LMFDB - Embedded newform 264.2.q.d.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [264,2,Mod(25,264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(264, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

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

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

chi := DirichletCharacter("264.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.q (of order $5$, degree $4$, 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:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	264.25
Dual form			264.2.q.d.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{5} +(0.690983 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{5} +(0.690983 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.80902 - 1.76336i) q^{11} +(0.190983 - 0.138757i) q^{13} +(0.500000 - 1.53884i) q^{15} +(2.11803 + 1.53884i) q^{17} +(-1.11803 - 3.44095i) q^{19} -2.23607 q^{21} +3.47214 q^{23} +(-0.736068 - 2.26538i) q^{25} +(0.809017 + 0.587785i) q^{27} +(0.618034 - 1.90211i) q^{29} +(-2.50000 + 1.81636i) q^{31} +(-2.54508 - 2.12663i) q^{33} +(2.92705 - 2.12663i) q^{35} +(-2.07295 + 6.37988i) q^{37} +(-0.190983 - 0.138757i) q^{39} +(2.54508 + 7.83297i) q^{41} -11.9443 q^{43} -1.61803 q^{45} +(2.28115 + 7.02067i) q^{47} +(1.61803 + 1.17557i) q^{49} +(0.809017 - 2.48990i) q^{51} +(-9.35410 + 6.79615i) q^{53} +(5.35410 + 0.363271i) q^{55} +(-2.92705 + 2.12663i) q^{57} +(-0.881966 + 2.71441i) q^{59} +(3.54508 + 2.57565i) q^{61} +(0.690983 + 2.12663i) q^{63} +0.381966 q^{65} -14.0902 q^{67} +(-1.07295 - 3.30220i) q^{69} +(7.16312 + 5.20431i) q^{71} +(4.09017 - 12.5882i) q^{73} +(-1.92705 + 1.40008i) q^{75} +(-1.80902 - 7.19218i) q^{77} +(1.42705 - 1.03681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-7.42705 - 5.39607i) q^{83} +(1.30902 + 4.02874i) q^{85} -2.00000 q^{87} -12.2361 q^{89} +(-0.163119 - 0.502029i) q^{91} +(2.50000 + 1.81636i) q^{93} +(1.80902 - 5.56758i) q^{95} +(4.78115 - 3.47371i) q^{97} +(-1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9}+O(q^{10}) $ 4 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9	$ 4 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9} + 9 q^{11} + 3 q^{13} + 2 q^{15} + 4 q^{17} - 4 q^{23} + 6 q^{25} + q^{27} - 2 q^{29} - 10 q^{31} + q^{33} + 5 q^{35} - 15 q^{37} - 3 q^{39} - q^{41} - 12 q^{43} - 2 q^{45} - 11 q^{47} + 2 q^{49} + q^{51} - 24 q^{53} + 8 q^{55} - 5 q^{57} - 8 q^{59} + 3 q^{61} + 5 q^{63} + 6 q^{65} - 34 q^{67} - 11 q^{69} + 13 q^{71} - 6 q^{73} - q^{75} - 5 q^{77} - q^{79} - q^{81} - 23 q^{83} + 3 q^{85} - 8 q^{87} - 40 q^{89} + 15 q^{91} + 10 q^{93} + 5 q^{95} - q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9 + 9 * q^11 + 3 * q^13 + 2 * q^15 + 4 * q^17 - 4 * q^23 + 6 * q^25 + q^27 - 2 * q^29 - 10 * q^31 + q^33 + 5 * q^35 - 15 * q^37 - 3 * q^39 - q^41 - 12 * q^43 - 2 * q^45 - 11 * q^47 + 2 * q^49 + q^51 - 24 * q^53 + 8 * q^55 - 5 * q^57 - 8 * q^59 + 3 * q^61 + 5 * q^63 + 6 * q^65 - 34 * q^67 - 11 * q^69 + 13 * q^71 - 6 * q^73 - q^75 - 5 * q^77 - q^79 - q^81 - 23 * q^83 + 3 * q^85 - 8 * q^87 - 40 * q^89 + 15 * q^91 + 10 * q^93 + 5 * q^95 - q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	0.840670	−	0.541547i	$-0.182161\pi$
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	−0.255260	+	0.966872i	$0.582161\pi$
$6$		0			0
$7$	0.690983	−	2.12663i	0.261167	−	0.803789i	−0.731385	−	0.681965i	$-0.761126\pi$
$7$	0.690983	−	2.12663i	0.261167	−	0.803789i	0.992552	−	0.121824i	$-0.0388744\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	2.80902	−	1.76336i	0.846950	−	0.531672i
$11$	2.80902	−	1.76336i	0.846950	−	0.531672i
$12$		0			0
$13$	0.190983	−	0.138757i	0.0529692	−	0.0384843i	−0.560986	−	0.827826i	$-0.689578\pi$
$13$	0.190983	−	0.138757i	0.0529692	−	0.0384843i	0.613955	+	0.789341i	$0.289578\pi$
$14$		0			0
$15$	0.500000	−	1.53884i	0.129099	−	0.397327i
$16$		0			0
$17$	2.11803	+	1.53884i	0.513699	+	0.373224i	0.814225	−	0.580550i	$-0.197162\pi$
$17$	2.11803	+	1.53884i	0.513699	+	0.373224i	−0.300526	+	0.953774i	$0.597162\pi$
$18$		0			0
$19$	−1.11803	−	3.44095i	−0.256495	−	0.789409i	−0.993532	−	0.113557i	$-0.963776\pi$
$19$	−1.11803	−	3.44095i	−0.256495	−	0.789409i	0.737037	−	0.675852i	$-0.236224\pi$
$20$		0			0
$21$	−2.23607			−0.487950
$22$		0			0
$23$	3.47214			0.723990			0.361995	−	0.932180i	$-0.382096\pi$
$23$	3.47214			0.723990			0.361995	+	0.932180i	$0.382096\pi$
$24$		0			0
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	0.618034	−	1.90211i	0.114766	−	0.353214i	−0.877132	−	0.480249i	$-0.840546\pi$
$29$	0.618034	−	1.90211i	0.114766	−	0.353214i	0.991898	+	0.127036i	$0.0405463\pi$
$30$		0			0
$31$	−2.50000	+	1.81636i	−0.449013	+	0.326227i	−0.789206	−	0.614128i	$-0.789508\pi$
$31$	−2.50000	+	1.81636i	−0.449013	+	0.326227i	0.340193	+	0.940356i	$0.389508\pi$
$32$		0			0
$33$	−2.54508	−	2.12663i	−0.443042	−	0.370198i
$34$		0			0
$35$	2.92705	−	2.12663i	0.494762	−	0.359466i
$36$		0			0
$37$	−2.07295	+	6.37988i	−0.340791	+	1.04885i	0.623008	+	0.782215i	$0.285910\pi$
$37$	−2.07295	+	6.37988i	−0.340791	+	1.04885i	−0.963799	+	0.266631i	$0.914090\pi$
$38$		0			0
$39$	−0.190983	−	0.138757i	−0.0305818	−	0.0222189i
$40$		0			0
$41$	2.54508	+	7.83297i	0.397475	+	1.22330i	0.927017	+	0.375020i	$0.122364\pi$
$41$	2.54508	+	7.83297i	0.397475	+	1.22330i	−0.529541	+	0.848284i	$0.677636\pi$
$42$		0			0
$43$	−11.9443			−1.82148			−0.910742	−	0.412975i	$-0.864490\pi$
$43$	−11.9443			−1.82148			−0.910742	+	0.412975i	$0.864490\pi$
$44$		0			0
$45$	−1.61803			−0.241202
$46$		0			0
$47$	2.28115	+	7.02067i	0.332740	+	1.02407i	0.967824	+	0.251626i	$0.0809654\pi$
$47$	2.28115	+	7.02067i	0.332740	+	1.02407i	−0.635084	+	0.772443i	$0.719035\pi$
$48$		0			0
$49$	1.61803	+	1.17557i	0.231148	+	0.167939i
$50$		0			0
$51$	0.809017	−	2.48990i	0.113285	−	0.348655i
$52$		0			0
$53$	−9.35410	+	6.79615i	−1.28488	+	0.933523i	−0.999689	−	0.0249458i	$-0.992059\pi$
$53$	−9.35410	+	6.79615i	−1.28488	+	0.933523i	−0.285196	+	0.958469i	$0.592059\pi$
$54$		0			0
$55$	5.35410	+	0.363271i	0.721947	+	0.0489835i
$56$		0			0
$57$	−2.92705	+	2.12663i	−0.387697	+	0.281679i
$58$		0			0
$59$	−0.881966	+	2.71441i	−0.114822	+	0.353386i	−0.991910	−	0.126944i	$-0.959483\pi$
$59$	−0.881966	+	2.71441i	−0.114822	+	0.353386i	0.877088	+	0.480330i	$0.159483\pi$
$60$		0			0
$61$	3.54508	+	2.57565i	0.453902	+	0.329779i	0.791134	−	0.611643i	$-0.209491\pi$
$61$	3.54508	+	2.57565i	0.453902	+	0.329779i	−0.337233	+	0.941421i	$0.609491\pi$
$62$		0			0
$63$	0.690983	+	2.12663i	0.0870557	+	0.267930i
$64$		0			0
$65$	0.381966			0.0473771
$66$		0			0
$67$	−14.0902			−1.72139			−0.860694	−	0.509122i	$-0.829970\pi$
$67$	−14.0902			−1.72139			−0.860694	+	0.509122i	$0.829970\pi$
$68$		0			0
$69$	−1.07295	−	3.30220i	−0.129168	−	0.397538i
