LMFDB - Embedded newform 352.2.w.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(49,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("352.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.w (of order $10$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	352.113
Dual form			352.2.w.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.32812 + 0.756451i) q^{3} +(0.117836 - 0.162187i) q^{5} +(0.725001 - 2.23132i) q^{7} +(2.42086 - 1.75886i) q^{9} +(1.47592 + 2.97013i) q^{11} +(-0.959026 - 1.31999i) q^{13} +(-0.151649 + 0.466727i) q^{15} +(2.69920 + 1.96108i) q^{17} +(4.68224 - 1.52135i) q^{19} +5.74321i q^{21} +9.25109 q^{23} +(1.53267 + 4.71706i) q^{25} +(0.0110111 - 0.0151554i) q^{27} +(5.88863 + 1.91333i) q^{29} +(-6.68182 + 4.85463i) q^{31} +(-5.68286 - 5.79835i) q^{33} +(-0.276461 - 0.380516i) q^{35} +(-1.21740 - 0.395559i) q^{37} +(3.23123 + 2.34763i) q^{39} +(-1.86354 - 5.73540i) q^{41} -2.47184i q^{43} -0.599888i q^{45} +(-1.47060 - 4.52605i) q^{47} +(1.20994 + 0.879070i) q^{49} +(-7.76750 - 2.52381i) q^{51} +(-5.14997 - 7.08833i) q^{53} +(0.655632 + 0.110613i) q^{55} +(-9.74997 + 7.08377i) q^{57} +(1.81173 + 0.588668i) q^{59} +(3.75888 - 5.17366i) q^{61} +(-2.16946 - 6.67690i) q^{63} -0.327092 q^{65} +8.27349i q^{67} +(-21.5376 + 6.99800i) q^{69} +(-1.00994 - 0.733765i) q^{71} +(2.13073 - 6.55770i) q^{73} +(-7.13645 - 9.82248i) q^{75} +(7.69737 - 1.13990i) q^{77} +(-11.8293 + 8.59451i) q^{79} +(-2.78823 + 8.58129i) q^{81} +(5.50905 - 7.58255i) q^{83} +(0.636123 - 0.206689i) q^{85} -15.1568 q^{87} +5.11129 q^{89} +(-3.64061 + 1.18291i) q^{91} +(11.8838 - 16.3566i) q^{93} +(0.304992 - 0.938668i) q^{95} +(-0.242496 + 0.176183i) q^{97} +(8.79702 + 4.59434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{7} + 18 q^{15} - 6 q^{17} + 8 q^{23} - 4 q^{25} + 6 q^{31} - 10 q^{33} + 34 q^{39} - 14 q^{41} + 6 q^{47} - 4 q^{49} + 2 q^{55} - 26 q^{57} - 60 q^{63} - 36 q^{65} - 22 q^{71} - 6 q^{73} - 74 q^{79}+ \cdots + 10 q^{97}+O(q^{100}) $ 40 * q + 10 * q^7 + 18 * q^15 - 6 * q^17 + 8 * q^23 - 4 * q^25 + 6 * q^31 - 10 * q^33 + 34 * q^39 - 14 * q^41 + 6 * q^47 - 4 * q^49 + 2 * q^55 - 26 * q^57 - 60 * q^63 - 36 * q^65 - 22 * q^71 - 6 * q^73 - 74 * q^79 - 4 * q^81 - 68 * q^87 - 16 * q^89 - 66 * q^95 + 10 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.32812	+	0.756451i	−1.34414	+	0.436737i	−0.890717	−	0.454559i	$-0.849797\pi$
$3$	−2.32812	+	0.756451i	−1.34414	+	0.436737i	−0.453422	+	0.891296i	$0.649797\pi$
$4$		0			0
$5$	0.117836	−	0.162187i	0.0526977	−	0.0725322i	−0.781855	−	0.623460i	$-0.785726\pi$
$5$	0.117836	−	0.162187i	0.0526977	−	0.0725322i	0.834553	+	0.550928i	$0.185726\pi$
$6$		0			0
$7$	0.725001	−	2.23132i	0.274025	−	0.843361i	−0.715451	−	0.698663i	$-0.753779\pi$
$7$	0.725001	−	2.23132i	0.274025	−	0.843361i	0.989476	−	0.144699i	$-0.0462212\pi$
$8$		0			0
$9$	2.42086	−	1.75886i	0.806953	−	0.586286i
$10$		0			0
$11$	1.47592	+	2.97013i	0.445005	+	0.895528i
$11$	1.47592	+	2.97013i	0.445005	+	0.895528i
$12$		0			0
$13$	−0.959026	−	1.31999i	−0.265986	−	0.366098i	0.655044	−	0.755591i	$-0.272650\pi$
$13$	−0.959026	−	1.31999i	−0.265986	−	0.366098i	−0.921029	+	0.389493i	$0.872650\pi$
$14$		0			0
$15$	−0.151649	+	0.466727i	−0.0391556	+	0.120508i
$16$		0			0
$17$	2.69920	+	1.96108i	0.654651	+	0.475632i	0.864852	−	0.502026i	$-0.167412\pi$
$17$	2.69920	+	1.96108i	0.654651	+	0.475632i	−0.210201	+	0.977658i	$0.567412\pi$
$18$		0			0
$19$	4.68224	−	1.52135i	1.07418	−	0.349022i	0.282065	−	0.959395i	$-0.408981\pi$
$19$	4.68224	−	1.52135i	1.07418	−	0.349022i	0.792114	+	0.610373i	$0.208981\pi$
$20$		0			0
$21$			5.74321i			1.25327i
$22$		0			0
$23$	9.25109			1.92899			0.964493	−	0.264108i	$-0.0850776\pi$
$23$	9.25109			1.92899			0.964493	+	0.264108i	$0.0850776\pi$
$24$		0			0
$25$	1.53267	+	4.71706i	0.306533	+	0.943412i
$26$		0			0
$27$	0.0110111	−	0.0151554i	0.00211908	−	0.00291667i
$28$		0			0
$29$	5.88863	+	1.91333i	1.09349	+	0.355297i	0.799595	−	0.600540i	$-0.205048\pi$
$29$	5.88863	+	1.91333i	1.09349	+	0.355297i	0.293897	+	0.955837i	$0.405048\pi$
$30$		0			0
$31$	−6.68182	+	4.85463i	−1.20009	+	0.871917i	−0.994294	−	0.106678i	$-0.965979\pi$
$31$	−6.68182	+	4.85463i	−1.20009	+	0.871917i	−0.205797	+	0.978595i	$0.565979\pi$
$32$		0			0
$33$	−5.68286	−	5.79835i	−0.989259	−	1.00936i
$34$		0			0
$35$	−0.276461	−	0.380516i	−0.0467304	−	0.0643189i
$36$		0			0
$37$	−1.21740	−	0.395559i	−0.200140	−	0.0650295i	0.207232	−	0.978292i	$-0.433555\pi$
$37$	−1.21740	−	0.395559i	−0.200140	−	0.0650295i	−0.407372	+	0.913262i	$0.633555\pi$
$38$		0			0
$39$	3.23123	+	2.34763i	0.517411	+	0.375921i
$40$		0			0
$41$	−1.86354	−	5.73540i	−0.291037	−	0.895718i	−0.984524	−	0.175250i	$-0.943927\pi$
$41$	−1.86354	−	5.73540i	−0.291037	−	0.895718i	0.693487	−	0.720469i	$-0.256073\pi$
$42$		0			0
$43$		−	2.47184i		−	0.376952i	−0.982078	−	0.188476i	$-0.939645\pi$
$43$		−	2.47184i		−	0.376952i	0.982078	−	0.188476i	$-0.0603549\pi$
$44$		0			0
$45$		−	0.599888i		−	0.0894261i
$46$		0			0
$47$	−1.47060	−	4.52605i	−0.214509	−	0.660192i	−0.999188	−	0.0402894i	$-0.987172\pi$
$47$	−1.47060	−	4.52605i	−0.214509	−	0.660192i	0.784679	−	0.619903i	$-0.212828\pi$
$48$		0			0
$49$	1.20994	+	0.879070i	0.172848	+	0.125581i
$50$		0			0
$51$	−7.76750	−	2.52381i	−1.08767	−	0.353405i
$52$		0			0
$53$	−5.14997	−	7.08833i	−0.707403	−	0.973657i	−0.999849	−	0.0173746i	$-0.994469\pi$
$53$	−5.14997	−	7.08833i	−0.707403	−	0.973657i	0.292446	−	0.956282i	$-0.405531\pi$
$54$		0			0
$55$	0.655632	+	0.110613i	0.0884054	+	0.0149151i
$56$		0			0
$57$	−9.74997	+	7.08377i	−1.29142	+	0.938268i
$58$		0			0
$59$	1.81173	+	0.588668i	0.235868	+	0.0766381i	0.424566	−	0.905397i	$-0.360427\pi$
$59$	1.81173	+	0.588668i	0.235868	+	0.0766381i	−0.188698	+	0.982035i	$0.560427\pi$
$60$		0			0
$61$	3.75888	−	5.17366i	0.481276	−	0.662419i	−0.497474	−	0.867479i	$-0.665739\pi$
$61$	3.75888	−	5.17366i	0.481276	−	0.662419i	0.978749	+	0.205060i	$0.0657389\pi$
$62$		0			0
$63$	−2.16946	−	6.67690i	−0.273326	−	0.841210i
$64$		0			0
$65$	−0.327092			−0.0405708
$66$		0			0
$67$			8.27349i			1.01077i	0.862895	+	0.505384i	$0.168649\pi$
$67$			8.27349i			1.01077i	−0.862895	+	0.505384i	$0.831351\pi$
$68$		0			0
$69$	−21.5376	+	6.99800i	−2.59283	+	0.842460i
$70$		0			0
$71$	−1.00994	−	0.733765i	−0.119858	−	0.0870819i	0.526241	−	0.850335i	$-0.323601\pi$
$71$	−1.00994	−	0.733765i	−0.119858	−	0.0870819i	−0.646099	+	0.763253i	$0.723601\pi$
$72$		0			0
$73$	2.13073	−	6.55770i	0.249383	−	0.767521i	−0.745502	−	0.666503i	$-0.767790\pi$
$73$	2.13073	−	6.55770i	0.249383	−	0.767521i	0.994885	−	0.101017i	$-0.0322098\pi$
$74$		0			0
$75$	−7.13645	−	9.82248i	−0.824046	−	1.13420i
$76$		0			0
$77$	7.69737	−	1.13990i	0.877196	−	0.129904i
$78$		0			0
$79$	−11.8293	+	8.59451i	−1.33090	+	0.966958i	−0.331177	+	0.943569i	$0.607446\pi$
$79$	−11.8293	+	8.59451i	−1.33090	+	0.966958i	−0.999726	+	0.0233897i	$0.992554\pi$
