Properties

Label 441.2.h.h.373.9
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.9
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.h.214.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.29987 q^{2} +(-1.47364 + 0.910162i) q^{3} -0.310333 q^{4} +(1.76292 + 3.05347i) q^{5} +(-1.91554 + 1.18309i) q^{6} -3.00314 q^{8} +(1.34321 - 2.68250i) q^{9} +O(q^{10})\) \(q+1.29987 q^{2} +(-1.47364 + 0.910162i) q^{3} -0.310333 q^{4} +(1.76292 + 3.05347i) q^{5} +(-1.91554 + 1.18309i) q^{6} -3.00314 q^{8} +(1.34321 - 2.68250i) q^{9} +(2.29157 + 3.96912i) q^{10} +(-0.589267 + 1.02064i) q^{11} +(0.457317 - 0.282453i) q^{12} +(-1.61030 + 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} -3.28303 q^{16} +(-2.45159 - 4.24627i) q^{17} +(1.74600 - 3.48690i) q^{18} +(-3.43318 + 5.94645i) q^{19} +(-0.547092 - 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +(2.14994 + 3.72380i) q^{23} +(4.42553 - 2.73334i) q^{24} +(-3.71578 + 6.43592i) q^{25} +(-2.09319 + 3.62551i) q^{26} +(0.462101 + 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(-6.98948 - 3.76334i) q^{30} +1.92080 q^{31} +1.73876 q^{32} +(-0.0605825 - 2.04038i) q^{33} +(-3.18675 - 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} +(4.88229 - 8.45637i) q^{37} +(-4.46270 + 7.72962i) q^{38} +(-0.165555 - 5.57579i) q^{39} +(-5.29429 - 9.16998i) q^{40} +(3.32673 - 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(0.182869 - 0.316738i) q^{44} +(10.5589 - 0.627577i) q^{45} +(2.79464 + 4.84046i) q^{46} -0.633218 q^{47} +(4.83799 - 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(7.47754 + 4.02612i) q^{51} +(0.499729 - 0.865557i) q^{52} +(1.11378 + 1.92912i) q^{53} +(0.600672 + 6.72757i) q^{54} -4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} +(1.76965 + 3.06512i) q^{58} -8.21304 q^{59} +(1.66868 + 0.898462i) q^{60} +9.65916 q^{61} +2.49680 q^{62} +8.82622 q^{64} -11.3553 q^{65} +(-0.0787495 - 2.65224i) q^{66} +5.33301 q^{67} +(0.760807 + 1.31776i) q^{68} +(-6.55748 - 3.53074i) q^{69} -3.27719 q^{71} +(-4.03385 + 8.05590i) q^{72} +(0.519036 + 0.898997i) q^{73} +(6.34635 - 10.9922i) q^{74} +(-0.382019 - 12.8662i) q^{75} +(1.06543 - 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +1.00408 q^{79} +(-5.78772 - 10.0246i) q^{80} +(-5.39157 - 7.20631i) q^{81} +(4.32432 - 7.48994i) q^{82} +(3.65598 + 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +(6.28411 + 10.8844i) q^{86} +(-4.15239 - 2.23577i) q^{87} +(1.76965 - 3.06512i) q^{88} +(6.02144 - 10.4294i) q^{89} +(13.7252 - 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(-2.83056 + 1.74824i) q^{93} -0.823103 q^{94} -24.2097 q^{95} +(-2.56230 + 1.58255i) q^{96} +(5.46454 + 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + 20q^{11} + 4q^{15} + 24q^{16} - 32q^{18} + 32q^{23} - 12q^{25} + 16q^{29} - 84q^{30} - 96q^{32} - 4q^{36} - 12q^{37} + 8q^{39} + 56q^{44} + 24q^{46} - 4q^{50} + 64q^{51} + 32q^{53} - 12q^{57} + 32q^{60} + 96q^{64} - 120q^{65} + 24q^{67} - 112q^{71} + 68q^{74} - 60q^{78} - 24q^{79} - 40q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 32q^{93} - 128q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29987 0.919148 0.459574 0.888139i \(-0.348002\pi\)
0.459574 + 0.888139i \(0.348002\pi\)
\(3\) −1.47364 + 0.910162i −0.850805 + 0.525482i
\(4\) −0.310333 −0.155166
\(5\) 1.76292 + 3.05347i 0.788402 + 1.36555i 0.926945 + 0.375196i \(0.122425\pi\)
−0.138543 + 0.990356i \(0.544242\pi\)
\(6\) −1.91554 + 1.18309i −0.782016 + 0.482996i
\(7\) 0 0
\(8\) −3.00314 −1.06177
\(9\) 1.34321 2.68250i 0.447737 0.894165i
\(10\) 2.29157 + 3.96912i 0.724659 + 1.25515i
\(11\) −0.589267 + 1.02064i −0.177671 + 0.307735i −0.941082 0.338178i \(-0.890190\pi\)
0.763412 + 0.645912i \(0.223523\pi\)
\(12\) 0.457317 0.282453i 0.132016 0.0815371i
\(13\) −1.61030 + 2.78913i −0.446618 + 0.773564i −0.998163 0.0605803i \(-0.980705\pi\)
0.551546 + 0.834145i \(0.314038\pi\)
\(14\) 0 0
\(15\) −5.37706 2.89516i −1.38835 0.747527i
\(16\) −3.28303 −0.820757
\(17\) −2.45159 4.24627i −0.594597 1.02987i −0.993604 0.112924i \(-0.963978\pi\)
0.399006 0.916948i \(-0.369355\pi\)
\(18\) 1.74600 3.48690i 0.411537 0.821871i
\(19\) −3.43318 + 5.94645i −0.787627 + 1.36421i 0.139791 + 0.990181i \(0.455357\pi\)
−0.927417 + 0.374028i \(0.877976\pi\)
\(20\) −0.547092 0.947591i −0.122333 0.211888i
\(21\) 0 0
\(22\) −0.765972 + 1.32670i −0.163306 + 0.282854i
\(23\) 2.14994 + 3.72380i 0.448293 + 0.776466i 0.998275 0.0587106i \(-0.0186989\pi\)
−0.549982 + 0.835176i \(0.685366\pi\)
\(24\) 4.42553 2.73334i 0.903358 0.557941i
\(25\) −3.71578 + 6.43592i −0.743156 + 1.28718i
\(26\) −2.09319 + 3.62551i −0.410508 + 0.711020i
\(27\) 0.462101 + 5.17556i 0.0889314 + 0.996038i
\(28\) 0 0
\(29\) 1.36140 + 2.35802i 0.252806 + 0.437873i 0.964297 0.264822i \(-0.0853131\pi\)
−0.711491 + 0.702695i \(0.751980\pi\)
\(30\) −6.98948 3.76334i −1.27610 0.687088i
\(31\) 1.92080 0.344986 0.172493 0.985011i \(-0.444818\pi\)
0.172493 + 0.985011i \(0.444818\pi\)
\(32\) 1.73876 0.307372
\(33\) −0.0605825 2.04038i −0.0105461 0.355185i
\(34\) −3.18675 5.51961i −0.546523 0.946606i
\(35\) 0 0
\(36\) −0.416842 + 0.832466i −0.0694737 + 0.138744i
\(37\) 4.88229 8.45637i 0.802643 1.39022i −0.115228 0.993339i \(-0.536760\pi\)
0.917871 0.396879i \(-0.129907\pi\)
\(38\) −4.46270 + 7.72962i −0.723946 + 1.25391i
\(39\) −0.165555 5.57579i −0.0265100 0.892842i
\(40\) −5.29429 9.16998i −0.837101 1.44990i
