# Properties

 Label 4284.2.a.m.1.1 Level $4284$ Weight $2$ Character 4284.1 Self dual yes Analytic conductor $34.208$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4284,2,Mod(1,4284)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4284, 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("4284.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4284.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: $$34.2079122259$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 476) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 4284.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.618034 q^{5} -1.00000 q^{7} +O(q^{10})$$ $$q-0.618034 q^{5} -1.00000 q^{7} +0.763932 q^{11} +1.23607 q^{13} -1.00000 q^{17} -8.47214 q^{19} +7.70820 q^{23} -4.61803 q^{25} +5.70820 q^{29} +6.32624 q^{31} +0.618034 q^{35} +0.472136 q^{37} +0.0901699 q^{41} -12.0902 q^{43} +8.47214 q^{47} +1.00000 q^{49} -10.7984 q^{53} -0.472136 q^{55} -7.32624 q^{61} -0.763932 q^{65} -13.0902 q^{67} -10.9443 q^{71} +7.14590 q^{73} -0.763932 q^{77} +2.94427 q^{79} -15.4164 q^{83} +0.618034 q^{85} -2.00000 q^{89} -1.23607 q^{91} +5.23607 q^{95} +15.0902 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{5} - 2 q^{7}+O(q^{10})$$ 2 * q + q^5 - 2 * q^7 $$2 q + q^{5} - 2 q^{7} + 6 q^{11} - 2 q^{13} - 2 q^{17} - 8 q^{19} + 2 q^{23} - 7 q^{25} - 2 q^{29} - 3 q^{31} - q^{35} - 8 q^{37} - 11 q^{41} - 13 q^{43} + 8 q^{47} + 2 q^{49} + 3 q^{53} + 8 q^{55} + q^{61} - 6 q^{65} - 15 q^{67} - 4 q^{71} + 21 q^{73} - 6 q^{77} - 12 q^{79} - 4 q^{83} - q^{85} - 4 q^{89} + 2 q^{91} + 6 q^{95} + 19 q^{97}+O(q^{100})$$ 2 * q + q^5 - 2 * q^7 + 6 * q^11 - 2 * q^13 - 2 * q^17 - 8 * q^19 + 2 * q^23 - 7 * q^25 - 2 * q^29 - 3 * q^31 - q^35 - 8 * q^37 - 11 * q^41 - 13 * q^43 + 8 * q^47 + 2 * q^49 + 3 * q^53 + 8 * q^55 + q^61 - 6 * q^65 - 15 * q^67 - 4 * q^71 + 21 * q^73 - 6 * q^77 - 12 * q^79 - 4 * q^83 - q^85 - 4 * q^89 + 2 * q^91 + 6 * q^95 + 19 * q^97

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −0.618034 −0.276393 −0.138197 0.990405i $$-0.544131\pi$$
−0.138197 + 0.990405i $$0.544131\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0.763932 0.230334 0.115167 0.993346i $$-0.463260\pi$$
0.115167 + 0.993346i $$0.463260\pi$$
$$12$$ 0 0
$$13$$ 1.23607 0.342824 0.171412 0.985199i $$-0.445167\pi$$
0.171412 + 0.985199i $$0.445167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.00000 −0.242536
$$18$$ 0 0
$$19$$ −8.47214 −1.94364 −0.971821 0.235722i $$-0.924255\pi$$
−0.971821 + 0.235722i $$0.924255\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 7.70820 1.60727 0.803636 0.595121i $$-0.202896\pi$$
0.803636 + 0.595121i $$0.202896\pi$$
$$24$$ 0 0
$$25$$ −4.61803 −0.923607
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 5.70820 1.05999 0.529993 0.848002i $$-0.322194\pi$$
0.529993 + 0.848002i $$0.322194\pi$$
$$30$$ 0 0
$$31$$ 6.32624 1.13623 0.568113 0.822951i $$-0.307674\pi$$
0.568113 + 0.822951i $$0.307674\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0.618034 0.104467
$$36$$ 0 0
$$37$$ 0.472136 0.0776187 0.0388093 0.999247i $$-0.487644\pi$$
0.0388093 + 0.999247i $$0.487644\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.0901699 0.0140822 0.00704109 0.999975i $$-0.497759\pi$$
0.00704109 + 0.999975i $$0.497759\pi$$
$$42$$ 0 0
$$43$$ −12.0902 −1.84373 −0.921867 0.387507i $$-0.873336\pi$$
−0.921867 + 0.387507i $$0.873336\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.47214 1.23579 0.617894 0.786261i $$-0.287986\pi$$
0.617894 + 0.786261i $$0.287986\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −10.7984 −1.48327 −0.741635 0.670803i $$-0.765950\pi$$
−0.741635 + 0.670803i $$0.765950\pi$$
$$54$$ 0 0
$$55$$ −0.472136 −0.0636628
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −7.32624 −0.938029 −0.469014 0.883191i $$-0.655391\pi$$
−0.469014 + 0.883191i $$0.655391\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −0.763932 −0.0947541
$$66$$ 0 0
$$67$$ −13.0902 −1.59922 −0.799609 0.600520i $$-0.794960\pi$$