$80$		0			0
$81$	−2.78823	+	8.58129i	−0.309803	+	0.953476i
$82$		0			0
$83$	5.50905	−	7.58255i	0.604697	−	0.832293i	−0.391432	−	0.920207i	$-0.628020\pi$
$83$	5.50905	−	7.58255i	0.604697	−	0.832293i	0.996128	+	0.0879138i	$0.0280200\pi$
$84$		0			0
$85$	0.636123	−	0.206689i	0.0689973	−	0.0224186i
$86$		0			0
$87$	−15.1568			−1.62498
$88$		0			0
$89$	5.11129			0.541795			0.270898	−	0.962608i	$-0.412680\pi$
$89$	5.11129			0.541795			0.270898	+	0.962608i	$0.412680\pi$
$90$		0			0
$91$	−3.64061	+	1.18291i	−0.381640	+	0.124002i
$92$		0			0
$93$	11.8838	−	16.3566i	1.23229	−	1.69610i
$94$		0			0
$95$	0.304992	−	0.938668i	0.0312915	−	0.0963053i
$96$		0			0
$97$	−0.242496	+	0.176183i	−0.0246217	+	0.0178887i	−0.600028	−	0.799979i	$-0.704844\pi$
$97$	−0.242496	+	0.176183i	−0.0246217	+	0.0178887i	0.575406	+	0.817868i	$0.304844\pi$
$98$		0			0
$99$	8.79702	+	4.59434i	0.884134	+	0.461749i
$100$		0			0
$101$	8.82844	+	12.1513i	0.878462	+	1.20910i	0.976844	+	0.213951i	$0.0686332\pi$
$101$	8.82844	+	12.1513i	0.878462	+	1.20910i	−0.0983822	+	0.995149i	$0.531367\pi$
$102$		0			0
$103$	−0.872910	+	2.68654i	−0.0860104	+	0.264713i	−0.984807	−	0.173653i	$-0.944443\pi$
$103$	−0.872910	+	2.68654i	−0.0860104	+	0.264713i	0.898796	+	0.438366i	$0.144443\pi$
$104$		0			0
$105$	0.931474	+	0.676756i	0.0909026	+	0.0660446i
$106$		0			0
$107$	0.849631	−	0.276062i	0.0821369	−	0.0266879i	−0.267660	−	0.963513i	$-0.586250\pi$
$107$	0.849631	−	0.276062i	0.0821369	−	0.0266879i	0.349797	+	0.936825i	$0.386250\pi$
$108$		0			0
$109$		−	1.35318i		−	0.129611i	−0.997898	−	0.0648057i	$-0.979357\pi$
$109$		−	1.35318i		−	0.129611i	0.997898	−	0.0648057i	$-0.0206428\pi$
$110$		0			0
$111$	3.13348			0.297417
$112$		0			0
$113$	−1.16461	−	3.58429i	−0.109557	−	0.337182i	0.881216	−	0.472714i	$-0.156726\pi$
$113$	−1.16461	−	3.58429i	−0.109557	−	0.337182i	−0.990773	+	0.135532i	$0.956726\pi$
$114$		0			0
$115$	1.09011	−	1.50041i	0.101653	−	0.139914i
$116$		0			0
$117$	−4.64333	−	1.50871i	−0.429276	−	0.139480i
$118$		0			0
$119$	6.33273	−	4.60099i	0.580520	−	0.421772i
$120$		0			0
$121$	−6.64335	+	8.76732i	−0.603940	+	0.797029i
$122$		0			0
$123$	8.67709	+	11.9430i	0.782387	+	1.07686i
$124$		0			0
$125$	1.89896	+	0.617009i	0.169848	+	0.0551870i
$126$		0			0
$127$	5.94849	+	4.32183i	0.527843	+	0.383500i	0.819550	−	0.573007i	$-0.194223\pi$
$127$	5.94849	+	4.32183i	0.527843	+	0.383500i	−0.291707	+	0.956508i	$0.594223\pi$
$128$		0			0
$129$	1.86983	+	5.75474i	0.164629	+	0.506677i
$130$		0			0
$131$			6.85311i			0.598759i	0.954134	+	0.299380i	$0.0967797\pi$
$131$			6.85311i			0.598759i	−0.954134	+	0.299380i	$0.903220\pi$
$132$		0			0
$133$		−	11.5506i		−	1.00156i
$134$		0			0
$135$	−0.00116052	−	0.00357171i	−9.98815e−5	−	0.000307404i
$136$		0			0
$137$	−2.26770	−	1.64758i	−0.193743	−	0.140762i	0.486685	−	0.873578i	$-0.338206\pi$
$137$	−2.26770	−	1.64758i	−0.193743	−	0.140762i	−0.680428	+	0.732815i	$0.738206\pi$
$138$		0			0
$139$	−8.46925	−	2.75183i	−0.718352	−	0.233407i	−0.0730436	−	0.997329i	$-0.523271\pi$
$139$	−8.46925	−	2.75183i	−0.718352	−	0.233407i	−0.645309	+	0.763922i	$0.723271\pi$
$140$		0			0
$141$	6.84747	+	9.42474i	0.576661	+	0.793706i
$142$		0			0
$143$	2.50509	−	4.79662i	0.209486	−	0.401114i
$144$		0			0
$145$	1.00421	−	0.729601i	0.0833950	−	0.0605900i
$146$		0			0
$147$	−3.48185	−	1.13132i	−0.287178	−	0.0933098i
$148$		0			0
$149$	−7.08039	+	9.74532i	−0.580048	+	0.798368i	−0.993701	−	0.112067i	$-0.964253\pi$
$149$	−7.08039	+	9.74532i	−0.580048	+	0.798368i	0.413653	+	0.910435i	$0.364253\pi$
$150$		0			0
$151$	−1.63679	−	5.03752i	−0.133200	−	0.409947i	0.862106	−	0.506728i	$-0.169145\pi$
$151$	−1.63679	−	5.03752i	−0.133200	−	0.409947i	−0.995306	+	0.0967811i	$0.969145\pi$
$152$		0			0
$153$	9.98363			0.807129
$154$		0			0
$155$			1.65575i			0.132993i
$156$		0			0
$157$	−3.75714	+	1.22077i	−0.299853	+	0.0974281i	−0.455080	−	0.890451i	$-0.650389\pi$
$157$	−3.75714	+	1.22077i	−0.299853	+	0.0974281i	0.155227	+	0.987879i	$0.450389\pi$
$158$		0			0
$159$	17.3517	+	12.6068i	1.37608	+	0.999781i
$160$		0			0
$161$	6.70705	−	20.6422i	0.528590	−	1.62683i
$162$		0			0
$163$	−9.43913	−	12.9918i	−0.739330	−	1.01760i	−0.998657	−	0.0518106i	$-0.983501\pi$
$163$	−9.43913	−	12.9918i	−0.739330	−	1.01760i	0.259327	−	0.965790i	$-0.416499\pi$
$164$		0			0
$165$	−1.61006	+	0.238433i	−0.125343	+	0.0185620i
$166$		0			0
$167$	7.50715	−	5.45426i	0.580921	−	0.422064i	−0.258135	−	0.966109i	$-0.583108\pi$
$167$	7.50715	−	5.45426i	0.580921	−	0.422064i	0.839056	+	0.544045i	$0.183108\pi$
$168$		0			0
$169$	3.19459	−	9.83193i	0.245738	−	0.756303i
$170$		0			0
$171$	8.65920	−	11.9184i	0.662186	−	0.911420i
$172$		0			0
$173$	−8.40944	+	2.73239i	−0.639358	+	0.207740i	−0.610716	−	0.791850i	$-0.709118\pi$
$173$	−8.40944	+	2.73239i	−0.639358	+	0.207740i	−0.0286420	+	0.999590i	$0.509118\pi$
$174$		0			0
$175$	11.6365			0.879635
$176$		0			0
$177$	−4.66323			−0.350510
$178$		0			0
$179$	−10.1324	+	3.29223i	−0.757334	+	0.246073i	−0.662134	−	0.749385i	$-0.730349\pi$
$179$	−10.1324	+	3.29223i	−0.757334	+	0.246073i	−0.0952002	+	0.995458i	$0.530349\pi$
$180$		0			0
$181$	−7.88600	+	10.8542i	−0.586162	+	0.806783i	−0.994354	−	0.106113i	$-0.966159\pi$
$181$	−7.88600	+	10.8542i	−0.586162	+	0.806783i	0.408192	+	0.912896i	$0.366159\pi$
$182$		0			0
$183$	−4.83750	+	14.8883i	−0.357598	+	1.10057i
$184$		0			0
$185$	−0.207608	+	0.150836i	−0.0152637	+	0.0110897i
$186$		0			0
$187$	−1.84088	+	10.9113i	−0.134618	+	0.797917i
$188$		0			0
$189$	−0.0258337	−	0.0355570i	−0.00187912	−	0.00258639i
$190$		0			0
$191$	4.57929	−	14.0936i	0.331346	−	1.01978i	−0.637148	−	0.770741i	$-0.719886\pi$
$191$	4.57929	−	14.0936i	0.331346	−	1.01978i	0.968494	−	0.249036i	$-0.0801139\pi$
$192$		0			0
$193$	3.61949	+	2.62972i	0.260537	+	0.189291i	0.710384	−	0.703815i	$-0.248521\pi$
$193$	3.61949	+	2.62972i	0.260537	+	0.189291i	−0.449847	+	0.893106i	$0.648521\pi$
$194$		0			0
$195$	0.761509	−	0.247429i	0.0545328	−	0.0177188i
$196$		0			0
$197$			20.3350i			1.44881i	0.689373	+	0.724406i	$0.257886\pi$
$197$			20.3350i			1.44881i	−0.689373	+	0.724406i	$0.742114\pi$
$198$		0			0
$199$	−10.4142			−0.738245			−0.369122	−	0.929381i	$-0.620342\pi$
$199$	−10.4142			−0.738245			−0.369122	+	0.929381i	$0.620342\pi$
$200$		0			0
$201$	−6.25849	−	19.2616i	−0.441440	−	1.35861i
$202$		0			0
$203$	8.53853	−	11.7523i	0.599287	−	0.824848i
$204$		0			0
$205$	−1.14980	−	0.373592i	−0.0803054	−	0.0260928i
$206$		0			0
$207$	22.3956	−	16.2714i	1.55660	−	1.13094i
$208$		0			0
$209$	11.4292	+	11.6615i	0.790574	+	0.806641i
$210$		0			0
$211$	11.0079	+	15.1511i	0.757817	+	1.04305i	0.997393	+	0.0721675i	$0.0229916\pi$
$211$	11.0079	+	15.1511i	0.757817	+	1.04305i	−0.239576	+	0.970878i	$0.577008\pi$
$212$		0			0
$213$	2.90632	+	0.944320i	0.199138	+	0.0647037i
$214$		0			0
$215$	−0.400901	−	0.291271i	−0.0273412	−	0.0198645i
