LMFDB - Embedded newform 275.2.h.d.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 25x^{12} + 57x^{10} + 194x^{8} + 303x^{6} + 235x^{4} + 33x^{2} + 121 $ x^16 + 7x^14 + 25x^12 + 57x^10 + 194x^8 + 303x^6 + 235x^4 + 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$0.625353 + 1.92464i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.d.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63719 + 1.18949i) q^{2} +(0.809808 + 2.49233i) q^{3} +(0.647481 - 1.99274i) q^{4} +(-4.29042 - 3.11717i) q^{6} +(-0.298456 + 0.918552i) q^{7} +(0.0595923 + 0.183406i) q^{8} +(-3.12889 + 2.27327i) q^{9} +O(q^{10})$	\(q+(-1.63719 + 1.18949i) q^{2} +(0.809808 + 2.49233i) q^{3} +(0.647481 - 1.99274i) q^{4} +(-4.29042 - 3.11717i) q^{6} +(-0.298456 + 0.918552i) q^{7} +(0.0595923 + 0.183406i) q^{8} +(-3.12889 + 2.27327i) q^{9} +(-3.31118 + 0.189896i) q^{11} +5.49092 q^{12} +(-3.66088 + 2.65978i) q^{13} +(-0.603980 - 1.85886i) q^{14} +(3.07453 + 2.23378i) q^{16} +(-2.69944 - 1.96126i) q^{17} +(2.41856 - 7.44357i) q^{18} +(1.01283 + 3.11717i) q^{19} -2.53103 q^{21} +(5.19517 - 4.24952i) q^{22} +3.36643 q^{23} +(-0.408851 + 0.297048i) q^{24} +(2.82978 - 8.70916i) q^{26} +(-1.83923 - 1.33628i) q^{27} +(1.63719 + 1.18949i) q^{28} +(1.51820 - 4.67254i) q^{29} +(0.338464 - 0.245909i) q^{31} -8.07636 q^{32} +(-3.15471 - 8.09880i) q^{33} +6.75241 q^{34} +(2.50415 + 7.70697i) q^{36} +(-1.95841 + 6.02737i) q^{37} +(-5.36605 - 3.89867i) q^{38} +(-9.59368 - 6.97021i) q^{39} +(1.78786 + 5.50247i) q^{41} +(4.14379 - 3.01064i) q^{42} +2.26205 q^{43} +(-1.76552 + 6.72129i) q^{44} +(-5.51149 + 4.00433i) q^{46} +(-1.33626 - 4.11260i) q^{47} +(-3.07754 + 9.47169i) q^{48} +(4.90846 + 3.56620i) q^{49} +(2.70208 - 8.31615i) q^{51} +(2.92991 + 9.01735i) q^{52} +(-2.15255 + 1.56392i) q^{53} +4.60066 q^{54} -0.186254 q^{56} +(-6.94884 + 5.04863i) q^{57} +(3.07235 + 9.45574i) q^{58} +(-3.12889 + 9.62972i) q^{59} +(1.99897 + 1.45233i) q^{61} +(-0.261626 + 0.805201i) q^{62} +(-1.15428 - 3.55252i) q^{63} +(7.07350 - 5.13920i) q^{64} +(14.7983 + 9.50680i) q^{66} +9.60059 q^{67} +(-5.65612 + 4.10941i) q^{68} +(2.72616 + 8.39026i) q^{69} +(4.41166 + 3.20526i) q^{71} +(-0.603390 - 0.438388i) q^{72} +(-0.443607 + 1.36528i) q^{73} +(-3.96321 - 12.1975i) q^{74} +6.86752 q^{76} +(0.813812 - 3.09817i) q^{77} +23.9977 q^{78} +(-0.812218 + 0.590111i) q^{79} +(-1.74436 + 5.36858i) q^{81} +(-9.47221 - 6.88197i) q^{82} +(5.98302 + 4.34692i) q^{83} +(-1.63880 + 5.04369i) q^{84} +(-3.70342 + 2.69069i) q^{86} +12.8750 q^{87} +(-0.232149 - 0.595976i) q^{88} -12.1964 q^{89} +(-1.35054 - 4.15654i) q^{91} +(2.17970 - 6.70842i) q^{92} +(0.886978 + 0.644427i) q^{93} +(7.07962 + 5.14365i) q^{94} +(-6.54030 - 20.1290i) q^{96} +(-2.44262 + 1.77467i) q^{97} -12.2781 q^{98} +(9.92863 - 8.12138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9	$ 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46} + 10 q^{49} - 42 q^{51} + 40 q^{54} - 20 q^{56} - 2 q^{59} - 40 q^{61} + 8 q^{64} + 58 q^{66} - 26 q^{69} + 36 q^{71} - 48 q^{74} + 56 q^{76} - 38 q^{79} + 68 q^{81} - 12 q^{84} + 22 q^{86} - 24 q^{89} - 20 q^{91} - 14 q^{94} - 86 q^{96} + 72 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.63719	+	1.18949i	−1.15767	+	0.841097i	−0.989482	−	0.144657i	$-0.953792\pi$
$2$	−1.63719	+	1.18949i	−1.15767	+	0.841097i	−0.168189	+	0.985755i	$0.553792\pi$
$3$	0.809808	+	2.49233i	0.467543	+	1.43895i	0.855756	+	0.517380i	$0.173093\pi$
$3$	0.809808	+	2.49233i	0.467543	+	1.43895i	−0.388213	+	0.921570i	$0.626907\pi$
$4$	0.647481	−	1.99274i	0.323741	−	0.996371i
$5$		0			0
$5$		0			0
$6$	−4.29042	−	3.11717i	−1.75156	−	1.27258i
$7$	−0.298456	+	0.918552i	−0.112806	+	0.347180i	−0.991483	−	0.130236i	$-0.958427\pi$
$7$	−0.298456	+	0.918552i	−0.112806	+	0.347180i	0.878677	+	0.477416i	$0.158427\pi$
$8$	0.0595923	+	0.183406i	0.0210691	+	0.0648439i
$9$	−3.12889	+	2.27327i	−1.04296	+	0.757756i
$10$		0			0
$11$	−3.31118	+	0.189896i	−0.998360	+	0.0572559i
$11$	−3.31118	+	0.189896i	−0.998360	+	0.0572559i
$12$	5.49092			1.58509
$13$	−3.66088	+	2.65978i	−1.01534	+	0.737691i	−0.965323	−	0.261057i	$-0.915929\pi$
$13$	−3.66088	+	2.65978i	−1.01534	+	0.737691i	−0.0500213	+	0.998748i	$0.515929\pi$
$14$	−0.603980	−	1.85886i	−0.161420	−	0.496801i
$15$		0			0
$16$	3.07453	+	2.23378i	0.768633	+	0.558445i
$17$	−2.69944	−	1.96126i	−0.654710	−	0.475675i	0.210162	−	0.977667i	$-0.432601\pi$
$17$	−2.69944	−	1.96126i	−0.654710	−	0.475675i	−0.864872	+	0.501992i	$0.832601\pi$
$18$	2.41856	−	7.44357i	0.570060	−	1.75447i
$19$	1.01283	+	3.11717i	0.232359	+	0.715129i	0.997461	+	0.0712189i	$0.0226889\pi$
$19$	1.01283	+	3.11717i	0.232359	+	0.715129i	−0.765101	+	0.643910i	$0.777311\pi$
$20$		0			0
$21$	−2.53103			−0.552316
$22$	5.19517	−	4.24952i	1.10761	−	0.906001i
$23$	3.36643			0.701948			0.350974	−	0.936385i	$-0.385851\pi$
$23$	3.36643			0.701948			0.350974	+	0.936385i	$0.385851\pi$
$24$	−0.408851	+	0.297048i	−0.0834565	+	0.0606347i
$25$		0			0
$26$	2.82978	−	8.70916i	0.554965	−	1.70801i
$27$	−1.83923	−	1.33628i	−0.353959	−	0.257167i
$28$	1.63719	+	1.18949i	0.309401	+	0.224793i
$29$	1.51820	−	4.67254i	0.281923	−	0.867668i	−0.705382	−	0.708828i	$-0.749224\pi$
$29$	1.51820	−	4.67254i	0.281923	−	0.867668i	0.987304	−	0.158841i	$-0.0507756\pi$
$30$		0			0
$31$	0.338464	−	0.245909i	0.0607900	−	0.0441665i	−0.556975	−	0.830529i	$-0.688038\pi$
$31$	0.338464	−	0.245909i	0.0607900	−	0.0441665i	0.617765	+	0.786363i	$0.288038\pi$
$32$	−8.07636			−1.42771
$33$	−3.15471	−	8.09880i	−0.549164	−	1.40982i
$34$	6.75241			1.15803
$35$		0			0
$36$	2.50415	+	7.70697i	0.417358	+	1.28449i
$37$	−1.95841	+	6.02737i	−0.321961	+	0.990894i	0.650833	+	0.759221i	$0.274420\pi$
$37$	−1.95841	+	6.02737i	−0.321961	+	0.990894i	−0.972794	+	0.231673i	$0.925580\pi$
$38$	−5.36605	−	3.89867i	−0.870489	−	0.632447i
$39$	−9.59368	−	6.97021i	−1.53622	−	1.11613i
$40$		0			0
$41$	1.78786	+	5.50247i	0.279217	+	0.859341i	0.988073	+	0.153988i	$0.0492117\pi$
$41$	1.78786	+	5.50247i	0.279217	+	0.859341i	−0.708856	+	0.705353i	$0.750788\pi$
$42$	4.14379	−	3.01064i	0.639401	−	0.464552i
$43$	2.26205			0.344960			0.172480	−	0.985013i	$-0.444822\pi$
$43$	2.26205			0.344960			0.172480	+	0.985013i	$0.444822\pi$
$44$	−1.76552	+	6.72129i	−0.266161	+	1.01327i
$45$		0			0
$46$	−5.51149	+	4.00433i	−0.812625	+	0.590407i
$47$	−1.33626	−	4.11260i	−0.194914	−	0.599884i	−0.999978	−	0.00669531i	$-0.997869\pi$
$47$	−1.33626	−	4.11260i	−0.194914	−	0.599884i	0.805063	−	0.593189i	$-0.202131\pi$
$48$	−3.07754	+	9.47169i	−0.444205	+	1.36712i
$49$	4.90846	+	3.56620i	0.701208	+	0.509457i
$50$		0			0
$51$	2.70208	−	8.31615i	0.378367	−	1.16449i
$52$	2.92991	+	9.01735i	0.406306	+	1.25048i
$53$	−2.15255	+	1.56392i	−0.295676	+	0.214821i	−0.725726	−	0.687984i	$-0.758496\pi$
$53$	−2.15255	+	1.56392i	−0.295676	+	0.214821i	0.430050	+	0.902805i	$0.358496\pi$
$54$	4.60066			0.626071
$55$		0			0
$56$	−0.186254			−0.0248892
$57$	−6.94884	+	5.04863i	−0.920396	+	0.668707i
$58$	3.07235	+	9.45574i	0.403420	+	1.24160i
$59$	−3.12889	+	9.62972i	−0.407346	+	1.25368i	0.511574	+	0.859239i	$0.329063\pi$
$59$	−3.12889	+	9.62972i	−0.407346	+	1.25368i	−0.918920	+	0.394444i	$0.870937\pi$
$60$		0			0
$61$	1.99897	+	1.45233i	0.255941	+	0.185952i	0.708356	−	0.705856i	$-0.249437\pi$
$61$	1.99897	+	1.45233i	0.255941	+	0.185952i	−0.452414	+	0.891808i	$0.649437\pi$
$62$	−0.261626	+	0.805201i	−0.0332265	+	0.102261i
$63$	−1.15428	−	3.55252i	−0.145426	−	0.447575i
$64$	7.07350	−	5.13920i	0.884187	−	0.642400i
$65$		0			0
$66$	14.7983	+	9.50680i	1.82155	+	1.17021i
$67$	9.60059			1.17290			0.586449	−	0.809986i	$-0.300525\pi$
$67$	9.60059			1.17290			0.586449	+	0.809986i	$0.300525\pi$
$68$	−5.65612	+	4.10941i	−0.685905	+	0.498339i
$69$	2.72616	+	8.39026i	0.328191	+	1.01007i
$70$		0			0
$71$	4.41166	+	3.20526i	0.523567	+	0.380394i	0.817946	−	0.575295i	$-0.195113\pi$
$71$	4.41166	+	3.20526i	0.523567	+	0.380394i	−0.294379	+	0.955689i	$0.595113\pi$
$72$	−0.603390	−	0.438388i	−0.0711102	−	0.0516646i
$73$	−0.443607	+	1.36528i	−0.0519203	+	0.159794i	−0.973655	−	0.228028i	$-0.926772\pi$
$73$	−0.443607	+	1.36528i	−0.0519203	+	0.159794i	0.921734	+	0.387822i	$0.126772\pi$
$74$	−3.96321	−	12.1975i	−0.460713	−	1.41793i
