Properties

 Label 882.4.g.e.361.1 Level $882$ Weight $4$ Character 882.361 Analytic conductor $52.040$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

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

Newform invariants

 Self dual: no Analytic conductor: $$52.0396846251$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.361 Dual form 882.4.g.e.667.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +O(q^{10})$$ $$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(-15.0000 + 25.9808i) q^{11} +2.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-33.0000 + 57.1577i) q^{17} +(26.0000 + 45.0333i) q^{19} +24.0000 q^{20} +60.0000 q^{22} +(-57.0000 - 98.7269i) q^{23} +(44.5000 - 77.0763i) q^{25} +(-2.00000 - 3.46410i) q^{26} +72.0000 q^{29} +(98.0000 - 169.741i) q^{31} +(-16.0000 + 27.7128i) q^{32} +132.000 q^{34} +(143.000 + 247.683i) q^{37} +(52.0000 - 90.0666i) q^{38} +(-24.0000 - 41.5692i) q^{40} -378.000 q^{41} +164.000 q^{43} +(-60.0000 - 103.923i) q^{44} +(-114.000 + 197.454i) q^{46} +(114.000 + 197.454i) q^{47} -178.000 q^{50} +(-4.00000 + 6.92820i) q^{52} +(174.000 - 301.377i) q^{53} +180.000 q^{55} +(-72.0000 - 124.708i) q^{58} +(174.000 - 301.377i) q^{59} +(53.0000 + 91.7987i) q^{61} -392.000 q^{62} +64.0000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-298.000 + 516.151i) q^{67} +(-132.000 - 228.631i) q^{68} +630.000 q^{71} +(521.000 - 902.398i) q^{73} +(286.000 - 495.367i) q^{74} -208.000 q^{76} +(44.0000 + 76.2102i) q^{79} +(-48.0000 + 83.1384i) q^{80} +(378.000 + 654.715i) q^{82} -1440.00 q^{83} +396.000 q^{85} +(-164.000 - 284.056i) q^{86} +(-120.000 + 207.846i) q^{88} +(-687.000 - 1189.92i) q^{89} +456.000 q^{92} +(228.000 - 394.908i) q^{94} +(156.000 - 270.200i) q^{95} -34.0000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{2} - 4q^{4} - 6q^{5} + 16q^{8} + O(q^{10})$$ $$2q - 2q^{2} - 4q^{4} - 6q^{5} + 16q^{8} - 12q^{10} - 30q^{11} + 4q^{13} - 16q^{16} - 66q^{17} + 52q^{19} + 48q^{20} + 120q^{22} - 114q^{23} + 89q^{25} - 4q^{26} + 144q^{29} + 196q^{31} - 32q^{32} + 264q^{34} + 286q^{37} + 104q^{38} - 48q^{40} - 756q^{41} + 328q^{43} - 120q^{44} - 228q^{46} + 228q^{47} - 356q^{50} - 8q^{52} + 348q^{53} + 360q^{55} - 144q^{58} + 348q^{59} + 106q^{61} - 784q^{62} + 128q^{64} - 12q^{65} - 596q^{67} - 264q^{68} + 1260q^{71} + 1042q^{73} + 572q^{74} - 416q^{76} + 88q^{79} - 96q^{80} + 756q^{82} - 2880q^{83} + 792q^{85} - 328q^{86} - 240q^{88} - 1374q^{89} + 912q^{92} + 456q^{94} + 312q^{95} - 68q^{97} + O(q^{100})$$

Character values

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

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

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
$$5$$ −3.00000 5.19615i −0.268328 0.464758i 0.700102 0.714043i $$-0.253138\pi$$
−0.968430 + 0.249285i $$0.919804\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 8.00000 0.353553
$$9$$ 0 0
$$10$$ −6.00000 + 10.3923i −0.189737 + 0.328634i
$$11$$ −15.0000 + 25.9808i −0.411152 + 0.712136i −0.995016 0.0997155i $$-0.968207\pi$$
0.583864 + 0.811851i $$0.301540\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.0426692 0.0213346 0.999772i $$-0.493208\pi$$
0.0213346 + 0.999772i $$0.493208\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −8.00000 13.8564i −0.125000 0.216506i
$$17$$ −33.0000 + 57.1577i −0.470804 + 0.815457i −0.999442 0.0333902i $$-0.989370\pi$$
0.528638 + 0.848847i $$0.322703\pi$$
$$18$$ 0 0
$$19$$ 26.0000 + 45.0333i 0.313937 + 0.543755i 0.979211 0.202844i $$-0.0650185\pi$$
−0.665274 + 0.746600i $$0.731685\pi$$
$$20$$ 24.0000 0.268328
$$21$$ 0 0
$$22$$ 60.0000 0.581456
$$23$$ −57.0000 98.7269i −0.516753 0.895043i −0.999811 0.0194541i $$-0.993807\pi$$
0.483058 0.875589i $$-0.339526\pi$$
$$24$$ 0 0
$$25$$ 44.5000 77.0763i 0.356000 0.616610i
$$26$$ −2.00000 3.46410i −0.0150859 0.0261295i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 72.0000 0.461037 0.230518 0.973068i $$-0.425958\pi$$
0.230518 + 0.973068i $$0.425958\pi$$
$$30$$ 0 0
$$31$$ 98.0000 169.741i 0.567785 0.983432i −0.429000 0.903304i $$-0.641134\pi$$
0.996785 0.0801272i $$-0.0255326\pi$$
$$32$$ −16.0000 + 27.7128i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 132.000 0.665818
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 143.000 + 247.683i 0.635380 + 1.10051i 0.986435 + 0.164155i $$0.0524898\pi$$
−0.351055 + 0.936355i $$0.614177\pi$$
$$38$$ 52.0000 90.0666i 0.221987 0.384493i
$$39$$ 0 0
$$40$$ −24.0000 41.5692i −0.0948683 0.164317i
$$41$$ −378.000 −1.43985 −0.719923 0.694054i $$-0.755823\pi$$
−0.719923 + 0.694054i $$0.755823\pi$$
