Properties

Label 210.3.l.b.43.7
Level 210
Weight 3
Character 210.43
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 43.7
Root \(-3.48873 + 3.48873i\) 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 \(\chi\) \(=\) 210.43
Dual form 210.3.l.b.127.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-1.66827 + 4.71348i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-1.66827 + 4.71348i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-3.04521 - 6.38175i) q^{10} -5.03576 q^{11} +(2.44949 - 2.44949i) q^{12} +(-2.44923 - 2.44923i) q^{13} -3.74166i q^{14} +(-7.81601 + 3.72961i) q^{15} -4.00000 q^{16} +(-18.2815 + 18.2815i) q^{17} +(-3.00000 - 3.00000i) q^{18} -9.56449i q^{19} +(9.42696 + 3.33654i) q^{20} -4.58258 q^{21} +(5.03576 - 5.03576i) q^{22} +(16.4256 + 16.4256i) q^{23} +4.89898i q^{24} +(-19.4338 - 15.7267i) q^{25} +4.89847 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} +4.18550i q^{29} +(4.08641 - 11.5456i) q^{30} -55.1410 q^{31} +(4.00000 - 4.00000i) q^{32} +(-6.16752 - 6.16752i) q^{33} -36.5631i q^{34} +(-5.69707 - 11.9392i) q^{35} +6.00000 q^{36} +(-1.23603 + 1.23603i) q^{37} +(9.56449 + 9.56449i) q^{38} -5.99937i q^{39} +(-12.7635 + 6.09042i) q^{40} -12.2171 q^{41} +(4.58258 - 4.58258i) q^{42} +(36.1249 + 36.1249i) q^{43} +10.0715i q^{44} +(-14.1404 - 5.00481i) q^{45} -32.8512 q^{46} +(18.6917 - 18.6917i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +(35.1605 - 3.70706i) q^{50} -44.7804 q^{51} +(-4.89847 + 4.89847i) q^{52} +(37.8979 + 37.8979i) q^{53} -7.34847i q^{54} +(8.40100 - 23.7359i) q^{55} -7.48331 q^{56} +(11.7141 - 11.7141i) q^{57} +(-4.18550 - 4.18550i) q^{58} +71.7488i q^{59} +(7.45921 + 15.6320i) q^{60} +60.8100 q^{61} +(55.1410 - 55.1410i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +(15.6304 - 7.45843i) q^{65} +12.3350 q^{66} +(30.4868 - 30.4868i) q^{67} +(36.5631 + 36.5631i) q^{68} +40.2344i q^{69} +(17.6362 + 6.24209i) q^{70} +115.195 q^{71} +(-6.00000 + 6.00000i) q^{72} +(54.8705 + 54.8705i) q^{73} -2.47206i q^{74} +(-4.54020 - 43.0626i) q^{75} -19.1290 q^{76} +(9.42104 - 9.42104i) q^{77} +(5.99937 + 5.99937i) q^{78} +62.5991i q^{79} +(6.67307 - 18.8539i) q^{80} -9.00000 q^{81} +(12.2171 - 12.2171i) q^{82} +(52.8767 + 52.8767i) q^{83} +9.16515i q^{84} +(-55.6711 - 116.668i) q^{85} -72.2499 q^{86} +(-5.12617 + 5.12617i) q^{87} +(-10.0715 - 10.0715i) q^{88} +16.5994i q^{89} +(19.1452 - 9.13563i) q^{90} +9.16419 q^{91} +(32.8512 - 32.8512i) q^{92} +(-67.5336 - 67.5336i) q^{93} +37.3834i q^{94} +(45.0820 + 15.9561i) q^{95} +9.79796 q^{96} +(71.1722 - 71.1722i) q^{97} +(7.00000 + 7.00000i) q^{98} -15.1073i 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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(5\) −1.66827 + 4.71348i −0.333654 + 0.942696i
\(6\) −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
\(10\) −3.04521 6.38175i −0.304521 0.638175i
\(11\) −5.03576 −0.457796 −0.228898 0.973450i \(-0.573512\pi\)
−0.228898 + 0.973450i \(0.573512\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) −2.44923 2.44923i −0.188403 0.188403i 0.606603 0.795005i \(-0.292532\pi\)
−0.795005 + 0.606603i \(0.792532\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −7.81601 + 3.72961i −0.521067 + 0.248640i
\(16\) −4.00000 −0.250000
\(17\) −18.2815 + 18.2815i −1.07538 + 1.07538i −0.0784682 + 0.996917i \(0.525003\pi\)
−0.996917 + 0.0784682i \(0.974997\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 9.56449i 0.503394i −0.967806 0.251697i \(-0.919011\pi\)
0.967806 0.251697i \(-0.0809887\pi\)
\(20\) 9.42696 + 3.33654i 0.471348 + 0.166827i
\(21\) −4.58258 −0.218218
\(22\) 5.03576 5.03576i 0.228898 0.228898i
\(23\) 16.4256 + 16.4256i 0.714157 + 0.714157i 0.967402 0.253245i \(-0.0814979\pi\)
−0.253245 + 0.967402i \(0.581498\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −19.4338 15.7267i −0.777350 0.629068i
\(26\) 4.89847 0.188403
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 3.74166 + 3.74166i 0.133631 + 0.133631i
\(29\) 4.18550i 0.144328i 0.997393 + 0.0721639i \(0.0229905\pi\)
−0.997393 + 0.0721639i \(0.977010\pi\)
\(30\) 4.08641 11.5456i 0.136214 0.384854i
\(31\) −55.1410 −1.77874 −0.889370 0.457188i \(-0.848857\pi\)
−0.889370 + 0.457188i \(0.848857\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −6.16752 6.16752i −0.186894 0.186894i
\(34\) 36.5631i 1.07538i
\(35\) −5.69707 11.9392i −0.162773 0.341119i
\(36\) 6.00000 0.166667
\(37\) −1.23603 + 1.23603i −0.0334062 + 0.0334062i −0.723613 0.690206i \(-0.757520\pi\)
0.690206 + 0.723613i \(0.257520\pi\)
\(38\) 9.56449 + 9.56449i 0.251697 + 0.251697i
\(39\) 5.99937i 0.153830i
\(40\) −12.7635 + 6.09042i −0.319087 + 0.152260i
\(41\) −12.2171 −0.297979 −0.148989 0.988839i \(-0.547602\pi\)
−0.148989 + 0.988839i \(0.547602\pi\)
\(42\) 4.58258 4.58258i 0.109109 0.109109i
\(43\) 36.1249 + 36.1249i 0.840115 + 0.840115i 0.988874 0.148759i \(-0.0475278\pi\)
−0.148759 + 0.988874i \(0.547528\pi\)
\(44\) 10.0715i 0.228898i
\(45\) −14.1404 5.00481i −0.314232 0.111218i
\(46\) −32.8512 −0.714157
\(47\) 18.6917 18.6917i 0.397696 0.397696i −0.479724 0.877419i \(-0.659263\pi\)
0.877419 + 0.479724i \(0.159263\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) 35.1605 3.70706i 0.703209 0.0741412i
\(51\) −44.7804 −0.878048
\(52\) −4.89847 + 4.89847i −0.0942013 + 0.0942013i
