Properties

Label 210.3.l.b.127.5
Level 210
Weight 3
Character 210.127
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.5
Root \(3.60306 + 3.60306i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.b.43.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.39814 + 2.37832i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.39814 + 2.37832i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.77646 + 2.01982i) q^{10} -14.7776 q^{11} +(2.44949 + 2.44949i) q^{12} +(-13.2827 + 13.2827i) q^{13} -3.74166i q^{14} +(-2.47376 + 8.29943i) q^{15} -4.00000 q^{16} +(1.17963 + 1.17963i) q^{17} +(-3.00000 + 3.00000i) q^{18} +15.1298i q^{19} +(-4.75664 - 8.79627i) q^{20} +4.58258 q^{21} +(14.7776 + 14.7776i) q^{22} +(-22.5070 + 22.5070i) q^{23} -4.89898i q^{24} +(13.6872 - 20.9203i) q^{25} +26.5654 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -3.29748i q^{29} +(10.7732 - 5.82567i) q^{30} +50.0892 q^{31} +(4.00000 + 4.00000i) q^{32} +(-18.0988 + 18.0988i) q^{33} -2.35927i q^{34} +(-12.6776 - 3.77873i) q^{35} +6.00000 q^{36} +(6.15735 + 6.15735i) q^{37} +(15.1298 - 15.1298i) q^{38} +32.5359i q^{39} +(-4.03963 + 13.5529i) q^{40} -35.1369 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-58.9417 + 58.9417i) q^{43} -29.5552i q^{44} +(7.13496 + 13.1944i) q^{45} +45.0141 q^{46} +(-20.1645 - 20.1645i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-34.6075 + 7.23315i) q^{50} +2.88950 q^{51} +(-26.5654 - 26.5654i) q^{52} +(10.9028 - 10.9028i) q^{53} +7.34847i q^{54} +(64.9939 - 35.1459i) q^{55} +7.48331 q^{56} +(18.5302 + 18.5302i) q^{57} +(-3.29748 + 3.29748i) q^{58} -66.6774i q^{59} +(-16.5989 - 4.94752i) q^{60} -4.45593 q^{61} +(-50.0892 - 50.0892i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(26.8286 - 90.0098i) q^{65} +36.1976 q^{66} +(-88.4424 - 88.4424i) q^{67} +(-2.35927 + 2.35927i) q^{68} +55.1307i q^{69} +(8.89886 + 16.4563i) q^{70} +69.3188 q^{71} +(-6.00000 - 6.00000i) q^{72} +(58.4166 - 58.4166i) q^{73} -12.3147i q^{74} +(-8.85877 - 42.3854i) q^{75} -30.2597 q^{76} +(-27.6464 - 27.6464i) q^{77} +(32.5359 - 32.5359i) q^{78} -52.8307i q^{79} +(17.5925 - 9.51328i) q^{80} -9.00000 q^{81} +(35.1369 + 35.1369i) q^{82} +(-53.4286 + 53.4286i) q^{83} +9.16515i q^{84} +(-7.99374 - 2.38264i) q^{85} +117.883 q^{86} +(-4.03857 - 4.03857i) q^{87} +(-29.5552 + 29.5552i) q^{88} -21.3553i q^{89} +(6.05945 - 20.3294i) q^{90} -49.6994 q^{91} +(-45.0141 - 45.0141i) q^{92} +(61.3464 - 61.3464i) q^{93} +40.3290i q^{94} +(-35.9836 - 66.5431i) q^{95} +9.79796 q^{96} +(90.3562 + 90.3562i) q^{97} +(7.00000 - 7.00000i) q^{98} +44.3328i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.39814 + 2.37832i −0.879627 + 0.475664i
\(6\) −2.44949 −0.408248
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.77646 + 2.01982i 0.677646 + 0.201982i
\(11\) −14.7776 −1.34342 −0.671710 0.740814i \(-0.734440\pi\)
−0.671710 + 0.740814i \(0.734440\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −13.2827 + 13.2827i −1.02175 + 1.02175i −0.0219895 + 0.999758i \(0.507000\pi\)
−0.999758 + 0.0219895i \(0.993000\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −2.47376 + 8.29943i −0.164917 + 0.553295i
\(16\) −4.00000 −0.250000
\(17\) 1.17963 + 1.17963i 0.0693902 + 0.0693902i 0.740950 0.671560i \(-0.234375\pi\)
−0.671560 + 0.740950i \(0.734375\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 15.1298i 0.796307i 0.917319 + 0.398154i \(0.130349\pi\)
−0.917319 + 0.398154i \(0.869651\pi\)
\(20\) −4.75664 8.79627i −0.237832 0.439814i
\(21\) 4.58258 0.218218
\(22\) 14.7776 + 14.7776i 0.671710 + 0.671710i
\(23\) −22.5070 + 22.5070i −0.978567 + 0.978567i −0.999775 0.0212084i \(-0.993249\pi\)
0.0212084 + 0.999775i \(0.493249\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 13.6872 20.9203i 0.547488 0.836814i
\(26\) 26.5654 1.02175
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −3.74166 + 3.74166i −0.133631 + 0.133631i
\(29\) 3.29748i 0.113706i −0.998383 0.0568530i \(-0.981893\pi\)
0.998383 0.0568530i \(-0.0181066\pi\)
\(30\) 10.7732 5.82567i 0.359106 0.194189i
\(31\) 50.0892 1.61578 0.807890 0.589334i \(-0.200610\pi\)
0.807890 + 0.589334i \(0.200610\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −18.0988 + 18.0988i −0.548449 + 0.548449i
\(34\) 2.35927i 0.0693902i
\(35\) −12.6776 3.77873i −0.362217 0.107964i
\(36\) 6.00000 0.166667
\(37\) 6.15735 + 6.15735i 0.166415 + 0.166415i 0.785401 0.618987i \(-0.212457\pi\)
−0.618987 + 0.785401i \(0.712457\pi\)
\(38\) 15.1298 15.1298i 0.398154 0.398154i
\(39\) 32.5359i 0.834254i
\(40\) −4.03963 + 13.5529i −0.100991 + 0.338823i
\(41\) −35.1369 −0.856998 −0.428499 0.903542i \(-0.640957\pi\)
−0.428499 + 0.903542i \(0.640957\pi\)
\(42\) −4.58258 4.58258i −0.109109 0.109109i
\(43\) −58.9417 + 58.9417i −1.37074 + 1.37074i −0.511388 + 0.859350i \(0.670869\pi\)
−0.859350 + 0.511388i \(0.829131\pi\)
\(44\) 29.5552i 0.671710i
\(45\) 7.13496 + 13.1944i 0.158555 + 0.293209i
\(46\) 45.0141 0.978567
\(47\) −20.1645 20.1645i −0.429032 0.429032i 0.459266 0.888299i \(-0.348112\pi\)
−0.888299 + 0.459266i \(0.848112\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −34.6075 + 7.23315i −0.692151 + 0.144663i
\(51\) 2.88950 0.0566569
\(52\) −26.5654 26.5654i −0.510874 0.510874i
\(53\) 10.9028 10.9028i 0.205712 0.205712i −0.596730 0.802442i \(-0.703534\pi\)
