LMFDB - Embedded newform 729.2.c.c.244.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.1
Root			$0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.c.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 1.70574i) q^{2} +(-0.939693 + 1.62760i) q^{4} +(1.85083 - 3.20574i) q^{5} +(1.17365 + 2.03282i) q^{7} -0.237565 q^{8} +O(q^{10})$	\(q+(-0.984808 - 1.70574i) q^{2} +(-0.939693 + 1.62760i) q^{4} +(1.85083 - 3.20574i) q^{5} +(1.17365 + 2.03282i) q^{7} -0.237565 q^{8} -7.29086 q^{10} +(-1.08926 - 1.88666i) q^{11} +(2.35844 - 4.08494i) q^{13} +(2.31164 - 4.00387i) q^{14} +(2.11334 + 3.66041i) q^{16} +2.93512 q^{17} -6.22668 q^{19} +(3.47843 + 6.02481i) q^{20} +(-2.14543 + 3.71599i) q^{22} +(0.259515 - 0.449493i) q^{23} +(-4.35117 - 7.53644i) q^{25} -9.29044 q^{26} -4.41147 q^{28} +(-1.74638 - 3.02481i) q^{29} +(2.15270 - 3.72859i) q^{31} +(3.92490 - 6.79813i) q^{32} +(-2.89053 - 5.00654i) q^{34} +8.68891 q^{35} +2.41147 q^{37} +(6.13208 + 10.6211i) q^{38} +(-0.439693 + 0.761570i) q^{40} +(1.24930 - 2.16385i) q^{41} +(-0.532089 - 0.921605i) q^{43} +4.09429 q^{44} -1.02229 q^{46} +(-0.118782 - 0.205737i) q^{47} +(0.745100 - 1.29055i) q^{49} +(-8.57013 + 14.8439i) q^{50} +(4.43242 + 7.67717i) q^{52} -4.66717 q^{53} -8.06418 q^{55} +(-0.278817 - 0.482926i) q^{56} +(-3.43969 + 5.95772i) q^{58} +(-6.65609 + 11.5287i) q^{59} +(1.83750 + 3.18264i) q^{61} -8.48000 q^{62} -7.00774 q^{64} +(-8.73016 - 15.1211i) q^{65} +(-7.14930 + 12.3830i) q^{67} +(-2.75811 + 4.77719i) q^{68} +(-8.55690 - 14.8210i) q^{70} -1.20307 q^{71} -4.68004 q^{73} +(-2.37484 - 4.11334i) q^{74} +(5.85117 - 10.1345i) q^{76} +(2.55682 - 4.42855i) q^{77} +(6.40033 + 11.0857i) q^{79} +15.6458 q^{80} -4.92127 q^{82} +(-5.65198 - 9.78952i) q^{83} +(5.43242 - 9.40923i) q^{85} +(-1.04801 + 1.81521i) q^{86} +(0.258770 + 0.448204i) q^{88} -0.699287 q^{89} +11.0719 q^{91} +(0.487728 + 0.844770i) q^{92} +(-0.233956 + 0.405223i) q^{94} +(-11.5245 + 19.9611i) q^{95} +(3.54323 + 6.13706i) q^{97} -2.93512 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{7}+O(q^{10}) $ 12 * q + 12 * q^7	$ 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) $ 12 * q + 12 * q^7 - 24 * q^10 + 12 * q^13 + 12 * q^16 - 48 * q^19 + 6 * q^22 - 12 * q^28 + 30 * q^31 - 12 * q^37 + 6 * q^40 + 12 * q^43 + 12 * q^46 + 6 * q^49 + 6 * q^52 - 60 * q^55 - 30 * q^58 + 12 * q^61 + 12 * q^64 - 6 * q^67 - 30 * q^70 + 24 * q^73 + 18 * q^76 + 48 * q^79 - 24 * q^82 + 18 * q^85 - 42 * q^88 - 12 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.984808	−	1.70574i	−0.696364	−	1.20614i	−0.969719	−	0.244225i	$-0.921467\pi$
$2$	−0.984808	−	1.70574i	−0.696364	−	1.20614i	0.273354	−	0.961913i	$-0.411867\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	+	1.62760i	−0.469846	+	0.813798i
$5$	1.85083	−	3.20574i	0.827718	−	1.43365i	−0.0721067	−	0.997397i	$-0.522972\pi$
$5$	1.85083	−	3.20574i	0.827718	−	1.43365i	0.899824	−	0.436252i	$-0.143694\pi$
$6$		0			0
$7$	1.17365	+	2.03282i	0.443597	+	0.768333i	0.997953	−	0.0639466i	$-0.0203687\pi$
$7$	1.17365	+	2.03282i	0.443597	+	0.768333i	−0.554356	+	0.832280i	$0.687035\pi$
$8$	−0.237565			−0.0839918
$9$		0			0
$10$	−7.29086			−2.30557
$11$	−1.08926	−	1.88666i	−0.328425	−	0.568849i	0.653774	−	0.756690i	$-0.273185\pi$
$11$	−1.08926	−	1.88666i	−0.328425	−	0.568849i	−0.982200	+	0.187840i	$0.939851\pi$
$12$		0			0
$13$	2.35844	−	4.08494i	0.654114	−	1.13296i	−0.328001	−	0.944677i	$-0.606375\pi$
$13$	2.35844	−	4.08494i	0.654114	−	1.13296i	0.982115	−	0.188281i	$-0.0602916\pi$
$14$	2.31164	−	4.00387i	0.617811	−	1.07008i
$15$		0			0
$16$	2.11334	+	3.66041i	0.528335	+	0.915103i
$17$	2.93512			0.711871			0.355936	−	0.934510i	$-0.384162\pi$
$17$	2.93512			0.711871			0.355936	+	0.934510i	$0.384162\pi$
$18$		0			0
$19$	−6.22668			−1.42850			−0.714249	−	0.699891i	$-0.753232\pi$
$19$	−6.22668			−1.42850			−0.714249	+	0.699891i	$0.753232\pi$
$20$	3.47843	+	6.02481i	0.777800	+	1.34719i
$21$		0			0
$22$	−2.14543	+	3.71599i	−0.457407	+	0.792252i
$23$	0.259515	−	0.449493i	0.0541126	−	0.0937257i	−0.837700	−	0.546130i	$-0.816100\pi$
$23$	0.259515	−	0.449493i	0.0541126	−	0.0937257i	0.891813	+	0.452405i	$0.149434\pi$
$24$		0			0
$25$	−4.35117	−	7.53644i	−0.870233	−	1.50729i
$26$	−9.29044			−1.82201
$27$		0			0
$28$	−4.41147			−0.833690
$29$	−1.74638	−	3.02481i	−0.324294	−	0.561694i	0.657075	−	0.753825i	$-0.271793\pi$
$29$	−1.74638	−	3.02481i	−0.324294	−	0.561694i	−0.981369	+	0.192131i	$0.938460\pi$
$30$		0			0
$31$	2.15270	−	3.72859i	0.386637	−	0.669675i	−0.605358	−	0.795953i	$-0.706970\pi$
$31$	2.15270	−	3.72859i	0.386637	−	0.669675i	0.991995	+	0.126279i	$0.0403033\pi$
$32$	3.92490	−	6.79813i	0.693832	−	1.20175i
$33$		0			0
$34$	−2.89053	−	5.00654i	−0.495722	−	0.858615i
$35$	8.68891			1.46869
$36$		0			0
$37$	2.41147			0.396444			0.198222	−	0.980157i	$-0.436483\pi$
$37$	2.41147			0.396444			0.198222	+	0.980157i	$0.436483\pi$
$38$	6.13208	+	10.6211i	0.994755	+	1.72297i
$39$		0			0
$40$	−0.439693	+	0.761570i	−0.0695215	+	0.120415i
$41$	1.24930	−	2.16385i	0.195108	−	0.337936i	−0.751828	−	0.659359i	$-0.770828\pi$
$41$	1.24930	−	2.16385i	0.195108	−	0.337936i	0.946936	+	0.321423i	$0.104161\pi$
$42$		0			0
$43$	−0.532089	−	0.921605i	−0.0811428	−	0.140543i	0.822598	−	0.568623i	$-0.192524\pi$
$43$	−0.532089	−	0.921605i	−0.0811428	−	0.140543i	−0.903741	+	0.428080i	$0.859190\pi$
$44$	4.09429			0.617237
$45$		0			0
$46$	−1.02229			−0.150728
$47$	−0.118782	−	0.205737i	−0.0173262	−	0.0300098i	0.857232	−	0.514930i	$-0.172182\pi$
$47$	−0.118782	−	0.205737i	−0.0173262	−	0.0300098i	−0.874558	+	0.484920i	$0.838849\pi$
$48$		0			0
$49$	0.745100	−	1.29055i	0.106443	−	0.184364i
$50$	−8.57013	+	14.8439i	−1.21200	+	2.09924i
$51$		0			0
$52$	4.43242	+	7.67717i	0.614666	+	1.06463i
$53$	−4.66717			−0.641085			−0.320543	−	0.947234i	$-0.603865\pi$
$53$	−4.66717			−0.641085			−0.320543	+	0.947234i	$0.603865\pi$
$54$		0			0
$55$	−8.06418			−1.08737
$56$	−0.278817	−	0.482926i	−0.0372585	−	0.0645337i
$57$		0			0
$58$	−3.43969	+	5.95772i	−0.451654	+	0.782287i
$59$	−6.65609	+	11.5287i	−0.866549	+	1.50091i	−0.00104825	+	0.999999i	$0.500334\pi$
$59$	−6.65609	+	11.5287i	−0.866549	+	1.50091i	−0.865501	+	0.500908i	$0.833000\pi$
$60$		0			0
$61$	1.83750	+	3.18264i	0.235267	+	0.407495i	0.959350	−	0.282218i	$-0.0910701\pi$
$61$	1.83750	+	3.18264i	0.235267	+	0.407495i	−0.724083	+	0.689713i	$0.757737\pi$
$62$	−8.48000			−1.07696
$63$		0			0
$64$	−7.00774			−0.875968
$65$	−8.73016	−	15.1211i	−1.08284	−	1.87554i
$66$		0			0
$67$	−7.14930	+	12.3830i	−0.873426	+	1.51282i	−0.0149960	+	0.999888i	$0.504774\pi$
$67$	−7.14930	+	12.3830i	−0.873426	+	1.51282i	−0.858430	+	0.512931i	$0.828560\pi$
$68$	−2.75811	+	4.77719i	−0.334470	+	0.579319i
$69$		0			0
$70$	−8.55690	−	14.8210i	−1.02275	−	1.77145i
$71$	−1.20307			−0.142778			−0.0713891	−	0.997449i	$-0.522743\pi$
$71$	−1.20307			−0.142778			−0.0713891	+	0.997449i	$0.522743\pi$
$72$		0			0
$73$	−4.68004			−0.547758			−0.273879	−	0.961764i	$-0.588307\pi$
$73$	−4.68004			−0.547758			−0.273879	+	0.961764i	$0.588307\pi$
