LMFDB - Embedded newform 1156.2.h.a.757.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1156,2,Mod(733,1156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1156.733"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1156, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1156 = 2^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1156.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,0,0,4,0,4,0,-4,0,0,0,4,0,0,0,4,0,0,0,12,0,-4,0,-4,0, 8,0,4,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(33)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.23070647366$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			757.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1156.757
Dual form			1156.2.h.a.733.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70711 - 0.707107i) q^{3} +(-0.707107 + 1.70711i) q^{5} +(0.292893 + 0.707107i) q^{7} +(0.292893 + 0.292893i) q^{9} +(-3.12132 + 1.29289i) q^{11} -6.82843i q^{13} +(2.41421 - 2.41421i) q^{15} +(-1.82843 + 1.82843i) q^{19} -1.41421i q^{21} +(6.53553 - 2.70711i) q^{23} +(1.12132 + 1.12132i) q^{25} +(1.82843 + 4.41421i) q^{27} +(-1.53553 + 3.70711i) q^{29} +(5.94975 + 2.46447i) q^{31} +6.24264 q^{33} -1.41421 q^{35} +(-6.12132 - 2.53553i) q^{37} +(-4.82843 + 11.6569i) q^{39} +(0.464466 + 1.12132i) q^{41} +(3.00000 + 3.00000i) q^{43} +(-0.707107 + 0.292893i) q^{45} +3.65685i q^{47} +(4.53553 - 4.53553i) q^{49} +(4.17157 - 4.17157i) q^{53} -6.24264i q^{55} +(4.41421 - 1.82843i) q^{57} +(9.82843 + 9.82843i) q^{59} +(-0.707107 - 1.70711i) q^{61} +(-0.121320 + 0.292893i) q^{63} +(11.6569 + 4.82843i) q^{65} +11.3137 q^{67} -13.0711 q^{69} +(1.12132 + 0.464466i) q^{71} +(3.29289 - 7.94975i) q^{73} +(-1.12132 - 2.70711i) q^{75} +(-1.82843 - 1.82843i) q^{77} +(10.5355 - 4.36396i) q^{79} -10.0711i q^{81} +(-0.171573 + 0.171573i) q^{83} +(5.24264 - 5.24264i) q^{87} +10.8284i q^{89} +(4.82843 - 2.00000i) q^{91} +(-8.41421 - 8.41421i) q^{93} +(-1.82843 - 4.41421i) q^{95} +(-0.363961 + 0.878680i) q^{97} +(-1.29289 - 0.535534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{7} + 4 q^{9} - 4 q^{11} + 4 q^{15} + 4 q^{19} + 12 q^{23} - 4 q^{25} - 4 q^{27} + 8 q^{29} + 4 q^{31} + 8 q^{33} - 16 q^{37} - 8 q^{39} + 16 q^{41} + 12 q^{43} + 4 q^{49} + 28 q^{53}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^7 + 4 * q^9 - 4 * q^11 + 4 * q^15 + 4 * q^19 + 12 * q^23 - 4 * q^25 - 4 * q^27 + 8 * q^29 + 4 * q^31 + 8 * q^33 - 16 * q^37 - 8 * q^39 + 16 * q^41 + 12 * q^43 + 4 * q^49 + 28 * q^53 + 12 * q^57 + 28 * q^59 + 8 * q^63 + 24 * q^65 - 24 * q^69 - 4 * q^71 + 16 * q^73 + 4 * q^75 + 4 * q^77 + 28 * q^79 - 12 * q^83 + 4 * q^87 + 8 * q^91 - 28 * q^93 + 4 * q^95 + 24 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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
$3$	−1.70711	−	0.707107i	−0.985599	−	0.408248i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	−1.70711	−	0.707107i	−0.985599	−	0.408248i	−0.816497	+	0.577350i	$0.804087\pi$
$4$		0			0
$5$	−0.707107	+	1.70711i	−0.316228	+	0.763441i	0.683220	+	0.730213i	$0.260579\pi$
$5$	−0.707107	+	1.70711i	−0.316228	+	0.763441i	−0.999448	+	0.0332288i	$0.989421\pi$
$6$		0			0
$7$	0.292893	+	0.707107i	0.110703	+	0.267261i	0.969516	−	0.245029i	$-0.0787974\pi$
$7$	0.292893	+	0.707107i	0.110703	+	0.267261i	−0.858813	+	0.512290i	$0.828797\pi$
$8$		0			0
$9$	0.292893	+	0.292893i	0.0976311	+	0.0976311i
$10$		0			0
$11$	−3.12132	+	1.29289i	−0.941113	+	0.389822i	−0.799884	−	0.600155i	$-0.795106\pi$
$11$	−3.12132	+	1.29289i	−0.941113	+	0.389822i	−0.141230	+	0.989977i	$0.545106\pi$
$12$		0			0
$13$		−	6.82843i		−	1.89386i	−0.321433	−	0.946932i	$-0.604164\pi$
$13$		−	6.82843i		−	1.89386i	0.321433	−	0.946932i	$-0.395836\pi$
$14$		0			0
$15$	2.41421	−	2.41421i	0.623347	−	0.623347i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$	−1.82843	+	1.82843i	−0.419470	+	0.419470i	−0.885021	−	0.465551i	$-0.845856\pi$
$19$	−1.82843	+	1.82843i	−0.419470	+	0.419470i	0.465551	+	0.885021i	$0.345856\pi$
$20$		0			0
$21$		−	1.41421i		−	0.308607i
$22$		0			0
$23$	6.53553	−	2.70711i	1.36275	−	0.564471i	0.422939	−	0.906158i	$-0.360998\pi$
$23$	6.53553	−	2.70711i	1.36275	−	0.564471i	0.939814	+	0.341687i	$0.110998\pi$
$24$		0			0
$25$	1.12132	+	1.12132i	0.224264	+	0.224264i
$26$		0			0
$27$	1.82843	+	4.41421i	0.351881	+	0.849516i
$28$		0			0
$29$	−1.53553	+	3.70711i	−0.285141	+	0.688392i	−0.999940	−	0.0109378i	$-0.996518\pi$
$29$	−1.53553	+	3.70711i	−0.285141	+	0.688392i	0.714799	+	0.699330i	$0.246518\pi$
$30$		0			0
$31$	5.94975	+	2.46447i	1.06861	+	0.442631i	0.846499	−	0.532391i	$-0.178706\pi$
$31$	5.94975	+	2.46447i	1.06861	+	0.442631i	0.222108	+	0.975022i	$0.428706\pi$
$32$		0			0
$33$	6.24264			1.08670
$34$		0			0
$35$	−1.41421			−0.239046
$36$		0			0
$37$	−6.12132	−	2.53553i	−1.00634	−	0.416839i	−0.182221	−	0.983258i	$-0.558329\pi$
$37$	−6.12132	−	2.53553i	−1.00634	−	0.416839i	−0.824118	+	0.566418i	$0.808329\pi$
$38$		0			0
$39$	−4.82843	+	11.6569i	−0.773167	+	1.86659i
$40$		0			0
$41$	0.464466	+	1.12132i	0.0725374	+	0.175121i	0.955990	−	0.293400i	$-0.0947869\pi$
$41$	0.464466	+	1.12132i	0.0725374	+	0.175121i	−0.883452	+	0.468521i	$0.844787\pi$
$42$		0			0
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	0.897833	−	0.440337i	$-0.145141\pi$
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	−0.440337	+	0.897833i	$0.645141\pi$
$44$		0			0
$45$	−0.707107	+	0.292893i	−0.105409	+	0.0436619i
$46$		0			0
$47$			3.65685i			0.533407i	0.963779	+	0.266704i	$0.0859344\pi$
$47$			3.65685i			0.533407i	−0.963779	+	0.266704i	$0.914066\pi$
$48$		0			0
$49$	4.53553	−	4.53553i	0.647933	−	0.647933i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.17157	−	4.17157i	0.573010	−	0.573010i	−0.359959	−	0.932968i	$-0.617209\pi$
$53$	4.17157	−	4.17157i	0.573010	−	0.573010i	0.932968	+	0.359959i	$0.117209\pi$
$54$		0			0
$55$		−	6.24264i		−	0.841757i
$56$		0			0
$57$	4.41421	−	1.82843i	0.584677	−	0.242181i
$58$		0			0
$59$	9.82843	+	9.82843i	1.27955	+	1.27955i	0.940918	+	0.338634i	$0.109965\pi$
$59$	9.82843	+	9.82843i	1.27955	+	1.27955i	0.338634	+	0.940918i	$0.390035\pi$
$60$		0			0
$61$	−0.707107	−	1.70711i	−0.0905357	−	0.218573i	0.872125	−	0.489283i	$-0.162741\pi$
$61$	−0.707107	−	1.70711i	−0.0905357	−	0.218573i	−0.962661	+	0.270710i	$0.912741\pi$
$62$		0			0
$63$	−0.121320	+	0.292893i	−0.0152849	+	0.0369011i
$64$		0			0
$65$	11.6569	+	4.82843i	1.44585	+	0.598893i
$66$		0			0
$67$	11.3137			1.38219			0.691095	−	0.722764i	$-0.257129\pi$
$67$	11.3137			1.38219			0.691095	+	0.722764i	$0.257129\pi$
$68$		0			0
$69$	−13.0711			−1.57357
$70$		0			0
