# Properties

 Label 9280.2.a.bu.1.1 Level $9280$ Weight $2$ Character 9280.1 Self dual yes Analytic conductor $74.101$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9280,2,Mod(1,9280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9280.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$9280 = 2^{6} \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9280.a (trivial)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$74.1011730757$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.148.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - x^{2} - 3x + 1$$ x^3 - x^2 - 3*x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 145) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$2.17009$$ of defining polynomial Character $$\chi$$ $$=$$ 9280.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.70928 q^{3} +1.00000 q^{5} +0.630898 q^{7} -0.0783777 q^{9} +O(q^{10})$$ $$q-1.70928 q^{3} +1.00000 q^{5} +0.630898 q^{7} -0.0783777 q^{9} -0.290725 q^{11} +0.921622 q^{13} -1.70928 q^{15} +4.97107 q^{17} +6.04945 q^{19} -1.07838 q^{21} +2.29072 q^{23} +1.00000 q^{25} +5.26180 q^{27} -1.00000 q^{29} +10.0494 q^{31} +0.496928 q^{33} +0.630898 q^{35} -1.55252 q^{37} -1.57531 q^{39} +0.340173 q^{41} +5.70928 q^{43} -0.0783777 q^{45} -1.12783 q^{47} -6.60197 q^{49} -8.49693 q^{51} +0.340173 q^{53} -0.290725 q^{55} -10.3402 q^{57} -9.75872 q^{59} -3.07838 q^{61} -0.0494483 q^{63} +0.921622 q^{65} +5.70928 q^{67} -3.91548 q^{69} +9.07838 q^{71} -6.94441 q^{73} -1.70928 q^{75} -0.183417 q^{77} +12.3896 q^{79} -8.75872 q^{81} -2.78765 q^{83} +4.97107 q^{85} +1.70928 q^{87} +4.73820 q^{89} +0.581449 q^{91} -17.1773 q^{93} +6.04945 q^{95} -15.8927 q^{97} +0.0227863 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10})$$ 3 * q + 2 * q^3 + 3 * q^5 - 2 * q^7 + 3 * q^9 $$3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 3 q^{9} - 8 q^{11} + 6 q^{13} + 2 q^{15} + 14 q^{23} + 3 q^{25} + 8 q^{27} - 3 q^{29} + 12 q^{31} - 16 q^{33} - 2 q^{35} - 4 q^{37} + 16 q^{39} - 10 q^{41} + 10 q^{43} + 3 q^{45} + 18 q^{47} - q^{49} - 8 q^{51} - 10 q^{53} - 8 q^{55} - 20 q^{57} - 4 q^{59} - 6 q^{61} + 18 q^{63} + 6 q^{65} + 10 q^{67} + 20 q^{69} + 24 q^{71} - 4 q^{73} + 2 q^{75} + 4 q^{77} + 8 q^{79} - q^{81} + 2 q^{83} - 2 q^{87} + 22 q^{89} + 16 q^{91} - 12 q^{93} - 36 q^{97} - 20 q^{99}+O(q^{100})$$ 3 * q + 2 * q^3 + 3 * q^5 - 2 * q^7 + 3 * q^9 - 8 * q^11 + 6 * q^13 + 2 * q^15 + 14 * q^23 + 3 * q^25 + 8 * q^27 - 3 * q^29 + 12 * q^31 - 16 * q^33 - 2 * q^35 - 4 * q^37 + 16 * q^39 - 10 * q^41 + 10 * q^43 + 3 * q^45 + 18 * q^47 - q^49 - 8 * q^51 - 10 * q^53 - 8 * q^55 - 20 * q^57 - 4 * q^59 - 6 * q^61 + 18 * q^63 + 6 * q^65 + 10 * q^67 + 20 * q^69 + 24 * q^71 - 4 * q^73 + 2 * q^75 + 4 * q^77 + 8 * q^79 - q^81 + 2 * q^83 - 2 * q^87 + 22 * q^89 + 16 * q^91 - 12 * q^93 - 36 * q^97 - 20 * q^99

## 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
$$3$$ −1.70928 −0.986851 −0.493425 0.869788i $$-0.664255\pi$$
−0.493425 + 0.869788i $$0.664255\pi$$
$$4$$ 0 0
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 0.630898 0.238457 0.119228 0.992867i $$-0.461958\pi$$
0.119228 + 0.992867i $$0.461958\pi$$
$$8$$ 0 0
$$9$$ −0.0783777 −0.0261259
$$10$$ 0 0
$$11$$ −0.290725 −0.0876568 −0.0438284 0.999039i $$-0.513955\pi$$
−0.0438284 + 0.999039i $$0.513955\pi$$
$$12$$ 0 0
$$13$$ 0.921622 0.255612 0.127806 0.991799i $$-0.459207\pi$$
0.127806 + 0.991799i $$0.459207\pi$$
$$14$$ 0 0
$$15$$ −1.70928 −0.441333
$$16$$ 0 0
$$17$$ 4.97107 1.20566 0.602831 0.797869i $$-0.294039\pi$$
0.602831 + 0.797869i $$0.294039\pi$$
$$18$$ 0 0
$$19$$ 6.04945 1.38784 0.693919 0.720053i $$-0.255882\pi$$
0.693919 + 0.720053i $$0.255882\pi$$
$$20$$ 0 0
$$21$$ −1.07838 −0.235321
$$22$$ 0 0
$$23$$ 2.29072 0.477649 0.238825 0.971063i $$-0.423238\pi$$
0.238825 + 0.971063i $$0.423238\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 5.26180 1.01263
$$28$$ 0 0
$$29$$ −1.00000 −0.185695
$$30$$ 0 0
$$31$$ 10.0494 1.80493 0.902467 0.430759i $$-0.141754\pi$$
0.902467 + 0.430759i $$0.141754\pi$$
$$32$$ 0 0
$$33$$ 0.496928 0.0865041
$$34$$ 0 0
$$35$$ 0.630898 0.106641
$$36$$ 0 0
$$37$$ −1.55252 −0.255233 −0.127616 0.991824i $$-0.540733\pi$$
−0.127616 + 0.991824i $$0.540733\pi$$
$$38$$ 0 0
$$39$$ −1.57531 −0.252251
$$40$$ 0 0
$$41$$ 0.340173 0.0531261 0.0265630 0.999647i $$-0.491544\pi$$
0.0265630 + 0.999647i $$0.491544\pi$$
$$42$$ 0 0
