Properties

Label 300.2.m.b.121.2
Level $300$
Weight $2$
Character 300.121
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 121.2
Root \(-0.0272949 - 1.41395i\) of defining polynomial
Character \(\chi\) \(=\) 300.121
Dual form 300.2.m.b.181.2

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 −0.787902 0.615801i \(-0.788833\pi\)
0.999385 0.0350761i \(-0.0111674\pi\)
\(12\) 0 0
\(13\) 0.819443 + 2.52199i 0.227273 + 0.699473i 0.998053 + 0.0623720i \(0.0198665\pi\)
−0.770780 + 0.637101i \(0.780133\pi\)
\(14\) 0 0
\(15\) 1.02729 + 1.98612i 0.265246 + 0.512813i
\(16\) 0 0
\(17\) −1.68949 + 1.22749i −0.409762 + 0.297710i −0.773506 0.633790i \(-0.781499\pi\)
0.363743 + 0.931499i \(0.381499\pi\)
\(18\) 0 0
\(19\) −1.42464 + 1.03506i −0.326835 + 0.237459i −0.739086 0.673611i \(-0.764742\pi\)
0.412252 + 0.911070i \(0.364742\pi\)
\(20\) 0 0
\(21\) −0.0714590 0.0519180i −0.0155936 0.0113294i
\(22\) 0 0
\(23\) 1.46477 4.50810i 0.305426 0.940005i −0.674092 0.738647i \(-0.735465\pi\)
0.979518 0.201357i \(-0.0645352\pi\)
\(24\) 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 0.273480 0.961878i \(-0.411825\pi\)
−0.830290 + 0.557332i \(0.811825\pi\)
\(30\) 0 0
\(31\) 3.32199 2.41356i 0.596646 0.433489i −0.248041 0.968750i \(-0.579787\pi\)
0.844687 + 0.535261i \(0.179787\pi\)
\(32\) 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 0.952044 + 0.305963i \(0.0989782\pi\)
−0.590379 + 0.807126i \(0.701022\pi\)
\(38\) 0 0
\(39\) −0.819443 + 2.52199i −0.131216 + 0.403841i
\(40\) 0 0
\(41\) −2.03623 6.26687i −0.318006 0.978721i −0.974499 0.224390i \(-0.927961\pi\)
0.656494 0.754332i \(-0.272039\pi\)
\(42\) 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 −0.199578 0.979882i \(-0.563957\pi\)
−0.993596 + 0.112990i \(0.963957\pi\)
\(48\) 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 0.639923 0.768439i \(-0.278966\pi\)
−0.533081 + 0.846064i \(0.678966\pi\)
\(54\) 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 −0.952332 0.305063i \(-0.901323\pi\)
0.591142 0.806568i \(-0.298677\pi\)
\(60\) 0 0
\(61\) 2.92521 9.00287i 0.374535 1.15270i −0.569257 0.822159i \(-0.692769\pi\)
0.943792 0.330540i \(-0.107231\pi\)
\(62\) 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 −0.376825 + 0.926285i \(0.622984\pi\)
−0.997394 + 0.0721440i \(0.977016\pi\)
\(68\) 0 0
\(69\) 3.83482 2.78616i 0.461658 0.335414i
\(70\) 0 0
\(71\) −4.97363 3.61355i −0.590261 0.428850i 0.252148 0.967689i \(-0.418863\pi\)
−0.842409 + 0.538839i \(0.818863\pi\)
\(72\) 0 0
\(73\) −0.975766 + 3.00310i −0.114205 + 0.351486i −0.991780 0.127952i \(-0.959160\pi\)
0.877576 + 0.479438i \(0.159160\pi\)
\(74\) 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 −0.219631 0.975583i \(-0.570485\pi\)
−0.995704 + 0.0925903i \(0.970485\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) 12.7982 9.29846i 1.40479 1.02064i 0.410734 0.911755i \(-0.365272\pi\)
0.994054 0.108884i \(-0.0347276\pi\)
\(84\) 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 0.630568 + 0.776134i \(0.282822\pi\)
−0.966340 + 0.257267i \(0.917178\pi\)
\(90\) 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 0.972605 0.232465i \(-0.0746790\pi\)
