LMFDB - Embedded newform 504.2.q.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	504.121
Dual form			504.2.q.d.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65097 - 0.523731i) q^{3} +(-0.841578 - 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +(2.45141 + 1.72933i) q^{9} +O(q^{10})$	\(q+(-1.65097 - 0.523731i) q^{3} +(-0.841578 - 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +(2.45141 + 1.72933i) q^{9} +(-0.622490 + 1.07818i) q^{11} +(1.96039 - 3.39550i) q^{13} +(0.626001 + 2.84731i) q^{15} +(-1.62691 - 2.81788i) q^{17} +(2.36192 - 4.09097i) q^{19} +(-1.65131 - 4.27471i) q^{21} +(0.199068 + 0.344795i) q^{23} +(1.08349 - 1.87667i) q^{25} +(-3.14150 - 4.13895i) q^{27} +(-3.19896 - 5.54076i) q^{29} -0.578367 q^{31} +(1.59239 - 1.45403i) q^{33} +(1.61605 - 4.14963i) q^{35} +(2.72146 - 4.71371i) q^{37} +(-5.01488 + 4.57916i) q^{39} +(4.20216 - 7.27836i) q^{41} +(2.46299 + 4.26603i) q^{43} +(0.457714 - 5.02868i) q^{45} -0.425190 q^{47} +(-1.52179 + 6.83258i) q^{49} +(1.21016 + 5.50430i) q^{51} +(-0.466315 - 0.807681i) q^{53} +2.09550 q^{55} +(-6.04204 + 5.51707i) q^{57} +6.05054 q^{59} +10.2092 q^{61} +(0.487470 + 7.92227i) q^{63} -6.59930 q^{65} -9.41952 q^{67} +(-0.148075 - 0.673505i) q^{69} +8.46617 q^{71} +(6.82340 + 11.8185i) q^{73} +(-2.77168 + 2.53086i) q^{75} +(-3.25582 + 0.499480i) q^{77} -5.53340 q^{79} +(3.01883 + 8.47860i) q^{81} +(-8.03669 - 13.9199i) q^{83} +(-2.73833 + 4.74293i) q^{85} +(2.37952 + 10.8230i) q^{87} +(-6.03776 + 10.4577i) q^{89} +(10.2535 - 1.57300i) q^{91} +(0.954867 + 0.302909i) q^{93} -7.95097 q^{95} +(-5.86046 - 10.1506i) q^{97} +(-3.39052 + 1.56658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.65097	−	0.523731i	−0.953189	−	0.302376i
$3$	−1.65097	−	0.523731i	−0.953189	−	0.302376i
$4$		0			0
$5$	−0.841578	−	1.45766i	−0.376365	−	0.651883i	0.614165	−	0.789177i	$-0.289493\pi$
$5$	−0.841578	−	1.45766i	−0.376365	−	0.651883i	−0.990530	+	0.137294i	$0.956159\pi$
$6$		0			0
$7$	1.65502	+	2.06419i	0.625540	+	0.780192i
$7$	1.65502	+	2.06419i	0.625540	+	0.780192i
$8$		0			0
$9$	2.45141	+	1.72933i	0.817137	+	0.576443i
$10$		0			0
$11$	−0.622490	+	1.07818i	−0.187688	+	0.325085i	−0.944479	−	0.328572i	$-0.893433\pi$
$11$	−0.622490	+	1.07818i	−0.187688	+	0.325085i	0.756791	+	0.653657i	$0.226766\pi$
$12$		0			0
$13$	1.96039	−	3.39550i	0.543715	−	0.941743i	−0.454971	−	0.890506i	$-0.650350\pi$
$13$	1.96039	−	3.39550i	0.543715	−	0.941743i	0.998687	−	0.0512366i	$-0.0163162\pi$
$14$		0			0
$15$	0.626001	+	2.84731i	0.161633	+	0.735172i
$16$		0			0
$17$	−1.62691	−	2.81788i	−0.394582	−	0.683437i	0.598465	−	0.801149i	$-0.295777\pi$
$17$	−1.62691	−	2.81788i	−0.394582	−	0.683437i	−0.993048	+	0.117712i	$0.962444\pi$
$18$		0			0
$19$	2.36192	−	4.09097i	0.541863	−	0.938534i	−0.456935	−	0.889500i	$-0.651053\pi$
$19$	2.36192	−	4.09097i	0.541863	−	0.938534i	0.998797	−	0.0490333i	$-0.0156140\pi$
$20$		0			0
$21$	−1.65131	−	4.27471i	−0.360346	−	0.932819i
$22$		0			0
$23$	0.199068	+	0.344795i	0.0415085	+	0.0718948i	0.886033	−	0.463622i	$-0.153450\pi$
$23$	0.199068	+	0.344795i	0.0415085	+	0.0718948i	−0.844525	+	0.535516i	$0.820117\pi$
$24$		0			0
$25$	1.08349	−	1.87667i	0.216699	−	0.375333i
$26$		0			0
$27$	−3.14150	−	4.13895i	−0.604583	−	0.796542i
$28$		0			0
$29$	−3.19896	−	5.54076i	−0.594032	−	1.02889i	−0.993683	−	0.112226i	$-0.964202\pi$
$29$	−3.19896	−	5.54076i	−0.594032	−	1.02889i	0.399651	−	0.916667i	$-0.369131\pi$
$30$		0			0
$31$	−0.578367			−0.103878			−0.0519389	−	0.998650i	$-0.516540\pi$
$31$	−0.578367			−0.103878			−0.0519389	+	0.998650i	$0.516540\pi$
$32$		0			0
$33$	1.59239	−	1.45403i	0.277200	−	0.253115i
$34$		0			0
$35$	1.61605	−	4.14963i	0.273163	−	0.701416i
$36$		0			0
$37$	2.72146	−	4.71371i	0.447405	−	0.774928i	−0.550811	−	0.834630i	$-0.685682\pi$
$37$	2.72146	−	4.71371i	0.447405	−	0.774928i	0.998216	+	0.0597015i	$0.0190149\pi$
$38$		0			0
$39$	−5.01488	+	4.57916i	−0.803024	+	0.733252i
$40$		0			0
$41$	4.20216	−	7.27836i	0.656267	−	1.13669i	−0.325307	−	0.945608i	$-0.605468\pi$
$41$	4.20216	−	7.27836i	0.656267	−	1.13669i	0.981574	−	0.191080i	$-0.0611990\pi$
$42$		0			0
$43$	2.46299	+	4.26603i	0.375603	+	0.650563i	0.990417	−	0.138109i	$-0.0441024\pi$
$43$	2.46299	+	4.26603i	0.375603	+	0.650563i	−0.614814	+	0.788672i	$0.710769\pi$
$44$		0			0
$45$	0.457714	−	5.02868i	0.0682320	−	0.749631i
$46$		0			0
$47$	−0.425190			−0.0620203			−0.0310101	−	0.999519i	$-0.509872\pi$
$47$	−0.425190			−0.0620203			−0.0310101	+	0.999519i	$0.509872\pi$
$48$		0			0
$49$	−1.52179	+	6.83258i	−0.217399	+	0.976083i
$50$		0			0
$51$	1.21016	+	5.50430i	0.169456	+	0.770757i
$52$		0			0
$53$	−0.466315	−	0.807681i	−0.0640533	−	0.110944i	0.832220	−	0.554445i	$-0.187069\pi$
$53$	−0.466315	−	0.807681i	−0.0640533	−	0.110944i	−0.896274	+	0.443501i	$0.853736\pi$
$54$		0			0
$55$	2.09550			0.282557
$56$		0			0
$57$	−6.04204	+	5.51707i	−0.800288	+	0.730753i
$58$		0			0
$59$	6.05054			0.787713			0.393856	−	0.919172i	$-0.371141\pi$
$59$	6.05054			0.787713			0.393856	+	0.919172i	$0.371141\pi$
$60$		0			0
$61$	10.2092			1.30715			0.653575	−	0.756862i	$-0.273268\pi$
$61$	10.2092			1.30715			0.653575	+	0.756862i	$0.273268\pi$
$62$		0			0
$63$	0.487470	+	7.92227i	0.0614154	+	0.998112i
$64$		0			0
$65$	−6.59930			−0.818542
$66$		0			0
$67$	−9.41952			−1.15078			−0.575389	−	0.817880i	$-0.695149\pi$
$67$	−9.41952			−1.15078			−0.575389	+	0.817880i	$0.695149\pi$
$68$		0			0
$69$	−0.148075	−	0.673505i	−0.0178261	−	0.0810805i
$70$		0			0
$71$	8.46617			1.00475			0.502375	−	0.864650i	$-0.332460\pi$
$71$	8.46617			1.00475			0.502375	+	0.864650i	$0.332460\pi$
$72$		0			0
$73$	6.82340	+	11.8185i	0.798619	+	1.38325i	0.920516	+	0.390705i	$0.127769\pi$
$73$	6.82340	+	11.8185i	0.798619	+	1.38325i	−0.121897	+	0.992543i	$0.538898\pi$
$74$		0			0
$75$	−2.77168	+	2.53086i	−0.320047	+	0.292239i
$76$		0			0
$77$	−3.25582	+	0.499480i	−0.371035	+	0.0569211i
$78$		0			0
$79$	−5.53340			−0.622556			−0.311278	−	0.950319i	$-0.600757\pi$
$79$	−5.53340			−0.622556			−0.311278	+	0.950319i	$0.600757\pi$
$80$		0			0
$81$	3.01883	+	8.47860i	0.335426	+	0.942067i
$82$		0			0
$83$	−8.03669	−	13.9199i	−0.882141	−	1.52791i	−0.848956	−	0.528463i	$-0.822768\pi$
$83$	−8.03669	−	13.9199i	−0.882141	−	1.52791i	−0.0331848	−	0.999449i	$-0.510565\pi$
$84$		0			0
$85$	−2.73833	+	4.74293i	−0.297014	+	0.514444i
$86$		0			0
$87$	2.37952	+	10.8230i	0.255111	+	1.16035i
$88$		0			0
$89$	−6.03776	+	10.4577i	−0.640001	+	1.10851i	0.345431	+	0.938444i	$0.387733\pi$