$75$		0			0
$76$	6.86752			0.787758
$77$	0.813812	−	3.09817i	0.0927425	−	0.353069i
$78$	23.9977			2.71721
$79$	−0.812218	+	0.590111i	−0.0913817	+	0.0663927i	−0.632538	−	0.774529i	$-0.717987\pi$
$79$	−0.812218	+	0.590111i	−0.0913817	+	0.0663927i	0.541156	+	0.840922i	$0.317987\pi$
$80$		0			0
$81$	−1.74436	+	5.36858i	−0.193818	+	0.596509i
$82$	−9.47221	−	6.88197i	−1.04603	−	0.759986i
$83$	5.98302	+	4.34692i	0.656721	+	0.477136i	0.865554	−	0.500815i	$-0.166966\pi$
$83$	5.98302	+	4.34692i	0.656721	+	0.477136i	−0.208833	+	0.977951i	$0.566966\pi$
$84$	−1.63880	+	5.04369i	−0.178807	+	0.550312i
$85$		0			0
$86$	−3.70342	+	2.69069i	−0.399350	+	0.290145i
$87$	12.8750			1.38034
$88$	−0.232149	−	0.595976i	−0.0247472	−	0.0635312i
$89$	−12.1964			−1.29282			−0.646410	−	0.762991i	$-0.723730\pi$
$89$	−12.1964			−1.29282			−0.646410	+	0.762991i	$0.723730\pi$
$90$		0			0
$91$	−1.35054	−	4.15654i	−0.141575	−	0.435723i
$92$	2.17970	−	6.70842i	0.227249	−	0.699401i
$93$	0.886978	+	0.644427i	0.0919754	+	0.0668240i
$94$	7.07962	+	5.14365i	0.730207	+	0.530527i
$95$		0			0
$96$	−6.54030	−	20.1290i	−0.667517	−	2.05440i
$97$	−2.44262	+	1.77467i	−0.248010	+	0.180190i	−0.704844	−	0.709362i	$-0.748983\pi$
$97$	−2.44262	+	1.77467i	−0.248010	+	0.180190i	0.456834	+	0.889552i	$0.348983\pi$
$98$	−12.2781			−1.24027
$99$	9.92863	−	8.12138i	0.997865	−	0.816229i
$100$		0			0
$101$	−12.2940	+	8.93210i	−1.22330	+	0.888777i	−0.996369	−	0.0851342i	$-0.972868\pi$
$101$	−12.2940	+	8.93210i	−1.22330	+	0.888777i	−0.226928	+	0.973912i	$0.572868\pi$
$102$	5.46815	+	16.8292i	0.541428	+	1.66634i
$103$	3.01196	−	9.26987i	0.296778	−	0.913387i	−0.685841	−	0.727751i	$-0.740565\pi$
$103$	3.01196	−	9.26987i	0.296778	−	0.913387i	0.982619	−	0.185636i	$-0.0594345\pi$
$104$	−0.705981	−	0.512925i	−0.0692272	−	0.0502965i
$105$		0			0
$106$	1.66387	−	5.12088i	0.161610	−	0.497384i
$107$	−2.36144	−	7.26778i	−0.228289	−	0.702602i	−0.997941	−	0.0641384i	$-0.979570\pi$
$107$	−2.36144	−	7.26778i	−0.228289	−	0.702602i	0.769652	−	0.638464i	$-0.220430\pi$
$108$	−3.85372	+	2.79989i	−0.370825	+	0.269420i
$109$	−9.85576			−0.944010			−0.472005	−	0.881596i	$-0.656470\pi$
$109$	−9.85576			−0.944010			−0.472005	+	0.881596i	$0.656470\pi$
$110$		0			0
$111$	−16.6082			−1.57638
$112$	−2.96945	+	2.15743i	−0.280587	+	0.203858i
$113$	−1.55084	−	4.77298i	−0.145890	−	0.449004i	0.851234	−	0.524786i	$-0.175855\pi$
$113$	−1.55084	−	4.77298i	−0.145890	−	0.449004i	−0.997124	+	0.0757819i	$0.975855\pi$
$114$	5.37130	−	16.5312i	0.503068	−	1.54829i
$115$		0			0
$116$	−8.32816	−	6.05076i	−0.773250	−	0.561799i
$117$	5.40807	−	16.6443i	0.499976	−	1.53877i
$118$	−6.33188	−	19.4875i	−0.582896	−	1.79397i
$119$	2.60718	−	1.89423i	0.239000	−	0.173644i
$120$		0			0
$121$	10.9279	−	1.25756i	0.993444	−	0.114324i
$122$	−5.00023			−0.452700
$123$	−12.2662	+	8.91189i	−1.10600	+	0.803558i
$124$	−0.270884	−	0.833694i	−0.0243261	−	0.0748679i
$125$		0			0
$126$	6.11547	+	4.44315i	0.544810	+	0.395827i
$127$	5.73626	+	4.16764i	0.509011	+	0.369818i	0.812448	−	0.583033i	$-0.198134\pi$
$127$	5.73626	+	4.16764i	0.509011	+	0.369818i	−0.303438	+	0.952851i	$0.598134\pi$
$128$	−0.476198	+	1.46559i	−0.0420903	+	0.129541i
$129$	1.83183	+	5.63779i	0.161284	+	0.496380i
$130$		0			0
$131$	7.21704			0.630556			0.315278	−	0.948999i	$-0.397902\pi$
$131$	7.21704			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$132$	−18.1814	+	1.04271i	−1.58249	+	0.0907559i
$133$	−3.16557			−0.274490
$134$	−15.7180	+	11.4198i	−1.35783	+	0.986521i
$135$		0			0
$136$	0.198841	−	0.611970i	0.0170505	−	0.0524760i
$137$	6.86920	+	4.99076i	0.586875	+	0.426390i	0.841196	−	0.540730i	$-0.181852\pi$
$137$	6.86920	+	4.99076i	0.586875	+	0.426390i	−0.254321	+	0.967120i	$0.581852\pi$
$138$	−14.4434	−	10.4937i	−1.22950	−	0.893286i
$139$	2.39184	−	7.36133i	0.202873	−	0.624380i	−0.796921	−	0.604084i	$-0.793539\pi$
$139$	2.39184	−	7.36133i	0.202873	−	0.624380i	0.999794	−	0.0202958i	$-0.00646080\pi$
$140$		0			0
$141$	9.16785	−	6.66083i	0.772072	−	0.560943i
$142$	−11.0354			−0.926067
$143$	11.6168	−	9.50222i	0.971442	−	0.794615i
$144$	−14.6978			−1.22482
$145$		0			0
$146$	−0.897720	−	2.76290i	−0.0742958	−	0.228659i
$147$	−4.91326	+	15.1215i	−0.405239	+	1.24720i
$148$	10.7430	+	7.80522i	0.883067	+	0.641585i
$149$	13.6589	+	9.92376i	1.11898	+	0.812986i	0.984054	−	0.177870i	$-0.0569206\pi$
$149$	13.6589	+	9.92376i	1.11898	+	0.812986i	0.134925	+	0.990856i	$0.456921\pi$
$150$		0			0
$151$	−3.79555	−	11.6815i	−0.308877	−	0.950626i	−0.978202	−	0.207656i	$-0.933416\pi$
$151$	−3.79555	−	11.6815i	−0.308877	−	0.950626i	0.669325	−	0.742970i	$-0.266584\pi$
$152$	−0.511353	+	0.371519i	−0.0414762	+	0.0301342i
$153$	12.9047			1.04328
$154$	2.35288	+	6.04033i	0.189600	+	0.486744i
$155$		0			0
$156$	−20.1016	+	14.6046i	−1.60941	+	1.16931i
$157$	−1.30087	−	4.00368i	−0.103821	−	0.319528i	0.885631	−	0.464390i	$-0.153726\pi$
$157$	−1.30087	−	4.00368i	−0.103821	−	0.319528i	−0.989452	+	0.144862i	$0.953726\pi$
$158$	0.627827	−	1.93225i	0.0499472	−	0.153722i
$159$	−5.64096	−	4.09840i	−0.447357	−	0.325024i
$160$		0			0
$161$	−1.00473	+	3.09224i	−0.0791837	+	0.243702i
$162$	−3.53003	−	10.8643i	−0.277345	−	0.853581i
$163$	−13.4083	+	9.74169i	−1.05022	+	0.763028i	−0.972254	−	0.233928i	$-0.924842\pi$
$163$	−13.4083	+	9.74169i	−1.05022	+	0.763028i	−0.0779643	+	0.996956i	$0.524842\pi$
$164$	12.1226			0.946617
$165$		0			0
$166$	−14.9660			−1.16159
$167$	7.41608	−	5.38810i	0.573874	−	0.416944i	−0.262637	−	0.964895i	$-0.584592\pi$
$167$	7.41608	−	5.38810i	0.573874	−	0.416944i	0.836510	+	0.547951i	$0.184592\pi$
$168$	−0.150830	−	0.464207i	−0.0116368	−	0.0358144i
$169$	2.31036	−	7.11055i	0.177720	−	0.546965i
$170$		0			0
$171$	−10.2552	−	7.45085i	−0.784236	−	0.569781i
$172$	1.46464	−	4.50769i	0.111678	−	0.343708i
$173$	1.26996	+	3.90853i	0.0965531	+	0.297160i	0.987655	−	0.156643i	$-0.0500671\pi$
$173$	1.26996	+	3.90853i	0.0965531	+	0.297160i	−0.891102	+	0.453803i	$0.850067\pi$
$174$	−21.0788	+	15.3147i	−1.59798	+	1.16100i
$175$		0			0
$176$	−10.6045	−	6.81261i	−0.799346	−	0.513520i
$177$	−26.5343			−1.99444
$178$	19.9679	−	14.5075i	1.49666	−	1.08739i
$179$	−5.03576	−	15.4985i	−0.376390	−	1.15841i	−0.942536	−	0.334105i	$-0.891566\pi$
$179$	−5.03576	−	15.4985i	−0.376390	−	1.15841i	0.566145	−	0.824305i	$-0.308434\pi$
$180$		0			0
$181$	4.48753	+	3.26038i	0.333555	+	0.242342i	0.741938	−	0.670469i	$-0.233907\pi$
$181$	4.48753	+	3.26038i	0.333555	+	0.242342i	−0.408382	+	0.912811i	$0.633907\pi$
$182$	7.15526	+	5.19860i	0.530383	+	0.385346i
$183$	−2.00092	+	6.15820i	−0.147912	+	0.455227i
$184$	0.200613	+	0.617424i	0.0147894	+	0.0455171i
$185$		0			0
$186$	−2.21870			−0.162683
$187$	9.31078	+	5.98147i	0.680871	+	0.437408i
$188$	−9.06056			−0.660809
$189$	1.77637	−	1.29061i	0.129212	−	0.0938779i
$190$		0			0
$191$	6.74155	−	20.7484i	0.487802	−	1.50130i	−0.340080	−	0.940396i	$-0.610454\pi$
$191$	6.74155	−	20.7484i	0.487802	−	1.50130i	0.827882	−	0.560903i	$-0.189546\pi$
$192$	18.5368	+	13.4678i	1.33778	+	0.971951i
$193$	18.1858	+	13.2128i	1.30904	+	0.951076i	1.00000		2.83481e-5i	$9.02350e-6\pi$
$193$	18.1858	+	13.2128i	1.30904	+	0.951076i	0.309044	+	0.951048i	$0.399991\pi$
$194$	1.88809	−	5.81094i	0.135557	−	0.417201i
$195$		0			0
$196$	10.2847	−	7.47224i	0.734619	−	0.533732i
$197$	25.7479			1.83446			0.917230	−	0.398358i	$-0.130420\pi$
$197$	25.7479			1.83446			0.917230	+	0.398358i	$0.130420\pi$
$198$	−6.59480	+	25.1063i	−0.468672	+	1.78423i
$199$	16.9671			1.20277			0.601385	−	0.798960i	$-0.294616\pi$
$199$	16.9671			1.20277			0.601385	+	0.798960i	$0.294616\pi$
$200$		0			0
$201$	7.77463	+	23.9279i	0.548380	+	1.68774i
$202$	9.50298	−	29.2472i	0.668627	−	2.05782i
$203$	3.83886	+	2.78909i	0.269435	+	0.195756i
$204$	−14.8224	−	10.7691i	−1.03778	−	0.753988i
$205$		0			0
$206$	6.09526	+	18.7593i	0.424677	+	1.30702i
$207$	−10.5332	+	7.65279i	−0.732106	+	0.531906i
$208$	−17.1969			−1.19239
$209$	−3.94561	−	10.1292i	−0.272924	−	0.700652i
$210$		0			0
$211$	4.71363	−	3.42465i	0.324500	−	0.235763i	−0.413593	−	0.910462i	$-0.635726\pi$
$211$	4.71363	−	3.42465i	0.324500	−	0.235763i	0.738093	+	0.674699i	$0.235726\pi$
$212$	1.72275	+	5.30209i	0.118319	+	0.364149i
