# Properties

 Label 882.4.g.b.667.1 Level $882$ Weight $4$ Character 882.667 Analytic conductor $52.040$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 882.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$52.0396846251$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 667.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.667 Dual form 882.4.g.b.361.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.00000 + 12.1244i) q^{5} +8.00000 q^{8} +O(q^{10})$$ $$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.00000 + 12.1244i) q^{5} +8.00000 q^{8} +(-14.0000 - 24.2487i) q^{10} +(-14.0000 - 24.2487i) q^{11} +18.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(37.0000 + 64.0859i) q^{17} +(-40.0000 + 69.2820i) q^{19} +56.0000 q^{20} +56.0000 q^{22} +(-56.0000 + 96.9948i) q^{23} +(-35.5000 - 61.4878i) q^{25} +(-18.0000 + 31.1769i) q^{26} -190.000 q^{29} +(-36.0000 - 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} -148.000 q^{34} +(173.000 - 299.645i) q^{37} +(-80.0000 - 138.564i) q^{38} +(-56.0000 + 96.9948i) q^{40} -162.000 q^{41} -412.000 q^{43} +(-56.0000 + 96.9948i) q^{44} +(-112.000 - 193.990i) q^{46} +(12.0000 - 20.7846i) q^{47} +142.000 q^{50} +(-36.0000 - 62.3538i) q^{52} +(159.000 + 275.396i) q^{53} +392.000 q^{55} +(190.000 - 329.090i) q^{58} +(-100.000 - 173.205i) q^{59} +(99.0000 - 171.473i) q^{61} +144.000 q^{62} +64.0000 q^{64} +(-126.000 + 218.238i) q^{65} +(358.000 + 620.074i) q^{67} +(148.000 - 256.344i) q^{68} -392.000 q^{71} +(-269.000 - 465.922i) q^{73} +(346.000 + 599.290i) q^{74} +320.000 q^{76} +(-120.000 + 207.846i) q^{79} +(-112.000 - 193.990i) q^{80} +(162.000 - 280.592i) q^{82} +1072.00 q^{83} -1036.00 q^{85} +(412.000 - 713.605i) q^{86} +(-112.000 - 193.990i) q^{88} +(405.000 - 701.481i) q^{89} +448.000 q^{92} +(24.0000 + 41.5692i) q^{94} +(-560.000 - 969.948i) q^{95} +1354.00 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{2} - 4q^{4} - 14q^{5} + 16q^{8} + O(q^{10})$$ $$2q - 2q^{2} - 4q^{4} - 14q^{5} + 16q^{8} - 28q^{10} - 28q^{11} + 36q^{13} - 16q^{16} + 74q^{17} - 80q^{19} + 112q^{20} + 112q^{22} - 112q^{23} - 71q^{25} - 36q^{26} - 380q^{29} - 72q^{31} - 32q^{32} - 296q^{34} + 346q^{37} - 160q^{38} - 112q^{40} - 324q^{41} - 824q^{43} - 112q^{44} - 224q^{46} + 24q^{47} + 284q^{50} - 72q^{52} + 318q^{53} + 784q^{55} + 380q^{58} - 200q^{59} + 198q^{61} + 288q^{62} + 128q^{64} - 252q^{65} + 716q^{67} + 296q^{68} - 784q^{71} - 538q^{73} + 692q^{74} + 640q^{76} - 240q^{79} - 224q^{80} + 324q^{82} + 2144q^{83} - 2072q^{85} + 824q^{86} - 224q^{88} + 810q^{89} + 896q^{92} + 48q^{94} - 1120q^{95} + 2708q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 + 1.73205i −0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −2.00000 3.46410i −0.250000 0.433013i
$$5$$ −7.00000 + 12.1244i −0.626099 + 1.08444i 0.362228 + 0.932089i $$0.382016\pi$$
−0.988327 + 0.152346i $$0.951317\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 8.00000 0.353553
$$9$$ 0 0
$$10$$ −14.0000 24.2487i −0.442719 0.766812i
$$11$$ −14.0000 24.2487i −0.383742 0.664660i 0.607852 0.794050i $$-0.292031\pi$$
−0.991594 + 0.129390i $$0.958698\pi$$
$$12$$ 0 0
$$13$$ 18.0000 0.384023 0.192012 0.981393i $$-0.438499\pi$$
0.192012 + 0.981393i $$0.438499\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −8.00000 + 13.8564i −0.125000 + 0.216506i
$$17$$ 37.0000 + 64.0859i 0.527872 + 0.914301i 0.999472 + 0.0324882i $$0.0103431\pi$$
−0.471600 + 0.881812i $$0.656324\pi$$
$$18$$ 0 0
$$19$$ −40.0000 + 69.2820i −0.482980 + 0.836547i −0.999809 0.0195422i $$-0.993779\pi$$
0.516829 + 0.856089i $$0.327112\pi$$
$$20$$ 56.0000 0.626099
$$21$$ 0 0
$$22$$ 56.0000 0.542693
$$23$$ −56.0000 + 96.9948i −0.507687 + 0.879340i 0.492273 + 0.870441i $$0.336166\pi$$
−0.999960 + 0.00889936i $$0.997167\pi$$
$$24$$ 0 0
$$25$$ −35.5000 61.4878i −0.284000 0.491902i
$$26$$ −18.0000 + 31.1769i −0.135773 + 0.235165i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −190.000 −1.21662 −0.608312 0.793698i $$-0.708153\pi$$
−0.608312 + 0.793698i $$0.708153\pi$$
$$30$$ 0 0
$$31$$ −36.0000 62.3538i −0.208574 0.361261i 0.742692 0.669634i $$-0.233549\pi$$
−0.951266 + 0.308373i $$0.900216\pi$$
$$32$$ −16.0000 27.7128i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −148.000 −0.746523
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 173.000 299.645i 0.768676 1.33139i −0.169605 0.985512i $$-0.554249\pi$$
0.938281 0.345874i $$-0.112418\pi$$
$$38$$ −80.0000 138.564i −0.341519 0.591528i
$$39$$ 0 0
$$40$$ −56.0000 + 96.9948i −0.221359 + 0.383406i
