LMFDB - Embedded newform 1024.2.g.d.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, 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:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			385.1
Root			$-0.793353 - 0.608761i$ of defining polynomial
Character	$\chi$	$=$	1024.385
Dual form			1024.2.g.d.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70868 + 1.12197i) q^{3} +(-0.151613 + 0.366025i) q^{5} +(3.06528 + 3.06528i) q^{7} +(3.95680 - 3.95680i) q^{9} +O(q^{10})$	\(q+(-2.70868 + 1.12197i) q^{3} +(-0.151613 + 0.366025i) q^{5} +(3.06528 + 3.06528i) q^{7} +(3.95680 - 3.95680i) q^{9} +(3.66515 + 1.51815i) q^{11} +(-0.780239 - 1.88366i) q^{13} -1.16155i q^{15} -4.54587i q^{17} +(-0.221474 - 0.534684i) q^{19} +(-11.7420 - 4.86370i) q^{21} +(4.41794 - 4.41794i) q^{23} +(3.42455 + 3.42455i) q^{25} +(-2.91236 + 7.03106i) q^{27} +(4.74737 - 1.96642i) q^{29} +0.0539984 q^{31} -11.6310 q^{33} +(-1.58671 + 0.657235i) q^{35} +(0.330749 - 0.798499i) q^{37} +(4.22683 + 4.22683i) q^{39} +(0.621063 - 0.621063i) q^{41} +(-2.06923 - 0.857104i) q^{43} +(0.848387 + 2.04819i) q^{45} +9.44387i q^{47} +11.7919i q^{49} +(5.10033 + 12.3133i) q^{51} +(10.0582 + 4.16622i) q^{53} +(-1.11137 + 1.11137i) q^{55} +(1.19980 + 1.19980i) q^{57} +(-2.97354 + 7.17877i) q^{59} +(9.72911 - 4.02993i) q^{61} +24.2574 q^{63} +0.807763 q^{65} +(-7.53875 + 3.12265i) q^{67} +(-7.00997 + 16.9236i) q^{69} +(-2.99152 - 2.99152i) q^{71} +(-2.91724 + 2.91724i) q^{73} +(-13.1182 - 5.43375i) q^{75} +(6.58114 + 15.8883i) q^{77} -5.74836i q^{79} -5.52520i q^{81} +(1.36905 + 3.30517i) q^{83} +(1.66390 + 0.689211i) q^{85} +(-10.6528 + 10.6528i) q^{87} +(2.38134 + 2.38134i) q^{89} +(3.38231 - 8.16561i) q^{91} +(-0.146264 + 0.0605847i) q^{93} +0.229286 q^{95} -13.2672 q^{97} +(20.5093 - 8.49522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^5 + 16 * q^9	$ 16 q - 8 q^{5} + 16 q^{9} + 24 q^{13} - 48 q^{21} + 32 q^{25} - 8 q^{29} - 80 q^{33} + 8 q^{37} + 16 q^{41} + 8 q^{45} + 40 q^{53} + 16 q^{57} + 8 q^{61} - 32 q^{65} - 32 q^{73} + 32 q^{77} - 32 q^{85} - 32 q^{89} + 48 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 16 * q^9 + 24 * q^13 - 48 * q^21 + 32 * q^25 - 8 * q^29 - 80 * q^33 + 8 * q^37 + 16 * q^41 + 8 * q^45 + 40 * q^53 + 16 * q^57 + 8 * q^61 - 32 * q^65 - 32 * q^73 + 32 * q^77 - 32 * q^85 - 32 * q^89 + 48 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.70868	+	1.12197i	−1.56386	+	0.647770i	−0.985754	−	0.168194i	$-0.946206\pi$
$3$	−2.70868	+	1.12197i	−1.56386	+	0.647770i	−0.578102	+	0.815965i	$0.696206\pi$
$4$		0			0
$5$	−0.151613	+	0.366025i	−0.0678033	+	0.163692i	−0.954149	−	0.299333i	$-0.903236\pi$
$5$	−0.151613	+	0.366025i	−0.0678033	+	0.163692i	0.886345	+	0.463025i	$0.153236\pi$
$6$		0			0
$7$	3.06528	+	3.06528i	1.15857	+	1.15857i	0.984784	+	0.173784i	$0.0555994\pi$
$7$	3.06528	+	3.06528i	1.15857	+	1.15857i	0.173784	+	0.984784i	$0.444401\pi$
$8$		0			0
$9$	3.95680	−	3.95680i	1.31893	−	1.31893i
$10$		0			0
$11$	3.66515	+	1.51815i	1.10508	+	0.457741i	0.859242	−	0.511569i	$-0.170936\pi$
$11$	3.66515	+	1.51815i	1.10508	+	0.457741i	0.245842	+	0.969310i	$0.420936\pi$
$12$		0			0
$13$	−0.780239	−	1.88366i	−0.216399	−	0.522434i	0.777983	−	0.628286i	$-0.216243\pi$
$13$	−0.780239	−	1.88366i	−0.216399	−	0.522434i	−0.994382	+	0.105852i	$0.966243\pi$
$14$		0			0
$15$		−	1.16155i		−	0.299911i
$16$		0			0
$17$		−	4.54587i		−	1.10253i	−0.834329	−	0.551267i	$-0.814144\pi$
$17$		−	4.54587i		−	1.10253i	0.834329	−	0.551267i	$-0.185856\pi$
$18$		0			0
$19$	−0.221474	−	0.534684i	−0.0508095	−	0.122665i	0.896437	−	0.443172i	$-0.146147\pi$
$19$	−0.221474	−	0.534684i	−0.0508095	−	0.122665i	−0.947246	+	0.320507i	$0.896147\pi$
$20$		0			0
$21$	−11.7420	−	4.86370i	−2.56232	−	1.06135i
$22$		0			0
$23$	4.41794	−	4.41794i	0.921203	−	0.921203i	−0.0759114	−	0.997115i	$-0.524187\pi$
$23$	4.41794	−	4.41794i	0.921203	−	0.921203i	0.997115	+	0.0759114i	$0.0241866\pi$
$24$		0			0
$25$	3.42455	+	3.42455i	0.684909	+	0.684909i
$26$		0			0
$27$	−2.91236	+	7.03106i	−0.560484	+	1.35313i
$28$		0			0
$29$	4.74737	−	1.96642i	0.881564	−	0.365156i	0.104461	−	0.994529i	$-0.466688\pi$
$29$	4.74737	−	1.96642i	0.881564	−	0.365156i	0.777103	+	0.629373i	$0.216688\pi$
$30$		0			0
$31$	0.0539984			0.00969841			0.00484920	−	0.999988i	$-0.498456\pi$
$31$	0.0539984			0.00969841			0.00484920	+	0.999988i	$0.498456\pi$
$32$		0			0
$33$	−11.6310			−2.02470
$34$		0			0
$35$	−1.58671	+	0.657235i	−0.268202	+	0.111093i
$36$		0			0
$37$	0.330749	−	0.798499i	0.0543748	−	0.131272i	−0.894358	−	0.447353i	$-0.852367\pi$
$37$	0.330749	−	0.798499i	0.0543748	−	0.131272i	0.948732	+	0.316080i	$0.102367\pi$
$38$		0			0
$39$	4.22683	+	4.22683i	0.676835	+	0.676835i
$40$		0			0
$41$	0.621063	−	0.621063i	0.0969937	−	0.0969937i	−0.656945	−	0.753939i	$-0.728152\pi$
$41$	0.621063	−	0.621063i	0.0969937	−	0.0969937i	0.753939	+	0.656945i	$0.228152\pi$
$42$		0			0
$43$	−2.06923	−	0.857104i	−0.315555	−	0.130707i	0.219284	−	0.975661i	$-0.429628\pi$
$43$	−2.06923	−	0.857104i	−0.315555	−	0.130707i	−0.534839	+	0.844954i	$0.679628\pi$
$44$		0			0
$45$	0.848387	+	2.04819i	0.126470	+	0.305326i
$46$		0			0
$47$			9.44387i			1.37753i	0.724984	+	0.688765i	$0.241847\pi$
$47$			9.44387i			1.37753i	−0.724984	+	0.688765i	$0.758153\pi$
$48$		0			0
$49$			11.7919i			1.68456i
$50$		0			0
$51$	5.10033	+	12.3133i	0.714189	+	1.72420i
$52$		0			0
$53$	10.0582	+	4.16622i	1.38159	+	0.572275i	0.944907	−	0.327339i	$-0.106152\pi$
$53$	10.0582	+	4.16622i	1.38159	+	0.572275i	0.436687	+	0.899614i	$0.356152\pi$
$54$		0			0
$55$	−1.11137	+	1.11137i	−0.149857	+	0.149857i
$56$		0			0
$57$	1.19980	+	1.19980i	0.158918	+	0.158918i
$58$		0			0
$59$	−2.97354	+	7.17877i	−0.387123	+	0.934596i	0.603424	+	0.797420i	$0.293803\pi$
$59$	−2.97354	+	7.17877i	−0.387123	+	0.934596i	−0.990547	+	0.137176i	$0.956197\pi$
$60$		0			0
$61$	9.72911	−	4.02993i	1.24568	−	0.515979i	0.340198	−	0.940354i	$-0.389506\pi$
$61$	9.72911	−	4.02993i	1.24568	−	0.515979i	0.905487	+	0.424375i	$0.139506\pi$
$62$		0			0
$63$	24.2574			3.05614
$64$		0			0
$65$	0.807763			0.100191
$66$		0			0
$67$	−7.53875	+	3.12265i	−0.921004	+	0.381493i	−0.792259	−	0.610185i	$-0.791095\pi$
$67$	−7.53875	+	3.12265i	−0.921004	+	0.381493i	−0.128746	+	0.991678i	$0.541095\pi$
$68$		0			0
$69$	−7.00997	+	16.9236i	−0.843901	+	2.03736i
$70$		0			0
$71$	−2.99152	−	2.99152i	−0.355028	−	0.355028i	0.506948	−	0.861976i	$-0.330773\pi$
$71$	−2.99152	−	2.99152i	−0.355028	−	0.355028i	−0.861976	+	0.506948i	$0.830773\pi$
$72$		0			0
$73$	−2.91724	+	2.91724i	−0.341437	+	0.341437i	−0.856907	−	0.515470i	$-0.827617\pi$
$73$	−2.91724	+	2.91724i	−0.341437	+	0.341437i	0.515470	+	0.856907i	$0.327617\pi$