0.802442 + 0.596730i \(0.203534\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 64.9939 35.1459i 1.18171 0.639016i
\(56\) 7.48331 0.133631
\(57\) 18.5302 + 18.5302i 0.325091 + 0.325091i
\(58\) −3.29748 + 3.29748i −0.0568530 + 0.0568530i
\(59\) 66.6774i 1.13013i −0.825048 0.565063i \(-0.808852\pi\)
0.825048 0.565063i \(-0.191148\pi\)
\(60\) −16.5989 4.94752i −0.276648 0.0824586i
\(61\) −4.45593 −0.0730481 −0.0365241 0.999333i \(-0.511629\pi\)
−0.0365241 + 0.999333i \(0.511629\pi\)
\(62\) −50.0892 50.0892i −0.807890 0.807890i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 26.8286 90.0098i 0.412748 1.38477i
\(66\) 36.1976 0.548449
\(67\) −88.4424 88.4424i −1.32004 1.32004i −0.913743 0.406293i \(-0.866821\pi\)
−0.406293 0.913743i \(-0.633179\pi\)
\(68\) −2.35927 + 2.35927i −0.0346951 + 0.0346951i
\(69\) 55.1307i 0.798996i
\(70\) 8.89886 + 16.4563i 0.127127 + 0.235090i
\(71\) 69.3188 0.976321 0.488161 0.872754i \(-0.337668\pi\)
0.488161 + 0.872754i \(0.337668\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 58.4166 58.4166i 0.800227 0.800227i −0.182903 0.983131i \(-0.558550\pi\)
0.983131 + 0.182903i \(0.0585496\pi\)
\(74\) 12.3147i 0.166415i
\(75\) −8.85877 42.3854i −0.118117 0.565139i
\(76\) −30.2597 −0.398154
\(77\) −27.6464 27.6464i −0.359044 0.359044i
\(78\) 32.5359 32.5359i 0.417127 0.417127i
\(79\) 52.8307i 0.668744i −0.942441 0.334372i \(-0.891476\pi\)
0.942441 0.334372i \(-0.108524\pi\)
\(80\) 17.5925 9.51328i 0.219907 0.118916i
\(81\) −9.00000 −0.111111
\(82\) 35.1369 + 35.1369i 0.428499 + 0.428499i
\(83\) −53.4286 + 53.4286i −0.643718 + 0.643718i −0.951468 0.307749i \(-0.900424\pi\)
0.307749 + 0.951468i \(0.400424\pi\)
\(84\) 9.16515i 0.109109i
\(85\) −7.99374 2.38264i −0.0940440 0.0280311i
\(86\) 117.883 1.37074
\(87\) −4.03857 4.03857i −0.0464203 0.0464203i
\(88\) −29.5552 + 29.5552i −0.335855 + 0.335855i
\(89\) 21.3553i 0.239947i −0.992777 0.119973i \(-0.961719\pi\)
0.992777 0.119973i \(-0.0382809\pi\)
\(90\) 6.05945 20.3294i 0.0673272 0.225882i
\(91\) −49.6994 −0.546147
\(92\) −45.0141 45.0141i −0.489283 0.489283i
\(93\) 61.3464 61.3464i 0.659639 0.659639i
\(94\) 40.3290i 0.429032i
\(95\) −35.9836 66.5431i −0.378775 0.700453i
\(96\) 9.79796 0.102062
\(97\) 90.3562 + 90.3562i 0.931507 + 0.931507i 0.997800 0.0662929i \(-0.0211172\pi\)
−0.0662929 + 0.997800i \(0.521117\pi\)
\(98\) 7.00000 7.00000i 0.0714286 0.0714286i
\(99\) 44.3328i 0.447806i
\(100\) 41.8407 + 27.3744i 0.418407 + 0.273744i
\(101\) 43.6109 0.431791 0.215896 0.976416i \(-0.430733\pi\)
0.215896 + 0.976416i \(0.430733\pi\)
\(102\) −2.88950 2.88950i −0.0283284 0.0283284i
\(103\) −48.8638 + 48.8638i −0.474405 + 0.474405i −0.903337 0.428932i \(-0.858890\pi\)
0.428932 + 0.903337i \(0.358890\pi\)
\(104\) 53.1309i 0.510874i
\(105\) −20.1548 + 10.8988i −0.191950 + 0.103798i
\(106\) −21.8055 −0.205712
\(107\) 23.1497 + 23.1497i 0.216352 + 0.216352i 0.806959 0.590607i \(-0.201112\pi\)
−0.590607 + 0.806959i \(0.701112\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 141.834i 1.30123i 0.759409 + 0.650613i \(0.225488\pi\)
−0.759409 + 0.650613i \(0.774512\pi\)
\(110\) −100.140 29.8481i −0.910362 0.271346i
\(111\) 15.0824 0.135877
\(112\) −7.48331 7.48331i −0.0668153 0.0668153i
\(113\) −113.746 + 113.746i −1.00660 + 1.00660i −0.00662298 + 0.999978i \(0.502108\pi\)
−0.999978 + 0.00662298i \(0.997892\pi\)
\(114\) 37.0604i 0.325091i
\(115\) 45.4601 152.518i 0.395305 1.32624i
\(116\) 6.59495 0.0568530
\(117\) 39.8482 + 39.8482i 0.340583 + 0.340583i
\(118\) −66.6774 + 66.6774i −0.565063 + 0.565063i
\(119\) 4.41379i 0.0370906i
\(120\) 11.6513 + 21.5464i 0.0970945 + 0.179553i
\(121\) 97.3779 0.804776
\(122\) 4.45593 + 4.45593i 0.0365241 + 0.0365241i
\(123\) −43.0338 + 43.0338i −0.349868 + 0.349868i
\(124\) 100.178i 0.807890i
\(125\) −10.4429 + 124.563i −0.0835428 + 0.996504i
\(126\) −11.2250 −0.0890871
\(127\) −172.678 172.678i −1.35967 1.35967i −0.874325 0.485341i \(-0.838695\pi\)
−0.485341 0.874325i \(-0.661305\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 144.377i 1.11920i
\(130\) −116.838 + 63.1811i −0.898757 + 0.486009i
\(131\) 147.540 1.12626 0.563129 0.826369i \(-0.309597\pi\)
0.563129 + 0.826369i \(0.309597\pi\)
\(132\) −36.1976 36.1976i −0.274224 0.274224i
\(133\) −28.3053 + 28.3053i −0.212822 + 0.212822i
\(134\) 176.885i 1.32004i
\(135\) 24.8983 + 7.42128i 0.184432 + 0.0549724i
\(136\) 4.71854 0.0346951
\(137\) 96.5907 + 96.5907i 0.705042 + 0.705042i 0.965488 0.260447i \(-0.0838698\pi\)
−0.260447 + 0.965488i \(0.583870\pi\)
\(138\) 55.1307 55.1307i 0.399498 0.399498i
\(139\) 184.197i 1.32516i −0.748993 0.662578i \(-0.769462\pi\)
0.748993 0.662578i \(-0.230538\pi\)
\(140\) 7.55746 25.3552i 0.0539818 0.181108i
\(141\) −49.3928 −0.350303
\(142\) −69.3188 69.3188i −0.488161 0.488161i
\(143\) 196.287 196.287i 1.37264 1.37264i
\(144\) 12.0000i 0.0833333i
\(145\) 7.84245 + 14.5027i 0.0540859 + 0.100019i
\(146\) −116.833 −0.800227
\(147\) 8.57321 + 8.57321i 0.0583212 + 0.0583212i
\(148\) −12.3147 + 12.3147i −0.0832074 + 0.0832074i
\(149\) 206.358i 1.38495i 0.721442 + 0.692475i \(0.243480\pi\)
−0.721442 + 0.692475i \(0.756520\pi\)
\(150\) −33.5266 + 51.2442i −0.223511 + 0.341628i
\(151\) 51.4825 0.340944 0.170472 0.985363i \(-0.445471\pi\)
0.170472 + 0.985363i \(0.445471\pi\)
\(152\) 30.2597 + 30.2597i 0.199077 + 0.199077i
