# Properties

 Label 882.4.g.u.667.1 Level $882$ Weight $4$ Character 882.667 Analytic conductor $52.040$ 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] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

 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

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: $$52.0396846251$$ 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: $$\Z[a_1, \ldots, a_{5}]$$ 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.u.361.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} -8.00000 q^{8} +O(q^{10})$$ $$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} -8.00000 q^{8} +(-9.00000 - 15.5885i) q^{10} +(-28.5000 - 49.3634i) q^{11} +70.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-25.5000 - 44.1673i) q^{17} +(2.50000 - 4.33013i) q^{19} -36.0000 q^{20} -114.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(22.0000 + 38.1051i) q^{25} +(70.0000 - 121.244i) q^{26} -114.000 q^{29} +(11.5000 + 19.9186i) q^{31} +(16.0000 + 27.7128i) q^{32} -102.000 q^{34} +(126.500 - 219.104i) q^{37} +(-5.00000 - 8.66025i) q^{38} +(-36.0000 + 62.3538i) q^{40} -42.0000 q^{41} -124.000 q^{43} +(-114.000 + 197.454i) q^{44} +(-69.0000 - 119.512i) q^{46} +(-100.500 + 174.071i) q^{47} +88.0000 q^{50} +(-140.000 - 242.487i) q^{52} +(-196.500 - 340.348i) q^{53} -513.000 q^{55} +(-114.000 + 197.454i) q^{58} +(-109.500 - 189.660i) q^{59} +(-354.500 + 614.012i) q^{61} +46.0000 q^{62} +64.0000 q^{64} +(315.000 - 545.596i) q^{65} +(-209.500 - 362.865i) q^{67} +(-102.000 + 176.669i) q^{68} +96.0000 q^{71} +(-156.500 - 271.066i) q^{73} +(-253.000 - 438.209i) q^{74} -20.0000 q^{76} +(-230.500 + 399.238i) q^{79} +(72.0000 + 124.708i) q^{80} +(-42.0000 + 72.7461i) q^{82} -588.000 q^{83} -459.000 q^{85} +(-124.000 + 214.774i) q^{86} +(228.000 + 394.908i) q^{88} +(508.500 - 880.748i) q^{89} -276.000 q^{92} +(201.000 + 348.142i) q^{94} +(-22.5000 - 38.9711i) q^{95} +1834.00 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - 4 q^{4} + 9 q^{5} - 16 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 - 4 * q^4 + 9 * q^5 - 16 * q^8 $$2 q + 2 q^{2} - 4 q^{4} + 9 q^{5} - 16 q^{8} - 18 q^{10} - 57 q^{11} + 140 q^{13} - 16 q^{16} - 51 q^{17} + 5 q^{19} - 72 q^{20} - 228 q^{22} + 69 q^{23} + 44 q^{25} + 140 q^{26} - 228 q^{29} + 23 q^{31} + 32 q^{32} - 204 q^{34} + 253 q^{37} - 10 q^{38} - 72 q^{40} - 84 q^{41} - 248 q^{43} - 228 q^{44} - 138 q^{46} - 201 q^{47} + 176 q^{50} - 280 q^{52} - 393 q^{53} - 1026 q^{55} - 228 q^{58} - 219 q^{59} - 709 q^{61} + 92 q^{62} + 128 q^{64} + 630 q^{65} - 419 q^{67} - 204 q^{68} + 192 q^{71} - 313 q^{73} - 506 q^{74} - 40 q^{76} - 461 q^{79} + 144 q^{80} - 84 q^{82} - 1176 q^{83} - 918 q^{85} - 248 q^{86} + 456 q^{88} + 1017 q^{89} - 552 q^{92} + 402 q^{94} - 45 q^{95} + 3668 q^{97}+O(q^{100})$$ 2 * q + 2 * q^2 - 4 * q^4 + 9 * q^5 - 16 * q^8 - 18 * q^10 - 57 * q^11 + 140 * q^13 - 16 * q^16 - 51 * q^17 + 5 * q^19 - 72 * q^20 - 228 * q^22 + 69 * q^23 + 44 * q^25 + 140 * q^26 - 228 * q^29 + 23 * q^31 + 32 * q^32 - 204 * q^34 + 253 * q^37 - 10 * q^38 - 72 * q^40 - 84 * q^41 - 248 * q^43 - 228 * q^44 - 138 * q^46 - 201 * q^47 + 176 * q^50 - 280 * q^52 - 393 * q^53 - 1026 * q^55 - 228 * q^58 - 219 * q^59 - 709 * q^61 + 92 * q^62 + 128 * q^64 + 630 * q^65 - 419 * q^67 - 204 * q^68 + 192 * q^71 - 313 * q^73 - 506 * q^74 - 40 * q^76 - 461 * q^79 + 144 * q^80 - 84 * q^82 - 1176 * q^83 - 918 * q^85 - 248 * q^86 + 456 * q^88 + 1017 * q^89 - 552 * q^92 + 402 * q^94 - 45 * q^95 + 3668 * q^97

## 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
$$5$$ 4.50000 7.79423i 0.402492 0.697137i −0.591534 0.806280i $$-0.701477\pi$$
0.994026 + 0.109143i $$0.0348107\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ −9.00000 15.5885i −0.284605 0.492950i
$$11$$ −28.5000 49.3634i −0.781188 1.35306i −0.931250 0.364381i $$-0.881280\pi$$
0.150061 0.988677i $$-0.452053\pi$$
$$12$$ 0 0
$$13$$ 70.0000 1.49342 0.746712 0.665148i $$-0.231631\pi$$
0.746712 + 0.665148i $$0.231631\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −8.00000 + 13.8564i −0.125000 + 0.216506i
$$17$$ −25.5000 44.1673i −0.363803 0.630126i 0.624780 0.780801i $$-0.285189\pi$$
−0.988583 + 0.150675i $$0.951855\pi$$
$$18$$ 0 0
$$19$$ 2.50000 4.33013i 0.0301863 0.0522842i −0.850538 0.525914i $$-0.823723\pi$$
0.880724 + 0.473630i $$0.157057\pi$$
$$20$$ −36.0000 −0.402492
$$21$$ 0 0
$$22$$ −114.000 −1.10477
$$23$$ 34.5000 59.7558i 0.312772 0.541736i −0.666190 0.745782i $$-0.732076\pi$$
0.978961 + 0.204046i $$0.0654092\pi$$
$$24$$ 0 0
$$25$$ 22.0000 + 38.1051i 0.176000 + 0.304841i
