# Properties

 Label 720.4.a.a.1.1 Level $720$ Weight $4$ Character 720.1 Self dual yes Analytic conductor $42.481$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 720.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$42.4813752041$$ 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 $$\chi$$ $$=$$ 720.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-5.00000 q^{5} -34.0000 q^{7} +O(q^{10})$$ $$q-5.00000 q^{5} -34.0000 q^{7} -18.0000 q^{11} +12.0000 q^{13} -106.000 q^{17} +44.0000 q^{19} -56.0000 q^{23} +25.0000 q^{25} +270.000 q^{29} -204.000 q^{31} +170.000 q^{35} +120.000 q^{37} +80.0000 q^{41} -536.000 q^{43} +536.000 q^{47} +813.000 q^{49} +542.000 q^{53} +90.0000 q^{55} +174.000 q^{59} +186.000 q^{61} -60.0000 q^{65} -332.000 q^{67} +132.000 q^{71} -602.000 q^{73} +612.000 q^{77} +548.000 q^{79} +492.000 q^{83} +530.000 q^{85} -1052.00 q^{89} -408.000 q^{91} -220.000 q^{95} +482.000 q^{97} +O(q^{100})$$

## 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
$$5$$ −5.00000 −0.447214
$$6$$ 0 0
$$7$$ −34.0000 −1.83583 −0.917914 0.396780i $$-0.870128\pi$$
−0.917914 + 0.396780i $$0.870128\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −18.0000 −0.493382 −0.246691 0.969094i $$-0.579343\pi$$
−0.246691 + 0.969094i $$0.579343\pi$$
$$12$$ 0 0
$$13$$ 12.0000 0.256015 0.128008 0.991773i $$-0.459142\pi$$
0.128008 + 0.991773i $$0.459142\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −106.000 −1.51228 −0.756140 0.654409i $$-0.772917\pi$$
−0.756140 + 0.654409i $$0.772917\pi$$
$$18$$ 0 0
$$19$$ 44.0000 0.531279 0.265639 0.964072i $$-0.414417\pi$$
0.265639 + 0.964072i $$0.414417\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −56.0000 −0.507687 −0.253844 0.967245i $$-0.581695\pi$$
−0.253844 + 0.967245i $$0.581695\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 270.000 1.72889 0.864444 0.502729i $$-0.167671\pi$$
0.864444 + 0.502729i $$0.167671\pi$$
$$30$$ 0 0
$$31$$ −204.000 −1.18192 −0.590959 0.806701i $$-0.701251\pi$$
−0.590959 + 0.806701i $$0.701251\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 170.000 0.821007
$$36$$ 0 0
$$37$$ 120.000 0.533186 0.266593 0.963809i $$-0.414102\pi$$
0.266593 + 0.963809i $$0.414102\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 80.0000 0.304729 0.152365 0.988324i $$-0.451311\pi$$
0.152365 + 0.988324i $$0.451311\pi$$
$$42$$ 0 0
$$43$$ −536.000 −1.90091 −0.950456 0.310858i $$-0.899383\pi$$
−0.950456 + 0.310858i $$0.899383\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 536.000 1.66348 0.831741 0.555164i $$-0.187345\pi$$
0.831741 + 0.555164i $$0.187345\pi$$
$$48$$ 0 0
$$49$$ 813.000 2.37026
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 542.000 1.40471 0.702353 0.711829i $$-0.252133\pi$$
0.702353 + 0.711829i $$0.252133\pi$$
$$54$$ 0 0
$$55$$ 90.0000 0.220647
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 174.000 0.383947 0.191973 0.981400i $$-0.438511\pi$$
0.191973 + 0.981400i $$0.438511\pi$$
$$60$$ 0 0
$$61$$ 186.000 0.390408 0.195204 0.980763i $$-0.437463\pi$$
0.195204 + 0.980763i $$0.437463\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −60.0000 −0.114494
$$66$$ 0 0
$$67$$ −332.000 −0.605377 −0.302688 0.953090i $$-0.597884\pi$$
−0.302688 + 0.953090i $$0.597884\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 132.000 0.220641 0.110321 0.993896i $$-0.464812\pi$$
0.110321 + 0.993896i $$0.464812\pi$$
$$72$$ 0 0
$$73$$ −602.000 −0.965189 −0.482594 0.875844i $$-0.660305\pi$$
−0.482594 + 0.875844i $$0.660305\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 612.000 0.905765
$$78$$ 0 0
$$79$$ 548.000 0.780441 0.390220 0.920721i $$-0.372399\pi$$
0.390220 + 0.920721i $$0.372399\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 492.000 0.650651 0.325325 0.945602i $$-0.394526\pi$$
0.325325 + 0.945602i $$0.394526\pi$$
$$84$$ 0 0
$$85$$ 530.000 0.676313
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −1052.00 −1.25294 −0.626471 0.779445i $$-0.715501\pi$$
