Properties

Label 300.2.m.b.181.2
Level $300$
Weight $2$
Character 300.181
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 2 x^{6} + x^{4} + 8 x^{2} - 24 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.2
Root \(-0.0272949 + 1.41395i\) of defining polynomial
Character \(\chi\) \(=\) 300.181
Dual form 300.2.m.b.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{3} +(1.99851 - 1.00297i) q^{5} -0.0883282 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{3} +(1.99851 - 1.00297i) q^{5} -0.0883282 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.701409 + 2.15871i) q^{11} +(0.819443 - 2.52199i) q^{13} +(1.02729 - 1.98612i) q^{15} +(-1.68949 - 1.22749i) q^{17} +(-1.42464 - 1.03506i) q^{19} +(-0.0714590 + 0.0519180i) q^{21} +(1.46477 + 4.50810i) q^{23} +(2.98808 - 4.00891i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(-2.99851 + 2.17855i) q^{29} +(3.32199 + 2.41356i) q^{31} +(1.83631 + 1.33416i) q^{33} +(-0.176525 + 0.0885909i) q^{35} +(2.19992 - 6.77065i) q^{37} +(-0.819443 - 2.52199i) q^{39} +(-2.03623 + 6.26687i) q^{41} +1.79469 q^{43} +(-0.336312 - 2.21063i) q^{45} +(-8.17999 + 5.94311i) q^{47} -6.99220 q^{49} -2.08833 q^{51} +(0.777821 - 0.565120i) q^{53} +(3.56691 + 3.61072i) q^{55} -1.76095 q^{57} +(-2.77436 + 8.53860i) q^{59} +(2.92521 + 9.00287i) q^{61} +(-0.0272949 + 0.0840051i) q^{63} +(-0.891823 - 5.86209i) q^{65} +(-11.2485 - 8.17249i) q^{67} +(3.83482 + 2.78616i) q^{69} +(-4.97363 + 3.61355i) q^{71} +(-0.975766 - 3.00310i) q^{73} +(0.0610333 - 4.99963i) q^{75} +(-0.0619542 - 0.190675i) q^{77} +(-10.8021 + 7.84821i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(12.7982 + 9.29846i) q^{83} +(-4.60761 - 0.758630i) q^{85} +(-1.14533 + 3.52496i) q^{87} +(-3.16767 - 9.74909i) q^{89} +(-0.0723799 + 0.222762i) q^{91} +4.10620 q^{93} +(-3.88530 - 0.639703i) q^{95} +(10.3617 - 7.52820i) q^{97} +2.26981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} - 5q^{5} + 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q + 2q^{3} - 5q^{5} + 8q^{7} - 2q^{9} + 8q^{11} + 5q^{15} + 3q^{17} + 5q^{19} + 7q^{21} - 7q^{23} + 5q^{25} + 2q^{27} - 3q^{29} - 3q^{31} + 7q^{33} - 10q^{35} - q^{37} + 10q^{41} - 12q^{43} + 5q^{45} - 33q^{47} - 8q^{49} - 8q^{51} - 19q^{53} - 15q^{55} + 10q^{57} - 38q^{59} + 46q^{61} + 3q^{63} + 25q^{65} - 8q^{67} + 2q^{69} - 25q^{71} - 26q^{73} - 5q^{75} + 23q^{77} - 16q^{79} - 2q^{81} + 8q^{83} - 30q^{85} + 3q^{87} - 30q^{89} + 25q^{91} - 22q^{93} - 25q^{95} - 14q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.809017 0.587785i 0.467086 0.339358i
\(4\) 0 0
\(5\) 1.99851 1.00297i 0.893761 0.448544i
\(6\) 0 0
\(7\) −0.0883282 −0.0333849 −0.0166925 0.999861i \(-0.505314\pi\)
−0.0166925 + 0.999861i \(0.505314\pi\)
\(8\) 0 0
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0 0
\(11\) 0.701409 + 2.15871i 0.211483 + 0.650877i 0.999385 + 0.0350761i \(0.0111674\pi\)
−0.787902 + 0.615801i \(0.788833\pi\)
\(12\) 0 0
\(13\) 0.819443 2.52199i 0.227273 0.699473i −0.770780 0.637101i \(-0.780133\pi\)
0.998053 0.0623720i \(-0.0198665\pi\)
\(14\) 0 0
\(15\) 1.02729 1.98612i 0.265246 0.512813i
\(16\) 0 0
\(17\) −1.68949 1.22749i −0.409762 0.297710i 0.363743 0.931499i \(-0.381499\pi\)
−0.773506 + 0.633790i \(0.781499\pi\)
\(18\) 0 0
\(19\) −1.42464 1.03506i −0.326835 0.237459i 0.412252 0.911070i \(-0.364742\pi\)
−0.739086 + 0.673611i \(0.764742\pi\)
\(20\) 0 0
\(21\) −0.0714590 + 0.0519180i −0.0155936 + 0.0113294i
\(22\) 0 0
\(23\) 1.46477 + 4.50810i 0.305426 + 0.940005i 0.979518 + 0.201357i \(0.0645352\pi\)
−0.674092 + 0.738647i \(0.735465\pi\)
\(24\) 0 0
\(25\) 2.98808 4.00891i 0.597617 0.801782i
\(26\) 0 0
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) 0 0
\(29\) −2.99851 + 2.17855i −0.556809 + 0.404546i −0.830290 0.557332i \(-0.811825\pi\)
0.273480 + 0.961878i \(0.411825\pi\)
\(30\) 0 0
\(31\) 3.32199 + 2.41356i 0.596646 + 0.433489i 0.844687 0.535261i \(-0.179787\pi\)
−0.248041 + 0.968750i \(0.579787\pi\)
\(32\) 0 0
\(33\) 1.83631 + 1.33416i 0.319661 + 0.232247i
\(34\) 0 0
\(35\) −0.176525 + 0.0885909i −0.0298381 + 0.0149746i
\(36\) 0 0
\(37\) 2.19992 6.77065i 0.361664 1.11309i −0.590379 0.807126i \(-0.701022\pi\)
0.952044 0.305963i \(-0.0989782\pi\)
\(38\) 0 0
\(39\) −0.819443 2.52199i −0.131216 0.403841i
\(40\) 0 0
\(41\) −2.03623 + 6.26687i −0.318006 + 0.978721i 0.656494 + 0.754332i \(0.272039\pi\)