$$26$$ 70.0000 121.244i 0.528005 0.914531i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −114.000 −0.729975 −0.364987 0.931012i $$-0.618927\pi$$
−0.364987 + 0.931012i $$0.618927\pi$$
$$30$$ 0 0
$$31$$ 11.5000 + 19.9186i 0.0666278 + 0.115403i 0.897415 0.441188i $$-0.145443\pi$$
−0.830787 + 0.556590i $$0.812109\pi$$
$$32$$ 16.0000 + 27.7128i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ −102.000 −0.514496
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 126.500 219.104i 0.562067 0.973528i −0.435249 0.900310i $$-0.643340\pi$$
0.997316 0.0732182i $$-0.0233270\pi$$
$$38$$ −5.00000 8.66025i −0.0213449 0.0369705i
$$39$$ 0 0
$$40$$ −36.0000 + 62.3538i −0.142302 + 0.246475i
$$41$$ −42.0000 −0.159983 −0.0799914 0.996796i $$-0.525489\pi$$
−0.0799914 + 0.996796i $$0.525489\pi$$
$$42$$ 0 0
$$43$$ −124.000 −0.439763 −0.219882 0.975527i $$-0.570567\pi$$
−0.219882 + 0.975527i $$0.570567\pi$$
$$44$$ −114.000 + 197.454i −0.390594 + 0.676529i
$$45$$ 0 0
$$46$$ −69.0000 119.512i −0.221163 0.383065i
$$47$$ −100.500 + 174.071i −0.311903 + 0.540231i −0.978774 0.204941i $$-0.934300\pi$$
0.666871 + 0.745173i $$0.267633\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 88.0000 0.248902
$$51$$ 0 0
$$52$$ −140.000 242.487i −0.373356 0.646671i
$$53$$ −196.500 340.348i −0.509271 0.882083i −0.999942 0.0107383i $$-0.996582\pi$$
0.490672 0.871345i $$-0.336751\pi$$
$$54$$ 0 0
$$55$$ −513.000 −1.25769
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −114.000 + 197.454i −0.258085 + 0.447016i
$$59$$ −109.500 189.660i −0.241622 0.418501i 0.719555 0.694436i $$-0.244346\pi$$
−0.961176 + 0.275935i $$0.911013\pi$$
$$60$$ 0 0
$$61$$ −354.500 + 614.012i −0.744083 + 1.28879i 0.206539 + 0.978438i $$0.433780\pi$$
−0.950622 + 0.310351i $$0.899553\pi$$
$$62$$ 46.0000 0.0942259
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 315.000 545.596i 0.601091 1.04112i
$$66$$ 0 0
$$67$$ −209.500 362.865i −0.382007 0.661656i 0.609342 0.792908i $$-0.291434\pi$$
−0.991349 + 0.131251i $$0.958100\pi$$
$$68$$ −102.000 + 176.669i −0.181902 + 0.315063i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 96.0000 0.160466 0.0802331 0.996776i $$-0.474434\pi$$
0.0802331 + 0.996776i $$0.474434\pi$$
$$72$$ 0 0
$$73$$ −156.500 271.066i −0.250917 0.434601i 0.712862 0.701305i $$-0.247399\pi$$
−0.963779 + 0.266704i $$0.914065\pi$$
$$74$$ −253.000 438.209i −0.397441 0.688388i
$$75$$ 0 0
$$76$$ −20.0000 −0.0301863
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −230.500 + 399.238i −0.328269 + 0.568579i −0.982169 0.188003i $$-0.939799\pi$$
0.653899 + 0.756582i $$0.273132\pi$$
$$80$$ 72.0000 + 124.708i 0.100623 + 0.174284i
$$81$$ 0 0
$$82$$ −42.0000 + 72.7461i −0.0565625 + 0.0979691i
$$83$$ −588.000 −0.777607 −0.388804 0.921321i $$-0.627112\pi$$
−0.388804 + 0.921321i $$0.627112\pi$$
$$84$$ 0 0
$$85$$ −459.000 −0.585712
$$86$$ −124.000 + 214.774i −0.155480 + 0.269299i
$$87$$ 0 0
$$88$$ 228.000 + 394.908i 0.276192 + 0.478378i
$$89$$ 508.500 880.748i 0.605628 1.04898i −0.386324 0.922363i $$-0.626255\pi$$
0.991952 0.126615i $$-0.0404114\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −276.000 −0.312772
$$93$$ 0 0
$$94$$ 201.000 + 348.142i 0.220549 + 0.382001i
$$95$$ −22.5000 38.9711i −0.0242995 0.0420879i
$$96$$ 0 0
$$97$$ 1834.00 1.91974 0.959868 0.280451i $$-0.0904839\pi$$
0.959868 + 0.280451i $$0.0904839\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 88.0000 152.420i 0.0880000 0.152420i
$$101$$ 142.500 + 246.817i 0.140389 + 0.243161i 0.927643 0.373468i $$-0.121831\pi$$
−0.787254 + 0.616629i $$0.788498\pi$$
$$102$$ 0 0
$$103$$ −249.500 + 432.147i −0.238679 + 0.413405i −0.960336 0.278847i $$-0.910048\pi$$
0.721656 + 0.692252i $$0.243381\pi$$
$$104$$ −560.000 −0.528005
$$105$$ 0 0
$$106$$ −786.000 −0.720218
$$107$$ −553.500 + 958.690i −0.500083 + 0.866169i 0.499917 + 0.866073i $$0.333364\pi$$
−1.00000 9.56665e-5i $$0.999970\pi$$
$$108$$ 0 0
$$109$$ −461.500 799.341i −0.405538 0.702413i 0.588846 0.808246i $$-0.299583\pi$$
−0.994384 + 0.105832i $$0.966249\pi$$
$$110$$ −513.000 + 888.542i −0.444660 + 0.770174i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1542.00 −1.28371 −0.641855 0.766826i $$-0.721835\pi$$
−0.641855 + 0.766826i $$0.721835\pi$$
$$114$$ 0 0
$$115$$ −310.500 537.802i −0.251776 0.436089i
$$116$$ 228.000 + 394.908i 0.182494 + 0.316088i
$$117$$ 0 0
$$118$$ −438.000 −0.341705
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −959.000 + 1661.04i −0.720511 + 1.24796i
$$122$$ 709.000 + 1228.02i 0.526146 + 0.911312i
$$123$$ 0 0
$$124$$ 46.0000 79.6743i 0.0333139 0.0577013i
$$125$$ 1521.00 1.08834
$$126$$ 0 0
$$127$$ −2056.00 −1.43654 −0.718270 0.695765i $$-0.755066\pi$$
