Properties

Label 370.2.c.a.369.8
Level $370$
Weight $2$
Character 370.369
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 19 x^{8} + 103 x^{6} + 210 x^{4} + 140 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.8
Root \(1.76216i\) of defining polynomial
Character \(\chi\) \(=\) 370.369
Dual form 370.2.c.a.369.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.76216i q^{3} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.76216i q^{6} -1.22131i q^{7} -1.00000 q^{8} -0.105209 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.76216i q^{3} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.76216i q^{6} -1.22131i q^{7} -1.00000 q^{8} -0.105209 q^{9} +(1.62868 + 1.53213i) q^{10} +1.87120 q^{11} +1.76216i q^{12} +6.50491 q^{13} +1.22131i q^{14} +(2.69985 - 2.86999i) q^{15} +1.00000 q^{16} -0.765994 q^{17} +0.105209 q^{18} +3.34507i q^{19} +(-1.62868 - 1.53213i) q^{20} +2.15215 q^{21} -1.87120 q^{22} +1.38964 q^{23} -1.76216i q^{24} +(0.305180 + 4.99068i) q^{25} -6.50491 q^{26} +5.10109i q^{27} -1.22131i q^{28} -1.72909i q^{29} +(-2.69985 + 2.86999i) q^{30} +4.11288i q^{31} -1.00000 q^{32} +3.29736i q^{33} +0.765994 q^{34} +(-1.87120 + 1.98912i) q^{35} -0.105209 q^{36} +(1.76599 - 5.82076i) q^{37} -3.34507i q^{38} +11.4627i q^{39} +(1.62868 + 1.53213i) q^{40} +3.73892 q^{41} -2.15215 q^{42} +4.91814 q^{43} +1.87120 q^{44} +(0.171351 + 0.161193i) q^{45} -1.38964 q^{46} -6.30775i q^{47} +1.76216i q^{48} +5.50840 q^{49} +(-0.305180 - 4.99068i) q^{50} -1.34980i q^{51} +6.50491 q^{52} -2.57768i q^{53} -5.10109i q^{54} +(-3.04759 - 2.86692i) q^{55} +1.22131i q^{56} -5.89455 q^{57} +1.72909i q^{58} +10.5664i q^{59} +(2.69985 - 2.86999i) q^{60} -11.1550i q^{61} -4.11288i q^{62} +0.128493i q^{63} +1.00000 q^{64} +(-10.5944 - 9.96634i) q^{65} -3.29736i q^{66} -11.1219i q^{67} -0.765994 q^{68} +2.44877i q^{69} +(1.87120 - 1.98912i) q^{70} +0.963126 q^{71} +0.105209 q^{72} +9.03119i q^{73} +(-1.76599 + 5.82076i) q^{74} +(-8.79437 + 0.537776i) q^{75} +3.34507i q^{76} -2.28532i q^{77} -11.4627i q^{78} +10.3333i q^{79} +(-1.62868 - 1.53213i) q^{80} -9.30456 q^{81} -3.73892 q^{82} -0.00656819i q^{83} +2.15215 q^{84} +(1.24756 + 1.17360i) q^{85} -4.91814 q^{86} +3.04694 q^{87} -1.87120 q^{88} -4.70144i q^{89} +(-0.171351 - 0.161193i) q^{90} -7.94452i q^{91} +1.38964 q^{92} -7.24756 q^{93} +6.30775i q^{94} +(5.12507 - 5.44804i) q^{95} -1.76216i q^{96} -0.403430 q^{97} -5.50840 q^{98} -0.196867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(-1\) \(-1\)

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 −0.707107
\(3\) 1.76216i 1.01738i 0.860949 + 0.508692i \(0.169871\pi\)
−0.860949 + 0.508692i \(0.830129\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.62868 1.53213i −0.728367 0.685188i
\(6\) 1.76216i 0.719399i
\(7\) 1.22131i 0.461612i −0.973000 0.230806i \(-0.925864\pi\)
0.973000 0.230806i \(-0.0741363\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.105209 −0.0350696
\(10\) 1.62868 + 1.53213i 0.515033 + 0.484501i
\(11\) 1.87120 0.564189 0.282094 0.959387i \(-0.408971\pi\)
0.282094 + 0.959387i \(0.408971\pi\)
\(12\) 1.76216i 0.508692i
\(13\) 6.50491 1.80414 0.902069 0.431592i \(-0.142048\pi\)
0.902069 + 0.431592i \(0.142048\pi\)
\(14\) 1.22131i 0.326409i
\(15\) 2.69985 2.86999i 0.697099 0.741028i
\(16\) 1.00000 0.250000
\(17\) −0.765994 −0.185781 −0.0928904 0.995676i \(-0.529611\pi\)
−0.0928904 + 0.995676i \(0.529611\pi\)
\(18\) 0.105209 0.0247979
\(19\) 3.34507i 0.767412i 0.923455 + 0.383706i \(0.125352\pi\)
−0.923455 + 0.383706i \(0.874648\pi\)
\(20\) −1.62868 1.53213i −0.364183 0.342594i
\(21\) 2.15215 0.469637
\(22\) −1.87120 −0.398942
\(23\) 1.38964 0.289760 0.144880 0.989449i \(-0.453720\pi\)
0.144880 + 0.989449i \(0.453720\pi\)
\(24\) 1.76216i 0.359699i
\(25\) 0.305180 + 4.99068i 0.0610360 + 0.998136i
\(26\) −6.50491 −1.27572
\(27\) 5.10109i 0.981704i
\(28\) 1.22131i 0.230806i
\(29\) 1.72909i 0.321084i −0.987029 0.160542i \(-0.948676\pi\)
0.987029 0.160542i \(-0.0513243\pi\)
\(30\) −2.69985 + 2.86999i −0.492923 + 0.523986i
\(31\) 4.11288i 0.738695i 0.929291 + 0.369348i \(0.120419\pi\)
−0.929291 + 0.369348i \(0.879581\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.29736i 0.573996i
\(34\) 0.765994 0.131367
\(35\) −1.87120 + 1.98912i −0.316291 + 0.336223i
\(36\) −0.105209 −0.0175348
\(37\) 1.76599 5.82076i 0.290328 0.956927i
\(38\) 3.34507i 0.542642i
\(39\) 11.4627i 1.83550i
\(40\) 1.62868 + 1.53213i 0.257517 + 0.242250i
\(41\) 3.73892 0.583921 0.291960 0.956430i \(-0.405692\pi\)
0.291960 + 0.956430i \(0.405692\pi\)
\(42\) −2.15215 −0.332083
\(43\) 4.91814 0.750009 0.375005 0.927023i \(-0.377641\pi\)
0.375005 + 0.927023i \(0.377641\pi\)
