# Properties

 Label 585.2.h.e.64.2 Level $585$ Weight $2$ Character 585.64 Analytic conductor $4.671$ Analytic rank $0$ Dimension $4$ CM discriminant -195 Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(64,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("585.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.h (of order $$2$$, degree $$1$$, minimal)

## 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: no Analytic conductor: $$4.67124851824$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-5}, \sqrt{13})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 2x^{3} + 5x^{2} - 4x + 69$$ x^4 - 2*x^3 + 5*x^2 - 4*x + 69 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 64.2 Root $$2.30278 + 2.23607i$$ of defining polynomial Character $$\chi$$ $$=$$ 585.64 Dual form 585.2.h.e.64.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-2.00000 q^{4} -2.23607i q^{5} +3.60555 q^{7} +O(q^{10})$$ $$q-2.00000 q^{4} -2.23607i q^{5} +3.60555 q^{7} +2.23607i q^{11} -3.60555 q^{13} +4.00000 q^{16} -8.06226i q^{17} +4.47214i q^{20} -8.06226i q^{23} -5.00000 q^{25} -7.21110 q^{28} -8.06226i q^{35} +3.60555 q^{37} -11.1803i q^{41} -4.47214i q^{44} +6.00000 q^{49} +7.21110 q^{52} -8.06226i q^{53} +5.00000 q^{55} +8.94427i q^{59} -7.00000 q^{61} -8.00000 q^{64} +8.06226i q^{65} +14.4222 q^{67} +16.1245i q^{68} +15.6525i q^{71} -7.21110 q^{73} +8.06226i q^{77} +11.0000 q^{79} -8.94427i q^{80} -18.0278 q^{85} +2.23607i q^{89} -13.0000 q^{91} +16.1245i q^{92} +3.60555 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{4}+O(q^{10})$$ 4 * q - 8 * q^4 $$4 q - 8 q^{4} + 16 q^{16} - 20 q^{25} + 24 q^{49} + 20 q^{55} - 28 q^{61} - 32 q^{64} + 44 q^{79} - 52 q^{91}+O(q^{100})$$ 4 * q - 8 * q^4 + 16 * q^16 - 20 * q^25 + 24 * q^49 + 20 * q^55 - 28 * q^61 - 32 * q^64 + 44 * q^79 - 52 * q^91

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$496$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 0 0
$$4$$ −2.00000 −1.00000
$$5$$ − 2.23607i − 1.00000i
$$6$$ 0 0
$$7$$ 3.60555 1.36277 0.681385 0.731925i $$-0.261378\pi$$
0.681385 + 0.731925i $$0.261378\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.23607i 0.674200i 0.941469 + 0.337100i $$0.109446\pi$$
−0.941469 + 0.337100i $$0.890554\pi$$
$$12$$ 0 0
$$13$$ −3.60555 −1.00000
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.00000 1.00000
$$17$$ − 8.06226i − 1.95538i −0.210042 0.977692i $$-0.567360\pi$$
0.210042 0.977692i $$-0.432640\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 4.47214i 1.00000i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ − 8.06226i − 1.68110i −0.541736 0.840548i $$-0.682233\pi$$
0.541736 0.840548i $$-0.317767\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −7.21110 −1.36277
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ − 8.06226i − 1.36277i
$$36$$ 0 0
$$37$$ 3.60555 0.592749 0.296374 0.955072i $$-0.404222\pi$$
0.296374 + 0.955072i $$0.404222\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ − 11.1803i − 1.74608i −0.487652 0.873038i $$-0.662147\pi$$
0.487652 0.873038i $$-0.337853\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ − 4.47214i − 0.674200i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 6.00000 0.857143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 7.21110 1.00000
$$53$$ − 8.06226i − 1.10744i −0.832704 0.553718i $$-0.813209\pi$$
0.832704 0.553718i $$-0.186791\pi$$
$$54$$ 0 0
$$55$$ 5.00000 0.674200
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 8.94427i 1.16445i 0.813029 + 0.582223i $$0.197817\pi$$
−0.813029 + 0.582223i $$0.802183\pi$$
$$60$$ 0 0
$$61$$ −7.00000 −0.896258 −0.448129 0.893969i $$-0.647910\pi$$
−0.448129 + 0.893969i $$0.647910\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 8.06226i 1.00000i
$$66$$ 0 0
$$67$$ 14.4222 1.76195 0.880976 0.473160i $$-0.156887\pi$$
0.880976 + 0.473160i $$0.156887\pi$$
$$68$$ 16.1245i 1.95538i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 15.6525i 1.85761i 0.370572 + 0.928804i $$0.379162\pi$$
−0.370572 + 0.928804i $$0.620838\pi$$
$$72$$ 0 0
$$73$$ −7.21110 −0.843996 −0.421998 0.906597i $$-0.638671\pi$$
−0.421998 + 0.906597i $$0.638671\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 8.06226i 0.918780i
$$78$$ 0 0
$$79$$ 11.0000 1.23760 0.618798 0.785550i $$-0.287620\pi$$
0.618798 + 0.785550i $$0.287620\pi$$
$$80$$ − 8.94427i − 1.00000i
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −18.0278 −1.95538
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.23607i 0.237023i 0.992953 + 0.118511i $$0.0378122\pi$$