$213$	−4.41597	+	13.5910i	−0.302577	+	0.931238i
$214$	12.5111	+	9.08984i	0.855241	+	0.621369i
$215$		0			0
$216$	0.135478	−	0.416958i	0.00921810	−	0.0283704i
$217$	0.124863	+	0.384290i	0.00847628	+	0.0260873i
$218$	16.1358	−	11.7233i	1.09285	−	0.794005i
$219$	−3.76197			−0.254211
$220$		0			0
$221$	15.0988			1.01566
$222$	27.1908	−	19.7553i	1.82493	−	1.32589i
$223$	−5.87820	−	18.0913i	−0.393634	−	1.21148i	−0.930020	−	0.367508i	$-0.880211\pi$
$223$	−5.87820	−	18.0913i	−0.393634	−	1.21148i	0.536387	−	0.843972i	$-0.319789\pi$
$224$	2.41043	−	7.41856i	0.161054	−	0.495673i
$225$		0			0
$226$	8.21644	+	5.96959i	0.546549	+	0.397091i
$227$	−8.79646	+	27.0727i	−0.583841	+	1.79688i	0.0200332	+	0.999799i	$0.493623\pi$
$227$	−8.79646	+	27.0727i	−0.583841	+	1.79688i	−0.603874	+	0.797079i	$0.706377\pi$
$228$	5.56137	+	17.1161i	0.368311	+	1.13354i
$229$	20.5420	−	14.9247i	1.35746	−	0.986250i	0.358854	−	0.933394i	$-0.383168\pi$
$229$	20.5420	−	14.9247i	1.35746	−	0.986250i	0.998602	−	0.0528558i	$-0.0168324\pi$
$230$		0			0
$231$	8.38071	−	0.480634i	0.551410	−	0.0316234i
$232$	0.947446			0.0622029
$233$	10.1268	−	7.35755i	0.663429	−	0.482009i	−0.204390	−	0.978890i	$-0.565521\pi$
$233$	10.1268	−	7.35755i	0.663429	−	0.482009i	0.867819	+	0.496880i	$0.165521\pi$
$234$	10.9442	+	33.6828i	0.715446	+	2.20192i
$235$		0			0
$236$	17.1637	+	12.4701i	1.11726	+	0.811737i
$237$	−2.12849	−	1.54644i	−0.138261	−	0.100452i
$238$	−2.01529	+	6.20244i	−0.130632	+	0.402044i
$239$	6.30011	+	19.3897i	0.407520	+	1.25422i	0.918773	+	0.394787i	$0.129182\pi$
$239$	6.30011	+	19.3897i	0.407520	+	1.25422i	−0.511252	+	0.859431i	$0.670818\pi$
$240$		0			0
$241$	−22.7935			−1.46826			−0.734129	−	0.679010i	$-0.762409\pi$
$241$	−22.7935			−1.46826			−0.734129	+	0.679010i	$0.762409\pi$
$242$	−16.3952	+	15.0575i	−1.05392	+	0.967932i
$243$	−21.6131			−1.38648
$244$	4.18842	−	3.04307i	0.268136	−	0.194812i
$245$		0			0
$246$	9.48148	−	29.1810i	0.604517	−	1.86051i
$247$	−11.9989	−	8.71768i	−0.763469	−	0.554693i
$248$	0.0652711	+	0.0474222i	0.00414472	+	0.00301132i
$249$	−5.98887	+	18.4318i	−0.379529	+	1.16807i
$250$		0			0
$251$	−13.7151	+	9.96460i	−0.865689	+	0.628960i	−0.929427	−	0.369007i	$-0.879698\pi$
$251$	−13.7151	+	9.96460i	−0.865689	+	0.628960i	0.0637374	+	0.997967i	$0.479698\pi$
$252$	−7.82663			−0.493031
$253$	−11.1469	+	0.639272i	−0.700797	+	0.0401907i
$254$	−14.3487			−0.900320
$255$		0			0
$256$	4.44000	+	13.6649i	0.277500	+	0.854057i
$257$	−1.46346	+	4.50405i	−0.0912879	+	0.280955i	−0.986268	−	0.165150i	$-0.947189\pi$
$257$	−1.46346	+	4.50405i	−0.0912879	+	0.280955i	0.894981	+	0.446105i	$0.147189\pi$
$258$	−9.70516	−	7.05121i	−0.604217	−	0.438989i
$259$	−4.95196	−	3.59781i	−0.307700	−	0.223557i
$260$		0			0
$261$	5.87166	+	18.0711i	0.363447	+	1.11857i
$262$	−11.8157	+	8.58461i	−0.729976	+	0.530359i
$263$	18.1037			1.11632			0.558162	−	0.829732i	$-0.311507\pi$
$263$	18.1037			1.11632			0.558162	+	0.829732i	$0.311507\pi$
$264$	1.29737	−	1.06122i	0.0798479	−	0.0653136i
$265$		0			0
$266$	5.18266	−	3.76542i	0.317769	−	0.230873i
$267$	−9.87677	−	30.3976i	−0.604449	−	1.86030i
$268$	6.21620	−	19.1315i	0.379715	−	1.16864i
$269$	1.85914	+	1.35074i	0.113354	+	0.0823562i	0.643018	−	0.765851i	$-0.277682\pi$
$269$	1.85914	+	1.35074i	0.113354	+	0.0823562i	−0.529664	+	0.848207i	$0.677682\pi$
$270$		0			0
$271$	0.248971	−	0.766255i	0.0151239	−	0.0465467i	−0.943210	−	0.332198i	$-0.892210\pi$
$271$	0.248971	−	0.766255i	0.0151239	−	0.0465467i	0.958334	+	0.285651i	$0.0922098\pi$
$272$	−3.91850	−	12.0599i	−0.237594	−	0.731239i
$273$	9.26579	−	6.73199i	0.560791	−	0.407439i
$274$	−17.1827			−1.03804
$275$		0			0
$276$	18.4848			1.11265
$277$	−9.57302	+	6.95521i	−0.575187	+	0.417898i	−0.836986	−	0.547225i	$-0.815684\pi$
$277$	−9.57302	+	6.95521i	−0.575187	+	0.417898i	0.261799	+	0.965122i	$0.415684\pi$
$278$	4.84033	+	14.8970i	0.290304	+	0.893462i
$279$	−0.500000	+	1.53884i	−0.0299342	+	0.0921280i
$280$		0			0
$281$	−5.03960	−	3.66148i	−0.300637	−	0.218426i	0.427231	−	0.904142i	$-0.359489\pi$
$281$	−5.03960	−	3.66148i	−0.300637	−	0.218426i	−0.727869	+	0.685717i	$0.759489\pi$
$282$	−7.08655	+	21.8101i	−0.421998	+	1.29878i
$283$	2.67165	+	8.22250i	0.158813	+	0.488777i	0.998527	−	0.0542519i	$-0.0172774\pi$
$283$	2.67165	+	8.22250i	0.158813	+	0.488777i	−0.839714	+	0.543029i	$0.817277\pi$
$284$	9.24372	−	6.71596i	0.548514	−	0.398519i
$285$		0			0
$286$	−7.71608	+	29.3750i	−0.456261	+	1.73698i
$287$	−5.58790			−0.329843
$288$	25.2700	−	18.3597i	1.48905	−	1.08186i
$289$	−1.81285	−	5.57937i	−0.106638	−	0.328198i
$290$		0			0
$291$	−6.40111	−	4.65068i	−0.375240	−	0.272628i
$292$	2.43343	+	1.76799i	0.142406	+	0.103464i
$293$	−1.79554	+	5.52610i	−0.104896	+	0.322838i	−0.989706	−	0.143115i	$-0.954288\pi$
$293$	−1.79554	+	5.52610i	−0.104896	+	0.322838i	0.884810	+	0.465953i	$0.154288\pi$
$294$	−9.94288	−	30.6010i	−0.579880	−	1.78469i
$295$		0			0
$296$	−1.22216			−0.0710369
$297$	6.34377	+	4.07540i	0.368103	+	0.236478i
$298$	−34.1665			−1.97921
$299$	−12.3241	+	8.95396i	−0.712719	+	0.517821i
$300$		0			0
$301$	−0.675123	+	2.07781i	−0.0389134	+	0.119763i
$302$	20.1091	+	14.6101i	1.15715	+	0.840717i
$303$	−32.2176	−	23.4074i	−1.85085	−	1.34472i
$304$	−3.84909	+	11.8463i	−0.220761	+	0.679432i
$305$		0			0
$306$	−21.1275	+	15.3500i	−1.20778	+	0.877503i
$307$	−18.4721			−1.05426			−0.527130	−	0.849785i	$-0.676732\pi$
$307$	−18.4721			−1.05426			−0.527130	+	0.849785i	$0.676732\pi$
$308$	−5.64693	−	3.62773i	−0.321764	−	0.206709i
$309$	25.5427			1.45307
$310$		0			0
$311$	−3.50158	−	10.7768i	−0.198557	−	0.611094i	−0.999917	−	0.0129120i	$-0.995890\pi$
$311$	−3.50158	−	10.7768i	−0.198557	−	0.611094i	0.801360	−	0.598182i	$-0.204110\pi$
$312$	0.706672	−	2.17491i	0.0400074	−	0.123130i
$313$	−4.13811	−	3.00651i	−0.233900	−	0.169938i	0.464661	−	0.885488i	$-0.346176\pi$
$313$	−4.13811	−	3.00651i	−0.233900	−	0.169938i	−0.698561	+	0.715550i	$0.746176\pi$
$314$	6.89212	+	5.00742i	0.388945	+	0.282585i
$315$		0			0
$316$	0.650043	+	2.00063i	0.0365678	+	0.112544i
$317$	9.55715	−	6.94368i	0.536783	−	0.389996i	−0.286106	−	0.958198i	$-0.592361\pi$
$317$	9.55715	−	6.94368i	0.536783	−	0.389996i	0.822889	+	0.568202i	$0.192361\pi$
$318$	14.1104			0.791270
$319$	−4.13974	+	15.7599i	−0.231781	+	0.882387i
$320$		0			0
$321$	16.2014	−	11.7710i	0.904274	−	0.656994i
$322$	−2.03325	−	6.25771i	−0.113309	−	0.348729i
$323$	3.37951	−	10.4010i	0.188041	−	0.578730i
$324$	9.56877	+	6.95212i	0.531598	+	0.386229i
$325$		0			0
$326$	10.3643	−	31.8981i	0.574026	−	1.76667i
$327$	−7.98127	−	24.5638i	−0.441365	−	1.35838i
$328$	−0.902645	+	0.655810i	−0.0498402	+	0.0362110i
$329$	4.17645			0.230255
$330$		0			0
$331$	29.2692			1.60878			0.804391	−	0.594100i	$-0.202492\pi$
$331$	29.2692			1.60878			0.804391	+	0.594100i	$0.202492\pi$
$332$	12.5362	−	9.10807i	0.688012	−	0.499870i
$333$	−7.57419	−	23.3110i	−0.415063	−	1.27743i
$334$	−5.73247	+	17.6427i	−0.313667	+	0.965367i
$335$		0			0
$336$	−7.78174	−	5.65376i	−0.424529	−	0.308438i
$337$	8.23348	−	25.3400i	0.448506	−	1.38036i	−0.430087	−	0.902788i	$-0.641517\pi$
$337$	8.23348	−	25.3400i	0.448506	−	1.38036i	0.878593	−	0.477572i	$-0.158483\pi$
$338$	4.67543	+	14.3895i	0.254310	+	0.782685i
$339$	10.6400	−	7.73040i	0.577885	−	0.419858i
$340$		0			0
$341$	−1.07402	+	0.878523i	−0.0581615	+	0.0475747i
$342$	25.6525			1.38713
$343$	−10.2103	+	7.41820i	−0.551303	+	0.400545i
$344$	0.134801	+	0.414875i	0.00726798	+	0.0223686i
$345$		0			0
$346$	−6.72833	−	4.88842i	−0.361717	−	0.262803i
$347$	3.48790	+	2.53411i	0.187240	+	0.136038i	0.677457	−	0.735563i	$-0.263082\pi$
$347$	3.48790	+	2.53411i	0.187240	+	0.136038i	−0.490216	+	0.871601i	$0.663082\pi$
$348$	8.33631	−	25.6565i	0.446873	−	1.37533i
$349$	−4.06960	−	12.5249i	−0.217841	−	0.670444i	−0.998940	−	0.0460373i	$-0.985341\pi$
$349$	−4.06960	−	12.5249i	−0.217841	−	0.670444i	0.781099	−	0.624407i	$-0.214659\pi$
$350$		0			0
$351$	10.2874			0.549100
$352$	26.7423	−	1.53367i	1.42537	−	0.0817449i
$353$	−25.4904			−1.35672			−0.678358	−	0.734732i	$-0.737308\pi$
$353$	−25.4904			−1.35672			−0.678358	+	0.734732i	$0.737308\pi$
$354$	43.4418	−	31.5623i	2.30890	−	1.67752i
$355$		0			0
