LMFDB - Embedded newform 968.2.i.j.753.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, degree $4$, not 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			753.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	968.753
Dual form			968.2.i.j.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.42705 + 1.76336i) q^{3} +(-0.927051 + 2.85317i) q^{5} +(1.61803 - 1.17557i) q^{7} +(1.85410 + 5.70634i) q^{9} +O(q^{10})$	\(q+(2.42705 + 1.76336i) q^{3} +(-0.927051 + 2.85317i) q^{5} +(1.61803 - 1.17557i) q^{7} +(1.85410 + 5.70634i) q^{9} +(-7.28115 + 5.29007i) q^{15} +(-1.85410 + 5.70634i) q^{17} +(-3.23607 - 2.35114i) q^{19} +6.00000 q^{21} +1.00000 q^{23} +(-3.23607 - 2.35114i) q^{25} +(-2.78115 + 8.55951i) q^{27} +(6.47214 - 4.70228i) q^{29} +(-2.16312 - 6.65740i) q^{31} +(1.85410 + 5.70634i) q^{35} +(0.809017 - 0.587785i) q^{37} +(-3.23607 - 2.35114i) q^{41} +6.00000 q^{43} -18.0000 q^{45} +(6.47214 + 4.70228i) q^{47} +(-0.927051 + 2.85317i) q^{49} +(-14.5623 + 10.5801i) q^{51} +(0.618034 + 1.90211i) q^{53} +(-3.70820 - 11.4127i) q^{57} +(0.809017 - 0.587785i) q^{59} +(1.23607 - 3.80423i) q^{61} +(9.70820 + 7.05342i) q^{63} -5.00000 q^{67} +(2.42705 + 1.76336i) q^{69} +(0.927051 - 2.85317i) q^{71} +(-12.9443 + 9.40456i) q^{73} +(-3.70820 - 11.4127i) q^{75} +(0.618034 + 1.90211i) q^{79} +(-7.28115 + 5.29007i) q^{81} +(-0.618034 + 1.90211i) q^{83} +(-14.5623 - 10.5801i) q^{85} +24.0000 q^{87} +15.0000 q^{89} +(6.48936 - 19.9722i) q^{93} +(9.70820 - 7.05342i) q^{95} +(-2.16312 - 6.65740i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9	$ 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9} - 9 q^{15} + 6 q^{17} - 4 q^{19} + 24 q^{21} + 4 q^{23} - 4 q^{25} + 9 q^{27} + 8 q^{29} + 7 q^{31} - 6 q^{35} + q^{37} - 4 q^{41} + 24 q^{43} - 72 q^{45} + 8 q^{47} + 3 q^{49} - 18 q^{51} - 2 q^{53} + 12 q^{57} + q^{59} - 4 q^{61} + 12 q^{63} - 20 q^{67} + 3 q^{69} - 3 q^{71} - 16 q^{73} + 12 q^{75} - 2 q^{79} - 9 q^{81} + 2 q^{83} - 18 q^{85} + 96 q^{87} + 60 q^{89} - 21 q^{93} + 12 q^{95} + 7 q^{97}+O(q^{100}) $ 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9 - 9 * q^15 + 6 * q^17 - 4 * q^19 + 24 * q^21 + 4 * q^23 - 4 * q^25 + 9 * q^27 + 8 * q^29 + 7 * q^31 - 6 * q^35 + q^37 - 4 * q^41 + 24 * q^43 - 72 * q^45 + 8 * q^47 + 3 * q^49 - 18 * q^51 - 2 * q^53 + 12 * q^57 + q^59 - 4 * q^61 + 12 * q^63 - 20 * q^67 + 3 * q^69 - 3 * q^71 - 16 * q^73 + 12 * q^75 - 2 * q^79 - 9 * q^81 + 2 * q^83 - 18 * q^85 + 96 * q^87 + 60 * q^89 - 21 * q^93 + 12 * q^95 + 7 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	2.42705	+	1.76336i	1.40126	+	1.01807i	0.994522	+	0.104528i	$0.0333333\pi$
$3$	2.42705	+	1.76336i	1.40126	+	1.01807i	0.406737	+	0.913545i	$0.366667\pi$
$4$		0			0
$5$	−0.927051	+	2.85317i	−0.414590	+	1.27598i	0.498027	+	0.867161i	$0.334058\pi$
$5$	−0.927051	+	2.85317i	−0.414590	+	1.27598i	−0.912617	+	0.408815i	$0.865942\pi$
$6$		0			0
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	−0.238404	−	0.971166i	$-0.576624\pi$
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	0.849963	+	0.526842i	$0.176624\pi$
$8$		0			0
$9$	1.85410	+	5.70634i	0.618034	+	1.90211i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$13$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$14$		0			0
$15$	−7.28115	+	5.29007i	−1.87999	+	1.36589i
$16$		0			0
$17$	−1.85410	+	5.70634i	−0.449686	+	1.38399i	0.427576	+	0.903979i	$0.359367\pi$
$17$	−1.85410	+	5.70634i	−0.449686	+	1.38399i	−0.877262	+	0.480011i	$0.840633\pi$
$18$		0			0
$19$	−3.23607	−	2.35114i	−0.742405	−	0.539389i	0.151058	−	0.988525i	$-0.451732\pi$
$19$	−3.23607	−	2.35114i	−0.742405	−	0.539389i	−0.893463	+	0.449136i	$0.851732\pi$
$20$		0			0
$21$	6.00000			1.30931
$22$		0			0
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$		0			0
$25$	−3.23607	−	2.35114i	−0.647214	−	0.470228i
$26$		0			0
$27$	−2.78115	+	8.55951i	−0.535233	+	1.64728i
$28$		0			0
$29$	6.47214	−	4.70228i	1.20185	−	0.873192i	0.207380	−	0.978260i	$-0.433506\pi$
$29$	6.47214	−	4.70228i	1.20185	−	0.873192i	0.994465	+	0.105069i	$0.0335062\pi$
$30$		0			0
$31$	−2.16312	−	6.65740i	−0.388508	−	1.19570i	−0.933904	−	0.357525i	$-0.883621\pi$
$31$	−2.16312	−	6.65740i	−0.388508	−	1.19570i	0.545396	−	0.838179i	$-0.316379\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.85410	+	5.70634i	0.313400	+	0.964547i
$36$		0			0
$37$	0.809017	−	0.587785i	0.133002	−	0.0966313i	−0.519295	−	0.854595i	$-0.673806\pi$
$37$	0.809017	−	0.587785i	0.133002	−	0.0966313i	0.652297	+	0.757964i	$0.273806\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.23607	−	2.35114i	−0.505389	−	0.367187i	0.305683	−	0.952133i	$-0.401115\pi$
$41$	−3.23607	−	2.35114i	−0.505389	−	0.367187i	−0.811072	+	0.584947i	$0.801115\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−18.0000			−2.68328
$46$		0			0
$47$	6.47214	+	4.70228i	0.944058	+	0.685898i	0.949394	−	0.314087i	$-0.101699\pi$
$47$	6.47214	+	4.70228i	0.944058	+	0.685898i	−0.00533600	+	0.999986i	$0.501699\pi$
$48$		0			0
$49$	−0.927051	+	2.85317i	−0.132436	+	0.407596i
$50$		0			0
$51$	−14.5623	+	10.5801i	−2.03913	+	1.48152i
$52$		0			0
$53$	0.618034	+	1.90211i	0.0848935	+	0.261275i	0.984488	−	0.175450i	$-0.0561381\pi$
$53$	0.618034	+	1.90211i	0.0848935	+	0.261275i	−0.899595	+	0.436726i	$0.856138\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.70820	−	11.4127i	−0.491164	−	1.51165i
$58$		0			0
$59$	0.809017	−	0.587785i	0.105325	−	0.0765231i	−0.533876	−	0.845563i	$-0.679265\pi$
$59$	0.809017	−	0.587785i	0.105325	−	0.0765231i	0.639201	+	0.769040i	$0.279265\pi$
$60$		0			0
$61$	1.23607	−	3.80423i	0.158262	−	0.487081i	−0.840215	−	0.542254i	$-0.817571\pi$
$61$	1.23607	−	3.80423i	0.158262	−	0.487081i	0.998477	+	0.0551729i	$0.0175710\pi$
$62$		0			0
$63$	9.70820	+	7.05342i	1.22312	+	0.888648i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.00000			−0.610847			−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000			−0.610847			−0.305424	+	0.952217i	$0.598798\pi$
$68$		0			0
$69$	2.42705	+	1.76336i	0.292183	+	0.212283i
$70$		0			0
$71$	0.927051	−	2.85317i	0.110021	−	0.338609i	−0.880855	−	0.473386i	$-0.843032\pi$
$71$	0.927051	−	2.85317i	0.110021	−	0.338609i	0.990876	+	0.134777i	$0.0430317\pi$
$72$		0			0
$73$	−12.9443	+	9.40456i	−1.51501	+	1.10072i	−0.551121	+	0.834425i	$0.685800\pi$