−0.974499 + 0.224390i \(0.927961\pi\)
\(42\) 0 0
\(43\) 1.79469 0.273688 0.136844 0.990593i \(-0.456304\pi\)
0.136844 + 0.990593i \(0.456304\pi\)
\(44\) 0 0
\(45\) −0.336312 2.21063i −0.0501344 0.329542i
\(46\) 0 0
\(47\) −8.17999 + 5.94311i −1.19317 + 0.866892i −0.993596 0.112990i \(-0.963957\pi\)
−0.199578 + 0.979882i \(0.563957\pi\)
\(48\) 0 0
\(49\) −6.99220 −0.998885
\(50\) 0 0
\(51\) −2.08833 −0.292424
\(52\) 0 0
\(53\) 0.777821 0.565120i 0.106842 0.0776252i −0.533081 0.846064i \(-0.678966\pi\)
0.639923 + 0.768439i \(0.278966\pi\)
\(54\) 0 0
\(55\) 3.56691 + 3.61072i 0.480962 + 0.486869i
\(56\) 0 0
\(57\) −1.76095 −0.233244
\(58\) 0 0
\(59\) −2.77436 + 8.53860i −0.361191 + 1.11163i 0.591142 + 0.806568i \(0.298677\pi\)
−0.952332 + 0.305063i \(0.901323\pi\)
\(60\) 0 0
\(61\) 2.92521 + 9.00287i 0.374535 + 1.15270i 0.943792 + 0.330540i \(0.107231\pi\)
−0.569257 + 0.822159i \(0.692769\pi\)
\(62\) 0 0
\(63\) −0.0272949 + 0.0840051i −0.00343883 + 0.0105836i
\(64\) 0 0
\(65\) −0.891823 5.86209i −0.110617 0.727103i
\(66\) 0 0
\(67\) −11.2485 8.17249i −1.37422 0.998429i −0.997394 0.0721440i \(-0.977016\pi\)
−0.376825 0.926285i \(-0.622984\pi\)
\(68\) 0 0
\(69\) 3.83482 + 2.78616i 0.461658 + 0.335414i
\(70\) 0 0
\(71\) −4.97363 + 3.61355i −0.590261 + 0.428850i −0.842409 0.538839i \(-0.818863\pi\)
0.252148 + 0.967689i \(0.418863\pi\)
\(72\) 0 0
\(73\) −0.975766 3.00310i −0.114205 0.351486i 0.877576 0.479438i \(-0.159160\pi\)
−0.991780 + 0.127952i \(0.959160\pi\)
\(74\) 0 0
\(75\) 0.0610333 4.99963i 0.00704751 0.577307i
\(76\) 0 0
\(77\) −0.0619542 0.190675i −0.00706033 0.0217295i
\(78\) 0 0
\(79\) −10.8021 + 7.84821i −1.21534 + 0.882993i −0.995704 0.0925903i \(-0.970485\pi\)
−0.219631 + 0.975583i \(0.570485\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) 12.7982 + 9.29846i 1.40479 + 1.02064i 0.994054 + 0.108884i \(0.0347276\pi\)
0.410734 + 0.911755i \(0.365272\pi\)
\(84\) 0 0
\(85\) −4.60761 0.758630i −0.499765 0.0822849i
\(86\) 0 0
\(87\) −1.14533 + 3.52496i −0.122792 + 0.377915i
\(88\) 0 0
\(89\) −3.16767 9.74909i −0.335772 1.03340i −0.966340 0.257267i \(-0.917178\pi\)
0.630568 0.776134i \(-0.282822\pi\)
\(90\) 0 0
\(91\) −0.0723799 + 0.222762i −0.00758747 + 0.0233518i
\(92\) 0 0
\(93\) 4.10620 0.425793
\(94\) 0 0
\(95\) −3.88530 0.639703i −0.398623 0.0656322i
\(96\) 0 0
\(97\) 10.3617 7.52820i 1.05207 0.764373i 0.0794643 0.996838i \(-0.474679\pi\)
0.972605 + 0.232465i \(0.0746790\pi\)
\(98\) 0 0
\(99\) 2.26981 0.228124
\(100\) 0 0
\(101\) −2.72537 −0.271185 −0.135592 0.990765i \(-0.543294\pi\)
−0.135592 + 0.990765i \(0.543294\pi\)
\(102\) 0 0
\(103\) 0.291227 0.211589i 0.0286954 0.0208485i −0.573345 0.819314i \(-0.694355\pi\)
0.602041 + 0.798466i \(0.294355\pi\)
\(104\) 0 0
\(105\) −0.0907391 + 0.175430i −0.00885523 + 0.0171202i
\(106\) 0 0
\(107\) 0.0286533 0.00277002 0.00138501 0.999999i \(-0.499559\pi\)
0.00138501 + 0.999999i \(0.499559\pi\)
\(108\) 0 0
\(109\) −5.84714 + 17.9956i −0.560054 + 1.72367i 0.122153 + 0.992511i \(0.461020\pi\)
−0.682207 + 0.731159i \(0.738980\pi\)
\(110\) 0 0
\(111\) −2.19992 6.77065i −0.208807 0.642642i
\(112\) 0 0
\(113\) 1.51227 4.65428i 0.142262 0.437838i −0.854387 0.519638i \(-0.826067\pi\)
0.996649 + 0.0818000i \(0.0260669\pi\)
\(114\) 0 0
\(115\) 7.44887 + 7.54036i 0.694611 + 0.703142i
\(116\) 0 0
\(117\) −2.14533 1.55867i −0.198336 0.144099i
\(118\) 0 0
\(119\) 0.149230 + 0.108422i 0.0136799 + 0.00993901i
\(120\) 0 0
\(121\) 4.73111 3.43736i 0.430101 0.312487i
\(122\) 0 0
\(123\) 2.03623 + 6.26687i 0.183601 + 0.565065i
\(124\) 0 0
\(125\) 1.95088 11.0088i 0.174492 0.984659i
\(126\) 0 0
\(127\) −1.01048 3.10993i −0.0896652 0.275961i 0.896161 0.443728i \(-0.146344\pi\)
−0.985827 + 0.167767i \(0.946344\pi\)
\(128\) 0 0
\(129\) 1.45193 1.05489i 0.127836 0.0928781i
\(130\) 0 0
\(131\) −2.90882 2.11338i −0.254145 0.184647i 0.453417 0.891299i \(-0.350205\pi\)
−0.707562 + 0.706651i \(0.750205\pi\)
\(132\) 0 0
\(133\) 0.125836 + 0.0914251i 0.0109114 + 0.00792756i
\(134\) 0 0
\(135\) −1.57146 1.59076i −0.135250 0.136911i
\(136\) 0 0
\(137\) 5.25938 16.1867i 0.449339 1.38292i −0.428315 0.903629i \(-0.640893\pi\)
0.877654 0.479294i \(-0.159107\pi\)
\(138\) 0 0
\(139\) −5.86699 18.0567i −0.497632 1.53155i −0.812815 0.582522i \(-0.802066\pi\)
0.315184 0.949031i \(-0.397934\pi\)
\(140\) 0 0
\(141\) −3.12448 + 9.61615i −0.263128 + 0.809826i
\(142\) 0 0
