LMFDB - Embedded newform 1792.2.m.d.1345.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (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:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.1
Root			$0.500000 - 2.10607i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.d.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.898966 - 0.898966i) q^{3} +(-0.786578 + 0.786578i) q^{5} -1.00000i q^{7} -1.38372i q^{9} +O(q^{10})$	\(q+(-0.898966 - 0.898966i) q^{3} +(-0.786578 + 0.786578i) q^{5} -1.00000i q^{7} -1.38372i q^{9} +(-2.15894 + 2.15894i) q^{11} +(1.31318 + 1.31318i) q^{13} +1.41421 q^{15} -1.79793 q^{17} +(-0.531306 - 0.531306i) q^{19} +(-0.898966 + 0.898966i) q^{21} -5.95687i q^{23} +3.76259i q^{25} +(-3.94082 + 3.94082i) q^{27} +(5.62636 + 5.62636i) q^{29} -4.34059 q^{31} +3.88163 q^{33} +(0.786578 + 0.786578i) q^{35} +(2.12845 - 2.12845i) q^{37} -2.36101i q^{39} +0.712611i q^{41} +(-2.96951 + 2.96951i) q^{43} +(1.08840 + 1.08840i) q^{45} +2.20207 q^{47} -1.00000 q^{49} +(1.61628 + 1.61628i) q^{51} +(-3.38372 + 3.38372i) q^{53} -3.39635i q^{55} +0.955252i q^{57} +(-2.41549 + 2.41549i) q^{59} +(7.09505 + 7.09505i) q^{61} -1.38372 q^{63} -2.06584 q^{65} +(6.76744 + 6.76744i) q^{67} +(-5.35503 + 5.35503i) q^{69} -1.96788i q^{71} +10.3633i q^{73} +(3.38244 - 3.38244i) q^{75} +(2.15894 + 2.15894i) q^{77} +14.2449 q^{79} +2.93416 q^{81} +(-5.95217 - 5.95217i) q^{83} +(1.41421 - 1.41421i) q^{85} -10.1158i q^{87} +16.9417i q^{89} +(1.31318 - 1.31318i) q^{91} +(3.90205 + 3.90205i) q^{93} +0.835826 q^{95} +17.6796 q^{97} +(2.98737 + 2.98737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^5	$ 8 q + 4 q^{3} + 4 q^{5} - 8 q^{11} - 12 q^{13} + 8 q^{17} + 4 q^{19} + 4 q^{21} - 8 q^{27} + 8 q^{31} - 16 q^{33} - 4 q^{35} + 8 q^{37} - 24 q^{43} - 12 q^{45} + 40 q^{47} - 8 q^{49} + 24 q^{51} - 16 q^{53} - 52 q^{59} + 20 q^{61} - 24 q^{65} + 32 q^{67} - 8 q^{69} - 28 q^{75} + 8 q^{77} + 16 q^{81} - 12 q^{83} - 12 q^{91} + 40 q^{93} + 80 q^{95} + 72 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^11 - 12 * q^13 + 8 * q^17 + 4 * q^19 + 4 * q^21 - 8 * q^27 + 8 * q^31 - 16 * q^33 - 4 * q^35 + 8 * q^37 - 24 * q^43 - 12 * q^45 + 40 * q^47 - 8 * q^49 + 24 * q^51 - 16 * q^53 - 52 * q^59 + 20 * q^61 - 24 * q^65 + 32 * q^67 - 8 * q^69 - 28 * q^75 + 8 * q^77 + 16 * q^81 - 12 * q^83 - 12 * q^91 + 40 * q^93 + 80 * q^95 + 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−0.898966	−	0.898966i	−0.519018	−	0.519018i	0.398256	−	0.917274i	$-0.369616\pi$
$3$	−0.898966	−	0.898966i	−0.519018	−	0.519018i	−0.917274	+	0.398256i	$0.869616\pi$
$4$		0			0
$5$	−0.786578	+	0.786578i	−0.351768	+	0.351768i	−0.860767	−	0.508999i	$-0.830016\pi$
$5$	−0.786578	+	0.786578i	−0.351768	+	0.351768i	0.508999	+	0.860767i	$0.330016\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	1.38372i		−	0.461240i
$10$		0			0
$11$	−2.15894	+	2.15894i	−0.650945	+	0.650945i	−0.953221	−	0.302275i	$-0.902254\pi$
$11$	−2.15894	+	2.15894i	−0.650945	+	0.650945i	0.302275	+	0.953221i	$0.402254\pi$
$12$		0			0
$13$	1.31318	+	1.31318i	0.364211	+	0.364211i	0.865360	−	0.501150i	$-0.167089\pi$
$13$	1.31318	+	1.31318i	0.364211	+	0.364211i	−0.501150	+	0.865360i	$0.667089\pi$
$14$		0			0
$15$	1.41421			0.365148
$16$		0			0
$17$	−1.79793			−0.436063			−0.218031	−	0.975942i	$-0.569964\pi$
$17$	−1.79793			−0.436063			−0.218031	+	0.975942i	$0.569964\pi$
$18$		0			0
$19$	−0.531306	−	0.531306i	−0.121890	−	0.121890i	0.643531	−	0.765420i	$-0.277469\pi$
$19$	−0.531306	−	0.531306i	−0.121890	−	0.121890i	−0.765420	+	0.643531i	$0.777469\pi$
$20$		0			0
$21$	−0.898966	+	0.898966i	−0.196171	+	0.196171i
$22$		0			0
$23$		−	5.95687i		−	1.24209i	−0.783773	−	0.621047i	$-0.786708\pi$
$23$		−	5.95687i		−	1.24209i	0.783773	−	0.621047i	$-0.213292\pi$
$24$		0			0
$25$			3.76259i			0.752518i
$26$		0			0
$27$	−3.94082	+	3.94082i	−0.758410	+	0.758410i
$28$		0			0
$29$	5.62636	+	5.62636i	1.04479	+	1.04479i	0.998949	+	0.0458400i	$0.0145964\pi$
$29$	5.62636	+	5.62636i	1.04479	+	1.04479i	0.0458400	+	0.998949i	$0.485404\pi$
$30$		0			0
$31$	−4.34059			−0.779594			−0.389797	−	0.920901i	$-0.627455\pi$
$31$	−4.34059			−0.779594			−0.389797	+	0.920901i	$0.627455\pi$
$32$		0			0
$33$	3.88163			0.675705
$34$		0			0
$35$	0.786578	+	0.786578i	0.132956	+	0.132956i
$36$		0			0
$37$	2.12845	−	2.12845i	0.349915	−	0.349915i	−0.510163	−	0.860078i	$-0.670415\pi$
$37$	2.12845	−	2.12845i	0.349915	−	0.349915i	0.860078	+	0.510163i	$0.170415\pi$
$38$		0			0
$39$		−	2.36101i		−	0.378064i
$40$		0			0
$41$			0.712611i			0.111291i	0.998451	+	0.0556456i	$0.0177217\pi$
$41$			0.712611i			0.111291i	−0.998451	+	0.0556456i	$0.982278\pi$
$42$		0			0
$43$	−2.96951	+	2.96951i	−0.452845	+	0.452845i	−0.896298	−	0.443453i	$-0.853753\pi$
$43$	−2.96951	+	2.96951i	−0.452845	+	0.452845i	0.443453	+	0.896298i	$0.353753\pi$
$44$		0			0
$45$	1.08840	+	1.08840i	0.162249	+	0.162249i
$46$		0			0
$47$	2.20207			0.321205			0.160602	−	0.987019i	$-0.448656\pi$
$47$	2.20207			0.321205			0.160602	+	0.987019i	$0.448656\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	1.61628	+	1.61628i	0.226325	+	0.226325i
$52$		0			0
$53$	−3.38372	+	3.38372i	−0.464790	+	0.464790i	−0.900222	−	0.435432i	$-0.856596\pi$
$53$	−3.38372	+	3.38372i	−0.464790	+	0.464790i	0.435432	+	0.900222i	$0.356596\pi$
$54$		0			0
$55$		−	3.39635i		−	0.457964i
$56$		0			0
$57$			0.955252i			0.126526i
$58$		0			0
$59$	−2.41549	+	2.41549i	−0.314470	+	0.314470i	−0.846638	−	0.532168i	$-0.821377\pi$
$59$	−2.41549	+	2.41549i	−0.314470	+	0.314470i	0.532168	+	0.846638i	$0.321377\pi$
$60$		0			0
$61$	7.09505	+	7.09505i	0.908429	+	0.908429i	0.996145	−	0.0877169i	$-0.0279571\pi$
$61$	7.09505	+	7.09505i	0.908429	+	0.908429i	−0.0877169	+	0.996145i	$0.527957\pi$
$62$		0			0
$63$	−1.38372			−0.174332
$64$		0			0
$65$	−2.06584			−0.256235
$66$		0			0
$67$	6.76744	+	6.76744i	0.826774	+	0.826774i	0.987069	−	0.160295i	$-0.0512446\pi$
$67$	6.76744	+	6.76744i	0.826774	+	0.826774i	−0.160295	+	0.987069i	$0.551245\pi$
$68$		0			0
$69$	−5.35503	+	5.35503i	−0.644670	+	0.644670i
$70$		0			0
$71$		−	1.96788i		−	0.233545i	−0.993159	−	0.116772i	$-0.962745\pi$
$71$		−	1.96788i		−	0.233545i	0.993159	−	0.116772i	$-0.0372548\pi$
