# Properties

 Label 6400.2.a.bv.1.1 Level $6400$ Weight $2$ Character 6400.1 Self dual yes Analytic conductor $51.104$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6400 = 2^{8} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6400.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$51.1042572936$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{6})$$ Defining polynomial: $$x^{2} - 6$$ x^2 - 6 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 640) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-2.44949$$ of defining polynomial Character $$\chi$$ $$=$$ 6400.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.44949 q^{3} -2.44949 q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-2.44949 q^{3} -2.44949 q^{7} +3.00000 q^{9} -4.89898 q^{11} -4.00000 q^{17} +4.89898 q^{19} +6.00000 q^{21} -2.44949 q^{23} +8.00000 q^{29} -9.79796 q^{31} +12.0000 q^{33} -4.00000 q^{37} -8.00000 q^{41} -7.34847 q^{43} -12.2474 q^{47} -1.00000 q^{49} +9.79796 q^{51} -8.00000 q^{53} -12.0000 q^{57} -4.89898 q^{59} +6.00000 q^{61} -7.34847 q^{63} -2.44949 q^{67} +6.00000 q^{69} +9.79796 q^{71} -4.00000 q^{73} +12.0000 q^{77} -9.79796 q^{79} -9.00000 q^{81} +2.44949 q^{83} -19.5959 q^{87} +2.00000 q^{89} +24.0000 q^{93} +4.00000 q^{97} -14.6969 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 6 q^{9}+O(q^{10})$$ 2 * q + 6 * q^9 $$2 q + 6 q^{9} - 8 q^{17} + 12 q^{21} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 16 q^{41} - 2 q^{49} - 16 q^{53} - 24 q^{57} + 12 q^{61} + 12 q^{69} - 8 q^{73} + 24 q^{77} - 18 q^{81} + 4 q^{89} + 48 q^{93} + 8 q^{97}+O(q^{100})$$ 2 * q + 6 * q^9 - 8 * q^17 + 12 * q^21 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 16 * q^41 - 2 * q^49 - 16 * q^53 - 24 * q^57 + 12 * q^61 + 12 * q^69 - 8 * q^73 + 24 * q^77 - 18 * q^81 + 4 * q^89 + 48 * q^93 + 8 * 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
$$3$$ −2.44949 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −2.44949 −0.925820 −0.462910 0.886405i $$-0.653195\pi$$
−0.462910 + 0.886405i $$0.653195\pi$$
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ −4.89898 −1.47710 −0.738549 0.674200i $$-0.764489\pi$$
−0.738549 + 0.674200i $$0.764489\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ 4.89898 1.12390 0.561951 0.827170i $$-0.310051\pi$$
0.561951 + 0.827170i $$0.310051\pi$$
$$20$$ 0 0
$$21$$ 6.00000 1.30931
$$22$$ 0 0
$$23$$ −2.44949 −0.510754 −0.255377 0.966842i $$-0.582200\pi$$
−0.255377 + 0.966842i $$0.582200\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 8.00000 1.48556 0.742781 0.669534i $$-0.233506\pi$$
0.742781 + 0.669534i $$0.233506\pi$$
$$30$$ 0 0
$$31$$ −9.79796 −1.75977 −0.879883 0.475191i $$-0.842379\pi$$
−0.879883 + 0.475191i $$0.842379\pi$$
$$32$$ 0 0
$$33$$ 12.0000 2.08893
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −8.00000 −1.24939 −0.624695 0.780869i $$-0.714777\pi$$
−0.624695 + 0.780869i $$0.714777\pi$$
$$42$$ 0 0
$$43$$ −7.34847 −1.12063 −0.560316 0.828279i $$-0.689320\pi$$
−0.560316 + 0.828279i $$0.689320\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −12.2474 −1.78647 −0.893237 0.449586i $$-0.851571\pi$$
−0.893237 + 0.449586i $$0.851571\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 9.79796 1.37199
$$52$$ 0 0
$$53$$ −8.00000 −1.09888 −0.549442 0.835532i $$-0.685160\pi$$
−0.549442 + 0.835532i $$0.685160\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −12.0000 −1.58944
$$58$$ 0 0
$$59$$ −4.89898 −0.637793 −0.318896 0.947790i $$-0.603312\pi$$
−0.318896 + 0.947790i $$0.603312\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 0 0
$$63$$ −7.34847 −0.925820
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.44949 −0.299253 −0.149626 0.988743i $$-0.547807\pi$$
−0.149626 + 0.988743i $$0.547807\pi$$
$$68$$ 0 0
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ 9.79796 1.16280 0.581402 0.813617i $$-0.302504\pi$$
0.581402 + 0.813617i $$0.302504\pi$$
$$72$$ 0 0
$$73$$ −4.00000 −0.468165 −0.234082 0.972217i $$-0.575209\pi$$
−0.234082 + 0.972217i $$0.575209\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 12.0000 1.36753
