LMFDB - Embedded newform 1024.2.g.a.897.4

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			897.4
Root			$-0.793353 - 0.608761i$ of defining polynomial
Character	$\chi$	$=$	1024.897
Dual form			1024.2.g.a.129.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12197 + 2.70868i) q^{3} +(0.366025 + 0.151613i) q^{5} +(3.06528 + 3.06528i) q^{7} +(-3.95680 + 3.95680i) q^{9} +O(q^{10})$	\(q+(1.12197 + 2.70868i) q^{3} +(0.366025 + 0.151613i) q^{5} +(3.06528 + 3.06528i) q^{7} +(-3.95680 + 3.95680i) q^{9} +(-1.51815 + 3.66515i) q^{11} +(1.88366 - 0.780239i) q^{13} +1.16155i q^{15} -4.54587i q^{17} +(-0.534684 + 0.221474i) q^{19} +(-4.86370 + 11.7420i) q^{21} +(4.41794 - 4.41794i) q^{23} +(-3.42455 - 3.42455i) q^{25} +(-7.03106 - 2.91236i) q^{27} +(1.96642 + 4.74737i) q^{29} -0.0539984 q^{31} -11.6310 q^{33} +(0.657235 + 1.58671i) q^{35} +(-0.798499 - 0.330749i) q^{37} +(4.22683 + 4.22683i) q^{39} +(-0.621063 + 0.621063i) q^{41} +(0.857104 - 2.06923i) q^{43} +(-2.04819 + 0.848387i) q^{45} -9.44387i q^{47} +11.7919i q^{49} +(12.3133 - 5.10033i) q^{51} +(4.16622 - 10.0582i) q^{53} +(-1.11137 + 1.11137i) q^{55} +(-1.19980 - 1.19980i) q^{57} +(-7.17877 - 2.97354i) q^{59} +(4.02993 + 9.72911i) q^{61} -24.2574 q^{63} +0.807763 q^{65} +(3.12265 + 7.53875i) q^{67} +(16.9236 + 7.00997i) q^{69} +(-2.99152 - 2.99152i) q^{71} +(2.91724 - 2.91724i) q^{73} +(5.43375 - 13.1182i) q^{75} +(-15.8883 + 6.58114i) q^{77} +5.74836i q^{79} -5.52520i q^{81} +(3.30517 - 1.36905i) q^{83} +(0.689211 - 1.66390i) q^{85} +(-10.6528 + 10.6528i) q^{87} +(-2.38134 - 2.38134i) q^{89} +(8.16561 + 3.38231i) q^{91} +(-0.0605847 - 0.146264i) q^{93} -0.229286 q^{95} -13.2672 q^{97} +(-8.49522 - 20.5093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 8 q^{13} - 16 q^{21} - 32 q^{25} + 24 q^{29} - 80 q^{33} - 40 q^{37} - 16 q^{41} - 24 q^{45} + 56 q^{53} - 16 q^{57} - 8 q^{61} - 32 q^{65} + 64 q^{69} + 32 q^{73} - 64 q^{77} + 48 q^{85} + 32 q^{89} - 80 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 - 16 * q^9 + 8 * q^13 - 16 * q^21 - 32 * q^25 + 24 * q^29 - 80 * q^33 - 40 * q^37 - 16 * q^41 - 24 * q^45 + 56 * q^53 - 16 * q^57 - 8 * q^61 - 32 * q^65 + 64 * q^69 + 32 * q^73 - 64 * q^77 + 48 * q^85 + 32 * q^89 - 80 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.12197	+	2.70868i	0.647770	+	1.56386i	0.815965	+	0.578102i	$0.196206\pi$
$3$	1.12197	+	2.70868i	0.647770	+	1.56386i	−0.168194	+	0.985754i	$0.553794\pi$
$4$		0			0
$5$	0.366025	+	0.151613i	0.163692	+	0.0678033i	0.463025	−	0.886345i	$-0.346764\pi$
$5$	0.366025	+	0.151613i	0.163692	+	0.0678033i	−0.299333	+	0.954149i	$0.596764\pi$
$6$		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
$11$	−1.51815	+	3.66515i	−0.457741	+	1.10508i	0.511569	+	0.859242i	$0.329064\pi$
$11$	−1.51815	+	3.66515i	−0.457741	+	1.10508i	−0.969310	+	0.245842i	$0.920936\pi$
$12$		0			0
$13$	1.88366	−	0.780239i	0.522434	−	0.216399i	−0.105852	−	0.994382i	$-0.533757\pi$
$13$	1.88366	−	0.780239i	0.522434	−	0.216399i	0.628286	+	0.777983i	$0.283757\pi$
$14$		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
$19$	−0.534684	+	0.221474i	−0.122665	+	0.0508095i	−0.443172	−	0.896437i	$-0.646147\pi$
$19$	−0.534684	+	0.221474i	−0.122665	+	0.0508095i	0.320507	+	0.947246i	$0.396147\pi$
$20$		0			0
$21$	−4.86370	+	11.7420i	−1.06135	+	2.56232i
$22$		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
$27$	−7.03106	−	2.91236i	−1.35313	−	0.560484i
$28$		0			0
$29$	1.96642	+	4.74737i	0.365156	+	0.881564i	0.994529	+	0.104461i	$0.0333117\pi$
$29$	1.96642	+	4.74737i	0.365156	+	0.881564i	−0.629373	+	0.777103i	$0.716688\pi$
$30$		0			0
$31$	−0.0539984			−0.00969841			−0.00484920	−	0.999988i	$-0.501544\pi$
$31$	−0.0539984			−0.00969841			−0.00484920	+	0.999988i	$0.501544\pi$
$32$		0			0
$33$	−11.6310			−2.02470
$34$		0			0
$35$	0.657235	+	1.58671i	0.111093	+	0.268202i
$36$		0			0
$37$	−0.798499	−	0.330749i	−0.131272	−	0.0543748i	0.316080	−	0.948732i	$-0.397633\pi$
$37$	−0.798499	−	0.330749i	−0.131272	−	0.0543748i	−0.447353	+	0.894358i	$0.647633\pi$
$38$		0			0
$39$	4.22683	+	4.22683i	0.676835	+	0.676835i
$40$		0			0
$41$	−0.621063	+	0.621063i	−0.0969937	+	0.0969937i	−0.753939	−	0.656945i	$-0.771848\pi$
$41$	−0.621063	+	0.621063i	−0.0969937	+	0.0969937i	0.656945	+	0.753939i	$0.271848\pi$
$42$		0			0
$43$	0.857104	−	2.06923i	0.130707	−	0.315555i	−0.844954	−	0.534839i	$-0.820372\pi$
$43$	0.857104	−	2.06923i	0.130707	−	0.315555i	0.975661	+	0.219284i	$0.0703722\pi$
$44$		0			0
$45$	−2.04819	+	0.848387i	−0.305326	+	0.126470i
$46$		0			0
$47$		−	9.44387i		−	1.37753i	−0.724984	−	0.688765i	$-0.758153\pi$
$47$		−	9.44387i		−	1.37753i	0.724984	−	0.688765i	$-0.241847\pi$
$48$		0			0
$49$			11.7919i			1.68456i
$50$		0			0
$51$	12.3133	−	5.10033i	1.72420	−	0.714189i
$52$		0			0
$53$	4.16622	−	10.0582i	0.572275	−	1.38159i	−0.327339	−	0.944907i	$-0.606152\pi$
$53$	4.16622	−	10.0582i	0.572275	−	1.38159i	0.899614	−	0.436687i	$-0.143848\pi$
$54$		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
$59$	−7.17877	−	2.97354i	−0.934596	−	0.387123i	−0.137176	−	0.990547i	$-0.543803\pi$
$59$	−7.17877	−	2.97354i	−0.934596	−	0.387123i	−0.797420	+	0.603424i	$0.793803\pi$
$60$		0			0
$61$	4.02993	+	9.72911i	0.515979	+	1.24568i	0.940354	+	0.340198i	$0.110494\pi$
$61$	4.02993	+	9.72911i	0.515979	+	1.24568i	−0.424375	+	0.905487i	$0.639506\pi$
$62$		0			0
$63$	−24.2574			−3.05614
$64$		0			0
$65$	0.807763			0.100191
$66$		0			0
$67$	3.12265	+	7.53875i	0.381493	+	0.921004i	0.991678	+	0.128746i	$0.0410951\pi$
