LMFDB - Embedded newform 880.2.bo.h.641.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.1
Root			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.h.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.177837 - 0.547326i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.12773 - 3.47080i) q^{7} +(2.15911 - 1.56869i) q^{9} +O(q^{10})$	\(q+(-0.177837 - 0.547326i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.12773 - 3.47080i) q^{7} +(2.15911 - 1.56869i) q^{9} +(-0.490303 + 3.28018i) q^{11} +(2.29029 - 1.66399i) q^{13} +(0.177837 - 0.547326i) q^{15} +(-2.98685 - 2.17008i) q^{17} +(0.0293950 + 0.0904686i) q^{19} -2.10021 q^{21} -1.16215 q^{23} +(0.309017 + 0.951057i) q^{25} +(-2.63930 - 1.91757i) q^{27} +(-2.08707 + 6.42333i) q^{29} +(5.48382 - 3.98423i) q^{31} +(1.88253 - 0.314983i) q^{33} +(2.95244 - 2.14507i) q^{35} +(3.04066 - 9.35820i) q^{37} +(-1.31805 - 0.957617i) q^{39} +(-2.57047 - 7.91110i) q^{41} +2.96862 q^{43} +2.66881 q^{45} +(0.687534 + 2.11601i) q^{47} +(-5.11155 - 3.71376i) q^{49} +(-0.656567 + 2.02070i) q^{51} +(-2.42214 + 1.75979i) q^{53} +(-2.32471 + 2.36553i) q^{55} +(0.0442883 - 0.0321774i) q^{57} +(2.62930 - 8.09216i) q^{59} +(6.86076 + 4.98464i) q^{61} +(-3.00970 - 9.26289i) q^{63} +2.83095 q^{65} +13.4153 q^{67} +(0.206673 + 0.636074i) q^{69} +(6.71734 + 4.88043i) q^{71} +(-0.407912 + 1.25542i) q^{73} +(0.465584 - 0.338266i) q^{75} +(10.8319 + 5.40091i) q^{77} +(-11.2179 + 8.15028i) q^{79} +(1.89395 - 5.82899i) q^{81} +(-8.61155 - 6.25666i) q^{83} +(-1.14088 - 3.51126i) q^{85} +3.88682 q^{87} -12.1612 q^{89} +(-3.19256 - 9.82567i) q^{91} +(-3.15590 - 2.29290i) q^{93} +(-0.0293950 + 0.0904686i) q^{95} +(3.50412 - 2.54589i) q^{97} +(4.08696 + 7.85141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9	$ 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9} - 3 q^{11} - 2 q^{13} - 5 q^{15} - 13 q^{17} - 15 q^{19} - 20 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - 9 q^{29} + 10 q^{31} + 5 q^{33} + 4 q^{35} + 24 q^{37} - 21 q^{39} + 8 q^{41} + 38 q^{43} + q^{49} - q^{51} + 13 q^{53} - 7 q^{55} - 45 q^{57} + 27 q^{59} + 6 q^{61} - 25 q^{63} + 2 q^{65} + 38 q^{67} - q^{69} + 20 q^{71} + 13 q^{73} - 5 q^{75} + 34 q^{77} - 37 q^{79} + 8 q^{81} - 27 q^{83} - 12 q^{85} - 38 q^{87} - 16 q^{89} - 44 q^{91} - 35 q^{93} + 15 q^{95} + 24 q^{97} + 20 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9 - 3 * q^11 - 2 * q^13 - 5 * q^15 - 13 * q^17 - 15 * q^19 - 20 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - 9 * q^29 + 10 * q^31 + 5 * q^33 + 4 * q^35 + 24 * q^37 - 21 * q^39 + 8 * q^41 + 38 * q^43 + q^49 - q^51 + 13 * q^53 - 7 * q^55 - 45 * q^57 + 27 * q^59 + 6 * q^61 - 25 * q^63 + 2 * q^65 + 38 * q^67 - q^69 + 20 * q^71 + 13 * q^73 - 5 * q^75 + 34 * q^77 - 37 * q^79 + 8 * q^81 - 27 * q^83 - 12 * q^85 - 38 * q^87 - 16 * q^89 - 44 * q^91 - 35 * q^93 + 15 * q^95 + 24 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.177837	−	0.547326i	−0.102674	−	0.315999i	0.886503	−	0.462722i	$-0.153127\pi$
$3$	−0.177837	−	0.547326i	−0.102674	−	0.315999i	−0.989178	+	0.146723i	$0.953127\pi$
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	1.12773	−	3.47080i	0.426242	−	1.31184i	−0.475558	−	0.879685i	$-0.657754\pi$
$7$	1.12773	−	3.47080i	0.426242	−	1.31184i	0.901800	−	0.432154i	$-0.142246\pi$
$8$		0			0
$9$	2.15911	−	1.56869i	0.719704	−	0.522895i
$10$		0			0
$11$	−0.490303	+	3.28018i	−0.147832	+	0.989012i
$11$	−0.490303	+	3.28018i	−0.147832	+	0.989012i
$12$		0			0
$13$	2.29029	−	1.66399i	0.635212	−	0.461509i	−0.222990	−	0.974821i	$-0.571582\pi$
$13$	2.29029	−	1.66399i	0.635212	−	0.461509i	0.858202	+	0.513312i	$0.171582\pi$
$14$		0			0
$15$	0.177837	−	0.547326i	0.0459174	−	0.141319i
$16$		0			0
$17$	−2.98685	−	2.17008i	−0.724419	−	0.526321i	0.163374	−	0.986564i	$-0.447762\pi$
$17$	−2.98685	−	2.17008i	−0.724419	−	0.526321i	−0.887793	+	0.460243i	$0.847762\pi$
$18$		0			0
$19$	0.0293950	+	0.0904686i	0.00674368	+	0.0207549i	0.954372	−	0.298621i	$-0.0965267\pi$
$19$	0.0293950	+	0.0904686i	0.00674368	+	0.0207549i	−0.947628	+	0.319376i	$0.896527\pi$
$20$		0			0
$21$	−2.10021			−0.458304
$22$		0			0
$23$	−1.16215			−0.242324			−0.121162	−	0.992633i	$-0.538662\pi$
$23$	−1.16215			−0.242324			−0.121162	+	0.992633i	$0.538662\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−2.63930	−	1.91757i	−0.507934	−	0.369036i
$28$		0			0
$29$	−2.08707	+	6.42333i	−0.387559	+	1.19278i	0.547049	+	0.837101i	$0.315751\pi$
$29$	−2.08707	+	6.42333i	−0.387559	+	1.19278i	−0.934607	+	0.355682i	$0.884249\pi$
$30$		0			0
$31$	5.48382	−	3.98423i	0.984923	−	0.715588i	0.0261194	−	0.999659i	$-0.491685\pi$
$31$	5.48382	−	3.98423i	0.984923	−	0.715588i	0.958803	+	0.284071i	$0.0916850\pi$
$32$		0			0
$33$	1.88253	−	0.314983i	0.327706	−	0.0548314i
$34$		0			0
$35$	2.95244	−	2.14507i	0.499053	−	0.362583i
$36$		0			0
$37$	3.04066	−	9.35820i	0.499882	−	1.53848i	−0.309326	−	0.950956i	$-0.600103\pi$
$37$	3.04066	−	9.35820i	0.499882	−	1.53848i	0.809208	−	0.587523i	$-0.199897\pi$
$38$		0			0
$39$	−1.31805	−	0.957617i	−0.211056	−	0.153341i
$40$		0			0
$41$	−2.57047	−	7.91110i	−0.401440	−	1.23551i	−0.923831	−	0.382800i	$-0.874960\pi$
$41$	−2.57047	−	7.91110i	−0.401440	−	1.23551i	0.522391	−	0.852706i	$-0.325040\pi$
$42$		0			0
$43$	2.96862			0.452710			0.226355	−	0.974045i	$-0.427319\pi$
$43$	2.96862			0.452710			0.226355	+	0.974045i	$0.427319\pi$
$44$		0			0
$45$	2.66881			0.397842
$46$		0			0
$47$	0.687534	+	2.11601i	0.100287	+	0.308652i	0.988595	−	0.150595i	$-0.0481191\pi$
$47$	0.687534	+	2.11601i	0.100287	+	0.308652i	−0.888308	+	0.459248i	$0.848119\pi$
$48$		0			0
$49$	−5.11155	−	3.71376i	−0.730221	−	0.530537i
$50$		0			0
$51$	−0.656567	+	2.02070i	−0.0919377	+	0.282955i
$52$		0			0
$53$	−2.42214	+	1.75979i	−0.332706	+	0.241725i	−0.741578	−	0.670867i	$-0.765922\pi$
$53$	−2.42214	+	1.75979i	−0.332706	+	0.241725i	0.408872	+	0.912592i	$0.365922\pi$
$54$		0			0
$55$	−2.32471	+	2.36553i	−0.313463	+	0.318968i
$56$		0			0
$57$	0.0442883	−	0.0321774i	0.00586613	−	0.00426200i
$58$		0			0
$59$	2.62930	−	8.09216i	0.342306	−	1.05351i	−0.620704	−	0.784045i	$-0.713153\pi$
$59$	2.62930	−	8.09216i	0.342306	−	1.05351i	0.963010	−	0.269465i	$-0.0868468\pi$
$60$		0			0
$61$	6.86076	+	4.98464i	0.878431	+	0.638217i	0.932836	−	0.360302i	$-0.117326\pi$
$61$	6.86076	+	4.98464i	0.878431	+	0.638217i	−0.0544052	+	0.998519i	$0.517326\pi$
$62$		0			0
$63$	−3.00970	−	9.26289i	−0.379186	−	1.16702i
$64$		0			0
$65$	2.83095			0.351137
$66$		0			0
$67$	13.4153			1.63894			0.819469	−	0.573123i	$-0.194268\pi$
$67$	13.4153			1.63894			0.819469	+	0.573123i	$0.194268\pi$
$68$		0			0
$69$	0.206673	+	0.636074i	0.0248805	+	0.0765743i
$70$		0			0
$71$	6.71734	+	4.88043i	0.797202	+	0.579201i	0.910092	−	0.414406i	$-0.136011\pi$
$71$	6.71734	+	4.88043i	0.797202	+	0.579201i	−0.112890	+	0.993607i	$0.536011\pi$
$72$		0			0
$73$	−0.407912	+	1.25542i	−0.0477425	+	0.146936i	−0.972086	−	0.234625i	$-0.924614\pi$