$$78$$ 0 0
$$79$$ −9.79796 −1.10236 −0.551178 0.834388i $$-0.685822\pi$$
−0.551178 + 0.834388i $$0.685822\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 0 0
$$83$$ 2.44949 0.268866 0.134433 0.990923i $$-0.457079\pi$$
0.134433 + 0.990923i $$0.457079\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −19.5959 −2.10090
$$88$$ 0 0
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 24.0000 2.48868
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 4.00000 0.406138 0.203069 0.979164i $$-0.434908\pi$$
0.203069 + 0.979164i $$0.434908\pi$$
$$98$$ 0 0
$$99$$ −14.6969 −1.47710
$$100$$ 0 0
$$101$$ 8.00000 0.796030 0.398015 0.917379i $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ 0 0
$$103$$ −2.44949 −0.241355 −0.120678 0.992692i $$-0.538507\pi$$
−0.120678 + 0.992692i $$0.538507\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −7.34847 −0.710403 −0.355202 0.934790i $$-0.615588\pi$$
−0.355202 + 0.934790i $$0.615588\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ 9.79796 0.929981
$$112$$ 0 0
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 9.79796 0.898177
$$120$$ 0 0
$$121$$ 13.0000 1.18182
$$122$$ 0 0
$$123$$ 19.5959 1.76690
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −7.34847 −0.652071 −0.326036 0.945357i $$-0.605713\pi$$
−0.326036 + 0.945357i $$0.605713\pi$$
$$128$$ 0 0
$$129$$ 18.0000 1.58481
$$130$$ 0 0
$$131$$ −4.89898 −0.428026 −0.214013 0.976831i $$-0.568653\pi$$
−0.214013 + 0.976831i $$0.568653\pi$$
$$132$$ 0 0
$$133$$ −12.0000 −1.04053
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.00000 −0.683486 −0.341743 0.939793i $$-0.611017\pi$$
−0.341743 + 0.939793i $$0.611017\pi$$
$$138$$ 0 0
$$139$$ 4.89898 0.415526 0.207763 0.978179i $$-0.433382\pi$$
0.207763 + 0.978179i $$0.433382\pi$$
$$140$$ 0 0
$$141$$ 30.0000 2.52646
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 2.44949 0.202031
$$148$$ 0 0
$$149$$ 2.00000 0.163846 0.0819232 0.996639i $$-0.473894\pi$$
0.0819232 + 0.996639i $$0.473894\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ −12.0000 −0.970143
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −20.0000 −1.59617 −0.798087 0.602542i $$-0.794154\pi$$
−0.798087 + 0.602542i $$0.794154\pi$$
$$158$$ 0 0
$$159$$ 19.5959 1.55406
$$160$$ 0 0
$$161$$ 6.00000 0.472866
$$162$$ 0 0
$$163$$ −2.44949 −0.191859 −0.0959294 0.995388i $$-0.530582\pi$$
−0.0959294 + 0.995388i $$0.530582\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.44949 0.189547 0.0947736 0.995499i $$-0.469787\pi$$
0.0947736 + 0.995499i $$0.469787\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 14.6969 1.12390
$$172$$ 0 0
$$173$$ −4.00000 −0.304114 −0.152057 0.988372i $$-0.548590\pi$$
−0.152057 + 0.988372i $$0.548590\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 12.0000 0.901975
$$178$$ 0 0
$$179$$ 14.6969 1.09850 0.549250 0.835658i $$-0.314913\pi$$
0.549250 + 0.835658i $$0.314913\pi$$
$$180$$ 0 0
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ 0 0
$$183$$ −14.6969 −1.08643
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 19.5959 1.43300
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 19.5959 1.41791 0.708955 0.705253i $$-0.249167\pi$$
0.708955 + 0.705253i $$0.249167\pi$$
$$192$$ 0 0
$$193$$ −12.0000 −0.863779 −0.431889 0.901927i $$-0.642153\pi$$
−0.431889 + 0.901927i $$0.642153\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −8.00000 −0.569976 −0.284988 0.958531i $$-0.591990\pi$$
−0.284988 + 0.958531i $$0.591990\pi$$
$$198$$ 0 0
$$199$$ −9.79796 −0.694559 −0.347279 0.937762i $$-0.612894\pi$$
−0.347279 + 0.937762i $$0.612894\pi$$
$$200$$ 0 0
$$201$$ 6.00000 0.423207
$$202$$ 0 0
$$203$$ −19.5959 −1.37536
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −7.34847 −0.510754
$$208$$ 0 0
$$209$$ −24.0000 −1.66011
$$210$$ 0 0
$$211$$ −24.4949 −1.68630 −0.843149 0.537680i $$-0.819301\pi$$
−0.843149 + 0.537680i $$0.819301\pi$$
$$212$$ 0 0
$$213$$ −24.0000 −1.64445
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 24.0000 1.62923
$$218$$ 0 0
