LMFDB - Embedded newform 512.2.i.b.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	512.289
Dual form			512.2.i.b.225.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.572535 + 0.856859i) q^{3} +(0.690473 + 3.47124i) q^{5} +(0.983337 + 2.37399i) q^{7} +(0.741639 - 1.79047i) q^{9} +(-1.29020 - 0.862086i) q^{11} +(0.115716 - 0.581745i) q^{13} +(-2.57905 + 2.57905i) q^{15} +(4.30936 + 4.30936i) q^{17} +(-3.59299 - 0.714690i) q^{19} +(-1.47118 + 2.20177i) q^{21} +(-7.79200 - 3.22755i) q^{23} +(-6.95338 + 2.88018i) q^{25} +(4.99100 - 0.992772i) q^{27} +(0.373179 - 0.249351i) q^{29} +1.08345i q^{31} -1.59910i q^{33} +(-7.56172 + 5.05258i) q^{35} +(4.16040 - 0.827556i) q^{37} +(0.564725 - 0.233917i) q^{39} +(5.15990 + 2.13730i) q^{41} +(1.55896 - 2.33315i) q^{43} +(6.72725 + 1.33813i) q^{45} +(6.43269 + 6.43269i) q^{47} +(0.280888 - 0.280888i) q^{49} +(-1.22526 + 6.15978i) q^{51} +(1.22184 + 0.816410i) q^{53} +(2.10166 - 5.07385i) q^{55} +(-1.44472 - 3.48787i) q^{57} +(1.46423 + 7.36119i) q^{59} +(-6.45980 - 9.66777i) q^{61} +4.97984 q^{63} +2.09928 q^{65} +(-3.30637 - 4.94834i) q^{67} +(-1.69564 - 8.52453i) q^{69} +(-3.75143 - 9.05676i) q^{71} +(-1.19724 + 2.89039i) q^{73} +(-6.44896 - 4.30906i) q^{75} +(0.777876 - 3.91064i) q^{77} +(-0.934789 + 0.934789i) q^{79} +(-0.402918 - 0.402918i) q^{81} +(16.5833 + 3.29862i) q^{83} +(-11.9833 + 17.9343i) q^{85} +(0.427317 + 0.177000i) q^{87} +(-6.15337 + 2.54881i) q^{89} +(1.49484 - 0.297343i) q^{91} +(-0.928361 + 0.620311i) q^{93} -12.9656i q^{95} -5.79443i q^{97} +(-2.50041 + 1.67072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$1$

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
$3$	0.572535	+	0.856859i	0.330553	+	0.494708i	0.959101	−	0.283063i	$-0.0913505\pi$
$3$	0.572535	+	0.856859i	0.330553	+	0.494708i	−0.628548	+	0.777771i	$0.716350\pi$
$4$		0			0
$5$	0.690473	+	3.47124i	0.308789	+	1.55239i	0.753947	+	0.656935i	$0.228147\pi$
$5$	0.690473	+	3.47124i	0.308789	+	1.55239i	−0.445158	+	0.895452i	$0.646853\pi$
$6$		0			0
$7$	0.983337	+	2.37399i	0.371667	+	0.897283i	0.993468	+	0.114108i	$0.0364010\pi$
$7$	0.983337	+	2.37399i	0.371667	+	0.897283i	−0.621802	+	0.783175i	$0.713599\pi$
$8$		0			0
$9$	0.741639	−	1.79047i	0.247213	−	0.596825i
$10$		0			0
$11$	−1.29020	−	0.862086i	−0.389011	−	0.259929i	0.345650	−	0.938364i	$-0.387659\pi$
$11$	−1.29020	−	0.862086i	−0.389011	−	0.259929i	−0.734660	+	0.678435i	$0.762659\pi$
$12$		0			0
$13$	0.115716	−	0.581745i	0.0320939	−	0.161347i	−0.961415	−	0.275103i	$-0.911288\pi$
$13$	0.115716	−	0.581745i	0.0320939	−	0.161347i	0.993509	+	0.113756i	$0.0362881\pi$
$14$		0			0
$15$	−2.57905	+	2.57905i	−0.665907	+	0.665907i
$16$		0			0
$17$	4.30936	+	4.30936i	1.04517	+	1.04517i	0.998930	+	0.0462432i	$0.0147249\pi$
$17$	4.30936	+	4.30936i	1.04517	+	1.04517i	0.0462432	+	0.998930i	$0.485275\pi$
$18$		0			0
$19$	−3.59299	−	0.714690i	−0.824288	−	0.163961i	−0.235115	−	0.971968i	$-0.575547\pi$
$19$	−3.59299	−	0.714690i	−0.824288	−	0.163961i	−0.589174	+	0.808006i	$0.700547\pi$
$20$		0			0
$21$	−1.47118	+	2.20177i	−0.321037	+	0.480466i
$22$		0			0
$23$	−7.79200	−	3.22755i	−1.62474	−	0.672991i	−0.630116	−	0.776501i	$-0.716993\pi$
$23$	−7.79200	−	3.22755i	−1.62474	−	0.672991i	−0.994628	+	0.103510i	$0.966993\pi$
$24$		0			0
$25$	−6.95338	+	2.88018i	−1.39068	+	0.576037i
$26$		0			0
$27$	4.99100	−	0.992772i	0.960519	−	0.191059i
$28$		0			0
$29$	0.373179	−	0.249351i	0.0692977	−	0.0463032i	−0.520439	−	0.853899i	$-0.674232\pi$
$29$	0.373179	−	0.249351i	0.0692977	−	0.0463032i	0.589736	+	0.807596i	$0.299232\pi$
$30$		0			0
$31$			1.08345i			0.194593i	0.995255	+	0.0972963i	$0.0310195\pi$
$31$			1.08345i			0.194593i	−0.995255	+	0.0972963i	$0.968981\pi$
$32$		0			0
$33$		−	1.59910i		−	0.278367i
$34$		0			0
$35$	−7.56172	+	5.05258i	−1.27816	+	0.854041i
$36$		0			0
$37$	4.16040	−	0.827556i	0.683966	−	0.136049i	0.159136	−	0.987257i	$-0.449129\pi$
$37$	4.16040	−	0.827556i	0.683966	−	0.136049i	0.524830	+	0.851207i	$0.324129\pi$
$38$		0			0
$39$	0.564725	−	0.233917i	0.0904284	−	0.0374567i
$40$		0			0
$41$	5.15990	+	2.13730i	0.805841	+	0.333790i	0.747293	−	0.664494i	$-0.231353\pi$
$41$	5.15990	+	2.13730i	0.805841	+	0.333790i	0.0585477	+	0.998285i	$0.481353\pi$
$42$		0			0
$43$	1.55896	−	2.33315i	0.237739	−	0.355802i	−0.693345	−	0.720605i	$-0.743864\pi$
$43$	1.55896	−	2.33315i	0.237739	−	0.355802i	0.931084	+	0.364804i	$0.118864\pi$
$44$		0			0
$45$	6.72725	+	1.33813i	1.00284	+	0.199477i
$46$		0			0
$47$	6.43269	+	6.43269i	0.938304	+	0.938304i	0.998204	−	0.0599006i	$-0.0190784\pi$
$47$	6.43269	+	6.43269i	0.938304	+	0.938304i	−0.0599006	+	0.998204i	$0.519078\pi$
$48$		0			0
$49$	0.280888	−	0.280888i	0.0401268	−	0.0401268i
$50$		0			0
$51$	−1.22526	+	6.15978i	−0.171570	+	0.862541i
$52$		0			0
$53$	1.22184	+	0.816410i	0.167833	+	0.112143i	0.636650	−	0.771153i	$-0.280320\pi$
$53$	1.22184	+	0.816410i	0.167833	+	0.112143i	−0.468817	+	0.883295i	$0.655320\pi$
$54$		0			0
$55$	2.10166	−	5.07385i	0.283388	−	0.684158i
$56$		0			0
$57$	−1.44472	−	3.48787i	−0.191358	−	0.461980i
$58$		0			0
$59$	1.46423	+	7.36119i	0.190627	+	0.958345i	0.951078	+	0.308950i	$0.0999776\pi$
$59$	1.46423	+	7.36119i	0.190627	+	0.958345i	−0.760452	+	0.649395i	$0.775022\pi$
$60$		0			0
$61$	−6.45980	−	9.66777i	−0.827092	−	1.23783i	−0.968781	−	0.247920i	$-0.920253\pi$
$61$	−6.45980	−	9.66777i	−0.827092	−	1.23783i	0.141688	−	0.989911i	$-0.454747\pi$
$62$		0			0
$63$	4.97984			0.627401
$64$		0			0
$65$	2.09928			0.260383
$66$		0			0
$67$	−3.30637	−	4.94834i	−0.403938	−	0.604535i	0.572612	−	0.819826i	$-0.305930\pi$
$67$	−3.30637	−	4.94834i	−0.403938	−	0.604535i	−0.976550	+	0.215291i	$0.930930\pi$
$68$		0			0
$69$	−1.69564	−	8.52453i	−0.204131	−	1.02623i
$70$		0			0
$71$	−3.75143	−	9.05676i	−0.445213	−	1.07484i	−0.974094	−	0.226143i	$-0.927388\pi$
$71$	−3.75143	−	9.05676i	−0.445213	−	1.07484i	0.528881	−	0.848696i	$-0.322612\pi$
$72$		0			0
$73$	−1.19724	+	2.89039i	−0.140126	+	0.338295i	−0.978327	−	0.207068i	$-0.933608\pi$
$73$	−1.19724	+	2.89039i	−0.140126	+	0.338295i	0.838200	+	0.545362i	$0.183608\pi$
$74$		0			0
$75$	−6.44896	−	4.30906i	−0.744662	−	0.497567i
$76$		0			0
$77$	0.777876	−	3.91064i	0.0886472	−	0.445659i
$78$		0			0
$79$	−0.934789	+	0.934789i	−0.105172	+	0.105172i	−0.757735	−	0.652563i	$-0.773694\pi$
$79$	−0.934789	+	0.934789i	−0.105172	+	0.105172i	0.652563	+	0.757735i	$0.273694\pi$
$80$		0			0
$81$	−0.402918	−	0.402918i	−0.0447687	−	0.0447687i
$82$		0			0
$83$	16.5833	+	3.29862i	1.82025	+	0.362070i	0.982834	−	0.184494i	$-0.0590645\pi$
$83$	16.5833	+	3.29862i	1.82025	+	0.362070i	0.837417	+	0.546564i	$0.184064\pi$
