LMFDB - Embedded newform 135.2.f.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(53,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("135.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$135 = 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	135.f (of order $4$ , degree $2$ , 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} + 23x^{4} + 1$ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.3
Root			$0.323042 + 0.323042i$ of defining polynomial
Character	$\chi$	$=$	135.53
Dual form			135.2.f.a.107.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.323042 + 0.323042i) q^{2} -1.79129i q^{4} +(-1.22474 - 1.87083i) q^{5} +(1.79129 - 1.79129i) q^{7} +(1.22474 - 1.22474i) q^{8} +(0.208712 - 1.00000i) q^{10} +5.54506i q^{11} +(1.79129 + 1.79129i) q^{13} +1.15732 q^{14} -2.79129 q^{16} +(-1.87083 - 1.87083i) q^{17} +3.00000i q^{19} +(-3.35119 + 2.19387i) q^{20} +(-1.79129 + 1.79129i) q^{22} +(4.32032 - 4.32032i) q^{23} +(-2.00000 + 4.58258i) q^{25} +1.15732i q^{26} +(-3.20871 - 3.20871i) q^{28} +4.38774 q^{29} -1.00000 q^{31} +(-3.35119 - 3.35119i) q^{32} -1.20871i q^{34} +(-5.54506 - 1.15732i) q^{35} +(-5.00000 + 5.00000i) q^{37} +(-0.969126 + 0.969126i) q^{38} +(-3.79129 - 0.791288i) q^{40} +5.54506i q^{41} +(3.20871 + 3.20871i) q^{43} +9.93280 q^{44} +2.79129 q^{46} +(-0.646084 - 0.646084i) q^{47} +0.582576i q^{49} +(-2.12645 + 0.834280i) q^{50} +(3.20871 - 3.20871i) q^{52} +(-0.0674228 + 0.0674228i) q^{53} +(10.3739 - 6.79129i) q^{55} -4.38774i q^{56} +(1.41742 + 1.41742i) q^{58} -4.38774 q^{59} -1.00000 q^{61} +(-0.323042 - 0.323042i) q^{62} +3.41742i q^{64} +(1.15732 - 5.54506i) q^{65} +(8.58258 - 8.58258i) q^{67} +(-3.35119 + 3.35119i) q^{68} +(-1.41742 - 2.16515i) q^{70} +5.54506i q^{71} +(-10.3739 - 10.3739i) q^{73} -3.23042 q^{74} +5.37386 q^{76} +(9.93280 + 9.93280i) q^{77} -10.5826i q^{79} +(3.41862 + 5.22202i) q^{80} +(-1.79129 + 1.79129i) q^{82} +(8.70806 - 8.70806i) q^{83} +(-1.20871 + 5.79129i) q^{85} +2.07310i q^{86} +(6.79129 + 6.79129i) q^{88} -16.6352 q^{89} +6.41742 q^{91} +(-7.73893 - 7.73893i) q^{92} -0.417424i q^{94} +(5.61249 - 3.67423i) q^{95} +(-3.58258 + 3.58258i) q^{97} +(-0.188196 + 0.188196i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 4 q^{7} + 20 q^{10} - 4 q^{13} - 4 q^{16} + 4 q^{22} - 16 q^{25} - 44 q^{28} - 8 q^{31} - 40 q^{37} - 12 q^{40} + 44 q^{43} + 4 q^{46} + 44 q^{52} + 28 q^{55} + 48 q^{58} - 8 q^{61} + 32 q^{67} - 48 q^{70}+ \cdots + 8 q^{97}+O(q^{100})$ 8 * q - 4 * q^7 + 20 * q^10 - 4 * q^13 - 4 * q^16 + 4 * q^22 - 16 * q^25 - 44 * q^28 - 8 * q^31 - 40 * q^37 - 12 * q^40 + 44 * q^43 + 4 * q^46 + 44 * q^52 + 28 * q^55 + 48 * q^58 - 8 * q^61 + 32 * q^67 - 48 * q^70 - 28 * q^73 - 12 * q^76 + 4 * q^82 - 28 * q^85 + 36 * q^88 + 88 * q^91 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$ .

$n$	$56$	$82$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.323042	+	0.323042i	0.228425	+	0.228425i	0.812035	−	0.583609i	$-0.198360\pi$
$2$	0.323042	+	0.323042i	0.228425	+	0.228425i	−0.583609	+	0.812035i	$0.698360\pi$
$3$		0			0
$3$		0			0
$4$		−	1.79129i		−	0.895644i
$5$	−1.22474	−	1.87083i	−0.547723	−	0.836660i
$5$	−1.22474	−	1.87083i	−0.547723	−	0.836660i
$6$		0			0
$7$	1.79129	−	1.79129i	0.677043	−	0.677043i	−0.282287	−	0.959330i	$-0.591093\pi$
$7$	1.79129	−	1.79129i	0.677043	−	0.677043i	0.959330	+	0.282287i	$0.0910930\pi$
$8$	1.22474	−	1.22474i	0.433013	−	0.433013i
$9$		0			0
$10$	0.208712	−	1.00000i	0.0660006	−	0.316228i
$11$			5.54506i			1.67190i	0.548806	+	0.835950i	$0.315083\pi$
$11$			5.54506i			1.67190i	−0.548806	+	0.835950i	$0.684917\pi$
$12$		0			0
$13$	1.79129	+	1.79129i	0.496814	+	0.496814i	0.910445	−	0.413631i	$-0.135740\pi$
$13$	1.79129	+	1.79129i	0.496814	+	0.496814i	−0.413631	+	0.910445i	$0.635740\pi$
$14$	1.15732			0.309307
$15$		0			0
$16$	−2.79129			−0.697822
$17$	−1.87083	−	1.87083i	−0.453743	−	0.453743i	0.442852	−	0.896595i	$-0.353967\pi$
$17$	−1.87083	−	1.87083i	−0.453743	−	0.453743i	−0.896595	+	0.442852i	$0.853967\pi$
$18$		0			0
$19$			3.00000i			0.688247i	0.938924	+	0.344124i	$0.111824\pi$
$19$			3.00000i			0.688247i	−0.938924	+	0.344124i	$0.888176\pi$
$20$	−3.35119	+	2.19387i	−0.749349	+	0.490564i
$21$		0			0
$22$	−1.79129	+	1.79129i	−0.381904	+	0.381904i
$23$	4.32032	−	4.32032i	0.900849	−	0.900849i	−0.0946609	−	0.995510i	$-0.530177\pi$
$23$	4.32032	−	4.32032i	0.900849	−	0.900849i	0.995510	+	0.0946609i	$0.0301767\pi$
$24$		0			0
$25$	−2.00000	+	4.58258i	−0.400000	+	0.916515i
$26$			1.15732i			0.226970i
$27$		0			0
$28$	−3.20871	−	3.20871i	−0.606390	−	0.606390i
$29$	4.38774			0.814783			0.407392	−	0.913254i	$-0.366438\pi$
$29$	4.38774			0.814783			0.407392	+	0.913254i	$0.366438\pi$
$30$		0			0
$31$	−1.00000			−0.179605			−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000			−0.179605			−0.0898027	+	0.995960i	$0.528624\pi$
$32$	−3.35119	−	3.35119i	−0.592413	−	0.592413i
$33$		0			0
$34$		−	1.20871i		−	0.207292i
$35$	−5.54506	−	1.15732i	−0.937287	−	0.195623i
$36$		0			0
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	0.164399	+	0.986394i	$0.447432\pi$
$38$	−0.969126	+	0.969126i	−0.157213	+	0.157213i
$39$		0			0
$40$	−3.79129	−	0.791288i	−0.599455	−	0.125114i
$41$			5.54506i			0.865993i	0.901396	+	0.432997i	$0.142544\pi$
$41$			5.54506i			0.865993i	−0.901396	+	0.432997i	$0.857456\pi$
$42$		0			0
$43$	3.20871	+	3.20871i	0.489324	+	0.489324i	0.908093	−	0.418769i	$-0.137538\pi$
$43$	3.20871	+	3.20871i	0.489324	+	0.489324i	−0.418769	+	0.908093i	$0.637538\pi$
$44$	9.93280			1.49743
$45$		0			0
$46$	2.79129			0.411553
$47$	−0.646084	−	0.646084i	−0.0942410	−	0.0942410i	0.658415	−	0.752656i	$-0.271227\pi$
$47$	−0.646084	−	0.646084i	−0.0942410	−	0.0942410i	−0.752656	+	0.658415i	$0.771227\pi$
$48$		0			0
$49$			0.582576i			0.0832251i
$50$	−2.12645	+	0.834280i	−0.300725	+	0.117985i
$51$		0			0
$52$	3.20871	−	3.20871i	0.444968	−	0.444968i
$53$	−0.0674228	+	0.0674228i	−0.00926123	+	0.00926123i	−0.711722	−	0.702461i	$-0.752085\pi$
$53$	−0.0674228	+	0.0674228i	−0.00926123	+	0.00926123i	0.702461	+	0.711722i	$0.252085\pi$
$54$		0			0
$55$	10.3739	−	6.79129i	1.39881	−	0.915737i
$56$		−	4.38774i		−	0.586337i
$57$		0			0
$58$	1.41742	+	1.41742i	0.186117	+	0.186117i
$59$	−4.38774			−0.571235			−0.285618	−	0.958344i	$-0.592199\pi$
$59$	−4.38774			−0.571235			−0.285618	+	0.958344i	$0.592199\pi$
$60$		0			0
$61$	−1.00000			−0.128037			−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000			−0.128037			−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−0.323042	−	0.323042i	−0.0410264	−	0.0410264i
$63$		0			0
$64$			3.41742i			0.427178i
$65$	1.15732	−	5.54506i	0.143548	−	0.687780i
$66$		0			0
$67$	8.58258	−	8.58258i	1.04853	−	1.04853i	0.0497677	−	0.998761i	$-0.484152\pi$