$73$	−12.9443	+	9.40456i	−1.51501	+	1.10072i	−0.963891	+	0.266296i	$0.914200\pi$
$74$		0			0
$75$	−3.70820	−	11.4127i	−0.428187	−	1.31782i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.618034	+	1.90211i	0.0695343	+	0.214004i	0.979785	−	0.200053i	$-0.0641114\pi$
$79$	0.618034	+	1.90211i	0.0695343	+	0.214004i	−0.910251	+	0.414057i	$0.864111\pi$
$80$		0			0
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$		0			0
$83$	−0.618034	+	1.90211i	−0.0678380	+	0.208784i	−0.979229	−	0.202758i	$-0.935010\pi$
$83$	−0.618034	+	1.90211i	−0.0678380	+	0.208784i	0.911391	+	0.411542i	$0.135010\pi$
$84$		0			0
$85$	−14.5623	−	10.5801i	−1.57950	−	1.14758i
$86$		0			0
$87$	24.0000			2.57307
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.48936	−	19.9722i	0.672915	−	2.07102i
$94$		0			0
$95$	9.70820	−	7.05342i	0.996041	−	0.723666i
$96$		0			0
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	−0.998792	−	0.0491321i	$-0.984354\pi$
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	0.779161	−	0.626824i	$-0.215646\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.09017	−	9.51057i	−0.307483	−	0.946337i	−0.978739	−	0.205110i	$-0.934245\pi$
$101$	−3.09017	−	9.51057i	−0.307483	−	0.946337i	0.671255	−	0.741226i	$-0.265755\pi$
$102$		0			0
$103$	12.9443	−	9.40456i	1.27544	−	0.926659i	0.276032	−	0.961148i	$-0.410980\pi$
$103$	12.9443	−	9.40456i	1.27544	−	0.926659i	0.999405	+	0.0344892i	$0.0109804\pi$
$104$		0			0
$105$	−5.56231	+	17.1190i	−0.542825	+	1.67065i
$106$		0			0
$107$	−1.61803	−	1.17557i	−0.156421	−	0.113647i	0.506822	−	0.862051i	$-0.330820\pi$
$107$	−1.61803	−	1.17557i	−0.156421	−	0.113647i	−0.663243	+	0.748404i	$0.730820\pi$
$108$		0			0
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$	3.00000			0.284747
$112$		0			0
$113$	5.66312	+	4.11450i	0.532741	+	0.387059i	0.821382	−	0.570378i	$-0.193203\pi$
$113$	5.66312	+	4.11450i	0.532741	+	0.387059i	−0.288641	+	0.957437i	$0.593203\pi$
$114$		0			0
$115$	−0.927051	+	2.85317i	−0.0864479	+	0.266059i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.70820	+	11.4127i	0.339930	+	1.04620i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−3.70820	−	11.4127i	−0.334357	−	1.02905i
$124$		0			0
$125$	−2.42705	+	1.76336i	−0.217082	+	0.157719i
$126$		0			0
$127$	1.23607	−	3.80423i	0.109683	−	0.337570i	−0.881118	−	0.472897i	$-0.843208\pi$
$127$	1.23607	−	3.80423i	0.109683	−	0.337570i	0.990801	+	0.135326i	$0.0432083\pi$
$128$		0			0
$129$	14.5623	+	10.5801i	1.28214	+	0.931529i
$130$		0			0
$131$	−2.00000			−0.174741			−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000			−0.174741			−0.0873704	+	0.996176i	$0.527846\pi$
$132$		0			0
$133$	−8.00000			−0.693688
$134$		0			0
$135$	−21.8435	−	15.8702i	−1.87999	−	1.36589i
$136$		0			0
$137$	−4.63525	+	14.2658i	−0.396017	+	1.21881i	0.532150	+	0.846650i	$0.321384\pi$
$137$	−4.63525	+	14.2658i	−0.396017	+	1.21881i	−0.928167	+	0.372164i	$0.878616\pi$
$138$		0			0
$139$	17.7984	−	12.9313i	1.50964	−	1.09682i	0.543301	−	0.839538i	$-0.317174\pi$
$139$	17.7984	−	12.9313i	1.50964	−	1.09682i	0.966337	−	0.257279i	$-0.0828258\pi$
$140$		0			0
$141$	7.41641	+	22.8254i	0.624574	+	1.92224i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	7.41641	+	22.8254i	0.615899	+	1.89554i
$146$		0			0
$147$	−7.28115	+	5.29007i	−0.600539	+	0.436317i
$148$		0			0
$149$	5.56231	−	17.1190i	0.455682	−	1.40244i	−0.414651	−	0.909981i	$-0.636096\pi$
$149$	5.56231	−	17.1190i	0.455682	−	1.40244i	0.870333	−	0.492464i	$-0.163904\pi$
$150$		0			0
$151$	14.5623	+	10.5801i	1.18506	+	0.860999i	0.992734	−	0.120331i	$-0.0383957\pi$
$151$	14.5623	+	10.5801i	1.18506	+	0.860999i	0.192330	+	0.981330i	$0.438396\pi$
$152$		0			0
$153$	−36.0000			−2.91043
$154$		0			0
$155$	21.0000			1.68676
$156$		0			0
$157$	8.89919	+	6.46564i	0.710232	+	0.516014i	0.883249	−	0.468905i	$-0.155351\pi$
$157$	8.89919	+	6.46564i	0.710232	+	0.516014i	−0.173016	+	0.984919i	$0.555351\pi$
$158$		0			0
$159$	−1.85410	+	5.70634i	−0.147040	+	0.452542i
$160$		0			0
$161$	1.61803	−	1.17557i	0.127519	−	0.0926479i
$162$		0			0
$163$	−1.23607	−	3.80423i	−0.0968163	−	0.297970i	0.890906	−	0.454187i	$-0.150070\pi$
$163$	−1.23607	−	3.80423i	−0.0968163	−	0.297970i	−0.987723	+	0.156217i	$0.950070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.94427	+	15.2169i	0.382599	+	1.17752i	0.938207	+	0.346075i	$0.112486\pi$
$167$	4.94427	+	15.2169i	0.382599	+	1.17752i	−0.555608	+	0.831445i	$0.687514\pi$
$168$		0			0
$169$	10.5172	−	7.64121i	0.809017	−	0.587785i
$170$		0			0
$171$	7.41641	−	22.8254i	0.567147	−	1.74550i
$172$		0			0
$173$	−14.5623	−	10.5801i	−1.10715	−	0.804393i	−0.124939	−	0.992164i	$-0.539873\pi$
$173$	−14.5623	−	10.5801i	−1.10715	−	0.804393i	−0.982213	+	0.187772i	$0.939873\pi$
$174$		0			0
$175$	−8.00000			−0.604743
$176$		0			0
$177$	3.00000			0.225494
$178$		0			0
$179$	4.04508	+	2.93893i	0.302344	+	0.219666i	0.728604	−	0.684935i	$-0.240169\pi$
$179$	4.04508	+	2.93893i	0.302344	+	0.219666i	−0.426261	+	0.904600i	$0.640169\pi$
$180$		0			0
$181$	−1.54508	+	4.75528i	−0.114845	+	0.353457i	−0.991915	−	0.126906i	$-0.959495\pi$
$181$	−1.54508	+	4.75528i	−0.114845	+	0.353457i	0.877069	+	0.480364i	$0.159495\pi$
$182$		0			0
$183$	9.70820	−	7.05342i	0.717651	−	0.521404i
$184$		0			0
$185$	0.927051	+	2.85317i	0.0681581	+	0.209769i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	5.56231	+	17.1190i	0.404598	+	1.24523i
$190$		0			0
$191$	7.28115	−	5.29007i	0.526846	−	0.382776i	−0.292331	−	0.956317i	$-0.594431\pi$
$191$	7.28115	−	5.29007i	0.526846	−	0.382776i	0.819177	+	0.573541i	$0.194431\pi$
$192$		0			0
$193$	1.23607	−	3.80423i	0.0889741	−	0.273834i	−0.896662	−	0.442715i	$-0.854015\pi$
$193$	1.23607	−	3.80423i	0.0889741	−	0.273834i	0.985636	+	0.168881i	$0.0540153\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	−12.1353	−	8.81678i	−0.855955	−	0.621888i
$202$		0			0
$203$	4.94427	−	15.2169i	0.347020	−	1.06802i
$204$		0			0
$205$	9.70820	−	7.05342i	0.678050	−	0.492632i
$206$		0			0
$207$	1.85410	+	5.70634i	0.128869	+	0.396618i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	6.18034	+	19.0211i	0.425472	+	1.30947i	0.902541	+	0.430603i	$0.141699\pi$
$211$	6.18034	+	19.0211i	0.425472	+	1.30947i	−0.477069	+	0.878866i	$0.658301\pi$
$212$		0			0
