LMFDB - Embedded newform 576.2.bb.e.529.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			529.14
Character	$\chi$	$=$	576.529
Dual form			576.2.bb.e.49.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22967 + 1.21980i) q^{3} +(0.174734 + 0.0468197i) q^{5} +(4.04791 + 2.33706i) q^{7} +(0.0241875 + 2.99990i) q^{9} +O(q^{10})$	\(q+(1.22967 + 1.21980i) q^{3} +(0.174734 + 0.0468197i) q^{5} +(4.04791 + 2.33706i) q^{7} +(0.0241875 + 2.99990i) q^{9} +(-0.160430 - 0.598734i) q^{11} +(1.18229 - 4.41237i) q^{13} +(0.157754 + 0.270713i) q^{15} -4.34691 q^{17} +(1.23918 + 1.23918i) q^{19} +(2.12686 + 7.81146i) q^{21} +(-3.86311 + 2.23037i) q^{23} +(-4.30179 - 2.48364i) q^{25} +(-3.62953 + 3.71840i) q^{27} +(8.64910 - 2.31752i) q^{29} +(2.25376 + 3.90364i) q^{31} +(0.533058 - 0.931939i) q^{33} +(0.597886 + 0.597886i) q^{35} +(2.79692 - 2.79692i) q^{37} +(6.83604 - 3.98362i) q^{39} +(-3.67211 + 2.12009i) q^{41} +(-0.00351694 - 0.0131254i) q^{43} +(-0.136228 + 0.525316i) q^{45} +(1.17465 - 2.03456i) q^{47} +(7.42373 + 12.8583i) q^{49} +(-5.34528 - 5.30235i) q^{51} +(-0.519418 + 0.519418i) q^{53} -0.112130i q^{55} +(0.0122364 + 3.03533i) q^{57} +(-11.0349 - 2.95679i) q^{59} +(-2.19745 + 0.588805i) q^{61} +(-6.91305 + 12.1999i) q^{63} +(0.413172 - 0.715636i) q^{65} +(1.88714 - 7.04291i) q^{67} +(-7.47096 - 1.96959i) q^{69} -7.55145i q^{71} +2.92707i q^{73} +(-2.26025 - 8.30137i) q^{75} +(0.749872 - 2.79856i) q^{77} +(-1.45885 + 2.52680i) q^{79} +(-8.99883 + 0.145120i) q^{81} +(7.44148 - 1.99394i) q^{83} +(-0.759552 - 0.203521i) q^{85} +(13.4625 + 7.70036i) q^{87} -3.18821i q^{89} +(15.0978 - 15.0978i) q^{91} +(-1.99025 + 7.54933i) q^{93} +(0.158508 + 0.274544i) q^{95} +(8.03868 - 13.9234i) q^{97} +(1.79226 - 0.495757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22967	+	1.21980i	0.709952	+	0.704250i
$3$	1.22967	+	1.21980i	0.709952	+	0.704250i
$4$		0			0
$5$	0.174734	+	0.0468197i	0.0781432	+	0.0209384i	0.297679	−	0.954666i	$-0.403788\pi$
$5$	0.174734	+	0.0468197i	0.0781432	+	0.0209384i	−0.219536	+	0.975604i	$0.570454\pi$
$6$		0			0
$7$	4.04791	+	2.33706i	1.52997	+	0.883327i	0.999362	+	0.0357075i	$0.0113685\pi$
$7$	4.04791	+	2.33706i	1.52997	+	0.883327i	0.530605	+	0.847619i	$0.321965\pi$
$8$		0			0
$9$	0.0241875	+	2.99990i	0.00806251	+	0.999967i
$10$		0			0
$11$	−0.160430	−	0.598734i	−0.0483716	−	0.180525i	0.937513	−	0.347949i	$-0.113122\pi$
$11$	−0.160430	−	0.598734i	−0.0483716	−	0.180525i	−0.985885	+	0.167424i	$0.946455\pi$
$12$		0			0
$13$	1.18229	−	4.41237i	0.327909	−	1.22377i	−0.583446	−	0.812152i	$-0.698296\pi$
$13$	1.18229	−	4.41237i	0.327909	−	1.22377i	0.911355	−	0.411621i	$-0.135037\pi$
$14$		0			0
$15$	0.157754	+	0.270713i	0.0407320	+	0.0698977i
$16$		0			0
$17$	−4.34691			−1.05428			−0.527141	−	0.849778i	$-0.676736\pi$
$17$	−4.34691			−1.05428			−0.527141	+	0.849778i	$0.676736\pi$
$18$		0			0
$19$	1.23918	+	1.23918i	0.284287	+	0.284287i	0.834816	−	0.550529i	$-0.185574\pi$
$19$	1.23918	+	1.23918i	0.284287	+	0.284287i	−0.550529	+	0.834816i	$0.685574\pi$
$20$		0			0
$21$	2.12686	+	7.81146i	0.464119	+	1.70460i
$22$		0			0
$23$	−3.86311	+	2.23037i	−0.805515	+	0.465064i	−0.845396	−	0.534140i	$-0.820635\pi$
$23$	−3.86311	+	2.23037i	−0.805515	+	0.465064i	0.0398812	+	0.999204i	$0.487302\pi$
$24$		0			0
$25$	−4.30179	−	2.48364i	−0.860357	−	0.496728i
$26$		0			0
$27$	−3.62953	+	3.71840i	−0.698504	+	0.715607i
$28$		0			0
$29$	8.64910	−	2.31752i	1.60610	−	0.430353i	0.659221	−	0.751949i	$-0.270886\pi$
$29$	8.64910	−	2.31752i	1.60610	−	0.430353i	0.946877	+	0.321597i	$0.104220\pi$
$30$		0			0
$31$	2.25376	+	3.90364i	0.404788	+	0.701114i	0.994297	−	0.106648i	$-0.0340119\pi$
$31$	2.25376	+	3.90364i	0.404788	+	0.701114i	−0.589509	+	0.807762i	$0.700679\pi$
$32$		0			0
$33$	0.533058	−	0.931939i	0.0927935	−	0.162230i
$34$		0			0
$35$	0.597886	+	0.597886i	0.101061	+	0.101061i
$36$		0			0
$37$	2.79692	−	2.79692i	0.459811	−	0.459811i	−0.438783	−	0.898593i	$-0.644590\pi$
$37$	2.79692	−	2.79692i	0.459811	−	0.459811i	0.898593	+	0.438783i	$0.144590\pi$
$38$		0			0
$39$	6.83604	−	3.98362i	1.09464	−	0.637889i
$40$		0			0
$41$	−3.67211	+	2.12009i	−0.573487	+	0.331103i	−0.758541	−	0.651626i	$-0.774087\pi$
$41$	−3.67211	+	2.12009i	−0.573487	+	0.331103i	0.185054	+	0.982728i	$0.440754\pi$
$42$		0			0
$43$	−0.00351694	−	0.0131254i	−0.000536329	−	0.00200161i	0.965657	−	0.259820i	$-0.0836631\pi$
$43$	−0.00351694	−	0.0131254i	−0.000536329	−	0.00200161i	−0.966193	+	0.257818i	$0.916996\pi$
$44$		0			0
$45$	−0.136228	+	0.525316i	−0.0203077	+	0.0783095i
$46$		0			0
$47$	1.17465	−	2.03456i	0.171341	−	0.296771i	−0.767548	−	0.640991i	$-0.778523\pi$
$47$	1.17465	−	2.03456i	0.171341	−	0.296771i	0.938889	+	0.344221i	$0.111857\pi$
$48$		0			0
$49$	7.42373	+	12.8583i	1.06053	+	1.83690i
$50$		0			0
$51$	−5.34528	−	5.30235i	−0.748489	−	0.742478i
$52$		0			0
$53$	−0.519418	+	0.519418i	−0.0713476	+	0.0713476i	−0.741880	−	0.670533i	$-0.766066\pi$
$53$	−0.519418	+	0.519418i	−0.0713476	+	0.0713476i	0.670533	+	0.741880i	$0.266066\pi$
$54$		0			0
$55$		−	0.112130i		−	0.0151196i
$56$		0			0
$57$	0.0122364	+	3.03533i	0.00162075	+	0.402040i
$58$		0			0
$59$	−11.0349	−	2.95679i	−1.43662	−	0.384942i	−0.545273	−	0.838258i	$-0.683574\pi$
$59$	−11.0349	−	2.95679i	−1.43662	−	0.384942i	−0.891350	+	0.453317i	$0.850241\pi$
$60$		0			0
$61$	−2.19745	+	0.588805i	−0.281355	+	0.0753887i	−0.396737	−	0.917932i	$-0.629857\pi$
$61$	−2.19745	+	0.588805i	−0.281355	+	0.0753887i	0.115382	+	0.993321i	$0.463191\pi$
$62$		0			0
$63$	−6.91305	+	12.1999i	−0.870963	+	1.53704i
$64$		0			0
$65$	0.413172	−	0.715636i	0.0512477	−	0.0887637i
$66$		0			0
$67$	1.88714	−	7.04291i	0.230551	−	0.860428i	−0.749553	−	0.661944i	$-0.769732\pi$
$67$	1.88714	−	7.04291i	0.230551	−	0.860428i	0.980104	−	0.198484i	$-0.0636018\pi$
$68$		0			0
$69$	−7.47096	−	1.96959i	−0.899398	−	0.237111i
$70$		0			0
$71$		−	7.55145i		−	0.896193i	−0.893985	−	0.448096i	$-0.852102\pi$
$71$		−	7.55145i		−	0.896193i	0.893985	−	0.448096i	$-0.147898\pi$
$72$		0			0
$73$			2.92707i			0.342588i	0.985220	+	0.171294i	$0.0547948\pi$
$73$			2.92707i			0.342588i	−0.985220	+	0.171294i	$0.945205\pi$
$74$		0			0
$75$	−2.26025	−	8.30137i	−0.260991	−	0.958560i
$76$		0			0
$77$	0.749872	−	2.79856i	0.0854558	−	0.318925i
$78$		0			0
$79$	−1.45885	+	2.52680i	−0.164133	+	0.284287i	−0.936347	−	0.351076i	$-0.885816\pi$
$79$	−1.45885	+	2.52680i	−0.164133	+	0.284287i	0.772214	+	0.635362i	$0.219149\pi$
$80$		0			0
$81$	−8.99883	+	0.145120i	−0.999870	+	0.0161245i
$82$		0			0
$83$	7.44148	−	1.99394i	0.816808	−	0.218863i	0.173858	−	0.984771i	$-0.444377\pi$
$83$	7.44148	−	1.99394i	0.816808	−	0.218863i	0.642950	+	0.765908i	$0.277710\pi$
$84$		0			0
$85$	−0.759552	−	0.203521i	−0.0823850	−	0.0220750i
