LMFDB - Embedded newform 1148.2.r.a.737.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			737.23
Character	$\chi$	$=$	1148.737
Dual form			1148.2.r.a.81.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79608 - 1.03697i) q^{3} +(-0.904853 + 1.56725i) q^{5} +(-2.10654 - 1.60077i) q^{7} +(0.650613 - 1.12689i) q^{9} +O(q^{10})$	\(q+(1.79608 - 1.03697i) q^{3} +(-0.904853 + 1.56725i) q^{5} +(-2.10654 - 1.60077i) q^{7} +(0.650613 - 1.12689i) q^{9} +(-2.79436 + 1.61332i) q^{11} +6.58011i q^{13} +3.75322i q^{15} +(-4.75257 + 2.74390i) q^{17} +(-4.51856 - 2.60879i) q^{19} +(-5.44348 - 0.690702i) q^{21} +(0.901915 - 1.56216i) q^{23} +(0.862481 + 1.49386i) q^{25} +3.52316i q^{27} -5.39334i q^{29} +(-2.38433 - 4.12978i) q^{31} +(-3.34594 + 5.79534i) q^{33} +(4.41493 - 1.85302i) q^{35} +(-4.15338 + 7.19386i) q^{37} +(6.82338 + 11.8184i) q^{39} +(3.53942 + 5.33596i) q^{41} +5.81689 q^{43} +(1.17742 + 2.03935i) q^{45} +(-2.28612 - 1.31989i) q^{47} +(1.87505 + 6.74420i) q^{49} +(-5.69068 + 9.85655i) q^{51} +(8.66082 - 5.00033i) q^{53} -5.83929i q^{55} -10.8210 q^{57} +(-4.69687 - 8.13521i) q^{59} +(2.70825 - 4.69083i) q^{61} +(-3.17445 + 1.33237i) q^{63} +(-10.3127 - 5.95404i) q^{65} +(-9.69812 + 5.59921i) q^{67} -3.74103i q^{69} -2.46402i q^{71} +(7.19507 + 12.4622i) q^{73} +(3.09818 + 1.78873i) q^{75} +(8.46901 + 1.07460i) q^{77} +(-6.86759 - 3.96500i) q^{79} +(5.60524 + 9.70857i) q^{81} +0.937138 q^{83} -9.93130i q^{85} +(-5.59273 - 9.68689i) q^{87} +(-7.40854 - 4.27732i) q^{89} +(10.5333 - 13.8613i) q^{91} +(-8.56491 - 4.94495i) q^{93} +(8.17727 - 4.72115i) q^{95} +8.46243i q^{97} +4.19860i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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
$3$	1.79608	−	1.03697i	1.03697	−	0.598695i	0.117996	−	0.993014i	$-0.462353\pi$
$3$	1.79608	−	1.03697i	1.03697	−	0.598695i	0.918974	+	0.394319i	$0.129020\pi$
$4$		0			0
$5$	−0.904853	+	1.56725i	−0.404663	+	0.700896i	−0.994282	−	0.106785i	$-0.965944\pi$
$5$	−0.904853	+	1.56725i	−0.404663	+	0.700896i	0.589619	+	0.807681i	$0.299278\pi$
$6$		0			0
$7$	−2.10654	−	1.60077i	−0.796199	−	0.605035i
$7$	−2.10654	−	1.60077i	−0.796199	−	0.605035i
$8$		0			0
$9$	0.650613	−	1.12689i	0.216871	−	0.375631i
$10$		0			0
$11$	−2.79436	+	1.61332i	−0.842531	+	0.486436i	−0.858124	−	0.513443i	$-0.828370\pi$
$11$	−2.79436	+	1.61332i	−0.842531	+	0.486436i	0.0155924	+	0.999878i	$0.495037\pi$
$12$		0			0
$13$			6.58011i			1.82500i	0.409082	+	0.912498i	$0.365849\pi$
$13$			6.58011i			1.82500i	−0.409082	+	0.912498i	$0.634151\pi$
$14$		0			0
$15$			3.75322i			0.969078i
$16$		0			0
$17$	−4.75257	+	2.74390i	−1.15267	+	0.665493i	−0.949536	−	0.313658i	$-0.898445\pi$
$17$	−4.75257	+	2.74390i	−1.15267	+	0.665493i	−0.203132	+	0.979151i	$0.565112\pi$
$18$		0			0
$19$	−4.51856	−	2.60879i	−1.03663	−	0.598498i	−0.117752	−	0.993043i	$-0.537569\pi$
$19$	−4.51856	−	2.60879i	−1.03663	−	0.598498i	−0.918877	+	0.394545i	$0.870902\pi$
$20$		0			0
$21$	−5.44348	−	0.690702i	−1.18787	−	0.150724i
$22$		0			0
$23$	0.901915	−	1.56216i	0.188062	−	0.325733i	−0.756542	−	0.653945i	$-0.773113\pi$
$23$	0.901915	−	1.56216i	0.188062	−	0.325733i	0.944604	+	0.328212i	$0.106446\pi$
$24$		0			0
$25$	0.862481	+	1.49386i	0.172496	+	0.298772i
$26$		0			0
$27$			3.52316i			0.678032i
$28$		0			0
$29$		−	5.39334i		−	1.00152i	−0.865587	−	0.500759i	$-0.833054\pi$
$29$		−	5.39334i		−	1.00152i	0.865587	−	0.500759i	$-0.166946\pi$
$30$		0			0
$31$	−2.38433	−	4.12978i	−0.428238	−	0.741730i	0.568479	−	0.822698i	$-0.307532\pi$
$31$	−2.38433	−	4.12978i	−0.428238	−	0.741730i	−0.996717	+	0.0809679i	$0.974199\pi$
$32$		0			0
$33$	−3.34594	+	5.79534i	−0.582453	+	1.00884i
$34$		0			0
$35$	4.41493	−	1.85302i	0.746259	−	0.313217i
$36$		0			0
$37$	−4.15338	+	7.19386i	−0.682811	+	1.18266i	0.291308	+	0.956629i	$0.405910\pi$
$37$	−4.15338	+	7.19386i	−0.682811	+	1.18266i	−0.974119	+	0.226035i	$0.927424\pi$
$38$		0			0
$39$	6.82338	+	11.8184i	1.09262	+	1.89247i
$40$		0			0
$41$	3.53942	+	5.33596i	0.552765	+	0.833337i
$41$	3.53942	+	5.33596i	0.552765	+	0.833337i
$42$		0			0
$43$	5.81689			0.887067			0.443534	−	0.896258i	$-0.353725\pi$
$43$	5.81689			0.887067			0.443534	+	0.896258i	$0.353725\pi$
$44$		0			0
$45$	1.17742	+	2.03935i	0.175519	+	0.304008i
$46$		0			0
$47$	−2.28612	−	1.31989i	−0.333464	−	0.192526i	0.323914	−	0.946087i	$-0.395001\pi$
$47$	−2.28612	−	1.31989i	−0.333464	−	0.192526i	−0.657378	+	0.753561i	$0.728335\pi$
$48$		0			0
$49$	1.87505	+	6.74420i	0.267864	+	0.963457i
$50$		0			0
$51$	−5.69068	+	9.85655i	−0.796855	+	1.38019i
$52$		0			0
$53$	8.66082	−	5.00033i	1.18966	−	0.686848i	0.231427	−	0.972852i	$-0.425660\pi$
$53$	8.66082	−	5.00033i	1.18966	−	0.686848i	0.958228	+	0.286004i	$0.0923272\pi$
$54$		0			0
$55$		−	5.83929i		−	0.787370i
$56$		0			0
$57$	−10.8210			−1.43327
$58$		0			0
$59$	−4.69687	−	8.13521i	−0.611480	−	1.05911i	−0.990991	−	0.133927i	$-0.957241\pi$
$59$	−4.69687	−	8.13521i	−0.611480	−	1.05911i	0.379511	−	0.925187i	$-0.376092\pi$
$60$		0			0
$61$	2.70825	−	4.69083i	0.346756	−	0.600600i	−0.638915	−	0.769278i	$-0.720616\pi$
$61$	2.70825	−	4.69083i	0.346756	−	0.600600i	0.985671	+	0.168678i	$0.0539497\pi$
$62$		0			0
$63$	−3.17445	+	1.33237i	−0.399943	+	0.167863i
$64$		0			0
$65$	−10.3127	−	5.95404i	−1.27913	−	0.738508i
$66$		0			0
$67$	−9.69812	+	5.59921i	−1.18481	+	0.684052i	−0.957123	−	0.289681i	$-0.906451\pi$
$67$	−9.69812	+	5.59921i	−1.18481	+	0.684052i	−0.227690	+	0.973734i	$0.573117\pi$
$68$		0			0
$69$		−	3.74103i		−	0.450368i
$70$		0			0
$71$		−	2.46402i		−	0.292426i	−0.989253	−	0.146213i	$-0.953292\pi$
$71$		−	2.46402i		−	0.292426i	0.989253	−	0.146213i	$-0.0467084\pi$
$72$		0			0
$73$	7.19507	+	12.4622i	0.842120	+	1.45859i	0.888099	+	0.459652i	$0.152026\pi$
$73$	7.19507	+	12.4622i	0.842120	+	1.45859i	−0.0459796	+	0.998942i	$0.514641\pi$
$74$		0			0
$75$	3.09818	+	1.78873i	0.357747	+	0.206545i
$76$		0			0
$77$	8.46901	+	1.07460i	0.965133	+	0.122462i
$78$		0			0
$79$	−6.86759	−	3.96500i	−0.772664	−	0.446098i	0.0611600	−	0.998128i	$-0.480520\pi$
$79$	−6.86759	−	3.96500i	−0.772664	−	0.446098i	−0.833824	+	0.552030i	$0.813853\pi$
$80$		0			0
$81$	5.60524	+	9.70857i	0.622805	+	1.07873i
$82$		0			0
$83$	0.937138			0.102864			0.0514321	−	0.998676i	$-0.483621\pi$