$$42$$ 0 0
$$43$$ 164.000 0.581622 0.290811 0.956780i $$-0.406075\pi$$
0.290811 + 0.956780i $$0.406075\pi$$
$$44$$ −60.0000 103.923i −0.205576 0.356068i
$$45$$ 0 0
$$46$$ −114.000 + 197.454i −0.365400 + 0.632891i
$$47$$ 114.000 + 197.454i 0.353800 + 0.612800i 0.986912 0.161261i $$-0.0515560\pi$$
−0.633112 + 0.774060i $$0.718223\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −178.000 −0.503460
$$51$$ 0 0
$$52$$ −4.00000 + 6.92820i −0.0106673 + 0.0184763i
$$53$$ 174.000 301.377i 0.450957 0.781081i −0.547488 0.836813i $$-0.684416\pi$$
0.998446 + 0.0557323i $$0.0177493\pi$$
$$54$$ 0 0
$$55$$ 180.000 0.441294
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −72.0000 124.708i −0.163001 0.282326i
$$59$$ 174.000 301.377i 0.383947 0.665016i −0.607676 0.794185i $$-0.707898\pi$$
0.991622 + 0.129170i $$0.0412312\pi$$
$$60$$ 0 0
$$61$$ 53.0000 + 91.7987i 0.111245 + 0.192682i 0.916273 0.400555i $$-0.131183\pi$$
−0.805027 + 0.593238i $$0.797849\pi$$
$$62$$ −392.000 −0.802969
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −6.00000 10.3923i −0.0114494 0.0198309i
$$66$$ 0 0
$$67$$ −298.000 + 516.151i −0.543381 + 0.941163i 0.455326 + 0.890325i $$0.349523\pi$$
−0.998707 + 0.0508381i $$0.983811\pi$$
$$68$$ −132.000 228.631i −0.235402 0.407729i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 630.000 1.05306 0.526530 0.850157i $$-0.323493\pi$$
0.526530 + 0.850157i $$0.323493\pi$$
$$72$$ 0 0
$$73$$ 521.000 902.398i 0.835321 1.44682i −0.0584477 0.998290i $$-0.518615\pi$$
0.893769 0.448528i $$-0.148052\pi$$
$$74$$ 286.000 495.367i 0.449281 0.778178i
$$75$$ 0 0
$$76$$ −208.000 −0.313937
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 44.0000 + 76.2102i 0.0626631 + 0.108536i 0.895655 0.444750i $$-0.146707\pi$$
−0.832992 + 0.553285i $$0.813374\pi$$
$$80$$ −48.0000 + 83.1384i −0.0670820 + 0.116190i
$$81$$ 0 0
$$82$$ 378.000 + 654.715i 0.509062 + 0.881722i
$$83$$ −1440.00 −1.90434 −0.952172 0.305563i $$-0.901155\pi$$
−0.952172 + 0.305563i $$0.901155\pi$$
$$84$$ 0 0
$$85$$ 396.000 0.505320
$$86$$ −164.000 284.056i −0.205635 0.356170i
$$87$$ 0 0
$$88$$ −120.000 + 207.846i −0.145364 + 0.251778i
$$89$$ −687.000 1189.92i −0.818223 1.41720i −0.906990 0.421152i $$-0.861626\pi$$
0.0887672 0.996052i $$-0.471707\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 456.000 0.516753
$$93$$ 0 0
$$94$$ 228.000 394.908i 0.250175 0.433315i
$$95$$ 156.000 270.200i 0.168476 0.291810i
$$96$$ 0 0
$$97$$ −34.0000 −0.0355895 −0.0177947 0.999842i $$-0.505665\pi$$
−0.0177947 + 0.999842i $$0.505665\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 178.000 + 308.305i 0.178000 + 0.308305i
$$101$$ 219.000 379.319i 0.215756 0.373700i −0.737750 0.675074i $$-0.764112\pi$$
0.953506 + 0.301374i $$0.0974452\pi$$
$$102$$ 0 0
$$103$$ −838.000 1451.46i −0.801656 1.38851i −0.918525 0.395362i $$-0.870619\pi$$
0.116869 0.993147i $$-0.462714\pi$$
$$104$$ 16.0000 0.0150859
$$105$$ 0 0
$$106$$ −696.000 −0.637750
$$107$$ −1011.00 1751.10i −0.913430 1.58211i −0.809183 0.587557i $$-0.800090\pi$$
−0.104247 0.994551i $$-0.533243\pi$$
$$108$$ 0 0
$$109$$ 251.000 434.745i 0.220564 0.382027i −0.734416 0.678700i $$-0.762544\pi$$
0.954979 + 0.296673i $$0.0958770\pi$$
$$110$$ −180.000 311.769i −0.156021 0.270237i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2016.00 1.67831 0.839156 0.543890i $$-0.183049\pi$$
0.839156 + 0.543890i $$0.183049\pi$$
$$114$$ 0 0
$$115$$ −342.000 + 592.361i −0.277319 + 0.480330i
$$116$$ −144.000 + 249.415i −0.115259 + 0.199635i
$$117$$ 0 0
$$118$$ −696.000 −0.542983
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 215.500 + 373.257i 0.161908 + 0.280433i
$$122$$ 106.000 183.597i 0.0786622 0.136247i
$$123$$ 0 0
$$124$$ 392.000 + 678.964i 0.283892 + 0.491716i
$$125$$ −1284.00 −0.918756
$$126$$ 0 0
$$127$$ 1784.00 1.24649 0.623246 0.782026i $$-0.285814\pi$$
0.623246 + 0.782026i $$0.285814\pi$$
$$128$$ −64.0000 110.851i −0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −12.0000 + 20.7846i −0.00809592 + 0.0140225i
$$131$$ −804.000 1392.57i −0.536228 0.928773i −0.999103 0.0423499i $$-0.986516\pi$$
0.462875 0.886423i $$-0.346818\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 1192.00 0.768456
$$135$$ 0 0
$$136$$ −264.000 + 457.261i −0.166455 + 0.288308i
$$137$$ 1290.00 2234.35i 0.804468 1.39338i −0.112181 0.993688i $$-0.535784\pi$$
0.916650 0.399692i $$-0.130883\pi$$
$$138$$ 0 0
$$139$$ 2144.00 1.30829 0.654143 0.756371i $$-0.273030\pi$$
0.654143 + 0.756371i $$0.273030\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −630.000 1091.19i −0.372313 0.644865i
