LMFDB - Embedded newform 432.2.y.e.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, 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("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$432 = 2^{4} \cdot 3^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	432.y (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:	$3.44953736732$
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			37.7
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.297230 - 1.38263i) q^{2} +(-1.82331 + 0.821916i) q^{4} +(0.0112878 - 0.00302457i) q^{5} +(1.05753 - 0.610563i) q^{7} +(1.67835 + 2.27665i) q^{8} +(-0.00753693 - 0.0147079i) q^{10} +(0.490535 - 1.83070i) q^{11} +(-1.35786 - 5.06759i) q^{13} +(-1.15851 - 1.28069i) q^{14} +(2.64891 - 2.99721i) q^{16} +1.54238 q^{17} +(4.06823 - 4.06823i) q^{19} +(-0.0180953 + 0.0147924i) q^{20} +(-2.67698 - 0.134086i) q^{22} +(-5.20660 - 3.00603i) q^{23} +(-4.33001 + 2.49993i) q^{25} +(-6.60298 + 3.38365i) q^{26} +(-1.42637 + 1.98244i) q^{28} +(2.98082 + 0.798708i) q^{29} +(2.92831 - 5.07198i) q^{31} +(-4.93136 - 2.77158i) q^{32} +(-0.458442 - 2.13254i) q^{34} +(0.0100905 - 0.0100905i) q^{35} +(0.923082 + 0.923082i) q^{37} +(-6.83404 - 4.41564i) q^{38} +(0.0258308 + 0.0206222i) q^{40} +(-3.20829 - 1.85231i) q^{41} +(1.29691 - 4.84015i) q^{43} +(0.610287 + 3.74111i) q^{44} +(-2.60866 + 8.09227i) q^{46} +(1.31218 + 2.27277i) q^{47} +(-2.75442 + 4.77080i) q^{49} +(4.74348 + 5.24373i) q^{50} +(6.64092 + 8.12373i) q^{52} +(8.88508 + 8.88508i) q^{53} -0.0221483i q^{55} +(3.16494 + 1.38289i) q^{56} +(0.218325 - 4.35876i) q^{58} +(8.78724 - 2.35453i) q^{59} +(-12.1194 - 3.24737i) q^{61} +(-7.88303 - 2.54121i) q^{62} +(-2.36631 + 7.64203i) q^{64} +(-0.0306545 - 0.0530952i) q^{65} +(3.18324 + 11.8800i) q^{67} +(-2.81224 + 1.26771i) q^{68} +(-0.0169506 - 0.0109522i) q^{70} -14.2363i q^{71} -4.32091i q^{73} +(1.00191 - 1.55065i) q^{74} +(-4.07389 + 10.7614i) q^{76} +(-0.599006 - 2.23552i) q^{77} +(-0.261880 - 0.453589i) q^{79} +(0.0208352 - 0.0418439i) q^{80} +(-1.60745 + 4.98643i) q^{82} +(10.8824 + 2.91592i) q^{83} +(0.0174101 - 0.00466503i) q^{85} +(-7.07759 - 0.354508i) q^{86} +(4.99116 - 1.95577i) q^{88} +10.7103i q^{89} +(-4.53005 - 4.53005i) q^{91} +(11.9640 + 1.20153i) q^{92} +(2.75237 - 2.48980i) q^{94} +(0.0336169 - 0.0582262i) q^{95} +(8.78820 + 15.2216i) q^{97} +(7.41493 + 2.39031i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32}+ \cdots - 88 q^{98}+O(q^{100})$ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$ .

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.297230	−	1.38263i	−0.210174	−	0.977664i
$2$	−0.297230	−	1.38263i	−0.210174	−	0.977664i
$3$		0			0
$3$		0			0
$4$	−1.82331	+	0.821916i	−0.911654	+	0.410958i
$5$	0.0112878	−	0.00302457i	0.00504807	−	0.00135263i	−0.256294	−	0.966599i	$-0.582502\pi$
$5$	0.0112878	−	0.00302457i	0.00504807	−	0.00135263i	0.261342	+	0.965246i	$0.415835\pi$
$6$		0			0
$7$	1.05753	−	0.610563i	0.399708	−	0.230771i	−0.286650	−	0.958035i	$-0.592542\pi$
$7$	1.05753	−	0.610563i	0.399708	−	0.230771i	0.686358	+	0.727264i	$0.259208\pi$
$8$	1.67835	+	2.27665i	0.593385	+	0.804919i
$9$		0			0
$10$	−0.00753693	−	0.0147079i	−0.00238339	−	0.00465104i
$11$	0.490535	−	1.83070i	0.147902	−	0.551977i	−0.851707	−	0.524018i	$-0.824432\pi$
$11$	0.490535	−	1.83070i	0.147902	−	0.551977i	0.999609	−	0.0279594i	$-0.00890090\pi$
$12$		0			0
$13$	−1.35786	−	5.06759i	−0.376602	−	1.40550i	−0.850991	−	0.525181i	$-0.823998\pi$
$13$	−1.35786	−	5.06759i	−0.376602	−	1.40550i	0.474389	−	0.880315i	$-0.342669\pi$
$14$	−1.15851	−	1.28069i	−0.309625	−	0.342278i
$15$		0			0
$16$	2.64891	−	2.99721i	0.662227	−	0.749304i
$17$	1.54238			0.374082			0.187041	−	0.982352i	$-0.440110\pi$
$17$	1.54238			0.374082			0.187041	+	0.982352i	$0.440110\pi$
$18$		0			0
$19$	4.06823	−	4.06823i	0.933317	−	0.933317i	−0.0645950	−	0.997912i	$-0.520576\pi$
$19$	4.06823	−	4.06823i	0.933317	−	0.933317i	0.997912	+	0.0645950i	$0.0205756\pi$
$20$	−0.0180953	+	0.0147924i	−0.00404623	+	0.00330768i
$21$		0			0
$22$	−2.67698	−	0.134086i	−0.570734	−	0.0285873i
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.153236	−	0.988190i	$-0.548970\pi$
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.932415	+	0.361388i	$0.882303\pi$
$24$		0			0
$25$	−4.33001	+	2.49993i	−0.866002	+	0.499986i
$26$	−6.60298	+	3.38365i	−1.29495	+	0.663588i
$27$		0			0
$28$	−1.42637	+	1.98244i	−0.269558	+	0.374647i
$29$	2.98082	+	0.798708i	0.553524	+	0.148316i	0.524730	−	0.851269i	$-0.324166\pi$
$29$	2.98082	+	0.798708i	0.553524	+	0.148316i	0.0287946	+	0.999585i	$0.490833\pi$
$30$		0			0
$31$	2.92831	−	5.07198i	0.525939	−	0.910954i	−0.473604	−	0.880738i	$-0.657047\pi$
$31$	2.92831	−	5.07198i	0.525939	−	0.910954i	0.999543	−	0.0302159i	$-0.00961949\pi$
$32$	−4.93136	−	2.77158i	−0.871750	−	0.489951i
$33$		0			0
$34$	−0.458442	−	2.13254i	−0.0786222	−	0.365727i
$35$	0.0100905	−	0.0100905i	0.00170561	−	0.00170561i
$36$		0			0
$37$	0.923082	+	0.923082i	0.151754	+	0.151754i	0.778901	−	0.627147i	$-0.215777\pi$
$37$	0.923082	+	0.923082i	0.151754	+	0.151754i	−0.627147	+	0.778901i	$0.715777\pi$
$38$	−6.83404	−	4.41564i	−1.10863	−	0.716312i
$39$		0			0
$40$	0.0258308	+	0.0206222i	0.00408421	+	0.00326066i
$41$	−3.20829	−	1.85231i	−0.501051	−	0.289282i	0.228096	−	0.973639i	$-0.426750\pi$
$41$	−3.20829	−	1.85231i	−0.501051	−	0.289282i	−0.729147	+	0.684357i	$0.760083\pi$
$42$		0			0
$43$	1.29691	−	4.84015i	0.197777	−	0.738115i	−0.793753	−	0.608240i	$-0.791876\pi$
$43$	1.29691	−	4.84015i	0.197777	−	0.738115i	0.991530	−	0.129875i	$-0.0414576\pi$
$44$	0.610287	+	3.74111i	0.0920043	+	0.563994i
$45$		0			0
$46$	−2.60866	+	8.09227i	−0.384626	+	1.19314i
$47$	1.31218	+	2.27277i	0.191402	+	0.331517i	0.945715	−	0.324997i	$-0.105363\pi$
$47$	1.31218	+	2.27277i	0.191402	+	0.331517i	−0.754313	+	0.656515i	$0.772030\pi$
$48$		0			0
$49$	−2.75442	+	4.77080i	−0.393489	+	0.681543i
$50$	4.74348	+	5.24373i	0.670829	+	0.741575i
$51$		0			0
$52$	6.64092	+	8.12373i	0.920931	+	1.12656i
$53$	8.88508	+	8.88508i	1.22046	+	1.22046i	0.967469	+	0.252991i	$0.0814144\pi$
$53$	8.88508	+	8.88508i	1.22046	+	1.22046i	0.252991	+	0.967469i	$0.418586\pi$
$54$		0			0
$55$		−	0.0221483i		−	0.00298648i
$56$	3.16494	+	1.38289i	0.422932	+	0.184796i
$57$		0			0
$58$	0.218325	−	4.35876i	0.0286674	−	0.572333i
$59$	8.78724	−	2.35453i	1.14400	−	0.306534i	0.363443	−	0.931617i	$-0.381601\pi$
$59$	8.78724	−	2.35453i	1.14400	−	0.306534i	0.780559	+	0.625082i	$0.214935\pi$
$60$		0			0
$61$	−12.1194	−	3.24737i	−1.55172	−	0.415783i	−0.621692	−	0.783262i	$-0.713555\pi$
$61$	−12.1194	−	3.24737i	−1.55172	−	0.415783i	−0.930032	+	0.367478i	$0.880221\pi$
$62$	−7.88303	−	2.54121i	−1.00115	−	0.322734i
$63$		0			0
$64$	−2.36631	+	7.64203i	−0.295789	+	0.955253i
$65$	−0.0306545	−	0.0530952i	−0.00380223	−	0.00658565i
$66$		0			0
$67$	3.18324	+	11.8800i	0.388895	+	1.45137i	0.831935	+	0.554873i	$0.187233\pi$
$67$	3.18324	+	11.8800i	0.388895	+	1.45137i	−0.443041	+	0.896501i	$0.646100\pi$
$68$	−2.81224	+	1.26771i	−0.341034	+	0.153732i
$69$		0			0
$70$	−0.0169506	−	0.0109522i	−0.00202598	−	0.00130904i
$71$		−	14.2363i		−	1.68954i	−0.535129	−	0.844771i	$-0.679737\pi$
$71$		−	14.2363i		−	1.68954i	0.535129	−	0.844771i	$-0.320263\pi$
$72$		0			0
$73$		−	4.32091i		−	0.505724i	−0.967502	−	0.252862i	$-0.918628\pi$
$73$		−	4.32091i		−	0.505724i	0.967502	−	0.252862i	$-0.0813718\pi$
$74$	1.00191	−	1.55065i	0.116470	−	0.180259i
$75$		0			0