0.0794643 + 0.996838i \(0.474679\pi\)
\(98\) 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 0.602041 0.798466i \(-0.294355\pi\)
−0.573345 + 0.819314i \(0.694355\pi\)
\(104\) 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 −0.682207 0.731159i \(-0.738980\pi\)
0.122153 0.992511i \(-0.461020\pi\)
\(110\) 0 0
\(111\) −2.19992 + 6.77065i −0.208807 + 0.642642i
\(112\) 0 0
\(113\) 1.51227 + 4.65428i 0.142262 + 0.437838i 0.996649 0.0818000i \(-0.0260669\pi\)
−0.854387 + 0.519638i \(0.826067\pi\)
\(114\) 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 −0.985827 0.167767i \(-0.946344\pi\)
0.896161 + 0.443728i \(0.146344\pi\)
\(128\) 0 0
\(129\) 1.45193 + 1.05489i 0.127836 + 0.0928781i
\(130\) 0 0
\(131\) −2.90882 + 2.11338i −0.254145 + 0.184647i −0.707562 0.706651i \(-0.750205\pi\)
0.453417 + 0.891299i \(0.350205\pi\)
\(132\) 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 0.877654 + 0.479294i \(0.159107\pi\)
−0.428315 + 0.903629i \(0.640893\pi\)
\(138\) 0 0
\(139\) −5.86699 + 18.0567i −0.497632 + 1.53155i 0.315184 + 0.949031i \(0.397934\pi\)
−0.812815 + 0.582522i \(0.802066\pi\)
\(140\) 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 0.950215 + 0.311596i \(0.100863\pi\)
−0.585589 + 0.810608i \(0.699137\pi\)
\(164\) 0 0
\(165\) 5.00801 0.824555i 0.389873 0.0641916i
\(166\) 0 0
\(167\) 2.79215 2.02861i 0.216063 0.156979i −0.474490 0.880261i \(-0.657367\pi\)
0.690553 + 0.723282i \(0.257367\pi\)
\(168\) 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 −0.975406 0.220417i \(-0.929258\pi\)
0.918678 + 0.395008i \(0.129258\pi\)
\(174\) 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 0.703986 0.710214i \(-0.251402\pi\)
−0.457910 + 0.888999i \(0.651402\pi\)
\(180\) 0 0
\(181\) 10.7893 7.83888i 0.801962 0.582660i −0.109527 0.993984i \(-0.534934\pi\)
0.911489 + 0.411324i \(0.134934\pi\)
\(182\) 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 0.668998 + 0.743264i \(0.266723\pi\)
−0.104351 + 0.994541i \(0.533277\pi\)
\(192\) 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 −0.0967697 0.995307i \(-0.530851\pi\)
−0.976496 + 0.215533i \(0.930851\pi\)
\(198\) 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 −0.999247 0.0387958i \(-0.987648\pi\)
0.831212 + 0.555956i \(0.187648\pi\)
\(212\) 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 −0.999999 0.00167090i \(-0.999468\pi\)
0.809998 + 0.586433i \(0.199468\pi\)
\(224\) 0 0
\(225\) −2.88933 + 4.08066i −0.192622 + 0.272044i
\(226\) 0 0
\(227\) 3.57392 10.9994i 0.237209 0.730056i −0.759611 0.650377i \(-0.774611\pi\)
0.996821 0.0796781i \(-0.0253892\pi\)
\(228\) 0 0
\(229\) −20.1820 14.6631i −1.33366 0.968962i −0.999652 0.0263923i \(-0.991598\pi\)
−0.334010 0.942570i \(-0.608402\pi\)
\(230\) 0 0
\(231\) −0.162198 + 0.117844i −0.0106718 + 0.00775355i
\(232\) 0 0
\(233\) −10.5334 + 7.65295i −0.690065 + 0.501361i −0.876681 0.481071i \(-0.840248\pi\)
0.186617 + 0.982433i \(0.440248\pi\)
\(234\) 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 0.230693 + 0.973027i \(0.425901\pi\)
−0.758565 + 0.651597i \(0.774099\pi\)
\(240\) 0 0
\(241\) −1.92700 5.93070i −0.124129 0.382030i 0.869612 0.493735i \(-0.164369\pi\)
