# Properties

 Label 666.2.a.k.1.2 Level $666$ Weight $2$ Character 666.1 Self dual yes Analytic conductor $5.318$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(1,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.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: $$5.31803677462$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{17})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 4$$ x^2 - x - 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-1.56155$$ of defining polynomial Character $$\chi$$ $$=$$ 666.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} +2.56155 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} +2.56155 q^{7} +1.00000 q^{8} +2.00000 q^{10} +2.56155 q^{11} -5.68466 q^{13} +2.56155 q^{14} +1.00000 q^{16} -0.561553 q^{17} +0.561553 q^{19} +2.00000 q^{20} +2.56155 q^{22} -3.68466 q^{23} -1.00000 q^{25} -5.68466 q^{26} +2.56155 q^{28} +7.12311 q^{29} -0.876894 q^{31} +1.00000 q^{32} -0.561553 q^{34} +5.12311 q^{35} -1.00000 q^{37} +0.561553 q^{38} +2.00000 q^{40} +2.87689 q^{41} -7.12311 q^{43} +2.56155 q^{44} -3.68466 q^{46} +6.24621 q^{47} -0.438447 q^{49} -1.00000 q^{50} -5.68466 q^{52} +2.56155 q^{53} +5.12311 q^{55} +2.56155 q^{56} +7.12311 q^{58} +9.12311 q^{59} +4.24621 q^{61} -0.876894 q^{62} +1.00000 q^{64} -11.3693 q^{65} -14.2462 q^{67} -0.561553 q^{68} +5.12311 q^{70} -14.2462 q^{71} -0.561553 q^{73} -1.00000 q^{74} +0.561553 q^{76} +6.56155 q^{77} -6.00000 q^{79} +2.00000 q^{80} +2.87689 q^{82} -13.9309 q^{83} -1.12311 q^{85} -7.12311 q^{86} +2.56155 q^{88} +15.9309 q^{89} -14.5616 q^{91} -3.68466 q^{92} +6.24621 q^{94} +1.12311 q^{95} +11.1231 q^{97} -0.438447 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 + 2 * q^4 + 4 * q^5 + q^7 + 2 * q^8 $$2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} + q^{7} + 2 q^{8} + 4 q^{10} + q^{11} + q^{13} + q^{14} + 2 q^{16} + 3 q^{17} - 3 q^{19} + 4 q^{20} + q^{22} + 5 q^{23} - 2 q^{25} + q^{26} + q^{28} + 6 q^{29} - 10 q^{31} + 2 q^{32} + 3 q^{34} + 2 q^{35} - 2 q^{37} - 3 q^{38} + 4 q^{40} + 14 q^{41} - 6 q^{43} + q^{44} + 5 q^{46} - 4 q^{47} - 5 q^{49} - 2 q^{50} + q^{52} + q^{53} + 2 q^{55} + q^{56} + 6 q^{58} + 10 q^{59} - 8 q^{61} - 10 q^{62} + 2 q^{64} + 2 q^{65} - 12 q^{67} + 3 q^{68} + 2 q^{70} - 12 q^{71} + 3 q^{73} - 2 q^{74} - 3 q^{76} + 9 q^{77} - 12 q^{79} + 4 q^{80} + 14 q^{82} + q^{83} + 6 q^{85} - 6 q^{86} + q^{88} + 3 q^{89} - 25 q^{91} + 5 q^{92} - 4 q^{94} - 6 q^{95} + 14 q^{97} - 5 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 + 2 * q^4 + 4 * q^5 + q^7 + 2 * q^8 + 4 * q^10 + q^11 + q^13 + q^14 + 2 * q^16 + 3 * q^17 - 3 * q^19 + 4 * q^20 + q^22 + 5 * q^23 - 2 * q^25 + q^26 + q^28 + 6 * q^29 - 10 * q^31 + 2 * q^32 + 3 * q^34 + 2 * q^35 - 2 * q^37 - 3 * q^38 + 4 * q^40 + 14 * q^41 - 6 * q^43 + q^44 + 5 * q^46 - 4 * q^47 - 5 * q^49 - 2 * q^50 + q^52 + q^53 + 2 * q^55 + q^56 + 6 * q^58 + 10 * q^59 - 8 * q^61 - 10 * q^62 + 2 * q^64 + 2 * q^65 - 12 * q^67 + 3 * q^68 + 2 * q^70 - 12 * q^71 + 3 * q^73 - 2 * q^74 - 3 * q^76 + 9 * q^77 - 12 * q^79 + 4 * q^80 + 14 * q^82 + q^83 + 6 * q^85 - 6 * q^86 + q^88 + 3 * q^89 - 25 * q^91 + 5 * q^92 - 4 * q^94 - 6 * q^95 + 14 * q^97 - 5 * q^98

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 2.00000 0.894427 0.447214 0.894427i $$-0.352416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ 0 0
$$7$$ 2.56155 0.968176 0.484088 0.875019i $$-0.339151\pi$$
0.484088 + 0.875019i $$0.339151\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 2.00000 0.632456
$$11$$ 2.56155 0.772337 0.386169 0.922428i $$-0.373798\pi$$
0.386169 + 0.922428i $$0.373798\pi$$
$$12$$ 0 0
$$13$$ −5.68466 −1.57664 −0.788320 0.615265i $$-0.789049\pi$$
−0.788320 + 0.615265i $$0.789049\pi$$
$$14$$ 2.56155 0.684604
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −0.561553 −0.136197 −0.0680983 0.997679i $$-0.521693\pi$$
−0.0680983 + 0.997679i $$0.521693\pi$$
$$18$$ 0 0
$$19$$ 0.561553 0.128829 0.0644145 0.997923i $$-0.479482\pi$$
0.0644145 + 0.997923i $$0.479482\pi$$
$$20$$ 2.00000 0.447214
$$21$$ 0 0
$$22$$ 2.56155 0.546125
$$23$$ −3.68466 −0.768304 −0.384152 0.923270i $$-0.625506\pi$$
−0.384152 + 0.923270i $$0.625506\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ −5.68466 −1.11485
$$27$$ 0 0
$$28$$ 2.56155 0.484088
$$29$$ 7.12311 1.32273 0.661364 0.750065i $$-0.269978\pi$$
0.661364 + 0.750065i $$0.269978\pi$$
$$30$$ 0 0
$$31$$ −0.876894 −0.157495 −0.0787474 0.996895i $$-0.525092\pi$$
−0.0787474 + 0.996895i $$0.525092\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −0.561553 −0.0963055
$$35$$ 5.12311 0.865963
$$36$$ 0 0
$$37$$ −1.00000 −0.164399
$$38$$ 0.561553 0.0910959