\(143\) 6.01901 0.503335
\(144\) 0 0
\(145\) −3.80753 + 7.36127i −0.316198 + 0.611320i
\(146\) 0 0
\(147\) −5.65681 + 4.10991i −0.466566 + 0.338980i
\(148\) 0 0
\(149\) 20.3441 1.66665 0.833327 0.552780i \(-0.186433\pi\)
0.833327 + 0.552780i \(0.186433\pi\)
\(150\) 0 0
\(151\) 13.2609 1.07915 0.539577 0.841936i \(-0.318584\pi\)
0.539577 + 0.841936i \(0.318584\pi\)
\(152\) 0 0
\(153\) −1.68949 + 1.22749i −0.136587 + 0.0992366i
\(154\) 0 0
\(155\) 9.05976 + 1.49166i 0.727698 + 0.119813i
\(156\) 0 0
\(157\) 12.8066 1.02208 0.511039 0.859558i \(-0.329261\pi\)
0.511039 + 0.859558i \(0.329261\pi\)
\(158\) 0 0
\(159\) 0.297101 0.914384i 0.0235617 0.0725153i
\(160\) 0 0
\(161\) −0.129381 0.398193i −0.0101966 0.0313820i
\(162\) 0 0
\(163\) 4.65524 14.3273i 0.364626 1.12220i −0.585589 0.810608i \(-0.699137\pi\)
0.950215 0.311596i \(-0.100863\pi\)
\(164\) 0 0
\(165\) 5.00801 + 0.824555i 0.389873 + 0.0641916i
\(166\) 0 0
\(167\) 2.79215 + 2.02861i 0.216063 + 0.156979i 0.690553 0.723282i \(-0.257367\pi\)
−0.474490 + 0.880261i \(0.657367\pi\)
\(168\) 0 0
\(169\) 4.82830 + 3.50796i 0.371407 + 0.269843i
\(170\) 0 0
\(171\) −1.42464 + 1.03506i −0.108945 + 0.0791531i
\(172\) 0 0
\(173\) −0.746142 2.29639i −0.0567281 0.174591i 0.918678 0.395008i \(-0.129258\pi\)
−0.975406 + 0.220417i \(0.929258\pi\)
\(174\) 0 0
\(175\) −0.263932 + 0.354100i −0.0199514 + 0.0267674i
\(176\) 0 0
\(177\) 2.77436 + 8.53860i 0.208533 + 0.641800i
\(178\) 0 0
\(179\) 3.29228 2.39198i 0.246077 0.178785i −0.457910 0.888999i \(-0.651402\pi\)
0.703986 + 0.710214i \(0.251402\pi\)
\(180\) 0 0
\(181\) 10.7893 + 7.83888i 0.801962 + 0.582660i 0.911489 0.411324i \(-0.134934\pi\)
−0.109527 + 0.993984i \(0.534934\pi\)
\(182\) 0 0
\(183\) 7.65830 + 5.56408i 0.566118 + 0.411309i
\(184\) 0 0
\(185\) −2.39423 15.7377i −0.176028 1.15706i
\(186\) 0 0
\(187\) 1.46477 4.50810i 0.107115 0.329665i
\(188\) 0 0
\(189\) 0.0272949 + 0.0840051i 0.00198541 + 0.00611047i
\(190\) 0 0
\(191\) 7.80358 24.0169i 0.564647 1.73780i −0.104351 0.994541i \(-0.533277\pi\)
0.668998 0.743264i \(-0.266723\pi\)
\(192\) 0 0
\(193\) −24.6399 −1.77362 −0.886808 0.462139i \(-0.847082\pi\)
−0.886808 + 0.462139i \(0.847082\pi\)
\(194\) 0 0
\(195\) −4.16715 4.21833i −0.298416 0.302081i
\(196\) 0 0
\(197\) −15.0640 + 10.9446i −1.07327 + 0.779774i −0.976496 0.215533i \(-0.930851\pi\)
−0.0967697 + 0.995307i \(0.530851\pi\)
\(198\) 0 0
\(199\) 9.85708 0.698750 0.349375 0.936983i \(-0.386394\pi\)
0.349375 + 0.936983i \(0.386394\pi\)
\(200\) 0 0
\(201\) −13.9039 −0.980703
\(202\) 0 0
\(203\) 0.264853 0.192427i 0.0185890 0.0135057i
\(204\) 0 0
\(205\) 2.21609 + 14.5667i 0.154778 + 1.01738i
\(206\) 0 0
\(207\) 4.74010 0.329460
\(208\) 0 0
\(209\) 1.23515 3.80139i 0.0854369 0.262948i
\(210\) 0 0
\(211\) −2.44086 7.51219i −0.168036 0.517161i 0.831212 0.555956i \(-0.187648\pi\)
−0.999247 + 0.0387958i \(0.987648\pi\)
\(212\) 0 0
\(213\) −1.89976 + 5.84685i −0.130169 + 0.400619i
\(214\) 0 0
\(215\) 3.58671 1.80003i 0.244611 0.122761i
\(216\) 0 0
\(217\) −0.293425 0.213186i −0.0199190 0.0144720i
\(218\) 0 0
\(219\) −2.55459 1.85602i −0.172623 0.125418i
\(220\) 0 0
\(221\) −4.48015 + 3.25502i −0.301368 + 0.218956i
\(222\) 0 0
\(223\) −2.83731 8.73235i −0.190001 0.584762i 0.809998 0.586433i \(-0.199468\pi\)
−0.999999 + 0.00167090i \(0.999468\pi\)
\(224\) 0 0
\(225\) −2.88933 4.08066i −0.192622 0.272044i
\(226\) 0 0
\(227\) 3.57392 + 10.9994i 0.237209 + 0.730056i 0.996821 + 0.0796781i \(0.0253892\pi\)
−0.759611 + 0.650377i \(0.774611\pi\)
\(228\) 0 0
\(229\) −20.1820 + 14.6631i −1.33366 + 0.968962i −0.334010 + 0.942570i \(0.608402\pi\)
−0.999652 + 0.0263923i \(0.991598\pi\)
\(230\) 0 0
\(231\) −0.162198 0.117844i −0.0106718 0.00775355i
\(232\) 0 0
\(233\) −10.5334 7.65295i −0.690065 0.501361i 0.186617 0.982433i \(-0.440248\pi\)
−0.876681 + 0.481071i \(0.840248\pi\)
\(234\) 0 0
\(235\) −10.3870 + 20.0817i −0.677573 + 1.30998i
\(236\) 0 0
\(237\) −4.12605 + 12.6987i −0.268016 + 0.824867i
\(238\) 0 0
\(239\) −8.16071 25.1161i −0.527872 1.62462i −0.758565 0.651597i \(-0.774099\pi\)
0.230693 0.973027i \(-0.425901\pi\)
\(240\) 0 0
\(241\) −1.92700 + 5.93070i −0.124129 + 0.382030i −0.993741 0.111705i \(-0.964369\pi\)
0.869612 + 0.493735i \(0.164369\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −13.9740 + 7.01300i −0.892765 + 0.448044i
\(246\) 0 0
\(247\) −3.77782 + 2.74475i −0.240377 + 0.174644i