$71$	1.12132	+	0.464466i	0.133076	+	0.0551220i	0.448228	−	0.893919i	$-0.352055\pi$
$71$	1.12132	+	0.464466i	0.133076	+	0.0551220i	−0.315152	+	0.949041i	$0.602055\pi$
$72$		0			0
$73$	3.29289	−	7.94975i	0.385404	−	0.930448i	−0.605496	−	0.795848i	$-0.707025\pi$
$73$	3.29289	−	7.94975i	0.385404	−	0.930448i	0.990900	−	0.134599i	$-0.0429747\pi$
$74$		0			0
$75$	−1.12132	−	2.70711i	−0.129479	−	0.312590i
$76$		0			0
$77$	−1.82843	−	1.82843i	−0.208369	−	0.208369i
$78$		0			0
$79$	10.5355	−	4.36396i	1.18534	−	0.490984i	0.299105	−	0.954220i	$-0.403312\pi$
$79$	10.5355	−	4.36396i	1.18534	−	0.490984i	0.886235	+	0.463236i	$0.153312\pi$
$80$		0			0
$81$		−	10.0711i		−	1.11901i
$82$		0			0
$83$	−0.171573	+	0.171573i	−0.0188326	+	0.0188326i	−0.716460	−	0.697628i	$-0.754239\pi$
$83$	−0.171573	+	0.171573i	−0.0188326	+	0.0188326i	0.697628	+	0.716460i	$0.254239\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.24264	−	5.24264i	0.562070	−	0.562070i
$88$		0			0
$89$			10.8284i			1.14781i	0.818922	+	0.573905i	$0.194572\pi$
$89$			10.8284i			1.14781i	−0.818922	+	0.573905i	$0.805428\pi$
$90$		0			0
$91$	4.82843	−	2.00000i	0.506157	−	0.209657i
$92$		0			0
$93$	−8.41421	−	8.41421i	−0.872513	−	0.872513i
$94$		0			0
$95$	−1.82843	−	4.41421i	−0.187593	−	0.452889i
$96$		0			0
$97$	−0.363961	+	0.878680i	−0.0369546	+	0.0892164i	−0.941279	−	0.337629i	$-0.890375\pi$
$97$	−0.363961	+	0.878680i	−0.0369546	+	0.0892164i	0.904325	+	0.426845i	$0.140375\pi$
$98$		0			0
$99$	−1.29289	−	0.535534i	−0.129941	−	0.0538232i
$100$		0			0
$101$	12.8284			1.27648			0.638238	−	0.769839i	$-0.279664\pi$
$101$	12.8284			1.27648			0.638238	+	0.769839i	$0.279664\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	2.41421	+	1.00000i	0.235603	+	0.0975900i
$106$		0			0
$107$	−1.46447	+	3.53553i	−0.141575	+	0.341793i	−0.978724	−	0.205183i	$-0.934221\pi$
$107$	−1.46447	+	3.53553i	−0.141575	+	0.341793i	0.837148	+	0.546976i	$0.184221\pi$
$108$		0			0
$109$	−1.87868	−	4.53553i	−0.179945	−	0.434425i	0.808010	−	0.589169i	$-0.200545\pi$
$109$	−1.87868	−	4.53553i	−0.179945	−	0.434425i	−0.987955	+	0.154744i	$0.950545\pi$
$110$		0			0
$111$	8.65685	+	8.65685i	0.821672	+	0.821672i
$112$		0			0
$113$	−1.29289	+	0.535534i	−0.121625	+	0.0503788i	−0.442666	−	0.896687i	$-0.645967\pi$
$113$	−1.29289	+	0.535534i	−0.121625	+	0.0503788i	0.321041	+	0.947065i	$0.395967\pi$
$114$		0			0
$115$			13.0711i			1.21888i
$116$		0			0
$117$	2.00000	−	2.00000i	0.184900	−	0.184900i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.292893	−	0.292893i	0.0266267	−	0.0266267i
$122$		0			0
$123$		−	2.24264i		−	0.202212i
$124$		0			0
$125$	−11.2426	+	4.65685i	−1.00557	+	0.416522i
$126$		0			0
$127$	0.171573	+	0.171573i	0.0152246	+	0.0152246i	0.714678	−	0.699453i	$-0.246573\pi$
$127$	0.171573	+	0.171573i	0.0152246	+	0.0152246i	−0.699453	+	0.714678i	$0.746573\pi$
$128$		0			0
$129$	−3.00000	−	7.24264i	−0.264135	−	0.637679i
$130$		0			0
$131$	4.19239	−	10.1213i	0.366291	−	0.884304i	−0.628061	−	0.778164i	$-0.716151\pi$
$131$	4.19239	−	10.1213i	0.366291	−	0.884304i	0.994351	−	0.106139i	$-0.0338490\pi$
$132$		0			0
$133$	−1.82843	−	0.757359i	−0.158545	−	0.0656714i
$134$		0			0
$135$	−8.82843			−0.759830
$136$		0			0
$137$	12.1421			1.03737			0.518686	−	0.854965i	$-0.326421\pi$
$137$	12.1421			1.03737			0.518686	+	0.854965i	$0.326421\pi$
$138$		0			0
$139$	−16.1924	−	6.70711i	−1.37342	−	0.568889i	−0.430707	−	0.902492i	$-0.641736\pi$
$139$	−16.1924	−	6.70711i	−1.37342	−	0.568889i	−0.942714	+	0.333603i	$0.891736\pi$
$140$		0			0
$141$	2.58579	−	6.24264i	0.217763	−	0.525725i
$142$		0			0
$143$	8.82843	+	21.3137i	0.738270	+	1.78234i
$144$		0			0
$145$	−5.24264	−	5.24264i	−0.435378	−	0.435378i
$146$		0			0
$147$	−10.9497	+	4.53553i	−0.903120	+	0.374085i
$148$		0			0
$149$		−	9.65685i		−	0.791120i	−0.918440	−	0.395560i	$-0.870550\pi$
$149$		−	9.65685i		−	0.791120i	0.918440	−	0.395560i	$-0.129450\pi$
$150$		0			0
$151$	−10.3137	+	10.3137i	−0.839318	+	0.839318i	−0.988769	−	0.149451i	$-0.952249\pi$
$151$	−10.3137	+	10.3137i	−0.839318	+	0.839318i	0.149451	+	0.988769i	$0.452249\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.41421	+	8.41421i	−0.675846	+	0.675846i
$156$		0			0
$157$		−	2.34315i		−	0.187003i	−0.995619	−	0.0935017i	$-0.970194\pi$
$157$		−	2.34315i		−	0.187003i	0.995619	−	0.0935017i	$-0.0298061\pi$
$158$		0			0
$159$	−10.0711	+	4.17157i	−0.798688	+	0.330827i
$160$		0			0
$161$	3.82843	+	3.82843i	0.301722	+	0.301722i
$162$		0			0
$163$	2.77817	+	6.70711i	0.217603	+	0.525341i	0.994554	−	0.104220i	$-0.0332347\pi$
$163$	2.77817	+	6.70711i	0.217603	+	0.525341i	−0.776951	+	0.629561i	$0.783235\pi$
$164$		0			0
$165$	−4.41421	+	10.6569i	−0.343646	+	0.829635i
$166$		0			0
$167$	−11.3640	−	4.70711i	−0.879370	−	0.364247i	−0.103117	−	0.994669i	$-0.532882\pi$
$167$	−11.3640	−	4.70711i	−0.879370	−	0.364247i	−0.776252	+	0.630422i	$0.782882\pi$
$168$		0			0
$169$	−33.6274			−2.58672
$170$		0			0
$171$	−1.07107			−0.0819066
$172$		0			0
$173$	23.1924	+	9.60660i	1.76328	+	0.730376i	0.996028	+	0.0890357i	$0.0283785\pi$
$173$	23.1924	+	9.60660i	1.76328	+	0.730376i	0.767256	+	0.641341i	$0.221621\pi$
$174$		0			0
$175$	−0.464466	+	1.12132i	−0.0351103	+	0.0847639i
$176$		0			0
$177$	−9.82843	−	23.7279i	−0.738750	−	1.78350i
$178$		0			0
$179$	−13.0000	−	13.0000i	−0.971666	−	0.971666i	0.0279439	−	0.999609i	$-0.491104\pi$
$179$	−13.0000	−	13.0000i	−0.971666	−	0.971666i	−0.999609	+	0.0279439i	$0.991104\pi$
$180$		0			0
$181$	3.53553	−	1.46447i	0.262794	−	0.108853i	−0.247396	−	0.968914i	$-0.579575\pi$
$181$	3.53553	−	1.46447i	0.262794	−	0.108853i	0.510190	+	0.860061i	$0.329575\pi$
$182$		0			0
$183$			3.41421i			0.252386i
$184$		0			0
$185$	8.65685	−	8.65685i	0.636465	−	0.636465i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−2.58579	+	2.58579i	−0.188088	+	0.188088i
$190$		0			0
$191$		−	0.343146i		−	0.0248292i	−0.999923	−	0.0124146i	$-0.996048\pi$
$191$		−	0.343146i		−	0.0248292i	0.999923	−	0.0124146i	$-0.00395178\pi$
$192$		0			0
$193$	14.3640	−	5.94975i	1.03394	−	0.428272i	0.199807	−	0.979835i	$-0.435968\pi$
$193$	14.3640	−	5.94975i	1.03394	−	0.428272i	0.834133	+	0.551563i	$0.185968\pi$
$194$		0			0
$195$	−16.4853	−	16.4853i	−1.18054	−	1.18054i
$196$		0			0
$197$	4.80761	+	11.6066i	0.342528	+	0.826936i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$	4.80761	+	11.6066i	0.342528	+	0.826936i	−0.654931	+	0.755689i	$0.727302\pi$
$198$		0			0
$199$	−0.636039	+	1.53553i	−0.0450876	+	0.108851i	−0.944819	−	0.327593i	$-0.893762\pi$
$199$	−0.636039	+	1.53553i	−0.0450876	+	0.108851i	0.899731	+	0.436444i	$0.143762\pi$
