LMFDB - Embedded newform 2548.2.u.d.589.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(589,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("2548.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.u (of order $6$, 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 188 x^{14} - 49 x^{13} + 1116 x^{12} - x^{11} + 4649 x^{10} + \cdots + 16 $ x^18 - x^17 + 17x^16 - 6x^15 + 188x^14 - 49x^13 + 1116x^12 - x^11 + 4649x^10 + 106x^9 + 9589x^8 + 3532x^7 + 12349x^6 + 753x^5 + 2622x^4 - 883x^3 + 541x^2 - 92*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			589.3
Root			$0.893365 - 1.54735i$ of defining polynomial
Character	$\chi$	$=$	2548.589
Dual form			2548.2.u.d.1765.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.893365 + 1.54735i) q^{3} +1.41239i q^{5} +(-0.0962010 - 0.166625i) q^{9} +(1.44649 + 0.835132i) q^{11} +(-2.45155 - 2.64384i) q^{13} +(-2.18546 - 1.26178i) q^{15} +(-3.38930 - 5.87045i) q^{17} +(4.90862 - 2.83399i) q^{19} +(0.576127 - 0.997882i) q^{23} +3.00517 q^{25} -5.01642 q^{27} +(1.79209 - 3.10400i) q^{29} -5.14475i q^{31} +(-2.58449 + 1.49215i) q^{33} +(4.91950 + 2.84027i) q^{37} +(6.28108 - 1.43150i) q^{39} +(-6.63082 - 3.82831i) q^{41} +(-2.20385 - 3.81717i) q^{43} +(0.235339 - 0.135873i) q^{45} -11.7333i q^{47} +12.1115 q^{51} -3.16988 q^{53} +(-1.17953 + 2.04300i) q^{55} +10.1272i q^{57} +(6.77778 - 3.91315i) q^{59} +(2.00285 + 3.46904i) q^{61} +(3.73412 - 3.46254i) q^{65} +(-11.8853 - 6.86196i) q^{67} +(1.02938 + 1.78294i) q^{69} +(-2.78064 + 1.60540i) q^{71} +12.1870i q^{73} +(-2.68471 + 4.65006i) q^{75} +11.4664 q^{79} +(4.77009 - 8.26204i) q^{81} +6.72074i q^{83} +(8.29133 - 4.78700i) q^{85} +(3.20199 + 5.54600i) q^{87} +(6.22521 + 3.59413i) q^{89} +(7.96075 + 4.59614i) q^{93} +(4.00269 + 6.93286i) q^{95} +(-2.06757 + 1.19371i) q^{97} -0.321362i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{3} - 6 q^{9} + 6 q^{11} + 4 q^{13} + 6 q^{15} + 10 q^{17} + 21 q^{19} - 6 q^{23} - 10 q^{25} + 20 q^{27} + 2 q^{29} + 12 q^{33} - 18 q^{37} - 25 q^{39} + 9 q^{41} - 14 q^{43} + 30 q^{45} - 4 q^{51}+ \cdots + 18 q^{97}+O(q^{100}) $ 18 * q - q^3 - 6 * q^9 + 6 * q^11 + 4 * q^13 + 6 * q^15 + 10 * q^17 + 21 * q^19 - 6 * q^23 - 10 * q^25 + 20 * q^27 + 2 * q^29 + 12 * q^33 - 18 * q^37 - 25 * q^39 + 9 * q^41 - 14 * q^43 + 30 * q^45 - 4 * q^51 + 26 * q^53 + q^55 - 21 * q^61 - 18 * q^65 - 15 * q^67 + q^69 - 45 * q^71 - 25 * q^75 + 28 * q^79 - q^81 - 30 * q^85 - 2 * q^87 - 9 * q^89 - 21 * q^93 + 30 * q^95 + 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.893365	+	1.54735i	−0.515784	+	0.893365i	0.484048	+	0.875042i	$0.339166\pi$
$3$	−0.893365	+	1.54735i	−0.515784	+	0.893365i	−0.999832	+	0.0183231i	$0.994167\pi$
$4$		0			0
$5$			1.41239i			0.631638i	0.948819	+	0.315819i	$0.102279\pi$
$5$			1.41239i			0.631638i	−0.948819	+	0.315819i	$0.897721\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.0962010	−	0.166625i	−0.0320670	−	0.0555417i
$10$		0			0
$11$	1.44649	+	0.835132i	0.436133	+	0.251802i	0.701956	−	0.712220i	$-0.252310\pi$
$11$	1.44649	+	0.835132i	0.436133	+	0.251802i	−0.265823	+	0.964022i	$0.585644\pi$
$12$		0			0
$13$	−2.45155	−	2.64384i	−0.679938	−	0.733270i
$13$	−2.45155	−	2.64384i	−0.679938	−	0.733270i
$14$		0			0
$15$	−2.18546	−	1.26178i	−0.564283	−	0.325789i
$16$		0			0
$17$	−3.38930	−	5.87045i	−0.822027	−	1.42379i	−0.904170	−	0.427172i	$-0.859510\pi$
$17$	−3.38930	−	5.87045i	−0.822027	−	1.42379i	0.0821435	−	0.996621i	$-0.473823\pi$
$18$		0			0
$19$	4.90862	−	2.83399i	1.12611	−	0.650163i	0.183160	−	0.983083i	$-0.441367\pi$
$19$	4.90862	−	2.83399i	1.12611	−	0.650163i	0.942955	+	0.332920i	$0.108034\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.576127	−	0.997882i	0.120131	−	0.208073i	−0.799688	−	0.600415i	$-0.795002\pi$
$23$	0.576127	−	0.997882i	0.120131	−	0.208073i	0.919819	+	0.392343i	$0.128335\pi$
$24$		0			0
$25$	3.00517			0.601033
$26$		0			0
$27$	−5.01642			−0.965410
$28$		0			0
$29$	1.79209	−	3.10400i	0.332784	−	0.576398i	−0.650273	−	0.759701i	$-0.725345\pi$
$29$	1.79209	−	3.10400i	0.332784	−	0.576398i	0.983057	+	0.183303i	$0.0586788\pi$
$30$		0			0
$31$		−	5.14475i		−	0.924025i	−0.886874	−	0.462012i	$-0.847128\pi$
$31$		−	5.14475i		−	0.924025i	0.886874	−	0.462012i	$-0.152872\pi$
$32$		0			0
$33$	−2.58449	+	1.49215i	−0.449902	+	0.259751i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.91950	+	2.84027i	0.808761	+	0.466938i	0.846525	−	0.532348i	$-0.178690\pi$
$37$	4.91950	+	2.84027i	0.808761	+	0.466938i	−0.0377646	+	0.999287i	$0.512024\pi$
$38$		0			0
$39$	6.28108	−	1.43150i	1.00578	−	0.229224i
$40$		0			0
$41$	−6.63082	−	3.82831i	−1.03556	−	0.597881i	−0.116987	−	0.993133i	$-0.537324\pi$
$41$	−6.63082	−	3.82831i	−1.03556	−	0.597881i	−0.918572	+	0.395253i	$0.870657\pi$
$42$		0			0
$43$	−2.20385	−	3.81717i	−0.336083	−	0.582113i	0.647609	−	0.761973i	$-0.275769\pi$
$43$	−2.20385	−	3.81717i	−0.336083	−	0.582113i	−0.983692	+	0.179860i	$0.942436\pi$
$44$		0			0
$45$	0.235339	−	0.135873i	0.0350822	−	0.0202547i
$46$		0			0
$47$		−	11.7333i		−	1.71148i	−0.517408	−	0.855739i	$-0.673103\pi$
$47$		−	11.7333i		−	1.71148i	0.517408	−	0.855739i	$-0.326897\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	12.1115			1.69595
$52$		0			0
$53$	−3.16988			−0.435417			−0.217708	−	0.976014i	$-0.569858\pi$
$53$	−3.16988			−0.435417			−0.217708	+	0.976014i	$0.569858\pi$
$54$		0			0
$55$	−1.17953	+	2.04300i	−0.159048	+	0.275478i
$56$		0			0
$57$			10.1272i			1.34137i
$58$		0			0
$59$	6.77778	−	3.91315i	0.882391	−	0.509449i	0.0109453	−	0.999940i	$-0.496516\pi$
$59$	6.77778	−	3.91315i	0.882391	−	0.509449i	0.871446	+	0.490491i	$0.163183\pi$
$60$		0			0
$61$	2.00285	+	3.46904i	0.256439	+	0.444165i	0.965285	−	0.261198i	$-0.0841175\pi$
$61$	2.00285	+	3.46904i	0.256439	+	0.444165i	−0.708847	+	0.705363i	$0.750784\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.73412	−	3.46254i	0.463161	−	0.429475i
$66$		0			0
$67$	−11.8853	−	6.86196i	−1.45202	−	0.838322i	−0.453421	−	0.891296i	$-0.649797\pi$
$67$	−11.8853	−	6.86196i	−1.45202	−	0.838322i	−0.998596	+	0.0529740i	$0.983130\pi$
$68$		0			0
$69$	1.02938	+	1.78294i	0.123923	+	0.214641i
$70$		0			0
$71$	−2.78064	+	1.60540i	−0.330001	+	0.190526i	−0.655841	−	0.754899i	$-0.727686\pi$
$71$	−2.78064	+	1.60540i	−0.330001	+	0.190526i	0.325841	+	0.945425i	$0.394353\pi$
