LMFDB - Embedded newform 1456.2.s.h.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(113,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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("1456.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.s (of order $3$, degree $2$, 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1456.113
Dual form			1456.2.s.h.1121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 + 0.330792i) q^{3} +0.381966 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.42705 + 2.47172i) q^{9} +O(q^{10})$	\(q+(-0.190983 + 0.330792i) q^{3} +0.381966 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.42705 + 2.47172i) q^{9} +(-2.42705 + 4.20378i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(-0.0729490 + 0.126351i) q^{15} +(-3.73607 - 6.47106i) q^{17} +(2.42705 + 4.20378i) q^{19} -0.381966 q^{21} +(2.23607 - 3.87298i) q^{23} -4.85410 q^{25} -2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} -8.70820 q^{31} +(-0.927051 - 1.60570i) q^{33} +(0.190983 + 0.330792i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-0.381966 - 1.32317i) q^{39} +(-2.61803 + 4.53457i) q^{41} +(-3.78115 - 6.54915i) q^{43} +(0.545085 + 0.944115i) q^{45} -2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} +2.85410 q^{51} +8.23607 q^{53} +(-0.927051 + 1.60570i) q^{55} -1.85410 q^{57} +(1.11803 + 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-1.42705 + 2.47172i) q^{63} +(-0.954915 + 0.992377i) q^{65} +(0.354102 - 0.613323i) q^{67} +(0.854102 + 1.47935i) q^{69} +(4.09017 + 7.08438i) q^{71} -2.00000 q^{73} +(0.927051 - 1.60570i) q^{75} -4.85410 q^{77} -4.00000 q^{79} +(-3.85410 + 6.67550i) q^{81} +6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(0.781153 + 1.35300i) q^{87} +(-8.04508 + 13.9345i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(1.66312 - 2.88061i) q^{93} +(0.927051 + 1.60570i) q^{95} +(-6.07295 - 10.5187i) q^{97} -13.8541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9	$ 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} - 3 q^{11} - 10 q^{13} - 7 q^{15} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 6 q^{25} - 3 q^{29} - 8 q^{31} + 3 q^{33} + 3 q^{35} - 8 q^{37} - 6 q^{39} - 6 q^{41} + 5 q^{43} - 9 q^{45} - 2 q^{49} - 2 q^{51} + 24 q^{53} + 3 q^{55} + 6 q^{57} + 12 q^{61} + q^{63} - 15 q^{65} - 12 q^{67} - 10 q^{69} - 6 q^{71} - 8 q^{73} - 3 q^{75} - 6 q^{77} - 16 q^{79} - 2 q^{81} + q^{85} - 17 q^{87} - 21 q^{89} - 14 q^{91} - 9 q^{93} - 3 q^{95} - 31 q^{97} - 42 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9 - 3 * q^11 - 10 * q^13 - 7 * q^15 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 6 * q^25 - 3 * q^29 - 8 * q^31 + 3 * q^33 + 3 * q^35 - 8 * q^37 - 6 * q^39 - 6 * q^41 + 5 * q^43 - 9 * q^45 - 2 * q^49 - 2 * q^51 + 24 * q^53 + 3 * q^55 + 6 * q^57 + 12 * q^61 + q^63 - 15 * q^65 - 12 * q^67 - 10 * q^69 - 6 * q^71 - 8 * q^73 - 3 * q^75 - 6 * q^77 - 16 * q^79 - 2 * q^81 + q^85 - 17 * q^87 - 21 * q^89 - 14 * q^91 - 9 * q^93 - 3 * q^95 - 31 * q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−0.190983	+	0.330792i	−0.110264	+	0.190983i	−0.915877	−	0.401460i	$-0.868503\pi$
$3$	−0.190983	+	0.330792i	−0.110264	+	0.190983i	0.805613	+	0.592443i	$0.201836\pi$
$4$		0			0
$5$	0.381966			0.170820			0.0854102	−	0.996346i	$-0.472780\pi$
$5$	0.381966			0.170820			0.0854102	+	0.996346i	$0.472780\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	1.42705	+	2.47172i	0.475684	+	0.823908i
$10$		0			0
$11$	−2.42705	+	4.20378i	−0.731783	+	1.26749i	0.224337	+	0.974512i	$0.427978\pi$
$11$	−2.42705	+	4.20378i	−0.731783	+	1.26749i	−0.956120	+	0.292974i	$0.905355\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$		0			0
$15$	−0.0729490	+	0.126351i	−0.0188354	+	0.0326238i
$16$		0			0
$17$	−3.73607	−	6.47106i	−0.906130	−	1.56946i	−0.819394	−	0.573231i	$-0.805690\pi$
$17$	−3.73607	−	6.47106i	−0.906130	−	1.56946i	−0.0867359	−	0.996231i	$-0.527644\pi$
$18$		0			0
$19$	2.42705	+	4.20378i	0.556804	+	0.964412i	0.997761	+	0.0668841i	$0.0213058\pi$
$19$	2.42705	+	4.20378i	0.556804	+	0.964412i	−0.440957	+	0.897528i	$0.645361\pi$
$20$		0			0
$21$	−0.381966			−0.0833518
$22$		0			0
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	−0.533005	−	0.846112i	$-0.678937\pi$
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	0.999257	+	0.0385394i	$0.0122705\pi$
$24$		0			0
$25$	−4.85410			−0.970820
$26$		0			0
$27$	−2.23607			−0.430331
$28$		0			0
$29$	2.04508	−	3.54219i	0.379763	−	0.657768i	−0.611265	−	0.791426i	$-0.709339\pi$
$29$	2.04508	−	3.54219i	0.379763	−	0.657768i	0.991028	+	0.133658i	$0.0426723\pi$
$30$		0			0
$31$	−8.70820			−1.56404			−0.782020	−	0.623254i	$-0.785810\pi$
$31$	−8.70820			−1.56404			−0.782020	+	0.623254i	$0.785810\pi$
$32$		0			0
$33$	−0.927051	−	1.60570i	−0.161379	−	0.279516i
$34$		0			0
$35$	0.190983	+	0.330792i	0.0322820	+	0.0559141i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	−0.381966	−	1.32317i	−0.0611635	−	0.211877i
$40$		0			0
$41$	−2.61803	+	4.53457i	−0.408868	+	0.708181i	−0.994763	−	0.102206i	$-0.967410\pi$
$41$	−2.61803	+	4.53457i	−0.408868	+	0.708181i	0.585895	+	0.810387i	$0.300743\pi$
$42$		0			0
$43$	−3.78115	−	6.54915i	−0.576620	−	0.998736i	−0.995864	−	0.0908618i	$-0.971038\pi$
$43$	−3.78115	−	6.54915i	−0.576620	−	0.998736i	0.419243	−	0.907874i	$-0.362296\pi$
$44$		0			0
$45$	0.545085	+	0.944115i	0.0812565	+	0.140740i
$46$		0			0
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	2.85410			0.399654
$52$		0			0
$53$	8.23607			1.13131			0.565655	−	0.824642i	$-0.308623\pi$
$53$	8.23607			1.13131			0.565655	+	0.824642i	$0.308623\pi$
$54$		0			0
$55$	−0.927051	+	1.60570i	−0.125004	+	0.216512i
$56$		0			0
$57$	−1.85410			−0.245582
$58$		0			0
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	0.929580	−	0.368620i	$-0.120170\pi$
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	−0.784024	+	0.620730i	$0.786836\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		0			0
$63$	−1.42705	+	2.47172i	−0.179792	+	0.311408i
$64$		0			0
$65$	−0.954915	+	0.992377i	−0.118443	+	0.123089i
$66$		0			0
$67$	0.354102	−	0.613323i	0.0432604	−	0.0749293i	−0.843584	−	0.536997i	$-0.819559\pi$
$67$	0.354102	−	0.613323i	0.0432604	−	0.0749293i	0.886845	+	0.462067i	$0.152892\pi$
$68$		0			0
$69$	0.854102	+	1.47935i	0.102822	+	0.178093i
$70$		0			0
$71$	4.09017	+	7.08438i	0.485414	+	0.840761i	0.999860	−	0.0167615i	$-0.00533560\pi$