$86$		0			0
$87$	13.4625	+	7.70036i	1.44333	+	0.825566i
$88$		0			0
$89$		−	3.18821i		−	0.337950i	−0.985620	−	0.168975i	$-0.945954\pi$
$89$		−	3.18821i		−	0.337950i	0.985620	−	0.168975i	$-0.0540457\pi$
$90$		0			0
$91$	15.0978	−	15.0978i	1.58268	−	1.58268i
$92$		0			0
$93$	−1.99025	+	7.54933i	−0.206380	+	0.782829i
$94$		0			0
$95$	0.158508	+	0.274544i	0.0162626	+	0.0281676i
$96$		0			0
$97$	8.03868	−	13.9234i	0.816204	−	1.41371i	−0.0922553	−	0.995735i	$-0.529408\pi$
$97$	8.03868	−	13.9234i	0.816204	−	1.41371i	0.908460	−	0.417972i	$-0.137259\pi$
$98$		0			0
$99$	1.79226	−	0.495757i	0.180129	−	0.0498255i
$100$		0			0
$101$	−4.56339	−	17.0308i	−0.454074	−	1.69463i	−0.690795	−	0.723051i	$-0.742739\pi$
$101$	−4.56339	−	17.0308i	−0.454074	−	1.69463i	0.236720	−	0.971578i	$-0.423928\pi$
$102$		0			0
$103$	−8.05916	+	4.65296i	−0.794093	+	0.458470i	−0.841401	−	0.540411i	$-0.818269\pi$
$103$	−8.05916	+	4.65296i	−0.794093	+	0.458470i	0.0473086	+	0.998880i	$0.484936\pi$
$104$		0			0
$105$	0.00590388	+	1.46450i	0.000576159	+	0.142921i
$106$		0			0
$107$	−9.51927	+	9.51927i	−0.920263	+	0.920263i	−0.997048	−	0.0767848i	$-0.975535\pi$
$107$	−9.51927	+	9.51927i	−0.920263	+	0.920263i	0.0767848	+	0.997048i	$0.475535\pi$
$108$		0			0
$109$	−6.35255	−	6.35255i	−0.608464	−	0.608464i	0.334081	−	0.942544i	$-0.391574\pi$
$109$	−6.35255	−	6.35255i	−0.608464	−	0.608464i	−0.942544	+	0.334081i	$0.891574\pi$
$110$		0			0
$111$	6.85097	−	0.0276184i	0.650265	−	0.00262143i
$112$		0			0
$113$	5.34598	+	9.25951i	0.502908	+	0.871062i	0.999994	+	0.00336088i	$0.00106980\pi$
$113$	5.34598	+	9.25951i	0.502908	+	0.871062i	−0.497087	+	0.867701i	$0.665597\pi$
$114$		0			0
$115$	−0.779441	+	0.208851i	−0.0726832	+	0.0194754i
$116$		0			0
$117$	13.2653	+	3.44004i	1.22638	+	0.318032i
$118$		0			0
$119$	−17.5959	−	10.1590i	−1.61302	−	0.931275i
$120$		0			0
$121$	9.19353	−	5.30789i	0.835776	−	0.482535i
$122$		0			0
$123$	−7.10157	−	1.87221i	−0.640327	−	0.168811i
$124$		0			0
$125$	−1.27495	−	1.27495i	−0.114035	−	0.114035i
$126$		0			0
$127$	11.5283			1.02297			0.511484	−	0.859293i	$-0.329096\pi$
$127$	11.5283			1.02297			0.511484	+	0.859293i	$0.329096\pi$
$128$		0			0
$129$	0.0116857	−	0.0204299i	0.00102886	−	0.00179875i
$130$		0			0
$131$	−0.917160	+	3.42289i	−0.0801327	+	0.299059i	−0.994348	−	0.106169i	$-0.966141\pi$
$131$	−0.917160	+	3.42289i	−0.0801327	+	0.299059i	0.914215	+	0.405229i	$0.132808\pi$
$132$		0			0
$133$	2.12005	+	7.91213i	0.183832	+	0.686069i
$134$		0			0
$135$	−0.808296	+	0.479796i	−0.0695670	+	0.0412943i
$136$		0			0
$137$	−13.0194	−	7.51678i	−1.11233	−	0.642202i	−0.172895	−	0.984940i	$-0.555312\pi$
$137$	−13.0194	−	7.51678i	−1.11233	−	0.642202i	−0.939431	+	0.342739i	$0.888646\pi$
$138$		0			0
$139$	9.76161	+	2.61562i	0.827969	+	0.221854i	0.647828	−	0.761787i	$-0.275678\pi$
$139$	9.76161	+	2.61562i	0.827969	+	0.221854i	0.180142	+	0.983641i	$0.442344\pi$
$140$		0			0
$141$	3.92619	−	1.06900i	0.330645	−	0.0900261i
$142$		0			0
$143$	−2.83152			−0.236783
$144$		0			0
$145$	1.61979			0.134517
$146$		0			0
$147$	−6.55574	+	24.8669i	−0.540708	+	2.05099i
$148$		0			0
$149$	−5.14811	−	1.37943i	−0.421749	−	0.113007i	0.0417013	−	0.999130i	$-0.486722\pi$
$149$	−5.14811	−	1.37943i	−0.421749	−	0.113007i	−0.463451	+	0.886123i	$0.653389\pi$
$150$		0			0
$151$	−9.86458	−	5.69532i	−0.802768	−	0.463479i	0.0416699	−	0.999131i	$-0.486732\pi$
$151$	−9.86458	−	5.69532i	−0.802768	−	0.463479i	−0.844438	+	0.535653i	$0.820066\pi$
$152$		0			0
$153$	−0.105141	−	13.0403i	−0.00850015	−	1.05425i
$154$		0			0
$155$	0.211041	+	0.787617i	0.0169512	+	0.0632629i
$156$		0			0
$157$	1.46607	−	5.47145i	0.117005	−	0.436670i	−0.882424	−	0.470455i	$-0.844090\pi$
$157$	1.46607	−	5.47145i	0.117005	−	0.436670i	0.999429	+	0.0337857i	$0.0107564\pi$
$158$		0			0
$159$	−1.27230	+	0.00512904i	−0.100900	+	0.000406760i
$160$		0			0
$161$	−20.8501			−1.64321
$162$		0			0
$163$	−15.0117	−	15.0117i	−1.17581	−	1.17581i	−0.980802	−	0.195004i	$-0.937528\pi$
$163$	−15.0117	−	15.0117i	−1.17581	−	1.17581i	−0.195004	−	0.980802i	$-0.562472\pi$
$164$		0			0
$165$	0.136776	−	0.137884i	0.0106480	−	0.0107342i
$166$		0			0
$167$	7.81918	−	4.51441i	0.605066	−	0.349335i	−0.165966	−	0.986132i	$-0.553074\pi$
$167$	7.81918	−	4.51441i	0.605066	−	0.349335i	0.771032	+	0.636796i	$0.219741\pi$
$168$		0			0
$169$	−6.81291	−	3.93343i	−0.524070	−	0.302572i
$170$		0			0
$171$	−3.68744	+	3.74739i	−0.281986	+	0.286570i
$172$		0			0
$173$	5.00520	−	1.34114i	0.380539	−	0.101965i	−0.0634788	−	0.997983i	$-0.520220\pi$
$173$	5.00520	−	1.34114i	0.380539	−	0.101965i	0.444017	+	0.896018i	$0.353553\pi$
$174$		0			0
$175$	−11.6088	−	20.1071i	−0.877546	−	1.51995i
$176$		0			0
$177$	−9.96263	−	17.0962i	−0.748837	−	1.28503i
$178$		0			0
$179$	−1.96093	−	1.96093i	−0.146566	−	0.146566i	0.630016	−	0.776582i	$-0.283048\pi$
$179$	−1.96093	−	1.96093i	−0.146566	−	0.146566i	−0.776582	+	0.630016i	$0.783048\pi$
$180$		0			0
$181$	−0.224256	+	0.224256i	−0.0166688	+	0.0166688i	−0.715392	−	0.698723i	$-0.753752\pi$
$181$	−0.224256	+	0.224256i	−0.0166688	+	0.0166688i	0.698723	+	0.715392i	$0.253752\pi$
$182$		0			0
$183$	−3.42037	−	1.95641i	−0.252841	−	0.144622i
$184$		0			0
$185$	0.619667	−	0.357765i	0.0455588	−	0.0263034i
$186$		0			0
$187$	0.697377	+	2.60265i	0.0509972	+	0.190324i
$188$		0			0
$189$	−23.3822	+	6.56932i	−1.70080	+	0.477847i
$190$		0			0
$191$	10.3893	−	17.9947i	0.751741	−	1.30205i	−0.195237	−	0.980756i	$-0.562548\pi$
$191$	10.3893	−	17.9947i	0.751741	−	1.30205i	0.946978	−	0.321298i	$-0.104119\pi$
$192$		0			0
$193$	7.69572	+	13.3294i	0.553950	+	0.959469i	0.997984	+	0.0634596i	$0.0202134\pi$
$193$	7.69572	+	13.3294i	0.553950	+	0.959469i	−0.444035	+	0.896010i	$0.646453\pi$
$194$		0			0
$195$	1.38100	−	0.376010i	0.0988953	−	0.0269267i
$196$		0			0
$197$	−0.905158	+	0.905158i	−0.0644898	+	0.0644898i	−0.738616	−	0.674126i	$-0.764520\pi$
$197$	−0.905158	+	0.905158i	−0.0644898	+	0.0644898i	0.674126	+	0.738616i	$0.264520\pi$
$198$		0			0
$199$			16.5201i			1.17108i	0.810645	+	0.585538i	$0.199117\pi$
$199$			16.5201i			1.17108i	−0.810645	+	0.585538i	$0.800883\pi$
$200$		0			0
$201$	10.9115	−	6.35854i	0.769637	−	0.448497i
$202$		0			0
$203$	40.4270	+	10.8324i	2.83742	+	0.760284i
$204$		0			0
$205$	−0.740902	+	0.198524i	−0.0517469	+	0.0138655i
$206$		0			0
$207$	−6.78433	−	11.5350i	−0.471543	−	0.801739i
$208$		0			0
$209$	0.543137	−	0.940741i	0.0375696	−	0.0650724i
$210$		0			0
$211$	−6.75305	+	25.2027i	−0.464899	+	1.73503i	0.192325	+	0.981331i	$0.438397\pi$
$211$	−6.75305	+	25.2027i	−0.464899	+	1.73503i	−0.657224	+	0.753695i	$0.728270\pi$
$212$		0			0
$213$	9.21125	−	9.28581i	0.631144	−	0.636253i
$214$		0			0
$215$		−	0.00245811i		−	0.000167642i
$216$		0			0
$217$			21.0688i			1.43024i