\(41\) 3.32673 5.76206i 0.519547 0.899883i −0.480194 0.877162i \(-0.659434\pi\)
0.999742 0.0227205i \(-0.00723278\pi\)
\(42\) 0 0
\(43\) 4.83441 + 8.37344i 0.737240 + 1.27694i 0.953734 + 0.300653i \(0.0972047\pi\)
−0.216493 + 0.976284i \(0.569462\pi\)
\(44\) 0.182869 0.316738i 0.0275685 0.0477501i
\(45\) 10.5589 0.627577i 1.57403 0.0935537i
\(46\) 2.79464 + 4.84046i 0.412047 + 0.713687i
\(47\) −0.633218 −0.0923644 −0.0461822 0.998933i \(-0.514705\pi\)
−0.0461822 + 0.998933i \(0.514705\pi\)
\(48\) 4.83799 2.98809i 0.698304 0.431293i
\(49\) 0 0
\(50\) −4.83004 + 8.36587i −0.683071 + 1.18311i
\(51\) 7.47754 + 4.02612i 1.04707 + 0.563770i
\(52\) 0.499729 0.865557i 0.0693000 0.120031i
\(53\) 1.11378 + 1.92912i 0.152989 + 0.264985i 0.932325 0.361621i \(-0.117777\pi\)
−0.779336 + 0.626606i \(0.784443\pi\)
\(54\) 0.600672 + 6.72757i 0.0817412 + 0.915506i
\(55\) −4.15533 −0.560304
\(56\) 0 0
\(57\) −0.352965 11.8877i −0.0467514 1.57456i
\(58\) 1.76965 + 3.06512i 0.232366 + 0.402471i
\(59\) −8.21304 −1.06925 −0.534623 0.845091i \(-0.679546\pi\)
−0.534623 + 0.845091i \(0.679546\pi\)
\(60\) 1.66868 + 0.898462i 0.215425 + 0.115991i
\(61\) 9.65916 1.23673 0.618364 0.785892i \(-0.287796\pi\)
0.618364 + 0.785892i \(0.287796\pi\)
\(62\) 2.49680 0.317093
\(63\) 0 0
\(64\) 8.82622 1.10328
\(65\) −11.3553 −1.40846
\(66\) −0.0787495 2.65224i −0.00969340 0.326468i
\(67\) 5.33301 0.651531 0.325766 0.945451i \(-0.394378\pi\)
0.325766 + 0.945451i \(0.394378\pi\)
\(68\) 0.760807 + 1.31776i 0.0922614 + 0.159801i
\(69\) −6.55748 3.53074i −0.789428 0.425051i
\(70\) 0 0
\(71\) −3.27719 −0.388931 −0.194466 0.980909i \(-0.562297\pi\)
−0.194466 + 0.980909i \(0.562297\pi\)
\(72\) −4.03385 + 8.05590i −0.475393 + 0.949397i
\(73\) 0.519036 + 0.898997i 0.0607486 + 0.105220i 0.894800 0.446467i \(-0.147318\pi\)
−0.834052 + 0.551686i \(0.813985\pi\)
\(74\) 6.34635 10.9922i 0.737748 1.27782i
\(75\) −0.382019 12.8662i −0.0441118 1.48566i
\(76\) 1.06543 1.84538i 0.122213 0.211679i
\(77\) 0 0
\(78\) −0.215200 7.24782i −0.0243666 0.820654i
\(79\) 1.00408 0.112968 0.0564838 0.998404i \(-0.482011\pi\)
0.0564838 + 0.998404i \(0.482011\pi\)
\(80\) −5.78772 10.0246i −0.647087 1.12079i
\(81\) −5.39157 7.20631i −0.599063 0.800702i
\(82\) 4.32432 7.48994i 0.477541 0.827126i
\(83\) 3.65598 + 6.33234i 0.401296 + 0.695064i 0.993883 0.110442i \(-0.0352267\pi\)
−0.592587 + 0.805506i \(0.701893\pi\)
\(84\) 0 0
\(85\) 8.64391 14.9717i 0.937563 1.62391i
\(86\) 6.28411 + 10.8844i 0.677633 + 1.17369i
\(87\) −4.15239 2.23577i −0.445183 0.239699i
\(88\) 1.76965 3.06512i 0.188645 0.326743i
\(89\) 6.02144 10.4294i 0.638271 1.10552i −0.347541 0.937665i \(-0.612983\pi\)
0.985812 0.167853i \(-0.0536834\pi\)
\(90\) 13.7252 0.815770i 1.44676 0.0859897i
\(91\) 0 0
\(92\) −0.667195 1.15562i −0.0695599 0.120481i
\(93\) −2.83056 + 1.74824i −0.293516 + 0.181284i
\(94\) −0.823103 −0.0848966
\(95\) −24.2097 −2.48387
\(96\) −2.56230 + 1.58255i −0.261513 + 0.161518i
\(97\) 5.46454 + 9.46487i 0.554840 + 0.961012i 0.997916 + 0.0645275i \(0.0205540\pi\)
−0.443076 + 0.896484i \(0.646113\pi\)
\(98\) 0 0
\(99\) 1.94636 + 2.95164i 0.195616 + 0.296651i
\(100\) 1.15313 1.99728i 0.115313 0.199728i
\(101\) −0.797546 + 1.38139i −0.0793588 + 0.137453i −0.902973 0.429696i \(-0.858621\pi\)
0.823615 + 0.567150i \(0.191954\pi\)
\(102\) 9.71985 + 5.23344i 0.962409 + 0.518188i
\(103\) 1.16778 + 2.02265i 0.115065 + 0.199298i 0.917806 0.397030i \(-0.129959\pi\)
−0.802741 + 0.596328i \(0.796626\pi\)
\(104\) 4.83596 8.37613i 0.474205 0.821347i
\(105\) 0 0
\(106\) 1.44777 + 2.50761i 0.140620 + 0.243561i
\(107\) 1.11181 1.92571i 0.107483 0.186166i −0.807267 0.590186i \(-0.799054\pi\)
0.914750 + 0.404021i \(0.132388\pi\)
\(108\) −0.143405 1.60615i −0.0137992 0.154551i
\(109\) 0.459782 + 0.796366i 0.0440391 + 0.0762780i 0.887205 0.461376i \(-0.152644\pi\)
−0.843166 + 0.537654i \(0.819311\pi\)
\(110\) −5.40139 −0.515003
\(111\) 0.501947 + 16.9053i 0.0476427 + 1.60458i
\(112\) 0 0
\(113\) 1.19327 2.06681i 0.112254 0.194429i −0.804425 0.594054i \(-0.797526\pi\)
0.916679 + 0.399625i \(0.130860\pi\)
\(114\) −0.458810 15.4524i −0.0429715 1.44725i
\(115\) −7.58033 + 13.1295i −0.706870 + 1.22433i
\(116\) −0.422488 0.731770i −0.0392270 0.0679432i
\(117\) 5.31884 + 8.06601i 0.491727 + 0.745703i
\(118\) −10.6759 −0.982796
\(119\) 0 0
\(120\) 16.1480 + 8.69456i 1.47411 + 0.793701i
\(121\) 4.80553 + 8.32342i 0.436866 + 0.756674i
\(122\) 12.5557 1.13674
\(123\) 0.342020 + 11.5190i 0.0308389 + 1.03864i
\(124\) −0.596087 −0.0535302
\(125\) −8.57330 −0.766819
\(126\) 0 0
\(127\) −3.04170 −0.269907 −0.134954 0.990852i \(-0.543089\pi\)
−0.134954 + 0.990852i \(0.543089\pi\)
\(128\) 7.99544 0.706704
\(129\) −14.7453 7.93931i −1.29826 0.699018i
\(130\) −14.7605 −1.29458
\(131\) −1.63088 2.82476i −0.142490 0.246801i 0.785943 0.618298i \(-0.212178\pi\)
−0.928434 + 0.371498i \(0.878844\pi\)
\(132\) 0.0188007 + 0.633197i 0.00163639 + 0.0551127i
\(133\) 0 0
\(134\) 6.93223 0.598854
\(135\) −14.9888 + 10.5351i −1.29003 + 0.906719i
\(136\) 7.36245 + 12.7521i 0.631325 + 1.09349i
\(137\) −10.4669 + 18.1292i −0.894246 + 1.54888i −0.0595120 + 0.998228i \(0.518954\pi\)
−0.834734 + 0.550653i \(0.814379\pi\)
\(138\) −8.52389 4.58951i −0.725602 0.390685i
\(139\) 8.31195 14.3967i 0.705010 1.22111i −0.261677 0.965155i \(-0.584276\pi\)
0.966688 0.255958i \(-0.0823910\pi\)
\(140\) 0 0
\(141\) 0.933134 0.576331i 0.0785840 0.0485358i