$200$		0			0
$201$	−19.3137	−	8.00000i	−1.36228	−	0.564276i
$202$		0			0
$203$	−3.07107			−0.215547
$204$		0			0
$205$	−2.24264			−0.156633
$206$		0			0
$207$	2.70711	+	1.12132i	0.188157	+	0.0779372i
$208$		0			0
$209$	3.34315	−	8.07107i	0.231250	−	0.558287i
$210$		0			0
$211$	0.778175	+	1.87868i	0.0535717	+	0.129334i	0.948399	−	0.317078i	$-0.102702\pi$
$211$	0.778175	+	1.87868i	0.0535717	+	0.129334i	−0.894828	+	0.446412i	$0.852702\pi$
$212$		0			0
$213$	−1.58579	−	1.58579i	−0.108656	−	0.108656i
$214$		0			0
$215$	−7.24264	+	3.00000i	−0.493944	+	0.204598i
$216$		0			0
$217$			4.92893i			0.334598i
$218$		0			0
$219$	−11.2426	+	11.2426i	−0.759707	+	0.759707i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−12.1716	+	12.1716i	−0.815069	+	0.815069i	−0.985389	−	0.170320i	$-0.945520\pi$
$223$	−12.1716	+	12.1716i	−0.815069	+	0.815069i	0.170320	+	0.985389i	$0.445520\pi$
$224$		0			0
$225$			0.656854i			0.0437903i
$226$		0			0
$227$	−17.9497	+	7.43503i	−1.19137	+	0.493480i	−0.888200	−	0.459457i	$-0.848044\pi$
$227$	−17.9497	+	7.43503i	−1.19137	+	0.493480i	−0.303167	+	0.952938i	$0.598044\pi$
$228$		0			0
$229$	2.65685	+	2.65685i	0.175570	+	0.175570i	0.789421	−	0.613852i	$-0.210381\pi$
$229$	2.65685	+	2.65685i	0.175570	+	0.175570i	−0.613852	+	0.789421i	$0.710381\pi$
$230$		0			0
$231$	1.82843	+	4.41421i	0.120302	+	0.290434i
$232$		0			0
$233$	3.43503	−	8.29289i	0.225036	−	0.543285i	−0.770524	−	0.637411i	$-0.780005\pi$
$233$	3.43503	−	8.29289i	0.225036	−	0.543285i	0.995560	+	0.0941253i	$0.0300054\pi$
$234$		0			0
$235$	−6.24264	−	2.58579i	−0.407225	−	0.168678i
$236$		0			0
$237$	−21.0711			−1.36871
$238$		0			0
$239$	22.6274			1.46365			0.731823	−	0.681495i	$-0.238670\pi$
$239$	22.6274			1.46365			0.731823	+	0.681495i	$0.238670\pi$
$240$		0			0
$241$	18.3640	+	7.60660i	1.18293	+	0.489984i	0.885445	−	0.464743i	$-0.153853\pi$
$241$	18.3640	+	7.60660i	1.18293	+	0.489984i	0.297481	+	0.954728i	$0.403853\pi$
$242$		0			0
$243$	−1.63604	+	3.94975i	−0.104952	+	0.253376i
$244$		0			0
$245$	4.53553	+	10.9497i	0.289765	+	0.699554i
$246$		0			0
$247$	12.4853	+	12.4853i	0.794419	+	0.794419i
$248$		0			0
$249$	0.414214	−	0.171573i	0.0262497	−	0.0108730i
$250$		0			0
$251$			22.9706i			1.44989i	0.688807	+	0.724945i	$0.258135\pi$
$251$			22.9706i			1.44989i	−0.688807	+	0.724945i	$0.741865\pi$
$252$		0			0
$253$	−16.8995	+	16.8995i	−1.06246	+	1.06246i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.65685	−	2.65685i	0.165730	−	0.165730i	−0.619370	−	0.785100i	$-0.712612\pi$
$257$	2.65685	−	2.65685i	0.165730	−	0.165730i	0.785100	+	0.619370i	$0.212612\pi$
$258$		0			0
$259$		−	5.07107i		−	0.315101i
$260$		0			0
$261$	−1.53553	+	0.636039i	−0.0950472	+	0.0393698i
$262$		0			0
$263$	9.34315	+	9.34315i	0.576123	+	0.576123i	0.933833	−	0.357710i	$-0.116442\pi$
$263$	9.34315	+	9.34315i	0.576123	+	0.576123i	−0.357710	+	0.933833i	$0.616442\pi$
$264$		0			0
$265$	4.17157	+	10.0711i	0.256258	+	0.618661i
$266$		0			0
$267$	7.65685	−	18.4853i	0.468592	−	1.13128i
$268$		0			0
$269$	−7.77817	−	3.22183i	−0.474244	−	0.196438i	0.132742	−	0.991151i	$-0.457622\pi$
$269$	−7.77817	−	3.22183i	−0.474244	−	0.196438i	−0.606986	+	0.794712i	$0.707622\pi$
$270$		0			0
$271$	−11.3137			−0.687259			−0.343629	−	0.939105i	$-0.611656\pi$
$271$	−11.3137			−0.687259			−0.343629	+	0.939105i	$0.611656\pi$
$272$		0			0
$273$	−9.65685			−0.584459
$274$		0			0
$275$	−4.94975	−	2.05025i	−0.298481	−	0.123635i
$276$		0			0
$277$	5.77817	−	13.9497i	0.347177	−	0.838159i	−0.649774	−	0.760127i	$-0.725136\pi$
$277$	5.77817	−	13.9497i	0.347177	−	0.838159i	0.996951	−	0.0780317i	$-0.0248635\pi$
$278$		0			0
$279$	1.02082	+	2.46447i	0.0611146	+	0.147544i
$280$		0			0
$281$	−10.6569	−	10.6569i	−0.635735	−	0.635735i	0.313766	−	0.949500i	$-0.398409\pi$
$281$	−10.6569	−	10.6569i	−0.635735	−	0.635735i	−0.949500	+	0.313766i	$0.898409\pi$
$282$		0			0
$283$	6.53553	−	2.70711i	0.388497	−	0.160921i	−0.179881	−	0.983688i	$-0.557571\pi$
$283$	6.53553	−	2.70711i	0.388497	−	0.160921i	0.568378	+	0.822768i	$0.307571\pi$
$284$		0			0
$285$			8.82843i			0.522951i
$286$		0			0
$287$	−0.656854	+	0.656854i	−0.0387729	+	0.0387729i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	1.24264	−	1.24264i	0.0728449	−	0.0728449i
$292$		0			0
$293$			8.00000i			0.467365i	0.972313	+	0.233682i	$0.0750776\pi$
$293$			8.00000i			0.467365i	−0.972313	+	0.233682i	$0.924922\pi$
$294$		0			0
$295$	−23.7279	+	9.82843i	−1.38149	+	0.572233i
$296$		0			0
$297$	−11.4142	−	11.4142i	−0.662320	−	0.662320i
$298$		0			0
$299$	−18.4853	−	44.6274i	−1.06903	−	2.58087i
$300$		0			0
$301$	−1.24264	+	3.00000i	−0.0716246	+	0.172917i
$302$		0			0
$303$	−21.8995	−	9.07107i	−1.25809	−	0.521119i
$304$		0			0
$305$	3.41421			0.195497
$306$		0			0
$307$	6.34315			0.362022			0.181011	−	0.983481i	$-0.442063\pi$
$307$	6.34315			0.362022			0.181011	+	0.983481i	$0.442063\pi$
$308$		0			0
$309$	−6.82843	−	2.82843i	−0.388456	−	0.160904i
$310$		0			0
$311$	4.87868	−	11.7782i	0.276645	−	0.667879i	−0.723094	−	0.690750i	$-0.757281\pi$
$311$	4.87868	−	11.7782i	0.276645	−	0.667879i	0.999738	+	0.0228708i	$0.00728062\pi$
$312$		0			0
$313$	−8.70711	−	21.0208i	−0.492155	−	1.18817i	−0.953621	−	0.301009i	$-0.902677\pi$
$313$	−8.70711	−	21.0208i	−0.492155	−	1.18817i	0.461466	−	0.887158i	$-0.347323\pi$
$314$		0			0
$315$	−0.414214	−	0.414214i	−0.0233383	−	0.0233383i
$316$		0			0
$317$	0.363961	−	0.150758i	0.0204421	−	0.00846739i	−0.372439	−	0.928057i	$-0.621478\pi$
$317$	0.363961	−	0.150758i	0.0204421	−	0.00846739i	0.392881	+	0.919589i	$0.371478\pi$
$318$		0			0
$319$		−	13.5563i		−	0.759010i
$320$		0			0
$321$	5.00000	−	5.00000i	0.279073	−	0.279073i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	7.65685	−	7.65685i	0.424726	−	0.424726i
$326$		0			0
$327$			9.07107i			0.501631i
$328$		0			0
$329$	−2.58579	+	1.07107i	−0.142559	+	0.0590499i
$330$		0			0
$331$	−20.3137	−	20.3137i	−1.11654	−	1.11654i	−0.992245	−	0.124297i	$-0.960332\pi$
$331$	−20.3137	−	20.3137i	−1.11654	−	1.11654i	−0.124297	−	0.992245i	$-0.539668\pi$
$332$		0			0
$333$	−1.05025	−	2.53553i	−0.0575535	−	0.138946i
$334$		0			0
$335$	−8.00000	+	19.3137i	−0.437087	+	1.05522i
$336$		0			0
$337$	24.0208	+	9.94975i	1.30850	+	0.541997i	0.924445	−	0.381314i	$-0.124528\pi$
$337$	24.0208	+	9.94975i	1.30850	+	0.541997i	0.384052	+	0.923312i	$0.374528\pi$
$338$		0			0
$339$	2.58579			0.140441
$340$		0			0
$341$	−21.7574			−1.17823
$342$		0			0
$343$	9.48528	+	3.92893i	0.512157	+	0.212142i
$344$		0			0
$345$	9.24264	−	22.3137i	0.497607	−	1.20133i
$346$		0			0
$347$	2.97918	+	7.19239i	0.159931	+	0.386108i	0.983450	−	0.181182i	$-0.0579922\pi$