$$143$$ −30.0000 + 51.9615i −0.0175435 + 0.0303863i
$$144$$ 0 0
$$145$$ −216.000 374.123i −0.123709 0.214270i
$$146$$ −2084.00 −1.18132
$$147$$ 0 0
$$148$$ −1144.00 −0.635380
$$149$$ −750.000 1299.04i −0.412365 0.714237i 0.582783 0.812628i $$-0.301964\pi$$
−0.995148 + 0.0983907i $$0.968631\pi$$
$$150$$ 0 0
$$151$$ 620.000 1073.87i 0.334138 0.578745i −0.649181 0.760634i $$-0.724888\pi$$
0.983319 + 0.181890i $$0.0582214\pi$$
$$152$$ 208.000 + 360.267i 0.110994 + 0.192247i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1176.00 −0.609410
$$156$$ 0 0
$$157$$ −307.000 + 531.740i −0.156059 + 0.270302i −0.933444 0.358723i $$-0.883212\pi$$
0.777385 + 0.629025i $$0.216546\pi$$
$$158$$ 88.0000 152.420i 0.0443095 0.0767463i
$$159$$ 0 0
$$160$$ 192.000 0.0948683
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −46.0000 79.6743i −0.0221043 0.0382857i 0.854762 0.519021i $$-0.173703\pi$$
−0.876866 + 0.480735i $$0.840370\pi$$
$$164$$ 756.000 1309.43i 0.359961 0.623472i
$$165$$ 0 0
$$166$$ 1440.00 + 2494.15i 0.673287 + 1.16617i
$$167$$ −3924.00 −1.81825 −0.909126 0.416520i $$-0.863250\pi$$
−0.909126 + 0.416520i $$0.863250\pi$$
$$168$$ 0 0
$$169$$ −2193.00 −0.998179
$$170$$ −396.000 685.892i −0.178658 0.309444i
$$171$$ 0 0
$$172$$ −328.000 + 568.113i −0.145406 + 0.251850i
$$173$$ 951.000 + 1647.18i 0.417938 + 0.723889i 0.995732 0.0922934i $$-0.0294198\pi$$
−0.577794 + 0.816182i $$0.696086\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 480.000 0.205576
$$177$$ 0 0
$$178$$ −1374.00 + 2379.84i −0.578571 + 1.00211i
$$179$$ 3.00000 5.19615i 0.00125268 0.00216971i −0.865398 0.501084i $$-0.832935\pi$$
0.866651 + 0.498915i $$0.166268\pi$$
$$180$$ 0 0
$$181$$ −2878.00 −1.18188 −0.590939 0.806716i $$-0.701243\pi$$
−0.590939 + 0.806716i $$0.701243\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −456.000 789.815i −0.182700 0.316445i
$$185$$ 858.000 1486.10i 0.340981 0.590596i
$$186$$ 0 0
$$187$$ −990.000 1714.73i −0.387144 0.670553i
$$188$$ −912.000 −0.353800
$$189$$ 0 0
$$190$$ −624.000 −0.238262
$$191$$ 177.000 + 306.573i 0.0670538 + 0.116141i 0.897603 0.440804i $$-0.145307\pi$$
−0.830549 + 0.556945i $$0.811973\pi$$
$$192$$ 0 0
$$193$$ 2429.00 4207.15i 0.905924 1.56911i 0.0862509 0.996273i $$-0.472511\pi$$
0.819673 0.572832i $$-0.194155\pi$$
$$194$$ 34.0000 + 58.8897i 0.0125828 + 0.0217940i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −396.000 −0.143217 −0.0716087 0.997433i $$-0.522813\pi$$
−0.0716087 + 0.997433i $$0.522813\pi$$
$$198$$ 0 0
$$199$$ −856.000 + 1482.64i −0.304926 + 0.528147i −0.977245 0.212115i $$-0.931965\pi$$
0.672319 + 0.740262i $$0.265298\pi$$
$$200$$ 356.000 616.610i 0.125865 0.218005i
$$201$$ 0 0
$$202$$ −876.000 −0.305124
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1134.00 + 1964.15i 0.386351 + 0.669180i
$$206$$ −1676.00 + 2902.92i −0.566857 + 0.981824i
$$207$$ 0 0
$$208$$ −16.0000 27.7128i −0.00533366 0.00923816i
$$209$$ −1560.00 −0.516304
$$210$$ 0 0
$$211$$ −772.000 −0.251880 −0.125940 0.992038i $$-0.540195\pi$$
−0.125940 + 0.992038i $$0.540195\pi$$
$$212$$ 696.000 + 1205.51i 0.225479 + 0.390540i
$$213$$ 0 0
$$214$$ −2022.00 + 3502.21i −0.645893 + 1.11872i
$$215$$ −492.000 852.169i −0.156066 0.270314i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1004.00 −0.311924
$$219$$ 0 0
$$220$$ −360.000 + 623.538i −0.110324 + 0.191086i
$$221$$ −66.0000 + 114.315i −0.0200889 + 0.0347949i
$$222$$ 0 0
$$223$$ 776.000 0.233026 0.116513 0.993189i $$-0.462828\pi$$
0.116513 + 0.993189i $$0.462828\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −2016.00 3491.81i −0.593373 1.02775i
$$227$$ 894.000 1548.45i 0.261396 0.452751i −0.705217 0.708991i $$-0.749151\pi$$
0.966613 + 0.256240i $$0.0824839\pi$$
$$228$$ 0 0
$$229$$ −2701.00 4678.27i −0.779420 1.34999i −0.932277 0.361746i $$-0.882181\pi$$
0.152857 0.988248i $$-0.451153\pi$$
$$230$$ 1368.00 0.392188
$$231$$ 0 0
$$232$$ 576.000 0.163001
$$233$$ −1506.00 2608.47i −0.423439 0.733418i 0.572834 0.819671i $$-0.305844\pi$$
−0.996273 + 0.0862531i $$0.972511\pi$$
$$234$$ 0 0
$$235$$ 684.000 1184.72i 0.189869 0.328863i
$$236$$ 696.000 + 1205.51i 0.191973 + 0.332508i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3546.00 0.959714 0.479857 0.877347i $$-0.340689\pi$$
0.479857 + 0.877347i $$0.340689\pi$$
$$240$$ 0 0
$$241$$ 1781.00 3084.78i 0.476034 0.824516i −0.523589 0.851971i $$-0.675407\pi$$
0.999623 + 0.0274554i $$0.00874043\pi$$
$$242$$ 431.000 746.514i 0.114486 0.198296i
$$243$$ 0 0
$$244$$ −424.000 −0.111245
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 52.0000 + 90.0666i 0.0133955 + 0.0232016i