−0.799609 + 0.600520i $$0.794960\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10.9443 −1.29885 −0.649423 0.760427i $$-0.724990\pi$$
−0.649423 + 0.760427i $$0.724990\pi$$
$$72$$ 0 0
$$73$$ 7.14590 0.836364 0.418182 0.908363i $$-0.362667\pi$$
0.418182 + 0.908363i $$0.362667\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.763932 −0.0870581
$$78$$ 0 0
$$79$$ 2.94427 0.331256 0.165628 0.986188i $$-0.447035\pi$$
0.165628 + 0.986188i $$0.447035\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −15.4164 −1.69217 −0.846085 0.533048i $$-0.821047\pi$$
−0.846085 + 0.533048i $$0.821047\pi$$
$$84$$ 0 0
$$85$$ 0.618034 0.0670352
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −2.00000 −0.212000 −0.106000 0.994366i $$-0.533804\pi$$
−0.106000 + 0.994366i $$0.533804\pi$$
$$90$$ 0 0
$$91$$ −1.23607 −0.129575
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 5.23607 0.537209
$$96$$ 0 0
$$97$$ 15.0902 1.53217 0.766087 0.642737i $$-0.222201\pi$$
0.766087 + 0.642737i $$0.222201\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0.472136 0.0469793 0.0234896 0.999724i $$-0.492522\pi$$
0.0234896 + 0.999724i $$0.492522\pi$$
$$102$$ 0 0
$$103$$ 15.4164 1.51902 0.759512 0.650493i $$-0.225438\pi$$
0.759512 + 0.650493i $$0.225438\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −10.7639 −1.04059 −0.520294 0.853987i $$-0.674178\pi$$
−0.520294 + 0.853987i $$0.674178\pi$$
$$108$$ 0 0
$$109$$ −3.52786 −0.337908 −0.168954 0.985624i $$-0.554039\pi$$
−0.168954 + 0.985624i $$0.554039\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ −4.76393 −0.444239
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1.00000 0.0916698
$$120$$ 0 0
$$121$$ −10.4164 −0.946946
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 5.94427 0.531672
$$126$$ 0 0
$$127$$ −7.85410 −0.696939 −0.348469 0.937320i $$-0.613298\pi$$
−0.348469 + 0.937320i $$0.613298\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ 0 0
$$133$$ 8.47214 0.734627
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.38197 −0.203505 −0.101753 0.994810i $$-0.532445\pi$$
−0.101753 + 0.994810i $$0.532445\pi$$
$$138$$ 0 0
$$139$$ −14.0344 −1.19039 −0.595193 0.803583i $$-0.702924\pi$$
−0.595193 + 0.803583i $$0.702924\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0.944272 0.0789640
$$144$$ 0 0
$$145$$ −3.52786 −0.292973
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 13.6180 1.11563 0.557816 0.829964i $$-0.311639\pi$$
0.557816 + 0.829964i $$0.311639\pi$$
$$150$$ 0 0
$$151$$ −15.1459 −1.23256 −0.616278 0.787529i $$-0.711360\pi$$
−0.616278 + 0.787529i $$0.711360\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.90983 −0.314045
$$156$$ 0 0
$$157$$ −2.18034 −0.174010 −0.0870050 0.996208i $$-0.527730\pi$$
−0.0870050 + 0.996208i $$0.527730\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −7.70820 −0.607492
$$162$$ 0 0
$$163$$ 5.70820 0.447101 0.223551 0.974692i $$-0.428235\pi$$
0.223551 + 0.974692i $$0.428235\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −14.3820 −1.11291 −0.556455 0.830878i $$-0.687839\pi$$
−0.556455 + 0.830878i $$0.687839\pi$$
$$168$$ 0 0
$$169$$ −11.4721 −0.882472
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 11.9098 0.905488 0.452744 0.891641i $$-0.350445\pi$$
0.452744 + 0.891641i $$0.350445\pi$$
$$174$$ 0 0
$$175$$ 4.61803 0.349091
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 18.3820 1.37393 0.686966 0.726689i $$-0.258942\pi$$
0.686966 + 0.726689i $$0.258942\pi$$
$$180$$ 0 0
$$181$$ −12.4721 −0.927047 −0.463523 0.886085i $$-0.653415\pi$$
−0.463523 + 0.886085i $$0.653415\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.291796 −0.0214533
$$186$$ 0 0
$$187$$ −0.763932 −0.0558642
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −20.7984 −1.50492 −0.752459 0.658639i $$-0.771132\pi$$
−0.752459 + 0.658639i $$0.771132\pi$$
$$192$$ 0 0
$$193$$ −14.1803 −1.02072 −0.510362 0.859960i $$-0.670488\pi$$