$70$		0			0
$71$	7.16312	+	5.20431i	0.850106	+	0.617638i	0.925175	−	0.379540i	$-0.123918\pi$
$71$	7.16312	+	5.20431i	0.850106	+	0.617638i	−0.0750694	+	0.997178i	$0.523918\pi$
$72$		0			0
$73$	4.09017	−	12.5882i	0.478718	−	1.47334i	−0.362159	−	0.932116i	$-0.617960\pi$
$73$	4.09017	−	12.5882i	0.478718	−	1.47334i	0.840877	−	0.541227i	$-0.182040\pi$
$74$		0			0
$75$	−1.92705	+	1.40008i	−0.222517	+	0.161668i
$76$		0			0
$77$	−1.80902	−	7.19218i	−0.206157	−	0.819625i
$78$		0			0
$79$	1.42705	−	1.03681i	0.160556	−	0.116651i	−0.504606	−	0.863349i	$-0.668362\pi$
$79$	1.42705	−	1.03681i	0.160556	−	0.116651i	0.665162	+	0.746699i	$0.268362\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−7.42705	−	5.39607i	−0.815225	−	0.592295i	0.100116	−	0.994976i	$-0.468079\pi$
$83$	−7.42705	−	5.39607i	−0.815225	−	0.592295i	−0.915341	+	0.402680i	$0.868079\pi$
$84$		0			0
$85$	1.30902	+	4.02874i	0.141983	+	0.436978i
$86$		0			0
$87$	−2.00000			−0.214423
$88$		0			0
$89$	−12.2361			−1.29702			−0.648510	−	0.761206i	$-0.724608\pi$
$89$	−12.2361			−1.29702			−0.648510	+	0.761206i	$0.724608\pi$
$90$		0			0
$91$	−0.163119	−	0.502029i	−0.0170995	−	0.0526269i
$92$		0			0
$93$	2.50000	+	1.81636i	0.259238	+	0.188347i
$94$		0			0
$95$	1.80902	−	5.56758i	0.185601	−	0.571222i
$96$		0			0
$97$	4.78115	−	3.47371i	0.485453	−	0.352702i	−0.317980	−	0.948097i	$-0.603005\pi$
$97$	4.78115	−	3.47371i	0.485453	−	0.352702i	0.803433	+	0.595395i	$0.203005\pi$
$98$		0			0
$99$	−1.23607	+	3.07768i	−0.124230	+	0.309319i
$100$		0			0
$101$	10.2812	−	7.46969i	1.02301	−	0.743262i	0.0561146	−	0.998424i	$-0.482129\pi$
$101$	10.2812	−	7.46969i	1.02301	−	0.743262i	0.966898	+	0.255162i	$0.0821288\pi$
$102$		0			0
$103$	−5.09017	+	15.6659i	−0.501549	+	1.54361i	0.304946	+	0.952370i	$0.401362\pi$
$103$	−5.09017	+	15.6659i	−0.501549	+	1.54361i	−0.806495	+	0.591241i	$0.798638\pi$
$104$		0			0
$105$	−2.92705	−	2.12663i	−0.285651	−	0.207538i
$106$		0			0
$107$	1.60081	+	4.92680i	0.154756	+	0.476291i	0.998136	−	0.0610267i	$-0.0194375\pi$
$107$	1.60081	+	4.92680i	0.154756	+	0.476291i	−0.843380	+	0.537318i	$0.819437\pi$
$108$		0			0
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	6.70820			0.636715
$112$		0			0
$113$	−0.635255	−	1.95511i	−0.0597598	−	0.183922i	0.916720	−	0.399530i	$-0.130827\pi$
$113$	−0.635255	−	1.95511i	−0.0597598	−	0.183922i	−0.976480	+	0.215608i	$0.930827\pi$
$114$		0			0
$115$	4.54508	+	3.30220i	0.423831	+	0.307932i
$116$		0			0
$117$	−0.0729490	+	0.224514i	−0.00674414	+	0.0207563i
$118$		0			0
$119$	4.73607	−	3.44095i	0.434155	−	0.315432i
$120$		0			0
$121$	4.78115	−	9.90659i	0.434650	−	0.900599i
$122$		0			0
$123$	6.66312	−	4.84104i	0.600793	−	0.436502i
$124$		0			0
$125$	3.69098	−	11.3597i	0.330132	−	1.01604i
$126$		0			0
$127$	10.3262	+	7.50245i	0.916305	+	0.665735i	0.942602	−	0.333919i	$-0.108371\pi$
$127$	10.3262	+	7.50245i	0.916305	+	0.665735i	−0.0262962	+	0.999654i	$0.508371\pi$
$128$		0			0
$129$	3.69098	+	11.3597i	0.324973	+	1.00016i
$130$		0			0
$131$	−17.2705			−1.50893			−0.754466	−	0.656339i	$-0.772104\pi$
$131$	−17.2705			−1.50893			−0.754466	+	0.656339i	$0.772104\pi$
$132$		0			0
$133$	−8.09017			−0.701507
$134$		0			0
$135$	0.500000	+	1.53884i	0.0430331	+	0.132442i
$136$		0			0
$137$	5.80902	+	4.22050i	0.496298	+	0.360581i	0.807601	−	0.589729i	$-0.200765\pi$
$137$	5.80902	+	4.22050i	0.496298	+	0.360581i	−0.311303	+	0.950311i	$0.600765\pi$
$138$		0			0
$139$	0.718847	−	2.21238i	0.0609718	−	0.187652i	−0.915931	−	0.401336i	$-0.868546\pi$
$139$	0.718847	−	2.21238i	0.0609718	−	0.187652i	0.976903	+	0.213684i	$0.0685461\pi$
$140$		0			0
$141$	5.97214	−	4.33901i	0.502945	−	0.365411i
$142$		0			0
$143$	0.291796	−	0.726543i	0.0244012	−	0.0607565i
$144$		0			0
$145$	2.61803	−	1.90211i	0.217416	−	0.157962i
$146$		0			0
$147$	0.618034	−	1.90211i	0.0509746	−	0.156884i
$148$		0			0
$149$	−5.04508	−	3.66547i	−0.413309	−	0.300287i	0.361631	−	0.932321i	$-0.382220\pi$
$149$	−5.04508	−	3.66547i	−0.413309	−	0.300287i	−0.774940	+	0.632034i	$0.782220\pi$
$150$		0			0
$151$	−2.90983	−	8.95554i	−0.236799	−	0.728791i	−0.996878	−	0.0789607i	$-0.974840\pi$
$151$	−2.90983	−	8.95554i	−0.236799	−	0.728791i	0.760079	−	0.649831i	$-0.225160\pi$
$152$		0			0
$153$	−2.61803			−0.211656
$154$		0			0
$155$	−5.00000			−0.401610
$156$		0			0
$157$	−4.70820	−	14.4904i	−0.375756	−	1.15646i	−0.942967	−	0.332885i	$-0.891978\pi$
$157$	−4.70820	−	14.4904i	−0.375756	−	1.15646i	0.567212	−	0.823572i	$-0.308022\pi$
$158$		0			0
$159$	9.35410	+	6.79615i	0.741829	+	0.538970i
$160$		0			0
$161$	2.39919	−	7.38394i	0.189082	−	0.581936i
$162$		0			0
$163$	9.97214	−	7.24518i	0.781078	−	0.567486i	−0.124224	−	0.992254i	$-0.539644\pi$
$163$	9.97214	−	7.24518i	0.781078	−	0.567486i	0.905302	+	0.424768i	$0.139644\pi$
$164$		0			0
$165$	−1.30902	−	5.20431i	−0.101907	−	0.405155i
$166$		0			0
$167$	8.16312	−	5.93085i	0.631681	−	0.458943i	−0.225301	−	0.974289i	$-0.572337\pi$
$167$	8.16312	−	5.93085i	0.631681	−	0.458943i	0.856982	+	0.515346i	$0.172337\pi$
$168$		0			0
$169$	−4.00000	+	12.3107i	−0.307692	+	0.946980i
$170$		0			0
$171$	2.92705	+	2.12663i	0.223837	+	0.162627i
$172$		0			0
$173$	−2.06231	−	6.34712i	−0.156794	−	0.482563i	0.841544	−	0.540188i	$-0.181647\pi$
$173$	−2.06231	−	6.34712i	−0.156794	−	0.482563i	−0.998338	+	0.0576255i	$0.981647\pi$
$174$		0			0
$175$	−5.32624			−0.402626
$176$		0			0
$177$	2.85410			0.214527
$178$		0			0
$179$	−1.30902	−	4.02874i	−0.0978405	−	0.301122i	0.890143	−	0.455681i	$-0.150604\pi$
$179$	−1.30902	−	4.02874i	−0.0978405	−	0.301122i	−0.987984	+	0.154559i	$0.950604\pi$
$180$		0			0
$181$	18.6074	+	13.5191i	1.38308	+	1.00486i	0.996585	+	0.0825708i	$0.0263131\pi$
$181$	18.6074	+	13.5191i	1.38308	+	1.00486i	0.386491	+	0.922293i	$0.373687\pi$
$182$		0			0
$183$	1.35410	−	4.16750i	0.100098	−	0.308070i
$184$		0			0
$185$	−8.78115	+	6.37988i	−0.645603	+	0.469058i
$186$		0			0
$187$	8.66312	+	0.587785i	0.633510	+	0.0429831i
$188$		0			0
$189$	1.80902	−	1.31433i	0.131587	−	0.0956033i
$190$		0			0
$191$	−5.54508	+	17.0660i	−0.401228	+	1.23485i	0.522776	+	0.852470i	$0.324897\pi$
$191$	−5.54508	+	17.0660i	−0.401228	+	1.23485i	−0.924004	+	0.382383i	$0.875103\pi$
$192$		0			0
$193$	−11.4443	−	8.31475i	−0.823777	−	0.598509i	0.0940151	−	0.995571i	$-0.470030\pi$
$193$	−11.4443	−	8.31475i	−0.823777	−	0.598509i	−0.917792	+	0.397062i	$0.870030\pi$
$194$		0			0
$195$	−0.118034	−	0.363271i	−0.00845259	−	0.0260144i
$196$		0			0
$197$	−7.38197			−0.525943			−0.262972	−	0.964804i	$-0.584703\pi$
$197$	−7.38197			−0.525943			−0.262972	+	0.964804i	$0.584703\pi$
$198$		0			0
$199$	2.41641			0.171295			0.0856473	−	0.996326i	$-0.472704\pi$
$199$	2.41641			0.171295			0.0856473	+	0.996326i	$0.472704\pi$
$200$		0			0
$201$	4.35410	+	13.4005i	0.307115	+	0.945202i
