LMFDB - Embedded newform 276.2.k.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	276.53
Dual form			276.2.k.a.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67064 - 0.457117i) q^{3} +(1.12657 + 2.46685i) q^{5} +(-1.33973 - 4.56271i) q^{7} +(2.58209 + 1.52736i) q^{9} +O(q^{10})$	\(q+(-1.67064 - 0.457117i) q^{3} +(1.12657 + 2.46685i) q^{5} +(-1.33973 - 4.56271i) q^{7} +(2.58209 + 1.52736i) q^{9} +(3.05906 + 3.53034i) q^{11} +(5.00588 + 1.46986i) q^{13} +(-0.754461 - 4.63621i) q^{15} +(0.651083 - 4.52838i) q^{17} +(1.22401 - 0.175986i) q^{19} +(0.152520 + 8.23506i) q^{21} +(3.62548 + 3.13941i) q^{23} +(-1.54190 + 1.77944i) q^{25} +(-3.61556 - 3.73198i) q^{27} +(1.04528 + 0.150289i) q^{29} +(2.01881 + 1.29741i) q^{31} +(-3.49681 - 7.29628i) q^{33} +(9.74622 - 8.44515i) q^{35} +(-3.27904 - 1.49749i) q^{37} +(-7.69114 - 4.74388i) q^{39} +(-0.361197 + 0.164953i) q^{41} +(-2.00725 - 3.12335i) q^{43} +(-0.858855 + 8.09032i) q^{45} +2.95968i q^{47} +(-13.1346 + 8.44111i) q^{49} +(-3.15773 + 7.26768i) q^{51} +(-12.1886 + 3.57890i) q^{53} +(-5.26258 + 11.5234i) q^{55} +(-2.12533 - 0.265506i) q^{57} +(-1.28015 + 4.35978i) q^{59} +(5.47649 - 8.52159i) q^{61} +(3.50958 - 13.8276i) q^{63} +(2.01357 + 14.0047i) q^{65} +(1.58000 + 1.36908i) q^{67} +(-4.62180 - 6.90210i) q^{69} +(-12.6008 - 10.9187i) q^{71} +(-0.0116824 - 0.0812528i) q^{73} +(3.38937 - 2.26799i) q^{75} +(12.0096 - 18.6873i) q^{77} +(-3.92739 + 13.3755i) q^{79} +(4.33435 + 7.88755i) q^{81} +(0.287324 - 0.629151i) q^{83} +(11.9043 - 3.49543i) q^{85} +(-1.67759 - 0.728895i) q^{87} +(1.94506 - 1.25001i) q^{89} -24.8096i q^{91} +(-2.77963 - 3.09033i) q^{93} +(1.81307 + 2.82119i) q^{95} +(7.40873 - 3.38345i) q^{97} +(2.50666 + 13.7879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$	$-1$

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
$3$	−1.67064	−	0.457117i	−0.964545	−	0.263917i
$3$	−1.67064	−	0.457117i	−0.964545	−	0.263917i
$4$		0			0
$5$	1.12657	+	2.46685i	0.503819	+	1.10321i	0.975209	+	0.221286i	$0.0710253\pi$
$5$	1.12657	+	2.46685i	0.503819	+	1.10321i	−0.471390	+	0.881925i	$0.656247\pi$
$6$		0			0
$7$	−1.33973	−	4.56271i	−0.506371	−	1.72454i	−0.674038	−	0.738697i	$-0.735442\pi$
$7$	−1.33973	−	4.56271i	−0.506371	−	1.72454i	0.167667	−	0.985844i	$-0.446377\pi$
$8$		0			0
$9$	2.58209	+	1.52736i	0.860696	+	0.509119i
$10$		0			0
$11$	3.05906	+	3.53034i	0.922340	+	1.06444i	0.997734	+	0.0672832i	$0.0214331\pi$
$11$	3.05906	+	3.53034i	0.922340	+	1.06444i	−0.0753940	+	0.997154i	$0.524021\pi$
$12$		0			0
$13$	5.00588	+	1.46986i	1.38838	+	0.407666i	0.888678	−	0.458531i	$-0.151624\pi$
$13$	5.00588	+	1.46986i	1.38838	+	0.407666i	0.499703	+	0.866197i	$0.333442\pi$
$14$		0			0
$15$	−0.754461	−	4.63621i	−0.194801	−	1.19706i
$16$		0			0
$17$	0.651083	−	4.52838i	0.157911	−	1.09829i	−0.744564	−	0.667551i	$-0.767343\pi$
$17$	0.651083	−	4.52838i	0.157911	−	1.09829i	0.902475	−	0.430742i	$-0.141748\pi$
$18$		0			0
$19$	1.22401	−	0.175986i	0.280807	−	0.0403740i	−0.000472281	−	1.00000i	$-0.500150\pi$
$19$	1.22401	−	0.175986i	0.280807	−	0.0403740i	0.281279	+	0.959626i	$0.409241\pi$
$20$		0			0
$21$	0.152520	+	8.23506i	0.0332826	+	1.79704i
$22$		0			0
$23$	3.62548	+	3.13941i	0.755965	+	0.654613i
$23$	3.62548	+	3.13941i	0.755965	+	0.654613i
$24$		0			0
$25$	−1.54190	+	1.77944i	−0.308379	+	0.355889i
$26$		0			0
$27$	−3.61556	−	3.73198i	−0.695815	−	0.718221i
$28$		0			0
$29$	1.04528	+	0.150289i	0.194104	+	0.0279079i	0.238681	−	0.971098i	$-0.423285\pi$
$29$	1.04528	+	0.150289i	0.194104	+	0.0279079i	−0.0445771	+	0.999006i	$0.514194\pi$
$30$		0			0
$31$	2.01881	+	1.29741i	0.362588	+	0.233021i	0.709231	−	0.704976i	$-0.249042\pi$
$31$	2.01881	+	1.29741i	0.362588	+	0.233021i	−0.346643	+	0.937997i	$0.612679\pi$
$32$		0			0
$33$	−3.49681	−	7.29628i	−0.608716	−	1.27012i
$34$		0			0
$35$	9.74622	−	8.44515i	1.64741	−	1.42749i
$36$		0			0
$37$	−3.27904	−	1.49749i	−0.539070	−	0.246185i	0.127224	−	0.991874i	$-0.459393\pi$
$37$	−3.27904	−	1.49749i	−0.539070	−	0.246185i	−0.666294	+	0.745689i	$0.732121\pi$
$38$		0			0
$39$	−7.69114	−	4.74388i	−1.23157	−	0.759629i
$40$		0			0
$41$	−0.361197	+	0.164953i	−0.0564095	+	0.0257614i	−0.443420	−	0.896314i	$-0.646235\pi$
$41$	−0.361197	+	0.164953i	−0.0564095	+	0.0257614i	0.387011	+	0.922075i	$0.373508\pi$
$42$		0			0
$43$	−2.00725	−	3.12335i	−0.306103	−	0.476306i	0.653788	−	0.756678i	$-0.273179\pi$
$43$	−2.00725	−	3.12335i	−0.306103	−	0.476306i	−0.959892	+	0.280371i	$0.909542\pi$
$44$		0			0
$45$	−0.858855	+	8.09032i	−0.128031	+	1.20603i
$46$		0			0
$47$			2.95968i			0.431714i	0.976425	+	0.215857i	$0.0692545\pi$
$47$			2.95968i			0.431714i	−0.976425	+	0.215857i	$0.930746\pi$
$48$		0			0
$49$	−13.1346	+	8.44111i	−1.87638	+	1.20587i
$50$		0			0
$51$	−3.15773	+	7.26768i	−0.442170	+	1.01768i
$52$		0			0
$53$	−12.1886	+	3.57890i	−1.67424	+	0.491600i	−0.974797	−	0.223092i	$-0.928385\pi$
$53$	−12.1886	+	3.57890i	−1.67424	+	0.491600i	−0.699439	+	0.714692i	$0.746567\pi$
$54$		0			0
$55$	−5.26258	+	11.5234i	−0.709606	+	1.55382i
$56$		0			0
$57$	−2.12533	−	0.265506i	−0.281507	−	0.0351672i
$58$		0			0
$59$	−1.28015	+	4.35978i	−0.166661	+	0.567595i	0.833231	+	0.552924i	$0.186488\pi$
$59$	−1.28015	+	4.35978i	−0.166661	+	0.567595i	−0.999892	+	0.0146706i	$0.995330\pi$
$60$		0			0
$61$	5.47649	−	8.52159i	0.701193	−	1.09108i	−0.289790	−	0.957090i	$-0.593585\pi$
$61$	5.47649	−	8.52159i	0.701193	−	1.09108i	0.990983	−	0.133988i	$-0.0427782\pi$
$62$		0			0
$63$	3.50958	−	13.8276i	0.442166	−	1.74211i
$64$		0			0
$65$	2.01357	+	14.0047i	0.249753	+	1.73707i
$66$		0			0
$67$	1.58000	+	1.36908i	0.193028	+	0.167259i	0.746013	−	0.665932i	$-0.231966\pi$
$67$	1.58000	+	1.36908i	0.193028	+	0.167259i	−0.552985	+	0.833191i	$0.686511\pi$
$68$		0			0
$69$	−4.62180	−	6.90210i	−0.556399	−	0.830915i
$70$		0			0
$71$	−12.6008	−	10.9187i	−1.49544	−	1.29581i	−0.842915	−	0.538047i	$-0.819162\pi$
$71$	−12.6008	−	10.9187i	−1.49544	−	1.29581i	−0.652530	−	0.757763i	$-0.726292\pi$
$72$		0			0
$73$	−0.0116824	−	0.0812528i	−0.00136732	−	0.00950992i	0.989126	−	0.147068i	$-0.0469837\pi$
$73$	−0.0116824	−	0.0812528i	−0.00136732	−	0.00950992i	−0.990494	+	0.137558i	$0.956075\pi$
$74$		0			0
$75$	3.38937	−	2.26799i	0.391371	−	0.261884i
$76$		0			0
$77$	12.0096	−	18.6873i	1.36862	−	2.12961i
$78$		0			0
$79$	−3.92739	+	13.3755i	−0.441866	+	1.50486i	0.374446	+	0.927249i	$0.377833\pi$
$79$	−3.92739	+	13.3755i	−0.441866	+	1.50486i	−0.816313	+	0.577610i	$0.803985\pi$
$80$		0			0
$81$	4.33435	+	7.88755i	0.481595	+	0.876394i
$82$		0			0
$83$	0.287324	−	0.629151i	0.0315379	−	0.0690583i	−0.893207	−	0.449645i	$-0.851551\pi$
$83$	0.287324	−	0.629151i	0.0315379	−	0.0690583i	0.924745	+	0.380586i	$0.124278\pi$