−0.510362 + 0.859960i $$0.670488\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −9.70820 −0.691681 −0.345840 0.938293i $$-0.612406\pi$$
−0.345840 + 0.938293i $$0.612406\pi$$
$$198$$ 0 0
$$199$$ −12.0902 −0.857049 −0.428525 0.903530i $$-0.640967\pi$$
−0.428525 + 0.903530i $$0.640967\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −5.70820 −0.400637
$$204$$ 0 0
$$205$$ −0.0557281 −0.00389222
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −6.47214 −0.447687
$$210$$ 0 0
$$211$$ −2.29180 −0.157774 −0.0788869 0.996884i $$-0.525137\pi$$
−0.0788869 + 0.996884i $$0.525137\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 7.47214 0.509595
$$216$$ 0 0
$$217$$ −6.32624 −0.429453
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.23607 −0.0831469
$$222$$ 0 0
$$223$$ 2.94427 0.197163 0.0985815 0.995129i $$-0.468569\pi$$
0.0985815 + 0.995129i $$0.468569\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −25.7426 −1.70860 −0.854300 0.519781i $$-0.826014\pi$$
−0.854300 + 0.519781i $$0.826014\pi$$
$$228$$ 0 0
$$229$$ −19.2361 −1.27116 −0.635578 0.772037i $$-0.719238\pi$$
−0.635578 + 0.772037i $$0.719238\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.47214 −0.424004 −0.212002 0.977269i $$-0.567998\pi$$
−0.212002 + 0.977269i $$0.567998\pi$$
$$234$$ 0 0
$$235$$ −5.23607 −0.341563
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −11.9098 −0.770383 −0.385191 0.922837i $$-0.625865\pi$$
−0.385191 + 0.922837i $$0.625865\pi$$
$$240$$ 0 0
$$241$$ 4.03444 0.259881 0.129941 0.991522i $$-0.458521\pi$$
0.129941 + 0.991522i $$0.458521\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −0.618034 −0.0394847
$$246$$ 0 0
$$247$$ −10.4721 −0.666326
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 17.4164 1.09931 0.549657 0.835390i $$-0.314758\pi$$
0.549657 + 0.835390i $$0.314758\pi$$
$$252$$ 0 0
$$253$$ 5.88854 0.370210
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −25.7082 −1.60363 −0.801817 0.597570i $$-0.796133\pi$$
−0.801817 + 0.597570i $$0.796133\pi$$
$$258$$ 0 0
$$259$$ −0.472136 −0.0293371
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 16.9443 1.04483 0.522414 0.852692i $$-0.325031\pi$$
0.522414 + 0.852692i $$0.325031\pi$$
$$264$$ 0 0
$$265$$ 6.67376 0.409966
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 0 0
$$271$$ 3.70820 0.225257 0.112629 0.993637i $$-0.464073\pi$$
0.112629 + 0.993637i $$0.464073\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −3.52786 −0.212738
$$276$$ 0 0
$$277$$ 2.76393 0.166069 0.0830343 0.996547i $$-0.473539\pi$$
0.0830343 + 0.996547i $$0.473539\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 8.90983 0.531516 0.265758 0.964040i $$-0.414378\pi$$
0.265758 + 0.964040i $$0.414378\pi$$
$$282$$ 0 0
$$283$$ −4.43769 −0.263794 −0.131897 0.991263i $$-0.542107\pi$$
−0.131897 + 0.991263i $$0.542107\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −0.0901699 −0.00532256
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 6.29180 0.367571 0.183785 0.982966i $$-0.441165\pi$$
0.183785 + 0.982966i $$0.441165\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 9.52786 0.551011
$$300$$ 0 0
$$301$$ 12.0902 0.696866
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.52786 0.259265
$$306$$ 0 0
$$307$$ 1.05573 0.0602536 0.0301268 0.999546i $$-0.490409\pi$$
0.0301268 + 0.999546i $$0.490409\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −26.6180 −1.50937 −0.754685 0.656087i $$-0.772210\pi$$
−0.754685 + 0.656087i $$0.772210\pi$$
$$312$$ 0 0
$$313$$ −1.27051 −0.0718135 −0.0359067 0.999355i $$-0.511432\pi$$
−0.0359067 + 0.999355i $$0.511432\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 28.1803 1.58277 0.791383 0.611321i $$-0.209362\pi$$
0.791383 + 0.611321i $$0.209362\pi$$
$$318$$ 0 0
$$319$$ 4.36068 0.244151
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.47214 0.471402
$$324$$ 0 0
$$325$$ −5.70820 −0.316634
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −8.47214 −0.467084
$$330$$ 0 0
$$331$$ 18.0344 0.991263 0.495631 0.868533i $$-0.334937\pi$$