$202$		0			0
$203$	−3.61803	−	2.62866i	−0.253936	−	0.184495i
$204$		0			0
$205$	−4.11803	+	12.6740i	−0.287616	+	0.885191i
$206$		0			0
$207$	−2.80902	+	2.04087i	−0.195240	+	0.141850i
$208$		0			0
$209$	−9.20820	−	7.69421i	−0.636945	−	0.532220i
$210$		0			0
$211$	0.972136	−	0.706298i	0.0669246	−	0.0486236i	−0.553820	−	0.832636i	$-0.686830\pi$
$211$	0.972136	−	0.706298i	0.0669246	−	0.0486236i	0.620745	+	0.784013i	$0.286830\pi$
$212$		0			0
$213$	2.73607	−	8.42075i	0.187472	−	0.576980i
$214$		0			0
$215$	−15.6353	−	11.3597i	−1.06632	−	0.774724i
$216$		0			0
$217$	2.13525	+	6.57164i	0.144951	+	0.446112i
$218$		0			0
$219$	−13.2361			−0.894411
$220$		0			0
$221$	0.618034			0.0415735
$222$		0			0
$223$	−1.39919	−	4.30625i	−0.0936965	−	0.288368i	0.893215	−	0.449629i	$-0.148444\pi$
$223$	−1.39919	−	4.30625i	−0.0936965	−	0.288368i	−0.986912	+	0.161261i	$0.948444\pi$
$224$		0			0
$225$	1.92705	+	1.40008i	0.128470	+	0.0933390i
$226$		0			0
$227$	−1.21885	+	3.75123i	−0.0808977	+	0.248978i	−0.983323	−	0.181869i	$-0.941785\pi$
$227$	−1.21885	+	3.75123i	−0.0808977	+	0.248978i	0.902425	+	0.430847i	$0.141785\pi$
$228$		0			0
$229$	−21.3262	+	15.4944i	−1.40928	+	1.02390i	−0.415850	+	0.909433i	$0.636516\pi$
$229$	−21.3262	+	15.4944i	−1.40928	+	1.02390i	−0.993427	+	0.114467i	$0.963484\pi$
$230$		0			0
$231$	−6.28115	+	3.94298i	−0.413270	+	0.259429i
$232$		0			0
$233$	−16.4894	+	11.9802i	−1.08025	+	0.784850i	−0.977727	−	0.209880i	$-0.932693\pi$
$233$	−16.4894	+	11.9802i	−1.08025	+	0.784850i	−0.102527	+	0.994730i	$0.532693\pi$
$234$		0			0
$235$	−3.69098	+	11.3597i	−0.240773	+	0.741024i
$236$		0			0
$237$	−1.42705	−	1.03681i	−0.0926969	−	0.0673483i
$238$		0			0
$239$	0.281153	+	0.865300i	0.0181863	+	0.0559716i	0.959738	−	0.280897i	$-0.0906321\pi$
$239$	0.281153	+	0.865300i	0.0181863	+	0.0559716i	−0.941552	+	0.336869i	$0.890632\pi$
$240$		0			0
$241$	28.1803			1.81526			0.907628	−	0.419776i	$-0.137891\pi$
$241$	28.1803			1.81526			0.907628	+	0.419776i	$0.137891\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	1.00000	+	3.07768i	0.0638877	+	0.196626i
$246$		0			0
$247$	−0.690983	−	0.502029i	−0.0439662	−	0.0319433i
$248$		0			0
$249$	−2.83688	+	8.73102i	−0.179780	+	0.553306i
$250$		0			0
$251$	17.0623	−	12.3965i	1.07696	−	0.782460i	0.0998123	−	0.995006i	$-0.468176\pi$
$251$	17.0623	−	12.3965i	1.07696	−	0.782460i	0.977151	+	0.212547i	$0.0681758\pi$
$252$		0			0
$253$	9.75329	−	6.12261i	0.613184	−	0.384925i
$254$		0			0
$255$	3.42705	−	2.48990i	0.214610	−	0.155923i
$256$		0			0
$257$	1.35410	−	4.16750i	0.0844666	−	0.259961i	−0.899899	−	0.436098i	$-0.856360\pi$
$257$	1.35410	−	4.16750i	0.0844666	−	0.259961i	0.984366	+	0.176137i	$0.0563601\pi$
$258$		0			0
$259$	12.1353	+	8.81678i	0.754048	+	0.547848i
$260$		0			0
$261$	0.618034	+	1.90211i	0.0382553	+	0.117738i
$262$		0			0
$263$	−31.5066			−1.94278			−0.971389	−	0.237492i	$-0.923675\pi$
$263$	−31.5066			−1.94278			−0.971389	+	0.237492i	$0.923675\pi$
$264$		0			0
$265$	−18.7082			−1.14924
$266$		0			0
$267$	3.78115	+	11.6372i	0.231403	+	0.712185i
$268$		0			0
$269$	21.3262	+	15.4944i	1.30028	+	0.944711i	0.999958	−	0.00912545i	$-0.00290476\pi$
$269$	21.3262	+	15.4944i	1.30028	+	0.944711i	0.300325	+	0.953837i	$0.402905\pi$
$270$		0			0
$271$	2.02786	−	6.24112i	0.123184	−	0.379121i	−0.870382	−	0.492377i	$-0.836128\pi$
$271$	2.02786	−	6.24112i	0.123184	−	0.379121i	0.993566	+	0.113256i	$0.0361280\pi$
$272$		0			0
$273$	−0.427051	+	0.310271i	−0.0258463	+	0.0187784i
$274$		0			0
$275$	−6.06231	−	5.06555i	−0.365571	−	0.305464i
$276$		0			0
$277$	−25.6803	+	18.6579i	−1.54298	+	1.12104i	−0.594551	+	0.804058i	$0.702670\pi$
$277$	−25.6803	+	18.6579i	−1.54298	+	1.12104i	−0.948431	+	0.316984i	$0.897330\pi$
$278$		0			0
$279$	0.954915	−	2.93893i	0.0571693	−	0.175949i
$280$		0			0
$281$	8.70820	+	6.32688i	0.519488	+	0.377430i	0.816411	−	0.577471i	$-0.195960\pi$
$281$	8.70820	+	6.32688i	0.519488	+	0.377430i	−0.296923	+	0.954901i	$0.595960\pi$
$282$		0			0
$283$	−7.61803	−	23.4459i	−0.452845	−	1.39371i	−0.873647	−	0.486561i	$-0.838251\pi$
$283$	−7.61803	−	23.4459i	−0.452845	−	1.39371i	0.420801	−	0.907153i	$-0.361749\pi$
$284$		0			0
$285$	−5.85410			−0.346767
$286$		0			0
$287$	18.4164			1.08709
$288$		0			0
$289$	−3.13525	−	9.64932i	−0.184427	−	0.567607i
$290$		0			0
$291$	−4.78115	−	3.47371i	−0.280276	−	0.203633i
$292$		0			0
$293$	−4.98278	+	15.3354i	−0.291097	+	0.895905i	0.693407	+	0.720546i	$0.256109\pi$
$293$	−4.98278	+	15.3354i	−0.291097	+	0.895905i	−0.984505	+	0.175359i	$0.943891\pi$
$294$		0			0
$295$	−3.73607	+	2.71441i	−0.217522	+	0.158039i
$296$		0			0
$297$	3.30902	+	0.224514i	0.192009	+	0.0130276i
$298$		0			0
$299$	0.663119	−	0.481784i	0.0383492	−	0.0278623i
$300$		0			0
$301$	−8.25329	+	25.4010i	−0.475712	+	1.46409i
$302$		0			0
$303$	−10.2812	−	7.46969i	−0.590637	−	0.429123i
$304$		0			0
$305$	2.19098	+	6.74315i	0.125455	+	0.386112i
$306$		0			0
$307$	27.7426			1.58336			0.791678	−	0.610938i	$-0.209208\pi$
$307$	27.7426			1.58336			0.791678	+	0.610938i	$0.209208\pi$
$308$		0			0
$309$	16.4721			0.937067
$310$		0			0
$311$	4.01722	+	12.3637i	0.227796	+	0.701083i	0.997996	+	0.0632807i	$0.0201563\pi$
$311$	4.01722	+	12.3637i	0.227796	+	0.701083i	−0.770200	+	0.637802i	$0.779844\pi$
$312$		0			0
$313$	−21.3713	−	15.5272i	−1.20798	−	0.877648i	−0.212933	−	0.977067i	$-0.568302\pi$
$313$	−21.3713	−	15.5272i	−1.20798	−	0.877648i	−0.995046	+	0.0994190i	$0.968302\pi$
$314$		0			0
$315$	−1.11803	+	3.44095i	−0.0629941	+	0.193876i
$316$		0			0
$317$	−8.66312	+	6.29412i	−0.486569	+	0.353513i	−0.803863	−	0.594814i	$-0.797226\pi$
$317$	−8.66312	+	6.29412i	−0.486569	+	0.353513i	0.317294	+	0.948327i	$0.397226\pi$
$318$		0			0
$319$	−1.61803	−	6.43288i	−0.0905925	−	0.360172i
$320$		0			0
$321$	4.19098	−	3.04493i	0.233918	−	0.169951i
$322$		0			0
$323$	2.92705	−	9.00854i	0.162865	−	0.501248i
$324$		0			0
$325$	−0.454915	−	0.330515i	−0.0252341	−	0.0183337i
$326$		0			0
$327$	−3.70820	−	11.4127i	−0.205064	−	0.631123i
$328$		0			0
$329$	16.5066			0.910037
$330$		0			0
$331$	−13.4721			−0.740496			−0.370248	−	0.928933i	$-0.620727\pi$
$331$	−13.4721			−0.740496			−0.370248	+	0.928933i	$0.620727\pi$
$332$		0			0
$333$	−2.07295	−	6.37988i	−0.113597	−	0.349615i
$334$		0			0
$335$	−18.4443	−	13.4005i	−1.00772	−	0.732150i
$336$		0			0
$337$	4.81966	−	14.8334i	0.262544	−	0.808026i	−0.729706	−	0.683762i	$-0.760343\pi$
$337$	4.81966	−	14.8334i	0.262544	−	0.808026i	0.992249	−	0.124265i	$-0.0396572\pi$
$338$		0			0
$339$	−1.66312	+	1.20833i	−0.0903282	+	0.0656273i
$340$		0			0
$341$	−3.81966	+	9.51057i	−0.206846	+	0.515026i
$342$		0			0
$343$	16.2812	−	11.8290i	0.879100	−	0.638703i
$344$		0			0
$345$	1.73607	−	5.34307i	0.0934668	−	0.287661i
$346$		0			0