$73$	−0.407912	+	1.25542i	−0.0477425	+	0.146936i	0.924343	+	0.381562i	$0.124614\pi$
$74$		0			0
$75$	0.465584	−	0.338266i	0.0537610	−	0.0390596i
$76$		0			0
$77$	10.8319	+	5.40091i	1.23441	+	0.615491i
$78$		0			0
$79$	−11.2179	+	8.15028i	−1.26211	+	0.916978i	−0.998859	−	0.0477484i	$-0.984795\pi$
$79$	−11.2179	+	8.15028i	−1.26211	+	0.916978i	−0.263253	+	0.964727i	$0.584795\pi$
$80$		0			0
$81$	1.89395	−	5.82899i	0.210439	−	0.647665i
$82$		0			0
$83$	−8.61155	−	6.25666i	−0.945240	−	0.686757i	0.00443607	−	0.999990i	$-0.498588\pi$
$83$	−8.61155	−	6.25666i	−0.945240	−	0.686757i	−0.949676	+	0.313233i	$0.898588\pi$
$84$		0			0
$85$	−1.14088	−	3.51126i	−0.123745	−	0.380849i
$86$		0			0
$87$	3.88682			0.416710
$88$		0			0
$89$	−12.1612			−1.28908			−0.644540	−	0.764570i	$-0.722951\pi$
$89$	−12.1612			−1.28908			−0.644540	+	0.764570i	$0.722951\pi$
$90$		0			0
$91$	−3.19256	−	9.82567i	−0.334671	−	1.03001i
$92$		0			0
$93$	−3.15590	−	2.29290i	−0.327252	−	0.237762i
$94$		0			0
$95$	−0.0293950	+	0.0904686i	−0.00301587	+	0.00928188i
$96$		0			0
$97$	3.50412	−	2.54589i	0.355789	−	0.258496i	−0.395504	−	0.918464i	$-0.629430\pi$
$97$	3.50412	−	2.54589i	0.355789	−	0.258496i	0.751294	+	0.659968i	$0.229430\pi$
$98$		0			0
$99$	4.08696	+	7.85141i	0.410755	+	0.789096i
$100$		0			0
$101$	−8.01388	+	5.82242i	−0.797411	+	0.579353i	−0.910153	−	0.414271i	$-0.864036\pi$
$101$	−8.01388	+	5.82242i	−0.797411	+	0.579353i	0.112743	+	0.993624i	$0.464036\pi$
$102$		0			0
$103$	−1.25643	+	3.86690i	−0.123800	+	0.381017i	−0.993681	−	0.112245i	$-0.964196\pi$
$103$	−1.25643	+	3.86690i	−0.123800	+	0.381017i	0.869880	+	0.493263i	$0.164196\pi$
$104$		0			0
$105$	−1.69911	−	1.23447i	−0.165816	−	0.120472i
$106$		0			0
$107$	−0.599053	−	1.84369i	−0.0579126	−	0.178237i	0.917916	−	0.396776i	$-0.129871\pi$
$107$	−0.599053	−	1.84369i	−0.0579126	−	0.178237i	−0.975828	+	0.218539i	$0.929871\pi$
$108$		0			0
$109$	6.12664			0.586825			0.293413	−	0.955986i	$-0.405209\pi$
$109$	6.12664			0.586825			0.293413	+	0.955986i	$0.405209\pi$
$110$		0			0
$111$	−5.66273			−0.537483
$112$		0			0
$113$	1.78775	+	5.50212i	0.168177	+	0.517596i	0.999256	−	0.0385582i	$-0.0122765\pi$
$113$	1.78775	+	5.50212i	0.168177	+	0.517596i	−0.831079	+	0.556154i	$0.812276\pi$
$114$		0			0
$115$	−0.940197	−	0.683093i	−0.0876738	−	0.0636987i
$116$		0			0
$117$	2.33471	−	7.18549i	0.215844	−	0.664299i
$118$		0			0
$119$	−10.9003	+	7.91951i	−0.999226	+	0.725980i
$120$		0			0
$121$	−10.5192	−	3.21657i	−0.956291	−	0.292415i
$122$		0			0
$123$	−3.87283	+	2.81377i	−0.349201	+	0.253710i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	1.97224	+	1.43292i	0.175008	+	0.127151i	0.671841	−	0.740695i	$-0.265504\pi$
$127$	1.97224	+	1.43292i	0.175008	+	0.127151i	−0.496833	+	0.867846i	$0.665504\pi$
$128$		0			0
$129$	−0.527931	−	1.62480i	−0.0464817	−	0.143056i
$130$		0			0
$131$	−7.04156			−0.615224			−0.307612	−	0.951512i	$-0.599530\pi$
$131$	−7.04156			−0.615224			−0.307612	+	0.951512i	$0.599530\pi$
$132$		0			0
$133$	0.347148			0.0301016
$134$		0			0
$135$	−1.00812	−	3.10269i	−0.0867655	−	0.267037i
$136$		0			0
$137$	7.74461	+	5.62678i	0.661666	+	0.480729i	0.867225	−	0.497916i	$-0.165901\pi$
$137$	7.74461	+	5.62678i	0.661666	+	0.480729i	−0.205559	+	0.978645i	$0.565901\pi$
$138$		0			0
$139$	−0.159299	+	0.490271i	−0.0135116	+	0.0415843i	−0.957585	−	0.288151i	$-0.906959\pi$
$139$	−0.159299	+	0.490271i	−0.0135116	+	0.0415843i	0.944073	+	0.329735i	$0.106959\pi$
$140$		0			0
$141$	1.03588	−	0.752611i	0.0872369	−	0.0633813i
$142$		0			0
$143$	4.33527	+	8.32843i	0.362533	+	0.696459i
$144$		0			0
$145$	−5.46401	+	3.96984i	−0.453761	+	0.329677i
$146$		0			0
$147$	−1.12361	+	3.45813i	−0.0926742	+	0.285222i
$148$		0			0
$149$	6.60144	+	4.79623i	0.540811	+	0.392922i	0.824386	−	0.566028i	$-0.191521\pi$
$149$	6.60144	+	4.79623i	0.540811	+	0.392922i	−0.283575	+	0.958950i	$0.591521\pi$
$150$		0			0
$151$	−0.599563	−	1.84526i	−0.0487917	−	0.150165i	0.923692	−	0.383135i	$-0.125156\pi$
$151$	−0.599563	−	1.84526i	−0.0487917	−	0.150165i	−0.972484	+	0.232970i	$0.925156\pi$
$152$		0			0
$153$	−9.85312			−0.796577
$154$		0			0
$155$	6.77837			0.544452
$156$		0			0
$157$	6.57418	+	20.2332i	0.524676	+	1.61479i	0.764955	+	0.644084i	$0.222761\pi$
$157$	6.57418	+	20.2332i	0.524676	+	1.61479i	−0.240279	+	0.970704i	$0.577239\pi$
$158$		0			0
$159$	1.39392	+	1.01274i	0.110545	+	0.0803159i
$160$		0			0
$161$	−1.31059	+	4.03358i	−0.103289	+	0.317891i
$162$		0			0
$163$	−12.9289	+	9.39337i	−1.01267	+	0.735746i	−0.964767	−	0.263107i	$-0.915253\pi$
$163$	−12.9289	+	9.39337i	−1.01267	+	0.735746i	−0.0479001	+	0.998852i	$0.515253\pi$
$164$		0			0
$165$	1.70814	+	0.851694i	0.132978	+	0.0663043i
$166$		0			0
$167$	14.3269	−	10.4091i	1.10865	−	0.805481i	0.126199	−	0.992005i	$-0.459722\pi$
$167$	14.3269	−	10.4091i	1.10865	−	0.805481i	0.982450	+	0.186524i	$0.0597223\pi$
$168$		0			0
$169$	−1.54066	+	4.74168i	−0.118513	+	0.364744i
$170$		0			0
$171$	0.205384	+	0.149220i	0.0157061	+	0.0114112i
$172$		0			0
$173$	4.90888	+	15.1080i	0.373216	+	1.14864i	0.944675	+	0.328009i	$0.106378\pi$
$173$	4.90888	+	15.1080i	0.373216	+	1.14864i	−0.571459	+	0.820631i	$0.693622\pi$
$174$		0			0
$175$	3.64941			0.275870
$176$		0			0
$177$	−4.89664			−0.368054
$178$		0			0
$179$	5.21653	+	16.0548i	0.389902	+	1.19999i	0.932862	+	0.360235i	$0.117304\pi$
$179$	5.21653	+	16.0548i	0.389902	+	1.19999i	−0.542960	+	0.839759i	$0.682696\pi$
$180$		0			0
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.986187	+	0.165636i	$0.0529676\pi$
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.462277	+	0.886735i	$0.347032\pi$
$182$		0			0
$183$	1.50812	−	4.64153i	0.111484	−	0.343112i
$184$		0			0
$185$	7.96056	−	5.78369i	0.585272	−	0.425225i
$186$		0			0
$187$	8.58271	−	8.73343i	0.627630	−	0.638652i
$188$		0			0
$189$	−9.63191	+	6.99800i	−0.700619	+	0.509029i
$190$		0			0
$191$	−1.66337	+	5.11934i	−0.120358	+	0.370422i	−0.993027	−	0.117890i	$-0.962387\pi$
$191$	−1.66337	+	5.11934i	−0.120358	+	0.370422i	0.872669	+	0.488312i	$0.162387\pi$
$192$		0			0
$193$	−14.7921	−	10.7471i	−1.06476	−	0.773593i	−0.0897961	−	0.995960i	$-0.528622\pi$
$193$	−14.7921	−	10.7471i	−1.06476	−	0.773593i	−0.974963	+	0.222367i	$0.928622\pi$
$194$		0			0
$195$	−0.503449	−	1.54946i	−0.0360527	−	0.110959i
$196$		0			0
$197$	2.64566			0.188496			0.0942478	−	0.995549i	$-0.469955\pi$
$197$	2.64566			0.188496			0.0942478	+	0.995549i	$0.469955\pi$
$198$		0			0
$199$	−6.52800			−0.462757			−0.231379	−	0.972864i	$-0.574324\pi$
$199$	−6.52800			−0.462757			−0.231379	+	0.972864i	$0.574324\pi$
$200$		0			0
$201$	−2.38574	−	7.34254i	−0.168277	−	0.517903i
$202$		0			0
$203$	19.9404	+	14.4876i	1.39954	+	1.01683i
$204$		0			0
$205$	2.57047	−	7.91110i	0.179530	−	0.552535i
$206$		0			0
$207$	−2.50920	+	1.82304i	−0.174402	+	0.126710i
$208$		0			0
$209$	−0.311166	+	0.0520641i	−0.0215238	+	0.00360135i
$210$		0			0