\(44\) 1.87120 0.282094
\(45\) 0.171351 + 0.161193i 0.0255435 + 0.0240292i
\(46\) −1.38964 −0.204891
\(47\) 6.30775i 0.920080i −0.887898 0.460040i \(-0.847835\pi\)
0.887898 0.460040i \(-0.152165\pi\)
\(48\) 1.76216i 0.254346i
\(49\) 5.50840 0.786914
\(50\) −0.305180 4.99068i −0.0431590 0.705788i
\(51\) 1.34980i 0.189010i
\(52\) 6.50491 0.902069
\(53\) 2.57768i 0.354072i −0.984204 0.177036i \(-0.943349\pi\)
0.984204 0.177036i \(-0.0566509\pi\)
\(54\) 5.10109i 0.694170i
\(55\) −3.04759 2.86692i −0.410936 0.386575i
\(56\) 1.22131i 0.163205i
\(57\) −5.89455 −0.780752
\(58\) 1.72909i 0.227041i
\(59\) 10.5664i 1.37563i 0.725887 + 0.687814i \(0.241429\pi\)
−0.725887 + 0.687814i \(0.758571\pi\)
\(60\) 2.69985 2.86999i 0.348549 0.370514i
\(61\) 11.1550i 1.42825i −0.700020 0.714123i \(-0.746826\pi\)
0.700020 0.714123i \(-0.253174\pi\)
\(62\) 4.11288i 0.522337i
\(63\) 0.128493i 0.0161886i
\(64\) 1.00000 0.125000
\(65\) −10.5944 9.96634i −1.31407 1.23617i
\(66\) 3.29736i 0.405877i
\(67\) 11.1219i 1.35875i −0.733789 0.679377i \(-0.762250\pi\)
0.733789 0.679377i \(-0.237750\pi\)
\(68\) −0.765994 −0.0928904
\(69\) 2.44877i 0.294797i
\(70\) 1.87120 1.98912i 0.223651 0.237746i
\(71\) 0.963126 0.114302 0.0571510 0.998366i \(-0.481798\pi\)
0.0571510 + 0.998366i \(0.481798\pi\)
\(72\) 0.105209 0.0123990
\(73\) 9.03119i 1.05702i 0.848927 + 0.528511i \(0.177249\pi\)
−0.848927 + 0.528511i \(0.822751\pi\)
\(74\) −1.76599 + 5.82076i −0.205293 + 0.676650i
\(75\) −8.79437 + 0.537776i −1.01549 + 0.0620971i
\(76\) 3.34507i 0.383706i
\(77\) 2.28532i 0.260436i
\(78\) 11.4627i 1.29789i
\(79\) 10.3333i 1.16259i 0.813694 + 0.581293i \(0.197453\pi\)
−0.813694 + 0.581293i \(0.802547\pi\)
\(80\) −1.62868 1.53213i −0.182092 0.171297i
\(81\) −9.30456 −1.03384
\(82\) −3.73892 −0.412894
\(83\) 0.00656819i 0.000720953i −1.00000 0.000360477i \(-0.999885\pi\)
1.00000 0.000360477i \(-0.000114743\pi\)
\(84\) 2.15215 0.234818
\(85\) 1.24756 + 1.17360i 0.135317 + 0.127295i
\(86\) −4.91814 −0.530337
\(87\) 3.04694 0.326666
\(88\) −1.87120 −0.199471
\(89\) 4.70144i 0.498352i −0.968458 0.249176i \(-0.919840\pi\)
0.968458 0.249176i \(-0.0801598\pi\)
\(90\) −0.171351 0.161193i −0.0180620 0.0169912i
\(91\) 7.94452i 0.832812i
\(92\) 1.38964 0.144880
\(93\) −7.24756 −0.751537
\(94\) 6.30775i 0.650595i
\(95\) 5.12507 5.44804i 0.525821 0.558957i
\(96\) 1.76216i 0.179850i
\(97\) −0.403430 −0.0409621 −0.0204811 0.999790i \(-0.506520\pi\)
−0.0204811 + 0.999790i \(0.506520\pi\)
\(98\) −5.50840 −0.556432
\(99\) −0.196867 −0.0197859
\(100\) 0.305180 + 4.99068i 0.0305180 + 0.499068i
\(101\) −19.3724 −1.92762 −0.963812 0.266582i \(-0.914106\pi\)
−0.963812 + 0.266582i \(0.914106\pi\)
\(102\) 1.34980i 0.133650i
\(103\) −5.56165 −0.548005 −0.274003 0.961729i \(-0.588348\pi\)
−0.274003 + 0.961729i \(0.588348\pi\)
\(104\) −6.50491 −0.637859
\(105\) −3.50515 3.29736i −0.342068 0.321789i
\(106\) 2.57768i 0.250367i
\(107\) 1.93484i 0.187048i 0.995617 + 0.0935241i \(0.0298132\pi\)
−0.995617 + 0.0935241i \(0.970187\pi\)
\(108\) 5.10109i 0.490852i
\(109\) 8.70619i 0.833901i −0.908929 0.416951i \(-0.863099\pi\)
0.908929 0.416951i \(-0.136901\pi\)
\(110\) 3.04759 + 2.86692i 0.290576 + 0.273350i
\(111\) 10.2571 + 3.11196i 0.973562 + 0.295375i
\(112\) 1.22131i 0.115403i
\(113\) −14.7585 −1.38837 −0.694183 0.719798i \(-0.744234\pi\)
−0.694183 + 0.719798i \(0.744234\pi\)
\(114\) 5.89455 0.552075
\(115\) −2.26327 2.12910i −0.211051 0.198540i
\(116\) 1.72909i 0.160542i
\(117\) −0.684374 −0.0632704
\(118\) 10.5664i 0.972715i
\(119\) 0.935517i 0.0857587i
\(120\) −2.69985 + 2.86999i −0.246462 + 0.261993i
\(121\) −7.49860 −0.681691
\(122\) 11.1550i 1.00992i
\(123\) 6.58857i 0.594072i
\(124\) 4.11288i 0.369348i
\(125\) 7.14931 8.59578i 0.639453 0.768830i
\(126\) 0.128493i 0.0114470i
\(127\) 11.1280i 0.987453i 0.869617 + 0.493727i \(0.164366\pi\)
−0.869617 + 0.493727i \(0.835634\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.66655i 0.763047i
\(130\) 10.5944 + 9.96634i 0.929191 + 0.874106i
\(131\) 12.8363i 1.12152i −0.827980 0.560758i \(-0.810510\pi\)
0.827980 0.560758i \(-0.189490\pi\)
\(132\) 3.29736i 0.286998i
\(133\) 4.08537 0.354247
\(134\) 11.1219i 0.960785i
\(135\) 7.81551 8.30802i 0.672652 0.715041i
\(136\) 0.765994 0.0656834
\(137\) 12.0355i 1.02826i −0.857713 0.514129i \(-0.828115\pi\)
0.857713 0.514129i \(-0.171885\pi\)
\(138\) 2.44877i 0.208453i
\(139\) −9.78562 −0.830005 −0.415003 0.909820i \(-0.636219\pi\)
−0.415003 + 0.909820i \(0.636219\pi\)
\(140\) −1.87120 + 1.98912i −0.158145 + 0.168111i
\(141\) 11.1153 0.936075
\(142\) −0.963126 −0.0808237
\(143\) 12.1720 1.01787
\(144\) −0.105209 −0.00876740
