 + 0.273141i \(0.911938\pi\)
\(564\) 21.7958i 0.0386450i
\(565\) 60.8487 44.5555i 0.107697 0.0788594i
\(566\) −309.513 −0.546843
\(567\) −77.6560 77.6560i −0.136960 0.136960i
\(568\) −255.933 + 255.933i −0.450585 + 0.450585i
\(569\) 132.973i 0.233696i −0.993150 0.116848i \(-0.962721\pi\)
0.993150 0.116848i \(-0.0372790\pi\)
\(570\) 40.4379 261.603i 0.0709437 0.458953i
\(571\) 331.378 0.580347 0.290174 0.956974i \(-0.406287\pi\)
0.290174 + 0.956974i \(0.406287\pi\)
\(572\) 27.2821 + 27.2821i 0.0476959 + 0.0476959i
\(573\) −6.74043 + 6.74043i −0.0117634 + 0.0117634i
\(574\) 794.848i 1.38475i
\(575\) 106.420 55.2240i 0.185079 0.0960417i
\(576\) −24.0000 −0.0416667
\(577\) 342.624 + 342.624i 0.593803 + 0.593803i 0.938656 0.344854i \(-0.112072\pi\)
−0.344854 + 0.938656i \(0.612072\pi\)
\(578\) 42.0941 42.0941i 0.0728271 0.0728271i
\(579\) 440.809i 0.761329i
\(580\) −405.819 62.7305i −0.699688 0.108156i
\(581\) −1053.76 −1.81370
\(582\) −273.631 273.631i −0.470156 0.470156i
\(583\) 101.288 101.288i 0.173736 0.173736i
\(584\) 238.463i 0.408327i
\(585\) −17.1602 23.4354i −0.0293338 0.0400605i
\(586\) 625.800 1.06792
\(587\) −761.501 761.501i −1.29728 1.29728i −0.930185 0.367091i \(-0.880354\pi\)
−0.367091 0.930185i \(-0.619646\pi\)
\(588\) 244.705 244.705i 0.416164 0.416164i
\(589\) 857.105i 1.45519i
\(590\) −478.536 + 350.401i −0.811078 + 0.593900i
\(591\) −357.295 −0.604560
\(592\) 191.554 + 191.554i 0.323572 + 0.323572i
\(593\) 9.06060 9.06060i 0.0152793 0.0152793i −0.699426 0.714705i \(-0.746561\pi\)
0.714705 + 0.699426i \(0.246561\pi\)
\(594\) 73.2079i 0.123246i
\(595\) 169.595 1097.15i 0.285033 1.84395i
\(596\) 271.147 0.454945
\(597\) 115.317 + 115.317i 0.193160 + 0.193160i
\(598\) 9.28677 9.28677i 0.0155297 0.0155297i
\(599\) 730.067i 1.21881i 0.792859 + 0.609405i \(0.208592\pi\)
−0.792859 + 0.609405i \(0.791408\pi\)
\(600\) −36.9800 + 116.758i −0.0616333 + 0.194597i
\(601\) −1150.36 −1.91407 −0.957036 0.289969i \(-0.906355\pi\)
−0.957036 + 0.289969i \(0.906355\pi\)
\(602\) 733.550 + 733.550i 1.21852 + 1.21852i
\(603\) −72.2514 + 72.2514i −0.119820 + 0.119820i
\(604\) 444.847i 0.736502i
\(605\) 107.483 + 16.6144i 0.177658 + 0.0274619i
\(606\) 190.370 0.314141
\(607\) −121.692 121.692i −0.200481 0.200481i 0.599725 0.800206i \(-0.295277\pi\)
−0.800206 + 0.599725i \(0.795277\pi\)
\(608\) −86.4539 + 86.4539i −0.142194 + 0.142194i
\(609\) 867.898i 1.42512i
\(610\) −396.729 541.805i −0.650375 0.888205i
\(611\) −12.1838 −0.0199408
\(612\) 77.1991 + 77.1991i 0.126142 + 0.126142i
\(613\) 624.795 624.795i 1.01924 1.01924i 0.0194306 0.999811i \(-0.493815\pi\)
0.999811 0.0194306i \(-0.00618533\pi\)
\(614\) 132.062i 0.215085i
\(615\) −321.834 + 235.659i −0.523308 + 0.383185i
