LMFDB - Embedded newform 528.2.y.f.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(49,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("528.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.y (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.21610122672$
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:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			433.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	528.433
Dual form			528.2.y.f.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.224514i) q^{5} +(-0.927051 - 2.85317i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.224514i) q^{5} +(-0.927051 - 2.85317i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.80902 - 1.76336i) q^{11} +(-5.04508 - 3.66547i) q^{13} +(0.118034 + 0.363271i) q^{15} +(0.500000 - 0.363271i) q^{17} +(0.263932 - 0.812299i) q^{19} +3.00000 q^{21} +5.47214 q^{23} +(-1.50000 + 4.61653i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-1.38197 - 4.25325i) q^{29} +(-3.11803 - 2.26538i) q^{31} +(2.54508 - 2.12663i) q^{33} +(-0.927051 - 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(5.04508 - 3.66547i) q^{39} +(1.83688 - 5.65334i) q^{41} -1.76393 q^{43} -0.381966 q^{45} +(0.190983 - 0.587785i) q^{47} +(-1.61803 + 1.17557i) q^{49} +(0.190983 + 0.587785i) q^{51} +(5.97214 + 4.33901i) q^{53} +(-1.26393 + 0.0857567i) q^{55} +(0.690983 + 0.502029i) q^{57} +(1.64590 + 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(-0.927051 + 2.85317i) q^{63} -2.38197 q^{65} -10.5623 q^{67} +(-1.69098 + 5.20431i) q^{69} +(11.7812 - 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(-3.92705 - 2.85317i) q^{75} +(-2.42705 + 9.64932i) q^{77} +(0.427051 + 0.310271i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-10.2812 + 7.46969i) q^{83} +(0.0729490 - 0.224514i) q^{85} +4.47214 q^{87} +9.47214 q^{89} +(-5.78115 + 17.7926i) q^{91} +(3.11803 - 2.26538i) q^{93} +(-0.100813 - 0.310271i) q^{95} +(-12.1631 - 8.83702i) q^{97} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9}+O(q^{10}) $ 4 * q + q^3 - q^5 + 3 * q^7 - q^9	$ 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9} - 9 q^{11} - 9 q^{13} - 4 q^{15} + 2 q^{17} + 10 q^{19} + 12 q^{21} + 4 q^{23} - 6 q^{25} + q^{27} - 10 q^{29} - 8 q^{31} - q^{33} + 3 q^{35} - 3 q^{37} + 9 q^{39} + 23 q^{41} - 16 q^{43} - 6 q^{45} + 3 q^{47} - 2 q^{49} + 3 q^{51} + 6 q^{53} - 14 q^{55} + 5 q^{57} + 20 q^{59} + 3 q^{61} + 3 q^{63} - 14 q^{65} - 2 q^{67} - 9 q^{69} + 27 q^{71} + 6 q^{73} - 9 q^{75} - 3 q^{77} - 5 q^{79} - q^{81} - 21 q^{83} + 7 q^{85} + 20 q^{89} - 3 q^{91} + 8 q^{93} - 25 q^{95} - 33 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + q^3 - q^5 + 3 * q^7 - q^9 - 9 * q^11 - 9 * q^13 - 4 * q^15 + 2 * q^17 + 10 * q^19 + 12 * q^21 + 4 * q^23 - 6 * q^25 + q^27 - 10 * q^29 - 8 * q^31 - q^33 + 3 * q^35 - 3 * q^37 + 9 * q^39 + 23 * q^41 - 16 * q^43 - 6 * q^45 + 3 * q^47 - 2 * q^49 + 3 * q^51 + 6 * q^53 - 14 * q^55 + 5 * q^57 + 20 * q^59 + 3 * q^61 + 3 * q^63 - 14 * q^65 - 2 * q^67 - 9 * q^69 + 27 * q^71 + 6 * q^73 - 9 * q^75 - 3 * q^77 - 5 * q^79 - q^81 - 21 * q^83 + 7 * q^85 + 20 * q^89 - 3 * q^91 + 8 * q^93 - 25 * q^95 - 33 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	0.309017	−	0.224514i	0.138197	−	0.100406i	−0.516539	−	0.856264i	$-0.672780\pi$
$5$	0.309017	−	0.224514i	0.138197	−	0.100406i	0.654736	+	0.755858i	$0.272780\pi$
$6$		0			0
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	−0.958633	−	0.284644i	$-0.908125\pi$
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	0.608241	−	0.793752i	$-0.291875\pi$
$8$		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
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.994777	−	0.102070i	$-0.967453\pi$
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.404478	−	0.914548i	$-0.632547\pi$
$14$		0			0
$15$	0.118034	+	0.363271i	0.0304762	+	0.0937962i
$16$		0			0
$17$	0.500000	−	0.363271i	0.121268	−	0.0881062i	−0.525498	−	0.850795i	$-0.676121\pi$
$17$	0.500000	−	0.363271i	0.121268	−	0.0881062i	0.646766	+	0.762688i	$0.276121\pi$
$18$		0			0
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	−0.916206	−	0.400707i	$-0.868764\pi$
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	0.976756	+	0.214353i	$0.0687644\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$		0			0
$23$	5.47214			1.14102			0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214			1.14102			0.570510	+	0.821291i	$0.306746\pi$
$24$		0			0
$25$	−1.50000	+	4.61653i	−0.300000	+	0.923305i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$		0			0
$31$	−3.11803	−	2.26538i	−0.560015	−	0.406875i	0.271449	−	0.962453i	$-0.412497\pi$
$31$	−3.11803	−	2.26538i	−0.560015	−	0.406875i	−0.831465	+	0.555578i	$0.812497\pi$
$32$		0			0
$33$	2.54508	−	2.12663i	0.443042	−	0.370198i
$34$		0			0
$35$	−0.927051	−	0.673542i	−0.156700	−	0.113849i
$36$		0			0
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	−0.999139	−	0.0414819i	$-0.986792\pi$
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	0.783938	−	0.620839i	$-0.213208\pi$
$38$		0			0
$39$	5.04508	−	3.66547i	0.807860	−	0.586945i
$40$		0			0
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	−0.698958	−	0.715162i	$-0.746353\pi$
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	0.985831	−	0.167741i	$-0.0536472\pi$
$42$		0			0
$43$	−1.76393			−0.268997			−0.134499	−	0.990914i	$-0.542942\pi$
$43$	−1.76393			−0.268997			−0.134499	+	0.990914i	$0.542942\pi$
$44$		0			0
$45$	−0.381966			−0.0569401
$46$		0			0
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	−0.936161	−	0.351572i	$-0.885647\pi$
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	0.964019	+	0.265834i	$0.0856474\pi$
$48$		0			0
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$		0			0
$51$	0.190983	+	0.587785i	0.0267430	+	0.0823064i
$52$		0			0
$53$	5.97214	+	4.33901i	0.820336	+	0.596009i	0.916809	−	0.399327i	$-0.130756\pi$
$53$	5.97214	+	4.33901i	0.820336	+	0.596009i	−0.0964728	+	0.995336i	$0.530756\pi$
$54$		0			0
$55$	−1.26393	+	0.0857567i	−0.170429	+	0.0115634i
$56$		0			0
$57$	0.690983	+	0.502029i	0.0915229	+	0.0664953i
$58$		0			0
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	0.999204	+	0.0398899i	$0.0127007\pi$
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	−0.784926	+	0.619589i	$0.787299\pi$
$60$		0			0
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	−0.645550	−	0.763718i	$-0.723372\pi$
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	0.526853	+	0.849956i	$0.323372\pi$
$62$		0			0
$63$	−0.927051	+	2.85317i	−0.116797	+	0.359466i
$64$		0			0
$65$	−2.38197			−0.295447
$66$		0			0
$67$	−10.5623			−1.29039			−0.645196	−	0.764017i	$-0.723224\pi$
$67$	−10.5623			−1.29039			−0.645196	+	0.764017i	$0.723224\pi$
$68$		0			0
$69$	−1.69098	+	5.20431i	−0.203570	+	0.626525i
$70$		0			0
$71$	11.7812	−	8.55951i	1.39817	−	1.01583i	0.403253	−	0.915089i	$-0.367880\pi$
$71$	11.7812	−	8.55951i	1.39817	−	1.01583i	0.994913	−	0.100738i	$-0.0321204\pi$
$72$		0			0
