# Properties

 Label 98.4.c.f.79.1 Level $98$ Weight $4$ Character 98.79 Analytic conductor $5.782$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 98.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.78218718056$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 79.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 98.79 Dual form 98.4.c.f.67.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.00000 + 12.1244i) q^{5} +16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.00000 + 12.1244i) q^{5} +16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(14.0000 + 24.2487i) q^{10} +(14.0000 + 24.2487i) q^{11} +(16.0000 - 27.7128i) q^{12} -18.0000 q^{13} -112.000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(37.0000 + 64.0859i) q^{17} +(37.0000 + 64.0859i) q^{18} +(40.0000 - 69.2820i) q^{19} +56.0000 q^{20} +56.0000 q^{22} +(56.0000 - 96.9948i) q^{23} +(-32.0000 - 55.4256i) q^{24} +(-35.5000 - 61.4878i) q^{25} +(-18.0000 + 31.1769i) q^{26} -80.0000 q^{27} +190.000 q^{29} +(-112.000 + 193.990i) q^{30} +(36.0000 + 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-112.000 + 193.990i) q^{33} +148.000 q^{34} +148.000 q^{36} +(173.000 - 299.645i) q^{37} +(-80.0000 - 138.564i) q^{38} +(-72.0000 - 124.708i) q^{39} +(56.0000 - 96.9948i) q^{40} -162.000 q^{41} -412.000 q^{43} +(56.0000 - 96.9948i) q^{44} +(-259.000 - 448.601i) q^{45} +(-112.000 - 193.990i) q^{46} +(12.0000 - 20.7846i) q^{47} -128.000 q^{48} -142.000 q^{50} +(-296.000 + 512.687i) q^{51} +(36.0000 + 62.3538i) q^{52} +(-159.000 - 275.396i) q^{53} +(-80.0000 + 138.564i) q^{54} -392.000 q^{55} +640.000 q^{57} +(190.000 - 329.090i) q^{58} +(-100.000 - 173.205i) q^{59} +(224.000 + 387.979i) q^{60} +(-99.0000 + 171.473i) q^{61} +144.000 q^{62} +64.0000 q^{64} +(126.000 - 218.238i) q^{65} +(224.000 + 387.979i) q^{66} +(358.000 + 620.074i) q^{67} +(148.000 - 256.344i) q^{68} +896.000 q^{69} +392.000 q^{71} +(148.000 - 256.344i) q^{72} +(269.000 + 465.922i) q^{73} +(-346.000 - 599.290i) q^{74} +(284.000 - 491.902i) q^{75} -320.000 q^{76} -288.000 q^{78} +(-120.000 + 207.846i) q^{79} +(-112.000 - 193.990i) q^{80} +(179.500 + 310.903i) q^{81} +(-162.000 + 280.592i) q^{82} +1072.00 q^{83} -1036.00 q^{85} +(-412.000 + 713.605i) q^{86} +(760.000 + 1316.36i) q^{87} +(-112.000 - 193.990i) q^{88} +(405.000 - 701.481i) q^{89} -1036.00 q^{90} -448.000 q^{92} +(-288.000 + 498.831i) q^{93} +(-24.0000 - 41.5692i) q^{94} +(560.000 + 969.948i) q^{95} +(-128.000 + 221.703i) q^{96} -1354.00 q^{97} -1036.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 8 q^{3} - 4 q^{4} - 14 q^{5} + 32 q^{6} - 16 q^{8} - 37 q^{9}+O(q^{10})$$ 2 * q + 2 * q^2 + 8 * q^3 - 4 * q^4 - 14 * q^5 + 32 * q^6 - 16 * q^8 - 37 * q^9 $$2 q + 2 q^{2} + 8 q^{3} - 4 q^{4} - 14 q^{5} + 32 q^{6} - 16 q^{8} - 37 q^{9} + 28 q^{10} + 28 q^{11} + 32 q^{12} - 36 q^{13} - 224 q^{15} - 16 q^{16} + 74 q^{17} + 74 q^{18} + 80 q^{19} + 112 q^{20} + 112 q^{22} + 112 q^{23} - 64 q^{24} - 71 q^{25} - 36 q^{26} - 160 q^{27} + 380 q^{29} - 224 q^{30} + 72 q^{31} + 32 q^{32} - 224 q^{33} + 296 q^{34} + 296 q^{36} + 346 q^{37} - 160 q^{38} - 144 q^{39} + 112 q^{40} - 324 q^{41} - 824 q^{43} + 112 q^{44} - 518 q^{45} - 224 q^{46} + 24 q^{47} - 256 q^{48} - 284 q^{50} - 592 q^{51} + 72 q^{52} - 318 q^{53} - 160 q^{54} - 784 q^{55} + 1280 q^{57} + 380 q^{58} - 200 q^{59} + 448 q^{60} - 198 q^{61} + 288 q^{62} + 128 q^{64} + 252 q^{65} + 448 q^{66} + 716 q^{67} + 296 q^{68} + 1792 q^{69} + 784 q^{71} + 296 q^{72} + 538 q^{73} - 692 q^{74} + 568 q^{75} - 640 q^{76} - 576 q^{78} - 240 q^{79} - 224 q^{80} + 359 q^{81} - 324 q^{82} + 2144 q^{83} - 2072 q^{85} - 824 q^{86} + 1520 q^{87} - 224 q^{88} + 810 q^{89} - 2072 q^{90} - 896 q^{92} - 576 q^{93} - 48 q^{94} + 1120 q^{95} - 256 q^{96} - 2708 q^{97} - 2072 q^{99}+O(q^{100})$$ 2 * q + 2 * q^2 + 8 * q^3 - 4 * q^4 - 14 * q^5 + 32 * q^6 - 16 * q^8 - 37 * q^9 + 28 * q^10 + 28 * q^11 + 32 * q^12 - 36 * q^13 - 224 * q^15 - 16 * q^16 + 74 * q^17 + 74 * q^18 + 80 * q^19 + 112 * q^20 + 112 * q^22 + 112 * q^23 - 64 * q^24 - 71 * q^25 - 36 * q^26 - 160 * q^27 + 380 * q^29 - 224 * q^30 + 72 * q^31 + 32 * q^32 - 224 * q^33 + 296 * q^34 + 296 * q^36 + 346 * q^37 - 160 * q^38 - 144 * q^39 + 112 * q^40 - 324 * q^41 - 824 * q^43 + 112 * q^44 - 518 * q^45 - 224 * q^46 + 24 * q^47 - 256 * q^48 - 284 * q^50 - 592 * q^51 + 72 * q^52 - 318 * q^53 - 160 * q^54 - 784 * q^55 + 1280 * q^57 + 380 * q^58 - 200 * q^59 + 448 * q^60 - 198 * q^61 + 288 * q^62 + 128 * q^64 + 252 * q^65 + 448 * q^66 + 716 * q^67 + 296 * q^68 + 1792 * q^69 + 784 * q^71 + 296 * q^72 + 538 * q^73 - 692 * q^74 + 568 * q^75 - 640 * q^76 - 576 * q^78 - 240 * q^79 - 224 * q^80 + 359 * q^81 - 324 * q^82 + 2144 * q^83 - 2072 * q^85 - 824 * q^86 + 1520 * q^87 - 224 * q^88 + 810 * q^89 - 2072 * q^90 - 896 * q^92 - 576 * q^93 - 48 * q^94 + 1120 * q^95 - 256 * q^96 - 2708 * q^97 - 2072 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$$.