$213$	7.28115	−	5.29007i	0.498896	−	0.362469i
$214$		0			0
$215$	−5.56231	+	17.1190i	−0.379346	+	1.16751i
$216$		0			0
$217$	−11.3262	−	8.22899i	−0.768875	−	0.558620i
$218$		0			0
$219$	−48.0000			−3.24354
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−23.4615	−	17.0458i	−1.57110	−	1.14147i	−0.926096	−	0.377288i	$-0.876857\pi$
$223$	−23.4615	−	17.0458i	−1.57110	−	1.14147i	−0.645002	−	0.764181i	$-0.723143\pi$
$224$		0			0
$225$	7.41641	−	22.8254i	0.494427	−	1.52169i
$226$		0			0
$227$	−14.5623	+	10.5801i	−0.966534	+	0.702228i	−0.954659	−	0.297701i	$-0.903780\pi$
$227$	−14.5623	+	10.5801i	−0.966534	+	0.702228i	−0.0118751	+	0.999929i	$0.503780\pi$
$228$		0			0
$229$	−6.48936	−	19.9722i	−0.428829	−	1.31980i	−0.899280	−	0.437373i	$-0.855909\pi$
$229$	−6.48936	−	19.9722i	−0.428829	−	1.31980i	0.470451	−	0.882426i	$-0.344091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.94427	−	15.2169i	−0.323910	−	0.996893i	−0.971930	−	0.235269i	$-0.924403\pi$
$233$	−4.94427	−	15.2169i	−0.323910	−	0.996893i	0.648020	−	0.761623i	$-0.275597\pi$
$234$		0			0
$235$	−19.4164	+	14.1068i	−1.26659	+	0.920229i
$236$		0			0
$237$	−1.85410	+	5.70634i	−0.120437	+	0.370667i
$238$		0			0
$239$	1.61803	+	1.17557i	0.104662	+	0.0760413i	0.638885	−	0.769302i	$-0.279396\pi$
$239$	1.61803	+	1.17557i	0.104662	+	0.0760413i	−0.534223	+	0.845343i	$0.679396\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.28115	−	5.29007i	−0.465176	−	0.337970i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−4.85410	+	3.52671i	−0.307616	+	0.223496i
$250$		0			0
$251$	−4.01722	−	12.3637i	−0.253565	−	0.780392i	−0.994109	−	0.108384i	$-0.965432\pi$
$251$	−4.01722	−	12.3637i	−0.253565	−	0.780392i	0.740544	−	0.672008i	$-0.234568\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−16.6869	−	51.3571i	−1.04498	−	3.21610i
$256$		0			0
$257$	8.09017	−	5.87785i	0.504651	−	0.366650i	−0.306140	−	0.951987i	$-0.599037\pi$
$257$	8.09017	−	5.87785i	0.504651	−	0.366650i	0.810791	+	0.585336i	$0.199037\pi$
$258$		0			0
$259$	0.618034	−	1.90211i	0.0384028	−	0.118192i
$260$		0			0
$261$	38.8328	+	28.2137i	2.40369	+	1.74638i
$262$		0			0
$263$	14.0000			0.863277			0.431638	−	0.902047i	$-0.357936\pi$
$263$	14.0000			0.863277			0.431638	+	0.902047i	$0.357936\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	36.4058	+	26.4503i	2.22800	+	1.61873i
$268$		0			0
$269$	8.03444	−	24.7275i	0.489869	−	1.50766i	−0.334935	−	0.942241i	$-0.608714\pi$
$269$	8.03444	−	24.7275i	0.489869	−	1.50766i	0.824804	−	0.565419i	$-0.191286\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.618034	−	1.90211i	−0.0371341	−	0.114287i	0.930771	−	0.365602i	$-0.119137\pi$
$277$	−0.618034	−	1.90211i	−0.0371341	−	0.114287i	−0.967905	+	0.251315i	$0.919137\pi$
$278$		0			0
$279$	33.9787	−	24.6870i	2.03425	−	1.47797i
$280$		0			0
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	−0.880399	−	0.474234i	$-0.842725\pi$
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	0.991005	+	0.133822i	$0.0427251\pi$
$282$		0			0
$283$	−3.23607	−	2.35114i	−0.192364	−	0.139761i	0.487434	−	0.873160i	$-0.337933\pi$
$283$	−3.23607	−	2.35114i	−0.192364	−	0.139761i	−0.679799	+	0.733399i	$0.737933\pi$
$284$		0			0
$285$	36.0000			2.13246
$286$		0			0
$287$	−8.00000			−0.472225
$288$		0			0
$289$	−15.3713	−	11.1679i	−0.904195	−	0.656936i
$290$		0			0
$291$	6.48936	−	19.9722i	0.380413	−	1.17079i
$292$		0			0
$293$	−9.70820	+	7.05342i	−0.567159	+	0.412065i	−0.834072	−	0.551655i	$-0.813996\pi$
$293$	−9.70820	+	7.05342i	−0.567159	+	0.412065i	0.266913	+	0.963721i	$0.413996\pi$
$294$		0			0
$295$	0.927051	+	2.85317i	0.0539750	+	0.166118i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	9.70820	−	7.05342i	0.559572	−	0.406553i
$302$		0			0
$303$	9.27051	−	28.5317i	0.532577	−	1.63910i
$304$		0			0
$305$	9.70820	+	7.05342i	0.555890	+	0.403878i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	48.0000			2.73062
$310$		0			0
$311$	9.70820	+	7.05342i	0.550502	+	0.399963i	0.827970	−	0.560772i	$-0.189495\pi$
$311$	9.70820	+	7.05342i	0.550502	+	0.399963i	−0.277469	+	0.960735i	$0.589495\pi$
$312$		0			0
$313$	−2.78115	+	8.55951i	−0.157200	+	0.483812i	−0.998377	−	0.0569477i	$-0.981863\pi$
$313$	−2.78115	+	8.55951i	−0.157200	+	0.483812i	0.841177	+	0.540760i	$0.181863\pi$
$314$		0			0
$315$	−29.1246	+	21.1603i	−1.64099	+	1.19225i
$316$		0			0
$317$	−4.63525	−	14.2658i	−0.260342	−	0.801250i	−0.992730	−	0.120362i	$-0.961594\pi$
$317$	−4.63525	−	14.2658i	−0.260342	−	0.801250i	0.732388	−	0.680887i	$-0.238406\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.85410	−	5.70634i	−0.103486	−	0.318497i
$322$		0			0
$323$	19.4164	−	14.1068i	1.08036	−	0.784926i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−33.9787	−	24.6870i	−1.87903	−	1.36519i
$328$		0			0
$329$	16.0000			0.882109
$330$		0			0
$331$	−35.0000			−1.92377			−0.961887	−	0.273447i	$-0.911836\pi$
$331$	−35.0000			−1.92377			−0.961887	+	0.273447i	$0.911836\pi$
$332$		0			0
$333$	4.85410	+	3.52671i	0.266003	+	0.193263i
$334$		0			0
$335$	4.63525	−	14.2658i	0.253251	−	0.779427i
$336$		0			0
$337$	8.09017	−	5.87785i	0.440700	−	0.320187i	−0.345213	−	0.938524i	$-0.612193\pi$
$337$	8.09017	−	5.87785i	0.440700	−	0.320187i	0.785913	+	0.618337i	$0.212193\pi$
$338$		0			0
$339$	6.48936	+	19.9722i	0.352453	+	1.08474i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	6.18034	+	19.0211i	0.333707	+	1.02704i
$344$		0			0
$345$	−7.28115	+	5.29007i	−0.392004	+	0.284808i
$346$		0			0
$347$	−9.88854	+	30.4338i	−0.530845	+	1.63377i	0.221615	+	0.975134i	$0.428867\pi$
$347$	−9.88854	+	30.4338i	−0.530845	+	1.63377i	−0.752460	+	0.658638i	$0.771133\pi$
$348$		0			0
$349$	11.3262	+	8.22899i	0.606280	+	0.440488i	0.848102	−	0.529833i	$-0.177745\pi$
$349$	11.3262	+	8.22899i	0.606280	+	0.440488i	−0.241823	+	0.970320i	$0.577745\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$		0			0
$355$	7.28115	+	5.29007i	0.386443	+	0.280768i
$356$		0			0
$357$	−11.1246	+	34.2380i	−0.588777	+	1.81207i
$358$		0			0
$359$	−19.4164	+	14.1068i	−1.02476	+	0.744531i	−0.967253	−	0.253814i	$-0.918315\pi$
$359$	−19.4164	+	14.1068i	−1.02476	+	0.744531i	−0.0575058	+	0.998345i	$0.518315\pi$
$360$		0			0
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−14.8328	−	45.6507i	−0.776385	−	2.38947i
$366$		0			0