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	0.970918	−	0.239412i	$-0.0769548\pi$
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	−0.926212	+	0.377003i	$0.876955\pi$
$74$		0			0
$75$	−3.92705	−	2.85317i	−0.453457	−	0.329456i
$76$		0			0
$77$	−2.42705	+	9.64932i	−0.276588	+	1.09964i
$78$		0			0
$79$	0.427051	+	0.310271i	0.0480470	+	0.0349082i	0.611550	−	0.791206i	$-0.290547\pi$
$79$	0.427051	+	0.310271i	0.0480470	+	0.0349082i	−0.563503	+	0.826114i	$0.690547\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.985476	−	0.169813i	$-0.945684\pi$
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.143027	+	0.989719i	$0.545684\pi$
$84$		0			0
$85$	0.0729490	−	0.224514i	0.00791243	−	0.0243520i
$86$		0			0
$87$	4.47214			0.479463
$88$		0			0
$89$	9.47214			1.00404			0.502022	−	0.864855i	$-0.332590\pi$
$89$	9.47214			1.00404			0.502022	+	0.864855i	$0.332590\pi$
$90$		0			0
$91$	−5.78115	+	17.7926i	−0.606029	+	1.86517i
$92$		0			0
$93$	3.11803	−	2.26538i	0.323325	−	0.234909i
$94$		0			0
$95$	−0.100813	−	0.310271i	−0.0103432	−	0.0318331i
$96$		0			0
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.237724	−	0.971333i	$-0.576402\pi$
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.997253	+	0.0740689i	$0.976402\pi$
$98$		0			0
$99$	1.23607	+	3.07768i	0.124230	+	0.309319i
$100$		0			0
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$		0			0
$103$	1.85410	+	5.70634i	0.182690	+	0.562262i	0.999901	−	0.0140765i	$-0.00448085\pi$
$103$	1.85410	+	5.70634i	0.182690	+	0.562262i	−0.817211	+	0.576339i	$0.804481\pi$
$104$		0			0
$105$	0.927051	−	0.673542i	0.0904709	−	0.0657310i
$106$		0			0
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	−0.954521	−	0.298145i	$-0.903632\pi$
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	0.947468	+	0.319849i	$0.103632\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	4.23607			0.402070
$112$		0			0
$113$	−3.92705	+	12.0862i	−0.369426	+	1.13698i	0.577737	+	0.816223i	$0.303936\pi$
$113$	−3.92705	+	12.0862i	−0.369426	+	1.13698i	−0.947163	+	0.320753i	$0.896064\pi$
$114$		0			0
$115$	1.69098	−	1.22857i	0.157685	−	0.114565i
$116$		0			0
$117$	1.92705	+	5.93085i	0.178156	+	0.548308i
$118$		0			0
$119$	−1.50000	−	1.08981i	−0.137505	−	0.0999031i
$120$		0			0
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$		0			0
$123$	4.80902	+	3.49396i	0.433614	+	0.315039i
$124$		0			0
$125$	1.16312	+	3.57971i	0.104033	+	0.320179i
$126$		0			0
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	−0.181995	−	0.983299i	$-0.558255\pi$
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	0.878934	+	0.476944i	$0.158255\pi$
$128$		0			0
$129$	0.545085	−	1.67760i	0.0479921	−	0.147704i
$130$		0			0
$131$	13.8541			1.21044			0.605219	−	0.796059i	$-0.293085\pi$
$131$	13.8541			1.21044			0.605219	+	0.796059i	$0.293085\pi$
$132$		0			0
$133$	−2.56231			−0.222180
$134$		0			0
$135$	0.118034	−	0.363271i	0.0101587	−	0.0312654i
$136$		0			0
$137$	1.19098	−	0.865300i	0.101753	−	0.0739276i	−0.535746	−	0.844379i	$-0.679969\pi$
$137$	1.19098	−	0.865300i	0.101753	−	0.0739276i	0.637498	+	0.770452i	$0.279969\pi$
$138$		0			0
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	0.844561	−	0.535460i	$-0.179862\pi$
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	−0.997999	+	0.0632239i	$0.979862\pi$
$140$		0			0
$141$	0.500000	+	0.363271i	0.0421076	+	0.0305930i
$142$		0			0
$143$	7.70820	+	19.1926i	0.644592	+	1.60497i
$144$		0			0
$145$	−1.38197	−	1.00406i	−0.114766	−	0.0833824i
$146$		0			0
$147$	−0.618034	−	1.90211i	−0.0509746	−	0.156884i
$148$		0			0
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.960828	−	0.277146i	$-0.910612\pi$
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.0333309	+	0.999444i	$0.510612\pi$
$150$		0			0
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	−0.973050	−	0.230596i	$-0.925932\pi$
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	0.922755	+	0.385388i	$0.125932\pi$
$152$		0			0
$153$	−0.618034			−0.0499651
$154$		0			0
$155$	−1.47214			−0.118245
$156$		0			0
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$		0			0
$159$	−5.97214	+	4.33901i	−0.473621	+	0.344106i
$160$		0			0
$161$	−5.07295	−	15.6129i	−0.399804	−	1.23047i
$162$		0			0
$163$	−12.3541	−	8.97578i	−0.967648	−	0.703037i	−0.0127336	−	0.999919i	$-0.504053\pi$
$163$	−12.3541	−	8.97578i	−0.967648	−	0.703037i	−0.954914	+	0.296882i	$0.904053\pi$
$164$		0			0
$165$	0.309017	−	1.22857i	0.0240569	−	0.0956441i
$166$		0			0
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.198190	−	0.980164i	$-0.563506\pi$
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.993435	+	0.114398i	$0.963506\pi$
$168$		0			0
$169$	8.00000	+	24.6215i	0.615385	+	1.89396i
$170$		0			0
$171$	−0.690983	+	0.502029i	−0.0528408	+	0.0383911i
$172$		0			0
$173$	5.44427	−	16.7557i	0.413920	−	1.27392i	−0.499293	−	0.866433i	$-0.666407\pi$
$173$	5.44427	−	16.7557i	0.413920	−	1.27392i	0.913213	−	0.407482i	$-0.133593\pi$
$174$		0			0
$175$	14.5623			1.10081
$176$		0			0
$177$	−5.32624			−0.400345
$178$		0			0
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	−0.973553	−	0.228460i	$-0.926631\pi$
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	0.921907	+	0.387412i	$0.126631\pi$
$180$		0			0
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	−0.301077	−	0.953600i	$-0.597346\pi$
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	0.813889	+	0.581020i	$0.197346\pi$
$182$		0			0
$183$	−0.354102	−	1.08981i	−0.0261760	−	0.0805614i
$184$		0			0
$185$	−1.30902	−	0.951057i	−0.0962408	−	0.0699231i
$186$		0			0
$187$	−2.04508	+	0.138757i	−0.149551	+	0.0101469i
$188$		0			0
$189$	−2.42705	−	1.76336i	−0.176542	−	0.128265i
$190$		0			0
$191$	−0.454915	−	1.40008i	−0.0329165	−	0.101307i	0.933248	−	0.359232i	$-0.116961\pi$
$191$	−0.454915	−	1.40008i	−0.0329165	−	0.101307i	−0.966165	+	0.257925i	$0.916961\pi$
$192$		0			0
$193$	−1.26393	+	0.918300i	−0.0909798	+	0.0661007i	−0.632345	−	0.774687i	$-0.717908\pi$
$193$	−1.26393	+	0.918300i	−0.0909798	+	0.0661007i	0.541365	+	0.840787i	$0.317908\pi$
$194$		0			0
$195$	0.736068	−	2.26538i	0.0527109	−	0.162228i
$196$		0			0
$197$	26.6180			1.89646			0.948228	−	0.317590i	$-0.102873\pi$
$197$	26.6180			1.89646			0.948228	+	0.317590i	$0.102873\pi$
$198$		0			0
$199$	3.29180			0.233349			0.116675	−	0.993170i	$-0.462777\pi$
$199$	3.29180			0.233349			0.116675	+	0.993170i	$0.462777\pi$
$200$		0			0
$201$	3.26393	−	10.0453i	0.230220	−	0.708544i
$202$		0			0
$203$	−10.8541	+	7.88597i	−0.761809	+	0.553486i
$204$		0			0
$205$	−0.701626	−	2.15938i	−0.0490037	−	0.150818i
$206$		0			0
$207$	−4.42705	−	3.21644i	−0.307701	−	0.223558i
$208$		0			0
$209$	−2.17376	+	1.81636i	−0.150362	+	0.125640i
$210$		0			0
$211$	9.11803	+	6.62464i	0.627711	+	0.456059i	0.855607	−	0.517627i	$-0.173184\pi$
$211$	9.11803	+	6.62464i	0.627711	+	0.456059i	−0.227895	+	0.973686i	$0.573184\pi$
$212$		0			0
$213$	4.50000	+	13.8496i	0.308335	+	0.948957i
$214$		0			0
$215$	−0.545085	+	0.396027i	−0.0371745	+	0.0270088i