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

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 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
$$3$$ 4.00000 + 6.92820i 0.769800 + 1.33333i 0.937671 + 0.347524i $$0.112978\pi$$
−0.167871 + 0.985809i $$0.553689\pi$$
$$4$$ −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 $$0.951317\pi$$
$$6$$ 16.0000 1.08866
$$7$$ 0 0
$$8$$ −8.00000 −0.353553
$$9$$ −18.5000 + 32.0429i −0.685185 + 1.18678i
$$10$$ 14.0000 + 24.2487i 0.442719 + 0.766812i
$$11$$ 14.0000 + 24.2487i 0.383742 + 0.664660i 0.991594 0.129390i $$-0.0413020\pi$$
−0.607852 + 0.794050i $$0.707969\pi$$
$$12$$ 16.0000 27.7128i 0.384900 0.666667i
$$13$$ −18.0000 −0.384023 −0.192012 0.981393i $$-0.561501\pi$$
−0.192012 + 0.981393i $$0.561501\pi$$
$$14$$ 0 0
$$15$$ −112.000 −1.92789
$$16$$ −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 $$0.656324\pi$$
$$18$$ 37.0000 + 64.0859i 0.484499 + 0.839177i
$$19$$ 40.0000 69.2820i 0.482980 0.836547i −0.516829 0.856089i $$-0.672888\pi$$
0.999809 + 0.0195422i $$0.00622087\pi$$
$$20$$ 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 $$-0.663834\pi$$
0.999960 0.00889936i $$-0.00283279\pi$$
$$24$$ −32.0000 55.4256i −0.272166 0.471405i
$$25$$ −35.5000 61.4878i −0.284000 0.491902i
$$26$$ −18.0000 + 31.1769i −0.135773 + 0.235165i
$$27$$ −80.0000 −0.570222
$$28$$ 0 0
$$29$$ 190.000 1.21662 0.608312 0.793698i $$-0.291847\pi$$
0.608312 + 0.793698i $$0.291847\pi$$
$$30$$ −112.000 + 193.990i −0.681610 + 1.18058i
$$31$$ 36.0000 + 62.3538i 0.208574 + 0.361261i 0.951266 0.308373i $$-0.0997845\pi$$
−0.742692 + 0.669634i $$0.766451\pi$$
$$32$$ 16.0000 + 27.7128i 0.0883883 + 0.153093i
$$33$$ −112.000 + 193.990i −0.590809 + 1.02331i
$$34$$ 148.000 0.746523
$$35$$ 0 0
$$36$$ 148.000 0.685185
$$37$$ 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
$$39$$ −72.0000 124.708i −0.295621 0.512031i
$$40$$ 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
$$45$$ −259.000 448.601i −0.857988 1.48608i
$$46$$ −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 $$0.154809\pi$$
$$48$$ −128.000 −0.384900
$$49$$ 0 0
$$50$$ −142.000 −0.401637
$$51$$ −296.000 + 512.687i −0.812712 + 1.40766i
$$52$$ 36.0000 + 62.3538i 0.0960058 + 0.166287i
$$53$$ −159.000 275.396i −0.412082 0.713746i 0.583036 0.812447i $$-0.301865\pi$$
−0.995117 + 0.0987002i $$0.968532\pi$$
$$54$$ −80.0000 + 138.564i −0.201604 + 0.349189i
$$55$$ −392.000 −0.961041
$$56$$ 0 0
$$57$$ 640.000 1.48719
$$58$$ 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 $$0.904154\pi$$
$$60$$ 224.000 + 387.979i 0.481971 + 0.834799i
$$61$$ −99.0000 + 171.473i −0.207798 + 0.359916i −0.951020 0.309128i $$-0.899963\pi$$
0.743223 + 0.669044i $$0.233296\pi$$
$$62$$ 144.000 0.294968
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 126.000 218.238i 0.240437 0.416448i
$$66$$ 224.000 + 387.979i 0.417765 + 0.723590i
$$67$$ 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
$$69$$ 896.000 1.56327
$$70$$ 0 0
$$71$$ 392.000 0.655237 0.327619 0.944810i $$-0.393754\pi$$
0.327619 + 0.944810i $$0.393754\pi$$
$$72$$ 148.000 256.344i 0.242250 0.419589i
$$73$$ 269.000 + 465.922i 0.431289 + 0.747014i 0.996985 0.0776001i $$-0.0247257\pi$$
−0.565696 + 0.824614i $$0.691392\pi$$
$$74$$ −346.000 599.290i −0.543536 0.941432i
$$75$$ 284.000 491.902i 0.437247 0.757333i
$$76$$ −320.000 −0.482980
$$77$$ 0 0
$$78$$ −288.000 −0.418072
$$79$$ −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
$$81$$ 179.500 + 310.903i 0.246228 + 0.426479i
$$82$$ −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
$$87$$ 760.000 + 1316.36i 0.936558 + 1.62217i
$$88$$ −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 $$0.00644690\pi$$
$$90$$ −1036.00 −1.21338
$$91$$ 0 0
$$92$$ −448.000 −0.507687
$$93$$ −288.000 + 498.831i −0.321121 + 0.556197i
$$94$$ −24.0000 41.5692i −0.0263342 0.0456121i
$$95$$ 560.000 + 969.948i 0.604787 + 1.04752i
$$96$$ −128.000 + 221.703i −0.136083 + 0.235702i
$$97$$ −1354.00 −1.41730 −0.708649 0.705561i $$-0.750695\pi$$
−0.708649 + 0.705561i $$0.750695\pi$$
$$98$$ 0 0
$$99$$ −1036.00 −1.05174
$$100$$ −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 $$-0.399919\pi$$
$$102$$ 592.000 + 1025.37i 0.574674 + 0.995364i
$$103$$ −416.000 + 720.533i −0.397958 + 0.689284i −0.993474 0.114060i $$-0.963614\pi$$