$84$		0			0
$85$	−11.9833	+	17.9343i	−1.29978	+	1.94525i
$86$		0			0
$87$	0.427317	+	0.177000i	0.0458132	+	0.0189764i
$88$		0			0
$89$	−6.15337	+	2.54881i	−0.652256	+	0.270173i	−0.684176	−	0.729317i	$-0.739838\pi$
$89$	−6.15337	+	2.54881i	−0.652256	+	0.270173i	0.0319199	+	0.999490i	$0.489838\pi$
$90$		0			0
$91$	1.49484	−	0.297343i	0.156702	−	0.0311700i
$92$		0			0
$93$	−0.928361	+	0.620311i	−0.0962666	+	0.0643233i
$94$		0			0
$95$		−	12.9656i		−	1.33024i
$96$		0			0
$97$		−	5.79443i		−	0.588336i	−0.955754	−	0.294168i	$-0.904958\pi$
$97$		−	5.79443i		−	0.588336i	0.955754	−	0.294168i	$-0.0950425\pi$
$98$		0			0
$99$	−2.50041	+	1.67072i	−0.251300	+	0.167914i
$100$		0			0
$101$	−0.921112	+	0.183220i	−0.0916540	+	0.0182311i	−0.240704	−	0.970599i	$-0.577378\pi$
$101$	−0.921112	+	0.183220i	−0.0916540	+	0.0182311i	0.149050	+	0.988830i	$0.452378\pi$
$102$		0			0
$103$	12.7902	−	5.29788i	1.26026	−	0.522015i	0.350268	−	0.936649i	$-0.386090\pi$
$103$	12.7902	−	5.29788i	1.26026	−	0.522015i	0.909988	+	0.414634i	$0.136090\pi$
$104$		0			0
$105$	−8.65870	−	3.58655i	−0.845002	−	0.350011i
$106$		0			0
$107$	8.24793	−	12.3439i	0.797358	−	1.19333i	−0.180400	−	0.983593i	$-0.557739\pi$
$107$	8.24793	−	12.3439i	0.797358	−	1.19333i	0.977758	−	0.209737i	$-0.0672608\pi$
$108$		0			0
$109$	6.63883	+	1.32055i	0.635885	+	0.126485i	0.502497	−	0.864579i	$-0.332415\pi$
$109$	6.63883	+	1.32055i	0.635885	+	0.126485i	0.133387	+	0.991064i	$0.457415\pi$
$110$		0			0
$111$	3.09108	+	3.09108i	0.293392	+	0.293392i
$112$		0			0
$113$	−3.62032	+	3.62032i	−0.340571	+	0.340571i	−0.856582	−	0.516011i	$-0.827416\pi$
$113$	−3.62032	+	3.62032i	−0.340571	+	0.340571i	0.516011	+	0.856582i	$0.327416\pi$
$114$		0			0
$115$	5.82345	−	29.2765i	0.543039	−	2.73004i
$116$		0			0
$117$	−0.955779	−	0.638631i	−0.0883618	−	0.0590415i
$118$		0			0
$119$	−5.99281	+	14.4679i	−0.549360	+	1.32627i
$120$		0			0
$121$	−3.28809	−	7.93814i	−0.298917	−	0.721649i
$122$		0			0
$123$	1.12286	+	5.64499i	0.101245	+	0.508991i
$124$		0			0
$125$	−4.96743	−	7.43428i	−0.444300	−	0.664942i
$126$		0			0
$127$	−5.27774			−0.468324			−0.234162	−	0.972198i	$-0.575235\pi$
$127$	−5.27774			−0.468324			−0.234162	+	0.972198i	$0.575235\pi$
$128$		0			0
$129$	2.89174			0.254603
$130$		0			0
$131$	3.19779	+	4.78583i	0.279392	+	0.418140i	0.944452	−	0.328651i	$-0.106594\pi$
$131$	3.19779	+	4.78583i	0.279392	+	0.418140i	−0.665060	+	0.746790i	$0.731594\pi$
$132$		0			0
$133$	−1.83646	−	9.23249i	−0.159241	−	0.800558i
$134$		0			0
$135$	6.89231	+	16.6395i	0.593195	+	1.43210i
$136$		0			0
$137$	3.78991	−	9.14965i	0.323794	−	0.781707i	−0.675233	−	0.737604i	$-0.735957\pi$
$137$	3.78991	−	9.14965i	0.323794	−	0.781707i	0.999027	−	0.0441030i	$-0.0140430\pi$
$138$		0			0
$139$	1.75609	+	1.17338i	0.148950	+	0.0995250i	0.627812	−	0.778365i	$-0.283951\pi$
$139$	1.75609	+	1.17338i	0.148950	+	0.0995250i	−0.478862	+	0.877890i	$0.658951\pi$
$140$		0			0
$141$	−1.82897	+	9.19485i	−0.154027	+	0.774346i
$142$		0			0
$143$	−0.650811	+	0.650811i	−0.0544236	+	0.0544236i
$144$		0			0
$145$	1.12323	+	1.12323i	0.0932789	+	0.0932789i
$146$		0			0
$147$	0.401500	+	0.0798632i	0.0331151	+	0.00658701i
$148$		0			0
$149$	10.0124	−	14.9845i	0.820244	−	1.22758i	−0.150772	−	0.988569i	$-0.548176\pi$
$149$	10.0124	−	14.9845i	0.820244	−	1.22758i	0.971016	−	0.239013i	$-0.0768240\pi$
$150$		0			0
$151$	−4.99222	−	2.06785i	−0.406261	−	0.168279i	0.170188	−	0.985412i	$-0.445562\pi$
$151$	−4.99222	−	2.06785i	−0.406261	−	0.168279i	−0.576450	+	0.817133i	$0.695562\pi$
$152$		0			0
$153$	10.9118	−	4.51981i	0.882166	−	0.365405i
$154$		0			0
$155$	−3.76090	+	0.748090i	−0.302083	+	0.0600881i
$156$		0			0
$157$	−7.04496	+	4.70729i	−0.562249	+	0.375683i	−0.803976	−	0.594662i	$-0.797286\pi$
$157$	−7.04496	+	4.70729i	−0.562249	+	0.375683i	0.241727	+	0.970344i	$0.422286\pi$
$158$		0			0
$159$			1.51437i			0.120098i
$160$		0			0
$161$		−	21.6719i		−	1.70798i
$162$		0			0
$163$	−0.919897	+	0.614656i	−0.0720519	+	0.0481435i	−0.591074	−	0.806617i	$-0.701296\pi$
$163$	−0.919897	+	0.614656i	−0.0720519	+	0.0481435i	0.519023	+	0.854761i	$0.326296\pi$
$164$		0			0
$165$	5.55085	−	1.10413i	0.432133	−	0.0859567i
$166$		0			0
$167$	−2.61833	+	1.08455i	−0.202612	+	0.0839247i	−0.481682	−	0.876346i	$-0.659974\pi$
$167$	−2.61833	+	1.08455i	−0.202612	+	0.0839247i	0.279070	+	0.960271i	$0.409974\pi$
$168$		0			0
$169$	11.6854	+	4.84025i	0.898877	+	0.372327i
$170$		0			0
$171$	−3.94433	+	5.90311i	−0.301631	+	0.451422i
$172$		0			0
$173$	−10.2464	−	2.03813i	−0.779016	−	0.154956i	−0.210462	−	0.977602i	$-0.567497\pi$
$173$	−10.2464	−	2.03813i	−0.779016	−	0.154956i	−0.568554	+	0.822646i	$0.692497\pi$
$174$		0			0
$175$	−13.6750	−	13.6750i	−1.03374	−	1.03374i
$176$		0			0
$177$	−5.46918	+	5.46918i	−0.411089	+	0.411089i
$178$		0			0
$179$	−3.79507	+	19.0791i	−0.283657	+	1.42604i	0.531627	+	0.846979i	$0.321581\pi$
$179$	−3.79507	+	19.0791i	−0.283657	+	1.42604i	−0.815284	+	0.579061i	$0.803419\pi$
$180$		0			0
$181$	−3.32947	−	2.22468i	−0.247477	−	0.165359i	0.425645	−	0.904890i	$-0.360047\pi$
$181$	−3.32947	−	2.22468i	−0.247477	−	0.165359i	−0.673122	+	0.739531i	$0.735047\pi$
$182$		0			0
$183$	4.58546	−	11.0703i	0.338967	−	0.818339i
$184$		0			0
$185$	5.74529	+	13.8704i	0.422402	+	1.01977i
$186$		0			0
$187$	−1.84491	−	9.27499i	−0.134913	−	0.678254i
$188$		0			0
$189$	7.26467	+	10.8723i	0.528427	+	0.790847i
$190$		0			0
$191$	16.2586			1.17643			0.588215	−	0.808704i	$-0.299831\pi$
$191$	16.2586			1.17643			0.588215	+	0.808704i	$0.299831\pi$
$192$		0			0
$193$	−24.9345			−1.79482			−0.897411	−	0.441196i	$-0.854554\pi$
$193$	−24.9345			−1.79482			−0.897411	+	0.441196i	$0.854554\pi$
$194$		0			0
$195$	1.20191	+	1.79878i	0.0860705	+	0.128814i
$196$		0			0
$197$	0.816489	+	4.10477i	0.0581724	+	0.292452i	0.998910	−	0.0466836i	$-0.0148653\pi$
$197$	0.816489	+	4.10477i	0.0581724	+	0.292452i	−0.940737	+	0.339136i	$0.889865\pi$
$198$		0			0
$199$	−0.744172	−	1.79659i	−0.0527529	−	0.127357i	0.895306	−	0.445452i	$-0.146957\pi$
$199$	−0.744172	−	1.79659i	−0.0527529	−	0.127357i	−0.948059	+	0.318095i	$0.896957\pi$
$200$		0			0
$201$	2.34701	−	5.66619i	0.165546	−	0.399662i
$202$		0			0
$203$	0.958916	+	0.640727i	0.0673027	+	0.0449702i
$204$		0			0
$205$	−3.85632	+	19.3870i	−0.269337	+	1.35405i
$206$		0			0
$207$	−11.5577	+	11.5577i	−0.803315	+	0.803315i
$208$		0			0
$209$	4.01956	+	4.01956i	0.278039	+	0.278039i
$210$		0			0
$211$	−14.6646	−	2.91696i	−1.00955	−	0.200812i	−0.337507	−	0.941323i	$-0.609584\pi$
$211$	−14.6646	−	2.91696i	−1.00955	−	0.200812i	−0.672044	+	0.740511i	$0.734584\pi$
$212$		0			0
$213$	5.61254	−	8.39976i	0.384565	−	0.575542i