\(142\) −4.25993 −0.357486
\(143\) −1.89780 3.28708i −0.158702 0.274880i
\(144\) −4.40980 + 8.80671i −0.367483 + 0.733893i
\(145\) −4.80009 + 8.31401i −0.398626 + 0.690441i
\(146\) 0.674681 + 1.16858i 0.0558370 + 0.0967124i
\(147\) 0 0
\(148\) −1.51513 + 2.62429i −0.124543 + 0.215715i
\(149\) −0.564221 0.977260i −0.0462228 0.0800602i 0.841988 0.539496i \(-0.181385\pi\)
−0.888211 + 0.459435i \(0.848052\pi\)
\(150\) −0.496576 16.7244i −0.0405452 1.36554i
\(151\) 9.81476 16.9997i 0.798714 1.38341i −0.121740 0.992562i \(-0.538847\pi\)
0.920454 0.390851i \(-0.127819\pi\)
\(152\) 10.3103 17.8580i 0.836278 1.44848i
\(153\) −14.6836 + 0.872733i −1.18710 + 0.0705563i
\(154\) 0 0
\(155\) 3.38622 + 5.86511i 0.271988 + 0.471097i
\(156\) 0.0513771 + 1.73035i 0.00411346 + 0.138539i
\(157\) −9.33237 −0.744804 −0.372402 0.928071i \(-0.621466\pi\)
−0.372402 + 0.928071i \(0.621466\pi\)
\(158\) 1.30517 0.103834
\(159\) −3.39712 1.82910i −0.269409 0.145057i
\(160\) 3.06529 + 5.30924i 0.242332 + 0.419732i
\(161\) 0 0
\(162\) −7.00835 9.36729i −0.550628 0.735964i
\(163\) −8.45056 + 14.6368i −0.661899 + 1.14644i 0.318217 + 0.948018i \(0.396916\pi\)
−0.980116 + 0.198425i \(0.936417\pi\)
\(164\) −1.03239 + 1.78815i −0.0806162 + 0.139631i
\(165\) 6.12344 3.78202i 0.476709 0.294430i
\(166\) 4.75230 + 8.23123i 0.368850 + 0.638867i
\(167\) −2.57319 + 4.45689i −0.199119 + 0.344885i −0.948243 0.317545i \(-0.897141\pi\)
0.749124 + 0.662430i \(0.230475\pi\)
\(168\) 0 0
\(169\) 1.31385 + 2.27566i 0.101066 + 0.175051i
\(170\) 11.2360 19.4613i 0.861760 1.49261i
\(171\) 11.3398 + 17.1968i 0.867179 + 1.31508i
\(172\) −1.50027 2.59855i −0.114395 0.198138i
\(173\) −9.73669 −0.740266 −0.370133 0.928979i \(-0.620688\pi\)
−0.370133 + 0.928979i \(0.620688\pi\)
\(174\) −5.39758 2.90621i −0.409190 0.220319i
\(175\) 0 0
\(176\) 1.93458 3.35079i 0.145825 0.252576i
\(177\) 12.1030 7.47519i 0.909720 0.561870i
\(178\) 7.82710 13.5569i 0.586666 1.01613i
\(179\) −0.687990 1.19163i −0.0514228 0.0890668i 0.839168 0.543872i \(-0.183042\pi\)
−0.890591 + 0.454805i \(0.849709\pi\)
\(180\) −3.27677 + 0.194758i −0.244236 + 0.0145164i
\(181\) 5.66560 0.421120 0.210560 0.977581i \(-0.432471\pi\)
0.210560 + 0.977581i \(0.432471\pi\)
\(182\) 0 0
\(183\) −14.2341 + 8.79140i −1.05221 + 0.649879i
\(184\) −6.45655 11.1831i −0.475983 0.824427i
\(185\) 34.4283 2.53122
\(186\) −3.67937 + 2.27249i −0.269785 + 0.166627i
\(187\) 5.77856 0.422570
\(188\) 0.196508 0.0143318
\(189\) 0 0
\(190\) −31.4696 −2.28304
\(191\) −25.0129 −1.80987 −0.904936 0.425547i \(-0.860082\pi\)
−0.904936 + 0.425547i \(0.860082\pi\)
\(192\) −13.0066 + 8.03329i −0.938673 + 0.579753i
\(193\) 17.5338 1.26211 0.631054 0.775739i \(-0.282623\pi\)
0.631054 + 0.775739i \(0.282623\pi\)
\(194\) 7.10321 + 12.3031i 0.509981 + 0.883312i
\(195\) 16.7337 10.3352i 1.19832 0.740119i
\(196\) 0 0
\(197\) −19.7540 −1.40741 −0.703707 0.710490i \(-0.748473\pi\)
−0.703707 + 0.710490i \(0.748473\pi\)
\(198\) 2.53001 + 3.83676i 0.179800 + 0.272667i
\(199\) −9.51110 16.4737i −0.674224 1.16779i −0.976695 0.214631i \(-0.931145\pi\)
0.302471 0.953158i \(-0.402188\pi\)
\(200\) 11.1590 19.3279i 0.789060 1.36669i
\(201\) −7.85892 + 4.85390i −0.554326 + 0.342368i
\(202\) −1.03671 + 1.79563i −0.0729425 + 0.126340i
\(203\) 0 0
\(204\) −2.32053 1.24944i −0.162469 0.0874781i
\(205\) 23.4590 1.63845
\(206\) 1.51796 + 2.62919i 0.105761 + 0.183184i
\(207\) 12.8769 0.765349i 0.895006 0.0531955i
\(208\) 5.28667 9.15678i 0.366565 0.634908i
\(209\) −4.04613 7.00810i −0.279876 0.484760i
\(210\) 0 0
\(211\) 3.71809 6.43993i 0.255964 0.443343i −0.709193 0.705015i \(-0.750940\pi\)
0.965157 + 0.261672i \(0.0842738\pi\)
\(212\) −0.345642 0.598669i −0.0237388 0.0411168i
\(213\) 4.82939 2.98278i 0.330904 0.204376i
\(214\) 1.44521 2.50318i 0.0987927 0.171114i
\(215\) −17.0454 + 29.5234i −1.16248 + 2.01348i
\(216\) −1.38775 15.5429i −0.0944246 1.05756i
\(217\) 0 0
\(218\) 0.597658 + 1.03517i 0.0404785 + 0.0701108i
\(219\) −1.58310 0.852388i −0.106976 0.0575990i
\(220\) 1.28953 0.0869403
\(221\) 15.7912 1.06223
\(222\) 0.652467 + 21.9747i 0.0437907 + 1.47485i
\(223\) −1.64565 2.85034i −0.110201 0.190873i 0.805650 0.592391i \(-0.201816\pi\)
−0.915851 + 0.401518i \(0.868483\pi\)
\(224\) 0 0
\(225\) 12.2733 + 18.6124i 0.818217 + 1.24082i
\(226\) 1.55110 2.68659i 0.103178 0.178709i
\(227\) −9.00847 + 15.6031i −0.597913 + 1.03562i 0.395215 + 0.918589i \(0.370670\pi\)
−0.993129 + 0.117028i \(0.962663\pi\)
\(228\) 0.109537 + 3.68913i 0.00725424 + 0.244318i
\(229\) 2.12746 + 3.68486i 0.140586 + 0.243503i 0.927718 0.373283i \(-0.121768\pi\)
−0.787131 + 0.616785i \(0.788435\pi\)
\(230\) −9.85347 + 17.0667i −0.649718 + 1.12535i
\(231\) 0 0
\(232\) −4.08848 7.08146i −0.268422 0.464920i
\(233\) 7.35275 12.7353i 0.481695 0.834320i −0.518084 0.855330i \(-0.673355\pi\)
0.999779 + 0.0210095i \(0.00668801\pi\)
\(234\) 6.91382 + 10.4848i 0.451970 + 0.685412i
\(235\) −1.11631 1.93351i −0.0728203 0.126128i
\(236\) 2.54877 0.165911
\(237\) −1.47965 + 0.913873i −0.0961133 + 0.0593624i
\(238\) 0 0
\(239\) 7.08187 12.2662i 0.458088 0.793432i −0.540772 0.841169i \(-0.681868\pi\)
0.998860 + 0.0477377i \(0.0152011\pi\)
\(240\) 17.6530 + 9.50489i 1.13950 + 0.613538i
\(241\) 3.96752 6.87194i 0.255570 0.442661i −0.709480 0.704726i \(-0.751070\pi\)
0.965050 + 0.262065i \(0.0844035\pi\)
\(242\) 6.24657 + 10.8194i 0.401545 + 0.695496i