$67$	8.58258	−	8.58258i	1.04853	−	1.04853i	0.998761	−	0.0497677i	$-0.0158481\pi$
$68$	−3.35119	+	3.35119i	−0.406392	+	0.406392i
$69$		0			0
$70$	−1.41742	−	2.16515i	−0.169415	−	0.258785i
$71$			5.54506i			0.658078i	0.944316	+	0.329039i	$0.106725\pi$
$71$			5.54506i			0.658078i	−0.944316	+	0.329039i	$0.893275\pi$
$72$		0			0
$73$	−10.3739	−	10.3739i	−1.21417	−	1.21417i	−0.969643	−	0.244526i	$-0.921368\pi$
$73$	−10.3739	−	10.3739i	−1.21417	−	1.21417i	−0.244526	−	0.969643i	$-0.578632\pi$
$74$	−3.23042			−0.375529
$75$		0			0
$76$	5.37386			0.616424
$77$	9.93280	+	9.93280i	1.13195	+	1.13195i
$78$		0			0
$79$		−	10.5826i		−	1.19063i	−0.803491	−	0.595316i	$-0.797027\pi$
$79$		−	10.5826i		−	1.19063i	0.803491	−	0.595316i	$-0.202973\pi$
$80$	3.41862	+	5.22202i	0.382213	+	0.583840i
$81$		0			0
$82$	−1.79129	+	1.79129i	−0.197815	+	0.197815i
$83$	8.70806	−	8.70806i	0.955834	−	0.955834i	−0.0432314	−	0.999065i	$-0.513765\pi$
$83$	8.70806	−	8.70806i	0.955834	−	0.955834i	0.999065	+	0.0432314i	$0.0137653\pi$
$84$		0			0
$85$	−1.20871	+	5.79129i	−0.131103	+	0.628153i
$86$			2.07310i			0.223548i
$87$		0			0
$88$	6.79129	+	6.79129i	0.723954	+	0.723954i
$89$	−16.6352			−1.76333			−0.881663	−	0.471879i	$-0.843576\pi$
$89$	−16.6352			−1.76333			−0.881663	+	0.471879i	$0.843576\pi$
$90$		0			0
$91$	6.41742			0.672729
$92$	−7.73893	−	7.73893i	−0.806840	−	0.806840i
$93$		0			0
$94$		−	0.417424i		−	0.0430540i
$95$	5.61249	−	3.67423i	0.575829	−	0.376969i
$96$		0			0
$97$	−3.58258	+	3.58258i	−0.363755	+	0.363755i	−0.865194	−	0.501438i	$-0.832805\pi$
$97$	−3.58258	+	3.58258i	−0.363755	+	0.363755i	0.501438	+	0.865194i	$0.332805\pi$
$98$	−0.188196	+	0.188196i	−0.0190107	+	0.0190107i
$99$		0			0
$100$	8.20871	+	3.58258i	0.820871	+	0.358258i
$101$		−	11.0901i		−	1.10351i	−0.834007	−	0.551754i	$-0.813959\pi$
$101$		−	11.0901i		−	1.10351i	0.834007	−	0.551754i	$-0.186041\pi$
$102$		0			0
$103$	−3.58258	−	3.58258i	−0.353002	−	0.353002i	0.508224	−	0.861225i	$-0.330302\pi$
$103$	−3.58258	−	3.58258i	−0.353002	−	0.353002i	−0.861225	+	0.508224i	$0.830302\pi$
$104$	4.38774			0.430253
$105$		0			0
$106$	−0.0435608			−0.00423100
$107$	3.74166	+	3.74166i	0.361720	+	0.361720i	0.864446	−	0.502726i	$-0.167670\pi$
$107$	3.74166	+	3.74166i	0.361720	+	0.361720i	−0.502726	+	0.864446i	$0.667670\pi$
$108$		0			0
$109$			13.7477i			1.31679i	0.752671	+	0.658397i	$0.228765\pi$
$109$			13.7477i			1.31679i	−0.752671	+	0.658397i	$0.771235\pi$
$110$	5.54506	+	1.15732i	0.528701	+	0.110346i
$111$		0			0
$112$	−5.00000	+	5.00000i	−0.472456	+	0.472456i
$113$	−8.64064	+	8.64064i	−0.812843	+	0.812843i	−0.985059	−	0.172216i	$-0.944907\pi$
$113$	−8.64064	+	8.64064i	−0.812843	+	0.812843i	0.172216	+	0.985059i	$0.444907\pi$
$114$		0			0
$115$	−13.3739	−	2.79129i	−1.24712	−	0.260289i
$116$		−	7.85971i		−	0.729756i
$117$		0			0
$118$	−1.41742	−	1.41742i	−0.130484	−	0.130484i
$119$	−6.70239			−0.614407
$120$		0			0
$121$	−19.7477			−1.79525
$122$	−0.323042	−	0.323042i	−0.0292468	−	0.0292468i
$123$		0			0
$124$			1.79129i			0.160862i
$125$	11.0227	−	1.87083i	0.985901	−	0.167332i
$126$		0			0
$127$	−5.00000	+	5.00000i	−0.443678	+	0.443678i	−0.893246	−	0.449568i	$-0.851578\pi$
$127$	−5.00000	+	5.00000i	−0.443678	+	0.443678i	0.449568	+	0.893246i	$0.351578\pi$
$128$	−7.80636	+	7.80636i	−0.689991	+	0.689991i
$129$		0			0
$130$	2.16515	−	1.41742i	0.189896	−	0.124316i
$131$		−	7.61816i		−	0.665602i	−0.942997	−	0.332801i	$-0.892006\pi$
$131$		−	7.61816i		−	0.665602i	0.942997	−	0.332801i	$-0.107994\pi$
$132$		0			0
$133$	5.37386	+	5.37386i	0.465973	+	0.465973i
$134$	5.54506			0.479021
$135$		0			0
$136$	−4.58258			−0.392953
$137$	10.3766	+	10.3766i	0.886534	+	0.886534i	0.994188	−	0.107654i	$-0.0343339\pi$
$137$	10.3766	+	10.3766i	0.886534	+	0.886534i	−0.107654	+	0.994188i	$0.534334\pi$
$138$		0			0
$139$		−	3.16515i		−	0.268465i	−0.990950	−	0.134232i	$-0.957143\pi$
$139$		−	3.16515i		−	0.268465i	0.990950	−	0.134232i	$-0.0428568\pi$
$140$	−2.07310	+	9.93280i	−0.175209	+	0.839475i
$141$		0			0
$142$	−1.79129	+	1.79129i	−0.150322	+	0.150322i
$143$	−9.93280	+	9.93280i	−0.830623	+	0.830623i
$144$		0			0
$145$	−5.37386	−	8.20871i	−0.446275	−	0.681696i
$146$		−	6.70239i		−	0.554693i
$147$		0			0
$148$	8.95644	+	8.95644i	0.736215	+	0.736215i
$149$	−7.85971			−0.643892			−0.321946	−	0.946758i	$-0.604337\pi$
$149$	−7.85971			−0.643892			−0.321946	+	0.946758i	$0.604337\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	3.67423	+	3.67423i	0.298020	+	0.298020i
$153$		0			0
$154$			6.41742i			0.517131i
$155$	1.22474	+	1.87083i	0.0983739	+	0.150269i
$156$		0			0
$157$	3.20871	−	3.20871i	0.256083	−	0.256083i	−0.567376	−	0.823459i	$-0.692041\pi$
$157$	3.20871	−	3.20871i	0.256083	−	0.256083i	0.823459	+	0.567376i	$0.192041\pi$
$158$	3.41862	−	3.41862i	0.271970	−	0.271970i
$159$		0			0
$160$	−2.16515	+	10.3739i	−0.171170	+	0.820126i
$161$		−	15.4779i		−	1.21983i
$162$		0			0
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	0.483638	−	0.875268i	$-0.339315\pi$
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	−0.875268	+	0.483638i	$0.839315\pi$
$164$	9.93280			0.775622
$165$		0			0
$166$	5.62614			0.436673
$167$	−10.6463	−	10.6463i	−0.823836	−	0.823836i	0.162820	−	0.986656i	$-0.447941\pi$
$167$	−10.6463	−	10.6463i	−0.823836	−	0.823836i	−0.986656	+	0.162820i	$0.947941\pi$
$168$		0			0
$169$		−	6.58258i		−	0.506352i
$170$	−2.26129	+	1.48036i	−0.173433	+	0.113539i
$171$		0			0
$172$	5.74773	−	5.74773i	0.438260	−	0.438260i
$173$	−7.92713	+	7.92713i	−0.602689	+	0.602689i	−0.941025	−	0.338337i	$-0.890136\pi$
$173$	−7.92713	+	7.92713i	−0.602689	+	0.602689i	0.338337	+	0.941025i	$0.390136\pi$
$174$		0			0
$175$	4.62614	+	11.7913i	0.349703	+	0.891338i
$176$		−	15.4779i		−	1.16669i
$177$		0			0
$178$	−5.37386	−	5.37386i	−0.402788	−	0.402788i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	9.74773			0.724543			0.362271	−	0.932073i	$-0.382001\pi$
$181$	9.74773			0.724543			0.362271	+	0.932073i	$0.382001\pi$
$182$	2.07310	+	2.07310i	0.153668	+	0.153668i
$183$		0			0
$184$		−	10.5826i		−	0.780158i
$185$	15.4779	+	3.23042i	1.13796	+	0.237505i
$186$		0			0
$187$	10.3739	−	10.3739i	0.758612	−	0.758612i
$188$	−1.15732	+	1.15732i	−0.0844064	+	0.0844064i
$189$		0			0
$190$	3.00000	+	0.626136i	0.217643	+	0.0454247i
$191$			18.7083i			1.35368i	0.736128	+	0.676842i	$0.236652\pi$
$191$			18.7083i			1.35368i	−0.736128	+	0.676842i	$0.763348\pi$
$192$		0			0
$193$	1.79129	+	1.79129i	0.128940	+	0.128940i	0.768632	−	0.639692i	$-0.220938\pi$
$193$	1.79129	+	1.79129i	0.128940	+	0.128940i	−0.639692	+	0.768632i	$0.720938\pi$
$194$	−2.31464			−0.166182
$195$		0			0
$196$	1.04356			0.0745401