$$219$$ 9.79796 0.662085
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 7.34847 0.492090 0.246045 0.969258i $$-0.420869\pi$$
0.246045 + 0.969258i $$0.420869\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2.44949 0.162578 0.0812892 0.996691i $$-0.474096\pi$$
0.0812892 + 0.996691i $$0.474096\pi$$
$$228$$ 0 0
$$229$$ 8.00000 0.528655 0.264327 0.964433i $$-0.414850\pi$$
0.264327 + 0.964433i $$0.414850\pi$$
$$230$$ 0 0
$$231$$ −29.3939 −1.93398
$$232$$ 0 0
$$233$$ −20.0000 −1.31024 −0.655122 0.755523i $$-0.727383\pi$$
−0.655122 + 0.755523i $$0.727383\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 24.0000 1.55897
$$238$$ 0 0
$$239$$ 9.79796 0.633777 0.316889 0.948463i $$-0.397362\pi$$
0.316889 + 0.948463i $$0.397362\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 0 0
$$243$$ 22.0454 1.41421
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −6.00000 −0.380235
$$250$$ 0 0
$$251$$ −4.89898 −0.309221 −0.154610 0.987976i $$-0.549412\pi$$
−0.154610 + 0.987976i $$0.549412\pi$$
$$252$$ 0 0
$$253$$ 12.0000 0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 8.00000 0.499026 0.249513 0.968371i $$-0.419729\pi$$
0.249513 + 0.968371i $$0.419729\pi$$
$$258$$ 0 0
$$259$$ 9.79796 0.608816
$$260$$ 0 0
$$261$$ 24.0000 1.48556
$$262$$ 0 0
$$263$$ 22.0454 1.35938 0.679689 0.733500i $$-0.262115\pi$$
0.679689 + 0.733500i $$0.262115\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −4.89898 −0.299813
$$268$$ 0 0
$$269$$ 26.0000 1.58525 0.792624 0.609711i $$-0.208714\pi$$
0.792624 + 0.609711i $$0.208714\pi$$
$$270$$ 0 0
$$271$$ −9.79796 −0.595184 −0.297592 0.954693i $$-0.596183\pi$$
−0.297592 + 0.954693i $$0.596183\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 12.0000 0.721010 0.360505 0.932757i $$-0.382604\pi$$
0.360505 + 0.932757i $$0.382604\pi$$
$$278$$ 0 0
$$279$$ −29.3939 −1.75977
$$280$$ 0 0
$$281$$ −16.0000 −0.954480 −0.477240 0.878773i $$-0.658363\pi$$
−0.477240 + 0.878773i $$0.658363\pi$$
$$282$$ 0 0
$$283$$ 26.9444 1.60168 0.800839 0.598880i $$-0.204387\pi$$
0.800839 + 0.598880i $$0.204387\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 19.5959 1.15671
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ −9.79796 −0.574367
$$292$$ 0 0
$$293$$ 20.0000 1.16841 0.584206 0.811605i $$-0.301406\pi$$
0.584206 + 0.811605i $$0.301406\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 18.0000 1.03750
$$302$$ 0 0
$$303$$ −19.5959 −1.12576
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 17.1464 0.978598 0.489299 0.872116i $$-0.337253\pi$$
0.489299 + 0.872116i $$0.337253\pi$$
$$308$$ 0 0
$$309$$ 6.00000 0.341328
$$310$$ 0 0
$$311$$ −19.5959 −1.11118 −0.555591 0.831456i $$-0.687508\pi$$
−0.555591 + 0.831456i $$0.687508\pi$$
$$312$$ 0 0
$$313$$ −24.0000 −1.35656 −0.678280 0.734803i $$-0.737274\pi$$
−0.678280 + 0.734803i $$0.737274\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 8.00000 0.449325 0.224662 0.974437i $$-0.427872\pi$$
0.224662 + 0.974437i $$0.427872\pi$$
$$318$$ 0 0
$$319$$ −39.1918 −2.19432
$$320$$ 0 0
$$321$$ 18.0000 1.00466
$$322$$ 0 0
$$323$$ −19.5959 −1.09035
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 24.4949 1.35457
$$328$$ 0 0
$$329$$ 30.0000 1.65395
$$330$$ 0 0
$$331$$ 4.89898 0.269272 0.134636 0.990895i $$-0.457013\pi$$
0.134636 + 0.990895i $$0.457013\pi$$
$$332$$ 0 0
$$333$$ −12.0000 −0.657596
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 16.0000 0.871576 0.435788 0.900049i $$-0.356470\pi$$
0.435788 + 0.900049i $$0.356470\pi$$
$$338$$ 0 0
$$339$$ −39.1918 −2.12861
$$340$$ 0 0
$$341$$ 48.0000 2.59935
$$342$$ 0 0
$$343$$ 19.5959 1.05808
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −12.2474 −0.657477 −0.328739 0.944421i $$-0.606624\pi$$
−0.328739 + 0.944421i $$0.606624\pi$$
$$348$$ 0 0
$$349$$ 24.0000 1.28469 0.642345 0.766415i $$-0.277962\pi$$
0.642345 + 0.766415i $$0.277962\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8.00000 0.425797 0.212899 0.977074i $$-0.431710\pi$$
0.212899 + 0.977074i $$0.431710\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −24.0000 −1.27021