$76$	−4.07389	+	10.7614i	−0.467308	+	1.23442i
$77$	−0.599006	−	2.23552i	−0.0682630	−	0.254761i
$78$		0			0
$79$	−0.261880	−	0.453589i	−0.0294638	−	0.0510328i	0.850918	−	0.525299i	$-0.176047\pi$
$79$	−0.261880	−	0.453589i	−0.0294638	−	0.0510328i	−0.880381	+	0.474267i	$0.842713\pi$
$80$	0.0208352	−	0.0418439i	0.00232944	−	0.00467829i
$81$		0			0
$82$	−1.60745	+	4.98643i	−0.177513	+	0.550659i
$83$	10.8824	+	2.91592i	1.19450	+	0.320064i	0.800661	−	0.599117i	$-0.204482\pi$
$83$	10.8824	+	2.91592i	1.19450	+	0.320064i	0.393834	+	0.919181i	$0.371148\pi$
$84$		0			0
$85$	0.0174101	−	0.00466503i	0.00188839	−	0.000505994i
$86$	−7.07759	−	0.354508i	−0.763196	−	0.0382276i
$87$		0			0
$88$	4.99116	−	1.95577i	0.532060	−	0.208486i
$89$			10.7103i			1.13529i	0.823274	+	0.567644i	$0.192145\pi$
$89$			10.7103i			1.13529i	−0.823274	+	0.567644i	$0.807855\pi$
$90$		0			0
$91$	−4.53005	−	4.53005i	−0.474879	−	0.474879i
$92$	11.9640	+	1.20153i	1.24733	+	0.125269i
$93$		0			0
$94$	2.75237	−	2.48980i	0.283885	−	0.256803i
$95$	0.0336169	−	0.0582262i	0.00344902	−	0.00597388i
$96$		0			0
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.837104	+	0.547044i	$0.184247\pi$
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.0552025	+	0.998475i	$0.482420\pi$
$98$	7.41493	+	2.39031i	0.749022	+	0.241458i
$99$		0			0
$100$	5.84021	−	8.11705i	0.584021	−	0.811705i
$101$	1.80361	−	6.73117i	0.179466	−	0.669776i	−0.816282	−	0.577654i	$-0.803968\pi$
$101$	1.80361	−	6.73117i	0.179466	−	0.669776i	0.995748	−	0.0921222i	$-0.0293650\pi$
$102$		0			0
$103$	2.20609	+	1.27369i	0.217373	+	0.125500i	0.604733	−	0.796428i	$-0.293280\pi$
$103$	2.20609	+	1.27369i	0.217373	+	0.125500i	−0.387360	+	0.921928i	$0.626613\pi$
$104$	9.25820	−	11.5965i	0.907841	−	1.13713i
$105$		0			0
$106$	9.64383	−	14.9257i	0.936691	−	1.44971i
$107$	−3.52175	−	3.52175i	−0.340460	−	0.340460i	0.516080	−	0.856540i	$-0.327391\pi$
$107$	−3.52175	−	3.52175i	−0.340460	−	0.340460i	−0.856540	+	0.516080i	$0.827391\pi$
$108$		0			0
$109$	3.14334	−	3.14334i	0.301077	−	0.301077i	−0.540358	−	0.841435i	$-0.681711\pi$
$109$	3.14334	−	3.14334i	0.301077	−	0.301077i	0.841435	+	0.540358i	$0.181711\pi$
$110$	−0.0306228	+	0.00658315i	−0.00291977	+	0.000627679i
$111$		0			0
$112$	0.971300	−	4.78696i	0.0917793	−	0.452325i
$113$	−7.90904	+	13.6989i	−0.744020	+	1.28868i	0.206631	+	0.978419i	$0.433750\pi$
$113$	−7.90904	+	13.6989i	−0.744020	+	1.28868i	−0.950651	+	0.310262i	$0.899583\pi$
$114$		0			0
$115$	−0.0678632	−	0.0181839i	−0.00632828	−	0.00169566i
$116$	−6.09142	+	0.993693i	−0.565574	+	0.0922621i
$117$		0			0
$118$	−5.86727	−	11.4496i	−0.540126	−	1.05402i
$119$	1.63111	−	0.941721i	0.149523	−	0.0863274i
$120$		0			0
$121$	6.41543	+	3.70395i	0.583221	+	0.336723i
$122$	−0.887661	+	17.7218i	−0.0803650	+	1.60445i
$123$		0			0
$124$	−1.17047	+	11.6546i	−0.105111	+	1.04661i
$125$	−0.0826316	+	0.0826316i	−0.00739079	+	0.00739079i
$126$		0			0
$127$	−5.72603			−0.508103			−0.254052	−	0.967191i	$-0.581763\pi$
$127$	−5.72603			−0.508103			−0.254052	+	0.967191i	$0.581763\pi$
$128$	11.2694	+	1.00029i	0.996084	+	0.0884136i
$129$		0			0
$130$	−0.0642993	+	0.0581652i	−0.00563942	+	0.00510143i
$131$	1.75835	+	6.56224i	0.153628	+	0.573346i	0.999219	+	0.0395151i	$0.0125813\pi$
$131$	1.75835	+	6.56224i	0.153628	+	0.573346i	−0.845591	+	0.533831i	$0.820752\pi$
$132$		0			0
$133$	1.81835	−	6.78618i	0.157671	−	0.588436i
$134$	15.4795	−	7.93233i	1.33722	−	0.685249i
$135$		0			0
$136$	2.58865	+	3.51147i	0.221975	+	0.301106i
$137$	−3.64923	+	2.10688i	−0.311775	+	0.180003i	−0.647720	−	0.761878i	$-0.724278\pi$
$137$	−3.64923	+	2.10688i	−0.311775	+	0.180003i	0.335946	+	0.941881i	$0.390944\pi$
$138$		0			0
$139$	15.6519	−	4.19392i	1.32758	−	0.355724i	0.475767	−	0.879571i	$-0.342170\pi$
$139$	15.6519	−	4.19392i	1.32758	−	0.355724i	0.851812	+	0.523847i	$0.175504\pi$
$140$	−0.0101045	+	0.0266916i	−0.000853990	+	0.00225586i
$141$		0			0
$142$	−19.6835	+	4.23147i	−1.65180	+	0.355097i
$143$	−9.94332			−0.831502
$144$		0			0
$145$	0.0360627			0.00299485
$146$	−5.97420	+	1.28430i	−0.494428	+	0.106290i
$147$		0			0
$148$	−2.44176	−	0.924367i	−0.200711	−	0.0759825i
$149$	3.76477	−	1.00877i	0.308422	−	0.0826415i	−0.101288	−	0.994857i	$-0.532296\pi$
$149$	3.76477	−	1.00877i	0.308422	−	0.0826415i	0.409710	+	0.912216i	$0.365630\pi$
$150$		0			0
$151$	−13.0073	+	7.50979i	−1.05852	+	0.611138i	−0.925023	−	0.379911i	$-0.875955\pi$
$151$	−13.0073	+	7.50979i	−1.05852	+	0.611138i	−0.133499	+	0.991049i	$0.542621\pi$
$152$	16.0899	+	2.43406i	1.30506	+	0.197428i
$153$		0			0
$154$	−2.91284	+	1.49266i	−0.234724	+	0.120282i
$155$	0.0177137	−	0.0661085i	0.00142280	−	0.00530996i
$156$		0			0
$157$	2.53825	+	9.47288i	0.202574	+	0.756018i	0.990175	+	0.139832i	$0.0446564\pi$
$157$	2.53825	+	9.47288i	0.202574	+	0.756018i	−0.787601	+	0.616186i	$0.788677\pi$
$158$	−0.549305	+	0.496902i	−0.0437004	+	0.0395314i
$159$		0			0
$160$	−0.0640473	−	0.0163700i	−0.00506338	−	0.00129416i
$161$	−7.34150			−0.578591
$162$		0			0
$163$	5.22606	−	5.22606i	0.409336	−	0.409336i	−0.472171	−	0.881507i	$-0.656529\pi$
$163$	5.22606	−	5.22606i	0.409336	−	0.409336i	0.881507	+	0.472171i	$0.156529\pi$
$164$	7.37215	+	0.740381i	0.575668	+	0.0578140i
$165$		0			0
$166$	0.797060	−	15.9129i	0.0618638	−	1.23508i
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	0.235364	−	0.971907i	$-0.424372\pi$
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	−0.724015	+	0.689785i	$0.757705\pi$
$168$		0			0
$169$	−12.5783	+	7.26211i	−0.967565	+	0.558624i
$170$	−0.0116248	−	0.0226851i	−0.000891583	−	0.00173987i
$171$		0			0
$172$	1.61352	+	9.89103i	0.123030	+	0.754184i
$173$	−22.9394	−	6.14659i	−1.74405	−	0.467317i	−0.760710	−	0.649092i	$-0.775149\pi$
$173$	−22.9394	−	6.14659i	−1.74405	−	0.467317i	−0.983340	+	0.181775i	$0.941816\pi$
$174$		0			0
$175$	−3.05273	+	5.28749i	−0.230765	+	0.399697i
$176$	−4.18762	−	6.31960i	−0.315654	−	0.476358i
$177$		0			0
$178$	14.8083	−	3.18342i	1.10993	−	0.238608i
$179$	−11.4489	+	11.4489i	−0.855732	+	0.855732i	−0.990832	−	0.135100i	$-0.956864\pi$
$179$	−11.4489	+	11.4489i	−0.855732	+	0.855732i	0.135100	+	0.990832i	$0.456864\pi$
$180$		0			0
$181$	−3.01327	−	3.01327i	−0.223974	−	0.223974i	0.586195	−	0.810170i	$-0.300625\pi$
$181$	−3.01327	−	3.01327i	−0.223974	−	0.223974i	−0.810170	+	0.586195i	$0.800625\pi$
$182$	−4.91690	+	7.60984i	−0.364465	+	0.564079i
$183$		0			0
$184$	−1.89478	−	16.8988i	−0.139685	−	1.24580i
$185$	0.0132115	+	0.00762768i	0.000971331	+	0.000560798i
$186$		0			0
$187$	0.756592	−	2.82364i	0.0553275	−	0.206485i
$188$	−4.26054	−	3.06545i	−0.310732	−	0.223571i
$189$		0			0
$190$	−0.0904970	−	0.0291730i	−0.00656534	−	0.00211643i
$191$	2.25702	+	3.90928i	0.163313	+	0.282866i	0.936055	−	0.351854i	$-0.114449\pi$
$191$	2.25702	+	3.90928i	0.163313	+	0.282866i	−0.772742	+	0.634720i	$0.781115\pi$
$192$		0			0
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	−0.922333	−	0.386395i	$-0.873720\pi$
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	0.795795	+	0.605566i	$0.207053\pi$
$194$	18.4337	−	16.6751i	1.32346	−	1.19720i
$195$		0			0
$196$	1.10096	−	10.9626i	0.0786403	−	0.783040i
$197$	4.81922	+	4.81922i	0.343355	+	0.343355i	0.857627	−	0.514272i	$-0.171938\pi$
$197$	4.81922	+	4.81922i	0.343355	+	0.343355i	−0.514272	+	0.857627i	$0.671938\pi$
$198$		0			0
$199$			4.66322i			0.330567i	0.986246	+	0.165284i	$0.0528539\pi$
$199$			4.66322i			0.330567i	−0.986246	+	0.165284i	$0.947146\pi$
