LMFDB - Embedded newform 572.2.x.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(25,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("572.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.x (of order $10$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	572.25
Dual form			572.2.x.a.389.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.129602 - 0.398873i) q^{3} +(2.17400 - 2.99226i) q^{5} +(1.13565 + 0.368994i) q^{7} +(2.28475 - 1.65997i) q^{9} +O(q^{10})$	\(q+(-0.129602 - 0.398873i) q^{3} +(2.17400 - 2.99226i) q^{5} +(1.13565 + 0.368994i) q^{7} +(2.28475 - 1.65997i) q^{9} +(1.49532 + 2.96041i) q^{11} +(-3.59591 + 0.263553i) q^{13} +(-1.47529 - 0.479349i) q^{15} +(-0.532445 - 0.386844i) q^{17} +(5.66127 - 1.83946i) q^{19} -0.500802i q^{21} -8.51470 q^{23} +(-2.68223 - 8.25505i) q^{25} +(-1.97613 - 1.43574i) q^{27} +(0.362283 - 1.11499i) q^{29} +(3.52465 + 4.85126i) q^{31} +(0.987030 - 0.980119i) q^{33} +(3.57302 - 2.59595i) q^{35} +(-3.56700 - 1.15899i) q^{37} +(0.571160 + 1.40015i) q^{39} +(6.62747 - 2.15339i) q^{41} +6.13179 q^{43} -10.4453i q^{45} +(5.41207 - 1.75849i) q^{47} +(-4.50958 - 3.27640i) q^{49} +(-0.0852960 + 0.262514i) q^{51} +(-8.76734 + 6.36984i) q^{53} +(12.1091 + 1.96154i) q^{55} +(-1.46742 - 2.01973i) q^{57} +(-7.30625 - 2.37394i) q^{59} +(11.7568 + 8.54180i) q^{61} +(3.20719 - 1.04208i) q^{63} +(-7.02889 + 11.3328i) q^{65} -0.370212i q^{67} +(1.10352 + 3.39629i) q^{69} +(-1.21775 + 1.67609i) q^{71} +(-6.53174 - 2.12229i) q^{73} +(-2.94510 + 2.13974i) q^{75} +(0.605787 + 3.91374i) q^{77} +(1.45827 - 1.05950i) q^{79} +(2.30152 - 7.08335i) q^{81} +(-3.82093 + 5.25906i) q^{83} +(-2.31507 + 0.752213i) q^{85} -0.491694 q^{87} +0.0928121i q^{89} +(-4.18093 - 1.02757i) q^{91} +(1.47824 - 2.03462i) q^{93} +(6.80347 - 20.9389i) q^{95} +(-1.04163 - 1.43368i) q^{97} +(8.33061 + 4.28160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^9	$ 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) $ 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.129602	−	0.398873i	−0.0748256	−	0.230290i	0.906648	−	0.421889i	$-0.138633\pi$
$3$	−0.129602	−	0.398873i	−0.0748256	−	0.230290i	−0.981473	+	0.191599i	$0.938633\pi$
$4$		0			0
$5$	2.17400	−	2.99226i	0.972243	−	1.33818i	0.0313370	−	0.999509i	$-0.490023\pi$
$5$	2.17400	−	2.99226i	0.972243	−	1.33818i	0.940906	−	0.338669i	$-0.109977\pi$
$6$		0			0
$7$	1.13565	+	0.368994i	0.429234	+	0.139467i	0.515663	−	0.856791i	$-0.327546\pi$
$7$	1.13565	+	0.368994i	0.429234	+	0.139467i	−0.0864289	+	0.996258i	$0.527546\pi$
$8$		0			0
$9$	2.28475	−	1.65997i	0.761583	−	0.553322i
$10$		0			0
$11$	1.49532	+	2.96041i	0.450857	+	0.892596i
$11$	1.49532	+	2.96041i	0.450857	+	0.892596i
$12$		0			0
$13$	−3.59591	+	0.263553i	−0.997325	+	0.0730964i
$13$	−3.59591	+	0.263553i	−0.997325	+	0.0730964i
$14$		0			0
$15$	−1.47529	−	0.479349i	−0.380917	−	0.123767i
$16$		0			0
$17$	−0.532445	−	0.386844i	−0.129137	−	0.0938235i	0.521342	−	0.853348i	$-0.325432\pi$
$17$	−0.532445	−	0.386844i	−0.129137	−	0.0938235i	−0.650479	+	0.759524i	$0.725432\pi$
$18$		0			0
$19$	5.66127	−	1.83946i	1.29878	−	0.422000i	0.423625	−	0.905837i	$-0.360757\pi$
$19$	5.66127	−	1.83946i	1.29878	−	0.422000i	0.875158	+	0.483837i	$0.160757\pi$
$20$		0			0
$21$		−	0.500802i		−	0.109284i
$22$		0			0
$23$	−8.51470			−1.77544			−0.887719	−	0.460386i	$-0.847711\pi$
$23$	−8.51470			−1.77544			−0.887719	+	0.460386i	$0.847711\pi$
$24$		0			0
$25$	−2.68223	−	8.25505i	−0.536446	−	1.65101i
$26$		0			0
$27$	−1.97613	−	1.43574i	−0.380306	−	0.276309i
$28$		0			0
$29$	0.362283	−	1.11499i	0.0672743	−	0.207049i	−0.911768	−	0.410705i	$-0.865282\pi$
$29$	0.362283	−	1.11499i	0.0672743	−	0.207049i	0.979042	+	0.203656i	$0.0652825\pi$
$30$		0			0
$31$	3.52465	+	4.85126i	0.633046	+	0.871313i	0.998221	−	0.0596260i	$-0.0189908\pi$
$31$	3.52465	+	4.85126i	0.633046	+	0.871313i	−0.365175	+	0.930939i	$0.618991\pi$
$32$		0			0
$33$	0.987030	−	0.980119i	0.171820	−	0.170617i
$34$		0			0
$35$	3.57302	−	2.59595i	0.603951	−	0.438796i
$36$		0			0
$37$	−3.56700	−	1.15899i	−0.586411	−	0.190537i	0.000759424	−	1.00000i	$-0.499758\pi$
$37$	−3.56700	−	1.15899i	−0.586411	−	0.190537i	−0.587171	+	0.809463i	$0.699758\pi$
$38$		0			0
$39$	0.571160	+	1.40015i	0.0914588	+	0.224204i
$40$		0			0
$41$	6.62747	−	2.15339i	1.03504	−	0.336304i	0.258257	−	0.966076i	$-0.416852\pi$
$41$	6.62747	−	2.15339i	1.03504	−	0.336304i	0.776779	+	0.629773i	$0.216852\pi$
$42$		0			0
$43$	6.13179			0.935090			0.467545	−	0.883969i	$-0.345139\pi$
$43$	6.13179			0.935090			0.467545	+	0.883969i	$0.345139\pi$
$44$		0			0
$45$		−	10.4453i		−	1.55710i
$46$		0			0
$47$	5.41207	−	1.75849i	0.789432	−	0.256502i	0.113570	−	0.993530i	$-0.463771\pi$
$47$	5.41207	−	1.75849i	0.789432	−	0.256502i	0.675862	+	0.737028i	$0.263771\pi$
$48$		0			0
$49$	−4.50958	−	3.27640i	−0.644226	−	0.468057i
$50$		0			0
$51$	−0.0852960	+	0.262514i	−0.0119438	+	0.0367593i
$52$		0			0
$53$	−8.76734	+	6.36984i	−1.20429	+	0.874965i	−0.994699	−	0.102825i	$-0.967212\pi$
$53$	−8.76734	+	6.36984i	−1.20429	+	0.874965i	−0.209587	+	0.977790i	$0.567212\pi$
$54$		0			0
$55$	12.1091	+	1.96154i	1.63279	+	0.264494i
$56$		0			0
$57$	−1.46742	−	2.01973i	−0.194365	−	0.267520i
$58$		0			0
$59$	−7.30625	−	2.37394i	−0.951192	−	0.309061i	−0.207992	−	0.978130i	$-0.566693\pi$
$59$	−7.30625	−	2.37394i	−0.951192	−	0.309061i	−0.743200	+	0.669069i	$0.766693\pi$
$60$		0			0
$61$	11.7568	+	8.54180i	1.50530	+	1.09367i	0.968209	+	0.250143i	$0.0804776\pi$
$61$	11.7568	+	8.54180i	1.50530	+	1.09367i	0.537093	+	0.843523i	$0.319522\pi$
$62$		0			0
$63$	3.20719	−	1.04208i	0.404067	−	0.131289i
$64$		0			0
$65$	−7.02889	+	11.3328i	−0.871826	+	1.40567i
$66$		0			0
$67$		−	0.370212i		−	0.0452286i	−0.999744	−	0.0226143i	$-0.992801\pi$
$67$		−	0.370212i		−	0.0452286i	0.999744	−	0.0226143i	$-0.00719896\pi$
$68$		0			0
$69$	1.10352	+	3.39629i	0.132848	+	0.408865i
$70$		0			0
$71$	−1.21775	+	1.67609i	−0.144521	+	0.198916i	−0.875141	−	0.483869i	$-0.839231\pi$
$71$	−1.21775	+	1.67609i	−0.144521	+	0.198916i	0.730620	+	0.682784i	$0.239231\pi$
$72$		0			0
$73$	−6.53174	−	2.12229i	−0.764482	−	0.248395i	−0.0992809	−	0.995059i	$-0.531654\pi$
$73$	−6.53174	−	2.12229i	−0.764482	−	0.248395i	−0.665201	+	0.746664i	$0.731654\pi$
$74$		0			0
$75$	−2.94510	+	2.13974i	−0.340071	+	0.247076i
$76$		0			0
$77$	0.605787	+	3.91374i	0.0690359	+	0.446013i
$78$		0			0
$79$	1.45827	−	1.05950i	0.164068	−	0.119203i	−0.502721	−	0.864448i	$-0.667668\pi$
$79$	1.45827	−	1.05950i	0.164068	−	0.119203i	0.666790	+	0.745246i	$0.267668\pi$
$80$		0			0
