# Properties

 Label 10.6.b.a.9.2 Level $10$ Weight $6$ Character 10.9 Analytic conductor $1.604$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$10 = 2 \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 10.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.60383819813$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 9.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 10.9 Dual form 10.6.b.a.9.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+4.00000i q^{2} +14.0000i q^{3} -16.0000 q^{4} +(55.0000 + 10.0000i) q^{5} -56.0000 q^{6} -158.000i q^{7} -64.0000i q^{8} +47.0000 q^{9} +O(q^{10})$$ $$q+4.00000i q^{2} +14.0000i q^{3} -16.0000 q^{4} +(55.0000 + 10.0000i) q^{5} -56.0000 q^{6} -158.000i q^{7} -64.0000i q^{8} +47.0000 q^{9} +(-40.0000 + 220.000i) q^{10} -148.000 q^{11} -224.000i q^{12} +684.000i q^{13} +632.000 q^{14} +(-140.000 + 770.000i) q^{15} +256.000 q^{16} -2048.00i q^{17} +188.000i q^{18} -2220.00 q^{19} +(-880.000 - 160.000i) q^{20} +2212.00 q^{21} -592.000i q^{22} -1246.00i q^{23} +896.000 q^{24} +(2925.00 + 1100.00i) q^{25} -2736.00 q^{26} +4060.00i q^{27} +2528.00i q^{28} +270.000 q^{29} +(-3080.00 - 560.000i) q^{30} -2048.00 q^{31} +1024.00i q^{32} -2072.00i q^{33} +8192.00 q^{34} +(1580.00 - 8690.00i) q^{35} -752.000 q^{36} +4372.00i q^{37} -8880.00i q^{38} -9576.00 q^{39} +(640.000 - 3520.00i) q^{40} -2398.00 q^{41} +8848.00i q^{42} +2294.00i q^{43} +2368.00 q^{44} +(2585.00 + 470.000i) q^{45} +4984.00 q^{46} +10682.0i q^{47} +3584.00i q^{48} -8157.00 q^{49} +(-4400.00 + 11700.0i) q^{50} +28672.0 q^{51} -10944.0i q^{52} +2964.00i q^{53} -16240.0 q^{54} +(-8140.00 - 1480.00i) q^{55} -10112.0 q^{56} -31080.0i q^{57} +1080.00i q^{58} +39740.0 q^{59} +(2240.00 - 12320.0i) q^{60} -42298.0 q^{61} -8192.00i q^{62} -7426.00i q^{63} -4096.00 q^{64} +(-6840.00 + 37620.0i) q^{65} +8288.00 q^{66} -32098.0i q^{67} +32768.0i q^{68} +17444.0 q^{69} +(34760.0 + 6320.00i) q^{70} -4248.00 q^{71} -3008.00i q^{72} +30104.0i q^{73} -17488.0 q^{74} +(-15400.0 + 40950.0i) q^{75} +35520.0 q^{76} +23384.0i q^{77} -38304.0i q^{78} -35280.0 q^{79} +(14080.0 + 2560.00i) q^{80} -45419.0 q^{81} -9592.00i q^{82} -27826.0i q^{83} -35392.0 q^{84} +(20480.0 - 112640. i) q^{85} -9176.00 q^{86} +3780.00i q^{87} +9472.00i q^{88} +85210.0 q^{89} +(-1880.00 + 10340.0i) q^{90} +108072. q^{91} +19936.0i q^{92} -28672.0i q^{93} -42728.0 q^{94} +(-122100. - 22200.0i) q^{95} -14336.0 q^{96} +97232.0i q^{97} -32628.0i q^{98} -6956.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 32q^{4} + 110q^{5} - 112q^{6} + 94q^{9} + O(q^{10})$$ $$2q - 32q^{4} + 110q^{5} - 112q^{6} + 94q^{9} - 80q^{10} - 296q^{11} + 1264q^{14} - 280q^{15} + 512q^{16} - 4440q^{19} - 1760q^{20} + 4424q^{21} + 1792q^{24} + 5850q^{25} - 5472q^{26} + 540q^{29} - 6160q^{30} - 4096q^{31} + 16384q^{34} + 3160q^{35} - 1504q^{36} - 19152q^{39} + 1280q^{40} - 4796q^{41} + 4736q^{44} + 5170q^{45} + 9968q^{46} - 16314q^{49} - 8800q^{50} + 57344q^{51} - 32480q^{54} - 16280q^{55} - 20224q^{56} + 79480q^{59} + 4480q^{60} - 84596q^{61} - 8192q^{64} - 13680q^{65} + 16576q^{66} + 34888q^{69} + 69520q^{70} - 8496q^{71} - 34976q^{74} - 30800q^{75} + 71040q^{76} - 70560q^{79} + 28160q^{80} - 90838q^{81} - 70784q^{84} + 40960q^{85} - 18352q^{86} + 170420q^{89} - 3760q^{90} + 216144q^{91} - 85456q^{94} - 244200q^{95} - 28672q^{96} - 13912q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$$.

 $$n$$ $$7$$ $$\chi(n)$$ $$-1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000i 0.707107i
$$3$$ 14.0000i 0.898100i 0.893507 + 0.449050i $$0.148238\pi$$
−0.893507 + 0.449050i $$0.851762\pi$$
$$4$$ −16.0000 −0.500000
$$5$$ 55.0000 + 10.0000i 0.983870 + 0.178885i
$$6$$ −56.0000 −0.635053
$$7$$ 158.000i 1.21874i −0.792885 0.609371i $$-0.791422\pi$$
0.792885 0.609371i $$-0.208578\pi$$
$$8$$ 64.0000i 0.353553i
$$9$$ 47.0000 0.193416
$$10$$ −40.0000 + 220.000i −0.126491 + 0.695701i
$$11$$ −148.000 −0.368791 −0.184395 0.982852i $$-0.559033\pi$$
−0.184395 + 0.982852i $$0.559033\pi$$
$$12$$ 224.000i 0.449050i
$$13$$ 684.000i 1.12253i 0.827636 + 0.561265i $$0.189685\pi$$
−0.827636 + 0.561265i $$0.810315\pi$$
$$14$$ 632.000 0.861781
$$15$$ −140.000 + 770.000i −0.160657 + 0.883614i
$$16$$ 256.000 0.250000
$$17$$ 2048.00i 1.71873i −0.511363 0.859365i $$-0.670859\pi$$
0.511363 0.859365i $$-0.329141\pi$$
$$18$$ 188.000i 0.136766i
$$19$$ −2220.00 −1.41081 −0.705406 0.708804i $$-0.749235\pi$$
−0.705406 + 0.708804i $$0.749235\pi$$
$$20$$ −880.000 160.000i −0.491935 0.0894427i
$$21$$ 2212.00 1.09455
$$22$$ 592.000i 0.260774i
$$23$$ 1246.00i 0.491132i −0.969380 0.245566i $$-0.921026\pi$$
0.969380 0.245566i $$-0.0789738\pi$$
$$24$$ 896.000 0.317526
$$25$$ 2925.00 + 1100.00i 0.936000 + 0.352000i
$$26$$ −2736.00 −0.793748
$$27$$ 4060.00i 1.07181i
$$28$$ 2528.00i 0.609371i
$$29$$ 270.000 0.0596168 0.0298084 0.999556i $$-0.490510\pi$$
