# Properties

 Label 1800.4.a.be.1.1 Level $1800$ Weight $4$ Character 1800.1 Self dual yes Analytic conductor $106.203$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1800.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$106.203438010$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 360) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1800.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+18.0000 q^{7} +O(q^{10})$$ $$q+18.0000 q^{7} +34.0000 q^{11} -12.0000 q^{13} +102.000 q^{17} +164.000 q^{19} -48.0000 q^{23} +146.000 q^{29} +100.000 q^{31} -328.000 q^{37} -288.000 q^{41} -120.000 q^{43} -16.0000 q^{47} -19.0000 q^{49} +126.000 q^{53} +642.000 q^{59} +602.000 q^{61} -436.000 q^{67} +652.000 q^{71} -1062.00 q^{73} +612.000 q^{77} +388.000 q^{79} +444.000 q^{83} -820.000 q^{89} -216.000 q^{91} +766.000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 18.0000 0.971909 0.485954 0.873984i $$-0.338472\pi$$
0.485954 + 0.873984i $$0.338472\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 34.0000 0.931944 0.465972 0.884799i $$-0.345705\pi$$
0.465972 + 0.884799i $$0.345705\pi$$
$$12$$ 0 0
$$13$$ −12.0000 −0.256015 −0.128008 0.991773i $$-0.540858\pi$$
−0.128008 + 0.991773i $$0.540858\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 102.000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ 164.000 1.98022 0.990110 0.140293i $$-0.0448045\pi$$
0.990110 + 0.140293i $$0.0448045\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −48.0000 −0.435161 −0.217580 0.976042i $$-0.569816\pi$$
−0.217580 + 0.976042i $$0.569816\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 146.000 0.934880 0.467440 0.884025i $$-0.345176\pi$$
0.467440 + 0.884025i $$0.345176\pi$$
$$30$$ 0 0
$$31$$ 100.000 0.579372 0.289686 0.957122i $$-0.406449\pi$$
0.289686 + 0.957122i $$0.406449\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −328.000 −1.45737 −0.728687 0.684846i $$-0.759869\pi$$
−0.728687 + 0.684846i $$0.759869\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −288.000 −1.09703 −0.548513 0.836142i $$-0.684806\pi$$
−0.548513 + 0.836142i $$0.684806\pi$$
$$42$$ 0 0
$$43$$ −120.000 −0.425577 −0.212789 0.977098i $$-0.568255\pi$$
−0.212789 + 0.977098i $$0.568255\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −16.0000 −0.0496562 −0.0248281 0.999692i $$-0.507904\pi$$
−0.0248281 + 0.999692i $$0.507904\pi$$
$$48$$ 0 0
$$49$$ −19.0000 −0.0553936
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 126.000 0.326555 0.163278 0.986580i $$-0.447793\pi$$
0.163278 + 0.986580i $$0.447793\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 642.000 1.41663 0.708316 0.705896i $$-0.249455\pi$$
0.708316 + 0.705896i $$0.249455\pi$$
$$60$$ 0 0
$$61$$ 602.000 1.26358 0.631789 0.775141i $$-0.282321\pi$$
0.631789 + 0.775141i $$0.282321\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −436.000 −0.795013 −0.397507 0.917599i $$-0.630124\pi$$
−0.397507 + 0.917599i $$0.630124\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 652.000 1.08983 0.544917 0.838490i $$-0.316561\pi$$
0.544917 + 0.838490i $$0.316561\pi$$
$$72$$ 0 0
$$73$$ −1062.00 −1.70271 −0.851354 0.524591i $$-0.824218\pi$$
−0.851354 + 0.524591i $$0.824218\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 612.000 0.905765
$$78$$ 0 0
$$79$$ 388.000 0.552575 0.276287 0.961075i $$-0.410896\pi$$
0.276287 + 0.961075i $$0.410896\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 444.000 0.587173 0.293586 0.955933i $$-0.405151\pi$$
0.293586 + 0.955933i $$0.405151\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −820.000 −0.976627 −0.488314 0.872668i $$-0.662388\pi$$