$216$		0			0
$217$	−3.57295	+	10.9964i	−0.242548	+	0.746485i
$218$		0			0
$219$	−1.23607			−0.0835257
$220$		0			0
$221$	−3.85410			−0.259255
$222$		0			0
$223$	3.92705	−	12.0862i	0.262975	−	0.809353i	−0.729178	−	0.684324i	$-0.760097\pi$
$223$	3.92705	−	12.0862i	0.262975	−	0.809353i	0.992153	−	0.125029i	$-0.0399025\pi$
$224$		0			0
$225$	3.92705	−	2.85317i	0.261803	−	0.190211i
$226$		0			0
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	−0.998457	−	0.0555264i	$-0.982316\pi$
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	0.775131	−	0.631800i	$-0.217684\pi$
$228$		0			0
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	0.287467	−	0.957790i	$-0.407187\pi$
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	−0.822081	+	0.569371i	$0.807187\pi$
$230$		0			0
$231$	−8.42705	−	5.29007i	−0.554459	−	0.348061i
$232$		0			0
$233$	−7.01722	−	5.09831i	−0.459713	−	0.334001i	0.333705	−	0.942677i	$-0.391701\pi$
$233$	−7.01722	−	5.09831i	−0.459713	−	0.334001i	−0.793419	+	0.608676i	$0.791701\pi$
$234$		0			0
$235$	−0.0729490	−	0.224514i	−0.00475867	−	0.0146457i
$236$		0			0
$237$	−0.427051	+	0.310271i	−0.0277399	+	0.0201542i
$238$		0			0
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	−0.607220	−	0.794534i	$-0.707715\pi$
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	0.958266	−	0.285877i	$-0.0922848\pi$
$240$		0			0
$241$	17.1246			1.10309			0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246			1.10309			0.551547	+	0.834144i	$0.314038\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−0.236068	+	0.726543i	−0.0150818	+	0.0464171i
$246$		0			0
$247$	−4.30902	+	3.13068i	−0.274176	+	0.199201i
$248$		0			0
$249$	−3.92705	−	12.0862i	−0.248867	−	0.765933i
$250$		0			0
$251$	13.5902	+	9.87384i	0.857804	+	0.623231i	0.927287	−	0.374352i	$-0.122135\pi$
$251$	13.5902	+	9.87384i	0.857804	+	0.623231i	−0.0694827	+	0.997583i	$0.522135\pi$
$252$		0			0
$253$	−15.3713	−	9.64932i	−0.966387	−	0.606648i
$254$		0			0
$255$	0.190983	+	0.138757i	0.0119598	+	0.00868932i
$256$		0			0
$257$	−8.44427	−	25.9888i	−0.526739	−	1.62114i	−0.760851	−	0.648927i	$-0.775218\pi$
$257$	−8.44427	−	25.9888i	−0.526739	−	1.62114i	0.234112	−	0.972210i	$-0.424782\pi$
$258$		0			0
$259$	−10.2812	+	7.46969i	−0.638840	+	0.464144i
$260$		0			0
$261$	−1.38197	+	4.25325i	−0.0855415	+	0.263270i
$262$		0			0
$263$	0.673762			0.0415459			0.0207730	−	0.999784i	$-0.493387\pi$
$263$	0.673762			0.0415459			0.0207730	+	0.999784i	$0.493387\pi$
$264$		0			0
$265$	2.81966			0.173210
$266$		0			0
$267$	−2.92705	+	9.00854i	−0.179133	+	0.551313i
$268$		0			0
$269$	−19.7984	+	14.3844i	−1.20713	+	0.877030i	−0.994967	−	0.100205i	$-0.968050\pi$
$269$	−19.7984	+	14.3844i	−1.20713	+	0.877030i	−0.212161	+	0.977235i	$0.568050\pi$
$270$		0			0
$271$	−1.93769	−	5.96361i	−0.117707	−	0.362263i	0.874795	−	0.484493i	$-0.160996\pi$
$271$	−1.93769	−	5.96361i	−0.117707	−	0.362263i	−0.992502	+	0.122229i	$0.960996\pi$
$272$		0			0
$273$	−15.1353	−	10.9964i	−0.916027	−	0.665533i
$274$		0			0
$275$	12.3541	−	10.3229i	0.744980	−	0.622492i
$276$		0			0
$277$	−8.44427	−	6.13512i	−0.507367	−	0.368624i	0.304457	−	0.952526i	$-0.401525\pi$
$277$	−8.44427	−	6.13512i	−0.507367	−	0.368624i	−0.811824	+	0.583902i	$0.801525\pi$
$278$		0			0
$279$	1.19098	+	3.66547i	0.0713023	+	0.219446i
$280$		0			0
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	−0.454221	−	0.890889i	$-0.650082\pi$
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	0.706924	+	0.707290i	$0.250082\pi$
$282$		0			0
$283$	6.85410	−	21.0948i	0.407434	−	1.25395i	−0.511412	−	0.859336i	$-0.670877\pi$
$283$	6.85410	−	21.0948i	0.407434	−	1.25395i	0.918846	−	0.394617i	$-0.129123\pi$
$284$		0			0
$285$	0.326238			0.0193247
$286$		0			0
$287$	−17.8328			−1.05264
$288$		0			0
$289$	−5.13525	+	15.8047i	−0.302074	+	0.929688i
$290$		0			0
$291$	12.1631	−	8.83702i	0.713015	−	0.518035i
$292$		0			0
$293$	5.54508	+	17.0660i	0.323947	+	0.997007i	0.971914	+	0.235338i	$0.0756198\pi$
$293$	5.54508	+	17.0660i	0.323947	+	0.997007i	−0.647966	+	0.761669i	$0.724380\pi$
$294$		0			0
$295$	1.64590	+	1.19581i	0.0958279	+	0.0696230i
$296$		0			0
$297$	−3.30902	+	0.224514i	−0.192009	+	0.0130276i
$298$		0			0
$299$	−27.6074	−	20.0579i	−1.59658	−	1.15998i
$300$		0			0
$301$	1.63525	+	5.03280i	0.0942545	+	0.290086i
$302$		0			0
$303$	−2.42705	+	1.76336i	−0.139430	+	0.101302i
$304$		0			0
$305$	−0.135255	+	0.416272i	−0.00774467	+	0.0238357i
$306$		0			0
$307$	19.5623			1.11648			0.558240	−	0.829680i	$-0.311477\pi$
$307$	19.5623			1.11648			0.558240	+	0.829680i	$0.311477\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$		0			0
$311$	−3.54508	+	10.9106i	−0.201023	+	0.618686i	0.798830	+	0.601557i	$0.205453\pi$
$311$	−3.54508	+	10.9106i	−0.201023	+	0.618686i	−0.999853	+	0.0171293i	$0.994547\pi$
$312$		0			0
$313$	22.5172	−	16.3597i	1.27275	−	0.924706i	0.273440	−	0.961889i	$-0.411838\pi$
$313$	22.5172	−	16.3597i	1.27275	−	0.924706i	0.999308	+	0.0371831i	$0.0118385\pi$
$314$		0			0
$315$	0.354102	+	1.08981i	0.0199514	+	0.0614041i
$316$		0			0
$317$	−20.5172	−	14.9066i	−1.15236	−	0.837240i	−0.163569	−	0.986532i	$-0.552301\pi$
$317$	−20.5172	−	14.9066i	−1.15236	−	0.837240i	−0.988793	+	0.149292i	$0.952301\pi$
$318$		0			0
$319$	−3.61803	+	14.3844i	−0.202571	+	0.805370i
$320$		0			0
$321$	−0.190983	−	0.138757i	−0.0106596	−	0.00774468i
$322$		0			0
$323$	−0.163119	−	0.502029i	−0.00907618	−	0.0279336i
$324$		0			0
$325$	24.4894	−	17.7926i	1.35843	−	0.986954i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.85410			−0.102220
$330$		0			0
$331$	22.5967			1.24203			0.621015	−	0.783799i	$-0.286721\pi$
$331$	22.5967			1.24203			0.621015	+	0.783799i	$0.286721\pi$
$332$		0			0
$333$	−1.30902	+	4.02874i	−0.0717337	+	0.220774i
$334$		0			0
$335$	−3.26393	+	2.37139i	−0.178328	+	0.129563i
$336$		0			0
$337$	−4.23607	−	13.0373i	−0.230753	−	0.710186i	−0.997656	−	0.0684228i	$-0.978203\pi$
$337$	−4.23607	−	13.0373i	−0.230753	−	0.710186i	0.766903	−	0.641763i	$-0.221797\pi$
$338$		0			0
$339$	−10.2812	−	7.46969i	−0.558396	−	0.405698i
$340$		0			0
$341$	4.76393	+	11.8617i	0.257981	+	0.642347i
$342$		0			0
$343$	−12.1353	−	8.81678i	−0.655242	−	0.476061i
$344$		0			0
$345$	0.645898	+	1.98787i	0.0347740	+	0.107023i
$346$		0			0
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	−0.652160	−	0.758081i	$-0.726137\pi$
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	0.519449	+	0.854501i	$0.326137\pi$
$348$		0			0
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	−0.313449	−	0.949605i	$-0.601485\pi$
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	0.811750	−	0.584006i	$-0.198515\pi$
$350$		0			0
$351$	−6.23607			−0.332857
$352$		0			0
$353$	−1.52786			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$353$	−1.52786			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$354$		0			0
$355$	1.71885	−	5.29007i	0.0912269	−	0.280768i
$356$		0			0
$357$	1.50000	−	1.08981i	0.0793884	−	0.0576791i
$358$		0			0