\(53\) 37.8979 + 37.8979i 0.715056 + 0.715056i 0.967588 0.252533i \(-0.0812636\pi\)
−0.252533 + 0.967588i \(0.581264\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 8.40100 23.7359i 0.152745 0.431562i
\(56\) −7.48331 −0.133631
\(57\) 11.7141 11.7141i 0.205510 0.205510i
\(58\) −4.18550 4.18550i −0.0721639 0.0721639i
\(59\) 71.7488i 1.21608i 0.793906 + 0.608041i \(0.208044\pi\)
−0.793906 + 0.608041i \(0.791956\pi\)
\(60\) 7.45921 + 15.6320i 0.124320 + 0.260534i
\(61\) 60.8100 0.996885 0.498442 0.866923i \(-0.333906\pi\)
0.498442 + 0.866923i \(0.333906\pi\)
\(62\) 55.1410 55.1410i 0.889370 0.889370i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 15.6304 7.45843i 0.240467 0.114745i
\(66\) 12.3350 0.186894
\(67\) 30.4868 30.4868i 0.455027 0.455027i −0.441992 0.897019i \(-0.645728\pi\)
0.897019 + 0.441992i \(0.145728\pi\)
\(68\) 36.5631 + 36.5631i 0.537692 + 0.537692i
\(69\) 40.2344i 0.583107i
\(70\) 17.6362 + 6.24209i 0.251946 + 0.0891727i
\(71\) 115.195 1.62246 0.811229 0.584728i \(-0.198799\pi\)
0.811229 + 0.584728i \(0.198799\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) 54.8705 + 54.8705i 0.751651 + 0.751651i 0.974787 0.223136i \(-0.0716294\pi\)
−0.223136 + 0.974787i \(0.571629\pi\)
\(74\) 2.47206i 0.0334062i
\(75\) −4.54020 43.0626i −0.0605361 0.574168i
\(76\) −19.1290 −0.251697
\(77\) 9.42104 9.42104i 0.122351 0.122351i
\(78\) 5.99937 + 5.99937i 0.0769150 + 0.0769150i
\(79\) 62.5991i 0.792394i 0.918165 + 0.396197i \(0.129670\pi\)
−0.918165 + 0.396197i \(0.870330\pi\)
\(80\) 6.67307 18.8539i 0.0834134 0.235674i
\(81\) −9.00000 −0.111111
\(82\) 12.2171 12.2171i 0.148989 0.148989i
\(83\) 52.8767 + 52.8767i 0.637069 + 0.637069i 0.949831 0.312762i \(-0.101254\pi\)
−0.312762 + 0.949831i \(0.601254\pi\)
\(84\) 9.16515i 0.109109i
\(85\) −55.6711 116.668i −0.654954 1.37257i
\(86\) −72.2499 −0.840115
\(87\) −5.12617 + 5.12617i −0.0589215 + 0.0589215i
\(88\) −10.0715 10.0715i −0.114449 0.114449i
\(89\) 16.5994i 0.186511i 0.995642 + 0.0932553i \(0.0297273\pi\)
−0.995642 + 0.0932553i \(0.970273\pi\)
\(90\) 19.1452 9.13563i 0.212725 0.101507i
\(91\) 9.16419 0.100705
\(92\) 32.8512 32.8512i 0.357079 0.357079i
\(93\) −67.5336 67.5336i −0.726168 0.726168i
\(94\) 37.3834i 0.397696i
\(95\) 45.0820 + 15.9561i 0.474548 + 0.167959i
\(96\) 9.79796 0.102062
\(97\) 71.1722 71.1722i 0.733734 0.733734i −0.237623 0.971357i \(-0.576368\pi\)
0.971357 + 0.237623i \(0.0763684\pi\)
\(98\) 7.00000 + 7.00000i 0.0714286 + 0.0714286i
\(99\) 15.1073i 0.152599i
\(100\) −31.4534 + 38.8675i −0.314534 + 0.388675i
\(101\) −145.577 −1.44136 −0.720679 0.693269i \(-0.756170\pi\)
−0.720679 + 0.693269i \(0.756170\pi\)
\(102\) 44.7804 44.7804i 0.439024 0.439024i
\(103\) 105.102 + 105.102i 1.02041 + 1.02041i 0.999787 + 0.0206221i \(0.00656470\pi\)
0.0206221 + 0.999787i \(0.493435\pi\)
\(104\) 9.79693i 0.0942013i
\(105\) 7.64497 21.5999i 0.0728092 0.205713i
\(106\) −75.7959 −0.715056
\(107\) −45.6173 + 45.6173i −0.426330 + 0.426330i −0.887376 0.461046i \(-0.847474\pi\)
0.461046 + 0.887376i \(0.347474\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 156.303i 1.43397i −0.697087 0.716987i \(-0.745521\pi\)
0.697087 0.716987i \(-0.254479\pi\)
\(110\) 15.3349 + 32.1369i 0.139409 + 0.292154i
\(111\) −3.02764 −0.0272760
\(112\) 7.48331 7.48331i 0.0668153 0.0668153i
\(113\) −78.3428 78.3428i −0.693299 0.693299i 0.269657 0.962956i \(-0.413090\pi\)
−0.962956 + 0.269657i \(0.913090\pi\)
\(114\) 23.4281i 0.205510i
\(115\) −104.824 + 50.0194i −0.911514 + 0.434952i
\(116\) 8.37101 0.0721639
\(117\) 7.34770 7.34770i 0.0628009 0.0628009i
\(118\) −71.7488 71.7488i −0.608041 0.608041i
\(119\) 68.4033i 0.574817i
\(120\) −23.0912 8.17281i −0.192427 0.0681068i
\(121\) −95.6411 −0.790423
\(122\) −60.8100 + 60.8100i −0.498442 + 0.498442i
\(123\) −14.9629 14.9629i −0.121649 0.121649i
\(124\) 110.282i 0.889370i
\(125\) 106.548 65.3642i 0.852385 0.522914i
\(126\) 11.2250 0.0890871
\(127\) 84.9960 84.9960i 0.669260 0.669260i −0.288285 0.957545i \(-0.593085\pi\)
0.957545 + 0.288285i \(0.0930851\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 88.4877i 0.685951i
\(130\) −8.17196 + 23.0888i −0.0628612 + 0.177606i
\(131\) −220.554 −1.68362 −0.841808 0.539776i \(-0.818509\pi\)
−0.841808 + 0.539776i \(0.818509\pi\)
\(132\) −12.3350 + 12.3350i −0.0934472 + 0.0934472i
\(133\) 17.8935 + 17.8935i 0.134538 + 0.134538i
\(134\) 60.9737i 0.455027i
\(135\) −11.1888 23.4480i −0.0828801 0.173689i
\(136\) −73.1262 −0.537692
\(137\) −116.039 + 116.039i −0.846999 + 0.846999i −0.989758 0.142759i \(-0.954403\pi\)
0.142759 + 0.989758i \(0.454403\pi\)
\(138\) −40.2344 40.2344i −0.291553 0.291553i
\(139\) 270.544i 1.94636i 0.230046 + 0.973180i \(0.426112\pi\)
−0.230046 + 0.973180i \(0.573888\pi\)
\(140\) −23.8783 + 11.3941i −0.170559 + 0.0813867i
\(141\) 45.7851 0.324717
\(142\) −115.195 + 115.195i −0.811229 + 0.811229i
\(143\) 12.3337 + 12.3337i 0.0862500 + 0.0862500i
\(144\) 12.0000i 0.0833333i
\(145\) −19.7283 6.98255i −0.136057 0.0481555i
\(146\) −109.741 −0.751651
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) 2.47206 + 2.47206i 0.0167031 + 0.0167031i
\(149\) 101.794i 0.683184i −0.939848 0.341592i \(-0.889034\pi\)
0.939848 0.341592i \(-0.110966\pi\)
\(150\) 47.6028 + 38.5224i 0.317352 + 0.256816i
\(151\) 166.350 1.10165 0.550826 0.834620i \(-0.314313\pi\)
0.550826 + 0.834620i \(0.314313\pi\)