$72$		0			0
$73$			10.3633i			1.21293i	0.795109	+	0.606466i	$0.207414\pi$
$73$			10.3633i			1.21293i	−0.795109	+	0.606466i	$0.792586\pi$
$74$		0			0
$75$	3.38244	−	3.38244i	0.390571	−	0.390571i
$76$		0			0
$77$	2.15894	+	2.15894i	0.246034	+	0.246034i
$78$		0			0
$79$	14.2449			1.60268			0.801340	−	0.598209i	$-0.204121\pi$
$79$	14.2449			1.60268			0.801340	+	0.598209i	$0.204121\pi$
$80$		0			0
$81$	2.93416			0.326018
$82$		0			0
$83$	−5.95217	−	5.95217i	−0.653336	−	0.653336i	0.300459	−	0.953795i	$-0.402860\pi$
$83$	−5.95217	−	5.95217i	−0.653336	−	0.653336i	−0.953795	+	0.300459i	$0.902860\pi$
$84$		0			0
$85$	1.41421	−	1.41421i	0.153393	−	0.153393i
$86$		0			0
$87$		−	10.1158i		−	1.08453i
$88$		0			0
$89$			16.9417i			1.79582i	0.440184	+	0.897908i	$0.354913\pi$
$89$			16.9417i			1.79582i	−0.440184	+	0.897908i	$0.645087\pi$
$90$		0			0
$91$	1.31318	−	1.31318i	0.137659	−	0.137659i
$92$		0			0
$93$	3.90205	+	3.90205i	0.404623	+	0.404623i
$94$		0			0
$95$	0.835826			0.0857540
$96$		0			0
$97$	17.6796			1.79509			0.897544	−	0.440925i	$-0.145350\pi$
$97$	17.6796			1.79509			0.897544	+	0.440925i	$0.145350\pi$
$98$		0			0
$99$	2.98737	+	2.98737i	0.300242	+	0.300242i
$100$		0			0
$101$	−6.66156	+	6.66156i	−0.662850	+	0.662850i	−0.956051	−	0.293201i	$-0.905279\pi$
$101$	−6.66156	+	6.66156i	−0.662850	+	0.662850i	0.293201	+	0.956051i	$0.405279\pi$
$102$		0			0
$103$		−	1.88418i		−	0.185654i	−0.995682	−	0.0928271i	$-0.970410\pi$
$103$		−	1.88418i		−	0.185654i	0.995682	−	0.0928271i	$-0.0295904\pi$
$104$		0			0
$105$		−	1.41421i		−	0.138013i
$106$		0			0
$107$	−8.94909	+	8.94909i	−0.865141	+	0.865141i	−0.991930	−	0.126789i	$-0.959533\pi$
$107$	−8.94909	+	8.94909i	−0.865141	+	0.865141i	0.126789	+	0.991930i	$0.459533\pi$
$108$		0			0
$109$	−4.73210	−	4.73210i	−0.453253	−	0.453253i	0.443180	−	0.896433i	$-0.353850\pi$
$109$	−4.73210	−	4.73210i	−0.453253	−	0.453253i	−0.896433	+	0.443180i	$0.853850\pi$
$110$		0			0
$111$	−3.82680			−0.363224
$112$		0			0
$113$	−7.93416			−0.746383			−0.373192	−	0.927754i	$-0.621737\pi$
$113$	−7.93416			−0.746383			−0.373192	+	0.927754i	$0.621737\pi$
$114$		0			0
$115$	4.68554	+	4.68554i	0.436929	+	0.436929i
$116$		0			0
$117$	1.81707	−	1.81707i	0.167988	−	0.167988i
$118$		0			0
$119$			1.79793i			0.164816i
$120$		0			0
$121$			1.67794i			0.152540i
$122$		0			0
$123$	0.640613	−	0.640613i	0.0577622	−	0.0577622i
$124$		0			0
$125$	−6.89246	−	6.89246i	−0.616480	−	0.616480i
$126$		0			0
$127$	7.93161			0.703817			0.351908	−	0.936034i	$-0.385533\pi$
$127$	7.93161			0.703817			0.351908	+	0.936034i	$0.385533\pi$
$128$		0			0
$129$	5.33897			0.470070
$130$		0			0
$131$	5.98429	+	5.98429i	0.522850	+	0.522850i	0.918431	−	0.395581i	$-0.129457\pi$
$131$	5.98429	+	5.98429i	0.522850	+	0.522850i	−0.395581	+	0.918431i	$0.629457\pi$
$132$		0			0
$133$	−0.531306	+	0.531306i	−0.0460700	+	0.0460700i
$134$		0			0
$135$		−	6.19951i		−	0.533569i
$136$		0			0
$137$			12.3380i			1.05411i	0.849831	+	0.527055i	$0.176704\pi$
$137$			12.3380i			1.05411i	−0.849831	+	0.527055i	$0.823296\pi$
$138$		0			0
$139$	−13.0393	+	13.0393i	−1.10598	+	1.10598i	−0.112305	+	0.993674i	$0.535823\pi$
$139$	−13.0393	+	13.0393i	−1.10598	+	1.10598i	−0.993674	+	0.112305i	$0.964177\pi$
$140$		0			0
$141$	−1.97958	−	1.97958i	−0.166711	−	0.166711i
$142$		0			0
$143$	−5.67016			−0.474162
$144$		0			0
$145$	−8.85114			−0.735047
$146$		0			0
$147$	0.898966	+	0.898966i	0.0741455	+	0.0741455i
$148$		0			0
$149$	8.62798	−	8.62798i	0.706832	−	0.706832i	−0.259036	−	0.965868i	$-0.583405\pi$
$149$	8.62798	−	8.62798i	0.706832	−	0.706832i	0.965868	+	0.259036i	$0.0834048\pi$
$150$		0			0
$151$			9.55274i			0.777391i	0.921366	+	0.388695i	$0.127074\pi$
$151$			9.55274i			0.777391i	−0.921366	+	0.388695i	$0.872926\pi$
$152$		0			0
$153$			2.48783i			0.201129i
$154$		0			0
$155$	3.41421	−	3.41421i	0.274236	−	0.274236i
$156$		0			0
$157$	8.25742	+	8.25742i	0.659014	+	0.659014i	0.955147	−	0.296133i	$-0.0956971\pi$
$157$	8.25742	+	8.25742i	0.659014	+	0.659014i	−0.296133	+	0.955147i	$0.595697\pi$
$158$		0			0
$159$	6.08370			0.482469
$160$		0			0
$161$	−5.95687			−0.469467
$162$		0			0
$163$	1.01263	+	1.01263i	0.0793154	+	0.0793154i	0.745652	−	0.666336i	$-0.232138\pi$
$163$	1.01263	+	1.01263i	0.0793154	+	0.0793154i	−0.666336	+	0.745652i	$0.732138\pi$
$164$		0			0
$165$	−3.05320	+	3.05320i	−0.237692	+	0.237692i
$166$		0			0
$167$			5.79793i			0.448657i	0.974514	+	0.224329i	$0.0720189\pi$
$167$			5.79793i			0.448657i	−0.974514	+	0.224329i	$0.927981\pi$
$168$		0			0
$169$		−	9.55112i		−	0.734701i
$170$		0			0
$171$	−0.735178	+	0.735178i	−0.0562205	+	0.0562205i
$172$		0			0
$173$	−2.65215	−	2.65215i	−0.201639	−	0.201639i	0.599063	−	0.800702i	$-0.295540\pi$
$173$	−2.65215	−	2.65215i	−0.201639	−	0.201639i	−0.800702	+	0.599063i	$0.795540\pi$
$174$		0			0
$175$	3.76259			0.284425
$176$		0			0
$177$	4.34289			0.326431
$178$		0			0
$179$	−1.55045	−	1.55045i	−0.115886	−	0.115886i	0.646786	−	0.762672i	$-0.276113\pi$
$179$	−1.55045	−	1.55045i	−0.115886	−	0.115886i	−0.762672	+	0.646786i	$0.776113\pi$
$180$		0			0
$181$	11.0315	−	11.0315i	0.819966	−	0.819966i	−0.166137	−	0.986103i	$-0.553129\pi$
$181$	11.0315	−	11.0315i	0.819966	−	0.819966i	0.986103	+	0.166137i	$0.0531293\pi$
$182$		0			0
$183$		−	12.7564i		−	0.942982i
$184$		0			0
$185$			3.34838i			0.246178i
$186$		0			0
$187$	3.88163	−	3.88163i	0.283853	−	0.283853i
$188$		0			0
$189$	3.94082	+	3.94082i	0.286652	+	0.286652i
$190$		0			0
$191$	16.5664			1.19870			0.599352	−	0.800485i	$-0.295425\pi$
$191$	16.5664			1.19870			0.599352	+	0.800485i	$0.295425\pi$
$192$		0			0
$193$	17.3795			1.25101			0.625503	−	0.780221i	$-0.284894\pi$
$193$	17.3795			1.25101			0.625503	+	0.780221i	$0.284894\pi$
$194$		0			0
$195$	1.85712	+	1.85712i	0.132991	+	0.132991i
$196$		0			0
$197$	1.44110	−	1.44110i	0.102674	−	0.102674i	−0.653904	−	0.756578i	$-0.726870\pi$
$197$	1.44110	−	1.44110i	0.102674	−	0.102674i	0.756578	+	0.653904i	$0.226870\pi$
$198$		0			0
$199$			13.1438i			0.931736i	0.884854	+	0.465868i	$0.154258\pi$
$199$			13.1438i			0.931736i	−0.884854	+	0.465868i	$0.845742\pi$
$200$		0			0
$201$		−	12.1674i		−	0.858222i
$202$		0			0