$67$	3.12265	+	7.53875i	0.381493	+	0.921004i	−0.610185	+	0.792259i	$0.708905\pi$
$68$		0			0
$69$	16.9236	+	7.00997i	2.03736	+	0.843901i
$70$		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	−0.515470	−	0.856907i	$-0.672383\pi$
$73$	2.91724	−	2.91724i	0.341437	−	0.341437i	0.856907	+	0.515470i	$0.172383\pi$
$74$		0			0
$75$	5.43375	−	13.1182i	0.627435	−	1.51476i
$76$		0			0
$77$	−15.8883	+	6.58114i	−1.81064	+	0.749991i
$78$		0			0
$79$			5.74836i			0.646741i	0.946272	+	0.323370i	$0.104816\pi$
$79$			5.74836i			0.646741i	−0.946272	+	0.323370i	$0.895184\pi$
$80$		0			0
$81$		−	5.52520i		−	0.613911i
$82$		0			0
$83$	3.30517	−	1.36905i	0.362790	−	0.150272i	−0.193840	−	0.981033i	$-0.562094\pi$
$83$	3.30517	−	1.36905i	0.362790	−	0.150272i	0.556630	+	0.830761i	$0.312094\pi$
$84$		0			0
$85$	0.689211	−	1.66390i	0.0747554	−	0.180476i
$86$		0			0
$87$	−10.6528	+	10.6528i	−1.14210	+	1.14210i
$88$		0			0
$89$	−2.38134	−	2.38134i	−0.252422	−	0.252422i	0.569541	−	0.821963i	$-0.307121\pi$
$89$	−2.38134	−	2.38134i	−0.252422	−	0.252422i	−0.821963	+	0.569541i	$0.807121\pi$
$90$		0			0
$91$	8.16561	+	3.38231i	0.855989	+	0.354562i
$92$		0			0
$93$	−0.0605847	−	0.146264i	−0.00628234	−	0.0151669i
$94$		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
$99$	−8.49522	−	20.5093i	−0.853801	−	2.06126i
$100$		0			0
$101$	−13.6610	−	5.65855i	−1.35932	−	0.563047i	−0.420446	−	0.907318i	$-0.638126\pi$
$101$	−13.6610	−	5.65855i	−1.35932	−	0.563047i	−0.938870	+	0.344271i	$0.888126\pi$
$102$		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
$107$	−3.16083	+	7.63093i	−0.305569	+	0.737710i	0.694269	+	0.719716i	$0.255728\pi$
$107$	−3.16083	+	7.63093i	−0.305569	+	0.737710i	−0.999838	+	0.0179938i	$0.994272\pi$
$108$		0			0
$109$	−2.46240	+	1.01996i	−0.235855	+	0.0976945i	−0.497481	−	0.867475i	$-0.665741\pi$
$109$	−2.46240	+	1.01996i	−0.235855	+	0.0976945i	0.261625	+	0.965169i	$0.415741\pi$
$110$		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
$115$	2.28689	−	0.947262i	0.213254	−	0.0883326i
$116$		0			0
$117$	−4.36603	+	10.5405i	−0.403639	+	0.974471i
$118$		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
$123$	−2.37907	−	0.985444i	−0.214514	−	0.0888545i
$124$		0			0
$125$	−1.49233	−	3.60280i	−0.133478	−	0.322244i
$126$		0			0
$127$	15.4530			1.37123			0.685614	−	0.727965i	$-0.259534\pi$
$127$	15.4530			1.37123			0.685614	+	0.727965i	$0.259534\pi$
$128$		0			0
$129$	6.56653			0.578151
$130$		0			0
$131$	4.00352	+	9.66535i	0.349789	+	0.844465i	0.996644	+	0.0818527i	$0.0260837\pi$
$131$	4.00352	+	9.66535i	0.349789	+	0.844465i	−0.646855	+	0.762613i	$0.723916\pi$
$132$		0			0
$133$	−2.31784	−	0.960080i	−0.200982	−	0.0832495i
$134$		0			0
$135$	−2.13200	−	2.13200i	−0.183493	−	0.183493i
$136$		0			0
$137$	11.4887	−	11.4887i	0.981544	−	0.981544i	−0.0182885	−	0.999833i	$-0.505822\pi$
$137$	11.4887	−	11.4887i	0.981544	−	0.981544i	0.999833	+	0.0182885i	$0.00582173\pi$
$138$		0			0
$139$	−2.86897	+	6.92630i	−0.243343	+	0.587481i	−0.997611	−	0.0690854i	$-0.977992\pi$
$139$	−2.86897	+	6.92630i	−0.243343	+	0.587481i	0.754268	+	0.656567i	$0.227992\pi$
$140$		0			0
$141$	25.5804	−	10.5958i	2.15426	−	0.892323i
$142$		0			0
$143$			8.08843i			0.676388i
$144$		0			0
$145$			2.03579i			0.169063i
$146$		0			0
$147$	−31.9405	+	13.2302i	−2.63441	+	1.09121i
$148$		0			0
$149$	2.42248	−	5.84839i	0.198457	−	0.479119i	−0.793052	−	0.609154i	$-0.791509\pi$
$149$	2.42248	−	5.84839i	0.198457	−	0.479119i	0.991509	+	0.130035i	$0.0415091\pi$
$150$		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
$155$	−0.0197648	−	0.00818685i	−0.00158755	−	0.000657583i
$156$		0			0
$157$	−3.12025	−	7.53295i	−0.249023	−	0.601195i	0.749098	−	0.662459i	$-0.230487\pi$
$157$	−3.12025	−	7.53295i	−0.249023	−	0.601195i	−0.998122	+	0.0612635i	$0.980487\pi$
$158$		0			0
$159$	31.9187			2.53132
$160$		0			0
$161$	27.0844			2.13455
$162$		0			0
$163$	2.28073	+	5.50617i	0.178640	+	0.431276i	0.987682	−	0.156475i	$-0.0500132\pi$
$163$	2.28073	+	5.50617i	0.178640	+	0.431276i	−0.809041	+	0.587752i	$0.800013\pi$
$164$		0			0
$165$	−4.25725	−	1.76341i	−0.331427	−	0.137281i
$166$		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
$171$	1.23931	−	2.99196i	0.0947725	−	0.228801i
$172$		0			0
$173$	16.0158	−	6.63397i	1.21766	−	0.504372i	0.320996	−	0.947081i	$-0.395982\pi$
$173$	16.0158	−	6.63397i	1.21766	−	0.504372i	0.896665	+	0.442709i	$0.145982\pi$
$174$		0			0
$175$		−	20.9944i		−	1.58703i
$176$		0			0
$177$		−	22.7812i		−	1.71234i
$178$		0			0
$179$	8.69109	−	3.59997i	0.649602	−	0.269074i	−0.0334535	−	0.999440i	$-0.510651\pi$
$179$	8.69109	−	3.59997i	0.649602	−	0.269074i	0.683056	+	0.730366i	$0.260651\pi$
$180$		0			0
$181$	0.276217	−	0.666847i	0.0205310	−	0.0495663i	−0.913282	−	0.407329i	$-0.866460\pi$
$181$	0.276217	−	0.666847i	0.0205310	−	0.0495663i	0.933813	+	0.357763i	$0.116460\pi$
$182$		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
$187$	16.6613	+	6.90133i	1.21839	+	0.504675i
$188$		0			0
$189$	−12.6250	−	30.4794i	−0.918332	−	2.21705i
$190$		0			0
$191$	−10.1746			−0.736209			−0.368105	−	0.929784i	$-0.619993\pi$
$191$	−10.1746			−0.736209			−0.368105	+	0.929784i	$0.619993\pi$
$192$		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
$195$	0.906286	+	2.18797i	0.0649005	+	0.156684i
$196$		0			0
$197$	−14.5064	−	6.00875i	−1.03354	−	0.428106i	−0.199550	−	0.979888i	$-0.563948\pi$
$197$	−14.5064	−	6.00875i	−1.03354	−	0.428106i	−0.833988	+	0.551782i	$0.813948\pi$
$198$		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
$203$	−8.52437	+	20.5797i	−0.598294	+	1.44441i
$204$		0			0
