Properties

Label 27.8.e.a.4.11
Level 27
Weight 8
Character 27.4
Analytic conductor 8.434
Analytic rank 0
Dimension 120
CM No

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 27.e (of order \(9\) and degree \(6\))

Newform invariants

Self dual: No
Analytic conductor: \(8.43439568807\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{9})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.11
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.493529 - 0.179630i) q^{2} +(-38.9037 + 25.9520i) q^{3} +(-97.8424 - 82.0995i) q^{4} +(-47.2754 + 268.112i) q^{5} +(23.8618 - 5.81978i) q^{6} +(932.688 - 782.618i) q^{7} +(67.1535 + 116.313i) q^{8} +(839.991 - 2019.25i) q^{9} +O(q^{10})\) \(q+(-0.493529 - 0.179630i) q^{2} +(-38.9037 + 25.9520i) q^{3} +(-97.8424 - 82.0995i) q^{4} +(-47.2754 + 268.112i) q^{5} +(23.8618 - 5.81978i) q^{6} +(932.688 - 782.618i) q^{7} +(67.1535 + 116.313i) q^{8} +(839.991 - 2019.25i) q^{9} +(71.4927 - 123.829i) q^{10} +(163.525 + 927.398i) q^{11} +(5937.07 + 654.770i) q^{12} +(7907.66 - 2878.15i) q^{13} +(-600.890 + 218.706i) q^{14} +(-5118.85 - 11657.4i) q^{15} +(2826.67 + 16030.9i) q^{16} +(10208.4 - 17681.4i) q^{17} +(-777.278 + 845.672i) q^{18} +(-23788.0 - 41202.0i) q^{19} +(26637.4 - 22351.5i) q^{20} +(-15974.5 + 54651.8i) q^{21} +(85.8839 - 487.072i) q^{22} +(62547.7 + 52483.8i) q^{23} +(-5631.07 - 2782.25i) q^{24} +(3764.23 + 1370.07i) q^{25} -4419.66 q^{26} +(19724.8 + 100356. i) q^{27} -155509. q^{28} +(-147074. - 53530.6i) q^{29} +(432.277 + 6672.78i) q^{30} +(-79745.9 - 66914.7i) q^{31} +(4469.81 - 25349.6i) q^{32} +(-30429.5 - 31835.4i) q^{33} +(-8214.22 + 6892.55i) q^{34} +(165736. + 287064. i) q^{35} +(-247966. + 128606. i) q^{36} +(108488. - 187906. i) q^{37} +(4338.95 + 24607.4i) q^{38} +(-232943. + 317190. i) q^{39} +(-34359.7 + 12505.9i) q^{40} +(708955. - 258038. i) q^{41} +(17701.0 - 24102.7i) q^{42} +(-51214.9 - 290454. i) q^{43} +(60139.2 - 104164. i) q^{44} +(501676. + 320673. i) q^{45} +(-21441.5 - 37137.7i) q^{46} +(708465. - 594473. i) q^{47} +(-526000. - 550301. i) q^{48} +(114409. - 648846. i) q^{49} +(-1611.65 - 1352.34i) q^{50} +(61724.3 + 952798. i) q^{51} +(-1.01000e6 - 367610. i) q^{52} +161235. q^{53} +(8292.11 - 53071.6i) q^{54} -256378. q^{55} +(153662. + 55928.4i) q^{56} +(1.99471e6 + 985564. i) q^{57} +(62969.6 + 52837.8i) q^{58} +(124070. - 703638. i) q^{59} +(-456230. + 1.56085e6i) q^{60} +(-768904. + 645187. i) q^{61} +(27337.0 + 47349.1i) q^{62} +(-796854. - 2.54073e6i) q^{63} +(1.03504e6 - 1.79275e6i) q^{64} +(397830. + 2.25621e6i) q^{65} +(9299.27 + 21177.7i) q^{66} +(270542. - 98469.2i) q^{67} +(-2.45044e6 + 891889. i) q^{68} +(-3.79539e6 - 418575. i) q^{69} +(-30230.5 - 171445. i) q^{70} +(331804. - 574701. i) q^{71} +(291274. - 37897.8i) q^{72} +(1.60739e6 + 2.78409e6i) q^{73} +(-87295.3 + 73249.4i) q^{74} +(-181999. + 44388.5i) q^{75} +(-1.05519e6 + 5.98428e6i) q^{76} +(878317. + 736995. i) q^{77} +(171941. - 114699. i) q^{78} +(-385748. - 140401. i) q^{79} -4.43170e6 q^{80} +(-3.37180e6 - 3.39231e6i) q^{81} -396241. q^{82} +(-9.30945e6 - 3.38836e6i) q^{83} +(6.04987e6 - 4.03576e6i) q^{84} +(4.25800e6 + 3.57288e6i) q^{85} +(-26898.2 + 152547. i) q^{86} +(7.11095e6 - 1.73433e6i) q^{87} +(-96887.4 + 81298.2i) q^{88} +(5.57596e6 + 9.65785e6i) q^{89} +(-189989. - 248377. i) q^{90} +(5.12289e6 - 8.87310e6i) q^{91} +(-1.81093e6 - 1.02703e7i) q^{92} +(4.83897e6 + 533667. i) q^{93} +(-456433. + 166128. i) q^{94} +(1.21713e7 - 4.43001e6i) q^{95} +(483979. + 1.10219e6i) q^{96} +(270092. + 1.53177e6i) q^{97} +(-173016. + 299673. i) q^{98} +(2.01001e6 + 448807. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} + O(q^{10}) \) \( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} - 3q^{10} + 9399q^{11} - 10545q^{12} - 6q^{13} + 16647q^{14} + 11709q^{15} + 378q^{16} - 58959q^{17} - 156051q^{18} - 3q^{19} + 240243q^{20} - 516q^{21} + 105762q^{22} - 144084q^{23} - 150894q^{24} - 107997q^{25} + 443202q^{26} + 114363q^{27} - 12q^{28} + 107886q^{29} - 179901q^{30} + 297975q^{31} - 639576q^{32} - 31338q^{33} - 265806q^{34} - 450672q^{35} + 51264q^{36} - 3q^{37} - 145596q^{38} + 1919661q^{39} + 283521q^{40} + 227085q^{41} + 3792042q^{42} - 1080969q^{43} - 1205115q^{44} - 4430925q^{45} - 3q^{46} - 5184339q^{47} - 2424039q^{48} + 976008q^{49} + 2324559q^{50} + 2918034q^{51} - 3366135q^{52} + 5631750q^{53} + 11971422q^{54} - 12q^{55} + 5254923q^{56} - 284637q^{57} + 3884295q^{58} - 12534492q^{59} - 29390886q^{60} + 3865440q^{61} - 9923646q^{62} + 3292389q^{63} - 10223619q^{64} + 17158395q^{65} + 39100653q^{66} + 5567061q^{67} + 19858455q^{68} - 12682935q^{69} - 1020993q^{70} - 18563877q^{71} - 33138540q^{72} + 3770934q^{73} - 36278085q^{74} - 26317941q^{75} - 1156998q^{76} + 8471751q^{77} + 36593658q^{78} + 16415526q^{79} + 101080590q^{80} + 45736524q^{81} - 12q^{82} + 3147699q^{83} - 27588054q^{84} - 7672131q^{85} - 70854834q^{86} - 55384731q^{87} - 34323078q^{88} - 54647613q^{89} - 25256970q^{90} + 3315066q^{91} + 73858515q^{92} + 69808065q^{93} + 22126539q^{94} + 32541447q^{95} + 33014034q^{96} + 41250117q^{97} - 88493274q^{98} - 111262167q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.493529 0.179630i −0.0436222 0.0158772i 0.320117 0.947378i \(-0.396278\pi\)
−0.363739 + 0.931501i \(0.618500\pi\)
\(3\) −38.9037 + 25.9520i −0.831891 + 0.554940i
\(4\) −97.8424 82.0995i −0.764394 0.641402i
\(5\) −47.2754 + 268.112i −0.169138 + 0.959228i 0.775557 + 0.631277i \(0.217469\pi\)
−0.944695 + 0.327950i \(0.893642\pi\)
\(6\) 23.8618 5.81978i 0.0450998 0.0109996i
\(7\) 932.688 782.618i 1.02776 0.862396i 0.0371805 0.999309i \(-0.488162\pi\)
0.990583 + 0.136912i \(0.0437179\pi\)
\(8\) 67.1535 + 116.313i 0.0463717 + 0.0803182i
\(9\) 839.991 2019.25i 0.384084 0.923298i
\(10\) 71.4927 123.829i 0.0226080 0.0391582i
\(11\) 163.525 + 927.398i 0.0370434 + 0.210083i 0.997711 0.0676158i \(-0.0215392\pi\)
−0.960668 + 0.277699i \(0.910428\pi\)
\(12\) 5937.07 + 654.770i 0.991832 + 0.109384i
\(13\) 7907.66 2878.15i 0.998266 0.363339i 0.209350 0.977841i \(-0.432865\pi\)
0.788916 + 0.614502i \(0.210643\pi\)
\(14\) −600.890 + 218.706i −0.0585257 + 0.0213016i
\(15\) −5118.85 11657.4i −0.391610 0.891834i
\(16\) 2826.67 + 16030.9i 0.172526 + 0.978446i
\(17\) 10208.4 17681.4i 0.503947 0.872861i −0.496043 0.868298i \(-0.665214\pi\)
0.999990 0.00456334i \(-0.00145256\pi\)
\(18\) −777.278 + 845.672i −0.0314139 + 0.0341781i
\(19\) −23788.0 41202.0i −0.795646 1.37810i −0.922428 0.386169i \(-0.873798\pi\)
0.126782 0.991931i \(-0.459535\pi\)
\(20\) 26637.4 22351.5i 0.744539 0.624742i