$$358$$ 0 0
$$359$$ 19.5959 1.03423 0.517116 0.855915i $$-0.327005\pi$$
0.517116 + 0.855915i $$0.327005\pi$$
$$360$$ 0 0
$$361$$ 5.00000 0.263158
$$362$$ 0 0
$$363$$ −31.8434 −1.67134
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 31.8434 1.66221 0.831105 0.556115i $$-0.187709\pi$$
0.831105 + 0.556115i $$0.187709\pi$$
$$368$$ 0 0
$$369$$ −24.0000 −1.24939
$$370$$ 0 0
$$371$$ 19.5959 1.01737
$$372$$ 0 0
$$373$$ 20.0000 1.03556 0.517780 0.855514i $$-0.326758\pi$$
0.517780 + 0.855514i $$0.326758\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −14.6969 −0.754931 −0.377466 0.926024i $$-0.623204\pi$$
−0.377466 + 0.926024i $$0.623204\pi$$
$$380$$ 0 0
$$381$$ 18.0000 0.922168
$$382$$ 0 0
$$383$$ 26.9444 1.37679 0.688397 0.725334i $$-0.258315\pi$$
0.688397 + 0.725334i $$0.258315\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −22.0454 −1.12063
$$388$$ 0 0
$$389$$ 2.00000 0.101404 0.0507020 0.998714i $$-0.483854\pi$$
0.0507020 + 0.998714i $$0.483854\pi$$
$$390$$ 0 0
$$391$$ 9.79796 0.495504
$$392$$ 0 0
$$393$$ 12.0000 0.605320
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 0 0
$$399$$ 29.3939 1.47153
$$400$$ 0 0
$$401$$ 10.0000 0.499376 0.249688 0.968326i $$-0.419672\pi$$
0.249688 + 0.968326i $$0.419672\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 19.5959 0.971334
$$408$$ 0 0
$$409$$ −24.0000 −1.18672 −0.593362 0.804936i $$-0.702200\pi$$
−0.593362 + 0.804936i $$0.702200\pi$$
$$410$$ 0 0
$$411$$ 19.5959 0.966595
$$412$$ 0 0
$$413$$ 12.0000 0.590481
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −12.0000 −0.587643
$$418$$ 0 0
$$419$$ 14.6969 0.717992 0.358996 0.933339i $$-0.383119\pi$$
0.358996 + 0.933339i $$0.383119\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −0.0974740 −0.0487370 0.998812i $$-0.515520\pi$$
−0.0487370 + 0.998812i $$0.515520\pi$$
$$422$$ 0 0
$$423$$ −36.7423 −1.78647
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −14.6969 −0.711235
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −29.3939 −1.41585 −0.707927 0.706286i $$-0.750369\pi$$
−0.707927 + 0.706286i $$0.750369\pi$$
$$432$$ 0 0
$$433$$ −36.0000 −1.73005 −0.865025 0.501729i $$-0.832697\pi$$
−0.865025 + 0.501729i $$0.832697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −12.0000 −0.574038
$$438$$ 0 0
$$439$$ 19.5959 0.935262 0.467631 0.883924i $$-0.345108\pi$$
0.467631 + 0.883924i $$0.345108\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 26.9444 1.28017 0.640083 0.768306i $$-0.278900\pi$$
0.640083 + 0.768306i $$0.278900\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −4.89898 −0.231714
$$448$$ 0 0
$$449$$ 32.0000 1.51017 0.755087 0.655625i $$-0.227595\pi$$
0.755087 + 0.655625i $$0.227595\pi$$
$$450$$ 0 0
$$451$$ 39.1918 1.84547
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 32.0000 1.49690 0.748448 0.663193i $$-0.230799\pi$$
0.748448 + 0.663193i $$0.230799\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 8.00000 0.372597 0.186299 0.982493i $$-0.440351\pi$$
0.186299 + 0.982493i $$0.440351\pi$$
$$462$$ 0 0
$$463$$ 31.8434 1.47989 0.739943 0.672669i $$-0.234852\pi$$
0.739943 + 0.672669i $$0.234852\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −36.7423 −1.70023 −0.850117 0.526595i $$-0.823469\pi$$
−0.850117 + 0.526595i $$0.823469\pi$$
$$468$$ 0 0
$$469$$ 6.00000 0.277054
$$470$$ 0 0
$$471$$ 48.9898 2.25733
$$472$$ 0 0
$$473$$ 36.0000 1.65528
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −24.0000 −1.09888
$$478$$ 0 0
$$479$$ −19.5959 −0.895360 −0.447680 0.894194i $$-0.647750\pi$$
−0.447680 + 0.894194i $$0.647750\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ −14.6969 −0.668734
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 17.1464 0.776979 0.388489 0.921453i $$-0.372997\pi$$
0.388489 + 0.921453i $$0.372997\pi$$
$$488$$ 0 0
$$489$$ 6.00000 0.271329
$$490$$ 0 0
$$491$$ −14.6969 −0.663264 −0.331632 0.943409i $$-0.607599\pi$$
−0.331632 + 0.943409i $$0.607599\pi$$
$$492$$ 0 0
$$493$$ −32.0000 −1.44121
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −24.0000 −1.07655
