Properties

Label 441.2.h.h.214.10
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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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 214.10
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.h.373.10

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.138543 + 0.990356i \(0.455758\pi\)
−0.926945 + 0.375196i \(0.877575\pi\)
\(6\) 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 0.763412 0.645912i \(-0.223523\pi\)
−0.941082 + 0.338178i \(0.890190\pi\)
\(12\) −0.457317 0.282453i −0.132016 0.0815371i
\(13\) 1.61030 + 2.78913i 0.446618 + 0.773564i 0.998163 0.0605803i \(-0.0192951\pi\)
−0.551546 + 0.834145i \(0.685962\pi\)
\(14\) 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 −0.399006 0.916948i \(-0.630645\pi\)
0.993604 0.112924i \(-0.0360218\pi\)
\(18\) 1.74600 + 3.48690i 0.411537 + 0.821871i
\(19\) 3.43318 + 5.94645i 0.787627 + 1.36421i 0.927417 + 0.374028i \(0.122024\pi\)
−0.139791 + 0.990181i \(0.544643\pi\)
\(20\) 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 −0.549982 0.835176i \(-0.685366\pi\)
0.998275 + 0.0587106i \(0.0186989\pi\)
\(24\) −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 −0.711491 0.702695i \(-0.751980\pi\)
0.964297 + 0.264822i \(0.0853131\pi\)
\(30\) −6.98948 + 3.76334i −1.27610 + 0.687088i
\(31\) −1.92080 −0.344986 −0.172493 0.985011i \(-0.555182\pi\)
−0.172493 + 0.985011i \(0.555182\pi\)
\(32\) 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 0.917871 + 0.396879i \(0.129907\pi\)
−0.115228 + 0.993339i \(0.536760\pi\)
\(38\) 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 −0.999742 0.0227205i \(-0.992767\pi\)
0.480194 0.877162i \(-0.340566\pi\)
\(42\) 0 0
\(43\) 4.83441 8.37344i 0.737240 1.27694i −0.216493 0.976284i \(-0.569462\pi\)
0.953734 0.300653i \(-0.0972047\pi\)
\(44\) 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 \(-0.485295\pi\)
0.0461822 + 0.998933i \(0.485295\pi\)
\(48\) −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 −0.779336 0.626606i \(-0.784443\pi\)
0.932325 + 0.361621i \(0.117777\pi\)
\(54\) −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 \(-0.320454\pi\)
0.534623 + 0.845091i \(0.320454\pi\)
\(60\) 1.66868 0.898462i 0.215425 0.115991i
\(61\) −9.65916 −1.23673 −0.618364 0.785892i \(-0.712204\pi\)
−0.618364 + 0.785892i \(0.712204\pi\)
\(62\) −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 \(-0.852682\pi\)
0.834052 + 0.551686i \(0.186015\pi\)
\(74\) 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 \(-0.964773\pi\)
0.592587 + 0.805506i \(0.298107\pi\)
\(84\) 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 −0.985812 0.167853i \(-0.946317\pi\)
0.347541 0.937665i \(-0.387017\pi\)
\(90\) −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 0.443076 + 0.896484i \(0.353887\pi\)
−0.997916 + 0.0645275i \(0.979446\pi\)
\(98\) 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 \(-0.141379\pi\)
−0.823615 + 0.567150i \(0.808046\pi\)
\(102\) 9.71985 5.23344i 0.962409 0.518188i
\(103\) −1.16778 + 2.02265i −0.115065 + 0.199298i −0.917806 0.397030i \(-0.870041\pi\)
0.802741 + 0.596328i \(0.203374\pi\)
\(104\) −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 0.914750 0.404021i \(-0.132388\pi\)
−0.807267 + 0.590186i \(0.799054\pi\)
\(108\) 0.143405 1.60615i 0.0137992 0.154551i
\(109\) 0.459782 0.796366i 0.0440391 0.0762780i −0.843166 0.537654i \(-0.819311\pi\)
0.887205 + 0.461376i \(0.152644\pi\)
\(110\) 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 0.916679 0.399625i \(-0.130860\pi\)
−0.804425 + 0.594054i \(0.797526\pi\)
\(114\) −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 \(-0.787822\pi\)
0.928434 + 0.371498i \(0.121156\pi\)
\(132\) −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 −0.834734 0.550653i \(-0.814379\pi\)
−0.0595120 0.998228i \(-0.518954\pi\)
\(138\) 8.52389 4.58951i 0.725602 0.390685i