−0.718270 + 0.695765i $$0.755066\pi$$
$$128$$ 64.0000 110.851i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −630.000 1091.19i −0.425036 0.736184i
$$131$$ −1024.50 + 1774.49i −0.683290 + 1.18349i 0.290681 + 0.956820i $$0.406118\pi$$
−0.973971 + 0.226673i $$0.927215\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −838.000 −0.540240
$$135$$ 0 0
$$136$$ 204.000 + 353.338i 0.128624 + 0.222783i
$$137$$ −70.5000 122.110i −0.0439651 0.0761498i 0.843205 0.537591i $$-0.180666\pi$$
−0.887171 + 0.461442i $$0.847332\pi$$
$$138$$ 0 0
$$139$$ −1484.00 −0.905548 −0.452774 0.891625i $$-0.649566\pi$$
−0.452774 + 0.891625i $$0.649566\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 96.0000 166.277i 0.0567334 0.0982651i
$$143$$ −1995.00 3455.44i −1.16665 2.02069i
$$144$$ 0 0
$$145$$ −513.000 + 888.542i −0.293809 + 0.508892i
$$146$$ −626.000 −0.354850
$$147$$ 0 0
$$148$$ −1012.00 −0.562067
$$149$$ −28.5000 + 49.3634i −0.0156699 + 0.0271410i −0.873754 0.486368i $$-0.838321\pi$$
0.858084 + 0.513509i $$0.171655\pi$$
$$150$$ 0 0
$$151$$ −419.500 726.595i −0.226082 0.391586i 0.730561 0.682847i $$-0.239258\pi$$
−0.956644 + 0.291261i $$0.905925\pi$$
$$152$$ −20.0000 + 34.6410i −0.0106725 + 0.0184852i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 207.000 0.107269
$$156$$ 0 0
$$157$$ −1416.50 2453.45i −0.720057 1.24718i −0.960976 0.276631i $$-0.910782\pi$$
0.240919 0.970545i $$-0.422551\pi$$
$$158$$ 461.000 + 798.475i 0.232121 + 0.402046i
$$159$$ 0 0
$$160$$ 288.000 0.142302
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1155.50 2001.38i 0.555250 0.961721i −0.442634 0.896702i $$-0.645956\pi$$
0.997884 0.0650188i $$-0.0207107\pi$$
$$164$$ 84.0000 + 145.492i 0.0399957 + 0.0692746i
$$165$$ 0 0
$$166$$ −588.000 + 1018.45i −0.274926 + 0.476185i
$$167$$ 1260.00 0.583843 0.291921 0.956442i $$-0.405705\pi$$
0.291921 + 0.956442i $$0.405705\pi$$
$$168$$ 0 0
$$169$$ 2703.00 1.23031
$$170$$ −459.000 + 795.011i −0.207081 + 0.358674i
$$171$$ 0 0
$$172$$ 248.000 + 429.549i 0.109941 + 0.190423i
$$173$$ −1633.50 + 2829.30i −0.717877 + 1.24340i 0.243962 + 0.969785i $$0.421553\pi$$
−0.961839 + 0.273615i $$0.911781\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 912.000 0.390594
$$177$$ 0 0
$$178$$ −1017.00 1761.50i −0.428244 0.741740i
$$179$$ 643.500 + 1114.57i 0.268701 + 0.465403i 0.968527 0.248910i $$-0.0800724\pi$$
−0.699826 + 0.714314i $$0.746739\pi$$
$$180$$ 0 0
$$181$$ 2674.00 1.09810 0.549052 0.835788i $$-0.314989\pi$$
0.549052 + 0.835788i $$0.314989\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −276.000 + 478.046i −0.110581 + 0.191533i
$$185$$ −1138.50 1971.94i −0.452455 0.783675i
$$186$$ 0 0
$$187$$ −1453.50 + 2517.54i −0.568398 + 0.984494i
$$188$$ 804.000 0.311903
$$189$$ 0 0
$$190$$ −90.0000 −0.0343647
$$191$$ 2092.50 3624.32i 0.792712 1.37302i −0.131570 0.991307i $$-0.542002\pi$$
0.924282 0.381711i $$-0.124665\pi$$
$$192$$ 0 0
$$193$$ 42.5000 + 73.6122i 0.0158509 + 0.0274545i 0.873842 0.486210i $$-0.161621\pi$$
−0.857991 + 0.513664i $$0.828288\pi$$
$$194$$ 1834.00 3176.58i 0.678730 1.17559i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 390.000 0.141047 0.0705237 0.997510i $$-0.477533\pi$$
0.0705237 + 0.997510i $$0.477533\pi$$
$$198$$ 0 0
$$199$$ −1416.50 2453.45i −0.504588 0.873972i −0.999986 0.00530596i $$-0.998311\pi$$
0.495398 0.868666i $$-0.335022\pi$$
$$200$$ −176.000 304.841i −0.0622254 0.107778i
$$201$$ 0 0
$$202$$ 570.000 0.198540
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −189.000 + 327.358i −0.0643919 + 0.111530i
$$206$$ 499.000 + 864.293i 0.168772 + 0.292321i
$$207$$ 0 0
$$208$$ −560.000 + 969.948i −0.186678 + 0.323336i
$$209$$ −285.000 −0.0943247
$$210$$ 0 0
$$211$$ −124.000 −0.0404574 −0.0202287 0.999795i $$-0.506439\pi$$
−0.0202287 + 0.999795i $$0.506439\pi$$
$$212$$ −786.000 + 1361.39i −0.254635 + 0.441041i
$$213$$ 0 0
$$214$$ 1107.00 + 1917.38i 0.353612 + 0.612474i
$$215$$ −558.000 + 966.484i −0.177001 + 0.306575i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1846.00 −0.573518
$$219$$ 0 0
$$220$$ 1026.00 + 1777.08i 0.314422 + 0.544595i
$$221$$ −1785.00 3091.71i −0.543313 0.941045i
$$222$$ 0 0
$$223$$ −56.0000 −0.0168163 −0.00840816 0.999965i $$-0.502676\pi$$
−0.00840816 + 0.999965i $$0.502676\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −1542.00 + 2670.82i −0.453860 + 0.786108i
$$227$$ 1528.50 + 2647.44i 0.446917 + 0.774083i 0.998184 0.0602465i $$-0.0191887\pi$$
−0.551267 + 0.834329i $$0.685855\pi$$
$$228$$ 0 0
$$229$$ −480.500 + 832.250i −0.138656 + 0.240160i −0.926988 0.375090i $$-0.877612\pi$$
0.788332 + 0.615250i $$0.210945\pi$$
$$230$$ −1242.00 −0.356065
$$231$$ 0 0