$72$		0			0
$73$			12.1870i			1.42638i	0.700970	+	0.713190i	$0.252751\pi$
$73$			12.1870i			1.42638i	−0.700970	+	0.713190i	$0.747249\pi$
$74$		0			0
$75$	−2.68471	+	4.65006i	−0.310004	+	0.536942i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	11.4664			1.29007			0.645037	−	0.764152i	$-0.276842\pi$
$79$	11.4664			1.29007			0.645037	+	0.764152i	$0.276842\pi$
$80$		0			0
$81$	4.77009	−	8.26204i	0.530010	−	0.918005i
$82$		0			0
$83$			6.72074i			0.737697i	0.929490	+	0.368848i	$0.120248\pi$
$83$			6.72074i			0.737697i	−0.929490	+	0.368848i	$0.879752\pi$
$84$		0			0
$85$	8.29133	−	4.78700i	0.899321	−	0.519223i
$86$		0			0
$87$	3.20199	+	5.54600i	0.343289	+	0.594594i
$88$		0			0
$89$	6.22521	+	3.59413i	0.659871	+	0.380977i	0.792228	−	0.610225i	$-0.208921\pi$
$89$	6.22521	+	3.59413i	0.659871	+	0.380977i	−0.132357	+	0.991202i	$0.542254\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	7.96075	+	4.59614i	0.825491	+	0.476597i
$94$		0			0
$95$	4.00269	+	6.93286i	0.410667	+	0.711297i
$96$		0			0
$97$	−2.06757	+	1.19371i	−0.209930	+	0.121203i	−0.601279	−	0.799039i	$-0.705342\pi$
$97$	−2.06757	+	1.19371i	−0.209930	+	0.121203i	0.391349	+	0.920242i	$0.372009\pi$
$98$		0			0
$99$		−	0.321362i		−	0.0322981i
$100$		0			0
$101$	4.97642	−	8.61941i	0.495172	−	0.857663i	−0.504813	−	0.863229i	$-0.668438\pi$
$101$	4.97642	−	8.61941i	0.495172	−	0.857663i	0.999985	+	0.00556600i	$0.00177172\pi$
$102$		0			0
$103$	−14.7252			−1.45091			−0.725456	−	0.688268i	$-0.758371\pi$
$103$	−14.7252			−1.45091			−0.725456	+	0.688268i	$0.758371\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.521717	+	0.903640i	−0.0504362	+	0.0873581i	−0.890141	−	0.455685i	$-0.849395\pi$
$107$	−0.521717	+	0.903640i	−0.0504362	+	0.0873581i	0.839705	+	0.543043i	$0.182728\pi$
$108$		0			0
$109$			11.8166i			1.13182i	0.824466	+	0.565912i	$0.191476\pi$
$109$			11.8166i			1.13182i	−0.824466	+	0.565912i	$0.808524\pi$
$110$		0			0
$111$	−8.78981	+	5.07480i	−0.834292	+	0.481679i
$112$		0			0
$113$	−7.69833	−	13.3339i	−0.724198	−	1.25435i	−0.959303	−	0.282378i	$-0.908877\pi$
$113$	−7.69833	−	13.3339i	−0.724198	−	1.25435i	0.235105	−	0.971970i	$-0.424457\pi$
$114$		0			0
$115$	1.40939	+	0.813714i	0.131427	+	0.0758792i
$116$		0			0
$117$	−0.204688	+	0.662830i	−0.0189234	+	0.0612786i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.10511	−	7.11026i	−0.373192	−	0.646387i
$122$		0			0
$123$	11.8475	−	6.84015i	1.06825	−	0.616755i
$124$		0			0
$125$			11.3064i			1.01127i
$126$		0			0
$127$	−0.493081	+	0.854041i	−0.0437538	+	0.0757839i	−0.887073	−	0.461629i	$-0.847265\pi$
$127$	−0.493081	+	0.854041i	−0.0437538	+	0.0757839i	0.843319	+	0.537413i	$0.180598\pi$
$128$		0			0
$129$	7.87535			0.693386
$130$		0			0
$131$	12.6165			1.10231			0.551155	−	0.834403i	$-0.314187\pi$
$131$	12.6165			1.10231			0.551155	+	0.834403i	$0.314187\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		−	7.08512i		−	0.609790i
$136$		0			0
$137$	16.0896	−	9.28931i	1.37462	−	0.793639i	0.383118	−	0.923700i	$-0.374850\pi$
$137$	16.0896	−	9.28931i	1.37462	−	0.793639i	0.991506	+	0.130060i	$0.0415170\pi$
$138$		0			0
$139$	−4.75252	−	8.23161i	−0.403104	−	0.698196i	0.590995	−	0.806675i	$-0.298735\pi$
$139$	−4.75252	−	8.23161i	−0.403104	−	0.698196i	−0.994099	+	0.108479i	$0.965402\pi$
$140$		0			0
$141$	18.1556	+	10.4821i	1.52897	+	0.882753i
$142$		0			0
$143$	−1.33819	−	5.87166i	−0.111905	−	0.491013i
$144$		0			0
$145$	4.38404	+	2.53113i	0.364075	+	0.210199i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.63123	−	0.941790i	0.133635	−	0.0771545i	−0.431692	−	0.902021i	$-0.642083\pi$
$149$	1.63123	−	0.941790i	0.133635	−	0.0771545i	0.565327	+	0.824867i	$0.308750\pi$
$150$		0			0
$151$		−	1.66686i		−	0.135648i	−0.997697	−	0.0678238i	$-0.978394\pi$
$151$		−	1.66686i		−	0.135648i	0.997697	−	0.0678238i	$-0.0216056\pi$
$152$		0			0
$153$	−0.652109	+	1.12949i	−0.0527199	+	0.0913135i
$154$		0			0
$155$	7.26637			0.583649
$156$		0			0
$157$	9.62483			0.768145			0.384072	−	0.923303i	$-0.374521\pi$
$157$	9.62483			0.768145			0.384072	+	0.923303i	$0.374521\pi$
$158$		0			0
$159$	2.83186	−	4.90492i	0.224581	−	0.388986i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.43825	−	1.40773i	0.190979	−	0.110262i	−0.401462	−	0.915876i	$-0.631498\pi$
$163$	2.43825	−	1.40773i	0.190979	−	0.110262i	0.592441	+	0.805614i	$0.298164\pi$
$164$		0			0
$165$	−2.10750	−	3.65029i	−0.164068	−	0.284175i
$166$		0			0
$167$	−3.82773	−	2.20994i	−0.296198	−	0.171010i	0.344535	−	0.938773i	$-0.388036\pi$
$167$	−3.82773	−	2.20994i	−0.296198	−	0.171010i	−0.640734	+	0.767763i	$0.721370\pi$
$168$		0			0
$169$	−0.979788	+	12.9630i	−0.0753683	+	0.997156i
$170$		0			0
$171$	−0.944428	−	0.545266i	−0.0722222	−	0.0416975i
$172$		0			0
$173$	9.25463	+	16.0295i	0.703617	+	1.21870i	0.967189	+	0.254060i	$0.0817660\pi$
$173$	9.25463	+	16.0295i	0.703617	+	1.21870i	−0.263572	+	0.964640i	$0.584901\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			13.9835i			1.05106i
$178$		0			0
$179$	2.99156	−	5.18154i	0.223600	−	0.387286i	−0.732299	−	0.680984i	$-0.761552\pi$
$179$	2.99156	−	5.18154i	0.223600	−	0.387286i	0.955898	+	0.293697i	$0.0948858\pi$
$180$		0			0
$181$	2.08148			0.154715			0.0773575	−	0.997003i	$-0.475352\pi$
$181$	2.08148			0.154715			0.0773575	+	0.997003i	$0.475352\pi$
$182$		0			0
$183$	−7.15710			−0.529068
$184$		0			0
$185$	−4.01156	+	6.94823i	−0.294936	+	0.510844i
$186$		0			0
$187$		−	11.3221i		−	0.827951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.0441	−	22.5930i	−0.943838	−	1.63478i	−0.758061	−	0.652183i	$-0.773853\pi$
$191$	−13.0441	−	22.5930i	−0.943838	−	1.63478i	−0.185777	−	0.982592i	$-0.559480\pi$
$192$		0			0
$193$	11.6454	+	6.72345i	0.838252	+	0.483965i	0.856670	−	0.515866i	$-0.172530\pi$
$193$	11.6454	+	6.72345i	0.838252	+	0.483965i	−0.0184180	+	0.999830i	$0.505863\pi$
$194$		0			0
$195$	2.02183	+	8.87131i	0.144786	+	0.635288i
$196$		0			0
$197$	4.44601	+	2.56691i	0.316765	+	0.182885i	0.649950	−	0.759977i	$-0.274790\pi$
$197$	4.44601	+	2.56691i	0.316765	+	0.182885i	−0.333184	+	0.942862i	$0.608123\pi$
$198$		0			0
$199$	9.31361	+	16.1316i	0.660224	+	1.14354i	0.980556	+	0.196237i	$0.0628722\pi$
$199$	9.31361	+	16.1316i	0.660224	+	1.14354i	−0.320332	+	0.947305i	$0.603794\pi$
$200$		0			0