\(248\) 0 0
\(249\) 15.8195 1.00252
\(250\) 0 0
\(251\) 7.46802 0.471377 0.235689 0.971829i \(-0.424265\pi\)
0.235689 + 0.971829i \(0.424265\pi\)
\(252\) 0 0
\(253\) −8.70430 + 6.32405i −0.547235 + 0.397589i
\(254\) 0 0
\(255\) −4.17354 + 2.09454i −0.261358 + 0.131165i
\(256\) 0 0
\(257\) 8.39880 0.523903 0.261951 0.965081i \(-0.415634\pi\)
0.261951 + 0.965081i \(0.415634\pi\)
\(258\) 0 0
\(259\) −0.194315 + 0.598039i −0.0120741 + 0.0371604i
\(260\) 0 0
\(261\) 1.14533 + 3.52496i 0.0708941 + 0.218190i
\(262\) 0 0
\(263\) −3.09783 + 9.53415i −0.191021 + 0.587901i 0.808979 + 0.587837i \(0.200020\pi\)
−1.00000 6.39037e-5i \(0.999980\pi\)
\(264\) 0 0
\(265\) 0.987682 1.90953i 0.0606728 0.117302i
\(266\) 0 0
\(267\) −8.29307 6.02527i −0.507528 0.368740i
\(268\) 0 0
\(269\) 14.2542 + 10.3563i 0.869094 + 0.631434i 0.930344 0.366689i \(-0.119509\pi\)
−0.0612496 + 0.998122i \(0.519509\pi\)
\(270\) 0 0
\(271\) 3.92718 2.85327i 0.238559 0.173324i −0.462082 0.886837i \(-0.652897\pi\)
0.700641 + 0.713514i \(0.252897\pi\)
\(272\) 0 0
\(273\) 0.0723799 + 0.222762i 0.00438063 + 0.0134822i
\(274\) 0 0
\(275\) 10.7500 + 3.63854i 0.648247 + 0.219412i
\(276\) 0 0
\(277\) 6.98748 + 21.5053i 0.419837 + 1.29213i 0.907852 + 0.419291i \(0.137721\pi\)
−0.488015 + 0.872835i \(0.662279\pi\)
\(278\) 0 0
\(279\) 3.32199 2.41356i 0.198882 0.144496i
\(280\) 0 0
\(281\) −23.6671 17.1952i −1.41186 1.02578i −0.993048 0.117708i \(-0.962445\pi\)
−0.418815 0.908071i \(-0.637555\pi\)
\(282\) 0 0
\(283\) −23.6661 17.1944i −1.40680 1.02210i −0.993778 0.111383i \(-0.964472\pi\)
−0.413026 0.910719i \(-0.635528\pi\)
\(284\) 0 0
\(285\) −3.51928 + 1.76619i −0.208464 + 0.104620i
\(286\) 0 0
\(287\) 0.179857 0.553541i 0.0106166 0.0326745i
\(288\) 0 0
\(289\) −3.90563 12.0203i −0.229743 0.707076i
\(290\) 0 0
\(291\) 3.95781 12.1809i 0.232011 0.714056i
\(292\) 0 0
\(293\) −13.4104 −0.783447 −0.391723 0.920083i \(-0.628121\pi\)
−0.391723 + 0.920083i \(0.628121\pi\)
\(294\) 0 0
\(295\) 3.01941 + 19.8471i 0.175797 + 1.15554i
\(296\) 0 0
\(297\) 1.83631 1.33416i 0.106554 0.0774157i
\(298\) 0 0
\(299\) 12.5697 0.726923
\(300\) 0 0
\(301\) −0.158522 −0.00913704
\(302\) 0 0
\(303\) −2.20487 + 1.60193i −0.126667 + 0.0920287i
\(304\) 0 0
\(305\) 14.8757 + 15.0584i 0.851781 + 0.862242i
\(306\) 0 0
\(307\) 13.5444 0.773022 0.386511 0.922285i \(-0.373680\pi\)
0.386511 + 0.922285i \(0.373680\pi\)
\(308\) 0 0
\(309\) 0.111239 0.342358i 0.00632815 0.0194761i
\(310\) 0 0
\(311\) −0.630031 1.93904i −0.0357258 0.109953i 0.931603 0.363477i \(-0.118410\pi\)
−0.967329 + 0.253524i \(0.918410\pi\)
\(312\) 0 0
\(313\) −5.64839 + 17.3840i −0.319266 + 0.982599i 0.654697 + 0.755892i \(0.272796\pi\)
−0.973963 + 0.226708i \(0.927204\pi\)
\(314\) 0 0
\(315\) 0.0297058 + 0.195261i 0.00167373 + 0.0110017i
\(316\) 0 0
\(317\) 15.2078 + 11.0491i 0.854153 + 0.620579i 0.926288 0.376816i \(-0.122981\pi\)
−0.0721348 + 0.997395i \(0.522981\pi\)
\(318\) 0 0
\(319\) −6.80604 4.94488i −0.381065 0.276860i
\(320\) 0 0
\(321\) 0.0231810 0.0168420i 0.00129384 0.000940029i
\(322\) 0 0
\(323\) 1.13639 + 3.49746i 0.0632306 + 0.194604i
\(324\) 0 0
\(325\) −7.66185 10.8210i −0.425003 0.600240i
\(326\) 0 0
\(327\) 5.84714 + 17.9956i 0.323348 + 0.995161i
\(328\) 0 0
\(329\) 0.722523 0.524944i 0.0398340 0.0289411i
\(330\) 0 0
\(331\) 6.73111 + 4.89044i 0.369976 + 0.268803i 0.757201 0.653182i \(-0.226566\pi\)
−0.387225 + 0.921985i \(0.626566\pi\)
\(332\) 0 0
\(333\) −5.75946 4.18449i −0.315617 0.229309i
\(334\) 0 0
\(335\) −30.6770 5.05088i −1.67606 0.275959i
\(336\) 0 0
\(337\) 5.43691 16.7331i 0.296167 0.911509i −0.686660 0.726979i \(-0.740924\pi\)
0.982827 0.184530i \(-0.0590763\pi\)
\(338\) 0 0
\(339\) −1.51227 4.65428i −0.0821351 0.252786i
\(340\) 0 0
\(341\) −2.88012 + 8.86411i −0.155967 + 0.480019i
\(342\) 0 0
\(343\) 1.23591 0.0667326
\(344\) 0 0
\(345\) 10.4584 + 1.72194i 0.563060 + 0.0927063i
\(346\) 0 0
\(347\) −24.9333 + 18.1151i −1.33849 + 0.972469i −0.338990 + 0.940790i \(0.610085\pi\)
−0.999498 + 0.0316789i \(0.989915\pi\)
\(348\) 0 0
\(349\) 22.0376 1.17964 0.589822 0.807533i \(-0.299198\pi\)
0.589822 + 0.807533i \(0.299198\pi\)
\(350\) 0 0
\(351\) −2.65177 −0.141541
\(352\) 0 0
\(353\) −4.94803 + 3.59496i −0.263357 + 0.191340i −0.711626 0.702559i \(-0.752041\pi\)
0.448269 + 0.893899i \(0.352041\pi\)
\(354\) 0 0
\(355\) −6.31554 + 12.2101i −0.335194 + 0.648047i