$$39$$ 0 0
$$40$$ 2.00000 0.316228
$$41$$ 2.87689 0.449295 0.224648 0.974440i $$-0.427877\pi$$
0.224648 + 0.974440i $$0.427877\pi$$
$$42$$ 0 0
$$43$$ −7.12311 −1.08626 −0.543132 0.839648i $$-0.682762\pi$$
−0.543132 + 0.839648i $$0.682762\pi$$
$$44$$ 2.56155 0.386169
$$45$$ 0 0
$$46$$ −3.68466 −0.543273
$$47$$ 6.24621 0.911104 0.455552 0.890209i $$-0.349442\pi$$
0.455552 + 0.890209i $$0.349442\pi$$
$$48$$ 0 0
$$49$$ −0.438447 −0.0626353
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ −5.68466 −0.788320
$$53$$ 2.56155 0.351856 0.175928 0.984403i $$-0.443707\pi$$
0.175928 + 0.984403i $$0.443707\pi$$
$$54$$ 0 0
$$55$$ 5.12311 0.690799
$$56$$ 2.56155 0.342302
$$57$$ 0 0
$$58$$ 7.12311 0.935310
$$59$$ 9.12311 1.18773 0.593864 0.804566i $$-0.297602\pi$$
0.593864 + 0.804566i $$0.297602\pi$$
$$60$$ 0 0
$$61$$ 4.24621 0.543672 0.271836 0.962344i $$-0.412369\pi$$
0.271836 + 0.962344i $$0.412369\pi$$
$$62$$ −0.876894 −0.111366
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −11.3693 −1.41019
$$66$$ 0 0
$$67$$ −14.2462 −1.74045 −0.870226 0.492653i $$-0.836027\pi$$
−0.870226 + 0.492653i $$0.836027\pi$$
$$68$$ −0.561553 −0.0680983
$$69$$ 0 0
$$70$$ 5.12311 0.612328
$$71$$ −14.2462 −1.69071 −0.845357 0.534202i $$-0.820612\pi$$
−0.845357 + 0.534202i $$0.820612\pi$$
$$72$$ 0 0
$$73$$ −0.561553 −0.0657248 −0.0328624 0.999460i $$-0.510462\pi$$
−0.0328624 + 0.999460i $$0.510462\pi$$
$$74$$ −1.00000 −0.116248
$$75$$ 0 0
$$76$$ 0.561553 0.0644145
$$77$$ 6.56155 0.747758
$$78$$ 0 0
$$79$$ −6.00000 −0.675053 −0.337526 0.941316i $$-0.609590\pi$$
−0.337526 + 0.941316i $$0.609590\pi$$
$$80$$ 2.00000 0.223607
$$81$$ 0 0
$$82$$ 2.87689 0.317700
$$83$$ −13.9309 −1.52911 −0.764556 0.644558i $$-0.777042\pi$$
−0.764556 + 0.644558i $$0.777042\pi$$
$$84$$ 0 0
$$85$$ −1.12311 −0.121818
$$86$$ −7.12311 −0.768104
$$87$$ 0 0
$$88$$ 2.56155 0.273062
$$89$$ 15.9309 1.68867 0.844334 0.535817i $$-0.179996\pi$$
0.844334 + 0.535817i $$0.179996\pi$$
$$90$$ 0 0
$$91$$ −14.5616 −1.52647
$$92$$ −3.68466 −0.384152
$$93$$ 0 0
$$94$$ 6.24621 0.644247
$$95$$ 1.12311 0.115228
$$96$$ 0 0
$$97$$ 11.1231 1.12938 0.564690 0.825303i $$-0.308996\pi$$
0.564690 + 0.825303i $$0.308996\pi$$
$$98$$ −0.438447 −0.0442899
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ −2.87689 −0.286262 −0.143131 0.989704i $$-0.545717\pi$$
−0.143131 + 0.989704i $$0.545717\pi$$
$$102$$ 0 0
$$103$$ −10.0000 −0.985329 −0.492665 0.870219i $$-0.663977\pi$$
−0.492665 + 0.870219i $$0.663977\pi$$
$$104$$ −5.68466 −0.557427
$$105$$ 0 0
$$106$$ 2.56155 0.248800
$$107$$ −10.5616 −1.02102 −0.510512 0.859871i $$-0.670544\pi$$
−0.510512 + 0.859871i $$0.670544\pi$$
$$108$$ 0 0
$$109$$ −0.561553 −0.0537870 −0.0268935 0.999638i $$-0.508561\pi$$
−0.0268935 + 0.999638i $$0.508561\pi$$
$$110$$ 5.12311 0.488469
$$111$$ 0 0
$$112$$ 2.56155 0.242044
$$113$$ 4.24621 0.399450 0.199725 0.979852i $$-0.435995\pi$$
0.199725 + 0.979852i $$0.435995\pi$$
$$114$$ 0 0
$$115$$ −7.36932 −0.687192
$$116$$ 7.12311 0.661364
$$117$$ 0 0
$$118$$ 9.12311 0.839850
$$119$$ −1.43845 −0.131862
$$120$$ 0 0
$$121$$ −4.43845 −0.403495
$$122$$ 4.24621 0.384434
$$123$$ 0 0
$$124$$ −0.876894 −0.0787474
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 1.43845 0.127642 0.0638208 0.997961i $$-0.479671\pi$$
0.0638208 + 0.997961i $$0.479671\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ −11.3693 −0.997155
$$131$$ 6.87689 0.600837 0.300419 0.953807i $$-0.402874\pi$$
0.300419 + 0.953807i $$0.402874\pi$$
$$132$$ 0 0
$$133$$ 1.43845 0.124729
$$134$$ −14.2462 −1.23069
$$135$$ 0 0
$$136$$ −0.561553 −0.0481528
$$137$$ −22.2462 −1.90062 −0.950311 0.311302i $$-0.899235\pi$$
−0.950311 + 0.311302i $$0.899235\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 5.12311 0.432981
$$141$$ 0 0
$$142$$ −14.2462 −1.19552
$$143$$ −14.5616 −1.21770
$$144$$ 0 0
$$145$$ 14.2462 1.18308
$$146$$ −0.561553 −0.0464744
$$147$$ 0 0
$$148$$ −1.00000 −0.0821995
$$149$$ −5.12311 −0.419701 −0.209851 0.977733i $$-0.567298\pi$$
−0.209851 + 0.977733i $$0.567298\pi$$
$$150$$ 0 0
$$151$$ 15.6847 1.27640 0.638200 0.769871i $$-0.279679\pi$$
0.638200 + 0.769871i $$0.279679\pi$$
$$152$$ 0.561553 0.0455479
$$153$$ 0 0
$$154$$ 6.56155 0.528745
$$155$$ −1.75379 −0.140868
$$156$$ 0 0
$$157$$ 22.4924 1.79509 0.897545 0.440922i $$-0.145349\pi$$
0.897545 + 0.440922i $$0.145349\pi$$
$$158$$ −6.00000 −0.477334
$$159$$ 0 0
$$160$$ 2.00000 0.158114
$$161$$ −9.43845 −0.743854
$$162$$ 0 0
$$163$$ 7.93087 0.621194 0.310597 0.950542i $$-0.399471\pi$$
0.310597 + 0.950542i $$0.399471\pi$$
$$164$$ 2.87689 0.224648
$$165$$ 0 0
$$166$$ −13.9309 −1.08125
$$167$$ −4.31534 −0.333931 −0.166966 0.985963i $$-0.553397\pi$$