$$232$$ 912.000 0.258085
$$233$$ −1414.50 + 2449.99i −0.397712 + 0.688858i −0.993443 0.114326i $$-0.963529\pi$$
0.595731 + 0.803184i $$0.296862\pi$$
$$234$$ 0 0
$$235$$ 904.500 + 1566.64i 0.251077 + 0.434878i
$$236$$ −438.000 + 758.638i −0.120811 + 0.209251i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3540.00 0.958090 0.479045 0.877790i $$-0.340983\pi$$
0.479045 + 0.877790i $$0.340983\pi$$
$$240$$ 0 0
$$241$$ 2615.50 + 4530.18i 0.699084 + 1.21085i 0.968785 + 0.247904i $$0.0797419\pi$$
−0.269701 + 0.962944i $$0.586925\pi$$
$$242$$ 1918.00 + 3322.07i 0.509478 + 0.882442i
$$243$$ 0 0
$$244$$ 2836.00 0.744083
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 175.000 303.109i 0.0450809 0.0780824i
$$248$$ −92.0000 159.349i −0.0235565 0.0408010i
$$249$$ 0 0
$$250$$ 1521.00 2634.45i 0.384786 0.666469i
$$251$$ 5040.00 1.26742 0.633709 0.773571i $$-0.281532\pi$$
0.633709 + 0.773571i $$0.281532\pi$$
$$252$$ 0 0
$$253$$ −3933.00 −0.977334
$$254$$ −2056.00 + 3561.10i −0.507893 + 0.879697i
$$255$$ 0 0
$$256$$ −128.000 221.703i −0.0312500 0.0541266i
$$257$$ 718.500 1244.48i 0.174392 0.302056i −0.765559 0.643366i $$-0.777537\pi$$
0.939951 + 0.341310i $$0.110871\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −2520.00 −0.601091
$$261$$ 0 0
$$262$$ 2049.00 + 3548.97i 0.483159 + 0.836856i
$$263$$ −1162.50 2013.51i −0.272558 0.472085i 0.696958 0.717112i $$-0.254536\pi$$
−0.969516 + 0.245027i $$0.921203\pi$$
$$264$$ 0 0
$$265$$ −3537.00 −0.819910
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −838.000 + 1451.46i −0.191004 + 0.330828i
$$269$$ 1192.50 + 2065.47i 0.270290 + 0.468156i 0.968936 0.247311i $$-0.0795471\pi$$
−0.698646 + 0.715467i $$0.746214\pi$$
$$270$$ 0 0
$$271$$ −165.500 + 286.654i −0.0370975 + 0.0642547i −0.883978 0.467528i $$-0.845145\pi$$
0.846881 + 0.531783i $$0.178478\pi$$
$$272$$ 816.000 0.181902
$$273$$ 0 0
$$274$$ −282.000 −0.0621761
$$275$$ 1254.00 2171.99i 0.274978 0.476276i
$$276$$ 0 0
$$277$$ −2435.50 4218.41i −0.528285 0.915017i −0.999456 0.0329750i $$-0.989502\pi$$
0.471171 0.882042i $$-0.343831\pi$$
$$278$$ −1484.00 + 2570.36i −0.320160 + 0.554533i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 7026.00 1.49159 0.745794 0.666177i $$-0.232070\pi$$
0.745794 + 0.666177i $$0.232070\pi$$
$$282$$ 0 0
$$283$$ −2676.50 4635.83i −0.562196 0.973752i −0.997305 0.0733738i $$-0.976623\pi$$
0.435109 0.900378i $$-0.356710\pi$$
$$284$$ −192.000 332.554i −0.0401166 0.0694839i
$$285$$ 0 0
$$286$$ −7980.00 −1.64989
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1156.00 2002.25i 0.235294 0.407541i
$$290$$ 1026.00 + 1777.08i 0.207754 + 0.359841i
$$291$$ 0 0
$$292$$ −626.000 + 1084.26i −0.125458 + 0.217300i
$$293$$ 4158.00 0.829054 0.414527 0.910037i $$-0.363947\pi$$
0.414527 + 0.910037i $$0.363947\pi$$
$$294$$ 0 0
$$295$$ −1971.00 −0.389004
$$296$$ −1012.00 + 1752.84i −0.198721 + 0.344194i
$$297$$ 0 0
$$298$$ 57.0000 + 98.7269i 0.0110803 + 0.0191916i
$$299$$ 2415.00 4182.90i 0.467101 0.809042i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −1678.00 −0.319729
$$303$$ 0 0
$$304$$ 40.0000 + 69.2820i 0.00754657 + 0.0130710i
$$305$$ 3190.50 + 5526.11i 0.598975 + 1.03746i
$$306$$ 0 0
$$307$$ 9604.00 1.78544 0.892719 0.450615i $$-0.148795\pi$$
0.892719 + 0.450615i $$0.148795\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 207.000 358.535i 0.0379252 0.0656884i
$$311$$ −5065.50 8773.70i −0.923595 1.59971i −0.793805 0.608173i $$-0.791903\pi$$
−0.129791 0.991541i $$-0.541430\pi$$
$$312$$ 0 0
$$313$$ 5399.50 9352.21i 0.975073 1.68888i 0.295378 0.955380i $$-0.404554\pi$$
0.679695 0.733495i $$-0.262112\pi$$
$$314$$ −5666.00 −1.01831
$$315$$ 0 0
$$316$$ 1844.00 0.328269
$$317$$ 265.500 459.859i 0.0470409 0.0814772i −0.841546 0.540185i $$-0.818354\pi$$
0.888587 + 0.458708i $$0.151688\pi$$
$$318$$ 0 0
$$319$$ 3249.00 + 5627.43i 0.570248 + 0.987698i
$$320$$ 288.000 498.831i 0.0503115 0.0871421i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −255.000 −0.0439275
$$324$$ 0 0
$$325$$ 1540.00 + 2667.36i 0.262843 + 0.455257i
$$326$$ −2311.00 4002.77i −0.392621 0.680040i
$$327$$ 0 0
$$328$$ 336.000 0.0565625
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 3507.50 6075.17i 0.582446 1.00883i −0.412743 0.910848i $$-0.635429\pi$$
0.995189 0.0979784i $$-0.0312376\pi$$
$$332$$ 1176.00 + 2036.89i 0.194402 + 0.336714i
$$333$$ 0 0
$$334$$ 1260.00 2182.38i 0.206420 0.357529i
$$335$$ −3771.00 −0.615020
$$336$$ 0 0
$$337$$ 8990.00 1.45316 0.726582 0.687079i $$-0.241108\pi$$
0.726582 + 0.687079i $$0.241108\pi$$
$$338$$ 2703.00 4681.73i 0.434982 0.753410i
$$339$$ 0 0
$$340$$ 918.000 + 1590.02i 0.146428 + 0.253621i