$74$	−2.37484	−	4.11334i	−0.276069	−	0.478166i
$75$		0			0
$76$	5.85117	−	10.1345i	0.671175	−	1.16251i
$77$	2.55682	−	4.42855i	0.291377	−	0.504680i
$78$		0			0
$79$	6.40033	+	11.0857i	0.720093	+	1.24724i	0.960962	+	0.276681i	$0.0892344\pi$
$79$	6.40033	+	11.0857i	0.720093	+	1.24724i	−0.240869	+	0.970558i	$0.577432\pi$
$80$	15.6458			1.74925
$81$		0			0
$82$	−4.92127			−0.543464
$83$	−5.65198	−	9.78952i	−0.620385	−	1.07454i	−0.989414	−	0.145121i	$-0.953643\pi$
$83$	−5.65198	−	9.78952i	−0.620385	−	1.07454i	0.369029	−	0.929418i	$-0.379690\pi$
$84$		0			0
$85$	5.43242	−	9.40923i	0.589229	−	1.02057i
$86$	−1.04801	+	1.81521i	−0.113010	+	0.195739i
$87$		0			0
$88$	0.258770	+	0.448204i	0.0275850	+	0.0477787i
$89$	−0.699287			−0.0741242			−0.0370621	−	0.999313i	$-0.511800\pi$
$89$	−0.699287			−0.0741242			−0.0370621	+	0.999313i	$0.511800\pi$
$90$		0			0
$91$	11.0719			1.16065
$92$	0.487728	+	0.844770i	0.0508492	+	0.0880734i
$93$		0			0
$94$	−0.233956	+	0.405223i	−0.0241307	+	0.0417956i
$95$	−11.5245	+	19.9611i	−1.18239	+	2.04797i
$96$		0			0
$97$	3.54323	+	6.13706i	0.359761	+	0.623124i	0.987921	−	0.154960i	$-0.0495250\pi$
$97$	3.54323	+	6.13706i	0.359761	+	0.623124i	−0.628160	+	0.778084i	$0.716192\pi$
$98$	−2.93512			−0.296492
$99$		0			0
$100$	16.3550			1.63550
$101$	2.33856	+	4.05051i	0.232696	+	0.403041i	0.958600	−	0.284755i	$-0.0919121\pi$
$101$	2.33856	+	4.05051i	0.232696	+	0.403041i	−0.725905	+	0.687795i	$0.758579\pi$
$102$		0			0
$103$	6.81180	−	11.7984i	0.671187	−	1.16253i	−0.306381	−	0.951909i	$-0.599118\pi$
$103$	6.81180	−	11.7984i	0.671187	−	1.16253i	0.977568	−	0.210621i	$-0.0675486\pi$
$104$	−0.560282	+	0.970437i	−0.0549402	+	0.0951592i
$105$		0			0
$106$	4.59627	+	7.96097i	0.446429	+	0.773238i
$107$	−11.6340			−1.12470			−0.562350	−	0.826900i	$-0.690102\pi$
$107$	−11.6340			−1.12470			−0.562350	+	0.826900i	$0.690102\pi$
$108$		0			0
$109$	14.6040			1.39881			0.699405	−	0.714725i	$-0.253448\pi$
$109$	14.6040			1.39881			0.699405	+	0.714725i	$0.253448\pi$
$110$	7.94166	+	13.7554i	0.757208	+	1.31152i
$111$		0			0
$112$	−4.96064	+	8.59208i	−0.468736	+	0.811875i
$113$	2.34791	−	4.06670i	0.220873	−	0.382563i	−0.734200	−	0.678933i	$-0.762443\pi$
$113$	2.34791	−	4.06670i	0.220873	−	0.382563i	0.955073	+	0.296370i	$0.0957760\pi$
$114$		0			0
$115$	−0.960637	−	1.66387i	−0.0895799	−	0.155157i
$116$	6.56423			0.609474
$117$		0			0
$118$	26.2199			2.41374
$119$	3.44480	+	5.96657i	0.315784	+	0.546954i
$120$		0			0
$121$	3.12701	−	5.41614i	0.284274	−	0.492377i
$122$	3.61916	−	6.26857i	0.327663	−	0.567530i
$123$		0			0
$124$	4.04576	+	7.00746i	0.363320	+	0.629289i
$125$	−13.7048			−1.22579
$126$		0			0
$127$	6.09152			0.540535			0.270267	−	0.962785i	$-0.412888\pi$
$127$	6.09152			0.540535			0.270267	+	0.962785i	$0.412888\pi$
$128$	−0.948531	−	1.64290i	−0.0838391	−	0.145214i
$129$		0			0
$130$	−17.1951	+	29.7827i	−1.50811	+	2.61212i
$131$	5.17420	−	8.96198i	0.452072	−	0.783012i	−0.546442	−	0.837497i	$-0.684018\pi$
$131$	5.17420	−	8.96198i	0.452072	−	0.783012i	0.998515	+	0.0544847i	$0.0173516\pi$
$132$		0			0
$133$	−7.30793	−	12.6577i	−0.633678	−	1.09756i
$134$	28.1627			2.43289
$135$		0			0
$136$	−0.697281			−0.0597914
$137$	9.54233	+	16.5278i	0.815257	+	1.41207i	0.909143	+	0.416483i	$0.136737\pi$
$137$	9.54233	+	16.5278i	0.815257	+	1.41207i	−0.0938868	+	0.995583i	$0.529929\pi$
$138$		0			0
$139$	11.6518	−	20.1816i	0.988295	−	1.71178i	0.362031	−	0.932166i	$-0.382083\pi$
$139$	11.6518	−	20.1816i	0.988295	−	1.71178i	0.626264	−	0.779611i	$-0.284583\pi$
$140$	−8.16490	+	14.1420i	−0.690060	+	1.19522i
$141$		0			0
$142$	1.18479	+	2.05212i	0.0994256	+	0.172210i
$143$	−10.2759			−0.859310
$144$		0			0
$145$	−12.9290			−1.07370
$146$	4.60894	+	7.98293i	0.381439	+	0.660672i
$147$		0			0
$148$	−2.26604	+	3.92490i	−0.186268	+	0.322625i
$149$	7.75298	−	13.4285i	0.635149	−	1.10011i	−0.351335	−	0.936250i	$-0.614272\pi$
$149$	7.75298	−	13.4285i	0.635149	−	1.10011i	0.986484	−	0.163860i	$-0.0523945\pi$
$150$		0			0
$151$	2.95084	+	5.11100i	0.240136	+	0.415927i	0.960753	−	0.277406i	$-0.0894747\pi$
$151$	2.95084	+	5.11100i	0.240136	+	0.415927i	−0.720617	+	0.693333i	$0.756141\pi$
$152$	1.47924			0.119982
$153$		0			0
$154$	−10.0719			−0.811618
$155$	−7.96859	−	13.8020i	−0.640053	−	1.10860i
$156$		0			0
$157$	0.606067	−	1.04974i	0.0483694	−	0.0837783i	−0.840827	−	0.541304i	$-0.817931\pi$
$157$	0.606067	−	1.04974i	0.0483694	−	0.0837783i	0.889196	+	0.457526i	$0.151264\pi$
$158$	12.6062	−	21.8346i	1.00289	−	1.73706i
$159$		0			0
$160$	−14.5287	−	25.1644i	−1.14859	−	1.98942i
$161$	1.21832			0.0960168
$162$		0			0
$163$	2.77332			0.217223			0.108612	−	0.994084i	$-0.465360\pi$
$163$	2.77332			0.217223			0.108612	+	0.994084i	$0.465360\pi$
$164$	2.34791	+	4.06670i	0.183341	+	0.317556i
$165$		0			0
$166$	−11.1322	+	19.2816i	−0.864028	+	1.49654i
$167$	−1.91404	+	3.31521i	−0.148113	+	0.256538i	−0.930530	−	0.366216i	$-0.880653\pi$
$167$	−1.91404	+	3.31521i	−0.148113	+	0.256538i	0.782417	+	0.622754i	$0.213986\pi$
$168$		0			0
$169$	−4.62449	−	8.00984i	−0.355730	−	0.616142i
$170$	−21.3996			−1.64127
$171$		0			0
$172$	2.00000			0.152499
$173$	−3.51471	−	6.08765i	−0.267218	−	0.462835i	0.700924	−	0.713236i	$-0.252771\pi$
$173$	−3.51471	−	6.08765i	−0.267218	−	0.462835i	−0.968142	+	0.250400i	$0.919438\pi$
$174$		0			0
$175$	10.2135	−	17.6903i	0.772066	−	1.33726i
$176$	4.60397	−	7.97431i	0.347037	−	0.601086i
$177$		0			0
$178$	0.688663	+	1.19280i	0.0516175	+	0.0894041i
$179$	14.3854			1.07521			0.537607	−	0.843195i	$-0.319328\pi$
$179$	14.3854			1.07521			0.537607	+	0.843195i	$0.319328\pi$
$180$		0			0
$181$	13.2003			0.981169			0.490584	−	0.871394i	$-0.336783\pi$
$181$	13.2003			0.981169			0.490584	+	0.871394i	$0.336783\pi$
$182$	−10.9037	−	18.8858i	−0.808237	−	1.39991i
$183$		0			0
$184$	−0.0616516	+	0.106784i	−0.00454501	+	0.00787219i
$185$	4.46324	−	7.73055i	0.328144	−	0.568361i
$186$		0			0
$187$	−3.19712	−	5.53757i	−0.233796	−	0.404947i
$188$	0.446476			0.0325626
$189$		0			0
$190$	45.3979			3.29351
$191$	6.71167	+	11.6250i	0.485639	+	0.841152i	0.999864	−	0.0165036i	$-0.00525351\pi$
$191$	6.71167	+	11.6250i	0.485639	+	0.841152i	−0.514224	+	0.857656i	$0.671920\pi$
$192$		0			0
$193$	−7.50253	+	12.9948i	−0.540044	+	0.935383i	0.458857	+	0.888510i	$0.348259\pi$
$193$	−7.50253	+	12.9948i	−0.540044	+	0.935383i	−0.998901	+	0.0468730i	$0.985074\pi$
$194$	6.97881	−	12.0876i	0.501049	−	0.867843i
$195$		0			0
$196$	1.40033	+	2.42544i	0.100024	+	0.173246i
$197$	22.3212			1.59032			0.795158	−	0.606402i	$-0.207388\pi$
$197$	22.3212			1.59032			0.795158	+	0.606402i	$0.207388\pi$
$198$		0			0
$199$	−9.10101			−0.645154			−0.322577	−	0.946543i	$-0.604549\pi$
$199$	−9.10101			−0.645154			−0.322577	+	0.946543i	$0.604549\pi$
$200$	1.03368	+	1.79039i	0.0730925	+	0.126600i
$201$		0			0
$202$	4.60607	−	7.97794i	0.324082	−	0.561326i
$203$	4.09927	−	7.10014i	0.287712	−	0.498332i
$204$		0			0
$205$	−4.62449	−	8.00984i	−0.322988	−	0.559432i
$206$	−26.8333			−1.86956
$207$		0			0
$208$	19.9368			1.38237
$209$	6.78250	+	11.7476i	0.469155	+	0.812600i
