Properties

 Label 9800.2.a.cg.1.3 Level $9800$ Weight $2$ Character 9800.1 Self dual yes Analytic conductor $78.253$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$9800 = 2^{3} \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9800.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$78.2533939809$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.568.1 Defining polynomial: $$x^{3} - x^{2} - 6 x - 2$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.3 Root $$3.12489$$ of defining polynomial Character $$\chi$$ $$=$$ 9800.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+3.12489 q^{3} +6.76491 q^{9} +O(q^{10})$$ $$q+3.12489 q^{3} +6.76491 q^{9} +2.48486 q^{11} -4.15516 q^{13} +5.76491 q^{17} +1.60975 q^{19} -7.28005 q^{23} +11.7649 q^{27} +1.45459 q^{29} +2.24977 q^{31} +7.76491 q^{33} +6.00000 q^{37} -12.9844 q^{39} -11.2800 q^{41} +5.28005 q^{43} +3.45459 q^{47} +18.0147 q^{51} +9.21949 q^{53} +5.03028 q^{57} +5.92007 q^{59} -5.35998 q^{61} +7.52982 q^{67} -22.7493 q^{69} -4.24977 q^{71} +7.28005 q^{73} +16.9844 q^{79} +16.4693 q^{81} -10.1093 q^{83} +4.54541 q^{87} +11.4693 q^{89} +7.03028 q^{93} -2.73463 q^{97} +16.8099 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3q + q^{3} + 4q^{9} + O(q^{10})$$ $$3q + q^{3} + 4q^{9} + 7q^{11} - 5q^{13} + q^{17} - 4q^{19} - 6q^{23} + 19q^{27} + 3q^{29} - 10q^{31} + 7q^{33} + 18q^{37} - 5q^{39} - 18q^{41} + 9q^{47} + 21q^{51} + 10q^{53} + 16q^{57} - 6q^{59} - 24q^{61} - 10q^{67} - 18q^{69} + 4q^{71} + 6q^{73} + 17q^{79} + 15q^{81} + 12q^{83} + 15q^{87} + 22q^{93} + 9q^{97} + 2q^{99} + O(q^{100})$$

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
$$3$$ 3.12489 1.80415 0.902077 0.431576i $$-0.142042\pi$$
0.902077 + 0.431576i $$0.142042\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 6.76491 2.25497
$$10$$ 0 0
$$11$$ 2.48486 0.749214 0.374607 0.927184i $$-0.377778\pi$$
0.374607 + 0.927184i $$0.377778\pi$$
$$12$$ 0 0
$$13$$ −4.15516 −1.15243 −0.576217 0.817297i $$-0.695472\pi$$
−0.576217 + 0.817297i $$0.695472\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 5.76491 1.39820 0.699098 0.715026i $$-0.253585\pi$$
0.699098 + 0.715026i $$0.253585\pi$$
$$18$$ 0 0
$$19$$ 1.60975 0.369301 0.184651 0.982804i $$-0.440885\pi$$
0.184651 + 0.982804i $$0.440885\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −7.28005 −1.51799 −0.758997 0.651094i $$-0.774310\pi$$
−0.758997 + 0.651094i $$0.774310\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 11.7649 2.26416
$$28$$ 0 0
$$29$$ 1.45459 0.270110 0.135055 0.990838i $$-0.456879\pi$$
0.135055 + 0.990838i $$0.456879\pi$$
$$30$$ 0 0
$$31$$ 2.24977 0.404071 0.202035 0.979378i $$-0.435244\pi$$
0.202035 + 0.979378i $$0.435244\pi$$
$$32$$ 0 0
$$33$$ 7.76491 1.35170
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 0 0
$$39$$ −12.9844 −2.07917
$$40$$ 0 0
$$41$$ −11.2800 −1.76165 −0.880824 0.473444i $$-0.843010\pi$$
−0.880824 + 0.473444i $$0.843010\pi$$
$$42$$ 0 0
$$43$$ 5.28005 0.805200 0.402600 0.915376i $$-0.368107\pi$$
0.402600 + 0.915376i $$0.368107\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.45459 0.503903 0.251952 0.967740i $$-0.418928\pi$$
0.251952 + 0.967740i $$0.418928\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 18.0147 2.52256
$$52$$ 0 0
$$53$$ 9.21949 1.26639 0.633197 0.773990i $$-0.281742\pi$$
0.633197 + 0.773990i $$0.281742\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 5.03028 0.666276
$$58$$ 0 0
$$59$$ 5.92007 0.770728 0.385364 0.922765i $$-0.374076\pi$$
0.385364 + 0.922765i $$0.374076\pi$$
$$60$$ 0 0
$$61$$ −5.35998 −0.686275 −0.343137 0.939285i $$-0.611490\pi$$
−0.343137 + 0.939285i $$0.611490\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 7.52982 0.919914 0.459957 0.887941i $$-0.347865\pi$$
0.459957 + 0.887941i $$0.347865\pi$$
$$68$$ 0 0
$$69$$ −22.7493 −2.73870
$$70$$ 0 0
$$71$$ −4.24977 −0.504355 −0.252178 0.967681i $$-0.581147\pi$$
−0.252178 + 0.967681i $$0.581147\pi$$
$$72$$ 0 0
$$73$$ 7.28005 0.852065 0.426033 0.904708i $$-0.359911\pi$$