$203$	5.62636	−	5.62636i	0.394893	−	0.394893i
$204$		0			0
$205$	−0.560524	−	0.560524i	−0.0391487	−	0.0391487i
$206$		0			0
$207$	−8.24264			−0.572903
$208$		0			0
$209$	2.29412			0.158687
$210$		0			0
$211$	−3.59587	−	3.59587i	−0.247550	−	0.247550i	0.572415	−	0.819964i	$-0.306007\pi$
$211$	−3.59587	−	3.59587i	−0.247550	−	0.247550i	−0.819964	+	0.572415i	$0.806007\pi$
$212$		0			0
$213$	−1.76906	+	1.76906i	−0.121214	+	0.121214i
$214$		0			0
$215$		−	4.67149i		−	0.318593i
$216$		0			0
$217$			4.34059i			0.294659i
$218$		0			0
$219$	9.31626	−	9.31626i	0.629535	−	0.629535i
$220$		0			0
$221$	−2.36101	−	2.36101i	−0.158819	−	0.158819i
$222$		0			0
$223$	−27.5132			−1.84242			−0.921211	−	0.389064i	$-0.872799\pi$
$223$	−27.5132			−1.84242			−0.921211	+	0.389064i	$0.872799\pi$
$224$		0			0
$225$	5.20637			0.347091
$226$		0			0
$227$	−11.0418	−	11.0418i	−0.732873	−	0.732873i	0.238315	−	0.971188i	$-0.423405\pi$
$227$	−11.0418	−	11.0418i	−0.732873	−	0.732873i	−0.971188	+	0.238315i	$0.923405\pi$
$228$		0			0
$229$	−11.9717	+	11.9717i	−0.791109	+	0.791109i	−0.981675	−	0.190565i	$-0.938968\pi$
$229$	−11.9717	+	11.9717i	−0.791109	+	0.791109i	0.190565	+	0.981675i	$0.438968\pi$
$230$		0			0
$231$		−	3.88163i		−	0.255393i
$232$		0			0
$233$		−	28.7013i		−	1.88029i	−0.340778	−	0.940144i	$-0.610690\pi$
$233$		−	28.7013i		−	1.88029i	0.340778	−	0.940144i	$-0.389310\pi$
$234$		0			0
$235$	−1.73210	+	1.73210i	−0.112990	+	0.112990i
$236$		0			0
$237$	−12.8057	−	12.8057i	−0.831821	−	0.831821i
$238$		0			0
$239$	16.6348			1.07602			0.538008	−	0.842939i	$-0.319177\pi$
$239$	16.6348			1.07602			0.538008	+	0.842939i	$0.319177\pi$
$240$		0			0
$241$	−3.77267			−0.243019			−0.121510	−	0.992590i	$-0.538773\pi$
$241$	−3.77267			−0.243019			−0.121510	+	0.992590i	$0.538773\pi$
$242$		0			0
$243$	9.18473	+	9.18473i	0.589201	+	0.589201i
$244$		0			0
$245$	0.786578	−	0.786578i	0.0502526	−	0.0502526i
$246$		0			0
$247$		−	1.39540i		−	0.0887872i
$248$		0			0
$249$			10.7016i			0.678186i
$250$		0			0
$251$	−20.1264	+	20.1264i	−1.27037	+	1.27037i	−0.324474	+	0.945895i	$0.605187\pi$
$251$	−20.1264	+	20.1264i	−1.27037	+	1.27037i	−0.945895	+	0.324474i	$0.894813\pi$
$252$		0			0
$253$	12.8605	+	12.8605i	0.808535	+	0.808535i
$254$		0			0
$255$	−2.54266			−0.159228
$256$		0			0
$257$	−25.8408			−1.61190			−0.805952	−	0.591980i	$-0.798346\pi$
$257$	−25.8408			−1.61190			−0.805952	+	0.591980i	$0.798346\pi$
$258$		0			0
$259$	−2.12845	−	2.12845i	−0.132255	−	0.132255i
$260$		0			0
$261$	7.78530	−	7.78530i	0.481898	−	0.481898i
$262$		0			0
$263$			2.24035i			0.138146i	0.997612	+	0.0690728i	$0.0220041\pi$
$263$			2.24035i			0.138146i	−0.997612	+	0.0690728i	$0.977996\pi$
$264$		0			0
$265$		−	5.32312i		−	0.326996i
$266$		0			0
$267$	15.2300	−	15.2300i	0.932061	−	0.932061i
$268$		0			0
$269$	−13.3489	−	13.3489i	−0.813897	−	0.813897i	0.171319	−	0.985216i	$-0.445197\pi$
$269$	−13.3489	−	13.3489i	−0.813897	−	0.813897i	−0.985216	+	0.171319i	$0.945197\pi$
$270$		0			0
$271$	−13.5670			−0.824136			−0.412068	−	0.911153i	$-0.635193\pi$
$271$	−13.5670			−0.824136			−0.412068	+	0.911153i	$0.635193\pi$
$272$		0			0
$273$	−2.36101			−0.142895
$274$		0			0
$275$	−8.12322	−	8.12322i	−0.489848	−	0.489848i
$276$		0			0
$277$	8.22060	−	8.22060i	0.493928	−	0.493928i	−0.415613	−	0.909541i	$-0.636433\pi$
$277$	8.22060	−	8.22060i	0.493928	−	0.493928i	0.909541	+	0.415613i	$0.136433\pi$
$278$		0			0
$279$			6.00616i			0.359580i
$280$		0			0
$281$		−	4.95365i		−	0.295510i	−0.989024	−	0.147755i	$-0.952795\pi$
$281$		−	4.95365i		−	0.295510i	0.989024	−	0.147755i	$-0.0472047\pi$
$282$		0			0
$283$	15.6184	−	15.6184i	0.928419	−	0.928419i	−0.0691845	−	0.997604i	$-0.522040\pi$
$283$	15.6184	−	15.6184i	0.928419	−	0.928419i	0.997604	+	0.0691845i	$0.0220397\pi$
$284$		0			0
$285$	−0.751380	−	0.751380i	−0.0445079	−	0.0445079i
$286$		0			0
$287$	0.712611			0.0420641
$288$		0			0
$289$	−13.7674			−0.809849
$290$		0			0
$291$	−15.8933	−	15.8933i	−0.931684	−	0.931684i
$292$		0			0
$293$	−14.6749	+	14.6749i	−0.857315	+	0.857315i	−0.991021	−	0.133706i	$-0.957312\pi$
$293$	−14.6749	+	14.6749i	−0.857315	+	0.857315i	0.133706	+	0.991021i	$0.457312\pi$
$294$		0			0
$295$		−	3.79994i		−	0.221241i
$296$		0			0
$297$		−	17.0160i		−	0.987367i
$298$		0			0
$299$	7.82245	−	7.82245i	0.452384	−	0.452384i
$300$		0			0
$301$	2.96951	+	2.96951i	0.171159	+	0.171159i
$302$		0			0
$303$	11.9770			0.688063
$304$		0			0
$305$	−11.1616			−0.639113
$306$		0			0
$307$	−9.72484	−	9.72484i	−0.555026	−	0.555026i	0.372861	−	0.927887i	$-0.378377\pi$
$307$	−9.72484	−	9.72484i	−0.555026	−	0.555026i	−0.927887	+	0.372861i	$0.878377\pi$
$308$		0			0
$309$	−1.69382	+	1.69382i	−0.0963579	+	0.0963579i
$310$		0			0
$311$			27.1376i			1.53883i	0.638748	+	0.769416i	$0.279453\pi$
$311$			27.1376i			1.53883i	−0.638748	+	0.769416i	$0.720547\pi$
$312$		0			0
$313$		−	13.1116i		−	0.741114i	−0.928810	−	0.370557i	$-0.879167\pi$
$313$		−	13.1116i		−	0.741114i	0.928810	−	0.370557i	$-0.120833\pi$
$314$		0			0
$315$	1.08840	−	1.08840i	0.0613245	−	0.0613245i
$316$		0			0
$317$	11.4901	+	11.4901i	0.645350	+	0.645350i	0.951866	−	0.306516i	$-0.0991632\pi$
$317$	11.4901	+	11.4901i	0.645350	+	0.645350i	−0.306516	+	0.951866i	$0.599163\pi$
$318$		0			0
$319$	−24.2940			−1.36020
$320$		0			0
$321$	16.0899			0.898048
$322$		0			0
$323$	0.955252	+	0.955252i	0.0531516	+	0.0531516i
$324$		0			0
$325$	−4.94096	+	4.94096i	−0.274075	+	0.274075i
$326$		0			0
$327$			8.50799i			0.470493i
$328$		0			0
$329$		−	2.20207i		−	0.121404i
$330$		0			0
$331$	11.4094	−	11.4094i	0.627116	−	0.627116i	−0.320226	−	0.947341i	$-0.603759\pi$
$331$	11.4094	−	11.4094i	0.627116	−	0.627116i	0.947341	+	0.320226i	$0.103759\pi$
$332$		0			0
$333$	−2.94517	−	2.94517i	−0.161394	−	0.161394i
$334$		0			0
$335$	−10.6462			−0.581666
$336$		0			0
$337$	−30.6355			−1.66882			−0.834411	−	0.551142i	$-0.814192\pi$
$337$	−30.6355			−1.66882			−0.834411	+	0.551142i	$0.814192\pi$
$338$		0			0
$339$	7.13255	+	7.13255i	0.387387	+	0.387387i
$340$		0			0
$341$	9.37109	−	9.37109i	0.507473	−	0.507473i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	8.42429i		−	0.453549i
$346$		0			0
$347$	−4.28321	+	4.28321i	−0.229935	+	0.229935i	−0.812665	−	0.582730i	$-0.801984\pi$