$89$	−6.03776	+	10.4577i	−0.640001	+	1.10851i	−0.985432	+	0.170070i	$0.945601\pi$
$90$		0			0
$91$	10.2535	−	1.57300i	1.07486	−	0.164895i
$92$		0			0
$93$	0.954867	+	0.302909i	0.0990151	+	0.0314102i
$94$		0			0
$95$	−7.95097			−0.815753
$96$		0			0
$97$	−5.86046	−	10.1506i	−0.595040	−	1.03064i	−0.993541	−	0.113472i	$-0.963803\pi$
$97$	−5.86046	−	10.1506i	−0.595040	−	1.03064i	0.398501	−	0.917168i	$-0.369530\pi$
$98$		0			0
$99$	−3.39052	+	1.56658i	−0.340760	+	0.157447i
$100$		0			0
$101$	−2.70302	+	4.68177i	−0.268961	+	0.465854i	−0.968594	−	0.248649i	$-0.920014\pi$
$101$	−2.70302	+	4.68177i	−0.268961	+	0.465854i	0.699633	+	0.714502i	$0.253347\pi$
$102$		0			0
$103$	−7.31018	−	12.6616i	−0.720294	−	1.24759i	−0.960882	−	0.276958i	$-0.910674\pi$
$103$	−7.31018	−	12.6616i	−0.720294	−	1.24759i	0.240588	−	0.970627i	$-0.422660\pi$
$104$		0			0
$105$	−4.84135	+	6.00455i	−0.472467	+	0.585984i
$106$		0			0
$107$	−3.40209	+	5.89259i	−0.328892	+	0.569658i	−0.982292	−	0.187354i	$-0.940009\pi$
$107$	−3.40209	+	5.89259i	−0.328892	+	0.569658i	0.653400	+	0.757013i	$0.273342\pi$
$108$		0			0
$109$	8.37636	+	14.5083i	0.802310	+	1.38964i	0.918092	+	0.396367i	$0.129729\pi$
$109$	8.37636	+	14.5083i	0.802310	+	1.38964i	−0.115783	+	0.993275i	$0.536938\pi$
$110$		0			0
$111$	−6.96176	+	6.35688i	−0.660781	+	0.603368i
$112$		0			0
$113$	6.77154	−	11.7287i	0.637013	−	1.10334i	−0.349072	−	0.937096i	$-0.613503\pi$
$113$	6.77154	−	11.7287i	0.637013	−	1.10334i	0.986085	−	0.166243i	$-0.0531636\pi$
$114$		0			0
$115$	0.335062	−	0.580344i	0.0312447	−	0.0541174i
$116$		0			0
$117$	10.6777	−	4.93360i	0.987151	−	0.456112i
$118$		0			0
$119$	3.12409	−	8.02191i	0.286385	−	0.735367i
$120$		0			0
$121$	4.72501	+	8.18396i	0.429547	+	0.743996i
$122$		0			0
$123$	−10.7496	+	9.81556i	−0.969254	+	0.885039i
$124$		0			0
$125$	−12.0632			−1.07896
$126$		0			0
$127$	10.5904			0.939748			0.469874	−	0.882734i	$-0.344299\pi$
$127$	10.5904			0.939748			0.469874	+	0.882734i	$0.344299\pi$
$128$		0			0
$129$	−1.83208	−	8.33304i	−0.161305	−	0.733683i
$130$		0			0
$131$	11.1819	+	19.3676i	0.976968	+	1.69216i	0.673282	+	0.739385i	$0.264884\pi$
$131$	11.1819	+	19.3676i	0.976968	+	1.69216i	0.303685	+	0.952772i	$0.401783\pi$
$132$		0			0
$133$	12.3536	−	1.89519i	1.07119	−	0.164333i
$134$		0			0
$135$	−3.38935	+	8.06249i	−0.291709	+	0.693908i
$136$		0			0
$137$	−8.97700	+	15.5486i	−0.766957	+	1.32841i	0.172249	+	0.985053i	$0.444896\pi$
$137$	−8.97700	+	15.5486i	−0.766957	+	1.32841i	−0.939206	+	0.343354i	$0.888437\pi$
$138$		0			0
$139$	0.570825	−	0.988699i	0.0484168	−	0.0838603i	−0.840801	−	0.541344i	$-0.817916\pi$
$139$	0.570825	−	0.988699i	0.0484168	−	0.0838603i	0.889218	+	0.457483i	$0.151249\pi$
$140$		0			0
$141$	0.701976	+	0.222685i	0.0591170	+	0.0187535i
$142$		0			0
$143$	2.44065	+	4.22733i	0.204098	+	0.353507i
$144$		0			0
$145$	−5.38434	+	9.32596i	−0.447145	+	0.774479i
$146$		0			0
$147$	6.09087	−	10.4834i	0.502367	−	0.864655i
$148$		0			0
$149$	−8.82916	−	15.2925i	−0.723313	−	1.25281i	−0.959665	−	0.281147i	$-0.909285\pi$
$149$	−8.82916	−	15.2925i	−0.723313	−	1.25281i	0.236352	−	0.971667i	$-0.424048\pi$
$150$		0			0
$151$	7.61769	−	13.1942i	0.619919	−	1.07373i	−0.369581	−	0.929198i	$-0.620499\pi$
$151$	7.61769	−	13.1942i	0.619919	−	1.07373i	0.989500	−	0.144532i	$-0.0461678\pi$
$152$		0			0
$153$	0.884835	−	9.72124i	0.0715347	−	0.785916i
$154$		0			0
$155$	0.486741	+	0.843060i	0.0390960	+	0.0677162i
$156$		0			0
$157$	−13.6288			−1.08769			−0.543847	−	0.839184i	$-0.683033\pi$
$157$	−13.6288			−1.08769			−0.543847	+	0.839184i	$0.683033\pi$
$158$		0			0
$159$	0.346865	+	1.57768i	0.0275082	+	0.125118i
$160$		0			0
$161$	−0.382263	+	0.981559i	−0.0301265	+	0.0773577i
$162$		0			0
$163$	−4.04726	+	7.01005i	−0.317006	+	0.549070i	−0.979862	−	0.199677i	$-0.936011\pi$
$163$	−4.04726	+	7.01005i	−0.317006	+	0.549070i	0.662856	+	0.748747i	$0.269344\pi$
$164$		0			0
$165$	−3.45960	−	1.09748i	−0.269330	−	0.0854384i
$166$		0			0
$167$	−2.07739	+	3.59814i	−0.160753	+	0.278433i	−0.935139	−	0.354281i	$-0.884726\pi$
$167$	−2.07739	+	3.59814i	−0.160753	+	0.278433i	0.774386	+	0.632714i	$0.218059\pi$
$168$		0			0
$169$	−1.18629	−	2.05471i	−0.0912529	−	0.158055i
$170$		0			0
$171$	12.8647	−	5.94411i	0.983788	−	0.454557i
$172$		0			0
$173$	13.8346			1.05183			0.525913	−	0.850539i	$-0.323724\pi$
$173$	13.8346			1.05183			0.525913	+	0.850539i	$0.323724\pi$
$174$		0			0
$175$	5.66701	−	0.869385i	0.428386	−	0.0657193i
$176$		0			0
$177$	−9.98926	−	3.16886i	−0.750839	−	0.238186i
$178$		0			0
$179$	−4.71167	−	8.16084i	−0.352166	−	0.609970i	0.634462	−	0.772954i	$-0.281222\pi$
$179$	−4.71167	−	8.16084i	−0.352166	−	0.609970i	−0.986629	+	0.162984i	$0.947888\pi$
$180$		0			0
$181$	1.32133			0.0982136			0.0491068	−	0.998794i	$-0.484363\pi$
$181$	1.32133			0.0982136			0.0491068	+	0.998794i	$0.484363\pi$
$182$		0			0
$183$	−16.8550	−	5.34686i	−1.24596	−	0.395251i
$184$		0			0
$185$	−9.16128			−0.673551
$186$		0			0
$187$	4.05093			0.296233
$188$		0			0
$189$	3.34434	−	13.3347i	0.243265	−	0.969960i
$190$		0			0
$191$	16.2854			1.17837			0.589186	−	0.807997i	$-0.299449\pi$
$191$	16.2854			1.17837			0.589186	+	0.807997i	$0.299449\pi$
$192$		0			0
$193$	2.56155			0.184384			0.0921921	−	0.995741i	$-0.470613\pi$
$193$	2.56155			0.184384			0.0921921	+	0.995741i	$0.470613\pi$
$194$		0			0
$195$	10.8952	+	3.45626i	0.780225	+	0.247508i
$196$		0			0
$197$	21.6916			1.54546			0.772730	−	0.634735i	$-0.218891\pi$
$197$	21.6916			1.54546			0.772730	+	0.634735i	$0.218891\pi$
$198$		0			0
$199$	−5.59684	−	9.69402i	−0.396750	−	0.687191i	0.596573	−	0.802559i	$-0.296529\pi$
$199$	−5.59684	−	9.69402i	−0.396750	−	0.687191i	−0.993323	+	0.115368i	$0.963195\pi$
$200$		0			0
$201$	15.5514	+	4.93330i	1.09691	+	0.347968i
$202$		0			0
$203$	6.14285	−	15.7734i	0.431143	−	1.10707i
$204$		0			0
$205$	−14.1458			−0.987985
$206$		0			0
$207$	−0.108268	+	1.18949i	−0.00752516	+	0.0826752i
$208$		0			0
$209$	2.94055	+	5.09318i	0.203402	+	0.352303i
$210$		0			0
$211$	−14.1807	+	24.5616i	−0.976237	+	1.69089i	−0.300444	+	0.953799i	$0.597135\pi$
$211$	−14.1807	+	24.5616i	−0.976237	+	1.69089i	−0.675793	+	0.737092i	$0.736199\pi$
$212$		0			0
$213$	−13.9774	−	4.43400i	−0.957716	−	0.303813i
$214$		0			0
$215$	4.14560	−	7.18039i	0.282728	−	0.489699i
$216$		0			0
$217$	−0.957211	−	1.19386i	−0.0649797	−	0.0810446i
$218$		0			0
$219$	−5.07553	−	23.0856i	−0.342973	−	1.55998i
$220$		0			0
$221$	−12.7575			−0.858162
