Properties

Label 27.8.e.a.4.19
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 4.19
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.19

$q$-expansion

\(f(q)\) \(=\) \(q+(17.6042 + 6.40739i) q^{2} +(-7.16273 + 46.2136i) q^{3} +(170.798 + 143.317i) q^{4} +(-14.0863 + 79.8875i) q^{5} +(-422.203 + 767.657i) q^{6} +(245.838 - 206.282i) q^{7} +(889.502 + 1540.66i) q^{8} +(-2084.39 - 662.031i) q^{9} +O(q^{10})\) \(q+(17.6042 + 6.40739i) q^{2} +(-7.16273 + 46.2136i) q^{3} +(170.798 + 143.317i) q^{4} +(-14.0863 + 79.8875i) q^{5} +(-422.203 + 767.657i) q^{6} +(245.838 - 206.282i) q^{7} +(889.502 + 1540.66i) q^{8} +(-2084.39 - 662.031i) q^{9} +(-759.849 + 1316.10i) q^{10} +(695.757 + 3945.83i) q^{11} +(-7846.57 + 6866.66i) q^{12} +(3689.99 - 1343.05i) q^{13} +(5649.50 - 2056.25i) q^{14} +(-3590.99 - 1223.19i) q^{15} +(831.554 + 4715.98i) q^{16} +(16679.4 - 28889.6i) q^{17} +(-32452.1 - 25010.0i) q^{18} +(22676.0 + 39275.9i) q^{19} +(-13855.2 + 11625.9i) q^{20} +(7772.17 + 12838.6i) q^{21} +(-13034.3 + 73921.1i) q^{22} +(-28585.9 - 23986.4i) q^{23} +(-77570.8 + 30071.7i) q^{24} +(67229.9 + 24469.7i) q^{25} +73564.6 q^{26} +(45524.7 - 91585.2i) q^{27} +71552.3 q^{28} +(41425.0 + 15077.4i) q^{29} +(-55379.0 - 44542.2i) q^{30} +(-181152. - 152004. i) q^{31} +(23963.5 - 135904. i) q^{32} +(-187335. + 3890.48i) q^{33} +(478734. - 401705. i) q^{34} +(13016.4 + 22545.1i) q^{35} +(-261130. - 411802. i) q^{36} +(162257. - 281038. i) q^{37} +(147535. + 836714. i) q^{38} +(35636.6 + 180147. i) q^{39} +(-135610. + 49357.8i) q^{40} +(-85992.6 + 31298.7i) q^{41} +(54560.8 + 275812. i) q^{42} +(-50011.7 - 283630. i) q^{43} +(-446670. + 773656. i) q^{44} +(82249.4 - 157191. i) q^{45} +(-349541. - 605422. i) q^{46} +(-831447. + 697667. i) q^{47} +(-223899. + 4649.82i) q^{48} +(-125123. + 709608. i) q^{49} +(1.02674e6 + 861537. i) q^{50} +(1.21562e6 + 977743. i) q^{51} +(822725. + 299447. i) q^{52} -1.18896e6 q^{53} +(1.38825e6 - 1.32059e6i) q^{54} -325024. q^{55} +(536484. + 195264. i) q^{56} +(-1.97750e6 + 766615. i) q^{57} +(632645. + 530852. i) q^{58} +(26424.9 - 149863. i) q^{59} +(-438032. - 723569. i) q^{60} +(-301592. + 253066. i) q^{61} +(-2.21507e6 - 3.83662e6i) q^{62} +(-648987. + 267221. i) q^{63} +(1.59913e6 - 2.76977e6i) q^{64} +(55314.2 + 313703. i) q^{65} +(-3.32280e6 - 1.13184e6i) q^{66} +(287638. - 104692. i) q^{67} +(6.98917e6 - 2.54385e6i) q^{68} +(1.31325e6 - 1.14925e6i) q^{69} +(84688.0 + 480289. i) q^{70} +(-2.52803e6 + 4.37868e6i) q^{71} +(-834103. - 3.80022e6i) q^{72} +(-2.37317e6 - 4.11045e6i) q^{73} +(4.65713e6 - 3.90779e6i) q^{74} +(-1.61238e6 + 2.93166e6i) q^{75} +(-1.75588e6 + 9.95812e6i) q^{76} +(984998. + 826512. i) q^{77} +(-526923. + 3.39968e6i) q^{78} +(5.52321e6 + 2.01028e6i) q^{79} -388462. q^{80} +(3.90640e6 + 2.75986e6i) q^{81} -1.71437e6 q^{82} +(-1.83860e6 - 669195. i) q^{83} +(-512510. + 3.30669e6i) q^{84} +(2.07296e6 + 1.73942e6i) q^{85} +(936917. - 5.31352e6i) q^{86} +(-993499. + 1.80640e6i) q^{87} +(-5.46032e6 + 4.58175e6i) q^{88} +(-6.02973e6 - 1.04438e7i) q^{89} +(2.45512e6 - 2.24022e6i) q^{90} +(630091. - 1.09135e6i) q^{91} +(-1.44477e6 - 8.19368e6i) q^{92} +(8.32221e6 - 7.28291e6i) q^{93} +(-1.91072e7 + 6.95443e6i) q^{94} +(-3.45708e6 + 1.25827e6i) q^{95} +(6.10897e6 + 2.08089e6i) q^{96} +(-2.26494e6 - 1.28451e7i) q^{97} +(-6.74942e6 + 1.16903e7i) q^{98} +(1.16203e6 - 8.68527e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 17.6042 + 6.40739i 1.55600 + 0.566339i 0.969816 0.243837i \(-0.0784061\pi\)
0.586187 + 0.810176i \(0.300628\pi\)
\(3\) −7.16273 + 46.2136i −0.153163 + 0.988201i
\(4\) 170.798 + 143.317i 1.33436 + 1.11966i
\(5\) −14.0863 + 79.8875i −0.0503968 + 0.285814i −0.999582 0.0289030i \(-0.990799\pi\)
0.949185 + 0.314717i \(0.101910\pi\)
\(6\) −422.203 + 767.657i −0.797979 + 1.45090i
\(7\) 245.838 206.282i 0.270898 0.227310i −0.497211 0.867630i \(-0.665643\pi\)
0.768109 + 0.640320i \(0.221198\pi\)
\(8\) 889.502 + 1540.66i 0.614231 + 1.06388i
\(9\) −2084.39 662.031i −0.953082 0.302712i
\(10\) −759.849 + 1316.10i −0.240285 + 0.416186i
\(11\) 695.757 + 3945.83i 0.157610 + 0.893849i 0.956361 + 0.292188i \(0.0943833\pi\)
−0.798751 + 0.601662i \(0.794506\pi\)
\(12\) −7846.57 + 6866.66i −1.31083 + 1.14713i
\(13\) 3689.99 1343.05i 0.465825 0.169547i −0.0984349 0.995143i \(-0.531384\pi\)
0.564260 + 0.825597i \(0.309161\pi\)
\(14\) 5649.50 2056.25i 0.550252 0.200275i
\(15\) −3590.99 1223.19i −0.274723 0.0935784i
\(16\) 831.554 + 4715.98i 0.0507541 + 0.287841i
\(17\) 16679.4 28889.6i 0.823397 1.42616i −0.0797419 0.996816i \(-0.525410\pi\)
0.903139 0.429349i \(-0.141257\pi\)
\(18\) −32452.1 25010.0i −1.31156 1.01079i
\(19\) 22676.0 + 39275.9i 0.758453 + 1.31368i 0.943639 + 0.330975i \(0.107378\pi\)
−0.185187 + 0.982703i \(0.559289\pi\)
\(20\) −13855.2 + 11625.9i −0.387263 + 0.324952i
\(21\) 7772.17 + 12838.6i 0.183136 + 0.302517i
\(22\) −13034.3 + 73921.1i −0.260980 + 1.48009i
\(23\) −28585.9 23986.4i −0.489897 0.411072i 0.364093 0.931363i \(-0.381379\pi\)
−0.853989 + 0.520291i \(0.825824\pi\)
\(24\) −77570.8 + 30071.7i −1.14540 + 0.444037i
\(25\) 67229.9 + 24469.7i 0.860543 + 0.313212i
\(26\) 73564.6 0.820847
\(27\) 45524.7 91585.2i 0.445117 0.895472i
\(28\) 71552.3 0.615986
\(29\) 41425.0 + 15077.4i 0.315405 + 0.114798i 0.494872 0.868966i \(-0.335215\pi\)
−0.179467 + 0.983764i \(0.557437\pi\)
\(30\) −55379.0 44542.2i −0.374473 0.301195i
\(31\) −181152. 152004.i −1.09214 0.916411i −0.0952644 0.995452i \(-0.530370\pi\)
−0.996871 + 0.0790413i \(0.974814\pi\)
\(32\) 23963.5 135904.i 0.129278 0.733175i
\(33\) −187335. + 3890.48i −0.907443 + 0.0188453i
\(34\) 478734. 401705.i 2.08890 1.75280i
\(35\) 13016.4 + 22545.1i 0.0513161 + 0.0888821i
\(36\) −261130. 411802.i −0.932821 1.47106i
\(37\) 162257. 281038.i 0.526621 0.912135i −0.472897 0.881117i \(-0.656792\pi\)
0.999519 0.0310175i \(-0.00987477\pi\)
\(38\) 147535. + 836714.i 0.436168 + 2.47363i
\(39\) 35636.6 + 180147.i 0.0961988 + 0.486297i
\(40\) −135610. + 49357.8i −0.335027 + 0.121940i
\(41\) −85992.6 + 31298.7i −0.194858 + 0.0709224i −0.437606 0.899167i \(-0.644173\pi\)
0.242748 + 0.970089i \(0.421951\pi\)
\(42\) 54560.8 + 275812.i 0.113634 + 0.574434i
\(43\) −50011.7 283630.i −0.0959250 0.544018i −0.994460 0.105116i \(-0.966479\pi\)
0.898535 0.438902i \(-0.144632\pi\)
