# Properties

 Label 2160.4.a.bo.1.3 Level $2160$ Weight $4$ Character 2160.1 Self dual yes Analytic conductor $127.444$ Analytic rank $1$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2160 = 2^{4} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2160.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$127.444125612$$ Analytic rank: $$1$$ Dimension: $$3$$ Coefficient field: 3.3.985.1 Defining polynomial: $$x^{3} - x^{2} - 6x + 1$$ x^3 - x^2 - 6*x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{3}\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 1080) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-2.09376$$ of defining polynomial Character $$\chi$$ $$=$$ 2160.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} +12.8657 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} +12.8657 q^{7} -18.2595 q^{11} +20.2595 q^{13} +6.65336 q^{17} -150.972 q^{19} +88.1068 q^{23} +25.0000 q^{25} -201.867 q^{29} +268.330 q^{31} +64.3283 q^{35} -123.539 q^{37} +275.174 q^{41} -488.679 q^{43} -436.725 q^{47} -177.475 q^{49} +340.573 q^{53} -91.2975 q^{55} -548.360 q^{59} -206.793 q^{61} +101.298 q^{65} -499.621 q^{67} +460.900 q^{71} -416.818 q^{73} -234.921 q^{77} +289.912 q^{79} -909.471 q^{83} +33.2668 q^{85} +186.814 q^{89} +260.652 q^{91} -754.862 q^{95} +648.440 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 15 q^{5} - 6 q^{7}+O(q^{10})$$ 3 * q + 15 * q^5 - 6 * q^7 $$3 q + 15 q^{5} - 6 q^{7} - 12 q^{11} + 18 q^{13} - 21 q^{17} - 57 q^{19} - 87 q^{23} + 75 q^{25} + 138 q^{29} - 117 q^{31} - 30 q^{35} + 150 q^{37} - 180 q^{43} - 684 q^{47} - 81 q^{49} + 87 q^{53} - 60 q^{55} - 714 q^{59} - 513 q^{61} + 90 q^{65} + 174 q^{67} - 768 q^{71} - 252 q^{73} + 888 q^{77} - 207 q^{79} - 1689 q^{83} - 105 q^{85} + 312 q^{89} - 900 q^{91} - 285 q^{95} - 1080 q^{97}+O(q^{100})$$ 3 * q + 15 * q^5 - 6 * q^7 - 12 * q^11 + 18 * q^13 - 21 * q^17 - 57 * q^19 - 87 * q^23 + 75 * q^25 + 138 * q^29 - 117 * q^31 - 30 * q^35 + 150 * q^37 - 180 * q^43 - 684 * q^47 - 81 * q^49 + 87 * q^53 - 60 * q^55 - 714 * q^59 - 513 * q^61 + 90 * q^65 + 174 * q^67 - 768 * q^71 - 252 * q^73 + 888 * q^77 - 207 * q^79 - 1689 * q^83 - 105 * q^85 + 312 * q^89 - 900 * q^91 - 285 * q^95 - 1080 * q^97

## 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
$$7$$ 12.8657 0.694680 0.347340 0.937739i $$-0.387085\pi$$
0.347340 + 0.937739i $$0.387085\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −18.2595 −0.500495 −0.250248 0.968182i $$-0.580512\pi$$
−0.250248 + 0.968182i $$0.580512\pi$$
$$12$$ 0 0
$$13$$ 20.2595 0.432229 0.216114 0.976368i $$-0.430662\pi$$
0.216114 + 0.976368i $$0.430662\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.65336 0.0949222 0.0474611 0.998873i $$-0.484887\pi$$
0.0474611 + 0.998873i $$0.484887\pi$$
$$18$$ 0 0
$$19$$ −150.972 −1.82292 −0.911459 0.411390i $$-0.865043\pi$$
−0.911459 + 0.411390i $$0.865043\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 88.1068 0.798762 0.399381 0.916785i $$-0.369225\pi$$
0.399381 + 0.916785i $$0.369225\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −201.867 −1.29261 −0.646306 0.763078i $$-0.723687\pi$$
−0.646306 + 0.763078i $$0.723687\pi$$
$$30$$ 0 0
$$31$$ 268.330 1.55463 0.777313 0.629114i $$-0.216582\pi$$
0.777313 + 0.629114i $$0.216582\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 64.3283 0.310670
$$36$$ 0 0
$$37$$ −123.539 −0.548909 −0.274455 0.961600i $$-0.588497\pi$$
−0.274455 + 0.961600i $$0.588497\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 275.174 1.04817 0.524084 0.851666i $$-0.324408\pi$$
0.524084 + 0.851666i $$0.324408\pi$$
$$42$$ 0 0
$$43$$ −488.679 −1.73309 −0.866545 0.499098i $$-0.833665\pi$$
−0.866545 + 0.499098i $$0.833665\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −436.725 −1.35538 −0.677691 0.735347i $$-0.737019\pi$$
−0.677691 + 0.735347i $$0.737019\pi$$
$$48$$ 0 0
$$49$$ −177.475 −0.517420
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 340.573 0.882665 0.441332 0.897344i $$-0.354506\pi$$
0.441332 + 0.897344i $$0.354506\pi$$
$$54$$ 0 0
$$55$$ −91.2975 −0.223828