$367$	−26.6976	+	19.3969i	−1.39360	+	1.01251i	−0.398142	+	0.917324i	$0.630345\pi$
$367$	−26.6976	+	19.3969i	−1.39360	+	1.01251i	−0.995459	+	0.0951868i	$0.969655\pi$
$368$		0			0
$369$	7.41641	−	22.8254i	0.386083	−	1.18824i
$370$		0			0
$371$	3.23607	+	2.35114i	0.168008	+	0.122065i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−9.00000			−0.464758
$376$		0			0
$377$		0			0
$378$		0			0
$379$	7.72542	−	23.7764i	0.396828	−	1.22131i	−0.530700	−	0.847560i	$-0.678071\pi$
$379$	7.72542	−	23.7764i	0.396828	−	1.22131i	0.927528	−	0.373753i	$-0.121929\pi$
$380$		0			0
$381$	9.70820	−	7.05342i	0.497366	−	0.361358i
$382$		0			0
$383$	0.309017	+	0.951057i	0.0157900	+	0.0485967i	0.958641	−	0.284618i	$-0.0918667\pi$
$383$	0.309017	+	0.951057i	0.0157900	+	0.0485967i	−0.942851	+	0.333214i	$0.891867\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	11.1246	+	34.2380i	0.565496	+	1.74042i
$388$		0			0
$389$	−10.5172	+	7.64121i	−0.533244	+	0.387425i	−0.821570	−	0.570108i	$-0.806901\pi$
$389$	−10.5172	+	7.64121i	−0.533244	+	0.387425i	0.288326	+	0.957532i	$0.406901\pi$
$390$		0			0
$391$	−1.85410	+	5.70634i	−0.0937660	+	0.288582i
$392$		0			0
$393$	−4.85410	−	3.52671i	−0.244857	−	0.177899i
$394$		0			0
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−26.0000			−1.30490			−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000			−1.30490			−0.652451	+	0.757831i	$0.726259\pi$
$398$		0			0
$399$	−19.4164	−	14.1068i	−0.972036	−	0.706226i
$400$		0			0
$401$	−1.85410	+	5.70634i	−0.0925894	+	0.284961i	−0.986618	−	0.163049i	$-0.947867\pi$
$401$	−1.85410	+	5.70634i	−0.0925894	+	0.284961i	0.894029	+	0.448010i	$0.147867\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−8.34346	−	25.6785i	−0.414590	−	1.27598i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	10.5066	+	32.3359i	0.519517	+	1.59891i	0.774910	+	0.632071i	$0.217795\pi$
$409$	10.5066	+	32.3359i	0.519517	+	1.59891i	−0.255393	+	0.966837i	$0.582205\pi$
$410$		0			0
$411$	−36.4058	+	26.4503i	−1.79576	+	1.30470i
$412$		0			0
$413$	0.618034	−	1.90211i	0.0304115	−	0.0935969i
$414$		0			0
$415$	−4.85410	−	3.52671i	−0.238278	−	0.173119i
$416$		0			0
$417$	66.0000			3.23203
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	−24.2705	−	17.6336i	−1.18287	−	0.859407i	−0.190380	−	0.981711i	$-0.560972\pi$
$421$	−24.2705	−	17.6336i	−1.18287	−	0.859407i	−0.992493	+	0.122304i	$0.960972\pi$
$422$		0			0
$423$	−14.8328	+	45.6507i	−0.721196	+	2.21961i
$424$		0			0
$425$	19.4164	−	14.1068i	0.941834	−	0.684283i
$426$		0			0
$427$	−2.47214	−	7.60845i	−0.119635	−	0.368199i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.03444	−	24.7275i	−0.387005	−	1.19108i	−0.935015	−	0.354608i	$-0.884614\pi$
$431$	−8.03444	−	24.7275i	−0.387005	−	1.19108i	0.548010	−	0.836472i	$-0.315386\pi$
$432$		0			0
$433$	−10.5172	+	7.64121i	−0.505425	+	0.367213i	−0.811085	−	0.584928i	$-0.801123\pi$
$433$	−10.5172	+	7.64121i	−0.505425	+	0.367213i	0.305660	+	0.952141i	$0.401123\pi$
$434$		0			0
$435$	−22.2492	+	68.4761i	−1.06677	+	3.28318i
$436$		0			0
$437$	−3.23607	−	2.35114i	−0.154802	−	0.112470i
$438$		0			0
$439$	−32.0000			−1.52728			−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000			−1.52728			−0.763638	+	0.645644i	$0.776589\pi$
$440$		0			0
$441$	−18.0000			−0.857143
$442$		0			0
$443$	7.28115	+	5.29007i	0.345938	+	0.251339i	0.747163	−	0.664641i	$-0.231415\pi$
$443$	7.28115	+	5.29007i	0.345938	+	0.251339i	−0.401225	+	0.915980i	$0.631415\pi$
$444$		0			0
$445$	−13.9058	+	42.7975i	−0.659196	+	2.02880i
$446$		0			0
$447$	43.6869	−	31.7404i	2.06632	−	1.50127i
$448$		0			0
$449$	−6.48936	−	19.9722i	−0.306252	−	0.942546i	−0.979207	−	0.202863i	$-0.934975\pi$
$449$	−6.48936	−	19.9722i	−0.306252	−	0.942546i	0.672955	−	0.739683i	$-0.265025\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	16.6869	+	51.3571i	0.784020	+	2.41296i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.70820	−	11.4127i	0.173462	−	0.533863i	−0.826097	−	0.563527i	$-0.809444\pi$
$457$	3.70820	−	11.4127i	0.173462	−	0.533863i	0.999560	+	0.0296647i	$0.00944396\pi$
$458$		0			0
$459$	−43.6869	−	31.7404i	−2.03913	−	1.48152i
$460$		0			0
$461$	−28.0000			−1.30409			−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000			−1.30409			−0.652045	+	0.758180i	$0.726089\pi$
$462$		0			0
$463$	27.0000			1.25480			0.627398	−	0.778699i	$-0.284120\pi$
$463$	27.0000			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$464$		0			0
$465$	50.9681	+	37.0305i	2.36359	+	1.71725i
$466$		0			0
$467$	−10.1976	+	31.3849i	−0.471887	+	1.45232i	0.378224	+	0.925714i	$0.376535\pi$
$467$	−10.1976	+	31.3849i	−0.471887	+	1.45232i	−0.850111	+	0.526604i	$0.823465\pi$
$468$		0			0
$469$	−8.09017	+	5.87785i	−0.373569	+	0.271414i
$470$		0			0
$471$	10.1976	+	31.3849i	0.469879	+	1.44614i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.94427	+	15.2169i	0.226859	+	0.698199i
$476$		0			0
$477$	−9.70820	+	7.05342i	−0.444508	+	0.322954i
$478$		0			0
$479$	2.47214	−	7.60845i	0.112955	−	0.347639i	−0.878560	−	0.477632i	$-0.841495\pi$
$479$	2.47214	−	7.60845i	0.112955	−	0.347639i	0.991515	+	0.129993i	$0.0414954\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	6.00000			0.273009
$484$		0			0
$485$	21.0000			0.953561
$486$		0			0
$487$	−7.28115	−	5.29007i	−0.329941	−	0.239716i	0.410465	−	0.911876i	$-0.365366\pi$
$487$	−7.28115	−	5.29007i	−0.329941	−	0.239716i	−0.740405	+	0.672161i	$0.765366\pi$
$488$		0			0
$489$	3.70820	−	11.4127i	0.167691	−	0.516099i
$490$		0			0
$491$	−6.47214	+	4.70228i	−0.292083	+	0.212211i	−0.724171	−	0.689621i	$-0.757777\pi$
$491$	−6.47214	+	4.70228i	−0.292083	+	0.212211i	0.432087	+	0.901832i	$0.357777\pi$
$492$		0			0
$493$	14.8328	+	45.6507i	0.668036	+	2.05600i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.85410	−	5.70634i	−0.0831678	−	0.255964i
$498$		0			0
$499$	16.1803	−	11.7557i	0.724331	−	0.526258i	−0.163434	−	0.986554i	$-0.552257\pi$
$499$	16.1803	−	11.7557i	0.724331	−	0.526258i	0.887765	+	0.460297i	$0.152257\pi$
$500$		0			0
$501$	−14.8328	+	45.6507i	−0.662681	+	2.03952i
$502$		0			0
$503$	24.2705	+	17.6336i	1.08217	+	0.786241i	0.978060	−	0.208324i	$-0.0668010\pi$
$503$	24.2705	+	17.6336i	1.08217	+	0.786241i	0.104109	+	0.994566i	$0.466801\pi$
$504$		0			0
$505$	30.0000			1.33498
$506$		0			0
$507$	39.0000			1.73205