$84$		0			0
$85$	11.9043	−	3.49543i	1.29121	−	0.379133i
$86$		0			0
$87$	−1.67759	−	0.728895i	−0.179857	−	0.0781458i
$88$		0			0
$89$	1.94506	−	1.25001i	0.206176	−	0.132501i	−0.433478	−	0.901164i	$-0.642714\pi$
$89$	1.94506	−	1.25001i	0.206176	−	0.132501i	0.639654	+	0.768663i	$0.279078\pi$
$90$		0			0
$91$		−	24.8096i		−	2.60075i
$92$		0			0
$93$	−2.77963	−	3.09033i	−0.288235	−	0.320453i
$94$		0			0
$95$	1.81307	+	2.82119i	0.186017	+	0.289448i
$96$		0			0
$97$	7.40873	−	3.38345i	0.752243	−	0.343538i	−0.00211815	−	0.999998i	$-0.500674\pi$
$97$	7.40873	−	3.38345i	0.752243	−	0.343538i	0.754361	+	0.656460i	$0.227947\pi$
$98$		0			0
$99$	2.50666	+	13.7879i	0.251929	+	1.38574i
$100$		0			0
$101$	1.20156	+	0.548736i	0.119560	+	0.0546012i	0.474297	−	0.880365i	$-0.342702\pi$
$101$	1.20156	+	0.548736i	0.119560	+	0.0546012i	−0.354737	+	0.934966i	$0.615430\pi$
$102$		0			0
$103$	5.89540	−	5.10840i	0.580891	−	0.503345i	−0.314123	−	0.949382i	$-0.601710\pi$
$103$	5.89540	−	5.10840i	0.580891	−	0.503345i	0.895015	+	0.446037i	$0.147165\pi$
$104$		0			0
$105$	−20.1429	+	9.65365i	−1.96574	+	0.942100i
$106$		0			0
$107$	6.95661	+	4.47074i	0.672521	+	0.432203i	0.831834	−	0.555025i	$-0.187291\pi$
$107$	6.95661	+	4.47074i	0.672521	+	0.432203i	−0.159312	+	0.987228i	$0.550928\pi$
$108$		0			0
$109$	4.84909	+	0.697194i	0.464459	+	0.0667791i	0.370572	−	0.928804i	$-0.379162\pi$
$109$	4.84909	+	0.697194i	0.464459	+	0.0667791i	0.0938869	+	0.995583i	$0.470071\pi$
$110$		0			0
$111$	4.79357	+	4.00067i	0.454985	+	0.379726i
$112$		0			0
$113$	3.62917	−	4.18829i	0.341404	−	0.394001i	−0.558920	−	0.829222i	$-0.688784\pi$
$113$	3.62917	−	4.18829i	0.341404	−	0.394001i	0.900324	+	0.435220i	$0.143330\pi$
$114$		0			0
$115$	−3.66010	+	12.4803i	−0.341306	+	1.16379i
$116$		0			0
$117$	10.6806	+	11.4411i	0.987424	+	1.05773i
$118$		0			0
$119$	−21.5339	+	3.09611i	−1.97401	+	0.283820i
$120$		0			0
$121$	−1.54000	+	10.7110i	−0.140000	+	0.973724i
$122$		0			0
$123$	0.678834	−	0.110468i	0.0612084	−	0.00996059i
$124$		0			0
$125$	6.88368	+	2.02123i	0.615695	+	0.180784i
$126$		0			0
$127$	−7.76550	−	8.96186i	−0.689076	−	0.795236i	0.298157	−	0.954517i	$-0.403628\pi$
$127$	−7.76550	−	8.96186i	−0.689076	−	0.795236i	−0.987233	+	0.159280i	$0.949083\pi$
$128$		0			0
$129$	1.92567	+	6.13555i	0.169545	+	0.540205i
$130$		0			0
$131$	0.120476	+	0.410305i	0.0105261	+	0.0358485i	0.964589	−	0.263759i	$-0.0849624\pi$
$131$	0.120476	+	0.410305i	0.0105261	+	0.0358485i	−0.954063	+	0.299608i	$0.903144\pi$
$132$		0			0
$133$	−2.44282	−	5.34902i	−0.211819	−	0.463819i
$134$		0			0
$135$	5.13306	−	13.1234i	0.441784	−	1.12948i
$136$		0			0
$137$	−8.03221			−0.686238			−0.343119	−	0.939292i	$-0.611483\pi$
$137$	−8.03221			−0.686238			−0.343119	+	0.939292i	$0.611483\pi$
$138$		0			0
$139$	4.45044			0.377481			0.188741	−	0.982027i	$-0.439559\pi$
$139$	4.45044			0.377481			0.188741	+	0.982027i	$0.439559\pi$
$140$		0			0
$141$	1.35292	−	4.94457i	0.113937	−	0.416408i
$142$		0			0
$143$	10.1242	+	22.1688i	0.846625	+	1.85385i
$144$		0			0
$145$	0.806848	+	2.74787i	0.0670050	+	0.228198i
$146$		0			0
$147$	25.8018	−	8.09801i	2.12810	−	0.667913i
$148$		0			0
$149$	−11.6544	−	13.4499i	−0.954763	−	1.10186i	−0.994717	−	0.102654i	$-0.967267\pi$
$149$	−11.6544	−	13.4499i	−0.954763	−	1.10186i	0.0399538	−	0.999202i	$-0.487279\pi$
$150$		0			0
$151$	−11.3723	−	3.33920i	−0.925463	−	0.271741i	−0.215927	−	0.976410i	$-0.569277\pi$
$151$	−11.3723	−	3.33920i	−0.925463	−	0.271741i	−0.709536	+	0.704669i	$0.751096\pi$
$152$		0			0
$153$	8.59761	−	10.6982i	0.695075	−	0.864901i
$154$		0			0
$155$	−0.926180	+	6.44173i	−0.0743926	+	0.517412i
$156$		0			0
$157$	−17.8347	+	2.56424i	−1.42336	+	0.204648i	−0.810591	−	0.585613i	$-0.800854\pi$
$157$	−17.8347	+	2.56424i	−1.42336	+	0.204648i	−0.612770	+	0.790261i	$0.709945\pi$
$158$		0			0
$159$	21.9988	−	0.407436i	1.74462	−	0.0323118i
$160$		0			0
$161$	9.46704	−	20.7480i	0.746108	−	1.63517i
$162$		0			0
$163$	7.96596	−	9.19320i	0.623942	−	0.720067i	−0.352509	−	0.935809i	$-0.614671\pi$
$163$	7.96596	−	9.19320i	0.623942	−	0.720067i	0.976451	+	0.215741i	$0.0692168\pi$
$164$		0			0
$165$	14.0594	−	16.8459i	1.09453	−	1.31145i
$166$		0			0
$167$	2.31350	+	0.332631i	0.179024	+	0.0257398i	0.231244	−	0.972896i	$-0.425721\pi$
$167$	2.31350	+	0.332631i	0.179024	+	0.0257398i	−0.0522197	+	0.998636i	$0.516630\pi$
$168$		0			0
$169$	11.9621	+	7.68755i	0.920159	+	0.591350i
$170$		0			0
$171$	3.42929	+	1.41509i	0.262245	+	0.108215i
$172$		0			0
$173$	−12.9677	+	11.2365i	−0.985913	+	0.854298i	−0.989329	−	0.145696i	$-0.953458\pi$
$173$	−12.9677	+	11.2365i	−0.985913	+	0.854298i	0.00341649	+	0.999994i	$0.498912\pi$
$174$		0			0
$175$	10.1848	+	4.65124i	0.769899	+	0.351601i
$176$		0			0
$177$	4.13160	−	6.69845i	0.310550	−	0.503487i
$178$		0			0
$179$	−18.5511	+	8.47199i	−1.38657	+	0.633226i	−0.962220	−	0.272272i	$-0.912225\pi$
$179$	−18.5511	+	8.47199i	−1.38657	+	0.633226i	−0.424351	+	0.905498i	$0.639498\pi$
$180$		0			0
$181$	0.575468	+	0.895446i	0.0427742	+	0.0665580i	0.861982	−	0.506939i	$-0.169223\pi$
$181$	0.575468	+	0.895446i	0.0427742	+	0.0665580i	−0.819208	+	0.573497i	$0.805587\pi$
$182$		0			0
$183$	−13.0446	+	11.7331i	−0.964286	+	0.867338i
$184$		0			0
$185$		−	9.77594i		−	0.718741i
$186$		0			0
$187$	17.9784	−	11.5540i	1.31471	−	0.844914i
$188$		0			0
$189$	−12.1841	+	21.4966i	−0.886260	+	1.56365i
$190$		0			0
$191$	−8.72912	+	2.56310i	−0.631617	+	0.185459i	−0.581843	−	0.813301i	$-0.697668\pi$
$191$	−8.72912	+	2.56310i	−0.631617	+	0.185459i	−0.0497737	+	0.998761i	$0.515850\pi$
$192$		0			0
$193$	−2.13658	+	4.67845i	−0.153794	+	0.336762i	−0.970809	−	0.239855i	$-0.922900\pi$
$193$	−2.13658	+	4.67845i	−0.153794	+	0.336762i	0.817015	+	0.576617i	$0.195627\pi$
$194$		0			0
$195$	3.03783	−	24.3172i	0.217543	−	1.74139i
$196$		0			0
$197$	−6.71965	+	22.8850i	−0.478755	+	1.63049i	0.266589	+	0.963810i	$0.414103\pi$
$197$	−6.71965	+	22.8850i	−0.478755	+	1.63049i	−0.745344	+	0.666680i	$0.767715\pi$
$198$		0			0
$199$	−5.72633	+	8.91034i	−0.405929	+	0.631637i	−0.982686	−	0.185278i	$-0.940681\pi$
$199$	−5.72633	+	8.91034i	−0.405929	+	0.631637i	0.576758	+	0.816915i	$0.304318\pi$
$200$		0			0
$201$	−2.01378	−	3.00948i	−0.142041	−	0.212273i
$202$		0			0
$203$	−0.714673	−	4.97066i	−0.0501602	−	0.348872i
$204$		0			0
$205$	−0.813831	−	0.705189i	−0.0568404	−	0.0492525i
$206$		0			0
$207$	4.56630	+	13.6436i	0.317380	+	0.948299i
$208$		0			0
$209$	4.36560	+	3.78282i	0.301975	+	0.261663i
$210$		0			0
$211$	0.628734	+	4.37294i	0.0432838	+	0.301046i	0.999951	+	0.00986312i	$0.00313958\pi$
$211$	0.628734	+	4.37294i	0.0432838	+	0.301046i	−0.956668	+	0.291182i	$0.905951\pi$