0.0298084 + 0.999556i $$0.490510\pi$$
$$30$$ −3080.00 560.000i −0.624809 0.113602i
$$31$$ −2048.00 −0.382759 −0.191380 0.981516i $$-0.561296\pi$$
−0.191380 + 0.981516i $$0.561296\pi$$
$$32$$ 1024.00i 0.176777i
$$33$$ 2072.00i 0.331211i
$$34$$ 8192.00 1.21533
$$35$$ 1580.00 8690.00i 0.218015 1.19908i
$$36$$ −752.000 −0.0967078
$$37$$ 4372.00i 0.525020i 0.964929 + 0.262510i $$0.0845503\pi$$
−0.964929 + 0.262510i $$0.915450\pi$$
$$38$$ 8880.00i 0.997594i
$$39$$ −9576.00 −1.00814
$$40$$ 640.000 3520.00i 0.0632456 0.347851i
$$41$$ −2398.00 −0.222787 −0.111393 0.993776i $$-0.535531\pi$$
−0.111393 + 0.993776i $$0.535531\pi$$
$$42$$ 8848.00i 0.773966i
$$43$$ 2294.00i 0.189200i 0.995515 + 0.0946002i $$0.0301573\pi$$
−0.995515 + 0.0946002i $$0.969843\pi$$
$$44$$ 2368.00 0.184395
$$45$$ 2585.00 + 470.000i 0.190296 + 0.0345992i
$$46$$ 4984.00 0.347283
$$47$$ 10682.0i 0.705355i 0.935745 + 0.352678i $$0.114729\pi$$
−0.935745 + 0.352678i $$0.885271\pi$$
$$48$$ 3584.00i 0.224525i
$$49$$ −8157.00 −0.485333
$$50$$ −4400.00 + 11700.0i −0.248902 + 0.661852i
$$51$$ 28672.0 1.54359
$$52$$ 10944.0i 0.561265i
$$53$$ 2964.00i 0.144940i 0.997371 + 0.0724700i $$0.0230882\pi$$
−0.997371 + 0.0724700i $$0.976912\pi$$
$$54$$ −16240.0 −0.757882
$$55$$ −8140.00 1480.00i −0.362842 0.0659713i
$$56$$ −10112.0 −0.430891
$$57$$ 31080.0i 1.26705i
$$58$$ 1080.00i 0.0421555i
$$59$$ 39740.0 1.48627 0.743135 0.669141i $$-0.233338\pi$$
0.743135 + 0.669141i $$0.233338\pi$$
$$60$$ 2240.00 12320.0i 0.0803285 0.441807i
$$61$$ −42298.0 −1.45544 −0.727722 0.685873i $$-0.759421\pi$$
−0.727722 + 0.685873i $$0.759421\pi$$
$$62$$ 8192.00i 0.270652i
$$63$$ 7426.00i 0.235724i
$$64$$ −4096.00 −0.125000
$$65$$ −6840.00 + 37620.0i −0.200804 + 1.10442i
$$66$$ 8288.00 0.234202
$$67$$ 32098.0i 0.873556i −0.899569 0.436778i $$-0.856119\pi$$
0.899569 0.436778i $$-0.143881\pi$$
$$68$$ 32768.0i 0.859365i
$$69$$ 17444.0 0.441086
$$70$$ 34760.0 + 6320.00i 0.847881 + 0.154160i
$$71$$ −4248.00 −0.100009 −0.0500044 0.998749i $$-0.515924\pi$$
−0.0500044 + 0.998749i $$0.515924\pi$$
$$72$$ 3008.00i 0.0683828i
$$73$$ 30104.0i 0.661176i 0.943775 + 0.330588i $$0.107247\pi$$
−0.943775 + 0.330588i $$0.892753\pi$$
$$74$$ −17488.0 −0.371245
$$75$$ −15400.0 + 40950.0i −0.316131 + 0.840622i
$$76$$ 35520.0 0.705406
$$77$$ 23384.0i 0.449461i
$$78$$ 38304.0i 0.712866i
$$79$$ −35280.0 −0.636005 −0.318003 0.948090i $$-0.603012\pi$$
−0.318003 + 0.948090i $$0.603012\pi$$
$$80$$ 14080.0 + 2560.00i 0.245967 + 0.0447214i
$$81$$ −45419.0 −0.769175
$$82$$ 9592.00i 0.157534i
$$83$$ 27826.0i 0.443359i −0.975120 0.221680i $$-0.928846\pi$$
0.975120 0.221680i $$-0.0711539\pi$$
$$84$$ −35392.0 −0.547277
$$85$$ 20480.0 112640.i 0.307456 1.69101i
$$86$$ −9176.00 −0.133785
$$87$$ 3780.00i 0.0535419i
$$88$$ 9472.00i 0.130387i
$$89$$ 85210.0 1.14029 0.570145 0.821544i $$-0.306887\pi$$
0.570145 + 0.821544i $$0.306887\pi$$
$$90$$ −1880.00 + 10340.0i −0.0244654 + 0.134559i
$$91$$ 108072. 1.36807
$$92$$ 19936.0i 0.245566i
$$93$$ 28672.0i 0.343756i
$$94$$ −42728.0 −0.498762
$$95$$ −122100. 22200.0i −1.38805 0.252374i
$$96$$ −14336.0 −0.158763
$$97$$ 97232.0i 1.04925i 0.851333 + 0.524626i $$0.175795\pi$$
−0.851333 + 0.524626i $$0.824205\pi$$
$$98$$ 32628.0i 0.343183i
$$99$$ −6956.00 −0.0713299
$$100$$ −46800.0 17600.0i −0.468000 0.176000i
$$101$$ −4298.00 −0.0419240 −0.0209620 0.999780i $$-0.506673\pi$$
−0.0209620 + 0.999780i $$0.506673\pi$$
$$102$$ 114688.i 1.09148i
$$103$$ 124114.i 1.15273i 0.817192 + 0.576365i $$0.195529\pi$$
−0.817192 + 0.576365i $$0.804471\pi$$
$$104$$ 43776.0 0.396874
$$105$$ 121660. + 22120.0i 1.07690 + 0.195800i
$$106$$ −11856.0 −0.102488
$$107$$ 42342.0i 0.357530i 0.983892 + 0.178765i $$0.0572101\pi$$
−0.983892 + 0.178765i $$0.942790\pi$$
$$108$$ 64960.0i 0.535904i
$$109$$ 35990.0 0.290145 0.145073 0.989421i $$-0.453658\pi$$
0.145073 + 0.989421i $$0.453658\pi$$
$$110$$ 5920.00 32560.0i 0.0466487 0.256568i
$$111$$ −61208.0 −0.471521
$$112$$ 40448.0i 0.304686i
$$113$$ 228816.i 1.68574i −0.538118 0.842869i $$-0.680865\pi$$
0.538118 0.842869i $$-0.319135\pi$$
$$114$$ 124320. 0.895940
$$115$$ 12460.0 68530.0i 0.0878564 0.483210i
$$116$$ −4320.00 −0.0298084
$$117$$ 32148.0i 0.217115i
$$118$$ 158960.i 1.05095i
$$119$$ −323584. −2.09469
$$120$$ 49280.0 + 8960.00i 0.312405 + 0.0568009i
$$121$$ −139147. −0.863993
$$122$$ 169192.i 1.02915i
$$123$$ 33572.0i 0.200085i
$$124$$ 32768.0 0.191380
$$125$$ 149875. + 89750.0i 0.857935 + 0.513759i
$$126$$ 29704.0 0.166682
$$127$$ 175238.i 0.964093i −0.876146 0.482047i $$-0.839894\pi$$
0.876146 0.482047i $$-0.160106\pi$$
$$128$$ 16384.0i 0.0883883i
$$129$$ −32116.0 −0.169921
$$130$$ −150480. 27360.0i −0.780945 0.141990i
$$131$$ 299652. 1.52559 0.762797 0.646638i $$-0.223826\pi$$
0.762797 + 0.646638i $$0.223826\pi$$
$$132$$ 33152.0i 0.165606i
$$133$$ 350760.i 1.71942i
$$134$$ 128392. 0.617698