\(21\) −15974.5 + 54651.8i −0.376409 + 1.28777i
\(22\) 85.8839 487.072i 0.00171962 0.00975244i
\(23\) 62547.7 + 52483.8i 1.07192 + 0.899452i 0.995225 0.0976027i \(-0.0311174\pi\)
0.0766992 + 0.997054i \(0.475562\pi\)
\(24\) −5631.07 2782.25i −0.0831480 0.0410824i
\(25\) 3764.23 + 1370.07i 0.0481822 + 0.0175369i
\(26\) −4419.66 −0.0493154
\(27\) 19724.8 + 100356.i 0.192859 + 0.981226i
\(28\) −155509. −1.33876
\(29\) −147074. 53530.6i −1.11981 0.407576i −0.285225 0.958460i \(-0.592068\pi\)
−0.834582 + 0.550884i \(0.814291\pi\)
\(30\) 432.277 + 6672.78i 0.00292306 + 0.0451214i
\(31\) −79745.9 66914.7i −0.480775 0.403418i 0.369931 0.929059i \(-0.379381\pi\)
−0.850707 + 0.525641i \(0.823826\pi\)
\(32\) 4469.81 25349.6i 0.0241137 0.136756i
\(33\) −30429.5 31835.4i −0.147400 0.154210i
\(34\) −8214.22 + 6892.55i −0.0358418 + 0.0300749i
\(35\) 165736. + 287064.i 0.653401 + 1.13172i
\(36\) −247966. + 128606.i −0.885797 + 0.459411i
\(37\) 108488. 187906.i 0.352107 0.609866i −0.634512 0.772913i \(-0.718799\pi\)
0.986618 + 0.163047i \(0.0521321\pi\)
\(38\) 4338.95 + 24607.4i 0.0128275 + 0.0727483i
\(39\) −232943. + 317190.i −0.628817 + 0.856236i
\(40\) −34359.7 + 12505.9i −0.0848867 + 0.0308962i
\(41\) 708955. 258038.i 1.60648 0.584711i 0.625740 0.780032i \(-0.284797\pi\)
0.980739 + 0.195321i \(0.0625750\pi\)
\(42\) 17701.0 24102.7i 0.0368659 0.0501989i
\(43\) −51214.9 290454.i −0.0982329 0.557106i −0.993709 0.111996i \(-0.964276\pi\)
0.895476 0.445110i \(-0.146835\pi\)
\(44\) 60139.2 104164.i 0.106432 0.184346i
\(45\) 501676. + 320673.i 0.820690 + 0.524588i
\(46\) −21441.5 37137.7i −0.0324789 0.0562552i
\(47\) 708465. 594473.i 0.995350 0.835198i 0.00901683 0.999959i \(-0.497130\pi\)
0.986333 + 0.164761i \(0.0526854\pi\)
\(48\) −526000. 550301.i −0.686501 0.718218i
\(49\) 114409. 648846.i 0.138923 0.787871i
\(50\) −1611.65 1352.34i −0.00182338 0.00152999i
\(51\) 61724.3 + 952798.i 0.0651569 + 1.00579i
\(52\) −1.01000e6 367610.i −0.996115 0.362556i
\(53\) 161235. 0.148763 0.0743815 0.997230i \(-0.476302\pi\)
0.0743815 + 0.997230i \(0.476302\pi\)
\(54\) 8292.11 53071.6i 0.00716617 0.0458653i
\(55\) −256378. −0.207783
\(56\) 153662. + 55928.4i 0.116925 + 0.0425573i
\(57\) 1.99471e6 + 985564.i 1.42665 + 0.704892i
\(58\) 62969.6 + 52837.8i 0.0423773 + 0.0355588i
\(59\) 124070. 703638.i 0.0786477 0.446034i −0.919900 0.392154i \(-0.871730\pi\)
0.998547 0.0538798i \(-0.0171588\pi\)
\(60\) −456230. + 1.56085e6i −0.272681 + 0.932891i
\(61\) −768904. + 645187.i −0.433728 + 0.363941i −0.833356 0.552736i \(-0.813584\pi\)
0.399628 + 0.916677i \(0.369139\pi\)
\(62\) 27337.0 + 47349.1i 0.0145673 + 0.0252314i
\(63\) −796854. 2.54073e6i −0.401501 1.28016i
\(64\) 1.03504e6 1.79275e6i 0.493547 0.854848i
\(65\) 397830. + 2.25621e6i 0.179681 + 1.01902i
\(66\) 9299.27 + 21177.7i 0.00398148 + 0.00906725i
\(67\) 270542. 98469.2i 0.109894 0.0399980i −0.286488 0.958084i \(-0.592488\pi\)
0.396382 + 0.918086i \(0.370266\pi\)
\(68\) −2.45044e6 + 891889.i −0.945069 + 0.343977i
\(69\) −3.79539e6 418575.i −1.39087 0.153392i
\(70\) −30230.5 171445.i −0.0105342 0.0597424i
\(71\) 331804. 574701.i 0.110021 0.190563i −0.805757 0.592246i \(-0.798241\pi\)
0.915779 + 0.401683i \(0.131575\pi\)
\(72\) 291274. 37897.8i 0.0919683 0.0119660i
\(73\) 1.60739e6 + 2.78409e6i 0.483606 + 0.837631i 0.999823 0.0188276i \(-0.00599336\pi\)
−0.516217 + 0.856458i \(0.672660\pi\)
\(74\) −87295.3 + 73249.4i −0.0250426 + 0.0210133i
\(75\) −181999. + 44388.5i −0.0498142 + 0.0121494i
\(76\) −1.05519e6 + 5.98428e6i −0.275730 + 1.56374i
\(77\) 878317. + 736995.i 0.219247 + 0.183970i
\(78\) 171941. 114699.i 0.0410250 0.0273670i
\(79\) −385748. 140401.i −0.0880255 0.0320387i 0.297632 0.954681i \(-0.403803\pi\)
−0.385658 + 0.922642i \(0.626025\pi\)
\(80\) −4.43170e6 −0.967733
\(81\) −3.37180e6 3.39231e6i −0.704959 0.709248i
\(82\) −396241. −0.0793617
\(83\) −9.30945e6 3.38836e6i −1.78711 0.650454i −0.999408 0.0343953i \(-0.989049\pi\)
−0.787700 0.616059i \(-0.788728\pi\)
\(84\) 6.04987e6 4.03576e6i 1.11370 0.742931i
\(85\) 4.25800e6 + 3.57288e6i 0.752037 + 0.631034i
\(86\) −26898.2 + 152547.i −0.00456014 + 0.0258619i
\(87\) 7.11095e6 1.73433e6i 1.15774 0.282366i
\(88\) −96887.4 + 81298.2i −0.0151558 + 0.0127172i
\(89\) 5.57596e6 + 9.65785e6i 0.838407 + 1.45216i 0.891226 + 0.453559i \(0.149846\pi\)
−0.0528195 + 0.998604i \(0.516821\pi\)
\(90\) −189989. 248377.i −0.0274713 0.0359139i
\(91\) 5.12289e6 8.87310e6i 0.712639 1.23433i
\(92\) −1.81093e6 1.02703e7i −0.242462 1.37507i
\(93\) 4.83897e6 + 533667.i 0.623825 + 0.0687986i
\(94\) −456433. + 166128.i −0.0566799 + 0.0206298i
\(95\) 1.21713e7 4.43001e6i 1.45649 0.530117i
\(96\) 483979. + 1.10219e6i 0.0558312 + 0.127147i
\(97\) 270092. + 1.53177e6i 0.0300476 + 0.170409i 0.996139 0.0877928i \(-0.0279813\pi\)
−0.966091 + 0.258201i \(0.916870\pi\)
\(98\) −173016. + 299673.i −0.0185693 + 0.0321630i
\(99\) 2.01001e6 + 448807.i 0.208197 + 0.0464876i
\(100\) −255820. 443093.i −0.0255820 0.0443093i
\(101\) −9.96415e6 + 8.36091e6i −0.962311 + 0.807474i −0.981327 0.192345i \(-0.938391\pi\)
0.0190169 + 0.999819i \(0.493946\pi\)
\(102\) 140688. 481321.i 0.0131267 0.0449091i
\(103\) −194321. + 1.10205e6i −0.0175223 + 0.0993737i −0.992315 0.123740i \(-0.960511\pi\)
0.974792 + 0.223114i \(0.0716222\pi\)
\(104\) 865794. + 726487.i 0.0754741 + 0.0633303i
\(105\) −1.38976e7 6.86665e6i −1.17160 0.578872i
\(106\) −79574.3 28962.7i −0.00648937 0.00236194i
\(107\) −1.73090e7 −1.36593 −0.682966 0.730451i \(-0.739310\pi\)
−0.682966 + 0.730451i \(0.739310\pi\)
\(108\) 6.30924e6 1.14384e7i 0.481941 0.873744i
\(109\) 3.57204e6 0.264195 0.132097 0.991237i \(-0.457829\pi\)
0.132097 + 0.991237i \(0.457829\pi\)
\(110\) 126530. + 46053.1i 0.00906396 + 0.00329901i
\(111\) 655965. + 1.01257e7i 0.0455250 + 0.702740i
\(112\) 1.51824e7 + 1.27396e7i 1.02112 + 0.856825i
\(113\) 1.47474e6 8.36366e6i 0.0961481 0.545283i −0.898241 0.439502i \(-0.855155\pi\)
0.994390 0.105780i \(-0.0337341\pi\)
\(114\) −807411. 844714.i −0.0510420 0.0534002i
\(115\) −1.70285e7 + 1.42886e7i −1.04408 + 0.876089i
\(116\) 9.99525e6 + 1.73123e7i 0.594553 + 1.02980i
\(117\) 830646. 1.83852e7i 0.0479474 1.06125i
\(118\) −187627. + 324979.i −0.0105125 + 0.0182083i
\(119\) −4.31657e6 2.44805e7i −0.234814 1.33170i
\(120\) 1.01217e6 1.37823e6i 0.0534709 0.0728093i
\(121\) 1.74786e7 6.36170e6i 0.896930 0.326456i
\(122\) 495371. 180300.i 0.0246985 0.00898953i
\(123\) −2.08843e7 + 2.84374e7i −1.01194 + 1.37791i
\(124\) 2.30886e6 + 1.30942e7i 0.108748 + 0.616741i
\(125\) −1.11800e7 + 1.93643e7i −0.511984 + 0.886782i