\(356\) 0 0
\(357\) 0.184458 0.00976256
\(358\) 0 0
\(359\) 4.57676 14.0858i 0.241552 0.743422i −0.754632 0.656148i \(-0.772185\pi\)
0.996184 0.0872735i \(-0.0278154\pi\)
\(360\) 0 0
\(361\) −4.91308 15.1209i −0.258583 0.795836i
\(362\) 0 0
\(363\) 1.80712 5.56176i 0.0948495 0.291917i
\(364\) 0 0
\(365\) −4.96211 5.02306i −0.259729 0.262919i
\(366\) 0 0
\(367\) −10.7692 7.82431i −0.562150 0.408426i 0.270095 0.962834i \(-0.412945\pi\)
−0.832245 + 0.554408i \(0.812945\pi\)
\(368\) 0 0
\(369\) 5.33092 + 3.87314i 0.277517 + 0.201628i
\(370\) 0 0
\(371\) −0.0687035 + 0.0499160i −0.00356691 + 0.00259151i
\(372\) 0 0
\(373\) −5.26035 16.1897i −0.272371 0.838271i −0.989903 0.141746i \(-0.954728\pi\)
0.717532 0.696525i \(-0.245272\pi\)
\(374\) 0 0
\(375\) −4.89252 10.0530i −0.252649 0.519136i
\(376\) 0 0
\(377\) 3.03715 + 9.34739i 0.156421 + 0.481415i
\(378\) 0 0
\(379\) 2.29328 1.66617i 0.117798 0.0855852i −0.527326 0.849663i \(-0.676806\pi\)
0.645124 + 0.764078i \(0.276806\pi\)
\(380\) 0 0
\(381\) −2.64546 1.92204i −0.135531 0.0984691i
\(382\) 0 0
\(383\) −8.12938 5.90634i −0.415392 0.301800i 0.360389 0.932802i \(-0.382644\pi\)
−0.775781 + 0.631002i \(0.782644\pi\)
\(384\) 0 0
\(385\) −0.315058 0.318928i −0.0160569 0.0162541i
\(386\) 0 0
\(387\) 0.554590 1.70685i 0.0281914 0.0867642i
\(388\) 0 0
\(389\) 2.58687 + 7.96156i 0.131159 + 0.403667i 0.994973 0.100144i \(-0.0319305\pi\)
−0.863813 + 0.503812i \(0.831930\pi\)
\(390\) 0 0
\(391\) 3.05892 9.41440i 0.154696 0.476107i
\(392\) 0 0
\(393\) −3.59550 −0.181369
\(394\) 0 0
\(395\) −13.7166 + 26.5190i −0.690158 + 1.33432i
\(396\) 0 0
\(397\) 6.78277 4.92797i 0.340418 0.247328i −0.404420 0.914573i \(-0.632527\pi\)
0.744838 + 0.667245i \(0.232527\pi\)
\(398\) 0 0
\(399\) 0.155542 0.00778682
\(400\) 0 0
\(401\) 2.14450 0.107091 0.0535455 0.998565i \(-0.482948\pi\)
0.0535455 + 0.998565i \(0.482948\pi\)
\(402\) 0 0
\(403\) 8.80915 6.40022i 0.438815 0.318818i
\(404\) 0 0
\(405\) −2.20636 0.363271i −0.109635 0.0180511i
\(406\) 0 0
\(407\) 16.1589 0.800969
\(408\) 0 0
\(409\) −1.10861 + 3.41195i −0.0548173 + 0.168710i −0.974717 0.223444i \(-0.928270\pi\)
0.919900 + 0.392154i \(0.128270\pi\)
\(410\) 0 0
\(411\) −5.25938 16.1867i −0.259426 0.798431i
\(412\) 0 0
\(413\) 0.245054 0.754199i 0.0120583 0.0371117i
\(414\) 0 0
\(415\) 34.9035 + 5.74677i 1.71335 + 0.282098i
\(416\) 0 0
\(417\) −15.3600 11.1597i −0.752181 0.546492i
\(418\) 0 0
\(419\) 7.44874 + 5.41183i 0.363895 + 0.264385i 0.754675 0.656099i \(-0.227795\pi\)
−0.390780 + 0.920484i \(0.627795\pi\)
\(420\) 0 0
\(421\) 33.0957 24.0454i 1.61299 1.17190i 0.760095 0.649812i \(-0.225152\pi\)
0.852890 0.522090i \(-0.174848\pi\)
\(422\) 0 0
\(423\) 3.12448 + 9.61615i 0.151917 + 0.467553i
\(424\) 0 0
\(425\) −9.96924 + 3.10518i −0.483579 + 0.150624i
\(426\) 0 0
\(427\) −0.258378 0.795207i −0.0125038 0.0384828i
\(428\) 0 0
\(429\) 4.86948 3.53789i 0.235101 0.170811i
\(430\) 0 0
\(431\) −1.83058 1.32999i −0.0881758 0.0640634i 0.542824 0.839847i \(-0.317355\pi\)
−0.631000 + 0.775783i \(0.717355\pi\)
\(432\) 0 0
\(433\) 3.70141 + 2.68923i 0.177878 + 0.129236i 0.673162 0.739495i \(-0.264936\pi\)
−0.495283 + 0.868731i \(0.664936\pi\)
\(434\) 0 0
\(435\) 1.24649 + 8.19340i 0.0597648 + 0.392844i
\(436\) 0 0
\(437\) 2.57939 7.93855i 0.123389 0.379753i
\(438\) 0 0
\(439\) −0.541703 1.66719i −0.0258541 0.0795706i 0.937297 0.348532i \(-0.113320\pi\)
−0.963151 + 0.268961i \(0.913320\pi\)
\(440\) 0 0
\(441\) −2.16071 + 6.64998i −0.102891 + 0.316666i
\(442\) 0 0
\(443\) 20.8364 0.989967 0.494983 0.868902i \(-0.335174\pi\)
0.494983 + 0.868902i \(0.335174\pi\)
\(444\) 0 0
\(445\) −16.1087 16.3066i −0.763626 0.773005i
\(446\) 0 0
\(447\) 16.4587 11.9580i 0.778471 0.565592i
\(448\) 0 0
\(449\) 25.1952 1.18904 0.594518 0.804082i \(-0.297343\pi\)
0.594518 + 0.804082i \(0.297343\pi\)
\(450\) 0 0
\(451\) −14.9566 −0.704280
\(452\) 0 0
\(453\) 10.7283 7.79454i 0.504058 0.366220i
\(454\) 0 0
\(455\) 0.0787731 + 0.517788i 0.00369294 + 0.0242743i
\(456\) 0 0
\(457\) 39.5166 1.84851 0.924255 0.381775i \(-0.124687\pi\)
0.924255 + 0.381775i \(0.124687\pi\)
\(458\) 0 0
\(459\) −0.645329 + 1.98612i −0.0301214 + 0.0927041i
\(460\) 0 0
\(461\) 4.50731 + 13.8721i 0.209927 + 0.646087i 0.999475 + 0.0323993i \(0.0103148\pi\)
−0.789548 + 0.613688i \(0.789685\pi\)
\(462\) 0 0