−0.626471 + 0.779445i $$0.715501\pi$$
$$90$$ 0 0
$$91$$ −408.000 −0.470000
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −220.000 −0.237595
$$96$$ 0 0
$$97$$ 482.000 0.504533 0.252266 0.967658i $$-0.418824\pi$$
0.252266 + 0.967658i $$0.418824\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1214.00 1.19601 0.598007 0.801491i $$-0.295959\pi$$
0.598007 + 0.801491i $$0.295959\pi$$
$$102$$ 0 0
$$103$$ −898.000 −0.859054 −0.429527 0.903054i $$-0.641320\pi$$
−0.429527 + 0.903054i $$0.641320\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1364.00 −1.23236 −0.616182 0.787604i $$-0.711321\pi$$
−0.616182 + 0.787604i $$0.711321\pi$$
$$108$$ 0 0
$$109$$ 218.000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1386.00 1.15384 0.576920 0.816801i $$-0.304254\pi$$
0.576920 + 0.816801i $$0.304254\pi$$
$$114$$ 0 0
$$115$$ 280.000 0.227045
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 3604.00 2.77629
$$120$$ 0 0
$$121$$ −1007.00 −0.756574
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −125.000 −0.0894427
$$126$$ 0 0
$$127$$ 814.000 0.568747 0.284373 0.958714i $$-0.408214\pi$$
0.284373 + 0.958714i $$0.408214\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1282.00 0.855029 0.427515 0.904008i $$-0.359389\pi$$
0.427515 + 0.904008i $$0.359389\pi$$
$$132$$ 0 0
$$133$$ −1496.00 −0.975336
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3066.00 1.91202 0.956008 0.293342i $$-0.0947675\pi$$
0.956008 + 0.293342i $$0.0947675\pi$$
$$138$$ 0 0
$$139$$ 1332.00 0.812797 0.406398 0.913696i $$-0.366784\pi$$
0.406398 + 0.913696i $$0.366784\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −216.000 −0.126313
$$144$$ 0 0
$$145$$ −1350.00 −0.773182
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1470.00 −0.808236 −0.404118 0.914707i $$-0.632421\pi$$
−0.404118 + 0.914707i $$0.632421\pi$$
$$150$$ 0 0
$$151$$ 2592.00 1.39691 0.698457 0.715652i $$-0.253870\pi$$
0.698457 + 0.715652i $$0.253870\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1020.00 0.528570
$$156$$ 0 0
$$157$$ −3332.00 −1.69377 −0.846887 0.531773i $$-0.821526\pi$$
−0.846887 + 0.531773i $$0.821526\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1904.00 0.932026
$$162$$ 0 0
$$163$$ 748.000 0.359435 0.179717 0.983718i $$-0.442482\pi$$
0.179717 + 0.983718i $$0.442482\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2560.00 1.18622 0.593110 0.805121i $$-0.297900\pi$$
0.593110 + 0.805121i $$0.297900\pi$$
$$168$$ 0 0
$$169$$ −2053.00 −0.934456
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1206.00 0.530003 0.265001 0.964248i $$-0.414628\pi$$
0.265001 + 0.964248i $$0.414628\pi$$
$$174$$ 0 0
$$175$$ −850.000 −0.367165
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1694.00 0.707349 0.353675 0.935369i $$-0.384932\pi$$
0.353675 + 0.935369i $$0.384932\pi$$
$$180$$ 0 0
$$181$$ 3722.00 1.52848 0.764238 0.644935i $$-0.223115\pi$$
0.764238 + 0.644935i $$0.223115\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −600.000 −0.238448
$$186$$ 0 0
$$187$$ 1908.00 0.746133
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2836.00 −1.07438 −0.537188 0.843463i $$-0.680513\pi$$
−0.537188 + 0.843463i $$0.680513\pi$$
$$192$$ 0 0
$$193$$ −234.000 −0.0872730 −0.0436365 0.999047i $$-0.513894\pi$$
−0.0436365 + 0.999047i $$0.513894\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3814.00 −1.37937 −0.689686 0.724109i $$-0.742251\pi$$
−0.689686 + 0.724109i $$0.742251\pi$$
$$198$$ 0 0
$$199$$ −2352.00 −0.837833 −0.418917 0.908025i $$-0.637590\pi$$
−0.418917 + 0.908025i $$0.637590\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −9180.00 −3.17394
$$204$$ 0 0
$$205$$ −400.000 −0.136279
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −792.000 −0.262123
$$210$$ 0 0
$$211$$ 3660.00 1.19415 0.597073 0.802187i $$-0.296330\pi$$
0.597073 + 0.802187i $$0.296330\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 2680.00 0.850114
$$216$$ 0 0
$$217$$ 6936.00 2.16980