$83$	0.937138			0.102864			0.0514321	+	0.998676i	$0.483621\pi$
$84$		0			0
$85$		−	9.93130i		−	1.07720i
$86$		0			0
$87$	−5.59273	−	9.68689i	−0.599604	−	1.03854i
$88$		0			0
$89$	−7.40854	−	4.27732i	−0.785304	−	0.453396i	0.0530027	−	0.998594i	$-0.483121\pi$
$89$	−7.40854	−	4.27732i	−0.785304	−	0.453396i	−0.838307	+	0.545199i	$0.816454\pi$
$90$		0			0
$91$	10.5333	−	13.8613i	1.10419	−	1.45306i
$92$		0			0
$93$	−8.56491	−	4.94495i	−0.888140	−	0.512768i
$94$		0			0
$95$	8.17727	−	4.72115i	0.838970	−	0.484380i
$96$		0			0
$97$			8.46243i			0.859230i	0.903012	+	0.429615i	$0.141351\pi$
$97$			8.46243i			0.859230i	−0.903012	+	0.429615i	$0.858649\pi$
$98$		0			0
$99$			4.19860i			0.421975i
$100$		0			0
$101$	11.5065	−	6.64326i	1.14494	−	0.661029i	0.197288	−	0.980346i	$-0.436787\pi$
$101$	11.5065	−	6.64326i	1.14494	−	0.661029i	0.947648	+	0.319316i	$0.103453\pi$
$102$		0			0
$103$	−1.14792	+	1.98826i	−0.113108	+	0.195909i	−0.917022	−	0.398837i	$-0.869414\pi$
$103$	−1.14792	+	1.98826i	−0.113108	+	0.195909i	0.803914	+	0.594746i	$0.202747\pi$
$104$		0			0
$105$	6.00806	−	7.90633i	0.586326	−	0.771578i
$106$		0			0
$107$	0.339200	−	0.587512i	0.0327917	−	0.0567969i	−0.849164	−	0.528130i	$-0.822894\pi$
$107$	0.339200	−	0.587512i	0.0327917	−	0.0567969i	0.881956	+	0.471333i	$0.156227\pi$
$108$		0			0
$109$	1.50809	−	0.870698i	0.144449	−	0.0833978i	−0.426034	−	0.904707i	$-0.640089\pi$
$109$	1.50809	−	0.870698i	0.144449	−	0.0833978i	0.570483	+	0.821310i	$0.306756\pi$
$110$		0			0
$111$			17.2277i			1.63518i
$112$		0			0
$113$	−6.09345			−0.573224			−0.286612	−	0.958047i	$-0.592529\pi$
$113$	−6.09345			−0.573224			−0.286612	+	0.958047i	$0.592529\pi$
$114$		0			0
$115$	1.63220	+	2.82706i	0.152204	+	0.263624i
$116$		0			0
$117$	7.41509	+	4.28111i	0.685526	+	0.395788i
$118$		0			0
$119$	14.4039	+	1.82765i	1.32040	+	0.167540i
$120$		0			0
$121$	−0.294365	+	0.509856i	−0.0267605	+	0.0463505i
$122$		0			0
$123$	11.8903	+	5.91356i	1.07212	+	0.533208i
$124$		0			0
$125$	−12.1702			−1.08854
$126$		0			0
$127$	6.62708			0.588059			0.294029	−	0.955796i	$-0.405004\pi$
$127$	6.62708			0.588059			0.294029	+	0.955796i	$0.405004\pi$
$128$		0			0
$129$	10.4476	−	6.03194i	0.919862	−	0.531083i
$130$		0			0
$131$	−8.14767	+	14.1122i	−0.711865	+	1.23299i	0.252291	+	0.967651i	$0.418816\pi$
$131$	−8.14767	+	14.1122i	−0.711865	+	1.23299i	−0.964156	+	0.265335i	$0.914517\pi$
$132$		0			0
$133$	5.34246	+	12.7287i	0.463250	+	1.10372i
$134$		0			0
$135$	−5.52167	−	3.18794i	−0.475230	−	0.274374i
$136$		0			0
$137$	2.26523	−	1.30783i	0.193532	−	0.111736i	−0.400103	−	0.916470i	$-0.631026\pi$
$137$	2.26523	−	1.30783i	0.193532	−	0.111736i	0.593635	+	0.804735i	$0.297692\pi$
$138$		0			0
$139$	−5.49421			−0.466013			−0.233007	−	0.972475i	$-0.574856\pi$
$139$	−5.49421			−0.466013			−0.233007	+	0.972475i	$0.574856\pi$
$140$		0			0
$141$	−5.47474			−0.461056
$142$		0			0
$143$	−10.6159	−	18.3872i	−0.887743	−	1.53762i
$144$		0			0
$145$	8.45272	+	4.88018i	0.701960	+	0.405277i
$146$		0			0
$147$	10.3613	+	10.1688i	0.854584	+	0.838707i
$148$		0			0
$149$	15.7064	+	9.06812i	1.28672	+	0.742889i	0.978068	−	0.208285i	$-0.0667883\pi$
$149$	15.7064	+	9.06812i	1.28672	+	0.742889i	0.308654	+	0.951175i	$0.400122\pi$
$150$		0			0
$151$	−10.0095	+	5.77896i	−0.814558	+	0.470285i	−0.848536	−	0.529138i	$-0.822516\pi$
$151$	−10.0095	+	5.77896i	−0.814558	+	0.470285i	0.0339785	+	0.999423i	$0.489182\pi$
$152$		0			0
$153$			7.14086i			0.577304i
$154$		0			0
$155$	8.62987			0.693168
$156$		0			0
$157$	−8.66570	+	5.00314i	−0.691598	+	0.399294i	−0.804210	−	0.594345i	$-0.797412\pi$
$157$	−8.66570	+	5.00314i	−0.691598	+	0.399294i	0.112612	+	0.993639i	$0.464078\pi$
$158$		0			0
$159$	10.3704	−	17.9620i	0.822425	−	1.42448i
$160$		0			0
$161$	−4.40059	+	1.84700i	−0.346815	+	0.145564i
$162$		0			0
$163$	6.89659	−	11.9452i	0.540182	−	0.935623i	−0.458711	−	0.888586i	$-0.651689\pi$
$163$	6.89659	−	11.9452i	0.540182	−	0.935623i	0.998893	−	0.0470376i	$-0.0149780\pi$
$164$		0			0
$165$	−6.05517	−	10.4879i	−0.471394	−	0.816479i
$166$		0			0
$167$			16.3149i			1.26249i	0.775585	+	0.631244i	$0.217455\pi$
$167$			16.3149i			1.26249i	−0.775585	+	0.631244i	$0.782545\pi$
$168$		0			0
$169$	−30.2979			−2.33061
$170$		0			0
$171$	−5.87966	+	3.39463i	−0.449629	+	0.259594i
$172$		0			0
$173$	2.11386	−	3.66131i	0.160714	−	0.278364i	−0.774411	−	0.632683i	$-0.781954\pi$
$173$	2.11386	−	3.66131i	0.160714	−	0.278364i	0.935125	+	0.354318i	$0.115287\pi$
$174$		0			0
$175$	0.574479	−	4.52752i	0.0434265	−	0.342248i
$176$		0			0
$177$	−16.8719	−	9.74102i	−1.26817	−	0.732180i
$178$		0			0
$179$	13.0457	−	7.53191i	0.975078	−	0.562961i	0.0742972	−	0.997236i	$-0.476329\pi$
$179$	13.0457	−	7.53191i	0.975078	−	0.562961i	0.900780	+	0.434275i	$0.142995\pi$
$180$		0			0
$181$		−	15.4408i		−	1.14770i	−0.818959	−	0.573852i	$-0.805449\pi$
$181$		−	15.4408i		−	1.14770i	0.818959	−	0.573852i	$-0.194551\pi$
$182$		0			0
$183$		−	11.2335i		−	0.830405i
$184$		0			0
$185$	−7.51640	−	13.0188i	−0.552617	−	0.957160i
$186$		0			0
$187$	8.85360	−	15.3349i	0.647439	−	1.12140i
$188$		0			0
$189$	5.63977	−	7.42168i	0.410233	−	0.539848i
$190$		0			0
$191$	−13.9876	−	8.07573i	−1.01211	−	0.584339i	−0.100298	−	0.994957i	$-0.531980\pi$
$191$	−13.9876	−	8.07573i	−1.01211	−	0.584339i	−0.911807	+	0.410618i	$0.865313\pi$
$192$		0			0
$193$	6.01375	−	3.47204i	0.432879	−	0.249923i	−0.267693	−	0.963504i	$-0.586261\pi$
$193$	6.01375	−	3.47204i	0.432879	−	0.249923i	0.700572	+	0.713581i	$0.252928\pi$
$194$		0			0
$195$	−24.6966			−1.76856
$196$		0			0
$197$	2.77407			0.197644			0.0988221	−	0.995105i	$-0.468493\pi$
$197$	2.77407			0.197644			0.0988221	+	0.995105i	$0.468493\pi$
$198$		0			0
$199$	−13.2066	+	7.62482i	−0.936190	+	0.540509i	−0.888764	−	0.458366i	$-0.848435\pi$
$199$	−13.2066	+	7.62482i	−0.936190	+	0.540509i	−0.0474257	+	0.998875i	$0.515102\pi$
$200$		0			0
$201$	−11.6124	+	20.1133i	−0.819077	+	1.41868i
$202$		0			0
$203$	−8.63352	+	11.3613i	−0.605954	+	0.797407i
$204$		0			0
$205$	−11.5655	+	0.718903i	−0.807766	+	0.0502104i
$206$		0			0
$207$	−1.17359	−	2.03273i	−0.0815705	−	0.141284i
$208$		0			0
$209$	16.8353			1.16452
$210$		0			0
$211$			22.7059i			1.56314i	0.623818	+	0.781569i	$0.285581\pi$