−0.993741 + 0.111705i \(0.964369\pi\)
\(242\) 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 −1.00000 6.39037e-5i \(-0.999980\pi\)
0.808979 0.587837i \(-0.200020\pi\)
\(264\) 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 −0.0612496 0.998122i \(-0.519509\pi\)
0.930344 + 0.366689i \(0.119509\pi\)
\(270\) 0 0
\(271\) 3.92718 + 2.85327i 0.238559 + 0.173324i 0.700641 0.713514i \(-0.252897\pi\)
−0.462082 + 0.886837i \(0.652897\pi\)
\(272\) 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 −0.488015 0.872835i \(-0.662279\pi\)
0.907852 0.419291i \(-0.137721\pi\)
\(278\) 0 0
\(279\) 3.32199 + 2.41356i 0.198882 + 0.144496i
\(280\) 0 0
\(281\) −23.6671 + 17.1952i −1.41186 + 1.02578i −0.418815 + 0.908071i \(0.637555\pi\)
−0.993048 + 0.117708i \(0.962445\pi\)
\(282\) 0 0
\(283\) −23.6661 + 17.1944i −1.40680 + 1.02210i −0.413026 + 0.910719i \(0.635528\pi\)
−0.993778 + 0.111383i \(0.964472\pi\)
\(284\) 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 −0.967329 0.253524i \(-0.918410\pi\)
0.931603 + 0.363477i \(0.118410\pi\)
\(312\) 0 0
\(313\) −5.64839 17.3840i −0.319266 0.982599i −0.973963 0.226708i \(-0.927204\pi\)
0.654697 0.755892i \(-0.272796\pi\)
\(314\) 0 0
\(315\) 0.0297058 0.195261i 0.00167373 0.0110017i
\(316\) 0 0
\(317\) 15.2078 11.0491i 0.854153 0.620579i −0.0721348 0.997395i \(-0.522981\pi\)
0.926288 + 0.376816i \(0.122981\pi\)
\(318\) 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 −0.387225 0.921985i \(-0.626566\pi\)
0.757201 + 0.653182i \(0.226566\pi\)
\(332\) 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 0.982827 + 0.184530i \(0.0590763\pi\)
−0.686660 + 0.726979i \(0.740924\pi\)
\(338\) 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 −0.999498 0.0316789i \(-0.989915\pi\)
−0.338990 0.940790i \(-0.610085\pi\)
\(348\) 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 0.448269 0.893899i \(-0.352041\pi\)
−0.711626 + 0.702559i \(0.752041\pi\)
\(354\) 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 0.996184 + 0.0872735i \(0.0278154\pi\)
−0.754632 + 0.656148i \(0.772185\pi\)
\(360\) 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 −0.832245 0.554408i \(-0.812945\pi\)
0.270095 + 0.962834i \(0.412945\pi\)
\(368\) 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 0.717532 + 0.696525i \(0.245272\pi\)
−0.989903 + 0.141746i \(0.954728\pi\)
\(374\) 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 0.645124 0.764078i \(-0.276806\pi\)
−0.527326 + 0.849663i \(0.676806\pi\)
\(380\) 0 0
\(381\) −2.64546 + 1.92204i −0.135531 + 0.0984691i
\(382\) 0 0
\(383\) −8.12938 + 5.90634i −0.415392 + 0.301800i −0.775781 0.631002i \(-0.782644\pi\)
0.360389 + 0.932802i \(0.382644\pi\)
\(384\) 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 −0.863813 0.503812i \(-0.831930\pi\)
0.994973 + 0.100144i \(0.0319305\pi\)
\(390\) 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 0.744838 0.667245i \(-0.232527\pi\)
−0.404420 + 0.914573i \(0.632527\pi\)
\(398\) 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 0.919900 0.392154i \(-0.128270\pi\)
−0.974717 + 0.223444i \(0.928270\pi\)
\(410\) 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 −0.390780 0.920484i \(-0.627795\pi\)