0.595516 + 0.803344i $$0.296948\pi$$
$$104$$ 144.000 0.135773
$$105$$ 0 0
$$106$$ −636.000 −0.582772
$$107$$ −222.000 + 384.515i −0.200575 + 0.347406i −0.948714 0.316136i $$-0.897614\pi$$
0.748139 + 0.663542i $$0.230948\pi$$
$$108$$ 160.000 + 277.128i 0.142556 + 0.246914i
$$109$$ −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
$$111$$ 2768.00 2.36691
$$112$$ 0 0
$$113$$ 1378.00 1.14718 0.573590 0.819143i $$-0.305550\pi$$
0.573590 + 0.819143i $$0.305550\pi$$
$$114$$ 640.000 1108.51i 0.525803 0.910717i
$$115$$ 784.000 + 1357.93i 0.635725 + 1.10111i
$$116$$ −380.000 658.179i −0.304156 0.526814i
$$117$$ 333.000 576.773i 0.263127 0.455749i
$$118$$ −400.000 −0.312059
$$119$$ 0 0
$$120$$ 896.000 0.681610
$$121$$ 273.500 473.716i 0.205485 0.355910i
$$122$$ 198.000 + 342.946i 0.146935 + 0.254499i
$$123$$ −648.000 1122.37i −0.475026 0.822769i
$$124$$ 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
$$129$$ −1648.00 2854.42i −1.12479 1.94820i
$$130$$ −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 $$0.257926\pi$$
$$132$$ 896.000 0.590809
$$133$$ 0 0
$$134$$ 1432.00 0.923179
$$135$$ 560.000 969.948i 0.357016 0.618369i
$$136$$ −296.000 512.687i −0.186631 0.323254i
$$137$$ 1483.00 + 2568.63i 0.924827 + 1.60185i 0.791840 + 0.610729i $$0.209123\pi$$
0.132987 + 0.991118i $$0.457543\pi$$
$$138$$ 896.000 1551.92i 0.552700 0.957304i
$$139$$ −2800.00 −1.70858 −0.854291 0.519795i $$-0.826008\pi$$
−0.854291 + 0.519795i $$0.826008\pi$$
$$140$$ 0 0
$$141$$ 192.000 0.114676
$$142$$ 392.000 678.964i 0.231661 0.401249i
$$143$$ −252.000 436.477i −0.147366 0.255245i
$$144$$ −296.000 512.687i −0.171296 0.296694i
$$145$$ −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 −0.927573 0.373641i $$-0.878109\pi$$
0.787369 + 0.616482i $$0.211443\pi$$
$$150$$ −568.000 983.805i −0.309180 0.535516i
$$151$$ −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
$$153$$ −2738.00 −1.44676
$$154$$ 0 0
$$155$$ −1008.00 −0.522352
$$156$$ −288.000 + 498.831i −0.147811 + 0.256015i
$$157$$ −1343.00 2326.14i −0.682695 1.18246i −0.974155 0.225879i $$-0.927475\pi$$
0.291461 0.956583i $$-0.405859\pi$$
$$158$$ 240.000 + 415.692i 0.120844 + 0.209308i
$$159$$ 1272.00 2203.17i 0.634441 1.09888i
$$160$$ −448.000 −0.221359
$$161$$ 0 0
$$162$$ 718.000 0.348219
$$163$$ 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
$$165$$ −1568.00 2715.86i −0.739810 1.28139i
$$166$$ 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
$$171$$ 1480.00 + 2563.44i 0.661862 + 1.14638i
$$172$$ 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 $$0.0327992\pi$$
$$174$$ 3040.00 1.32449
$$175$$ 0 0
$$176$$ −448.000 −0.191871
$$177$$ 800.000 1385.64i 0.339727 0.588424i
$$178$$ −810.000 1402.96i −0.341079 0.590766i
$$179$$ 150.000 + 259.808i 0.0626342 + 0.108486i 0.895642 0.444775i $$-0.146717\pi$$
−0.833008 + 0.553261i $$0.813383\pi$$
$$180$$ −1036.00 + 1794.40i −0.428994 + 0.743039i
$$181$$ 2358.00 0.968336 0.484168 0.874975i $$-0.339122\pi$$
0.484168 + 0.874975i $$0.339122\pi$$
$$182$$ 0 0
$$183$$ −1584.00 −0.639851
$$184$$ −448.000 + 775.959i −0.179495 + 0.310894i
$$185$$ 2422.00 + 4195.03i 0.962535 + 1.66716i
$$186$$ 576.000 + 997.661i 0.227067 + 0.393291i
$$187$$ −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 −0.967214 0.253962i $$-0.918266\pi$$
0.703545 + 0.710651i $$0.251599\pi$$
$$192$$ 256.000 + 443.405i 0.0962250 + 0.166667i
$$193$$ −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
$$195$$ 2016.00 0.740353
$$196$$ 0 0
$$197$$ 1214.00 0.439055 0.219528 0.975606i $$-0.429548\pi$$
0.219528 + 0.975606i $$0.429548\pi$$
$$198$$ −1036.00 + 1794.40i −0.371845 + 0.644054i
$$199$$ 520.000 + 900.666i 0.185235 + 0.320837i 0.943656 0.330929i $$-0.107362\pi$$
−0.758420 + 0.651766i $$0.774029\pi$$
$$200$$ 284.000 + 491.902i 0.100409 + 0.173914i
$$201$$ −2864.00 + 4960.59i −1.00503 + 1.74076i
$$202$$ −2716.00 −0.946025
$$203$$ 0 0
$$204$$ 2368.00 0.812712
$$205$$ 1134.00 1964.15i 0.386351 0.669180i
$$206$$ 832.000 + 1441.07i 0.281399 + 0.487397i
$$207$$ 2072.00 + 3588.81i 0.695720 + 1.20502i
$$208$$ 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
$$213$$ 1568.00 + 2715.86i 0.504402 + 0.873650i
$$214$$ 444.000 + 769.031i 0.141828 + 0.245653i
$$215$$ 2884.00 4995.23i 0.914824 1.58452i
$$216$$ 640.000 0.201604