$$43$$ 5.70928 0.870656 0.435328 0.900272i $$-0.356632\pi$$
0.435328 + 0.900272i $$0.356632\pi$$
$$44$$ 0 0
$$45$$ −0.0783777 −0.0116839
$$46$$ 0 0
$$47$$ −1.12783 −0.164510 −0.0822552 0.996611i $$-0.526212\pi$$
−0.0822552 + 0.996611i $$0.526212\pi$$
$$48$$ 0 0
$$49$$ −6.60197 −0.943138
$$50$$ 0 0
$$51$$ −8.49693 −1.18981
$$52$$ 0 0
$$53$$ 0.340173 0.0467264 0.0233632 0.999727i $$-0.492563\pi$$
0.0233632 + 0.999727i $$0.492563\pi$$
$$54$$ 0 0
$$55$$ −0.290725 −0.0392013
$$56$$ 0 0
$$57$$ −10.3402 −1.36959
$$58$$ 0 0
$$59$$ −9.75872 −1.27048 −0.635239 0.772316i $$-0.719098\pi$$
−0.635239 + 0.772316i $$0.719098\pi$$
$$60$$ 0 0
$$61$$ −3.07838 −0.394146 −0.197073 0.980389i $$-0.563144\pi$$
−0.197073 + 0.980389i $$0.563144\pi$$
$$62$$ 0 0
$$63$$ −0.0494483 −0.00622990
$$64$$ 0 0
$$65$$ 0.921622 0.114313
$$66$$ 0 0
$$67$$ 5.70928 0.697499 0.348749 0.937216i $$-0.386606\pi$$
0.348749 + 0.937216i $$0.386606\pi$$
$$68$$ 0 0
$$69$$ −3.91548 −0.471368
$$70$$ 0 0
$$71$$ 9.07838 1.07741 0.538703 0.842496i $$-0.318915\pi$$
0.538703 + 0.842496i $$0.318915\pi$$
$$72$$ 0 0
$$73$$ −6.94441 −0.812782 −0.406391 0.913699i $$-0.633213\pi$$
−0.406391 + 0.913699i $$0.633213\pi$$
$$74$$ 0 0
$$75$$ −1.70928 −0.197370
$$76$$ 0 0
$$77$$ −0.183417 −0.0209024
$$78$$ 0 0
$$79$$ 12.3896 1.39394 0.696971 0.717100i $$-0.254531\pi$$
0.696971 + 0.717100i $$0.254531\pi$$
$$80$$ 0 0
$$81$$ −8.75872 −0.973192
$$82$$ 0 0
$$83$$ −2.78765 −0.305985 −0.152992 0.988227i $$-0.548891\pi$$
−0.152992 + 0.988227i $$0.548891\pi$$
$$84$$ 0 0
$$85$$ 4.97107 0.539188
$$86$$ 0 0
$$87$$ 1.70928 0.183254
$$88$$ 0 0
$$89$$ 4.73820 0.502249 0.251124 0.967955i $$-0.419200\pi$$
0.251124 + 0.967955i $$0.419200\pi$$
$$90$$ 0 0
$$91$$ 0.581449 0.0609524
$$92$$ 0 0
$$93$$ −17.1773 −1.78120
$$94$$ 0 0
$$95$$ 6.04945 0.620660
$$96$$ 0 0
$$97$$ −15.8927 −1.61366 −0.806829 0.590785i $$-0.798818\pi$$
−0.806829 + 0.590785i $$0.798818\pi$$
$$98$$ 0 0
$$99$$ 0.0227863 0.00229011
$$100$$ 0 0
$$101$$ 12.2557 1.21948 0.609741 0.792600i $$-0.291273\pi$$
0.609741 + 0.792600i $$0.291273\pi$$
$$102$$ 0 0
$$103$$ −7.86603 −0.775063 −0.387532 0.921856i $$-0.626672\pi$$
−0.387532 + 0.921856i $$0.626672\pi$$
$$104$$ 0 0
$$105$$ −1.07838 −0.105239
$$106$$ 0 0
$$107$$ −12.7298 −1.23064 −0.615318 0.788279i $$-0.710972\pi$$
−0.615318 + 0.788279i $$0.710972\pi$$
$$108$$ 0 0
$$109$$ −12.4391 −1.19145 −0.595723 0.803190i $$-0.703135\pi$$
−0.595723 + 0.803190i $$0.703135\pi$$
$$110$$ 0 0
$$111$$ 2.65368 0.251877
$$112$$ 0 0
$$113$$ 12.5730 1.18277 0.591386 0.806389i $$-0.298581\pi$$
0.591386 + 0.806389i $$0.298581\pi$$
$$114$$ 0 0
$$115$$ 2.29072 0.213611
$$116$$ 0 0
$$117$$ −0.0722347 −0.00667810
$$118$$ 0 0
$$119$$ 3.13624 0.287498
$$120$$ 0 0
$$121$$ −10.9155 −0.992316
$$122$$ 0 0
$$123$$ −0.581449 −0.0524275
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −20.9132 −1.85575 −0.927874 0.372895i $$-0.878365\pi$$
−0.927874 + 0.372895i $$0.878365\pi$$
$$128$$ 0 0
$$129$$ −9.75872 −0.859208
$$130$$ 0 0
$$131$$ 13.4680 1.17670 0.588352 0.808605i $$-0.299777\pi$$
0.588352 + 0.808605i $$0.299777\pi$$
$$132$$ 0 0
$$133$$ 3.81658 0.330940
$$134$$ 0 0
$$135$$ 5.26180 0.452863
$$136$$ 0 0
$$137$$ −13.5525 −1.15787 −0.578935 0.815374i $$-0.696531\pi$$
−0.578935 + 0.815374i $$0.696531\pi$$
$$138$$ 0 0
$$139$$ 4.89496 0.415185 0.207593 0.978215i $$-0.433437\pi$$
0.207593 + 0.978215i $$0.433437\pi$$
$$140$$ 0 0
$$141$$ 1.92777 0.162347
$$142$$ 0 0
$$143$$ −0.267938 −0.0224061
$$144$$ 0 0
$$145$$ −1.00000 −0.0830455
$$146$$ 0 0
$$147$$ 11.2846 0.930737
$$148$$ 0 0
$$149$$ 12.5236 1.02597 0.512986 0.858397i $$-0.328539\pi$$
0.512986 + 0.858397i $$0.328539\pi$$
$$150$$ 0 0
$$151$$ 7.60197 0.618639 0.309320 0.950958i $$-0.399899\pi$$
0.309320 + 0.950958i $$0.399899\pi$$
$$152$$ 0 0
$$153$$ −0.389621 −0.0314990
$$154$$ 0 0
$$155$$ 10.0494 0.807191
$$156$$ 0 0
$$157$$ 24.8865 1.98616 0.993081 0.117428i $$-0.0374648\pi$$
0.993081 + 0.117428i $$0.0374648\pi$$
$$158$$ 0 0
$$159$$ −0.581449 −0.0461119
$$160$$ 0 0
$$161$$ 1.44521 0.113899
$$162$$ 0 0
$$163$$ −0.447480 −0.0350493 −0.0175247 0.999846i $$-0.505579\pi$$
−0.0175247 + 0.999846i $$0.505579\pi$$
$$164$$ 0 0
$$165$$ 0.496928 0.0386858
$$166$$ 0 0
$$167$$ 19.8660 1.53728 0.768640 0.639682i $$-0.220934\pi$$
0.768640 + 0.639682i $$0.220934\pi$$
$$168$$ 0 0
$$169$$ −12.1506 −0.934662
$$170$$ 0 0
$$171$$ −0.474142 −0.0362586
$$172$$ 0 0