$81$	2.30152	−	7.08335i	0.255724	−	0.787038i
$82$		0			0
$83$	−3.82093	+	5.25906i	−0.419402	+	0.577257i	−0.965480	−	0.260477i	$-0.916120\pi$
$83$	−3.82093	+	5.25906i	−0.419402	+	0.577257i	0.546078	+	0.837734i	$0.316120\pi$
$84$		0			0
$85$	−2.31507	+	0.752213i	−0.251105	+	0.0815890i
$86$		0			0
$87$	−0.491694			−0.0527151
$88$		0			0
$89$			0.0928121i			0.00983807i	0.999988	+	0.00491903i	$0.00156578\pi$
$89$			0.0928121i			0.00983807i	−0.999988	+	0.00491903i	$0.998434\pi$
$90$		0			0
$91$	−4.18093	−	1.02757i	−0.438281	−	0.107718i
$92$		0			0
$93$	1.47824	−	2.03462i	0.153286	−	0.210980i
$94$		0			0
$95$	6.80347	−	20.9389i	0.698022	−	2.14829i
$96$		0			0
$97$	−1.04163	−	1.43368i	−0.105761	−	0.145568i	0.752856	−	0.658186i	$-0.228676\pi$
$97$	−1.04163	−	1.43368i	−0.105761	−	0.145568i	−0.858617	+	0.512618i	$0.828676\pi$
$98$		0			0
$99$	8.33061	+	4.28160i	0.837258	+	0.430317i
$100$		0			0
$101$	−8.16272	+	5.93056i	−0.812221	+	0.590113i	−0.914474	−	0.404646i	$-0.867395\pi$
$101$	−8.16272	+	5.93056i	−0.812221	+	0.590113i	0.102253	+	0.994758i	$0.467395\pi$
$102$		0			0
$103$	−4.22468	+	13.0022i	−0.416270	+	1.28115i	0.494840	+	0.868984i	$0.335227\pi$
$103$	−4.22468	+	13.0022i	−0.416270	+	1.28115i	−0.911110	+	0.412163i	$0.864773\pi$
$104$		0			0
$105$	−1.49853	−	1.08874i	−0.146241	−	0.106250i
$106$		0			0
$107$	0.222542	+	0.684915i	0.0215140	+	0.0662132i	0.961237	−	0.275723i	$-0.0889173\pi$
$107$	0.222542	+	0.684915i	0.0215140	+	0.0662132i	−0.939723	+	0.341936i	$0.888917\pi$
$108$		0			0
$109$			15.8267i			1.51592i	0.652300	+	0.757961i	$0.273804\pi$
$109$			15.8267i			1.51592i	−0.652300	+	0.757961i	$0.726196\pi$
$110$		0			0
$111$			1.57299i			0.149301i
$112$		0			0
$113$	−0.806320	−	2.48160i	−0.0758522	−	0.233449i	0.905940	−	0.423405i	$-0.139165\pi$
$113$	−0.806320	−	2.48160i	−0.0758522	−	0.233449i	−0.981793	+	0.189956i	$0.939165\pi$
$114$		0			0
$115$	−18.5110	+	25.4782i	−1.72616	+	2.37585i
$116$		0			0
$117$	−7.77825	+	6.57123i	−0.719099	+	0.607511i
$118$		0			0
$119$	−0.461927	−	0.635788i	−0.0423448	−	0.0582826i
$120$		0			0
$121$	−6.52802	+	8.85353i	−0.593456	+	0.804866i
$122$		0			0
$123$	−1.71786	−	2.36444i	−0.154894	−	0.213194i
$124$		0			0
$125$	−12.9444	−	4.20588i	−1.15778	−	0.376185i
$126$		0			0
$127$	14.8844	+	10.8141i	1.32078	+	0.959599i	0.999922	+	0.0124705i	$0.00396960\pi$
$127$	14.8844	+	10.8141i	1.32078	+	0.959599i	0.320853	+	0.947129i	$0.396030\pi$
$128$		0			0
$129$	−0.794691	−	2.44581i	−0.0699687	−	0.215341i
$130$		0			0
$131$	−7.19800			−0.628892			−0.314446	−	0.949275i	$-0.601819\pi$
$131$	−7.19800			−0.628892			−0.314446	+	0.949275i	$0.601819\pi$
$132$		0			0
$133$	7.10795			0.616337
$134$		0			0
$135$	−8.59221	+	2.79178i	−0.739500	+	0.240278i
$136$		0			0
$137$	10.4266	−	14.3510i	0.890804	−	1.22609i	−0.0825061	−	0.996591i	$-0.526292\pi$
$137$	10.4266	−	14.3510i	0.890804	−	1.22609i	0.973310	−	0.229495i	$-0.0737076\pi$
$138$		0			0
$139$	−0.848588	+	2.61168i	−0.0719763	+	0.221520i	−0.980573	−	0.196154i	$-0.937155\pi$
$139$	−0.848588	+	2.61168i	−0.0719763	+	0.221520i	0.908597	+	0.417674i	$0.137155\pi$
$140$		0			0
$141$	−1.40283	−	1.93083i	−0.118139	−	0.162605i
$142$		0			0
$143$	−6.15727	−	10.2512i	−0.514896	−	0.857252i
$144$		0			0
$145$	−2.54874	−	3.50804i	−0.211661	−	0.291327i
$146$		0			0
$147$	−0.722420	+	2.22338i	−0.0595842	+	0.183381i
$148$		0			0
$149$	7.05406	−	9.70907i	0.577891	−	0.795398i	−0.415571	−	0.909561i	$-0.636418\pi$
$149$	7.05406	−	9.70907i	0.577891	−	0.795398i	0.993462	+	0.114162i	$0.0364184\pi$
$150$		0			0
$151$	−19.2798	+	6.26440i	−1.56897	+	0.509790i	−0.959186	−	0.282776i	$-0.908745\pi$
$151$	−19.2798	+	6.26440i	−1.56897	+	0.509790i	−0.609786	+	0.792566i	$0.708745\pi$
$152$		0			0
$153$	−1.85865			−0.150263
$154$		0			0
$155$	22.1788			1.78145
$156$		0			0
$157$	−1.21895	−	3.75153i	−0.0972824	−	0.299405i	0.890559	−	0.454867i	$-0.150313\pi$
$157$	−1.21895	−	3.75153i	−0.0972824	−	0.299405i	−0.987842	+	0.155462i	$0.950313\pi$
$158$		0			0
$159$	3.67702	+	2.67151i	0.291607	+	0.211865i
$160$		0			0
$161$	−9.66970	−	3.14187i	−0.762079	−	0.247614i
$162$		0			0
$163$	9.81055	+	13.5031i	0.768422	+	1.05764i	0.996466	+	0.0839912i	$0.0267668\pi$
$163$	9.81055	+	13.5031i	0.768422	+	1.05764i	−0.228045	+	0.973651i	$0.573233\pi$
$164$		0			0
$165$	−0.786960	−	5.08423i	−0.0612648	−	0.395806i
$166$		0			0
$167$	10.4918	+	14.4407i	0.811878	+	1.11745i	0.991031	+	0.133633i	$0.0426644\pi$
$167$	10.4918	+	14.4407i	0.811878	+	1.11745i	−0.179153	+	0.983821i	$0.557336\pi$
$168$		0			0
$169$	12.8611	−	1.89542i	0.989314	−	0.145802i
$170$		0			0
$171$	9.88113	−	13.6002i	0.755629	−	1.04003i
$172$		0			0
$173$	6.63469	+	20.4195i	0.504426	+	1.55246i	0.801733	+	0.597682i	$0.203912\pi$
$173$	6.63469	+	20.4195i	0.504426	+	1.55246i	−0.297307	+	0.954782i	$0.596088\pi$
$174$		0			0
$175$		−	10.3646i		−	0.783487i
$176$		0			0
$177$			3.22193i			0.242175i
$178$		0			0
$179$	3.22082	+	9.91267i	0.240736	+	0.740908i	0.996309	+	0.0858434i	$0.0273585\pi$
$179$	3.22082	+	9.91267i	0.240736	+	0.740908i	−0.755573	+	0.655064i	$0.772642\pi$
$180$		0			0
$181$	−3.20224	−	2.32656i	−0.238020	−	0.172932i	0.462381	−	0.886682i	$-0.346995\pi$
$181$	−3.20224	−	2.32656i	−0.238020	−	0.172932i	−0.700401	+	0.713750i	$0.746995\pi$
$182$		0			0
$183$	1.88340	−	5.79650i	0.139225	−	0.428490i
$184$		0			0
$185$	−11.2227	+	8.15373i	−0.825106	+	0.599475i
$186$		0			0
$187$	0.349038	−	2.15471i	0.0255242	−	0.157568i
$188$		0			0
$189$	−1.71441	−	2.35968i	−0.124705	−	0.171641i
$190$		0			0
$191$	3.98057	−	12.2509i	0.288024	−	0.886447i	−0.697452	−	0.716632i	$-0.745683\pi$
$191$	3.98057	−	12.2509i	0.288024	−	0.886447i	0.985476	−	0.169815i	$-0.0543171\pi$
$192$		0			0
$193$	−5.53185	+	7.61394i	−0.398191	+	0.548063i	−0.960289	−	0.279008i	$-0.909995\pi$
$193$	−5.53185	+	7.61394i	−0.398191	+	0.548063i	0.562098	+	0.827071i	$0.309995\pi$
$194$		0			0
$195$	5.43132	+	1.33488i	0.388945	+	0.0955927i
$196$		0			0
$197$		−	8.93791i		−	0.636799i	−0.947957	−	0.318400i	$-0.896855\pi$
$197$		−	8.93791i		−	0.636799i	0.947957	−	0.318400i	$-0.103145\pi$
$198$		0			0
$199$	−6.29310			−0.446106			−0.223053	−	0.974806i	$-0.571602\pi$
$199$	−6.29310			−0.446106			−0.223053	+	0.974806i	$0.571602\pi$
$200$		0			0
$201$	−0.147668	+	0.0479801i	−0.0104157	+	0.00338426i
$202$		0			0
$203$	0.822852	−	1.13256i	0.0577529	−	0.0794901i
$204$		0			0
$205$	7.96461	−	24.5126i	0.556273	−	1.71203i
$206$		0			0
$207$	−19.4539	+	14.1341i	−1.35214	+	0.982389i
$208$		0			0
$209$	13.9110	+	14.0091i	0.962241	+	0.969027i
$210$		0			0