−0.992953 + 0.118511i $$0.962188\pi$$
$$90$$ 0 0
$$91$$ −13.0000 −1.36277
$$92$$ 16.1245i 1.68110i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 3.60555 0.366088 0.183044 0.983105i $$-0.441405\pi$$
0.183044 + 0.983105i $$0.441405\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 10.0000 1.00000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ − 8.06226i − 0.779408i −0.920940 0.389704i $$-0.872577\pi$$
0.920940 0.389704i $$-0.127423\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 14.4222 1.36277
$$113$$ 16.1245i 1.51687i 0.651751 + 0.758433i $$0.274035\pi$$
−0.651751 + 0.758433i $$0.725965\pi$$
$$114$$ 0 0
$$115$$ −18.0278 −1.68110
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ − 29.0689i − 2.66474i
$$120$$ 0 0
$$121$$ 6.00000 0.545455
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 11.1803i 1.00000i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ −19.0000 −1.61156 −0.805779 0.592216i $$-0.798253\pi$$
−0.805779 + 0.592216i $$0.798253\pi$$
$$140$$ 16.1245i 1.36277i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ − 8.06226i − 0.674200i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −7.21110 −0.592749
$$149$$ 15.6525i 1.28230i 0.767415 + 0.641150i $$0.221543\pi$$
−0.767415 + 0.641150i $$0.778457\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ − 29.0689i − 2.29095i
$$162$$ 0 0
$$163$$ 25.2389 1.97686 0.988430 0.151678i $$-0.0484676\pi$$
0.988430 + 0.151678i $$0.0484676\pi$$
$$164$$ 22.3607i 1.74608i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 16.1245i 1.22592i 0.790112 + 0.612962i $$0.210022\pi$$
−0.790112 + 0.612962i $$0.789978\pi$$
$$174$$ 0 0
$$175$$ −18.0278 −1.36277
$$176$$ 8.94427i 0.674200i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 23.0000 1.70958 0.854788 0.518977i $$-0.173687\pi$$
0.854788 + 0.518977i $$0.173687\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ − 8.06226i − 0.592749i
$$186$$ 0 0
$$187$$ 18.0278 1.31832
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 25.2389 1.81673 0.908366 0.418175i $$-0.137330\pi$$
0.908366 + 0.418175i $$0.137330\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −12.0000 −0.857143
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −25.0000 −1.74608
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −14.4222 −1.00000
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ 16.1245i 1.10744i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −10.0000 −0.674200
$$221$$ 29.0689i 1.95538i
$$222$$ 0 0
$$223$$ −28.8444 −1.93156 −0.965782 0.259354i $$-0.916490\pi$$
−0.965782 + 0.259354i $$0.916490\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ − 8.06226i − 0.528176i −0.964499 0.264088i $$-0.914929\pi$$
0.964499 0.264088i $$-0.0850709\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ − 17.8885i − 1.16445i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ − 24.5967i − 1.59103i −0.605933 0.795516i $$-0.707200\pi$$
0.605933 0.795516i $$-0.292800\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 14.0000 0.896258
$$245$$ − 13.4164i − 0.857143i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 18.0278 1.13340
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 16.1245i 1.00582i 0.864339 + 0.502910i $$0.167737\pi$$
−0.864339 + 0.502910i $$0.832263\pi$$
$$258$$ 0 0
$$259$$ 13.0000 0.807781
$$260$$ − 16.1245i − 1.00000i
$$261$$ 0 0
$$262$$ 0 0
$$263$$ − 32.2490i − 1.98856i −0.106803 0.994280i $$-0.534061\pi$$
0.106803 0.994280i $$-0.465939\pi$$
$$264$$ 0 0
$$265$$ −18.0278 −1.10744
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −28.8444 −1.76195
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ − 32.2490i − 1.95538i
$$273$$ 0 0
$$274$$ 0 0
$$275$$ − 11.1803i − 0.674200i
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 22.3607i 1.33393i 0.745091 + 0.666963i $$0.232406\pi$$
−0.745091 + 0.666963i $$0.767594\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ − 31.3050i − 1.85761i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ − 40.3113i − 2.37950i
$$288$$ 0 0
$$289$$ −48.0000 −2.82353
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 14.4222 0.843996
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 20.0000 1.16445
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 29.0689i 1.68110i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 15.6525i 0.896258i
$$306$$ 0 0
$$307$$ 3.60555 0.205780 0.102890 0.994693i $$-0.467191\pi$$
0.102890 + 0.994693i $$0.467191\pi$$