$197$	−1.87083	−	1.87083i	−0.133291	−	0.133291i	0.637314	−	0.770605i	$-0.280046\pi$
$197$	−1.87083	−	1.87083i	−0.133291	−	0.133291i	−0.770605	+	0.637314i	$0.780046\pi$
$198$		0			0
$199$		−	16.7477i		−	1.18721i	−0.804755	−	0.593607i	$-0.797703\pi$
$199$		−	16.7477i		−	1.18721i	0.804755	−	0.593607i	$-0.202297\pi$
$200$	3.16300	+	8.06198i	0.223658	+	0.570068i
$201$		0			0
$202$	3.58258	−	3.58258i	0.252069	−	0.252069i
$203$	7.85971	−	7.85971i	0.551643	−	0.551643i
$204$		0			0
$205$	10.3739	−	6.79129i	0.724542	−	0.474324i
$206$		−	2.31464i		−	0.161269i
$207$		0			0
$208$	−5.00000	−	5.00000i	−0.346688	−	0.346688i
$209$	−16.6352			−1.15068
$210$		0			0
$211$	9.74773			0.671061			0.335531	−	0.942029i	$-0.391084\pi$
$211$	9.74773			0.671061			0.335531	+	0.942029i	$0.391084\pi$
$212$	0.120774	+	0.120774i	0.00829476	+	0.00829476i
$213$		0			0
$214$			2.41742i			0.165252i
$215$	2.07310	−	9.93280i	0.141384	−	0.677412i
$216$		0			0
$217$	−1.79129	+	1.79129i	−0.121601	+	0.121601i
$218$	−4.44109	+	4.44109i	−0.300789	+	0.300789i
$219$		0			0
$220$	−12.1652	−	18.5826i	−0.820174	−	1.25284i
$221$		−	6.70239i		−	0.450851i
$222$		0			0
$223$	8.58258	+	8.58258i	0.574732	+	0.574732i	0.933447	−	0.358715i	$-0.116785\pi$
$223$	8.58258	+	8.58258i	0.574732	+	0.574732i	−0.358715	+	0.933447i	$0.616785\pi$
$224$	−12.0059			−0.802178
$225$		0			0
$226$	−5.58258			−0.371347
$227$	6.90465	+	6.90465i	0.458278	+	0.458278i	0.898090	−	0.439812i	$-0.144955\pi$
$227$	6.90465	+	6.90465i	0.458278	+	0.458278i	−0.439812	+	0.898090i	$0.644955\pi$
$228$		0			0
$229$			5.83485i			0.385578i	0.981240	+	0.192789i	$0.0617532\pi$
$229$			5.83485i			0.385578i	−0.981240	+	0.192789i	$0.938247\pi$
$230$	−3.41862	−	5.22202i	−0.225417	−	0.344330i
$231$		0			0
$232$	5.37386	−	5.37386i	0.352811	−	0.352811i
$233$	16.7700	−	16.7700i	1.09864	−	1.09864i	0.104072	−	0.994570i	$-0.466813\pi$
$233$	16.7700	−	16.7700i	1.09864	−	1.09864i	0.994570	−	0.104072i	$-0.0331872\pi$
$234$		0			0
$235$	−0.417424	+	2.00000i	−0.0272298	+	0.130466i
$236$			7.85971i			0.511623i
$237$		0			0
$238$	−2.16515	−	2.16515i	−0.140346	−	0.140346i
$239$	12.2474			0.792222			0.396111	−	0.918203i	$-0.370360\pi$
$239$	12.2474			0.792222			0.396111	+	0.918203i	$0.370360\pi$
$240$		0			0
$241$	−11.7477			−0.756738			−0.378369	−	0.925655i	$-0.623515\pi$
$241$	−11.7477			−0.756738			−0.378369	+	0.925655i	$0.623515\pi$
$242$	−6.37934	−	6.37934i	−0.410080	−	0.410080i
$243$		0			0
$244$			1.79129i			0.114675i
$245$	1.08990	−	0.713507i	0.0696311	−	0.0455843i
$246$		0			0
$247$	−5.37386	+	5.37386i	−0.341931	+	0.341931i
$248$	−1.22474	+	1.22474i	−0.0777714	+	0.0777714i
$249$		0			0
$250$	4.16515	+	2.95644i	0.263427	+	0.186982i
$251$			22.1803i			1.40001i	0.714140	+	0.700003i	$0.246818\pi$
$251$			22.1803i			1.40001i	−0.714140	+	0.700003i	$0.753182\pi$
$252$		0			0
$253$	23.9564	+	23.9564i	1.50613	+	1.50613i
$254$	−3.23042			−0.202695
$255$		0			0
$256$	1.79129			0.111955
$257$	2.51691	+	2.51691i	0.157001	+	0.157001i	0.781236	−	0.624236i	$-0.214589\pi$
$257$	2.51691	+	2.51691i	0.157001	+	0.157001i	−0.624236	+	0.781236i	$0.714589\pi$
$258$		0			0
$259$			17.9129i			1.11305i
$260$	−9.93280	−	2.07310i	−0.616006	−	0.128568i
$261$		0			0
$262$	2.46099	−	2.46099i	0.152040	−	0.152040i
$263$	−0.780929	+	0.780929i	−0.0481542	+	0.0481542i	−0.730774	−	0.682620i	$-0.760841\pi$
$263$	−0.780929	+	0.780929i	−0.0481542	+	0.0481542i	0.682620	+	0.730774i	$0.260841\pi$
$264$		0			0
$265$	0.208712	+	0.0435608i	0.0128211	+	0.00267592i
$266$			3.47197i			0.212880i
$267$		0			0
$268$	−15.3739	−	15.3739i	−0.939108	−	0.939108i
$269$	3.47197			0.211690			0.105845	−	0.994383i	$-0.466245\pi$
$269$	3.47197			0.211690			0.105845	+	0.994383i	$0.466245\pi$
$270$		0			0
$271$	−1.00000			−0.0607457			−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000			−0.0607457			−0.0303728	+	0.999539i	$0.509669\pi$
$272$	5.22202	+	5.22202i	0.316632	+	0.316632i
$273$		0			0
$274$			6.70417i			0.405013i
$275$	−25.4107	−	11.0901i	−1.53232	−	0.668760i
$276$		0			0
$277$	−13.2087	+	13.2087i	−0.793635	+	0.793635i	−0.982083	−	0.188448i	$-0.939654\pi$
$277$	−13.2087	+	13.2087i	−0.793635	+	0.793635i	0.188448	+	0.982083i	$0.439654\pi$
$278$	1.02248	−	1.02248i	0.0613241	−	0.0613241i
$279$		0			0
$280$	−8.20871	+	5.37386i	−0.490564	+	0.321150i
$281$			2.07310i			0.123671i	0.998086	+	0.0618353i	$0.0196954\pi$
$281$			2.07310i			0.123671i	−0.998086	+	0.0618353i	$0.980305\pi$
$282$		0			0
$283$	−13.2087	−	13.2087i	−0.785176	−	0.785176i	0.195523	−	0.980699i	$-0.437360\pi$
$283$	−13.2087	−	13.2087i	−0.785176	−	0.785176i	−0.980699	+	0.195523i	$0.937360\pi$
$284$	9.93280			0.589404
$285$		0			0
$286$	−6.41742			−0.379470
$287$	9.93280	+	9.93280i	0.586315	+	0.586315i
$288$		0			0
$289$		−	10.0000i		−	0.588235i
$290$	0.915775	−	4.38774i	0.0537762	−	0.257657i
$291$		0			0
$292$	−18.5826	+	18.5826i	−1.08746	+	1.08746i
$293$	−12.3149	+	12.3149i	−0.719442	+	0.719442i	−0.968491	−	0.249049i	$-0.919882\pi$
$293$	−12.3149	+	12.3149i	−0.719442	+	0.719442i	0.249049	+	0.968491i	$0.419882\pi$
$294$		0			0
$295$	5.37386	+	8.20871i	0.312878	+	0.477930i
$296$			12.2474i			0.711868i
$297$		0			0
$298$	−2.53901	−	2.53901i	−0.147081	−	0.147081i
$299$	15.4779			0.895108
$300$		0			0
$301$	11.4955			0.662587
$302$	0.646084	+	0.646084i	0.0371779	+	0.0371779i
$303$		0			0
$304$		−	8.37386i		−	0.480274i
$305$	1.22474	+	1.87083i	0.0701287	+	0.107123i
$306$		0			0
$307$	−15.7477	+	15.7477i	−0.898770	+	0.898770i	−0.995327	−	0.0965572i	$-0.969217\pi$
$307$	−15.7477	+	15.7477i	−0.898770	+	0.898770i	0.0965572	+	0.995327i	$0.469217\pi$
$308$	17.7925	−	17.7925i	1.01382	−	1.01382i
$309$		0			0
$310$	−0.208712	+	1.00000i	−0.0118541	+	0.0567962i
$311$			9.01703i			0.511309i	0.966768	+	0.255654i	$0.0822909\pi$
$311$			9.01703i			0.511309i	−0.966768	+	0.255654i	$0.917709\pi$
$312$		0			0
$313$	−17.1652	−	17.1652i	−0.970232	−	0.970232i	0.0293378	−	0.999570i	$-0.490660\pi$
$313$	−17.1652	−	17.1652i	−0.970232	−	0.970232i	−0.999570	+	0.0293378i	$0.990660\pi$
$314$	2.07310			0.116992
$315$		0			0
$316$	−18.9564			−1.06638
$317$	−22.8938	−	22.8938i	−1.28584	−	1.28584i	−0.937289	−	0.348552i	$-0.886673\pi$
$317$	−22.8938	−	22.8938i	−1.28584	−	1.28584i	−0.348552	−	0.937289i	$-0.613327\pi$
$318$		0			0
$319$			24.3303i			1.36224i
$320$	6.39342	−	4.18547i	0.357403	−	0.233975i
$321$		0			0
$322$	5.00000	−	5.00000i	0.278639	−	0.278639i
$323$	5.61249	−	5.61249i	0.312287	−	0.312287i
$324$		0			0
$325$	−11.7913	+	4.62614i	−0.654063	+	0.256612i
$326$		−	3.23042i		−	0.178916i
$327$		0			0
$328$	6.79129	+	6.79129i	0.374986	+	0.374986i
$329$	−2.31464			−0.127610
$330$		0			0
$331$	12.7477			0.700678			0.350339	−	0.936623i	$-0.386066\pi$
$331$	12.7477			0.700678			0.350339	+	0.936623i	$0.386066\pi$