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1272.00 −0.387167
$$222$$ 0 0
$$223$$ 2646.00 0.794571 0.397285 0.917695i $$-0.369952\pi$$
0.397285 + 0.917695i $$0.369952\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −240.000 −0.0701734 −0.0350867 0.999384i $$-0.511171\pi$$
−0.0350867 + 0.999384i $$0.511171\pi$$
$$228$$ 0 0
$$229$$ −4698.00 −1.35569 −0.677844 0.735206i $$-0.737086\pi$$
−0.677844 + 0.735206i $$0.737086\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3814.00 1.07238 0.536188 0.844099i $$-0.319864\pi$$
0.536188 + 0.844099i $$0.319864\pi$$
$$234$$ 0 0
$$235$$ −2680.00 −0.743932
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2148.00 0.581350 0.290675 0.956822i $$-0.406120\pi$$
0.290675 + 0.956822i $$0.406120\pi$$
$$240$$ 0 0
$$241$$ −3370.00 −0.900750 −0.450375 0.892839i $$-0.648710\pi$$
−0.450375 + 0.892839i $$0.648710\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −4065.00 −1.06001
$$246$$ 0 0
$$247$$ 528.000 0.136016
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −6134.00 −1.54253 −0.771264 0.636515i $$-0.780375\pi$$
−0.771264 + 0.636515i $$0.780375\pi$$
$$252$$ 0 0
$$253$$ 1008.00 0.250484
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −4566.00 −1.10825 −0.554123 0.832435i $$-0.686946\pi$$
−0.554123 + 0.832435i $$0.686946\pi$$
$$258$$ 0 0
$$259$$ −4080.00 −0.978837
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1920.00 0.450161 0.225080 0.974340i $$-0.427736\pi$$
0.225080 + 0.974340i $$0.427736\pi$$
$$264$$ 0 0
$$265$$ −2710.00 −0.628204
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −5802.00 −1.31507 −0.657536 0.753423i $$-0.728401\pi$$
−0.657536 + 0.753423i $$0.728401\pi$$
$$270$$ 0 0
$$271$$ −1640.00 −0.367612 −0.183806 0.982963i $$-0.558842\pi$$
−0.183806 + 0.982963i $$0.558842\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −450.000 −0.0986764
$$276$$ 0 0
$$277$$ −2792.00 −0.605614 −0.302807 0.953052i $$-0.597924\pi$$
−0.302807 + 0.953052i $$0.597924\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1108.00 0.235223 0.117612 0.993060i $$-0.462476\pi$$
0.117612 + 0.993060i $$0.462476\pi$$
$$282$$ 0 0
$$283$$ −6028.00 −1.26617 −0.633087 0.774080i $$-0.718213\pi$$
−0.633087 + 0.774080i $$0.718213\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −2720.00 −0.559430
$$288$$ 0 0
$$289$$ 6323.00 1.28699
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 7994.00 1.59391 0.796953 0.604041i $$-0.206444\pi$$
0.796953 + 0.604041i $$0.206444\pi$$
$$294$$ 0 0
$$295$$ −870.000 −0.171706
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −672.000 −0.129976
$$300$$ 0 0
$$301$$ 18224.0 3.48975
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −930.000 −0.174596
$$306$$ 0 0
$$307$$ −736.000 −0.136827 −0.0684133 0.997657i $$-0.521794\pi$$
−0.0684133 + 0.997657i $$0.521794\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 5380.00 0.980938 0.490469 0.871459i $$-0.336825\pi$$
0.490469 + 0.871459i $$0.336825\pi$$
$$312$$ 0 0
$$313$$ −1370.00 −0.247402 −0.123701 0.992320i $$-0.539476\pi$$
−0.123701 + 0.992320i $$0.539476\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 5770.00 1.02232 0.511160 0.859486i $$-0.329216\pi$$
0.511160 + 0.859486i $$0.329216\pi$$
$$318$$ 0 0
$$319$$ −4860.00 −0.853002
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −4664.00 −0.803442
$$324$$ 0 0
$$325$$ 300.000 0.0512031
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −18224.0 −3.05387
$$330$$ 0 0
$$331$$ 4172.00 0.692791 0.346396 0.938089i $$-0.387406\pi$$
0.346396 + 0.938089i $$0.387406\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1660.00 0.270733
$$336$$ 0 0
$$337$$ 8206.00 1.32644 0.663219 0.748426i $$-0.269190\pi$$
0.663219 + 0.748426i $$0.269190\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3672.00 0.583138
$$342$$ 0 0
$$343$$ −15980.0 −2.51557
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −10848.0 −1.67825 −0.839123 0.543942i $$-0.816931\pi$$