$222$		0			0
$223$	−12.6962	−	21.9905i	−0.850202	−	1.47259i	−0.881026	−	0.473068i	$-0.843147\pi$
$223$	−12.6962	−	21.9905i	−0.850202	−	1.47259i	0.0308242	−	0.999525i	$-0.490187\pi$
$224$		0			0
$225$	5.90146	−	2.72676i	0.393431	−	0.181784i
$226$		0			0
$227$	−2.31430	+	4.00849i	−0.153606	+	0.266053i	−0.932550	−	0.361040i	$-0.882422\pi$
$227$	−2.31430	+	4.00849i	−0.153606	+	0.266053i	0.778945	+	0.627092i	$0.215755\pi$
$228$		0			0
$229$	−1.16296	−	2.01431i	−0.0768506	−	0.133109i	0.825039	−	0.565076i	$-0.191153\pi$
$229$	−1.16296	−	2.01431i	−0.0768506	−	0.133109i	−0.901890	+	0.431967i	$0.857820\pi$
$230$		0			0
$231$	5.63685	+	0.880546i	0.370878	+	0.0579357i
$232$		0			0
$233$	−6.37989	+	11.0503i	−0.417960	+	0.723929i	−0.995734	−	0.0922683i	$-0.970588\pi$
$233$	−6.37989	+	11.0503i	−0.417960	+	0.723929i	0.577774	+	0.816197i	$0.303922\pi$
$234$		0			0
$235$	0.357830	+	0.619780i	0.0233423	+	0.0404300i
$236$		0			0
$237$	9.13548	+	2.89801i	0.593413	+	0.188246i
$238$		0			0
$239$	−11.0492	+	19.1378i	−0.714714	+	1.23792i	0.248355	+	0.968669i	$0.420110\pi$
$239$	−11.0492	+	19.1378i	−0.714714	+	1.23792i	−0.963070	+	0.269252i	$0.913223\pi$
$240$		0			0
$241$	−10.0088	+	17.3358i	−0.644726	+	1.11670i	0.339639	+	0.940556i	$0.389695\pi$
$241$	−10.0088	+	17.3358i	−0.644726	+	1.11670i	−0.984365	+	0.176142i	$0.943638\pi$
$242$		0			0
$243$	−0.543501	−	15.5790i	−0.0348656	−	0.999392i
$244$		0			0
$245$	11.2403	−	3.53190i	0.718114	−	0.225645i
$246$		0			0
$247$	−9.26060	−	16.0398i	−0.589238	−	1.02059i
$248$		0			0
$249$	5.97802	+	27.1905i	0.378842	+	1.72313i
$250$		0			0
$251$	−2.12390			−0.134059			−0.0670297	−	0.997751i	$-0.521352\pi$
$251$	−2.12390			−0.134059			−0.0670297	+	0.997751i	$0.521352\pi$
$252$		0			0
$253$	−0.495671			−0.0311625
$254$		0			0
$255$	7.00493	−	6.39630i	0.438666	−	0.400552i
$256$		0			0
$257$	6.38150	+	11.0531i	0.398067	+	0.689472i	0.993487	−	0.113942i	$-0.0363478\pi$
$257$	6.38150	+	11.0531i	0.398067	+	0.689472i	−0.595420	+	0.803414i	$0.703014\pi$
$258$		0			0
$259$	14.2341	−	2.18367i	0.884463	−	0.135687i
$260$		0			0
$261$	1.73984	−	19.1147i	0.107693	−	1.18317i
$262$		0			0
$263$	5.53432	−	9.58572i	0.341261	−	0.591081i	−0.643406	−	0.765525i	$-0.722479\pi$
$263$	5.53432	−	9.58572i	0.341261	−	0.591081i	0.984667	+	0.174444i	$0.0558127\pi$
$264$		0			0
$265$	−0.784881	+	1.35945i	−0.0482148	+	0.0835105i
$266$		0			0
$267$	15.4452	−	14.1032i	0.945230	−	0.863102i
$268$		0			0
$269$	−1.77479	−	3.07403i	−0.108211	−	0.187427i	0.806835	−	0.590777i	$-0.201179\pi$
$269$	−1.77479	−	3.07403i	−0.108211	−	0.187427i	−0.915046	+	0.403351i	$0.867846\pi$
$270$		0			0
$271$	−0.687666	+	1.19107i	−0.0417727	+	0.0723525i	−0.886156	−	0.463387i	$-0.846634\pi$
$271$	−0.687666	+	1.19107i	−0.0417727	+	0.0723525i	0.844383	+	0.535740i	$0.179967\pi$
$272$		0			0
$273$	−17.7520	−	2.77308i	−1.07440	−	0.167835i
$274$		0			0
$275$	1.34893	+	2.33641i	0.0813434	+	0.140891i
$276$		0			0
$277$	14.5809	−	25.2548i	0.876079	−	1.51741i	0.0204692	−	0.999790i	$-0.493484\pi$
$277$	14.5809	−	25.2548i	0.876079	−	1.51741i	0.855609	−	0.517622i	$-0.173183\pi$
$278$		0			0
$279$	−1.41782	−	1.00019i	−0.0848824	−	0.0598797i
$280$		0			0
$281$	6.29603	+	10.9050i	0.375590	+	0.650540i	0.990415	−	0.138123i	$-0.0441069\pi$
$281$	6.29603	+	10.9050i	0.375590	+	0.650540i	−0.614826	+	0.788663i	$0.710774\pi$
$282$		0			0
$283$	−9.46056			−0.562372			−0.281186	−	0.959653i	$-0.590728\pi$
$283$	−9.46056			−0.562372			−0.281186	+	0.959653i	$0.590728\pi$
$284$		0			0
$285$	13.1268	+	4.16417i	0.777566	+	0.246664i
$286$		0			0
$287$	21.9786	−	3.37178i	1.29736	−	0.199030i
$288$		0			0
$289$	3.20636	−	5.55358i	0.188609	−	0.326681i
$290$		0			0
$291$	4.35926	+	19.8277i	0.255544	+	1.16232i
$292$		0			0
$293$	−8.32726	+	14.4232i	−0.486484	+	0.842614i	−0.999879	−	0.0155376i	$-0.995054\pi$
$293$	−8.32726	+	14.4232i	−0.486484	+	0.842614i	0.513396	+	0.858152i	$0.328387\pi$
$294$		0			0
$295$	−5.09200	−	8.81960i	−0.296468	−	0.513497i
$296$		0			0
$297$	6.41811	−	0.810664i	0.372417	−	0.0470395i
$298$		0			0
$299$	1.56100			0.0902752
$300$		0			0
$301$	−4.72960	+	12.1445i	−0.272610	+	0.699996i
$302$		0			0
$303$	6.91460	−	6.31381i	0.397234	−	0.362719i
$304$		0			0
$305$	−8.59181	−	14.8815i	−0.491966	−	0.852110i
$306$		0			0
$307$	−9.55966			−0.545599			−0.272799	−	0.962071i	$-0.587949\pi$
$307$	−9.55966			−0.545599			−0.272799	+	0.962071i	$0.587949\pi$
$308$		0			0
$309$	5.43762	+	24.7325i	0.309335	+	1.40698i
$310$		0			0
$311$	26.3702			1.49532			0.747658	−	0.664084i	$-0.231178\pi$
$311$	26.3702			1.49532			0.747658	+	0.664084i	$0.231178\pi$
$312$		0			0
$313$	−12.7018			−0.717949			−0.358975	−	0.933347i	$-0.616874\pi$
$313$	−12.7018			−0.717949			−0.358975	+	0.933347i	$0.616874\pi$
$314$		0			0
$315$	11.1377	−	7.37777i	0.627538	−	0.415690i
$316$		0			0
$317$	0.0331536			0.00186209			0.000931047	−	1.00000i	$-0.499704\pi$
$317$	0.0331536			0.00186209			0.000931047		1.00000i	$0.499704\pi$
$318$		0			0
$319$	7.96528			0.445970
$320$		0			0
$321$	8.70289	−	7.94672i	0.485748	−	0.443543i
$322$		0			0
$323$	−15.3705			−0.855238
$324$		0			0
$325$	−4.24815	−	7.35801i	−0.235645	−	0.408149i
$326$		0			0
$327$	−6.23069	−	28.3397i	−0.344558	−	1.56719i
$328$		0			0
$329$	−0.703699	−	0.877674i	−0.0387962	−	0.0483877i
$330$		0			0
$331$	−4.85388			−0.266793			−0.133397	−	0.991063i	$-0.542588\pi$
$331$	−4.85388			−0.266793			−0.133397	+	0.991063i	$0.542588\pi$
$332$		0			0
$333$	14.8230	−	6.84893i	0.812294	−	0.375319i
$334$		0			0
$335$	7.92726	+	13.7304i	0.433112	+	0.750173i
$336$		0			0
$337$	−4.32200	+	7.48592i	−0.235434	+	0.407784i	−0.959399	−	0.282053i	$-0.908985\pi$
$337$	−4.32200	+	7.48592i	−0.235434	+	0.407784i	0.723965	+	0.689837i	$0.242318\pi$
$338$		0			0
$339$	−17.3223	+	15.8172i	−0.940817	+	0.859072i
$340$		0			0
$341$	0.360028	−	0.623586i	0.0194966	−	0.0337691i
$342$		0			0
$343$	−16.6224	+	8.16680i	−0.897524	+	0.440966i
$344$		0			0
$345$	−0.857122	+	0.782649i	−0.0461459	+	0.0421364i
$346$		0			0
$347$	−23.2232			−1.24669			−0.623344	−	0.781948i	$-0.714226\pi$
$347$	−23.2232			−1.24669			−0.623344	+	0.781948i	$0.714226\pi$
$348$		0			0
$349$	−3.76025	−	6.51295i	−0.201282	−	0.348630i	0.747660	−	0.664082i	$-0.231177\pi$
$349$	−3.76025	−	6.51295i	−0.201282	−	0.348630i	−0.948942	+	0.315452i	$0.897844\pi$
$350$		0			0
$351$	−20.2124	+	2.55300i	−1.07886	+	0.136269i
$352$		0			0
$353$	0.459528	−	0.795925i	0.0244582	−	0.0423628i	−0.853537	−	0.521032i	$-0.825547\pi$