$201$	21.2358	−	12.2605i	1.49786	−	0.864787i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.40704	−	9.36527i	0.377644	−	0.654099i
$206$		0			0
$207$	−0.221696			−0.0154089
$208$		0			0
$209$	9.46703			0.654848
$210$		0			0
$211$	0.720035	−	1.24714i	0.0495692	−	0.0858564i	−0.840176	−	0.542314i	$-0.817548\pi$
$211$	0.720035	−	1.24714i	0.0495692	−	0.0858564i	0.889745	+	0.456457i	$0.150882\pi$
$212$		0			0
$213$		−	5.73683i		−	0.393081i
$214$		0			0
$215$	5.39132	−	3.11268i	0.367685	−	0.212283i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−18.8576	−	10.8874i	−1.27428	−	0.735705i
$220$		0			0
$221$	−7.21147	+	23.3525i	−0.485096	+	1.57086i
$222$		0			0
$223$	−0.263960	−	0.152397i	−0.0176761	−	0.0102053i	0.491136	−	0.871083i	$-0.336582\pi$
$223$	−0.263960	−	0.152397i	−0.0176761	−	0.0102053i	−0.508812	+	0.860878i	$0.669915\pi$
$224$		0			0
$225$	−0.289100	−	0.500736i	−0.0192733	−	0.0333824i
$226$		0			0
$227$	2.18239	−	1.26001i	0.144851	−	0.0836295i	−0.425823	−	0.904806i	$-0.640015\pi$
$227$	2.18239	−	1.26001i	0.144851	−	0.0836295i	0.570674	+	0.821177i	$0.306682\pi$
$228$		0			0
$229$		−	7.34531i		−	0.485392i	−0.970102	−	0.242696i	$-0.921968\pi$
$229$		−	7.34531i		−	0.485392i	0.970102	−	0.242696i	$-0.0780317\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	24.4856			1.60411			0.802053	−	0.597252i	$-0.203741\pi$
$233$	24.4856			1.60411			0.802053	+	0.597252i	$0.203741\pi$
$234$		0			0
$235$	16.5719			1.08103
$236$		0			0
$237$	−10.2437	+	17.7426i	−0.665400	+	1.15251i
$238$		0			0
$239$			1.44381i			0.0933922i	0.998909	+	0.0466961i	$0.0148692\pi$
$239$			1.44381i			0.0933922i	−0.998909	+	0.0466961i	$0.985131\pi$
$240$		0			0
$241$	−9.51138	+	5.49140i	−0.612682	+	0.353732i	−0.774014	−	0.633168i	$-0.781754\pi$
$241$	−9.51138	+	5.49140i	−0.612682	+	0.353732i	0.161333	+	0.986900i	$0.448421\pi$
$242$		0			0
$243$	0.998240	+	1.72900i	0.0640371	+	0.110916i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−19.5264	−	6.02993i	−1.24243	−	0.383675i
$248$		0			0
$249$	−10.3994	−	6.00407i	−0.659032	−	0.380493i
$250$		0			0
$251$	−8.01603	−	13.8842i	−0.505967	−	0.876361i	−0.999976	−	0.00690401i	$-0.997802\pi$
$251$	−8.01603	−	13.8842i	−0.505967	−	0.876361i	0.494009	−	0.869457i	$-0.335531\pi$
$252$		0			0
$253$	1.66673	−	0.962284i	0.104786	−	0.0604983i
$254$		0			0
$255$			17.1062i			1.07123i
$256$		0			0
$257$	−13.7003	+	23.7296i	−0.854600	+	1.48021i	0.0224155	+	0.999749i	$0.492864\pi$
$257$	−13.7003	+	23.7296i	−0.854600	+	1.48021i	−0.877016	+	0.480462i	$0.840469\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.689605			−0.0426855
$262$		0			0
$263$	−10.1003	+	17.4943i	−0.622814	+	1.07875i	0.366145	+	0.930558i	$0.380677\pi$
$263$	−10.1003	+	17.4943i	−0.622814	+	1.07875i	−0.988959	+	0.148188i	$0.952656\pi$
$264$		0			0
$265$		−	4.47709i		−	0.275026i
$266$		0			0
$267$	−11.1228	+	6.42174i	−0.680703	+	0.393004i
$268$		0			0
$269$	−4.54691	−	7.87548i	−0.277230	−	0.480176i	0.693465	−	0.720490i	$-0.256083\pi$
$269$	−4.54691	−	7.87548i	−0.277230	−	0.480176i	−0.970695	+	0.240314i	$0.922750\pi$
$270$		0			0
$271$	1.56769	+	0.905105i	0.0952303	+	0.0549812i	0.546859	−	0.837225i	$-0.315823\pi$
$271$	1.56769	+	0.905105i	0.0952303	+	0.0549812i	−0.451629	+	0.892206i	$0.649157\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.34695	+	2.50971i	0.262131	+	0.151341i
$276$		0			0
$277$	4.04743	+	7.01035i	0.243186	+	0.421211i	0.961620	−	0.274384i	$-0.0884740\pi$
$277$	4.04743	+	7.01035i	0.243186	+	0.421211i	−0.718434	+	0.695595i	$0.755141\pi$
$278$		0			0
$279$	−0.857244	+	0.494930i	−0.0513218	+	0.0296307i
$280$		0			0
$281$		−	16.0935i		−	0.960059i	−0.877252	−	0.480030i	$-0.840626\pi$
$281$		−	16.0935i		−	0.960059i	0.877252	−	0.480030i	$-0.159374\pi$
$282$		0			0
$283$	5.59555	−	9.69177i	0.332621	−	0.576116i	−0.650404	−	0.759588i	$-0.725400\pi$
$283$	5.59555	−	9.69177i	0.332621	−	0.576116i	0.983025	+	0.183472i	$0.0587338\pi$
$284$		0			0
$285$	−14.3035			−0.847263
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−14.4748	+	25.0710i	−0.851457	+	1.47477i
$290$		0			0
$291$		−	4.26568i		−	0.250059i
$292$		0			0
$293$	12.9552	−	7.47966i	0.756848	−	0.436967i	−0.0713148	−	0.997454i	$-0.522719\pi$
$293$	12.9552	−	7.47966i	0.756848	−	0.436967i	0.828163	+	0.560487i	$0.189386\pi$
$294$		0			0
$295$	5.52688	+	9.57283i	0.321787	+	0.557352i
$296$		0			0
$297$	−7.25620	−	4.18937i	−0.421048	−	0.243092i
$298$		0			0
$299$	−4.05065	+	0.923170i	−0.234255	+	0.0533883i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	8.89151	+	15.4005i	0.510804	+	0.884738i
$304$		0			0
$305$	−4.89962	+	2.82880i	−0.280551	+	0.161976i
$306$		0			0
$307$		−	10.4783i		−	0.598030i	−0.954248	−	0.299015i	$-0.903342\pi$
$307$		−	10.4783i		−	0.598030i	0.954248	−	0.299015i	$-0.0966581\pi$
$308$		0			0
$309$	13.1549	−	22.7850i	0.748358	−	1.29619i
$310$		0			0
$311$	9.67828			0.548805			0.274403	−	0.961615i	$-0.411520\pi$
$311$	9.67828			0.548805			0.274403	+	0.961615i	$0.411520\pi$
$312$		0			0
$313$	−31.5355			−1.78249			−0.891247	−	0.453519i	$-0.850169\pi$
$313$	−31.5355			−1.78249			−0.891247	+	0.453519i	$0.850169\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	2.23755i		−	0.125673i	−0.998024	−	0.0628367i	$-0.979985\pi$
$317$		−	2.23755i		−	0.125673i	0.998024	−	0.0628367i	$-0.0200147\pi$
$318$		0			0
$319$	5.18450	−	2.99327i	0.290276	−	0.167591i
$320$		0			0
$321$	−0.932166	−	1.61456i	−0.0520284	−	0.0901159i
$322$		0			0
$323$	−33.2736	−	19.2105i	−1.85139	−	1.06890i
$324$		0			0
$325$	−7.36732	−	7.94518i	−0.408666	−	0.440720i
$326$		0			0
$327$	−18.2844	−	10.5565i	−1.01113	−	0.583777i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	18.2345	−	10.5277i	1.00226	−	0.578656i	0.0933448	−	0.995634i	$-0.470244\pi$
$331$	18.2345	−	10.5277i	1.00226	−	0.578656i	0.908917	+	0.416978i	$0.136911\pi$
$332$		0			0
$333$		−	1.09295i		−	0.0598932i
$334$		0			0
$335$	9.69174	−	16.7866i	0.529516	−	0.917149i
$336$		0			0
$337$	24.6487			1.34270			0.671349	−	0.741141i	$-0.265715\pi$
$337$	24.6487			1.34270			0.671349	+	0.741141i	$0.265715\pi$
$338$		0			0
$339$	27.5097			1.49412
$340$		0			0
$341$	4.29655	−	7.44184i	0.232671	−	0.402998i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.51820	+	1.45389i	−0.135576	+	0.0782746i
$346$		0			0
$347$	−16.8055	−	29.1080i	−0.902167	−	1.56260i	−0.824676	−	0.565606i	$-0.808642\pi$