\(152\) 19.1290 19.1290i 0.125849 0.125849i
\(153\) −54.8446 54.8446i −0.358462 0.358462i
\(154\) 18.8421i 0.122351i
\(155\) 91.9899 259.906i 0.593483 1.67681i
\(156\) −11.9987 −0.0769150
\(157\) −106.083 + 106.083i −0.675686 + 0.675686i −0.959021 0.283335i \(-0.908559\pi\)
0.283335 + 0.959021i \(0.408559\pi\)
\(158\) −62.5991 62.5991i −0.396197 0.396197i
\(159\) 92.8306i 0.583840i
\(160\) 12.1808 + 25.5270i 0.0761302 + 0.159544i
\(161\) −61.4590 −0.381733
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) 54.7674 + 54.7674i 0.335996 + 0.335996i 0.854858 0.518862i \(-0.173644\pi\)
−0.518862 + 0.854858i \(0.673644\pi\)
\(164\) 24.4342i 0.148989i
\(165\) 39.3595 18.7814i 0.238543 0.113827i
\(166\) −105.753 −0.637069
\(167\) 12.2483 12.2483i 0.0733432 0.0733432i −0.669484 0.742827i \(-0.733485\pi\)
0.742827 + 0.669484i \(0.233485\pi\)
\(168\) −9.16515 9.16515i −0.0545545 0.0545545i
\(169\) 157.003i 0.929009i
\(170\) 172.339 + 60.9970i 1.01376 + 0.358806i
\(171\) 28.6935 0.167798
\(172\) 72.2499 72.2499i 0.420057 0.420057i
\(173\) −210.627 210.627i −1.21750 1.21750i −0.968506 0.248992i \(-0.919901\pi\)
−0.248992 0.968506i \(-0.580099\pi\)
\(174\) 10.2523i 0.0589215i
\(175\) 65.7792 6.93528i 0.375881 0.0396302i
\(176\) 20.1430 0.114449
\(177\) −87.8740 + 87.8740i −0.496463 + 0.496463i
\(178\) −16.5994 16.5994i −0.0932553 0.0932553i
\(179\) 141.089i 0.788208i −0.919066 0.394104i \(-0.871055\pi\)
0.919066 0.394104i \(-0.128945\pi\)
\(180\) −10.0096 + 28.2809i −0.0556090 + 0.157116i
\(181\) −14.5190 −0.0802153 −0.0401077 0.999195i \(-0.512770\pi\)
−0.0401077 + 0.999195i \(0.512770\pi\)
\(182\) −9.16419 + 9.16419i −0.0503527 + 0.0503527i
\(183\) 74.4767 + 74.4767i 0.406976 + 0.406976i
\(184\) 65.7025i 0.357079i
\(185\) −3.76396 7.88802i −0.0203458 0.0426379i
\(186\) 135.067 0.726168
\(187\) 92.0614 92.0614i 0.492307 0.492307i
\(188\) −37.3834 37.3834i −0.198848 0.198848i
\(189\) 13.7477i 0.0727393i
\(190\) −61.0382 + 29.1259i −0.321254 + 0.153294i
\(191\) 336.312 1.76080 0.880398 0.474235i \(-0.157275\pi\)
0.880398 + 0.474235i \(0.157275\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) 15.7585 + 15.7585i 0.0816500 + 0.0816500i 0.746752 0.665102i \(-0.231612\pi\)
−0.665102 + 0.746752i \(0.731612\pi\)
\(194\) 142.344i 0.733734i
\(195\) 28.2779 + 10.0086i 0.145015 + 0.0513260i
\(196\) −14.0000 −0.0714286
\(197\) −160.208 + 160.208i −0.813239 + 0.813239i −0.985118 0.171879i \(-0.945016\pi\)
0.171879 + 0.985118i \(0.445016\pi\)
\(198\) 15.1073 + 15.1073i 0.0762994 + 0.0762994i
\(199\) 161.286i 0.810483i −0.914210 0.405242i \(-0.867187\pi\)
0.914210 0.405242i \(-0.132813\pi\)
\(200\) −7.41412 70.3209i −0.0370706 0.351605i
\(201\) 74.6772 0.371528
\(202\) 145.577 145.577i 0.720679 0.720679i
\(203\) −7.83036 7.83036i −0.0385732 0.0385732i
\(204\) 89.5609i 0.439024i
\(205\) 20.3814 57.5852i 0.0994217 0.280903i
\(206\) −210.204 −1.02041
\(207\) −49.2768 + 49.2768i −0.238052 + 0.238052i
\(208\) 9.79693 + 9.79693i 0.0471006 + 0.0471006i
\(209\) 48.1645i 0.230452i
\(210\) 13.9549 + 29.2448i 0.0664519 + 0.139261i
\(211\) −76.5522 −0.362806 −0.181403 0.983409i \(-0.558064\pi\)
−0.181403 + 0.983409i \(0.558064\pi\)
\(212\) 75.7959 75.7959i 0.357528 0.357528i
\(213\) 141.084 + 141.084i 0.662366 + 0.662366i
\(214\) 91.2347i 0.426330i
\(215\) −230.540 + 110.008i −1.07228 + 0.511665i
\(216\) −14.6969 −0.0680414
\(217\) 103.159 103.159i 0.475388 0.475388i
\(218\) 156.303 + 156.303i 0.716987 + 0.716987i
\(219\) 134.405i 0.613721i
\(220\) −47.4719 16.8020i −0.215781 0.0763727i
\(221\) 89.5515 0.405210
\(222\) 3.02764 3.02764i 0.0136380 0.0136380i
\(223\) 247.136 + 247.136i 1.10823 + 1.10823i 0.993383 + 0.114852i \(0.0366394\pi\)
0.114852 + 0.993383i \(0.463361\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 47.1801 58.3013i 0.209689 0.259117i
\(226\) 156.686 0.693299
\(227\) −195.992 + 195.992i −0.863402 + 0.863402i −0.991732 0.128330i \(-0.959038\pi\)
0.128330 + 0.991732i \(0.459038\pi\)
\(228\) −23.4281 23.4281i −0.102755 0.102755i
\(229\) 70.9486i 0.309819i −0.987929 0.154910i \(-0.950491\pi\)
0.987929 0.154910i \(-0.0495086\pi\)
\(230\) 54.8047 154.844i 0.238281 0.673233i
\(231\) 23.0767 0.0998993
\(232\) −8.37101 + 8.37101i −0.0360819 + 0.0360819i
\(233\) −13.5120 13.5120i −0.0579912 0.0579912i 0.677516 0.735508i \(-0.263056\pi\)
−0.735508 + 0.677516i \(0.763056\pi\)
\(234\) 14.6954i 0.0628009i
\(235\) 56.9201 + 119.286i 0.242213 + 0.507599i
\(236\) 143.498 0.608041
\(237\) −76.6680 + 76.6680i −0.323494 + 0.323494i
\(238\) 68.4033 + 68.4033i 0.287409 + 0.287409i
\(239\) 157.888i 0.660617i −0.943873 0.330309i \(-0.892847\pi\)
0.943873 0.330309i \(-0.107153\pi\)
\(240\) 31.2640 14.9184i 0.130267 0.0621601i
\(241\) 142.701 0.592119 0.296060 0.955169i \(-0.404327\pi\)
0.296060 + 0.955169i \(0.404327\pi\)
\(242\) 95.6411 95.6411i 0.395211 0.395211i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 121.620i 0.498442i
\(245\) 32.9943 + 11.6779i 0.134671 + 0.0476648i
\(246\) 29.9257 0.121649
\(247\) −23.4257 + 23.4257i −0.0948408 + 0.0948408i
\(248\) −110.282 110.282i −0.444685 0.444685i
\(249\) 129.521i 0.520165i
\(250\) −41.1839 + 171.912i −0.164736 + 0.687650i
\(251\) 81.9263 0.326400 0.163200 0.986593i \(-0.447818\pi\)
0.163200 + 0.986593i \(0.447818\pi\)
\(252\) −11.2250 + 11.2250i −0.0445435 + 0.0445435i