$200$	−12.9587	−	5.66219i	−0.916321	−	0.400377i
$201$		0			0
$202$	−9.84277	−	0.493012i	−0.692535	−	0.0346882i
$203$	3.63996	−	0.975324i	0.255475	−	0.0684543i
$204$		0			0
$205$	−0.0418171	−	0.0112049i	−0.00292063	−	0.000782581i
$206$	1.10532	−	3.42878i	0.0770110	−	0.238894i
$207$		0			0
$208$	−18.7855	−	9.35378i	−1.30254	−	0.648568i
$209$	−5.45211	−	9.44333i	−0.377130	−	0.653209i
$210$		0			0
$211$	4.67442	+	17.4452i	0.321800	+	1.20097i	0.917490	+	0.397760i	$0.130212\pi$
$211$	4.67442	+	17.4452i	0.321800	+	1.20097i	−0.595689	+	0.803215i	$0.703121\pi$
$212$	−23.5030	−	8.89745i	−1.61420	−	0.611079i
$213$		0			0
$214$	−3.82249	+	5.91603i	−0.261300	+	0.404411i
$215$		−	0.0585574i		−	0.00399358i
$216$		0			0
$217$		−	7.15167i		−	0.485487i
$218$	−5.28036	−	3.41177i	−0.357631	−	0.231074i
$219$		0			0
$220$	0.0182041	+	0.0403832i	0.00122732	+	0.00272264i
$221$	−2.09433	−	7.81615i	−0.140880	−	0.525771i
$222$		0			0
$223$	2.85769	+	4.94966i	0.191365	+	0.331454i	0.945703	−	0.325032i	$-0.105375\pi$
$223$	2.85769	+	4.94966i	0.191365	+	0.331454i	−0.754338	+	0.656486i	$0.772042\pi$
$224$	−6.90727	+	0.0798841i	−0.461512	+	0.00533748i
$225$		0			0
$226$	21.2912	+	6.86353i	1.41627	+	0.456555i
$227$	−19.6766	−	5.27233i	−1.30598	−	0.349937i	−0.462272	−	0.886738i	$-0.652966\pi$
$227$	−19.6766	−	5.27233i	−1.30598	−	0.349937i	−0.843709	+	0.536802i	$0.819632\pi$
$228$		0			0
$229$	3.70525	−	0.992819i	0.244850	−	0.0656073i	−0.134307	−	0.990940i	$-0.542881\pi$
$229$	3.70525	−	0.992819i	0.244850	−	0.0656073i	0.379157	+	0.925332i	$0.376214\pi$
$230$	−0.00497052	+	0.0992343i	−0.000327747	+	0.00654332i
$231$		0			0
$232$	3.18446	+	8.12680i	0.209070	+	0.533551i
$233$		−	5.33043i		−	0.349208i	−0.984639	−	0.174604i	$-0.944136\pi$
$233$		−	5.33043i		−	0.349208i	0.984639	−	0.174604i	$-0.0558645\pi$
$234$		0			0
$235$	0.0216859	+	0.0216859i	0.00141463	+	0.00141463i
$236$	−14.0866	+	11.5154i	−0.916961	+	0.749590i
$237$		0			0
$238$	−1.78686	−	1.97530i	−0.115825	−	0.128040i
$239$	13.8380	−	23.9681i	0.895104	−	1.55037i	0.0614282	−	0.998112i	$-0.480434\pi$
$239$	13.8380	−	23.9681i	0.895104	−	1.55037i	0.833676	−	0.552254i	$-0.186232\pi$
$240$		0			0
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	0.892021	−	0.451993i	$-0.149287\pi$
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	−0.837448	+	0.546517i	$0.815954\pi$
$242$	3.21432	−	9.97107i	0.206624	−	0.640965i
$243$		0			0
$244$	24.7664	−	4.04014i	1.58551	−	0.258643i
$245$	−0.0166619	+	0.0621830i	−0.00106449	+	0.00397273i
$246$		0			0
$247$	−26.1402	−	15.0921i	−1.66326	−	0.960284i
$248$	16.4618	−	1.84578i	1.04533	−	0.117207i
$249$		0			0
$250$	0.138809	+	0.0896880i	0.00877906	+	0.00567236i
$251$	−0.987980	−	0.987980i	−0.0623607	−	0.0623607i	0.675239	−	0.737599i	$-0.264041\pi$
$251$	−0.987980	−	0.987980i	−0.0623607	−	0.0623607i	−0.737599	+	0.675239i	$0.764041\pi$
$252$		0			0
$253$	−8.05717	+	8.05717i	−0.506550	+	0.506550i
$254$	1.70195	+	7.91696i	0.106790	+	0.496754i
$255$		0			0
$256$	−1.96659	−	15.8787i	−0.122912	−	0.992418i
$257$	−11.8214	+	20.4753i	−0.737401	+	1.27722i	0.216260	+	0.976336i	$0.430614\pi$
$257$	−11.8214	+	20.4753i	−0.737401	+	1.27722i	−0.953662	+	0.300881i	$0.902719\pi$
$258$		0			0
$259$	1.53978	+	0.412584i	0.0956776	+	0.0256367i
$260$	0.0995325	+	0.0716134i	0.00617274	+	0.00444128i
$261$		0			0
$262$	8.55049	−	4.38163i	0.528251	−	0.270698i
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.991271	−	0.131841i	$-0.957911\pi$
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.381458	+	0.924386i	$0.624578\pi$
$264$		0			0
$265$	0.127167	+	0.0734198i	0.00781180	+	0.00451015i
$266$	−9.92321	−	0.497042i	−0.608431	−	0.0304756i
$267$		0			0
$268$	−15.5684	−	19.0446i	−0.950991	−	1.16333i
$269$	13.6891	−	13.6891i	0.834637	−	0.834637i	−0.153510	−	0.988147i	$-0.549058\pi$
$269$	13.6891	−	13.6891i	0.834637	−	0.834637i	0.988147	+	0.153510i	$0.0490577\pi$
$270$		0			0
$271$	−7.11000			−0.431902			−0.215951	−	0.976404i	$-0.569285\pi$
$271$	−7.11000			−0.431902			−0.215951	+	0.976404i	$0.569285\pi$
$272$	4.08562	−	4.62284i	0.247727	−	0.280301i
$273$		0			0
$274$	3.99770	+	4.41929i	0.241510	+	0.266979i
$275$	2.45261	+	9.15326i	0.147898	+	0.551962i
$276$		0			0
$277$	5.81917	−	21.7174i	0.349640	−	1.30487i	−0.537457	−	0.843291i	$-0.680615\pi$
$277$	5.81917	−	21.7174i	0.349640	−	1.30487i	0.887097	−	0.461583i	$-0.152718\pi$
$278$	−10.4509	−	20.3942i	−0.626801	−	1.22316i
$279$		0			0
$280$	0.0399079	+	0.00603724i	0.00238496	+	0.000360794i
$281$	19.7952	−	11.4288i	1.18088	−	0.681783i	0.224664	−	0.974436i	$-0.427872\pi$
$281$	19.7952	−	11.4288i	1.18088	−	0.681783i	0.956218	+	0.292654i	$0.0945383\pi$
$282$		0			0
$283$	−5.96971	+	1.59958i	−0.354862	+	0.0950851i	−0.431846	−	0.901947i	$-0.642138\pi$
$283$	−5.96971	+	1.59958i	−0.354862	+	0.0950851i	0.0769838	+	0.997032i	$0.475471\pi$
$284$	11.7011	+	25.9572i	0.694331	+	1.54028i
$285$		0			0
$286$	2.95546	+	13.7479i	0.174760	+	0.812930i
$287$	−4.52381			−0.267032
$288$		0			0
$289$	−14.6211			−0.860063
$290$	−0.0107189	−	0.0498613i	−0.000629438	−	0.00292796i
$291$		0			0
$292$	3.55142	+	7.87834i	0.207831	+	0.461045i
$293$	3.76752	−	1.00950i	0.220101	−	0.0589758i	−0.147083	−	0.989124i	$-0.546989\pi$
$293$	3.76752	−	1.00950i	0.220101	−	0.0589758i	0.367184	+	0.930148i	$0.380322\pi$
$294$		0			0
$295$	0.0920675	−	0.0531552i	0.00536038	−	0.00309482i
$296$	−0.552289	+	3.65079i	−0.0321011	+	0.212198i
$297$		0			0
$298$	−2.51375	−	4.90543i	−0.145618	−	0.284164i
$299$	−8.16352	+	30.4667i	−0.472109	+	1.76193i
$300$		0			0
$301$	−1.58370	−	5.91043i	−0.0912827	−	0.340672i
$302$	14.2494	+	15.7521i	0.819961	+	0.906434i
$303$		0			0
$304$	−1.41700	−	22.9697i	−0.0812703	−	1.31740i
$305$	−0.146623			−0.00839562
$306$		0			0
$307$	10.8111	−	10.8111i	0.617023	−	0.617023i	−0.327743	−	0.944767i	$-0.606288\pi$
$307$	10.8111	−	10.8111i	0.617023	−	0.617023i	0.944767	+	0.327743i	$0.106288\pi$
$308$	2.92958	+	3.58371i	0.166928	+	0.204201i
$309$		0			0
$310$	−0.0966684	−	0.00484200i	−0.00549040	−	0.000275007i
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.938273	−	0.345897i	$-0.112425\pi$
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.169581	+	0.985516i	$0.445759\pi$
$312$		0			0
$313$	5.17232	−	2.98624i	0.292357	−	0.168792i	−0.346647	−	0.937996i	$-0.612680\pi$
$313$	5.17232	−	2.98624i	0.292357	−	0.168792i	0.639004	+	0.769203i	$0.279347\pi$
$314$	12.3430	−	6.32508i	0.696556	−	0.356945i
$315$		0			0
$316$	0.850300	+	0.611789i	0.0478331	+	0.0344158i
$317$	17.9792	+	4.81751i	1.00981	+	0.270579i	0.725551	−	0.688168i	$-0.241585\pi$
$317$	17.9792	+	4.81751i	1.00981	+	0.270579i	0.284262	+	0.958747i	$0.408252\pi$
$318$		0			0
$319$	2.92439	−	5.06520i	0.163735	−	0.283597i
$320$	−0.00359675	+	0.0934190i	−0.000201064	+	0.00522228i
$321$		0			0
$322$	2.18211	+	10.1505i	0.121605	+	0.565668i
$323$	6.27476	−	6.27476i	0.349137	−	0.349137i
$324$		0			0
$325$	18.5482	+	18.5482i	1.02887	+	1.02887i
$326$	−8.77903	−	5.67234i	−0.486225	−	0.314162i
$327$		0			0
$328$	−1.16756	−	10.4130i	−0.0644675	−	0.574961i
$329$	2.77534	+	1.60234i	0.153009	+	0.0883400i
$330$		0			0
$331$	2.72957	−	10.1869i	0.150031	−	0.559923i	−0.849449	−	0.527671i	$-0.823065\pi$
$331$	2.72957	−	10.1869i	0.150031	−	0.559923i	0.999480	−	0.0322521i	$-0.0102679\pi$
$332$	−22.2386	+	3.62777i	−1.22050	+	0.199100i
$333$		0			0
$334$	−3.16388	+	9.81461i	−0.173120	+	0.537031i
$335$	0.0718638	+	0.124472i	0.00392634	+	0.00680062i