$$41$$ −162.000 −0.617077 −0.308538 0.951212i $$-0.599840\pi$$
−0.308538 + 0.951212i $$0.599840\pi$$
$$42$$ 0 0
$$43$$ −412.000 −1.46115 −0.730575 0.682833i $$-0.760748\pi$$
−0.730575 + 0.682833i $$0.760748\pi$$
$$44$$ −56.0000 + 96.9948i −0.191871 + 0.332330i
$$45$$ 0 0
$$46$$ −112.000 193.990i −0.358989 0.621787i
$$47$$ 12.0000 20.7846i 0.0372421 0.0645053i −0.846804 0.531906i $$-0.821476\pi$$
0.884046 + 0.467401i $$0.154809\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 142.000 0.401637
$$51$$ 0 0
$$52$$ −36.0000 62.3538i −0.0960058 0.166287i
$$53$$ 159.000 + 275.396i 0.412082 + 0.713746i 0.995117 0.0987002i $$-0.0314685\pi$$
−0.583036 + 0.812447i $$0.698135\pi$$
$$54$$ 0 0
$$55$$ 392.000 0.961041
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 190.000 329.090i 0.430142 0.745027i
$$59$$ −100.000 173.205i −0.220659 0.382193i 0.734349 0.678772i $$-0.237488\pi$$
−0.955008 + 0.296579i $$0.904154\pi$$
$$60$$ 0 0
$$61$$ 99.0000 171.473i 0.207798 0.359916i −0.743223 0.669044i $$-0.766704\pi$$
0.951020 + 0.309128i $$0.100037\pi$$
$$62$$ 144.000 0.294968
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −126.000 + 218.238i −0.240437 + 0.416448i
$$66$$ 0 0
$$67$$ 358.000 + 620.074i 0.652786 + 1.13066i 0.982444 + 0.186558i $$0.0597332\pi$$
−0.329658 + 0.944100i $$0.606933\pi$$
$$68$$ 148.000 256.344i 0.263936 0.457150i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −392.000 −0.655237 −0.327619 0.944810i $$-0.606246\pi$$
−0.327619 + 0.944810i $$0.606246\pi$$
$$72$$ 0 0
$$73$$ −269.000 465.922i −0.431289 0.747014i 0.565696 0.824614i $$-0.308608\pi$$
−0.996985 + 0.0776001i $$0.975274\pi$$
$$74$$ 346.000 + 599.290i 0.543536 + 0.941432i
$$75$$ 0 0
$$76$$ 320.000 0.482980
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −120.000 + 207.846i −0.170899 + 0.296006i −0.938735 0.344641i $$-0.888001\pi$$
0.767835 + 0.640647i $$0.221334\pi$$
$$80$$ −112.000 193.990i −0.156525 0.271109i
$$81$$ 0 0
$$82$$ 162.000 280.592i 0.218170 0.377881i
$$83$$ 1072.00 1.41768 0.708839 0.705370i $$-0.249219\pi$$
0.708839 + 0.705370i $$0.249219\pi$$
$$84$$ 0 0
$$85$$ −1036.00 −1.32200
$$86$$ 412.000 713.605i 0.516594 0.894767i
$$87$$ 0 0
$$88$$ −112.000 193.990i −0.135673 0.234993i
$$89$$ 405.000 701.481i 0.482359 0.835470i −0.517436 0.855722i $$-0.673114\pi$$
0.999795 + 0.0202521i $$0.00644690\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 448.000 0.507687
$$93$$ 0 0
$$94$$ 24.0000 + 41.5692i 0.0263342 + 0.0456121i
$$95$$ −560.000 969.948i −0.604787 1.04752i
$$96$$ 0 0
$$97$$ 1354.00 1.41730 0.708649 0.705561i $$-0.249305\pi$$
0.708649 + 0.705561i $$0.249305\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −142.000 + 245.951i −0.142000 + 0.245951i
$$101$$ −679.000 1176.06i −0.668941 1.15864i −0.978201 0.207662i $$-0.933415\pi$$
0.309260 0.950978i $$-0.399919\pi$$
$$102$$ 0 0
$$103$$ 416.000 720.533i 0.397958 0.689284i −0.595516 0.803344i $$-0.703052\pi$$
0.993474 + 0.114060i $$0.0363856\pi$$
$$104$$ 144.000 0.135773
$$105$$ 0 0
$$106$$ −636.000 −0.582772
$$107$$ 222.000 384.515i 0.200575 0.347406i −0.748139 0.663542i $$-0.769052\pi$$
0.948714 + 0.316136i $$0.102386\pi$$
$$108$$ 0 0
$$109$$ −935.000 1619.47i −0.821622 1.42309i −0.904474 0.426529i $$-0.859736\pi$$
0.0828525 0.996562i $$-0.473597\pi$$
$$110$$ −392.000 + 678.964i −0.339779 + 0.588515i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1378.00 −1.14718 −0.573590 0.819143i $$-0.694450\pi$$
−0.573590 + 0.819143i $$0.694450\pi$$
$$114$$ 0 0
$$115$$ −784.000 1357.93i −0.635725 1.10111i
$$116$$ 380.000 + 658.179i 0.304156 + 0.526814i
$$117$$ 0 0
$$118$$ 400.000 0.312059
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 273.500 473.716i 0.205485 0.355910i
$$122$$ 198.000 + 342.946i 0.146935 + 0.254499i
$$123$$ 0 0
$$124$$ −144.000 + 249.415i −0.104287 + 0.180630i
$$125$$ −756.000 −0.540950
$$126$$ 0 0
$$127$$ 1944.00 1.35828 0.679142 0.734007i $$-0.262352\pi$$
0.679142 + 0.734007i $$0.262352\pi$$
$$128$$ −64.0000 + 110.851i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −252.000 436.477i −0.170014 0.294473i
$$131$$ −424.000 + 734.390i −0.282787 + 0.489801i −0.972070 0.234691i $$-0.924592\pi$$
0.689283 + 0.724492i $$0.257926\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1432.00 −0.923179
$$135$$ 0 0
$$136$$ 296.000 + 512.687i 0.186631 + 0.323254i
$$137$$ −1483.00 2568.63i −0.924827 1.60185i −0.791840 0.610729i $$-0.790877\pi$$
−0.132987 0.991118i $$-0.542457\pi$$
$$138$$ 0 0
$$139$$ 2800.00 1.70858 0.854291 0.519795i $$-0.173992\pi$$
