LMFDB - Embedded newform 360.2.d.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(109,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.d (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.2
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	360.109
Dual form			360.2.d.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.41421 - 1.73205i) q^{5} +2.44949i q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.41421 - 1.73205i) q^{5} +2.44949i q^{7} +2.82843 q^{8} +(3.12132 - 0.507306i) q^{10} +3.46410i q^{11} +(-3.00000 - 1.73205i) q^{14} +(-2.00000 + 3.46410i) q^{16} +4.89898i q^{17} +3.46410i q^{19} +(-1.58579 + 4.18154i) q^{20} +(-4.24264 - 2.44949i) q^{22} +2.44949i q^{23} +(-1.00000 + 4.89898i) q^{25} +(4.24264 - 2.44949i) q^{28} +4.00000 q^{31} +(-2.82843 - 4.89898i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(4.24264 - 3.46410i) q^{35} -8.48528 q^{37} +(-4.24264 - 2.44949i) q^{38} +(-4.00000 - 4.89898i) q^{40} +4.24264 q^{43} +(6.00000 - 3.46410i) q^{44} +(-3.00000 - 1.73205i) q^{46} -7.34847i q^{47} +1.00000 q^{49} +(-5.29289 - 4.68885i) q^{50} -5.65685 q^{53} +(6.00000 - 4.89898i) q^{55} +6.92820i q^{56} +10.3923i q^{59} +3.46410i q^{61} +(-2.82843 + 4.89898i) q^{62} +8.00000 q^{64} -4.24264 q^{67} +(8.48528 - 4.89898i) q^{68} +(1.24264 + 7.64564i) q^{70} +12.0000 q^{71} -4.89898i q^{73} +(6.00000 - 10.3923i) q^{74} +(6.00000 - 3.46410i) q^{76} -8.48528 q^{77} -4.00000 q^{79} +(8.82843 - 1.43488i) q^{80} +9.89949 q^{83} +(8.48528 - 6.92820i) q^{85} +(-3.00000 + 5.19615i) q^{86} +9.79796i q^{88} -6.00000 q^{89} +(4.24264 - 2.44949i) q^{92} +(9.00000 + 5.19615i) q^{94} +(6.00000 - 4.89898i) q^{95} +4.89898i q^{97} +(-0.707107 + 1.22474i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} + 4 q^{10} - 12 q^{14} - 8 q^{16} - 12 q^{20} - 4 q^{25} + 16 q^{31} - 24 q^{34} - 16 q^{40} + 24 q^{44} - 12 q^{46} + 4 q^{49} - 24 q^{50} + 24 q^{55} + 32 q^{64} - 12 q^{70} + 48 q^{71} + 24 q^{74} + 24 q^{76} - 16 q^{79} + 24 q^{80} - 12 q^{86} - 24 q^{89} + 36 q^{94} + 24 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^10 - 12 * q^14 - 8 * q^16 - 12 * q^20 - 4 * q^25 + 16 * q^31 - 24 * q^34 - 16 * q^40 + 24 * q^44 - 12 * q^46 + 4 * q^49 - 24 * q^50 + 24 * q^55 + 32 * q^64 - 12 * q^70 + 48 * q^71 + 24 * q^74 + 24 * q^76 - 16 * q^79 + 24 * q^80 - 12 * q^86 - 24 * q^89 + 36 * q^94 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 (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 $

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$6$		0			0
$7$			2.44949i			0.925820i	0.886405	+	0.462910i	$0.153195\pi$
$7$			2.44949i			0.925820i	−0.886405	+	0.462910i	$0.846805\pi$
$8$	2.82843			1.00000
$9$		0			0
$10$	3.12132	−	0.507306i	0.987048	−	0.160424i
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−3.00000	−	1.73205i	−0.801784	−	0.462910i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$			4.89898i			1.18818i	0.804400	+	0.594089i	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$		0			0
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.58579	+	4.18154i	−0.354593	+	0.935021i
$21$		0			0
$22$	−4.24264	−	2.44949i	−0.904534	−	0.522233i
$23$			2.44949i			0.510754i	0.966842	+	0.255377i	$0.0821996\pi$
$23$			2.44949i			0.510754i	−0.966842	+	0.255377i	$0.917800\pi$
$24$		0			0
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$		0			0
$27$		0			0
$28$	4.24264	−	2.44949i	0.801784	−	0.462910i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−2.82843	−	4.89898i	−0.500000	−	0.866025i
$33$		0			0
$34$	−6.00000	−	3.46410i	−1.02899	−	0.594089i
$35$	4.24264	−	3.46410i	0.717137	−	0.585540i
$36$		0			0
$37$	−8.48528			−1.39497			−0.697486	−	0.716599i	$-0.745698\pi$
$37$	−8.48528			−1.39497			−0.697486	+	0.716599i	$0.745698\pi$
$38$	−4.24264	−	2.44949i	−0.688247	−	0.397360i
$39$		0			0
$40$	−4.00000	−	4.89898i	−0.632456	−	0.774597i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	4.24264			0.646997			0.323498	−	0.946229i	$-0.395141\pi$
$43$	4.24264			0.646997			0.323498	+	0.946229i	$0.395141\pi$
$44$	6.00000	−	3.46410i	0.904534	−	0.522233i
$45$		0			0
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$		−	7.34847i		−	1.07188i	−0.844255	−	0.535942i	$-0.819956\pi$
$47$		−	7.34847i		−	1.07188i	0.844255	−	0.535942i	$-0.180044\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−5.29289	−	4.68885i	−0.748528	−	0.663103i
$51$		0			0
$52$		0			0
$53$	−5.65685			−0.777029			−0.388514	−	0.921443i	$-0.627012\pi$
$53$	−5.65685			−0.777029			−0.388514	+	0.921443i	$0.627012\pi$
$54$		0			0
$55$	6.00000	−	4.89898i	0.809040	−	0.660578i
$56$			6.92820i			0.925820i
$57$		0			0
$58$		0			0
$59$			10.3923i			1.35296i	0.736460	+	0.676481i	$0.236496\pi$
$59$			10.3923i			1.35296i	−0.736460	+	0.676481i	$0.763504\pi$
$60$		0			0
$61$			3.46410i			0.443533i	0.975100	+	0.221766i	$0.0711822\pi$
$61$			3.46410i			0.443533i	−0.975100	+	0.221766i	$0.928818\pi$
$62$	−2.82843	+	4.89898i	−0.359211	+	0.622171i
$63$		0			0
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	−4.24264			−0.518321			−0.259161	−	0.965834i	$-0.583446\pi$
$67$	−4.24264			−0.518321			−0.259161	+	0.965834i	$0.583446\pi$
$68$	8.48528	−	4.89898i	1.02899	−	0.594089i
$69$		0			0
$70$	1.24264	+	7.64564i	0.148524	+	0.913829i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$		−	4.89898i		−	0.573382i	−0.958023	−	0.286691i	$-0.907445\pi$
$73$		−	4.89898i		−	0.573382i	0.958023	−	0.286691i	$-0.0925553\pi$
$74$	6.00000	−	10.3923i	0.697486	−	1.20808i
$75$		0			0
$76$	6.00000	−	3.46410i	0.688247	−	0.397360i
$77$	−8.48528			−0.966988
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	8.82843	−	1.43488i	0.987048	−	0.160424i
$81$		0			0
$82$		0			0
$83$	9.89949			1.08661			0.543305	−	0.839535i	$-0.317173\pi$
$83$	9.89949			1.08661			0.543305	+	0.839535i	$0.317173\pi$
$84$		0			0
$85$	8.48528	−	6.92820i	0.920358	−	0.751469i
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$		0			0