\(153\) 3.53890 3.53890i 0.0231301 0.0231301i
\(154\) 55.2928i 0.359044i
\(155\) −220.299 + 119.128i −1.42128 + 0.768568i
\(156\) −65.0718 −0.417127
\(157\) 91.7859 + 91.7859i 0.584624 + 0.584624i 0.936170 0.351547i \(-0.114344\pi\)
−0.351547 + 0.936170i \(0.614344\pi\)
\(158\) −52.8307 + 52.8307i −0.334372 + 0.334372i
\(159\) 26.7062i 0.167963i
\(160\) −27.1058 8.07926i −0.169411 0.0504954i
\(161\) −84.2136 −0.523066
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −11.1451 + 11.1451i −0.0683748 + 0.0683748i −0.740467 0.672092i \(-0.765396\pi\)
0.672092 + 0.740467i \(0.265396\pi\)
\(164\) 70.2739i 0.428499i
\(165\) 36.5563 122.646i 0.221553 0.743308i
\(166\) 106.857 0.643718
\(167\) 224.811 + 224.811i 1.34617 + 1.34617i 0.889776 + 0.456397i \(0.150860\pi\)
0.456397 + 0.889776i \(0.349140\pi\)
\(168\) 9.16515 9.16515i 0.0545545 0.0545545i
\(169\) 183.861i 1.08794i
\(170\) 5.61109 + 10.3764i 0.0330064 + 0.0610375i
\(171\) 45.3895 0.265436
\(172\) −117.883 117.883i −0.685369 0.685369i
\(173\) 43.4546 43.4546i 0.251183 0.251183i −0.570273 0.821455i \(-0.693162\pi\)
0.821455 + 0.570273i \(0.193162\pi\)
\(174\) 8.07713i 0.0464203i
\(175\) 64.7448 13.5320i 0.369970 0.0773257i
\(176\) 59.1105 0.335855
\(177\) −81.6628 81.6628i −0.461372 0.461372i
\(178\) −21.3553 + 21.3553i −0.119973 + 0.119973i
\(179\) 167.373i 0.935046i 0.883981 + 0.467523i \(0.154854\pi\)
−0.883981 + 0.467523i \(0.845146\pi\)
\(180\) −26.3888 + 14.2699i −0.146605 + 0.0792773i
\(181\) 225.762 1.24730 0.623652 0.781702i \(-0.285648\pi\)
0.623652 + 0.781702i \(0.285648\pi\)
\(182\) 49.6994 + 49.6994i 0.273074 + 0.273074i
\(183\) −5.45738 + 5.45738i −0.0298218 + 0.0298218i
\(184\) 90.0281i 0.489283i
\(185\) −41.7250 12.4367i −0.225540 0.0672254i
\(186\) −122.693 −0.659639
\(187\) −17.4322 17.4322i −0.0932202 0.0932202i
\(188\) 40.3290 40.3290i 0.214516 0.214516i
\(189\) 13.7477i 0.0727393i
\(190\) −30.5595 + 102.527i −0.160839 + 0.539614i
\(191\) −148.626 −0.778145 −0.389073 0.921207i \(-0.627204\pi\)
−0.389073 + 0.921207i \(0.627204\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −158.063 + 158.063i −0.818979 + 0.818979i −0.985960 0.166982i \(-0.946598\pi\)
0.166982 + 0.985960i \(0.446598\pi\)
\(194\) 180.712i 0.931507i
\(195\) −77.3807 143.097i −0.396824 0.733832i
\(196\) −14.0000 −0.0714286
\(197\) 26.7707 + 26.7707i 0.135892 + 0.135892i 0.771781 0.635889i \(-0.219366\pi\)
−0.635889 + 0.771781i \(0.719366\pi\)
\(198\) 44.3328 44.3328i 0.223903 0.223903i
\(199\) 171.790i 0.863269i −0.902049 0.431634i \(-0.857937\pi\)
0.902049 0.431634i \(-0.142063\pi\)
\(200\) −14.4663 69.2151i −0.0723315 0.346075i
\(201\) −216.639 −1.07780
\(202\) −43.6109 43.6109i −0.215896 0.215896i
\(203\) 6.16901 6.16901i 0.0303892 0.0303892i
\(204\) 5.77900i 0.0283284i
\(205\) 154.537 83.5668i 0.753839 0.407643i
\(206\) 97.7275 0.474405
\(207\) 67.5211 + 67.5211i 0.326189 + 0.326189i
\(208\) 53.1309 53.1309i 0.255437 0.255437i
\(209\) 223.583i 1.06977i
\(210\) 31.0536 + 9.25596i 0.147874 + 0.0440760i
\(211\) −302.432 −1.43333 −0.716664 0.697419i \(-0.754332\pi\)
−0.716664 + 0.697419i \(0.754332\pi\)
\(212\) 21.8055 + 21.8055i 0.102856 + 0.102856i
\(213\) 84.8978 84.8978i 0.398581 0.398581i
\(214\) 46.2994i 0.216352i
\(215\) 119.051 399.416i 0.553728 1.85775i
\(216\) −14.6969 −0.0680414
\(217\) 93.7082 + 93.7082i 0.431835 + 0.431835i
\(218\) 141.834 141.834i 0.650613 0.650613i
\(219\) 143.091i 0.653383i
\(220\) 70.2918 + 129.988i 0.319508 + 0.590854i
\(221\) −31.3375 −0.141799
\(222\) −15.0824 15.0824i −0.0679385 0.0679385i
\(223\) −170.784 + 170.784i −0.765850 + 0.765850i −0.977373 0.211523i \(-0.932158\pi\)
0.211523 + 0.977373i \(0.432158\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −62.7610 41.0616i −0.278938 0.182496i
\(226\) 227.492 1.00660
\(227\) 154.323 + 154.323i 0.679838 + 0.679838i 0.959963 0.280125i \(-0.0903760\pi\)
−0.280125 + 0.959963i \(0.590376\pi\)
\(228\) −37.0604 + 37.0604i −0.162546 + 0.162546i
\(229\) 33.7243i 0.147267i −0.997285 0.0736337i \(-0.976540\pi\)
0.997285 0.0736337i \(-0.0234596\pi\)
\(230\) −197.978 + 107.058i −0.860774 + 0.465469i
\(231\) −67.7195 −0.293158
\(232\) −6.59495 6.59495i −0.0284265 0.0284265i
\(233\) −207.998 + 207.998i −0.892697 + 0.892697i −0.994776 0.102079i \(-0.967450\pi\)
0.102079 + 0.994776i \(0.467450\pi\)
\(234\) 79.6963i 0.340583i
\(235\) 136.644 + 40.7286i 0.581464 + 0.173313i
\(236\) 133.355 0.565063
\(237\) −64.7042 64.7042i −0.273013 0.273013i
\(238\) 4.41379 4.41379i 0.0185453 0.0185453i
\(239\) 49.7163i 0.208018i 0.994576 + 0.104009i \(0.0331670\pi\)
−0.994576 + 0.104009i \(0.966833\pi\)
\(240\) 9.89504 33.1977i 0.0412293 0.138324i
\(241\) −49.9716 −0.207351 −0.103676 0.994611i \(-0.533060\pi\)
−0.103676 + 0.994611i \(0.533060\pi\)
\(242\) −97.3779 97.3779i −0.402388 0.402388i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 8.91187i 0.0365241i
\(245\) −16.6482 30.7869i −0.0679520 0.125661i
\(246\) 86.0675 0.349868
\(247\) −200.965 200.965i −0.813625 0.813625i
\(248\) 100.178 100.178i 0.403945 0.403945i
\(249\) 130.873i 0.525594i
\(250\) 135.006 114.120i 0.540023 0.456481i
\(251\) −315.486 −1.25692 −0.628459 0.777843i \(-0.716314\pi\)
−0.628459 + 0.777843i \(0.716314\pi\)
\(252\) 11.2250 + 11.2250i 0.0445435 + 0.0445435i
\(253\) 332.600 332.600i 1.31463 1.31463i