0.754675 + 0.656099i \(0.227795\pi\)
\(420\) 0 0
\(421\) 33.0957 + 24.0454i 1.61299 + 1.17190i 0.852890 + 0.522090i \(0.174848\pi\)
0.760095 + 0.649812i \(0.225152\pi\)
\(422\) 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 −0.631000 0.775783i \(-0.717355\pi\)
0.542824 + 0.839847i \(0.317355\pi\)
\(432\) 0 0
\(433\) 3.70141 2.68923i 0.177878 0.129236i −0.495283 0.868731i \(-0.664936\pi\)
0.673162 + 0.739495i \(0.264936\pi\)
\(434\) 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 −0.963151 0.268961i \(-0.913320\pi\)
0.937297 + 0.348532i \(0.113320\pi\)
\(440\) 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 −0.789548 0.613688i \(-0.789685\pi\)
0.999475 0.0323993i \(-0.0103148\pi\)
\(462\) 0 0
\(463\) 3.05096 + 9.38989i 0.141790 + 0.436385i 0.996584 0.0825821i \(-0.0263167\pi\)
−0.854794 + 0.518967i \(0.826317\pi\)
\(464\) 0 0
\(465\) 8.20628 + 4.11841i 0.380557 + 0.190987i
\(466\) 0 0
\(467\) 17.1041 12.4268i 0.791481 0.575045i −0.116921 0.993141i \(-0.537303\pi\)
0.908403 + 0.418096i \(0.137303\pi\)
\(468\) 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 −0.955055 0.296429i \(-0.904204\pi\)
−0.577049 0.816710i \(-0.695796\pi\)
\(480\) 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 0.918781 0.394768i \(-0.129175\pi\)
−0.975348 + 0.220671i \(0.929175\pi\)
\(488\) 0 0
\(489\) −4.65524 + 14.3273i −0.210517 + 0.647905i
\(490\) 0 0
\(491\) 8.95383 + 27.5570i 0.404081 + 1.24363i 0.921661 + 0.387997i \(0.126833\pi\)
−0.517580 + 0.855635i \(0.673167\pi\)
\(492\) 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 0.320540 0.947235i \(-0.396136\pi\)
−0.801822 + 0.597563i \(0.796136\pi\)
\(504\) 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 0.854570 0.519336i \(-0.173821\pi\)
−0.996620 + 0.0821518i \(0.973821\pi\)
\(510\) 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 −0.0770169 0.997030i \(-0.524540\pi\)
−0.972031 + 0.234852i \(0.924540\pi\)
\(522\) 0 0
\(523\) 0.661227 2.03505i 0.0289134 0.0889864i −0.935558 0.353172i \(-0.885103\pi\)
0.964472 + 0.264185i \(0.0851031\pi\)
\(524\) 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 0.877408 0.479745i \(-0.159271\pi\)
−0.991825 + 0.127605i \(0.959271\pi\)
\(542\) 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 0.106479 0.994315i \(-0.466042\pi\)
−0.912746 + 0.408528i \(0.866042\pi\)
\(548\) 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 0.856347 0.516400i \(-0.172728\pi\)
−0.996332 + 0.0855718i \(0.972728\pi\)
\(564\) 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 −0.708363 0.705848i \(-0.750566\pi\)
0.452405 + 0.891812i \(0.350566\pi\)
\(570\) 0 0
\(571\) −23.9648 17.4115i −1.00290 0.728647i −0.0401891 0.999192i \(-0.512796\pi\)
−0.962707 + 0.270545i \(0.912796\pi\)
\(572\) 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 −0.799511 0.600651i \(-0.794908\pi\)
0.999872 0.0159961i \(-0.00509192\pi\)
\(578\) 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 0.811287 + 0.584649i \(0.198768\pi\)
−0.312697 + 0.949853i \(0.601232\pi\)
\(588\) 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 −0.999711 0.0240235i \(-0.992352\pi\)