0.426033 + 0.904708i $$0.359911\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 16.9844 1.91089 0.955447 0.295162i $$-0.0953735\pi$$
0.955447 + 0.295162i $$0.0953735\pi$$
$$80$$ 0 0
$$81$$ 16.4693 1.82992
$$82$$ 0 0
$$83$$ −10.1093 −1.10964 −0.554819 0.831971i $$-0.687213\pi$$
−0.554819 + 0.831971i $$0.687213\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 4.54541 0.487320
$$88$$ 0 0
$$89$$ 11.4693 1.21574 0.607870 0.794037i $$-0.292024\pi$$
0.607870 + 0.794037i $$0.292024\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 7.03028 0.729006
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −2.73463 −0.277660 −0.138830 0.990316i $$-0.544334\pi$$
−0.138830 + 0.990316i $$0.544334\pi$$
$$98$$ 0 0
$$99$$ 16.8099 1.68945
$$100$$ 0 0
$$101$$ 4.57947 0.455674 0.227837 0.973699i $$-0.426835\pi$$
0.227837 + 0.973699i $$0.426835\pi$$
$$102$$ 0 0
$$103$$ −2.48486 −0.244841 −0.122420 0.992478i $$-0.539066\pi$$
−0.122420 + 0.992478i $$0.539066\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −9.95413 −0.953433 −0.476716 0.879057i $$-0.658173\pi$$
−0.476716 + 0.879057i $$0.658173\pi$$
$$110$$ 0 0
$$111$$ 18.7493 1.77961
$$112$$ 0 0
$$113$$ 18.4995 1.74029 0.870145 0.492795i $$-0.164025\pi$$
0.870145 + 0.492795i $$0.164025\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −28.1093 −2.59870
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −4.82546 −0.438678
$$122$$ 0 0
$$123$$ −35.2489 −3.17828
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 7.15894 0.635253 0.317627 0.948216i $$-0.397114\pi$$
0.317627 + 0.948216i $$0.397114\pi$$
$$128$$ 0 0
$$129$$ 16.4995 1.45270
$$130$$ 0 0
$$131$$ −7.85952 −0.686689 −0.343345 0.939209i $$-0.611560\pi$$
−0.343345 + 0.939209i $$0.611560\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.5601 0.902210 0.451105 0.892471i $$-0.351030\pi$$
0.451105 + 0.892471i $$0.351030\pi$$
$$138$$ 0 0
$$139$$ −9.79897 −0.831137 −0.415569 0.909562i $$-0.636417\pi$$
−0.415569 + 0.909562i $$0.636417\pi$$
$$140$$ 0 0
$$141$$ 10.7952 0.909119
$$142$$ 0 0
$$143$$ −10.3250 −0.863420
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2.49954 0.204770 0.102385 0.994745i $$-0.467353\pi$$
0.102385 + 0.994745i $$0.467353\pi$$
$$150$$ 0 0
$$151$$ −3.76491 −0.306384 −0.153192 0.988196i $$-0.548955\pi$$
−0.153192 + 0.988196i $$0.548955\pi$$
$$152$$ 0 0
$$153$$ 38.9991 3.15289
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −5.67030 −0.452539 −0.226270 0.974065i $$-0.572653\pi$$
−0.226270 + 0.974065i $$0.572653\pi$$
$$158$$ 0 0
$$159$$ 28.8099 2.28477
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 10.2498 0.802824 0.401412 0.915898i $$-0.368520\pi$$
0.401412 + 0.915898i $$0.368520\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.95504 0.228668 0.114334 0.993442i $$-0.463527\pi$$
0.114334 + 0.993442i $$0.463527\pi$$
$$168$$ 0 0
$$169$$ 4.26537 0.328105
$$170$$ 0 0
$$171$$ 10.8898 0.832763
$$172$$ 0 0
$$173$$ −22.4049 −1.70342 −0.851708 0.524017i $$-0.824433\pi$$
−0.851708 + 0.524017i $$0.824433\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 18.4995 1.39051
$$178$$ 0 0
$$179$$ 14.5601 1.08827 0.544136 0.838997i $$-0.316857\pi$$
0.544136 + 0.838997i $$0.316857\pi$$
$$180$$ 0 0
$$181$$ 9.67030 0.718788 0.359394 0.933186i $$-0.382983\pi$$
0.359394 + 0.933186i $$0.382983\pi$$
$$182$$ 0 0
$$183$$ −16.7493 −1.23814
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 14.3250 1.04755
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.01468 0.579922 0.289961 0.957038i $$-0.406358\pi$$
0.289961 + 0.957038i $$0.406358\pi$$
$$192$$ 0 0
$$193$$ 3.46927 0.249723 0.124862 0.992174i $$-0.460151\pi$$
0.124862 + 0.992174i $$0.460151\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −16.2791 −1.15984 −0.579920 0.814673i $$-0.696916\pi$$
−0.579920 + 0.814673i $$0.696916\pi$$
$$198$$ 0 0
$$199$$ −26.8704 −1.90479 −0.952397 0.304862i $$-0.901390\pi$$
−0.952397 + 0.304862i $$0.901390\pi$$
$$200$$ 0 0
$$201$$ 23.5298 1.65967