$353$	0.459528	−	0.795925i	0.0244582	−	0.0423628i	0.877995	+	0.478669i	$0.158881\pi$
$354$		0			0
$355$	−7.12495	−	12.3408i	−0.378153	−	0.654980i
$356$		0			0
$357$	−9.35911	+	11.6078i	−0.495336	+	0.614348i
$358$		0			0
$359$	8.24300	−	14.2773i	0.435049	−	0.753527i	−0.562251	−	0.826967i	$-0.690064\pi$
$359$	8.24300	−	14.2773i	0.435049	−	0.753527i	0.997300	+	0.0734398i	$0.0233977\pi$
$360$		0			0
$361$	−1.65737	−	2.87066i	−0.0872302	−	0.151087i
$362$		0			0
$363$	−3.51466	−	15.9861i	−0.184472	−	0.839054i
$364$		0			0
$365$	11.4848	−	19.8923i	0.601144	−	1.04121i
$366$		0			0
$367$	6.33921	−	10.9798i	0.330904	−	0.573143i	−0.651785	−	0.758404i	$-0.725980\pi$
$367$	6.33921	−	10.9798i	0.330904	−	0.573143i	0.982689	+	0.185261i	$0.0593130\pi$
$368$		0			0
$369$	22.8879	−	10.5753i	1.19150	−	0.550529i
$370$		0			0
$371$	0.895448	−	2.29930i	0.0464894	−	0.119373i
$372$		0			0
$373$	−11.3410	−	19.6433i	−0.587217	−	1.01709i	−0.994595	−	0.103830i	$-0.966890\pi$
$373$	−11.3410	−	19.6433i	−0.587217	−	1.01709i	0.407378	−	0.913259i	$-0.366443\pi$
$374$		0			0
$375$	19.9159	+	6.31785i	1.02845	+	0.326252i
$376$		0			0
$377$	−25.0849			−1.29194
$378$		0			0
$379$	19.0925			0.980717			0.490358	−	0.871521i	$-0.336866\pi$
$379$	19.0925			0.980717			0.490358	+	0.871521i	$0.336866\pi$
$380$		0			0
$381$	−17.4845	−	5.54653i	−0.895757	−	0.284158i
$382$		0			0
$383$	3.03963	+	5.26479i	0.155318	+	0.269018i	0.933175	−	0.359423i	$-0.117027\pi$
$383$	3.03963	+	5.26479i	0.155318	+	0.269018i	−0.777857	+	0.628441i	$0.783693\pi$
$384$		0			0
$385$	3.46809	+	4.32551i	0.176750	+	0.220448i
$386$		0			0
$387$	−1.33956	+	14.7171i	−0.0680939	+	0.748113i
$388$		0			0
$389$	0.315781	−	0.546948i	0.0160107	−	0.0277314i	−0.857909	−	0.513802i	$-0.828237\pi$
$389$	0.315781	−	0.546948i	0.0160107	−	0.0277314i	0.873920	+	0.486070i	$0.161570\pi$
$390$		0			0
$391$	0.647728	−	1.12190i	0.0327570	−	0.0567368i
$392$		0			0
$393$	−8.31757	−	37.8317i	−0.419566	−	1.90836i
$394$		0			0
$395$	4.65679	+	8.06579i	0.234308	+	0.405834i
$396$		0			0
$397$	−18.1830	+	31.4939i	−0.912578	+	1.58063i	−0.102170	+	0.994767i	$0.532579\pi$
$397$	−18.1830	+	31.4939i	−0.912578	+	1.58063i	−0.810408	+	0.585865i	$0.800755\pi$
$398$		0			0
$399$	−21.3880	−	3.34107i	−1.07074	−	0.167263i
$400$		0			0
$401$	15.8069	+	27.3783i	0.789357	+	1.36721i	0.926361	+	0.376636i	$0.122919\pi$
$401$	15.8069	+	27.3783i	0.789357	+	1.36721i	−0.137004	+	0.990571i	$0.543747\pi$
$402$		0			0
$403$	−1.13383	+	1.96385i	−0.0564800	+	0.0978262i
$404$		0			0
$405$	9.81829	−	11.5358i	0.487875	−	0.573220i
$406$		0			0
$407$	3.38816	+	5.86847i	0.167945	+	0.290889i
$408$		0			0
$409$	20.1812			0.997896			0.498948	−	0.866632i	$-0.333720\pi$
$409$	20.1812			0.997896			0.498948	+	0.866632i	$0.333720\pi$
$410$		0			0
$411$	22.9641	−	20.9688i	1.13273	−	1.03431i
$412$		0			0
$413$	10.0138	+	12.4895i	0.492746	+	0.614567i
$414$		0			0
$415$	−13.5270	+	23.4294i	−0.664014	+	1.15011i
$416$		0			0
$417$	−1.46023	+	1.33335i	−0.0715077	+	0.0652946i
$418$		0			0
$419$	−12.4159	+	21.5049i	−0.606555	+	1.05058i	0.385248	+	0.922813i	$0.374116\pi$
$419$	−12.4159	+	21.5049i	−0.606555	+	1.05058i	−0.991804	+	0.127772i	$0.959217\pi$
$420$		0			0
$421$	−5.71841	−	9.90458i	−0.278698	−	0.482720i	0.692363	−	0.721549i	$-0.256570\pi$
$421$	−5.71841	−	9.90458i	−0.278698	−	0.482720i	−0.971062	+	0.238829i	$0.923236\pi$
$422$		0			0
$423$	−1.04231	−	0.735293i	−0.0506791	−	0.0357512i
$424$		0			0
$425$	−7.05096			−0.342022
$426$		0			0
$427$	16.8964	+	21.0737i	0.817675	+	1.01983i
$428$		0			0
$429$	−1.81546	−	8.25745i	−0.0876512	−	0.398673i
$430$		0			0
$431$	2.80157	+	4.85246i	0.134947	+	0.233735i	0.925577	−	0.378559i	$-0.123580\pi$
$431$	2.80157	+	4.85246i	0.134947	+	0.233735i	−0.790630	+	0.612294i	$0.790247\pi$
$432$		0			0
$433$	−4.22555			−0.203067			−0.101534	−	0.994832i	$-0.532375\pi$
$433$	−4.22555			−0.203067			−0.101534	+	0.994832i	$0.532375\pi$
$434$		0			0
$435$	13.7737	−	12.5769i	0.660398	−	0.603018i
$436$		0			0
$437$	1.88073			0.0899676
$438$		0			0
$439$	−35.4631			−1.69256			−0.846281	−	0.532737i	$-0.821164\pi$
$439$	−35.4631			−1.69256			−0.846281	+	0.532737i	$0.821164\pi$
$440$		0			0
$441$	−15.5463	+	14.1178i	−0.740301	+	0.672275i
$442$		0			0
$443$	−22.9315			−1.08951			−0.544755	−	0.838595i	$-0.683377\pi$
$443$	−22.9315			−1.08951			−0.544755	+	0.838595i	$0.683377\pi$
$444$		0			0
$445$	20.3250			0.963496
$446$		0			0
$447$	6.56750	+	29.8717i	0.310632	+	1.41288i
$448$		0			0
$449$	20.4850			0.966747			0.483373	−	0.875414i	$-0.339411\pi$
$449$	20.4850			0.966747			0.483373	+	0.875414i	$0.339411\pi$
$450$		0			0
$451$	5.23161	+	9.06141i	0.246347	+	0.426685i
$452$		0			0
$453$	−19.4868	+	17.7937i	−0.915570	+	0.836019i
$454$		0			0
$455$	−10.9220	−	13.6222i	−0.512031	−	0.638620i
$456$		0			0
$457$	15.4535			0.722886			0.361443	−	0.932394i	$-0.382284\pi$
$457$	15.4535			0.722886			0.361443	+	0.932394i	$0.382284\pi$
$458$		0			0
$459$	−6.55216	+	15.5861i	−0.305828	+	0.727496i
$460$		0			0
$461$	14.0815	+	24.3898i	0.655839	+	1.13595i	0.981683	+	0.190523i	$0.0610183\pi$
$461$	14.0815	+	24.3898i	0.655839	+	1.13595i	−0.325844	+	0.945424i	$0.605648\pi$
$462$		0			0
$463$	−15.3193	+	26.5338i	−0.711948	+	1.23313i	0.252177	+	0.967681i	$0.418854\pi$
$463$	−15.3193	+	26.5338i	−0.711948	+	1.23313i	−0.964125	+	0.265449i	$0.914480\pi$
$464$		0			0
$465$	−0.362058	−	1.64679i	−0.0167901	−	0.0763680i
$466$		0			0
$467$	−6.61798	+	11.4627i	−0.306244	+	0.530429i	−0.977537	−	0.210762i	$-0.932406\pi$
$467$	−6.61798	+	11.4627i	−0.306244	+	0.530429i	0.671294	+	0.741191i	$0.265739\pi$
$468$		0			0
$469$	−15.5895	−	19.4437i	−0.719857	−	0.897827i
$470$		0			0
$471$	22.5007	+	7.13781i	1.03678	+	0.328893i
$472$		0			0
$473$	−6.13275			−0.281984
$474$		0			0
$475$	−5.11826	−	8.86508i	−0.234842	−	0.406758i
$476$		0			0
$477$	0.253618	−	2.78637i	0.0116124	−	0.127579i
$478$		0			0
$479$	−7.04358	+	12.1998i	−0.321829	+	0.557425i	−0.980866	−	0.194687i	$-0.937631\pi$
$479$	−7.04358	+	12.1998i	−0.321829	+	0.557425i	0.659036	+	0.752111i	$0.270964\pi$
$480$		0			0
$481$	−10.6703	−	18.4814i	−0.486522	−	0.842681i
$482$		0			0
$483$	1.14518	−	1.42032i	0.0521074	−	0.0646269i
$484$		0			0
$485$	−9.86407	+	17.0851i	−0.447904	+	0.775793i
$486$		0			0
$487$	3.45654	+	5.98690i	0.156631	+	0.271292i	0.933652	−	0.358183i	$-0.116603\pi$
$487$	3.45654	+	5.98690i	0.156631	+	0.271292i	−0.777021	+	0.629475i	$0.783270\pi$
$488$		0			0
$489$	10.3533	−	9.45372i	0.468192	−	0.427512i