$74$		0			0
$75$	−13.1182	−	5.43375i	−1.51476	−	0.627435i
$76$		0			0
$77$	6.58114	+	15.8883i	0.749991	+	1.81064i
$78$		0			0
$79$		−	5.74836i		−	0.646741i	−0.946272	−	0.323370i	$-0.895184\pi$
$79$		−	5.74836i		−	0.646741i	0.946272	−	0.323370i	$-0.104816\pi$
$80$		0			0
$81$		−	5.52520i		−	0.613911i
$82$		0			0
$83$	1.36905	+	3.30517i	0.150272	+	0.362790i	0.981033	−	0.193840i	$-0.0620942\pi$
$83$	1.36905	+	3.30517i	0.150272	+	0.362790i	−0.830761	+	0.556630i	$0.812094\pi$
$84$		0			0
$85$	1.66390	+	0.689211i	0.180476	+	0.0747554i
$86$		0			0
$87$	−10.6528	+	10.6528i	−1.14210	+	1.14210i
$88$		0			0
$89$	2.38134	+	2.38134i	0.252422	+	0.252422i	0.821963	−	0.569541i	$-0.192879\pi$
$89$	2.38134	+	2.38134i	0.252422	+	0.252422i	−0.569541	+	0.821963i	$0.692879\pi$
$90$		0			0
$91$	3.38231	−	8.16561i	0.354562	−	0.855989i
$92$		0			0
$93$	−0.146264	+	0.0605847i	−0.0151669	+	0.00628234i
$94$		0			0
$95$	0.229286			0.0235243
$96$		0			0
$97$	−13.2672			−1.34708			−0.673541	−	0.739150i	$-0.735228\pi$
$97$	−13.2672			−1.34708			−0.673541	+	0.739150i	$0.735228\pi$
$98$		0			0
$99$	20.5093	−	8.49522i	2.06126	−	0.853801i
$100$		0			0
$101$	5.65855	−	13.6610i	0.563047	−	1.35932i	−0.344271	−	0.938870i	$-0.611874\pi$
$101$	5.65855	−	13.6610i	0.563047	−	1.35932i	0.907318	−	0.420446i	$-0.138126\pi$
$102$		0			0
$103$	−4.66978	−	4.66978i	−0.460127	−	0.460127i	0.438570	−	0.898697i	$-0.355485\pi$
$103$	−4.66978	−	4.66978i	−0.460127	−	0.460127i	−0.898697	+	0.438570i	$0.855485\pi$
$104$		0			0
$105$	3.56048	−	3.56048i	0.347467	−	0.347467i
$106$		0			0
$107$	7.63093	+	3.16083i	0.737710	+	0.305569i	0.719716	−	0.694269i	$-0.244272\pi$
$107$	7.63093	+	3.16083i	0.737710	+	0.305569i	0.0179938	+	0.999838i	$0.494272\pi$
$108$		0			0
$109$	1.01996	+	2.46240i	0.0976945	+	0.235855i	0.965169	−	0.261625i	$-0.0842585\pi$
$109$	1.01996	+	2.46240i	0.0976945	+	0.235855i	−0.867475	+	0.497481i	$0.834259\pi$
$110$		0			0
$111$			2.53397i			0.240514i
$112$		0			0
$113$			4.96472i			0.467042i	0.972352	+	0.233521i	$0.0750247\pi$
$113$			4.96472i			0.467042i	−0.972352	+	0.233521i	$0.924975\pi$
$114$		0			0
$115$	0.947262	+	2.28689i	0.0883326	+	0.213254i
$116$		0			0
$117$	−10.5405	−	4.36603i	−0.974471	−	0.403639i
$118$		0			0
$119$	13.9344	−	13.9344i	1.27736	−	1.27736i
$120$		0			0
$121$	3.35034	+	3.35034i	0.304577	+	0.304577i
$122$		0			0
$123$	−0.985444	+	2.37907i	−0.0888545	+	0.214514i
$124$		0			0
$125$	−3.60280	+	1.49233i	−0.322244	+	0.133478i
$126$		0			0
$127$	−15.4530			−1.37123			−0.685614	−	0.727965i	$-0.740466\pi$
$127$	−15.4530			−1.37123			−0.685614	+	0.727965i	$0.740466\pi$
$128$		0			0
$129$	6.56653			0.578151
$130$		0			0
$131$	−9.66535	+	4.00352i	−0.844465	+	0.349789i	−0.762613	−	0.646855i	$-0.776084\pi$
$131$	−9.66535	+	4.00352i	−0.844465	+	0.349789i	−0.0818527	+	0.996644i	$0.526084\pi$
$132$		0			0
$133$	0.960080	−	2.31784i	0.0832495	−	0.200982i
$134$		0			0
$135$	−2.13200	−	2.13200i	−0.183493	−	0.183493i
$136$		0			0
$137$	−11.4887	+	11.4887i	−0.981544	+	0.981544i	−0.999833	−	0.0182885i	$-0.994178\pi$
$137$	−11.4887	+	11.4887i	−0.981544	+	0.981544i	0.0182885	+	0.999833i	$0.494178\pi$
$138$		0			0
$139$	6.92630	+	2.86897i	0.587481	+	0.243343i	0.656567	−	0.754268i	$-0.272008\pi$
$139$	6.92630	+	2.86897i	0.587481	+	0.243343i	−0.0690854	+	0.997611i	$0.522008\pi$
$140$		0			0
$141$	−10.5958	−	25.5804i	−0.892323	−	2.15426i
$142$		0			0
$143$		−	8.08843i		−	0.676388i
$144$		0			0
$145$			2.03579i			0.169063i
$146$		0			0
$147$	−13.2302	−	31.9405i	−1.09121	−	2.63441i
$148$		0			0
$149$	5.84839	+	2.42248i	0.479119	+	0.198457i	0.609154	−	0.793052i	$-0.291509\pi$
$149$	5.84839	+	2.42248i	0.479119	+	0.198457i	−0.130035	+	0.991509i	$0.541509\pi$
$150$		0			0
$151$	7.57293	−	7.57293i	0.616276	−	0.616276i	−0.328298	−	0.944574i	$-0.606475\pi$
$151$	7.57293	−	7.57293i	0.616276	−	0.616276i	0.944574	+	0.328298i	$0.106475\pi$
$152$		0			0
$153$	−17.9871	−	17.9871i	−1.45417	−	1.45417i
$154$		0			0
$155$	−0.00818685	+	0.0197648i	−0.000657583	+	0.00158755i
$156$		0			0
$157$	−7.53295	+	3.12025i	−0.601195	+	0.249023i	−0.662459	−	0.749098i	$-0.730487\pi$
$157$	−7.53295	+	3.12025i	−0.601195	+	0.249023i	0.0612635	+	0.998122i	$0.480487\pi$
$158$		0			0
$159$	−31.9187			−2.53132
$160$		0			0
$161$	27.0844			2.13455
$162$		0			0
$163$	−5.50617	+	2.28073i	−0.431276	+	0.178640i	−0.587752	−	0.809041i	$-0.699987\pi$
$163$	−5.50617	+	2.28073i	−0.431276	+	0.178640i	0.156475	+	0.987682i	$0.449987\pi$
$164$		0			0
$165$	1.76341	−	4.25725i	0.137281	−	0.331427i
$166$		0			0
$167$	14.4145	+	14.4145i	1.11543	+	1.11543i	0.992404	+	0.123021i	$0.0392583\pi$
$167$	14.4145	+	14.4145i	1.11543	+	1.11543i	0.123021	+	0.992404i	$0.460742\pi$
$168$		0			0
$169$	6.25297	−	6.25297i	0.480998	−	0.480998i
$170$		0			0
$171$	−2.99196	−	1.23931i	−0.228801	−	0.0947725i
$172$		0			0
$173$	−6.63397	−	16.0158i	−0.504372	−	1.21766i	−0.947081	−	0.320996i	$-0.895982\pi$
$173$	−6.63397	−	16.0158i	−0.504372	−	1.21766i	0.442709	−	0.896665i	$-0.354018\pi$
$174$		0			0
$175$			20.9944i			1.58703i
$176$		0			0
$177$		−	22.7812i		−	1.71234i
$178$		0			0
$179$	3.59997	+	8.69109i	0.269074	+	0.649602i	0.999440	−	0.0334535i	$-0.0106506\pi$
$179$	3.59997	+	8.69109i	0.269074	+	0.649602i	−0.730366	+	0.683056i	$0.760651\pi$
$180$		0			0
$181$	0.666847	+	0.276217i	0.0495663	+	0.0205310i	0.407329	−	0.913282i	$-0.366460\pi$
$181$	0.666847	+	0.276217i	0.0495663	+	0.0205310i	−0.357763	+	0.933813i	$0.616460\pi$
$182$		0			0
$183$	−21.8316	+	21.8316i	−1.61383	+	1.61383i
$184$		0			0
$185$	0.242125	+	0.242125i	0.0178014	+	0.0178014i
$186$		0			0
$187$	6.90133	−	16.6613i	0.504675	−	1.21839i
$188$		0			0
$189$	−30.4794	+	12.6250i	−2.21705	+	0.918332i
$190$		0			0
$191$	10.1746			0.736209			0.368105	−	0.929784i	$-0.380007\pi$
$191$	10.1746			0.736209			0.368105	+	0.929784i	$0.380007\pi$
$192$		0			0
$193$	11.7515			0.845889			0.422945	−	0.906156i	$-0.360996\pi$
$193$	11.7515			0.845889			0.422945	+	0.906156i	$0.360996\pi$
$194$		0			0
$195$	−2.18797	+	0.906286i	−0.156684	+	0.0649005i
$196$		0			0
$197$	6.00875	−	14.5064i	0.428106	−	1.03354i	−0.551782	−	0.833988i	$-0.686052\pi$
$197$	6.00875	−	14.5064i	0.428106	−	1.03354i	0.979888	−	0.199550i	$-0.0639480\pi$
$198$		0			0
$199$	2.32691	+	2.32691i	0.164951	+	0.164951i	0.784756	−	0.619805i	$-0.212788\pi$
$199$	2.32691	+	2.32691i	0.164951	+	0.164951i	−0.619805	+	0.784756i	$0.712788\pi$
$200$		0			0
$201$	16.9165	−	16.9165i	1.19320	−	1.19320i
$202$		0			0
$203$	20.5797	+	8.52437i	1.44441	+	0.598294i
$204$		0			0
$205$	0.133164	+	0.321486i	0.00930056	+	0.0224535i
$206$		0			0
$207$		−	34.9617i		−	2.43001i
$208$		0			0
$209$		−	2.29593i		−	0.158813i
$210$		0			0