$211$	−13.1454	+	9.55072i	−0.904969	+	0.657499i	−0.939738	−	0.341897i	$-0.888931\pi$
$211$	−13.1454	+	9.55072i	−0.904969	+	0.657499i	0.0347683	+	0.999395i	$0.488931\pi$
$212$		0			0
$213$	0.826372	+	0.268504i	0.0566221	+	0.0183976i
$214$		0			0
$215$	13.3305	−	18.3479i	0.909134	−	1.25132i
$216$		0			0
$217$	2.21267	+	6.80990i	0.150206	+	0.462286i
$218$		0			0
$219$			2.88039i			0.194639i
$220$		0			0
$221$	2.01658	+	1.25073i	0.135650	+	0.0841331i
$222$		0			0
$223$	7.67435	−	2.49355i	0.513913	−	0.166980i	−0.0405683	−	0.999177i	$-0.512917\pi$
$223$	7.67435	−	2.49355i	0.513913	−	0.166980i	0.554481	+	0.832196i	$0.312917\pi$
$224$		0			0
$225$	−19.8313	−	14.4083i	−1.32209	−	0.960553i
$226$		0			0
$227$	−4.08060	−	1.32587i	−0.270839	−	0.0880009i	0.170449	−	0.985367i	$-0.445478\pi$
$227$	−4.08060	−	1.32587i	−0.270839	−	0.0880009i	−0.441288	+	0.897366i	$0.645478\pi$
$228$		0			0
$229$	13.5716	+	18.6798i	0.896840	+	1.23439i	0.971465	+	0.237182i	$0.0762239\pi$
$229$	13.5716	+	18.6798i	0.896840	+	1.23439i	−0.0746254	+	0.997212i	$0.523776\pi$
$230$		0			0
$231$	1.48258	−	0.748861i	0.0975464	−	0.0492714i
$232$		0			0
$233$	17.5946	−	12.7832i	1.15266	−	0.837456i	0.163828	−	0.986489i	$-0.447616\pi$
$233$	17.5946	−	12.7832i	1.15266	−	0.837456i	0.988832	+	0.149033i	$0.0476160\pi$
$234$		0			0
$235$	6.50400	−	20.0173i	0.424274	−	1.30578i
$236$		0			0
$237$	−0.611599	−	0.444353i	−0.0397277	−	0.0288638i
$238$		0			0
$239$	−5.79470	+	1.88281i	−0.374828	+	0.121789i	−0.490372	−	0.871513i	$-0.663139\pi$
$239$	−5.79470	+	1.88281i	−0.374828	+	0.121789i	0.115544	+	0.993302i	$0.463139\pi$
$240$		0			0
$241$		−	12.8242i		−	0.826080i	−0.910713	−	0.413040i	$-0.864467\pi$
$241$		−	12.8242i		−	0.826080i	0.910713	−	0.413040i	$-0.135533\pi$
$242$		0			0
$243$	−10.4515			−0.670466
$244$		0			0
$245$	−19.6077	+	6.37092i	−1.25269	+	0.407023i
$246$		0			0
$247$	−19.8726	+	8.10656i	−1.26446	+	0.515808i
$248$		0			0
$249$	2.59290	+	0.842484i	0.164318	+	0.0533902i
$250$		0			0
$251$	−9.56629	+	6.95032i	−0.603819	+	0.438700i	−0.847232	−	0.531222i	$-0.821733\pi$
$251$	−9.56629	+	6.95032i	−0.603819	+	0.438700i	0.243413	+	0.969923i	$0.421733\pi$
$252$		0			0
$253$	−12.7322	−	25.2070i	−0.800468	−	1.58475i
$254$		0			0
$255$	0.600075	+	0.825933i	0.0375782	+	0.0517219i
$256$		0			0
$257$	7.24010	−	22.2827i	0.451625	−	1.38996i	−0.423427	−	0.905930i	$-0.639173\pi$
$257$	7.24010	−	22.2827i	0.451625	−	1.38996i	0.875052	−	0.484029i	$-0.160827\pi$
$258$		0			0
$259$	−3.62319	−	2.63241i	−0.225134	−	0.163570i
$260$		0			0
$261$	−1.02313	−	3.14886i	−0.0633299	−	0.194909i
$262$		0			0
$263$	−20.1480			−1.24238			−0.621189	−	0.783660i	$-0.713350\pi$
$263$	−20.1480			−1.24238			−0.621189	+	0.783660i	$0.713350\pi$
$264$		0			0
$265$			40.0822i			2.46223i
$266$		0			0
$267$	0.0370203	−	0.0120286i	0.00226560	−	0.000736139i
$268$		0			0
$269$	−14.8710	−	10.8044i	−0.906702	−	0.658757i	0.0334767	−	0.999439i	$-0.489342\pi$
$269$	−14.8710	−	10.8044i	−0.906702	−	0.658757i	−0.940179	+	0.340682i	$0.889342\pi$
$270$		0			0
$271$	11.4326	+	3.71467i	0.694480	+	0.225650i	0.634924	−	0.772575i	$-0.281031\pi$
$271$	11.4326	+	3.71467i	0.694480	+	0.225650i	0.0595561	+	0.998225i	$0.481031\pi$
$272$		0			0
$273$	0.131988	+	1.80084i	0.00798826	+	0.108992i
$274$		0			0
$275$	20.4275	−	20.2845i	1.23183	−	1.22320i
$276$		0			0
$277$	5.08781	−	3.69651i	0.305697	−	0.222102i	−0.424351	−	0.905498i	$-0.639498\pi$
$277$	5.08781	−	3.69651i	0.305697	−	0.222102i	0.730048	+	0.683396i	$0.239498\pi$
$278$		0			0
$279$	16.1059	+	5.23312i	0.964233	+	0.313298i
$280$		0			0
$281$	17.1779	−	23.6433i	1.02474	−	1.41044i	0.115922	−	0.993258i	$-0.463018\pi$
$281$	17.1779	−	23.6433i	1.02474	−	1.41044i	0.908823	−	0.417182i	$-0.136982\pi$
$282$		0			0
$283$	4.83308	+	14.8747i	0.287297	+	0.884208i	0.985701	+	0.168505i	$0.0538939\pi$
$283$	4.83308	+	14.8747i	0.287297	+	0.884208i	−0.698404	+	0.715704i	$0.746106\pi$
$284$		0			0
$285$	−9.23372			−0.546959
$286$		0			0
$287$	8.32105			0.491176
$288$		0			0
$289$	−5.11944	−	15.7560i	−0.301143	−	0.926824i
$290$		0			0
$291$	−0.436859	+	0.601284i	−0.0256091	+	0.0352479i
$292$		0			0
$293$	−18.5395	−	6.02385i	−1.08309	−	0.351917i	−0.287517	−	0.957776i	$-0.592830\pi$
$293$	−18.5395	−	6.02385i	−1.08309	−	0.351917i	−0.795572	+	0.605858i	$0.792830\pi$
$294$		0			0
$295$	−22.9872	+	16.7012i	−1.33837	+	0.972382i
$296$		0			0
$297$	1.29543	−	7.99704i	0.0751683	−	0.464036i
$298$		0			0
$299$	30.6181	−	2.24407i	1.77069	−	0.129778i
$300$		0			0
$301$	6.96356	+	2.26260i	0.401373	+	0.130414i
$302$		0			0
$303$	3.42344	+	2.48728i	0.196672	+	0.142890i
$304$		0			0
$305$	51.1185	−	16.6094i	2.92704	−	0.951052i
$306$		0			0
$307$		−	14.3442i		−	0.818669i	−0.912384	−	0.409334i	$-0.865761\pi$
$307$		−	14.3442i		−	0.818669i	0.912384	−	0.409334i	$-0.134239\pi$
$308$		0			0
$309$	5.73377			0.326183
$310$		0			0
$311$	−3.20507	−	9.86420i	−0.181743	−	0.559348i	0.818134	−	0.575028i	$-0.195009\pi$
$311$	−3.20507	−	9.86420i	−0.181743	−	0.559348i	−0.999877	+	0.0156800i	$0.995009\pi$
$312$		0			0
$313$	22.1273	+	16.0764i	1.25071	+	0.908694i	0.998263	−	0.0589173i	$-0.0187648\pi$
$313$	22.1273	+	16.0764i	1.25071	+	0.908694i	0.252447	+	0.967611i	$0.418765\pi$
$314$		0			0
$315$	3.85426	−	11.8622i	0.217163	−	0.668359i
$316$		0			0
$317$	9.50224	+	13.0787i	0.533699	+	0.734574i	0.987689	−	0.156433i	$-0.0499996\pi$
$317$	9.50224	+	13.0787i	0.533699	+	0.734574i	−0.453989	+	0.891007i	$0.650000\pi$
$318$		0			0
$319$	3.84256	−	0.594770i	0.215142	−	0.0333007i
$320$		0			0
$321$	0.244352	−	0.177532i	0.0136384	−	0.00990889i
$322$		0			0
$323$	−3.72590	−	1.21062i	−0.207315	−	0.0673606i
$324$		0			0
$325$	11.8207	+	28.9775i	0.655694	+	1.60738i
$326$		0			0
$327$	6.31284	−	2.05117i	0.349101	−	0.113430i
$328$		0			0
$329$	6.79508			0.374625
$330$		0			0
$331$		−	27.9080i		−	1.53396i	−0.641670	−	0.766981i	$-0.721758\pi$
$331$		−	27.9080i		−	1.53396i	0.641670	−	0.766981i	$-0.278242\pi$
$332$		0			0
$333$	−10.0736	+	3.27310i	−0.552029	+	0.179365i
$334$		0			0
$335$	−1.10777	−	0.804841i	−0.0605238	−	0.0439732i
$336$		0			0
$337$	−2.55427	+	7.86124i	−0.139140	+	0.428229i	−0.996211	−	0.0869695i	$-0.972282\pi$
$337$	−2.55427	+	7.86124i	−0.139140	+	0.428229i	0.857071	+	0.515198i	$0.172282\pi$
$338$		0			0
$339$	−0.885343	+	0.643239i	−0.0480852	+	0.0349360i
$340$		0			0
$341$	−9.09122	+	17.6886i	−0.492317	+	0.957892i
$342$		0			0
$343$	−8.82540	−	12.1471i	−0.476527	−	0.655883i
$344$		0			0
$345$	12.5616	+	4.08151i	0.676294	+	0.219741i
$346$		0			0
$347$	−11.3437	−	8.24167i	−0.608961	−	0.442436i	0.240087	−	0.970751i	$-0.422824\pi$