$508$		0			0
$509$	10.5172	+	7.64121i	0.466168	+	0.338691i	0.795946	−	0.605368i	$-0.206974\pi$
$509$	10.5172	+	7.64121i	0.466168	+	0.338691i	−0.329778	+	0.944058i	$0.606974\pi$
$510$		0			0
$511$	−9.88854	+	30.4338i	−0.437443	+	1.34631i
$512$		0			0
$513$	29.1246	−	21.1603i	1.28588	−	0.934249i
$514$		0			0
$515$	14.8328	+	45.6507i	0.653612	+	2.01161i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−16.6869	−	51.3571i	−0.732474	−	2.25432i
$520$		0			0
$521$	−29.9336	+	21.7481i	−1.31142	+	0.952800i	−0.311419	+	0.950273i	$0.600804\pi$
$521$	−29.9336	+	21.7481i	−1.31142	+	0.952800i	−0.999997	+	0.00252695i	$0.999196\pi$
$522$		0			0
$523$	13.5967	−	41.8465i	0.594544	−	1.82982i	0.0375627	−	0.999294i	$-0.488041\pi$
$523$	13.5967	−	41.8465i	0.594544	−	1.82982i	0.556982	−	0.830525i	$-0.311959\pi$
$524$		0			0
$525$	−19.4164	−	14.1068i	−0.847402	−	0.615673i
$526$		0			0
$527$	42.0000			1.82955
$528$		0			0
$529$	−22.0000			−0.956522
$530$		0			0
$531$	4.85410	+	3.52671i	0.210650	+	0.153046i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4.85410	−	3.52671i	0.209861	−	0.152473i
$536$		0			0
$537$	4.63525	+	14.2658i	0.200026	+	0.615617i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	3.70820	+	11.4127i	0.159428	+	0.490669i	0.998583	−	0.0532238i	$-0.0169497\pi$
$541$	3.70820	+	11.4127i	0.159428	+	0.490669i	−0.839154	+	0.543893i	$0.816950\pi$
$542$		0			0
$543$	−12.1353	+	8.81678i	−0.520774	+	0.378364i
$544$		0			0
$545$	12.9787	−	39.9444i	0.555947	−	1.71103i
$546$		0			0
$547$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$547$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$548$		0			0
$549$	24.0000			1.02430
$550$		0			0
$551$	−32.0000			−1.36325
$552$		0			0
$553$	3.23607	+	2.35114i	0.137612	+	0.0999807i
$554$		0			0
$555$	−2.78115	+	8.55951i	−0.118053	+	0.363331i
$556$		0			0
$557$	−33.9787	+	24.6870i	−1.43972	+	1.04602i	−0.451624	+	0.892208i	$0.649155\pi$
$557$	−33.9787	+	24.6870i	−1.43972	+	1.04602i	−0.988100	+	0.153813i	$0.950845\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.70820	−	11.4127i	−0.156282	−	0.480987i	0.842006	−	0.539468i	$-0.181374\pi$
$563$	−3.70820	−	11.4127i	−0.156282	−	0.480987i	−0.998289	+	0.0584805i	$0.981374\pi$
$564$		0			0
$565$	−16.9894	+	12.3435i	−0.714748	+	0.519295i
$566$		0			0
$567$	−5.56231	+	17.1190i	−0.233595	+	0.718931i
$568$		0			0
$569$	19.4164	+	14.1068i	0.813978	+	0.591390i	0.914981	−	0.403496i	$-0.132205\pi$
$569$	19.4164	+	14.1068i	0.813978	+	0.591390i	−0.101003	+	0.994886i	$0.532205\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	27.0000			1.12794
$574$		0			0
$575$	−3.23607	−	2.35114i	−0.134953	−	0.0980494i
$576$		0			0
$577$	−7.10739	+	21.8743i	−0.295885	+	0.910639i	0.687038	+	0.726621i	$0.258910\pi$
$577$	−7.10739	+	21.8743i	−0.295885	+	0.910639i	−0.982923	+	0.184018i	$0.941090\pi$
$578$		0			0
$579$	9.70820	−	7.05342i	0.403459	−	0.293130i
$580$		0			0
$581$	1.23607	+	3.80423i	0.0512807	+	0.157826i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.70820	+	7.05342i	−0.400700	+	0.291126i	−0.769826	−	0.638254i	$-0.779657\pi$
$587$	−9.70820	+	7.05342i	−0.400700	+	0.291126i	0.369126	+	0.929379i	$0.379657\pi$
$588$		0			0
$589$	−8.65248	+	26.6296i	−0.356519	+	1.09725i
$590$		0			0
$591$	14.5623	+	10.5801i	0.599013	+	0.435209i
$592$		0			0
$593$	−4.00000			−0.164260			−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000			−0.164260			−0.0821302	+	0.996622i	$0.526172\pi$
$594$		0			0
$595$	−36.0000			−1.47586
$596$		0			0
$597$	19.4164	+	14.1068i	0.794661	+	0.577355i
$598$		0			0
$599$	14.8328	−	45.6507i	0.606052	−	1.86524i	0.116664	−	0.993171i	$-0.462780\pi$
$599$	14.8328	−	45.6507i	0.606052	−	1.86524i	0.489388	−	0.872066i	$-0.337220\pi$
$600$		0			0
$601$	−30.7426	+	22.3358i	−1.25402	+	0.911098i	−0.998448	−	0.0556925i	$-0.982263\pi$
$601$	−30.7426	+	22.3358i	−1.25402	+	0.911098i	−0.255571	+	0.966790i	$0.582263\pi$
$602$		0			0
$603$	−9.27051	−	28.5317i	−0.377524	−	1.16190i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−5.56231	−	17.1190i	−0.225767	−	0.694839i	−0.998213	−	0.0597588i	$-0.980967\pi$
$607$	−5.56231	−	17.1190i	−0.225767	−	0.694839i	0.772446	−	0.635081i	$-0.219033\pi$
$608$		0			0
$609$	38.8328	−	28.2137i	1.57359	−	1.14328i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	12.9443	+	9.40456i	0.522814	+	0.379847i	0.817663	−	0.575697i	$-0.195269\pi$
$613$	12.9443	+	9.40456i	0.522814	+	0.379847i	−0.294849	+	0.955544i	$0.595269\pi$
$614$		0			0
$615$	36.0000			1.45166
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	2.42705	+	1.76336i	0.0975514	+	0.0708753i	0.635492	−	0.772108i	$-0.280797\pi$
$619$	2.42705	+	1.76336i	0.0975514	+	0.0708753i	−0.537940	+	0.842983i	$0.680797\pi$
$620$		0			0
$621$	−2.78115	+	8.55951i	−0.111604	+	0.343481i
$622$		0			0
$623$	24.2705	−	17.6336i	0.972377	−	0.706474i
$624$		0			0
$625$	−8.96149	−	27.5806i	−0.358460	−	1.10323i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.85410	+	5.70634i	0.0739279	+	0.227527i
$630$		0			0
$631$	−7.28115	+	5.29007i	−0.289858	+	0.210594i	−0.723206	−	0.690633i	$-0.757332\pi$
$631$	−7.28115	+	5.29007i	−0.289858	+	0.210594i	0.433348	+	0.901227i	$0.357332\pi$
$632$		0			0
$633$	−18.5410	+	57.0634i	−0.736939	+	2.26807i
$634$		0			0
$635$	9.70820	+	7.05342i	0.385258	+	0.279907i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	18.0000			0.712069
$640$		0			0
$641$	7.28115	+	5.29007i	0.287588	+	0.208945i	0.722220	−	0.691663i	$-0.243122\pi$
$641$	7.28115	+	5.29007i	0.287588	+	0.208945i	−0.434632	+	0.900608i	$0.643122\pi$
$642$		0			0
$643$	2.16312	−	6.65740i	0.0853051	−	0.262542i	−0.899301	−	0.437330i	$-0.855924\pi$
$643$	2.16312	−	6.65740i	0.0853051	−	0.262542i	0.984606	+	0.174788i	$0.0559241\pi$
$644$		0			0
$645$	−43.6869	+	31.7404i	−1.72017	+	1.24978i
$646$		0			0
$647$	4.63525	+	14.2658i	0.182231	+	0.560848i	0.999890	−	0.0148545i	$-0.00472851\pi$
$647$	4.63525	+	14.2658i	0.182231	+	0.560848i	−0.817659	+	0.575703i	$0.804729\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−12.9787	−	39.9444i	−0.508676	−	1.56554i
$652$		0			0
$653$	−8.89919	+	6.46564i	−0.348252	+	0.253020i	−0.748135	−	0.663546i	$-0.769051\pi$
$653$	−8.89919	+	6.46564i	−0.348252	+	0.253020i	0.399883	+	0.916566i	$0.369051\pi$
$654$		0			0
$655$	1.85410	−	5.70634i	0.0724458	−	0.222965i