$$248$$ 784.000 1357.93i 0.200742 0.347696i
$$249$$ 0 0
$$250$$ 1284.00 + 2223.95i 0.324829 + 0.562621i
$$251$$ 3348.00 0.841928 0.420964 0.907077i $$-0.361692\pi$$
0.420964 + 0.907077i $$0.361692\pi$$
$$252$$ 0 0
$$253$$ 3420.00 0.849856
$$254$$ −1784.00 3089.98i −0.440701 0.763317i
$$255$$ 0 0
$$256$$ −128.000 + 221.703i −0.0312500 + 0.0541266i
$$257$$ −183.000 316.965i −0.0444172 0.0769329i 0.842962 0.537973i $$-0.180810\pi$$
−0.887379 + 0.461040i $$0.847476\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 48.0000 0.0114494
$$261$$ 0 0
$$262$$ −1608.00 + 2785.14i −0.379170 + 0.656742i
$$263$$ −2085.00 + 3611.33i −0.488846 + 0.846707i −0.999918 0.0128315i $$-0.995915\pi$$
0.511071 + 0.859538i $$0.329249\pi$$
$$264$$ 0 0
$$265$$ −2088.00 −0.484018
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1192.00 2064.60i −0.271690 0.470581i
$$269$$ −3039.00 + 5263.70i −0.688814 + 1.19306i 0.283407 + 0.959000i $$0.408535\pi$$
−0.972222 + 0.234062i $$0.924798\pi$$
$$270$$ 0 0
$$271$$ −1234.00 2137.35i −0.276606 0.479095i 0.693933 0.720039i $$-0.255876\pi$$
−0.970539 + 0.240944i $$0.922543\pi$$
$$272$$ 1056.00 0.235402
$$273$$ 0 0
$$274$$ −5160.00 −1.13769
$$275$$ 1335.00 + 2312.29i 0.292740 + 0.507041i
$$276$$ 0 0
$$277$$ 197.000 341.214i 0.0427313 0.0740129i −0.843869 0.536550i $$-0.819727\pi$$
0.886600 + 0.462537i $$0.153061\pi$$
$$278$$ −2144.00 3713.52i −0.462549 0.801158i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −396.000 −0.0840690 −0.0420345 0.999116i $$-0.513384\pi$$
−0.0420345 + 0.999116i $$0.513384\pi$$
$$282$$ 0 0
$$283$$ 674.000 1167.40i 0.141573 0.245212i −0.786516 0.617570i $$-0.788117\pi$$
0.928089 + 0.372358i $$0.121451\pi$$
$$284$$ −1260.00 + 2182.38i −0.263265 + 0.455988i
$$285$$ 0 0
$$286$$ 120.000 0.0248103
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 278.500 + 482.376i 0.0566863 + 0.0981836i
$$290$$ −432.000 + 748.246i −0.0874756 + 0.151512i
$$291$$ 0 0
$$292$$ 2084.00 + 3609.59i 0.417661 + 0.723409i
$$293$$ 7506.00 1.49660 0.748302 0.663358i $$-0.230869\pi$$
0.748302 + 0.663358i $$0.230869\pi$$
$$294$$ 0 0
$$295$$ −2088.00 −0.412095
$$296$$ 1144.00 + 1981.47i 0.224641 + 0.389089i
$$297$$ 0 0
$$298$$ −1500.00 + 2598.08i −0.291586 + 0.505042i
$$299$$ −114.000 197.454i −0.0220495 0.0381908i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −2480.00 −0.472543
$$303$$ 0 0
$$304$$ 416.000 720.533i 0.0784843 0.135939i
$$305$$ 318.000 550.792i 0.0597004 0.103404i
$$306$$ 0 0
$$307$$ 1748.00 0.324963 0.162481 0.986712i $$-0.448050\pi$$
0.162481 + 0.986712i $$0.448050\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1176.00 + 2036.89i 0.215459 + 0.373186i
$$311$$ 570.000 987.269i 0.103928 0.180009i −0.809371 0.587297i $$-0.800192\pi$$
0.913300 + 0.407288i $$0.133525\pi$$
$$312$$ 0 0
$$313$$ −73.0000 126.440i −0.0131828 0.0228332i 0.859359 0.511373i $$-0.170863\pi$$
−0.872542 + 0.488540i $$0.837530\pi$$
$$314$$ 1228.00 0.220701
$$315$$ 0 0
$$316$$ −352.000 −0.0626631
$$317$$ 4074.00 + 7056.37i 0.721825 + 1.25024i 0.960267 + 0.279081i $$0.0900300\pi$$
−0.238442 + 0.971157i $$0.576637\pi$$
$$318$$ 0 0
$$319$$ −1080.00 + 1870.61i −0.189556 + 0.328321i
$$320$$ −192.000 332.554i −0.0335410 0.0580948i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −3432.00 −0.591212
$$324$$ 0 0
$$325$$ 89.0000 154.153i 0.0151903 0.0263103i
$$326$$ −92.0000 + 159.349i −0.0156301 + 0.0270721i
$$327$$ 0 0
$$328$$ −3024.00 −0.509062
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 4850.00 + 8400.45i 0.805378 + 1.39496i 0.916036 + 0.401097i $$0.131371\pi$$
−0.110658 + 0.993859i $$0.535296\pi$$
$$332$$ 2880.00 4988.31i 0.476086 0.824605i
$$333$$ 0 0
$$334$$ 3924.00 + 6796.57i 0.642849 + 1.11345i
$$335$$ 3576.00 0.583217
$$336$$ 0 0
$$337$$ 8174.00 1.32126 0.660632 0.750710i $$-0.270288\pi$$
0.660632 + 0.750710i $$0.270288\pi$$
$$338$$ 2193.00 + 3798.39i 0.352910 + 0.611258i
$$339$$ 0 0
$$340$$ −792.000 + 1371.78i −0.126330 + 0.218810i
$$341$$ 2940.00 + 5092.23i 0.466891 + 0.808679i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 1312.00 0.205635
$$345$$ 0 0
$$346$$ 1902.00 3294.36i 0.295526 0.511867i
$$347$$ 2019.00 3497.01i 0.312350 0.541007i −0.666520 0.745487i $$-0.732217\pi$$
0.978871 + 0.204480i $$0.0655504\pi$$
$$348$$ 0 0
$$349$$ 10766.0 1.65126 0.825631 0.564210i $$-0.190819\pi$$
0.825631 + 0.564210i $$0.190819\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −480.000 831.384i −0.0726821 0.125889i
$$353$$ −1833.00 + 3174.85i −0.276376 + 0.478697i −0.970481 0.241176i $$-0.922467\pi$$