$210$		0			0
$211$	2.98886	−	5.17685i	0.205761	−	0.356389i	−0.744614	−	0.667496i	$-0.767366\pi$
$211$	2.98886	−	5.17685i	0.205761	−	0.356389i	0.950375	+	0.311107i	$0.100700\pi$
$212$	4.38571	−	7.59627i	0.301212	−	0.521714i
$213$		0			0
$214$	11.4572	+	19.8445i	0.783200	+	1.35654i
$215$	−3.93923			−0.268653
$216$		0			0
$217$	10.1061			0.686045
$218$	−14.3821	−	24.9106i	−0.974081	−	1.68716i
$219$		0			0
$220$	7.57785	−	13.1252i	0.510898	−	0.884902i
$221$	6.92231	−	11.9898i	0.465645	−	0.806521i
$222$		0			0
$223$	4.45084	+	7.70908i	0.298050	+	0.516238i	0.975690	−	0.219156i	$-0.0703304\pi$
$223$	4.45084	+	7.70908i	0.298050	+	0.516238i	−0.677640	+	0.735394i	$0.736997\pi$
$224$	18.4258			1.23113
$225$		0			0
$226$	−9.24897			−0.615232
$227$	−5.33424	−	9.23917i	−0.354046	−	0.613225i	0.632908	−	0.774227i	$-0.281861\pi$
$227$	−5.33424	−	9.23917i	−0.354046	−	0.613225i	−0.986954	+	0.161001i	$0.948528\pi$
$228$		0			0
$229$	4.13563	−	7.16312i	0.273290	−	0.473352i	−0.696412	−	0.717642i	$-0.745221\pi$
$229$	4.13563	−	7.16312i	0.273290	−	0.473352i	0.969702	+	0.244290i	$0.0785548\pi$
$230$	−1.89209	+	3.27719i	−0.124760	+	0.216091i
$231$		0			0
$232$	0.414878	+	0.718589i	0.0272381	+	0.0471777i
$233$	−12.7393			−0.834579			−0.417290	−	0.908774i	$-0.637020\pi$
$233$	−12.7393			−0.834579			−0.417290	+	0.908774i	$0.637020\pi$
$234$		0			0
$235$	−0.879385			−0.0573648
$236$	−12.5094	−	21.6668i	−0.814290	−	1.41039i
$237$		0			0
$238$	6.78493	−	11.7518i	0.439802	−	0.761759i
$239$	7.50779	−	13.0039i	0.485638	−	0.841150i	−0.514225	−	0.857655i	$-0.671921\pi$
$239$	7.50779	−	13.0039i	0.485638	−	0.841150i	0.999864	+	0.0165047i	$0.00525384\pi$
$240$		0			0
$241$	−0.397804	−	0.689016i	−0.0256248	−	0.0443834i	0.852929	−	0.522028i	$-0.174824\pi$
$241$	−0.397804	−	0.689016i	−0.0256248	−	0.0443834i	−0.878553	+	0.477644i	$0.841491\pi$
$242$	−12.3180			−0.791832
$243$		0			0
$244$	−6.90673			−0.442158
$245$	−2.75811	−	4.77719i	−0.176209	−	0.305203i
$246$		0			0
$247$	−14.6853	+	25.4356i	−0.934401	+	1.61843i
$248$	−0.511406	+	0.885782i	−0.0324743	+	0.0562472i
$249$		0			0
$250$	13.4966	+	23.3768i	0.853600	+	1.47848i
$251$	−8.31499			−0.524837			−0.262419	−	0.964954i	$-0.584520\pi$
$251$	−8.31499			−0.524837			−0.262419	+	0.964954i	$0.584520\pi$
$252$		0			0
$253$	−1.13072			−0.0710877
$254$	−5.99898	−	10.3905i	−0.376409	−	0.651960i
$255$		0			0
$256$	−8.87598	+	15.3737i	−0.554749	+	0.960853i
$257$	−12.8101	+	22.1878i	−0.799074	+	1.38404i	0.121146	+	0.992635i	$0.461343\pi$
$257$	−12.8101	+	22.1878i	−0.799074	+	1.38404i	−0.920220	+	0.391401i	$0.871990\pi$
$258$		0			0
$259$	2.83022	+	4.90209i	0.175861	+	0.304601i
$260$	32.8147			2.03508
$261$		0			0
$262$	−20.3824			−1.25923
$263$	14.0325	+	24.3050i	0.865281	+	1.49871i	0.866768	+	0.498711i	$0.166193\pi$
$263$	14.0325	+	24.3050i	0.865281	+	1.49871i	−0.00148730	+	0.999999i	$0.500473\pi$
$264$		0			0
$265$	−8.63816	+	14.9617i	−0.530638	+	0.919091i
$266$	−14.3938	+	24.9308i	−0.882542	+	1.52861i
$267$		0			0
$268$	−13.4363	−	23.2723i	−0.820752	−	1.42158i
$269$	30.1710			1.83956			0.919778	−	0.392439i	$-0.128369\pi$
$269$	30.1710			1.83956			0.919778	+	0.392439i	$0.128369\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	6.20291	+	10.7438i	0.376107	+	0.651436i
$273$		0			0
$274$	18.7947	−	32.5534i	1.13543	−	1.96662i
$275$	−9.47913	+	16.4183i	−0.571613	+	0.990063i
$276$		0			0
$277$	−10.5608	−	18.2918i	−0.634535	−	1.09905i	−0.986613	−	0.163077i	$-0.947858\pi$
$277$	−10.5608	−	18.2918i	−0.634535	−	1.09905i	0.352078	−	0.935971i	$-0.385475\pi$
$278$	−45.8992			−2.75285
$279$		0			0
$280$	−2.06418			−0.123358
$281$	−0.873649	−	1.51320i	−0.0521175	−	0.0902702i	0.838790	−	0.544456i	$-0.183264\pi$
$281$	−0.873649	−	1.51320i	−0.0521175	−	0.0902702i	−0.890907	+	0.454185i	$0.849930\pi$
$282$		0			0
$283$	3.64409	−	6.31174i	0.216618	−	0.375194i	−0.737154	−	0.675725i	$-0.763831\pi$
$283$	3.64409	−	6.31174i	0.216618	−	0.375194i	0.953772	+	0.300531i	$0.0971639\pi$
$284$	1.13052	−	1.95811i	0.0670838	−	0.116193i
$285$		0			0
$286$	10.1197	+	17.5279i	0.598393	+	1.03645i
$287$	5.86495			0.346197
$288$		0			0
$289$	−8.38507			−0.493239
$290$	12.7326	+	22.0535i	0.747684	+	1.29503i
$291$		0			0
$292$	4.39780	−	7.61722i	0.257362	−	0.445764i
$293$	−7.67545	+	13.2943i	−0.448404	+	0.776659i	−0.998282	−	0.0585858i	$-0.981341\pi$
$293$	−7.67545	+	13.2943i	−0.448404	+	0.776659i	0.549878	+	0.835245i	$0.314674\pi$
$294$		0			0
$295$	24.6386	+	42.6753i	1.43452	+	2.48465i
$296$	−0.572881			−0.0332980
$297$		0			0
$298$	−30.5408			−1.76918
$299$	−1.22410	−	2.12020i	−0.0707916	−	0.122615i
$300$		0			0
$301$	1.24897	−	2.16328i	0.0719895	−	0.124689i
$302$	5.81201	−	10.0667i	0.334444	−	0.579274i
$303$		0			0
$304$	−13.1591	−	22.7922i	−0.754726	−	1.30722i
$305$	13.6036			0.778940
$306$		0			0
$307$	16.7638			0.956762			0.478381	−	0.878152i	$-0.341224\pi$
$307$	16.7638			0.956762			0.478381	+	0.878152i	$0.341224\pi$
$308$	4.80526	+	8.32295i	0.273805	+	0.474244i
$309$		0			0
$310$	−15.6951	+	27.1846i	−0.891419	+	1.54398i
$311$	8.01157	−	13.8764i	0.454295	−	0.786861i	−0.544353	−	0.838856i	$-0.683225\pi$
$311$	8.01157	−	13.8764i	0.454295	−	0.786861i	0.998647	+	0.0519952i	$0.0165580\pi$
$312$		0			0
$313$	−17.2028	−	29.7961i	−0.972360	−	1.68418i	−0.688386	−	0.725344i	$-0.741681\pi$
$313$	−17.2028	−	29.7961i	−0.972360	−	1.68418i	−0.283974	−	0.958832i	$-0.591653\pi$
$314$	−2.38744			−0.134731
$315$		0			0
$316$	−24.0574			−1.35333
$317$	8.15555	+	14.1258i	0.458061	+	0.793386i	0.998858	−	0.0477675i	$-0.0152106\pi$
$317$	8.15555	+	14.1258i	0.458061	+	0.793386i	−0.540797	+	0.841153i	$0.681877\pi$
$318$		0			0
$319$	−3.80453	+	6.58964i	−0.213013	+	0.368949i
$320$	−12.9702	+	22.4650i	−0.725054	+	1.25583i
$321$		0			0
$322$	−1.19981	−	2.07813i	−0.0668626	−	0.115809i
$323$	−18.2761			−1.01691
$324$		0			0
$325$	−41.0479			−2.27693
$326$	−2.73119	−	4.73055i	−0.151266	−	0.262001i
$327$		0			0
$328$	−0.296789	+	0.514054i	−0.0163874	+	0.0283839i
$329$	0.278817	−	0.482926i	0.0153717	−	0.0266246i
$330$		0			0
$331$	15.7900	+	27.3491i	0.867896	+	1.50324i	0.864143	+	0.503247i	$0.167861\pi$
$331$	15.7900	+	27.3491i	0.867896	+	1.50324i	0.00375320	+	0.999993i	$0.498805\pi$
$332$	21.2445			1.16594
$333$		0			0
$334$	7.53983			0.412561
$335$	26.4643	+	45.8376i	1.44590	+	2.50437i
$336$		0			0
$337$	−3.00253	+	5.20053i	−0.163558	+	0.283291i	−0.936142	−	0.351621i	$-0.885630\pi$
$337$	−3.00253	+	5.20053i	−0.163558	+	0.283291i	0.772584	+	0.634912i	$0.218964\pi$
$338$	−9.10846	+	15.7763i	−0.495435	+	0.858118i
$339$		0			0
$340$	10.2096	+	17.6836i	0.553694	+	0.959026i
$341$	−9.37944			−0.507925
$342$		0			0
$343$	19.9290			1.07607
$344$	0.126406	+	0.218941i	0.00681533	+	0.0118045i
$345$		0			0
$346$	−6.92262	+	11.9903i	−0.372162	+	0.644604i
$347$	−11.5152	+	19.9449i	−0.618168	+	1.07070i	0.371652	+	0.928372i	$0.378792\pi$
$347$	−11.5152	+	19.9449i	−0.618168	+	1.07070i	−0.989820	+	0.142326i	$0.954542\pi$
$348$		0			0
$349$	5.78312	+	10.0167i	0.309563	+	0.536179i	0.978267	−	0.207350i	$-0.0664838\pi$