$336$		0			0
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	−0.320192	−	0.947353i	$-0.603747\pi$
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	0.980527	−	0.196382i	$-0.0629194\pi$
$338$	13.7794	+	15.2326i	0.749503	+	0.828546i
$339$		0			0
$340$	−0.0279098	+	0.0228155i	−0.00151362	+	0.00123734i
$341$	−7.84884	−	7.84884i	−0.425038	−	0.425038i
$342$		0			0
$343$			15.2749i			0.824767i
$344$	13.1960	−	5.17081i	0.711481	−	0.278792i
$345$		0			0
$346$	−1.68016	+	33.5436i	−0.0903257	+	1.80331i
$347$	18.5696	−	4.97570i	0.996867	−	0.267110i	0.276735	−	0.960946i	$-0.410748\pi$
$347$	18.5696	−	4.97570i	0.996867	−	0.267110i	0.720132	+	0.693837i	$0.244081\pi$
$348$		0			0
$349$	15.6423	+	4.19134i	0.837313	+	0.224357i	0.651901	−	0.758304i	$-0.273972\pi$
$349$	15.6423	+	4.19134i	0.837313	+	0.224357i	0.185411	+	0.982661i	$0.440638\pi$
$350$	8.21798	+	2.64919i	0.439270	+	0.141605i
$351$		0			0
$352$	−7.49295	+	7.66829i	−0.399376	+	0.408721i
$353$	7.69391	+	13.3262i	0.409505	+	0.709284i	0.994834	−	0.101512i	$-0.0323680\pi$
$353$	7.69391	+	13.3262i	0.409505	+	0.709284i	−0.585329	+	0.810796i	$0.699035\pi$
$354$		0			0
$355$	−0.0430587	−	0.160697i	−0.00228532	−	0.00852893i
$356$	−8.80297	−	19.5282i	−0.466556	−	1.03499i
$357$		0			0
$358$	19.2325	+	12.4266i	1.01647	+	0.656766i
$359$			2.97883i			0.157217i	0.996906	+	0.0786083i	$0.0250476\pi$
$359$			2.97883i			0.157217i	−0.996906	+	0.0786083i	$0.974952\pi$
$360$		0			0
$361$		−	14.1010i		−	0.742159i
$362$	−3.27059	+	5.06185i	−0.171898	+	0.266045i
$363$		0			0
$364$	11.9830	+	4.53636i	0.628080	+	0.237770i
$365$	−0.0130689	−	0.0487737i	−0.000684056	−	0.00255293i
$366$		0			0
$367$	12.5585	+	21.7519i	0.655547	+	1.13544i	0.981756	+	0.190143i	$0.0608952\pi$
$367$	12.5585	+	21.7519i	0.655547	+	1.13544i	−0.326210	+	0.945297i	$0.605772\pi$
$368$	−22.8015	+	7.64260i	−1.18861	+	0.398398i
$369$		0			0
$370$	0.00661936	−	0.0205338i	0.000344124	−	0.00106750i
$371$	14.8211	+	3.97131i	0.769474	+	0.206180i
$372$		0			0
$373$	−28.8046	+	7.71816i	−1.49144	+	0.399631i	−0.910224	−	0.414116i	$-0.864091\pi$
$373$	−28.8046	+	7.71816i	−1.49144	+	0.399631i	−0.581220	+	0.813747i	$0.697424\pi$
$374$	−4.12892	−	0.206812i	−0.213501	−	0.0106940i
$375$		0			0
$376$	−2.97201	+	6.80188i	−0.153270	+	0.350780i
$377$		−	16.1901i		−	0.833832i
$378$		0			0
$379$	10.1985	+	10.1985i	0.523864	+	0.523864i	0.918736	−	0.394872i	$-0.129211\pi$
$379$	10.1985	+	10.1985i	0.523864	+	0.523864i	−0.394872	+	0.918736i	$0.629211\pi$
$380$	−0.0134369	+	0.133795i	−0.000689300	+	0.00686352i
$381$		0			0
$382$	4.73422	−	4.28258i	0.242224	−	0.219116i
$383$	−10.5750	+	18.3164i	−0.540356	+	0.935924i	0.458528	+	0.888680i	$0.348377\pi$
$383$	−10.5750	+	18.3164i	−0.540356	+	0.935924i	−0.998883	+	0.0472436i	$0.984956\pi$
$384$		0			0
$385$	−0.0135230	−	0.0234224i	−0.000689194	−	0.00119372i
$386$	4.73236	+	1.52555i	0.240871	+	0.0776482i
$387$		0			0
$388$	−28.5345	−	20.5305i	−1.44862	−	1.04228i
$389$	8.13193	−	30.3488i	0.412305	−	1.53874i	−0.377867	−	0.925860i	$-0.623342\pi$
$389$	8.13193	−	30.3488i	0.412305	−	1.53874i	0.790173	−	0.612884i	$-0.209991\pi$
$390$		0			0
$391$	−8.03056	−	4.63645i	−0.406123	−	0.234475i
$392$	−15.4843	+	1.73618i	−0.782078	+	0.0876904i
$393$		0			0
$394$	5.23076	−	8.09560i	0.263522	−	0.407850i
$395$	−0.00432797	−	0.00432797i	−0.000217764	−	0.000217764i
$396$		0			0
$397$	−3.24113	+	3.24113i	−0.162668	+	0.162668i	−0.783747	−	0.621080i	$-0.786694\pi$
$397$	−3.24113	+	3.24113i	−0.162668	+	0.162668i	0.621080	+	0.783747i	$0.286694\pi$
$398$	6.44749	−	1.38605i	0.323184	−	0.0694765i
$399$		0			0
$400$	−3.97696	+	19.6000i	−0.198848	+	0.980002i
$401$	10.7429	−	18.6073i	0.536476	−	0.929203i	−0.462614	−	0.886560i	$-0.653089\pi$
$401$	10.7429	−	18.6073i	0.536476	−	0.929203i	0.999090	−	0.0426439i	$-0.0135781\pi$
$402$		0			0
$403$	−29.6789	−	7.95244i	−1.47841	−	0.396139i
$404$	2.24392	+	13.7554i	0.111639	+	0.684357i
$405$		0			0
$406$	−2.43041	−	4.74280i	−0.120619	−	0.235381i
$407$	2.14269	−	1.23708i	0.106209	−	0.0613200i
$408$		0			0
$409$	23.1426	+	13.3614i	1.14433	+	0.660678i	0.947499	−	0.319760i	$-0.103602\pi$
$409$	23.1426	+	13.3614i	1.14433	+	0.660678i	0.196829	+	0.980438i	$0.436936\pi$
$410$	−0.00306282	+	0.0611478i	−0.000151262	+	0.00301988i
$411$		0			0
$412$	−5.06925	−	0.509102i	−0.249744	−	0.0250817i
$413$	7.85515	−	7.85515i	0.386527	−	0.386527i
$414$		0			0
$415$	0.131658			0.00646283
$416$	−7.34917	+	28.7535i	−0.360323	+	1.40976i
$417$		0			0
$418$	−11.4361	+	10.3451i	−0.559356	+	0.505994i
$419$	−2.36864	−	8.83989i	−0.115716	−	0.431857i	0.883624	−	0.468198i	$-0.155097\pi$
$419$	−2.36864	−	8.83989i	−0.115716	−	0.431857i	−0.999339	+	0.0363407i	$0.988430\pi$
$420$		0			0
$421$	7.75295	−	28.9344i	0.377856	−	1.41018i	−0.471272	−	0.881988i	$-0.656205\pi$
$421$	7.75295	−	28.9344i	0.377856	−	1.41018i	0.849127	−	0.528188i	$-0.177128\pi$
$422$	22.7308	−	11.6482i	1.10652	−	0.567026i
$423$		0			0
$424$	−5.31603	+	35.1405i	−0.258169	+	1.70657i
$425$	−6.67852	+	3.85585i	−0.323956	+	0.187036i
$426$		0			0
$427$	−14.7993	+	3.96545i	−0.716187	+	0.191902i
$428$	9.31581	+	3.52665i	0.450297	+	0.170467i
$429$		0			0
$430$	−0.0809629	+	0.0174050i	−0.00390438	+	0.000839345i
$431$	7.05544			0.339849			0.169924	−	0.985457i	$-0.445648\pi$
$431$	7.05544			0.339849			0.169924	+	0.985457i	$0.445648\pi$
$432$		0			0
$433$	13.1552			0.632201			0.316100	−	0.948726i	$-0.397626\pi$
$433$	13.1552			0.632201			0.316100	+	0.948726i	$0.397626\pi$
$434$	−9.88808	+	2.12569i	−0.474643	+	0.102036i
$435$		0			0
$436$	−3.14771	+	8.31484i	−0.150748	+	0.398209i
$437$	−33.4109	+	8.95243i	−1.59826	+	0.428253i
$438$		0			0
$439$	12.8757	−	7.43381i	0.614525	−	0.354796i	−0.160209	−	0.987083i	$-0.551217\pi$
$439$	12.8757	−	7.43381i	0.614525	−	0.354796i	0.774734	+	0.632287i	$0.217884\pi$
$440$	0.0504241	−	0.0371725i	0.00240387	−	0.00177213i
$441$		0			0
$442$	−10.1843	+	5.21887i	−0.484418	+	0.248236i
$443$	−0.797625	+	2.97678i	−0.0378963	+	0.141431i	−0.982282	−	0.187409i	$-0.939991\pi$
$443$	−0.797625	+	2.97678i	−0.0378963	+	0.141431i	0.944386	+	0.328840i	$0.106658\pi$
$444$		0			0
$445$	0.0323940	+	0.120896i	0.00153562	+	0.00573102i
$446$	5.99414	−	5.42231i	0.283831	−	0.256754i
$447$		0			0
$448$	2.16350	+	9.52643i	0.102216	+	0.450082i
$449$	21.8550			1.03140			0.515701	−	0.856769i	$-0.327532\pi$
$449$	21.8550			1.03140			0.515701	+	0.856769i	$0.327532\pi$
$450$		0			0
$451$	−4.96480	+	4.96480i	−0.233783	+	0.233783i
$452$	3.16130	−	31.4778i	0.148695	−	1.48059i
$453$		0			0
$454$	−1.44118	+	28.7724i	−0.0676378	+	1.35036i
$455$	−0.0648360	−	0.0374331i	−0.00303956	−	0.00175489i
$456$		0			0
$457$	2.32261	−	1.34096i	0.108647	−	0.0627275i	−0.444692	−	0.895684i	$-0.646687\pi$
$457$	2.32261	−	1.34096i	0.108647	−	0.0627275i	0.553339	+	0.832956i	$0.313353\pi$
$458$	−2.47401	−	4.82788i	−0.115603	−	0.225592i
$459$		0			0
$460$	0.138681	−	0.0226231i	0.00646605	−	0.00105481i
$461$	10.2573	+	2.74844i	0.477732	+	0.128008i	0.489646	−	0.871921i	$-0.337126\pi$
$461$	10.2573	+	2.74844i	0.477732	+	0.128008i	−0.0119146	+	0.999929i	$0.503793\pi$
$462$		0			0
$463$	11.8249	−	20.4814i	0.549550	−	0.951849i	−0.448755	−	0.893655i	$-0.648132\pi$
$463$	11.8249	−	20.4814i	0.549550	−	0.951849i	0.998305	−	0.0581943i	$-0.0185343\pi$
$464$	10.2898	−	6.81845i	0.477692	−	0.316539i
$465$		0			0
$466$	−7.36999	+	1.58436i	−0.341408	+	0.0733942i
$467$	−2.22540	+	2.22540i	−0.102979	+	0.102979i	−0.756719	−	0.653740i	$-0.773199\pi$