\(254\) 345.355i 1.35967i
\(255\) −12.7084 + 6.87216i −0.0498369 + 0.0269496i
\(256\) 16.0000 0.0625000
\(257\) 275.744 + 275.744i 1.07293 + 1.07293i 0.997122 + 0.0758107i \(0.0241545\pi\)
0.0758107 + 0.997122i \(0.475846\pi\)
\(258\) 144.377 144.377i 0.559601 0.559601i
\(259\) 23.0387i 0.0889524i
\(260\) 180.020 + 53.6573i 0.692383 + 0.206374i
\(261\) −9.89243 −0.0379020
\(262\) −147.540 147.540i −0.563129 0.563129i
\(263\) 122.744 122.744i 0.466708 0.466708i −0.434138 0.900846i \(-0.642947\pi\)
0.900846 + 0.434138i \(0.142947\pi\)
\(264\) 72.3952i 0.274224i
\(265\) −22.0216 + 73.8820i −0.0831002 + 0.278800i
\(266\) 56.6107 0.212822
\(267\) −26.1547 26.1547i −0.0979578 0.0979578i
\(268\) 176.885 176.885i 0.660018 0.660018i
\(269\) 62.3232i 0.231685i 0.993268 + 0.115842i \(0.0369567\pi\)
−0.993268 + 0.115842i \(0.963043\pi\)
\(270\) −17.4770 32.3196i −0.0647297 0.119702i
\(271\) 127.663 0.471081 0.235541 0.971864i \(-0.424314\pi\)
0.235541 + 0.971864i \(0.424314\pi\)
\(272\) −4.71854 4.71854i −0.0173476 0.0173476i
\(273\) −60.8691 + 60.8691i −0.222964 + 0.222964i
\(274\) 193.181i 0.705042i
\(275\) −202.264 + 309.153i −0.735506 + 1.12419i
\(276\) −110.261 −0.399498
\(277\) −57.6863 57.6863i −0.208254 0.208254i 0.595271 0.803525i \(-0.297045\pi\)
−0.803525 + 0.595271i \(0.797045\pi\)
\(278\) −184.197 + 184.197i −0.662578 + 0.662578i
\(279\) 150.267i 0.538593i
\(280\) −32.9126 + 17.7977i −0.117545 + 0.0635633i
\(281\) 119.372 0.424812 0.212406 0.977182i \(-0.431870\pi\)
0.212406 + 0.977182i \(0.431870\pi\)
\(282\) 49.3928 + 49.3928i 0.175152 + 0.175152i
\(283\) −175.257 + 175.257i −0.619282 + 0.619282i −0.945347 0.326065i \(-0.894277\pi\)
0.326065 + 0.945347i \(0.394277\pi\)
\(284\) 138.638i 0.488161i
\(285\) −125.569 37.4276i −0.440593 0.131325i
\(286\) −392.574 −1.37264
\(287\) −65.7352 65.7352i −0.229042 0.229042i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 286.217i 0.990370i
\(290\) 6.66029 22.3452i 0.0229665 0.0770524i
\(291\) 221.327 0.760572
\(292\) 116.833 + 116.833i 0.400114 + 0.400114i
\(293\) 224.254 224.254i 0.765372 0.765372i −0.211916 0.977288i \(-0.567970\pi\)
0.977288 + 0.211916i \(0.0679703\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 158.580 + 293.256i 0.537560 + 0.994089i
\(296\) 24.6294 0.0832074
\(297\) 54.2964 + 54.2964i 0.182816 + 0.182816i
\(298\) 206.358 206.358i 0.692475 0.692475i
\(299\) 597.909i 1.99970i
\(300\) 84.7708 17.7175i 0.282569 0.0590585i
\(301\) −220.540 −0.732690
\(302\) −51.4825 51.4825i −0.170472 0.170472i
\(303\) 53.4123 53.4123i 0.176278 0.176278i
\(304\) 60.5194i 0.199077i
\(305\) 19.5978 10.5976i 0.0642551 0.0347464i
\(306\) −7.07780 −0.0231301
\(307\) 202.366 + 202.366i 0.659172 + 0.659172i 0.955184 0.296012i \(-0.0956569\pi\)
−0.296012 + 0.955184i \(0.595657\pi\)
\(308\) 55.2928 55.2928i 0.179522 0.179522i
\(309\) 119.691i 0.387350i
\(310\) 339.427 + 101.171i 1.09493 + 0.326358i
\(311\) −382.114 −1.22866 −0.614331 0.789049i \(-0.710574\pi\)
−0.614331 + 0.789049i \(0.710574\pi\)
\(312\) 65.0718 + 65.0718i 0.208563 + 0.208563i
\(313\) −235.445 + 235.445i −0.752220 + 0.752220i −0.974893 0.222674i \(-0.928522\pi\)
0.222674 + 0.974893i \(0.428522\pi\)
\(314\) 183.572i 0.584624i
\(315\) −11.3362 + 38.0328i −0.0359879 + 0.120739i
\(316\) 105.661 0.334372
\(317\) 297.704 + 297.704i 0.939129 + 0.939129i 0.998251 0.0591213i \(-0.0188299\pi\)
−0.0591213 + 0.998251i \(0.518830\pi\)
\(318\) −26.7062 + 26.7062i −0.0839817 + 0.0839817i
\(319\) 48.7288i 0.152755i
\(320\) 19.0266 + 35.1851i 0.0594580 + 0.109953i
\(321\) 56.7049 0.176651
\(322\) 84.2136 + 84.2136i 0.261533 + 0.261533i
\(323\) −17.8477 + 17.8477i −0.0552559 + 0.0552559i
\(324\) 18.0000i 0.0555556i
\(325\) 96.0760 + 459.682i 0.295618 + 1.41441i
\(326\) 22.2902 0.0683748
\(327\) 173.710 + 173.710i 0.531223 + 0.531223i
\(328\) −70.2739 + 70.2739i −0.214250 + 0.214250i
\(329\) 75.4487i 0.229327i
\(330\) −159.202 + 86.0895i −0.482430 + 0.260877i
\(331\) −197.349 −0.596221 −0.298110 0.954531i \(-0.596356\pi\)
−0.298110 + 0.954531i \(0.596356\pi\)
\(332\) −106.857 106.857i −0.321859 0.321859i
\(333\) 18.4720 18.4720i 0.0554716 0.0554716i
\(334\) 449.622i 1.34617i
\(335\) 599.326 + 178.637i 1.78903 + 0.533246i
\(336\) −18.3303 −0.0545545
\(337\) −259.060 259.060i −0.768723 0.768723i 0.209159 0.977882i \(-0.432927\pi\)
−0.977882 + 0.209159i \(0.932927\pi\)
\(338\) −183.861 + 183.861i −0.543968 + 0.543968i
\(339\) 278.619i 0.821886i
\(340\) 4.76529 15.9875i 0.0140155 0.0470220i
\(341\) −740.198 −2.17067
\(342\) −45.3895 45.3895i −0.132718 0.132718i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 235.767i 0.685369i
\(345\) −131.119 242.472i −0.380054 0.702819i
\(346\) −86.9092 −0.251183
\(347\) −316.016 316.016i −0.910710 0.910710i 0.0856183 0.996328i \(-0.472713\pi\)
−0.996328 + 0.0856183i \(0.972713\pi\)
\(348\) 8.07713 8.07713i 0.0232102 0.0232102i
\(349\) 64.9155i 0.186004i −0.995666 0.0930022i \(-0.970354\pi\)
0.995666 0.0930022i \(-0.0296464\pi\)
\(350\) −78.2768 51.2128i −0.223648 0.146322i
\(351\) 97.6077 0.278085
\(352\) −59.1105 59.1105i −0.167927 0.167927i
\(353\) 328.571 328.571i 0.930796 0.930796i −0.0669597 0.997756i \(-0.521330\pi\)
0.997756 + 0.0669597i \(0.0213299\pi\)
\(354\) 163.326i 0.461372i
\(355\) −304.873 + 164.862i −0.858798 + 0.464401i