$$217$$ 0 0
$$218$$ −3740.00 −1.16195
$$219$$ −2152.00 + 3727.37i −0.664012 + 1.15010i
$$220$$ 784.000 + 1357.93i 0.240260 + 0.416143i
$$221$$ −666.000 1153.55i −0.202715 0.351113i
$$222$$ 2768.00 4794.32i 0.836829 1.44943i
$$223$$ −3968.00 −1.19156 −0.595778 0.803149i $$-0.703156\pi$$
−0.595778 + 0.803149i $$0.703156\pi$$
$$224$$ 0 0
$$225$$ 2627.00 0.778370
$$226$$ 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 $$-0.361829\pi$$
$$228$$ −1280.00 2217.03i −0.371799 0.643974i
$$229$$ 2405.00 4165.58i 0.694004 1.20205i −0.276512 0.961011i $$-0.589178\pi$$
0.970515 0.241039i $$-0.0774883\pi$$
$$230$$ 3136.00 0.899051
$$231$$ 0 0
$$232$$ −1520.00 −0.430142
$$233$$ 1091.00 1889.67i 0.306754 0.531314i −0.670896 0.741551i $$-0.734090\pi$$
0.977650 + 0.210237i $$0.0674236\pi$$
$$234$$ −666.000 1153.55i −0.186059 0.322263i
$$235$$ 168.000 + 290.985i 0.0466345 + 0.0807734i
$$236$$ −400.000 + 692.820i −0.110330 + 0.191096i
$$237$$ −1920.00 −0.526234
$$238$$ 0 0
$$239$$ −3000.00 −0.811941 −0.405970 0.913886i $$-0.633066\pi$$
−0.405970 + 0.913886i $$0.633066\pi$$
$$240$$ 896.000 1551.92i 0.240986 0.417399i
$$241$$ 1021.00 + 1768.42i 0.272898 + 0.472673i 0.969603 0.244685i $$-0.0786845\pi$$
−0.696705 + 0.717358i $$0.745351\pi$$
$$242$$ −547.000 947.432i −0.145300 0.251666i
$$243$$ −2516.00 + 4357.84i −0.664204 + 1.15043i
$$244$$ 792.000 0.207798
$$245$$ 0 0
$$246$$ −2592.00 −0.671788
$$247$$ −720.000 + 1247.08i −0.185476 + 0.321253i
$$248$$ −288.000 498.831i −0.0737420 0.127725i
$$249$$ 4288.00 + 7427.03i 1.09133 + 1.89024i
$$250$$ −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
$$255$$ −4144.00 7177.62i −1.01768 1.76267i
$$256$$ −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 $$-0.0729785\pi$$
$$258$$ −6592.00 −1.59070
$$259$$ 0 0
$$260$$ −1008.00 −0.240437
$$261$$ −3515.00 + 6088.16i −0.833613 + 1.44386i
$$262$$ 848.000 + 1468.78i 0.199960 + 0.346342i
$$263$$ −84.0000 145.492i −0.0196945 0.0341119i 0.856010 0.516959i $$-0.172936\pi$$
−0.875705 + 0.482847i $$0.839603\pi$$
$$264$$ 896.000 1551.92i 0.208883 0.361795i
$$265$$ 4452.00 1.03202
$$266$$ 0 0
$$267$$ 6480.00 1.48528
$$268$$ 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 $$0.880765\pi$$
$$270$$ −1120.00 1939.90i −0.252448 0.437253i
$$271$$ −1104.00 + 1912.18i −0.247466 + 0.428623i −0.962822 0.270137i $$-0.912931\pi$$
0.715356 + 0.698760i $$0.246264\pi$$
$$272$$ −1184.00 −0.263936
$$273$$ 0 0
$$274$$ 5932.00 1.30790
$$275$$ 994.000 1721.66i 0.217965 0.377527i
$$276$$ −1792.00 3103.84i −0.390818 0.676916i
$$277$$ −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
$$279$$ −2664.00 −0.571647
$$280$$ 0 0
$$281$$ 3242.00 0.688262 0.344131 0.938922i $$-0.388174\pi$$
0.344131 + 0.938922i $$0.388174\pi$$
$$282$$ 192.000 332.554i 0.0405441 0.0702244i
$$283$$ −796.000 1378.71i −0.167199 0.289597i 0.770235 0.637760i $$-0.220139\pi$$
−0.937434 + 0.348163i $$0.886806\pi$$
$$284$$ −784.000 1357.93i −0.163809 0.283726i
$$285$$ −4480.00 + 7759.59i −0.931131 + 1.61277i
$$286$$ −1008.00 −0.208407
$$287$$ 0 0
$$288$$ −1184.00 −0.242250
$$289$$ −281.500 + 487.572i −0.0572970 + 0.0992413i
$$290$$ 2660.00 + 4607.26i 0.538623 + 0.932922i
$$291$$ −5416.00 9380.79i −1.09104 1.88973i
$$292$$ 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
$$297$$ −1120.00 1939.90i −0.218818 0.379004i
$$298$$ 510.000 + 883.346i 0.0991393 + 0.171714i
$$299$$ −1008.00 + 1745.91i −0.194964 + 0.337687i
$$300$$ −2272.00 −0.437247
$$301$$ 0 0
$$302$$ −1184.00 −0.225601
$$303$$ 5432.00 9408.50i 1.02990 1.78384i
$$304$$ 640.000 + 1108.51i 0.120745 + 0.209137i
$$305$$ −1386.00 2400.62i −0.260204 0.450686i
$$306$$ −2738.00 + 4742.36i −0.511507 + 0.885956i
$$307$$ 9536.00 1.77280 0.886398 0.462924i $$-0.153200\pi$$
0.886398 + 0.462924i $$0.153200\pi$$
$$308$$ 0 0
$$309$$ −6656.00 −1.22539
$$310$$ −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 $$0.861460\pi$$
$$312$$ 576.000 + 997.661i 0.104518 + 0.181030i
$$313$$ 1529.00 2648.31i 0.276116 0.478246i −0.694300 0.719685i $$-0.744286\pi$$
0.970416 + 0.241439i $$0.0776194\pi$$
$$314$$ −5372.00 −0.965476
$$315$$ 0 0
$$316$$ 960.000 0.170899
$$317$$ 2493.00 4318.00i 0.441706 0.765057i −0.556110 0.831109i $$-0.687707\pi$$
0.997816 + 0.0660512i $$0.0210401\pi$$
$$318$$ −2544.00 4406.34i −0.448618 0.777029i