$211$	−22.2057	+	16.1334i	−1.52871	+	1.11067i	−0.571752	+	0.820426i	$0.693736\pi$
$211$	−22.2057	+	16.1334i	−1.52871	+	1.11067i	−0.956953	+	0.290243i	$0.906264\pi$
$212$		0			0
$213$	1.47660	−	4.54450i	0.101175	−	0.311384i
$214$		0			0
$215$	2.40166	+	1.74491i	0.163792	+	0.119002i
$216$		0			0
$217$	−7.64418	−	23.5264i	−0.518921	−	1.59707i
$218$		0			0
$219$	0.759669			0.0513337
$220$		0			0
$221$	−10.4518			−0.703061
$222$		0			0
$223$	1.57040	+	4.83321i	0.105162	+	0.323656i	0.989768	−	0.142683i	$-0.0455729\pi$
$223$	1.57040	+	4.83321i	0.105162	+	0.323656i	−0.884606	+	0.466338i	$0.845573\pi$
$224$		0			0
$225$	2.15911	+	1.56869i	0.143941	+	0.104579i
$226$		0			0
$227$	−1.15566	+	3.55676i	−0.0767040	+	0.236071i	−0.982055	−	0.188593i	$-0.939607\pi$
$227$	−1.15566	+	3.55676i	−0.0767040	+	0.236071i	0.905351	+	0.424663i	$0.139607\pi$
$228$		0			0
$229$	−21.7821	+	15.8256i	−1.43940	+	1.04578i	−0.451232	+	0.892407i	$0.649015\pi$
$229$	−21.7821	+	15.8256i	−1.43940	+	1.04578i	−0.988168	+	0.153378i	$0.950985\pi$
$230$		0			0
$231$	1.02974	−	6.88908i	0.0677520	−	0.453268i
$232$		0			0
$233$	−14.8185	+	10.7663i	−0.970794	+	0.705323i	−0.955632	−	0.294562i	$-0.904826\pi$
$233$	−14.8185	+	10.7663i	−0.970794	+	0.705323i	−0.0151615	+	0.999885i	$0.504826\pi$
$234$		0			0
$235$	−0.687534	+	2.11601i	−0.0448498	+	0.138033i
$236$		0			0
$237$	6.45582	+	4.69043i	0.419351	+	0.304676i
$238$		0			0
$239$	3.38555	+	10.4196i	0.218993	+	0.673991i	0.998846	+	0.0480283i	$0.0152938\pi$
$239$	3.38555	+	10.4196i	0.218993	+	0.673991i	−0.779853	+	0.625963i	$0.784706\pi$
$240$		0			0
$241$	−9.99444			−0.643798			−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444			−0.643798			−0.321899	+	0.946774i	$0.604321\pi$
$242$		0			0
$243$	−13.3143			−0.854110
$244$		0			0
$245$	−1.95244	−	6.00899i	−0.124737	−	0.383900i
$246$		0			0
$247$	0.217862	+	0.158286i	0.0138622	+	0.0100715i
$248$		0			0
$249$	−1.89298	+	5.82599i	−0.119963	+	0.369207i
$250$		0			0
$251$	7.81303	−	5.67650i	0.493154	−	0.358297i	−0.313242	−	0.949673i	$-0.601415\pi$
$251$	7.81303	−	5.67650i	0.493154	−	0.358297i	0.806396	+	0.591376i	$0.201415\pi$
$252$		0			0
$253$	0.569804	−	3.81206i	0.0358233	−	0.239662i
$254$		0			0
$255$	−1.71891	+	1.24886i	−0.107643	+	0.0782069i
$256$		0			0
$257$	3.22230	−	9.91721i	0.201001	−	0.618618i	−0.798853	−	0.601527i	$-0.794559\pi$
$257$	3.22230	−	9.91721i	0.201001	−	0.618618i	0.999854	−	0.0170916i	$-0.00544069\pi$
$258$		0			0
$259$	−29.0514	−	21.1071i	−1.80517	−	1.31153i
$260$		0			0
$261$	5.56998	+	17.1426i	0.344773	+	1.06110i
$262$		0			0
$263$	10.9619			0.675937			0.337968	−	0.941157i	$-0.390260\pi$
$263$	10.9619			0.675937			0.337968	+	0.941157i	$0.390260\pi$
$264$		0			0
$265$	−2.99393			−0.183915
$266$		0			0
$267$	2.16271	+	6.65613i	0.132355	+	0.407348i
$268$		0			0
$269$	0.0722816	+	0.0525156i	0.00440708	+	0.00320193i	0.589987	−	0.807413i	$-0.299133\pi$
$269$	0.0722816	+	0.0525156i	0.00440708	+	0.00320193i	−0.585580	+	0.810615i	$0.699133\pi$
$270$		0			0
$271$	4.14069	−	12.7437i	0.251529	−	0.774126i	−0.742965	−	0.669330i	$-0.766581\pi$
$271$	4.14069	−	12.7437i	0.251529	−	0.774126i	0.994494	−	0.104796i	$-0.0334190\pi$
$272$		0			0
$273$	−4.81010	+	3.49474i	−0.291120	+	0.211511i
$274$		0			0
$275$	−3.27115	+	0.547326i	−0.197258	+	0.0330050i
$276$		0			0
$277$	3.16057	−	2.29629i	0.189901	−	0.137971i	−0.488773	−	0.872411i	$-0.662555\pi$
$277$	3.16057	−	2.29629i	0.189901	−	0.137971i	0.678673	+	0.734440i	$0.262555\pi$
$278$		0			0
$279$	5.59017	−	17.2048i	0.334675	−	1.03002i
$280$		0			0
$281$	1.24381	+	0.903680i	0.0741994	+	0.0539090i	0.624267	−	0.781211i	$-0.285398\pi$
$281$	1.24381	+	0.903680i	0.0741994	+	0.0539090i	−0.550067	+	0.835120i	$0.685398\pi$
$282$		0			0
$283$	1.67231	+	5.14683i	0.0994083	+	0.305947i	0.988377	−	0.152020i	$-0.0485778\pi$
$283$	1.67231	+	5.14683i	0.0994083	+	0.305947i	−0.888969	+	0.457967i	$0.848578\pi$
$284$		0			0
$285$	0.0547434			0.00324272
$286$		0			0
$287$	−30.3566			−1.79190
$288$		0			0
$289$	−1.04122	−	3.20456i	−0.0612484	−	0.188503i
$290$		0			0
$291$	−2.01659	−	1.46514i	−0.118215	−	0.0858881i
$292$		0			0
$293$	3.52789	−	10.8577i	0.206102	−	0.634315i	−0.793565	−	0.608486i	$-0.791777\pi$
$293$	3.52789	−	10.8577i	0.206102	−	0.634315i	0.999666	−	0.0258295i	$-0.00822271\pi$
$294$		0			0
$295$	6.88361	−	5.00123i	0.400779	−	0.291183i
$296$		0			0
$297$	7.58403	−	7.71721i	0.440070	−	0.447798i
$298$		0			0
$299$	−2.66165	+	1.93381i	−0.153927	+	0.111835i
$300$		0			0
$301$	3.34780	−	10.3035i	0.192964	−	0.593883i
$302$		0			0
$303$	4.61193	+	3.35077i	0.264949	+	0.192496i
$304$		0			0
$305$	2.62058	+	8.06531i	0.150054	+	0.461818i
$306$		0			0
$307$	4.25008			0.242565			0.121282	−	0.992618i	$-0.461299\pi$
$307$	4.25008			0.242565			0.121282	+	0.992618i	$0.461299\pi$
$308$		0			0
$309$	2.33990			0.133112
$310$		0			0
$311$	5.13570	+	15.8061i	0.291219	+	0.896279i	0.984465	+	0.175579i	$0.0561796\pi$
$311$	5.13570	+	15.8061i	0.291219	+	0.896279i	−0.693247	+	0.720700i	$0.743820\pi$
$312$		0			0
$313$	21.5012	+	15.6215i	1.21532	+	0.882982i	0.995703	−	0.0926041i	$-0.0295191\pi$
$313$	21.5012	+	15.6215i	1.21532	+	0.882982i	0.219617	+	0.975586i	$0.429519\pi$
$314$		0			0
$315$	3.00970	−	9.26289i	0.169577	−	0.521905i
$316$		0			0
$317$	−4.68982	+	3.40736i	−0.263407	+	0.191376i	−0.711648	−	0.702537i	$-0.752051\pi$
$317$	−4.68982	+	3.40736i	−0.263407	+	0.191376i	0.448241	+	0.893913i	$0.352051\pi$
$318$		0			0
$319$	−20.0464	−	9.99534i	−1.12238	−	0.559632i
$320$		0			0
$321$	−0.902569	+	0.655755i	−0.0503765	+	0.0366007i
$322$		0			0
$323$	0.108525	−	0.334006i	0.00603850	−	0.0185846i
$324$		0			0
$325$	2.29029	+	1.66399i	0.127042	+	0.0923018i
$326$		0			0
$327$	−1.08954	−	3.35327i	−0.0602519	−	0.185436i
$328$		0			0
$329$	8.11961			0.447648
$330$		0			0
$331$	12.9230			0.710311			0.355155	−	0.934807i	$-0.384428\pi$
$331$	12.9230			0.710311			0.355155	+	0.934807i	$0.384428\pi$
$332$		0			0
$333$	−8.11495	−	24.9752i	−0.444696	−	1.36863i
$334$		0			0
$335$	10.8532	+	7.88531i	0.592974	+	0.430820i
$336$		0			0
$337$	4.13631	−	12.7303i	0.225319	−	0.693461i	−0.772940	−	0.634479i	$-0.781215\pi$
$337$	4.13631	−	12.7303i	0.225319	−	0.693461i	0.998259	−	0.0589818i	$-0.0187854\pi$
$338$		0			0
$339$	2.69353	−	1.95696i	0.146292	−	0.106288i
$340$		0			0
$341$	10.3803	+	19.9414i	0.562123	+	1.07989i
$342$		0			0
$343$	2.01291	−	1.46246i	0.108687	−	0.0789656i
$344$		0			0
$345$	−0.206673	+	0.636074i	−0.0111269	+	0.0342451i
$346$		0			0
$347$	−6.83538	−	4.96619i	−0.366942	−	0.266599i	0.389000	−	0.921238i	$-0.372821\pi$
$347$	−6.83538	−	4.96619i	−0.366942	−	0.266599i	−0.755942	+	0.654639i	$0.772821\pi$
$348$		0			0
$349$	−3.21341	−	9.88987i	−0.172010	−	0.529393i	0.827474	−	0.561504i	$-0.189777\pi$
$349$	−3.21341	−	9.88987i	−0.172010	−	0.529393i	−0.999484	+	0.0321111i	$0.989777\pi$
$350$		0			0
$351$	−9.23559			−0.492959
$352$		0			0
$353$	19.1073			1.01698			0.508489	−	0.861069i	$-0.330204\pi$