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	0.987538	+	0.157379i	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$		0			0
$363$	−10.8992	+	1.48584i	−0.572059	+	0.0779864i
$364$		0			0
$365$	0.381966	+	0.277515i	0.0199930	+	0.0145258i
$366$		0			0
$367$	4.50000	+	13.8496i	0.234898	+	0.722942i	0.997135	+	0.0756437i	$0.0241012\pi$
$367$	4.50000	+	13.8496i	0.234898	+	0.722942i	−0.762237	+	0.647298i	$0.775899\pi$
$368$		0			0
$369$	−4.80902	+	3.49396i	−0.250347	+	0.181888i
$370$		0			0
$371$	6.84346	−	21.0620i	0.355295	−	1.09348i
$372$		0			0
$373$	22.4164			1.16068			0.580339	−	0.814375i	$-0.302920\pi$
$373$	22.4164			1.16068			0.580339	+	0.814375i	$0.302920\pi$
$374$		0			0
$375$	−3.76393			−0.194369
$376$		0			0
$377$	−8.61803	+	26.5236i	−0.443851	+	1.36603i
$378$		0			0
$379$	22.9894	−	16.7027i	1.18088	−	0.857962i	0.188613	−	0.982052i	$-0.439601\pi$
$379$	22.9894	−	16.7027i	1.18088	−	0.857962i	0.992271	+	0.124089i	$0.0396009\pi$
$380$		0			0
$381$	3.00000	+	9.23305i	0.153695	+	0.473024i
$382$		0			0
$383$	−7.19098	−	5.22455i	−0.367442	−	0.266962i	0.388707	−	0.921361i	$-0.372922\pi$
$383$	−7.19098	−	5.22455i	−0.367442	−	0.266962i	−0.756149	+	0.654399i	$0.772922\pi$
$384$		0			0
$385$	1.41641	+	3.52671i	0.0721868	+	0.179738i
$386$		0			0
$387$	1.42705	+	1.03681i	0.0725411	+	0.0527042i
$388$		0			0
$389$	−2.86475	−	8.81678i	−0.145248	−	0.447028i	0.851795	−	0.523876i	$-0.175515\pi$
$389$	−2.86475	−	8.81678i	−0.145248	−	0.447028i	−0.997043	+	0.0768476i	$0.975515\pi$
$390$		0			0
$391$	2.73607	−	1.98787i	0.138369	−	0.100531i
$392$		0			0
$393$	−4.28115	+	13.1760i	−0.215956	+	0.664643i
$394$		0			0
$395$	0.201626			0.0101449
$396$		0			0
$397$	−25.2918			−1.26936			−0.634679	−	0.772776i	$-0.718868\pi$
$397$	−25.2918			−1.26936			−0.634679	+	0.772776i	$0.718868\pi$
$398$		0			0
$399$	0.791796	−	2.43690i	0.0396394	−	0.121997i
$400$		0			0
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	−0.244354	−	0.969686i	$-0.578576\pi$
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	0.846717	+	0.532044i	$0.178576\pi$
$402$		0			0
$403$	7.42705	+	22.8581i	0.369968	+	1.13864i
$404$		0			0
$405$	0.309017	+	0.224514i	0.0153552	+	0.0111562i
$406$		0			0
$407$	−3.42705	+	13.6251i	−0.169873	+	0.675369i
$408$		0			0
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.989507	−	0.144486i	$-0.0461529\pi$
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.168360	+	0.985726i	$0.446153\pi$
$410$		0			0
$411$	0.454915	+	1.40008i	0.0224393	+	0.0690611i
$412$		0			0
$413$	12.9271	−	9.39205i	0.636099	−	0.462153i
$414$		0			0
$415$	−1.50000	+	4.61653i	−0.0736321	+	0.226616i
$416$		0			0
$417$	5.85410			0.286677
$418$		0			0
$419$	21.5066			1.05067			0.525333	−	0.850897i	$-0.323941\pi$
$419$	21.5066			1.05067			0.525333	+	0.850897i	$0.323941\pi$
$420$		0			0
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	−0.975205	−	0.221304i	$-0.928969\pi$
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	0.919037	+	0.394172i	$0.128969\pi$
$422$		0			0
$423$	−0.500000	+	0.363271i	−0.0243108	+	0.0176629i
$424$		0			0
$425$	0.927051	+	2.85317i	0.0449686	+	0.138399i
$426$		0			0
$427$	2.78115	+	2.02063i	0.134589	+	0.0977849i
$428$		0			0
$429$	−20.6353	+	1.40008i	−0.996279	+	0.0675967i
$430$		0			0
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	0.558306	−	0.829635i	$-0.311451\pi$
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	−0.616503	+	0.787352i	$0.711451\pi$
$432$		0			0
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$		0			0
$435$	1.38197	−	1.00406i	0.0662602	−	0.0481409i
$436$		0			0
$437$	1.44427	−	4.44501i	0.0690889	−	0.212634i
$438$		0			0
$439$	−16.7082			−0.797439			−0.398720	−	0.917073i	$-0.630545\pi$
$439$	−16.7082			−0.797439			−0.398720	+	0.917073i	$0.630545\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$		0			0
$443$	0.270510	−	0.832544i	0.0128523	−	0.0395553i	−0.944425	−	0.328728i	$-0.893380\pi$
$443$	0.270510	−	0.832544i	0.0128523	−	0.0395553i	0.957277	+	0.289172i	$0.0933801\pi$
$444$		0			0
$445$	2.92705	−	2.12663i	0.138756	−	0.100812i
$446$		0			0
$447$	−4.63525	−	14.2658i	−0.219240	−	0.674751i
$448$		0			0
$449$	12.5623	+	9.12705i	0.592852	+	0.430732i	0.843334	−	0.537389i	$-0.180589\pi$
$449$	12.5623	+	9.12705i	0.592852	+	0.430732i	−0.250483	+	0.968121i	$0.580589\pi$
$450$		0			0
$451$	−15.1287	+	12.6412i	−0.712382	+	0.595253i
$452$		0			0
$453$	−1.61803	−	1.17557i	−0.0760219	−	0.0552331i
$454$		0			0
$455$	2.20820	+	6.79615i	0.103522	+	0.318609i
$456$		0			0
$457$	−26.5344	+	19.2784i	−1.24123	+	0.901806i	−0.997680	−	0.0680830i	$-0.978312\pi$
$457$	−26.5344	+	19.2784i	−1.24123	+	0.901806i	−0.243549	+	0.969889i	$0.578312\pi$
$458$		0			0
$459$	0.190983	−	0.587785i	0.00891432	−	0.0274355i
$460$		0			0
$461$	−9.90983			−0.461547			−0.230773	−	0.973008i	$-0.574126\pi$
$461$	−9.90983			−0.461547			−0.230773	+	0.973008i	$0.574126\pi$
$462$		0			0
$463$	−8.79837			−0.408895			−0.204448	−	0.978878i	$-0.565540\pi$
$463$	−8.79837			−0.408895			−0.204448	+	0.978878i	$0.565540\pi$
$464$		0			0
$465$	0.454915	−	1.40008i	0.0210962	−	0.0649274i
$466$		0			0
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	−0.821461	−	0.570264i	$-0.806841\pi$
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	0.288508	+	0.957478i	$0.406841\pi$
$468$		0			0
$469$	9.79180	+	30.1360i	0.452143	+	1.39155i
$470$		0			0
$471$	7.85410	+	5.70634i	0.361898	+	0.262934i
$472$		0			0
$473$	4.95492	+	3.11044i	0.227827	+	0.143018i
$474$		0			0
$475$	3.35410	+	2.43690i	0.153897	+	0.111813i
$476$		0			0
$477$	−2.28115	−	7.02067i	−0.104447	−	0.321454i
$478$		0			0
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	−0.854689	−	0.519140i	$-0.826252\pi$
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	0.229618	+	0.973281i	$0.426252\pi$
$480$		0			0
$481$	−8.16312	+	25.1235i	−0.372206	+	1.14553i
$482$		0			0
$483$	16.4164			0.746972
$484$		0			0
$485$	−5.74265			−0.260760
$486$		0			0
$487$	−12.1074	+	37.2627i	−0.548638	+	1.68853i	0.163540	+	0.986537i	$0.447709\pi$
$487$	−12.1074	+	37.2627i	−0.548638	+	1.68853i	−0.712179	+	0.701998i	$0.752291\pi$
$488$		0			0
$489$	12.3541	−	8.97578i	0.558672	−	0.405899i
$490$		0			0
$491$	8.10081	+	24.9317i	0.365585	+	1.12515i	0.949614	+	0.313421i	$0.101475\pi$
$491$	8.10081	+	24.9317i	0.365585	+	1.12515i	−0.584030	+	0.811732i	$0.698525\pi$
$492$		0			0
$493$	−2.23607	−	1.62460i	−0.100707	−	0.0731682i
$494$		0			0
$495$	1.07295	+	0.673542i	0.0482255	+	0.0302735i
$496$		0			0
$497$	−35.3435	−	25.6785i	−1.58537	−	1.15184i
$498$		0			0
$499$	−0.791796	−	2.43690i	−0.0354457	−	0.109091i	0.931768	−	0.363054i	$-0.118266\pi$
$499$	−0.791796	−	2.43690i	−0.0354457	−	0.109091i	−0.967214	+	0.253963i	$0.918266\pi$
$500$		0			0
$501$	15.3992	−	11.1882i	0.687985	−	0.499850i
$502$		0			0
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	−0.498574	−	0.866847i	$-0.666143\pi$
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	0.912875	−	0.408239i	$-0.133857\pi$
$504$		0			0