\(243\) 14.5041 + 5.71229i 0.930440 + 0.366443i
\(244\) −2.99755 −0.191899
\(245\) 0 0
\(246\) 0.444583 + 14.9733i 0.0283456 + 0.954662i
\(247\) −11.0569 19.1512i −0.703536 1.21856i
\(248\) −5.76843 −0.366296
\(249\) −11.1510 6.00403i −0.706668 0.380490i
\(250\) −11.1442 −0.704821
\(251\) −8.05097 −0.508173 −0.254087 0.967181i \(-0.581775\pi\)
−0.254087 + 0.967181i \(0.581775\pi\)
\(252\) 0 0
\(253\) −5.06755 −0.318594
\(254\) −3.95382 −0.248085
\(255\) 0.888679 + 29.9302i 0.0556513 + 1.87430i
\(256\) −7.25938 −0.453712
\(257\) −8.77687 15.2020i −0.547486 0.948273i −0.998446 0.0557293i \(-0.982252\pi\)
0.450960 0.892544i \(-0.351082\pi\)
\(258\) −19.1671 10.3201i −1.19329 0.642501i
\(259\) 0 0
\(260\) 3.52393 0.218545
\(261\) 8.15403 0.484642i 0.504722 0.0299986i
\(262\) −2.11993 3.67183i −0.130970 0.226846i
\(263\) 11.6743 20.2205i 0.719867 1.24685i −0.241185 0.970479i \(-0.577536\pi\)
0.961052 0.276367i \(-0.0891306\pi\)
\(264\) 0.181938 + 6.12755i 0.0111975 + 0.377125i
\(265\) −3.92701 + 6.80177i −0.241234 + 0.417830i
\(266\) 0 0
\(267\) 0.619063 + 20.8497i 0.0378861 + 1.27598i
\(268\) −1.65501 −0.101096
\(269\) 0.269244 + 0.466344i 0.0164161 + 0.0284335i 0.874117 0.485716i \(-0.161441\pi\)
−0.857701 + 0.514149i \(0.828108\pi\)
\(270\) −19.4835 + 13.6943i −1.18573 + 0.833409i
\(271\) −7.20749 + 12.4837i −0.437824 + 0.758334i −0.997521 0.0703635i \(-0.977584\pi\)
0.559697 + 0.828697i \(0.310917\pi\)
\(272\) 8.04863 + 13.9406i 0.488020 + 0.845275i
\(273\) 0 0
\(274\) −13.6056 + 23.5656i −0.821945 + 1.42365i
\(275\) −4.37918 7.58495i −0.264074 0.457390i
\(276\) 2.03500 + 1.09570i 0.122493 + 0.0659535i
\(277\) −10.9533 + 18.9717i −0.658121 + 1.13990i 0.322980 + 0.946406i \(0.395315\pi\)
−0.981101 + 0.193494i \(0.938018\pi\)
\(278\) 10.8045 18.7139i 0.648009 1.12238i
\(279\) 2.58004 5.15254i 0.154463 0.308475i
\(280\) 0 0
\(281\) −0.776622 1.34515i −0.0463294 0.0802449i 0.841931 0.539586i \(-0.181419\pi\)
−0.888260 + 0.459341i \(0.848086\pi\)
\(282\) 1.21295 0.749157i 0.0722304 0.0446116i
\(283\) 2.65142 0.157610 0.0788051 0.996890i \(-0.474890\pi\)
0.0788051 + 0.996890i \(0.474890\pi\)
\(284\) 1.01702 0.0603490
\(285\) 35.6763 22.0348i 2.11328 1.30523i
\(286\) −2.46689 4.27279i −0.145870 0.252655i
\(287\) 0 0
\(288\) 2.33552 4.66421i 0.137622 0.274841i
\(289\) −3.52056 + 6.09778i −0.207091 + 0.358693i
\(290\) −6.23951 + 10.8071i −0.366396 + 0.634617i
\(291\) −16.6673 8.97416i −0.977055 0.526074i
\(292\) −0.161074 0.278988i −0.00942613 0.0163265i
\(293\) 5.19314 8.99478i 0.303386 0.525481i −0.673514 0.739174i \(-0.735216\pi\)
0.976901 + 0.213694i \(0.0685494\pi\)
\(294\) 0 0
\(295\) −14.4789 25.0783i −0.842996 1.46011i
\(296\) −14.6622 + 25.3956i −0.852221 + 1.47609i
\(297\) −5.55469 2.57815i −0.322316 0.149600i
\(298\) −0.733415 1.27031i −0.0424856 0.0735872i
\(299\) −13.8482 −0.800861
\(300\) 0.118553 + 3.99279i 0.00684466 + 0.230524i
\(301\) 0 0
\(302\) 12.7579 22.0974i 0.734137 1.27156i
\(303\) −0.0819956 2.76156i −0.00471053 0.158648i
\(304\) 11.2712 19.5224i 0.646450 1.11968i
\(305\) 17.0283 + 29.4939i 0.975039 + 1.68882i
\(306\) −19.0868 + 1.13444i −1.09112 + 0.0648517i
\(307\) 10.6425 0.607400 0.303700 0.952768i \(-0.401778\pi\)
0.303700 + 0.952768i \(0.401778\pi\)
\(308\) 0 0
\(309\) −3.56182 1.91779i −0.202625 0.109099i
\(310\) 4.40165 + 7.62389i 0.249997 + 0.433008i
\(311\) 13.7096 0.777399 0.388699 0.921365i \(-0.372925\pi\)
0.388699 + 0.921365i \(0.372925\pi\)
\(312\) 0.497184 + 16.7449i 0.0281475 + 0.947992i
\(313\) −21.2179 −1.19931 −0.599653 0.800260i \(-0.704695\pi\)
−0.599653 + 0.800260i \(0.704695\pi\)
\(314\) −12.1309 −0.684586
\(315\) 0 0
\(316\) −0.311598 −0.0175288
\(317\) 3.57043 0.200535 0.100268 0.994961i \(-0.468030\pi\)
0.100268 + 0.994961i \(0.468030\pi\)
\(318\) −4.41582 2.37760i −0.247627 0.133329i
\(319\) −3.20892 −0.179665
\(320\) 15.5599 + 26.9506i 0.869826 + 1.50658i
\(321\) 0.114305 + 3.84973i 0.00637989 + 0.214871i
\(322\) 0 0
\(323\) 33.6670 1.87328
\(324\) 1.67318 + 2.23635i 0.0929544 + 0.124242i
\(325\) −11.9671 20.7276i −0.663813 1.14976i
\(326\) −10.9846 + 19.0260i −0.608383 + 1.05375i
\(327\) −1.40237 0.755078i −0.0775514 0.0417559i
\(328\) −9.99062 + 17.3043i −0.551639 + 0.955468i
\(329\) 0 0
\(330\) 7.95969 4.91614i 0.438167 0.270625i
\(331\) −23.9456 −1.31617 −0.658085 0.752944i \(-0.728633\pi\)
−0.658085 + 0.752944i \(0.728633\pi\)
\(332\) −1.13457 1.96513i −0.0622675 0.107851i
\(333\) −16.1262 24.4554i −0.883712 1.34015i
\(334\) −3.34482 + 5.79339i −0.183020 + 0.317000i
\(335\) 9.40168 + 16.2842i 0.513669 + 0.889700i
\(336\) 0 0
\(337\) −13.7468 + 23.8102i −0.748838 + 1.29703i 0.199542 + 0.979889i \(0.436055\pi\)
−0.948380 + 0.317137i \(0.897279\pi\)
\(338\) 1.70784 + 2.95806i 0.0928942 + 0.160897i
\(339\) 0.122680 + 4.13180i 0.00666309 + 0.224409i
\(340\) −2.68249 + 4.64620i −0.145478 + 0.251976i
\(341\) −1.13187 + 1.96045i −0.0612940 + 0.106164i
\(342\) 14.7403 + 22.3537i 0.797066 + 1.20875i
\(343\) 0 0
\(344\) −14.5184 25.1466i −0.782779 1.35581i
\(345\) −0.779333 26.2475i −0.0419579 1.41312i
\(346\) −12.6564 −0.680415
\(347\) −5.12824 −0.275299 −0.137649 0.990481i \(-0.543955\pi\)
−0.137649 + 0.990481i \(0.543955\pi\)
\(348\) 1.28862 + 0.693831i 0.0690774 + 0.0371933i
\(349\) 7.56980 + 13.1113i 0.405202 + 0.701830i 0.994345 0.106198i \(-0.0338679\pi\)
−0.589143 + 0.808029i \(0.700535\pi\)
\(350\) 0 0