0.794663 0.607051i \(-0.207648\pi\)
\(614\) 0 0
\(615\) 10.3549 10.4821i 0.417552 0.422680i
\(616\) 0 0
\(617\) 3.06226 2.22486i 0.123282 0.0895696i −0.524436 0.851450i \(-0.675724\pi\)
0.647718 + 0.761880i \(0.275724\pi\)
\(618\) 0 0
\(619\) 0.341478 0.248098i 0.0137252 0.00997192i −0.580902 0.813974i \(-0.697300\pi\)
0.594627 + 0.804002i \(0.297300\pi\)
\(620\) 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 0.139805 0.990179i \(-0.455353\pi\)
0.984918 + 0.173020i \(0.0553525\pi\)
\(632\) 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 0.970870 0.239605i \(-0.0770180\pi\)
−0.926287 + 0.376819i \(0.877018\pi\)
\(642\) 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 −0.0379623 0.999279i \(-0.512087\pi\)
−0.962102 + 0.272690i \(0.912087\pi\)
\(648\) 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 0.981753 0.190161i \(-0.0609011\pi\)
0.122524 + 0.992466i \(0.460901\pi\)
\(654\) 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 −0.773555 0.633729i \(-0.781523\pi\)
0.253323 0.967382i \(-0.418477\pi\)
\(660\) 0 0
\(661\) −3.10111 + 9.54425i −0.120619 + 0.371228i −0.993078 0.117461i \(-0.962525\pi\)
0.872458 + 0.488689i \(0.162525\pi\)
\(662\) 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 −0.599429 0.800428i \(-0.704606\pi\)
0.955428 0.295224i \(-0.0953944\pi\)
\(674\) 0 0
\(675\) −4.73607 + 1.60302i −0.182291 + 0.0617001i
\(676\) 0 0
\(677\) −6.99242 + 21.5205i −0.268740 + 0.827098i 0.722068 + 0.691823i \(0.243192\pi\)
−0.990808 + 0.135276i \(0.956808\pi\)
\(678\) 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 −0.909253 0.416243i \(-0.863346\pi\)
0.114896 + 0.993378i \(0.463346\pi\)
\(684\) 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 −0.922733 0.385440i \(-0.874050\pi\)
0.519950 0.854196i \(-0.325950\pi\)
\(692\) 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 −0.996257 0.0864398i \(-0.972451\pi\)
0.755181 0.655516i \(-0.227549\pi\)
\(710\) 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 −0.904393 0.426701i \(-0.859676\pi\)
0.126344 + 0.991986i \(0.459676\pi\)
\(720\) 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 −0.990016 0.140958i \(-0.954982\pi\)
0.883792 + 0.467879i \(0.154982\pi\)
\(728\) 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 −0.227265 0.973833i \(-0.572978\pi\)
0.855941 + 0.517073i \(0.172978\pi\)
\(734\) 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 −0.988695 0.149938i \(-0.952093\pi\)
0.888003 + 0.459838i \(0.152093\pi\)
\(740\) 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 −0.479330 0.877635i \(-0.659120\pi\)
0.903647 0.428279i \(-0.140880\pi\)
\(762\) 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 −0.775261 0.631640i \(-0.782382\pi\)
0.361157 + 0.932505i \(0.382382\pi\)
\(770\) 0 0
\(771\) 6.79477 + 4.93669i 0.244708 + 0.177791i
\(772\) 0 0
\(773\) −11.2415 + 34.5978i −0.404329 + 1.24440i 0.517126 + 0.855910i \(0.327002\pi\)
−0.921454 + 0.388487i \(0.872998\pi\)
\(774\) 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 −0.940431 0.339985i \(-0.889578\pi\)
0.560986 0.827825i \(-0.310422\pi\)
\(788\) 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 + 0.0753798i