$218$		0			0
$219$	−3.57044	+	3.59934i	−0.241268	+	0.243221i
$220$		0			0
$221$	−5.13932	+	19.1802i	−0.345708	+	1.29020i
$222$		0			0
$223$	−6.47927	+	11.2224i	−0.433884	+	0.751510i	−0.997204	−	0.0747295i	$-0.976191\pi$
$223$	−6.47927	+	11.2224i	−0.433884	+	0.751510i	0.563320	+	0.826239i	$0.309524\pi$
$224$		0			0
$225$	7.34662	−	12.9650i	0.489775	−	0.864334i
$226$		0			0
$227$	13.1401	−	3.52089i	0.872142	−	0.233690i	0.205128	−	0.978735i	$-0.434239\pi$
$227$	13.1401	−	3.52089i	0.872142	−	0.233690i	0.667014	+	0.745045i	$0.267572\pi$
$228$		0			0
$229$	−16.2371	−	4.35071i	−1.07298	−	0.287503i	−0.321260	−	0.946991i	$-0.604106\pi$
$229$	−16.2371	−	4.35071i	−1.07298	−	0.287503i	−0.751715	+	0.659488i	$0.770773\pi$
$230$		0			0
$231$	4.33577	−	2.52662i	0.285273	−	0.166239i
$232$		0			0
$233$			10.0493i			0.658351i	0.944269	+	0.329176i	$0.106771\pi$
$233$			10.0493i			0.658351i	−0.944269	+	0.329176i	$0.893229\pi$
$234$		0			0
$235$	0.300509	−	0.300509i	0.0196030	−	0.0196030i
$236$		0			0
$237$	−4.87608	+	1.32763i	−0.316735	+	0.0862390i
$238$		0			0
$239$	3.38365	+	5.86066i	0.218870	+	0.379094i	0.954463	−	0.298330i	$-0.0964295\pi$
$239$	3.38365	+	5.86066i	0.218870	+	0.379094i	−0.735593	+	0.677424i	$0.763096\pi$
$240$		0			0
$241$	−1.07804	+	1.86722i	−0.0694428	+	0.120278i	−0.898656	−	0.438654i	$-0.855455\pi$
$241$	−1.07804	+	1.86722i	−0.0694428	+	0.120278i	0.829213	+	0.558932i	$0.188789\pi$
$242$		0			0
$243$	−11.2426	−	10.7983i	−0.721215	−	0.692711i
$244$		0			0
$245$	0.695154	+	2.59435i	0.0444118	+	0.165747i
$246$		0			0
$247$	6.93279	−	4.00265i	0.441123	−	0.254683i
$248$		0			0
$249$	11.5828	+	6.62520i	0.734029	+	0.419855i
$250$		0			0
$251$	−3.65289	+	3.65289i	−0.230568	+	0.230568i	−0.812930	−	0.582362i	$-0.802129\pi$
$251$	−3.65289	+	3.65289i	−0.230568	+	0.230568i	0.582362	+	0.812930i	$0.302129\pi$
$252$		0			0
$253$	1.95516	+	1.95516i	0.122920	+	0.122920i
$254$		0			0
$255$	−0.685745	−	1.17676i	−0.0429430	−	0.0736918i
$256$		0			0
$257$	−5.09689	−	8.82807i	−0.317935	−	0.550680i	0.662122	−	0.749396i	$-0.269656\pi$
$257$	−5.09689	−	8.82807i	−0.317935	−	0.550680i	−0.980057	+	0.198716i	$0.936323\pi$
$258$		0			0
$259$	17.8583	−	4.78511i	1.10966	−	0.297332i
$260$		0			0
$261$	7.16153	+	25.8904i	0.443288	+	1.60258i
$262$		0			0
$263$	14.5937	+	8.42569i	0.899888	+	0.519550i	0.877164	−	0.480191i	$-0.159433\pi$
$263$	14.5937	+	8.42569i	0.899888	+	0.519550i	0.0227239	+	0.999742i	$0.492766\pi$
$264$		0			0
$265$	−0.115079	+	0.0664408i	−0.00706924	+	0.00408143i
$266$		0			0
$267$	3.88897	−	3.92045i	0.238001	−	0.239928i
$268$		0			0
$269$	18.2219	+	18.2219i	1.11101	+	1.11101i	0.993014	+	0.117993i	$0.0376461\pi$
$269$	18.2219	+	18.2219i	1.11101	+	1.11101i	0.117993	+	0.993014i	$0.462354\pi$
$270$		0			0
$271$	−9.95663			−0.604822			−0.302411	−	0.953178i	$-0.597792\pi$
$271$	−9.95663			−0.604822			−0.302411	+	0.953178i	$0.597792\pi$
$272$		0			0
$273$	36.9816	−	0.149085i	2.23823	−	0.00902302i
$274$		0			0
$275$	−0.796902	+	2.97408i	−0.0480550	+	0.179344i
$276$		0			0
$277$	−0.706690	−	2.63740i	−0.0424609	−	0.158466i	0.941440	−	0.337180i	$-0.109473\pi$
$277$	−0.706690	−	2.63740i	−0.0424609	−	0.158466i	−0.983901	+	0.178714i	$0.942806\pi$
$278$		0			0
$279$	−11.6560	+	6.85549i	−0.697827	+	0.410428i
$280$		0			0
$281$	21.8517	+	12.6161i	1.30356	+	0.752612i	0.981013	−	0.193941i	$-0.0621271\pi$
$281$	21.8517	+	12.6161i	1.30356	+	0.752612i	0.322549	+	0.946553i	$0.395460\pi$
$282$		0			0
$283$	−8.63704	−	2.31429i	−0.513419	−	0.137570i	−0.00719814	−	0.999974i	$-0.502291\pi$
$283$	−8.63704	−	2.31429i	−0.513419	−	0.137570i	−0.506221	+	0.862404i	$0.668958\pi$
$284$		0			0
$285$	−0.139975	+	0.530947i	−0.00829142	+	0.0314506i
$286$		0			0
$287$	−19.8192			−1.16989
$288$		0			0
$289$	1.89565			0.111509
$290$		0			0
$291$	26.8687	−	7.31566i	1.57507	−	0.428852i
$292$		0			0
$293$	20.1100	+	5.38845i	1.17484	+	0.314796i	0.792876	−	0.609383i	$-0.208583\pi$
$293$	20.1100	+	5.38845i	1.17484	+	0.314796i	0.381960	+	0.924179i	$0.375249\pi$
$294$		0			0
$295$	−1.78973	−	1.03330i	−0.104202	−	0.0601612i
$296$		0			0
$297$	2.80862	+	1.57658i	0.162973	+	0.0914825i
$298$		0			0
$299$	5.27390	+	19.6824i	0.304997	+	1.13827i
$300$		0			0
$301$	0.0164386	−	0.0613498i	0.000947507	−	0.00353615i
$302$		0			0
$303$	15.1627	−	26.5087i	0.871072	−	1.52289i
$304$		0			0
$305$	−0.411536			−0.0235645
$306$		0			0
$307$	−11.4523	−	11.4523i	−0.653619	−	0.653619i	0.300243	−	0.953863i	$-0.402932\pi$
$307$	−11.4523	−	11.4523i	−0.653619	−	0.653619i	−0.953863	+	0.300243i	$0.902932\pi$
$308$		0			0
$309$	−15.5858	−	4.10893i	−0.886645	−	0.233749i
$310$		0			0
$311$	−15.6387	+	9.02903i	−0.886792	+	0.511989i	−0.872892	−	0.487914i	$-0.837758\pi$
$311$	−15.6387	+	9.02903i	−0.886792	+	0.511989i	−0.0138999	+	0.999903i	$0.504425\pi$
$312$		0			0
$313$	22.1825	+	12.8070i	1.25383	+	0.723897i	0.971867	−	0.235529i	$-0.0756823\pi$
$313$	22.1825	+	12.8070i	1.25383	+	0.723897i	0.281959	+	0.959426i	$0.409016\pi$
$314$		0			0
$315$	−1.77914	+	1.80806i	−0.100243	+	0.101873i
$316$		0			0
$317$	3.31301	−	0.887719i	0.186077	−	0.0498593i	−0.164577	−	0.986364i	$-0.552626\pi$
$317$	3.31301	−	0.887719i	0.186077	−	0.0498593i	0.350654	+	0.936505i	$0.385959\pi$
$318$		0			0
$319$	−2.77516	−	4.80671i	−0.155379	−	0.269124i
$320$		0			0
$321$	−23.3172	+	0.0939989i	−1.30144	+	0.00524651i
$322$		0			0
$323$	−5.38660	−	5.38660i	−0.299719	−	0.299719i
$324$		0			0
$325$	−16.0447	+	16.0447i	−0.890001	+	0.890001i
$326$		0			0
$327$	−0.0627288	−	15.5604i	−0.00346891	−	0.860491i
$328$		0			0
$329$	9.50978	−	5.49047i	0.524291	−	0.302700i
$330$		0			0
$331$	4.07910	+	15.2234i	0.224207	+	0.836753i	0.982721	+	0.185096i	$0.0592595\pi$
$331$	4.07910	+	15.2234i	0.224207	+	0.836753i	−0.758513	+	0.651658i	$0.774074\pi$
$332$		0			0
$333$	8.45813	+	8.32283i	0.463503	+	0.456088i
$334$		0			0
$335$	0.659494	−	1.14228i	0.0360320	−	0.0624093i
$336$		0			0
$337$	−8.67225	−	15.0208i	−0.472407	−	0.818233i	0.527094	−	0.849807i	$-0.323282\pi$
$337$	−8.67225	−	15.0208i	−0.472407	−	0.818233i	−0.999501	+	0.0315734i	$0.989948\pi$
$338$		0			0
$339$	−4.72093	+	17.9072i	−0.256406	+	0.972585i
$340$		0			0
$341$	1.97567	−	1.97567i	0.106988	−	0.106988i
$342$		0			0
$343$			36.6800i			1.98053i
$344$		0			0
$345$	−1.21321	−	0.693942i	−0.0653171	−	0.0373606i
$346$		0			0
$347$	−6.92193	−	1.85473i	−0.371589	−	0.0995669i	0.0681917	−	0.997672i	$-0.478277\pi$
$347$	−6.92193	−	1.85473i	−0.371589	−	0.0995669i	−0.439780	+	0.898105i	$0.644944\pi$
$348$		0			0
$349$	−1.10009	+	0.294768i	−0.0588865	+	0.0157786i	−0.288142	−	0.957588i	$-0.593038\pi$
$349$	−1.10009	+	0.294768i	−0.0588865	+	0.0157786i	0.229256	+	0.973366i	$0.426371\pi$
$350$		0			0
$351$	12.1158	+	20.4111i	0.646694	+	1.08946i