$$135$$ −40600.0 + 223300.i −0.191731 + 1.05452i
$$136$$ −131072. −0.607663
$$137$$ 107928.i 0.491284i −0.969361 0.245642i $$-0.921001\pi$$
0.969361 0.245642i $$-0.0789988\pi$$
$$138$$ 69776.0i 0.311895i
$$139$$ 196460. 0.862456 0.431228 0.902243i $$-0.358080\pi$$
0.431228 + 0.902243i $$0.358080\pi$$
$$140$$ −25280.0 + 139040.i −0.109008 + 0.599542i
$$141$$ −149548. −0.633480
$$142$$ 16992.0i 0.0707170i
$$143$$ 101232.i 0.413978i
$$144$$ 12032.0 0.0483539
$$145$$ 14850.0 + 2700.00i 0.0586552 + 0.0106646i
$$146$$ −120416. −0.467522
$$147$$ 114198.i 0.435878i
$$148$$ 69952.0i 0.262510i
$$149$$ −138850. −0.512366 −0.256183 0.966628i $$-0.582465\pi$$
−0.256183 + 0.966628i $$0.582465\pi$$
$$150$$ −163800. 61600.0i −0.594410 0.223539i
$$151$$ 416152. 1.48528 0.742642 0.669688i $$-0.233572\pi$$
0.742642 + 0.669688i $$0.233572\pi$$
$$152$$ 142080.i 0.498797i
$$153$$ 96256.0i 0.332429i
$$154$$ −93536.0 −0.317817
$$155$$ −112640. 20480.0i −0.376585 0.0684701i
$$156$$ 153216. 0.504072
$$157$$ 433108.i 1.40232i −0.713004 0.701160i $$-0.752666\pi$$
0.713004 0.701160i $$-0.247334\pi$$
$$158$$ 141120.i 0.449724i
$$159$$ −41496.0 −0.130171
$$160$$ −10240.0 + 56320.0i −0.0316228 + 0.173925i
$$161$$ −196868. −0.598564
$$162$$ 181676.i 0.543889i
$$163$$ 149134.i 0.439651i 0.975539 + 0.219825i $$0.0705487\pi$$
−0.975539 + 0.219825i $$0.929451\pi$$
$$164$$ 38368.0 0.111393
$$165$$ 20720.0 113960.i 0.0592488 0.325869i
$$166$$ 111304. 0.313502
$$167$$ 559602.i 1.55270i 0.630301 + 0.776351i $$0.282932\pi$$
−0.630301 + 0.776351i $$0.717068\pi$$
$$168$$ 141568.i 0.386983i
$$169$$ −96563.0 −0.260072
$$170$$ 450560. + 81920.0i 1.19572 + 0.217404i
$$171$$ −104340. −0.272873
$$172$$ 36704.0i 0.0946002i
$$173$$ 343804.i 0.873365i 0.899616 + 0.436682i $$0.143847\pi$$
−0.899616 + 0.436682i $$0.856153\pi$$
$$174$$ −15120.0 −0.0378598
$$175$$ 173800. 462150.i 0.428997 1.14074i
$$176$$ −37888.0 −0.0921977
$$177$$ 556360.i 1.33482i
$$178$$ 340840.i 0.806307i
$$179$$ −23980.0 −0.0559392 −0.0279696 0.999609i $$-0.508904\pi$$
−0.0279696 + 0.999609i $$0.508904\pi$$
$$180$$ −41360.0 7520.00i −0.0951479 0.0172996i
$$181$$ −651898. −1.47905 −0.739526 0.673128i $$-0.764950\pi$$
−0.739526 + 0.673128i $$0.764950\pi$$
$$182$$ 432288.i 0.967375i
$$183$$ 592172.i 1.30713i
$$184$$ −79744.0 −0.173641
$$185$$ −43720.0 + 240460.i −0.0939184 + 0.516551i
$$186$$ 114688. 0.243072
$$187$$ 303104.i 0.633852i
$$188$$ 170912.i 0.352678i
$$189$$ 641480. 1.30626
$$190$$ 88800.0 488400.i 0.178455 0.981503i
$$191$$ 202752. 0.402144 0.201072 0.979576i $$-0.435557\pi$$
0.201072 + 0.979576i $$0.435557\pi$$
$$192$$ 57344.0i 0.112263i
$$193$$ 452656.i 0.874732i −0.899284 0.437366i $$-0.855911\pi$$
0.899284 0.437366i $$-0.144089\pi$$
$$194$$ −388928. −0.741933
$$195$$ −526680. 95760.0i −0.991883 0.180342i
$$196$$ 130512. 0.242667
$$197$$ 337468.i 0.619537i −0.950812 0.309768i $$-0.899748\pi$$
0.950812 0.309768i $$-0.100252\pi$$
$$198$$ 27824.0i 0.0504379i
$$199$$ 561000. 1.00422 0.502112 0.864803i $$-0.332557\pi$$
0.502112 + 0.864803i $$0.332557\pi$$
$$200$$ 70400.0 187200.i 0.124451 0.330926i
$$201$$ 449372. 0.784541
$$202$$ 17192.0i 0.0296448i
$$203$$ 42660.0i 0.0726576i
$$204$$ −458752. −0.771796
$$205$$ −131890. 23980.0i −0.219193 0.0398533i
$$206$$ −496456. −0.815103
$$207$$ 58562.0i 0.0949927i
$$208$$ 175104.i 0.280632i
$$209$$ 328560. 0.520294
$$210$$ −88480.0 + 486640.i −0.138451 + 0.761482i
$$211$$ −805548. −1.24562 −0.622810 0.782373i $$-0.714009\pi$$
−0.622810 + 0.782373i $$0.714009\pi$$
$$212$$ 47424.0i 0.0724700i
$$213$$ 59472.0i 0.0898180i
$$214$$ −169368. −0.252812
$$215$$ −22940.0 + 126170.i −0.0338452 + 0.186149i
$$216$$ 259840. 0.378941
$$217$$ 323584.i 0.466485i
$$218$$ 143960.i 0.205164i
$$219$$ −421456. −0.593802
$$220$$ 130240. + 23680.0i 0.181421 + 0.0329856i
$$221$$ 1.40083e6 1.92932
$$222$$ 244832.i 0.333415i
$$223$$ 1.21855e6i 1.64090i 0.571717 + 0.820451i $$0.306278\pi$$
−0.571717 + 0.820451i $$0.693722\pi$$
$$224$$ 161792. 0.215445
$$225$$ 137475. + 51700.0i 0.181037 + 0.0680823i
$$226$$ 915264. 1.19200
$$227$$ 564338.i 0.726900i −0.931614 0.363450i $$-0.881599\pi$$
0.931614 0.363450i $$-0.118401\pi$$
$$228$$ 497280.i 0.633525i
$$229$$ −560330. −0.706082 −0.353041 0.935608i $$-0.614852\pi$$
−0.353041 + 0.935608i $$0.614852\pi$$
$$230$$ 274120. + 49840.0i 0.341681 + 0.0621239i
$$231$$ −327376. −0.403661
$$232$$ 17280.0i 0.0210777i
$$233$$ 293576.i 0.354267i −0.984187 0.177134i $$-0.943318\pi$$
0.984187 0.177134i $$-0.0566824\pi$$
$$234$$ −128592. −0.153523
$$235$$ −106820. + 587510.i −0.126178 + 0.693978i
$$236$$ −635840. −0.743135
$$237$$ 493920.i 0.571197i
$$238$$ 1.29434e6i 1.48117i
$$239$$ −584240. −0.661602 −0.330801 0.943701i $$-0.607319\pi$$
−0.330801 + 0.943701i $$0.607319\pi$$
$$240$$ −35840.0 + 197120.i −0.0401643 + 0.220903i
$$241$$ −563798. −0.625289 −0.312645 0.949870i $$-0.601215\pi$$