$216$		0			0
$217$	5.98792	+	18.4289i	0.406486	+	1.25104i
$218$		0			0
$219$			16.8789i			1.14057i
$220$		0			0
$221$		−	5.44363i		−	0.366178i
$222$		0			0
$223$	−4.50465	−	13.8639i	−0.301654	−	0.928394i	−0.980905	−	0.194488i	$-0.937695\pi$
$223$	−4.50465	−	13.8639i	−0.301654	−	0.928394i	0.679251	−	0.733906i	$-0.262305\pi$
$224$		0			0
$225$	12.0070	+	8.72360i	0.800467	+	0.581573i
$226$		0			0
$227$	3.97727	+	1.29229i	0.263981	+	0.0857725i	0.438017	−	0.898967i	$-0.355681\pi$
$227$	3.97727	+	1.29229i	0.263981	+	0.0857725i	−0.174036	+	0.984739i	$0.555681\pi$
$228$		0			0
$229$	−13.6608	−	18.8025i	−0.902733	−	1.24251i	−0.969588	−	0.244743i	$-0.921296\pi$
$229$	−13.6608	−	18.8025i	−0.902733	−	1.24251i	0.0668544	−	0.997763i	$-0.478704\pi$
$230$		0			0
$231$	−17.0581	+	8.47650i	−1.12234	+	0.557713i
$232$		0			0
$233$	11.3120	−	8.21868i	0.741077	−	0.538424i	−0.151971	−	0.988385i	$-0.548562\pi$
$233$	11.3120	−	8.21868i	0.741077	−	0.538424i	0.893048	+	0.449961i	$0.148562\pi$
$234$		0			0
$235$	−0.907356	−	0.294818i	−0.0591894	−	0.0192318i
$236$		0			0
$237$	21.0387	−	28.9573i	1.36661	−	1.88098i
$238$		0			0
$239$	7.39672	+	22.7648i	0.478454	+	1.47253i	0.841242	+	0.540659i	$0.181825\pi$
$239$	7.39672	+	22.7648i	0.478454	+	1.47253i	−0.362788	+	0.931872i	$0.618175\pi$
$240$		0			0
$241$	−26.1842			−1.68667			−0.843336	−	0.537387i	$-0.819412\pi$
$241$	−26.1842			−1.68667			−0.843336	+	0.537387i	$0.819412\pi$
$242$		0			0
$243$		−	22.0312i		−	1.41330i
$244$		0			0
$245$	0.285148	−	0.0926500i	0.0182174	−	0.00591919i
$246$		0			0
$247$	−6.49855	−	4.72147i	−0.413493	−	0.300420i
$248$		0			0
$249$	−7.08988	+	21.8204i	−0.449303	+	1.38281i
$250$		0			0
$251$	11.3303	+	15.5948i	0.715161	+	0.984335i	0.999671	+	0.0256619i	$0.00816933\pi$
$251$	11.3303	+	15.5948i	0.715161	+	0.984335i	−0.284509	+	0.958673i	$0.591831\pi$
$252$		0			0
$253$	13.6538	+	27.4769i	0.858409	+	1.72746i
$254$		0			0
$255$	−1.32462	+	0.962392i	−0.0829509	+	0.0602673i
$256$		0			0
$257$	2.27691	−	7.00760i	0.142030	−	0.437122i	−0.854587	−	0.519308i	$-0.826190\pi$
$257$	2.27691	−	7.00760i	0.142030	−	0.437122i	0.996617	+	0.0821853i	$0.0261899\pi$
$258$		0			0
$259$	−1.76524	+	2.42964i	−0.109687	+	0.150971i
$260$		0			0
$261$	17.6208	−	5.72536i	1.09070	−	0.354391i
$262$		0			0
$263$	−2.69244			−0.166023			−0.0830114	−	0.996549i	$-0.526454\pi$
$263$	−2.69244			−0.166023			−0.0830114	+	0.996549i	$0.526454\pi$
$264$		0			0
$265$	−1.75649			−0.107900
$266$		0			0
$267$	−11.8997	+	3.86644i	−0.728248	+	0.236622i
$268$		0			0
$269$	9.14422	−	12.5859i	0.557533	−	0.767378i	−0.433477	−	0.901164i	$-0.642714\pi$
$269$	9.14422	−	12.5859i	0.557533	−	0.767378i	0.991010	+	0.133786i	$0.0427136\pi$
$270$		0			0
$271$	0.288637	−	0.888332i	0.0175334	−	0.0539623i	−0.941907	−	0.335874i	$-0.890968\pi$
$271$	0.288637	−	0.888332i	0.0175334	−	0.0539623i	0.959440	+	0.281911i	$0.0909684\pi$
$272$		0			0
$273$	7.58096	−	5.50789i	0.458821	−	0.333353i
$274$		0			0
$275$	−11.7482	+	11.5142i	−0.708443	+	0.694332i
$276$		0			0
$277$	7.97055	+	10.9705i	0.478904	+	0.659155i	0.978294	−	0.207223i	$-0.0664424\pi$
$277$	7.97055	+	10.9705i	0.478904	+	0.659155i	−0.499390	+	0.866377i	$0.666442\pi$
$278$		0			0
$279$	−7.63715	+	23.5047i	−0.457224	+	1.40719i
$280$		0			0
$281$	12.5780	+	9.13844i	0.750339	+	0.545153i	0.895932	−	0.444191i	$-0.146509\pi$
$281$	12.5780	+	9.13844i	0.750339	+	0.545153i	−0.145593	+	0.989345i	$0.546509\pi$
$282$		0			0
$283$	−2.22890	+	0.724213i	−0.132494	+	0.0430500i	−0.374514	−	0.927221i	$-0.622190\pi$
$283$	−2.22890	+	0.724213i	−0.132494	+	0.0430500i	0.242019	+	0.970271i	$0.422190\pi$
$284$		0			0
$285$			2.41604i			0.143114i
$286$		0			0
$287$	−14.1486			−0.835166
$288$		0			0
$289$	−1.81347	−	5.58129i	−0.106675	−	0.328311i
$290$		0			0
$291$	0.431284	−	0.593612i	0.0252823	−	0.0347981i
$292$		0			0
$293$	−17.4944	−	5.68428i	−1.02203	−	0.332079i	−0.250398	−	0.968143i	$-0.580562\pi$
$293$	−17.4944	−	5.68428i	−1.02203	−	0.332079i	−0.771637	+	0.636064i	$0.780562\pi$
$294$		0			0
$295$	0.308961	−	0.224474i	0.0179884	−	0.0130694i
$296$		0			0
$297$	0.0612651	+	0.0103362i	0.00355496	+	0.000599765i
$298$		0			0
$299$	−8.87204	−	12.2113i	−0.513083	−	0.706198i
$300$		0			0
$301$	−5.51548	−	1.79209i	−0.317907	−	0.103294i
$302$		0			0
$303$	−29.7455	−	21.6114i	−1.70883	−	1.24154i
$304$		0			0
$305$	−0.396169	−	1.21928i	−0.0226846	−	0.0698160i
$306$		0			0
$307$		−	20.3704i		−	1.16260i	−0.813690	−	0.581299i	$-0.802545\pi$
$307$		−	20.3704i		−	1.16260i	0.813690	−	0.581299i	$-0.197455\pi$
$308$		0			0
$309$		−	6.91490i		−	0.393375i
$310$		0			0
$311$	−6.70833	−	20.6461i	−0.380395	−	1.17073i	−0.939766	−	0.341818i	$-0.888957\pi$
$311$	−6.70833	−	20.6461i	−0.380395	−	1.17073i	0.559372	−	0.828917i	$-0.311043\pi$
$312$		0			0
$313$	−21.7038	−	15.7687i	−1.22677	−	0.891301i	−0.230127	−	0.973161i	$-0.573914\pi$
$313$	−21.7038	−	15.7687i	−1.22677	−	0.891301i	−0.996644	+	0.0818590i	$0.973914\pi$
$314$		0			0
$315$	−1.33855	−	0.434920i	−0.0754185	−	0.0245050i
$316$		0			0
$317$	−2.23951	−	3.08242i	−0.125783	−	0.173126i	0.741481	−	0.670974i	$-0.234124\pi$
$317$	−2.23951	−	3.08242i	−0.125783	−	0.173126i	−0.867264	+	0.497848i	$0.834124\pi$
$318$		0			0
$319$	3.00828	+	20.3139i	0.168431	+	1.13736i
$320$		0			0
$321$	−1.76921	+	1.28541i	−0.0987478	+	0.0717445i
$322$		0			0
$323$	15.6218	+	5.07582i	0.869218	+	0.282426i
$324$		0			0
$325$	4.75659	−	6.54688i	0.263848	−	0.363156i
$326$		0			0
$327$	1.02362	+	3.15037i	0.0566061	+	0.174216i
$328$		0			0
$329$	−11.1653			−0.615562
$330$		0			0
$331$		−	28.2300i		−	1.55166i	−0.630941	−	0.775831i	$-0.717331\pi$
$331$		−	28.2300i		−	1.55166i	0.630941	−	0.775831i	$-0.282669\pi$
$332$		0			0
$333$	−3.64290	+	1.18365i	−0.199630	+	0.0648636i
$334$		0			0
$335$	1.34185	+	0.974912i	0.0733132	+	0.0532652i
$336$		0			0
$337$	−6.34988	+	19.5429i	−0.345900	+	1.06457i	0.615200	+	0.788371i	$0.289075\pi$
$337$	−6.34988	+	19.5429i	−0.345900	+	1.06457i	−0.961100	+	0.276200i	$0.910925\pi$
$338$		0			0
$339$	5.42269	+	7.46369i	0.294520	+	0.405372i
$340$		0			0
$341$	−24.2807	−	12.6809i	−1.31487	−	0.686707i
$342$		0			0
$343$	16.1252	−	11.7157i	0.870681	−	0.632587i
$344$		0			0
$345$	−1.40292	+	4.31774i	−0.0755306	+	0.232459i
$346$		0			0
$347$	−2.21490	+	3.04855i	−0.118902	+	0.163655i	−0.864319	−	0.502944i	$-0.832250\pi$
$347$	−2.21490	+	3.04855i	−0.118902	+	0.163655i	0.745417	+	0.666598i	$0.232250\pi$
$348$		0			0
$349$	−29.9260	+	9.72356i	−1.60190	+	0.520490i	−0.967577	−	0.252575i	$-0.918722\pi$
$349$	−29.9260	+	9.72356i	−1.60190	+	0.520490i	−0.634326	+	0.773065i	$0.718722\pi$
$350$		0			0
$351$	−0.0305649			−0.00163143
$352$		0			0
$353$	−30.7625			−1.63732			−0.818662	−	0.574276i	$-0.805284\pi$
$353$	−30.7625			−1.63732			−0.818662	+	0.574276i	$0.805284\pi$
$354$		0			0
$355$	−0.238014	+	0.0773355i	−0.0126325	+	0.00410454i
$356$		0			0
$357$	−11.2629	+	15.5021i	−0.596096	+	0.820456i