$71$	4.09017	+	7.08438i	0.485414	+	0.840761i	−0.514446	+	0.857523i	$0.672002\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$	0.927051	−	1.60570i	0.107047	−	0.185410i
$76$		0			0
$77$	−4.85410			−0.553176
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−3.85410	+	6.67550i	−0.428234	+	0.741722i
$82$		0			0
$83$	6.70820			0.736321			0.368161	−	0.929762i	$-0.379988\pi$
$83$	6.70820			0.736321			0.368161	+	0.929762i	$0.379988\pi$
$84$		0			0
$85$	−1.42705	−	2.47172i	−0.154785	−	0.268096i
$86$		0			0
$87$	0.781153	+	1.35300i	0.0837484	+	0.145056i
$88$		0			0
$89$	−8.04508	+	13.9345i	−0.852777	+	1.47705i	0.0259145	+	0.999664i	$0.491750\pi$
$89$	−8.04508	+	13.9345i	−0.852777	+	1.47705i	−0.878692	+	0.477389i	$0.841583\pi$
$90$		0			0
$91$	−3.50000	−	0.866025i	−0.366900	−	0.0907841i
$92$		0			0
$93$	1.66312	−	2.88061i	0.172457	−	0.298705i
$94$		0			0
$95$	0.927051	+	1.60570i	0.0951134	+	0.164741i
$96$		0			0
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	−0.990099	−	0.140371i	$-0.955170\pi$
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	0.373484	−	0.927636i	$-0.378163\pi$
$98$		0			0
$99$	−13.8541			−1.39239
$100$		0			0
$101$	−4.28115	+	7.41517i	−0.425991	+	0.737837i	−0.996512	−	0.0834451i	$-0.973408\pi$
$101$	−4.28115	+	7.41517i	−0.425991	+	0.737837i	0.570522	+	0.821283i	$0.306741\pi$
$102$		0			0
$103$	−4.70820			−0.463913			−0.231957	−	0.972726i	$-0.574513\pi$
$103$	−4.70820			−0.463913			−0.231957	+	0.972726i	$0.574513\pi$
$104$		0			0
$105$	−0.145898			−0.0142382
$106$		0			0
$107$	−2.80902	+	4.86536i	−0.271558	+	0.470352i	−0.969261	−	0.246035i	$-0.920872\pi$
$107$	−2.80902	+	4.86536i	−0.271558	+	0.470352i	0.697703	+	0.716387i	$0.254206\pi$
$108$		0			0
$109$	10.7082			1.02566			0.512830	−	0.858490i	$-0.328597\pi$
$109$	10.7082			1.02566			0.512830	+	0.858490i	$0.328597\pi$
$110$		0			0
$111$	−0.763932	−	1.32317i	−0.0725092	−	0.125590i
$112$		0			0
$113$	3.73607	+	6.47106i	0.351460	+	0.608746i	0.986505	−	0.163728i	$-0.0523521\pi$
$113$	3.73607	+	6.47106i	0.351460	+	0.608746i	−0.635046	+	0.772475i	$0.719019\pi$
$114$		0			0
$115$	0.854102	−	1.47935i	0.0796454	−	0.137950i
$116$		0			0
$117$	−9.98936	−	2.47172i	−0.923516	−	0.228511i
$118$		0			0
$119$	3.73607	−	6.47106i	0.342485	−	0.593201i
$120$		0			0
$121$	−6.28115	−	10.8793i	−0.571014	−	0.989025i
$122$		0			0
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$		0			0
$125$	−3.76393			−0.336656
$126$		0			0
$127$	−7.07295	+	12.2507i	−0.627623	+	1.08707i	0.360405	+	0.932796i	$0.382639\pi$
$127$	−7.07295	+	12.2507i	−0.627623	+	1.08707i	−0.988027	+	0.154278i	$0.950695\pi$
$128$		0			0
$129$	2.88854			0.254322
$130$		0			0
$131$	−0.326238			−0.0285035			−0.0142518	−	0.999898i	$-0.504537\pi$
$131$	−0.326238			−0.0285035			−0.0142518	+	0.999898i	$0.504537\pi$
$132$		0			0
$133$	−2.42705	+	4.20378i	−0.210452	+	0.364514i
$134$		0			0
$135$	−0.854102			−0.0735094
$136$		0			0
$137$	0.190983	+	0.330792i	0.0163168	+	0.0282615i	0.874069	−	0.485803i	$-0.161473\pi$
$137$	0.190983	+	0.330792i	0.0163168	+	0.0282615i	−0.857752	+	0.514064i	$0.828139\pi$
$138$		0			0
$139$	−7.78115	−	13.4774i	−0.659989	−	1.14313i	−0.980618	−	0.195929i	$-0.937228\pi$
$139$	−7.78115	−	13.4774i	−0.659989	−	1.14313i	0.320629	−	0.947205i	$-0.396106\pi$
$140$		0			0
$141$	0.427051	−	0.739674i	0.0359642	−	0.0622918i
$142$		0			0
$143$	−4.85410	−	16.8151i	−0.405920	−	1.40615i
$144$		0			0
$145$	0.781153	−	1.35300i	0.0648712	−	0.112360i
$146$		0			0
$147$	−0.190983	−	0.330792i	−0.0157520	−	0.0272833i
$148$		0			0
$149$	2.42705	+	4.20378i	0.198832	+	0.344387i	0.948150	−	0.317823i	$-0.102952\pi$
$149$	2.42705	+	4.20378i	0.198832	+	0.344387i	−0.749318	+	0.662210i	$0.769619\pi$
$150$		0			0
$151$	14.7082			1.19694			0.598468	−	0.801146i	$-0.295776\pi$
$151$	14.7082			1.19694			0.598468	+	0.801146i	$0.295776\pi$
$152$		0			0
$153$	10.6631	−	18.4691i	0.862062	−	1.49314i
$154$		0			0
$155$	−3.32624			−0.267170
$156$		0			0
$157$	8.14590			0.650113			0.325057	−	0.945695i	$-0.394617\pi$
$157$	8.14590			0.650113			0.325057	+	0.945695i	$0.394617\pi$
$158$		0			0
$159$	−1.57295	+	2.72443i	−0.124743	+	0.216061i
$160$		0			0
$161$	4.47214			0.352454
$162$		0			0
$163$	4.85410	+	8.40755i	0.380203	+	0.658530i	0.991091	−	0.133186i	$-0.0425209\pi$
$163$	4.85410	+	8.40755i	0.380203	+	0.658530i	−0.610888	+	0.791717i	$0.709188\pi$
$164$		0			0
$165$	−0.354102	−	0.613323i	−0.0275668	−	0.0477471i
$166$		0			0
$167$	4.88197	−	8.45581i	0.377778	−	0.654330i	−0.612961	−	0.790113i	$-0.710022\pi$
$167$	4.88197	−	8.45581i	0.377778	−	0.654330i	0.990739	+	0.135783i	$0.0433550\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−6.92705	+	11.9980i	−0.529725	+	0.917510i
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	−2.42705	−	4.20378i	−0.183468	−	0.317776i
$176$		0			0
$177$	−0.854102			−0.0641982
$178$		0			0
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	−3.70820			−0.275629			−0.137814	−	0.990458i	$-0.544008\pi$
$181$	−3.70820			−0.275629			−0.137814	+	0.990458i	$0.544008\pi$
$182$		0			0
$183$	−2.29180			−0.169414
$184$		0			0
$185$	−0.763932	+	1.32317i	−0.0561654	+	0.0972813i
$186$		0			0
$187$	36.2705			2.65236
$188$		0			0
$189$	−1.11803	−	1.93649i	−0.0813250	−	0.140859i
$190$		0			0
$191$	11.8090	+	20.4538i	0.854470	+	1.47999i	0.877135	+	0.480243i	$0.159452\pi$
$191$	11.8090	+	20.4538i	0.854470	+	1.47999i	−0.0226649	+	0.999743i	$0.507215\pi$
$192$		0			0
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$		0			0
$195$	−0.145898	−	0.505406i	−0.0104480	−	0.0361928i
$196$		0			0
$197$	−3.89919	+	6.75359i	−0.277806	+	0.481173i	−0.970839	−	0.239732i	$-0.922940\pi$
$197$	−3.89919	+	6.75359i	−0.277806	+	0.481173i	0.693034	+	0.720905i	$0.256274\pi$
$198$		0			0
$199$	1.20820	+	2.09267i	0.0856473	+	0.148345i	0.905667	−	0.423990i	$-0.139371\pi$
$199$	1.20820	+	2.09267i	0.0856473	+	0.148345i	−0.820020	+	0.572336i	$0.806038\pi$
$200$		0			0
$201$	0.135255	+	0.234268i	0.00954015	+	0.0165240i
$202$		0			0
$203$	4.09017			0.287074
$204$		0			0
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$		0			0
$207$	12.7639			0.887155
$208$		0			0
$209$	−23.5623			−1.62984
$210$		0			0
$211$	−4.35410	+	7.54153i	−0.299749	+	0.519180i	−0.976078	−	0.217419i	$-0.930236\pi$
$211$	−4.35410	+	7.54153i	−0.299749	+	0.519180i	0.676330	+	0.736599i	$0.263570\pi$
$212$		0			0
$213$	−3.12461			−0.214095
$214$		0			0
$215$	−1.44427	−	2.50155i	−0.0984985	−	0.170604i
$216$		0			0
$217$	−4.35410	−	7.54153i	−0.295576	−	0.511952i
$218$		0			0