$656$		0			0
$657$	−77.6656	−	56.4274i	−3.03002	−	2.20144i
$658$		0			0
$659$	22.0000			0.856998			0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000			0.856998			0.428499	+	0.903542i	$0.359042\pi$
$660$		0			0
$661$	−7.00000			−0.272268			−0.136134	−	0.990690i	$-0.543468\pi$
$661$	−7.00000			−0.272268			−0.136134	+	0.990690i	$0.543468\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.41641	−	22.8254i	0.287596	−	0.885129i
$666$		0			0
$667$	6.47214	−	4.70228i	0.250602	−	0.182073i
$668$		0			0
$669$	−26.8845	−	82.7419i	−1.03941	−	3.19899i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−10.5066	−	32.3359i	−0.404999	−	1.24646i	−0.920896	−	0.389808i	$-0.872541\pi$
$673$	−10.5066	−	32.3359i	−0.404999	−	1.24646i	0.515897	−	0.856650i	$-0.327459\pi$
$674$		0			0
$675$	29.1246	−	21.1603i	1.12101	−	0.814459i
$676$		0			0
$677$	−9.27051	+	28.5317i	−0.356295	+	1.09656i	0.598960	+	0.800779i	$0.295581\pi$
$677$	−9.27051	+	28.5317i	−0.356295	+	1.09656i	−0.955255	+	0.295783i	$0.904419\pi$
$678$		0			0
$679$	−11.3262	−	8.22899i	−0.434661	−	0.315800i
$680$		0			0
$681$	−54.0000			−2.06928
$682$		0			0
$683$	8.00000			0.306111			0.153056	−	0.988218i	$-0.451089\pi$
$683$	8.00000			0.306111			0.153056	+	0.988218i	$0.451089\pi$
$684$		0			0
$685$	−36.4058	−	26.4503i	−1.39099	−	1.01062i
$686$		0			0
$687$	19.4681	−	59.9166i	0.742753	−	2.28596i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−8.96149	−	27.5806i	−0.340911	−	1.04922i	−0.963736	−	0.266856i	$-0.914015\pi$
$691$	−8.96149	−	27.5806i	−0.340911	−	1.04922i	0.622825	−	0.782361i	$-0.285985\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	20.3951	+	62.7697i	0.773631	+	2.38099i
$696$		0			0
$697$	19.4164	−	14.1068i	0.735449	−	0.534335i
$698$		0			0
$699$	14.8328	−	45.6507i	0.561029	−	1.72667i
$700$		0			0
$701$	8.09017	+	5.87785i	0.305562	+	0.222003i	0.729990	−	0.683458i	$-0.239525\pi$
$701$	8.09017	+	5.87785i	0.305562	+	0.222003i	−0.424428	+	0.905462i	$0.639525\pi$
$702$		0			0
$703$	−4.00000			−0.150863
$704$		0			0
$705$	−72.0000			−2.71168
$706$		0			0
$707$	−16.1803	−	11.7557i	−0.608524	−	0.442119i
$708$		0			0
$709$	5.87132	−	18.0701i	0.220502	−	0.678636i	−0.778215	−	0.627998i	$-0.783875\pi$
$709$	5.87132	−	18.0701i	0.220502	−	0.678636i	0.998717	−	0.0506378i	$-0.0161254\pi$
$710$		0			0
$711$	−9.70820	+	7.05342i	−0.364086	+	0.264524i
$712$		0			0
$713$	−2.16312	−	6.65740i	−0.0810094	−	0.249321i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.85410	+	5.70634i	0.0692427	+	0.213107i
$718$		0			0
$719$	18.6074	−	13.5191i	0.693939	−	0.504176i	−0.184014	−	0.982924i	$-0.558909\pi$
$719$	18.6074	−	13.5191i	0.693939	−	0.504176i	0.877953	+	0.478748i	$0.158909\pi$
$720$		0			0
$721$	9.88854	−	30.4338i	0.368269	−	1.13341i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−32.0000			−1.18845
$726$		0			0
$727$	−35.0000			−1.29808			−0.649039	−	0.760755i	$-0.724829\pi$
$727$	−35.0000			−1.29808			−0.649039	+	0.760755i	$0.724829\pi$
$728$		0			0
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$		0			0
$731$	−11.1246	+	34.2380i	−0.411459	+	1.26634i
$732$		0			0
$733$	−3.23607	+	2.35114i	−0.119527	+	0.0868414i	−0.645943	−	0.763386i	$-0.723536\pi$
$733$	−3.23607	+	2.35114i	−0.119527	+	0.0868414i	0.526416	+	0.850227i	$0.323536\pi$
$734$		0			0
$735$	−8.34346	−	25.6785i	−0.307753	−	0.947167i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−8.03444	−	24.7275i	−0.295552	−	0.909615i	−0.983036	−	0.183415i	$-0.941285\pi$
$739$	−8.03444	−	24.7275i	−0.295552	−	0.909615i	0.687484	−	0.726200i	$-0.258715\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.1246	+	34.2380i	−0.408122	+	1.25607i	0.510137	+	0.860093i	$0.329595\pi$
$743$	−11.1246	+	34.2380i	−0.408122	+	1.25607i	−0.918260	+	0.395979i	$0.870405\pi$
$744$		0			0
$745$	43.6869	+	31.7404i	1.60056	+	1.16288i
$746$		0			0
$747$	−12.0000			−0.439057
$748$		0			0
$749$	−4.00000			−0.146157
$750$		0			0
$751$	−18.6074	−	13.5191i	−0.678993	−	0.493318i	0.194030	−	0.980996i	$-0.437844\pi$
$751$	−18.6074	−	13.5191i	−0.678993	−	0.493318i	−0.873024	+	0.487678i	$0.837844\pi$
$752$		0			0
$753$	12.0517	−	37.0912i	0.439187	−	1.35168i
$754$		0			0
$755$	−43.6869	+	31.7404i	−1.58993	+	1.15515i
$756$		0			0
$757$	3.09017	+	9.51057i	0.112314	+	0.345667i	0.991377	−	0.131038i	$-0.0418309\pi$
$757$	3.09017	+	9.51057i	0.112314	+	0.345667i	−0.879063	+	0.476705i	$0.841831\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$	−22.6525	+	16.4580i	−0.820075	+	0.595819i
$764$		0			0
$765$	33.3738	−	102.714i	1.20663	−	3.71364i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	16.0000			0.576975			0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000			0.576975			0.288487	+	0.957484i	$0.406848\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$		0			0
$773$	4.85410	+	3.52671i	0.174590	+	0.126847i	0.671648	−	0.740870i	$-0.265587\pi$
$773$	4.85410	+	3.52671i	0.174590	+	0.126847i	−0.497059	+	0.867717i	$0.665587\pi$
$774$		0			0
$775$	−8.65248	+	26.6296i	−0.310806	+	0.956563i
$776$		0			0
$777$	4.85410	−	3.52671i	0.174140	−	0.126520i
$778$		0			0
$779$	4.94427	+	15.2169i	0.177147	+	0.545202i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	22.2492	+	68.4761i	0.795122	+	2.44714i
$784$		0			0
$785$	−26.6976	+	19.3969i	−0.952877	+	0.692306i
$786$		0			0
$787$	7.41641	−	22.8254i	0.264366	−	0.813636i	−0.727472	−	0.686137i	$-0.759305\pi$
$787$	7.41641	−	22.8254i	0.264366	−	0.813636i	0.991839	−	0.127499i	$-0.0406950\pi$
$788$		0			0
$789$	33.9787	+	24.6870i	1.20967	+	0.878880i
$790$		0			0
$791$	14.0000			0.497783
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−14.5623	−	10.5801i	−0.516472	−	0.375239i
$796$		0			0
$797$	0.309017	−	0.951057i	0.0109459	−	0.0336882i	−0.945434	−	0.325813i	$-0.894362\pi$
$797$	0.309017	−	0.951057i	0.0109459	−	0.0336882i	0.956380	+	0.292124i	$0.0943621\pi$
$798$		0			0
$799$	−38.8328	+	28.2137i	−1.37381	+	0.998129i
$800$		0			0
$801$	27.8115	+	85.5951i	0.982672	+	3.02435i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	1.85410	+	5.70634i	0.0653485	+	0.201122i
$806$		0			0
$807$	63.1033	−	45.8472i	2.22134	−	1.61390i
$808$		0			0
$809$	3.70820	−	11.4127i	0.130374	−	0.401248i	−0.864468	−	0.502687i	$-0.832345\pi$
$809$	3.70820	−	11.4127i	0.130374	−	0.401248i	0.994842	+	0.101439i	$0.0323447\pi$