−0.488314 + 0.872668i $$0.662388\pi$$
$$90$$ 0 0
$$91$$ −216.000 −0.248824
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 766.000 0.801809 0.400905 0.916120i $$-0.368696\pi$$
0.400905 + 0.916120i $$0.368696\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −798.000 −0.786178 −0.393089 0.919500i $$-0.628594\pi$$
−0.393089 + 0.919500i $$0.628594\pi$$
$$102$$ 0 0
$$103$$ 402.000 0.384565 0.192283 0.981340i $$-0.438411\pi$$
0.192283 + 0.981340i $$0.438411\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1444.00 −1.30464 −0.652321 0.757943i $$-0.726205\pi$$
−0.652321 + 0.757943i $$0.726205\pi$$
$$108$$ 0 0
$$109$$ −198.000 −0.173990 −0.0869952 0.996209i $$-0.527726\pi$$
−0.0869952 + 0.996209i $$0.527726\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2010.00 1.67332 0.836659 0.547724i $$-0.184506\pi$$
0.836659 + 0.547724i $$0.184506\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1836.00 1.41433
$$120$$ 0 0
$$121$$ −175.000 −0.131480
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 866.000 0.605079 0.302540 0.953137i $$-0.402166\pi$$
0.302540 + 0.953137i $$0.402166\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −2098.00 −1.39926 −0.699630 0.714505i $$-0.746652\pi$$
−0.699630 + 0.714505i $$0.746652\pi$$
$$132$$ 0 0
$$133$$ 2952.00 1.92459
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −886.000 −0.552526 −0.276263 0.961082i $$-0.589096\pi$$
−0.276263 + 0.961082i $$0.589096\pi$$
$$138$$ 0 0
$$139$$ −500.000 −0.305104 −0.152552 0.988295i $$-0.548749\pi$$
−0.152552 + 0.988295i $$0.548749\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −408.000 −0.238592
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2302.00 1.26569 0.632843 0.774280i $$-0.281888\pi$$
0.632843 + 0.774280i $$0.281888\pi$$
$$150$$ 0 0
$$151$$ −2384.00 −1.28482 −0.642408 0.766363i $$-0.722064\pi$$
−0.642408 + 0.766363i $$0.722064\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −1452.00 −0.738103 −0.369052 0.929409i $$-0.620317\pi$$
−0.369052 + 0.929409i $$0.620317\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −864.000 −0.422936
$$162$$ 0 0
$$163$$ −604.000 −0.290239 −0.145119 0.989414i $$-0.546357\pi$$
−0.145119 + 0.989414i $$0.546357\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 664.000 0.307676 0.153838 0.988096i $$-0.450837\pi$$
0.153838 + 0.988096i $$0.450837\pi$$
$$168$$ 0 0
$$169$$ −2053.00 −0.934456
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 4118.00 1.80974 0.904872 0.425684i $$-0.139966\pi$$
0.904872 + 0.425684i $$0.139966\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1746.00 0.729062 0.364531 0.931191i $$-0.381229\pi$$
0.364531 + 0.931191i $$0.381229\pi$$
$$180$$ 0 0
$$181$$ −1270.00 −0.521538 −0.260769 0.965401i $$-0.583976\pi$$
−0.260769 + 0.965401i $$0.583976\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3468.00 1.35618
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 2676.00 1.01376 0.506881 0.862016i $$-0.330798\pi$$
0.506881 + 0.862016i $$0.330798\pi$$
$$192$$ 0 0
$$193$$ 3146.00 1.17334 0.586668 0.809827i $$-0.300439\pi$$
0.586668 + 0.809827i $$0.300439\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3674.00 1.32874 0.664370 0.747404i $$-0.268700\pi$$
0.664370 + 0.747404i $$0.268700\pi$$
$$198$$ 0 0
$$199$$ −1392.00 −0.495861 −0.247930 0.968778i $$-0.579750\pi$$
−0.247930 + 0.968778i $$0.579750\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 2628.00 0.908618
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 5576.00 1.84545
$$210$$ 0 0
$$211$$ −540.000 −0.176185 −0.0880927 0.996112i $$-0.528077\pi$$