$$308$$ − 16.1245i − 0.918780i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −22.0000 −1.23760
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 17.8885i 1.00000i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 18.0278 1.00000
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ − 32.2490i − 1.76195i
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 36.0555 1.95538
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −3.60555 −0.194681
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ − 8.06226i − 0.432805i −0.976304 0.216402i $$-0.930568\pi$$
0.976304 0.216402i $$-0.0694323\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 35.0000 1.85761
$$356$$ − 4.47214i − 0.237023i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 35.7771i 1.88824i 0.329598 + 0.944121i $$0.393087\pi$$
−0.329598 + 0.944121i $$0.606913\pi$$
$$360$$ 0 0
$$361$$ 19.0000 1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 26.0000 1.36277
$$365$$ 16.1245i 0.843996i
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ − 32.2490i − 1.68110i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ − 29.0689i − 1.50918i
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 18.0278 0.918780
$$386$$ 0 0
$$387$$ 0 0
$$388$$ −7.21110 −0.366088
$$389$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$390$$ 0 0
$$391$$ −65.0000 −3.28719
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ − 24.5967i − 1.23760i
$$396$$ 0 0
$$397$$ −39.6611 −1.99053 −0.995266 0.0971897i $$-0.969015\pi$$
−0.995266 + 0.0971897i $$0.969015\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −20.0000 −1.00000
$$401$$ − 31.3050i − 1.56329i −0.623721 0.781647i $$-0.714380\pi$$
0.623721 0.781647i $$-0.285620\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 8.06226i 0.399631i
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 32.2490i 1.58687i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 40.3113i 1.95538i
$$426$$ 0 0
$$427$$ −25.2389 −1.22139
$$428$$ 16.1245i 0.779408i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ − 17.8885i − 0.861661i −0.902433 0.430830i $$-0.858221\pi$$
0.902433 0.430830i $$-0.141779\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −1.00000 −0.0477274 −0.0238637 0.999715i $$-0.507597\pi$$
−0.0238637 + 0.999715i $$0.507597\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 40.3113i 1.91525i 0.288023 + 0.957624i $$0.407002\pi$$
−0.288023 + 0.957624i $$0.592998\pi$$
$$444$$ 0 0
$$445$$ 5.00000 0.237023
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −28.8444 −1.36277
$$449$$ − 38.0132i − 1.79395i −0.442080 0.896976i $$-0.645759\pi$$
0.442080 0.896976i $$-0.354241\pi$$
$$450$$ 0 0
$$451$$ 25.0000 1.17720
$$452$$ − 32.2490i − 1.51687i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 29.0689i 1.36277i
$$456$$ 0 0
$$457$$ 3.60555 0.168661 0.0843303 0.996438i $$-0.473125\pi$$
0.0843303 + 0.996438i $$0.473125\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 36.0555 1.68110
$$461$$ 42.4853i 1.97874i 0.145429 + 0.989369i $$0.453544\pi$$
−0.145429 + 0.989369i $$0.546456\pi$$
$$462$$ 0 0
$$463$$ 25.2389 1.17295 0.586475 0.809968i $$-0.300515\pi$$
0.586475 + 0.809968i $$0.300515\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 40.3113i 1.86538i 0.360674 + 0.932692i $$0.382547\pi$$
−0.360674 + 0.932692i $$0.617453\pi$$
$$468$$ 0 0
$$469$$ 52.0000 2.40114
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 58.1378i 2.66474i
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 2.23607i 0.102169i 0.998694 + 0.0510843i $$0.0162677\pi$$
−0.998694 + 0.0510843i $$0.983732\pi$$
$$480$$ 0 0
$$481$$ −13.0000 −0.592749
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −12.0000 −0.545455
$$485$$ − 8.06226i − 0.366088i
$$486$$ 0 0
$$487$$ −39.6611 −1.79721 −0.898607 0.438754i $$-0.855420\pi$$
−0.898607 + 0.438754i $$0.855420\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 56.4358i 2.53149i
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ − 22.3607i − 1.00000i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ − 32.2490i − 1.43791i −0.695055 0.718957i $$-0.744620\pi$$
0.695055 0.718957i $$-0.255380\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ − 11.1803i − 0.495560i −0.968816 0.247780i $$-0.920299\pi$$
0.968816 0.247780i $$-0.0797010\pi$$
$$510$$ 0 0
$$511$$ −26.0000 −1.15017
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −42.0000 −1.82609
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 40.3113i 1.74608i
$$534$$ 0 0
$$535$$ −18.0278 −0.779408
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 13.4164i 0.577886i