$347$	−4.28321	+	4.28321i	−0.229935	+	0.229935i	0.582730	+	0.812665i	$0.301984\pi$
$348$		0			0
$349$	−22.9861	−	22.9861i	−1.23042	−	1.23042i	−0.963803	−	0.266614i	$-0.914095\pi$
$349$	−22.9861	−	22.9861i	−1.23042	−	1.23042i	−0.266614	−	0.963803i	$-0.585905\pi$
$350$		0			0
$351$	−10.3500			−0.552442
$352$		0			0
$353$	16.0523			0.854376			0.427188	−	0.904163i	$-0.359504\pi$
$353$	16.0523			0.854376			0.427188	+	0.904163i	$0.359504\pi$
$354$		0			0
$355$	1.54789	+	1.54789i	0.0821536	+	0.0821536i
$356$		0			0
$357$	1.61628	−	1.61628i	0.0855427	−	0.0855427i
$358$		0			0
$359$			15.8317i			0.835563i	0.908548	+	0.417781i	$0.137192\pi$
$359$			15.8317i			0.835563i	−0.908548	+	0.417781i	$0.862808\pi$
$360$		0			0
$361$		−	18.4354i		−	0.970286i
$362$		0			0
$363$	1.50841	−	1.50841i	0.0791712	−	0.0791712i
$364$		0			0
$365$	−8.15154	−	8.15154i	−0.426671	−	0.426671i
$366$		0			0
$367$	−37.3527			−1.94979			−0.974897	−	0.222656i	$-0.928527\pi$
$367$	−37.3527			−1.94979			−0.974897	+	0.222656i	$0.928527\pi$
$368$		0			0
$369$	0.986054			0.0513319
$370$		0			0
$371$	3.38372	+	3.38372i	0.175674	+	0.175674i
$372$		0			0
$373$	12.4321	−	12.4321i	0.643709	−	0.643709i	−0.307757	−	0.951465i	$-0.599578\pi$
$373$	12.4321	−	12.4321i	0.643709	−	0.643709i	0.951465	+	0.307757i	$0.0995782\pi$
$374$		0			0
$375$			12.3922i			0.639929i
$376$		0			0
$377$			14.7768i			0.761046i
$378$		0			0
$379$	−2.68374	+	2.68374i	−0.137854	+	0.137854i	−0.772667	−	0.634812i	$-0.781077\pi$
$379$	−2.68374	+	2.68374i	−0.137854	+	0.137854i	0.634812	+	0.772667i	$0.281077\pi$
$380$		0			0
$381$	−7.13025	−	7.13025i	−0.365294	−	0.365294i
$382$		0			0
$383$	10.7195			0.547739			0.273870	−	0.961767i	$-0.411696\pi$
$383$	10.7195			0.547739			0.273870	+	0.961767i	$0.411696\pi$
$384$		0			0
$385$	−3.39635			−0.173094
$386$		0			0
$387$	4.10896	+	4.10896i	0.208870	+	0.208870i
$388$		0			0
$389$	−18.4499	+	18.4499i	−0.935449	+	0.935449i	−0.998039	−	0.0625902i	$-0.980064\pi$
$389$	−18.4499	+	18.4499i	−0.935449	+	0.935449i	0.0625902	+	0.998039i	$0.480064\pi$
$390$		0			0
$391$			10.7101i			0.541631i
$392$		0			0
$393$		−	10.7593i		−	0.542737i
$394$		0			0
$395$	−11.2047	+	11.2047i	−0.563772	+	0.563772i
$396$		0			0
$397$	8.43982	+	8.43982i	0.423583	+	0.423583i	0.886435	−	0.462853i	$-0.153174\pi$
$397$	8.43982	+	8.43982i	0.423583	+	0.423583i	−0.462853	+	0.886435i	$0.653174\pi$
$398$		0			0
$399$	0.955252			0.0478224
$400$		0			0
$401$	−33.3744			−1.66664			−0.833320	−	0.552791i	$-0.813563\pi$
$401$	−33.3744			−1.66664			−0.833320	+	0.552791i	$0.813563\pi$
$402$		0			0
$403$	−5.69998	−	5.69998i	−0.283936	−	0.283936i
$404$		0			0
$405$	−2.30795	+	2.30795i	−0.114683	+	0.114683i
$406$		0			0
$407$			9.19039i			0.455551i
$408$		0			0
$409$			8.19011i			0.404975i	0.979285	+	0.202487i	$0.0649025\pi$
$409$			8.19011i			0.404975i	−0.979285	+	0.202487i	$0.935097\pi$
$410$		0			0
$411$	11.0915	−	11.0915i	0.547103	−	0.547103i
$412$		0			0
$413$	2.41549	+	2.41549i	0.118858	+	0.118858i
$414$		0			0
$415$	9.36369			0.459645
$416$		0			0
$417$	23.4438			1.14805
$418$		0			0
$419$	−21.7021	−	21.7021i	−1.06022	−	1.06022i	−0.998067	−	0.0621518i	$-0.980204\pi$
$419$	−21.7021	−	21.7021i	−1.06022	−	1.06022i	−0.0621518	−	0.998067i	$-0.519796\pi$
$420$		0			0
$421$	27.4513	−	27.4513i	1.33789	−	1.33789i	0.439798	−	0.898097i	$-0.355050\pi$
$421$	27.4513	−	27.4513i	1.33789	−	1.33789i	0.898097	−	0.439798i	$-0.144950\pi$
$422$		0			0
$423$		−	3.04704i		−	0.148152i
$424$		0			0
$425$		−	6.76489i		−	0.328145i
$426$		0			0
$427$	7.09505	−	7.09505i	0.343354	−	0.343354i
$428$		0			0
$429$	5.09728	+	5.09728i	0.246099	+	0.246099i
$430$		0			0
$431$	−6.85598			−0.330241			−0.165121	−	0.986273i	$-0.552801\pi$
$431$	−6.85598			−0.330241			−0.165121	+	0.986273i	$0.552801\pi$
$432$		0			0
$433$	39.3144			1.88933			0.944665	−	0.328037i	$-0.106387\pi$
$433$	39.3144			1.88933			0.944665	+	0.328037i	$0.106387\pi$
$434$		0			0
$435$	7.95687	+	7.95687i	0.381503	+	0.381503i
$436$		0			0
$437$	−3.16492	+	3.16492i	−0.151399	+	0.151399i
$438$		0			0
$439$			1.76192i			0.0840918i	0.999116	+	0.0420459i	$0.0133876\pi$
$439$			1.76192i			0.0840918i	−0.999116	+	0.0420459i	$0.986612\pi$
$440$		0			0
$441$			1.38372i			0.0658914i
$442$		0			0
$443$	13.1344	−	13.1344i	0.624032	−	0.624032i	−0.322528	−	0.946560i	$-0.604533\pi$
$443$	13.1344	−	13.1344i	0.624032	−	0.624032i	0.946560	+	0.322528i	$0.104533\pi$
$444$		0			0
$445$	−13.3260	−	13.3260i	−0.631711	−	0.631711i
$446$		0			0
$447$	−15.5125			−0.733718
$448$		0			0
$449$	−19.8852			−0.938443			−0.469221	−	0.883081i	$-0.655465\pi$
$449$	−19.8852			−0.938443			−0.469221	+	0.883081i	$0.655465\pi$
$450$		0			0
$451$	−1.53849	−	1.53849i	−0.0724445	−	0.0724445i
$452$		0			0
$453$	8.58759	−	8.58759i	0.403480	−	0.403480i
$454$		0			0
$455$			2.06584i			0.0968479i
$456$		0			0
$457$		−	16.7983i		−	0.785792i	−0.919583	−	0.392896i	$-0.871473\pi$
$457$		−	16.7983i		−	0.785792i	0.919583	−	0.392896i	$-0.128527\pi$
$458$		0			0
$459$	7.08532	−	7.08532i	0.330714	−	0.330714i
$460$		0			0
$461$	−23.5576	−	23.5576i	−1.09719	−	1.09719i	−0.994738	−	0.102450i	$-0.967332\pi$
$461$	−23.5576	−	23.5576i	−1.09719	−	1.09719i	−0.102450	−	0.994738i	$-0.532668\pi$
$462$		0			0
$463$	13.6063			0.632340			0.316170	−	0.948703i	$-0.397603\pi$
$463$	13.6063			0.632340			0.316170	+	0.948703i	$0.397603\pi$
$464$		0			0
$465$	−6.13853			−0.284667
$466$		0			0
$467$	−17.8703	−	17.8703i	−0.826938	−	0.826938i	0.160154	−	0.987092i	$-0.448801\pi$
$467$	−17.8703	−	17.8703i	−0.826938	−	0.826938i	−0.987092	+	0.160154i	$0.948801\pi$
$468$		0			0
$469$	6.76744	−	6.76744i	0.312491	−	0.312491i
$470$		0			0
$471$		−	14.8463i		−	0.684081i
$472$		0			0
$473$		−	12.8220i		−	0.589555i
$474$		0			0
$475$	1.99909	−	1.99909i	0.0917244	−	0.0917244i
$476$		0			0
$477$	4.68212	+	4.68212i	0.214379	+	0.214379i
$478$		0			0
$479$	37.3075			1.70463			0.852313	−	0.523033i	$-0.175199\pi$
$479$	37.3075			1.70463			0.852313	+	0.523033i	$0.175199\pi$
$480$		0			0
$481$	5.59007			0.254885
$482$		0			0
$483$	5.35503	+	5.35503i	0.243662	+	0.243662i
$484$		0			0
$485$	−13.9063	+	13.9063i	−0.631455	+	0.631455i
$486$		0			0