$$173$$ 25.4329 1.93363 0.966815 0.255478i $$-0.0822329\pi$$
0.966815 + 0.255478i $$0.0822329\pi$$
$$174$$ 0 0
$$175$$ 0.630898 0.0476914
$$176$$ 0 0
$$177$$ 16.6803 1.25377
$$178$$ 0 0
$$179$$ −14.8371 −1.10898 −0.554489 0.832191i $$-0.687086\pi$$
−0.554489 + 0.832191i $$0.687086\pi$$
$$180$$ 0 0
$$181$$ 5.91548 0.439694 0.219847 0.975534i $$-0.429444\pi$$
0.219847 + 0.975534i $$0.429444\pi$$
$$182$$ 0 0
$$183$$ 5.26180 0.388963
$$184$$ 0 0
$$185$$ −1.55252 −0.114144
$$186$$ 0 0
$$187$$ −1.44521 −0.105684
$$188$$ 0 0
$$189$$ 3.31965 0.241469
$$190$$ 0 0
$$191$$ 7.02893 0.508595 0.254298 0.967126i $$-0.418156\pi$$
0.254298 + 0.967126i $$0.418156\pi$$
$$192$$ 0 0
$$193$$ 17.8660 1.28603 0.643013 0.765856i $$-0.277684\pi$$
0.643013 + 0.765856i $$0.277684\pi$$
$$194$$ 0 0
$$195$$ −1.57531 −0.112810
$$196$$ 0 0
$$197$$ −6.09890 −0.434528 −0.217264 0.976113i $$-0.569713\pi$$
−0.217264 + 0.976113i $$0.569713\pi$$
$$198$$ 0 0
$$199$$ −9.75872 −0.691778 −0.345889 0.938276i $$-0.612423\pi$$
−0.345889 + 0.938276i $$0.612423\pi$$
$$200$$ 0 0
$$201$$ −9.75872 −0.688327
$$202$$ 0 0
$$203$$ −0.630898 −0.0442803
$$204$$ 0 0
$$205$$ 0.340173 0.0237587
$$206$$ 0 0
$$207$$ −0.179542 −0.0124790
$$208$$ 0 0
$$209$$ −1.75872 −0.121653
$$210$$ 0 0
$$211$$ −9.86603 −0.679206 −0.339603 0.940569i $$-0.610293\pi$$
−0.339603 + 0.940569i $$0.610293\pi$$
$$212$$ 0 0
$$213$$ −15.5174 −1.06324
$$214$$ 0 0
$$215$$ 5.70928 0.389369
$$216$$ 0 0
$$217$$ 6.34017 0.430399
$$218$$ 0 0
$$219$$ 11.8699 0.802094
$$220$$ 0 0
$$221$$ 4.58145 0.308182
$$222$$ 0 0
$$223$$ 10.9711 0.734677 0.367339 0.930087i $$-0.380269\pi$$
0.367339 + 0.930087i $$0.380269\pi$$
$$224$$ 0 0
$$225$$ −0.0783777 −0.00522518
$$226$$ 0 0
$$227$$ 12.5464 0.832732 0.416366 0.909197i $$-0.363303\pi$$
0.416366 + 0.909197i $$0.363303\pi$$
$$228$$ 0 0
$$229$$ −23.3607 −1.54372 −0.771859 0.635794i $$-0.780673\pi$$
−0.771859 + 0.635794i $$0.780673\pi$$
$$230$$ 0 0
$$231$$ 0.313511 0.0206275
$$232$$ 0 0
$$233$$ 12.4703 0.816954 0.408477 0.912769i $$-0.366060\pi$$
0.408477 + 0.912769i $$0.366060\pi$$
$$234$$ 0 0
$$235$$ −1.12783 −0.0735713
$$236$$ 0 0
$$237$$ −21.1773 −1.37561
$$238$$ 0 0
$$239$$ 13.7587 0.889978 0.444989 0.895536i $$-0.353208\pi$$
0.444989 + 0.895536i $$0.353208\pi$$
$$240$$ 0 0
$$241$$ −14.6803 −0.945644 −0.472822 0.881158i $$-0.656765\pi$$
−0.472822 + 0.881158i $$0.656765\pi$$
$$242$$ 0 0
$$243$$ −0.814315 −0.0522383
$$244$$ 0 0
$$245$$ −6.60197 −0.421784
$$246$$ 0 0
$$247$$ 5.57531 0.354748
$$248$$ 0 0
$$249$$ 4.76487 0.301961
$$250$$ 0 0
$$251$$ −15.4413 −0.974649 −0.487324 0.873221i $$-0.662027\pi$$
−0.487324 + 0.873221i $$0.662027\pi$$
$$252$$ 0 0
$$253$$ −0.665970 −0.0418692
$$254$$ 0 0
$$255$$ −8.49693 −0.532098
$$256$$ 0 0
$$257$$ −6.28231 −0.391880 −0.195940 0.980616i $$-0.562776\pi$$
−0.195940 + 0.980616i $$0.562776\pi$$
$$258$$ 0 0
$$259$$ −0.979481 −0.0608620
$$260$$ 0 0
$$261$$ 0.0783777 0.00485146
$$262$$ 0 0
$$263$$ 10.0761 0.621320 0.310660 0.950521i $$-0.399450\pi$$
0.310660 + 0.950521i $$0.399450\pi$$
$$264$$ 0 0
$$265$$ 0.340173 0.0208967
$$266$$ 0 0
$$267$$ −8.09890 −0.495644
$$268$$ 0 0
$$269$$ −28.1711 −1.71762 −0.858812 0.512291i $$-0.828797\pi$$
−0.858812 + 0.512291i $$0.828797\pi$$
$$270$$ 0 0
$$271$$ 28.8020 1.74960 0.874799 0.484485i $$-0.160993\pi$$
0.874799 + 0.484485i $$0.160993\pi$$
$$272$$ 0 0
$$273$$ −0.993857 −0.0601510
$$274$$ 0 0
$$275$$ −0.290725 −0.0175314
$$276$$ 0 0
$$277$$ −0.0266620 −0.00160196 −0.000800982 1.00000i $$-0.500255\pi$$
−0.000800982 1.00000i $$0.500255\pi$$
$$278$$ 0 0
$$279$$ −0.787653 −0.0471556
$$280$$ 0 0
$$281$$ −28.0722 −1.67465 −0.837325 0.546706i $$-0.815881\pi$$
−0.837325 + 0.546706i $$0.815881\pi$$
$$282$$ 0 0
$$283$$ 20.8143 1.23728 0.618641 0.785674i $$-0.287683\pi$$
0.618641 + 0.785674i $$0.287683\pi$$
$$284$$ 0 0
$$285$$ −10.3402 −0.612499
$$286$$ 0 0
$$287$$ 0.214614 0.0126683
$$288$$ 0 0
$$289$$ 7.71154 0.453620
$$290$$ 0 0
$$291$$ 27.1650 1.59244
$$292$$ 0 0
$$293$$ 15.4101 0.900270 0.450135 0.892961i $$-0.351376\pi$$
0.450135 + 0.892961i $$0.351376\pi$$
$$294$$ 0 0
$$295$$ −9.75872 −0.568175
$$296$$ 0 0
$$297$$ −1.52973 −0.0887641
$$298$$ 0 0
$$299$$ 2.11118 0.122093
$$300$$ 0 0
$$301$$ 3.60197 0.207614
$$302$$ 0 0
$$303$$ −20.9483 −1.20345
$$304$$ 0 0
$$305$$ −3.07838 −0.176267
$$306$$ 0 0
$$307$$ 28.4307 1.62262 0.811312 0.584614i $$-0.198754\pi$$