−0.0880927 + 0.996112i $$0.528077\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1800.00 0.563097
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1224.00 −0.372557
$$222$$ 0 0
$$223$$ −4166.00 −1.25101 −0.625507 0.780219i $$-0.715108\pi$$
−0.625507 + 0.780219i $$0.715108\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5024.00 1.46896 0.734481 0.678629i $$-0.237425\pi$$
0.734481 + 0.678629i $$0.237425\pi$$
$$228$$ 0 0
$$229$$ 4454.00 1.28528 0.642639 0.766169i $$-0.277840\pi$$
0.642639 + 0.766169i $$0.277840\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1526.00 0.429063 0.214531 0.976717i $$-0.431178\pi$$
0.214531 + 0.976717i $$0.431178\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 6828.00 1.84798 0.923989 0.382420i $$-0.124909\pi$$
0.923989 + 0.382420i $$0.124909\pi$$
$$240$$ 0 0
$$241$$ 5782.00 1.54544 0.772721 0.634746i $$-0.218895\pi$$
0.772721 + 0.634746i $$0.218895\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1968.00 −0.506967
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −6394.00 −1.60791 −0.803956 0.594689i $$-0.797275\pi$$
−0.803956 + 0.594689i $$0.797275\pi$$
$$252$$ 0 0
$$253$$ −1632.00 −0.405545
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1862.00 −0.451939 −0.225970 0.974134i $$-0.572555\pi$$
−0.225970 + 0.974134i $$0.572555\pi$$
$$258$$ 0 0
$$259$$ −5904.00 −1.41644
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6504.00 1.52492 0.762460 0.647036i $$-0.223992\pi$$
0.762460 + 0.647036i $$0.223992\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 8298.00 1.88081 0.940405 0.340056i $$-0.110446\pi$$
0.940405 + 0.340056i $$0.110446\pi$$
$$270$$ 0 0
$$271$$ 1848.00 0.414236 0.207118 0.978316i $$-0.433592\pi$$
0.207118 + 0.978316i $$0.433592\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −2824.00 −0.612555 −0.306277 0.951942i $$-0.599084\pi$$
−0.306277 + 0.951942i $$0.599084\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1940.00 −0.411853 −0.205927 0.978567i $$-0.566021\pi$$
−0.205927 + 0.978567i $$0.566021\pi$$
$$282$$ 0 0
$$283$$ −6548.00 −1.37540 −0.687700 0.725995i $$-0.741380\pi$$
−0.687700 + 0.725995i $$0.741380\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −5184.00 −1.06621
$$288$$ 0 0
$$289$$ 5491.00 1.11765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −6566.00 −1.30918 −0.654590 0.755984i $$-0.727159\pi$$
−0.654590 + 0.755984i $$0.727159\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 576.000 0.111408
$$300$$ 0 0
$$301$$ −2160.00 −0.413622
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −8432.00 −1.56756 −0.783778 0.621041i $$-0.786710\pi$$
−0.783778 + 0.621041i $$0.786710\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4916.00 −0.896337 −0.448168 0.893949i $$-0.647924\pi$$
−0.448168 + 0.893949i $$0.647924\pi$$
$$312$$ 0 0
$$313$$ 10106.0 1.82500 0.912500 0.409077i $$-0.134149\pi$$
0.912500 + 0.409077i $$0.134149\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −3382.00 −0.599218 −0.299609 0.954062i $$-0.596856\pi$$
−0.299609 + 0.954062i $$0.596856\pi$$
$$318$$ 0 0
$$319$$ 4964.00 0.871256
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 16728.0 2.88164
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −288.000 −0.0482613
$$330$$ 0 0
$$331$$ −6460.00 −1.07273 −0.536365 0.843986i $$-0.680203\pi$$
−0.536365 + 0.843986i $$0.680203\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −5294.00 −0.855735 −0.427867 0.903842i $$-0.640735\pi$$
−0.427867 + 0.903842i $$0.640735\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3400.00 0.539942
$$342$$ 0 0
$$343$$ −6516.00 −1.02575
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 12096.0 1.87132 0.935659 0.352906i $$-0.114806\pi$$