$$498$$ 0 0
$$499$$ −4.89898 −0.219308 −0.109654 0.993970i $$-0.534974\pi$$
−0.109654 + 0.993970i $$0.534974\pi$$
$$500$$ 0 0
$$501$$ −6.00000 −0.268060
$$502$$ 0 0
$$503$$ 17.1464 0.764521 0.382261 0.924055i $$-0.375146\pi$$
0.382261 + 0.924055i $$0.375146\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 31.8434 1.41421
$$508$$ 0 0
$$509$$ 8.00000 0.354594 0.177297 0.984157i $$-0.443265\pi$$
0.177297 + 0.984157i $$0.443265\pi$$
$$510$$ 0 0
$$511$$ 9.79796 0.433436
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 60.0000 2.63880
$$518$$ 0 0
$$519$$ 9.79796 0.430083
$$520$$ 0 0
$$521$$ 22.0000 0.963837 0.481919 0.876216i $$-0.339940\pi$$
0.481919 + 0.876216i $$0.339940\pi$$
$$522$$ 0 0
$$523$$ −31.8434 −1.39241 −0.696207 0.717841i $$-0.745130\pi$$
−0.696207 + 0.717841i $$0.745130\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 39.1918 1.70722
$$528$$ 0 0
$$529$$ −17.0000 −0.739130
$$530$$ 0 0
$$531$$ −14.6969 −0.637793
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −36.0000 −1.55351
$$538$$ 0 0
$$539$$ 4.89898 0.211014
$$540$$ 0 0
$$541$$ 8.00000 0.343947 0.171973 0.985102i $$-0.444986\pi$$
0.171973 + 0.985102i $$0.444986\pi$$
$$542$$ 0 0
$$543$$ −19.5959 −0.840941
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 22.0454 0.942594 0.471297 0.881975i $$-0.343786\pi$$
0.471297 + 0.881975i $$0.343786\pi$$
$$548$$ 0 0
$$549$$ 18.0000 0.768221
$$550$$ 0 0
$$551$$ 39.1918 1.66963
$$552$$ 0 0
$$553$$ 24.0000 1.02058
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −4.00000 −0.169485 −0.0847427 0.996403i $$-0.527007\pi$$
−0.0847427 + 0.996403i $$0.527007\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −48.0000 −2.02656
$$562$$ 0 0
$$563$$ −2.44949 −0.103234 −0.0516168 0.998667i $$-0.516437\pi$$
−0.0516168 + 0.998667i $$0.516437\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 22.0454 0.925820
$$568$$ 0 0
$$569$$ −8.00000 −0.335377 −0.167689 0.985840i $$-0.553630\pi$$
−0.167689 + 0.985840i $$0.553630\pi$$
$$570$$ 0 0
$$571$$ −44.0908 −1.84514 −0.922572 0.385826i $$-0.873917\pi$$
−0.922572 + 0.385826i $$0.873917\pi$$
$$572$$ 0 0
$$573$$ −48.0000 −2.00523
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −24.0000 −0.999133 −0.499567 0.866276i $$-0.666507\pi$$
−0.499567 + 0.866276i $$0.666507\pi$$
$$578$$ 0 0
$$579$$ 29.3939 1.22157
$$580$$ 0 0
$$581$$ −6.00000 −0.248922
$$582$$ 0 0
$$583$$ 39.1918 1.62316
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.2474 −0.505506 −0.252753 0.967531i $$-0.581336\pi$$
−0.252753 + 0.967531i $$0.581336\pi$$
$$588$$ 0 0
$$589$$ −48.0000 −1.97781
$$590$$ 0 0
$$591$$ 19.5959 0.806068
$$592$$ 0 0
$$593$$ 8.00000 0.328521 0.164260 0.986417i $$-0.447476\pi$$
0.164260 + 0.986417i $$0.447476\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 24.0000 0.982255
$$598$$ 0 0
$$599$$ 9.79796 0.400334 0.200167 0.979762i $$-0.435852\pi$$
0.200167 + 0.979762i $$0.435852\pi$$
$$600$$ 0 0
$$601$$ −16.0000 −0.652654 −0.326327 0.945257i $$-0.605811\pi$$
−0.326327 + 0.945257i $$0.605811\pi$$
$$602$$ 0 0
$$603$$ −7.34847 −0.299253
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 7.34847 0.298265 0.149133 0.988817i $$-0.452352\pi$$
0.149133 + 0.988817i $$0.452352\pi$$
$$608$$ 0 0
$$609$$ 48.0000 1.94506
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 16.0000 0.646234 0.323117 0.946359i $$-0.395269\pi$$
0.323117 + 0.946359i $$0.395269\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −28.0000 −1.12724 −0.563619 0.826035i $$-0.690591\pi$$
−0.563619 + 0.826035i $$0.690591\pi$$
$$618$$ 0 0
$$619$$ −24.4949 −0.984533 −0.492267 0.870445i $$-0.663831\pi$$
−0.492267 + 0.870445i $$0.663831\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4.89898 −0.196273
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 58.7878 2.34776
$$628$$ 0 0
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 60.0000 2.38479
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 29.3939 1.16280
$$640$$ 0 0
$$641$$ −16.0000 −0.631962 −0.315981 0.948766i $$-0.602334\pi$$
−0.315981 + 0.948766i $$0.602334\pi$$