\(351\) −15.1794 7.04537i −0.810218 0.376054i
\(352\) −1.02459 + 1.77465i −0.0546110 + 0.0945889i
\(353\) 16.4878 28.5578i 0.877559 1.51998i 0.0235477 0.999723i \(-0.492504\pi\)
0.854011 0.520254i \(-0.174163\pi\)
\(354\) 15.7324 9.71680i 0.836168 0.516442i
\(355\) −5.77743 10.0068i −0.306634 0.531106i
\(356\) −1.86865 + 3.23659i −0.0990381 + 0.171539i
\(357\) 0 0
\(358\) −0.894299 1.54897i −0.0472651 0.0818656i
\(359\) 12.0178 20.8154i 0.634274 1.09859i −0.352395 0.935851i \(-0.614633\pi\)
0.986669 0.162743i \(-0.0520341\pi\)
\(360\) −31.7098 + 1.88470i −1.67125 + 0.0993324i
\(361\) −14.0735 24.3760i −0.740711 1.28295i
\(362\) 7.36455 0.387072
\(363\) −14.6573 7.89189i −0.769307 0.414217i
\(364\) 0 0
\(365\) −1.83004 + 3.16972i −0.0957886 + 0.165911i
\(366\) −18.5025 + 11.4277i −0.967141 + 0.597335i
\(367\) −1.32751 + 2.29931i −0.0692952 + 0.120023i −0.898591 0.438787i \(-0.855408\pi\)
0.829296 + 0.558810i \(0.188742\pi\)
\(368\) −7.05830 12.2253i −0.367939 0.637290i
\(369\) −10.9882 16.6636i −0.572023 0.867472i
\(370\) 44.7524 2.32657
\(371\) 0 0
\(372\) 0.878416 0.542536i 0.0455438 0.0281292i
\(373\) 15.9592 + 27.6421i 0.826334 + 1.43125i 0.900896 + 0.434036i \(0.142911\pi\)
−0.0745621 + 0.997216i \(0.523756\pi\)
\(374\) 7.51139 0.388405
\(375\) 12.6339 7.80309i 0.652413 0.402950i
\(376\) 1.90164 0.0980697
\(377\) −8.76909 −0.451631
\(378\) 0 0
\(379\) 30.2681 1.55477 0.777384 0.629027i \(-0.216546\pi\)
0.777384 + 0.629027i \(0.216546\pi\)
\(380\) 7.51307 0.385412
\(381\) 4.48236 2.76844i 0.229638 0.141831i
\(382\) −32.5136 −1.66354
\(383\) 0.866526 + 1.50087i 0.0442774 + 0.0766907i 0.887315 0.461164i \(-0.152568\pi\)
−0.843037 + 0.537855i \(0.819235\pi\)
\(384\) −11.7824 + 7.27715i −0.601267 + 0.371360i
\(385\) 0 0
\(386\) 22.7917 1.16006
\(387\) 28.9553 1.72099i 1.47188 0.0874826i
\(388\) −1.69583 2.93726i −0.0860925 0.149117i
\(389\) 5.54175 9.59859i 0.280978 0.486668i −0.690648 0.723191i \(-0.742675\pi\)
0.971626 + 0.236523i \(0.0760079\pi\)
\(390\) 21.7516 13.4344i 1.10144 0.680279i
\(391\) 10.5415 18.2584i 0.533107 0.923368i
\(392\) 0 0
\(393\) 4.97431 + 2.67831i 0.250921 + 0.135103i
\(394\) −25.6777 −1.29362
\(395\) 1.77011 + 3.06592i 0.0890639 + 0.154263i
\(396\) −0.604017 0.915991i −0.0303530 0.0460303i
\(397\) 12.6696 21.9443i 0.635867 1.10135i −0.350464 0.936576i \(-0.613976\pi\)
0.986331 0.164777i \(-0.0526905\pi\)
\(398\) −12.3632 21.4137i −0.619712 1.07337i
\(399\) 0 0
\(400\) 12.1990 21.1293i 0.609951 1.05647i
\(401\) 17.4122 + 30.1588i 0.869524 + 1.50606i 0.862483 + 0.506085i \(0.168908\pi\)
0.00704089 + 0.999975i \(0.497759\pi\)
\(402\) −10.2156 + 6.30945i −0.509507 + 0.314687i
\(403\) −3.09307 + 5.35736i −0.154077 + 0.266869i
\(404\) 0.247505 0.428690i 0.0123138 0.0213281i
\(405\) 12.4993 29.1672i 0.621097 1.44933i
\(406\) 0 0
\(407\) 5.75394 + 9.96612i 0.285212 + 0.494002i
\(408\) −22.4561 12.0910i −1.11174 0.598594i
\(409\) 18.2462 0.902215 0.451107 0.892470i \(-0.351029\pi\)
0.451107 + 0.892470i \(0.351029\pi\)
\(410\) 30.4937 1.50598
\(411\) −1.07610 36.2424i −0.0530801 1.78771i
\(412\) −0.362400 0.627695i −0.0178541 0.0309243i
\(413\) 0 0
\(414\) 16.7383 0.994856i 0.822643 0.0488945i
\(415\) −12.8904 + 22.3268i −0.632765 + 1.09598i
\(416\) −2.79992 + 4.84961i −0.137278 + 0.237772i
\(417\) 0.854551 + 28.7808i 0.0418475 + 1.40940i
\(418\) −5.25945 9.10963i −0.257248 0.445567i
\(419\) 4.20719 7.28708i 0.205535 0.355997i −0.744768 0.667323i \(-0.767440\pi\)
0.950303 + 0.311326i \(0.100773\pi\)
\(420\) 0 0
\(421\) 0.144291 + 0.249919i 0.00703230 + 0.0121803i 0.869520 0.493897i \(-0.164428\pi\)
−0.862488 + 0.506078i \(0.831095\pi\)
\(422\) 4.83304 8.37108i 0.235269 0.407498i
\(423\) −0.850546 + 1.69861i −0.0413549 + 0.0825890i
\(424\) −3.34483 5.79341i −0.162439 0.281353i
\(425\) 36.4382 1.76751
\(426\) 6.27759 3.87723i 0.304150 0.187852i
\(427\) 0 0
\(428\) −0.345031 + 0.597612i −0.0166777 + 0.0288866i
\(429\) 5.78844 + 3.11666i 0.279469 + 0.150474i
\(430\) −22.1568 + 38.3767i −1.06849 + 1.85069i
\(431\) 6.74795 + 11.6878i 0.325037 + 0.562981i 0.981520 0.191360i \(-0.0612898\pi\)
−0.656482 + 0.754341i \(0.727956\pi\)
\(432\) −1.51709 16.9915i −0.0729911 0.817505i
\(433\) 4.85211 0.233177 0.116589 0.993180i \(-0.462804\pi\)
0.116589 + 0.993180i \(0.462804\pi\)
\(434\) 0 0
\(435\) −0.493497 16.6207i −0.0236614 0.796901i
\(436\) −0.142685 0.247138i −0.00683339 0.0118358i
\(437\) −29.5245 −1.41235
\(438\) −2.05783 1.10800i −0.0983270 0.0529421i
\(439\) −2.54793 −0.121606 −0.0608031 0.998150i \(-0.519366\pi\)
−0.0608031 + 0.998150i \(0.519366\pi\)
\(440\) 12.4790 0.594914
\(441\) 0 0
\(442\) 20.5265 0.976347
\(443\) −0.645506 −0.0306689 −0.0153345 0.999882i \(-0.504881\pi\)
−0.0153345 + 0.999882i \(0.504881\pi\)
\(444\) −0.155771 5.24626i −0.00739255 0.248976i
\(445\) 42.4613 2.01286
\(446\) −2.13913 3.70508i −0.101291 0.175441i
\(447\) 1.72092 + 0.926593i 0.0813968 + 0.0438264i
\(448\) 0 0
\(449\) −5.22658 −0.246658 −0.123329 0.992366i \(-0.539357\pi\)
−0.123329 + 0.992366i \(0.539357\pi\)
\(450\) 15.9537 + 24.1937i 0.752063 + 1.14050i
\(451\) 3.92066 + 6.79079i 0.184617 + 0.319766i
\(452\) −0.370312 + 0.641399i −0.0174180 + 0.0301689i
\(453\) 1.00905 + 33.9844i 0.0474095 + 1.59672i
\(454\) −11.7099 + 20.2821i −0.549571 + 0.951885i
\(455\) 0 0
\(456\) 1.06000 + 35.7003i 0.0496392 + 1.67182i
\(457\) −2.86075 −0.133820 −0.0669101 0.997759i \(-0.521314\pi\)