$347$	−16.8055	−	29.1080i	−0.902167	−	1.56260i	−0.0774912	−	0.996993i	$-0.524691\pi$
$348$		0			0
$349$	2.46776	+	1.42476i	0.132096	+	0.0762658i	0.564592	−	0.825370i	$-0.309034\pi$
$349$	2.46776	+	1.42476i	0.132096	+	0.0762658i	−0.432496	+	0.901636i	$0.642367\pi$
$350$		0			0
$351$	12.2980	+	13.2626i	0.656419	+	0.707906i
$352$		0			0
$353$	−24.7665	−	14.2990i	−1.31819	−	0.761057i	−0.334752	−	0.942306i	$-0.608652\pi$
$353$	−24.7665	−	14.2990i	−1.31819	−	0.761057i	−0.983437	+	0.181250i	$0.941986\pi$
$354$		0			0
$355$	−2.26744	−	3.92733i	−0.120343	−	0.208441i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			2.68544i			0.141732i	0.997486	+	0.0708660i	$0.0225763\pi$
$359$			2.68544i			0.141732i	−0.997486	+	0.0708660i	$0.977424\pi$
$360$		0			0
$361$	6.56304	−	11.3675i	0.345423	−	0.598290i
$362$		0			0
$363$	14.6694			0.769946
$364$		0			0
$365$	−17.2127			−0.900956
$366$		0			0
$367$	0.569817	−	0.986952i	0.0297442	−	0.0515185i	−0.850770	−	0.525538i	$-0.823864\pi$
$367$	0.569817	−	0.986952i	0.0297442	−	0.0515185i	0.880514	+	0.474020i	$0.157197\pi$
$368$		0			0
$369$			1.47315i			0.0766889i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	11.5364	+	19.9817i	0.597334	+	1.03461i	0.993213	+	0.116310i	$0.0371066\pi$
$373$	11.5364	+	19.9817i	0.597334	+	1.03461i	−0.395879	+	0.918303i	$0.629560\pi$
$374$		0			0
$375$	−17.4950	−	10.1007i	−0.903436	−	0.521599i
$376$		0			0
$377$	−12.5999	+	2.87160i	−0.648927	+	0.147895i
$378$		0			0
$379$	−15.5083	−	8.95374i	−0.796609	−	0.459923i	0.0456749	−	0.998956i	$-0.485456\pi$
$379$	−15.5083	−	8.95374i	−0.796609	−	0.459923i	−0.842284	+	0.539034i	$0.818789\pi$
$380$		0			0
$381$	−0.881002	−	1.52594i	−0.0451351	−	0.0781763i
$382$		0			0
$383$	30.5724	−	17.6510i	1.56217	−	0.901922i	0.565138	−	0.824997i	$-0.308823\pi$
$383$	30.5724	−	17.6510i	1.56217	−	0.901922i	0.997037	−	0.0769251i	$-0.0245102\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.424024	+	0.734431i	−0.0215544	+	0.0373332i
$388$		0			0
$389$	−31.8724			−1.61600			−0.807999	−	0.589184i	$-0.799449\pi$
$389$	−31.8724			−1.61600			−0.807999	+	0.589184i	$0.799449\pi$
$390$		0			0
$391$	−7.81068			−0.395003
$392$		0			0
$393$	−11.2712	+	19.5222i	−0.568555	+	0.984765i
$394$		0			0
$395$			16.1950i			0.814859i
$396$		0			0
$397$	7.70707	−	4.44968i	0.386807	−	0.223323i	−0.293969	−	0.955815i	$-0.594976\pi$
$397$	7.70707	−	4.44968i	0.386807	−	0.223323i	0.680776	+	0.732492i	$0.261643\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.84908	+	4.53167i	0.391964	+	0.226301i	0.683011	−	0.730408i	$-0.260670\pi$
$401$	7.84908	+	4.53167i	0.391964	+	0.226301i	−0.291047	+	0.956709i	$0.594003\pi$
$402$		0			0
$403$	−13.6019	+	12.6126i	−0.677559	+	0.628279i
$404$		0			0
$405$	11.6692	+	6.73721i	0.579847	+	0.334775i
$406$		0			0
$407$	4.74401	+	8.21686i	0.235152	+	0.407295i
$408$		0			0
$409$	−10.2498	+	5.91773i	−0.506820	+	0.292613i	−0.731526	−	0.681814i	$-0.761191\pi$
$409$	−10.2498	+	5.91773i	−0.506820	+	0.292613i	0.224705	+	0.974427i	$0.427858\pi$
$410$		0			0
$411$			33.1950i			1.63739i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−9.49227			−0.465957
$416$		0			0
$417$	16.9829			0.831658
$418$		0			0
$419$	8.87793	−	15.3770i	0.433715	−	0.751217i	−0.563475	−	0.826133i	$-0.690536\pi$
$419$	8.87793	−	15.3770i	0.433715	−	0.751217i	0.997190	+	0.0749167i	$0.0238691\pi$
$420$		0			0
$421$			22.6045i			1.10168i	0.834612	+	0.550838i	$0.185692\pi$
$421$			22.6045i			1.10168i	−0.834612	+	0.550838i	$0.814308\pi$
$422$		0			0
$423$	−1.95506	+	1.12875i	−0.0950583	+	0.0548819i
$424$		0			0
$425$	−10.1854	−	17.6417i	−0.494066	−	0.855747i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	10.2810	+	3.17488i	0.496373	+	0.153285i
$430$		0			0
$431$	−18.2515	−	10.5375i	−0.879142	−	0.507573i	−0.00876660	−	0.999962i	$-0.502791\pi$
$431$	−18.2515	−	10.5375i	−0.879142	−	0.507573i	−0.870375	+	0.492389i	$0.836124\pi$
$432$		0			0
$433$	12.8663	+	22.2851i	0.618316	+	1.07095i	0.989793	+	0.142512i	$0.0455181\pi$
$433$	12.8663	+	22.2851i	0.618316	+	1.07095i	−0.371477	+	0.928442i	$0.621149\pi$
$434$		0			0
$435$	−7.83310	+	4.52244i	−0.375568	+	0.216834i
$436$		0			0
$437$		−	6.53096i		−	0.312418i
$438$		0			0
$439$	−15.8732	+	27.4931i	−0.757585	+	1.31218i	0.186494	+	0.982456i	$0.440288\pi$
$439$	−15.8732	+	27.4931i	−0.757585	+	1.31218i	−0.944079	+	0.329720i	$0.893046\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.8364			−0.942454			−0.471227	−	0.882012i	$-0.656189\pi$
$443$	−19.8364			−0.942454			−0.471227	+	0.882012i	$0.656189\pi$
$444$		0			0
$445$	−5.07630	+	8.79240i	−0.240640	+	0.416800i
$446$		0			0
$447$			3.36545i			0.159180i
$448$		0			0
$449$	−15.2765	+	8.81989i	−0.720942	+	0.416236i	−0.815099	−	0.579321i	$-0.803318\pi$
$449$	−15.2765	+	8.81989i	−0.720942	+	0.416236i	0.0941570	+	0.995557i	$0.469984\pi$
$450$		0			0
$451$	−6.39428	−	11.0752i	−0.301095	−	0.521512i
$452$		0			0
$453$	2.57923	+	1.48912i	0.121183	+	0.0699649i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−23.1212	−	13.3490i	−1.08156	−	0.624441i	−0.150246	−	0.988649i	$-0.548007\pi$
$457$	−23.1212	−	13.3490i	−1.08156	−	0.624441i	−0.931318	+	0.364207i	$0.881340\pi$
$458$		0			0
$459$	17.0022	+	29.4486i	0.793593	+	1.37454i
$460$		0			0
$461$	−3.64848	+	2.10645i	−0.169927	+	0.0981071i	−0.582551	−	0.812794i	$-0.697945\pi$
$461$	−3.64848	+	2.10645i	−0.169927	+	0.0981071i	0.412625	+	0.910901i	$0.364612\pi$
$462$		0			0
$463$		−	34.4422i		−	1.60067i	−0.599556	−	0.800333i	$-0.704656\pi$
$463$		−	34.4422i		−	1.60067i	0.599556	−	0.800333i	$-0.295344\pi$
$464$		0			0
$465$	−6.49152	+	11.2436i	−0.301037	+	0.521411i
$466$		0			0
$467$	−26.8826			−1.24398			−0.621988	−	0.783027i	$-0.713675\pi$
$467$	−26.8826			−1.24398			−0.621988	+	0.783027i	$0.713675\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−8.59848	+	14.8930i	−0.396197	+	0.686234i
$472$		0			0
$473$		−	7.36201i		−	0.338505i
$474$		0			0
$475$	14.7512	−	8.51662i	0.676833	−	0.390770i
$476$		0			0
$477$	0.304946	+	0.528181i	0.0139625	+	0.0241838i
$478$		0			0
$479$	−30.8084	−	17.7873i	−1.40767	−	0.812720i	−0.412510	−	0.910953i	$-0.635348\pi$
$479$	−30.8084	−	17.7873i	−1.40767	−	0.812720i	−0.995163	+	0.0982329i	$0.968681\pi$
$480$		0			0
$481$	−4.55117	−	19.9695i	−0.207516	−	0.910529i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.68598	−	2.92021i	−0.0765565	−	0.132600i