$332$	−15.5986	−	15.5986i	−0.856087	−	0.856087i
$333$		0			0
$334$		−	6.87841i		−	0.376370i
$335$	−26.5680	−	5.54506i	−1.45156	−	0.302959i
$336$		0			0
$337$	18.2087	−	18.2087i	0.991892	−	0.991892i	−0.00807564	−	0.999967i	$-0.502571\pi$
$337$	18.2087	−	18.2087i	0.991892	−	0.991892i	0.999967	+	0.00807564i	$0.00257058\pi$
$338$	2.12645	−	2.12645i	0.115664	−	0.115664i
$339$		0			0
$340$	10.3739	+	2.16515i	0.562602	+	0.117422i
$341$		−	5.54506i		−	0.300282i
$342$		0			0
$343$	13.5826	+	13.5826i	0.733390	+	0.733390i
$344$	7.85971			0.423767
$345$		0			0
$346$	−5.12159			−0.275338
$347$	−8.50579	−	8.50579i	−0.456615	−	0.456615i	0.440928	−	0.897543i	$-0.354649\pi$
$347$	−8.50579	−	8.50579i	−0.456615	−	0.456615i	−0.897543	+	0.440928i	$0.854649\pi$
$348$		0			0
$349$			19.4174i			1.03939i	0.854352	+	0.519695i	$0.173955\pi$
$349$			19.4174i			1.03939i	−0.854352	+	0.519695i	$0.826045\pi$
$350$	−2.31464	+	5.30352i	−0.123723	+	0.283485i
$351$		0			0
$352$	18.5826	−	18.5826i	0.990455	−	0.990455i
$353$	12.3823	−	12.3823i	0.659043	−	0.659043i	−0.296111	−	0.955154i	$-0.595690\pi$
$353$	12.3823	−	12.3823i	0.659043	−	0.659043i	0.955154	+	0.296111i	$0.0956897\pi$
$354$		0			0
$355$	10.3739	−	6.79129i	0.550588	−	0.360444i
$356$			29.7984i			1.57931i
$357$		0			0
$358$		0			0
$359$	29.7984			1.57270			0.786350	−	0.617781i	$-0.211968\pi$
$359$	29.7984			1.57270			0.786350	+	0.617781i	$0.211968\pi$
$360$		0			0
$361$	10.0000			0.526316
$362$	3.14892	+	3.14892i	0.165504	+	0.165504i
$363$		0			0
$364$		−	11.4955i		−	0.602526i
$365$	−6.70239	+	32.1131i	−0.350819	+	1.68087i
$366$		0			0
$367$	−8.95644	+	8.95644i	−0.467522	+	0.467522i	−0.901111	−	0.433589i	$-0.857247\pi$
$367$	−8.95644	+	8.95644i	−0.467522	+	0.467522i	0.433589	+	0.901111i	$0.357247\pi$
$368$	−12.0593	+	12.0593i	−0.628632	+	0.628632i
$369$		0			0
$370$	3.95644	+	6.04356i	0.205685	+	0.314190i
$371$			0.241547i			0.0125405i
$372$		0			0
$373$	−3.58258	−	3.58258i	−0.185499	−	0.185499i	0.608248	−	0.793747i	$-0.291873\pi$
$373$	−3.58258	−	3.58258i	−0.185499	−	0.185499i	−0.793747	+	0.608248i	$0.791873\pi$
$374$	6.70239			0.346572
$375$		0			0
$376$	−1.58258			−0.0816151
$377$	7.85971	+	7.85971i	0.404796	+	0.404796i
$378$		0			0
$379$		−	7.74773i		−	0.397974i	−0.980002	−	0.198987i	$-0.936235\pi$
$379$		−	7.74773i		−	0.397974i	0.980002	−	0.198987i	$-0.0637652\pi$
$380$	−6.58161	−	10.0536i	−0.337630	−	0.515738i
$381$		0			0
$382$	−6.04356	+	6.04356i	−0.309215	+	0.309215i
$383$	20.9555	−	20.9555i	1.07078	−	1.07078i	0.0734797	−	0.997297i	$-0.476590\pi$
$383$	20.9555	−	20.9555i	1.07078	−	1.07078i	0.997297	−	0.0734797i	$-0.0234104\pi$
$384$		0			0
$385$	6.41742	−	30.7477i	0.327062	−	1.56705i
$386$			1.15732i			0.0589061i
$387$		0			0
$388$	6.41742	+	6.41742i	0.325795	+	0.325795i
$389$	7.85971			0.398503			0.199251	−	0.979948i	$-0.436149\pi$
$389$	7.85971			0.398503			0.199251	+	0.979948i	$0.436149\pi$
$390$		0			0
$391$	−16.1652			−0.817507
$392$	0.713507	+	0.713507i	0.0360375	+	0.0360375i
$393$		0			0
$394$		−	1.20871i		−	0.0608940i
$395$	−19.7982	+	12.9610i	−0.996155	+	0.652136i
$396$		0			0
$397$	26.1216	−	26.1216i	1.31101	−	1.31101i	0.390330	−	0.920675i	$-0.372361\pi$
$397$	26.1216	−	26.1216i	1.31101	−	1.31101i	0.920675	−	0.390330i	$-0.127639\pi$
$398$	5.41022	−	5.41022i	0.271190	−	0.271190i
$399$		0			0
$400$	5.58258	−	12.7913i	0.279129	−	0.639564i
$401$			18.7083i			0.934247i	0.884192	+	0.467124i	$0.154710\pi$
$401$			18.7083i			0.934247i	−0.884192	+	0.467124i	$0.845290\pi$
$402$		0			0
$403$	−1.79129	−	1.79129i	−0.0892304	−	0.0892304i
$404$	−19.8656			−0.988351
$405$		0			0
$406$	5.07803			0.252018
$407$	−27.7253	−	27.7253i	−1.37429	−	1.37429i
$408$		0			0
$409$		−	24.1652i		−	1.19489i	−0.801910	−	0.597445i	$-0.796183\pi$
$409$		−	24.1652i		−	1.19489i	0.801910	−	0.597445i	$-0.203817\pi$
$410$	5.54506	+	1.15732i	0.273851	+	0.0571561i
$411$		0			0
$412$	−6.41742	+	6.41742i	−0.316164	+	0.316164i
$413$	−7.85971	+	7.85971i	−0.386751	+	0.386751i
$414$		0			0
$415$	−26.9564	−	5.62614i	−1.32324	−	0.276176i
$416$		−	12.0059i		−	0.588638i
$417$		0			0
$418$	−5.37386	−	5.37386i	−0.262844	−	0.262844i
$419$	−0.915775			−0.0447385			−0.0223693	−	0.999750i	$-0.507121\pi$
$419$	−0.915775			−0.0447385			−0.0223693	+	0.999750i	$0.507121\pi$
$420$		0			0
$421$	39.7477			1.93719			0.968593	−	0.248652i	$-0.0799876\pi$
$421$	39.7477			1.93719			0.968593	+	0.248652i	$0.0799876\pi$
$422$	3.14892	+	3.14892i	0.153287	+	0.153287i
$423$		0			0
$424$			0.165151i			0.00802046i
$425$	12.3149	−	4.83156i	0.597359	−	0.234365i
$426$		0			0
$427$	−1.79129	+	1.79129i	−0.0866865	+	0.0866865i
$428$	6.70239	−	6.70239i	0.323972	−	0.323972i
$429$		0			0
$430$	3.87841	−	2.53901i	0.187034	−	0.122442i
$431$			9.01703i			0.434335i	0.976134	+	0.217168i	$0.0696818\pi$
$431$			9.01703i			0.434335i	−0.976134	+	0.217168i	$0.930318\pi$
$432$		0			0
$433$	4.62614	+	4.62614i	0.222318	+	0.222318i	0.809474	−	0.587156i	$-0.199752\pi$
$433$	4.62614	+	4.62614i	0.222318	+	0.222318i	−0.587156	+	0.809474i	$0.699752\pi$
$434$	−1.15732			−0.0555532
$435$		0			0
$436$	24.6261			1.17938
$437$	12.9610	+	12.9610i	0.620007	+	0.620007i
$438$		0			0
$439$		−	10.5826i		−	0.505079i	−0.967587	−	0.252539i	$-0.918734\pi$
$439$		−	10.5826i		−	0.505079i	0.967587	−	0.252539i	$-0.0812657\pi$
$440$	4.38774	−	21.0229i	0.209177	−	1.00223i
$441$		0			0
$442$	2.16515	−	2.16515i	0.102986	−	0.102986i
$443$	−7.92713	+	7.92713i	−0.376629	+	0.376629i	−0.869885	−	0.493255i	$-0.835807\pi$
$443$	−7.92713	+	7.92713i	−0.376629	+	0.376629i	0.493255	+	0.869885i	$0.335807\pi$
$444$		0			0
$445$	20.3739	+	31.1216i	0.965814	+	1.47530i
$446$			5.54506i			0.262566i
$447$		0			0
$448$	6.12159	+	6.12159i	0.289218	+	0.289218i
$449$	13.1632			0.621211			0.310605	−	0.950539i	$-0.399468\pi$
$449$	13.1632			0.621211			0.310605	+	0.950539i	$0.399468\pi$
$450$		0			0
$451$	−30.7477			−1.44785
$452$	15.4779	+	15.4779i	0.728018	+	0.728018i
$453$		0			0
$454$			4.46099i			0.209364i
$455$	−7.85971	−	12.0059i	−0.368469	−	0.562845i
$456$		0			0
$457$	−3.58258	+	3.58258i	−0.167586	+	0.167586i	−0.785917	−	0.618332i	$-0.787809\pi$
$457$	−3.58258	+	3.58258i	−0.167586	+	0.167586i	0.618332	+	0.785917i	$0.287809\pi$
$458$	−1.88490	+	1.88490i	−0.0880756	+	0.0880756i
$459$		0			0
$460$	−5.00000	+	23.9564i	−0.233126	+	1.11697i
$461$		−	14.5621i		−	0.678224i	−0.940746	−	0.339112i	$-0.889873\pi$
$461$		−	14.5621i		−	0.678224i	0.940746	−	0.339112i	$-0.110127\pi$
$462$		0			0
$463$	−7.83485	−	7.83485i	−0.364116	−	0.364116i	0.501210	−	0.865326i	$-0.332889\pi$
$463$	−7.83485	−	7.83485i	−0.364116	−	0.364116i	−0.865326	+	0.501210i	$0.832889\pi$
$464$	−12.2474			−0.568574
$465$		0			0
$466$	10.8348			0.501915