$347$	16.4721	+	11.9677i	0.884271	+	0.642460i	0.934378	−	0.356284i	$-0.115956\pi$
$347$	16.4721	+	11.9677i	0.884271	+	0.642460i	−0.0501073	+	0.998744i	$0.515956\pi$
$348$		0			0
$349$	−3.63525	−	11.1882i	−0.194591	−	0.598889i	−0.999981	−	0.00614397i	$-0.998044\pi$
$349$	−3.63525	−	11.1882i	−0.194591	−	0.598889i	0.805390	−	0.592745i	$-0.201956\pi$
$350$		0			0
$351$	0.236068			0.0126004
$352$		0			0
$353$	15.0557			0.801336			0.400668	−	0.916223i	$-0.368778\pi$
$353$	15.0557			0.801336			0.400668	+	0.916223i	$0.368778\pi$
$354$		0			0
$355$	4.42705	+	13.6251i	0.234963	+	0.723143i
$356$		0			0
$357$	−4.73607	−	3.44095i	−0.250659	−	0.182115i
$358$		0			0
$359$	7.90983	−	24.3440i	0.417465	−	1.28482i	−0.492563	−	0.870277i	$-0.663940\pi$
$359$	7.90983	−	24.3440i	0.417465	−	1.28482i	0.910028	−	0.414548i	$-0.136060\pi$
$360$		0			0
$361$	4.78115	−	3.47371i	0.251640	−	0.182827i
$362$		0			0
$363$	−10.8992	−	1.48584i	−0.572059	−	0.0779864i
$364$		0			0
$365$	17.3262	−	12.5882i	0.906897	−	0.658899i
$366$		0			0
$367$	−0.881966	+	2.71441i	−0.0460383	+	0.141691i	−0.971433	−	0.237313i	$-0.923733\pi$
$367$	−0.881966	+	2.71441i	−0.0460383	+	0.141691i	0.925395	+	0.379004i	$0.123733\pi$
$368$		0			0
$369$	−6.66312	−	4.84104i	−0.346868	−	0.252014i
$370$		0			0
$371$	7.98936	+	24.5887i	0.414787	+	1.27658i
$372$		0			0
$373$	−12.4164			−0.642897			−0.321449	−	0.946927i	$-0.604170\pi$
$373$	−12.4164			−0.642897			−0.321449	+	0.946927i	$0.604170\pi$
$374$		0			0
$375$	−11.9443			−0.616800
$376$		0			0
$377$	−0.145898	−	0.449028i	−0.00751413	−	0.0231261i
$378$		0			0
$379$	−4.95492	−	3.59996i	−0.254517	−	0.184917i	0.453209	−	0.891404i	$-0.350279\pi$
$379$	−4.95492	−	3.59996i	−0.254517	−	0.184917i	−0.707726	+	0.706487i	$0.750279\pi$
$380$		0			0
$381$	3.94427	−	12.1392i	0.202071	−	0.621911i
$382$		0			0
$383$	15.6631	−	11.3799i	0.800348	−	0.581487i	−0.110668	−	0.993857i	$-0.535299\pi$
$383$	15.6631	−	11.3799i	0.800348	−	0.581487i	0.911016	+	0.412371i	$0.135299\pi$
$384$		0			0
$385$	4.47214	−	11.1352i	0.227921	−	0.567500i
$386$		0			0
$387$	9.66312	−	7.02067i	0.491204	−	0.356881i
$388$		0			0
$389$	10.3369	−	31.8136i	0.524101	−	1.61302i	−0.241987	−	0.970280i	$-0.577799\pi$
$389$	10.3369	−	31.8136i	0.524101	−	1.61302i	0.766087	−	0.642736i	$-0.222201\pi$
$390$		0			0
$391$	7.35410	+	5.34307i	0.371913	+	0.270211i
$392$		0			0
$393$	5.33688	+	16.4252i	0.269210	+	0.828543i
$394$		0			0
$395$	2.85410			0.143605
$396$		0			0
$397$	12.8197			0.643400			0.321700	−	0.946842i	$-0.395746\pi$
$397$	12.8197			0.643400			0.321700	+	0.946842i	$0.395746\pi$
$398$		0			0
$399$	2.50000	+	7.69421i	0.125157	+	0.385192i
$400$		0			0
$401$	13.9721	+	10.1514i	0.697735	+	0.506934i	0.879194	−	0.476464i	$-0.158082\pi$
$401$	13.9721	+	10.1514i	0.697735	+	0.506934i	−0.181459	+	0.983399i	$0.558082\pi$
$402$		0			0
$403$	−0.225425	+	0.693786i	−0.0112292	+	0.0345600i
$404$		0			0
$405$	1.30902	−	0.951057i	0.0650456	−	0.0472584i
$406$		0			0
$407$	5.42705	+	21.5765i	0.269009	+	1.06951i
$408$		0			0
$409$	−18.9443	+	13.7638i	−0.936734	+	0.680577i	−0.947632	−	0.319364i	$-0.896531\pi$
$409$	−18.9443	+	13.7638i	−0.936734	+	0.680577i	0.0108983	+	0.999941i	$0.496531\pi$
$410$		0			0
$411$	2.21885	−	6.82891i	0.109448	−	0.336845i
$412$		0			0
$413$	5.16312	+	3.75123i	0.254060	+	0.184586i
$414$		0			0
$415$	−4.59017	−	14.1271i	−0.225323	−	0.693472i
$416$		0			0
$417$	−2.32624			−0.113916
$418$		0			0
$419$	23.7984			1.16263			0.581313	−	0.813680i	$-0.302539\pi$
$419$	23.7984			1.16263			0.581313	+	0.813680i	$0.302539\pi$
$420$		0			0
$421$	−7.73607	−	23.8092i	−0.377033	−	1.16039i	−0.942097	−	0.335341i	$-0.891149\pi$
$421$	−7.73607	−	23.8092i	−0.377033	−	1.16039i	0.565064	−	0.825047i	$-0.308851\pi$
$422$		0			0
$423$	−5.97214	−	4.33901i	−0.290375	−	0.210970i
$424$		0			0
$425$	1.92705	−	5.93085i	0.0934757	−	0.287689i
$426$		0			0
$427$	7.92705	−	5.75934i	0.383617	−	0.278714i
$428$		0			0
$429$	−0.781153	−	0.0530006i	−0.0377144	−	0.00255889i
$430$		0			0
$431$	−21.4443	+	15.5802i	−1.03293	+	0.750471i	−0.968894	−	0.247477i	$-0.920399\pi$
$431$	−21.4443	+	15.5802i	−1.03293	+	0.750471i	−0.0640404	+	0.997947i	$0.520399\pi$
$432$		0			0
$433$	6.32624	−	19.4702i	0.304020	−	0.935676i	−0.676022	−	0.736882i	$-0.736297\pi$
$433$	6.32624	−	19.4702i	0.304020	−	0.935676i	0.980041	−	0.198794i	$-0.0637026\pi$
$434$		0			0
$435$	−2.61803	−	1.90211i	−0.125525	−	0.0911993i
$436$		0			0
$437$	−3.88197	−	11.9475i	−0.185700	−	0.571525i
$438$		0			0
$439$	27.9443			1.33371			0.666854	−	0.745189i	$-0.267641\pi$
$439$	27.9443			1.33371			0.666854	+	0.745189i	$0.267641\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$		0			0
$443$	7.03444	+	21.6498i	0.334216	+	1.02861i	0.967107	+	0.254371i	$0.0818684\pi$
$443$	7.03444	+	21.6498i	0.334216	+	1.02861i	−0.632890	+	0.774241i	$0.718132\pi$
$444$		0			0
$445$	−16.0172	−	11.6372i	−0.759289	−	0.551656i
$446$		0			0
$447$	−1.92705	+	5.93085i	−0.0911464	+	0.280520i
$448$		0			0
$449$	12.0902	−	8.78402i	0.570570	−	0.414544i	−0.264742	−	0.964319i	$-0.585287\pi$
$449$	12.0902	−	8.78402i	0.570570	−	0.414544i	0.835312	+	0.549776i	$0.185287\pi$
$450$		0			0
$451$	20.9615	+	17.5150i	0.987038	+	0.824751i
$452$		0			0
$453$	−7.61803	+	5.53483i	−0.357926	+	0.260049i
$454$		0			0
$455$	0.263932	−	0.812299i	0.0123733	−	0.0380812i
$456$		0			0
$457$	8.88197	+	6.45313i	0.415481	+	0.301865i	0.775817	−	0.630958i	$-0.217338\pi$
$457$	8.88197	+	6.45313i	0.415481	+	0.301865i	−0.360336	+	0.932823i	$0.617338\pi$
$458$		0			0
$459$	0.809017	+	2.48990i	0.0377617	+	0.116218i
$460$		0			0
$461$	24.2705			1.13039			0.565195	−	0.824957i	$-0.308801\pi$
$461$	24.2705			1.13039			0.565195	+	0.824957i	$0.308801\pi$
$462$		0			0
$463$	−27.4508			−1.27575			−0.637875	−	0.770140i	$-0.720186\pi$
$463$	−27.4508			−1.27575			−0.637875	+	0.770140i	$0.720186\pi$
$464$		0			0
$465$	1.54508	+	4.75528i	0.0716516	+	0.220521i
$466$		0			0
$467$	−5.42705	−	3.94298i	−0.251134	−	0.182460i	0.455095	−	0.890443i	$-0.349605\pi$
$467$	−5.42705	−	3.94298i	−0.251134	−	0.182460i	−0.706229	+	0.707983i	$0.749605\pi$
$468$		0			0
$469$	−9.73607	+	29.9645i	−0.449570	+	1.38363i
$470$		0			0
$471$	−12.3262	+	8.95554i	−0.567963	+	0.412649i
$472$		0			0
$473$	−33.5517	+	21.0620i	−1.54271	+	0.968432i
$474$		0			0
$475$	−6.97214	+	5.06555i	−0.319904	+	0.232424i
$476$		0			0
$477$	3.57295	−	10.9964i	0.163594	−	0.503491i
$478$		0			0
$479$	−6.97214	−	5.06555i	−0.318565	−	0.231451i	0.416998	−	0.908907i	$-0.363082\pi$
$479$	−6.97214	−	5.06555i	−0.318565	−	0.231451i	−0.735563	+	0.677456i	$0.763082\pi$
$480$		0			0
$481$	0.489357	+	1.50609i	0.0223128	+	0.0686716i
$482$		0			0
$483$	−7.76393			−0.353271
$484$		0			0
$485$	9.56231			0.434202
$486$		0			0
$487$	−2.78115	−	8.55951i	−0.126026	−	0.387868i	0.868061	−	0.496458i	$-0.165366\pi$