$211$			22.7059i			1.56314i	−0.623818	+	0.781569i	$0.714419\pi$
$212$		0			0
$213$	−2.55512	−	4.42559i	−0.175074	−	0.303237i
$214$		0			0
$215$	−5.26343	+	9.11653i	−0.358963	+	0.621742i
$216$		0			0
$217$	−1.58815	+	12.5163i	−0.107811	+	0.849664i
$218$		0			0
$219$	25.8459	+	14.9221i	1.74651	+	1.00835i
$220$		0			0
$221$	−18.0552	−	31.2725i	−1.21452	−	2.10361i
$222$		0			0
$223$	27.2535			1.82503			0.912516	−	0.409040i	$-0.134136\pi$
$223$	27.2535			1.82503			0.912516	+	0.409040i	$0.134136\pi$
$224$		0			0
$225$	2.24456			0.149638
$226$		0			0
$227$	−0.0702538	+	0.0405611i	−0.00466291	+	0.00269213i	−0.502330	−	0.864676i	$-0.667524\pi$
$227$	−0.0702538	+	0.0405611i	−0.00466291	+	0.00269213i	0.497667	+	0.867368i	$0.334190\pi$
$228$		0			0
$229$	−4.69420	−	2.71020i	−0.310201	−	0.179095i	0.336815	−	0.941571i	$-0.390650\pi$
$229$	−4.69420	−	2.71020i	−0.310201	−	0.179095i	−0.647017	+	0.762476i	$0.723984\pi$
$230$		0			0
$231$	16.3254	−	6.85204i	1.07413	−	0.450831i
$232$		0			0
$233$	−19.7775	−	11.4186i	−1.29567	−	0.748055i	−0.316016	−	0.948754i	$-0.602345\pi$
$233$	−19.7775	−	11.4186i	−1.29567	−	0.748055i	−0.979653	+	0.200699i	$0.935679\pi$
$234$		0			0
$235$	4.13720	−	2.38861i	0.269881	−	0.155816i
$236$		0			0
$237$	−16.4464			−1.06831
$238$		0			0
$239$			18.6179i			1.20429i	0.798386	+	0.602146i	$0.205687\pi$
$239$			18.6179i			1.20429i	−0.798386	+	0.602146i	$0.794313\pi$
$240$		0			0
$241$	8.75467	+	15.1635i	0.563938	+	0.976769i	0.997148	+	0.0754759i	$0.0240476\pi$
$241$	8.75467	+	15.1635i	0.563938	+	0.976769i	−0.433210	+	0.901293i	$0.642619\pi$
$242$		0			0
$243$	10.9816	+	6.34020i	0.704467	+	0.406724i
$244$		0			0
$245$	−12.2665	−	3.16383i	−0.783678	−	0.202130i
$246$		0			0
$247$	17.1662	−	29.7326i	1.09226	−	1.89184i
$248$		0			0
$249$	1.68318	−	0.971784i	0.106667	−	0.0615843i
$250$		0			0
$251$	9.67147			0.610458			0.305229	−	0.952279i	$-0.401267\pi$
$251$	9.67147			0.610458			0.305229	+	0.952279i	$0.401267\pi$
$252$		0			0
$253$			5.82033i			0.365921i
$254$		0			0
$255$	−10.2985	−	17.8375i	−0.644915	−	1.11702i
$256$		0			0
$257$	2.40805	+	1.39029i	0.150210	+	0.0867237i	0.573221	−	0.819401i	$-0.305694\pi$
$257$	2.40805	+	1.39029i	0.150210	+	0.0867237i	−0.423011	+	0.906124i	$0.639027\pi$
$258$		0			0
$259$	20.2650	−	8.50557i	1.25921	−	0.528510i
$260$		0			0
$261$	−6.07772	−	3.50897i	−0.376202	−	0.217200i
$262$		0			0
$263$	18.4998	−	10.6808i	1.14074	−	0.658609i	0.194129	−	0.980976i	$-0.437812\pi$
$263$	18.4998	−	10.6808i	1.14074	−	0.658609i	0.946615	+	0.322367i	$0.104479\pi$
$264$		0			0
$265$			18.0983i			1.11177i
$266$		0			0
$267$	−17.7418			−1.08578
$268$		0			0
$269$	−5.23832	−	9.07304i	−0.319386	−	0.553193i	0.660974	−	0.750409i	$-0.270143\pi$
$269$	−5.23832	−	9.07304i	−0.319386	−	0.553193i	−0.980360	+	0.197216i	$0.936810\pi$
$270$		0			0
$271$	−12.1929	+	21.1187i	−0.740666	+	1.28287i	0.211527	+	0.977372i	$0.432156\pi$
$271$	−12.1929	+	21.1187i	−0.740666	+	1.28287i	−0.952193	+	0.305498i	$0.901177\pi$
$272$		0			0
$273$	4.54490	−	35.8187i	0.275070	−	2.16785i
$274$		0			0
$275$	−4.82017	−	2.78292i	−0.290667	−	0.167817i
$276$		0			0
$277$	−11.4453	−	19.8238i	−0.687680	−	1.19110i	−0.972587	−	0.232541i	$-0.925296\pi$
$277$	−11.4453	−	19.8238i	−0.687680	−	1.19110i	0.284907	−	0.958555i	$-0.408037\pi$
$278$		0			0
$279$	−6.20510			−0.371489
$280$		0			0
$281$		−	9.08718i		−	0.542096i	−0.962566	−	0.271048i	$-0.912630\pi$
$281$		−	9.08718i		−	0.542096i	0.962566	−	0.271048i	$-0.0873701\pi$
$282$		0			0
$283$	9.06792	+	15.7061i	0.539032	+	0.933630i	0.998956	+	0.0456723i	$0.0145430\pi$
$283$	9.06792	+	15.7061i	0.539032	+	0.933630i	−0.459925	+	0.887958i	$0.652124\pi$
$284$		0			0
$285$	9.79138	−	16.9592i	0.579991	−	1.00457i
$286$		0			0
$287$	1.08572	−	16.9062i	0.0640880	−	0.997944i
$288$		0			0
$289$	6.55796	−	11.3587i	0.385762	−	0.668160i
$290$		0			0
$291$	8.77529	+	15.1992i	0.514416	+	0.890995i
$292$		0			0
$293$			15.6806i			0.916071i	0.888934	+	0.458035i	$0.151447\pi$
$293$			15.6806i			0.916071i	−0.888934	+	0.458035i	$0.848553\pi$
$294$		0			0
$295$	16.9999			0.989772
$296$		0			0
$297$	−5.68400	−	9.84497i	−0.329819	−	0.571263i
$298$		0			0
$299$	10.2792	+	5.93470i	0.594462	+	0.343213i
$300$		0			0
$301$	−12.2535	−	9.31152i	−0.706282	−	0.536707i
$302$		0			0
$303$	13.7777	−	23.8637i	0.791510	−	1.37093i
$304$		0			0
$305$	4.90115	+	8.48904i	0.280639	+	0.486081i
$306$		0			0
$307$	8.64929			0.493641			0.246820	−	0.969061i	$-0.420614\pi$
$307$	8.64929			0.493641			0.246820	+	0.969061i	$0.420614\pi$
$308$		0			0
$309$			4.76145i			0.270870i
$310$		0			0
$311$	21.3264	−	12.3128i	1.20931	−	0.698196i	0.246703	−	0.969091i	$-0.420653\pi$
$311$	21.3264	−	12.3128i	1.20931	−	0.698196i	0.962609	+	0.270895i	$0.0873196\pi$
$312$		0			0
$313$	19.0693	+	11.0097i	1.07786	+	0.622305i	0.930319	−	0.366751i	$-0.119530\pi$
$313$	19.0693	+	11.0097i	1.07786	+	0.622305i	0.147544	+	0.989055i	$0.452863\pi$
$314$		0			0
$315$	0.784252	−	6.18075i	0.0441876	−	0.348246i
$316$		0			0
$317$	−23.3867	−	13.5023i	−1.31353	−	0.758365i	−0.330849	−	0.943684i	$-0.607335\pi$
$317$	−23.3867	−	13.5023i	−1.31353	−	0.758365i	−0.982679	+	0.185318i	$0.940668\pi$
$318$		0			0
$319$	8.70121	+	15.0709i	0.487174	+	0.843811i
$320$		0			0
$321$		−	1.40696i		−	0.0785289i
$322$		0			0
$323$	28.6330			1.59319
$324$		0			0
$325$	−9.82977	+	5.67522i	−0.545258	+	0.314805i
$326$		0			0
$327$	1.80578	−	3.12770i	0.0998596	−	0.172962i
$328$		0			0
$329$	2.70296	+	6.43996i	0.149019	+	0.355046i
$330$		0			0
$331$	15.8049	+	9.12496i	0.868715	+	0.501553i	0.866921	−	0.498445i	$-0.166096\pi$
$331$	15.8049	+	9.12496i	0.868715	+	0.501553i	0.00179432	+	0.999998i	$0.499429\pi$
$332$		0			0
$333$	5.40448	+	9.36084i	0.296164	+	0.512971i
$334$		0			0
$335$		−	20.2659i		−	1.10724i
$336$		0			0
$337$	32.2331			1.75585			0.877924	−	0.478800i	$-0.158928\pi$
$337$	32.2331			1.75585			0.877924	+	0.478800i	$0.158928\pi$
$338$		0			0
$339$	−10.9444	+	6.31873i	−0.594416	+	0.343186i
$340$		0			0
$341$	13.3253	+	7.69339i	0.721608	+	0.416621i
$342$		0			0
$343$	6.84606	−	17.2085i	0.369652	−	0.929170i
$344$		0			0
$345$	5.86314	+	3.38509i	0.315661	+	0.182247i
$346$		0			0
$347$	−5.23540	+	3.02266i	−0.281051	+	0.162265i	−0.633899	−	0.773416i	$-0.718547\pi$
$347$	−5.23540	+	3.02266i	−0.281051	+	0.162265i	0.352848	+	0.935681i	$0.385213\pi$