$505$	1.14590			0.0509918
$506$		0			0
$507$	−25.8885			−1.14975
$508$		0			0
$509$	6.60739	−	20.3355i	0.292867	−	0.901353i	−0.691062	−	0.722796i	$-0.742857\pi$
$509$	6.60739	−	20.3355i	0.292867	−	0.901353i	0.983929	−	0.178558i	$-0.0571432\pi$
$510$		0			0
$511$	3.00000	−	2.17963i	0.132712	−	0.0964210i
$512$		0			0
$513$	−0.263932	−	0.812299i	−0.0116529	−	0.0358639i
$514$		0			0
$515$	1.85410	+	1.34708i	0.0817015	+	0.0593596i
$516$		0			0
$517$	−1.57295	+	1.31433i	−0.0691782	+	0.0578041i
$518$		0			0
$519$	14.2533	+	10.3556i	0.625650	+	0.454561i
$520$		0			0
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	0.762869	+	0.646553i	$0.223790\pi$
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	−0.237139	+	0.971476i	$0.576210\pi$
$522$		0			0
$523$	28.2984	−	20.5600i	1.23740	−	0.899025i	0.239979	−	0.970778i	$-0.422859\pi$
$523$	28.2984	−	20.5600i	1.23740	−	0.899025i	0.997422	+	0.0717533i	$0.0228594\pi$
$524$		0			0
$525$	−4.50000	+	13.8496i	−0.196396	+	0.604445i
$526$		0			0
$527$	−2.38197			−0.103760
$528$		0			0
$529$	6.94427			0.301925
$530$		0			0
$531$	1.64590	−	5.06555i	0.0714259	−	0.219826i
$532$		0			0
$533$	−29.9894	+	21.7885i	−1.29898	+	0.943767i
$534$		0			0
$535$	0.0278640	+	0.0857567i	0.00120467	+	0.00370759i
$536$		0			0
$537$	−1.80902	−	1.31433i	−0.0780648	−	0.0567174i
$538$		0			0
$539$	6.61803	−	0.449028i	0.285059	−	0.0193410i
$540$		0			0
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	0.597521	−	0.801853i	$-0.296152\pi$
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	−0.577963	+	0.816063i	$0.696152\pi$
$542$		0			0
$543$	2.63525	+	8.11048i	0.113090	+	0.348054i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−5.98936	+	18.4333i	−0.256086	+	0.788153i	0.737527	+	0.675317i	$0.235993\pi$
$547$	−5.98936	+	18.4333i	−0.256086	+	0.788153i	−0.993614	+	0.112836i	$0.964007\pi$
$548$		0			0
$549$	1.14590			0.0489057
$550$		0			0
$551$	−3.81966			−0.162723
$552$		0			0
$553$	0.489357	−	1.50609i	0.0208096	−	0.0640453i
$554$		0			0
$555$	1.30902	−	0.951057i	0.0555647	−	0.0403701i
$556$		0			0
$557$	8.06231	+	24.8132i	0.341611	+	1.05137i	0.963373	+	0.268164i	$0.0864170\pi$
$557$	8.06231	+	24.8132i	0.341611	+	1.05137i	−0.621762	+	0.783206i	$0.713583\pi$
$558$		0			0
$559$	8.89919	+	6.46564i	0.376396	+	0.273467i
$560$		0			0
$561$	0.500000	−	1.98787i	0.0211100	−	0.0839279i
$562$		0			0
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	0.942723	−	0.333575i	$-0.108255\pi$
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	−0.0259316	+	0.999664i	$0.508255\pi$
$564$		0			0
$565$	1.50000	+	4.61653i	0.0631055	+	0.194219i
$566$		0			0
$567$	2.42705	−	1.76336i	0.101927	−	0.0740540i
$568$		0			0
$569$	10.5279	−	32.4014i	0.441351	−	1.35834i	−0.445085	−	0.895488i	$-0.646827\pi$
$569$	10.5279	−	32.4014i	0.441351	−	1.35834i	0.886436	−	0.462851i	$-0.153173\pi$
$570$		0			0
$571$	25.6869			1.07496			0.537482	−	0.843275i	$-0.319376\pi$
$571$	25.6869			1.07496			0.537482	+	0.843275i	$0.319376\pi$
$572$		0			0
$573$	1.47214			0.0614994
$574$		0			0
$575$	−8.20820	+	25.2623i	−0.342306	+	1.05351i
$576$		0			0
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	−0.814016	−	0.580842i	$-0.802723\pi$
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	0.300868	+	0.953666i	$0.402723\pi$
$578$		0			0
$579$	−0.482779	−	1.48584i	−0.0200636	−	0.0617495i
$580$		0			0
$581$	30.8435	+	22.4091i	1.27960	+	0.929685i
$582$		0			0
$583$	−9.12461	−	22.7194i	−0.377903	−	0.940940i
$584$		0			0
$585$	1.92705	+	1.40008i	0.0796738	+	0.0578864i
$586$		0			0
$587$	−7.51064	−	23.1154i	−0.309997	−	0.954074i	−0.977765	−	0.209704i	$-0.932750\pi$
$587$	−7.51064	−	23.1154i	−0.309997	−	0.954074i	0.667767	−	0.744370i	$-0.267250\pi$
$588$		0			0
$589$	−2.66312	+	1.93487i	−0.109732	+	0.0797249i
$590$		0			0
$591$	−8.22542	+	25.3153i	−0.338349	+	1.04133i
$592$		0			0
$593$	−29.2148			−1.19971			−0.599854	−	0.800110i	$-0.704775\pi$
$593$	−29.2148			−1.19971			−0.599854	+	0.800110i	$0.704775\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$		0			0
$597$	−1.01722	+	3.13068i	−0.0416321	+	0.128130i
$598$		0			0
$599$	−17.5623	+	12.7598i	−0.717576	+	0.521350i	−0.885609	−	0.464432i	$-0.846259\pi$
$599$	−17.5623	+	12.7598i	−0.717576	+	0.521350i	0.168033	+	0.985781i	$0.446259\pi$
$600$		0			0
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	−0.994775	−	0.102093i	$-0.967446\pi$
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	0.744781	−	0.667309i	$-0.232554\pi$
$602$		0			0
$603$	8.54508	+	6.20837i	0.347983	+	0.252824i
$604$		0			0
$605$	3.70163	+	1.98787i	0.150493	+	0.0808184i
$606$		0			0
$607$	−1.88197	−	1.36733i	−0.0763866	−	0.0554981i	0.548937	−	0.835864i	$-0.315033\pi$
$607$	−1.88197	−	1.36733i	−0.0763866	−	0.0554981i	−0.625323	+	0.780366i	$0.715033\pi$
$608$		0			0
$609$	−4.14590	−	12.7598i	−0.168000	−	0.517052i
$610$		0			0
$611$	−3.11803	+	2.26538i	−0.126142	+	0.0916476i
$612$		0			0
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	−0.927990	−	0.372604i	$-0.878465\pi$
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	0.969771	+	0.244016i	$0.0784650\pi$
$614$		0			0
$615$	2.27051			0.0915558
$616$		0			0
$617$	46.4164			1.86865			0.934327	−	0.356417i	$-0.116002\pi$
$617$	46.4164			1.86865			0.934327	+	0.356417i	$0.116002\pi$
$618$		0			0
$619$	9.63525	−	29.6543i	0.387274	−	1.19191i	−0.547544	−	0.836777i	$-0.684437\pi$
$619$	9.63525	−	29.6543i	0.387274	−	1.19191i	0.934817	−	0.355129i	$-0.115563\pi$
$620$		0			0
$621$	4.42705	−	3.21644i	0.177651	−	0.129071i
$622$		0			0
$623$	−8.78115	−	27.0256i	−0.351809	−	1.08276i
$624$		0			0
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$		0			0
$627$	−1.05573	−	2.62866i	−0.0421617	−	0.104978i
$628$		0			0
$629$	−2.11803	−	1.53884i	−0.0844515	−	0.0613576i
$630$		0			0
$631$	−3.93363	−	12.1065i	−0.156595	−	0.481951i	0.841724	−	0.539908i	$-0.181541\pi$
$631$	−3.93363	−	12.1065i	−0.156595	−	0.481951i	−0.998319	+	0.0579577i	$0.981541\pi$
$632$		0			0
$633$	−9.11803	+	6.62464i	−0.362409	+	0.263306i
$634$		0			0
$635$	1.14590	−	3.52671i	0.0454736	−	0.139953i
$636$		0			0
$637$	12.4721			0.494164
$638$		0			0
$639$	−14.5623			−0.576076
$640$		0			0
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	−0.983736	−	0.179623i	$-0.942512\pi$
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	0.901439	+	0.432907i	$0.142512\pi$
$642$		0			0
$643$	−14.9164	+	10.8374i	−0.588246	+	0.427386i	−0.841687	−	0.539965i	$-0.818437\pi$
$643$	−14.9164	+	10.8374i	−0.588246	+	0.427386i	0.253442	+	0.967351i	$0.418437\pi$
$644$		0			0
$645$	−0.208204	−	0.640786i	−0.00819802	−	0.0252309i
$646$		0			0
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	0.637535	−	0.770421i	$-0.279954\pi$
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	−0.535705	+	0.844405i	$0.679954\pi$
$648$		0			0
$649$	4.30902	−	17.1315i	0.169144	−	0.672471i
$650$		0			0
$651$	−9.35410	−	6.79615i	−0.366616	−	0.266362i
$652$		0			0
$653$	6.78773	+	20.8905i	0.265624	+	0.817508i	0.991549	+	0.129734i	$0.0414122\pi$