−0.0669101 + 0.997759i \(0.521314\pi\)
\(458\) 2.76542 + 4.78985i 0.129220 + 0.223815i
\(459\) 20.8440 14.6506i 0.972913 0.683829i
\(460\) 2.35242 4.07452i 0.109682 0.189975i
\(461\) −1.82624 3.16314i −0.0850566 0.147322i 0.820359 0.571849i \(-0.193774\pi\)
−0.905415 + 0.424527i \(0.860440\pi\)
\(462\) 0 0
\(463\) −15.4052 + 26.6825i −0.715939 + 1.24004i 0.246657 + 0.969103i \(0.420668\pi\)
−0.962596 + 0.270940i \(0.912666\pi\)
\(464\) −4.46953 7.74145i −0.207493 0.359388i
\(465\) −10.3283 5.56103i −0.478962 0.257887i
\(466\) 9.55764 16.5543i 0.442749 0.766864i
\(467\) 10.2885 17.8202i 0.476096 0.824622i −0.523529 0.852008i \(-0.675385\pi\)
0.999625 + 0.0273858i \(0.00871825\pi\)
\(468\) −1.65061 2.50315i −0.0762995 0.115708i
\(469\) 0 0
\(470\) −1.45107 2.51332i −0.0669327 0.115931i
\(471\) 13.7525 8.49397i 0.633683 0.391381i
\(472\) 24.6649 1.13529
\(473\) −11.3950 −0.523944
\(474\) −1.92335 + 1.18792i −0.0883424 + 0.0545629i
\(475\) −25.5139 44.1914i −1.17066 2.02764i
\(476\) 0 0
\(477\) 6.67090 0.396491i 0.305439 0.0181541i
\(478\) 9.20552 15.9444i 0.421051 0.729281i
\(479\) 12.5916 21.8093i 0.575325 0.996492i −0.420682 0.907208i \(-0.638209\pi\)
0.996006 0.0892833i \(-0.0284577\pi\)
\(480\) −9.34939 5.03398i −0.426739 0.229769i
\(481\) 15.7239 + 27.2346i 0.716949 + 1.24179i
\(482\) 5.15726 8.93264i 0.234907 0.406871i
\(483\) 0 0
\(484\) −1.49131 2.58303i −0.0677869 0.117410i
\(485\) −19.2671 + 33.3716i −0.874875 + 1.51533i
\(486\) 18.8535 + 7.42524i 0.855213 + 0.336816i
\(487\) 16.3807 + 28.3723i 0.742282 + 1.28567i 0.951454 + 0.307791i \(0.0995896\pi\)
−0.209173 + 0.977879i \(0.567077\pi\)
\(488\) −29.0078 −1.31312
\(489\) −0.868801 29.2607i −0.0392886 1.32321i
\(490\) 0 0
\(491\) 1.76000 3.04841i 0.0794278 0.137573i −0.823575 0.567207i \(-0.808024\pi\)
0.903003 + 0.429634i \(0.141357\pi\)
\(492\) −0.106140 3.57473i −0.00478516 0.161161i
\(493\) 6.67520 11.5618i 0.300636 0.520716i
\(494\) −14.3726 24.8941i −0.646654 1.12004i
\(495\) −5.58148 + 11.1466i −0.250869 + 0.501005i
\(496\) −6.30605 −0.283150
\(497\) 0 0
\(498\) −14.4949 7.80448i −0.649533 0.349727i
\(499\) −7.82082 13.5461i −0.350108 0.606405i 0.636160 0.771557i \(-0.280522\pi\)
−0.986268 + 0.165152i \(0.947188\pi\)
\(500\) 2.66057 0.118984
\(501\) −0.264549 8.90986i −0.0118192 0.398063i
\(502\) −10.4652 −0.467086
\(503\) 36.5427 1.62936 0.814678 0.579913i \(-0.196914\pi\)
0.814678 + 0.579913i \(0.196914\pi\)
\(504\) 0 0
\(505\) −5.62404 −0.250267
\(506\) −6.58716 −0.292835
\(507\) −4.00736 2.15768i −0.177973 0.0958257i
\(508\) 0.943938 0.0418805
\(509\) −18.8229 32.6023i −0.834311 1.44507i −0.894590 0.446888i \(-0.852532\pi\)
0.0602789 0.998182i \(-0.480801\pi\)
\(510\) 1.15517 + 38.9054i 0.0511518 + 1.72276i
\(511\) 0 0
\(512\) −25.4272 −1.12373
\(513\) −32.3627 15.0208i −1.42885 0.663185i
\(514\) −11.4088 19.7606i −0.503221 0.871604i
\(515\) −4.11740 + 7.13155i −0.181434 + 0.314254i
\(516\) 4.57596 + 2.46383i 0.201445 + 0.108464i
\(517\) 0.373135 0.646289i 0.0164105 0.0284237i
\(518\) 0 0
\(519\) 14.3483 8.86196i 0.629822 0.388997i
\(520\) 34.1017 1.49546
\(521\) −7.17115 12.4208i −0.314174 0.544165i 0.665088 0.746765i \(-0.268394\pi\)
−0.979262 + 0.202600i \(0.935061\pi\)
\(522\) 10.5992 0.629973i 0.463914 0.0275732i
\(523\) 5.24222 9.07980i 0.229226 0.397032i −0.728353 0.685202i \(-0.759714\pi\)
0.957579 + 0.288171i \(0.0930471\pi\)
\(524\) 0.506114 + 0.876616i 0.0221097 + 0.0382951i
\(525\) 0 0
\(526\) 15.1751 26.2840i 0.661665 1.14604i
\(527\) −4.70901 8.15625i −0.205128 0.355292i
\(528\) 0.198894 + 6.69863i 0.00865576 + 0.291521i
\(529\) 2.25555 3.90673i 0.0980674 0.169858i
\(530\) −5.10461 + 8.84144i −0.221730 + 0.384047i
\(531\) −11.0318 + 22.0314i −0.478741 + 0.956083i
\(532\) 0 0
\(533\) 10.7141 + 18.5573i 0.464078 + 0.803807i
\(534\) 0.804703 + 27.1019i 0.0348229 + 1.17281i
\(535\) 7.84014 0.338959
\(536\) −16.0158 −0.691776
\(537\) 2.09843 + 1.12985i 0.0905538 + 0.0487567i
\(538\) 0.349983 + 0.606188i 0.0150888 + 0.0261346i
\(539\) 0 0
\(540\) 4.65150 3.26939i 0.200169 0.140692i
\(541\) 23.0461 39.9170i 0.990830 1.71617i 0.378399 0.925643i \(-0.376475\pi\)
0.612430 0.790524i \(-0.290192\pi\)
\(542\) −9.36882 + 16.2273i −0.402425 + 0.697021i
\(543\) −8.34903 + 5.15661i −0.358291 + 0.221291i
\(544\) −4.26271 7.38323i −0.182762 0.316554i
\(545\) −1.62112 + 2.80786i −0.0694411 + 0.120275i
\(546\) 0 0
\(547\) −12.1793 21.0951i −0.520747 0.901961i −0.999709 0.0241250i \(-0.992320\pi\)
0.478962 0.877836i \(-0.341013\pi\)
\(548\) 3.24822 5.62607i 0.138757 0.240334i
\(549\) 12.9743 25.9107i 0.553729 1.10584i
\(550\) −5.69237 9.85947i −0.242723 0.420409i
\(551\) −18.6958 −0.796468
\(552\) 19.6930 + 10.6033i 0.838191 + 0.451306i
\(553\) 0 0
\(554\) −14.2379 + 24.6608i −0.604911 + 1.04774i
\(555\) −50.7349 + 31.3354i −2.15357 + 1.33011i
\(556\) −2.57947 + 4.46777i −0.109394 + 0.189476i
\(557\) −15.2888 26.4809i −0.647806 1.12203i −0.983646 0.180114i \(-0.942353\pi\)
0.335840 0.941919i \(-0.390980\pi\)
\(558\) 3.35372 6.69765i 0.141974 0.283534i
\(559\) −31.1394 −1.31706
\(560\) 0 0
\(561\) −8.51550 + 5.25943i −0.359525 + 0.222053i
\(562\) −1.00951 1.74852i −0.0425836 0.0737570i
\(563\) −8.82714 −0.372019 −0.186010 0.982548i \(-0.559556\pi\)
−0.186010 + 0.982548i \(0.559556\pi\)
\(564\) −0.289582 + 0.178854i −0.0121936 + 0.00753113i
\(565\) 8.41459 0.354005
\(566\) 3.44650 0.144867
\(567\) 0 0
\(568\) 9.84186 0.412955