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −548.360 −1.21001 −0.605004 0.796223i $$-0.706828\pi$$
−0.605004 + 0.796223i $$0.706828\pi$$
$$60$$ 0 0
$$61$$ −206.793 −0.434051 −0.217025 0.976166i $$-0.569635\pi$$
−0.217025 + 0.976166i $$0.569635\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 101.298 0.193299
$$66$$ 0 0
$$67$$ −499.621 −0.911021 −0.455511 0.890230i $$-0.650543\pi$$
−0.455511 + 0.890230i $$0.650543\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 460.900 0.770406 0.385203 0.922832i $$-0.374131\pi$$
0.385203 + 0.922832i $$0.374131\pi$$
$$72$$ 0 0
$$73$$ −416.818 −0.668285 −0.334143 0.942522i $$-0.608447\pi$$
−0.334143 + 0.942522i $$0.608447\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −234.921 −0.347684
$$78$$ 0 0
$$79$$ 289.912 0.412882 0.206441 0.978459i $$-0.433812\pi$$
0.206441 + 0.978459i $$0.433812\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −909.471 −1.20274 −0.601370 0.798971i $$-0.705378\pi$$
−0.601370 + 0.798971i $$0.705378\pi$$
$$84$$ 0 0
$$85$$ 33.2668 0.0424505
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 186.814 0.222497 0.111249 0.993793i $$-0.464515\pi$$
0.111249 + 0.993793i $$0.464515\pi$$
$$90$$ 0 0
$$91$$ 260.652 0.300261
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −754.862 −0.815234
$$96$$ 0 0
$$97$$ 648.440 0.678754 0.339377 0.940651i $$-0.389784\pi$$
0.339377 + 0.940651i $$0.389784\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1415.88 1.39490 0.697450 0.716634i $$-0.254318\pi$$
0.697450 + 0.716634i $$0.254318\pi$$
$$102$$ 0 0
$$103$$ 1199.94 1.14790 0.573949 0.818891i $$-0.305411\pi$$
0.573949 + 0.818891i $$0.305411\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1597.84 −1.44363 −0.721817 0.692084i $$-0.756693\pi$$
−0.721817 + 0.692084i $$0.756693\pi$$
$$108$$ 0 0
$$109$$ 1316.75 1.15708 0.578541 0.815653i $$-0.303622\pi$$
0.578541 + 0.815653i $$0.303622\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −806.519 −0.671425 −0.335712 0.941965i $$-0.608977\pi$$
−0.335712 + 0.941965i $$0.608977\pi$$
$$114$$ 0 0
$$115$$ 440.534 0.357217
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 85.5999 0.0659406
$$120$$ 0 0
$$121$$ −997.590 −0.749504
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ −1480.02 −1.03410 −0.517050 0.855955i $$-0.672970\pi$$
−0.517050 + 0.855955i $$0.672970\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 95.0432 0.0633890 0.0316945 0.999498i $$-0.489910\pi$$
0.0316945 + 0.999498i $$0.489910\pi$$
$$132$$ 0 0
$$133$$ −1942.36 −1.26635
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 793.417 0.494790 0.247395 0.968915i $$-0.420425\pi$$
0.247395 + 0.968915i $$0.420425\pi$$
$$138$$ 0 0
$$139$$ 24.6768 0.0150580 0.00752900 0.999972i $$-0.497603\pi$$
0.00752900 + 0.999972i $$0.497603\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −369.929 −0.216329
$$144$$ 0 0
$$145$$ −1009.33 −0.578074
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 3092.28 1.70020 0.850098 0.526624i $$-0.176543\pi$$
0.850098 + 0.526624i $$0.176543\pi$$
$$150$$ 0 0
$$151$$ −2056.52 −1.10832 −0.554162 0.832409i $$-0.686961\pi$$
−0.554162 + 0.832409i $$0.686961\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1341.65 0.695250
$$156$$ 0 0
$$157$$ −649.944 −0.330390 −0.165195 0.986261i $$-0.552825\pi$$
−0.165195 + 0.986261i $$0.552825\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1133.55 0.554884
$$162$$ 0 0
$$163$$ −3183.46 −1.52974 −0.764870 0.644185i $$-0.777197\pi$$
−0.764870 + 0.644185i $$0.777197\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −743.307 −0.344424 −0.172212 0.985060i $$-0.555091\pi$$
−0.172212 + 0.985060i $$0.555091\pi$$
$$168$$ 0 0
$$169$$ −1786.55 −0.813178
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2152.84 0.946113 0.473057 0.881032i $$-0.343151\pi$$
0.473057 + 0.881032i $$0.343151\pi$$
$$174$$ 0 0
$$175$$ 321.641 0.138936
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 597.624 0.249545 0.124772 0.992185i $$-0.460180\pi$$
0.124772 + 0.992185i $$0.460180\pi$$
$$180$$ 0 0
$$181$$ −736.338 −0.302384 −0.151192 0.988504i $$-0.548311\pi$$