$486$		0			0
$487$	−21.6293	+	12.4877i	−0.980117	+	0.565871i	−0.902305	−	0.431097i	$-0.858127\pi$
$487$	−21.6293	+	12.4877i	−0.980117	+	0.565871i	−0.0778114	+	0.996968i	$0.524793\pi$
$488$		0			0
$489$			5.03045i			0.227485i
$490$		0			0
$491$	18.6406	−	32.2865i	0.841240	−	1.45707i	−0.0476065	−	0.998866i	$-0.515159\pi$
$491$	18.6406	−	32.2865i	0.841240	−	1.45707i	0.888847	−	0.458205i	$-0.151507\pi$
$492$		0			0
$493$	−24.2958			−1.09423
$494$		0			0
$495$	0.453887			0.0204007
$496$		0			0
$497$		0			0
$498$		0			0
$499$			3.00566i			0.134552i	0.997734	+	0.0672759i	$0.0214308\pi$
$499$			3.00566i			0.134552i	−0.997734	+	0.0672759i	$0.978569\pi$
$500$		0			0
$501$	6.83911	−	3.94856i	0.305549	−	0.176409i
$502$		0			0
$503$	−6.70811	−	11.6188i	−0.299100	−	0.518056i	0.676831	−	0.736139i	$-0.263353\pi$
$503$	−6.70811	−	11.6188i	−0.299100	−	0.518056i	−0.975930	+	0.218083i	$0.930020\pi$
$504$		0			0
$505$	12.1739	+	7.02862i	0.541733	+	0.312769i
$506$		0			0
$507$	−19.1831	−	13.0968i	−0.851950	−	0.581649i
$508$		0			0
$509$	36.1416	+	20.8664i	1.60195	+	0.924886i	0.991097	+	0.133143i	$0.0425068\pi$
$509$	36.1416	+	20.8664i	1.60195	+	0.924886i	0.610853	+	0.791744i	$0.290827\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−24.6237	+	14.2165i	−1.08716	+	0.627674i
$514$		0			0
$515$		−	20.7976i		−	0.916452i
$516$		0			0
$517$	9.79886	−	16.9721i	0.430953	−	0.746433i
$518$		0			0
$519$	−33.0710			−1.45166
$520$		0			0
$521$	−20.4568			−0.896230			−0.448115	−	0.893976i	$-0.647904\pi$
$521$	−20.4568			−0.896230			−0.448115	+	0.893976i	$0.647904\pi$
$522$		0			0
$523$	−1.30125	+	2.25383i	−0.0568996	+	0.0985529i	−0.893072	−	0.449913i	$-0.851455\pi$
$523$	−1.30125	+	2.25383i	−0.0568996	+	0.0985529i	0.836173	+	0.548466i	$0.184788\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−30.2020	+	17.4371i	−1.31562	+	0.759573i
$528$		0			0
$529$	10.8362	+	18.7688i	0.471137	+	0.816034i
$530$		0			0
$531$	−1.30406	−	0.752898i	−0.0565913	−	0.0326730i
$532$		0			0
$533$	6.13437	+	26.9161i	0.265709	+	1.16587i
$534$		0			0
$535$	−1.27629	−	0.736865i	−0.0551787	−	0.0318574i
$536$		0			0
$537$	5.34511	+	9.25800i	0.230659	+	0.399512i
$538$		0			0
$539$		0			0
$540$		0			0
$541$			14.7308i			0.633328i	0.948538	+	0.316664i	$0.102563\pi$
$541$			14.7308i			0.633328i	−0.948538	+	0.316664i	$0.897437\pi$
$542$		0			0
$543$	−1.85952	+	3.22078i	−0.0797996	+	0.138217i
$544$		0			0
$545$	−16.6896			−0.714903
$546$		0			0
$547$	−0.154082			−0.00658808			−0.00329404	−	0.999995i	$-0.501049\pi$
$547$	−0.154082			−0.00658808			−0.00329404	+	0.999995i	$0.501049\pi$
$548$		0			0
$549$	0.385352	−	0.667449i	0.0164464	−	0.0284861i
$550$		0			0
$551$		−	20.3151i		−	0.865454i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−7.16758	−	12.4146i	−0.304247	−	0.526971i
$556$		0			0
$557$	−23.3779	−	13.4972i	−0.990552	−	0.571896i	−0.0851130	−	0.996371i	$-0.527125\pi$
$557$	−23.3779	−	13.4972i	−0.990552	−	0.571896i	−0.905439	+	0.424476i	$0.860458\pi$
$558$		0			0
$559$	−4.68915	+	15.1846i	−0.198330	+	0.642241i
$560$		0			0
$561$	17.5192	+	10.1147i	0.739663	+	0.427044i
$562$		0			0
$563$	20.2361	+	35.0500i	0.852852	+	1.47718i	0.878624	+	0.477515i	$0.158462\pi$
$563$	20.2361	+	35.0500i	0.852852	+	1.47718i	−0.0257722	+	0.999668i	$0.508204\pi$
$564$		0			0
$565$	18.8326	−	10.8730i	0.792294	−	0.457431i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.74231	+	4.74982i	−0.114964	+	0.199123i	−0.917765	−	0.397124i	$-0.870008\pi$
$569$	−2.74231	+	4.74982i	−0.114964	+	0.199123i	0.802802	+	0.596246i	$0.203342\pi$
$570$		0			0
$571$	19.4650			0.814585			0.407293	−	0.913298i	$-0.366473\pi$
$571$	19.4650			0.814585			0.407293	+	0.913298i	$0.366473\pi$
$572$		0			0
$573$	46.6126			1.94727
$574$		0			0
$575$	1.73136	−	2.99880i	0.0722026	−	0.125059i
$576$		0			0
$577$		−	29.0779i		−	1.21053i	−0.796025	−	0.605264i	$-0.793068\pi$
$577$		−	29.0779i		−	1.21053i	0.796025	−	0.605264i	$-0.206932\pi$
$578$		0			0
$579$	−20.8071	+	12.0130i	−0.864714	+	0.499243i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.58520	−	2.64727i	−0.189900	−	0.109639i
$584$		0			0
$585$	−0.936171	−	0.289099i	−0.0387059	−	0.0119528i
$586$		0			0
$587$	−21.2641	−	12.2768i	−0.877662	−	0.506718i	−0.00777502	−	0.999970i	$-0.502475\pi$
$587$	−21.2641	−	12.2768i	−0.877662	−	0.506718i	−0.869887	+	0.493252i	$0.835808\pi$
$588$		0			0
$589$	−14.5802	−	25.2536i	−0.600766	−	1.04056i
$590$		0			0
$591$	−7.94382	+	4.58637i	−0.326765	+	0.188658i
$592$		0			0
$593$			26.6457i			1.09421i	0.837064	+	0.547104i	$0.184270\pi$
$593$			26.6457i			1.09421i	−0.837064	+	0.547104i	$0.815730\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−33.2818			−1.36213
$598$		0			0
$599$	2.19399			0.0896441			0.0448220	−	0.998995i	$-0.485728\pi$
$599$	2.19399			0.0896441			0.0448220	+	0.998995i	$0.485728\pi$
$600$		0			0
$601$	2.47046	−	4.27896i	0.100772	−	0.174542i	−0.811231	−	0.584726i	$-0.801202\pi$
$601$	2.47046	−	4.27896i	0.100772	−	0.174542i	0.912003	+	0.410184i	$0.134535\pi$
$602$		0			0
$603$			2.64051i			0.107530i
$604$		0			0
$605$	10.0424	−	5.79800i	0.408283	−	0.235722i
$606$		0			0
$607$	4.08158	+	7.06950i	0.165666	+	0.286942i	0.936892	−	0.349620i	$-0.113689\pi$
$607$	4.08158	+	7.06950i	0.165666	+	0.286942i	−0.771226	+	0.636562i	$0.780356\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−31.0210	+	28.7648i	−1.25497	+	1.16370i
$612$		0			0
$613$	−18.0862	−	10.4421i	−0.730495	−	0.421751i	0.0881084	−	0.996111i	$-0.471918\pi$
$613$	−18.0862	−	10.4421i	−0.730495	−	0.421751i	−0.818603	+	0.574360i	$0.805251\pi$
$614$		0			0
$615$	9.66092	+	16.7332i	0.389566	+	0.674748i
$616$		0			0
$617$	−32.3343	+	18.6682i	−1.30173	+	0.751555i	−0.980701	−	0.195514i	$-0.937362\pi$
$617$	−32.3343	+	18.6682i	−1.30173	+	0.751555i	−0.321030	+	0.947069i	$0.604029\pi$
$618$		0			0
$619$			13.3505i			0.536603i	0.963335	+	0.268302i	$0.0864624\pi$
$619$			13.3505i			0.536603i	−0.963335	+	0.268302i	$0.913538\pi$
$620$		0			0
$621$	−2.89009	+	5.00579i	−0.115976	+	0.200875i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.943131			−0.0377253
$626$		0			0
$627$	−8.45751	+	14.6488i	−0.337761	+	0.585018i
$628$		0			0
$629$		−	38.5062i		−	1.53534i
$630$		0			0