$356$	−7.89696	+	24.3044i	−0.418538	+	1.28813i
$357$	6.83237	+	4.96400i	0.361607	+	0.262723i
$358$	26.6798	+	19.3840i	1.41007	+	1.02448i
$359$	8.11915	−	24.9882i	0.428512	−	1.31883i	−0.471078	−	0.882091i	$-0.656135\pi$
$359$	8.11915	−	24.9882i	0.428512	−	1.31883i	0.899591	−	0.436734i	$-0.143865\pi$
$360$		0			0
$361$	6.68037	−	4.85358i	0.351599	−	0.255451i
$362$	−11.2252			−0.589981
$363$	11.9838	+	26.2175i	0.628984	+	1.37606i
$364$	−9.15736			−0.479976
$365$		0			0
$366$	−4.04923	−	12.4622i	−0.211657	−	0.651412i
$367$	−0.623823	+	1.91993i	−0.0325633	+	0.100220i	−0.966017	−	0.258478i	$-0.916779\pi$
$367$	−0.623823	+	1.91993i	−0.0325633	+	0.100220i	0.933454	+	0.358698i	$0.116779\pi$
$368$	10.3502	+	7.51985i	0.539541	+	0.391999i
$369$	−18.1026	−	13.1523i	−0.942384	−	0.684682i
$370$		0			0
$371$	−0.794101	−	2.44399i	−0.0412277	−	0.126886i
$372$	1.85848	−	1.35026i	0.0963577	−	0.0700080i
$373$	8.87153			0.459351			0.229675	−	0.973267i	$-0.426234\pi$
$373$	8.87153			0.459351			0.229675	+	0.973267i	$0.426234\pi$
$374$	−22.3585	+	1.28226i	−1.15613	+	0.0663040i
$375$		0			0
$376$	0.674645	−	0.490159i	0.0347922	−	0.0252780i
$377$	6.86999	+	21.1437i	0.353823	+	1.08895i
$378$	−1.37309	+	4.22595i	−0.0706243	+	0.217359i
$379$	−17.0412	−	12.3812i	−0.875348	−	0.635978i	0.0566685	−	0.998393i	$-0.481952\pi$
$379$	−17.0412	−	12.3812i	−0.875348	−	0.635978i	−0.932017	+	0.362415i	$0.881952\pi$
$380$		0			0
$381$	−5.74187	+	17.6717i	−0.294165	+	0.905346i
$382$	13.6428	+	41.9881i	0.698025	+	2.14830i
$383$	21.0179	−	15.2704i	1.07396	−	0.780281i	0.0973436	−	0.995251i	$-0.468965\pi$
$383$	21.0179	−	15.2704i	1.07396	−	0.780281i	0.976621	+	0.214970i	$0.0689654\pi$
$384$	−4.03836			−0.206082
$385$		0			0
$386$	−45.4902			−2.31539
$387$	−7.07771	+	5.14225i	−0.359780	+	0.261396i
$388$	1.95490	+	6.01657i	0.0992451	+	0.305445i
$389$	−0.507965	+	1.56335i	−0.0257548	+	0.0792652i	−0.963108	−	0.269116i	$-0.913269\pi$
$389$	−0.507965	+	1.56335i	−0.0257548	+	0.0792652i	0.937353	+	0.348381i	$0.113269\pi$
$390$		0			0
$391$	−9.08746	−	6.60243i	−0.459573	−	0.333899i
$392$	−0.361558	+	1.11276i	−0.0182614	+	0.0562029i
$393$	5.84442	+	17.9873i	0.294812	+	0.907338i
$394$	−42.1543	+	30.6269i	−2.12370	+	1.54296i
$395$		0			0
$396$	−9.75521	−	25.0437i	−0.490218	−	1.25849i
$397$	−16.7088			−0.838588			−0.419294	−	0.907850i	$-0.637722\pi$
$397$	−16.7088			−0.838588			−0.419294	+	0.907850i	$0.637722\pi$
$398$	−27.7785	+	20.1823i	−1.39241	+	1.01165i
$399$	−2.56351	−	7.88966i	−0.128336	−	0.394977i
$400$		0			0
$401$	−22.4842	−	16.3357i	−1.12281	−	0.815766i	−0.138174	−	0.990408i	$-0.544123\pi$
$401$	−22.4842	−	16.3357i	−1.12281	−	0.815766i	−0.984632	+	0.174641i	$0.944123\pi$
$402$	−41.1906	−	29.9267i	−2.05440	−	1.49261i
$403$	−0.585013	+	1.80048i	−0.0291416	+	0.0896885i
$404$	9.83926	+	30.2821i	0.489521	+	1.50659i
$405$		0			0
$406$	−9.60255			−0.476567
$407$	5.34009	−	20.3296i	0.264698	−	1.00770i
$408$	1.68626			0.0834822
$409$	−31.9019	+	23.1781i	−1.57745	+	1.14608i	−0.657902	+	0.753104i	$0.728556\pi$
$409$	−31.9019	+	23.1781i	−1.57745	+	1.14608i	−0.919547	+	0.392980i	$0.871444\pi$
$410$		0			0
$411$	−6.87591	+	21.1619i	−0.339164	+	1.04384i
$412$	−16.5223	−	12.0041i	−0.813994	−	0.591401i
$413$	−7.91157	−	5.74809i	−0.389303	−	0.282845i
$414$	8.14191	−	25.0582i	0.400153	−	1.23154i
$415$		0			0
$416$	29.5665	−	21.4814i	1.44962	−	1.05321i
$417$	20.2838			0.993303
$418$	18.5083	+	11.8902i	0.905272	+	0.581569i
$419$	14.7812			0.722111			0.361055	−	0.932544i	$-0.382417\pi$
$419$	14.7812			0.722111			0.361055	+	0.932544i	$0.382417\pi$
$420$		0			0
$421$	−3.33036	−	10.2498i	−0.162312	−	0.499545i	0.836516	−	0.547942i	$-0.184589\pi$
$421$	−3.33036	−	10.2498i	−0.162312	−	0.499545i	−0.998828	+	0.0483974i	$0.984589\pi$
$422$	−3.64354	+	11.2136i	−0.177365	+	0.545872i
$423$	13.5301	+	9.83016i	0.657854	+	0.477959i
$424$	−0.415108	−	0.301594i	−0.0201594	−	0.0146467i
$425$		0			0
$426$	−8.93653	−	27.5038i	−0.432976	−	1.33256i
$427$	−1.93065	+	1.40270i	−0.0934306	+	0.0678813i
$428$	−16.0118			−0.773960
$429$	33.0900	+	21.2579i	1.59760	+	1.02634i
$430$		0			0
$431$	−26.0435	+	18.9217i	−1.25447	+	0.911428i	−0.998473	−	0.0552489i	$-0.982405\pi$
$431$	−26.0435	+	18.9217i	−1.25447	+	0.911428i	−0.256000	+	0.966677i	$0.582405\pi$
$432$	−2.66982	−	8.21685i	−0.128452	−	0.395334i
$433$	−0.118240	+	0.363904i	−0.00568223	+	0.0174881i	−0.953857	−	0.300260i	$-0.902927\pi$
$433$	−0.118240	+	0.363904i	−0.00568223	+	0.0174881i	0.948175	+	0.317748i	$0.102927\pi$
$434$	−0.661536	−	0.480634i	−0.0317547	−	0.0230712i
$435$		0			0
$436$	−6.38142	+	19.6400i	−0.305615	+	0.940585i
$437$	3.40962	+	10.4937i	0.163104	+	0.501983i
$438$	6.15908	−	4.47484i	0.294292	−	0.213816i
$439$	26.5331			1.26635			0.633177	−	0.774007i	$-0.281751\pi$
$439$	26.5331			1.26635			0.633177	+	0.774007i	$0.281751\pi$
$440$		0			0
$441$	−23.4649			−1.11738
$442$	−24.7197	+	17.9599i	−1.17580	+	0.854267i
$443$	4.48106	+	13.7913i	0.212901	+	0.655243i	0.999296	+	0.0375185i	$0.0119453\pi$
$443$	4.48106	+	13.7913i	0.212901	+	0.655243i	−0.786395	+	0.617725i	$0.788055\pi$
$444$	−10.7535	+	33.0958i	−0.510337	+	1.57066i
$445$		0			0
$446$	31.1432	+	22.6268i	1.47467	+	1.07141i
$447$	−13.6722	+	42.0788i	−0.646675	+	1.99026i
$448$	2.60950	+	8.03120i	0.123287	+	0.379439i
$449$	−8.18240	+	5.94486i	−0.386151	+	0.280555i	−0.763876	−	0.645362i	$-0.776706\pi$
$449$	−8.18240	+	5.94486i	−0.386151	+	0.280555i	0.377725	+	0.925918i	$0.376706\pi$
$450$		0			0
$451$	−6.96483	−	17.8802i	−0.327961	−	0.841945i
$452$	−10.5155			−0.494606
$453$	26.0405	−	18.9195i	1.22349	−	0.888917i
$454$	−17.8012	−	54.7866i	−0.835454	−	2.57126i
$455$		0			0
$456$	−1.34005	−	0.973602i	−0.0627535	−	0.0455931i
$457$	31.6235	+	22.9758i	1.47928	+	1.07476i	0.977787	+	0.209602i	$0.0672170\pi$
$457$	31.6235	+	22.9758i	1.47928	+	1.07476i	0.501496	+	0.865160i	$0.332783\pi$
$458$	−15.8785	+	48.8691i	−0.741956	+	2.28351i
$459$	2.34410	+	7.21440i	0.109413	+	0.336739i
$460$		0			0
$461$	39.1322			1.82257			0.911285	−	0.411776i	$-0.135092\pi$
$461$	39.1322			1.82257			0.911285	+	0.411776i	$0.135092\pi$
$462$	−13.1491	+	10.7557i	−0.611753	+	0.500399i
$463$	12.9189			0.600392			0.300196	−	0.953878i	$-0.402948\pi$
$463$	12.9189			0.600392			0.300196	+	0.953878i	$0.402948\pi$
$464$	15.1052	−	10.9745i	0.701240	−	0.509481i
$465$		0			0
$466$	−7.82780	+	24.0915i	−0.362616	+	1.11602i
$467$	−9.10071	−	6.61206i	−0.421131	−	0.305969i	0.356962	−	0.934119i	$-0.383813\pi$
$467$	−9.10071	−	6.61206i	−0.421131	−	0.305969i	−0.778093	+	0.628150i	$0.783813\pi$
$468$	−29.6662	−	21.5538i	−1.37132	−	0.996324i
$469$	−2.86535	+	8.81864i	−0.132310	+	0.407207i
$470$		0			0
$471$	8.92504	−	6.48442i	0.411244	−	0.298786i
$472$	−1.95261			−0.0898762
$473$	−7.49007	+	0.429556i	−0.344394	+	0.0197510i
$474$	5.32424			0.244550
$475$		0			0
$476$	−2.08661	−	6.42192i	−0.0956395	−	0.294348i
$477$	3.17988	−	9.78665i	0.145597	−	0.448100i
$478$	−33.3784	−	24.2508i	−1.52669	−	1.10921i
$479$	−16.9621	−	12.3237i	−0.775017	−	0.563083i	0.128462	−	0.991714i	$-0.458996\pi$
$479$	−16.9621	−	12.3237i	−0.775017	−	0.563083i	−0.903479	+	0.428632i	$0.858996\pi$
$480$		0			0
$481$	−8.86200	−	27.2744i	−0.404072	−	1.24361i
$482$	37.3174	−	27.1126i	1.69976	−	1.23495i
$483$	−8.52053			−0.387697
$484$	4.56960	−	22.5907i	0.207709	−	1.02685i
$485$		0			0
$486$	35.3849	−	25.7086i	1.60509	−	1.16617i
$487$	−6.97424	−	21.4645i	−0.316033	−	0.972649i	−0.975327	−	0.220764i	$-0.929145\pi$
$487$	−6.97424	−	21.4645i	−0.316033	−	0.972649i	0.659294	−	0.751885i	$-0.270855\pi$
$488$	−0.147244	+	0.453171i	−0.00666543	+	0.0205141i
$489$	−35.1377	−	25.5290i	−1.58898	−	1.15446i
$490$		0			0
$491$	−6.20389	+	19.0936i	−0.279977	+	0.861682i	0.707882	+	0.706331i	$0.249651\pi$
$491$	−6.20389	+	19.0936i	−0.279977	+	0.861682i	−0.987859	+	0.155351i	$0.950349\pi$
$492$	9.81699	+	30.2136i	0.442584	+	1.36213i
$493$	−13.2623	+	9.63565i	−0.597306	+	0.433968i
$494$	30.0141			1.35040
$495$		0			0
$496$	1.58993			0.0713898
$497$	−4.26088	+	3.09571i	−0.191127	+	0.138862i
$498$	−12.1196	−	37.3002i	−0.543091	−	1.67146i
$499$	1.43750	−	4.42417i	0.0643513	−	0.198053i	−0.913711	−	0.406364i	$-0.866797\pi$
$499$	1.43750	−	4.42417i	0.0643513	−	0.198053i	0.978063	+	0.208311i	$0.0667966\pi$