−0.166966 + 0.985963i $$0.553397\pi$$
$$168$$ 0 0
$$169$$ 19.3153 1.48580
$$170$$ −1.12311 −0.0861383
$$171$$ 0 0
$$172$$ −7.12311 −0.543132
$$173$$ −2.56155 −0.194751 −0.0973756 0.995248i $$-0.531045\pi$$
−0.0973756 + 0.995248i $$0.531045\pi$$
$$174$$ 0 0
$$175$$ −2.56155 −0.193635
$$176$$ 2.56155 0.193084
$$177$$ 0 0
$$178$$ 15.9309 1.19407
$$179$$ −1.12311 −0.0839449 −0.0419724 0.999119i $$-0.513364\pi$$
−0.0419724 + 0.999119i $$0.513364\pi$$
$$180$$ 0 0
$$181$$ −18.4924 −1.37453 −0.687265 0.726406i $$-0.741189\pi$$
−0.687265 + 0.726406i $$0.741189\pi$$
$$182$$ −14.5616 −1.07937
$$183$$ 0 0
$$184$$ −3.68466 −0.271637
$$185$$ −2.00000 −0.147043
$$186$$ 0 0
$$187$$ −1.43845 −0.105190
$$188$$ 6.24621 0.455552
$$189$$ 0 0
$$190$$ 1.12311 0.0814786
$$191$$ 6.56155 0.474777 0.237389 0.971415i $$-0.423709\pi$$
0.237389 + 0.971415i $$0.423709\pi$$
$$192$$ 0 0
$$193$$ 25.3693 1.82612 0.913062 0.407821i $$-0.133711\pi$$
0.913062 + 0.407821i $$0.133711\pi$$
$$194$$ 11.1231 0.798592
$$195$$ 0 0
$$196$$ −0.438447 −0.0313177
$$197$$ −8.80776 −0.627527 −0.313764 0.949501i $$-0.601590\pi$$
−0.313764 + 0.949501i $$0.601590\pi$$
$$198$$ 0 0
$$199$$ 4.87689 0.345714 0.172857 0.984947i $$-0.444700\pi$$
0.172857 + 0.984947i $$0.444700\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 0 0
$$202$$ −2.87689 −0.202418
$$203$$ 18.2462 1.28063
$$204$$ 0 0
$$205$$ 5.75379 0.401862
$$206$$ −10.0000 −0.696733
$$207$$ 0 0
$$208$$ −5.68466 −0.394160
$$209$$ 1.43845 0.0994995
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 2.56155 0.175928
$$213$$ 0 0
$$214$$ −10.5616 −0.721973
$$215$$ −14.2462 −0.971584
$$216$$ 0 0
$$217$$ −2.24621 −0.152483
$$218$$ −0.561553 −0.0380332
$$219$$ 0 0
$$220$$ 5.12311 0.345400
$$221$$ 3.19224 0.214733
$$222$$ 0 0
$$223$$ −4.49242 −0.300835 −0.150417 0.988623i $$-0.548062\pi$$
−0.150417 + 0.988623i $$0.548062\pi$$
$$224$$ 2.56155 0.171151
$$225$$ 0 0
$$226$$ 4.24621 0.282454
$$227$$ 19.3693 1.28559 0.642793 0.766040i $$-0.277775\pi$$
0.642793 + 0.766040i $$0.277775\pi$$
$$228$$ 0 0
$$229$$ 2.63068 0.173840 0.0869202 0.996215i $$-0.472297\pi$$
0.0869202 + 0.996215i $$0.472297\pi$$
$$230$$ −7.36932 −0.485918
$$231$$ 0 0
$$232$$ 7.12311 0.467655
$$233$$ −16.0000 −1.04819 −0.524097 0.851658i $$-0.675597\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ 0 0
$$235$$ 12.4924 0.814916
$$236$$ 9.12311 0.593864
$$237$$ 0 0
$$238$$ −1.43845 −0.0932407
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ 8.24621 0.531185 0.265593 0.964085i $$-0.414432\pi$$
0.265593 + 0.964085i $$0.414432\pi$$
$$242$$ −4.43845 −0.285314
$$243$$ 0 0
$$244$$ 4.24621 0.271836
$$245$$ −0.876894 −0.0560227
$$246$$ 0 0
$$247$$ −3.19224 −0.203117
$$248$$ −0.876894 −0.0556828
$$249$$ 0 0
$$250$$ −12.0000 −0.758947
$$251$$ −1.12311 −0.0708898 −0.0354449 0.999372i $$-0.511285\pi$$
−0.0354449 + 0.999372i $$0.511285\pi$$
$$252$$ 0 0
$$253$$ −9.43845 −0.593390
$$254$$ 1.43845 0.0902562
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 19.4384 1.21254 0.606269 0.795260i $$-0.292666\pi$$
0.606269 + 0.795260i $$0.292666\pi$$
$$258$$ 0 0
$$259$$ −2.56155 −0.159167
$$260$$ −11.3693 −0.705095
$$261$$ 0 0
$$262$$ 6.87689 0.424856
$$263$$ 30.2462 1.86506 0.932531 0.361091i $$-0.117596\pi$$
0.932531 + 0.361091i $$0.117596\pi$$
$$264$$ 0 0
$$265$$ 5.12311 0.314710
$$266$$ 1.43845 0.0881969
$$267$$ 0 0
$$268$$ −14.2462 −0.870226
$$269$$ −19.0540 −1.16174 −0.580871 0.813996i $$-0.697288\pi$$
−0.580871 + 0.813996i $$0.697288\pi$$
$$270$$ 0 0
$$271$$ −22.2462 −1.35136 −0.675681 0.737195i $$-0.736150\pi$$
−0.675681 + 0.737195i $$0.736150\pi$$
$$272$$ −0.561553 −0.0340491
$$273$$ 0 0
$$274$$ −22.2462 −1.34394
$$275$$ −2.56155 −0.154467
$$276$$ 0 0
$$277$$ 23.4384 1.40828 0.704140 0.710061i $$-0.251333\pi$$
0.704140 + 0.710061i $$0.251333\pi$$
$$278$$ −12.0000 −0.719712
$$279$$ 0 0
$$280$$ 5.12311 0.306164
$$281$$ 15.9309 0.950356 0.475178 0.879890i $$-0.342384\pi$$
0.475178 + 0.879890i $$0.342384\pi$$
$$282$$ 0 0
$$283$$ −26.8078 −1.59356 −0.796778 0.604272i $$-0.793464\pi$$
−0.796778 + 0.604272i $$0.793464\pi$$
$$284$$ −14.2462 −0.845357
$$285$$ 0 0
$$286$$ −14.5616 −0.861043
$$287$$ 7.36932 0.434997
$$288$$ 0 0
$$289$$ −16.6847 −0.981450
$$290$$ 14.2462 0.836566
$$291$$ 0 0
$$292$$ −0.561553 −0.0328624
$$293$$ 25.3002 1.47805 0.739026 0.673677i $$-0.235286\pi$$
0.739026 + 0.673677i $$0.235286\pi$$
$$294$$ 0 0
$$295$$ 18.2462 1.06234
$$296$$ −1.00000 −0.0581238
$$297$$ 0 0
$$298$$ −5.12311 −0.296774
$$299$$ 20.9460 1.21134
$$300$$ 0 0
$$301$$ −18.2462 −1.05169
$$302$$ 15.6847 0.902551
$$303$$ 0 0
$$304$$ 0.561553 0.0322073