\(44\) −446670. + 773656.i −0.790501 + 1.36919i
\(45\) 82249.4 157191.i 0.134552 0.257149i
\(46\) −349541. 605422.i −0.529475 0.917077i
\(47\) −831447. + 697667.i −1.16813 + 0.980179i −0.999984 0.00558270i \(-0.998223\pi\)
−0.168148 + 0.985762i \(0.553779\pi\)
\(48\) −223899. + 4649.82i −0.292218 + 0.00606864i
\(49\) −125123. + 709608.i −0.151933 + 0.861652i
\(50\) 1.02674e6 + 861537.i 1.16162 + 0.974717i
\(51\) 1.21562e6 + 977743.i 1.28322 + 1.03212i
\(52\) 822725. + 299447.i 0.811415 + 0.295331i
\(53\) −1.18896e6 −1.09699 −0.548495 0.836154i \(-0.684799\pi\)
−0.548495 + 0.836154i \(0.684799\pi\)
\(54\) 1.38825e6 1.32059e6i 1.19974 1.14127i
\(55\) −325024. −0.263418
\(56\) 536484. + 195264.i 0.408224 + 0.148581i
\(57\) −1.97750e6 + 766615.i −1.41435 + 0.548296i
\(58\) 632645. + 530852.i 0.425757 + 0.357253i
\(59\) 26424.9 149863.i 0.0167506 0.0949974i −0.975286 0.220945i \(-0.929086\pi\)
0.992037 + 0.125947i \(0.0401970\pi\)
\(60\) −438032. 723569.i −0.261804 0.432465i
\(61\) −301592. + 253066.i −0.170124 + 0.142751i −0.723875 0.689932i \(-0.757641\pi\)
0.553750 + 0.832683i \(0.313196\pi\)
\(62\) −2.21507e6 3.83662e6i −1.18037 2.04446i
\(63\) −648987. + 267221.i −0.326997 + 0.134641i
\(64\) 1.59913e6 2.76977e6i 0.762523 1.32073i
\(65\) 55314.2 + 313703.i 0.0249827 + 0.141684i
\(66\) −3.32280e6 1.13184e6i −1.42266 0.484597i
\(67\) 287638. 104692.i 0.116838 0.0425255i −0.282940 0.959138i \(-0.591310\pi\)
0.399778 + 0.916612i \(0.369087\pi\)
\(68\) 6.98917e6 2.54385e6i 2.69553 0.981094i
\(69\) 1.31325e6 1.14925e6i 0.481256 0.421155i
\(70\) 84688.0 + 480289.i 0.0295106 + 0.167363i
\(71\) −2.52803e6 + 4.37868e6i −0.838259 + 1.45191i 0.0530894 + 0.998590i \(0.483093\pi\)
−0.891349 + 0.453318i \(0.850240\pi\)
\(72\) −834103. 3.80022e6i −0.263364 1.19990i
\(73\) −2.37317e6 4.11045e6i −0.714001 1.23669i −0.963344 0.268271i \(-0.913548\pi\)
0.249343 0.968415i \(-0.419785\pi\)
\(74\) 4.65713e6 3.90779e6i 1.33600 1.12104i
\(75\) −1.61238e6 + 2.93166e6i −0.441320 + 0.802416i
\(76\) −1.75588e6 + 9.95812e6i −0.458826 + 2.60213i
\(77\) 984998. + 826512.i 0.245877 + 0.206315i
\(78\) −526923. + 3.39968e6i −0.125723 + 0.811162i
\(79\) 5.52321e6 + 2.01028e6i 1.26037 + 0.458736i 0.883892 0.467691i \(-0.154914\pi\)
0.376474 + 0.926427i \(0.377136\pi\)
\(80\) −388462. −0.0848268
\(81\) 3.90640e6 + 2.75986e6i 0.816731 + 0.577019i
\(82\) −1.71437e6 −0.343365
\(83\) −1.83860e6 669195.i −0.352950 0.128463i 0.159460 0.987204i \(-0.449025\pi\)
−0.512410 + 0.858741i \(0.671247\pi\)
\(84\) −512510. + 3.30669e6i −0.0943463 + 0.608718i
\(85\) 2.07296e6 + 1.73942e6i 0.366122 + 0.307213i
\(86\) 936917. 5.31352e6i 0.158839 0.900819i
\(87\) −993499. + 1.80640e6i −0.161752 + 0.294101i
\(88\) −5.46032e6 + 4.58175e6i −0.854139 + 0.716708i
\(89\) −6.02973e6 1.04438e7i −0.906635 1.57034i −0.818707 0.574212i \(-0.805309\pi\)
−0.0879287 0.996127i \(-0.528025\pi\)
\(90\) 2.45512e6 2.24022e6i 0.354996 0.323923i
\(91\) 630091. 1.09135e6i 0.0876513 0.151817i
\(92\) −1.44477e6 8.19368e6i −0.193437 1.09704i
\(93\) 8.32221e6 7.28291e6i 1.07287 0.938889i
\(94\) −1.91072e7 + 6.95443e6i −2.37273 + 0.863603i
\(95\) −3.45708e6 + 1.25827e6i −0.413692 + 0.150571i
\(96\) 6.10897e6 + 2.08089e6i 0.704723 + 0.240048i
\(97\) −2.26494e6 1.28451e7i −0.251974 1.42901i −0.803723 0.595004i \(-0.797151\pi\)
0.551749 0.834010i \(-0.313961\pi\)
\(98\) −6.74942e6 + 1.16903e7i −0.724395 + 1.25469i
\(99\) 1.16203e6 8.68527e6i 0.120364 0.899622i
\(100\) 7.97584e6 + 1.38146e7i 0.797584 + 1.38146i
\(101\) −1.05222e7 + 8.82914e6i −1.01620 + 0.852695i −0.989146 0.146939i \(-0.953058\pi\)
−0.0270565 + 0.999634i \(0.508613\pi\)
\(102\) 1.51352e7 + 2.50013e7i 1.41217 + 2.33272i
\(103\) 2.11875e6 1.20160e7i 0.191051 1.08350i −0.726880 0.686765i \(-0.759030\pi\)
0.917931 0.396740i \(-0.129859\pi\)
\(104\) 5.35143e6 + 4.49038e6i 0.466502 + 0.391441i
\(105\) −1.13512e6 + 440051.i −0.0956931 + 0.0370972i
\(106\) −2.09307e7 7.61814e6i −1.70692 0.621268i
\(107\) 1.62855e7 1.28516 0.642580 0.766218i \(-0.277864\pi\)
0.642580 + 0.766218i \(0.277864\pi\)
\(108\) 2.09013e7 9.11814e6i 1.59657 0.696503i
\(109\) 1.20009e7 0.887608 0.443804 0.896124i \(-0.353629\pi\)
0.443804 + 0.896124i \(0.353629\pi\)
\(110\) −5.72177e6 2.08255e6i −0.409879 0.149184i
\(111\) 1.18256e7 + 9.51150e6i 0.820714 + 0.660113i
\(112\) 1.17725e6 + 987830.i 0.0791782 + 0.0664384i
\(113\) −2.04855e6 + 1.16179e7i −0.133559 + 0.757448i 0.842294 + 0.539018i \(0.181205\pi\)
−0.975853 + 0.218430i \(0.929907\pi\)
\(114\) −3.97243e7 + 824976.i −2.51125 + 0.0521524i
\(115\) 2.31889e6 1.94578e6i 0.142180 0.119303i
\(116\) 4.91446e6 + 8.51210e6i 0.292330 + 0.506330i
\(117\) −8.58051e6 + 356546.i −0.495294 + 0.0205809i
\(118\) 1.42542e6 2.46890e6i 0.0798647 0.138330i
\(119\) −1.85898e6 1.05428e7i −0.101125 0.573511i
\(120\) −1.30967e6 6.62054e6i −0.0691874 0.349751i
\(121\) 3.22642e6 1.17432e6i 0.165567 0.0602613i
\(122\) −6.93077e6 + 2.52260e6i −0.345559 + 0.125773i
\(123\) −830485. 4.19821e6i −0.0402406 0.203421i
\(124\) −9.15564e6 5.19242e7i −0.431234 2.44565i
\(125\) −6.07059e6 + 1.05146e7i −0.278001 + 0.481511i
\(126\) −1.31371e7 + 545884.i −0.585061 + 0.0243110i
\(127\) 6.66057e6 + 1.15364e7i 0.288535 + 0.499757i 0.973460 0.228856i \(-0.0734986\pi\)
−0.684925 + 0.728613i \(0.740165\pi\)
\(128\) 3.23669e7 2.71590e7i 1.36416 1.14467i
\(129\) 1.34658e7 279651.i 0.552291 0.0114697i
\(130\) −1.03625e6 + 5.87689e6i −0.0413680 + 0.234610i
\(131\) 3.07251e6 + 2.57815e6i 0.119411 + 0.100198i 0.700538 0.713615i \(-0.252944\pi\)
−0.581127 + 0.813813i \(0.697388\pi\)
\(132\) −3.25540e7 2.61837e7i −1.23196 0.990883i
\(133\) 1.36765e7 + 4.97785e6i 0.504075 + 0.183468i
\(134\) 5.73442e6 0.205884
\(135\) 6.67524e6 + 4.92696e6i 0.233506 + 0.172350i
\(136\) 5.93454e7 2.02302
\(137\) −8.33682e6 3.03435e6i −0.276999 0.100819i 0.199785 0.979840i \(-0.435976\pi\)
−0.476784 + 0.879020i \(0.658198\pi\)
\(138\) 3.04824e7 1.18171e7i 0.987353 0.382765i
\(139\) 1.95127e7 + 1.63731e7i 0.616263 + 0.517106i 0.896626 0.442788i \(-0.146011\pi\)
−0.280363 + 0.959894i \(0.590455\pi\)
\(140\) −1.00791e6 + 5.71614e6i −0.0310437 + 0.176058i
\(141\) −2.62862e7 4.34213e7i −0.789699 1.30448i
\(142\) −7.25598e7 + 6.08849e7i −2.12661 + 1.78443i
\(143\) 7.86677e6 + 1.36256e7i 0.224968 + 0.389656i
\(144\) 1.38884e6 1.03805e7i 0.0387600 0.289700i