$467$	−2.22540	+	2.22540i	−0.102979	+	0.102979i	0.653740	+	0.756719i	$0.273199\pi$
$468$		0			0
$469$	10.6199	+	10.6199i	0.490380	+	0.490380i
$470$	0.0235377	−	0.0364291i	0.00108572	−	0.00168035i
$471$		0			0
$472$	20.1085	+	16.0538i	0.925568	+	0.738936i
$473$	−8.22468	−	4.74852i	−0.378171	−	0.218337i
$474$		0			0
$475$	−7.44518	+	27.7858i	−0.341608	+	1.27490i
$476$	−2.20000	+	3.05768i	−0.100837	+	0.140149i
$477$		0			0
$478$	−37.2519	−	12.0087i	−1.70386	−	0.549265i
$479$	6.23896	+	10.8062i	0.285066	+	0.493748i	0.972625	−	0.232380i	$-0.0746513\pi$
$479$	6.23896	+	10.8062i	0.285066	+	0.493748i	−0.687559	+	0.726128i	$0.741318\pi$
$480$		0			0
$481$	3.42439	−	5.93121i	0.156139	−	0.270440i
$482$	1.77705	−	1.60752i	0.0809423	−	0.0732205i
$483$		0			0
$484$	−14.7417	−	1.48050i	−0.670075	−	0.0672953i
$485$	0.145238	+	0.145238i	0.00659494	+	0.00659494i
$486$		0			0
$487$			12.5314i			0.567853i	0.958846	+	0.283927i	$0.0916372\pi$
$487$			12.5314i			0.567853i	−0.958846	+	0.283927i	$0.908363\pi$
$488$	−12.9473	−	33.0418i	−0.586098	−	1.49573i
$489$		0			0
$490$	0.0909282	+	0.00455448i	0.00410772	+	0.000205751i
$491$	−14.6898	+	3.93613i	−0.662942	+	0.177635i	−0.574574	−	0.818453i	$-0.694832\pi$
$491$	−14.6898	+	3.93613i	−0.662942	+	0.177635i	−0.0883688	+	0.996088i	$0.528165\pi$
$492$		0			0
$493$	4.59756	+	1.23191i	0.207064	+	0.0554825i
$494$	−13.0970	+	40.6279i	−0.589262	+	1.82794i
$495$		0			0
$496$	−7.44499	−	22.2120i	−0.334290	−	0.997346i
$497$	−8.69218	−	15.0553i	−0.389898	−	0.675322i
$498$		0			0
$499$	−7.88570	−	29.4298i	−0.353012	−	1.31746i	−0.882967	−	0.469434i	$-0.844458\pi$
$499$	−7.88570	−	29.4298i	−0.353012	−	1.31746i	0.529955	−	0.848026i	$-0.322209\pi$
$500$	0.0827466	−	0.218579i	0.00370054	−	0.00977516i
$501$		0			0
$502$	−1.07235	+	1.65966i	−0.0478613	+	0.0740744i
$503$			1.90106i			0.0847639i	0.999101	+	0.0423820i	$0.0134946\pi$
$503$			1.90106i			0.0847639i	−0.999101	+	0.0423820i	$0.986505\pi$
$504$		0			0
$505$		−	0.0814355i		−	0.00362383i
$506$	13.5349	+	8.74522i	0.601699	+	0.388772i
$507$		0			0
$508$	10.4403	−	4.70632i	0.463214	−	0.208809i
$509$	3.34659	+	12.4896i	0.148335	+	0.553593i	0.999584	+	0.0288320i	$0.00917879\pi$
$509$	3.34659	+	12.4896i	0.148335	+	0.553593i	−0.851249	+	0.524761i	$0.824155\pi$
$510$		0			0
$511$	−2.63819	−	4.56947i	−0.116706	−	0.202142i
$512$	−21.3697	+	7.43868i	−0.944418	+	0.328746i
$513$		0			0
$514$	31.8234	+	10.2587i	1.40367	+	0.452494i
$515$	0.0287544	+	0.00770471i	0.00126707	+	0.000339510i
$516$		0			0
$517$	4.80444	−	1.28734i	0.211299	−	0.0566174i
$518$	0.112779	−	2.25158i	0.00495522	−	0.0989287i
$519$		0			0
$520$	0.0694305	−	0.158902i	0.00304473	−	0.00696831i
$521$			1.24885i			0.0547130i	0.999626	+	0.0273565i	$0.00870893\pi$
$521$			1.24885i			0.0547130i	−0.999626	+	0.0273565i	$0.991291\pi$
$522$		0			0
$523$	9.58031	+	9.58031i	0.418918	+	0.418918i	0.884831	−	0.465913i	$-0.154274\pi$
$523$	9.58031	+	9.58031i	0.418918	+	0.418918i	−0.465913	+	0.884831i	$0.654274\pi$
$524$	−8.59962	−	10.5198i	−0.375676	−	0.459559i
$525$		0			0
$526$	24.3877	+	26.9596i	1.06335	+	1.17550i
$527$	4.51656	−	7.82292i	0.196745	−	0.340772i
$528$		0			0
$529$	6.57248	+	11.3839i	0.285760	+	0.494951i
$530$	0.0637143	−	0.197647i	0.00276757	−	0.00858523i
$531$		0			0
$532$	2.26226	+	13.8678i	0.0980813	+	0.601247i
$533$	−5.03034	+	18.7735i	−0.217888	+	0.813169i
$534$		0			0
$535$	−0.0504047	−	0.0291012i	−0.00217918	−	0.00125815i
$536$	−21.7041	+	27.1859i	−0.937475	+	1.17425i
$537$		0			0
$538$	−22.9957	−	14.8581i	−0.991413	−	0.640576i
$539$	7.38278	+	7.38278i	0.317999	+	0.317999i
$540$		0			0
$541$	13.0165	−	13.0165i	0.559622	−	0.559622i	−0.369578	−	0.929200i	$-0.620498\pi$
$541$	13.0165	−	13.0165i	0.559622	−	0.559622i	0.929200	+	0.369578i	$0.120498\pi$
$542$	2.11331	+	9.83047i	0.0907743	+	0.422255i
$543$		0			0
$544$	−7.60603	−	4.27484i	−0.326106	−	0.183282i
$545$	0.0259743	−	0.0449887i	0.00111262	−	0.00192711i
$546$		0			0
$547$	−9.76080	−	2.61540i	−0.417341	−	0.111826i	0.0440366	−	0.999030i	$-0.485978\pi$
$547$	−9.76080	−	2.61540i	−0.417341	−	0.111826i	−0.461378	+	0.887204i	$0.652645\pi$
$548$	4.92199	−	6.84086i	0.210257	−	0.292227i
$549$		0			0
$550$	11.9265	−	6.11167i	0.508550	−	0.260602i
$551$	15.3760	−	8.87733i	0.655039	−	0.378187i
$552$		0			0
$553$	−0.553890	−	0.319788i	−0.0235538	−	0.0135988i
$554$	−31.7567	−	1.59066i	−1.34921	−	0.0675805i
$555$		0			0
$556$	−25.0912	+	20.5114i	−1.06411	+	0.869877i
$557$	−26.6259	+	26.6259i	−1.12818	+	1.12818i	−0.137702	+	0.990474i	$0.543971\pi$
$557$	−26.6259	+	26.6259i	−1.12818	+	1.12818i	−0.990474	+	0.137702i	$0.956029\pi$
$558$		0			0
$559$	−26.2889			−1.11190
$560$	−0.00351460	−	0.0569722i	−0.000148519	−	0.00240751i
$561$		0			0
$562$	−21.6854	−	23.9724i	−0.914745	−	1.01121i
$563$	−5.67141	−	21.1660i	−0.239021	−	0.892039i	−0.976295	−	0.216445i	$-0.930554\pi$
$563$	−5.67141	−	21.1660i	−0.239021	−	0.892039i	0.737274	−	0.675594i	$-0.236113\pi$
$564$		0			0
$565$	−0.0478429	+	0.178552i	−0.00201276	+	0.00751174i
$566$	3.98600	+	7.77843i	0.167544	+	0.326952i
$567$		0			0
$568$	32.4112	−	23.8935i	1.35994	−	1.00255i
$569$	8.15901	−	4.71061i	0.342044	−	0.197479i	−0.319132	−	0.947710i	$-0.603391\pi$
$569$	8.15901	−	4.71061i	0.342044	−	0.197479i	0.661175	+	0.750231i	$0.270058\pi$
$570$		0			0
$571$	−28.4258	+	7.61666i	−1.18958	+	0.318747i	−0.798720	−	0.601702i	$-0.794489\pi$
$571$	−28.4258	+	7.61666i	−1.18958	+	0.318747i	−0.390861	+	0.920450i	$0.627823\pi$
$572$	18.1297	−	8.17258i	0.758042	−	0.341713i
$573$		0			0
$574$	1.34461	+	6.25473i	0.0561230	+	0.261067i
$575$	30.0595			1.25357
$576$		0			0
$577$	−42.9309			−1.78724			−0.893618	−	0.448828i	$-0.851842\pi$
$577$	−42.9309			−1.78724			−0.893618	+	0.448828i	$0.851842\pi$
$578$	4.34582	+	20.2155i	0.180762	+	0.840852i
$579$		0			0
$580$	−0.0657535	+	0.0296406i	−0.00273027	+	0.00123076i
$581$	13.2888	−	3.56071i	0.551310	−	0.147723i
$582$		0			0
$583$	20.6244	−	11.9075i	0.854175	−	0.493158i
$584$	9.83721	−	7.25197i	0.407067	−	0.300089i
$585$		0			0
$586$	−2.51559	−	4.90901i	−0.103918	−	0.202789i
$587$	8.13523	−	30.3611i	0.335777	−	1.25314i	−0.567247	−	0.823548i	$-0.691992\pi$
$587$	8.13523	−	30.3611i	0.335777	−	1.25314i	0.903024	−	0.429589i	$-0.141342\pi$
$588$		0			0
$589$	−8.72095	−	32.5470i	−0.359340	−	1.34108i
$590$	−0.100859	−	0.111496i	−0.00415230	−	0.00459020i
$591$		0			0
$592$	5.21184	−	0.321517i	0.214205	−	0.0132143i
$593$	−0.434128			−0.0178275			−0.00891374	−	0.999960i	$-0.502837\pi$
$593$	−0.434128			−0.0178275			−0.00891374	+	0.999960i	$0.502837\pi$
$594$		0			0
$595$	0.0155634	−	0.0155634i	0.000638037	−	0.000638037i
$596$	−6.03522	+	4.93362i	−0.247212	+	0.202089i
$597$		0			0
$598$	44.5505	+	2.23148i	1.82180	+	0.0912519i
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	0.569045	−	0.822306i	$-0.307313\pi$
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	−0.427615	+	0.903961i	$0.640646\pi$
$600$		0			0
$601$	3.54563	−	2.04707i	0.144629	−	0.0835019i	−0.425939	−	0.904752i	$-0.640056\pi$
$601$	3.54563	−	2.04707i	0.144629	−	0.0835019i	0.570569	+	0.821250i	$0.306723\pi$
$602$	−7.70119	+	3.94642i	−0.313877	+	0.160844i
$603$		0			0
$604$	17.5440	−	24.3836i	0.713854	−	0.992155i
$605$	0.0836192	+	0.0224057i	0.00339961	+	0.000910922i
$606$		0			0
$607$	16.8996	−	29.2709i	0.685932	−	1.18807i	−0.287211	−	0.957867i	$-0.592728\pi$
$607$	16.8996	−	29.2709i	0.685932	−	1.18807i	0.973143	−	0.230202i	$-0.0739386\pi$