0.935659 + 0.352906i $$0.114806\pi$$
$$348$$ 0 0
$$349$$ −862.000 −0.132211 −0.0661057 0.997813i $$-0.521057\pi$$
−0.0661057 + 0.997813i $$0.521057\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6878.00 1.03705 0.518525 0.855062i $$-0.326481\pi$$
0.518525 + 0.855062i $$0.326481\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 6216.00 0.913838 0.456919 0.889508i $$-0.348953\pi$$
0.456919 + 0.889508i $$0.348953\pi$$
$$360$$ 0 0
$$361$$ 20037.0 2.92127
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 13274.0 1.88800 0.944002 0.329941i $$-0.107029\pi$$
0.944002 + 0.329941i $$0.107029\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 2268.00 0.317382
$$372$$ 0 0
$$373$$ −1300.00 −0.180460 −0.0902298 0.995921i $$-0.528760\pi$$
−0.0902298 + 0.995921i $$0.528760\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −1752.00 −0.239344
$$378$$ 0 0
$$379$$ 13324.0 1.80583 0.902913 0.429824i $$-0.141424\pi$$
0.902913 + 0.429824i $$0.141424\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −6192.00 −0.826100 −0.413050 0.910708i $$-0.635537\pi$$
−0.413050 + 0.910708i $$0.635537\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 2022.00 0.263546 0.131773 0.991280i $$-0.457933\pi$$
0.131773 + 0.991280i $$0.457933\pi$$
$$390$$ 0 0
$$391$$ −4896.00 −0.633252
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7856.00 −0.993152 −0.496576 0.867993i $$-0.665410\pi$$
−0.496576 + 0.867993i $$0.665410\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1148.00 0.142964 0.0714818 0.997442i $$-0.477227\pi$$
0.0714818 + 0.997442i $$0.477227\pi$$
$$402$$ 0 0
$$403$$ −1200.00 −0.148328
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −11152.0 −1.35819
$$408$$ 0 0
$$409$$ −6310.00 −0.762859 −0.381430 0.924398i $$-0.624568\pi$$
−0.381430 + 0.924398i $$0.624568\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 11556.0 1.37684
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −13362.0 −1.55794 −0.778969 0.627062i $$-0.784257\pi$$
−0.778969 + 0.627062i $$0.784257\pi$$
$$420$$ 0 0
$$421$$ −5146.00 −0.595726 −0.297863 0.954609i $$-0.596274\pi$$
−0.297863 + 0.954609i $$0.596274\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 10836.0 1.22808
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −6368.00 −0.711684 −0.355842 0.934546i $$-0.615806\pi$$
−0.355842 + 0.934546i $$0.615806\pi$$
$$432$$ 0 0
$$433$$ 6138.00 0.681232 0.340616 0.940202i $$-0.389364\pi$$
0.340616 + 0.940202i $$0.389364\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −7872.00 −0.861714
$$438$$ 0 0
$$439$$ −4424.00 −0.480970 −0.240485 0.970653i $$-0.577307\pi$$
−0.240485 + 0.970653i $$0.577307\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 488.000 0.0523377 0.0261688 0.999658i $$-0.491669\pi$$
0.0261688 + 0.999658i $$0.491669\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 16884.0 1.77462 0.887311 0.461172i $$-0.152571\pi$$
0.887311 + 0.461172i $$0.152571\pi$$
$$450$$ 0 0
$$451$$ −9792.00 −1.02237
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5398.00 0.552533 0.276267 0.961081i $$-0.410903\pi$$
0.276267 + 0.961081i $$0.410903\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −6122.00 −0.618503 −0.309252 0.950980i $$-0.600079\pi$$
−0.309252 + 0.950980i $$0.600079\pi$$
$$462$$ 0 0
$$463$$ −8162.00 −0.819266 −0.409633 0.912250i $$-0.634343\pi$$
−0.409633 + 0.912250i $$0.634343\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2660.00 0.263576 0.131788 0.991278i $$-0.457928\pi$$
0.131788 + 0.991278i $$0.457928\pi$$
$$468$$ 0 0
$$469$$ −7848.00 −0.772680
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −4080.00 −0.396614