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −49.2489 −3.42303
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 17.2342 1.18645 0.593225 0.805037i $$-0.297855\pi$$
0.593225 + 0.805037i $$0.297855\pi$$
$$212$$ 0 0
$$213$$ −13.2800 −0.909934
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 22.7493 1.53726
$$220$$ 0 0
$$221$$ −23.9541 −1.61133
$$222$$ 0 0
$$223$$ 0.235091 0.0157429 0.00787143 0.999969i $$-0.497494\pi$$
0.00787143 + 0.999969i $$0.497494\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0.564792 0.0374865 0.0187433 0.999824i $$-0.494033\pi$$
0.0187433 + 0.999824i $$0.494033\pi$$
$$228$$ 0 0
$$229$$ −7.11021 −0.469856 −0.234928 0.972013i $$-0.575485\pi$$
−0.234928 + 0.972013i $$0.575485\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.49954 0.556823 0.278412 0.960462i $$-0.410192\pi$$
0.278412 + 0.960462i $$0.410192\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 53.0743 3.44755
$$238$$ 0 0
$$239$$ −7.26537 −0.469958 −0.234979 0.972001i $$-0.575502\pi$$
−0.234979 + 0.972001i $$0.575502\pi$$
$$240$$ 0 0
$$241$$ −7.28005 −0.468949 −0.234475 0.972122i $$-0.575337\pi$$
−0.234475 + 0.972122i $$0.575337\pi$$
$$242$$ 0 0
$$243$$ 16.1698 1.03730
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.68876 −0.425596
$$248$$ 0 0
$$249$$ −31.5904 −2.00196
$$250$$ 0 0
$$251$$ −22.9192 −1.44664 −0.723322 0.690511i $$-0.757386\pi$$
−0.723322 + 0.690511i $$0.757386\pi$$
$$252$$ 0 0
$$253$$ −18.0899 −1.13730
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −0.719953 −0.0449094 −0.0224547 0.999748i $$-0.507148\pi$$
−0.0224547 + 0.999748i $$0.507148\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 9.84014 0.609089
$$262$$ 0 0
$$263$$ −18.5601 −1.14446 −0.572232 0.820092i $$-0.693922\pi$$
−0.572232 + 0.820092i $$0.693922\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 35.8401 2.19338
$$268$$ 0 0
$$269$$ 22.1698 1.35172 0.675860 0.737030i $$-0.263773\pi$$
0.675860 + 0.737030i $$0.263773\pi$$
$$270$$ 0 0
$$271$$ 7.87890 0.478609 0.239304 0.970945i $$-0.423081\pi$$
0.239304 + 0.970945i $$0.423081\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −2.78051 −0.167064 −0.0835322 0.996505i $$-0.526620\pi$$
−0.0835322 + 0.996505i $$0.526620\pi$$
$$278$$ 0 0
$$279$$ 15.2195 0.911167
$$280$$ 0 0
$$281$$ −23.7044 −1.41408 −0.707042 0.707172i $$-0.749971\pi$$
−0.707042 + 0.707172i $$0.749971\pi$$
$$282$$ 0 0
$$283$$ −26.8439 −1.59571 −0.797853 0.602852i $$-0.794031\pi$$
−0.797853 + 0.602852i $$0.794031\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 16.2342 0.954951
$$290$$ 0 0
$$291$$ −8.54541 −0.500941
$$292$$ 0 0
$$293$$ 9.93475 0.580394 0.290197 0.956967i $$-0.406279\pi$$
0.290197 + 0.956967i $$0.406279\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 29.2342 1.69634
$$298$$ 0 0
$$299$$ 30.2498 1.74939
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 14.3103 0.822107
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 32.0946 1.83174 0.915868 0.401479i $$-0.131504\pi$$
0.915868 + 0.401479i $$0.131504\pi$$
$$308$$ 0 0
$$309$$ −7.76491 −0.441730
$$310$$ 0 0
$$311$$ 10.0606 0.570482 0.285241 0.958456i $$-0.407926\pi$$
0.285241 + 0.958456i $$0.407926\pi$$
$$312$$ 0 0
$$313$$ −20.8245 −1.17707 −0.588536 0.808471i $$-0.700296\pi$$
−0.588536 + 0.808471i $$0.700296\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 15.7502 0.884621 0.442311 0.896862i $$-0.354159\pi$$
0.442311 + 0.896862i $$0.354159\pi$$
$$318$$ 0 0
$$319$$ 3.61445 0.202370
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 9.28005 0.516356
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −31.1055 −1.72014
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −25.7796 −1.41697 −0.708487 0.705724i $$-0.750622\pi$$
−0.708487 + 0.705724i $$0.750622\pi$$
$$332$$ 0 0
$$333$$ 40.5895 2.22429
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.0605522 0.00329849 0.00164924 0.999999i $$-0.499475\pi$$
0.00164924 + 0.999999i $$0.499475\pi$$
$$338$$ 0 0
$$339$$ 57.8089 3.13975
$$340$$ 0 0
$$341$$ 5.59037 0.302736