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 39.6611 1.68656
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 38.0000 1.61156
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ − 32.2490i − 1.36277i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ − 8.06226i − 0.339784i −0.985463 0.169892i $$-0.945658\pi$$
0.985463 0.169892i $$-0.0543418\pi$$
$$564$$ 0 0
$$565$$ 36.0555 1.51687
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 23.0000 0.962520 0.481260 0.876578i $$-0.340179\pi$$
0.481260 + 0.876578i $$0.340179\pi$$
$$572$$ 16.1245i 0.674200i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 40.3113i 1.68110i
$$576$$ 0 0
$$577$$ −39.6611 −1.65111 −0.825556 0.564320i $$-0.809138\pi$$
−0.825556 + 0.564320i $$0.809138\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 18.0278 0.746633
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 14.4222 0.592749
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ −65.0000 −2.66474
$$596$$ − 31.3050i − 1.28230i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 47.0000 1.91717 0.958585 0.284807i $$-0.0919294\pi$$
0.958585 + 0.284807i $$0.0919294\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ − 13.4164i − 0.545455i
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 25.2389 1.01939 0.509694 0.860356i $$-0.329759\pi$$
0.509694 + 0.860356i $$0.329759\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 8.06226i 0.323008i
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ − 29.0689i − 1.15905i
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −21.6333 −0.857143
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$642$$ 0 0
$$643$$ 46.8722 1.84846 0.924229 0.381839i $$-0.124709\pi$$
0.924229 + 0.381839i $$0.124709\pi$$
$$644$$ 58.1378i 2.29095i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ − 8.06226i − 0.316960i −0.987362 0.158480i $$-0.949341\pi$$
0.987362 0.158480i $$-0.0506593\pi$$
$$648$$ 0 0
$$649$$ −20.0000 −0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −50.4777 −1.97686
$$653$$ 16.1245i 0.631001i 0.948925 + 0.315501i $$0.102172\pi$$
−0.948925 + 0.315501i $$0.897828\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ − 44.7214i − 1.74608i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ − 15.6525i − 0.604257i
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −26.0000 −1.00000
$$677$$ 40.3113i 1.54929i 0.632397 + 0.774644i $$0.282071\pi$$
−0.632397 + 0.774644i $$0.717929\pi$$
$$678$$ 0 0
$$679$$ 13.0000 0.498894
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 29.0689i 1.10744i
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ − 32.2490i − 1.22592i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 42.4853i 1.61156i
$$696$$ 0 0
$$697$$ −90.1388 −3.41425
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 36.0555 1.36277
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ − 17.8885i − 0.674200i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −18.0278 −0.674200
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ −46.0000 −1.70958
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 46.8722 1.73126 0.865631 0.500682i $$-0.166917\pi$$
0.865631 + 0.500682i $$0.166917\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 32.2490i 1.18791i
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 16.1245i 0.592749i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 35.0000 1.28230
$$746$$ 0 0
$$747$$ 0 0
$$748$$ −36.0555 −1.31832
$$749$$ − 29.0689i − 1.06215i
$$750$$ 0 0
$$751$$ 53.0000 1.93400 0.966999 0.254781i $$-0.0820034\pi$$
0.966999 + 0.254781i $$0.0820034\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 49.1935i 1.78326i 0.452762 + 0.891631i $$0.350439\pi$$
−0.452762 + 0.891631i $$0.649561\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ − 32.2490i − 1.16445i
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −50.4777 −1.81673
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −35.0000 −1.25240
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 24.0000 0.857143
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 14.4222 0.514096 0.257048 0.966399i $$-0.417250\pi$$
0.257048 + 0.966399i $$0.417250\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 58.1378i 2.06714i
$$792$$ 0 0
$$793$$ 25.2389 0.896258
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 8.00000 0.283552
$$797$$ − 56.4358i − 1.99906i −0.0306762 0.999529i $$-0.509766\pi$$
0.0306762 0.999529i $$-0.490234\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ − 16.1245i − 0.569022i