$348$		0			0
$349$	−22.7177			−1.21605			−0.608026	−	0.793917i	$-0.708038\pi$
$349$	−22.7177			−1.21605			−0.608026	+	0.793917i	$0.708038\pi$
$350$		0			0
$351$	−23.1828			−1.23740
$352$		0			0
$353$	−14.9822	−	25.9499i	−0.797420	−	1.38117i	−0.921291	−	0.388874i	$-0.872864\pi$
$353$	−14.9822	−	25.9499i	−0.797420	−	1.38117i	0.123871	−	0.992298i	$-0.460469\pi$
$354$		0			0
$355$	3.86175	+	2.22958i	0.204960	+	0.118334i
$356$		0			0
$357$	27.7658	−	11.6538i	1.46952	−	0.616782i
$358$		0			0
$359$	−11.9544	+	20.7057i	−0.630930	+	1.09280i	0.356432	+	0.934321i	$0.383993\pi$
$359$	−11.9544	+	20.7057i	−0.630930	+	1.09280i	−0.987362	+	0.158482i	$0.949340\pi$
$360$		0			0
$361$	4.11159	+	7.12149i	0.216400	+	0.374815i
$362$		0			0
$363$			1.22099i			0.0640855i
$364$		0			0
$365$	−26.0419			−1.36310
$366$		0			0
$367$	1.80073	+	3.11895i	0.0939972	+	0.162808i	0.909190	−	0.416382i	$-0.136702\pi$
$367$	1.80073	+	3.11895i	0.0939972	+	0.162808i	−0.815192	+	0.579190i	$0.803369\pi$
$368$		0			0
$369$	8.31586	−	0.516910i	0.432906	−	0.0269092i
$370$		0			0
$371$	−26.2488	−	3.33061i	−1.36277	−	0.172916i
$372$		0			0
$373$	8.60309	−	14.9010i	0.445451	−	0.771544i	−0.552632	−	0.833425i	$-0.686377\pi$
$373$	8.60309	−	14.9010i	0.445451	−	0.771544i	0.998084	+	0.0618811i	$0.0197100\pi$
$374$		0			0
$375$	−21.8587	+	12.6201i	−1.12878	+	0.651701i
$376$		0			0
$377$	35.4888			1.82777
$378$		0			0
$379$	0.871934			0.0447883			0.0223941	−	0.999749i	$-0.492871\pi$
$379$	0.871934			0.0447883			0.0223941	+	0.999749i	$0.492871\pi$
$380$		0			0
$381$	11.9028	−	6.87209i	0.609799	−	0.352068i
$382$		0			0
$383$	−28.6112	−	16.5187i	−1.46197	−	0.844067i	−0.462864	−	0.886429i	$-0.653178\pi$
$383$	−28.6112	−	16.5187i	−1.46197	−	0.844067i	−0.999102	+	0.0423626i	$0.986512\pi$
$384$		0			0
$385$	−9.34738	+	12.3007i	−0.476387	+	0.626903i
$386$		0			0
$387$	3.78454	−	6.55502i	0.192379	−	0.333210i
$388$		0			0
$389$	18.1539	+	31.4435i	0.920440	+	1.59425i	0.798735	+	0.601682i	$0.205503\pi$
$389$	18.1539	+	31.4435i	0.920440	+	1.59425i	0.121705	+	0.992566i	$0.461164\pi$
$390$		0			0
$391$			9.89905i			0.500617i
$392$		0			0
$393$			33.7956i			1.70476i
$394$		0			0
$395$	12.4283	−	7.17549i	0.625337	−	0.361038i
$396$		0			0
$397$	−0.585885	−	0.338261i	−0.0294047	−	0.0169768i	0.485226	−	0.874389i	$-0.338737\pi$
$397$	−0.585885	−	0.338261i	−0.0294047	−	0.0169768i	−0.514630	+	0.857412i	$0.672071\pi$
$398$		0			0
$399$	22.7948	+	17.3219i	1.14117	+	0.867179i
$400$		0			0
$401$	9.42440	−	16.3235i	0.470632	−	0.815159i	−0.528804	−	0.848744i	$-0.677359\pi$
$401$	9.42440	−	16.3235i	0.470632	−	0.815159i	0.999436	+	0.0335855i	$0.0106926\pi$
$402$		0			0
$403$	27.1744	−	15.6892i	1.35365	−	0.781533i
$404$		0			0
$405$	−20.2877			−1.00810
$406$		0			0
$407$		−	26.8030i		−	1.32858i
$408$		0			0
$409$	18.3099	+	31.7136i	0.905364	+	1.56814i	0.820428	+	0.571750i	$0.193735\pi$
$409$	18.3099	+	31.7136i	0.905364	+	1.56814i	0.0849361	+	0.996386i	$0.472931\pi$
$410$		0			0
$411$	2.71236	−	4.69795i	0.133791	−	0.231733i
$412$		0			0
$413$	−3.12848	+	24.6558i	−0.153942	+	1.21323i
$414$		0			0
$415$	−0.847973	+	1.46873i	−0.0416253	+	0.0720972i
$416$		0			0
$417$	−9.86807	+	5.69733i	−0.483242	+	0.279000i
$418$		0			0
$419$	−28.7296			−1.40353			−0.701766	−	0.712408i	$-0.747605\pi$
$419$	−28.7296			−1.40353			−0.701766	+	0.712408i	$0.747605\pi$
$420$		0			0
$421$		−	14.3246i		−	0.698138i	−0.937097	−	0.349069i	$-0.886498\pi$
$421$		−	14.3246i		−	0.698138i	0.937097	−	0.349069i	$-0.113502\pi$
$422$		0			0
$423$	−2.97475	+	1.71747i	−0.144637	+	0.0835064i
$424$		0			0
$425$	−8.19800	−	4.73312i	−0.397662	−	0.229590i
$426$		0			0
$427$	−13.2140	+	5.54614i	−0.639471	+	0.268397i
$428$		0			0
$429$	−38.1340	−	22.0167i	−1.84113	−	1.06297i
$430$		0			0
$431$	−4.38370	−	7.59279i	−0.211155	−	0.365732i	0.740921	−	0.671592i	$-0.234389\pi$
$431$	−4.38370	−	7.59279i	−0.211155	−	0.365732i	−0.952076	+	0.305860i	$0.901056\pi$
$432$		0			0
$433$	−28.3215			−1.36104			−0.680522	−	0.732728i	$-0.738247\pi$
$433$	−28.3215			−1.36104			−0.680522	+	0.732728i	$0.738247\pi$
$434$		0			0
$435$	20.2424			0.970549
$436$		0			0
$437$	−8.15072	+	4.70582i	−0.389902	+	0.225110i
$438$		0			0
$439$	31.6083	+	18.2490i	1.50858	+	0.870979i	0.999950	+	0.00999364i	$0.00318113\pi$
$439$	31.6083	+	18.2490i	1.50858	+	0.870979i	0.508630	+	0.860985i	$0.330152\pi$
$440$		0			0
$441$	8.81993	+	2.27488i	0.419996	+	0.108328i
$442$		0			0
$443$	8.99921	−	15.5871i	0.427565	−	0.740565i	−0.569091	−	0.822275i	$-0.692705\pi$
$443$	8.99921	−	15.5871i	0.427565	−	0.740565i	0.996656	+	0.0817100i	$0.0260381\pi$
$444$		0			0
$445$	13.4073	−	7.74070i	0.635567	−	0.366945i
$446$		0			0
$447$	37.6135			1.77906
$448$		0			0
$449$	3.70183			0.174700			0.0873502	−	0.996178i	$-0.472160\pi$
$449$	3.70183			0.174700			0.0873502	+	0.996178i	$0.472160\pi$
$450$		0			0
$451$	−18.4991	−	9.20036i	−0.871087	−	0.433228i
$452$		0			0
$453$	−11.9852	+	20.7590i	−0.563114	+	0.975343i
$454$		0			0
$455$	12.1931	+	29.0507i	0.571620	+	1.36192i
$456$		0			0
$457$	2.38636	+	1.37777i	0.111629	+	0.0644492i	0.554775	−	0.832000i	$-0.312804\pi$
$457$	2.38636	+	1.37777i	0.111629	+	0.0644492i	−0.443146	+	0.896450i	$0.646138\pi$
$458$		0			0
$459$	−9.66718	−	16.7441i	−0.451225	−	0.781545i
$460$		0			0
$461$	−31.8522			−1.48351			−0.741753	−	0.670673i	$-0.766006\pi$
$461$	−31.8522			−1.48351			−0.741753	+	0.670673i	$0.766006\pi$
$462$		0			0
$463$		−	10.1179i		−	0.470220i	−0.971969	−	0.235110i	$-0.924455\pi$
$463$		−	10.1179i		−	0.470220i	0.971969	−	0.235110i	$-0.0755451\pi$
$464$		0			0
$465$	15.5000	−	8.94892i	0.718794	−	0.414996i
$466$		0			0
$467$	0.153712	−	0.266237i	0.00711295	−	0.0123200i	−0.862447	−	0.506147i	$-0.831069\pi$
$467$	0.153712	−	0.266237i	0.00711295	−	0.0123200i	0.869560	+	0.493827i	$0.164403\pi$
$468$		0			0
$469$	29.3926	+	3.72951i	1.35722	+	0.172213i
$470$		0			0
$471$	−10.3762	+	17.9721i	−0.478111	+	0.828112i
$472$		0			0
$473$	−16.2545	+	9.38453i	−0.747382	+	0.431501i
$474$		0			0
$475$		−	9.00013i		−	0.412954i
$476$		0			0
$477$		−	13.0131i		−	0.595829i
$478$		0			0
$479$	−20.4749	+	11.8212i	−0.935520	+	0.540123i	−0.888553	−	0.458774i	$-0.848289\pi$
$479$	−20.4749	+	11.8212i	−0.935520	+	0.540123i	−0.0469668	+	0.998896i	$0.514955\pi$