$211$	−7.00267	−	16.9059i	−0.482083	−	1.16385i	−0.958618	−	0.284696i	$-0.908107\pi$
$211$	−7.00267	−	16.9059i	−0.482083	−	1.16385i	0.476534	−	0.879156i	$-0.341893\pi$
$212$		0			0
$213$	11.4595	+	4.74666i	0.785189	+	0.325236i
$214$		0			0
$215$	0.627444	−	0.627444i	0.0427913	−	0.0427913i
$216$		0			0
$217$	0.165520	+	0.165520i	0.0112363	+	0.0112363i
$218$		0			0
$219$	4.62880	−	11.1749i	0.312786	−	0.755131i
$220$		0			0
$221$	−8.56288	+	3.54686i	−0.576002	+	0.238588i
$222$		0			0
$223$	−21.6471			−1.44959			−0.724797	−	0.688962i	$-0.758066\pi$
$223$	−21.6471			−1.44959			−0.724797	+	0.688962i	$0.758066\pi$
$224$		0			0
$225$	27.1005			1.80670
$226$		0			0
$227$	8.86440	−	3.67176i	0.588351	−	0.243703i	−0.0685901	−	0.997645i	$-0.521850\pi$
$227$	8.86440	−	3.67176i	0.588351	−	0.243703i	0.656941	+	0.753942i	$0.271850\pi$
$228$		0			0
$229$	−11.0093	+	26.5787i	−0.727513	+	1.75637i	−0.0768003	+	0.997046i	$0.524470\pi$
$229$	−11.0093	+	26.5787i	−0.727513	+	1.75637i	−0.650712	+	0.759324i	$0.725530\pi$
$230$		0			0
$231$	−35.6524	−	35.6524i	−2.34575	−	2.34575i
$232$		0			0
$233$	−18.0722	+	18.0722i	−1.18395	+	1.18395i	−0.205239	+	0.978712i	$0.565797\pi$
$233$	−18.0722	+	18.0722i	−1.18395	+	1.18395i	−0.978712	+	0.205239i	$0.934203\pi$
$234$		0			0
$235$	−3.45670	−	1.43181i	−0.225490	−	0.0934011i
$236$		0			0
$237$	6.44949	+	15.5704i	0.418939	+	1.01141i
$238$		0			0
$239$		−	24.0765i		−	1.55738i	−0.627409	−	0.778690i	$-0.715884\pi$
$239$		−	24.0765i		−	1.55738i	0.627409	−	0.778690i	$-0.284116\pi$
$240$		0			0
$241$		−	10.3823i		−	0.668785i	−0.942434	−	0.334393i	$-0.891469\pi$
$241$		−	10.3823i		−	0.668785i	0.942434	−	0.334393i	$-0.108531\pi$
$242$		0			0
$243$	−2.53797	−	6.12719i	−0.162811	−	0.393060i
$244$		0			0
$245$	−4.31614	−	1.78780i	−0.275748	−	0.114219i
$246$		0			0
$247$	−0.834363	+	0.834363i	−0.0530893	+	0.0530893i
$248$		0			0
$249$	−7.41662	−	7.41662i	−0.470009	−	0.470009i
$250$		0			0
$251$	9.54203	−	23.0365i	0.602288	−	1.45405i	−0.268933	−	0.963159i	$-0.586671\pi$
$251$	9.54203	−	23.0365i	0.602288	−	1.45405i	0.871221	−	0.490892i	$-0.163329\pi$
$252$		0			0
$253$	22.8995	−	9.48528i	1.43968	−	0.596335i
$254$		0			0
$255$	−5.28025			−0.330662
$256$		0			0
$257$	−18.7121			−1.16723			−0.583613	−	0.812032i	$-0.698362\pi$
$257$	−18.7121			−1.16723			−0.583613	+	0.812032i	$0.698362\pi$
$258$		0			0
$259$	3.46146	−	1.43379i	0.215085	−	0.0890911i
$260$		0			0
$261$	11.0036	−	26.5651i	0.681107	−	1.64434i
$262$		0			0
$263$	0.884682	+	0.884682i	0.0545518	+	0.0545518i	0.733856	−	0.679305i	$-0.237718\pi$
$263$	0.884682	+	0.884682i	0.0545518	+	0.0545518i	−0.679305	+	0.733856i	$0.737718\pi$
$264$		0			0
$265$	−3.04989	+	3.04989i	−0.187353	+	0.187353i
$266$		0			0
$267$	−9.12208	−	3.77849i	−0.558262	−	0.231240i
$268$		0			0
$269$	5.44363	+	13.1421i	0.331904	+	0.801286i	0.998441	+	0.0558149i	$0.0177757\pi$
$269$	5.44363	+	13.1421i	0.331904	+	0.801286i	−0.666537	+	0.745472i	$0.732224\pi$
$270$		0			0
$271$			17.5598i			1.06668i	0.845900	+	0.533341i	$0.179064\pi$
$271$			17.5598i			1.06668i	−0.845900	+	0.533341i	$0.820936\pi$
$272$		0			0
$273$			25.9129i			1.56832i
$274$		0			0
$275$	7.35248	+	17.7505i	0.443371	+	1.07039i
$276$		0			0
$277$	24.3747	+	10.0964i	1.46454	+	0.606631i	0.965606	−	0.260011i	$-0.0837261\pi$
$277$	24.3747	+	10.0964i	1.46454	+	0.606631i	0.498931	+	0.866642i	$0.333726\pi$
$278$		0			0
$279$	0.213661	−	0.213661i	0.0127915	−	0.0127915i
$280$		0			0
$281$	16.9764	+	16.9764i	1.01273	+	1.01273i	0.999918	+	0.0128071i	$0.00407675\pi$
$281$	16.9764	+	16.9764i	1.01273	+	1.01273i	0.0128071	+	0.999918i	$0.495923\pi$
$282$		0			0
$283$	−1.34744	+	3.25301i	−0.0800972	+	0.193372i	−0.958855	−	0.283896i	$-0.908373\pi$
$283$	−1.34744	+	3.25301i	−0.0800972	+	0.193372i	0.878758	+	0.477268i	$0.158373\pi$
$284$		0			0
$285$	−0.621063	+	0.257253i	−0.0367886	+	0.0152383i
$286$		0			0
$287$	3.80746			0.224747
$288$		0			0
$289$	−3.66490			−0.215582
$290$		0			0
$291$	35.9366	−	14.8854i	2.10664	−	0.872600i
$292$		0			0
$293$	1.19545	−	2.88607i	0.0698388	−	0.168606i	−0.885106	−	0.465390i	$-0.845914\pi$
$293$	1.19545	−	2.88607i	0.0698388	−	0.168606i	0.954945	+	0.296784i	$0.0959141\pi$
$294$		0			0
$295$	−2.17679	−	2.17679i	−0.126737	−	0.126737i
$296$		0			0
$297$	−21.3485	+	21.3485i	−1.23876	+	1.23876i
$298$		0			0
$299$	−11.7689	−	4.87486i	−0.680616	−	0.281920i
$300$		0			0
$301$	−3.71552	−	8.97005i	−0.214159	−	0.517025i
$302$		0			0
$303$			43.3519i			2.49050i
$304$		0			0
$305$			4.17209i			0.238893i
$306$		0			0
$307$	−3.26318	−	7.87800i	−0.186239	−	0.449621i	0.802991	−	0.595992i	$-0.203241\pi$
$307$	−3.26318	−	7.87800i	−0.186239	−	0.449621i	−0.989230	+	0.146370i	$0.953241\pi$
$308$		0			0
$309$	17.8883	+	7.40957i	1.01763	+	0.421516i
$310$		0			0
$311$	3.38586	−	3.38586i	0.191995	−	0.191995i	−0.604563	−	0.796557i	$-0.706652\pi$
$311$	3.38586	−	3.38586i	0.191995	−	0.191995i	0.796557	+	0.604563i	$0.206652\pi$
$312$		0			0
$313$	−21.0698	−	21.0698i	−1.19094	−	1.19094i	−0.976805	−	0.214132i	$-0.931308\pi$
$313$	−21.0698	−	21.0698i	−1.19094	−	1.19094i	−0.214132	−	0.976805i	$-0.568692\pi$
$314$		0			0
$315$	−3.67773	+	8.87882i	−0.207216	+	0.500265i
$316$		0			0
$317$	−26.0404	+	10.7863i	−1.46258	+	0.605818i	−0.965152	−	0.261690i	$-0.915720\pi$
$317$	−26.0404	+	10.7863i	−1.46258	+	0.605818i	−0.497423	+	0.867508i	$0.665720\pi$
$318$		0			0
$319$	20.3851			1.14135
$320$		0			0
$321$	−24.2161			−1.35161
$322$		0			0
$323$	−2.43060	+	1.00679i	−0.135242	+	0.0560192i
$324$		0			0
$325$	3.77873	−	9.12266i	0.209606	−	0.506034i
$326$		0			0
$327$	−5.52549	−	5.52549i	−0.305560	−	0.305560i
$328$		0			0
$329$	−28.9481	+	28.9481i	−1.59596	+	1.59596i
$330$		0			0
$331$	−28.9852	−	12.0060i	−1.59317	−	0.659912i	−0.602740	−	0.797938i	$-0.705924\pi$
$331$	−28.9852	−	12.0060i	−1.59317	−	0.659912i	−0.990429	+	0.138026i	$0.955924\pi$
$332$		0			0
$333$	−1.85079	−	4.46821i	−0.101423	−	0.244856i
$334$		0			0
$335$		−	3.23281i		−	0.176627i
$336$		0			0
$337$			35.6957i			1.94447i	0.234010	+	0.972234i	$0.424815\pi$
$337$			35.6957i			1.94447i	−0.234010	+	0.972234i	$0.575185\pi$
$338$		0			0
$339$	−5.57028	−	13.4478i	−0.302536	−	0.730386i
$340$		0			0
$341$	0.197912	+	0.0819780i	0.0107176	+	0.00443935i
$342$		0			0
$343$	−14.6885	+	14.6885i	−0.793107	+	0.793107i
$344$		0			0
$345$	−5.13165	−	5.13165i	−0.276279	−	0.276279i
$346$		0			0
$347$	−10.8129	+	26.1047i	−0.580468	+	1.40137i	0.311921	+	0.950108i	$0.399027\pi$
$347$	−10.8129	+	26.1047i	−0.580468	+	1.40137i	−0.892389	+	0.451266i	$0.850973\pi$
$348$		0			0
$349$	12.0652	−	4.99757i	0.645836	−	0.267514i	−0.0356289	−	0.999365i	$-0.511343\pi$
$349$	12.0652	−	4.99757i	0.645836	−	0.267514i	0.681464	+	0.731851i	$0.261343\pi$