\(356\) 42.7105 0.119973
\(357\) 5.40576 + 5.40576i 0.0151422 + 0.0151422i
\(358\) 167.373 167.373i 0.467523 0.467523i
\(359\) 110.889i 0.308883i −0.988002 0.154442i \(-0.950642\pi\)
0.988002 0.154442i \(-0.0493579\pi\)
\(360\) 40.6587 + 12.1189i 0.112941 + 0.0336636i
\(361\) 132.088 0.365895
\(362\) −225.762 225.762i −0.623652 0.623652i
\(363\) 119.263 119.263i 0.328548 0.328548i
\(364\) 99.3988i 0.273074i
\(365\) −117.991 + 395.857i −0.323262 + 1.08454i
\(366\) 10.9148 0.0298218
\(367\) −347.342 347.342i −0.946436 0.946436i 0.0522011 0.998637i \(-0.483376\pi\)
−0.998637 + 0.0522011i \(0.983376\pi\)
\(368\) 90.0281 90.0281i 0.244642 0.244642i
\(369\) 105.411i 0.285666i
\(370\) 29.2883 + 54.1617i 0.0791575 + 0.146383i
\(371\) 40.7944 0.109958
\(372\) 122.693 + 122.693i 0.329820 + 0.329820i
\(373\) −433.660 + 433.660i −1.16263 + 1.16263i −0.178728 + 0.983899i \(0.557198\pi\)
−0.983899 + 0.178728i \(0.942802\pi\)
\(374\) 34.8644i 0.0932202i
\(375\) 139.768 + 165.348i 0.372715 + 0.440927i
\(376\) −80.6581 −0.214516
\(377\) 43.7995 + 43.7995i 0.116179 + 0.116179i
\(378\) −13.7477 + 13.7477i −0.0363696 + 0.0363696i
\(379\) 5.82662i 0.0153737i 0.999970 + 0.00768684i \(0.00244682\pi\)
−0.999970 + 0.00768684i \(0.997553\pi\)
\(380\) 133.086 71.9672i 0.350227 0.189387i
\(381\) −422.972 −1.11016
\(382\) 148.626 + 148.626i 0.389073 + 0.389073i
\(383\) −84.7856 + 84.7856i −0.221372 + 0.221372i −0.809076 0.587704i \(-0.800032\pi\)
0.587704 + 0.809076i \(0.300032\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 187.344 + 55.8406i 0.486609 + 0.145041i
\(386\) 316.126 0.818979
\(387\) 176.825 + 176.825i 0.456913 + 0.456913i
\(388\) −180.712 + 180.712i −0.465754 + 0.465754i
\(389\) 287.140i 0.738150i −0.929400 0.369075i \(-0.879675\pi\)
0.929400 0.369075i \(-0.120325\pi\)
\(390\) −65.7165 + 220.478i −0.168504 + 0.565328i
\(391\) −53.1001 −0.135806
\(392\) 14.0000 + 14.0000i 0.0357143 + 0.0357143i
\(393\) 180.699 180.699i 0.459793 0.459793i
\(394\) 53.5413i 0.135892i
\(395\) 125.648 + 232.357i 0.318097 + 0.588245i
\(396\) −88.6657 −0.223903
\(397\) 89.5514 + 89.5514i 0.225570 + 0.225570i 0.810839 0.585269i \(-0.199011\pi\)
−0.585269 + 0.810839i \(0.699011\pi\)
\(398\) −171.790 + 171.790i −0.431634 + 0.431634i
\(399\) 69.3336i 0.173768i
\(400\) −54.7488 + 83.6814i −0.136872 + 0.209203i
\(401\) −649.944 −1.62081 −0.810405 0.585871i \(-0.800753\pi\)
−0.810405 + 0.585871i \(0.800753\pi\)
\(402\) 216.639 + 216.639i 0.538902 + 0.538902i
\(403\) −665.320 + 665.320i −1.65092 + 1.65092i
\(404\) 87.2218i 0.215896i
\(405\) 39.5832 21.4049i 0.0977363 0.0528515i
\(406\) −12.3380 −0.0303892
\(407\) −90.9909 90.9909i −0.223565 0.223565i
\(408\) 5.77900 5.77900i 0.0141642 0.0141642i
\(409\) 717.337i 1.75388i 0.480600 + 0.876940i \(0.340419\pi\)
−0.480600 + 0.876940i \(0.659581\pi\)
\(410\) −238.104 70.9701i −0.580741 0.173098i
\(411\) 236.598 0.575664
\(412\) −97.7275 97.7275i −0.237203 0.237203i
\(413\) 124.742 124.742i 0.302039 0.302039i
\(414\) 135.042i 0.326189i
\(415\) 107.916 362.057i 0.260038 0.872426i
\(416\) −106.262 −0.255437
\(417\) −225.594 225.594i −0.540992 0.540992i
\(418\) −223.583 + 223.583i −0.534887 + 0.534887i
\(419\) 680.885i 1.62502i 0.582945 + 0.812511i \(0.301900\pi\)
−0.582945 + 0.812511i \(0.698100\pi\)
\(420\) −21.7977 40.3096i −0.0518992 0.0959752i
\(421\) 710.333 1.68725 0.843626 0.536931i \(-0.180416\pi\)
0.843626 + 0.536931i \(0.180416\pi\)
\(422\) 302.432 + 302.432i 0.716664 + 0.716664i
\(423\) −60.4936 + 60.4936i −0.143011 + 0.143011i
\(424\) 43.6110i 0.102856i
\(425\) 40.8242 8.53247i 0.0960570 0.0200764i
\(426\) −169.796 −0.398581
\(427\) −8.33629 8.33629i −0.0195229 0.0195229i
\(428\) −46.2994 + 46.2994i −0.108176 + 0.108176i
\(429\) 480.803i 1.12075i
\(430\) −518.467 + 280.365i −1.20574 + 0.652011i
\(431\) 785.543 1.82261 0.911303 0.411737i \(-0.135078\pi\)
0.911303 + 0.411737i \(0.135078\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 484.429 484.429i 1.11877 1.11877i 0.126852 0.991922i \(-0.459513\pi\)
0.991922 0.126852i \(-0.0404874\pi\)
\(434\) 187.416i 0.431835i
\(435\) 27.3672 + 8.15716i 0.0629130 + 0.0187521i
\(436\) −283.667 −0.650613
\(437\) −340.528 340.528i −0.779240 0.779240i
\(438\) −143.091 + 143.091i −0.326691 + 0.326691i
\(439\) 558.366i 1.27190i 0.771728 + 0.635952i \(0.219392\pi\)
−0.771728 + 0.635952i \(0.780608\pi\)
\(440\) 59.6961 200.280i 0.135673 0.455181i
\(441\) 21.0000 0.0476190
\(442\) 31.3375 + 31.3375i 0.0708993 + 0.0708993i
\(443\) 94.3596 94.3596i 0.213001 0.213001i −0.592540 0.805541i \(-0.701875\pi\)
0.805541 + 0.592540i \(0.201875\pi\)
\(444\) 30.1647i 0.0679385i
\(445\) 50.7896 + 93.9233i 0.114134 + 0.211064i
\(446\) 341.569 0.765850
\(447\) 252.735 + 252.735i 0.565404 + 0.565404i
\(448\) 14.9666 14.9666i 0.0334077 0.0334077i
\(449\) 642.007i 1.42986i −0.699197 0.714929i \(-0.746459\pi\)
0.699197 0.714929i \(-0.253541\pi\)
\(450\) 21.6995 + 103.823i 0.0482210 + 0.230717i
\(451\) 519.240 1.15131
\(452\) −227.492 227.492i −0.503301 0.503301i
\(453\) 63.0529 63.0529i 0.139190 0.139190i
\(454\) 308.647i 0.679838i
\(455\) 218.585 118.201i 0.480406 0.259782i
\(456\) 74.1208 0.162546
\(457\) 320.594 + 320.594i 0.701519 + 0.701519i 0.964736 0.263218i \(-0.0847838\pi\)
−0.263218 + 0.964736i \(0.584784\pi\)
\(458\) −33.7243 + 33.7243i −0.0736337 + 0.0736337i