$358$		0			0
$359$	3.84845	−	11.8443i	0.203113	−	0.625118i	−0.796672	−	0.604411i	$-0.793408\pi$
$359$	3.84845	−	11.8443i	0.203113	−	0.625118i	0.999786	−	0.0207068i	$-0.00659164\pi$
$360$		0			0
$361$	4.23752	−	3.07874i	0.223028	−	0.162039i
$362$		0			0
$363$	8.83443	−	25.4367i	0.463688	−	1.33508i
$364$		0			0
$365$	−0.812498	−	1.11831i	−0.0425281	−	0.0585349i
$366$		0			0
$367$	1.43633	−	4.42056i	0.0749757	−	0.230752i	−0.906544	−	0.422110i	$-0.861289\pi$
$367$	1.43633	−	4.42056i	0.0749757	−	0.230752i	0.981520	+	0.191359i	$0.0612894\pi$
$368$		0			0
$369$	−14.5991	−	10.6069i	−0.760000	−	0.552172i
$370$		0			0
$371$	−19.5501	+	6.35221i	−1.01499	+	0.329790i
$372$		0			0
$373$		−	18.0242i		−	0.933256i	−0.884454	−	0.466628i	$-0.845469\pi$
$373$		−	18.0242i		−	0.933256i	0.884454	−	0.466628i	$-0.154531\pi$
$374$		0			0
$375$	−4.88774			−0.252402
$376$		0			0
$377$	−3.12178	−	9.60785i	−0.160780	−	0.494829i
$378$		0			0
$379$	−8.17433	+	11.2510i	−0.419887	+	0.577925i	−0.965595	−	0.260050i	$-0.916261\pi$
$379$	−8.17433	+	11.2510i	−0.419887	+	0.577925i	0.545708	+	0.837975i	$0.316261\pi$
$380$		0			0
$381$	−17.1180	−	5.56198i	−0.876983	−	0.284949i
$382$		0			0
$383$	−18.2628	+	13.2687i	−0.933184	+	0.677998i	−0.946770	−	0.321910i	$-0.895675\pi$
$383$	−18.2628	+	13.2687i	−0.933184	+	0.677998i	0.0135866	+	0.999908i	$0.495675\pi$
$384$		0			0
$385$	0.722148	−	1.38273i	0.0368041	−	0.0704706i
$386$		0			0
$387$	−4.34762	−	5.98398i	−0.221002	−	0.304183i
$388$		0			0
$389$	22.3165	+	7.25108i	1.13149	+	0.367644i	0.814143	−	0.580665i	$-0.197207\pi$
$389$	22.3165	+	7.25108i	1.13149	+	0.367644i	0.317349	+	0.948309i	$0.397207\pi$
$390$		0			0
$391$	24.9705	+	18.1421i	1.26281	+	0.917487i
$392$		0			0
$393$	−5.18404	−	15.9548i	−0.261500	−	0.804816i
$394$		0			0
$395$			2.93130i			0.147490i
$396$		0			0
$397$			29.9901i			1.50516i	0.658500	+	0.752581i	$0.271191\pi$
$397$			29.9901i			1.50516i	−0.658500	+	0.752581i	$0.728809\pi$
$398$		0			0
$399$	8.73745	+	26.8911i	0.437419	+	1.34624i
$400$		0			0
$401$	16.3663	+	11.8908i	0.817292	+	0.593797i	0.915936	−	0.401325i	$-0.131450\pi$
$401$	16.3663	+	11.8908i	0.817292	+	0.593797i	−0.0986435	+	0.995123i	$0.531450\pi$
$402$		0			0
$403$	12.8161	+	4.16420i	0.638414	+	0.207433i
$404$		0			0
$405$	1.06322	+	1.46340i	0.0528318	+	0.0727168i
$406$		0			0
$407$	−0.621926	−	4.19966i	−0.0308277	−	0.208170i
$408$		0			0
$409$	−3.58977	+	2.60812i	−0.177503	+	0.128963i	−0.672989	−	0.739652i	$-0.734990\pi$
$409$	−3.58977	+	2.60812i	−0.177503	+	0.128963i	0.495486	+	0.868616i	$0.334990\pi$
$410$		0			0
$411$	6.52578	+	2.12036i	0.321893	+	0.104589i
$412$		0			0
$413$	2.62702	−	3.61578i	0.129267	−	0.177921i
$414$		0			0
$415$	−0.580629	−	1.78699i	−0.0285019	−	0.0877200i
$416$		0			0
$417$	21.7990			1.06750
$418$		0			0
$419$			6.01641i			0.293921i	0.989142	+	0.146960i	$0.0469490\pi$
$419$			6.01641i			0.293921i	−0.989142	+	0.146960i	$0.953051\pi$
$420$		0			0
$421$	26.1104	−	8.48380i	1.27254	−	0.413475i	0.406596	−	0.913608i	$-0.366716\pi$
$421$	26.1104	−	8.48380i	1.27254	−	0.413475i	0.865949	+	0.500133i	$0.166716\pi$
$422$		0			0
$423$	−11.5208	−	8.37035i	−0.560161	−	0.406980i
$424$		0			0
$425$	−5.11357	+	15.7379i	−0.248044	+	0.763402i
$426$		0			0
$427$	−8.81892	−	12.1382i	−0.426777	−	0.587409i
$428$		0			0
$429$	−2.20373	+	13.0621i	−0.106397	+	0.630643i
$430$		0			0
$431$	−20.1455	+	14.6365i	−0.970373	+	0.705017i	−0.955537	−	0.294873i	$-0.904723\pi$
$431$	−20.1455	+	14.6365i	−0.970373	+	0.705017i	−0.0148364	+	0.999890i	$0.504723\pi$
$432$		0			0
$433$	4.18538	−	12.8813i	0.201137	−	0.619035i	−0.798713	−	0.601712i	$-0.794486\pi$
$433$	4.18538	−	12.8813i	0.201137	−	0.619035i	0.999850	−	0.0173233i	$-0.00551447\pi$
$434$		0			0
$435$	−1.78601	+	2.45823i	−0.0856326	+	0.117863i
$436$		0			0
$437$	43.3158	−	14.0742i	2.07208	−	0.673259i
$438$		0			0
$439$	30.1967			1.44121			0.720606	−	0.693345i	$-0.243864\pi$
$439$	30.1967			1.44121			0.720606	+	0.693345i	$0.243864\pi$
$440$		0			0
$441$	4.47525			0.213107
$442$		0			0
$443$	−13.2565	+	4.30729i	−0.629835	+	0.204646i	−0.606502	−	0.795082i	$-0.707428\pi$
$443$	−13.2565	+	4.30729i	−0.629835	+	0.204646i	−0.0233328	+	0.999728i	$0.507428\pi$
$444$		0			0
$445$	0.602292	−	0.828984i	0.0285514	−	0.0392976i
$446$		0			0
$447$	9.11212	−	28.0442i	0.430988	−	1.32645i
$448$		0			0
$449$	−5.70957	+	4.14825i	−0.269451	+	0.195768i	−0.714303	−	0.699836i	$-0.753256\pi$
$449$	−5.70957	+	4.14825i	−0.269451	+	0.195768i	0.444852	+	0.895604i	$0.353256\pi$
$450$		0			0
$451$	14.2844	−	13.9999i	0.672628	−	0.659231i
$452$		0			0
$453$	7.62127	+	10.4898i	0.358079	+	0.492853i
$454$		0			0
$455$	−0.237142	+	0.729849i	−0.0111174	+	0.0342158i
$456$		0			0
$457$	−5.07195	−	3.68499i	−0.237256	−	0.172377i	0.462804	−	0.886461i	$-0.346843\pi$
$457$	−5.07195	−	3.68499i	−0.237256	−	0.172377i	−0.700060	+	0.714084i	$0.746843\pi$
$458$		0			0
$459$	0.0594421	−	0.0193139i	0.00277452	−	0.000901496i
$460$		0			0
$461$		−	18.0857i		−	0.842334i	−0.906983	−	0.421167i	$-0.861621\pi$
$461$		−	18.0857i		−	0.842334i	0.906983	−	0.421167i	$-0.138379\pi$
$462$		0			0
$463$	−9.95458			−0.462628			−0.231314	−	0.972879i	$-0.574303\pi$
$463$	−9.95458			−0.462628			−0.231314	+	0.972879i	$0.574303\pi$
$464$		0			0
$465$	−1.25250	−	3.85479i	−0.0580831	−	0.178761i
$466$		0			0
$467$	19.1724	−	26.3885i	0.887191	−	1.22111i	−0.0871856	−	0.996192i	$-0.527787\pi$
$467$	19.1724	−	26.3885i	0.887191	−	1.22111i	0.974377	−	0.224922i	$-0.0722127\pi$
$468$		0			0
$469$	18.4608	+	5.99829i	0.852442	+	0.276975i
$470$		0			0
$471$	7.82362	−	5.68419i	0.360493	−	0.261914i
$472$		0			0
$473$	7.34169	−	3.64823i	0.337571	−	0.167746i
$474$		0			0
$475$	14.3526	+	19.7547i	0.658543	+	0.906407i
$476$		0			0
$477$	−24.9347	−	8.10178i	−1.14168	−	0.370955i
$478$		0			0
$479$	6.88599	+	5.00296i	0.314629	+	0.228591i	0.733880	−	0.679279i	$-0.237707\pi$
$479$	6.88599	+	5.00296i	0.314629	+	0.228591i	−0.419251	+	0.907870i	$0.637707\pi$
$480$		0			0
$481$	0.645391	+	1.98631i	0.0294273	+	0.0905679i
$482$		0			0
$483$			53.1310i			2.41754i
$484$		0			0
$485$			0.0600903i			0.00272856i
$486$		0			0
$487$	−2.20485	−	6.78582i	−0.0999112	−	0.307495i	0.888591	−	0.458700i	$-0.151685\pi$
$487$	−2.20485	−	6.78582i	−0.0999112	−	0.307495i	−0.988502	+	0.151205i	$0.951685\pi$
$488$		0			0
$489$	31.8031	+	23.1063i	1.43819	+	1.04490i
$490$		0			0
$491$	11.5079	+	3.73913i	0.519343	+	0.168745i	0.556947	−	0.830548i	$-0.311973\pi$
$491$	11.5079	+	3.73913i	0.519343	+	0.168745i	−0.0376042	+	0.999293i	$0.511973\pi$
$492$		0			0
$493$	12.1424	+	16.7125i	0.546865	+	0.752695i
$494$		0			0
$495$	1.78175	−	0.885385i	0.0800835	−	0.0397951i
$496$		0			0
$497$	−2.36948	+	1.72153i	−0.106286	+	0.0772210i
$498$		0			0
$499$	−13.3674	−	4.34332i	−0.598405	−	0.194434i	−0.00587615	−	0.999983i	$-0.501870\pi$
$499$	−13.3674	−	4.34332i	−0.598405	−	0.194434i	−0.592529	+	0.805549i	$0.701870\pi$