$467$	−5.34279	−	5.34279i	−0.247235	−	0.247235i	0.572600	−	0.819835i	$-0.305935\pi$
$467$	−5.34279	−	5.34279i	−0.247235	−	0.247235i	−0.819835	+	0.572600i	$0.805935\pi$
$468$		0			0
$469$		−	30.7477i		−	1.41980i
$470$	−0.780929	+	0.511238i	−0.0360216	+	0.0235817i
$471$		0			0
$472$	−5.37386	+	5.37386i	−0.247352	+	0.247352i
$473$	−17.7925	+	17.7925i	−0.818101	+	0.818101i
$474$		0			0
$475$	−13.7477	−	6.00000i	−0.630789	−	0.275299i
$476$			12.0059i			0.550290i
$477$		0			0
$478$	3.95644	+	3.95644i	0.180963	+	0.180963i
$479$	7.85971			0.359119			0.179560	−	0.983747i	$-0.442533\pi$
$479$	7.85971			0.359119			0.179560	+	0.983747i	$0.442533\pi$
$480$		0			0
$481$	−17.9129			−0.816757
$482$	−3.79501	−	3.79501i	−0.172858	−	0.172858i
$483$		0			0
$484$			35.3739i			1.60790i
$485$	11.0901	+	2.31464i	0.503577	+	0.105103i
$486$		0			0
$487$	0.373864	−	0.373864i	0.0169414	−	0.0169414i	−0.698585	−	0.715527i	$-0.746187\pi$
$487$	0.373864	−	0.373864i	0.0169414	−	0.0169414i	0.715527	+	0.698585i	$0.246187\pi$
$488$	−1.22474	+	1.22474i	−0.0554416	+	0.0554416i
$489$		0			0
$490$	0.582576	+	0.121591i	0.0263181	+	0.00549290i
$491$		−	14.5621i		−	0.657178i	−0.944473	−	0.328589i	$-0.893427\pi$
$491$		−	14.5621i		−	0.657178i	0.944473	−	0.328589i	$-0.106573\pi$
$492$		0			0
$493$	−8.20871	−	8.20871i	−0.369702	−	0.369702i
$494$	−3.47197			−0.156211
$495$		0			0
$496$	2.79129			0.125333
$497$	9.93280	+	9.93280i	0.445547	+	0.445547i
$498$		0			0
$499$			27.3303i			1.22347i	0.791062	+	0.611736i	$0.209529\pi$
$499$			27.3303i			1.22347i	−0.791062	+	0.611736i	$0.790471\pi$
$500$	−3.35119	−	19.7448i	−0.149870	−	0.883016i
$501$		0			0
$502$	−7.16515	+	7.16515i	−0.319796	+	0.319796i
$503$	16.5678	−	16.5678i	0.738720	−	0.738720i	−0.233610	−	0.972330i	$-0.575054\pi$
$503$	16.5678	−	16.5678i	0.738720	−	0.738720i	0.972330	+	0.233610i	$0.0750539\pi$
$504$		0			0
$505$	−20.7477	+	13.5826i	−0.923262	+	0.604417i
$506$			15.4779i			0.688075i
$507$		0			0
$508$	8.95644	+	8.95644i	0.397378	+	0.397378i
$509$	−17.5510			−0.777933			−0.388966	−	0.921252i	$-0.627168\pi$
$509$	−17.5510			−0.777933			−0.388966	+	0.921252i	$0.627168\pi$
$510$		0			0
$511$	−37.1652			−1.64409
$512$	16.1914	+	16.1914i	0.715564	+	0.715564i
$513$		0			0
$514$			1.62614i			0.0717258i
$515$	−2.31464	+	11.0901i	−0.101995	+	0.488689i
$516$		0			0
$517$	3.58258	−	3.58258i	0.157561	−	0.157561i
$518$	−5.78661	+	5.78661i	−0.254249	+	0.254249i
$519$		0			0
$520$	−5.37386	−	8.20871i	−0.235660	−	0.359976i
$521$		−	27.7253i		−	1.21467i	−0.794447	−	0.607334i	$-0.792239\pi$
$521$		−	27.7253i		−	1.21467i	0.794447	−	0.607334i	$-0.207761\pi$
$522$		0			0
$523$	15.3739	+	15.3739i	0.672252	+	0.672252i	0.958235	−	0.285983i	$-0.0923200\pi$
$523$	15.3739	+	15.3739i	0.672252	+	0.672252i	−0.285983	+	0.958235i	$0.592320\pi$
$524$	−13.6463			−0.596142
$525$		0			0
$526$	−0.504546			−0.0219992
$527$	1.87083	+	1.87083i	0.0814946	+	0.0814946i
$528$		0			0
$529$		−	14.3303i		−	0.623057i
$530$	0.0533508	+	0.0814947i	0.00231741	+	0.00353990i
$531$		0			0
$532$	9.62614	−	9.62614i	0.417346	−	0.417346i
$533$	−9.93280	+	9.93280i	−0.430238	+	0.430238i
$534$		0			0
$535$	2.41742	−	11.5826i	0.104514	−	0.500758i
$536$		−	21.0229i		−	0.908052i
$537$		0			0
$538$	1.12159	+	1.12159i	0.0483552	+	0.0483552i
$539$	−3.23042			−0.139144
$540$		0			0
$541$	−19.4955			−0.838175			−0.419088	−	0.907946i	$-0.637650\pi$
$541$	−19.4955			−0.838175			−0.419088	+	0.907946i	$0.637650\pi$
$542$	−0.323042	−	0.323042i	−0.0138758	−	0.0138758i
$543$		0			0
$544$			12.5390i			0.537606i
$545$	25.7196	−	16.8375i	1.10171	−	0.721237i
$546$		0			0
$547$	−23.9564	+	23.9564i	−1.02430	+	1.02430i	−0.0246062	+	0.999697i	$0.507833\pi$
$547$	−23.9564	+	23.9564i	−1.02430	+	1.02430i	−0.999697	+	0.0246062i	$0.992167\pi$
$548$	18.5875	−	18.5875i	0.794019	−	0.794019i
$549$		0			0
$550$	−4.62614	−	11.7913i	−0.197259	−	0.502782i
$551$			13.1632i			0.560772i
$552$		0			0
$553$	−18.9564	−	18.9564i	−0.806110	−	0.806110i
$554$	−8.53394			−0.362572
$555$		0			0
$556$	−5.66970			−0.240449
$557$	−26.0568	−	26.0568i	−1.10406	−	1.10406i	−0.993916	−	0.110145i	$-0.964869\pi$
$557$	−26.0568	−	26.0568i	−1.10406	−	1.10406i	−0.110145	−	0.993916i	$-0.535131\pi$
$558$		0			0
$559$			11.4955i			0.486206i
$560$	15.4779	+	3.23042i	0.654059	+	0.136510i
$561$		0			0
$562$	−0.669697	+	0.669697i	−0.0282495	+	0.0282495i
$563$	−8.64064	+	8.64064i	−0.364159	+	0.364159i	−0.865342	−	0.501182i	$-0.832899\pi$
$563$	−8.64064	+	8.64064i	−0.364159	+	0.364159i	0.501182	+	0.865342i	$0.332899\pi$
$564$		0			0
$565$	26.7477	+	5.58258i	1.12529	+	0.234861i
$566$		−	8.53394i		−	0.358708i
$567$		0			0
$568$	6.79129	+	6.79129i	0.284956	+	0.284956i
$569$	−28.8826			−1.21082			−0.605412	−	0.795913i	$-0.706991\pi$
$569$	−28.8826			−1.21082			−0.605412	+	0.795913i	$0.706991\pi$
$570$		0			0
$571$	−22.4955			−0.941405			−0.470703	−	0.882292i	$-0.656000\pi$
$571$	−22.4955			−0.941405			−0.470703	+	0.882292i	$0.656000\pi$
$572$	17.7925	+	17.7925i	0.743942	+	0.743942i
$573$		0			0
$574$			6.41742i			0.267858i
$575$	11.1575	+	28.4388i	0.465302	+	1.18598i
$576$		0			0
$577$	−10.3739	+	10.3739i	−0.431870	+	0.431870i	−0.889264	−	0.457394i	$-0.848783\pi$
$577$	−10.3739	+	10.3739i	−0.431870	+	0.431870i	0.457394	+	0.889264i	$0.348783\pi$
$578$	3.23042	−	3.23042i	0.134368	−	0.134368i
$579$		0			0
$580$	−14.7042	+	9.62614i	−0.610557	+	0.399704i
$581$		−	31.1973i		−	1.29428i
$582$		0			0
$583$	−0.373864	−	0.373864i	−0.0154838	−	0.0154838i
$584$	−25.4107			−1.05150
$585$		0			0
$586$	−7.95644			−0.328677
$587$	27.0118	+	27.0118i	1.11490	+	1.11490i	0.992479	+	0.122418i	$0.0390649\pi$
$587$	27.0118	+	27.0118i	1.11490	+	1.11490i	0.122418	+	0.992479i	$0.460935\pi$
$588$		0			0
$589$		−	3.00000i		−	0.123613i
$590$	−0.915775	+	4.38774i	−0.0377019	+	0.180640i
$591$		0			0
$592$	13.9564	−	13.9564i	0.573606	−	0.573606i
$593$	−29.8658	+	29.8658i	−1.22644	+	1.22644i	−0.261143	+	0.965300i	$0.584099\pi$
$593$	−29.8658	+	29.8658i	−1.22644	+	1.22644i	−0.965300	+	0.261143i	$0.915901\pi$
$594$		0			0
$595$	8.20871	+	12.5390i	0.336524	+	0.514049i
$596$			14.0790i			0.576698i
$597$		0			0
$598$	5.00000	+	5.00000i	0.204465	+	0.204465i
$599$	28.8826			1.18011			0.590056	−	0.807362i	$-0.299106\pi$
$599$	28.8826			1.18011			0.590056	+	0.807362i	$0.299106\pi$
$600$		0			0
$601$	39.7477			1.62134			0.810672	−	0.585501i	$-0.199102\pi$
$601$	39.7477			1.62134			0.810672	+	0.585501i	$0.199102\pi$
$602$	3.71351	+	3.71351i	0.151352	+	0.151352i
$603$		0			0
$604$		−	3.58258i		−	0.145773i
$605$	24.1859	+	36.9446i	0.983298	+	1.50201i
$606$		0			0
$607$	13.9564	−	13.9564i	0.566474	−	0.566474i	−0.364665	−	0.931139i	$-0.618816\pi$
$607$	13.9564	−	13.9564i	0.566474	−	0.566474i	0.931139	+	0.364665i	$0.118816\pi$