$88$			9.79796i			1.04447i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$		0			0
$92$	4.24264	−	2.44949i	0.442326	−	0.255377i
$93$		0			0
$94$	9.00000	+	5.19615i	0.928279	+	0.535942i
$95$	6.00000	−	4.89898i	0.615587	−	0.502625i
$96$		0			0
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$	−0.707107	+	1.22474i	−0.0714286	+	0.123718i
$99$		0			0
$100$	9.48528	−	3.16693i	0.948528	−	0.316693i
$101$		−	13.8564i		−	1.37876i	−0.724398	−	0.689382i	$-0.757882\pi$
$101$		−	13.8564i		−	1.37876i	0.724398	−	0.689382i	$-0.242118\pi$
$102$		0			0
$103$			7.34847i			0.724066i	0.932165	+	0.362033i	$0.117917\pi$
$103$			7.34847i			0.724066i	−0.932165	+	0.362033i	$0.882083\pi$
$104$		0			0
$105$		0			0
$106$	4.00000	−	6.92820i	0.388514	−	0.672927i
$107$	−1.41421			−0.136717			−0.0683586	−	0.997661i	$-0.521776\pi$
$107$	−1.41421			−0.136717			−0.0683586	+	0.997661i	$0.521776\pi$
$108$		0			0
$109$		−	3.46410i		−	0.331801i	−0.986143	−	0.165900i	$-0.946947\pi$
$109$		−	3.46410i		−	0.331801i	0.986143	−	0.165900i	$-0.0530530\pi$
$110$	1.75736	+	10.8126i	0.167558	+	1.03094i
$111$		0			0
$112$	−8.48528	−	4.89898i	−0.801784	−	0.462910i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$	4.24264	−	3.46410i	0.395628	−	0.323029i
$116$		0			0
$117$		0			0
$118$	−12.7279	−	7.34847i	−1.17170	−	0.676481i
$119$	−12.0000			−1.10004
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−4.24264	−	2.44949i	−0.384111	−	0.221766i
$123$		0			0
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$		0			0
$127$		−	17.1464i		−	1.52150i	−0.649045	−	0.760750i	$-0.724831\pi$
$127$		−	17.1464i		−	1.52150i	0.649045	−	0.760750i	$-0.275169\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$		−	3.46410i		−	0.302660i	−0.988483	−	0.151330i	$-0.951644\pi$
$131$		−	3.46410i		−	0.302660i	0.988483	−	0.151330i	$-0.0483556\pi$
$132$		0			0
$133$	−8.48528			−0.735767
$134$	3.00000	−	5.19615i	0.259161	−	0.448879i
$135$		0			0
$136$			13.8564i			1.18818i
$137$		−	9.79796i		−	0.837096i	−0.908195	−	0.418548i	$-0.862539\pi$
$137$		−	9.79796i		−	0.837096i	0.908195	−	0.418548i	$-0.137461\pi$
$138$		0			0
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$	−10.2426	−	3.88437i	−0.865661	−	0.328289i
$141$		0			0
$142$	−8.48528	+	14.6969i	−0.712069	+	1.23334i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	6.00000	+	3.46410i	0.496564	+	0.286691i
$147$		0			0
$148$	8.48528	+	14.6969i	0.697486	+	1.20808i
$149$			17.3205i			1.41895i	0.704730	+	0.709476i	$0.251068\pi$
$149$			17.3205i			1.41895i	−0.704730	+	0.709476i	$0.748932\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$			9.79796i			0.794719i
$153$		0			0
$154$	6.00000	−	10.3923i	0.483494	−	0.837436i
$155$	−5.65685	−	6.92820i	−0.454369	−	0.556487i
$156$		0			0
$157$	8.48528			0.677199			0.338600	−	0.940931i	$-0.390047\pi$
$157$	8.48528			0.677199			0.338600	+	0.940931i	$0.390047\pi$
$158$	2.82843	−	4.89898i	0.225018	−	0.389742i
$159$		0			0
$160$	−4.48528	+	11.8272i	−0.354593	+	0.935021i
$161$	−6.00000			−0.472866
$162$		0			0
$163$	21.2132			1.66155			0.830773	−	0.556611i	$-0.187899\pi$
$163$	21.2132			1.66155			0.830773	+	0.556611i	$0.187899\pi$
$164$		0			0
$165$		0			0
$166$	−7.00000	+	12.1244i	−0.543305	+	0.941033i
$167$			12.2474i			0.947736i	0.880596	+	0.473868i	$0.157143\pi$
$167$			12.2474i			0.947736i	−0.880596	+	0.473868i	$0.842857\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	2.48528	+	15.2913i	0.190612	+	1.17279i
$171$		0			0
$172$	−4.24264	−	7.34847i	−0.323498	−	0.560316i
$173$	−2.82843			−0.215041			−0.107521	−	0.994203i	$-0.534291\pi$
$173$	−2.82843			−0.215041			−0.107521	+	0.994203i	$0.534291\pi$
$174$		0			0
$175$	−12.0000	−	2.44949i	−0.907115	−	0.185164i
$176$	−12.0000	−	6.92820i	−0.904534	−	0.522233i
$177$		0			0
$178$	4.24264	−	7.34847i	0.317999	−	0.550791i
$179$			3.46410i			0.258919i	0.991585	+	0.129460i	$0.0413242\pi$
$179$			3.46410i			0.258919i	−0.991585	+	0.129460i	$0.958676\pi$
$180$		0			0
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$		0			0
$183$		0			0
$184$			6.92820i			0.510754i
$185$	12.0000	+	14.6969i	0.882258	+	1.08054i
$186$		0			0
$187$	−16.9706			−1.24101
$188$	−12.7279	+	7.34847i	−0.928279	+	0.535942i
$189$		0			0
$190$	1.75736	+	10.8126i	0.127492	+	0.784426i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$		−	24.4949i		−	1.76318i	−0.472015	−	0.881591i	$-0.656473\pi$
$193$		−	24.4949i		−	1.76318i	0.472015	−	0.881591i	$-0.343527\pi$
$194$	−6.00000	−	3.46410i	−0.430775	−	0.248708i
$195$		0			0
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	5.65685			0.403034			0.201517	−	0.979485i	$-0.435413\pi$
$197$	5.65685			0.403034			0.201517	+	0.979485i	$0.435413\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	−2.82843	+	13.8564i	−0.200000	+	0.979796i
$201$		0			0
$202$	16.9706	+	9.79796i	1.19404	+	0.689382i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−9.00000	−	5.19615i	−0.627060	−	0.362033i
$207$		0			0
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$		−	24.2487i		−	1.66935i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$		−	24.2487i		−	1.66935i	0.550743	−	0.834675i	$-0.314345\pi$
$212$	5.65685	+	9.79796i	0.388514	+	0.672927i
$213$		0			0
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$	−6.00000	−	7.34847i	−0.409197	−	0.501161i
$216$		0			0
$217$			9.79796i			0.665129i
$218$	4.24264	+	2.44949i	0.287348	+	0.165900i
$219$		0			0
$220$	−14.4853	−	5.49333i	−0.976597	−	0.370360i
$221$		0			0
$222$		0			0
$223$			22.0454i			1.47627i	0.674653	+	0.738135i	$0.264293\pi$
$223$			22.0454i			1.47627i	−0.674653	+	0.738135i	$0.735707\pi$
$224$	12.0000	−	6.92820i	0.801784	−	0.462910i
$225$		0			0
$226$		0			0
$227$	1.41421			0.0938647			0.0469323	−	0.998898i	$-0.485055\pi$
$227$	1.41421			0.0938647			0.0469323	+	0.998898i	$0.485055\pi$
$228$		0			0
$229$			27.7128i			1.83131i	0.401960	+	0.915657i	$0.368329\pi$
$229$			27.7128i			1.83131i	−0.401960	+	0.915657i	$0.631671\pi$
$230$	1.24264	+	7.64564i	0.0819373	+	0.504139i