$500$		0			0
$501$	−13.3516	+	18.3770i	−0.596507	+	0.821022i
$502$		0			0
$503$	8.50938	+	26.1892i	0.379415	+	1.16772i	0.940452	+	0.339928i	$0.110403\pi$
$503$	8.50938	+	26.1892i	0.379415	+	1.16772i	−0.561037	+	0.827791i	$0.689597\pi$
$504$		0			0
$505$	3.01109			0.133992
$506$		0			0
$507$			25.3064i			1.12390i
$508$		0			0
$509$	−0.286361	+	0.0930445i	−0.0126927	+	0.00412412i	−0.315356	−	0.948973i	$-0.602124\pi$
$509$	−0.286361	+	0.0930445i	−0.0126927	+	0.00412412i	0.302664	+	0.953097i	$0.402124\pi$
$510$		0			0
$511$	−13.0876	−	9.50868i	−0.578960	−	0.420639i
$512$		0			0
$513$	0.0284997	−	0.0877131i	0.00125829	−	0.00387263i
$514$		0			0
$515$	0.332862	+	0.458145i	0.0146677	+	0.0201883i
$516$		0			0
$517$	11.2725	−	11.0480i	0.495763	−	0.485888i
$518$		0			0
$519$	17.5112	−	12.7227i	0.768658	−	0.558463i
$520$		0			0
$521$	−5.15755	+	15.8733i	−0.225956	+	0.695422i	0.772237	+	0.635335i	$0.219138\pi$
$521$	−5.15755	+	15.8733i	−0.225956	+	0.695422i	−0.998193	+	0.0600874i	$0.980862\pi$
$522$		0			0
$523$	−3.37114	+	4.63997i	−0.147409	+	0.202892i	−0.876336	−	0.481700i	$-0.840019\pi$
$523$	−3.37114	+	4.63997i	−0.147409	+	0.202892i	0.728927	+	0.684592i	$0.240019\pi$
$524$		0			0
$525$	−27.0911	+	8.80242i	−1.18235	+	0.384169i
$526$		0			0
$527$	−27.5559			−1.20035
$528$		0			0
$529$	62.5827			2.72099
$530$		0			0
$531$	5.42134	−	1.76150i	0.235266	−	0.0764426i
$532$		0			0
$533$	−5.78346	+	7.96024i	−0.250509	+	0.344796i
$534$		0			0
$535$	0.0553432	−	0.170329i	0.00239270	−	0.00736396i
$536$		0			0
$537$	21.0991	−	15.3294i	0.910494	−	0.661512i
$538$		0			0
$539$	−0.825189	+	4.89110i	−0.0355434	+	0.210675i
$540$		0			0
$541$	−14.1771	−	19.5131i	−0.609522	−	0.838935i	0.387016	−	0.922073i	$-0.373506\pi$
$541$	−14.1771	−	19.5131i	−0.609522	−	0.838935i	−0.996538	+	0.0831377i	$0.973506\pi$
$542$		0			0
$543$	10.1489	−	31.2351i	0.435531	−	1.34043i
$544$		0			0
$545$	−0.219469	−	0.159453i	−0.00940101	−	0.00683023i
$546$		0			0
$547$	−7.03428	+	2.28558i	−0.300764	+	0.0977241i	−0.455511	−	0.890230i	$-0.650544\pi$
$547$	−7.03428	+	2.28558i	−0.300764	+	0.0977241i	0.154747	+	0.987954i	$0.450544\pi$
$548$		0			0
$549$		−	19.1360i		−	0.816707i
$550$		0			0
$551$	30.4828			1.29861
$552$		0			0
$553$	10.6009	+	32.6261i	0.450795	+	1.38740i
$554$		0			0
$555$	0.369236	−	0.508210i	0.0156732	−	0.0215723i
$556$		0			0
$557$	−10.8601	−	3.52867i	−0.460158	−	0.149514i	0.0697589	−	0.997564i	$-0.477777\pi$
$557$	−10.8601	−	3.52867i	−0.460158	−	0.149514i	−0.529917	+	0.848049i	$0.677777\pi$
$558$		0			0
$559$	−3.26280	+	2.37056i	−0.138002	+	0.100264i
$560$		0			0
$561$	−3.96812	−	26.7954i	−0.167534	−	1.13130i
$562$		0			0
$563$	−5.71080	−	7.86025i	−0.240682	−	0.331270i	0.671539	−	0.740969i	$-0.265634\pi$
$563$	−5.71080	−	7.86025i	−0.240682	−	0.331270i	−0.912221	+	0.409699i	$0.865634\pi$
$564$		0			0
$565$	−0.718558	−	0.233474i	−0.0302300	−	0.00982231i
$566$		0			0
$567$	17.1262	+	12.4429i	0.719231	+	0.522552i
$568$		0			0
$569$	−7.44871	−	22.9248i	−0.312266	−	0.961057i	−0.976865	−	0.213856i	$-0.931398\pi$
$569$	−7.44871	−	22.9248i	−0.312266	−	0.961057i	0.664599	−	0.747200i	$-0.268602\pi$
$570$		0			0
$571$		−	12.8180i		−	0.536415i	−0.963361	−	0.268207i	$-0.913569\pi$
$571$		−	12.8180i		−	0.536415i	0.963361	−	0.268207i	$-0.0864312\pi$
$572$		0			0
$573$			36.2756i			1.51543i
$574$		0			0
$575$	14.1788	+	43.6380i	0.591298	+	1.81983i
$576$		0			0
$577$	−18.4866	−	13.4313i	−0.769608	−	0.559153i	0.132234	−	0.991219i	$-0.457785\pi$
$577$	−18.4866	−	13.4313i	−0.769608	−	0.559153i	−0.901842	+	0.432065i	$0.857785\pi$
$578$		0			0
$579$	−10.4159	−	3.38432i	−0.432868	−	0.140647i
$580$		0			0
$581$	−12.9251	−	17.7898i	−0.536222	−	0.738047i
$582$		0			0
$583$	13.4523	−	25.7579i	0.557139	−	1.06678i
$584$		0			0
$585$	−0.791844	+	0.575308i	−0.0327387	+	0.0237861i
$586$		0			0
$587$	−27.8685	−	9.05504i	−1.15026	−	0.373741i	−0.329017	−	0.944324i	$-0.606717\pi$
$587$	−27.8685	−	9.05504i	−1.15026	−	0.373741i	−0.821240	+	0.570583i	$0.806717\pi$
$588$		0			0
$589$	−23.9003	+	32.8959i	−0.984794	+	1.35545i
$590$		0			0
$591$	−15.3825	−	47.3424i	−0.632750	−	1.94741i
$592$		0			0
$593$	10.3694			0.425820			0.212910	−	0.977072i	$-0.431706\pi$
$593$	10.3694			0.425820			0.212910	+	0.977072i	$0.431706\pi$
$594$		0			0
$595$		−	1.56925i		−	0.0643329i
$596$		0			0
$597$	24.2455	−	7.87785i	0.992303	−	0.322419i
$598$		0			0
$599$	−16.8754	−	12.2607i	−0.689508	−	0.500957i	0.186990	−	0.982362i	$-0.440127\pi$
$599$	−16.8754	−	12.2607i	−0.689508	−	0.500957i	−0.876498	+	0.481405i	$0.840127\pi$
$600$		0			0
$601$	12.1139	−	37.2827i	0.494135	−	1.52079i	−0.324164	−	0.946001i	$-0.605083\pi$
$601$	12.1139	−	37.2827i	0.494135	−	1.52079i	0.818300	−	0.574792i	$-0.194917\pi$
$602$		0			0
$603$	14.5519	+	20.0290i	0.592599	+	0.815642i
$604$		0			0
$605$	0.639122	+	2.11057i	0.0259840	+	0.0858068i
$606$		0			0
$607$	−21.5873	+	15.6841i	−0.876203	+	0.636599i	−0.932244	−	0.361830i	$-0.882152\pi$
$607$	−21.5873	+	15.6841i	−0.876203	+	0.636599i	0.0560410	+	0.998428i	$0.482152\pi$
$608$		0			0
$609$	−10.9887	+	33.8197i	−0.445284	+	1.37044i
$610$		0			0
$611$	−4.56398	+	6.28177i	−0.184639	+	0.254133i
$612$		0			0
$613$	29.2625	−	9.50796i	1.18190	−	0.384023i	0.348828	−	0.937187i	$-0.386580\pi$
$613$	29.2625	−	9.50796i	1.18190	−	0.384023i	0.833073	+	0.553164i	$0.186580\pi$
$614$		0			0
$615$	2.95947			0.119337
$616$		0			0
$617$	10.0183			0.403323			0.201662	−	0.979455i	$-0.435366\pi$
$617$	10.0183			0.403323			0.201662	+	0.979455i	$0.435366\pi$
$618$		0			0
$619$	30.5262	−	9.91856i	1.22695	−	0.398660i	0.377342	−	0.926074i	$-0.376838\pi$
$619$	30.5262	−	9.91856i	1.22695	−	0.398660i	0.849609	+	0.527414i	$0.176838\pi$
$620$		0			0
$621$	0.101864	−	0.140204i	0.00408768	−	0.00562621i
$622$		0			0
$623$	3.70569	−	11.4049i	0.148465	−	0.456929i
$624$		0			0
$625$	−19.7390	+	14.3412i	−0.789561	+	0.573649i
$626$		0			0
$627$	−35.4299	−	18.5036i	−1.41493	−	0.738964i
$628$		0			0
$629$	−2.51029	−	3.45512i	−0.100092	−	0.137765i
$630$		0			0
$631$	0.865296	−	2.66311i	0.0344469	−	0.106017i	−0.932355	−	0.361545i	$-0.882249\pi$
$631$	0.865296	−	2.66311i	0.0344469	−	0.106017i	0.966802	+	0.255528i	$0.0822494\pi$
$632$		0			0
$633$	−37.0888	−	26.9466i	−1.47415	−	1.07103i
$634$		0			0
$635$	1.40189	−	0.455501i	0.0556322	−	0.0180760i
$636$		0			0
$637$		−	2.44015i		−	0.0966823i
$638$		0			0
$639$	−3.73551			−0.147775
$640$		0			0
$641$	5.21567	+	16.0522i	0.206007	+	0.634023i	0.999671	+	0.0256668i	$0.00817089\pi$
$641$	5.21567	+	16.0522i	0.206007	+	0.634023i	−0.793664	+	0.608356i	$0.791829\pi$
$642$		0			0
$643$	−28.8449	+	39.7016i	−1.13753	+	1.56568i	−0.364630	+	0.931153i	$0.618804\pi$
$643$	−28.8449	+	39.7016i	−1.13753	+	1.56568i	−0.772902	+	0.634525i	$0.781196\pi$
$644$		0			0
$645$	1.15368	+	0.374852i	0.0454260	+	0.0147598i
$646$		0			0