$$341$$ 655.500 1135.36i 0.104098 0.180303i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 992.000 0.155480
$$345$$ 0 0
$$346$$ 3267.00 + 5658.61i 0.507616 + 0.879216i
$$347$$ −4354.50 7542.22i −0.673665 1.16682i −0.976857 0.213893i $$-0.931386\pi$$
0.303192 0.952929i $$-0.401948\pi$$
$$348$$ 0 0
$$349$$ −6482.00 −0.994193 −0.497097 0.867695i $$-0.665601\pi$$
−0.497097 + 0.867695i $$0.665601\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 912.000 1579.63i 0.138096 0.239189i
$$353$$ 1066.50 + 1847.23i 0.160805 + 0.278522i 0.935158 0.354232i $$-0.115258\pi$$
−0.774353 + 0.632754i $$0.781924\pi$$
$$354$$ 0 0
$$355$$ 432.000 748.246i 0.0645864 0.111867i
$$356$$ −4068.00 −0.605628
$$357$$ 0 0
$$358$$ 2574.00 0.380000
$$359$$ 1924.50 3333.33i 0.282928 0.490046i −0.689176 0.724594i $$-0.742028\pi$$
0.972105 + 0.234548i $$0.0753608\pi$$
$$360$$ 0 0
$$361$$ 3417.00 + 5918.42i 0.498178 + 0.862869i
$$362$$ 2674.00 4631.50i 0.388238 0.672449i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2817.00 −0.403969
$$366$$ 0 0
$$367$$ 3245.50 + 5621.37i 0.461618 + 0.799545i 0.999042 0.0437668i $$-0.0139358\pi$$
−0.537424 + 0.843312i $$0.680603\pi$$
$$368$$ 552.000 + 956.092i 0.0781929 + 0.135434i
$$369$$ 0 0
$$370$$ −4554.00 −0.639868
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −461.500 + 799.341i −0.0640632 + 0.110961i −0.896278 0.443493i $$-0.853739\pi$$
0.832215 + 0.554453i $$0.187073\pi$$
$$374$$ 2907.00 + 5035.07i 0.401918 + 0.696143i
$$375$$ 0 0
$$376$$ 804.000 1392.57i 0.110274 0.191001i
$$377$$ −7980.00 −1.09016
$$378$$ 0 0
$$379$$ 6344.00 0.859814 0.429907 0.902873i $$-0.358546\pi$$
0.429907 + 0.902873i $$0.358546\pi$$
$$380$$ −90.0000 + 155.885i −0.0121497 + 0.0210440i
$$381$$ 0 0
$$382$$ −4185.00 7248.63i −0.560532 0.970870i
$$383$$ 2503.50 4336.19i 0.334002 0.578509i −0.649290 0.760541i $$-0.724934\pi$$
0.983293 + 0.182032i $$0.0582673\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 170.000 0.0224165
$$387$$ 0 0
$$388$$ −3668.00 6353.16i −0.479934 0.831270i
$$389$$ 6145.50 + 10644.3i 0.801001 + 1.38737i 0.918958 + 0.394355i $$0.129032\pi$$
−0.117958 + 0.993019i $$0.537635\pi$$
$$390$$ 0 0
$$391$$ −3519.00 −0.455150
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 390.000 675.500i 0.0498678 0.0863736i
$$395$$ 2074.50 + 3593.14i 0.264252 + 0.457697i
$$396$$ 0 0
$$397$$ 443.500 768.165i 0.0560671 0.0971110i −0.836630 0.547769i $$-0.815477\pi$$
0.892697 + 0.450658i $$0.148811\pi$$
$$398$$ −5666.00 −0.713595
$$399$$ 0 0
$$400$$ −704.000 −0.0880000
$$401$$ 5977.50 10353.3i 0.744394 1.28933i −0.206083 0.978535i $$-0.566072\pi$$
0.950477 0.310794i $$-0.100595\pi$$
$$402$$ 0 0
$$403$$ 805.000 + 1394.30i 0.0995035 + 0.172345i
$$404$$ 570.000 987.269i 0.0701945 0.121580i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −14421.0 −1.75632
$$408$$ 0 0
$$409$$ −1710.50 2962.67i −0.206794 0.358178i 0.743909 0.668281i $$-0.232970\pi$$
−0.950703 + 0.310103i $$0.899636\pi$$
$$410$$ 378.000 + 654.715i 0.0455319 + 0.0788636i
$$411$$ 0 0
$$412$$ 1996.00 0.238679
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −2646.00 + 4583.01i −0.312981 + 0.542099i
$$416$$ 1120.00 + 1939.90i 0.132001 + 0.228633i
$$417$$ 0 0
$$418$$ −285.000 + 493.634i −0.0333488 + 0.0577618i
$$419$$ −5460.00 −0.636607 −0.318304 0.947989i $$-0.603113\pi$$
−0.318304 + 0.947989i $$0.603113\pi$$
$$420$$ 0 0
$$421$$ 7730.00 0.894863 0.447431 0.894318i $$-0.352339\pi$$
0.447431 + 0.894318i $$0.352339\pi$$
$$422$$ −124.000 + 214.774i −0.0143039 + 0.0247750i
$$423$$ 0 0
$$424$$ 1572.00 + 2722.78i 0.180054 + 0.311863i
$$425$$ 1122.00 1943.36i 0.128059 0.221804i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 4428.00 0.500083
$$429$$ 0 0
$$430$$ 1116.00 + 1932.97i 0.125159 + 0.216781i
$$431$$ −5656.50 9797.35i −0.632167 1.09495i −0.987108 0.160057i $$-0.948832\pi$$
0.354941 0.934889i $$-0.384501\pi$$
$$432$$ 0 0
$$433$$ −4214.00 −0.467695 −0.233847 0.972273i $$-0.575132\pi$$
−0.233847 + 0.972273i $$0.575132\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1846.00 + 3197.37i −0.202769 + 0.351207i
$$437$$ −172.500 298.779i −0.0188828 0.0327060i
$$438$$ 0 0
$$439$$ 8276.50 14335.3i 0.899808 1.55851i 0.0720696 0.997400i $$-0.477040\pi$$
0.827739 0.561114i $$-0.189627\pi$$
$$440$$ 4104.00 0.444660
$$441$$ 0 0
$$442$$ −7140.00 −0.768360
$$443$$ −8197.50 + 14198.5i −0.879176 + 1.52278i −0.0269294 + 0.999637i $$0.508573\pi$$
−0.852247 + 0.523140i $$0.824760\pi$$
$$444$$ 0 0
$$445$$ −4576.50 7926.73i −0.487521 0.844411i
$$446$$ −56.0000 + 96.9948i −0.00594546 + 0.0102978i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 15090.0 1.58606 0.793030 0.609182i $$-0.208502\pi$$