0.811312 + 0.584614i $$0.198754\pi$$
$$308$$ 0 0
$$309$$ 13.4452 0.764871
$$310$$ 0 0
$$311$$ −19.6248 −1.11282 −0.556409 0.830909i $$-0.687821\pi$$
−0.556409 + 0.830909i $$0.687821\pi$$
$$312$$ 0 0
$$313$$ 22.9093 1.29491 0.647456 0.762103i $$-0.275833\pi$$
0.647456 + 0.762103i $$0.275833\pi$$
$$314$$ 0 0
$$315$$ −0.0494483 −0.00278610
$$316$$ 0 0
$$317$$ −22.8599 −1.28394 −0.641970 0.766730i $$-0.721882\pi$$
−0.641970 + 0.766730i $$0.721882\pi$$
$$318$$ 0 0
$$319$$ 0.290725 0.0162775
$$320$$ 0 0
$$321$$ 21.7587 1.21445
$$322$$ 0 0
$$323$$ 30.0722 1.67326
$$324$$ 0 0
$$325$$ 0.921622 0.0511224
$$326$$ 0 0
$$327$$ 21.2618 1.17578
$$328$$ 0 0
$$329$$ −0.711543 −0.0392286
$$330$$ 0 0
$$331$$ −24.0905 −1.32413 −0.662066 0.749445i $$-0.730320\pi$$
−0.662066 + 0.749445i $$0.730320\pi$$
$$332$$ 0 0
$$333$$ 0.121683 0.00666819
$$334$$ 0 0
$$335$$ 5.70928 0.311931
$$336$$ 0 0
$$337$$ 12.7877 0.696588 0.348294 0.937385i $$-0.386761\pi$$
0.348294 + 0.937385i $$0.386761\pi$$
$$338$$ 0 0
$$339$$ −21.4908 −1.16722
$$340$$ 0 0
$$341$$ −2.92162 −0.158215
$$342$$ 0 0
$$343$$ −8.58145 −0.463355
$$344$$ 0 0
$$345$$ −3.91548 −0.210802
$$346$$ 0 0
$$347$$ −8.41628 −0.451810 −0.225905 0.974149i $$-0.572534\pi$$
−0.225905 + 0.974149i $$0.572534\pi$$
$$348$$ 0 0
$$349$$ −22.1978 −1.18822 −0.594110 0.804384i $$-0.702496\pi$$
−0.594110 + 0.804384i $$0.702496\pi$$
$$350$$ 0 0
$$351$$ 4.84939 0.258841
$$352$$ 0 0
$$353$$ −6.18342 −0.329110 −0.164555 0.986368i $$-0.552619\pi$$
−0.164555 + 0.986368i $$0.552619\pi$$
$$354$$ 0 0
$$355$$ 9.07838 0.481830
$$356$$ 0 0
$$357$$ −5.36069 −0.283718
$$358$$ 0 0
$$359$$ 5.05559 0.266824 0.133412 0.991061i $$-0.457407\pi$$
0.133412 + 0.991061i $$0.457407\pi$$
$$360$$ 0 0
$$361$$ 17.5958 0.926096
$$362$$ 0 0
$$363$$ 18.6576 0.979268
$$364$$ 0 0
$$365$$ −6.94441 −0.363487
$$366$$ 0 0
$$367$$ 29.5402 1.54199 0.770994 0.636843i $$-0.219760\pi$$
0.770994 + 0.636843i $$0.219760\pi$$
$$368$$ 0 0
$$369$$ −0.0266620 −0.00138797
$$370$$ 0 0
$$371$$ 0.214614 0.0111422
$$372$$ 0 0
$$373$$ −14.4124 −0.746246 −0.373123 0.927782i $$-0.621713\pi$$
−0.373123 + 0.927782i $$0.621713\pi$$
$$374$$ 0 0
$$375$$ −1.70928 −0.0882666
$$376$$ 0 0
$$377$$ −0.921622 −0.0474660
$$378$$ 0 0
$$379$$ −14.1340 −0.726013 −0.363007 0.931787i $$-0.618250\pi$$
−0.363007 + 0.931787i $$0.618250\pi$$
$$380$$ 0 0
$$381$$ 35.7464 1.83135
$$382$$ 0 0
$$383$$ −15.7815 −0.806397 −0.403199 0.915112i $$-0.632102\pi$$
−0.403199 + 0.915112i $$0.632102\pi$$
$$384$$ 0 0
$$385$$ −0.183417 −0.00934782
$$386$$ 0 0
$$387$$ −0.447480 −0.0227467
$$388$$ 0 0
$$389$$ 13.8166 0.700529 0.350264 0.936651i $$-0.386092\pi$$
0.350264 + 0.936651i $$0.386092\pi$$
$$390$$ 0 0
$$391$$ 11.3874 0.575883
$$392$$ 0 0
$$393$$ −23.0205 −1.16123
$$394$$ 0 0
$$395$$ 12.3896 0.623390
$$396$$ 0 0
$$397$$ −9.05172 −0.454293 −0.227146 0.973861i $$-0.572940\pi$$
−0.227146 + 0.973861i $$0.572940\pi$$
$$398$$ 0 0
$$399$$ −6.52359 −0.326588
$$400$$ 0 0
$$401$$ 19.7587 0.986704 0.493352 0.869830i $$-0.335772\pi$$
0.493352 + 0.869830i $$0.335772\pi$$
$$402$$ 0 0
$$403$$ 9.26180 0.461363
$$404$$ 0 0
$$405$$ −8.75872 −0.435224
$$406$$ 0 0
$$407$$ 0.451356 0.0223729
$$408$$ 0 0
$$409$$ −1.71769 −0.0849341 −0.0424670 0.999098i $$-0.513522\pi$$
−0.0424670 + 0.999098i $$0.513522\pi$$
$$410$$ 0 0
$$411$$ 23.1650 1.14264
$$412$$ 0 0
$$413$$ −6.15676 −0.302954
$$414$$ 0 0
$$415$$ −2.78765 −0.136841
$$416$$ 0 0
$$417$$ −8.36683 −0.409726
$$418$$ 0 0
$$419$$ 35.5318 1.73584 0.867922 0.496701i $$-0.165456\pi$$
0.867922 + 0.496701i $$0.165456\pi$$
$$420$$ 0 0
$$421$$ 12.0722 0.588365 0.294182 0.955749i $$-0.404953\pi$$
0.294182 + 0.955749i $$0.404953\pi$$
$$422$$ 0 0
$$423$$ 0.0883965 0.00429798
$$424$$ 0 0
$$425$$ 4.97107 0.241132
$$426$$ 0 0
$$427$$ −1.94214 −0.0939868
$$428$$ 0 0
$$429$$ 0.457980 0.0221115
$$430$$ 0 0
$$431$$ 19.8310 0.955224 0.477612 0.878571i $$-0.341503\pi$$
0.477612 + 0.878571i $$0.341503\pi$$
$$432$$ 0 0
$$433$$ 14.8143 0.711931 0.355965 0.934499i $$-0.384152\pi$$
0.355965 + 0.934499i $$0.384152\pi$$
$$434$$ 0 0
$$435$$ 1.70928 0.0819535
$$436$$ 0 0
$$437$$ 13.8576 0.662900
$$438$$ 0 0
$$439$$ −17.8576 −0.852298 −0.426149 0.904653i $$-0.640130\pi$$
−0.426149 + 0.904653i $$0.640130\pi$$
$$440$$ 0 0
$$441$$ 0.517447 0.0246404
$$442$$ 0 0
$$443$$ −33.5936 −1.59608 −0.798039 0.602606i $$-0.794129\pi$$
−0.798039 + 0.602606i $$0.794129\pi$$
$$444$$ 0 0
$$445$$ 4.73820 0.224612