\(253\) −82.7154 82.7154i −0.326938 0.326938i
\(254\) 169.992i 0.669260i
\(255\) 74.7058 211.072i 0.292964 0.827732i
\(256\) 16.0000 0.0625000
\(257\) −266.743 + 266.743i −1.03791 + 1.03791i −0.0386594 + 0.999252i \(0.512309\pi\)
−0.999252 + 0.0386594i \(0.987691\pi\)
\(258\) −88.4877 88.4877i −0.342975 0.342975i
\(259\) 4.62479i 0.0178563i
\(260\) −14.9169 31.2608i −0.0573725 0.120234i
\(261\) −12.5565 −0.0481092
\(262\) 220.554 220.554i 0.841808 0.841808i
\(263\) −77.4514 77.4514i −0.294492 0.294492i 0.544360 0.838852i \(-0.316773\pi\)
−0.838852 + 0.544360i \(0.816773\pi\)
\(264\) 24.6701i 0.0934472i
\(265\) −241.855 + 115.407i −0.912661 + 0.435499i
\(266\) −35.7871 −0.134538
\(267\) −20.3301 + 20.3301i −0.0761427 + 0.0761427i
\(268\) −60.9737 60.9737i −0.227514 0.227514i
\(269\) 51.5262i 0.191547i −0.995403 0.0957737i \(-0.969467\pi\)
0.995403 0.0957737i \(-0.0305325\pi\)
\(270\) 34.6369 + 12.2592i 0.128285 + 0.0454045i
\(271\) 143.162 0.528273 0.264137 0.964485i \(-0.414913\pi\)
0.264137 + 0.964485i \(0.414913\pi\)
\(272\) 73.1262 73.1262i 0.268846 0.268846i
\(273\) 11.2238 + 11.2238i 0.0411128 + 0.0411128i
\(274\) 232.078i 0.846999i
\(275\) 97.8637 + 79.1958i 0.355868 + 0.287985i
\(276\) 80.4688 0.291553
\(277\) −66.2523 + 66.2523i −0.239178 + 0.239178i −0.816510 0.577332i \(-0.804094\pi\)
0.577332 + 0.816510i \(0.304094\pi\)
\(278\) −270.544 270.544i −0.973180 0.973180i
\(279\) 165.423i 0.592913i
\(280\) 12.4842 35.2724i 0.0445864 0.125973i
\(281\) 484.413 1.72389 0.861945 0.507002i \(-0.169246\pi\)
0.861945 + 0.507002i \(0.169246\pi\)
\(282\) −45.7851 + 45.7851i −0.162359 + 0.162359i
\(283\) 248.349 + 248.349i 0.877559 + 0.877559i 0.993282 0.115723i \(-0.0369184\pi\)
−0.115723 + 0.993282i \(0.536918\pi\)
\(284\) 230.389i 0.811229i
\(285\) 35.6718 + 74.7562i 0.125164 + 0.262302i
\(286\) −24.6675 −0.0862500
\(287\) 22.8561 22.8561i 0.0796381 0.0796381i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 379.430i 1.31290i
\(290\) 26.7108 12.7457i 0.0921063 0.0439508i
\(291\) 174.336 0.599091
\(292\) 109.741 109.741i 0.375826 0.375826i
\(293\) −201.337 201.337i −0.687158 0.687158i 0.274445 0.961603i \(-0.411506\pi\)
−0.961603 + 0.274445i \(0.911506\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) −338.187 119.696i −1.14640 0.405750i
\(296\) −4.94411 −0.0167031
\(297\) 18.5026 18.5026i 0.0622982 0.0622982i
\(298\) 101.794 + 101.794i 0.341592 + 0.341592i
\(299\) 80.4603i 0.269098i
\(300\) −86.1252 + 9.08041i −0.287084 + 0.0302680i
\(301\) −135.167 −0.449060
\(302\) −166.350 + 166.350i −0.550826 + 0.550826i
\(303\) −178.295 178.295i −0.588432 0.588432i
\(304\) 38.2580i 0.125849i
\(305\) −101.447 + 286.626i −0.332614 + 0.939759i
\(306\) 109.689 0.358462
\(307\) −2.87888 + 2.87888i −0.00937745 + 0.00937745i −0.711780 0.702403i \(-0.752111\pi\)
0.702403 + 0.711780i \(0.252111\pi\)
\(308\) −18.8421 18.8421i −0.0611756 0.0611756i
\(309\) 257.447i 0.833161i
\(310\) 167.916 + 351.896i 0.541664 + 1.13515i
\(311\) −127.446 −0.409793 −0.204897 0.978784i \(-0.565686\pi\)
−0.204897 + 0.978784i \(0.565686\pi\)
\(312\) 11.9987 11.9987i 0.0384575 0.0384575i
\(313\) −73.9562 73.9562i −0.236282 0.236282i 0.579027 0.815309i \(-0.303433\pi\)
−0.815309 + 0.579027i \(0.803433\pi\)
\(314\) 212.165i 0.675686i
\(315\) 35.8175 17.0912i 0.113706 0.0542578i
\(316\) 125.198 0.396197
\(317\) 377.411 377.411i 1.19057 1.19057i 0.213664 0.976907i \(-0.431460\pi\)
0.976907 0.213664i \(-0.0685397\pi\)
\(318\) −92.8306 92.8306i −0.291920 0.291920i
\(319\) 21.0772i 0.0660727i
\(320\) −37.7078 13.3461i −0.117837 0.0417067i
\(321\) −111.739 −0.348097
\(322\) 61.4590 61.4590i 0.190867 0.190867i
\(323\) 174.854 + 174.854i 0.541343 + 0.541343i
\(324\) 18.0000i 0.0555556i
\(325\) 9.07946 + 86.1162i 0.0279368 + 0.264973i
\(326\) −109.535 −0.335996
\(327\) 191.431 191.431i 0.585417 0.585417i
\(328\) −24.4342 24.4342i −0.0744947 0.0744947i
\(329\) 69.9379i 0.212577i
\(330\) −20.5782 + 58.1409i −0.0623580 + 0.176185i
\(331\) −505.056 −1.52585 −0.762924 0.646488i \(-0.776237\pi\)
−0.762924 + 0.646488i \(0.776237\pi\)
\(332\) 105.753 105.753i 0.318535 0.318535i
\(333\) −3.70808 3.70808i −0.0111354 0.0111354i
\(334\) 24.4966i 0.0733432i
\(335\) 92.8388 + 194.559i 0.277131 + 0.580774i
\(336\) 18.3303 0.0545545
\(337\) −389.840 + 389.840i −1.15680 + 1.15680i −0.171635 + 0.985161i \(0.554905\pi\)
−0.985161 + 0.171635i \(0.945095\pi\)
\(338\) 157.003 + 157.003i 0.464504 + 0.464504i
\(339\) 191.900i 0.566076i
\(340\) −233.336 + 111.342i −0.686283 + 0.327477i
\(341\) 277.676 0.814300
\(342\) −28.6935 + 28.6935i −0.0838991 + 0.0838991i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 144.500i 0.420057i
\(345\) −189.644 67.1218i −0.549692 0.194556i
\(346\) 421.254 1.21750
\(347\) −306.559 + 306.559i −0.883456 + 0.883456i −0.993884 0.110428i \(-0.964778\pi\)
0.110428 + 0.993884i \(0.464778\pi\)
\(348\) 10.2523 + 10.2523i 0.0294608 + 0.0294608i
\(349\) 509.585i 1.46013i 0.683379 + 0.730064i \(0.260510\pi\)
−0.683379 + 0.730064i \(0.739490\pi\)
\(350\) −58.8439 + 72.7145i −0.168125 + 0.207756i
\(351\) 17.9981 0.0512767
\(352\) −20.1430 + 20.1430i −0.0572245 + 0.0572245i
\(353\) 330.387 + 330.387i 0.935941 + 0.935941i 0.998068 0.0621272i \(-0.0197884\pi\)
−0.0621272 + 0.998068i \(0.519788\pi\)
\(354\) 175.748i 0.496463i
\(355\) −192.176 + 542.967i −0.541340 + 1.52949i