$480$		0			0
$481$	−47.3365	−	27.3297i	−2.15836	−	1.24613i
$482$		0			0
$483$	−5.98855	+	7.88065i	−0.272488	+	0.358582i
$484$		0			0
$485$	−13.2628	−	7.65726i	−0.602231	−	0.347698i
$486$		0			0
$487$	3.67369	+	6.36302i	0.166471	+	0.288336i	0.937177	−	0.348855i	$-0.113430\pi$
$487$	3.67369	+	6.36302i	0.166471	+	0.288336i	−0.770706	+	0.637191i	$0.780096\pi$
$488$		0			0
$489$		−	28.6062i		−	1.29362i
$490$		0			0
$491$	−13.4939			−0.608971			−0.304485	−	0.952517i	$-0.598484\pi$
$491$	−13.4939			−0.608971			−0.304485	+	0.952517i	$0.598484\pi$
$492$		0			0
$493$	14.7988	+	25.6322i	0.666503	+	1.15442i
$494$		0			0
$495$	−6.58026	−	3.79912i	−0.295761	−	0.170758i
$496$		0			0
$497$	−3.94434	+	5.19057i	−0.176928	+	0.232829i
$498$		0			0
$499$	9.52683	+	5.50032i	0.426480	+	0.246228i	0.697846	−	0.716248i	$-0.254142\pi$
$499$	9.52683	+	5.50032i	0.426480	+	0.246228i	−0.271366	+	0.962476i	$0.587475\pi$
$500$		0			0
$501$	16.9181	+	29.3030i	0.755844	+	1.30916i
$502$		0			0
$503$		−	2.00925i		−	0.0895880i	−0.998996	−	0.0447940i	$-0.985737\pi$
$503$		−	2.00925i		−	0.0895880i	0.998996	−	0.0447940i	$-0.0142631\pi$
$504$		0			0
$505$			24.0447i			1.06998i
$506$		0			0
$507$	−54.4176	+	31.4180i	−2.41677	+	1.39532i
$508$		0			0
$509$	27.9699	+	16.1484i	1.23974	+	0.715766i	0.969042	−	0.246897i	$-0.0794110\pi$
$509$	27.9699	+	16.1484i	1.23974	+	0.715766i	0.270702	+	0.962663i	$0.412744\pi$
$510$		0			0
$511$	4.79248	−	37.7699i	0.212007	−	1.67084i
$512$		0			0
$513$	9.19118	−	15.9196i	0.405801	−	0.702867i
$514$		0			0
$515$	−2.07741	−	3.59818i	−0.0915415	−	0.158555i
$516$		0			0
$517$	8.51764			0.374606
$518$		0			0
$519$		−	8.76803i		−	0.384874i
$520$		0			0
$521$	−21.9898	+	12.6958i	−0.963390	+	0.556213i	−0.897215	−	0.441595i	$-0.854413\pi$
$521$	−21.9898	+	12.6958i	−0.963390	+	0.556213i	−0.0661749	+	0.997808i	$0.521080\pi$
$522$		0			0
$523$	−14.0212	+	24.2854i	−0.613104	+	1.06193i	0.377610	+	0.925965i	$0.376746\pi$
$523$	−14.0212	+	24.2854i	−0.613104	+	1.06193i	−0.990714	+	0.135962i	$0.956587\pi$
$524$		0			0
$525$	−3.66309	−	8.72752i	−0.159870	−	0.380900i
$526$		0			0
$527$	22.6634	+	13.0847i	0.987233	+	0.569979i
$528$		0			0
$529$	9.87310	+	17.1007i	0.429265	+	0.743509i
$530$		0			0
$531$	−12.2234			−0.530449
$532$		0			0
$533$	−35.1112	+	23.2898i	−1.52084	+	1.00879i
$534$		0			0
$535$	0.613853	+	1.06322i	0.0265392	+	0.0459672i
$536$		0			0
$537$	15.6207	−	27.0559i	0.674084	−	1.16755i
$538$		0			0
$539$	−16.1201	−	15.8207i	−0.694344	−	0.681444i
$540$		0			0
$541$	11.5535	−	20.0112i	0.496722	−	0.860347i	−0.503271	−	0.864129i	$-0.667870\pi$
$541$	11.5535	−	20.0112i	0.496722	−	0.860347i	0.999993	+	0.00378117i	$0.00120359\pi$
$542$		0			0
$543$	−16.0116	−	27.7329i	−0.687124	−	1.19013i
$544$		0			0
$545$			3.15142i			0.134992i
$546$		0			0
$547$			11.5069i			0.492002i	0.969270	+	0.246001i	$0.0791166\pi$
$547$			11.5069i			0.492002i	−0.969270	+	0.246001i	$0.920883\pi$
$548$		0			0
$549$	−3.52405	−	6.10383i	−0.150403	−	0.260505i
$550$		0			0
$551$	−14.0701	+	24.3701i	−0.599407	+	1.03820i
$552$		0			0
$553$	8.11980	+	19.3459i	0.345289	+	0.822672i
$554$		0			0
$555$	−27.0002	−	15.5886i	−1.14609	−	0.661697i
$556$		0			0
$557$	10.9602	−	6.32788i	0.464399	−	0.268121i	−0.249493	−	0.968377i	$-0.580264\pi$
$557$	10.9602	−	6.32788i	0.464399	−	0.268121i	0.713892	+	0.700256i	$0.246931\pi$
$558$		0			0
$559$			38.2758i			1.61889i
$560$		0			0
$561$		−	36.7237i		−	1.55047i
$562$		0			0
$563$	−29.8766	+	17.2493i	−1.25915	+	0.726969i	−0.972909	−	0.231189i	$-0.925738\pi$
$563$	−29.8766	+	17.2493i	−1.25915	+	0.726969i	−0.286239	+	0.958158i	$0.592405\pi$
$564$		0			0
$565$	5.51368	−	9.54998i	0.231962	−	0.401771i
$566$		0			0
$567$	3.73353	−	29.4242i	0.156793	−	1.23570i
$568$		0			0
$569$	−1.40942	+	2.44120i	−0.0590862	+	0.102340i	−0.894055	−	0.447956i	$-0.852152\pi$
$569$	−1.40942	+	2.44120i	−0.0590862	+	0.102340i	0.834969	+	0.550297i	$0.185485\pi$
$570$		0			0
$571$	−17.7405	+	10.2425i	−0.742418	+	0.428635i	−0.822948	−	0.568117i	$-0.807672\pi$
$571$	−17.7405	+	10.2425i	−0.742418	+	0.428635i	0.0805296	+	0.996752i	$0.474339\pi$
$572$		0			0
$573$	−33.4972			−1.39936
$574$		0			0
$575$	3.11154			0.129760
$576$		0			0
$577$	−20.7779	+	11.9961i	−0.864995	+	0.499405i	−0.865682	−	0.500595i	$-0.833115\pi$
$577$	−20.7779	+	11.9961i	−0.864995	+	0.499405i	0.000686611		1.00000i	$0.499781\pi$
$578$		0			0
$579$	7.20080	−	12.4722i	0.299255	−	0.518325i
$580$		0			0
$581$	−1.97412	−	1.50015i	−0.0819004	−	0.0622365i
$582$		0			0
$583$	−16.1343	+	27.9454i	−0.668215	+	1.15738i
$584$		0			0
$585$	−13.4191	+	7.74755i	−0.554813	+	0.320322i
$586$		0			0
$587$			2.01697i			0.0832491i	0.999133	+	0.0416245i	$0.0132533\pi$
$587$			2.01697i			0.0832491i	−0.999133	+	0.0416245i	$0.986747\pi$
$588$		0			0
$589$			24.8809i			1.02520i
$590$		0			0
$591$	4.98246	−	2.87662i	0.204951	−	0.118329i
$592$		0			0
$593$	39.3416	+	22.7139i	1.61557	+	0.932748i	0.988048	+	0.154146i	$0.0492625\pi$
$593$	39.3416	+	22.7139i	1.61557	+	0.932748i	0.627518	+	0.778602i	$0.284071\pi$
$594$		0			0
$595$	−15.8978	+	20.9207i	−0.651745	+	0.857666i
$596$		0			0
$597$	−15.8134	+	27.3896i	−0.647200	+	1.12098i
$598$		0			0
$599$	−6.01561	−	10.4193i	−0.245791	−	0.425723i	0.716562	−	0.697523i	$-0.245714\pi$
$599$	−6.01561	−	10.4193i	−0.245791	−	0.425723i	−0.962354	+	0.271800i	$0.912381\pi$
$600$		0			0
$601$			41.9703i			1.71200i	0.516973	+	0.856002i	$0.327059\pi$
$601$			41.9703i			1.71200i	−0.516973	+	0.856002i	$0.672941\pi$
$602$		0			0
$603$			14.5717i			0.593404i
$604$		0			0
$605$	−0.532715	−	0.922689i	−0.0216579	−	0.0375127i
$606$		0			0
$607$	−3.31033	+	5.73366i	−0.134362	+	0.232722i	−0.925354	−	0.379105i	$-0.876232\pi$
$607$	−3.31033	+	5.73366i	−0.134362	+	0.232722i	0.790991	+	0.611827i	$0.209565\pi$
$608$		0			0
$609$	−3.72519	+	29.3586i	−0.150952	+	1.18967i
$610$		0			0
$611$	8.68503	−	15.0429i	0.351359	−	0.608571i
$612$		0			0
$613$	−3.82717	−	6.62885i	−0.154578	−	0.267737i	0.778327	−	0.627859i	$-0.216068\pi$
$613$	−3.82717	−	6.62885i	−0.154578	−	0.267737i	−0.932905	+	0.360122i	$0.882735\pi$
$614$		0			0
$615$	−20.0271	+	13.2842i	−0.807569	+	0.535672i
$616$		0			0
$617$	−3.11259			−0.125308			−0.0626540	−	0.998035i	$-0.519956\pi$