$487$	−2.78115	−	8.55951i	−0.126026	−	0.387868i	−0.994087	+	0.108590i	$0.965366\pi$
$488$		0			0
$489$	−9.97214	−	7.24518i	−0.450956	−	0.327638i
$490$		0			0
$491$	−2.86475	+	8.81678i	−0.129284	+	0.397896i	−0.994657	−	0.103232i	$-0.967081\pi$
$491$	−2.86475	+	8.81678i	−0.129284	+	0.397896i	0.865373	+	0.501128i	$0.167081\pi$
$492$		0			0
$493$	4.23607	−	3.07768i	0.190783	−	0.138612i
$494$		0			0
$495$	−4.54508	+	2.85317i	−0.204286	+	0.128240i
$496$		0			0
$497$	16.0172	−	11.6372i	0.718471	−	0.521999i
$498$		0			0
$499$	−2.64590	+	8.14324i	−0.118447	+	0.364541i	−0.992650	−	0.121018i	$-0.961384\pi$
$499$	−2.64590	+	8.14324i	−0.118447	+	0.364541i	0.874204	+	0.485559i	$0.161384\pi$
$500$		0			0
$501$	−8.16312	−	5.93085i	−0.364701	−	0.264971i
$502$		0			0
$503$	4.81966	+	14.8334i	0.214898	+	0.661388i	0.999161	+	0.0409593i	$0.0130414\pi$
$503$	4.81966	+	14.8334i	0.214898	+	0.661388i	−0.784263	+	0.620429i	$0.786959\pi$
$504$		0			0
$505$	20.5623			0.915011
$506$		0			0
$507$	12.9443			0.574875
$508$		0			0
$509$	−11.2467	−	34.6138i	−0.498502	−	1.53423i	−0.811428	−	0.584453i	$-0.801309\pi$
$509$	−11.2467	−	34.6138i	−0.498502	−	1.53423i	0.312926	−	0.949778i	$-0.398691\pi$
$510$		0			0
$511$	−23.9443	−	17.3965i	−1.05923	−	0.769577i
$512$		0			0
$513$	1.11803	−	3.44095i	0.0493624	−	0.151922i
$514$		0			0
$515$	−21.5623	+	15.6659i	−0.950149	+	0.690323i
$516$		0			0
$517$	18.7877	+	15.6987i	0.826283	+	0.690428i
$518$		0			0
$519$	−5.39919	+	3.92274i	−0.236998	+	0.172189i
$520$		0			0
$521$	0.652476	−	2.00811i	0.0285855	−	0.0879771i	−0.935746	−	0.352675i	$-0.885272\pi$
$521$	0.652476	−	2.00811i	0.0285855	−	0.0879771i	0.964331	+	0.264698i	$0.0852722\pi$
$522$		0			0
$523$	6.73607	+	4.89404i	0.294548	+	0.214001i	0.725238	−	0.688498i	$-0.241730\pi$
$523$	6.73607	+	4.89404i	0.294548	+	0.214001i	−0.430690	+	0.902500i	$0.641730\pi$
$524$		0			0
$525$	1.64590	+	5.06555i	0.0718329	+	0.221079i
$526$		0			0
$527$	−8.09017			−0.352413
$528$		0			0
$529$	−10.9443			−0.475838
$530$		0			0
$531$	−0.881966	−	2.71441i	−0.0382741	−	0.117795i
$532$		0			0
$533$	1.57295	+	1.14281i	0.0681320	+	0.0495008i
$534$		0			0
$535$	−2.59017	+	7.97172i	−0.111983	+	0.344648i
$536$		0			0
$537$	−3.42705	+	2.48990i	−0.147888	+	0.107447i
$538$		0			0
$539$	6.61803	+	0.449028i	0.285059	+	0.0193410i
$540$		0			0
$541$	−2.30902	+	1.67760i	−0.0992724	+	0.0721256i	−0.636314	−	0.771430i	$-0.719542\pi$
$541$	−2.30902	+	1.67760i	−0.0992724	+	0.0721256i	0.537042	+	0.843556i	$0.319542\pi$
$542$		0			0
$543$	7.10739	−	21.8743i	0.305007	−	0.938716i
$544$		0			0
$545$	15.7082	+	11.4127i	0.672866	+	0.488865i
$546$		0			0
$547$	−4.62868	−	14.2456i	−0.197908	−	0.609098i	−0.999930	−	0.0118040i	$-0.996243\pi$
$547$	−4.62868	−	14.2456i	−0.197908	−	0.609098i	0.802022	−	0.597294i	$-0.203757\pi$
$548$		0			0
$549$	−4.38197			−0.187018
$550$		0			0
$551$	−7.23607			−0.308267
$552$		0			0
$553$	−1.21885	−	3.75123i	−0.0518306	−	0.159518i
$554$		0			0
$555$	8.78115	+	6.37988i	0.372739	+	0.270811i
$556$		0			0
$557$	−12.8607	+	39.5811i	−0.544924	+	1.67711i	0.176245	+	0.984346i	$0.443605\pi$
$557$	−12.8607	+	39.5811i	−0.544924	+	1.67711i	−0.721169	+	0.692759i	$0.756395\pi$
$558$		0			0
$559$	−2.28115	+	1.65735i	−0.0964825	+	0.0700986i
$560$		0			0
$561$	−2.11803	−	8.42075i	−0.0894235	−	0.355524i
$562$		0			0
$563$	−14.9894	+	10.8904i	−0.631726	+	0.458976i	−0.856998	−	0.515320i	$-0.827673\pi$
$563$	−14.9894	+	10.8904i	−0.631726	+	0.458976i	0.225272	+	0.974296i	$0.427673\pi$
$564$		0			0
$565$	1.02786	−	3.16344i	0.0432426	−	0.133087i
$566$		0			0
$567$	−1.80902	−	1.31433i	−0.0759716	−	0.0551966i
$568$		0			0
$569$	−2.81966	−	8.67802i	−0.118206	−	0.363802i	0.874396	−	0.485213i	$-0.161258\pi$
$569$	−2.81966	−	8.67802i	−0.118206	−	0.363802i	−0.992602	+	0.121411i	$0.961258\pi$
$570$		0			0
$571$	−19.1459			−0.801231			−0.400615	−	0.916246i	$-0.631204\pi$
$571$	−19.1459			−0.801231			−0.400615	+	0.916246i	$0.631204\pi$
$572$		0			0
$573$	17.9443			0.749633
$574$		0			0
$575$	−2.55573	−	7.86572i	−0.106581	−	0.328023i
$576$		0			0
$577$	−36.0344	−	26.1806i	−1.50013	−	1.08991i	−0.970328	−	0.241791i	$-0.922265\pi$
$577$	−36.0344	−	26.1806i	−1.50013	−	1.08991i	−0.529805	−	0.848119i	$-0.677735\pi$
$578$		0			0
$579$	−4.37132	+	13.4535i	−0.181666	+	0.559110i
$580$		0			0
$581$	−16.6074	+	12.0660i	−0.688991	+	0.500581i
$582$		0			0
$583$	−14.2918	+	35.5851i	−0.591906	+	1.47379i
$584$		0			0
$585$	−0.309017	+	0.224514i	−0.0127763	+	0.00928251i
$586$		0			0
$587$	7.10739	−	21.8743i	0.293353	−	0.902849i	−0.690416	−	0.723412i	$-0.742573\pi$
$587$	7.10739	−	21.8743i	0.293353	−	0.902849i	0.983770	−	0.179437i	$-0.0574275\pi$
$588$		0			0
$589$	9.04508	+	6.57164i	0.372696	+	0.270780i
$590$		0			0
$591$	2.28115	+	7.02067i	0.0938341	+	0.288792i
$592$		0			0
$593$	−16.2016			−0.665321			−0.332661	−	0.943047i	$-0.607946\pi$
$593$	−16.2016			−0.665321			−0.332661	+	0.943047i	$0.607946\pi$
$594$		0			0
$595$	9.47214			0.388320
$596$		0			0
$597$	−0.746711	−	2.29814i	−0.0305609	−	0.0940566i
$598$		0			0
$599$	−31.2705	−	22.7194i	−1.27768	−	0.928288i	−0.278198	−	0.960524i	$-0.589737\pi$
$599$	−31.2705	−	22.7194i	−1.27768	−	0.928288i	−0.999480	+	0.0322360i	$0.989737\pi$
$600$		0			0
$601$	−1.83688	+	5.65334i	−0.0749279	+	0.230604i	−0.981505	−	0.191435i	$-0.938686\pi$
$601$	−1.83688	+	5.65334i	−0.0749279	+	0.230604i	0.906577	+	0.422040i	$0.138686\pi$
$602$		0			0
$603$	11.3992	−	8.28199i	0.464211	−	0.337269i
$604$		0			0
$605$	15.6803	−	8.42075i	0.637496	−	0.342352i
$606$		0			0
$607$	−5.73607	+	4.16750i	−0.232820	+	0.169153i	−0.698078	−	0.716021i	$-0.745961\pi$
$607$	−5.73607	+	4.16750i	−0.232820	+	0.169153i	0.465259	+	0.885175i	$0.345961\pi$
$608$		0			0
$609$	−1.38197	+	4.25325i	−0.0560001	+	0.172351i
$610$		0			0
$611$	1.40983	+	1.02430i	0.0570356	+	0.0414388i
$612$		0			0
$613$	−1.90983	−	5.87785i	−0.0771373	−	0.237404i	0.905051	−	0.425303i	$-0.139832\pi$
$613$	−1.90983	−	5.87785i	−0.0771373	−	0.237404i	−0.982188	+	0.187899i	$0.939832\pi$
$614$		0			0
$615$	13.3262			0.537366
$616$		0			0
$617$	−19.6525			−0.791179			−0.395589	−	0.918427i	$-0.629460\pi$
$617$	−19.6525			−0.791179			−0.395589	+	0.918427i	$0.629460\pi$
$618$		0			0
$619$	5.83688	+	17.9641i	0.234604	+	0.722037i	0.997174	+	0.0751309i	$0.0239375\pi$
$619$	5.83688	+	17.9641i	0.234604	+	0.722037i	−0.762570	+	0.646906i	$0.776063\pi$
$620$		0			0
$621$	2.80902	+	2.04087i	0.112722	+	0.0818973i
$622$		0			0
$623$	−8.45492	+	26.0216i	−0.338739	+	1.04253i
$624$		0			0
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$		0			0
$627$	−4.47214	+	11.1352i	−0.178600	+	0.444696i
$628$		0			0
$629$	−14.2082	+	10.3229i	−0.566518	+	0.411600i
$630$		0			0
$631$	−8.28115	+	25.4868i	−0.329667	+	1.01461i	0.639622	+	0.768690i	$0.279091\pi$