−0.312645 + 0.949870i $$0.601215\pi$$
$$242$$ 556588.i 0.610936i
$$243$$ 350714.i 0.381011i
$$244$$ 676768. 0.727722
$$245$$ −448635. 81570.0i −0.477505 0.0868191i
$$246$$ 134288. 0.141481
$$247$$ 1.51848e6i 1.58368i
$$248$$ 131072.i 0.135326i
$$249$$ 389564. 0.398181
$$250$$ −359000. + 599500.i −0.363282 + 0.606651i
$$251$$ −1.01975e6 −1.02167 −0.510833 0.859680i $$-0.670663\pi$$
−0.510833 + 0.859680i $$0.670663\pi$$
$$252$$ 118816.i 0.117862i
$$253$$ 184408.i 0.181125i
$$254$$ 700952. 0.681717
$$255$$ 1.57696e6 + 286720.i 1.51869 + 0.276126i
$$256$$ 65536.0 0.0625000
$$257$$ 657408.i 0.620872i −0.950594 0.310436i $$-0.899525\pi$$
0.950594 0.310436i $$-0.100475\pi$$
$$258$$ 128464.i 0.120152i
$$259$$ 690776. 0.639864
$$260$$ 109440. 601920.i 0.100402 0.552211i
$$261$$ 12690.0 0.0115308
$$262$$ 1.19861e6i 1.07876i
$$263$$ 562366.i 0.501337i −0.968073 0.250668i $$-0.919350\pi$$
0.968073 0.250668i $$-0.0806504\pi$$
$$264$$ −132608. −0.117101
$$265$$ −29640.0 + 163020.i −0.0259277 + 0.142602i
$$266$$ −1.40304e6 −1.21581
$$267$$ 1.19294e6i 1.02410i
$$268$$ 513568.i 0.436778i
$$269$$ −366570. −0.308870 −0.154435 0.988003i $$-0.549356\pi$$
−0.154435 + 0.988003i $$0.549356\pi$$
$$270$$ −893200. 162400.i −0.745657 0.135574i
$$271$$ 1.16075e6 0.960099 0.480050 0.877241i $$-0.340619\pi$$
0.480050 + 0.877241i $$0.340619\pi$$
$$272$$ 524288.i 0.429682i
$$273$$ 1.51301e6i 1.22867i
$$274$$ 431712. 0.347390
$$275$$ −432900. 162800.i −0.345188 0.129814i
$$276$$ −279104. −0.220543
$$277$$ 2.51501e6i 1.96943i 0.174172 + 0.984715i $$0.444275\pi$$
−0.174172 + 0.984715i $$0.555725\pi$$
$$278$$ 785840.i 0.609849i
$$279$$ −96256.0 −0.0740316
$$280$$ −556160. 101120.i −0.423940 0.0770800i
$$281$$ 2.08600e6 1.57597 0.787987 0.615692i $$-0.211124\pi$$
0.787987 + 0.615692i $$0.211124\pi$$
$$282$$ 598192.i 0.447938i
$$283$$ 2.23803e6i 1.66111i −0.556935 0.830556i $$-0.688023\pi$$
0.556935 0.830556i $$-0.311977\pi$$
$$284$$ 67968.0 0.0500044
$$285$$ 310800. 1.70940e6i 0.226657 1.24661i
$$286$$ 404928. 0.292727
$$287$$ 378884.i 0.271520i
$$288$$ 48128.0i 0.0341914i
$$289$$ −2.77445e6 −1.95403
$$290$$ −10800.0 + 59400.0i −0.00754100 + 0.0414755i
$$291$$ −1.36125e6 −0.942334
$$292$$ 481664.i 0.330588i
$$293$$ 975756.i 0.664006i −0.943278 0.332003i $$-0.892276\pi$$
0.943278 0.332003i $$-0.107724\pi$$
$$294$$ 456792. 0.308212
$$295$$ 2.18570e6 + 397400.i 1.46230 + 0.265872i
$$296$$ 279808. 0.185623
$$297$$ 600880.i 0.395273i
$$298$$ 555400.i 0.362297i
$$299$$ 852264. 0.551310
$$300$$ 246400. 655200.i 0.158066 0.420311i
$$301$$ 362452. 0.230587
$$302$$ 1.66461e6i 1.05025i
$$303$$ 60172.0i 0.0376520i
$$304$$ −568320. −0.352703
$$305$$ −2.32639e6 422980.i −1.43197 0.260358i
$$306$$ 385024. 0.235063
$$307$$ 87858.0i 0.0532029i −0.999646 0.0266015i $$-0.991531\pi$$
0.999646 0.0266015i $$-0.00846850\pi$$
$$308$$ 374144.i 0.224730i
$$309$$ −1.73760e6 −1.03527
$$310$$ 81920.0 450560.i 0.0484156 0.266286i
$$311$$ 599352. 0.351383 0.175692 0.984445i $$-0.443784\pi$$
0.175692 + 0.984445i $$0.443784\pi$$
$$312$$ 612864.i 0.356433i
$$313$$ 2.09342e6i 1.20780i −0.797060 0.603900i $$-0.793613\pi$$
0.797060 0.603900i $$-0.206387\pi$$
$$314$$ 1.73243e6 0.991590
$$315$$ 74260.0 408430.i 0.0421676 0.231922i
$$316$$ 564480. 0.318003
$$317$$ 2.41625e6i 1.35050i 0.737590 + 0.675249i $$0.235964\pi$$
−0.737590 + 0.675249i $$0.764036\pi$$
$$318$$ 165984.i 0.0920446i
$$319$$ −39960.0 −0.0219861
$$320$$ −225280. 40960.0i −0.122984 0.0223607i
$$321$$ −592788. −0.321097
$$322$$ 787472.i 0.423249i
$$323$$ 4.54656e6i 2.42480i
$$324$$ 726704. 0.384587
$$325$$ −752400. + 2.00070e6i −0.395130 + 1.05069i
$$326$$ −596536. −0.310880
$$327$$ 503860.i 0.260580i
$$328$$ 153472.i 0.0787670i
$$329$$ 1.68776e6 0.859647
$$330$$ 455840. + 82880.0i 0.230424 + 0.0418953i
$$331$$ −1.64095e6 −0.823237 −0.411618 0.911356i $$-0.635036\pi$$
−0.411618 + 0.911356i $$0.635036\pi$$
$$332$$ 445216.i 0.221680i
$$333$$ 205484.i 0.101547i
$$334$$ −2.23841e6 −1.09793
$$335$$ 320980. 1.76539e6i 0.156267 0.859466i
$$336$$ 566272. 0.273638
$$337$$ 2.18773e6i 1.04935i −0.851304 0.524673i $$-0.824188\pi$$
0.851304 0.524673i $$-0.175812\pi$$
$$338$$ 386252.i 0.183899i
$$339$$ 3.20342e6 1.51396
$$340$$ −327680. + 1.80224e6i −0.153728 + 0.845503i
$$341$$ 303104. 0.141158
$$342$$ 417360.i 0.192950i
$$343$$ 1.36670e6i 0.627246i
$$344$$ 146816. 0.0668925
$$345$$ 959420. + 174440.i 0.433971 + 0.0789039i
$$346$$ −1.37522e6 −0.617562
$$347$$ 2.74502e6i 1.22383i −0.790923 0.611916i $$-0.790399\pi$$
0.790923 0.611916i $$-0.209601\pi$$
$$348$$ 60480.0i 0.0267709i
$$349$$ 2.65115e6 1.16512 0.582560 0.812788i $$-0.302051\pi$$
0.582560 + 0.812788i $$0.302051\pi$$
$$350$$ 1.84860e6 + 695200.i 0.806627 + 0.303347i
$$351$$ −2.77704e6 −1.20313
$$352$$ 151552.i 0.0651936i
$$353$$ 3.05766e6i 1.30603i 0.757345 + 0.653015i $$0.226496\pi$$