$347$	2.97918	+	7.19239i	0.159931	+	0.386108i	−0.823519	+	0.567289i	$0.807992\pi$
$348$		0			0
$349$	−19.8284	−	19.8284i	−1.06139	−	1.06139i	−0.997988	−	0.0634034i	$-0.979805\pi$
$349$	−19.8284	−	19.8284i	−1.06139	−	1.06139i	−0.0634034	−	0.997988i	$-0.520195\pi$
$350$		0			0
$351$	30.1421	−	12.4853i	1.60887	−	0.666415i
$352$		0			0
$353$			15.3137i			0.815066i	0.913190	+	0.407533i	$0.133611\pi$
$353$			15.3137i			0.815066i	−0.913190	+	0.407533i	$0.866389\pi$
$354$		0			0
$355$	−1.58579	+	1.58579i	−0.0841648	+	0.0841648i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	21.4853	−	21.4853i	1.13395	−	1.13395i	0.144436	−	0.989514i	$-0.453863\pi$
$359$	21.4853	−	21.4853i	1.13395	−	1.13395i	0.989514	−	0.144436i	$-0.0461366\pi$
$360$		0			0
$361$			12.3137i			0.648090i
$362$		0			0
$363$	−0.707107	+	0.292893i	−0.0371135	+	0.0153729i
$364$		0			0
$365$	11.2426	+	11.2426i	0.588467	+	0.588467i
$366$		0			0
$367$	1.46447	+	3.53553i	0.0764445	+	0.184553i	0.957482	−	0.288493i	$-0.0931542\pi$
$367$	1.46447	+	3.53553i	0.0764445	+	0.184553i	−0.881037	+	0.473047i	$0.843154\pi$
$368$		0			0
$369$	−0.192388	+	0.464466i	−0.0100153	+	0.0241791i
$370$		0			0
$371$	4.17157	+	1.72792i	0.216577	+	0.0897092i
$372$		0			0
$373$	18.4853			0.957132			0.478566	−	0.878052i	$-0.341157\pi$
$373$	18.4853			0.957132			0.478566	+	0.878052i	$0.341157\pi$
$374$		0			0
$375$	22.4853			1.16113
$376$		0			0
$377$	25.3137	+	10.4853i	1.30372	+	0.540019i
$378$		0			0
$379$	4.19239	−	10.1213i	0.215349	−	0.519897i	−0.778881	−	0.627172i	$-0.784212\pi$
$379$	4.19239	−	10.1213i	0.215349	−	0.519897i	0.994229	+	0.107275i	$0.0342124\pi$
$380$		0			0
$381$	−0.171573	−	0.414214i	−0.00878994	−	0.0212208i
$382$		0			0
$383$	18.3137	+	18.3137i	0.935787	+	0.935787i	0.998059	−	0.0622724i	$-0.0198348\pi$
$383$	18.3137	+	18.3137i	0.935787	+	0.935787i	−0.0622724	+	0.998059i	$0.519835\pi$
$384$		0			0
$385$	4.41421	−	1.82843i	0.224969	−	0.0931853i
$386$		0			0
$387$			1.75736i			0.0893316i
$388$		0			0
$389$	1.48528	−	1.48528i	0.0753068	−	0.0753068i	−0.668450	−	0.743757i	$-0.733042\pi$
$389$	1.48528	−	1.48528i	0.0753068	−	0.0753068i	0.743757	+	0.668450i	$0.233042\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−14.3137	+	14.3137i	−0.722031	+	0.722031i
$394$		0			0
$395$			21.0711i			1.06020i
$396$		0			0
$397$	−17.4350	+	7.22183i	−0.875039	+	0.362453i	−0.774571	−	0.632487i	$-0.782034\pi$
$397$	−17.4350	+	7.22183i	−0.875039	+	0.362453i	−0.100468	+	0.994940i	$0.532034\pi$
$398$		0			0
$399$	2.58579	+	2.58579i	0.129451	+	0.129451i
$400$		0			0
$401$	−3.53553	−	8.53553i	−0.176556	−	0.426244i	0.810684	−	0.585484i	$-0.199096\pi$
$401$	−3.53553	−	8.53553i	−0.176556	−	0.426244i	−0.987240	+	0.159240i	$0.949096\pi$
$402$		0			0
$403$	16.8284	−	40.6274i	0.838284	−	2.02380i
$404$		0			0
$405$	17.1924	+	7.12132i	0.854297	+	0.353861i
$406$		0			0
$407$	22.3848			1.10957
$408$		0			0
$409$	−11.6569			−0.576394			−0.288197	−	0.957571i	$-0.593056\pi$
$409$	−11.6569			−0.576394			−0.288197	+	0.957571i	$0.593056\pi$
$410$		0			0
$411$	−20.7279	−	8.58579i	−1.02243	−	0.423506i
$412$		0			0
$413$	−4.07107	+	9.82843i	−0.200324	+	0.483625i
$414$		0			0
$415$	−0.171573	−	0.414214i	−0.00842218	−	0.0203329i
$416$		0			0
$417$	22.8995	+	22.8995i	1.12139	+	1.12139i
$418$		0			0
$419$	−32.9203	+	13.6360i	−1.60826	+	0.666164i	−0.992553	−	0.121810i	$-0.961130\pi$
$419$	−32.9203	+	13.6360i	−1.60826	+	0.666164i	−0.615709	+	0.787974i	$0.711130\pi$
$420$		0			0
$421$		−	1.17157i		−	0.0570990i	−0.999592	−	0.0285495i	$-0.990911\pi$
$421$		−	1.17157i		−	0.0570990i	0.999592	−	0.0285495i	$-0.00908882\pi$
$422$		0			0
$423$	−1.07107	+	1.07107i	−0.0520771	+	0.0520771i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.00000	−	1.00000i	0.0483934	−	0.0483934i
$428$		0			0
$429$		−	42.6274i		−	2.05807i
$430$		0			0
$431$	19.0208	−	7.87868i	0.916200	−	0.379503i	0.125774	−	0.992059i	$-0.459859\pi$
$431$	19.0208	−	7.87868i	0.916200	−	0.379503i	0.790427	+	0.612556i	$0.209859\pi$
$432$		0			0
$433$	−5.82843	−	5.82843i	−0.280096	−	0.280096i	0.553051	−	0.833147i	$-0.313463\pi$
$433$	−5.82843	−	5.82843i	−0.280096	−	0.280096i	−0.833147	+	0.553051i	$0.813463\pi$
$434$		0			0
$435$	5.24264	+	12.6569i	0.251365	+	0.606850i
$436$		0			0
$437$	−7.00000	+	16.8995i	−0.334855	+	0.808412i
$438$		0			0
$439$	−13.7071	−	5.67767i	−0.654205	−	0.270980i	0.0307930	−	0.999526i	$-0.490197\pi$
$439$	−13.7071	−	5.67767i	−0.654205	−	0.270980i	−0.684998	+	0.728545i	$0.740197\pi$
$440$		0			0
$441$	2.65685			0.126517
$442$		0			0
$443$	−21.6569			−1.02895			−0.514474	−	0.857506i	$-0.672013\pi$
$443$	−21.6569			−1.02895			−0.514474	+	0.857506i	$0.672013\pi$
$444$		0			0
$445$	−18.4853	−	7.65685i	−0.876286	−	0.362970i
$446$		0			0
$447$	−6.82843	+	16.4853i	−0.322974	+	0.779727i
$448$		0			0
$449$	8.12132	+	19.6066i	0.383269	+	0.925293i	0.991329	+	0.131402i	$0.0419479\pi$
$449$	8.12132	+	19.6066i	0.383269	+	0.925293i	−0.608060	+	0.793891i	$0.708052\pi$
$450$		0			0
$451$	−2.89949	−	2.89949i	−0.136532	−	0.136532i
$452$		0			0
$453$	24.8995	−	10.3137i	1.16988	−	0.484580i
$454$		0			0
$455$			9.65685i			0.452720i
$456$		0			0
$457$	−3.00000	+	3.00000i	−0.140334	+	0.140334i	−0.773784	−	0.633450i	$-0.781638\pi$
$457$	−3.00000	+	3.00000i	−0.140334	+	0.140334i	0.633450	+	0.773784i	$0.281638\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.48528	+	5.48528i	−0.255475	+	0.255475i	−0.823211	−	0.567736i	$-0.807820\pi$
$461$	−5.48528	+	5.48528i	−0.255475	+	0.255475i	0.567736	+	0.823211i	$0.307820\pi$
$462$		0			0
$463$		−	7.65685i		−	0.355844i	−0.984045	−	0.177922i	$-0.943062\pi$
$463$		−	7.65685i		−	0.355844i	0.984045	−	0.177922i	$-0.0569375\pi$
$464$		0			0
$465$	20.3137	−	8.41421i	0.942026	−	0.390200i
$466$		0			0
$467$	19.9706	+	19.9706i	0.924127	+	0.924127i	0.997318	−	0.0731905i	$-0.0233181\pi$
$467$	19.9706	+	19.9706i	0.924127	+	0.924127i	−0.0731905	+	0.997318i	$0.523318\pi$
$468$		0			0
$469$	3.31371	+	8.00000i	0.153013	+	0.369406i
$470$		0			0
$471$	−1.65685	+	4.00000i	−0.0763438	+	0.184310i
$472$		0			0
$473$	−13.2426	−	5.48528i	−0.608897	−	0.252214i
$474$		0			0
$475$	−4.10051			−0.188144
$476$		0			0
$477$	2.44365			0.111887
$478$		0			0
$479$	7.60660	+	3.15076i	0.347555	+	0.143962i	0.549630	−	0.835408i	$-0.314769\pi$
$479$	7.60660	+	3.15076i	0.347555	+	0.143962i	−0.202076	+	0.979370i	$0.564769\pi$
$480$		0			0
$481$	−17.3137	+	41.7990i	−0.789437	+	1.90587i
$482$		0			0
$483$	−3.82843	−	9.24264i	−0.174199	−	0.420555i
$484$		0			0
$485$	−1.24264	−	1.24264i	−0.0564254	−	0.0564254i
$486$		0			0