$$446$$ 0 0
$$447$$ −21.4063 −1.01248
$$448$$ 0 0
$$449$$ 7.07838 0.334049 0.167025 0.985953i $$-0.446584\pi$$
0.167025 + 0.985953i $$0.446584\pi$$
$$450$$ 0 0
$$451$$ −0.0988967 −0.00465686
$$452$$ 0 0
$$453$$ −12.9939 −0.610505
$$454$$ 0 0
$$455$$ 0.581449 0.0272588
$$456$$ 0 0
$$457$$ −5.81658 −0.272088 −0.136044 0.990703i $$-0.543439\pi$$
−0.136044 + 0.990703i $$0.543439\pi$$
$$458$$ 0 0
$$459$$ 26.1568 1.22089
$$460$$ 0 0
$$461$$ 32.3090 1.50478 0.752390 0.658718i $$-0.228901\pi$$
0.752390 + 0.658718i $$0.228901\pi$$
$$462$$ 0 0
$$463$$ 1.44134 0.0669846 0.0334923 0.999439i $$-0.489337\pi$$
0.0334923 + 0.999439i $$0.489337\pi$$
$$464$$ 0 0
$$465$$ −17.1773 −0.796577
$$466$$ 0 0
$$467$$ 11.7503 0.543740 0.271870 0.962334i $$-0.412358\pi$$
0.271870 + 0.962334i $$0.412358\pi$$
$$468$$ 0 0
$$469$$ 3.60197 0.166323
$$470$$ 0 0
$$471$$ −42.5380 −1.96005
$$472$$ 0 0
$$473$$ −1.65983 −0.0763189
$$474$$ 0 0
$$475$$ 6.04945 0.277568
$$476$$ 0 0
$$477$$ −0.0266620 −0.00122077
$$478$$ 0 0
$$479$$ 17.1689 0.784465 0.392233 0.919866i $$-0.371703\pi$$
0.392233 + 0.919866i $$0.371703\pi$$
$$480$$ 0 0
$$481$$ −1.43084 −0.0652405
$$482$$ 0 0
$$483$$ −2.47027 −0.112401
$$484$$ 0 0
$$485$$ −15.8927 −0.721650
$$486$$ 0 0
$$487$$ −4.10277 −0.185914 −0.0929572 0.995670i $$-0.529632\pi$$
−0.0929572 + 0.995670i $$0.529632\pi$$
$$488$$ 0 0
$$489$$ 0.764867 0.0345885
$$490$$ 0 0
$$491$$ −40.7708 −1.83996 −0.919981 0.391963i $$-0.871796\pi$$
−0.919981 + 0.391963i $$0.871796\pi$$
$$492$$ 0 0
$$493$$ −4.97107 −0.223886
$$494$$ 0 0
$$495$$ 0.0227863 0.00102417
$$496$$ 0 0
$$497$$ 5.72753 0.256915
$$498$$ 0 0
$$499$$ 18.4703 0.826843 0.413421 0.910540i $$-0.364334\pi$$
0.413421 + 0.910540i $$0.364334\pi$$
$$500$$ 0 0
$$501$$ −33.9565 −1.51707
$$502$$ 0 0
$$503$$ −21.4947 −0.958400 −0.479200 0.877706i $$-0.659073\pi$$
−0.479200 + 0.877706i $$0.659073\pi$$
$$504$$ 0 0
$$505$$ 12.2557 0.545369
$$506$$ 0 0
$$507$$ 20.7687 0.922372
$$508$$ 0 0
$$509$$ −3.75872 −0.166602 −0.0833012 0.996524i $$-0.526546\pi$$
−0.0833012 + 0.996524i $$0.526546\pi$$
$$510$$ 0 0
$$511$$ −4.38121 −0.193813
$$512$$ 0 0
$$513$$ 31.8310 1.40537
$$514$$ 0 0
$$515$$ −7.86603 −0.346619
$$516$$ 0 0
$$517$$ 0.327887 0.0144204
$$518$$ 0 0
$$519$$ −43.4719 −1.90820
$$520$$ 0 0
$$521$$ 12.8059 0.561037 0.280518 0.959849i $$-0.409494\pi$$
0.280518 + 0.959849i $$0.409494\pi$$
$$522$$ 0 0
$$523$$ 21.1278 0.923855 0.461928 0.886918i $$-0.347158\pi$$
0.461928 + 0.886918i $$0.347158\pi$$
$$524$$ 0 0
$$525$$ −1.07838 −0.0470643
$$526$$ 0 0
$$527$$ 49.9565 2.17614
$$528$$ 0 0
$$529$$ −17.7526 −0.771851
$$530$$ 0 0
$$531$$ 0.764867 0.0331924
$$532$$ 0 0
$$533$$ 0.313511 0.0135797
$$534$$ 0 0
$$535$$ −12.7298 −0.550357
$$536$$ 0 0
$$537$$ 25.3607 1.09439
$$538$$ 0 0
$$539$$ 1.91935 0.0826725
$$540$$ 0 0
$$541$$ −32.7382 −1.40753 −0.703763 0.710435i $$-0.748498\pi$$
−0.703763 + 0.710435i $$0.748498\pi$$
$$542$$ 0 0
$$543$$ −10.1112 −0.433912
$$544$$ 0 0
$$545$$ −12.4391 −0.532831
$$546$$ 0 0
$$547$$ 22.1073 0.945240 0.472620 0.881266i $$-0.343308\pi$$
0.472620 + 0.881266i $$0.343308\pi$$
$$548$$ 0 0
$$549$$ 0.241276 0.0102974
$$550$$ 0 0
$$551$$ −6.04945 −0.257715
$$552$$ 0 0
$$553$$ 7.81658 0.332395
$$554$$ 0 0
$$555$$ 2.65368 0.112643
$$556$$ 0 0
$$557$$ 39.8720 1.68943 0.844715 0.535216i $$-0.179770\pi$$
0.844715 + 0.535216i $$0.179770\pi$$
$$558$$ 0 0
$$559$$ 5.26180 0.222550
$$560$$ 0 0
$$561$$ 2.47027 0.104295
$$562$$ 0 0
$$563$$ −10.1217 −0.426578 −0.213289 0.976989i $$-0.568418\pi$$
−0.213289 + 0.976989i $$0.568418\pi$$
$$564$$ 0 0
$$565$$ 12.5730 0.528952
$$566$$ 0 0
$$567$$ −5.52586 −0.232064
$$568$$ 0 0
$$569$$ −24.4391 −1.02454 −0.512270 0.858825i $$-0.671195\pi$$
−0.512270 + 0.858825i $$0.671195\pi$$
$$570$$ 0 0
$$571$$ 28.2511 1.18227 0.591136 0.806572i $$-0.298680\pi$$
0.591136 + 0.806572i $$0.298680\pi$$
$$572$$ 0 0
$$573$$ −12.0144 −0.501908
$$574$$ 0 0
$$575$$ 2.29072 0.0955298
$$576$$ 0 0
$$577$$ 46.1171 1.91988 0.959941 0.280202i $$-0.0904015\pi$$
0.959941 + 0.280202i $$0.0904015\pi$$
$$578$$ 0 0
$$579$$ −30.5380 −1.26911
$$580$$ 0 0
$$581$$ −1.75872 −0.0729642
$$582$$ 0 0
$$583$$ −0.0988967 −0.00409588
$$584$$ 0 0
$$585$$ −0.0722347 −0.00298654
$$586$$ 0 0
$$587$$ 0.715418 0.0295285 0.0147642 0.999891i $$-0.495300\pi$$
0.0147642 + 0.999891i $$0.495300\pi$$
$$588$$ 0 0
$$589$$ 60.7936 2.50496
$$590$$ 0 0
$$591$$ 10.4247 0.428815