\(356\) 33.1989 0.0932553
\(357\) 83.7765 83.7765i 0.234668 0.234668i
\(358\) 141.089 + 141.089i 0.394104 + 0.394104i
\(359\) 152.593i 0.425051i −0.977155 0.212526i \(-0.931831\pi\)
0.977155 0.212526i \(-0.0681689\pi\)
\(360\) −18.2713 38.2905i −0.0507535 0.106362i
\(361\) 269.520 0.746594
\(362\) 14.5190 14.5190i 0.0401077 0.0401077i
\(363\) −117.136 117.136i −0.322689 0.322689i
\(364\) 18.3284i 0.0503527i
\(365\) −350.170 + 167.092i −0.959370 + 0.457787i
\(366\) −148.953 −0.406976
\(367\) −105.176 + 105.176i −0.286583 + 0.286583i −0.835727 0.549145i \(-0.814954\pi\)
0.549145 + 0.835727i \(0.314954\pi\)
\(368\) −65.7025 65.7025i −0.178539 0.178539i
\(369\) 36.6514i 0.0993262i
\(370\) 11.6520 + 4.12405i 0.0314918 + 0.0111461i
\(371\) −141.801 −0.382213
\(372\) −135.067 + 135.067i −0.363084 + 0.363084i
\(373\) −304.851 304.851i −0.817294 0.817294i 0.168421 0.985715i \(-0.446133\pi\)
−0.985715 + 0.168421i \(0.946133\pi\)
\(374\) 184.123i 0.492307i
\(375\) 210.549 + 50.4398i 0.561464 + 0.134506i
\(376\) 74.7668 0.198848
\(377\) 10.2513 10.2513i 0.0271917 0.0271917i
\(378\) 13.7477 + 13.7477i 0.0363696 + 0.0363696i
\(379\) 157.708i 0.416117i −0.978116 0.208059i \(-0.933286\pi\)
0.978116 0.208059i \(-0.0667145\pi\)
\(380\) 31.9123 90.1641i 0.0839797 0.237274i
\(381\) 208.197 0.546448
\(382\) −336.312 + 336.312i −0.880398 + 0.880398i
\(383\) −429.631 429.631i −1.12175 1.12175i −0.991478 0.130275i \(-0.958414\pi\)
−0.130275 0.991478i \(-0.541586\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 28.6890 + 60.1227i 0.0745170 + 0.156163i
\(386\) −31.5169 −0.0816500
\(387\) −108.375 + 108.375i −0.280038 + 0.280038i
\(388\) −142.344 142.344i −0.366867 0.366867i
\(389\) 168.931i 0.434269i −0.976142 0.217135i \(-0.930329\pi\)
0.976142 0.217135i \(-0.0696711\pi\)
\(390\) −38.2865 + 18.2693i −0.0981704 + 0.0468445i
\(391\) −600.571 −1.53599
\(392\) 14.0000 14.0000i 0.0357143 0.0357143i
\(393\) −270.122 270.122i −0.687334 0.687334i
\(394\) 320.416i 0.813239i
\(395\) −295.060 104.432i −0.746987 0.264385i
\(396\) −30.2145 −0.0762994
\(397\) 514.413 514.413i 1.29575 1.29575i 0.364579 0.931172i \(-0.381213\pi\)
0.931172 0.364579i \(-0.118787\pi\)
\(398\) 161.286 + 161.286i 0.405242 + 0.405242i
\(399\) 43.8300i 0.109850i
\(400\) 77.7350 + 62.9068i 0.194338 + 0.157267i
\(401\) 542.884 1.35383 0.676913 0.736063i \(-0.263317\pi\)
0.676913 + 0.736063i \(0.263317\pi\)
\(402\) −74.6772 + 74.6772i −0.185764 + 0.185764i
\(403\) 135.053 + 135.053i 0.335119 + 0.335119i
\(404\) 291.154i 0.720679i
\(405\) 15.0144 42.4213i 0.0370726 0.104744i
\(406\) 15.6607 0.0385732
\(407\) 6.22434 6.22434i 0.0152932 0.0152932i
\(408\) −89.5609 89.5609i −0.219512 0.219512i
\(409\) 454.920i 1.11227i −0.831091 0.556137i \(-0.812283\pi\)
0.831091 0.556137i \(-0.187717\pi\)
\(410\) 37.2037 + 77.9666i 0.0907408 + 0.190162i
\(411\) −284.236 −0.691572
\(412\) 210.204 210.204i 0.510205 0.510205i
\(413\) −134.230 134.230i −0.325012 0.325012i
\(414\) 98.5537i 0.238052i
\(415\) −337.446 + 161.021i −0.813123 + 0.388002i
\(416\) −19.5939 −0.0471006
\(417\) −331.347 + 331.347i −0.794598 + 0.794598i
\(418\) −48.1645 48.1645i −0.115226 0.115226i
\(419\) 597.925i 1.42703i 0.700641 + 0.713514i \(0.252898\pi\)
−0.700641 + 0.713514i \(0.747102\pi\)
\(420\) −43.1997 15.2899i −0.102857 0.0364046i
\(421\) −607.858 −1.44384 −0.721921 0.691975i \(-0.756741\pi\)
−0.721921 + 0.691975i \(0.756741\pi\)
\(422\) 76.5522 76.5522i 0.181403 0.181403i
\(423\) 56.0751 + 56.0751i 0.132565 + 0.132565i
\(424\) 151.592i 0.357528i
\(425\) 642.787 67.7708i 1.51244 0.159461i
\(426\) −282.168 −0.662366
\(427\) −113.765 + 113.765i −0.266429 + 0.266429i
\(428\) 91.2347 + 91.2347i 0.213165 + 0.213165i
\(429\) 30.2114i 0.0704228i
\(430\) 120.532 340.548i 0.280307 0.791973i
\(431\) 291.207 0.675655 0.337827 0.941208i \(-0.390308\pi\)
0.337827 + 0.941208i \(0.390308\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) −47.9051 47.9051i −0.110635 0.110635i 0.649622 0.760257i \(-0.274927\pi\)
−0.760257 + 0.649622i \(0.774927\pi\)
\(434\) 206.319i 0.475388i
\(435\) −15.6103 32.7140i −0.0358857 0.0752045i
\(436\) −312.606 −0.716987
\(437\) 157.103 157.103i 0.359503 0.359503i
\(438\) −134.405 134.405i −0.306860 0.306860i
\(439\) 652.062i 1.48533i −0.669660 0.742667i \(-0.733560\pi\)
0.669660 0.742667i \(-0.266440\pi\)
\(440\) 64.2739 30.6699i 0.146077 0.0697043i
\(441\) 21.0000 0.0476190
\(442\) −89.5515 + 89.5515i −0.202605 + 0.202605i
\(443\) −146.273 146.273i −0.330187 0.330187i 0.522470 0.852657i \(-0.325011\pi\)
−0.852657 + 0.522470i \(0.825011\pi\)
\(444\) 6.05527i 0.0136380i
\(445\) −78.2411 27.6923i −0.175823 0.0622300i
\(446\) −494.273 −1.10823
\(447\) 124.672 124.672i 0.278909 0.278909i
\(448\) −14.9666 14.9666i −0.0334077 0.0334077i
\(449\) 213.815i 0.476203i 0.971240 + 0.238101i \(0.0765251\pi\)
−0.971240 + 0.238101i \(0.923475\pi\)
\(450\) 11.1212 + 105.481i 0.0247137 + 0.234403i
\(451\) 61.5225 0.136413
\(452\) −156.686 + 156.686i −0.346650 + 0.346650i
\(453\) 203.736 + 203.736i 0.449748 + 0.449748i
\(454\) 391.984i 0.863402i
\(455\) −15.2883 + 43.1952i −0.0336007 + 0.0949345i
\(456\) 46.8562 0.102755
\(457\) 339.531 339.531i 0.742956 0.742956i −0.230189 0.973146i \(-0.573935\pi\)
0.973146 + 0.230189i \(0.0739346\pi\)
\(458\) 70.9486 + 70.9486i 0.154910 + 0.154910i