$231$		0			0
$232$		0			0
$233$		−	14.6969i		−	0.962828i	−0.876493	−	0.481414i	$-0.840123\pi$
$233$		−	14.6969i		−	0.962828i	0.876493	−	0.481414i	$-0.159877\pi$
$234$		0			0
$235$	−12.7279	+	10.3923i	−0.830278	+	0.677919i
$236$	18.0000	−	10.3923i	1.17170	−	0.676481i
$237$		0			0
$238$	8.48528	−	14.6969i	0.550019	−	0.952661i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$	0.707107	−	1.22474i	0.0454545	−	0.0787296i
$243$		0			0
$244$	6.00000	−	3.46410i	0.384111	−	0.221766i
$245$	−1.41421	−	1.73205i	−0.0903508	−	0.110657i
$246$		0			0
$247$		0			0
$248$	11.3137			0.718421
$249$		0			0
$250$	−0.636039	+	15.7986i	−0.0402266	+	0.999191i
$251$		−	10.3923i		−	0.655956i	−0.944685	−	0.327978i	$-0.893633\pi$
$251$		−	10.3923i		−	0.655956i	0.944685	−	0.327978i	$-0.106367\pi$
$252$		0			0
$253$	−8.48528			−0.533465
$254$	21.0000	+	12.1244i	1.31766	+	0.760750i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$			9.79796i			0.611180i	0.952163	+	0.305590i	$0.0988537\pi$
$257$			9.79796i			0.611180i	−0.952163	+	0.305590i	$0.901146\pi$
$258$		0			0
$259$		−	20.7846i		−	1.29149i
$260$		0			0
$261$		0			0
$262$	4.24264	+	2.44949i	0.262111	+	0.151330i
$263$			7.34847i			0.453126i	0.973997	+	0.226563i	$0.0727489\pi$
$263$			7.34847i			0.453126i	−0.973997	+	0.226563i	$0.927251\pi$
$264$		0			0
$265$	8.00000	+	9.79796i	0.491436	+	0.601884i
$266$	6.00000	−	10.3923i	0.367884	−	0.637193i
$267$		0			0
$268$	4.24264	+	7.34847i	0.259161	+	0.448879i
$269$			10.3923i			0.633630i	0.948487	+	0.316815i	$0.102613\pi$
$269$			10.3923i			0.633630i	−0.948487	+	0.316815i	$0.897387\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−16.9706	−	9.79796i	−1.02899	−	0.594089i
$273$		0			0
$274$	12.0000	+	6.92820i	0.724947	+	0.418548i
$275$	−16.9706	−	3.46410i	−1.02336	−	0.208893i
$276$		0			0
$277$	25.4558			1.52949			0.764747	−	0.644331i	$-0.222864\pi$
$277$	25.4558			1.52949			0.764747	+	0.644331i	$0.222864\pi$
$278$	−12.7279	−	7.34847i	−0.763370	−	0.440732i
$279$		0			0
$280$	12.0000	−	9.79796i	0.717137	−	0.585540i
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	−21.2132			−1.26099			−0.630497	−	0.776192i	$-0.717149\pi$
$283$	−21.2132			−1.26099			−0.630497	+	0.776192i	$0.717149\pi$
$284$	−12.0000	−	20.7846i	−0.712069	−	1.23334i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−7.00000			−0.411765
$290$		0			0
$291$		0			0
$292$	−8.48528	+	4.89898i	−0.496564	+	0.286691i
$293$	19.7990			1.15667			0.578335	−	0.815800i	$-0.303703\pi$
$293$	19.7990			1.15667			0.578335	+	0.815800i	$0.303703\pi$
$294$		0			0
$295$	18.0000	−	14.6969i	1.04800	−	0.855689i
$296$	−24.0000			−1.39497
$297$		0			0
$298$	−21.2132	−	12.2474i	−1.22885	−	0.709476i
$299$		0			0
$300$		0			0
$301$			10.3923i			0.599002i
$302$	11.3137	−	19.5959i	0.651031	−	1.12762i
$303$		0			0
$304$	−12.0000	−	6.92820i	−0.688247	−	0.397360i
$305$	6.00000	−	4.89898i	0.343559	−	0.280515i
$306$		0			0
$307$	29.6985			1.69498			0.847491	−	0.530810i	$-0.178112\pi$
$307$	29.6985			1.69498			0.847491	+	0.530810i	$0.178112\pi$
$308$	8.48528	+	14.6969i	0.483494	+	0.837436i
$309$		0			0
$310$	12.4853	−	2.02922i	0.709116	−	0.115252i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$		−	9.79796i		−	0.553813i	−0.960897	−	0.276907i	$-0.910691\pi$
$313$		−	9.79796i		−	0.553813i	0.960897	−	0.276907i	$-0.0893093\pi$
$314$	−6.00000	+	10.3923i	−0.338600	+	0.586472i
$315$		0			0
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	28.2843			1.58860			0.794301	−	0.607524i	$-0.207837\pi$
$317$	28.2843			1.58860			0.794301	+	0.607524i	$0.207837\pi$
$318$		0			0
$319$		0			0
$320$	−11.3137	−	13.8564i	−0.632456	−	0.774597i
$321$		0			0
$322$	4.24264	−	7.34847i	0.236433	−	0.409514i
$323$	−16.9706			−0.944267
$324$		0			0
$325$		0			0
$326$	−15.0000	+	25.9808i	−0.830773	+	1.43894i
$327$		0			0
$328$		0			0
$329$	18.0000			0.992372
$330$		0			0
$331$			31.1769i			1.71364i	0.515617	+	0.856819i	$0.327563\pi$
$331$			31.1769i			1.71364i	−0.515617	+	0.856819i	$0.672437\pi$
$332$	−9.89949	−	17.1464i	−0.543305	−	0.941033i
$333$		0			0
$334$	−15.0000	−	8.66025i	−0.820763	−	0.473868i
$335$	6.00000	+	7.34847i	0.327815	+	0.401490i
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	9.19239	−	15.9217i	0.500000	−	0.866025i
$339$		0			0
$340$	−20.4853	−	7.76874i	−1.11097	−	0.421319i
$341$			13.8564i			0.750366i
$342$		0			0
$343$			19.5959i			1.05808i
$344$	12.0000			0.646997
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	−15.5563			−0.835109			−0.417554	−	0.908652i	$-0.637113\pi$
$347$	−15.5563			−0.835109			−0.417554	+	0.908652i	$0.637113\pi$
$348$		0			0
$349$		−	13.8564i		−	0.741716i	−0.928689	−	0.370858i	$-0.879064\pi$
$349$		−	13.8564i		−	0.741716i	0.928689	−	0.370858i	$-0.120936\pi$
$350$	11.4853	−	12.9649i	0.613914	−	0.693002i
$351$		0			0
$352$	16.9706	−	9.79796i	0.904534	−	0.522233i
$353$		−	29.3939i		−	1.56448i	−0.622978	−	0.782239i	$-0.714078\pi$
$353$		−	29.3939i		−	1.56448i	0.622978	−	0.782239i	$-0.285922\pi$
$354$		0			0
$355$	−16.9706	−	20.7846i	−0.900704	−	1.10313i
$356$	6.00000	+	10.3923i	0.317999	+	0.550791i
$357$		0			0
$358$	−4.24264	−	2.44949i	−0.224231	−	0.129460i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$	16.9706	+	9.79796i	0.891953	+	0.514969i
$363$		0			0
$364$		0			0
$365$	−8.48528	+	6.92820i	−0.444140	+	0.362639i
$366$		0			0
$367$			12.2474i			0.639312i	0.947534	+	0.319656i	$0.103567\pi$
$367$			12.2474i			0.639312i	−0.947534	+	0.319656i	$0.896433\pi$
$368$	−8.48528	−	4.89898i	−0.442326	−	0.255377i
$369$		0			0
$370$	−26.4853	+	4.30463i	−1.37690	+	0.223787i
$371$		−	13.8564i		−	0.719389i
$372$		0			0
$373$	−8.48528			−0.439351			−0.219676	−	0.975573i	$-0.570500\pi$
$373$	−8.48528			−0.439351			−0.219676	+	0.975573i	$0.570500\pi$
$374$	12.0000	−	20.7846i	0.620505	−	1.07475i
$375$		0			0
$376$		−	20.7846i		−	1.07188i
$377$		0			0
$378$		0			0
$379$			24.2487i			1.24557i	0.782392	+	0.622786i	$0.213999\pi$