\(463\) 3.05096 9.38989i 0.141790 0.436385i −0.854794 0.518967i \(-0.826317\pi\)
0.996584 + 0.0825821i \(0.0263167\pi\)
\(464\) 0 0
\(465\) 8.20628 4.11841i 0.380557 0.190987i
\(466\) 0 0
\(467\) 17.1041 + 12.4268i 0.791481 + 0.575045i 0.908403 0.418096i \(-0.137303\pi\)
−0.116921 + 0.993141i \(0.537303\pi\)
\(468\) 0 0
\(469\) 0.993557 + 0.721861i 0.0458782 + 0.0333324i
\(470\) 0 0
\(471\) 10.3608 7.52753i 0.477399 0.346850i
\(472\) 0 0
\(473\) 1.25881 + 3.87422i 0.0578802 + 0.178137i
\(474\) 0 0
\(475\) −8.40641 + 2.61840i −0.385713 + 0.120140i
\(476\) 0 0
\(477\) −0.297101 0.914384i −0.0136033 0.0418667i
\(478\) 0 0
\(479\) −33.5317 + 24.3622i −1.53210 + 1.11314i −0.577049 + 0.816710i \(0.695796\pi\)
−0.955055 + 0.296429i \(0.904204\pi\)
\(480\) 0 0
\(481\) −15.2728 11.0963i −0.696379 0.505949i
\(482\) 0 0
\(483\) −0.338723 0.246097i −0.0154124 0.0111978i
\(484\) 0 0
\(485\) 13.1573 25.4377i 0.597443 1.15507i
\(486\) 0 0
\(487\) −1.24834 + 3.84198i −0.0565675 + 0.174097i −0.975348 0.220671i \(-0.929175\pi\)
0.918781 + 0.394768i \(0.129175\pi\)
\(488\) 0 0
\(489\) −4.65524 14.3273i −0.210517 0.647905i
\(490\) 0 0
\(491\) 8.95383 27.5570i 0.404081 1.24363i −0.517580 0.855635i \(-0.673167\pi\)
0.921661 0.387997i \(-0.126833\pi\)
\(492\) 0 0
\(493\) 7.74010 0.348597
\(494\) 0 0
\(495\) 4.53623 2.27656i 0.203888 0.102324i
\(496\) 0 0
\(497\) 0.439311 0.319178i 0.0197058 0.0143171i
\(498\) 0 0
\(499\) 23.6824 1.06017 0.530086 0.847944i \(-0.322160\pi\)
0.530086 + 0.847944i \(0.322160\pi\)
\(500\) 0 0
\(501\) 3.45128 0.154192
\(502\) 0 0
\(503\) −10.7940 + 7.84233i −0.481282 + 0.349672i −0.801822 0.597563i \(-0.796136\pi\)
0.320540 + 0.947235i \(0.396136\pi\)
\(504\) 0 0
\(505\) −5.44668 + 2.73348i −0.242374 + 0.121638i
\(506\) 0 0
\(507\) 5.96810 0.265053
\(508\) 0 0
\(509\) −3.20479 + 9.86333i −0.142050 + 0.437184i −0.996620 0.0821518i \(-0.973821\pi\)
0.854570 + 0.519336i \(0.173821\pi\)
\(510\) 0 0
\(511\) 0.0861877 + 0.265258i 0.00381272 + 0.0117343i
\(512\) 0 0
\(513\) −0.544164 + 1.67476i −0.0240254 + 0.0739427i
\(514\) 0 0
\(515\) 0.369802 0.714955i 0.0162954 0.0315047i
\(516\) 0 0
\(517\) −18.5670 13.4897i −0.816575 0.593277i
\(518\) 0 0
\(519\) −1.95343 1.41925i −0.0857458 0.0622980i
\(520\) 0 0
\(521\) −23.9450 + 17.3970i −1.04905 + 0.762178i −0.972031 0.234852i \(-0.924540\pi\)
−0.0770169 + 0.997030i \(0.524540\pi\)
\(522\) 0 0
\(523\) 0.661227 + 2.03505i 0.0289134 + 0.0889864i 0.964472 0.264185i \(-0.0851031\pi\)
−0.935558 + 0.353172i \(0.885103\pi\)
\(524\) 0 0
\(525\) −0.00539096 + 0.441608i −0.000235281 + 0.0192734i
\(526\) 0 0
\(527\) −2.64985 8.15540i −0.115429 0.355255i
\(528\) 0 0
\(529\) 0.429950 0.312377i 0.0186935 0.0135816i
\(530\) 0 0
\(531\) 7.26336 + 5.27714i 0.315203 + 0.229008i
\(532\) 0 0
\(533\) 14.1364 + 10.2707i 0.612315 + 0.444873i
\(534\) 0 0
\(535\) 0.0572639 0.0287385i 0.00247574 0.00124248i
\(536\) 0 0
\(537\) 1.25754 3.87031i 0.0542668 0.167016i
\(538\) 0 0
\(539\) −4.90439 15.0942i −0.211247 0.650151i
\(540\) 0 0
\(541\) −2.66128 + 8.19057i −0.114417 + 0.352140i −0.991825 0.127605i \(-0.959271\pi\)
0.877408 + 0.479745i \(0.159271\pi\)
\(542\) 0 0
\(543\) 13.3363 0.572316
\(544\) 0 0
\(545\) 6.36361 + 41.8290i 0.272587 + 1.79176i
\(546\) 0 0
\(547\) −18.8570 + 13.7004i −0.806267 + 0.585787i −0.912746 0.408528i \(-0.866042\pi\)
0.106479 + 0.994315i \(0.466042\pi\)
\(548\) 0 0
\(549\) 9.46618 0.404007
\(550\) 0 0
\(551\) 6.52673 0.278048
\(552\) 0 0
\(553\) 0.954133 0.693218i 0.0405739 0.0294786i
\(554\) 0 0
\(555\) −11.1874 11.3248i −0.474877 0.480709i
\(556\) 0 0
\(557\) −37.2790 −1.57956 −0.789781 0.613389i \(-0.789806\pi\)
−0.789781 + 0.613389i \(0.789806\pi\)
\(558\) 0 0
\(559\) 1.47065 4.52618i 0.0622017 0.191437i
\(560\) 0 0
\(561\) −1.46477 4.50810i −0.0618427 0.190332i
\(562\) 0 0
\(563\) −3.32150 + 10.2225i −0.139985 + 0.430828i −0.996332 0.0855718i \(-0.972728\pi\)
0.856347 + 0.516400i \(0.172728\pi\)
\(564\) 0 0
\(565\) −1.64584 10.8184i −0.0692411 0.455133i
\(566\) 0 0
\(567\) 0.0714590 + 0.0519180i 0.00300100 + 0.00218035i
\(568\) 0 0
\(569\) −6.10555 4.43594i −0.255958 0.185964i 0.452405 0.891812i \(-0.350566\pi\)
−0.708363 + 0.705848i \(0.750566\pi\)
\(570\) 0 0
\(571\) −23.9648 + 17.4115i −1.00290 + 0.728647i −0.962707 0.270545i \(-0.912796\pi\)
−0.0401891 + 0.999192i \(0.512796\pi\)
\(572\) 0 0
\(573\) −7.80358 24.0169i −0.325999 1.00332i
\(574\) 0 0