$212$		0			0
$213$	16.0604	+	24.0013i	1.10044	+	1.64454i
$214$		0			0
$215$	5.44352	−	8.47029i	0.371245	−	0.577669i
$216$		0			0
$217$	3.21503	−	10.9494i	0.218251	−	0.743293i
$218$		0			0
$219$	−0.0176250	+	0.141085i	−0.00119098	+	0.00953361i
$220$		0			0
$221$	9.91532	−	21.7115i	0.666977	−	1.46048i
$222$		0			0
$223$	−12.5809	+	3.69408i	−0.842477	+	0.247374i	−0.674369	−	0.738395i	$-0.735584\pi$
$223$	−12.5809	+	3.69408i	−0.842477	+	0.247374i	−0.168109	+	0.985768i	$0.553766\pi$
$224$		0			0
$225$	−6.69916	+	2.23965i	−0.446611	+	0.149310i
$226$		0			0
$227$	−9.42482	+	6.05697i	−0.625548	+	0.402015i	−0.814659	−	0.579941i	$-0.803076\pi$
$227$	−9.42482	+	6.05697i	−0.625548	+	0.402015i	0.189111	+	0.981956i	$0.439439\pi$
$228$		0			0
$229$		−	15.5638i		−	1.02848i	−0.857645	−	0.514242i	$-0.828073\pi$
$229$		−	15.5638i		−	1.02848i	0.857645	−	0.514242i	$-0.171927\pi$
$230$		0			0
$231$	−28.6060	+	25.7300i	−1.88214	+	1.69291i
$232$		0			0
$233$	1.10918	+	1.72592i	0.0726651	+	0.113069i	0.875684	−	0.482884i	$-0.160411\pi$
$233$	1.10918	+	1.72592i	0.0726651	+	0.113069i	−0.803019	+	0.595953i	$0.796774\pi$
$234$		0			0
$235$	−7.30110	+	3.33430i	−0.476271	+	0.217506i
$236$		0			0
$237$	12.6754	−	20.5503i	0.823358	−	1.33489i
$238$		0			0
$239$	−4.96502	−	2.26745i	−0.321161	−	0.146669i	0.248310	−	0.968680i	$-0.420125\pi$
$239$	−4.96502	−	2.26745i	−0.321161	−	0.146669i	−0.569471	+	0.822011i	$0.692852\pi$
$240$		0			0
$241$	4.73039	−	4.09891i	0.304711	−	0.264034i	−0.489060	−	0.872250i	$-0.662660\pi$
$241$	4.73039	−	4.09891i	0.304711	−	0.264034i	0.793771	+	0.608216i	$0.208115\pi$
$242$		0			0
$243$	−3.63562	−	15.1586i	−0.233225	−	0.972423i
$244$		0			0
$245$	−35.6201	−	22.8917i	−2.27569	−	1.46249i
$246$		0			0
$247$	6.38592	+	0.918157i	0.406326	+	0.0584209i
$248$		0			0
$249$	−0.767611	+	0.919745i	−0.0486453	+	0.0582865i
$250$		0			0
$251$	18.5079	−	21.3593i	1.16821	−	1.34819i	0.242409	−	0.970174i	$-0.422062\pi$
$251$	18.5079	−	21.3593i	1.16821	−	1.34819i	0.925801	−	0.378012i	$-0.123392\pi$
$252$		0			0
$253$	0.00735549	+	22.4028i	0.000462436	+	1.40845i
$254$		0			0
$255$	−21.4857	+	0.397933i	−1.34549	+	0.0249195i
$256$		0			0
$257$	6.55820	−	0.942927i	0.409089	−	0.0588182i	0.0653016	−	0.997866i	$-0.479199\pi$
$257$	6.55820	−	0.942927i	0.409089	−	0.0588182i	0.343788	+	0.939047i	$0.388290\pi$
$258$		0			0
$259$	−2.43956	+	16.9675i	−0.151587	+	1.05431i
$260$		0			0
$261$	2.46947	+	1.98458i	0.152856	+	0.122842i
$262$		0			0
$263$	−6.02257	−	1.76839i	−0.371368	−	0.109043i	0.0907228	−	0.995876i	$-0.471082\pi$
$263$	−6.02257	−	1.76839i	−0.371368	−	0.109043i	−0.462090	+	0.886833i	$0.652900\pi$
$264$		0			0
$265$	−22.5600	−	26.0357i	−1.38585	−	1.59936i
$266$		0			0
$267$	−3.82089	+	1.19920i	−0.233835	+	0.0733901i
$268$		0			0
$269$	−0.773440	−	2.63409i	−0.0471575	−	0.160604i	0.932548	−	0.361046i	$-0.117580\pi$
$269$	−0.773440	−	2.63409i	−0.0471575	−	0.160604i	−0.979705	+	0.200442i	$0.935762\pi$
$270$		0			0
$271$	6.03397	+	13.2125i	0.366537	+	0.802605i	0.999594	+	0.0284992i	$0.00907280\pi$
$271$	6.03397	+	13.2125i	0.366537	+	0.802605i	−0.633056	+	0.774106i	$0.718200\pi$
$272$		0			0
$273$	−11.3409	+	41.4479i	−0.686381	+	2.50854i
$274$		0			0
$275$	−10.9988			−0.663252
$276$		0			0
$277$	−6.22116			−0.373793			−0.186897	−	0.982380i	$-0.559843\pi$
$277$	−6.22116			−0.373793			−0.186897	+	0.982380i	$0.559843\pi$
$278$		0			0
$279$	3.23113	+	6.43346i	0.193443	+	0.385161i
$280$		0			0
$281$	−8.52437	−	18.6658i	−0.508521	−	1.11351i	−0.973605	−	0.228239i	$-0.926703\pi$
$281$	−8.52437	−	18.6658i	−0.508521	−	1.11351i	0.465084	−	0.885267i	$-0.346024\pi$
$282$		0			0
$283$	−3.78212	−	12.8807i	−0.224824	−	0.765679i	−0.992219	−	0.124505i	$-0.960266\pi$
$283$	−3.78212	−	12.8807i	−0.224824	−	0.765679i	0.767395	−	0.641174i	$-0.221552\pi$
$284$		0			0
$285$	−1.73938	−	5.54199i	−0.103032	−	0.328279i
$286$		0			0
$287$	1.23654	+	1.42704i	0.0729906	+	0.0842357i
$288$		0			0
$289$	−3.77093	−	1.10724i	−0.221819	−	0.0651320i
$290$		0			0
$291$	−13.9240	+	2.26588i	−0.816238	+	0.132828i
$292$		0			0
$293$	−0.537117	+	3.73573i	−0.0313787	+	0.218244i	−0.999477	−	0.0323254i	$-0.989709\pi$
$293$	−0.537117	+	3.73573i	−0.0313787	+	0.218244i	0.968099	+	0.250569i	$0.0806178\pi$
$294$		0			0
$295$	−12.1971	+	1.75368i	−0.710144	+	0.102103i
$296$		0			0
$297$	2.11496	−	24.1805i	0.122723	−	1.40310i
$298$		0			0
$299$	13.5342	+	21.0445i	0.782704	+	1.21703i
$300$		0			0
$301$	−11.5617	+	13.3430i	−0.666407	+	0.769075i
$302$		0			0
$303$	−1.75655	−	1.46600i	−0.100911	−	0.0842193i
$304$		0			0
$305$	27.1912	+	3.90950i	1.55696	+	0.223858i
$306$		0			0
$307$	27.7828	+	17.8549i	1.58565	+	1.01904i	0.973613	+	0.228206i	$0.0732861\pi$
$307$	27.7828	+	17.8549i	1.58565	+	1.01904i	0.612037	+	0.790829i	$0.290350\pi$
$308$		0			0
$309$	−12.1842	+	5.83941i	−0.693137	+	0.332192i
$310$		0			0
$311$	−12.7794	+	11.0734i	−0.724655	+	0.627917i	−0.937021	−	0.349273i	$-0.886429\pi$
$311$	−12.7794	+	11.0734i	−0.724655	+	0.627917i	0.212366	+	0.977190i	$0.431883\pi$
$312$		0			0
$313$	−19.7375	−	9.01381i	−1.11563	−	0.509491i	−0.229677	−	0.973267i	$-0.573767\pi$
$313$	−19.7375	−	9.01381i	−1.11563	−	0.509491i	−0.885952	+	0.463776i	$0.846494\pi$
$314$		0			0
$315$	38.0644	−	6.92015i	2.14468	−	0.389906i
$316$		0			0
$317$	−5.86062	+	2.67646i	−0.329165	+	0.150325i	−0.573141	−	0.819456i	$-0.694275\pi$
$317$	−5.86062	+	2.67646i	−0.329165	+	0.150325i	0.243976	+	0.969781i	$0.421548\pi$
$318$		0			0
$319$	2.66701	+	4.14994i	0.149324	+	0.232352i
$320$		0			0
$321$	−9.57836	−	10.6490i	−0.534612	−	0.594369i
$322$		0			0
$323$		−	5.65736i		−	0.314784i
$324$		0			0
$325$	−10.3341	+	6.64131i	−0.573232	+	0.368394i
$326$		0			0
$327$	−7.78240	−	3.38136i	−0.430368	−	0.186990i
$328$		0			0
$329$	13.5042	−	3.96518i	0.744508	−	0.218607i
$330$		0			0
$331$	−7.61924	+	16.6838i	−0.418791	+	0.917025i	0.576223	+	0.817293i	$0.304526\pi$
$331$	−7.61924	+	16.6838i	−0.418791	+	0.917025i	−0.995014	+	0.0997325i	$0.968201\pi$
$332$		0			0
$333$	−6.17956	−	8.87490i	−0.338638	−	0.486342i
$334$		0			0
$335$	−1.59733	+	5.44000i	−0.0872713	+	0.297219i
$336$		0			0
$337$	10.3663	−	16.1303i	0.564688	−	0.878671i	−0.435076	−	0.900394i	$-0.643279\pi$
$337$	10.3663	−	16.1303i	0.564688	−	0.878671i	0.999764	+	0.0217223i	$0.00691495\pi$
$338$		0			0
$339$	−7.97759	+	5.33817i	−0.433283	+	0.289930i
$340$		0			0
$341$	1.59535	+	11.0959i	0.0863931	+	0.600877i
$342$		0			0
$343$	30.9543	+	26.8221i	1.67138	+	1.44825i
$344$		0			0
$345$	11.8197	−	19.1770i	0.636350	−	1.03246i
$346$		0			0
$347$	18.0456	+	15.6366i	0.968739	+	0.839417i	0.987050	−	0.160416i	$-0.0512834\pi$