$487$	3.36396	−	1.39340i	0.152436	−	0.0631409i	−0.305161	−	0.952301i	$-0.598710\pi$
$487$	3.36396	−	1.39340i	0.152436	−	0.0631409i	0.457597	+	0.889160i	$0.348710\pi$
$488$		0			0
$489$		−	13.4142i		−	0.606612i
$490$		0			0
$491$	16.7990	−	16.7990i	0.758128	−	0.758128i	−0.217854	−	0.975981i	$-0.569906\pi$
$491$	16.7990	−	16.7990i	0.758128	−	0.758128i	0.975981	+	0.217854i	$0.0699055\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	1.82843	−	1.82843i	0.0821817	−	0.0821817i
$496$		0			0
$497$			0.928932i			0.0416683i
$498$		0			0
$499$	34.6777	−	14.3640i	1.55239	−	0.643019i	0.568640	−	0.822587i	$-0.307470\pi$
$499$	34.6777	−	14.3640i	1.55239	−	0.643019i	0.983746	+	0.179567i	$0.0574698\pi$
$500$		0			0
$501$	16.0711	+	16.0711i	0.718002	+	0.718002i
$502$		0			0
$503$	−3.02082	−	7.29289i	−0.134691	−	0.325174i	0.842115	−	0.539298i	$-0.181310\pi$
$503$	−3.02082	−	7.29289i	−0.134691	−	0.325174i	−0.976806	+	0.214124i	$0.931310\pi$
$504$		0			0
$505$	−9.07107	+	21.8995i	−0.403657	+	0.974515i
$506$		0			0
$507$	57.4056	+	23.7782i	2.54947	+	1.05603i
$508$		0			0
$509$	6.68629			0.296365			0.148182	−	0.988960i	$-0.452658\pi$
$509$	6.68629			0.296365			0.148182	+	0.988960i	$0.452658\pi$
$510$		0			0
$511$	6.58579			0.291338
$512$		0			0
$513$	−11.4142	−	4.72792i	−0.503950	−	0.208743i
$514$		0			0
$515$	−2.82843	+	6.82843i	−0.124635	+	0.300896i
$516$		0			0
$517$	−4.72792	−	11.4142i	−0.207934	−	0.501997i
$518$		0			0
$519$	−32.7990	−	32.7990i	−1.43972	−	1.43972i
$520$		0			0
$521$	−25.4350	+	10.5355i	−1.11433	+	0.461570i	−0.862426	−	0.506183i	$-0.831056\pi$
$521$	−25.4350	+	10.5355i	−1.11433	+	0.461570i	−0.251902	+	0.967753i	$0.581056\pi$
$522$		0			0
$523$		−	34.0000i		−	1.48672i	−0.668894	−	0.743358i	$-0.733232\pi$
$523$		−	34.0000i		−	1.48672i	0.668894	−	0.743358i	$-0.266768\pi$
$524$		0			0
$525$	1.58579	−	1.58579i	0.0692094	−	0.0692094i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.1213	−	19.1213i	0.831362	−	0.831362i
$530$		0			0
$531$			5.75736i			0.249848i
$532$		0			0
$533$	7.65685	−	3.17157i	0.331655	−	0.137376i
$534$		0			0
$535$	−5.00000	−	5.00000i	−0.216169	−	0.216169i
$536$		0			0
$537$	13.0000	+	31.3848i	0.560991	+	1.35435i
$538$		0			0
$539$	−8.29289	+	20.0208i	−0.357200	+	0.862358i
$540$		0			0
$541$	−7.29289	−	3.02082i	−0.313546	−	0.129875i	0.220361	−	0.975418i	$-0.429277\pi$
$541$	−7.29289	−	3.02082i	−0.313546	−	0.129875i	−0.533907	+	0.845543i	$0.679277\pi$
$542$		0			0
$543$	−7.07107			−0.303449
$544$		0			0
$545$	9.07107			0.388562
$546$		0			0
$547$	−22.6777	−	9.39340i	−0.969627	−	0.401633i	−0.159054	−	0.987270i	$-0.550844\pi$
$547$	−22.6777	−	9.39340i	−0.969627	−	0.401633i	−0.810573	+	0.585637i	$0.800844\pi$
$548$		0			0
$549$	0.292893	−	0.707107i	0.0125004	−	0.0301786i
$550$		0			0
$551$	−3.97056	−	9.58579i	−0.169152	−	0.408368i
$552$		0			0
$553$	6.17157	+	6.17157i	0.262442	+	0.262442i
$554$		0			0
$555$	−20.8995	+	8.65685i	−0.887134	+	0.367463i
$556$		0			0
$557$		−	22.8284i		−	0.967272i	−0.875269	−	0.483636i	$-0.839316\pi$
$557$		−	22.8284i		−	0.967272i	0.875269	−	0.483636i	$-0.160684\pi$
$558$		0			0
$559$	20.4853	−	20.4853i	0.866435	−	0.866435i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−27.2843	+	27.2843i	−1.14989	+	1.14989i	−0.163322	+	0.986573i	$0.552221\pi$
$563$	−27.2843	+	27.2843i	−1.14989	+	1.14989i	−0.986573	+	0.163322i	$0.947779\pi$
$564$		0			0
$565$		−	2.58579i		−	0.108785i
$566$		0			0
$567$	7.12132	−	2.94975i	0.299067	−	0.123878i
$568$		0			0
$569$	19.4853	+	19.4853i	0.816865	+	0.816865i	0.985653	−	0.168787i	$-0.0539850\pi$
$569$	19.4853	+	19.4853i	0.816865	+	0.816865i	−0.168787	+	0.985653i	$0.553985\pi$
$570$		0			0
$571$	9.74874	+	23.5355i	0.407972	+	0.984931i	0.985671	+	0.168681i	$0.0539509\pi$
$571$	9.74874	+	23.5355i	0.407972	+	0.984931i	−0.577699	+	0.816250i	$0.696049\pi$
$572$		0			0
$573$	−0.242641	+	0.585786i	−0.0101365	+	0.0244716i
$574$		0			0
$575$	10.3640	+	4.29289i	0.432207	+	0.179026i
$576$		0			0
$577$	1.79899			0.0748929			0.0374465	−	0.999299i	$-0.488078\pi$
$577$	1.79899			0.0748929			0.0374465	+	0.999299i	$0.488078\pi$
$578$		0			0
$579$	−28.7279			−1.19389
$580$		0			0
$581$	−0.171573	−	0.0710678i	−0.00711804	−	0.00294839i
$582$		0			0
$583$	−7.62742	+	18.4142i	−0.315895	+	0.762639i
$584$		0			0
$585$	2.00000	+	4.82843i	0.0826898	+	0.199631i
$586$		0			0
$587$	20.6569	+	20.6569i	0.852600	+	0.852600i	0.990453	−	0.137853i	$-0.0440202\pi$
$587$	20.6569	+	20.6569i	0.852600	+	0.852600i	−0.137853	+	0.990453i	$0.544020\pi$
$588$		0			0
$589$	−15.3848	+	6.37258i	−0.633919	+	0.262578i
$590$		0			0
$591$		−	23.2132i		−	0.954864i
$592$		0			0
$593$	23.4853	−	23.4853i	0.964425	−	0.964425i	−0.0349637	−	0.999389i	$-0.511132\pi$
$593$	23.4853	−	23.4853i	0.964425	−	0.964425i	0.999389	+	0.0349637i	$0.0111316\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.17157	−	2.17157i	0.0888766	−	0.0888766i
$598$		0			0
$599$		−	37.3137i		−	1.52460i	−0.647226	−	0.762298i	$-0.724071\pi$
$599$		−	37.3137i		−	1.52460i	0.647226	−	0.762298i	$-0.275929\pi$
$600$		0			0
$601$	4.70711	−	1.94975i	0.192007	−	0.0795319i	−0.284608	−	0.958644i	$-0.591864\pi$
$601$	4.70711	−	1.94975i	0.192007	−	0.0795319i	0.476615	+	0.879112i	$0.341864\pi$
$602$		0			0
$603$	3.31371	+	3.31371i	0.134945	+	0.134945i
$604$		0			0
$605$	0.292893	+	0.707107i	0.0119078	+	0.0287480i
$606$		0			0
$607$	−6.09188	+	14.7071i	−0.247262	+	0.596943i	−0.997970	−	0.0636914i	$-0.979713\pi$
$607$	−6.09188	+	14.7071i	−0.247262	+	0.596943i	0.750708	+	0.660634i	$0.229713\pi$
$608$		0			0
$609$	5.24264	+	2.17157i	0.212443	+	0.0879966i
$610$		0			0
$611$	24.9706			1.01020
$612$		0			0
$613$	0.343146			0.0138595			0.00692976	−	0.999976i	$-0.497794\pi$
$613$	0.343146			0.0138595			0.00692976	+	0.999976i	$0.497794\pi$
$614$		0			0
$615$	3.82843	+	1.58579i	0.154377	+	0.0639451i
$616$		0			0
$617$	−13.0503	+	31.5061i	−0.525383	+	1.26839i	0.409135	+	0.912474i	$0.365830\pi$
$617$	−13.0503	+	31.5061i	−0.525383	+	1.26839i	−0.934519	+	0.355914i	$0.884170\pi$
$618$		0			0
$619$	5.12132	+	12.3640i	0.205843	+	0.496950i	0.992761	−	0.120109i	$-0.0383243\pi$
$619$	5.12132	+	12.3640i	0.205843	+	0.496950i	−0.786918	+	0.617058i	$0.788324\pi$
$620$		0			0
$621$	23.8995	+	23.8995i	0.959054	+	0.959054i
$622$		0			0
$623$	−7.65685	+	3.17157i	−0.306765	+	0.127066i
$624$		0			0
$625$		−	14.5563i		−	0.582254i
$626$		0			0
$627$	−11.4142	+	11.4142i	−0.455840	+	0.455840i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−10.3137	+	10.3137i	−0.410582	+	0.410582i	−0.881941	−	0.471359i	$-0.843764\pi$
$631$	−10.3137	+	10.3137i	−0.410582	+	0.410582i	0.471359	+	0.881941i	$0.343764\pi$