$214$		0			0
$215$	9.17534	+	3.80055i	0.625753	+	0.259195i
$216$		0			0
$217$	−2.57209	+	1.06539i	−0.174605	+	0.0723236i
$218$		0			0
$219$	−3.16212	+	0.628985i	−0.213676	+	0.0425028i
$220$		0			0
$221$	3.00561	−	2.00828i	0.202179	−	0.135092i
$222$		0			0
$223$		−	14.8634i		−	0.995330i	−0.867369	−	0.497665i	$-0.834191\pi$
$223$		−	14.8634i		−	0.995330i	0.867369	−	0.497665i	$-0.165809\pi$
$224$		0			0
$225$			14.5859i			0.972393i
$226$		0			0
$227$	6.90248	−	4.61209i	0.458133	−	0.306115i	−0.305004	−	0.952351i	$-0.598658\pi$
$227$	6.90248	−	4.61209i	0.458133	−	0.306115i	0.763138	+	0.646236i	$0.223658\pi$
$228$		0			0
$229$	3.63468	−	0.722983i	0.240187	−	0.0477761i	−0.0735290	−	0.997293i	$-0.523426\pi$
$229$	3.63468	−	0.722983i	0.240187	−	0.0477761i	0.313716	+	0.949517i	$0.398426\pi$
$230$		0			0
$231$	3.79623	−	1.57245i	0.249774	−	0.103460i
$232$		0			0
$233$	17.7828	+	7.36589i	1.16499	+	0.482556i	0.879534	−	0.475836i	$-0.157854\pi$
$233$	17.7828	+	7.36589i	1.16499	+	0.482556i	0.285458	+	0.958391i	$0.407854\pi$
$234$		0			0
$235$	−17.8878	+	26.7710i	−1.16687	+	1.74635i
$236$		0			0
$237$	−1.33618	−	0.265783i	−0.0867944	−	0.0172645i
$238$		0			0
$239$	−1.69651	−	1.69651i	−0.109738	−	0.109738i	0.650106	−	0.759844i	$-0.274725\pi$
$239$	−1.69651	−	1.69651i	−0.109738	−	0.109738i	−0.759844	+	0.650106i	$0.774725\pi$
$240$		0			0
$241$	−12.7520	+	12.7520i	−0.821432	+	0.821432i	−0.986313	−	0.164882i	$-0.947276\pi$
$241$	−12.7520	+	12.7520i	−0.821432	+	0.821432i	0.164882	+	0.986313i	$0.447276\pi$
$242$		0			0
$243$	3.09288	−	15.5489i	0.198408	−	0.997465i
$244$		0			0
$245$	1.16898	+	0.781085i	0.0746831	+	0.0499017i
$246$		0			0
$247$	−0.831534	+	2.00750i	−0.0529093	+	0.127734i
$248$		0			0
$249$	6.66806	+	16.0981i	0.422571	+	1.02018i
$250$		0			0
$251$	−0.0325488	−	0.163634i	−0.00205446	−	0.0103285i	0.979744	−	0.200252i	$-0.0641760\pi$
$251$	−0.0325488	−	0.163634i	−0.00205446	−	0.0103285i	−0.981799	+	0.189923i	$0.939176\pi$
$252$		0			0
$253$	7.27083	+	10.8816i	0.457113	+	0.684118i
$254$		0			0
$255$	−22.2281			−1.39198
$256$		0			0
$257$	1.30561			0.0814417			0.0407209	−	0.999171i	$-0.487035\pi$
$257$	1.30561			0.0814417			0.0407209	+	0.999171i	$0.487035\pi$
$258$		0			0
$259$	6.05569	+	9.06297i	0.376282	+	0.563146i
$260$		0			0
$261$	−0.169691	−	0.853096i	−0.0105036	−	0.0528053i
$262$		0			0
$263$	4.45700	+	10.7602i	0.274831	+	0.663500i	0.999677	−	0.0254106i	$-0.00808933\pi$
$263$	4.45700	+	10.7602i	0.274831	+	0.663500i	−0.724846	+	0.688910i	$0.758089\pi$
$264$		0			0
$265$	−1.99031	+	4.80503i	−0.122264	+	0.295170i
$266$		0			0
$267$	−5.70699	−	3.81329i	−0.349262	−	0.233370i
$268$		0			0
$269$	2.48406	−	12.4882i	0.151456	−	0.761419i	−0.828153	−	0.560502i	$-0.810608\pi$
$269$	2.48406	−	12.4882i	0.151456	−	0.761419i	0.979608	−	0.200916i	$-0.0643919\pi$
$270$		0			0
$271$	5.90740	−	5.90740i	0.358849	−	0.358849i	−0.504540	−	0.863389i	$-0.668338\pi$
$271$	5.90740	−	5.90740i	0.358849	−	0.358849i	0.863389	+	0.504540i	$0.168338\pi$
$272$		0			0
$273$	1.11063	+	1.11063i	0.0672184	+	0.0672184i
$274$		0			0
$275$	11.4542	+	2.27839i	0.690716	+	0.137392i
$276$		0			0
$277$	0.0619322	−	0.0926880i	0.00372114	−	0.00556908i	−0.829604	−	0.558352i	$-0.811434\pi$
$277$	0.0619322	−	0.0926880i	0.00372114	−	0.00556908i	0.833326	+	0.552783i	$0.186434\pi$
$278$		0			0
$279$	1.93988	+	0.803526i	0.116138	+	0.0481058i
$280$		0			0
$281$	−8.41645	+	3.48621i	−0.502083	+	0.207970i	−0.619327	−	0.785133i	$-0.712594\pi$
$281$	−8.41645	+	3.48621i	−0.502083	+	0.207970i	0.117243	+	0.993103i	$0.462594\pi$
$282$		0			0
$283$	−11.6331	+	2.31397i	−0.691518	+	0.137551i	−0.528324	−	0.849043i	$-0.677179\pi$
$283$	−11.6331	+	2.31397i	−0.691518	+	0.137551i	−0.163193	+	0.986594i	$0.552179\pi$
$284$		0			0
$285$	11.1097	−	7.42327i	0.658082	−	0.439717i
$286$		0			0
$287$			14.3512i			0.847126i
$288$		0			0
$289$			20.1412i			1.18478i
$290$		0			0
$291$	4.96502	−	3.31752i	0.291054	−	0.194476i
$292$		0			0
$293$	−0.100300	+	0.0199510i	−0.00585961	+	0.00116555i	−0.198019	−	0.980198i	$-0.563451\pi$
$293$	−0.100300	+	0.0199510i	−0.00585961	+	0.00116555i	0.192160	+	0.981364i	$0.438451\pi$
$294$		0			0
$295$	−24.5415	+	10.1654i	−1.42886	+	0.591853i
$296$		0			0
$297$	−7.29526	−	3.02180i	−0.423314	−	0.175342i
$298$		0			0
$299$	−2.77927	+	4.15947i	−0.160729	+	0.240549i
$300$		0			0
$301$	7.07185	+	1.40668i	0.407614	+	0.0810795i
$302$		0			0
$303$	−0.684363	−	0.684363i	−0.0393156	−	0.0393156i
$304$		0			0
$305$	29.0989	−	29.0989i	1.66620	−	1.66620i
$306$		0			0
$307$	−4.46728	+	22.4585i	−0.254961	+	1.28178i	0.614950	+	0.788566i	$0.289176\pi$
$307$	−4.46728	+	22.4585i	−0.254961	+	1.28178i	−0.869911	+	0.493209i	$0.835824\pi$
$308$		0			0
$309$	11.8624	+	7.92619i	0.674827	+	0.450905i
$310$		0			0
$311$	−6.48708	+	15.6612i	−0.367848	+	0.888064i	0.626254	+	0.779619i	$0.284587\pi$
$311$	−6.48708	+	15.6612i	−0.367848	+	0.888064i	−0.994102	+	0.108445i	$0.965413\pi$
$312$		0			0
$313$	−6.94583	−	16.7687i	−0.392602	−	0.947824i	−0.989371	−	0.145411i	$-0.953549\pi$
$313$	−6.94583	−	16.7687i	−0.392602	−	0.947824i	0.596770	−	0.802413i	$-0.296451\pi$
$314$		0			0
$315$	3.43845	+	17.2862i	0.193735	+	0.973970i
$316$		0			0
$317$	10.9936	+	16.4530i	0.617459	+	0.924093i	1.00000		0.000154534i	$4.91898e-5\pi$
$317$	10.9936	+	16.4530i	0.617459	+	0.924093i	−0.382541	+	0.923939i	$0.624951\pi$
$318$		0			0
$319$	−0.696439			−0.0389931
$320$		0			0
$321$	15.2992			0.853919
$322$		0			0
$323$	−12.4036	−	18.5633i	−0.690156	−	1.03289i
$324$		0			0
$325$	0.870913	+	4.37837i	0.0483095	+	0.242868i
$326$		0			0
$327$	2.66944	+	6.44460i	0.147620	+	0.356387i
$328$		0			0
$329$	−8.94561	+	21.5966i	−0.493187	+	1.19066i
$330$		0			0
$331$	5.97462	+	3.99211i	0.328395	+	0.219426i	0.708827	−	0.705382i	$-0.249225\pi$
$331$	5.97462	+	3.99211i	0.328395	+	0.219426i	−0.380432	+	0.924809i	$0.624225\pi$
$332$		0			0
$333$	1.60380	−	8.06284i	0.0878876	−	0.441841i
$334$		0			0
$335$	14.8939	−	14.8939i	0.813741	−	0.813741i
$336$		0			0
$337$	−18.4718	−	18.4718i	−1.00622	−	1.00622i	−0.999981	−	0.00624304i	$-0.998013\pi$
$337$	−18.4718	−	18.4718i	−1.00622	−	1.00622i	−0.00624304	−	0.999981i	$-0.501987\pi$
$338$		0			0
$339$	−5.17487	−	1.02935i	−0.281060	−	0.0559064i
$340$		0			0
$341$	0.934023	−	1.39786i	0.0505802	−	0.0756986i
$342$		0			0
$343$	17.5609	+	7.27398i	0.948201	+	0.392758i
$344$		0			0
$345$	28.4199	−	11.7719i	1.53008	−	0.633779i
$346$		0			0
$347$	−9.12297	+	1.81467i	−0.489747	+	0.0974167i	−0.433785	−	0.901016i	$-0.642822\pi$
$347$	−9.12297	+	1.81467i	−0.489747	+	0.0974167i	−0.0559615	+	0.998433i	$0.517822\pi$
$348$		0			0