$500$		0			0
$501$	19.4346	+	14.1200i	0.868272	+	0.630836i
$502$	10.6015	−	32.6280i	0.473167	−	1.45626i
$503$	−4.01636	−	12.3611i	−0.179081	−	0.551154i	0.820716	−	0.571337i	$-0.193575\pi$
$503$	−4.01636	−	12.3611i	−0.179081	−	0.551154i	−0.999796	+	0.0201833i	$0.993575\pi$
$504$	0.582768	−	0.423406i	0.0259585	−	0.0188600i
$505$		0			0
$506$	17.4892	−	14.3057i	0.777488	−	0.635966i
$507$	19.5928			0.870147
$508$	12.0191	−	8.73242i	0.533263	−	0.387439i
$509$	9.12976	+	28.0985i	0.404669	+	1.24544i	0.921171	+	0.389158i	$0.127234\pi$
$509$	9.12976	+	28.0985i	0.404669	+	1.24544i	−0.516501	+	0.856286i	$0.672766\pi$
$510$		0			0
$511$	−1.12169	−	0.814952i	−0.0496205	−	0.0360514i
$512$	−26.0168	−	18.9023i	−1.14979	−	0.835373i
$513$	2.30258	−	7.08662i	0.101661	−	0.312882i
$514$	−2.96157	−	9.11478i	−0.130629	−	0.402036i
$515$		0			0
$516$	12.4207			0.546793
$517$	5.20558	+	13.3638i	0.228941	+	0.587740i
$518$	12.3869			0.544248
$519$	−8.71293	+	6.33032i	−0.382455	+	0.277870i
$520$		0			0
$521$	−9.71896	+	29.9119i	−0.425796	+	1.31046i	0.476435	+	0.879210i	$0.341929\pi$
$521$	−9.71896	+	29.9119i	−0.425796	+	1.31046i	−0.902230	+	0.431254i	$0.858071\pi$
$522$	−31.1085	−	22.6016i	−1.36158	−	0.989247i
$523$	7.29750	+	5.30194i	0.319097	+	0.231838i	0.735790	−	0.677210i	$-0.236811\pi$
$523$	7.29750	+	5.30194i	0.319097	+	0.231838i	−0.416693	+	0.909047i	$0.636811\pi$
$524$	4.67290	−	14.3817i	0.204137	−	0.628268i
$525$		0			0
$526$	−29.6393	+	21.5342i	−1.29234	+	0.938937i
$527$	−1.39595			−0.0608088
$528$	8.39166	−	31.9469i	0.365200	−	1.39031i
$529$	−11.6672			−0.507269
$530$		0			0
$531$	−12.1010	−	37.2431i	−0.525140	−	1.61621i
$532$	−2.04965	+	6.30817i	−0.0888636	+	0.273494i
$533$	−21.1805	−	15.3885i	−0.917430	−	0.666552i
$534$	52.3279	+	38.0184i	2.26445	+	1.64522i
$535$		0			0
$536$	0.572121	+	1.76081i	0.0247119	+	0.0760553i
$537$	34.5494	−	25.1016i	1.49092	−	1.08321i
$538$	−4.65046			−0.200496
$539$	−16.9300	−	10.8763i	−0.729227	−	0.468473i
$540$		0			0
$541$	6.91720	−	5.02564i	0.297394	−	0.216069i	−0.429075	−	0.903269i	$-0.641160\pi$
$541$	6.91720	−	5.02564i	0.297394	−	0.216069i	0.726468	+	0.687200i	$0.241160\pi$
$542$	0.503839	+	1.55066i	0.0216417	+	0.0666064i
$543$	−4.49192	+	13.8247i	−0.192767	+	0.593275i
$544$	21.8016	+	15.8398i	0.934737	+	0.679126i
$545$		0			0
$546$	−7.16226	+	22.0432i	−0.306516	+	0.943360i
$547$	10.4849	+	32.2693i	0.448304	+	1.37974i	0.878820	+	0.477154i	$0.158332\pi$
$547$	10.4849	+	32.2693i	0.448304	+	1.37974i	−0.430516	+	0.902583i	$0.641668\pi$
$548$	14.3930	−	10.4571i	0.614838	−	0.446706i
$549$	−9.55608			−0.407844
$550$		0			0
$551$	16.1028			0.686002
$552$	−1.37637	+	0.999990i	−0.0585821	+	0.0425624i
$553$	−0.299637	−	0.922187i	−0.0127418	−	0.0392154i
$554$	7.39974	−	22.7740i	0.314385	−	0.967577i
$555$		0			0
$556$	−13.1206	−	9.53265i	−0.556436	−	0.404274i
$557$	7.08904	−	21.8178i	0.300372	−	0.924451i	−0.680991	−	0.732291i	$-0.738451\pi$
$557$	7.08904	−	21.8178i	0.300372	−	0.924451i	0.981364	−	0.192160i	$-0.0615491\pi$
$558$	−1.01184	−	3.11413i	−0.0428347	−	0.131832i
$559$	−8.28110	+	6.01657i	−0.350253	+	0.254474i
$560$		0			0
$561$	−7.36788	+	28.0494i	−0.311072	+	1.18425i
$562$	12.6061			0.531757
$563$	7.50980	−	5.45619i	0.316500	−	0.229951i	−0.418180	−	0.908364i	$-0.637332\pi$
$563$	7.50980	−	5.45619i	0.316500	−	0.229951i	0.734681	+	0.678413i	$0.237332\pi$
$564$	−7.33731	−	22.5819i	−0.308957	−	0.950871i
$565$		0			0
$566$	−14.1546	−	10.2839i	−0.594962	−	0.432266i
$567$	−4.41071	−	3.20457i	−0.185232	−	0.134579i
$568$	−0.324963	+	1.00013i	−0.0136352	+	0.0419647i
$569$	9.55701	+	29.4135i	0.400651	+	1.23308i	0.924473	+	0.381248i	$0.124506\pi$
$569$	9.55701	+	29.4135i	0.400651	+	1.23308i	−0.523822	+	0.851828i	$0.675494\pi$
$570$		0			0
$571$	−2.63736			−0.110370			−0.0551851	−	0.998476i	$-0.517575\pi$
$571$	−2.63736			−0.110370			−0.0551851	+	0.998476i	$0.517575\pi$
$572$	−11.4138	−	29.3017i	−0.477237	−	1.22517i
$573$	57.1712			2.38836
$574$	9.14848	−	6.64676i	0.381850	−	0.277430i
$575$		0			0
$576$	−10.4494	+	32.1599i	−0.435391	+	1.34000i
$577$	−29.6347	−	21.5309i	−1.23371	−	0.896342i	−0.236546	−	0.971620i	$-0.576015\pi$
$577$	−29.6347	−	21.5309i	−1.23371	−	0.896342i	−0.997163	+	0.0752785i	$0.976015\pi$
$578$	9.60459	+	6.97814i	0.399498	+	0.290252i
$579$	−18.2036	+	56.0249i	−0.756516	+	2.32832i
$580$		0			0
$581$	−5.77854	+	4.19835i	−0.239734	+	0.174177i
$582$	16.0118			0.663710
$583$	6.83051	−	5.58719i	0.282891	−	0.231398i
$584$	−0.276837			−0.0114556
$585$		0			0
$586$	−3.63360	−	11.1831i	−0.150103	−	0.461968i
$587$	−4.24973	+	13.0793i	−0.175405	+	0.539842i	−0.999652	−	0.0263892i	$-0.991599\pi$
$587$	−4.24973	+	13.0793i	−0.175405	+	0.539842i	0.824246	+	0.566231i	$0.191599\pi$
$588$	26.9519	+	19.5817i	1.11148	+	0.807536i
$589$	1.10935	+	0.805989i	0.0457099	+	0.0332102i
$590$		0			0
$591$	20.8508	+	64.1723i	0.857689	+	2.63970i
$592$	−19.4850	+	14.1567i	−0.800829	+	0.581837i
$593$	−20.1550			−0.827668			−0.413834	−	0.910352i	$-0.635811\pi$
$593$	−20.1550			−0.827668			−0.413834	+	0.910352i	$0.635811\pi$
$594$	−15.2336	+	0.873649i	−0.625044	+	0.0358463i
$595$		0			0
$596$	28.6194	−	20.7932i	1.17230	−	0.851722i
$597$	13.7401	+	42.2878i	0.562346	+	1.73072i
$598$	9.52624	−	29.3187i	0.389557	−	1.19893i
$599$	−3.49753	−	2.54110i	−0.142905	−	0.103827i	0.514036	−	0.857769i	$-0.328150\pi$
$599$	−3.49753	−	2.54110i	−0.142905	−	0.103827i	−0.656941	+	0.753942i	$0.728150\pi$
$600$		0			0
$601$	11.1214	−	34.2281i	0.453650	−	1.39619i	−0.419063	−	0.907957i	$-0.637641\pi$
$601$	11.1214	−	34.2281i	0.453650	−	1.39619i	0.872713	−	0.488234i	$-0.162359\pi$
$602$	−1.36623	−	4.20484i	−0.0556836	−	0.171376i
$603$	−30.0391	+	21.8247i	−1.22329	+	0.888771i
$604$	−25.7358			−1.04717
$605$		0			0
$606$	80.5893			3.27372
$607$	32.0774	−	23.3056i	1.30198	−	0.945945i	0.302009	−	0.953305i	$-0.402343\pi$
$607$	32.0774	−	23.3056i	1.30198	−	0.945945i	0.999973	+	0.00736018i	$0.00234284\pi$
$608$	−8.17999	−	25.1754i	−0.331742	−	1.02100i
$609$	−3.84261	+	11.8263i	−0.155710	+	0.479227i
$610$		0			0
$611$	15.8305	+	11.5015i	0.640434	+	0.465303i
$612$	8.35556	−	25.7158i	0.337753	−	1.03950i
$613$	1.17887	+	3.62818i	0.0476139	+	0.146541i	0.972037	−	0.234828i	$-0.0754528\pi$
$613$	1.17887	+	3.62818i	0.0476139	+	0.146541i	−0.924423	+	0.381369i	$0.875453\pi$
$614$	30.2424	−	21.9724i	1.22049	−	0.886735i
$615$		0			0
$616$	0.616721	−	0.0353690i	0.0248484	−	0.00142506i
$617$	−28.4055			−1.14356			−0.571781	−	0.820407i	$-0.693747\pi$
$617$	−28.4055			−1.14356			−0.571781	+	0.820407i	$0.693747\pi$
$618$	−41.8184	+	30.3828i	−1.68218	+	1.22218i
$619$	7.43830	+	22.8927i	0.298971	+	0.920137i	0.981859	+	0.189614i	$0.0607236\pi$
$619$	7.43830	+	22.8927i	0.298971	+	0.920137i	−0.682888	+	0.730523i	$0.739276\pi$
$620$		0			0
$621$	−6.19162	−	4.49848i	−0.248461	−	0.180518i
$622$	18.5516	+	13.4786i	0.743853	+	0.540441i
$623$	3.64010	−	11.2031i	0.145837	−	0.448841i
$624$	−13.9262	−	42.8603i	−0.557492	−	1.71579i
$625$		0			0
$626$	10.3511			0.413714
$627$	22.0502	−	18.0365i	0.880599	−	0.720308i
$628$	−8.82059			−0.351980
$629$	17.1078	−	12.4296i	0.682135	−	0.495600i
$630$		0			0
$631$	5.90889	−	18.1857i	0.235229	−	0.723961i	−0.761862	−	0.647740i	$-0.775714\pi$
$631$	5.90889	−	18.1857i	0.235229	−	0.723961i	0.997091	−	0.0762213i	$-0.0242855\pi$
$632$	−0.156632	−	0.113800i	−0.00623049	−	0.00452672i
$633$	12.3525	+	8.97463i	0.490969	+	0.356710i
$634$	−7.38747	+	22.7363i	−0.293394	+	0.902974i
$635$		0			0
$636$	−11.8195	+	8.58735i	−0.468673	+	0.340511i
$637$	−27.4546			−1.08779
$638$	−11.9687	−	30.7263i	−0.473847	−	1.21646i
$639$	−21.0900			−0.834307
$640$		0			0
$641$	3.70172	+	11.3927i	0.146209	+	0.449985i	0.997165	−	0.0752526i	$-0.0239763\pi$
$641$	3.70172	+	11.3927i	0.146209	+	0.449985i	−0.850955	+	0.525238i	$0.823976\pi$
$642$	−12.5233	+	38.5429i	−0.494257	+	1.52117i
$643$	20.8248	+	15.1301i	0.821248	+	0.596672i	0.917070	−	0.398727i	$-0.130548\pi$
$643$	20.8248	+	15.1301i	0.821248	+	0.596672i	−0.0958216	+	0.995399i	$0.530548\pi$
$644$	5.51149	+	4.00433i	0.217183	+	0.157793i
$645$		0			0
$646$	6.83905	+	21.0484i	0.269079	+	0.828139i
$647$	−7.52570	+	5.46774i	−0.295866	+	0.214959i	−0.725808	−	0.687897i	$-0.758534\pi$