$219$	0.381966	−	0.661585i	0.0258109	−	0.0447057i
$220$		0			0
$221$	26.1525	+	6.47106i	1.75921	+	0.435291i
$222$		0			0
$223$	−6.63525	+	11.4926i	−0.444330	+	0.769601i	−0.998005	−	0.0631310i	$-0.979891\pi$
$223$	−6.63525	+	11.4926i	−0.444330	+	0.769601i	0.553676	+	0.832732i	$0.313225\pi$
$224$		0			0
$225$	−6.92705	−	11.9980i	−0.461803	−	0.799867i
$226$		0			0
$227$	−3.73607	−	6.47106i	−0.247972	−	0.429499i	0.714991	−	0.699133i	$-0.246431\pi$
$227$	−3.73607	−	6.47106i	−0.247972	−	0.429499i	−0.962963	+	0.269634i	$0.913097\pi$
$228$		0			0
$229$	27.1246			1.79244			0.896222	−	0.443605i	$-0.146301\pi$
$229$	27.1246			1.79244			0.896222	+	0.443605i	$0.146301\pi$
$230$		0			0
$231$	0.927051	−	1.60570i	0.0609955	−	0.105647i
$232$		0			0
$233$	0.381966			0.0250234			0.0125117	−	0.999922i	$-0.496017\pi$
$233$	0.381966			0.0250234			0.0125117	+	0.999922i	$0.496017\pi$
$234$		0			0
$235$	−0.854102			−0.0557155
$236$		0			0
$237$	0.763932	−	1.32317i	0.0496227	−	0.0859491i
$238$		0			0
$239$	11.2918			0.730406			0.365203	−	0.930928i	$-0.381000\pi$
$239$	11.2918			0.730406			0.365203	+	0.930928i	$0.381000\pi$
$240$		0			0
$241$	−2.21885	−	3.84316i	−0.142929	−	0.247559i	0.785670	−	0.618646i	$-0.212319\pi$
$241$	−2.21885	−	3.84316i	−0.142929	−	0.247559i	−0.928598	+	0.371087i	$0.878985\pi$
$242$		0			0
$243$	−4.82624	−	8.35929i	−0.309603	−	0.536249i
$244$		0			0
$245$	−0.190983	+	0.330792i	−0.0122015	+	0.0211335i
$246$		0			0
$247$	−16.9894	−	4.20378i	−1.08101	−	0.267480i
$248$		0			0
$249$	−1.28115	+	2.21902i	−0.0811898	+	0.140625i
$250$		0			0
$251$	2.61803	+	4.53457i	0.165249	+	0.286219i	0.936744	−	0.350016i	$-0.113824\pi$
$251$	2.61803	+	4.53457i	0.165249	+	0.286219i	−0.771495	+	0.636236i	$0.780491\pi$
$252$		0			0
$253$	10.8541	+	18.7999i	0.682392	+	1.18194i
$254$		0			0
$255$	1.09017			0.0682691
$256$		0			0
$257$	12.8713	−	22.2938i	0.802891	−	1.39065i	−0.114815	−	0.993387i	$-0.536627\pi$
$257$	12.8713	−	22.2938i	0.802891	−	1.39065i	0.917706	−	0.397261i	$-0.130039\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$		0			0
$261$	11.6738			0.722588
$262$		0			0
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	3.14590			0.193251
$266$		0			0
$267$	−3.07295	−	5.32250i	−0.188061	−	0.325732i
$268$		0			0
$269$	−6.87132	−	11.9015i	−0.418952	−	0.725646i	0.576882	−	0.816827i	$-0.304269\pi$
$269$	−6.87132	−	11.9015i	−0.418952	−	0.725646i	−0.995834	+	0.0911812i	$0.970936\pi$
$270$		0			0
$271$	9.20820	−	15.9491i	0.559359	−	0.968837i	−0.438192	−	0.898882i	$-0.644381\pi$
$271$	9.20820	−	15.9491i	0.559359	−	0.968837i	0.997550	−	0.0699558i	$-0.0222858\pi$
$272$		0			0
$273$	0.954915	−	0.992377i	0.0577941	−	0.0600614i
$274$		0			0
$275$	11.7812	−	20.4056i	0.710430	−	1.23050i
$276$		0			0
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$		0			0
$279$	−12.4271	−	21.5243i	−0.743988	−	1.28863i
$280$		0			0
$281$	−2.18034			−0.130068			−0.0650341	−	0.997883i	$-0.520716\pi$
$281$	−2.18034			−0.130068			−0.0650341	+	0.997883i	$0.520716\pi$
$282$		0			0
$283$	−6.70820	+	11.6190i	−0.398761	+	0.690675i	−0.993573	−	0.113190i	$-0.963893\pi$
$283$	−6.70820	+	11.6190i	−0.398761	+	0.690675i	0.594812	+	0.803865i	$0.297226\pi$
$284$		0			0
$285$	−0.708204			−0.0419504
$286$		0			0
$287$	−5.23607			−0.309075
$288$		0			0
$289$	−19.4164	+	33.6302i	−1.14214	+	1.97825i
$290$		0			0
$291$	4.63932			0.271962
$292$		0			0
$293$	5.61803	+	9.73072i	0.328209	+	0.568475i	0.982157	−	0.188065i	$-0.0602216\pi$
$293$	5.61803	+	9.73072i	0.328209	+	0.568475i	−0.653947	+	0.756540i	$0.726888\pi$
$294$		0			0
$295$	0.427051	+	0.739674i	0.0248639	+	0.0430655i
$296$		0			0
$297$	5.42705	−	9.39993i	0.314909	−	0.545439i
$298$		0			0
$299$	4.47214	+	15.4919i	0.258630	+	0.895922i
$300$		0			0
$301$	3.78115	−	6.54915i	0.217942	−	0.377487i
$302$		0			0
$303$	−1.63525	−	2.83234i	−0.0939429	−	0.162714i
$304$		0			0
$305$	1.14590	+	1.98475i	0.0656139	+	0.113647i
$306$		0			0
$307$	−1.85410			−0.105819			−0.0529096	−	0.998599i	$-0.516850\pi$
$307$	−1.85410			−0.105819			−0.0529096	+	0.998599i	$0.516850\pi$
$308$		0			0
$309$	0.899187	−	1.55744i	0.0511530	−	0.0885995i
$310$		0			0
$311$	12.3262			0.698957			0.349478	−	0.936944i	$-0.386359\pi$
$311$	12.3262			0.698957			0.349478	+	0.936944i	$0.386359\pi$
$312$		0			0
$313$	−15.1246			−0.854894			−0.427447	−	0.904041i	$-0.640587\pi$
$313$	−15.1246			−0.854894			−0.427447	+	0.904041i	$0.640587\pi$
$314$		0			0
$315$	−0.545085	+	0.944115i	−0.0307121	+	0.0531948i
$316$		0			0
$317$	21.7639			1.22238			0.611192	−	0.791482i	$-0.290690\pi$
$317$	21.7639			1.22238			0.611192	+	0.791482i	$0.290690\pi$
$318$		0			0
$319$	9.92705	+	17.1942i	0.555808	+	0.962688i
$320$		0			0
$321$	−1.07295	−	1.85840i	−0.0598862	−	0.103726i
$322$		0			0
$323$	18.1353	−	31.4112i	1.00907	−	1.74776i
$324$		0			0
$325$	12.1353	−	12.6113i	0.673143	−	0.699551i
$326$		0			0
$327$	−2.04508	+	3.54219i	−0.113093	+	0.195884i
$328$		0			0
$329$	−1.11803	−	1.93649i	−0.0616392	−	0.106762i
$330$		0			0
$331$	−8.42705	−	14.5961i	−0.463193	−	0.802273i	0.535925	−	0.844265i	$-0.319963\pi$
$331$	−8.42705	−	14.5961i	−0.463193	−	0.802273i	−0.999118	+	0.0419923i	$0.986630\pi$
$332$		0			0
$333$	−11.4164			−0.625615
$334$		0			0
$335$	0.135255	−	0.234268i	0.00738977	−	0.0127994i
$336$		0			0
$337$	8.56231			0.466419			0.233209	−	0.972427i	$-0.425077\pi$
$337$	8.56231			0.466419			0.233209	+	0.972427i	$0.425077\pi$
$338$		0			0
$339$	−2.85410			−0.155014
$340$		0			0
$341$	21.1353	−	36.6073i	1.14454	−	1.98240i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	0.326238	+	0.565061i	0.0175641	+	0.0304218i
$346$		0			0
$347$	17.6180	+	30.5153i	0.945786	+	1.63815i	0.754171	+	0.656679i	$0.228039\pi$
$347$	17.6180	+	30.5153i	0.945786	+	1.63815i	0.191615	+	0.981470i	$0.438627\pi$
$348$		0			0
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	−0.946953	−	0.321372i	$-0.895856\pi$
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	0.751793	+	0.659400i	$0.229189\pi$
$350$		0			0
$351$	5.59017	−	5.80948i	0.298381	−	0.310087i
$352$		0			0
$353$	−14.4271	+	24.9884i	−0.767874	+	1.33000i	0.170839	+	0.985299i	$0.445352\pi$
$353$	−14.4271	+	24.9884i	−0.767874	+	1.33000i	−0.938713	+	0.344699i	$0.887981\pi$
$354$		0			0
$355$	1.56231	+	2.70599i	0.0829186	+	0.143619i
$356$		0			0
$357$	1.42705	+	2.47172i	0.0755275	+	0.130818i
$358$		0			0
$359$	10.9098			0.575799			0.287899	−	0.957661i	$-0.407043\pi$
$359$	10.9098			0.575799			0.287899	+	0.957661i	$0.407043\pi$