$490$		0			0
$491$	−15.3481	+	26.5837i	−0.692651	+	1.19971i	0.278315	+	0.960490i	$0.410224\pi$
$491$	−15.3481	+	26.5837i	−0.692651	+	1.19971i	−0.970966	+	0.239217i	$0.923109\pi$
$492$		0			0
$493$	−10.4088	+	18.0286i	−0.468789	+	0.811966i
$494$		0			0
$495$	5.13692	+	3.62380i	0.230887	+	0.162878i
$496$		0			0
$497$	14.0117	+	17.4758i	0.628511	+	0.783898i
$498$		0			0
$499$	11.0186	+	19.0847i	0.493259	+	0.854350i	0.999970	−	0.00776631i	$-0.00247212\pi$
$499$	11.0186	+	19.0847i	0.493259	+	0.854350i	−0.506711	+	0.862116i	$0.669139\pi$
$500$		0			0
$501$	5.31417	−	4.85244i	0.237419	−	0.216791i
$502$		0			0
$503$	38.9653			1.73737			0.868687	−	0.495361i	$-0.164964\pi$
$503$	38.9653			1.73737			0.868687	+	0.495361i	$0.164964\pi$
$504$		0			0
$505$	9.09922			0.404910
$506$		0			0
$507$	0.882411	+	4.01357i	0.0391892	+	0.178249i
$508$		0			0
$509$	14.1471	+	24.5034i	0.627058	+	1.08610i	0.988139	+	0.153561i	$0.0490743\pi$
$509$	14.1471	+	24.5034i	0.627058	+	1.08610i	−0.361082	+	0.932534i	$0.617592\pi$
$510$		0			0
$511$	−13.1027	+	33.6447i	−0.579631	+	1.48835i
$512$		0			0
$513$	−24.3524	+	3.07591i	−1.07518	+	0.135805i
$514$		0			0
$515$	−12.3042	+	21.3115i	−0.542187	+	0.939095i
$516$		0			0
$517$	0.264676	−	0.458433i	0.0116405	−	0.0201619i
$518$		0			0
$519$	−22.8405	−	7.24561i	−1.00259	−	0.318047i
$520$		0			0
$521$	−5.98150	−	10.3603i	−0.262054	−	0.453892i	0.704733	−	0.709472i	$-0.251067\pi$
$521$	−5.98150	−	10.3603i	−0.262054	−	0.453892i	−0.966788	+	0.255581i	$0.917733\pi$
$522$		0			0
$523$	−3.15056	+	5.45693i	−0.137764	+	0.238615i	−0.926650	−	0.375925i	$-0.877325\pi$
$523$	−3.15056	+	5.45693i	−0.137764	+	0.238615i	0.788886	+	0.614540i	$0.210658\pi$
$524$		0			0
$525$	−9.81139	−	1.53266i	−0.428204	−	0.0668908i
$526$		0			0
$527$	0.940948	+	1.62977i	0.0409884	+	0.0709939i
$528$		0			0
$529$	11.4207	−	19.7813i	0.496554	−	0.860057i
$530$		0			0
$531$	14.8324	+	10.4634i	0.643669	+	0.454072i
$532$		0			0
$533$	−16.4758	−	28.5369i	−0.713645	−	1.23607i
$534$		0			0
$535$	11.4525			0.495135
$536$		0			0
$537$	3.50473	+	15.9410i	0.151240	+	0.687903i
$538$		0			0
$539$	−6.41948	−	5.89399i	−0.276507	−	0.253872i
$540$		0			0
$541$	9.88191	−	17.1160i	0.424857	−	0.735873i	−0.571550	−	0.820567i	$-0.693658\pi$
$541$	9.88191	−	17.1160i	0.424857	−	0.735873i	0.996407	+	0.0846937i	$0.0269912\pi$
$542$		0			0
$543$	−2.18148	−	0.692021i	−0.0936161	−	0.0296975i
$544$		0			0
$545$	14.0987	−	24.4197i	0.603923	−	1.04602i
$546$		0			0
$547$	21.6125	+	37.4340i	0.924085	+	1.60056i	0.793026	+	0.609188i	$0.208504\pi$
$547$	21.6125	+	37.4340i	0.924085	+	1.60056i	0.131059	+	0.991375i	$0.458162\pi$
$548$		0			0
$549$	25.0269	+	17.6550i	1.06812	+	0.753498i
$550$		0			0
$551$	−30.2228			−1.28753
$552$		0			0
$553$	−9.15791	−	11.4220i	−0.389434	−	0.485713i
$554$		0			0
$555$	15.1250	+	4.79805i	0.642021	+	0.203666i
$556$		0			0
$557$	−14.0838	−	24.3938i	−0.596748	−	1.03360i	−0.993298	−	0.115584i	$-0.963126\pi$
$557$	−14.0838	−	24.3938i	−0.596748	−	1.03360i	0.396550	−	0.918013i	$-0.370207\pi$
$558$		0			0
$559$	19.3137			0.816884
$560$		0			0
$561$	−6.68797	−	2.12160i	−0.282366	−	0.0895739i
$562$		0			0
$563$	25.6944			1.08289			0.541445	−	0.840736i	$-0.317878\pi$
$563$	25.6944			1.08289			0.541445	+	0.840736i	$0.317878\pi$
$564$		0			0
$565$	−22.7951			−0.958998
$566$		0			0
$567$	−12.5052	+	20.2637i	−0.525170	+	0.850997i
$568$		0			0
$569$	35.4881			1.48774			0.743870	−	0.668324i	$-0.232988\pi$
$569$	35.4881			1.48774			0.743870	+	0.668324i	$0.232988\pi$
$570$		0			0
$571$	21.6824			0.907378			0.453689	−	0.891160i	$-0.350108\pi$
$571$	21.6824			0.907378			0.453689	+	0.891160i	$0.350108\pi$
$572$		0			0
$573$	−26.8868	−	8.52919i	−1.12321	−	0.356312i
$574$		0			0
$575$	0.862754			0.0359793
$576$		0			0
$577$	−7.60727	−	13.1762i	−0.316695	−	0.548531i	0.663102	−	0.748529i	$-0.269240\pi$
$577$	−7.60727	−	13.1762i	−0.316695	−	0.548531i	−0.979796	+	0.199998i	$0.935906\pi$
$578$		0			0
$579$	−4.22904	−	1.34156i	−0.175753	−	0.0557534i
$580$		0			0
$581$	15.4326	−	39.6271i	0.640251	−	1.64401i
$582$		0			0
$583$	1.16111			0.0480881
$584$		0			0
$585$	−16.1776	−	11.4124i	−0.668861	−	0.471843i
$586$		0			0
$587$	−19.1924	−	33.2423i	−0.792157	−	1.37206i	−0.924629	−	0.380869i	$-0.875625\pi$
$587$	−19.1924	−	33.2423i	−0.792157	−	1.37206i	0.132472	−	0.991187i	$-0.457708\pi$
$588$		0			0
$589$	−1.36606	+	2.36608i	−0.0562875	+	0.0974928i
$590$		0			0
$591$	−35.8121	−	11.3605i	−1.47311	−	0.467310i
$592$		0			0
$593$	−9.25559	+	16.0311i	−0.380081	+	0.658320i	−0.991074	−	0.133316i	$-0.957437\pi$
$593$	−9.25559	+	16.0311i	−0.380081	+	0.658320i	0.610992	+	0.791637i	$0.290771\pi$
$594$		0			0
$595$	−14.3223	+	2.19721i	−0.587159	+	0.0900770i
$596$		0			0
$597$	4.16317	+	18.9358i	0.170387	+	0.774990i
$598$		0			0
$599$	−21.6825			−0.885924			−0.442962	−	0.896540i	$-0.646072\pi$
$599$	−21.6825			−0.885924			−0.442962	+	0.896540i	$0.646072\pi$
$600$		0			0
$601$	3.95776	+	6.85505i	0.161441	+	0.279623i	0.935386	−	0.353630i	$-0.115053\pi$
$601$	3.95776	+	6.85505i	0.161441	+	0.279623i	−0.773945	+	0.633253i	$0.781719\pi$
$602$		0			0
$603$	−23.0911	−	16.2895i	−0.940343	−	0.663358i
$604$		0			0
$605$	7.95293	−	13.7749i	0.323333	−	0.560029i
$606$		0			0
$607$	−17.9623	−	31.1117i	−0.729068	−	1.26278i	−0.957277	−	0.289171i	$-0.906620\pi$
$607$	−17.9623	−	31.1117i	−0.729068	−	1.26278i	0.228209	−	0.973612i	$-0.426713\pi$
$608$		0			0
$609$	−18.4027	+	22.8241i	−0.745714	+	0.924881i
$610$		0			0
$611$	−0.833539	+	1.44373i	−0.0337214	+	0.0584072i
$612$		0			0
$613$	−1.60252	−	2.77565i	−0.0647253	−	0.112108i	0.831847	−	0.555005i	$-0.187284\pi$
$613$	−1.60252	−	2.77565i	−0.0647253	−	0.112108i	−0.896572	+	0.442898i	$0.853950\pi$
$614$		0			0
$615$	23.3543	+	7.40859i	0.941736	+	0.298743i
$616$		0			0
$617$	15.9357	−	27.6015i	0.641549	−	1.11120i	−0.343538	−	0.939139i	$-0.611626\pi$
$617$	15.9357	−	27.6015i	0.641549	−	1.11120i	0.985087	−	0.172056i	$-0.0550411\pi$
$618$		0			0
$619$	10.4863	−	18.1628i	0.421480	−	0.730024i	−0.574605	−	0.818431i	$-0.694844\pi$
$619$	10.4863	−	18.1628i	0.421480	−	0.730024i	0.996084	+	0.0884070i	$0.0281776\pi$
$620$		0			0
$621$	0.801720	−	1.90711i	0.0321719	−	0.0765296i
$622$		0			0
$623$	−31.5793	+	4.84464i	−1.26520	+	0.194096i
$624$		0			0
$625$	4.73462	+	8.20060i	0.189385	+	0.328024i
$626$		0			0
$627$	−2.18730	−	9.94875i	−0.0873525	−	0.397315i
$628$		0			0
$629$	−17.7102			−0.706153
$630$		0			0
$631$	26.4435			1.05270			0.526349	−	0.850268i	$-0.323560\pi$