0.854291 + 0.519795i $$0.173992\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 392.000 678.964i 0.231661 0.401249i
$$143$$ −252.000 436.477i −0.147366 0.255245i
$$144$$ 0 0
$$145$$ 1330.00 2303.63i 0.761728 1.31935i
$$146$$ 1076.00 0.609934
$$147$$ 0 0
$$148$$ −1384.00 −0.768676
$$149$$ 255.000 441.673i 0.140204 0.242841i −0.787369 0.616482i $$-0.788557\pi$$
0.927573 + 0.373641i $$0.121891\pi$$
$$150$$ 0 0
$$151$$ −296.000 512.687i −0.159524 0.276304i 0.775173 0.631749i $$-0.217663\pi$$
−0.934697 + 0.355445i $$0.884329\pi$$
$$152$$ −320.000 + 554.256i −0.170759 + 0.295764i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1008.00 0.522352
$$156$$ 0 0
$$157$$ 1343.00 + 2326.14i 0.682695 + 1.18246i 0.974155 + 0.225879i $$0.0725254\pi$$
−0.291461 + 0.956583i $$0.594141\pi$$
$$158$$ −240.000 415.692i −0.120844 0.209308i
$$159$$ 0 0
$$160$$ 448.000 0.221359
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 506.000 876.418i 0.243147 0.421143i −0.718462 0.695566i $$-0.755154\pi$$
0.961609 + 0.274423i $$0.0884869\pi$$
$$164$$ 324.000 + 561.184i 0.154269 + 0.267202i
$$165$$ 0 0
$$166$$ −1072.00 + 1856.76i −0.501225 + 0.868147i
$$167$$ −544.000 −0.252072 −0.126036 0.992026i $$-0.540225\pi$$
−0.126036 + 0.992026i $$0.540225\pi$$
$$168$$ 0 0
$$169$$ −1873.00 −0.852526
$$170$$ 1036.00 1794.40i 0.467397 0.809556i
$$171$$ 0 0
$$172$$ 824.000 + 1427.21i 0.365287 + 0.632696i
$$173$$ 929.000 1609.08i 0.408269 0.707143i −0.586427 0.810002i $$-0.699466\pi$$
0.994696 + 0.102859i $$0.0327992\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 448.000 0.191871
$$177$$ 0 0
$$178$$ 810.000 + 1402.96i 0.341079 + 0.590766i
$$179$$ −150.000 259.808i −0.0626342 0.108486i 0.833008 0.553261i $$-0.186617\pi$$
−0.895642 + 0.444775i $$0.853283\pi$$
$$180$$ 0 0
$$181$$ −2358.00 −0.968336 −0.484168 0.874975i $$-0.660878\pi$$
−0.484168 + 0.874975i $$0.660878\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −448.000 + 775.959i −0.179495 + 0.310894i
$$185$$ 2422.00 + 4195.03i 0.962535 + 1.66716i
$$186$$ 0 0
$$187$$ 1036.00 1794.40i 0.405133 0.701710i
$$188$$ −96.0000 −0.0372421
$$189$$ 0 0
$$190$$ 2240.00 0.855298
$$191$$ 696.000 1205.51i 0.263669 0.456688i −0.703545 0.710651i $$-0.748401\pi$$
0.967214 + 0.253962i $$0.0817340\pi$$
$$192$$ 0 0
$$193$$ −889.000 1539.79i −0.331563 0.574284i 0.651256 0.758858i $$-0.274243\pi$$
−0.982818 + 0.184575i $$0.940909\pi$$
$$194$$ −1354.00 + 2345.20i −0.501090 + 0.867914i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1214.00 −0.439055 −0.219528 0.975606i $$-0.570452\pi$$
−0.219528 + 0.975606i $$0.570452\pi$$
$$198$$ 0 0
$$199$$ −520.000 900.666i −0.185235 0.320837i 0.758420 0.651766i $$-0.225971\pi$$
−0.943656 + 0.330929i $$0.892638\pi$$
$$200$$ −284.000 491.902i −0.100409 0.173914i
$$201$$ 0 0
$$202$$ 2716.00 0.946025
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1134.00 1964.15i 0.386351 0.669180i
$$206$$ 832.000 + 1441.07i 0.281399 + 0.487397i
$$207$$ 0 0
$$208$$ −144.000 + 249.415i −0.0480029 + 0.0831435i
$$209$$ 2240.00 0.741359
$$210$$ 0 0
$$211$$ −3868.00 −1.26201 −0.631005 0.775779i $$-0.717357\pi$$
−0.631005 + 0.775779i $$0.717357\pi$$
$$212$$ 636.000 1101.58i 0.206041 0.356873i
$$213$$ 0 0
$$214$$ 444.000 + 769.031i 0.141828 + 0.245653i
$$215$$ 2884.00 4995.23i 0.914824 1.58452i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 3740.00 1.16195
$$219$$ 0 0
$$220$$ −784.000 1357.93i −0.240260 0.416143i
$$221$$ 666.000 + 1153.55i 0.202715 + 0.351113i
$$222$$ 0 0
$$223$$ 3968.00 1.19156 0.595778 0.803149i $$-0.296844\pi$$
0.595778 + 0.803149i $$0.296844\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1378.00 2386.77i 0.405589 0.702501i
$$227$$ −1968.00 3408.68i −0.575422 0.996660i −0.995996 0.0894015i $$-0.971505\pi$$
0.420574 0.907258i $$-0.361829\pi$$
$$228$$ 0 0
$$229$$ −2405.00 + 4165.58i −0.694004 + 1.20205i 0.276512 + 0.961011i $$0.410822\pi$$
−0.970515 + 0.241039i $$0.922512\pi$$
$$230$$ 3136.00 0.899051
$$231$$ 0 0
$$232$$ −1520.00 −0.430142
$$233$$ −1091.00 + 1889.67i −0.306754 + 0.531314i −0.977650 0.210237i $$-0.932576\pi$$
0.670896 + 0.741551i $$0.265910\pi$$
$$234$$ 0 0
$$235$$ 168.000 + 290.985i 0.0466345 + 0.0807734i
$$236$$ −400.000 + 692.820i −0.110330 + 0.191096i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3000.00 0.811941 0.405970 0.913886i $$-0.366934\pi$$
0.405970 + 0.913886i $$0.366934\pi$$
$$240$$ 0 0
$$241$$ −1021.00 1768.42i −0.272898 0.472673i 0.696705 0.717358i $$-0.254649\pi$$
−0.969603 + 0.244685i $$0.921315\pi$$
$$242$$ 547.000 + 947.432i 0.145300 + 0.251666i
$$243$$ 0 0
$$244$$ −792.000 −0.207798