$487$		−	7.61373i		−	0.345011i	−0.985009	−	0.172505i	$-0.944814\pi$
$487$		−	7.61373i		−	0.345011i	0.985009	−	0.172505i	$-0.0551863\pi$
$488$		0			0
$489$		−	1.82064i		−	0.0823323i
$490$		0			0
$491$	25.1091	−	25.1091i	1.13316	−	1.13316i	0.143508	−	0.989649i	$-0.454162\pi$
$491$	25.1091	−	25.1091i	1.13316	−	1.13316i	0.989649	−	0.143508i	$-0.0458383\pi$
$492$		0			0
$493$	−10.1158	−	10.1158i	−0.455593	−	0.455593i
$494$		0			0
$495$	−4.69959			−0.211231
$496$		0			0
$497$	−1.96788			−0.0882716
$498$		0			0
$499$	16.5674	+	16.5674i	0.741658	+	0.741658i	0.972897	−	0.231239i	$-0.0742780\pi$
$499$	16.5674	+	16.5674i	0.741658	+	0.741658i	−0.231239	+	0.972897i	$0.574278\pi$
$500$		0			0
$501$	5.21215	−	5.21215i	0.232862	−	0.232862i
$502$		0			0
$503$			32.9297i			1.46826i	0.679007	+	0.734132i	$0.262411\pi$
$503$			32.9297i			1.46826i	−0.679007	+	0.734132i	$0.737589\pi$
$504$		0			0
$505$		−	10.4797i		−	0.466339i
$506$		0			0
$507$	−8.58613	+	8.58613i	−0.381324	+	0.381324i
$508$		0			0
$509$	0.330168	+	0.330168i	0.0146345	+	0.0146345i	0.714386	−	0.699752i	$-0.246706\pi$
$509$	0.330168	+	0.330168i	0.0146345	+	0.0146345i	−0.699752	+	0.714386i	$0.746706\pi$
$510$		0			0
$511$	10.3633			0.458446
$512$		0			0
$513$	4.18756			0.184885
$514$		0			0
$515$	1.48206	+	1.48206i	0.0653072	+	0.0653072i
$516$		0			0
$517$	−4.75413	+	4.75413i	−0.209087	+	0.209087i
$518$		0			0
$519$			4.76839i			0.209309i
$520$		0			0
$521$			5.94331i			0.260381i	0.991489	+	0.130191i	$0.0415589\pi$
$521$			5.94331i			0.260381i	−0.991489	+	0.130191i	$0.958441\pi$
$522$		0			0
$523$	14.4703	−	14.4703i	0.632743	−	0.632743i	−0.316012	−	0.948755i	$-0.602344\pi$
$523$	14.4703	−	14.4703i	0.632743	−	0.632743i	0.948755	+	0.316012i	$0.102344\pi$
$524$		0			0
$525$	−3.38244	−	3.38244i	−0.147622	−	0.147622i
$526$		0			0
$527$	7.80409			0.339952
$528$		0			0
$529$	−12.4844			−0.542798
$530$		0			0
$531$	3.34236	+	3.34236i	0.145046	+	0.145046i
$532$		0			0
$533$	−0.935787	+	0.935787i	−0.0405334	+	0.0405334i
$534$		0			0
$535$		−	14.0783i		−	0.608658i
$536$		0			0
$537$			2.78760i			0.120294i
$538$		0			0
$539$	2.15894	−	2.15894i	0.0929922	−	0.0929922i
$540$		0			0
$541$	8.23256	+	8.23256i	0.353945	+	0.353945i	0.861575	−	0.507630i	$-0.169478\pi$
$541$	8.23256	+	8.23256i	0.353945	+	0.353945i	−0.507630	+	0.861575i	$0.669478\pi$
$542$		0			0
$543$	−19.8339			−0.851155
$544$		0			0
$545$	7.44432			0.318880
$546$		0			0
$547$	16.9144	+	16.9144i	0.723208	+	0.723208i	0.969257	−	0.246049i	$-0.0791324\pi$
$547$	16.9144	+	16.9144i	0.723208	+	0.723208i	−0.246049	+	0.969257i	$0.579132\pi$
$548$		0			0
$549$	9.81756	−	9.81756i	0.419003	−	0.419003i
$550$		0			0
$551$		−	5.97863i		−	0.254698i
$552$		0			0
$553$		−	14.2449i		−	0.605756i
$554$		0			0
$555$	3.01008	−	3.01008i	0.127771	−	0.127771i
$556$		0			0
$557$	−28.0529	−	28.0529i	−1.18864	−	1.18864i	−0.977443	−	0.211198i	$-0.932263\pi$
$557$	−28.0529	−	28.0529i	−1.18864	−	1.18864i	−0.211198	−	0.977443i	$-0.567737\pi$
$558$		0			0
$559$	−7.79899			−0.329862
$560$		0			0
$561$	−6.97891			−0.294650
$562$		0			0
$563$	10.7240	+	10.7240i	0.451961	+	0.451961i	0.896005	−	0.444044i	$-0.146457\pi$
$563$	10.7240	+	10.7240i	0.451961	+	0.451961i	−0.444044	+	0.896005i	$0.646457\pi$
$564$		0			0
$565$	6.24084	−	6.24084i	0.262554	−	0.262554i
$566$		0			0
$567$		−	2.93416i		−	0.123223i
$568$		0			0
$569$			7.70067i			0.322829i	0.986887	+	0.161414i	$0.0516056\pi$
$569$			7.70067i			0.322829i	−0.986887	+	0.161414i	$0.948394\pi$
$570$		0			0
$571$	−33.1892	+	33.1892i	−1.38892	+	1.38892i	−0.561336	+	0.827588i	$0.689712\pi$
$571$	−33.1892	+	33.1892i	−1.38892	+	1.38892i	−0.827588	+	0.561336i	$0.810288\pi$
$572$		0			0
$573$	−14.8927	−	14.8927i	−0.622150	−	0.622150i
$574$		0			0
$575$	22.4133			0.934699
$576$		0			0
$577$	7.15827			0.298003			0.149001	−	0.988837i	$-0.452394\pi$
$577$	7.15827			0.298003			0.149001	+	0.988837i	$0.452394\pi$
$578$		0			0
$579$	−15.6236	−	15.6236i	−0.649296	−	0.649296i
$580$		0			0
$581$	−5.95217	+	5.95217i	−0.246938	+	0.246938i
$582$		0			0
$583$		−	14.6105i		−	0.605105i
$584$		0			0
$585$			2.85854i			0.118186i
$586$		0			0
$587$	−18.8145	+	18.8145i	−0.776558	+	0.776558i	−0.979244	−	0.202686i	$-0.935033\pi$
$587$	−18.8145	+	18.8145i	−0.776558	+	0.776558i	0.202686	+	0.979244i	$0.435033\pi$
$588$		0			0
$589$	2.30618	+	2.30618i	0.0950246	+	0.0950246i
$590$		0			0
$591$	−2.59100			−0.106579
$592$		0			0
$593$	−4.45182			−0.182814			−0.0914072	−	0.995814i	$-0.529136\pi$
$593$	−4.45182			−0.182814			−0.0914072	+	0.995814i	$0.529136\pi$
$594$		0			0
$595$	−1.41421	−	1.41421i	−0.0579771	−	0.0579771i
$596$		0			0
$597$	11.8158	−	11.8158i	0.483588	−	0.483588i
$598$		0			0
$599$			29.5201i			1.20616i	0.797682	+	0.603079i	$0.206060\pi$
$599$			29.5201i			1.20616i	−0.797682	+	0.603079i	$0.793940\pi$
$600$		0			0
$601$			24.5564i			1.00168i	0.865541	+	0.500838i	$0.166975\pi$
$601$			24.5564i			1.00168i	−0.865541	+	0.500838i	$0.833025\pi$
$602$		0			0
$603$	9.36423	−	9.36423i	0.381341	−	0.381341i
$604$		0			0
$605$	−1.31983	−	1.31983i	−0.0536588	−	0.0536588i
$606$		0			0
$607$	36.1536			1.46743			0.733714	−	0.679458i	$-0.237785\pi$
$607$	36.1536			1.46743			0.733714	+	0.679458i	$0.237785\pi$
$608$		0			0
$609$	−10.1158			−0.409914
$610$		0			0
$611$	2.89171	+	2.89171i	0.116986	+	0.116986i
$612$		0			0
$613$	3.35616	−	3.35616i	0.135554	−	0.135554i	−0.636074	−	0.771628i	$-0.719443\pi$
$613$	3.35616	−	3.35616i	0.135554	−	0.135554i	0.771628	+	0.636074i	$0.219443\pi$
$614$		0			0
$615$			1.00778i			0.0406378i
$616$		0			0
$617$			25.5502i			1.02861i	0.857607	+	0.514306i	$0.171950\pi$
$617$			25.5502i			1.02861i	−0.857607	+	0.514306i	$0.828050\pi$
$618$		0			0
$619$	−11.1501	+	11.1501i	−0.448159	+	0.448159i	−0.894742	−	0.446583i	$-0.852641\pi$
$619$	−11.1501	+	11.1501i	−0.448159	+	0.448159i	0.446583	+	0.894742i	$0.352641\pi$
$620$		0			0
$621$	23.4749	+	23.4749i	0.942017	+	0.942017i
$622$		0			0
$623$	16.9417			0.678755
$624$		0			0
$625$	−7.97005			−0.318802
$626$		0			0
$627$	−2.06233	−	2.06233i	−0.0823616	−	0.0823616i
$628$		0			0
$629$	−3.82680	+	3.82680i	−0.152585	+	0.152585i
$630$		0			0
$631$			25.7069i			1.02337i	0.859172	+	0.511687i	$0.170979\pi$