$350$		0			0
$351$	15.5165			0.828209
$352$		0			0
$353$	16.4488			0.875479			0.437740	−	0.899102i	$-0.355779\pi$
$353$	16.4488			0.875479			0.437740	+	0.899102i	$0.355779\pi$
$354$		0			0
$355$	1.54852	−	0.641420i	0.0821871	−	0.0340430i
$356$		0			0
$357$	−22.1097	+	53.3776i	−1.17017	+	2.82504i
$358$		0			0
$359$	3.92378	+	3.92378i	0.207089	+	0.207089i	0.803029	−	0.595940i	$-0.203220\pi$
$359$	3.92378	+	3.92378i	0.207089	+	0.207089i	−0.595940	+	0.803029i	$0.703220\pi$
$360$		0			0
$361$	13.1982	−	13.1982i	0.694642	−	0.694642i
$362$		0			0
$363$	−12.8340	−	5.31601i	−0.673610	−	0.279018i
$364$		0			0
$365$	−0.625493	−	1.51007i	−0.0327398	−	0.0790409i
$366$		0			0
$367$		−	18.9285i		−	0.988061i	−0.869444	−	0.494031i	$-0.835523\pi$
$367$		−	18.9285i		−	0.988061i	0.869444	−	0.494031i	$-0.164477\pi$
$368$		0			0
$369$		−	4.91484i		−	0.255856i
$370$		0			0
$371$	18.0604	+	43.6017i	0.937651	+	2.26369i
$372$		0			0
$373$	−14.2960	−	5.92159i	−0.740218	−	0.306608i	−0.0194748	−	0.999810i	$-0.506199\pi$
$373$	−14.2960	−	5.92159i	−0.740218	−	0.306608i	−0.720743	+	0.693202i	$0.756199\pi$
$374$		0			0
$375$	8.08448	−	8.08448i	0.417481	−	0.417481i
$376$		0			0
$377$	−7.40816	−	7.40816i	−0.381540	−	0.381540i
$378$		0			0
$379$	−8.23798	+	19.8882i	−0.423157	+	1.02159i	0.558254	+	0.829670i	$0.311471\pi$
$379$	−8.23798	+	19.8882i	−0.423157	+	1.02159i	−0.981411	+	0.191920i	$0.938529\pi$
$380$		0			0
$381$	41.8571	−	17.3378i	2.14440	−	0.888241i
$382$		0			0
$383$	14.8953			0.761113			0.380556	−	0.924758i	$-0.375732\pi$
$383$	14.8953			0.761113			0.380556	+	0.924758i	$0.375732\pi$
$384$		0			0
$385$	−6.81330			−0.347238
$386$		0			0
$387$	−11.5789	+	4.79614i	−0.588589	+	0.243802i
$388$		0			0
$389$	7.61723	−	18.3896i	0.386209	−	0.932390i	−0.604527	−	0.796585i	$-0.706638\pi$
$389$	7.61723	−	18.3896i	0.386209	−	0.932390i	0.990736	−	0.135805i	$-0.0433622\pi$
$390$		0			0
$391$	−20.0833	−	20.0833i	−1.01566	−	1.01566i
$392$		0			0
$393$	21.6885	−	21.6885i	1.09404	−	1.09404i
$394$		0			0
$395$	2.10404	+	0.871524i	0.105866	+	0.0438511i
$396$		0			0
$397$	6.23072	+	15.0423i	0.312711	+	0.754951i	0.999603	+	0.0281913i	$0.00897477\pi$
$397$	6.23072	+	15.0423i	0.312711	+	0.754951i	−0.686891	+	0.726760i	$0.741025\pi$
$398$		0			0
$399$			7.35546i			0.368233i
$400$		0			0
$401$		−	26.1297i		−	1.30485i	−0.757852	−	0.652427i	$-0.773751\pi$
$401$		−	26.1297i		−	1.30485i	0.757852	−	0.652427i	$-0.226249\pi$
$402$		0			0
$403$	−0.0421317	−	0.101715i	−0.00209873	−	0.00506678i
$404$		0			0
$405$	2.02236	+	0.837691i	0.100492	+	0.0416252i
$406$		0			0
$407$	2.42449	−	2.42449i	0.120177	−	0.120177i
$408$		0			0
$409$	15.4495	+	15.4495i	0.763928	+	0.763928i	0.977030	−	0.213102i	$-0.0683566\pi$
$409$	15.4495	+	15.4495i	0.763928	+	0.763928i	−0.213102	+	0.977030i	$0.568357\pi$
$410$		0			0
$411$	18.2292	−	44.0091i	0.899179	−	2.17081i
$412$		0			0
$413$	−31.1197	+	12.8902i	−1.53130	+	0.634286i
$414$		0			0
$415$	−1.41734			−0.0695746
$416$		0			0
$417$	−21.9800			−1.07637
$418$		0			0
$419$	−10.2918	+	4.26299i	−0.502786	+	0.208261i	−0.619637	−	0.784889i	$-0.712720\pi$
$419$	−10.2918	+	4.26299i	−0.502786	+	0.208261i	0.116851	+	0.993149i	$0.462720\pi$
$420$		0			0
$421$	10.0453	−	24.2514i	0.489576	−	1.18194i	−0.465357	−	0.885123i	$-0.654074\pi$
$421$	10.0453	−	24.2514i	0.489576	−	1.18194i	0.954934	−	0.296819i	$-0.0959259\pi$
$422$		0			0
$423$	37.3675	+	37.3675i	1.81687	+	1.81687i
$424$		0			0
$425$	15.5675	−	15.5675i	0.755136	−	0.755136i
$426$		0			0
$427$	42.1753	+	17.4696i	2.04101	+	0.845413i
$428$		0			0
$429$	9.07498	+	21.9089i	0.438144	+	1.05777i
$430$		0			0
$431$		−	11.4592i		−	0.551972i	−0.961162	−	0.275986i	$-0.910996\pi$
$431$		−	11.4592i		−	0.551972i	0.961162	−	0.275986i	$-0.0890043\pi$
$432$		0			0
$433$		−	15.0019i		−	0.720946i	−0.932770	−	0.360473i	$-0.882615\pi$
$433$		−	15.0019i		−	0.720946i	0.932770	−	0.360473i	$-0.117385\pi$
$434$		0			0
$435$	−2.28410	−	5.51430i	−0.109514	−	0.264391i
$436$		0			0
$437$	−3.34066	−	1.38375i	−0.159805	−	0.0661935i
$438$		0			0
$439$	−13.9503	+	13.9503i	−0.665812	+	0.665812i	−0.956744	−	0.290932i	$-0.906035\pi$
$439$	−13.9503	+	13.9503i	−0.665812	+	0.665812i	0.290932	+	0.956744i	$0.406035\pi$
$440$		0			0
$441$	46.6582	+	46.6582i	2.22182	+	2.22182i
$442$		0			0
$443$	−4.47872	+	10.8126i	−0.212791	+	0.513722i	−0.993850	−	0.110735i	$-0.964680\pi$
$443$	−4.47872	+	10.8126i	−0.212791	+	0.513722i	0.781059	+	0.624457i	$0.214680\pi$
$444$		0			0
$445$	−1.23267	+	0.510590i	−0.0584343	+	0.0242043i
$446$		0			0
$447$	−18.5594			−0.877827
$448$		0			0
$449$	4.74061			0.223723			0.111862	−	0.993724i	$-0.464319\pi$
$449$	4.74061			0.223723			0.111862	+	0.993724i	$0.464319\pi$
$450$		0			0
$451$	3.21916	−	1.33342i	0.151584	−	0.0627882i
$452$		0			0
$453$	−12.0160	+	29.0092i	−0.564562	+	1.36297i
$454$		0			0
$455$	2.47602	+	2.47602i	0.116078	+	0.116078i
$456$		0			0
$457$	15.1910	−	15.1910i	0.710605	−	0.710605i	−0.256057	−	0.966662i	$-0.582423\pi$
$457$	15.1910	−	15.1910i	0.710605	−	0.710605i	0.966662	+	0.256057i	$0.0824235\pi$
$458$		0			0
$459$	31.9623	+	13.2392i	1.49187	+	0.617953i
$460$		0			0
$461$	6.16815	+	14.8912i	0.287279	+	0.693554i	0.999969	−	0.00792626i	$-0.00252303\pi$
$461$	6.16815	+	14.8912i	0.287279	+	0.693554i	−0.712689	+	0.701480i	$0.752523\pi$
$462$		0			0
$463$		−	11.4145i		−	0.530477i	−0.964183	−	0.265238i	$-0.914549\pi$
$463$		−	11.4145i		−	0.530477i	0.964183	−	0.265238i	$-0.0854506\pi$
$464$		0			0
$465$		−	0.0627219i		−	0.00290866i
$466$		0			0
$467$	2.64610	+	6.38825i	0.122447	+	0.295613i	0.973203	−	0.229948i	$-0.0738556\pi$
$467$	2.64610	+	6.38825i	0.122447	+	0.295613i	−0.850756	+	0.525561i	$0.823856\pi$
$468$		0			0
$469$	−32.6802	−	13.5366i	−1.50903	−	0.625061i
$470$		0			0
$471$	16.9035	−	16.9035i	0.778873	−	0.778873i
$472$		0			0
$473$	−6.28283	−	6.28283i	−0.288885	−	0.288885i
$474$		0			0
$475$	1.07260	−	2.58950i	0.0492145	−	0.118814i
$476$		0			0
$477$	56.2830	−	23.3132i	2.57702	−	1.06744i
$478$		0			0
$479$	16.2733			0.743545			0.371772	−	0.928324i	$-0.378750\pi$
$479$	16.2733			0.743545			0.371772	+	0.928324i	$0.378750\pi$
$480$		0			0
$481$	−1.76217			−0.0803479
$482$		0			0
$483$	−73.3630	+	30.3880i	−3.33813	+	1.38270i
$484$		0			0
$485$	2.01148	−	4.85614i	0.0913366	−	0.220506i
$486$		0			0
$487$	13.0573	+	13.0573i	0.591683	+	0.591683i	0.938086	−	0.346403i	$-0.112597\pi$
$487$	13.0573	+	13.0573i	0.591683	+	0.591683i	−0.346403	+	0.938086i	$0.612597\pi$
$488$		0			0
$489$	12.3555	−	12.3555i	0.558736	−	0.558736i
$490$		0			0
$491$	13.2438	+	5.48577i	0.597686	+	0.247569i	0.660953	−	0.750427i	$-0.270152\pi$
$491$	13.2438	+	5.48577i	0.597686	+	0.247569i	−0.0632676	+	0.997997i	$0.520152\pi$