\(145\) −2.64919 + 2.81613i −0.220003 + 0.233867i
\(146\) 9.03119i 0.747427i
\(147\) 9.70668i 0.800594i
\(148\) 1.76599 5.82076i 0.145164 0.478464i
\(149\) −11.8876 −0.973868 −0.486934 0.873439i \(-0.661885\pi\)
−0.486934 + 0.873439i \(0.661885\pi\)
\(150\) 8.79437 0.537776i 0.718058 0.0439093i
\(151\) 21.3141 1.73452 0.867259 0.497857i \(-0.165880\pi\)
0.867259 + 0.497857i \(0.165880\pi\)
\(152\) 3.34507i 0.271321i
\(153\) 0.0805893 0.00651526
\(154\) 2.28532i 0.184156i
\(155\) 6.30145 6.69856i 0.506145 0.538041i
\(156\) 11.4627i 0.917750i
\(157\) 15.3009i 1.22115i 0.791960 + 0.610573i \(0.209061\pi\)
−0.791960 + 0.610573i \(0.790939\pi\)
\(158\) 10.3333i 0.822072i
\(159\) 4.54229 0.360227
\(160\) 1.62868 + 1.53213i 0.128758 + 0.121125i
\(161\) 1.69718i 0.133757i
\(162\) 9.30456 0.731035
\(163\) −14.9177 −1.16844 −0.584221 0.811595i \(-0.698600\pi\)
−0.584221 + 0.811595i \(0.698600\pi\)
\(164\) 3.73892 0.291960
\(165\) 5.05197 5.37033i 0.393295 0.418080i
\(166\) 0.00656819i 0.000509791i
\(167\) 17.3041 1.33903 0.669514 0.742800i \(-0.266502\pi\)
0.669514 + 0.742800i \(0.266502\pi\)
\(168\) −2.15215 −0.166042
\(169\) 29.3139 2.25491
\(170\) −1.24756 1.17360i −0.0956832 0.0900109i
\(171\) 0.351931i 0.0269128i
\(172\) 4.91814 0.375005
\(173\) 19.7322i 1.50021i 0.661317 + 0.750107i \(0.269998\pi\)
−0.661317 + 0.750107i \(0.730002\pi\)
\(174\) −3.04694 −0.230988
\(175\) 6.09517 0.372720i 0.460752 0.0281750i
\(176\) 1.87120 0.141047
\(177\) −18.6197 −1.39954
\(178\) 4.70144i 0.352388i
\(179\) 3.70357i 0.276818i −0.990375 0.138409i \(-0.955801\pi\)
0.990375 0.138409i \(-0.0441988\pi\)
\(180\) 0.171351 + 0.161193i 0.0127718 + 0.0120146i
\(181\) −10.4093 −0.773714 −0.386857 0.922140i \(-0.626439\pi\)
−0.386857 + 0.922140i \(0.626439\pi\)
\(182\) 7.94452i 0.588887i
\(183\) 19.6568 1.45307
\(184\) −1.38964 −0.102446
\(185\) −11.7944 + 6.77442i −0.867140 + 0.498065i
\(186\) 7.24756 0.531417
\(187\) −1.43333 −0.104815
\(188\) 6.30775i 0.460040i
\(189\) 6.23001 0.453167
\(190\) −5.12507 + 5.44804i −0.371812 + 0.395242i
\(191\) 23.0954i 1.67113i 0.549395 + 0.835563i \(0.314858\pi\)
−0.549395 + 0.835563i \(0.685142\pi\)
\(192\) 1.76216i 0.127173i
\(193\) −12.4951 −0.899418 −0.449709 0.893175i \(-0.648472\pi\)
−0.449709 + 0.893175i \(0.648472\pi\)
\(194\) 0.403430 0.0289646
\(195\) 17.5623 18.6690i 1.25766 1.33692i
\(196\) 5.50840 0.393457
\(197\) 5.51302i 0.392786i −0.980525 0.196393i \(-0.937077\pi\)
0.980525 0.196393i \(-0.0629229\pi\)
\(198\) 0.196867 0.0139907
\(199\) 18.8033i 1.33293i −0.745537 0.666464i \(-0.767807\pi\)
0.745537 0.666464i \(-0.232193\pi\)
\(200\) −0.305180 4.99068i −0.0215795 0.352894i
\(201\) 19.5985 1.38237
\(202\) 19.3724 1.36304
\(203\) −2.11176 −0.148216
\(204\) 1.34980i 0.0945052i
\(205\) −6.08949 5.72849i −0.425309 0.400095i
\(206\) 5.56165 0.387498
\(207\) −0.146202 −0.0101618
\(208\) 6.50491 0.451034
\(209\) 6.25931i 0.432965i
\(210\) 3.50515 + 3.29736i 0.241878 + 0.227539i
\(211\) −26.6632 −1.83557 −0.917784 0.397081i \(-0.870023\pi\)
−0.917784 + 0.397081i \(0.870023\pi\)
\(212\) 2.57768i 0.177036i
\(213\) 1.69718i 0.116289i
\(214\) 1.93484i 0.132263i
\(215\) −8.01006 7.53521i −0.546282 0.513897i
\(216\) 5.10109i 0.347085i
\(217\) 5.02311 0.340991
\(218\) 8.70619i 0.589657i
\(219\) −15.9144 −1.07540
\(220\) −3.04759 2.86692i −0.205468 0.193288i
\(221\) −4.98272 −0.335174
\(222\) −10.2571 3.11196i −0.688412 0.208861i
\(223\) 10.8630i 0.727441i 0.931508 + 0.363721i \(0.118494\pi\)
−0.931508 + 0.363721i \(0.881506\pi\)
\(224\) 1.22131i 0.0816023i
\(225\) −0.0321076 0.525063i −0.00214051 0.0350042i
\(226\) 14.7585 0.981723
\(227\) 6.82427 0.452942 0.226471 0.974018i \(-0.427281\pi\)
0.226471 + 0.974018i \(0.427281\pi\)
\(228\) −5.89455 −0.390376
\(229\) 2.56189 0.169294 0.0846471 0.996411i \(-0.473024\pi\)
0.0846471 + 0.996411i \(0.473024\pi\)
\(230\) 2.26327 + 2.12910i 0.149236 + 0.140389i
\(231\) 4.02710 0.264964
\(232\) 1.72909i 0.113520i
\(233\) 23.3423i 1.52921i 0.644502 + 0.764603i \(0.277065\pi\)
−0.644502 + 0.764603i \(0.722935\pi\)
\(234\) 0.684374 0.0447389
\(235\) −9.66427 + 10.2733i −0.630428 + 0.670156i
\(236\) 10.5664i 0.687814i
\(237\) −18.2089 −1.18280
\(238\) 0.935517i 0.0606405i
\(239\) 5.19256i 0.335879i −0.985797 0.167940i \(-0.946289\pi\)
0.985797 0.167940i \(-0.0537113\pi\)
\(240\) 2.69985 2.86999i 0.174275 0.185257i
\(241\) 15.5243i 1.00001i −0.866022 0.500005i \(-0.833331\pi\)
0.866022 0.500005i \(-0.166669\pi\)
\(242\) 7.49860 0.482028
\(243\) 1.09286i 0.0701072i
\(244\) 11.1550i 0.714123i
\(245\) −8.97140 8.43956i −0.573162 0.539184i
\(246\) 6.58857i 0.420072i
\(247\) 21.7594i 1.38452i
\(248\) 4.11288i 0.261168i