$205$	−0.321486	+	0.133164i	−0.0224535	+	0.00930056i
$206$		0			0
$207$			34.9617i			2.43001i
$208$		0			0
$209$		−	2.29593i		−	0.158813i
$210$		0			0
$211$	−16.9059	+	7.00267i	−1.16385	+	0.482083i	−0.879156	−	0.476534i	$-0.841893\pi$
$211$	−16.9059	+	7.00267i	−1.16385	+	0.482083i	−0.284696	+	0.958618i	$0.591893\pi$
$212$		0			0
$213$	4.74666	−	11.4595i	0.325236	−	0.785189i
$214$		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
$219$	11.1749	+	4.62880i	0.755131	+	0.312786i
$220$		0			0
$221$	−3.54686	−	8.56288i	−0.238588	−	0.576002i
$222$		0			0
$223$	21.6471			1.44959			0.724797	−	0.688962i	$-0.241934\pi$
$223$	21.6471			1.44959			0.724797	+	0.688962i	$0.241934\pi$
$224$		0			0
$225$	27.1005			1.80670
$226$		0			0
$227$	−3.67176	−	8.86440i	−0.243703	−	0.588351i	0.753942	−	0.656941i	$-0.228150\pi$
$227$	−3.67176	−	8.86440i	−0.243703	−	0.588351i	−0.997645	+	0.0685901i	$0.978150\pi$
$228$		0			0
$229$	26.5787	+	11.0093i	1.75637	+	0.727513i	0.997046	+	0.0768003i	$0.0244704\pi$
$229$	26.5787	+	11.0093i	1.75637	+	0.727513i	0.759324	+	0.650712i	$0.225530\pi$
$230$		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	$-0.434203\pi$
$233$	18.0722	−	18.0722i	1.18395	−	1.18395i	0.978712	−	0.205239i	$-0.0657972\pi$
$234$		0			0
$235$	1.43181	−	3.45670i	0.0934011	−	0.225490i
$236$		0			0
$237$	−15.5704	+	6.44949i	−1.01141	+	0.418939i
$238$		0			0
$239$			24.0765i			1.55738i	0.627409	+	0.778690i	$0.284116\pi$
$239$			24.0765i			1.55738i	−0.627409	+	0.778690i	$0.715884\pi$
$240$		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
$243$	−6.12719	+	2.53797i	−0.393060	+	0.162811i
$244$		0			0
$245$	−1.78780	+	4.31614i	−0.114219	+	0.275748i
$246$		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
$251$	23.0365	+	9.54203i	1.45405	+	0.602288i	0.963159	−	0.268933i	$-0.0866710\pi$
$251$	23.0365	+	9.54203i	1.45405	+	0.602288i	0.490892	+	0.871221i	$0.336671\pi$
$252$		0			0
$253$	9.48528	+	22.8995i	0.596335	+	1.43968i
$254$		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
$259$	−1.43379	−	3.46146i	−0.0890911	−	0.215085i
$260$		0			0
$261$	−26.5651	−	11.0036i	−1.64434	−	0.681107i
$262$		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
$267$	3.77849	−	9.12208i	0.231240	−	0.558262i
$268$		0			0
$269$	−13.1421	+	5.44363i	−0.801286	+	0.331904i	−0.745472	−	0.666537i	$-0.767776\pi$
$269$	−13.1421	+	5.44363i	−0.801286	+	0.331904i	−0.0558149	+	0.998441i	$0.517776\pi$
$270$		0			0
$271$		−	17.5598i		−	1.06668i	−0.845900	−	0.533341i	$-0.820936\pi$
$271$		−	17.5598i		−	1.06668i	0.845900	−	0.533341i	$-0.179064\pi$
$272$		0			0
$273$			25.9129i			1.56832i
$274$		0			0
$275$	17.7505	−	7.35248i	1.07039	−	0.443371i
$276$		0			0
$277$	10.0964	−	24.3747i	0.606631	−	1.46454i	−0.260011	−	0.965606i	$-0.583726\pi$
$277$	10.0964	−	24.3747i	0.606631	−	1.46454i	0.866642	−	0.498931i	$-0.166274\pi$
$278$		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	$-0.995923\pi$
$281$	−16.9764	−	16.9764i	−1.01273	−	1.01273i	−0.0128071	−	0.999918i	$-0.504077\pi$
$282$		0			0
$283$	−3.25301	−	1.34744i	−0.193372	−	0.0800972i	0.283896	−	0.958855i	$-0.408373\pi$
$283$	−3.25301	−	1.34744i	−0.193372	−	0.0800972i	−0.477268	+	0.878758i	$0.658373\pi$
$284$		0			0
$285$	−0.257253	−	0.621063i	−0.0152383	−	0.0367886i
$286$		0			0
$287$	−3.80746			−0.224747
$288$		0			0
$289$	−3.66490			−0.215582
$290$		0			0
$291$	−14.8854	−	35.9366i	−0.872600	−	2.10664i
$292$		0			0
$293$	−2.88607	−	1.19545i	−0.168606	−	0.0698388i	0.296784	−	0.954945i	$-0.404086\pi$
$293$	−2.88607	−	1.19545i	−0.168606	−	0.0698388i	−0.465390	+	0.885106i	$0.654086\pi$
$294$		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
$299$	4.87486	−	11.7689i	0.281920	−	0.680616i
$300$		0			0
$301$	8.97005	−	3.71552i	0.517025	−	0.214159i
$302$		0			0
$303$		−	43.3519i		−	2.49050i
$304$		0			0
$305$			4.17209i			0.238893i
$306$		0			0
$307$	−7.87800	+	3.26318i	−0.449621	+	0.186239i	−0.595992	−	0.802991i	$-0.703241\pi$
$307$	−7.87800	+	3.26318i	−0.449621	+	0.186239i	0.146370	+	0.989230i	$0.453241\pi$
$308$		0			0
$309$	7.40957	−	17.8883i	0.421516	−	1.01763i
$310$		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	$0.0686923\pi$
$313$	21.0698	+	21.0698i	1.19094	+	1.19094i	0.214132	+	0.976805i	$0.431308\pi$
$314$		0			0
$315$	−8.87882	−	3.67773i	−0.500265	−	0.207216i
$316$		0			0
$317$	−10.7863	−	26.0404i	−0.605818	−	1.46258i	−0.867508	−	0.497423i	$-0.834280\pi$
$317$	−10.7863	−	26.0404i	−0.605818	−	1.46258i	0.261690	−	0.965152i	$-0.415720\pi$
$318$		0			0
$319$	−20.3851			−1.14135
$320$		0			0
$321$	−24.2161			−1.35161
$322$		0			0
$323$	1.00679	+	2.43060i	0.0560192	+	0.135242i
$324$		0			0
$325$	−9.12266	−	3.77873i	−0.506034	−	0.209606i
$326$		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
$331$	12.0060	−	28.9852i	0.659912	−	1.59317i	−0.138026	−	0.990429i	$-0.544076\pi$
$331$	12.0060	−	28.9852i	0.659912	−	1.59317i	0.797938	−	0.602740i	$-0.205924\pi$
$332$		0			0
$333$	4.46821	−	1.85079i	0.244856	−	0.101423i
$334$		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
$339$	−13.4478	+	5.57028i	−0.730386	+	0.302536i
$340$		0			0
$341$	0.0819780	−	0.197912i	0.00443935	−	0.0107176i
$342$		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
$347$	−26.1047	−	10.8129i	−1.40137	−	0.580468i	−0.451266	−	0.892389i	$-0.649027\pi$
$347$	−26.1047	−	10.8129i	−1.40137	−	0.580468i	−0.950108	+	0.311921i	$0.899027\pi$
$348$		0			0
$349$	4.99757	+	12.0652i	0.267514	+	0.645836i	0.999365	−	0.0356289i	$-0.0113434\pi$
$349$	4.99757	+	12.0652i	0.267514	+	0.645836i	−0.731851	+	0.681464i	$0.761343\pi$