\(139\) −8.31195 14.3967i −0.705010 1.22111i −0.966688 0.255958i \(-0.917609\pi\)
0.261677 0.965155i \(-0.415724\pi\)
\(140\) 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 −0.888211 0.459435i \(-0.848052\pi\)
0.841988 + 0.539496i \(0.181385\pi\)
\(150\) 0.496576 16.7244i 0.0405452 1.36554i
\(151\) 9.81476 + 16.9997i 0.798714 + 1.38341i 0.920454 + 0.390851i \(0.127819\pi\)
−0.121740 + 0.992562i \(0.538847\pi\)
\(152\) −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 \(-0.378534\pi\)
0.372402 + 0.928071i \(0.378534\pi\)
\(158\) 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 −0.980116 0.198425i \(-0.936417\pi\)
0.318217 0.948018i \(-0.396916\pi\)
\(164\) 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 \(-0.102859\pi\)
−0.749124 + 0.662430i \(0.769525\pi\)
\(168\) 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 \(-0.379312\pi\)
0.370133 + 0.928979i \(0.379312\pi\)
\(174\) 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 −0.890591 0.454805i \(-0.849709\pi\)
0.839168 + 0.543872i \(0.183042\pi\)
\(180\) 3.27677 + 0.194758i 0.244236 + 0.0145164i
\(181\) −5.66560 −0.421120 −0.210560 0.977581i \(-0.567529\pi\)
−0.210560 + 0.977581i \(0.567529\pi\)
\(182\) 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 −0.302471 0.953158i \(-0.597812\pi\)
0.976695 0.214631i \(-0.0688550\pi\)
\(200\) 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 0.965157 0.261672i \(-0.0842738\pi\)
−0.709193 + 0.705015i \(0.750940\pi\)
\(212\) −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 \(-0.798184\pi\)
0.915851 + 0.401518i \(0.131517\pi\)
\(224\) 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 0.993129 + 0.117028i \(0.0373366\pi\)
−0.395215 + 0.918589i \(0.629330\pi\)
\(228\) 0.109537 3.68913i 0.00725424 0.244318i
\(229\) −2.12746 + 3.68486i −0.140586 + 0.243503i −0.927718 0.373283i \(-0.878232\pi\)
0.787131 + 0.616785i \(0.211565\pi\)
\(230\) 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 0.999779 0.0210095i \(-0.00668801\pi\)
−0.518084 + 0.855330i \(0.673355\pi\)
\(234\) −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 0.998860 0.0477377i \(-0.0152011\pi\)
−0.540772 + 0.841169i \(0.681868\pi\)
\(240\) 17.6530 9.50489i 1.13950 0.613538i
\(241\) −3.96752 6.87194i −0.255570 0.442661i 0.709480 0.704726i \(-0.248930\pi\)
−0.965050 + 0.262065i \(0.915597\pi\)
\(242\) 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 \(-0.418225\pi\)
0.254087 + 0.967181i \(0.418225\pi\)
\(252\) 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 −0.450960 0.892544i \(-0.648918\pi\)
0.998446 0.0557293i \(-0.0177484\pi\)
\(258\) 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 0.961052 + 0.276367i \(0.0891306\pi\)
−0.241185 + 0.970479i \(0.577536\pi\)
\(264\) −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 \(-0.838559\pi\)
0.857701 + 0.514149i \(0.171892\pi\)
\(270\) −19.4835 13.6943i −1.18573 0.833409i
\(271\) 7.20749 + 12.4837i 0.437824 + 0.758334i 0.997521 0.0703635i \(-0.0224159\pi\)
−0.559697 + 0.828697i \(0.689083\pi\)
\(272\) −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 −0.981101 0.193494i \(-0.938018\pi\)
0.322980 0.946406i \(-0.395315\pi\)
\(278\) −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 −0.888260 0.459341i \(-0.848086\pi\)
0.841931 + 0.539586i \(0.181419\pi\)
\(282\) 1.21295 + 0.749157i 0.0722304 + 0.0446116i
\(283\) −2.65142 −0.157610 −0.0788051 0.996890i \(-0.525110\pi\)
−0.0788051 + 0.996890i \(0.525110\pi\)
\(284\) 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 \(-0.264784\pi\)
−0.976901 + 0.213694i \(0.931451\pi\)
\(294\) 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 \(-0.598222\pi\)
−0.303700 + 0.952768i \(0.598222\pi\)
\(308\) 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 \(-0.627075\pi\)
−0.388699 + 0.921365i \(0.627075\pi\)
\(312\) 0.497184 16.7449i 0.0281475 0.947992i
\(313\) 21.2179 1.19931 0.599653 0.800260i \(-0.295305\pi\)