$608$	−31.3374	+	8.78648i	−1.27090	+	0.356339i
$609$		0			0
$610$	0.0435809	+	0.202725i	0.00176454	+	0.00820810i
$611$	9.73570	−	9.73570i	0.393864	−	0.393864i
$612$		0			0
$613$	1.73094	+	1.73094i	0.0699119	+	0.0699119i	0.741198	−	0.671286i	$-0.234258\pi$
$613$	1.73094	+	1.73094i	0.0699119	+	0.0699119i	−0.671286	+	0.741198i	$0.734258\pi$
$614$	−18.1611	−	11.7343i	−0.732924	−	0.473560i
$615$		0			0
$616$	4.08417	−	5.11570i	0.164556	−	0.206117i
$617$	−14.9093	−	8.60788i	−0.600225	−	0.346540i	0.168905	−	0.985632i	$-0.445977\pi$
$617$	−14.9093	−	8.60788i	−0.600225	−	0.346540i	−0.769130	+	0.639092i	$0.779310\pi$
$618$		0			0
$619$	−1.70053	+	6.34645i	−0.0683499	+	0.255085i	−0.991643	−	0.129010i	$-0.958820\pi$
$619$	−1.70053	+	6.34645i	−0.0683499	+	0.255085i	0.923293	+	0.384095i	$0.125487\pi$
$620$	0.0220381	+	0.135095i	0.000885071	+	0.00542556i
$621$		0			0
$622$	9.78871	−	30.3653i	0.392491	−	1.21754i
$623$	6.53931	+	11.3264i	0.261992	+	0.453783i
$624$		0			0
$625$	12.4990	−	21.6489i	0.499959	−	0.865954i
$626$	−5.66623	−	6.26379i	−0.226468	−	0.250351i
$627$		0			0
$628$	−12.4139	−	15.1858i	−0.495370	−	0.605978i
$629$	1.42374	+	1.42374i	0.0567684	+	0.0567684i
$630$		0			0
$631$		−	13.3295i		−	0.530639i	−0.964161	−	0.265319i	$-0.914523\pi$
$631$		−	13.3295i		−	0.530639i	0.964161	−	0.265319i	$-0.0854774\pi$
$632$	0.593141	−	1.35749i	0.0235939	−	0.0539980i
$633$		0			0
$634$	1.31686	−	26.2904i	0.0522990	−	1.04413i
$635$	−0.0646345	+	0.0173188i	−0.00256494	+	0.000687274i
$636$		0			0
$637$	27.9166	+	7.48023i	1.10610	+	0.296377i
$638$	−7.87249	−	2.53781i	−0.311675	−	0.100473i
$639$		0			0
$640$	0.130233	−	0.0227940i	0.00514790	−	0.000901012i
$641$	−8.26044	−	14.3075i	−0.326268	−	0.565113i	0.655500	−	0.755195i	$-0.272458\pi$
$641$	−8.26044	−	14.3075i	−0.326268	−	0.565113i	−0.981768	+	0.190082i	$0.939124\pi$
$642$		0			0
$643$	6.43213	+	24.0050i	0.253659	+	0.946667i	0.968832	+	0.247719i	$0.0796811\pi$
$643$	6.43213	+	24.0050i	0.253659	+	0.946667i	−0.715173	+	0.698947i	$0.753652\pi$
$644$	13.3858	−	6.03410i	0.527475	−	0.237777i
$645$		0			0
$646$	−10.5407	−	6.81060i	−0.414718	−	0.267959i
$647$			26.9660i			1.06014i	0.847954	+	0.530071i	$0.177835\pi$
$647$			26.9660i			1.06014i	−0.847954	+	0.530071i	$0.822165\pi$
$648$		0			0
$649$		−	17.2418i		−	0.676800i
$650$	20.1321	−	31.1582i	0.789645	−	1.22213i
$651$		0			0
$652$	−5.23333	+	13.8241i	−0.204953	+	0.541393i
$653$	1.41419	+	5.27782i	0.0553414	+	0.206537i	0.988060	−	0.154067i	$-0.0492372\pi$
$653$	1.41419	+	5.27782i	0.0553414	+	0.206537i	−0.932719	+	0.360604i	$0.882571\pi$
$654$		0			0
$655$	0.0396959	+	0.0687553i	0.00155105	+	0.00268649i
$656$	−14.0502	+	4.70935i	−0.548569	+	0.183869i
$657$		0			0
$658$	1.39053	−	4.31352i	0.0542083	−	0.168159i
$659$	−0.689165	−	0.184661i	−0.0268460	−	0.00719337i	0.245371	−	0.969429i	$-0.421090\pi$
$659$	−0.689165	−	0.184661i	−0.0268460	−	0.00719337i	−0.272217	+	0.962236i	$0.587757\pi$
$660$		0			0
$661$	−36.9228	+	9.89344i	−1.43613	+	0.384810i	−0.891177	−	0.453656i	$-0.850120\pi$
$661$	−36.9228	+	9.89344i	−1.43613	+	0.384810i	−0.544954	+	0.838466i	$0.683453\pi$
$662$	−14.8960	−	0.746122i	−0.578949	−	0.0289989i
$663$		0			0
$664$	11.6258	+	29.6693i	0.451170	+	1.15139i
$665$		−	0.0821010i		−	0.00318374i
$666$		0			0
$667$	−13.1190	−	13.1190i	−0.507970	−	0.507970i
$668$	14.5103	+	1.45726i	0.561421	+	0.0563833i
$669$		0			0
$670$	0.150738	−	0.136357i	0.00582351	−	0.00526795i
$671$	−11.8899	+	20.5940i	−0.459006	+	0.795022i
$672$		0			0
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	0.716137	−	0.697960i	$-0.245909\pi$
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	−0.962520	+	0.271212i	$0.912575\pi$
$674$	−32.6329	−	10.5197i	−1.25697	−	0.405204i
$675$		0			0
$676$	16.9654	−	23.5794i	0.652514	−	0.906901i
$677$	−6.82184	+	25.4595i	−0.262185	+	0.978487i	0.701766	+	0.712407i	$0.252395\pi$
$677$	−6.82184	+	25.4595i	−0.262185	+	0.978487i	−0.963951	+	0.266079i	$0.914272\pi$
$678$		0			0
$679$	18.5875	+	10.7315i	0.713323	+	0.411837i
$680$	0.0398409	+	0.0318073i	0.00152783	+	0.00121976i
$681$		0			0
$682$	−8.51910	+	13.1849i	−0.326213	+	0.504877i
$683$	−9.42670	−	9.42670i	−0.360703	−	0.360703i	0.503369	−	0.864072i	$-0.332094\pi$
$683$	−9.42670	−	9.42670i	−0.360703	−	0.360703i	−0.864072	+	0.503369i	$0.832094\pi$
$684$		0			0
$685$	−0.0348195	+	0.0348195i	−0.00133039	+	0.00133039i
$686$	21.1195	−	4.54016i	0.806345	−	0.173344i
$687$		0			0
$688$	−11.0716	−	16.7082i	−0.422099	−	0.636995i
$689$	32.9613	−	57.0906i	1.25572	−	2.17498i
$690$		0			0
$691$	−15.1910	−	4.07041i	−0.577891	−	0.154846i	−0.0419780	−	0.999119i	$-0.513366\pi$
$691$	−15.1910	−	4.07041i	−0.577891	−	0.154846i	−0.535913	+	0.844273i	$0.680033\pi$
$692$	46.8776	−	7.64714i	1.78202	−	0.290700i
$693$		0			0
$694$	−12.3990	−	24.1958i	−0.470659	−	0.918462i
$695$	0.163992	−	0.0946807i	0.00622056	−	0.00359144i
$696$		0			0
$697$	−4.94841	−	2.85696i	−0.187434	−	0.108215i
$698$	1.14569	−	22.8732i	0.0433651	−	0.865764i
$699$		0			0
$700$	1.22020	−	12.1498i	0.0461192	−	0.459220i
$701$	−9.62303	+	9.62303i	−0.363457	+	0.363457i	−0.865084	−	0.501627i	$-0.832735\pi$
$701$	−9.62303	+	9.62303i	−0.363457	+	0.363457i	0.501627	+	0.865084i	$0.332735\pi$
$702$		0			0
$703$	7.51063			0.283269
$704$	12.8295	+	8.08070i	0.483530	+	0.304553i
$705$		0			0
$706$	16.1383	−	14.5988i	0.607374	−	0.549431i
$707$	−2.20244	−	8.21961i	−0.0828312	−	0.309130i
$708$		0			0
$709$	−10.8223	+	40.3893i	−0.406439	+	1.51685i	0.394947	+	0.918704i	$0.370763\pi$
$709$	−10.8223	+	40.3893i	−0.406439	+	1.51685i	−0.801386	+	0.598148i	$0.795904\pi$
$710$	−0.209386	+	0.107298i	−0.00785812	+	0.00402683i
$711$		0			0
$712$	−24.3836	+	17.9756i	−0.913816	+	0.673663i
$713$	−30.4931	+	17.6052i	−1.14197	+	0.659319i
$714$		0			0
$715$	−0.112239	+	0.0300742i	−0.00419749	+	0.00112471i
$716$	11.4648	−	30.2850i	0.428462	−	1.13180i
$717$		0			0
$718$	4.11861	−	0.885398i	0.153705	−	0.0330428i
$719$	−48.7757			−1.81903			−0.909514	−	0.415674i	$-0.863546\pi$
$719$	−48.7757			−1.81903			−0.909514	+	0.415674i	$0.863546\pi$
$720$		0			0
$721$	3.11067			0.115847
$722$	−19.4964	+	4.19125i	−0.725583	+	0.155982i
$723$		0			0
$724$	7.97077	+	3.01746i	0.296231	+	0.112143i
$725$	−14.9037	+	3.99343i	−0.553509	+	0.148312i
$726$		0			0
$727$	34.9918	−	20.2025i	1.29777	−	0.749270i	0.317755	−	0.948173i	$-0.397071\pi$
$727$	34.9918	−	20.2025i	1.29777	−	0.749270i	0.980019	+	0.198902i	$0.0637377\pi$
$728$	2.71037	−	17.9164i	0.100453	−	0.664024i
$729$		0			0
$730$	−0.0635513	+	0.0325664i	−0.00235214	+	0.00120534i
$731$	2.00033	−	7.46535i	0.0739850	−	0.276116i
$732$		0			0
$733$	7.60991	+	28.4006i	0.281078	+	1.04900i	0.951658	+	0.307161i	$0.0993789\pi$
$733$	7.60991	+	28.4006i	0.281078	+	1.04900i	−0.670579	+	0.741838i	$0.733954\pi$
$734$	26.3420	−	23.8290i	0.972301	−	0.879544i
$735$		0			0
$736$	17.3442	+	29.2544i	0.639314	+	1.07833i
$737$	23.3102			0.858644
$738$		0			0
$739$	15.4222	−	15.4222i	0.567316	−	0.567316i	−0.364060	−	0.931376i	$-0.618610\pi$
$739$	15.4222	−	15.4222i	0.567316	−	0.567316i	0.931376	+	0.364060i	$0.118610\pi$
$740$	−0.0303580	−	0.00304884i	−0.00111598	−	0.000112078i
$741$		0			0
$742$	1.08555	−	21.6725i	0.0398517	−	0.795621i
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	0.0486373	−	0.998817i	$-0.484512\pi$
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	−0.840682	+	0.541529i	$0.817845\pi$
$744$		0			0