$347$	−11.3437	−	8.24167i	−0.608961	−	0.442436i	−0.849048	+	0.528315i	$0.822824\pi$
$348$		0			0
$349$	−5.13634	+	1.66890i	−0.274942	+	0.0893341i	−0.443243	−	0.896402i	$-0.646172\pi$
$349$	−5.13634	+	1.66890i	−0.274942	+	0.0893341i	0.168301	+	0.985736i	$0.446172\pi$
$350$		0			0
$351$	7.48437	+	4.64198i	0.399486	+	0.247770i
$352$		0			0
$353$		−	19.4683i		−	1.03619i	−0.855322	−	0.518097i	$-0.826641\pi$
$353$		−	19.4683i		−	1.03619i	0.855322	−	0.518097i	$-0.173359\pi$
$354$		0			0
$355$	2.36790	+	7.28766i	0.125675	+	0.386789i
$356$		0			0
$357$	−0.193732	+	0.266650i	−0.0102534	+	0.0141126i
$358$		0			0
$359$	19.1380	+	6.21830i	1.01006	+	0.328189i	0.766880	−	0.641791i	$-0.221808\pi$
$359$	19.1380	+	6.21830i	1.01006	+	0.328189i	0.243184	+	0.969980i	$0.421808\pi$
$360$		0			0
$361$	13.2950	−	9.65939i	0.699737	−	0.508389i
$362$		0			0
$363$	4.37748	+	1.45642i	0.229758	+	0.0764421i
$364$		0			0
$365$	−20.5504	+	14.9308i	−1.07566	+	0.781512i
$366$		0			0
$367$	4.46245	−	13.7340i	0.232938	−	0.716910i	−0.764450	−	0.644683i	$-0.776989\pi$
$367$	4.46245	−	13.7340i	0.232938	−	0.716910i	0.997388	−	0.0722268i	$-0.0230105\pi$
$368$		0			0
$369$	11.5675	−	15.9213i	0.602181	−	0.828831i
$370$		0			0
$371$	−12.3070	+	3.99880i	−0.638950	+	0.207607i
$372$		0			0
$373$	−28.9141			−1.49711			−0.748557	−	0.663070i	$-0.769253\pi$
$373$	−28.9141			−1.49711			−0.748557	+	0.663070i	$0.769253\pi$
$374$		0			0
$375$			5.70824i			0.294772i
$376$		0			0
$377$	−1.00888	+	4.10489i	−0.0519598	+	0.211413i
$378$		0			0
$379$	−6.49748	+	8.94302i	−0.333753	+	0.459372i	−0.942604	−	0.333913i	$-0.891631\pi$
$379$	−6.49748	+	8.94302i	−0.333753	+	0.459372i	0.608851	+	0.793285i	$0.291631\pi$
$380$		0			0
$381$	2.38443	−	7.33851i	0.122158	−	0.375963i
$382$		0			0
$383$	−19.9883	−	27.5116i	−1.02136	−	1.40578i	−0.911249	−	0.411855i	$-0.864881\pi$
$383$	−19.9883	−	27.5116i	−1.02136	−	1.40578i	−0.110106	−	0.993920i	$-0.535119\pi$
$384$		0			0
$385$	13.0279	+	6.69581i	0.663963	+	0.341250i
$386$		0			0
$387$	14.0096	−	10.1786i	0.712148	−	0.517406i
$388$		0			0
$389$	8.74880	−	26.9260i	0.443582	−	1.36520i	−0.440450	−	0.897777i	$-0.645181\pi$
$389$	8.74880	−	26.9260i	0.443582	−	1.36520i	0.884032	−	0.467427i	$-0.154819\pi$
$390$		0			0
$391$	4.53361	+	3.29386i	0.229275	+	0.166578i
$392$		0			0
$393$	0.932873	+	2.87109i	0.0470572	+	0.144827i
$394$		0			0
$395$		−	6.66687i		−	0.335447i
$396$		0			0
$397$			21.1136i			1.05966i	0.848104	+	0.529830i	$0.177744\pi$
$397$			21.1136i			1.05966i	−0.848104	+	0.529830i	$0.822256\pi$
$398$		0			0
$399$	−0.921203	−	2.83517i	−0.0461178	−	0.141936i
$400$		0			0
$401$	−8.14909	+	11.2163i	−0.406946	+	0.560113i	−0.962470	−	0.271387i	$-0.912518\pi$
$401$	−8.14909	+	11.2163i	−0.406946	+	0.560113i	0.555524	+	0.831500i	$0.312518\pi$
$402$		0			0
$403$	−13.9529	−	16.5158i	−0.695042	−	0.822709i
$404$		0			0
$405$	−16.1917	−	22.2859i	−0.804571	−	1.10740i
$406$		0			0
$407$	−1.90274	−	12.2928i	−0.0943154	−	0.609333i
$408$		0			0
$409$	18.6950	+	25.7315i	0.924409	+	1.27234i	0.962001	+	0.273047i	$0.0880314\pi$
$409$	18.6950	+	25.7315i	0.924409	+	1.27234i	−0.0375915	+	0.999293i	$0.511969\pi$
$410$		0			0
$411$	−7.07552	−	2.29898i	−0.349010	−	0.113400i
$412$		0			0
$413$	−7.42135	−	5.39193i	−0.365181	−	0.265319i
$414$		0			0
$415$	7.42975	+	22.8664i	0.364712	+	1.12247i
$416$		0			0
$417$	1.15171			0.0563995
$418$		0			0
$419$	−25.5405			−1.24773			−0.623867	−	0.781530i	$-0.714439\pi$
$419$	−25.5405			−1.24773			−0.623867	+	0.781530i	$0.714439\pi$
$420$		0			0
$421$	0.419034	−	0.136152i	0.0204224	−	0.00663566i	−0.298788	−	0.954320i	$-0.596582\pi$
$421$	0.419034	−	0.136152i	0.0204224	−	0.00663566i	0.319210	+	0.947684i	$0.396582\pi$
$422$		0			0
$423$	9.44619	−	13.0016i	0.459289	−	0.632158i
$424$		0			0
$425$	−1.76528	+	5.43297i	−0.0856286	+	0.263538i
$426$		0			0
$427$	10.1997	+	14.0387i	0.493597	+	0.679379i
$428$		0			0
$429$	−3.29096	+	3.78455i	−0.158889	+	0.182720i
$430$		0			0
$431$	−9.78818	−	13.4723i	−0.471480	−	0.648936i	0.505360	−	0.862909i	$-0.331360\pi$
$431$	−9.78818	−	13.4723i	−0.471480	−	0.648936i	−0.976840	+	0.213972i	$0.931360\pi$
$432$		0			0
$433$	−3.02804	+	9.31934i	−0.145518	+	0.447859i	−0.997077	−	0.0763996i	$-0.975658\pi$
$433$	−3.02804	+	9.31934i	−0.145518	+	0.447859i	0.851559	+	0.524259i	$0.175658\pi$
$434$		0			0
$435$	−1.06894	+	1.47127i	−0.0512519	+	0.0705421i
$436$		0			0
$437$	−48.2040	+	15.6624i	−2.30591	+	0.749235i
$438$		0			0
$439$	−1.45142			−0.0692725			−0.0346363	−	0.999400i	$-0.511027\pi$
$439$	−1.45142			−0.0692725			−0.0346363	+	0.999400i	$0.511027\pi$
$440$		0			0
$441$	−15.7420			−0.749618
$442$		0			0
$443$	0.607630	+	1.87009i	0.0288694	+	0.0888507i	0.964453	−	0.264254i	$-0.0851258\pi$
$443$	0.607630	+	1.87009i	0.0288694	+	0.0888507i	−0.935584	+	0.353105i	$0.885126\pi$
$444$		0			0
$445$	0.277718	+	0.201774i	0.0131651	+	0.00956499i
$446$		0			0
$447$	−4.78691	−	1.55536i	−0.226413	−	0.0735660i
$448$		0			0
$449$	17.1973	+	23.6700i	0.811589	+	1.11706i	0.991076	+	0.133296i	$0.0425561\pi$
$449$	17.1973	+	23.6700i	0.811589	+	1.11706i	−0.179488	+	0.983760i	$0.557444\pi$
$450$		0			0
$451$	16.2851	+	16.4000i	0.766837	+	0.772245i
$452$		0			0
$453$	4.99741	+	6.87834i	0.234799	+	0.323173i
$454$		0			0
$455$	−12.1641	+	10.2765i	−0.570261	+	0.481769i
$456$		0			0
$457$	−4.39419	+	6.04808i	−0.205551	+	0.282917i	−0.899330	−	0.437272i	$-0.855945\pi$
$457$	−4.39419	+	6.04808i	−0.205551	+	0.282917i	0.693778	+	0.720189i	$0.255945\pi$
$458$		0			0
$459$	0.496772	+	1.52891i	0.0231874	+	0.0713633i
$460$		0			0
$461$			9.98474i			0.465036i	0.972592	+	0.232518i	$0.0746964\pi$
$461$			9.98474i			0.465036i	−0.972592	+	0.232518i	$0.925304\pi$
$462$		0			0
$463$			3.51426i			0.163321i	0.996660	+	0.0816607i	$0.0260224\pi$
$463$			3.51426i			0.163321i	−0.996660	+	0.0816607i	$0.973978\pi$
$464$		0			0
$465$	−2.87441	−	8.84654i	−0.133298	−	0.410248i
$466$		0			0
$467$	−19.6811	−	14.2992i	−0.910733	−	0.661687i	0.0304669	−	0.999536i	$-0.490301\pi$
$467$	−19.6811	−	14.2992i	−0.910733	−	0.661687i	−0.941200	+	0.337849i	$0.890301\pi$
$468$		0			0
$469$	0.136606	−	0.420430i	0.00630788	−	0.0194137i
$470$		0			0
$471$	−1.33841	+	0.972409i	−0.0616705	+	0.0448063i
$472$		0			0
$473$	9.16902	+	18.1526i	0.421592	+	0.834658i
$474$		0			0
$475$	−30.3696	−	41.8002i	−1.39345	−	1.91792i
$476$		0			0
$477$	−9.45743	+	29.1070i	−0.433026	+	1.33272i
$478$		0			0
$479$	−23.0845	+	31.7731i	−1.05476	+	1.45175i	−0.170147	+	0.985419i	$0.554424\pi$