$647$	−28.5917	+	20.7731i	−1.12406	+	0.816675i	−0.984819	−	0.173585i	$-0.944465\pi$
$647$	−28.5917	+	20.7731i	−1.12406	+	0.816675i	−0.139237	+	0.990259i	$0.544465\pi$
$648$		0			0
$649$	0.925546	+	6.24991i	0.0363309	+	0.245330i
$650$		0			0
$651$	−27.8812	−	38.3751i	−1.09275	−	1.50404i
$652$		0			0
$653$	−0.182805	−	0.0593970i	−0.00715372	−	0.00232438i	0.305438	−	0.952212i	$-0.401197\pi$
$653$	−0.182805	−	0.0593970i	−0.00715372	−	0.00232438i	−0.312592	+	0.949888i	$0.601197\pi$
$654$		0			0
$655$	1.11149	+	0.807542i	0.0434293	+	0.0315533i
$656$		0			0
$657$	−6.37587	−	19.6229i	−0.248746	−	0.765563i
$658$		0			0
$659$		−	46.4826i		−	1.81071i	−0.424660	−	0.905353i	$-0.639606\pi$
$659$		−	46.4826i		−	1.81071i	0.424660	−	0.905353i	$-0.360394\pi$
$660$		0			0
$661$		−	24.0904i		−	0.937007i	−0.883462	−	0.468503i	$-0.844793\pi$
$661$		−	24.0904i		−	0.937007i	0.883462	−	0.468503i	$-0.155207\pi$
$662$		0			0
$663$	4.11784	+	12.6734i	0.159924	+	0.492194i
$664$		0			0
$665$	−1.87335	−	1.36107i	−0.0726455	−	0.0527801i
$666$		0			0
$667$	54.4763	+	17.7004i	2.10933	+	0.685363i
$668$		0			0
$669$	20.9747	+	28.8692i	0.810929	+	1.11615i
$670$		0			0
$671$	20.9142	+	3.52849i	0.807385	+	0.136216i
$672$		0			0
$673$	6.12494	−	4.45003i	0.236099	−	0.171536i	−0.463444	−	0.886126i	$-0.653387\pi$
$673$	6.12494	−	4.45003i	0.236099	−	0.171536i	0.699544	+	0.714590i	$0.253387\pi$
$674$		0			0
$675$	0.0883654	+	0.0287117i	0.00340119	+	0.00110511i
$676$		0			0
$677$	−12.1390	+	16.7079i	−0.466540	+	0.642137i	−0.975849	−	0.218447i	$-0.929901\pi$
$677$	−12.1390	+	16.7079i	−0.466540	+	0.642137i	0.509309	+	0.860584i	$0.329901\pi$
$678$		0			0
$679$	0.217313	+	0.668820i	0.00833969	+	0.0256669i
$680$		0			0
$681$	−10.2371			−0.392287
$682$		0			0
$683$			14.6272i			0.559694i	0.960045	+	0.279847i	$0.0902837\pi$
$683$			14.6272i			0.559694i	−0.960045	+	0.279847i	$0.909716\pi$
$684$		0			0
$685$	−0.534432	+	0.173648i	−0.0204196	+	0.00663473i
$686$		0			0
$687$	46.0272	+	33.4407i	1.75605	+	1.27584i
$688$		0			0
$689$	−4.41754	+	13.5958i	−0.168295	+	0.517958i
$690$		0			0
$691$	13.4854	+	18.5610i	0.513008	+	0.706095i	0.984423	−	0.175817i	$-0.0562566\pi$
$691$	13.4854	+	18.5610i	0.513008	+	0.706095i	−0.471415	+	0.881911i	$0.656257\pi$
$692$		0			0
$693$	16.6293	−	16.2981i	0.631696	−	0.619114i
$694$		0			0
$695$	−1.44429	+	1.04934i	−0.0547851	+	0.0398037i
$696$		0			0
$697$	6.21750	−	19.1355i	0.235505	−	0.724809i
$698$		0			0
$699$	−20.1187	+	27.6911i	−0.760960	+	1.04737i
$700$		0			0
$701$	−0.666479	+	0.216552i	−0.0251726	+	0.00817907i	−0.321576	−	0.946884i	$-0.604213\pi$
$701$	−0.666479	+	0.216552i	−0.0251726	+	0.00817907i	0.296404	+	0.955063i	$0.404213\pi$
$702$		0			0
$703$	−6.30196			−0.237683
$704$		0			0
$705$	2.33545			0.0879580
$706$		0			0
$707$	33.5141	−	10.8894i	1.26043	−	0.409538i
$708$		0			0
$709$	2.38215	−	3.27875i	0.0894636	−	0.123136i	−0.761939	−	0.647649i	$-0.775752\pi$
$709$	2.38215	−	3.27875i	0.0894636	−	0.123136i	0.851403	+	0.524513i	$0.175752\pi$
$710$		0			0
$711$	−13.5206	+	41.6122i	−0.507063	+	1.56058i
$712$		0			0
$713$	−61.8141	+	44.9106i	−2.31496	+	1.68192i
$714$		0			0
$715$	−0.482760	−	0.971506i	−0.0180542	−	0.0363323i
$716$		0			0
$717$	−34.4409	−	47.4038i	−1.28622	−	1.77033i
$718$		0			0
$719$	−3.11822	+	9.59690i	−0.116290	+	0.357904i	−0.992214	−	0.124545i	$-0.960253\pi$
$719$	−3.11822	+	9.59690i	−0.116290	+	0.357904i	0.875924	+	0.482449i	$0.160253\pi$
$720$		0			0
$721$	5.36169	+	3.89549i	0.199680	+	0.145076i
$722$		0			0
$723$	60.9599	−	19.8071i	2.26712	−	0.736632i
$724$		0			0
$725$			30.7095i			1.14052i
$726$		0			0
$727$	13.6615			0.506675			0.253338	−	0.967378i	$-0.418472\pi$
$727$	13.6615			0.506675			0.253338	+	0.967378i	$0.418472\pi$
$728$		0			0
$729$	8.30084	+	25.5474i	0.307438	+	0.946198i
$730$		0			0
$731$	4.84748	−	6.67199i	0.179291	−	0.246772i
$732$		0			0
$733$	17.0433	+	5.53772i	0.629510	+	0.204540i	0.606358	−	0.795192i	$-0.292630\pi$
$733$	17.0433	+	5.53772i	0.629510	+	0.204540i	0.0231521	+	0.999732i	$0.492630\pi$
$734$		0			0
$735$	−0.593772	+	0.431400i	−0.0219016	+	0.0159124i
$736$		0			0
$737$	−24.5733	+	12.2110i	−0.905170	+	0.449797i
$738$		0			0
$739$	−13.8476	−	19.0596i	−0.509393	−	0.701120i	0.474424	−	0.880297i	$-0.342656\pi$
$739$	−13.8476	−	19.0596i	−0.509393	−	0.701120i	−0.983817	+	0.179177i	$0.942656\pi$
$740$		0			0
$741$	18.7010	+	6.07631i	0.686997	+	0.223219i
$742$		0			0
$743$	−11.0265	−	8.01121i	−0.404523	−	0.293903i	0.366858	−	0.930277i	$-0.380434\pi$
$743$	−11.0265	−	8.01121i	−0.404523	−	0.293903i	−0.771381	+	0.636374i	$0.780434\pi$
$744$		0			0
$745$	0.746241	+	2.29669i	0.0273402	+	0.0841444i
$746$		0			0
$747$		−	28.0459i		−	1.02615i
$748$		0			0
$749$		−	2.09595i		−	0.0765842i
$750$		0			0
$751$	3.77972	+	11.6328i	0.137924	+	0.424486i	0.996033	−	0.0889809i	$-0.0283610\pi$
$751$	3.77972	+	11.6328i	0.137924	+	0.424486i	−0.858110	+	0.513467i	$0.828361\pi$
$752$		0			0
$753$	−38.1749	−	27.7357i	−1.39117	−	1.01075i
$754$		0			0
$755$	−1.00989	−	0.328134i	−0.0367537	−	0.0119420i
$756$		0			0
$757$	−12.5436	−	17.2648i	−0.455906	−	0.627501i	0.517747	−	0.855534i	$-0.326771\pi$
$757$	−12.5436	−	17.2648i	−0.455906	−	0.627501i	−0.973654	+	0.228033i	$0.926771\pi$
$758$		0			0
$759$	−52.5727	−	53.6411i	−1.90827	−	1.94705i
$760$		0			0
$761$	−9.57071	+	6.95353i	−0.346938	+	0.252065i	−0.747583	−	0.664168i	$-0.768786\pi$
$761$	−9.57071	+	6.95353i	−0.346938	+	0.252065i	0.400645	+	0.916233i	$0.368786\pi$
$762$		0			0
$763$	−3.01939	−	0.981060i	−0.109309	−	0.0355167i
$764$		0			0
$765$	1.17643	−	1.61922i	0.0425339	−	0.0585429i
$766$		0			0
$767$	−0.960466	−	2.95601i	−0.0346804	−	0.106735i
$768$		0			0
$769$	2.94327			0.106137			0.0530685	−	0.998591i	$-0.483100\pi$
$769$	2.94327			0.106137			0.0530685	+	0.998591i	$0.483100\pi$
$770$		0			0
$771$			18.0369i			0.649583i
$772$		0			0
$773$	−7.56561	+	2.45822i	−0.272116	+	0.0884159i	−0.441896	−	0.897066i	$-0.645694\pi$
$773$	−7.56561	+	2.45822i	−0.272116	+	0.0884159i	0.169780	+	0.985482i	$0.445694\pi$
$774$		0			0
$775$	−33.1406	−	24.0780i	−1.19044	−	0.864908i
$776$		0			0
$777$	2.27178	−	6.99182i	0.0814996	−	0.250830i
$778$		0			0
$779$	−17.4511	−	24.0194i	−0.625251	−	0.860584i
$780$		0			0
$781$	0.688790	−	4.08263i	0.0246468	−	0.146088i
$782$		0			0
$783$	0.0938376	−	0.0681770i	0.00335348	−	0.00243645i
$784$		0			0
$785$	−0.244733	+	0.753210i	−0.00873489	+	0.0268832i
$786$		0			0
$787$	−1.60061	+	2.20304i	−0.0570554	+	0.0785300i	−0.836591	−	0.547828i	$-0.815455\pi$
$787$	−1.60061	+	2.20304i	−0.0570554	+	0.0785300i	0.779536	+	0.626358i	$0.215455\pi$
$788$		0			0
$789$	6.26831	−	2.03670i	0.223158	−	0.0725083i
$790$		0			0
$791$	−8.84207			−0.314388
$792$		0			0
$793$	−10.4340			−0.370523
$794$		0			0
$795$	4.08930	−	1.32870i	0.145033	−	0.0471240i
$796$		0			0
$797$	−16.4925	+	22.7000i	−0.584196	+	0.804077i	−0.994148	−	0.108031i	$-0.965546\pi$