$631$			25.7069i			1.02337i	−0.859172	+	0.511687i	$0.829021\pi$
$632$		0			0
$633$			6.46512i			0.256966i
$634$		0			0
$635$	−6.23883	+	6.23883i	−0.247580	+	0.247580i
$636$		0			0
$637$	−1.31318	−	1.31318i	−0.0520301	−	0.0520301i
$638$		0			0
$639$	−2.72300			−0.107720
$640$		0			0
$641$	−7.39970			−0.292271			−0.146135	−	0.989265i	$-0.546683\pi$
$641$	−7.39970			−0.292271			−0.146135	+	0.989265i	$0.546683\pi$
$642$		0			0
$643$	17.2666	+	17.2666i	0.680929	+	0.680929i	0.960210	−	0.279280i	$-0.0900959\pi$
$643$	17.2666	+	17.2666i	0.680929	+	0.680929i	−0.279280	+	0.960210i	$0.590096\pi$
$644$		0			0
$645$	−4.19951	+	4.19951i	−0.165356	+	0.165356i
$646$		0			0
$647$			7.71205i			0.303192i	0.988443	+	0.151596i	$0.0484412\pi$
$647$			7.71205i			0.303192i	−0.988443	+	0.151596i	$0.951559\pi$
$648$		0			0
$649$		−	10.4298i		−	0.409406i
$650$		0			0
$651$	3.90205	−	3.90205i	0.152933	−	0.152933i
$652$		0			0
$653$	4.78463	+	4.78463i	0.187237	+	0.187237i	0.794501	−	0.607263i	$-0.207733\pi$
$653$	4.78463	+	4.78463i	0.187237	+	0.187237i	−0.607263	+	0.794501i	$0.707733\pi$
$654$		0			0
$655$	−9.41421			−0.367844
$656$		0			0
$657$	14.3399			0.559453
$658$		0			0
$659$	−28.1016	−	28.1016i	−1.09468	−	1.09468i	−0.995022	−	0.0996599i	$-0.968225\pi$
$659$	−28.1016	−	28.1016i	−1.09468	−	1.09468i	−0.0996599	−	0.995022i	$-0.531775\pi$
$660$		0			0
$661$	10.0875	−	10.0875i	0.392357	−	0.392357i	−0.483170	−	0.875527i	$-0.660515\pi$
$661$	10.0875	−	10.0875i	0.392357	−	0.392357i	0.875527	+	0.483170i	$0.160515\pi$
$662$		0			0
$663$			4.24494i			0.164860i
$664$		0			0
$665$		−	0.835826i		−	0.0324120i
$666$		0			0
$667$	33.5155	−	33.5155i	1.29773	−	1.29773i
$668$		0			0
$669$	24.7335	+	24.7335i	0.956251	+	0.956251i
$670$		0			0
$671$	−30.6356			−1.18267
$672$		0			0
$673$	31.2930			1.20626			0.603129	−	0.797644i	$-0.293920\pi$
$673$	31.2930			1.20626			0.603129	+	0.797644i	$0.293920\pi$
$674$		0			0
$675$	−14.8277	−	14.8277i	−0.570718	−	0.570718i
$676$		0			0
$677$	−3.75969	+	3.75969i	−0.144497	+	0.144497i	−0.775654	−	0.631158i	$-0.782580\pi$
$677$	−3.75969	+	3.75969i	−0.144497	+	0.144497i	0.631158	+	0.775654i	$0.282580\pi$
$678$		0			0
$679$		−	17.6796i		−	0.678479i
$680$		0			0
$681$			19.8525i			0.760750i
$682$		0			0
$683$	−8.31693	+	8.31693i	−0.318239	+	0.318239i	−0.848090	−	0.529852i	$-0.822248\pi$
$683$	−8.31693	+	8.31693i	−0.318239	+	0.318239i	0.529852	+	0.848090i	$0.322248\pi$
$684$		0			0
$685$	−9.70483	−	9.70483i	−0.370802	−	0.370802i
$686$		0			0
$687$	21.5242			0.821201
$688$		0			0
$689$	−8.88686			−0.338563
$690$		0			0
$691$	33.6065	+	33.6065i	1.27845	+	1.27845i	0.941535	+	0.336916i	$0.109384\pi$
$691$	33.6065	+	33.6065i	1.27845	+	1.27845i	0.336916	+	0.941535i	$0.390616\pi$
$692$		0			0
$693$	2.98737	−	2.98737i	0.113481	−	0.113481i
$694$		0			0
$695$		−	20.5128i		−	0.778096i
$696$		0			0
$697$		−	1.28123i		−	0.0485299i
$698$		0			0
$699$	−25.8015	+	25.8015i	−0.975904	+	0.975904i
$700$		0			0
$701$	33.3319	+	33.3319i	1.25893	+	1.25893i	0.951606	+	0.307322i	$0.0994329\pi$
$701$	33.3319	+	33.3319i	1.25893	+	1.25893i	0.307322	+	0.951606i	$0.400567\pi$
$702$		0			0
$703$	−2.26171			−0.0853021
$704$		0			0
$705$	3.11419			0.117287
$706$		0			0
$707$	6.66156	+	6.66156i	0.250534	+	0.250534i
$708$		0			0
$709$	−16.4665	+	16.4665i	−0.618412	+	0.618412i	−0.945124	−	0.326712i	$-0.894059\pi$
$709$	−16.4665	+	16.4665i	−0.618412	+	0.618412i	0.326712	+	0.945124i	$0.394059\pi$
$710$		0			0
$711$		−	19.7110i		−	0.739220i
$712$		0			0
$713$			25.8564i			0.968329i
$714$		0			0
$715$	4.46002	−	4.46002i	0.166795	−	0.166795i
$716$		0			0
$717$	−14.9541	−	14.9541i	−0.558473	−	0.558473i
$718$		0			0
$719$	25.5122			0.951443			0.475722	−	0.879596i	$-0.342187\pi$
$719$	25.5122			0.951443			0.475722	+	0.879596i	$0.342187\pi$
$720$		0			0
$721$	−1.88418			−0.0701707
$722$		0			0
$723$	3.39150	+	3.39150i	0.126131	+	0.126131i
$724$		0			0
$725$	−21.1697	+	21.1697i	−0.786223	+	0.786223i
$726$		0			0
$727$			10.8327i			0.401764i	0.979615	+	0.200882i	$0.0643807\pi$
$727$			10.8327i			0.401764i	−0.979615	+	0.200882i	$0.935619\pi$
$728$		0			0
$729$		−	25.3160i		−	0.937630i
$730$		0			0
$731$	5.33897	−	5.33897i	0.197469	−	0.197469i
$732$		0			0
$733$	−3.64351	−	3.64351i	−0.134576	−	0.134576i	0.636610	−	0.771186i	$-0.280336\pi$
$733$	−3.64351	−	3.64351i	−0.134576	−	0.134576i	−0.771186	+	0.636610i	$0.780336\pi$
$734$		0			0
$735$	−1.41421			−0.0521641
$736$		0			0
$737$	−29.2210			−1.07637
$738$		0			0
$739$	1.72954	+	1.72954i	0.0636223	+	0.0636223i	0.738202	−	0.674580i	$-0.235675\pi$
$739$	1.72954	+	1.72954i	0.0636223	+	0.0636223i	−0.674580	+	0.738202i	$0.735675\pi$
$740$		0			0
$741$	−1.25442	+	1.25442i	−0.0460822	+	0.0460822i
$742$		0			0
$743$		−	38.1023i		−	1.39784i	−0.715202	−	0.698918i	$-0.753665\pi$
$743$		−	38.1023i		−	1.39784i	0.715202	−	0.698918i	$-0.246335\pi$
$744$		0			0
$745$			13.5732i			0.497282i
$746$		0			0
$747$	−8.23613	+	8.23613i	−0.301344	+	0.301344i
$748$		0			0
$749$	8.94909	+	8.94909i	0.326993	+	0.326993i
$750$		0			0
$751$	−33.6119			−1.22651			−0.613257	−	0.789883i	$-0.710141\pi$
$751$	−33.6119			−1.22651			−0.613257	+	0.789883i	$0.710141\pi$
$752$		0			0
$753$	36.1860			1.31869
$754$		0			0
$755$	−7.51397	−	7.51397i	−0.273461	−	0.273461i
$756$		0			0
$757$	−2.39019	+	2.39019i	−0.0868729	+	0.0868729i	−0.749208	−	0.662335i	$-0.769566\pi$
$757$	−2.39019	+	2.39019i	−0.0868729	+	0.0868729i	0.662335	+	0.749208i	$0.269566\pi$
$758$		0			0
$759$		−	23.1224i		−	0.839290i
$760$		0			0
$761$			3.87733i			0.140553i	0.997528	+	0.0702765i	$0.0223882\pi$
$761$			3.87733i			0.140553i	−0.997528	+	0.0702765i	$0.977612\pi$
$762$		0			0
$763$	−4.73210	+	4.73210i	−0.171313	+	0.171313i
$764$		0			0
$765$	−1.95687	−	1.95687i	−0.0707509	−	0.0707509i
$766$		0			0
$767$	−6.34395			−0.229067
$768$		0			0
$769$	24.8126			0.894764			0.447382	−	0.894343i	$-0.352356\pi$
$769$	24.8126			0.894764			0.447382	+	0.894343i	$0.352356\pi$
$770$		0			0
$771$	23.2300	+	23.2300i	0.836608	+	0.836608i
$772$		0			0
$773$	8.49465	−	8.49465i	0.305531	−	0.305531i	−0.537642	−	0.843173i	$-0.680685\pi$
$773$	8.49465	−	8.49465i	0.305531	−	0.305531i	0.843173	+	0.537642i	$0.180685\pi$