$745$	0.0394451	−	0.0227736i	0.00144515	−	0.000834361i
$746$	19.2329	+	37.5319i	0.704167	+	1.37414i
$747$		0			0
$748$	0.941295	+	5.77022i	0.0344172	+	0.210980i
$749$	−5.87459	−	1.57409i	−0.214653	−	0.0575161i
$750$		0			0
$751$	−21.2809	+	36.8596i	−0.776551	+	1.34503i	0.157368	+	0.987540i	$0.449699\pi$
$751$	−21.2809	+	36.8596i	−0.776551	+	1.34503i	−0.933919	+	0.357486i	$0.883634\pi$
$752$	10.2878	+	2.08746i	0.375159	+	0.0761217i
$753$		0			0
$754$	−22.3848	+	4.81218i	−0.815208	+	0.175249i
$755$	−0.124111	+	0.124111i	−0.00451686	+	0.00451686i
$756$		0			0
$757$	1.80855	+	1.80855i	0.0657328	+	0.0657328i	0.739209	−	0.673476i	$-0.235200\pi$
$757$	1.80855	+	1.80855i	0.0657328	+	0.0657328i	−0.673476	+	0.739209i	$0.735200\pi$
$758$	11.0694	−	17.1321i	0.402060	−	0.622265i
$759$		0			0
$760$	0.188982	−	0.0211896i	0.00685509	−	0.000768626i
$761$	18.5805	+	10.7275i	0.673543	+	0.388870i	0.797418	−	0.603428i	$-0.206199\pi$
$761$	18.5805	+	10.7275i	0.673543	+	0.388870i	−0.123875	+	0.992298i	$0.539532\pi$
$762$		0			0
$763$	1.40496	−	5.24337i	0.0508629	−	0.189823i
$764$	−7.32835	−	5.27274i	−0.265130	−	0.190761i
$765$		0			0
$766$	28.4679	+	9.17705i	1.02859	+	0.331580i
$767$	−23.8636	−	41.3330i	−0.861665	−	1.49245i
$768$		0			0
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	−0.987965	−	0.154680i	$-0.950565\pi$
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	0.627939	+	0.778263i	$0.283899\pi$
$770$	−0.0283650	+	0.0256590i	−0.00102221	+	0.000924688i
$771$		0			0
$772$	0.702657	−	6.99653i	0.0252892	−	0.251810i
$773$	−24.8049	−	24.8049i	−0.892171	−	0.892171i	0.102557	−	0.994727i	$-0.467298\pi$
$773$	−24.8049	−	24.8049i	−0.892171	−	0.892171i	−0.994727	+	0.102557i	$0.967298\pi$
$774$		0			0
$775$			29.2823i			1.05185i
$776$	−19.9047	+	45.5548i	−0.714537	+	1.63532i
$777$		0			0
$778$	−44.3781	−	2.22284i	−1.59103	−	0.0796927i
$779$	−20.5877	+	5.51646i	−0.737631	+	0.197648i
$780$		0			0
$781$	−26.0625	−	6.98342i	−0.932589	−	0.249886i
$782$	−4.02355	+	12.4814i	−0.143882	+	0.446332i
$783$		0			0
$784$	7.00291	+	20.8930i	0.250104	+	0.746179i
$785$	0.0573027	+	0.0992512i	0.00204522	+	0.00354243i
$786$		0			0
$787$	−2.76911	−	10.3344i	−0.0987080	−	0.368383i	0.898848	−	0.438261i	$-0.144406\pi$
$787$	−2.76911	−	10.3344i	−0.0987080	−	0.368383i	−0.997556	+	0.0698783i	$0.977739\pi$
$788$	−12.7479	−	4.82593i	−0.454126	−	0.171917i
$789$		0			0
$790$	−0.00469756	+	0.00727036i	−0.000167132	+	0.000258668i
$791$			19.3159i			0.686794i
$792$		0			0
$793$			65.8254i			2.33753i
$794$	5.44463	+	3.51791i	0.193223	+	0.124846i
$795$		0			0
$796$	−3.83278	−	8.50250i	−0.135849	−	0.301363i
$797$	12.5408	+	46.8027i	0.444216	+	1.65784i	0.717997	+	0.696046i	$0.245059\pi$
$797$	12.5408	+	46.8027i	0.444216	+	1.65784i	−0.273781	+	0.961792i	$0.588274\pi$
$798$		0			0
$799$	2.02389	+	3.50547i	0.0716000	+	0.124015i
$800$	28.2816	−	0.327083i	0.999906	−	0.0115641i
$801$		0			0
$802$	−28.9200	−	9.32279i	−1.02120	−	0.329199i
$803$	−7.91029	−	2.11956i	−0.279148	−	0.0747975i
$804$		0			0
$805$	−0.0828696	+	0.0222048i	−0.00292077	+	0.000782618i
$806$	−2.17378	+	43.3985i	−0.0765681	+	1.52865i
$807$		0			0
$808$	18.3516	−	7.19102i	0.645608	−	0.252979i
$809$			51.3577i			1.80564i	0.430019	+	0.902820i	$0.358507\pi$
$809$			51.3577i			1.80564i	−0.430019	+	0.902820i	$0.641493\pi$
$810$		0			0
$811$	−2.55652	−	2.55652i	−0.0897715	−	0.0897715i	0.660795	−	0.750566i	$-0.270219\pi$
$811$	−2.55652	−	2.55652i	−0.0897715	−	0.0897715i	−0.750566	+	0.660795i	$0.770219\pi$
$812$	−5.83513	+	4.77006i	−0.204773	+	0.167396i
$813$		0			0
$814$	−2.34730	−	2.59484i	−0.0822728	−	0.0909492i
$815$	0.0431843	−	0.0747975i	0.00151268	−	0.00262004i
$816$		0			0
$817$	−14.4147	−	24.9670i	−0.504306	−	0.873484i
$818$	11.5951	−	35.9690i	0.405414	−	1.25763i
$819$		0			0
$820$	0.0854549	−	0.0139403i	0.00298422	−	0.000486815i
$821$	0.0479933	−	0.179113i	0.00167498	−	0.00625110i	−0.965083	−	0.261943i	$-0.915637\pi$
$821$	0.0479933	−	0.179113i	0.00167498	−	0.00625110i	0.966758	+	0.255692i	$0.0823033\pi$
$822$		0			0
$823$	16.8590	+	9.73353i	0.587667	+	0.339290i	0.764174	−	0.645010i	$-0.223147\pi$
$823$	16.8590	+	9.73353i	0.587667	+	0.339290i	−0.176508	+	0.984299i	$0.556480\pi$
$824$	0.802836	+	7.16019i	0.0279681	+	0.249437i
$825$		0			0
$826$	−13.1955	−	8.52595i	−0.459131	−	0.296656i
$827$	−7.70731	−	7.70731i	−0.268009	−	0.268009i	0.560288	−	0.828298i	$-0.310690\pi$
$827$	−7.70731	−	7.70731i	−0.268009	−	0.268009i	−0.828298	+	0.560288i	$0.810690\pi$
$828$		0			0
$829$	−23.8166	+	23.8166i	−0.827184	+	0.827184i	−0.987126	−	0.159942i	$-0.948869\pi$
$829$	−23.8166	+	23.8166i	−0.827184	+	0.827184i	0.159942	+	0.987126i	$0.448869\pi$
$830$	−0.0391327	−	0.182034i	−0.00135832	−	0.00631848i
$831$		0			0
$832$	41.9398	+	1.61473i	1.45400	+	0.0559808i
$833$	−4.24837	+	7.35839i	−0.147197	+	0.254953i
$834$		0			0
$835$	−0.0823071	−	0.0220541i	−0.00284835	−	0.000763214i
$836$	17.7025	+	12.7369i	0.612254	+	0.440516i
$837$		0			0
$838$	−11.5182	+	5.90243i	−0.397891	+	0.203896i
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	−0.141662	−	0.989915i	$-0.545245\pi$
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	0.786461	+	0.617640i	$0.211911\pi$
$840$		0			0
$841$	−16.8674	−	9.73839i	−0.581634	−	0.335807i
$842$	−42.3099	−	2.11925i	−1.45809	−	0.0730341i
$843$		0			0
$844$	−22.8614	−	27.9659i	−0.786921	−	0.962627i
$845$	−0.120018	+	0.120018i	−0.00412873	+	0.00412873i
$846$		0			0
$847$	9.04599			0.310824
$848$	50.1663	−	3.09474i	1.72272	−	0.106274i
$849$		0			0
$850$	7.31625	+	8.08782i	0.250945	+	0.277410i
$851$	−2.03131	−	7.58094i	−0.0696323	−	0.259871i
$852$		0			0
$853$	−10.3419	+	38.5967i	−0.354102	+	1.32153i	0.527510	+	0.849549i	$0.323126\pi$
$853$	−10.3419	+	38.5967i	−0.354102	+	1.32153i	−0.881611	+	0.471976i	$0.843541\pi$
$854$	9.88153	+	19.2832i	0.338139	+	0.659857i
$855$		0			0
$856$	2.10709	−	13.9285i	0.0720190	−	0.476067i
$857$	14.5777	−	8.41643i	0.497964	−	0.287500i	−0.229908	−	0.973212i	$-0.573843\pi$
$857$	14.5777	−	8.41643i	0.497964	−	0.287500i	0.727872	+	0.685713i	$0.240509\pi$
$858$		0			0
$859$	20.7346	−	5.55582i	0.707455	−	0.189562i	0.112888	−	0.993608i	$-0.463990\pi$
$859$	20.7346	−	5.55582i	0.707455	−	0.189562i	0.594568	+	0.804046i	$0.297323\pi$
$860$	0.0481293	+	0.106768i	0.00164119	+	0.00364076i
$861$		0			0
$862$	−2.09709	−	9.75503i	−0.0714272	−	0.332258i
$863$	−20.3421			−0.692455			−0.346227	−	0.938151i	$-0.612537\pi$
$863$	−20.3421			−0.692455			−0.346227	+	0.938151i	$0.612537\pi$
$864$		0			0
$865$	−0.277527			−0.00943620
$866$	−3.91014	−	18.1888i	−0.132872	−	0.618080i
$867$		0			0
$868$	5.87807	+	13.0397i	0.199515	+	0.442596i
$869$	−0.958848	+	0.256922i	−0.0325267	+	0.00871550i
$870$		0			0
$871$	55.8806	−	32.2627i	1.89344	−	1.09318i
$872$	12.4319	+	1.88069i	0.420997	+	0.0636882i
$873$		0			0
$874$	22.3086	+	43.5339i	0.754599	+	1.47255i
$875$	−0.0369333	+	0.137837i	−0.00124857	+	0.00465974i
$876$		0			0
$877$	4.98805	+	18.6156i	0.168434	+	0.628606i	0.997577	+	0.0695688i	$0.0221624\pi$
$877$	4.98805	+	18.6156i	0.168434	+	0.628606i	−0.829143	+	0.559037i	$0.811171\pi$
$878$	−14.1052	−	15.5928i	−0.476029	−	0.526230i
$879$		0			0
$880$	−0.0663833	−	0.0586688i	−0.00223778	−	0.00197773i
$881$	−37.3378			−1.25794			−0.628972	−	0.777428i	$-0.716524\pi$
$881$	−37.3378			−1.25794			−0.628972	+	0.777428i	$0.716524\pi$
$882$		0			0
$883$	−16.7468	+	16.7468i	−0.563576	+	0.563576i	−0.930321	−	0.366745i	$-0.880472\pi$