\(569\) 7.12055 0.298509 0.149254 0.988799i \(-0.452313\pi\)
0.149254 + 0.988799i \(0.452313\pi\)
\(570\) 46.3747 28.6424i 1.94242 1.19970i
\(571\) 6.66361 0.278863 0.139432 0.990232i \(-0.455472\pi\)
0.139432 + 0.990232i \(0.455472\pi\)
\(572\) 0.588948 + 1.02009i 0.0246252 + 0.0426520i
\(573\) 36.8600 22.7658i 1.53985 0.951056i
\(574\) 0 0
\(575\) −31.9548 −1.33261
\(576\) 11.8555 23.6763i 0.493978 0.986512i
\(577\) 3.95629 + 6.85250i 0.164703 + 0.285273i 0.936550 0.350535i \(-0.114000\pi\)
−0.771847 + 0.635808i \(0.780667\pi\)
\(578\) −4.57627 + 7.92633i −0.190348 + 0.329692i
\(579\) −25.8384 + 15.9586i −1.07381 + 0.663215i
\(580\) 1.48963 2.58011i 0.0618533 0.107133i
\(581\) 0 0
\(582\) −21.6654 11.6653i −0.898059 0.483540i
\(583\) −2.62525 −0.108727
\(584\) −1.55874 2.69981i −0.0645010 0.111719i
\(585\) −15.2526 + 30.4607i −0.630618 + 1.25939i
\(586\) 6.75042 11.6921i 0.278857 0.482995i
\(587\) 9.13891 + 15.8291i 0.377203 + 0.653335i 0.990654 0.136398i \(-0.0435525\pi\)
−0.613451 + 0.789733i \(0.710219\pi\)
\(588\) 0 0
\(589\) −6.59447 + 11.4220i −0.271720 + 0.470633i
\(590\) −18.8208 32.5985i −0.774839 1.34206i
\(591\) 29.1102 17.9793i 1.19743 0.739571i
\(592\) −16.0287 + 27.7625i −0.658775 + 1.14103i
\(593\) −14.1908 + 24.5792i −0.582745 + 1.00934i 0.412407 + 0.911000i \(0.364688\pi\)
−0.995152 + 0.0983450i \(0.968645\pi\)
\(594\) −7.22039 3.35127i −0.296256 0.137504i
\(595\) 0 0
\(596\) 0.175096 + 0.303275i 0.00717222 + 0.0124226i
\(597\) 29.0096 + 15.6196i 1.18729 + 0.639268i
\(598\) −18.0009 −0.736111
\(599\) 9.38902 0.383625 0.191813 0.981432i \(-0.438563\pi\)
0.191813 + 0.981432i \(0.438563\pi\)
\(600\) 1.14726 + 38.6389i 0.0468365 + 1.57743i
\(601\) 6.31432 + 10.9367i 0.257566 + 0.446118i 0.965589 0.260071i \(-0.0837460\pi\)
−0.708023 + 0.706189i \(0.750413\pi\)
\(602\) 0 0
\(603\) 7.16336 14.3058i 0.291714 0.582577i
\(604\) −3.04584 + 5.27555i −0.123934 + 0.214659i
\(605\) −16.9435 + 29.3471i −0.688853 + 1.19313i
\(606\) −0.106584 3.58968i −0.00432967 0.145821i
\(607\) 12.0133 + 20.8076i 0.487604 + 0.844554i 0.999898 0.0142555i \(-0.00453781\pi\)
−0.512295 + 0.858810i \(0.671204\pi\)
\(608\) −5.96947 + 10.3394i −0.242094 + 0.419319i
\(609\) 0 0
\(610\) 22.1347 + 38.3383i 0.896206 + 1.55227i
\(611\) 1.01967 1.76613i 0.0412516 0.0714498i
\(612\) 4.55680 0.270837i 0.184198 0.0109480i
\(613\) 14.2708 + 24.7177i 0.576390 + 0.998337i 0.995889 + 0.0905814i \(0.0288725\pi\)
−0.419499 + 0.907756i \(0.637794\pi\)
\(614\) 13.8339 0.558291
\(615\) −34.5701 + 21.3515i −1.39400 + 0.860976i
\(616\) 0 0
\(617\) −6.05549 + 10.4884i −0.243785 + 0.422248i −0.961789 0.273791i \(-0.911722\pi\)
0.718004 + 0.696039i \(0.245056\pi\)
\(618\) −4.62991 2.49288i −0.186242 0.100278i
\(619\) −13.2870 + 23.0137i −0.534048 + 0.924998i 0.465161 + 0.885226i \(0.345997\pi\)
−0.999209 + 0.0397721i \(0.987337\pi\)
\(620\) −1.05085 1.82013i −0.0422033 0.0730983i
\(621\) −18.2793 + 12.8479i −0.733522 + 0.515569i
\(622\) 17.8207 0.714545
\(623\) 0 0
\(624\) 0.543522 + 18.3055i 0.0217583 + 0.732806i
\(625\) 3.46486 + 6.00131i 0.138594 + 0.240052i
\(626\) −27.5806 −1.10234
\(627\) 12.3410 + 6.64476i 0.492853 + 0.265366i
\(628\) 2.89614 0.115569
\(629\) −47.8774 −1.90900
\(630\) 0 0
\(631\) 3.30962 0.131754 0.0658770 0.997828i \(-0.479015\pi\)
0.0658770 + 0.997828i \(0.479015\pi\)
\(632\) −3.01538 −0.119945
\(633\) 0.382257 + 12.8742i 0.0151933 + 0.511703i
\(634\) 4.64110 0.184322
\(635\) −5.36227 9.28773i −0.212795 0.368572i
\(636\) 1.05424 + 0.567631i 0.0418032 + 0.0225080i
\(637\) 0 0
\(638\) −4.17119 −0.165139
\(639\) −4.40196 + 8.79106i −0.174139 + 0.347769i
\(640\) 14.0953 + 24.4138i 0.557167 + 0.965041i
\(641\) −16.2922 + 28.2189i −0.643503 + 1.11458i 0.341142 + 0.940012i \(0.389186\pi\)
−0.984645 + 0.174568i \(0.944147\pi\)
\(642\) 0.148582 + 5.00416i 0.00586407 + 0.197498i
\(643\) −21.5327 + 37.2957i −0.849166 + 1.47080i 0.0327873 + 0.999462i \(0.489562\pi\)
−0.881953 + 0.471337i \(0.843772\pi\)
\(644\) 0 0
\(645\) −1.75243 59.0208i −0.0690019 2.32394i
\(646\) 43.7628 1.72182
\(647\) 23.0988 + 40.0082i 0.908106 + 1.57289i 0.816692 + 0.577074i \(0.195805\pi\)
0.0914143 + 0.995813i \(0.470861\pi\)
\(648\) 16.1916 + 21.6415i 0.636067 + 0.850160i
\(649\) 4.83968 8.38256i 0.189974 0.329044i
\(650\) −15.5556 26.9432i −0.610143 1.05680i
\(651\) 0 0
\(652\) 2.62248 4.54228i 0.102704 0.177889i
\(653\) −16.0002 27.7132i −0.626138 1.08450i −0.988320 0.152395i \(-0.951301\pi\)
0.362182 0.932107i \(-0.382032\pi\)
\(654\) −1.82291 0.981504i −0.0712812 0.0383799i
\(655\) 5.75022 9.95967i 0.224680 0.389156i
\(656\) −10.9217 + 18.9170i −0.426422 + 0.738585i
\(657\) 3.10873 0.184770i 0.121283 0.00720857i
\(658\) 0 0
\(659\) 19.2070 + 33.2674i 0.748197 + 1.29591i 0.948686 + 0.316219i \(0.102413\pi\)
−0.200490 + 0.979696i \(0.564253\pi\)
\(660\) −1.90030 + 1.17368i −0.0739692 + 0.0456856i
\(661\) −28.0260 −1.09009 −0.545043 0.838408i \(-0.683487\pi\)
−0.545043 + 0.838408i \(0.683487\pi\)
\(662\) −31.1262 −1.20976
\(663\) −23.2705 + 14.3725i −0.903750 + 0.558183i
\(664\) −10.9794 19.0169i −0.426083 0.737998i
\(665\) 0 0
\(666\) −20.9620 31.7889i −0.812263 1.23179i
\(667\) −5.85386 + 10.1392i −0.226662 + 0.392591i
\(668\) 0.798544 1.38312i 0.0308966 0.0535145i
\(669\) 5.01936 + 2.70256i 0.194060 + 0.104487i
\(670\) 12.2210 + 21.1674i 0.472138 + 0.817766i
\(671\) −5.69183 + 9.85853i −0.219730 + 0.380584i