\(459\) 8.66850i 0.0188856i
\(460\) 305.036 + 90.9201i 0.663121 + 0.197652i
\(461\) −300.193 −0.651177 −0.325589 0.945512i \(-0.605562\pi\)
−0.325589 + 0.945512i \(0.605562\pi\)
\(462\) 67.7195 + 67.7195i 0.146579 + 0.146579i
\(463\) 58.9154 58.9154i 0.127247 0.127247i −0.640615 0.767862i \(-0.721321\pi\)
0.767862 + 0.640615i \(0.221321\pi\)
\(464\) 13.1899i 0.0284265i
\(465\) −123.908 + 415.711i −0.266470 + 0.894003i
\(466\) 415.997 0.892697
\(467\) −362.497 362.497i −0.776226 0.776226i 0.202961 0.979187i \(-0.434943\pi\)
−0.979187 + 0.202961i \(0.934943\pi\)
\(468\) −79.6963 + 79.6963i −0.170291 + 0.170291i
\(469\) 330.921i 0.705589i
\(470\) −95.9153 177.373i −0.204075 0.377388i
\(471\) 224.829 0.477343
\(472\) −133.355 133.355i −0.282531 0.282531i
\(473\) 871.018 871.018i 1.84148 1.84148i
\(474\) 129.408i 0.273013i
\(475\) 316.521 + 207.085i 0.666361 + 0.435968i
\(476\) −8.82757 −0.0185453
\(477\) −32.7083 32.7083i −0.0685708 0.0685708i
\(478\) 49.7163 49.7163i 0.104009 0.104009i
\(479\) 233.704i 0.487900i −0.969788 0.243950i \(-0.921557\pi\)
0.969788 0.243950i \(-0.0784433\pi\)
\(480\) −43.0928 + 23.3027i −0.0897766 + 0.0485472i
\(481\) −163.573 −0.340068
\(482\) 49.9716 + 49.9716i 0.103676 + 0.103676i
\(483\) −103.140 + 103.140i −0.213541 + 0.213541i
\(484\) 194.756i 0.402388i
\(485\) −612.295 182.503i −1.26246 0.376295i
\(486\) 22.0454 0.0453609
\(487\) 234.027 + 234.027i 0.480549 + 0.480549i 0.905307 0.424758i \(-0.139641\pi\)
−0.424758 + 0.905307i \(0.639641\pi\)
\(488\) −8.91187 + 8.91187i −0.0182620 + 0.0182620i
\(489\) 27.2998i 0.0558278i
\(490\) −14.1387 + 47.4352i −0.0288545 + 0.0968065i
\(491\) 29.6268 0.0603398 0.0301699 0.999545i \(-0.490395\pi\)
0.0301699 + 0.999545i \(0.490395\pi\)
\(492\) −86.0675 86.0675i −0.174934 0.174934i
\(493\) 3.88981 3.88981i 0.00789009 0.00789009i
\(494\) 401.931i 0.813625i
\(495\) −105.438 194.982i −0.213005 0.393903i
\(496\) −200.357 −0.403945
\(497\) 129.684 + 129.684i 0.260933 + 0.260933i
\(498\) 130.873 130.873i 0.262797 0.262797i
\(499\) 322.566i 0.646426i −0.946326 0.323213i \(-0.895237\pi\)
0.946326 0.323213i \(-0.104763\pi\)
\(500\) −249.126 20.8857i −0.498252 0.0417714i
\(501\) 550.672 1.09915
\(502\) 315.486 + 315.486i 0.628459 + 0.628459i
\(503\) −350.402 + 350.402i −0.696625 + 0.696625i −0.963681 0.267056i \(-0.913949\pi\)
0.267056 + 0.963681i \(0.413949\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −191.807 + 103.721i −0.379815 + 0.205388i
\(506\) −665.200 −1.31463
\(507\) −225.183 225.183i −0.444148 0.444148i
\(508\) 345.355 345.355i 0.679833 0.679833i
\(509\) 66.4967i 0.130642i 0.997864 + 0.0653210i \(0.0208071\pi\)
−0.997864 + 0.0653210i \(0.979193\pi\)
\(510\) 19.5806 + 5.83626i 0.0383933 + 0.0114436i
\(511\) 218.575 0.427740
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 55.5906 55.5906i 0.108364 0.108364i
\(514\) 551.488i 1.07293i
\(515\) 98.6958 331.123i 0.191642 0.642957i
\(516\) −288.754 −0.559601
\(517\) 297.983 + 297.983i 0.576370 + 0.576370i
\(518\) 23.0387 23.0387i 0.0444762 0.0444762i
\(519\) 106.442i 0.205090i
\(520\) −126.362 233.677i −0.243004 0.449378i
\(521\) −603.618 −1.15858 −0.579288 0.815123i \(-0.696669\pi\)
−0.579288 + 0.815123i \(0.696669\pi\)
\(522\) 9.89243 + 9.89243i 0.0189510 + 0.0189510i
\(523\) −294.450 + 294.450i −0.563002 + 0.563002i −0.930159 0.367157i \(-0.880331\pi\)
0.367157 + 0.930159i \(0.380331\pi\)
\(524\) 295.080i 0.563129i
\(525\) 62.7226 95.8691i 0.119472 0.182608i
\(526\) −245.488 −0.466708
\(527\) 59.0869 + 59.0869i 0.112119 + 0.112119i
\(528\) 72.3952 72.3952i 0.137112 0.137112i
\(529\) 484.133i 0.915185i
\(530\) 95.9036 51.8605i 0.180950 0.0978499i
\(531\) −200.032 −0.376709
\(532\) −56.6107 56.6107i −0.106411 0.106411i
\(533\) 466.714 466.714i 0.875636 0.875636i
\(534\) 52.3095i 0.0979578i
\(535\) −156.873 46.7581i −0.293220 0.0873983i
\(536\) −353.770 −0.660018
\(537\) 204.990 + 204.990i 0.381731 + 0.381731i
\(538\) 62.3232 62.3232i 0.115842 0.115842i
\(539\) 103.443i 0.191917i
\(540\) −14.8426 + 49.7966i −0.0274862 + 0.0922159i
\(541\) −248.513 −0.459358 −0.229679 0.973266i \(-0.573768\pi\)
−0.229679 + 0.973266i \(0.573768\pi\)
\(542\) −127.663 127.663i −0.235541 0.235541i
\(543\) 276.501 276.501i 0.509209 0.509209i
\(544\) 9.43707i 0.0173476i
\(545\) −337.326 623.804i −0.618946 1.14459i
\(546\) 121.738 0.222964
\(547\) −246.861 246.861i −0.451299 0.451299i 0.444487 0.895786i \(-0.353386\pi\)
−0.895786 + 0.444487i \(0.853386\pi\)
\(548\) −193.181 + 193.181i −0.352521 + 0.352521i
\(549\) 13.3678i 0.0243494i
\(550\) 511.417 106.889i 0.929849 0.194343i
\(551\) 49.8903 0.0905450
\(552\) 110.261 + 110.261i 0.199749 + 0.199749i
\(553\) 98.8373 98.8373i 0.178729 0.178729i
\(554\) 115.373i 0.208254i
\(555\) −66.3343 + 35.8707i −0.119521 + 0.0646318i
\(556\) 368.393 0.662578
\(557\) −333.317 333.317i −0.598416 0.598416i 0.341475 0.939891i \(-0.389073\pi\)
−0.939891 + 0.341475i \(0.889073\pi\)
\(558\) −150.267 + 150.267i −0.269297 + 0.269297i
\(559\) 1565.81i 2.80110i
\(560\) 50.7103 + 15.1149i 0.0905542 + 0.0269909i
\(561\) −42.6999 −0.0761140
\(562\) −119.372 119.372i −0.212406 0.212406i
\(563\) 499.267 499.267i 0.886798 0.886798i −0.107416 0.994214i \(-0.534258\pi\)
0.994214 + 0.107416i \(0.0342577\pi\)
\(564\) 98.7856i 0.175152i
\(565\) 229.746 770.794i 0.406630 1.36424i