\(126\) −63119.4 + 1.39706e6i −0.00281103 + 0.0622183i
\(127\) −1.53527e7 2.65916e7i −0.665076 1.15194i −0.979265 0.202584i \(-0.935066\pi\)
0.314189 0.949360i \(-0.398267\pi\)
\(128\) −3.35682e6 + 2.81670e6i −0.141479 + 0.118715i
\(129\) 9.53030e6 + 9.97061e6i 0.390879 + 0.408938i
\(130\) 208941. 1.18497e6i 0.00834109 0.0473047i
\(131\) 2.22439e7 + 1.86648e7i 0.864491 + 0.725394i 0.962931 0.269749i \(-0.0869407\pi\)
−0.0984395 + 0.995143i \(0.531385\pi\)
\(132\) 363629. + 5.61310e6i 0.0137610 + 0.212419i
\(133\) −5.44322e7 1.98117e7i −2.00620 0.730198i
\(134\) −151208. −0.00542886
\(135\) −2.78391e7 + 544109.i −0.973839 + 0.0190335i
\(136\) 2.74211e6 0.0934756
\(137\) 1.88277e7 + 6.85273e6i 0.625570 + 0.227689i 0.635302 0.772264i \(-0.280876\pi\)
−0.00973224 + 0.999953i \(0.503098\pi\)
\(138\) 1.79795e6 + 888345.i 0.0582372 + 0.0287743i
\(139\) −5.45170e6 4.57452e6i −0.172179 0.144475i 0.552626 0.833429i \(-0.313626\pi\)
−0.724805 + 0.688954i \(0.758070\pi\)
\(140\) 7.35176e6 4.16939e7i 0.226435 1.28417i
\(141\) −1.21342e7 + 4.15132e7i −0.364538 + 1.24715i
\(142\) −266988. + 224030.i −0.00782498 + 0.00656594i
\(143\) 3.96230e6 + 6.86290e6i 0.113311 + 0.196260i
\(144\) 3.47447e7 + 7.75801e6i 0.969662 + 0.216512i
\(145\) 2.13052e7 3.69017e7i 0.580360 1.00521i
\(146\) −293190. 1.66276e6i −0.00779675 0.0442176i
\(147\) 1.23879e7 + 2.82116e7i 0.321652 + 0.732516i
\(148\) −2.60417e7 + 9.47840e6i −0.660318 + 0.240336i
\(149\) 4.44226e7 1.61685e7i 1.10015 0.400422i 0.272779 0.962077i \(-0.412057\pi\)
0.827372 + 0.561655i \(0.189835\pi\)
\(150\) 97795.0 + 10785.3i 0.00236590 + 0.000260924i
\(151\) −1.09228e7 6.19465e7i −0.258176 1.46419i −0.787787 0.615948i \(-0.788773\pi\)
0.529611 0.848241i \(-0.322338\pi\)
\(152\) 3.19489e6 5.53371e6i 0.0737910 0.127810i
\(153\) −2.71283e7 3.54655e7i −0.612354 0.800545i
\(154\) −301088. 521500.i −0.00664311 0.0115062i
\(155\) 2.17107e7 1.82174e7i 0.468287 0.392940i
\(156\) 4.88329e7 1.19101e7i 1.02986 0.251177i
\(157\) −1.01165e7 + 5.73735e7i −0.208632 + 1.18321i 0.682989 + 0.730429i \(0.260680\pi\)
−0.891621 + 0.452783i \(0.850431\pi\)
\(158\) 165157. + 138584.i 0.00333118 + 0.00279519i
\(159\) −6.27265e6 + 4.18438e6i −0.123755 + 0.0825545i
\(160\) 6.58522e6 + 2.39682e6i 0.127101 + 0.0462611i
\(161\) 9.94123e7 1.87737
\(162\) 1.05472e6 + 2.27988e6i 0.0194910 + 0.0421317i
\(163\) 7.61459e7 1.37718 0.688589 0.725152i \(-0.258231\pi\)
0.688589 + 0.725152i \(0.258231\pi\)
\(164\) −9.05507e7 3.29577e7i −1.60302 0.583451i
\(165\) 9.97403e6 6.65350e6i 0.172853 0.115307i
\(166\) 3.98583e6 + 3.34451e6i 0.0676302 + 0.0567485i
\(167\) −2.03305e6 + 1.15300e7i −0.0337785 + 0.191567i −0.997028 0.0770413i \(-0.975453\pi\)
0.963249 + 0.268608i \(0.0865638\pi\)
\(168\) −7.42947e6 + 1.81201e6i −0.120886 + 0.0294835i
\(169\) 6.17918e6 5.18495e6i 0.0984754 0.0826306i
\(170\) −1.45965e6 2.52818e6i −0.0227864 0.0394673i
\(171\) −1.03179e8 + 1.34246e7i −1.57799 + 0.205313i
\(172\) −1.88352e7 + 3.26234e7i −0.282241 + 0.488855i
\(173\) 6.93835e6 + 3.93493e7i 0.101881 + 0.577798i 0.992420 + 0.122891i \(0.0392165\pi\)
−0.890539 + 0.454907i \(0.849672\pi\)
\(174\) −3.82099e6 421399.i −0.0549862 0.00606416i
\(175\) 4.58310e6 1.66811e6i 0.0646437 0.0235284i
\(176\) −1.44048e7 + 5.24290e6i −0.199164 + 0.0724899i
\(177\) 1.34340e7 + 3.05940e7i 0.182095 + 0.414696i
\(178\) −1.01706e6 5.76803e6i −0.0135169 0.0766581i
\(179\) −2.91501e7 + 5.04894e7i −0.379886 + 0.657983i −0.991045 0.133525i \(-0.957370\pi\)
0.611159 + 0.791508i \(0.290704\pi\)
\(180\) −2.27580e7 7.25628e7i −0.290858 0.927385i
\(181\) −5.86779e7 1.01633e8i −0.735529 1.27397i −0.954491 0.298240i \(-0.903600\pi\)
0.218962 0.975733i \(-0.429733\pi\)
\(182\) −4.12216e6 + 3.45891e6i −0.0506845 + 0.0425294i
\(183\) 1.31693e7 4.50547e7i 0.158849 0.543452i
\(184\) −1.90426e6 + 1.07996e7i −0.0225353 + 0.127804i
\(185\) 4.52511e7 + 3.79702e7i 0.525446 + 0.440902i
\(186\) −2.29231e6 1.13260e6i −0.0261203 0.0129057i
\(187\) 1.80670e7 + 6.57586e6i 0.202042 + 0.0735371i
\(188\) −1.18124e8 −1.29654
\(189\) 9.69374e7 + 7.81636e7i 1.04442 + 0.842148i
\(190\) −6.80267e6 −0.0719518
\(191\) −1.26890e7 4.61841e6i −0.131768 0.0479596i 0.275295 0.961360i \(-0.411225\pi\)
−0.407062 + 0.913400i \(0.633447\pi\)
\(192\) 6.25833e6 + 9.66058e7i 0.0638122 + 0.985029i
\(193\) 5.06168e7 + 4.24725e7i 0.506809 + 0.425263i 0.860005 0.510286i \(-0.170461\pi\)
−0.353196 + 0.935549i \(0.614905\pi\)
\(194\) 141853. 804487.i 0.00139486 0.00791066i
\(195\) −7.40301e7 7.74503e7i −0.714969 0.748000i
\(196\) −6.44640e7 + 5.40917e7i −0.611534 + 0.513138i
\(197\) −3.78903e7 6.56279e7i −0.353098 0.611584i 0.633692 0.773585i \(-0.281539\pi\)
−0.986791 + 0.162001i \(0.948205\pi\)
\(198\) −911379. 582557.i −0.00834394 0.00533348i
\(199\) −2.14710e7 + 3.71888e7i −0.193137 + 0.334523i −0.946288 0.323324i \(-0.895200\pi\)
0.753151 + 0.657847i \(0.228533\pi\)
\(200\) 93424.2 + 529835.i 0.000825761 + 0.00468312i
\(201\) −7.96961e6 + 1.08519e7i −0.0692230 + 0.0942584i
\(202\) 6.41946e6 2.33649e6i 0.0547985 0.0199450i
\(203\) −1.79068e8 + 6.51755e7i −1.50239 + 0.546825i
\(204\) 7.21850e7 9.82916e7i 0.595308 0.810608i
\(205\) 3.56671e7 + 2.02278e8i 0.289154 + 1.63988i
\(206\) 293864. 508988.i 0.00234213 0.00405669i
\(207\) 1.58518e8 8.22138e7i 1.24217 0.644241i
\(208\) 6.84916e7 + 1.18631e8i 0.527735 + 0.914063i
\(209\) 3.43207e7 2.87985e7i 0.260042 0.218202i
\(210\) 5.62542e6 + 5.88532e6i 0.0419167 + 0.0438533i
\(211\) 2.58685e7 1.46708e8i 0.189576 1.07514i −0.730358 0.683064i \(-0.760647\pi\)
0.919934 0.392073i \(-0.128242\pi\)
\(212\) −1.57757e7 1.32374e7i −0.113714 0.0954170i
\(213\) 2.00624e6 + 3.09690e7i 0.0142250 + 0.219583i
\(214\) 8.54249e6 + 3.10921e6i 0.0595849 + 0.0216871i
\(215\) 8.02955e7 0.551007
\(216\) −1.03481e7 + 9.03350e6i −0.0698671 + 0.0609913i
\(217\) −1.26747e8 −0.842030
\(218\) −1.76291e6 641645.i −0.0115247 0.00419466i
\(219\) −1.34786e8 6.65961e7i −0.867142 0.428445i
\(220\) 2.50846e7 + 2.10485e7i 0.158828 + 0.133273i
\(221\) 2.98345e7 1.69200e8i 0.185928 1.05445i
\(222\) 1.49514e6 5.11516e6i 0.00917163 0.0313779i
\(223\) 1.38018e8 1.15811e8i 0.833428 0.699329i −0.122647 0.992450i \(-0.539138\pi\)
0.956075 + 0.293121i \(0.0946939\pi\)
\(224\) −1.56701e7 2.71414e7i −0.0931544 0.161348i
\(225\) 5.92844e6 6.45010e6i 0.0346978 0.0377509i
\(226\) −2.23019e6 + 3.86280e6i −0.0128517 + 0.0222599i
\(227\) 2.53958e6 + 1.44027e7i 0.0144103 + 0.0817246i 0.991165 0.132636i \(-0.0423442\pi\)
−0.976755 + 0.214361i \(0.931233\pi\)
\(228\) −1.14253e8 2.60195e8i −0.638405 1.45387i