\(575\) 22.4494 + 7.59846i 0.936206 + 0.316878i
\(576\) 0 0
\(577\) 4.81283 + 14.8124i 0.200361 + 0.616647i 0.999872 + 0.0159961i \(0.00509192\pi\)
−0.799511 + 0.600651i \(0.794908\pi\)
\(578\) 0 0
\(579\) −19.9341 + 14.4829i −0.828431 + 0.601891i
\(580\) 0 0
\(581\) −1.13044 0.821316i −0.0468987 0.0340739i
\(582\) 0 0
\(583\) 1.76550 + 1.28271i 0.0731197 + 0.0531246i
\(584\) 0 0
\(585\) −5.85077 0.963313i −0.241900 0.0398281i
\(586\) 0 0
\(587\) 12.0799 37.1780i 0.498590 1.53450i −0.312697 0.949853i \(-0.601232\pi\)
0.811287 0.584649i \(-0.198768\pi\)
\(588\) 0 0
\(589\) −2.23445 6.87692i −0.0920688 0.283358i
\(590\) 0 0
\(591\) −5.75394 + 17.7088i −0.236685 + 0.728443i
\(592\) 0 0
\(593\) −18.6722 −0.766775 −0.383387 0.923588i \(-0.625243\pi\)
−0.383387 + 0.923588i \(0.625243\pi\)
\(594\) 0 0
\(595\) 0.406982 + 0.0670084i 0.0166846 + 0.00274708i
\(596\) 0 0
\(597\) 7.97455 5.79385i 0.326376 0.237126i
\(598\) 0 0
\(599\) −14.0186 −0.572783 −0.286392 0.958113i \(-0.592456\pi\)
−0.286392 + 0.958113i \(0.592456\pi\)
\(600\) 0 0
\(601\) −9.89791 −0.403744 −0.201872 0.979412i \(-0.564703\pi\)
−0.201872 + 0.979412i \(0.564703\pi\)
\(602\) 0 0
\(603\) −11.2485 + 8.17249i −0.458073 + 0.332810i
\(604\) 0 0
\(605\) 6.00760 11.6148i 0.244244 0.472208i
\(606\) 0 0
\(607\) −22.2953 −0.904939 −0.452469 0.891780i \(-0.649457\pi\)
−0.452469 + 0.891780i \(0.649457\pi\)
\(608\) 0 0
\(609\) 0.101165 0.311353i 0.00409940 0.0126167i
\(610\) 0 0
\(611\) 8.28540 + 25.4998i 0.335192 + 1.03161i
\(612\) 0 0
\(613\) −5.07676 + 15.6247i −0.205049 + 0.631075i 0.794663 + 0.607051i \(0.207648\pi\)
−0.999711 + 0.0240235i \(0.992352\pi\)
\(614\) 0 0
\(615\) 10.3549 + 10.4821i 0.417552 + 0.422680i
\(616\) 0 0
\(617\) 3.06226 + 2.22486i 0.123282 + 0.0895696i 0.647718 0.761880i \(-0.275724\pi\)
−0.524436 + 0.851450i \(0.675724\pi\)
\(618\) 0 0
\(619\) 0.341478 + 0.248098i 0.0137252 + 0.00997192i 0.594627 0.804002i \(-0.297300\pi\)
−0.580902 + 0.813974i \(0.697300\pi\)
\(620\) 0 0
\(621\) 3.83482 2.78616i 0.153886 0.111805i
\(622\) 0 0
\(623\) 0.279795 + 0.861119i 0.0112097 + 0.0345000i
\(624\) 0 0
\(625\) −7.14271 23.9579i −0.285708 0.958317i
\(626\) 0 0
\(627\) −1.23515 3.80139i −0.0493270 0.151813i
\(628\) 0 0
\(629\) −12.0276 + 8.73860i −0.479574 + 0.348431i
\(630\) 0 0
\(631\) 28.2527 + 20.5268i 1.12472 + 0.817159i 0.984918 0.173020i \(-0.0553525\pi\)
0.139805 + 0.990179i \(0.455353\pi\)
\(632\) 0 0
\(633\) −6.39025 4.64279i −0.253990 0.184534i
\(634\) 0 0
\(635\) −5.13862 5.20174i −0.203920 0.206425i
\(636\) 0 0
\(637\) −5.72971 + 17.6342i −0.227019 + 0.698693i
\(638\) 0 0
\(639\) 1.89976 + 5.84685i 0.0751532 + 0.231298i
\(640\) 0 0
\(641\) 1.12876 3.47396i 0.0445833 0.137213i −0.926287 0.376819i \(-0.877018\pi\)
0.970870 + 0.239605i \(0.0770180\pi\)
\(642\) 0 0
\(643\) 34.3967 1.35647 0.678236 0.734844i \(-0.262745\pi\)
0.678236 + 0.734844i \(0.262745\pi\)
\(644\) 0 0
\(645\) 1.84368 3.56447i 0.0725947 0.140351i
\(646\) 0 0
\(647\) −25.4378 + 18.4817i −1.00006 + 0.726589i −0.962102 0.272690i \(-0.912087\pi\)
−0.0379623 + 0.999279i \(0.512087\pi\)
\(648\) 0 0
\(649\) −20.3783 −0.799920
\(650\) 0 0
\(651\) −0.362693 −0.0142151
\(652\) 0 0
\(653\) 28.2185 20.5020i 1.10428 0.802304i 0.122524 0.992466i \(-0.460901\pi\)
0.981753 + 0.190161i \(0.0609011\pi\)
\(654\) 0 0
\(655\) −7.93298 1.30614i −0.309967 0.0510352i
\(656\) 0 0
\(657\) −3.15765 −0.123192
\(658\) 0 0
\(659\) −13.3549 + 41.1021i −0.520232 + 1.60111i 0.253323 + 0.967382i \(0.418477\pi\)
−0.773555 + 0.633729i \(0.781523\pi\)
\(660\) 0 0
\(661\) −3.10111 9.54425i −0.120619 0.371228i 0.872458 0.488689i \(-0.162525\pi\)
−0.993078 + 0.117461i \(0.962525\pi\)
\(662\) 0 0
\(663\) −1.71127 + 5.26673i −0.0664600 + 0.204543i
\(664\) 0 0
\(665\) 0.343181 + 0.0565038i 0.0133080 + 0.00219112i
\(666\) 0 0
\(667\) −14.2132 10.3265i −0.550339 0.399845i
\(668\) 0 0
\(669\) −7.42818 5.39689i −0.287190 0.208656i
\(670\) 0 0
\(671\) −17.3829 + 12.6294i −0.671058 + 0.487552i
\(672\) 0 0
\(673\) 9.23541 + 28.4237i 0.355999 + 1.09565i 0.955428 + 0.295224i \(0.0953944\pi\)
−0.599429 + 0.800428i \(0.704606\pi\)
\(674\) 0 0
\(675\) −4.73607 1.60302i −0.182291 0.0617001i
\(676\) 0 0
\(677\) −6.99242 21.5205i −0.268740 0.827098i −0.990808 0.135276i \(-0.956808\pi\)
0.722068 0.691823i \(-0.243192\pi\)
\(678\) 0 0
\(679\) −0.915228 + 0.664952i −0.0351232 + 0.0255185i