$810$		0			0
$811$	21.0344	+	15.2824i	0.738619	+	0.536638i	0.892278	−	0.451486i	$-0.149106\pi$
$811$	21.0344	+	15.2824i	0.738619	+	0.536638i	−0.153659	+	0.988124i	$0.549106\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.0000			0.420342
$816$		0			0
$817$	−19.4164	−	14.1068i	−0.679294	−	0.493536i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	27.5066	−	19.9847i	0.959986	−	0.697471i	0.00683865	−	0.999977i	$-0.497823\pi$
$821$	27.5066	−	19.9847i	0.959986	−	0.697471i	0.953148	+	0.302506i	$0.0978232\pi$
$822$		0			0
$823$	−9.57953	−	29.4828i	−0.333921	−	1.02770i	−0.967251	−	0.253822i	$-0.918312\pi$
$823$	−9.57953	−	29.4828i	−0.333921	−	1.02770i	0.633330	−	0.773882i	$-0.281688\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.94427	−	15.2169i	−0.171929	−	0.529144i	0.827551	−	0.561391i	$-0.189734\pi$
$827$	−4.94427	−	15.2169i	−0.171929	−	0.529144i	−0.999480	+	0.0322473i	$0.989734\pi$
$828$		0			0
$829$	28.3156	−	20.5725i	0.983441	−	0.714512i	0.0249662	−	0.999688i	$-0.492052\pi$
$829$	28.3156	−	20.5725i	0.983441	−	0.714512i	0.958475	+	0.285176i	$0.0920522\pi$
$830$		0			0
$831$	1.85410	−	5.70634i	0.0643181	−	0.197951i
$832$		0			0
$833$	−14.5623	−	10.5801i	−0.504554	−	0.366580i
$834$		0			0
$835$	−48.0000			−1.66111
$836$		0			0
$837$	63.0000			2.17760
$838$		0			0
$839$	−16.9894	−	12.3435i	−0.586538	−	0.426145i	0.254537	−	0.967063i	$-0.418077\pi$
$839$	−16.9894	−	12.3435i	−0.586538	−	0.426145i	−0.841075	+	0.540918i	$0.818077\pi$
$840$		0			0
$841$	10.8156	−	33.2870i	0.372952	−	1.14783i
$842$		0			0
$843$	14.5623	−	10.5801i	0.501552	−	0.364399i
$844$		0			0
$845$	12.0517	+	37.0912i	0.414590	+	1.27598i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.70820	−	11.4127i	−0.127265	−	0.391682i
$850$		0			0
$851$	0.809017	−	0.587785i	0.0277327	−	0.0201490i
$852$		0			0
$853$	−8.03444	+	24.7275i	−0.275094	+	0.846652i	0.714100	+	0.700043i	$0.246836\pi$
$853$	−8.03444	+	24.7275i	−0.275094	+	0.846652i	−0.989194	+	0.146609i	$0.953164\pi$
$854$		0			0
$855$	58.2492	+	42.3205i	1.99208	+	1.44733i
$856$		0			0
$857$	−24.0000			−0.819824			−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000			−0.819824			−0.409912	+	0.912125i	$0.634441\pi$
$858$		0			0
$859$	11.0000			0.375315			0.187658	−	0.982235i	$-0.439910\pi$
$859$	11.0000			0.375315			0.187658	+	0.982235i	$0.439910\pi$
$860$		0			0
$861$	−19.4164	−	14.1068i	−0.661709	−	0.480760i
$862$		0			0
$863$	−4.94427	+	15.2169i	−0.168305	+	0.517989i	−0.999265	−	0.0383432i	$-0.987792\pi$
$863$	−4.94427	+	15.2169i	−0.168305	+	0.517989i	0.830960	+	0.556333i	$0.187792\pi$
$864$		0			0
$865$	43.6869	−	31.7404i	1.48540	−	1.07921i
$866$		0			0
$867$	−17.6140	−	54.2102i	−0.598202	−	1.84108i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	33.9787	−	24.6870i	1.15001	−	0.835528i
$874$		0			0
$875$	−1.85410	+	5.70634i	−0.0626801	+	0.192909i
$876$		0			0
$877$	−45.3050	−	32.9160i	−1.52984	−	1.11149i	−0.956328	−	0.292296i	$-0.905581\pi$
$877$	−45.3050	−	32.9160i	−1.52984	−	1.11149i	−0.573512	−	0.819197i	$-0.694419\pi$
$878$		0			0
$879$	−36.0000			−1.21425
$880$		0			0
$881$	−19.0000			−0.640126			−0.320063	−	0.947396i	$-0.603704\pi$
$881$	−19.0000			−0.640126			−0.320063	+	0.947396i	$0.603704\pi$
$882$		0			0
$883$	22.6525	+	16.4580i	0.762317	+	0.553855i	0.899620	−	0.436674i	$-0.143844\pi$
$883$	22.6525	+	16.4580i	0.762317	+	0.553855i	−0.137303	+	0.990529i	$0.543844\pi$
$884$		0			0
$885$	−2.78115	+	8.55951i	−0.0934874	+	0.287725i
$886$		0			0
$887$	27.5066	−	19.9847i	0.923580	−	0.671021i	−0.0208321	−	0.999783i	$-0.506632\pi$
$887$	27.5066	−	19.9847i	0.923580	−	0.671021i	0.944413	+	0.328762i	$0.106632\pi$
$888$		0			0
$889$	−2.47214	−	7.60845i	−0.0829128	−	0.255179i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.88854	−	30.4338i	−0.330908	−	1.01843i
$894$		0			0
$895$	−12.1353	+	8.81678i	−0.405637	+	0.294712i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−45.3050	−	32.9160i	−1.51100	−	1.09781i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$	36.0000			1.19800
$904$		0			0
$905$	−12.1353	−	8.81678i	−0.403390	−	0.293080i
$906$		0			0
$907$	8.65248	−	26.6296i	0.287301	−	0.884221i	−0.698399	−	0.715709i	$-0.746104\pi$
$907$	8.65248	−	26.6296i	0.287301	−	0.884221i	0.985700	−	0.168512i	$-0.0538962\pi$
$908$		0			0
$909$	48.5410	−	35.2671i	1.61000	−	1.16974i
$910$		0			0
$911$	11.1246	+	34.2380i	0.368575	+	1.13436i	0.947712	+	0.319127i	$0.103390\pi$
$911$	11.1246	+	34.2380i	0.368575	+	1.13436i	−0.579137	+	0.815230i	$0.696610\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	11.1246	+	34.2380i	0.367768	+	1.13187i
$916$		0			0
$917$	−3.23607	+	2.35114i	−0.106864	+	0.0776415i
$918$		0			0
$919$	−15.4508	+	47.5528i	−0.509677	+	1.56862i	0.283087	+	0.959094i	$0.408641\pi$
$919$	−15.4508	+	47.5528i	−0.509677	+	1.56862i	−0.792764	+	0.609529i	$0.791359\pi$
$920$		0			0
$921$	−9.70820	−	7.05342i	−0.319896	−	0.232418i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	77.6656	+	56.4274i	2.55087	+	1.85332i
$928$		0			0
$929$	−6.79837	+	20.9232i	−0.223047	+	0.686469i	0.775437	+	0.631426i	$0.217530\pi$
$929$	−6.79837	+	20.9232i	−0.223047	+	0.686469i	−0.998484	+	0.0550438i	$0.982470\pi$
$930$		0			0
$931$	9.70820	−	7.05342i	0.318174	−	0.231167i
$932$		0			0
$933$	11.1246	+	34.2380i	0.364203	+	1.12090i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.23607	+	3.80423i	0.0403806	+	0.124279i	0.969215	−	0.246217i	$-0.0791877\pi$
$937$	1.23607	+	3.80423i	0.0403806	+	0.124279i	−0.928834	+	0.370496i	$0.879188\pi$
$938$		0			0
$939$	−21.8435	+	15.8702i	−0.712834	+	0.517904i
$940$		0			0
$941$	3.09017	−	9.51057i	0.100737	−	0.310036i	−0.887970	−	0.459902i	$-0.847884\pi$
$941$	3.09017	−	9.51057i	0.100737	−	0.310036i	0.988706	+	0.149867i	$0.0478844\pi$
$942$		0			0
$943$	−3.23607	−	2.35114i	−0.105381	−	0.0765637i
$944$		0			0
$945$	−54.0000			−1.75662
$946$		0			0
$947$	47.0000			1.52729			0.763647	−	0.645634i	$-0.223407\pi$
$947$	47.0000			1.52729			0.763647	+	0.645634i	$0.223407\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	13.9058	−	42.7975i	0.450925	−	1.38781i
$952$		0			0
$953$	27.5066	−	19.9847i	0.891025	−	0.647368i	−0.0451197	−	0.998982i	$-0.514367\pi$
$953$	27.5066	−	19.9847i	0.891025	−	0.647368i	0.936145	+	0.351614i	$0.114367\pi$