\(145\) −1.78803e6 + 3.09695e6i −0.0487064 + 0.0843619i
\(146\) −1.54404e7 8.75669e7i −0.410605 2.32865i
\(147\) −3.18973e7 1.08651e7i −0.828215 0.282113i
\(148\) 6.79908e7 2.47466e7i 1.72399 0.627480i
\(149\) −2.03541e6 + 740827.i −0.0504080 + 0.0183470i −0.367101 0.930181i \(-0.619650\pi\)
0.316693 + 0.948528i \(0.397427\pi\)
\(150\) −4.71690e7 + 4.12784e7i −1.14113 + 0.998626i
\(151\) −810566. 4.59695e6i −0.0191588 0.108655i 0.973729 0.227711i \(-0.0731243\pi\)
−0.992888 + 0.119056i \(0.962013\pi\)
\(152\) −4.03406e7 + 6.98721e7i −0.931731 + 1.61380i
\(153\) −5.38922e7 + 4.91749e7i −1.21648 + 1.11000i
\(154\) 1.20443e7 + 2.08613e7i 0.265741 + 0.460277i
\(155\) 1.46950e7 1.23306e7i 0.316963 0.265964i
\(156\) −1.97315e7 + 3.58762e7i −0.416125 + 0.756607i
\(157\) −9.43329e6 + 5.34989e7i −0.194542 + 1.10331i 0.718526 + 0.695500i \(0.244817\pi\)
−0.913069 + 0.407805i \(0.866294\pi\)
\(158\) 8.43508e7 + 7.07788e7i 1.70133 + 1.42759i
\(159\) 8.51621e6 5.49462e7i 0.168018 1.08405i
\(160\) 1.05195e7 + 3.82878e6i 0.203037 + 0.0738993i
\(161\) −1.19755e7 −0.226153
\(162\) 5.10854e7 + 7.36149e7i 0.944048 + 1.36039i
\(163\) 1.62948e7 0.294707 0.147354 0.989084i \(-0.452924\pi\)
0.147354 + 0.989084i \(0.452924\pi\)
\(164\) −1.91730e7 6.97841e6i −0.339420 0.123539i
\(165\) 2.32806e6 1.50205e7i 0.0403459 0.260310i
\(166\) −2.80792e7 2.35612e7i −0.476438 0.399779i
\(167\) −1.60885e7 + 9.12427e7i −0.267306 + 1.51597i 0.495080 + 0.868847i \(0.335139\pi\)
−0.762386 + 0.647122i \(0.775972\pi\)
\(168\) −1.28666e7 + 2.33942e7i −0.209353 + 0.380650i
\(169\) −3.62559e7 + 3.04223e7i −0.577797 + 0.484829i
\(170\) 2.53476e7 + 4.39034e7i 0.395700 + 0.685373i
\(171\) −2.12637e7 9.68786e7i −0.325202 1.48164i
\(172\) 3.21071e7 5.56111e7i 0.481118 0.833320i
\(173\) 4.66254e6 + 2.64426e7i 0.0684639 + 0.388278i 0.999714 + 0.0238984i \(0.00760782\pi\)
−0.931251 + 0.364380i \(0.881281\pi\)
\(174\) −2.90640e7 + 2.54344e7i −0.418248 + 0.366016i
\(175\) 2.15753e7 7.85276e6i 0.304315 0.110762i
\(176\) −1.80299e7 + 6.56235e6i −0.249287 + 0.0907330i
\(177\) 6.73642e6 + 2.29461e6i 0.0913110 + 0.0311031i
\(178\) −3.92308e7 2.22489e8i −0.521384 2.95691i
\(179\) 4.88225e7 8.45630e7i 0.636259 1.10203i −0.349988 0.936754i \(-0.613814\pi\)
0.986247 0.165279i \(-0.0528524\pi\)
\(180\) 3.65762e7 1.50603e7i 0.467461 0.192477i
\(181\) −4.56030e7 7.89867e7i −0.571634 0.990099i −0.996398 0.0847953i \(-0.972976\pi\)
0.424764 0.905304i \(-0.360357\pi\)
\(182\) 1.80849e7 1.51751e7i 0.222365 0.186587i
\(183\) −9.53486e6 1.57503e7i −0.115010 0.189981i
\(184\) 1.15278e7 6.53772e7i 0.136421 0.773685i
\(185\) 2.01658e7 + 1.69211e7i 0.234161 + 0.196485i
\(186\) 1.93170e8 7.48858e7i 2.20112 0.853305i
\(187\) 1.25598e8 + 4.57140e7i 1.40455 + 0.511215i
\(188\) −2.41997e8 −2.65618
\(189\) −7.70070e6 3.19060e7i −0.0829687 0.343761i
\(190\) −6.89213e7 −0.728980
\(191\) −5.04854e7 1.83752e7i −0.524262 0.190816i 0.0663123 0.997799i \(-0.478877\pi\)
−0.590575 + 0.806983i \(0.701099\pi\)
\(192\) 1.16547e8 + 9.37405e7i 1.18836 + 0.955813i
\(193\) 1.43673e7 + 1.20556e7i 0.143855 + 0.120709i 0.711875 0.702306i \(-0.247846\pi\)
−0.568020 + 0.823014i \(0.692291\pi\)
\(194\) 4.24313e7 2.40640e8i 0.417234 2.36625i
\(195\) −1.48935e7 + 309302.i −0.143839 + 0.00298718i
\(196\) −1.23070e8 + 1.03268e8i −1.16749 + 0.979643i
\(197\) 2.53140e7 + 4.38451e7i 0.235901 + 0.408592i 0.959534 0.281593i \(-0.0908627\pi\)
−0.723633 + 0.690184i \(0.757529\pi\)
\(198\) 7.61066e7 1.45451e8i 0.696778 1.33165i
\(199\) −3.88425e6 + 6.72771e6i −0.0349398 + 0.0605176i −0.882967 0.469436i \(-0.844457\pi\)
0.848027 + 0.529953i \(0.177791\pi\)
\(200\) 2.21016e7 + 1.25344e8i 0.195352 + 1.10790i
\(201\) 2.77790e6 + 1.40426e7i 0.0241285 + 0.121973i
\(202\) −2.41806e8 + 8.80100e7i −2.06413 + 0.751281i
\(203\) 1.32940e7 4.83863e6i 0.111537 0.0405963i
\(204\) 6.74989e7 + 3.41216e8i 0.556661 + 2.81400i
\(205\) −1.28906e6 7.31062e6i −0.0104504 0.0592674i
\(206\) 1.14290e8 1.97957e8i 0.910907 1.57774i
\(207\) 4.37044e7 + 6.89218e7i 0.342475 + 0.540083i
\(208\) 9.40220e6 + 1.62851e7i 0.0724449 + 0.125478i
\(209\) −1.39199e8 + 1.16802e8i −1.05469 + 0.884991i
\(210\) −2.28025e7 + 473551.i −0.169908 + 0.00352858i
\(211\) −4.07236e7 + 2.30955e8i −0.298441 + 1.69254i 0.354439 + 0.935079i \(0.384672\pi\)
−0.652879 + 0.757462i \(0.726439\pi\)
\(212\) −2.03073e8 1.70398e8i −1.46378 1.22826i
\(213\) −1.84247e8 1.48193e8i −1.30639 1.05075i
\(214\) 2.86692e8 + 1.04347e8i 1.99971 + 0.727836i
\(215\) 2.33630e7 0.160322
\(216\) 1.81596e8 1.13269e7i 1.22608 0.0764759i
\(217\) −7.58897e7 −0.504166
\(218\) 2.11266e8 + 7.68945e7i 1.38112 + 0.502687i
\(219\) 2.06957e8 8.02306e7i 1.33145 0.516162i
\(220\) −5.55135e7 4.65814e7i −0.351495 0.294939i
\(221\) 2.27468e7 1.29003e8i 0.141758 0.803948i
\(222\) 1.47235e8 + 2.43213e8i 0.903185 + 1.49194i
\(223\) 1.26841e8 1.06432e8i 0.765937 0.642697i −0.173728 0.984794i \(-0.555581\pi\)
0.939665 + 0.342096i \(0.111137\pi\)
\(224\) −2.21434e7 3.83536e7i −0.131637 0.228001i
\(225\) −1.23934e8 9.55126e7i −0.725355 0.559013i
\(226\) −1.10503e8 + 1.91397e8i −0.636790 + 1.10295i
\(227\) 2.29622e7 + 1.30225e8i 0.130294 + 0.738933i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.847728 + 0.530431i \(0.822030\pi\)
\(228\) −4.47623e8 1.52473e8i −2.50116 0.851964i
\(229\) −1.94255e8 + 7.07030e7i −1.06893 + 0.389057i −0.815775 0.578369i \(-0.803689\pi\)
−0.253151 + 0.967427i \(0.581467\pi\)
\(230\) 5.32894e7 1.93958e7i 0.288798 0.105114i
\(231\) −4.52513e7 + 3.96002e7i −0.241540 + 0.211376i
\(232\) 1.36183e7 + 7.72333e7i 0.0716004 + 0.406066i
\(233\) 8.13152e7 1.40842e8i 0.421140 0.729435i −0.574912 0.818216i \(-0.694964\pi\)
0.996051 + 0.0887803i \(0.0282969\pi\)
\(234\) −1.53337e8 4.87020e7i −0.782334 0.248480i
\(235\) −4.40228e7 7.62498e7i −0.221279 0.383267i
\(236\) 2.59912e7 2.18092e7i 0.128716 0.108006i
\(237\) −1.32464e8 + 2.40848e8i −0.646365 + 1.17523i
\(238\) 3.48261e7 1.97508e8i 0.167450 0.949656i
\(239\) 2.06553e8 + 1.73318e8i 0.978675 + 0.821206i 0.983889 0.178781i \(-0.0572152\pi\)
−0.00521402 + 0.999986i \(0.501660\pi\)
\(240\) 2.78245e6 1.79522e7i 0.0129923 0.0838259i
\(241\) 2.65340e8 + 9.65760e7i 1.22108 + 0.444436i 0.870533 0.492110i \(-0.163774\pi\)
0.350545 + 0.936546i \(0.385996\pi\)
\(242\) 6.43229e7 0.291750