0.793030 + 0.609182i $$0.208502\pi$$
$$450$$ 0 0
$$451$$ 1197.00 + 2073.26i 0.124977 + 0.216466i
$$452$$ 3084.00 + 5341.64i 0.320927 + 0.555862i
$$453$$ 0 0
$$454$$ 6114.00 0.632036
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 7392.50 12804.2i 0.756688 1.31062i −0.187842 0.982199i $$-0.560149\pi$$
0.944531 0.328423i $$-0.106517\pi$$
$$458$$ 961.000 + 1664.50i 0.0980449 + 0.169819i
$$459$$ 0 0
$$460$$ −1242.00 + 2151.21i −0.125888 + 0.218045i
$$461$$ 2898.00 0.292784 0.146392 0.989227i $$-0.453234\pi$$
0.146392 + 0.989227i $$0.453234\pi$$
$$462$$ 0 0
$$463$$ 464.000 0.0465743 0.0232872 0.999729i $$-0.492587\pi$$
0.0232872 + 0.999729i $$0.492587\pi$$
$$464$$ 912.000 1579.63i 0.0912468 0.158044i
$$465$$ 0 0
$$466$$ 2829.00 + 4899.97i 0.281225 + 0.487096i
$$467$$ −2116.50 + 3665.89i −0.209721 + 0.363248i −0.951627 0.307256i $$-0.900589\pi$$
0.741905 + 0.670505i $$0.233922\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 3618.00 0.355076
$$471$$ 0 0
$$472$$ 876.000 + 1517.28i 0.0854262 + 0.147963i
$$473$$ 3534.00 + 6121.07i 0.343538 + 0.595025i
$$474$$ 0 0
$$475$$ 220.000 0.0212511
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 3540.00 6131.46i 0.338736 0.586708i
$$479$$ −1369.50 2372.04i −0.130635 0.226266i 0.793287 0.608848i $$-0.208368\pi$$
−0.923921 + 0.382582i $$0.875035\pi$$
$$480$$ 0 0
$$481$$ 8855.00 15337.3i 0.839404 1.45389i
$$482$$ 10462.0 0.988654
$$483$$ 0 0
$$484$$ 7672.00 0.720511
$$485$$ 8253.00 14294.6i 0.772679 1.33832i
$$486$$ 0 0
$$487$$ −8525.50 14766.6i −0.793280 1.37400i −0.923926 0.382572i $$-0.875038\pi$$
0.130646 0.991429i $$-0.458295\pi$$
$$488$$ 2836.00 4912.10i 0.263073 0.455656i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 4296.00 0.394859 0.197429 0.980317i $$-0.436741\pi$$
0.197429 + 0.980317i $$0.436741\pi$$
$$492$$ 0 0
$$493$$ 2907.00 + 5035.07i 0.265567 + 0.459976i
$$494$$ −350.000 606.218i −0.0318770 0.0552126i
$$495$$ 0 0
$$496$$ −368.000 −0.0333139
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1700.50 + 2945.35i −0.152555 + 0.264233i −0.932166 0.362031i $$-0.882083\pi$$
0.779611 + 0.626264i $$0.215417\pi$$
$$500$$ −3042.00 5268.90i −0.272085 0.471265i
$$501$$ 0 0
$$502$$ 5040.00 8729.54i 0.448100 0.776132i
$$503$$ 16800.0 1.48921 0.744607 0.667503i $$-0.232637\pi$$
0.744607 + 0.667503i $$0.232637\pi$$
$$504$$ 0 0
$$505$$ 2565.00 0.226022
$$506$$ −3933.00 + 6812.16i −0.345540 + 0.598493i
$$507$$ 0 0
$$508$$ 4112.00 + 7122.19i 0.359135 + 0.622040i
$$509$$ −919.500 + 1592.62i −0.0800710 + 0.138687i −0.903280 0.429051i $$-0.858848\pi$$
0.823209 + 0.567738i $$0.192181\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ −1437.00 2488.96i −0.123314 0.213586i
$$515$$ 2245.50 + 3889.32i 0.192133 + 0.332784i
$$516$$ 0 0
$$517$$ 11457.0 0.974620
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −2520.00 + 4364.77i −0.212518 + 0.368092i
$$521$$ −151.500 262.406i −0.0127396 0.0220656i 0.859585 0.510992i $$-0.170722\pi$$
−0.872325 + 0.488927i $$0.837389\pi$$
$$522$$ 0 0
$$523$$ −10833.5 + 18764.2i −0.905767 + 1.56883i −0.0858815 + 0.996305i $$0.527371\pi$$
−0.819885 + 0.572528i $$0.805963\pi$$
$$524$$ 8196.00 0.683290
$$525$$ 0 0
$$526$$ −4650.00 −0.385456
$$527$$ 586.500 1015.85i 0.0484788 0.0839678i
$$528$$ 0 0
$$529$$ 3703.00 + 6413.78i 0.304348 + 0.527146i
$$530$$ −3537.00 + 6126.26i −0.289882 + 0.502090i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2940.00 −0.238922
$$534$$ 0 0
$$535$$ 4981.50 + 8628.21i 0.402559 + 0.697253i
$$536$$ 1676.00 + 2902.92i 0.135060 + 0.233931i
$$537$$ 0 0
$$538$$ 4770.00 0.382248
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −2519.50 + 4363.90i −0.200225 + 0.346800i −0.948601 0.316475i $$-0.897501\pi$$
0.748376 + 0.663275i $$0.230834\pi$$
$$542$$ 331.000 + 573.309i 0.0262319 + 0.0454349i
$$543$$ 0 0
$$544$$ 816.000 1413.35i 0.0643120 0.111392i
$$545$$ −8307.00 −0.652904
$$546$$ 0 0
$$547$$ −2392.00 −0.186974 −0.0934868 0.995621i $$-0.529801\pi$$
−0.0934868 + 0.995621i $$0.529801\pi$$
$$548$$ −282.000 + 488.438i −0.0219826 + 0.0380749i
$$549$$ 0 0
$$550$$ −2508.00 4343.98i −0.194439 0.336778i
$$551$$ −285.000 + 493.634i −0.0220352 + 0.0381661i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −9742.00 −0.747108
$$555$$ 0 0
$$556$$ 2968.00 + 5140.73i 0.226387 + 0.392114i
$$557$$ −11074.5 19181.6i −0.842445 1.45916i −0.887822 0.460187i $$-0.847782\pi$$
0.0453775 0.998970i $$-0.485551\pi$$
$$558$$ 0 0
$$559$$ −8680.00 −0.656753
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 7026.00 12169.4i 0.527356 0.913407i
$$563$$ 4174.50 + 7230.45i 0.312494 + 0.541256i 0.978902 0.204332i $$-0.0655022\pi$$