0.599653 + 0.800260i \(0.295305\pi\)
\(314\) 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 −0.948380 0.317137i \(-0.897279\pi\)
0.199542 0.979889i \(-0.436055\pi\)
\(338\) 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 \(-0.966132\pi\)
0.589143 + 0.808029i \(0.299465\pi\)
\(350\) 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 −0.854011 0.520254i \(-0.825837\pi\)
−0.0235477 0.999723i \(-0.507496\pi\)
\(354\) 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 0.986669 + 0.162743i \(0.0520341\pi\)
−0.352395 + 0.935851i \(0.614633\pi\)
\(360\) 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 \(-0.144592\pi\)
−0.829296 + 0.558810i \(0.811258\pi\)
\(368\) −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 −0.0745621 0.997216i \(-0.523756\pi\)
0.900896 0.434036i \(-0.142911\pi\)
\(374\) −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 \(-0.847432\pi\)
0.843037 + 0.537855i \(0.180765\pi\)
\(384\) 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 0.971626 0.236523i \(-0.0760079\pi\)
−0.690648 + 0.723191i \(0.742675\pi\)
\(390\) −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 −0.986331 0.164777i \(-0.947310\pi\)
0.350464 0.936576i \(-0.386024\pi\)
\(398\) 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 0.00704089 0.999975i \(-0.497759\pi\)
0.862483 0.506085i \(-0.168908\pi\)
\(402\) 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 \(-0.648971\pi\)
−0.451107 + 0.892470i \(0.648971\pi\)
\(410\) 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 \(-0.232560\pi\)
−0.950303 + 0.311326i \(0.899227\pi\)
\(420\) 0 0
\(421\) 0.144291 0.249919i 0.00703230 0.0121803i −0.862488 0.506078i \(-0.831095\pi\)
0.869520 + 0.493897i \(0.164428\pi\)
\(422\) 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 −0.656482 0.754341i \(-0.727956\pi\)
0.981520 + 0.191360i \(0.0612898\pi\)
\(432\) 1.51709 16.9915i 0.0729911 0.817505i
\(433\) −4.85211 −0.233177 −0.116589 0.993180i \(-0.537196\pi\)
−0.116589 + 0.993180i \(0.537196\pi\)
\(434\) 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 \(-0.480634\pi\)
0.0608031 + 0.998150i \(0.480634\pi\)
\(440\) −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 \(-0.806226\pi\)
0.905415 + 0.424527i \(0.139560\pi\)
\(462\) 0 0
\(463\) −15.4052 26.6825i −0.715939 1.24004i −0.962596 0.270940i \(-0.912666\pi\)
0.246657 0.969103i \(-0.420668\pi\)
\(464\) −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 \(-0.324615\pi\)
−0.999625 + 0.0273858i \(0.991282\pi\)
\(468\) 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 −0.996006 0.0892833i \(-0.971542\pi\)
0.420682 0.907208i \(-0.361791\pi\)
\(480\) −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 −0.209173 0.977879i \(-0.567077\pi\)
0.951454 0.307791i \(-0.0995896\pi\)
\(488\) 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 0.903003 0.429634i \(-0.141357\pi\)
−0.823575 + 0.567207i \(0.808024\pi\)
\(492\) −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 −0.986268 0.165152i \(-0.947188\pi\)
0.636160 + 0.771557i \(0.280522\pi\)
\(500\) −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 \(-0.803086\pi\)
−0.814678 + 0.579913i \(0.803086\pi\)
\(504\) 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 −0.0602789 0.998182i \(-0.519199\pi\)
0.894590 0.446888i \(-0.147468\pi\)
\(510\) −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 \(-0.731606\pi\)
0.979262 + 0.202600i \(0.0649392\pi\)
\(522\) 10.5992 + 0.629973i 0.463914 + 0.0275732i
\(523\) −5.24222 9.07980i −0.229226 0.397032i 0.728353 0.685202i \(-0.240286\pi\)
−0.957579 + 0.288171i \(0.906953\pi\)
\(524\) −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 0.612430 + 0.790524i \(0.290192\pi\)
0.378399 + 0.925643i \(0.376475\pi\)
\(542\) 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 0.478962 + 0.877836i \(0.341013\pi\)
−0.999709 + 0.0241250i \(0.992320\pi\)