$$305$$ 8.49242 0.486275
$$306$$ 0 0
$$307$$ 7.36932 0.420589 0.210295 0.977638i $$-0.432558\pi$$
0.210295 + 0.977638i $$0.432558\pi$$
$$308$$ 6.56155 0.373879
$$309$$ 0 0
$$310$$ −1.75379 −0.0996085
$$311$$ 13.7538 0.779906 0.389953 0.920835i $$-0.372491\pi$$
0.389953 + 0.920835i $$0.372491\pi$$
$$312$$ 0 0
$$313$$ −11.1231 −0.628715 −0.314358 0.949305i $$-0.601789\pi$$
−0.314358 + 0.949305i $$0.601789\pi$$
$$314$$ 22.4924 1.26932
$$315$$ 0 0
$$316$$ −6.00000 −0.337526
$$317$$ 1.12311 0.0630799 0.0315399 0.999502i $$-0.489959\pi$$
0.0315399 + 0.999502i $$0.489959\pi$$
$$318$$ 0 0
$$319$$ 18.2462 1.02159
$$320$$ 2.00000 0.111803
$$321$$ 0 0
$$322$$ −9.43845 −0.525984
$$323$$ −0.315342 −0.0175461
$$324$$ 0 0
$$325$$ 5.68466 0.315328
$$326$$ 7.93087 0.439250
$$327$$ 0 0
$$328$$ 2.87689 0.158850
$$329$$ 16.0000 0.882109
$$330$$ 0 0
$$331$$ 1.36932 0.0752645 0.0376322 0.999292i $$-0.488018\pi$$
0.0376322 + 0.999292i $$0.488018\pi$$
$$332$$ −13.9309 −0.764556
$$333$$ 0 0
$$334$$ −4.31534 −0.236125
$$335$$ −28.4924 −1.55671
$$336$$ 0 0
$$337$$ 23.9309 1.30360 0.651799 0.758392i $$-0.274015\pi$$
0.651799 + 0.758392i $$0.274015\pi$$
$$338$$ 19.3153 1.05062
$$339$$ 0 0
$$340$$ −1.12311 −0.0609090
$$341$$ −2.24621 −0.121639
$$342$$ 0 0
$$343$$ −19.0540 −1.02882
$$344$$ −7.12311 −0.384052
$$345$$ 0 0
$$346$$ −2.56155 −0.137710
$$347$$ −29.6155 −1.58984 −0.794922 0.606711i $$-0.792488\pi$$
−0.794922 + 0.606711i $$0.792488\pi$$
$$348$$ 0 0
$$349$$ 26.4924 1.41811 0.709053 0.705155i $$-0.249122\pi$$
0.709053 + 0.705155i $$0.249122\pi$$
$$350$$ −2.56155 −0.136921
$$351$$ 0 0
$$352$$ 2.56155 0.136531
$$353$$ 26.0000 1.38384 0.691920 0.721974i $$-0.256765\pi$$
0.691920 + 0.721974i $$0.256765\pi$$
$$354$$ 0 0
$$355$$ −28.4924 −1.51222
$$356$$ 15.9309 0.844334
$$357$$ 0 0
$$358$$ −1.12311 −0.0593580
$$359$$ 4.49242 0.237101 0.118550 0.992948i $$-0.462175\pi$$
0.118550 + 0.992948i $$0.462175\pi$$
$$360$$ 0 0
$$361$$ −18.6847 −0.983403
$$362$$ −18.4924 −0.971940
$$363$$ 0 0
$$364$$ −14.5616 −0.763233
$$365$$ −1.12311 −0.0587860
$$366$$ 0 0
$$367$$ 12.3153 0.642856 0.321428 0.946934i $$-0.395837\pi$$
0.321428 + 0.946934i $$0.395837\pi$$
$$368$$ −3.68466 −0.192076
$$369$$ 0 0
$$370$$ −2.00000 −0.103975
$$371$$ 6.56155 0.340659
$$372$$ 0 0
$$373$$ 2.63068 0.136212 0.0681058 0.997678i $$-0.478304\pi$$
0.0681058 + 0.997678i $$0.478304\pi$$
$$374$$ −1.43845 −0.0743803
$$375$$ 0 0
$$376$$ 6.24621 0.322124
$$377$$ −40.4924 −2.08547
$$378$$ 0 0
$$379$$ −2.24621 −0.115380 −0.0576901 0.998335i $$-0.518374\pi$$
−0.0576901 + 0.998335i $$0.518374\pi$$
$$380$$ 1.12311 0.0576141
$$381$$ 0 0
$$382$$ 6.56155 0.335718
$$383$$ −8.80776 −0.450056 −0.225028 0.974352i $$-0.572247\pi$$
−0.225028 + 0.974352i $$0.572247\pi$$
$$384$$ 0 0
$$385$$ 13.1231 0.668815
$$386$$ 25.3693 1.29126
$$387$$ 0 0
$$388$$ 11.1231 0.564690
$$389$$ −32.7386 −1.65991 −0.829957 0.557827i $$-0.811635\pi$$
−0.829957 + 0.557827i $$0.811635\pi$$
$$390$$ 0 0
$$391$$ 2.06913 0.104640
$$392$$ −0.438447 −0.0221449
$$393$$ 0 0
$$394$$ −8.80776 −0.443729
$$395$$ −12.0000 −0.603786
$$396$$ 0 0
$$397$$ 18.4924 0.928108 0.464054 0.885807i $$-0.346394\pi$$
0.464054 + 0.885807i $$0.346394\pi$$
$$398$$ 4.87689 0.244457
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ 7.43845 0.371458 0.185729 0.982601i $$-0.440535\pi$$
0.185729 + 0.982601i $$0.440535\pi$$
$$402$$ 0 0
$$403$$ 4.98485 0.248313
$$404$$ −2.87689 −0.143131
$$405$$ 0 0
$$406$$ 18.2462 0.905544
$$407$$ −2.56155 −0.126971
$$408$$ 0 0
$$409$$ 3.75379 0.185613 0.0928065 0.995684i $$-0.470416\pi$$
0.0928065 + 0.995684i $$0.470416\pi$$
$$410$$ 5.75379 0.284159
$$411$$ 0 0
$$412$$ −10.0000 −0.492665
$$413$$ 23.3693 1.14993
$$414$$ 0 0
$$415$$ −27.8617 −1.36768
$$416$$ −5.68466 −0.278713
$$417$$ 0 0
$$418$$ 1.43845 0.0703568
$$419$$ 35.6847 1.74331 0.871655 0.490120i $$-0.163047\pi$$
0.871655 + 0.490120i $$0.163047\pi$$
$$420$$ 0 0
$$421$$ 3.75379 0.182948 0.0914742 0.995807i $$-0.470842\pi$$
0.0914742 + 0.995807i $$0.470842\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ 2.56155 0.124400
$$425$$ 0.561553 0.0272393
$$426$$ 0 0
$$427$$ 10.8769 0.526370
$$428$$ −10.5616 −0.510512
$$429$$ 0 0
$$430$$ −14.2462 −0.687013
$$431$$ 8.17708 0.393876 0.196938 0.980416i $$-0.436900\pi$$
0.196938 + 0.980416i $$0.436900\pi$$
$$432$$ 0 0
$$433$$ 24.5616 1.18035 0.590176 0.807274i $$-0.299058\pi$$
0.590176 + 0.807274i $$0.299058\pi$$
$$434$$ −2.24621 −0.107822
$$435$$ 0 0
$$436$$ −0.561553 −0.0268935
$$437$$ −2.06913 −0.0989799
$$438$$ 0 0
$$439$$ 22.4924 1.07350 0.536752 0.843740i $$-0.319651\pi$$
0.536752 + 0.843740i $$0.319651\pi$$
$$440$$ 5.12311 0.244234