−0.151192 + 0.988504i $$0.548311\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −617.693 −0.245480
$$186$$ 0 0
$$187$$ −121.487 −0.0475081
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3355.19 −1.27106 −0.635531 0.772075i $$-0.719219\pi$$
−0.635531 + 0.772075i $$0.719219\pi$$
$$192$$ 0 0
$$193$$ 1521.54 0.567475 0.283737 0.958902i $$-0.408426\pi$$
0.283737 + 0.958902i $$0.408426\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 364.341 0.131768 0.0658838 0.997827i $$-0.479013\pi$$
0.0658838 + 0.997827i $$0.479013\pi$$
$$198$$ 0 0
$$199$$ 171.730 0.0611738 0.0305869 0.999532i $$-0.490262\pi$$
0.0305869 + 0.999532i $$0.490262\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −2597.15 −0.897952
$$204$$ 0 0
$$205$$ 1375.87 0.468755
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2756.68 0.912362
$$210$$ 0 0
$$211$$ −904.632 −0.295154 −0.147577 0.989051i $$-0.547147\pi$$
−0.147577 + 0.989051i $$0.547147\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −2443.40 −0.775062
$$216$$ 0 0
$$217$$ 3452.24 1.07997
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 134.794 0.0410281
$$222$$ 0 0
$$223$$ −405.423 −0.121745 −0.0608724 0.998146i $$-0.519388\pi$$
−0.0608724 + 0.998146i $$0.519388\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −556.762 −0.162791 −0.0813956 0.996682i $$-0.525938\pi$$
−0.0813956 + 0.996682i $$0.525938\pi$$
$$228$$ 0 0
$$229$$ −4584.45 −1.32292 −0.661461 0.749979i $$-0.730063\pi$$
−0.661461 + 0.749979i $$0.730063\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4593.97 1.29168 0.645839 0.763473i $$-0.276508\pi$$
0.645839 + 0.763473i $$0.276508\pi$$
$$234$$ 0 0
$$235$$ −2183.63 −0.606145
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1754.22 −0.474775 −0.237387 0.971415i $$-0.576291\pi$$
−0.237387 + 0.971415i $$0.576291\pi$$
$$240$$ 0 0
$$241$$ −4394.90 −1.17469 −0.587346 0.809336i $$-0.699827\pi$$
−0.587346 + 0.809336i $$0.699827\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −887.375 −0.231397
$$246$$ 0 0
$$247$$ −3058.63 −0.787918
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −2260.13 −0.568360 −0.284180 0.958771i $$-0.591721\pi$$
−0.284180 + 0.958771i $$0.591721\pi$$
$$252$$ 0 0
$$253$$ −1608.79 −0.399777
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −570.878 −0.138562 −0.0692809 0.997597i $$-0.522070\pi$$
−0.0692809 + 0.997597i $$0.522070\pi$$
$$258$$ 0 0
$$259$$ −1589.41 −0.381316
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6248.85 1.46510 0.732549 0.680715i $$-0.238331\pi$$
0.732549 + 0.680715i $$0.238331\pi$$
$$264$$ 0 0
$$265$$ 1702.86 0.394740
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1718.42 −0.389494 −0.194747 0.980853i $$-0.562389\pi$$
−0.194747 + 0.980853i $$0.562389\pi$$
$$270$$ 0 0
$$271$$ −883.253 −0.197985 −0.0989923 0.995088i $$-0.531562\pi$$
−0.0989923 + 0.995088i $$0.531562\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −456.488 −0.100099
$$276$$ 0 0
$$277$$ −4889.06 −1.06049 −0.530244 0.847845i $$-0.677900\pi$$
−0.530244 + 0.847845i $$0.677900\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −3590.34 −0.762212 −0.381106 0.924531i $$-0.624457\pi$$
−0.381106 + 0.924531i $$0.624457\pi$$
$$282$$ 0 0
$$283$$ 2003.82 0.420900 0.210450 0.977605i $$-0.432507\pi$$
0.210450 + 0.977605i $$0.432507\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 3540.29 0.728142
$$288$$ 0 0
$$289$$ −4868.73 −0.990990
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 4348.62 0.867062 0.433531 0.901139i $$-0.357267\pi$$
0.433531 + 0.901139i $$0.357267\pi$$
$$294$$ 0 0
$$295$$ −2741.80 −0.541132
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1785.00 0.345248
$$300$$ 0 0
$$301$$ −6287.18 −1.20394
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1033.96 −0.194113
$$306$$ 0 0
$$307$$ −7513.36 −1.39678 −0.698388 0.715719i $$-0.746099\pi$$
−0.698388 + 0.715719i $$0.746099\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 624.265 0.113823 0.0569113 0.998379i $$-0.481875\pi$$
0.0569113 + 0.998379i $$0.481875\pi$$
$$312$$ 0 0