0.694105 + 0.719873i $$0.255800\pi$$
$$354$$ 0 0
$$355$$ −1890.00 3273.58i −0.282566 0.489418i
$$356$$ 5496.00 0.818223
$$357$$ 0 0
$$358$$ −12.0000 −0.00177156
$$359$$ 2553.00 + 4421.93i 0.375326 + 0.650084i 0.990376 0.138404i $$-0.0441973\pi$$
−0.615049 + 0.788489i $$0.710864\pi$$
$$360$$ 0 0
$$361$$ 2077.50 3598.34i 0.302887 0.524615i
$$362$$ 2878.00 + 4984.84i 0.417857 + 0.723750i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −6252.00 −0.896561
$$366$$ 0 0
$$367$$ 2888.00 5002.16i 0.410769 0.711473i −0.584205 0.811606i $$-0.698593\pi$$
0.994974 + 0.100133i $$0.0319268\pi$$
$$368$$ −912.000 + 1579.63i −0.129188 + 0.223761i
$$369$$ 0 0
$$370$$ −3432.00 −0.482219
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −4231.00 7328.31i −0.587327 1.01728i −0.994581 0.103965i $$-0.966847\pi$$
0.407254 0.913315i $$-0.366486\pi$$
$$374$$ −1980.00 + 3429.46i −0.273752 + 0.474153i
$$375$$ 0 0
$$376$$ 912.000 + 1579.63i 0.125087 + 0.216657i
$$377$$ 144.000 0.0196721
$$378$$ 0 0
$$379$$ 6860.00 0.929748 0.464874 0.885377i $$-0.346100\pi$$
0.464874 + 0.885377i $$0.346100\pi$$
$$380$$ 624.000 + 1080.80i 0.0842382 + 0.145905i
$$381$$ 0 0
$$382$$ 354.000 613.146i 0.0474142 0.0821238i
$$383$$ 348.000 + 602.754i 0.0464281 + 0.0804159i 0.888306 0.459253i $$-0.151883\pi$$
−0.841877 + 0.539669i $$0.818549\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −9716.00 −1.28117
$$387$$ 0 0
$$388$$ 68.0000 117.779i 0.00889736 0.0154107i
$$389$$ −5568.00 + 9644.06i −0.725730 + 1.25700i 0.232943 + 0.972490i $$0.425164\pi$$
−0.958673 + 0.284510i $$0.908169\pi$$
$$390$$ 0 0
$$391$$ 7524.00 0.973159
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 396.000 + 685.892i 0.0506350 + 0.0877024i
$$395$$ 264.000 457.261i 0.0336286 0.0582464i
$$396$$ 0 0
$$397$$ −5419.00 9385.98i −0.685068 1.18657i −0.973416 0.229046i $$-0.926439\pi$$
0.288348 0.957526i $$-0.406894\pi$$
$$398$$ 3424.00 0.431230
$$399$$ 0 0
$$400$$ −1424.00 −0.178000
$$401$$ 4182.00 + 7243.44i 0.520796 + 0.902045i 0.999708 + 0.0241817i $$0.00769804\pi$$
−0.478912 + 0.877863i $$0.658969\pi$$
$$402$$ 0 0
$$403$$ 196.000 339.482i 0.0242269 0.0419623i
$$404$$ 876.000 + 1517.28i 0.107878 + 0.186850i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −8580.00 −1.04495
$$408$$ 0 0
$$409$$ 881.000 1525.94i 0.106510 0.184481i −0.807844 0.589396i $$-0.799366\pi$$
0.914354 + 0.404915i $$0.132699\pi$$
$$410$$ 2268.00 3928.29i 0.273192 0.473182i
$$411$$ 0 0
$$412$$ 6704.00 0.801656
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4320.00 + 7482.46i 0.510989 + 0.885059i
$$416$$ −32.0000 + 55.4256i −0.00377146 + 0.00653237i
$$417$$ 0 0
$$418$$ 1560.00 + 2702.00i 0.182541 + 0.316170i
$$419$$ 14580.0 1.69995 0.849976 0.526822i $$-0.176617\pi$$
0.849976 + 0.526822i $$0.176617\pi$$
$$420$$ 0 0
$$421$$ 8534.00 0.987938 0.493969 0.869480i $$-0.335546\pi$$
0.493969 + 0.869480i $$0.335546\pi$$
$$422$$ 772.000 + 1337.14i 0.0890530 + 0.154244i
$$423$$ 0 0
$$424$$ 1392.00 2411.01i 0.159437 0.276154i
$$425$$ 2937.00 + 5087.03i 0.335213 + 0.580606i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 8088.00 0.913430
$$429$$ 0 0
$$430$$ −984.000 + 1704.34i −0.110355 + 0.191141i
$$431$$ −2967.00 + 5138.99i −0.331590 + 0.574331i −0.982824 0.184546i $$-0.940918\pi$$
0.651234 + 0.758877i $$0.274252\pi$$
$$432$$ 0 0
$$433$$ −14758.0 −1.63793 −0.818966 0.573843i $$-0.805452\pi$$
−0.818966 + 0.573843i $$0.805452\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1004.00 + 1738.98i 0.110282 + 0.191014i
$$437$$ 2964.00 5133.80i 0.324456 0.561975i
$$438$$ 0 0
$$439$$ 5696.00 + 9865.76i 0.619260 + 1.07259i 0.989621 + 0.143702i $$0.0459007\pi$$
−0.370361 + 0.928888i $$0.620766\pi$$
$$440$$ 1440.00 0.156021
$$441$$ 0 0
$$442$$ 264.000 0.0284100
$$443$$ −3513.00 6084.69i −0.376767 0.652579i 0.613823 0.789444i $$-0.289631\pi$$
−0.990590 + 0.136865i $$0.956298\pi$$
$$444$$ 0 0
$$445$$ −4122.00 + 7139.51i −0.439105 + 0.760551i
$$446$$ −776.000 1344.07i −0.0823871 0.142699i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −3384.00 −0.355681 −0.177841 0.984059i $$-0.556911\pi$$
−0.177841 + 0.984059i $$0.556911\pi$$
$$450$$ 0 0
$$451$$ 5670.00 9820.73i 0.591995 1.02537i
$$452$$ −4032.00 + 6983.63i −0.419578 + 0.726731i
$$453$$ 0 0
$$454$$ −3576.00 −0.369670
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2141.00 + 3708.32i 0.219150 + 0.379580i 0.954548 0.298056i $$-0.0963381\pi$$
−0.735398 + 0.677635i $$0.763005\pi$$
$$458$$ −5402.00 + 9356.54i −0.551133 + 0.954590i
$$459$$ 0 0
$$460$$ −1368.00 2369.45i −0.138659 0.240165i