−0.839123 + 0.543942i $$0.816931\pi$$
$$348$$ 0 0
$$349$$ −1694.00 −0.259822 −0.129911 0.991526i $$-0.541469\pi$$
−0.129911 + 0.991526i $$0.541469\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −6642.00 −1.00147 −0.500734 0.865601i $$-0.666936\pi$$
−0.500734 + 0.865601i $$0.666936\pi$$
$$354$$ 0 0
$$355$$ −660.000 −0.0986737
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10376.0 1.52542 0.762708 0.646743i $$-0.223869\pi$$
0.762708 + 0.646743i $$0.223869\pi$$
$$360$$ 0 0
$$361$$ −4923.00 −0.717743
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3010.00 0.431645
$$366$$ 0 0
$$367$$ 2198.00 0.312629 0.156314 0.987707i $$-0.450039\pi$$
0.156314 + 0.987707i $$0.450039\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −18428.0 −2.57880
$$372$$ 0 0
$$373$$ −12220.0 −1.69632 −0.848160 0.529740i $$-0.822290\pi$$
−0.848160 + 0.529740i $$0.822290\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3240.00 0.442622
$$378$$ 0 0
$$379$$ 10388.0 1.40790 0.703952 0.710247i $$-0.251417\pi$$
0.703952 + 0.710247i $$0.251417\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −10552.0 −1.40779 −0.703893 0.710306i $$-0.748557\pi$$
−0.703893 + 0.710306i $$0.748557\pi$$
$$384$$ 0 0
$$385$$ −3060.00 −0.405070
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −8262.00 −1.07686 −0.538432 0.842669i $$-0.680983\pi$$
−0.538432 + 0.842669i $$0.680983\pi$$
$$390$$ 0 0
$$391$$ 5936.00 0.767766
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −2740.00 −0.349024
$$396$$ 0 0
$$397$$ 2864.00 0.362066 0.181033 0.983477i $$-0.442056\pi$$
0.181033 + 0.983477i $$0.442056\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −12588.0 −1.56762 −0.783809 0.621002i $$-0.786726\pi$$
−0.783809 + 0.621002i $$0.786726\pi$$
$$402$$ 0 0
$$403$$ −2448.00 −0.302589
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −2160.00 −0.263064
$$408$$ 0 0
$$409$$ 10330.0 1.24886 0.624432 0.781079i $$-0.285330\pi$$
0.624432 + 0.781079i $$0.285330\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −5916.00 −0.704860
$$414$$ 0 0
$$415$$ −2460.00 −0.290980
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1250.00 0.145743 0.0728717 0.997341i $$-0.476784\pi$$
0.0728717 + 0.997341i $$0.476784\pi$$
$$420$$ 0 0
$$421$$ 5670.00 0.656387 0.328193 0.944611i $$-0.393560\pi$$
0.328193 + 0.944611i $$0.393560\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2650.00 −0.302456
$$426$$ 0 0
$$427$$ −6324.00 −0.716721
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12976.0 1.45019 0.725095 0.688649i $$-0.241796\pi$$
0.725095 + 0.688649i $$0.241796\pi$$
$$432$$ 0 0
$$433$$ −9050.00 −1.00442 −0.502212 0.864745i $$-0.667480\pi$$
−0.502212 + 0.864745i $$0.667480\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2464.00 −0.269723
$$438$$ 0 0
$$439$$ 17528.0 1.90562 0.952808 0.303572i $$-0.0981794\pi$$
0.952808 + 0.303572i $$0.0981794\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −2568.00 −0.275416 −0.137708 0.990473i $$-0.543974\pi$$
−0.137708 + 0.990473i $$0.543974\pi$$
$$444$$ 0 0
$$445$$ 5260.00 0.560332
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 12652.0 1.32981 0.664905 0.746928i $$-0.268472\pi$$
0.664905 + 0.746928i $$0.268472\pi$$
$$450$$ 0 0
$$451$$ −1440.00 −0.150348
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 2040.00 0.210190
$$456$$ 0 0
$$457$$ −6230.00 −0.637696 −0.318848 0.947806i $$-0.603296\pi$$
−0.318848 + 0.947806i $$0.603296\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 5290.00 0.534447 0.267223 0.963635i $$-0.413894\pi$$
0.267223 + 0.963635i $$0.413894\pi$$
$$462$$ 0 0
$$463$$ −8110.00 −0.814047 −0.407023 0.913418i $$-0.633433\pi$$
−0.407023 + 0.913418i $$0.633433\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2020.00 0.200159 0.100080 0.994979i $$-0.468090\pi$$
0.100080 + 0.994979i $$0.468090\pi$$
$$468$$ 0 0
$$469$$ 11288.0 1.11137
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 9648.00 0.937876
$$474$$ 0 0
$$475$$ 1100.00 0.106256