$352$		0			0
$353$	−12.2507	+	21.2188i	−0.652037	+	1.12936i	0.330591	+	0.943774i	$0.392752\pi$
$353$	−12.2507	+	21.2188i	−0.652037	+	1.12936i	−0.982628	+	0.185587i	$0.940581\pi$
$354$		0			0
$355$	0.353557	−	1.31949i	0.0187649	−	0.0700314i
$356$		0			0
$357$	−9.24528	−	33.9557i	−0.489312	−	1.79713i
$358$		0			0
$359$		−	11.6859i		−	0.616757i	−0.951264	−	0.308378i	$-0.900214\pi$
$359$		−	11.6859i		−	0.616757i	0.951264	−	0.308378i	$-0.0997863\pi$
$360$		0			0
$361$		−	15.9289i		−	0.838362i
$362$		0			0
$363$	17.7796	+	4.68729i	0.933186	+	0.246019i
$364$		0			0
$365$	−0.137045	+	0.511458i	−0.00717325	+	0.0267709i
$366$		0			0
$367$	5.61911	−	9.73258i	0.293315	−	0.508037i	−0.681276	−	0.732026i	$-0.738575\pi$
$367$	5.61911	−	9.73258i	0.293315	−	0.508037i	0.974592	+	0.223990i	$0.0719082\pi$
$368$		0			0
$369$	−6.44889	−	10.9647i	−0.335716	−	0.570798i
$370$		0			0
$371$	−3.31647	+	0.888646i	−0.172183	+	0.0461362i
$372$		0			0
$373$	−11.5685	−	3.09978i	−0.598996	−	0.160501i	−0.0534347	−	0.998571i	$-0.517017\pi$
$373$	−11.5685	−	3.09978i	−0.598996	−	0.160501i	−0.545561	+	0.838071i	$0.683684\pi$
$374$		0			0
$375$	−0.0125896	−	3.12296i	−0.000650126	−	0.161269i
$376$		0			0
$377$		−	40.9031i		−	2.10661i
$378$		0			0
$379$	−11.6135	+	11.6135i	−0.596544	+	0.596544i	−0.939391	−	0.342847i	$-0.888609\pi$
$379$	−11.6135	+	11.6135i	−0.596544	+	0.596544i	0.342847	+	0.939391i	$0.388609\pi$
$380$		0			0
$381$	14.1760	+	14.0622i	0.726258	+	0.720426i
$382$		0			0
$383$	14.5294	+	25.1657i	0.742418	+	1.28591i	0.951391	+	0.307985i	$0.0996546\pi$
$383$	14.5294	+	25.1657i	0.742418	+	1.28591i	−0.208973	+	0.977921i	$0.567012\pi$
$384$		0			0
$385$	0.262056	−	0.453894i	0.0133556	−	0.0231326i
$386$		0			0
$387$	0.0392899	−	0.0108680i	0.00199722	−	0.000552449i
$388$		0			0
$389$	3.65693	+	13.6478i	0.185414	+	0.691973i	0.994542	+	0.104341i	$0.0332732\pi$
$389$	3.65693	+	13.6478i	0.185414	+	0.691973i	−0.809128	+	0.587632i	$0.800060\pi$
$390$		0			0
$391$	16.7926	−	9.69522i	0.849239	−	0.490308i
$392$		0			0
$393$	−5.30304	+	3.09028i	−0.267503	+	0.155884i
$394$		0			0
$395$	−0.373213	+	0.373213i	−0.0187784	+	0.0187784i
$396$		0			0
$397$	−1.83996	−	1.83996i	−0.0923450	−	0.0923450i	0.659425	−	0.751770i	$-0.270800\pi$
$397$	−1.83996	−	1.83996i	−0.0923450	−	0.0923450i	−0.751770	+	0.659425i	$0.770800\pi$
$398$		0			0
$399$	−7.04423	+	12.3154i	−0.352653	+	0.616539i
$400$		0			0
$401$	14.5786	+	25.2509i	0.728021	+	1.26097i	0.957718	+	0.287708i	$0.0928931\pi$
$401$	14.5786	+	25.2509i	0.728021	+	1.26097i	−0.229697	+	0.973262i	$0.573774\pi$
$402$		0			0
$403$	19.8889	−	5.32922i	0.990737	−	0.265467i
$404$		0			0
$405$	−1.57919	−	0.395965i	−0.0784707	−	0.0196757i
$406$		0			0
$407$	−2.12332	−	1.22590i	−0.105249	−	0.0607656i
$408$		0			0
$409$	−9.18277	+	5.30167i	−0.454059	+	0.262151i	−0.709543	−	0.704662i	$-0.751099\pi$
$409$	−9.18277	+	5.30167i	−0.454059	+	0.262151i	0.255484	+	0.966813i	$0.417765\pi$
$410$		0			0
$411$	−6.84070	−	25.1243i	−0.337427	−	1.23929i
$412$		0			0
$413$	−37.7581	−	37.7581i	−1.85796	−	1.85796i
$414$		0			0
$415$	1.39363			0.0684107
$416$		0			0
$417$	8.81306	+	15.1235i	0.431577	+	0.740603i
$418$		0			0
$419$	−3.70507	+	13.8275i	−0.181005	+	0.675519i	0.814446	+	0.580240i	$0.197041\pi$
$419$	−3.70507	+	13.8275i	−0.181005	+	0.675519i	−0.995451	+	0.0952792i	$0.969626\pi$
$420$		0			0
$421$	5.16753	+	19.2855i	0.251850	+	0.939918i	0.969816	+	0.243839i	$0.0784068\pi$
$421$	5.16753	+	19.2855i	0.251850	+	0.939918i	−0.717966	+	0.696079i	$0.754926\pi$
$422$		0			0
$423$	6.13189	+	3.47463i	0.298143	+	0.168942i
$424$		0			0
$425$	18.6995	+	10.7962i	0.907059	+	0.523691i
$426$		0			0
$427$	−10.2712	−	2.75215i	−0.497056	−	0.133186i
$428$		0			0
$429$	−3.48184	−	3.45388i	−0.168105	−	0.166755i
$430$		0			0
$431$	8.92159			0.429738			0.214869	−	0.976643i	$-0.431068\pi$
$431$	8.92159			0.429738			0.214869	+	0.976643i	$0.431068\pi$
$432$		0			0
$433$	−29.8178			−1.43295			−0.716476	−	0.697612i	$-0.754246\pi$
$433$	−29.8178			−1.43295			−0.716476	+	0.697612i	$0.754246\pi$
$434$		0			0
$435$	1.99182	+	1.97582i	0.0955003	+	0.0947334i
$436$		0			0
$437$	−7.55091	−	2.02326i	−0.361209	−	0.0967857i
$438$		0			0
$439$	−27.0574	−	15.6216i	−1.29138	−	0.745579i	−0.312481	−	0.949924i	$-0.601160\pi$
$439$	−27.0574	−	15.6216i	−1.29138	−	0.745579i	−0.978899	+	0.204345i	$0.934493\pi$
$440$		0			0
$441$	−38.3940	+	22.5815i	−1.82829	+	1.07531i
$442$		0			0
$443$	−2.84043	−	10.6006i	−0.134953	−	0.503651i	−0.999998	−	0.00195701i	$-0.999377\pi$
$443$	−2.84043	−	10.6006i	−0.134953	−	0.503651i	0.865045	−	0.501694i	$-0.167290\pi$
$444$		0			0
$445$	0.149271	−	0.557087i	0.00707613	−	0.0264085i
$446$		0			0
$447$	−4.64786	−	7.97590i	−0.219836	−	0.377247i
$448$		0			0
$449$	27.4967			1.29765			0.648824	−	0.760938i	$-0.275261\pi$
$449$	27.4967			1.29765			0.648824	+	0.760938i	$0.275261\pi$
$450$		0			0
$451$	1.85849	+	1.85849i	0.0875128	+	0.0875128i
$452$		0			0
$453$	−5.18307	−	19.0362i	−0.243522	−	0.894397i
$454$		0			0
$455$	3.34497	−	1.93122i	0.156815	−	0.0905370i
$456$		0			0
$457$	−16.8184	−	9.71008i	−0.786729	−	0.454218i	0.0520805	−	0.998643i	$-0.483415\pi$
$457$	−16.8184	−	9.71008i	−0.786729	−	0.454218i	−0.838810	+	0.544424i	$0.816748\pi$
$458$		0			0
$459$	15.7773	−	16.1636i	0.736419	−	0.754451i
$460$		0			0
$461$	4.03437	−	1.08101i	0.187900	−	0.0503475i	−0.163642	−	0.986520i	$-0.552324\pi$
$461$	4.03437	−	1.08101i	0.187900	−	0.0503475i	0.351542	+	0.936172i	$0.385658\pi$
$462$		0			0
$463$	0.773244	+	1.33930i	0.0359357	+	0.0622425i	0.883434	−	0.468556i	$-0.155226\pi$
$463$	0.773244	+	1.33930i	0.0359357	+	0.0622425i	−0.847498	+	0.530798i	$0.821892\pi$
$464$		0			0
$465$	−0.701222	+	1.22594i	−0.0325184	+	0.0568515i
$466$		0			0
$467$	2.13196	+	2.13196i	0.0986553	+	0.0986553i	0.754712	−	0.656056i	$-0.227777\pi$
$467$	2.13196	+	2.13196i	0.0986553	+	0.0986553i	−0.656056	+	0.754712i	$0.727777\pi$
$468$		0			0
$469$	24.0987	−	24.0987i	1.11277	−	1.11277i
$470$		0			0
$471$	8.47685	−	4.93978i	0.390593	−	0.227613i
$472$		0			0
$473$	−0.00729441	+	0.00421143i	−0.000335397	+	0.000193642i
$474$		0			0
$475$	−2.25301	−	8.40836i	−0.103375	−	0.385802i
$476$		0			0
$477$	−1.57077	−	1.54564i	−0.0719205	−	0.0707700i
$478$		0			0
$479$	−14.5113	+	25.1343i	−0.663037	+	1.14841i	0.316777	+	0.948500i	$0.397399\pi$
$479$	−14.5113	+	25.1343i	−0.663037	+	1.14841i	−0.979814	+	0.199914i	$0.935934\pi$
$480$		0			0
$481$	−9.03428	−	15.6478i	−0.411928	−	0.713480i
$482$		0			0
$483$	−25.6387	−	25.4328i	−1.16660	−	1.15723i
$484$		0			0
$485$	2.05652	−	2.05652i	0.0933817	−	0.0933817i
$486$		0			0
$487$			3.59517i			0.162913i	0.996677	+	0.0814564i	$0.0259571\pi$
$487$			3.59517i			0.162913i	−0.996677	+	0.0814564i	$0.974043\pi$
$488$		0			0