$774$		0			0
$775$		−	16.3319i		−	0.586658i
$776$		0			0
$777$			3.82680i			0.137286i
$778$		0			0
$779$	0.378614	−	0.378614i	0.0135653	−	0.0135653i
$780$		0			0
$781$	4.24854	+	4.24854i	0.152025	+	0.152025i
$782$		0			0
$783$	−44.3449			−1.58476
$784$		0			0
$785$	−12.9902			−0.463640
$786$		0			0
$787$	−1.92149	−	1.92149i	−0.0684939	−	0.0684939i	0.672030	−	0.740524i	$-0.265423\pi$
$787$	−1.92149	−	1.92149i	−0.0684939	−	0.0684939i	−0.740524	+	0.672030i	$0.765423\pi$
$788$		0			0
$789$	2.01400	−	2.01400i	0.0717001	−	0.0717001i
$790$		0			0
$791$			7.93416i			0.282106i
$792$		0			0
$793$			18.6342i			0.661719i
$794$		0			0
$795$	−4.78530	+	4.78530i	−0.169717	+	0.169717i
$796$		0			0
$797$	8.95191	+	8.95191i	0.317093	+	0.317093i	0.847650	−	0.530557i	$-0.178017\pi$
$797$	8.95191	+	8.95191i	0.317093	+	0.317093i	−0.530557	+	0.847650i	$0.678017\pi$
$798$		0			0
$799$	−3.95917			−0.140065
$800$		0			0
$801$	23.4425			0.828301
$802$		0			0
$803$	−22.3738	−	22.3738i	−0.789553	−	0.789553i
$804$		0			0
$805$	4.68554	−	4.68554i	0.165144	−	0.165144i
$806$		0			0
$807$			24.0004i			0.844855i
$808$		0			0
$809$			3.51709i			0.123654i	0.998087	+	0.0618272i	$0.0196928\pi$
$809$			3.51709i			0.123654i	−0.998087	+	0.0618272i	$0.980307\pi$
$810$		0			0
$811$	−16.7994	+	16.7994i	−0.589907	+	0.589907i	−0.937606	−	0.347699i	$-0.886963\pi$
$811$	−16.7994	+	16.7994i	−0.589907	+	0.589907i	0.347699	+	0.937606i	$0.386963\pi$
$812$		0			0
$813$	12.1963	+	12.1963i	0.427742	+	0.427742i
$814$		0			0
$815$	−1.59303			−0.0558013
$816$		0			0
$817$	3.15543			0.110395
$818$		0			0
$819$	−1.81707	−	1.81707i	−0.0634936	−	0.0634936i
$820$		0			0
$821$	−27.2771	+	27.2771i	−0.951976	+	0.951976i	−0.998899	−	0.0469228i	$-0.985059\pi$
$821$	−27.2771	+	27.2771i	−0.951976	+	0.951976i	0.0469228	+	0.998899i	$0.485059\pi$
$822$		0			0
$823$		−	48.5252i		−	1.69148i	−0.533593	−	0.845742i	$-0.679158\pi$
$823$		−	48.5252i		−	1.69148i	0.533593	−	0.845742i	$-0.320842\pi$
$824$		0			0
$825$			14.6050i			0.508481i
$826$		0			0
$827$	−12.1041	+	12.1041i	−0.420901	+	0.420901i	−0.885514	−	0.464613i	$-0.846194\pi$
$827$	−12.1041	+	12.1041i	−0.420901	+	0.420901i	0.464613	+	0.885514i	$0.346194\pi$
$828$		0			0
$829$	0.264075	+	0.264075i	0.00917169	+	0.00917169i	0.711678	−	0.702506i	$-0.247936\pi$
$829$	0.264075	+	0.264075i	0.00917169	+	0.00917169i	−0.702506	+	0.711678i	$0.747936\pi$
$830$		0			0
$831$	−14.7801			−0.512716
$832$		0			0
$833$	1.79793			0.0622947
$834$		0			0
$835$	−4.56052	−	4.56052i	−0.157823	−	0.157823i
$836$		0			0
$837$	17.1055	−	17.1055i	0.591252	−	0.591252i
$838$		0			0
$839$		−	2.31074i		−	0.0797757i	−0.999204	−	0.0398878i	$-0.987300\pi$
$839$		−	2.31074i		−	0.0797757i	0.999204	−	0.0398878i	$-0.0127001\pi$
$840$		0			0
$841$			34.3118i			1.18317i
$842$		0			0
$843$	−4.45316	+	4.45316i	−0.153375	+	0.153375i
$844$		0			0
$845$	7.51269	+	7.51269i	0.258445	+	0.258445i
$846$		0			0
$847$	1.67794			0.0576548
$848$		0			0
$849$	−28.0809			−0.963734
$850$		0			0
$851$	−12.6789	−	12.6789i	−0.434627	−	0.434627i
$852$		0			0
$853$	−35.5400	+	35.5400i	−1.21687	+	1.21687i	−0.248143	+	0.968723i	$0.579820\pi$
$853$	−35.5400	+	35.5400i	−1.21687	+	1.21687i	−0.968723	+	0.248143i	$0.920180\pi$
$854$		0			0
$855$		−	1.15655i		−	0.0395531i
$856$		0			0
$857$		−	24.9222i		−	0.851327i	−0.904882	−	0.425664i	$-0.860041\pi$
$857$		−	24.9222i		−	0.851327i	0.904882	−	0.425664i	$-0.139959\pi$
$858$		0			0
$859$	−0.931083	+	0.931083i	−0.0317682	+	0.0317682i	−0.722812	−	0.691044i	$-0.757151\pi$
$859$	−0.931083	+	0.931083i	−0.0317682	+	0.0317682i	0.691044	+	0.722812i	$0.257151\pi$
$860$		0			0
$861$	−0.640613	−	0.640613i	−0.0218320	−	0.0218320i
$862$		0			0
$863$	27.9398			0.951081			0.475541	−	0.879694i	$-0.342252\pi$
$863$	27.9398			0.951081			0.475541	+	0.879694i	$0.342252\pi$
$864$		0			0
$865$	4.17224			0.141861
$866$		0			0
$867$	12.3765	+	12.3765i	0.420327	+	0.420327i
$868$		0			0
$869$	−30.7540	+	30.7540i	−1.04326	+	1.04326i
$870$		0			0
$871$			17.7737i			0.602240i
$872$		0			0
$873$		−	24.4636i		−	0.827966i
$874$		0			0
$875$	−6.89246	+	6.89246i	−0.233008	+	0.233008i
$876$		0			0
$877$	37.7935	+	37.7935i	1.27620	+	1.27620i	0.942780	+	0.333416i	$0.108201\pi$
$877$	37.7935	+	37.7935i	1.27620	+	1.27620i	0.333416	+	0.942780i	$0.391799\pi$
$878$		0			0
$879$	26.3844			0.889924
$880$		0			0
$881$	36.6692			1.23542			0.617709	−	0.786407i	$-0.288061\pi$
$881$	36.6692			1.23542			0.617709	+	0.786407i	$0.288061\pi$
$882$		0			0
$883$	20.2105	+	20.2105i	0.680138	+	0.680138i	0.960031	−	0.279893i	$-0.0902990\pi$
$883$	20.2105	+	20.2105i	0.680138	+	0.680138i	−0.279893	+	0.960031i	$0.590299\pi$
$884$		0			0
$885$	−3.41602	+	3.41602i	−0.114828	+	0.114828i
$886$		0			0
$887$		−	30.7180i		−	1.03141i	−0.856767	−	0.515704i	$-0.827530\pi$
$887$		−	30.7180i		−	1.03141i	0.856767	−	0.515704i	$-0.172470\pi$
$888$		0			0
$889$		−	7.93161i		−	0.266018i
$890$		0			0
$891$	−6.33469	+	6.33469i	−0.212220	+	0.212220i
$892$		0			0
$893$	−1.16997	−	1.16997i	−0.0391516	−	0.0391516i
$894$		0			0
$895$	2.43909			0.0815298
$896$		0			0
$897$	−14.0642			−0.469591
$898$		0			0
$899$	−24.4217	−	24.4217i	−0.814511	−	0.814511i
$900$		0			0
$901$	6.08370	−	6.08370i	0.202677	−	0.202677i
$902$		0			0
$903$		−	5.33897i		−	0.177670i
$904$		0			0
$905$			17.3543i			0.576876i
$906$		0			0
$907$	−4.77429	+	4.77429i	−0.158528	+	0.158528i	−0.781914	−	0.623386i	$-0.785756\pi$
$907$	−4.77429	+	4.77429i	−0.158528	+	0.158528i	0.623386	+	0.781914i	$0.285756\pi$
$908$		0			0
$909$	9.21772	+	9.21772i	0.305733	+	0.305733i
$910$		0			0
$911$	8.31693			0.275552			0.137776	−	0.990463i	$-0.456005\pi$
$911$	8.31693			0.275552			0.137776	+	0.990463i	$0.456005\pi$
$912$		0			0
$913$	25.7008			0.850572
$914$		0			0
$915$	10.0339	+	10.0339i	0.331711	+	0.331711i
$916$		0			0
$917$	5.98429	−	5.98429i	0.197619	−	0.197619i
$918$		0			0
$919$		−	21.2142i		−	0.699790i	−0.936789	−	0.349895i	$-0.886217\pi$
$919$		−	21.2142i		−	0.699790i	0.936789	−	0.349895i	$-0.113783\pi$
$920$		0			0
$921$			17.4846i			0.576137i
$922$		0			0
$923$	2.58418	−	2.58418i	0.0850595	−	0.0850595i
$924$		0			0
$925$	8.00848	+	8.00848i	0.263317	+	0.263317i
$926$		0			0