$631$	26.4435			1.05270			0.526349	+	0.850268i	$0.323560\pi$
$632$		0			0
$633$	36.2755	−	33.1237i	1.44182	−	1.31655i
$634$		0			0
$635$	−8.91266	−	15.4372i	−0.353688	−	0.612606i
$636$		0			0
$637$	20.2167	+	18.5618i	0.801016	+	0.735445i
$638$		0			0
$639$	20.7541	+	14.6408i	0.821019	+	0.579182i
$640$		0			0
$641$	13.9809	−	24.2157i	0.552213	−	0.956461i	−0.445901	−	0.895082i	$-0.647117\pi$
$641$	13.9809	−	24.2157i	0.552213	−	0.956461i	0.998115	−	0.0613792i	$-0.0195499\pi$
$642$		0			0
$643$	−6.12936	+	10.6164i	−0.241718	+	0.418669i	−0.961204	−	0.275839i	$-0.911044\pi$
$643$	−6.12936	+	10.6164i	−0.241718	+	0.418669i	0.719485	+	0.694508i	$0.244378\pi$
$644$		0			0
$645$	−10.6049	+	9.68344i	−0.417566	+	0.381285i
$646$		0			0
$647$	4.49923	+	7.79290i	0.176883	+	0.306371i	0.940811	−	0.338931i	$-0.110065\pi$
$647$	4.49923	+	7.79290i	0.176883	+	0.306371i	−0.763928	+	0.645301i	$0.776732\pi$
$648$		0			0
$649$	−3.76640	+	6.52360i	−0.147844	+	0.256074i
$650$		0			0
$651$	0.955065	+	2.47235i	0.0374320	+	0.0968991i
$652$		0			0
$653$	11.3950	+	19.7368i	0.445922	+	0.772359i	0.998116	−	0.0613562i	$-0.0195426\pi$
$653$	11.3950	+	19.7368i	0.445922	+	0.772359i	−0.552194	+	0.833716i	$0.686209\pi$
$654$		0			0
$655$	18.8209	−	32.5987i	0.735393	−	1.27374i
$656$		0			0
$657$	−3.71109	+	40.7719i	−0.144783	+	1.59066i
$658$		0			0
$659$	−19.3311	−	33.4824i	−0.753033	−	1.30429i	−0.946347	−	0.323154i	$-0.895257\pi$
$659$	−19.3311	−	33.4824i	−0.753033	−	1.30429i	0.193314	−	0.981137i	$-0.438076\pi$
$660$		0			0
$661$	−11.5080			−0.447609			−0.223804	−	0.974634i	$-0.571848\pi$
$661$	−11.5080			−0.447609			−0.223804	+	0.974634i	$0.571848\pi$
$662$		0			0
$663$	21.0623	+	6.68150i	0.817990	+	0.259488i
$664$		0			0
$665$	−13.1590	−	16.4124i	−0.510286	−	0.636444i
$666$		0			0
$667$	1.27362	−	2.20597i	0.0493147	−	0.0854156i
$668$		0			0
$669$	9.44398	+	42.9551i	0.365125	+	1.66074i
$670$		0			0
$671$	−6.35511	+	11.0074i	−0.245336	+	0.424935i
$672$		0			0
$673$	−10.6642	−	18.4709i	−0.411075	−	0.712002i	0.583933	−	0.811802i	$-0.301513\pi$
$673$	−10.6642	−	18.4709i	−0.411075	−	0.712002i	−0.995008	+	0.0997997i	$0.968180\pi$
$674$		0			0
$675$	−11.1712	+	1.41102i	−0.429981	+	0.0543103i
$676$		0			0
$677$	27.7599			1.06690			0.533449	−	0.845832i	$-0.320896\pi$
$677$	27.7599			1.06690			0.533449	+	0.845832i	$0.320896\pi$
$678$		0			0
$679$	11.2536	−	28.8966i	0.431875	−	1.10895i
$680$		0			0
$681$	5.92021	−	5.40582i	0.226863	−	0.207152i
$682$		0			0
$683$	−8.66854	−	15.0143i	−0.331692	−	0.574508i	0.651151	−	0.758948i	$-0.274286\pi$
$683$	−8.66854	−	15.0143i	−0.331692	−	0.574508i	−0.982844	+	0.184440i	$0.940953\pi$
$684$		0			0
$685$	30.2194			1.15462
$686$		0			0
$687$	0.865059	+	3.93464i	0.0330041	+	0.150116i
$688$		0			0
$689$	−3.65664			−0.139307
$690$		0			0
$691$	39.6046			1.50663			0.753315	−	0.657660i	$-0.228453\pi$
$691$	39.6046			1.50663			0.753315	+	0.657660i	$0.228453\pi$
$692$		0			0
$693$	−8.84511	−	4.40595i	−0.335998	−	0.167368i
$694$		0			0
$695$	−1.92158			−0.0728895
$696$		0			0
$697$	−27.3461			−1.03581
$698$		0			0
$699$	16.3204	−	14.9024i	0.617294	−	0.563659i
$700$		0			0
$701$	7.28469			0.275139			0.137570	−	0.990492i	$-0.456071\pi$
$701$	7.28469			0.275139			0.137570	+	0.990492i	$0.456071\pi$
$702$		0			0
$703$	−12.8558	−	22.2668i	−0.484864	−	0.839809i
$704$		0			0
$705$	−0.266169	−	1.21065i	−0.0100245	−	0.0455956i
$706$		0			0
$707$	−14.1377	+	2.16888i	−0.531701	+	0.0815691i
$708$		0			0
$709$	12.0108			0.451075			0.225538	−	0.974234i	$-0.427586\pi$
$709$	12.0108			0.451075			0.225538	+	0.974234i	$0.427586\pi$
$710$		0			0
$711$	−13.5646	−	9.56908i	−0.508714	−	0.358868i
$712$		0			0
$713$	−0.115134	−	0.199418i	−0.00431181	−	0.00746827i
$714$		0			0
$715$	4.10800	−	7.11526i	0.153630	−	0.266096i
$716$		0			0
$717$	28.2650	−	25.8091i	1.05558	−	0.963860i
$718$		0			0
$719$	−2.15819	+	3.73809i	−0.0804868	+	0.139407i	−0.903459	−	0.428674i	$-0.858981\pi$
$719$	−2.15819	+	3.73809i	−0.0804868	+	0.139407i	0.822972	+	0.568081i	$0.192314\pi$
$720$		0			0
$721$	14.0375	−	36.0449i	0.522783	−	1.34238i
$722$		0			0
$723$	25.6036	−	23.3790i	0.952208	−	0.869473i
$724$		0			0
$725$	−13.8642			−0.514903
$726$		0			0
$727$	10.2483	+	17.7506i	0.380090	+	0.658334i	0.991075	−	0.133308i	$-0.0425598\pi$
$727$	10.2483	+	17.7506i	0.380090	+	0.658334i	−0.610985	+	0.791642i	$0.709226\pi$
$728$		0			0
$729$	−7.26189	+	26.0051i	−0.268959	+	0.963152i
$730$		0			0
$731$	8.01411	−	13.8808i	0.296413	−	0.513402i
$732$		0			0
$733$	−12.6661	−	21.9383i	−0.467833	−	0.810310i	0.531491	−	0.847064i	$-0.321632\pi$
$733$	−12.6661	−	21.9383i	−0.467833	−	0.810310i	−0.999324	+	0.0367533i	$0.988298\pi$
$734$		0			0
$735$	−20.4071	−	0.0558159i	−0.752727	−	0.00205880i
$736$		0			0
$737$	5.86356	−	10.1560i	0.215987	−	0.374100i
$738$		0			0
$739$	−6.63391	−	11.4903i	−0.244032	−	0.422676i	0.717827	−	0.696222i	$-0.245137\pi$
$739$	−6.63391	−	11.4903i	−0.244032	−	0.422676i	−0.961859	+	0.273545i	$0.911804\pi$
$740$		0			0
$741$	6.88843	+	31.3314i	0.253053	+	1.15099i
$742$		0			0
$743$	22.6116	−	39.1644i	0.829538	−	1.43680i	−0.0688624	−	0.997626i	$-0.521937\pi$
$743$	22.6116	−	39.1644i	0.829538	−	1.43680i	0.898401	−	0.439176i	$-0.144730\pi$
$744$		0			0
$745$	−14.8608	+	25.7397i	−0.544459	+	0.943031i
$746$		0			0
$747$	4.37096	−	48.0216i	0.159925	−	1.75702i
$748$		0			0
$749$	−17.7940	+	2.72981i	−0.650178	+	0.0997449i
$750$		0			0
$751$	14.1898	+	24.5775i	0.517795	+	0.896847i	0.999786	+	0.0206709i	$0.00658022\pi$
$751$	14.1898	+	24.5775i	0.517795	+	0.896847i	−0.481992	+	0.876176i	$0.660086\pi$
$752$		0			0
$753$	3.50650	+	1.11235i	0.127784	+	0.0405364i
$754$		0			0
$755$	−25.6435			−0.933263
$756$		0			0
$757$	5.08483			0.184811			0.0924056	−	0.995721i	$-0.470544\pi$
$757$	5.08483			0.184811			0.0924056	+	0.995721i	$0.470544\pi$
$758$		0			0
$759$	0.818338	+	0.259598i	0.0297038	+	0.00942282i
$760$		0			0
$761$	−18.8612	−	32.6686i	−0.683720	−	1.18424i	−0.973837	−	0.227246i	$-0.927028\pi$
$761$	−18.8612	−	32.6686i	−0.683720	−	1.18424i	0.290118	−	0.956991i	$-0.406306\pi$
$762$		0			0
$763$	−16.0848	+	41.3020i	−0.582310	+	1.49523i
$764$		0			0
$765$	−14.9149	+	6.89140i	−0.539249	+	0.249159i
$766$		0			0
$767$	11.8614	−	20.5446i	0.428292	−	0.741823i
$768$		0			0
$769$	11.8729	−	20.5644i	0.428147	−	0.741572i	−0.568562	−	0.822641i	$-0.692500\pi$
$769$	11.8729	−	20.5644i	0.428147	−	0.741572i	0.996709	+	0.0810688i	$0.0258333\pi$
$770$		0			0