$360$		0			0
$361$	−2.28115	+	3.95107i	−0.120061	+	0.207951i
$362$		0			0
$363$	4.79837			0.251849
$364$		0			0
$365$	−0.763932			−0.0399860
$366$		0			0
$367$	12.7082	−	22.0113i	0.663363	−	1.14898i	−0.316364	−	0.948638i	$-0.602462\pi$
$367$	12.7082	−	22.0113i	0.663363	−	1.14898i	0.979726	−	0.200340i	$-0.0642047\pi$
$368$		0			0
$369$	−14.9443			−0.777968
$370$		0			0
$371$	4.11803	+	7.13264i	0.213798	+	0.370308i
$372$		0			0
$373$	0.218847	+	0.379054i	0.0113315	+	0.0196267i	0.871636	−	0.490155i	$-0.163060\pi$
$373$	0.218847	+	0.379054i	0.0113315	+	0.0196267i	−0.860304	+	0.509781i	$0.829726\pi$
$374$		0			0
$375$	0.718847	−	1.24508i	0.0371211	−	0.0642956i
$376$		0			0
$377$	4.09017	+	14.1688i	0.210654	+	0.729728i
$378$		0			0
$379$	−6.42705	+	11.1320i	−0.330135	+	0.571811i	−0.982538	−	0.186061i	$-0.940428\pi$
$379$	−6.42705	+	11.1320i	−0.330135	+	0.571811i	0.652403	+	0.757872i	$0.273761\pi$
$380$		0			0
$381$	−2.70163	−	4.67935i	−0.138408	−	0.239731i
$382$		0			0
$383$	12.4894	+	21.6322i	0.638176	+	1.10535i	0.985833	+	0.167732i	$0.0536443\pi$
$383$	12.4894	+	21.6322i	0.638176	+	1.10535i	−0.347656	+	0.937622i	$0.613022\pi$
$384$		0			0
$385$	−1.85410			−0.0944938
$386$		0			0
$387$	10.7918	−	18.6919i	0.548578	−	0.950165i
$388$		0			0
$389$	23.8885			1.21120			0.605599	−	0.795770i	$-0.292934\pi$
$389$	23.8885			1.21120			0.605599	+	0.795770i	$0.292934\pi$
$390$		0			0
$391$	−33.4164			−1.68994
$392$		0			0
$393$	0.0623059	−	0.107917i	0.00314292	−	0.00544369i
$394$		0			0
$395$	−1.52786			−0.0768752
$396$		0			0
$397$	12.7082	+	22.0113i	0.637806	+	1.10471i	0.985913	+	0.167258i	$0.0534914\pi$
$397$	12.7082	+	22.0113i	0.637806	+	1.10471i	−0.348107	+	0.937455i	$0.613175\pi$
$398$		0			0
$399$	−0.927051	−	1.60570i	−0.0464106	−	0.0803855i
$400$		0			0
$401$	10.2254	−	17.7110i	0.510633	−	0.884443i	−0.489291	−	0.872121i	$-0.662744\pi$
$401$	10.2254	−	17.7110i	0.510633	−	0.884443i	0.999924	−	0.0123222i	$-0.00392237\pi$
$402$		0			0
$403$	21.7705	−	22.6246i	1.08447	−	1.12701i
$404$		0			0
$405$	−1.47214	+	2.54981i	−0.0731510	+	0.126701i
$406$		0			0
$407$	−9.70820	−	16.8151i	−0.481218	−	0.833494i
$408$		0			0
$409$	−17.2812	−	29.9318i	−0.854498	−	1.48003i	−0.877110	−	0.480290i	$-0.840532\pi$
$409$	−17.2812	−	29.9318i	−0.854498	−	1.48003i	0.0226119	−	0.999744i	$-0.492802\pi$
$410$		0			0
$411$	−0.145898			−0.00719662
$412$		0			0
$413$	−1.11803	+	1.93649i	−0.0550149	+	0.0952885i
$414$		0			0
$415$	2.56231			0.125779
$416$		0			0
$417$	5.94427			0.291092
$418$		0			0
$419$	2.97214	−	5.14789i	0.145198	−	0.251491i	−0.784249	−	0.620447i	$-0.786951\pi$
$419$	2.97214	−	5.14789i	0.145198	−	0.251491i	0.929447	+	0.368956i	$0.120285\pi$
$420$		0			0
$421$	−25.4164			−1.23872			−0.619360	−	0.785107i	$-0.712608\pi$
$421$	−25.4164			−1.23872			−0.619360	+	0.785107i	$0.712608\pi$
$422$		0			0
$423$	−3.19098	−	5.52694i	−0.155151	−	0.268729i
$424$		0			0
$425$	18.1353	+	31.4112i	0.879689	+	1.52367i
$426$		0			0
$427$	−3.00000	+	5.19615i	−0.145180	+	0.251459i
$428$		0			0
$429$	6.48936	+	1.60570i	0.313309	+	0.0775239i
$430$		0			0
$431$	−8.39919	+	14.5478i	−0.404575	+	0.700744i	−0.994272	−	0.106881i	$-0.965914\pi$
$431$	−8.39919	+	14.5478i	−0.404575	+	0.700744i	0.589697	+	0.807624i	$0.299247\pi$
$432$		0			0
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$		0			0
$435$	0.298374	+	0.516799i	0.0143059	+	0.0247786i
$436$		0			0
$437$	21.7082			1.03844
$438$		0			0
$439$	4.07295	−	7.05455i	0.194391	−	0.336696i	−0.752310	−	0.658810i	$-0.771060\pi$
$439$	4.07295	−	7.05455i	0.194391	−	0.336696i	0.946701	+	0.322114i	$0.104394\pi$
$440$		0			0
$441$	−2.85410			−0.135910
$442$		0			0
$443$	0.763932			0.0362955			0.0181478	−	0.999835i	$-0.494223\pi$
$443$	0.763932			0.0362955			0.0181478	+	0.999835i	$0.494223\pi$
$444$		0			0
$445$	−3.07295	+	5.32250i	−0.145672	+	0.252311i
$446$		0			0
$447$	−1.85410			−0.0876960
$448$		0			0
$449$	−14.2361	−	24.6576i	−0.671842	−	1.16366i	−0.977381	−	0.211484i	$-0.932170\pi$
$449$	−14.2361	−	24.6576i	−0.671842	−	1.16366i	0.305540	−	0.952179i	$-0.401163\pi$
$450$		0			0
$451$	−12.7082	−	22.0113i	−0.598406	−	1.03647i
$452$		0			0
$453$	−2.80902	+	4.86536i	−0.131979	+	0.228595i
$454$		0			0
$455$	−1.33688	−	0.330792i	−0.0626739	−	0.0155078i
$456$		0			0
$457$	5.70820	−	9.88690i	0.267019	−	0.462490i	−0.701072	−	0.713091i	$-0.747295\pi$
$457$	5.70820	−	9.88690i	0.267019	−	0.462490i	0.968090	+	0.250601i	$0.0806282\pi$
$458$		0			0
$459$	8.35410	+	14.4697i	0.389936	+	0.675389i
$460$		0			0
$461$	−19.6074	−	33.9610i	−0.913207	−	1.58172i	−0.809505	−	0.587113i	$-0.800264\pi$
$461$	−19.6074	−	33.9610i	−0.913207	−	1.58172i	−0.103702	−	0.994608i	$-0.533069\pi$
$462$		0			0
$463$	6.70820			0.311757			0.155878	−	0.987776i	$-0.450179\pi$
$463$	6.70820			0.311757			0.155878	+	0.987776i	$0.450179\pi$
$464$		0			0
$465$	0.635255	−	1.10029i	0.0294592	−	0.0510249i
$466$		0			0
$467$	−33.6525			−1.55725			−0.778625	−	0.627489i	$-0.784083\pi$
$467$	−33.6525			−1.55725			−0.778625	+	0.627489i	$0.784083\pi$
$468$		0			0
$469$	0.708204			0.0327018
$470$		0			0
$471$	−1.55573	+	2.69460i	−0.0716842	+	0.124161i
$472$		0			0
$473$	36.7082			1.68785
$474$		0			0
$475$	−11.7812	−	20.4056i	−0.540556	−	0.936271i
$476$		0			0
$477$	11.7533	+	20.3573i	0.538146	+	0.932096i
$478$		0			0
$479$	−10.9894	+	19.0341i	−0.502117	+	0.869691i	0.497880	+	0.867246i	$0.334112\pi$
$479$	−10.9894	+	19.0341i	−0.502117	+	0.869691i	−0.999997	+	0.00244569i	$0.999222\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$		0			0
$483$	−0.854102	+	1.47935i	−0.0388630	+	0.0673127i
$484$		0			0
$485$	−2.31966	−	4.01777i	−0.105330	−	0.182438i
$486$		0			0
$487$	−8.48936	−	14.7040i	−0.384689	−	0.666302i	0.607037	−	0.794674i	$-0.292358\pi$
$487$	−8.48936	−	14.7040i	−0.384689	−	0.666302i	−0.991726	+	0.128372i	$0.959025\pi$
$488$		0			0
$489$	−3.70820			−0.167691
$490$		0			0
$491$	7.30902	−	12.6596i	0.329851	−	0.571319i	−0.652631	−	0.757676i	$-0.726335\pi$
$491$	7.30902	−	12.6596i	0.329851	−	0.571319i	0.982482	+	0.186357i	$0.0596680\pi$
$492$		0			0
$493$	−30.5623			−1.37646
$494$		0			0
$495$	−5.29180			−0.237849
$496$		0			0
$497$	−4.09017	+	7.08438i	−0.183469	+	0.317778i
$498$		0			0
$499$	−8.14590			−0.364660			−0.182330	−	0.983237i	$-0.558364\pi$
$499$	−8.14590			−0.364660			−0.182330	+	0.983237i	$0.558364\pi$
$500$		0			0
$501$	1.86475	+	3.22983i	0.0833107	+	0.144298i
$502$		0			0
$503$	12.1910	+	21.1154i	0.543569	+	0.941489i	0.998695	+	0.0510624i	$0.0162607\pi$