−0.666408 + 0.745588i $$0.732169\pi$$
$$564$$ 0 0
$$565$$ −6939.00 + 12018.7i −0.516683 + 0.894921i
$$566$$ −10706.0 −0.795065
$$567$$ 0 0
$$568$$ −768.000 −0.0567334
$$569$$ −7672.50 + 13289.2i −0.565286 + 0.979105i 0.431737 + 0.902000i $$0.357901\pi$$
−0.997023 + 0.0771050i $$0.975432\pi$$
$$570$$ 0 0
$$571$$ 5796.50 + 10039.8i 0.424827 + 0.735821i 0.996404 0.0847268i $$-0.0270017\pi$$
−0.571578 + 0.820548i $$0.693668\pi$$
$$572$$ −7980.00 + 13821.8i −0.583323 + 1.01034i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3036.00 0.220191
$$576$$ 0 0
$$577$$ −7296.50 12637.9i −0.526442 0.911825i −0.999525 0.0308071i $$-0.990192\pi$$
0.473083 0.881018i $$-0.343141\pi$$
$$578$$ −2312.00 4004.50i −0.166378 0.288175i
$$579$$ 0 0
$$580$$ 4104.00 0.293809
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −11200.5 + 19399.8i −0.795673 + 1.37815i
$$584$$ 1252.00 + 2168.53i 0.0887125 + 0.153655i
$$585$$ 0 0
$$586$$ 4158.00 7201.87i 0.293115 0.507690i
$$587$$ −15372.0 −1.08087 −0.540435 0.841386i $$-0.681740\pi$$
−0.540435 + 0.841386i $$0.681740\pi$$
$$588$$ 0 0
$$589$$ 115.000 0.00804498
$$590$$ −1971.00 + 3413.87i −0.137534 + 0.238215i
$$591$$ 0 0
$$592$$ 2024.00 + 3505.67i 0.140517 + 0.243382i
$$593$$ 7186.50 12447.4i 0.497663 0.861978i −0.502333 0.864674i $$-0.667525\pi$$
0.999996 + 0.00269639i $$0.000858288\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 228.000 0.0156699
$$597$$ 0 0
$$598$$ −4830.00 8365.81i −0.330290 0.572079i
$$599$$ 1273.50 + 2205.77i 0.0868678 + 0.150459i 0.906186 0.422880i $$-0.138981\pi$$
−0.819318 + 0.573340i $$0.805648\pi$$
$$600$$ 0 0
$$601$$ 7042.00 0.477952 0.238976 0.971025i $$-0.423188\pi$$
0.238976 + 0.971025i $$0.423188\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1678.00 + 2906.38i −0.113041 + 0.195793i
$$605$$ 8631.00 + 14949.3i 0.580000 + 1.00459i
$$606$$ 0 0
$$607$$ −11295.5 + 19564.4i −0.755305 + 1.30823i 0.189917 + 0.981800i $$0.439178\pi$$
−0.945223 + 0.326427i $$0.894155\pi$$
$$608$$ 160.000 0.0106725
$$609$$ 0 0
$$610$$ 12762.0 0.847079
$$611$$ −7035.00 + 12185.0i −0.465803 + 0.806794i
$$612$$ 0 0
$$613$$ 4242.50 + 7348.23i 0.279532 + 0.484163i 0.971268 0.237987i $$-0.0764874\pi$$
−0.691737 + 0.722150i $$0.743154\pi$$
$$614$$ 9604.00 16634.6i 0.631247 1.09335i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18282.0 1.19288 0.596439 0.802658i $$-0.296582\pi$$
0.596439 + 0.802658i $$0.296582\pi$$
$$618$$ 0 0
$$619$$ 1145.50 + 1984.06i 0.0743805 + 0.128831i 0.900817 0.434200i $$-0.142969\pi$$
−0.826436 + 0.563030i $$0.809635\pi$$
$$620$$ −414.000 717.069i −0.0268172 0.0464487i
$$621$$ 0 0
$$622$$ −20262.0 −1.30616
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 4094.50 7091.88i 0.262048 0.453880i
$$626$$ −10799.0 18704.4i −0.689481 1.19422i
$$627$$ 0 0
$$628$$ −5666.00 + 9813.80i −0.360029 + 0.623588i
$$629$$ −12903.0 −0.817927
$$630$$ 0 0
$$631$$ −6928.00 −0.437083 −0.218541 0.975828i $$-0.570130\pi$$
−0.218541 + 0.975828i $$0.570130\pi$$
$$632$$ 1844.00 3193.90i 0.116061 0.201023i
$$633$$ 0 0
$$634$$ −531.000 919.719i −0.0332629 0.0576131i
$$635$$ −9252.00 + 16024.9i −0.578196 + 1.00146i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 12996.0 0.806452
$$639$$ 0 0
$$640$$ −576.000 997.661i −0.0355756 0.0616188i
$$641$$ 12487.5 + 21629.0i 0.769464 + 1.33275i 0.937854 + 0.347031i $$0.112810\pi$$
−0.168390 + 0.985721i $$0.553857\pi$$
$$642$$ 0 0
$$643$$ −9548.00 −0.585593 −0.292797 0.956175i $$-0.594586\pi$$
−0.292797 + 0.956175i $$0.594586\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −255.000 + 441.673i −0.0155307 + 0.0269000i
$$647$$ −5065.50 8773.70i −0.307798 0.533122i 0.670082 0.742287i $$-0.266259\pi$$
−0.977880 + 0.209165i $$0.932925\pi$$
$$648$$ 0 0
$$649$$ −6241.50 + 10810.6i −0.377504 + 0.653857i
$$650$$ 6160.00 0.371716
$$651$$ 0 0
$$652$$ −9244.00 −0.555250
$$653$$ 8329.50 14427.1i 0.499171 0.864589i −0.500829 0.865546i $$-0.666971\pi$$
1.00000 0.000957229i $$0.000304695\pi$$
$$654$$ 0 0
$$655$$ 9220.50 + 15970.4i 0.550038 + 0.952693i
$$656$$ 336.000 581.969i 0.0199979 0.0346373i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −29556.0 −1.74710 −0.873550 0.486735i $$-0.838188\pi$$
−0.873550 + 0.486735i $$0.838188\pi$$
$$660$$ 0 0
$$661$$ 95.5000 + 165.411i 0.00561955 + 0.00973334i 0.868822 0.495125i $$-0.164878\pi$$
−0.863202 + 0.504859i $$0.831545\pi$$
$$662$$ −7015.00 12150.3i −0.411852 0.713348i
$$663$$ 0 0
$$664$$ 4704.00 0.274926
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −3933.00 + 6812.16i −0.228315 + 0.395454i
$$668$$ −2520.00 4364.77i −0.145961 0.252811i
$$669$$ 0 0
$$670$$ −3771.00 + 6531.56i −0.217442 + 0.376621i