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −20.9310 −1.12363 −0.561817 0.827262i $$-0.689897\pi$$
−0.561817 + 0.827262i $$0.689897\pi$$
$$348$$ 0 0
$$349$$ −5.48108 −0.293396 −0.146698 0.989181i $$-0.546864\pi$$
−0.146698 + 0.989181i $$0.546864\pi$$
$$350$$ 0 0
$$351$$ −48.8851 −2.60929
$$352$$ 0 0
$$353$$ 26.9239 1.43301 0.716506 0.697581i $$-0.245740\pi$$
0.716506 + 0.697581i $$0.245740\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 6.06055 0.319864 0.159932 0.987128i $$-0.448873\pi$$
0.159932 + 0.987128i $$0.448873\pi$$
$$360$$ 0 0
$$361$$ −16.4087 −0.863616
$$362$$ 0 0
$$363$$ −15.0790 −0.791443
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −30.7034 −1.60271 −0.801353 0.598191i $$-0.795886\pi$$
−0.801353 + 0.598191i $$0.795886\pi$$
$$368$$ 0 0
$$369$$ −76.3085 −3.97246
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −10.8099 −0.559714 −0.279857 0.960042i $$-0.590287\pi$$
−0.279857 + 0.960042i $$0.590287\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −6.04404 −0.311284
$$378$$ 0 0
$$379$$ −9.28005 −0.476684 −0.238342 0.971181i $$-0.576604\pi$$
−0.238342 + 0.971181i $$0.576604\pi$$
$$380$$ 0 0
$$381$$ 22.3709 1.14609
$$382$$ 0 0
$$383$$ 5.28005 0.269798 0.134899 0.990859i $$-0.456929\pi$$
0.134899 + 0.990859i $$0.456929\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 35.7190 1.81570
$$388$$ 0 0
$$389$$ 5.48395 0.278047 0.139024 0.990289i $$-0.455604\pi$$
0.139024 + 0.990289i $$0.455604\pi$$
$$390$$ 0 0
$$391$$ −41.9688 −2.12245
$$392$$ 0 0
$$393$$ −24.5601 −1.23889
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −6.40493 −0.321454 −0.160727 0.986999i $$-0.551384\pi$$
−0.160727 + 0.986999i $$0.551384\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.20482 −0.0601656 −0.0300828 0.999547i $$-0.509577\pi$$
−0.0300828 + 0.999547i $$0.509577\pi$$
$$402$$ 0 0
$$403$$ −9.34816 −0.465665
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 14.9092 0.739020
$$408$$ 0 0
$$409$$ 2.31032 0.114238 0.0571191 0.998367i $$-0.481809\pi$$
0.0571191 + 0.998367i $$0.481809\pi$$
$$410$$ 0 0
$$411$$ 32.9991 1.62772
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −30.6206 −1.49950
$$418$$ 0 0
$$419$$ 19.7384 0.964285 0.482142 0.876093i $$-0.339859\pi$$
0.482142 + 0.876093i $$0.339859\pi$$
$$420$$ 0 0
$$421$$ 30.1433 1.46910 0.734548 0.678556i $$-0.237394\pi$$
0.734548 + 0.678556i $$0.237394\pi$$
$$422$$ 0 0
$$423$$ 23.3700 1.13629
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −32.2645 −1.55774
$$430$$ 0 0
$$431$$ −4.61353 −0.222226 −0.111113 0.993808i $$-0.535442\pi$$
−0.111113 + 0.993808i $$0.535442\pi$$
$$432$$ 0 0
$$433$$ 11.4399 0.549767 0.274883 0.961478i $$-0.411361\pi$$
0.274883 + 0.961478i $$0.411361\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −11.7190 −0.560598
$$438$$ 0 0
$$439$$ −12.0294 −0.574130 −0.287065 0.957911i $$-0.592680\pi$$
−0.287065 + 0.957911i $$0.592680\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −14.4390 −0.686017 −0.343009 0.939332i $$-0.611446\pi$$
−0.343009 + 0.939332i $$0.611446\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 7.81078 0.369437
$$448$$ 0 0
$$449$$ 19.2342 0.907717 0.453858 0.891074i $$-0.350047\pi$$
0.453858 + 0.891074i $$0.350047\pi$$
$$450$$ 0 0
$$451$$ −28.0294 −1.31985
$$452$$ 0 0
$$453$$ −11.7649 −0.552764
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 34.8780 1.63152 0.815762 0.578388i $$-0.196318\pi$$
0.815762 + 0.578388i $$0.196318\pi$$
$$458$$ 0 0
$$459$$ 67.8236 3.16574
$$460$$ 0 0
$$461$$ 15.2607 0.710760 0.355380 0.934722i $$-0.384351\pi$$
0.355380 + 0.934722i $$0.384351\pi$$
$$462$$ 0 0
$$463$$ 24.9991 1.16181 0.580903 0.813973i $$-0.302700\pi$$
0.580903 + 0.813973i $$0.302700\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −5.06433 −0.234349 −0.117175 0.993111i $$-0.537384\pi$$
−0.117175 + 0.993111i $$0.537384\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −17.7190 −0.816450
$$472$$ 0 0
$$473$$ 13.1202 0.603267
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 62.3690 2.85568