$$319$$ 2660.00 + 4607.26i 0.466870 + 0.808642i
$$320$$ −448.000 + 775.959i −0.0782624 + 0.135554i
$$321$$ −3552.00 −0.617612
$$322$$ 0 0
$$323$$ 5920.00 1.01981
$$324$$ 718.000 1243.61i 0.123114 0.213239i
$$325$$ 639.000 + 1106.78i 0.109063 + 0.188902i
$$326$$ −1012.00 1752.84i −0.171931 0.297793i
$$327$$ 7480.00 12955.7i 1.26497 2.19099i
$$328$$ 1296.00 0.218170
$$329$$ 0 0
$$330$$ −6272.00 −1.04625
$$331$$ −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
$$333$$ 6401.00 + 11086.9i 1.05337 + 1.82449i
$$334$$ −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
$$339$$ 5512.00 + 9547.06i 0.883100 + 1.52957i
$$340$$ 2072.00 + 3588.81i 0.330500 + 0.572443i
$$341$$ −1008.00 + 1745.91i −0.160077 + 0.277262i
$$342$$ 5920.00 0.936014
$$343$$ 0 0
$$344$$ 3296.00 0.516594
$$345$$ −6272.00 + 10863.4i −0.978763 + 1.69527i
$$346$$ −1858.00 3218.15i −0.288690 0.500026i
$$347$$ −1002.00 1735.51i −0.155015 0.268494i 0.778050 0.628203i $$-0.216209\pi$$
−0.933064 + 0.359709i $$0.882876\pi$$
$$348$$ 3040.00 5265.43i 0.468279 0.811083i
$$349$$ −1330.00 −0.203992 −0.101996 0.994785i $$-0.532523\pi$$
−0.101996 + 0.994785i $$0.532523\pi$$
$$350$$ 0 0
$$351$$ 1440.00 0.218979
$$352$$ −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 $$0.809843\pi$$
$$354$$ −1600.00 2771.28i −0.240223 0.416079i
$$355$$ −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 $$-0.581328\pi$$
0.964276 0.264899i $$-0.0853385\pi$$
$$360$$ 2072.00 + 3588.81i 0.303344 + 0.525408i
$$361$$ 229.500 + 397.506i 0.0334597 + 0.0579539i
$$362$$ 2358.00 4084.18i 0.342358 0.592982i
$$363$$ 4376.00 0.632728
$$364$$ 0 0
$$365$$ −7532.00 −1.08012
$$366$$ −1584.00 + 2743.57i −0.226221 + 0.391827i
$$367$$ −4328.00 7496.32i −0.615585 1.06622i −0.990282 0.139077i $$-0.955586\pi$$
0.374696 0.927148i $$-0.377747\pi$$
$$368$$ 896.000 + 1551.92i 0.126922 + 0.219835i
$$369$$ 2997.00 5190.96i 0.422812 0.732332i
$$370$$ 9688.00 1.36123
$$371$$ 0 0
$$372$$ 2304.00 0.321121
$$373$$ −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
$$375$$ −3024.00 5237.72i −0.416423 0.721266i
$$376$$ −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
$$381$$ 7776.00 + 13468.4i 1.04561 + 1.81105i
$$382$$ 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 $$0.303136\pi$$
$$384$$ 1024.00 0.136083
$$385$$ 0 0
$$386$$ −3556.00 −0.468901
$$387$$ 7622.00 13201.7i 1.00116 1.73406i
$$388$$ 2708.00 + 4690.39i 0.354324 + 0.613708i
$$389$$ 7405.00 + 12825.8i 0.965163 + 1.67171i 0.709177 + 0.705031i $$0.249067\pi$$
0.255986 + 0.966680i $$0.417600\pi$$
$$390$$ 2016.00 3491.81i 0.261754 0.453372i
$$391$$ 8288.00 1.07197
$$392$$ 0 0
$$393$$ −6784.00 −0.870757
$$394$$ 1214.00 2102.71i 0.155230 0.268865i
$$395$$ −1680.00 2909.85i −0.214000 0.370659i
$$396$$ 2072.00 + 3588.81i 0.262934 + 0.455415i
$$397$$ 2577.00 4463.49i 0.325783 0.564273i −0.655887 0.754859i $$-0.727705\pi$$
0.981671 + 0.190586i $$0.0610387\pi$$
$$398$$ 2080.00 0.261962
$$399$$ 0 0
$$400$$ 1136.00 0.142000
$$401$$ −1641.00 + 2842.30i −0.204358 + 0.353959i −0.949928 0.312469i $$-0.898844\pi$$
0.745570 + 0.666427i $$0.232177\pi$$
$$402$$ 5728.00 + 9921.19i 0.710663 + 1.23091i
$$403$$ −648.000 1122.37i −0.0800972 0.138732i
$$404$$ −2716.00 + 4704.25i −0.334470 + 0.579320i
$$405$$ −5026.00 −0.616652
$$406$$ 0 0
$$407$$ 9688.00 1.17989
$$408$$ 2368.00 4101.50i 0.287337 0.497682i
$$409$$ 2905.00 + 5031.61i 0.351205 + 0.608306i 0.986461 0.163996i $$-0.0524386\pi$$
−0.635256 + 0.772302i $$0.719105\pi$$
$$410$$ −2268.00 3928.29i −0.273192 0.473182i
$$411$$ −11864.0 + 20549.1i −1.42386 + 2.46620i
$$412$$ 3328.00 0.397958
$$413$$ 0 0
$$414$$ 8288.00 0.983896
$$415$$ −7504.00 + 12997.3i −0.887607 + 1.53738i
$$416$$ −288.000 498.831i −0.0339432 0.0587913i
$$417$$ −11200.0 19399.0i −1.31527 2.27811i
$$418$$ 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
$$423$$ 444.000 + 769.031i 0.0510355 + 0.0883961i
$$424$$ 1272.00 + 2203.17i 0.145693 + 0.252347i
$$425$$ 2627.00 4550.10i 0.299831 0.519323i
$$426$$ 6272.00 0.713332
$$427$$ 0 0
$$428$$ 1776.00 0.200575
$$429$$ 2016.00 3491.81i 0.226884 0.392975i
$$430$$ −5768.00 9990.47i −0.646878 1.12043i
$$431$$ −636.000 1101.58i −0.0710790 0.123112i 0.828295 0.560292i $$-0.189311\pi$$
−0.899374 + 0.437179i $$0.855978\pi$$