$$461$$ 16650.0 1.68214 0.841071 0.540924i $$-0.181925\pi$$
0.841071 + 0.540924i $$0.181925\pi$$
$$462$$ 0 0
$$463$$ −9664.00 −0.970031 −0.485015 0.874506i $$-0.661186\pi$$
−0.485015 + 0.874506i $$0.661186\pi$$
$$464$$ −576.000 997.661i −0.0576296 0.0998174i
$$465$$ 0 0
$$466$$ −3012.00 + 5216.94i −0.299417 + 0.518605i
$$467$$ 6162.00 + 10672.9i 0.610585 + 1.05756i 0.991142 + 0.132807i $$0.0423991\pi$$
−0.380557 + 0.924758i $$0.624268\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −2736.00 −0.268515
$$471$$ 0 0
$$472$$ 1392.00 2411.01i 0.135746 0.235119i
$$473$$ −2460.00 + 4260.84i −0.239135 + 0.414194i
$$474$$ 0 0
$$475$$ 4628.00 0.447047
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −3546.00 6141.85i −0.339310 0.587702i
$$479$$ −9330.00 + 16160.0i −0.889976 + 1.54148i −0.0500744 + 0.998745i $$0.515946\pi$$
−0.839902 + 0.542738i $$0.817387\pi$$
$$480$$ 0 0
$$481$$ 286.000 + 495.367i 0.0271112 + 0.0469579i
$$482$$ −7124.00 −0.673214
$$483$$ 0 0
$$484$$ −1724.00 −0.161908
$$485$$ 102.000 + 176.669i 0.00954965 + 0.0165405i
$$486$$ 0 0
$$487$$ 1700.00 2944.49i 0.158181 0.273978i −0.776031 0.630694i $$-0.782770\pi$$
0.934213 + 0.356716i $$0.116104\pi$$
$$488$$ 424.000 + 734.390i 0.0393311 + 0.0681235i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2970.00 0.272982 0.136491 0.990641i $$-0.456418\pi$$
0.136491 + 0.990641i $$0.456418\pi$$
$$492$$ 0 0
$$493$$ −2376.00 + 4115.35i −0.217058 + 0.375956i
$$494$$ 104.000 180.133i 0.00947203 0.0164060i
$$495$$ 0 0
$$496$$ −3136.00 −0.283892
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 494.000 + 855.633i 0.0443176 + 0.0767603i 0.887333 0.461129i $$-0.152555\pi$$
−0.843016 + 0.537889i $$0.819222\pi$$
$$500$$ 2568.00 4447.91i 0.229689 0.397833i
$$501$$ 0 0
$$502$$ −3348.00 5798.91i −0.297666 0.515573i
$$503$$ 5184.00 0.459529 0.229765 0.973246i $$-0.426204\pi$$
0.229765 + 0.973246i $$0.426204\pi$$
$$504$$ 0 0
$$505$$ −2628.00 −0.231573
$$506$$ −3420.00 5923.61i −0.300469 0.520428i
$$507$$ 0 0
$$508$$ −3568.00 + 6179.96i −0.311623 + 0.539747i
$$509$$ −8427.00 14596.0i −0.733831 1.27103i −0.955234 0.295851i $$-0.904397\pi$$
0.221403 0.975182i $$-0.428936\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 512.000 0.0441942
$$513$$ 0 0
$$514$$ −366.000 + 633.931i −0.0314077 + 0.0543998i
$$515$$ −5028.00 + 8708.75i −0.430214 + 0.745152i
$$516$$ 0 0
$$517$$ −6840.00 −0.581862
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −48.0000 83.1384i −0.00404796 0.00701127i
$$521$$ 2199.00 3808.78i 0.184914 0.320280i −0.758634 0.651517i $$-0.774133\pi$$
0.943547 + 0.331238i $$0.107466\pi$$
$$522$$ 0 0
$$523$$ 5336.00 + 9242.22i 0.446132 + 0.772723i 0.998130 0.0611220i $$-0.0194679\pi$$
−0.551998 + 0.833845i $$0.686135\pi$$
$$524$$ 6432.00 0.536228
$$525$$ 0 0
$$526$$ 8340.00 0.691333
$$527$$ 6468.00 + 11202.9i 0.534631 + 0.926008i
$$528$$ 0 0
$$529$$ −414.500 + 717.935i −0.0340676 + 0.0590067i
$$530$$ 2088.00 + 3616.52i 0.171126 + 0.296399i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −756.000 −0.0614371
$$534$$ 0 0
$$535$$ −6066.00 + 10506.6i −0.490198 + 0.849048i
$$536$$ −2384.00 + 4129.21i −0.192114 + 0.332751i
$$537$$ 0 0
$$538$$ 12156.0 0.974131
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −10351.0 17928.5i −0.822596 1.42478i −0.903743 0.428075i $$-0.859192\pi$$
0.0811474 0.996702i $$-0.474142\pi$$
$$542$$ −2468.00 + 4274.70i −0.195590 + 0.338771i
$$543$$ 0 0
$$544$$ −1056.00 1829.05i −0.0832273 0.144154i
$$545$$ −3012.00 −0.236734
$$546$$ 0 0
$$547$$ −22876.0 −1.78813 −0.894065 0.447937i $$-0.852159\pi$$
−0.894065 + 0.447937i $$0.852159\pi$$
$$548$$ 5160.00 + 8937.38i 0.402234 + 0.696690i
$$549$$ 0 0
$$550$$ 2670.00 4624.58i 0.206999 0.358532i
$$551$$ 1872.00 + 3242.40i 0.144737 + 0.250691i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −788.000 −0.0604312
$$555$$ 0 0
$$556$$ −4288.00 + 7427.03i −0.327071 + 0.566504i
$$557$$ 6438.00 11150.9i 0.489743 0.848260i −0.510187 0.860063i $$-0.670424\pi$$
0.999930 + 0.0118036i $$0.00375730\pi$$
$$558$$ 0 0
$$559$$ 328.000 0.0248174
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 396.000 + 685.892i 0.0297229 + 0.0514815i
$$563$$ 3450.00 5975.58i 0.258260 0.447319i −0.707516 0.706697i $$-0.750184\pi$$
0.965776 + 0.259378i $$0.0835177\pi$$
$$564$$ 0 0
$$565$$ −6048.00 10475.4i −0.450339 0.780009i
$$566$$ −2696.00 −0.200214
$$567$$ 0 0
$$568$$ 5040.00 0.372313
$$569$$ −7338.00 12709.8i −0.540641 0.936418i −0.998867 0.0475826i $$-0.984848\pi$$
0.458226 0.888836i $$-0.348485\pi$$
$$570$$ 0 0
$$571$$ −190.000 + 329.090i −0.0139251 + 0.0241190i −0.872904 0.487892i $$-0.837766\pi$$