$$441$$ 0 0
$$442$$ 3.19224 0.151839
$$443$$ 30.7386 1.46044 0.730218 0.683214i $$-0.239418\pi$$
0.730218 + 0.683214i $$0.239418\pi$$
$$444$$ 0 0
$$445$$ 31.8617 1.51039
$$446$$ −4.49242 −0.212722
$$447$$ 0 0
$$448$$ 2.56155 0.121022
$$449$$ 15.7538 0.743467 0.371734 0.928339i $$-0.378763\pi$$
0.371734 + 0.928339i $$0.378763\pi$$
$$450$$ 0 0
$$451$$ 7.36932 0.347008
$$452$$ 4.24621 0.199725
$$453$$ 0 0
$$454$$ 19.3693 0.909047
$$455$$ −29.1231 −1.36531
$$456$$ 0 0
$$457$$ −35.6155 −1.66602 −0.833012 0.553255i $$-0.813386\pi$$
−0.833012 + 0.553255i $$0.813386\pi$$
$$458$$ 2.63068 0.122924
$$459$$ 0 0
$$460$$ −7.36932 −0.343596
$$461$$ 38.9848 1.81571 0.907853 0.419289i $$-0.137721\pi$$
0.907853 + 0.419289i $$0.137721\pi$$
$$462$$ 0 0
$$463$$ 13.3693 0.621325 0.310662 0.950520i $$-0.399449\pi$$
0.310662 + 0.950520i $$0.399449\pi$$
$$464$$ 7.12311 0.330682
$$465$$ 0 0
$$466$$ −16.0000 −0.741186
$$467$$ 21.6155 1.00025 0.500124 0.865954i $$-0.333288\pi$$
0.500124 + 0.865954i $$0.333288\pi$$
$$468$$ 0 0
$$469$$ −36.4924 −1.68506
$$470$$ 12.4924 0.576232
$$471$$ 0 0
$$472$$ 9.12311 0.419925
$$473$$ −18.2462 −0.838962
$$474$$ 0 0
$$475$$ −0.561553 −0.0257658
$$476$$ −1.43845 −0.0659311
$$477$$ 0 0
$$478$$ 8.00000 0.365911
$$479$$ 4.94602 0.225990 0.112995 0.993596i $$-0.463956\pi$$
0.112995 + 0.993596i $$0.463956\pi$$
$$480$$ 0 0
$$481$$ 5.68466 0.259198
$$482$$ 8.24621 0.375605
$$483$$ 0 0
$$484$$ −4.43845 −0.201748
$$485$$ 22.2462 1.01015
$$486$$ 0 0
$$487$$ 4.87689 0.220993 0.110497 0.993877i $$-0.464756\pi$$
0.110497 + 0.993877i $$0.464756\pi$$
$$488$$ 4.24621 0.192217
$$489$$ 0 0
$$490$$ −0.876894 −0.0396140
$$491$$ −29.9309 −1.35076 −0.675381 0.737469i $$-0.736021\pi$$
−0.675381 + 0.737469i $$0.736021\pi$$
$$492$$ 0 0
$$493$$ −4.00000 −0.180151
$$494$$ −3.19224 −0.143625
$$495$$ 0 0
$$496$$ −0.876894 −0.0393737
$$497$$ −36.4924 −1.63691
$$498$$ 0 0
$$499$$ 28.4233 1.27240 0.636201 0.771524i $$-0.280505\pi$$
0.636201 + 0.771524i $$0.280505\pi$$
$$500$$ −12.0000 −0.536656
$$501$$ 0 0
$$502$$ −1.12311 −0.0501267
$$503$$ −32.9848 −1.47072 −0.735361 0.677676i $$-0.762987\pi$$
−0.735361 + 0.677676i $$0.762987\pi$$
$$504$$ 0 0
$$505$$ −5.75379 −0.256040
$$506$$ −9.43845 −0.419590
$$507$$ 0 0
$$508$$ 1.43845 0.0638208
$$509$$ 39.0540 1.73104 0.865519 0.500877i $$-0.166989\pi$$
0.865519 + 0.500877i $$0.166989\pi$$
$$510$$ 0 0
$$511$$ −1.43845 −0.0636332
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 19.4384 0.857393
$$515$$ −20.0000 −0.881305
$$516$$ 0 0
$$517$$ 16.0000 0.703679
$$518$$ −2.56155 −0.112548
$$519$$ 0 0
$$520$$ −11.3693 −0.498578
$$521$$ 24.0000 1.05146 0.525730 0.850652i $$-0.323792\pi$$
0.525730 + 0.850652i $$0.323792\pi$$
$$522$$ 0 0
$$523$$ −20.8769 −0.912883 −0.456441 0.889753i $$-0.650876\pi$$
−0.456441 + 0.889753i $$0.650876\pi$$
$$524$$ 6.87689 0.300419
$$525$$ 0 0
$$526$$ 30.2462 1.31880
$$527$$ 0.492423 0.0214503
$$528$$ 0 0
$$529$$ −9.42329 −0.409708
$$530$$ 5.12311 0.222533
$$531$$ 0 0
$$532$$ 1.43845 0.0623646
$$533$$ −16.3542 −0.708377
$$534$$ 0 0
$$535$$ −21.1231 −0.913231
$$536$$ −14.2462 −0.615343
$$537$$ 0 0
$$538$$ −19.0540 −0.821475
$$539$$ −1.12311 −0.0483756
$$540$$ 0 0
$$541$$ −31.9309 −1.37282 −0.686408 0.727217i $$-0.740813\pi$$
−0.686408 + 0.727217i $$0.740813\pi$$
$$542$$ −22.2462 −0.955557
$$543$$ 0 0
$$544$$ −0.561553 −0.0240764
$$545$$ −1.12311 −0.0481086
$$546$$ 0 0
$$547$$ −22.8078 −0.975190 −0.487595 0.873070i $$-0.662126\pi$$
−0.487595 + 0.873070i $$0.662126\pi$$
$$548$$ −22.2462 −0.950311
$$549$$ 0 0
$$550$$ −2.56155 −0.109225
$$551$$ 4.00000 0.170406
$$552$$ 0 0
$$553$$ −15.3693 −0.653570
$$554$$ 23.4384 0.995804
$$555$$ 0 0
$$556$$ −12.0000 −0.508913
$$557$$ −34.0000 −1.44063 −0.720313 0.693649i $$-0.756002\pi$$
−0.720313 + 0.693649i $$0.756002\pi$$
$$558$$ 0 0
$$559$$ 40.4924 1.71265
$$560$$ 5.12311 0.216491
$$561$$ 0 0
$$562$$ 15.9309 0.672003
$$563$$ −17.1231 −0.721653 −0.360826 0.932633i $$-0.617505\pi$$
−0.360826 + 0.932633i $$0.617505\pi$$
$$564$$ 0 0
$$565$$ 8.49242 0.357279
$$566$$ −26.8078 −1.12681
$$567$$ 0 0
$$568$$ −14.2462 −0.597758
$$569$$ 15.3002 0.641417 0.320709 0.947178i $$-0.396079\pi$$
0.320709 + 0.947178i $$0.396079\pi$$
$$570$$ 0 0
$$571$$ −38.7386 −1.62116 −0.810581 0.585627i $$-0.800848\pi$$
−0.810581 + 0.585627i $$0.800848\pi$$
$$572$$ −14.5616 −0.608849
$$573$$ 0 0
$$574$$ 7.36932 0.307589
$$575$$ 3.68466 0.153661
$$576$$ 0 0
$$577$$ −0.876894 −0.0365056 −0.0182528 0.999833i $$-0.505810\pi$$
−0.0182528 + 0.999833i $$0.505810\pi$$
$$578$$ −16.6847 −0.693990
$$579$$ 0 0
$$580$$ 14.2462 0.591542
$$581$$ −35.6847 −1.48045
$$582$$ 0 0
$$583$$ 6.56155 0.271752