$379$			24.2487i			1.24557i	−0.782392	+	0.622786i	$0.786001\pi$
$380$	−14.4853	−	5.49333i	−0.743079	−	0.281802i
$381$		0			0
$382$	16.9706	−	29.3939i	0.868290	−	1.50392i
$383$			26.9444i			1.37679i	0.725334	+	0.688397i	$0.241685\pi$
$383$			26.9444i			1.37679i	−0.725334	+	0.688397i	$0.758315\pi$
$384$		0			0
$385$	12.0000	+	14.6969i	0.611577	+	0.749025i
$386$	30.0000	+	17.3205i	1.52696	+	0.881591i
$387$		0			0
$388$	8.48528	−	4.89898i	0.430775	−	0.248708i
$389$			3.46410i			0.175637i	0.996136	+	0.0878185i	$0.0279895\pi$
$389$			3.46410i			0.175637i	−0.996136	+	0.0878185i	$0.972010\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	2.82843			0.142857
$393$		0			0
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	5.65685	+	6.92820i	0.284627	+	0.348596i
$396$		0			0
$397$	−16.9706			−0.851728			−0.425864	−	0.904787i	$-0.640030\pi$
$397$	−16.9706			−0.851728			−0.425864	+	0.904787i	$0.640030\pi$
$398$	−2.82843	+	4.89898i	−0.141776	+	0.245564i
$399$		0			0
$400$	−14.9706	−	13.2621i	−0.748528	−	0.663103i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$		0			0
$403$		0			0
$404$	−24.0000	+	13.8564i	−1.19404	+	0.689382i
$405$		0			0
$406$		0			0
$407$		−	29.3939i		−	1.45700i
$408$		0			0
$409$	32.0000			1.58230			0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000			1.58230			0.791149	+	0.611623i	$0.209483\pi$
$410$		0			0
$411$		0			0
$412$	12.7279	−	7.34847i	0.627060	−	0.362033i
$413$	−25.4558			−1.25260
$414$		0			0
$415$	−14.0000	−	17.1464i	−0.687233	−	0.841685i
$416$		0			0
$417$		0			0
$418$	8.48528	−	14.6969i	0.415029	−	0.718851i
$419$		−	10.3923i		−	0.507697i	−0.967244	−	0.253849i	$-0.918303\pi$
$419$		−	10.3923i		−	0.507697i	0.967244	−	0.253849i	$-0.0816965\pi$
$420$		0			0
$421$			24.2487i			1.18181i	0.806741	+	0.590905i	$0.201229\pi$
$421$			24.2487i			1.18181i	−0.806741	+	0.590905i	$0.798771\pi$
$422$	29.6985	+	17.1464i	1.44570	+	0.834675i
$423$		0			0
$424$	−16.0000			−0.777029
$425$	−24.0000	−	4.89898i	−1.16417	−	0.237635i
$426$		0			0
$427$	−8.48528			−0.410632
$428$	1.41421	+	2.44949i	0.0683586	+	0.118401i
$429$		0			0
$430$	13.2426	−	2.15232i	0.638617	−	0.103794i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$			4.89898i			0.235430i	0.993047	+	0.117715i	$0.0375569\pi$
$433$			4.89898i			0.235430i	−0.993047	+	0.117715i	$0.962443\pi$
$434$	−12.0000	−	6.92820i	−0.576018	−	0.332564i
$435$		0			0
$436$	−6.00000	+	3.46410i	−0.287348	+	0.165900i
$437$	−8.48528			−0.405906
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	16.9706	−	13.8564i	0.809040	−	0.660578i
$441$		0			0
$442$		0			0
$443$	−1.41421			−0.0671913			−0.0335957	−	0.999436i	$-0.510696\pi$
$443$	−1.41421			−0.0671913			−0.0335957	+	0.999436i	$0.510696\pi$
$444$		0			0
$445$	8.48528	+	10.3923i	0.402241	+	0.492642i
$446$	−27.0000	−	15.5885i	−1.27849	−	0.738135i
$447$		0			0
$448$			19.5959i			0.925820i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.00000	+	1.73205i	−0.0469323	+	0.0812892i
$455$		0			0
$456$		0			0
$457$		−	19.5959i		−	0.916658i	−0.888783	−	0.458329i	$-0.848448\pi$
$457$		−	19.5959i		−	0.916658i	0.888783	−	0.458329i	$-0.151552\pi$
$458$	−33.9411	−	19.5959i	−1.58596	−	0.915657i
$459$		0			0
$460$	−10.2426	−	3.88437i	−0.477566	−	0.181110i
$461$			13.8564i			0.645357i	0.946509	+	0.322679i	$0.104583\pi$
$461$			13.8564i			0.645357i	−0.946509	+	0.322679i	$0.895417\pi$
$462$		0			0
$463$			17.1464i			0.796862i	0.917198	+	0.398431i	$0.130445\pi$
$463$			17.1464i			0.796862i	−0.917198	+	0.398431i	$0.869555\pi$
$464$		0			0
$465$		0			0
$466$	18.0000	+	10.3923i	0.833834	+	0.481414i
$467$	7.07107			0.327210			0.163605	−	0.986526i	$-0.447688\pi$
$467$	7.07107			0.327210			0.163605	+	0.986526i	$0.447688\pi$
$468$		0			0
$469$		−	10.3923i		−	0.479872i
$470$	−3.72792	−	22.9369i	−0.171956	−	1.05800i
$471$		0			0
$472$			29.3939i			1.35296i
$473$			14.6969i			0.675766i
$474$		0			0
$475$	−16.9706	−	3.46410i	−0.778663	−	0.158944i
$476$	12.0000	+	20.7846i	0.550019	+	0.952661i
$477$		0			0
$478$	−8.48528	+	14.6969i	−0.388108	+	0.672222i
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$		0			0
$482$	−2.82843	+	4.89898i	−0.128831	+	0.223142i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	8.48528	−	6.92820i	0.385297	−	0.314594i
$486$		0			0
$487$		−	7.34847i		−	0.332991i	−0.986042	−	0.166495i	$-0.946755\pi$
$487$		−	7.34847i		−	0.332991i	0.986042	−	0.166495i	$-0.0532451\pi$
$488$			9.79796i			0.443533i
$489$		0			0
$490$	3.12132	−	0.507306i	0.141007	−	0.0229177i
$491$			24.2487i			1.09433i	0.837025	+	0.547165i	$0.184293\pi$
$491$			24.2487i			1.09433i	−0.837025	+	0.547165i	$0.815707\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−8.00000	+	13.8564i	−0.359211	+	0.622171i
$497$			29.3939i			1.31850i
$498$		0			0
$499$		−	17.3205i		−	0.775372i	−0.921791	−	0.387686i	$-0.873274\pi$
$499$		−	17.3205i		−	0.775372i	0.921791	−	0.387686i	$-0.126726\pi$
$500$	−18.8995	−	11.9503i	−0.845211	−	0.534433i
$501$		0			0
$502$	12.7279	+	7.34847i	0.568075	+	0.327978i
$503$			12.2474i			0.546087i	0.962002	+	0.273043i	$0.0880303\pi$
$503$			12.2474i			0.546087i	−0.962002	+	0.273043i	$0.911970\pi$
$504$		0			0
$505$	−24.0000	+	19.5959i	−1.06799	+	0.872007i
$506$	6.00000	−	10.3923i	0.266733	−	0.461994i
$507$		0			0
$508$	−29.6985	+	17.1464i	−1.31766	+	0.760750i
$509$		−	27.7128i		−	1.22835i	−0.789170	−	0.614174i	$-0.789489\pi$
$509$		−	27.7128i		−	1.22835i	0.789170	−	0.614174i	$-0.210511\pi$
$510$		0			0
$511$	12.0000			0.530849
$512$	22.6274			1.00000
$513$		0			0
$514$	−12.0000	−	6.92820i	−0.529297	−	0.305590i
$515$	12.7279	−	10.3923i	0.560859	−	0.457940i
$516$		0			0
$517$	25.4558			1.11955
$518$	25.4558	+	14.6969i	1.11847	+	0.645746i
$519$		0			0
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	12.7279			0.556553			0.278277	−	0.960501i	$-0.410237\pi$
$523$	12.7279			0.556553			0.278277	+	0.960501i	$0.410237\pi$
$524$	−6.00000	+	3.46410i	−0.262111	+	0.151330i
$525$		0			0
$526$	−9.00000	−	5.19615i	−0.392419	−	0.226563i