$349$	−9.46721	+	6.32579i	−0.506768	+	0.338612i	−0.782528	−	0.622615i	$-0.786070\pi$
$349$	−9.46721	+	6.32579i	−0.506768	+	0.338612i	0.275760	+	0.961226i	$0.411070\pi$
$350$		0			0
$351$		−	3.01837i		−	0.161109i
$352$		0			0
$353$			12.2587i			0.652465i	0.945290	+	0.326233i	$0.105779\pi$
$353$			12.2587i			0.652465i	−0.945290	+	0.326233i	$0.894221\pi$
$354$		0			0
$355$	28.8479	−	19.2756i	1.53109	−	1.02304i
$356$		0			0
$357$	−15.8281	+	3.14840i	−0.837710	+	0.166631i
$358$		0			0
$359$	−6.95121	+	2.87929i	−0.366871	+	0.151963i	−0.558500	−	0.829505i	$-0.688623\pi$
$359$	−6.95121	+	2.87929i	−0.366871	+	0.151963i	0.191629	+	0.981467i	$0.438623\pi$
$360$		0			0
$361$	−5.15492	−	2.13524i	−0.271311	−	0.112381i
$362$		0			0
$363$	4.91933	−	7.36230i	0.258198	−	0.386420i
$364$		0			0
$365$	−10.8599	−	2.16017i	−0.568433	−	0.113068i
$366$		0			0
$367$	−1.10049	−	1.10049i	−0.0574452	−	0.0574452i	0.677801	−	0.735246i	$-0.262933\pi$
$367$	−1.10049	−	1.10049i	−0.0574452	−	0.0574452i	−0.735246	+	0.677801i	$0.762933\pi$
$368$		0			0
$369$	7.65356	−	7.65356i	0.398429	−	0.398429i
$370$		0			0
$371$	−0.736662	+	3.70345i	−0.0382456	+	0.192273i
$372$		0			0
$373$	−29.9517	−	20.0131i	−1.55084	−	1.03624i	−0.975946	−	0.218014i	$-0.930042\pi$
$373$	−29.9517	−	20.0131i	−1.55084	−	1.03624i	−0.574897	−	0.818226i	$-0.694958\pi$
$374$		0			0
$375$	3.52611	−	8.51278i	0.182087	−	0.439598i
$376$		0			0
$377$	−0.101875	−	0.245949i	−0.00524685	−	0.0126670i
$378$		0			0
$379$	−3.70680	−	18.6353i	−0.190405	−	0.957233i	−0.951279	−	0.308332i	$-0.900229\pi$
$379$	−3.70680	−	18.6353i	−0.190405	−	0.957233i	0.760873	−	0.648900i	$-0.224771\pi$
$380$		0			0
$381$	−3.02169	−	4.52229i	−0.154806	−	0.231684i
$382$		0			0
$383$	−22.9884			−1.17465			−0.587327	−	0.809350i	$-0.699820\pi$
$383$	−22.9884			−1.17465			−0.587327	+	0.809350i	$0.699820\pi$
$384$		0			0
$385$	14.1119			0.719209
$386$		0			0
$387$	−3.02126	−	4.52163i	−0.153579	−	0.229847i
$388$		0			0
$389$	5.01123	+	25.1931i	0.254079	+	1.27734i	0.871377	+	0.490614i	$0.163227\pi$
$389$	5.01123	+	25.1931i	0.254079	+	1.27734i	−0.617298	+	0.786729i	$0.711773\pi$
$390$		0			0
$391$	−19.6698	−	47.4872i	−0.994747	−	2.40153i
$392$		0			0
$393$	−2.26994	+	5.48011i	−0.114503	+	0.276435i
$394$		0			0
$395$	−3.89033	−	2.59943i	−0.195744	−	0.130792i
$396$		0			0
$397$	−0.319222	+	1.60484i	−0.0160213	+	0.0805445i	−0.987969	−	0.154654i	$-0.950574\pi$
$397$	−0.319222	+	1.60484i	−0.0160213	+	0.0805445i	0.971947	+	0.235198i	$0.0755739\pi$
$398$		0			0
$399$	6.85951	−	6.85951i	0.343405	−	0.343405i
$400$		0			0
$401$	−21.7278	−	21.7278i	−1.08503	−	1.08503i	−0.996031	−	0.0890025i	$-0.971632\pi$
$401$	−21.7278	−	21.7278i	−1.08503	−	1.08503i	−0.0890025	−	0.996031i	$-0.528368\pi$
$402$		0			0
$403$	0.630289	+	0.125372i	0.0313969	+	0.00624524i
$404$		0			0
$405$	1.12042	−	1.67683i	0.0556742	−	0.0833224i
$406$		0			0
$407$	−6.08119	−	2.51891i	−0.301433	−	0.124858i
$408$		0			0
$409$	17.9000	−	7.41442i	0.885097	−	0.366619i	0.106626	−	0.994299i	$-0.465995\pi$
$409$	17.9000	−	7.41442i	0.885097	−	0.366619i	0.778472	+	0.627680i	$0.215995\pi$
$410$		0			0
$411$	10.0098	−	1.99108i	0.493748	−	0.0982126i
$412$		0			0
$413$	−16.0355	+	10.7146i	−0.789056	+	0.527231i
$414$		0			0
$415$			59.8422i			2.93754i
$416$		0			0
$417$			2.17653i			0.106585i
$418$		0			0
$419$	−27.8129	+	18.5840i	−1.35875	+	0.907886i	−0.999677	−	0.0254236i	$-0.991907\pi$
$419$	−27.8129	+	18.5840i	−1.35875	+	0.907886i	−0.359071	+	0.933310i	$0.616907\pi$
$420$		0			0
$421$	−19.7735	+	3.93320i	−0.963703	+	0.191693i	−0.651774	−	0.758413i	$-0.725975\pi$
$421$	−19.7735	+	3.93320i	−0.963703	+	0.191693i	−0.311929	+	0.950105i	$0.600975\pi$
$422$		0			0
$423$	16.2883	−	6.74683i	0.791964	−	0.328042i
$424$		0			0
$425$	−42.3764	−	17.5529i	−2.05556	−	0.851439i
$426$		0			0
$427$	16.5990	−	24.8422i	0.803282	−	1.20220i
$428$		0			0
$429$	−0.930266	−	0.185041i	−0.0449137	−	0.00893388i
$430$		0			0
$431$	13.5229	+	13.5229i	0.651373	+	0.651373i	0.953324	−	0.301950i	$-0.0976377\pi$
$431$	13.5229	+	13.5229i	0.651373	+	0.651373i	−0.301950	+	0.953324i	$0.597638\pi$
$432$		0			0
$433$	−17.9120	+	17.9120i	−0.860797	+	0.860797i	−0.991431	−	0.130634i	$-0.958299\pi$
$433$	−17.9120	+	17.9120i	−0.860797	+	0.860797i	0.130634	+	0.991431i	$0.458299\pi$
$434$		0			0
$435$	−0.319361	+	1.60553i	−0.0153122	+	0.0769795i
$436$		0			0
$437$	25.6899	+	17.1654i	1.22891	+	0.821134i
$438$		0			0
$439$	2.81785	−	6.80290i	0.134489	−	0.324685i	−0.842260	−	0.539071i	$-0.818775\pi$
$439$	2.81785	−	6.80290i	0.134489	−	0.324685i	0.976749	+	0.214387i	$0.0687753\pi$
$440$		0			0
$441$	−0.294605	−	0.711240i	−0.0140288	−	0.0338686i
$442$		0			0
$443$	−5.64485	−	28.3786i	−0.268195	−	1.34831i	−0.846458	−	0.532456i	$-0.821269\pi$
$443$	−5.64485	−	28.3786i	−0.268195	−	1.34831i	0.578263	−	0.815850i	$-0.303731\pi$
$444$		0			0
$445$	−13.0963	−	19.6000i	−0.620823	−	0.929127i
$446$		0			0
$447$	18.5721			0.878429
$448$		0			0
$449$	−0.0955370			−0.00450867			−0.00225433	−	0.999997i	$-0.500718\pi$
$449$	−0.0955370			−0.00450867			−0.00225433	+	0.999997i	$0.500718\pi$
$450$		0			0
$451$	−4.81478	−	7.20583i	−0.226719	−	0.339309i
$452$		0			0
$453$	−1.08637	−	5.46155i	−0.0510421	−	0.256606i
$454$		0			0
$455$	2.06430	+	4.98365i	0.0967757	+	0.233637i
$456$		0			0
$457$	11.4359	−	27.6087i	0.534949	−	1.29148i	−0.393262	−	0.919426i	$-0.628654\pi$
$457$	11.4359	−	27.6087i	0.534949	−	1.29148i	0.928211	−	0.372054i	$-0.121346\pi$
$458$		0			0
$459$	25.7862	+	17.2298i	1.20360	+	0.804219i
$460$		0			0
$461$	5.29789	−	26.6343i	0.246747	−	1.24048i	−0.636390	−	0.771368i	$-0.719573\pi$
$461$	5.29789	−	26.6343i	0.246747	−	1.24048i	0.883137	−	0.469115i	$-0.155427\pi$
$462$		0			0
$463$	21.3463	−	21.3463i	0.992048	−	0.992048i	−0.00792071	−	0.999969i	$-0.502521\pi$
$463$	21.3463	−	21.3463i	0.992048	−	0.992048i	0.999969	+	0.00792071i	$0.00252127\pi$
$464$		0			0
$465$	−2.79426	−	2.79426i	−0.129581	−	0.129581i
$466$		0			0
$467$	−32.0458	−	6.37431i	−1.48290	−	0.294968i	−0.613746	−	0.789503i	$-0.710338\pi$
$467$	−32.0458	−	6.37431i	−1.48290	−	0.294968i	−0.869157	+	0.494535i	$0.835338\pi$
$468$		0			0
$469$	8.49600	−	12.7152i	0.392309	−	0.587132i
$470$		0			0
$471$	−8.06697	−	3.34145i	−0.371707	−	0.153966i
$472$		0			0
$473$	−4.02275	+	1.66628i	−0.184966	+	0.0766155i
$474$		0			0
$475$	27.0418	−	5.37896i	1.24077	−	0.246804i
$476$		0			0
$477$	2.36793	−	1.58220i	0.108420	−	0.0724439i
$478$		0			0
$479$		−	0.620601i		−	0.0283560i	−0.999899	−	0.0141780i	$-0.995487\pi$
$479$		−	0.620601i		−	0.0283560i	0.999899	−	0.0141780i	$-0.00451315\pi$
$480$		0			0
$481$		−	2.51605i		−	0.114722i
$482$		0			0