$353$	19.1073			1.01698			0.508489	+	0.861069i	$0.330204\pi$
$354$		0			0
$355$	2.56580	+	7.89671i	0.136178	+	0.419114i
$356$		0			0
$357$	6.27303	+	4.55762i	0.332004	+	0.241215i
$358$		0			0
$359$	1.36405	−	4.19813i	0.0719920	−	0.221569i	−0.908586	−	0.417698i	$-0.862837\pi$
$359$	1.36405	−	4.19813i	0.0719920	−	0.221569i	0.980578	+	0.196129i	$0.0628371\pi$
$360$		0			0
$361$	15.3640	−	11.1626i	0.808632	−	0.587505i
$362$		0			0
$363$	0.110193	+	6.32946i	0.00578362	+	0.332211i
$364$		0			0
$365$	−1.06793	+	0.775895i	−0.0558979	+	0.0406122i
$366$		0			0
$367$	9.07327	−	27.9247i	0.473621	−	1.45766i	−0.374188	−	0.927353i	$-0.622078\pi$
$367$	9.07327	−	27.9247i	0.473621	−	1.45766i	0.847809	−	0.530302i	$-0.177922\pi$
$368$		0			0
$369$	−17.9600	−	13.0487i	−0.934958	−	0.679287i
$370$		0			0
$371$	3.37634	+	10.3913i	0.175291	+	0.539490i
$372$		0			0
$373$	−4.96478			−0.257067			−0.128533	−	0.991705i	$-0.541027\pi$
$373$	−4.96478			−0.257067			−0.128533	+	0.991705i	$0.541027\pi$
$374$		0			0
$375$	0.575493			0.0297183
$376$		0			0
$377$	5.90839	+	18.1842i	0.304298	+	0.936532i
$378$		0			0
$379$	6.40996	+	4.65711i	0.329258	+	0.239220i	0.740116	−	0.672480i	$-0.234771\pi$
$379$	6.40996	+	4.65711i	0.329258	+	0.239220i	−0.410858	+	0.911699i	$0.634771\pi$
$380$		0			0
$381$	0.433536	−	1.33429i	0.0222107	−	0.0683576i
$382$		0			0
$383$	−19.8335	+	14.4099i	−1.01344	+	0.736309i	−0.964928	−	0.262514i	$-0.915449\pi$
$383$	−19.8335	+	14.4099i	−1.01344	+	0.736309i	−0.0485140	+	0.998823i	$0.515449\pi$
$384$		0			0
$385$	5.58864	+	10.7363i	0.284823	+	0.547171i
$386$		0			0
$387$	6.40958	−	4.65683i	0.325817	−	0.236720i
$388$		0			0
$389$	1.68752	−	5.19366i	0.0855608	−	0.263329i	−0.899118	−	0.437706i	$-0.855791\pi$
$389$	1.68752	−	5.19366i	0.0855608	−	0.263329i	0.984679	+	0.174377i	$0.0557911\pi$
$390$		0			0
$391$	3.47116	+	2.52195i	0.175544	+	0.127540i
$392$		0			0
$393$	1.25225	+	3.85403i	0.0631677	+	0.194410i
$394$		0			0
$395$	−13.8661			−0.697679
$396$		0			0
$397$	−6.43455			−0.322941			−0.161470	−	0.986878i	$-0.551624\pi$
$397$	−6.43455			−0.322941			−0.161470	+	0.986878i	$0.551624\pi$
$398$		0			0
$399$	−0.0617358	−	0.190003i	−0.00309066	−	0.00951206i
$400$		0			0
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	0.843741	−	0.536751i	$-0.180348\pi$
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	−0.249750	+	0.968310i	$0.580348\pi$
$402$		0			0
$403$	5.92981	−	18.2501i	0.295385	−	0.909101i
$404$		0			0
$405$	4.95843	−	3.60251i	0.246386	−	0.179010i
$406$		0			0
$407$	29.2058	+	14.5623i	1.44768	+	0.721826i
$408$		0			0
$409$	−3.55625	+	2.58376i	−0.175845	+	0.127759i	−0.672226	−	0.740346i	$-0.734662\pi$
$409$	−3.55625	+	2.58376i	−0.175845	+	0.127759i	0.496381	+	0.868105i	$0.334662\pi$
$410$		0			0
$411$	1.70241	−	5.23948i	0.0839737	−	0.258444i
$412$		0			0
$413$	−25.1211	−	18.2516i	−1.23613	−	0.898101i
$414$		0			0
$415$	−3.28932	−	10.1235i	−0.161466	−	0.496942i
$416$		0			0
$417$	0.296668			0.0145279
$418$		0			0
$419$	−17.8526			−0.872159			−0.436079	−	0.899908i	$-0.643633\pi$
$419$	−17.8526			−0.872159			−0.436079	+	0.899908i	$0.643633\pi$
$420$		0			0
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	0.908090	−	0.418776i	$-0.137541\pi$
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	−0.980810	+	0.194965i	$0.937541\pi$
$422$		0			0
$423$	4.80382	+	3.49018i	0.233570	+	0.169698i
$424$		0			0
$425$	1.14088	−	3.51126i	0.0553407	−	0.170321i
$426$		0			0
$427$	25.0378	−	18.1910i	1.21166	−	0.880324i
$428$		0			0
$429$	3.78740	−	3.85391i	0.182857	−	0.186069i
$430$		0			0
$431$	−20.1234	+	14.6205i	−0.969312	+	0.704247i	−0.955295	−	0.295655i	$-0.904462\pi$
$431$	−20.1234	+	14.6205i	−0.969312	+	0.704247i	−0.0140175	+	0.999902i	$0.504462\pi$
$432$		0			0
$433$	−6.56669	+	20.2102i	−0.315575	+	0.971240i	0.659942	+	0.751316i	$0.270581\pi$
$433$	−6.56669	+	20.2102i	−0.315575	+	0.971240i	−0.975517	+	0.219923i	$0.929419\pi$
$434$		0			0
$435$	3.14450	+	2.28461i	0.150767	+	0.109539i
$436$		0			0
$437$	−0.0341614	−	0.105138i	−0.00163416	−	0.00502943i
$438$		0			0
$439$	15.9119			0.759434			0.379717	−	0.925103i	$-0.376021\pi$
$439$	15.9119			0.759434			0.379717	+	0.925103i	$0.376021\pi$
$440$		0			0
$441$	−16.8621			−0.802958
$442$		0			0
$443$	−8.12332	−	25.0010i	−0.385951	−	1.18783i	−0.935788	−	0.352562i	$-0.885310\pi$
$443$	−8.12332	−	25.0010i	−0.385951	−	1.18783i	0.549838	−	0.835272i	$-0.314690\pi$
$444$		0			0
$445$	−9.83859	−	7.14815i	−0.466394	−	0.338855i
$446$		0			0
$447$	1.45112	−	4.46609i	0.0686356	−	0.211239i
$448$		0			0
$449$	6.62554	−	4.81373i	0.312678	−	0.227174i	−0.420366	−	0.907354i	$-0.638098\pi$
$449$	6.62554	−	4.81373i	0.312678	−	0.227174i	0.733045	+	0.680180i	$0.238098\pi$
$450$		0			0
$451$	27.2102	−	4.55278i	1.28128	−	0.214382i
$452$		0			0
$453$	−0.903337	+	0.656313i	−0.0424425	+	0.0308363i
$454$		0			0
$455$	3.19256	−	9.82567i	0.149669	−	0.460635i
$456$		0			0
$457$	−9.64056	−	7.00428i	−0.450966	−	0.327646i	0.339011	−	0.940782i	$-0.389908\pi$
$457$	−9.64056	−	7.00428i	−0.450966	−	0.327646i	−0.789977	+	0.613136i	$0.789908\pi$
$458$		0			0
$459$	3.72195	+	11.4550i	0.173726	+	0.534673i
$460$		0			0
$461$	6.96172			0.324240			0.162120	−	0.986771i	$-0.448167\pi$
$461$	6.96172			0.324240			0.162120	+	0.986771i	$0.448167\pi$
$462$		0			0
$463$	−12.4762			−0.579817			−0.289909	−	0.957054i	$-0.593625\pi$
$463$	−12.4762			−0.579817			−0.289909	+	0.957054i	$0.593625\pi$
$464$		0			0
$465$	−1.20545	−	3.70998i	−0.0559012	−	0.172046i
$466$		0			0
$467$	−4.97235	−	3.61263i	−0.230093	−	0.167172i	0.466765	−	0.884381i	$-0.345419\pi$
$467$	−4.97235	−	3.61263i	−0.230093	−	0.167172i	−0.696858	+	0.717209i	$0.745419\pi$
$468$		0			0
$469$	15.1288	−	46.5618i	0.698585	−	2.15002i
$470$		0			0
$471$	9.90505	−	7.19644i	0.456401	−	0.331594i
$472$		0			0
$473$	−1.45552	+	9.73762i	−0.0669250	+	0.447736i
$474$		0			0
$475$	−0.0769572	+	0.0559127i	−0.00353104	+	0.00256545i
$476$		0			0
$477$	−2.46911	+	7.59915i	−0.113053	+	0.347941i
$478$		0			0
$479$	17.9555	+	13.0454i	0.820406	+	0.596060i	0.916829	−	0.399281i	$-0.130740\pi$
$479$	17.9555	+	13.0454i	0.820406	+	0.596060i	−0.0964228	+	0.995340i	$0.530740\pi$
$480$		0			0
$481$	−8.60798	−	26.4926i	−0.392490	−	1.20796i
$482$		0			0
$483$	2.44076			0.111058
$484$		0			0
$485$	4.33133			0.196675
$486$		0			0
$487$	10.5778	+	32.5553i	0.479328	+	1.47522i	0.840030	+	0.542539i	$0.182537\pi$
$487$	10.5778	+	32.5553i	0.479328	+	1.47522i	−0.360702	+	0.932681i	$0.617463\pi$
$488$		0			0
$489$	7.44047	+	5.40582i	0.336470	+	0.244460i
$490$		0			0
$491$	5.25197	−	16.1639i	0.237018	−	0.729467i	−0.759829	−	0.650123i	$-0.774717\pi$
$491$	5.25197	−	16.1639i	0.237018	−	0.729467i	0.996847	−	0.0793441i	$-0.0252826\pi$
$492$		0			0
$493$	20.1729	−	14.6565i	0.908541	−	0.660094i
$494$		0			0
$495$	−1.30852	+	8.75418i	−0.0588138	+	0.393471i
$496$		0			0
$497$	24.5144	−	17.8107i	1.09962	−	0.798920i