$$313$$ −1963.18 −0.354521 −0.177261 0.984164i $$-0.556724\pi$$
−0.177261 + 0.984164i $$0.556724\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2928.29 0.518829 0.259415 0.965766i $$-0.416470\pi$$
0.259415 + 0.965766i $$0.416470\pi$$
$$318$$ 0 0
$$319$$ 3685.99 0.646946
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1004.47 −0.173035
$$324$$ 0 0
$$325$$ 506.488 0.0864458
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −5618.76 −0.941556
$$330$$ 0 0
$$331$$ −3619.06 −0.600972 −0.300486 0.953786i $$-0.597149\pi$$
−0.300486 + 0.953786i $$0.597149\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −2498.11 −0.407421
$$336$$ 0 0
$$337$$ −9440.02 −1.52591 −0.762954 0.646453i $$-0.776251\pi$$
−0.762954 + 0.646453i $$0.776251\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −4899.57 −0.778083
$$342$$ 0 0
$$343$$ −6696.25 −1.05412
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1657.99 −0.256500 −0.128250 0.991742i $$-0.540936\pi$$
−0.128250 + 0.991742i $$0.540936\pi$$
$$348$$ 0 0
$$349$$ −4537.03 −0.695879 −0.347939 0.937517i $$-0.613119\pi$$
−0.347939 + 0.937517i $$0.613119\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −8627.43 −1.30083 −0.650413 0.759580i $$-0.725404\pi$$
−0.650413 + 0.759580i $$0.725404\pi$$
$$354$$ 0 0
$$355$$ 2304.50 0.344536
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −10116.5 −1.48726 −0.743631 0.668590i $$-0.766898\pi$$
−0.743631 + 0.668590i $$0.766898\pi$$
$$360$$ 0 0
$$361$$ 15933.7 2.32303
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2084.09 −0.298866
$$366$$ 0 0
$$367$$ −4707.74 −0.669597 −0.334798 0.942290i $$-0.608668\pi$$
−0.334798 + 0.942290i $$0.608668\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 4381.69 0.613170
$$372$$ 0 0
$$373$$ −14191.2 −1.96995 −0.984973 0.172706i $$-0.944749\pi$$
−0.984973 + 0.172706i $$0.944749\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4089.73 −0.558704
$$378$$ 0 0
$$379$$ −8841.08 −1.19825 −0.599124 0.800656i $$-0.704484\pi$$
−0.599124 + 0.800656i $$0.704484\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 6225.37 0.830553 0.415276 0.909695i $$-0.363685\pi$$
0.415276 + 0.909695i $$0.363685\pi$$
$$384$$ 0 0
$$385$$ −1174.60 −0.155489
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3967.13 0.517074 0.258537 0.966001i $$-0.416760\pi$$
0.258537 + 0.966001i $$0.416760\pi$$
$$390$$ 0 0
$$391$$ 586.206 0.0758203
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 1449.56 0.184646
$$396$$ 0 0
$$397$$ 10510.6 1.32875 0.664375 0.747399i $$-0.268698\pi$$
0.664375 + 0.747399i $$0.268698\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 6440.92 0.802105 0.401052 0.916055i $$-0.368645\pi$$
0.401052 + 0.916055i $$0.368645\pi$$
$$402$$ 0 0
$$403$$ 5436.22 0.671954
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2255.76 0.274726
$$408$$ 0 0
$$409$$ −4820.75 −0.582813 −0.291407 0.956599i $$-0.594123\pi$$
−0.291407 + 0.956599i $$0.594123\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −7055.01 −0.840568
$$414$$ 0 0
$$415$$ −4547.36 −0.537882
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 17003.8 1.98255 0.991276 0.131803i $$-0.0420767\pi$$
0.991276 + 0.131803i $$0.0420767\pi$$
$$420$$ 0 0
$$421$$ 1582.86 0.183239 0.0916197 0.995794i $$-0.470796\pi$$
0.0916197 + 0.995794i $$0.470796\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 166.334 0.0189844
$$426$$ 0 0
$$427$$ −2660.52 −0.301526
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 10518.7 1.17557 0.587784 0.809018i $$-0.300001\pi$$
0.587784 + 0.809018i $$0.300001\pi$$
$$432$$ 0 0
$$433$$ −5469.93 −0.607086 −0.303543 0.952818i $$-0.598170\pi$$
−0.303543 + 0.952818i $$0.598170\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −13301.7 −1.45608
$$438$$ 0 0
$$439$$ 12068.3 1.31205 0.656024 0.754740i $$-0.272237\pi$$
0.656024 + 0.754740i $$0.272237\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 9948.23 1.06694 0.533470 0.845819i $$-0.320888\pi$$
0.533470 + 0.845819i $$0.320888\pi$$
$$444$$ 0 0
$$445$$ 934.071 0.0995039