$347$	18.0456	+	15.6366i	0.968739	+	0.839417i	−0.0183109	+	0.999832i	$0.505829\pi$
$348$		0			0
$349$	−2.31036	−	16.0689i	−0.123671	−	0.860150i	−0.953341	−	0.301896i	$-0.902380\pi$
$349$	−2.31036	−	16.0689i	−0.123671	−	0.860150i	0.829670	−	0.558254i	$-0.188529\pi$
$350$		0			0
$351$	−12.6136	−	23.9962i	−0.673263	−	1.28082i
$352$		0			0
$353$	1.75655	−	2.73324i	0.0934917	−	0.145476i	−0.791357	−	0.611354i	$-0.790625\pi$
$353$	1.75655	−	2.73324i	0.0934917	−	0.145476i	0.884849	+	0.465878i	$0.154262\pi$
$354$		0			0
$355$	12.7390	−	43.3852i	0.676118	−	2.30265i
$356$		0			0
$357$	37.3908	+	4.67104i	1.97893	+	0.247217i
$358$		0			0
$359$	6.45161	−	14.1271i	0.340503	−	0.745597i	−0.659478	−	0.751724i	$-0.729223\pi$
$359$	6.45161	−	14.1271i	0.340503	−	0.745597i	0.999981	+	0.00612628i	$0.00195007\pi$
$360$		0			0
$361$	−16.7631	+	4.92210i	−0.882270	+	0.259058i
$362$		0			0
$363$	7.46896	−	17.1902i	0.392019	−	0.902253i
$364$		0			0
$365$	0.187278	−	0.120356i	0.00980257	−	0.00629973i
$366$		0			0
$367$		−	17.8731i		−	0.932967i	−0.884530	−	0.466484i	$-0.845521\pi$
$367$		−	17.8731i		−	0.932967i	0.884530	−	0.466484i	$-0.154479\pi$
$368$		0			0
$369$	−1.18459	−	0.125754i	−0.0616670	−	0.00654647i
$370$		0			0
$371$	32.6590	+	50.8184i	1.69557	+	2.63836i
$372$		0			0
$373$	−8.68292	+	3.96536i	−0.449584	+	0.205318i	−0.627323	−	0.778759i	$-0.715849\pi$
$373$	−8.68292	+	3.96536i	−0.449584	+	0.205318i	0.177738	+	0.984078i	$0.443122\pi$
$374$		0			0
$375$	−10.5762	−	6.52340i	−0.546154	−	0.336867i
$376$		0			0
$377$	5.01165	+	2.28875i	0.258113	+	0.117876i
$378$		0			0
$379$	−17.1855	+	14.8913i	−0.882760	+	0.764916i	−0.972952	−	0.231009i	$-0.925797\pi$
$379$	−17.1855	+	14.8913i	−0.882760	+	0.764916i	0.0901920	+	0.995924i	$0.471252\pi$
$380$		0			0
$381$	8.87674	+	18.5218i	0.454769	+	0.948900i
$382$		0			0
$383$	−18.9736	−	12.1936i	−0.969507	−	0.623064i	−0.0428936	−	0.999080i	$-0.513658\pi$
$383$	−18.9736	−	12.1936i	−0.969507	−	0.623064i	−0.926613	+	0.376015i	$0.877294\pi$
$384$		0			0
$385$	59.6285	+	8.57328i	3.03895	+	0.436935i
$386$		0			0
$387$	−0.412435	−	11.1306i	−0.0209653	−	0.565798i
$388$		0			0
$389$	−8.16330	+	9.42095i	−0.413896	+	0.477661i	−0.923968	−	0.382471i	$-0.875073\pi$
$389$	−8.16330	+	9.42095i	−0.413896	+	0.477661i	0.510072	+	0.860132i	$0.329619\pi$
$390$		0			0
$391$	16.5769	−	14.3735i	0.838331	−	0.726900i
$392$		0			0
$393$	−0.0137155	−	0.740544i	−0.000691854	−	0.0373555i
$394$		0			0
$395$	−37.4199	+	5.38016i	−1.88280	+	0.270705i
$396$		0			0
$397$	4.42118	−	30.7500i	0.221893	−	1.54330i	−0.508976	−	0.860781i	$-0.669976\pi$
$397$	4.42118	−	30.7500i	0.221893	−	1.54330i	0.730869	−	0.682518i	$-0.239115\pi$
$398$		0			0
$399$	1.63594	+	10.0530i	0.0818995	+	0.503277i
$400$		0			0
$401$	31.3069	+	9.19252i	1.56339	+	0.459053i	0.945068	−	0.326873i	$-0.105995\pi$
$401$	31.3069	+	9.19252i	1.56339	+	0.459053i	0.618321	+	0.785926i	$0.287813\pi$
$402$		0			0
$403$	8.19889	+	9.46203i	0.408416	+	0.471337i
$404$		0			0
$405$	−14.5745	+	19.5781i	−0.724210	+	0.972845i
$406$		0			0
$407$	−4.74412	−	16.1570i	−0.235157	−	0.800873i
$408$		0			0
$409$	9.37333	+	20.5247i	0.463481	+	1.01488i	0.986680	+	0.162672i	$0.0520112\pi$
$409$	9.37333	+	20.5247i	0.463481	+	1.01488i	−0.523199	+	0.852211i	$0.675261\pi$
$410$		0			0
$411$	13.4190	+	3.67166i	0.661908	+	0.181110i
$412$		0			0
$413$	21.6074			1.06323
$414$		0			0
$415$	1.87572			0.0920752
$416$		0			0
$417$	−7.43509	−	2.03437i	−0.364098	−	0.0996236i
$418$		0			0
$419$	2.31233	+	5.06330i	0.112965	+	0.247358i	0.957667	−	0.287878i	$-0.0929498\pi$
$419$	2.31233	+	5.06330i	0.112965	+	0.247358i	−0.844702	+	0.535236i	$0.820222\pi$
$420$		0			0
$421$	8.00794	+	27.2725i	0.390283	+	1.32918i	0.887201	+	0.461384i	$0.152647\pi$
$421$	8.00794	+	27.2725i	0.390283	+	1.32918i	−0.496918	+	0.867798i	$0.665535\pi$
$422$		0			0
$423$	−4.52049	+	7.64216i	−0.219794	+	0.371574i
$424$		0			0
$425$	7.05409	+	8.14086i	0.342174	+	0.394889i
$426$		0			0
$427$	−46.2185	−	13.5710i	−2.23667	−	0.656746i
$428$		0			0
$429$	−6.78010	−	41.6641i	−0.327346	−	2.01156i
$430$		0			0
$431$	2.95655	−	20.5633i	0.142412	−	0.990499i	−0.785809	−	0.618470i	$-0.787753\pi$
$431$	2.95655	−	20.5633i	0.142412	−	0.990499i	0.928221	−	0.372029i	$-0.121338\pi$
$432$		0			0
$433$	−2.12330	+	0.305284i	−0.102039	+	0.0146710i	−0.193145	−	0.981170i	$-0.561869\pi$
$433$	−2.12330	+	0.305284i	−0.102039	+	0.0146710i	0.0911061	+	0.995841i	$0.470960\pi$
$434$		0			0
$435$	−0.0918545	−	4.95953i	−0.00440409	−	0.237791i
$436$		0			0
$437$	4.99011	+	3.20464i	0.238710	+	0.153299i
$438$		0			0
$439$	22.6384	−	26.1260i	1.08047	−	1.24693i	0.113093	−	0.993584i	$-0.463924\pi$
$439$	22.6384	−	26.1260i	1.08047	−	1.24693i	0.967376	−	0.253344i	$-0.0815304\pi$
$440$		0			0
$441$	−46.8074	+	1.73442i	−2.22892	+	0.0825912i
$442$		0			0
$443$	2.55339	+	0.367122i	0.121315	+	0.0174425i	0.202705	−	0.979240i	$-0.435027\pi$
$443$	2.55339	+	0.367122i	0.121315	+	0.0174425i	−0.0813897	+	0.996682i	$0.525936\pi$
$444$		0			0
$445$	5.27485	+	3.38994i	0.250052	+	0.160699i
$446$		0			0
$447$	13.3221	+	27.7973i	0.630115	+	1.31477i
$448$		0			0
$449$	0.532986	−	0.461835i	0.0251532	−	0.0217953i	−0.642193	−	0.766543i	$-0.721975\pi$
$449$	0.532986	−	0.461835i	0.0251532	−	0.0217953i	0.667347	+	0.744747i	$0.267430\pi$
$450$		0			0
$451$	−1.68726	−	0.770547i	−0.0794501	−	0.0362836i
$452$		0			0
$453$	17.4726	+	10.7771i	0.820934	+	0.506351i
$454$		0			0
$455$	61.2016	−	27.9498i	2.86918	−	1.31031i
$456$		0			0
$457$	−15.8700	−	24.6942i	−0.742367	−	1.15514i	−0.982835	−	0.184488i	$-0.940937\pi$
$457$	−15.8700	−	24.6942i	−0.742367	−	1.15514i	0.240468	−	0.970657i	$-0.422699\pi$
$458$		0			0
$459$	−19.2539	+	13.9428i	−0.898694	+	0.650794i
$460$		0			0
$461$			28.3275i			1.31934i	0.751555	+	0.659671i	$0.229304\pi$
$461$			28.3275i			1.31934i	−0.751555	+	0.659671i	$0.770696\pi$
$462$		0			0
$463$	−31.4195	+	20.1921i	−1.46019	+	0.938407i	−0.461505	+	0.887138i	$0.652690\pi$
$463$	−31.4195	+	20.1921i	−1.46019	+	0.938407i	−0.998685	+	0.0512694i	$0.983673\pi$
$464$		0			0
$465$	4.49194	−	10.3384i	0.208309	−	0.479434i
$466$		0			0
$467$	35.2298	−	10.3444i	1.63024	−	0.478682i	0.666497	−	0.745508i	$-0.267793\pi$
$467$	35.2298	−	10.3444i	1.63024	−	0.478682i	0.963745	+	0.266826i	$0.0859748\pi$
$468$		0			0
$469$	4.12992	−	9.04327i	0.190702	−	0.417579i
$470$		0			0
$471$	30.9675	+	3.86861i	1.42691	+	0.178256i
$472$		0			0
$473$	4.88617	−	16.6408i	0.224667	−	0.765144i
$474$		0			0
$475$	−1.57414	+	2.44941i	−0.0722265	+	0.112387i
$476$		0			0
$477$	−36.9384	−	9.37535i	−1.69129	−	0.429268i
$478$		0			0
$479$	−2.09689	−	14.5842i	−0.0958092	−	0.666367i	−0.979964	−	0.199174i	$-0.936174\pi$