$617$	−3.11259			−0.125308			−0.0626540	+	0.998035i	$0.519956\pi$
$618$		0			0
$619$	3.60498	+	6.24400i	0.144896	+	0.250968i	0.929334	−	0.369240i	$-0.120382\pi$
$619$	3.60498	+	6.24400i	0.144896	+	0.250968i	−0.784438	+	0.620207i	$0.787048\pi$
$620$		0			0
$621$	5.50374	+	3.17759i	0.220858	+	0.127512i
$622$		0			0
$623$	8.75939	+	20.8698i	0.350938	+	0.836130i
$624$		0			0
$625$	6.69985	−	11.6045i	0.267994	−	0.464179i
$626$		0			0
$627$	30.2376	−	17.4577i	1.20758	−	0.697194i
$628$		0			0
$629$		−	45.5858i		−	1.81763i
$630$		0			0
$631$	11.4665			0.456476			0.228238	−	0.973605i	$-0.426704\pi$
$631$	11.4665			0.456476			0.228238	+	0.973605i	$0.426704\pi$
$632$		0			0
$633$	23.5453	+	40.7817i	0.935843	+	1.62093i
$634$		0			0
$635$	−5.99654	+	10.3863i	−0.237965	+	0.412168i
$636$		0			0
$637$	−44.3776	+	12.3380i	−1.75830	+	0.488851i
$638$		0			0
$639$	−2.77669	−	1.60312i	−0.109844	−	0.0634186i
$640$		0			0
$641$	−1.63445	+	0.943653i	−0.0645571	+	0.0372720i	−0.531931	−	0.846788i	$-0.678533\pi$
$641$	−1.63445	+	0.943653i	−0.0645571	+	0.0372720i	0.467374	+	0.884060i	$0.345200\pi$
$642$		0			0
$643$			24.4961i			0.966031i	0.875612	+	0.483016i	$0.160459\pi$
$643$			24.4961i			0.966031i	−0.875612	+	0.483016i	$0.839541\pi$
$644$		0			0
$645$			21.8321i			0.859637i
$646$		0			0
$647$	20.0050	+	34.6496i	0.786477	+	1.36222i	0.928113	+	0.372299i	$0.121430\pi$
$647$	20.0050	+	34.6496i	0.786477	+	1.36222i	−0.141636	+	0.989919i	$0.545236\pi$
$648$		0			0
$649$	26.2495	+	15.1551i	1.03038	+	0.594891i
$650$		0			0
$651$	10.1266	+	24.1272i	0.396893	+	0.945621i
$652$		0			0
$653$	16.8842	+	9.74810i	0.660730	+	0.381472i	0.792555	−	0.609800i	$-0.208750\pi$
$653$	16.8842	+	9.74810i	0.660730	+	0.381472i	−0.131825	+	0.991273i	$0.542084\pi$
$654$		0			0
$655$	−14.7449	−	25.5389i	−0.576131	−	0.997888i
$656$		0			0
$657$	18.7248			0.730525
$658$		0			0
$659$		−	23.9290i		−	0.932143i	−0.884747	−	0.466072i	$-0.845669\pi$
$659$		−	23.9290i		−	0.932143i	0.884747	−	0.466072i	$-0.154331\pi$
$660$		0			0
$661$	−4.52168	−	7.83178i	−0.175873	−	0.304621i	0.764590	−	0.644517i	$-0.222941\pi$
$661$	−4.52168	−	7.83178i	−0.175873	−	0.304621i	−0.940463	+	0.339896i	$0.889608\pi$
$662$		0			0
$663$	−64.8572	−	37.4453i	−2.51885	−	1.45426i
$664$		0			0
$665$	−24.7833	−	3.14465i	−0.961054	−	0.121944i
$666$		0			0
$667$	−8.42528	−	4.86433i	−0.326228	−	0.188348i
$668$		0			0
$669$	48.9497	−	28.2611i	1.89250	−	1.09264i
$670$		0			0
$671$			17.4772i			0.674699i
$672$		0			0
$673$			6.33559i			0.244219i	0.992517	+	0.122110i	$0.0389659\pi$
$673$			6.33559i			0.244219i	−0.992517	+	0.122110i	$0.961034\pi$
$674$		0			0
$675$	−5.26310	+	3.03865i	−0.202577	+	0.116958i
$676$		0			0
$677$	2.72125	−	4.71334i	0.104586	−	0.181148i	−0.808983	−	0.587832i	$-0.799982\pi$
$677$	2.72125	−	4.71334i	0.104586	−	0.181148i	0.913569	+	0.406684i	$0.133315\pi$
$678$		0			0
$679$	13.5464	−	17.8265i	0.519865	−	0.684118i
$680$		0			0
$681$	−0.0841212	+	0.145702i	−0.00322353	+	0.00558332i
$682$		0			0
$683$	−11.7286	+	6.77152i	−0.448783	+	0.259105i	−0.707316	−	0.706897i	$-0.750094\pi$
$683$	−11.7286	+	6.77152i	−0.448783	+	0.259105i	0.258533	+	0.966002i	$0.416761\pi$
$684$		0			0
$685$			4.73358i			0.180861i
$686$		0			0
$687$	−11.2416			−0.428893
$688$		0			0
$689$	32.9027	+	56.9892i	1.25349	+	2.17112i
$690$		0			0
$691$	−15.9271	−	9.19549i	−0.605894	−	0.349813i	0.165463	−	0.986216i	$-0.447088\pi$
$691$	−15.9271	−	9.19549i	−0.605894	−	0.349813i	−0.771357	+	0.636403i	$0.780422\pi$
$692$		0			0
$693$	6.72100	−	8.84453i	0.255310	−	0.335976i
$694$		0			0
$695$	4.97146	−	8.61082i	0.188578	−	0.326627i
$696$		0			0
$697$	−31.4627	−	15.6477i	−1.19173	−	0.592700i
$698$		0			0
$699$	−47.3628			−1.79143
$700$		0			0
$701$	27.4115			1.03532			0.517659	−	0.855587i	$-0.326803\pi$
$701$	27.4115			1.03532			0.517659	+	0.855587i	$0.326803\pi$
$702$		0			0
$703$	37.5346	−	21.6706i	1.41564	−	0.817322i
$704$		0			0
$705$	4.95384	−	8.58030i	0.186572	−	0.323153i
$706$		0			0
$707$	−34.8732	−	4.42493i	−1.31154	−	0.166417i
$708$		0			0
$709$	−18.5656	−	10.7189i	−0.697247	−	0.402556i	0.109074	−	0.994034i	$-0.465211\pi$
$709$	−18.5656	−	10.7189i	−0.697247	−	0.402556i	−0.806321	+	0.591478i	$0.798545\pi$
$710$		0			0
$711$	−8.93628	+	5.15936i	−0.335137	+	0.193491i
$712$		0			0
$713$	−8.60185			−0.322142
$714$		0			0
$715$	38.4232			1.43695
$716$		0			0
$717$	19.3062	+	33.4393i	0.721003	+	1.24881i
$718$		0			0
$719$	33.8080	+	19.5191i	1.26083	+	0.727938i	0.973234	−	0.229816i	$-0.0738123\pi$
$719$	33.8080	+	19.5191i	1.26083	+	0.727938i	0.287591	+	0.957753i	$0.407146\pi$
$720$		0			0
$721$	5.60091	−	2.35080i	0.208589	−	0.0875483i
$722$		0			0
$723$	31.4482	+	18.1567i	1.16957	+	0.675253i
$724$		0			0
$725$	8.05690	−	4.65165i	0.299226	−	0.172758i
$726$		0			0
$727$			29.1135i			1.07976i	0.841742	+	0.539880i	$0.181530\pi$
$727$			29.1135i			1.07976i	−0.841742	+	0.539880i	$0.818470\pi$
$728$		0			0
$729$	−7.33307			−0.271595
$730$		0			0
$731$	−27.6452	+	15.9610i	−1.02249	+	0.590337i
$732$		0			0
$733$	−0.764500	+	1.32415i	−0.0282375	+	0.0489087i	−0.879799	−	0.475346i	$-0.842323\pi$
$733$	−0.764500	+	1.32415i	−0.0282375	+	0.0489087i	0.851561	+	0.524255i	$0.175656\pi$
$734$		0			0
$735$	−25.3125	+	7.03748i	−0.933665	+	0.259581i
$736$		0			0
$737$	18.0667	−	31.2924i	0.665495	−	1.15267i
$738$		0			0
$739$	6.52787	+	11.3066i	0.240132	+	0.415920i	0.960752	−	0.277410i	$-0.0894761\pi$
$739$	6.52787	+	11.3066i	0.240132	+	0.415920i	−0.720620	+	0.693330i	$0.756143\pi$
$740$		0			0
$741$		−	71.2031i		−	2.61571i
$742$		0			0
$743$	−5.00616			−0.183658			−0.0918292	−	0.995775i	$-0.529271\pi$
$743$	−5.00616			−0.183658			−0.0918292	+	0.995775i	$0.529271\pi$
$744$		0			0
$745$	−28.4240	+	16.4106i	−1.04138	+	0.601239i
$746$		0			0
$747$	0.609714	−	1.05606i	0.0223083	−	0.0386390i
$748$		0			0
$749$	−1.65501	+	0.694637i	−0.0604729	+	0.0253815i
$750$		0			0
$751$	4.55769	+	2.63138i	0.166312	+	0.0960205i	0.580846	−	0.814014i	$-0.302722\pi$
$751$	4.55769	+	2.63138i	0.166312	+	0.0960205i	−0.414533	+	0.910034i	$0.636055\pi$
$752$		0			0
$753$	17.3708	−	10.0290i	0.633026	−	0.365478i
$754$		0			0
$755$		−	20.9164i		−	0.761227i
$756$		0			0
$757$		−	7.70894i		−	0.280186i	−0.990138	−	0.140093i	$-0.955260\pi$