$349$	5.78312	+	10.0167i	0.309563	+	0.536179i	−0.668704	+	0.743529i	$0.733150\pi$
$350$	−40.2332			−2.15056
$351$		0			0
$352$	−17.1010			−0.911487
$353$	1.06731	+	1.84864i	0.0568073	+	0.0983932i	0.893031	−	0.449996i	$-0.148575\pi$
$353$	1.06731	+	1.84864i	0.0568073	+	0.0983932i	−0.836223	+	0.548389i	$0.815241\pi$
$354$		0			0
$355$	−2.22668	+	3.85673i	−0.118180	+	0.204694i
$356$	0.657115	−	1.13816i	0.0348270	−	0.0603221i
$357$		0			0
$358$	−14.1668	−	24.5377i	−0.748741	−	1.29686i
$359$	24.2235			1.27847			0.639234	−	0.769012i	$-0.279251\pi$
$359$	24.2235			1.27847			0.639234	+	0.769012i	$0.279251\pi$
$360$		0			0
$361$	19.7716			1.04061
$362$	−12.9997	−	22.5162i	−0.683251	−	1.18343i
$363$		0			0
$364$	−10.4042	+	18.0206i	−0.545328	+	0.944536i
$365$	−8.66198	+	15.0030i	−0.453389	+	0.785293i
$366$		0			0
$367$	1.41740	+	2.45502i	0.0739879	+	0.128151i	0.900646	−	0.434554i	$-0.143094\pi$
$367$	1.41740	+	2.45502i	0.0739879	+	0.128151i	−0.826658	+	0.562705i	$0.809761\pi$
$368$	2.19377			0.114358
$369$		0			0
$370$	−17.5817			−0.914030
$371$	−5.47762	−	9.48751i	−0.284384	−	0.492567i
$372$		0			0
$373$	14.4167	−	24.9704i	0.746468	−	1.29292i	−0.203038	−	0.979171i	$-0.565081\pi$
$373$	14.4167	−	24.9704i	0.746468	−	1.29292i	0.949506	−	0.313749i	$-0.101585\pi$
$374$	−6.29710	+	10.9069i	−0.325615	+	0.563982i
$375$		0			0
$376$	0.0282185	+	0.0488759i	0.00145526	+	0.00252058i
$377$	−16.4749			−0.848501
$378$		0			0
$379$	32.1985			1.65393			0.826963	−	0.562256i	$-0.190066\pi$
$379$	32.1985			1.65393			0.826963	+	0.562256i	$0.190066\pi$
$380$	−21.6591	−	37.5146i	−1.11109	−	1.92446i
$381$		0			0
$382$	13.2194	−	22.8967i	0.676364	−	1.17150i
$383$	−0.336125	+	0.582186i	−0.0171752	+	0.0297483i	−0.874485	−	0.485052i	$-0.838801\pi$
$383$	−0.336125	+	0.582186i	−0.0171752	+	0.0297483i	0.857310	+	0.514800i	$0.172134\pi$
$384$		0			0
$385$	−9.46451	−	16.3930i	−0.482356	−	0.835465i
$386$	29.5542			1.50427
$387$		0			0
$388$	−13.3182			−0.676129
$389$	2.12965	+	3.68866i	0.107978	+	0.187023i	0.914951	−	0.403565i	$-0.132229\pi$
$389$	2.12965	+	3.68866i	0.107978	+	0.187023i	−0.806973	+	0.590588i	$0.798896\pi$
$390$		0			0
$391$	0.761707	−	1.31932i	0.0385212	−	0.0667207i
$392$	−0.177009	+	0.306589i	−0.00894033	+	0.0154851i
$393$		0			0
$394$	−21.9820	−	38.0740i	−1.10744	−	1.91814i
$395$	47.3838			2.38414
$396$		0			0
$397$	−8.86484			−0.444913			−0.222457	−	0.974943i	$-0.571408\pi$
$397$	−8.86484			−0.444913			−0.222457	+	0.974943i	$0.571408\pi$
$398$	8.96275	+	15.5239i	0.449262	+	0.778145i
$399$		0			0
$400$	18.3910	−	31.8541i	0.919550	−	1.59271i
$401$	−18.5420	+	32.1156i	−0.925941	+	1.60378i	−0.135901	+	0.990722i	$0.543393\pi$
$401$	−18.5420	+	32.1156i	−0.925941	+	1.60378i	−0.790040	+	0.613055i	$0.789940\pi$
$402$		0			0
$403$	−10.1540	−	17.5873i	−0.505809	−	0.876087i
$404$	−8.79012			−0.437325
$405$		0			0
$406$	−16.1480			−0.801410
$407$	−2.62673	−	4.54963i	−0.130202	−	0.225517i
$408$		0			0
$409$	1.69459	−	2.93512i	0.0837922	−	0.145132i	−0.821084	−	0.570808i	$-0.806630\pi$
$409$	1.69459	−	2.93512i	0.0837922	−	0.145132i	0.904876	+	0.425675i	$0.139963\pi$
$410$	−9.10846	+	15.7763i	−0.449835	+	0.779136i
$411$		0			0
$412$	12.8020	+	22.1737i	0.630709	+	1.09242i
$413$	−31.2476			−1.53760
$414$		0			0
$415$	−41.8435			−2.05402
$416$	−18.5133	−	32.0660i	−0.907690	−	1.57216i
$417$		0			0
$418$	13.3589	−	23.1383i	0.653406	−	1.13173i
$419$	10.3282	−	17.8889i	0.504565	−	0.873932i	−0.495421	−	0.868653i	$-0.664986\pi$
$419$	10.3282	−	17.8889i	0.504565	−	0.873932i	0.999986	−	0.00527895i	$-0.00168035\pi$
$420$		0			0
$421$	−13.7665	−	23.8443i	−0.670939	−	1.16210i	−0.977638	−	0.210294i	$-0.932558\pi$
$421$	−13.7665	−	23.8443i	−0.670939	−	1.16210i	0.306700	−	0.951806i	$-0.400775\pi$
$422$	−11.7738			−0.573139
$423$		0			0
$424$	1.10876			0.0538459
$425$	−12.7712	−	22.1204i	−0.619494	−	1.07300i
$426$		0			0
$427$	−4.31315	+	7.47059i	−0.208728	+	0.361527i
$428$	10.9324	−	18.9354i	0.528436	−	0.915278i
$429$		0			0
$430$	3.87939	+	6.71929i	0.187081	+	0.324033i
$431$	−2.58110			−0.124327			−0.0621636	−	0.998066i	$-0.519800\pi$
$431$	−2.58110			−0.124327			−0.0621636	+	0.998066i	$0.519800\pi$
$432$		0			0
$433$	−27.0137			−1.29820			−0.649098	−	0.760704i	$-0.724854\pi$
$433$	−27.0137			−1.29820			−0.649098	+	0.760704i	$0.724854\pi$
$434$	−9.95253	−	17.2383i	−0.477737	−	0.827465i
$435$		0			0
$436$	−13.7233	+	23.7694i	−0.657226	+	1.13835i
$437$	−1.61592	+	2.79885i	−0.0772997	+	0.133887i
$438$		0			0
$439$	−5.85504	−	10.1412i	−0.279446	−	0.484014i	0.691801	−	0.722088i	$-0.256817\pi$
$439$	−5.85504	−	10.1412i	−0.279446	−	0.484014i	−0.971247	+	0.238074i	$0.923484\pi$
$440$	1.91576			0.0913305
$441$		0			0
$442$	−27.2686			−1.29703
$443$	−1.04039	−	1.80200i	−0.0494303	−	0.0856158i	0.840252	−	0.542197i	$-0.182407\pi$
$443$	−1.04039	−	1.80200i	−0.0494303	−	0.0856158i	−0.889682	+	0.456581i	$0.849074\pi$
$444$		0			0
$445$	−1.29426	+	2.24173i	−0.0613539	+	0.106268i
$446$	8.76644	−	15.1839i	0.415103	−	0.718979i
$447$		0			0
$448$	−8.22462	−	14.2455i	−0.388577	−	0.673035i
$449$	10.5508			0.497924			0.248962	−	0.968513i	$-0.419911\pi$
$449$	10.5508			0.497924			0.248962	+	0.968513i	$0.419911\pi$
$450$		0			0
$451$	−5.44326			−0.256313
$452$	4.41263	+	7.64290i	0.207553	+	0.359492i
$453$		0			0
$454$	−10.5064	+	18.1976i	−0.493090	+	0.854056i
$455$	20.4923	−	35.4937i	0.960693	−	1.66397i
$456$		0			0
$457$	3.95471	+	6.84975i	0.184993	+	0.320418i	0.943574	−	0.331161i	$-0.107440\pi$
$457$	3.95471	+	6.84975i	0.184993	+	0.320418i	−0.758581	+	0.651579i	$0.774107\pi$
$458$	−16.2912			−0.761238
$459$		0			0
$460$	3.61081			0.168355
$461$	19.5464	+	33.8553i	0.910366	+	1.57680i	0.813548	+	0.581498i	$0.197533\pi$
$461$	19.5464	+	33.8553i	0.910366	+	1.57680i	0.0968187	+	0.995302i	$0.469133\pi$
$462$		0			0
$463$	−11.8464	+	20.5186i	−0.550550	+	0.953580i	0.447685	+	0.894191i	$0.352249\pi$
$463$	−11.8464	+	20.5186i	−0.550550	+	0.953580i	−0.998235	+	0.0593889i	$0.981085\pi$
$464$	7.38138	−	12.7849i	0.342672	−	0.593525i
$465$		0			0
$466$	12.5458	+	21.7299i	0.581171	+	1.00662i
$467$	−34.7152			−1.60643			−0.803214	−	0.595691i	$-0.796878\pi$
$467$	−34.7152			−1.60643			−0.803214	+	0.595691i	$0.796878\pi$
$468$		0			0
$469$	−33.5631			−1.54980
$470$	0.866025	+	1.50000i	0.0399468	+	0.0691898i
$471$		0			0
$472$	1.58125	−	2.73881i	0.0727830	−	0.126064i
$473$	−1.15917	+	2.00774i	−0.0532987	+	0.0923160i
$474$		0			0
$475$	27.0933	+	46.9270i	1.24313	+	2.15316i
$476$	−12.9482			−0.593480
$477$		0			0
$478$	−29.5749			−1.35272
$479$	3.24086	+	5.61334i	0.148079	+	0.256480i	0.930517	−	0.366248i	$-0.119358\pi$
$479$	3.24086	+	5.61334i	0.148079	+	0.256480i	−0.782439	+	0.622728i	$0.786024\pi$
$480$		0			0
$481$	5.68732	−	9.85073i	0.259319	−	0.449154i
$482$	−0.783520	+	1.35710i	−0.0356884	+	0.0618141i
$483$		0			0
$484$	5.87686	+	10.1790i	0.267130	+	0.462683i
$485$	26.2317			1.19112
$486$		0			0
$487$	19.9828			0.905505			0.452753	−	0.891636i	$-0.350442\pi$
$487$	19.9828			0.905505			0.452753	+	0.891636i	$0.350442\pi$
$488$	−0.436524	−	0.756082i	−0.0197605	−	0.0342262i