0.858979 + 0.512011i $$0.171099\pi$$
$$572$$ −120.000 207.846i −0.00877177 0.0151932i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −10146.0 −0.735856
$$576$$ 0 0
$$577$$ 5903.00 10224.3i 0.425901 0.737683i −0.570603 0.821226i $$-0.693290\pi$$
0.996504 + 0.0835434i $$0.0266237\pi$$
$$578$$ 557.000 964.752i 0.0400833 0.0694263i
$$579$$ 0 0
$$580$$ 1728.00 0.123709
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 5220.00 + 9041.31i 0.370824 + 0.642286i
$$584$$ 4168.00 7219.19i 0.295331 0.511528i
$$585$$ 0 0
$$586$$ −7506.00 13000.8i −0.529130 0.916480i
$$587$$ −19188.0 −1.34919 −0.674594 0.738189i $$-0.735681\pi$$
−0.674594 + 0.738189i $$0.735681\pi$$
$$588$$ 0 0
$$589$$ 10192.0 0.712995
$$590$$ 2088.00 + 3616.52i 0.145698 + 0.252356i
$$591$$ 0 0
$$592$$ 2288.00 3962.93i 0.158845 0.275128i
$$593$$ −345.000 597.558i −0.0238912 0.0413807i 0.853833 0.520548i $$-0.174272\pi$$
−0.877724 + 0.479167i $$0.840939\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6000.00 0.412365
$$597$$ 0 0
$$598$$ −228.000 + 394.908i −0.0155913 + 0.0270050i
$$599$$ 10245.0 17744.9i 0.698830 1.21041i −0.270042 0.962849i $$-0.587038\pi$$
0.968872 0.247561i $$-0.0796291\pi$$
$$600$$ 0 0
$$601$$ −11590.0 −0.786632 −0.393316 0.919403i $$-0.628672\pi$$
−0.393316 + 0.919403i $$0.628672\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 2480.00 + 4295.49i 0.167069 + 0.289372i
$$605$$ 1293.00 2239.54i 0.0868891 0.150496i
$$606$$ 0 0
$$607$$ 3212.00 + 5563.35i 0.214779 + 0.372009i 0.953204 0.302327i $$-0.0977634\pi$$
−0.738425 + 0.674336i $$0.764430\pi$$
$$608$$ −1664.00 −0.110994
$$609$$ 0 0
$$610$$ −1272.00 −0.0844291
$$611$$ 228.000 + 394.908i 0.0150964 + 0.0261477i
$$612$$ 0 0
$$613$$ 4841.00 8384.86i 0.318966 0.552465i −0.661307 0.750116i $$-0.729998\pi$$
0.980273 + 0.197650i $$0.0633311\pi$$
$$614$$ −1748.00 3027.62i −0.114892 0.198998i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 5076.00 0.331203 0.165601 0.986193i $$-0.447044\pi$$
0.165601 + 0.986193i $$0.447044\pi$$
$$618$$ 0 0
$$619$$ −11332.0 + 19627.6i −0.735818 + 1.27447i 0.218545 + 0.975827i $$0.429869\pi$$
−0.954363 + 0.298648i $$0.903464\pi$$
$$620$$ 2352.00 4073.78i 0.152353 0.263882i
$$621$$ 0 0
$$622$$ −2280.00 −0.146977
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −1710.50 2962.67i −0.109472 0.189611i
$$626$$ −146.000 + 252.879i −0.00932162 + 0.0161455i
$$627$$ 0 0
$$628$$ −1228.00 2126.96i −0.0780295 0.135151i
$$629$$ −18876.0 −1.19656
$$630$$ 0 0
$$631$$ −8584.00 −0.541559 −0.270779 0.962641i $$-0.587281\pi$$
−0.270779 + 0.962641i $$0.587281\pi$$
$$632$$ 352.000 + 609.682i 0.0221548 + 0.0383732i
$$633$$ 0 0
$$634$$ 8148.00 14112.7i 0.510408 0.884052i
$$635$$ −5352.00 9269.94i −0.334469 0.579317i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 4320.00 0.268073
$$639$$ 0 0
$$640$$ −384.000 + 665.108i −0.0237171 + 0.0410792i
$$641$$ −186.000 + 322.161i −0.0114611 + 0.0198512i −0.871699 0.490042i $$-0.836982\pi$$
0.860238 + 0.509893i $$0.170315\pi$$
$$642$$ 0 0
$$643$$ 3188.00 0.195525 0.0977624 0.995210i $$-0.468831\pi$$
0.0977624 + 0.995210i $$0.468831\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 3432.00 + 5944.40i 0.209025 + 0.362042i
$$647$$ 6366.00 11026.2i 0.386821 0.669994i −0.605199 0.796074i $$-0.706906\pi$$
0.992020 + 0.126080i $$0.0402397\pi$$
$$648$$ 0 0
$$649$$ 5220.00 + 9041.31i 0.315721 + 0.546845i
$$650$$ −356.000 −0.0214823
$$651$$ 0 0
$$652$$ 368.000 0.0221043
$$653$$ 1788.00 + 3096.91i 0.107151 + 0.185592i 0.914615 0.404326i $$-0.132494\pi$$
−0.807464 + 0.589917i $$0.799160\pi$$
$$654$$ 0 0
$$655$$ −4824.00 + 8355.41i −0.287770 + 0.498432i
$$656$$ 3024.00 + 5237.72i 0.179981 + 0.311736i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 11430.0 0.675644 0.337822 0.941210i $$-0.390310\pi$$
0.337822 + 0.941210i $$0.390310\pi$$
$$660$$ 0 0
$$661$$ −11323.0 + 19612.0i −0.666284 + 1.15404i 0.312652 + 0.949868i $$0.398783\pi$$
−0.978936 + 0.204170i $$0.934551\pi$$
$$662$$ 9700.00 16800.9i 0.569488 0.986383i
$$663$$ 0 0
$$664$$ −11520.0 −0.673287
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4104.00 7108.34i −0.238242 0.412648i
$$668$$ 7848.00 13593.1i 0.454563 0.787327i
$$669$$ 0 0
$$670$$ −3576.00 6193.81i −0.206198 0.357146i
$$671$$ −3180.00 −0.182955
$$672$$ 0 0
$$673$$ −13570.0 −0.777244 −0.388622 0.921397i $$-0.627049\pi$$
−0.388622 + 0.921397i $$0.627049\pi$$
$$674$$ −8174.00 14157.8i −0.467138 0.809106i
$$675$$ 0 0
$$676$$ 4386.00 7596.77i 0.249545 0.432224i
$$677$$ 1419.00 + 2457.78i 0.0805563 + 0.139528i 0.903489 0.428611i $$-0.140997\pi$$