$498$		0			0
$499$	−1.61599	+	4.97352i	−0.0723418	+	0.222645i	−0.980690	−	0.195570i	$-0.937344\pi$
$499$	−1.61599	+	4.97352i	−0.0723418	+	0.222645i	0.908348	+	0.418215i	$0.137344\pi$
$500$		0			0
$501$	−8.24504	−	5.99037i	−0.368361	−	0.267630i
$502$		0			0
$503$	−12.9617	−	39.8919i	−0.577931	−	1.77869i	−0.625973	−	0.779845i	$-0.715298\pi$
$503$	−12.9617	−	39.8919i	−0.577931	−	1.77869i	0.0480416	−	0.998845i	$-0.484702\pi$
$504$		0			0
$505$	−9.90570			−0.440798
$506$		0			0
$507$	2.86923			0.127427
$508$		0			0
$509$	6.29399	+	19.3709i	0.278976	+	0.858601i	0.988140	+	0.153557i	$0.0490728\pi$
$509$	6.29399	+	19.3709i	0.278976	+	0.858601i	−0.709163	+	0.705044i	$0.750927\pi$
$510$		0			0
$511$	3.89731	+	2.83156i	0.172407	+	0.125261i
$512$		0			0
$513$	0.0958972	−	0.295141i	0.00423396	−	0.0130308i
$514$		0			0
$515$	−3.28939	+	2.38988i	−0.144948	+	0.105311i
$516$		0			0
$517$	−7.27801	+	1.21775i	−0.320086	+	0.0535566i
$518$		0			0
$519$	7.39602	−	5.37352i	0.324649	−	0.235872i
$520$		0			0
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	−0.803958	−	0.594686i	$-0.797276\pi$
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	0.999963	−	0.00855656i	$-0.00272367\pi$
$522$		0			0
$523$	9.02873	+	6.55975i	0.394799	+	0.286838i	0.767419	−	0.641146i	$-0.221541\pi$
$523$	9.02873	+	6.55975i	0.394799	+	0.286838i	−0.372620	+	0.927984i	$0.621541\pi$
$524$		0			0
$525$	−0.649001	−	1.99742i	−0.0283247	−	0.0871746i
$526$		0			0
$527$	−25.0254			−1.09013
$528$		0			0
$529$	−21.6494			−0.941279
$530$		0			0
$531$	−7.01710	−	21.5964i	−0.304516	−	0.937205i
$532$		0			0
$533$	−19.0511	−	13.8415i	−0.825197	−	0.599540i
$534$		0			0
$535$	0.599053	−	1.84369i	0.0258993	−	0.0797099i
$536$		0			0
$537$	7.85954	−	5.71029i	0.339164	−	0.246417i
$538$		0			0
$539$	14.6880	−	14.9459i	0.632658	−	0.643768i
$540$		0			0
$541$	−8.64094	+	6.27801i	−0.371503	+	0.269913i	−0.757834	−	0.652447i	$-0.773742\pi$
$541$	−8.64094	+	6.27801i	−0.371503	+	0.269913i	0.386331	+	0.922360i	$0.373742\pi$
$542$		0			0
$543$	4.28363	−	13.1837i	0.183828	−	0.565765i
$544$		0			0
$545$	4.95655	+	3.60115i	0.212315	+	0.154256i
$546$		0			0
$547$	−0.540038	−	1.66207i	−0.0230904	−	0.0710648i	0.938847	−	0.344334i	$-0.111895\pi$
$547$	−0.540038	−	1.66207i	−0.0230904	−	0.0710648i	−0.961938	+	0.273269i	$0.911895\pi$
$548$		0			0
$549$	22.6325			0.965930
$550$		0			0
$551$	−0.642459			−0.0273697
$552$		0			0
$553$	15.6372	+	48.1264i	0.664962	+	2.04654i
$554$		0			0
$555$	−4.58125	−	3.32847i	−0.194463	−	0.141286i
$556$		0			0
$557$	−6.02100	+	18.5307i	−0.255118	+	0.785173i	0.738688	+	0.674047i	$0.235446\pi$
$557$	−6.02100	+	18.5307i	−0.255118	+	0.785173i	−0.993806	+	0.111126i	$0.964554\pi$
$558$		0			0
$559$	6.79900	−	4.93976i	0.287567	−	0.208930i
$560$		0			0
$561$	−6.30636	−	3.14442i	−0.266255	−	0.132757i
$562$		0			0
$563$	−11.8838	+	8.63407i	−0.500842	+	0.363883i	−0.809338	−	0.587343i	$-0.800174\pi$
$563$	−11.8838	+	8.63407i	−0.500842	+	0.363883i	0.308497	+	0.951225i	$0.400174\pi$
$564$		0			0
$565$	−1.78775	+	5.50212i	−0.0752111	+	0.231476i
$566$		0			0
$567$	−18.0954	−	13.1471i	−0.759934	−	0.552124i
$568$		0			0
$569$	6.15980	+	18.9579i	0.258232	+	0.794758i	0.993176	+	0.116629i	$0.0372088\pi$
$569$	6.15980	+	18.9579i	0.258232	+	0.794758i	−0.734943	+	0.678129i	$0.762791\pi$
$570$		0			0
$571$	−5.24422			−0.219464			−0.109732	−	0.993961i	$-0.534999\pi$
$571$	−5.24422			−0.219464			−0.109732	+	0.993961i	$0.534999\pi$
$572$		0			0
$573$	3.09776			0.129411
$574$		0			0
$575$	−0.359123	−	1.10527i	−0.0149765	−	0.0460928i
$576$		0			0
$577$	−30.4194	−	22.1010i	−1.26637	−	0.920075i	−0.267323	−	0.963607i	$-0.586139\pi$
$577$	−30.4194	−	22.1010i	−1.26637	−	0.920075i	−0.999052	+	0.0435320i	$0.986139\pi$
$578$		0			0
$579$	−3.25158	+	10.0073i	−0.135131	+	0.415891i
$580$		0			0
$581$	−31.4271	+	22.8331i	−1.30382	+	0.947278i
$582$		0			0
$583$	−4.58484	−	8.80789i	−0.189885	−	0.364785i
$584$		0			0
$585$	6.11235	−	4.44088i	0.252714	−	0.183608i
$586$		0			0
$587$	−7.90191	+	24.3196i	−0.326147	+	1.00378i	0.644774	+	0.764373i	$0.276952\pi$
$587$	−7.90191	+	24.3196i	−0.326147	+	1.00378i	−0.970920	+	0.239403i	$0.923048\pi$
$588$		0			0
$589$	0.521644	+	0.378997i	0.0214940	+	0.0156163i
$590$		0			0
$591$	−0.470497	−	1.44804i	−0.0193536	−	0.0595644i
$592$		0			0
$593$	40.2260			1.65188			0.825942	−	0.563754i	$-0.190644\pi$
$593$	40.2260			1.65188			0.825942	+	0.563754i	$0.190644\pi$
$594$		0			0
$595$	−13.4735			−0.552358
$596$		0			0
$597$	1.16092	+	3.57295i	0.0475133	+	0.146231i
$598$		0			0
$599$	3.98843	+	2.89776i	0.162963	+	0.118399i	0.666278	−	0.745704i	$-0.267886\pi$
$599$	3.98843	+	2.89776i	0.162963	+	0.118399i	−0.503315	+	0.864103i	$0.667886\pi$
$600$		0			0
$601$	14.2425	−	43.8338i	0.580963	−	1.78802i	−0.0339497	−	0.999424i	$-0.510809\pi$
$601$	14.2425	−	43.8338i	0.580963	−	1.78802i	0.614912	−	0.788596i	$-0.289191\pi$
$602$		0			0
$603$	28.9651	−	21.0444i	1.17955	−	0.856993i
$604$		0			0
$605$	−6.61956	−	8.78529i	−0.269124	−	0.357173i
$606$		0			0
$607$	−36.5162	+	26.5306i	−1.48215	+	1.07684i	−0.505288	+	0.862951i	$0.668614\pi$
$607$	−36.5162	+	26.5306i	−1.48215	+	1.07684i	−0.976857	+	0.213891i	$0.931386\pi$
$608$		0			0
$609$	4.38328	−	13.4904i	0.177620	−	0.546657i
$610$		0			0
$611$	5.09568	+	3.70223i	0.206149	+	0.149776i
$612$		0			0
$613$	1.46294	+	4.50247i	0.0590877	+	0.181853i	0.976244	−	0.216675i	$-0.0695212\pi$
$613$	1.46294	+	4.50247i	0.0590877	+	0.181853i	−0.917156	+	0.398528i	$0.869521\pi$
$614$		0			0
$615$	−4.78708			−0.193034
$616$		0			0
$617$	17.8468			0.718486			0.359243	−	0.933244i	$-0.383035\pi$
$617$	17.8468			0.718486			0.359243	+	0.933244i	$0.383035\pi$
$618$		0			0
$619$	−0.110304	−	0.339482i	−0.00443351	−	0.0136449i	0.948815	−	0.315832i	$-0.102283\pi$
$619$	−0.110304	−	0.339482i	−0.00443351	−	0.0136449i	−0.953249	+	0.302187i	$0.902283\pi$
$620$		0			0
$621$	3.06726	+	2.22850i	0.123085	+	0.0894264i
$622$		0			0
$623$	−13.7145	+	42.2089i	−0.549461	+	1.69107i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	0.0838329	+	0.161051i	0.00334796	+	0.00643174i
$628$		0			0
$629$	−29.3900	+	21.3531i	−1.17186	+	0.851404i
$630$		0			0
$631$	9.88614	−	30.4264i	0.393561	−	1.21126i	−0.536516	−	0.843890i	$-0.680260\pi$
$631$	9.88614	−	30.4264i	0.393561	−	1.21126i	0.930077	−	0.367366i	$-0.119740\pi$
$632$		0			0
$633$	12.7792	+	9.28466i	0.507929	+	0.369032i
$634$		0			0
$635$	0.753330	+	2.31851i	0.0298950	+	0.0920073i
$636$		0			0
$637$	−17.8866			−0.708693
$638$		0			0
$639$	22.1594			0.876610
$640$		0			0
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	0.957047	−	0.289932i	$-0.0936326\pi$
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	−0.944685	+	0.327979i	$0.893633\pi$
$642$		0			0
$643$	−12.1130	−	8.80057i	−0.477688	−	0.347061i	0.322742	−	0.946487i	$-0.395395\pi$
$643$	−12.1130	−	8.80057i	−0.477688	−	0.347061i	−0.800430	+	0.599426i	$0.795395\pi$
$644$		0			0