\(243\) −1.55524e8 + 1.60761e8i −0.695303 + 0.718716i
\(244\) −8.77801e7 −0.386840
\(245\) −5.49263e7 1.99915e7i −0.238616 0.0868490i
\(246\) 1.22796e7 7.92272e7i 0.0525909 0.339314i
\(247\) 1.36423e8 + 1.14473e8i 0.576036 + 0.483352i
\(248\) 7.30526e7 4.14302e8i 0.304127 1.72479i
\(249\) 4.40953e7 8.01749e7i 0.181007 0.329110i
\(250\) −1.74239e8 + 1.46204e8i −0.705269 + 0.591791i
\(251\) −1.42767e8 2.47280e8i −0.569863 0.987032i −0.996579 0.0826461i \(-0.973663\pi\)
0.426716 0.904386i \(-0.359670\pi\)
\(252\) −1.49143e8 4.73699e7i −0.587085 0.186466i
\(253\) 7.47576e7 1.29484e8i 0.290224 0.502683i
\(254\) 4.33352e7 + 2.45766e8i 0.165929 + 0.941032i
\(255\) −9.52331e7 + 8.33401e7i −0.359664 + 0.314748i
\(256\) 3.59122e8 1.30710e8i 1.33783 0.486931i
\(257\) −2.35071e8 + 8.55587e7i −0.863838 + 0.314411i −0.735669 0.677341i \(-0.763132\pi\)
−0.128169 + 0.991752i \(0.540910\pi\)
\(258\) 2.38846e8 + 8.13576e7i 0.865862 + 0.294937i
\(259\) −1.80842e7 1.02561e8i −0.0646770 0.366801i
\(260\) −3.55113e7 + 6.15074e7i −0.125302 + 0.217030i
\(261\) −7.63640e7 5.88519e7i −0.265856 0.204889i
\(262\) 3.75699e7 + 6.50729e7i 0.129058 + 0.223535i
\(263\) −1.24431e8 + 1.04410e8i −0.421779 + 0.353914i −0.828839 0.559487i \(-0.810998\pi\)
0.407061 + 0.913401i \(0.366554\pi\)
\(264\) −1.72628e8 2.85159e8i −0.577429 0.953835i
\(265\) 1.67481e7 9.49832e7i 0.0552847 0.313535i
\(266\) 2.08869e8 + 1.75262e8i 0.680437 + 0.570955i
\(267\) 5.25835e8 2.03849e8i 1.69067 0.655420i
\(268\) 6.41321e7 + 2.33422e7i 0.203518 + 0.0740747i
\(269\) −8.57986e7 −0.268749 −0.134375 0.990931i \(-0.542903\pi\)
−0.134375 + 0.990931i \(0.542903\pi\)
\(270\) 8.59431e7 + 1.29506e8i 0.265728 + 0.400421i
\(271\) −3.21130e8 −0.980142 −0.490071 0.871683i \(-0.663029\pi\)
−0.490071 + 0.871683i \(0.663029\pi\)
\(272\) 1.50112e8 + 5.46364e7i 0.452299 + 0.164623i
\(273\) 4.59220e7 + 3.69358e7i 0.136600 + 0.109870i
\(274\) −1.27320e8 1.06835e8i −0.373914 0.313751i
\(275\) −4.97776e7 + 2.82303e8i −0.144334 + 0.818561i
\(276\) 3.89008e8 8.07873e6i 1.11372 0.0231292i
\(277\) −6.32828e7 + 5.31006e7i −0.178898 + 0.150114i −0.727840 0.685747i \(-0.759476\pi\)
0.548941 + 0.835861i \(0.315031\pi\)
\(278\) 2.38596e8 + 4.13261e8i 0.666050 + 1.15363i
\(279\) 2.76959e8 + 4.36765e8i 0.763487 + 1.20402i
\(280\) −2.31563e7 + 4.01078e7i −0.0630399 + 0.109188i
\(281\) −5.88430e7 3.33715e8i −0.158206 0.897230i −0.955796 0.294030i \(-0.905003\pi\)
0.797590 0.603200i \(-0.206108\pi\)
\(282\) −1.84530e8 9.32823e8i −0.489999 2.47701i
\(283\) 5.08679e8 1.85144e8i 1.33411 0.485576i 0.426157 0.904649i \(-0.359867\pi\)
0.907953 + 0.419073i \(0.137645\pi\)
\(284\) −1.05932e9 + 3.85562e8i −2.74419 + 0.998803i
\(285\) −3.33872e7 1.68777e8i −0.0854325 0.431873i
\(286\) 5.11831e7 + 2.90274e8i 0.129373 + 0.733713i
\(287\) −1.46838e7 + 2.54331e7i −0.0366651 + 0.0635058i
\(288\) −1.39922e8 + 2.67412e8i −0.345154 + 0.659641i
\(289\) −3.51235e8 6.08357e8i −0.855964 1.48257i
\(290\) −5.13201e7 + 4.30627e7i −0.123565 + 0.103683i
\(291\) 6.09841e8 1.26649e7i 1.45075 0.0301284i
\(292\) 1.83763e8 1.04217e9i 0.431935 2.44963i
\(293\) 9.51058e7 + 7.98033e7i 0.220887 + 0.185346i 0.746516 0.665368i \(-0.231725\pi\)
−0.525628 + 0.850714i \(0.676170\pi\)
\(294\) −4.91908e8 3.95650e8i −1.12893 0.908020i
\(295\) 1.15999e7 + 4.22203e6i 0.0263075 + 0.00957513i
\(296\) 5.77313e8 1.29387
\(297\) 3.93054e8 + 1.15912e8i 0.870572 + 0.256733i
\(298\) −4.05784e7 −0.0888256
\(299\) −1.37697e8 5.01174e7i −0.297902 0.108428i
\(300\) −6.95549e8 + 2.69642e8i −1.48732 + 0.576585i
\(301\) −7.08026e7 5.94104e7i −0.149646 0.125568i
\(302\) 1.51851e7 8.61191e7i 0.0317244 0.179918i
\(303\) −3.32659e8 5.49507e8i −0.686989 1.13481i
\(304\) −1.66368e8 + 1.39600e8i −0.339635 + 0.284988i
\(305\) −1.59685e7 2.76582e7i −0.0322266 0.0558181i
\(306\) −1.26381e9 + 5.20374e8i −2.52149 + 1.03822i
\(307\) 2.74504e8 4.75456e8i 0.541458 0.937833i −0.457362 0.889280i \(-0.651206\pi\)
0.998821 0.0485528i \(-0.0154609\pi\)
\(308\) 4.97830e7 + 2.82334e8i 0.0970854 + 0.550599i
\(309\) 5.40128e8 + 1.83983e8i 1.04146 + 0.354750i
\(310\) 3.37700e8 1.22913e8i 0.643822 0.234332i
\(311\) −2.29330e8 + 8.34692e7i −0.432314 + 0.157349i −0.549005 0.835819i \(-0.684993\pi\)
0.116692 + 0.993168i \(0.462771\pi\)
\(312\) −2.45848e8 + 2.15145e8i −0.458274 + 0.401043i
\(313\) −4.97421e7 2.82102e8i −0.0916894 0.519996i −0.995712 0.0925110i \(-0.970511\pi\)
0.904022 0.427485i \(-0.140600\pi\)
\(314\) −5.08853e8 + 8.81360e8i −0.927553 + 1.60657i
\(315\) −1.22058e7 5.56101e7i −0.0220028 0.100246i
\(316\) 6.55248e8 + 1.13492e9i 1.16816 + 2.02330i
\(317\) 9.06900e7 7.60980e7i 0.159901 0.134173i −0.559326 0.828947i \(-0.688940\pi\)
0.719228 + 0.694774i \(0.244496\pi\)
\(318\) 5.01983e8 9.12715e8i 0.875374 1.59162i
\(319\) −3.06714e7 + 1.73946e8i −0.0529013 + 0.300018i
\(320\) 1.98744e8 + 1.66766e8i 0.339055 + 0.284501i
\(321\) −1.16649e8 + 7.52610e8i −0.196839 + 1.27000i
\(322\) −2.10818e8 7.67315e7i −0.351894 0.128079i
\(323\) 1.51289e9 2.49803
\(324\) 2.71672e8 + 1.03123e9i 0.443749 + 1.68442i
\(325\) 2.80941e8 0.453967
\(326\) 2.86856e8 + 1.04407e8i 0.458566 + 0.166904i
\(327\) −8.59593e7 + 5.54605e8i −0.135949 + 0.877135i
\(328\) −1.24711e8 1.04645e8i −0.195141 0.163742i
\(329\) −6.04846e7 + 3.43025e8i −0.0936395 + 0.531056i
\(330\) 1.37226e8 2.49507e8i 0.210202 0.382194i
\(331\) −5.17169e7 + 4.33956e7i −0.0783852 + 0.0657730i −0.681138 0.732155i \(-0.738515\pi\)
0.602753 + 0.797928i \(0.294070\pi\)
\(332\) −2.18123e8 3.77799e8i −0.327128 0.566602i
\(333\) −5.24264e8 + 4.78374e8i −0.778028 + 0.709925i
\(334\) −8.67853e8 + 1.50317e9i −1.27448 + 2.20747i
\(335\) 4.31179e6 + 2.44534e7i 0.00626615 + 0.0355371i
\(336\) −5.40835e7 + 4.73294e7i −0.0777816 + 0.0680680i
\(337\) −1.15668e8 + 4.20995e7i −0.164629 + 0.0599201i −0.423020 0.906120i \(-0.639030\pi\)
0.258391 + 0.966040i \(0.416808\pi\)
\(338\) −8.33183e8 + 3.03254e8i −1.17363 + 0.427167i
\(339\) −5.22231e8 1.77887e8i −0.728054 0.247996i
\(340\) 1.04770e8 + 5.94181e8i 0.144564 + 0.819866i
\(341\) 4.73746e8 8.20553e8i 0.647002 1.12064i
\(342\) 2.46410e8 1.84171e9i 0.333093 2.48960i
\(343\) 2.47764e8 + 4.29141e8i 0.331520 + 0.574209i
\(344\) 3.92493e8 3.29341e8i 0.519849 0.436205i
\(345\) 7.33118e7 + 1.21101e8i 0.0961185 + 0.158775i
\(346\) −8.73479e7 + 4.95375e8i −0.113367 + 0.642936i