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 9684.00 0.923744 0.461872 0.886947i $$-0.347178\pi$$
0.461872 + 0.886947i $$0.347178\pi$$
$$480$$ 0 0
$$481$$ 1440.00 0.136504
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2410.00 −0.225634
$$486$$ 0 0
$$487$$ 18426.0 1.71450 0.857250 0.514900i $$-0.172171\pi$$
0.857250 + 0.514900i $$0.172171\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −4558.00 −0.418940 −0.209470 0.977815i $$-0.567174\pi$$
−0.209470 + 0.977815i $$0.567174\pi$$
$$492$$ 0 0
$$493$$ −28620.0 −2.61456
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −4488.00 −0.405059
$$498$$ 0 0
$$499$$ 460.000 0.0412674 0.0206337 0.999787i $$-0.493432\pi$$
0.0206337 + 0.999787i $$0.493432\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 8568.00 0.759499 0.379750 0.925089i $$-0.376010\pi$$
0.379750 + 0.925089i $$0.376010\pi$$
$$504$$ 0 0
$$505$$ −6070.00 −0.534874
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 16374.0 1.42586 0.712932 0.701233i $$-0.247367\pi$$
0.712932 + 0.701233i $$0.247367\pi$$
$$510$$ 0 0
$$511$$ 20468.0 1.77192
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 4490.00 0.384181
$$516$$ 0 0
$$517$$ −9648.00 −0.820732
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 21620.0 1.81802 0.909011 0.416772i $$-0.136839\pi$$
0.909011 + 0.416772i $$0.136839\pi$$
$$522$$ 0 0
$$523$$ −16524.0 −1.38154 −0.690769 0.723076i $$-0.742728\pi$$
−0.690769 + 0.723076i $$0.742728\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 21624.0 1.78739
$$528$$ 0 0
$$529$$ −9031.00 −0.742254
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 960.000 0.0780154
$$534$$ 0 0
$$535$$ 6820.00 0.551130
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −14634.0 −1.16945
$$540$$ 0 0
$$541$$ −4990.00 −0.396556 −0.198278 0.980146i $$-0.563535\pi$$
−0.198278 + 0.980146i $$0.563535\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1090.00 −0.0856706
$$546$$ 0 0
$$547$$ 15224.0 1.19000 0.595001 0.803725i $$-0.297152\pi$$
0.595001 + 0.803725i $$0.297152\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 11880.0 0.918521
$$552$$ 0 0
$$553$$ −18632.0 −1.43275
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −5698.00 −0.433451 −0.216725 0.976233i $$-0.569538\pi$$
−0.216725 + 0.976233i $$0.569538\pi$$
$$558$$ 0 0
$$559$$ −6432.00 −0.486663
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −5976.00 −0.447351 −0.223675 0.974664i $$-0.571806\pi$$
−0.223675 + 0.974664i $$0.571806\pi$$
$$564$$ 0 0
$$565$$ −6930.00 −0.516013
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 16460.0 1.21272 0.606361 0.795189i $$-0.292629\pi$$
0.606361 + 0.795189i $$0.292629\pi$$
$$570$$ 0 0
$$571$$ 18236.0 1.33652 0.668260 0.743928i $$-0.267039\pi$$
0.668260 + 0.743928i $$0.267039\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1400.00 −0.101537
$$576$$ 0 0
$$577$$ 20842.0 1.50375 0.751875 0.659306i $$-0.229150\pi$$
0.751875 + 0.659306i $$0.229150\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −16728.0 −1.19448
$$582$$ 0 0
$$583$$ −9756.00 −0.693057
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 11772.0 0.827738 0.413869 0.910336i $$-0.364177\pi$$
0.413869 + 0.910336i $$0.364177\pi$$
$$588$$ 0 0
$$589$$ −8976.00 −0.627928
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 4514.00 0.312593 0.156297 0.987710i $$-0.450044\pi$$
0.156297 + 0.987710i $$0.450044\pi$$
$$594$$ 0 0
$$595$$ −18020.0 −1.24159
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −25096.0 −1.71184 −0.855922 0.517105i $$-0.827010\pi$$
−0.855922 + 0.517105i $$0.827010\pi$$
$$600$$ 0 0
$$601$$ 16262.0 1.10373 0.551864 0.833934i $$-0.313917\pi$$
0.551864 + 0.833934i $$0.313917\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 5035.00 0.338350
$$606$$ 0 0
$$607$$ −2262.00 −0.151255 −0.0756275 0.997136i $$-0.524096\pi$$
−0.0756275 + 0.997136i $$0.524096\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 6432.00 0.425877
$$612$$ 0 0