$503$	12.1910	+	21.1154i	0.543569	+	0.941489i	−0.455126	+	0.890427i	$0.650406\pi$
$504$		0			0
$505$	−1.63525	+	2.83234i	−0.0727679	+	0.126038i
$506$		0			0
$507$	4.39261	+	2.31555i	0.195083	+	0.102837i
$508$		0			0
$509$	−15.2984	+	26.4976i	−0.678089	+	1.17448i	0.297467	+	0.954732i	$0.403858\pi$
$509$	−15.2984	+	26.4976i	−0.678089	+	1.17448i	−0.975556	+	0.219752i	$0.929475\pi$
$510$		0			0
$511$	−1.00000	−	1.73205i	−0.0442374	−	0.0766214i
$512$		0			0
$513$	−5.42705	−	9.39993i	−0.239610	−	0.415017i
$514$		0			0
$515$	−1.79837			−0.0792458
$516$		0			0
$517$	5.42705	−	9.39993i	0.238681	−	0.413408i
$518$		0			0
$519$	−3.43769			−0.150898
$520$		0			0
$521$	−12.6525			−0.554315			−0.277158	−	0.960824i	$-0.589392\pi$
$521$	−12.6525			−0.554315			−0.277158	+	0.960824i	$0.589392\pi$
$522$		0			0
$523$	−19.5623	+	33.8829i	−0.855400	+	1.48160i	0.0208736	+	0.999782i	$0.493355\pi$
$523$	−19.5623	+	33.8829i	−0.855400	+	1.48160i	−0.876274	+	0.481814i	$0.839978\pi$
$524$		0			0
$525$	1.85410			0.0809196
$526$		0			0
$527$	32.5344	+	56.3513i	1.41722	+	2.45470i
$528$		0			0
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$		0			0
$531$	−3.19098	+	5.52694i	−0.138477	+	0.239849i
$532$		0			0
$533$	−5.23607	−	18.1383i	−0.226799	−	0.785656i
$534$		0			0
$535$	−1.07295	+	1.85840i	−0.0463876	+	0.0803457i
$536$		0			0
$537$	−1.71885	−	2.97713i	−0.0741737	−	0.128473i
$538$		0			0
$539$	−2.42705	−	4.20378i	−0.104540	−	0.181069i
$540$		0			0
$541$	1.72949			0.0743566			0.0371783	−	0.999309i	$-0.488163\pi$
$541$	1.72949			0.0743566			0.0371783	+	0.999309i	$0.488163\pi$
$542$		0			0
$543$	0.708204	−	1.22665i	0.0303919	−	0.0526404i
$544$		0			0
$545$	4.09017			0.175204
$546$		0			0
$547$	3.00000			0.128271			0.0641354	−	0.997941i	$-0.479571\pi$
$547$	3.00000			0.128271			0.0641354	+	0.997941i	$0.479571\pi$
$548$		0			0
$549$	−8.56231	+	14.8303i	−0.365430	+	0.632944i
$550$		0			0
$551$	19.8541			0.845813
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$		0			0
$555$	−0.291796	−	0.505406i	−0.0123861	−	0.0214533i
$556$		0			0
$557$	−9.48936	+	16.4360i	−0.402077	+	0.696418i	−0.993976	−	0.109594i	$-0.965045\pi$
$557$	−9.48936	+	16.4360i	−0.402077	+	0.696418i	0.591899	+	0.806012i	$0.298378\pi$
$558$		0			0
$559$	26.4681	+	6.54915i	1.11948	+	0.276999i
$560$		0			0
$561$	−6.92705	+	11.9980i	−0.292460	+	0.506556i
$562$		0			0
$563$	−19.4721	−	33.7267i	−0.820653	−	1.42141i	−0.905197	−	0.424992i	$-0.860277\pi$
$563$	−19.4721	−	33.7267i	−0.820653	−	1.42141i	0.0845442	−	0.996420i	$-0.473057\pi$
$564$		0			0
$565$	1.42705	+	2.47172i	0.0600365	+	0.103986i
$566$		0			0
$567$	−7.70820			−0.323714
$568$		0			0
$569$	1.47214	−	2.54981i	0.0617151	−	0.106894i	−0.833517	−	0.552494i	$-0.813676\pi$
$569$	1.47214	−	2.54981i	0.0617151	−	0.106894i	0.895232	+	0.445600i	$0.147010\pi$
$570$		0			0
$571$	35.6869			1.49345			0.746726	−	0.665132i	$-0.231625\pi$
$571$	35.6869			1.49345			0.746726	+	0.665132i	$0.231625\pi$
$572$		0			0
$573$	−9.02129			−0.376870
$574$		0			0
$575$	−10.8541	+	18.7999i	−0.452647	+	0.784008i
$576$		0			0
$577$	9.83282			0.409345			0.204673	−	0.978830i	$-0.434387\pi$
$577$	9.83282			0.409345			0.204673	+	0.978830i	$0.434387\pi$
$578$		0			0
$579$	1.14590	+	1.98475i	0.0476219	+	0.0824835i
$580$		0			0
$581$	3.35410	+	5.80948i	0.139152	+	0.241018i
$582$		0			0
$583$	−19.9894	+	34.6226i	−0.827875	+	1.43392i
$584$		0			0
$585$	−3.81559	−	0.944115i	−0.157755	−	0.0390343i
$586$		0			0
$587$	−15.5451	+	26.9249i	−0.641614	+	1.11131i	0.343458	+	0.939168i	$0.388402\pi$
$587$	−15.5451	+	26.9249i	−0.641614	+	1.11131i	−0.985072	+	0.172141i	$0.944932\pi$
$588$		0			0
$589$	−21.1353	−	36.6073i	−0.870863	−	1.50838i
$590$		0			0
$591$	−1.48936	−	2.57964i	−0.0612640	−	0.106112i
$592$		0			0
$593$	19.2016			0.788516			0.394258	−	0.919000i	$-0.371002\pi$
$593$	19.2016			0.788516			0.394258	+	0.919000i	$0.371002\pi$
$594$		0			0
$595$	1.42705	−	2.47172i	0.0585034	−	0.101331i
$596$		0			0
$597$	−0.922986			−0.0377753
$598$		0			0
$599$	8.50658			0.347569			0.173785	−	0.984784i	$-0.444400\pi$
$599$	8.50658			0.347569			0.173785	+	0.984784i	$0.444400\pi$
$600$		0			0
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	−0.293535	−	0.955948i	$-0.594832\pi$
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	0.974643	−	0.223765i	$-0.0718348\pi$
$602$		0			0
$603$	2.02129			0.0823131
$604$		0			0
$605$	−2.39919	−	4.15551i	−0.0975408	−	0.168946i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$		0			0
$609$	−0.781153	+	1.35300i	−0.0316539	+	0.0548262i
$610$		0			0
$611$	5.59017	−	5.80948i	0.226154	−	0.235026i
$612$		0			0
$613$	−7.21885	+	12.5034i	−0.291566	+	0.505008i	−0.974180	−	0.225771i	$-0.927510\pi$
$613$	−7.21885	+	12.5034i	−0.291566	+	0.505008i	0.682614	+	0.730779i	$0.260843\pi$
$614$		0			0
$615$	−0.381966	−	0.661585i	−0.0154024	−	0.0266777i
$616$		0			0
$617$	−8.97214	−	15.5402i	−0.361205	−	0.625625i	0.626955	−	0.779056i	$-0.284301\pi$
$617$	−8.97214	−	15.5402i	−0.361205	−	0.625625i	−0.988159	+	0.153431i	$0.950968\pi$
$618$		0			0
$619$	17.4164			0.700025			0.350012	−	0.936745i	$-0.386177\pi$
$619$	17.4164			0.700025			0.350012	+	0.936745i	$0.386177\pi$
$620$		0			0
$621$	−5.00000	+	8.66025i	−0.200643	+	0.347524i
$622$		0			0
$623$	−16.0902			−0.644639
$624$		0			0
$625$	22.8328			0.913313
$626$		0			0
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$		0			0
$629$	29.8885			1.19173
$630$		0			0
$631$	−19.6976	−	34.1172i	−0.784148	−	1.35818i	−0.929507	−	0.368804i	$-0.879767\pi$
$631$	−19.6976	−	34.1172i	−0.784148	−	1.35818i	0.145360	−	0.989379i	$-0.453566\pi$
$632$		0			0
$633$	−1.66312	−	2.88061i	−0.0661030	−	0.114494i
$634$		0			0
$635$	−2.70163	+	4.67935i	−0.107211	+	0.185694i
$636$		0			0
$637$	−1.00000	−	3.46410i	−0.0396214	−	0.137253i
$638$		0			0
$639$	−11.6738	+	20.2195i	−0.461807	+	0.799873i
$640$		0			0
$641$	4.74671	+	8.22154i	0.187484	+	0.324731i	0.944411	−	0.328768i	$-0.106633\pi$
$641$	4.74671	+	8.22154i	0.187484	+	0.324731i	−0.756927	+	0.653500i	$0.773300\pi$
$642$		0			0
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	0.788723	−	0.614749i	$-0.210743\pi$
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$	1.10333			0.0434434
$646$		0			0
$647$	14.6180	−	25.3192i	0.574694	−	0.995400i	−0.421381	−	0.906884i	$-0.638454\pi$
$647$	14.6180	−	25.3192i	0.574694	−	0.995400i	0.996075	−	0.0885157i	$-0.0282123\pi$
$648$		0			0
$649$	−10.8541			−0.426061
$650$		0			0