$489$	−0.148234	−	36.7707i	−0.00670339	−	1.66283i
$490$		0			0
$491$	−19.9964	−	5.35801i	−0.902424	−	0.241804i	−0.222367	−	0.974963i	$-0.571378\pi$
$491$	−19.9964	−	5.35801i	−0.902424	−	0.241804i	−0.680057	+	0.733159i	$0.738045\pi$
$492$		0			0
$493$	−37.5969	+	10.0741i	−1.69328	+	0.453713i
$494$		0			0
$495$	0.336380	−	0.00271215i	0.0151192	−	0.000121902i
$496$		0			0
$497$	17.6482	−	30.5676i	0.791631	−	1.37115i
$498$		0			0
$499$	−3.94988	+	14.7412i	−0.176821	+	0.659905i	0.819413	+	0.573203i	$0.194299\pi$
$499$	−3.94988	+	14.7412i	−0.176821	+	0.659905i	−0.996234	+	0.0867019i	$0.972367\pi$
$500$		0			0
$501$	15.1217	+	3.98658i	0.675587	+	0.178107i
$502$		0			0
$503$			11.1260i			0.496085i	0.968749	+	0.248042i	$0.0797872\pi$
$503$			11.1260i			0.496085i	−0.968749	+	0.248042i	$0.920213\pi$
$504$		0			0
$505$		−	3.18951i		−	0.141931i
$506$		0			0
$507$	−3.57965	−	13.1472i	−0.158978	−	0.583888i
$508$		0			0
$509$	6.47918	−	24.1806i	0.287185	−	1.07179i	−0.660044	−	0.751227i	$-0.729462\pi$
$509$	6.47918	−	24.1806i	0.287185	−	1.07179i	0.947228	−	0.320560i	$-0.103871\pi$
$510$		0			0
$511$	−6.84076	+	11.8485i	−0.302617	+	0.524149i
$512$		0			0
$513$	−9.10540	+	0.110125i	−0.402013	+	0.00486214i
$514$		0			0
$515$	−1.62606	+	0.435701i	−0.0716526	+	0.0191993i
$516$		0			0
$517$	−1.40661	−	0.376900i	−0.0618626	−	0.0165760i
$518$		0			0
$519$	7.79068	+	4.45617i	0.341973	+	0.195604i
$520$		0			0
$521$			44.7974i			1.96261i	0.192458	+	0.981305i	$0.438354\pi$
$521$			44.7974i			1.96261i	−0.192458	+	0.981305i	$0.561646\pi$
$522$		0			0
$523$	−7.02267	+	7.02267i	−0.307080	+	0.307080i	−0.843776	−	0.536696i	$-0.819672\pi$
$523$	−7.02267	+	7.02267i	−0.307080	+	0.307080i	0.536696	+	0.843776i	$0.319672\pi$
$524$		0			0
$525$	10.2515	−	38.8856i	0.447413	−	1.69711i
$526$		0			0
$527$	−9.79692	−	16.9688i	−0.426761	−	0.739171i
$528$		0			0
$529$	−1.55091	+	2.68626i	−0.0674309	+	0.116794i
$530$		0			0
$531$	8.60319	−	33.1752i	0.373347	−	1.43968i
$532$		0			0
$533$	5.01314	+	18.7093i	0.217143	+	0.810389i
$534$		0			0
$535$	−2.10903	+	1.21765i	−0.0911812	+	0.0526435i
$536$		0			0
$537$	−0.0193633	−	4.80323i	−0.000835590	−	0.207275i
$538$		0			0
$539$	6.50770	−	6.50770i	0.280306	−	0.280306i
$540$		0			0
$541$	14.9663	+	14.9663i	0.643452	+	0.643452i	0.951402	−	0.307950i	$-0.0996431\pi$
$541$	14.9663	+	14.9663i	0.643452	+	0.643452i	−0.307950	+	0.951402i	$0.599643\pi$
$542$		0			0
$543$	−0.549309	+	0.00221444i	−0.0235731	+	9.50308e-5i
$544$		0			0
$545$	−0.812579	−	1.40743i	−0.0348071	−	0.0602876i
$546$		0			0
$547$	5.15670	−	1.38173i	0.220485	−	0.0590787i	−0.146885	−	0.989154i	$-0.546925\pi$
$547$	5.15670	−	1.38173i	0.220485	−	0.0590787i	0.367370	+	0.930075i	$0.380258\pi$
$548$		0			0
$549$	−1.81951	−	6.57789i	−0.0776547	−	0.280738i
$550$		0			0
$551$	13.5896	+	7.84596i	0.578937	+	0.334249i
$552$		0			0
$553$	−11.8106	+	6.81883i	−0.502236	+	0.289966i
$554$		0			0
$555$	1.19839	+	0.315935i	0.0508687	+	0.0134107i
$556$		0			0
$557$	7.66230	+	7.66230i	0.324662	+	0.324662i	0.850552	−	0.525890i	$-0.176268\pi$
$557$	7.66230	+	7.66230i	0.324662	+	0.324662i	−0.525890	+	0.850552i	$0.676268\pi$
$558$		0			0
$559$	−0.0620723			−0.00262538
$560$		0			0
$561$	−2.31716	+	4.05106i	−0.0978304	+	0.171036i
$562$		0			0
$563$	−5.71152	+	21.3157i	−0.240712	+	0.898349i	0.734779	+	0.678307i	$0.237286\pi$
$563$	−5.71152	+	21.3157i	−0.240712	+	0.898349i	−0.975490	+	0.220042i	$0.929381\pi$
$564$		0			0
$565$	0.500595	+	1.86825i	0.0210602	+	0.0785977i
$566$		0			0
$567$	−36.7656	−	20.4434i	−1.54401	−	0.858542i
$568$		0			0
$569$	−38.6354	−	22.3061i	−1.61968	−	0.935122i	−0.987002	−	0.160706i	$-0.948623\pi$
$569$	−38.6354	−	22.3061i	−1.61968	−	0.935122i	−0.632676	−	0.774416i	$-0.718044\pi$
$570$		0			0
$571$	−9.47469	−	2.53873i	−0.396503	−	0.106243i	0.0550573	−	0.998483i	$-0.482466\pi$
$571$	−9.47469	−	2.53873i	−0.396503	−	0.106243i	−0.451561	+	0.892240i	$0.649133\pi$
$572$		0			0
$573$	34.7253	−	9.45483i	1.45067	−	0.394981i
$574$		0			0
$575$	22.1577			0.924041
$576$		0			0
$577$	−0.565932			−0.0235600			−0.0117800	−	0.999931i	$-0.503750\pi$
$577$	−0.565932			−0.0235600			−0.0117800	+	0.999931i	$0.503750\pi$
$578$		0			0
$579$	−6.79593	+	25.7780i	−0.282429	+	1.07130i
$580$		0			0
$581$	34.7824	+	9.31992i	1.44302	+	0.386655i
$582$		0			0
$583$	0.394324	+	0.227663i	0.0163312	+	0.00942884i
$584$		0			0
$585$	2.15683	+	1.22217i	0.0891740	+	0.0505304i
$586$		0			0
$587$	−10.6937	−	39.9093i	−0.441375	−	1.64723i	−0.725334	−	0.688397i	$-0.758315\pi$
$587$	−10.6937	−	39.9093i	−0.441375	−	1.64723i	0.283960	−	0.958836i	$-0.408352\pi$
$588$		0			0
$589$	−2.04448	+	7.63012i	−0.0842415	+	0.314394i
$590$		0			0
$591$	−2.21716	+	0.00893807i	−0.0912017	+	0.000367663i
$592$		0			0
$593$	−12.9281			−0.530893			−0.265447	−	0.964126i	$-0.585519\pi$
$593$	−12.9281			−0.530893			−0.265447	+	0.964126i	$0.585519\pi$
$594$		0			0
$595$	−2.59896	−	2.59896i	−0.106547	−	0.106547i
$596$		0			0
$597$	−20.1511	+	20.3143i	−0.824731	+	0.831408i
$598$		0			0
$599$	39.9617	−	23.0719i	1.63279	−	0.942692i	0.649563	−	0.760308i	$-0.274952\pi$
$599$	39.9617	−	23.0719i	1.63279	−	0.942692i	0.983227	−	0.182384i	$-0.0583814\pi$
$600$		0			0
$601$	−28.4107	−	16.4029i	−1.15890	−	0.669090i	−0.207858	−	0.978159i	$-0.566649\pi$
$601$	−28.4107	−	16.4029i	−1.15890	−	0.669090i	−0.951040	+	0.309069i	$0.899983\pi$
$602$		0			0
$603$	21.1737	+	5.49089i	0.862259	+	0.223606i
$604$		0			0
$605$	1.85493	−	0.497028i	0.0754138	−	0.0202071i
$606$		0			0
$607$	6.36706	+	11.0281i	0.258431	+	0.447616i	0.965822	−	0.259207i	$-0.0834611\pi$
$607$	6.36706	+	11.0281i	0.258431	+	0.447616i	−0.707391	+	0.706823i	$0.750128\pi$
$608$		0			0
$609$	36.4986	+	62.6330i	1.47900	+	2.53802i
$610$		0			0
$611$	−7.58845	−	7.58845i	−0.306996	−	0.306996i
$612$		0			0
$613$	29.9303	−	29.9303i	1.20888	−	1.20888i	0.237483	−	0.971392i	$-0.423677\pi$
$613$	29.9303	−	29.9303i	1.20888	−	1.20888i	0.971392	−	0.237483i	$-0.0763225\pi$
$614$		0			0
$615$	−1.15323	−	0.659631i	−0.0465026	−	0.0265989i
$616$		0			0
$617$	−2.50740	+	1.44765i	−0.100944	+	0.0582802i	−0.549622	−	0.835413i	$-0.685228\pi$
$617$	−2.50740	+	1.44765i	−0.100944	+	0.0582802i	0.448678	+	0.893693i	$0.351895\pi$
$618$		0			0
$619$	−1.48762	−	5.55188i	−0.0597926	−	0.223149i	0.929564	−	0.368661i	$-0.120184\pi$
$619$	−1.48762	−	5.55188i	−0.0597926	−	0.223149i	−0.989356	+	0.145512i	$0.953517\pi$
$620$		0			0
$621$	5.72788	−	22.4598i	0.229852	−	0.901280i
$622$		0			0
$623$	7.45105	−	12.9056i	0.298520	−	0.517052i
$624$		0			0
$625$	12.2551	+	21.2265i	0.490204	+	0.849059i
$626$		0			0
$627$	1.81539	−	0.494286i	0.0724999	−	0.0197399i
$628$		0			0
$629$	−12.1580	+	12.1580i	−0.484770	+	0.484770i
$630$		0			0
$631$		−	33.4420i		−	1.33130i	−0.746262	−	0.665652i	$-0.768154\pi$