$647$	−7.52570	+	5.46774i	−0.295866	+	0.214959i	0.429942	+	0.902856i	$0.358534\pi$
$648$	−1.08858			−0.0427636
$649$	8.53167	−	32.4800i	0.334897	−	1.27495i
$650$		0			0
$651$	−0.856664	+	0.622403i	−0.0335753	+	0.0243939i
$652$	10.7311	+	33.0268i	0.420261	+	1.29343i
$653$	−11.5729	+	35.6177i	−0.452882	+	1.39383i	0.420723	+	0.907189i	$0.361777\pi$
$653$	−11.5729	+	35.6177i	−0.452882	+	1.39383i	−0.873604	+	0.486637i	$0.838223\pi$
$654$	42.2854	+	30.7221i	1.65349	+	1.20133i
$655$		0			0
$656$	−6.79446	+	20.9112i	−0.265279	+	0.816445i
$657$	−1.71566	−	5.28025i	−0.0669342	−	0.206002i
$658$	−6.83766	+	4.96785i	−0.266560	+	0.193667i
$659$	−4.93753			−0.192339			−0.0961693	−	0.995365i	$-0.530659\pi$
$659$	−4.93753			−0.192339			−0.0961693	+	0.995365i	$0.530659\pi$
$660$		0			0
$661$	−4.82155			−0.187537			−0.0937683	−	0.995594i	$-0.529891\pi$
$661$	−4.82155			−0.187537			−0.0937683	+	0.995594i	$0.529891\pi$
$662$	−47.9194	+	34.8155i	−1.86244	+	1.35314i
$663$	12.2272	+	37.6313i	0.474864	+	1.46148i
$664$	−0.440710	+	1.35637i	−0.0171029	+	0.0526372i
$665$		0			0
$666$	40.1286	+	29.1551i	1.55495	+	1.12974i
$667$	5.11091	−	15.7297i	0.197895	−	0.609058i
$668$	−5.93532	−	18.2670i	−0.229645	−	0.706773i
$669$	40.3292	−	29.3009i	1.55922	−	1.13284i
$670$		0			0
$671$	−6.89474	−	4.42935i	−0.266168	−	0.170993i
$672$	20.4415			0.788548
$673$	−26.6280	+	19.3464i	−1.02644	+	0.745749i	−0.967592	−	0.252518i	$-0.918741\pi$
$673$	−26.6280	+	19.3464i	−1.02644	+	0.745749i	−0.0588431	+	0.998267i	$0.518741\pi$
$674$	16.6619	+	51.2802i	0.641794	+	1.97524i
$675$		0			0
$676$	−12.6736	−	9.20789i	−0.487445	−	0.354150i
$677$	−13.8686	−	10.0761i	−0.533014	−	0.387258i	0.288470	−	0.957489i	$-0.406854\pi$
$677$	−13.8686	−	10.0761i	−0.533014	−	0.387258i	−0.821484	+	0.570231i	$0.806854\pi$
$678$	−8.22448	+	25.3123i	−0.315859	+	0.972114i
$679$	−0.901110	−	2.77333i	−0.0345814	−	0.106431i
$680$		0			0
$681$	−74.5977			−2.85859
$682$	0.713386	−	2.71585i	0.0273170	−	0.103995i
$683$	19.3586			0.740737			0.370368	−	0.928885i	$-0.379231\pi$
$683$	19.3586			0.740737			0.370368	+	0.928885i	$0.379231\pi$
$684$	−21.4877	+	15.6117i	−0.821602	+	0.596929i
$685$		0			0
$686$	7.89232	−	24.2901i	0.301330	−	0.927399i
$687$	53.8324	+	39.1115i	2.05383	+	1.49220i
$688$	6.95475	+	5.05292i	0.265148	+	0.192641i
$689$	3.72054	−	11.4506i	0.141741	−	0.436234i
$690$		0			0
$691$	7.39559	−	5.37321i	0.281342	−	0.204407i	−0.438161	−	0.898897i	$-0.644370\pi$
$691$	7.39559	−	5.37321i	0.281342	−	0.204407i	0.719502	+	0.694490i	$0.244370\pi$
$692$	8.61097			0.327340
$693$	4.49665	+	11.5438i	0.170814	+	0.438514i
$694$	−8.72467			−0.331184
$695$		0			0
$696$	0.767250	+	2.36135i	0.0290825	+	0.0895068i
$697$	5.96554	−	18.3600i	0.225961	−	0.695436i
$698$	21.5610	+	15.6650i	0.816096	+	0.592929i
$699$	26.5383	+	19.2812i	1.00377	+	0.729281i
$700$		0			0
$701$	−4.72594	−	14.5450i	−0.178496	−	0.549355i	0.821279	−	0.570526i	$-0.193261\pi$
$701$	−4.72594	−	14.5450i	−0.178496	−	0.549355i	−0.999776	+	0.0211707i	$0.993261\pi$
$702$	−16.8425	+	12.2368i	−0.635678	+	0.461847i
$703$	−20.7719			−0.783428
$704$	−22.4457	+	18.3601i	−0.845956	+	0.691971i
$705$		0			0
$706$	41.7327	−	30.3206i	1.57063	−	1.14113i
$707$	−4.53539	−	13.9585i	−0.170571	−	0.524964i
$708$	−17.1805	+	52.8760i	−0.645681	+	1.98720i
$709$	−34.7172	−	25.2235i	−1.30383	−	0.947290i	−0.303848	−	0.952721i	$-0.598271\pi$
$709$	−34.7172	−	25.2235i	−1.30383	−	0.947290i	−0.999985	+	0.00543044i	$0.998271\pi$
$710$		0			0
$711$	1.19986	−	3.69278i	0.0449982	−	0.138490i
$712$	−0.726814	−	2.23690i	−0.0272385	−	0.0838315i
$713$	1.13942	−	0.827834i	0.0426714	−	0.0310026i
$714$	−17.0905			−0.639598
$715$		0			0
$716$	−34.1450			−1.27606
$717$	−43.2238	+	31.4039i	−1.61422	+	1.17280i
$718$	16.4306	+	50.5682i	0.613184	+	1.88719i
$719$	1.48738	−	4.57768i	0.0554699	−	0.170719i	−0.919483	−	0.393129i	$-0.871393\pi$
$719$	1.48738	−	4.57768i	0.0554699	−	0.170719i	0.974953	+	0.222411i	$0.0713925\pi$
$720$		0			0
$721$	7.61592	+	5.53329i	0.283632	+	0.206071i
$722$	−5.16378	+	15.8925i	−0.192176	+	0.591457i
$723$	−18.4584	−	56.8090i	−0.686473	−	2.11275i
$724$	9.40269	−	6.83146i	0.349448	−	0.253889i
$725$		0			0
$726$	−50.8053	−	28.6686i	−1.88556	−	1.06399i
$727$	21.8922			0.811937			0.405969	−	0.913887i	$-0.366934\pi$
$727$	21.8922			0.811937			0.405969	+	0.913887i	$0.366934\pi$
$728$	0.681853	−	0.495395i	0.0252712	−	0.0183606i
$729$	−12.2694	−	37.7614i	−0.454423	−	1.39857i
$730$		0			0
$731$	−6.10627	−	4.43647i	−0.225849	−	0.164089i
$732$	10.9762	+	7.97464i	0.405690	+	0.294751i
$733$	14.8419	−	45.6788i	0.548199	−	1.68718i	−0.165060	−	0.986284i	$-0.552782\pi$
$733$	14.8419	−	45.6788i	0.548199	−	1.68718i	0.713259	−	0.700901i	$-0.247218\pi$
$734$	−1.26242	−	3.88533i	−0.0465968	−	0.143410i
$735$		0			0
$736$	−27.1885			−1.00218
$737$	−31.7893	+	1.82312i	−1.17097	+	0.0671554i
$738$	45.2820			1.66685
$739$	27.5934	−	20.0478i	1.01504	−	0.737470i	0.0497805	−	0.998760i	$-0.484148\pi$
$739$	27.5934	−	20.0478i	1.01504	−	0.737470i	0.965260	+	0.261290i	$0.0841478\pi$
$740$		0			0
$741$	12.0106	−	36.9648i	0.441220	−	1.35794i
$742$	4.20720	+	3.05671i	0.154451	+	0.112215i
$743$	−21.3906	−	15.5411i	−0.784743	−	0.570149i	0.121656	−	0.992572i	$-0.461180\pi$
$743$	−21.3906	−	15.5411i	−0.784743	−	0.570149i	−0.906399	+	0.422423i	$0.861180\pi$
$744$	−0.0653350	+	0.201080i	−0.00239530	+	0.00737196i
$745$		0			0
$746$	−14.5244	+	10.5526i	−0.531777	+	0.386359i
$747$	−28.6019			−1.04649
$748$	17.9481	−	14.6811i	0.656247	−	0.536794i
$749$	7.38062			0.269682
$750$		0			0
$751$	14.1963	+	43.6918i	0.518032	+	1.59434i	0.777697	+	0.628639i	$0.216388\pi$
$751$	14.1963	+	43.6918i	0.518032	+	1.59434i	−0.259666	+	0.965699i	$0.583612\pi$
$752$	5.07825	−	15.6292i	0.185185	−	0.569939i
$753$	−35.9417	−	26.1132i	−1.30979	−	0.951617i
$754$	−36.3977	−	26.4445i	−1.32553	−	0.963052i
$755$		0			0
$756$	−1.42168	−	4.37549i	−0.0517061	−	0.159135i
$757$	−24.9628	+	18.1365i	−0.907288	+	0.659183i	−0.940327	−	0.340271i	$-0.889481\pi$
$757$	−24.9628	+	18.1365i	−0.907288	+	0.659183i	0.0330398	+	0.999454i	$0.489481\pi$
$758$	42.6271			1.54828
$759$	−10.6201	−	27.2640i	−0.385485	−	0.989620i
$760$		0			0
$761$	11.4860	−	8.34507i	0.416367	−	0.302508i	−0.359807	−	0.933027i	$-0.617158\pi$
$761$	11.4860	−	8.34507i	0.416367	−	0.302508i	0.776175	+	0.630518i	$0.217158\pi$
$762$	−11.6197	−	35.7618i	−0.420938	−	1.29551i
$763$	2.94151	−	9.05303i	0.106490	−	0.327742i
$764$	−36.9811	−	26.8684i	−1.33793	−	0.972063i
$765$		0			0
$766$	−16.2464	+	50.0012i	−0.587005	+	1.80662i
$767$	−14.1585	−	43.5754i	−0.511234	−	1.57342i
$768$	−30.4620	+	22.1319i	−1.09920	+	0.798617i
$769$	−30.0208			−1.08258			−0.541290	−	0.840836i	$-0.682064\pi$
$769$	−30.0208			−1.08258			−0.541290	+	0.840836i	$0.682064\pi$
$770$		0			0
$771$	−12.4107			−0.446961
$772$	38.1046	−	27.6846i	1.37142	−	0.996392i
$773$	9.40320	+	28.9401i	0.338209	+	1.04090i	0.965119	+	0.261810i	$0.0843194\pi$
$773$	9.40320	+	28.9401i	0.338209	+	1.04090i	−0.626910	+	0.779092i	$0.715681\pi$
$774$	5.47091	−	16.8377i	0.196648	−	0.605220i
$775$		0			0
$776$	−0.471046	−	0.342235i	−0.0169096	−	0.0122855i
$777$	4.95680	−	15.2555i	0.177824	−	0.547287i
$778$	−1.02796	−	3.16373i	−0.0368541	−	0.113425i
$779$	−15.3414	+	11.1461i	−0.549661	+	0.399352i
$780$		0			0
$781$	−15.2165	−	9.77544i	−0.544488	−	0.349793i
$782$	22.7315			0.812876
$783$	−9.03612	+	6.56512i	−0.322925	+	0.234618i
$784$	7.12510	+	21.9288i	0.254468	+	0.783172i
$785$		0			0
$786$	−30.9642	−	22.4968i	−1.10445	−	0.802433i
$787$	24.6465	+	17.9067i	0.878553	+	0.638306i	0.932868	−	0.360218i	$-0.117298\pi$
$787$	24.6465	+	17.9067i	0.878553	+	0.638306i	−0.0543151	+	0.998524i	$0.517298\pi$
$788$	16.6713	−	51.3089i	0.593890	−	1.82780i
$789$	14.6605	+	45.1205i	0.521929	+	1.60633i
$790$		0			0
$791$	4.84709			0.172343
$792$	2.08118	+	1.33700i	0.0739516	+	0.0475083i
$793$	−11.1809			−0.397044
$794$	27.3555	−	19.8749i	0.970810	−	0.705334i
$795$		0			0
$796$	10.9859	−	33.8112i	0.389385	−	1.19840i
$797$	−26.7341	−	19.4235i	−0.946970	−	0.688014i	0.00311796	−	0.999995i	$-0.499008\pi$
$797$	−26.7341	−	19.4235i	−0.946970	−	0.688014i	−0.950088	+	0.311981i	$0.899008\pi$