\(680\) 0 0
\(681\) 9.35664 + 6.79800i 0.358547 + 0.260500i
\(682\) 0 0
\(683\) −20.7599 15.0830i −0.794357 0.577134i 0.114896 0.993378i \(-0.463346\pi\)
−0.909253 + 0.416243i \(0.863346\pi\)
\(684\) 0 0
\(685\) −5.72393 37.6243i −0.218700 1.43755i
\(686\) 0 0
\(687\) −7.70882 + 23.7253i −0.294110 + 0.905177i
\(688\) 0 0
\(689\) −0.787845 2.42474i −0.0300145 0.0923751i
\(690\) 0 0
\(691\) −10.5879 + 32.5862i −0.402782 + 1.23964i 0.519950 + 0.854196i \(0.325950\pi\)
−0.922733 + 0.385440i \(0.874050\pi\)
\(692\) 0 0
\(693\) −0.200488 −0.00761590
\(694\) 0 0
\(695\) −29.8357 30.2021i −1.13173 1.14563i
\(696\) 0 0
\(697\) 11.1327 8.08839i 0.421682 0.306370i
\(698\) 0 0
\(699\) −13.0200 −0.492461
\(700\) 0 0
\(701\) 42.0813 1.58939 0.794695 0.607009i \(-0.207631\pi\)
0.794695 + 0.607009i \(0.207631\pi\)
\(702\) 0 0
\(703\) −10.1421 + 7.36869i −0.382518 + 0.277916i
\(704\) 0 0
\(705\) 3.40046 + 22.3517i 0.128069 + 0.841816i
\(706\) 0 0
\(707\) 0.240727 0.00905347
\(708\) 0 0
\(709\) −6.41915 + 19.7561i −0.241076 + 0.741956i 0.755181 + 0.655516i \(0.227549\pi\)
−0.996257 + 0.0864398i \(0.972451\pi\)
\(710\) 0 0
\(711\) 4.12605 + 12.6987i 0.154739 + 0.476237i
\(712\) 0 0
\(713\) −6.01464 + 18.5112i −0.225250 + 0.693249i
\(714\) 0 0
\(715\) 12.0291 6.03691i 0.449861 0.225768i
\(716\) 0 0
\(717\) −21.3650 15.5226i −0.797891 0.579702i
\(718\) 0 0
\(719\) −20.8627 15.1577i −0.778049 0.565285i 0.126344 0.991986i \(-0.459676\pi\)
−0.904393 + 0.426701i \(0.859676\pi\)
\(720\) 0 0
\(721\) −0.0257235 + 0.0186892i −0.000957995 + 0.000696024i
\(722\) 0 0
\(723\) 1.92700 + 5.93070i 0.0716659 + 0.220565i
\(724\) 0 0
\(725\) −0.226211 + 18.5304i −0.00840128 + 0.688203i
\(726\) 0 0
\(727\) −2.86409 8.81476i −0.106223 0.326921i 0.883792 0.467879i \(-0.154982\pi\)
−0.990016 + 0.140958i \(0.954982\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) −3.03212 2.20296i −0.112147 0.0814795i
\(732\) 0 0
\(733\) 17.0208 + 12.3663i 0.628676 + 0.456760i 0.855941 0.517073i \(-0.172978\pi\)
−0.227265 + 0.973833i \(0.572978\pi\)
\(734\) 0 0
\(735\) −7.18305 + 13.8873i −0.264951 + 0.512242i
\(736\) 0 0
\(737\) 9.75230 30.0145i 0.359230 1.10560i
\(738\) 0 0
\(739\) −2.73729 8.42450i −0.100693 0.309900i 0.888003 0.459838i \(-0.152093\pi\)
−0.988695 + 0.149938i \(0.952093\pi\)
\(740\) 0 0
\(741\) −1.44300 + 4.44110i −0.0530099 + 0.163148i
\(742\) 0 0
\(743\) 13.9773 0.512778 0.256389 0.966574i \(-0.417467\pi\)
0.256389 + 0.966574i \(0.417467\pi\)
\(744\) 0 0
\(745\) 40.6579 20.4046i 1.48959 0.747568i
\(746\) 0 0
\(747\) 12.7982 9.29846i 0.468263 0.340213i
\(748\) 0 0
\(749\) −0.00253090 −9.24769e−5
\(750\) 0 0
\(751\) −32.8762 −1.19967 −0.599834 0.800124i \(-0.704767\pi\)
−0.599834 + 0.800124i \(0.704767\pi\)
\(752\) 0 0
\(753\) 6.04175 4.38959i 0.220174 0.159966i
\(754\) 0 0
\(755\) 26.5020 13.3003i 0.964506 0.484048i
\(756\) 0 0
\(757\) −31.4556 −1.14327 −0.571636 0.820507i \(-0.693691\pi\)
−0.571636 + 0.820507i \(0.693691\pi\)
\(758\) 0 0
\(759\) −3.32475 + 10.2325i −0.120681 + 0.371417i
\(760\) 0 0
\(761\) 11.7053 + 36.0252i 0.424317 + 1.30591i 0.903647 + 0.428279i \(0.140880\pi\)
−0.479330 + 0.877635i \(0.659120\pi\)
\(762\) 0 0
\(763\) 0.516467 1.58952i 0.0186974 0.0575446i
\(764\) 0 0
\(765\) −2.14533 + 4.14767i −0.0775645 + 0.149959i
\(766\) 0 0
\(767\) 19.2608 + 13.9938i 0.695467 + 0.505286i
\(768\) 0 0
\(769\) −11.4835 8.34323i −0.414105 0.300865i 0.361157 0.932505i \(-0.382382\pi\)
−0.775261 + 0.631640i \(0.782382\pi\)
\(770\) 0 0
\(771\) 6.79477 4.93669i 0.244708 0.177791i
\(772\) 0 0
\(773\) −11.2415 34.5978i −0.404329 1.24440i −0.921454 0.388487i \(-0.872998\pi\)
0.517126 0.855910i \(-0.327002\pi\)
\(774\) 0 0
\(775\) 19.6021 6.10561i 0.704129 0.219320i
\(776\) 0 0
\(777\) 0.194315 + 0.598039i 0.00697100 + 0.0214545i
\(778\) 0 0
\(779\) 9.38750 6.82041i 0.336342 0.244367i
\(780\) 0 0
\(781\) −11.2892 8.20206i −0.403958 0.293493i
\(782\) 0 0
\(783\) 2.99851 + 2.17855i 0.107158 + 0.0778548i
\(784\) 0 0
\(785\) 25.5941 12.8447i 0.913493 0.458447i
\(786\) 0 0
\(787\) −10.6448 + 32.7612i −0.379445 + 1.16781i 0.560986 + 0.827825i \(0.310422\pi\)
−0.940431 + 0.339985i \(0.889578\pi\)
\(788\) 0 0
\(789\) 3.09783 + 9.53415i 0.110286 + 0.339425i
\(790\) 0 0
\(791\) −0.133576 + 0.411104i −0.00474941 + 0.0146172i
\(792\) 0 0
\(793\) 25.1021 0.891403
\(794\) 0 0
\(795\) −0.323344 2.12539i −0.0114678