−0.757345 + 0.653015i $$0.773504\pi$$
$$354$$ −2.22544e6 −0.943860
$$355$$ −233640. 42480.0i −0.0983957 0.0178901i
$$356$$ −1.36336e6 −0.570145
$$357$$ 4.53018e6i 1.88124i
$$358$$ 95920.0i 0.0395550i
$$359$$ −3.79356e6 −1.55350 −0.776749 0.629810i $$-0.783133\pi$$
−0.776749 + 0.629810i $$0.783133\pi$$
$$360$$ 30080.0 165440.i 0.0122327 0.0672797i
$$361$$ 2.45230e6 0.990389
$$362$$ 2.60759e6i 1.04585i
$$363$$ 1.94806e6i 0.775953i
$$364$$ −1.72915e6 −0.684037
$$365$$ −301040. + 1.65572e6i −0.118275 + 0.650511i
$$366$$ 2.36869e6 0.924283
$$367$$ 3.11060e6i 1.20553i 0.797917 + 0.602767i $$0.205935\pi$$
−0.797917 + 0.602767i $$0.794065\pi$$
$$368$$ 318976.i 0.122783i
$$369$$ −112706. −0.0430905
$$370$$ −961840. 174880.i −0.365257 0.0664104i
$$371$$ 468312. 0.176645
$$372$$ 458752.i 0.171878i
$$373$$ 1.41520e6i 0.526677i −0.964703 0.263339i $$-0.915176\pi$$
0.964703 0.263339i $$-0.0848236\pi$$
$$374$$ −1.21242e6 −0.448201
$$375$$ −1.25650e6 + 2.09825e6i −0.461407 + 0.770511i
$$376$$ 683648. 0.249381
$$377$$ 184680.i 0.0669216i
$$378$$ 2.56592e6i 0.923663i
$$379$$ 3.90262e6 1.39559 0.697796 0.716297i $$-0.254164\pi$$
0.697796 + 0.716297i $$0.254164\pi$$
$$380$$ 1.95360e6 + 355200.i 0.694027 + 0.126187i
$$381$$ 2.45333e6 0.865852
$$382$$ 811008.i 0.284359i
$$383$$ 695674.i 0.242331i 0.992632 + 0.121165i $$0.0386632\pi$$
−0.992632 + 0.121165i $$0.961337\pi$$
$$384$$ 229376. 0.0793816
$$385$$ −233840. + 1.28612e6i −0.0804020 + 0.442211i
$$386$$ 1.81062e6 0.618529
$$387$$ 107818.i 0.0365943i
$$388$$ 1.55571e6i 0.524626i
$$389$$ −498290. −0.166958 −0.0834792 0.996510i $$-0.526603\pi$$
−0.0834792 + 0.996510i $$0.526603\pi$$
$$390$$ 383040. 2.10672e6i 0.127521 0.701367i
$$391$$ −2.55181e6 −0.844124
$$392$$ 522048.i 0.171591i
$$393$$ 4.19513e6i 1.37014i
$$394$$ 1.34987e6 0.438079
$$395$$ −1.94040e6 352800.i −0.625747 0.113772i
$$396$$ 111296. 0.0356649
$$397$$ 1.09567e6i 0.348901i −0.984666 0.174451i $$-0.944185\pi$$
0.984666 0.174451i $$-0.0558150\pi$$
$$398$$ 2.24400e6i 0.710093i
$$399$$ −4.91064e6 −1.54421
$$400$$ 748800. + 281600.i 0.234000 + 0.0880000i
$$401$$ −2.49160e6 −0.773779 −0.386890 0.922126i $$-0.626451\pi$$
−0.386890 + 0.922126i $$0.626451\pi$$
$$402$$ 1.79749e6i 0.554755i
$$403$$ 1.40083e6i 0.429659i
$$404$$ 68768.0 0.0209620
$$405$$ −2.49805e6 454190.i −0.756768 0.137594i
$$406$$ 170640. 0.0513766
$$407$$ 647056.i 0.193623i
$$408$$ 1.83501e6i 0.545742i
$$409$$ 3.63349e6 1.07403 0.537014 0.843573i $$-0.319552\pi$$
0.537014 + 0.843573i $$0.319552\pi$$
$$410$$ 95920.0 527560.i 0.0281806 0.154993i
$$411$$ 1.51099e6 0.441222
$$412$$ 1.98582e6i 0.576365i
$$413$$ 6.27892e6i 1.81138i
$$414$$ 234248. 0.0671700
$$415$$ 278260. 1.53043e6i 0.0793105 0.436208i
$$416$$ −700416. −0.198437
$$417$$ 2.75044e6i 0.774572i
$$418$$ 1.31424e6i 0.367904i
$$419$$ 3.64378e6 1.01395 0.506976 0.861960i $$-0.330763\pi$$
0.506976 + 0.861960i $$0.330763\pi$$
$$420$$ −1.94656e6 353920.i −0.538449 0.0978998i
$$421$$ −1.82530e6 −0.501913 −0.250957 0.967998i $$-0.580745\pi$$
−0.250957 + 0.967998i $$0.580745\pi$$
$$422$$ 3.22219e6i 0.880786i
$$423$$ 502054.i 0.136427i
$$424$$ 189696. 0.0512441
$$425$$ 2.25280e6 5.99040e6i 0.604993 1.60873i
$$426$$ 237888. 0.0635109
$$427$$ 6.68308e6i 1.77381i
$$428$$ 677472.i 0.178765i
$$429$$ 1.41725e6 0.371794
$$430$$ −504680. 91760.0i −0.131627 0.0239322i
$$431$$ 2.85435e6 0.740141 0.370070 0.929004i $$-0.379334\pi$$
0.370070 + 0.929004i $$0.379334\pi$$
$$432$$ 1.03936e6i 0.267952i
$$433$$ 587776.i 0.150658i −0.997159 0.0753290i $$-0.975999\pi$$
0.997159 0.0753290i $$-0.0240007\pi$$
$$434$$ −1.29434e6 −0.329855
$$435$$ −37800.0 + 207900.i −0.00957786 + 0.0526783i
$$436$$ −575840. −0.145073
$$437$$ 2.76612e6i 0.692895i
$$438$$ 1.68582e6i 0.419882i
$$439$$ −6.11604e6 −1.51464 −0.757319 0.653045i $$-0.773491\pi$$
−0.757319 + 0.653045i $$0.773491\pi$$
$$440$$ −94720.0 + 520960.i −0.0233244 + 0.128284i
$$441$$ −383379. −0.0938711
$$442$$ 5.60333e6i 1.36424i
$$443$$ 2.35771e6i 0.570795i −0.958409 0.285398i $$-0.907874\pi$$
0.958409 0.285398i $$-0.0921257\pi$$
$$444$$ 979328. 0.235760
$$445$$ 4.68655e6 + 852100.i 1.12190 + 0.203981i
$$446$$ −4.87422e6 −1.16029
$$447$$ 1.94390e6i 0.460156i
$$448$$ 647168.i 0.152343i
$$449$$ −5.49735e6 −1.28688 −0.643439 0.765497i $$-0.722493\pi$$
−0.643439 + 0.765497i $$0.722493\pi$$
$$450$$ −206800. + 549900.i −0.0481415 + 0.128013i
$$451$$ 354904. 0.0821617
$$452$$ 3.66106e6i 0.842869i
$$453$$ 5.82613e6i 1.33393i
$$454$$ 2.25735e6 0.513996
$$455$$ 5.94396e6 + 1.08072e6i 1.34601 + 0.244729i
$$456$$ −1.98912e6 −0.447970
$$457$$ 1.16039e6i 0.259905i 0.991520 + 0.129952i $$0.0414824\pi$$
−0.991520 + 0.129952i $$0.958518\pi$$
$$458$$ 2.24132e6i 0.499275i
$$459$$ 8.31488e6 1.84215
$$460$$ −199360. + 1.09648e6i −0.0439282 + 0.241605i
$$461$$ −2.30330e6 −0.504775 −0.252387 0.967626i $$-0.581216\pi$$
−0.252387 + 0.967626i $$0.581216\pi$$