$$432$$ 640.000 1108.51i 0.0712778 0.123457i
$$433$$ 5062.00 0.561811 0.280906 0.959735i $$-0.409365\pi$$
0.280906 + 0.959735i $$0.409365\pi$$
$$434$$ 0 0
$$435$$ −21280.0 −2.34551
$$436$$ −3740.00 + 6477.87i −0.410811 + 0.711545i
$$437$$ −4480.00 7759.59i −0.490406 0.849408i
$$438$$ 4304.00 + 7454.75i 0.469528 + 0.813246i
$$439$$ 2820.00 4884.38i 0.306586 0.531023i −0.671027 0.741433i $$-0.734147\pi$$
0.977613 + 0.210410i $$0.0674800\pi$$
$$440$$ 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 $$0.421575\pi$$
−0.961820 + 0.273683i $$0.911758\pi$$
$$444$$ −5536.00 9588.63i −0.591727 1.02490i
$$445$$ 5670.00 + 9820.73i 0.604008 + 1.04617i
$$446$$ −3968.00 + 6872.78i −0.421279 + 0.729676i
$$447$$ −4080.00 −0.431717
$$448$$ 0 0
$$449$$ −3230.00 −0.339495 −0.169747 0.985488i $$-0.554295\pi$$
−0.169747 + 0.985488i $$0.554295\pi$$
$$450$$ 2627.00 4550.10i 0.275195 0.476653i
$$451$$ −2268.00 3928.29i −0.236798 0.410146i
$$452$$ −2756.00 4773.53i −0.286795 0.496743i
$$453$$ 2368.00 4101.50i 0.245603 0.425398i
$$454$$ −7872.00 −0.813769
$$455$$ 0 0
$$456$$ −5120.00 −0.525803
$$457$$ 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
$$459$$ −2960.00 5126.87i −0.301004 0.521355i
$$460$$ 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
$$465$$ −4032.00 6983.63i −0.402107 0.696469i
$$466$$ −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 $$0.211222\pi$$
$$468$$ −2664.00 −0.263127
$$469$$ 0 0
$$470$$ 672.000 0.0659512
$$471$$ 10744.0 18609.2i 1.05108 1.82052i
$$472$$ 800.000 + 1385.64i 0.0780148 + 0.135126i
$$473$$ −5768.00 9990.47i −0.560704 0.971168i
$$474$$ −1920.00 + 3325.54i −0.186052 + 0.322251i
$$475$$ −5680.00 −0.548666
$$476$$ 0 0
$$477$$ 11766.0 1.12941
$$478$$ −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 $$0.881491\pi$$
$$480$$ −1792.00 3103.84i −0.170403 0.295146i
$$481$$ −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
$$486$$ 5032.00 + 8715.68i 0.469663 + 0.813480i
$$487$$ 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
$$489$$ 8096.00 0.748699
$$490$$ 0 0
$$491$$ −11268.0 −1.03568 −0.517839 0.855478i $$-0.673263\pi$$
−0.517839 + 0.855478i $$0.673263\pi$$
$$492$$ −2592.00 + 4489.48i −0.237513 + 0.411385i
$$493$$ 7030.00 + 12176.3i 0.642222 + 1.11236i
$$494$$ 1440.00 + 2494.15i 0.131151 + 0.227160i
$$495$$ 7252.00 12560.8i 0.658491 1.14054i
$$496$$ −1152.00 −0.104287
$$497$$ 0 0
$$498$$ 17152.0 1.54337
$$499$$ 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
$$501$$ −2176.00 3768.94i −0.194045 0.336096i
$$502$$ 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
$$507$$ −7492.00 12976.5i −0.656275 1.13670i
$$508$$ −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 $$0.995074\pi$$
$$510$$ −16576.0 −1.43921
$$511$$ 0 0
$$512$$ −512.000 −0.0441942
$$513$$ −3200.00 + 5542.56i −0.275406 + 0.477018i
$$514$$ −5634.00 9758.37i −0.483473 0.837400i
$$515$$ −5824.00 10087.5i −0.498323 0.863120i
$$516$$ −6592.00 + 11417.7i −0.562397 + 0.974099i
$$517$$ 672.000 0.0571654
$$518$$ 0 0
$$519$$ 14864.0 1.25714
$$520$$ −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 $$0.815095\pi$$
$$522$$ 7030.00 + 12176.3i 0.589454 + 1.02096i
$$523$$ 3484.00 6034.47i 0.291290 0.504529i −0.682825 0.730582i $$-0.739249\pi$$
0.974115 + 0.226053i $$0.0725822\pi$$
$$524$$ 3392.00 0.282787
$$525$$ 0 0
$$526$$ −336.000 −0.0278523
$$527$$ −2664.00 + 4614.18i −0.220200 + 0.381398i
$$528$$ −1792.00 3103.84i −0.147702 0.255828i
$$529$$ −188.500 326.492i −0.0154927 0.0268342i
$$530$$ 4452.00 7711.09i 0.364873 0.631978i
$$531$$ 7400.00 0.604770
$$532$$ 0 0
$$533$$ 2916.00 0.236972
$$534$$ 6480.00 11223.7i 0.525126 0.909544i
$$535$$ −3108.00 5383.21i −0.251160 0.435022i
$$536$$ −2864.00 4960.59i −0.230795 0.399748i
$$537$$ −1200.00 + 2078.46i −0.0964317 + 0.167025i
$$538$$ −2620.00 −0.209956
$$539$$ 0 0
$$540$$ −4480.00 −0.357016
$$541$$ −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
$$543$$ 9432.00 + 16336.7i 0.745425 + 1.29111i
$$544$$ −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
$$549$$ −3663.00 6344.50i −0.284760 0.493218i
$$550$$ −1988.00 3443.32i −0.154125 0.266952i
$$551$$ 7600.00 13163.6i 0.587606 1.01776i
$$552$$ −7168.00 −0.552700
$$553$$ 0 0
$$554$$ −10588.0 −0.811987
$$555$$ −19376.0 + 33560.2i −1.48192 + 2.56676i
$$556$$ 5600.00 + 9699.48i 0.427146 + 0.739838i