$492$		0			0
$493$	−8.93910	−	21.5809i	−0.402597	−	0.971955i
$494$		0			0
$495$			8.79490i			0.395301i
$496$		0			0
$497$		−	18.3397i		−	0.822648i
$498$		0			0
$499$	−9.43511	−	22.7784i	−0.422374	−	1.01970i	−0.981645	−	0.190716i	$-0.938919\pi$
$499$	−9.43511	−	22.7784i	−0.422374	−	1.01970i	0.559272	−	0.828984i	$-0.311081\pi$
$500$		0			0
$501$	−55.2168	−	22.8715i	−2.46690	−	1.02182i
$502$		0			0
$503$	29.0166	−	29.0166i	1.29378	−	1.29378i	0.361357	−	0.932428i	$-0.382314\pi$
$503$	29.0166	−	29.0166i	1.29378	−	1.29378i	0.932428	−	0.361357i	$-0.117686\pi$
$504$		0			0
$505$	4.14235	+	4.14235i	0.184332	+	0.184332i
$506$		0			0
$507$	−9.92163	+	23.9529i	−0.440635	+	1.06379i
$508$		0			0
$509$	0.240941	−	0.0998009i	0.0106795	−	0.00442360i	−0.377337	−	0.926076i	$-0.623160\pi$
$509$	0.240941	−	0.0998009i	0.0106795	−	0.00442360i	0.388017	+	0.921652i	$0.373160\pi$
$510$		0			0
$511$	−17.8843			−0.791156
$512$		0			0
$513$	4.40441			0.194459
$514$		0			0
$515$	2.41726	−	1.00126i	0.106517	−	0.0441208i
$516$		0			0
$517$	−14.3373	+	34.6132i	−0.630552	+	1.52229i
$518$		0			0
$519$	35.9386	+	35.9386i	1.57753	+	1.57753i
$520$		0			0
$521$	6.59451	−	6.59451i	0.288911	−	0.288911i	−0.547739	−	0.836649i	$-0.684511\pi$
$521$	6.59451	−	6.59451i	0.288911	−	0.288911i	0.836649	+	0.547739i	$0.184511\pi$
$522$		0			0
$523$	−30.1535	−	12.4900i	−1.31852	−	0.546148i	−0.391160	−	0.920323i	$-0.627926\pi$
$523$	−30.1535	−	12.4900i	−1.31852	−	0.546148i	−0.927358	+	0.374174i	$0.877926\pi$
$524$		0			0
$525$	−23.5551	−	56.8671i	−1.02803	−	2.48188i
$526$		0			0
$527$		−	0.245470i		−	0.0106928i
$528$		0			0
$529$		−	16.0363i		−	0.697231i
$530$		0			0
$531$	16.6392	+	40.1706i	0.722081	+	1.74326i
$532$		0			0
$533$	−1.65445	−	0.685296i	−0.0716622	−	0.0296835i
$534$		0			0
$535$	−2.31389	+	2.31389i	−0.100038	+	0.100038i
$536$		0			0
$537$	−19.5023	−	19.5023i	−0.841586	−	0.841586i
$538$		0			0
$539$	−17.9019	+	43.2191i	−0.771091	+	1.86158i
$540$		0			0
$541$	−13.1850	+	5.46141i	−0.566867	+	0.234804i	−0.647664	−	0.761926i	$-0.724254\pi$
$541$	−13.1850	+	5.46141i	−0.566867	+	0.234804i	0.0807961	+	0.996731i	$0.474254\pi$
$542$		0			0
$543$	−2.11618			−0.0908140
$544$		0			0
$545$	−1.05594			−0.0452315
$546$		0			0
$547$	22.8546	−	9.46669i	0.977192	−	0.404766i	0.163807	−	0.986492i	$-0.447622\pi$
$547$	22.8546	−	9.46669i	0.977192	−	0.404766i	0.813385	+	0.581726i	$0.197622\pi$
$548$		0			0
$549$	22.5505	−	54.4417i	0.962431	−	2.32351i
$550$		0			0
$551$	−2.10283	−	2.10283i	−0.0895837	−	0.0895837i
$552$		0			0
$553$	17.6203	−	17.6203i	0.749293	−	0.749293i
$554$		0			0
$555$	−0.927497	−	0.384182i	−0.0393700	−	0.0163076i
$556$		0			0
$557$	−7.31400	−	17.6576i	−0.309904	−	0.748175i	−0.999708	−	0.0241782i	$-0.992303\pi$
$557$	−7.31400	−	17.6576i	−0.309904	−	0.748175i	0.689804	−	0.723997i	$-0.257697\pi$
$558$		0			0
$559$			4.56648i			0.193142i
$560$		0			0
$561$			52.8731i			2.23230i
$562$		0			0
$563$	−12.0464	−	29.0826i	−0.507695	−	1.22568i	−0.945207	−	0.326472i	$-0.894140\pi$
$563$	−12.0464	−	29.0826i	−0.507695	−	1.22568i	0.437512	−	0.899213i	$-0.355860\pi$
$564$		0			0
$565$	−1.81722	−	0.752715i	−0.0764508	−	0.0316670i
$566$		0			0
$567$	16.9363	−	16.9363i	0.711258	−	0.711258i
$568$		0			0
$569$	−18.1317	−	18.1317i	−0.760118	−	0.760118i	0.216225	−	0.976344i	$-0.430625\pi$
$569$	−18.1317	−	18.1317i	−0.760118	−	0.760118i	−0.976344	+	0.216225i	$0.930625\pi$
$570$		0			0
$571$	−3.21852	+	7.77020i	−0.134691	+	0.325173i	−0.976806	−	0.214125i	$-0.931310\pi$
$571$	−3.21852	+	7.77020i	−0.134691	+	0.325173i	0.842115	+	0.539297i	$0.181310\pi$
$572$		0			0
$573$	−27.5597	+	11.4156i	−1.15133	+	0.476894i
$574$		0			0
$575$	30.2588			1.26188
$576$		0			0
$577$	−13.2275			−0.550669			−0.275335	−	0.961348i	$-0.588789\pi$
$577$	−13.2275			−0.550669			−0.275335	+	0.961348i	$0.588789\pi$
$578$		0			0
$579$	−31.8309	+	13.1848i	−1.32285	+	0.547942i
$580$		0			0
$581$	−5.93477	+	14.3278i	−0.246216	+	0.594418i
$582$		0			0
$583$	30.5397	+	30.5397i	1.26482	+	1.26482i
$584$		0			0
$585$	3.19615	−	3.19615i	0.132145	−	0.132145i
$586$		0			0
$587$	32.0438	+	13.2730i	1.32259	+	0.547835i	0.928533	−	0.371251i	$-0.121071\pi$
$587$	32.0438	+	13.2730i	1.32259	+	0.547835i	0.394058	+	0.919086i	$0.371071\pi$
$588$		0			0
$589$	−0.0119592	−	0.0288721i	−0.000492771	−	0.00118966i
$590$		0			0
$591$			46.0348i			1.89362i
$592$		0			0
$593$		−	37.4869i		−	1.53940i	−0.638405	−	0.769700i	$-0.720406\pi$
$593$		−	37.4869i		−	1.53940i	0.638405	−	0.769700i	$-0.279594\pi$
$594$		0			0
$595$	2.98770	+	7.21296i	0.122484	+	0.295702i
$596$		0			0
$597$	−8.91359	−	3.69213i	−0.364809	−	0.151109i
$598$		0			0
$599$	−4.05549	+	4.05549i	−0.165703	+	0.165703i	−0.785088	−	0.619385i	$-0.787382\pi$
$599$	−4.05549	+	4.05549i	−0.165703	+	0.165703i	0.619385	+	0.785088i	$0.287382\pi$
$600$		0			0
$601$	0.796070	+	0.796070i	0.0324724	+	0.0324724i	0.723157	−	0.690684i	$-0.242691\pi$
$601$	0.796070	+	0.796070i	0.0324724	+	0.0324724i	−0.690684	+	0.723157i	$0.742691\pi$
$602$		0			0
$603$	−17.4736	+	42.1850i	−0.711579	+	1.71790i
$604$		0			0
$605$	−1.73427	+	0.718357i	−0.0705079	+	0.0292053i
$606$		0			0
$607$	13.8854			0.563591			0.281795	−	0.959475i	$-0.409070\pi$
$607$	13.8854			0.563591			0.281795	+	0.959475i	$0.409070\pi$
$608$		0			0
$609$	−65.3078			−2.64640
$610$		0			0
$611$	17.7891	−	7.36848i	0.719669	−	0.298097i
$612$		0			0
$613$	−3.91967	+	9.46292i	−0.158314	+	0.382204i	−0.983056	−	0.183305i	$-0.941320\pi$
$613$	−3.91967	+	9.46292i	−0.158314	+	0.382204i	0.824742	+	0.565509i	$0.191320\pi$
$614$		0			0
$615$	−0.721395	−	0.721395i	−0.0290895	−	0.0290895i
$616$		0			0
$617$	5.39736	−	5.39736i	0.217290	−	0.217290i	−0.590066	−	0.807355i	$-0.700898\pi$
$617$	5.39736	−	5.39736i	0.217290	−	0.217290i	0.807355	+	0.590066i	$0.200898\pi$
$618$		0			0
$619$	−31.2161	−	12.9301i	−1.25468	−	0.519706i	−0.346408	−	0.938084i	$-0.612599\pi$
$619$	−31.2161	−	12.9301i	−1.25468	−	0.519706i	−0.908273	+	0.418379i	$0.862599\pi$
$620$		0			0
$621$	18.1962	+	43.9294i	0.730186	+	1.76283i
$622$		0			0
$623$			14.5990i			0.584895i
$624$		0			0
$625$			22.6702i			0.906809i
$626$		0			0
$627$	2.57597	+	6.21893i	0.102874	+	0.248360i
$628$		0			0
$629$	−3.62987	−	1.50354i	−0.144732	−	0.0599501i
$630$		0			0
$631$	−21.8697	+	21.8697i	−0.870620	+	0.870620i	−0.992540	−	0.121920i	$-0.961095\pi$
$631$	−21.8697	+	21.8697i	−0.870620	+	0.870620i	0.121920	+	0.992540i	$0.461095\pi$
$632$		0			0
$633$	37.9359	+	37.9359i	1.50782	+	1.50782i
$634$		0			0
$635$	2.34286	−	5.65618i	0.0929737	−	0.224458i
$636$		0			0
$637$	22.2120	−	9.20050i	0.880071	−	0.364537i
$638$		0			0
$639$	−23.6737			−0.936515
$640$		0			0