$631$	37.7929	−	21.8198i	1.50451	−	0.868631i	0.504527	−	0.863396i	$-0.331667\pi$
$631$	37.7929	−	21.8198i	1.50451	−	0.868631i	0.999986	−	0.00523510i	$-0.00166639\pi$
$632$		0			0
$633$	1.28651	+	2.22830i	0.0511341	+	0.0885668i
$634$		0			0
$635$	−1.20623	−	0.696420i	−0.0478680	−	0.0276366i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.535000	+	0.308882i	0.0211643	+	0.0122192i
$640$		0			0
$641$	−13.0431	−	22.5914i	−0.515173	−	0.892306i	−0.999845	−	0.0176101i	$-0.994394\pi$
$641$	−13.0431	−	22.5914i	−0.515173	−	0.892306i	0.484672	−	0.874696i	$-0.338939\pi$
$642$		0			0
$643$	38.2452	−	22.0809i	1.50825	−	0.870786i	0.508291	−	0.861185i	$-0.330277\pi$
$643$	38.2452	−	22.0809i	1.50825	−	0.870786i	0.999954	−	0.00960062i	$-0.00305602\pi$
$644$		0			0
$645$			11.1230i			0.437969i
$646$		0			0
$647$	−7.76036	+	13.4413i	−0.305091	+	0.528433i	−0.977282	−	0.211945i	$-0.932020\pi$
$647$	−7.76036	+	13.4413i	−0.305091	+	0.528433i	0.672190	+	0.740378i	$0.265354\pi$
$648$		0			0
$649$	13.0720			0.513121
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.1084	−	33.0967i	0.747769	−	1.29517i	−0.201121	−	0.979566i	$-0.564458\pi$
$653$	19.1084	−	33.0967i	0.747769	−	1.29517i	0.948890	−	0.315608i	$-0.102208\pi$
$654$		0			0
$655$			17.8194i			0.696261i
$656$		0			0
$657$	2.03066	−	1.17240i	0.0792236	−	0.0457397i
$658$		0			0
$659$	−10.2159	−	17.6944i	−0.397955	−	0.689277i	0.595519	−	0.803341i	$-0.296946\pi$
$659$	−10.2159	−	17.6944i	−0.397955	−	0.689277i	−0.993473	+	0.114064i	$0.963613\pi$
$660$		0			0
$661$	7.49575	+	4.32767i	0.291551	+	0.168327i	0.638641	−	0.769505i	$-0.279497\pi$
$661$	7.49575	+	4.32767i	0.291551	+	0.168327i	−0.347090	+	0.937832i	$0.612830\pi$
$662$		0			0
$663$	−29.6921	−	32.0210i	−1.15314	−	1.24359i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.06495	−	3.57660i	−0.0799551	−	0.138486i
$668$		0			0
$669$	0.471625	−	0.272293i	0.0182341	−	0.0105275i
$670$		0			0
$671$			6.69058i			0.258287i
$672$		0			0
$673$	−13.0726	+	22.6424i	−0.503912	+	0.872801i	0.496078	+	0.868278i	$0.334773\pi$
$673$	−13.0726	+	22.6424i	−0.503912	+	0.872801i	−0.999990	+	0.00452265i	$0.998560\pi$
$674$		0			0
$675$	−15.0752			−0.580244
$676$		0			0
$677$	−0.319797			−0.0122908			−0.00614539	−	0.999981i	$-0.501956\pi$
$677$	−0.319797			−0.0122908			−0.00614539	+	0.999981i	$0.501956\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			4.50258i			0.172539i
$682$		0			0
$683$	4.50473	−	2.60081i	0.172369	−	0.0995170i	−0.411334	−	0.911485i	$-0.634937\pi$
$683$	4.50473	−	2.60081i	0.172369	−	0.0995170i	0.583702	+	0.811968i	$0.301604\pi$
$684$		0			0
$685$	13.1201	+	22.7247i	0.501293	+	0.868265i
$686$		0			0
$687$	11.3658	+	6.56204i	0.433632	+	0.250357i
$688$		0			0
$689$	7.77113	+	8.38066i	0.296056	+	0.319278i
$690$		0			0
$691$	−5.48965	−	3.16945i	−0.208836	−	0.120572i	0.391934	−	0.919993i	$-0.371806\pi$
$691$	−5.48965	−	3.16945i	−0.208836	−	0.120572i	−0.600770	+	0.799422i	$0.705139\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.6262	−	6.71239i	0.441007	−	0.254616i
$696$		0			0
$697$			51.9012i			1.96590i
$698$		0			0
$699$	−21.8746	+	37.8879i	−0.827373	+	1.43305i
$700$		0			0
$701$	39.6964			1.49931			0.749655	−	0.661828i	$-0.230219\pi$
$701$	39.6964			1.49931			0.749655	+	0.661828i	$0.230219\pi$
$702$		0			0
$703$	32.1973			1.21434
$704$		0			0
$705$	−14.8048	+	25.6426i	−0.557581	+	0.965758i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	26.3165	−	15.1938i	0.988337	−	0.570617i	0.0835602	−	0.996503i	$-0.473371\pi$
$709$	26.3165	−	15.1938i	0.988337	−	0.570617i	0.904777	+	0.425886i	$0.140038\pi$
$710$		0			0
$711$	−1.10308	−	1.91059i	−0.0413688	−	0.0716528i
$712$		0			0
$713$	−5.13385	−	2.96403i	−0.192264	−	0.111004i
$714$		0			0
$715$	8.29305	−	1.89004i	0.310142	−	0.0706836i
$716$		0			0
$717$	−2.23408	−	1.28985i	−0.0834333	−	0.0481702i
$718$		0			0
$719$	11.1395	+	19.2941i	0.415432	+	0.719550i	0.995474	−	0.0950371i	$-0.0302970\pi$
$719$	11.1395	+	19.2941i	0.415432	+	0.719550i	−0.580041	+	0.814587i	$0.696964\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		−	19.6233i		−	0.729798i
$724$		0			0
$725$	5.38554	−	9.32803i	0.200014	−	0.346434i
$726$		0			0
$727$	39.0166			1.44705			0.723523	−	0.690300i	$-0.242522\pi$
$727$	39.0166			1.44705			0.723523	+	0.690300i	$0.242522\pi$
$728$		0			0
$729$	25.0534			0.927903
$730$		0			0
$731$	−14.9390	+	25.8751i	−0.552539	+	0.957026i
$732$		0			0
$733$		−	35.7643i		−	1.32098i	−0.750834	−	0.660491i	$-0.770348\pi$
$733$		−	35.7643i		−	1.32098i	0.750834	−	0.660491i	$-0.229652\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.4613	−	19.8515i	−0.422182	−	0.731241i
$738$		0			0
$739$	−16.9984	−	9.81403i	−0.625297	−	0.361015i	0.153632	−	0.988128i	$-0.450903\pi$
$739$	−16.9984	−	9.81403i	−0.625297	−	0.361015i	−0.778928	+	0.627113i	$0.784236\pi$
$740$		0			0
$741$	26.7746	−	24.8273i	0.983589	−	0.912052i
$742$		0			0
$743$	−20.5695	−	11.8758i	−0.754621	−	0.435681i	0.0727399	−	0.997351i	$-0.476826\pi$
$743$	−20.5695	−	11.8758i	−0.754621	−	0.435681i	−0.827361	+	0.561670i	$0.810159\pi$
$744$		0			0
$745$	1.33017	+	2.30392i	0.0487337	+	0.0844092i
$746$		0			0
$747$	1.11984	−	0.646542i	0.0409729	−	0.0236557i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.26053	+	14.3077i	−0.301431	+	0.522094i	−0.976460	−	0.215697i	$-0.930798\pi$
$751$	−8.26053	+	14.3077i	−0.301431	+	0.522094i	0.675029	+	0.737791i	$0.264131\pi$
$752$		0			0
$753$	28.6449			1.04388
$754$		0			0
$755$	2.35426			0.0856801
$756$		0			0
$757$	−5.76790	+	9.99030i	−0.209638	+	0.363104i	−0.951601	−	0.307338i	$-0.900562\pi$
$757$	−5.76790	+	9.99030i	−0.209638	+	0.363104i	0.741963	+	0.670441i	$0.233895\pi$
$758$		0			0
$759$			3.43868i			0.124816i
$760$		0			0
$761$	−10.5574	+	6.09530i	−0.382704	+	0.220954i	−0.678994	−	0.734144i	$-0.737584\pi$
$761$	−10.5574	+	6.09530i	−0.382704	+	0.220954i	0.296290	+	0.955098i	$0.404251\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.59527	−	0.921029i	−0.0576771	−	0.0332999i
$766$		0			0
$767$	−26.9618	−	8.32607i	−0.973535	−	0.300637i
$768$		0			0
$769$	−12.3254	−	7.11605i	−0.444464	−	0.256611i	0.261026	−	0.965332i	$-0.415939\pi$
$769$	−12.3254	−	7.11605i	−0.444464	−	0.256611i	−0.705489	+	0.708721i	$0.749273\pi$
$770$		0			0
$771$	−24.4787	−	42.3983i	−0.881579	−	1.52694i
$772$		0			0
$773$	40.0536	−	23.1250i	1.44063	−	0.831748i	0.442738	−	0.896651i	$-0.354007\pi$