$653$	6.78773	+	20.8905i	0.265624	+	0.817508i	−0.725924	+	0.687774i	$0.758588\pi$
$654$		0			0
$655$	4.28115	−	3.11044i	0.167278	−	0.121535i
$656$		0			0
$657$	0.381966	−	1.17557i	0.0149019	−	0.0458634i
$658$		0			0
$659$	−20.6525			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$659$	−20.6525			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$660$		0			0
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$		0			0
$663$	1.19098	−	3.66547i	0.0462539	−	0.142355i
$664$		0			0
$665$	−0.791796	+	0.575274i	−0.0307045	+	0.0223082i
$666$		0			0
$667$	−7.56231	−	23.2744i	−0.292814	−	0.901188i
$668$		0			0
$669$	10.2812	+	7.46969i	0.397492	+	0.288795i
$670$		0			0
$671$	3.79180	−	0.257270i	0.146381	−	0.00993180i
$672$		0			0
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	0.789430	−	0.613841i	$-0.210376\pi$
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	−0.339850	+	0.940480i	$0.610376\pi$
$674$		0			0
$675$	1.50000	+	4.61653i	0.0577350	+	0.177690i
$676$		0			0
$677$	−18.1803	+	13.2088i	−0.698727	+	0.507655i	−0.879517	−	0.475867i	$-0.842134\pi$
$677$	−18.1803	+	13.2088i	−0.698727	+	0.507655i	0.180790	+	0.983522i	$0.442134\pi$
$678$		0			0
$679$	−13.9377	+	42.8958i	−0.534880	+	1.64619i
$680$		0			0
$681$	10.8885			0.417250
$682$		0			0
$683$	38.8885			1.48803			0.744014	−	0.668164i	$-0.232919\pi$
$683$	38.8885			1.48803			0.744014	+	0.668164i	$0.232919\pi$
$684$		0			0
$685$	0.173762	−	0.534785i	0.00663911	−	0.0204331i
$686$		0			0
$687$	8.09017	−	5.87785i	0.308659	−	0.224254i
$688$		0			0
$689$	−14.2254	−	43.7814i	−0.541946	−	1.66794i
$690$		0			0
$691$	−32.1246	−	23.3399i	−1.22208	−	0.887892i	−0.225807	−	0.974172i	$-0.572502\pi$
$691$	−32.1246	−	23.3399i	−1.22208	−	0.887892i	−0.996271	+	0.0862806i	$0.972502\pi$
$692$		0			0
$693$	7.63525	−	6.37988i	0.290039	−	0.242352i
$694$		0			0
$695$	−1.80902	−	1.31433i	−0.0686199	−	0.0498553i
$696$		0			0
$697$	−1.13525	−	3.49396i	−0.0430008	−	0.132343i
$698$		0			0
$699$	7.01722	−	5.09831i	0.265416	−	0.192836i
$700$		0			0
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	−0.0388752	−	0.999244i	$-0.512377\pi$
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	0.618792	−	0.785555i	$-0.287623\pi$
$702$		0			0
$703$	−3.61803			−0.136457
$704$		0			0
$705$	0.236068			0.00889083
$706$		0			0
$707$	2.78115	−	8.55951i	0.104596	−	0.321913i
$708$		0			0
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	−0.678773	−	0.734348i	$-0.737488\pi$
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	0.488654	+	0.872478i	$0.337488\pi$
$710$		0			0
$711$	−0.163119	−	0.502029i	−0.00611744	−	0.0188275i
$712$		0			0
$713$	−17.0623	−	12.3965i	−0.638988	−	0.464252i
$714$		0			0
$715$	6.69098	+	4.20025i	0.250229	+	0.157081i
$716$		0			0
$717$	14.2082	+	10.3229i	0.530615	+	0.385514i
$718$		0			0
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	0.970308	+	0.241873i	$0.0777618\pi$
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	−0.642826	+	0.766012i	$0.722238\pi$
$720$		0			0
$721$	14.5623	−	10.5801i	0.542329	−	0.394025i
$722$		0			0
$723$	−5.29180	+	16.2865i	−0.196804	+	0.605700i
$724$		0			0
$725$	21.7082			0.806222
$726$		0			0
$727$	−32.1459			−1.19223			−0.596113	−	0.802901i	$-0.703289\pi$
$727$	−32.1459			−1.19223			−0.596113	+	0.802901i	$0.703289\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−0.881966	+	0.640786i	−0.0326207	+	0.0237003i
$732$		0			0
$733$	−7.50658	−	23.1029i	−0.277262	−	0.853324i	−0.988612	−	0.150486i	$-0.951916\pi$
$733$	−7.50658	−	23.1029i	−0.277262	−	0.853324i	0.711350	−	0.702838i	$-0.248084\pi$
$734$		0			0
$735$	−0.618034	−	0.449028i	−0.0227965	−	0.0165626i
$736$		0			0
$737$	29.6697	+	18.6251i	1.09290	+	0.686064i
$738$		0			0
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	0.149958	−	0.988692i	$-0.452086\pi$
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	−0.893963	+	0.448142i	$0.852086\pi$
$740$		0			0
$741$	−1.64590	−	5.06555i	−0.0604636	−	0.186088i
$742$		0			0
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	−0.381059	−	0.924551i	$-0.624441\pi$
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	0.761546	+	0.648111i	$0.224441\pi$
$744$		0			0
$745$	−1.77051	+	5.44907i	−0.0648665	+	0.199638i
$746$		0			0
$747$	12.7082			0.464969
$748$		0			0
$749$	0.708204			0.0258772
$750$		0			0
$751$	16.3541	−	50.3328i	0.596770	−	1.83667i	0.0510571	−	0.998696i	$-0.483741\pi$
$751$	16.3541	−	50.3328i	0.596770	−	1.83667i	0.545713	−	0.837972i	$-0.316259\pi$
$752$		0			0
$753$	−13.5902	+	9.87384i	−0.495253	+	0.359823i
$754$		0			0
$755$	0.236068	+	0.726543i	0.00859139	+	0.0264416i
$756$		0			0
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	0.796985	−	0.603999i	$-0.206427\pi$
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	−0.328156	+	0.944624i	$0.606427\pi$
$758$		0			0
$759$	13.9271	−	11.6372i	0.505520	−	0.422403i
$760$		0			0
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	0.513791	−	0.857916i	$-0.328241\pi$
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	−0.657156	+	0.753754i	$0.728241\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.190983	+	0.138757i	−0.00690501	+	0.00501678i
$766$		0			0
$767$	10.2639	−	31.5891i	0.370609	−	1.14062i
$768$		0			0
$769$	−47.6869			−1.71963			−0.859817	−	0.510602i	$-0.829423\pi$
$769$	−47.6869			−1.71963			−0.859817	+	0.510602i	$0.829423\pi$
$770$		0			0
$771$	27.3262			0.984130
$772$		0			0
$773$	15.2188	−	46.8388i	0.547384	−	1.68467i	−0.167870	−	0.985809i	$-0.553689\pi$
$773$	15.2188	−	46.8388i	0.547384	−	1.68467i	0.715253	−	0.698865i	$-0.246311\pi$
$774$		0			0
$775$	15.1353	−	10.9964i	0.543674	−	0.395003i
$776$		0			0
$777$	−3.92705	−	12.0862i	−0.140882	−	0.433591i
$778$		0			0
$779$	−4.10739	−	2.98419i	−0.147163	−	0.106920i
$780$		0			0
$781$	−48.1869	+	3.26944i	−1.72426	+	0.116990i
$782$		0			0
$783$	−3.61803	−	2.62866i	−0.129298	−	0.0939405i
$784$		0			0
$785$	−1.14590	−	3.52671i	−0.0408989	−	0.125874i
$786$		0			0
$787$	−19.1803	+	13.9353i	−0.683705	+	0.496741i	−0.874585	−	0.484873i	$-0.838866\pi$
$787$	−19.1803	+	13.9353i	−0.683705	+	0.496741i	0.190880	+	0.981613i	$0.438866\pi$
$788$		0			0
$789$	−0.208204	+	0.640786i	−0.00741226	+	0.0228126i
$790$		0			0
$791$	38.1246			1.35556
$792$		0			0
$793$	7.14590			0.253758
$794$		0			0
$795$	−0.871323	+	2.68166i	−0.0309026	+	0.0951085i
$796$		0			0
$797$	−12.3262	+	8.95554i	−0.436618	+	0.317221i	−0.784290	−	0.620395i	$-0.786972\pi$
$797$	−12.3262	+	8.95554i	−0.436618	+	0.317221i	0.347672	+	0.937616i	$0.386972\pi$
$798$		0			0
$799$	−0.118034	−	0.363271i	−0.00417574	−	0.0128516i
$800$		0			0
$801$	−7.66312	−	5.56758i	−0.270763	−	0.196721i
$802$		0			0
$803$	1.00000	−	3.97574i	0.0352892	−	0.140301i
$804$		0			0
$805$	−5.07295	−	3.68571i	−0.178798	−	0.129904i
$806$		0			0
$807$	−7.56231	−	23.2744i	−0.266206	−	0.819297i
$808$		0			0
$809$	−20.4894	+	14.8864i	−0.720367	+	0.523378i	−0.886502	−	0.462726i	$-0.846872\pi$