\(229\) 1.58874e8 5.78255e7i 0.874238 0.318197i 0.134356 0.990933i \(-0.457103\pi\)
0.739882 + 0.672737i \(0.234881\pi\)
\(230\) 1.09707e7 3.99302e6i 0.0594550 0.0216398i
\(231\) −5.32962e7 5.87778e6i −0.284482 0.0313741i
\(232\) −3.65022e6 2.07014e7i −0.0191916 0.108841i
\(233\) −1.09328e8 + 1.89362e8i −0.566223 + 0.980726i 0.430712 + 0.902489i \(0.358262\pi\)
−0.996935 + 0.0782370i \(0.975071\pi\)
\(234\) −3.71248e6 + 8.92441e6i −0.0189412 + 0.0455328i
\(235\) 1.25892e8 + 2.18052e8i 0.632794 + 1.09603i
\(236\) −6.99077e7 + 5.86595e7i −0.346205 + 0.290500i
\(237\) 1.86507e7 4.54881e6i 0.0910071 0.0221962i
\(238\) −2.26707e6 + 1.28572e7i −0.0109005 + 0.0618197i
\(239\) 1.10737e8 + 9.29198e7i 0.524689 + 0.440266i 0.866263 0.499589i \(-0.166516\pi\)
−0.341574 + 0.939855i \(0.610960\pi\)
\(240\) 1.72409e8 1.15011e8i 0.805048 0.537033i
\(241\) 1.95586e8 + 7.11875e7i 0.900074 + 0.327600i 0.750282 0.661118i \(-0.229918\pi\)
0.149791 + 0.988718i \(0.452140\pi\)
\(242\) −9.76895e6 −0.0443092
\(243\) 2.19212e8 + 4.44685e7i 0.980039 + 0.198807i
\(244\) 1.28201e8 0.564972
\(245\) 1.68555e8 + 6.13489e7i 0.732251 + 0.266517i
\(246\) 1.54152e7 1.02832e7i 0.0660202 0.0440410i
\(247\) −3.06693e8 2.57346e8i −1.29498 1.08662i
\(248\) 2.42786e6 1.37691e7i 0.0101075 0.0573222i
\(249\) 4.50107e8 1.09779e8i 1.84764 0.450631i
\(250\) 8.99605e6 7.54859e6i 0.0364135 0.0305545i
\(251\) −1.32238e8 2.29043e8i −0.527836 0.914238i −0.999473 0.0324457i \(-0.989670\pi\)
0.471638 0.881792i \(-0.343663\pi\)
\(252\) −1.30626e8 + 3.14012e8i −0.514196 + 1.23607i
\(253\) −3.84452e7 + 6.65891e7i −0.149252 + 0.258512i
\(254\) 2.80034e6 + 1.58815e7i 0.0107224 + 0.0608099i
\(255\) −2.58375e8 2.84949e7i −0.975798 0.107616i
\(256\) −2.46829e8 + 8.98382e7i −0.919508 + 0.334673i
\(257\) −5.02354e8 + 1.82842e8i −1.84605 + 0.671908i −0.858895 + 0.512151i \(0.828849\pi\)
−0.987156 + 0.159757i \(0.948929\pi\)
\(258\) −2.91246e6 6.63271e6i −0.0105582 0.0240448i
\(259\) −4.58736e7 2.60162e8i −0.164064 0.930454i
\(260\) 1.46309e8 2.53414e8i 0.516255 0.894179i
\(261\) −2.31633e8 + 2.52015e8i −0.806414 + 0.877372i
\(262\) −7.62523e6 1.32073e7i −0.0261938 0.0453690i
\(263\) 1.24293e7 1.04295e7i 0.0421311 0.0353522i −0.621479 0.783431i \(-0.713468\pi\)
0.663610 + 0.748079i \(0.269023\pi\)
\(264\) 1.65943e6 5.67721e6i 0.00555066 0.0189898i
\(265\) −7.62248e6 + 4.32292e7i −0.0251614 + 0.142698i
\(266\) 2.33051e7 + 1.95553e7i 0.0759215 + 0.0637057i
\(267\) −4.67566e8 2.31019e8i −1.50333 0.742776i
\(268\) −3.45548e7 1.25769e7i −0.109657 0.0399118i
\(269\) 3.33238e8 1.04381 0.521905 0.853004i \(-0.325222\pi\)
0.521905 + 0.853004i \(0.325222\pi\)
\(270\) 1.38371e7 + 4.73220e6i 0.0427832 + 0.0146315i
\(271\) −5.43961e8 −1.66026 −0.830128 0.557573i \(-0.811733\pi\)
−0.830128 + 0.557573i \(0.811733\pi\)
\(272\) 3.12304e8 + 1.13669e8i 0.940991 + 0.342493i
\(273\) 3.09753e7 + 4.78145e8i 0.0921394 + 1.42230i
\(274\) −8.06106e6 6.76404e6i −0.0236737 0.0198646i
\(275\) −655052. + 3.71499e6i −0.00189938 + 0.0107719i
\(276\) 3.36986e8 + 3.52554e8i 0.964783 + 1.00936i
\(277\) 7.64733e7 6.41687e7i 0.216187 0.181403i −0.528262 0.849081i \(-0.677156\pi\)
0.744450 + 0.667678i \(0.232712\pi\)
\(278\) 1.86885e6 + 3.23695e6i 0.00521697 + 0.00903605i
\(279\) −2.02104e8 + 1.04819e8i −0.557134 + 0.288953i
\(280\) −2.22595e7 + 3.85547e7i −0.0605987 + 0.104960i
\(281\) 4.45544e7 + 2.52681e8i 0.119789 + 0.679360i 0.984267 + 0.176688i \(0.0565384\pi\)
−0.864477 + 0.502672i \(0.832351\pi\)
\(282\) 1.34456e7 1.83083e7i 0.0357032 0.0486157i
\(283\) −2.67750e8 + 9.74530e7i −0.702226 + 0.255589i −0.668361 0.743837i \(-0.733004\pi\)
−0.0338650 + 0.999426i \(0.510782\pi\)
\(284\) −7.96472e7 + 2.89892e7i −0.206327 + 0.0750969i
\(285\) −3.58543e8 + 4.88214e8i −0.917453 + 1.24926i
\(286\) −722726. 4.09878e6i −0.00182681 0.0103603i
\(287\) 4.59288e8 7.95510e8i 1.14683 1.98637i
\(288\) −4.74326e7 3.03191e7i −0.117005 0.0747898i
\(289\) −3.25180e6 5.63228e6i −0.00792468 0.0137259i
\(290\) −1.71434e7 + 1.43850e7i −0.0412765 + 0.0346351i
\(291\) −5.02599e7 5.25819e7i −0.119563 0.125087i
\(292\) 7.13009e7 4.04368e8i 0.167593 0.950466i
\(293\) 1.46126e8 + 1.22615e8i 0.339385 + 0.284778i 0.796511 0.604624i \(-0.206677\pi\)
−0.457126 + 0.889402i \(0.651121\pi\)
\(294\) −1.04613e6 1.61485e7i −0.00240088 0.0370609i
\(295\) 1.82789e8 + 6.65296e7i 0.414545 + 0.150882i
\(296\) 2.91413e7 0.0653112
\(297\) −8.98443e7 + 3.47035e7i −0.198995 + 0.0768645i
\(298\) −2.48282e7 −0.0543485
\(299\) 6.45663e8 + 2.35002e8i 1.39687 + 0.508420i
\(300\) 2.14514e7 + 1.05989e7i 0.0458704 + 0.0226640i
\(301\) −2.75082e8 2.30821e8i −0.581406 0.487858i
\(302\) −5.73670e6 + 3.25344e7i −0.0119850 + 0.0679702i
\(303\) 1.70660e8 5.83859e8i 0.352437 1.20575i
\(304\) 5.93262e8 4.97806e8i 1.21113 1.01625i
\(305\) −1.36632e8 2.36654e8i −0.275743 0.477600i
\(306\) 7.01793e6 + 2.23763e7i 0.0140018 + 0.0446440i
\(307\) 1.66397e7 2.88208e7i 0.0328217 0.0568489i −0.849148 0.528155i \(-0.822884\pi\)
0.881970 + 0.471306i \(0.156217\pi\)
\(308\) −2.54297e7 1.44219e8i −0.0495922 0.281251i
\(309\) −2.10406e7 4.79168e7i −0.0405698 0.0923918i
\(310\) −1.39872e7 + 5.09094e6i −0.0266665 + 0.00970581i
\(311\) −8.73039e8 + 3.17760e8i −1.64578 + 0.599015i −0.988036 0.154225i \(-0.950712\pi\)
−0.657745 + 0.753240i \(0.728490\pi\)
\(312\) −5.25363e7 5.79397e6i −0.0979307 0.0108003i
\(313\) 6.38144e7 + 3.61910e8i 0.117629 + 0.667106i 0.985415 + 0.170168i \(0.0544311\pi\)
−0.867786 + 0.496938i \(0.834458\pi\)
\(314\) 1.52988e7 2.64982e7i 0.0278870 0.0483018i
\(315\) 7.18872e8 9.35326e7i 1.29588 0.168607i
\(316\) 2.62156e7 + 4.54068e7i 0.0467365 + 0.0809499i
\(317\) 1.18778e8 9.96668e7i 0.209425 0.175729i −0.532041 0.846718i \(-0.678575\pi\)
0.741467 + 0.670990i \(0.234130\pi\)
\(318\) 3.84737e6 938355.i 0.00670918 0.00163634i
\(319\) 2.55938e7 1.45150e8i 0.0441436 0.250351i
\(320\) 4.31725e8 + 3.62260e8i 0.736517 + 0.618011i
\(321\) 6.73384e8 4.49203e8i 1.13631 0.758009i
\(322\) −4.90628e7 1.78574e7i −0.0818949 0.0298073i
\(323\) −9.71345e8 −1.60385
\(324\) 5.13978e7 + 6.08735e8i 0.0839531 + 0.994307i
\(325\) 3.37096e7 0.0544705
\(326\) −3.75802e7 1.36781e7i −0.0600755 0.0218657i
\(327\) −1.38966e8 + 9.27015e7i −0.219781 + 0.146612i
\(328\) 7.76221e7 + 6.51326e7i 0.121458 + 0.101915i
\(329\) 1.95532e8 1.10892e9i 0.302713 1.71677i
\(330\) −6.11764e6 + 1.49206e6i −0.00937098 + 0.00228554i
\(331\) −7.15687e8 + 6.00533e8i −1.08474 + 0.910204i −0.996306 0.0858781i \(-0.972630\pi\)
−0.0884332 + 0.996082i \(0.528186\pi\)
\(332\) 6.32676e8 + 1.09583e9i 0.948851 + 1.64346i