$$804$$ 0 0
$$805$$ −65.0000 −2.29095
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ − 56.4358i − 1.97686i
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 50.0000 1.74608
$$821$$ − 11.1803i − 0.390197i −0.980784 0.195098i $$-0.937497\pi$$
0.980784 0.195098i $$-0.0625026\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 28.8444 1.00000
$$833$$ − 48.3735i − 1.67604i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ − 38.0132i − 1.31236i −0.754604 0.656180i $$-0.772171\pi$$
0.754604 0.656180i $$-0.227829\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ −16.0000 −0.550743
$$845$$ − 29.0689i − 1.00000i
$$846$$ 0 0
$$847$$ 21.6333 0.743329
$$848$$ − 32.2490i − 1.10744i
$$849$$ 0 0
$$850$$ 0 0
$$851$$ − 29.0689i − 0.996468i
$$852$$ 0 0
$$853$$ 46.8722 1.60487 0.802436 0.596738i $$-0.203537\pi$$
0.802436 + 0.596738i $$0.203537\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ − 56.4358i − 1.92781i −0.266246 0.963905i $$-0.585783\pi$$
0.266246 0.963905i $$-0.414217\pi$$
$$858$$ 0 0
$$859$$ 41.0000 1.39890 0.699451 0.714681i $$-0.253428\pi$$
0.699451 + 0.714681i $$0.253428\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 36.0555 1.22592
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 24.5967i 0.834388i
$$870$$ 0 0
$$871$$ −52.0000 −1.76195
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 40.3113i 1.36277i
$$876$$ 0 0
$$877$$ −50.4777 −1.70451 −0.852256 0.523125i $$-0.824766\pi$$
−0.852256 + 0.523125i $$0.824766\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 20.0000 0.674200
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ − 58.1378i − 1.95538i
$$885$$ 0 0
$$886$$ 0 0
$$887$$ − 56.4358i − 1.89493i −0.319861 0.947464i $$-0.603636\pi$$
0.319861 0.947464i $$-0.396364\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 57.6888 1.93156
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −65.0000 −2.16546
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ − 51.4296i − 1.70958i
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 59.0000 1.94623 0.973115 0.230319i $$-0.0739769\pi$$
0.973115 + 0.230319i $$0.0739769\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ − 56.4358i − 1.85761i
$$924$$ 0 0
$$925$$ −18.0278 −0.592749
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 42.4853i 1.39390i 0.717121 + 0.696949i $$0.245459\pi$$
−0.717121 + 0.696949i $$0.754541\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 16.1245i 0.528176i
$$933$$ 0 0
$$934$$ 0 0
$$935$$ − 40.3113i − 1.31832i
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ − 24.5967i − 0.801831i −0.916115 0.400916i $$-0.868692\pi$$
0.916115 0.400916i $$-0.131308\pi$$
$$942$$ 0 0
$$943$$ −90.1388 −2.93532
$$944$$ 35.7771i 1.16445i
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 26.0000 0.843996
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 40.3113i 1.30581i 0.757439 + 0.652905i $$0.226450\pi$$
−0.757439 + 0.652905i $$0.773550\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 49.1935i 1.59103i
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 31.0000 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ − 56.4358i − 1.81673i
$$966$$ 0 0
$$967$$ 57.6888 1.85515 0.927574 0.373640i $$-0.121891\pi$$
0.927574 + 0.373640i $$0.121891\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ −68.5055 −2.19618
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −28.0000 −0.896258
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ −5.00000 −0.159801
$$980$$ 26.8328i 0.857143i
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 47.0000 1.49300 0.746502 0.665383i $$-0.231732\pi$$
0.746502 + 0.665383i $$0.231732\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 8.94427i 0.283552i
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 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 585.2.h.e.64.2 yes 4
3.2 odd 2 inner 585.2.h.e.64.4 yes 4
5.4 even 2 inner 585.2.h.e.64.1 4
13.12 even 2 inner 585.2.h.e.64.3 yes 4
15.14 odd 2 inner 585.2.h.e.64.3 yes 4
39.38 odd 2 inner 585.2.h.e.64.1 4
65.64 even 2 inner 585.2.h.e.64.4 yes 4
195.194 odd 2 CM 585.2.h.e.64.2 yes 4

By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.h.e.64.1 4 5.4 even 2 inner
585.2.h.e.64.1 4 39.38 odd 2 inner
585.2.h.e.64.2 yes 4 1.1 even 1 trivial
585.2.h.e.64.2 yes 4 195.194 odd 2 CM
585.2.h.e.64.3 yes 4 13.12 even 2 inner
585.2.h.e.64.3 yes 4 15.14 odd 2 inner
585.2.h.e.64.4 yes 4 3.2 odd 2 inner
585.2.h.e.64.4 yes 4 65.64 even 2 inner