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −12449.4 −1.30852 −0.654258 0.756271i $$-0.727019\pi$$
−0.654258 + 0.756271i $$0.727019\pi$$
$$450$$ 0 0
$$451$$ −5024.54 −0.524603
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 1303.26 0.134281
$$456$$ 0 0
$$457$$ 15270.3 1.56305 0.781524 0.623875i $$-0.214442\pi$$
0.781524 + 0.623875i $$0.214442\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 11670.3 1.17905 0.589524 0.807751i $$-0.299315\pi$$
0.589524 + 0.807751i $$0.299315\pi$$
$$462$$ 0 0
$$463$$ 9205.75 0.924033 0.462017 0.886871i $$-0.347126\pi$$
0.462017 + 0.886871i $$0.347126\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −12090.0 −1.19799 −0.598994 0.800754i $$-0.704433\pi$$
−0.598994 + 0.800754i $$0.704433\pi$$
$$468$$ 0 0
$$469$$ −6427.95 −0.632868
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 8923.04 0.867404
$$474$$ 0 0
$$475$$ −3774.31 −0.364584
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −3804.88 −0.362942 −0.181471 0.983396i $$-0.558086\pi$$
−0.181471 + 0.983396i $$0.558086\pi$$
$$480$$ 0 0
$$481$$ −2502.83 −0.237254
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 3242.20 0.303548
$$486$$ 0 0
$$487$$ −5679.19 −0.528437 −0.264218 0.964463i $$-0.585114\pi$$
−0.264218 + 0.964463i $$0.585114\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7710.36 −0.708684 −0.354342 0.935116i $$-0.615295\pi$$
−0.354342 + 0.935116i $$0.615295\pi$$
$$492$$ 0 0
$$493$$ −1343.09 −0.122698
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 5929.78 0.535185
$$498$$ 0 0
$$499$$ 7766.60 0.696755 0.348378 0.937354i $$-0.386733\pi$$
0.348378 + 0.937354i $$0.386733\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −8393.87 −0.744064 −0.372032 0.928220i $$-0.621339\pi$$
−0.372032 + 0.928220i $$0.621339\pi$$
$$504$$ 0 0
$$505$$ 7079.38 0.623818
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −14775.6 −1.28667 −0.643337 0.765583i $$-0.722451\pi$$
−0.643337 + 0.765583i $$0.722451\pi$$
$$510$$ 0 0
$$511$$ −5362.63 −0.464245
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 5999.70 0.513356
$$516$$ 0 0
$$517$$ 7974.39 0.678362
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −21089.0 −1.77337 −0.886684 0.462376i $$-0.846997\pi$$
−0.886684 + 0.462376i $$0.846997\pi$$
$$522$$ 0 0
$$523$$ −860.536 −0.0719476 −0.0359738 0.999353i $$-0.511453\pi$$
−0.0359738 + 0.999353i $$0.511453\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 1785.29 0.147569
$$528$$ 0 0
$$529$$ −4404.19 −0.361979
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 5574.88 0.453049
$$534$$ 0 0
$$535$$ −7989.19 −0.645613
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3240.61 0.258966
$$540$$ 0 0
$$541$$ −23226.2 −1.84579 −0.922895 0.385051i $$-0.874184\pi$$
−0.922895 + 0.385051i $$0.874184\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 6583.76 0.517463
$$546$$ 0 0
$$547$$ −11800.1 −0.922371 −0.461185 0.887304i $$-0.652576\pi$$
−0.461185 + 0.887304i $$0.652576\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 30476.3 2.35633
$$552$$ 0 0
$$553$$ 3729.91 0.286821
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −13654.7 −1.03872 −0.519361 0.854555i $$-0.673830\pi$$
−0.519361 + 0.854555i $$0.673830\pi$$
$$558$$ 0 0
$$559$$ −9900.40 −0.749092
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12390.2 0.927502 0.463751 0.885966i $$-0.346503\pi$$
0.463751 + 0.885966i $$0.346503\pi$$
$$564$$ 0 0
$$565$$ −4032.60 −0.300270
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −12361.4 −0.910753 −0.455376 0.890299i $$-0.650495\pi$$
−0.455376 + 0.890299i $$0.650495\pi$$
$$570$$ 0 0
$$571$$ 20577.3 1.50812 0.754058 0.656807i $$-0.228094\pi$$
0.754058 + 0.656807i $$0.228094\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 2202.67 0.159752
$$576$$ 0 0
$$577$$ 18345.2 1.32361 0.661803 0.749678i $$-0.269791\pi$$
0.661803 + 0.749678i $$0.269791\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −11700.9 −0.835520
$$582$$ 0 0
$$583$$ −6218.69 −0.441770
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 19713.9 1.38617 0.693085 0.720856i $$-0.256251\pi$$
0.693085 + 0.720856i $$0.256251\pi$$