$631$	−8.28115	+	25.4868i	−0.329667	+	1.01461i	−0.969289	+	0.245923i	$0.920909\pi$
$632$		0			0
$633$	−0.972136	−	0.706298i	−0.0386389	−	0.0280728i
$634$		0			0
$635$	6.38197	+	19.6417i	0.253261	+	0.779456i
$636$		0			0
$637$	0.472136			0.0187067
$638$		0			0
$639$	−8.85410			−0.350263
$640$		0			0
$641$	5.46556	+	16.8213i	0.215877	+	0.664400i	0.999090	+	0.0426471i	$0.0135791\pi$
$641$	5.46556	+	16.8213i	0.215877	+	0.664400i	−0.783214	+	0.621753i	$0.786421\pi$
$642$		0			0
$643$	14.3541	+	10.4289i	0.566071	+	0.411274i	0.833676	−	0.552254i	$-0.186232\pi$
$643$	14.3541	+	10.4289i	0.566071	+	0.411274i	−0.267605	+	0.963529i	$0.586232\pi$
$644$		0			0
$645$	−5.97214	+	18.3803i	−0.235153	+	0.723725i
$646$		0			0
$647$	16.3541	−	11.8820i	0.642946	−	0.467128i	−0.217915	−	0.975968i	$-0.569926\pi$
$647$	16.3541	−	11.8820i	0.642946	−	0.467128i	0.860861	+	0.508840i	$0.169926\pi$
$648$		0			0
$649$	2.30902	+	9.18005i	0.0906368	+	0.360348i
$650$		0			0
$651$	5.59017	−	4.06150i	0.219096	−	0.159183i
$652$		0			0
$653$	1.62868	−	5.01255i	0.0637351	−	0.196156i	−0.914118	−	0.405448i	$-0.867116\pi$
$653$	1.62868	−	5.01255i	0.0637351	−	0.196156i	0.977853	+	0.209291i	$0.0671157\pi$
$654$		0			0
$655$	−22.6074	−	16.4252i	−0.883344	−	0.641787i
$656$		0			0
$657$	4.09017	+	12.5882i	0.159573	+	0.491114i
$658$		0			0
$659$	27.1246			1.05662			0.528312	−	0.849050i	$-0.322825\pi$
$659$	27.1246			1.05662			0.528312	+	0.849050i	$0.322825\pi$
$660$		0			0
$661$	21.3820			0.831662			0.415831	−	0.909442i	$-0.363491\pi$
$661$	21.3820			0.831662			0.415831	+	0.909442i	$0.363491\pi$
$662$		0			0
$663$	−0.190983	−	0.587785i	−0.00741717	−	0.0228277i
$664$		0			0
$665$	−10.5902	−	7.69421i	−0.410669	−	0.298369i
$666$		0			0
$667$	2.14590	−	6.60440i	0.0830895	−	0.255723i
$668$		0			0
$669$	−3.66312	+	2.66141i	−0.141624	+	0.102896i
$670$		0			0
$671$	14.5000	+	0.983813i	0.559766	+	0.0379797i
$672$		0			0
$673$	13.6631	−	9.92684i	0.526675	−	0.382651i	−0.292438	−	0.956285i	$-0.594466\pi$
$673$	13.6631	−	9.92684i	0.526675	−	0.382651i	0.819112	+	0.573633i	$0.194466\pi$
$674$		0			0
$675$	0.736068	−	2.26538i	0.0283313	−	0.0871947i
$676$		0			0
$677$	−30.1803	−	21.9273i	−1.15992	−	0.842735i	−0.170156	−	0.985417i	$-0.554427\pi$
$677$	−30.1803	−	21.9273i	−1.15992	−	0.842735i	−0.989769	+	0.142682i	$0.954427\pi$
$678$		0			0
$679$	−4.08359	−	12.5680i	−0.156714	−	0.482316i
$680$		0			0
$681$	3.94427			0.151145
$682$		0			0
$683$	16.5279			0.632421			0.316211	−	0.948689i	$-0.397589\pi$
$683$	16.5279			0.632421			0.316211	+	0.948689i	$0.397589\pi$
$684$		0			0
$685$	3.59017	+	11.0494i	0.137173	+	0.422176i
$686$		0			0
$687$	21.3262	+	15.4944i	0.813647	+	0.591149i
$688$		0			0
$689$	−0.843459	+	2.59590i	−0.0321332	+	0.0988959i
$690$		0			0
$691$	−5.76393	+	4.18774i	−0.219270	+	0.159309i	−0.691998	−	0.721899i	$-0.743269\pi$
$691$	−5.76393	+	4.18774i	−0.219270	+	0.159309i	0.472728	+	0.881208i	$0.343269\pi$
$692$		0			0
$693$	5.69098	+	4.75528i	0.216183	+	0.180638i
$694$		0			0
$695$	3.04508	−	2.21238i	0.115507	−	0.0839205i
$696$		0			0
$697$	−6.66312	+	20.5070i	−0.252384	+	0.776757i
$698$		0			0
$699$	16.4894	+	11.9802i	0.623685	+	0.453133i
$700$		0			0
$701$	−15.0967	−	46.4630i	−0.570196	−	1.75488i	−0.651983	−	0.758234i	$-0.726063\pi$
$701$	−15.0967	−	46.4630i	−0.570196	−	1.75488i	0.0817864	−	0.996650i	$-0.473937\pi$
$702$		0			0
$703$	24.2705			0.915380
$704$		0			0
$705$	11.9443			0.449847
$706$		0			0
$707$	−8.78115	−	27.0256i	−0.330249	−	1.01640i
$708$		0			0
$709$	−4.88197	−	3.54696i	−0.183346	−	0.133209i	0.492326	−	0.870411i	$-0.336147\pi$
$709$	−4.88197	−	3.54696i	−0.183346	−	0.133209i	−0.675672	+	0.737202i	$0.736147\pi$
$710$		0			0
$711$	−0.545085	+	1.67760i	−0.0204423	+	0.0629149i
$712$		0			0
$713$	−8.68034	+	6.30664i	−0.325081	+	0.236185i
$714$		0			0
$715$	1.07295	−	0.673542i	0.0401260	−	0.0251890i
$716$		0			0
$717$	0.736068	−	0.534785i	0.0274890	−	0.0199719i
$718$		0			0
$719$	14.1631	−	43.5896i	0.528195	−	1.62562i	−0.229714	−	0.973258i	$-0.573779\pi$
$719$	14.1631	−	43.5896i	0.528195	−	1.62562i	0.757910	−	0.652360i	$-0.226221\pi$
$720$		0			0
$721$	29.7984	+	21.6498i	1.10975	+	0.806280i
$722$		0			0
$723$	−8.70820	−	26.8011i	−0.323862	−	0.996743i
$724$		0			0
$725$	−4.76393			−0.176928
$726$		0			0
$727$	37.5623			1.39311			0.696554	−	0.717504i	$-0.254715\pi$
$727$	37.5623			1.39311			0.696554	+	0.717504i	$0.254715\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−25.2984	−	18.3803i	−0.935694	−	0.679822i
$732$		0			0
$733$	−0.673762	+	2.07363i	−0.0248860	+	0.0765911i	−0.962728	−	0.270471i	$-0.912821\pi$
$733$	−0.673762	+	2.07363i	−0.0248860	+	0.0765911i	0.937842	+	0.347062i	$0.112821\pi$
$734$		0			0
$735$	2.61803	−	1.90211i	0.0965676	−	0.0701605i
$736$		0			0
$737$	−39.5795	+	24.8460i	−1.45793	+	0.915214i
$738$		0			0
$739$	−17.5172	+	12.7270i	−0.644381	+	0.468170i	−0.861353	−	0.508008i	$-0.830382\pi$
$739$	−17.5172	+	12.7270i	−0.644381	+	0.468170i	0.216971	+	0.976178i	$0.430382\pi$
$740$		0			0
$741$	−0.263932	+	0.812299i	−0.00969579	+	0.0298406i
$742$		0			0
$743$	−20.3713	−	14.8006i	−0.747351	−	0.542983i	0.147653	−	0.989039i	$-0.452828\pi$
$743$	−20.3713	−	14.8006i	−0.747351	−	0.542983i	−0.895005	+	0.446057i	$0.852828\pi$
$744$		0			0
$745$	−3.11803	−	9.59632i	−0.114236	−	0.351582i
$746$		0			0
$747$	9.18034			0.335891
$748$		0			0
$749$	11.5836			0.423255
$750$		0			0
$751$	−12.9164	−	39.7526i	−0.471326	−	1.45059i	−0.850849	−	0.525411i	$-0.823912\pi$
$751$	−12.9164	−	39.7526i	−0.471326	−	1.45059i	0.379522	−	0.925183i	$-0.376088\pi$
$752$		0			0
$753$	−17.0623	−	12.3965i	−0.621785	−	0.451753i
$754$		0			0
$755$	4.70820	−	14.4904i	0.171349	−	0.527358i
$756$		0			0
$757$	31.8435	−	23.1356i	1.15737	−	0.840879i	0.167927	−	0.985799i	$-0.446293\pi$
$757$	31.8435	−	23.1356i	1.15737	−	0.840879i	0.989443	+	0.144921i	$0.0462927\pi$
$758$		0			0
$759$	−8.83688	−	7.38394i	−0.320758	−	0.268020i
$760$		0			0
$761$	2.19098	−	1.59184i	0.0794231	−	0.0577042i	−0.547365	−	0.836894i	$-0.684369\pi$
$761$	2.19098	−	1.59184i	0.0794231	−	0.0577042i	0.626788	+	0.779190i	$0.284369\pi$
$762$		0			0
$763$	8.29180	−	25.5195i	0.300183	−	0.923869i
$764$		0			0
$765$	−3.42705	−	2.48990i	−0.123905	−	0.0900225i
$766$		0			0
$767$	0.208204	+	0.640786i	0.00751781	+	0.0231374i
$768$		0			0
$769$	24.0902			0.868714			0.434357	−	0.900741i	$-0.356976\pi$
$769$	24.0902			0.868714			0.434357	+	0.900741i	$0.356976\pi$
$770$		0			0
$771$	−4.38197			−0.157813
$772$		0			0
$773$	11.9271	+	36.7077i	0.428986	+	1.32028i	0.899125	+	0.437691i	$0.144204\pi$
$773$	11.9271	+	36.7077i	0.428986	+	1.32028i	−0.470139	+	0.882592i	$0.655796\pi$
$774$		0			0
$775$	5.95492	+	4.32650i	0.213907	+	0.155412i
$776$		0			0