$632$		0			0
$633$		−	3.75736i		−	0.149342i
$634$		0			0
$635$	−0.414214	+	0.171573i	−0.0164376	+	0.00680866i
$636$		0			0
$637$	−30.9706	−	30.9706i	−1.22710	−	1.22710i
$638$		0			0
$639$	0.192388	+	0.464466i	0.00761076	+	0.0183740i
$640$		0			0
$641$	17.7782	−	42.9203i	0.702196	−	1.69525i	−0.0164412	−	0.999865i	$-0.505234\pi$
$641$	17.7782	−	42.9203i	0.702196	−	1.69525i	0.718637	−	0.695385i	$-0.244766\pi$
$642$		0			0
$643$	5.12132	+	2.12132i	0.201965	+	0.0836567i	0.481373	−	0.876516i	$-0.340138\pi$
$643$	5.12132	+	2.12132i	0.201965	+	0.0836567i	−0.279408	+	0.960172i	$0.590138\pi$
$644$		0			0
$645$	14.4853			0.570357
$646$		0			0
$647$	32.9706			1.29621			0.648103	−	0.761552i	$-0.275563\pi$
$647$	32.9706			1.29621			0.648103	+	0.761552i	$0.275563\pi$
$648$		0			0
$649$	−43.3848	−	17.9706i	−1.70300	−	0.705406i
$650$		0			0
$651$	3.48528	−	8.41421i	0.136599	−	0.329779i
$652$		0			0
$653$	17.2929	+	41.7487i	0.676723	+	1.63375i	0.769946	+	0.638109i	$0.220283\pi$
$653$	17.2929	+	41.7487i	0.676723	+	1.63375i	−0.0932228	+	0.995645i	$0.529717\pi$
$654$		0			0
$655$	14.3137	+	14.3137i	0.559283	+	0.559283i
$656$		0			0
$657$	3.29289	−	1.36396i	0.128468	−	0.0532132i
$658$		0			0
$659$		−	2.68629i		−	0.104643i	−0.998630	−	0.0523215i	$-0.983338\pi$
$659$		−	2.68629i		−	0.104643i	0.998630	−	0.0523215i	$-0.0166621\pi$
$660$		0			0
$661$	−9.00000	+	9.00000i	−0.350059	+	0.350059i	−0.860132	−	0.510072i	$-0.829619\pi$
$661$	−9.00000	+	9.00000i	−0.350059	+	0.350059i	0.510072	+	0.860132i	$0.329619\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.58579	−	2.58579i	0.100272	−	0.100272i
$666$		0			0
$667$			28.3848i			1.09906i
$668$		0			0
$669$	29.3848	−	12.1716i	1.13608	−	0.470580i
$670$		0			0
$671$	4.41421	+	4.41421i	0.170409	+	0.170409i
$672$		0			0
$673$	−11.8787	−	28.6777i	−0.457889	−	1.10544i	−0.969250	−	0.246077i	$-0.920858\pi$
$673$	−11.8787	−	28.6777i	−0.457889	−	1.10544i	0.511361	−	0.859366i	$-0.329142\pi$
$674$		0			0
$675$	−2.89949	+	7.00000i	−0.111602	+	0.269430i
$676$		0			0
$677$	1.53553	+	0.636039i	0.0590154	+	0.0244450i	0.411996	−	0.911186i	$-0.364832\pi$
$677$	1.53553	+	0.636039i	0.0590154	+	0.0244450i	−0.352981	+	0.935631i	$0.614832\pi$
$678$		0			0
$679$	−0.727922			−0.0279351
$680$		0			0
$681$	35.8995			1.37567
$682$		0			0
$683$	3.94975	+	1.63604i	0.151133	+	0.0626013i	0.456968	−	0.889483i	$-0.348936\pi$
$683$	3.94975	+	1.63604i	0.151133	+	0.0626013i	−0.305835	+	0.952085i	$0.598936\pi$
$684$		0			0
$685$	−8.58579	+	20.7279i	−0.328046	+	0.791973i
$686$		0			0
$687$	−2.65685	−	6.41421i	−0.101365	−	0.244718i
$688$		0			0
$689$	−28.4853	−	28.4853i	−1.08520	−	1.08520i
$690$		0			0
$691$	6.53553	−	2.70711i	0.248623	−	0.102983i	−0.254892	−	0.966970i	$-0.582040\pi$
$691$	6.53553	−	2.70711i	0.248623	−	0.102983i	0.503515	+	0.863986i	$0.332040\pi$
$692$		0			0
$693$		−	1.07107i		−	0.0406865i
$694$		0			0
$695$	22.8995	−	22.8995i	0.868627	−	0.868627i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−11.7279	+	11.7279i	−0.443591	+	0.443591i
$700$		0			0
$701$			19.5147i			0.737061i	0.929616	+	0.368530i	$0.120139\pi$
$701$			19.5147i			0.737061i	−0.929616	+	0.368530i	$0.879861\pi$
$702$		0			0
$703$	15.8284	−	6.55635i	0.596980	−	0.247277i
$704$		0			0
$705$	8.82843	+	8.82843i	0.332498	+	0.332498i
$706$		0			0
$707$	3.75736	+	9.07107i	0.141310	+	0.341153i
$708$		0			0
$709$	1.29289	−	3.12132i	0.0485556	−	0.117224i	−0.897741	−	0.440524i	$-0.854793\pi$
$709$	1.29289	−	3.12132i	0.0485556	−	0.117224i	0.946296	+	0.323301i	$0.104793\pi$
$710$		0			0
$711$	4.36396	+	1.80761i	0.163661	+	0.0677907i
$712$		0			0
$713$	45.5563			1.70610
$714$		0			0
$715$	−42.6274			−1.59418
$716$		0			0
$717$	−38.6274	−	16.0000i	−1.44257	−	0.597531i
$718$		0			0
$719$	−5.74874	+	13.8787i	−0.214392	+	0.517587i	−0.994089	−	0.108569i	$-0.965373\pi$
$719$	−5.74874	+	13.8787i	−0.214392	+	0.517587i	0.779697	+	0.626157i	$0.215373\pi$
$720$		0			0
$721$	1.17157	+	2.82843i	0.0436317	+	0.105336i
$722$		0			0
$723$	−25.9706	−	25.9706i	−0.965856	−	0.965856i
$724$		0			0
$725$	−5.87868	+	2.43503i	−0.218329	+	0.0904347i
$726$		0			0
$727$			19.6569i			0.729032i	0.931197	+	0.364516i	$0.118766\pi$
$727$			19.6569i			0.729032i	−0.931197	+	0.364516i	$0.881234\pi$
$728$		0			0
$729$	−15.7782	+	15.7782i	−0.584377	+	0.584377i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−3.34315	+	3.34315i	−0.123482	+	0.123482i	−0.766147	−	0.642665i	$-0.777829\pi$
$733$	−3.34315	+	3.34315i	−0.123482	+	0.123482i	0.642665	+	0.766147i	$0.277829\pi$
$734$		0			0
$735$		−	21.8995i		−	0.807775i
$736$		0			0
$737$	−35.3137	+	14.6274i	−1.30080	+	0.538808i
$738$		0			0
$739$	11.9706	+	11.9706i	0.440344	+	0.440344i	0.892128	−	0.451783i	$-0.149212\pi$
$739$	11.9706	+	11.9706i	0.440344	+	0.440344i	−0.451783	+	0.892128i	$0.649212\pi$
$740$		0			0
$741$	−12.4853	−	30.1421i	−0.458658	−	1.10730i
$742$		0			0
$743$	−10.7782	+	26.0208i	−0.395413	+	0.954611i	0.593326	+	0.804962i	$0.297814\pi$
$743$	−10.7782	+	26.0208i	−0.395413	+	0.954611i	−0.988739	+	0.149649i	$0.952186\pi$
$744$		0			0
$745$	16.4853	+	6.82843i	0.603974	+	0.250174i
$746$		0			0
$747$	−0.100505			−0.00367729
$748$		0			0
$749$	−2.92893			−0.107021
$750$		0			0
$751$	42.5772	+	17.6360i	1.55366	+	0.643548i	0.983974	−	0.178312i	$-0.0570637\pi$
$751$	42.5772	+	17.6360i	1.55366	+	0.643548i	0.569689	+	0.821860i	$0.307064\pi$
$752$		0			0
$753$	16.2426	−	39.2132i	0.591915	−	1.42901i
$754$		0			0
$755$	−10.3137	−	24.8995i	−0.375354	−	0.906185i
$756$		0			0
$757$	33.0000	+	33.0000i	1.19941	+	1.19941i	0.974345	+	0.225061i	$0.0722580\pi$
$757$	33.0000	+	33.0000i	1.19941	+	1.19941i	0.225061	+	0.974345i	$0.427742\pi$
$758$		0			0
$759$	40.7990	−	16.8995i	1.48091	−	0.613413i
$760$		0			0
$761$		−	17.8579i		−	0.647347i	−0.946169	−	0.323674i	$-0.895082\pi$
$761$		−	17.8579i		−	0.647347i	0.946169	−	0.323674i	$-0.104918\pi$
$762$		0			0
$763$	2.65685	−	2.65685i	0.0961846	−	0.0961846i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	67.1127	−	67.1127i	2.42330	−	2.42330i
$768$		0			0
$769$		−	3.79899i		−	0.136995i	−0.997651	−	0.0684975i	$-0.978179\pi$
$769$		−	3.79899i		−	0.136995i	0.997651	−	0.0684975i	$-0.0218205\pi$
$770$		0			0
$771$	−6.41421	+	2.65685i	−0.231002	+	0.0956843i
$772$		0			0
$773$	−14.7990	−	14.7990i	−0.532283	−	0.532283i	0.388968	−	0.921251i	$-0.372832\pi$
$773$	−14.7990	−	14.7990i	−0.532283	−	0.532283i	−0.921251	+	0.388968i	$0.872832\pi$
$774$		0			0
$775$	3.90812	+	9.43503i	0.140384	+	0.338916i
$776$		0			0
$777$	−3.58579	+	8.65685i	−0.128639	+	0.310563i
$778$		0			0
$779$	−2.89949	−	1.20101i	−0.103885	−	0.0430307i