$350$		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
$355$	−0.641420	−	1.54852i	−0.0340430	−	0.0821871i
$356$		0			0
$357$	53.3776	+	22.1097i	2.82504	+	1.17017i
$358$		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
$363$	5.31601	−	12.8340i	0.279018	−	0.673610i
$364$		0			0
$365$	1.51007	−	0.625493i	0.0790409	−	0.0327398i
$366$		0			0
$367$			18.9285i			0.988061i	0.869444	+	0.494031i	$0.164477\pi$
$367$			18.9285i			0.988061i	−0.869444	+	0.494031i	$0.835523\pi$
$368$		0			0
$369$		−	4.91484i		−	0.255856i
$370$		0			0
$371$	43.6017	−	18.0604i	2.26369	−	0.937651i
$372$		0			0
$373$	−5.92159	+	14.2960i	−0.306608	+	0.740218i	0.693202	+	0.720743i	$0.256199\pi$
$373$	−5.92159	+	14.2960i	−0.306608	+	0.740218i	−0.999810	+	0.0194748i	$0.993801\pi$
$374$		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
$379$	−19.8882	−	8.23798i	−1.02159	−	0.423157i	−0.191920	−	0.981411i	$-0.561471\pi$
$379$	−19.8882	−	8.23798i	−1.02159	−	0.423157i	−0.829670	+	0.558254i	$0.811471\pi$
$380$		0			0
$381$	17.3378	+	41.8571i	0.888241	+	2.14440i
$382$		0			0
$383$	−14.8953			−0.761113			−0.380556	−	0.924758i	$-0.624268\pi$
$383$	−14.8953			−0.761113			−0.380556	+	0.924758i	$0.624268\pi$
$384$		0			0
$385$	−6.81330			−0.347238
$386$		0			0
$387$	4.79614	+	11.5789i	0.243802	+	0.588589i
$388$		0			0
$389$	−18.3896	−	7.61723i	−0.932390	−	0.386209i	−0.135805	−	0.990736i	$-0.543362\pi$
$389$	−18.3896	−	7.61723i	−0.932390	−	0.386209i	−0.796585	+	0.604527i	$0.793362\pi$
$390$		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
$395$	−0.871524	+	2.10404i	−0.0438511	+	0.105866i
$396$		0			0
$397$	−15.0423	+	6.23072i	−0.754951	+	0.312711i	−0.726760	−	0.686891i	$-0.758975\pi$
$397$	−15.0423	+	6.23072i	−0.754951	+	0.312711i	−0.0281913	+	0.999603i	$0.508975\pi$
$398$		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
$403$	−0.101715	+	0.0421317i	−0.00506678	+	0.00209873i
$404$		0			0
$405$	0.837691	−	2.02236i	0.0416252	−	0.100492i
$406$		0			0
$407$	2.42449	−	2.42449i	0.120177	−	0.120177i
$408$		0			0
$409$	−15.4495	−	15.4495i	−0.763928	−	0.763928i	0.213102	−	0.977030i	$-0.431643\pi$
$409$	−15.4495	−	15.4495i	−0.763928	−	0.763928i	−0.977030	+	0.213102i	$0.931643\pi$
$410$		0			0
$411$	44.0091	+	18.2292i	2.17081	+	0.899179i
$412$		0			0
$413$	−12.8902	−	31.1197i	−0.634286	−	1.53130i
$414$		0			0
$415$	1.41734			0.0695746
$416$		0			0
$417$	−21.9800			−1.07637
$418$		0			0
$419$	4.26299	+	10.2918i	0.208261	+	0.502786i	0.993149	−	0.116851i	$-0.0372799\pi$
$419$	4.26299	+	10.2918i	0.208261	+	0.502786i	−0.784889	+	0.619637i	$0.787280\pi$
$420$		0			0
$421$	−24.2514	−	10.0453i	−1.18194	−	0.489576i	−0.296819	−	0.954934i	$-0.595926\pi$
$421$	−24.2514	−	10.0453i	−1.18194	−	0.489576i	−0.885123	+	0.465357i	$0.845926\pi$
$422$		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
$427$	−17.4696	+	42.1753i	−0.845413	+	2.04101i
$428$		0			0
$429$	−21.9089	+	9.07498i	−1.05777	+	0.438144i
$430$		0			0
$431$			11.4592i			0.551972i	0.961162	+	0.275986i	$0.0890043\pi$
$431$			11.4592i			0.551972i	−0.961162	+	0.275986i	$0.910996\pi$
$432$		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
$435$	−5.51430	+	2.28410i	−0.264391	+	0.109514i
$436$		0			0
$437$	−1.38375	+	3.34066i	−0.0661935	+	0.159805i
$438$		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
$443$	−10.8126	−	4.47872i	−0.513722	−	0.212791i	0.110735	−	0.993850i	$-0.464680\pi$
$443$	−10.8126	−	4.47872i	−0.513722	−	0.212791i	−0.624457	+	0.781059i	$0.714680\pi$
$444$		0			0
$445$	−0.510590	−	1.23267i	−0.0242043	−	0.0584343i
$446$		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
$451$	−1.33342	−	3.21916i	−0.0627882	−	0.151584i
$452$		0			0
$453$	29.0092	+	12.0160i	1.36297	+	0.564562i
$454$		0			0
$455$	2.47602	+	2.47602i	0.116078	+	0.116078i
$456$		0			0
$457$	−15.1910	+	15.1910i	−0.710605	+	0.710605i	−0.966662	−	0.256057i	$-0.917577\pi$
$457$	−15.1910	+	15.1910i	−0.710605	+	0.710605i	0.256057	+	0.966662i	$0.417577\pi$
$458$		0			0
$459$	−13.2392	+	31.9623i	−0.617953	+	1.49187i
$460$		0			0
$461$	−14.8912	+	6.16815i	−0.693554	+	0.287279i	−0.701480	−	0.712689i	$-0.747477\pi$
$461$	−14.8912	+	6.16815i	−0.693554	+	0.287279i	0.00792626	+	0.999969i	$0.497477\pi$
$462$		0			0
$463$			11.4145i			0.530477i	0.964183	+	0.265238i	$0.0854506\pi$
$463$			11.4145i			0.530477i	−0.964183	+	0.265238i	$0.914549\pi$
$464$		0			0
$465$		−	0.0627219i		−	0.00290866i
$466$		0			0
$467$	6.38825	−	2.64610i	0.295613	−	0.122447i	−0.229948	−	0.973203i	$-0.573856\pi$
$467$	6.38825	−	2.64610i	0.295613	−	0.122447i	0.525561	+	0.850756i	$0.323856\pi$
$468$		0			0
$469$	−13.5366	+	32.6802i	−0.625061	+	1.50903i
$470$		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
$475$	2.58950	+	1.07260i	0.118814	+	0.0492145i
$476$		0			0
$477$	23.3132	+	56.2830i	1.06744	+	2.57702i
$478$		0			0
$479$	−16.2733			−0.743545			−0.371772	−	0.928324i	$-0.621250\pi$
$479$	−16.2733			−0.743545			−0.371772	+	0.928324i	$0.621250\pi$
$480$		0			0
$481$	−1.76217			−0.0803479
$482$		0			0
$483$	30.3880	+	73.3630i	1.38270	+	3.33813i
$484$		0			0
$485$	−4.85614	−	2.01148i	−0.220506	−	0.0913366i
$486$		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
$491$	−5.48577	+	13.2438i	−0.247569	+	0.597686i	−0.997997	−	0.0632676i	$-0.979848\pi$
$491$	−5.48577	+	13.2438i	−0.247569	+	0.597686i	0.750427	+	0.660953i	$0.229848\pi$
$492$		0			0
$493$	21.5809	−	8.93910i	0.971955	−	0.402597i
$494$		0			0
$495$		−	8.79490i		−	0.395301i
$496$		0			0
$497$		−	18.3397i		−	0.822648i
$498$		0			0