\(347\) −9.89146e8 8.29992e8i −1.27089 1.06640i −0.994433 0.105375i \(-0.966396\pi\)
−0.276456 0.961027i \(-0.589160\pi\)
\(348\) −4.28575e8 + 1.66145e8i −0.545130 + 0.211329i
\(349\) −9.35821e8 3.40611e8i −1.17843 0.428913i −0.322783 0.946473i \(-0.604618\pi\)
−0.855647 + 0.517560i \(0.826841\pi\)
\(350\) 4.30131e8 0.536244
\(351\) 4.49826e7 3.99090e8i 0.0555226 0.492602i
\(352\) 5.52927e8 0.675723
\(353\) −5.38723e8 1.96079e8i −0.651860 0.237258i −0.00514183 0.999987i \(-0.501637\pi\)
−0.646718 + 0.762729i \(0.723859\pi\)
\(354\) 1.03887e8 + 8.35577e7i 0.124465 + 0.100109i
\(355\) −3.14191e8 2.63638e8i −0.372731 0.312758i
\(356\) 4.66904e8 2.64794e9i 0.548470 3.11053i
\(357\) 5.00536e8 1.03949e7i 0.582233 0.0120915i
\(358\) 1.40131e9 1.17584e9i 1.61415 1.35443i
\(359\) −5.12115e8 8.87008e8i −0.584166 1.01181i −0.994979 0.100086i \(-0.968088\pi\)
0.410812 0.911720i \(-0.365245\pi\)
\(360\) 3.15340e8 1.31033e7i 0.356221 0.0148021i
\(361\) −5.81464e8 + 1.00713e9i −0.650501 + 1.12670i
\(362\) −2.96704e8 1.68269e9i −0.328733 1.86434i
\(363\) 3.11596e7 + 1.57516e8i 0.0341916 + 0.172843i
\(364\) 2.64027e8 9.60981e7i 0.286942 0.104438i
\(365\) 3.61803e8 1.31686e8i 0.389446 0.141747i
\(366\) −6.69349e7 3.38365e8i −0.0713623 0.360746i
\(367\) 1.38527e8 + 7.85628e8i 0.146287 + 0.829633i 0.966325 + 0.257324i \(0.0828409\pi\)
−0.820038 + 0.572308i \(0.806048\pi\)
\(368\) 8.93487e7 1.54757e8i 0.0934590 0.161876i
\(369\) 1.99963e8 8.30905e6i 0.207184 0.00860913i
\(370\) 2.46582e8 + 4.27093e8i 0.253079 + 0.438345i
\(371\) −2.92291e8 + 2.45262e8i −0.297172 + 0.249357i
\(372\) 2.46518e9 5.11957e7i 2.48284 0.0515624i
\(373\) −1.20779e8 + 6.84974e8i −0.120507 + 0.683429i 0.863368 + 0.504574i \(0.168350\pi\)
−0.983875 + 0.178855i \(0.942761\pi\)
\(374\) 1.91814e9 + 1.60951e9i 1.89597 + 1.59090i
\(375\) −4.42434e8 3.55857e8i −0.433251 0.348470i
\(376\) −1.81444e9 6.60403e8i −1.76030 0.640695i
\(377\) 1.73107e8 0.166387
\(378\) 6.88699e7 6.11020e8i 0.0655856 0.581881i
\(379\) −3.48313e8 −0.328649 −0.164325 0.986406i \(-0.552544\pi\)
−0.164325 + 0.986406i \(0.552544\pi\)
\(380\) −7.70795e8 2.80547e8i −0.720604 0.262278i
\(381\) −5.80848e8 + 2.25176e8i −0.538053 + 0.208586i
\(382\) −7.71016e8 6.46959e8i −0.707687 0.593820i
\(383\) 5.90291e7 3.34771e8i 0.0536872 0.304475i −0.946126 0.323798i \(-0.895040\pi\)
0.999813 + 0.0193232i \(0.00615114\pi\)
\(384\) 1.02328e9 + 1.69032e9i 0.922222 + 1.52339i
\(385\) −7.99030e7 + 6.70466e7i −0.0713593 + 0.0598776i
\(386\) 1.75679e8 + 3.04286e8i 0.155477 + 0.269294i
\(387\) −8.35282e7 + 6.24306e8i −0.0732562 + 0.547531i
\(388\) 1.45407e9 2.51853e9i 1.26379 2.18895i
\(389\) 3.48743e8 + 1.97782e9i 0.300387 + 1.70358i 0.644460 + 0.764638i \(0.277082\pi\)
−0.344073 + 0.938943i \(0.611807\pi\)
\(390\) −2.64170e8 8.99837e7i −0.225506 0.0768135i
\(391\) −1.16975e9 + 4.25755e8i −0.989636 + 0.360198i
\(392\) −1.20456e9 + 4.38425e8i −1.01002 + 0.367616i
\(393\) −1.41153e8 + 1.23525e8i −0.117305 + 0.102655i
\(394\) 1.64699e8 + 9.34054e8i 0.135661 + 0.769370i
\(395\) −2.38398e8 + 4.12918e8i −0.194632 + 0.337112i
\(396\) 1.44322e9 1.31689e9i 1.16788 1.06566i
\(397\) −1.19548e9 2.07064e9i −0.958908 1.66088i −0.725160 0.688580i \(-0.758234\pi\)
−0.233748 0.972297i \(-0.575099\pi\)
\(398\) −1.11486e8 + 9.35479e7i −0.0886400 + 0.0743778i
\(399\) −3.28006e8 + 5.96387e8i −0.258509 + 0.470027i
\(400\) −5.94932e7 + 3.37403e8i −0.0464791 + 0.263596i
\(401\) 1.05158e9 + 8.82380e8i 0.814399 + 0.683362i 0.951653 0.307174i \(-0.0993834\pi\)
−0.137255 + 0.990536i \(0.543828\pi\)
\(402\) −4.10741e7 + 2.65008e8i −0.0315339 + 0.203455i
\(403\) −8.72597e8 3.17599e8i −0.664119 0.241720i
\(404\) −3.06253e9 −2.31071
\(405\) −2.75505e8 + 2.73196e8i −0.206081 + 0.204354i
\(406\) 2.65033e8 0.196544
\(407\) 1.22182e9 + 4.44707e8i 0.898312 + 0.326959i
\(408\) −4.25075e8 + 2.74256e9i −0.309853 + 1.99915i
\(409\) 1.94837e9 + 1.63488e9i 1.40812 + 1.18155i 0.957356 + 0.288910i \(0.0932929\pi\)
0.450764 + 0.892643i \(0.351152\pi\)
\(410\) 2.41492e7 1.36957e8i 0.0173045 0.0981387i
\(411\) 1.99943e8 3.63540e8i 0.142056 0.258289i
\(412\) 2.08398e9 1.74867e9i 1.46809 1.23187i
\(413\) −2.44178e7 4.22929e7i −0.0170562 0.0295421i
\(414\) 3.27771e8 + 1.49334e9i 0.227023 + 1.03433i
\(415\) 7.93594e7 1.37455e8i 0.0545042 0.0944041i
\(416\) −9.41001e7 5.33668e8i −0.0640861 0.363450i
\(417\) −8.96425e8 + 7.84477e8i −0.605394 + 0.529790i
\(418\) −3.19889e9 + 1.16430e9i −2.14231 + 0.779736i
\(419\) −4.53747e8 + 1.65151e8i −0.301346 + 0.109681i −0.488268 0.872694i \(-0.662371\pi\)
0.186922 + 0.982375i \(0.440149\pi\)
\(420\) −2.56944e8 8.75223e7i −0.169226 0.0576430i
\(421\) 2.22751e8 + 1.26328e9i 0.145490 + 0.825114i 0.966973 + 0.254881i \(0.0820361\pi\)
−0.821483 + 0.570233i \(0.806853\pi\)
\(422\) −2.19673e9 + 3.80484e9i −1.42293 + 2.46458i
\(423\) 2.19494e9 9.03766e8i 1.41004 0.580584i
\(424\) −1.05758e9 1.83179e9i −0.673805 1.16706i
\(425\) 1.82827e9 1.53410e9i 1.15526 0.969378i
\(426\) −2.29398e9 3.78935e9i −1.43766 2.37482i
\(427\) −2.19397e7 + 1.24426e8i −0.0136374 + 0.0773418i
\(428\) 2.78153e9 + 2.33398e9i 1.71487 + 1.43895i
\(429\) −6.86037e8 + 2.65955e8i −0.419515 + 0.162632i
\(430\) 4.11286e8 + 1.49696e8i 0.249462 + 0.0907968i
\(431\) −2.38745e9 −1.43636 −0.718181 0.695856i \(-0.755025\pi\)
−0.718181 + 0.695856i \(0.755025\pi\)
\(432\) 4.69770e8 + 1.38536e8i 0.280345 + 0.0826739i
\(433\) −2.19572e8 −0.129978 −0.0649891 0.997886i \(-0.520701\pi\)
−0.0649891 + 0.997886i \(0.520701\pi\)
\(434\) −1.33597e9 4.86255e8i −0.784484 0.285529i
\(435\) −1.30314e8 1.04814e8i −0.0759065 0.0610528i
\(436\) 2.04974e9 + 1.71993e9i 1.18439 + 0.993822i
\(437\) 2.93876e8 1.66665e9i 0.168453 0.955346i
\(438\) 4.15738e9 8.63384e7i 2.36407 0.0490958i
\(439\) −7.57191e8 + 6.35359e8i −0.427149 + 0.358421i −0.830875 0.556459i \(-0.812159\pi\)
0.403726 + 0.914880i \(0.367715\pi\)
\(440\) −2.89109e8 5.00752e8i −0.161800 0.280245i
\(441\) 7.30587e8 1.39626e9i 0.405637 0.775234i
\(442\) 1.22701e9 2.12525e9i 0.675882 1.17066i
\(443\) −1.50525e8 8.53670e8i −0.0822613 0.466527i −0.997914 0.0645568i \(-0.979437\pi\)
0.915653 0.401970i \(-0.131674\pi\)
\(444\) 6.56630e8 + 3.31935e9i 0.356025 + 1.79975i
\(445\) 9.19266e8 3.34585e8i 0.494517 0.179989i
\(446\) 2.91489e9 1.06093e9i 1.55578 0.566259i