\(566\) 350.514 0.619282
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 138.638 138.638i 0.244080 0.244080i
\(569\) 990.818i 1.74133i 0.491874 + 0.870666i \(0.336312\pi\)
−0.491874 + 0.870666i \(0.663688\pi\)
\(570\) 88.1414 + 162.997i 0.154634 + 0.285959i
\(571\) −172.474 −0.302057 −0.151028 0.988529i \(-0.548258\pi\)
−0.151028 + 0.988529i \(0.548258\pi\)
\(572\) 392.574 + 392.574i 0.686318 + 0.686318i
\(573\) −182.029 + 182.029i −0.317676 + 0.317676i
\(574\) 131.470i 0.229042i
\(575\) 162.797 + 778.913i 0.283125 + 1.35463i
\(576\) −24.0000 −0.0416667
\(577\) −75.2134 75.2134i −0.130352 0.130352i 0.638920 0.769273i \(-0.279381\pi\)
−0.769273 + 0.638920i \(0.779381\pi\)
\(578\) −286.217 + 286.217i −0.495185 + 0.495185i
\(579\) 387.173i 0.668693i
\(580\) −29.0055 + 15.6849i −0.0500095 + 0.0270429i
\(581\) −199.912 −0.344082
\(582\) −221.327 221.327i −0.380286 0.380286i
\(583\) −161.117 + 161.117i −0.276358 + 0.276358i
\(584\) 233.666i 0.400114i
\(585\) −270.029 80.4859i −0.461588 0.137583i
\(586\) −448.508 −0.765372
\(587\) 371.013 + 371.013i 0.632050 + 0.632050i 0.948582 0.316532i \(-0.102519\pi\)
−0.316532 + 0.948582i \(0.602519\pi\)
\(588\) −17.1464 + 17.1464i −0.0291606 + 0.0291606i
\(589\) 757.841i 1.28666i
\(590\) 134.676 451.836i 0.228265 0.765824i
\(591\) 65.5745 0.110955
\(592\) −24.6294 24.6294i −0.0416037 0.0416037i
\(593\) 106.940 106.940i 0.180337 0.180337i −0.611166 0.791503i \(-0.709299\pi\)
0.791503 + 0.611166i \(0.209299\pi\)
\(594\) 108.593i 0.182816i
\(595\) −10.4974 19.4124i −0.0176427 0.0326259i
\(596\) −412.715 −0.692475
\(597\) −210.399 210.399i −0.352428 0.352428i
\(598\) −597.909 + 597.909i −0.999848 + 0.999848i
\(599\) 382.077i 0.637859i 0.947778 + 0.318929i \(0.103323\pi\)
−0.947778 + 0.318929i \(0.896677\pi\)
\(600\) −102.488 67.0533i −0.170814 0.111755i
\(601\) 618.446 1.02903 0.514514 0.857482i \(-0.327972\pi\)
0.514514 + 0.857482i \(0.327972\pi\)
\(602\) 220.540 + 220.540i 0.366345 + 0.366345i
\(603\) −265.327 + 265.327i −0.440012 + 0.440012i
\(604\) 102.965i 0.170472i
\(605\) −428.281 + 231.596i −0.707903 + 0.382803i
\(606\) −106.825 −0.176278
\(607\) 222.670 + 222.670i 0.366837 + 0.366837i 0.866322 0.499485i \(-0.166477\pi\)
−0.499485 + 0.866322i \(0.666477\pi\)
\(608\) −60.5194 + 60.5194i −0.0995384 + 0.0995384i
\(609\) 15.1109i 0.0248127i
\(610\) −30.1954 9.00017i −0.0495007 0.0147544i
\(611\) 535.679 0.876725
\(612\) 7.07780 + 7.07780i 0.0115650 + 0.0115650i
\(613\) 422.055 422.055i 0.688508 0.688508i −0.273394 0.961902i \(-0.588146\pi\)
0.961902 + 0.273394i \(0.0881464\pi\)
\(614\) 404.731i 0.659172i
\(615\) 86.9203 291.616i 0.141334 0.474173i
\(616\) −110.586 −0.179522
\(617\) −651.882 651.882i −1.05653 1.05653i −0.998303 0.0582314i \(-0.981454\pi\)
−0.0582314 0.998303i \(-0.518546\pi\)
\(618\) 119.691 119.691i 0.193675 0.193675i
\(619\) 687.434i 1.11056i 0.831665 + 0.555278i \(0.187388\pi\)
−0.831665 + 0.555278i \(0.812612\pi\)
\(620\) −238.256 440.598i −0.384284 0.710642i
\(621\) 165.392 0.266332
\(622\) 382.114 + 382.114i 0.614331 + 0.614331i
\(623\) 39.9520 39.9520i 0.0641284 0.0641284i
\(624\) 130.144i 0.208563i
\(625\) −250.322 572.681i −0.400515 0.916290i
\(626\) 470.889 0.752220
\(627\) −273.832 273.832i −0.436734 0.436734i
\(628\) −183.572 + 183.572i −0.292312 + 0.292312i
\(629\) 14.5268i 0.0230951i
\(630\) 49.3689 26.6966i 0.0783634 0.0423755i
\(631\) 589.381 0.934043 0.467021 0.884246i \(-0.345327\pi\)
0.467021 + 0.884246i \(0.345327\pi\)
\(632\) −105.661 105.661i −0.167186 0.167186i
\(633\) −370.402 + 370.402i −0.585154 + 0.585154i
\(634\) 595.408i 0.939129i
\(635\) 1170.14 + 348.777i 1.84274 + 0.549255i
\(636\) 53.4124 0.0839817
\(637\) −92.9790 92.9790i −0.145964 0.145964i
\(638\) 48.7288 48.7288i 0.0763775 0.0763775i
\(639\) 207.956i 0.325440i
\(640\) 16.1585 54.2116i 0.0252477 0.0847057i
\(641\) 410.799 0.640872 0.320436 0.947270i \(-0.396171\pi\)
0.320436 + 0.947270i \(0.396171\pi\)
\(642\) −56.7049 56.7049i −0.0883254 0.0883254i
\(643\) 216.800 216.800i 0.337169 0.337169i −0.518132 0.855301i \(-0.673372\pi\)
0.855301 + 0.518132i \(0.173372\pi\)
\(644\) 168.427i 0.261533i
\(645\) −343.375 634.990i −0.532364 0.984481i
\(646\) 35.6953 0.0552559
\(647\) −411.008 411.008i −0.635252 0.635252i 0.314129 0.949380i \(-0.398288\pi\)
−0.949380 + 0.314129i \(0.898288\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 985.333i 1.51823i
\(650\) 363.606 555.758i 0.559394 0.855013i
\(651\) 229.537 0.352592
\(652\) −22.2902 22.2902i −0.0341874 0.0341874i
\(653\) −46.1020 + 46.1020i −0.0706003 + 0.0706003i −0.741525 0.670925i \(-0.765897\pi\)
0.670925 + 0.741525i \(0.265897\pi\)
\(654\) 347.420i 0.531223i
\(655\) −648.900 + 350.897i −0.990687 + 0.535720i
\(656\) 140.548 0.214250
\(657\) −175.250 175.250i −0.266742 0.266742i
\(658\) −75.4487 + 75.4487i −0.114664 + 0.114664i
\(659\) 911.116i 1.38257i 0.722580 + 0.691287i \(0.242956\pi\)
−0.722580 + 0.691287i \(0.757044\pi\)
\(660\) 245.292 + 73.1125i 0.371654 + 0.110777i
\(661\) 24.2084 0.0366239 0.0183120 0.999832i \(-0.494171\pi\)
0.0183120 + 0.999832i \(0.494171\pi\)
\(662\) 197.349 + 197.349i 0.298110 + 0.298110i
\(663\) −38.3804 + 38.3804i −0.0578890 + 0.0578890i
\(664\) 213.714i 0.321859i
\(665\) 57.1716 191.810i 0.0859723 0.288436i
\(666\) −36.9441 −0.0554716