0.495631 + 0.868533i $$0.334937\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 8.09017 0.442013
$$336$$ 0 0
$$337$$ 9.52786 0.519016 0.259508 0.965741i $$-0.416440\pi$$
0.259508 + 0.965741i $$0.416440\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 4.83282 0.261712
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −30.9443 −1.66118 −0.830588 0.556888i $$-0.811995\pi$$
−0.830588 + 0.556888i $$0.811995\pi$$
$$348$$ 0 0
$$349$$ −15.5279 −0.831188 −0.415594 0.909550i $$-0.636426\pi$$
−0.415594 + 0.909550i $$0.636426\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 12.7639 0.679356 0.339678 0.940542i $$-0.389682\pi$$
0.339678 + 0.940542i $$0.389682\pi$$
$$354$$ 0 0
$$355$$ 6.76393 0.358992
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −19.5623 −1.03246 −0.516230 0.856450i $$-0.672665\pi$$
−0.516230 + 0.856450i $$0.672665\pi$$
$$360$$ 0 0
$$361$$ 52.7771 2.77774
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −4.41641 −0.231165
$$366$$ 0 0
$$367$$ −19.5066 −1.01824 −0.509118 0.860697i $$-0.670028\pi$$
−0.509118 + 0.860697i $$0.670028\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 10.7984 0.560624
$$372$$ 0 0
$$373$$ −16.8541 −0.872672 −0.436336 0.899784i $$-0.643724\pi$$
−0.436336 + 0.899784i $$0.643724\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 7.05573 0.363388
$$378$$ 0 0
$$379$$ 10.6525 0.547181 0.273590 0.961846i $$-0.411789\pi$$
0.273590 + 0.961846i $$0.411789\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 30.6525 1.56627 0.783134 0.621853i $$-0.213620\pi$$
0.783134 + 0.621853i $$0.213620\pi$$
$$384$$ 0 0
$$385$$ 0.472136 0.0240623
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 21.5623 1.09325 0.546626 0.837377i $$-0.315912\pi$$
0.546626 + 0.837377i $$0.315912\pi$$
$$390$$ 0 0
$$391$$ −7.70820 −0.389821
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1.81966 −0.0915570
$$396$$ 0 0
$$397$$ −6.79837 −0.341201 −0.170600 0.985340i $$-0.554571\pi$$
−0.170600 + 0.985340i $$0.554571\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 10.4721 0.522954 0.261477 0.965210i $$-0.415791\pi$$
0.261477 + 0.965210i $$0.415791\pi$$
$$402$$ 0 0
$$403$$ 7.81966 0.389525
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0.360680 0.0178782
$$408$$ 0 0
$$409$$ −8.18034 −0.404492 −0.202246 0.979335i $$-0.564824\pi$$
−0.202246 + 0.979335i $$0.564824\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 9.52786 0.467704
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −37.4508 −1.82959 −0.914797 0.403914i $$-0.867649\pi$$
−0.914797 + 0.403914i $$0.867649\pi$$
$$420$$ 0 0
$$421$$ −29.2148 −1.42384 −0.711921 0.702260i $$-0.752174\pi$$
−0.711921 + 0.702260i $$0.752174\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 4.61803 0.224008
$$426$$ 0 0
$$427$$ 7.32624 0.354542
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −5.05573 −0.243526 −0.121763 0.992559i $$-0.538855\pi$$
−0.121763 + 0.992559i $$0.538855\pi$$
$$432$$ 0 0
$$433$$ 16.9443 0.814290 0.407145 0.913364i $$-0.366524\pi$$
0.407145 + 0.913364i $$0.366524\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −65.3050 −3.12396
$$438$$ 0 0
$$439$$ −3.32624 −0.158753 −0.0793763 0.996845i $$-0.525293\pi$$
−0.0793763 + 0.996845i $$0.525293\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −25.8885 −1.23000 −0.615001 0.788526i $$-0.710844\pi$$
−0.615001 + 0.788526i $$0.710844\pi$$
$$444$$ 0 0
$$445$$ 1.23607 0.0585952
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −17.7082 −0.835702 −0.417851 0.908516i $$-0.637217\pi$$
−0.417851 + 0.908516i $$0.637217\pi$$
$$450$$ 0 0
$$451$$ 0.0688837 0.00324361
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0.763932 0.0358137
$$456$$ 0 0
$$457$$ 0.618034 0.0289104 0.0144552 0.999896i $$-0.495399\pi$$
0.0144552 + 0.999896i $$0.495399\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 12.9443 0.602875 0.301437 0.953486i $$-0.402534\pi$$
0.301437 + 0.953486i $$0.402534\pi$$
$$462$$ 0 0