$527$			19.5959i			0.853612i
$528$		0			0
$529$	17.0000			0.739130
$530$	−17.6569	+	2.86976i	−0.766965	+	0.124654i
$531$		0			0
$532$	8.48528	+	14.6969i	0.367884	+	0.637193i
$533$		0			0
$534$		0			0
$535$	2.00000	+	2.44949i	0.0864675	+	0.105901i
$536$	−12.0000			−0.518321
$537$		0			0
$538$	−12.7279	−	7.34847i	−0.548740	−	0.316815i
$539$			3.46410i			0.149209i
$540$		0			0
$541$		−	41.5692i		−	1.78720i	−0.448864	−	0.893600i	$-0.648171\pi$
$541$		−	41.5692i		−	1.78720i	0.448864	−	0.893600i	$-0.351829\pi$
$542$	−14.1421	+	24.4949i	−0.607457	+	1.05215i
$543$		0			0
$544$	24.0000	−	13.8564i	1.02899	−	0.594089i
$545$	−6.00000	+	4.89898i	−0.257012	+	0.209849i
$546$		0			0
$547$	4.24264			0.181402			0.0907011	−	0.995878i	$-0.471089\pi$
$547$	4.24264			0.181402			0.0907011	+	0.995878i	$0.471089\pi$
$548$	−16.9706	+	9.79796i	−0.724947	+	0.418548i
$549$		0			0
$550$	16.2426	−	18.3351i	0.692589	−	0.781812i
$551$		0			0
$552$		0			0
$553$		−	9.79796i		−	0.416652i
$554$	−18.0000	+	31.1769i	−0.764747	+	1.32458i
$555$		0			0
$556$	18.0000	−	10.3923i	0.763370	−	0.440732i
$557$	14.1421			0.599222			0.299611	−	0.954062i	$-0.403143\pi$
$557$	14.1421			0.599222			0.299611	+	0.954062i	$0.403143\pi$
$558$		0			0
$559$		0			0
$560$	3.51472	+	21.6251i	0.148524	+	0.913829i
$561$		0			0
$562$	−8.48528	+	14.6969i	−0.357930	+	0.619953i
$563$	41.0122			1.72846			0.864229	−	0.503099i	$-0.167807\pi$
$563$	41.0122			1.72846			0.864229	+	0.503099i	$0.167807\pi$
$564$		0			0
$565$		0			0
$566$	15.0000	−	25.9808i	0.630497	−	1.09205i
$567$		0			0
$568$	33.9411			1.42414
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$		−	3.46410i		−	0.144968i	−0.997370	−	0.0724841i	$-0.976907\pi$
$571$		−	3.46410i		−	0.144968i	0.997370	−	0.0724841i	$-0.0230926\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000	−	2.44949i	−0.500435	−	0.102151i
$576$		0			0
$577$			29.3939i			1.22368i	0.790980	+	0.611842i	$0.209571\pi$
$577$			29.3939i			1.22368i	−0.790980	+	0.611842i	$0.790429\pi$
$578$	4.94975	−	8.57321i	0.205882	−	0.356599i
$579$		0			0
$580$		0			0
$581$			24.2487i			1.00601i
$582$		0			0
$583$		−	19.5959i		−	0.811580i
$584$		−	13.8564i		−	0.573382i
$585$		0			0
$586$	−14.0000	+	24.2487i	−0.578335	+	1.00171i
$587$	−9.89949			−0.408596			−0.204298	−	0.978909i	$-0.565491\pi$
$587$	−9.89949			−0.408596			−0.204298	+	0.978909i	$0.565491\pi$
$588$		0			0
$589$			13.8564i			0.570943i
$590$	5.27208	+	32.4377i	0.217048	+	1.33544i
$591$		0			0
$592$	16.9706	−	29.3939i	0.697486	−	1.20808i
$593$			9.79796i			0.402354i	0.979555	+	0.201177i	$0.0644766\pi$
$593$			9.79796i			0.402354i	−0.979555	+	0.201177i	$0.935523\pi$
$594$		0			0
$595$	16.9706	+	20.7846i	0.695725	+	0.852086i
$596$	30.0000	−	17.3205i	1.22885	−	0.709476i
$597$		0			0
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	−12.7279	−	7.34847i	−0.518751	−	0.299501i
$603$		0			0
$604$	16.0000	+	27.7128i	0.651031	+	1.12762i
$605$	1.41421	+	1.73205i	0.0574960	+	0.0704179i
$606$		0			0
$607$			7.34847i			0.298265i	0.988817	+	0.149133i	$0.0476481\pi$
$607$			7.34847i			0.298265i	−0.988817	+	0.149133i	$0.952352\pi$
$608$	16.9706	−	9.79796i	0.688247	−	0.397360i
$609$		0			0
$610$	1.75736	+	10.8126i	0.0711534	+	0.437788i
$611$		0			0
$612$		0			0
$613$	−33.9411			−1.37087			−0.685435	−	0.728134i	$-0.740388\pi$
$613$	−33.9411			−1.37087			−0.685435	+	0.728134i	$0.740388\pi$
$614$	−21.0000	+	36.3731i	−0.847491	+	1.46790i
$615$		0			0
$616$	−24.0000			−0.966988
$617$		−	34.2929i		−	1.38058i	−0.723534	−	0.690289i	$-0.757483\pi$
$617$		−	34.2929i		−	1.38058i	0.723534	−	0.690289i	$-0.242517\pi$
$618$		0			0
$619$		−	10.3923i		−	0.417702i	−0.977947	−	0.208851i	$-0.933028\pi$
$619$		−	10.3923i		−	0.417702i	0.977947	−	0.208851i	$-0.0669724\pi$
$620$	−6.34315	+	16.7262i	−0.254747	+	0.671739i
$621$		0			0
$622$	−16.9706	+	29.3939i	−0.680458	+	1.17859i
$623$		−	14.6969i		−	0.588820i
$624$		0			0
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	12.0000	+	6.92820i	0.479616	+	0.276907i
$627$		0			0
$628$	−8.48528	−	14.6969i	−0.338600	−	0.586472i
$629$		−	41.5692i		−	1.65747i
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	−11.3137			−0.450035
$633$		0			0
$634$	−20.0000	+	34.6410i	−0.794301	+	1.37577i
$635$	−29.6985	+	24.2487i	−1.17855	+	0.962281i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	24.9706	−	4.05845i	0.987048	−	0.160424i
$641$	−12.0000			−0.473972			−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000			−0.473972			−0.236986	+	0.971513i	$0.576159\pi$
$642$		0			0
$643$	29.6985			1.17119			0.585597	−	0.810602i	$-0.300860\pi$
$643$	29.6985			1.17119			0.585597	+	0.810602i	$0.300860\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$		−	12.2474i		−	0.481497i	−0.970588	−	0.240748i	$-0.922607\pi$
$647$		−	12.2474i		−	0.481497i	0.970588	−	0.240748i	$-0.0773929\pi$
$648$		0			0
$649$	−36.0000			−1.41312
$650$		0			0
$651$		0			0
$652$	−21.2132	−	36.7423i	−0.830773	−	1.43894i
$653$	−11.3137			−0.442740			−0.221370	−	0.975190i	$-0.571053\pi$
$653$	−11.3137			−0.442740			−0.221370	+	0.975190i	$0.571053\pi$
$654$		0			0
$655$	−6.00000	+	4.89898i	−0.234439	+	0.191419i
$656$		0			0
$657$		0			0
$658$	−12.7279	+	22.0454i	−0.496186	+	0.859419i
$659$		−	24.2487i		−	0.944596i	−0.881439	−	0.472298i	$-0.843425\pi$
$659$		−	24.2487i		−	0.944596i	0.881439	−	0.472298i	$-0.156575\pi$
$660$		0			0
$661$		−	10.3923i		−	0.404214i	−0.979363	−	0.202107i	$-0.935221\pi$
$661$		−	10.3923i		−	0.404214i	0.979363	−	0.202107i	$-0.0647788\pi$
$662$	−38.1838	−	22.0454i	−1.48405	−	0.856819i
$663$		0			0
$664$	28.0000			1.08661
$665$	12.0000	+	14.6969i	0.465340	+	0.569923i
$666$		0			0
$667$		0			0
$668$	21.2132	−	12.2474i	0.820763	−	0.473868i
$669$		0			0
$670$	−13.2426	+	2.15232i	−0.511608	+	0.0831513i
$671$	−12.0000			−0.463255
$672$		0			0
$673$		−	34.2929i		−	1.32189i	−0.750433	−	0.660946i	$-0.770155\pi$
$673$		−	34.2929i		−	1.32189i	0.750433	−	0.660946i	$-0.229845\pi$
