# Properties

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

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(67,98)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$5.78218718056$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field 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.d.67.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} -16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})$$ $$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 $$-0.887022\pi$$
0.167871 0.985809i $$-0.446311\pi$$
$$4$$ −2.00000 3.46410i −0.250000 0.433013i
$$5$$ 7.00000 12.1244i 0.626099 1.08444i −0.362228 0.932089i $$-0.617984\pi$$
0.988327 0.152346i $$-0.0486828\pi$$
$$6$$ −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 $$-0.438499\pi$$
0.192012 + 0.981393i $$0.438499\pi$$
$$14$$ 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 $$-0.989657\pi$$
0.471600 0.881812i $$-0.343676\pi$$
$$18$$ 37.0000 + 64.0859i 0.484499 + 0.839177i
$$19$$ −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 $$-0.663834\pi$$
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 0.742692 0.669634i $$-0.233549\pi$$
−0.951266 + 0.308373i $$0.900216\pi$$
$$32$$ 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 $$-0.400160\pi$$
0.308538 + 0.951212i $$0.400160\pi$$
$$42$$ 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 −0.884046 0.467401i $$-0.845191\pi$$
0.846804 + 0.531906i $$0.178524\pi$$
$$48$$ 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 0.955008 0.296579i $$-0.0958458\pi$$
−0.734349 + 0.678772i $$0.762512\pi$$
$$60$$ 224.000 + 387.979i 0.481971 + 0.834799i
$$61$$ 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
$$66$$ −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 0.565696 0.824614i $$-0.308608\pi$$
−0.996985 + 0.0776001i $$0.975274\pi$$
$$74$$ −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 $$-0.750781\pi$$
−0.708839 + 0.705370i $$0.750781\pi$$
$$84$$ 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 −0.999795 0.0202521i $$-0.993553\pi$$
0.517436 + 0.855722i $$0.326886\pi$$
$$90$$ 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 $$-0.249305\pi$$
0.708649 + 0.705561i $$0.249305\pi$$
$$98$$ 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 $$0.0665854\pi$$
−0.309260 + 0.950978i $$0.600081\pi$$
$$102$$ 592.000 + 1025.37i 0.574674 + 0.995364i
$$103$$ 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 −0.948714 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 −0.689283 0.724492i $$-0.742074\pi$$
0.972070 + 0.234691i $$0.0754078\pi$$
$$132$$ −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 $$-0.173992\pi$$
0.854291 + 0.519795i $$0.173992\pi$$
$$140$$ 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 $$0.0725254\pi$$
−0.291461 + 0.956583i $$0.594141\pi$$
$$158$$ 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 $$-0.459775\pi$$
0.126036 + 0.992026i $$0.459775\pi$$
$$168$$ 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 −0.994696 0.102859i $$-0.967201\pi$$
0.586427 + 0.810002i $$0.300534\pi$$
$$174$$ −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 $$-0.660878\pi$$
−0.484168 + 0.874975i $$0.660878\pi$$
$$182$$ 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 0.758420 0.651766i $$-0.225971\pi$$
−0.943656 + 0.330929i $$0.892638\pi$$
$$200$$ 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 $$-0.296844\pi$$
0.595778 + 0.803149i $$0.296844\pi$$
$$224$$ 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 $$0.0284954\pi$$
−0.420574 + 0.907258i $$0.638171\pi$$
$$228$$ −1280.00 2217.03i −0.371799 0.643974i
$$229$$ −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 −0.670896 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 0.696705 0.717358i $$-0.254649\pi$$
−0.969603 + 0.244685i $$0.921315\pi$$
$$242$$ −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 $$-0.521148\pi$$
−0.0663886 + 0.997794i $$0.521148\pi$$
$$252$$ 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 $$0.406312\pi$$
−0.973833 + 0.227265i $$0.927022\pi$$
$$258$$ 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 0.930659 0.365888i $$-0.119235\pi$$
−0.782198 + 0.623030i $$0.785901\pi$$
$$270$$ −1120.00 1939.90i −0.252448 0.437253i
$$271$$ 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
$$276$$ 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 0.937434 0.348163i $$-0.113194\pi$$
−0.770235 + 0.637760i $$0.779861\pi$$
$$284$$ −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 $$-0.666910\pi$$
−0.500663 + 0.865642i $$0.666910\pi$$
$$294$$ 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 $$-0.846800\pi$$