$$463$$ −13.0344 −0.605762 −0.302881 0.953028i $$-0.597948\pi$$
−0.302881 + 0.953028i $$0.597948\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −10.4721 −0.484593 −0.242296 0.970202i $$-0.577901\pi$$
−0.242296 + 0.970202i $$0.577901\pi$$
$$468$$ 0 0
$$469$$ 13.0902 0.604448
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −9.23607 −0.424675
$$474$$ 0 0
$$475$$ 39.1246 1.79516
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 24.2705 1.10895 0.554474 0.832201i $$-0.312920\pi$$
0.554474 + 0.832201i $$0.312920\pi$$
$$480$$ 0 0
$$481$$ 0.583592 0.0266095
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −9.32624 −0.423483
$$486$$ 0 0
$$487$$ −22.3607 −1.01326 −0.506630 0.862164i $$-0.669109\pi$$
−0.506630 + 0.862164i $$0.669109\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 1.09017 0.0491987 0.0245993 0.999697i $$-0.492169\pi$$
0.0245993 + 0.999697i $$0.492169\pi$$
$$492$$ 0 0
$$493$$ −5.70820 −0.257085
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 10.9443 0.490918
$$498$$ 0 0
$$499$$ 17.0557 0.763519 0.381760 0.924262i $$-0.375318\pi$$
0.381760 + 0.924262i $$0.375318\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 10.6180 0.473435 0.236717 0.971579i $$-0.423928\pi$$
0.236717 + 0.971579i $$0.423928\pi$$
$$504$$ 0 0
$$505$$ −0.291796 −0.0129848
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0.763932 0.0338607 0.0169303 0.999857i $$-0.494611\pi$$
0.0169303 + 0.999857i $$0.494611\pi$$
$$510$$ 0 0
$$511$$ −7.14590 −0.316116
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −9.52786 −0.419848
$$516$$ 0 0
$$517$$ 6.47214 0.284644
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 26.7426 1.17162 0.585808 0.810450i $$-0.300777\pi$$
0.585808 + 0.810450i $$0.300777\pi$$
$$522$$ 0 0
$$523$$ 34.1803 1.49460 0.747301 0.664486i $$-0.231349\pi$$
0.747301 + 0.664486i $$0.231349\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −6.32624 −0.275575
$$528$$ 0 0
$$529$$ 36.4164 1.58332
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0.111456 0.00482770
$$534$$ 0 0
$$535$$ 6.65248 0.287612
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0.763932 0.0329049
$$540$$ 0 0
$$541$$ −5.23607 −0.225116 −0.112558 0.993645i $$-0.535904\pi$$
−0.112558 + 0.993645i $$0.535904\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 2.18034 0.0933955
$$546$$ 0 0
$$547$$ −40.6525 −1.73817 −0.869087 0.494659i $$-0.835293\pi$$
−0.869087 + 0.494659i $$0.835293\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −48.3607 −2.06023
$$552$$ 0 0
$$553$$ −2.94427 −0.125203
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −34.3607 −1.45591 −0.727954 0.685626i $$-0.759529\pi$$
−0.727954 + 0.685626i $$0.759529\pi$$
$$558$$ 0 0
$$559$$ −14.9443 −0.632075
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 29.1246 1.22746 0.613728 0.789518i $$-0.289669\pi$$
0.613728 + 0.789518i $$0.289669\pi$$
$$564$$ 0 0
$$565$$ 3.70820 0.156005
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 43.5066 1.82389 0.911945 0.410312i $$-0.134580\pi$$
0.911945 + 0.410312i $$0.134580\pi$$
$$570$$ 0 0
$$571$$ 8.47214 0.354548 0.177274 0.984162i $$-0.443272\pi$$
0.177274 + 0.984162i $$0.443272\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −35.5967 −1.48449
$$576$$ 0 0
$$577$$ 17.1246 0.712907 0.356453 0.934313i $$-0.383986\pi$$
0.356453 + 0.934313i $$0.383986\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 15.4164 0.639580
$$582$$ 0 0
$$583$$ −8.24922 −0.341648
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 42.8328 1.76790 0.883950 0.467582i $$-0.154875\pi$$
0.883950 + 0.467582i $$0.154875\pi$$
$$588$$ 0 0
$$589$$ −53.5967 −2.20842
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 22.3607 0.918243 0.459122 0.888373i $$-0.348164\pi$$
0.459122 + 0.888373i $$0.348164\pi$$
$$594$$ 0 0
$$595$$ −0.618034 −0.0253369
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −36.0902 −1.47460 −0.737302 0.675563i $$-0.763901\pi$$
−0.737302 + 0.675563i $$0.763901\pi$$
$$600$$ 0 0