$$671$$ 40413.0 2.32508
$$672$$ 0 0
$$673$$ 2606.00 0.149263 0.0746314 0.997211i $$-0.476222\pi$$
0.0746314 + 0.997211i $$0.476222\pi$$
$$674$$ 8990.00 15571.1i 0.513771 0.889878i
$$675$$ 0 0
$$676$$ −5406.00 9363.47i −0.307579 0.532742i
$$677$$ 2104.50 3645.10i 0.119472 0.206931i −0.800087 0.599885i $$-0.795213\pi$$
0.919559 + 0.392953i $$0.128547\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 3672.00 0.207081
$$681$$ 0 0
$$682$$ −1311.00 2270.72i −0.0736082 0.127493i
$$683$$ 12151.5 + 21047.0i 0.680768 + 1.17912i 0.974747 + 0.223312i $$0.0716869\pi$$
−0.293979 + 0.955812i $$0.594980\pi$$
$$684$$ 0 0
$$685$$ −1269.00 −0.0707825
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 992.000 1718.19i 0.0549704 0.0952116i
$$689$$ −13755.0 23824.4i −0.760557 1.31732i
$$690$$ 0 0
$$691$$ 7520.50 13025.9i 0.414028 0.717117i −0.581298 0.813691i $$-0.697455\pi$$
0.995326 + 0.0965734i $$0.0307882\pi$$
$$692$$ 13068.0 0.717877
$$693$$ 0 0
$$694$$ −17418.0 −0.952706
$$695$$ −6678.00 + 11566.6i −0.364476 + 0.631291i
$$696$$ 0 0
$$697$$ 1071.00 + 1855.03i 0.0582023 + 0.100809i
$$698$$ −6482.00 + 11227.2i −0.351500 + 0.608817i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −24726.0 −1.33222 −0.666111 0.745852i $$-0.732042\pi$$
−0.666111 + 0.745852i $$0.732042\pi$$
$$702$$ 0 0
$$703$$ −632.500 1095.52i −0.0339334 0.0587744i
$$704$$ −1824.00 3159.26i −0.0976486 0.169132i
$$705$$ 0 0
$$706$$ 4266.00 0.227412
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 2478.50 4292.89i 0.131286 0.227395i −0.792886 0.609370i $$-0.791423\pi$$
0.924173 + 0.381975i $$0.124756\pi$$
$$710$$ −864.000 1496.49i −0.0456695 0.0791019i
$$711$$ 0 0
$$712$$ −4068.00 + 7045.98i −0.214122 + 0.370870i
$$713$$ 1587.00 0.0833571
$$714$$ 0 0
$$715$$ −35910.0 −1.87826
$$716$$ 2574.00 4458.30i 0.134350 0.232702i
$$717$$ 0 0
$$718$$ −3849.00 6666.66i −0.200060 0.346515i
$$719$$ −13834.5 + 23962.1i −0.717580 + 1.24288i 0.244376 + 0.969680i $$0.421417\pi$$
−0.961956 + 0.273204i $$0.911917\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 13668.0 0.704529
$$723$$ 0 0
$$724$$ −5348.00 9263.01i −0.274526 0.475493i
$$725$$ −2508.00 4343.98i −0.128476 0.222526i
$$726$$ 0 0
$$727$$ 13888.0 0.708497 0.354249 0.935151i $$-0.384737\pi$$
0.354249 + 0.935151i $$0.384737\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −2817.00 + 4879.19i −0.142824 + 0.247379i
$$731$$ 3162.00 + 5476.74i 0.159987 + 0.277106i
$$732$$ 0 0
$$733$$ 7121.50 12334.8i 0.358852 0.621550i −0.628917 0.777472i $$-0.716502\pi$$
0.987769 + 0.155922i $$0.0498349\pi$$
$$734$$ 12982.0 0.652826
$$735$$ 0 0
$$736$$ 2208.00 0.110581
$$737$$ −11941.5 + 20683.3i −0.596840 + 1.03376i
$$738$$ 0 0
$$739$$ −18479.5 32007.4i −0.919864 1.59325i −0.799620 0.600507i $$-0.794966\pi$$
−0.120244 0.992744i $$-0.538368\pi$$
$$740$$ −4554.00 + 7887.76i −0.226228 + 0.391838i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 12528.0 0.618584 0.309292 0.950967i $$-0.399908\pi$$
0.309292 + 0.950967i $$0.399908\pi$$
$$744$$ 0 0
$$745$$ 256.500 + 444.271i 0.0126140 + 0.0218481i
$$746$$ 923.000 + 1598.68i 0.0452995 + 0.0784610i
$$747$$ 0 0
$$748$$ 11628.0 0.568398
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 8883.50 15386.7i 0.431643 0.747627i −0.565372 0.824836i $$-0.691268\pi$$
0.997015 + 0.0772090i $$0.0246009\pi$$
$$752$$ −1608.00 2785.14i −0.0779757 0.135058i
$$753$$ 0 0
$$754$$ −7980.00 + 13821.8i −0.385430 + 0.667585i
$$755$$ −7551.00 −0.363985
$$756$$ 0 0
$$757$$ −28726.0 −1.37921 −0.689606 0.724184i $$-0.742216\pi$$
−0.689606 + 0.724184i $$0.742216\pi$$
$$758$$ 6344.00 10988.1i 0.303990 0.526526i
$$759$$ 0 0
$$760$$ 180.000 + 311.769i 0.00859117 + 0.0148803i
$$761$$ 13234.5 22922.8i 0.630421 1.09192i −0.357045 0.934087i $$-0.616216\pi$$
0.987466 0.157834i $$-0.0504510\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −16740.0 −0.792712
$$765$$ 0 0
$$766$$ −5007.00 8672.38i −0.236175 0.409068i
$$767$$ −7665.00 13276.2i −0.360844 0.625000i
$$768$$ 0 0
$$769$$ −5054.00 −0.236999 −0.118499 0.992954i $$-0.537808\pi$$
−0.118499 + 0.992954i $$0.537808\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 170.000 294.449i 0.00792543 0.0137273i
$$773$$ 17782.5 + 30800.2i 0.827415 + 1.43313i 0.900059 + 0.435767i $$0.143523\pi$$
−0.0726439 + 0.997358i $$0.523144\pi$$
$$774$$ 0 0
$$775$$ −506.000 + 876.418i −0.0234530 + 0.0406217i
$$776$$ −14672.0 −0.678730
$$777$$ 0 0
$$778$$ 24582.0 1.13279
$$779$$ −105.000 + 181.865i −0.00482929 + 0.00836457i
$$780$$ 0 0
$$781$$ −2736.00 4738.89i −0.125354 0.217120i
$$782$$ −3519.00 + 6095.09i −0.160920 + 0.278721i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −25497.0 −1.15927