$883$	−16.7468	+	16.7468i	−0.563576	+	0.563576i	0.366745	+	0.930321i	$0.380472\pi$
$884$	10.2428	+	12.5299i	0.344504	+	0.421426i
$885$		0			0
$886$	4.35285	+	0.218029i	0.146237	+	0.00732482i
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.965983	−	0.258606i	$-0.0832630\pi$
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.259033	+	0.965869i	$0.416596\pi$
$888$		0			0
$889$	−6.05543	+	3.49611i	−0.203093	+	0.117256i
$890$	0.157526	−	0.0807228i	0.00528027	−	0.00270583i
$891$		0			0
$892$	−9.27866	−	6.67598i	−0.310673	−	0.223528i
$893$	14.5844	+	3.90788i	0.488049	+	0.130772i
$894$		0			0
$895$	−0.0946055	+	0.163862i	−0.00316231	+	0.00547729i
$896$	12.5284	−	5.82286i	0.418546	−	0.194528i
$897$		0			0
$898$	−6.49597	−	30.2173i	−0.216773	−	1.00836i
$899$	12.7798	−	12.7798i	0.426229	−	0.426229i
$900$		0			0
$901$	13.7042	+	13.7042i	0.456552	+	0.456552i
$902$	8.34016	+	5.38878i	0.277697	+	0.179427i
$903$		0			0
$904$	−44.4617	+	4.98526i	−1.47877	+	0.165807i
$905$	−0.0431271	−	0.0248994i	−0.00143359	−	0.000827685i
$906$		0			0
$907$	−0.275009	+	1.02635i	−0.00913154	+	0.0340794i	−0.970341	−	0.241739i	$-0.922282\pi$
$907$	−0.275009	+	1.02635i	−0.00913154	+	0.0340794i	0.961210	+	0.275818i	$0.0889489\pi$
$908$	40.2099	−	6.55943i	1.33441	−	0.217682i
$909$		0			0
$910$	−0.0324847	+	0.100770i	−0.00107686	+	0.00334050i
$911$	−1.91307	−	3.31354i	−0.0633829	−	0.109782i	0.832593	−	0.553886i	$-0.186856\pi$
$911$	−1.91307	−	3.31354i	−0.0633829	−	0.109782i	−0.895976	+	0.444103i	$0.853522\pi$
$912$		0			0
$913$	10.6764	−	18.4920i	0.353336	−	0.611996i
$914$	−2.54440	−	2.81273i	−0.0841611	−	0.0930368i
$915$		0			0
$916$	−5.93980	+	4.85562i	−0.196256	+	0.160434i
$917$	5.86616	+	5.86616i	0.193718	+	0.193718i
$918$		0			0
$919$			5.73779i			0.189272i	0.995512	+	0.0946361i	$0.0301688\pi$
$919$			5.73779i			0.189272i	−0.995512	+	0.0946361i	$0.969831\pi$
$920$	−0.0724995	−	0.185020i	−0.00239024	−	0.00609993i
$921$		0			0
$922$	0.751280	−	14.9990i	0.0247421	−	0.493965i
$923$	−72.1438	+	19.3309i	−2.37464	+	0.636284i
$924$		0			0
$925$	−6.30460	−	1.68931i	−0.207294	−	0.0555442i
$926$	−31.8328	−	10.2618i	−1.04609	−	0.337222i
$927$		0			0
$928$	−12.4858	−	12.2003i	−0.409867	−	0.400495i
$929$	20.2911	+	35.1451i	0.665728	+	1.15307i	0.979087	+	0.203440i	$0.0652122\pi$
$929$	20.2911	+	35.1451i	0.665728	+	1.15307i	−0.313359	+	0.949635i	$0.601454\pi$
$930$		0			0
$931$	8.20310	+	30.6144i	0.268846	+	1.00335i
$932$	4.38117	+	9.71901i	0.143510	+	0.318357i
$933$		0			0
$934$	3.73835	+	2.41544i	0.122323	+	0.0790355i
$935$		−	0.0341611i		−	0.00111719i
$936$		0			0
$937$		−	27.9974i		−	0.914635i	−0.889304	−	0.457317i	$-0.848810\pi$
$937$		−	27.9974i		−	0.914635i	0.889304	−	0.457317i	$-0.151190\pi$
$938$	11.5267	−	17.8398i	0.376362	−	0.582491i
$939$		0			0
$940$	−0.0573640	−	0.0217160i	−0.00187101	−	0.000708299i
$941$	−9.68215	−	36.1343i	−0.315629	−	1.17794i	−0.923402	−	0.383833i	$-0.874604\pi$
$941$	−9.68215	−	36.1343i	−0.315629	−	1.17794i	0.607773	−	0.794111i	$-0.292063\pi$
$942$		0			0
$943$	11.1362	+	19.2885i	0.362645	+	0.628119i
$944$	16.2195	−	32.5742i	0.527901	−	1.06020i
$945$		0			0
$946$	−4.12081	+	12.7831i	−0.133979	+	0.415613i
$947$	−18.3948	−	4.92887i	−0.597751	−	0.160167i	−0.0527575	−	0.998607i	$-0.516801\pi$
$947$	−18.3948	−	4.92887i	−0.597751	−	0.160167i	−0.544993	+	0.838441i	$0.683468\pi$
$948$		0			0
$949$	−21.8966	+	5.86717i	−0.710793	+	0.190456i
$950$	40.6303	+	2.03512i	1.31822	+	0.0660280i
$951$		0			0
$952$	4.88154	+	2.13294i	0.158212	+	0.0691289i
$953$		−	2.49861i		−	0.0809380i	−0.999181	−	0.0404690i	$-0.987115\pi$
$953$		−	2.49861i		−	0.0809380i	0.999181	−	0.0404690i	$-0.0128852\pi$
$954$		0			0
$955$	0.0373008	+	0.0373008i	0.00120703	+	0.00120703i
$956$	−5.53114	+	55.0748i	−0.178890	+	1.78125i
$957$		0			0
$958$	13.0865	−	11.8381i	0.422807	−	0.382471i
$959$	−2.57277	+	4.45617i	−0.0830792	+	0.143897i
$960$		0			0
$961$	−1.64996	−	2.85782i	−0.0532246	−	0.0921877i
$962$	−9.21848	−	2.97171i	−0.297216	−	0.0958118i
$963$		0			0
$964$	−2.75079	−	1.97919i	−0.0885970	−	0.0637454i
$965$	−0.0106340	+	0.0396865i	−0.000342319	+	0.00127755i
$966$		0			0
$967$	3.08638	+	1.78192i	0.0992513	+	0.0573028i	0.548804	−	0.835951i	$-0.315083\pi$
$967$	3.08638	+	1.78192i	0.0992513	+	0.0573028i	−0.449553	+	0.893254i	$0.648417\pi$
$968$	2.33469	+	20.8222i	0.0750399	+	0.669252i
$969$		0			0
$970$	0.157641	−	0.243980i	0.00506155	−	0.00783372i
$971$	0.578866	+	0.578866i	0.0185767	+	0.0185767i	0.716334	−	0.697757i	$-0.245819\pi$
$971$	0.578866	+	0.578866i	0.0185767	+	0.0185767i	−0.697757	+	0.716334i	$0.745819\pi$
$972$		0			0
$973$	13.9917	−	13.9917i	0.448553	−	0.448553i
$974$	17.3263	−	3.72472i	0.555170	−	0.119348i
$975$		0			0
$976$	−41.8361	+	27.7223i	−1.33914	+	0.887370i
$977$	−10.3841	+	17.9859i	−0.332218	+	0.575418i	−0.982946	−	0.183892i	$-0.941130\pi$
$977$	−10.3841	+	17.9859i	−0.332218	+	0.575418i	0.650728	+	0.759310i	$0.274464\pi$
$978$		0			0
$979$	19.6074	+	5.25377i	0.626654	+	0.167911i
$980$	−0.0207295	−	0.127073i	−0.000662179	−	0.00405921i
$981$		0			0
$982$	9.80845	+	19.1406i	0.313000	+	0.610801i
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	−0.347220	−	0.937784i	$-0.612874\pi$
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	0.638534	+	0.769593i	$0.279541\pi$
$984$		0			0
$985$	0.0689747	+	0.0398225i	0.00219772	+	0.00126885i
$986$	0.336740	−	6.72286i	0.0107240	−	0.214100i
$987$		0			0
$988$	60.0661	+	6.03240i	1.91096	+	0.191916i
$989$	−21.3022	+	21.3022i	−0.677369	+	0.677369i
$990$		0			0
$991$	−24.1374			−0.766749			−0.383374	−	0.923593i	$-0.625238\pi$
$991$	−24.1374			−0.766749			−0.383374	+	0.923593i	$0.625238\pi$
$992$	−28.4979	+	16.8957i	−0.904811	+	0.536439i
$993$		0			0
$994$	−18.2323	+	16.4929i	−0.578292	+	0.523124i
$995$	0.0141042	+	0.0526377i	0.000447134	+	0.00166873i
$996$		0			0
$997$	6.02848	−	22.4986i	0.190924	−	0.712538i	−0.802361	−	0.596840i	$-0.796423\pi$
$997$	6.02848	−	22.4986i	0.190924	−	0.712538i	0.993284	−	0.115698i	$-0.0369105\pi$
$998$	−38.3466	+	19.6504i	−1.21384	+	0.622023i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.7		72
3.2	odd	2		144.2.x.e.85.12	yes	72
4.3	odd	2		1728.2.bc.e.1009.9		72
9.2	odd	6		144.2.x.e.133.13	yes	72
9.7	even	3	inner	432.2.y.e.181.6		72
12.11	even	2		576.2.bb.e.49.4		72
16.3	odd	4		1728.2.bc.e.145.10		72
16.13	even	4	inner	432.2.y.e.253.6		72
36.7	odd	6		1728.2.bc.e.1585.10		72
36.11	even	6		576.2.bb.e.241.14		72
48.29	odd	4		144.2.x.e.13.13	✓	72
48.35	even	4		576.2.bb.e.337.14		72
144.29	odd	12		144.2.x.e.61.12	yes	72
144.61	even	12	inner	432.2.y.e.397.7		72
144.83	even	12		576.2.bb.e.529.4		72
144.115	odd	12		1728.2.bc.e.721.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.13	✓	72	48.29	odd	4
144.2.x.e.61.12	yes	72	144.29	odd	12
144.2.x.e.85.12	yes	72	3.2	odd	2
144.2.x.e.133.13	yes	72	9.2	odd	6
432.2.y.e.37.7		72	1.1	even	1	trivial
432.2.y.e.181.6		72	9.7	even	3	inner
432.2.y.e.253.6		72	16.13	even	4	inner
432.2.y.e.397.7		72	144.61	even	12	inner
576.2.bb.e.49.4		72	12.11	even	2
576.2.bb.e.241.14		72	36.11	even	6
576.2.bb.e.337.14		72	48.35	even	4
576.2.bb.e.529.4		72	144.83	even	12
1728.2.bc.e.145.10		72	16.3	odd	4
1728.2.bc.e.721.9		72	144.115	odd	12
1728.2.bc.e.1009.9		72	4.3	odd	2
1728.2.bc.e.1585.10		72	36.7	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	432.2.y.e.37.7

Level	$432$
Weight	$2$
Character	432.37
Analytic conductor	$3.450$
Analytic rank	$0$
Dimension	$72$
Inner twists	$4$