$798$	13.5816	+	9.86764i	0.480785	+	0.349311i
$799$	−4.45870	+	13.7225i	−0.157737	+	0.485466i
$800$		0			0
$801$	38.1613	−	27.7258i	1.34836	−	0.979642i
$802$	56.2421			1.98598
$803$	1.20960	−	4.60494i	0.0426859	−	0.162505i
$804$	52.7160			1.85915
$805$		0			0
$806$	−1.18388	−	3.64361i	−0.0417004	−	0.128341i
$807$	−1.86095	+	5.72743i	−0.0655087	+	0.201615i
$808$	−2.37083	−	1.72251i	−0.0834056	−	0.0605977i
$809$	−8.89072	−	6.45948i	−0.312581	−	0.227103i	0.420422	−	0.907329i	$-0.361882\pi$
$809$	−8.89072	−	6.45948i	−0.312581	−	0.227103i	−0.733003	+	0.680225i	$0.761882\pi$
$810$		0			0
$811$	12.5951	+	38.7638i	0.442275	+	1.36118i	0.885445	+	0.464744i	$0.153854\pi$
$811$	12.5951	+	38.7638i	0.442275	+	1.36118i	−0.443171	+	0.896437i	$0.646146\pi$
$812$	8.04353	−	5.84397i	0.282273	−	0.205083i
$813$	2.11138			0.0740494
$814$	15.4392	+	39.6355i	0.541142	+	1.38923i
$815$		0			0
$816$	26.8841	−	19.5324i	0.941130	−	0.683771i
$817$	2.29108	+	7.05121i	0.0801547	+	0.246691i
$818$	24.6595	−	75.8941i	0.862199	−	2.65358i
$819$	13.6746	+	9.93519i	0.477830	+	0.347164i
$820$		0			0
$821$	4.66851	−	14.3682i	0.162932	−	0.501454i	−0.835946	−	0.548812i	$-0.815080\pi$
$821$	4.66851	−	14.3682i	0.162932	−	0.501454i	0.998878	+	0.0473584i	$0.0150803\pi$
$822$	−13.9147	−	42.8250i	−0.485330	−	1.49369i
$823$	29.4735	−	21.4138i	1.02738	−	0.746437i	0.0595989	−	0.998222i	$-0.481018\pi$
$823$	29.4735	−	21.4138i	1.02738	−	0.746437i	0.967783	+	0.251786i	$0.0810178\pi$
$824$	1.87964			0.0654805
$825$		0			0
$826$	19.7901			0.688585
$827$	3.07703	−	2.23560i	0.106999	−	0.0777393i	−0.532999	−	0.846116i	$-0.678935\pi$
$827$	3.07703	−	2.23560i	0.106999	−	0.0777393i	0.639998	+	0.768376i	$0.278935\pi$
$828$	8.43002	+	25.9449i	0.292963	+	0.901649i
$829$	−8.43810	+	25.9698i	−0.293067	+	0.901969i	0.690796	+	0.723049i	$0.257260\pi$
$829$	−8.43810	+	25.9698i	−0.293067	+	0.901969i	−0.983864	+	0.178919i	$0.942740\pi$
$830$		0			0
$831$	−25.0870	−	18.2268i	−0.870259	−	0.632280i
$832$	−12.2261	+	37.6279i	−0.423862	+	1.30451i
$833$	−6.25584	−	19.2535i	−0.216752	−	0.667094i
$834$	−33.2085	+	24.1274i	−1.14992	+	0.835464i
$835$		0			0
$836$	−22.7396	+	1.30412i	−0.786466	+	0.0451038i
$837$	−0.951115			−0.0328754
$838$	−24.1998	+	17.5821i	−0.835967	+	0.607365i
$839$	8.75291	+	26.9387i	0.302184	+	0.930026i	0.980713	+	0.195453i	$0.0626177\pi$
$839$	8.75291	+	26.9387i	0.302184	+	0.930026i	−0.678529	+	0.734573i	$0.737382\pi$
$840$		0			0
$841$	3.93381	+	2.85808i	0.135649	+	0.0985546i
$842$	17.6445	+	12.8195i	0.608070	+	0.441788i
$843$	5.04453	−	15.5255i	0.173743	−	0.534725i
$844$	−3.77247	−	11.6105i	−0.129854	−	0.399649i
$845$		0			0
$846$	−33.8442			−1.16359
$847$	−2.10635	+	10.4132i	−0.0723750	+	0.357800i
$848$	−10.1115			−0.347232
$849$	−18.3297	+	13.3173i	−0.629073	+	0.457048i
$850$		0			0
$851$	−6.59285	+	20.2907i	−0.226000	+	0.695556i
$852$	24.2240	+	17.5998i	0.829902	+	0.602959i
$853$	6.74977	+	4.90400i	0.231108	+	0.167910i	0.697313	−	0.716767i	$-0.254379\pi$
$853$	6.74977	+	4.90400i	0.231108	+	0.167910i	−0.466205	+	0.884677i	$0.654379\pi$
$854$	1.49235	−	4.59298i	0.0510671	−	0.157168i
$855$		0			0
$856$	1.19223	−	0.866207i	0.0407497	−	0.0296064i
$857$	8.59547			0.293616			0.146808	−	0.989165i	$-0.453100\pi$
$857$	8.59547			0.293616			0.146808	+	0.989165i	$0.453100\pi$
$858$	−79.4609	+	4.55708i	−2.71275	+	0.155576i
$859$	9.40807			0.320999			0.160500	−	0.987036i	$-0.448689\pi$
$859$	9.40807			0.320999			0.160500	+	0.987036i	$0.448689\pi$
$860$		0			0
$861$	−4.52513	−	13.9269i	−0.154216	−	0.474628i
$862$	20.1311	−	61.9571i	0.685667	−	2.11027i
$863$	−8.35396	−	6.06951i	−0.284372	−	0.206608i	0.436450	−	0.899728i	$-0.356236\pi$
$863$	−8.35396	−	6.06951i	−0.284372	−	0.206608i	−0.720822	+	0.693120i	$0.756236\pi$
$864$	14.8543	+	10.7922i	0.505352	+	0.367160i
$865$		0			0
$866$	−0.239279	−	0.736426i	−0.00813104	−	0.0250248i
$867$	12.4376	−	9.03644i	0.422403	−	0.306893i
$868$	0.846638			0.0287368
$869$	2.57734	−	2.10820i	0.0874304	−	0.0715159i
$870$		0			0
$871$	−35.1466	+	25.5355i	−1.19090	+	0.865237i
$872$	−0.587328	−	1.80761i	−0.0198894	−	0.0612133i
$873$	3.60838	−	11.1055i	0.122125	−	0.375863i
$874$	−18.0644	−	13.1246i	−0.611038	−	0.443945i
$875$		0			0
$876$	−2.43581	+	7.49665i	−0.0822984	+	0.253288i
$877$	−9.20969	−	28.3445i	−0.310989	−	0.957126i	−0.977374	−	0.211518i	$-0.932159\pi$
$877$	−9.20969	−	28.3445i	−0.310989	−	0.957126i	0.666385	−	0.745608i	$-0.267841\pi$
$878$	−43.4398	+	31.5608i	−1.46602	+	1.06513i
$879$	−15.2269			−0.513591
$880$		0			0
$881$	30.1175			1.01469			0.507343	−	0.861744i	$-0.330628\pi$
$881$	30.1175			1.01469			0.507343	+	0.861744i	$0.330628\pi$
$882$	38.4167	−	27.9113i	1.29356	−	0.939824i
$883$	−15.5627	−	47.8970i	−0.523726	−	1.61186i	−0.766822	−	0.641860i	$-0.778163\pi$
$883$	−15.5627	−	47.8970i	−0.523726	−	1.61186i	0.243096	−	0.970002i	$-0.421837\pi$
$884$	9.77622	−	30.0881i	0.328810	−	1.01197i
$885$		0			0
$886$	−23.7410	−	17.2488i	−0.797593	−	0.579485i
$887$	−12.7950	+	39.3789i	−0.429613	+	1.32221i	0.468893	+	0.883255i	$0.344653\pi$
$887$	−12.7950	+	39.3789i	−0.429613	+	1.32221i	−0.898507	+	0.438959i	$0.855347\pi$
$888$	−0.989719	−	3.04604i	−0.0332128	−	0.102218i
$889$	−5.54021	+	4.02520i	−0.185813	+	0.135001i
$890$		0			0
$891$	4.75642	−	18.1076i	0.159346	−	0.606628i
$892$	−39.8572			−1.33452
$893$	11.4663	−	8.33074i	0.383704	−	0.278777i
$894$	−27.6683	−	85.1542i	−0.925366	−	2.84798i
$895$		0			0
$896$	−1.20409	−	0.874825i	−0.0402259	−	0.0292258i
$897$	−32.2964	−	23.4647i	−1.07835	−	0.783464i
$898$	6.32481	−	19.4658i	0.211062	−	0.649581i
$899$	−0.635162	−	1.95483i	−0.0211838	−	0.0651971i
$900$		0			0
$901$	8.87793			0.295767
$902$	32.6711	+	20.9887i	1.08783	+	0.698848i
$903$	−5.72532			−0.190527
$904$	0.782977	−	0.568866i	0.0260414	−	0.0189202i
$905$		0			0
$906$	−20.1287	+	61.9499i	−0.668733	+	2.05815i
$907$	−3.74749	−	2.72271i	−0.124433	−	0.0904062i	0.523828	−	0.851824i	$-0.324504\pi$
$907$	−3.74749	−	2.72271i	−0.124433	−	0.0904062i	−0.648261	+	0.761418i	$0.724504\pi$
$908$	48.2534	+	35.0582i	1.60135	+	1.16345i
$909$	18.1614	−	55.8951i	0.602376	−	1.85392i
$910$		0			0
$911$	−5.64577	+	4.10189i	−0.187053	+	0.135902i	−0.677371	−	0.735642i	$-0.736881\pi$
$911$	−5.64577	+	4.10189i	−0.187053	+	0.135902i	0.490318	+	0.871544i	$0.336881\pi$
$912$	−32.6419			−1.08088
$913$	−20.6363	−	13.2573i	−0.682963	−	0.438752i
$914$	−79.1032			−2.61650
$915$		0			0
$916$	−16.4404	−	50.5984i	−0.543207	−	1.67182i
$917$	−2.15397	+	6.62923i	−0.0711303	+	0.218916i
$918$	−12.4192	−	9.02308i	−0.409895	−	0.297806i
$919$	18.9477	+	13.7663i	0.625027	+	0.454109i	0.854674	−	0.519165i	$-0.173757\pi$
$919$	18.9477	+	13.7663i	0.625027	+	0.454109i	−0.229647	+	0.973274i	$0.573757\pi$
$920$		0			0
$921$	−14.9589	−	46.0387i	−0.492912	−	1.51703i
$922$	−64.0671	+	46.5474i	−2.10994	+	1.53296i
$923$	−24.6758			−0.812215
$924$	4.46857	−	17.0118i	0.147005	−	0.559647i
$925$		0			0
$926$	−21.1507	+	15.3669i	−0.695057	+	0.504988i
$927$	11.6488	+	35.8514i	0.382597	+	1.17751i
$928$	−12.2615	+	37.7371i	−0.402504	+	1.23878i
$929$	14.6355	+	10.6333i	0.480175	+	0.348868i	0.801394	−	0.598137i	$-0.204092\pi$
$929$	14.6355	+	10.6333i	0.480175	+	0.348868i	−0.321218	+	0.947005i	$0.604092\pi$
$930$		0			0
$931$	−6.14504	+	18.9125i	−0.201395	+	0.619831i
$932$	−8.10480	−	24.9440i	−0.265481	−	0.817068i
$933$	24.0237	−	17.4542i	0.786500	−	0.571426i
$934$	22.7646			0.744881
$935$		0			0
$936$	3.37495			0.110314
$937$	8.90696	−	6.47128i	0.290978	−	0.211408i	−0.432714	−	0.901531i	$-0.642444\pi$
$937$	8.90696	−	6.47128i	0.290978	−	0.211408i	0.723691	+	0.690124i	$0.242444\pi$
$938$	−5.79856	−	17.8461i	−0.189330	−	0.582697i
$939$	4.14216	−	12.7483i	0.135174	−	0.416023i
$940$		0			0
$941$	−27.3293	−	19.8559i	−0.890908	−	0.647283i	0.0452063	−	0.998978i	$-0.485605\pi$
$941$	−27.3293	−	19.8559i	−0.890908	−	0.647283i	−0.936115	+	0.351695i	$0.885605\pi$
$942$	−6.89886	+	21.2325i	−0.224777	+	0.691793i
$943$	6.01870	+	18.5237i	0.195996	+	0.603213i
$944$	−31.1305	+	22.6177i	−1.01321	+	0.736142i
$945$		0			0
$946$	11.7517	−	9.61264i	0.382082	−	0.312534i
$947$	46.9853			1.52682			0.763409	−	0.645915i	$-0.223524\pi$
$947$	46.9853			1.52682			0.763409	+	0.645915i	$0.223524\pi$