$651$	3.32624			0.130366
$652$		0			0
$653$	1.30902	−	2.26728i	0.0512258	−	0.0887257i	−0.839275	−	0.543706i	$-0.817021\pi$
$653$	1.30902	−	2.26728i	0.0512258	−	0.0887257i	0.890501	+	0.454981i	$0.150354\pi$
$654$		0			0
$655$	−0.124612			−0.00486899
$656$		0			0
$657$	−2.85410	−	4.94345i	−0.111349	−	0.192862i
$658$		0			0
$659$	5.94427	+	10.2958i	0.231556	+	0.401067i	0.958266	−	0.285877i	$-0.0922850\pi$
$659$	5.94427	+	10.2958i	0.231556	+	0.401067i	−0.726710	+	0.686944i	$0.758952\pi$
$660$		0			0
$661$	−9.27051	+	16.0570i	−0.360581	+	0.624545i	−0.988057	−	0.154092i	$-0.950755\pi$
$661$	−9.27051	+	16.0570i	−0.360581	+	0.624545i	0.627476	+	0.778636i	$0.284088\pi$
$662$		0			0
$663$	−7.13525	+	7.41517i	−0.277110	+	0.287982i
$664$		0			0
$665$	−0.927051	+	1.60570i	−0.0359495	+	0.0622664i
$666$		0			0
$667$	−9.14590	−	15.8412i	−0.354131	−	0.613372i
$668$		0			0
$669$	−2.53444	−	4.38978i	−0.0979872	−	0.169719i
$670$		0			0
$671$	−29.1246			−1.12434
$672$		0			0
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	0.127806	+	0.991799i	$0.459207\pi$
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	−0.922826	+	0.385216i	$0.874127\pi$
$674$		0			0
$675$	10.8541			0.417775
$676$		0			0
$677$	1.25735			0.0483240			0.0241620	−	0.999708i	$-0.492308\pi$
$677$	1.25735			0.0483240			0.0241620	+	0.999708i	$0.492308\pi$
$678$		0			0
$679$	6.07295	−	10.5187i	0.233058	−	0.403669i
$680$		0			0
$681$	2.85410			0.109369
$682$		0			0
$683$	−3.73607	−	6.47106i	−0.142957	−	0.247608i	0.785652	−	0.618669i	$-0.212328\pi$
$683$	−3.73607	−	6.47106i	−0.142957	−	0.247608i	−0.928609	+	0.371060i	$0.878994\pi$
$684$		0			0
$685$	0.0729490	+	0.126351i	0.00278724	+	0.00482764i
$686$		0			0
$687$	−5.18034	+	8.97261i	−0.197642	+	0.342326i
$688$		0			0
$689$	−20.5902	+	21.3979i	−0.784423	+	0.815196i
$690$		0			0
$691$	0.427051	−	0.739674i	0.0162458	−	0.0281385i	−0.857788	−	0.514003i	$-0.828162\pi$
$691$	0.427051	−	0.739674i	0.0162458	−	0.0281385i	0.874034	+	0.485865i	$0.161495\pi$
$692$		0			0
$693$	−6.92705	−	11.9980i	−0.263137	−	0.455766i
$694$		0			0
$695$	−2.97214	−	5.14789i	−0.112740	−	0.195271i
$696$		0			0
$697$	39.1246			1.48195
$698$		0			0
$699$	−0.0729490	+	0.126351i	−0.00275919	+	0.00477905i
$700$		0			0
$701$	6.76393			0.255470			0.127735	−	0.991808i	$-0.459229\pi$
$701$	6.76393			0.255470			0.127735	+	0.991808i	$0.459229\pi$
$702$		0			0
$703$	−19.4164			−0.732304
$704$		0			0
$705$	0.163119	−	0.282530i	0.00614342	−	0.0106407i
$706$		0			0
$707$	−8.56231			−0.322019
$708$		0			0
$709$	−1.71885	−	2.97713i	−0.0645527	−	0.111808i	0.831943	−	0.554861i	$-0.187229\pi$
$709$	−1.71885	−	2.97713i	−0.0645527	−	0.111808i	−0.896495	+	0.443053i	$0.853895\pi$
$710$		0			0
$711$	−5.70820	−	9.88690i	−0.214074	−	0.370788i
$712$		0			0
$713$	−19.4721	+	33.7267i	−0.729237	+	1.26308i
$714$		0			0
$715$	−1.85410	−	6.42280i	−0.0693395	−	0.240199i
$716$		0			0
$717$	−2.15654	+	3.73524i	−0.0805375	+	0.139495i
$718$		0			0
$719$	−16.0623	−	27.8207i	−0.599023	−	1.03754i	−0.992966	−	0.118403i	$-0.962222\pi$
$719$	−16.0623	−	27.8207i	−0.599023	−	1.03754i	0.393943	−	0.919135i	$-0.371111\pi$
$720$		0			0
$721$	−2.35410	−	4.07742i	−0.0876713	−	0.151851i
$722$		0			0
$723$	1.69505			0.0630395
$724$		0			0
$725$	−9.92705	+	17.1942i	−0.368681	+	0.638575i
$726$		0			0
$727$	17.2918			0.641317			0.320659	−	0.947195i	$-0.396096\pi$
$727$	17.2918			0.641317			0.320659	+	0.947195i	$0.396096\pi$
$728$		0			0
$729$	−19.4377			−0.719915
$730$		0			0
$731$	−28.2533	+	48.9361i	−1.04499	+	1.80997i
$732$		0			0
$733$	1.27051			0.0469274			0.0234637	−	0.999725i	$-0.492531\pi$
$733$	1.27051			0.0469274			0.0234637	+	0.999725i	$0.492531\pi$
$734$		0			0
$735$	−0.0729490	−	0.126351i	−0.00269077	−	0.00466054i
$736$		0			0
$737$	1.71885	+	2.97713i	0.0633145	+	0.109664i
$738$		0			0
$739$	−23.5623	+	40.8111i	−0.866753	+	1.50126i	−0.00145790	+	0.999999i	$0.500464\pi$
$739$	−23.5623	+	40.8111i	−0.866753	+	1.50126i	−0.865296	+	0.501262i	$0.832869\pi$
$740$		0			0
$741$	4.63525	−	4.81710i	0.170280	−	0.176961i
$742$		0			0
$743$	11.8369	−	20.5021i	0.434253	−	0.752148i	−0.562981	−	0.826470i	$-0.690346\pi$
$743$	11.8369	−	20.5021i	0.434253	−	0.752148i	0.997234	+	0.0743213i	$0.0236790\pi$
$744$		0			0
$745$	0.927051	+	1.60570i	0.0339645	+	0.0588283i
$746$		0			0
$747$	9.57295	+	16.5808i	0.350256	+	0.606661i
$748$		0			0
$749$	−5.61803			−0.205278
$750$		0			0
$751$	4.64590	−	8.04693i	0.169531	−	0.293637i	−0.768724	−	0.639581i	$-0.779108\pi$
$751$	4.64590	−	8.04693i	0.169531	−	0.293637i	0.938255	+	0.345944i	$0.112441\pi$
$752$		0			0
$753$	−2.00000			−0.0728841
$754$		0			0
$755$	5.61803			0.204461
$756$		0			0
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$		0			0
$759$	−8.29180			−0.300973
$760$		0			0
$761$	11.0729	+	19.1789i	0.401394	+	0.695235i	0.993894	−	0.110335i	$-0.0351925\pi$
$761$	11.0729	+	19.1789i	0.401394	+	0.695235i	−0.592500	+	0.805570i	$0.701859\pi$
$762$		0			0
$763$	5.35410	+	9.27358i	0.193832	+	0.335726i
$764$		0			0
$765$	4.07295	−	7.05455i	0.147258	−	0.255058i
$766$		0			0
$767$	−7.82624	−	1.93649i	−0.282589	−	0.0699227i
$768$		0			0
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	−0.931872	−	0.362788i	$-0.881825\pi$
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	0.780120	+	0.625630i	$0.215158\pi$
$770$		0			0
$771$	4.91641	+	8.51547i	0.177060	+	0.306677i
$772$		0			0
$773$	9.68034	+	16.7668i	0.348178	+	0.603061i	0.985926	−	0.167184i	$-0.0534673\pi$
$773$	9.68034	+	16.7668i	0.348178	+	0.603061i	−0.637748	+	0.770245i	$0.720134\pi$
$774$		0			0
$775$	42.2705			1.51840
$776$		0			0
$777$	0.763932	−	1.32317i	0.0274059	−	0.0474684i
$778$		0			0
$779$	−25.4164			−0.910637
$780$		0			0
$781$	−39.7082			−1.42087
$782$		0			0
$783$	−4.57295	+	7.92058i	−0.163424	+	0.283058i
$784$		0			0
$785$	3.11146			0.111053
$786$		0			0
$787$	14.7082	+	25.4754i	0.524291	+	0.908098i	0.999600	+	0.0282796i	$0.00900287\pi$
$787$	14.7082	+	25.4754i	0.524291	+	0.908098i	−0.475309	+	0.879819i	$0.657664\pi$
$788$		0			0
$789$	1.71885	+	2.97713i	0.0611926	+	0.105989i
$790$		0			0
$791$	−3.73607	+	6.47106i	−0.132839	+	0.230084i
$792$		0			0
$793$	−21.0000	−	5.19615i	−0.745732	−	0.184521i
$794$		0			0
$795$	−0.600813	+	1.04064i	−0.0213086	+	0.0369077i
$796$		0			0
$797$	−7.09017	−	12.2805i	−0.251147	−	0.434999i	0.712695	−	0.701474i	$-0.247474\pi$
$797$	−7.09017	−	12.2805i	−0.251147	−	0.434999i	−0.963842	+	0.266475i	$0.914141\pi$
$798$		0			0