$608$	10.0536	−	10.0536i	0.407726	−	0.407726i
$609$		0			0
$610$	−0.208712	+	1.00000i	−0.00845051	+	0.0404888i
$611$		−	2.31464i		−	0.0936405i
$612$		0			0
$613$	10.0000	+	10.0000i	0.403896	+	0.403896i	0.879604	−	0.475707i	$-0.157808\pi$
$613$	10.0000	+	10.0000i	0.403896	+	0.403896i	−0.475707	+	0.879604i	$0.657808\pi$
$614$	−10.1744			−0.410603
$615$		0			0
$616$	24.3303			0.980296
$617$	−14.1183	−	14.1183i	−0.568380	−	0.568380i	0.363294	−	0.931675i	$-0.381652\pi$
$617$	−14.1183	−	14.1183i	−0.568380	−	0.568380i	−0.931675	+	0.363294i	$0.881652\pi$
$618$		0			0
$619$		−	19.5826i		−	0.787090i	−0.919305	−	0.393545i	$-0.871249\pi$
$619$		−	19.5826i		−	0.787090i	0.919305	−	0.393545i	$-0.128751\pi$
$620$	3.35119	−	2.19387i	0.134587	−	0.0881080i
$621$		0			0
$622$	−2.91288	+	2.91288i	−0.116796	+	0.116796i
$623$	−29.7984	+	29.7984i	−1.19385	+	1.19385i
$624$		0			0
$625$	−17.0000	−	18.3303i	−0.680000	−	0.733212i
$626$		−	11.0901i		−	0.443251i
$627$		0			0
$628$	−5.74773	−	5.74773i	−0.229359	−	0.229359i
$629$	18.7083			0.745948
$630$		0			0
$631$	39.7477			1.58233			0.791166	−	0.611601i	$-0.209474\pi$
$631$	39.7477			1.58233			0.791166	+	0.611601i	$0.209474\pi$
$632$	−12.9610	−	12.9610i	−0.515559	−	0.515559i
$633$		0			0
$634$		−	14.7913i		−	0.587437i
$635$	15.4779	+	3.23042i	0.614220	+	0.128195i
$636$		0			0
$637$	−1.04356	+	1.04356i	−0.0413474	+	0.0413474i
$638$	−7.85971	+	7.85971i	−0.311169	+	0.311169i
$639$		0			0
$640$	24.1652	+	5.04356i	0.955211	+	0.199364i
$641$		−	37.4166i		−	1.47787i	−0.673779	−	0.738933i	$-0.735330\pi$
$641$		−	37.4166i		−	1.47787i	0.673779	−	0.738933i	$-0.264670\pi$
$642$		0			0
$643$	1.79129	+	1.79129i	0.0706415	+	0.0706415i	0.741545	−	0.670903i	$-0.234093\pi$
$643$	1.79129	+	1.79129i	0.0706415	+	0.0706415i	−0.670903	+	0.741545i	$0.734093\pi$
$644$	−27.7253			−1.09253
$645$		0			0
$646$	3.62614			0.142668
$647$	−18.5060	−	18.5060i	−0.727547	−	0.727547i	0.242584	−	0.970130i	$-0.422005\pi$
$647$	−18.5060	−	18.5060i	−0.727547	−	0.727547i	−0.970130	+	0.242584i	$0.922005\pi$
$648$		0			0
$649$		−	24.3303i		−	0.955048i
$650$	−5.30352	−	2.31464i	−0.208021	−	0.0907878i
$651$		0			0
$652$	−8.95644	+	8.95644i	−0.350761	+	0.350761i
$653$	17.4835	−	17.4835i	0.684184	−	0.684184i	−0.276756	−	0.960940i	$-0.589259\pi$
$653$	17.4835	−	17.4835i	0.684184	−	0.684184i	0.960940	+	0.276756i	$0.0892595\pi$
$654$		0			0
$655$	−14.2523	+	9.33030i	−0.556882	+	0.364565i
$656$		−	15.4779i		−	0.604309i
$657$		0			0
$658$	−0.747727	−	0.747727i	−0.0291494	−	0.0291494i
$659$	37.6581			1.46695			0.733476	−	0.679715i	$-0.237897\pi$
$659$	37.6581			1.46695			0.733476	+	0.679715i	$0.237897\pi$
$660$		0			0
$661$	23.4955			0.913867			0.456934	−	0.889501i	$-0.348948\pi$
$661$	23.4955			0.913867			0.456934	+	0.889501i	$0.348948\pi$
$662$	4.11805	+	4.11805i	0.160053	+	0.160053i
$663$		0			0
$664$		−	21.3303i		−	0.827776i
$665$	3.47197	−	16.6352i	0.134637	−	0.645085i
$666$		0			0
$667$	18.9564	−	18.9564i	0.733996	−	0.733996i
$668$	−19.0706	+	19.0706i	−0.737864	+	0.737864i
$669$		0			0
$670$	−6.79129	−	10.3739i	−0.262370	−	0.400777i
$671$		−	5.54506i		−	0.214065i
$672$		0			0
$673$	−22.5390	−	22.5390i	−0.868815	−	0.868815i	0.123526	−	0.992341i	$-0.460580\pi$
$673$	−22.5390	−	22.5390i	−0.868815	−	0.868815i	−0.992341	+	0.123526i	$0.960580\pi$
$674$	11.7644			0.453146
$675$		0			0
$676$	−11.7913			−0.453511
$677$	12.5171	+	12.5171i	0.481073	+	0.481073i	0.905474	−	0.424401i	$-0.139515\pi$
$677$	12.5171	+	12.5171i	0.481073	+	0.481073i	−0.424401	+	0.905474i	$0.639515\pi$
$678$		0			0
$679$			12.8348i			0.492556i
$680$	5.61249	+	8.57321i	0.215229	+	0.328768i
$681$		0			0
$682$	1.79129	−	1.79129i	0.0685920	−	0.0685920i
$683$	−0.0674228	+	0.0674228i	−0.00257986	+	0.00257986i	−0.708396	−	0.705816i	$-0.750581\pi$
$683$	−0.0674228	+	0.0674228i	−0.00257986	+	0.00257986i	0.705816	+	0.708396i	$0.250581\pi$
$684$		0			0
$685$	6.70417	−	32.1216i	0.256153	−	1.22730i
$686$			8.77548i			0.335049i
$687$		0			0
$688$	−8.95644	−	8.95644i	−0.341461	−	0.341461i
$689$	−0.241547			−0.00920221
$690$		0			0
$691$	−11.7477			−0.446905			−0.223452	−	0.974715i	$-0.571733\pi$
$691$	−11.7477			−0.446905			−0.223452	+	0.974715i	$0.571733\pi$
$692$	14.1998	+	14.1998i	0.539794	+	0.539794i
$693$		0			0
$694$		−	5.49545i		−	0.208605i
$695$	−5.92146	+	3.87650i	−0.224614	+	0.147044i
$696$		0			0
$697$	10.3739	−	10.3739i	0.392938	−	0.392938i
$698$	−6.27264	+	6.27264i	−0.237423	+	0.237423i
$699$		0			0
$700$	21.1216	−	8.28674i	0.798321	−	0.313209i
$701$		−	47.8325i		−	1.80661i	−0.429001	−	0.903304i	$-0.641134\pi$
$701$		−	47.8325i		−	1.80661i	0.429001	−	0.903304i	$-0.358866\pi$
$702$		0			0
$703$	−15.0000	−	15.0000i	−0.565736	−	0.565736i
$704$	−18.9498			−0.714199
$705$		0			0
$706$	8.00000			0.301084
$707$	−19.8656	−	19.8656i	−0.747123	−	0.747123i
$708$		0			0
$709$			42.6606i			1.60215i	0.598562	+	0.801076i	$0.295739\pi$
$709$			42.6606i			1.60215i	−0.598562	+	0.801076i	$0.704261\pi$
$710$	5.54506	+	1.15732i	0.208103	+	0.0434335i
$711$		0			0
$712$	−20.3739	+	20.3739i	−0.763543	+	0.763543i
$713$	−4.32032	+	4.32032i	−0.161797	+	0.161797i
$714$		0			0
$715$	30.7477	+	6.41742i	1.14990	+	0.239998i
$716$		0			0
$717$		0			0
$718$	9.62614	+	9.62614i	0.359244	+	0.359244i
$719$	−29.7984			−1.11129			−0.555647	−	0.831419i	$-0.687529\pi$
$719$	−29.7984			−1.11129			−0.555647	+	0.831419i	$0.687529\pi$
$720$		0			0
$721$	−12.8348			−0.477995
$722$	3.23042	+	3.23042i	0.120224	+	0.120224i
$723$		0			0
$724$		−	17.4610i		−	0.648932i
$725$	−8.77548	+	20.1072i	−0.325913	+	0.746761i
$726$		0			0
$727$	37.1652	−	37.1652i	1.37838	−	1.37838i	0.531020	−	0.847359i	$-0.321809\pi$
$727$	37.1652	−	37.1652i	1.37838	−	1.37838i	0.847359	−	0.531020i	$-0.178191\pi$
$728$	7.85971	−	7.85971i	0.291300	−	0.291300i
$729$		0			0
$730$	−12.5390	+	8.20871i	−0.464090	+	0.303818i
$731$		−	12.0059i		−	0.444054i
$732$		0			0
$733$	26.4174	+	26.4174i	0.975750	+	0.975750i	0.999713	−	0.0239630i	$-0.00762839\pi$
$733$	26.4174	+	26.4174i	0.975750	+	0.975750i	−0.0239630	+	0.999713i	$0.507628\pi$
$734$	−5.78661			−0.213588
$735$		0			0
$736$	−28.9564			−1.06735
$737$	47.5909	+	47.5909i	1.75303	+	1.75303i
$738$		0			0
$739$			24.4955i			0.901080i	0.892756	+	0.450540i	$0.148769\pi$
$739$			24.4955i			0.901080i	−0.892756	+	0.450540i	$0.851231\pi$
$740$	5.78661	−	27.7253i	0.212720	−	1.01920i
$741$		0			0
$742$	−0.0780299	+	0.0780299i	−0.00286457	+	0.00286457i
$743$	−12.1126	+	12.1126i	−0.444368	+	0.444368i	−0.893477	−	0.449109i	$-0.851742\pi$
$743$	−12.1126	+	12.1126i	−0.444368	+	0.444368i	0.449109	+	0.893477i	$0.351742\pi$
$744$		0			0
$745$	9.62614	+	14.7042i	0.352674	+	0.538719i
$746$		−	2.31464i		−	0.0847451i
$747$		0			0