$631$		−	33.4420i		−	1.33130i	0.746262	−	0.665652i	$-0.231846\pi$
$632$		0			0
$633$	−39.0462	+	22.7537i	−1.55195	+	0.904379i
$634$		0			0
$635$	2.01438	+	0.539750i	0.0799381	+	0.0214193i
$636$		0			0
$637$	65.5126	−	17.5540i	2.59570	−	0.695516i
$638$		0			0
$639$	22.6536	−	0.182651i	0.896164	−	0.00722556i
$640$		0			0
$641$	9.42170	−	16.3189i	0.372135	−	0.644557i	−0.617759	−	0.786368i	$-0.711959\pi$
$641$	9.42170	−	16.3189i	0.372135	−	0.644557i	0.989894	+	0.141811i	$0.0452925\pi$
$642$		0			0
$643$	−3.18391	+	11.8825i	−0.125561	+	0.468601i	−0.999859	−	0.0167890i	$-0.994656\pi$
$643$	−3.18391	+	11.8825i	−0.125561	+	0.468601i	0.874298	+	0.485390i	$0.161322\pi$
$644$		0			0
$645$	0.00299840	−	0.00302267i	0.000118062	−	0.000119018i
$646$		0			0
$647$			8.72393i			0.342973i	0.985186	+	0.171487i	$0.0548570\pi$
$647$			8.72393i			0.342973i	−0.985186	+	0.171487i	$0.945143\pi$
$648$		0			0
$649$			7.08134i			0.277967i
$650$		0			0
$651$	−25.6996	+	25.9077i	−1.00725	+	1.01540i
$652$		0			0
$653$	−5.07099	+	18.9252i	−0.198443	+	0.740600i	0.792906	+	0.609345i	$0.208567\pi$
$653$	−5.07099	+	18.9252i	−0.198443	+	0.740600i	−0.991349	+	0.131255i	$0.958099\pi$
$654$		0			0
$655$	−0.320517	+	0.555152i	−0.0125237	+	0.0216916i
$656$		0			0
$657$	−8.78094	+	0.0707987i	−0.342577	+	0.00276212i
$658$		0			0
$659$	−37.3628	+	10.0113i	−1.45545	+	0.389986i	−0.897915	−	0.440168i	$-0.854919\pi$
$659$	−37.3628	+	10.0113i	−1.45545	+	0.389986i	−0.557533	+	0.830155i	$0.688252\pi$
$660$		0			0
$661$	−26.6308	−	7.13570i	−1.03582	−	0.277546i	−0.299438	−	0.954116i	$-0.596799\pi$
$661$	−26.6308	−	7.13570i	−1.03582	−	0.277546i	−0.736379	+	0.676569i	$0.763466\pi$
$662$		0			0
$663$	−29.7157	+	17.3164i	−1.15406	+	0.672515i
$664$		0			0
$665$			1.48177i			0.0574608i
$666$		0			0
$667$	−28.2435	+	28.2435i	−1.09359	+	1.09359i
$668$		0			0
$669$	−21.6565	+	5.89651i	−0.837288	+	0.227972i
$670$		0			0
$671$	0.705075	+	1.22123i	0.0272191	+	0.0471449i
$672$		0			0
$673$	10.0608	−	17.4258i	0.387815	−	0.671716i	−0.604340	−	0.796726i	$-0.706563\pi$
$673$	10.0608	−	17.4258i	0.387815	−	0.671716i	0.992155	+	0.125011i	$0.0398965\pi$
$674$		0			0
$675$	24.8486	−	6.98133i	0.956424	−	0.268711i
$676$		0			0
$677$	−5.24998	−	19.5932i	−0.201773	−	0.753027i	−0.990409	−	0.138167i	$-0.955879\pi$
$677$	−5.24998	−	19.5932i	−0.201773	−	0.753027i	0.788636	−	0.614860i	$-0.210788\pi$
$678$		0			0
$679$	65.0798	−	37.5738i	2.49753	−	1.44195i
$680$		0			0
$681$	20.4528	+	11.6988i	0.783755	+	0.448298i
$682$		0			0
$683$	18.4322	−	18.4322i	0.705287	−	0.705287i	−0.260253	−	0.965540i	$-0.583806\pi$
$683$	18.4322	−	18.4322i	0.705287	−	0.705287i	0.965540	+	0.260253i	$0.0838061\pi$
$684$		0			0
$685$	−1.92300	−	1.92300i	−0.0734741	−	0.0734741i
$686$		0			0
$687$	−14.6593	−	25.1559i	−0.559286	−	0.959756i
$688$		0			0
$689$	1.67776	+	2.90597i	0.0639177	+	0.110709i
$690$		0			0
$691$	−15.6519	+	4.19392i	−0.595427	+	0.159544i	−0.543932	−	0.839129i	$-0.683065\pi$
$691$	−15.6519	+	4.19392i	−0.595427	+	0.159544i	−0.0514946	+	0.998673i	$0.516399\pi$
$692$		0			0
$693$	8.41354	+	2.18185i	0.319604	+	0.0828817i
$694$		0			0
$695$	1.58322	+	0.914072i	0.0600549	+	0.0346727i
$696$		0			0
$697$	15.9623	−	9.21585i	0.604616	−	0.349075i
$698$		0			0
$699$	−12.2581	+	12.3573i	−0.463644	+	0.467397i
$700$		0			0
$701$	2.97647	+	2.97647i	0.112420	+	0.112420i	0.761079	−	0.648659i	$-0.224670\pi$
$701$	2.97647	+	2.97647i	0.112420	+	0.112420i	−0.648659	+	0.761079i	$0.724670\pi$
$702$		0			0
$703$	6.93177			0.261437
$704$		0			0
$705$	0.736087	−	0.00296740i	0.0277226	−	0.000111759i
$706$		0			0
$707$	21.3299	−	79.6042i	0.802192	−	2.99382i
$708$		0			0
$709$	10.0033	+	37.3329i	0.375682	+	1.40207i	0.852345	+	0.522980i	$0.175180\pi$
$709$	10.0033	+	37.3329i	0.375682	+	1.40207i	−0.476663	+	0.879086i	$0.658154\pi$
$710$		0			0
$711$	−7.61542	−	4.31528i	−0.285601	−	0.161836i
$712$		0			0
$713$	−17.4131	−	10.0535i	−0.652125	−	0.376505i
$714$		0			0
$715$	−0.494761	−	0.132571i	−0.0185030	−	0.00495787i
$716$		0			0
$717$	−2.98803	+	11.3341i	−0.111590	+	0.423278i
$718$		0			0
$719$	−38.3674			−1.43086			−0.715431	−	0.698683i	$-0.753770\pi$
$719$	−38.3674			−1.43086			−0.715431	+	0.698683i	$0.753770\pi$
$720$		0			0
$721$	−43.4970			−1.61991
$722$		0			0
$723$	−3.60327	+	0.981080i	−0.134007	+	0.0364867i
$724$		0			0
$725$	−42.9625	−	11.5118i	−1.59559	−	0.427536i
$726$		0			0
$727$	14.8899	+	8.59667i	0.552235	+	0.318833i	0.750023	−	0.661412i	$-0.230042\pi$
$727$	14.8899	+	8.59667i	0.552235	+	0.318833i	−0.197788	+	0.980245i	$0.563376\pi$
$728$		0			0
$729$	−0.653006	−	26.9921i	−0.0241854	−	0.999707i
$730$		0			0
$731$	0.0152878	+	0.0570550i	0.000565441	+	0.00211026i
$732$		0			0
$733$	3.41130	−	12.7311i	0.125999	−	0.470235i	−0.873874	−	0.486152i	$-0.838400\pi$
$733$	3.41130	−	12.7311i	0.125999	−	0.470235i	0.999873	+	0.0159168i	$0.00506670\pi$
$734$		0			0
$735$	−2.30977	+	4.03815i	−0.0851972	+	0.148949i
$736$		0			0
$737$	−4.51959			−0.166481
$738$		0			0
$739$	15.2048	+	15.2048i	0.559316	+	0.559316i	0.929113	−	0.369797i	$-0.120573\pi$
$739$	15.2048	+	15.2048i	0.559316	+	0.559316i	−0.369797	+	0.929113i	$0.620573\pi$
$740$		0			0
$741$	13.4075	+	3.53466i	0.492536	+	0.129849i
$742$		0			0
$743$	−36.6127	+	21.1384i	−1.34319	+	0.775491i	−0.987274	−	0.159027i	$-0.949164\pi$
$743$	−36.6127	+	21.1384i	−1.34319	+	0.775491i	−0.355916	+	0.934518i	$0.615831\pi$
$744$		0			0
$745$	−0.834963	−	0.482066i	−0.0305907	−	0.0176615i
$746$		0			0
$747$	6.16161	+	22.2755i	0.225441	+	0.815017i
$748$		0			0
$749$	−60.7803	+	16.2860i	−2.22086	+	0.595079i
$750$		0			0
$751$	9.72823	+	16.8498i	0.354988	+	0.614857i	0.987116	−	0.160007i	$-0.0511516\pi$
$751$	9.72823	+	16.8498i	0.354988	+	0.614857i	−0.632128	+	0.774864i	$0.717818\pi$
$752$		0			0
$753$	−8.94764	+	0.0360708i	−0.326070	+	0.00131449i
$754$		0			0
$755$	−1.45702	−	1.45702i	−0.0530264	−	0.0530264i
$756$		0			0
$757$	26.9716	−	26.9716i	0.980300	−	0.980300i	−0.0195093	−	0.999810i	$-0.506210\pi$
$757$	26.9716	−	26.9716i	0.980300	−	0.980300i	0.999810	+	0.0195093i	$0.00621039\pi$
$758$		0			0
$759$	0.0193064	+	4.78910i	0.000700778	+	0.173833i
$760$		0			0
$761$	−15.0417	+	8.68435i	−0.545263	+	0.314808i	−0.747209	−	0.664589i	$-0.768607\pi$
$761$	−15.0417	+	8.68435i	−0.545263	+	0.314808i	0.201946	+	0.979397i	$0.435273\pi$
$762$		0			0
$763$	−10.8683	−	40.5609i	−0.393457	−	1.46840i
$764$		0			0
$765$	0.592172	−	2.28350i	0.0214100	−	0.0825603i
$766$		0			0
$767$	−26.0930	+	45.1944i	−0.942163	+	1.63187i
$768$		0			0
$769$	15.0664	+	26.0957i	0.543307	+	0.941036i	0.998711	+	0.0507510i	$0.0161615\pi$
$769$	15.0664	+	26.0957i	0.543307	+	0.941036i	−0.455404	+	0.890285i	$0.650505\pi$
$770$		0			0