\(249\) 0.0115742 0.000733486
\(250\) −7.14931 + 8.59578i −0.452162 + 0.543645i
\(251\) 3.85199i 0.243136i 0.992583 + 0.121568i \(0.0387922\pi\)
−0.992583 + 0.121568i \(0.961208\pi\)
\(252\) 0.128493i 0.00809428i
\(253\) 2.60030 0.163479
\(254\) 11.1280i 0.698235i
\(255\) −2.06807 + 2.19840i −0.129508 + 0.137669i
\(256\) 1.00000 0.0625000
\(257\) 3.34529 0.208673 0.104337 0.994542i \(-0.466728\pi\)
0.104337 + 0.994542i \(0.466728\pi\)
\(258\) 8.66655i 0.539556i
\(259\) −7.10896 2.15683i −0.441729 0.134019i
\(260\) −10.5944 9.96634i −0.657037 0.618086i
\(261\) 0.181916i 0.0112603i
\(262\) 12.8363i 0.793031i
\(263\) 1.14405i 0.0705454i 0.999378 + 0.0352727i \(0.0112300\pi\)
−0.999378 + 0.0352727i \(0.988770\pi\)
\(264\) 3.29736i 0.202938i
\(265\) −3.94934 + 4.19821i −0.242606 + 0.257894i
\(266\) −4.08537 −0.250490
\(267\) 8.28470 0.507015
\(268\) 11.1219i 0.679377i
\(269\) 15.1344 0.922760 0.461380 0.887203i \(-0.347355\pi\)
0.461380 + 0.887203i \(0.347355\pi\)
\(270\) −7.81551 + 8.30802i −0.475637 + 0.505610i
\(271\) −18.2842 −1.11069 −0.555344 0.831621i \(-0.687413\pi\)
−0.555344 + 0.831621i \(0.687413\pi\)
\(272\) −0.765994 −0.0464452
\(273\) 13.9995 0.847289
\(274\) 12.0355i 0.727088i
\(275\) 0.571054 + 9.33857i 0.0344359 + 0.563137i
\(276\) 2.44877i 0.147398i
\(277\) 2.58352 0.155229 0.0776145 0.996983i \(-0.475270\pi\)
0.0776145 + 0.996983i \(0.475270\pi\)
\(278\) 9.78562 0.586902
\(279\) 0.432711i 0.0259057i
\(280\) 1.87120 1.98912i 0.111826 0.118873i
\(281\) 19.3056i 1.15168i 0.817563 + 0.575839i \(0.195325\pi\)
−0.817563 + 0.575839i \(0.804675\pi\)
\(282\) −11.1153 −0.661905
\(283\) 9.02942 0.536743 0.268372 0.963315i \(-0.413514\pi\)
0.268372 + 0.963315i \(0.413514\pi\)
\(284\) 0.963126 0.0571510
\(285\) 9.60032 + 9.03119i 0.568674 + 0.534962i
\(286\) −12.1720 −0.719746
\(287\) 4.56638i 0.269545i
\(288\) 0.105209 0.00619949
\(289\) −16.4133 −0.965485
\(290\) 2.64919 2.81613i 0.155566 0.165369i
\(291\) 0.710909i 0.0416742i
\(292\) 9.03119i 0.528511i
\(293\) 13.0845i 0.764405i −0.924079 0.382203i \(-0.875166\pi\)
0.924079 0.382203i \(-0.124834\pi\)
\(294\) 9.70668i 0.566105i
\(295\) 16.1890 17.2092i 0.942563 1.00196i
\(296\) −1.76599 + 5.82076i −0.102646 + 0.338325i
\(297\) 9.54517i 0.553867i
\(298\) 11.8876 0.688629
\(299\) 9.03948 0.522767
\(300\) −8.79437 + 0.537776i −0.507743 + 0.0310485i
\(301\) 6.00658i 0.346213i
\(302\) −21.3141 −1.22649
\(303\) 34.1373i 1.96113i
\(304\) 3.34507i 0.191853i
\(305\) −17.0908 + 18.1678i −0.978616 + 1.04029i
\(306\) −0.0805893 −0.00460698
\(307\) 7.60942i 0.434293i 0.976139 + 0.217146i \(0.0696749\pi\)
−0.976139 + 0.217146i \(0.930325\pi\)
\(308\) 2.28532i 0.130218i
\(309\) 9.80051i 0.557532i
\(310\) −6.30145 + 6.69856i −0.357898 + 0.380453i
\(311\) 15.2359i 0.863950i 0.901886 + 0.431975i \(0.142183\pi\)
−0.901886 + 0.431975i \(0.857817\pi\)
\(312\) 11.4627i 0.648947i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 15.3009i 0.863480i
\(315\) 0.196867 0.209273i 0.0110922 0.0117912i
\(316\) 10.3333i 0.581293i
\(317\) 34.1403i 1.91751i −0.284230 0.958756i \(-0.591738\pi\)
0.284230 0.958756i \(-0.408262\pi\)
\(318\) −4.54229 −0.254719
\(319\) 3.23548i 0.181152i
\(320\) −1.62868 1.53213i −0.0910458 0.0856484i
\(321\) −3.40950 −0.190300
\(322\) 1.69718i 0.0945803i
\(323\) 2.56230i 0.142570i
\(324\) −9.30456 −0.516920
\(325\) 1.98517 + 32.4639i 0.110117 + 1.80077i
\(326\) 14.9177 0.826213
\(327\) 15.3417 0.848398
\(328\) −3.73892 −0.206447
\(329\) −7.70373 −0.424720
\(330\) −5.05197 + 5.37033i −0.278102 + 0.295627i
\(331\) 27.2567i 1.49817i −0.662476 0.749083i \(-0.730494\pi\)
0.662476 0.749083i \(-0.269506\pi\)
\(332\) 0.00656819i 0.000360477i
\(333\) −0.185798 + 0.612395i −0.0101817 + 0.0335590i
\(334\) −17.3041 −0.946836
\(335\) −17.0401 + 18.1140i −0.931002 + 0.989672i
\(336\) 2.15215 0.117409
\(337\) 22.5315i 1.22737i −0.789552 0.613683i \(-0.789687\pi\)
0.789552 0.613683i \(-0.210313\pi\)
\(338\) −29.3139 −1.59446
\(339\) 26.0069i 1.41250i
\(340\) 1.24756 + 1.17360i 0.0676583 + 0.0636473i
\(341\) 7.69603i 0.416764i
\(342\) 0.351931i 0.0190302i
\(343\) 15.2766i 0.824861i
\(344\) −4.91814 −0.265168
\(345\) 3.75182 3.98825i 0.201991 0.214720i
\(346\) 19.7322i 1.06081i
\(347\) −34.7252 −1.86415 −0.932073 0.362272i \(-0.882001\pi\)
−0.932073 + 0.362272i \(0.882001\pi\)
\(348\) 3.04694 0.163333
\(349\) 15.9343 0.852942 0.426471 0.904501i \(-0.359757\pi\)
0.426471 + 0.904501i \(0.359757\pi\)
\(350\) −6.09517 + 0.372720i −0.325801 + 0.0199227i
\(351\) 33.1821i 1.77113i
\(352\) −1.87120 −0.0997354
\(353\) 20.1925 1.07474 0.537370 0.843347i \(-0.319418\pi\)
0.537370 + 0.843347i \(0.319418\pi\)
\(354\) 18.6197 0.989625