$777$	4.63525	−	14.2658i	0.166289	−	0.511784i
$778$		0			0
$779$	24.1074	−	17.5150i	0.863737	−	0.627542i
$780$		0			0
$781$	29.2984	+	1.98787i	1.04838	+	0.0711316i
$782$		0			0
$783$	1.61803	−	1.17557i	0.0578238	−	0.0420115i
$784$		0			0
$785$	7.61803	−	23.4459i	0.271899	−	0.836820i
$786$		0			0
$787$	2.23607	+	1.62460i	0.0797072	+	0.0579107i	0.626925	−	0.779079i	$-0.284313\pi$
$787$	2.23607	+	1.62460i	0.0797072	+	0.0579107i	−0.547218	+	0.836990i	$0.684313\pi$
$788$		0			0
$789$	9.73607	+	29.9645i	0.346613	+	1.06677i
$790$		0			0
$791$	−4.59675			−0.163442
$792$		0			0
$793$	1.03444			0.0367341
$794$		0			0
$795$	5.78115	+	17.7926i	0.205036	+	0.631037i
$796$		0			0
$797$	−21.0902	−	15.3229i	−0.747052	−	0.542765i	0.147860	−	0.989008i	$-0.452762\pi$
$797$	−21.0902	−	15.3229i	−0.747052	−	0.542765i	−0.894912	+	0.446243i	$0.852762\pi$
$798$		0			0
$799$	−5.97214	+	18.3803i	−0.211279	+	0.650250i
$800$		0			0
$801$	9.89919	−	7.19218i	0.349771	−	0.254123i
$802$		0			0
$803$	−10.7082	−	42.5730i	−0.377884	−	1.50237i
$804$		0			0
$805$	10.1631	−	7.38394i	0.358203	−	0.260250i
$806$		0			0
$807$	8.14590	−	25.0705i	0.286749	−	0.882523i
$808$		0			0
$809$	−8.25329	−	5.99637i	−0.290170	−	0.210821i	0.433171	−	0.901312i	$-0.357395\pi$
$809$	−8.25329	−	5.99637i	−0.290170	−	0.210821i	−0.723341	+	0.690491i	$0.757395\pi$
$810$		0			0
$811$	−12.8435	−	39.5281i	−0.450995	−	1.38802i	−0.875774	−	0.482722i	$-0.839648\pi$
$811$	−12.8435	−	39.5281i	−0.450995	−	1.38802i	0.424779	−	0.905297i	$-0.360352\pi$
$812$		0			0
$813$	−6.56231			−0.230150
$814$		0			0
$815$	19.9443			0.698617
$816$		0			0
$817$	13.3541	+	41.0997i	0.467201	+	1.43790i
$818$		0			0
$819$	0.427051	+	0.310271i	0.0149224	+	0.0108417i
$820$		0			0
$821$	−3.34346	+	10.2901i	−0.116688	+	0.359127i	−0.992295	−	0.123896i	$-0.960461\pi$
$821$	−3.34346	+	10.2901i	−0.116688	+	0.359127i	0.875608	+	0.483023i	$0.160461\pi$
$822$		0			0
$823$	0.663119	−	0.481784i	0.0231149	−	0.0167939i	−0.576168	−	0.817331i	$-0.695453\pi$
$823$	0.663119	−	0.481784i	0.0231149	−	0.0167939i	0.599283	+	0.800537i	$0.295453\pi$
$824$		0			0
$825$	−2.94427	+	7.33094i	−0.102506	+	0.255230i
$826$		0			0
$827$	−28.8885	+	20.9888i	−1.00455	+	0.729851i	−0.963060	−	0.269288i	$-0.913212\pi$
$827$	−28.8885	+	20.9888i	−1.00455	+	0.729851i	−0.0414935	+	0.999139i	$0.513212\pi$
$828$		0			0
$829$	1.28115	−	3.94298i	0.0444963	−	0.136945i	−0.926340	−	0.376688i	$-0.877063\pi$
$829$	1.28115	−	3.94298i	0.0444963	−	0.136945i	0.970837	+	0.239742i	$0.0770630\pi$
$830$		0			0
$831$	25.6803	+	18.6579i	0.890841	+	0.647234i
$832$		0			0
$833$	1.61803	+	4.97980i	0.0560616	+	0.172540i
$834$		0			0
$835$	16.3262			0.564993
$836$		0			0
$837$	−3.09017			−0.106812
$838$		0			0
$839$	3.63525	+	11.1882i	0.125503	+	0.386258i	0.993992	−	0.109449i	$-0.0349087\pi$
$839$	3.63525	+	11.1882i	0.125503	+	0.386258i	−0.868489	+	0.495708i	$0.834909\pi$
$840$		0			0
$841$	20.2254	+	14.6946i	0.697428	+	0.506711i
$842$		0			0
$843$	3.32624	−	10.2371i	0.114562	−	0.352585i
$844$		0			0
$845$	−16.9443	+	12.3107i	−0.582901	+	0.423502i
$846$		0			0
$847$	−17.7639	−	17.0130i	−0.610376	−	0.584574i
$848$		0			0
$849$	−19.9443	+	14.4904i	−0.684486	+	0.497308i
$850$		0			0
$851$	−7.19756	+	22.1518i	−0.246729	+	0.759354i
$852$		0			0
$853$	2.04508	+	1.48584i	0.0700224	+	0.0508742i	0.622246	−	0.782822i	$-0.286220\pi$
$853$	2.04508	+	1.48584i	0.0700224	+	0.0508742i	−0.552223	+	0.833696i	$0.686220\pi$
$854$		0			0
$855$	1.80902	+	5.56758i	0.0618671	+	0.190407i
$856$		0			0
$857$	45.6525			1.55946			0.779729	−	0.626117i	$-0.215357\pi$
$857$	45.6525			1.55946			0.779729	+	0.626117i	$0.215357\pi$
$858$		0			0
$859$	−13.0689			−0.445905			−0.222952	−	0.974829i	$-0.571569\pi$
$859$	−13.0689			−0.445905			−0.222952	+	0.974829i	$0.571569\pi$
$860$		0			0
$861$	−5.69098	−	17.5150i	−0.193948	−	0.596911i
$862$		0			0
$863$	19.0344	+	13.8293i	0.647940	+	0.470756i	0.862569	−	0.505940i	$-0.168854\pi$
$863$	19.0344	+	13.8293i	0.647940	+	0.470756i	−0.214629	+	0.976696i	$0.568854\pi$
$864$		0			0
$865$	3.33688	−	10.2699i	0.113457	−	0.349186i
$866$		0			0
$867$	−8.20820	+	5.96361i	−0.278765	+	0.202535i
$868$		0			0
$869$	2.18034	−	5.42882i	0.0739630	−	0.184160i
$870$		0			0
$871$	−2.69098	+	1.95511i	−0.0911805	+	0.0662465i
$872$		0			0
$873$	−1.82624	+	5.62058i	−0.0618088	+	0.190228i
$874$		0			0
$875$	−21.6074	−	15.6987i	−0.730463	−	0.530713i
$876$		0			0
$877$	3.21885	+	9.90659i	0.108693	+	0.334522i	0.990579	−	0.136940i	$-0.0437266\pi$
$877$	3.21885	+	9.90659i	0.108693	+	0.334522i	−0.881887	+	0.471461i	$0.843727\pi$
$878$		0			0
$879$	16.1246			0.543870
$880$		0			0
$881$	−27.9656			−0.942184			−0.471092	−	0.882084i	$-0.656140\pi$
$881$	−27.9656			−0.942184			−0.471092	+	0.882084i	$0.656140\pi$
$882$		0			0
$883$	−1.96556	−	6.04937i	−0.0661463	−	0.203577i	0.912521	−	0.409031i	$-0.134133\pi$
$883$	−1.96556	−	6.04937i	−0.0661463	−	0.203577i	−0.978667	+	0.205453i	$0.934133\pi$
$884$		0			0
$885$	3.73607	+	2.71441i	0.125587	+	0.0912440i
$886$		0			0
$887$	−0.600813	+	1.84911i	−0.0201733	+	0.0620871i	−0.960636	−	0.277809i	$-0.910392\pi$
$887$	−0.600813	+	1.84911i	−0.0201733	+	0.0620871i	0.940463	+	0.339896i	$0.110392\pi$
$888$		0			0
$889$	23.0902	−	16.7760i	0.774419	−	0.562649i
$890$		0			0
$891$	−0.809017	−	3.21644i	−0.0271031	−	0.107755i
$892$		0			0
$893$	21.6074	−	15.6987i	0.723064	−	0.525337i
$894$		0			0
$895$	2.11803	−	6.51864i	0.0707981	−	0.217894i
$896$		0			0
$897$	−0.663119	−	0.481784i	−0.0221409	−	0.0160863i
$898$		0			0
$899$	1.90983	+	5.87785i	0.0636964	+	0.196037i
$900$		0			0
$901$	−30.2705			−1.00846
$902$		0			0
$903$	26.7082			0.888793
$904$		0			0
$905$	11.5000	+	35.3934i	0.382273	+	1.17652i
$906$		0			0
$907$	−20.8713	−	15.1639i	−0.693021	−	0.503509i	0.184631	−	0.982808i	$-0.440891\pi$
$907$	−20.8713	−	15.1639i	−0.693021	−	0.503509i	−0.877652	+	0.479299i	$0.840891\pi$
$908$		0			0
$909$	−3.92705	+	12.0862i	−0.130252	+	0.400875i
$910$		0			0
$911$	1.28115	−	0.930812i	0.0424465	−	0.0308392i	−0.566360	−	0.824158i	$-0.691649\pi$
$911$	1.28115	−	0.930812i	0.0424465	−	0.0308392i	0.608806	+	0.793319i	$0.291649\pi$
$912$		0			0
$913$	−30.3779	−	2.06111i	−1.00536	−	0.0682129i
$914$		0			0
$915$	5.73607	−	4.16750i	0.189629	−	0.137773i
$916$		0			0
$917$	−11.9336	+	36.7279i	−0.394083	+	1.21286i
$918$		0			0
$919$	17.6631	+	12.8330i	0.582653	+	0.423322i	0.839679	−	0.543082i	$-0.182743\pi$
$919$	17.6631	+	12.8330i	0.582653	+	0.423322i	−0.257027	+	0.966404i	$0.582743\pi$
$920$		0			0
$921$	−8.57295	−	26.3848i	−0.282488	−	0.869410i
$922$		0			0
$923$	2.09017			0.0687988
$924$		0			0
$925$	15.9787			0.525377
$926$		0			0
$927$	−5.09017	−	15.6659i	−0.167183	−	0.514537i
$928$		0			0
$929$	−18.8435	−	13.6906i	−0.618234	−	0.449173i	0.234070	−	0.972220i	$-0.424795\pi$