$757$		−	7.70894i		−	0.280186i	0.990138	−	0.140093i	$-0.0447402\pi$
$758$		0			0
$759$	6.03550	+	10.4538i	0.219075	+	0.379449i
$760$		0			0
$761$	−18.5083	+	32.0572i	−0.670924	+	1.16207i	0.306719	+	0.951800i	$0.400769\pi$
$761$	−18.5083	+	32.0572i	−0.670924	+	1.16207i	−0.977643	+	0.210274i	$0.932564\pi$
$762$		0			0
$763$	−4.57066	−	0.579953i	−0.165469	−	0.0209957i
$764$		0			0
$765$	−11.1915	−	6.46143i	−0.404630	−	0.233614i
$766$		0			0
$767$	53.5306	−	30.9059i	1.93288	−	1.11595i
$768$		0			0
$769$	1.18808			0.0428433			0.0214217	−	0.999771i	$-0.493181\pi$
$769$	1.18808			0.0428433			0.0214217	+	0.999771i	$0.493181\pi$
$770$		0			0
$771$	5.76674			0.207684
$772$		0			0
$773$	46.5478	−	26.8744i	1.67421	−	0.966603i	0.708965	−	0.705244i	$-0.249163\pi$
$773$	46.5478	−	26.8744i	1.67421	−	0.966603i	0.965242	−	0.261360i	$-0.0841708\pi$
$774$		0			0
$775$	4.11288	−	7.12371i	0.147739	−	0.255891i
$776$		0			0
$777$	27.5777	−	36.2909i	0.989343	−	1.30193i
$778$		0			0
$779$	−2.07268	−	33.3445i	−0.0742614	−	1.19469i
$780$		0			0
$781$	3.97527	+	6.88537i	0.142246	+	0.246378i
$782$		0			0
$783$	19.0016			0.679061
$784$		0			0
$785$		−	18.1084i		−	0.646318i
$786$		0			0
$787$	−11.0272	−	19.0997i	−0.393077	−	0.680830i	0.599776	−	0.800168i	$-0.295256\pi$
$787$	−11.0272	−	19.0997i	−0.393077	−	0.680830i	−0.992854	+	0.119338i	$0.961923\pi$
$788$		0			0
$789$	22.1514	−	38.3674i	0.788611	−	1.36591i
$790$		0			0
$791$	12.8361	+	9.75424i	0.456400	+	0.346821i
$792$		0			0
$793$	30.8662	+	17.8206i	1.09609	+	0.632829i
$794$		0			0
$795$	18.7673	+	32.5060i	0.665609	+	1.15287i
$796$		0			0
$797$	−5.20879			−0.184505			−0.0922523	−	0.995736i	$-0.529407\pi$
$797$	−5.20879			−0.184505			−0.0922523	+	0.995736i	$0.529407\pi$
$798$		0			0
$799$	14.4866			0.512498
$800$		0			0
$801$	−9.64018	+	5.56576i	−0.340619	+	0.196657i
$802$		0			0
$803$	−40.2113	−	23.2160i	−1.41902	−	0.819274i
$804$		0			0
$805$	1.08717	−	8.56810i	0.0383178	−	0.301986i
$806$		0			0
$807$	−18.8169	−	10.8640i	−0.662388	−	0.382430i
$808$		0			0
$809$	39.2732	−	22.6744i	1.38077	−	0.797189i	0.388521	−	0.921440i	$-0.372986\pi$
$809$	39.2732	−	22.6744i	1.38077	−	0.797189i	0.992251	+	0.124251i	$0.0396529\pi$
$810$		0			0
$811$	29.5981			1.03933			0.519664	−	0.854370i	$-0.326057\pi$
$811$	29.5981			1.03933			0.519664	+	0.854370i	$0.326057\pi$
$812$		0			0
$813$			50.5747i			1.77373i
$814$		0			0
$815$	12.4808	+	21.6174i	0.437183	+	0.757224i
$816$		0			0
$817$	−26.2840	−	15.1751i	−0.919560	−	0.530908i
$818$		0			0
$819$	−8.76713	−	20.8882i	−0.306348	−	0.729893i
$820$		0			0
$821$	−18.5854	+	32.1908i	−0.648634	+	1.12347i	0.334815	+	0.942284i	$0.391326\pi$
$821$	−18.5854	+	32.1908i	−0.648634	+	1.12347i	−0.983449	+	0.181183i	$0.942007\pi$
$822$		0			0
$823$	−30.9267	+	17.8555i	−1.07804	+	0.622405i	−0.930366	−	0.366632i	$-0.880511\pi$
$823$	−30.9267	+	17.8555i	−1.07804	+	0.622405i	−0.147671	+	0.989037i	$0.547178\pi$
$824$		0			0
$825$	−11.5432			−0.401884
$826$		0			0
$827$			15.6336i			0.543635i	0.962349	+	0.271817i	$0.0876247\pi$
$827$			15.6336i			0.543635i	−0.962349	+	0.271817i	$0.912375\pi$
$828$		0			0
$829$	10.5579	+	18.2868i	0.366690	+	0.635125i	0.989046	−	0.147609i	$-0.0471577\pi$
$829$	10.5579	+	18.2868i	0.366690	+	0.635125i	−0.622356	+	0.782734i	$0.713824\pi$
$830$		0			0
$831$	−41.1133	−	23.7368i	−1.42621	−	0.823420i
$832$		0			0
$833$	−27.4167	−	26.9073i	−0.949932	−	0.932284i
$834$		0			0
$835$	−25.5696	−	14.7626i	−0.884873	−	0.510881i
$836$		0			0
$837$	14.5499	−	8.40036i	0.502917	−	0.290359i
$838$		0			0
$839$			11.1518i			0.385003i	0.981297	+	0.192502i	$0.0616601\pi$
$839$			11.1518i			0.385003i	−0.981297	+	0.192502i	$0.938340\pi$
$840$		0			0
$841$	−0.0881166			−0.00303851
$842$		0			0
$843$	−9.42313	−	16.3213i	−0.324550	−	0.562137i
$844$		0			0
$845$	27.4152	−	47.4845i	0.943110	−	1.63352i
$846$		0			0
$847$	1.43626	−	0.602821i	0.0493504	−	0.0207132i
$848$		0			0
$849$	32.5735	+	18.8063i	1.11792	+	0.645431i
$850$		0			0
$851$	7.49199	+	12.9765i	0.256822	+	0.444829i
$852$		0			0
$853$	−8.86518			−0.303538			−0.151769	−	0.988416i	$-0.548497\pi$
$853$	−8.86518			−0.303538			−0.151769	+	0.988416i	$0.548497\pi$
$854$		0			0
$855$		−	12.2866i		−	0.420191i
$856$		0			0
$857$	−26.3997	−	45.7257i	−0.901798	−	1.56196i	−0.825159	−	0.564901i	$-0.808914\pi$
$857$	−26.3997	−	45.7257i	−0.901798	−	1.56196i	−0.0766390	−	0.997059i	$-0.524419\pi$
$858$		0			0
$859$	−26.6155	+	46.0994i	−0.908110	+	1.57289i	−0.0914216	+	0.995812i	$0.529141\pi$
$859$	−26.6155	+	46.0994i	−0.908110	+	1.57289i	−0.816688	+	0.577080i	$0.804192\pi$
$860$		0			0
$861$	−15.5812	−	31.4909i	−0.531007	−	1.07321i
$862$		0			0
$863$	−7.85354	+	13.6027i	−0.267338	+	0.463042i	−0.968173	−	0.250280i	$-0.919477\pi$
$863$	−7.85354	+	13.6027i	−0.267338	+	0.463042i	0.700836	+	0.713323i	$0.252811\pi$
$864$		0			0
$865$	3.82546	+	6.62590i	0.130070	+	0.225287i
$866$		0			0
$867$		−	27.2016i		−	0.923815i
$868$		0			0
$869$	25.5874			0.867992
$870$		0			0
$871$	−36.8434	−	63.8147i	−1.24839	−	2.16228i
$872$		0			0
$873$	9.53627	+	5.50577i	0.322754	+	0.186342i
$874$		0			0
$875$	25.6371	+	19.4817i	0.866691	+	0.658603i
$876$		0			0
$877$	−8.98930	+	15.5699i	−0.303547	+	0.525759i	−0.976937	−	0.213529i	$-0.931504\pi$
$877$	−8.98930	+	15.5699i	−0.303547	+	0.525759i	0.673390	+	0.739288i	$0.264838\pi$
$878$		0			0
$879$	16.2603	+	28.1637i	0.548447	+	0.949938i
$880$		0			0
$881$	7.98020			0.268860			0.134430	−	0.990923i	$-0.457080\pi$
$881$	7.98020			0.268860			0.134430	+	0.990923i	$0.457080\pi$
$882$		0			0
$883$		−	44.2495i		−	1.48912i	−0.667558	−	0.744558i	$-0.732660\pi$
$883$		−	44.2495i		−	1.48912i	0.667558	−	0.744558i	$-0.267340\pi$
$884$		0			0
$885$	30.5333	−	17.6284i	1.02636	−	0.592572i
$886$		0			0
$887$	15.2720	+	8.81729i	0.512783	+	0.296056i	0.733977	−	0.679174i	$-0.237662\pi$
$887$	15.2720	+	8.81729i	0.512783	+	0.296056i	−0.221194	+	0.975230i	$0.570995\pi$
$888$		0			0
$889$	−13.9602	−	10.6085i	−0.468211	−	0.355796i
$890$		0			0
$891$	−31.3261	−	18.0862i	−1.04947	−	0.605909i
$892$		0			0
$893$	6.88664	+	11.9280i	0.230452	+	0.399155i
$894$		0			0
$895$			27.2611i			0.911238i
$896$		0			0
$897$	24.6164			0.821919
$898$		0			0
$899$	−22.2733	+	12.8595i	−0.742856	+	0.428888i
$900$		0			0
$901$	−27.4408	+	47.5288i	−0.914185	+	1.58342i