$$584$$ −0.561553 −0.0232372
$$585$$ 0 0
$$586$$ 25.3002 1.04514
$$587$$ −30.2462 −1.24839 −0.624197 0.781267i $$-0.714574\pi$$
−0.624197 + 0.781267i $$0.714574\pi$$
$$588$$ 0 0
$$589$$ −0.492423 −0.0202899
$$590$$ 18.2462 0.751185
$$591$$ 0 0
$$592$$ −1.00000 −0.0410997
$$593$$ 8.63068 0.354420 0.177210 0.984173i $$-0.443293\pi$$
0.177210 + 0.984173i $$0.443293\pi$$
$$594$$ 0 0
$$595$$ −2.87689 −0.117941
$$596$$ −5.12311 −0.209851
$$597$$ 0 0
$$598$$ 20.9460 0.856547
$$599$$ −17.7538 −0.725400 −0.362700 0.931906i $$-0.618145\pi$$
−0.362700 + 0.931906i $$0.618145\pi$$
$$600$$ 0 0
$$601$$ −21.6847 −0.884536 −0.442268 0.896883i $$-0.645826\pi$$
−0.442268 + 0.896883i $$0.645826\pi$$
$$602$$ −18.2462 −0.743660
$$603$$ 0 0
$$604$$ 15.6847 0.638200
$$605$$ −8.87689 −0.360897
$$606$$ 0 0
$$607$$ −21.8617 −0.887341 −0.443670 0.896190i $$-0.646324\pi$$
−0.443670 + 0.896190i $$0.646324\pi$$
$$608$$ 0.561553 0.0227740
$$609$$ 0 0
$$610$$ 8.49242 0.343848
$$611$$ −35.5076 −1.43648
$$612$$ 0 0
$$613$$ 34.9848 1.41302 0.706512 0.707701i $$-0.250268\pi$$
0.706512 + 0.707701i $$0.250268\pi$$
$$614$$ 7.36932 0.297401
$$615$$ 0 0
$$616$$ 6.56155 0.264372
$$617$$ −14.8769 −0.598921 −0.299461 0.954109i $$-0.596807\pi$$
−0.299461 + 0.954109i $$0.596807\pi$$
$$618$$ 0 0
$$619$$ −30.7386 −1.23549 −0.617745 0.786378i $$-0.711954\pi$$
−0.617745 + 0.786378i $$0.711954\pi$$
$$620$$ −1.75379 −0.0704339
$$621$$ 0 0
$$622$$ 13.7538 0.551477
$$623$$ 40.8078 1.63493
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ −11.1231 −0.444569
$$627$$ 0 0
$$628$$ 22.4924 0.897545
$$629$$ 0.561553 0.0223906
$$630$$ 0 0
$$631$$ 36.7386 1.46254 0.731271 0.682087i $$-0.238928\pi$$
0.731271 + 0.682087i $$0.238928\pi$$
$$632$$ −6.00000 −0.238667
$$633$$ 0 0
$$634$$ 1.12311 0.0446042
$$635$$ 2.87689 0.114166
$$636$$ 0 0
$$637$$ 2.49242 0.0987534
$$638$$ 18.2462 0.722374
$$639$$ 0 0
$$640$$ 2.00000 0.0790569
$$641$$ 35.8617 1.41645 0.708227 0.705985i $$-0.249495\pi$$
0.708227 + 0.705985i $$0.249495\pi$$
$$642$$ 0 0
$$643$$ 22.8078 0.899450 0.449725 0.893167i $$-0.351522\pi$$
0.449725 + 0.893167i $$0.351522\pi$$
$$644$$ −9.43845 −0.371927
$$645$$ 0 0
$$646$$ −0.315342 −0.0124069
$$647$$ −13.9309 −0.547679 −0.273840 0.961775i $$-0.588294\pi$$
−0.273840 + 0.961775i $$0.588294\pi$$
$$648$$ 0 0
$$649$$ 23.3693 0.917326
$$650$$ 5.68466 0.222971
$$651$$ 0 0
$$652$$ 7.93087 0.310597
$$653$$ −32.7386 −1.28116 −0.640581 0.767891i $$-0.721306\pi$$
−0.640581 + 0.767891i $$0.721306\pi$$
$$654$$ 0 0
$$655$$ 13.7538 0.537405
$$656$$ 2.87689 0.112324
$$657$$ 0 0
$$658$$ 16.0000 0.623745
$$659$$ −1.75379 −0.0683179 −0.0341590 0.999416i $$-0.510875\pi$$
−0.0341590 + 0.999416i $$0.510875\pi$$
$$660$$ 0 0
$$661$$ −15.4384 −0.600486 −0.300243 0.953863i $$-0.597068\pi$$
−0.300243 + 0.953863i $$0.597068\pi$$
$$662$$ 1.36932 0.0532200
$$663$$ 0 0
$$664$$ −13.9309 −0.540623
$$665$$ 2.87689 0.111561
$$666$$ 0 0
$$667$$ −26.2462 −1.01626
$$668$$ −4.31534 −0.166966
$$669$$ 0 0
$$670$$ −28.4924 −1.10076
$$671$$ 10.8769 0.419898
$$672$$ 0 0
$$673$$ −37.0540 −1.42833 −0.714163 0.699980i $$-0.753192\pi$$
−0.714163 + 0.699980i $$0.753192\pi$$
$$674$$ 23.9309 0.921783
$$675$$ 0 0
$$676$$ 19.3153 0.742898
$$677$$ −26.5616 −1.02084 −0.510422 0.859924i $$-0.670511\pi$$
−0.510422 + 0.859924i $$0.670511\pi$$
$$678$$ 0 0
$$679$$ 28.4924 1.09344
$$680$$ −1.12311 −0.0430691
$$681$$ 0 0
$$682$$ −2.24621 −0.0860119
$$683$$ −50.1080 −1.91733 −0.958664 0.284542i $$-0.908159\pi$$
−0.958664 + 0.284542i $$0.908159\pi$$
$$684$$ 0 0
$$685$$ −44.4924 −1.69997
$$686$$ −19.0540 −0.727484
$$687$$ 0 0
$$688$$ −7.12311 −0.271566
$$689$$ −14.5616 −0.554751
$$690$$ 0 0
$$691$$ −22.8769 −0.870278 −0.435139 0.900363i $$-0.643301\pi$$
−0.435139 + 0.900363i $$0.643301\pi$$
$$692$$ −2.56155 −0.0973756
$$693$$ 0 0
$$694$$ −29.6155 −1.12419
$$695$$ −24.0000 −0.910372
$$696$$ 0 0
$$697$$ −1.61553 −0.0611925
$$698$$ 26.4924 1.00275
$$699$$ 0 0
$$700$$ −2.56155 −0.0968176
$$701$$ 45.3693 1.71358 0.856788 0.515669i $$-0.172457\pi$$
0.856788 + 0.515669i $$0.172457\pi$$
$$702$$ 0 0
$$703$$ −0.561553 −0.0211794
$$704$$ 2.56155 0.0965422
$$705$$ 0 0
$$706$$ 26.0000 0.978523
$$707$$ −7.36932 −0.277152
$$708$$ 0 0
$$709$$ 11.3002 0.424387 0.212194 0.977228i $$-0.431939\pi$$
0.212194 + 0.977228i $$0.431939\pi$$
$$710$$ −28.4924 −1.06930
$$711$$ 0 0
$$712$$ 15.9309 0.597035
$$713$$ 3.23106 0.121004
$$714$$ 0 0
$$715$$ −29.1231 −1.08914
$$716$$ −1.12311 −0.0419724
$$717$$ 0 0
$$718$$ 4.49242 0.167656
$$719$$ 47.3693 1.76658 0.883289 0.468829i $$-0.155324\pi$$
0.883289 + 0.468829i $$0.155324\pi$$
$$720$$ 0 0
$$721$$ −25.6155 −0.953972