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −720.000 + 1247.08i −0.185476 + 0.321253i
$$248$$ −288.000 498.831i −0.0737420 0.127725i
$$249$$ 0 0
$$250$$ 756.000 1309.43i 0.191255 0.331263i
$$251$$ 528.000 0.132777 0.0663886 0.997794i $$-0.478852\pi$$
0.0663886 + 0.997794i $$0.478852\pi$$
$$252$$ 0 0
$$253$$ 3136.00 0.779283
$$254$$ −1944.00 + 3367.11i −0.480226 + 0.831776i
$$255$$ 0 0
$$256$$ −128.000 221.703i −0.0312500 0.0541266i
$$257$$ 2817.00 4879.19i 0.683734 1.18426i −0.290099 0.956997i $$-0.593688\pi$$
0.973833 0.227265i $$-0.0729785\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 1008.00 0.240437
$$261$$ 0 0
$$262$$ −848.000 1468.78i −0.199960 0.346342i
$$263$$ 84.0000 + 145.492i 0.0196945 + 0.0341119i 0.875705 0.482847i $$-0.160397\pi$$
−0.856010 + 0.516959i $$0.827064\pi$$
$$264$$ 0 0
$$265$$ −4452.00 −1.03202
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 1432.00 2480.30i 0.326393 0.565329i
$$269$$ −655.000 1134.49i −0.148461 0.257142i 0.782198 0.623030i $$-0.214099\pi$$
−0.930659 + 0.365888i $$0.880765\pi$$
$$270$$ 0 0
$$271$$ 1104.00 1912.18i 0.247466 0.428623i −0.715356 0.698760i $$-0.753736\pi$$
0.962822 + 0.270137i $$0.0870689\pi$$
$$272$$ −1184.00 −0.263936
$$273$$ 0 0
$$274$$ 5932.00 1.30790
$$275$$ −994.000 + 1721.66i −0.217965 + 0.377527i
$$276$$ 0 0
$$277$$ −2647.00 4584.74i −0.574162 0.994477i −0.996132 0.0878678i $$-0.971995\pi$$
0.421970 0.906610i $$-0.361339\pi$$
$$278$$ −2800.00 + 4849.74i −0.604075 + 1.04629i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −3242.00 −0.688262 −0.344131 0.938922i $$-0.611826\pi$$
−0.344131 + 0.938922i $$0.611826\pi$$
$$282$$ 0 0
$$283$$ 796.000 + 1378.71i 0.167199 + 0.289597i 0.937434 0.348163i $$-0.113194\pi$$
−0.770235 + 0.637760i $$0.779861\pi$$
$$284$$ 784.000 + 1357.93i 0.163809 + 0.283726i
$$285$$ 0 0
$$286$$ 1008.00 0.208407
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −281.500 + 487.572i −0.0572970 + 0.0992413i
$$290$$ 2660.00 + 4607.26i 0.538623 + 0.932922i
$$291$$ 0 0
$$292$$ −1076.00 + 1863.69i −0.215644 + 0.373507i
$$293$$ 5022.00 1.00133 0.500663 0.865642i $$-0.333090\pi$$
0.500663 + 0.865642i $$0.333090\pi$$
$$294$$ 0 0
$$295$$ 2800.00 0.552618
$$296$$ 1384.00 2397.16i 0.271768 0.470716i
$$297$$ 0 0
$$298$$ 510.000 + 883.346i 0.0991393 + 0.171714i
$$299$$ −1008.00 + 1745.91i −0.194964 + 0.337687i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 1184.00 0.225601
$$303$$ 0 0
$$304$$ −640.000 1108.51i −0.120745 0.209137i
$$305$$ 1386.00 + 2400.62i 0.260204 + 0.450686i
$$306$$ 0 0
$$307$$ −9536.00 −1.77280 −0.886398 0.462924i $$-0.846800\pi$$
−0.886398 + 0.462924i $$0.846800\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −1008.00 + 1745.91i −0.184679 + 0.319874i
$$311$$ −484.000 838.313i −0.0882480 0.152850i 0.818523 0.574474i $$-0.194793\pi$$
−0.906771 + 0.421624i $$0.861460\pi$$
$$312$$ 0 0
$$313$$ −1529.00 + 2648.31i −0.276116 + 0.478246i −0.970416 0.241439i $$-0.922381\pi$$
0.694300 + 0.719685i $$0.255714\pi$$
$$314$$ −5372.00 −0.965476
$$315$$ 0 0
$$316$$ 960.000 0.170899
$$317$$ −2493.00 + 4318.00i −0.441706 + 0.765057i −0.997816 0.0660512i $$-0.978960\pi$$
0.556110 + 0.831109i $$0.312293\pi$$
$$318$$ 0 0
$$319$$ 2660.00 + 4607.26i 0.466870 + 0.808642i
$$320$$ −448.000 + 775.959i −0.0782624 + 0.135554i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −5920.00 −1.01981
$$324$$ 0 0
$$325$$ −639.000 1106.78i −0.109063 0.188902i
$$326$$ 1012.00 + 1752.84i 0.171931 + 0.297793i
$$327$$ 0 0
$$328$$ −1296.00 −0.218170
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −4306.00 + 7458.21i −0.715043 + 1.23849i 0.247900 + 0.968786i $$0.420259\pi$$
−0.962943 + 0.269705i $$0.913074\pi$$
$$332$$ −2144.00 3713.52i −0.354420 0.613873i
$$333$$ 0 0
$$334$$ 544.000 942.236i 0.0891208 0.154362i
$$335$$ −10024.0 −1.63483
$$336$$ 0 0
$$337$$ −10206.0 −1.64972 −0.824861 0.565336i $$-0.808747\pi$$
−0.824861 + 0.565336i $$0.808747\pi$$
$$338$$ 1873.00 3244.13i 0.301414 0.522064i
$$339$$ 0 0
$$340$$ 2072.00 + 3588.81i 0.330500 + 0.572443i
$$341$$ −1008.00 + 1745.91i −0.160077 + 0.277262i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −3296.00 −0.516594
$$345$$ 0 0
$$346$$ 1858.00 + 3218.15i 0.288690 + 0.500026i
$$347$$ 1002.00 + 1735.51i 0.155015 + 0.268494i 0.933064 0.359709i $$-0.117124\pi$$
−0.778050 + 0.628203i $$0.783791\pi$$
$$348$$ 0 0
$$349$$ 1330.00 0.203992 0.101996 0.994785i $$-0.467477\pi$$
0.101996 + 0.994785i $$0.467477\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −448.000 + 775.959i −0.0678366 + 0.117496i