$$592$$ 0 0
$$593$$ 15.5441 0.638320 0.319160 0.947701i $$-0.396599\pi$$
0.319160 + 0.947701i $$0.396599\pi$$
$$594$$ 0 0
$$595$$ 3.13624 0.128573
$$596$$ 0 0
$$597$$ 16.6803 0.682681
$$598$$ 0 0
$$599$$ −9.59809 −0.392167 −0.196084 0.980587i $$-0.562822\pi$$
−0.196084 + 0.980587i $$0.562822\pi$$
$$600$$ 0 0
$$601$$ 6.81044 0.277804 0.138902 0.990306i $$-0.455643\pi$$
0.138902 + 0.990306i $$0.455643\pi$$
$$602$$ 0 0
$$603$$ −0.447480 −0.0182228
$$604$$ 0 0
$$605$$ −10.9155 −0.443777
$$606$$ 0 0
$$607$$ 31.6970 1.28654 0.643271 0.765639i $$-0.277577\pi$$
0.643271 + 0.765639i $$0.277577\pi$$
$$608$$ 0 0
$$609$$ 1.07838 0.0436981
$$610$$ 0 0
$$611$$ −1.03943 −0.0420508
$$612$$ 0 0
$$613$$ −1.20394 −0.0486265 −0.0243133 0.999704i $$-0.507740\pi$$
−0.0243133 + 0.999704i $$0.507740\pi$$
$$614$$ 0 0
$$615$$ −0.581449 −0.0234463
$$616$$ 0 0
$$617$$ −37.9337 −1.52715 −0.763577 0.645716i $$-0.776559\pi$$
−0.763577 + 0.645716i $$0.776559\pi$$
$$618$$ 0 0
$$619$$ 4.60424 0.185060 0.0925299 0.995710i $$-0.470505\pi$$
0.0925299 + 0.995710i $$0.470505\pi$$
$$620$$ 0 0
$$621$$ 12.0533 0.483683
$$622$$ 0 0
$$623$$ 2.98932 0.119765
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 3.00614 0.120054
$$628$$ 0 0
$$629$$ −7.71769 −0.307724
$$630$$ 0 0
$$631$$ −8.41241 −0.334893 −0.167446 0.985881i $$-0.553552\pi$$
−0.167446 + 0.985881i $$0.553552\pi$$
$$632$$ 0 0
$$633$$ 16.8638 0.670274
$$634$$ 0 0
$$635$$ −20.9132 −0.829915
$$636$$ 0 0
$$637$$ −6.08452 −0.241077
$$638$$ 0 0
$$639$$ −0.711543 −0.0281482
$$640$$ 0 0
$$641$$ 32.5380 1.28517 0.642586 0.766213i $$-0.277861\pi$$
0.642586 + 0.766213i $$0.277861\pi$$
$$642$$ 0 0
$$643$$ 2.09293 0.0825372 0.0412686 0.999148i $$-0.486860\pi$$
0.0412686 + 0.999148i $$0.486860\pi$$
$$644$$ 0 0
$$645$$ −9.75872 −0.384249
$$646$$ 0 0
$$647$$ 45.1955 1.77682 0.888410 0.459051i $$-0.151811\pi$$
0.888410 + 0.459051i $$0.151811\pi$$
$$648$$ 0 0
$$649$$ 2.83710 0.111366
$$650$$ 0 0
$$651$$ −10.8371 −0.424739
$$652$$ 0 0
$$653$$ 2.14834 0.0840712 0.0420356 0.999116i $$-0.486616\pi$$
0.0420356 + 0.999116i $$0.486616\pi$$
$$654$$ 0 0
$$655$$ 13.4680 0.526238
$$656$$ 0 0
$$657$$ 0.544287 0.0212347
$$658$$ 0 0
$$659$$ 45.0843 1.75624 0.878118 0.478444i $$-0.158799\pi$$
0.878118 + 0.478444i $$0.158799\pi$$
$$660$$ 0 0
$$661$$ 36.3234 1.41281 0.706407 0.707806i $$-0.250315\pi$$
0.706407 + 0.707806i $$0.250315\pi$$
$$662$$ 0 0
$$663$$ −7.83096 −0.304129
$$664$$ 0 0
$$665$$ 3.81658 0.148001
$$666$$ 0 0
$$667$$ −2.29072 −0.0886972
$$668$$ 0 0
$$669$$ −18.7526 −0.725017
$$670$$ 0 0
$$671$$ 0.894960 0.0345496
$$672$$ 0 0
$$673$$ −17.4719 −0.673491 −0.336746 0.941596i $$-0.609326\pi$$
−0.336746 + 0.941596i $$0.609326\pi$$
$$674$$ 0 0
$$675$$ 5.26180 0.202527
$$676$$ 0 0
$$677$$ 40.0372 1.53875 0.769377 0.638796i $$-0.220567\pi$$
0.769377 + 0.638796i $$0.220567\pi$$
$$678$$ 0 0
$$679$$ −10.0267 −0.384788
$$680$$ 0 0
$$681$$ −21.4452 −0.821782
$$682$$ 0 0
$$683$$ −2.07611 −0.0794402 −0.0397201 0.999211i $$-0.512647\pi$$
−0.0397201 + 0.999211i $$0.512647\pi$$
$$684$$ 0 0
$$685$$ −13.5525 −0.517815
$$686$$ 0 0
$$687$$ 39.9299 1.52342
$$688$$ 0 0
$$689$$ 0.313511 0.0119438
$$690$$ 0 0
$$691$$ −26.7070 −1.01598 −0.507991 0.861362i $$-0.669612\pi$$
−0.507991 + 0.861362i $$0.669612\pi$$
$$692$$ 0 0
$$693$$ 0.0143758 0.000546093 0
$$694$$ 0 0
$$695$$ 4.89496 0.185676
$$696$$ 0 0
$$697$$ 1.69102 0.0640521
$$698$$ 0 0
$$699$$ −21.3151 −0.806212
$$700$$ 0 0
$$701$$ 21.9155 0.827736 0.413868 0.910337i $$-0.364177\pi$$
0.413868 + 0.910337i $$0.364177\pi$$
$$702$$ 0 0
$$703$$ −9.39189 −0.354222
$$704$$ 0 0
$$705$$ 1.92777 0.0726038
$$706$$ 0 0
$$707$$ 7.73206 0.290794
$$708$$ 0 0
$$709$$ 4.60811 0.173061 0.0865306 0.996249i $$-0.472422\pi$$
0.0865306 + 0.996249i $$0.472422\pi$$
$$710$$ 0 0
$$711$$ −0.971071 −0.0364180
$$712$$ 0 0
$$713$$ 23.0205 0.862125
$$714$$ 0 0
$$715$$ −0.267938 −0.0100203
$$716$$ 0 0
$$717$$ −23.5174 −0.878275
$$718$$ 0 0
$$719$$ 6.80590 0.253817 0.126909 0.991914i $$-0.459494\pi$$
0.126909 + 0.991914i $$0.459494\pi$$
$$720$$ 0 0
$$721$$ −4.96266 −0.184819
$$722$$ 0 0
$$723$$ 25.0928 0.933210
$$724$$ 0 0
$$725$$ −1.00000 −0.0371391
$$726$$ 0 0
$$727$$ −26.9711 −1.00030 −0.500151 0.865938i $$-0.666722\pi$$
−0.500151 + 0.865938i $$0.666722\pi$$
$$728$$ 0 0
$$729$$ 27.6681 1.02474
$$730$$ 0 0
$$731$$ 28.3812 1.04972
$$732$$ 0 0
$$733$$ 30.0638 1.11043 0.555216 0.831706i $$-0.312635\pi$$