$479$	−2.09689	−	14.5842i	−0.0958092	−	0.666367i	0.884155	−	0.467194i	$-0.154735\pi$
$480$		0			0
$481$	−14.2134	−	12.3160i	−0.648074	−	0.561559i
$482$		0			0
$483$	−25.3003	+	30.3349i	−1.15120	+	1.38028i
$484$		0			0
$485$	16.6930	+	14.4645i	0.757989	+	0.656801i
$486$		0			0
$487$	−2.93543	−	20.4164i	−0.133017	−	0.925155i	−0.941591	−	0.336760i	$-0.890669\pi$
$487$	−2.93543	−	20.4164i	−0.133017	−	0.925155i	0.808573	−	0.588395i	$-0.200240\pi$
$488$		0			0
$489$	−17.5106	+	11.7172i	−0.791858	+	0.529869i
$490$		0			0
$491$	6.13364	−	9.54413i	0.276807	−	0.430720i	−0.674817	−	0.737985i	$-0.735777\pi$
$491$	6.13364	−	9.54413i	0.276807	−	0.430720i	0.951624	+	0.307265i	$0.0994137\pi$
$492$		0			0
$493$	1.36113	−	4.63558i	0.0613022	−	0.208776i
$494$		0			0
$495$	−31.1888	+	21.7167i	−1.40183	+	0.976092i
$496$		0			0
$497$	−32.9370	+	72.1220i	−1.47743	+	3.23512i
$498$		0			0
$499$	11.9530	−	3.50971i	0.535089	−	0.157116i	−0.00301403	−	0.999995i	$-0.500959\pi$
$499$	11.9530	−	3.50971i	0.535089	−	0.157116i	0.538103	+	0.842879i	$0.319141\pi$
$500$		0			0
$501$	−3.71298	−	1.61325i	−0.165884	−	0.0720746i
$502$		0			0
$503$	1.36699	−	0.878509i	0.0609509	−	0.0391708i	−0.509811	−	0.860287i	$-0.670284\pi$
$503$	1.36699	−	0.878509i	0.0609509	−	0.0391708i	0.570761	+	0.821116i	$0.306648\pi$
$504$		0			0
$505$			3.58227i			0.159409i
$506$		0			0
$507$	−16.4702	−	18.3112i	−0.731468	−	0.813229i
$508$		0			0
$509$	−3.66091	−	5.69649i	−0.162267	−	0.252493i	0.750593	−	0.660765i	$-0.229768\pi$
$509$	−3.66091	−	5.69649i	−0.162267	−	0.252493i	−0.912860	+	0.408272i	$0.866132\pi$
$510$		0			0
$511$	−0.355081	+	0.162160i	−0.0157079	+	0.00717355i
$512$		0			0
$513$	−5.08226	−	3.93170i	−0.224387	−	0.173589i
$514$		0			0
$515$	19.2433	+	8.78811i	0.847960	+	0.387250i
$516$		0			0
$517$	−10.4487	+	9.05383i	−0.459532	+	0.398187i
$518$		0			0
$519$	26.8007	−	12.8445i	1.17642	−	0.563811i
$520$		0			0
$521$	−11.3165	−	7.27265i	−0.495783	−	0.318621i	0.268744	−	0.963212i	$-0.413391\pi$
$521$	−11.3165	−	7.27265i	−0.495783	−	0.318621i	−0.764528	+	0.644591i	$0.777028\pi$
$522$		0			0
$523$	−5.01050	−	0.720401i	−0.219094	−	0.0315009i	0.0318937	−	0.999491i	$-0.489846\pi$
$523$	−5.01050	−	0.720401i	−0.219094	−	0.0315009i	−0.250987	+	0.967990i	$0.580755\pi$
$524$		0			0
$525$	−14.8890	−	12.4262i	−0.649809	−	0.542324i
$526$		0			0
$527$	7.18956	−	8.29720i	0.313182	−	0.361432i
$528$		0			0
$529$	3.28819	+	22.7637i	0.142965	+	0.989728i
$530$		0			0
$531$	−9.96440	+	9.30209i	−0.432418	+	0.403676i
$532$		0			0
$533$	−2.05057	+	0.294827i	−0.0888200	+	0.0127704i
$534$		0			0
$535$	−3.19153	+	22.1976i	−0.137982	+	0.959685i
$536$		0			0
$537$	34.8649	−	5.67365i	1.50453	−	0.244836i
$538$		0			0
$539$	−69.9795	−	20.5478i	−3.01423	−	0.885058i
$540$		0			0
$541$	26.4588	+	30.5351i	1.13755	+	1.31281i	0.943333	+	0.331847i	$0.107672\pi$
$541$	26.4588	+	30.5351i	1.13755	+	1.31281i	0.194219	+	0.980958i	$0.437783\pi$
$542$		0			0
$543$	−0.552077	−	1.75903i	−0.0236919	−	0.0754870i
$544$		0			0
$545$	3.74299	+	12.7474i	0.160332	+	0.546041i
$546$		0			0
$547$	5.49347	+	12.0290i	0.234884	+	0.514324i	0.989966	−	0.141307i	$-0.0451303\pi$
$547$	5.49347	+	12.0290i	0.234884	+	0.514324i	−0.755082	+	0.655630i	$0.772403\pi$
$548$		0			0
$549$	27.1563	−	13.6389i	1.15900	−	0.582095i
$550$		0			0
$551$	1.30588			0.0556325
$552$		0			0
$553$	66.2900			2.81894
$554$		0			0
$555$	−4.46875	+	16.3321i	−0.189688	+	0.693258i
$556$		0			0
$557$	−14.9460	−	32.7272i	−0.633282	−	1.38669i	−0.905453	−	0.424446i	$-0.860469\pi$
$557$	−14.9460	−	32.7272i	−0.633282	−	1.38669i	0.272171	−	0.962249i	$-0.412258\pi$
$558$		0			0
$559$	−5.45719	−	18.5855i	−0.230815	−	0.786082i
$560$		0			0
$561$	−35.3170	+	11.0844i	−1.49109	+	0.467983i
$562$		0			0
$563$	−27.8803	−	32.1756i	−1.17502	−	1.35604i	−0.921344	−	0.388749i	$-0.872907\pi$
$563$	−27.8803	−	32.1756i	−1.17502	−	1.35604i	−0.253672	−	0.967290i	$-0.581638\pi$
$564$		0			0
$565$	14.4204	+	4.23422i	0.606672	+	0.178135i
$566$		0			0
$567$	30.1817	−	30.3436i	1.26751	−	1.27431i
$568$		0			0
$569$	0.911663	−	6.34075i	0.0382189	−	0.265818i	−0.961748	−	0.273935i	$-0.911675\pi$
$569$	0.911663	−	6.34075i	0.0382189	−	0.265818i	0.999967	+	0.00811690i	$0.00258372\pi$
$570$		0			0
$571$	20.9737	−	3.01556i	0.877721	−	0.126197i	0.311299	−	0.950312i	$-0.399236\pi$
$571$	20.9737	−	3.01556i	0.877721	−	0.126197i	0.566423	+	0.824115i	$0.308327\pi$
$572$		0			0
$573$	15.7549	−	0.291793i	0.658169	−	0.0121898i
$574$		0			0
$575$	−11.1765	+	1.61069i	−0.466093	+	0.0671703i
$576$		0			0
$577$	14.3018	−	16.5052i	0.595394	−	0.687121i	−0.375448	−	0.926844i	$-0.622511\pi$
$577$	14.3018	−	16.5052i	0.595394	−	0.687121i	0.970841	+	0.239723i	$0.0770565\pi$
$578$		0			0
$579$	5.70805	−	6.83935i	0.237219	−	0.284234i
$580$		0			0
$581$	−3.25557	−	0.468080i	−0.135064	−	0.0194192i
$582$		0			0
$583$	−49.9204	−	32.0819i	−2.06749	−	1.32870i
$584$		0			0
$585$	−16.1910	+	39.2368i	−0.669414	+	1.62224i
$586$		0			0
$587$	7.68594	−	6.65991i	0.317233	−	0.274884i	−0.481659	−	0.876359i	$-0.659966\pi$
$587$	7.68594	−	6.65991i	0.317233	−	0.274884i	0.798892	+	0.601475i	$0.205420\pi$
$588$		0			0
$589$	2.69936	+	1.23276i	0.111225	+	0.0507949i
$590$		0			0
$591$	21.6873	−	35.1610i	0.892095	−	1.44633i
$592$		0			0
$593$	9.16582	−	4.18589i	0.376395	−	0.171894i	−0.218229	−	0.975898i	$-0.570028\pi$
$593$	9.16582	−	4.18589i	0.376395	−	0.171894i	0.594624	+	0.804004i	$0.297301\pi$
$594$		0			0
$595$	−31.8972	−	49.6331i	−1.30766	−	2.03476i
$596$		0			0
$597$	13.6397	−	12.2684i	0.558236	−	0.502111i
$598$		0			0
$599$			35.8720i			1.46569i	0.680395	+	0.732845i	$0.261808\pi$
$599$			35.8720i			1.46569i	−0.680395	+	0.732845i	$0.738192\pi$
$600$		0			0
$601$	−23.9026	+	15.3613i	−0.975007	+	0.626599i	−0.928112	−	0.372301i	$-0.878569\pi$
$601$	−23.9026	+	15.3613i	−0.975007	+	0.626599i	−0.0468950	+	0.998900i	$0.514933\pi$
$602$		0			0
$603$	1.98863	+	5.94830i	0.0809831	+	0.242234i
$604$		0			0
$605$	−28.1573	+	8.26774i	−1.14476	+	0.336131i
$606$		0			0
$607$	−9.38766	+	20.5561i	−0.381034	+	0.834347i	0.617813	+	0.786325i	$0.288019\pi$
$607$	−9.38766	+	20.5561i	−0.381034	+	0.834347i	−0.998846	+	0.0480218i	$0.984708\pi$
$608$		0			0
$609$	−1.07821	+	8.63088i	−0.0436913	+	0.349741i
$610$		0			0
$611$	−4.35031	+	14.8158i	−0.175995	+	0.599384i
$612$		0			0
$613$	−11.2256	+	17.4674i	−0.453399	+	0.705503i	−0.990423	−	0.138064i	$-0.955912\pi$
$613$	−11.2256	+	17.4674i	−0.453399	+	0.705503i	0.537024	+	0.843567i	$0.319548\pi$
$614$		0			0
$615$	1.03727	+	1.55013i	0.0418266	+	0.0625074i
$616$		0			0
$617$	3.66574	+	25.4958i	0.147577	+	1.02642i	0.920170	+	0.391519i	$0.128050\pi$
$617$	3.66574	+	25.4958i	0.147577	+	1.02642i	−0.772593	+	0.634902i	$0.781041\pi$