$$462$$ 1.30950e6i 0.285431i
$$463$$ 2.71343e6i 0.588257i 0.955766 + 0.294128i $$0.0950293\pi$$
−0.955766 + 0.294128i $$0.904971\pi$$
$$464$$ 69120.0 0.0149042
$$465$$ 286720. 1.57696e6i 0.0614930 0.338211i
$$466$$ 1.17430e6 0.250505
$$467$$ 4.05050e6i 0.859441i −0.902962 0.429721i $$-0.858612\pi$$
0.902962 0.429721i $$-0.141388\pi$$
$$468$$ 514368.i 0.108557i
$$469$$ −5.07148e6 −1.06464
$$470$$ −2.35004e6 427280.i −0.490716 0.0892212i
$$471$$ 6.06351e6 1.25942
$$472$$ 2.54336e6i 0.525476i
$$473$$ 339512.i 0.0697754i
$$474$$ 1.97568e6 0.403897
$$475$$ −6.49350e6 2.44200e6i −1.32052 0.496606i
$$476$$ 5.17734e6 1.04734
$$477$$ 139308.i 0.0280337i
$$478$$ 2.33696e6i 0.467823i
$$479$$ −5.60528e6 −1.11624 −0.558121 0.829759i $$-0.688478\pi$$
−0.558121 + 0.829759i $$0.688478\pi$$
$$480$$ −788480. 143360.i −0.156202 0.0284004i
$$481$$ −2.99045e6 −0.589350
$$482$$ 2.25519e6i 0.442146i
$$483$$ 2.75615e6i 0.537570i
$$484$$ 2.22635e6 0.431997
$$485$$ −972320. + 5.34776e6i −0.187696 + 1.03233i
$$486$$ −1.40286e6 −0.269415
$$487$$ 7.13168e6i 1.36260i −0.732003 0.681301i $$-0.761414\pi$$
0.732003 0.681301i $$-0.238586\pi$$
$$488$$ 2.70707e6i 0.514577i
$$489$$ −2.08788e6 −0.394850
$$490$$ 326280. 1.79454e6i 0.0613904 0.337647i
$$491$$ 5.88145e6 1.10098 0.550492 0.834841i $$-0.314440\pi$$
0.550492 + 0.834841i $$0.314440\pi$$
$$492$$ 537152.i 0.100042i
$$493$$ 552960.i 0.102465i
$$494$$ 6.07392e6 1.11983
$$495$$ −382580. 69560.0i −0.0701793 0.0127599i
$$496$$ −524288. −0.0956898
$$497$$ 671184.i 0.121885i
$$498$$ 1.55826e6i 0.281556i
$$499$$ −1.75710e6 −0.315897 −0.157948 0.987447i $$-0.550488\pi$$
−0.157948 + 0.987447i $$0.550488\pi$$
$$500$$ −2.39800e6 1.43600e6i −0.428967 0.256879i
$$501$$ −7.83443e6 −1.39448
$$502$$ 4.07899e6i 0.722426i
$$503$$ 4.91411e6i 0.866015i 0.901390 + 0.433007i $$0.142548\pi$$
−0.901390 + 0.433007i $$0.857452\pi$$
$$504$$ −475264. −0.0833410
$$505$$ −236390. 42980.0i −0.0412478 0.00749960i
$$506$$ −737632. −0.128075
$$507$$ 1.35188e6i 0.233571i
$$508$$ 2.80381e6i 0.482047i
$$509$$ 5.75499e6 0.984578 0.492289 0.870432i $$-0.336160\pi$$
0.492289 + 0.870432i $$0.336160\pi$$
$$510$$ −1.14688e6 + 6.30784e6i −0.195251 + 1.07388i
$$511$$ 4.75643e6 0.805803
$$512$$ 262144.i 0.0441942i
$$513$$ 9.01320e6i 1.51212i
$$514$$ 2.62963e6 0.439023
$$515$$ −1.24114e6 + 6.82627e6i −0.206207 + 1.13414i
$$516$$ 513856. 0.0849605
$$517$$ 1.58094e6i 0.260128i
$$518$$ 2.76310e6i 0.452452i
$$519$$ −4.81326e6 −0.784369
$$520$$ 2.40768e6 + 437760.i 0.390472 + 0.0709950i
$$521$$ −1.61980e6 −0.261437 −0.130718 0.991420i $$-0.541728\pi$$
−0.130718 + 0.991420i $$0.541728\pi$$
$$522$$ 50760.0i 0.00815352i
$$523$$ 1.19117e7i 1.90422i 0.305751 + 0.952112i $$0.401093\pi$$
−0.305751 + 0.952112i $$0.598907\pi$$
$$524$$ −4.79443e6 −0.762797
$$525$$ 6.47010e6 + 2.43320e6i 1.02450 + 0.385283i
$$526$$ 2.24946e6 0.354499
$$527$$ 4.19430e6i 0.657860i
$$528$$ 530432.i 0.0828028i
$$529$$ 4.88383e6 0.758789
$$530$$ −652080. 118560.i −0.100835 0.0183336i
$$531$$ 1.86778e6 0.287468
$$532$$ 5.61216e6i 0.859708i
$$533$$ 1.64023e6i 0.250085i
$$534$$ −4.77176e6 −0.724145
$$535$$ −423420. + 2.32881e6i −0.0639568 + 0.351763i
$$536$$ −2.05427e6 −0.308849
$$537$$ 335720.i 0.0502391i
$$538$$ 1.46628e6i 0.218404i
$$539$$ 1.20724e6 0.178986
$$540$$ 649600. 3.57280e6i 0.0958653 0.527259i
$$541$$ 4.07630e6 0.598788 0.299394 0.954130i $$-0.403215\pi$$
0.299394 + 0.954130i $$0.403215\pi$$
$$542$$ 4.64301e6i 0.678893i
$$543$$ 9.12657e6i 1.32834i
$$544$$ 2.09715e6 0.303831
$$545$$ 1.97945e6 + 359900.i 0.285465 + 0.0519028i
$$546$$ −6.05203e6 −0.868800
$$547$$ 1.23680e7i 1.76739i −0.468065 0.883694i $$-0.655049\pi$$
0.468065 0.883694i $$-0.344951\pi$$
$$548$$ 1.72685e6i 0.245642i
$$549$$ −1.98801e6 −0.281505
$$550$$ 651200. 1.73160e6i 0.0917926 0.244085i
$$551$$ −599400. −0.0841081
$$552$$ 1.11642e6i 0.155947i
$$553$$ 5.57424e6i 0.775127i
$$554$$ −1.00600e7 −1.39260
$$555$$ −3.36644e6 612080.i −0.463915 0.0843482i
$$556$$ −3.14336e6 −0.431228
$$557$$ 130308.i 0.0177964i −0.999960 0.00889822i $$-0.997168\pi$$
0.999960 0.00889822i $$-0.00283243\pi$$
$$558$$ 385024.i 0.0523483i
$$559$$ −1.56910e6 −0.212383
$$560$$ 404480. 2.22464e6i 0.0545038 0.299771i
$$561$$ −4.24346e6 −0.569262
$$562$$ 8.34401e6i 1.11438i
$$563$$ 5.91687e6i 0.786721i −0.919384 0.393361i $$-0.871312\pi$$
0.919384 0.393361i $$-0.128688\pi$$
$$564$$ 2.39277e6 0.316740
$$565$$ 2.28816e6 1.25849e7i 0.301554 1.65855i
$$566$$ 8.95210e6 1.17458
$$567$$ 7.17620e6i 0.937426i
$$568$$ 271872.i 0.0353585i
$$569$$ 9.03013e6 1.16927 0.584633 0.811298i $$-0.301239\pi$$
0.584633 + 0.811298i $$0.301239\pi$$
$$570$$ 6.83760e6 + 1.24320e6i 0.881488 + 0.160271i
$$571$$ −1.07093e7 −1.37459 −0.687294 0.726379i $$-0.741202\pi$$
−0.687294 + 0.726379i $$0.741202\pi$$
$$572$$ 1.61971e6i 0.206989i
$$573$$ 2.83853e6i 0.361166i
$$574$$ −1.51554e6 −0.191994