\(355\) −1.56862 1.47563i −0.0832538 0.0783183i
\(356\) 4.70144i 0.249176i
\(357\) −1.64853 −0.0872495
\(358\) 3.70357i 0.195740i
\(359\) −30.8657 −1.62903 −0.814515 0.580143i \(-0.802997\pi\)
−0.814515 + 0.580143i \(0.802997\pi\)
\(360\) −0.171351 0.161193i −0.00903100 0.00849562i
\(361\) 7.81050 0.411079
\(362\) 10.4093 0.547099
\(363\) 13.2137i 0.693541i
\(364\) 7.94452i 0.416406i
\(365\) 13.8369 14.7089i 0.724258 0.769899i
\(366\) −19.6568 −1.02748
\(367\) 28.9254i 1.50989i 0.655786 + 0.754947i \(0.272337\pi\)
−0.655786 + 0.754947i \(0.727663\pi\)
\(368\) 1.38964 0.0724400
\(369\) −0.393367 −0.0204779
\(370\) 11.7944 6.77442i 0.613160 0.352185i
\(371\) −3.14815 −0.163444
\(372\) −7.24756 −0.375768
\(373\) 27.8899i 1.44408i −0.691849 0.722042i \(-0.743204\pi\)
0.691849 0.722042i \(-0.256796\pi\)
\(374\) 1.43333 0.0741157
\(375\) 15.1471 + 12.5982i 0.782195 + 0.650570i
\(376\) 6.30775i 0.325298i
\(377\) 11.2476i 0.579280i
\(378\) −6.23001 −0.320437
\(379\) −5.73365 −0.294518 −0.147259 0.989098i \(-0.547045\pi\)
−0.147259 + 0.989098i \(0.547045\pi\)
\(380\) 5.12507 5.44804i 0.262911 0.279479i
\(381\) −19.6094 −1.00462
\(382\) 23.0954i 1.18166i
\(383\) 17.8363 0.911391 0.455696 0.890136i \(-0.349391\pi\)
0.455696 + 0.890136i \(0.349391\pi\)
\(384\) 1.76216i 0.0899249i
\(385\) −3.50140 + 3.72205i −0.178448 + 0.189693i
\(386\) 12.4951 0.635985
\(387\) −0.517431 −0.0263025
\(388\) −0.403430 −0.0204811
\(389\) 29.8974i 1.51586i −0.652337 0.757929i \(-0.726211\pi\)
0.652337 0.757929i \(-0.273789\pi\)
\(390\) −17.5623 + 18.6690i −0.889301 + 0.945343i
\(391\) −1.06446 −0.0538318
\(392\) −5.50840 −0.278216
\(393\) 22.6197 1.14101
\(394\) 5.51302i 0.277742i
\(395\) 15.8319 16.8296i 0.796589 0.846789i
\(396\) −0.196867 −0.00989293
\(397\) 13.2064i 0.662812i −0.943488 0.331406i \(-0.892477\pi\)
0.943488 0.331406i \(-0.107523\pi\)
\(398\) 18.8033i 0.942523i
\(399\) 7.19908i 0.360405i
\(400\) 0.305180 + 4.99068i 0.0152590 + 0.249534i
\(401\) 23.0269i 1.14991i 0.818185 + 0.574954i \(0.194980\pi\)
−0.818185 + 0.574954i \(0.805020\pi\)
\(402\) −19.5985 −0.977487
\(403\) 26.7539i 1.33271i
\(404\) −19.3724 −0.963812
\(405\) 15.1541 + 14.2558i 0.753014 + 0.708374i
\(406\) 2.11176 0.104805
\(407\) 3.30453 10.8918i 0.163800 0.539888i
\(408\) 1.34980i 0.0668252i
\(409\) 9.77049i 0.483120i −0.970386 0.241560i \(-0.922341\pi\)
0.970386 0.241560i \(-0.0776590\pi\)
\(410\) 6.08949 + 5.72849i 0.300739 + 0.282910i
\(411\) 21.2084 1.04613
\(412\) −5.56165 −0.274003
\(413\) 12.9049 0.635006
\(414\) 0.146202 0.00718545
\(415\) −0.0100633 + 0.0106975i −0.000493988 + 0.000525118i
\(416\) −6.50491 −0.318930
\(417\) 17.2438i 0.844434i
\(418\) 6.25931i 0.306153i
\(419\) 2.06109 0.100691 0.0503455 0.998732i \(-0.483968\pi\)
0.0503455 + 0.998732i \(0.483968\pi\)
\(420\) −3.50515 3.29736i −0.171034 0.160895i
\(421\) 12.8910i 0.628271i 0.949378 + 0.314135i \(0.101715\pi\)
−0.949378 + 0.314135i \(0.898285\pi\)
\(422\) 26.6632 1.29794
\(423\) 0.663631i 0.0322668i
\(424\) 2.57768i 0.125183i
\(425\) −0.233766 3.82283i −0.0113393 0.185434i
\(426\) 1.69718i 0.0822288i
\(427\) −13.6237 −0.659296
\(428\) 1.93484i 0.0935241i
\(429\) 21.4490i 1.03557i
\(430\) 8.01006 + 7.53521i 0.386280 + 0.363380i
\(431\) 9.41662i 0.453582i −0.973943 0.226791i \(-0.927176\pi\)
0.973943 0.226791i \(-0.0728235\pi\)
\(432\) 5.10109i 0.245426i
\(433\) 3.07581i 0.147814i −0.997265 0.0739069i \(-0.976453\pi\)
0.997265 0.0739069i \(-0.0235468\pi\)
\(434\) −5.02311 −0.241117
\(435\) −4.96248 4.66829i −0.237933 0.223827i
\(436\) 8.70619i 0.416951i
\(437\) 4.64844i 0.222365i
\(438\) 15.9144 0.760420
\(439\) 1.93763i 0.0924780i 0.998930 + 0.0462390i \(0.0147236\pi\)
−0.998930 + 0.0462390i \(0.985276\pi\)
\(440\) 3.04759 + 2.86692i 0.145288 + 0.136675i
\(441\) −0.579532 −0.0275968
\(442\) 4.98272 0.237004
\(443\) 26.5690i 1.26233i 0.775649 + 0.631165i \(0.217423\pi\)
−0.775649 + 0.631165i \(0.782577\pi\)
\(444\) 10.2571 + 3.11196i 0.486781 + 0.147687i
\(445\) −7.20320 + 7.65713i −0.341465 + 0.362983i
\(446\) 10.8630i 0.514379i
\(447\) 20.9478i 0.990798i
\(448\) 1.22131i 0.0577015i
\(449\) 0.777045i 0.0366710i −0.999832 0.0183355i \(-0.994163\pi\)
0.999832 0.0183355i \(-0.00583670\pi\)
\(450\) 0.0321076 + 0.525063i 0.00151357 + 0.0247517i
\(451\) 6.99627 0.329442
\(452\) −14.7585 −0.694183
\(453\) 37.5589i 1.76467i
\(454\) −6.82427 −0.320279
\(455\) −12.1720 + 12.9391i −0.570633 + 0.606593i
\(456\) 5.89455 0.276038
\(457\) 21.1753 0.990537 0.495268 0.868740i \(-0.335070\pi\)
0.495268 + 0.868740i \(0.335070\pi\)
\(458\) −2.56189 −0.119709
\(459\) 3.90740i 0.182382i
\(460\) −2.26327 2.12910i −0.105526 0.0992699i