$674$		0			0
$675$		0			0
$676$	13.0000	+	22.5167i	0.500000	+	0.866025i
$677$	−22.6274			−0.869642			−0.434821	−	0.900517i	$-0.643188\pi$
$677$	−22.6274			−0.869642			−0.434821	+	0.900517i	$0.643188\pi$
$678$		0			0
$679$	−12.0000			−0.460518
$680$	24.0000	−	19.5959i	0.920358	−	0.751469i
$681$		0			0
$682$	−16.9706	−	9.79796i	−0.649836	−	0.375183i
$683$	−15.5563			−0.595247			−0.297624	−	0.954683i	$-0.596194\pi$
$683$	−15.5563			−0.595247			−0.297624	+	0.954683i	$0.596194\pi$
$684$		0			0
$685$	−16.9706	+	13.8564i	−0.648412	+	0.529426i
$686$	−24.0000	−	13.8564i	−0.916324	−	0.529040i
$687$		0			0
$688$	−8.48528	+	14.6969i	−0.323498	+	0.560316i
$689$		0			0
$690$		0			0
$691$			3.46410i			0.131781i	0.997827	+	0.0658903i	$0.0209887\pi$
$691$			3.46410i			0.131781i	−0.997827	+	0.0658903i	$0.979011\pi$
$692$	2.82843	+	4.89898i	0.107521	+	0.186231i
$693$		0			0
$694$	11.0000	−	19.0526i	0.417554	−	0.723225i
$695$	18.0000	−	14.6969i	0.682779	−	0.557487i
$696$		0			0
$697$		0			0
$698$	16.9706	+	9.79796i	0.642345	+	0.370858i
$699$		0			0
$700$	7.75736	+	23.2341i	0.293201	+	0.878166i
$701$		−	24.2487i		−	0.915861i	−0.888988	−	0.457931i	$-0.848591\pi$
$701$		−	24.2487i		−	0.915861i	0.888988	−	0.457931i	$-0.151409\pi$
$702$		0			0
$703$		−	29.3939i		−	1.10861i
$704$			27.7128i			1.04447i
$705$		0			0
$706$	36.0000	+	20.7846i	1.35488	+	0.782239i
$707$	33.9411			1.27649
$708$		0			0
$709$		−	41.5692i		−	1.56116i	−0.625053	−	0.780582i	$-0.714923\pi$
$709$		−	41.5692i		−	1.56116i	0.625053	−	0.780582i	$-0.285077\pi$
$710$	37.4558	−	6.08767i	1.40569	−	0.228466i
$711$		0			0
$712$	−16.9706			−0.635999
$713$			9.79796i			0.366936i
$714$		0			0
$715$		0			0
$716$	6.00000	−	3.46410i	0.224231	−	0.129460i
$717$		0			0
$718$	16.9706	−	29.3939i	0.633336	−	1.09697i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	−18.0000			−0.670355
$722$	−4.94975	+	8.57321i	−0.184211	+	0.319062i
$723$		0			0
$724$	−24.0000	+	13.8564i	−0.891953	+	0.514969i
$725$		0			0
$726$		0			0
$727$		−	46.5403i		−	1.72608i	−0.505132	−	0.863042i	$-0.668556\pi$
$727$		−	46.5403i		−	1.72608i	0.505132	−	0.863042i	$-0.331444\pi$
$728$		0			0
$729$		0			0
$730$	−2.48528	−	15.2913i	−0.0919844	−	0.565956i
$731$			20.7846i			0.768747i
$732$		0			0
$733$	42.4264			1.56706			0.783528	−	0.621357i	$-0.213418\pi$
$733$	42.4264			1.56706			0.783528	+	0.621357i	$0.213418\pi$
$734$	−15.0000	−	8.66025i	−0.553660	−	0.319656i
$735$		0			0
$736$	12.0000	−	6.92820i	0.442326	−	0.255377i
$737$		−	14.6969i		−	0.541369i
$738$		0			0
$739$		−	3.46410i		−	0.127429i	−0.997968	−	0.0637145i	$-0.979705\pi$
$739$		−	3.46410i		−	0.127429i	0.997968	−	0.0637145i	$-0.0202947\pi$
$740$	13.4558	−	35.4815i	0.494647	−	1.30433i
$741$		0			0
$742$	16.9706	+	9.79796i	0.623009	+	0.359694i
$743$		−	51.4393i		−	1.88712i	−0.331195	−	0.943562i	$-0.607452\pi$
$743$		−	51.4393i		−	1.88712i	0.331195	−	0.943562i	$-0.392548\pi$
$744$		0			0
$745$	30.0000	−	24.4949i	1.09911	−	0.897424i
$746$	6.00000	−	10.3923i	0.219676	−	0.380489i
$747$		0			0
$748$	16.9706	+	29.3939i	0.620505	+	1.07475i
$749$		−	3.46410i		−	0.126576i
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$	25.4558	+	14.6969i	0.928279	+	0.535942i
$753$		0			0
$754$		0			0
$755$	22.6274	+	27.7128i	0.823496	+	1.00857i
$756$		0			0
$757$	−25.4558			−0.925208			−0.462604	−	0.886565i	$-0.653085\pi$
$757$	−25.4558			−0.925208			−0.462604	+	0.886565i	$0.653085\pi$
$758$	−29.6985	−	17.1464i	−1.07870	−	0.622786i
$759$		0			0
$760$	16.9706	−	13.8564i	0.615587	−	0.502625i
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	8.48528			0.307188
$764$	24.0000	+	41.5692i	0.868290	+	1.50392i
$765$		0			0
$766$	−33.0000	−	19.0526i	−1.19234	−	0.688397i
$767$		0			0
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$	−26.4853	+	4.30463i	−0.954463	+	0.155128i
$771$		0			0
$772$	−42.4264	+	24.4949i	−1.52696	+	0.881591i
$773$	−28.2843			−1.01731			−0.508657	−	0.860969i	$-0.669858\pi$
$773$	−28.2843			−1.01731			−0.508657	+	0.860969i	$0.669858\pi$
$774$		0			0
$775$	−4.00000	+	19.5959i	−0.143684	+	0.703906i
$776$			13.8564i			0.497416i
$777$		0			0
$778$	−4.24264	−	2.44949i	−0.152106	−	0.0878185i
$779$		0			0
$780$		0			0
$781$			41.5692i			1.48746i
$782$	8.48528	−	14.6969i	0.303433	−	0.525561i
$783$		0			0
$784$	−2.00000	+	3.46410i	−0.0714286	+	0.123718i
$785$	−12.0000	−	14.6969i	−0.428298	−	0.524556i
$786$		0			0
$787$	−21.2132			−0.756169			−0.378085	−	0.925771i	$-0.623417\pi$
$787$	−21.2132			−0.756169			−0.378085	+	0.925771i	$0.623417\pi$
$788$	−5.65685	−	9.79796i	−0.201517	−	0.349038i
$789$		0			0
$790$	−12.4853	+	2.02922i	−0.444206	+	0.0721965i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	12.0000	−	20.7846i	0.425864	−	0.737618i
$795$		0			0
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−39.5980			−1.40263			−0.701316	−	0.712850i	$-0.747404\pi$
$797$	−39.5980			−1.40263			−0.701316	+	0.712850i	$0.747404\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$	26.8284	−	8.95743i	0.948528	−	0.316693i
$801$		0			0
$802$	−12.7279	+	22.0454i	−0.449439	+	0.778450i
$803$	16.9706			0.598878
$804$		0			0
$805$	8.48528	+	10.3923i	0.299067	+	0.366281i
$806$		0			0
$807$		0			0
$808$		−	39.1918i		−	1.37876i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$		0			0
$814$	36.0000	+	20.7846i	1.26180	+	0.728500i
$815$	−30.0000	−	36.7423i	−1.05085	−	1.28703i
$816$		0			0
$817$			14.6969i			0.514181i
$818$	−22.6274	+	39.1918i	−0.791149	+	1.37031i
$819$		0			0
$820$		0			0
$821$		−	31.1769i		−	1.08808i	−0.839059	−	0.544041i	$-0.816894\pi$
$821$		−	31.1769i		−	1.08808i	0.839059	−	0.544041i	$-0.183106\pi$
$822$		0			0
$823$			26.9444i			0.939222i	0.882873	+	0.469611i	$0.155606\pi$
$823$			26.9444i			0.939222i	−0.882873	+	0.469611i	$0.844394\pi$
$824$			20.7846i			0.724066i
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	35.3553			1.22943			0.614713	−	0.788751i	$-0.289272\pi$
$827$	35.3553			1.22943			0.614713	+	0.788751i	$0.289272\pi$