$$642$$ 0 0
$$643$$ 2.44949 0.0965984 0.0482992 0.998833i $$-0.484620\pi$$
0.0482992 + 0.998833i $$0.484620\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −22.0454 −0.866694 −0.433347 0.901227i $$-0.642668\pi$$
−0.433347 + 0.901227i $$0.642668\pi$$
$$648$$ 0 0
$$649$$ 24.0000 0.942082
$$650$$ 0 0
$$651$$ −58.7878 −2.30407
$$652$$ 0 0
$$653$$ 16.0000 0.626128 0.313064 0.949732i $$-0.398644\pi$$
0.313064 + 0.949732i $$0.398644\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −12.0000 −0.468165
$$658$$ 0 0
$$659$$ 14.6969 0.572511 0.286256 0.958153i $$-0.407589\pi$$
0.286256 + 0.958153i $$0.407589\pi$$
$$660$$ 0 0
$$661$$ −30.0000 −1.16686 −0.583432 0.812162i $$-0.698291\pi$$
−0.583432 + 0.812162i $$0.698291\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −19.5959 −0.758757
$$668$$ 0 0
$$669$$ −18.0000 −0.695920
$$670$$ 0 0
$$671$$ −29.3939 −1.13474
$$672$$ 0 0
$$673$$ −36.0000 −1.38770 −0.693849 0.720121i $$-0.744086\pi$$
−0.693849 + 0.720121i $$0.744086\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −32.0000 −1.22986 −0.614930 0.788582i $$-0.710816\pi$$
−0.614930 + 0.788582i $$0.710816\pi$$
$$678$$ 0 0
$$679$$ −9.79796 −0.376011
$$680$$ 0 0
$$681$$ −6.00000 −0.229920
$$682$$ 0 0
$$683$$ −7.34847 −0.281181 −0.140591 0.990068i $$-0.544900\pi$$
−0.140591 + 0.990068i $$0.544900\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −19.5959 −0.747631
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 14.6969 0.559098 0.279549 0.960131i $$-0.409815\pi$$
0.279549 + 0.960131i $$0.409815\pi$$
$$692$$ 0 0
$$693$$ 36.0000 1.36753
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 32.0000 1.21209
$$698$$ 0 0
$$699$$ 48.9898 1.85296
$$700$$ 0 0
$$701$$ 26.0000 0.982006 0.491003 0.871158i $$-0.336630\pi$$
0.491003 + 0.871158i $$0.336630\pi$$
$$702$$ 0 0
$$703$$ −19.5959 −0.739074
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −19.5959 −0.736980
$$708$$ 0 0
$$709$$ −40.0000 −1.50223 −0.751116 0.660171i $$-0.770484\pi$$
−0.751116 + 0.660171i $$0.770484\pi$$
$$710$$ 0 0
$$711$$ −29.3939 −1.10236
$$712$$ 0 0
$$713$$ 24.0000 0.898807
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −24.0000 −0.896296
$$718$$ 0 0
$$719$$ −48.9898 −1.82701 −0.913506 0.406826i $$-0.866635\pi$$
−0.913506 + 0.406826i $$0.866635\pi$$
$$720$$ 0 0
$$721$$ 6.00000 0.223452
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 36.7423 1.36270 0.681349 0.731959i $$-0.261394\pi$$
0.681349 + 0.731959i $$0.261394\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 29.3939 1.08717
$$732$$ 0 0
$$733$$ −12.0000 −0.443230 −0.221615 0.975134i $$-0.571133\pi$$
−0.221615 + 0.975134i $$0.571133\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 12.0000 0.442026
$$738$$ 0 0
$$739$$ 14.6969 0.540636 0.270318 0.962771i $$-0.412871\pi$$
0.270318 + 0.962771i $$0.412871\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −17.1464 −0.629041 −0.314521 0.949251i $$-0.601844\pi$$
−0.314521 + 0.949251i $$0.601844\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 7.34847 0.268866
$$748$$ 0 0
$$749$$ 18.0000 0.657706
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 12.0000 0.437304
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −12.0000 −0.436147 −0.218074 0.975932i $$-0.569977\pi$$
−0.218074 + 0.975932i $$0.569977\pi$$
$$758$$ 0 0
$$759$$ −29.3939 −1.06693
$$760$$ 0 0
$$761$$ −22.0000 −0.797499 −0.398750 0.917060i $$-0.630556\pi$$
−0.398750 + 0.917060i $$0.630556\pi$$
$$762$$ 0 0
$$763$$ 24.4949 0.886775
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 26.0000 0.937584 0.468792 0.883309i $$-0.344689\pi$$
0.468792 + 0.883309i $$0.344689\pi$$
$$770$$ 0 0
$$771$$ −19.5959 −0.705730
$$772$$ 0 0
$$773$$ −8.00000 −0.287740 −0.143870 0.989597i $$-0.545955\pi$$
−0.143870 + 0.989597i $$0.545955\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −24.0000 −0.860995
$$778$$ 0 0
$$779$$ −39.1918 −1.40419
$$780$$ 0 0
$$781$$ −48.0000 −1.71758
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −41.6413 −1.48435 −0.742176 0.670205i $$-0.766206\pi$$