\(461\) 23.9797i 1.11685i 0.829556 + 0.558424i \(0.188594\pi\)
−0.829556 + 0.558424i \(0.811406\pi\)
\(462\) −4.02710 −0.187358
\(463\) −25.1591 −1.16924 −0.584622 0.811306i \(-0.698757\pi\)
−0.584622 + 0.811306i \(0.698757\pi\)
\(464\) 1.72909i 0.0802711i
\(465\) 11.8039 + 11.1042i 0.547394 + 0.514944i
\(466\) 23.3423i 1.08131i
\(467\) 15.6162 0.722632 0.361316 0.932443i \(-0.382328\pi\)
0.361316 + 0.932443i \(0.382328\pi\)
\(468\) −0.684374 −0.0316352
\(469\) −13.5833 −0.627218
\(470\) 9.66427 10.2733i 0.445780 0.473872i
\(471\) −26.9626 −1.24237
\(472\) 10.5664i 0.486358i
\(473\) 9.20284 0.423147
\(474\) 18.2089 0.836363
\(475\) −16.6942 + 1.02085i −0.765981 + 0.0468398i
\(476\) 0.935517i 0.0428793i
\(477\) 0.271195i 0.0124172i
\(478\) 5.19256i 0.237502i
\(479\) 31.4974i 1.43915i 0.694414 + 0.719576i \(0.255664\pi\)
−0.694414 + 0.719576i \(0.744336\pi\)
\(480\) −2.69985 + 2.86999i −0.123231 + 0.130997i
\(481\) 11.4876 37.8635i 0.523791 1.72643i
\(482\) 15.5243i 0.707114i
\(483\) 2.99071 0.136082
\(484\) −7.49860 −0.340845
\(485\) 0.657058 + 0.618106i 0.0298355 + 0.0280667i
\(486\) 1.09286i 0.0495733i
\(487\) 24.2768 1.10009 0.550043 0.835137i \(-0.314611\pi\)
0.550043 + 0.835137i \(0.314611\pi\)
\(488\) 11.1550i 0.504961i
\(489\) 26.2873i 1.18875i
\(490\) 8.97140 + 8.43956i 0.405287 + 0.381260i
\(491\) 16.5129 0.745218 0.372609 0.927988i \(-0.378463\pi\)
0.372609 + 0.927988i \(0.378463\pi\)
\(492\) 6.58857i 0.297036i
\(493\) 1.32447i 0.0596513i
\(494\) 21.7594i 0.979001i
\(495\) 0.320633 + 0.301625i 0.0144114 + 0.0135570i
\(496\) 4.11288i 0.184674i
\(497\) 1.17628i 0.0527632i
\(498\) −0.0115742 −0.000518653
\(499\) 22.8436i 1.02262i −0.859397 0.511310i \(-0.829161\pi\)
0.859397 0.511310i \(-0.170839\pi\)
\(500\) 7.14931 8.59578i 0.319727 0.384415i
\(501\) 30.4925i 1.36231i
\(502\) 3.85199i 0.171923i
\(503\) −37.0666 −1.65272 −0.826359 0.563144i \(-0.809592\pi\)
−0.826359 + 0.563144i \(0.809592\pi\)
\(504\) 0.128493i 0.00572352i
\(505\) 31.5514 + 29.6809i 1.40402 + 1.32078i
\(506\) −2.60030 −0.115597
\(507\) 51.6557i 2.29411i
\(508\) 11.1280i 0.493727i
\(509\) 20.0939 0.890645 0.445323 0.895370i \(-0.353089\pi\)
0.445323 + 0.895370i \(0.353089\pi\)
\(510\) 2.06807 2.19840i 0.0915757 0.0973466i
\(511\) 11.0299 0.487934
\(512\) −1.00000 −0.0441942
\(513\) −17.0635 −0.753372
\(514\) −3.34529 −0.147554
\(515\) 9.05813 + 8.52114i 0.399149 + 0.375486i
\(516\) 8.66655i 0.381524i
\(517\) 11.8031i 0.519099i
\(518\) 7.10896 + 2.15683i 0.312350 + 0.0947656i
\(519\) −34.7713 −1.52629
\(520\) 10.5944 + 9.96634i 0.464595 + 0.437053i
\(521\) 32.3101 1.41553 0.707766 0.706447i \(-0.249703\pi\)
0.707766 + 0.706447i \(0.249703\pi\)
\(522\) 0.181916i 0.00796223i
\(523\) −38.5348 −1.68501 −0.842505 0.538688i \(-0.818920\pi\)
−0.842505 + 0.538688i \(0.818920\pi\)
\(524\) 12.8363i 0.560758i
\(525\) 0.656792 + 10.7407i 0.0286648 + 0.468761i
\(526\) 1.14405i 0.0498831i
\(527\) 3.15044i 0.137235i
\(528\) 3.29736i 0.143499i
\(529\) −21.0689 −0.916039
\(530\) 3.94934 4.19821i 0.171548 0.182359i
\(531\) 1.11168i 0.0482427i
\(532\) 4.08537 0.177123
\(533\) 24.3213 1.05347
\(534\) −8.28470 −0.358514
\(535\) 2.96442 3.15123i 0.128163 0.136240i
\(536\) 11.1219i 0.480392i
\(537\) 6.52628 0.281630
\(538\) −15.1344 −0.652490
\(539\) 10.3073 0.443968
\(540\) 7.81551 8.30802i 0.336326 0.357520i
\(541\) 40.6354i 1.74705i −0.486776 0.873527i \(-0.661827\pi\)
0.486776 0.873527i \(-0.338173\pi\)
\(542\) 18.2842 0.785374
\(543\) 18.3428i 0.787164i
\(544\) 0.765994 0.0328417
\(545\) −13.3390 + 14.1796i −0.571379 + 0.607386i
\(546\) −13.9995 −0.599124
\(547\) −26.6260 −1.13845 −0.569223 0.822183i \(-0.692756\pi\)
−0.569223 + 0.822183i \(0.692756\pi\)
\(548\) 12.0355i 0.514129i
\(549\) 1.17360i 0.0500880i
\(550\) −0.571054 9.33857i −0.0243498 0.398198i
\(551\) 5.78394 0.246404
\(552\) 2.44877i 0.104226i
\(553\) 12.6202 0.536664
\(554\) −2.58352 −0.109763
\(555\) −11.9376 20.7836i −0.506723 0.882214i
\(556\) −9.78562 −0.415003
\(557\) −31.8613 −1.35001 −0.675004 0.737814i \(-0.735858\pi\)
−0.675004 + 0.737814i \(0.735858\pi\)
\(558\) 0.432711i 0.0183181i
\(559\) 31.9921 1.35312
\(560\) −1.87120 + 1.98912i −0.0790727 + 0.0840557i
\(561\) 2.52576i 0.106638i
\(562\) 19.3056i 0.814360i
\(563\) −0.477178 −0.0201107 −0.0100553 0.999949i \(-0.503201\pi\)
−0.0100553 + 0.999949i \(0.503201\pi\)
\(564\) 11.1153 0.468037
\(565\) 24.0369 + 22.6119i 1.01124 + 0.951291i
\(566\) −9.02942 −0.379535
\(567\) 11.3638i 0.477233i
\(568\) −0.963126 −0.0404119
\(569\) 10.3567i 0.434175i −0.976152 0.217087i \(-0.930344\pi\)
0.976152 0.217087i \(-0.0696557\pi\)
\(570\) −9.60032 9.03119i −0.402113 0.378275i