\(667\) 74.2164 + 74.2164i 0.111269 + 0.111269i
\(668\) −449.622 + 449.622i −0.673087 + 0.673087i
\(669\) 418.335i 0.625314i
\(670\) −420.689 777.963i −0.627894 1.16114i
\(671\) 65.8481 0.0981343
\(672\) 18.3303 + 18.3303i 0.0272772 + 0.0272772i
\(673\) 522.406 522.406i 0.776235 0.776235i −0.202954 0.979188i \(-0.565054\pi\)
0.979188 + 0.202954i \(0.0650541\pi\)
\(674\) 518.119i 0.768723i
\(675\) −127.156 + 26.5763i −0.188380 + 0.0393723i
\(676\) 367.723 0.543968
\(677\) −283.980 283.980i −0.419468 0.419468i 0.465552 0.885020i \(-0.345856\pi\)
−0.885020 + 0.465552i \(0.845856\pi\)
\(678\) 278.619 278.619i 0.410943 0.410943i
\(679\) 338.082i 0.497912i
\(680\) −20.7528 + 11.2222i −0.0305188 + 0.0165032i
\(681\) 378.013 0.555086
\(682\) 740.198 + 740.198i 1.08533 + 1.08533i
\(683\) −549.911 + 549.911i −0.805141 + 0.805141i −0.983894 0.178753i \(-0.942794\pi\)
0.178753 + 0.983894i \(0.442794\pi\)
\(684\) 90.7790i 0.132718i
\(685\) −654.542 195.095i −0.955536 0.284811i
\(686\) 26.1916 0.0381802
\(687\) −41.3036 41.3036i −0.0601217 0.0601217i
\(688\) 235.767 235.767i 0.342685 0.342685i
\(689\) 289.636i 0.420372i
\(690\) −111.354 + 373.591i −0.161383 + 0.541436i
\(691\) −1119.58 −1.62023 −0.810117 0.586268i \(-0.800597\pi\)
−0.810117 + 0.586268i \(0.800597\pi\)
\(692\) 86.9092 + 86.9092i 0.125591 + 0.125591i
\(693\) −82.9392 + 82.9392i −0.119681 + 0.119681i
\(694\) 632.033i 0.910710i
\(695\) 438.078 + 810.122i 0.630329 + 1.16564i
\(696\) −16.1543 −0.0232102
\(697\) −41.4487 41.4487i −0.0594673 0.0594673i
\(698\) −64.9155 + 64.9155i −0.0930022 + 0.0930022i
\(699\) 509.490i 0.728884i
\(700\) 27.0640 + 129.490i 0.0386628 + 0.184985i
\(701\) 693.405 0.989166 0.494583 0.869130i \(-0.335321\pi\)
0.494583 + 0.869130i \(0.335321\pi\)
\(702\) −97.6077 97.6077i −0.139042 0.139042i
\(703\) −93.1597 + 93.1597i −0.132517 + 0.132517i
\(704\) 118.221i 0.167927i
\(705\) 217.236 117.472i 0.308136 0.166627i
\(706\) −657.142 −0.930796
\(707\) 81.5886 + 81.5886i 0.115401 + 0.115401i
\(708\) 163.326 163.326i 0.230686 0.230686i
\(709\) 774.547i 1.09245i 0.837638 + 0.546225i \(0.183936\pi\)
−0.837638 + 0.546225i \(0.816064\pi\)
\(710\) 469.736 + 140.011i 0.661600 + 0.197199i
\(711\) −158.492 −0.222915
\(712\) −42.7105 42.7105i −0.0599867 0.0599867i
\(713\) −1127.36 + 1127.36i −1.58115 + 1.58115i
\(714\) 10.8115i 0.0151422i
\(715\) −396.463 + 1330.13i −0.554494 + 1.86032i
\(716\) −334.747 −0.467523
\(717\) 60.8897 + 60.8897i 0.0849229 + 0.0849229i
\(718\) −110.889 + 110.889i −0.154442 + 0.154442i
\(719\) 8.61314i 0.0119793i −0.999982 0.00598966i \(-0.998093\pi\)
0.999982 0.00598966i \(-0.00190658\pi\)
\(720\) −28.5398 52.7776i −0.0396387 0.0733023i
\(721\) −182.831 −0.253580
\(722\) −132.088 132.088i −0.182947 0.182947i
\(723\) −61.2025 + 61.2025i −0.0846507 + 0.0846507i
\(724\) 451.524i 0.623652i
\(725\) −68.9843 45.1332i −0.0951508 0.0622527i
\(726\) −238.526 −0.328548
\(727\) −305.108 305.108i −0.419681 0.419681i 0.465413 0.885094i \(-0.345906\pi\)
−0.885094 + 0.465413i \(0.845906\pi\)
\(728\) −99.3988 + 99.3988i −0.136537 + 0.136537i
\(729\) 27.0000i 0.0370370i
\(730\) 513.848 277.867i 0.703902 0.380639i
\(731\) −139.059 −0.190232
\(732\) −10.9148 10.9148i −0.0149109 0.0149109i
\(733\) −73.0619 + 73.0619i −0.0996751 + 0.0996751i −0.755186 0.655511i \(-0.772453\pi\)
0.655511 + 0.755186i \(0.272453\pi\)
\(734\) 694.684i 0.946436i
\(735\) −58.0960 17.3163i −0.0790422 0.0235596i
\(736\) −180.056 −0.244642
\(737\) 1306.97 + 1306.97i 1.77336 + 1.77336i
\(738\) 105.411 105.411i 0.142833 0.142833i
\(739\) 81.9526i 0.110897i 0.998462 + 0.0554483i \(0.0176588\pi\)
−0.998462 + 0.0554483i \(0.982341\pi\)
\(740\) 24.8734 83.4500i 0.0336127 0.112770i
\(741\) −492.263 −0.664322
\(742\) −40.7944 40.7944i −0.0549789 0.0549789i
\(743\) 225.872 225.872i 0.304000 0.304000i −0.538577 0.842577i \(-0.681038\pi\)
0.842577 + 0.538577i \(0.181038\pi\)
\(744\) 245.386i 0.329820i
\(745\) −490.784 907.589i −0.658771 1.21824i
\(746\) 867.319 1.16263
\(747\) 160.286 + 160.286i 0.214573 + 0.214573i
\(748\) 34.8644 34.8644i 0.0466101 0.0466101i
\(749\) 86.6182i 0.115645i
\(750\) 25.5797 305.116i 0.0341062 0.406821i
\(751\) 795.157 1.05880 0.529399 0.848373i \(-0.322417\pi\)
0.529399 + 0.848373i \(0.322417\pi\)
\(752\) 80.6581 + 80.6581i 0.107258 + 0.107258i
\(753\) −386.390 + 386.390i −0.513134 + 0.513134i
\(754\) 87.5989i 0.116179i
\(755\) −226.427 + 122.442i −0.299903 + 0.162175i
\(756\) 27.4955 0.0363696
\(757\) −43.3607 43.3607i −0.0572796 0.0572796i 0.677887 0.735166i \(-0.262896\pi\)
−0.735166 + 0.677887i \(0.762896\pi\)
\(758\) 5.82662 5.82662i 0.00768684 0.00768684i
\(759\) 814.701i 1.07339i
\(760\) −205.053 61.1190i −0.269807 0.0804197i
\(761\) 448.207 0.588972 0.294486 0.955656i \(-0.404852\pi\)
0.294486 + 0.955656i \(0.404852\pi\)
\(762\) 422.972 + 422.972i 0.555081 + 0.555081i
\(763\) −265.346 + 265.346i −0.347767 + 0.347767i
\(764\) 297.251i 0.389073i
\(765\) −7.14793 + 23.9812i −0.00934370 + 0.0313480i
\(766\) 169.571 0.221372
\(767\) 885.657 + 885.657i 1.15470 + 1.15470i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 126.308i 0.164249i 0.996622 + 0.0821245i \(0.0261705\pi\)
−0.996622 + 0.0821245i \(0.973829\pi\)
\(770\) −131.504 243.185i −0.170784 0.315825i
\(771\) 675.432 0.876046
\(772\) −316.126 316.126i −0.409489 0.409489i