$645$	0.527931	−	1.62480i	0.0207873	−	0.0639766i
$646$		0			0
$647$	14.4712	−	10.5139i	0.568920	−	0.413345i	−0.265793	−	0.964030i	$-0.585634\pi$
$647$	14.4712	−	10.5139i	0.568920	−	0.413345i	0.834713	+	0.550686i	$0.185634\pi$
$648$		0			0
$649$	25.2546	+	12.5922i	0.991331	+	0.494287i
$650$		0			0
$651$	−11.5172	+	8.36772i	−0.451394	+	0.327957i
$652$		0			0
$653$	14.1419	−	43.5244i	0.553416	−	1.70324i	−0.146673	−	0.989185i	$-0.546856\pi$
$653$	14.1419	−	43.5244i	0.553416	−	1.70324i	0.700089	−	0.714055i	$-0.253144\pi$
$654$		0			0
$655$	−5.69674	−	4.13892i	−0.222590	−	0.161721i
$656$		0			0
$657$	1.08864	+	3.35049i	0.0424719	+	0.130715i
$658$		0			0
$659$	9.54036			0.371640			0.185820	−	0.982584i	$-0.440506\pi$
$659$	9.54036			0.371640			0.185820	+	0.982584i	$0.440506\pi$
$660$		0			0
$661$	15.7769			0.613651			0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769			0.613651			0.306825	+	0.951766i	$0.400733\pi$
$662$		0			0
$663$	1.85871	+	5.72052i	0.0721863	+	0.222167i
$664$		0			0
$665$	0.280849	+	0.204048i	0.0108908	+	0.00791266i
$666$		0			0
$667$	2.42548	−	7.46486i	0.0939149	−	0.289040i
$668$		0			0
$669$	2.36607	−	1.71905i	0.0914774	−	0.0664622i
$670$		0			0
$671$	−19.7144	+	20.0606i	−0.761065	+	0.774430i
$672$		0			0
$673$	−38.2690	+	27.8041i	−1.47516	+	1.07177i	−0.496086	+	0.868273i	$0.665230\pi$
$673$	−38.2690	+	27.8041i	−1.47516	+	1.07177i	−0.979076	+	0.203494i	$0.934770\pi$
$674$		0			0
$675$	1.00812	−	3.10269i	0.0388027	−	0.119423i
$676$		0			0
$677$	−22.2828	−	16.1894i	−0.856399	−	0.622210i	0.0705039	−	0.997512i	$-0.477539\pi$
$677$	−22.2828	−	16.1894i	−0.856399	−	0.622210i	−0.926903	+	0.375301i	$0.877539\pi$
$678$		0			0
$679$	−4.88457	−	15.0332i	−0.187453	−	0.576920i
$680$		0			0
$681$	2.15223			0.0824736
$682$		0			0
$683$	27.1617			1.03931			0.519656	−	0.854375i	$-0.326060\pi$
$683$	27.1617			1.03931			0.519656	+	0.854375i	$0.326060\pi$
$684$		0			0
$685$	2.95818	+	9.10433i	0.113026	+	0.347859i
$686$		0			0
$687$	12.5354	+	9.10752i	0.478256	+	0.347474i
$688$		0			0
$689$	−2.61913	+	8.06084i	−0.0997808	+	0.307094i
$690$		0			0
$691$	−6.08931	+	4.42414i	−0.231648	+	0.168302i	−0.697554	−	0.716532i	$-0.745728\pi$
$691$	−6.08931	+	4.42414i	−0.231648	+	0.168302i	0.465906	+	0.884834i	$0.345728\pi$
$692$		0			0
$693$	31.8597	−	5.33073i	1.21025	−	0.202498i
$694$		0			0
$695$	−0.417050	+	0.303004i	−0.0158196	+	0.0114936i
$696$		0			0
$697$	−9.49007	+	29.2074i	−0.359462	+	1.10631i
$698$		0			0
$699$	8.52796	+	6.19593i	0.322557	+	0.234351i
$700$		0			0
$701$	−9.83315	−	30.2633i	−0.371393	−	1.14303i	−0.945880	−	0.324516i	$-0.894799\pi$
$701$	−9.83315	−	30.2633i	−0.371393	−	1.14303i	0.574487	−	0.818513i	$-0.305201\pi$
$702$		0			0
$703$	0.936004			0.0353021
$704$		0			0
$705$	1.28042			0.0482234
$706$		0			0
$707$	11.1710	+	34.3807i	0.420127	+	1.29302i
$708$		0			0
$709$	11.6807	+	8.48651i	0.438677	+	0.318718i	0.785109	−	0.619357i	$-0.212607\pi$
$709$	11.6807	+	8.48651i	0.438677	+	0.318718i	−0.346432	+	0.938075i	$0.612607\pi$
$710$		0			0
$711$	−11.4355	+	35.1947i	−0.428863	+	1.31991i
$712$		0			0
$713$	−6.37300	+	4.63026i	−0.238671	+	0.173405i
$714$		0			0
$715$	−1.38803	+	9.28605i	−0.0519092	+	0.347279i
$716$		0			0
$717$	5.10087	−	3.70600i	0.190496	−	0.138403i
$718$		0			0
$719$	−1.67179	+	5.14526i	−0.0623474	+	0.191886i	−0.977378	−	0.211498i	$-0.932166\pi$
$719$	−1.67179	+	5.14526i	−0.0623474	+	0.191886i	0.915031	+	0.403383i	$0.132166\pi$
$720$		0			0
$721$	12.0043	+	8.72166i	0.447065	+	0.324811i
$722$		0			0
$723$	1.77738	+	5.47022i	0.0661016	+	0.203440i
$724$		0			0
$725$	−6.75389			−0.250833
$726$		0			0
$727$	16.7753			0.622161			0.311080	−	0.950384i	$-0.399309\pi$
$727$	16.7753			0.622161			0.311080	+	0.950384i	$0.399309\pi$
$728$		0			0
$729$	−3.31409	−	10.1997i	−0.122744	−	0.377767i
$730$		0			0
$731$	−8.86684	−	6.44213i	−0.327952	−	0.238271i
$732$		0			0
$733$	−4.35252	+	13.3957i	−0.160764	+	0.494781i	−0.998699	−	0.0509889i	$-0.983763\pi$
$733$	−4.35252	+	13.3957i	−0.160764	+	0.494781i	0.837935	+	0.545770i	$0.183763\pi$
$734$		0			0
$735$	−2.94166	+	2.13724i	−0.108505	+	0.0788334i
$736$		0			0
$737$	−6.57756	+	44.0046i	−0.242287	+	1.62093i
$738$		0			0
$739$	−29.4043	+	21.3635i	−1.08165	+	0.785868i	−0.977971	−	0.208743i	$-0.933063\pi$
$739$	−29.4043	+	21.3635i	−1.08165	+	0.785868i	−0.103683	+	0.994610i	$0.533063\pi$
$740$		0			0
$741$	0.0478902	−	0.147391i	0.00175929	−	0.00541454i
$742$		0			0
$743$	−1.58338	−	1.15039i	−0.0580884	−	0.0422037i	0.558362	−	0.829597i	$-0.311430\pi$
$743$	−1.58338	−	1.15039i	−0.0580884	−	0.0422037i	−0.616451	+	0.787394i	$0.711430\pi$
$744$		0			0
$745$	2.52153	+	7.76046i	0.0923815	+	0.284321i
$746$		0			0
$747$	−28.4080			−1.03939
$748$		0			0
$749$	−7.07466			−0.258503
$750$		0			0
$751$	−5.78189	−	17.7948i	−0.210984	−	0.649342i	−0.999414	−	0.0342181i	$-0.989106\pi$
$751$	−5.78189	−	17.7948i	−0.210984	−	0.649342i	0.788430	−	0.615124i	$-0.210894\pi$
$752$		0			0
$753$	−4.49634	−	3.26678i	−0.163856	−	0.119048i
$754$		0			0
$755$	0.599563	−	1.84526i	0.0218203	−	0.0671560i
$756$		0			0
$757$	11.7688	−	8.55054i	0.427744	−	0.310775i	−0.353002	−	0.935623i	$-0.614839\pi$
$757$	11.7688	−	8.55054i	0.427744	−	0.310775i	0.780746	+	0.624848i	$0.214839\pi$
$758$		0			0
$759$	−2.18777	+	0.366056i	−0.0794111	+	0.0132870i
$760$		0			0
$761$	−10.6309	+	7.72383i	−0.385371	+	0.279989i	−0.763556	−	0.645741i	$-0.776548\pi$
$761$	−10.6309	+	7.72383i	−0.385371	+	0.279989i	0.378185	+	0.925730i	$0.376548\pi$
$762$		0			0
$763$	6.90920	−	21.2643i	0.250130	−	0.769820i
$764$		0			0
$765$	−7.97134	−	5.79152i	−0.288204	−	0.209393i
$766$		0			0
$767$	−7.44344	−	22.9085i	−0.268767	−	0.827180i
$768$		0			0
$769$	38.9767			1.40554			0.702768	−	0.711419i	$-0.251947\pi$
$769$	38.9767			1.40554			0.702768	+	0.711419i	$0.251947\pi$
$770$		0			0
$771$	−6.00099			−0.216121
$772$		0			0
$773$	−11.9756	−	36.8571i	−0.430733	−	1.32566i	−0.897397	−	0.441225i	$-0.854544\pi$
$773$	−11.9756	−	36.8571i	−0.430733	−	1.32566i	0.466664	−	0.884435i	$-0.345456\pi$
$774$		0			0
$775$	5.48382	+	3.98423i	0.196985	+	0.143118i
$776$		0			0
$777$	−6.38604	+	19.6542i	−0.229098	+	0.705091i
$778$		0			0
$779$	0.640147	−	0.465094i	0.0229356	−	0.0166637i
$780$		0			0
$781$	−19.3023	+	19.6412i	−0.690689	+	0.702818i
$782$		0			0
$783$	17.8256	−	12.9510i	0.637034	−	0.462832i
$784$		0			0
$785$	−6.57418	+	20.2332i	−0.234642	+	0.722155i
$786$		0			0
$787$	−17.3002	−	12.5693i	−0.616685	−	0.448048i	0.235077	−	0.971977i	$-0.424466\pi$
$787$	−17.3002	−	12.5693i	−0.616685	−	0.448048i	−0.851762	+	0.523929i	$0.824466\pi$
$788$		0			0
$789$	−1.94943	−	5.99971i	−0.0694014	−	0.213595i
$790$		0			0
$791$	21.1128			0.750686
$792$		0			0
$793$	24.0075			0.852533
$794$		0			0
$795$	0.532431	+	1.63866i	0.0188834	+	0.0581171i
$796$		0			0
$797$	1.79970	+	1.30756i	0.0637488	+	0.0463162i	0.619203	−	0.785231i	$-0.287456\pi$
$797$	1.79970	+	1.30756i	0.0637488	+	0.0463162i	−0.555454	+	0.831547i	$0.687456\pi$