−0.742176 + 0.670205i $$0.766206\pi$$
$$788$$ 0 0
$$789$$ −54.0000 −1.92245
$$790$$ 0 0
$$791$$ −39.1918 −1.39350
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 8.00000 0.283375 0.141687 0.989911i $$-0.454747\pi$$
0.141687 + 0.989911i $$0.454747\pi$$
$$798$$ 0 0
$$799$$ 48.9898 1.73313
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 0 0
$$803$$ 19.5959 0.691525
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −63.6867 −2.24188
$$808$$ 0 0
$$809$$ 10.0000 0.351581 0.175791 0.984428i $$-0.443752\pi$$
0.175791 + 0.984428i $$0.443752\pi$$
$$810$$ 0 0
$$811$$ 53.8888 1.89229 0.946145 0.323742i $$-0.104941\pi$$
0.946145 + 0.323742i $$0.104941\pi$$
$$812$$ 0 0
$$813$$ 24.0000 0.841717
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −36.0000 −1.25948
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −14.0000 −0.488603 −0.244302 0.969699i $$-0.578559\pi$$
−0.244302 + 0.969699i $$0.578559\pi$$
$$822$$ 0 0
$$823$$ −22.0454 −0.768455 −0.384227 0.923239i $$-0.625532\pi$$
−0.384227 + 0.923239i $$0.625532\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 46.5403 1.61836 0.809182 0.587557i $$-0.199910\pi$$
0.809182 + 0.587557i $$0.199910\pi$$
$$828$$ 0 0
$$829$$ −22.0000 −0.764092 −0.382046 0.924143i $$-0.624780\pi$$
−0.382046 + 0.924143i $$0.624780\pi$$
$$830$$ 0 0
$$831$$ −29.3939 −1.01966
$$832$$ 0 0
$$833$$ 4.00000 0.138592
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −39.1918 −1.35305 −0.676526 0.736419i $$-0.736515\pi$$
−0.676526 + 0.736419i $$0.736515\pi$$
$$840$$ 0 0
$$841$$ 35.0000 1.20690
$$842$$ 0 0
$$843$$ 39.1918 1.34984
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −31.8434 −1.09415
$$848$$ 0 0
$$849$$ −66.0000 −2.26511
$$850$$ 0 0
$$851$$ 9.79796 0.335870
$$852$$ 0 0
$$853$$ 32.0000 1.09566 0.547830 0.836590i $$-0.315454\pi$$
0.547830 + 0.836590i $$0.315454\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −32.0000 −1.09310 −0.546550 0.837427i $$-0.684059\pi$$
−0.546550 + 0.837427i $$0.684059\pi$$
$$858$$ 0 0
$$859$$ −24.4949 −0.835755 −0.417878 0.908503i $$-0.637226\pi$$
−0.417878 + 0.908503i $$0.637226\pi$$
$$860$$ 0 0
$$861$$ −48.0000 −1.63584
$$862$$ 0 0
$$863$$ 51.4393 1.75101 0.875507 0.483206i $$-0.160528\pi$$
0.875507 + 0.483206i $$0.160528\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 2.44949 0.0831890
$$868$$ 0 0
$$869$$ 48.0000 1.62829
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 12.0000 0.406138
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −28.0000 −0.945493 −0.472746 0.881199i $$-0.656737\pi$$
−0.472746 + 0.881199i $$0.656737\pi$$
$$878$$ 0 0
$$879$$ −48.9898 −1.65238
$$880$$ 0 0
$$881$$ −8.00000 −0.269527 −0.134763 0.990878i $$-0.543027\pi$$
−0.134763 + 0.990878i $$0.543027\pi$$
$$882$$ 0 0
$$883$$ 36.7423 1.23648 0.618239 0.785990i $$-0.287846\pi$$
0.618239 + 0.785990i $$0.287846\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.44949 −0.0822458 −0.0411229 0.999154i $$-0.513094\pi$$
−0.0411229 + 0.999154i $$0.513094\pi$$
$$888$$ 0 0
$$889$$ 18.0000 0.603701
$$890$$ 0 0
$$891$$ 44.0908 1.47710
$$892$$ 0 0
$$893$$ −60.0000 −2.00782
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −78.3837 −2.61424
$$900$$ 0 0
$$901$$ 32.0000 1.06607
$$902$$ 0 0
$$903$$ −44.0908 −1.46725
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 12.2474 0.406670 0.203335 0.979109i $$-0.434822\pi$$
0.203335 + 0.979109i $$0.434822\pi$$
$$908$$ 0 0
$$909$$ 24.0000 0.796030
$$910$$ 0 0
$$911$$ 29.3939 0.973863 0.486931 0.873440i $$-0.338116\pi$$
0.486931 + 0.873440i $$0.338116\pi$$
$$912$$ 0 0
$$913$$ −12.0000 −0.397142
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 12.0000 0.396275
$$918$$ 0 0
$$919$$ 48.9898 1.61602 0.808012 0.589166i $$-0.200544\pi$$
0.808012 + 0.589166i $$0.200544\pi$$
$$920$$ 0 0
$$921$$ −42.0000 −1.38395
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −7.34847 −0.241355
$$928$$ 0 0
$$929$$ 16.0000 0.524943 0.262471 0.964940i $$-0.415462\pi$$
0.262471 + 0.964940i $$0.415462\pi$$
$$930$$ 0 0
$$931$$ −4.89898 −0.160558
$$932$$ 0 0
$$933$$ 48.0000 1.57145