$$601$$ 48.2492 1.96813 0.984063 0.177818i $$-0.0569037\pi$$
0.984063 + 0.177818i $$0.0569037\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 6.43769 0.261729
$$606$$ 0 0
$$607$$ −39.8541 −1.61763 −0.808814 0.588064i $$-0.799890\pi$$
−0.808814 + 0.588064i $$0.799890\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 10.4721 0.423657
$$612$$ 0 0
$$613$$ −17.5623 −0.709335 −0.354667 0.934993i $$-0.615406\pi$$
−0.354667 + 0.934993i $$0.615406\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 35.0132 1.40958 0.704788 0.709418i $$-0.251042\pi$$
0.704788 + 0.709418i $$0.251042\pi$$
$$618$$ 0 0
$$619$$ −32.0000 −1.28619 −0.643094 0.765787i $$-0.722350\pi$$
−0.643094 + 0.765787i $$0.722350\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 2.00000 0.0801283
$$624$$ 0 0
$$625$$ 19.4164 0.776656
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −0.472136 −0.0188253
$$630$$ 0 0
$$631$$ −37.0902 −1.47654 −0.738268 0.674507i $$-0.764356\pi$$
−0.738268 + 0.674507i $$0.764356\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 4.85410 0.192629
$$636$$ 0 0
$$637$$ 1.23607 0.0489748
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −21.0557 −0.831651 −0.415826 0.909444i $$-0.636507\pi$$
−0.415826 + 0.909444i $$0.636507\pi$$
$$642$$ 0 0
$$643$$ 3.14590 0.124062 0.0620311 0.998074i $$-0.480242\pi$$
0.0620311 + 0.998074i $$0.480242\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 20.7639 0.816314 0.408157 0.912912i $$-0.366172\pi$$
0.408157 + 0.912912i $$0.366172\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 32.4721 1.27073 0.635366 0.772211i $$-0.280849\pi$$
0.635366 + 0.772211i $$0.280849\pi$$
$$654$$ 0 0
$$655$$ −4.94427 −0.193189
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.74265 −0.0678838 −0.0339419 0.999424i $$-0.510806\pi$$
−0.0339419 + 0.999424i $$0.510806\pi$$
$$660$$ 0 0
$$661$$ 30.8328 1.19926 0.599629 0.800278i $$-0.295315\pi$$
0.599629 + 0.800278i $$0.295315\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −5.23607 −0.203046
$$666$$ 0 0
$$667$$ 44.0000 1.70369
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −5.59675 −0.216060
$$672$$ 0 0
$$673$$ −14.4721 −0.557860 −0.278930 0.960311i $$-0.589980\pi$$
−0.278930 + 0.960311i $$0.589980\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 33.7771 1.29816 0.649079 0.760721i $$-0.275154\pi$$
0.649079 + 0.760721i $$0.275154\pi$$
$$678$$ 0 0
$$679$$ −15.0902 −0.579108
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −28.1803 −1.07829 −0.539145 0.842213i $$-0.681253\pi$$
−0.539145 + 0.842213i $$0.681253\pi$$
$$684$$ 0 0
$$685$$ 1.47214 0.0562474
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −13.3475 −0.508500
$$690$$ 0 0
$$691$$ 8.49342 0.323105 0.161553 0.986864i $$-0.448350\pi$$
0.161553 + 0.986864i $$0.448350\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 8.67376 0.329015
$$696$$ 0 0
$$697$$ −0.0901699 −0.00341543
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 45.4164 1.71535 0.857677 0.514189i $$-0.171907\pi$$
0.857677 + 0.514189i $$0.171907\pi$$
$$702$$ 0 0
$$703$$ −4.00000 −0.150863
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −0.472136 −0.0177565
$$708$$ 0 0
$$709$$ 40.6525 1.52674 0.763368 0.645964i $$-0.223544\pi$$
0.763368 + 0.645964i $$0.223544\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 48.7639 1.82622
$$714$$ 0 0
$$715$$ −0.583592 −0.0218251
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 39.1459 1.45990 0.729948 0.683503i $$-0.239544\pi$$
0.729948 + 0.683503i $$0.239544\pi$$
$$720$$ 0 0
$$721$$ −15.4164 −0.574137
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −26.3607 −0.979011
$$726$$ 0 0
$$727$$ 16.4721 0.610918 0.305459 0.952205i $$-0.401190\pi$$
0.305459 + 0.952205i $$0.401190\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 12.0902 0.447171
$$732$$ 0 0
$$733$$ 36.0000 1.32969 0.664845 0.746981i $$-0.268498\pi$$
0.664845 + 0.746981i $$0.268498\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −10.0000 −0.368355
$$738$$ 0 0