$798$		0			0
$799$	2.53834	−	7.81222i	0.0898002	−	0.276377i
$800$		0			0
$801$	−26.2573	+	19.0770i	−0.927756	+	0.674054i
$802$		0			0
$803$	−3.91802	−	1.95356i	−0.138264	−	0.0689398i
$804$		0			0
$805$	−3.43117	+	2.49289i	−0.120933	+	0.0878628i
$806$		0			0
$807$	0.0158888	−	0.0489008i	0.000559314	−	0.00172139i
$808$		0			0
$809$	−17.1254	−	12.4424i	−0.602098	−	0.437450i	0.244525	−	0.969643i	$-0.421368\pi$
$809$	−17.1254	−	12.4424i	−0.602098	−	0.437450i	−0.846623	+	0.532193i	$0.821368\pi$
$810$		0			0
$811$	11.3462	+	34.9201i	0.398420	+	1.22621i	0.926266	+	0.376871i	$0.123000\pi$
$811$	11.3462	+	34.9201i	0.398420	+	1.22621i	−0.527845	+	0.849341i	$0.677000\pi$
$812$		0			0
$813$	−7.71135			−0.270449
$814$		0			0
$815$	−15.9810			−0.559788
$816$		0			0
$817$	0.0872627	+	0.268567i	0.00305294	+	0.00939597i
$818$		0			0
$819$	−22.3065	−	16.2066i	−0.779451	−	0.566305i
$820$		0			0
$821$	−12.2585	+	37.7278i	−0.427825	+	1.31671i	0.472439	+	0.881363i	$0.343374\pi$
$821$	−12.2585	+	37.7278i	−0.427825	+	1.31671i	−0.900264	+	0.435345i	$0.856626\pi$
$822$		0			0
$823$	−37.1568	+	26.9960i	−1.29520	+	0.941021i	−0.999897	−	0.0143810i	$-0.995422\pi$
$823$	−37.1568	+	26.9960i	−1.29520	+	0.941021i	−0.295308	+	0.955402i	$0.595422\pi$
$824$		0			0
$825$	0.881299	+	1.69305i	0.0306829	+	0.0589445i
$826$		0			0
$827$	−32.1139	+	23.3321i	−1.11671	+	0.811337i	−0.983707	−	0.179779i	$-0.942462\pi$
$827$	−32.1139	+	23.3321i	−1.11671	+	0.811337i	−0.133002	+	0.991116i	$0.542462\pi$
$828$		0			0
$829$	2.36578	−	7.28113i	0.0821671	−	0.252884i	−0.901530	−	0.432716i	$-0.857555\pi$
$829$	2.36578	−	7.28113i	0.0821671	−	0.252884i	0.983697	+	0.179832i	$0.0575553\pi$
$830$		0			0
$831$	−1.81889	−	1.32150i	−0.0630966	−	0.0458423i
$832$		0			0
$833$	7.20831	+	22.1849i	0.249753	+	0.768661i
$834$		0			0
$835$	17.7090			0.612846
$836$		0			0
$837$	−22.1135			−0.764354
$838$		0			0
$839$	−8.52536	−	26.2383i	−0.294328	−	0.905848i	−0.983446	−	0.181200i	$-0.942002\pi$
$839$	−8.52536	−	26.2383i	−0.294328	−	0.905848i	0.689118	−	0.724649i	$-0.257998\pi$
$840$		0			0
$841$	−13.4418	−	9.76607i	−0.463512	−	0.336761i
$842$		0			0
$843$	0.273412	−	0.841477i	0.00941683	−	0.0289820i
$844$		0			0
$845$	−4.03351	+	2.93052i	−0.138757	+	0.100813i
$846$		0			0
$847$	−23.0269	+	32.8826i	−0.791213	+	1.12986i
$848$		0			0
$849$	2.51960	−	1.83059i	0.0864724	−	0.0628258i
$850$		0			0
$851$	−3.53370	+	10.8756i	−0.121134	+	0.372811i
$852$		0			0
$853$	−34.0998	−	24.7749i	−1.16755	−	0.848277i	−0.176840	−	0.984240i	$-0.556587\pi$
$853$	−34.0998	−	24.7749i	−1.16755	−	0.848277i	−0.990714	+	0.135962i	$0.956587\pi$
$854$		0			0
$855$	0.0784497	+	0.241443i	0.00268292	+	0.00825719i
$856$		0			0
$857$	−45.0850			−1.54008			−0.770038	−	0.637998i	$-0.779763\pi$
$857$	−45.0850			−1.54008			−0.770038	+	0.637998i	$0.779763\pi$
$858$		0			0
$859$	11.8257			0.403488			0.201744	−	0.979438i	$-0.435339\pi$
$859$	11.8257			0.403488			0.201744	+	0.979438i	$0.435339\pi$
$860$		0			0
$861$	5.39854	+	16.6150i	0.183982	+	0.566237i
$862$		0			0
$863$	22.5484	+	16.3823i	0.767555	+	0.557662i	0.901218	−	0.433365i	$-0.142674\pi$
$863$	22.5484	+	16.3823i	0.767555	+	0.557662i	−0.133663	+	0.991027i	$0.542674\pi$
$864$		0			0
$865$	−4.90888	+	15.1080i	−0.166907	+	0.513687i
$866$		0			0
$867$	−1.56877	+	1.13978i	−0.0532782	+	0.0387089i
$868$		0			0
$869$	−21.2342	−	40.7929i	−0.720323	−	1.38380i
$870$		0			0
$871$	30.7249	−	22.3230i	1.04107	−	0.756384i
$872$		0			0
$873$	3.57207	−	10.9937i	0.120896	−	0.372081i
$874$		0			0
$875$	2.95244	+	2.14507i	0.0998106	+	0.0725167i
$876$		0			0
$877$	−3.53736	−	10.8869i	−0.119448	−	0.367624i	0.873401	−	0.487003i	$-0.161910\pi$
$877$	−3.53736	−	10.8869i	−0.119448	−	0.367624i	−0.992849	+	0.119379i	$0.961910\pi$
$878$		0			0
$879$	−6.57011			−0.221604
$880$		0			0
$881$	47.0037			1.58360			0.791798	−	0.610783i	$-0.209145\pi$
$881$	47.0037			1.58360			0.791798	+	0.610783i	$0.209145\pi$
$882$		0			0
$883$	14.4974	+	44.6185i	0.487877	+	1.50153i	0.827770	+	0.561067i	$0.189609\pi$
$883$	14.4974	+	44.6185i	0.487877	+	1.50153i	−0.339894	+	0.940464i	$0.610391\pi$
$884$		0			0
$885$	−3.96147	−	2.87817i	−0.133163	−	0.0967488i
$886$		0			0
$887$	8.60386	−	26.4800i	0.288889	−	0.889110i	−0.696316	−	0.717735i	$-0.745179\pi$
$887$	8.60386	−	26.4800i	0.288889	−	0.889110i	0.985206	−	0.171375i	$-0.0548210\pi$
$888$		0			0
$889$	7.19754	−	5.22932i	0.241398	−	0.175386i
$890$		0			0
$891$	18.1915	+	9.07048i	0.609439	+	0.303872i
$892$		0			0
$893$	−0.171223	+	0.124401i	−0.00572975	+	0.00416290i
$894$		0			0
$895$	−5.21653	+	16.0548i	−0.174369	+	0.536653i
$896$		0			0
$897$	1.53176	+	1.11289i	0.0511441	+	0.0371584i
$898$		0			0
$899$	14.1469	+	43.5397i	0.471826	+	1.45213i
$900$		0			0
$901$	11.0534			0.368244
$902$		0			0
$903$	−6.23473			−0.207479
$904$		0			0
$905$	7.44341	+	22.9085i	0.247427	+	0.761503i
$906$		0			0
$907$	−23.1567	−	16.8243i	−0.768907	−	0.558643i	0.132723	−	0.991153i	$-0.457628\pi$
$907$	−23.1567	−	16.8243i	−0.768907	−	0.558643i	−0.901629	+	0.432510i	$0.857628\pi$
$908$		0			0
$909$	−8.16930	+	25.1425i	−0.270959	+	0.833925i
$910$		0			0
$911$	4.14883	−	3.01430i	0.137457	−	0.0998682i	−0.516932	−	0.856026i	$-0.672926\pi$
$911$	4.14883	−	3.01430i	0.137457	−	0.0998682i	0.654389	+	0.756158i	$0.272926\pi$
$912$		0			0
$913$	24.7452	−	25.1798i	0.818948	−	0.833330i
$914$		0			0
$915$	3.94832	−	2.86862i	0.130527	−	0.0948338i
$916$		0			0
$917$	−7.94098	+	24.4398i	−0.262234	+	0.807074i
$918$		0			0
$919$	28.5429	+	20.7376i	0.941544	+	0.684072i	0.948792	−	0.315902i	$-0.102307\pi$
$919$	28.5429	+	20.7376i	0.941544	+	0.684072i	−0.00724799	+	0.999974i	$0.502307\pi$
$920$		0			0
$921$	−0.755822	−	2.32618i	−0.0249052	−	0.0766503i
$922$		0			0
$923$	23.5057			0.773699
$924$		0			0
$925$	9.83980			0.323531
$926$		0			0
$927$	3.35318	+	10.3200i	0.110133	+	0.338954i
$928$		0			0
$929$	47.8474	+	34.7632i	1.56982	+	1.14054i	0.927325	+	0.374256i	$0.122102\pi$
$929$	47.8474	+	34.7632i	1.56982	+	1.14054i	0.642498	+	0.766287i	$0.277898\pi$
$930$		0			0
$931$	0.185724	−	0.571601i	0.00608687	−	0.0187335i
$932$		0			0
$933$	7.73775	−	5.62181i	0.253323	−	0.184050i
$934$		0			0
$935$	12.0769	−	2.02070i	0.394958	−	0.0660841i
$936$		0			0
$937$	−11.6843	+	8.48911i	−0.381708	+	0.277327i	−0.762049	−	0.647519i	$-0.775807\pi$
$937$	−11.6843	+	8.48911i	−0.381708	+	0.277327i	0.380341	+	0.924846i	$0.375807\pi$
$938$		0			0
$939$	4.72637	−	14.5463i	0.154239	−	0.474700i
$940$		0			0
$941$	15.0955	+	10.9675i	0.492100	+	0.357532i	0.805991	−	0.591927i	$-0.201633\pi$
$941$	15.0955	+	10.9675i	0.492100	+	0.357532i	−0.313891	+	0.949459i	$0.601633\pi$
$942$		0			0
$943$	2.98727	+	9.19386i	0.0972788	+	0.299393i
$944$		0			0
$945$	−11.9057			−0.387292
$946$		0			0
$947$	0.991391			0.0322159			0.0161079	−	0.999870i	$-0.494872\pi$
$947$	0.991391			0.0322159			0.0161079	+	0.999870i	$0.494872\pi$
$948$		0			0