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 9788.00 0.933664 0.466832 0.884346i $$-0.345395\pi$$
0.466832 + 0.884346i $$0.345395\pi$$
$$480$$ 0 0
$$481$$ 3936.00 0.373111
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −4714.00 −0.438628 −0.219314 0.975654i $$-0.570382\pi$$
−0.219314 + 0.975654i $$0.570382\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −6690.00 −0.614899 −0.307450 0.951564i $$-0.599476\pi$$
−0.307450 + 0.951564i $$0.599476\pi$$
$$492$$ 0 0
$$493$$ 14892.0 1.36045
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 11736.0 1.05922
$$498$$ 0 0
$$499$$ −20636.0 −1.85129 −0.925646 0.378392i $$-0.876477\pi$$
−0.925646 + 0.378392i $$0.876477\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −15952.0 −1.41404 −0.707022 0.707191i $$-0.749962\pi$$
−0.707022 + 0.707191i $$0.749962\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −2230.00 −0.194191 −0.0970953 0.995275i $$-0.530955\pi$$
−0.0970953 + 0.995275i $$0.530955\pi$$
$$510$$ 0 0
$$511$$ −19116.0 −1.65488
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −544.000 −0.0462768
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1260.00 0.105953 0.0529766 0.998596i $$-0.483129\pi$$
0.0529766 + 0.998596i $$0.483129\pi$$
$$522$$ 0 0
$$523$$ −2900.00 −0.242463 −0.121231 0.992624i $$-0.538684\pi$$
−0.121231 + 0.992624i $$0.538684\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 10200.0 0.843110
$$528$$ 0 0
$$529$$ −9863.00 −0.810635
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3456.00 0.280855
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −646.000 −0.0516237
$$540$$ 0 0
$$541$$ 19554.0 1.55396 0.776980 0.629526i $$-0.216751\pi$$
0.776980 + 0.629526i $$0.216751\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2664.00 −0.208235 −0.104117 0.994565i $$-0.533202\pi$$
−0.104117 + 0.994565i $$0.533202\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 23944.0 1.85127
$$552$$ 0 0
$$553$$ 6984.00 0.537052
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 11358.0 0.864011 0.432005 0.901871i $$-0.357806\pi$$
0.432005 + 0.901871i $$0.357806\pi$$
$$558$$ 0 0
$$559$$ 1440.00 0.108954
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2440.00 0.182653 0.0913266 0.995821i $$-0.470889\pi$$
0.0913266 + 0.995821i $$0.470889\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −24156.0 −1.77974 −0.889870 0.456214i $$-0.849205\pi$$
−0.889870 + 0.456214i $$0.849205\pi$$
$$570$$ 0 0
$$571$$ −2220.00 −0.162704 −0.0813521 0.996685i $$-0.525924\pi$$
−0.0813521 + 0.996685i $$0.525924\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 5782.00 0.417171 0.208586 0.978004i $$-0.433114\pi$$
0.208586 + 0.978004i $$0.433114\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 7992.00 0.570678
$$582$$ 0 0
$$583$$ 4284.00 0.304331
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1684.00 −0.118409 −0.0592045 0.998246i $$-0.518856\pi$$
−0.0592045 + 0.998246i $$0.518856\pi$$
$$588$$ 0 0
$$589$$ 16400.0 1.14728
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −15246.0 −1.05578 −0.527891 0.849312i $$-0.677017\pi$$
−0.527891 + 0.849312i $$0.677017\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 9016.00 0.614998 0.307499 0.951548i $$-0.400508\pi$$
0.307499 + 0.951548i $$0.400508\pi$$
$$600$$ 0 0
$$601$$ −18682.0 −1.26798 −0.633989 0.773342i $$-0.718584\pi$$
−0.633989 + 0.773342i $$0.718584\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 22022.0 1.47256 0.736281 0.676676i $$-0.236580\pi$$
0.736281 + 0.676676i $$0.236580\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 192.000 0.0127127
$$612$$ 0 0