\(447\) −1.96572e7 9.93697e7i −0.0104099 0.0526233i
\(448\) −1.78229e8 1.01078e9i −0.0936493 0.531111i
\(449\) 1.49795e9 2.59453e9i 0.780973 1.35269i −0.150402 0.988625i \(-0.548057\pi\)
0.931375 0.364060i \(-0.118610\pi\)
\(450\) −1.56976e9 2.47551e9i −0.812064 1.28062i
\(451\) −1.83330e8 3.17536e8i −0.0941054 0.162995i
\(452\) −2.01493e9 + 1.69073e9i −1.02630 + 0.861169i
\(453\) 2.18247e8 4.53246e6i 0.110308 0.00229081i
\(454\) −4.30174e8 + 2.43964e9i −0.215749 + 1.22357i
\(455\) 7.83096e7 + 6.57095e7i 0.0389740 + 0.0327031i
\(456\) −2.94009e9 2.36476e9i −1.45206 1.16791i
\(457\) −1.68186e9 6.12147e8i −0.824295 0.300019i −0.104780 0.994495i \(-0.533414\pi\)
−0.719515 + 0.694476i \(0.755636\pi\)
\(458\) −3.87272e9 −1.88359
\(459\) −1.88653e9 2.84278e9i −0.910583 1.37214i
\(460\) 6.74925e8 0.323298
\(461\) 2.09714e9 + 7.63298e8i 0.996954 + 0.362862i 0.788409 0.615151i \(-0.210905\pi\)
0.208545 + 0.978013i \(0.433127\pi\)
\(462\) −1.05035e9 + 4.07186e8i −0.495548 + 0.192108i
\(463\) −1.54556e8 1.29688e8i −0.0723691 0.0607249i 0.605886 0.795552i \(-0.292819\pi\)
−0.678255 + 0.734827i \(0.737263\pi\)
\(464\) −3.66578e7 + 2.07897e8i −0.0170355 + 0.0966129i
\(465\) 4.64584e8 + 7.67430e8i 0.214279 + 0.353959i
\(466\) 2.33392e9 1.95839e9i 1.06840 0.896496i
\(467\) 8.63405e8 + 1.49546e9i 0.392288 + 0.679463i 0.992751 0.120190i \(-0.0383503\pi\)
−0.600463 + 0.799653i \(0.705017\pi\)
\(468\) −1.51664e9 1.16883e9i −0.683945 0.527099i
\(469\) 4.91161e7 8.50716e7i 0.0219846 0.0380785i
\(470\) −2.86423e8 1.62439e9i −0.127252 0.721683i
\(471\) −2.40481e9 8.19144e8i −1.06049 0.361233i
\(472\) 2.54393e8 9.25915e7i 0.111355 0.0405298i
\(473\) 1.08436e9 3.94675e8i 0.471151 0.171485i
\(474\) −3.87512e9 + 3.39119e9i −1.67133 + 1.46261i
\(475\) 5.63434e8 + 3.19539e9i 0.241221 + 1.36803i
\(476\) 1.19345e9 2.06712e9i 0.507201 0.878497i
\(477\) 2.47826e9 + 7.87129e8i 1.04552 + 0.332072i
\(478\) 2.52567e9 + 4.37459e9i 1.05774 + 1.83206i
\(479\) −8.12944e8 + 6.82141e8i −0.337976 + 0.283596i −0.795941 0.605375i \(-0.793023\pi\)
0.457964 + 0.888971i \(0.348579\pi\)
\(480\) −2.52290e8 + 4.58718e8i −0.104125 + 0.189322i
\(481\) 2.21281e8 1.25495e9i 0.0906643 0.514183i
\(482\) 4.05230e9 + 3.40028e9i 1.64830 + 1.38309i
\(483\) 8.57770e7 5.53429e8i 0.0346382 0.223484i
\(484\) 7.19368e8 + 2.61829e8i 0.288398 + 0.104968i
\(485\) 1.05807e9 0.421131
\(486\) −3.76792e9 + 1.83355e9i −1.48893 + 0.724548i
\(487\) 4.37594e9 1.71680 0.858400 0.512981i \(-0.171459\pi\)
0.858400 + 0.512981i \(0.171459\pi\)
\(488\) −6.58156e8 2.39549e8i −0.256365 0.0933094i
\(489\) −1.16715e8 + 7.53039e8i −0.0451383 + 0.291230i
\(490\) −8.38838e8 7.03869e8i −0.322101 0.270275i
\(491\) 1.90092e8 1.07806e9i 0.0724733 0.411016i −0.926890 0.375333i \(-0.877528\pi\)
0.999363 0.0356830i \(-0.0113607\pi\)
\(492\) 4.59829e8 8.36070e8i 0.174068 0.316493i
\(493\) 1.12652e9 9.45266e8i 0.423425 0.355296i
\(494\) 1.66815e9 + 2.88932e9i 0.622573 + 1.07833i
\(495\) 6.77476e8 + 2.15176e8i 0.251059 + 0.0797398i
\(496\) 5.66212e8 9.80708e8i 0.208350 0.360872i
\(497\) 2.81759e8 + 1.59793e9i 0.102951 + 0.583863i
\(498\) 1.28997e9 1.12888e9i 0.468034 0.409585i
\(499\) 3.72244e9 1.35486e9i 1.34115 0.488137i 0.430972 0.902365i \(-0.358171\pi\)
0.910173 + 0.414228i \(0.135948\pi\)
\(500\) −2.54376e9 + 9.25854e8i −0.910084 + 0.331244i
\(501\) −4.10141e9 1.39706e9i −1.45714 0.496343i
\(502\) −9.28878e8 5.26793e9i −0.327714 1.85856i
\(503\) 5.12159e8 8.87086e8i 0.179439 0.310798i −0.762250 0.647283i \(-0.775905\pi\)
0.941689 + 0.336486i \(0.109238\pi\)
\(504\) −9.88971e8 7.62176e8i −0.344094 0.265185i
\(505\) −5.57120e8 9.64960e8i −0.192499 0.333418i
\(506\) 2.14570e9 1.80046e9i 0.736279 0.617811i
\(507\) −1.14623e9 1.89342e9i −0.390612 0.645238i
\(508\) −5.15752e8 + 2.92498e9i −0.174549 + 0.989919i
\(509\) −3.76009e9 3.15509e9i −1.26382 1.06047i −0.995264 0.0972085i \(-0.969009\pi\)
−0.268557 0.963264i \(-0.586547\pi\)
\(510\) −2.21049e9 + 8.56937e8i −0.737893 + 0.286058i
\(511\) −1.43133e9 5.20960e8i −0.474532 0.172716i
\(512\) 1.75130e9 0.576655
\(513\) 4.62941e9 2.88757e8i 1.51396 0.0944324i
\(514\) −4.68643e9 −1.52220
\(515\) 9.30086e8 + 3.38524e8i 0.300053 + 0.109210i
\(516\) 2.34001e9 + 1.88211e9i 0.749798 + 0.603075i
\(517\) −3.33136e9 2.79534e9i −1.06024 0.889648i
\(518\) 3.38788e8 1.92136e9i 0.107096 0.607373i
\(519\) −1.25540e9 + 2.60716e7i −0.394183 + 0.00818620i
\(520\) −4.34108e8 + 3.64260e8i −0.135390 + 0.113606i
\(521\) 2.17406e9 + 3.76559e9i 0.673503 + 1.16654i 0.976904 + 0.213679i \(0.0685447\pi\)
−0.303400 + 0.952863i \(0.598122\pi\)
\(522\) −9.67238e8 1.52533e9i −0.297637 0.469373i
\(523\) −1.21067e9 + 2.09694e9i −0.370058 + 0.640959i −0.989574 0.144025i \(-0.953995\pi\)
0.619516 + 0.784984i \(0.287329\pi\)
\(524\) 1.55289e8 + 8.80686e8i 0.0471499 + 0.267400i
\(525\) 2.08366e8 + 1.05332e9i 0.0628449 + 0.317689i
\(526\) −2.85951e9 + 1.04078e9i −0.856724 + 0.311822i
\(527\) −7.41284e9 + 2.69805e9i −2.20621 + 0.802996i
\(528\) −1.74126e8 8.80231e8i −0.0514809 0.260242i
\(529\) −3.49436e8 1.98175e9i −0.102630 0.582042i
\(530\) 9.03431e8 1.56479e9i 0.263590 0.456552i
\(531\) −1.54294e8 + 2.94879e8i −0.0447216 + 0.0854697i
\(532\) 1.62252e9 + 2.81029e9i 0.467196 + 0.809207i
\(533\) −2.75276e8 + 2.30984e8i −0.0787450 + 0.0660749i
\(534\) 1.05630e10 2.19368e8i 3.00188 0.0623417i
\(535\) −2.29403e8 + 1.30101e9i −0.0647680 + 0.367317i
\(536\) 4.17149e8 + 3.50029e8i 0.117008 + 0.0981810i
\(537\) 3.55826e9 + 2.86196e9i 0.991579 + 0.797543i
\(538\) −1.51041e9 5.49745e8i −0.418175 0.152203i
\(539\) −2.88705e9 −0.794134
\(540\) 4.34004e8 + 1.79819e9i 0.118608 + 0.491425i
\(541\) 6.43755e9 1.74796 0.873978 0.485966i \(-0.161532\pi\)
0.873978 + 0.485966i \(0.161532\pi\)
\(542\) −5.65323e9 2.05761e9i −1.52510 0.555092i
\(543\) 3.97690e9 1.54172e9i 1.06597 0.413243i
\(544\) −3.52651e9 2.95909e9i −0.939180 0.788066i
\(545\) −1.69049e8 + 9.58723e8i −0.0447326 + 0.253691i
\(546\) 5.71756e8 + 9.44465e8i 0.150327 + 0.248320i
\(547\) −4.31221e9 + 3.61837e9i −1.12653 + 0.945274i −0.998916 0.0465499i \(-0.985177\pi\)
−0.127617 + 0.991823i \(0.540733\pi\)
\(548\) −9.89041e8 1.71307e9i −0.256733 0.444675i
\(549\) 7.96174e8 3.27825e8i 0.205355 0.0845549i
\(550\) −2.68512e9 + 4.65076e9i −0.688168 + 1.19194i
\(551\) 3.47170e8 + 1.96890e9i 0.0884121 + 0.501410i