$499$	−22.7784	+	9.43511i	−1.01970	+	0.422374i	−0.828984	−	0.559272i	$-0.811081\pi$
$499$	−22.7784	+	9.43511i	−1.01970	+	0.422374i	−0.190716	+	0.981645i	$0.561081\pi$
$500$		0			0
$501$	−22.8715	+	55.2168i	−1.02182	+	2.46690i
$502$		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
$507$	−23.9529	−	9.92163i	−1.06379	−	0.440635i
$508$		0			0
$509$	0.0998009	+	0.240941i	0.00442360	+	0.0106795i	0.926076	−	0.377337i	$-0.123160\pi$
$509$	0.0998009	+	0.240941i	0.00442360	+	0.0106795i	−0.921652	+	0.388017i	$0.873160\pi$
$510$		0			0
$511$	17.8843			0.791156
$512$		0			0
$513$	4.40441			0.194459
$514$		0			0
$515$	−1.00126	−	2.41726i	−0.0441208	−	0.106517i
$516$		0			0
$517$	34.6132	+	14.3373i	1.52229	+	0.630552i
$518$		0			0
$519$	35.9386	+	35.9386i	1.57753	+	1.57753i
$520$		0			0
$521$	−6.59451	+	6.59451i	−0.288911	+	0.288911i	−0.836649	−	0.547739i	$-0.815489\pi$
$521$	−6.59451	+	6.59451i	−0.288911	+	0.288911i	0.547739	+	0.836649i	$0.315489\pi$
$522$		0			0
$523$	12.4900	−	30.1535i	0.546148	−	1.31852i	−0.374174	−	0.927358i	$-0.622074\pi$
$523$	12.4900	−	30.1535i	0.546148	−	1.31852i	0.920323	−	0.391160i	$-0.127926\pi$
$524$		0			0
$525$	56.8671	−	23.5551i	2.48188	−	1.02803i
$526$		0			0
$527$			0.245470i			0.0106928i
$528$		0			0
$529$		−	16.0363i		−	0.697231i
$530$		0			0
$531$	40.1706	−	16.6392i	1.74326	−	0.722081i
$532$		0			0
$533$	−0.685296	+	1.65445i	−0.0296835	+	0.0716622i
$534$		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
$539$	−43.2191	−	17.9019i	−1.86158	−	0.771091i
$540$		0			0
$541$	−5.46141	−	13.1850i	−0.234804	−	0.566867i	0.761926	−	0.647664i	$-0.224254\pi$
$541$	−5.46141	−	13.1850i	−0.234804	−	0.566867i	−0.996731	+	0.0807961i	$0.974254\pi$
$542$		0			0
$543$	2.11618			0.0908140
$544$		0			0
$545$	−1.05594			−0.0452315
$546$		0			0
$547$	−9.46669	−	22.8546i	−0.404766	−	0.977192i	−0.986492	−	0.163807i	$-0.947622\pi$
$547$	−9.46669	−	22.8546i	−0.404766	−	0.977192i	0.581726	−	0.813385i	$-0.302378\pi$
$548$		0			0
$549$	−54.4417	−	22.5505i	−2.32351	−	0.962431i
$550$		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
$555$	0.384182	−	0.927497i	0.0163076	−	0.0393700i
$556$		0			0
$557$	17.6576	−	7.31400i	0.748175	−	0.309904i	0.0241782	−	0.999708i	$-0.492303\pi$
$557$	17.6576	−	7.31400i	0.748175	−	0.309904i	0.723997	+	0.689804i	$0.242303\pi$
$558$		0			0
$559$		−	4.56648i		−	0.193142i
$560$		0			0
$561$			52.8731i			2.23230i
$562$		0			0
$563$	−29.0826	+	12.0464i	−1.22568	+	0.507695i	−0.899213	−	0.437512i	$-0.855860\pi$
$563$	−29.0826	+	12.0464i	−1.22568	+	0.507695i	−0.326472	+	0.945207i	$0.605860\pi$
$564$		0			0
$565$	−0.752715	+	1.81722i	−0.0316670	+	0.0764508i
$566$		0			0
$567$	16.9363	−	16.9363i	0.711258	−	0.711258i
$568$		0			0
$569$	18.1317	+	18.1317i	0.760118	+	0.760118i	0.976344	−	0.216225i	$-0.0693745\pi$
$569$	18.1317	+	18.1317i	0.760118	+	0.760118i	−0.216225	+	0.976344i	$0.569375\pi$
$570$		0			0
$571$	−7.77020	−	3.21852i	−0.325173	−	0.134691i	0.214125	−	0.976806i	$-0.431310\pi$
$571$	−7.77020	−	3.21852i	−0.325173	−	0.134691i	−0.539297	+	0.842115i	$0.681310\pi$
$572$		0			0
$573$	−11.4156	−	27.5597i	−0.476894	−	1.15133i
$574$		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
$579$	13.1848	+	31.8309i	0.547942	+	1.32285i
$580$		0			0
$581$	14.3278	+	5.93477i	0.594418	+	0.246216i
$582$		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
$587$	−13.2730	+	32.0438i	−0.547835	+	1.32259i	0.371251	+	0.928533i	$0.378929\pi$
$587$	−13.2730	+	32.0438i	−0.547835	+	1.32259i	−0.919086	+	0.394058i	$0.871071\pi$
$588$		0			0
$589$	0.0288721	−	0.0119592i	0.00118966	−	0.000492771i
$590$		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
$595$	7.21296	−	2.98770i	0.295702	−	0.122484i
$596$		0			0
$597$	−3.69213	+	8.91359i	−0.151109	+	0.364809i
$598$		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	0.690684	−	0.723157i	$-0.257309\pi$
$601$	−0.796070	−	0.796070i	−0.0324724	−	0.0324724i	−0.723157	+	0.690684i	$0.757309\pi$
$602$		0			0
$603$	−42.1850	−	17.4736i	−1.71790	−	0.711579i
$604$		0			0
$605$	−0.718357	−	1.73427i	−0.0292053	−	0.0705079i
$606$		0			0
$607$	−13.8854			−0.563591			−0.281795	−	0.959475i	$-0.590930\pi$
$607$	−13.8854			−0.563591			−0.281795	+	0.959475i	$0.590930\pi$
$608$		0			0
$609$	−65.3078			−2.64640
$610$		0			0
$611$	−7.36848	−	17.7891i	−0.298097	−	0.719669i
$612$		0			0
$613$	9.46292	+	3.91967i	0.382204	+	0.158314i	0.565509	−	0.824742i	$-0.308680\pi$
$613$	9.46292	+	3.91967i	0.382204	+	0.158314i	−0.183305	+	0.983056i	$0.558680\pi$
$614$		0			0
$615$	−0.721395	−	0.721395i	−0.0290895	−	0.0290895i
$616$		0			0
$617$	−5.39736	+	5.39736i	−0.217290	+	0.217290i	−0.807355	−	0.590066i	$-0.799102\pi$
$617$	−5.39736	+	5.39736i	−0.217290	+	0.217290i	0.590066	+	0.807355i	$0.299102\pi$
$618$		0			0
$619$	12.9301	−	31.2161i	0.519706	−	1.25468i	−0.418379	−	0.908273i	$-0.637401\pi$
$619$	12.9301	−	31.2161i	0.519706	−	1.25468i	0.938084	−	0.346408i	$-0.112599\pi$
$620$		0			0
$621$	−43.9294	+	18.1962i	−1.76283	+	0.730186i
$622$		0			0
$623$		−	14.5990i		−	0.584895i
$624$		0			0
$625$			22.6702i			0.906809i
$626$		0			0
$627$	6.21893	−	2.57597i	0.248360	−	0.102874i
$628$		0			0
$629$	−1.50354	+	3.62987i	−0.0599501	+	0.144732i
$630$		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
$635$	5.65618	+	2.34286i	0.224458	+	0.0929737i
$636$		0			0
$637$	9.20050	+	22.2120i	0.364537	+	0.880071i
$638$		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
$643$	−3.89697	−	9.40811i	−0.153681	−	0.371020i	0.828223	−	0.560399i	$-0.189352\pi$
$643$	−3.89697	−	9.40811i	−0.153681	−	0.371020i	−0.981904	+	0.189380i	$0.939352\pi$