$$739$$ −1.43769 −0.0528864 −0.0264432 0.999650i $$-0.508418\pi$$
−0.0264432 + 0.999650i $$0.508418\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −4.65248 −0.170683 −0.0853414 0.996352i $$-0.527198\pi$$
−0.0853414 + 0.996352i $$0.527198\pi$$
$$744$$ 0 0
$$745$$ −8.41641 −0.308353
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 10.7639 0.393306
$$750$$ 0 0
$$751$$ 10.9443 0.399362 0.199681 0.979861i $$-0.436009\pi$$
0.199681 + 0.979861i $$0.436009\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 9.36068 0.340670
$$756$$ 0 0
$$757$$ −9.43769 −0.343019 −0.171509 0.985182i $$-0.554864\pi$$
−0.171509 + 0.985182i $$0.554864\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −30.1803 −1.09404 −0.547018 0.837121i $$-0.684237\pi$$
−0.547018 + 0.837121i $$0.684237\pi$$
$$762$$ 0 0
$$763$$ 3.52786 0.127717
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −7.12461 −0.256920 −0.128460 0.991715i $$-0.541003\pi$$
−0.128460 + 0.991715i $$0.541003\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −5.41641 −0.194815 −0.0974073 0.995245i $$-0.531055\pi$$
−0.0974073 + 0.995245i $$0.531055\pi$$
$$774$$ 0 0
$$775$$ −29.2148 −1.04943
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.763932 −0.0273707
$$780$$ 0 0
$$781$$ −8.36068 −0.299169
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 1.34752 0.0480952
$$786$$ 0 0
$$787$$ −12.0000 −0.427754 −0.213877 0.976861i $$-0.568609\pi$$
−0.213877 + 0.976861i $$0.568609\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ −9.05573 −0.321578
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −15.4164 −0.546077 −0.273039 0.962003i $$-0.588029\pi$$
−0.273039 + 0.962003i $$0.588029\pi$$
$$798$$ 0 0
$$799$$ −8.47214 −0.299723
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 5.45898 0.192643
$$804$$ 0 0
$$805$$ 4.76393 0.167907
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 53.4853 1.88044 0.940221 0.340564i $$-0.110618\pi$$
0.940221 + 0.340564i $$0.110618\pi$$
$$810$$ 0 0
$$811$$ −2.96556 −0.104135 −0.0520674 0.998644i $$-0.516581\pi$$
−0.0520674 + 0.998644i $$0.516581\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −3.52786 −0.123576
$$816$$ 0 0
$$817$$ 102.430 3.58356
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −14.3607 −0.501191 −0.250596 0.968092i $$-0.580626\pi$$
−0.250596 + 0.968092i $$0.580626\pi$$
$$822$$ 0 0
$$823$$ 47.4853 1.65523 0.827617 0.561294i $$-0.189696\pi$$
0.827617 + 0.561294i $$0.189696\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −27.5279 −0.957238 −0.478619 0.878023i $$-0.658862\pi$$
−0.478619 + 0.878023i $$0.658862\pi$$
$$828$$ 0 0
$$829$$ −6.18034 −0.214652 −0.107326 0.994224i $$-0.534229\pi$$
−0.107326 + 0.994224i $$0.534229\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1.00000 −0.0346479
$$834$$ 0 0
$$835$$ 8.88854 0.307601
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 13.5279 0.467034 0.233517 0.972353i $$-0.424977\pi$$
0.233517 + 0.972353i $$0.424977\pi$$
$$840$$ 0 0
$$841$$ 3.58359 0.123572
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 7.09017 0.243909
$$846$$ 0 0
$$847$$ 10.4164 0.357912
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 3.63932 0.124754
$$852$$ 0 0
$$853$$ −38.3607 −1.31344 −0.656722 0.754132i $$-0.728058\pi$$
−0.656722 + 0.754132i $$0.728058\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 15.0902 0.515470 0.257735 0.966216i $$-0.417024\pi$$
0.257735 + 0.966216i $$0.417024\pi$$
$$858$$ 0 0
$$859$$ 14.9443 0.509892 0.254946 0.966955i $$-0.417942\pi$$
0.254946 + 0.966955i $$0.417942\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 46.3262 1.57696 0.788482 0.615058i $$-0.210867\pi$$
0.788482 + 0.615058i $$0.210867\pi$$
$$864$$ 0 0
$$865$$ −7.36068 −0.250271
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 2.24922 0.0762997
$$870$$ 0 0
$$871$$ −16.1803 −0.548250
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −5.94427 −0.200953
$$876$$ 0 0
$$877$$ 18.2918 0.617670 0.308835 0.951116i $$-0.400061\pi$$