\(459\) 134.341i 0.292683i
\(460\) 100.039 + 209.648i 0.217476 + 0.455757i
\(461\) 580.456 1.25912 0.629562 0.776951i \(-0.283235\pi\)
0.629562 + 0.776951i \(0.283235\pi\)
\(462\) −23.0767 + 23.0767i −0.0499497 + 0.0499497i
\(463\) 551.037 + 551.037i 1.19014 + 1.19014i 0.977026 + 0.213119i \(0.0683621\pi\)
0.213119 + 0.977026i \(0.431638\pi\)
\(464\) 16.7420i 0.0360819i
\(465\) 430.982 205.654i 0.926844 0.442267i
\(466\) 27.0239 0.0579912
\(467\) 293.344 293.344i 0.628145 0.628145i −0.319456 0.947601i \(-0.603500\pi\)
0.947601 + 0.319456i \(0.103500\pi\)
\(468\) −14.6954 14.6954i −0.0314004 0.0314004i
\(469\) 114.071i 0.243222i
\(470\) −176.206 62.3655i −0.374906 0.132693i
\(471\) −259.848 −0.551695
\(472\) −143.498 + 143.498i −0.304021 + 0.304021i
\(473\) −181.916 181.916i −0.384601 0.384601i
\(474\) 153.336i 0.323494i
\(475\) −150.418 + 185.874i −0.316669 + 0.391314i
\(476\) −136.807 −0.287409
\(477\) −113.694 + 113.694i −0.238352 + 0.238352i
\(478\) 157.888 + 157.888i 0.330309 + 0.330309i
\(479\) 694.462i 1.44982i −0.688846 0.724908i \(-0.741882\pi\)
0.688846 0.724908i \(-0.258118\pi\)
\(480\) −16.3456 + 46.1825i −0.0340534 + 0.0962135i
\(481\) 6.05464 0.0125876
\(482\) −142.701 + 142.701i −0.296060 + 0.296060i
\(483\) −75.2716 75.2716i −0.155842 0.155842i
\(484\) 191.282i 0.395211i
\(485\) 216.734 + 454.203i 0.446875 + 0.936501i
\(486\) 22.0454 0.0453609
\(487\) 189.085 189.085i 0.388266 0.388266i −0.485803 0.874068i \(-0.661473\pi\)
0.874068 + 0.485803i \(0.161473\pi\)
\(488\) 121.620 + 121.620i 0.249221 + 0.249221i
\(489\) 134.152i 0.274340i
\(490\) −44.6722 + 21.3165i −0.0911678 + 0.0435030i
\(491\) 587.867 1.19729 0.598643 0.801016i \(-0.295707\pi\)
0.598643 + 0.801016i \(0.295707\pi\)
\(492\) −29.9257 + 29.9257i −0.0608246 + 0.0608246i
\(493\) −76.5175 76.5175i −0.155208 0.155208i
\(494\) 46.8513i 0.0948408i
\(495\) 71.2078 + 25.2030i 0.143854 + 0.0509151i
\(496\) 220.564 0.444685
\(497\) −215.509 + 215.509i −0.433620 + 0.433620i
\(498\) −129.521 129.521i −0.260082 0.260082i
\(499\) 13.5102i 0.0270745i 0.999908 + 0.0135373i \(0.00430918\pi\)
−0.999908 + 0.0135373i \(0.995691\pi\)
\(500\) −130.728 213.096i −0.261457 0.426193i
\(501\) 30.0021 0.0598845
\(502\) −81.9263 + 81.9263i −0.163200 + 0.163200i
\(503\) 231.640 + 231.640i 0.460516 + 0.460516i 0.898825 0.438309i \(-0.144422\pi\)
−0.438309 + 0.898825i \(0.644422\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) 242.862 686.175i 0.480914 1.35876i
\(506\) 165.431 0.326938
\(507\) 192.288 192.288i 0.379266 0.379266i
\(508\) −169.992 169.992i −0.334630 0.334630i
\(509\) 737.211i 1.44835i 0.689616 + 0.724176i \(0.257780\pi\)
−0.689616 + 0.724176i \(0.742220\pi\)
\(510\) 136.366 + 285.778i 0.267384 + 0.560348i
\(511\) −205.307 −0.401775
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) 35.1422 + 35.1422i 0.0685033 + 0.0685033i
\(514\) 533.487i 1.03791i
\(515\) −670.736 + 320.058i −1.30240 + 0.621472i
\(516\) 176.975 0.342975
\(517\) −94.1268 + 94.1268i −0.182063 + 0.182063i
\(518\) 4.62479 + 4.62479i 0.00892817 + 0.00892817i
\(519\) 515.929i 0.994083i
\(520\) 46.1776 + 16.3439i 0.0888031 + 0.0314306i
\(521\) 209.021 0.401191 0.200596 0.979674i \(-0.435712\pi\)
0.200596 + 0.979674i \(0.435712\pi\)
\(522\) 12.5565 12.5565i 0.0240546 0.0240546i
\(523\) 99.0847 + 99.0847i 0.189455 + 0.189455i 0.795460 0.606006i \(-0.207229\pi\)
−0.606006 + 0.795460i \(0.707229\pi\)
\(524\) 441.108i 0.841808i
\(525\) 89.0567 + 72.0688i 0.169632 + 0.137274i
\(526\) 154.903 0.294492
\(527\) 1008.06 1008.06i 1.91283 1.91283i
\(528\) 24.6701 + 24.6701i 0.0467236 + 0.0467236i
\(529\) 10.6017i 0.0200410i
\(530\) 126.448 357.262i 0.238581 0.674080i
\(531\) −215.247 −0.405361
\(532\) 35.7871 35.7871i 0.0672689 0.0672689i
\(533\) 29.9226 + 29.9226i 0.0561399 + 0.0561399i
\(534\) 40.6602i 0.0761427i
\(535\) −138.914 291.118i −0.259653 0.544147i
\(536\) 121.947 0.227514
\(537\) 172.798 172.798i 0.321784 0.321784i
\(538\) 51.5262 + 51.5262i 0.0957737 + 0.0957737i
\(539\) 35.2503i 0.0653994i
\(540\) −46.8961 + 22.3776i −0.0868446 + 0.0414401i
\(541\) 599.763 1.10862 0.554310 0.832311i \(-0.312982\pi\)
0.554310 + 0.832311i \(0.312982\pi\)
\(542\) −143.162 + 143.162i −0.264137 + 0.264137i
\(543\) −17.7820 17.7820i −0.0327478 0.0327478i
\(544\) 146.252i 0.268846i
\(545\) 736.731 + 260.756i 1.35180 + 0.478451i
\(546\) −22.4476 −0.0411128
\(547\) −332.261 + 332.261i −0.607424 + 0.607424i −0.942272 0.334848i \(-0.891315\pi\)
0.334848 + 0.942272i \(0.391315\pi\)
\(548\) 232.078 + 232.078i 0.423499 + 0.423499i
\(549\) 182.430i 0.332295i
\(550\) −177.060 + 18.6679i −0.321926 + 0.0339416i
\(551\) 40.0322 0.0726538
\(552\) −80.4688 + 80.4688i −0.145777 + 0.145777i
\(553\) −117.112 117.112i −0.211776 0.211776i
\(554\) 132.505i 0.239178i
\(555\) 5.05091 14.2707i 0.00910074 0.0257130i
\(556\) 541.088 0.973180
\(557\) −624.562 + 624.562i −1.12130 + 1.12130i −0.129750 + 0.991547i \(0.541417\pi\)
−0.991547 + 0.129750i \(0.958583\pi\)
\(558\) 165.423 + 165.423i 0.296457 + 0.296457i
\(559\) 176.957i 0.316560i
\(560\) 22.7883 + 47.7566i 0.0406933 + 0.0852797i
\(561\) 225.503 0.401967
\(562\) −484.413 + 484.413i −0.861945 + 0.861945i
\(563\) −385.579 385.579i −0.684865 0.684865i 0.276228 0.961092i \(-0.410916\pi\)
−0.961092 + 0.276228i \(0.910916\pi\)
\(564\) 91.5702i 0.162359i