$644$		0			0
$645$	2.40352	+	0.995569i	0.0946384	+	0.0392005i
$646$		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
$651$	0.262632	−	0.634051i	0.0102934	−	0.0248504i
$652$		0			0
$653$	−15.9705	+	6.61520i	−0.624974	+	0.258873i	−0.672616	−	0.739992i	$-0.734829\pi$
$653$	−15.9705	+	6.61520i	−0.624974	+	0.258873i	0.0476419	+	0.998864i	$0.484829\pi$
$654$		0			0
$655$			4.14475i			0.161949i
$656$		0			0
$657$			23.0858i			0.900665i
$658$		0			0
$659$	−3.12170	+	1.29305i	−0.121604	+	0.0503701i	−0.442656	−	0.896692i	$-0.645964\pi$
$659$	−3.12170	+	1.29305i	−0.121604	+	0.0503701i	0.321052	+	0.947062i	$0.395964\pi$
$660$		0			0
$661$	−17.7729	+	42.9077i	−0.691287	+	1.66892i	0.0508836	+	0.998705i	$0.483796\pi$
$661$	−17.7729	+	42.9077i	−0.691287	+	1.66892i	−0.742171	+	0.670211i	$0.766204\pi$
$662$		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
$667$	29.6611	+	12.2860i	1.14848	+	0.475717i
$668$		0			0
$669$	24.2874	+	58.6349i	0.939004	+	2.26696i
$670$		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
$675$	14.1047	+	34.0517i	0.542889	+	1.31065i
$676$		0			0
$677$	−10.2485	−	4.24507i	−0.393882	−	0.163151i	0.176947	−	0.984220i	$-0.443378\pi$
$677$	−10.2485	−	4.24507i	−0.393882	−	0.163151i	−0.570829	+	0.821069i	$0.693378\pi$
$678$		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
$683$	10.4720	−	25.2815i	0.400698	−	0.967371i	−0.586799	−	0.809733i	$-0.699612\pi$
$683$	10.4720	−	25.2815i	0.400698	−	0.967371i	0.987497	−	0.157638i	$-0.0503879\pi$
$684$		0			0
$685$	5.94698	−	2.46332i	0.227222	−	0.0941186i
$686$		0			0
$687$			84.3452i			3.21797i
$688$		0			0
$689$		−	22.1968i		−	0.845632i
$690$		0			0
$691$	28.0716	−	11.6277i	1.06790	−	0.442337i	0.221648	−	0.975127i	$-0.428856\pi$
$691$	28.0716	−	11.6277i	1.06790	−	0.442337i	0.846248	+	0.532790i	$0.178856\pi$
$692$		0			0
$693$	36.8265	−	88.9069i	1.39892	−	3.37729i
$694$		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
$699$	69.2284	+	28.6753i	2.61846	+	1.08460i
$700$		0			0
$701$	10.4808	+	25.3030i	0.395855	+	0.955679i	0.988638	+	0.150317i	$0.0480294\pi$
$701$	10.4808	+	25.3030i	0.395855	+	0.955679i	−0.592783	+	0.805363i	$0.701971\pi$
$702$		0			0
$703$	0.500197			0.0188653
$704$		0			0
$705$	10.9695			0.413136
$706$		0			0
$707$	−24.5296	−	59.2198i	−0.922531	−	2.22719i
$708$		0			0
$709$	44.0598	+	18.2502i	1.65470	+	0.685400i	0.997655	−	0.0684496i	$-0.0218052\pi$
$709$	44.0598	+	18.2502i	1.65470	+	0.685400i	0.657047	+	0.753850i	$0.271805\pi$
$710$		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
$715$	−1.22631	+	2.96057i	−0.0458613	+	0.110719i
$716$		0			0
$717$	−65.2155	+	27.0132i	−2.43552	+	1.00882i
$718$		0			0
$719$		−	20.5621i		−	0.766835i	−0.923575	−	0.383418i	$-0.874747\pi$
$719$		−	20.5621i		−	0.766835i	0.923575	−	0.383418i	$-0.125253\pi$
$720$		0			0
$721$		−	28.6284i		−	1.06618i
$722$		0			0
$723$	28.1224	−	11.6487i	1.04588	−	0.433219i
$724$		0			0
$725$	9.52347	−	22.9917i	0.353693	−	0.853890i
$726$		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
$731$	−9.40645	−	3.89628i	−0.347910	−	0.144109i
$732$		0			0
$733$	−18.3350	−	44.2647i	−0.677220	−	1.63495i	−0.769057	−	0.639180i	$-0.779274\pi$
$733$	−18.3350	−	44.2647i	−0.677220	−	1.63495i	0.0918368	−	0.995774i	$-0.470726\pi$
$734$		0			0
$735$	−13.6969			−0.505217
$736$		0			0
$737$	−32.3713			−1.19241
$738$		0			0
$739$	6.44435	+	15.5580i	0.237059	+	0.572312i	0.996976	−	0.0777085i	$-0.0247603\pi$
$739$	6.44435	+	15.5580i	0.237059	+	0.572312i	−0.759917	+	0.650020i	$0.774760\pi$
$740$		0			0
$741$	−3.19615	−	1.32389i	−0.117414	−	0.0486343i
$742$		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
$747$	−7.66085	+	18.4949i	−0.280296	+	0.676694i
$748$		0			0
$749$	−33.0798	+	13.7021i	−1.20871	+	0.500664i
$750$		0			0
$751$			4.40389i			0.160700i	0.996767	+	0.0803501i	$0.0256038\pi$
$751$			4.40389i			0.160700i	−0.996767	+	0.0803501i	$0.974396\pi$
$752$		0			0
$753$			73.1043i			2.66407i
$754$		0			0
$755$	3.92004	−	1.62373i	0.142665	−	0.0590937i
$756$		0			0
$757$	9.26500	−	22.3677i	0.336742	−	0.812968i	−0.661282	−	0.750137i	$-0.729987\pi$
$757$	9.26500	−	22.3677i	0.336742	−	0.812968i	0.998024	−	0.0628304i	$-0.0200127\pi$
$758$		0			0
$759$	−51.3851	+	51.3851i	−1.86516	+	1.86516i
$760$		0			0
$761$	6.81382	+	6.81382i	0.247001	+	0.247001i	0.819739	−	0.572738i	$-0.194119\pi$
$761$	6.81382	+	6.81382i	0.247001	+	0.247001i	−0.572738	+	0.819739i	$0.694119\pi$
$762$		0			0
$763$	−10.6744	−	4.42149i	−0.386440	−	0.160069i
$764$		0			0
$765$	3.85666	+	9.31079i	0.139438	+	0.336632i
$766$		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
$771$	−20.9944	−	50.6850i	−0.756095	−	1.82537i
$772$		0			0
$773$	−13.6437	−	5.65140i	−0.490730	−	0.203267i	0.123576	−	0.992335i	$-0.460564\pi$
$773$	−13.6437	−	5.65140i	−0.490730	−	0.203267i	−0.614305	+	0.789068i	$0.710564\pi$
$774$		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
$779$	0.194524	−	0.469621i	0.00696953	−	0.0168259i
$780$		0			0
$781$	15.5059	−	6.42277i	0.554846	−	0.229825i
$782$		0			0
$783$		−	39.1060i		−	1.39753i
$784$		0			0
$785$		−	3.23032i		−	0.115295i
$786$		0			0
$787$	9.06441	−	3.75460i	0.323111	−	0.133837i	−0.215231	−	0.976563i	$-0.569051\pi$
$787$	9.06441	−	3.75460i	0.323111	−	0.133837i	0.538343	+	0.842726i	$0.319051\pi$
$788$		0			0
$789$	−1.40373	+	3.38891i	−0.0499741	+	0.120648i
$790$		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
$795$	11.6830	+	4.83928i	0.414355	+	0.171631i
$796$		0			0
$797$	−14.4147	−	34.8002i	−0.510595	−	1.23269i	−0.943538	−	0.331264i	$-0.892525\pi$