$773$	40.0536	−	23.1250i	1.44063	−	0.831748i	0.997892	+	0.0649035i	$0.0206740\pi$
$774$		0			0
$775$		−	15.4608i		−	0.555370i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−43.3976			−1.55488
$780$		0			0
$781$	−5.36289			−0.191899
$782$		0			0
$783$	−8.98989	+	15.5710i	−0.321273	+	0.556460i
$784$		0			0
$785$			13.5940i			0.485189i
$786$		0			0
$787$	27.3472	−	15.7889i	0.974822	−	0.562814i	0.0741191	−	0.997249i	$-0.476385\pi$
$787$	27.3472	−	15.7889i	0.974822	−	0.562814i	0.900703	+	0.434436i	$0.143052\pi$
$788$		0			0
$789$	−18.0466	−	31.2576i	−0.642476	−	1.11280i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.26149	−	13.7997i	0.151330	−	0.490043i
$794$		0			0
$795$	6.92764	+	3.99968i	0.245698	+	0.141854i
$796$		0			0
$797$	2.40382	+	4.16354i	0.0851477	+	0.147480i	0.905454	−	0.424444i	$-0.139530\pi$
$797$	2.40382	+	4.16354i	0.0851477	+	0.147480i	−0.820306	+	0.571924i	$0.806197\pi$
$798$		0			0
$799$	−68.8797	+	39.7677i	−2.43679	+	1.40688i
$800$		0			0
$801$		−	1.38303i		−	0.0488671i
$802$		0			0
$803$	−10.1778	+	17.6284i	−0.359165	+	0.622092i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	16.2482			0.571964
$808$		0			0
$809$	0.758121	−	1.31310i	0.0266541	−	0.0461663i	−0.852391	−	0.522905i	$-0.824848\pi$
$809$	0.758121	−	1.31310i	0.0266541	−	0.0461663i	0.879045	+	0.476739i	$0.158181\pi$
$810$		0			0
$811$			44.4771i			1.56180i	0.624654	+	0.780901i	$0.285240\pi$
$811$			44.4771i			1.56180i	−0.624654	+	0.780901i	$0.714760\pi$
$812$		0			0
$813$	−2.80104	+	1.61718i	−0.0982366	+	0.0567169i
$814$		0			0
$815$	1.98825	+	3.44375i	0.0696454	+	0.120629i
$816$		0			0
$817$	−21.6357	−	12.4914i	−0.756937	−	0.437018i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.8647	−	6.27272i	−0.379179	−	0.218919i	0.298282	−	0.954478i	$-0.403586\pi$
$821$	−10.8647	−	6.27272i	−0.379179	−	0.218919i	−0.677461	+	0.735559i	$0.736920\pi$
$822$		0			0
$823$	19.3302	+	33.4809i	0.673808	+	1.16707i	0.976816	+	0.214082i	$0.0686760\pi$
$823$	19.3302	+	33.4809i	0.673808	+	1.16707i	−0.303007	+	0.952988i	$0.597991\pi$
$824$		0			0
$825$	−7.76682	+	4.48418i	−0.270406	+	0.156119i
$826$		0			0
$827$			10.4039i			0.361780i	0.983503	+	0.180890i	$0.0578977\pi$
$827$			10.4039i			0.361780i	−0.983503	+	0.180890i	$0.942102\pi$
$828$		0			0
$829$	−8.96371	+	15.5256i	−0.311323	+	0.539227i	−0.978649	−	0.205539i	$-0.934105\pi$
$829$	−8.96371	+	15.5256i	−0.311323	+	0.539227i	0.667326	+	0.744765i	$0.267439\pi$
$830$		0			0
$831$	−14.4633			−0.501727
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.12129	−	5.40622i	0.108017	−	0.187090i
$836$		0			0
$837$			25.8082i			0.892063i
$838$		0			0
$839$	8.61866	−	4.97598i	0.297549	−	0.171790i	−0.343792	−	0.939046i	$-0.611712\pi$
$839$	8.61866	−	4.97598i	0.297549	−	0.171790i	0.641341	+	0.767256i	$0.278378\pi$
$840$		0			0
$841$	8.07680	+	13.9894i	0.278510	+	0.482394i
$842$		0			0
$843$	24.9024	+	14.3774i	0.857683	+	0.495184i
$844$		0			0
$845$	−18.3088	−	1.38384i	−0.629841	−	0.0476055i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	9.99773	+	17.3166i	0.343121	+	0.594303i
$850$		0			0
$851$	5.66851	−	3.27272i	0.194314	−	0.112187i
$852$		0			0
$853$		−	21.5922i		−	0.739302i	−0.929171	−	0.369651i	$-0.879477\pi$
$853$		−	21.5922i		−	0.739302i	0.929171	−	0.369651i	$-0.120523\pi$
$854$		0			0
$855$	0.770125	−	1.33390i	0.0263377	−	0.0456183i
$856$		0			0
$857$	3.97270			0.135705			0.0678524	−	0.997695i	$-0.478385\pi$
$857$	3.97270			0.135705			0.0678524	+	0.997695i	$0.478385\pi$
$858$		0			0
$859$	49.8039			1.69929			0.849644	−	0.527357i	$-0.176817\pi$
$859$	49.8039			1.69929			0.849644	+	0.527357i	$0.176817\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			11.3284i			0.385624i	0.981236	+	0.192812i	$0.0617607\pi$
$863$			11.3284i			0.385624i	−0.981236	+	0.192812i	$0.938239\pi$
$864$		0			0
$865$	−22.6398	+	13.0711i	−0.769777	+	0.444431i
$866$		0			0
$867$	−25.8625	−	44.7951i	−0.878336	−	1.52132i
$868$		0			0
$869$	16.5861	+	9.57598i	0.562644	+	0.324843i
$870$		0			0
$871$	10.9954	+	48.2452i	0.372565	+	1.63473i
$872$		0			0
$873$	0.397805	+	0.229673i	0.0134636	+	0.00777324i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.51904	+	2.60907i	−0.152597	+	0.0881019i	−0.574354	−	0.818607i	$-0.694747\pi$
$877$	−4.51904	+	2.60907i	−0.152597	+	0.0881019i	0.421757	+	0.906709i	$0.361413\pi$
$878$		0			0
$879$			26.7283i			0.901522i
$880$		0			0
$881$	16.4160	−	28.4334i	0.553070	−	0.957946i	−0.444981	−	0.895540i	$-0.646789\pi$
$881$	16.4160	−	28.4334i	0.553070	−	0.957946i	0.998051	−	0.0624056i	$-0.0198772\pi$
$882$		0			0
$883$	45.6813			1.53730			0.768648	−	0.639672i	$-0.220930\pi$
$883$	45.6813			1.53730			0.768648	+	0.639672i	$0.220930\pi$
$884$		0			0
$885$	−19.7501			−0.663891
$886$		0			0
$887$	−3.32423	+	5.75774i	−0.111617	+	0.193326i	−0.916422	−	0.400213i	$-0.868936\pi$
$887$	−3.32423	+	5.75774i	−0.111617	+	0.193326i	0.804805	+	0.593539i	$0.202270\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	13.7998	−	7.96732i	0.462311	−	0.266915i
$892$		0			0
$893$	−33.2521	−	57.5943i	−1.11274	−	1.92732i
$894$		0			0
$895$	7.31833	+	4.22524i	0.244625	+	0.141234i
$896$		0			0
$897$	2.19023	−	7.09251i	0.0731298	−	0.236812i
$898$		0			0
$899$	−15.9693	−	9.21988i	−0.532606	−	0.307500i
$900$		0			0
$901$	10.7437	+	18.6086i	0.357924	+	0.619943i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			2.93985i			0.0977239i
$906$		0			0
$907$	12.3589	−	21.4063i	0.410372	−	0.710785i	−0.584558	−	0.811352i	$-0.698732\pi$
$907$	12.3589	−	21.4063i	0.410372	−	0.710785i	0.994930	+	0.100567i	$0.0320655\pi$
$908$		0			0
$909$	−1.91494			−0.0635147
$910$		0			0
$911$	−14.4092			−0.477397			−0.238698	−	0.971094i	$-0.576721\pi$
$911$	−14.4092			−0.477397			−0.238698	+	0.971094i	$0.576721\pi$
$912$		0			0
$913$	−5.61270	+	9.72149i	−0.185753	+	0.321734i
$914$		0			0
$915$		−	10.1086i		−	0.334180i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.86666	+	3.23315i	0.0615754	+	0.106652i	0.895170	−	0.445725i	$-0.147054\pi$
$919$	1.86666	+	3.23315i	0.0615754	+	0.106652i	−0.833594	+	0.552377i	$0.813721\pi$
$920$		0			0
$921$	16.2137	+	9.36098i	0.534259	+	0.308455i
$922$		0			0
$923$	11.0613	+	3.41583i	0.364087	+	0.112434i
$924$		0			0
$925$	14.7839	+	8.53550i	0.486092	+	0.280645i
$926$		0			0