$641$	34.0037			1.34307			0.671533	−	0.740975i	$-0.265636\pi$
$641$	34.0037			1.34307			0.671533	+	0.740975i	$0.265636\pi$
$642$		0			0
$643$	9.40811	−	3.89697i	0.371020	−	0.153681i	−0.189380	−	0.981904i	$-0.560648\pi$
$643$	9.40811	−	3.89697i	0.371020	−	0.153681i	0.560399	+	0.828223i	$0.310648\pi$
$644$		0			0
$645$	−0.995569	+	2.40352i	−0.0392005	+	0.0946384i
$646$		0			0
$647$	−11.9528	−	11.9528i	−0.469914	−	0.469914i	0.431973	−	0.901887i	$-0.357818\pi$
$647$	−11.9528	−	11.9528i	−0.469914	−	0.469914i	−0.901887	+	0.431973i	$0.857818\pi$
$648$		0			0
$649$	−21.7970	+	21.7970i	−0.855606	+	0.855606i
$650$		0			0
$651$	−0.634051	−	0.262632i	−0.0248504	−	0.0102934i
$652$		0			0
$653$	6.61520	+	15.9705i	0.258873	+	0.624974i	0.998864	−	0.0476419i	$-0.0151706\pi$
$653$	6.61520	+	15.9705i	0.258873	+	0.624974i	−0.739992	+	0.672616i	$0.765171\pi$
$654$		0			0
$655$		−	4.14475i		−	0.161949i
$656$		0			0
$657$			23.0858i			0.900665i
$658$		0			0
$659$	−1.29305	−	3.12170i	−0.0503701	−	0.121604i	0.896692	−	0.442656i	$-0.145964\pi$
$659$	−1.29305	−	3.12170i	−0.0503701	−	0.121604i	−0.947062	+	0.321052i	$0.895964\pi$
$660$		0			0
$661$	−42.9077	−	17.7729i	−1.66892	−	0.691287i	−0.670211	−	0.742171i	$-0.733796\pi$
$661$	−42.9077	−	17.7729i	−1.66892	−	0.691287i	−0.998705	+	0.0508836i	$0.983796\pi$
$662$		0			0
$663$	19.2146	−	19.2146i	0.746234	−	0.746234i
$664$		0			0
$665$	0.702827	+	0.702827i	0.0272545	+	0.0272545i
$666$		0			0
$667$	12.2860	−	29.6611i	0.475717	−	1.14848i
$668$		0			0
$669$	58.6349	−	24.2874i	2.26696	−	0.939004i
$670$		0			0
$671$	41.7767			1.61277
$672$		0			0
$673$	−0.107425			−0.00414091			−0.00207046	−	0.999998i	$-0.500659\pi$
$673$	−0.107425			−0.00414091			−0.00207046	+	0.999998i	$0.500659\pi$
$674$		0			0
$675$	−34.0517	+	14.1047i	−1.31065	+	0.542889i
$676$		0			0
$677$	4.24507	−	10.2485i	0.163151	−	0.393882i	−0.821069	−	0.570829i	$-0.806622\pi$
$677$	4.24507	−	10.2485i	0.163151	−	0.393882i	0.984220	+	0.176947i	$0.0566220\pi$
$678$		0			0
$679$	−40.6678	−	40.6678i	−1.56069	−	1.56069i
$680$		0			0
$681$	−19.8912	+	19.8912i	−0.762233	+	0.762233i
$682$		0			0
$683$	−25.2815	−	10.4720i	−0.967371	−	0.400698i	−0.157638	−	0.987497i	$-0.550388\pi$
$683$	−25.2815	−	10.4720i	−0.967371	−	0.400698i	−0.809733	+	0.586799i	$0.800388\pi$
$684$		0			0
$685$	−2.46332	−	5.94698i	−0.0941186	−	0.227222i
$686$		0			0
$687$		−	84.3452i		−	3.21797i
$688$		0			0
$689$		−	22.1968i		−	0.845632i
$690$		0			0
$691$	11.6277	+	28.0716i	0.442337	+	1.06790i	0.975127	+	0.221648i	$0.0711436\pi$
$691$	11.6277	+	28.0716i	0.442337	+	1.06790i	−0.532790	+	0.846248i	$0.678856\pi$
$692$		0			0
$693$	88.9069	+	36.8265i	3.37729	+	1.39892i
$694$		0			0
$695$	−2.10023	+	2.10023i	−0.0796663	+	0.0796663i
$696$		0			0
$697$	−2.82327	−	2.82327i	−0.106939	−	0.106939i
$698$		0			0
$699$	28.6753	−	69.2284i	1.08460	−	2.61846i
$700$		0			0
$701$	25.3030	−	10.4808i	0.955679	−	0.395855i	0.150317	−	0.988638i	$-0.451971\pi$
$701$	25.3030	−	10.4808i	0.955679	−	0.395855i	0.805363	+	0.592783i	$0.201971\pi$
$702$		0			0
$703$	−0.500197			−0.0188653
$704$		0			0
$705$	10.9695			0.413136
$706$		0			0
$707$	59.2198	−	24.5296i	2.22719	−	0.922531i
$708$		0			0
$709$	−18.2502	+	44.0598i	−0.685400	+	1.65470i	0.0684496	+	0.997655i	$0.478195\pi$
$709$	−18.2502	+	44.0598i	−0.685400	+	1.65470i	−0.753850	+	0.657047i	$0.771805\pi$
$710$		0			0
$711$	−22.7451	−	22.7451i	−0.853007	−	0.853007i
$712$		0			0
$713$	0.238562	−	0.238562i	0.00893420	−	0.00893420i
$714$		0			0
$715$	2.96057	+	1.22631i	0.110719	+	0.0458613i
$716$		0			0
$717$	27.0132	+	65.2155i	1.00882	+	2.43552i
$718$		0			0
$719$			20.5621i			0.766835i	0.923575	+	0.383418i	$0.125253\pi$
$719$			20.5621i			0.766835i	−0.923575	+	0.383418i	$0.874747\pi$
$720$		0			0
$721$		−	28.6284i		−	1.06618i
$722$		0			0
$723$	11.6487	+	28.1224i	0.433219	+	1.04588i
$724$		0			0
$725$	22.9917	+	9.52347i	0.853890	+	0.353693i
$726$		0			0
$727$	2.98129	−	2.98129i	0.110570	−	0.110570i	−0.649657	−	0.760227i	$-0.725088\pi$
$727$	2.98129	−	2.98129i	0.110570	−	0.110570i	0.760227	+	0.649657i	$0.225088\pi$
$728$		0			0
$729$	25.4698	+	25.4698i	0.943326	+	0.943326i
$730$		0			0
$731$	−3.89628	+	9.40645i	−0.144109	+	0.347910i
$732$		0			0
$733$	−44.2647	+	18.3350i	−1.63495	+	0.677220i	−0.995774	−	0.0918368i	$-0.970726\pi$
$733$	−44.2647	+	18.3350i	−1.63495	+	0.677220i	−0.639180	+	0.769057i	$0.720726\pi$
$734$		0			0
$735$	13.6969			0.505217
$736$		0			0
$737$	−32.3713			−1.19241
$738$		0			0
$739$	−15.5580	+	6.44435i	−0.572312	+	0.237059i	−0.650020	−	0.759917i	$-0.725240\pi$
$739$	−15.5580	+	6.44435i	−0.572312	+	0.237059i	0.0777085	+	0.996976i	$0.475240\pi$
$740$		0			0
$741$	1.32389	−	3.19615i	0.0486343	−	0.117414i
$742$		0			0
$743$	15.2184	+	15.2184i	0.558309	+	0.558309i	0.928826	−	0.370516i	$-0.120819\pi$
$743$	15.2184	+	15.2184i	0.558309	+	0.558309i	−0.370516	+	0.928826i	$0.620819\pi$
$744$		0			0
$745$	−1.77338	+	1.77338i	−0.0649716	+	0.0649716i
$746$		0			0
$747$	18.4949	+	7.66085i	0.676694	+	0.280296i
$748$		0			0
$749$	13.7021	+	33.0798i	0.500664	+	1.20871i
$750$		0			0
$751$		−	4.40389i		−	0.160700i	−0.996767	−	0.0803501i	$-0.974396\pi$
$751$		−	4.40389i		−	0.160700i	0.996767	−	0.0803501i	$-0.0256038\pi$
$752$		0			0
$753$			73.1043i			2.66407i
$754$		0			0
$755$	1.62373	+	3.92004i	0.0590937	+	0.142665i
$756$		0			0
$757$	22.3677	+	9.26500i	0.812968	+	0.336742i	0.750137	−	0.661282i	$-0.229987\pi$
$757$	22.3677	+	9.26500i	0.812968	+	0.336742i	0.0628304	+	0.998024i	$0.479987\pi$
$758$		0			0
$759$	−51.3851	+	51.3851i	−1.86516	+	1.86516i
$760$		0			0
$761$	−6.81382	−	6.81382i	−0.247001	−	0.247001i	0.572738	−	0.819739i	$-0.305881\pi$
$761$	−6.81382	−	6.81382i	−0.247001	−	0.247001i	−0.819739	+	0.572738i	$0.805881\pi$
$762$		0			0
$763$	−4.42149	+	10.6744i	−0.160069	+	0.386440i
$764$		0			0
$765$	9.31079	−	3.85666i	0.336632	−	0.139438i
$766$		0			0
$767$	15.8425			0.572038
$768$		0			0
$769$	−16.7366			−0.603538			−0.301769	−	0.953381i	$-0.597577\pi$
$769$	−16.7366			−0.603538			−0.301769	+	0.953381i	$0.597577\pi$
$770$		0			0
$771$	50.6850	−	20.9944i	1.82537	−	0.756095i
$772$		0			0
$773$	5.65140	−	13.6437i	0.203267	−	0.490730i	−0.789068	−	0.614305i	$-0.789436\pi$
$773$	5.65140	−	13.6437i	0.203267	−	0.490730i	0.992335	+	0.123576i	$0.0394363\pi$
$774$		0			0
$775$	0.184920	+	0.184920i	0.00664253	+	0.00664253i
$776$		0			0
$777$	−7.76733	+	7.76733i	−0.278651	+	0.278651i
$778$		0			0
$779$	−0.469621	−	0.194524i	−0.0168259	−	0.00696953i
$780$		0			0
$781$	−6.42277	−	15.5059i	−0.229825	−	0.554846i
$782$		0			0
$783$			39.1060i			1.39753i
$784$		0			0
$785$		−	3.23032i		−	0.115295i
$786$		0			0