$799$	8.35410	+	14.4697i	0.295547	+	0.511902i
$800$		0			0
$801$	−45.9230			−1.62261
$802$		0			0
$803$	4.85410	−	8.40755i	0.171298	−	0.296696i
$804$		0			0
$805$	1.70820			0.0602063
$806$		0			0
$807$	5.24922			0.184781
$808$		0			0
$809$	−11.2082	+	19.4132i	−0.394059	+	0.682531i	−0.992981	−	0.118277i	$-0.962263\pi$
$809$	−11.2082	+	19.4132i	−0.394059	+	0.682531i	0.598921	+	0.800808i	$0.295596\pi$
$810$		0			0
$811$	−5.72949			−0.201190			−0.100595	−	0.994927i	$-0.532075\pi$
$811$	−5.72949			−0.201190			−0.100595	+	0.994927i	$0.532075\pi$
$812$		0			0
$813$	3.51722	+	6.09201i	0.123354	+	0.213656i
$814$		0			0
$815$	1.85410	+	3.21140i	0.0649464	+	0.112490i
$816$		0			0
$817$	18.3541	−	31.7902i	0.642129	−	1.11220i
$818$		0			0
$819$	−2.85410	−	9.88690i	−0.0997304	−	0.345476i
$820$		0			0
$821$	−18.6803	+	32.3553i	−0.651948	+	1.12921i	0.330701	+	0.943736i	$0.392715\pi$
$821$	−18.6803	+	32.3553i	−0.651948	+	1.12921i	−0.982650	+	0.185472i	$0.940619\pi$
$822$		0			0
$823$	−5.79180	−	10.0317i	−0.201889	−	0.349683i	0.747248	−	0.664545i	$-0.231375\pi$
$823$	−5.79180	−	10.0317i	−0.201889	−	0.349683i	−0.949137	+	0.314863i	$0.898041\pi$
$824$		0			0
$825$	4.50000	+	7.79423i	0.156670	+	0.271360i
$826$		0			0
$827$	30.9787			1.07724			0.538618	−	0.842550i	$-0.318947\pi$
$827$	30.9787			1.07724			0.538618	+	0.842550i	$0.318947\pi$
$828$		0			0
$829$	6.28115	−	10.8793i	0.218153	−	0.377853i	−0.736090	−	0.676884i	$-0.763330\pi$
$829$	6.28115	−	10.8793i	0.218153	−	0.377853i	0.954243	+	0.299031i	$0.0966633\pi$
$830$		0			0
$831$	−1.90983			−0.0662513
$832$		0			0
$833$	7.47214			0.258894
$834$		0			0
$835$	1.86475	−	3.22983i	0.0645322	−	0.111773i
$836$		0			0
$837$	19.4721			0.673055
$838$		0			0
$839$	−14.3713	−	24.8919i	−0.496153	−	0.859362i	0.503837	−	0.863799i	$-0.331921\pi$
$839$	−14.3713	−	24.8919i	−0.496153	−	0.859362i	−0.999990	+	0.00443626i	$0.998588\pi$
$840$		0			0
$841$	6.13525	+	10.6266i	0.211561	+	0.366434i
$842$		0			0
$843$	0.416408	−	0.721240i	0.0143418	−	0.0248408i
$844$		0			0
$845$	−0.190983	−	4.96188i	−0.00657002	−	0.170694i
$846$		0			0
$847$	6.28115	−	10.8793i	0.215823	−	0.373816i
$848$		0			0
$849$	−2.56231	−	4.43804i	−0.0879381	−	0.152313i
$850$		0			0
$851$	8.94427	+	15.4919i	0.306606	+	0.531057i
$852$		0			0
$853$	−26.1246			−0.894490			−0.447245	−	0.894412i	$-0.647595\pi$
$853$	−26.1246			−0.894490			−0.447245	+	0.894412i	$0.647595\pi$
$854$		0			0
$855$	−2.64590	+	4.58283i	−0.0904878	+	0.156729i
$856$		0			0
$857$	29.4508			1.00602			0.503011	−	0.864280i	$-0.332226\pi$
$857$	29.4508			1.00602			0.503011	+	0.864280i	$0.332226\pi$
$858$		0			0
$859$	−36.2492			−1.23681			−0.618404	−	0.785861i	$-0.712220\pi$
$859$	−36.2492			−1.23681			−0.618404	+	0.785861i	$0.712220\pi$
$860$		0			0
$861$	1.00000	−	1.73205i	0.0340799	−	0.0590281i
$862$		0			0
$863$	23.8885			0.813175			0.406588	−	0.913612i	$-0.366719\pi$
$863$	23.8885			0.813175			0.406588	+	0.913612i	$0.366719\pi$
$864$		0			0
$865$	1.71885	+	2.97713i	0.0584426	+	0.101225i
$866$		0			0
$867$	−7.41641	−	12.8456i	−0.251874	−	0.436259i
$868$		0			0
$869$	9.70820	−	16.8151i	0.329328	−	0.570413i
$870$		0			0
$871$	0.708204	+	2.45329i	0.0239966	+	0.0831266i
$872$		0			0
$873$	17.3328	−	30.0213i	0.586627	−	1.01607i
$874$		0			0
$875$	−1.88197	−	3.25966i	−0.0636221	−	0.110197i
$876$		0			0
$877$	6.35410	+	11.0056i	0.214563	+	0.371634i	0.953137	−	0.302538i	$-0.0978340\pi$
$877$	6.35410	+	11.0056i	0.214563	+	0.371634i	−0.738574	+	0.674172i	$0.764501\pi$
$878$		0			0
$879$	−4.29180			−0.144759
$880$		0			0
$881$	−6.29837	+	10.9091i	−0.212198	+	0.367537i	−0.952402	−	0.304845i	$-0.901395\pi$
$881$	−6.29837	+	10.9091i	−0.212198	+	0.367537i	0.740204	+	0.672382i	$0.234729\pi$
$882$		0			0
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$		0			0
$885$	−0.326238			−0.0109664
$886$		0			0
$887$	11.6738	−	20.2195i	0.391967	−	0.678906i	−0.600742	−	0.799443i	$-0.705128\pi$
$887$	11.6738	−	20.2195i	0.391967	−	0.678906i	0.992709	+	0.120537i	$0.0384616\pi$
$888$		0			0
$889$	−14.1459			−0.474438
$890$		0			0
$891$	−18.7082	−	32.4036i	−0.626748	−	1.08556i
$892$		0			0
$893$	−5.42705	−	9.39993i	−0.181609	−	0.314557i
$894$		0			0
$895$	−1.71885	+	2.97713i	−0.0574547	+	0.0995145i
$896$		0			0
$897$	−5.97871	−	1.47935i	−0.199623	−	0.0493940i
$898$		0			0
$899$	−17.8090	+	30.8461i	−0.593964	+	1.02878i
$900$		0			0
$901$	−30.7705	−	53.2961i	−1.02511	−	1.77555i
$902$		0			0
$903$	1.44427	+	2.50155i	0.0480624	+	0.0832464i
$904$		0			0
$905$	−1.41641			−0.0470830
$906$		0			0
$907$	−12.0000	+	20.7846i	−0.398453	+	0.690142i	−0.993535	−	0.113523i	$-0.963786\pi$
$907$	−12.0000	+	20.7846i	−0.398453	+	0.690142i	0.595082	+	0.803665i	$0.297120\pi$
$908$		0			0
$909$	−24.4377			−0.810547
$910$		0			0
$911$	−37.6869			−1.24862			−0.624312	−	0.781175i	$-0.714620\pi$
$911$	−37.6869			−1.24862			−0.624312	+	0.781175i	$0.714620\pi$
$912$		0			0
$913$	−16.2812	+	28.1998i	−0.538828	+	0.933277i
$914$		0			0
$915$	−0.875388			−0.0289394
$916$		0			0
$917$	−0.163119	−	0.282530i	−0.00538666	−	0.00932997i
$918$		0			0
$919$	−15.0000	−	25.9808i	−0.494804	−	0.857026i	0.505178	−	0.863015i	$-0.331427\pi$
$919$	−15.0000	−	25.9808i	−0.494804	−	0.857026i	−0.999982	+	0.00598907i	$0.998094\pi$
$920$		0			0
$921$	0.354102	−	0.613323i	0.0116681	−	0.0202097i
$922$		0			0
$923$	−28.6312	−	7.08438i	−0.942407	−	0.233185i
$924$		0			0
$925$	9.70820	−	16.8151i	0.319204	−	0.552877i
$926$		0			0
$927$	−6.71885	−	11.6374i	−0.220676	−	0.382222i
$928$		0			0
$929$	23.5344	+	40.7628i	0.772140	+	1.33739i	0.936388	+	0.350967i	$0.114147\pi$
$929$	23.5344	+	40.7628i	0.772140	+	1.33739i	−0.164248	+	0.986419i	$0.552520\pi$
$930$		0			0
$931$	−4.85410			−0.159087
$932$		0			0
$933$	−2.35410	+	4.07742i	−0.0770698	+	0.133489i
$934$		0			0
$935$	13.8541			0.453078
$936$		0			0
$937$	−56.1246			−1.83351			−0.916756	−	0.399449i	$-0.869202\pi$
$937$	−56.1246			−1.83351			−0.916756	+	0.399449i	$0.869202\pi$
$938$		0			0
$939$	2.88854	−	5.00310i	0.0942641	−	0.163270i
$940$		0			0
$941$	51.6525			1.68382			0.841911	−	0.539616i	$-0.181431\pi$
$941$	51.6525			1.68382			0.841911	+	0.539616i	$0.181431\pi$
$942$		0			0
$943$	11.7082	+	20.2792i	0.381272	+	0.660382i
$944$		0			0
$945$	−0.427051	−	0.739674i	−0.0138920	−	0.0240616i
$946$		0			0
$947$	22.9336	−	39.7222i	0.745243	−	1.29080i	−0.204838	−	0.978796i	$-0.565667\pi$
$947$	22.9336	−	39.7222i	0.745243	−	1.29080i	0.950081	−	0.312003i	$-0.101000\pi$
$948$		0			0