$$588$$ 0 0
$$589$$ −40510.4 −2.83396
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −6553.49 −0.453827 −0.226914 0.973915i $$-0.572864\pi$$
−0.226914 + 0.973915i $$0.572864\pi$$
$$594$$ 0 0
$$595$$ 427.999 0.0294895
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −15005.2 −1.02354 −0.511768 0.859124i $$-0.671009\pi$$
−0.511768 + 0.859124i $$0.671009\pi$$
$$600$$ 0 0
$$601$$ −20290.4 −1.37714 −0.688572 0.725168i $$-0.741762\pi$$
−0.688572 + 0.725168i $$0.741762\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −4987.95 −0.335189
$$606$$ 0 0
$$607$$ −11867.6 −0.793563 −0.396781 0.917913i $$-0.629873\pi$$
−0.396781 + 0.917913i $$0.629873\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8847.84 −0.585835
$$612$$ 0 0
$$613$$ 27850.2 1.83501 0.917503 0.397730i $$-0.130202\pi$$
0.917503 + 0.397730i $$0.130202\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 4116.33 0.268586 0.134293 0.990942i $$-0.457124\pi$$
0.134293 + 0.990942i $$0.457124\pi$$
$$618$$ 0 0
$$619$$ 25022.4 1.62478 0.812388 0.583117i $$-0.198167\pi$$
0.812388 + 0.583117i $$0.198167\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 2403.49 0.154565
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −821.948 −0.0521037
$$630$$ 0 0
$$631$$ −17801.6 −1.12309 −0.561545 0.827446i $$-0.689793\pi$$
−0.561545 + 0.827446i $$0.689793\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −7400.10 −0.462463
$$636$$ 0 0
$$637$$ −3595.56 −0.223644
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 19325.4 1.19081 0.595405 0.803426i $$-0.296992\pi$$
0.595405 + 0.803426i $$0.296992\pi$$
$$642$$ 0 0
$$643$$ −267.444 −0.0164028 −0.00820138 0.999966i $$-0.502611\pi$$
−0.00820138 + 0.999966i $$0.502611\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18749.2 1.13927 0.569634 0.821898i $$-0.307085\pi$$
0.569634 + 0.821898i $$0.307085\pi$$
$$648$$ 0 0
$$649$$ 10012.8 0.605603
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −14996.0 −0.898684 −0.449342 0.893360i $$-0.648341\pi$$
−0.449342 + 0.893360i $$0.648341\pi$$
$$654$$ 0 0
$$655$$ 475.216 0.0283484
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −19249.4 −1.13786 −0.568929 0.822386i $$-0.692642\pi$$
−0.568929 + 0.822386i $$0.692642\pi$$
$$660$$ 0 0
$$661$$ 12989.7 0.764357 0.382178 0.924089i $$-0.375174\pi$$
0.382178 + 0.924089i $$0.375174\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −9711.80 −0.566327
$$666$$ 0 0
$$667$$ −17785.8 −1.03249
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 3775.93 0.217240
$$672$$ 0 0
$$673$$ −5909.54 −0.338478 −0.169239 0.985575i $$-0.554131\pi$$
−0.169239 + 0.985575i $$0.554131\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 23548.5 1.33684 0.668420 0.743784i $$-0.266971\pi$$
0.668420 + 0.743784i $$0.266971\pi$$
$$678$$ 0 0
$$679$$ 8342.60 0.471516
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 10065.3 0.563890 0.281945 0.959431i $$-0.409020\pi$$
0.281945 + 0.959431i $$0.409020\pi$$
$$684$$ 0 0
$$685$$ 3967.09 0.221277
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 6899.83 0.381513
$$690$$ 0 0
$$691$$ 28648.5 1.57720 0.788598 0.614910i $$-0.210807\pi$$
0.788598 + 0.614910i $$0.210807\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 123.384 0.00673414
$$696$$ 0 0
$$697$$ 1830.83 0.0994945
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30910.9 1.66546 0.832730 0.553679i $$-0.186777\pi$$
0.832730 + 0.553679i $$0.186777\pi$$
$$702$$ 0 0
$$703$$ 18650.9 1.00062
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 18216.2 0.969009
$$708$$ 0 0
$$709$$ 11680.0 0.618691 0.309345 0.950950i $$-0.399890\pi$$
0.309345 + 0.950950i $$0.399890\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 23641.7 1.24178
$$714$$ 0 0
$$715$$ −1849.64 −0.0967451
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −9205.71 −0.477489 −0.238745 0.971082i $$-0.576736\pi$$
−0.238745 + 0.971082i $$0.576736\pi$$
$$720$$ 0 0
$$721$$ 15438.0 0.797422
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −5046.67 −0.258522
$$726$$ 0 0
$$727$$ −8102.51 −0.413350 −0.206675 0.978410i $$-0.566264\pi$$