$929$	−18.8435	−	13.6906i	−0.618234	−	0.449173i	−0.852304	+	0.523046i	$0.824795\pi$
$930$		0			0
$931$	2.23607	−	6.88191i	0.0732842	−	0.225545i
$932$		0			0
$933$	10.5172	−	7.64121i	0.344318	−	0.250162i
$934$		0			0
$935$	10.7812	+	9.00854i	0.352581	+	0.294611i
$936$		0			0
$937$	−29.6074	+	21.5110i	−0.967231	+	0.702735i	−0.954819	−	0.297188i	$-0.903951\pi$
$937$	−29.6074	+	21.5110i	−0.967231	+	0.702735i	−0.0124124	+	0.999923i	$0.503951\pi$
$938$		0			0
$939$	−8.16312	+	25.1235i	−0.266393	+	0.819874i
$940$		0			0
$941$	8.29837	+	6.02912i	0.270519	+	0.196544i	0.714772	−	0.699358i	$-0.246531\pi$
$941$	8.29837	+	6.02912i	0.270519	+	0.196544i	−0.444252	+	0.895902i	$0.646531\pi$
$942$		0			0
$943$	8.83688	+	27.1971i	0.287768	+	0.885660i
$944$		0			0
$945$	3.61803			0.117695
$946$		0			0
$947$	−0.742646			−0.0241327			−0.0120664	−	0.999927i	$-0.503841\pi$
$947$	−0.742646			−0.0241327			−0.0120664	+	0.999927i	$0.503841\pi$
$948$		0			0
$949$	−0.965558	−	2.97168i	−0.0313433	−	0.0964649i
$950$		0			0
$951$	8.66312	+	6.29412i	0.280921	+	0.204101i
$952$		0			0
$953$	15.6525	−	48.1734i	0.507033	−	1.56049i	−0.290292	−	0.956938i	$-0.593752\pi$
$953$	15.6525	−	48.1734i	0.507033	−	1.56049i	0.797325	−	0.603550i	$-0.206248\pi$
$954$		0			0
$955$	−23.4894	+	17.0660i	−0.760098	+	0.552243i
$956$		0			0
$957$	−5.61803	+	3.52671i	−0.181605	+	0.114002i
$958$		0			0
$959$	12.9894	−	9.43732i	0.419448	−	0.304747i
$960$		0			0
$961$	−6.62868	+	20.4010i	−0.213828	+	0.658096i
$962$		0			0
$963$	−4.19098	−	3.04493i	−0.135053	−	0.0981214i
$964$		0			0
$965$	−7.07295	−	21.7683i	−0.227686	−	0.700746i
$966$		0			0
$967$	21.3951			0.688021			0.344010	−	0.938966i	$-0.388214\pi$
$967$	21.3951			0.688021			0.344010	+	0.938966i	$0.388214\pi$
$968$		0			0
$969$	−9.47214			−0.304289
$970$		0			0
$971$	−11.5623	−	35.5851i	−0.371052	−	1.14198i	−0.946104	−	0.323864i	$-0.895018\pi$
$971$	−11.5623	−	35.5851i	−0.371052	−	1.14198i	0.575052	−	0.818117i	$-0.304982\pi$
$972$		0			0
$973$	−4.20820	−	3.05744i	−0.134909	−	0.0980170i
$974$		0			0
$975$	−0.173762	+	0.534785i	−0.00556484	+	0.0171268i
$976$		0			0
$977$	−1.80902	+	1.31433i	−0.0578756	+	0.0420491i	−0.616347	−	0.787475i	$-0.711388\pi$
$977$	−1.80902	+	1.31433i	−0.0578756	+	0.0420491i	0.558471	+	0.829524i	$0.311388\pi$
$978$		0			0
$979$	−34.3713	+	21.5765i	−1.09851	+	0.689589i
$980$		0			0
$981$	−9.70820	+	7.05342i	−0.309959	+	0.225198i
$982$		0			0
$983$	−11.2016	+	34.4751i	−0.357276	+	1.09958i	0.597401	+	0.801942i	$0.296200\pi$
$983$	−11.2016	+	34.4751i	−0.357276	+	1.09958i	−0.954678	+	0.297641i	$0.903800\pi$
$984$		0			0
$985$	−9.66312	−	7.02067i	−0.307893	−	0.223697i
$986$		0			0
$987$	−5.10081	−	15.6987i	−0.162361	−	0.499695i
$988$		0			0
$989$	−41.4721			−1.31874
$990$		0			0
$991$	−48.9230			−1.55409			−0.777045	−	0.629445i	$-0.783282\pi$
$991$	−48.9230			−1.55409			−0.777045	+	0.629445i	$0.783282\pi$
$992$		0			0
$993$	4.16312	+	12.8128i	0.132113	+	0.406601i
$994$		0			0
$995$	3.16312	+	2.29814i	0.100278	+	0.0728560i
$996$		0			0
$997$	−2.44427	+	7.52270i	−0.0774109	+	0.238246i	−0.982272	−	0.187460i	$-0.939974\pi$
$997$	−2.44427	+	7.52270i	−0.0774109	+	0.238246i	0.904861	+	0.425706i	$0.139974\pi$
$998$		0			0
$999$	−5.42705	+	3.94298i	−0.171704	+	0.124750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.q.d.25.1	✓	4
3.2	odd	2		792.2.r.c.289.1		4
4.3	odd	2		528.2.y.c.289.1		4
11.2	odd	10		2904.2.a.p.1.1		2
11.4	even	5	inner	264.2.q.d.169.1	yes	4
11.9	even	5		2904.2.a.q.1.1		2
33.2	even	10		8712.2.a.bn.1.2		2
33.20	odd	10		8712.2.a.bo.1.2		2
33.26	odd	10		792.2.r.c.433.1		4
44.15	odd	10		528.2.y.c.433.1		4
44.31	odd	10		5808.2.a.ce.1.1		2
44.35	even	10		5808.2.a.cd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.d.25.1	✓	4	1.1	even	1	trivial
264.2.q.d.169.1	yes	4	11.4	even	5	inner
528.2.y.c.289.1		4	4.3	odd	2
528.2.y.c.433.1		4	44.15	odd	10
792.2.r.c.289.1		4	3.2	odd	2
792.2.r.c.433.1		4	33.26	odd	10
2904.2.a.p.1.1		2	11.2	odd	10
2904.2.a.q.1.1		2	11.9	even	5
5808.2.a.cd.1.1		2	44.35	even	10
5808.2.a.ce.1.1		2	44.31	odd	10
8712.2.a.bn.1.2		2	33.2	even	10
8712.2.a.bo.1.2		2	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{5} +(0.690983 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{5} +(0.690983 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.80902 - 1.76336i) q^{11} +(0.190983 - 0.138757i) q^{13} +(0.500000 - 1.53884i) q^{15} +(2.11803 + 1.53884i) q^{17} +(-1.11803 - 3.44095i) q^{19} -2.23607 q^{21} +3.47214 q^{23} +(-0.736068 - 2.26538i) q^{25} +(0.809017 + 0.587785i) q^{27} +(0.618034 - 1.90211i) q^{29} +(-2.50000 + 1.81636i) q^{31} +(-2.54508 - 2.12663i) q^{33} +(2.92705 - 2.12663i) q^{35} +(-2.07295 + 6.37988i) q^{37} +(-0.190983 - 0.138757i) q^{39} +(2.54508 + 7.83297i) q^{41} -11.9443 q^{43} -1.61803 q^{45} +(2.28115 + 7.02067i) q^{47} +(1.61803 + 1.17557i) q^{49} +(0.809017 - 2.48990i) q^{51} +(-9.35410 + 6.79615i) q^{53} +(5.35410 + 0.363271i) q^{55} +(-2.92705 + 2.12663i) q^{57} +(-0.881966 + 2.71441i) q^{59} +(3.54508 + 2.57565i) q^{61} +(0.690983 + 2.12663i) q^{63} +0.381966 q^{65} -14.0902 q^{67} +(-1.07295 - 3.30220i) q^{69} +(7.16312 + 5.20431i) q^{71} +(4.09017 - 12.5882i) q^{73} +(-1.92705 + 1.40008i) q^{75} +(-1.80902 - 7.19218i) q^{77} +(1.42705 - 1.03681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-7.42705 - 5.39607i) q^{83} +(1.30902 + 4.02874i) q^{85} -2.00000 q^{87} -12.2361 q^{89} +(-0.163119 - 0.502029i) q^{91} +(2.50000 + 1.81636i) q^{93} +(1.80902 - 5.56758i) q^{95} +(4.78115 - 3.47371i) q^{97} +(-1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9}+O(q^{10}) \) 4 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9	\( 4 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9} + 9 q^{11} + 3 q^{13} + 2 q^{15} + 4 q^{17} - 4 q^{23} + 6 q^{25} + q^{27} - 2 q^{29} - 10 q^{31} + q^{33} + 5 q^{35} - 15 q^{37} - 3 q^{39} - q^{41} - 12 q^{43} - 2 q^{45} - 11 q^{47} + 2 q^{49} + q^{51} - 24 q^{53} + 8 q^{55} - 5 q^{57} - 8 q^{59} + 3 q^{61} + 5 q^{63} + 6 q^{65} - 34 q^{67} - 11 q^{69} + 13 q^{71} - 6 q^{73} - q^{75} - 5 q^{77} - q^{79} - q^{81} - 23 q^{83} + 3 q^{85} - 8 q^{87} - 40 q^{89} + 15 q^{91} + 10 q^{93} + 5 q^{95} - q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9 + 9 * q^11 + 3 * q^13 + 2 * q^15 + 4 * q^17 - 4 * q^23 + 6 * q^25 + q^27 - 2 * q^29 - 10 * q^31 + q^33 + 5 * q^35 - 15 * q^37 - 3 * q^39 - q^41 - 12 * q^43 - 2 * q^45 - 11 * q^47 + 2 * q^49 + q^51 - 24 * q^53 + 8 * q^55 - 5 * q^57 - 8 * q^59 + 3 * q^61 + 5 * q^63 + 6 * q^65 - 34 * q^67 - 11 * q^69 + 13 * q^71 - 6 * q^73 - q^75 - 5 * q^77 - q^79 - q^81 - 23 * q^83 + 3 * q^85 - 8 * q^87 - 40 * q^89 + 15 * q^91 + 10 * q^93 + 5 * q^95 - q^97 + 4 * q^99

Introduction

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