$479$	−23.0845	+	31.7731i	−1.05476	+	1.45175i	−0.884610	+	0.466331i	$0.845576\pi$
$480$		0			0
$481$	13.1321	+	3.22752i	0.598770	+	0.147162i
$482$		0			0
$483$			4.26418i			0.194027i
$484$		0			0
$485$	−6.55443			−0.297621
$486$		0			0
$487$	34.9235	−	11.3473i	1.58254	−	0.514197i	0.619827	−	0.784738i	$-0.287203\pi$
$487$	34.9235	−	11.3473i	1.58254	−	0.514197i	0.962708	+	0.270541i	$0.0872027\pi$
$488$		0			0
$489$	4.11455	−	5.66319i	0.186066	−	0.256098i
$490$		0			0
$491$	−7.91580	+	24.3623i	−0.357235	+	1.09946i	0.597467	+	0.801893i	$0.296174\pi$
$491$	−7.91580	+	24.3623i	−0.357235	+	1.09946i	−0.954702	+	0.297563i	$0.903826\pi$
$492$		0			0
$493$	−0.624225	+	0.453526i	−0.0281137	+	0.0204258i
$494$		0			0
$495$	30.9224	−	15.6191i	1.38986	−	0.702028i
$496$		0			0
$497$	−2.00141	+	1.45411i	−0.0897754	+	0.0652256i
$498$		0			0
$499$	−19.2421	−	6.25215i	−0.861397	−	0.279885i	−0.155185	−	0.987885i	$-0.549597\pi$
$499$	−19.2421	−	6.25215i	−0.861397	−	0.279885i	−0.706212	+	0.708001i	$0.749597\pi$
$500$		0			0
$501$	4.40025	−	6.05643i	0.196589	−	0.270581i
$502$		0			0
$503$	−2.97208	−	9.14711i	−0.132518	−	0.407850i	0.862677	−	0.505755i	$-0.168786\pi$
$503$	−2.97208	−	9.14711i	−0.132518	−	0.407850i	−0.995196	+	0.0979050i	$0.968786\pi$
$504$		0			0
$505$			37.3180i			1.66063i
$506$		0			0
$507$	−2.42285	−	4.88429i	−0.107603	−	0.216919i
$508$		0			0
$509$	−8.93954	+	2.90463i	−0.396238	+	0.128746i	−0.500357	−	0.865819i	$-0.666798\pi$
$509$	−8.93954	+	2.90463i	−0.396238	+	0.128746i	0.104119	+	0.994565i	$0.466798\pi$
$510$		0			0
$511$	−6.63464	−	4.82035i	−0.293499	−	0.213240i
$512$		0			0
$513$	−13.8284	−	4.49311i	−0.610538	−	0.198376i
$514$		0			0
$515$	29.7215	+	40.9082i	1.30969	+	1.80263i
$516$		0			0
$517$	13.2986	+	13.3924i	0.584874	+	0.588998i
$518$		0			0
$519$	7.28492	−	5.29280i	0.319772	−	0.232328i
$520$		0			0
$521$	0.589316	−	1.81373i	0.0258184	−	0.0794609i	−0.937317	−	0.348478i	$-0.886699\pi$
$521$	0.589316	−	1.81373i	0.0258184	−	0.0794609i	0.963135	+	0.269017i	$0.0866987\pi$
$522$		0			0
$523$	−10.2423	−	7.44149i	−0.447866	−	0.325394i	0.340887	−	0.940104i	$-0.389273\pi$
$523$	−10.2423	−	7.44149i	−0.447866	−	0.325394i	−0.788753	+	0.614711i	$0.789273\pi$
$524$		0			0
$525$	−4.13414	+	1.34326i	−0.180429	+	0.0586249i
$526$		0			0
$527$		−	3.94652i		−	0.171913i
$528$		0			0
$529$	49.5001			2.15218
$530$		0			0
$531$	−20.6336	+	6.70426i	−0.895422	+	0.290940i
$532$		0			0
$533$	−23.2642	+	9.49009i	−1.00768	+	0.411061i
$534$		0			0
$535$	2.53325	+	0.823102i	0.109522	+	0.0355858i
$536$		0			0
$537$	3.53647	−	2.56940i	0.152610	−	0.110878i
$538$		0			0
$539$	2.95620	−	18.2495i	0.127333	−	0.786060i
$540$		0			0
$541$	−26.3282	−	36.2377i	−1.13194	−	1.55798i	−0.784336	−	0.620337i	$-0.786996\pi$
$541$	−26.3282	−	36.2377i	−1.13194	−	1.55798i	−0.347602	−	0.937642i	$-0.613004\pi$
$542$		0			0
$543$	−0.512987	+	1.57881i	−0.0220144	+	0.0677533i
$544$		0			0
$545$	47.3575	+	34.4072i	2.02857	+	1.47384i
$546$		0			0
$547$	−6.49037	−	19.9753i	−0.277508	−	0.854083i	−0.988545	−	0.150928i	$-0.951774\pi$
$547$	−6.49037	−	19.9753i	−0.277508	−	0.854083i	0.711037	−	0.703155i	$-0.248226\pi$
$548$		0			0
$549$	41.0404			1.75156
$550$		0			0
$551$		−	6.97868i		−	0.297302i
$552$		0			0
$553$	2.04703	−	0.665121i	0.0870486	−	0.0282838i
$554$		0			0
$555$	4.70678	+	3.41968i	0.199792	+	0.145157i
$556$		0			0
$557$	−24.6691	−	8.01548i	−1.04526	−	0.339627i	−0.264455	−	0.964398i	$-0.585192\pi$
$557$	−24.6691	−	8.01548i	−1.04526	−	0.339627i	−0.780808	+	0.624771i	$0.785192\pi$
$558$		0			0
$559$	−22.0494	+	1.61605i	−0.932588	+	0.0683517i
$560$		0			0
$561$	−0.904693	+	0.140033i	−0.0381962	+	0.00591218i
$562$		0			0
$563$	−5.70046	+	4.14163i	−0.240246	+	0.174549i	−0.701393	−	0.712775i	$-0.747438\pi$
$563$	−5.70046	+	4.14163i	−0.240246	+	0.174549i	0.461147	+	0.887324i	$0.347438\pi$
$564$		0			0
$565$	−9.17852	−	2.98228i	−0.386143	−	0.125466i
$566$		0			0
$567$	5.22743	−	7.19494i	0.219531	−	0.302159i
$568$		0			0
$569$	0.467394	+	1.43849i	0.0195942	+	0.0603047i	0.960376	−	0.278709i	$-0.0899066\pi$
$569$	0.467394	+	1.43849i	0.0195942	+	0.0603047i	−0.940781	+	0.339014i	$0.889907\pi$
$570$		0			0
$571$	−8.53319			−0.357103			−0.178551	−	0.983931i	$-0.557141\pi$
$571$	−8.53319			−0.357103			−0.178551	+	0.983931i	$0.557141\pi$
$572$		0			0
$573$	−5.40246			−0.225691
$574$		0			0
$575$	22.8384	+	70.2893i	0.952426	+	2.93127i
$576$		0			0
$577$	−11.5559	+	15.9053i	−0.481079	+	0.662148i	−0.978712	−	0.205240i	$-0.934203\pi$
$577$	−11.5559	+	15.9053i	−0.481079	+	0.662148i	0.497633	+	0.867388i	$0.334203\pi$
$578$		0			0
$579$	3.75394	+	1.21973i	0.156008	+	0.0506901i
$580$		0			0
$581$	−6.27979	+	4.56254i	−0.260530	+	0.189286i
$582$		0			0
$583$	−31.9673	−	16.4299i	−1.32395	−	0.680457i
$584$		0			0
$585$	2.75289	+	37.5604i	0.113818	+	1.55293i
$586$		0			0
$587$	−22.2587	−	7.23228i	−0.918714	−	0.298508i	−0.188775	−	0.982020i	$-0.560452\pi$
$587$	−22.2587	−	7.23228i	−0.918714	−	0.298508i	−0.729939	+	0.683512i	$0.760452\pi$
$588$		0			0
$589$	28.8777	+	20.9809i	1.18988	+	0.864501i
$590$		0			0
$591$	−3.56509	+	1.15837i	−0.146648	+	0.0476489i
$592$		0			0
$593$			16.5173i			0.678282i	0.940735	+	0.339141i	$0.110136\pi$
$593$			16.5173i			0.678282i	−0.940735	+	0.339141i	$0.889864\pi$
$594$		0			0
$595$	−2.90667			−0.119162
$596$		0			0
$597$	0.815597	+	2.51015i	0.0333802	+	0.102734i
$598$		0			0
$599$	−16.0884	−	11.6889i	−0.657356	−	0.477597i	0.208413	−	0.978041i	$-0.433170\pi$
$599$	−16.0884	−	11.6889i	−0.657356	−	0.477597i	−0.865769	+	0.500444i	$0.833170\pi$
$600$		0			0
$601$	13.1236	−	40.3903i	0.535323	−	1.64755i	−0.207627	−	0.978208i	$-0.566574\pi$
$601$	13.1236	−	40.3903i	0.535323	−	1.64755i	0.742950	−	0.669347i	$-0.233426\pi$
$602$		0			0
$603$	−0.614539	−	0.845841i	−0.0250260	−	0.0344453i
$604$		0			0
$605$	12.3001	+	38.7811i	0.500071	+	1.57667i
$606$		0			0
$607$	13.9243	−	10.1166i	0.565169	−	0.410620i	−0.268178	−	0.963369i	$-0.586421\pi$
$607$	13.9243	−	10.1166i	0.565169	−	0.410620i	0.833347	+	0.552750i	$0.186421\pi$
$608$		0			0
$609$	−0.558391	−	0.181432i	−0.0226271	−	0.00735200i
$610$		0			0
$611$	−18.9978	+	7.74973i	−0.768571	+	0.313520i
$612$		0			0
$613$	25.9197	−	8.42182i	1.04689	−	0.340154i	0.265441	−	0.964127i	$-0.414482\pi$
$613$	25.9197	−	8.42182i	1.04689	−	0.340154i	0.781446	+	0.623973i	$0.214482\pi$
$614$		0			0
$615$	−10.8096			−0.435886
$616$		0			0
$617$		−	29.5978i		−	1.19156i	−0.803146	−	0.595782i	$-0.796842\pi$
$617$		−	29.5978i		−	1.19156i	0.803146	−	0.595782i	$-0.203158\pi$
$618$		0			0
$619$	28.8843	−	9.38509i	1.16096	−	0.377219i	0.335698	−	0.941970i	$-0.391028\pi$