$771$	−4.74683	−	21.5905i	−0.170953	−	0.777563i
$772$		0			0
$773$	19.5347	+	33.8351i	0.702614	+	1.21696i	0.967546	+	0.252696i	$0.0813172\pi$
$773$	19.5347	+	33.8351i	0.702614	+	1.21696i	−0.264932	+	0.964267i	$0.585350\pi$
$774$		0			0
$775$	−0.626657	+	1.08540i	−0.0225102	+	0.0389888i
$776$		0			0
$777$	−24.6437	−	3.84965i	−0.884088	−	0.138105i
$778$		0			0
$779$	−19.8504	−	34.3819i	−0.711214	−	1.23186i
$780$		0			0
$781$	−5.27011	+	9.12810i	−0.188579	+	0.326629i
$782$		0			0
$783$	−12.8834	+	30.6467i	−0.460415	+	1.09522i
$784$		0			0
$785$	11.4697	+	19.8661i	0.409370	+	0.709050i
$786$		0			0
$787$	3.80915			0.135782			0.0678908	−	0.997693i	$-0.478373\pi$
$787$	3.80915			0.135782			0.0678908	+	0.997693i	$0.478373\pi$
$788$		0			0
$789$	−14.1573	+	12.9273i	−0.504015	+	0.460223i
$790$		0			0
$791$	35.4173	−	5.43342i	1.25929	−	0.193190i
$792$		0			0
$793$	20.0140	−	34.6653i	0.710718	−	1.23100i
$794$		0			0
$795$	2.00780	−	1.83335i	0.0712094	−	0.0650223i
$796$		0			0
$797$	−10.8239	+	18.7476i	−0.383404	+	0.664075i	−0.991546	−	0.129753i	$-0.958582\pi$
$797$	−10.8239	+	18.7476i	−0.383404	+	0.664075i	0.608143	+	0.793828i	$0.291915\pi$
$798$		0			0
$799$	0.691743	+	1.19813i	0.0244721	+	0.0423870i
$800$		0			0
$801$	−32.8858	+	15.1948i	−1.16196	+	0.536884i
$802$		0			0
$803$	−16.9900			−0.599564
$804$		0			0
$805$	1.75248	−	0.268851i	0.0617667	−	0.00947574i
$806$		0			0
$807$	1.32016	+	6.00464i	0.0464720	+	0.211374i
$808$		0			0
$809$	−18.5128	−	32.0652i	−0.650877	−	1.12735i	−0.982910	−	0.184084i	$-0.941068\pi$
$809$	−18.5128	−	32.0652i	−0.650877	−	1.12735i	0.332034	−	0.943268i	$-0.392265\pi$
$810$		0			0
$811$	5.37416			0.188712			0.0943561	−	0.995539i	$-0.469921\pi$
$811$	5.37416			0.188712			0.0943561	+	0.995539i	$0.469921\pi$
$812$		0			0
$813$	1.75912	−	1.60627i	0.0616950	−	0.0563345i
$814$		0			0
$815$	13.6243			0.477239
$816$		0			0
$817$	23.2696			0.814101
$818$		0			0
$819$	27.8557	+	13.8756i	0.973358	+	0.484851i
$820$		0			0
$821$	2.22239			0.0775619			0.0387809	−	0.999248i	$-0.487653\pi$
$821$	2.22239			0.0775619			0.0387809	+	0.999248i	$0.487653\pi$
$822$		0			0
$823$	37.1073			1.29348			0.646740	−	0.762710i	$-0.276132\pi$
$823$	37.1073			1.29348			0.646740	+	0.762710i	$0.276132\pi$
$824$		0			0
$825$	−1.00339	−	4.56382i	−0.0349335	−	0.158892i
$826$		0			0
$827$	19.4790			0.677351			0.338676	−	0.940903i	$-0.390021\pi$
$827$	19.4790			0.677351			0.338676	+	0.940903i	$0.390021\pi$
$828$		0			0
$829$	0.137129	+	0.237514i	0.00476267	+	0.00824919i	0.868397	−	0.495870i	$-0.165151\pi$
$829$	0.137129	+	0.237514i	0.00476267	+	0.00824919i	−0.863634	+	0.504119i	$0.831817\pi$
$830$		0			0
$831$	−37.2993	+	34.0585i	−1.29390	+	1.18147i
$832$		0			0
$833$	21.7292	−	6.82772i	0.752873	−	0.236566i
$834$		0			0
$835$	6.99314			0.242007
$836$		0			0
$837$	1.81694	+	2.39384i	0.0628027	+	0.0827430i
$838$		0			0
$839$	21.0711	+	36.4962i	0.727455	+	1.25999i	0.957956	+	0.286917i	$0.0926303\pi$
$839$	21.0711	+	36.4962i	0.727455	+	1.25999i	−0.230501	+	0.973072i	$0.574036\pi$
$840$		0			0
$841$	−5.96666	+	10.3346i	−0.205747	+	0.356364i
$842$		0			0
$843$	−4.68325	−	21.3013i	−0.161300	−	0.733657i
$844$		0			0
$845$	−1.99671	+	3.45840i	−0.0686888	+	0.118973i
$846$		0			0
$847$	−9.07328	+	23.2980i	−0.311762	+	0.800528i
$848$		0			0
$849$	15.6191	+	4.95479i	0.536047	+	0.170048i
$850$		0			0
$851$	2.16702			0.0742844
$852$		0			0
$853$	22.3086	+	38.6397i	0.763833	+	1.32300i	0.940862	+	0.338791i	$0.110018\pi$
$853$	22.3086	+	38.6397i	0.763833	+	1.32300i	−0.177029	+	0.984206i	$0.556649\pi$
$854$		0			0
$855$	−19.4911	−	13.7499i	−0.666582	−	0.470235i
$856$		0			0
$857$	3.66614	−	6.34993i	0.125233	−	0.216910i	−0.796591	−	0.604518i	$-0.793366\pi$
$857$	3.66614	−	6.34993i	0.125233	−	0.216910i	0.921824	+	0.387609i	$0.126699\pi$
$858$		0			0
$859$	1.35073	+	2.33953i	0.0460863	+	0.0798238i	0.888148	−	0.459557i	$-0.151992\pi$
$859$	1.35073	+	2.33953i	0.0460863	+	0.0798238i	−0.842062	+	0.539381i	$0.818658\pi$
$860$		0			0
$861$	−38.0520	−	5.94419i	−1.29681	−	0.202577i
$862$		0			0
$863$	7.40188	−	12.8204i	0.251963	−	0.436413i	−0.712103	−	0.702075i	$-0.752257\pi$
$863$	7.40188	−	12.8204i	0.251963	−	0.436413i	0.964066	+	0.265662i	$0.0855905\pi$
$864$		0			0
$865$	−11.6429	−	20.1661i	−0.395870	−	0.685668i
$866$		0			0
$867$	−8.20219	+	7.48953i	−0.278561	+	0.254358i
$868$		0			0
$869$	3.44449	−	5.96603i	0.116846	−	0.202384i
$870$		0			0
$871$	−18.4660	+	31.9840i	−0.625695	+	1.08374i
$872$		0			0
$873$	3.18737	−	35.0180i	0.107876	−	1.18518i
$874$		0			0
$875$	−19.9648	−	24.9007i	−0.674934	−	0.841797i
$876$		0			0
$877$	5.54807	+	9.60954i	0.187345	+	0.324491i	0.944364	−	0.328902i	$-0.106678\pi$
$877$	5.54807	+	9.60954i	0.187345	+	0.324491i	−0.757019	+	0.653393i	$0.773345\pi$
$878$		0			0
$879$	21.3020	−	19.4511i	0.718497	−	0.656069i
$880$		0			0
$881$	15.0536			0.507168			0.253584	−	0.967313i	$-0.418391\pi$
$881$	15.0536			0.507168			0.253584	+	0.967313i	$0.418391\pi$
$882$		0			0
$883$	2.39418			0.0805704			0.0402852	−	0.999188i	$-0.487173\pi$
$883$	2.39418			0.0805704			0.0402852	+	0.999188i	$0.487173\pi$
$884$		0			0
$885$	3.78764	+	17.2277i	0.127320	+	0.579104i
$886$		0			0
$887$	2.46697	+	4.27292i	0.0828328	+	0.143471i	0.904466	−	0.426546i	$-0.140270\pi$
$887$	2.46697	+	4.27292i	0.0828328	+	0.143471i	−0.821633	+	0.570017i	$0.806937\pi$
$888$		0			0
$889$	17.5274	+	21.8607i	0.587850	+	0.733184i
$890$		0			0
$891$	−11.0207	−	2.02298i	−0.369207	−	0.0677725i
$892$		0			0
$893$	−1.00427	+	1.73944i	−0.0336065	+	0.0582081i
$894$		0			0
$895$	−7.93047	+	13.7360i	−0.265086	+	0.459143i
$896$		0			0
$897$	−2.57717	−	0.817547i	−0.0860493	−	0.0272971i
$898$		0			0
$899$	1.85017	+	3.20459i	0.0617067	+	0.106879i
$900$		0			0
$901$	−1.51730	+	2.62804i	−0.0505486	+	0.0875527i
$902$		0			0
$903$	14.1689	−	17.5731i	0.471510	−	0.584797i
$904$		0			0
$905$	−1.11200	−	1.92604i	−0.0369642	−	0.0640238i
$906$		0			0
$907$	1.69815	−	2.94129i	0.0563863	−	0.0976639i	−0.836454	−	0.548036i	$-0.815376\pi$
$907$	1.69815	−	2.94129i	0.0563863	−	0.0976639i	0.892841	+	0.450373i	$0.148709\pi$
$908$		0			0
$909$	−14.7226	+	6.80253i	−0.488316	+	0.225626i
$910$		0			0
$911$	4.65142	+	8.05649i	0.154108	+	0.266924i	0.932734	−	0.360565i	$-0.117416\pi$
$911$	4.65142	+	8.05649i	0.154108	+	0.266924i	−0.778626	+	0.627489i	$0.784083\pi$
$912$		0			0
$913$	20.0110			0.662268
$914$		0			0
$915$	6.39095	+	29.0687i	0.211278	+	0.960980i
$916$		0			0
$917$	−21.4722	+	55.1355i	−0.709076	+	1.82073i