$$613$$ 22808.0 1.50278 0.751392 0.659856i $$-0.229383\pi$$
0.751392 + 0.659856i $$0.229383\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 9422.00 0.614774 0.307387 0.951585i $$-0.400545\pi$$
0.307387 + 0.951585i $$0.400545\pi$$
$$618$$ 0 0
$$619$$ 4172.00 0.270900 0.135450 0.990784i $$-0.456752\pi$$
0.135450 + 0.990784i $$0.456752\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −14760.0 −0.949192
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −33456.0 −2.12079
$$630$$ 0 0
$$631$$ −11572.0 −0.730070 −0.365035 0.930994i $$-0.618943\pi$$
−0.365035 + 0.930994i $$0.618943\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 228.000 0.0141816
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −936.000 −0.0576752 −0.0288376 0.999584i $$-0.509181\pi$$
−0.0288376 + 0.999584i $$0.509181\pi$$
$$642$$ 0 0
$$643$$ −15892.0 −0.974680 −0.487340 0.873212i $$-0.662033\pi$$
−0.487340 + 0.873212i $$0.662033\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −25056.0 −1.52249 −0.761247 0.648463i $$-0.775412\pi$$
−0.761247 + 0.648463i $$0.775412\pi$$
$$648$$ 0 0
$$649$$ 21828.0 1.32022
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −4054.00 −0.242948 −0.121474 0.992595i $$-0.538762\pi$$
−0.121474 + 0.992595i $$0.538762\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6758.00 0.399475 0.199738 0.979849i $$-0.435991\pi$$
0.199738 + 0.979849i $$0.435991\pi$$
$$660$$ 0 0
$$661$$ 25098.0 1.47685 0.738426 0.674335i $$-0.235569\pi$$
0.738426 + 0.674335i $$0.235569\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −7008.00 −0.406823
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 20468.0 1.17758
$$672$$ 0 0
$$673$$ −2830.00 −0.162093 −0.0810464 0.996710i $$-0.525826\pi$$
−0.0810464 + 0.996710i $$0.525826\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −10654.0 −0.604825 −0.302412 0.953177i $$-0.597792\pi$$
−0.302412 + 0.953177i $$0.597792\pi$$
$$678$$ 0 0
$$679$$ 13788.0 0.779286
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −17156.0 −0.961136 −0.480568 0.876957i $$-0.659570\pi$$
−0.480568 + 0.876957i $$0.659570\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1512.00 −0.0836032
$$690$$ 0 0
$$691$$ −812.000 −0.0447032 −0.0223516 0.999750i $$-0.507115\pi$$
−0.0223516 + 0.999750i $$0.507115\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −29376.0 −1.59641
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −30270.0 −1.63093 −0.815465 0.578806i $$-0.803519\pi$$
−0.815465 + 0.578806i $$0.803519\pi$$
$$702$$ 0 0
$$703$$ −53792.0 −2.88592
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −14364.0 −0.764093
$$708$$ 0 0
$$709$$ −394.000 −0.0208702 −0.0104351 0.999946i $$-0.503322\pi$$
−0.0104351 + 0.999946i $$0.503322\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −4800.00 −0.252120
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −37224.0 −1.93077 −0.965383 0.260836i $$-0.916002\pi$$
−0.965383 + 0.260836i $$0.916002\pi$$
$$720$$ 0 0
$$721$$ 7236.00 0.373762
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 12614.0 0.643504 0.321752 0.946824i $$-0.395728\pi$$
0.321752 + 0.946824i $$0.395728\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −12240.0 −0.619306
$$732$$ 0 0
$$733$$ 25664.0 1.29321 0.646604 0.762826i $$-0.276189\pi$$
0.646604 + 0.762826i $$0.276189\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −14824.0 −0.740908
$$738$$ 0 0
$$739$$ −18772.0 −0.934424 −0.467212 0.884145i $$-0.654741\pi$$
−0.467212 + 0.884145i $$0.654741\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 19376.0 0.956711 0.478356 0.878166i $$-0.341233\pi$$