\(552\) 2.93874e9 + 1.00102e9i 0.743661 + 0.253312i
\(553\) 1.77250e9 6.45137e8i 0.445705 0.162223i
\(554\) −1.45428e9 + 5.29314e8i −0.363382 + 0.132260i
\(555\) −9.26429e8 + 8.10734e8i −0.230031 + 0.201304i
\(556\) 9.86198e8 + 5.59300e9i 0.243334 + 1.38001i
\(557\) −2.86703e9 + 4.96584e9i −0.702973 + 1.21759i 0.264445 + 0.964401i \(0.414811\pi\)
−0.967418 + 0.253185i \(0.918522\pi\)
\(558\) 2.07712e9 + 9.46346e9i 0.506106 + 2.30585i
\(559\) −5.65471e8 9.79424e8i −0.136921 0.237154i
\(560\) −9.54984e7 + 8.01327e7i −0.0229794 + 0.0192820i
\(561\) −3.01223e9 + 5.47691e9i −0.720309 + 1.30968i
\(562\) 1.10236e9 6.25181e9i 0.261967 1.48569i
\(563\) −4.14449e9 3.47764e9i −0.978794 0.821306i 0.00511276 0.999987i \(-0.498373\pi\)
−0.983907 + 0.178681i \(0.942817\pi\)
\(564\) 1.73336e9 1.11836e10i 0.406829 2.62484i
\(565\) −8.99268e8 3.27307e8i −0.209759 0.0763459i
\(566\) 1.01412e10 2.35088
\(567\) 1.52965e9 1.27343e8i 0.352412 0.0293382i
\(568\) −8.99476e9 −2.05954
\(569\) 3.35730e9 + 1.22196e9i 0.764007 + 0.278076i 0.694488 0.719505i \(-0.255631\pi\)
0.0695197 + 0.997581i \(0.477853\pi\)
\(570\) 4.93665e8 3.18510e9i 0.111653 0.720379i
\(571\) 5.58433e9 + 4.68581e9i 1.25529 + 1.05332i 0.996167 + 0.0874716i \(0.0278787\pi\)
0.259125 + 0.965844i \(0.416566\pi\)
\(572\) −6.09153e8 + 3.45468e9i −0.136094 + 0.771830i
\(573\) 1.21080e9 2.20149e9i 0.268862 0.488851i
\(574\) −4.21457e8 + 3.53644e8i −0.0930168 + 0.0780504i
\(575\) −1.33489e9 2.31209e9i −0.292824 0.507187i
\(576\) −5.16688e9 + 4.71461e9i −1.12655 + 1.02794i
\(577\) 6.22876e7 1.07885e8i 0.0134985 0.0233801i −0.859197 0.511645i \(-0.829036\pi\)
0.872696 + 0.488264i \(0.162370\pi\)
\(578\) −2.28522e9 1.29601e10i −0.492244 2.79165i
\(579\) −6.60042e8 + 5.77614e8i −0.141318 + 0.123669i
\(580\) −7.49237e8 + 2.72700e8i −0.159449 + 0.0580346i
\(581\) −5.90039e8 + 2.14757e8i −0.124814 + 0.0454287i
\(582\) 1.08169e10 + 3.68454e9i 2.27443 + 0.774734i
\(583\) −8.27228e8 4.69144e9i −0.172896 0.980543i
\(584\) 4.22188e9 7.31251e9i 0.877123 1.51922i
\(585\) 9.23844e7 6.90499e8i 0.0190789 0.142599i
\(586\) 1.16293e9 + 2.01425e9i 0.238732 + 0.413496i
\(587\) −1.90340e9 + 1.59714e9i −0.388415 + 0.325919i −0.815995 0.578058i \(-0.803811\pi\)
0.427580 + 0.903977i \(0.359366\pi\)
\(588\) −3.89085e9 6.42716e9i −0.789267 1.30376i
\(589\) 1.86232e9 1.05618e10i 0.375536 2.12977i
\(590\) 1.77155e8 + 1.48651e8i 0.0355117 + 0.0297979i
\(591\) −2.20756e9 + 8.55800e8i −0.439902 + 0.170536i
\(592\) 1.46030e9 + 5.31504e8i 0.289278 + 0.105288i
\(593\) 3.85909e9 0.759964 0.379982 0.924994i \(-0.375930\pi\)
0.379982 + 0.924994i \(0.375930\pi\)
\(594\) 6.17670e9 + 4.55899e9i 1.20922 + 0.892516i
\(595\) 8.68425e8 0.169014
\(596\) −4.53817e8 1.65176e8i −0.0878049 0.0319584i
\(597\) −2.83090e8 2.27694e8i −0.0544520 0.0437966i
\(598\) −2.10291e9 1.76455e9i −0.402130 0.337427i
\(599\) −6.12552e8 + 3.47396e9i −0.116453 + 0.660436i 0.869568 + 0.493813i \(0.164397\pi\)
−0.986021 + 0.166623i \(0.946714\pi\)
\(600\) −5.95092e9 + 1.23586e8i −1.12475 + 0.0233582i
\(601\) −6.34144e9 + 5.32110e9i −1.19159 + 0.999864i −0.191761 + 0.981442i \(0.561420\pi\)
−0.999830 + 0.0184225i \(0.994136\pi\)
\(602\) −8.65755e8 1.49953e9i −0.161736 0.280135i
\(603\) −6.68858e8 + 2.77931e7i −0.124229 + 0.00516209i
\(604\) 5.20377e8 9.01319e8i 0.0960923 0.166437i
\(605\) 4.83653e7 + 2.74293e8i 0.00887952 + 0.0503583i
\(606\) −2.33527e9 1.18051e10i −0.426268 2.15484i
\(607\) 8.27765e9 3.01282e9i 1.50227 0.546780i 0.545620 0.838033i \(-0.316294\pi\)
0.956646 + 0.291253i \(0.0940720\pi\)
\(608\) 5.88116e9 2.14057e9i 1.06121 0.386248i
\(609\) 1.28389e8 + 6.49022e8i 0.0230339 + 0.116439i
\(610\) −1.03895e8 5.89217e8i −0.0185327 0.105104i
\(611\) −2.13103e9 + 3.69105e9i −0.377960 + 0.654645i
\(612\) −1.62523e10 + 6.75330e8i −2.86605 + 0.119093i
\(613\) −2.12297e9 3.67710e9i −0.372248 0.644753i 0.617663 0.786443i \(-0.288080\pi\)
−0.989911 + 0.141690i \(0.954746\pi\)
\(614\) 7.87885e9 6.61114e9i 1.37364 1.15262i
\(615\) 3.47083e8 7.20806e6i 0.0601687 0.00124955i
\(616\) −3.97218e8 + 2.25273e9i −0.0684693 + 0.388309i
\(617\) 1.16433e9 + 9.76986e8i 0.199561 + 0.167452i 0.737092 0.675792i \(-0.236198\pi\)
−0.537531 + 0.843244i \(0.680643\pi\)
\(618\) 8.32965e9 + 6.69967e9i 1.41960 + 1.14181i
\(619\) 3.05617e9 + 1.11236e9i 0.517917 + 0.188506i 0.587735 0.809053i \(-0.300020\pi\)
−0.0698180 + 0.997560i \(0.522242\pi\)
\(620\) 4.27707e9 0.720734
\(621\) −3.49817e9 + 1.52607e9i −0.586165 + 0.255714i
\(622\) −4.57198e9 −0.761794
\(623\) −3.63670e9 1.32365e9i −0.602559 0.219314i
\(624\) −8.19938e8 + 3.17864e8i −0.135094 + 0.0523715i
\(625\) 3.52727e9 + 2.95973e9i 0.577908 + 0.484923i
\(626\) 9.31867e8 5.28488e9i 0.151825 0.861043i
\(627\) −4.40080e9 7.26952e9i −0.713009 1.17779i
\(628\) −9.27848e9 + 7.78557e9i −1.49492 + 1.25439i
\(629\) −5.41271e9 9.37509e9i −0.867237 1.50210i
\(630\) 1.41444e8 1.05718e9i 0.0225367 0.168444i
\(631\) −6.16341e8 + 1.06753e9i −0.0976604 + 0.169153i −0.910716 0.413034i \(-0.864469\pi\)
0.813055 + 0.582186i \(0.197803\pi\)
\(632\) 1.81574e9 + 1.02976e10i 0.286117 + 1.62265i
\(633\) −1.03816e10 3.53626e9i −1.62686 0.554154i
\(634\) 2.08411e9 7.58555e8i 0.324794 0.118216i
\(635\) −1.01544e9 + 3.69590e8i −0.157379 + 0.0572813i
\(636\) 9.32927e9 8.16420e9i 1.43796 1.25839i
\(637\) 4.91333e8 + 2.78649e9i 0.0753162 + 0.427139i
\(638\) −1.65449e9 + 2.86565e9i −0.252227 + 0.436869i
\(639\) 8.16823e9 7.45325e9i 1.23844 1.13004i
\(640\) 1.71374e9 + 2.96828e9i 0.258413 + 0.447584i
\(641\) 2.81638e9 2.36323e9i 0.422366 0.354407i −0.406696 0.913563i \(-0.633319\pi\)
0.829062 + 0.559156i \(0.188875\pi\)
\(642\) −6.87577e9 + 1.25017e10i −1.02553 + 1.86464i
\(643\) −4.75458e8 + 2.69646e9i −0.0705300 + 0.399996i 0.929021 + 0.370027i \(0.120652\pi\)
−0.999551 + 0.0299682i \(0.990459\pi\)
\(644\) −2.04539e9 1.71628e9i −0.301769 0.253215i
\(645\) −1.67343e8 + 1.07969e9i −0.0245555 + 0.158431i
\(646\) 2.66331e10 + 9.69366e9i 3.88694 + 1.41473i
\(647\) −2.19801e9 −0.319055 −0.159528 0.987193i \(-0.550997\pi\)
−0.159528 + 0.987193i \(0.550997\pi\)
\(648\) −7.77266e8 + 8.47334e9i −0.112217 + 1.22333i
\(649\) 6.09719e8 0.0875535
\(650\) 4.94574e9 + 1.80010e9i 0.706374 + 0.257099i
\(651\) 5.43577e8 3.50713e9i 0.0772197 0.498217i
\(652\) 2.78312e9 + 2.33531e9i 0.393247 + 0.329973i