$619$	28.8843	−	9.38509i	1.16096	−	0.377219i	0.825261	+	0.564751i	$0.191028\pi$
$620$		0			0
$621$	16.8261	+	12.2249i	0.675210	+	0.490569i
$622$		0			0
$623$	−0.0342471	+	0.105402i	−0.00137208	+	0.00422284i
$624$		0			0
$625$	−5.61526	+	4.07973i	−0.224610	+	0.163189i
$626$		0			0
$627$	3.78496	−	7.36431i	0.151157	−	0.294102i
$628$		0			0
$629$	1.45089	+	1.99697i	0.0578506	+	0.0796245i
$630$		0			0
$631$	−35.9897	−	11.6938i	−1.43273	−	0.465522i	−0.513106	−	0.858325i	$-0.671505\pi$
$631$	−35.9897	−	11.6938i	−1.43273	−	0.465522i	−0.919622	+	0.392804i	$0.871505\pi$
$632$		0			0
$633$	5.51320	+	4.00557i	0.219130	+	0.159207i
$634$		0			0
$635$	64.7173	−	21.0279i	2.56823	−	0.834468i
$636$		0			0
$637$	17.0795	+	10.5931i	0.676716	+	0.419715i
$638$		0			0
$639$			5.85088i			0.231457i
$640$		0			0
$641$	−4.17242	−	12.8414i	−0.164801	−	0.507205i	0.834221	−	0.551431i	$-0.185918\pi$
$641$	−4.17242	−	12.8414i	−0.164801	−	0.507205i	−0.999022	+	0.0442260i	$0.985918\pi$
$642$		0			0
$643$	−8.79946	+	12.1114i	−0.347017	+	0.477627i	−0.946474	−	0.322779i	$-0.895383\pi$
$643$	−8.79946	+	12.1114i	−0.347017	+	0.477627i	0.599458	+	0.800406i	$0.295383\pi$
$644$		0			0
$645$	−9.04614	−	2.93927i	−0.356192	−	0.115734i
$646$		0			0
$647$	−35.8226	+	26.0267i	−1.40833	+	1.02321i	−0.414771	+	0.909926i	$0.636138\pi$
$647$	−35.8226	+	26.0267i	−1.40833	+	1.02321i	−0.993562	+	0.113288i	$0.963862\pi$
$648$		0			0
$649$	−3.89736	−	25.1793i	−0.152985	−	0.988373i
$650$		0			0
$651$	2.42952	−	1.76515i	0.0952205	−	0.0691817i
$652$		0			0
$653$	−5.26740	+	16.2114i	−0.206129	+	0.634401i	0.793536	+	0.608524i	$0.208238\pi$
$653$	−5.26740	+	16.2114i	−0.206129	+	0.634401i	−0.999665	+	0.0258772i	$0.991762\pi$
$654$		0			0
$655$	−15.6485	+	21.5383i	−0.611436	+	0.841569i
$656$		0			0
$657$	−18.4463	+	5.99357i	−0.719659	+	0.233831i
$658$		0			0
$659$	35.4119			1.37945			0.689726	−	0.724071i	$-0.257731\pi$
$659$	35.4119			1.37945			0.689726	+	0.724071i	$0.257731\pi$
$660$		0			0
$661$		−	8.61067i		−	0.334916i	−0.985879	−	0.167458i	$-0.946444\pi$
$661$		−	8.61067i		−	0.334916i	0.985879	−	0.167458i	$-0.0535559\pi$
$662$		0			0
$663$	0.237530	−	0.966455i	0.00922490	−	0.0375340i
$664$		0			0
$665$	15.4527	−	21.2688i	0.599230	−	0.824769i
$666$		0			0
$667$	−3.08473	+	9.49383i	−0.119441	+	0.367603i
$668$		0			0
$669$	−1.98922	−	2.73793i	−0.0769077	−	0.105854i
$670$		0			0
$671$	−7.70702	+	47.5776i	−0.297526	+	1.83671i
$672$		0			0
$673$	−28.8825	+	20.9844i	−1.11334	+	0.808889i	−0.983186	−	0.182605i	$-0.941547\pi$
$673$	−28.8825	+	20.9844i	−1.11334	+	0.808889i	−0.130153	+	0.991494i	$0.541547\pi$
$674$		0			0
$675$	−6.55169	+	20.1640i	−0.252175	+	0.776114i
$676$		0			0
$677$	−19.7344	−	14.3379i	−0.758454	−	0.551049i	0.139982	−	0.990154i	$-0.455296\pi$
$677$	−19.7344	−	14.3379i	−0.758454	−	0.551049i	−0.898436	+	0.439105i	$0.855296\pi$
$678$		0			0
$679$	−0.653903	−	2.01251i	−0.0250945	−	0.0772329i
$680$		0			0
$681$			1.79948i			0.0689561i
$682$		0			0
$683$		−	15.7973i		−	0.604465i	−0.953234	−	0.302233i	$-0.902268\pi$
$683$		−	15.7973i		−	0.604465i	0.953234	−	0.302233i	$-0.0977320\pi$
$684$		0			0
$685$	−20.2744	−	62.3980i	−0.774643	−	2.38411i
$686$		0			0
$687$	5.69195	−	7.83430i	0.217161	−	0.298897i
$688$		0			0
$689$	29.8477	−	25.2160i	1.13711	−	0.960654i
$690$		0			0
$691$	12.9580	+	17.8352i	0.492946	+	0.678482i	0.980928	−	0.194372i	$-0.0622668\pi$
$691$	12.9580	+	17.8352i	0.492946	+	0.678482i	−0.487982	+	0.872854i	$0.662267\pi$
$692$		0			0
$693$	7.88075	+	7.93633i	0.299365	+	0.301476i
$694$		0			0
$695$	5.97000	+	8.21700i	0.226455	+	0.311688i
$696$		0			0
$697$	−4.36179	−	1.41723i	−0.165215	−	0.0536815i
$698$		0			0
$699$	−7.37917	−	5.36128i	−0.279106	−	0.202782i
$700$		0			0
$701$	−6.16589	−	18.9767i	−0.232882	−	0.716739i	−0.997395	−	0.0721299i	$-0.977020\pi$
$701$	−6.16589	−	18.9767i	−0.232882	−	0.716739i	0.764513	−	0.644609i	$-0.222980\pi$
$702$		0			0
$703$	−22.3256			−0.842028
$704$		0			0
$705$	−8.82728			−0.332455
$706$		0			0
$707$	−11.4583	+	3.72303i	−0.430934	+	0.140019i
$708$		0			0
$709$	10.0958	−	13.8957i	0.379156	−	0.521864i	−0.576204	−	0.817306i	$-0.695467\pi$
$709$	10.0958	−	13.8957i	0.379156	−	0.521864i	0.955361	+	0.295442i	$0.0954668\pi$
$710$		0			0
$711$	1.57305	−	4.84136i	0.0589942	−	0.181565i
$712$		0			0
$713$	−30.0113	−	41.3071i	−1.12393	−	1.54696i
$714$		0			0
$715$	−44.0603	−	3.86211i	−1.64776	−	0.144435i
$716$		0			0
$717$	1.50201	+	2.06734i	0.0560935	+	0.0772061i
$718$		0			0
$719$	11.4012	−	35.0893i	0.425193	−	1.30861i	−0.477616	−	0.878569i	$-0.658499\pi$
$719$	11.4012	−	35.0893i	0.425193	−	1.30861i	0.902809	−	0.430042i	$-0.141501\pi$
$720$		0			0
$721$	−9.59549	+	13.2071i	−0.357355	+	0.491857i
$722$		0			0
$723$	−5.11523	+	1.66204i	−0.190238	+	0.0618119i
$724$		0			0
$725$	−10.1761			−0.377929
$726$		0			0
$727$	−0.595516			−0.0220865			−0.0110432	−	0.999939i	$-0.503515\pi$
$727$	−0.595516			−0.0220865			−0.0110432	+	0.999939i	$0.503515\pi$
$728$		0			0
$729$	−5.55002	−	17.0812i	−0.205556	−	0.632637i
$730$		0			0
$731$	−3.26485	−	2.37205i	−0.120755	−	0.0877334i
$732$		0			0
$733$	24.6508	+	8.00954i	0.910499	+	0.295839i	0.726563	−	0.687099i	$-0.241116\pi$
$733$	24.6508	+	8.00954i	0.910499	+	0.295839i	0.183935	+	0.982938i	$0.441116\pi$
$734$		0			0
$735$	5.08238	+	6.99529i	0.187466	+	0.258025i
$736$		0			0
$737$	1.09598	−	0.553586i	0.0403708	−	0.0203916i
$738$		0			0
$739$	18.9656	+	26.1040i	0.697662	+	0.960250i	0.999975	+	0.00704113i	$0.00224128\pi$
$739$	18.9656	+	26.1040i	0.697662	+	0.960250i	−0.302313	+	0.953209i	$0.597759\pi$
$740$		0			0
$741$	5.80901	+	6.87602i	0.213399	+	0.252597i
$742$		0			0
$743$	1.56391	−	2.15254i	0.0573744	−	0.0789691i	−0.779366	−	0.626569i	$-0.784459\pi$
$743$	1.56391	−	2.15254i	0.0573744	−	0.0789691i	0.836740	+	0.547600i	$0.184459\pi$
$744$		0			0
$745$	−13.7165	−	42.2151i	−0.502534	−	1.54664i
$746$		0			0
$747$			18.3582i			0.671693i
$748$		0			0
$749$			0.859938i			0.0314215i
$750$		0			0
$751$	−0.266340	−	0.819710i	−0.00971888	−	0.0299116i	0.946079	−	0.323935i	$-0.105006\pi$
$751$	−0.266340	−	0.819710i	−0.00971888	−	0.0299116i	−0.955798	+	0.294023i	$0.905006\pi$
$752$		0			0
$753$	4.01211	+	2.91497i	0.146209	+	0.106227i
$754$		0			0
$755$	−23.1697	+	71.3091i	−0.843232	+	2.59520i
$756$		0			0
$757$	25.9905	−	18.8832i	0.944640	−	0.686321i	−0.00489280	−	0.999988i	$-0.501557\pi$
$757$	25.9905	−	18.8832i	0.944640	−	0.686321i	0.949533	+	0.313667i	$0.101557\pi$
$758$		0			0
$759$	−8.40427	+	8.34541i	−0.305056	+	0.302919i