$949$	1.15478	+	3.55405i	0.0374858	+	0.115369i
$950$		0			0
$951$	2.69896	+	1.96091i	0.0875198	+	0.0635869i
$952$		0			0
$953$	−2.55373	+	7.85957i	−0.0827234	+	0.254597i	−0.983860	−	0.178938i	$-0.942734\pi$
$953$	−2.55373	+	7.85957i	−0.0827234	+	0.254597i	0.901137	+	0.433535i	$0.142734\pi$
$954$		0			0
$955$	−4.35477	+	3.16393i	−0.140917	+	0.102382i
$956$		0			0
$957$	−1.90572	+	12.7495i	−0.0616031	+	0.412132i
$958$		0			0
$959$	28.2633	−	20.5345i	0.912669	−	0.663093i
$960$		0			0
$961$	4.61867	−	14.2148i	0.148989	−	0.458542i
$962$		0			0
$963$	−4.18560	−	3.04102i	−0.134879	−	0.0979954i
$964$		0			0
$965$	−5.65008	−	17.3892i	−0.181883	−	0.559777i
$966$		0			0
$967$	−7.36029			−0.236691			−0.118345	−	0.992972i	$-0.537759\pi$
$967$	−7.36029			−0.236691			−0.118345	+	0.992972i	$0.537759\pi$
$968$		0			0
$969$	−0.202110			−0.00649271
$970$		0			0
$971$	1.53808	+	4.73372i	0.0493593	+	0.151912i	0.972698	−	0.232074i	$-0.0745511\pi$
$971$	1.53808	+	4.73372i	0.0493593	+	0.151912i	−0.923339	+	0.383986i	$0.874551\pi$
$972$		0			0
$973$	1.52199	+	1.10579i	0.0487927	+	0.0354500i
$974$		0			0
$975$	0.503449	−	1.54946i	0.0161233	−	0.0496223i
$976$		0			0
$977$	−8.36266	+	6.07583i	−0.267545	+	0.194383i	−0.713467	−	0.700689i	$-0.752876\pi$
$977$	−8.36266	+	6.07583i	−0.267545	+	0.194383i	0.445922	+	0.895072i	$0.352876\pi$
$978$		0			0
$979$	5.96266	−	39.8908i	0.190567	−	1.27492i
$980$		0			0
$981$	13.2281	−	9.61077i	0.422340	−	0.306848i
$982$		0			0
$983$	8.98045	−	27.6390i	0.286432	−	0.881547i	−0.699534	−	0.714599i	$-0.746609\pi$
$983$	8.98045	−	27.6390i	0.286432	−	0.881547i	0.985966	−	0.166947i	$-0.0533910\pi$
$984$		0			0
$985$	2.14038	+	1.55508i	0.0681983	+	0.0495490i
$986$		0			0
$987$	−1.44397	−	4.44408i	−0.0459620	−	0.141456i
$988$		0			0
$989$	−3.44997			−0.109703
$990$		0			0
$991$	−7.70381			−0.244719			−0.122360	−	0.992486i	$-0.539046\pi$
$991$	−7.70381			−0.244719			−0.122360	+	0.992486i	$0.539046\pi$
$992$		0			0
$993$	−2.29818	−	7.07308i	−0.0729307	−	0.224458i
$994$		0			0
$995$	−5.28126	−	3.83706i	−0.167427	−	0.121643i
$996$		0			0
$997$	−0.885080	+	2.72400i	−0.0280308	+	0.0862698i	−0.964093	−	0.265564i	$-0.914442\pi$
$997$	−0.885080	+	2.72400i	−0.0280308	+	0.0862698i	0.936062	+	0.351834i	$0.114442\pi$
$998$		0			0
$999$	−25.9702	+	18.8685i	−0.821661	+	0.596972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.h.641.1		8
4.3	odd	2		55.2.g.b.36.1	yes	8
11.2	odd	10		9680.2.a.cm.1.2		4
11.4	even	5	inner	880.2.bo.h.81.1		8
11.9	even	5		9680.2.a.cn.1.2		4
12.11	even	2		495.2.n.e.91.2		8
20.3	even	4		275.2.z.a.124.4		16
20.7	even	4		275.2.z.a.124.1		16
20.19	odd	2		275.2.h.a.201.2		8
44.3	odd	10		605.2.g.m.511.2		8
44.7	even	10		605.2.g.k.81.2		8
44.15	odd	10		55.2.g.b.26.1	✓	8
44.19	even	10		605.2.g.e.511.1		8
44.27	odd	10		605.2.g.m.251.2		8
44.31	odd	10		605.2.a.j.1.4		4
44.35	even	10		605.2.a.k.1.1		4
44.39	even	10		605.2.g.e.251.1		8
44.43	even	2		605.2.g.k.366.2		8
132.35	odd	10		5445.2.a.bi.1.4		4
132.59	even	10		495.2.n.e.136.2		8
132.119	even	10		5445.2.a.bp.1.1		4
220.59	odd	10		275.2.h.a.26.2		8
220.79	even	10		3025.2.a.w.1.4		4
220.103	even	20		275.2.z.a.224.1		16
220.119	odd	10		3025.2.a.bd.1.1		4
220.147	even	20		275.2.z.a.224.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	44.15	odd	10
55.2.g.b.36.1	yes	8	4.3	odd	2
275.2.h.a.26.2		8	220.59	odd	10
275.2.h.a.201.2		8	20.19	odd	2
275.2.z.a.124.1		16	20.7	even	4
275.2.z.a.124.4		16	20.3	even	4
275.2.z.a.224.1		16	220.103	even	20
275.2.z.a.224.4		16	220.147	even	20
495.2.n.e.91.2		8	12.11	even	2
495.2.n.e.136.2		8	132.59	even	10
605.2.a.j.1.4		4	44.31	odd	10
605.2.a.k.1.1		4	44.35	even	10
605.2.g.e.251.1		8	44.39	even	10
605.2.g.e.511.1		8	44.19	even	10
605.2.g.k.81.2		8	44.7	even	10
605.2.g.k.366.2		8	44.43	even	2
605.2.g.m.251.2		8	44.27	odd	10
605.2.g.m.511.2		8	44.3	odd	10
880.2.bo.h.81.1		8	11.4	even	5	inner
880.2.bo.h.641.1		8	1.1	even	1	trivial
3025.2.a.w.1.4		4	220.79	even	10
3025.2.a.bd.1.1		4	220.119	odd	10
5445.2.a.bi.1.4		4	132.35	odd	10
5445.2.a.bp.1.1		4	132.119	even	10
9680.2.a.cm.1.2		4	11.2	odd	10
9680.2.a.cn.1.2		4	11.9	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.177837 - 0.547326i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.12773 - 3.47080i) q^{7} +(2.15911 - 1.56869i) q^{9} +O(q^{10})\)	\(q+(-0.177837 - 0.547326i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.12773 - 3.47080i) q^{7} +(2.15911 - 1.56869i) q^{9} +(-0.490303 + 3.28018i) q^{11} +(2.29029 - 1.66399i) q^{13} +(0.177837 - 0.547326i) q^{15} +(-2.98685 - 2.17008i) q^{17} +(0.0293950 + 0.0904686i) q^{19} -2.10021 q^{21} -1.16215 q^{23} +(0.309017 + 0.951057i) q^{25} +(-2.63930 - 1.91757i) q^{27} +(-2.08707 + 6.42333i) q^{29} +(5.48382 - 3.98423i) q^{31} +(1.88253 - 0.314983i) q^{33} +(2.95244 - 2.14507i) q^{35} +(3.04066 - 9.35820i) q^{37} +(-1.31805 - 0.957617i) q^{39} +(-2.57047 - 7.91110i) q^{41} +2.96862 q^{43} +2.66881 q^{45} +(0.687534 + 2.11601i) q^{47} +(-5.11155 - 3.71376i) q^{49} +(-0.656567 + 2.02070i) q^{51} +(-2.42214 + 1.75979i) q^{53} +(-2.32471 + 2.36553i) q^{55} +(0.0442883 - 0.0321774i) q^{57} +(2.62930 - 8.09216i) q^{59} +(6.86076 + 4.98464i) q^{61} +(-3.00970 - 9.26289i) q^{63} +2.83095 q^{65} +13.4153 q^{67} +(0.206673 + 0.636074i) q^{69} +(6.71734 + 4.88043i) q^{71} +(-0.407912 + 1.25542i) q^{73} +(0.465584 - 0.338266i) q^{75} +(10.8319 + 5.40091i) q^{77} +(-11.2179 + 8.15028i) q^{79} +(1.89395 - 5.82899i) q^{81} +(-8.61155 - 6.25666i) q^{83} +(-1.14088 - 3.51126i) q^{85} +3.88682 q^{87} -12.1612 q^{89} +(-3.19256 - 9.82567i) q^{91} +(-3.15590 - 2.29290i) q^{93} +(-0.0293950 + 0.0904686i) q^{95} +(3.50412 - 2.54589i) q^{97} +(4.08696 + 7.85141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9	\( 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9} - 3 q^{11} - 2 q^{13} - 5 q^{15} - 13 q^{17} - 15 q^{19} - 20 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - 9 q^{29} + 10 q^{31} + 5 q^{33} + 4 q^{35} + 24 q^{37} - 21 q^{39} + 8 q^{41} + 38 q^{43} + q^{49} - q^{51} + 13 q^{53} - 7 q^{55} - 45 q^{57} + 27 q^{59} + 6 q^{61} - 25 q^{63} + 2 q^{65} + 38 q^{67} - q^{69} + 20 q^{71} + 13 q^{73} - 5 q^{75} + 34 q^{77} - 37 q^{79} + 8 q^{81} - 27 q^{83} - 12 q^{85} - 38 q^{87} - 16 q^{89} - 44 q^{91} - 35 q^{93} + 15 q^{95} + 24 q^{97} + 20 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9 - 3 * q^11 - 2 * q^13 - 5 * q^15 - 13 * q^17 - 15 * q^19 - 20 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - 9 * q^29 + 10 * q^31 + 5 * q^33 + 4 * q^35 + 24 * q^37 - 21 * q^39 + 8 * q^41 + 38 * q^43 + q^49 - q^51 + 13 * q^53 - 7 * q^55 - 45 * q^57 + 27 * q^59 + 6 * q^61 - 25 * q^63 + 2 * q^65 + 38 * q^67 - q^69 + 20 * q^71 + 13 * q^73 - 5 * q^75 + 34 * q^77 - 37 * q^79 + 8 * q^81 - 27 * q^83 - 12 * q^85 - 38 * q^87 - 16 * q^89 - 44 * q^91 - 35 * q^93 + 15 * q^95 + 24 * q^97 + 20 * q^99

Introduction

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