0.555216 + 0.831706i $$0.312635\pi$$
$$734$$ 0 0
$$735$$ 11.2846 0.416238
$$736$$ 0 0
$$737$$ −1.65983 −0.0611405
$$738$$ 0 0
$$739$$ −51.1422 −1.88130 −0.940648 0.339383i $$-0.889782\pi$$
−0.940648 + 0.339383i $$0.889782\pi$$
$$740$$ 0 0
$$741$$ −9.52973 −0.350084
$$742$$ 0 0
$$743$$ 11.1857 0.410363 0.205181 0.978724i $$-0.434222\pi$$
0.205181 + 0.978724i $$0.434222\pi$$
$$744$$ 0 0
$$745$$ 12.5236 0.458829
$$746$$ 0 0
$$747$$ 0.218490 0.00799413
$$748$$ 0 0
$$749$$ −8.03120 −0.293454
$$750$$ 0 0
$$751$$ −18.3630 −0.670074 −0.335037 0.942205i $$-0.608749\pi$$
−0.335037 + 0.942205i $$0.608749\pi$$
$$752$$ 0 0
$$753$$ 26.3935 0.961832
$$754$$ 0 0
$$755$$ 7.60197 0.276664
$$756$$ 0 0
$$757$$ −15.8927 −0.577630 −0.288815 0.957385i $$-0.593261\pi$$
−0.288815 + 0.957385i $$0.593261\pi$$
$$758$$ 0 0
$$759$$ 1.13833 0.0413186
$$760$$ 0 0
$$761$$ 13.8843 0.503305 0.251652 0.967818i $$-0.419026\pi$$
0.251652 + 0.967818i $$0.419026\pi$$
$$762$$ 0 0
$$763$$ −7.84778 −0.284109
$$764$$ 0 0
$$765$$ −0.389621 −0.0140868
$$766$$ 0 0
$$767$$ −8.99386 −0.324749
$$768$$ 0 0
$$769$$ −35.4063 −1.27678 −0.638391 0.769712i $$-0.720400\pi$$
−0.638391 + 0.769712i $$0.720400\pi$$
$$770$$ 0 0
$$771$$ 10.7382 0.386727
$$772$$ 0 0
$$773$$ 0.488518 0.0175708 0.00878539 0.999961i $$-0.497203\pi$$
0.00878539 + 0.999961i $$0.497203\pi$$
$$774$$ 0 0
$$775$$ 10.0494 0.360987
$$776$$ 0 0
$$777$$ 1.67420 0.0600617
$$778$$ 0 0
$$779$$ 2.05786 0.0737304
$$780$$ 0 0
$$781$$ −2.63931 −0.0944419
$$782$$ 0 0
$$783$$ −5.26180 −0.188041
$$784$$ 0 0
$$785$$ 24.8865 0.888239
$$786$$ 0 0
$$787$$ 1.99159 0.0709925 0.0354962 0.999370i $$-0.488699\pi$$
0.0354962 + 0.999370i $$0.488699\pi$$
$$788$$ 0 0
$$789$$ −17.2228 −0.613150
$$790$$ 0 0
$$791$$ 7.93230 0.282040
$$792$$ 0 0
$$793$$ −2.83710 −0.100748
$$794$$ 0 0
$$795$$ −0.581449 −0.0206219
$$796$$ 0 0
$$797$$ 17.2702 0.611742 0.305871 0.952073i $$-0.401052\pi$$
0.305871 + 0.952073i $$0.401052\pi$$
$$798$$ 0 0
$$799$$ −5.60650 −0.198344
$$800$$ 0 0
$$801$$ −0.371370 −0.0131217
$$802$$ 0 0
$$803$$ 2.01891 0.0712458
$$804$$ 0 0
$$805$$ 1.44521 0.0509371
$$806$$ 0 0
$$807$$ 48.1522 1.69504
$$808$$ 0 0
$$809$$ −56.5068 −1.98667 −0.993336 0.115254i $$-0.963232\pi$$
−0.993336 + 0.115254i $$0.963232\pi$$
$$810$$ 0 0
$$811$$ 8.77924 0.308281 0.154140 0.988049i $$-0.450739\pi$$
0.154140 + 0.988049i $$0.450739\pi$$
$$812$$ 0 0
$$813$$ −49.2306 −1.72659
$$814$$ 0 0
$$815$$ −0.447480 −0.0156745
$$816$$ 0 0
$$817$$ 34.5380 1.20833
$$818$$ 0 0
$$819$$ −0.0455727 −0.00159244
$$820$$ 0 0
$$821$$ 28.1568 0.982678 0.491339 0.870969i $$-0.336508\pi$$
0.491339 + 0.870969i $$0.336508\pi$$
$$822$$ 0 0
$$823$$ 20.7442 0.723096 0.361548 0.932353i $$-0.382248\pi$$
0.361548 + 0.932353i $$0.382248\pi$$
$$824$$ 0 0
$$825$$ 0.496928 0.0173008
$$826$$ 0 0
$$827$$ 9.12783 0.317406 0.158703 0.987326i $$-0.449269\pi$$
0.158703 + 0.987326i $$0.449269\pi$$
$$828$$ 0 0
$$829$$ −31.8576 −1.10646 −0.553230 0.833028i $$-0.686605\pi$$
−0.553230 + 0.833028i $$0.686605\pi$$
$$830$$ 0 0
$$831$$ 0.0455727 0.00158090
$$832$$ 0 0
$$833$$ −32.8188 −1.13711
$$834$$ 0 0
$$835$$ 19.8660 0.687492
$$836$$ 0 0
$$837$$ 52.8781 1.82774
$$838$$ 0 0
$$839$$ 27.4413 0.947380 0.473690 0.880692i $$-0.342922\pi$$
0.473690 + 0.880692i $$0.342922\pi$$
$$840$$ 0 0
$$841$$ 1.00000 0.0344828
$$842$$ 0 0
$$843$$ 47.9832 1.65263
$$844$$ 0 0
$$845$$ −12.1506 −0.417994
$$846$$ 0 0
$$847$$ −6.88655 −0.236625
$$848$$ 0 0
$$849$$ −35.5774 −1.22101
$$850$$ 0 0
$$851$$ −3.55640 −0.121912
$$852$$ 0 0
$$853$$ 56.0515 1.91917 0.959584 0.281422i $$-0.0908061\pi$$
0.959584 + 0.281422i $$0.0908061\pi$$
$$854$$ 0 0
$$855$$ −0.474142 −0.0162153
$$856$$ 0 0
$$857$$ −6.08452 −0.207843 −0.103922 0.994585i $$-0.533139\pi$$
−0.103922 + 0.994585i $$0.533139\pi$$
$$858$$ 0 0
$$859$$ −35.5936 −1.21444 −0.607218 0.794535i $$-0.707715\pi$$
−0.607218 + 0.794535i $$0.707715\pi$$
$$860$$ 0 0
$$861$$ −0.366835 −0.0125017
$$862$$ 0 0
$$863$$ −12.8287 −0.436694 −0.218347 0.975871i $$-0.570066\pi$$
−0.218347 + 0.975871i $$0.570066\pi$$
$$864$$ 0 0
$$865$$ 25.4329 0.864745
$$866$$ 0 0
$$867$$ −13.1812 −0.447655
$$868$$ 0 0
$$869$$ −3.60197 −0.122188
$$870$$ 0 0
$$871$$ 5.26180 0.178289
$$872$$ 0 0
$$873$$ 1.24563 0.0421583
$$874$$ 0 0
$$875$$ 0.630898 0.0213282
$$876$$ 0 0
$$877$$ 1.50307 0.0507551 0.0253776 0.999678i $$-0.491921\pi$$
0.0253776 + 0.999678i $$0.491921\pi$$