$$353$$ 489.000 + 846.973i 0.0737304 + 0.127705i 0.900533 0.434787i $$-0.143176\pi$$
−0.826803 + 0.562492i $$0.809843\pi$$
$$354$$ 0 0
$$355$$ 2744.00 4752.75i 0.410243 0.710562i
$$356$$ −3240.00 −0.482359
$$357$$ 0 0
$$358$$ 600.000 0.0885782
$$359$$ −4840.00 + 8383.13i −0.711547 + 1.23244i 0.252729 + 0.967537i $$0.418672\pi$$
−0.964276 + 0.264899i $$0.914661\pi$$
$$360$$ 0 0
$$361$$ 229.500 + 397.506i 0.0334597 + 0.0579539i
$$362$$ 2358.00 4084.18i 0.342358 0.592982i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 7532.00 1.08012
$$366$$ 0 0
$$367$$ 4328.00 + 7496.32i 0.615585 + 1.06622i 0.990282 + 0.139077i $$0.0444136\pi$$
−0.374696 + 0.927148i $$0.622253\pi$$
$$368$$ −896.000 1551.92i −0.126922 0.219835i
$$369$$ 0 0
$$370$$ −9688.00 −1.36123
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −2639.00 + 4570.88i −0.366333 + 0.634508i −0.988989 0.147988i $$-0.952720\pi$$
0.622656 + 0.782496i $$0.286054\pi$$
$$374$$ 2072.00 + 3588.81i 0.286472 + 0.496184i
$$375$$ 0 0
$$376$$ 96.0000 166.277i 0.0131671 0.0228061i
$$377$$ −3420.00 −0.467212
$$378$$ 0 0
$$379$$ 6340.00 0.859272 0.429636 0.903002i $$-0.358642\pi$$
0.429636 + 0.903002i $$0.358642\pi$$
$$380$$ −2240.00 + 3879.79i −0.302394 + 0.523761i
$$381$$ 0 0
$$382$$ 1392.00 + 2411.01i 0.186442 + 0.322927i
$$383$$ −3116.00 + 5397.07i −0.415718 + 0.720045i −0.995504 0.0947240i $$-0.969803\pi$$
0.579785 + 0.814769i $$0.303136\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 3556.00 0.468901
$$387$$ 0 0
$$388$$ −2708.00 4690.39i −0.354324 0.613708i
$$389$$ −7405.00 12825.8i −0.965163 1.67171i −0.709177 0.705031i $$-0.750933\pi$$
−0.255986 0.966680i $$-0.582400\pi$$
$$390$$ 0 0
$$391$$ −8288.00 −1.07197
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 1214.00 2102.71i 0.155230 0.268865i
$$395$$ −1680.00 2909.85i −0.214000 0.370659i
$$396$$ 0 0
$$397$$ −2577.00 + 4463.49i −0.325783 + 0.564273i −0.981671 0.190586i $$-0.938961\pi$$
0.655887 + 0.754859i $$0.272295\pi$$
$$398$$ 2080.00 0.261962
$$399$$ 0 0
$$400$$ 1136.00 0.142000
$$401$$ 1641.00 2842.30i 0.204358 0.353959i −0.745570 0.666427i $$-0.767823\pi$$
0.949928 + 0.312469i $$0.101156\pi$$
$$402$$ 0 0
$$403$$ −648.000 1122.37i −0.0800972 0.138732i
$$404$$ −2716.00 + 4704.25i −0.334470 + 0.579320i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −9688.00 −1.17989
$$408$$ 0 0
$$409$$ −2905.00 5031.61i −0.351205 0.608306i 0.635256 0.772302i $$-0.280895\pi$$
−0.986461 + 0.163996i $$0.947561\pi$$
$$410$$ 2268.00 + 3928.29i 0.273192 + 0.473182i
$$411$$ 0 0
$$412$$ −3328.00 −0.397958
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −7504.00 + 12997.3i −0.887607 + 1.53738i
$$416$$ −288.000 498.831i −0.0339432 0.0587913i
$$417$$ 0 0
$$418$$ −2240.00 + 3879.79i −0.262110 + 0.453988i
$$419$$ −13560.0 −1.58102 −0.790512 0.612446i $$-0.790186\pi$$
−0.790512 + 0.612446i $$0.790186\pi$$
$$420$$ 0 0
$$421$$ −738.000 −0.0854345 −0.0427172 0.999087i $$-0.513601\pi$$
−0.0427172 + 0.999087i $$0.513601\pi$$
$$422$$ 3868.00 6699.57i 0.446188 0.772820i
$$423$$ 0 0
$$424$$ 1272.00 + 2203.17i 0.145693 + 0.252347i
$$425$$ 2627.00 4550.10i 0.299831 0.519323i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1776.00 −0.200575
$$429$$ 0 0
$$430$$ 5768.00 + 9990.47i 0.646878 + 1.12043i
$$431$$ 636.000 + 1101.58i 0.0710790 + 0.123112i 0.899374 0.437179i $$-0.144022\pi$$
−0.828295 + 0.560292i $$0.810689\pi$$
$$432$$ 0 0
$$433$$ −5062.00 −0.561811 −0.280906 0.959735i $$-0.590635\pi$$
−0.280906 + 0.959735i $$0.590635\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −3740.00 + 6477.87i −0.410811 + 0.711545i
$$437$$ −4480.00 7759.59i −0.490406 0.849408i
$$438$$ 0 0
$$439$$ −2820.00 + 4884.38i −0.306586 + 0.531023i −0.977613 0.210410i $$-0.932520\pi$$
0.671027 + 0.741433i $$0.265853\pi$$
$$440$$ 3136.00 0.339779
$$441$$ 0 0
$$442$$ −2664.00 −0.286682
$$443$$ 6694.00 11594.3i 0.717927 1.24349i −0.243893 0.969802i $$-0.578425\pi$$
0.961820 0.273683i $$-0.0882421\pi$$
$$444$$ 0 0
$$445$$ 5670.00 + 9820.73i 0.604008 + 1.04617i
$$446$$ −3968.00 + 6872.78i −0.421279 + 0.729676i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 3230.00 0.339495 0.169747 0.985488i $$-0.445705\pi$$
0.169747 + 0.985488i $$0.445705\pi$$
$$450$$ 0 0
$$451$$ 2268.00 + 3928.29i 0.236798 + 0.410146i
$$452$$ 2756.00 + 4773.53i 0.286795 + 0.496743i
$$453$$ 0 0
$$454$$ 7872.00 0.813769
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5323.00 9219.71i 0.544857 0.943719i −0.453759 0.891124i $$-0.649917\pi$$
0.998616 0.0525950i $$-0.0167492\pi$$
$$458$$ −4810.00 8331.16i −0.490735 0.849978i
$$459$$ 0 0