$780$		0			0
$781$	−4.10051			−0.146728
$782$		0			0
$783$	−19.1716			−0.685136
$784$		0			0
$785$	4.00000	+	1.65685i	0.142766	+	0.0591357i
$786$		0			0
$787$	13.5061	−	32.6066i	0.481440	−	1.16230i	−0.477485	−	0.878640i	$-0.658451\pi$
$787$	13.5061	−	32.6066i	0.481440	−	1.16230i	0.958925	−	0.283660i	$-0.0915486\pi$
$788$		0			0
$789$	−9.34315	−	22.5563i	−0.332625	−	0.803027i
$790$		0			0
$791$	−0.757359	−	0.757359i	−0.0269286	−	0.0269286i
$792$		0			0
$793$	−11.6569	+	4.82843i	−0.413947	+	0.171462i
$794$		0			0
$795$		−	20.1421i		−	0.714368i
$796$		0			0
$797$	34.3137	−	34.3137i	1.21545	−	1.21545i	0.246247	−	0.969207i	$-0.420803\pi$
$797$	34.3137	−	34.3137i	1.21545	−	1.21545i	0.969207	−	0.246247i	$-0.0791974\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−3.17157	+	3.17157i	−0.112062	+	0.112062i
$802$		0			0
$803$			29.0711i			1.02590i
$804$		0			0
$805$	−9.24264	+	3.82843i	−0.325760	+	0.134934i
$806$		0			0
$807$	11.0000	+	11.0000i	0.387218	+	0.387218i
$808$		0			0
$809$	−11.3934	−	27.5061i	−0.400571	−	0.967063i	−0.987528	−	0.157445i	$-0.949674\pi$
$809$	−11.3934	−	27.5061i	−0.400571	−	0.967063i	0.586957	−	0.809618i	$-0.300326\pi$
$810$		0			0
$811$	−9.12132	+	22.0208i	−0.320293	+	0.773255i	0.678944	+	0.734190i	$0.262438\pi$
$811$	−9.12132	+	22.0208i	−0.320293	+	0.773255i	−0.999237	+	0.0390652i	$0.987562\pi$
$812$		0			0
$813$	19.3137	+	8.00000i	0.677361	+	0.280572i
$814$		0			0
$815$	−13.4142			−0.469879
$816$		0			0
$817$	−10.9706			−0.383811
$818$		0			0
$819$	2.00000	+	0.828427i	0.0698857	+	0.0289476i
$820$		0			0
$821$	2.26346	−	5.46447i	0.0789952	−	0.190711i	−0.879448	−	0.475995i	$-0.842088\pi$
$821$	2.26346	−	5.46447i	0.0789952	−	0.190711i	0.958443	+	0.285284i	$0.0920879\pi$
$822$		0			0
$823$	−11.5650	−	27.9203i	−0.403130	−	0.973241i	−0.986902	−	0.161323i	$-0.948424\pi$
$823$	−11.5650	−	27.9203i	−0.403130	−	0.973241i	0.583772	−	0.811918i	$-0.301576\pi$
$824$		0			0
$825$	7.00000	+	7.00000i	0.243709	+	0.243709i
$826$		0			0
$827$	3.36396	−	1.39340i	0.116976	−	0.0484532i	−0.323428	−	0.946253i	$-0.604835\pi$
$827$	3.36396	−	1.39340i	0.116976	−	0.0484532i	0.440404	+	0.897800i	$0.354835\pi$
$828$		0			0
$829$			29.6569i			1.03003i	0.857183	+	0.515013i	$0.172213\pi$
$829$			29.6569i			1.03003i	−0.857183	+	0.515013i	$0.827787\pi$
$830$		0			0
$831$	−19.7279	+	19.7279i	−0.684354	+	0.684354i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	16.0711	−	16.0711i	0.556162	−	0.556162i
$836$		0			0
$837$			30.7696i			1.06355i
$838$		0			0
$839$	−5.60660	+	2.32233i	−0.193561	+	0.0801758i	−0.477359	−	0.878709i	$-0.658406\pi$
$839$	−5.60660	+	2.32233i	−0.193561	+	0.0801758i	0.283797	+	0.958884i	$0.408406\pi$
$840$		0			0
$841$	9.12132	+	9.12132i	0.314528	+	0.314528i
$842$		0			0
$843$	10.6569	+	25.7279i	0.367042	+	0.886117i
$844$		0			0
$845$	23.7782	−	57.4056i	0.817994	−	1.97481i
$846$		0			0
$847$	0.292893	+	0.121320i	0.0100639	+	0.00416862i
$848$		0			0
$849$	−13.0711			−0.448598
$850$		0			0
$851$	−46.8701			−1.60668
$852$		0			0
$853$	20.0208	+	8.29289i	0.685500	+	0.283943i	0.698124	−	0.715977i	$-0.254018\pi$
$853$	20.0208	+	8.29289i	0.685500	+	0.283943i	−0.0126242	+	0.999920i	$0.504018\pi$
$854$		0			0
$855$	0.757359	−	1.82843i	0.0259011	−	0.0625309i
$856$		0			0
$857$	4.94975	+	11.9497i	0.169080	+	0.408196i	0.985594	−	0.169131i	$-0.0540960\pi$
$857$	4.94975	+	11.9497i	0.169080	+	0.408196i	−0.816513	+	0.577326i	$0.804096\pi$
$858$		0			0
$859$	−11.8284	−	11.8284i	−0.403581	−	0.403581i	0.475912	−	0.879493i	$-0.342118\pi$
$859$	−11.8284	−	11.8284i	−0.403581	−	0.403581i	−0.879493	+	0.475912i	$0.842118\pi$
$860$		0			0
$861$	1.58579	−	0.656854i	0.0540435	−	0.0223855i
$862$		0			0
$863$			14.0000i			0.476566i	0.971196	+	0.238283i	$0.0765845\pi$
$863$			14.0000i			0.476566i	−0.971196	+	0.238283i	$0.923415\pi$
$864$		0			0
$865$	−32.7990	+	32.7990i	−1.11520	+	1.11520i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−27.2426	+	27.2426i	−0.924143	+	0.924143i
$870$		0			0
$871$		−	77.2548i		−	2.61768i
$872$		0			0
$873$	−0.363961	+	0.150758i	−0.0123182	+	0.00510237i
$874$		0			0
$875$	−6.58579	−	6.58579i	−0.222640	−	0.222640i
$876$		0			0
$877$	3.29289	+	7.94975i	0.111193	+	0.268444i	0.969674	−	0.244401i	$-0.0785914\pi$
$877$	3.29289	+	7.94975i	0.111193	+	0.268444i	−0.858481	+	0.512845i	$0.828591\pi$
$878$		0			0
$879$	5.65685	−	13.6569i	0.190801	−	0.460634i
$880$		0			0
$881$	−8.94975	−	3.70711i	−0.301525	−	0.124896i	0.226791	−	0.973943i	$-0.427176\pi$
$881$	−8.94975	−	3.70711i	−0.301525	−	0.124896i	−0.528316	+	0.849048i	$0.677176\pi$
$882$		0			0
$883$	14.3431			0.482685			0.241343	−	0.970440i	$-0.422412\pi$
$883$	14.3431			0.482685			0.241343	+	0.970440i	$0.422412\pi$
$884$		0			0
$885$	47.4558			1.59521
$886$		0			0
$887$	32.7782	+	13.5772i	1.10058	+	0.455877i	0.857685	−	0.514175i	$-0.171902\pi$
$887$	32.7782	+	13.5772i	1.10058	+	0.455877i	0.242898	+	0.970052i	$0.421902\pi$
$888$		0			0
$889$	−0.0710678	+	0.171573i	−0.00238354	+	0.00575437i
$890$		0			0
$891$	13.0208	+	31.4350i	0.436214	+	1.05311i
$892$		0			0
$893$	−6.68629	−	6.68629i	−0.223748	−	0.223748i
$894$		0			0
$895$	31.3848	−	13.0000i	1.04908	−	0.434542i
$896$		0			0
$897$			89.2548i			2.98013i
$898$		0			0
$899$	−18.2721	+	18.2721i	−0.609408	+	0.609408i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	4.24264	−	4.24264i	0.141186	−	0.141186i
$904$		0			0
$905$			7.07107i			0.235050i
$906$		0			0
$907$	7.02082	−	2.90812i	0.233122	−	0.0965624i	−0.263064	−	0.964778i	$-0.584733\pi$
$907$	7.02082	−	2.90812i	0.233122	−	0.0965624i	0.496187	+	0.868216i	$0.334733\pi$
$908$		0			0
$909$	3.75736	+	3.75736i	0.124624	+	0.124624i
$910$		0			0
$911$	−1.16295	−	2.80761i	−0.0385303	−	0.0930203i	0.903443	−	0.428708i	$-0.141031\pi$
$911$	−1.16295	−	2.80761i	−0.0385303	−	0.0930203i	−0.941973	+	0.335688i	$0.891031\pi$
$912$		0			0
$913$	0.313708	−	0.757359i	0.0103822	−	0.0250649i
$914$		0			0
$915$	−5.82843	−	2.41421i	−0.192682	−	0.0798114i
$916$		0			0
$917$	8.38478			0.276890
$918$		0			0
$919$	−14.3431			−0.473137			−0.236568	−	0.971615i	$-0.576023\pi$
$919$	−14.3431			−0.473137			−0.236568	+	0.971615i	$0.576023\pi$
$920$		0			0
$921$	−10.8284	−	4.48528i	−0.356809	−	0.147795i
$922$		0			0
$923$	3.17157	−	7.65685i	0.104394	−	0.252028i
$924$		0			0
$925$	−4.02082	−	9.70711i	−0.132204	−	0.319168i
$926$		0			0
$927$	1.17157	+	1.17157i	0.0384795	+	0.0384795i
$928$		0			0
$929$	45.6777	−	18.9203i	1.49864	−	0.620755i	0.525460	−	0.850818i	$-0.323893\pi$
$929$	45.6777	−	18.9203i	1.49864	−	0.620755i	0.973176	+	0.230063i	$0.0738932\pi$
$930$		0			0