$$557$$ 3733.00 + 6465.75i 0.283972 + 0.491854i 0.972359 0.233490i $$-0.0750145\pi$$
−0.688388 + 0.725343i $$0.741681\pi$$
$$558$$ −2664.00 + 4614.18i −0.202108 + 0.350061i
$$559$$ 7416.00 0.561115
$$560$$ 0 0
$$561$$ −16576.0 −1.24749
$$562$$ 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 $$0.449158\pi$$
$$564$$ −384.000 665.108i −0.0286690 0.0496562i
$$565$$ −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 $$0.342582\pi$$
−0.999578 + 0.0290514i $$0.990751\pi$$
$$570$$ 8960.00 + 15519.2i 0.658409 + 1.14040i
$$571$$ −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
$$573$$ −11136.0 −0.811890
$$574$$ 0 0
$$575$$ −7952.00 −0.576733
$$576$$ −1184.00 + 2050.75i −0.0856481 + 0.148347i
$$577$$ −4183.00 7245.17i −0.301803 0.522739i 0.674741 0.738055i $$-0.264255\pi$$
−0.976545 + 0.215316i $$0.930922\pi$$
$$578$$ 563.000 + 975.145i 0.0405151 + 0.0701742i
$$579$$ 7112.00 12318.3i 0.510474 0.884167i
$$580$$ 10640.0 0.761728
$$581$$ 0 0
$$582$$ −21664.0 −1.54296
$$583$$ 4452.00 7711.09i 0.316266 0.547789i
$$584$$ −2152.00 3727.37i −0.152484 0.264109i
$$585$$ 4662.00 + 8074.82i 0.329487 + 0.570688i
$$586$$ 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
$$591$$ 4856.00 + 8410.84i 0.337985 + 0.585407i
$$592$$ 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 $$0.0613993\pi$$
$$594$$ −4480.00 −0.309456
$$595$$ 0 0
$$596$$ 2040.00 0.140204
$$597$$ −4160.00 + 7205.33i −0.285188 + 0.493961i
$$598$$ 2016.00 + 3491.81i 0.137860 + 0.238781i
$$599$$ 4500.00 + 7794.23i 0.306953 + 0.531659i 0.977694 0.210033i $$-0.0673571\pi$$
−0.670741 + 0.741692i $$0.734024\pi$$
$$600$$ −2272.00 + 3935.22i −0.154590 + 0.267758i
$$601$$ −7562.00 −0.513245 −0.256623 0.966512i $$-0.582610\pi$$
−0.256623 + 0.966512i $$0.582610\pi$$
$$602$$ 0 0
$$603$$ −26492.0 −1.78912
$$604$$ −1184.00 + 2050.75i −0.0797620 + 0.138152i
$$605$$ 3829.00 + 6632.02i 0.257307 + 0.445670i
$$606$$ −10864.0 18817.0i −0.728251 1.26137i
$$607$$ −1488.00 + 2577.29i −0.0994993 + 0.172338i −0.911478 0.411350i $$-0.865057\pi$$
0.811978 + 0.583688i $$0.198391\pi$$
$$608$$ 2560.00 0.170759
$$609$$ 0 0
$$610$$ −5544.00 −0.367984
$$611$$ −216.000 + 374.123i −0.0143018 + 0.0247715i
$$612$$ 5476.00 + 9484.71i 0.361690 + 0.626465i
$$613$$ −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
$$615$$ 18144.0 1.18965
$$616$$ 0 0
$$617$$ 18794.0 1.22629 0.613143 0.789972i $$-0.289905\pi$$
0.613143 + 0.789972i $$0.289905\pi$$
$$618$$ −6656.00 + 11528.5i −0.433242 + 0.750397i
$$619$$ 9020.00 + 15623.1i 0.585694 + 1.01445i 0.994789 + 0.101959i $$0.0325112\pi$$
−0.409095 + 0.912492i $$0.634155\pi$$
$$620$$ 2016.00 + 3491.81i 0.130588 + 0.226185i
$$621$$ −4480.00 + 7759.59i −0.289495 + 0.501420i
$$622$$ −1936.00 −0.124801
$$623$$ 0 0
$$624$$ 2304.00 0.147811
$$625$$ 9729.50 16852.0i 0.622688 1.07853i
$$626$$ −3058.00 5296.61i −0.195243 0.338171i
$$627$$ 8960.00 + 15519.2i 0.570698 + 0.988479i
$$628$$ −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
$$633$$ −15472.0 26798.3i −0.971496 1.68268i
$$634$$ −4986.00 8636.01i −0.312333 0.540977i
$$635$$ −13608.0 + 23569.7i −0.850420 + 1.47297i
$$636$$ −10176.0 −0.634441
$$637$$ 0 0
$$638$$ 10640.0 0.660253
$$639$$ −7252.00 + 12560.8i −0.448959 + 0.777619i
$$640$$ 896.000 + 1551.92i 0.0553399 + 0.0958514i
$$641$$ 5279.00 + 9143.50i 0.325285 + 0.563411i 0.981570 0.191102i $$-0.0612063\pi$$
−0.656285 + 0.754513i $$0.727873\pi$$
$$642$$ −3552.00 + 6152.24i −0.218359 + 0.378208i
$$643$$ 26152.0 1.60394 0.801971 0.597363i $$-0.203785\pi$$
0.801971 + 0.597363i $$0.203785\pi$$
$$644$$ 0 0
$$645$$ 46144.0 2.81693
$$646$$ 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 $$0.549928\pi$$
$$648$$ −1436.00 2487.22i −0.0870546 0.150783i
$$649$$ 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 −0.998711 0.0507630i $$-0.983835\pi$$
0.543317 + 0.839527i $$0.317168\pi$$
$$654$$ −14960.0 25911.5i −0.894468 1.54926i
$$655$$ −5936.00 10281.5i −0.354105 0.613328i
$$656$$ 1296.00 2244.74i 0.0771346 0.133601i
$$657$$ −19906.0 −1.18205
$$658$$ 0 0
$$659$$ −6100.00 −0.360580 −0.180290 0.983613i $$-0.557704\pi$$
−0.180290 + 0.983613i $$0.557704\pi$$
$$660$$ −6272.00 + 10863.4i −0.369905 + 0.640694i
$$661$$ −1159.00 2007.45i −0.0681995 0.118125i 0.829909 0.557898i $$-0.188392\pi$$