$489$		0			0
$490$	−5.43242	+	9.40923i	−0.245412	+	0.425065i
$491$	13.1135	−	22.7133i	0.591806	−	1.02504i	−0.402183	−	0.915559i	$-0.631749\pi$
$491$	13.1135	−	22.7133i	0.591806	−	1.02504i	0.993989	−	0.109478i	$-0.0349181\pi$
$492$		0			0
$493$	−5.12583	−	8.87820i	−0.230856	−	0.399854i
$494$	57.8486			2.60273
$495$		0			0
$496$	18.1976			0.817096
$497$	−1.41198	−	2.44562i	−0.0633360	−	0.109701i
$498$		0			0
$499$	−3.15863	+	5.47091i	−0.141400	+	0.244912i	−0.928024	−	0.372520i	$-0.878494\pi$
$499$	−3.15863	+	5.47091i	−0.141400	+	0.244912i	0.786624	+	0.617432i	$0.211827\pi$
$500$	12.8783	−	22.3059i	0.575935	−	0.997549i
$501$		0			0
$502$	8.18866	+	14.1832i	0.365478	+	0.633026i
$503$	−21.8261			−0.973179			−0.486589	−	0.873631i	$-0.661759\pi$
$503$	−21.8261			−0.973179			−0.486589	+	0.873631i	$0.661759\pi$
$504$		0			0
$505$	17.3131			0.770425
$506$	1.11354	+	1.92871i	0.0495030	+	0.0857416i
$507$		0			0
$508$	−5.72416	+	9.91453i	−0.253968	+	0.439886i
$509$	−14.5466	+	25.1954i	−0.644765	+	1.11676i	0.339591	+	0.940573i	$0.389711\pi$
$509$	−14.5466	+	25.1954i	−0.644765	+	1.11676i	−0.984356	+	0.176192i	$0.943622\pi$
$510$		0			0
$511$	−5.49273	−	9.51368i	−0.242984	−	0.420860i
$512$	31.1704			1.37755
$513$		0			0
$514$	50.4620			2.22579
$515$	−25.2150	−	43.6737i	−1.11111	−	1.92449i
$516$		0			0
$517$	−0.258770	+	0.448204i	−0.0113807	+	0.0197120i
$518$	5.57445	−	9.65523i	0.244927	−	0.424226i
$519$		0			0
$520$	2.07398	+	3.59224i	0.0909499	+	0.157530i
$521$	−13.6949			−0.599982			−0.299991	−	0.953942i	$-0.596984\pi$
$521$	−13.6949			−0.599982			−0.299991	+	0.953942i	$0.596984\pi$
$522$		0			0
$523$	13.1506			0.575038			0.287519	−	0.957775i	$-0.407170\pi$
$523$	13.1506			0.575038			0.287519	+	0.957775i	$0.407170\pi$
$524$	9.72432	+	16.8430i	0.424809	+	0.735791i
$525$		0			0
$526$	27.6386	−	47.8715i	1.20510	−	2.08730i
$527$	6.31844	−	10.9439i	0.275236	−	0.476722i
$528$		0			0
$529$	11.3653	+	19.6853i	0.494144	+	0.855882i
$530$	34.0277			1.47807
$531$		0			0
$532$	27.4688			1.19093
$533$	−5.89279	−	10.2066i	−0.255245	−	0.442098i
$534$		0			0
$535$	−21.5326	+	37.2955i	−0.930934	+	1.61242i
$536$	1.69842	−	2.94175i	0.0733606	−	0.127064i
$537$		0			0
$538$	−29.7126	−	51.4637i	−1.28100	−	2.21876i
$539$	−3.24644			−0.139834
$540$		0			0
$541$	6.26083			0.269174			0.134587	−	0.990902i	$-0.457029\pi$
$541$	6.26083			0.269174			0.134587	+	0.990902i	$0.457029\pi$
$542$	18.7113	+	32.4090i	0.803721	+	1.39209i
$543$		0			0
$544$	11.5201	−	19.9533i	0.493919	−	0.855492i
$545$	27.0296	−	46.8166i	1.15782	−	2.00540i
$546$		0			0
$547$	15.6891	+	27.1744i	0.670819	+	1.16189i	0.977672	+	0.210135i	$0.0673905\pi$
$547$	15.6891	+	27.1744i	0.670819	+	1.16189i	−0.306854	+	0.951757i	$0.599276\pi$
$548$	−35.8674			−1.53218
$549$		0			0
$550$	37.3405			1.59220
$551$	10.8741	+	18.8346i	0.463254	+	0.802379i
$552$		0			0
$553$	−15.0235	+	26.0214i	−0.638863	+	1.10654i
$554$	−20.8007	+	36.0278i	−0.883736	+	1.53067i
$555$		0			0
$556$	21.8983	+	37.9289i	0.928694	+	1.60854i
$557$	−43.4392			−1.84058			−0.920290	−	0.391237i	$-0.872047\pi$
$557$	−43.4392			−1.84058			−0.920290	+	0.391237i	$0.872047\pi$
$558$		0			0
$559$	−5.01960			−0.212306
$560$	18.3626	+	31.8050i	0.775962	+	1.34401i
$561$		0			0
$562$	−1.72075	+	2.98043i	−0.0725855	+	0.125722i
$563$	16.0088	−	27.7281i	0.674691	−	1.16860i	−0.301868	−	0.953350i	$-0.597610\pi$
$563$	16.0088	−	27.7281i	0.674691	−	1.16860i	0.976559	−	0.215250i	$-0.0690565\pi$
$564$		0			0
$565$	−8.69119	−	15.0536i	−0.365641	−	0.633309i
$566$	−14.3549			−0.603381
$567$		0			0
$568$	0.285807			0.0119922
$569$	3.38597	+	5.86468i	0.141947	+	0.245860i	0.928230	−	0.372007i	$-0.121330\pi$
$569$	3.38597	+	5.86468i	0.141947	+	0.245860i	−0.786283	+	0.617867i	$0.787997\pi$
$570$		0			0
$571$	10.5765	−	18.3190i	0.442613	−	0.766628i	−0.555270	−	0.831670i	$-0.687385\pi$
$571$	10.5765	−	18.3190i	0.442613	−	0.766628i	0.997883	+	0.0650424i	$0.0207182\pi$
$572$	9.65614	−	16.7249i	0.403744	−	0.699304i
$573$		0			0
$574$	−5.77584	−	10.0041i	−0.241079	−	0.417561i
$575$	−4.51677			−0.188362
$576$		0			0
$577$	11.9162			0.496079			0.248039	−	0.968750i	$-0.420214\pi$
$577$	11.9162			0.496079			0.248039	+	0.968750i	$0.420214\pi$
$578$	8.25768	+	14.3027i	0.343474	+	0.594915i
$579$		0			0
$580$	12.1493	−	21.0432i	0.504472	−	0.873772i
$581$	13.2669	−	22.9789i	0.550403	−	0.953325i
$582$		0			0
$583$	5.08378	+	8.80536i	0.210549	+	0.364681i
$584$	1.11181			0.0460072
$585$		0			0
$586$	30.2354			1.24901
$587$	0.0649308	+	0.112463i	0.00267998	+	0.00464186i	0.867362	−	0.497677i	$-0.165814\pi$
$587$	0.0649308	+	0.112463i	0.00267998	+	0.00464186i	−0.864682	+	0.502319i	$0.832480\pi$
$588$		0			0
$589$	−13.4042	+	23.2168i	−0.552310	+	0.956630i
$590$	48.5286	−	84.0540i	1.99789	−	3.46045i
$591$		0			0
$592$	5.09627	+	8.82699i	0.209455	+	0.362787i
$593$	26.2622			1.07846			0.539230	−	0.842158i	$-0.318715\pi$
$593$	26.2622			1.07846			0.539230	+	0.842158i	$0.318715\pi$
$594$		0			0
$595$	25.5030			1.04552
$596$	14.5708	+	25.2374i	0.596844	+	1.03376i
$597$		0			0
$598$	−2.41101	+	4.17599i	−0.0985934	+	0.170769i
$599$	−13.7976	+	23.8981i	−0.563754	+	0.976450i	0.433411	+	0.901197i	$0.357310\pi$
$599$	−13.7976	+	23.8981i	−0.563754	+	0.976450i	−0.997164	+	0.0752537i	$0.976023\pi$
$600$		0			0
$601$	−0.666374	−	1.15419i	−0.0271820	−	0.0470806i	0.852114	−	0.523356i	$-0.175320\pi$
$601$	−0.666374	−	1.15419i	−0.0271820	−	0.0470806i	−0.879296	+	0.476275i	$0.841987\pi$
$602$	−4.91998			−0.200524
$603$		0			0
$604$	−11.0915			−0.451308
$605$	−11.5752	−	20.0488i	−0.470597	−	0.815098i
$606$		0			0
$607$	6.28224	−	10.8812i	0.254988	−	0.441653i	−0.709904	−	0.704298i	$-0.751262\pi$
$607$	6.28224	−	10.8812i	0.254988	−	0.441653i	0.964892	+	0.262646i	$0.0845950\pi$
$608$	−24.4391	+	42.3298i	−0.991138	+	1.71670i
$609$		0			0
$610$	−13.3969	−	23.2042i	−0.542426	−	0.939509i
$611$	−1.12056			−0.0453332
$612$		0			0
$613$	−13.9982			−0.565384			−0.282692	−	0.959211i	$-0.591227\pi$
$613$	−13.9982			−0.565384			−0.282692	+	0.959211i	$0.591227\pi$
$614$	−16.5091	−	28.5947i	−0.666255	−	1.15399i
$615$		0			0
$616$	−0.607411	+	1.05207i	−0.0244733	+	0.0423890i
$617$	−12.0234	+	20.8251i	−0.484042	+	0.838386i	−0.999832	−	0.0183296i	$-0.994165\pi$
$617$	−12.0234	+	20.8251i	−0.484042	+	0.838386i	0.515790	+	0.856715i	$0.327499\pi$
$618$		0			0
$619$	−3.43582	−	5.95102i	−0.138097	−	0.239192i	0.788679	−	0.614805i	$-0.210765\pi$
$619$	−3.43582	−	5.95102i	−0.138097	−	0.239192i	−0.926776	+	0.375614i	$0.877432\pi$
$620$	29.9521			1.20291
$621$		0			0
$622$	−31.5594			−1.26542
$623$	−0.820717	−	1.42152i	−0.0328813	−	0.0569521i
$624$		0			0
$625$	−3.60947	+	6.25179i	−0.144379	+	0.250071i
$626$	−33.8829	+	58.6869i	−1.35423	+	2.34560i
$627$		0			0
$628$	1.13903	+	1.97286i	0.0454524	+	0.0787258i
$629$	7.07797			0.282217
$630$		0			0
$631$	−35.3773			−1.40835			−0.704175	−	0.710027i	$-0.748683\pi$
$631$	−35.3773			−1.40835			−0.704175	+	0.710027i	$0.748683\pi$
$632$	−1.52049	−	2.63357i	−0.0604819	−	0.104758i
$633$		0			0
$634$	16.0633	−	27.8225i	0.637955	−	1.10497i