\(565\) 499.964 238.570i 0.884892 0.422248i
\(566\) −496.698 −0.877559
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) 230.389 + 230.389i 0.405615 + 0.405615i
\(569\) 578.028i 1.01587i 0.861397 + 0.507933i \(0.169590\pi\)
−0.861397 + 0.507933i \(0.830410\pi\)
\(570\) −110.428 39.0844i −0.193733 0.0685691i
\(571\) −14.7710 −0.0258687 −0.0129344 0.999916i \(-0.504117\pi\)
−0.0129344 + 0.999916i \(0.504117\pi\)
\(572\) 24.6675 24.6675i 0.0431250 0.0431250i
\(573\) 411.897 + 411.897i 0.718842 + 0.718842i
\(574\) 45.7123i 0.0796381i
\(575\) −60.8908 577.532i −0.105897 1.00440i
\(576\) −24.0000 −0.0416667
\(577\) 359.827 359.827i 0.623617 0.623617i −0.322838 0.946454i \(-0.604637\pi\)
0.946454 + 0.322838i \(0.104637\pi\)
\(578\) 379.430 + 379.430i 0.656452 + 0.656452i
\(579\) 38.6002i 0.0666670i
\(580\) −13.9651 + 39.4566i −0.0240777 + 0.0680286i
\(581\) −197.847 −0.340528
\(582\) −174.336 + 174.336i −0.299546 + 0.299546i
\(583\) −190.845 190.845i −0.327350 0.327350i
\(584\) 219.482i 0.375826i
\(585\) 22.3753 + 46.8912i 0.0382484 + 0.0801558i
\(586\) 402.675 0.687158
\(587\) 628.762 628.762i 1.07115 1.07115i 0.0738780 0.997267i \(-0.476462\pi\)
0.997267 0.0738780i \(-0.0235375\pi\)
\(588\) −17.1464 17.1464i −0.0291606 0.0291606i
\(589\) 527.395i 0.895408i
\(590\) 457.883 218.490i 0.776073 0.370322i
\(591\) −392.428 −0.664007
\(592\) 4.94411 4.94411i 0.00835154 0.00835154i
\(593\) −221.183 221.183i −0.372991 0.372991i 0.495575 0.868565i \(-0.334957\pi\)
−0.868565 + 0.495575i \(0.834957\pi\)
\(594\) 37.0051i 0.0622982i
\(595\) 322.417 + 114.115i 0.541878 + 0.191790i
\(596\) −203.589 −0.341592
\(597\) 197.534 197.534i 0.330878 0.330878i
\(598\) 80.4603 + 80.4603i 0.134549 + 0.134549i
\(599\) 227.599i 0.379966i 0.981787 + 0.189983i \(0.0608432\pi\)
−0.981787 + 0.189983i \(0.939157\pi\)
\(600\) 77.0448 95.2056i 0.128408 0.158676i
\(601\) −772.444 −1.28527 −0.642633 0.766175i \(-0.722158\pi\)
−0.642633 + 0.766175i \(0.722158\pi\)
\(602\) 135.167 135.167i 0.224530 0.224530i
\(603\) 91.4605 + 91.4605i 0.151676 + 0.151676i
\(604\) 332.699i 0.550826i
\(605\) 159.555 450.802i 0.263727 0.745128i
\(606\) 356.590 0.588432
\(607\) −145.543 + 145.543i −0.239774 + 0.239774i −0.816757 0.576982i \(-0.804230\pi\)
0.576982 + 0.816757i \(0.304230\pi\)
\(608\) −38.2580 38.2580i −0.0629243 0.0629243i
\(609\) 19.1804i 0.0314949i
\(610\) −185.179 388.074i −0.303572 0.636187i
\(611\) −91.5606 −0.149854
\(612\) −109.689 + 109.689i −0.179231 + 0.179231i
\(613\) −443.832 443.832i −0.724033 0.724033i 0.245391 0.969424i \(-0.421084\pi\)
−0.969424 + 0.245391i \(0.921084\pi\)
\(614\) 5.75775i 0.00937745i
\(615\) 95.4892 45.5651i 0.155267 0.0740895i
\(616\) 37.6842 0.0611756
\(617\) −490.933 + 490.933i −0.795678 + 0.795678i −0.982411 0.186733i \(-0.940210\pi\)
0.186733 + 0.982411i \(0.440210\pi\)
\(618\) −257.447 257.447i −0.416580 0.416580i
\(619\) 570.340i 0.921390i 0.887559 + 0.460695i \(0.152400\pi\)
−0.887559 + 0.460695i \(0.847600\pi\)
\(620\) −519.811 183.980i −0.838405 0.296742i
\(621\) −120.703 −0.194369
\(622\) 127.446 127.446i 0.204897 0.204897i
\(623\) −31.0547 31.0547i −0.0498471 0.0498471i
\(624\) 23.9975i 0.0384575i
\(625\) 130.342 + 611.258i 0.208547 + 0.978012i
\(626\) 147.912 0.236282
\(627\) −58.9892 + 58.9892i −0.0940816 + 0.0940816i
\(628\) 212.165 + 212.165i 0.337843 + 0.337843i
\(629\) 45.1930i 0.0718489i
\(630\) −18.7263 + 52.9087i −0.0297242 + 0.0839820i
\(631\) 471.145 0.746665 0.373332 0.927698i \(-0.378215\pi\)
0.373332 + 0.927698i \(0.378215\pi\)
\(632\) −125.198 + 125.198i −0.198099 + 0.198099i
\(633\) −93.7569 93.7569i −0.148115 0.148115i
\(634\) 754.822i 1.19057i
\(635\) 258.831 + 542.423i 0.407607 + 0.854209i
\(636\) 185.661 0.291920
\(637\) −17.1446 + 17.1446i −0.0269147 + 0.0269147i
\(638\) 21.0772 + 21.0772i 0.0330363 + 0.0330363i
\(639\) 345.584i 0.540820i
\(640\) 51.0540 24.3617i 0.0797718 0.0380651i
\(641\) −684.550 −1.06794 −0.533971 0.845503i \(-0.679301\pi\)
−0.533971 + 0.845503i \(0.679301\pi\)
\(642\) 111.739 111.739i 0.174049 0.174049i
\(643\) −521.636 521.636i −0.811253 0.811253i 0.173569 0.984822i \(-0.444470\pi\)
−0.984822 + 0.173569i \(0.944470\pi\)
\(644\) 122.918i 0.190867i
\(645\) −417.085 147.621i −0.646643 0.228870i
\(646\) −349.707 −0.541343
\(647\) −72.9658 + 72.9658i −0.112776 + 0.112776i −0.761243 0.648467i \(-0.775410\pi\)
0.648467 + 0.761243i \(0.275410\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 361.310i 0.556718i
\(650\) −95.1956 77.0367i −0.146455 0.118518i
\(651\) 252.688 0.388153
\(652\) 109.535 109.535i 0.167998 0.167998i
\(653\) 334.041 + 334.041i 0.511549 + 0.511549i 0.915001 0.403452i \(-0.132190\pi\)
−0.403452 + 0.915001i \(0.632190\pi\)
\(654\) 382.863i 0.585417i
\(655\) 367.943 1039.58i 0.561745 1.58714i
\(656\) 48.8685 0.0744947
\(657\) −164.612 + 164.612i −0.250550 + 0.250550i
\(658\) −69.9379 69.9379i −0.106289 0.106289i
\(659\) 177.497i 0.269343i −0.990890 0.134672i \(-0.957002\pi\)
0.990890 0.134672i \(-0.0429980\pi\)
\(660\) −37.5628 78.7191i −0.0569133 0.119271i
\(661\) 917.415 1.38792 0.693960 0.720013i \(-0.255864\pi\)
0.693960 + 0.720013i \(0.255864\pi\)
\(662\) 505.056 505.056i 0.762924 0.762924i
\(663\) 109.678 + 109.678i 0.165426 + 0.165426i
\(664\) 211.507i 0.318535i
\(665\) −114.192 + 54.4895i −0.171717 + 0.0819392i
\(666\) 7.41617 0.0111354