$760$		0			0
$761$	5.31644	+	7.31745i	0.192721	+	0.265257i	0.894432	−	0.447204i	$-0.147580\pi$
$761$	5.31644	+	7.31745i	0.192721	+	0.265257i	−0.701711	+	0.712462i	$0.747580\pi$
$762$		0			0
$763$	−5.83995	+	17.9735i	−0.211421	+	0.650685i
$764$		0			0
$765$	−4.04071	+	5.56156i	−0.146092	+	0.201079i
$766$		0			0
$767$	26.8982	+	6.61090i	0.971239	+	0.238706i
$768$		0			0
$769$		−	26.5545i		−	0.957581i	−0.877929	−	0.478790i	$-0.841075\pi$
$769$		−	26.5545i		−	0.957581i	0.877929	−	0.478790i	$-0.158925\pi$
$770$		0			0
$771$	−9.82632			−0.353886
$772$		0			0
$773$	−19.7872	+	6.42924i	−0.711695	+	0.231244i	−0.642419	−	0.766354i	$-0.722069\pi$
$773$	−19.7872	+	6.42924i	−0.711695	+	0.231244i	−0.0692761	+	0.997598i	$0.522069\pi$
$774$		0			0
$775$	30.5935	−	42.1084i	1.09895	−	1.51258i
$776$		0			0
$777$	−0.580423	+	1.78636i	−0.0208226	+	0.0640853i
$778$		0			0
$779$	33.5588	−	24.3819i	1.20237	−	0.873571i
$780$		0			0
$781$	−6.78285	−	1.09874i	−0.242710	−	0.0393161i
$782$		0			0
$783$	−2.31676	+	1.68323i	−0.0827943	+	0.0601536i
$784$		0			0
$785$	−13.8755	−	4.50843i	−0.495239	−	0.160913i
$786$		0			0
$787$	20.6004	−	28.3540i	0.734325	−	1.01071i	−0.264600	−	0.964358i	$-0.585240\pi$
$787$	20.6004	−	28.3540i	0.734325	−	1.01071i	0.998925	−	0.0463538i	$-0.0147602\pi$
$788$		0			0
$789$	2.61122	+	8.03650i	0.0929618	+	0.286107i
$790$		0			0
$791$		−	3.11575i		−	0.110783i
$792$		0			0
$793$	−44.5275	−	27.6170i	−1.58122	−	0.980708i
$794$		0			0
$795$	15.9877	−	5.19472i	0.567025	−	0.184238i
$796$		0			0
$797$	33.4383	+	24.2944i	1.18445	+	0.860551i	0.992666	−	0.120887i	$-0.0385738\pi$
$797$	33.4383	+	24.2944i	1.18445	+	0.860551i	0.191780	+	0.981438i	$0.438574\pi$
$798$		0			0
$799$	−3.56189	−	1.15733i	−0.126011	−	0.0409434i
$800$		0			0
$801$	0.154065	+	0.212052i	0.00544362	+	0.00749250i
$802$		0			0
$803$	−3.48422	−	22.5101i	−0.122955	−	0.794365i
$804$		0			0
$805$	−30.4232	+	22.1038i	−1.07228	+	0.779055i
$806$		0			0
$807$	−2.38229	+	7.33192i	−0.0838605	+	0.258096i
$808$		0			0
$809$	−5.57943	−	4.05369i	−0.196162	−	0.142520i	0.485368	−	0.874310i	$-0.338685\pi$
$809$	−5.57943	−	4.05369i	−0.196162	−	0.142520i	−0.681531	+	0.731789i	$0.738685\pi$
$810$		0			0
$811$	−20.9987	+	6.82289i	−0.737364	+	0.239584i	−0.653535	−	0.756896i	$-0.726715\pi$
$811$	−20.9987	+	6.82289i	−0.737364	+	0.239584i	−0.0838288	+	0.996480i	$0.526715\pi$
$812$		0			0
$813$		−	5.04158i		−	0.176816i
$814$		0			0
$815$	61.7328			2.16240
$816$		0			0
$817$	34.7137	−	11.2792i	1.21448	−	0.394608i
$818$		0			0
$819$	−11.2581	+	4.59248i	−0.393390	+	0.160474i
$820$		0			0
$821$	3.31311	+	1.07649i	0.115628	+	0.0375699i	0.366260	−	0.930513i	$-0.380638\pi$
$821$	3.31311	+	1.07649i	0.115628	+	0.0375699i	−0.250631	+	0.968083i	$0.580638\pi$
$822$		0			0
$823$	13.2633	−	9.63633i	0.462329	−	0.335901i	−0.332115	−	0.943239i	$-0.607762\pi$
$823$	13.2633	−	9.63633i	0.462329	−	0.335901i	0.794444	+	0.607337i	$0.207762\pi$
$824$		0			0
$825$	−10.7384	−	5.51908i	−0.373862	−	0.192150i
$826$		0			0
$827$	−12.8797	−	17.7274i	−0.447871	−	0.616442i	0.524067	−	0.851677i	$-0.324414\pi$
$827$	−12.8797	−	17.7274i	−0.447871	−	0.616442i	−0.971939	+	0.235235i	$0.924414\pi$
$828$		0			0
$829$	−11.0635	+	34.0500i	−0.384251	+	1.18260i	0.552770	+	0.833334i	$0.313571\pi$
$829$	−11.0635	+	34.0500i	−0.384251	+	1.18260i	−0.937022	+	0.349271i	$0.886429\pi$
$830$		0			0
$831$	−2.13383	−	1.55032i	−0.0740217	−	0.0537799i
$832$		0			0
$833$	1.13365	+	3.48901i	0.0392786	+	0.120887i
$834$		0			0
$835$	66.0194			2.28469
$836$		0			0
$837$		−	14.6472i		−	0.506282i
$838$		0			0
$839$	28.7804	−	9.35132i	0.993610	−	0.322843i	0.233300	−	0.972405i	$-0.425047\pi$
$839$	28.7804	−	9.35132i	0.993610	−	0.322843i	0.760309	+	0.649561i	$0.225047\pi$
$840$		0			0
$841$	22.3495	+	16.2379i	0.770674	+	0.559927i
$842$		0			0
$843$	−11.6570	−	3.78757i	−0.401487	−	0.130451i
$844$		0			0
$845$	22.2884	−	42.6043i	0.766745	−	1.46563i
$846$		0			0
$847$	−10.6804	+	7.64569i	−0.366984	+	0.262709i
$848$		0			0
$849$	5.30674	−	3.85557i	0.182127	−	0.132323i
$850$		0			0
$851$	30.3719	+	9.86844i	1.04114	+	0.338286i
$852$		0			0
$853$	17.0396	−	23.4530i	0.583425	−	0.803016i	−0.410640	−	0.911797i	$-0.634695\pi$
$853$	17.0396	−	23.4530i	0.583425	−	0.803016i	0.994066	+	0.108781i	$0.0346948\pi$
$854$		0			0
$855$	−19.2137	−	59.1337i	−0.657095	−	2.02233i
$856$		0			0
$857$	−25.8527			−0.883110			−0.441555	−	0.897234i	$-0.645573\pi$
$857$	−25.8527			−0.883110			−0.441555	+	0.897234i	$0.645573\pi$
$858$		0			0
$859$	−9.77235			−0.333428			−0.166714	−	0.986005i	$-0.553316\pi$
$859$	−9.77235			−0.333428			−0.166714	+	0.986005i	$0.553316\pi$
$860$		0			0
$861$	−1.07842	−	3.31905i	−0.0367526	−	0.113113i
$862$		0			0
$863$	19.7330	−	27.1602i	0.671721	−	0.924544i	−0.328077	−	0.944651i	$-0.606401\pi$
$863$	19.7330	−	27.1602i	0.671721	−	0.924544i	0.999798	+	0.0201066i	$0.00640056\pi$
$864$		0			0
$865$	75.5241	+	24.5393i	2.56790	+	0.834361i
$866$		0			0
$867$	−5.62116	+	4.08401i	−0.190905	+	0.138700i
$868$		0			0
$869$	5.31713	+	2.73279i	0.180371	+	0.0927035i
$870$		0			0
$871$	0.0975703	+	1.33125i	0.00330605	+	0.0451076i
$872$		0			0
$873$	−4.75971	−	1.54652i	−0.161092	−	0.0523419i
$874$		0			0
$875$	−13.1483	−	9.55278i	−0.444493	−	0.322943i
$876$		0			0
$877$	47.6024	−	15.4670i	1.60742	−	0.522282i	0.638493	−	0.769628i	$-0.279558\pi$
$877$	47.6024	−	15.4670i	1.60742	−	0.522282i	0.968927	+	0.247346i	$0.0795583\pi$
$878$		0			0
$879$			8.17561i			0.275757i
$880$		0			0
$881$	−1.81666			−0.0612048			−0.0306024	−	0.999532i	$-0.509743\pi$
$881$	−1.81666			−0.0612048			−0.0306024	+	0.999532i	$0.509743\pi$
$882$		0			0
$883$	−0.840129	−	2.58565i	−0.0282726	−	0.0870141i	0.935925	−	0.352201i	$-0.114566\pi$
$883$	−0.840129	−	2.58565i	−0.0282726	−	0.0870141i	−0.964197	+	0.265186i	$0.914566\pi$
$884$		0			0
$885$	9.64085	+	7.00449i	0.324074	+	0.235453i
$886$		0			0
$887$	13.8904	−	42.7503i	0.466395	−	1.43541i	−0.390826	−	0.920465i	$-0.627810\pi$
$887$	13.8904	−	42.7503i	0.466395	−	1.43541i	0.857220	−	0.514950i	$-0.172190\pi$
$888$		0			0
$889$	12.9131	+	17.7733i	0.433090	+	0.596097i
$890$		0			0
$891$	24.4111	−	3.77846i	0.817803	−	0.126583i
$892$		0			0
$893$	27.4045	−	19.9105i	0.917057	−	0.666281i
$894$		0			0
$895$	36.6633	+	11.9126i	1.22552	+	0.398195i
$896$		0			0
$897$	−4.86326	−	11.9219i	−0.162379	−	0.398060i
$898$		0			0
$899$	6.68605	−	2.17243i	0.222992	−	0.0724546i
$900$		0			0
$901$	7.13227			0.237610
$902$		0			0
$903$		−	3.07081i		−	0.102190i
$904$		0			0
$905$	−13.9233	+	4.52396i	−0.462827	+	0.150382i
$906$		0			0