$618$		0			0
$619$	1.80663	+	1.56545i	0.0726144	+	0.0629208i	0.690412	−	0.723417i	$-0.257429\pi$
$619$	1.80663	+	1.56545i	0.0726144	+	0.0629208i	−0.617797	+	0.786337i	$0.711975\pi$
$620$		0			0
$621$	−1.39191	−	24.8810i	−0.0558553	−	0.998439i
$622$		0			0
$623$	−8.30929	−	7.20004i	−0.332905	−	0.288464i
$624$		0			0
$625$	4.44433	+	30.9110i	0.177773	+	1.23644i
$626$		0			0
$627$	−5.56417	−	8.31533i	−0.222212	−	0.332082i
$628$		0			0
$629$	−8.91611	+	13.8737i	−0.355508	+	0.553182i
$630$		0			0
$631$	−0.359574	+	1.22460i	−0.0143144	+	0.0487504i	−0.966341	−	0.257266i	$-0.917178\pi$
$631$	−0.359574	+	1.22460i	−0.0143144	+	0.0487504i	0.952026	+	0.306017i	$0.0989964\pi$
$632$		0			0
$633$	0.948557	−	7.59302i	0.0377017	−	0.301795i
$634$		0			0
$635$	13.3592	−	29.2525i	0.530143	−	1.16085i
$636$		0			0
$637$	−78.1576	+	22.9491i	−3.09672	+	0.909278i
$638$		0			0
$639$	−15.8597	−	47.4390i	−0.627401	−	1.87666i
$640$		0			0
$641$	12.6348	−	8.11992i	0.499046	−	0.320718i	−0.266788	−	0.963755i	$-0.585962\pi$
$641$	12.6348	−	8.11992i	0.499046	−	0.320718i	0.765835	+	0.643038i	$0.222326\pi$
$642$		0			0
$643$			25.7378i			1.01500i	0.861652	+	0.507500i	$0.169430\pi$
$643$			25.7378i			1.01500i	−0.861652	+	0.507500i	$0.830570\pi$
$644$		0			0
$645$	−12.9661	+	11.6625i	−0.510539	+	0.459210i
$646$		0			0
$647$	−13.9530	−	21.7112i	−0.548548	−	0.853557i	0.450687	−	0.892682i	$-0.351179\pi$
$647$	−13.9530	−	21.7112i	−0.548548	−	0.853557i	−0.999234	+	0.0391254i	$0.987543\pi$
$648$		0			0
$649$	−19.3075	+	8.81746i	−0.757887	+	0.346115i
$650$		0			0
$651$	−10.3763	+	16.8229i	−0.406680	+	0.659340i
$652$		0			0
$653$	−24.1284	−	11.0191i	−0.944218	−	0.431210i	−0.117026	−	0.993129i	$-0.537336\pi$
$653$	−24.1284	−	11.0191i	−0.944218	−	0.431210i	−0.827192	+	0.561919i	$0.810063\pi$
$654$		0			0
$655$	−0.876436	+	0.759436i	−0.0342452	+	0.0296736i
$656$		0			0
$657$	0.0939372	−	0.227645i	0.00366484	−	0.00888128i
$658$		0			0
$659$	21.1998	+	13.6243i	0.825826	+	0.530726i	0.883949	−	0.467583i	$-0.154875\pi$
$659$	21.1998	+	13.6243i	0.825826	+	0.530726i	−0.0581227	+	0.998309i	$0.518511\pi$
$660$		0			0
$661$	28.2714	+	4.06481i	1.09963	+	0.158103i	0.668155	−	0.744022i	$-0.267084\pi$
$661$	28.2714	+	4.06481i	1.09963	+	0.158103i	0.431475	+	0.902125i	$0.357993\pi$
$662$		0			0
$663$	−26.4897	+	31.7397i	−1.02877	+	1.23267i
$664$		0			0
$665$	10.4432	−	12.0521i	0.404972	−	0.467362i
$666$		0			0
$667$	3.31783	+	3.82644i	0.128467	+	0.148160i
$668$		0			0
$669$	22.7067	−	0.420547i	0.877894	−	0.0162593i
$670$		0			0
$671$	46.8370	−	6.73414i	1.80812	−	0.259969i
$672$		0			0
$673$	−6.11713	+	42.5456i	−0.235798	+	1.64001i	0.436481	+	0.899714i	$0.356225\pi$
$673$	−6.11713	+	42.5456i	−0.235798	+	1.64001i	−0.672279	+	0.740298i	$0.734684\pi$
$674$		0			0
$675$	12.2157	−	0.679354i	0.470182	−	0.0261484i
$676$		0			0
$677$	−13.7037	−	4.02376i	−0.526675	−	0.154646i	0.00757663	−	0.999971i	$-0.497588\pi$
$677$	−13.7037	−	4.02376i	−0.526675	−	0.154646i	−0.534251	+	0.845326i	$0.679406\pi$
$678$		0			0
$679$	−25.3634	−	29.2709i	−0.973358	−	1.12332i
$680$		0			0
$681$	18.5142	−	5.81077i	0.709468	−	0.222669i
$682$		0			0
$683$	−7.00603	−	23.8603i	−0.268078	−	0.912990i	−0.977982	−	0.208691i	$-0.933080\pi$
$683$	−7.00603	−	23.8603i	−0.268078	−	0.912990i	0.709903	−	0.704299i	$-0.248739\pi$
$684$		0			0
$685$	−9.04889	−	19.8143i	−0.345740	−	0.757066i
$686$		0			0
$687$	−7.11448	+	26.0015i	−0.271434	+	0.992020i
$688$		0			0
$689$	−66.2753			−2.52489
$690$		0			0
$691$	4.16231			0.158342			0.0791709	−	0.996861i	$-0.474773\pi$
$691$	4.16231			0.158342			0.0791709	+	0.996861i	$0.474773\pi$
$692$		0			0
$693$	59.5519	−	29.9092i	2.26219	−	1.13616i
$694$		0			0
$695$	5.01375	+	10.9786i	0.190182	+	0.416441i
$696$		0			0
$697$	0.511801	+	1.74304i	0.0193859	+	0.0660222i
$698$		0			0
$699$	−1.06410	−	3.39043i	−0.0402480	−	0.128238i
$700$		0			0
$701$	10.5425	+	12.1667i	0.398186	+	0.459532i	0.919069	−	0.394097i	$-0.128943\pi$
$701$	10.5425	+	12.1667i	0.398186	+	0.459532i	−0.520883	+	0.853628i	$0.674397\pi$
$702$		0			0
$703$	−4.27711	−	1.25587i	−0.161314	−	0.0473661i
$704$		0			0
$705$	13.7217	−	2.23296i	0.516789	−	0.0840983i
$706$		0			0
$707$	0.893947	−	6.21754i	0.0336203	−	0.233835i
$708$		0			0
$709$	28.3070	−	4.06993i	1.06309	−	0.152849i	0.411492	−	0.911413i	$-0.365008\pi$
$709$	28.3070	−	4.06993i	1.06309	−	0.152849i	0.651599	+	0.758564i	$0.274099\pi$
$710$		0			0
$711$	−30.5700	+	28.5381i	−1.14647	+	1.07026i
$712$		0			0
$713$	3.24604	+	11.0416i	0.121565	+	0.413511i
$714$		0			0
$715$	−43.2817	+	49.9497i	−1.61864	+	1.86801i
$716$		0			0
$717$	7.25828	+	6.05769i	0.271066	+	0.226229i
$718$		0			0
$719$	3.25173	+	0.467528i	0.121269	+	0.0174358i	0.202682	−	0.979245i	$-0.435034\pi$
$719$	3.25173	+	0.467528i	0.121269	+	0.0174358i	−0.0814131	+	0.996680i	$0.525943\pi$
$720$		0			0
$721$	−31.2064	−	20.0551i	−1.16219	−	0.746891i
$722$		0			0
$723$	−9.77647	+	4.68546i	−0.363591	+	0.174254i
$724$		0			0
$725$	−1.87915	+	1.62829i	−0.0697898	+	0.0604732i
$726$		0			0
$727$	48.0118	+	21.9263i	1.78066	+	0.813200i	0.975454	+	0.220204i	$0.0706722\pi$
$727$	48.0118	+	21.9263i	1.78066	+	0.813200i	0.805205	+	0.592996i	$0.202055\pi$
$728$		0			0
$729$	−0.855420	+	26.9864i	−0.0316822	+	0.999498i
$730$		0			0
$731$	−15.4506	+	7.05605i	−0.571461	+	0.260977i
$732$		0			0
$733$	−4.93677	−	7.68176i	−0.182344	−	0.283732i	0.738033	−	0.674764i	$-0.235755\pi$
$733$	−4.93677	−	7.68176i	−0.182344	−	0.283732i	−0.920377	+	0.391032i	$0.872118\pi$
$734$		0			0
$735$	49.0443	+	54.5263i	1.80903	+	2.01123i
$736$		0			0
$737$			9.76602i			0.359736i
$738$		0			0
$739$	16.8509	−	10.8294i	0.619872	−	0.398368i	−0.192675	−	0.981263i	$-0.561716\pi$
$739$	16.8509	−	10.8294i	0.619872	−	0.398368i	0.812548	+	0.582895i	$0.198080\pi$
$740$		0			0
$741$	−10.2489	−	4.45303i	−0.376502	−	0.163586i
$742$		0			0
$743$	−4.72466	+	1.38728i	−0.173331	+	0.0508945i	−0.367246	−	0.930124i	$-0.619699\pi$
$743$	−4.72466	+	1.38728i	−0.173331	+	0.0508945i	0.193916	+	0.981018i	$0.437881\pi$
$744$		0			0
$745$	20.0493	−	43.9019i	0.734551	−	1.60844i
$746$		0			0
$747$	1.70283	−	1.18568i	0.0623034	−	0.0433817i
$748$		0			0
$749$	11.0787	−	37.7306i	0.404807	−	1.37865i
$750$		0			0
$751$	−1.42127	+	2.21153i	−0.0518627	+	0.0807000i	−0.866217	−	0.499669i	$-0.833455\pi$
$751$	−1.42127	+	2.21153i	−0.0518627	+	0.0807000i	0.814354	+	0.580369i	$0.197091\pi$
$752$		0			0
$753$	−40.6838	+	27.2234i	−1.48260	+	0.992077i
$754$		0			0
$755$	−4.57440	−	31.8156i	−0.166479	−	1.15789i
$756$		0			0
$757$	31.0404	+	26.8966i	1.12818	+	0.977574i	0.999900	−	0.0141634i	$-0.00450849\pi$
$757$	31.0404	+	26.8966i	1.12818	+	0.977574i	0.128281	+	0.991738i	$0.459054\pi$