\(667\) −68.7495 + 68.7495i −0.103073 + 0.103073i
\(668\) −24.4966 24.4966i −0.0366716 0.0366716i
\(669\) 605.358i 0.904870i
\(670\) −287.398 101.720i −0.428952 0.151822i
\(671\) −306.224 −0.456370
\(672\) −18.3303 + 18.3303i −0.0272772 + 0.0272772i
\(673\) 725.252 + 725.252i 1.07764 + 1.07764i 0.996721 + 0.0809191i \(0.0257855\pi\)
0.0809191 + 0.996721i \(0.474214\pi\)
\(674\) 779.680i 1.15680i
\(675\) 129.188 13.6206i 0.191389 0.0201787i
\(676\) −314.005 −0.464504
\(677\) −378.779 + 378.779i −0.559496 + 0.559496i −0.929164 0.369668i \(-0.879472\pi\)
0.369668 + 0.929164i \(0.379472\pi\)
\(678\) 191.900 + 191.900i 0.283038 + 0.283038i
\(679\) 266.302i 0.392197i
\(680\) 121.994 344.679i 0.179403 0.506880i
\(681\) −480.081 −0.704965
\(682\) −277.676 + 277.676i −0.407150 + 0.407150i
\(683\) 19.0537 + 19.0537i 0.0278971 + 0.0278971i 0.720918 0.693021i \(-0.243721\pi\)
−0.693021 + 0.720918i \(0.743721\pi\)
\(684\) 57.3870i 0.0838991i
\(685\) −353.363 740.530i −0.515858 1.08107i
\(686\) −26.1916 −0.0381802
\(687\) 86.8939 86.8939i 0.126483 0.126483i
\(688\) −144.500 144.500i −0.210029 0.210029i
\(689\) 185.642i 0.269437i
\(690\) 256.766 122.522i 0.372124 0.177568i
\(691\) −1010.25 −1.46202 −0.731008 0.682369i \(-0.760950\pi\)
−0.731008 + 0.682369i \(0.760950\pi\)
\(692\) −421.254 + 421.254i −0.608749 + 0.608749i
\(693\) 28.2631 + 28.2631i 0.0407837 + 0.0407837i
\(694\) 613.118i 0.883456i
\(695\) −1275.20 451.340i −1.83482 0.649410i
\(696\) −20.5047 −0.0294608
\(697\) 223.348 223.348i 0.320442 0.320442i
\(698\) −509.585 509.585i −0.730064 0.730064i
\(699\) 33.0974i 0.0473496i
\(700\) −13.8706 131.558i −0.0198151 0.187941i
\(701\) 80.0820 0.114240 0.0571198 0.998367i \(-0.481808\pi\)
0.0571198 + 0.998367i \(0.481808\pi\)
\(702\) −17.9981 + 17.9981i −0.0256383 + 0.0256383i
\(703\) 11.8220 + 11.8220i 0.0168165 + 0.0168165i
\(704\) 40.2861i 0.0572245i
\(705\) −76.3819 + 215.807i −0.108343 + 0.306109i
\(706\) −660.774 −0.935941
\(707\) 272.350 272.350i 0.385219 0.385219i
\(708\) 175.748 + 175.748i 0.248232 + 0.248232i
\(709\) 1012.82i 1.42852i 0.699879 + 0.714261i \(0.253237\pi\)
−0.699879 + 0.714261i \(0.746763\pi\)
\(710\) −350.792 735.143i −0.494073 1.03541i
\(711\) −187.797 −0.264131
\(712\) −33.1989 + 33.1989i −0.0466277 + 0.0466277i
\(713\) −905.724 905.724i −1.27030 1.27030i
\(714\) 167.553i 0.234668i
\(715\) −78.7108 + 37.5588i −0.110085 + 0.0525298i
\(716\) −282.178 −0.394104
\(717\) 193.372 193.372i 0.269696 0.269696i
\(718\) 152.593 + 152.593i 0.212526 + 0.212526i
\(719\) 289.247i 0.402290i 0.979561 + 0.201145i \(0.0644663\pi\)
−0.979561 + 0.201145i \(0.935534\pi\)
\(720\) 56.5617 + 20.0192i 0.0785580 + 0.0278045i
\(721\) −393.256 −0.545432
\(722\) −269.520 + 269.520i −0.373297 + 0.373297i
\(723\) 174.772 + 174.772i 0.241732 + 0.241732i
\(724\) 29.0379i 0.0401077i
\(725\) 65.8242 81.3401i 0.0907919 0.112193i
\(726\) 234.272 0.322689
\(727\) 444.891 444.891i 0.611954 0.611954i −0.331501 0.943455i \(-0.607555\pi\)
0.943455 + 0.331501i \(0.107555\pi\)
\(728\) 18.3284 + 18.3284i 0.0251764 + 0.0251764i
\(729\) 27.0000i 0.0370370i
\(730\) 183.078 517.262i 0.250791 0.708578i
\(731\) −1320.84 −1.80689
\(732\) 148.953 148.953i 0.203488 0.203488i
\(733\) −169.024 169.024i −0.230592 0.230592i 0.582348 0.812940i \(-0.302134\pi\)
−0.812940 + 0.582348i \(0.802134\pi\)
\(734\) 210.352i 0.286583i
\(735\) 26.1072 + 54.7121i 0.0355200 + 0.0744382i
\(736\) 131.405 0.178539
\(737\) −153.524 + 153.524i −0.208310 + 0.208310i
\(738\) 36.6514 + 36.6514i 0.0496631 + 0.0496631i
\(739\) 153.342i 0.207499i 0.994603 + 0.103749i \(0.0330840\pi\)
−0.994603 + 0.103749i \(0.966916\pi\)
\(740\) −15.7760 + 7.52793i −0.0213190 + 0.0101729i
\(741\) −57.3809 −0.0774372
\(742\) 141.801 141.801i 0.191107 0.191107i
\(743\) −402.717 402.717i −0.542015 0.542015i 0.382104 0.924119i \(-0.375200\pi\)
−0.924119 + 0.382104i \(0.875200\pi\)
\(744\) 270.134i 0.363084i
\(745\) 479.806 + 169.821i 0.644035 + 0.227947i
\(746\) 609.701 0.817294
\(747\) −158.630 + 158.630i −0.212356 + 0.212356i
\(748\) −184.123 184.123i −0.246153 0.246153i
\(749\) 170.684i 0.227883i
\(750\) −260.989 + 160.109i −0.347985 + 0.213479i
\(751\) −549.263 −0.731376 −0.365688 0.930738i \(-0.619166\pi\)
−0.365688 + 0.930738i \(0.619166\pi\)
\(752\) −74.7668 + 74.7668i −0.0994239 + 0.0994239i
\(753\) 100.339 + 100.339i 0.133252 + 0.133252i
\(754\) 20.5026i 0.0271917i
\(755\) −277.516 + 784.085i −0.367571 + 1.03852i
\(756\) −27.4955 −0.0363696
\(757\) −838.559 + 838.559i −1.10774 + 1.10774i −0.114292 + 0.993447i \(0.536460\pi\)
−0.993447 + 0.114292i \(0.963540\pi\)
\(758\) 157.708 + 157.708i 0.208059 + 0.208059i
\(759\) 202.611i 0.266944i
\(760\) 58.2518 + 122.076i 0.0766471 + 0.160627i
\(761\) −1207.74 −1.58705 −0.793524 0.608538i \(-0.791756\pi\)
−0.793524 + 0.608538i \(0.791756\pi\)
\(762\) −208.197 + 208.197i −0.273224 + 0.273224i
\(763\) 292.416 + 292.416i 0.383246 + 0.383246i
\(764\) 672.624i 0.880398i
\(765\) 350.005 167.013i 0.457522 0.218318i
\(766\) 859.263 1.12175
\(767\) 175.730 175.730i 0.229113 0.229113i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 1284.27i 1.67006i 0.550206 + 0.835029i \(0.314549\pi\)
−0.550206 + 0.835029i \(0.685451\pi\)
\(770\) −88.8117 31.4336i −0.115340 0.0408229i
\(771\) −653.385 −0.847451
\(772\) 31.5169 31.5169i 0.0408250 0.0408250i
\(773\) 321.946