$$478$$ 0 0
$$479$$ −41.8089 −1.91030 −0.955150 0.296123i $$-0.904306\pi$$
−0.955150 + 0.296123i $$0.904306\pi$$
$$480$$ 0 0
$$481$$ −24.9310 −1.13675
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 21.3406 0.967035 0.483517 0.875335i $$-0.339359\pi$$
0.483517 + 0.875335i $$0.339359\pi$$
$$488$$ 0 0
$$489$$ 32.0294 1.44842
$$490$$ 0 0
$$491$$ 8.35620 0.377110 0.188555 0.982063i $$-0.439620\pi$$
0.188555 + 0.982063i $$0.439620\pi$$
$$492$$ 0 0
$$493$$ 8.38555 0.377666
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −38.8539 −1.73934 −0.869670 0.493634i $$-0.835668\pi$$
−0.869670 + 0.493634i $$0.835668\pi$$
$$500$$ 0 0
$$501$$ 9.23417 0.412552
$$502$$ 0 0
$$503$$ 17.7044 0.789398 0.394699 0.918810i $$-0.370849\pi$$
0.394699 + 0.918810i $$0.370849\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 13.3288 0.591952
$$508$$ 0 0
$$509$$ −7.11021 −0.315154 −0.157577 0.987507i $$-0.550368\pi$$
−0.157577 + 0.987507i $$0.550368\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 18.9385 0.836157
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 8.58417 0.377531
$$518$$ 0 0
$$519$$ −70.0128 −3.07322
$$520$$ 0 0
$$521$$ −18.1892 −0.796884 −0.398442 0.917194i $$-0.630449\pi$$
−0.398442 + 0.917194i $$0.630449\pi$$
$$522$$ 0 0
$$523$$ 13.9882 0.611661 0.305830 0.952086i $$-0.401066\pi$$
0.305830 + 0.952086i $$0.401066\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 12.9697 0.564970
$$528$$ 0 0
$$529$$ 29.9991 1.30431
$$530$$ 0 0
$$531$$ 40.0487 1.73797
$$532$$ 0 0
$$533$$ 46.8704 2.03018
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 45.4986 1.96341
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −20.8245 −0.895317 −0.447659 0.894205i $$-0.647742\pi$$
−0.447659 + 0.894205i $$0.647742\pi$$
$$542$$ 0 0
$$543$$ 30.2186 1.29680
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −3.09839 −0.132478 −0.0662388 0.997804i $$-0.521100\pi$$
−0.0662388 + 0.997804i $$0.521100\pi$$
$$548$$ 0 0
$$549$$ −36.2598 −1.54753
$$550$$ 0 0
$$551$$ 2.34152 0.0997519
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 18.8099 0.797000 0.398500 0.917168i $$-0.369531\pi$$
0.398500 + 0.917168i $$0.369531\pi$$
$$558$$ 0 0
$$559$$ −21.9394 −0.927940
$$560$$ 0 0
$$561$$ 44.7640 1.88994
$$562$$ 0 0
$$563$$ 28.9503 1.22011 0.610056 0.792358i $$-0.291147\pi$$
0.610056 + 0.792358i $$0.291147\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −29.9688 −1.25636 −0.628179 0.778069i $$-0.716199\pi$$
−0.628179 + 0.778069i $$0.716199\pi$$
$$570$$ 0 0
$$571$$ 0.280964 0.0117580 0.00587898 0.999983i $$-0.498129\pi$$
0.00587898 + 0.999983i $$0.498129\pi$$
$$572$$ 0 0
$$573$$ 25.0450 1.04627
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 25.9541 1.08048 0.540242 0.841510i $$-0.318333\pi$$
0.540242 + 0.841510i $$0.318333\pi$$
$$578$$ 0 0
$$579$$ 10.8411 0.450539
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 22.9092 0.948801
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −22.2304 −0.917547 −0.458773 0.888553i $$-0.651711\pi$$
−0.458773 + 0.888553i $$0.651711\pi$$
$$588$$ 0 0
$$589$$ 3.62156 0.149224
$$590$$ 0 0
$$591$$ −50.8704 −2.09253
$$592$$ 0 0
$$593$$ 35.0743 1.44033 0.720165 0.693803i $$-0.244066\pi$$
0.720165 + 0.693803i $$0.244066\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −83.9670 −3.43654
$$598$$ 0 0
$$599$$ −21.7262 −0.887707 −0.443853 0.896099i $$-0.646389\pi$$
−0.443853 + 0.896099i $$0.646389\pi$$
$$600$$ 0 0
$$601$$ 23.9688 0.977708 0.488854 0.872366i $$-0.337415\pi$$
0.488854 + 0.872366i $$0.337415\pi$$
$$602$$ 0 0
$$603$$ 50.9385 2.07438
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 43.3241 1.75847 0.879235 0.476388i $$-0.158054\pi$$
0.879235 + 0.476388i $$0.158054\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −14.3544 −0.580715
$$612$$ 0 0
$$613$$ 8.90917 0.359838 0.179919 0.983681i $$-0.442416\pi$$
0.179919 + 0.983681i $$0.442416\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −27.2413 −1.09669 −0.548347 0.836251i $$-0.684743\pi$$