$927$	1.41657	+	2.45358i	0.0465264	+	0.0805861i
$928$		0			0
$929$	22.0407	−	12.7252i	0.723130	−	0.417500i	−0.0927733	−	0.995687i	$-0.529573\pi$
$929$	22.0407	−	12.7252i	0.723130	−	0.417500i	0.815904	+	0.578188i	$0.196240\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−8.64624	+	14.9757i	−0.283065	+	0.490283i
$934$		0			0
$935$	15.9911			0.522966
$936$		0			0
$937$	−25.0364			−0.817905			−0.408952	−	0.912556i	$-0.634106\pi$
$937$	−25.0364			−0.817905			−0.408952	+	0.912556i	$0.634106\pi$
$938$		0			0
$939$	28.1727	−	48.7966i	0.919382	−	1.59242i
$940$		0			0
$941$			12.3808i			0.403604i	0.979426	+	0.201802i	$0.0646797\pi$
$941$			12.3808i			0.403604i	−0.979426	+	0.201802i	$0.935320\pi$
$942$		0			0
$943$	−7.64039	+	4.41118i	−0.248805	+	0.143648i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.5614	+	10.1391i	0.570669	+	0.329476i	0.757417	−	0.652932i	$-0.226461\pi$
$947$	17.5614	+	10.1391i	0.570669	+	0.329476i	−0.186747	+	0.982408i	$0.559795\pi$
$948$		0			0
$949$	32.2205	−	29.8771i	1.04592	−	0.969851i
$950$		0			0
$951$	3.46228	+	1.99895i	0.112272	+	0.0648204i
$952$		0			0
$953$	−0.542566	−	0.939751i	−0.0175754	−	0.0304415i	0.857104	−	0.515144i	$-0.172261\pi$
$953$	−0.542566	−	0.939751i	−0.0175754	−	0.0304415i	−0.874679	+	0.484702i	$0.838928\pi$
$954$		0			0
$955$	31.9101	−	18.4233i	1.03259	−	0.596164i
$956$		0			0
$957$			10.6963i			0.345763i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	4.53154			0.146179
$962$		0			0
$963$	0.200759			0.00646935
$964$		0			0
$965$	−9.49611	+	16.4477i	−0.305691	+	0.529472i
$966$		0			0
$967$			6.19597i			0.199249i	0.995025	+	0.0996245i	$0.0317642\pi$
$967$			6.19597i			0.199249i	−0.995025	+	0.0996245i	$0.968236\pi$
$968$		0			0
$969$	59.4509	−	34.3240i	1.90984	−	1.10265i
$970$		0			0
$971$	21.5123	+	37.2605i	0.690364	+	1.19575i	0.971719	+	0.236142i	$0.0758829\pi$
$971$	21.5123	+	37.2605i	0.690364	+	1.19575i	−0.281355	+	0.959604i	$0.590784\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	18.8757	−	4.30190i	0.604507	−	0.137771i
$976$		0			0
$977$	−49.7684	−	28.7338i	−1.59223	−	0.919275i	−0.992923	−	0.118756i	$-0.962109\pi$
$977$	−49.7684	−	28.7338i	−1.59223	−	0.919275i	−0.599307	−	0.800519i	$-0.704557\pi$
$978$		0			0
$979$	6.00315	+	10.3978i	0.191861	+	0.332314i
$980$		0			0
$981$	1.96894	−	1.13677i	0.0628634	−	0.0362942i
$982$		0			0
$983$		−	5.12560i		−	0.163481i	−0.996654	−	0.0817406i	$-0.973952\pi$
$983$		−	5.12560i		−	0.163481i	0.996654	−	0.0817406i	$-0.0260479\pi$
$984$		0			0
$985$	−3.62546	+	6.27949i	−0.115517	+	0.200081i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.07878			−0.161496
$990$		0			0
$991$	−17.7691	+	30.7771i	−0.564456	+	0.977666i	0.432645	+	0.901565i	$0.357580\pi$
$991$	−17.7691	+	30.7771i	−0.564456	+	0.977666i	−0.997100	+	0.0761011i	$0.975753\pi$
$992$		0			0
$993$			37.6204i			1.19385i
$994$		0			0
$995$	−22.7841	+	13.1544i	−0.722305	+	0.417023i
$996$		0			0
$997$	−20.5543	−	35.6011i	−0.650961	−	1.12750i	−0.982890	−	0.184193i	$-0.941033\pi$
$997$	−20.5543	−	35.6011i	−0.650961	−	1.12750i	0.331929	−	0.943304i	$-0.392301\pi$
$998$		0			0
$999$	−24.6783	−	14.2480i	−0.780786	−	0.450787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.u.d.589.3		18
7.2	even	3		2548.2.bb.f.1733.3		18
7.3	odd	6		364.2.bq.a.121.3	yes	18
7.4	even	3		2548.2.bq.f.1941.7		18
7.5	odd	6		364.2.bb.a.277.7	yes	18
7.6	odd	2		2548.2.u.e.589.7		18
13.10	even	6	inner	2548.2.u.d.1765.3		18
21.5	even	6		3276.2.hi.i.1369.7		18
21.17	even	6		3276.2.fe.i.2305.3		18
91.10	odd	6		364.2.bb.a.205.7	✓	18
91.23	even	6		2548.2.bq.f.361.7		18
91.62	odd	6		2548.2.u.e.1765.7		18
91.75	odd	6		364.2.bq.a.361.3	yes	18
91.88	even	6		2548.2.bb.f.569.3		18
273.101	even	6		3276.2.hi.i.1297.7		18
273.257	even	6		3276.2.fe.i.361.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.bb.a.205.7	✓	18	91.10	odd	6
364.2.bb.a.277.7	yes	18	7.5	odd	6
364.2.bq.a.121.3	yes	18	7.3	odd	6
364.2.bq.a.361.3	yes	18	91.75	odd	6
2548.2.u.d.589.3		18	1.1	even	1	trivial
2548.2.u.d.1765.3		18	13.10	even	6	inner
2548.2.u.e.589.7		18	7.6	odd	2
2548.2.u.e.1765.7		18	91.62	odd	6
2548.2.bb.f.569.3		18	91.88	even	6
2548.2.bb.f.1733.3		18	7.2	even	3
2548.2.bq.f.361.7		18	91.23	even	6
2548.2.bq.f.1941.7		18	7.4	even	3
3276.2.fe.i.361.3		18	273.257	even	6
3276.2.fe.i.2305.3		18	21.17	even	6
3276.2.hi.i.1297.7		18	273.101	even	6
3276.2.hi.i.1369.7		18	21.5	even	6

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.893365 + 1.54735i) q^{3} +1.41239i q^{5} +(-0.0962010 - 0.166625i) q^{9} +(1.44649 + 0.835132i) q^{11} +(-2.45155 - 2.64384i) q^{13} +(-2.18546 - 1.26178i) q^{15} +(-3.38930 - 5.87045i) q^{17} +(4.90862 - 2.83399i) q^{19} +(0.576127 - 0.997882i) q^{23} +3.00517 q^{25} -5.01642 q^{27} +(1.79209 - 3.10400i) q^{29} -5.14475i q^{31} +(-2.58449 + 1.49215i) q^{33} +(4.91950 + 2.84027i) q^{37} +(6.28108 - 1.43150i) q^{39} +(-6.63082 - 3.82831i) q^{41} +(-2.20385 - 3.81717i) q^{43} +(0.235339 - 0.135873i) q^{45} -11.7333i q^{47} +12.1115 q^{51} -3.16988 q^{53} +(-1.17953 + 2.04300i) q^{55} +10.1272i q^{57} +(6.77778 - 3.91315i) q^{59} +(2.00285 + 3.46904i) q^{61} +(3.73412 - 3.46254i) q^{65} +(-11.8853 - 6.86196i) q^{67} +(1.02938 + 1.78294i) q^{69} +(-2.78064 + 1.60540i) q^{71} +12.1870i q^{73} +(-2.68471 + 4.65006i) q^{75} +11.4664 q^{79} +(4.77009 - 8.26204i) q^{81} +6.72074i q^{83} +(8.29133 - 4.78700i) q^{85} +(3.20199 + 5.54600i) q^{87} +(6.22521 + 3.59413i) q^{89} +(7.96075 + 4.59614i) q^{93} +(4.00269 + 6.93286i) q^{95} +(-2.06757 + 1.19371i) q^{97} -0.321362i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{3} - 6 q^{9} + 6 q^{11} + 4 q^{13} + 6 q^{15} + 10 q^{17} + 21 q^{19} - 6 q^{23} - 10 q^{25} + 20 q^{27} + 2 q^{29} + 12 q^{33} - 18 q^{37} - 25 q^{39} + 9 q^{41} - 14 q^{43} + 30 q^{45} - 4 q^{51}+ \cdots + 18 q^{97}+O(q^{100}) \) 18 * q - q^3 - 6 * q^9 + 6 * q^11 + 4 * q^13 + 6 * q^15 + 10 * q^17 + 21 * q^19 - 6 * q^23 - 10 * q^25 + 20 * q^27 + 2 * q^29 + 12 * q^33 - 18 * q^37 - 25 * q^39 + 9 * q^41 - 14 * q^43 + 30 * q^45 - 4 * q^51 + 26 * q^53 + q^55 - 21 * q^61 - 18 * q^65 - 15 * q^67 + q^69 - 45 * q^71 - 25 * q^75 + 28 * q^79 - q^81 - 30 * q^85 - 2 * q^87 - 9 * q^89 - 21 * q^93 + 30 * q^95 + 18 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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