$$722$$ −18.6847 −0.695371
$$723$$ 0 0
$$724$$ −18.4924 −0.687265
$$725$$ −7.12311 −0.264546
$$726$$ 0 0
$$727$$ −6.63068 −0.245918 −0.122959 0.992412i $$-0.539238\pi$$
−0.122959 + 0.992412i $$0.539238\pi$$
$$728$$ −14.5616 −0.539687
$$729$$ 0 0
$$730$$ −1.12311 −0.0415680
$$731$$ 4.00000 0.147945
$$732$$ 0 0
$$733$$ 9.86174 0.364252 0.182126 0.983275i $$-0.441702\pi$$
0.182126 + 0.983275i $$0.441702\pi$$
$$734$$ 12.3153 0.454568
$$735$$ 0 0
$$736$$ −3.68466 −0.135818
$$737$$ −36.4924 −1.34422
$$738$$ 0 0
$$739$$ 6.38447 0.234857 0.117428 0.993081i $$-0.462535\pi$$
0.117428 + 0.993081i $$0.462535\pi$$
$$740$$ −2.00000 −0.0735215
$$741$$ 0 0
$$742$$ 6.56155 0.240882
$$743$$ 52.9848 1.94383 0.971913 0.235342i $$-0.0756209\pi$$
0.971913 + 0.235342i $$0.0756209\pi$$
$$744$$ 0 0
$$745$$ −10.2462 −0.375392
$$746$$ 2.63068 0.0963162
$$747$$ 0 0
$$748$$ −1.43845 −0.0525948
$$749$$ −27.0540 −0.988531
$$750$$ 0 0
$$751$$ 43.2311 1.57752 0.788762 0.614699i $$-0.210722\pi$$
0.788762 + 0.614699i $$0.210722\pi$$
$$752$$ 6.24621 0.227776
$$753$$ 0 0
$$754$$ −40.4924 −1.47465
$$755$$ 31.3693 1.14165
$$756$$ 0 0
$$757$$ 1.68466 0.0612300 0.0306150 0.999531i $$-0.490253\pi$$
0.0306150 + 0.999531i $$0.490253\pi$$
$$758$$ −2.24621 −0.0815861
$$759$$ 0 0
$$760$$ 1.12311 0.0407393
$$761$$ −34.1080 −1.23641 −0.618206 0.786016i $$-0.712140\pi$$
−0.618206 + 0.786016i $$0.712140\pi$$
$$762$$ 0 0
$$763$$ −1.43845 −0.0520753
$$764$$ 6.56155 0.237389
$$765$$ 0 0
$$766$$ −8.80776 −0.318237
$$767$$ −51.8617 −1.87262
$$768$$ 0 0
$$769$$ 35.6155 1.28433 0.642164 0.766567i $$-0.278037\pi$$
0.642164 + 0.766567i $$0.278037\pi$$
$$770$$ 13.1231 0.472924
$$771$$ 0 0
$$772$$ 25.3693 0.913062
$$773$$ −4.31534 −0.155212 −0.0776060 0.996984i $$-0.524728\pi$$
−0.0776060 + 0.996984i $$0.524728\pi$$
$$774$$ 0 0
$$775$$ 0.876894 0.0314990
$$776$$ 11.1231 0.399296
$$777$$ 0 0
$$778$$ −32.7386 −1.17374
$$779$$ 1.61553 0.0578823
$$780$$ 0 0
$$781$$ −36.4924 −1.30580
$$782$$ 2.06913 0.0739919
$$783$$ 0 0
$$784$$ −0.438447 −0.0156588
$$785$$ 44.9848 1.60558
$$786$$ 0 0
$$787$$ −47.2311 −1.68361 −0.841803 0.539785i $$-0.818505\pi$$
−0.841803 + 0.539785i $$0.818505\pi$$
$$788$$ −8.80776 −0.313764
$$789$$ 0 0
$$790$$ −12.0000 −0.426941
$$791$$ 10.8769 0.386738
$$792$$ 0 0
$$793$$ −24.1383 −0.857175
$$794$$ 18.4924 0.656272
$$795$$ 0 0
$$796$$ 4.87689 0.172857
$$797$$ 34.0000 1.20434 0.602171 0.798367i $$-0.294303\pi$$
0.602171 + 0.798367i $$0.294303\pi$$
$$798$$ 0 0
$$799$$ −3.50758 −0.124089
$$800$$ −1.00000 −0.0353553
$$801$$ 0 0
$$802$$ 7.43845 0.262661
$$803$$ −1.43845 −0.0507617
$$804$$ 0 0
$$805$$ −18.8769 −0.665323
$$806$$ 4.98485 0.175584
$$807$$ 0 0
$$808$$ −2.87689 −0.101209
$$809$$ 24.4233 0.858677 0.429339 0.903144i $$-0.358747\pi$$
0.429339 + 0.903144i $$0.358747\pi$$
$$810$$ 0 0
$$811$$ −7.36932 −0.258772 −0.129386 0.991594i $$-0.541301\pi$$
−0.129386 + 0.991594i $$0.541301\pi$$
$$812$$ 18.2462 0.640316
$$813$$ 0 0
$$814$$ −2.56155 −0.0897824
$$815$$ 15.8617 0.555612
$$816$$ 0 0
$$817$$ −4.00000 −0.139942
$$818$$ 3.75379 0.131248
$$819$$ 0 0
$$820$$ 5.75379 0.200931
$$821$$ −47.6847 −1.66421 −0.832103 0.554621i $$-0.812863\pi$$
−0.832103 + 0.554621i $$0.812863\pi$$
$$822$$ 0 0
$$823$$ −0.807764 −0.0281569 −0.0140784 0.999901i $$-0.504481\pi$$
−0.0140784 + 0.999901i $$0.504481\pi$$
$$824$$ −10.0000 −0.348367
$$825$$ 0 0
$$826$$ 23.3693 0.813123
$$827$$ −33.7538 −1.17373 −0.586867 0.809683i $$-0.699639\pi$$
−0.586867 + 0.809683i $$0.699639\pi$$
$$828$$ 0 0
$$829$$ −0.561553 −0.0195035 −0.00975177 0.999952i $$-0.503104\pi$$
−0.00975177 + 0.999952i $$0.503104\pi$$
$$830$$ −27.8617 −0.967095
$$831$$ 0 0
$$832$$ −5.68466 −0.197080
$$833$$ 0.246211 0.00853071
$$834$$ 0 0
$$835$$ −8.63068 −0.298677
$$836$$ 1.43845 0.0497497
$$837$$ 0 0
$$838$$ 35.6847 1.23271
$$839$$ 22.8769 0.789798 0.394899 0.918725i $$-0.370780\pi$$
0.394899 + 0.918725i $$0.370780\pi$$
$$840$$ 0 0
$$841$$ 21.7386 0.749608
$$842$$ 3.75379 0.129364
$$843$$ 0 0
$$844$$ −4.00000 −0.137686
$$845$$ 38.6307 1.32894
$$846$$ 0 0
$$847$$ −11.3693 −0.390654
$$848$$ 2.56155 0.0879641
$$849$$ 0 0
$$850$$ 0.561553 0.0192611
$$851$$ 3.68466 0.126308
$$852$$ 0 0
$$853$$ 40.5616 1.38880 0.694401 0.719589i $$-0.255670\pi$$
0.694401 + 0.719589i $$0.255670\pi$$
$$854$$ 10.8769 0.372200
$$855$$ 0 0
$$856$$ −10.5616 −0.360986
$$857$$ −34.6695 −1.18429 −0.592144 0.805832i $$-0.701718\pi$$
−0.592144 + 0.805832i $$0.701718\pi$$
$$858$$ 0 0
$$859$$ −37.0540 −1.26427 −0.632133 0.774860i $$-0.717820\pi$$
−0.632133 + 0.774860i $$0.717820\pi$$
$$860$$ −14.2462 −0.485792
$$861$$ 0 0
$$862$$ 8.17708 0.278512