\(548\) 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 0.335840 + 0.941919i \(0.390980\pi\)
−0.983646 + 0.180114i \(0.942353\pi\)
\(558\) −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 \(-0.440444\pi\)
0.186010 + 0.982548i \(0.440444\pi\)
\(564\) −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 \(-0.886000\pi\)
0.771847 + 0.635808i \(0.219333\pi\)
\(578\) −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 \(-0.956447\pi\)
0.613451 + 0.789733i \(0.289781\pi\)
\(588\) 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 0.995152 + 0.0983450i \(0.0313549\pi\)
−0.412407 + 0.911000i \(0.635312\pi\)
\(594\) 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 \(-0.916254\pi\)
0.708023 + 0.706189i \(0.249587\pi\)
\(602\) 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 \(-0.995462\pi\)
0.512295 + 0.858810i \(0.328796\pi\)
\(608\) 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 −0.419499 0.907756i \(-0.637794\pi\)
0.995889 0.0905814i \(-0.0288725\pi\)
\(614\) −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 0.718004 0.696039i \(-0.245056\pi\)
−0.961789 + 0.273791i \(0.911722\pi\)
\(618\) −4.62991 + 2.49288i −0.186242 + 0.100278i
\(619\) 13.2870 + 23.0137i 0.534048 + 0.924998i 0.999209 + 0.0397721i \(0.0126632\pi\)
−0.465161 + 0.885226i \(0.654003\pi\)
\(620\) −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 −0.984645 0.174568i \(-0.944147\pi\)
0.341142 0.940012i \(-0.389186\pi\)
\(642\) −0.148582 + 5.00416i −0.00586407 + 0.197498i
\(643\) 21.5327 + 37.2957i 0.849166 + 1.47080i 0.881953 + 0.471337i \(0.156228\pi\)
−0.0327873 + 0.999462i \(0.510438\pi\)
\(644\) 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 −0.0914143 + 0.995813i \(0.529139\pi\)
−0.816692 + 0.577074i \(0.804195\pi\)
\(648\) 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 0.362182 + 0.932107i \(0.382032\pi\)
−0.988320 + 0.152395i \(0.951301\pi\)
\(654\) 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 −0.200490 0.979696i \(-0.564253\pi\)
0.948686 0.316219i \(-0.102413\pi\)
\(660\) −1.90030 1.17368i −0.0739692 0.0456856i
\(661\) 28.0260 1.09009 0.545043 0.838408i \(-0.316513\pi\)
0.545043 + 0.838408i \(0.316513\pi\)
\(662\) −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 −0.850270 0.526347i \(-0.823561\pi\)
0.880965 + 0.473182i \(0.156895\pi\)
\(674\) −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 \(-0.799308\pi\)
−0.807737 + 0.589543i \(0.799308\pi\)
\(678\) −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 0.290321 + 0.956929i \(0.406238\pi\)
−0.973886 + 0.227039i \(0.927095\pi\)
\(684\) 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 \(-0.925358\pi\)
−0.972632 + 0.232351i \(0.925358\pi\)
\(692\) −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 \(-0.130299\pi\)
−0.803378 + 0.595470i \(0.796966\pi\)
\(720\) 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 0.0766087 + 0.997061i \(0.475591\pi\)
−0.901785 + 0.432186i \(0.857743\pi\)
\(728\) 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 \(-0.775183\pi\)
0.942449 + 0.334349i \(0.108516\pi\)
\(734\) 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 −0.969659 0.244461i \(-0.921389\pi\)
0.696539 + 0.717519i \(0.254722\pi\)
\(740\) 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 0.804815 0.593525i \(-0.202264\pi\)
−0.916416 + 0.400228i \(0.868931\pi\)
\(744\) 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 −0.994329 0.106349i \(-0.966084\pi\)
0.589266 + 0.807939i \(0.299417\pi\)
\(752\) −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 \(-0.794277\pi\)
0.920710 + 0.390247i \(0.127610\pi\)
\(762\) −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 −0.942757 0.333482i \(-0.891776\pi\)
0.182575 0.983192i \(-0.441557\pi\)
\(770\) 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 \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147774\pi\)
\(774\) 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 0.848713i