$828$		0			0
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$	30.8995	−	5.02207i	1.07254	−	0.174319i
$831$		0			0
$832$		0			0
$833$			4.89898i			0.169740i
$834$		0			0
$835$	21.2132	−	17.3205i	0.734113	−	0.599401i
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$		0			0
$838$	12.7279	+	7.34847i	0.439679	+	0.253849i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−29.6985	−	17.1464i	−1.02348	−	0.590905i
$843$		0			0
$844$	−42.0000	+	24.2487i	−1.44570	+	0.834675i
$845$	18.3848	+	22.5167i	0.632456	+	0.774597i
$846$		0			0
$847$		−	2.44949i		−	0.0841655i
$848$	11.3137	−	19.5959i	0.388514	−	0.672927i
$849$		0			0
$850$	22.9706	−	25.9298i	0.787884	−	0.889384i
$851$		−	20.7846i		−	0.712487i
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	6.00000	−	10.3923i	0.205316	−	0.355617i
$855$		0			0
$856$	−4.00000			−0.136717
$857$			39.1918i			1.33877i	0.742917	+	0.669384i	$0.233442\pi$
$857$			39.1918i			1.33877i	−0.742917	+	0.669384i	$0.766558\pi$
$858$		0			0
$859$			3.46410i			0.118194i	0.998252	+	0.0590968i	$0.0188221\pi$
$859$			3.46410i			0.118194i	−0.998252	+	0.0590968i	$0.981178\pi$
$860$	−6.72792	+	17.7408i	−0.229420	+	0.604955i
$861$		0			0
$862$	8.48528	−	14.6969i	0.289010	−	0.500580i
$863$			2.44949i			0.0833816i	0.999131	+	0.0416908i	$0.0132744\pi$
$863$			2.44949i			0.0833816i	−0.999131	+	0.0416908i	$0.986726\pi$
$864$		0			0
$865$	4.00000	+	4.89898i	0.136004	+	0.166570i
$866$	−6.00000	−	3.46410i	−0.203888	−	0.117715i
$867$		0			0
$868$	16.9706	−	9.79796i	0.576018	−	0.332564i
$869$		−	13.8564i		−	0.470046i
$870$		0			0
$871$		0			0
$872$		−	9.79796i		−	0.331801i
$873$		0			0
$874$	6.00000	−	10.3923i	0.202953	−	0.351525i
$875$	12.7279	+	24.2487i	0.430282	+	0.819756i
$876$		0			0
$877$	−8.48528			−0.286528			−0.143264	−	0.989685i	$-0.545760\pi$
$877$	−8.48528			−0.286528			−0.143264	+	0.989685i	$0.545760\pi$
$878$	5.65685	−	9.79796i	0.190910	−	0.330665i
$879$		0			0
$880$	4.97056	+	30.5826i	0.167558	+	1.03094i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	4.24264			0.142776			0.0713881	−	0.997449i	$-0.477257\pi$
$883$	4.24264			0.142776			0.0713881	+	0.997449i	$0.477257\pi$
$884$		0			0
$885$		0			0
$886$	1.00000	−	1.73205i	0.0335957	−	0.0581894i
$887$			26.9444i			0.904704i	0.891839	+	0.452352i	$0.149415\pi$
$887$			26.9444i			0.904704i	−0.891839	+	0.452352i	$0.850585\pi$
$888$		0			0
$889$	42.0000			1.40863
$890$	−18.7279	+	3.04384i	−0.627761	+	0.102030i
$891$		0			0
$892$	38.1838	−	22.0454i	1.27849	−	0.738135i
$893$	25.4558			0.851847
$894$		0			0
$895$	6.00000	−	4.89898i	0.200558	−	0.163755i
$896$	−24.0000	−	13.8564i	−0.801784	−	0.462910i
$897$		0			0
$898$	−8.48528	+	14.6969i	−0.283158	+	0.490443i
$899$		0			0
$900$		0			0
$901$		−	27.7128i		−	0.923248i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.0000	+	19.5959i	−0.797787	+	0.651390i
$906$		0			0
$907$	−4.24264			−0.140875			−0.0704373	−	0.997516i	$-0.522439\pi$
$907$	−4.24264			−0.140875			−0.0704373	+	0.997516i	$0.522439\pi$
$908$	−1.41421	−	2.44949i	−0.0469323	−	0.0812892i
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$			34.2929i			1.13493i
$914$	24.0000	+	13.8564i	0.793849	+	0.458329i
$915$		0			0
$916$	48.0000	−	27.7128i	1.58596	−	0.915657i
$917$	8.48528			0.280209
$918$		0			0
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	12.0000	−	9.79796i	0.395628	−	0.323029i
$921$		0			0
$922$	−16.9706	−	9.79796i	−0.558896	−	0.322679i
$923$		0			0
$924$		0			0
$925$	8.48528	−	41.5692i	0.278994	−	1.36679i
$926$	−21.0000	−	12.1244i	−0.690103	−	0.398431i
$927$		0			0
$928$		0			0
$929$	36.0000			1.18112			0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000			1.18112			0.590561	+	0.806993i	$0.298907\pi$
$930$		0			0
$931$			3.46410i			0.113531i
$932$	−25.4558	+	14.6969i	−0.833834	+	0.481414i
$933$		0			0
$934$	−5.00000	+	8.66025i	−0.163605	+	0.283372i
$935$	24.0000	+	29.3939i	0.784884	+	0.961283i
$936$		0			0
$937$			4.89898i			0.160043i	0.996793	+	0.0800213i	$0.0254988\pi$
$937$			4.89898i			0.160043i	−0.996793	+	0.0800213i	$0.974501\pi$
$938$	12.7279	+	7.34847i	0.415581	+	0.239936i
$939$		0			0
$940$	30.7279	+	11.6531i	1.00223	+	0.380082i
$941$		−	13.8564i		−	0.451706i	−0.974161	−	0.225853i	$-0.927483\pi$
$941$		−	13.8564i		−	0.451706i	0.974161	−	0.225853i	$-0.0725169\pi$
$942$		0			0
$943$		0			0
$944$	−36.0000	−	20.7846i	−1.17170	−	0.676481i
$945$		0			0
$946$	−18.0000	−	10.3923i	−0.585230	−	0.337883i
$947$	−41.0122			−1.33272			−0.666359	−	0.745631i	$-0.732148\pi$
$947$	−41.0122			−1.33272			−0.666359	+	0.745631i	$0.732148\pi$
$948$		0			0
$949$		0			0
$950$	16.2426	−	18.3351i	0.526981	−	0.594870i
$951$		0			0
$952$	−33.9411			−1.10004
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$	33.9411	+	41.5692i	1.09831	+	1.34515i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$	−16.9706	+	29.3939i	−0.548294	+	0.949673i
$959$	24.0000			0.775000
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$	−42.4264	+	34.6410i	−1.36575	+	1.11513i
$966$		0			0
$967$			17.1464i			0.551392i	0.961245	+	0.275696i	$0.0889083\pi$
$967$			17.1464i			0.551392i	−0.961245	+	0.275696i	$0.911092\pi$
$968$	−2.82843			−0.0909091
$969$		0			0
$970$	2.48528	+	15.2913i	0.0797976	+	0.490974i
$971$		−	3.46410i		−	0.111168i	−0.998454	−	0.0555842i	$-0.982298\pi$
$971$		−	3.46410i		−	0.111168i	0.998454	−	0.0555842i	$-0.0177021\pi$
$972$		0			0
$973$	−25.4558			−0.816077
$974$	9.00000	+	5.19615i	0.288379	+	0.166495i
$975$		0			0
$976$	−12.0000	−	6.92820i	−0.384111	−	0.221766i
$977$		−	44.0908i		−	1.41059i	−0.708914	−	0.705295i	$-0.750815\pi$
$977$		−	44.0908i		−	1.41059i	0.708914	−	0.705295i	$-0.249185\pi$
$978$		0			0
$979$		−	20.7846i		−	0.664279i
$980$	−1.58579	+	4.18154i	−0.0506561	+	0.133574i
$981$		0			0
$982$	−29.6985	−	17.1464i	−0.947717	−	0.547165i
$983$			56.3383i			1.79691i	0.439064	+	0.898456i	$0.355310\pi$
$983$			56.3383i			1.79691i	−0.439064	+	0.898456i	$0.644690\pi$
$984$		0			0