$483$	18.5697	−	12.4079i	0.844953	−	0.564579i
$484$		0			0
$485$	20.1139	−	4.00090i	0.913325	−	0.181672i
$486$		0			0
$487$	−11.7418	+	4.86361i	−0.532072	+	0.220391i	−0.632510	−	0.774552i	$-0.717975\pi$
$487$	−11.7418	+	4.86361i	−0.532072	+	0.220391i	0.100439	+	0.994943i	$0.467975\pi$
$488$		0			0
$489$	−1.05335	−	0.436311i	−0.0476340	−	0.0197306i
$490$		0			0
$491$	11.9335	−	17.8598i	0.538553	−	0.806002i	−0.458000	−	0.888952i	$-0.651434\pi$
$491$	11.9335	−	17.8598i	0.538553	−	0.806002i	0.996554	+	0.0829501i	$0.0264342\pi$
$492$		0			0
$493$	2.68271	+	0.533623i	0.120823	+	0.0240332i
$494$		0			0
$495$	−7.52593	−	7.52593i	−0.338266	−	0.338266i
$496$		0			0
$497$	17.8117	−	17.8117i	0.798964	−	0.798964i
$498$		0			0
$499$	−5.81742	+	29.2462i	−0.260424	+	1.30924i	0.600140	+	0.799895i	$0.295112\pi$
$499$	−5.81742	+	29.2462i	−0.260424	+	1.30924i	−0.860564	+	0.509343i	$0.829888\pi$
$500$		0			0
$501$	−2.42839	−	1.62260i	−0.108492	−	0.0724923i
$502$		0			0
$503$	10.2519	−	24.7502i	0.457108	−	1.10356i	−0.512455	−	0.858714i	$-0.671264\pi$
$503$	10.2519	−	24.7502i	0.457108	−	1.10356i	0.969563	−	0.244842i	$-0.0787362\pi$
$504$		0			0
$505$	−1.27201	−	3.07089i	−0.0566035	−	0.136653i
$506$		0			0
$507$	2.54289	+	12.7840i	0.112934	+	0.567755i
$508$		0			0
$509$	3.45815	+	5.17549i	0.153280	+	0.229399i	0.900160	−	0.435559i	$-0.143449\pi$
$509$	3.45815	+	5.17549i	0.153280	+	0.229399i	−0.746880	+	0.664958i	$0.768449\pi$
$510$		0			0
$511$	−8.03904			−0.355626
$512$		0			0
$513$	−18.6421			−0.823071
$514$		0			0
$515$	27.2215	+	40.7399i	1.19952	+	1.79521i
$516$		0			0
$517$	−2.75394	−	13.8450i	−0.121118	−	0.608902i
$518$		0			0
$519$	−4.12001	−	9.94659i	−0.180848	−	0.436607i
$520$		0			0
$521$	−13.3796	+	32.3011i	−0.586169	+	1.41514i	0.300969	+	0.953634i	$0.402690\pi$
$521$	−13.3796	+	32.3011i	−0.586169	+	1.41514i	−0.887138	+	0.461504i	$0.847310\pi$
$522$		0			0
$523$	29.7773	+	19.8966i	1.30207	+	0.870016i	0.996617	−	0.0821904i	$-0.0261916\pi$
$523$	29.7773	+	19.8966i	1.30207	+	0.870016i	0.305455	+	0.952207i	$0.401192\pi$
$524$		0			0
$525$	3.88814	−	19.5470i	0.169692	−	0.853102i
$526$		0			0
$527$	−4.66896	+	4.66896i	−0.203383	+	0.203383i
$528$		0			0
$529$	34.0347	+	34.0347i	1.47977	+	1.47977i
$530$		0			0
$531$	14.2659	+	2.83767i	0.619089	+	0.123145i
$532$		0			0
$533$	1.84045	−	2.75442i	0.0797186	−	0.119307i
$534$		0			0
$535$	48.5437	+	20.1074i	2.09873	+	0.869321i
$536$		0			0
$537$	−18.5209	+	7.67162i	−0.799237	+	0.331055i
$538$		0			0
$539$	−0.604552	+	0.120253i	−0.0260399	+	0.00517966i
$540$		0			0
$541$	33.4281	−	22.3359i	1.43718	−	0.960296i	0.439099	−	0.898439i	$-0.355298\pi$
$541$	33.4281	−	22.3359i	1.43718	−	0.960296i	0.998085	−	0.0618571i	$-0.0197023\pi$
$542$		0			0
$543$		−	4.12659i		−	0.177089i
$544$		0			0
$545$			23.9568i			1.02620i
$546$		0			0
$547$	2.75272	−	1.83931i	0.117698	−	0.0786432i	−0.495328	−	0.868706i	$-0.664952\pi$
$547$	2.75272	−	1.83931i	0.117698	−	0.0786432i	0.613026	+	0.790063i	$0.289952\pi$
$548$		0			0
$549$	−22.1007	+	4.39611i	−0.943236	+	0.187621i
$550$		0			0
$551$	−1.51904	+	0.629206i	−0.0647132	+	0.0268051i
$552$		0			0
$553$	−3.13839	−	1.29996i	−0.133458	−	0.0552801i
$554$		0			0
$555$	−8.59557	+	12.8642i	−0.364862	+	0.546054i
$556$		0			0
$557$	−42.1945	−	8.39301i	−1.78784	−	0.355623i	−0.813650	−	0.581355i	$-0.802523\pi$
$557$	−42.1945	−	8.39301i	−1.78784	−	0.355623i	−0.974190	+	0.225731i	$0.927523\pi$
$558$		0			0
$559$	−1.17690	−	1.17690i	−0.0497775	−	0.0497775i
$560$		0			0
$561$	6.89108	−	6.89108i	0.290942	−	0.290942i
$562$		0			0
$563$	2.34500	−	11.7891i	0.0988299	−	0.496852i	−0.899387	−	0.437154i	$-0.855986\pi$
$563$	2.34500	−	11.7891i	0.0988299	−	0.496852i	0.998217	−	0.0596975i	$-0.0190136\pi$
$564$		0			0
$565$	−15.0668	−	10.0673i	−0.633863	−	0.423534i
$566$		0			0
$567$	0.560318	−	1.35273i	0.0235311	−	0.0568092i
$568$		0			0
$569$	−2.83292	−	6.83927i	−0.118762	−	0.286717i	0.853308	−	0.521407i	$-0.174593\pi$
$569$	−2.83292	−	6.83927i	−0.118762	−	0.286717i	−0.972070	+	0.234690i	$0.924593\pi$
$570$		0			0
$571$	−6.93430	−	34.8611i	−0.290191	−	1.45889i	−0.800725	−	0.599032i	$-0.795552\pi$
$571$	−6.93430	−	34.8611i	−0.290191	−	1.45889i	0.510534	−	0.859858i	$-0.329448\pi$
$572$		0			0
$573$	9.30862	+	13.9313i	0.388873	+	0.581990i
$574$		0			0
$575$	63.4766			2.64716
$576$		0			0
$577$	24.2433			1.00926			0.504632	−	0.863335i	$-0.331628\pi$
$577$	24.2433			1.00926			0.504632	+	0.863335i	$0.331628\pi$
$578$		0			0
$579$	−14.2759	−	21.3653i	−0.593284	−	0.887913i
$580$		0			0
$581$	8.47608	+	42.6121i	0.351647	+	1.76785i
$582$		0			0
$583$	−0.872611	−	2.10667i	−0.0361398	−	0.0872493i
$584$		0			0
$585$	1.55690	−	3.75870i	0.0643701	−	0.155403i
$586$		0			0
$587$	−12.8222	−	8.56752i	−0.529229	−	0.353619i	0.262070	−	0.965049i	$-0.415595\pi$
$587$	−12.8222	−	8.56752i	−0.529229	−	0.353619i	−0.791299	+	0.611429i	$0.790595\pi$
$588$		0			0
$589$	0.774328	−	3.89281i	0.0319056	−	0.160400i
$590$		0			0
$591$	−3.04974	+	3.04974i	−0.125450	+	0.125450i
$592$		0			0
$593$	−7.17902	−	7.17902i	−0.294807	−	0.294807i	0.544169	−	0.838976i	$-0.316845\pi$
$593$	−7.17902	−	7.17902i	−0.294807	−	0.294807i	−0.838976	+	0.544169i	$0.816845\pi$
$594$		0			0
$595$	−54.3595	−	10.8128i	−2.22852	−	0.443281i
$596$		0			0
$597$	1.11336	−	1.66626i	0.0455668	−	0.0681955i
$598$		0			0
$599$	−37.8559	−	15.6804i	−1.54675	−	0.640685i	−0.564025	−	0.825758i	$-0.690748\pi$
$599$	−37.8559	−	15.6804i	−1.54675	−	0.640685i	−0.982725	+	0.185073i	$0.940748\pi$
$600$		0			0
$601$	−32.5429	+	13.4797i	−1.32745	+	0.549850i	−0.929928	−	0.367741i	$-0.880131\pi$
$601$	−32.5429	+	13.4797i	−1.32745	+	0.549850i	−0.397526	+	0.917591i	$0.630131\pi$
$602$		0			0
$603$	−11.3120	+	2.25010i	−0.460660	+	0.0916310i
$604$		0			0
$605$	25.2849	−	16.8948i	1.02798	−	0.686872i
$606$		0			0
$607$		−	37.4709i		−	1.52090i	−0.649399	−	0.760448i	$-0.724979\pi$
$607$		−	37.4709i		−	1.52090i	0.649399	−	0.760448i	$-0.275021\pi$
$608$		0			0
$609$			1.18850i			0.0481603i
$610$		0			0
$611$	4.48655	−	2.99781i	0.181506	−	0.121279i
$612$		0			0
$613$	−3.83710	+	0.763246i	−0.154979	+	0.0308272i	−0.271970	−	0.962306i	$-0.587675\pi$
$613$	−3.83710	+	0.763246i	−0.154979	+	0.0308272i	0.116991	+	0.993133i	$0.462675\pi$
$614$		0			0
$615$	−18.8198	+	7.79543i	−0.758889	+	0.314342i
$616$		0			0
$617$	−37.8776	−	15.6894i	−1.52490	−	0.631633i	−0.546331	−	0.837569i	$-0.683976\pi$
$617$	−37.8776	−	15.6894i	−1.52490	−	0.631633i	−0.978565	+	0.205937i	$0.933976\pi$
$618$		0			0
$619$	−22.0632	+	33.0200i	−0.886796	+	1.32718i	0.0575877	+	0.998340i	$0.481659\pi$
$619$	−22.0632	+	33.0200i	−0.886796	+	1.32718i	−0.944384	+	0.328844i	$0.893341\pi$