$$613$$ 14216.0 0.936670 0.468335 0.883551i $$-0.344854\pi$$
0.468335 + 0.883551i $$0.344854\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2558.00 0.166906 0.0834532 0.996512i $$-0.473405\pi$$
0.0834532 + 0.996512i $$0.473405\pi$$
$$618$$ 0 0
$$619$$ 17044.0 1.10671 0.553357 0.832944i $$-0.313346\pi$$
0.553357 + 0.832944i $$0.313346\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 35768.0 2.30018
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −12720.0 −0.806327
$$630$$ 0 0
$$631$$ −20980.0 −1.32361 −0.661807 0.749674i $$-0.730210\pi$$
−0.661807 + 0.749674i $$0.730210\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −4070.00 −0.254351
$$636$$ 0 0
$$637$$ 9756.00 0.606824
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 7176.00 0.442176 0.221088 0.975254i $$-0.429039\pi$$
0.221088 + 0.975254i $$0.429039\pi$$
$$642$$ 0 0
$$643$$ 2724.00 0.167067 0.0835335 0.996505i $$-0.473379\pi$$
0.0835335 + 0.996505i $$0.473379\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 10392.0 0.631455 0.315728 0.948850i $$-0.397751\pi$$
0.315728 + 0.948850i $$0.397751\pi$$
$$648$$ 0 0
$$649$$ −3132.00 −0.189433
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −11958.0 −0.716620 −0.358310 0.933603i $$-0.616647\pi$$
−0.358310 + 0.933603i $$0.616647\pi$$
$$654$$ 0 0
$$655$$ −6410.00 −0.382381
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −13366.0 −0.790084 −0.395042 0.918663i $$-0.629270\pi$$
−0.395042 + 0.918663i $$0.629270\pi$$
$$660$$ 0 0
$$661$$ 14698.0 0.864880 0.432440 0.901663i $$-0.357653\pi$$
0.432440 + 0.901663i $$0.357653\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 7480.00 0.436183
$$666$$ 0 0
$$667$$ −15120.0 −0.877734
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −3348.00 −0.192620
$$672$$ 0 0
$$673$$ −7570.00 −0.433584 −0.216792 0.976218i $$-0.569559\pi$$
−0.216792 + 0.976218i $$0.569559\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 21378.0 1.21362 0.606812 0.794845i $$-0.292448\pi$$
0.606812 + 0.794845i $$0.292448\pi$$
$$678$$ 0 0
$$679$$ −16388.0 −0.926235
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 15804.0 0.885393 0.442696 0.896672i $$-0.354022\pi$$
0.442696 + 0.896672i $$0.354022\pi$$
$$684$$ 0 0
$$685$$ −15330.0 −0.855079
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 6504.00 0.359627
$$690$$ 0 0
$$691$$ 22028.0 1.21271 0.606356 0.795193i $$-0.292630\pi$$
0.606356 + 0.795193i $$0.292630\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −6660.00 −0.363494
$$696$$ 0 0
$$697$$ −8480.00 −0.460836
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1762.00 −0.0949356 −0.0474678 0.998873i $$-0.515115\pi$$
−0.0474678 + 0.998873i $$0.515115\pi$$
$$702$$ 0 0
$$703$$ 5280.00 0.283270
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −41276.0 −2.19568
$$708$$ 0 0
$$709$$ −2474.00 −0.131048 −0.0655240 0.997851i $$-0.520872\pi$$
−0.0655240 + 0.997851i $$0.520872\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 11424.0 0.600045
$$714$$ 0 0
$$715$$ 1080.00 0.0564891
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 32040.0 1.66188 0.830939 0.556363i $$-0.187804\pi$$
0.830939 + 0.556363i $$0.187804\pi$$
$$720$$ 0 0
$$721$$ 30532.0 1.57708
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 6750.00 0.345778
$$726$$ 0 0
$$727$$ 12874.0 0.656768 0.328384 0.944544i $$-0.393496\pi$$
0.328384 + 0.944544i $$0.393496\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 56816.0 2.87471
$$732$$ 0 0
$$733$$ 28208.0 1.42140 0.710700 0.703495i $$-0.248378\pi$$
0.710700 + 0.703495i $$0.248378\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5976.00 0.298682
$$738$$ 0 0
$$739$$ −29068.0 −1.44693 −0.723467 0.690359i $$-0.757452\pi$$
−0.723467 + 0.690359i $$0.757452\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 28152.0 1.39004 0.695018 0.718992i $$-0.255396\pi$$
0.695018 + 0.718992i $$0.255396\pi$$
$$744$$ 0 0
$$745$$ 7350.00 0.361454
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 46376.0 2.26241