−0.548347 + 0.836251i $$0.684743\pi$$
$$618$$ 0 0
$$619$$ −24.1405 −0.970288 −0.485144 0.874434i $$-0.661233\pi$$
−0.485144 + 0.874434i $$0.661233\pi$$
$$620$$ 0 0
$$621$$ −85.6491 −3.43698
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 12.4995 0.499184
$$628$$ 0 0
$$629$$ 34.5895 1.37917
$$630$$ 0 0
$$631$$ 8.01468 0.319059 0.159530 0.987193i $$-0.449002\pi$$
0.159530 + 0.987193i $$0.449002\pi$$
$$632$$ 0 0
$$633$$ 53.8548 2.14054
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −28.7493 −1.13731
$$640$$ 0 0
$$641$$ −49.1495 −1.94129 −0.970645 0.240516i $$-0.922683\pi$$
−0.970645 + 0.240516i $$0.922683\pi$$
$$642$$ 0 0
$$643$$ 7.24599 0.285754 0.142877 0.989740i $$-0.454365\pi$$
0.142877 + 0.989740i $$0.454365\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 30.2791 1.19040 0.595198 0.803579i $$-0.297074\pi$$
0.595198 + 0.803579i $$0.297074\pi$$
$$648$$ 0 0
$$649$$ 14.7106 0.577440
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −7.96881 −0.311844 −0.155922 0.987769i $$-0.549835\pi$$
−0.155922 + 0.987769i $$0.549835\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 49.2489 1.92138
$$658$$ 0 0
$$659$$ 20.9239 0.815078 0.407539 0.913188i $$-0.366387\pi$$
0.407539 + 0.913188i $$0.366387\pi$$
$$660$$ 0 0
$$661$$ −46.1992 −1.79694 −0.898470 0.439034i $$-0.855321\pi$$
−0.898470 + 0.439034i $$0.855321\pi$$
$$662$$ 0 0
$$663$$ −74.8539 −2.90708
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −10.5895 −0.410025
$$668$$ 0 0
$$669$$ 0.734633 0.0284025
$$670$$ 0 0
$$671$$ −13.3188 −0.514167
$$672$$ 0 0
$$673$$ −40.3784 −1.55647 −0.778237 0.627970i $$-0.783886\pi$$
−0.778237 + 0.627970i $$0.783886\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −44.3737 −1.70542 −0.852711 0.522383i $$-0.825043\pi$$
−0.852711 + 0.522383i $$0.825043\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.76491 0.0676315
$$682$$ 0 0
$$683$$ −17.9394 −0.686434 −0.343217 0.939256i $$-0.611517\pi$$
−0.343217 + 0.939256i $$0.611517\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −22.2186 −0.847692
$$688$$ 0 0
$$689$$ −38.3085 −1.45944
$$690$$ 0 0
$$691$$ 12.7905 0.486573 0.243287 0.969954i $$-0.421774\pi$$
0.243287 + 0.969954i $$0.421774\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −65.0284 −2.46313
$$698$$ 0 0
$$699$$ 26.5601 1.00460
$$700$$ 0 0
$$701$$ −19.4234 −0.733611 −0.366806 0.930298i $$-0.619549\pi$$
−0.366806 + 0.930298i $$0.619549\pi$$
$$702$$ 0 0
$$703$$ 9.65848 0.364277
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −13.4839 −0.506400 −0.253200 0.967414i $$-0.581483\pi$$
−0.253200 + 0.967414i $$0.581483\pi$$
$$710$$ 0 0
$$711$$ 114.898 4.30901
$$712$$ 0 0
$$713$$ −16.3784 −0.613377
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −22.7034 −0.847876
$$718$$ 0 0
$$719$$ −15.3700 −0.573203 −0.286601 0.958050i $$-0.592526\pi$$
−0.286601 + 0.958050i $$0.592526\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −22.7493 −0.846056
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −13.1589 −0.488038 −0.244019 0.969770i $$-0.578466\pi$$
−0.244019 + 0.969770i $$0.578466\pi$$
$$728$$ 0 0
$$729$$ 1.12110 0.0415224
$$730$$ 0 0
$$731$$ 30.4390 1.12583
$$732$$ 0 0
$$733$$ 10.0265 0.370337 0.185169 0.982707i $$-0.440717\pi$$
0.185169 + 0.982707i $$0.440717\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.7106 0.689212
$$738$$ 0 0
$$739$$ 19.2266 0.707262 0.353631 0.935385i $$-0.384947\pi$$
0.353631 + 0.935385i $$0.384947\pi$$
$$740$$ 0 0
$$741$$ −20.9016 −0.767840
$$742$$ 0 0
$$743$$ −5.21949 −0.191485 −0.0957423 0.995406i $$-0.530522\pi$$
−0.0957423 + 0.995406i $$0.530522\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −68.3884 −2.50220
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 29.8548 1.08942 0.544709 0.838625i $$-0.316640\pi$$
0.544709 + 0.838625i $$0.316640\pi$$
$$752$$ 0 0
$$753$$ −71.6197 −2.60997
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −18.0294 −0.655288 −0.327644 0.944801i $$-0.606255\pi$$
−0.327644 + 0.944801i $$0.606255\pi$$