\(571\) −1.56306 −0.0654119 −0.0327059 0.999465i \(-0.510412\pi\)
−0.0327059 + 0.999465i \(0.510412\pi\)
\(572\) 12.1720 0.508937
\(573\) −40.6978 −1.70018
\(574\) 4.56638i 0.190597i
\(575\) 0.424091 + 6.93524i 0.0176858 + 0.289220i
\(576\) −0.105209 −0.00438370
\(577\) −19.1344 −0.796575 −0.398287 0.917261i \(-0.630395\pi\)
−0.398287 + 0.917261i \(0.630395\pi\)
\(578\) 16.4133 0.682701
\(579\) 22.0184i 0.915053i
\(580\) −2.64919 + 2.81613i −0.110001 + 0.116934i
\(581\) −0.00802181 −0.000332801
\(582\) 0.710909i 0.0294681i
\(583\) 4.82337i 0.199763i
\(584\) 9.03119i 0.373713i
\(585\) 1.11462 + 1.04855i 0.0460840 + 0.0433521i
\(586\) 13.0845i 0.540516i
\(587\) 7.16828 0.295867 0.147933 0.988997i \(-0.452738\pi\)
0.147933 + 0.988997i \(0.452738\pi\)
\(588\) 9.70668i 0.400297i
\(589\) −13.7579 −0.566884
\(590\) −16.1890 + 17.2092i −0.666492 + 0.708493i
\(591\) 9.71482 0.399614
\(592\) 1.76599 5.82076i 0.0725819 0.239232i
\(593\) 36.6287i 1.50416i 0.659071 + 0.752081i \(0.270950\pi\)
−0.659071 + 0.752081i \(0.729050\pi\)
\(594\) 9.54517i 0.391643i
\(595\) 1.43333 1.52366i 0.0587608 0.0624638i
\(596\) −11.8876 −0.486934
\(597\) 33.1344 1.35610
\(598\) −9.03948 −0.369652
\(599\) 38.3505 1.56696 0.783480 0.621417i \(-0.213443\pi\)
0.783480 + 0.621417i \(0.213443\pi\)
\(600\) 8.79437 0.537776i 0.359029 0.0219546i
\(601\) −20.5311 −0.837480 −0.418740 0.908106i \(-0.637528\pi\)
−0.418740 + 0.908106i \(0.637528\pi\)
\(602\) 6.00658i 0.244810i
\(603\) 1.17012i 0.0476510i
\(604\) 21.3141 0.867259
\(605\) 12.2128 + 11.4888i 0.496521 + 0.467086i
\(606\) 34.1373i 1.38673i
\(607\) −35.3953 −1.43665 −0.718326 0.695706i \(-0.755091\pi\)
−0.718326 + 0.695706i \(0.755091\pi\)
\(608\) 3.34507i 0.135661i
\(609\) 3.72126i 0.150793i
\(610\) 17.0908 18.1678i 0.691986 0.735594i
\(611\) 41.0314i 1.65995i
\(612\) 0.0805893 0.00325763
\(613\) 10.3293i 0.417198i −0.978001 0.208599i \(-0.933110\pi\)
0.978001 0.208599i \(-0.0668904\pi\)
\(614\) 7.60942i 0.307091i
\(615\) 10.0945 10.7307i 0.407050 0.432702i
\(616\) 2.28532i 0.0920782i
\(617\) 2.91338i 0.117288i −0.998279 0.0586441i \(-0.981322\pi\)
0.998279 0.0586441i \(-0.0186777\pi\)
\(618\) 9.80051i 0.394234i
\(619\) 30.7715 1.23681 0.618405 0.785860i \(-0.287779\pi\)
0.618405 + 0.785860i \(0.287779\pi\)
\(620\) 6.30145 6.69856i 0.253072 0.269021i
\(621\) 7.08867i 0.284459i
\(622\) 15.2359i 0.610905i
\(623\) −5.74193 −0.230045
\(624\) 11.4627i 0.458875i
\(625\) −24.8137 + 3.04611i −0.992549 + 0.121844i
\(626\) 10.0000 0.399680
\(627\) −11.0299 −0.440492
\(628\) 15.3009i 0.610573i
\(629\) −1.35274 + 4.45867i −0.0539373 + 0.177779i
\(630\) −0.196867 + 0.209273i −0.00784337 + 0.00833764i
\(631\) 12.8167i 0.510225i −0.966911 0.255113i \(-0.917887\pi\)
0.966911 0.255113i \(-0.0821126\pi\)
\(632\) 10.3333i 0.411036i
\(633\) 46.9847i 1.86748i
\(634\) 34.1403i 1.35589i
\(635\) 17.0495 18.1240i 0.676591 0.719228i
\(636\) 4.54229 0.180114
\(637\) 35.8316 1.41970
\(638\) 3.23548i 0.128094i
\(639\) −0.101329 −0.00400853
\(640\) 1.62868 + 1.53213i 0.0643791 + 0.0605626i
\(641\) 39.8277 1.57310 0.786550 0.617527i \(-0.211865\pi\)
0.786550 + 0.617527i \(0.211865\pi\)
\(642\) 3.40950 0.134562
\(643\) −15.9821 −0.630273 −0.315137 0.949046i \(-0.602050\pi\)
−0.315137 + 0.949046i \(0.602050\pi\)
\(644\) 1.69718i 0.0668784i
\(645\) 13.2782 14.1150i 0.522830 0.555778i
\(646\) 2.56230i 0.100812i
\(647\) 37.8647 1.48861 0.744307 0.667838i \(-0.232780\pi\)
0.744307 + 0.667838i \(0.232780\pi\)
\(648\) 9.30456 0.365518
\(649\) 19.7719i 0.776113i
\(650\) −1.98517 32.4639i −0.0778648 1.27334i
\(651\) 8.85152i 0.346919i
\(652\) −14.9177 −0.584221
\(653\) −9.60006 −0.375679 −0.187840 0.982200i \(-0.560149\pi\)
−0.187840 + 0.982200i \(0.560149\pi\)
\(654\) −15.3417 −0.599908
\(655\) −19.6669 + 20.9062i −0.768449 + 0.816875i
\(656\) 3.73892 0.145980
\(657\) 0.950161i 0.0370693i
\(658\) 7.70373 0.300323
\(659\) 30.3448 1.18207 0.591033 0.806647i \(-0.298720\pi\)
0.591033 + 0.806647i \(0.298720\pi\)
\(660\) 5.05197 5.37033i 0.196648 0.209040i
\(661\) 28.0304i 1.09026i 0.838353 + 0.545128i \(0.183519\pi\)
−0.838353 + 0.545128i \(0.816481\pi\)
\(662\) 27.2567i 1.05936i
\(663\) 8.78035i 0.341001i
\(664\) 0.00656819i 0.000254895i
\(665\) −6.65375 6.25931i −0.258022 0.242725i
\(666\) 0.185798 0.612395i 0.00719953 0.0237298i
\(667\) 2.40281i 0.0930374i
\(668\) 17.3041 0.669514
\(669\) −19.1424 −0.740087
\(670\) 17.0401 18.1140i 0.658318 0.699804i
\(671\) 20.8732i 0.805800i
\(672\) −2.15215 −0.0830208
\(673\) 1.70175i 0.0655975i 0.999462 + 0.0327987i \(0.0104420\pi\)
−0.999462 + 0.0327987i \(0.989558\pi\)
\(674\) 22.5315i 0.867879i
\(675\) −25.4579 + 1.55675i −0.979874 + 0.0599194i
\(676\) 29.3139 1.12746