\(616\) −343.838 −0.558179
\(617\) −136.943 136.943i −0.221951 0.221951i 0.587369 0.809319i \(-0.300164\pi\)
−0.809319 + 0.587369i \(0.800164\pi\)
\(618\) 103.702 103.702i 0.167802 0.167802i
\(619\) 57.3312i 0.0926191i −0.998927 0.0463095i \(-0.985254\pi\)
0.998927 0.0463095i \(-0.0147461\pi\)
\(620\) 60.5799 391.906i 0.0977094 0.632107i
\(621\) 24.9199 0.0401286
\(622\) 47.7193 + 47.7193i 0.0767191 + 0.0767191i
\(623\) −728.000 + 728.000i −1.16854 + 1.16854i
\(624\) 13.4160i 0.0214999i
\(625\) 511.040 + 359.810i 0.817664 + 0.575696i
\(626\) 685.004 1.09425
\(627\) 263.713 + 263.713i 0.420595 + 0.420595i
\(628\) 328.553 328.553i 0.523174 0.523174i
\(629\) 1232.32i 1.95917i
\(630\) 255.815 + 39.5433i 0.406056 + 0.0627671i
\(631\) −148.750 −0.235737 −0.117868 0.993029i \(-0.537606\pi\)
−0.117868 + 0.993029i \(0.537606\pi\)
\(632\) 54.2693 + 54.2693i 0.0858691 + 0.0858691i
\(633\) 44.1489 44.1489i 0.0697454 0.0697454i
\(634\) 531.789i 0.838783i
\(635\) −507.004 692.406i −0.798432 1.09040i
\(636\) 49.8083 0.0783150
\(637\) −136.789 136.789i −0.214740 0.214740i
\(638\) 409.092 409.092i 0.641210 0.641210i
\(639\) 383.899i 0.600781i
\(640\) 45.6410 33.4200i 0.0713141 0.0522187i
\(641\) −891.369 −1.39059 −0.695296 0.718724i \(-0.744727\pi\)
−0.695296 + 0.718724i \(0.744727\pi\)
\(642\) −262.015 262.015i −0.408123 0.408123i
\(643\) 518.375 518.375i 0.806182 0.806182i −0.177872 0.984054i \(-0.556921\pi\)
0.984054 + 0.177872i \(0.0569213\pi\)
\(644\) 117.042i 0.181742i
\(645\) −79.5301 + 514.500i −0.123302 + 0.797674i
\(646\) 556.180 0.860960
\(647\) 716.167 + 716.167i 1.10690 + 1.10690i 0.993555 + 0.113349i \(0.0361579\pi\)
0.113349 + 0.993555i \(0.463842\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 835.623i 1.28755i
\(650\) 65.2676 + 20.6717i 0.100412 + 0.0318027i
\(651\) −838.143 −1.28747
\(652\) 101.191 + 101.191i 0.155201 + 0.155201i
\(653\) 3.21608 3.21608i 0.00492509 0.00492509i −0.704640 0.709565i \(-0.748891\pi\)
0.709565 + 0.704640i \(0.248891\pi\)
\(654\) 89.4415i 0.136761i
\(655\) −931.667 144.015i −1.42239 0.219870i
\(656\) 184.239 0.280852
\(657\) −178.847 178.847i −0.272218 0.272218i
\(658\) 76.7768 76.7768i 0.116682 0.116682i
\(659\) 197.407i 0.299555i −0.988720 0.149778i \(-0.952144\pi\)
0.988720 0.149778i \(-0.0478558\pi\)
\(660\) −101.942 139.220i −0.154458 0.210940i
\(661\) 560.346 0.847725 0.423862 0.905727i \(-0.360674\pi\)
0.423862 + 0.905727i \(0.360674\pi\)
\(662\) 49.2824 + 49.2824i 0.0744447 + 0.0744447i
\(663\) 43.1541 43.1541i 0.0650892 0.0650892i
\(664\) 244.252i 0.367849i
\(665\) 1063.95 779.065i 1.59993 1.17153i
\(666\) 287.332 0.431429
\(667\) −139.254 139.254i −0.208777 0.208777i
\(668\) 258.064 258.064i 0.386323 0.386323i
\(669\) 167.637i 0.250578i