−0.886398 + 0.462924i $$0.846800\pi$$
$$308$$ 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 0.906771 0.421624i $$-0.138540\pi$$
−0.818523 + 0.574474i $$0.805207\pi$$
$$312$$ 576.000 + 997.661i 0.104518 + 0.181030i
$$313$$ −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 −0.556110 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 $$-0.467477\pi$$
0.101996 + 0.994785i $$0.467477\pi$$
$$350$$ 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 0.826803 0.562492i $$-0.190157\pi$$
−0.900533 + 0.434787i $$0.856824\pi$$
$$354$$ −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 $$0.0444136\pi$$
−0.374696 + 0.927148i $$0.622253\pi$$
$$368$$ 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 −0.579785 0.814769i $$-0.696864\pi$$
0.995504 + 0.0947240i $$0.0301968\pi$$
$$384$$ −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 −0.981671 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 −0.949928 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 0.635256 0.772302i $$-0.280895\pi$$
−0.986461 + 0.163996i $$0.947561\pi$$
$$410$$ −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 $$-0.209814\pi$$
0.790512 + 0.612446i $$0.209814\pi$$
$$420$$ 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 $$-0.590635\pi$$
−0.280906 + 0.959735i $$0.590635\pi$$
$$434$$ 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 −0.977613 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 $$0.421575\pi$$
−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 $$-0.380094\pi$$
0.367849 + 0.929886i $$0.380094\pi$$
$$462$$ 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 −0.787797 0.615935i $$-0.788778\pi$$
0.927314 + 0.374285i $$0.122112\pi$$
$$468$$ 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 0.931490 0.363766i $$-0.118509\pi$$
−0.780776 + 0.624811i $$0.785176\pi$$
$$480$$ −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 $$-0.521347\pi$$
−0.0670147 + 0.997752i $$0.521347\pi$$
$$504$$ 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 $$-0.661740\pi$$
0.999880 0.0154756i $$-0.00492624\pi$$
$$510$$ 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 0.835972 0.548773i $$-0.184905\pi$$
−0.893237 + 0.449586i $$0.851571\pi$$
$$522$$ 7030.00 + 12176.3i 0.589454 + 1.02096i
$$523$$ −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
$$528$$ 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 $$-0.782491\pi$$
−0.159048 0.987271i $$-0.550842\pi$$
$$564$$ −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 0.976545 0.215316i $$-0.0690780\pi$$
−0.674741 + 0.738055i $$0.735745\pi$$
$$578$$ 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 $$-0.245678\pi$$
0.716642 + 0.697441i $$0.245678\pi$$
$$588$$ 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 −0.981454 0.191698i $$-0.938601\pi$$
0.656742 + 0.754115i $$0.271934\pi$$
$$594$$ 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 $$-0.417390\pi$$
0.256623 + 0.966512i $$0.417390\pi$$
$$602$$ 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 −0.811978 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
$$612$$ −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 $$-0.967489\pi$$
0.409095 0.912492i $$-0.365845\pi$$
$$620$$ 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 $$-0.796215\pi$$
−0.801971 + 0.597363i $$0.796215\pi$$
$$644$$ 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 $$-0.883261\pi$$
0.156211 0.987724i $$-0.450072\pi$$
$$648$$ −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 0.898109 0.439773i $$-0.144941\pi$$
−0.829909 + 0.557898i $$0.811608\pi$$
$$662$$ 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 $$0.423416\pi$$
−0.960221 + 0.279242i $$0.909917\pi$$
$$678$$ −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 $$0.359348\pi$$
−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
$$696$$ 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 −0.511309 0.859397i $$-0.670839\pi$$
0.999914 + 0.0131086i $$0.00417273\pi$$
$$720$$ −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 $$-0.0940849\pi$$
0.956634 + 0.291291i $$0.0940849\pi$$
$$728$$ 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 −0.983686 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
$$738$$ 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 $$-0.525588\pi$$
0.903378 0.428844i $$-0.141079\pi$$
$$762$$ −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 $$-0.130231\pi$$
0.917467 + 0.397812i $$0.130231\pi$$
$$770$$ 0 0
$$771$$ 45072.0 2.10535
$$772$$ −3556.00 + 6159.17i −0.165781 + 0.287142i
$$773$$ 12991.0 + 22501.1i