\(677\) 3.49272i 0.134236i −0.997745 0.0671180i \(-0.978620\pi\)
0.997745 0.0671180i \(-0.0213804\pi\)
\(678\) 26.0069i 0.998789i
\(679\) 0.492714i 0.0189086i
\(680\) −1.24756 1.17360i −0.0478416 0.0450055i
\(681\) 12.0254i 0.460816i
\(682\) 7.69603i 0.294696i
\(683\) −18.9186 −0.723901 −0.361950 0.932197i \(-0.617889\pi\)
−0.361950 + 0.932197i \(0.617889\pi\)
\(684\) 0.351931i 0.0134564i
\(685\) −18.4398 + 19.6019i −0.704550 + 0.748949i
\(686\) 15.2766i 0.583265i
\(687\) 4.51446i 0.172237i
\(688\) 4.91814 0.187502
\(689\) 16.7676i 0.638795i
\(690\) −3.75182 + 3.98825i −0.142829 + 0.151830i
\(691\) 4.56018 0.173477 0.0867386 0.996231i \(-0.472355\pi\)
0.0867386 + 0.996231i \(0.472355\pi\)
\(692\) 19.7322i 0.750107i
\(693\) 0.240436i 0.00913340i
\(694\) 34.7252 1.31815
\(695\) 15.9376 + 14.9928i 0.604548 + 0.568709i
\(696\) −3.04694 −0.115494
\(697\) −2.86399 −0.108481
\(698\) −15.9343 −0.603121
\(699\) −41.1329 −1.55579
\(700\) 6.09517 0.372720i 0.230376 0.0140875i
\(701\) 18.9895i 0.717224i −0.933487 0.358612i \(-0.883250\pi\)
0.933487 0.358612i \(-0.116750\pi\)
\(702\) 33.1821i 1.25238i
\(703\) 19.4709 + 5.90737i 0.734357 + 0.222801i
\(704\) 1.87120 0.0705236
\(705\) −18.1032 17.0300i −0.681806 0.641387i
\(706\) −20.1925 −0.759956
\(707\) 23.6597i 0.889815i
\(708\) −18.6197 −0.699770
\(709\) 10.8195i 0.406336i −0.979144 0.203168i \(-0.934876\pi\)
0.979144 0.203168i \(-0.0651238\pi\)
\(710\) 1.56862 + 1.47563i 0.0588693 + 0.0553794i
\(711\) 1.08715i 0.0407714i
\(712\) 4.70144i 0.176194i
\(713\) 5.71542i 0.214044i
\(714\) 1.64853 0.0616947
\(715\) −19.8243 18.6490i −0.741386 0.697435i
\(716\) 3.70357i 0.138409i
\(717\) 9.15013 0.341718
\(718\) 30.8657 1.15190
\(719\) −8.43399 −0.314535 −0.157267 0.987556i \(-0.550268\pi\)
−0.157267 + 0.987556i \(0.550268\pi\)
\(720\) 0.171351 + 0.161193i 0.00638588 + 0.00600731i
\(721\) 6.79250i 0.252966i
\(722\) −7.81050 −0.290677
\(723\) 27.3564 1.01739
\(724\) −10.4093 −0.386857
\(725\) 8.62934 0.527685i 0.320486 0.0195977i
\(726\) 13.2137i 0.490408i
\(727\) −16.7156 −0.619947 −0.309974 0.950745i \(-0.600320\pi\)
−0.309974 + 0.950745i \(0.600320\pi\)
\(728\) 7.94452i 0.294444i
\(729\) −25.9879 −0.962514
\(730\) −13.8369 + 14.7089i −0.512128 + 0.544401i
\(731\) −3.76726 −0.139337
\(732\) 19.6568 0.726537
\(733\) 10.4157i 0.384711i −0.981325 0.192356i \(-0.938387\pi\)
0.981325 0.192356i \(-0.0616127\pi\)
\(734\) 28.9254i 1.06766i
\(735\) 14.8719 15.8091i 0.548557 0.583126i
\(736\) −1.38964 −0.0512228
\(737\) 20.8113i 0.766594i
\(738\) 0.393367 0.0144800
\(739\) −19.7975 −0.728261 −0.364131 0.931348i \(-0.618634\pi\)
−0.364131 + 0.931348i \(0.618634\pi\)
\(740\) −11.7944 + 6.77442i −0.433570 + 0.249033i
\(741\) −38.3435 −1.40858
\(742\) 3.14815 0.115572
\(743\) 34.4142i 1.26253i −0.775566 0.631267i \(-0.782535\pi\)
0.775566 0.631267i \(-0.217465\pi\)
\(744\) 7.24756 0.265708
\(745\) 19.3610 + 18.2133i 0.709333 + 0.667282i
\(746\) 27.8899i 1.02112i
\(747\) 0 0.000691032i 0 2.52835e-5i
\(748\) −1.43333 −0.0524077
\(749\) 2.36304 0.0863437
\(750\) −15.1471 12.5982i −0.553095 0.460022i
\(751\) −40.7020 −1.48524 −0.742618 0.669715i \(-0.766416\pi\)
−0.742618 + 0.669715i \(0.766416\pi\)
\(752\) 6.30775i 0.230020i
\(753\) −6.78783 −0.247362
\(754\) 11.2476i 0.409613i
\(755\) −34.7138 32.6559i −1.26337 1.18847i
\(756\) 6.23001 0.226583
\(757\) 2.06470 0.0750426 0.0375213 0.999296i \(-0.488054\pi\)
0.0375213 + 0.999296i \(0.488054\pi\)
\(758\) 5.73365 0.208256
\(759\) 4.58214i 0.166321i
\(760\) −5.12507 + 5.44804i −0.185906 + 0.197621i
\(761\) 9.07263 0.328883 0.164441 0.986387i \(-0.447418\pi\)
0.164441 + 0.986387i \(0.447418\pi\)
\(762\) 19.6094 0.710373
\(763\) −10.6330 −0.384939
\(764\) 23.0954i 0.835563i
\(765\) −0.131254 0.123473i −0.00474550 0.00446417i
\(766\) −17.8363 −0.644451
\(767\) 68.7335i 2.48182i
\(768\) 1.76216i 0.0635865i
\(769\) 50.9991i 1.83907i 0.393002 + 0.919537i \(0.371436\pi\)
−0.393002 + 0.919537i \(0.628564\pi\)
\(770\) 3.50140 3.72205i 0.126182 0.134133i
\(771\) 5.89493i 0.212301i
\(772\) −12.4951 −0.449709
\(773\) 40.9981i 1.47460i 0.675565 + 0.737300i \(0.263900\pi\)
−0.675565 + 0.737300i \(0.736100\pi\)
\(774\) 0.517431 0.0185987
\(775\) −20.5261 + 1.25517i −0.737318 + 0.0450870i
\(776\) 0.403430 0.0144823
\(777\) 3.80068 12.5271i 0.136349 0.449408i
\(778\) 29.8974i 1.07187i
\(779\) 12.5069i 0.448108i
\(780\) 17.5623 18.6690i 0.628831 0.668459i
\(781\) 1.80220 0.0644879
\(782\) 1.06446 0.0380648
\(783\) 8.82025 0.315210
\(784\) 5.50840 0.196729
\(785\) 23.4429 24.9202i 0.836713 0.889441i
\(786\) −22.6197 −0.806817
\(787\) 30.4357i 1.08492i −0.840083 0.542458i \(-0.817494\pi\)
0.840083