$787$	3.75460	+	9.06441i	0.133837	+	0.323111i	0.976563	−	0.215231i	$-0.0690506\pi$
$787$	3.75460	+	9.06441i	0.133837	+	0.323111i	−0.842726	+	0.538343i	$0.819051\pi$
$788$		0			0
$789$	−3.38891	−	1.40373i	−0.120648	−	0.0499741i
$790$		0			0
$791$	−15.2183	+	15.2183i	−0.541100	+	0.541100i
$792$		0			0
$793$	−15.1821	−	15.1821i	−0.539131	−	0.539131i
$794$		0			0
$795$	4.83928	−	11.6830i	0.171631	−	0.414355i
$796$		0			0
$797$	−34.8002	+	14.4147i	−1.23269	+	0.510595i	−0.901421	−	0.432943i	$-0.857475\pi$
$797$	−34.8002	+	14.4147i	−1.23269	+	0.510595i	−0.331264	+	0.943538i	$0.607475\pi$
$798$		0			0
$799$	42.9306			1.51878
$800$		0			0
$801$	18.8450			0.665854
$802$		0			0
$803$	−15.1209	+	6.26330i	−0.533606	+	0.221027i
$804$		0			0
$805$	−4.10634	+	9.91359i	−0.144730	+	0.349408i
$806$		0			0
$807$	−29.4901	−	29.4901i	−1.03810	−	1.03810i
$808$		0			0
$809$	−6.59383	+	6.59383i	−0.231827	+	0.231827i	−0.813455	−	0.581628i	$-0.802416\pi$
$809$	−6.59383	+	6.59383i	−0.231827	+	0.231827i	0.581628	+	0.813455i	$0.302416\pi$
$810$		0			0
$811$	−29.0036	−	12.0137i	−1.01845	−	0.421857i	−0.189922	−	0.981799i	$-0.560823\pi$
$811$	−29.0036	−	12.0137i	−1.01845	−	0.421857i	−0.828532	+	0.559942i	$0.810823\pi$
$812$		0			0
$813$	−19.7016	−	47.5638i	−0.690965	−	1.66814i
$814$		0			0
$815$		−	2.36118i		−	0.0827087i
$816$		0			0
$817$			1.29621i			0.0453487i
$818$		0			0
$819$	−18.9266	−	45.6928i	−0.661348	−	1.59663i
$820$		0			0
$821$	26.9988	+	11.1833i	0.942265	+	0.390299i	0.800318	−	0.599575i	$-0.204664\pi$
$821$	26.9988	+	11.1833i	0.942265	+	0.390299i	0.141947	+	0.989874i	$0.454664\pi$
$822$		0			0
$823$	0.497968	−	0.497968i	0.0173581	−	0.0173581i	−0.698374	−	0.715733i	$-0.746093\pi$
$823$	0.497968	−	0.497968i	0.0173581	−	0.0173581i	0.715733	+	0.698374i	$0.246093\pi$
$824$		0			0
$825$	−39.8310	−	39.8310i	−1.38674	−	1.38674i
$826$		0			0
$827$	−18.1468	+	43.8102i	−0.631025	+	1.52343i	0.207311	+	0.978275i	$0.433529\pi$
$827$	−18.1468	+	43.8102i	−0.631025	+	1.52343i	−0.838336	+	0.545154i	$0.816471\pi$
$828$		0			0
$829$	−29.0154	+	12.0186i	−1.00774	+	0.417422i	−0.824632	−	0.565670i	$-0.808618\pi$
$829$	−29.0154	+	12.0186i	−1.00774	+	0.417422i	−0.183113	+	0.983092i	$0.558618\pi$
$830$		0			0
$831$	−77.3512			−2.68328
$832$		0			0
$833$	53.6044			1.85728
$834$		0			0
$835$	−7.46148	+	3.09065i	−0.258215	+	0.106956i
$836$		0			0
$837$	−0.157263	+	0.379666i	−0.00543580	+	0.0131232i
$838$		0			0
$839$	−28.1636	−	28.1636i	−0.972317	−	0.972317i	0.0273102	−	0.999627i	$-0.491306\pi$
$839$	−28.1636	−	28.1636i	−0.972317	−	0.972317i	−0.999627	+	0.0273102i	$0.991306\pi$
$840$		0			0
$841$	−1.83543	+	1.83543i	−0.0632906	+	0.0632906i
$842$		0			0
$843$	−65.0305	−	26.9365i	−2.23977	−	0.927743i
$844$		0			0
$845$	1.34072	+	3.23678i	0.0461221	+	0.111349i
$846$		0			0
$847$			20.5395i			0.705746i
$848$		0			0
$849$		−	10.3232i		−	0.354290i
$850$		0			0
$851$	−2.06649	−	4.98895i	−0.0708383	−	0.171019i
$852$		0			0
$853$	7.62203	+	3.15715i	0.260973	+	0.108099i	0.509334	−	0.860569i	$-0.329892\pi$
$853$	7.62203	+	3.15715i	0.260973	+	0.108099i	−0.248361	+	0.968668i	$0.579892\pi$
$854$		0			0
$855$	0.907239	−	0.907239i	0.0310269	−	0.0310269i
$856$		0			0
$857$	8.53805	+	8.53805i	0.291654	+	0.291654i	0.837734	−	0.546079i	$-0.183880\pi$
$857$	8.53805	+	8.53805i	0.291654	+	0.291654i	−0.546079	+	0.837734i	$0.683880\pi$
$858$		0			0
$859$	3.77131	−	9.10474i	0.128675	−	0.310650i	−0.846392	−	0.532561i	$-0.821230\pi$
$859$	3.77131	−	9.10474i	0.128675	−	0.310650i	0.975067	+	0.221912i	$0.0712296\pi$
$860$		0			0
$861$	−10.3132	+	4.27186i	−0.351473	+	0.145585i
$862$		0			0
$863$	−17.7816			−0.605294			−0.302647	−	0.953103i	$-0.597870\pi$
$863$	−17.7816			−0.605294			−0.302647	+	0.953103i	$0.597870\pi$
$864$		0			0
$865$	6.86800			0.233519
$866$		0			0
$867$	9.92703	−	4.11191i	0.337140	−	0.139648i
$868$		0			0
$869$	8.72689	−	21.0686i	0.296040	−	0.714703i
$870$		0			0
$871$	11.7640	+	11.7640i	0.398610	+	0.398610i
$872$		0			0
$873$	−52.4957	+	52.4957i	−1.77671	+	1.77671i
$874$		0			0
$875$	−15.6180	−	6.46919i	−0.527985	−	0.218699i
$876$		0			0
$877$	−8.87297	−	21.4212i	−0.299619	−	0.723344i	−0.999955	−	0.00953022i	$-0.996966\pi$
$877$	−8.87297	−	21.4212i	−0.299619	−	0.723344i	0.700336	−	0.713814i	$-0.253034\pi$
$878$		0			0
$879$			9.15869i			0.308915i
$880$		0			0
$881$		−	21.5225i		−	0.725113i	−0.931962	−	0.362557i	$-0.881904\pi$
$881$		−	21.5225i		−	0.725113i	0.931962	−	0.362557i	$-0.118096\pi$
$882$		0			0
$883$	−11.5351	−	27.8481i	−0.388186	−	0.937165i	−0.990324	−	0.138773i	$-0.955684\pi$
$883$	−11.5351	−	27.8481i	−0.388186	−	0.937165i	0.602138	−	0.798392i	$-0.294316\pi$
$884$		0			0
$885$	8.33850	+	3.45392i	0.280296	+	0.116102i
$886$		0			0
$887$	25.2963	−	25.2963i	0.849368	−	0.849368i	−0.140686	−	0.990054i	$-0.544931\pi$
$887$	25.2963	−	25.2963i	0.849368	−	0.849368i	0.990054	+	0.140686i	$0.0449309\pi$
$888$		0			0
$889$	−47.3677	−	47.3677i	−1.58866	−	1.58866i
$890$		0			0
$891$	8.38811	−	20.2507i	0.281012	−	0.678423i
$892$		0			0
$893$	5.04949	−	2.09157i	0.168975	−	0.0699917i
$894$		0			0
$895$	−3.72696			−0.124579
$896$		0			0
$897$	37.3477			1.24700
$898$		0			0
$899$	0.256350	−	0.106184i	0.00854976	−	0.00354143i
$900$		0			0
$901$	18.9391	−	45.7230i	0.630953	−	1.52325i
$902$		0			0
$903$	20.1283	+	20.1283i	0.669827	+	0.669827i
$904$		0			0
$905$	−0.202205	+	0.202205i	−0.00672152	+	0.00672152i
$906$		0			0
$907$	18.5718	+	7.69269i	0.616666	+	0.255432i	0.669076	−	0.743194i	$-0.266690\pi$
$907$	18.5718	+	7.69269i	0.616666	+	0.255432i	−0.0524095	+	0.998626i	$0.516690\pi$
$908$		0			0
$909$	−31.6639	−	76.4434i	−1.05022	−	2.53547i
$910$		0			0
$911$		−	57.0332i		−	1.88960i	−0.327655	−	0.944798i	$-0.606258\pi$
$911$		−	57.0332i		−	1.88960i	0.327655	−	0.944798i	$-0.393742\pi$
$912$		0			0
$913$			14.1924i			0.469699i
$914$		0			0
$915$	−4.68096	−	11.3008i	−0.154748	−	0.373594i
$916$		0			0
$917$	−41.8989	−	17.3551i	−1.38362	−	0.573116i
$918$		0			0
$919$	−7.18487	+	7.18487i	−0.237007	+	0.237007i	−0.815610	−	0.578603i	$-0.803598\pi$
$919$	−7.18487	+	7.18487i	−0.237007	+	0.237007i	0.578603	+	0.815610i	$0.303598\pi$
$920$		0			0
$921$	17.6778	+	17.6778i	0.582503	+	0.582503i
$922$		0			0
$923$	−3.30092	+	7.96911i	−0.108651	+	0.262307i
$924$		0			0
$925$	3.86716	−	1.60183i	0.127152	−	0.0526679i
$926$		0			0
$927$	−36.9547			−1.21375
$928$		0			0
$929$	−23.2751			−0.763630			−0.381815	−	0.924239i	$-0.624701\pi$
$929$	−23.2751			−0.763630			−0.381815	+	0.924239i	$0.624701\pi$
$930$		0			0
$931$	6.30495	−	2.61160i	0.206636	−	0.0855916i
$932$		0			0
$933$	−5.37237	+	12.9700i	−0.175883	+	0.424620i
$934$		0			0
$935$	5.05212	+	5.05212i	0.165222	+	0.165222i
$936$		0			0