$635$	11.2744	−	19.5278i	0.447410	−	0.774937i
$636$		0			0
$637$	−3.51455	−	6.08738i	−0.139251	−	0.241191i
$638$	14.9869			0.593338
$639$		0			0
$640$	−7.02229			−0.277580
$641$	9.58683	+	16.6049i	0.378657	+	0.655854i	0.990867	−	0.134842i	$-0.0430526\pi$
$641$	9.58683	+	16.6049i	0.378657	+	0.655854i	−0.612210	+	0.790695i	$0.709719\pi$
$642$		0			0
$643$	−9.68820	+	16.7804i	−0.382065	+	0.661756i	−0.991357	−	0.131190i	$-0.958120\pi$
$643$	−9.68820	+	16.7804i	−0.382065	+	0.661756i	0.609292	+	0.792946i	$0.291454\pi$
$644$	−1.14484	+	1.98293i	−0.0451131	+	0.0781382i
$645$		0			0
$646$	17.9984	+	31.1742i	0.708138	+	1.22653i
$647$	8.77141			0.344840			0.172420	−	0.985024i	$-0.444841\pi$
$647$	8.77141			0.344840			0.172420	+	0.985024i	$0.444841\pi$
$648$		0			0
$649$	29.0009			1.13839
$650$	40.4243	+	70.0169i	1.58557	+	2.74629i
$651$		0			0
$652$	−2.60607	+	4.51384i	−0.102061	+	0.176776i
$653$	−16.4047	+	28.4138i	−0.641965	+	1.11192i	0.343029	+	0.939325i	$0.388547\pi$
$653$	−16.4047	+	28.4138i	−0.641965	+	1.11192i	−0.984994	+	0.172591i	$0.944786\pi$
$654$		0			0
$655$	−19.1532	−	33.1743i	−0.748376	−	1.29623i
$656$	10.5608			0.412329
$657$		0			0
$658$	−1.09833			−0.0428172
$659$	−9.32580	−	16.1528i	−0.363282	−	0.629222i	0.625217	−	0.780451i	$-0.285010\pi$
$659$	−9.32580	−	16.1528i	−0.363282	−	0.629222i	−0.988499	+	0.151229i	$0.951677\pi$
$660$		0			0
$661$	−18.2037	+	31.5297i	−0.708041	+	1.22636i	0.257542	+	0.966267i	$0.417087\pi$
$661$	−18.2037	+	31.5297i	−0.708041	+	1.22636i	−0.965583	+	0.260096i	$0.916246\pi$
$662$	31.1002	−	53.8671i	1.20874	−	2.09360i
$663$		0			0
$664$	1.34271	+	2.32564i	0.0521073	+	0.0902525i
$665$	−54.1031			−2.09803
$666$		0			0
$667$	−1.81284			−0.0701936
$668$	−3.59721	−	6.23055i	−0.139180	−	0.241067i
$669$		0			0
$670$	52.1245	−	90.2824i	2.01375	−	3.48791i
$671$	4.00303	−	6.93346i	0.154535	−	0.267663i
$672$		0			0
$673$	−19.6951	−	34.1128i	−0.759189	−	1.31495i	−0.943265	−	0.332041i	$-0.892263\pi$
$673$	−19.6951	−	34.1128i	−0.759189	−	1.31495i	0.184076	−	0.982912i	$-0.441071\pi$
$674$	11.8276			0.455584
$675$		0			0
$676$	17.3824			0.668553
$677$	−15.8377	−	27.4317i	−0.608692	−	1.05429i	−0.991456	−	0.130440i	$-0.958361\pi$
$677$	−15.8377	−	27.4317i	−0.608692	−	1.05429i	0.382764	−	0.923846i	$-0.374972\pi$
$678$		0			0
$679$	−8.31702	+	14.4055i	−0.319178	+	0.552832i
$680$	−1.29055	+	2.23530i	−0.0494904	+	0.0857198i
$681$		0			0
$682$	9.23695	+	15.9989i	0.353701	+	0.612628i
$683$	−29.0656			−1.11217			−0.556083	−	0.831127i	$-0.687696\pi$
$683$	−29.0656			−1.11217			−0.556083	+	0.831127i	$0.687696\pi$
$684$		0			0
$685$	70.6451			2.69921
$686$	−19.6262	−	33.9937i	−0.749334	−	1.29788i
$687$		0			0
$688$	2.24897	−	3.89533i	0.0857412	−	0.148508i
$689$	−11.0072	+	19.0651i	−0.419343	+	0.726323i
$690$		0			0
$691$	−2.67870	−	4.63965i	−0.101903	−	0.176500i	0.810566	−	0.585647i	$-0.199160\pi$
$691$	−2.67870	−	4.63965i	−0.101903	−	0.176500i	−0.912468	+	0.409147i	$0.865826\pi$
$692$	13.2110			0.502206
$693$		0			0
$694$	45.3610			1.72188
$695$	−43.1312	−	74.7054i	−1.63606	−	2.83374i
$696$		0			0
$697$	3.66684	−	6.35115i	0.138892	−	0.240567i
$698$	11.3905	−	19.7290i	0.431138	−	0.746752i
$699$		0			0
$700$	19.1951	+	33.2468i	0.725505	+	1.25661i
$701$	−25.6536			−0.968922			−0.484461	−	0.874813i	$-0.660984\pi$
$701$	−25.6536			−0.968922			−0.484461	+	0.874813i	$0.660984\pi$
$702$		0			0
$703$	−15.0155			−0.566320
$704$	7.63327	+	13.2212i	0.287690	+	0.498293i
$705$		0			0
$706$	2.10220	−	3.64111i	0.0791172	−	0.137035i
$707$	−5.48930	+	9.50774i	−0.206446	+	0.357575i
$708$		0			0
$709$	2.34524	+	4.06207i	0.0880772	+	0.152554i	0.906698	−	0.421780i	$-0.138594\pi$
$709$	2.34524	+	4.06207i	0.0880772	+	0.152554i	−0.818621	+	0.574334i	$0.805261\pi$
$710$	8.77141			0.329185
$711$		0			0
$712$	0.166126			0.00622583
$713$	−1.11732	−	1.93525i	−0.0418438	−	0.0724757i
$714$		0			0
$715$	−19.0189	+	32.9417i	−0.711266	+	1.23195i
$716$	−13.5178	+	23.4136i	−0.505185	+	0.875007i
$717$		0			0
$718$	−23.8555	−	41.3189i	−0.890280	−	1.54201i
$719$	39.0669			1.45695			0.728476	−	0.685072i	$-0.240229\pi$
$719$	39.0669			1.45695			0.728476	+	0.685072i	$0.240229\pi$
$720$		0			0
$721$	31.9786			1.19095
$722$	−19.4712	−	33.7251i	−0.724643	−	1.25512i
$723$		0			0
$724$	−12.4042	+	21.4847i	−0.460998	+	0.798473i
$725$	−15.1976	+	26.3229i	−0.564423	+	0.977610i
$726$		0			0
$727$	5.41266	+	9.37500i	0.200744	+	0.347699i	0.948768	−	0.315972i	$-0.102331\pi$
$727$	5.41266	+	9.37500i	0.200744	+	0.347699i	−0.748024	+	0.663672i	$0.768997\pi$
$728$	−2.63030			−0.0974853
$729$		0			0
$730$	34.1215			1.26290
$731$	−1.56175	−	2.70502i	−0.0577632	−	0.100049i
$732$		0			0
$733$	1.70620	−	2.95523i	0.0630201	−	0.109154i	−0.832794	−	0.553583i	$-0.813260\pi$
$733$	1.70620	−	2.95523i	0.0630201	−	0.109154i	0.895814	+	0.444429i	$0.146593\pi$
$734$	2.79174	−	4.83544i	0.103045	−	0.178479i
$735$		0			0
$736$	−2.03714	−	3.52843i	−0.0750900	−	0.130060i
$737$	31.1499			1.14742
$738$		0			0
$739$	26.3010			0.967497			0.483748	−	0.875207i	$-0.339275\pi$
$739$	26.3010			0.967497			0.483748	+	0.875207i	$0.339275\pi$
$740$	8.38814	+	14.5287i	0.308354	+	0.534085i
$741$		0			0
$742$	−10.7888	+	18.6867i	−0.396069	+	0.686012i
$743$	−14.4719	+	25.0662i	−0.530924	+	0.919588i	0.468424	+	0.883504i	$0.344822\pi$
$743$	−14.4719	+	25.0662i	−0.530924	+	0.919588i	−0.999349	+	0.0360843i	$0.988512\pi$
$744$		0			0
$745$	−28.6989	−	49.7080i	−1.05145	−	1.82116i
$746$	−56.7907			−2.07925
$747$		0			0
$748$	12.0172			0.439394
$749$	−13.6542	−	23.6498i	−0.498914	−	0.864144i
$750$		0			0
$751$	9.72416	−	16.8427i	0.354839	−	0.614600i	−0.632251	−	0.774764i	$-0.717869\pi$
$751$	9.72416	−	16.8427i	0.354839	−	0.614600i	0.987090	+	0.160164i	$0.0512022\pi$
$752$	0.502055	−	0.869585i	0.0183081	−	0.0317105i
$753$		0			0
$754$	16.2246	+	28.1019i	0.590866	+	1.02341i
$755$	21.8460			0.795058
$756$		0			0
$757$	6.59627			0.239745			0.119873	−	0.992789i	$-0.461751\pi$
$757$	6.59627			0.239745			0.119873	+	0.992789i	$0.461751\pi$
$758$	−31.7094	−	54.9222i	−1.15174	−	1.99486i
$759$		0			0
$760$	2.73783	−	4.74205i	0.0993114	−	0.172012i
$761$	−5.16485	+	8.94578i	−0.187226	+	0.324284i	−0.944324	−	0.329016i	$-0.893283\pi$
$761$	−5.16485	+	8.94578i	−0.187226	+	0.324284i	0.757099	+	0.653301i	$0.226616\pi$
$762$		0			0
$763$	17.1400	+	29.6873i	0.620508	+	1.07475i
$764$	−25.2276			−0.912703
$765$		0			0
$766$	1.32407			0.0478407
$767$	31.3960	+	54.3794i	1.13364	+	1.96353i
$768$		0			0
$769$	−22.4295	+	38.8490i	−0.808828	+	1.40093i	0.104848	+	0.994488i	$0.466564\pi$
$769$	−22.4295	+	38.8490i	−0.808828	+	1.40093i	−0.913676	+	0.406443i	$0.866769\pi$
$770$	−18.6414	+	32.2879i	−0.671791	+	1.16358i
$771$		0			0
$772$	−14.1001	−	24.4222i	−0.507475	−	0.878973i
$773$	42.9355			1.54428			0.772141	−	0.635452i	$-0.219186\pi$
$773$	42.9355			1.54428			0.772141	+	0.635452i	$0.219186\pi$
$774$		0			0
$775$	−37.4671			−1.34586
$776$	−0.841747	−	1.45795i	−0.0302170	−	0.0523373i
$777$		0			0
$778$	4.19459	−	7.26525i	0.150383	−	0.260472i
$779$	−7.77898	+	13.4736i	−0.278711	+	0.482742i