$985$	−8.00000	−	9.79796i	−0.254901	−	0.312189i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			10.3923i			0.330456i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−11.3137	−	19.5959i	−0.359211	−	0.622171i
$993$		0			0
$994$	−36.0000	−	20.7846i	−1.14185	−	0.659248i
$995$	−5.65685	−	6.92820i	−0.179334	−	0.219639i
$996$		0			0
$997$	−50.9117			−1.61239			−0.806195	−	0.591650i	$-0.798477\pi$
$997$	−50.9117			−1.61239			−0.806195	+	0.591650i	$0.798477\pi$
$998$	21.2132	+	12.2474i	0.671492	+	0.387686i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.d.b.109.2		4
3.2	odd	2		40.2.f.a.29.3	yes	4
4.3	odd	2		1440.2.d.c.1009.1		4
5.2	odd	4		1800.2.k.m.901.1		4
5.3	odd	4		1800.2.k.m.901.4		4
5.4	even	2	inner	360.2.d.b.109.3		4
8.3	odd	2		1440.2.d.c.1009.4		4
8.5	even	2	inner	360.2.d.b.109.4		4
12.11	even	2		160.2.f.a.49.4		4
15.2	even	4		200.2.d.e.101.4		4
15.8	even	4		200.2.d.e.101.1		4
15.14	odd	2		40.2.f.a.29.2	yes	4
20.3	even	4		7200.2.k.l.3601.1		4
20.7	even	4		7200.2.k.l.3601.3		4
20.19	odd	2		1440.2.d.c.1009.3		4
24.5	odd	2		40.2.f.a.29.1	✓	4
24.11	even	2		160.2.f.a.49.1		4
40.3	even	4		7200.2.k.l.3601.2		4
40.13	odd	4		1800.2.k.m.901.3		4
40.19	odd	2		1440.2.d.c.1009.2		4
40.27	even	4		7200.2.k.l.3601.4		4
40.29	even	2	inner	360.2.d.b.109.1		4
40.37	odd	4		1800.2.k.m.901.2		4
48.5	odd	4		1280.2.c.i.769.3		4
48.11	even	4		1280.2.c.k.769.1		4
48.29	odd	4		1280.2.c.i.769.2		4
48.35	even	4		1280.2.c.k.769.4		4
60.23	odd	4		800.2.d.f.401.3		4
60.47	odd	4		800.2.d.f.401.2		4
60.59	even	2		160.2.f.a.49.2		4
120.29	odd	2		40.2.f.a.29.4	yes	4
120.53	even	4		200.2.d.e.101.2		4
120.59	even	2		160.2.f.a.49.3		4
120.77	even	4		200.2.d.e.101.3		4
120.83	odd	4		800.2.d.f.401.1		4
120.107	odd	4		800.2.d.f.401.4		4
240.29	odd	4		1280.2.c.i.769.4		4
240.53	even	4		6400.2.a.co.1.1		4
240.59	even	4		1280.2.c.k.769.3		4
240.77	even	4		6400.2.a.co.1.2		4
240.83	odd	4		6400.2.a.cm.1.2		4
240.107	odd	4		6400.2.a.cm.1.1		4
240.149	odd	4		1280.2.c.i.769.1		4
240.173	even	4		6400.2.a.co.1.3		4
240.179	even	4		1280.2.c.k.769.2		4
240.197	even	4		6400.2.a.co.1.4		4
240.203	odd	4		6400.2.a.cm.1.4		4
240.227	odd	4		6400.2.a.cm.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.f.a.29.1	✓	4	24.5	odd	2
40.2.f.a.29.2	yes	4	15.14	odd	2
40.2.f.a.29.3	yes	4	3.2	odd	2
40.2.f.a.29.4	yes	4	120.29	odd	2
160.2.f.a.49.1		4	24.11	even	2
160.2.f.a.49.2		4	60.59	even	2
160.2.f.a.49.3		4	120.59	even	2
160.2.f.a.49.4		4	12.11	even	2
200.2.d.e.101.1		4	15.8	even	4
200.2.d.e.101.2		4	120.53	even	4
200.2.d.e.101.3		4	120.77	even	4
200.2.d.e.101.4		4	15.2	even	4
360.2.d.b.109.1		4	40.29	even	2	inner
360.2.d.b.109.2		4	1.1	even	1	trivial
360.2.d.b.109.3		4	5.4	even	2	inner
360.2.d.b.109.4		4	8.5	even	2	inner
800.2.d.f.401.1		4	120.83	odd	4
800.2.d.f.401.2		4	60.47	odd	4
800.2.d.f.401.3		4	60.23	odd	4
800.2.d.f.401.4		4	120.107	odd	4
1280.2.c.i.769.1		4	240.149	odd	4
1280.2.c.i.769.2		4	48.29	odd	4
1280.2.c.i.769.3		4	48.5	odd	4
1280.2.c.i.769.4		4	240.29	odd	4
1280.2.c.k.769.1		4	48.11	even	4
1280.2.c.k.769.2		4	240.179	even	4
1280.2.c.k.769.3		4	240.59	even	4
1280.2.c.k.769.4		4	48.35	even	4
1440.2.d.c.1009.1		4	4.3	odd	2
1440.2.d.c.1009.2		4	40.19	odd	2
1440.2.d.c.1009.3		4	20.19	odd	2
1440.2.d.c.1009.4		4	8.3	odd	2
1800.2.k.m.901.1		4	5.2	odd	4
1800.2.k.m.901.2		4	40.37	odd	4
1800.2.k.m.901.3		4	40.13	odd	4
1800.2.k.m.901.4		4	5.3	odd	4
6400.2.a.cm.1.1		4	240.107	odd	4
6400.2.a.cm.1.2		4	240.83	odd	4
6400.2.a.cm.1.3		4	240.227	odd	4
6400.2.a.cm.1.4		4	240.203	odd	4
6400.2.a.co.1.1		4	240.53	even	4
6400.2.a.co.1.2		4	240.77	even	4
6400.2.a.co.1.3		4	240.173	even	4
6400.2.a.co.1.4		4	240.197	even	4
7200.2.k.l.3601.1		4	20.3	even	4
7200.2.k.l.3601.2		4	40.3	even	4
7200.2.k.l.3601.3		4	20.7	even	4
7200.2.k.l.3601.4		4	40.27	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.41421 - 1.73205i) q^{5} +2.44949i q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.41421 - 1.73205i) q^{5} +2.44949i q^{7} +2.82843 q^{8} +(3.12132 - 0.507306i) q^{10} +3.46410i q^{11} +(-3.00000 - 1.73205i) q^{14} +(-2.00000 + 3.46410i) q^{16} +4.89898i q^{17} +3.46410i q^{19} +(-1.58579 + 4.18154i) q^{20} +(-4.24264 - 2.44949i) q^{22} +2.44949i q^{23} +(-1.00000 + 4.89898i) q^{25} +(4.24264 - 2.44949i) q^{28} +4.00000 q^{31} +(-2.82843 - 4.89898i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(4.24264 - 3.46410i) q^{35} -8.48528 q^{37} +(-4.24264 - 2.44949i) q^{38} +(-4.00000 - 4.89898i) q^{40} +4.24264 q^{43} +(6.00000 - 3.46410i) q^{44} +(-3.00000 - 1.73205i) q^{46} -7.34847i q^{47} +1.00000 q^{49} +(-5.29289 - 4.68885i) q^{50} -5.65685 q^{53} +(6.00000 - 4.89898i) q^{55} +6.92820i q^{56} +10.3923i q^{59} +3.46410i q^{61} +(-2.82843 + 4.89898i) q^{62} +8.00000 q^{64} -4.24264 q^{67} +(8.48528 - 4.89898i) q^{68} +(1.24264 + 7.64564i) q^{70} +12.0000 q^{71} -4.89898i q^{73} +(6.00000 - 10.3923i) q^{74} +(6.00000 - 3.46410i) q^{76} -8.48528 q^{77} -4.00000 q^{79} +(8.82843 - 1.43488i) q^{80} +9.89949 q^{83} +(8.48528 - 6.92820i) q^{85} +(-3.00000 + 5.19615i) q^{86} +9.79796i q^{88} -6.00000 q^{89} +(4.24264 - 2.44949i) q^{92} +(9.00000 + 5.19615i) q^{94} +(6.00000 - 4.89898i) q^{95} +4.89898i q^{97} +(-0.707107 + 1.22474i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} + 4 q^{10} - 12 q^{14} - 8 q^{16} - 12 q^{20} - 4 q^{25} + 16 q^{31} - 24 q^{34} - 16 q^{40} + 24 q^{44} - 12 q^{46} + 4 q^{49} - 24 q^{50} + 24 q^{55} + 32 q^{64} - 12 q^{70} + 48 q^{71} + 24 q^{74} + 24 q^{76} - 16 q^{79} + 24 q^{80} - 12 q^{86} - 24 q^{89} + 36 q^{94} + 24 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^10 - 12 * q^14 - 8 * q^16 - 12 * q^20 - 4 * q^25 + 16 * q^31 - 24 * q^34 - 16 * q^40 + 24 * q^44 - 12 * q^46 + 4 * q^49 - 24 * q^50 + 24 * q^55 + 32 * q^64 - 12 * q^70 + 48 * q^71 + 24 * q^74 + 24 * q^76 - 16 * q^79 + 24 * q^80 - 12 * q^86 - 24 * q^89 + 36 * q^94 + 24 * q^95

Introduction

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