\(672\) 0 0
\(673\) 0.796281 + 1.37920i 0.0306944 + 0.0531642i 0.880965 0.473182i \(-0.156895\pi\)
−0.850270 + 0.526347i \(0.823561\pi\)
\(674\) −17.8691 + 30.9503i −0.688293 + 1.19216i
\(675\) −35.0266 16.2572i −1.34817 0.625740i
\(676\) −0.407731 0.706211i −0.0156820 0.0271619i
\(677\) 42.0334 1.61547 0.807737 0.589543i \(-0.200692\pi\)
0.807737 + 0.589543i \(0.200692\pi\)
\(678\) 0.159469 + 5.37082i 0.00612437 + 0.206265i
\(679\) 0 0
\(680\) −25.9588 + 44.9620i −0.995476 + 1.72421i
\(681\) −0.926160 31.1925i −0.0354905 1.19530i
\(682\) −1.47128 + 2.54833i −0.0563382 + 0.0975807i
\(683\) −17.8645 30.9422i −0.683565 1.18397i −0.973886 0.227039i \(-0.927095\pi\)
0.290321 0.956929i \(-0.406238\pi\)
\(684\) −3.51912 5.33674i −0.134557 0.204055i
\(685\) −73.8092 −2.82010
\(686\) 0 0
\(687\) −6.48892 3.49382i −0.247568 0.133298i
\(688\) −15.8715 27.4902i −0.605095 1.04806i
\(689\) −7.17408 −0.273311
\(690\) −1.01303 34.1184i −0.0385655 1.29886i
\(691\) 51.1349 1.94526 0.972632 0.232351i \(-0.0746418\pi\)
0.972632 + 0.232351i \(0.0746418\pi\)
\(692\) 3.02161 0.114864
\(693\) 0 0
\(694\) −6.66606 −0.253040
\(695\) 58.6132 2.22333
\(696\) 12.4702 + 6.71432i 0.472682 + 0.254505i
\(697\) −32.6230 −1.23569
\(698\) 9.83977 + 17.0430i 0.372441 + 0.645086i
\(699\) 0.755936 + 25.4595i 0.0285921 + 0.962965i
\(700\) 0 0
\(701\) −24.5761 −0.928226 −0.464113 0.885776i \(-0.653627\pi\)
−0.464113 + 0.885776i \(0.653627\pi\)
\(702\) −19.7313 9.15807i −0.744710 0.345649i
\(703\) 33.5236 + 58.0645i 1.26437 + 2.18995i
\(704\) −5.20100 + 9.00840i −0.196020 + 0.339517i
\(705\) 3.40485 + 1.83327i 0.128234 + 0.0690449i
\(706\) 21.4321 37.1215i 0.806607 1.39708i
\(707\) 0 0
\(708\) −3.75597 + 2.31980i −0.141158 + 0.0871833i
\(709\) 30.8976 1.16038 0.580192 0.814480i \(-0.302978\pi\)
0.580192 + 0.814480i \(0.302978\pi\)
\(710\) −7.50992 13.0076i −0.281842 0.488165i
\(711\) 1.34869 2.69343i 0.0505797 0.101012i
\(712\) −18.0832 + 31.3210i −0.677697 + 1.17380i
\(713\) 4.12960 + 7.15268i 0.154655 + 0.267870i
\(714\) 0 0
\(715\) 6.69133 11.5897i 0.250242 0.433431i
\(716\) 0.213506 + 0.369803i 0.00797908 + 0.0138202i
\(717\) 0.728086 + 24.5215i 0.0271909 + 0.915772i
\(718\) 15.6216 27.0573i 0.582992 1.00977i
\(719\) −3.05690 + 5.29471i −0.114003 + 0.197459i −0.917381 0.398011i \(-0.869701\pi\)
0.803378 + 0.595470i \(0.203034\pi\)
\(720\) −34.6651 + 2.06035i −1.29189 + 0.0767848i
\(721\) 0 0
\(722\) −18.2938 31.6857i −0.680823 1.17922i
\(723\) 0.407900 + 13.7378i 0.0151700 + 0.510915i
\(724\) −1.75822 −0.0653437
\(725\) −20.2347 −0.751498
\(726\) −19.0526 10.2584i −0.707107 0.380727i
\(727\) 22.2492 + 38.5367i 0.825176 + 1.42925i 0.901785 + 0.432186i \(0.142257\pi\)
−0.0766087 + 0.997061i \(0.524409\pi\)
\(728\) 0 0
\(729\) −26.5729 + 4.78327i −0.984182 + 0.177158i
\(730\) −2.37882 + 4.12023i −0.0880440 + 0.152497i
\(731\) 23.7039 41.0564i 0.876722 1.51853i
\(732\) 4.41730 2.72826i 0.163268 0.100839i
\(733\) −4.91854 8.51916i −0.181670 0.314662i 0.760779 0.649011i \(-0.224817\pi\)
−0.942449 + 0.334349i \(0.891484\pi\)
\(734\) −1.72559 + 2.98881i −0.0636926 + 0.110319i
\(735\) 0 0
\(736\) 3.73821 + 6.47478i 0.137792 + 0.238663i
\(737\) −3.14257 + 5.44309i −0.115758 + 0.200499i
\(738\) −14.2833 21.6605i −0.525774 0.797335i
\(739\) −7.42464 12.8598i −0.273120 0.473057i 0.696539 0.717519i \(-0.254722\pi\)
−0.969659 + 0.244461i \(0.921389\pi\)
\(740\) −10.6842 −0.392760
\(741\) 33.7246 + 18.1583i 1.23890 + 0.667061i
\(742\) 0 0
\(743\) −3.04201 + 5.26892i −0.111601 + 0.193298i −0.916416 0.400228i \(-0.868931\pi\)
0.804815 + 0.593525i \(0.202264\pi\)
\(744\) 8.50057 5.25021i 0.311646 0.192482i
\(745\) 1.98935 3.44566i 0.0728843 0.126239i
\(746\) 20.7449 + 35.9311i 0.759523 + 1.31553i
\(747\) 21.8972 1.30148i 0.801177 0.0476187i
\(748\) −1.79328 −0.0655686
\(749\) 0 0
\(750\) 16.4225 10.1430i 0.599665 0.370371i
\(751\) −11.1005 19.2266i −0.405063 0.701590i 0.589266 0.807939i \(-0.299417\pi\)
−0.994329 + 0.106349i \(0.966084\pi\)
\(752\) 2.07887 0.0758087
\(753\) 11.8642 7.32769i 0.432356 0.267036i
\(754\) −11.3987 −0.415116
\(755\) 69.2106 2.51883
\(756\) 0 0
\(757\) 25.0464 0.910329 0.455164 0.890407i \(-0.349581\pi\)
0.455164 + 0.890407i \(0.349581\pi\)
\(758\) 39.3446 1.42906
\(759\) 7.46773 4.61229i 0.271061 0.167415i
\(760\) 72.7051 2.63729
\(761\) −3.37632 5.84796i −0.122392 0.211988i 0.798319 0.602235i \(-0.205723\pi\)
−0.920710 + 0.390247i \(0.872390\pi\)
\(762\) 5.82649 3.59862i 0.211072 0.130364i
\(763\) 0 0
\(764\) 7.76233 0.280831
\(765\) −28.5509 43.2974i −1.03226 1.56542i
\(766\) 1.12637 + 1.95094i 0.0406975 + 0.0704902i
\(767\) 13.2255 22.9072i 0.477544 0.827131i
\(768\) 10.6977 6.60722i 0.386020 0.238417i
\(769\) 21.0805 36.5125i 0.760182 1.31667i −0.182575 0.983192i \(-0.558443\pi\)
0.942757 0.333482i \(-0.108224\pi\)
\(770\) 0 0
\(771\) 26.7702 + 14.4138i 0.964104 + 0.519101i
\(772\) −5.44130 −0.195837
\(773\) −1.64926 2.85660i −0.0593197 0.102745i 0.834841 0.550492i \(-0.185560\pi\)
−0.894160 + 0.447747i \(0.852226\pi\)
\(774\) 37.6382 2.23706i 1.35288 0.0804095i
\(775\) −7.13728 + 12.3621i −0.256379 + 0.444061i
\(776\) −16.4108 28.4243i −0.589112 1.02037i
\(777\) 0 0
\(778\) 7.20356 12.4769i 0.258260 0.447320i
\(779\) 22.8425 + 39.5644i 0.818419 + 1.41754i
\(780\) −5.19300 + 3.20735i −0.185939 + 0.114842i
\(781\) 1.93114 3.34484i 0.0691017 0.119688i
\(782\) 13.7026 23.7336i 0.490004