$937$	7.60456	−	7.60456i	0.248430	−	0.248430i	−0.571896	−	0.820326i	$-0.693792\pi$
$937$	7.60456	−	7.60456i	0.248430	−	0.248430i	0.820326	+	0.571896i	$0.193792\pi$
$938$		0			0
$939$	80.7111	+	33.4316i	2.63391	+	1.09100i
$940$		0			0
$941$	−1.13773	−	2.74672i	−0.0370889	−	0.0895406i	0.904250	−	0.427004i	$-0.140431\pi$
$941$	−1.13773	−	2.74672i	−0.0370889	−	0.0895406i	−0.941339	+	0.337464i	$0.890431\pi$
$942$		0			0
$943$		−	5.48763i		−	0.178702i
$944$		0			0
$945$		−	13.0703i		−	0.425178i
$946$		0			0
$947$	−8.99679	−	21.7202i	−0.292357	−	0.705811i	0.707643	−	0.706570i	$-0.249758\pi$
$947$	−8.99679	−	21.7202i	−0.292357	−	0.705811i	−1.00000		0.000758845i	$0.999758\pi$
$948$		0			0
$949$	7.77124	+	3.21895i	0.252265	+	0.104492i
$950$		0			0
$951$	58.4332	−	58.4332i	1.89483	−	1.89483i
$952$		0			0
$953$	−0.594510	−	0.594510i	−0.0192581	−	0.0192581i	0.697412	−	0.716670i	$-0.254335\pi$
$953$	−0.594510	−	0.594510i	−0.0192581	−	0.0192581i	−0.716670	+	0.697412i	$0.754335\pi$
$954$		0			0
$955$	−1.54260	+	3.72417i	−0.0499174	+	0.120511i
$956$		0			0
$957$	−55.2168	+	22.8715i	−1.78490	+	0.739332i
$958$		0			0
$959$	−70.4321			−2.27437
$960$		0			0
$961$	−30.9971			−0.999906
$962$		0			0
$963$	42.7008	−	17.6872i	1.37601	−	0.569964i
$964$		0			0
$965$	−1.78167	+	4.30134i	−0.0573541	+	0.138465i
$966$		0			0
$967$	−5.28012	−	5.28012i	−0.169797	−	0.169797i	0.617093	−	0.786890i	$-0.288310\pi$
$967$	−5.28012	−	5.28012i	−0.169797	−	0.169797i	−0.786890	+	0.617093i	$0.788310\pi$
$968$		0			0
$969$	5.45413	−	5.45413i	0.175212	−	0.175212i
$970$		0			0
$971$	45.8066	+	18.9737i	1.47000	+	0.608895i	0.966860	−	0.255308i	$-0.0821770\pi$
$971$	45.8066	+	18.9737i	1.47000	+	0.608895i	0.503143	+	0.864203i	$0.332177\pi$
$972$		0			0
$973$	12.4369	+	30.0253i	0.398708	+	0.962566i
$974$		0			0
$975$			28.9500i			0.927141i
$976$		0			0
$977$			27.5870i			0.882586i	0.897363	+	0.441293i	$0.145480\pi$
$977$			27.5870i			0.882586i	−0.897363	+	0.441293i	$0.854520\pi$
$978$		0			0
$979$	5.11273	+	12.3432i	0.163403	+	0.394491i
$980$		0			0
$981$	13.7790	+	5.70745i	0.439929	+	0.182225i
$982$		0			0
$983$	−32.4856	+	32.4856i	−1.03613	+	1.03613i	−0.0368067	+	0.999322i	$0.511719\pi$
$983$	−32.4856	+	32.4856i	−1.03613	+	1.03613i	−0.999322	+	0.0368067i	$0.988281\pi$
$984$		0			0
$985$	4.39871	+	4.39871i	0.140155	+	0.140155i
$986$		0			0
$987$	45.9322	−	110.890i	1.46204	−	3.52967i
$988$		0			0
$989$	−12.9284	+	5.35510i	−0.411098	+	0.170282i
$990$		0			0
$991$	−43.6148			−1.38547			−0.692735	−	0.721192i	$-0.743595\pi$
$991$	−43.6148			−1.38547			−0.692735	+	0.721192i	$0.743595\pi$
$992$		0			0
$993$	91.9819			2.91896
$994$		0			0
$995$	−1.20450	+	0.498920i	−0.0381852	+	0.0158168i
$996$		0			0
$997$	12.6240	−	30.4769i	0.399805	−	0.965214i	−0.587907	−	0.808928i	$-0.700048\pi$
$997$	12.6240	−	30.4769i	0.399805	−	0.965214i	0.987712	−	0.156286i	$-0.0499520\pi$
$998$		0			0
$999$	4.65104	+	4.65104i	0.147152	+	0.147152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.d.385.1	yes	16
4.3	odd	2	inner	1024.2.g.d.385.4	yes	16
8.3	odd	2		1024.2.g.g.385.1	yes	16
8.5	even	2		1024.2.g.g.385.4	yes	16
16.3	odd	4		1024.2.g.a.897.4	yes	16
16.5	even	4		1024.2.g.f.897.4	yes	16
16.11	odd	4		1024.2.g.f.897.1	yes	16
16.13	even	4		1024.2.g.a.897.1	yes	16
32.3	odd	8	inner	1024.2.g.d.641.4	yes	16
32.5	even	8		1024.2.g.f.129.4	yes	16
32.11	odd	8		1024.2.g.a.129.4	yes	16
32.13	even	8		1024.2.g.g.641.4	yes	16
32.19	odd	8		1024.2.g.g.641.1	yes	16
32.21	even	8		1024.2.g.a.129.1	✓	16
32.27	odd	8		1024.2.g.f.129.1	yes	16
32.29	even	8	inner	1024.2.g.d.641.1	yes	16
64.3	odd	16		4096.2.a.i.1.1		8
64.29	even	16		4096.2.a.i.1.2		8
64.35	odd	16		4096.2.a.s.1.8		8
64.61	even	16		4096.2.a.s.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.129.1	✓	16	32.21	even	8
1024.2.g.a.129.4	yes	16	32.11	odd	8
1024.2.g.a.897.1	yes	16	16.13	even	4
1024.2.g.a.897.4	yes	16	16.3	odd	4
1024.2.g.d.385.1	yes	16	1.1	even	1	trivial
1024.2.g.d.385.4	yes	16	4.3	odd	2	inner
1024.2.g.d.641.1	yes	16	32.29	even	8	inner
1024.2.g.d.641.4	yes	16	32.3	odd	8	inner
1024.2.g.f.129.1	yes	16	32.27	odd	8
1024.2.g.f.129.4	yes	16	32.5	even	8
1024.2.g.f.897.1	yes	16	16.11	odd	4
1024.2.g.f.897.4	yes	16	16.5	even	4
1024.2.g.g.385.1	yes	16	8.3	odd	2
1024.2.g.g.385.4	yes	16	8.5	even	2
1024.2.g.g.641.1	yes	16	32.19	odd	8
1024.2.g.g.641.4	yes	16	32.13	even	8
4096.2.a.i.1.1		8	64.3	odd	16
4096.2.a.i.1.2		8	64.29	even	16
4096.2.a.s.1.7		8	64.61	even	16
4096.2.a.s.1.8		8	64.35	odd	16

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70868 + 1.12197i) q^{3} +(-0.151613 + 0.366025i) q^{5} +(3.06528 + 3.06528i) q^{7} +(3.95680 - 3.95680i) q^{9} +O(q^{10})\)	\(q+(-2.70868 + 1.12197i) q^{3} +(-0.151613 + 0.366025i) q^{5} +(3.06528 + 3.06528i) q^{7} +(3.95680 - 3.95680i) q^{9} +(3.66515 + 1.51815i) q^{11} +(-0.780239 - 1.88366i) q^{13} -1.16155i q^{15} -4.54587i q^{17} +(-0.221474 - 0.534684i) q^{19} +(-11.7420 - 4.86370i) q^{21} +(4.41794 - 4.41794i) q^{23} +(3.42455 + 3.42455i) q^{25} +(-2.91236 + 7.03106i) q^{27} +(4.74737 - 1.96642i) q^{29} +0.0539984 q^{31} -11.6310 q^{33} +(-1.58671 + 0.657235i) q^{35} +(0.330749 - 0.798499i) q^{37} +(4.22683 + 4.22683i) q^{39} +(0.621063 - 0.621063i) q^{41} +(-2.06923 - 0.857104i) q^{43} +(0.848387 + 2.04819i) q^{45} +9.44387i q^{47} +11.7919i q^{49} +(5.10033 + 12.3133i) q^{51} +(10.0582 + 4.16622i) q^{53} +(-1.11137 + 1.11137i) q^{55} +(1.19980 + 1.19980i) q^{57} +(-2.97354 + 7.17877i) q^{59} +(9.72911 - 4.02993i) q^{61} +24.2574 q^{63} +0.807763 q^{65} +(-7.53875 + 3.12265i) q^{67} +(-7.00997 + 16.9236i) q^{69} +(-2.99152 - 2.99152i) q^{71} +(-2.91724 + 2.91724i) q^{73} +(-13.1182 - 5.43375i) q^{75} +(6.58114 + 15.8883i) q^{77} -5.74836i q^{79} -5.52520i q^{81} +(1.36905 + 3.30517i) q^{83} +(1.66390 + 0.689211i) q^{85} +(-10.6528 + 10.6528i) q^{87} +(2.38134 + 2.38134i) q^{89} +(3.38231 - 8.16561i) q^{91} +(-0.146264 + 0.0605847i) q^{93} +0.229286 q^{95} -13.2672 q^{97} +(20.5093 - 8.49522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 + 16 * q^9	\( 16 q - 8 q^{5} + 16 q^{9} + 24 q^{13} - 48 q^{21} + 32 q^{25} - 8 q^{29} - 80 q^{33} + 8 q^{37} + 16 q^{41} + 8 q^{45} + 40 q^{53} + 16 q^{57} + 8 q^{61} - 32 q^{65} - 32 q^{73} + 32 q^{77} - 32 q^{85} - 32 q^{89} + 48 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 16 * q^9 + 24 * q^13 - 48 * q^21 + 32 * q^25 - 8 * q^29 - 80 * q^33 + 8 * q^37 + 16 * q^41 + 8 * q^45 + 40 * q^53 + 16 * q^57 + 8 * q^61 - 32 * q^65 - 32 * q^73 + 32 * q^77 - 32 * q^85 - 32 * q^89 + 48 * q^93 - 16 * q^97

Introduction

L-functions

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Groups

Database

Properties

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