−0.822933 + 0.568139i $$0.807664\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 3168.00 0.178658
$$681$$ 0 0
$$682$$ 5880.00 10184.5i 0.330142 0.571823i
$$683$$ 3279.00 5679.39i 0.183701 0.318179i −0.759437 0.650580i $$-0.774526\pi$$
0.943138 + 0.332402i $$0.107859\pi$$
$$684$$ 0 0
$$685$$ −15480.0 −0.863446
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1312.00 2272.45i −0.0727028 0.125925i
$$689$$ 348.000 602.754i 0.0192420 0.0333281i
$$690$$ 0 0
$$691$$ 10916.0 + 18907.1i 0.600961 + 1.04090i 0.992676 + 0.120809i $$0.0385487\pi$$
−0.391715 + 0.920087i $$0.628118\pi$$
$$692$$ −7608.00 −0.417938
$$693$$ 0 0
$$694$$ −8076.00 −0.441730
$$695$$ −6432.00 11140.6i −0.351050 0.608036i
$$696$$ 0 0
$$697$$ 12474.0 21605.6i 0.677886 1.17413i
$$698$$ −10766.0 18647.3i −0.583810 1.01119i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 16200.0 0.872847 0.436423 0.899741i $$-0.356245\pi$$
0.436423 + 0.899741i $$0.356245\pi$$
$$702$$ 0 0
$$703$$ −7436.00 + 12879.5i −0.398939 + 0.690982i
$$704$$ −960.000 + 1662.77i −0.0513940 + 0.0890170i
$$705$$ 0 0
$$706$$ 7332.00 0.390855
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −18361.0 31802.2i −0.972584 1.68456i −0.687689 0.726006i $$-0.741375\pi$$
−0.284895 0.958559i $$-0.591959\pi$$
$$710$$ −3780.00 + 6547.15i −0.199804 + 0.346071i
$$711$$ 0 0
$$712$$ −5496.00 9519.35i −0.289286 0.501057i
$$713$$ −22344.0 −1.17362
$$714$$ 0 0
$$715$$ 360.000 0.0188297
$$716$$ 12.0000 + 20.7846i 0.000626342 + 0.00108486i
$$717$$ 0 0
$$718$$ 5106.00 8843.85i 0.265396 0.459679i
$$719$$ −6888.00 11930.4i −0.357273 0.618814i 0.630231 0.776407i $$-0.282960\pi$$
−0.987504 + 0.157593i $$0.949627\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −8310.00 −0.428347
$$723$$ 0 0
$$724$$ 5756.00 9969.68i 0.295470 0.511769i
$$725$$ 3204.00 5549.49i 0.164129 0.284280i
$$726$$ 0 0
$$727$$ 34220.0 1.74574 0.872868 0.487957i $$-0.162258\pi$$
0.872868 + 0.487957i $$0.162258\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 6252.00 + 10828.8i 0.316982 + 0.549029i
$$731$$ −5412.00 + 9373.86i −0.273830 + 0.474288i
$$732$$ 0 0
$$733$$ 6875.00 + 11907.8i 0.346431 + 0.600036i 0.985613 0.169020i $$-0.0540601\pi$$
−0.639182 + 0.769056i $$0.720727\pi$$
$$734$$ −11552.0 −0.580916
$$735$$ 0 0
$$736$$ 3648.00 0.182700
$$737$$ −8940.00 15484.5i −0.446824 0.773922i
$$738$$ 0 0
$$739$$ −19918.0 + 34499.0i −0.991469 + 1.71727i −0.382853 + 0.923809i $$0.625059\pi$$
−0.608616 + 0.793465i $$0.708275\pi$$
$$740$$ 3432.00 + 5944.40i 0.170490 + 0.295298i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 34470.0 1.70199 0.850997 0.525170i $$-0.175998\pi$$
0.850997 + 0.525170i $$0.175998\pi$$
$$744$$ 0 0
$$745$$ −4500.00 + 7794.23i −0.221298 + 0.383300i
$$746$$ −8462.00 + 14656.6i −0.415303 + 0.719325i
$$747$$ 0 0
$$748$$ 7920.00 0.387144
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −2620.00 4537.97i −0.127304 0.220497i 0.795327 0.606180i $$-0.207299\pi$$
−0.922631 + 0.385684i $$0.873966\pi$$
$$752$$ 1824.00 3159.26i 0.0884500 0.153200i
$$753$$ 0 0
$$754$$ −144.000 249.415i −0.00695513 0.0120466i
$$755$$ −7440.00 −0.358635
$$756$$ 0 0
$$757$$ 18578.0 0.891980 0.445990 0.895038i $$-0.352852\pi$$
0.445990 + 0.895038i $$0.352852\pi$$
$$758$$ −6860.00 11881.9i −0.328716 0.569352i
$$759$$ 0 0
$$760$$ 1248.00 2161.60i 0.0595654 0.103170i
$$761$$ −15267.0 26443.2i −0.727238 1.25961i −0.958046 0.286614i $$-0.907470\pi$$
0.230808 0.972999i $$-0.425863\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −1416.00 −0.0670538
$$765$$ 0 0
$$766$$ 696.000 1205.51i 0.0328296 0.0568626i
$$767$$ 348.000 602.754i 0.0163827 0.0283757i
$$768$$ 0 0
$$769$$ −39958.0 −1.87376 −0.936881 0.349650i $$-0.886301\pi$$
−0.936881 + 0.349650i $$0.886301\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 9716.00 + 16828.6i 0.452962 + 0.784553i
$$773$$ 1983.00 3434.66i 0.0922685 0.159814i −0.816197 0.577774i $$-0.803922\pi$$
0.908465 + 0.417960i $$0.137255\pi$$
$$774$$ 0 0
$$775$$ −8722.00 15106.9i −0.404263 0.700203i
$$776$$ −272.000 −0.0125828
$$777$$ 0 0
$$778$$ 22272.0 1.02634
$$779$$ −9828.00 17022.6i −0.452021 0.782924i
$$780$$ 0 0
$$781$$ −9450.00 + 16367.9i −0.432967 + 0.749922i
$$782$$ −7524.00 13032.0i −0.344064 0.595936i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 3684.00 0.167500
$$786$$ 0 0
$$787$$ 1880.00 3256.26i 0.0851522 0.147488i −0.820304 0.571928i $$-0.806196\pi$$
0.905456 + 0.424440i $$0.139529\pi$$
$$788$$ 792.000 1371.78i 0.0358044 0.0620150i
$$789$$ 0 0
$$790$$ −1056.00 −0.0475580
$$791$$ 0