$$460$$ −3136.00 + 5431.71i −0.317863 + 0.550554i
$$461$$ −7282.00 −0.735698 −0.367849 0.929886i $$-0.619906\pi$$
−0.367849 + 0.929886i $$0.619906\pi$$
$$462$$ 0 0
$$463$$ 12688.0 1.27357 0.636783 0.771043i $$-0.280265\pi$$
0.636783 + 0.771043i $$0.280265\pi$$
$$464$$ 1520.00 2632.72i 0.152078 0.263407i
$$465$$ 0 0
$$466$$ −2182.00 3779.33i −0.216908 0.375696i
$$467$$ −1408.00 + 2438.73i −0.139517 + 0.241651i −0.927314 0.374285i $$-0.877888\pi$$
0.787797 + 0.615935i $$0.211222\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −672.000 −0.0659512
$$471$$ 0 0
$$472$$ −800.000 1385.64i −0.0780148 0.135126i
$$473$$ 5768.00 + 9990.47i 0.560704 + 0.971168i
$$474$$ 0 0
$$475$$ 5680.00 0.548666
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −3000.00 + 5196.15i −0.287064 + 0.497210i
$$479$$ −1580.00 2736.64i −0.150714 0.261044i 0.780776 0.624811i $$-0.214824\pi$$
−0.931490 + 0.363766i $$0.881491\pi$$
$$480$$ 0 0
$$481$$ 3114.00 5393.61i 0.295190 0.511283i
$$482$$ 4084.00 0.385936
$$483$$ 0 0
$$484$$ −2188.00 −0.205485
$$485$$ −9478.00 + 16416.4i −0.887369 + 1.53697i
$$486$$ 0 0
$$487$$ 7088.00 + 12276.8i 0.659523 + 1.14233i 0.980739 + 0.195322i $$0.0625752\pi$$
−0.321216 + 0.947006i $$0.604091\pi$$
$$488$$ 792.000 1371.78i 0.0734675 0.127249i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11268.0 1.03568 0.517839 0.855478i $$-0.326737\pi$$
0.517839 + 0.855478i $$0.326737\pi$$
$$492$$ 0 0
$$493$$ −7030.00 12176.3i −0.642222 1.11236i
$$494$$ −1440.00 2494.15i −0.131151 0.227160i
$$495$$ 0 0
$$496$$ 1152.00 0.104287
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 2230.00 3862.47i 0.200057 0.346509i −0.748489 0.663147i $$-0.769221\pi$$
0.948547 + 0.316638i $$0.102554\pi$$
$$500$$ 1512.00 + 2618.86i 0.135237 + 0.234238i
$$501$$ 0 0
$$502$$ −528.000 + 914.523i −0.0469438 + 0.0813091i
$$503$$ 1512.00 0.134029 0.0670147 0.997752i $$-0.478653\pi$$
0.0670147 + 0.997752i $$0.478653\pi$$
$$504$$ 0 0
$$505$$ 19012.0 1.67529
$$506$$ −3136.00 + 5431.71i −0.275518 + 0.477212i
$$507$$ 0 0
$$508$$ −3888.00 6734.21i −0.339571 0.588154i
$$509$$ −5895.00 + 10210.4i −0.513342 + 0.889135i 0.486538 + 0.873660i $$0.338260\pi$$
−0.999880 + 0.0154756i $$0.995074\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 512.000 0.0441942
$$513$$ 0 0
$$514$$ 5634.00 + 9758.37i 0.483473 + 0.837400i
$$515$$ 5824.00 + 10087.5i 0.498323 + 0.863120i
$$516$$ 0 0
$$517$$ −672.000 −0.0571654
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −1008.00 + 1745.91i −0.0850072 + 0.147237i
$$521$$ 681.000 + 1179.53i 0.0572652 + 0.0991862i 0.893237 0.449586i $$-0.148429\pi$$
−0.835972 + 0.548773i $$0.815095\pi$$
$$522$$ 0 0
$$523$$ −3484.00 + 6034.47i −0.291290 + 0.504529i −0.974115 0.226053i $$-0.927418\pi$$
0.682825 + 0.730582i $$0.260751\pi$$
$$524$$ 3392.00 0.282787
$$525$$ 0 0
$$526$$ −336.000 −0.0278523
$$527$$ 2664.00 4614.18i 0.220200 0.381398i
$$528$$ 0 0
$$529$$ −188.500 326.492i −0.0154927 0.0268342i
$$530$$ 4452.00 7711.09i 0.364873 0.631978i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2916.00 −0.236972
$$534$$ 0 0
$$535$$ 3108.00 + 5383.21i 0.251160 + 0.435022i
$$536$$ 2864.00 + 4960.59i 0.230795 + 0.399748i
$$537$$ 0 0
$$538$$ 2620.00 0.209956
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −3531.00 + 6115.87i −0.280609 + 0.486029i −0.971535 0.236896i $$-0.923870\pi$$
0.690926 + 0.722926i $$0.257203\pi$$
$$542$$ 2208.00 + 3824.37i 0.174985 + 0.303082i
$$543$$ 0 0
$$544$$ 1184.00 2050.75i 0.0933154 0.161627i
$$545$$ 26180.0 2.05767
$$546$$ 0 0
$$547$$ −8196.00 −0.640650 −0.320325 0.947308i $$-0.603792\pi$$
−0.320325 + 0.947308i $$0.603792\pi$$
$$548$$ −5932.00 + 10274.5i −0.462413 + 0.800923i
$$549$$ 0 0
$$550$$ −1988.00 3443.32i −0.154125 0.266952i
$$551$$ 7600.00 13163.6i 0.587606 1.01776i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 10588.0 0.811987
$$555$$ 0 0
$$556$$ −5600.00 9699.48i −0.427146 0.739838i
$$557$$ −3733.00 6465.75i −0.283972 0.491854i 0.688388 0.725343i $$-0.258319\pi$$
−0.972359 + 0.233490i $$0.924986\pi$$
$$558$$ 0 0
$$559$$ −7416.00 −0.561115
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 3242.00 5615.31i 0.243337 0.421472i
$$563$$ 12484.0 + 21622.9i 0.934526 + 1.61865i 0.775478 + 0.631375i $$0.217509\pi$$
0.159048 + 0.987271i $$0.449158\pi$$
$$564$$ 0 0
$$565$$ 9646.00 16707.4i 0.718248 1.24404i
$$566$$ −3184.00 −0.236455
$$567$$ 0 0
$$568$$ −3136.00 −0.231661
$$569$$ 7125.00 12340.9i 0.524948 0.909237i −0.474630 0.880186i $$-0.657418\pi$$
0.999578 0.0290514i $$-0.00924865\pi$$
$$570$$ 0 0