$797$	−16.4925	+	22.7000i	−0.584196	+	0.804077i	0.409952	+	0.912107i	$0.365546\pi$
$798$		0			0
$799$	4.90650	−	15.1007i	0.173580	−	0.534223i
$800$		0			0
$801$	12.3737	−	8.99002i	0.437203	−	0.317647i
$802$		0			0
$803$	22.6220	−	3.35008i	0.798313	−	0.118222i
$804$		0			0
$805$	−2.55756	−	3.52018i	−0.0901423	−	0.124070i
$806$		0			0
$807$	−11.7682	+	36.2187i	−0.414259	+	1.27496i
$808$		0			0
$809$	26.3156	+	19.1194i	0.925207	+	0.672202i	0.944815	−	0.327605i	$-0.106242\pi$
$809$	26.3156	+	19.1194i	0.925207	+	0.672202i	−0.0196074	+	0.999808i	$0.506242\pi$
$810$		0			0
$811$	−8.46947	+	2.75190i	−0.297403	+	0.0966322i	−0.453918	−	0.891043i	$-0.649974\pi$
$811$	−8.46947	+	2.75190i	−0.297403	+	0.0966322i	0.156515	+	0.987676i	$0.449974\pi$
$812$		0			0
$813$			2.28648i			0.0801904i
$814$		0			0
$815$	−3.21938			−0.112770
$816$		0			0
$817$	−3.76054	−	11.5738i	−0.131565	−	0.404915i
$818$		0			0
$819$	−6.73285	+	9.26697i	−0.235265	+	0.323814i
$820$		0			0
$821$	13.6833	+	4.44597i	0.477550	+	0.155165i	0.537895	−	0.843012i	$-0.319220\pi$
$821$	13.6833	+	4.44597i	0.477550	+	0.155165i	−0.0603443	+	0.998178i	$0.519220\pi$
$822$		0			0
$823$	−28.5715	+	20.7584i	−0.995940	+	0.723593i	−0.961214	−	0.275804i	$-0.911056\pi$
$823$	−28.5715	+	20.7584i	−0.995940	+	0.723593i	−0.0347264	+	0.999397i	$0.511056\pi$
$824$		0			0
$825$	18.6412	−	35.6933i	0.649005	−	1.24268i
$826$		0			0
$827$	−7.54322	−	10.3823i	−0.262303	−	0.361030i	0.657469	−	0.753481i	$-0.271627\pi$
$827$	−7.54322	−	10.3823i	−0.262303	−	0.361030i	−0.919773	+	0.392452i	$0.871627\pi$
$828$		0			0
$829$	−22.7234	−	7.38328i	−0.789216	−	0.256432i	−0.113446	−	0.993544i	$-0.536189\pi$
$829$	−22.7234	−	7.38328i	−0.789216	−	0.256432i	−0.675770	+	0.737112i	$0.736189\pi$
$830$		0			0
$831$	−26.8550	−	19.5113i	−0.931591	−	0.676840i
$832$		0			0
$833$	1.54193	+	4.74556i	0.0534246	+	0.164424i
$834$		0			0
$835$		−	1.86027i		−	0.0643773i
$836$		0			0
$837$			0.154721i			0.00534793i
$838$		0			0
$839$	−7.29937	−	22.4652i	−0.252002	−	0.775583i	−0.994406	−	0.105630i	$-0.966314\pi$
$839$	−7.29937	−	22.4652i	−0.252002	−	0.775583i	0.742403	−	0.669953i	$-0.233686\pi$
$840$		0			0
$841$	7.55366	+	5.48805i	0.260471	+	0.189243i
$842$		0			0
$843$	−36.1958	−	11.7607i	−1.24665	−	0.405061i
$844$		0			0
$845$	−1.21817	−	1.67667i	−0.0419065	−	0.0576793i
$846$		0			0
$847$	14.7463	+	21.1798i	0.506689	+	0.727746i
$848$		0			0
$849$	4.64131	−	3.37211i	0.159289	−	0.115730i
$850$		0			0
$851$	−11.2623	−	3.65935i	−0.386068	−	0.125441i
$852$		0			0
$853$	24.5116	−	33.7374i	0.839262	−	1.15515i	−0.146865	−	0.989156i	$-0.546918\pi$
$853$	24.5116	−	33.7374i	0.839262	−	1.15515i	0.986128	−	0.165989i	$-0.0530816\pi$
$854$		0			0
$855$	−0.912641	−	2.80882i	−0.0312117	−	0.0960596i
$856$		0			0
$857$	−4.35256			−0.148680			−0.0743402	−	0.997233i	$-0.523685\pi$
$857$	−4.35256			−0.148680			−0.0743402	+	0.997233i	$0.523685\pi$
$858$		0			0
$859$			7.91648i			0.270107i	0.990838	+	0.135053i	$0.0431206\pi$
$859$			7.91648i			0.270107i	−0.990838	+	0.135053i	$0.956879\pi$
$860$		0			0
$861$	32.9396	−	10.7027i	1.12258	−	0.364748i
$862$		0			0
$863$	−9.98178	−	7.25219i	−0.339784	−	0.246867i	0.404787	−	0.914411i	$-0.367346\pi$
$863$	−9.98178	−	7.25219i	−0.339784	−	0.246867i	−0.744571	+	0.667544i	$0.767346\pi$
$864$		0			0
$865$	−0.547774	+	1.68588i	−0.0186249	+	0.0573215i
$866$		0			0
$867$	8.44394	+	11.6221i	0.286771	+	0.394707i
$868$		0			0
$869$	−42.9859	−	22.4499i	−1.45820	−	0.761560i
$870$		0			0
$871$	10.9209	−	7.93449i	0.370040	−	0.268850i
$872$		0			0
$873$	−0.277166	+	0.853031i	−0.00938066	+	0.0288707i
$874$		0			0
$875$	2.75350	−	3.78986i	0.0930852	−	0.128121i
$876$		0			0
$877$	−55.4714	+	18.0237i	−1.87314	+	0.608619i	−0.882834	+	0.469686i	$0.844367\pi$
$877$	−55.4714	+	18.0237i	−1.87314	+	0.608619i	−0.990302	+	0.138933i	$0.955633\pi$
$878$		0			0
$879$	45.0289			1.51879
$880$		0			0
$881$	−25.8106			−0.869581			−0.434791	−	0.900532i	$-0.643178\pi$
$881$	−25.8106			−0.869581			−0.434791	+	0.900532i	$0.643178\pi$
$882$		0			0
$883$	−34.8110	+	11.3108i	−1.17148	+	0.380638i	−0.829196	−	0.558958i	$-0.811201\pi$
$883$	−34.8110	+	11.3108i	−1.17148	+	0.380638i	−0.342287	+	0.939596i	$0.611201\pi$
$884$		0			0
$885$	−0.549495	+	0.756315i	−0.0184711	+	0.0254232i
$886$		0			0
$887$	−6.76505	+	20.8207i	−0.227148	+	0.699091i	0.770918	+	0.636934i	$0.219798\pi$
$887$	−6.76505	+	20.8207i	−0.227148	+	0.699091i	−0.998066	+	0.0621563i	$0.980202\pi$
$888$		0			0
$889$	13.9561	−	10.1397i	0.468071	−	0.340074i
$890$		0			0
$891$	−29.6027	+	4.38385i	−0.991729	+	0.146865i
$892$		0			0
$893$	−13.7714	−	18.9547i	−0.460843	−	0.634296i
$894$		0			0
$895$	−0.660007	+	2.03129i	−0.0220616	+	0.0678986i
$896$		0			0
$897$	29.8924	+	21.7181i	0.998078	+	0.725146i
$898$		0			0
$899$	−48.6353	+	15.8026i	−1.62208	+	0.527045i
$900$		0			0
$901$		−	29.2323i		−	0.973869i
$902$		0			0
$903$	14.1963			0.472424
$904$		0			0
$905$	0.831149	+	2.55801i	0.0276283	+	0.0850313i
$906$		0			0
$907$	−16.9320	+	23.3049i	−0.562218	+	0.773827i	−0.991606	−	0.129293i	$-0.958729\pi$
$907$	−16.9320	+	23.3049i	−0.562218	+	0.773827i	0.429388	+	0.903120i	$0.358729\pi$
$908$		0			0
$909$	42.7448	+	13.8886i	1.41776	+	0.460657i
$910$		0			0
$911$	35.7732	−	25.9908i	1.18522	−	0.861113i	0.192469	−	0.981303i	$-0.438351\pi$
$911$	35.7732	−	25.9908i	1.18522	−	0.861113i	0.992751	+	0.120191i	$0.0383505\pi$
$912$		0			0
$913$	30.6521	+	5.17138i	1.01444	+	0.171148i
$914$		0			0
$915$	1.84466	+	2.53895i	0.0609825	+	0.0839352i
$916$		0			0
$917$	15.2915	+	4.96852i	0.504970	+	0.164075i
$918$		0			0
$919$	−15.3711	−	11.1678i	−0.507046	−	0.368390i	0.304656	−	0.952462i	$-0.401459\pi$
$919$	−15.3711	−	11.1678i	−0.507046	−	0.368390i	−0.811702	+	0.584072i	$0.801459\pi$
$920$		0			0
$921$	15.4092	+	47.4246i	0.507750	+	1.56269i
$922$		0			0
$923$			2.03681i			0.0670423i
$924$		0			0
$925$		−	6.34883i		−	0.208748i
$926$		0			0
$927$	2.61205	+	8.03907i	0.0857910	+	0.264038i
$928$		0			0
$929$	−22.7067	−	16.4974i	−0.744983	−	0.541262i	0.149285	−	0.988794i	$-0.452303\pi$
$929$	−22.7067	−	16.4974i	−0.744983	−	0.541262i	−0.894268	+	0.447532i	$0.852303\pi$
$930$		0			0
$931$	7.00259	+	2.27528i	0.229500	+	0.0745692i
$932$		0			0
$933$	31.2356	+	42.9921i	1.02261	+	1.40750i
$934$		0			0
$935$	1.55276	+	1.58431i	0.0507806	+	0.0518126i
$936$		0			0
$937$	−0.237551	+	0.172591i	−0.00776046	+	0.00563830i	−0.591659	−	0.806189i	$-0.701527\pi$
$937$	−0.237551	+	0.172591i	−0.00776046	+	0.00563830i	0.583898	+	0.811827i	$0.301527\pi$
$938$		0			0
$939$	62.4573	+	20.2936i	2.03822	+	0.662256i
$940$		0			0
$941$	−9.48051	+	13.0488i	−0.309056	+	0.425379i	−0.935087	−	0.354420i	$-0.884678\pi$
$941$	−9.48051	+	13.0488i	−0.309056	+	0.425379i	0.626031	+	0.779798i	$0.284678\pi$
$942$		0			0
$943$	−17.2398	−	53.0587i	−0.561405	−	1.72783i
$944$		0			0
$945$	−0.00881101			−0.000286622
$946$		0			0