$948$	−4.45982	+	3.24025i	−0.144848	+	0.105238i
$949$	−2.00736	−	6.17803i	−0.0651618	−	0.200547i
$950$		0			0
$951$	25.0454	+	18.1966i	0.812154	+	0.590064i
$952$	0.502781	+	0.365292i	0.0162952	+	0.0118392i
$953$	−13.1303	+	40.4110i	−0.425333	+	1.30904i	0.477341	+	0.878718i	$0.341600\pi$
$953$	−13.1303	+	40.4110i	−0.425333	+	1.30904i	−0.902675	+	0.430323i	$0.858400\pi$
$954$	6.43506	+	19.8051i	0.208343	+	0.641213i
$955$		0			0
$956$	42.7180			1.38160
$957$	−42.6314	+	2.44491i	−1.37808	+	0.0790328i
$958$	42.4291			1.37082
$959$	−6.63443	+	4.82019i	−0.214237	+	0.155652i
$960$		0			0
$961$	−9.52544	+	29.3163i	−0.307272	+	0.945687i
$962$	46.9515	+	34.1123i	1.51378	+	1.09982i
$963$	23.9103	+	17.3719i	0.770499	+	0.559800i
$964$	−14.7584	+	45.4216i	−0.475335	+	1.46293i
$965$		0			0
$966$	13.9498	−	10.1351i	0.448826	−	0.326091i
$967$	−54.1642			−1.74180			−0.870901	−	0.491458i	$-0.836464\pi$
$967$	−54.1642			−1.74180			−0.870901	+	0.491458i	$0.836464\pi$
$968$	0.881863	+	1.92930i	0.0283442	+	0.0620101i
$969$	28.6596			0.920680
$970$		0			0
$971$	1.61878	+	4.98209i	0.0519491	+	0.159883i	0.973665	−	0.227982i	$-0.0732127\pi$
$971$	1.61878	+	4.98209i	0.0519491	+	0.159883i	−0.921716	+	0.387865i	$0.873213\pi$
$972$	−13.9941	+	43.0694i	−0.448861	+	1.38145i
$973$	6.04791	+	4.39406i	0.193887	+	0.140867i
$974$	36.9500	+	26.8457i	1.18395	+	0.860193i
$975$		0			0
$976$	2.90169	+	8.93049i	0.0928809	+	0.285858i
$977$	−6.29530	+	4.57381i	−0.201405	+	0.146329i	−0.683916	−	0.729561i	$-0.739725\pi$
$977$	−6.29530	+	4.57381i	−0.201405	+	0.146329i	0.482512	+	0.875890i	$0.339725\pi$
$978$	87.8938			2.81053
$979$	40.3846	−	2.31606i	1.29070	−	0.0740216i
$980$		0			0
$981$	30.8376	−	22.4048i	0.984567	−	0.715330i
$982$	−12.5547	−	38.6394i	−0.400637	−	1.23303i
$983$	−15.9186	+	48.9924i	−0.507724	+	1.56261i	0.288419	+	0.957504i	$0.406871\pi$
$983$	−15.9186	+	48.9924i	−0.507724	+	1.56261i	−0.796143	+	0.605109i	$0.793129\pi$
$984$	−2.36547	−	1.71861i	−0.0754083	−	0.0547873i
$985$		0			0
$986$	10.2515	−	31.5509i	0.326474	−	1.00478i
$987$	3.38213	+	10.4091i	0.107654	+	0.331326i
$988$	−25.1411	+	18.2661i	−0.799846	+	0.581122i
$989$	7.61503			0.242144
$990$		0			0
$991$	−22.3382			−0.709596			−0.354798	−	0.934943i	$-0.615450\pi$
$991$	−22.3382			−0.709596			−0.354798	+	0.934943i	$0.615450\pi$
$992$	−2.73356	+	1.98605i	−0.0867906	+	0.0630571i
$993$	23.7025	+	72.9487i	0.752175	+	2.31496i
$994$	3.29357	−	10.1366i	0.104466	−	0.321512i
$995$		0			0
$996$	32.8522	+	23.8686i	1.04096	+	0.756304i
$997$	−0.0570278	+	0.175514i	−0.00180609	+	0.00555857i	−0.951955	−	0.306236i	$-0.900930\pi$
$997$	−0.0570278	+	0.175514i	−0.00180609	+	0.00555857i	0.950149	+	0.311795i	$0.100930\pi$
$998$	2.90904	+	8.95311i	0.0920841	+	0.283406i
$999$	11.6562	−	8.46873i	0.368786	−	0.267939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.d.201.1		16
5.2	odd	4		55.2.j.a.14.1	yes	16
5.3	odd	4		55.2.j.a.14.4	yes	16
5.4	even	2	inner	275.2.h.d.201.4		16
11.2	odd	10		3025.2.a.bk.1.1		8
11.4	even	5	inner	275.2.h.d.26.1		16
11.9	even	5		3025.2.a.bl.1.8		8
15.2	even	4		495.2.ba.a.289.4		16
15.8	even	4		495.2.ba.a.289.1		16
20.3	even	4		880.2.cd.c.289.4		16
20.7	even	4		880.2.cd.c.289.1		16
55.2	even	20		605.2.b.f.364.1		8
55.3	odd	20		605.2.j.h.269.4		16
55.4	even	10	inner	275.2.h.d.26.4		16
55.7	even	20		605.2.j.d.444.1		16
55.8	even	20		605.2.j.g.269.1		16
55.9	even	10		3025.2.a.bl.1.1		8
55.13	even	20		605.2.b.f.364.8		8
55.17	even	20		605.2.j.g.9.1		16
55.18	even	20		605.2.j.d.444.4		16
55.24	odd	10		3025.2.a.bk.1.8		8
55.27	odd	20		605.2.j.h.9.4		16
55.28	even	20		605.2.j.g.9.4		16
55.32	even	4		605.2.j.d.124.4		16
55.37	odd	20		55.2.j.a.4.4	yes	16
55.38	odd	20		605.2.j.h.9.1		16
55.42	odd	20		605.2.b.g.364.8		8
55.43	even	4		605.2.j.d.124.1		16
55.47	odd	20		605.2.j.h.269.1		16
55.48	odd	20		55.2.j.a.4.1	✓	16
55.52	even	20		605.2.j.g.269.4		16
55.53	odd	20		605.2.b.g.364.1		8
165.92	even	20		495.2.ba.a.334.1		16
165.158	even	20		495.2.ba.a.334.4		16
220.103	even	20		880.2.cd.c.609.1		16
220.147	even	20		880.2.cd.c.609.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	55.48	odd	20
55.2.j.a.4.4	yes	16	55.37	odd	20
55.2.j.a.14.1	yes	16	5.2	odd	4
55.2.j.a.14.4	yes	16	5.3	odd	4
275.2.h.d.26.1		16	11.4	even	5	inner
275.2.h.d.26.4		16	55.4	even	10	inner
275.2.h.d.201.1		16	1.1	even	1	trivial
275.2.h.d.201.4		16	5.4	even	2	inner
495.2.ba.a.289.1		16	15.8	even	4
495.2.ba.a.289.4		16	15.2	even	4
495.2.ba.a.334.1		16	165.92	even	20
495.2.ba.a.334.4		16	165.158	even	20
605.2.b.f.364.1		8	55.2	even	20
605.2.b.f.364.8		8	55.13	even	20
605.2.b.g.364.1		8	55.53	odd	20
605.2.b.g.364.8		8	55.42	odd	20
605.2.j.d.124.1		16	55.43	even	4
605.2.j.d.124.4		16	55.32	even	4
605.2.j.d.444.1		16	55.7	even	20
605.2.j.d.444.4		16	55.18	even	20
605.2.j.g.9.1		16	55.17	even	20
605.2.j.g.9.4		16	55.28	even	20
605.2.j.g.269.1		16	55.8	even	20
605.2.j.g.269.4		16	55.52	even	20
605.2.j.h.9.1		16	55.38	odd	20
605.2.j.h.9.4		16	55.27	odd	20
605.2.j.h.269.1		16	55.47	odd	20
605.2.j.h.269.4		16	55.3	odd	20
880.2.cd.c.289.1		16	20.7	even	4
880.2.cd.c.289.4		16	20.3	even	4
880.2.cd.c.609.1		16	220.103	even	20
880.2.cd.c.609.4		16	220.147	even	20
3025.2.a.bk.1.1		8	11.2	odd	10
3025.2.a.bk.1.8		8	55.24	odd	10
3025.2.a.bl.1.1		8	55.9	even	10
3025.2.a.bl.1.8		8	11.9	even	5

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63719 + 1.18949i) q^{2} +(0.809808 + 2.49233i) q^{3} +(0.647481 - 1.99274i) q^{4} +(-4.29042 - 3.11717i) q^{6} +(-0.298456 + 0.918552i) q^{7} +(0.0595923 + 0.183406i) q^{8} +(-3.12889 + 2.27327i) q^{9} +O(q^{10})\)	\(q+(-1.63719 + 1.18949i) q^{2} +(0.809808 + 2.49233i) q^{3} +(0.647481 - 1.99274i) q^{4} +(-4.29042 - 3.11717i) q^{6} +(-0.298456 + 0.918552i) q^{7} +(0.0595923 + 0.183406i) q^{8} +(-3.12889 + 2.27327i) q^{9} +(-3.31118 + 0.189896i) q^{11} +5.49092 q^{12} +(-3.66088 + 2.65978i) q^{13} +(-0.603980 - 1.85886i) q^{14} +(3.07453 + 2.23378i) q^{16} +(-2.69944 - 1.96126i) q^{17} +(2.41856 - 7.44357i) q^{18} +(1.01283 + 3.11717i) q^{19} -2.53103 q^{21} +(5.19517 - 4.24952i) q^{22} +3.36643 q^{23} +(-0.408851 + 0.297048i) q^{24} +(2.82978 - 8.70916i) q^{26} +(-1.83923 - 1.33628i) q^{27} +(1.63719 + 1.18949i) q^{28} +(1.51820 - 4.67254i) q^{29} +(0.338464 - 0.245909i) q^{31} -8.07636 q^{32} +(-3.15471 - 8.09880i) q^{33} +6.75241 q^{34} +(2.50415 + 7.70697i) q^{36} +(-1.95841 + 6.02737i) q^{37} +(-5.36605 - 3.89867i) q^{38} +(-9.59368 - 6.97021i) q^{39} +(1.78786 + 5.50247i) q^{41} +(4.14379 - 3.01064i) q^{42} +2.26205 q^{43} +(-1.76552 + 6.72129i) q^{44} +(-5.51149 + 4.00433i) q^{46} +(-1.33626 - 4.11260i) q^{47} +(-3.07754 + 9.47169i) q^{48} +(4.90846 + 3.56620i) q^{49} +(2.70208 - 8.31615i) q^{51} +(2.92991 + 9.01735i) q^{52} +(-2.15255 + 1.56392i) q^{53} +4.60066 q^{54} -0.186254 q^{56} +(-6.94884 + 5.04863i) q^{57} +(3.07235 + 9.45574i) q^{58} +(-3.12889 + 9.62972i) q^{59} +(1.99897 + 1.45233i) q^{61} +(-0.261626 + 0.805201i) q^{62} +(-1.15428 - 3.55252i) q^{63} +(7.07350 - 5.13920i) q^{64} +(14.7983 + 9.50680i) q^{66} +9.60059 q^{67} +(-5.65612 + 4.10941i) q^{68} +(2.72616 + 8.39026i) q^{69} +(4.41166 + 3.20526i) q^{71} +(-0.603390 - 0.438388i) q^{72} +(-0.443607 + 1.36528i) q^{73} +(-3.96321 - 12.1975i) q^{74} +6.86752 q^{76} +(0.813812 - 3.09817i) q^{77} +23.9977 q^{78} +(-0.812218 + 0.590111i) q^{79} +(-1.74436 + 5.36858i) q^{81} +(-9.47221 - 6.88197i) q^{82} +(5.98302 + 4.34692i) q^{83} +(-1.63880 + 5.04369i) q^{84} +(-3.70342 + 2.69069i) q^{86} +12.8750 q^{87} +(-0.232149 - 0.595976i) q^{88} -12.1964 q^{89} +(-1.35054 - 4.15654i) q^{91} +(2.17970 - 6.70842i) q^{92} +(0.886978 + 0.644427i) q^{93} +(7.07962 + 5.14365i) q^{94} +(-6.54030 - 20.1290i) q^{96} +(-2.44262 + 1.77467i) q^{97} -12.2781 q^{98} +(9.92863 - 8.12138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9	\( 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46} + 10 q^{49} - 42 q^{51} + 40 q^{54} - 20 q^{56} - 2 q^{59} - 40 q^{61} + 8 q^{64} + 58 q^{66} - 26 q^{69} + 36 q^{71} - 48 q^{74} + 56 q^{76} - 38 q^{79} + 68 q^{81} - 12 q^{84} + 22 q^{86} - 24 q^{89} - 20 q^{91} - 14 q^{94} - 86 q^{96} + 72 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more