$$571$$ −3186.00 5518.31i −0.233503 0.404438i 0.725334 0.688397i $$-0.241685\pi$$
−0.958836 + 0.283959i $$0.908352\pi$$
$$572$$ −1008.00 + 1745.91i −0.0736829 + 0.127622i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 7952.00 0.576733
$$576$$ 0 0
$$577$$ 4183.00 + 7245.17i 0.301803 + 0.522739i 0.976545 0.215316i $$-0.0690780\pi$$
−0.674741 + 0.738055i $$0.735745\pi$$
$$578$$ −563.000 975.145i −0.0405151 0.0701742i
$$579$$ 0 0
$$580$$ −10640.0 −0.761728
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 4452.00 7711.09i 0.316266 0.547789i
$$584$$ −2152.00 3727.37i −0.152484 0.264109i
$$585$$ 0 0
$$586$$ −5022.00 + 8698.36i −0.354022 + 0.613184i
$$587$$ −20384.0 −1.43328 −0.716642 0.697441i $$-0.754322\pi$$
−0.716642 + 0.697441i $$0.754322\pi$$
$$588$$ 0 0
$$589$$ 5760.00 0.402948
$$590$$ −2800.00 + 4849.74i −0.195380 + 0.338408i
$$591$$ 0 0
$$592$$ 2768.00 + 4794.32i 0.192169 + 0.332847i
$$593$$ 4689.00 8121.59i 0.324712 0.562417i −0.656742 0.754115i $$-0.728066\pi$$
0.981454 + 0.191698i $$0.0613993\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −2040.00 −0.140204
$$597$$ 0 0
$$598$$ −2016.00 3491.81i −0.137860 0.238781i
$$599$$ −4500.00 7794.23i −0.306953 0.531659i 0.670741 0.741692i $$-0.265976\pi$$
−0.977694 + 0.210033i $$0.932643\pi$$
$$600$$ 0 0
$$601$$ 7562.00 0.513245 0.256623 0.966512i $$-0.417390\pi$$
0.256623 + 0.966512i $$0.417390\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1184.00 + 2050.75i −0.0797620 + 0.138152i
$$605$$ 3829.00 + 6632.02i 0.257307 + 0.445670i
$$606$$ 0 0
$$607$$ 1488.00 2577.29i 0.0994993 0.172338i −0.811978 0.583688i $$-0.801609\pi$$
0.911478 + 0.411350i $$0.134943\pi$$
$$608$$ 2560.00 0.170759
$$609$$ 0 0
$$610$$ −5544.00 −0.367984
$$611$$ 216.000 374.123i 0.0143018 0.0247715i
$$612$$ 0 0
$$613$$ −2139.00 3704.86i −0.140935 0.244107i 0.786914 0.617063i $$-0.211678\pi$$
−0.927849 + 0.372956i $$0.878344\pi$$
$$614$$ 9536.00 16516.8i 0.626778 1.08561i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18794.0 −1.22629 −0.613143 0.789972i $$-0.710095\pi$$
−0.613143 + 0.789972i $$0.710095\pi$$
$$618$$ 0 0
$$619$$ −9020.00 15623.1i −0.585694 1.01445i −0.994789 0.101959i $$-0.967489\pi$$
0.409095 0.912492i $$-0.365845\pi$$
$$620$$ −2016.00 3491.81i −0.130588 0.226185i
$$621$$ 0 0
$$622$$ 1936.00 0.124801
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9729.50 16852.0i 0.622688 1.07853i
$$626$$ −3058.00 5296.61i −0.195243 0.338171i
$$627$$ 0 0
$$628$$ 5372.00 9304.58i 0.341347 0.591231i
$$629$$ 25604.0 1.62305
$$630$$ 0 0
$$631$$ −21688.0 −1.36828 −0.684141 0.729350i $$-0.739823\pi$$
−0.684141 + 0.729350i $$0.739823\pi$$
$$632$$ −960.000 + 1662.77i −0.0604221 + 0.104654i
$$633$$ 0 0
$$634$$ −4986.00 8636.01i −0.312333 0.540977i
$$635$$ −13608.0 + 23569.7i −0.850420 + 1.47297i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −10640.0 −0.660253
$$639$$ 0 0
$$640$$ −896.000 1551.92i −0.0553399 0.0958514i
$$641$$ −5279.00 9143.50i −0.325285 0.563411i 0.656285 0.754513i $$-0.272127\pi$$
−0.981570 + 0.191102i $$0.938794\pi$$
$$642$$ 0 0
$$643$$ −26152.0 −1.60394 −0.801971 0.597363i $$-0.796215\pi$$
−0.801971 + 0.597363i $$0.796215\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 5920.00 10253.7i 0.360556 0.624502i
$$647$$ 12792.0 + 22156.4i 0.777288 + 1.34630i 0.933499 + 0.358579i $$0.116739\pi$$
−0.156211 + 0.987724i $$0.549928\pi$$
$$648$$ 0 0
$$649$$ −2800.00 + 4849.74i −0.169352 + 0.293327i
$$650$$ 2556.00 0.154238
$$651$$ 0 0
$$652$$ −4048.00 −0.243147
$$653$$ 7599.00 13161.9i 0.455393 0.788764i −0.543317 0.839527i $$-0.682832\pi$$
0.998711 + 0.0507630i $$0.0161653\pi$$
$$654$$ 0 0
$$655$$ −5936.00 10281.5i −0.354105 0.613328i
$$656$$ 1296.00 2244.74i 0.0771346 0.133601i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6100.00 0.360580 0.180290 0.983613i $$-0.442296\pi$$
0.180290 + 0.983613i $$0.442296\pi$$
$$660$$ 0 0
$$661$$ 1159.00 + 2007.45i 0.0681995 + 0.118125i 0.898109 0.439773i $$-0.144941\pi$$
−0.829909 + 0.557898i $$0.811608\pi$$
$$662$$ −8612.00 14916.4i −0.505612 0.875745i
$$663$$ 0 0
$$664$$ 8576.00 0.501225
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 10640.0 18429.0i 0.617665 1.06983i
$$668$$ 1088.00 + 1884.47i 0.0630179 + 0.109150i
$$669$$ 0 0
$$670$$ 10024.0 17362.1i 0.578001 1.00113i
$$671$$ −5544.00 −0.318962
$$672$$ 0 0
$$673$$ −10222.0 −0.585482 −0.292741 0.956192i $$-0.594567\pi$$
−0.292741 + 0.956192i $$0.594567\pi$$
$$674$$ 10206.0 17677.3i 0.583265 1.01024i
$$675$$ 0 0
$$676$$ 3746.00 + 6488.26i 0.213132 + 0.369155i
$$677$$ 12717.0 22026.5i 0.721941 1.25044i −0.238280 0.971197i $$-0.576584\pi$$