$$758$$ 0 0
$$759$$ −56.5289 −2.05187
$$760$$ 0 0
$$761$$ −8.22041 −0.297990 −0.148995 0.988838i $$-0.547604\pi$$
−0.148995 + 0.988838i $$0.547604\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −24.5988 −0.888213
$$768$$ 0 0
$$769$$ −50.6888 −1.82788 −0.913942 0.405845i $$-0.866977\pi$$
−0.913942 + 0.405845i $$0.866977\pi$$
$$770$$ 0 0
$$771$$ −2.24977 −0.0810235
$$772$$ 0 0
$$773$$ −6.99622 −0.251637 −0.125818 0.992053i $$-0.540156\pi$$
−0.125818 + 0.992053i $$0.540156\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −18.1580 −0.650579
$$780$$ 0 0
$$781$$ −10.5601 −0.377870
$$782$$ 0 0
$$783$$ 17.1131 0.611571
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 14.3444 0.511322 0.255661 0.966767i $$-0.417707\pi$$
0.255661 + 0.966767i $$0.417707\pi$$
$$788$$ 0 0
$$789$$ −57.9982 −2.06479
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 22.2716 0.790887
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 13.9348 0.493594 0.246797 0.969067i $$-0.420622\pi$$
0.246797 + 0.969067i $$0.420622\pi$$
$$798$$ 0 0
$$799$$ 19.9154 0.704555
$$800$$ 0 0
$$801$$ 77.5885 2.74146
$$802$$ 0 0
$$803$$ 18.0899 0.638379
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 69.2782 2.43871
$$808$$ 0 0
$$809$$ −5.58325 −0.196297 −0.0981483 0.995172i $$-0.531292\pi$$
−0.0981483 + 0.995172i $$0.531292\pi$$
$$810$$ 0 0
$$811$$ 6.57947 0.231036 0.115518 0.993305i $$-0.463147\pi$$
0.115518 + 0.993305i $$0.463147\pi$$
$$812$$ 0 0
$$813$$ 24.6206 0.863484
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 8.49954 0.297361
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 16.3250 0.569747 0.284873 0.958565i $$-0.408048\pi$$
0.284873 + 0.958565i $$0.408048\pi$$
$$822$$ 0 0
$$823$$ 12.3491 0.430462 0.215231 0.976563i $$-0.430950\pi$$
0.215231 + 0.976563i $$0.430950\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 6.40963 0.222885 0.111442 0.993771i $$-0.464453\pi$$
0.111442 + 0.993771i $$0.464453\pi$$
$$828$$ 0 0
$$829$$ 26.1698 0.908916 0.454458 0.890768i $$-0.349833\pi$$
0.454458 + 0.890768i $$0.349833\pi$$
$$830$$ 0 0
$$831$$ −8.68876 −0.301410
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 26.4683 0.914880
$$838$$ 0 0
$$839$$ 1.12958 0.0389975 0.0194988 0.999810i $$-0.493793\pi$$
0.0194988 + 0.999810i $$0.493793\pi$$
$$840$$ 0 0
$$841$$ −26.8842 −0.927041
$$842$$ 0 0
$$843$$ −74.0734 −2.55122
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −83.8842 −2.87890
$$850$$ 0 0
$$851$$ −43.6803 −1.49734
$$852$$ 0 0
$$853$$ −6.29095 −0.215398 −0.107699 0.994184i $$-0.534348\pi$$
−0.107699 + 0.994184i $$0.534348\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 25.0596 0.856021 0.428010 0.903774i $$-0.359215\pi$$
0.428010 + 0.903774i $$0.359215\pi$$
$$858$$ 0 0
$$859$$ −53.7896 −1.83528 −0.917638 0.397417i $$-0.869907\pi$$
−0.917638 + 0.397417i $$0.869907\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −58.0899 −1.97740 −0.988702 0.149896i $$-0.952106\pi$$
−0.988702 + 0.149896i $$0.952106\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 50.7299 1.72288
$$868$$ 0 0
$$869$$ 42.2039 1.43167
$$870$$ 0 0
$$871$$ −31.2876 −1.06014
$$872$$ 0 0
$$873$$ −18.4995 −0.626115
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −24.0899 −0.813459 −0.406729 0.913549i $$-0.633331\pi$$
−0.406729 + 0.913549i $$0.633331\pi$$
$$878$$ 0 0
$$879$$ 31.0450 1.04712
$$880$$ 0 0
$$881$$ −40.9679 −1.38024 −0.690122 0.723693i $$-0.742443\pi$$
−0.690122 + 0.723693i $$0.742443\pi$$
$$882$$ 0 0
$$883$$ −43.8014 −1.47403 −0.737017 0.675874i $$-0.763766\pi$$
−0.737017 + 0.675874i $$0.763766\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.77959 0.0597527 0.0298764 0.999554i $$-0.490489\pi$$
0.0298764 + 0.999554i $$0.490489\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 40.9239 1.37100
$$892$$ 0 0
$$893$$ 5.56101 0.186092
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 94.5271 3.15617
$$898$$ 0 0
$$899$$ 3.27248 0.109143
$$900$$ 0 0
$$901$$ 53.1495 1.77067