$907$	−26.2015	−	19.0365i	−0.870008	−	0.632098i	0.0605811	−	0.998163i	$-0.480705\pi$
$907$	−26.2015	−	19.0365i	−0.870008	−	0.632098i	−0.930589	+	0.366065i	$0.880705\pi$
$908$		0			0
$909$	−8.80522	+	27.0997i	−0.292051	+	0.898839i
$910$		0			0
$911$	8.16130	−	5.92953i	0.270396	−	0.196454i	−0.444322	−	0.895867i	$-0.646555\pi$
$911$	8.16130	−	5.92953i	0.270396	−	0.196454i	0.714717	+	0.699413i	$0.246555\pi$
$912$		0			0
$913$	−21.2825	−	3.44751i	−0.704347	−	0.114096i
$914$		0			0
$915$	−13.2501	−	18.2372i	−0.438035	−	0.602903i
$916$		0			0
$917$	−8.17439	−	2.65602i	−0.269942	−	0.0877095i
$918$		0			0
$919$	−40.1659	−	29.1822i	−1.32495	−	0.962632i	−0.999856	−	0.0169501i	$-0.994604\pi$
$919$	−40.1659	−	29.1822i	−1.32495	−	0.962632i	−0.325093	−	0.945682i	$-0.605396\pi$
$920$		0			0
$921$	−5.72153	+	1.85904i	−0.188531	+	0.0612574i
$922$		0			0
$923$	3.93719	−	6.34802i	0.129594	−	0.208947i
$924$		0			0
$925$			32.5544i			1.07038i
$926$		0			0
$927$	11.9309	+	36.7196i	0.391863	+	1.20603i
$928$		0			0
$929$	−26.0445	+	35.8472i	−0.854493	+	1.17611i	0.128361	+	0.991727i	$0.459028\pi$
$929$	−26.0445	+	35.8472i	−0.854493	+	1.17611i	−0.982855	+	0.184382i	$0.940972\pi$
$930$		0			0
$931$	−31.5567	−	10.2534i	−1.03423	−	0.336042i
$932$		0			0
$933$	−3.51918	+	2.55684i	−0.115213	+	0.0837071i
$934$		0			0
$935$	−5.68864	−	5.72876i	−0.186038	−	0.187350i
$936$		0			0
$937$	14.8896	−	10.8179i	0.486421	−	0.353406i	−0.317385	−	0.948297i	$-0.602805\pi$
$937$	14.8896	−	10.8179i	0.486421	−	0.353406i	0.803806	+	0.594891i	$0.202805\pi$
$938$		0			0
$939$	3.54472	−	10.9095i	0.115678	−	0.356019i
$940$		0			0
$941$	12.3088	−	16.9416i	0.401256	−	0.552282i	−0.559803	−	0.828626i	$-0.689123\pi$
$941$	12.3088	−	16.9416i	0.401256	−	0.552282i	0.961059	+	0.276344i	$0.0891230\pi$
$942$		0			0
$943$	−56.4309	+	18.3355i	−1.83764	+	0.597086i
$944$		0			0
$945$	−10.7879			−0.350930
$946$		0			0
$947$			30.9450i			1.00558i	0.864410	+	0.502788i	$0.167692\pi$
$947$			30.9450i			1.00558i	−0.864410	+	0.502788i	$0.832308\pi$
$948$		0			0
$949$	24.0468	+	5.91010i	0.780594	+	0.191850i
$950$		0			0
$951$	3.98524	−	5.48521i	0.129230	−	0.177870i
$952$		0			0
$953$	2.34236	−	7.20904i	0.0758764	−	0.233524i	−0.905924	−	0.423441i	$-0.860822\pi$
$953$	2.34236	−	7.20904i	0.0758764	−	0.233524i	0.981800	+	0.189917i	$0.0608220\pi$
$954$		0			0
$955$	−28.0042	−	38.5444i	−0.906194	−	1.24727i
$956$		0			0
$957$	−0.735241	−	1.45561i	−0.0237670	−	0.0470533i
$958$		0			0
$959$	17.1364	−	12.4503i	0.553362	−	0.402041i
$960$		0			0
$961$	−1.53208	+	4.71527i	−0.0494221	+	0.152106i
$962$		0			0
$963$	1.64539	+	1.19544i	0.0530219	+	0.0385227i
$964$		0			0
$965$	10.7566	+	33.1054i	0.346267	+	1.06570i
$966$		0			0
$967$		−	49.9314i		−	1.60569i	−0.596190	−	0.802843i	$-0.703320\pi$
$967$		−	49.9314i		−	1.60569i	0.596190	−	0.802843i	$-0.296680\pi$
$968$		0			0
$969$			1.64306i			0.0527827i
$970$		0			0
$971$	0.0306440	+	0.0943124i	0.000983412	+	0.00302663i	0.951547	−	0.307503i	$-0.0994935\pi$
$971$	0.0306440	+	0.0943124i	0.000983412	+	0.00302663i	−0.950564	+	0.310530i	$0.899494\pi$
$972$		0			0
$973$	−1.92739	+	2.65283i	−0.0617894	+	0.0850458i
$974$		0			0
$975$	10.0264	−	8.47049i	0.321100	−	0.271273i
$976$		0			0
$977$	−13.9843	−	19.2477i	−0.447397	−	0.615789i	0.524439	−	0.851448i	$-0.324275\pi$
$977$	−13.9843	−	19.2477i	−0.447397	−	0.615789i	−0.971836	+	0.235659i	$0.924275\pi$
$978$		0			0
$979$	−0.274762	+	0.138784i	−0.00878142	+	0.00443556i
$980$		0			0
$981$	26.2718	+	36.1600i	0.838793	+	1.15450i
$982$		0			0
$983$	25.9669	+	8.43715i	0.828215	+	0.269103i	0.692293	−	0.721616i	$-0.256600\pi$
$983$	25.9669	+	8.43715i	0.828215	+	0.269103i	0.135922	+	0.990720i	$0.456600\pi$
$984$		0			0
$985$	−26.7445	−	19.4310i	−0.852151	−	0.619124i
$986$		0			0
$987$	−0.880654	−	2.71037i	−0.0280315	−	0.0862722i
$988$		0			0
$989$	−52.2104			−1.66019
$990$		0			0
$991$	−14.4756			−0.459834			−0.229917	−	0.973210i	$-0.573845\pi$
$991$	−14.4756			−0.459834			−0.229917	+	0.973210i	$0.573845\pi$
$992$		0			0
$993$	−11.1318	+	3.61693i	−0.353255	+	0.114780i
$994$		0			0
$995$	−13.6812	+	18.8306i	−0.433724	+	0.596969i
$996$		0			0
$997$	−15.1937	+	46.7614i	−0.481189	+	1.48095i	0.356236	+	0.934396i	$0.384060\pi$
$997$	−15.1937	+	46.7614i	−0.481189	+	1.48095i	−0.837425	+	0.546552i	$0.815940\pi$
$998$		0			0
$999$	5.38484	+	7.41160i	0.170369	+	0.234493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.x.a.25.6	yes	56
11.4	even	5	inner	572.2.x.a.389.5	yes	56
13.12	even	2	inner	572.2.x.a.25.5	✓	56
143.103	even	10	inner	572.2.x.a.389.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.x.a.25.5	✓	56	13.12	even	2	inner
572.2.x.a.25.6	yes	56	1.1	even	1	trivial
572.2.x.a.389.5	yes	56	11.4	even	5	inner
572.2.x.a.389.6	yes	56	143.103	even	10	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.129602 - 0.398873i) q^{3} +(2.17400 - 2.99226i) q^{5} +(1.13565 + 0.368994i) q^{7} +(2.28475 - 1.65997i) q^{9} +O(q^{10})\)	\(q+(-0.129602 - 0.398873i) q^{3} +(2.17400 - 2.99226i) q^{5} +(1.13565 + 0.368994i) q^{7} +(2.28475 - 1.65997i) q^{9} +(1.49532 + 2.96041i) q^{11} +(-3.59591 + 0.263553i) q^{13} +(-1.47529 - 0.479349i) q^{15} +(-0.532445 - 0.386844i) q^{17} +(5.66127 - 1.83946i) q^{19} -0.500802i q^{21} -8.51470 q^{23} +(-2.68223 - 8.25505i) q^{25} +(-1.97613 - 1.43574i) q^{27} +(0.362283 - 1.11499i) q^{29} +(3.52465 + 4.85126i) q^{31} +(0.987030 - 0.980119i) q^{33} +(3.57302 - 2.59595i) q^{35} +(-3.56700 - 1.15899i) q^{37} +(0.571160 + 1.40015i) q^{39} +(6.62747 - 2.15339i) q^{41} +6.13179 q^{43} -10.4453i q^{45} +(5.41207 - 1.75849i) q^{47} +(-4.50958 - 3.27640i) q^{49} +(-0.0852960 + 0.262514i) q^{51} +(-8.76734 + 6.36984i) q^{53} +(12.1091 + 1.96154i) q^{55} +(-1.46742 - 2.01973i) q^{57} +(-7.30625 - 2.37394i) q^{59} +(11.7568 + 8.54180i) q^{61} +(3.20719 - 1.04208i) q^{63} +(-7.02889 + 11.3328i) q^{65} -0.370212i q^{67} +(1.10352 + 3.39629i) q^{69} +(-1.21775 + 1.67609i) q^{71} +(-6.53174 - 2.12229i) q^{73} +(-2.94510 + 2.13974i) q^{75} +(0.605787 + 3.91374i) q^{77} +(1.45827 - 1.05950i) q^{79} +(2.30152 - 7.08335i) q^{81} +(-3.82093 + 5.25906i) q^{83} +(-2.31507 + 0.752213i) q^{85} -0.491694 q^{87} +0.0928121i q^{89} +(-4.18093 - 1.02757i) q^{91} +(1.47824 - 2.03462i) q^{93} +(6.80347 - 20.9389i) q^{95} +(-1.04163 - 1.43368i) q^{97} +(8.33061 + 4.28160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^9	\( 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) \) 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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