−0.206675 + 0.978410i $$0.566264\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −3251.36 −0.164509
$$732$$ 0 0
$$733$$ −33738.0 −1.70006 −0.850028 0.526737i $$-0.823415\pi$$
−0.850028 + 0.526737i $$0.823415\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 9122.84 0.455962
$$738$$ 0 0
$$739$$ 28667.6 1.42700 0.713502 0.700653i $$-0.247108\pi$$
0.713502 + 0.700653i $$0.247108\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2344.60 −0.115767 −0.0578837 0.998323i $$-0.518435\pi$$
−0.0578837 + 0.998323i $$0.518435\pi$$
$$744$$ 0 0
$$745$$ 15461.4 0.760351
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −20557.2 −1.00286
$$750$$ 0 0
$$751$$ 23466.1 1.14020 0.570101 0.821575i $$-0.306904\pi$$
0.570101 + 0.821575i $$0.306904\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10282.6 −0.495658
$$756$$ 0 0
$$757$$ 5711.42 0.274221 0.137110 0.990556i $$-0.456219\pi$$
0.137110 + 0.990556i $$0.456219\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 8101.10 0.385893 0.192947 0.981209i $$-0.438196\pi$$
0.192947 + 0.981209i $$0.438196\pi$$
$$762$$ 0 0
$$763$$ 16940.9 0.803802
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −11109.5 −0.523000
$$768$$ 0 0
$$769$$ 19468.4 0.912937 0.456468 0.889740i $$-0.349114\pi$$
0.456468 + 0.889740i $$0.349114\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 9632.96 0.448219 0.224110 0.974564i $$-0.428053\pi$$
0.224110 + 0.974564i $$0.428053\pi$$
$$774$$ 0 0
$$775$$ 6708.24 0.310925
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −41543.6 −1.91073
$$780$$ 0 0
$$781$$ −8415.81 −0.385584
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −3249.72 −0.147755
$$786$$ 0 0
$$787$$ −38781.5 −1.75656 −0.878278 0.478150i $$-0.841308\pi$$
−0.878278 + 0.478150i $$0.841308\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −10376.4 −0.466425
$$792$$ 0 0
$$793$$ −4189.52 −0.187609
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 7148.58 0.317711 0.158856 0.987302i $$-0.449220\pi$$
0.158856 + 0.987302i $$0.449220\pi$$
$$798$$ 0 0
$$799$$ −2905.69 −0.128656
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 7610.89 0.334474
$$804$$ 0 0
$$805$$ 5667.76 0.248152
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −9156.29 −0.397921 −0.198960 0.980008i $$-0.563757\pi$$
−0.198960 + 0.980008i $$0.563757\pi$$
$$810$$ 0 0
$$811$$ −21877.2 −0.947241 −0.473621 0.880729i $$-0.657053\pi$$
−0.473621 + 0.880729i $$0.657053\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −15917.3 −0.684120
$$816$$ 0 0
$$817$$ 73777.1 3.15928
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −33923.3 −1.44206 −0.721030 0.692903i $$-0.756331\pi$$
−0.721030 + 0.692903i $$0.756331\pi$$
$$822$$ 0 0
$$823$$ 6357.76 0.269280 0.134640 0.990895i $$-0.457012\pi$$
0.134640 + 0.990895i $$0.457012\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −8059.61 −0.338887 −0.169444 0.985540i $$-0.554197\pi$$
−0.169444 + 0.985540i $$0.554197\pi$$
$$828$$ 0 0
$$829$$ −25496.5 −1.06819 −0.534095 0.845425i $$-0.679347\pi$$
−0.534095 + 0.845425i $$0.679347\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1180.81 −0.0491146
$$834$$ 0 0
$$835$$ −3716.54 −0.154031
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 31917.6 1.31337 0.656686 0.754164i $$-0.271958\pi$$
0.656686 + 0.754164i $$0.271958\pi$$
$$840$$ 0 0
$$841$$ 16361.3 0.670846
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −8932.76 −0.363664
$$846$$ 0 0
$$847$$ −12834.7 −0.520666
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −10884.6 −0.438448
$$852$$ 0 0
$$853$$ −28295.7 −1.13579 −0.567893 0.823102i $$-0.692241\pi$$
−0.567893 + 0.823102i $$0.692241\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 41896.2 1.66995 0.834975 0.550288i $$-0.185482\pi$$
0.834975 + 0.550288i $$0.185482\pi$$
$$858$$ 0 0
$$859$$ 18124.5 0.719907 0.359953 0.932970i $$-0.382793\pi$$
0.359953 + 0.932970i $$0.382793\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −25361.4 −1.00036 −0.500182 0.865921i $$-0.666733\pi$$
−0.500182 + 0.865921i $$0.666733\pi$$
$$864$$ 0 0
$$865$$ 10764.2 0.423115