0.478356 + 0.878166i $$0.341233\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −25992.0 −1.26799
$$750$$ 0 0
$$751$$ 30092.0 1.46215 0.731074 0.682299i $$-0.239020\pi$$
0.731074 + 0.682299i $$0.239020\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −18136.0 −0.870758 −0.435379 0.900247i $$-0.643386\pi$$
−0.435379 + 0.900247i $$0.643386\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 10948.0 0.521504 0.260752 0.965406i $$-0.416029\pi$$
0.260752 + 0.965406i $$0.416029\pi$$
$$762$$ 0 0
$$763$$ −3564.00 −0.169103
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −7704.00 −0.362680
$$768$$ 0 0
$$769$$ 1422.00 0.0666822 0.0333411 0.999444i $$-0.489385\pi$$
0.0333411 + 0.999444i $$0.489385\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −26142.0 −1.21638 −0.608190 0.793791i $$-0.708104\pi$$
−0.608190 + 0.793791i $$0.708104\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −47232.0 −2.17235
$$780$$ 0 0
$$781$$ 22168.0 1.01566
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −23404.0 −1.06005 −0.530027 0.847981i $$-0.677818\pi$$
−0.530027 + 0.847981i $$0.677818\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 36180.0 1.62631
$$792$$ 0 0
$$793$$ −7224.00 −0.323495
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −1418.00 −0.0630215 −0.0315108 0.999503i $$-0.510032\pi$$
−0.0315108 + 0.999503i $$0.510032\pi$$
$$798$$ 0 0
$$799$$ −1632.00 −0.0722603
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −36108.0 −1.58683
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −17304.0 −0.752010 −0.376005 0.926618i $$-0.622702\pi$$
−0.376005 + 0.926618i $$0.622702\pi$$
$$810$$ 0 0
$$811$$ −28012.0 −1.21287 −0.606433 0.795135i $$-0.707400\pi$$
−0.606433 + 0.795135i $$0.707400\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −19680.0 −0.842737
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 32266.0 1.37161 0.685805 0.727786i $$-0.259450\pi$$
0.685805 + 0.727786i $$0.259450\pi$$
$$822$$ 0 0
$$823$$ −4962.00 −0.210163 −0.105082 0.994464i $$-0.533510\pi$$
−0.105082 + 0.994464i $$0.533510\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −5064.00 −0.212929 −0.106465 0.994316i $$-0.533953\pi$$
−0.106465 + 0.994316i $$0.533953\pi$$
$$828$$ 0 0
$$829$$ −8174.00 −0.342454 −0.171227 0.985232i $$-0.554773\pi$$
−0.171227 + 0.985232i $$0.554773\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1938.00 −0.0806095
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −28240.0 −1.16204 −0.581021 0.813889i $$-0.697347\pi$$
−0.581021 + 0.813889i $$0.697347\pi$$
$$840$$ 0 0
$$841$$ −3073.00 −0.125999
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −3150.00 −0.127787
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 15744.0 0.634192
$$852$$ 0 0
$$853$$ −10472.0 −0.420345 −0.210173 0.977664i $$-0.567403\pi$$
−0.210173 + 0.977664i $$0.567403\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 32102.0 1.27956 0.639780 0.768558i $$-0.279025\pi$$
0.639780 + 0.768558i $$0.279025\pi$$
$$858$$ 0 0
$$859$$ −11060.0 −0.439304 −0.219652 0.975578i $$-0.570492\pi$$
−0.219652 + 0.975578i $$0.570492\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −36088.0 −1.42346 −0.711732 0.702451i $$-0.752089\pi$$
−0.711732 + 0.702451i $$0.752089\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 13192.0 0.514969
$$870$$ 0 0
$$871$$ 5232.00 0.203536
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 34508.0 1.32868 0.664340 0.747431i $$-0.268713\pi$$
0.664340 + 0.747431i $$0.268713\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −6596.00 −0.252242 −0.126121 0.992015i $$-0.540253\pi$$
−0.126121 + 0.992015i $$0.540253\pi$$
$$882$$ 0 0