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 60.0000 1.96011 0.980057 0.198715i $$-0.0636769\pi$$
0.980057 + 0.198715i $$0.0636769\pi$$
$$938$$ 0 0
$$939$$ 58.7878 1.91847
$$940$$ 0 0
$$941$$ 8.00000 0.260793 0.130396 0.991462i $$-0.458375\pi$$
0.130396 + 0.991462i $$0.458375\pi$$
$$942$$ 0 0
$$943$$ 19.5959 0.638131
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 17.1464 0.557184 0.278592 0.960410i $$-0.410132\pi$$
0.278592 + 0.960410i $$0.410132\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −19.5959 −0.635441
$$952$$ 0 0
$$953$$ −32.0000 −1.03658 −0.518291 0.855204i $$-0.673432\pi$$
−0.518291 + 0.855204i $$0.673432\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 96.0000 3.10324
$$958$$ 0 0
$$959$$ 19.5959 0.632785
$$960$$ 0 0
$$961$$ 65.0000 2.09677
$$962$$ 0 0
$$963$$ −22.0454 −0.710403
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −17.1464 −0.551392 −0.275696 0.961245i $$-0.588908\pi$$
−0.275696 + 0.961245i $$0.588908\pi$$
$$968$$ 0 0
$$969$$ 48.0000 1.54198
$$970$$ 0 0
$$971$$ 24.4949 0.786079 0.393039 0.919522i $$-0.371424\pi$$
0.393039 + 0.919522i $$0.371424\pi$$
$$972$$ 0 0
$$973$$ −12.0000 −0.384702
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 4.00000 0.127971 0.0639857 0.997951i $$-0.479619\pi$$
0.0639857 + 0.997951i $$0.479619\pi$$
$$978$$ 0 0
$$979$$ −9.79796 −0.313144
$$980$$ 0 0
$$981$$ −30.0000 −0.957826
$$982$$ 0 0
$$983$$ 22.0454 0.703139 0.351570 0.936162i $$-0.385648\pi$$
0.351570 + 0.936162i $$0.385648\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −73.4847 −2.33904
$$988$$ 0 0
$$989$$ 18.0000 0.572367
$$990$$ 0 0
$$991$$ 39.1918 1.24497 0.622485 0.782632i $$-0.286123\pi$$
0.622485 + 0.782632i $$0.286123\pi$$
$$992$$ 0 0
$$993$$ −12.0000 −0.380808
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 56.0000 1.77354 0.886769 0.462213i $$-0.152944\pi$$
0.886769 + 0.462213i $$0.152944\pi$$
$$998$$ 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 6400.2.a.bv.1.1 2
4.3 odd 2 inner 6400.2.a.bv.1.2 2
5.2 odd 4 1280.2.c.m.769.3 4
5.3 odd 4 1280.2.c.m.769.2 4
5.4 even 2 6400.2.a.bx.1.2 2
8.3 odd 2 6400.2.a.bu.1.1 2
8.5 even 2 6400.2.a.bu.1.2 2
16.3 odd 4 3200.2.d.k.1601.3 4
16.5 even 4 3200.2.d.k.1601.4 4
16.11 odd 4 3200.2.d.k.1601.1 4
16.13 even 4 3200.2.d.k.1601.2 4
20.3 even 4 1280.2.c.m.769.4 4
20.7 even 4 1280.2.c.m.769.1 4
20.19 odd 2 6400.2.a.bx.1.1 2
40.3 even 4 1280.2.c.e.769.1 4
40.13 odd 4 1280.2.c.e.769.3 4
40.19 odd 2 6400.2.a.bw.1.2 2
40.27 even 4 1280.2.c.e.769.4 4
40.29 even 2 6400.2.a.bw.1.1 2
40.37 odd 4 1280.2.c.e.769.2 4
80.3 even 4 640.2.f.g.449.1 yes 4
80.13 odd 4 640.2.f.g.449.3 yes 4
80.19 odd 4 3200.2.d.l.1601.2 4
80.27 even 4 640.2.f.g.449.2 yes 4
80.29 even 4 3200.2.d.l.1601.3 4
80.37 odd 4 640.2.f.g.449.4 yes 4
80.43 even 4 640.2.f.c.449.4 yes 4
80.53 odd 4 640.2.f.c.449.2 yes 4
80.59 odd 4 3200.2.d.l.1601.4 4
80.67 even 4 640.2.f.c.449.3 yes 4
80.69 even 4 3200.2.d.l.1601.1 4
80.77 odd 4 640.2.f.c.449.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.f.c.449.1 4 80.77 odd 4
640.2.f.c.449.2 yes 4 80.53 odd 4
640.2.f.c.449.3 yes 4 80.67 even 4
640.2.f.c.449.4 yes 4 80.43 even 4
640.2.f.g.449.1 yes 4 80.3 even 4
640.2.f.g.449.2 yes 4 80.27 even 4
640.2.f.g.449.3 yes 4 80.13 odd 4
640.2.f.g.449.4 yes 4 80.37 odd 4
1280.2.c.e.769.1 4 40.3 even 4
1280.2.c.e.769.2 4 40.37 odd 4
1280.2.c.e.769.3 4 40.13 odd 4
1280.2.c.e.769.4 4 40.27 even 4
1280.2.c.m.769.1 4 20.7 even 4
1280.2.c.m.769.2 4 5.3 odd 4
1280.2.c.m.769.3 4 5.2 odd 4
1280.2.c.m.769.4 4 20.3 even 4
3200.2.d.k.1601.1 4 16.11 odd 4
3200.2.d.k.1601.2 4 16.13 even 4
3200.2.d.k.1601.3 4 16.3 odd 4
3200.2.d.k.1601.4 4 16.5 even 4
3200.2.d.l.1601.1 4 80.69 even 4
3200.2.d.l.1601.2 4 80.19 odd 4
3200.2.d.l.1601.3 4 80.29 even 4
3200.2.d.l.1601.4 4 80.59 odd 4
6400.2.a.bu.1.1 2 8.3 odd 2
6400.2.a.bu.1.2 2 8.5 even 2
6400.2.a.bv.1.1 2 1.1 even 1 trivial
6400.2.a.bv.1.2 2 4.3 odd 2 inner
6400.2.a.bw.1.1 2 40.29 even 2
6400.2.a.bw.1.2 2 40.19 odd 2
6400.2.a.bx.1.1 2 20.19 odd 2
6400.2.a.bx.1.2 2 5.4 even 2