$748$	−18.5826	−	18.5826i	−0.679446	−	0.679446i
$749$	13.4048			0.489800
$750$		0			0
$751$	9.74773			0.355700			0.177850	−	0.984058i	$-0.443086\pi$
$751$	9.74773			0.355700			0.177850	+	0.984058i	$0.443086\pi$
$752$	1.80341	+	1.80341i	0.0657634	+	0.0657634i
$753$		0			0
$754$			5.07803i			0.184931i
$755$	−2.44949	−	3.74166i	−0.0891461	−	0.136173i
$756$		0			0
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	−0.792108	−	0.610380i	$-0.791017\pi$
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	0.610380	+	0.792108i	$0.291017\pi$
$758$	2.50284	−	2.50284i	0.0909073	−	0.0909073i
$759$		0			0
$760$	2.37386	−	11.3739i	0.0861091	−	0.412573i
$761$			9.01703i			0.326867i	0.986554	+	0.163434i	$0.0522569\pi$
$761$			9.01703i			0.326867i	−0.986554	+	0.163434i	$0.947743\pi$
$762$		0			0
$763$	24.6261	+	24.6261i	0.891526	+	0.891526i
$764$	33.5119			1.21242
$765$		0			0
$766$	13.5390			0.489184
$767$	−7.85971	−	7.85971i	−0.283798	−	0.283798i
$768$		0			0
$769$			27.3303i			0.985556i	0.870155	+	0.492778i	$0.164019\pi$
$769$			27.3303i			0.985556i	−0.870155	+	0.492778i	$0.835981\pi$
$770$	12.0059	−	7.85971i	0.432663	−	0.283244i
$771$		0			0
$772$	3.20871	−	3.20871i	0.115484	−	0.115484i
$773$	−36.8098	+	36.8098i	−1.32396	+	1.32396i	−0.413411	+	0.910545i	$0.635663\pi$
$773$	−36.8098	+	36.8098i	−1.32396	+	1.32396i	−0.910545	+	0.413411i	$0.864337\pi$
$774$		0			0
$775$	2.00000	−	4.58258i	0.0718421	−	0.164611i
$776$			8.77548i			0.315021i
$777$		0			0
$778$	2.53901	+	2.53901i	0.0910281	+	0.0910281i
$779$	−16.6352			−0.596018
$780$		0			0
$781$	−30.7477			−1.10024
$782$	−5.22202	−	5.22202i	−0.186739	−	0.186739i
$783$		0			0
$784$		−	1.62614i		−	0.0580763i
$785$	−9.93280	−	2.07310i	−0.354517	−	0.0739920i
$786$		0			0
$787$	−37.5390	+	37.5390i	−1.33812	+	1.33812i	−0.440242	+	0.897879i	$0.645107\pi$
$787$	−37.5390	+	37.5390i	−1.33812	+	1.33812i	−0.897879	+	0.440242i	$0.854893\pi$
$788$	−3.35119	+	3.35119i	−0.119381	+	0.119381i
$789$		0			0
$790$	−10.5826	−	2.20871i	−0.376511	−	0.0785825i
$791$			30.9557i			1.10066i
$792$		0			0
$793$	−1.79129	−	1.79129i	−0.0636105	−	0.0636105i
$794$	16.8767			0.598933
$795$		0			0
$796$	−30.0000			−1.06332
$797$	2.51691	+	2.51691i	0.0891536	+	0.0891536i	0.750277	−	0.661123i	$-0.229920\pi$
$797$	2.51691	+	2.51691i	0.0891536	+	0.0891536i	−0.661123	+	0.750277i	$0.729920\pi$
$798$		0			0
$799$			2.41742i			0.0855223i
$800$	22.0595	−	8.65471i	0.779920	−	0.305990i
$801$		0			0
$802$	−6.04356	+	6.04356i	−0.213406	+	0.213406i
$803$	57.5237	−	57.5237i	2.02997	−	2.02997i
$804$		0			0
$805$	−28.9564	+	18.9564i	−1.02058	+	0.668127i
$806$		−	1.15732i		−	0.0407649i
$807$		0			0
$808$	−13.5826	−	13.5826i	−0.477833	−	0.477833i
$809$	−42.9616			−1.51045			−0.755225	−	0.655465i	$-0.772473\pi$
$809$	−42.9616			−1.51045			−0.755225	+	0.655465i	$0.772473\pi$
$810$		0			0
$811$	23.4955			0.825037			0.412518	−	0.910949i	$-0.364649\pi$
$811$	23.4955			0.825037			0.412518	+	0.910949i	$0.364649\pi$
$812$	−14.0790	−	14.0790i	−0.494076	−	0.494076i
$813$		0			0
$814$		−	17.9129i		−	0.627846i
$815$	−3.23042	+	15.4779i	−0.113157	+	0.542166i
$816$		0			0
$817$	−9.62614	+	9.62614i	−0.336776	+	0.336776i
$818$	7.80636	−	7.80636i	0.272943	−	0.272943i
$819$		0			0
$820$	−12.1652	−	18.5826i	−0.424826	−	0.648932i
$821$		−	7.61816i		−	0.265876i	−0.991124	−	0.132938i	$-0.957559\pi$
$821$		−	7.61816i		−	0.265876i	0.991124	−	0.132938i	$-0.0424411\pi$
$822$		0			0
$823$	−23.9564	−	23.9564i	−0.835069	−	0.835069i	0.153136	−	0.988205i	$-0.451063\pi$
$823$	−23.9564	−	23.9564i	−0.835069	−	0.835069i	−0.988205	+	0.153136i	$0.951063\pi$
$824$	−8.77548			−0.305708
$825$		0			0
$826$	−5.07803			−0.176687
$827$	−31.6692	−	31.6692i	−1.10125	−	1.10125i	−0.994260	−	0.106987i	$-0.965880\pi$
$827$	−31.6692	−	31.6692i	−1.10125	−	1.10125i	−0.106987	−	0.994260i	$-0.534120\pi$
$828$		0			0
$829$			34.7477i			1.20684i	0.797424	+	0.603419i	$0.206195\pi$
$829$			34.7477i			1.20684i	−0.797424	+	0.603419i	$0.793805\pi$
$830$	−6.89058	−	10.5255i	−0.239176	−	0.365347i
$831$		0			0
$832$	−6.12159	+	6.12159i	−0.212228	+	0.212228i
$833$	1.08990	−	1.08990i	0.0377628	−	0.0377628i
$834$		0			0
$835$	−6.87841	+	32.9564i	−0.238037	+	1.14050i
$836$			29.7984i			1.03060i
$837$		0			0
$838$	−0.295834	−	0.295834i	−0.0102194	−	0.0102194i
$839$	−35.1019			−1.21185			−0.605927	−	0.795521i	$-0.707197\pi$
$839$	−35.1019			−1.21185			−0.605927	+	0.795521i	$0.707197\pi$
$840$		0			0
$841$	−9.74773			−0.336129
$842$	12.8402	+	12.8402i	0.442502	+	0.442502i
$843$		0			0
$844$		−	17.4610i		−	0.601032i
$845$	−12.3149	+	8.06198i	−0.423644	+	0.277340i
$846$		0			0
$847$	−35.3739	+	35.3739i	−1.21546	+	1.21546i
$848$	0.188196	−	0.188196i	0.00646269	−	0.00646269i
$849$		0			0
$850$	5.53901	+	2.41742i	0.189987	+	0.0829170i
$851$			43.2032i			1.48099i
$852$		0			0
$853$	4.33030	+	4.33030i	0.148267	+	0.148267i	0.777343	−	0.629077i	$-0.216567\pi$
$853$	4.33030	+	4.33030i	0.148267	+	0.148267i	−0.629077	+	0.777343i	$0.716567\pi$
$854$	−1.15732			−0.0396027
$855$		0			0
$856$	9.16515			0.313258
$857$	−6.25857	−	6.25857i	−0.213789	−	0.213789i	0.592086	−	0.805875i	$-0.298305\pi$
$857$	−6.25857	−	6.25857i	−0.213789	−	0.213789i	−0.805875	+	0.592086i	$0.798305\pi$
$858$		0			0
$859$		−	45.6606i		−	1.55792i	−0.627074	−	0.778960i	$-0.715748\pi$
$859$		−	45.6606i		−	1.55792i	0.627074	−	0.778960i	$-0.284252\pi$
$860$	−17.7925	−	3.71351i	−0.606720	−	0.126630i
$861$		0			0
$862$	−2.91288	+	2.91288i	−0.0992130	+	0.0992130i
$863$	26.2590	−	26.2590i	0.893868	−	0.893868i	−0.101017	−	0.994885i	$-0.532210\pi$
$863$	26.2590	−	26.2590i	0.893868	−	0.893868i	0.994885	+	0.101017i	$0.0322097\pi$
$864$		0			0
$865$	24.5390	+	5.12159i	0.834352	+	0.174139i
$866$			2.98887i			0.101566i
$867$		0			0
$868$	3.20871	+	3.20871i	0.108911	+	0.108911i
$869$	58.6811			1.99062
$870$		0			0
$871$	30.7477			1.04185
$872$	16.8375	+	16.8375i	0.570188	+	0.570188i
$873$		0			0
$874$			8.37386i			0.283250i
$875$	16.3936	−	23.0960i	0.554206	−	0.780788i
$876$		0			0
$877$	3.20871	−	3.20871i	0.108351	−	0.108351i	−0.650853	−	0.759204i	$-0.725589\pi$
$877$	3.20871	−	3.20871i	0.108351	−	0.108351i	0.759204	+	0.650853i	$0.225589\pi$
$878$	3.41862	−	3.41862i	0.115373	−	0.115373i
$879$		0			0
$880$	−28.9564	+	18.9564i	−0.976121	+	0.639021i
$881$			35.3435i			1.19075i	0.803447	+	0.595376i	$0.202997\pi$
$881$			35.3435i			1.19075i	−0.803447	+	0.595376i	$0.797003\pi$
$882$		0			0
$883$	−25.3739	−	25.3739i	−0.853898	−	0.853898i	0.136712	−	0.990611i	$-0.456346\pi$
$883$	−25.3739	−	25.3739i	−0.853898	−	0.853898i	−0.990611	+	0.136712i	$0.956346\pi$
$884$	−12.0059			−0.403802
$885$		0			0
$886$	−5.12159			−0.172063
$887$	35.7873	+	35.7873i	1.20162	+	1.20162i	0.973674	+	0.227946i	$0.0732009\pi$