\(333\) −2.88301e8 3.76903e8i −0.427850 0.559339i
\(334\) 3.07450e6 5.32518e6i 0.00451504 0.00782027i
\(335\) 1.36108e7 + 7.71908e7i 0.0197801 + 0.112178i
\(336\) −9.21270e8 1.01602e8i −1.32495 0.146122i
\(337\) 9.90259e8 3.60425e8i 1.40943 0.512991i 0.478469 0.878105i \(-0.341192\pi\)
0.930963 + 0.365113i \(0.118970\pi\)
\(338\) −3.98098e6 + 1.44896e6i −0.00560765 + 0.00204102i
\(339\) 1.59681e8 + 3.63649e8i 0.222614 + 0.506972i
\(340\) −1.23281e8 6.99159e8i −0.170105 0.964716i
\(341\) 4.90161e7 8.48984e7i 0.0669420 0.115947i
\(342\) 5.33332e7 + 1.19086e7i 0.0720952 + 0.0160979i
\(343\) 1.00257e8 + 1.73650e8i 0.134148 + 0.232351i
\(344\) 3.03444e7 2.54620e7i 0.0401905 0.0337239i
\(345\) 2.91654e8 9.97804e8i 0.382385 1.30821i
\(346\) 3.64404e6 2.06664e7i 0.00472951 0.0268224i
\(347\) 6.56572e8 + 5.50929e8i 0.843585 + 0.707852i 0.958367 0.285539i \(-0.0921725\pi\)
−0.114782 + 0.993391i \(0.536617\pi\)
\(348\) −8.38139e8 4.14115e8i −1.06608 0.526736i
\(349\) 2.42413e8 + 8.82313e7i 0.305258 + 0.111105i 0.490108 0.871662i \(-0.336957\pi\)
−0.184849 + 0.982767i \(0.559180\pi\)
\(350\) −2.56153e6 −0.00319346
\(351\) 4.44817e8 + 7.36808e8i 0.549043 + 0.909452i
\(352\) 2.42401e7 0.0296234
\(353\) −1.07343e9 3.90697e8i −1.29886 0.472747i −0.402236 0.915536i \(-0.631767\pi\)
−0.896626 + 0.442789i \(0.853989\pi\)
\(354\) −1.13448e6 1.75122e7i −0.00135920 0.0209811i
\(355\) 1.38398e8 + 1.16130e8i 0.164184 + 0.137767i
\(356\) 2.47339e8 1.40273e9i 0.290548 1.64778i
\(357\) 8.03247e8 + 8.40357e8i 0.934351 + 0.977518i
\(358\) 2.34558e7 1.96817e7i 0.0270184 0.0226711i
\(359\) −3.07043e7 5.31814e7i −0.0350242 0.0606637i 0.847982 0.530025i \(-0.177818\pi\)
−0.883006 + 0.469361i \(0.844484\pi\)
\(360\) −3.60925e6 + 7.98858e7i −0.00407717 + 0.0902425i
\(361\) −6.84800e8 + 1.18611e9i −0.766106 + 1.32693i
\(362\) 1.07029e7 + 6.06992e7i 0.0118583 + 0.0672516i
\(363\) −5.14884e8 + 7.01098e8i −0.564984 + 0.769317i
\(364\) −1.22971e9 + 4.47579e8i −1.33644 + 0.486424i
\(365\) −8.22438e8 + 2.99343e8i −0.885275 + 0.322214i
\(366\) −1.45926e7 + 1.98702e7i −0.0155578 + 0.0211845i
\(367\) 1.95829e8 + 1.11060e9i 0.206798 + 1.17281i 0.894585 + 0.446898i \(0.147471\pi\)
−0.687787 + 0.725913i \(0.741418\pi\)
\(368\) −6.64558e8 + 1.15105e9i −0.695129 + 1.20400i
\(369\) 7.44709e7 1.64831e9i 0.0771604 1.70784i
\(370\) −1.55122e7 2.68678e7i −0.0159208 0.0275757i
\(371\) 1.50382e8 1.26186e8i 0.152893 0.128293i
\(372\) −4.29643e8 4.49493e8i −0.432721 0.452712i
\(373\) −1.54214e8 + 8.74591e8i −0.153866 + 0.872618i 0.805949 + 0.591985i \(0.201655\pi\)
−0.959815 + 0.280633i \(0.909456\pi\)
\(374\) −7.73537e6 6.49075e6i −0.00764594 0.00641570i
\(375\) −6.75992e7 1.04349e9i −0.0661961 1.02183i
\(376\) 1.16721e8 + 4.24829e7i 0.113238 + 0.0412152i
\(377\) −1.31708e9 −1.26595
\(378\) −3.38009e7 5.59888e7i −0.0321889 0.0533188i
\(379\) 1.67723e9 1.58255 0.791273 0.611464i \(-0.209419\pi\)
0.791273 + 0.611464i \(0.209419\pi\)
\(380\) −1.55458e9 5.65819e8i −1.45335 0.528975i
\(381\) 1.28738e9 + 6.36079e8i 1.19253 + 0.589215i
\(382\) 5.43277e6 + 4.55864e6i 0.00498654 + 0.00418421i
\(383\) −1.57548e8 + 8.93496e8i −0.143290 + 0.812638i 0.825434 + 0.564498i \(0.190930\pi\)
−0.968724 + 0.248140i \(0.920181\pi\)
\(384\) 5.74935e7 1.96696e8i 0.0518155 0.177270i
\(385\) −2.39120e8 + 2.00646e8i −0.213552 + 0.179192i
\(386\) −1.73515e7 3.00537e7i −0.0153561 0.0265976i
\(387\) −6.29521e8 1.40563e8i −0.552105 0.123277i
\(388\) 9.93308e7 1.72046e8i 0.0863322 0.149532i
\(389\) 1.16419e8 + 6.60245e8i 0.100277 + 0.568698i 0.993002 + 0.118097i \(0.0376793\pi\)
−0.892725 + 0.450601i \(0.851210\pi\)
\(390\) 2.26236e7 + 5.15219e7i 0.0193124 + 0.0439811i
\(391\) 1.56650e9 5.70158e8i 1.32529 0.482366i
\(392\) 8.31523e7 3.02650e7i 0.0697225 0.0253769i
\(393\) −1.34976e9 1.48858e8i −1.12171 0.123708i
\(394\) 6.91122e6 + 3.91955e7i 0.00569269 + 0.0322849i
\(395\) 5.58795e7 9.67862e7i 0.0456208 0.0790176i
\(396\) −1.59817e8 2.08933e8i −0.129328 0.169073i
\(397\) −9.62237e8 1.66664e9i −0.771819 1.33683i −0.936565 0.350493i \(-0.886014\pi\)
0.164747 0.986336i \(-0.447319\pi\)
\(398\) 1.72767e7 1.44969e7i 0.0137363 0.0115262i
\(399\) 2.63176e9 6.41874e8i 2.07416 0.505877i
\(400\) −1.13231e7 + 6.42166e7i −0.00884619 + 0.0501692i
\(401\) 4.40541e8 + 3.69658e8i 0.341178 + 0.286282i 0.797236 0.603668i \(-0.206295\pi\)
−0.456058 + 0.889950i \(0.650739\pi\)
\(402\) 5.88256e6 3.92415e6i 0.00451622 0.00301269i
\(403\) −8.23194e8 2.99618e8i −0.626519 0.228034i
\(404\) 1.66134e9 1.25350
\(405\) 1.06892e9 7.43648e8i 0.799565 0.556256i
\(406\) 1.00083e8 0.0742196
\(407\) 1.92004e8 + 6.98838e7i 0.141166 + 0.0513802i
\(408\) −1.06678e8 + 7.11630e7i −0.0777614 + 0.0518733i
\(409\) 1.96650e9 + 1.65009e9i 1.42122 + 1.19255i 0.950680 + 0.310172i \(0.100387\pi\)
0.470544 + 0.882377i \(0.344058\pi\)
\(410\) 1.87325e7 1.06237e8i 0.0134231 0.0761259i
\(411\) −9.10309e8 + 2.22020e8i −0.646759 + 0.157741i
\(412\) 1.09491e8 9.18736e7i 0.0771324 0.0647218i
\(413\) −4.34961e8 7.53375e8i −0.303826 0.526243i
\(414\) −9.30011e7 + 1.21004e7i −0.0644150 + 0.00838105i
\(415\) 1.34857e9 2.33579e9i 0.926201 1.60423i
\(416\) −3.76142e7 2.13320e8i −0.0256168 0.145280i
\(417\) 3.30809e8 + 3.64833e7i 0.223409 + 0.0246387i
\(418\) −2.21113e7 + 8.04786e6i −0.0148080 + 0.00538969i
\(419\) −1.13159e9 + 4.11865e8i −0.751519 + 0.273531i −0.689245 0.724528i \(-0.742058\pi\)
−0.0622744 + 0.998059i \(0.519835\pi\)
\(420\) 7.96028e8 + 1.81284e9i 0.524271 + 1.19395i
\(421\) −1.30060e7 7.37604e7i −0.00849483 0.0481766i 0.980266 0.197685i \(-0.0633422\pi\)
−0.988761 + 0.149508i \(0.952231\pi\)
\(422\) −3.91199e7 + 6.77577e7i −0.0253399 + 0.0438899i
\(423\) −6.05287e8 1.92992e9i −0.388839 1.23979i
\(424\) 1.08275e7 + 1.87538e7i 0.00689840 + 0.0119484i
\(425\) 6.26514e7 5.25708e7i 0.0395885 0.0332187i
\(426\) 4.57281e6 1.56445e7i 0.00286583 0.00980453i
\(427\) −2.12212e8 + 1.20352e9i −0.131909 + 0.748091i
\(428\) 1.69355e9 + 1.42106e9i 1.04411 + 0.876112i
\(429\) −3.32254e8 1.64163e8i −0.203174 0.100386i
\(430\) −3.96282e7 1.44235e7i −0.0240361 0.00874843i
\(431\) 1.51132e9 0.909258 0.454629 0.890681i \(-0.349772\pi\)
0.454629 + 0.890681i \(0.349772\pi\)
\(432\) −1.55303e9 + 5.99879e8i −0.926803 + 0.357990i
\(433\) −1.17888e9 −0.697851 −0.348926 0.937150i \(-0.613453\pi\)
−0.348926 + 0.937150i \(0.613453\pi\)
\(434\) 6.25531e7 + 2.27675e7i 0.0367312 + 0.0133691i
\(435\) 1.28821e8 + 1.98852e9i 0.0750367 + 1.15829i
\(436\) −3.49497e8 2.93263e8i −0.201949 0.169455i
\(437\) 6.74552e8 3.82558e9i 0.386661 2.19286i
\(438\) 5.45581e7 + 5.70787e7i 0.0310241 + 0.0324575i