\(670\) 36.7912 238.011i 0.0549122 0.355241i
\(671\) 946.104 1.40999
\(672\) −84.5412 84.5412i −0.125805 0.125805i
\(673\) −947.596 + 947.596i −1.40802 + 1.40802i −0.637889 + 0.770129i \(0.720192\pi\)
−0.770129 + 0.637889i \(0.779808\pi\)
\(674\) 393.356i 0.583614i
\(675\) 59.8337 + 115.304i 0.0886425 + 0.170820i
\(676\) −330.501 −0.488906
\(677\) −121.113 121.113i −0.178896 0.178896i 0.611978 0.790874i \(-0.290374\pi\)
−0.790874 + 0.611978i \(0.790374\pi\)
\(678\) −26.1253 + 26.1253i −0.0385329 + 0.0385329i
\(679\) 1927.76i 2.83911i
\(680\) −254.310 39.3106i −0.373985 0.0578097i
\(681\) 386.851 0.568063
\(682\) 395.067 + 395.067i 0.579277 + 0.579277i
\(683\) 446.080 446.080i 0.653119 0.653119i −0.300624 0.953743i \(-0.597195\pi\)
0.953743 + 0.300624i \(0.0971948\pi\)
\(684\) 129.681i 0.189592i
\(685\) 359.717 + 491.259i 0.525135 + 0.717167i
\(686\) 878.380 1.28044
\(687\) −341.391 341.391i −0.496930 0.496930i
\(688\) 170.031 170.031i 0.247137 0.247137i
\(689\) 27.8428i 0.0404104i
\(690\) −47.3904 + 34.7009i −0.0686817 + 0.0502912i
\(691\) −885.496 −1.28147 −0.640735 0.767762i \(-0.721370\pi\)
−0.640735 + 0.767762i \(0.721370\pi\)
\(692\) 62.1844 + 62.1844i 0.0898619 + 0.0898619i
\(693\) −257.878 + 257.878i −0.372119 + 0.372119i
\(694\) 323.124i 0.465596i
\(695\) 111.092 718.682i 0.159845 1.03407i
\(696\) 201.171 0.289039
\(697\) −592.628 592.628i −0.850255 0.850255i
\(698\) 69.2537 69.2537i 0.0992173 0.0992173i
\(699\) 644.737i 0.922371i
\(700\) −541.550 + 281.023i −0.773643 + 0.401461i
\(701\) 1097.97 1.56628 0.783142 0.621843i \(-0.213616\pi\)
0.783142 + 0.621843i \(0.213616\pi\)
\(702\) 10.0620 + 10.0620i 0.0143333 + 0.0143333i
\(703\) 1035.04 1035.04i 1.47232 1.47232i
\(704\) 79.6987i 0.113208i
\(705\) 53.8500 + 8.32399i 0.0763829 + 0.0118071i
\(706\) −375.848 −0.532363
\(707\) 670.586 + 670.586i 0.948496 + 0.948496i
\(708\) 205.459 205.459i 0.290196 0.290196i
\(709\) 567.023i 0.799750i −0.916570 0.399875i \(-0.869054\pi\)
0.916570 0.399875i \(-0.130946\pi\)
\(710\) −534.579 730.064i −0.752928 1.02826i
\(711\) 81.4039 0.114492
\(712\) 168.744 + 168.744i 0.237000 + 0.237000i
\(713\) 134.480 134.480i 0.188612 0.188612i
\(714\) 543.875i 0.761730i
\(715\) −77.8238 + 56.9854i −0.108845 + 0.0796998i
\(716\) 132.889 0.185599
\(717\) 58.6053 + 58.6053i 0.0817368 + 0.0817368i
\(718\) 327.086 327.086i 0.455551 0.455551i
\(719\) 1190.36i 1.65557i 0.561045 + 0.827785i \(0.310399\pi\)
−0.561045 + 0.827785i \(0.689601\pi\)
\(720\) 9.16579 59.2958i 0.0127303 0.0823552i
\(721\) 730.589 1.01330
\(722\) 106.142 + 106.142i 0.147011 + 0.147011i
\(723\) 112.134 112.134i 0.155095 0.155095i
\(724\) 115.719i 0.159833i
\(725\) 309.971 978.683i 0.427546 1.34991i
\(726\) −53.2810 −0.0733899