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 53.0284 1.76078 0.880390 0.474250i $$-0.157281\pi$$
0.880390 + 0.474250i $$0.157281\pi$$
$$908$$ 0 0
$$909$$ 30.9797 1.02753
$$910$$ 0 0
$$911$$ 28.1798 0.933639 0.466820 0.884353i $$-0.345400\pi$$
0.466820 + 0.884353i $$0.345400\pi$$
$$912$$ 0 0
$$913$$ −25.1202 −0.831357
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 38.4243 1.26750 0.633751 0.773538i $$-0.281515\pi$$
0.633751 + 0.773538i $$0.281515\pi$$
$$920$$ 0 0
$$921$$ 100.292 3.30473
$$922$$ 0 0
$$923$$ 17.6585 0.581236
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −16.8099 −0.552108
$$928$$ 0 0
$$929$$ 36.6576 1.20270 0.601348 0.798987i $$-0.294631\pi$$
0.601348 + 0.798987i $$0.294631\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 31.4381 1.02924
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −5.83302 −0.190557 −0.0952783 0.995451i $$-0.530374\pi$$
−0.0952783 + 0.995451i $$0.530374\pi$$
$$938$$ 0 0
$$939$$ −65.0743 −2.12362
$$940$$ 0 0
$$941$$ 2.23796 0.0729553 0.0364776 0.999334i $$-0.488386\pi$$
0.0364776 + 0.999334i $$0.488386\pi$$
$$942$$ 0 0
$$943$$ 82.1193 2.67417
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −17.7502 −0.576805 −0.288402 0.957509i $$-0.593124\pi$$
−0.288402 + 0.957509i $$0.593124\pi$$
$$948$$ 0 0
$$949$$ −30.2498 −0.981949
$$950$$ 0 0
$$951$$ 49.2177 1.59599
$$952$$ 0 0
$$953$$ −32.0294 −1.03753 −0.518766 0.854916i $$-0.673609\pi$$
−0.518766 + 0.854916i $$0.673609\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 11.2947 0.365107
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −25.9385 −0.836727
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 43.4305 1.39663 0.698316 0.715790i $$-0.253933\pi$$
0.698316 + 0.715790i $$0.253933\pi$$
$$968$$ 0 0
$$969$$ 28.9991 0.931585
$$970$$ 0 0
$$971$$ 1.79897 0.0577316 0.0288658 0.999583i $$-0.490810\pi$$
0.0288658 + 0.999583i $$0.490810\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −22.4390 −0.717887 −0.358943 0.933359i $$-0.616863\pi$$
−0.358943 + 0.933359i $$0.616863\pi$$
$$978$$ 0 0
$$979$$ 28.4995 0.910849
$$980$$ 0 0
$$981$$ −67.3388 −2.14996
$$982$$ 0 0
$$983$$ −37.6950 −1.20228 −0.601141 0.799143i $$-0.705287\pi$$
−0.601141 + 0.799143i $$0.705287\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −38.4390 −1.22229
$$990$$ 0 0
$$991$$ 13.5686 0.431020 0.215510 0.976502i $$-0.430859\pi$$
0.215510 + 0.976502i $$0.430859\pi$$
$$992$$ 0 0
$$993$$ −80.5583 −2.55644
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −14.2838 −0.452373 −0.226187 0.974084i $$-0.572626\pi$$
−0.226187 + 0.974084i $$0.572626\pi$$
$$998$$ 0 0
$$999$$ 70.5895 2.23335
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 9800.2.a.cg.1.3 3
5.2 odd 4 1960.2.g.c.1569.1 6
5.3 odd 4 1960.2.g.c.1569.6 6
5.4 even 2 9800.2.a.cd.1.1 3
7.6 odd 2 1400.2.a.s.1.1 3
28.27 even 2 2800.2.a.br.1.3 3
35.13 even 4 280.2.g.b.169.1 6
35.27 even 4 280.2.g.b.169.6 yes 6
35.34 odd 2 1400.2.a.t.1.3 3
105.62 odd 4 2520.2.t.g.1009.1 6
105.83 odd 4 2520.2.t.g.1009.2 6
140.27 odd 4 560.2.g.f.449.1 6
140.83 odd 4 560.2.g.f.449.6 6
140.139 even 2 2800.2.a.bq.1.1 3
280.13 even 4 2240.2.g.l.449.6 6
280.27 odd 4 2240.2.g.m.449.6 6
280.83 odd 4 2240.2.g.m.449.1 6
280.237 even 4 2240.2.g.l.449.1 6
420.83 even 4 5040.2.t.y.1009.2 6
420.167 even 4 5040.2.t.y.1009.1 6

By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.g.b.169.1 6 35.13 even 4
280.2.g.b.169.6 yes 6 35.27 even 4
560.2.g.f.449.1 6 140.27 odd 4
560.2.g.f.449.6 6 140.83 odd 4
1400.2.a.s.1.1 3 7.6 odd 2
1400.2.a.t.1.3 3 35.34 odd 2
1960.2.g.c.1569.1 6 5.2 odd 4
1960.2.g.c.1569.6 6 5.3 odd 4
2240.2.g.l.449.1 6 280.237 even 4
2240.2.g.l.449.6 6 280.13 even 4
2240.2.g.m.449.1 6 280.83 odd 4
2240.2.g.m.449.6 6 280.27 odd 4
2520.2.t.g.1009.1 6 105.62 odd 4
2520.2.t.g.1009.2 6 105.83 odd 4
2800.2.a.bq.1.1 3 140.139 even 2
2800.2.a.br.1.3 3 28.27 even 2
5040.2.t.y.1009.1 6 420.167 even 4
5040.2.t.y.1009.2 6 420.83 even 4
9800.2.a.cd.1.1 3 5.4 even 2
9800.2.a.cg.1.3 3 1.1 even 1 trivial