−0.898109 + 0.439773i $$0.855059\pi$$
$$662$$ 8612.00 + 14916.4i 0.505612 + 0.875745i
$$663$$ 5328.00 9228.37i 0.312100 0.540573i
$$664$$ −8576.00 −0.501225
$$665$$ 0 0
$$666$$ 25604.0 1.48969
$$667$$ 10640.0 18429.0i 0.617665 1.06983i
$$668$$ 1088.00 + 1884.47i 0.0630179 + 0.109150i
$$669$$ −15872.0 27491.1i −0.917260 1.58874i
$$670$$ −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
$$675$$ 2840.00 + 4919.02i 0.161943 + 0.280494i
$$676$$ 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 $$-0.0900831\pi$$
$$678$$ 22048.0 1.24889
$$679$$ 0 0
$$680$$ 8288.00 0.467397
$$681$$ 15744.0 27269.4i 0.885920 1.53446i
$$682$$ 2016.00 + 3491.81i 0.113192 + 0.196053i
$$683$$ 4266.00 + 7388.93i 0.238996 + 0.413952i 0.960426 0.278534i $$-0.0898485\pi$$
−0.721431 + 0.692487i $$0.756515\pi$$
$$684$$ 5920.00 10253.7i 0.330931 0.573189i
$$685$$ −41524.0 −2.31613
$$686$$ 0 0
$$687$$ 38480.0 2.13698
$$688$$ 3296.00 5708.84i 0.182644 0.316348i
$$689$$ 2862.00 + 4957.13i 0.158249 + 0.274095i
$$690$$ 12544.0 + 21726.8i 0.692090 + 1.19873i
$$691$$ 10336.0 17902.5i 0.569030 0.985589i −0.427632 0.903953i $$-0.640652\pi$$
0.996662 0.0816365i $$-0.0260146\pi$$
$$692$$ −7432.00 −0.408269
$$693$$ 0 0
$$694$$ −4008.00 −0.219224
$$695$$ 19600.0 33948.2i 1.06974 1.85285i
$$696$$ −6080.00 10530.9i −0.331123 0.573522i
$$697$$ −5994.00 10381.9i −0.325737 0.564194i
$$698$$ −1330.00 + 2303.63i −0.0721221 + 0.124919i
$$699$$ 17456.0 0.944559
$$700$$ 0 0
$$701$$ −21458.0 −1.15614 −0.578072 0.815985i $$-0.696195\pi$$
−0.578072 + 0.815985i $$0.696195\pi$$
$$702$$ 1440.00 2494.15i 0.0774207 0.134097i
$$703$$ −13840.0 23971.6i −0.742511 1.28607i
$$704$$ 896.000 + 1551.92i 0.0479677 + 0.0830825i
$$705$$ −1344.00 + 2327.88i −0.0717985 + 0.124359i
$$706$$ 1956.00 0.104271
$$707$$ 0 0
$$708$$ −6400.00 −0.339727
$$709$$ 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
$$711$$ −4440.00 7690.31i −0.234196 0.405639i
$$712$$ −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
$$717$$ −12000.0 20784.6i −0.625032 1.08259i
$$718$$ −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 $$0.329161\pi$$
$$720$$ 8288.00 0.428994
$$721$$ 0 0
$$722$$ 918.000 0.0473191
$$723$$ −8168.00 + 14147.4i −0.420154 + 0.727728i
$$724$$ −4716.00 8168.35i −0.242084 0.419302i
$$725$$ −6745.00 11682.7i −0.345521 0.598461i
$$726$$ 4376.00 7579.45i 0.223703 0.387465i
$$727$$ −37504.0 −1.91327 −0.956634 0.291291i $$-0.905915\pi$$
−0.956634 + 0.291291i $$0.905915\pi$$
$$728$$ 0 0
$$729$$ −30563.0 −1.55276
$$730$$ −7532.00 + 13045.8i −0.381879 + 0.661434i
$$731$$ −15244.0 26403.4i −0.771299 1.33593i
$$732$$ 3168.00 + 5487.14i 0.159963 + 0.277063i
$$733$$ 6669.00 11551.0i 0.336051 0.582057i −0.647635 0.761950i $$-0.724242\pi$$
0.983686 + 0.179894i $$0.0575753\pi$$
$$734$$ −17312.0 −0.870569
$$735$$ 0 0
$$736$$ 3584.00 0.179495
$$737$$ −10024.0 + 17362.1i −0.501002 + 0.867762i
$$738$$ −5994.00 10381.9i −0.298973 0.517837i
$$739$$ −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
$$741$$ −11520.0 −0.571117
$$742$$ 0 0
$$743$$ −19632.0 −0.969352 −0.484676 0.874694i $$-0.661062\pi$$
−0.484676 + 0.874694i $$0.661062\pi$$
$$744$$ 2304.00 3990.65i 0.113533 0.196645i
$$745$$ −3570.00 6183.42i −0.175563 0.304085i
$$746$$ 5278.00 + 9141.76i 0.259037 + 0.448665i
$$747$$ −19832.0 + 34350.0i −0.971372 + 1.68247i
$$748$$ 8288.00 0.405133
$$749$$ 0 0
$$750$$ −12096.0 −0.588911
$$751$$ −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
$$753$$ 2112.00 + 3658.09i 0.102212 + 0.177036i
$$754$$ −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
$$759$$ 12544.0 + 21726.8i 0.599892 + 1.03904i
$$760$$ −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 $$0.858921\pi$$
$$762$$ 31104.0 1.47871
$$763$$ 0 0
$$764$$ 5568.00 0.263669
$$765$$ 19166.0 33196.5i 0.905815 1.56892i
$$766$$ 6232.00 + 10794.1i 0.293957 + 0.509149i
$$767$$ 1800.00 + 3117.69i 0.0847382 + 0.146771i
$$768$$ 1024.00 1773.62i 0.0481125 0.0833333i
$$769$$ −39130.0 −1.83493 −0.917467 0.397812i $$-0.869769\pi$$
−0.917467 + 0.397812i $$0.869769\pi$$
$$770$$ 0 0
$$771$$ 45072.0 2.10535
$$772$$ −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 $$-0.373281\pi$$
$$774$$ −15244.0 26403.4i −0.707925 1.22616i
$$775$$ 2556.00 4427.12i 0.118470 0.205196i
$$776$$ 10832.0 0.501090
$$777$$ 0 0