$797$	−14.4147	−	34.8002i	−0.510595	−	1.23269i	0.432943	−	0.901421i	$-0.357475\pi$
$798$		0			0
$799$	−42.9306			−1.51878
$800$		0			0
$801$	18.8450			0.665854
$802$		0			0
$803$	6.26330	+	15.1209i	0.221027	+	0.533606i
$804$		0			0
$805$	9.91359	+	4.10634i	0.349408	+	0.144730i
$806$		0			0
$807$	−29.4901	−	29.4901i	−1.03810	−	1.03810i
$808$		0			0
$809$	6.59383	−	6.59383i	0.231827	−	0.231827i	−0.581628	−	0.813455i	$-0.697584\pi$
$809$	6.59383	−	6.59383i	0.231827	−	0.231827i	0.813455	+	0.581628i	$0.197584\pi$
$810$		0			0
$811$	12.0137	−	29.0036i	0.421857	−	1.01845i	−0.559942	−	0.828532i	$-0.689177\pi$
$811$	12.0137	−	29.0036i	0.421857	−	1.01845i	0.981799	−	0.189922i	$-0.0608234\pi$
$812$		0			0
$813$	47.5638	−	19.7016i	1.66814	−	0.690965i
$814$		0			0
$815$			2.36118i			0.0827087i
$816$		0			0
$817$			1.29621i			0.0453487i
$818$		0			0
$819$	−45.6928	+	18.9266i	−1.59663	+	0.661348i
$820$		0			0
$821$	11.1833	−	26.9988i	0.390299	−	0.942265i	−0.599575	−	0.800318i	$-0.704664\pi$
$821$	11.1833	−	26.9988i	0.390299	−	0.942265i	0.989874	−	0.141947i	$-0.0453362\pi$
$822$		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
$827$	−43.8102	−	18.1468i	−1.52343	−	0.631025i	−0.545154	−	0.838336i	$-0.683529\pi$
$827$	−43.8102	−	18.1468i	−1.52343	−	0.631025i	−0.978275	+	0.207311i	$0.933529\pi$
$828$		0			0
$829$	−12.0186	−	29.0154i	−0.417422	−	1.00774i	−0.983092	−	0.183113i	$-0.941382\pi$
$829$	−12.0186	−	29.0154i	−0.417422	−	1.00774i	0.565670	−	0.824632i	$-0.308618\pi$
$830$		0			0
$831$	77.3512			2.68328
$832$		0			0
$833$	53.6044			1.85728
$834$		0			0
$835$	3.09065	+	7.46148i	0.106956	+	0.258215i
$836$		0			0
$837$	0.379666	+	0.157263i	0.0131232	+	0.00543580i
$838$		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
$843$	26.9365	−	65.0305i	0.927743	−	2.23977i
$844$		0			0
$845$	−3.23678	+	1.34072i	−0.111349	+	0.0461221i
$846$		0			0
$847$		−	20.5395i		−	0.705746i
$848$		0			0
$849$		−	10.3232i		−	0.354290i
$850$		0			0
$851$	−4.98895	+	2.06649i	−0.171019	+	0.0708383i
$852$		0			0
$853$	3.15715	−	7.62203i	0.108099	−	0.260973i	−0.860569	−	0.509334i	$-0.829892\pi$
$853$	3.15715	−	7.62203i	0.108099	−	0.260973i	0.968668	+	0.248361i	$0.0798918\pi$
$854$		0			0
$855$	0.907239	−	0.907239i	0.0310269	−	0.0310269i
$856$		0			0
$857$	−8.53805	−	8.53805i	−0.291654	−	0.291654i	0.546079	−	0.837734i	$-0.316120\pi$
$857$	−8.53805	−	8.53805i	−0.291654	−	0.291654i	−0.837734	+	0.546079i	$0.816120\pi$
$858$		0			0
$859$	9.10474	+	3.77131i	0.310650	+	0.128675i	0.532561	−	0.846392i	$-0.321230\pi$
$859$	9.10474	+	3.77131i	0.310650	+	0.128675i	−0.221912	+	0.975067i	$0.571230\pi$
$860$		0			0
$861$	−4.27186	−	10.3132i	−0.145585	−	0.351473i
$862$		0			0
$863$	17.7816			0.605294			0.302647	−	0.953103i	$-0.402130\pi$
$863$	17.7816			0.605294			0.302647	+	0.953103i	$0.402130\pi$
$864$		0			0
$865$	6.86800			0.233519
$866$		0			0
$867$	−4.11191	−	9.92703i	−0.139648	−	0.337140i
$868$		0			0
$869$	−21.0686	−	8.72689i	−0.714703	−	0.296040i
$870$		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
$875$	6.46919	−	15.6180i	0.218699	−	0.527985i
$876$		0			0
$877$	21.4212	−	8.87297i	0.723344	−	0.299619i	0.00953022	−	0.999955i	$-0.496966\pi$
$877$	21.4212	−	8.87297i	0.723344	−	0.299619i	0.713814	+	0.700336i	$0.246966\pi$
$878$		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
$883$	−27.8481	+	11.5351i	−0.937165	+	0.388186i	−0.798392	−	0.602138i	$-0.794316\pi$
$883$	−27.8481	+	11.5351i	−0.937165	+	0.388186i	−0.138773	+	0.990324i	$0.544316\pi$
$884$		0			0
$885$	3.45392	−	8.33850i	0.116102	−	0.280296i
$886$		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
$891$	20.2507	+	8.38811i	0.678423	+	0.281012i
$892$		0			0
$893$	2.09157	+	5.04949i	0.0699917	+	0.168975i
$894$		0			0
$895$	3.72696			0.124579
$896$		0			0
$897$	37.3477			1.24700
$898$		0			0
$899$	−0.106184	−	0.256350i	−0.00354143	−	0.00854976i
$900$		0			0
$901$	−45.7230	−	18.9391i	−1.52325	−	0.630953i
$902$		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
$907$	−7.69269	+	18.5718i	−0.255432	+	0.616666i	−0.998626	−	0.0524095i	$-0.983310\pi$
$907$	−7.69269	+	18.5718i	−0.255432	+	0.616666i	0.743194	+	0.669076i	$0.233310\pi$
$908$		0			0
$909$	76.4434	−	31.6639i	2.53547	−	1.05022i
$910$		0			0
$911$			57.0332i			1.88960i	0.327655	+	0.944798i	$0.393742\pi$
$911$			57.0332i			1.88960i	−0.327655	+	0.944798i	$0.606258\pi$
$912$		0			0
$913$			14.1924i			0.469699i
$914$		0			0
$915$	−11.3008	+	4.68096i	−0.373594	+	0.154748i
$916$		0			0
$917$	−17.3551	+	41.8989i	−0.573116	+	1.38362i
$918$		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
$923$	−7.96911	−	3.30092i	−0.262307	−	0.108651i
$924$		0			0
$925$	1.60183	+	3.86716i	0.0526679	+	0.127152i
$926$		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
$931$	−2.61160	−	6.30495i	−0.0855916	−	0.206636i
$932$		0			0
$933$	12.9700	+	5.37237i	0.424620	+	0.175883i
$934$		0			0
$935$	5.05212	+	5.05212i	0.165222	+	0.165222i
$936$		0			0
$937$	−7.60456	+	7.60456i	−0.248430	+	0.248430i	−0.820326	−	0.571896i	$-0.806208\pi$
$937$	−7.60456	+	7.60456i	−0.248430	+	0.248430i	0.571896	+	0.820326i	$0.306208\pi$
$938$		0			0
$939$	−33.4316	+	80.7111i	−1.09100	+	2.63391i
$940$		0			0
$941$	2.74672	−	1.13773i	0.0895406	−	0.0370889i	−0.337464	−	0.941339i	$-0.609569\pi$
$941$	2.74672	−	1.13773i	0.0895406	−	0.0370889i	0.427004	+	0.904250i	$0.359569\pi$
$942$		0			0
$943$			5.48763i			0.178702i
$944$		0			0
$945$		−	13.0703i		−	0.425178i
$946$		0			0
$947$	−21.7202	+	8.99679i	−0.705811	+	0.292357i	−0.706570	−	0.707643i	$-0.749758\pi$