$$750$$ 0 0
$$751$$ 29916.0 1.45360 0.726798 0.686851i $$-0.241008\pi$$
0.726798 + 0.686851i $$0.241008\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −12960.0 −0.624719
$$756$$ 0 0
$$757$$ 32904.0 1.57981 0.789905 0.613229i $$-0.210130\pi$$
0.789905 + 0.613229i $$0.210130\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −21764.0 −1.03672 −0.518360 0.855162i $$-0.673457\pi$$
−0.518360 + 0.855162i $$0.673457\pi$$
$$762$$ 0 0
$$763$$ −7412.00 −0.351681
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 2088.00 0.0982964
$$768$$ 0 0
$$769$$ −3570.00 −0.167409 −0.0837045 0.996491i $$-0.526675\pi$$
−0.0837045 + 0.996491i $$0.526675\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −19486.0 −0.906679 −0.453339 0.891338i $$-0.649767\pi$$
−0.453339 + 0.891338i $$0.649767\pi$$
$$774$$ 0 0
$$775$$ −5100.00 −0.236384
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3520.00 0.161896
$$780$$ 0 0
$$781$$ −2376.00 −0.108860
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 16660.0 0.757479
$$786$$ 0 0
$$787$$ −19764.0 −0.895185 −0.447592 0.894238i $$-0.647718\pi$$
−0.447592 + 0.894238i $$0.647718\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −47124.0 −2.11825
$$792$$ 0 0
$$793$$ 2232.00 0.0999504
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 14390.0 0.639548 0.319774 0.947494i $$-0.396393\pi$$
0.319774 + 0.947494i $$0.396393\pi$$
$$798$$ 0 0
$$799$$ −56816.0 −2.51565
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 10836.0 0.476207
$$804$$ 0 0
$$805$$ −9520.00 −0.416815
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 28536.0 1.24014 0.620069 0.784547i $$-0.287104\pi$$
0.620069 + 0.784547i $$0.287104\pi$$
$$810$$ 0 0
$$811$$ −27732.0 −1.20074 −0.600371 0.799721i $$-0.704981\pi$$
−0.600371 + 0.799721i $$0.704981\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −3740.00 −0.160744
$$816$$ 0 0
$$817$$ −23584.0 −1.00991
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 8086.00 0.343731 0.171866 0.985120i $$-0.445021\pi$$
0.171866 + 0.985120i $$0.445021\pi$$
$$822$$ 0 0
$$823$$ −39854.0 −1.68800 −0.843999 0.536344i $$-0.819805\pi$$
−0.843999 + 0.536344i $$0.819805\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 17752.0 0.746430 0.373215 0.927745i $$-0.378255\pi$$
0.373215 + 0.927745i $$0.378255\pi$$
$$828$$ 0 0
$$829$$ 23858.0 0.999545 0.499772 0.866157i $$-0.333417\pi$$
0.499772 + 0.866157i $$0.333417\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −86178.0 −3.58450
$$834$$ 0 0
$$835$$ −12800.0 −0.530494
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −13888.0 −0.571474 −0.285737 0.958308i $$-0.592238\pi$$
−0.285737 + 0.958308i $$0.592238\pi$$
$$840$$ 0 0
$$841$$ 48511.0 1.98905
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 10265.0 0.417901
$$846$$ 0 0
$$847$$ 34238.0 1.38894
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −6720.00 −0.270692
$$852$$ 0 0
$$853$$ −16568.0 −0.665038 −0.332519 0.943097i $$-0.607899\pi$$
−0.332519 + 0.943097i $$0.607899\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −13034.0 −0.519525 −0.259763 0.965673i $$-0.583644\pi$$
−0.259763 + 0.965673i $$0.583644\pi$$
$$858$$ 0 0
$$859$$ 34356.0 1.36462 0.682312 0.731061i $$-0.260975\pi$$
0.682312 + 0.731061i $$0.260975\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −16016.0 −0.631739 −0.315870 0.948803i $$-0.602296\pi$$
−0.315870 + 0.948803i $$0.602296\pi$$
$$864$$ 0 0
$$865$$ −6030.00 −0.237024
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −9864.00 −0.385056
$$870$$ 0 0
$$871$$ −3984.00 −0.154986
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 4250.00 0.164201
$$876$$ 0 0
$$877$$ 19780.0 0.761600 0.380800 0.924657i $$-0.375649\pi$$
0.380800 + 0.924657i $$0.375649\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −41036.0 −1.56928 −0.784641 0.619950i $$-0.787153\pi$$
−0.784641 + 0.619950i $$0.787153\pi$$
$$882$$ 0 0
$$883$$ 35108.0 1.33803 0.669014 0.743250i $$-0.266717\pi$$