$$878$$ 0 0
$$879$$ −26.3402 −0.888432
$$880$$ 0 0
$$881$$ 23.4908 0.791425 0.395712 0.918375i $$-0.370498\pi$$
0.395712 + 0.918375i $$0.370498\pi$$
$$882$$ 0 0
$$883$$ 29.0433 0.977385 0.488693 0.872456i $$-0.337474\pi$$
0.488693 + 0.872456i $$0.337474\pi$$
$$884$$ 0 0
$$885$$ 16.6803 0.560704
$$886$$ 0 0
$$887$$ −19.0700 −0.640307 −0.320153 0.947366i $$-0.603734\pi$$
−0.320153 + 0.947366i $$0.603734\pi$$
$$888$$ 0 0
$$889$$ −13.1941 −0.442516
$$890$$ 0 0
$$891$$ 2.54638 0.0853068
$$892$$ 0 0
$$893$$ −6.82273 −0.228314
$$894$$ 0 0
$$895$$ −14.8371 −0.495950
$$896$$ 0 0
$$897$$ −3.60859 −0.120487
$$898$$ 0 0
$$899$$ −10.0494 −0.335168
$$900$$ 0 0
$$901$$ 1.69102 0.0563362
$$902$$ 0 0
$$903$$ −6.15676 −0.204884
$$904$$ 0 0
$$905$$ 5.91548 0.196637
$$906$$ 0 0
$$907$$ −5.54023 −0.183960 −0.0919802 0.995761i $$-0.529320\pi$$
−0.0919802 + 0.995761i $$0.529320\pi$$
$$908$$ 0 0
$$909$$ −0.960570 −0.0318601
$$910$$ 0 0
$$911$$ 53.2990 1.76587 0.882937 0.469492i $$-0.155563\pi$$
0.882937 + 0.469492i $$0.155563\pi$$
$$912$$ 0 0
$$913$$ 0.810439 0.0268216
$$914$$ 0 0
$$915$$ 5.26180 0.173950
$$916$$ 0 0
$$917$$ 8.49693 0.280593
$$918$$ 0 0
$$919$$ 37.5897 1.23997 0.619985 0.784614i $$-0.287139\pi$$
0.619985 + 0.784614i $$0.287139\pi$$
$$920$$ 0 0
$$921$$ −48.5958 −1.60129
$$922$$ 0 0
$$923$$ 8.36683 0.275398
$$924$$ 0 0
$$925$$ −1.55252 −0.0510465
$$926$$ 0 0
$$927$$ 0.616522 0.0202492
$$928$$ 0 0
$$929$$ 37.3197 1.22442 0.612209 0.790696i $$-0.290281\pi$$
0.612209 + 0.790696i $$0.290281\pi$$
$$930$$ 0 0
$$931$$ −39.9383 −1.30892
$$932$$ 0 0
$$933$$ 33.5441 1.09818
$$934$$ 0 0
$$935$$ −1.44521 −0.0472635
$$936$$ 0 0
$$937$$ −22.8638 −0.746927 −0.373463 0.927645i $$-0.621830\pi$$
−0.373463 + 0.927645i $$0.621830\pi$$
$$938$$ 0 0
$$939$$ −39.1584 −1.27788
$$940$$ 0 0
$$941$$ −0.523590 −0.0170686 −0.00853428 0.999964i $$-0.502717\pi$$
−0.00853428 + 0.999964i $$0.502717\pi$$
$$942$$ 0 0
$$943$$ 0.779243 0.0253756
$$944$$ 0 0
$$945$$ 3.31965 0.107988
$$946$$ 0 0
$$947$$ 10.0228 0.325697 0.162848 0.986651i $$-0.447932\pi$$
0.162848 + 0.986651i $$0.447932\pi$$
$$948$$ 0 0
$$949$$ −6.40012 −0.207757
$$950$$ 0 0
$$951$$ 39.0738 1.26706
$$952$$ 0 0
$$953$$ −8.15676 −0.264223 −0.132112 0.991235i $$-0.542176\pi$$
−0.132112 + 0.991235i $$0.542176\pi$$
$$954$$ 0 0
$$955$$ 7.02893 0.227451
$$956$$ 0 0
$$957$$ −0.496928 −0.0160634
$$958$$ 0 0
$$959$$ −8.55025 −0.276102
$$960$$ 0 0
$$961$$ 69.9914 2.25779
$$962$$ 0 0
$$963$$ 0.997733 0.0321515
$$964$$ 0 0
$$965$$ 17.8660 0.575128
$$966$$ 0 0
$$967$$ 15.7671 0.507037 0.253518 0.967331i $$-0.418412\pi$$
0.253518 + 0.967331i $$0.418412\pi$$
$$968$$ 0 0
$$969$$ −51.4017 −1.65126
$$970$$ 0 0
$$971$$ 17.8804 0.573810 0.286905 0.957959i $$-0.407374\pi$$
0.286905 + 0.957959i $$0.407374\pi$$
$$972$$ 0 0
$$973$$ 3.08822 0.0990037
$$974$$ 0 0
$$975$$ −1.57531 −0.0504502
$$976$$ 0 0
$$977$$ −55.1071 −1.76303 −0.881517 0.472153i $$-0.843477\pi$$
−0.881517 + 0.472153i $$0.843477\pi$$
$$978$$ 0 0
$$979$$ −1.37751 −0.0440255
$$980$$ 0 0
$$981$$ 0.974946 0.0311276
$$982$$ 0 0
$$983$$ −1.29687 −0.0413637 −0.0206818 0.999786i $$-0.506584\pi$$
−0.0206818 + 0.999786i $$0.506584\pi$$
$$984$$ 0 0
$$985$$ −6.09890 −0.194327
$$986$$ 0 0
$$987$$ 1.21622 0.0387128
$$988$$ 0 0
$$989$$ 13.0784 0.415868
$$990$$ 0 0
$$991$$ −3.11942 −0.0990915 −0.0495458 0.998772i $$-0.515777\pi$$
−0.0495458 + 0.998772i $$0.515777\pi$$
$$992$$ 0 0
$$993$$ 41.1773 1.30672
$$994$$ 0 0
$$995$$ −9.75872 −0.309372
$$996$$ 0 0
$$997$$ −30.2472 −0.957940 −0.478970 0.877831i $$-0.658990\pi$$
−0.478970 + 0.877831i $$0.658990\pi$$
$$998$$ 0 0
$$999$$ −8.16904 −0.258457
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 9280.2.a.bu.1.1 3
4.3 odd 2 9280.2.a.bm.1.3 3
8.3 odd 2 2320.2.a.s.1.1 3
8.5 even 2 145.2.a.d.1.2 3
24.5 odd 2 1305.2.a.o.1.2 3
40.13 odd 4 725.2.b.d.349.2 6
40.29 even 2 725.2.a.d.1.2 3
40.37 odd 4 725.2.b.d.349.5 6
56.13 odd 2 7105.2.a.p.1.2 3
120.29 odd 2 6525.2.a.bh.1.2 3
232.173 even 2 4205.2.a.e.1.2 3

By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.d.1.2 3 8.5 even 2
725.2.a.d.1.2 3 40.29 even 2
725.2.b.d.349.2 6 40.13 odd 4
725.2.b.d.349.5 6 40.37 odd 4
1305.2.a.o.1.2 3 24.5 odd 2
2320.2.a.s.1.1 3 8.3 odd 2
4205.2.a.e.1.2 3 232.173 even 2
6525.2.a.bh.1.2 3 120.29 odd 2
7105.2.a.p.1.2 3 56.13 odd 2
9280.2.a.bm.1.3 3 4.3 odd 2
9280.2.a.bu.1.1 3 1.1 even 1 trivial