$927$	−2.60718			−0.0856311
$928$		0			0
$929$	−48.9785			−1.60693			−0.803466	−	0.595351i	$-0.797013\pi$
$929$	−48.9785			−1.60693			−0.803466	+	0.595351i	$0.797013\pi$
$930$		0			0
$931$	0.531306	+	0.531306i	0.0174128	+	0.0174128i
$932$		0			0
$933$	24.3958	−	24.3958i	0.798682	−	0.798682i
$934$		0			0
$935$			6.10641i			0.199701i
$936$		0			0
$937$		−	1.92705i		−	0.0629540i	−0.999504	−	0.0314770i	$-0.989979\pi$
$937$		−	1.92705i		−	0.0629540i	0.999504	−	0.0314770i	$-0.0100211\pi$
$938$		0			0
$939$	−11.7869	+	11.7869i	−0.384652	+	0.384652i
$940$		0			0
$941$	12.2347	+	12.2347i	0.398840	+	0.398840i	0.877824	−	0.478984i	$-0.158995\pi$
$941$	12.2347	+	12.2347i	0.398840	+	0.398840i	−0.478984	+	0.877824i	$0.658995\pi$
$942$		0			0
$943$	4.24494			0.138234
$944$		0			0
$945$	−6.19951			−0.201670
$946$		0			0
$947$	17.2543	+	17.2543i	0.560690	+	0.560690i	0.929503	−	0.368813i	$-0.120236\pi$
$947$	17.2543	+	17.2543i	0.560690	+	0.560690i	−0.368813	+	0.929503i	$0.620236\pi$
$948$		0			0
$949$	−13.6089	+	13.6089i	−0.441763	+	0.441763i
$950$		0			0
$951$		−	20.6585i		−	0.669897i
$952$		0			0
$953$		−	1.34866i		−	0.0436875i	−0.999761	−	0.0218438i	$-0.993046\pi$
$953$		−	1.34866i		−	0.0436875i	0.999761	−	0.0218438i	$-0.00695364\pi$
$954$		0			0
$955$	−13.0308	+	13.0308i	−0.421666	+	0.421666i
$956$		0			0
$957$	21.8395	+	21.8395i	0.705969	+	0.705969i
$958$		0			0
$959$	12.3380			0.398416
$960$		0			0
$961$	−12.1592			−0.392234
$962$		0			0
$963$	12.3830	+	12.3830i	0.399037	+	0.399037i
$964$		0			0
$965$	−13.6704	+	13.6704i	−0.440064	+	0.440064i
$966$		0			0
$967$		−	36.7348i		−	1.18131i	−0.806924	−	0.590655i	$-0.798869\pi$
$967$		−	36.7348i		−	1.18131i	0.806924	−	0.590655i	$-0.201131\pi$
$968$		0			0
$969$		−	1.71748i		−	0.0551734i
$970$		0			0
$971$	−22.6384	+	22.6384i	−0.726501	+	0.726501i	−0.969921	−	0.243420i	$-0.921731\pi$
$971$	−22.6384	+	22.6384i	−0.726501	+	0.726501i	0.243420	+	0.969921i	$0.421731\pi$
$972$		0			0
$973$	13.0393	+	13.0393i	0.418021	+	0.418021i
$974$		0			0
$975$	8.88351			0.284500
$976$		0			0
$977$	42.4361			1.35765			0.678826	−	0.734300i	$-0.262489\pi$
$977$	42.4361			1.35765			0.678826	+	0.734300i	$0.262489\pi$
$978$		0			0
$979$	−36.5761	−	36.5761i	−1.16898	−	1.16898i
$980$		0			0
$981$	−6.54789	+	6.54789i	−0.209058	+	0.209058i
$982$		0			0
$983$		−	61.1841i		−	1.95147i	−0.218957	−	0.975734i	$-0.570266\pi$
$983$		−	61.1841i		−	1.95147i	0.218957	−	0.975734i	$-0.429734\pi$
$984$		0			0
$985$			2.26707i			0.0722349i
$986$		0			0
$987$	−1.97958	+	1.97958i	−0.0630109	+	0.0630109i
$988$		0			0
$989$	17.6890	+	17.6890i	0.562477	+	0.562477i
$990$		0			0
$991$	4.09769			0.130168			0.0650838	−	0.997880i	$-0.479269\pi$
$991$	4.09769			0.130168			0.0650838	+	0.997880i	$0.479269\pi$
$992$		0			0
$993$	−20.5133			−0.650969
$994$		0			0
$995$	−10.3386	−	10.3386i	−0.327755	−	0.327755i
$996$		0			0
$997$	7.08175	−	7.08175i	0.224281	−	0.224281i	−0.586017	−	0.810299i	$-0.699305\pi$
$997$	7.08175	−	7.08175i	0.224281	−	0.224281i	0.810299	+	0.586017i	$0.199305\pi$
$998$		0			0
$999$			16.7756i			0.530758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.d.1345.1	yes	8
4.3	odd	2		1792.2.m.b.1345.4	yes	8
8.3	odd	2		1792.2.m.c.1345.1	yes	8
8.5	even	2		1792.2.m.a.1345.4	yes	8
16.3	odd	4		1792.2.m.c.449.1	yes	8
16.5	even	4	inner	1792.2.m.d.449.1	yes	8
16.11	odd	4		1792.2.m.b.449.4	yes	8
16.13	even	4		1792.2.m.a.449.4	✓	8
32.5	even	8		7168.2.a.t.1.3		4
32.11	odd	8		7168.2.a.w.1.3		4
32.21	even	8		7168.2.a.x.1.2		4
32.27	odd	8		7168.2.a.s.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.a.449.4	✓	8	16.13	even	4
1792.2.m.a.1345.4	yes	8	8.5	even	2
1792.2.m.b.449.4	yes	8	16.11	odd	4
1792.2.m.b.1345.4	yes	8	4.3	odd	2
1792.2.m.c.449.1	yes	8	16.3	odd	4
1792.2.m.c.1345.1	yes	8	8.3	odd	2
1792.2.m.d.449.1	yes	8	16.5	even	4	inner
1792.2.m.d.1345.1	yes	8	1.1	even	1	trivial
7168.2.a.s.1.2		4	32.27	odd	8
7168.2.a.t.1.3		4	32.5	even	8
7168.2.a.w.1.3		4	32.11	odd	8
7168.2.a.x.1.2		4	32.21	even	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.898966 - 0.898966i) q^{3} +(-0.786578 + 0.786578i) q^{5} -1.00000i q^{7} -1.38372i q^{9} +O(q^{10})\)	\(q+(-0.898966 - 0.898966i) q^{3} +(-0.786578 + 0.786578i) q^{5} -1.00000i q^{7} -1.38372i q^{9} +(-2.15894 + 2.15894i) q^{11} +(1.31318 + 1.31318i) q^{13} +1.41421 q^{15} -1.79793 q^{17} +(-0.531306 - 0.531306i) q^{19} +(-0.898966 + 0.898966i) q^{21} -5.95687i q^{23} +3.76259i q^{25} +(-3.94082 + 3.94082i) q^{27} +(5.62636 + 5.62636i) q^{29} -4.34059 q^{31} +3.88163 q^{33} +(0.786578 + 0.786578i) q^{35} +(2.12845 - 2.12845i) q^{37} -2.36101i q^{39} +0.712611i q^{41} +(-2.96951 + 2.96951i) q^{43} +(1.08840 + 1.08840i) q^{45} +2.20207 q^{47} -1.00000 q^{49} +(1.61628 + 1.61628i) q^{51} +(-3.38372 + 3.38372i) q^{53} -3.39635i q^{55} +0.955252i q^{57} +(-2.41549 + 2.41549i) q^{59} +(7.09505 + 7.09505i) q^{61} -1.38372 q^{63} -2.06584 q^{65} +(6.76744 + 6.76744i) q^{67} +(-5.35503 + 5.35503i) q^{69} -1.96788i q^{71} +10.3633i q^{73} +(3.38244 - 3.38244i) q^{75} +(2.15894 + 2.15894i) q^{77} +14.2449 q^{79} +2.93416 q^{81} +(-5.95217 - 5.95217i) q^{83} +(1.41421 - 1.41421i) q^{85} -10.1158i q^{87} +16.9417i q^{89} +(1.31318 - 1.31318i) q^{91} +(3.90205 + 3.90205i) q^{93} +0.835826 q^{95} +17.6796 q^{97} +(2.98737 + 2.98737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^5	\( 8 q + 4 q^{3} + 4 q^{5} - 8 q^{11} - 12 q^{13} + 8 q^{17} + 4 q^{19} + 4 q^{21} - 8 q^{27} + 8 q^{31} - 16 q^{33} - 4 q^{35} + 8 q^{37} - 24 q^{43} - 12 q^{45} + 40 q^{47} - 8 q^{49} + 24 q^{51} - 16 q^{53} - 52 q^{59} + 20 q^{61} - 24 q^{65} + 32 q^{67} - 8 q^{69} - 28 q^{75} + 8 q^{77} + 16 q^{81} - 12 q^{83} - 12 q^{91} + 40 q^{93} + 80 q^{95} + 72 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^11 - 12 * q^13 + 8 * q^17 + 4 * q^19 + 4 * q^21 - 8 * q^27 + 8 * q^31 - 16 * q^33 - 4 * q^35 + 8 * q^37 - 24 * q^43 - 12 * q^45 + 40 * q^47 - 8 * q^49 + 24 * q^51 - 16 * q^53 - 52 * q^59 + 20 * q^61 - 24 * q^65 + 32 * q^67 - 8 * q^69 - 28 * q^75 + 8 * q^77 + 16 * q^81 - 12 * q^83 - 12 * q^91 + 40 * q^93 + 80 * q^95 + 72 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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