0.669014 + 0.743250i $$0.266717\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −18648.0 −0.705906 −0.352953 0.935641i $$-0.614822\pi$$
−0.352953 + 0.935641i $$0.614822\pi$$
$$888$$ 0 0
$$889$$ −27676.0 −1.04412
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 23584.0 0.883772
$$894$$ 0 0
$$895$$ −8470.00 −0.316336
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −55080.0 −2.04340
$$900$$ 0 0
$$901$$ −57452.0 −2.12431
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −18610.0 −0.683555
$$906$$ 0 0
$$907$$ −21688.0 −0.793978 −0.396989 0.917823i $$-0.629945\pi$$
−0.396989 + 0.917823i $$0.629945\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 42064.0 1.52979 0.764897 0.644153i $$-0.222790\pi$$
0.764897 + 0.644153i $$0.222790\pi$$
$$912$$ 0 0
$$913$$ −8856.00 −0.321020
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −43588.0 −1.56969
$$918$$ 0 0
$$919$$ 44420.0 1.59443 0.797215 0.603696i $$-0.206306\pi$$
0.797215 + 0.603696i $$0.206306\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 1584.00 0.0564875
$$924$$ 0 0
$$925$$ 3000.00 0.106637
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −17124.0 −0.604758 −0.302379 0.953188i $$-0.597781\pi$$
−0.302379 + 0.953188i $$0.597781\pi$$
$$930$$ 0 0
$$931$$ 35772.0 1.25927
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −9540.00 −0.333681
$$936$$ 0 0
$$937$$ −11110.0 −0.387351 −0.193675 0.981066i $$-0.562041\pi$$
−0.193675 + 0.981066i $$0.562041\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 12962.0 0.449043 0.224521 0.974469i $$-0.427918\pi$$
0.224521 + 0.974469i $$0.427918\pi$$
$$942$$ 0 0
$$943$$ −4480.00 −0.154707
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 25672.0 0.880916 0.440458 0.897773i $$-0.354816\pi$$
0.440458 + 0.897773i $$0.354816\pi$$
$$948$$ 0 0
$$949$$ −7224.00 −0.247103
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 2082.00 0.0707687 0.0353844 0.999374i $$-0.488734\pi$$
0.0353844 + 0.999374i $$0.488734\pi$$
$$954$$ 0 0
$$955$$ 14180.0 0.480475
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −104244. −3.51013
$$960$$ 0 0
$$961$$ 11825.0 0.396932
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 1170.00 0.0390297
$$966$$ 0 0
$$967$$ −5666.00 −0.188424 −0.0942121 0.995552i $$-0.530033\pi$$
−0.0942121 + 0.995552i $$0.530033\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −28622.0 −0.945956 −0.472978 0.881074i $$-0.656821\pi$$
−0.472978 + 0.881074i $$0.656821\pi$$
$$972$$ 0 0
$$973$$ −45288.0 −1.49215
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −24586.0 −0.805093 −0.402546 0.915400i $$-0.631875\pi$$
−0.402546 + 0.915400i $$0.631875\pi$$
$$978$$ 0 0
$$979$$ 18936.0 0.618179
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −40632.0 −1.31837 −0.659186 0.751980i $$-0.729099\pi$$
−0.659186 + 0.751980i $$0.729099\pi$$
$$984$$ 0 0
$$985$$ 19070.0 0.616874
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 30016.0 0.965069
$$990$$ 0 0
$$991$$ −8768.00 −0.281054 −0.140527 0.990077i $$-0.544880\pi$$
−0.140527 + 0.990077i $$0.544880\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 11760.0 0.374691
$$996$$ 0 0
$$997$$ 37212.0 1.18206 0.591031 0.806649i $$-0.298721\pi$$
0.591031 + 0.806649i $$0.298721\pi$$
$$998$$ 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 720.4.a.a.1.1 1
3.2 odd 2 720.4.a.p.1.1 1
4.3 odd 2 360.4.a.g.1.1 1
12.11 even 2 360.4.a.o.1.1 yes 1
20.3 even 4 1800.4.f.o.649.1 2
20.7 even 4 1800.4.f.o.649.2 2
20.19 odd 2 1800.4.a.b.1.1 1
60.23 odd 4 1800.4.f.i.649.1 2
60.47 odd 4 1800.4.f.i.649.2 2
60.59 even 2 1800.4.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
360.4.a.g.1.1 1 4.3 odd 2
360.4.a.o.1.1 yes 1 12.11 even 2
720.4.a.a.1.1 1 1.1 even 1 trivial
720.4.a.p.1.1 1 3.2 odd 2
1800.4.a.a.1.1 1 60.59 even 2
1800.4.a.b.1.1 1 20.19 odd 2
1800.4.f.i.649.1 2 60.23 odd 4
1800.4.f.i.649.2 2 60.47 odd 4
1800.4.f.o.649.1 2 20.3 even 4
1800.4.f.o.649.2 2 20.7 even 4