\(653\) 9.12954e8 5.17762e9i 0.128308 0.727669i −0.850980 0.525198i \(-0.823991\pi\)
0.979288 0.202472i \(-0.0648974\pi\)
\(654\) −5.06681e9 + 9.21258e9i −0.708293 + 1.28783i
\(655\) −2.49242e8 + 2.09139e8i −0.0346559 + 0.0290797i
\(656\) −2.19112e8 3.79513e8i −0.0303042 0.0524883i
\(657\) 2.22537e9 + 1.01389e10i 0.306142 + 1.39480i
\(658\) −3.26268e9 + 5.65113e9i −0.446461 + 0.773293i
\(659\) 1.58543e9 + 8.99142e9i 0.215798 + 1.22385i 0.879516 + 0.475870i \(0.157867\pi\)
−0.663717 + 0.747983i \(0.731022\pi\)
\(660\) 2.55032e9 2.23183e9i 0.345295 0.302174i
\(661\) −1.14174e10 + 4.15560e9i −1.53767 + 0.559666i −0.965485 0.260458i \(-0.916126\pi\)
−0.572185 + 0.820125i \(0.693904\pi\)
\(662\) −1.18849e9 + 4.32573e8i −0.159218 + 0.0579504i
\(663\) 5.79878e9 + 1.97523e9i 0.772750 + 0.263220i
\(664\) −6.04433e8 3.42791e9i −0.0801234 0.454403i
\(665\) −5.90320e8 + 1.02246e9i −0.0778416 + 0.134826i
\(666\) −1.22944e10 + 5.06221e9i −1.61267 + 0.664018i
\(667\) −8.22516e8 1.42464e9i −0.107326 0.185894i
\(668\) −1.58245e10 + 1.32783e10i −2.05406 + 1.72356i
\(669\) 4.01009e9 + 6.62413e9i 0.517801 + 0.855337i
\(670\) −8.07770e7 + 4.58109e8i −0.0103759 + 0.0588446i
\(671\) −1.20839e9 1.01396e9i −0.154411 0.129566i
\(672\) 1.93106e9 7.48611e8i 0.245473 0.0951621i
\(673\) 2.89680e9 + 1.05435e9i 0.366325 + 0.133331i 0.518623 0.855003i \(-0.326445\pi\)
−0.152298 + 0.988335i \(0.548667\pi\)
\(674\) −2.30598e9 −0.290099
\(675\) 5.30168e9 5.04329e9i 0.663515 0.631176i
\(676\) −1.05525e10 −1.31384
\(677\) 6.28818e9 + 2.28871e9i 0.778869 + 0.283485i 0.700701 0.713455i \(-0.252871\pi\)
0.0781680 + 0.996940i \(0.475093\pi\)
\(678\) −8.05366e9 6.47769e9i −0.992406 0.798208i
\(679\) −3.20652e9 2.69059e9i −0.393088 0.329840i
\(680\) −8.35959e8 + 4.74096e9i −0.101954 + 0.578209i
\(681\) −6.18265e9 + 1.28398e8i −0.750171 + 0.0155792i
\(682\) 1.35975e10 1.14097e10i 1.64140 1.37730i
\(683\) 1.96692e9 + 3.40681e9i 0.236219 + 0.409143i 0.959626 0.281278i \(-0.0907585\pi\)
−0.723407 + 0.690421i \(0.757425\pi\)
\(684\) 1.02525e10 1.95942e10i 1.22500 2.34115i
\(685\) 3.59842e8 6.23265e8i 0.0427755 0.0740894i
\(686\) 1.61201e9 + 9.14219e9i 0.190649 + 1.08122i
\(687\) −1.87604e9 9.48364e9i −0.220747 1.11590i
\(688\) 1.29601e9 4.71708e8i 0.151722 0.0552222i
\(689\) −4.38725e9 + 1.59683e9i −0.511005 + 0.185991i
\(690\) 5.14650e8 + 2.60162e9i 0.0596404 + 0.301490i
\(691\) −1.49778e9 8.49436e9i −0.172694 0.979394i −0.940772 0.339039i \(-0.889898\pi\)
0.768079 0.640355i \(-0.221213\pi\)
\(692\) −2.99331e9 + 5.18457e9i −0.343385 + 0.594760i
\(693\) −1.50594e9 2.37487e9i −0.171887 0.271065i
\(694\) −1.20950e10 2.09492e10i −1.37356 2.37908i
\(695\) −1.58287e9 + 1.32819e9i −0.178854 + 0.150076i
\(696\) −3.66677e9 + 7.61498e7i −0.412241 + 0.00856123i
\(697\) −5.30097e8 + 3.00633e9i −0.0592981 + 0.336296i
\(698\) −1.42919e10 1.19923e10i −1.59073 1.33478i
\(699\) 5.92638e9 + 4.76668e9i 0.656325 + 0.527893i
\(700\) 4.81046e9 + 1.75086e9i 0.530082 + 0.192934i
\(701\) 8.27163e9 0.906939 0.453469 0.891272i \(-0.350186\pi\)
0.453469 + 0.891272i \(0.350186\pi\)
\(702\) 3.34901e9 6.73743e9i 0.365373 0.735046i
\(703\) 1.47174e10 1.59767
\(704\) 1.20417e10 + 4.38280e9i 1.30071 + 0.473421i
\(705\) 3.83910e9 1.48830e9i 0.412636 0.159966i
\(706\) −8.22742e9 6.90362e9i −0.879928 0.738347i
\(707\) −7.65447e8 + 4.34107e9i −0.0814606 + 0.461986i
\(708\) 8.21713e8 + 1.35736e9i 0.0870169 + 0.143740i
\(709\) −3.19066e9 + 2.67728e9i −0.336216 + 0.282119i −0.795227 0.606312i \(-0.792648\pi\)
0.459011 + 0.888431i \(0.348204\pi\)
\(710\) −3.84185e9 6.65427e9i −0.402843 0.697744i
\(711\) −1.01817e10 7.84675e9i −1.06237 0.818741i
\(712\) 1.07269e10 1.85795e10i 1.11377 1.92910i
\(713\) 1.53235e9 + 8.69037e9i 0.158323 + 0.897893i
\(714\) 8.87812e9 + 3.02414e9i 0.912804 + 0.310926i
\(715\) −1.19933e9 + 4.36522e8i −0.122707 + 0.0446616i
\(716\) 2.04581e10 7.44614e9i 2.08291 0.758116i
\(717\) −9.48915e9 + 8.30411e9i −0.961413 + 0.841349i
\(718\) −3.33194e9 1.88964e10i −0.335940 1.90521i
\(719\) 5.06255e9 8.76859e9i 0.507947 0.879790i −0.492011 0.870589i \(-0.663738\pi\)
0.999958 0.00920063i \(-0.00292869\pi\)
\(720\) 8.09706e8 + 2.57174e8i 0.0808469 + 0.0256781i
\(721\) −1.95782e9 3.39105e9i −0.194536 0.336947i
\(722\) −1.66892e10 + 1.40039e10i −1.65028 + 1.38475i
\(723\) −6.36368e9 + 1.15706e10i −0.626217 + 1.13860i
\(724\) 3.53121e9 2.00265e10i 0.345810 1.96119i
\(725\) 2.41605e9 + 2.02731e9i 0.235464 + 0.197577i
\(726\) −4.60727e8 + 2.97259e9i −0.0446854 + 0.288308i
\(727\) 1.40807e10 + 5.12495e9i 1.35911 + 0.494674i 0.915778 0.401685i \(-0.131575\pi\)
0.443328 + 0.896359i \(0.353798\pi\)
\(728\) 2.24187e9 0.215353
\(729\) −6.31535e9 8.33879e9i −0.603741 0.797180i
\(730\) 7.21300e9 0.686256
\(731\) −9.02812e9 3.28597e9i −0.854843 0.311137i
\(732\) 6.28745e8 4.05663e9i 0.0592497 0.382276i
\(733\) 1.17920e9 + 9.89468e8i 0.110592 + 0.0927978i 0.696407 0.717647i \(-0.254781\pi\)
−0.585815 + 0.810445i \(0.699225\pi\)
\(734\) −2.59517e9 + 1.47179e10i −0.242231 + 1.37376i
\(735\) 1.31730e9 2.39515e9i 0.122371 0.222498i
\(736\) −3.94487e9 + 3.31014e9i −0.364721 + 0.306037i
\(737\) 6.13221e8 + 1.06213e9i 0.0564262 + 0.0977331i
\(738\) 3.57342e9 + 1.13497e9i 0.327255 + 0.103941i
\(739\) −9.37312e9 + 1.62347e10i −0.854336 + 1.47975i 0.0229236 + 0.999737i \(0.492703\pi\)
−0.877260 + 0.480016i \(0.840631\pi\)
\(740\) 1.01921e9 + 5.78021e9i 0.0924594 + 0.524363i
\(741\) −6.26737e9 + 5.48468e9i −0.565876 + 0.495208i
\(742\) −6.71703e9 + 2.44480e9i −0.603620 + 0.219700i
\(743\) 1.24688e10 4.53828e9i 1.11523 0.405910i 0.282320 0.959320i \(-0.408896\pi\)
0.832909 + 0.553410i \(0.186674\pi\)
\(744\) 1.86231e10 + 6.34355e9i 1.65786 + 0.564713i
\(745\) −3.05115e7 1.73039e8i −0.00270344 0.0153319i
\(746\) −6.51512e9 + 1.12845e10i −0.574562 + 0.995170i
\(747\) 3.38933e9 + 2.61207e9i 0.297503 + 0.229278i
\(748\) 1.49004e10 + 2.58082e10i 1.30179 + 2.25477i
\(749\) 4.00358e9 3.35940e9i 0.348147 0.292130i
\(750\) −5.50857e9 9.09941e9i −0.476787 0.787588i
\(751\) −2.07032e9 + 1.17414e10i −0.178360 + 1.01153i 0.755833 + 0.654765i \(0.227232\pi\)
−0.934193 + 0.356768i \(0.883879\pi\)
\(752\) −3.98157e9 3.34094e9i −0.341423 0.286488i
\(753\) 1.24503e10 4.82659e9i 1.06267 0.411962i
\(754\) 3.04741e9 + 1.10917e9i 0.258899 + 0.0942317i
\(755\) 3.78657e8 0.0320207
\(756\) 3.25740e9