$809$	−20.4894	+	14.8864i	−0.720367	+	0.523378i	0.166134	+	0.986103i	$0.446872\pi$
$810$		0			0
$811$	−14.1353	+	43.5038i	−0.496356	+	1.52763i	0.318477	+	0.947931i	$0.396829\pi$
$811$	−14.1353	+	43.5038i	−0.496356	+	1.52763i	−0.814833	+	0.579696i	$0.803171\pi$
$812$		0			0
$813$	6.27051			0.219916
$814$		0			0
$815$	−5.83282			−0.204315
$816$		0			0
$817$	−0.465558	+	1.43284i	−0.0162878	+	0.0501287i
$818$		0			0
$819$	15.1353	−	10.9964i	0.528869	−	0.384246i
$820$		0			0
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	0.997200	−	0.0747763i	$-0.0238243\pi$
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	−0.850704	+	0.525644i	$0.823824\pi$
$822$		0			0
$823$	−21.4615	−	15.5927i	−0.748101	−	0.543527i	0.147137	−	0.989116i	$-0.452994\pi$
$823$	−21.4615	−	15.5927i	−0.748101	−	0.543527i	−0.895238	+	0.445589i	$0.852994\pi$
$824$		0			0
$825$	6.00000	+	14.9394i	0.208893	+	0.520123i
$826$		0			0
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	0.753975	−	0.656903i	$-0.228134\pi$
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	−0.391761	+	0.920067i	$0.628134\pi$
$828$		0			0
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	−0.867407	−	0.497600i	$-0.834215\pi$
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	0.409265	−	0.912416i	$-0.365785\pi$
$830$		0			0
$831$	8.44427	−	6.13512i	0.292929	−	0.212825i
$832$		0			0
$833$	−0.381966	+	1.17557i	−0.0132343	+	0.0407311i
$834$		0			0
$835$	−7.27051			−0.251606
$836$		0			0
$837$	−3.85410			−0.133217
$838$		0			0
$839$	7.19756	−	22.1518i	0.248487	−	0.764766i	−0.746556	−	0.665323i	$-0.768294\pi$
$839$	7.19756	−	22.1518i	0.248487	−	0.764766i	0.995043	−	0.0994428i	$-0.0317060\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$		0			0
$843$	1.61803	+	4.97980i	0.0557281	+	0.171513i
$844$		0			0
$845$	8.00000	+	5.81234i	0.275208	+	0.199951i
$846$		0			0
$847$	23.8328	−	22.8254i	0.818905	−	0.784289i
$848$		0			0
$849$	17.9443	+	13.0373i	0.615846	+	0.447438i
$850$		0			0
$851$	−7.16312	−	22.0458i	−0.245549	−	0.755721i
$852$		0			0
$853$	−6.42705	+	4.66953i	−0.220058	+	0.159882i	−0.692353	−	0.721559i	$-0.743426\pi$
$853$	−6.42705	+	4.66953i	−0.220058	+	0.159882i	0.472295	+	0.881441i	$0.343426\pi$
$854$		0			0
$855$	−0.100813	+	0.310271i	−0.00344773	+	0.0106110i
$856$		0			0
$857$	−41.7214			−1.42517			−0.712587	−	0.701584i	$-0.752477\pi$
$857$	−41.7214			−1.42517			−0.712587	+	0.701584i	$0.752477\pi$
$858$		0			0
$859$	−42.8885			−1.46334			−0.731669	−	0.681660i	$-0.761258\pi$
$859$	−42.8885			−1.46334			−0.731669	+	0.681660i	$0.761258\pi$
$860$		0			0
$861$	5.51064	−	16.9600i	0.187802	−	0.577996i
$862$		0			0
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	−0.865944	−	0.500141i	$-0.833281\pi$
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	0.208071	+	0.978114i	$0.433281\pi$
$864$		0			0
$865$	−2.07953	−	6.40013i	−0.0707060	−	0.217611i
$866$		0			0
$867$	−13.4443	−	9.76784i	−0.456591	−	0.331733i
$868$		0			0
$869$	−0.652476	−	1.62460i	−0.0221337	−	0.0551107i
$870$		0			0
$871$	53.2877	+	38.7158i	1.80559	+	1.31183i
$872$		0			0
$873$	4.64590	+	14.2986i	0.157240	+	0.483934i
$874$		0			0
$875$	9.13525	−	6.63715i	0.308828	−	0.224377i
$876$		0			0
$877$	−6.30902	+	19.4172i	−0.213040	+	0.655671i	0.786247	+	0.617913i	$0.212022\pi$
$877$	−6.30902	+	19.4172i	−0.213040	+	0.655671i	−0.999287	+	0.0377579i	$0.987978\pi$
$878$		0			0
$879$	−17.9443			−0.605245
$880$		0			0
$881$	25.0902			0.845309			0.422655	−	0.906291i	$-0.361098\pi$
$881$	25.0902			0.845309			0.422655	+	0.906291i	$0.361098\pi$
$882$		0			0
$883$	−11.5623	+	35.5851i	−0.389103	+	1.19753i	0.544358	+	0.838853i	$0.316774\pi$
$883$	−11.5623	+	35.5851i	−0.389103	+	1.19753i	−0.933460	+	0.358681i	$0.883226\pi$
$884$		0			0
$885$	−1.64590	+	1.19581i	−0.0553263	+	0.0401969i
$886$		0			0
$887$	−0.927051	−	2.85317i	−0.0311273	−	0.0958001i	0.934286	−	0.356525i	$-0.116038\pi$
$887$	−0.927051	−	2.85317i	−0.0311273	−	0.0958001i	−0.965413	+	0.260725i	$0.916038\pi$
$888$		0			0
$889$	−23.5623	−	17.1190i	−0.790254	−	0.574153i
$890$		0			0
$891$	0.809017	−	3.21644i	0.0271031	−	0.107755i
$892$		0			0
$893$	−0.427051	−	0.310271i	−0.0142907	−	0.0103828i
$894$		0			0
$895$	0.263932	+	0.812299i	0.00882227	+	0.0271522i
$896$		0			0
$897$	27.6074	−	20.0579i	0.921784	−	0.669715i
$898$		0			0
$899$	−5.32624	+	16.3925i	−0.177640	+	0.546720i
$900$		0			0
$901$	4.56231			0.151992
$902$		0			0
$903$	−5.29180			−0.176100
$904$		0			0
$905$	1.00658	−	3.09793i	0.0334598	−	0.102979i
$906$		0			0
$907$	3.21885	−	2.33863i	0.106880	−	0.0776529i	−0.533061	−	0.846077i	$-0.678959\pi$
$907$	3.21885	−	2.33863i	0.106880	−	0.0776529i	0.639942	+	0.768424i	$0.278959\pi$
$908$		0			0
$909$	−0.927051	−	2.85317i	−0.0307483	−	0.0946337i
$910$		0			0
$911$	29.0795	+	21.1275i	0.963448	+	0.699986i	0.953949	−	0.299969i	$-0.0969764\pi$
$911$	29.0795	+	21.1275i	0.963448	+	0.699986i	0.00949880	+	0.999955i	$0.496976\pi$
$912$		0			0
$913$	42.0517	−	2.85317i	1.39171	−	0.0944261i
$914$		0			0
$915$	−0.354102	−	0.257270i	−0.0117062	−	0.00850509i
$916$		0			0
$917$	−12.8435	−	39.5281i	−0.424128	−	1.30533i
$918$		0			0
$919$	−37.9894	+	27.6009i	−1.25315	+	0.910469i	−0.998400	−	0.0565371i	$-0.981994\pi$
$919$	−37.9894	+	27.6009i	−1.25315	+	0.910469i	−0.254753	+	0.967006i	$0.581994\pi$
$920$		0			0
$921$	−6.04508	+	18.6049i	−0.199192	+	0.613051i
$922$		0			0
$923$	−90.8115			−2.98910
$924$		0			0
$925$	20.5623			0.676084
$926$		0			0
$927$	1.85410	−	5.70634i	0.0608967	−	0.187421i
$928$		0			0
$929$	−2.33688	+	1.69784i	−0.0766706	+	0.0557044i	−0.625460	−	0.780256i	$-0.715089\pi$
$929$	−2.33688	+	1.69784i	−0.0766706	+	0.0557044i	0.548790	+	0.835960i	$0.315089\pi$
$930$		0			0
$931$	0.527864	+	1.62460i	0.0173000	+	0.0532441i
$932$		0			0
$933$	−9.28115	−	6.74315i	−0.303851	−	0.220761i
$934$		0			0
$935$	−0.600813	+	0.502029i	−0.0196487	+	0.0164181i
$936$		0			0
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	0.0667827	−	0.997768i	$-0.478727\pi$
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	−0.928296	+	0.371841i	$0.878727\pi$
$938$		0			0
$939$	8.60081	+	26.4706i	0.280677	+	0.863835i
$940$		0			0
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	−0.935084	−	0.354426i	$-0.884676\pi$
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	0.0481221	+	0.998841i	$0.484676\pi$
$942$		0			0
$943$	10.0517	−	30.9358i	0.327327	−	1.00741i
$944$		0			0
$945$	−1.14590			−0.0372761
$946$		0			0
$947$	−2.67376			−0.0868856			−0.0434428	−	0.999056i	$-0.513833\pi$
$947$	−2.67376			−0.0868856			−0.0434428	+	0.999056i	$0.513833\pi$
$948$		0			0
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$		0			0
$951$	20.5172	−	14.9066i	0.665316	−	0.483381i
$952$		0			0
$953$	18.5967	+	57.2349i	0.602408	+	1.85402i	0.513714	+	0.857961i	$0.328269\pi$
$953$	18.5967	+	57.2349i	0.602408	+	1.85402i	0.0886937	+	0.996059i	$0.471731\pi$
$954$		0			0
$955$	−0.454915	−	0.330515i	−0.0147207	−	0.0106952i
$956$		0			0
$957$	−12.5623	−	7.88597i	−0.406082	−	0.254917i
$958$		0			0