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$		0			0
$951$	−4.15654	+	7.19934i	−0.134785	+	0.233455i
$952$		0			0
$953$	22.3885	+	38.7781i	0.725236	+	1.25615i	0.958877	+	0.283823i	$0.0916027\pi$
$953$	22.3885	+	38.7781i	0.725236	+	1.25615i	−0.233641	+	0.972323i	$0.575064\pi$
$954$		0			0
$955$	4.51064	+	7.81266i	0.145961	+	0.252812i
$956$		0			0
$957$	−7.58359			−0.245143
$958$		0			0
$959$	−0.190983	+	0.330792i	−0.00616716	+	0.0106818i
$960$		0			0
$961$	44.8328			1.44622
$962$		0			0
$963$	−16.0344			−0.516703
$964$		0			0
$965$	1.14590	−	1.98475i	0.0368878	−	0.0638915i
$966$		0			0
$967$	39.0000			1.25416			0.627078	−	0.778957i	$-0.284251\pi$
$967$	39.0000			1.25416			0.627078	+	0.778957i	$0.284251\pi$
$968$		0			0
$969$	6.92705	+	11.9980i	0.222529	+	0.385431i
$970$		0			0
$971$	29.2082	+	50.5901i	0.937336	+	1.62351i	0.770415	+	0.637543i	$0.220049\pi$
$971$	29.2082	+	50.5901i	0.937336	+	1.62351i	0.166921	+	0.985970i	$0.446617\pi$
$972$		0			0
$973$	7.78115	−	13.4774i	0.249452	−	0.432064i
$974$		0			0
$975$	1.85410	+	6.42280i	0.0593788	+	0.205694i
$976$		0			0
$977$	15.7361	−	27.2557i	0.503441	−	0.871986i	−0.496551	−	0.868008i	$-0.665400\pi$
$977$	15.7361	−	27.2557i	0.503441	−	0.871986i	0.999992	−	0.00397838i	$-0.00126636\pi$
$978$		0			0
$979$	−39.0517	−	67.6395i	−1.24810	−	2.16177i
$980$		0			0
$981$	15.2812	+	26.4677i	0.487890	+	0.845050i
$982$		0			0
$983$	−20.6180			−0.657613			−0.328807	−	0.944397i	$-0.606646\pi$
$983$	−20.6180			−0.657613			−0.328807	+	0.944397i	$0.606646\pi$
$984$		0			0
$985$	−1.48936	+	2.57964i	−0.0474549	+	0.0821942i
$986$		0			0
$987$	0.854102			0.0271864
$988$		0			0
$989$	−33.8197			−1.07540
$990$		0			0
$991$	−11.4271	+	19.7922i	−0.362992	+	0.628721i	−0.988452	−	0.151536i	$-0.951578\pi$
$991$	−11.4271	+	19.7922i	−0.362992	+	0.628721i	0.625460	+	0.780257i	$0.284912\pi$
$992$		0			0
$993$	6.43769			0.204294
$994$		0			0
$995$	0.461493	+	0.799329i	0.0146303	+	0.0253404i
$996$		0			0
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	0.158352	−	0.987383i	$-0.449382\pi$
$998$		0			0
$999$	4.47214	−	7.74597i	0.141492	−	0.245072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.h.113.2		4
4.3	odd	2		91.2.f.a.22.2	✓	4
12.11	even	2		819.2.o.c.568.1		4
13.3	even	3	inner	1456.2.s.h.1121.2		4
28.3	even	6		637.2.g.c.373.2		4
28.11	odd	6		637.2.g.b.373.2		4
28.19	even	6		637.2.h.f.165.1		4
28.23	odd	6		637.2.h.g.165.1		4
28.27	even	2		637.2.f.c.295.2		4
52.3	odd	6		91.2.f.a.29.2	yes	4
52.7	even	12		1183.2.c.c.337.3		4
52.19	even	12		1183.2.c.c.337.2		4
52.35	odd	6		1183.2.a.g.1.1		2
52.43	odd	6		1183.2.a.c.1.2		2
156.107	even	6		819.2.o.c.757.1		4
364.3	even	6		637.2.h.f.471.1		4
364.55	even	6		637.2.f.c.393.2		4
364.107	odd	6		637.2.g.b.263.2		4
364.139	even	6		8281.2.a.bb.1.1		2
364.159	even	6		637.2.g.c.263.2		4
364.251	even	6		8281.2.a.n.1.2		2
364.263	odd	6		637.2.h.g.471.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.2	✓	4	4.3	odd	2
91.2.f.a.29.2	yes	4	52.3	odd	6
637.2.f.c.295.2		4	28.27	even	2
637.2.f.c.393.2		4	364.55	even	6
637.2.g.b.263.2		4	364.107	odd	6
637.2.g.b.373.2		4	28.11	odd	6
637.2.g.c.263.2		4	364.159	even	6
637.2.g.c.373.2		4	28.3	even	6
637.2.h.f.165.1		4	28.19	even	6
637.2.h.f.471.1		4	364.3	even	6
637.2.h.g.165.1		4	28.23	odd	6
637.2.h.g.471.1		4	364.263	odd	6
819.2.o.c.568.1		4	12.11	even	2
819.2.o.c.757.1		4	156.107	even	6
1183.2.a.c.1.2		2	52.43	odd	6
1183.2.a.g.1.1		2	52.35	odd	6
1183.2.c.c.337.2		4	52.19	even	12
1183.2.c.c.337.3		4	52.7	even	12
1456.2.s.h.113.2		4	1.1	even	1	trivial
1456.2.s.h.1121.2		4	13.3	even	3	inner
8281.2.a.n.1.2		2	364.251	even	6
8281.2.a.bb.1.1		2	364.139	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.330792i) q^{3} +0.381966 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.42705 + 2.47172i) q^{9} +O(q^{10})\)	\(q+(-0.190983 + 0.330792i) q^{3} +0.381966 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.42705 + 2.47172i) q^{9} +(-2.42705 + 4.20378i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(-0.0729490 + 0.126351i) q^{15} +(-3.73607 - 6.47106i) q^{17} +(2.42705 + 4.20378i) q^{19} -0.381966 q^{21} +(2.23607 - 3.87298i) q^{23} -4.85410 q^{25} -2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} -8.70820 q^{31} +(-0.927051 - 1.60570i) q^{33} +(0.190983 + 0.330792i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-0.381966 - 1.32317i) q^{39} +(-2.61803 + 4.53457i) q^{41} +(-3.78115 - 6.54915i) q^{43} +(0.545085 + 0.944115i) q^{45} -2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} +2.85410 q^{51} +8.23607 q^{53} +(-0.927051 + 1.60570i) q^{55} -1.85410 q^{57} +(1.11803 + 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-1.42705 + 2.47172i) q^{63} +(-0.954915 + 0.992377i) q^{65} +(0.354102 - 0.613323i) q^{67} +(0.854102 + 1.47935i) q^{69} +(4.09017 + 7.08438i) q^{71} -2.00000 q^{73} +(0.927051 - 1.60570i) q^{75} -4.85410 q^{77} -4.00000 q^{79} +(-3.85410 + 6.67550i) q^{81} +6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(0.781153 + 1.35300i) q^{87} +(-8.04508 + 13.9345i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(1.66312 - 2.88061i) q^{93} +(0.927051 + 1.60570i) q^{95} +(-6.07295 - 10.5187i) q^{97} -13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9	\( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} - 3 q^{11} - 10 q^{13} - 7 q^{15} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 6 q^{25} - 3 q^{29} - 8 q^{31} + 3 q^{33} + 3 q^{35} - 8 q^{37} - 6 q^{39} - 6 q^{41} + 5 q^{43} - 9 q^{45} - 2 q^{49} - 2 q^{51} + 24 q^{53} + 3 q^{55} + 6 q^{57} + 12 q^{61} + q^{63} - 15 q^{65} - 12 q^{67} - 10 q^{69} - 6 q^{71} - 8 q^{73} - 3 q^{75} - 6 q^{77} - 16 q^{79} - 2 q^{81} + q^{85} - 17 q^{87} - 21 q^{89} - 14 q^{91} - 9 q^{93} - 3 q^{95} - 31 q^{97} - 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 + 6 * q^5 + 2 * q^7 - q^9 - 3 * q^11 - 10 * q^13 - 7 * q^15 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 6 * q^25 - 3 * q^29 - 8 * q^31 + 3 * q^33 + 3 * q^35 - 8 * q^37 - 6 * q^39 - 6 * q^41 + 5 * q^43 - 9 * q^45 - 2 * q^49 - 2 * q^51 + 24 * q^53 + 3 * q^55 + 6 * q^57 + 12 * q^61 + q^63 - 15 * q^65 - 12 * q^67 - 10 * q^69 - 6 * q^71 - 8 * q^73 - 3 * q^75 - 6 * q^77 - 16 * q^79 - 2 * q^81 + q^85 - 17 * q^87 - 21 * q^89 - 14 * q^91 - 9 * q^93 - 3 * q^95 - 31 * q^97 - 42 * q^99

Introduction

L-functions

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Database

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