\(439\) −7.43788e8 + 6.24112e8i −0.419588 + 0.352076i −0.828006 0.560719i \(-0.810525\pi\)
0.408418 + 0.912795i \(0.366081\pi\)
\(440\) −1.72166e7 2.98201e7i −0.00963528 0.0166888i
\(441\) −1.21408e9 7.76045e8i −0.674082 0.430876i
\(442\) −4.51175e7 + 7.81458e7i −0.0248523 + 0.0430455i
\(443\) −5.02807e8 2.85156e9i −0.274782 1.55837i −0.739653 0.672988i \(-0.765011\pi\)
0.464871 0.885378i \(-0.346101\pi\)
\(444\) 7.67134e8 1.04458e9i 0.415940 0.566370i
\(445\) −2.85299e9 + 1.03841e9i −1.53476 + 0.558607i
\(446\) −8.89188e7 + 3.23638e7i −0.0474593 + 0.0172738i
\(447\) −1.30860e9 + 1.78187e9i −0.692994 + 0.943624i
\(448\) −4.37664e8 2.48212e9i −0.229968 1.30421i
\(449\) −1.21249e8 + 2.10010e8i −0.0632145 + 0.109491i −0.895901 0.444255i \(-0.853469\pi\)
0.832686 + 0.553745i \(0.186802\pi\)
\(450\) −4.08449e6 + 2.11838e6i −0.00211297 + 0.00109587i
\(451\) 3.55236e8 + 6.15288e8i 0.182347 + 0.315835i
\(452\) −8.30944e8 + 6.97245e8i −0.423241 + 0.355141i
\(453\) 2.03257e9 + 2.12648e9i 1.02731 + 1.07477i
\(454\) 1.33379e6 7.56432e6i 0.000668950 0.00379380i
\(455\) 2.13680e9 + 1.79299e9i 1.06347 + 0.892355i
\(456\) 1.93177e7 + 2.98195e8i 0.00954068 + 0.147273i
\(457\) −2.44595e9 8.90252e8i −1.19878 0.436321i −0.335983 0.941868i \(-0.609068\pi\)
−0.862799 + 0.505547i \(0.831291\pi\)
\(458\) −8.87963e7 −0.0431882
\(459\) 1.97579e9 + 6.75705e8i 0.953665 + 0.326147i
\(460\) 2.83920e9 1.36001
\(461\) 1.37315e9 + 4.99786e8i 0.652777 + 0.237591i 0.647115 0.762393i \(-0.275976\pi\)
0.00566198 + 0.999984i \(0.498198\pi\)
\(462\) 2.52474e7 + 1.24744e7i 0.0119116 + 0.00588538i
\(463\) −6.34521e8 5.32427e8i −0.297107 0.249302i 0.482032 0.876154i \(-0.339899\pi\)
−0.779139 + 0.626851i \(0.784343\pi\)
\(464\) 4.42411e8 2.50904e9i 0.205595 1.16599i
\(465\) −3.71847e8 + 1.27216e9i −0.171506 + 0.586754i
\(466\) 8.79718e7 7.38171e7i 0.0402710 0.0337914i
\(467\) 1.48375e9 + 2.56994e9i 0.674144 + 1.16765i 0.976718 + 0.214526i \(0.0688205\pi\)
−0.302575 + 0.953126i \(0.597846\pi\)
\(468\) −1.59069e9 + 1.73066e9i −0.717339 + 0.780459i
\(469\) 1.75267e8 3.03572e8i 0.0784506 0.135880i
\(470\) −2.29629e7 1.30229e8i −0.0102020 0.0578583i
\(471\) −1.09539e9 2.49458e9i −0.483052 1.10008i
\(472\) 9.01742e7 3.28207e7i 0.0394717 0.0143665i
\(473\) 2.60992e8 9.49932e7i 0.113400 0.0412742i
\(474\) −1.00217e7 1.10525e6i −0.00432234 0.000476690i
\(475\) −3.30940e7 1.87685e8i −0.0141684 0.0803530i
\(476\) −1.58749e9 + 2.74962e9i −0.674663 + 1.16855i
\(477\) 1.35436e8 3.25575e8i 0.0571375 0.137353i
\(478\) −3.79610e7 6.57503e7i −0.0158979 0.0275360i
\(479\) −1.56470e9 + 1.31294e9i −0.650516 + 0.545848i −0.907228 0.420640i \(-0.861805\pi\)
0.256711 + 0.966488i \(0.417361\pi\)
\(480\) −3.18391e8 + 7.76541e7i −0.131407 + 0.0320494i
\(481\) 3.17061e8 1.79814e9i 0.129908 0.736743i
\(482\) −8.37399e7 7.02661e7i −0.0340618 0.0285813i
\(483\) −3.86750e9 + 2.57994e9i −1.56177 + 1.04183i
\(484\) −2.23244e9 8.12543e8i −0.894997 0.325752i
\(485\) −4.23454e8 −0.168543
\(486\) −1.00200e8 6.13236e7i −0.0395949 0.0242326i
\(487\) −2.70444e9 −1.06102 −0.530512 0.847677i \(-0.678000\pi\)
−0.530512 + 0.847677i \(0.678000\pi\)
\(488\) −1.26678e8 4.61071e7i −0.0493438 0.0179597i
\(489\) −2.96235e9 + 1.97614e9i −1.14566 + 0.764250i
\(490\) −7.21665e7 6.05549e7i −0.0277108 0.0232522i
\(491\) −2.52759e7 + 1.43347e8i −0.00963655 + 0.0546516i −0.989247 0.146256i \(-0.953278\pi\)
0.979610 + 0.200907i \(0.0643889\pi\)
\(492\) 4.37807e9 1.06779e9i 1.65731 0.404211i
\(493\) −2.44788e9 + 2.05402e9i −0.920081 + 0.772040i
\(494\) 1.05135e8 + 1.82099e8i 0.0392376 + 0.0679615i
\(495\) −2.15355e8 + 5.17691e8i −0.0798062 + 0.191846i
\(496\) 8.47285e8 1.46754e9i 0.311777 0.540013i
\(497\) −1.40302e8 7.95693e8i −0.0512645 0.290736i
\(498\) −2.41860e8 2.66736e7i −0.0877529 0.00967784i
\(499\) 4.86034e9 1.76902e9i 1.75111 0.637354i 0.751368 0.659883i \(-0.229394\pi\)
0.999746 + 0.0225293i \(0.00717192\pi\)
\(500\) 2.68368e9 9.76779e8i 0.960142 0.349463i
\(501\) −2.20133e8 5.01320e8i −0.0782082 0.178108i
\(502\) 2.41203e7 + 1.36793e8i 0.00850982 + 0.0482616i
\(503\) −7.77740e8 + 1.34709e9i −0.272488 + 0.471962i −0.969498 0.245098i \(-0.921180\pi\)
0.697011 + 0.717061i \(0.254513\pi\)
\(504\) 2.42008e8 2.63303e8i 0.0842022 0.0916114i
\(505\) −1.77060e9 3.06678e9i −0.611789 1.05965i
\(506\) 3.09352e7 2.59577e7i 0.0106152 0.00890717i
\(507\) −1.05833e8 + 3.62076e8i −0.0360657 + 0.123388i
\(508\) −6.81016e8 + 3.86223e9i −0.230481 + 1.30712i
\(509\) 5.10836e8 + 4.28643e8i 0.171700 + 0.144073i 0.724588 0.689182i \(-0.242030\pi\)
−0.552888 + 0.833255i \(0.686474\pi\)
\(510\) 1.22397e8 + 6.04749e7i 0.0408578 + 0.0201874i
\(511\) 3.67807e9 + 1.33871e9i 1.21940 + 0.443826i
\(512\) 6.98852e8 0.230113
\(513\) 3.66564e9 3.19996e9i 1.19878 1.04649i
\(514\) 2.80770e8 0.0911968
\(515\) −2.86287e8 1.04200e8i −0.0923583 0.0336157i
\(516\) −1.13886e8 1.75798e9i −0.0364918 0.563301i
\(517\) 6.67165e8 + 5.59818e8i 0.212332 + 0.178168i
\(518\) −2.40929e7 + 1.36638e8i −0.00761615 + 0.0431933i
\(519\) −1.29112e9 1.35077e9i −0.405397 0.424127i
\(520\) −2.35711e8 + 1.97785e8i −0.0735137 + 0.0616853i
\(521\) −1.48409e9 2.57052e9i −0.459758 0.796324i 0.539190 0.842184i \(-0.318730\pi\)
−0.998948 + 0.0458604i \(0.985397\pi\)
\(522\) 1.59587e8 8.27683e7i 0.0491078 0.0254693i
\(523\) 4.56446e8 7.90588e8i 0.139519 0.241654i −0.787796 0.615937i \(-0.788778\pi\)
0.927315 + 0.374283i \(0.122111\pi\)
\(524\) −6.44020e8 3.65242e9i −0.195542 1.10897i
\(525\) −1.35009e8 + 1.83836e8i −0.0407196 + 0.0554464i
\(526\) −8.00768e6 + 2.91456e6i −0.00239915 + 0.000873218i
\(527\) −1.99722e9 + 7.26929e8i −0.594414 + 0.216349i
\(528\) 4.24334e8 5.77800e8i 0.125455 0.170828i
\(529\) 5.66431e8 + 3.21239e9i 0.166361 + 0.943481i
\(530\) 1.15272e7 1.99656e7i 0.00336323 0.00582529i
\(531\) −1.31661e9 8.41580e8i −0.381615 0.243930i
\(532\) 3.69924e9 + 6.40728e9i 1.06518 + 1.84494i
\(533\) 4.86350e9 4.08096e9i 1.39125 1.16739i
\(534\) 1.89259e8 + 1.98003e8i 0.0537852 + 0.0562701i
\(535\) 8.18291e8 4.64076e9i 0.231031 1.31024i
\(536\) 2.96211e7 + 2.48551e7i 0.00830854 + 0.00697169i
\(537\) −1.76254e8 2.72072e9i −0.0491167 0.758184i
\(538\) −1.64462e8 5.98594e7i −0.0455332 0.0165727i
\(539\) 6.20447e8 0.170665
\(540\) 2.76852e9 + 2.23234e9i 0.756605 + 0.610074i
\(541\) −5.64421e9 −1.53254 −0.766271 0.642518i \(-0.777890\pi\)
−0.766271 + 0.642518i \(0.777890\pi\)
\(542\) 2.68460e8 + 9.77116e7i 0.0724240 + 0.0263602i
\(543\) 4.92037e9 + 2.43110e9i 1.31886 + 0.651632i
\(544\) −4.02586e8 3.37810e8i −0.107217 0.0899655i