\(727\) 100.239 + 100.239i 0.137881 + 0.137881i 0.772678 0.634798i \(-0.218917\pi\)
−0.634798 + 0.772678i \(0.718917\pi\)
\(728\) −47.2584 + 47.2584i −0.0649153 + 0.0649153i
\(729\) 27.0000i 0.0370370i
\(730\) 589.161 + 91.0710i 0.807069 + 0.124755i
\(731\) −1093.85 −1.49637
\(732\) 232.623 + 232.623i 0.317791 + 0.317791i
\(733\) 272.933 272.933i 0.372350 0.372350i −0.495982 0.868333i \(-0.665192\pi\)
0.868333 + 0.495982i \(0.165192\pi\)
\(734\) 981.612i 1.33735i
\(735\) 511.127 + 698.036i 0.695410 + 0.949709i
\(736\) 27.1293 0.0368605
\(737\) 239.931 + 239.931i 0.325551 + 0.325551i
\(738\) 138.179 138.179i 0.187235 0.187235i
\(739\) 1375.85i 1.86177i 0.365313 + 0.930885i \(0.380962\pi\)
−0.365313 + 0.930885i \(0.619038\pi\)
\(740\) −546.422 + 400.109i −0.738408 + 0.540688i
\(741\) 72.4913 0.0978291
\(742\) 175.452 + 175.452i 0.236459 + 0.236459i
\(743\) −200.083 + 200.083i −0.269291 + 0.269291i −0.828814 0.559524i \(-0.810984\pi\)
0.559524 + 0.828814i \(0.310984\pi\)
\(744\) 194.274i 0.261121i
\(745\) −103.553 + 669.911i −0.138998 + 0.899210i
\(746\) 42.0317 0.0563427
\(747\) 183.189 + 183.189i 0.245233 + 0.245233i
\(748\) 256.361 256.361i 0.342729 0.342729i
\(749\) 1845.92i 2.46451i
\(750\) −274.347 135.956i −0.365795 0.181274i
\(751\) 46.1912 0.0615063 0.0307531 0.999527i \(-0.490209\pi\)
0.0307531 + 0.999527i \(0.490209\pi\)
\(752\) −17.7962 17.7962i −0.0236652 0.0236652i
\(753\) −439.038 + 439.038i −0.583052 + 0.583052i
\(754\) 112.454i 0.149144i
\(755\) 1099.06 + 169.891i 1.45571 + 0.225021i
\(756\) −126.812 −0.167740
\(757\) −379.305 379.305i −0.501063 0.501063i 0.410705 0.911768i \(-0.365283\pi\)
−0.911768 + 0.410705i \(0.865283\pi\)
\(758\) −310.295 + 310.295i −0.409360 + 0.409360i
\(759\) 82.7534i 0.109029i
\(760\) −180.581 246.615i −0.237606 0.324494i
\(761\) −496.235 −0.652083 −0.326042 0.945355i \(-0.605715\pi\)
−0.326042 + 0.945355i \(0.605715\pi\)
\(762\) 297.284 + 297.284i 0.390136 + 0.390136i
\(763\) −315.062 + 315.062i −0.412926 + 0.412926i
\(764\) 11.0071i 0.0144072i
\(765\) −220.215 + 161.249i −0.287863 + 0.210784i
\(766\) −493.893 −0.644769
\(767\) −114.851 114.851i −0.149741 0.149741i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 128.084i 0.166560i −0.996526 0.0832798i \(-0.973460\pi\)
0.996526 0.0832798i \(-0.0265395\pi\)
\(770\) 131.314 849.506i 0.170538 1.10325i
\(771\) −110.763 −0.143662
\(772\) 359.919 + 359.919i 0.466217 + 0.466217i
\(773\) −52.1777 + 52.1777i −0.0675003 + 0.0675003i −0.740051 0.672551i \(-0.765199\pi\)
0.672551 + 0.740051i \(0.265199\pi\)
\(774\) 255.046i 0.329517i
\(775\) 945.130 + 299.344i 1.21952 + 0.386250i
\(776\) −446.837 −0.575821
\(777\) 1012.14 + 1012.14i 1.30263 + 1.30263i
\(778\) 467.057 467.057i 0.600330 0.600330i
\(779\)