$918$		0			0
$919$	8.92656	−	15.4613i	0.294460	−	0.510020i	−0.680399	−	0.732842i	$-0.738194\pi$
$919$	8.92656	−	15.4613i	0.294460	−	0.510020i	0.974859	+	0.222822i	$0.0715268\pi$
$920$		0			0
$921$	15.7827	+	5.00669i	0.520058	+	0.164976i
$922$		0			0
$923$	16.5970	−	28.7469i	0.546298	−	0.946216i
$924$		0			0
$925$	−5.89737	−	10.2145i	−0.193904	−	0.335852i
$926$		0			0
$927$	3.97584	−	43.6805i	0.130584	−	1.43466i
$928$		0			0
$929$	−47.2861			−1.55141			−0.775703	−	0.631098i	$-0.782605\pi$
$929$	−47.2861			−1.55141			−0.775703	+	0.631098i	$0.782605\pi$
$930$		0			0
$931$	24.3575	+	22.3637i	0.798286	+	0.732939i
$932$		0			0
$933$	−43.5364	−	13.8109i	−1.42532	−	0.452148i
$934$		0			0
$935$	−3.40917	−	5.90486i	−0.111492	−	0.193110i
$936$		0			0
$937$	21.2493			0.694183			0.347092	−	0.937831i	$-0.387169\pi$
$937$	21.2493			0.694183			0.347092	+	0.937831i	$0.387169\pi$
$938$		0			0
$939$	20.9703	+	6.65234i	0.684341	+	0.217091i
$940$		0			0
$941$	−60.0810			−1.95858			−0.979292	−	0.202455i	$-0.935108\pi$
$941$	−60.0810			−1.95858			−0.979292	+	0.202455i	$0.935108\pi$
$942$		0			0
$943$	3.34606			0.108963
$944$		0			0
$945$	−22.2520	+	6.34733i	−0.723857	+	0.206479i
$946$		0			0
$947$	3.66935			0.119238			0.0596189	−	0.998221i	$-0.481011\pi$
$947$	3.66935			0.119238			0.0596189	+	0.998221i	$0.481011\pi$
$948$		0			0
$949$	53.5062			1.73688
$950$		0			0
$951$	−0.0547357	−	0.0173636i	−0.00177493	−	0.000563053i
$952$		0			0
$953$	0.837421			0.0271267			0.0135634	−	0.999908i	$-0.495683\pi$
$953$	0.837421			0.0271267			0.0135634	+	0.999908i	$0.495683\pi$
$954$		0			0
$955$	−13.7055	−	23.7385i	−0.443498	−	0.768161i
$956$		0			0
$957$	−13.1504	−	4.17166i	−0.425094	−	0.134851i
$958$		0			0
$959$	−46.9525	+	7.20306i	−1.51618	+	0.232599i
$960$		0			0
$961$	−30.6655			−0.989209
$962$		0			0
$963$	−18.5302	+	8.56183i	−0.597126	+	0.275901i
$964$		0			0
$965$	−2.15574	−	3.73386i	−0.0693958	−	0.120197i
$966$		0			0
$967$	21.8856	−	37.9070i	0.703795	−	1.21901i	−0.263330	−	0.964706i	$-0.584821\pi$
$967$	21.8856	−	37.9070i	0.703795	−	1.21901i	0.967125	−	0.254302i	$-0.0818458\pi$
$968$		0			0
$969$	25.3763	+	8.05001i	0.815203	+	0.258604i
$970$		0			0
$971$	−20.3059	+	35.1709i	−0.651648	+	1.12869i	0.331075	+	0.943605i	$0.392589\pi$
$971$	−20.3059	+	35.1709i	−0.651648	+	1.12869i	−0.982723	+	0.185083i	$0.940745\pi$
$972$		0			0
$973$	2.98560	−	0.458025i	0.0957138	−	0.0146836i
$974$		0			0
$975$	3.15995	+	14.3727i	0.101199	+	0.460296i
$976$		0			0
$977$	57.4959			1.83946			0.919728	−	0.392556i	$-0.128409\pi$
$977$	57.4959			1.83946			0.919728	+	0.392556i	$0.128409\pi$
$978$		0			0
$979$	−7.51689	−	13.0196i	−0.240241	−	0.416109i
$980$		0			0
$981$	−4.55571	+	50.0513i	−0.145452	+	1.59801i
$982$		0			0
$983$	6.72971	−	11.6562i	0.214644	−	0.371775i	−0.738518	−	0.674234i	$-0.764474\pi$
$983$	6.72971	−	11.6562i	0.214644	−	0.371775i	0.953162	+	0.302459i	$0.0978075\pi$
$984$		0			0
$985$	−18.2551	−	31.6188i	−0.581657	−	1.00746i
$986$		0			0
$987$	0.702121	+	1.81756i	0.0223488	+	0.0578537i
$988$		0			0
$989$	−0.980604	+	1.69846i	−0.0311814	+	0.0540078i
$990$		0			0
$991$	−17.7821	−	30.7995i	−0.564867	−	0.978379i	−0.997062	−	0.0765983i	$-0.975594\pi$
$991$	−17.7821	−	30.7995i	−0.564867	−	0.978379i	0.432195	−	0.901780i	$-0.357739\pi$
$992$		0			0
$993$	8.01362	+	2.54213i	0.254304	+	0.0806720i
$994$		0			0
$995$	−9.42036	+	16.3165i	−0.298645	+	0.517269i
$996$		0			0
$997$	−16.3644	+	28.3440i	−0.518267	+	0.897665i	0.481508	+	0.876442i	$0.340089\pi$
$997$	−16.3644	+	28.3440i	−0.518267	+	0.897665i	−0.999775	+	0.0212228i	$0.993244\pi$
$998$		0			0
$999$	−28.0593	+	3.54413i	−0.887757	+	0.112131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.121.1	yes	22
3.2	odd	2		1512.2.q.c.793.8		22
4.3	odd	2		1008.2.q.k.625.11		22
7.4	even	3		504.2.t.d.193.6	yes	22
9.2	odd	6		1512.2.t.d.289.4		22
9.7	even	3		504.2.t.d.457.6	yes	22
12.11	even	2		3024.2.q.k.2305.8		22
21.11	odd	6		1512.2.t.d.361.4		22
28.11	odd	6		1008.2.t.k.193.6		22
36.7	odd	6		1008.2.t.k.961.6		22
36.11	even	6		3024.2.t.l.289.4		22
63.11	odd	6		1512.2.q.c.1369.8		22
63.25	even	3	inner	504.2.q.d.25.1	✓	22
84.11	even	6		3024.2.t.l.1873.4		22
252.11	even	6		3024.2.q.k.2881.8		22
252.151	odd	6		1008.2.q.k.529.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.1	✓	22	63.25	even	3	inner
504.2.q.d.121.1	yes	22	1.1	even	1	trivial
504.2.t.d.193.6	yes	22	7.4	even	3
504.2.t.d.457.6	yes	22	9.7	even	3
1008.2.q.k.529.11		22	252.151	odd	6
1008.2.q.k.625.11		22	4.3	odd	2
1008.2.t.k.193.6		22	28.11	odd	6
1008.2.t.k.961.6		22	36.7	odd	6
1512.2.q.c.793.8		22	3.2	odd	2
1512.2.q.c.1369.8		22	63.11	odd	6
1512.2.t.d.289.4		22	9.2	odd	6
1512.2.t.d.361.4		22	21.11	odd	6
3024.2.q.k.2305.8		22	12.11	even	2
3024.2.q.k.2881.8		22	252.11	even	6
3024.2.t.l.289.4		22	36.11	even	6
3024.2.t.l.1873.4		22	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65097 - 0.523731i) q^{3} +(-0.841578 - 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +(2.45141 + 1.72933i) q^{9} +O(q^{10})\)	\(q+(-1.65097 - 0.523731i) q^{3} +(-0.841578 - 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +(2.45141 + 1.72933i) q^{9} +(-0.622490 + 1.07818i) q^{11} +(1.96039 - 3.39550i) q^{13} +(0.626001 + 2.84731i) q^{15} +(-1.62691 - 2.81788i) q^{17} +(2.36192 - 4.09097i) q^{19} +(-1.65131 - 4.27471i) q^{21} +(0.199068 + 0.344795i) q^{23} +(1.08349 - 1.87667i) q^{25} +(-3.14150 - 4.13895i) q^{27} +(-3.19896 - 5.54076i) q^{29} -0.578367 q^{31} +(1.59239 - 1.45403i) q^{33} +(1.61605 - 4.14963i) q^{35} +(2.72146 - 4.71371i) q^{37} +(-5.01488 + 4.57916i) q^{39} +(4.20216 - 7.27836i) q^{41} +(2.46299 + 4.26603i) q^{43} +(0.457714 - 5.02868i) q^{45} -0.425190 q^{47} +(-1.52179 + 6.83258i) q^{49} +(1.21016 + 5.50430i) q^{51} +(-0.466315 - 0.807681i) q^{53} +2.09550 q^{55} +(-6.04204 + 5.51707i) q^{57} +6.05054 q^{59} +10.2092 q^{61} +(0.487470 + 7.92227i) q^{63} -6.59930 q^{65} -9.41952 q^{67} +(-0.148075 - 0.673505i) q^{69} +8.46617 q^{71} +(6.82340 + 11.8185i) q^{73} +(-2.77168 + 2.53086i) q^{75} +(-3.25582 + 0.499480i) q^{77} -5.53340 q^{79} +(3.01883 + 8.47860i) q^{81} +(-8.03669 - 13.9199i) q^{83} +(-2.73833 + 4.74293i) q^{85} +(2.37952 + 10.8230i) q^{87} +(-6.03776 + 10.4577i) q^{89} +(10.2535 - 1.57300i) q^{91} +(0.954867 + 0.302909i) q^{93} -7.95097 q^{95} +(-5.86046 - 10.1506i) q^{97} +(-3.39052 + 1.56658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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