$947$			29.0812i			0.945011i	0.881328	+	0.472505i	$0.156650\pi$
$947$			29.0812i			0.945011i	−0.881328	+	0.472505i	$0.843350\pi$
$948$		0			0
$949$	−10.6995	+	3.47648i	−0.347320	+	0.112851i
$950$		0			0
$951$	7.54554	+	5.48215i	0.244681	+	0.177771i
$952$		0			0
$953$	12.5355	−	38.5803i	0.406065	−	1.24974i	−0.513937	−	0.857828i	$-0.671814\pi$
$953$	12.5355	−	38.5803i	0.406065	−	1.24974i	0.920003	−	0.391912i	$-0.128186\pi$
$954$		0			0
$955$	−1.74620	−	2.40343i	−0.0565056	−	0.0777732i
$956$		0			0
$957$	−22.3701	−	45.0176i	−0.723123	−	1.45521i
$958$		0			0
$959$	−5.32037	+	3.86548i	−0.171804	+	0.124823i
$960$		0			0
$961$	11.4998	−	35.3927i	0.370961	−	1.14170i
$962$		0			0
$963$	1.57128	−	2.16269i	0.0506339	−	0.0696916i
$964$		0			0
$965$	0.853011	−	0.277160i	0.0274594	−	0.00892210i
$966$		0			0
$967$	−6.42732			−0.206689			−0.103344	−	0.994646i	$-0.532954\pi$
$967$	−6.42732			−0.206689			−0.103344	+	0.994646i	$0.532954\pi$
$968$		0			0
$969$	−40.2089			−1.29170
$970$		0			0
$971$	48.2270	−	15.6699i	1.54768	−	0.502871i	0.594195	−	0.804321i	$-0.297471\pi$
$971$	48.2270	−	15.6699i	1.54768	−	0.502871i	0.953482	+	0.301450i	$0.0974707\pi$
$972$		0			0
$973$	−12.2804	+	16.9026i	−0.393693	+	0.541871i
$974$		0			0
$975$	−6.12150	+	18.8400i	−0.196045	+	0.603364i
$976$		0			0
$977$	0.0813429	−	0.0590991i	0.00260239	−	0.00189075i	−0.586483	−	0.809961i	$-0.699488\pi$
$977$	0.0813429	−	0.0590991i	0.00260239	−	0.00189075i	0.589086	+	0.808071i	$0.299488\pi$
$978$		0			0
$979$	7.54383	+	15.1812i	0.241102	+	0.485193i
$980$		0			0
$981$	−2.38006	−	3.27587i	−0.0759894	−	0.104590i
$982$		0			0
$983$	−8.13927	+	25.0501i	−0.259603	+	0.798974i	0.733285	+	0.679921i	$0.237986\pi$
$983$	−8.13927	+	25.0501i	−0.259603	+	0.798974i	−0.992888	+	0.119053i	$0.962014\pi$
$984$		0			0
$985$	3.29808	+	2.39620i	0.105086	+	0.0763491i
$986$		0			0
$987$	25.9941	−	8.44599i	0.827400	−	0.268839i
$988$		0			0
$989$		−	22.8672i		−	0.727136i
$990$		0			0
$991$	27.9640			0.888306			0.444153	−	0.895951i	$-0.353505\pi$
$991$	27.9640			0.888306			0.444153	+	0.895951i	$0.353505\pi$
$992$		0			0
$993$	21.3546	+	65.7228i	0.677669	+	2.08565i
$994$		0			0
$995$	−1.22717	+	1.68905i	−0.0389038	+	0.0535465i
$996$		0			0
$997$	54.4887	+	17.7045i	1.72567	+	0.560706i	0.992813	−	0.119673i	$-0.0381846\pi$
$997$	54.4887	+	17.7045i	1.72567	+	0.560706i	0.732861	+	0.680378i	$0.238185\pi$
$998$		0			0
$999$	−0.0193998	+	0.0140948i	−0.000613783	+	0.000445939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.w.a.113.2		40
4.3	odd	2		88.2.o.a.69.2	yes	40
8.3	odd	2		88.2.o.a.69.7	yes	40
8.5	even	2	inner	352.2.w.a.113.9		40
11.2	odd	10		3872.2.c.i.1937.17		20
11.4	even	5	inner	352.2.w.a.81.9		40
11.9	even	5		3872.2.c.h.1937.17		20
12.11	even	2		792.2.br.b.685.9		40
24.11	even	2		792.2.br.b.685.4		40
44.3	odd	10		968.2.o.j.269.2		40
44.7	even	10		968.2.o.i.565.4		40
44.15	odd	10		88.2.o.a.37.7	yes	40
44.19	even	10		968.2.o.d.269.9		40
44.27	odd	10		968.2.o.j.493.10		40
44.31	odd	10		968.2.c.h.485.14		20
44.35	even	10		968.2.c.i.485.7		20
44.39	even	10		968.2.o.d.493.1		40
44.43	even	2		968.2.o.i.245.9		40
88.3	odd	10		968.2.o.j.269.10		40
88.13	odd	10		3872.2.c.i.1937.4		20
88.19	even	10		968.2.o.d.269.1		40
88.27	odd	10		968.2.o.j.493.2		40
88.35	even	10		968.2.c.i.485.8		20
88.37	even	10	inner	352.2.w.a.81.2		40
88.43	even	2		968.2.o.i.245.4		40
88.51	even	10		968.2.o.i.565.9		40
88.53	even	10		3872.2.c.h.1937.4		20
88.59	odd	10		88.2.o.a.37.2	✓	40
88.75	odd	10		968.2.c.h.485.13		20
88.83	even	10		968.2.o.d.493.9		40
132.59	even	10		792.2.br.b.37.4		40
264.59	even	10		792.2.br.b.37.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.2	✓	40	88.59	odd	10
88.2.o.a.37.7	yes	40	44.15	odd	10
88.2.o.a.69.2	yes	40	4.3	odd	2
88.2.o.a.69.7	yes	40	8.3	odd	2
352.2.w.a.81.2		40	88.37	even	10	inner
352.2.w.a.81.9		40	11.4	even	5	inner
352.2.w.a.113.2		40	1.1	even	1	trivial
352.2.w.a.113.9		40	8.5	even	2	inner
792.2.br.b.37.4		40	132.59	even	10
792.2.br.b.37.9		40	264.59	even	10
792.2.br.b.685.4		40	24.11	even	2
792.2.br.b.685.9		40	12.11	even	2
968.2.c.h.485.13		20	88.75	odd	10
968.2.c.h.485.14		20	44.31	odd	10
968.2.c.i.485.7		20	44.35	even	10
968.2.c.i.485.8		20	88.35	even	10
968.2.o.d.269.1		40	88.19	even	10
968.2.o.d.269.9		40	44.19	even	10
968.2.o.d.493.1		40	44.39	even	10
968.2.o.d.493.9		40	88.83	even	10
968.2.o.i.245.4		40	88.43	even	2
968.2.o.i.245.9		40	44.43	even	2
968.2.o.i.565.4		40	44.7	even	10
968.2.o.i.565.9		40	88.51	even	10
968.2.o.j.269.2		40	44.3	odd	10
968.2.o.j.269.10		40	88.3	odd	10
968.2.o.j.493.2		40	88.27	odd	10
968.2.o.j.493.10		40	44.27	odd	10
3872.2.c.h.1937.4		20	88.53	even	10
3872.2.c.h.1937.17		20	11.9	even	5
3872.2.c.i.1937.4		20	88.13	odd	10
3872.2.c.i.1937.17		20	11.2	odd	10

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.w (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.32812 + 0.756451i) q^{3} +(0.117836 - 0.162187i) q^{5} +(0.725001 - 2.23132i) q^{7} +(2.42086 - 1.75886i) q^{9} +(1.47592 + 2.97013i) q^{11} +(-0.959026 - 1.31999i) q^{13} +(-0.151649 + 0.466727i) q^{15} +(2.69920 + 1.96108i) q^{17} +(4.68224 - 1.52135i) q^{19} +5.74321i q^{21} +9.25109 q^{23} +(1.53267 + 4.71706i) q^{25} +(0.0110111 - 0.0151554i) q^{27} +(5.88863 + 1.91333i) q^{29} +(-6.68182 + 4.85463i) q^{31} +(-5.68286 - 5.79835i) q^{33} +(-0.276461 - 0.380516i) q^{35} +(-1.21740 - 0.395559i) q^{37} +(3.23123 + 2.34763i) q^{39} +(-1.86354 - 5.73540i) q^{41} -2.47184i q^{43} -0.599888i q^{45} +(-1.47060 - 4.52605i) q^{47} +(1.20994 + 0.879070i) q^{49} +(-7.76750 - 2.52381i) q^{51} +(-5.14997 - 7.08833i) q^{53} +(0.655632 + 0.110613i) q^{55} +(-9.74997 + 7.08377i) q^{57} +(1.81173 + 0.588668i) q^{59} +(3.75888 - 5.17366i) q^{61} +(-2.16946 - 6.67690i) q^{63} -0.327092 q^{65} +8.27349i q^{67} +(-21.5376 + 6.99800i) q^{69} +(-1.00994 - 0.733765i) q^{71} +(2.13073 - 6.55770i) q^{73} +(-7.13645 - 9.82248i) q^{75} +(7.69737 - 1.13990i) q^{77} +(-11.8293 + 8.59451i) q^{79} +(-2.78823 + 8.58129i) q^{81} +(5.50905 - 7.58255i) q^{83} +(0.636123 - 0.206689i) q^{85} -15.1568 q^{87} +5.11129 q^{89} +(-3.64061 + 1.18291i) q^{91} +(11.8838 - 16.3566i) q^{93} +(0.304992 - 0.938668i) q^{95} +(-0.242496 + 0.176183i) q^{97} +(8.79702 + 4.59434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{7} + 18 q^{15} - 6 q^{17} + 8 q^{23} - 4 q^{25} + 6 q^{31} - 10 q^{33} + 34 q^{39} - 14 q^{41} + 6 q^{47} - 4 q^{49} + 2 q^{55} - 26 q^{57} - 60 q^{63} - 36 q^{65} - 22 q^{71} - 6 q^{73} - 74 q^{79}+ \cdots + 10 q^{97}+O(q^{100}) \) 40 * q + 10 * q^7 + 18 * q^15 - 6 * q^17 + 8 * q^23 - 4 * q^25 + 6 * q^31 - 10 * q^33 + 34 * q^39 - 14 * q^41 + 6 * q^47 - 4 * q^49 + 2 * q^55 - 26 * q^57 - 60 * q^63 - 36 * q^65 - 22 * q^71 - 6 * q^73 - 74 * q^79 - 4 * q^81 - 68 * q^87 - 16 * q^89 - 66 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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