$758$		0			0
$759$	10.2284	−	37.4304i	0.371268	−	1.35864i
$760$		0			0
$761$	−8.57382	−	7.42926i	−0.310801	−	0.269310i	0.485467	−	0.874255i	$-0.338650\pi$
$761$	−8.57382	−	7.42926i	−0.310801	−	0.269310i	−0.796267	+	0.604945i	$0.793195\pi$
$762$		0			0
$763$	−3.31539	−	23.0590i	−0.120025	−	0.834793i
$764$		0			0
$765$	36.0768	+	9.15669i	1.30436	+	0.331061i
$766$		0			0
$767$	−12.8165	+	19.9429i	−0.462778	+	0.720097i
$768$		0			0
$769$	7.92568	−	26.9924i	0.285807	−	0.973370i	−0.683997	−	0.729485i	$-0.739760\pi$
$769$	7.92568	−	26.9924i	0.285807	−	0.973370i	0.969804	−	0.243885i	$-0.0784220\pi$
$770$		0			0
$771$	−11.3874	−	1.42257i	−0.410108	−	0.0512327i
$772$		0			0
$773$	−13.5172	+	29.5986i	−0.486182	+	1.06459i	0.494536	+	0.869157i	$0.335338\pi$
$773$	−13.5172	+	29.5986i	−0.486182	+	1.06459i	−0.980717	+	0.195432i	$0.937389\pi$
$774$		0			0
$775$	−5.42145	+	1.59188i	−0.194744	+	0.0571821i
$776$		0			0
$777$	11.8318	−	27.2315i	0.424462	−	0.976923i
$778$		0			0
$779$	−0.413079	+	0.265470i	−0.0148001	+	0.00951145i
$780$		0			0
$781$		−	77.8861i		−	2.78698i
$782$		0			0
$783$	−3.21841	−	4.44436i	−0.115016	−	0.158828i
$784$		0			0
$785$	−26.4177	−	41.1067i	−0.942887	−	1.46716i
$786$		0			0
$787$	45.8209	−	20.9257i	1.63334	−	0.745921i	0.633722	−	0.773561i	$-0.281526\pi$
$787$	45.8209	−	20.9257i	1.63334	−	0.745921i	0.999618	+	0.0276398i	$0.00879915\pi$
$788$		0			0
$789$	9.25320	+	5.70736i	0.329423	+	0.203187i
$790$		0			0
$791$	−23.9721	−	10.9477i	−0.852348	−	0.389254i
$792$		0			0
$793$	39.9402	−	34.6084i	1.41832	−	1.22898i
$794$		0			0
$795$	25.7884	+	53.8089i	0.914620	+	1.90840i
$796$		0			0
$797$	8.91823	+	5.73140i	0.315900	+	0.203016i	0.688976	−	0.724784i	$-0.258061\pi$
$797$	8.91823	+	5.73140i	0.315900	+	0.203016i	−0.373076	+	0.927801i	$0.621697\pi$
$798$		0			0
$799$	13.4026	+	1.92700i	0.474148	+	0.0681723i
$800$		0			0
$801$	6.93152	−	0.256843i	0.244913	−	0.00907510i
$802$		0			0
$803$	0.251113	−	0.289800i	0.00886158	−	0.0102268i
$804$		0			0
$805$	61.8475	−	0.0203064i	2.17984	−	0.000715705i
$806$		0			0
$807$	0.0880513	+	4.75418i	0.00309955	+	0.167355i
$808$		0			0
$809$	41.8000	−	6.00993i	1.46961	−	0.211298i	0.639454	−	0.768830i	$-0.279161\pi$
$809$	41.8000	−	6.00993i	1.46961	−	0.211298i	0.830156	+	0.557532i	$0.188252\pi$
$810$		0			0
$811$	3.35992	−	23.3688i	0.117983	−	0.820589i	−0.841789	−	0.539807i	$-0.818497\pi$
$811$	3.35992	−	23.3688i	0.117983	−	0.820589i	0.959772	−	0.280782i	$-0.0905937\pi$
$812$		0			0
$813$	−4.04092	−	24.8317i	−0.141721	−	0.870884i
$814$		0			0
$815$	31.6525	+	9.29402i	1.10874	+	0.325555i
$816$		0			0
$817$	−3.00656	−	3.46976i	−0.105186	−	0.121392i
$818$		0			0
$819$	37.8931	−	64.0605i	1.32409	−	2.23846i
$820$		0			0
$821$	−4.88735	−	16.6448i	−0.170570	−	0.580907i	−0.999759	−	0.0219394i	$-0.993016\pi$
$821$	−4.88735	−	16.6448i	−0.170570	−	0.580907i	0.829190	−	0.558967i	$-0.188802\pi$
$822$		0			0
$823$	18.9472	+	41.4886i	0.660458	+	1.44620i	0.882095	+	0.471072i	$0.156133\pi$
$823$	18.9472	+	41.4886i	0.660458	+	1.44620i	−0.221637	+	0.975129i	$0.571140\pi$
$824$		0			0
$825$	18.3750	+	5.02773i	0.639736	+	0.175043i
$826$		0			0
$827$	10.2175			0.355298			0.177649	−	0.984094i	$-0.443151\pi$
$827$	10.2175			0.355298			0.177649	+	0.984094i	$0.443151\pi$
$828$		0			0
$829$	−25.0099			−0.868631			−0.434316	−	0.900761i	$-0.643010\pi$
$829$	−25.0099			−0.868631			−0.434316	+	0.900761i	$0.643010\pi$
$830$		0			0
$831$	10.3933	+	2.84380i	0.360541	+	0.0986503i
$832$		0			0
$833$	29.6728	+	64.9744i	1.02810	+	2.25123i
$834$		0			0
$835$	1.78578	+	6.08180i	0.0617994	+	0.210469i
$836$		0			0
$837$	−2.45721	−	12.2250i	−0.0849337	−	0.422558i
$838$		0			0
$839$	21.4861	+	24.7963i	0.741783	+	0.856063i	0.993745	−	0.111674i	$-0.0356213\pi$
$839$	21.4861	+	24.7963i	0.741783	+	0.856063i	−0.251962	+	0.967737i	$0.581076\pi$
$840$		0			0
$841$	−26.7553	−	7.85606i	−0.922595	−	0.270898i
$842$		0			0
$843$	5.70872	+	35.0804i	0.196619	+	1.20823i
$844$		0			0
$845$	−5.48791	+	38.1693i	−0.188790	+	1.31306i
$846$		0			0
$847$	50.9342	−	7.32323i	1.75012	−	0.251629i
$848$		0			0
$849$	0.430571	+	23.2479i	0.0147771	+	0.797867i
$850$		0			0
$851$	−7.18685	−	15.7233i	−0.246362	−	0.538989i
$852$		0			0
$853$	20.5813	−	23.7521i	0.704691	−	0.813257i	−0.284687	−	0.958621i	$-0.591890\pi$
$853$	20.5813	−	23.7521i	0.704691	−	0.813257i	0.989378	+	0.145363i	$0.0464351\pi$
$854$		0			0
$855$	0.372536	+	10.0538i	0.0127405	+	0.343832i
$856$		0			0
$857$	−43.3036	−	6.22611i	−1.47922	−	0.212680i	−0.645031	−	0.764157i	$-0.723155\pi$
$857$	−43.3036	−	6.22611i	−1.47922	−	0.212680i	−0.834190	+	0.551477i	$0.814065\pi$
$858$		0			0
$859$	16.2644	+	10.4525i	0.554934	+	0.356634i	0.787854	−	0.615862i	$-0.211192\pi$
$859$	16.2644	+	10.4525i	0.554934	+	0.356634i	−0.232921	+	0.972496i	$0.574828\pi$
$860$		0			0
$861$	−1.41349	−	2.94932i	−0.0481716	−	0.100513i
$862$		0			0
$863$	−37.6720	+	32.6429i	−1.28237	+	1.11118i	−0.294539	+	0.955639i	$0.595166\pi$
$863$	−37.6720	+	32.6429i	−1.28237	+	1.11118i	−0.987830	+	0.155539i	$0.950288\pi$
$864$		0			0
$865$	−42.3279	−	19.3305i	−1.43919	−	0.657258i
$866$		0			0
$867$	5.79373	+	3.57356i	0.196765	+	0.121365i
$868$		0			0
$869$	−59.2341	+	27.0513i	−2.00938	+	0.917652i
$870$		0			0
$871$	5.89694	+	9.17582i	0.199810	+	0.310911i
$872$		0			0
$873$	24.2977	+	2.57941i	0.822354	+	0.0872998i
$874$		0			0
$875$		−	34.1161i		−	1.15333i
$876$		0			0
$877$	−15.5378	+	9.98554i	−0.524675	+	0.337188i	−0.776019	−	0.630710i	$-0.782764\pi$
$877$	−15.5378	+	9.98554i	−0.524675	+	0.337188i	0.251344	+	0.967898i	$0.419127\pi$
$878$		0			0
$879$	2.60500	−	5.99555i	0.0878644	−	0.202225i
$880$		0			0
$881$	38.2887	−	11.2426i	1.28998	−	0.378772i	0.436408	−	0.899749i	$-0.356251\pi$
$881$	38.2887	−	11.2426i	1.28998	−	0.378772i	0.853571	+	0.520977i	$0.174432\pi$
$882$		0			0
$883$	−18.8173	+	41.2041i	−0.633252	+	1.38663i	0.272225	+	0.962234i	$0.412241\pi$
$883$	−18.8173	+	41.2041i	−0.633252	+	1.38663i	−0.905477	+	0.424395i	$0.860487\pi$
$884$		0			0
$885$	21.1787	+	2.64574i	0.711913	+	0.0889356i
$886$		0			0
$887$	−14.6758	+	49.9813i	−0.492766	+	1.67821i	0.218946	+	0.975737i	$0.429738\pi$
$887$	−14.6758	+	49.9813i	−0.492766	+	1.67821i	−0.711712	+	0.702471i	$0.752080\pi$
$888$		0			0
$889$	−30.4866	+	47.4381i	−1.02249	+	1.59102i
$890$		0			0
$891$	−14.5867	+	39.4302i	−0.488672	+	1.32096i
$892$		0			0
$893$	0.520863	+	3.62268i	0.0174300	+	0.121228i
$894$		0			0
$895$	−41.7983	−	36.2184i	−1.39716	−	1.21065i
$896$		0			0
$897$	−12.9910	−	41.3445i	−0.433759	−	1.38045i
$898$		0			0
$899$	1.91524	+	1.65956i	0.0638767	+	0.0553495i
$900$		0			0
$901$	8.27083	+	57.5249i	0.275541	+	1.91643i
$902$		0			0