$771$	4.50096	−	17.0728i	0.162098	−	0.614862i
$772$		0			0
$773$	−9.37945	+	9.37945i	−0.337355	+	0.337355i	−0.855371	−	0.518016i	$-0.826671\pi$
$773$	−9.37945	+	9.37945i	−0.337355	+	0.337355i	0.518016	+	0.855371i	$0.326671\pi$
$774$		0			0
$775$		−	22.3901i		−	0.804278i
$776$		0			0
$777$	27.7967	+	15.8993i	0.997200	+	0.570386i
$778$		0			0
$779$	−7.17757	−	1.92322i	−0.257163	−	0.0689067i
$780$		0			0
$781$	−4.52131	+	1.21148i	−0.161785	+	0.0433502i
$782$		0			0
$783$	−22.7747	+	40.5723i	−0.813902	+	1.44994i
$784$		0			0
$785$	0.512344	−	0.887406i	0.0182863	−	0.0316729i
$786$		0			0
$787$	3.39895	−	12.6850i	0.121159	−	0.452173i	−0.878514	−	0.477716i	$-0.841465\pi$
$787$	3.39895	−	12.6850i	0.121159	−	0.452173i	0.999674	+	0.0255430i	$0.00813148\pi$
$788$		0			0
$789$	7.66786	+	28.1622i	0.272983	+	1.00260i
$790$		0			0
$791$			49.9756i			1.77693i
$792$		0			0
$793$			10.3921i			0.369035i
$794$		0			0
$795$	−0.222554	−	0.0586725i	−0.00789316	−	0.00208090i
$796$		0			0
$797$	4.30559	−	16.0687i	0.152512	−	0.569181i	−0.846794	−	0.531921i	$-0.821470\pi$
$797$	4.30559	−	16.0687i	0.152512	−	0.569181i	0.999306	−	0.0372602i	$-0.0118630\pi$
$798$		0			0
$799$	−5.10611	+	8.84405i	−0.180641	+	0.312880i
$800$		0			0
$801$	9.56432	−	0.0771149i	0.337939	−	0.00272472i
$802$		0			0
$803$	1.75254	−	0.469592i	0.0618458	−	0.0165715i
$804$		0			0
$805$	−3.64320	−	0.976194i	−0.128406	−	0.0344063i
$806$		0			0
$807$	0.179934	+	44.6339i	0.00633396	+	1.57119i
$808$		0			0
$809$			6.67548i			0.234697i	0.993091	+	0.117349i	$0.0374395\pi$
$809$			6.67548i			0.234697i	−0.993091	+	0.117349i	$0.962560\pi$
$810$		0			0
$811$	18.4521	−	18.4521i	0.647940	−	0.647940i	−0.304555	−	0.952495i	$-0.598508\pi$
$811$	18.4521	−	18.4521i	0.647940	−	0.647940i	0.952495	+	0.304555i	$0.0985076\pi$
$812$		0			0
$813$	−12.2434	−	12.1451i	−0.429395	−	0.425947i
$814$		0			0
$815$	−1.92020	−	3.32589i	−0.0672618	−	0.116501i
$816$		0			0
$817$	0.0119066	−	0.0206229i	0.000416560	−	0.000721502i
$818$		0			0
$819$	45.6572	+	44.9268i	1.59539	+	1.56987i
$820$		0			0
$821$	−3.30305	−	12.3271i	−0.115277	−	0.430220i	0.884030	−	0.467430i	$-0.154820\pi$
$821$	−3.30305	−	12.3271i	−0.115277	−	0.430220i	−0.999307	+	0.0372093i	$0.988153\pi$
$822$		0			0
$823$	−7.14088	+	4.12279i	−0.248915	+	0.143711i	−0.619268	−	0.785180i	$-0.712570\pi$
$823$	−7.14088	+	4.12279i	−0.248915	+	0.143711i	0.370352	+	0.928891i	$0.379237\pi$
$824$		0			0
$825$	−4.60770	+	2.68508i	−0.160420	+	0.0934826i
$826$		0			0
$827$	24.9396	−	24.9396i	0.867236	−	0.867236i	−0.124930	−	0.992166i	$-0.539870\pi$
$827$	24.9396	−	24.9396i	0.867236	−	0.867236i	0.992166	+	0.124930i	$0.0398705\pi$
$828$		0			0
$829$	22.7949	+	22.7949i	0.791701	+	0.791701i	0.981771	−	0.190069i	$-0.0608713\pi$
$829$	22.7949	+	22.7949i	0.791701	+	0.791701i	−0.190069	+	0.981771i	$0.560871\pi$
$830$		0			0
$831$	2.34810	−	4.10516i	0.0814548	−	0.142407i
$832$		0			0
$833$	−32.2703	−	55.8938i	−1.11810	−	1.93661i
$834$		0			0
$835$	1.57764	−	0.422726i	0.0545964	−	0.0146291i
$836$		0			0
$837$	−22.6954	−	5.78797i	−0.784467	−	0.200061i
$838$		0			0
$839$	29.5746	+	17.0749i	1.02103	+	0.589492i	0.914402	−	0.404807i	$-0.132661\pi$
$839$	29.5746	+	17.0749i	1.02103	+	0.589492i	0.106628	+	0.994299i	$0.465995\pi$
$840$		0			0
$841$	44.3213	−	25.5889i	1.52832	−	0.882377i
$842$		0			0
$843$	11.4813	+	42.1683i	0.395439	+	1.45235i
$844$		0			0
$845$	−1.00628	−	1.00628i	−0.0346171	−	0.0346171i
$846$		0			0
$847$	49.6195			1.70495
$848$		0			0
$849$	−7.79777	−	13.3813i	−0.267619	−	0.459244i
$850$		0			0
$851$	−4.56665	+	17.0430i	−0.156543	+	0.584225i
$852$		0			0
$853$	5.84290	+	21.8060i	0.200057	+	0.746624i	0.990900	+	0.134604i	$0.0429761\pi$
$853$	5.84290	+	21.8060i	0.200057	+	0.746624i	−0.790842	+	0.612020i	$0.790357\pi$
$854$		0			0
$855$	−0.819772	+	0.482150i	−0.0280356	+	0.0164892i
$856$		0			0
$857$	44.1400	+	25.4842i	1.50779	+	0.870525i	0.999959	+	0.00907074i	$0.00288735\pi$
$857$	44.1400	+	25.4842i	1.50779	+	0.870525i	0.507835	+	0.861454i	$0.330446\pi$
$858$		0			0
$859$	−17.4277	−	4.66973i	−0.594624	−	0.159329i	−0.0510584	−	0.998696i	$-0.516259\pi$
$859$	−17.4277	−	4.66973i	−0.594624	−	0.159329i	−0.543566	+	0.839367i	$0.682926\pi$
$860$		0			0
$861$	−24.3711	−	24.1754i	−0.830564	−	0.823894i
$862$		0			0
$863$	45.5523			1.55062			0.775309	−	0.631583i	$-0.217594\pi$
$863$	45.5523			1.55062			0.775309	+	0.631583i	$0.217594\pi$
$864$		0			0
$865$	0.937369			0.0318715
$866$		0			0
$867$	2.33103	+	2.31231i	0.0791660	+	0.0785303i
$868$		0			0
$869$	1.74692	+	0.468086i	0.0592603	+	0.0158787i
$870$		0			0
$871$	−28.8448	−	16.6536i	−0.977369	−	0.564284i
$872$		0			0
$873$	41.9633	+	23.7785i	1.42024	+	0.804780i
$874$		0			0
$875$	−2.18125	−	8.14054i	−0.0737398	−	0.275201i
$876$		0			0
$877$	−5.03203	+	18.7798i	−0.169919	+	0.634148i	0.827442	+	0.561551i	$0.189795\pi$
$877$	−5.03203	+	18.7798i	−0.169919	+	0.634148i	−0.997361	+	0.0725968i	$0.976871\pi$
$878$		0			0
$879$	18.1558	+	31.1561i	0.612381	+	1.05087i
$880$		0			0
$881$	51.8921			1.74829			0.874145	−	0.485666i	$-0.161423\pi$
$881$	51.8921			1.74829			0.874145	+	0.485666i	$0.161423\pi$
$882$		0			0
$883$	1.40472	+	1.40472i	0.0472726	+	0.0472726i	0.730348	−	0.683075i	$-0.239358\pi$
$883$	1.40472	+	1.40472i	0.0472726	+	0.0472726i	−0.683075	+	0.730348i	$0.739358\pi$
$884$		0			0
$885$	−0.940365	−	3.45374i	−0.0316100	−	0.116096i
$886$		0			0
$887$	6.52145	−	3.76516i	0.218969	−	0.126422i	−0.386504	−	0.922288i	$-0.626317\pi$
$887$	6.52145	−	3.76516i	0.218969	−	0.126422i	0.605473	+	0.795866i	$0.292984\pi$
$888$		0			0
$889$	46.6654	+	26.9423i	1.56511	+	0.903616i
$890$		0			0
$891$	1.53057	+	5.36463i	0.0512762	+	0.179722i
$892$		0			0
$893$	3.97679	−	1.06558i	0.133078	−	0.0356582i
$894$		0			0
$895$	−0.250830	−	0.434449i	−0.00838431	−	0.0145220i
$896$		0			0
$897$	−17.5234	+	30.6360i	−0.585091	+	1.02291i
$898$		0			0
$899$	28.5398	+	28.5398i	0.951855	+	0.951855i
$900$		0			0
$901$	2.25787	−	2.25787i	0.0752204	−	0.0752204i
$902$		0			0
$903$	0.0950485	−	0.0553884i	0.00316302	−	0.00184321i
$904$		0			0
$905$	−0.0496848	+	0.0286855i	−0.00165158	+	0.000953539i
$906$		0			0
$907$	5.17036	+	19.2960i	0.171679	+	0.640714i	0.997094	+	0.0761873i	$0.0242747\pi$
$907$	5.17036	+	19.2960i	0.171679	+	0.640714i	−0.825415	+	0.564527i	$0.809059\pi$
$908$		0			0
$909$	50.9804	−	14.1017i	1.69091	−	0.467723i
$910$		0			0
$911$	20.6774	−	35.8143i	0.685073	−	1.18658i	−0.288341	−	0.957528i	$-0.593104\pi$
$911$	20.6774	−	35.8143i	0.685073	−	1.18658i	0.973414	−	0.229053i	$-0.0735629\pi$
$912$		0			0
$913$	−2.38768	−	4.13558i	−0.0790206	−	0.136868i
$914$		0			0
$915$	−0.506054	−	0.501991i	−0.0167296	−	0.0165953i
$916$		0			0
$917$	−11.7121	+	11.7121i	−0.386767	+	0.386767i
$918$		0			0