$620$		0			0
$621$	−42.0941	−	8.37304i	−1.68918	−	0.335998i
$622$		0			0
$623$	−12.1017	−	12.1017i	−0.484843	−	0.484843i
$624$		0			0
$625$	−4.23310	+	4.23310i	−0.169324	+	0.169324i
$626$		0			0
$627$	−1.14286	+	5.74554i	−0.0456414	+	0.229455i
$628$		0			0
$629$	21.4949	+	14.3624i	0.857058	+	0.572668i
$630$		0			0
$631$	−0.295581	+	0.713596i	−0.0117669	+	0.0284078i	−0.929654	−	0.368434i	$-0.879894\pi$
$631$	−0.295581	+	0.713596i	−0.0117669	+	0.0284078i	0.917887	+	0.396842i	$0.129894\pi$
$632$		0			0
$633$	−5.89655	−	14.2355i	−0.234367	−	0.565812i
$634$		0			0
$635$	−3.64414	−	18.3203i	−0.144613	−	0.727020i
$636$		0			0
$637$	−0.130902	−	0.195908i	−0.00518652	−	0.00776217i
$638$		0			0
$639$	−18.9981			−0.751553
$640$		0			0
$641$	20.3094			0.802172			0.401086	−	0.916040i	$-0.368633\pi$
$641$	20.3094			0.802172			0.401086	+	0.916040i	$0.368633\pi$
$642$		0			0
$643$	6.26132	+	9.37072i	0.246922	+	0.369545i	0.934140	−	0.356906i	$-0.116168\pi$
$643$	6.26132	+	9.37072i	0.246922	+	0.369545i	−0.687218	+	0.726451i	$0.741168\pi$
$644$		0			0
$645$	1.99667	+	10.0379i	0.0786187	+	0.395243i
$646$		0			0
$647$	−0.189930	−	0.458531i	−0.00746691	−	0.0180267i	0.920102	−	0.391679i	$-0.128105\pi$
$647$	−0.189930	−	0.458531i	−0.00746691	−	0.0180267i	−0.927569	+	0.373652i	$0.878105\pi$
$648$		0			0
$649$	4.45682	−	10.7597i	0.174945	−	0.422356i
$650$		0			0
$651$	−2.38550	−	1.59394i	−0.0934952	−	0.0624715i
$652$		0			0
$653$	−4.73978	+	23.8285i	−0.185482	+	0.932481i	0.770138	+	0.637878i	$0.220187\pi$
$653$	−4.73978	+	23.8285i	−0.185482	+	0.932481i	−0.955620	+	0.294603i	$0.904813\pi$
$654$		0			0
$655$	−14.4048	+	14.4048i	−0.562842	+	0.562842i
$656$		0			0
$657$	4.28725	+	4.28725i	0.167262	+	0.167262i
$658$		0			0
$659$	38.0620	+	7.57099i	1.48268	+	0.294924i	0.869073	−	0.494685i	$-0.164716\pi$
$659$	38.0620	+	7.57099i	1.48268	+	0.294924i	0.613611	+	0.789609i	$0.289716\pi$
$660$		0			0
$661$	−5.84250	+	8.74392i	−0.227247	+	0.340099i	−0.927518	−	0.373778i	$-0.878062\pi$
$661$	−5.84250	+	8.74392i	−0.227247	+	0.340099i	0.700271	+	0.713877i	$0.253062\pi$
$662$		0			0
$663$	3.44164	+	1.42557i	0.133662	+	0.0553646i
$664$		0			0
$665$	30.7802	−	12.7496i	1.19360	−	0.494407i
$666$		0			0
$667$	−3.71261	+	0.738483i	−0.143753	+	0.0285942i
$668$		0			0
$669$	12.7359	−	8.50984i	0.492398	−	0.329010i
$670$		0			0
$671$			18.0423i			0.696515i
$672$		0			0
$673$		−	40.4801i		−	1.56039i	−0.625534	−	0.780197i	$-0.715119\pi$
$673$		−	40.4801i		−	1.56039i	0.625534	−	0.780197i	$-0.284881\pi$
$674$		0			0
$675$	−31.8450	+	21.2781i	−1.22571	+	0.818995i
$676$		0			0
$677$	−28.0273	+	5.57498i	−1.07718	+	0.214264i	−0.701632	−	0.712540i	$-0.747545\pi$
$677$	−28.0273	+	5.57498i	−1.07718	+	0.214264i	−0.375546	+	0.926804i	$0.622545\pi$
$678$		0			0
$679$	13.7559	−	5.69788i	0.527903	−	0.218665i
$680$		0			0
$681$	7.90382	+	3.27387i	0.302875	+	0.125455i
$682$		0			0
$683$	−10.1966	+	15.2603i	−0.390163	+	0.583920i	−0.973606	−	0.228234i	$-0.926705\pi$
$683$	−10.1966	+	15.2603i	−0.390163	+	0.583920i	0.583443	+	0.812154i	$0.301705\pi$
$684$		0			0
$685$	34.3775	+	6.83811i	1.31350	+	0.261271i
$686$		0			0
$687$	2.70048	+	2.70048i	0.103030	+	0.103030i
$688$		0			0
$689$	0.616329	−	0.616329i	0.0234803	−	0.0234803i
$690$		0			0
$691$	0.695696	−	3.49750i	0.0264655	−	0.133051i	−0.965294	−	0.261167i	$-0.915893\pi$
$691$	0.695696	−	3.49750i	0.0264655	−	0.133051i	0.991759	+	0.128115i	$0.0408928\pi$
$692$		0			0
$693$	−6.42501	−	4.29305i	−0.244066	−	0.163080i
$694$		0			0
$695$	−2.86056	+	6.90601i	−0.108507	+	0.261960i
$696$		0			0
$697$	13.0255	+	31.4463i	0.493375	+	1.19111i
$698$		0			0
$699$	3.86976	+	19.4546i	0.146368	+	0.735841i
$700$		0			0
$701$	−8.71090	−	13.0368i	−0.329006	−	0.492393i	0.629681	−	0.776853i	$-0.283185\pi$
$701$	−8.71090	−	13.0368i	−0.329006	−	0.492393i	−0.958688	+	0.284461i	$0.908185\pi$
$702$		0			0
$703$	−15.5397			−0.586092
$704$		0			0
$705$	−33.1804			−1.24965
$706$		0			0
$707$	−1.34073	−	2.00654i	−0.0504232	−	0.0754637i
$708$		0			0
$709$	0.737183	+	3.70607i	0.0276855	+	0.139184i	0.992156	−	0.125006i	$-0.0398952\pi$
$709$	0.737183	+	3.70607i	0.0276855	+	0.139184i	−0.964470	+	0.264191i	$0.914895\pi$
$710$		0			0
$711$	0.980440	+	2.36699i	0.0367694	+	0.0887692i
$712$		0			0
$713$	3.49688	−	8.44221i	0.130959	−	0.316163i
$714$		0			0
$715$	−2.70849	−	1.80976i	−0.101292	−	0.0676810i
$716$		0			0
$717$	0.482359	−	2.42498i	0.0180140	−	0.0905627i
$718$		0			0
$719$	−36.7070	+	36.7070i	−1.36894	+	1.36894i	−0.506985	+	0.861955i	$0.669240\pi$
$719$	−36.7070	+	36.7070i	−1.36894	+	1.36894i	−0.861955	+	0.506985i	$0.830760\pi$
$720$		0			0
$721$	25.1542	+	25.1542i	0.936790	+	0.936790i
$722$		0			0
$723$	−18.2277	−	3.62572i	−0.677896	−	0.134842i
$724$		0			0
$725$	−1.87668	+	2.80865i	−0.0696982	+	0.104311i
$726$		0			0
$727$	−3.90063	−	1.61569i	−0.144666	−	0.0599228i	0.309176	−	0.951005i	$-0.399947\pi$
$727$	−3.90063	−	1.61569i	−0.144666	−	0.0599228i	−0.453842	+	0.891082i	$0.649947\pi$
$728$		0			0
$729$	13.5147	−	5.59798i	0.500545	−	0.207333i
$730$		0			0
$731$	16.7725	−	3.33626i	0.620353	−	0.123396i
$732$		0			0
$733$	−10.5958	+	7.07991i	−0.391366	+	0.261502i	−0.735648	−	0.677364i	$-0.763122\pi$
$733$	−10.5958	+	7.07991i	−0.391366	+	0.261502i	0.344282	+	0.938866i	$0.388122\pi$
$734$		0			0
$735$			1.44885i			0.0534415i
$736$		0			0
$737$			9.23473i			0.340166i
$738$		0			0
$739$	5.97439	−	3.99196i	0.219772	−	0.146847i	−0.440811	−	0.897600i	$-0.645309\pi$
$739$	5.97439	−	3.99196i	0.219772	−	0.146847i	0.660583	+	0.750753i	$0.270309\pi$
$740$		0			0
$741$	−2.19623	+	0.436857i	−0.0806805	+	0.0160483i
$742$		0			0
$743$	−16.8050	+	6.96086i	−0.616515	+	0.255369i	−0.669011	−	0.743252i	$-0.733282\pi$
$743$	−16.8050	+	6.96086i	−0.616515	+	0.255369i	0.0524960	+	0.998621i	$0.483282\pi$
$744$		0			0
$745$	58.9283	+	24.4089i	2.15896	+	0.894272i
$746$		0			0
$747$	18.2049	−	27.2455i	0.666082	−	0.996862i
$748$		0			0
$749$	37.4148	+	7.44226i	1.36711	+	0.271934i
$750$		0			0
$751$	25.4171	+	25.4171i	0.927482	+	0.927482i	0.997543	−	0.0700603i	$-0.0223192\pi$
$751$	25.4171	+	25.4171i	0.927482	+	0.927482i	−0.0700603	+	0.997543i	$0.522319\pi$
$752$		0			0
$753$	0.121576	−	0.121576i	0.00443047	−	0.00443047i
$754$		0			0
$755$	3.73100	−	18.7570i	0.135785	−	0.682638i
$756$		0			0
$757$	28.3377	+	18.9346i	1.02995	+	0.688192i	0.951160	−	0.308700i	$-0.0998938\pi$
$757$	28.3377	+	18.9346i	1.02995	+	0.688192i	0.0787918	+	0.996891i	$0.474894\pi$
$758$		0			0
$759$	−5.16117	+	12.4602i	−0.187338	+	0.452275i
$760$		0			0
$761$	3.25313	+	7.85375i	0.117926	+	0.284698i	0.971810	−	0.235765i	$-0.0757594\pi$