$903$	25.4148	−	17.0062i	0.845752	−	0.565932i
$904$		0			0
$905$	−1.56063	+	2.42838i	−0.0518770	+	0.0807222i
$906$		0			0
$907$	−5.55986	+	18.9351i	−0.184612	+	0.628731i	0.814227	+	0.580547i	$0.197161\pi$
$907$	−5.55986	+	18.9351i	−0.184612	+	0.628731i	−0.998839	+	0.0481834i	$0.984657\pi$
$908$		0			0
$909$	2.26443	+	3.25210i	0.0751063	+	0.107865i
$910$		0			0
$911$	8.29088	−	18.1545i	0.274689	−	0.601485i	−0.721133	−	0.692796i	$-0.756379\pi$
$911$	8.29088	−	18.1545i	0.274689	−	0.601485i	0.995822	+	0.0913112i	$0.0291058\pi$
$912$		0			0
$913$	3.10005	−	0.910258i	0.102597	−	0.0301251i
$914$		0			0
$915$	−43.6397	−	18.9609i	−1.44268	−	0.626830i
$916$		0			0
$917$	1.71069	−	1.09940i	0.0564921	−	0.0363052i
$918$		0			0
$919$		−	30.4765i		−	1.00533i	−0.864482	−	0.502663i	$-0.832354\pi$
$919$		−	30.4765i		−	1.00533i	0.864482	−	0.502663i	$-0.167646\pi$
$920$		0			0
$921$	−38.2534	−	42.5292i	−1.26049	−	1.40139i
$922$		0			0
$923$	−47.0294	−	73.1791i	−1.54799	−	2.40872i
$924$		0			0
$925$	7.72063	−	3.52589i	0.253853	−	0.115931i
$926$		0			0
$927$	23.0248	−	4.18594i	0.756234	−	0.137484i
$928$		0			0
$929$	45.8296	+	20.9297i	1.50362	+	0.686680i	0.985663	−	0.168726i	$-0.0539653\pi$
$929$	45.8296	+	20.9297i	1.50362	+	0.686680i	0.517958	+	0.855406i	$0.326693\pi$
$930$		0			0
$931$	−14.5914	+	12.6435i	−0.478214	+	0.414374i
$932$		0			0
$933$	26.4117	−	12.6581i	0.864681	−	0.414406i
$934$		0			0
$935$	48.7561	+	31.3336i	1.59450	+	1.02472i
$936$		0			0
$937$	−25.9030	−	3.72429i	−0.846215	−	0.121667i	−0.294450	−	0.955667i	$-0.595136\pi$
$937$	−25.9030	−	3.72429i	−0.846215	−	0.121667i	−0.551765	+	0.834000i	$0.686045\pi$
$938$		0			0
$939$	28.8539	+	24.0812i	0.941612	+	0.785860i
$940$		0			0
$941$	−29.8715	+	34.4736i	−0.973784	+	1.12381i	0.0185012	+	0.999829i	$0.494111\pi$
$941$	−29.8715	+	34.4736i	−0.973784	+	1.12381i	−0.992285	+	0.123978i	$0.960435\pi$
$942$		0			0
$943$	−1.82737	−	0.535912i	−0.0595073	−	0.0174517i
$944$		0			0
$945$	−66.7552	−	5.83879i	−2.17155	−	0.189936i
$946$		0			0
$947$	−25.7521	+	3.70259i	−0.836831	+	0.120318i	−0.547390	−	0.836878i	$-0.684378\pi$
$947$	−25.7521	+	3.70259i	−0.836831	+	0.120318i	−0.289441	+	0.957196i	$0.593469\pi$
$948$		0			0
$949$	0.0609495	−	0.423913i	0.00197851	−	0.0137608i
$950$		0			0
$951$	11.0145	−	1.79241i	0.357168	−	0.0581228i
$952$		0			0
$953$	43.1696	+	12.6757i	1.39840	+	0.410607i	0.892134	−	0.451770i	$-0.149207\pi$
$953$	43.1696	+	12.6757i	1.39840	+	0.410607i	0.506266	+	0.862378i	$0.331025\pi$
$954$		0			0
$955$	−16.1568	−	18.6459i	−0.522822	−	0.603368i
$956$		0			0
$957$	−2.55860	−	8.15220i	−0.0827078	−	0.263523i
$958$		0			0
$959$	10.7610	+	36.6486i	0.347491	+	1.18345i
$960$		0			0
$961$	−10.4856	−	22.9602i	−0.338244	−	0.740650i
$962$		0			0
$963$	11.1342	+	22.1691i	0.358793	+	0.714389i
$964$		0			0
$965$	−13.9481			−0.449004
$966$		0			0
$967$	21.3455			0.686425			0.343212	−	0.939258i	$-0.388485\pi$
$967$	21.3455			0.686425			0.343212	+	0.939258i	$0.388485\pi$
$968$		0			0
$969$	−2.58608	+	9.45142i	−0.0830768	+	0.303623i
$970$		0			0
$971$	−11.0742	−	24.2490i	−0.355387	−	0.778188i	−0.999907	−	0.0136014i	$-0.995670\pi$
$971$	−11.0742	−	24.2490i	−0.355387	−	0.778188i	0.644521	−	0.764587i	$-0.277057\pi$
$972$		0			0
$973$	−5.96239	−	20.3060i	−0.191146	−	0.650982i
$974$		0			0
$975$	20.3004	−	6.37137i	0.650133	−	0.204047i
$976$		0			0
$977$	−29.1337	−	33.6221i	−0.932069	−	1.07567i	−0.996971	−	0.0777738i	$-0.975219\pi$
$977$	−29.1337	−	33.6221i	−0.932069	−	1.07567i	0.0649016	−	0.997892i	$-0.479327\pi$
$978$		0			0
$979$	10.3630	+	3.04285i	0.331203	+	0.0972500i
$980$		0			0
$981$	11.4559	+	9.20652i	0.365759	+	0.293941i
$982$		0			0
$983$	7.40483	−	51.5017i	0.236177	−	1.64265i	−0.434336	−	0.900751i	$-0.643017\pi$
$983$	7.40483	−	51.5017i	0.236177	−	1.64265i	0.670513	−	0.741898i	$-0.266074\pi$
$984$		0			0
$985$	−64.0242	+	9.20529i	−2.03998	+	0.293305i
$986$		0			0
$987$	−24.3732	+	0.451410i	−0.775806	+	0.0143686i
$988$		0			0
$989$	2.52822	−	17.6252i	0.0803927	−	0.560450i
$990$		0			0
$991$	20.2186	−	23.3335i	0.642265	−	0.741213i	−0.337509	−	0.941322i	$-0.609584\pi$
$991$	20.2186	−	23.3335i	0.642265	−	0.741213i	0.979774	+	0.200109i	$0.0641298\pi$
$992$		0			0
$993$	20.3555	−	24.3898i	0.645962	−	0.773986i
$994$		0			0
$995$	−28.4316	−	4.08785i	−0.901344	−	0.129594i
$996$		0			0
$997$	14.1810	+	9.11360i	0.449118	+	0.288631i	0.745583	−	0.666413i	$-0.232171\pi$
$997$	14.1810	+	9.11360i	0.449118	+	0.288631i	−0.296465	+	0.955044i	$0.595808\pi$
$998$		0			0
$999$	6.26697	+	17.6516i	0.198278	+	0.558471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.53.2	✓	80
3.2	odd	2	inner	276.2.k.a.53.5	yes	80
23.10	odd	22	inner	276.2.k.a.125.5	yes	80
69.56	even	22	inner	276.2.k.a.125.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.53.2	✓	80	1.1	even	1	trivial
276.2.k.a.53.5	yes	80	3.2	odd	2	inner
276.2.k.a.125.2	yes	80	69.56	even	22	inner
276.2.k.a.125.5	yes	80	23.10	odd	22	inner

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67064 - 0.457117i) q^{3} +(1.12657 + 2.46685i) q^{5} +(-1.33973 - 4.56271i) q^{7} +(2.58209 + 1.52736i) q^{9} +O(q^{10})\)	\(q+(-1.67064 - 0.457117i) q^{3} +(1.12657 + 2.46685i) q^{5} +(-1.33973 - 4.56271i) q^{7} +(2.58209 + 1.52736i) q^{9} +(3.05906 + 3.53034i) q^{11} +(5.00588 + 1.46986i) q^{13} +(-0.754461 - 4.63621i) q^{15} +(0.651083 - 4.52838i) q^{17} +(1.22401 - 0.175986i) q^{19} +(0.152520 + 8.23506i) q^{21} +(3.62548 + 3.13941i) q^{23} +(-1.54190 + 1.77944i) q^{25} +(-3.61556 - 3.73198i) q^{27} +(1.04528 + 0.150289i) q^{29} +(2.01881 + 1.29741i) q^{31} +(-3.49681 - 7.29628i) q^{33} +(9.74622 - 8.44515i) q^{35} +(-3.27904 - 1.49749i) q^{37} +(-7.69114 - 4.74388i) q^{39} +(-0.361197 + 0.164953i) q^{41} +(-2.00725 - 3.12335i) q^{43} +(-0.858855 + 8.09032i) q^{45} +2.95968i q^{47} +(-13.1346 + 8.44111i) q^{49} +(-3.15773 + 7.26768i) q^{51} +(-12.1886 + 3.57890i) q^{53} +(-5.26258 + 11.5234i) q^{55} +(-2.12533 - 0.265506i) q^{57} +(-1.28015 + 4.35978i) q^{59} +(5.47649 - 8.52159i) q^{61} +(3.50958 - 13.8276i) q^{63} +(2.01357 + 14.0047i) q^{65} +(1.58000 + 1.36908i) q^{67} +(-4.62180 - 6.90210i) q^{69} +(-12.6008 - 10.9187i) q^{71} +(-0.0116824 - 0.0812528i) q^{73} +(3.38937 - 2.26799i) q^{75} +(12.0096 - 18.6873i) q^{77} +(-3.92739 + 13.3755i) q^{79} +(4.33435 + 7.88755i) q^{81} +(0.287324 - 0.629151i) q^{83} +(11.9043 - 3.49543i) q^{85} +(-1.67759 - 0.728895i) q^{87} +(1.94506 - 1.25001i) q^{89} -24.8096i q^{91} +(-2.77963 - 3.09033i) q^{93} +(1.81307 + 2.82119i) q^{95} +(7.40873 - 3.38345i) q^{97} +(2.50666 + 13.7879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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