\(545\) −1.68870e8 + 9.57709e8i −0.0446853 + 0.253423i
\(546\) 7.06019e7 2.41542e8i 0.0185627 0.0635066i
\(547\) 3.67165e9 3.08088e9i 0.959193 0.804858i −0.0216288 0.999766i \(-0.506885\pi\)
0.980822 + 0.194908i \(0.0624408\pi\)
\(548\) −1.27954e9 2.21623e9i −0.332141 0.575286i
\(549\) 6.56923e8 + 2.09456e9i 0.169438 + 0.540244i
\(550\) 990609. 1.71579e6i 0.000253883 0.000439737i
\(551\) 1.29303e9 + 7.33313e9i 0.329289 + 1.86749i
\(552\) −2.06188e8 4.69563e8i −0.0521767 0.118825i
\(553\) −4.69662e8 + 1.70943e8i −0.118099 + 0.0429847i
\(554\) −4.92684e7 + 1.79322e7i −0.0123107 + 0.00448074i
\(555\) −2.74584e9 3.02825e8i −0.681788 0.0751910i
\(556\) 1.57842e8 + 8.95164e8i 0.0389457 + 0.220872i
\(557\) 1.25016e9 2.16535e9i 0.306531 0.530927i −0.671070 0.741394i \(-0.734165\pi\)
0.977601 + 0.210467i \(0.0674985\pi\)
\(558\) 1.18573e8 1.54275e7i 0.0288911 0.00375903i
\(559\) −1.24096e9 2.14941e9i −0.300481 0.520448i
\(560\) −4.13339e9 + 3.46833e9i −0.994601 + 0.834569i
\(561\) −8.73530e8 + 2.13050e8i −0.208885 + 0.0509461i
\(562\) 2.34001e7 1.32708e8i 0.00556084 0.0315371i
\(563\) −5.84216e8 4.90216e8i −0.137973 0.115773i 0.571189 0.820818i \(-0.306482\pi\)
−0.709162 + 0.705045i \(0.750927\pi\)
\(564\) 4.59545e9 3.06555e9i 1.07858 0.719500i
\(565\) 2.17268e9 + 7.90791e8i 0.506788 + 0.184456i
\(566\) 1.49648e8 0.0346907
\(567\) −5.79972e9 5.25136e8i −1.33618 0.120985i
\(568\) 8.91272e7 0.0204076
\(569\) −2.66975e9 9.71708e8i −0.607543 0.221128i 0.0198848 0.999802i \(-0.493670\pi\)
−0.627428 + 0.778675i \(0.715892\pi\)
\(570\) 2.64649e8 1.76543e8i 0.0598561 0.0399289i
\(571\) 1.72846e9 + 1.45035e9i 0.388537 + 0.326021i 0.816043 0.577991i \(-0.196163\pi\)
−0.427506 + 0.904013i \(0.640608\pi\)
\(572\) 1.75760e8 9.96785e8i 0.0392676 0.222698i
\(573\) 6.13504e8 1.49631e8i 0.136231 0.0332261i
\(574\) −3.69569e8 + 3.10105e8i −0.0815651 + 0.0684412i
\(575\) 1.63538e8 + 2.83256e8i 0.0358741 + 0.0621358i
\(576\) −2.75058e9 3.59590e9i −0.599716 0.784024i
\(577\) 1.39273e7 2.41228e7i 0.00301822 0.00522771i −0.864512 0.502612i \(-0.832373\pi\)
0.867531 + 0.497384i \(0.165706\pi\)
\(578\) 593131. + 3.36381e6i 0.000127763 + 0.000724577i
\(579\) −3.07143e9 3.38732e8i −0.657605 0.0725240i
\(580\) −5.11416e9 + 1.86140e9i −1.08837 + 0.396134i
\(581\) −1.13346e10 + 4.12546e9i −2.39767 + 0.872682i
\(582\) 1.53594e7 + 3.49789e7i 0.00322957 + 0.00735487i
\(583\) 2.63661e7 + 1.49529e8i 0.00551069 + 0.0312527i
\(584\) −2.15884e8 + 3.73922e8i −0.0448513 + 0.0776848i
\(585\) 4.89003e9 + 1.09187e9i 1.00987 + 0.225490i
\(586\) −5.00924e7 8.67625e7i −0.0102832 0.0178111i
\(587\) −2.99490e8 + 2.51302e8i −0.0611151 + 0.0512816i −0.672834 0.739794i \(-0.734923\pi\)
0.611718 + 0.791076i \(0.290479\pi\)
\(588\) 1.10410e9 3.77733e9i 0.223969 0.766239i
\(589\) −8.60027e8 + 4.87745e9i −0.173424 + 0.983535i
\(590\) −7.82608e7 6.56686e7i −0.0156878 0.0131636i
\(591\) 3.17724e9 + 1.56984e9i 0.633132 + 0.312823i
\(592\) 3.31895e9 + 1.20800e9i 0.657469 + 0.239299i
\(593\) −2.64778e9 −0.521423 −0.260712 0.965417i \(-0.583957\pi\)
−0.260712 + 0.965417i \(0.583957\pi\)
\(594\) 5.05745e7 988467.i 0.00990100 0.000193513i
\(595\) 6.76758e9 1.31712
\(596\) −5.67384e9 2.06511e9i −1.09778 0.399559i
\(597\) −1.29823e8 2.00399e9i −0.0249713 0.385466i
\(598\) −2.76440e8 2.31961e8i −0.0528623 0.0443568i
\(599\) −8.76454e8 + 4.97062e9i −0.166623 + 0.944967i 0.780752 + 0.624841i \(0.214836\pi\)
−0.947375 + 0.320126i \(0.896275\pi\)
\(600\) −1.73848e7 1.81880e7i −0.00328579 0.00343760i
\(601\) 2.40885e9 2.02126e9i 0.452636 0.379807i −0.387777 0.921753i \(-0.626757\pi\)
0.840413 + 0.541947i \(0.182312\pi\)
\(602\) 9.42986e7 + 1.63330e8i 0.0176164 + 0.0305125i
\(603\) 2.84186e7 6.29006e8i 0.00527828 0.116827i
\(604\) −4.01706e9 + 6.95775e9i −0.741786 + 1.28481i
\(605\) 8.79340e8 + 4.98699e9i 0.161441 + 0.915576i
\(606\) −1.89104e8 + 2.57496e8i −0.0345181 + 0.0470019i
\(607\) −1.30498e9 + 4.74974e8i −0.236834 + 0.0862004i −0.457710 0.889101i \(-0.651330\pi\)
0.220877 + 0.975302i \(0.429108\pi\)
\(608\) −1.15078e9 + 4.18850e8i −0.207649 + 0.0755780i
\(609\) 5.27498e9 7.18274e9i 0.946369 1.28863i
\(610\) 2.49218e7 + 1.41339e8i 0.00444555 + 0.0252120i
\(611\) 3.89132e9 6.73996e9i 0.690164 1.19540i
\(612\) −2.57402e8 + 5.69725e9i −0.0453924 + 1.00470i
\(613\) 4.61958e9 + 8.00135e9i 0.810011 + 1.40298i 0.912855 + 0.408283i \(0.133872\pi\)
−0.102844 + 0.994698i \(0.532794\pi\)
\(614\) −1.33893e7 + 1.12349e7i −0.00233436 + 0.00195876i
\(615\) −6.63710e9 6.94374e9i −1.15058 1.20373i
\(616\) −2.67403e7 + 1.51652e8i −0.00460928 + 0.0261405i
\(617\) −6.18123e8 5.18667e8i −0.105944 0.0888977i 0.588277 0.808660i \(-0.299807\pi\)
−0.694221 + 0.719762i \(0.744251\pi\)
\(618\) 1.77683e6 + 2.74278e7i 0.000302822 + 0.00467447i
\(619\) −1.20339e9 4.38000e8i −0.203934 0.0742261i 0.238033 0.971257i \(-0.423497\pi\)
−0.441968 + 0.897031i \(0.645719\pi\)
\(620\) −3.61987e9 −0.609988
\(621\) −4.03331e9 + 7.31226e9i −0.675835 + 1.22527i
\(622\) 4.87949e8 0.0813033
\(623\) 1.27590e10 + 4.64391e9i 2.11402 + 0.769442i
\(624\) −5.74328e9 2.83769e9i −0.946268 0.467540i
\(625\) −4.42353e9 3.71179e9i −0.724752 0.608139i
\(626\) 3.35155e7 1.90076e8i 0.00546054 0.0309682i
\(627\) −5.87824e8 + 2.01106e9i −0.0952382 + 0.325828i
\(628\) 5.70016e9 4.78300e9i 0.918392 0.770622i
\(629\) −2.21496e9 3.83642e9i −0.354886 0.614680i
\(630\) −3.71585e8 8.29697e7i −0.0592061 0.0132199i
\(631\) −2.29391e9 + 3.97317e9i −0.363474 + 0.629556i −0.988530 0.151024i \(-0.951743\pi\)
0.625056 + 0.780580i \(0.285076\pi\)
\(632\) −9.57384e6 5.42959e7i −0.00150861 0.00855574i
\(633\) 2.80097e9 + 6.37880e9i 0.438930 + 0.999600i
\(634\) −7.65236e7 + 2.78523e7i −0.0119257 + 0.00434059i
\(635\) 7.85534e9 2.85911e9i 1.21747 0.443122i
\(636\) 9.57267e8 + 1.05572e8i 0.147548 + 0.0162723i
\(637\) −9.62770e8 5.46014e9i −0.147582 0.836981i
\(638\) −3.87045e7 + 6.70382e7i −0.00590051 + 0.0102200i
\(639\) −8.81755e8 1.15274e9i −0.133689 0.174775i
\(640\) −5.96498e8 1.03316e9i −0.0899454 0.155790i
\(641\) 6.13384e9 5.14690e9i 0.919876 0.771868i −0.0540959 0.998536i \(-0.517228\pi\)
0.973972 + 0.226668i \(0.0727832\pi\)
\(642\) −4.13024e8 + 1.00735e8i −0.0616032 + 0.0150247i
\(643\) 1.66141e9 9.42234e9i 0.246456 1.39772i −0.570631 0.821206i \(-0.693301\pi\)
0.817087 0.576514i \(-0.195587\pi\)
\(644\) −9.72674e9 8.16170e9i −1.43505 1.20415i
\(645\) −3.12379e9 + 2.08383e9i −0.458377 + 0.305775i
\(646\) 4.79387e8 + 1.74482e8i 0.0699636 + 0.0254647i
\(647\) 1.45730e9 0.211536 0.105768 0.994391i \(-0.466270\pi\)
0.105768 + 0.994391i \(0.466270\pi\)