$919$		−	8.25699i		−	0.272373i	−0.990683	−	0.136187i	$-0.956515\pi$
$919$		−	8.25699i		−	0.272373i	0.990683	−	0.136187i	$-0.0434847\pi$
$920$		0			0
$921$	−0.113087	−	28.0521i	−0.00372635	−	0.924350i
$922$		0			0
$923$	−33.3198	−	8.92803i	−1.09674	−	0.293870i
$924$		0			0
$925$	−18.9783	+	5.08522i	−0.624002	+	0.167201i
$926$		0			0
$927$	−14.1534	−	24.0642i	−0.464857	−	0.790371i
$928$		0			0
$929$	−2.79783	+	4.84599i	−0.0917939	+	0.158992i	−0.908266	−	0.418393i	$-0.862593\pi$
$929$	−2.79783	+	4.84599i	−0.0917939	+	0.158992i	0.816472	+	0.577385i	$0.195927\pi$
$930$		0			0
$931$	−6.73438	+	25.1330i	−0.220710	+	0.823702i
$932$		0			0
$933$	−30.2441	−	7.97335i	−0.990148	−	0.261036i
$934$		0			0
$935$			0.487421i			0.0159404i
$936$		0			0
$937$		−	3.12869i		−	0.102210i	−0.998693	−	0.0511049i	$-0.983726\pi$
$937$		−	3.12869i		−	0.102210i	0.998693	−	0.0511049i	$-0.0162743\pi$
$938$		0			0
$939$	11.6551	+	42.8066i	0.380351	+	1.39694i
$940$		0			0
$941$	−3.45992	+	12.9126i	−0.112790	+	0.420939i	−0.999112	−	0.0421307i	$-0.986585\pi$
$941$	−3.45992	+	12.9126i	−0.112790	+	0.420939i	0.886322	+	0.463070i	$0.153252\pi$
$942$		0			0
$943$	9.45717	−	16.3803i	0.307968	−	0.533416i
$944$		0			0
$945$	−4.39322	+	0.0531337i	−0.142912	+	0.00172844i
$946$		0			0
$947$	21.8316	−	5.84975i	0.709431	−	0.190091i	0.113980	−	0.993483i	$-0.463640\pi$
$947$	21.8316	−	5.84975i	0.709431	−	0.190091i	0.595451	+	0.803392i	$0.296973\pi$
$948$		0			0
$949$	12.9154	+	3.46066i	0.419250	+	0.112338i
$950$		0			0
$951$	5.15676	+	2.94960i	0.167219	+	0.0956474i
$952$		0			0
$953$		−	13.2051i		−	0.427754i	−0.976861	−	0.213877i	$-0.931391\pi$
$953$		−	13.2051i		−	0.427754i	0.976861	−	0.213877i	$-0.0686092\pi$
$954$		0			0
$955$	2.65786	−	2.65786i	0.0860065	−	0.0860065i
$956$		0			0
$957$	2.45068	−	9.29581i	0.0792193	−	0.300491i
$958$		0			0
$959$	−35.1344	−	60.8545i	−1.13455	−	1.96509i
$960$		0			0
$961$	5.34109	−	9.25104i	0.172293	−	0.298421i
$962$		0			0
$963$	−28.7871	−	28.3266i	−0.927653	−	0.912813i
$964$		0			0
$965$	0.720623	+	2.68940i	0.0231977	+	0.0865749i
$966$		0			0
$967$	−26.0110	+	15.0175i	−0.836457	+	0.482929i	−0.856058	−	0.516879i	$-0.827094\pi$
$967$	−26.0110	+	15.0175i	−0.836457	+	0.482929i	0.0196013	+	0.999808i	$0.493760\pi$
$968$		0			0
$969$	−0.0531905	−	13.1943i	−0.00170873	−	0.423863i
$970$		0			0
$971$	−29.4184	+	29.4184i	−0.944081	+	0.944081i	−0.998517	−	0.0544362i	$-0.982664\pi$
$971$	−29.4184	+	29.4184i	−0.944081	+	0.944081i	0.0544362	+	0.998517i	$0.482664\pi$
$972$		0			0
$973$	33.4013	+	33.4013i	1.07080	+	1.07080i
$974$		0			0
$975$	−39.3010	+	0.158435i	−1.25864	+	0.00507398i
$976$		0			0
$977$	−1.26388	−	2.18911i	−0.0404352	−	0.0700358i	0.845100	−	0.534609i	$-0.179541\pi$
$977$	−1.26388	−	2.18911i	−0.0404352	−	0.0700358i	−0.885535	+	0.464573i	$0.846208\pi$
$978$		0			0
$979$	−1.90889	+	0.511486i	−0.0610084	+	0.0163472i
$980$		0			0
$981$	18.9034	−	19.2107i	0.603538	−	0.613350i
$982$		0			0
$983$	17.8779	+	10.3218i	0.570215	+	0.329214i	0.757235	−	0.653142i	$-0.226550\pi$
$983$	17.8779	+	10.3218i	0.570215	+	0.329214i	−0.187020	+	0.982356i	$0.559883\pi$
$984$		0			0
$985$	−0.200541	+	0.115782i	−0.00638976	+	0.00368913i
$986$		0			0
$987$	18.3912	+	4.84852i	0.585398	+	0.154330i
$988$		0			0
$989$	0.0428609	+	0.0428609i	0.00136290	+	0.00136290i
$990$		0			0
$991$	−32.9680			−1.04726			−0.523631	−	0.851945i	$-0.675423\pi$
$991$	−32.9680			−1.04726			−0.523631	+	0.851945i	$0.675423\pi$
$992$		0			0
$993$	−13.5535	+	23.6955i	−0.430108	+	0.751953i
$994$		0			0
$995$	−0.773465	+	2.88661i	−0.0245205	+	0.0915117i
$996$		0			0
$997$	2.23491	+	8.34081i	0.0707804	+	0.264156i	0.992243	−	0.124310i	$-0.0396717\pi$
$997$	2.23491	+	8.34081i	0.0707804	+	0.264156i	−0.921463	+	0.388466i	$0.873005\pi$
$998$		0			0
$999$	0.248561	+	20.5516i	0.00786411	+	0.650223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.529.14		72
3.2	odd	2		1728.2.bc.e.721.8		72
4.3	odd	2		144.2.x.e.61.9	yes	72
9.4	even	3	inner	576.2.bb.e.337.15		72
9.5	odd	6		1728.2.bc.e.145.11		72
12.11	even	2		432.2.y.e.397.10		72
16.5	even	4	inner	576.2.bb.e.241.15		72
16.11	odd	4		144.2.x.e.133.17	yes	72
36.23	even	6		432.2.y.e.253.2		72
36.31	odd	6		144.2.x.e.13.17	✓	72
48.5	odd	4		1728.2.bc.e.1585.11		72
48.11	even	4		432.2.y.e.181.2		72
144.5	odd	12		1728.2.bc.e.1009.8		72
144.59	even	12		432.2.y.e.37.10		72
144.85	even	12	inner	576.2.bb.e.49.14		72
144.139	odd	12		144.2.x.e.85.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.17	✓	72	36.31	odd	6
144.2.x.e.61.9	yes	72	4.3	odd	2
144.2.x.e.85.9	yes	72	144.139	odd	12
144.2.x.e.133.17	yes	72	16.11	odd	4
432.2.y.e.37.10		72	144.59	even	12
432.2.y.e.181.2		72	48.11	even	4
432.2.y.e.253.2		72	36.23	even	6
432.2.y.e.397.10		72	12.11	even	2
576.2.bb.e.49.14		72	144.85	even	12	inner
576.2.bb.e.241.15		72	16.5	even	4	inner
576.2.bb.e.337.15		72	9.4	even	3	inner
576.2.bb.e.529.14		72	1.1	even	1	trivial
1728.2.bc.e.145.11		72	9.5	odd	6
1728.2.bc.e.721.8		72	3.2	odd	2
1728.2.bc.e.1009.8		72	144.5	odd	12
1728.2.bc.e.1585.11		72	48.5	odd	4

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22967 + 1.21980i) q^{3} +(0.174734 + 0.0468197i) q^{5} +(4.04791 + 2.33706i) q^{7} +(0.0241875 + 2.99990i) q^{9} +O(q^{10})\)	\(q+(1.22967 + 1.21980i) q^{3} +(0.174734 + 0.0468197i) q^{5} +(4.04791 + 2.33706i) q^{7} +(0.0241875 + 2.99990i) q^{9} +(-0.160430 - 0.598734i) q^{11} +(1.18229 - 4.41237i) q^{13} +(0.157754 + 0.270713i) q^{15} -4.34691 q^{17} +(1.23918 + 1.23918i) q^{19} +(2.12686 + 7.81146i) q^{21} +(-3.86311 + 2.23037i) q^{23} +(-4.30179 - 2.48364i) q^{25} +(-3.62953 + 3.71840i) q^{27} +(8.64910 - 2.31752i) q^{29} +(2.25376 + 3.90364i) q^{31} +(0.533058 - 0.931939i) q^{33} +(0.597886 + 0.597886i) q^{35} +(2.79692 - 2.79692i) q^{37} +(6.83604 - 3.98362i) q^{39} +(-3.67211 + 2.12009i) q^{41} +(-0.00351694 - 0.0131254i) q^{43} +(-0.136228 + 0.525316i) q^{45} +(1.17465 - 2.03456i) q^{47} +(7.42373 + 12.8583i) q^{49} +(-5.34528 - 5.30235i) q^{51} +(-0.519418 + 0.519418i) q^{53} -0.112130i q^{55} +(0.0122364 + 3.03533i) q^{57} +(-11.0349 - 2.95679i) q^{59} +(-2.19745 + 0.588805i) q^{61} +(-6.91305 + 12.1999i) q^{63} +(0.413172 - 0.715636i) q^{65} +(1.88714 - 7.04291i) q^{67} +(-7.47096 - 1.96959i) q^{69} -7.55145i q^{71} +2.92707i q^{73} +(-2.26025 - 8.30137i) q^{75} +(0.749872 - 2.79856i) q^{77} +(-1.45885 + 2.52680i) q^{79} +(-8.99883 + 0.145120i) q^{81} +(7.44148 - 1.99394i) q^{83} +(-0.759552 - 0.203521i) q^{85} +(13.4625 + 7.70036i) q^{87} -3.18821i q^{89} +(15.0978 - 15.0978i) q^{91} +(-1.99025 + 7.54933i) q^{93} +(0.158508 + 0.274544i) q^{95} +(8.03868 - 13.9234i) q^{97} +(1.79226 - 0.495757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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