$$575$$ 1.37060e6 3.64455e6i 0.172879 0.459700i
$$576$$ −192512. −0.0241770
$$577$$ 1.22051e6i 0.152617i 0.997084 + 0.0763084i $$0.0243134\pi$$
−0.997084 + 0.0763084i $$0.975687\pi$$
$$578$$ 1.10978e7i 1.38171i
$$579$$ 6.33718e6 0.785597
$$580$$ −237600. 43200.0i −0.0293276 0.00533229i
$$581$$ −4.39651e6 −0.540341
$$582$$ 5.44499e6i 0.666331i
$$583$$ 438672.i 0.0534526i
$$584$$ 1.92666e6 0.233761
$$585$$ −321480. + 1.76814e6i −0.0388387 + 0.213613i
$$586$$ 3.90302e6 0.469523
$$587$$ 1.47104e7i 1.76210i 0.473026 + 0.881049i $$0.343162\pi$$
−0.473026 + 0.881049i $$0.656838\pi$$
$$588$$ 1.82717e6i 0.217939i
$$589$$ 4.54656e6 0.540001
$$590$$ −1.58960e6 + 8.74280e6i −0.188000 + 1.03400i
$$591$$ 4.72455e6 0.556406
$$592$$ 1.11923e6i 0.131255i
$$593$$ 8.52014e6i 0.994970i 0.867472 + 0.497485i $$0.165743\pi$$
−0.867472 + 0.497485i $$0.834257\pi$$
$$594$$ 2.40352e6 0.279500
$$595$$ −1.77971e7 3.23584e6i −2.06090 0.374709i
$$596$$ 2.22160e6 0.256183
$$597$$ 7.85400e6i 0.901893i
$$598$$ 3.40906e6i 0.389835i
$$599$$ −2.90100e6 −0.330355 −0.165177 0.986264i $$-0.552820\pi$$
−0.165177 + 0.986264i $$0.552820\pi$$
$$600$$ 2.62080e6 + 985600.i 0.297205 + 0.111769i
$$601$$ 5.72760e6 0.646825 0.323412 0.946258i $$-0.395170\pi$$
0.323412 + 0.946258i $$0.395170\pi$$
$$602$$ 1.44981e6i 0.163049i
$$603$$ 1.50861e6i 0.168959i
$$604$$ −6.65843e6 −0.742642
$$605$$ −7.65308e6 1.39147e6i −0.850057 0.154556i
$$606$$ 240688. 0.0266240
$$607$$ 8.79924e6i 0.969334i 0.874699 + 0.484667i $$0.161059\pi$$
−0.874699 + 0.484667i $$0.838941\pi$$
$$608$$ 2.27328e6i 0.249399i
$$609$$ 597240. 0.0652538
$$610$$ 1.69192e6 9.30556e6i 0.184101 1.01255i
$$611$$ −7.30649e6 −0.791782
$$612$$ 1.54010e6i 0.166215i
$$613$$ 1.03408e6i 0.111149i 0.998455 + 0.0555744i $$0.0176990\pi$$
−0.998455 + 0.0555744i $$0.982301\pi$$
$$614$$ 351432. 0.0376201
$$615$$ 335720. 1.84646e6i 0.0357923 0.196858i
$$616$$ 1.49658e6 0.158908
$$617$$ 1.29854e7i 1.37323i −0.727020 0.686616i $$-0.759095\pi$$
0.727020 0.686616i $$-0.240905\pi$$
$$618$$ 6.95038e6i 0.732045i
$$619$$ −7.92002e6 −0.830806 −0.415403 0.909637i $$-0.636359\pi$$
−0.415403 + 0.909637i $$0.636359\pi$$
$$620$$ 1.80224e6 + 327680.i 0.188293 + 0.0342350i
$$621$$ 5.05876e6 0.526399
$$622$$ 2.39741e6i 0.248465i
$$623$$ 1.34632e7i 1.38972i
$$624$$ −2.45146e6 −0.252036
$$625$$ 7.34562e6 + 6.43500e6i 0.752192 + 0.658944i
$$626$$ 8.37366e6 0.854043
$$627$$ 4.59984e6i 0.467276i
$$628$$ 6.92973e6i 0.701160i
$$629$$ 8.95386e6 0.902368
$$630$$ 1.63372e6 + 297040.i 0.163993 + 0.0298170i
$$631$$ 1.68218e7 1.68189 0.840945 0.541120i $$-0.181999\pi$$
0.840945 + 0.541120i $$0.181999\pi$$
$$632$$ 2.25792e6i 0.224862i
$$633$$ 1.12777e7i 1.11869i
$$634$$ −9.66501e6 −0.954947
$$635$$ 1.75238e6 9.63809e6i 0.172462 0.948542i
$$636$$ 663936. 0.0650854
$$637$$ 5.57939e6i 0.544801i
$$638$$ 159840.i 0.0155465i
$$639$$ −199656. −0.0193433
$$640$$ 163840. 901120.i 0.0158114 0.0869626i
$$641$$ −1.55154e7 −1.49148 −0.745741 0.666236i $$-0.767904\pi$$
−0.745741 + 0.666236i $$0.767904\pi$$
$$642$$ 2.37115e6i 0.227050i
$$643$$ 1.05801e7i 1.00916i 0.863364 + 0.504582i $$0.168354\pi$$
−0.863364 + 0.504582i $$0.831646\pi$$
$$644$$ 3.14989e6 0.299282
$$645$$ −1.76638e6 321160.i −0.167180 0.0303964i
$$646$$ −1.81862e7 −1.71460
$$647$$ 1.37883e7i 1.29494i −0.762090 0.647471i $$-0.775827\pi$$
0.762090 0.647471i $$-0.224173\pi$$
$$648$$ 2.90682e6i 0.271944i
$$649$$ −5.88152e6 −0.548123
$$650$$ −8.00280e6 3.00960e6i −0.742948 0.279399i
$$651$$ −4.53018e6 −0.418950
$$652$$ 2.38614e6i 0.219825i
$$653$$ 1.58924e6i 0.145850i −0.997337 0.0729248i $$-0.976767\pi$$
0.997337 0.0729248i $$-0.0232333\pi$$
$$654$$ −2.01544e6 −0.184258
$$655$$ 1.64809e7 + 2.99652e6i 1.50099 + 0.272907i
$$656$$ −613888. −0.0556967
$$657$$ 1.41489e6i 0.127882i
$$658$$ 6.75102e6i 0.607862i
$$659$$ 9.12434e6 0.818442 0.409221 0.912435i $$-0.365801\pi$$
0.409221 + 0.912435i $$0.365801\pi$$
$$660$$ −331520. + 1.82336e6i −0.0296244 + 0.162934i
$$661$$ 6.50310e6 0.578918 0.289459 0.957190i $$-0.406525\pi$$
0.289459 + 0.957190i $$0.406525\pi$$
$$662$$ 6.56379e6i 0.582116i
$$663$$ 1.96116e7i 1.73273i
$$664$$ −1.78086e6 −0.156751
$$665$$ −3.50760e6 + 1.92918e7i −0.307578 + 1.69168i
$$666$$ −821936. −0.0718046
$$667$$ 336420.i 0.0292797i
$$668$$ 8.95363e6i 0.776351i
$$669$$ −1.70598e7 −1.47369
$$670$$ 7.06156e6 + 1.28392e6i 0.607734 + 0.110497i
$$671$$ 6.26010e6 0.536754
$$672$$ 2.26509e6i 0.193492i
$$673$$ 2.17810e6i 0.185370i −0.995695 0.0926850i $$-0.970455\pi$$
0.995695 0.0926850i $$-0.0295449\pi$$
$$674$$ 8.75091e6 0.741999
$$675$$ −4.46600e6 + 1.18755e7i −0.377276 + 1.00321i
$$676$$ 1.54501e6 0.130036
$$677$$ 3.98419e6i 0.334094i −0.985949 0.167047i $$-0.946577\pi$$
0.985949 0.167047i $$-0.0534231\pi$$
$$678$$ 1.28137e7i 1.07053i
$$679$$ 1.53627e7 1.27877
$$680$$ −7.20896e6 1.31072e6i −0.597861 0.108702i
$$681$$ 7.90073e6 0.652829