$$863$$ 32.6307 1.11076 0.555381 0.831596i $$-0.312573\pi$$
0.555381 + 0.831596i $$0.312573\pi$$
$$864$$ 0 0
$$865$$ −5.12311 −0.174191
$$866$$ 24.5616 0.834636
$$867$$ 0 0
$$868$$ −2.24621 −0.0762414
$$869$$ −15.3693 −0.521368
$$870$$ 0 0
$$871$$ 80.9848 2.74407
$$872$$ −0.561553 −0.0190166
$$873$$ 0 0
$$874$$ −2.06913 −0.0699894
$$875$$ −30.7386 −1.03916
$$876$$ 0 0
$$877$$ 34.0000 1.14810 0.574049 0.818821i $$-0.305372\pi$$
0.574049 + 0.818821i $$0.305372\pi$$
$$878$$ 22.4924 0.759082
$$879$$ 0 0
$$880$$ 5.12311 0.172700
$$881$$ −16.4924 −0.555644 −0.277822 0.960633i $$-0.589613\pi$$
−0.277822 + 0.960633i $$0.589613\pi$$
$$882$$ 0 0
$$883$$ −32.5616 −1.09578 −0.547892 0.836549i $$-0.684569\pi$$
−0.547892 + 0.836549i $$0.684569\pi$$
$$884$$ 3.19224 0.107367
$$885$$ 0 0
$$886$$ 30.7386 1.03268
$$887$$ 14.8769 0.499517 0.249759 0.968308i $$-0.419649\pi$$
0.249759 + 0.968308i $$0.419649\pi$$
$$888$$ 0 0
$$889$$ 3.68466 0.123579
$$890$$ 31.8617 1.06801
$$891$$ 0 0
$$892$$ −4.49242 −0.150417
$$893$$ 3.50758 0.117377
$$894$$ 0 0
$$895$$ −2.24621 −0.0750826
$$896$$ 2.56155 0.0855755
$$897$$ 0 0
$$898$$ 15.7538 0.525711
$$899$$ −6.24621 −0.208323
$$900$$ 0 0
$$901$$ −1.43845 −0.0479216
$$902$$ 7.36932 0.245371
$$903$$ 0 0
$$904$$ 4.24621 0.141227
$$905$$ −36.9848 −1.22942
$$906$$ 0 0
$$907$$ −15.3002 −0.508034 −0.254017 0.967200i $$-0.581752\pi$$
−0.254017 + 0.967200i $$0.581752\pi$$
$$908$$ 19.3693 0.642793
$$909$$ 0 0
$$910$$ −29.1231 −0.965422
$$911$$ 3.50758 0.116211 0.0581056 0.998310i $$-0.481494\pi$$
0.0581056 + 0.998310i $$0.481494\pi$$
$$912$$ 0 0
$$913$$ −35.6847 −1.18099
$$914$$ −35.6155 −1.17806
$$915$$ 0 0
$$916$$ 2.63068 0.0869202
$$917$$ 17.6155 0.581716
$$918$$ 0 0
$$919$$ 27.7538 0.915513 0.457757 0.889078i $$-0.348653\pi$$
0.457757 + 0.889078i $$0.348653\pi$$
$$920$$ −7.36932 −0.242959
$$921$$ 0 0
$$922$$ 38.9848 1.28390
$$923$$ 80.9848 2.66565
$$924$$ 0 0
$$925$$ 1.00000 0.0328798
$$926$$ 13.3693 0.439343
$$927$$ 0 0
$$928$$ 7.12311 0.233827
$$929$$ 29.7538 0.976190 0.488095 0.872790i $$-0.337692\pi$$
0.488095 + 0.872790i $$0.337692\pi$$
$$930$$ 0 0
$$931$$ −0.246211 −0.00806925
$$932$$ −16.0000 −0.524097
$$933$$ 0 0
$$934$$ 21.6155 0.707282
$$935$$ −2.87689 −0.0940845
$$936$$ 0 0
$$937$$ −15.7538 −0.514654 −0.257327 0.966324i $$-0.582842\pi$$
−0.257327 + 0.966324i $$0.582842\pi$$
$$938$$ −36.4924 −1.19152
$$939$$ 0 0
$$940$$ 12.4924 0.407458
$$941$$ 7.86174 0.256285 0.128143 0.991756i $$-0.459098\pi$$
0.128143 + 0.991756i $$0.459098\pi$$
$$942$$ 0 0
$$943$$ −10.6004 −0.345196
$$944$$ 9.12311 0.296932
$$945$$ 0 0
$$946$$ −18.2462 −0.593235
$$947$$ 19.3693 0.629418 0.314709 0.949188i $$-0.398093\pi$$
0.314709 + 0.949188i $$0.398093\pi$$
$$948$$ 0 0
$$949$$ 3.19224 0.103624
$$950$$ −0.561553 −0.0182192
$$951$$ 0 0
$$952$$ −1.43845 −0.0466203
$$953$$ −7.86174 −0.254667 −0.127333 0.991860i $$-0.540642\pi$$
−0.127333 + 0.991860i $$0.540642\pi$$
$$954$$ 0 0
$$955$$ 13.1231 0.424654
$$956$$ 8.00000 0.258738
$$957$$ 0 0
$$958$$ 4.94602 0.159799
$$959$$ −56.9848 −1.84014
$$960$$ 0 0
$$961$$ −30.2311 −0.975195
$$962$$ 5.68466 0.183281
$$963$$ 0 0
$$964$$ 8.24621 0.265593
$$965$$ 50.7386 1.63333
$$966$$ 0 0
$$967$$ 21.3693 0.687191 0.343595 0.939118i $$-0.388355\pi$$
0.343595 + 0.939118i $$0.388355\pi$$
$$968$$ −4.43845 −0.142657
$$969$$ 0 0
$$970$$ 22.2462 0.714283
$$971$$ 26.2462 0.842281 0.421141 0.906995i $$-0.361630\pi$$
0.421141 + 0.906995i $$0.361630\pi$$
$$972$$ 0 0
$$973$$ −30.7386 −0.985435
$$974$$ 4.87689 0.156266
$$975$$ 0 0
$$976$$ 4.24621 0.135918
$$977$$ 60.9157 1.94887 0.974433 0.224677i $$-0.0721328\pi$$
0.974433 + 0.224677i $$0.0721328\pi$$
$$978$$ 0 0
$$979$$ 40.8078 1.30422
$$980$$ −0.876894 −0.0280114
$$981$$ 0 0
$$982$$ −29.9309 −0.955132
$$983$$ 21.6155 0.689428 0.344714 0.938708i $$-0.387976\pi$$
0.344714 + 0.938708i $$0.387976\pi$$
$$984$$ 0 0
$$985$$ −17.6155 −0.561277
$$986$$ −4.00000 −0.127386
$$987$$ 0 0
$$988$$ −3.19224 −0.101559
$$989$$ 26.2462 0.834581
$$990$$ 0 0
$$991$$ 11.2614 0.357729 0.178865 0.983874i $$-0.442758\pi$$
0.178865 + 0.983874i $$0.442758\pi$$
$$992$$ −0.876894 −0.0278414
$$993$$ 0 0
$$994$$ −36.4924 −1.15747
$$995$$ 9.75379 0.309216
$$996$$ 0 0
$$997$$ −8.06913 −0.255552 −0.127776 0.991803i $$-0.540784\pi$$
−0.127776 + 0.991803i $$0.540784\pi$$
$$998$$ 28.4233 0.899724
$$999$$ 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 666.2.a.k.1.2 yes 2
3.2 odd 2 666.2.a.h.1.2 2
4.3 odd 2 5328.2.a.bh.1.1 2
12.11 even 2 5328.2.a.y.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.a.h.1.2 2 3.2 odd 2
666.2.a.k.1.2 yes 2 1.1 even 1 trivial
5328.2.a.y.1.1 2 12.11 even 2
5328.2.a.bh.1.1 2 4.3 odd 2