$959$	−3.57295	−	2.59590i	−0.115377	−	0.0838260i
$960$		0			0
$961$	−4.98936	−	15.3557i	−0.160947	−	0.495344i
$962$		0			0
$963$	0.190983	−	0.138757i	0.00615434	−	0.00447139i
$964$		0			0
$965$	−0.184405	+	0.567541i	−0.00593621	+	0.0182698i
$966$		0			0
$967$	−25.6869			−0.826036			−0.413018	−	0.910723i	$-0.635525\pi$
$967$	−25.6869			−0.826036			−0.413018	+	0.910723i	$0.635525\pi$
$968$		0			0
$969$	0.527864			0.0169574
$970$		0			0
$971$	10.4377	−	32.1239i	0.334962	−	1.03091i	−0.631779	−	0.775148i	$-0.717675\pi$
$971$	10.4377	−	32.1239i	0.334962	−	1.03091i	0.966741	−	0.255757i	$-0.0823248\pi$
$972$		0			0
$973$	−14.2082	+	10.3229i	−0.455494	+	0.330936i
$974$		0			0
$975$	9.35410	+	28.7890i	0.299571	+	0.921985i
$976$		0			0
$977$	39.9336	+	29.0135i	1.27759	+	0.928223i	0.999477	−	0.0323250i	$-0.0102912\pi$
$977$	39.9336	+	29.0135i	1.27759	+	0.928223i	0.278113	+	0.960548i	$0.410291\pi$
$978$		0			0
$979$	−26.6074	−	16.7027i	−0.850376	−	0.533822i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.9098	−	33.5770i	−0.347970	−	1.07094i	−0.959975	−	0.280086i	$-0.909637\pi$
$983$	−10.9098	−	33.5770i	−0.347970	−	1.07094i	0.612005	−	0.790854i	$-0.290363\pi$
$984$		0			0
$985$	8.22542	−	5.97612i	0.262084	−	0.190415i
$986$		0			0
$987$	0.572949	−	1.76336i	0.0182372	−	0.0561282i
$988$		0			0
$989$	−9.65248			−0.306931
$990$		0			0
$991$	12.2705			0.389786			0.194893	−	0.980825i	$-0.437564\pi$
$991$	12.2705			0.389786			0.194893	+	0.980825i	$0.437564\pi$
$992$		0			0
$993$	−6.98278	+	21.4908i	−0.221592	+	0.681989i
$994$		0			0
$995$	1.01722	−	0.739054i	0.0322481	−	0.0234296i
$996$		0			0
$997$	10.5000	+	32.3157i	0.332538	+	1.02345i	0.967922	+	0.251251i	$0.0808420\pi$
$997$	10.5000	+	32.3157i	0.332538	+	1.02345i	−0.635384	+	0.772197i	$0.719158\pi$
$998$		0			0
$999$	−3.42705	−	2.48990i	−0.108427	−	0.0787769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.y.f.433.1		4
4.3	odd	2		33.2.e.a.4.1	✓	4
11.3	even	5	inner	528.2.y.f.289.1		4
11.5	even	5		5808.2.a.bl.1.2		2
11.6	odd	10		5808.2.a.bm.1.2		2
12.11	even	2		99.2.f.b.37.1		4
20.3	even	4		825.2.bx.b.499.1		8
20.7	even	4		825.2.bx.b.499.2		8
20.19	odd	2		825.2.n.f.301.1		4
36.7	odd	6		891.2.n.d.433.1		8
36.11	even	6		891.2.n.a.433.1		8
36.23	even	6		891.2.n.a.136.1		8
36.31	odd	6		891.2.n.d.136.1		8
44.3	odd	10		33.2.e.a.25.1	yes	4
44.7	even	10		363.2.e.c.130.1		4
44.15	odd	10		363.2.e.h.130.1		4
44.19	even	10		363.2.e.j.124.1		4
44.27	odd	10		363.2.a.h.1.2		2
44.31	odd	10		363.2.e.h.148.1		4
44.35	even	10		363.2.e.c.148.1		4
44.39	even	10		363.2.a.e.1.1		2
44.43	even	2		363.2.e.j.202.1		4
132.47	even	10		99.2.f.b.91.1		4
132.71	even	10		1089.2.a.m.1.1		2
132.83	odd	10		1089.2.a.s.1.2		2
220.3	even	20		825.2.bx.b.124.2		8
220.39	even	10		9075.2.a.bv.1.2		2
220.47	even	20		825.2.bx.b.124.1		8
220.159	odd	10		9075.2.a.x.1.1		2
220.179	odd	10		825.2.n.f.751.1		4
396.47	even	30		891.2.n.a.190.1		8
396.223	odd	30		891.2.n.d.190.1		8
396.311	even	30		891.2.n.a.784.1		8
396.355	odd	30		891.2.n.d.784.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	4.3	odd	2
33.2.e.a.25.1	yes	4	44.3	odd	10
99.2.f.b.37.1		4	12.11	even	2
99.2.f.b.91.1		4	132.47	even	10
363.2.a.e.1.1		2	44.39	even	10
363.2.a.h.1.2		2	44.27	odd	10
363.2.e.c.130.1		4	44.7	even	10
363.2.e.c.148.1		4	44.35	even	10
363.2.e.h.130.1		4	44.15	odd	10
363.2.e.h.148.1		4	44.31	odd	10
363.2.e.j.124.1		4	44.19	even	10
363.2.e.j.202.1		4	44.43	even	2
528.2.y.f.289.1		4	11.3	even	5	inner
528.2.y.f.433.1		4	1.1	even	1	trivial
825.2.n.f.301.1		4	20.19	odd	2
825.2.n.f.751.1		4	220.179	odd	10
825.2.bx.b.124.1		8	220.47	even	20
825.2.bx.b.124.2		8	220.3	even	20
825.2.bx.b.499.1		8	20.3	even	4
825.2.bx.b.499.2		8	20.7	even	4
891.2.n.a.136.1		8	36.23	even	6
891.2.n.a.190.1		8	396.47	even	30
891.2.n.a.433.1		8	36.11	even	6
891.2.n.a.784.1		8	396.311	even	30
891.2.n.d.136.1		8	36.31	odd	6
891.2.n.d.190.1		8	396.223	odd	30
891.2.n.d.433.1		8	36.7	odd	6
891.2.n.d.784.1		8	396.355	odd	30
1089.2.a.m.1.1		2	132.71	even	10
1089.2.a.s.1.2		2	132.83	odd	10
5808.2.a.bl.1.2		2	11.5	even	5
5808.2.a.bm.1.2		2	11.6	odd	10
9075.2.a.x.1.1		2	220.159	odd	10
9075.2.a.bv.1.2		2	220.39	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.y (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.224514i) q^{5} +(-0.927051 - 2.85317i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.224514i) q^{5} +(-0.927051 - 2.85317i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.80902 - 1.76336i) q^{11} +(-5.04508 - 3.66547i) q^{13} +(0.118034 + 0.363271i) q^{15} +(0.500000 - 0.363271i) q^{17} +(0.263932 - 0.812299i) q^{19} +3.00000 q^{21} +5.47214 q^{23} +(-1.50000 + 4.61653i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-1.38197 - 4.25325i) q^{29} +(-3.11803 - 2.26538i) q^{31} +(2.54508 - 2.12663i) q^{33} +(-0.927051 - 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(5.04508 - 3.66547i) q^{39} +(1.83688 - 5.65334i) q^{41} -1.76393 q^{43} -0.381966 q^{45} +(0.190983 - 0.587785i) q^{47} +(-1.61803 + 1.17557i) q^{49} +(0.190983 + 0.587785i) q^{51} +(5.97214 + 4.33901i) q^{53} +(-1.26393 + 0.0857567i) q^{55} +(0.690983 + 0.502029i) q^{57} +(1.64590 + 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(-0.927051 + 2.85317i) q^{63} -2.38197 q^{65} -10.5623 q^{67} +(-1.69098 + 5.20431i) q^{69} +(11.7812 - 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(-3.92705 - 2.85317i) q^{75} +(-2.42705 + 9.64932i) q^{77} +(0.427051 + 0.310271i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-10.2812 + 7.46969i) q^{83} +(0.0729490 - 0.224514i) q^{85} +4.47214 q^{87} +9.47214 q^{89} +(-5.78115 + 17.7926i) q^{91} +(3.11803 - 2.26538i) q^{93} +(-0.100813 - 0.310271i) q^{95} +(-12.1631 - 8.83702i) q^{97} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9}+O(q^{10}) \) 4 * q + q^3 - q^5 + 3 * q^7 - q^9	\( 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9} - 9 q^{11} - 9 q^{13} - 4 q^{15} + 2 q^{17} + 10 q^{19} + 12 q^{21} + 4 q^{23} - 6 q^{25} + q^{27} - 10 q^{29} - 8 q^{31} - q^{33} + 3 q^{35} - 3 q^{37} + 9 q^{39} + 23 q^{41} - 16 q^{43} - 6 q^{45} + 3 q^{47} - 2 q^{49} + 3 q^{51} + 6 q^{53} - 14 q^{55} + 5 q^{57} + 20 q^{59} + 3 q^{61} + 3 q^{63} - 14 q^{65} - 2 q^{67} - 9 q^{69} + 27 q^{71} + 6 q^{73} - 9 q^{75} - 3 q^{77} - 5 q^{79} - q^{81} - 21 q^{83} + 7 q^{85} + 20 q^{89} - 3 q^{91} + 8 q^{93} - 25 q^{95} - 33 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + q^3 - q^5 + 3 * q^7 - q^9 - 9 * q^11 - 9 * q^13 - 4 * q^15 + 2 * q^17 + 10 * q^19 + 12 * q^21 + 4 * q^23 - 6 * q^25 + q^27 - 10 * q^29 - 8 * q^31 - q^33 + 3 * q^35 - 3 * q^37 + 9 * q^39 + 23 * q^41 - 16 * q^43 - 6 * q^45 + 3 * q^47 - 2 * q^49 + 3 * q^51 + 6 * q^53 - 14 * q^55 + 5 * q^57 + 20 * q^59 + 3 * q^61 + 3 * q^63 - 14 * q^65 - 2 * q^67 - 9 * q^69 + 27 * q^71 + 6 * q^73 - 9 * q^75 - 3 * q^77 - 5 * q^79 - q^81 - 21 * q^83 + 7 * q^85 + 20 * q^89 - 3 * q^91 + 8 * q^93 - 25 * q^95 - 33 * q^97 - 4 * q^99

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