$887$	35.7873	+	35.7873i	1.20162	+	1.20162i	0.227946	+	0.973674i	$0.426799\pi$
$888$		0			0
$889$			17.9129i			0.600779i
$890$	−3.47197	+	16.6352i	−0.116381	+	0.557613i
$891$		0			0
$892$	15.3739	−	15.3739i	0.514755	−	0.514755i
$893$	1.93825	−	1.93825i	0.0648611	−	0.0648611i
$894$		0			0
$895$		0			0
$896$			27.9669i			0.934307i
$897$		0			0
$898$	4.25227	+	4.25227i	0.141900	+	0.141900i
$899$	−4.38774			−0.146339
$900$		0			0
$901$	0.252273			0.00840443
$902$	−9.93280	−	9.93280i	−0.330726	−	0.330726i
$903$		0			0
$904$			21.1652i			0.703942i
$905$	−11.9385	−	18.2363i	−0.396848	−	0.606196i
$906$		0			0
$907$	17.9129	−	17.9129i	0.594787	−	0.594787i	−0.344133	−	0.938921i	$-0.611827\pi$
$907$	17.9129	−	17.9129i	0.594787	−	0.594787i	0.938921	+	0.344133i	$0.111827\pi$
$908$	12.3682	−	12.3682i	0.410454	−	0.410454i
$909$		0			0
$910$	1.33939	−	6.41742i	0.0444005	−	0.212736i
$911$		−	24.2534i		−	0.803549i	−0.915739	−	0.401775i	$-0.868394\pi$
$911$		−	24.2534i		−	0.803549i	0.915739	−	0.401775i	$-0.131606\pi$
$912$		0			0
$913$	48.2867	+	48.2867i	1.59806	+	1.59806i
$914$	−2.31464			−0.0765616
$915$		0			0
$916$	10.4519			0.345340
$917$	−13.6463	−	13.6463i	−0.450641	−	0.450641i
$918$		0			0
$919$			24.0000i			0.791687i	0.918318	+	0.395843i	$0.129548\pi$
$919$			24.0000i			0.791687i	−0.918318	+	0.395843i	$0.870452\pi$
$920$	−19.7982	+	12.9610i	−0.652727	+	0.427310i
$921$		0			0
$922$	4.70417	−	4.70417i	0.154923	−	0.154923i
$923$	−9.93280	+	9.93280i	−0.326942	+	0.326942i
$924$		0			0
$925$	−12.9129	−	32.9129i	−0.424573	−	1.08217i
$926$		−	5.06197i		−	0.166347i
$927$		0			0
$928$	−14.7042	−	14.7042i	−0.482688	−	0.482688i
$929$	0.915775			0.0300456			0.0150228	−	0.999887i	$-0.495218\pi$
$929$	0.915775			0.0300456			0.0150228	+	0.999887i	$0.495218\pi$
$930$		0			0
$931$	−1.74773			−0.0572794
$932$	−30.0400	−	30.0400i	−0.983992	−	0.983992i
$933$		0			0
$934$		−	3.45189i		−	0.112949i
$935$	−32.1131	−	6.70239i	−1.05021	−	0.219191i
$936$		0			0
$937$	−0.747727	+	0.747727i	−0.0244272	+	0.0244272i	−0.719215	−	0.694788i	$-0.755498\pi$
$937$	−0.747727	+	0.747727i	−0.0244272	+	0.0244272i	0.694788	+	0.719215i	$0.255498\pi$
$938$	9.93280	−	9.93280i	0.324318	−	0.324318i
$939$		0			0
$940$	3.58258	+	0.747727i	0.116851	+	0.0243882i
$941$		−	14.5621i		−	0.474711i	−0.971423	−	0.237355i	$-0.923719\pi$
$941$		−	14.5621i		−	0.474711i	0.971423	−	0.237355i	$-0.0762806\pi$
$942$		0			0
$943$	23.9564	+	23.9564i	0.780129	+	0.780129i
$944$	12.2474			0.398621
$945$		0			0
$946$	−11.4955			−0.373749
$947$	−9.73054	−	9.73054i	−0.316200	−	0.316200i	0.531106	−	0.847306i	$-0.321777\pi$
$947$	−9.73054	−	9.73054i	−0.316200	−	0.316200i	−0.847306	+	0.531106i	$0.821777\pi$
$948$		0			0
$949$		−	37.1652i		−	1.20643i
$950$	−2.50284	−	6.37934i	−0.0812029	−	0.206973i
$951$		0			0
$952$	−8.20871	+	8.20871i	−0.266046	+	0.266046i
$953$	20.2420	−	20.2420i	0.655703	−	0.655703i	−0.298658	−	0.954360i	$-0.596539\pi$
$953$	20.2420	−	20.2420i	0.655703	−	0.655703i	0.954360	+	0.298658i	$0.0965388\pi$
$954$		0			0
$955$	35.0000	−	22.9129i	1.13257	−	0.741443i
$956$		−	21.9387i		−	0.709548i
$957$		0			0
$958$	2.53901	+	2.53901i	0.0820318	+	0.0820318i
$959$	37.1750			1.20044
$960$		0			0
$961$	−30.0000			−0.967742
$962$	−5.78661	−	5.78661i	−0.186568	−	0.186568i
$963$		0			0
$964$			21.0436i			0.677767i
$965$	1.15732	−	5.54506i	0.0372555	−	0.178502i
$966$		0			0
$967$	19.3303	−	19.3303i	0.621621	−	0.621621i	−0.324325	−	0.945946i	$-0.605137\pi$
$967$	19.3303	−	19.3303i	0.621621	−	0.621621i	0.945946	+	0.324325i	$0.105137\pi$
$968$	−24.1859	+	24.1859i	−0.777365	+	0.777365i
$969$		0			0
$970$	2.83485	+	4.33030i	0.0910215	+	0.139038i
$971$			18.7083i			0.600377i	0.953880	+	0.300189i	$0.0970497\pi$
$971$			18.7083i			0.600377i	−0.953880	+	0.300189i	$0.902950\pi$
$972$		0			0
$973$	−5.66970	−	5.66970i	−0.181762	−	0.181762i
$974$	0.241547			0.00773967
$975$		0			0
$976$	2.79129			0.0893469
$977$	−1.56186	−	1.56186i	−0.0499683	−	0.0499683i	0.681681	−	0.731649i	$-0.261249\pi$
$977$	−1.56186	−	1.56186i	−0.0499683	−	0.0499683i	−0.731649	+	0.681681i	$0.761249\pi$
$978$		0			0
$979$		−	92.2432i		−	2.94810i
$980$	−1.27810	−	1.95232i	−0.0408273	−	0.0623647i
$981$		0			0
$982$	4.70417	−	4.70417i	0.150116	−	0.150116i
$983$	12.1800	−	12.1800i	0.388482	−	0.388482i	−0.485663	−	0.874146i	$-0.661422\pi$
$983$	12.1800	−	12.1800i	0.388482	−	0.388482i	0.874146	+	0.485663i	$0.161422\pi$
$984$		0			0
$985$	−1.20871	+	5.79129i	−0.0385128	+	0.184526i
$986$		−	5.30352i		−	0.168898i
$987$		0			0
$988$	9.62614	+	9.62614i	0.306248	+	0.306248i
$989$	27.7253			0.881614
$990$		0			0
$991$	18.2523			0.579803			0.289901	−	0.957057i	$-0.406378\pi$
$991$	18.2523			0.579803			0.289901	+	0.957057i	$0.406378\pi$
$992$	3.35119	+	3.35119i	0.106400	+	0.106400i
$993$		0			0
$994$			6.41742i			0.203548i
$995$	−31.3321	+	20.5117i	−0.993295	+	0.650264i
$996$		0			0
$997$	16.7913	−	16.7913i	0.531785	−	0.531785i	−0.389318	−	0.921103i	$-0.627289\pi$
$997$	16.7913	−	16.7913i	0.531785	−	0.531785i	0.921103	+	0.389318i	$0.127289\pi$
$998$	−8.82883	+	8.82883i	−0.279472	+	0.279472i
$999$		0			0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.f.a.53.3	yes	8
3.2	odd	2	inner	135.2.f.a.53.2	✓	8
4.3	odd	2		2160.2.w.d.593.1		8
5.2	odd	4	inner	135.2.f.a.107.2	yes	8
5.3	odd	4		675.2.f.i.107.3		8
5.4	even	2		675.2.f.i.593.2		8
9.2	odd	6		405.2.m.c.53.2		16
9.4	even	3		405.2.m.c.188.2		16
9.5	odd	6		405.2.m.c.188.3		16
9.7	even	3		405.2.m.c.53.3		16
12.11	even	2		2160.2.w.d.593.4		8
15.2	even	4	inner	135.2.f.a.107.3	yes	8
15.8	even	4		675.2.f.i.107.2		8
15.14	odd	2		675.2.f.i.593.3		8
20.7	even	4		2160.2.w.d.1457.3		8
45.2	even	12		405.2.m.c.377.2		16
45.7	odd	12		405.2.m.c.377.3		16
45.22	odd	12		405.2.m.c.107.2		16
45.32	even	12		405.2.m.c.107.3		16
60.47	odd	4		2160.2.w.d.1457.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.f.a.53.2	✓	8	3.2	odd	2	inner
135.2.f.a.53.3	yes	8	1.1	even	1	trivial
135.2.f.a.107.2	yes	8	5.2	odd	4	inner
135.2.f.a.107.3	yes	8	15.2	even	4	inner
405.2.m.c.53.2		16	9.2	odd	6
405.2.m.c.53.3		16	9.7	even	3
405.2.m.c.107.2		16	45.22	odd	12
405.2.m.c.107.3		16	45.32	even	12
405.2.m.c.188.2		16	9.4	even	3
405.2.m.c.188.3		16	9.5	odd	6
405.2.m.c.377.2		16	45.2	even	12
405.2.m.c.377.3		16	45.7	odd	12
675.2.f.i.107.2		8	15.8	even	4
675.2.f.i.107.3		8	5.3	odd	4
675.2.f.i.593.2		8	5.4	even	2
675.2.f.i.593.3		8	15.14	odd	2
2160.2.w.d.593.1		8	4.3	odd	2
2160.2.w.d.593.4		8	12.11	even	2
2160.2.w.d.1457.2		8	60.47	odd	4
2160.2.w.d.1457.3		8	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	135.2.f.a.53.3

Level	$135$
Weight	$2$
Character	135.53
Analytic conductor	$1.078$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$