$780$		0			0
$781$	1.31046	+	2.26978i	0.0468919	+	0.0812192i
$782$	−3.00054			−0.107299
$783$		0			0
$784$	6.29860			0.224950
$785$	−2.24346	−	3.88578i	−0.0800724	−	0.138690i
$786$		0			0
$787$	−0.238703	+	0.413446i	−0.00850885	+	0.0147378i	−0.870248	−	0.492613i	$-0.836042\pi$
$787$	−0.238703	+	0.413446i	−0.00850885	+	0.0147378i	0.861740	+	0.507351i	$0.169375\pi$
$788$	−20.9750	+	36.3298i	−0.747204	+	1.29420i
$789$		0			0
$790$	−46.6639	−	80.8243i	−1.66023	−	2.87560i
$791$	11.0225			0.391915
$792$		0			0
$793$	17.3345			0.615566
$794$	8.73016	+	15.1211i	0.309822	+	0.536627i
$795$		0			0
$796$	8.55216	−	14.8128i	0.303123	−	0.525025i
$797$	−5.73448	+	9.93242i	−0.203126	+	0.351824i	−0.949534	−	0.313664i	$-0.898443\pi$
$797$	−5.73448	+	9.93242i	−0.203126	+	0.351824i	0.746408	+	0.665488i	$0.231777\pi$
$798$		0			0
$799$	−0.348641	−	0.603863i	−0.0123340	−	0.0213631i
$800$	−68.3116			−2.41518
$801$		0			0
$802$	73.0411			2.57917
$803$	5.09780	+	8.82965i	0.179897	+	0.311592i
$804$		0			0
$805$	2.25490	−	3.90560i	0.0794748	−	0.137654i
$806$	−19.9996	+	34.6403i	−0.704455	+	1.22015i
$807$		0			0
$808$	−0.555560	−	0.962258i	−0.0195445	−	0.0338521i
$809$	42.7873			1.50432			0.752161	−	0.658979i	$-0.229012\pi$
$809$	42.7873			1.50432			0.752161	+	0.658979i	$0.229012\pi$
$810$		0			0
$811$	−31.2098			−1.09592			−0.547962	−	0.836503i	$-0.684596\pi$
$811$	−31.2098			−1.09592			−0.547962	+	0.836503i	$0.684596\pi$
$812$	7.70410	+	13.3439i	0.270361	+	0.468279i
$813$		0			0
$814$	−5.17365	+	8.96102i	−0.181336	+	0.314084i
$815$	5.13295	−	8.89053i	0.179799	−	0.311422i
$816$		0			0
$817$	3.31315	+	5.73854i	0.115912	+	0.200766i
$818$	−6.67539			−0.233400
$819$		0			0
$820$	17.3824			0.607019
$821$	−13.6255	−	23.6001i	−0.475535	−	0.823650i	0.524072	−	0.851674i	$-0.324412\pi$
$821$	−13.6255	−	23.6001i	−0.475535	−	0.823650i	−0.999607	+	0.0280232i	$0.991079\pi$
$822$		0			0
$823$	7.22028	−	12.5059i	0.251683	−	0.435928i	−0.712306	−	0.701869i	$-0.752349\pi$
$823$	7.22028	−	12.5059i	0.251683	−	0.435928i	0.963989	+	0.265941i	$0.0856825\pi$
$824$	−1.61824	+	2.80288i	−0.0563742	+	0.0976430i
$825$		0			0
$826$	30.7729	+	53.3002i	1.07073	+	1.85455i
$827$	7.02757			0.244373			0.122186	−	0.992507i	$-0.461009\pi$
$827$	7.02757			0.244373			0.122186	+	0.992507i	$0.461009\pi$
$828$		0			0
$829$	−42.0806			−1.46152			−0.730760	−	0.682635i	$-0.760834\pi$
$829$	−42.0806			−1.46152			−0.730760	+	0.682635i	$0.760834\pi$
$830$	41.2078	+	71.3740i	1.43034	+	2.47743i
$831$		0			0
$832$	−16.5273	+	28.6262i	−0.572982	+	0.992435i
$833$	2.18696	−	3.78792i	0.0757736	−	0.131244i
$834$		0			0
$835$	7.08512	+	12.2718i	0.245191	+	0.424683i
$836$	−25.4938			−0.881723
$837$		0			0
$838$	−40.6851			−1.40544
$839$	19.9606	+	34.5729i	0.689118	+	1.19359i	0.972124	+	0.234469i	$0.0753352\pi$
$839$	19.9606	+	34.5729i	0.689118	+	1.19359i	−0.283006	+	0.959118i	$0.591331\pi$
$840$		0			0
$841$	8.40033	−	14.5498i	0.289667	−	0.501717i
$842$	−27.1147	+	46.9641i	−0.934435	+	1.61849i
$843$		0			0
$844$	5.61721	+	9.72930i	0.193352	+	0.334896i
$845$	−34.2366			−1.17777
$846$		0			0
$847$	14.6800			0.504412
$848$	−9.86332	−	17.0838i	−0.338708	−	0.586659i
$849$		0			0
$850$	−25.1544	+	43.5686i	−0.862787	+	1.49439i
$851$	0.625813	−	1.08394i	0.0214526	−	0.0371570i
$852$		0			0
$853$	11.7405	+	20.3352i	0.401988	+	0.696263i	0.993966	−	0.109691i	$-0.0349862\pi$
$853$	11.7405	+	20.3352i	0.401988	+	0.696263i	−0.591978	+	0.805954i	$0.701653\pi$
$854$	16.9905			0.581402
$855$		0			0
$856$	2.76382			0.0944655
$857$	4.01736	+	6.95827i	0.137230	+	0.237690i	0.926447	−	0.376425i	$-0.122847\pi$
$857$	4.01736	+	6.95827i	0.137230	+	0.237690i	−0.789217	+	0.614115i	$0.789513\pi$
$858$		0			0
$859$	12.1480	−	21.0409i	0.414483	−	0.717905i	−0.580891	−	0.813981i	$-0.697296\pi$
$859$	12.1480	−	21.0409i	0.414483	−	0.717905i	0.995374	+	0.0960758i	$0.0306291\pi$
$860$	3.70167	−	6.41147i	0.126226	−	0.218629i
$861$		0			0
$862$	2.54189	+	4.40268i	0.0865771	+	0.149956i
$863$	10.2828			0.350029			0.175015	−	0.984566i	$-0.444003\pi$
$863$	10.2828			0.350029			0.175015	+	0.984566i	$0.444003\pi$
$864$		0			0
$865$	−26.0205			−0.884725
$866$	26.6033	+	46.0783i	0.904018	+	1.56580i
$867$		0			0
$868$	−9.49660	+	16.4486i	−0.322335	+	0.558301i
$869$	13.9433	−	24.1505i	0.472994	−	0.819249i
$870$		0			0
$871$	33.7224	+	58.4089i	1.14264	+	1.97911i
$872$	−3.46940			−0.117489
$873$		0			0
$874$	6.36547			0.215315
$875$	−16.0846	−	27.8594i	−0.543759	−	0.941819i
$876$		0			0
$877$	13.1138	−	22.7138i	0.442822	−	0.766990i	−0.555076	−	0.831800i	$-0.687311\pi$
$877$	13.1138	−	22.7138i	0.442822	−	0.766990i	0.997898	+	0.0648099i	$0.0206441\pi$
$878$	−11.5322	+	19.9743i	−0.389192	+	0.674100i
$879$		0			0
$880$	−17.0424	−	29.5182i	−0.574498	−	0.995059i
$881$	39.2326			1.32178			0.660890	−	0.750483i	$-0.270179\pi$
$881$	39.2326			1.32178			0.660890	+	0.750483i	$0.270179\pi$
$882$		0			0
$883$	7.79830			0.262434			0.131217	−	0.991354i	$-0.458112\pi$
$883$	7.79830			0.262434			0.131217	+	0.991354i	$0.458112\pi$
$884$	13.0097	+	22.5334i	0.437563	+	0.757881i
$885$		0			0
$886$	−2.04916	+	3.54925i	−0.0688430	+	0.119240i
$887$	−11.4285	+	19.7948i	−0.383732	+	0.664644i	−0.991592	−	0.129400i	$-0.958695\pi$
$887$	−11.4285	+	19.7948i	−0.383732	+	0.664644i	0.607860	+	0.794044i	$0.292028\pi$
$888$		0			0
$889$	7.14930	+	12.3830i	0.239780	+	0.415311i
$890$	5.09840			0.170899
$891$		0			0
$892$	−16.7297			−0.560151
$893$	0.739620	+	1.28106i	0.0247504	+	0.0428690i
$894$		0			0
$895$	26.6250	−	46.1158i	0.889974	−	1.54148i
$896$	2.22648	−	3.85638i	0.0743816	−	0.128833i
$897$		0			0
$898$	−10.3905	−	17.9969i	−0.346736	−	0.600565i
$899$	−15.0377			−0.501537
$900$		0			0
$901$	−13.6987			−0.456370
$902$	5.36056	+	9.28477i	0.178487	+	0.309149i
$903$		0			0
$904$	−0.557781	+	0.966105i	−0.0185515	+	0.0321322i
$905$	24.4315	−	42.3166i	0.812131	−	1.40665i
$906$		0			0
$907$	18.9243	+	32.7778i	0.628370	+	1.08837i	0.987879	+	0.155227i	$0.0496109\pi$
$907$	18.9243	+	32.7778i	0.628370	+	1.08837i	−0.359509	+	0.933142i	$0.617056\pi$
$908$	20.0502			0.665388
$909$		0			0
$910$	−80.7238			−2.67597
$911$	−26.3522	−	45.6434i	−0.873089	−	1.51223i	−0.858785	−	0.512336i	$-0.828780\pi$
$911$	−26.3522	−	45.6434i	−0.873089	−	1.51223i	−0.0143040	−	0.999898i	$-0.504553\pi$
$912$		0			0
$913$	−12.3130	+	21.3267i	−0.407500	+	0.705811i
$914$	7.78925	−	13.4914i	0.257646	−	0.446255i
$915$		0			0
$916$	7.77244	+	13.4623i	0.256809	+	0.444806i
$917$	24.2908			0.802152
$918$		0			0
$919$	−49.1052			−1.61983			−0.809916	−	0.586545i	$-0.800488\pi$
$919$	−49.1052			−1.61983			−0.809916	+	0.586545i	$0.800488\pi$
$920$	0.228213	+	0.395277i	0.00752398	+	0.0130319i
$921$		0			0
$922$	38.4989	−	66.6820i	1.26789	−	2.19605i
$923$	−2.83737	+	4.91447i	−0.0933931	+	0.161762i
$924$		0			0
$925$	−10.4927	−	18.1739i	−0.344999	−	0.597555i
$926$	46.6658			1.53353
$927$		0			0
$928$	−27.4175			−0.900022
$929$	−8.97535	−	15.5458i	−0.294472	−	0.510040i	0.680390	−	0.732850i	$-0.261810\pi$
$929$	−8.97535	−	15.5458i	−0.294472	−	0.510040i	−0.974862	+	0.222810i	$0.928477\pi$