0.960221 0.279242i $$-0.0900831\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −8288.00 −0.467397
$$681$$ 0 0
$$682$$ −2016.00 3491.81i −0.113192 0.196053i
$$683$$ −4266.00 7388.93i −0.238996 0.413952i 0.721431 0.692487i $$-0.243485\pi$$
−0.960426 + 0.278534i $$0.910151\pi$$
$$684$$ 0 0
$$685$$ 41524.0 2.31613
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 3296.00 5708.84i 0.182644 0.316348i
$$689$$ 2862.00 + 4957.13i 0.158249 + 0.274095i
$$690$$ 0 0
$$691$$ −10336.0 + 17902.5i −0.569030 + 0.985589i 0.427632 + 0.903953i $$0.359348\pi$$
−0.996662 + 0.0816365i $$0.973985\pi$$
$$692$$ −7432.00 −0.408269
$$693$$ 0 0
$$694$$ −4008.00 −0.219224
$$695$$ −19600.0 + 33948.2i −1.06974 + 1.85285i
$$696$$ 0 0
$$697$$ −5994.00 10381.9i −0.325737 0.564194i
$$698$$ −1330.00 + 2303.63i −0.0721221 + 0.124919i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 21458.0 1.15614 0.578072 0.815985i $$-0.303805\pi$$
0.578072 + 0.815985i $$0.303805\pi$$
$$702$$ 0 0
$$703$$ 13840.0 + 23971.6i 0.742511 + 1.28607i
$$704$$ −896.000 1551.92i −0.0479677 0.0830825i
$$705$$ 0 0
$$706$$ −1956.00 −0.104271
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 4925.00 8530.35i 0.260878 0.451853i −0.705598 0.708613i $$-0.749321\pi$$
0.966475 + 0.256759i $$0.0826547\pi$$
$$710$$ 5488.00 + 9505.49i 0.290086 + 0.502443i
$$711$$ 0 0
$$712$$ 3240.00 5611.84i 0.170540 0.295383i
$$713$$ 8064.00 0.423561
$$714$$ 0 0
$$715$$ 7056.00 0.369062
$$716$$ −600.000 + 1039.23i −0.0313171 + 0.0542428i
$$717$$ 0 0
$$718$$ −9680.00 16766.3i −0.503140 0.871464i
$$719$$ −9420.00 + 16315.9i −0.488605 + 0.846288i −0.999914 0.0131086i $$-0.995827\pi$$
0.511309 + 0.859397i $$0.329161\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −918.000 −0.0473191
$$723$$ 0 0
$$724$$ 4716.00 + 8168.35i 0.242084 + 0.419302i
$$725$$ 6745.00 + 11682.7i 0.345521 + 0.598461i
$$726$$ 0 0
$$727$$ 37504.0 1.91327 0.956634 0.291291i $$-0.0940849\pi$$
0.956634 + 0.291291i $$0.0940849\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −7532.00 + 13045.8i −0.381879 + 0.661434i
$$731$$ −15244.0 26403.4i −0.771299 1.33593i
$$732$$ 0 0
$$733$$ −6669.00 + 11551.0i −0.336051 + 0.582057i −0.983686 0.179894i $$-0.942425\pi$$
0.647635 + 0.761950i $$0.275758\pi$$
$$734$$ −17312.0 −0.870569
$$735$$ 0 0
$$736$$ 3584.00 0.179495
$$737$$ 10024.0 17362.1i 0.501002 0.867762i
$$738$$ 0 0
$$739$$ −8550.00 14809.0i −0.425598 0.737157i 0.570878 0.821035i $$-0.306603\pi$$
−0.996476 + 0.0838776i $$0.973270\pi$$
$$740$$ 9688.00 16780.1i 0.481268 0.833580i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 19632.0 0.969352 0.484676 0.874694i $$-0.338938\pi$$
0.484676 + 0.874694i $$0.338938\pi$$
$$744$$ 0 0
$$745$$ 3570.00 + 6183.42i 0.175563 + 0.304085i
$$746$$ −5278.00 9141.76i −0.259037 0.448665i
$$747$$ 0 0
$$748$$ −8288.00 −0.405133
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −16956.0 + 29368.7i −0.823879 + 1.42700i 0.0788938 + 0.996883i $$0.474861\pi$$
−0.902773 + 0.430117i $$0.858472\pi$$
$$752$$ 192.000 + 332.554i 0.00931053 + 0.0161263i
$$753$$ 0 0
$$754$$ 3420.00 5923.61i 0.165184 0.286108i
$$755$$ 8288.00 0.399512
$$756$$ 0 0
$$757$$ −31386.0 −1.50693 −0.753463 0.657490i $$-0.771618\pi$$
−0.753463 + 0.657490i $$0.771618\pi$$
$$758$$ −6340.00 + 10981.2i −0.303798 + 0.526194i
$$759$$ 0 0
$$760$$ −4480.00 7759.59i −0.213825 0.370355i
$$761$$ −17279.0 + 29928.1i −0.823079 + 1.42561i 0.0802993 + 0.996771i $$0.474412\pi$$
−0.903378 + 0.428844i $$0.858921\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −5568.00 −0.263669
$$765$$ 0 0
$$766$$ −6232.00 10794.1i −0.293957 0.509149i
$$767$$ −1800.00 3117.69i −0.0847382 0.146771i
$$768$$ 0 0
$$769$$ 39130.0 1.83493 0.917467 0.397812i $$-0.130231\pi$$
0.917467 + 0.397812i $$0.130231\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −3556.00 + 6159.17i −0.165781 + 0.287142i
$$773$$ −12991.0 22501.1i −0.604468 1.04697i −0.992135 0.125170i $$-0.960052\pi$$
0.387667 0.921799i $$-0.373281\pi$$
$$774$$ 0 0
$$775$$ −2556.00 + 4427.12i −0.118470 + 0.205196i
$$776$$ 10832.0 0.501090
$$777$$ 0 0
$$778$$ 29620.0 1.36495
$$779$$ 6480.00 11223.7i 0.298036 0.516214i
$$780$$ 0 0
$$781$$ 5488.00 + 9505.49i 0.251442 + 0.435510i
$$782$$ 8288.00 14355.2i 0.379000 0.656448i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −37604.0 −1.70974
$$786$$ 0 0
$$787$$ −17712.0 30678.1i −0.802242 1.38952i −0.918137 0.396263i $$-0.870307\pi$$
0.115895 0.993261i $$-0.463026\pi$$
$$788$$ 2428.00 + 4205.42i 0.109764 + 0.190117i
$$789$$ 0 0
$$790$$ 6720.00 0.302642