$947$	−21.7202	+	8.99679i	−0.705811	+	0.292357i	0.000758845		1.00000i	$0.499758\pi$
$948$		0			0
$949$	3.21895	−	7.77124i	0.104492	−	0.252265i
$950$		0			0
$951$	58.4332	−	58.4332i	1.89483	−	1.89483i
$952$		0			0
$953$	0.594510	+	0.594510i	0.0192581	+	0.0192581i	0.716670	−	0.697412i	$-0.245665\pi$
$953$	0.594510	+	0.594510i	0.0192581	+	0.0192581i	−0.697412	+	0.716670i	$0.745665\pi$
$954$		0			0
$955$	−3.72417	−	1.54260i	−0.120511	−	0.0499174i
$956$		0			0
$957$	−22.8715	−	55.2168i	−0.739332	−	1.78490i
$958$		0			0
$959$	70.4321			2.27437
$960$		0			0
$961$	−30.9971			−0.999906
$962$		0			0
$963$	−17.6872	−	42.7008i	−0.569964	−	1.37601i
$964$		0			0
$965$	4.30134	+	1.78167i	0.138465	+	0.0573541i
$966$		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
$971$	−18.9737	+	45.8066i	−0.608895	+	1.47000i	0.255308	+	0.966860i	$0.417823\pi$
$971$	−18.9737	+	45.8066i	−0.608895	+	1.47000i	−0.864203	+	0.503143i	$0.832177\pi$
$972$		0			0
$973$	−30.0253	+	12.4369i	−0.962566	+	0.398708i
$974$		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
$979$	12.3432	−	5.11273i	0.394491	−	0.163403i
$980$		0			0
$981$	5.70745	−	13.7790i	0.182225	−	0.439929i
$982$		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
$987$	110.890	+	45.9322i	3.52967	+	1.46204i
$988$		0			0
$989$	−5.35510	−	12.9284i	−0.170282	−	0.411098i
$990$		0			0
$991$	43.6148			1.38547			0.692735	−	0.721192i	$-0.256405\pi$
$991$	43.6148			1.38547			0.692735	+	0.721192i	$0.256405\pi$
$992$		0			0
$993$	91.9819			2.91896
$994$		0			0
$995$	0.498920	+	1.20450i	0.0158168	+	0.0381852i
$996$		0			0
$997$	−30.4769	−	12.6240i	−0.965214	−	0.399805i	−0.156286	−	0.987712i	$-0.549952\pi$
$997$	−30.4769	−	12.6240i	−0.965214	−	0.399805i	−0.808928	+	0.587907i	$0.799952\pi$
$998$		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.a.897.4	yes	16
4.3	odd	2	inner	1024.2.g.a.897.1	yes	16
8.3	odd	2		1024.2.g.f.897.4	yes	16
8.5	even	2		1024.2.g.f.897.1	yes	16
16.3	odd	4		1024.2.g.g.385.4	yes	16
16.5	even	4		1024.2.g.d.385.4	yes	16
16.11	odd	4		1024.2.g.d.385.1	yes	16
16.13	even	4		1024.2.g.g.385.1	yes	16
32.3	odd	8		1024.2.g.f.129.4	yes	16
32.5	even	8		1024.2.g.g.641.1	yes	16
32.11	odd	8		1024.2.g.d.641.1	yes	16
32.13	even	8	inner	1024.2.g.a.129.4	yes	16
32.19	odd	8	inner	1024.2.g.a.129.1	✓	16
32.21	even	8		1024.2.g.d.641.4	yes	16
32.27	odd	8		1024.2.g.g.641.4	yes	16
32.29	even	8		1024.2.g.f.129.1	yes	16
64.13	even	16		4096.2.a.s.1.8		8
64.19	odd	16		4096.2.a.s.1.7		8
64.45	even	16		4096.2.a.i.1.1		8
64.51	odd	16		4096.2.a.i.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.129.1	✓	16	32.19	odd	8	inner
1024.2.g.a.129.4	yes	16	32.13	even	8	inner
1024.2.g.a.897.1	yes	16	4.3	odd	2	inner
1024.2.g.a.897.4	yes	16	1.1	even	1	trivial
1024.2.g.d.385.1	yes	16	16.11	odd	4
1024.2.g.d.385.4	yes	16	16.5	even	4
1024.2.g.d.641.1	yes	16	32.11	odd	8
1024.2.g.d.641.4	yes	16	32.21	even	8
1024.2.g.f.129.1	yes	16	32.29	even	8
1024.2.g.f.129.4	yes	16	32.3	odd	8
1024.2.g.f.897.1	yes	16	8.5	even	2
1024.2.g.f.897.4	yes	16	8.3	odd	2
1024.2.g.g.385.1	yes	16	16.13	even	4
1024.2.g.g.385.4	yes	16	16.3	odd	4
1024.2.g.g.641.1	yes	16	32.5	even	8
1024.2.g.g.641.4	yes	16	32.27	odd	8
4096.2.a.i.1.1		8	64.45	even	16
4096.2.a.i.1.2		8	64.51	odd	16
4096.2.a.s.1.7		8	64.19	odd	16
4096.2.a.s.1.8		8	64.13	even	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)

\(f(q)\)	\(=\)	\(q+(1.12197 + 2.70868i) q^{3} +(0.366025 + 0.151613i) q^{5} +(3.06528 + 3.06528i) q^{7} +(-3.95680 + 3.95680i) q^{9} +O(q^{10})\)	\(q+(1.12197 + 2.70868i) q^{3} +(0.366025 + 0.151613i) q^{5} +(3.06528 + 3.06528i) q^{7} +(-3.95680 + 3.95680i) q^{9} +(-1.51815 + 3.66515i) q^{11} +(1.88366 - 0.780239i) q^{13} +1.16155i q^{15} -4.54587i q^{17} +(-0.534684 + 0.221474i) q^{19} +(-4.86370 + 11.7420i) q^{21} +(4.41794 - 4.41794i) q^{23} +(-3.42455 - 3.42455i) q^{25} +(-7.03106 - 2.91236i) q^{27} +(1.96642 + 4.74737i) q^{29} -0.0539984 q^{31} -11.6310 q^{33} +(0.657235 + 1.58671i) q^{35} +(-0.798499 - 0.330749i) q^{37} +(4.22683 + 4.22683i) q^{39} +(-0.621063 + 0.621063i) q^{41} +(0.857104 - 2.06923i) q^{43} +(-2.04819 + 0.848387i) q^{45} -9.44387i q^{47} +11.7919i q^{49} +(12.3133 - 5.10033i) q^{51} +(4.16622 - 10.0582i) q^{53} +(-1.11137 + 1.11137i) q^{55} +(-1.19980 - 1.19980i) q^{57} +(-7.17877 - 2.97354i) q^{59} +(4.02993 + 9.72911i) q^{61} -24.2574 q^{63} +0.807763 q^{65} +(3.12265 + 7.53875i) q^{67} +(16.9236 + 7.00997i) q^{69} +(-2.99152 - 2.99152i) q^{71} +(2.91724 - 2.91724i) q^{73} +(5.43375 - 13.1182i) q^{75} +(-15.8883 + 6.58114i) q^{77} +5.74836i q^{79} -5.52520i q^{81} +(3.30517 - 1.36905i) q^{83} +(0.689211 - 1.66390i) q^{85} +(-10.6528 + 10.6528i) q^{87} +(-2.38134 - 2.38134i) q^{89} +(8.16561 + 3.38231i) q^{91} +(-0.0605847 - 0.146264i) q^{93} -0.229286 q^{95} -13.2672 q^{97} +(-8.49522 - 20.5093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 - 16 * q^9	\( 16 q - 8 q^{5} - 16 q^{9} + 8 q^{13} - 16 q^{21} - 32 q^{25} + 24 q^{29} - 80 q^{33} - 40 q^{37} - 16 q^{41} - 24 q^{45} + 56 q^{53} - 16 q^{57} - 8 q^{61} - 32 q^{65} + 64 q^{69} + 32 q^{73} - 64 q^{77} + 48 q^{85} + 32 q^{89} - 80 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 - 16 * q^9 + 8 * q^13 - 16 * q^21 - 32 * q^25 + 24 * q^29 - 80 * q^33 - 40 * q^37 - 16 * q^41 - 24 * q^45 + 56 * q^53 - 16 * q^57 - 8 * q^61 - 32 * q^65 + 64 * q^69 + 32 * q^73 - 64 * q^77 + 48 * q^85 + 32 * q^89 - 80 * q^93 - 16 * q^97

Introduction

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Database

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