$902$		0			0
$903$	−31.6641	−	4.01774i	−1.05372	−	0.133702i
$904$		0			0
$905$	24.1996	+	13.9716i	0.804421	+	0.464433i
$906$		0			0
$907$	−12.4587	−	21.5790i	−0.413683	−	0.716520i	0.581606	−	0.813470i	$-0.302424\pi$
$907$	−12.4587	−	21.5790i	−0.413683	−	0.716520i	−0.995289	+	0.0969505i	$0.969091\pi$
$908$		0			0
$909$		−	17.2888i		−	0.573432i
$910$		0			0
$911$	−20.2827			−0.671997			−0.335998	−	0.941863i	$-0.609074\pi$
$911$	−20.2827			−0.671997			−0.335998	+	0.941863i	$0.609074\pi$
$912$		0			0
$913$	−2.61870	+	1.51191i	−0.0866664	+	0.0500369i
$914$		0			0
$915$	17.6057	+	10.1647i	0.582028	+	0.336034i
$916$		0			0
$917$	39.7538	−	16.6853i	1.31279	−	0.550999i
$918$		0			0
$919$	12.6286	+	7.29111i	0.416578	+	0.240512i	0.693612	−	0.720348i	$-0.256018\pi$
$919$	12.6286	+	7.29111i	0.416578	+	0.240512i	−0.277034	+	0.960860i	$0.589351\pi$
$920$		0			0
$921$	15.5349	−	8.96905i	0.511891	−	0.295540i
$922$		0			0
$923$	16.2136			0.533676
$924$		0			0
$925$	−14.3288			−0.471129
$926$		0			0
$927$	1.49371	+	2.58718i	0.0490598	+	0.0849741i
$928$		0			0
$929$	10.0254	+	5.78814i	0.328921	+	0.189903i	0.655362	−	0.755315i	$-0.272516\pi$
$929$	10.0254	+	5.78814i	0.328921	+	0.189903i	−0.326441	+	0.945218i	$0.605849\pi$
$930$		0			0
$931$	9.12168	−	35.3657i	0.298951	−	1.15906i
$932$		0			0
$933$	25.5361	−	44.2298i	0.836013	−	1.44802i
$934$		0			0
$935$	16.0224	+	27.7516i	0.523989	+	0.907576i
$936$		0			0
$937$			19.8760i			0.649321i	0.945831	+	0.324661i	$0.105250\pi$
$937$			19.8760i			0.649321i	−0.945831	+	0.324661i	$0.894750\pi$
$938$		0			0
$939$	45.6669			1.49028
$940$		0			0
$941$	−9.05689	−	15.6870i	−0.295246	−	0.511381i	0.679796	−	0.733401i	$-0.262068\pi$
$941$	−9.05689	−	15.6870i	−0.295246	−	0.511381i	−0.975042	+	0.222020i	$0.928735\pi$
$942$		0			0
$943$	11.5279	−	0.716569i	0.375400	−	0.0233347i
$944$		0			0
$945$	6.52848	+	15.5545i	0.212371	+	0.505987i
$946$		0			0
$947$	−3.97722	+	6.88874i	−0.129242	+	0.223854i	−0.923383	−	0.383879i	$-0.874588\pi$
$947$	−3.97722	+	6.88874i	−0.129242	+	0.223854i	0.794141	+	0.607734i	$0.207921\pi$
$948$		0			0
$949$	−82.0029	+	47.3444i	−2.66193	+	1.53686i
$950$		0			0
$951$	−56.0060			−1.81612
$952$		0			0
$953$	−22.3275			−0.723258			−0.361629	−	0.932322i	$-0.617779\pi$
$953$	−22.3275			−0.723258			−0.361629	+	0.932322i	$0.617779\pi$
$954$		0			0
$955$	25.3134	−	14.6147i	0.819123	−	0.472921i
$956$		0			0
$957$	31.2562	+	18.0458i	1.01037	+	0.583337i
$958$		0			0
$959$	−6.86535	−	0.871117i	−0.221694	−	0.0281298i
$960$		0			0
$961$	4.12995	−	7.15329i	0.133224	−	0.230751i
$962$		0			0
$963$	−0.441376	−	0.764485i	−0.0142231	−	0.0246352i
$964$		0			0
$965$			12.5667i			0.404538i
$966$		0			0
$967$			35.1971i			1.13186i	0.824452	+	0.565931i	$0.191483\pi$
$967$			35.1971i			1.13186i	−0.824452	+	0.565931i	$0.808517\pi$
$968$		0			0
$969$	51.4274	−	29.6916i	1.65208	−	0.953832i
$970$		0			0
$971$	3.54662	+	2.04764i	0.113816	+	0.0657119i	0.555828	−	0.831298i	$-0.312401\pi$
$971$	3.54662	+	2.04764i	0.113816	+	0.0657119i	−0.442011	+	0.897010i	$0.645735\pi$
$972$		0			0
$973$	11.5738	+	8.79499i	0.371039	+	0.281955i
$974$		0			0
$975$	−11.7701	+	20.3864i	−0.376944	+	0.652886i
$976$		0			0
$977$	16.3470	−	9.43795i	0.522987	−	0.301947i	−0.215169	−	0.976577i	$-0.569030\pi$
$977$	16.3470	−	9.43795i	0.522987	−	0.301947i	0.738156	+	0.674630i	$0.235697\pi$
$978$		0			0
$979$	27.6029			0.882191
$980$		0			0
$981$		−	2.26595i		−	0.0723462i
$982$		0			0
$983$	−19.6628	−	34.0569i	−0.627145	−	1.08625i	−0.988122	−	0.153672i	$-0.950890\pi$
$983$	−19.6628	−	34.0569i	−0.627145	−	1.08625i	0.360977	−	0.932575i	$-0.382443\pi$
$984$		0			0
$985$	−2.51012	+	4.34766i	−0.0799792	+	0.138528i
$986$		0			0
$987$	11.5328	+	8.76382i	0.367092	+	0.278956i
$988$		0			0
$989$	5.24634	−	9.08693i	0.166824	−	0.288948i
$990$		0			0
$991$	−37.5542	+	21.6820i	−1.19295	+	0.688750i	−0.958974	−	0.283493i	$-0.908507\pi$
$991$	−37.5542	+	21.6820i	−1.19295	+	0.688750i	−0.233975	+	0.972243i	$0.575174\pi$
$992$		0			0
$993$	37.8492			1.20111
$994$		0			0
$995$		−	27.5974i		−	0.874896i
$996$		0			0
$997$	29.3178	−	16.9266i	0.928504	−	0.536072i	0.0421662	−	0.999111i	$-0.486574\pi$
$997$	29.3178	−	16.9266i	0.928504	−	0.536072i	0.886338	+	0.463038i	$0.153241\pi$
$998$		0			0
$999$	−25.3451	−	14.6330i	−0.801884	−	0.462968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.737.23	yes	56
7.4	even	3	inner	1148.2.r.a.81.6	✓	56
41.40	even	2	inner	1148.2.r.a.737.6	yes	56
287.81	even	6	inner	1148.2.r.a.81.23	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.6	✓	56	7.4	even	3	inner
1148.2.r.a.81.23	yes	56	287.81	even	6	inner
1148.2.r.a.737.6	yes	56	41.40	even	2	inner
1148.2.r.a.737.23	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79608 - 1.03697i) q^{3} +(-0.904853 + 1.56725i) q^{5} +(-2.10654 - 1.60077i) q^{7} +(0.650613 - 1.12689i) q^{9} +O(q^{10})\)	\(q+(1.79608 - 1.03697i) q^{3} +(-0.904853 + 1.56725i) q^{5} +(-2.10654 - 1.60077i) q^{7} +(0.650613 - 1.12689i) q^{9} +(-2.79436 + 1.61332i) q^{11} +6.58011i q^{13} +3.75322i q^{15} +(-4.75257 + 2.74390i) q^{17} +(-4.51856 - 2.60879i) q^{19} +(-5.44348 - 0.690702i) q^{21} +(0.901915 - 1.56216i) q^{23} +(0.862481 + 1.49386i) q^{25} +3.52316i q^{27} -5.39334i q^{29} +(-2.38433 - 4.12978i) q^{31} +(-3.34594 + 5.79534i) q^{33} +(4.41493 - 1.85302i) q^{35} +(-4.15338 + 7.19386i) q^{37} +(6.82338 + 11.8184i) q^{39} +(3.53942 + 5.33596i) q^{41} +5.81689 q^{43} +(1.17742 + 2.03935i) q^{45} +(-2.28612 - 1.31989i) q^{47} +(1.87505 + 6.74420i) q^{49} +(-5.69068 + 9.85655i) q^{51} +(8.66082 - 5.00033i) q^{53} -5.83929i q^{55} -10.8210 q^{57} +(-4.69687 - 8.13521i) q^{59} +(2.70825 - 4.69083i) q^{61} +(-3.17445 + 1.33237i) q^{63} +(-10.3127 - 5.95404i) q^{65} +(-9.69812 + 5.59921i) q^{67} -3.74103i q^{69} -2.46402i q^{71} +(7.19507 + 12.4622i) q^{73} +(3.09818 + 1.78873i) q^{75} +(8.46901 + 1.07460i) q^{77} +(-6.86759 - 3.96500i) q^{79} +(5.60524 + 9.70857i) q^{81} +0.937138 q^{83} -9.93130i q^{85} +(-5.59273 - 9.68689i) q^{87} +(-7.40854 - 4.27732i) q^{89} +(10.5333 - 13.8613i) q^{91} +(-8.56491 - 4.94495i) q^{93} +(8.17727 - 4.72115i) q^{95} +8.46243i q^{97} +4.19860i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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