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −5293.66 −0.206646
$$870$$ 0 0
$$871$$ −10122.1 −0.393770
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 1608.21 0.0621341
$$876$$ 0 0
$$877$$ 28128.7 1.08306 0.541528 0.840683i $$-0.317846\pi$$
0.541528 + 0.840683i $$0.317846\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −12198.2 −0.466481 −0.233240 0.972419i $$-0.574933\pi$$
−0.233240 + 0.972419i $$0.574933\pi$$
$$882$$ 0 0
$$883$$ 15725.2 0.599317 0.299658 0.954047i $$-0.403127\pi$$
0.299658 + 0.954047i $$0.403127\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −3176.83 −0.120257 −0.0601283 0.998191i $$-0.519151\pi$$
−0.0601283 + 0.998191i $$0.519151\pi$$
$$888$$ 0 0
$$889$$ −19041.4 −0.718368
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 65933.5 2.47075
$$894$$ 0 0
$$895$$ 2988.12 0.111600
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −54166.9 −2.00953
$$900$$ 0 0
$$901$$ 2265.95 0.0837845
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −3681.69 −0.135230
$$906$$ 0 0
$$907$$ 11400.8 0.417374 0.208687 0.977982i $$-0.433081\pi$$
0.208687 + 0.977982i $$0.433081\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 9547.78 0.347236 0.173618 0.984813i $$-0.444454\pi$$
0.173618 + 0.984813i $$0.444454\pi$$
$$912$$ 0 0
$$913$$ 16606.5 0.601966
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 1222.79 0.0440351
$$918$$ 0 0
$$919$$ 47127.5 1.69161 0.845807 0.533488i $$-0.179119\pi$$
0.845807 + 0.533488i $$0.179119\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 9337.61 0.332992
$$924$$ 0 0
$$925$$ −3088.47 −0.109782
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 25591.7 0.903807 0.451904 0.892067i $$-0.350745\pi$$
0.451904 + 0.892067i $$0.350745\pi$$
$$930$$ 0 0
$$931$$ 26793.8 0.943214
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −607.436 −0.0212463
$$936$$ 0 0
$$937$$ 47575.6 1.65873 0.829364 0.558709i $$-0.188703\pi$$
0.829364 + 0.558709i $$0.188703\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 42722.0 1.48002 0.740009 0.672597i $$-0.234821\pi$$
0.740009 + 0.672597i $$0.234821\pi$$
$$942$$ 0 0
$$943$$ 24244.7 0.837238
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 19523.9 0.669948 0.334974 0.942227i $$-0.391272\pi$$
0.334974 + 0.942227i $$0.391272\pi$$
$$948$$ 0 0
$$949$$ −8444.52 −0.288852
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 6129.73 0.208354 0.104177 0.994559i $$-0.466779\pi$$
0.104177 + 0.994559i $$0.466779\pi$$
$$954$$ 0 0
$$955$$ −16775.9 −0.568436
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 10207.8 0.343721
$$960$$ 0 0
$$961$$ 42209.8 1.41686
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 7607.68 0.253782
$$966$$ 0 0
$$967$$ 33974.3 1.12982 0.564912 0.825151i $$-0.308910\pi$$
0.564912 + 0.825151i $$0.308910\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −28328.7 −0.936262 −0.468131 0.883659i $$-0.655072\pi$$
−0.468131 + 0.883659i $$0.655072\pi$$
$$972$$ 0 0
$$973$$ 317.484 0.0104605
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −37587.6 −1.23084 −0.615421 0.788198i $$-0.711014\pi$$
−0.615421 + 0.788198i $$0.711014\pi$$
$$978$$ 0 0
$$979$$ −3411.14 −0.111359
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 5777.92 0.187474 0.0937371 0.995597i $$-0.470119\pi$$
0.0937371 + 0.995597i $$0.470119\pi$$
$$984$$ 0 0
$$985$$ 1821.71 0.0589283
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −43056.0 −1.38433
$$990$$ 0 0
$$991$$ 45377.5 1.45455 0.727277 0.686344i $$-0.240785\pi$$
0.727277 + 0.686344i $$0.240785\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 858.648 0.0273578
$$996$$ 0 0
$$997$$ −6994.90 −0.222197 −0.111099 0.993809i $$-0.535437\pi$$
−0.111099 + 0.993809i $$0.535437\pi$$
$$998$$ 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 2160.4.a.bo.1.3 3
3.2 odd 2 2160.4.a.bg.1.3 3
4.3 odd 2 1080.4.a.m.1.1 yes 3
12.11 even 2 1080.4.a.g.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
1080.4.a.g.1.1 3 12.11 even 2
1080.4.a.m.1.1 yes 3 4.3 odd 2
2160.4.a.bg.1.3 3 3.2 odd 2
2160.4.a.bo.1.3 3 1.1 even 1 trivial