$954$		0			0
$955$	8.34346	+	25.6785i	0.269988	+	0.830938i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.27051	+	28.5317i	0.299360	+	0.921337i
$960$		0			0
$961$	−14.5623	+	10.5801i	−0.469752	+	0.341295i
$962$		0			0
$963$	3.70820	−	11.4127i	0.119495	−	0.367768i
$964$		0			0
$965$	9.70820	+	7.05342i	0.312518	+	0.227058i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$	72.0000			2.31297
$970$		0			0
$971$	−42.8779	−	31.1526i	−1.37602	−	0.999735i	−0.997240	−	0.0742473i	$-0.976345\pi$
$971$	−42.8779	−	31.1526i	−1.37602	−	0.999735i	−0.378777	−	0.925488i	$-0.623655\pi$
$972$		0			0
$973$	13.5967	−	41.8465i	0.435892	−	1.34154i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.39919	−	10.4616i	−0.108750	−	0.334697i	0.881843	−	0.471544i	$-0.156303\pi$
$977$	−3.39919	−	10.4616i	−0.108750	−	0.334697i	−0.990592	+	0.136847i	$0.956303\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−25.9574	−	79.8887i	−0.828757	−	2.55065i
$982$		0			0
$983$	−20.2254	+	14.6946i	−0.645091	+	0.468686i	−0.861595	−	0.507596i	$-0.830534\pi$
$983$	−20.2254	+	14.6946i	−0.645091	+	0.468686i	0.216505	+	0.976282i	$0.430534\pi$
$984$		0			0
$985$	−5.56231	+	17.1190i	−0.177230	+	0.545457i
$986$		0			0
$987$	38.8328	+	28.2137i	1.23606	+	0.898052i
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	−84.9468	−	61.7175i	−2.69570	−	1.95854i
$994$		0			0
$995$	−7.41641	+	22.8254i	−0.235116	+	0.723612i
$996$		0			0
$997$	−1.61803	+	1.17557i	−0.0512437	+	0.0372307i	−0.613112	−	0.789996i	$-0.710083\pi$
$997$	−1.61803	+	1.17557i	−0.0512437	+	0.0372307i	0.561869	+	0.827227i	$0.310083\pi$
$998$		0			0
$999$	2.78115	+	8.55951i	0.0879918	+	0.270811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.j.753.1		4
11.2	odd	10		968.2.i.i.9.1		4
11.3	even	5		88.2.a.a.1.1	✓	1
11.4	even	5	inner	968.2.i.j.729.1		4
11.5	even	5	inner	968.2.i.j.81.1		4
11.6	odd	10		968.2.i.i.81.1		4
11.7	odd	10		968.2.i.i.729.1		4
11.8	odd	10		968.2.a.a.1.1		1
11.9	even	5	inner	968.2.i.j.9.1		4
11.10	odd	2		968.2.i.i.753.1		4
33.8	even	10		8712.2.a.x.1.1		1
33.14	odd	10		792.2.a.g.1.1		1
44.3	odd	10		176.2.a.c.1.1		1
44.19	even	10		1936.2.a.l.1.1		1
55.3	odd	20		2200.2.b.a.1849.1		2
55.14	even	10		2200.2.a.k.1.1		1
55.47	odd	20		2200.2.b.a.1849.2		2
77.69	odd	10		4312.2.a.l.1.1		1
88.3	odd	10		704.2.a.b.1.1		1
88.19	even	10		7744.2.a.b.1.1		1
88.69	even	10		704.2.a.l.1.1		1
88.85	odd	10		7744.2.a.bk.1.1		1
132.47	even	10		1584.2.a.q.1.1		1
176.3	odd	20		2816.2.c.d.1409.2		2
176.69	even	20		2816.2.c.i.1409.2		2
176.91	odd	20		2816.2.c.d.1409.1		2
176.157	even	20		2816.2.c.i.1409.1		2
220.3	even	20		4400.2.b.b.4049.2		2
220.47	even	20		4400.2.b.b.4049.1		2
220.179	odd	10		4400.2.a.a.1.1		1
264.179	even	10		6336.2.a.k.1.1		1
264.245	odd	10		6336.2.a.h.1.1		1
308.223	even	10		8624.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.a.a.1.1	✓	1	11.3	even	5
176.2.a.c.1.1		1	44.3	odd	10
704.2.a.b.1.1		1	88.3	odd	10
704.2.a.l.1.1		1	88.69	even	10
792.2.a.g.1.1		1	33.14	odd	10
968.2.a.a.1.1		1	11.8	odd	10
968.2.i.i.9.1		4	11.2	odd	10
968.2.i.i.81.1		4	11.6	odd	10
968.2.i.i.729.1		4	11.7	odd	10
968.2.i.i.753.1		4	11.10	odd	2
968.2.i.j.9.1		4	11.9	even	5	inner
968.2.i.j.81.1		4	11.5	even	5	inner
968.2.i.j.729.1		4	11.4	even	5	inner
968.2.i.j.753.1		4	1.1	even	1	trivial
1584.2.a.q.1.1		1	132.47	even	10
1936.2.a.l.1.1		1	44.19	even	10
2200.2.a.k.1.1		1	55.14	even	10
2200.2.b.a.1849.1		2	55.3	odd	20
2200.2.b.a.1849.2		2	55.47	odd	20
2816.2.c.d.1409.1		2	176.91	odd	20
2816.2.c.d.1409.2		2	176.3	odd	20
2816.2.c.i.1409.1		2	176.157	even	20
2816.2.c.i.1409.2		2	176.69	even	20
4312.2.a.l.1.1		1	77.69	odd	10
4400.2.a.a.1.1		1	220.179	odd	10
4400.2.b.b.4049.1		2	220.47	even	20
4400.2.b.b.4049.2		2	220.3	even	20
6336.2.a.h.1.1		1	264.245	odd	10
6336.2.a.k.1.1		1	264.179	even	10
7744.2.a.b.1.1		1	88.19	even	10
7744.2.a.bk.1.1		1	88.85	odd	10
8624.2.a.c.1.1		1	308.223	even	10
8712.2.a.x.1.1		1	33.8	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.42705 + 1.76336i) q^{3} +(-0.927051 + 2.85317i) q^{5} +(1.61803 - 1.17557i) q^{7} +(1.85410 + 5.70634i) q^{9} +O(q^{10})\)	\(q+(2.42705 + 1.76336i) q^{3} +(-0.927051 + 2.85317i) q^{5} +(1.61803 - 1.17557i) q^{7} +(1.85410 + 5.70634i) q^{9} +(-7.28115 + 5.29007i) q^{15} +(-1.85410 + 5.70634i) q^{17} +(-3.23607 - 2.35114i) q^{19} +6.00000 q^{21} +1.00000 q^{23} +(-3.23607 - 2.35114i) q^{25} +(-2.78115 + 8.55951i) q^{27} +(6.47214 - 4.70228i) q^{29} +(-2.16312 - 6.65740i) q^{31} +(1.85410 + 5.70634i) q^{35} +(0.809017 - 0.587785i) q^{37} +(-3.23607 - 2.35114i) q^{41} +6.00000 q^{43} -18.0000 q^{45} +(6.47214 + 4.70228i) q^{47} +(-0.927051 + 2.85317i) q^{49} +(-14.5623 + 10.5801i) q^{51} +(0.618034 + 1.90211i) q^{53} +(-3.70820 - 11.4127i) q^{57} +(0.809017 - 0.587785i) q^{59} +(1.23607 - 3.80423i) q^{61} +(9.70820 + 7.05342i) q^{63} -5.00000 q^{67} +(2.42705 + 1.76336i) q^{69} +(0.927051 - 2.85317i) q^{71} +(-12.9443 + 9.40456i) q^{73} +(-3.70820 - 11.4127i) q^{75} +(0.618034 + 1.90211i) q^{79} +(-7.28115 + 5.29007i) q^{81} +(-0.618034 + 1.90211i) q^{83} +(-14.5623 - 10.5801i) q^{85} +24.0000 q^{87} +15.0000 q^{89} +(6.48936 - 19.9722i) q^{93} +(9.70820 - 7.05342i) q^{95} +(-2.16312 - 6.65740i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9	\( 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9} - 9 q^{15} + 6 q^{17} - 4 q^{19} + 24 q^{21} + 4 q^{23} - 4 q^{25} + 9 q^{27} + 8 q^{29} + 7 q^{31} - 6 q^{35} + q^{37} - 4 q^{41} + 24 q^{43} - 72 q^{45} + 8 q^{47} + 3 q^{49} - 18 q^{51} - 2 q^{53} + 12 q^{57} + q^{59} - 4 q^{61} + 12 q^{63} - 20 q^{67} + 3 q^{69} - 3 q^{71} - 16 q^{73} + 12 q^{75} - 2 q^{79} - 9 q^{81} + 2 q^{83} - 18 q^{85} + 96 q^{87} + 60 q^{89} - 21 q^{93} + 12 q^{95} + 7 q^{97}+O(q^{100}) \) 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9 - 9 * q^15 + 6 * q^17 - 4 * q^19 + 24 * q^21 + 4 * q^23 - 4 * q^25 + 9 * q^27 + 8 * q^29 + 7 * q^31 - 6 * q^35 + q^37 - 4 * q^41 + 24 * q^43 - 72 * q^45 + 8 * q^47 + 3 * q^49 - 18 * q^51 - 2 * q^53 + 12 * q^57 + q^59 - 4 * q^61 + 12 * q^63 - 20 * q^67 + 3 * q^69 - 3 * q^71 - 16 * q^73 + 12 * q^75 - 2 * q^79 - 9 * q^81 + 2 * q^83 - 18 * q^85 + 96 * q^87 + 60 * q^89 - 21 * q^93 + 12 * q^95 + 7 * q^97

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