$931$			16.5858i			0.543577i
$932$		0			0
$933$	−16.6569	+	16.6569i	−0.545321	+	0.545321i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.5147	+	16.5147i	−0.539512	+	0.539512i	−0.923386	−	0.383873i	$-0.874590\pi$
$937$	−16.5147	+	16.5147i	−0.539512	+	0.539512i	0.383873	+	0.923386i	$0.374590\pi$
$938$		0			0
$939$			42.0416i			1.37198i
$940$		0			0
$941$	1.53553	−	0.636039i	0.0500570	−	0.0207343i	−0.357514	−	0.933908i	$-0.616376\pi$
$941$	1.53553	−	0.636039i	0.0500570	−	0.0207343i	0.407571	+	0.913173i	$0.366376\pi$
$942$		0			0
$943$	6.07107	+	6.07107i	0.197701	+	0.197701i
$944$		0			0
$945$	−2.58579	−	6.24264i	−0.0841156	−	0.203073i
$946$		0			0
$947$	−3.46447	+	8.36396i	−0.112580	+	0.271792i	−0.970120	−	0.242625i	$-0.921992\pi$
$947$	−3.46447	+	8.36396i	−0.112580	+	0.271792i	0.857540	+	0.514417i	$0.171992\pi$
$948$		0			0
$949$	−54.2843	−	22.4853i	−1.76214	−	0.729903i
$950$		0			0
$951$	−0.727922			−0.0236045
$952$		0			0
$953$	12.1421			0.393322			0.196661	−	0.980472i	$-0.436990\pi$
$953$	12.1421			0.393322			0.196661	+	0.980472i	$0.436990\pi$
$954$		0			0
$955$	0.585786	+	0.242641i	0.0189556	+	0.00785167i
$956$		0			0
$957$	−9.58579	+	23.1421i	−0.309864	+	0.748079i
$958$		0			0
$959$	3.55635	+	8.58579i	0.114841	+	0.277250i
$960$		0			0
$961$	7.40559	+	7.40559i	0.238890	+	0.238890i
$962$		0			0
$963$	−1.46447	+	0.606602i	−0.0471918	+	0.0195475i
$964$		0			0
$965$			28.7279i			0.924785i
$966$		0			0
$967$	23.3431	−	23.3431i	0.750665	−	0.750665i	−0.223938	−	0.974603i	$-0.571891\pi$
$967$	23.3431	−	23.3431i	0.750665	−	0.750665i	0.974603	+	0.223938i	$0.0718914\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−26.3137	+	26.3137i	−0.844447	+	0.844447i	−0.989434	−	0.144987i	$-0.953686\pi$
$971$	−26.3137	+	26.3137i	−0.844447	+	0.844447i	0.144987	+	0.989434i	$0.453686\pi$
$972$		0			0
$973$		−	13.4142i		−	0.430040i
$974$		0			0
$975$	−18.4853	+	7.65685i	−0.592003	+	0.245216i
$976$		0			0
$977$	−27.1421	−	27.1421i	−0.868354	−	0.868354i	0.123936	−	0.992290i	$-0.460448\pi$
$977$	−27.1421	−	27.1421i	−0.868354	−	0.868354i	−0.992290	+	0.123936i	$0.960448\pi$
$978$		0			0
$979$	−14.0000	−	33.7990i	−0.447442	−	1.08022i
$980$		0			0
$981$	0.778175	−	1.87868i	0.0248452	−	0.0599816i
$982$		0			0
$983$	−36.3345	−	15.0503i	−1.15889	−	0.480029i	−0.281386	−	0.959595i	$-0.590794\pi$
$983$	−36.3345	−	15.0503i	−1.15889	−	0.480029i	−0.877506	+	0.479566i	$0.840794\pi$
$984$		0			0
$985$	−23.2132			−0.739634
$986$		0			0
$987$	5.17157			0.164613
$988$		0			0
$989$	27.7279	+	11.4853i	0.881697	+	0.365211i
$990$		0			0
$991$	17.3640	−	41.9203i	0.551584	−	1.33164i	−0.364704	−	0.931123i	$-0.618830\pi$
$991$	17.3640	−	41.9203i	0.551584	−	1.33164i	0.916288	−	0.400519i	$-0.131170\pi$
$992$		0			0
$993$	20.3137	+	49.0416i	0.644636	+	1.55629i
$994$		0			0
$995$	−2.17157	−	2.17157i	−0.0688435	−	0.0688435i
$996$		0			0
$997$	−28.6066	+	11.8492i	−0.905980	+	0.375269i	−0.786516	−	0.617569i	$-0.788118\pi$
$997$	−28.6066	+	11.8492i	−0.905980	+	0.375269i	−0.119464	+	0.992839i	$0.538118\pi$
$998$		0			0
$999$		−	31.6569i		−	1.00158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.h.a.757.1		4
17.2	even	8	inner	1156.2.h.a.733.1		4
17.3	odd	16		1156.2.e.f.829.1		8
17.4	even	4		68.2.h.a.25.1	✓	4
17.5	odd	16		1156.2.e.f.905.4		8
17.6	odd	16		1156.2.a.g.1.1		4
17.7	odd	16		1156.2.b.d.577.4		4
17.8	even	8		1156.2.h.b.1001.1		4
17.9	even	8		68.2.h.a.49.1	yes	4
17.10	odd	16		1156.2.b.d.577.1		4
17.11	odd	16		1156.2.a.g.1.4		4
17.12	odd	16		1156.2.e.f.905.1		8
17.13	even	4		1156.2.h.b.977.1		4
17.14	odd	16		1156.2.e.f.829.4		8
17.15	even	8		1156.2.h.c.733.1		4
17.16	even	2		1156.2.h.c.757.1		4
51.26	odd	8		612.2.w.a.253.1		4
51.38	odd	4		612.2.w.a.433.1		4
68.11	even	16		4624.2.a.bl.1.1		4
68.23	even	16		4624.2.a.bl.1.4		4
68.43	odd	8		272.2.v.c.49.1		4
68.55	odd	4		272.2.v.c.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.h.a.25.1	✓	4	17.4	even	4
68.2.h.a.49.1	yes	4	17.9	even	8
272.2.v.c.49.1		4	68.43	odd	8
272.2.v.c.161.1		4	68.55	odd	4
612.2.w.a.253.1		4	51.26	odd	8
612.2.w.a.433.1		4	51.38	odd	4
1156.2.a.g.1.1		4	17.6	odd	16
1156.2.a.g.1.4		4	17.11	odd	16
1156.2.b.d.577.1		4	17.10	odd	16
1156.2.b.d.577.4		4	17.7	odd	16
1156.2.e.f.829.1		8	17.3	odd	16
1156.2.e.f.829.4		8	17.14	odd	16
1156.2.e.f.905.1		8	17.12	odd	16
1156.2.e.f.905.4		8	17.5	odd	16
1156.2.h.a.733.1		4	17.2	even	8	inner
1156.2.h.a.757.1		4	1.1	even	1	trivial
1156.2.h.b.977.1		4	17.13	even	4
1156.2.h.b.1001.1		4	17.8	even	8
1156.2.h.c.733.1		4	17.15	even	8
1156.2.h.c.757.1		4	17.16	even	2
4624.2.a.bl.1.1		4	68.11	even	16
4624.2.a.bl.1.4		4	68.23	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 0.707107i) q^{3} +(-0.707107 + 1.70711i) q^{5} +(0.292893 + 0.707107i) q^{7} +(0.292893 + 0.292893i) q^{9} +(-3.12132 + 1.29289i) q^{11} -6.82843i q^{13} +(2.41421 - 2.41421i) q^{15} +(-1.82843 + 1.82843i) q^{19} -1.41421i q^{21} +(6.53553 - 2.70711i) q^{23} +(1.12132 + 1.12132i) q^{25} +(1.82843 + 4.41421i) q^{27} +(-1.53553 + 3.70711i) q^{29} +(5.94975 + 2.46447i) q^{31} +6.24264 q^{33} -1.41421 q^{35} +(-6.12132 - 2.53553i) q^{37} +(-4.82843 + 11.6569i) q^{39} +(0.464466 + 1.12132i) q^{41} +(3.00000 + 3.00000i) q^{43} +(-0.707107 + 0.292893i) q^{45} +3.65685i q^{47} +(4.53553 - 4.53553i) q^{49} +(4.17157 - 4.17157i) q^{53} -6.24264i q^{55} +(4.41421 - 1.82843i) q^{57} +(9.82843 + 9.82843i) q^{59} +(-0.707107 - 1.70711i) q^{61} +(-0.121320 + 0.292893i) q^{63} +(11.6569 + 4.82843i) q^{65} +11.3137 q^{67} -13.0711 q^{69} +(1.12132 + 0.464466i) q^{71} +(3.29289 - 7.94975i) q^{73} +(-1.12132 - 2.70711i) q^{75} +(-1.82843 - 1.82843i) q^{77} +(10.5355 - 4.36396i) q^{79} -10.0711i q^{81} +(-0.171573 + 0.171573i) q^{83} +(5.24264 - 5.24264i) q^{87} +10.8284i q^{89} +(4.82843 - 2.00000i) q^{91} +(-8.41421 - 8.41421i) q^{93} +(-1.82843 - 4.41421i) q^{95} +(-0.363961 + 0.878680i) q^{97} +(-1.29289 - 0.535534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{7} + 4 q^{9} - 4 q^{11} + 4 q^{15} + 4 q^{19} + 12 q^{23} - 4 q^{25} - 4 q^{27} + 8 q^{29} + 4 q^{31} + 8 q^{33} - 16 q^{37} - 8 q^{39} + 16 q^{41} + 12 q^{43} + 4 q^{49} + 28 q^{53}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^7 + 4 * q^9 - 4 * q^11 + 4 * q^15 + 4 * q^19 + 12 * q^23 - 4 * q^25 - 4 * q^27 + 8 * q^29 + 4 * q^31 + 8 * q^33 - 16 * q^37 - 8 * q^39 + 16 * q^41 + 12 * q^43 + 4 * q^49 + 28 * q^53 + 12 * q^57 + 28 * q^59 + 8 * q^63 + 24 * q^65 - 24 * q^69 - 4 * q^71 + 16 * q^73 + 4 * q^75 + 4 * q^77 + 28 * q^79 - 12 * q^83 + 4 * q^87 + 8 * q^91 - 28 * q^93 + 4 * q^95 + 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more