0.308835 + 0.951116i $$0.400061\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 19.6738 0.662826 0.331413 0.943486i $$-0.392475\pi$$
0.331413 + 0.943486i $$0.392475\pi$$
$$882$$ 0 0
$$883$$ 14.9787 0.504074 0.252037 0.967718i $$-0.418900\pi$$
0.252037 + 0.967718i $$0.418900\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 16.5066 0.554237 0.277118 0.960836i $$-0.410621\pi$$
0.277118 + 0.960836i $$0.410621\pi$$
$$888$$ 0 0
$$889$$ 7.85410 0.263418
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −71.7771 −2.40193
$$894$$ 0 0
$$895$$ −11.3607 −0.379746
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 36.1115 1.20438
$$900$$ 0 0
$$901$$ 10.7984 0.359746
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 7.70820 0.256229
$$906$$ 0 0
$$907$$ −31.3050 −1.03946 −0.519732 0.854329i $$-0.673968\pi$$
−0.519732 + 0.854329i $$0.673968\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 14.4721 0.479483 0.239742 0.970837i $$-0.422937\pi$$
0.239742 + 0.970837i $$0.422937\pi$$
$$912$$ 0 0
$$913$$ −11.7771 −0.389765
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −8.00000 −0.264183
$$918$$ 0 0
$$919$$ −30.1591 −0.994855 −0.497428 0.867505i $$-0.665722\pi$$
−0.497428 + 0.867505i $$0.665722\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −13.5279 −0.445275
$$924$$ 0 0
$$925$$ −2.18034 −0.0716891
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −21.2705 −0.697863 −0.348931 0.937148i $$-0.613455\pi$$
−0.348931 + 0.937148i $$0.613455\pi$$
$$930$$ 0 0
$$931$$ −8.47214 −0.277663
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0.472136 0.0154405
$$936$$ 0 0
$$937$$ −5.30495 −0.173305 −0.0866526 0.996239i $$-0.527617\pi$$
−0.0866526 + 0.996239i $$0.527617\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −45.9787 −1.49886 −0.749432 0.662082i $$-0.769673\pi$$
−0.749432 + 0.662082i $$0.769673\pi$$
$$942$$ 0 0
$$943$$ 0.695048 0.0226339
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −6.87539 −0.223420 −0.111710 0.993741i $$-0.535633\pi$$
−0.111710 + 0.993741i $$0.535633\pi$$
$$948$$ 0 0
$$949$$ 8.83282 0.286725
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −32.3262 −1.04715 −0.523575 0.851980i $$-0.675402\pi$$
−0.523575 + 0.851980i $$0.675402\pi$$
$$954$$ 0 0
$$955$$ 12.8541 0.415949
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 2.38197 0.0769177
$$960$$ 0 0
$$961$$ 9.02129 0.291009
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 8.76393 0.282121
$$966$$ 0 0
$$967$$ 37.7984 1.21551 0.607757 0.794123i $$-0.292070\pi$$
0.607757 + 0.794123i $$0.292070\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −21.1246 −0.677921 −0.338961 0.940801i $$-0.610075\pi$$
−0.338961 + 0.940801i $$0.610075\pi$$
$$972$$ 0 0
$$973$$ 14.0344 0.449924
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 2.21478 0.0708571 0.0354286 0.999372i $$-0.488720\pi$$
0.0354286 + 0.999372i $$0.488720\pi$$
$$978$$ 0 0
$$979$$ −1.52786 −0.0488307
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −6.90983 −0.220389 −0.110195 0.993910i $$-0.535147\pi$$
−0.110195 + 0.993910i $$0.535147\pi$$
$$984$$ 0 0
$$985$$ 6.00000 0.191176
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −93.1935 −2.96338
$$990$$ 0 0
$$991$$ −28.2492 −0.897366 −0.448683 0.893691i $$-0.648107\pi$$
−0.448683 + 0.893691i $$0.648107\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 7.47214 0.236883
$$996$$ 0 0
$$997$$ 29.0344 0.919530 0.459765 0.888041i $$-0.347934\pi$$
0.459765 + 0.888041i $$0.347934\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4284.2.a.m.1.1 2
3.2 odd 2 476.2.a.b.1.1 2
12.11 even 2 1904.2.a.j.1.2 2
21.20 even 2 3332.2.a.l.1.2 2
24.5 odd 2 7616.2.a.u.1.2 2
24.11 even 2 7616.2.a.p.1.1 2
51.50 odd 2 8092.2.a.m.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
476.2.a.b.1.1 2 3.2 odd 2
1904.2.a.j.1.2 2 12.11 even 2
3332.2.a.l.1.2 2 21.20 even 2
4284.2.a.m.1.1 2 1.1 even 1 trivial
7616.2.a.p.1.1 2 24.11 even 2
7616.2.a.u.1.2 2 24.5 odd 2
8092.2.a.m.1.2 2 51.50 odd 2