$$682$$ 1.21242e6i 0.0998138i
$$683$$ 5.91563e6i 0.485231i −0.970122 0.242616i $$-0.921995\pi$$
0.970122 0.242616i $$-0.0780054\pi$$
$$684$$ 1.66944e6 0.136436
$$685$$ 1.07928e6 5.93604e6i 0.0878836 0.483360i
$$686$$ 5.46680e6 0.443530
$$687$$ 7.84462e6i 0.634133i
$$688$$ 587264.i 0.0473001i
$$689$$ −2.02738e6 −0.162700
$$690$$ −697760. + 3.83768e6i −0.0557935 + 0.306864i
$$691$$ −1.55471e7 −1.23867 −0.619335 0.785127i $$-0.712598\pi$$
−0.619335 + 0.785127i $$0.712598\pi$$
$$692$$ 5.50086e6i 0.436682i
$$693$$ 1.09905e6i 0.0869328i
$$694$$ 1.09801e7 0.865379
$$695$$ 1.08053e7 + 1.96460e6i 0.848545 + 0.154281i
$$696$$ 241920. 0.0189299
$$697$$ 4.91110e6i 0.382910i
$$698$$ 1.06046e7i 0.823864i
$$699$$ 4.11006e6 0.318167
$$700$$ −2.78080e6 + 7.39440e6i −0.214499 + 0.570372i
$$701$$ −2.27103e7 −1.74553 −0.872766 0.488139i $$-0.837676\pi$$
−0.872766 + 0.488139i $$0.837676\pi$$
$$702$$ 1.11082e7i 0.850745i
$$703$$ 9.70584e6i 0.740704i
$$704$$ 606208. 0.0460988
$$705$$ −8.22514e6 1.49548e6i −0.623262 0.113320i
$$706$$ −1.22307e7 −0.923502
$$707$$ 679084.i 0.0510946i
$$708$$ 8.90176e6i 0.667410i
$$709$$ −6.29841e6 −0.470560 −0.235280 0.971928i $$-0.575601\pi$$
−0.235280 + 0.971928i $$0.575601\pi$$
$$710$$ 169920. 934560.i 0.0126502 0.0695763i
$$711$$ −1.65816e6 −0.123013
$$712$$ 5.45344e6i 0.403154i
$$713$$ 2.55181e6i 0.187985i
$$714$$ 1.81207e7 1.33024
$$715$$ 1.01232e6 5.56776e6i 0.0740547 0.407301i
$$716$$ 383680. 0.0279696
$$717$$ 8.17936e6i 0.594185i
$$718$$ 1.51742e7i 1.09849i
$$719$$ −2.11911e7 −1.52873 −0.764367 0.644782i $$-0.776948\pi$$
−0.764367 + 0.644782i $$0.776948\pi$$
$$720$$ 661760. + 120320.i 0.0475740 + 0.00864981i
$$721$$ 1.96100e7 1.40488
$$722$$ 9.80920e6i 0.700311i
$$723$$ 7.89317e6i 0.561572i
$$724$$ 1.04304e7 0.739526
$$725$$ 789750. + 297000.i 0.0558013 + 0.0209851i
$$726$$ 7.79223e6 0.548682
$$727$$ 1.35610e7i 0.951605i −0.879552 0.475803i $$-0.842158\pi$$
0.879552 0.475803i $$-0.157842\pi$$
$$728$$ 6.91661e6i 0.483687i
$$729$$ −1.59468e7 −1.11136
$$730$$ −6.62288e6 1.20416e6i −0.459981 0.0836329i
$$731$$ 4.69811e6 0.325185
$$732$$ 9.47475e6i 0.653567i
$$733$$ 2.69413e7i 1.85208i 0.377429 + 0.926038i $$0.376808\pi$$
−0.377429 + 0.926038i $$0.623192\pi$$
$$734$$ −1.24424e7 −0.852441
$$735$$ 1.14198e6 6.28089e6i 0.0779723 0.428847i
$$736$$ 1.27590e6 0.0868207
$$737$$ 4.75050e6i 0.322160i
$$738$$ 450824.i 0.0304696i
$$739$$ −2.77414e6 −0.186860 −0.0934302 0.995626i $$-0.529783\pi$$
−0.0934302 + 0.995626i $$0.529783\pi$$
$$740$$ 699520. 3.84736e6i 0.0469592 0.258276i
$$741$$ 2.12587e7 1.42230
$$742$$ 1.87325e6i 0.124907i
$$743$$ 1.85538e7i 1.23299i 0.787358 + 0.616497i $$0.211449\pi$$
−0.787358 + 0.616497i $$0.788551\pi$$
$$744$$ −1.83501e6 −0.121536
$$745$$ −7.63675e6 1.38850e6i −0.504101 0.0916548i
$$746$$ 5.66078e6 0.372417
$$747$$ 1.30782e6i 0.0857526i
$$748$$ 4.84966e6i 0.316926i
$$749$$ 6.69004e6 0.435736
$$750$$ −8.39300e6 5.02600e6i −0.544834 0.326264i
$$751$$ −2.19285e6 −0.141876 −0.0709380 0.997481i $$-0.522599\pi$$
−0.0709380 + 0.997481i $$0.522599\pi$$
$$752$$ 2.73459e6i 0.176339i
$$753$$ 1.42765e7i 0.917558i
$$754$$ −738720. −0.0473207
$$755$$ 2.28884e7 + 4.16152e6i 1.46133 + 0.265696i
$$756$$ −1.02637e7 −0.653128
$$757$$ 9.48749e6i 0.601744i 0.953665 + 0.300872i $$0.0972777\pi$$
−0.953665 + 0.300872i $$0.902722\pi$$
$$758$$ 1.56105e7i 0.986832i
$$759$$ −2.58171e6 −0.162668
$$760$$ −1.42080e6 + 7.81440e6i −0.0892275 + 0.490752i
$$761$$ 9.69580e6 0.606907 0.303453 0.952846i $$-0.401860\pi$$
0.303453 + 0.952846i $$0.401860\pi$$
$$762$$ 9.81333e6i 0.612250i
$$763$$ 5.68642e6i 0.353612i
$$764$$ −3.24403e6 −0.201072
$$765$$ 962560. 5.29408e6i 0.0594668 0.327067i
$$766$$ −2.78270e6 −0.171354
$$767$$ 2.71822e7i 1.66838i
$$768$$ 917504.i 0.0561313i
$$769$$ −9.32787e6 −0.568809 −0.284405 0.958704i $$-0.591796\pi$$
−0.284405 + 0.958704i $$0.591796\pi$$
$$770$$ −5.14448e6 935360.i −0.312690 0.0568528i
$$771$$ 9.20371e6 0.557606
$$772$$ 7.24250e6i 0.437366i
$$773$$ 9.68080e6i 0.582723i −0.956613 0.291362i $$-0.905892\pi$$
0.956613 0.291362i $$-0.0941083\pi$$
$$774$$ −431272. −0.0258761
$$775$$ −5.99040e6 2.25280e6i −0.358263 0.134731i
$$776$$ 6.22285e6 0.370967
$$777$$ 9.67086e6i 0.574662i
$$778$$ 1.99316e6i 0.118057i
$$779$$ 5.32356e6 0.314310
$$780$$ 8.42688e6 + 1.53216e6i 0.495941 + 0.0901712i
$$781$$ 628704. 0.0368824
$$782$$ 1.02072e7i 0.596886i
$$783$$ 1.09620e6i 0.0638977i
$$784$$ −2.08819e6 −0.121333
$$785$$ 4.33108e6 2.38209e7i 0.250855 1.37970i
$$786$$ −1.67805e7 −0.968833
$$787$$ 5.52302e6i 0.317863i 0.987290 + 0.158931i $$0.0508049\pi$$
−0.987290 + 0.158931i $$0.949195\pi$$
$$788$$ 5.39949e6i 0.309768i
$$789$$ 7.87312e6 0.450251
$$790$$ 1.41120e6 7.76160e6i 0.0804490 0.442470i
$$791$$ −3.61529e7 −2.05448
$$792$$ 445184.i 0.0252189i
$$793$$ 2.89318e7i 1.63378i
$$794$$ 4.38267e6 0.246711
$$795$$ −2.28228e6