\(648\) 1.68143e8 6.19990e8i 0.0242753 0.0895101i
\(649\) 6.72842e8 0.0966176
\(650\) −1.66366e7 6.05524e6i −0.00237612 0.000864838i
\(651\) 4.93091e9 3.28933e9i 0.700477 0.467276i
\(652\) −7.45030e9 6.25154e9i −1.05271 0.883325i
\(653\) −6.46360e8 + 3.66569e9i −0.0908402 + 0.515181i 0.905103 + 0.425193i \(0.139794\pi\)
−0.995943 + 0.0899875i \(0.971317\pi\)
\(654\) 8.52355e7 2.07885e7i 0.0119151 0.00290604i
\(655\) −6.05585e9 + 5.08147e9i −0.842036 + 0.706552i
\(656\) 6.14056e9 + 1.06358e10i 0.849267 + 1.47097i
\(657\) 6.97197e9 9.07125e8i 0.959128 0.124792i
\(658\) −2.95695e8 + 5.12158e8i −0.0404625 + 0.0700831i
\(659\) 1.17426e9 + 6.65955e9i 0.159832 + 0.906455i 0.954234 + 0.299062i \(0.0966736\pi\)
−0.794401 + 0.607393i \(0.792215\pi\)
\(660\) −1.52213e9 1.67868e8i −0.206086 0.0227282i
\(661\) 3.10255e9 1.12924e9i 0.417844 0.152083i −0.124538 0.992215i \(-0.539745\pi\)
0.542382 + 0.840132i \(0.317523\pi\)
\(662\) 4.61086e8 1.67821e8i 0.0617702 0.0224825i
\(663\) 3.23039e9 + 7.35675e9i 0.430485 + 0.980367i
\(664\) −2.31051e8 1.31035e9i −0.0306280 0.173700i
\(665\) 7.88507e9 1.36573e10i 1.03975 1.80090i
\(666\) 7.45819e7 + 2.37800e8i 0.00978303 + 0.0311927i
\(667\) −6.38967e9 1.10672e10i −0.833754 1.44410i
\(668\) 1.14552e9 9.61209e8i 0.148692 0.124767i
\(669\) −2.36389e9 + 8.08730e9i −0.305236 + 1.04427i
\(670\) 7.14844e6 4.05408e7i 0.000918225 0.00520751i
\(671\) −7.24080e8 6.07576e8i −0.0925248 0.0776375i
\(672\) 1.31400e9 + 6.49230e8i 0.167033 + 0.0825289i
\(673\) 4.09856e9 + 1.49175e9i 0.518297 + 0.188645i 0.587905 0.808930i \(-0.299953\pi\)
−0.0696082 + 0.997574i \(0.522175\pi\)
\(674\) −5.53464e8 −0.0696274
\(675\) −6.32455e7 + 4.04787e8i −0.00791528 + 0.0506598i
\(676\) −1.03027e9 −0.128273
\(677\) 8.60130e9 + 3.13062e9i 1.06538 + 0.387766i 0.814446 0.580239i \(-0.197041\pi\)
0.250932 + 0.968005i \(0.419263\pi\)
\(678\) −1.34847e7 2.08155e8i −0.00166164 0.0256497i
\(679\) 1.45070e9 + 1.21728e9i 0.177842 + 0.149227i
\(680\) −1.29634e8 + 7.35192e8i −0.0158102 + 0.0896644i
\(681\) −4.72577e8 4.94410e8i −0.0573400 0.0599891i
\(682\) −3.94411e7 + 3.30951e7i −0.00476107 + 0.00399501i
\(683\) −2.69251e9 4.66357e9i −0.323359 0.560075i 0.657820 0.753175i \(-0.271479\pi\)
−0.981179 + 0.193101i \(0.938146\pi\)
\(684\) 1.11974e10 + 7.15744e9i 1.33789 + 0.855188i
\(685\) −2.72739e9 + 4.72398e9i −0.324213 + 0.561553i
\(686\) −1.82869e7 1.03710e8i −0.00216275 0.0122656i
\(687\) −4.68011e9 + 6.37273e9i −0.550690 + 0.749854i
\(688\) 4.51146e9 1.64204e9i 0.528150 0.192231i
\(689\) 1.27500e9 4.64060e8i 0.148505 0.0540514i
\(690\) −3.23175e8 + 4.40055e8i −0.0374512 + 0.0509959i
\(691\) 8.76863e8 + 4.97294e9i 0.101102 + 0.573377i 0.992706 + 0.120561i \(0.0384693\pi\)
−0.891604 + 0.452816i \(0.850420\pi\)
\(692\) 2.55170e9 4.41967e9i 0.292724 0.507012i
\(693\) 2.22596e9 1.15447e9i 0.254068 0.131770i
\(694\) −2.25074e8 3.89839e8i −0.0255603 0.0442718i
\(695\) 1.48422e9 1.24541e9i 0.167707 0.140723i
\(696\) 6.79250e8 + 7.10631e8i 0.0763655 + 0.0798936i
\(697\) 2.67479e9 1.51695e10i 0.299209 1.69690i
\(698\) −1.03789e8 8.70893e7i −0.0115520 0.00969328i
\(699\) −6.61048e8 1.02042e10i −0.0732088 1.13008i
\(700\) −5.85372e8 2.13058e8i −0.0645044 0.0234777i
\(701\) −6.31602e9 −0.692517 −0.346259 0.938139i \(-0.612548\pi\)
−0.346259 + 0.938139i \(0.612548\pi\)
\(702\) −8.71771e7 4.43538e8i −0.00951092 0.0483895i
\(703\) −1.03228e10 −1.12061
\(704\) 1.83185e9 + 6.66737e8i 0.197872 + 0.0720195i
\(705\) −1.05566e10 5.21587e9i −1.13465 0.560616i
\(706\) 4.59588e8 + 3.85640e8i 0.0491533 + 0.0412445i
\(707\) −2.75004e9 + 1.55962e10i −0.292665 + 1.65979i
\(708\) 1.19734e9 4.09631e9i 0.126794 0.433787i
\(709\) 2.03372e9 1.70649e9i 0.214303 0.179822i −0.529317 0.848424i \(-0.677552\pi\)
0.743620 + 0.668603i \(0.233107\pi\)
\(710\) −4.74432e7 8.21740e7i −0.00497473 0.00861648i
\(711\) −6.07529e8 + 6.60987e8i −0.0633904 + 0.0689683i
\(712\) −7.48890e8 + 1.29712e9i −0.0777568 + 0.134679i
\(713\) −1.47599e9 8.37073e9i −0.152500 0.864868i
\(714\) −2.45472e8 5.59027e8i −0.0252382 0.0574764i
\(715\) −2.02735e9 + 7.37894e8i −0.207423 + 0.0754958i
\(716\) 6.99726e9 2.54680e9i 0.712414 0.259298i
\(717\) −6.71954e9 7.41065e8i −0.680805 0.0750826i
\(718\) 5.60049e6 + 3.17619e7i 0.000564664 + 0.00320237i
\(719\) −8.09335e9 + 1.40181e10i −0.812039 + 1.40649i 0.0993955 + 0.995048i \(0.468309\pi\)
−0.911435 + 0.411445i \(0.865024\pi\)
\(720\) −3.72259e9 + 8.94873e9i −0.371691 + 0.893506i
\(721\) 6.81244e8 + 1.17995e9i 0.0676907 + 0.117244i
\(722\) 5.51029e8 4.62368e8i 0.0544872 0.0457202i
\(723\) −9.45647e9 + 2.30639e9i −0.930561 + 0.226959i
\(724\) −2.60284e9 + 1.47615e10i −0.254896 + 1.44559i
\(725\) −4.80281e8 4.03003e8i −0.0468072 0.0392759i
\(726\) 3.80048e8 2.53524e8i 0.0368604 0.0245890i
\(727\) −3.95063e9 1.43791e9i −0.381326 0.138791i 0.144243 0.989542i \(-0.453925\pi\)
−0.525569 + 0.850751i \(0.676147\pi\)
\(728\) 1.37608e9 0.132185
\(729\) −9.68221e9 + 3.95900e9i −0.925611 + 0.378477i
\(730\) 4.59668e8 0.0437335
\(731\) −5.65845e9 2.05951e9i −0.535781 0.195008i
\(732\) −4.98749e9 + 3.32707e9i −0.469995 + 0.313525i
\(733\) −3.20213e9 2.68691e9i −0.300314 0.251993i 0.480161 0.877180i \(-0.340578\pi\)
−0.780475 + 0.625187i \(0.785023\pi\)
\(734\) 1.02850e8 5.83292e8i 0.00959994 0.0544440i
\(735\) −8.14953e9 + 1.98763e9i −0.757054 + 0.184642i
\(736\) 1.61002e9 1.35096e9i 0.148853 0.124903i
\(737\) 1.35561e8 + 2.34798e8i 0.0124738 + 0.0216052i
\(738\) −3.32839e8 + 8.00111e8i −0.0304815 + 0.0732745i
\(739\) 4.03972e9 6.99701e9i 0.368210 0.637759i −0.621075 0.783751i \(-0.713304\pi\)
0.989286 + 0.145992i \(0.0466373\pi\)
\(740\) −1.31014e9 7.43019e9i −0.118852 0.674045i
\(741\) 1.86101e10 + 2.05242e9i 1.68029 + 0.185311i
\(742\) −9.68848e7 + 3.52632e7i −0.00870646 + 0.00316889i
\(743\) 8.80255e9 3.20387e9i 0.787314 0.286559i 0.0830947 0.996542i \(-0.473520\pi\)
0.704219 + 0.709983i \(0.251297\pi\)
\(744\) 2.62881e8 + 5.98674e8i 0.0234021 + 0.0532949i
\(745\) 2.23488e9 + 1.26746e10i 0.198019 + 1.12302i
\(746\) 2.33212e8 4.03934e8i 0.0205667 0.0356225i
\(747\) −1.46618e10 + 1.59519e10i −1.28696 + 1.40021i
\(748\) −1.22785e9 2.12669e9i −0.107272 0.185801i
\(749\) −1.61439e10 + 1.35463e10i −1.40385 + 1.17797i
\(750\) −1.54079e8 + 5.27133e8i −0.0133361 + 0.0456253i
\(751\) 3.39211e8 1.92376e9i 0.0292234 0.165734i −0.966703 0.255899i \(-0.917628\pi\)
0.995927 + 0.0901653i \(0.0287395\pi\)
\(752\) 1.15325e10 + 9.67692e9i 0.988920 + 0.829802i
\(753\) 1.10887e10 + 5.47878e9i 0.946448 + 0.467629i
\(754\) 6.50018e8 + 2.36587e8i 0.0552237 + 0.0200998i
\(755\) 1.71250e10 1.44816