$$883$$ −17620.0 −0.671529 −0.335765 0.941946i $$-0.608995\pi$$
−0.335765 + 0.941946i $$0.608995\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 50784.0 1.92239 0.961195 0.275870i $$-0.0889659\pi$$
0.961195 + 0.275870i $$0.0889659\pi$$
$$888$$ 0 0
$$889$$ 15588.0 0.588082
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −2624.00 −0.0983301
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 14600.0 0.541643
$$900$$ 0 0
$$901$$ 12852.0 0.475208
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −16072.0 −0.588381 −0.294191 0.955747i $$-0.595050\pi$$
−0.294191 + 0.955747i $$0.595050\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −41760.0 −1.51874 −0.759369 0.650660i $$-0.774492\pi$$
−0.759369 + 0.650660i $$0.774492\pi$$
$$912$$ 0 0
$$913$$ 15096.0 0.547212
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −37764.0 −1.35995
$$918$$ 0 0
$$919$$ 34100.0 1.22400 0.612000 0.790858i $$-0.290365\pi$$
0.612000 + 0.790858i $$0.290365\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −7824.00 −0.279014
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −22812.0 −0.805638 −0.402819 0.915280i $$-0.631970\pi$$
−0.402819 + 0.915280i $$0.631970\pi$$
$$930$$ 0 0
$$931$$ −3116.00 −0.109691
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 38982.0 1.35911 0.679555 0.733624i $$-0.262173\pi$$
0.679555 + 0.733624i $$0.262173\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 52766.0 1.82797 0.913986 0.405745i $$-0.132988\pi$$
0.913986 + 0.405745i $$0.132988\pi$$
$$942$$ 0 0
$$943$$ 13824.0 0.477382
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −13608.0 −0.466949 −0.233474 0.972363i $$-0.575010\pi$$
−0.233474 + 0.972363i $$0.575010\pi$$
$$948$$ 0 0
$$949$$ 12744.0 0.435920
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −6446.00 −0.219104 −0.109552 0.993981i $$-0.534942\pi$$
−0.109552 + 0.993981i $$0.534942\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −15948.0 −0.537005
$$960$$ 0 0
$$961$$ −19791.0 −0.664328
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 42642.0 1.41807 0.709035 0.705173i $$-0.249131\pi$$
0.709035 + 0.705173i $$0.249131\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −19938.0 −0.658950 −0.329475 0.944164i $$-0.606872\pi$$
−0.329475 + 0.944164i $$0.606872\pi$$
$$972$$ 0 0
$$973$$ −9000.00 −0.296533
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −49754.0 −1.62924 −0.814622 0.579992i $$-0.803056\pi$$
−0.814622 + 0.579992i $$0.803056\pi$$
$$978$$ 0 0
$$979$$ −27880.0 −0.910162
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −7936.00 −0.257497 −0.128748 0.991677i $$-0.541096\pi$$
−0.128748 + 0.991677i $$0.541096\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 5760.00 0.185194
$$990$$ 0 0
$$991$$ −33248.0 −1.06575 −0.532875 0.846194i $$-0.678888\pi$$
−0.532875 + 0.846194i $$0.678888\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 20196.0 0.641538 0.320769 0.947157i $$-0.396059\pi$$
0.320769 + 0.947157i $$0.396059\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1800.4.a.be.1.1 1
3.2 odd 2 1800.4.a.bc.1.1 1
5.2 odd 4 1800.4.f.s.649.2 2
5.3 odd 4 1800.4.f.s.649.1 2
5.4 even 2 360.4.a.j.1.1 yes 1
15.2 even 4 1800.4.f.e.649.2 2
15.8 even 4 1800.4.f.e.649.1 2
15.14 odd 2 360.4.a.a.1.1 1
20.19 odd 2 720.4.a.z.1.1 1
60.59 even 2 720.4.a.m.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
360.4.a.a.1.1 1 15.14 odd 2
360.4.a.j.1.1 yes 1 5.4 even 2
720.4.a.m.1.1 1 60.59 even 2
720.4.a.z.1.1 1 20.19 odd 2
1800.4.a.bc.1.1 1 3.2 odd 2
1800.4.a.be.1.1 1 1.1 even 1 trivial
1800.4.f.e.649.1 2 15.8 even 4
1800.4.f.e.649.2 2 15.2 even 4
1800.4.f.s.649.1 2 5.3 odd 4
1800.4.f.s.649.2 2 5.2 odd 4