$930$		0			0
$931$	−4.63950	+	8.03585i	−0.152053	+	0.263364i
$932$	11.9710	−	20.7344i	0.392124	−	0.679179i
$933$		0			0
$934$	34.1878	+	59.2150i	1.11866	+	1.93757i
$935$	−23.6693			−0.774070
$936$		0			0
$937$	−29.7980			−0.973457			−0.486729	−	0.873553i	$-0.661810\pi$
$937$	−29.7980			−0.973457			−0.486729	+	0.873553i	$0.661810\pi$
$938$	33.0532	+	57.2497i	1.07922	+	1.86927i
$939$		0			0
$940$	0.826352	−	1.43128i	0.0269526	−	0.0466833i
$941$	15.0056	−	25.9905i	0.489169	−	0.847266i	−0.510753	−	0.859728i	$-0.670633\pi$
$941$	15.0056	−	25.9905i	0.489169	−	0.847266i	0.999922	+	0.0124613i	$0.00396665\pi$
$942$		0			0
$943$	−0.648423	−	1.12310i	−0.0211155	−	0.0365732i
$944$	−56.2663			−1.83131
$945$		0			0
$946$	4.56624			0.148461
$947$	−22.8007	−	39.4919i	−0.740922	−	1.28331i	−0.952076	−	0.305862i	$-0.901055\pi$
$947$	−22.8007	−	39.4919i	−0.740922	−	1.28331i	0.211154	−	0.977453i	$-0.432278\pi$
$948$		0			0
$949$	−11.0376	+	19.1177i	−0.358296	+	0.620587i
$950$	53.3634	−	92.4282i	1.73134	−	2.99877i
$951$		0			0
$952$	−0.818363	−	1.41745i	−0.0265233	−	0.0459397i
$953$	−13.1957			−0.427451			−0.213726	−	0.976894i	$-0.568560\pi$
$953$	−13.1957			−0.427451			−0.213726	+	0.976894i	$0.568560\pi$
$954$		0			0
$955$	49.6887			1.60789
$956$	14.1100	+	24.4393i	0.456351	+	0.790423i
$957$		0			0
$958$	6.38326	−	11.0561i	0.206234	−	0.357207i
$959$	−22.3987	+	38.7957i	−0.723291	+	1.25278i
$960$		0			0
$961$	6.23173	+	10.7937i	0.201024	+	0.348183i
$962$	−22.4037			−0.722323
$963$		0			0
$964$	1.49525			0.0481588
$965$	27.7718	+	48.1023i	0.894007	+	1.54847i
$966$		0			0
$967$	10.0774	−	17.4545i	0.324067	−	0.561300i	−0.657256	−	0.753667i	$-0.728283\pi$
$967$	10.0774	−	17.4545i	0.324067	−	0.561300i	0.981323	+	0.192367i	$0.0616164\pi$
$968$	−0.742868	+	1.28668i	−0.0238767	+	0.0413556i
$969$		0			0
$970$	−25.8332	−	44.7444i	−0.829455	−	1.43666i
$971$	−26.5839			−0.853118			−0.426559	−	0.904460i	$-0.640274\pi$
$971$	−26.5839			−0.853118			−0.426559	+	0.904460i	$0.640274\pi$
$972$		0			0
$973$	54.7006			1.75362
$974$	−19.6792	−	34.0853i	−0.630562	−	1.09216i
$975$		0			0
$976$	−7.76651	+	13.4520i	−0.248600	+	0.430588i
$977$	−7.20204	+	12.4743i	−0.230414	+	0.399088i	−0.957930	−	0.287002i	$-0.907341\pi$
$977$	−7.20204	+	12.4743i	−0.230414	+	0.399088i	0.727516	+	0.686091i	$0.240675\pi$
$978$		0			0
$979$	0.761707	+	1.31932i	0.0243443	+	0.0421655i
$980$	10.3671			0.331165
$981$		0			0
$982$	−51.6573			−1.64845
$983$	21.4941	+	37.2288i	0.685554	+	1.18741i	0.973262	+	0.229696i	$0.0737733\pi$
$983$	21.4941	+	37.2288i	0.685554	+	1.18741i	−0.287708	+	0.957718i	$0.592893\pi$
$984$		0			0
$985$	41.3127	−	71.5558i	1.31633	−	2.27996i
$986$	−10.0959	+	17.4866i	−0.321519	+	0.556888i
$987$		0			0
$988$	−27.5993	−	47.8033i	−0.878049	−	1.52083i
$989$	−0.552340			−0.0175634
$990$		0			0
$991$	−15.5794			−0.494895			−0.247447	−	0.968901i	$-0.579592\pi$
$991$	−15.5794			−0.494895			−0.247447	+	0.968901i	$0.579592\pi$
$992$	−16.8983	−	29.2687i	−0.536522	−	0.929283i
$993$		0			0
$994$	−2.78106	+	4.81694i	−0.0882098	+	0.152784i
$995$	−16.8445	+	29.1755i	−0.534005	+	0.924924i
$996$		0			0
$997$	−20.3093	−	35.1767i	−0.643201	−	1.11406i	−0.984714	−	0.174180i	$-0.944273\pi$
$997$	−20.3093	−	35.1767i	−0.643201	−	1.11406i	0.341513	−	0.939877i	$-0.389061\pi$
$998$	12.4426			0.393863
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.c.244.1		12
3.2	odd	2	inner	729.2.c.c.244.6		12
9.2	odd	6	inner	729.2.c.c.487.6		12
9.4	even	3		729.2.a.c.1.6	yes	6
9.5	odd	6		729.2.a.c.1.1	✓	6
9.7	even	3	inner	729.2.c.c.487.1		12
27.2	odd	18		729.2.e.m.82.1		12
27.4	even	9		729.2.e.m.649.2		12
27.5	odd	18		729.2.e.r.163.2		12
27.7	even	9		729.2.e.r.568.1		12
27.11	odd	18		729.2.e.q.325.1		12
27.13	even	9		729.2.e.q.406.2		12
27.14	odd	18		729.2.e.q.406.1		12
27.16	even	9		729.2.e.q.325.2		12
27.20	odd	18		729.2.e.r.568.2		12
27.22	even	9		729.2.e.r.163.1		12
27.23	odd	18		729.2.e.m.649.1		12
27.25	even	9		729.2.e.m.82.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.1	✓	6	9.5	odd	6
729.2.a.c.1.6	yes	6	9.4	even	3
729.2.c.c.244.1		12	1.1	even	1	trivial
729.2.c.c.244.6		12	3.2	odd	2	inner
729.2.c.c.487.1		12	9.7	even	3	inner
729.2.c.c.487.6		12	9.2	odd	6	inner
729.2.e.m.82.1		12	27.2	odd	18
729.2.e.m.82.2		12	27.25	even	9
729.2.e.m.649.1		12	27.23	odd	18
729.2.e.m.649.2		12	27.4	even	9
729.2.e.q.325.1		12	27.11	odd	18
729.2.e.q.325.2		12	27.16	even	9
729.2.e.q.406.1		12	27.14	odd	18
729.2.e.q.406.2		12	27.13	even	9
729.2.e.r.163.1		12	27.22	even	9
729.2.e.r.163.2		12	27.5	odd	18
729.2.e.r.568.1		12	27.7	even	9
729.2.e.r.568.2		12	27.20	odd	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 1.70574i) q^{2} +(-0.939693 + 1.62760i) q^{4} +(1.85083 - 3.20574i) q^{5} +(1.17365 + 2.03282i) q^{7} -0.237565 q^{8} +O(q^{10})\)	\(q+(-0.984808 - 1.70574i) q^{2} +(-0.939693 + 1.62760i) q^{4} +(1.85083 - 3.20574i) q^{5} +(1.17365 + 2.03282i) q^{7} -0.237565 q^{8} -7.29086 q^{10} +(-1.08926 - 1.88666i) q^{11} +(2.35844 - 4.08494i) q^{13} +(2.31164 - 4.00387i) q^{14} +(2.11334 + 3.66041i) q^{16} +2.93512 q^{17} -6.22668 q^{19} +(3.47843 + 6.02481i) q^{20} +(-2.14543 + 3.71599i) q^{22} +(0.259515 - 0.449493i) q^{23} +(-4.35117 - 7.53644i) q^{25} -9.29044 q^{26} -4.41147 q^{28} +(-1.74638 - 3.02481i) q^{29} +(2.15270 - 3.72859i) q^{31} +(3.92490 - 6.79813i) q^{32} +(-2.89053 - 5.00654i) q^{34} +8.68891 q^{35} +2.41147 q^{37} +(6.13208 + 10.6211i) q^{38} +(-0.439693 + 0.761570i) q^{40} +(1.24930 - 2.16385i) q^{41} +(-0.532089 - 0.921605i) q^{43} +4.09429 q^{44} -1.02229 q^{46} +(-0.118782 - 0.205737i) q^{47} +(0.745100 - 1.29055i) q^{49} +(-8.57013 + 14.8439i) q^{50} +(4.43242 + 7.67717i) q^{52} -4.66717 q^{53} -8.06418 q^{55} +(-0.278817 - 0.482926i) q^{56} +(-3.43969 + 5.95772i) q^{58} +(-6.65609 + 11.5287i) q^{59} +(1.83750 + 3.18264i) q^{61} -8.48000 q^{62} -7.00774 q^{64} +(-8.73016 - 15.1211i) q^{65} +(-7.14930 + 12.3830i) q^{67} +(-2.75811 + 4.77719i) q^{68} +(-8.55690 - 14.8210i) q^{70} -1.20307 q^{71} -4.68004 q^{73} +(-2.37484 - 4.11334i) q^{74} +(5.85117 - 10.1345i) q^{76} +(2.55682 - 4.42855i) q^{77} +(6.40033 + 11.0857i) q^{79} +15.6458 q^{80} -4.92127 q^{82} +(-5.65198 - 9.78952i) q^{83} +(5.43242 - 9.40923i) q^{85} +(-1.04801 + 1.81521i) q^{86} +(0.258770 + 0.448204i) q^{88} -0.699287 q^{89} +11.0719 q^{91} +(0.487728 + 0.844770i) q^{92} +(-0.233956 + 0.405223i) q^{94} +(-11.5245 + 19.9611i) q^{95} +(3.54323 + 6.13706i) q^{97} -2.93512 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{7}+O(q^{10}) \) 12 * q + 12 * q^7	\( 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) \) 12 * q + 12 * q^7 - 24 * q^10 + 12 * q^13 + 12 * q^16 - 48 * q^19 + 6 * q^22 - 12 * q^28 + 30 * q^31 - 12 * q^37 + 6 * q^40 + 12 * q^43 + 12 * q^46 + 6 * q^49 + 6 * q^52 - 60 * q^55 - 30 * q^58 + 12 * q^61 + 12 * q^64 - 6 * q^67 - 30 * q^70 + 24 * q^73 + 18 * q^76 + 48 * q^79 - 24 * q^82 + 18 * q^85 - 42 * q^88 - 12 * q^94 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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