$761$	3.25313	+	7.85375i	0.117926	+	0.284698i	−0.853884	+	0.520463i	$0.825759\pi$
$762$		0			0
$763$	3.39325	+	17.0590i	0.122844	+	0.617578i
$764$		0			0
$765$	23.2237	+	34.7567i	0.839653	+	1.25663i
$766$		0			0
$767$	4.45177			0.160744
$768$		0			0
$769$	0.673777			0.0242970			0.0121485	−	0.999926i	$-0.496133\pi$
$769$	0.673777			0.0242970			0.0121485	+	0.999926i	$0.496133\pi$
$770$		0			0
$771$	0.747508	+	1.11872i	0.0269208	+	0.0402899i
$772$		0			0
$773$	−9.93498	−	49.9465i	−0.357336	−	1.79645i	−0.572534	−	0.819881i	$-0.694040\pi$
$773$	−9.93498	−	49.9465i	−0.357336	−	1.79645i	0.215198	−	0.976570i	$-0.430960\pi$
$774$		0			0
$775$	−3.12052	−	7.53361i	−0.112092	−	0.270615i
$776$		0			0
$777$	−4.29860	+	10.3777i	−0.154211	+	0.372299i
$778$		0			0
$779$	−17.0120	−	11.3670i	−0.609517	−	0.407266i
$780$		0			0
$781$	−2.96760	+	14.9191i	−0.106189	+	0.533848i
$782$		0			0
$783$	1.61499	−	1.61499i	0.0577151	−	0.0577151i
$784$		0			0
$785$	−21.2045	−	21.2045i	−0.756821	−	0.756821i
$786$		0			0
$787$	50.7402	+	10.0929i	1.80869	+	0.359772i	0.979854	−	0.199715i	$-0.0640015\pi$
$787$	50.7402	+	10.0929i	1.80869	+	0.359772i	0.828840	+	0.559486i	$0.189001\pi$
$788$		0			0
$789$	−6.66815	+	9.97959i	−0.237393	+	0.355283i
$790$		0			0
$791$	−12.1546	−	5.03460i	−0.432168	−	0.179010i
$792$		0			0
$793$	−6.37168	+	2.63924i	−0.226265	+	0.0937220i
$794$		0			0
$795$	−5.25675	+	1.04563i	−0.186438	+	0.0370848i
$796$		0			0
$797$	−39.8300	+	26.6136i	−1.41085	+	0.942701i	−0.411339	+	0.911482i	$0.634939\pi$
$797$	−39.8300	+	26.6136i	−1.41085	+	0.942701i	−0.999513	+	0.0312188i	$0.990061\pi$
$798$		0			0
$799$			55.4415i			1.96138i
$800$		0			0
$801$			12.9077i			0.456073i
$802$		0			0
$803$	4.03644	−	2.69707i	0.142443	−	0.0951774i
$804$		0			0
$805$	75.2283	−	14.9638i	2.65145	−	0.527406i
$806$		0			0
$807$	12.1228	−	5.02144i	0.426744	−	0.176763i
$808$		0			0
$809$	14.9757	+	6.20314i	0.526518	+	0.218091i	0.630077	−	0.776532i	$-0.283023\pi$
$809$	14.9757	+	6.20314i	0.526518	+	0.218091i	−0.103559	+	0.994623i	$0.533023\pi$
$810$		0			0
$811$	−0.427422	+	0.639682i	−0.0150088	+	0.0224623i	−0.838898	−	0.544288i	$-0.816800\pi$
$811$	−0.427422	+	0.639682i	−0.0150088	+	0.0224623i	0.823889	+	0.566751i	$0.191800\pi$
$812$		0			0
$813$	8.44401	+	1.67962i	0.296144	+	0.0589068i
$814$		0			0
$815$	−2.76878	−	2.76878i	−0.0969863	−	0.0969863i
$816$		0			0
$817$	−7.26880	+	7.26880i	−0.254303	+	0.254303i
$818$		0			0
$819$	0.576248	−	2.89700i	0.0201358	−	0.101229i
$820$		0			0
$821$	−11.8401	−	7.91128i	−0.413221	−	0.276105i	0.331534	−	0.943443i	$-0.392434\pi$
$821$	−11.8401	−	7.91128i	−0.413221	−	0.276105i	−0.744755	+	0.667338i	$0.767434\pi$
$822$		0			0
$823$	−20.8253	+	50.2767i	−0.725924	+	1.75254i	−0.0702021	+	0.997533i	$0.522364\pi$
$823$	−20.8253	+	50.2767i	−0.725924	+	1.75254i	−0.655722	+	0.755003i	$0.727636\pi$
$824$		0			0
$825$	4.60569	+	11.1191i	0.160350	+	0.387118i
$826$		0			0
$827$	5.39604	+	27.1277i	0.187639	+	0.943323i	0.953747	+	0.300611i	$0.0971906\pi$
$827$	5.39604	+	27.1277i	0.187639	+	0.943323i	−0.766108	+	0.642712i	$0.777809\pi$
$828$		0			0
$829$	−4.05663	−	6.07118i	−0.140893	−	0.210861i	0.754312	−	0.656516i	$-0.227971\pi$
$829$	−4.05663	−	6.07118i	−0.140893	−	0.210861i	−0.895205	+	0.445656i	$0.852971\pi$
$830$		0			0
$831$	0.114879			0.00398511
$832$		0			0
$833$	2.42089			0.0838790
$834$		0			0
$835$	−5.57261	−	8.34000i	−0.192848	−	0.288618i
$836$		0			0
$837$	1.07562	+	5.40748i	0.0371787	+	0.186910i
$838$		0			0
$839$	9.19848	+	22.2071i	0.317567	+	0.766674i	0.999382	+	0.0351498i	$0.0111908\pi$
$839$	9.19848	+	22.2071i	0.317567	+	0.766674i	−0.681815	+	0.731524i	$0.738809\pi$
$840$		0			0
$841$	−11.0207	+	26.6064i	−0.380025	+	0.917462i
$842$		0			0
$843$	−7.80591	−	5.21574i	−0.268850	−	0.179640i
$844$		0			0
$845$	−8.73323	+	43.9049i	−0.300432	+	1.51038i
$846$		0			0
$847$	15.6117	−	15.6117i	0.536426	−	0.536426i
$848$		0			0
$849$	−8.64313	−	8.64313i	−0.296631	−	0.296631i
$850$		0			0
$851$	−35.0888	−	6.97960i	−1.20283	−	0.239258i
$852$		0			0
$853$	−2.19782	+	3.28928i	−0.0752521	+	0.112623i	−0.867187	−	0.497983i	$-0.834074\pi$
$853$	−2.19782	+	3.28928i	−0.0752521	+	0.112623i	0.791935	+	0.610606i	$0.209074\pi$
$854$		0			0
$855$	−23.2146	−	9.61580i	−0.793923	−	0.328853i
$856$		0			0
$857$	25.6461	−	10.6230i	0.876055	−	0.362874i	0.101089	−	0.994877i	$-0.467767\pi$
$857$	25.6461	−	10.6230i	0.876055	−	0.362874i	0.774966	+	0.632003i	$0.217767\pi$
$858$		0			0
$859$	−48.0526	+	9.55825i	−1.63953	+	0.326123i	−0.926870	−	0.375383i	$-0.877511\pi$
$859$	−48.0526	+	9.55825i	−1.63953	+	0.326123i	−0.712663	+	0.701506i	$0.752511\pi$
$860$		0			0
$861$	−12.2970	+	8.21658i	−0.419080	+	0.280020i
$862$		0			0
$863$		−	49.1366i		−	1.67263i	−0.548250	−	0.836314i	$-0.684706\pi$
$863$		−	49.1366i		−	1.67263i	0.548250	−	0.836314i	$-0.315294\pi$
$864$		0			0
$865$		−	36.9749i		−	1.25718i
$866$		0			0
$867$	−17.2582	+	11.5315i	−0.586118	+	0.391631i
$868$		0			0
$869$	2.01194	−	0.400199i	0.0682503	−	0.0135758i
$870$		0			0
$871$	−3.26127	+	1.35086i	−0.110504	+	0.0457722i
$872$		0			0
$873$	−10.3748	−	4.29738i	−0.351133	−	0.145444i
$874$		0			0
$875$	12.7642	−	19.1030i	0.431510	−	0.645800i
$876$		0			0
$877$	19.6791	+	3.91441i	0.664515	+	0.132180i	0.515812	−	0.856702i	$-0.327490\pi$
$877$	19.6791	+	3.91441i	0.664515	+	0.132180i	0.148703	+	0.988882i	$0.452490\pi$
$878$		0			0
$879$	−0.0745207	−	0.0745207i	−0.00251352	−	0.00251352i
$880$		0			0
$881$	−11.5209	+	11.5209i	−0.388150	+	0.388150i	−0.874027	−	0.485877i	$-0.838500\pi$
$881$	−11.5209	+	11.5209i	−0.388150	+	0.388150i	0.485877	+	0.874027i	$0.338500\pi$
$882$		0			0
$883$	2.44651	−	12.2994i	0.0823317	−	0.413909i	−0.917536	−	0.397652i	$-0.869825\pi$
$883$	2.44651	−	12.2994i	0.0823317	−	0.413909i	0.999868	−	0.0162569i	$-0.00517497\pi$
$884$		0			0
$885$	−22.7612	−	15.2085i	−0.765108	−	0.511229i
$886$		0			0
$887$	17.4593	−	42.1504i	0.586224	−	1.41527i	−0.300862	−	0.953668i	$-0.597274\pi$
$887$	17.4593	−	42.1504i	0.586224	−	1.41527i	0.887087	−	0.461603i	$-0.152726\pi$
$888$		0			0
$889$	−5.18980	−	12.5293i	−0.174060	−	0.420219i
$890$		0			0
$891$	0.172496	+	0.867196i	0.00577883	+	0.0290522i
$892$		0			0
$893$	−18.5152	−	27.7100i	−0.619587	−	0.927278i
$894$		0			0
$895$	−68.8486			−2.30136
$896$		0			0
$897$	−5.15531			−0.172131
$898$		0			0
$899$	0.270158	+	0.404320i	0.00901027	+	0.0134848i
$900$		0			0
$901$	1.74716	+	8.78357i	0.0582064	+	0.292623i
$902$		0			0
$903$	2.84356	+	6.86495i	0.0946276	+	0.228451i
$904$		0			0
$905$	5.42350	−	13.0935i	0.180283	−	0.435242i
$906$		0			0
$907$	15.0921	+	10.0842i	0.501125	+	0.334841i	0.780306	−	0.625398i	$-0.215063\pi$
$907$	15.0921	+	10.0842i	0.501125	+	0.334841i	−0.279182	+	0.960238i	$0.590063\pi$
$908$		0			0
$909$	−0.355080	+	1.78511i	−0.0117773	+	0.0592084i
$910$		0			0
$911$	36.0258	−	36.0258i	1.19359	−	1.19359i	0.217537	−	0.976052i	$-0.430198\pi$
$911$	36.0258	−	36.0258i	1.19359	−	1.19359i	0.976052	−	0.217537i	$-0.0698022\pi$
$912$		0			0
$913$	−18.5521	−	18.5521i	−0.613985	−	0.613985i
$914$		0			0
$915$	41.5938	+	8.27351i	1.37505	+	0.273514i
$916$		0			0
$917$	−8.21699	+	12.2976i	−0.271349	+	0.406102i
$918$		0			0
$919$	23.4993	+	9.73374i	0.775171	+	0.321086i	0.734965	−	0.678105i	$-0.237199\pi$
$919$	23.4993	+	9.73374i	0.775171	+	0.321086i	0.0402060	+	0.999191i	$0.487199\pi$
$920$		0			0
$921$	−21.8015	+	9.03046i	−0.718383	+	0.297564i
$922$		0			0
$923$	−5.70282	+	1.13436i	−0.187711	+	0.0373380i
$924$		0			0
$925$	−26.5453	+	17.7370i	−0.872805	+	0.583190i
$926$		0			0
$927$		−	26.8296i		−	0.881201i
$928$		0			0
$929$			14.5115i			0.476107i	0.971252	+	0.238053i	$0.0765094\pi$
$929$			14.5115i			0.476107i	−0.971252	+	0.238053i	$0.923491\pi$
$930$		0			0
$931$	−1.20998	+	0.808480i	−0.0396553	+	0.0264968i
$932$		0			0
$933$	−17.1335	+	3.40807i	−0.560926	+	0.111575i
$934$		0			0
$935$	30.9219	−	12.8083i	1.01125	−	0.418875i
$936$		0			0
$937$	15.1545	+	6.27722i	0.495077	+	0.205068i	0.616230	−	0.787566i	$-0.288659\pi$
$937$	15.1545	+	6.27722i	0.495077	+	0.205068i	−0.121153	+	0.992634i	$0.538659\pi$
$938$		0			0
$939$	10.3917	−	15.5523i	0.339120	−	0.507530i
$940$		0			0
$941$	32.7794	+	6.52023i	1.06858	+	0.212553i	0.697891	−	0.716204i	$-0.254122\pi$
$941$	32.7794	+	6.52023i	1.06858	+	0.212553i	0.370688	+	0.928758i	$0.379122\pi$
$942$		0			0
$943$	−33.3077	−	33.3077i	−1.08465	−	1.08465i
$944$		0			0
$945$	−32.7245	+	32.7245i	−1.06453	+	1.06453i
$946$		0			0
$947$	−1.24368	+	6.25242i	−0.0404143	+	0.203176i	−0.995717	−	0.0924528i	$-0.970529\pi$
$947$	−1.24368	+	6.25242i	−0.0404143	+	0.203176i	0.955303	+	0.295629i	$0.0955293\pi$
$948$		0			0
$949$	1.54293	+	1.03095i	0.0500856	+	0.0334661i
$950$		0			0
$951$	−7.80372	+	18.8399i	−0.253053	+	0.610924i
$952$		0			0
$953$	0.417863	+	1.00881i	0.0135359	+	0.0326786i	0.930503	−	0.366284i	$-0.119370\pi$
$953$	0.417863	+	1.00881i	0.0135359	+	0.0326786i	−0.916967	+	0.398963i	$0.869370\pi$
$954$		0			0
$955$	11.2261	+	56.4375i	0.363269	+	1.82628i
$956$		0			0
$957$	−0.398736	−	0.596750i	−0.0128893	−	0.0192902i
$958$		0			0
$959$	25.4479			0.821756
$960$		0			0
$961$	29.8261			0.962134
$962$		0			0
$963$	−15.9845	−	23.9224i	−0.515092	−	0.770890i
$964$		0			0
$965$	−17.2166	−	86.5536i	−0.554221	−	2.78626i
$966$		0			0
$967$	12.0473	+	29.0848i	0.387416	+	0.935305i	0.990486	+	0.137617i	$0.0439442\pi$
$967$	12.0473	+	29.0848i	0.387416	+	0.935305i	−0.603069	+	0.797689i	$0.706056\pi$
$968$		0			0
$969$	8.80466	−	21.2563i	0.282847	−	0.682852i
$970$		0			0
$971$	−25.2097	−	16.8446i	−0.809017	−	0.540568i	0.0808828	−	0.996724i	$-0.474226\pi$
$971$	−25.2097	−	16.8446i	−0.809017	−	0.540568i	−0.889900	+	0.456156i	$0.849226\pi$
$972$		0			0
$973$	−1.05876	+	5.32277i	−0.0339424	+	0.170640i
$974$		0			0
$975$	−3.25302	+	3.25302i	−0.104180	+	0.104180i
$976$		0			0
$977$	27.6449	+	27.6449i	0.884440	+	0.884440i	0.993982	−	0.109543i	$-0.0349386\pi$
$977$	27.6449	+	27.6449i	0.884440	+	0.884440i	−0.109543	+	0.993982i	$0.534939\pi$
$978$		0			0
$979$	10.1364	+	2.01625i	0.323960	+	0.0644397i
$980$		0			0
$981$	7.28802	−	10.9073i	0.232688	−	0.348243i
$982$		0			0
$983$	25.5539	+	10.5848i	0.815043	+	0.337602i	0.750964	−	0.660343i	$-0.229589\pi$
$983$	25.5539	+	10.5848i	0.815043	+	0.337602i	0.0640791	+	0.997945i	$0.479589\pi$
$984$		0			0
$985$	−13.6849	+	5.66846i	−0.436036	+	0.180612i
$986$		0			0
$987$	−23.6269	+	4.69969i	−0.752054	+	0.149593i
$988$		0			0
$989$	−19.6778	+	13.1483i	−0.625717	+	0.418090i
$990$		0			0
$991$		−	31.6905i		−	1.00668i	−0.864088	−	0.503340i	$-0.832104\pi$
$991$		−	31.6905i		−	1.00668i	0.864088	−	0.503340i	$-0.167896\pi$
$992$		0			0
$993$			7.40504i			0.234992i
$994$		0			0
$995$	5.72257	−	3.82370i	0.181418	−	0.121219i
$996$		0			0
$997$	21.6259	−	4.30166i	0.684900	−	0.136235i	0.159638	−	0.987176i	$-0.448967\pi$
$997$	21.6259	−	4.30166i	0.684900	−	0.136235i	0.525262	+	0.850941i	$0.323967\pi$
$998$		0			0
$999$	19.9430	−	8.26066i	0.630969	−	0.261356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.289.5		56
4.3	odd	2		512.2.i.a.289.3		56
8.3	odd	2		256.2.i.a.17.5		56
8.5	even	2		64.2.i.a.45.4	yes	56
24.5	odd	2		576.2.bd.a.109.4		56
64.5	even	16		64.2.i.a.37.4	✓	56
64.27	odd	16		512.2.i.a.225.3		56
64.37	even	16	inner	512.2.i.b.225.5		56
64.59	odd	16		256.2.i.a.241.5		56
192.5	odd	16		576.2.bd.a.37.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.4	✓	56	64.5	even	16
64.2.i.a.45.4	yes	56	8.5	even	2
256.2.i.a.17.5		56	8.3	odd	2
256.2.i.a.241.5		56	64.59	odd	16
512.2.i.a.225.3		56	64.27	odd	16
512.2.i.a.289.3		56	4.3	odd	2
512.2.i.b.225.5		56	64.37	even	16	inner
512.2.i.b.289.5		56	1.1	even	1	trivial
576.2.bd.a.37.4		56	192.5	odd	16
576.2.bd.a.109.4		56	24.5	odd	2

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.572535 + 0.856859i) q^{3} +(0.690473 + 3.47124i) q^{5} +(0.983337 + 2.37399i) q^{7} +(0.741639 - 1.79047i) q^{9} +(-1.29020 - 0.862086i) q^{11} +(0.115716 - 0.581745i) q^{13} +(-2.57905 + 2.57905i) q^{15} +(4.30936 + 4.30936i) q^{17} +(-3.59299 - 0.714690i) q^{19} +(-1.47118 + 2.20177i) q^{21} +(-7.79200 - 3.22755i) q^{23} +(-6.95338 + 2.88018i) q^{25} +(4.99100 - 0.992772i) q^{27} +(0.373179 - 0.249351i) q^{29} +1.08345i q^{31} -1.59910i q^{33} +(-7.56172 + 5.05258i) q^{35} +(4.16040 - 0.827556i) q^{37} +(0.564725 - 0.233917i) q^{39} +(5.15990 + 2.13730i) q^{41} +(1.55896 - 2.33315i) q^{43} +(6.72725 + 1.33813i) q^{45} +(6.43269 + 6.43269i) q^{47} +(0.280888 - 0.280888i) q^{49} +(-1.22526 + 6.15978i) q^{51} +(1.22184 + 0.816410i) q^{53} +(2.10166 - 5.07385i) q^{55} +(-1.44472 - 3.48787i) q^{57} +(1.46423 + 7.36119i) q^{59} +(-6.45980 - 9.66777i) q^{61} +4.97984 q^{63} +2.09928 q^{65} +(-3.30637 - 4.94834i) q^{67} +(-1.69564 - 8.52453i) q^{69} +(-3.75143 - 9.05676i) q^{71} +(-1.19724 + 2.89039i) q^{73} +(-6.44896 - 4.30906i) q^{75} +(0.777876 - 3.91064i) q^{77} +(-0.934789 + 0.934789i) q^{79} +(-0.402918 - 0.402918i) q^{81} +(16.5833 + 3.29862i) q^{83} +(-11.9833 + 17.9343i) q^{85} +(0.427317 + 0.177000i) q^{87} +(-6.15337 + 2.54881i) q^{89} +(1.49484 - 0.297343i) q^{91} +(-0.928361 + 0.620311i) q^{93} -12.9656i q^{95} -5.79443i q^{97} +(-2.50041 + 1.67072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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