LMFDB - Embedded newform 432.2.k.c.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, degree $2$, 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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	432.109
Dual form			432.2.k.c.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37261 - 0.340511i) q^{2} +(1.76810 + 0.934777i) q^{4} +(2.75203 - 2.75203i) q^{5} +0.113492i q^{7} +(-2.10861 - 1.88514i) q^{8} +O(q^{10})$	\(q+(-1.37261 - 0.340511i) q^{2} +(1.76810 + 0.934777i) q^{4} +(2.75203 - 2.75203i) q^{5} +0.113492i q^{7} +(-2.10861 - 1.88514i) q^{8} +(-4.71455 + 2.84036i) q^{10} +(3.69189 - 3.69189i) q^{11} +(-1.53621 - 1.53621i) q^{13} +(0.0386454 - 0.155780i) q^{14} +(2.25239 + 3.30557i) q^{16} -6.62546 q^{17} +(3.27496 + 3.27496i) q^{19} +(7.43841 - 2.29334i) q^{20} +(-6.32464 + 3.81038i) q^{22} +6.20621i q^{23} -10.1473i q^{25} +(1.58552 + 2.63171i) q^{26} +(-0.106090 + 0.200666i) q^{28} +(-1.51869 - 1.51869i) q^{29} -1.10668 q^{31} +(-1.96606 - 5.30421i) q^{32} +(9.09416 + 2.25604i) q^{34} +(0.312334 + 0.312334i) q^{35} +(2.61794 - 2.61794i) q^{37} +(-3.38007 - 5.61040i) q^{38} +(-10.9909 + 0.614998i) q^{40} -9.18551i q^{41} +(3.18841 - 3.18841i) q^{43} +(9.97873 - 3.07655i) q^{44} +(2.11328 - 8.51869i) q^{46} +3.56868 q^{47} +6.98712 q^{49} +(-3.45528 + 13.9283i) q^{50} +(-1.28016 - 4.15219i) q^{52} +(-4.08624 + 4.08624i) q^{53} -20.3204i q^{55} +(0.213949 - 0.239311i) q^{56} +(1.56744 + 2.60170i) q^{58} +(-0.942793 + 0.942793i) q^{59} +(-0.437200 - 0.437200i) q^{61} +(1.51904 + 0.376837i) q^{62} +(0.892486 + 7.95006i) q^{64} -8.45538 q^{65} +(-3.26764 - 3.26764i) q^{67} +(-11.7145 - 6.19333i) q^{68} +(-0.322359 - 0.535066i) q^{70} +7.72504i q^{71} +10.2334i q^{73} +(-4.48485 + 2.70197i) q^{74} +(2.72911 + 8.85183i) q^{76} +(0.419001 + 0.419001i) q^{77} -1.25408 q^{79} +(15.2956 + 2.89838i) q^{80} +(-3.12777 + 12.6081i) q^{82} +(8.42400 + 8.42400i) q^{83} +(-18.2335 + 18.2335i) q^{85} +(-5.46213 + 3.29075i) q^{86} +(-14.7445 + 0.825028i) q^{88} +0.361163i q^{89} +(0.174348 - 0.174348i) q^{91} +(-5.80142 + 10.9732i) q^{92} +(-4.89840 - 1.21518i) q^{94} +18.0256 q^{95} +13.7287 q^{97} +(-9.59057 - 2.37919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{4}+O(q^{10}) $ 24 * q + 16 * q^4	$ 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) $ 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.37261	−	0.340511i	−0.970580	−	0.240778i
$2$	−1.37261	−	0.340511i	−0.970580	−	0.240778i
$3$		0			0
$3$		0			0
$4$	1.76810	+	0.934777i	0.884052	+	0.467388i
$5$	2.75203	−	2.75203i	1.23075	−	1.23075i	0.267067	−	0.963678i	$-0.413945\pi$
$5$	2.75203	−	2.75203i	1.23075	−	1.23075i	0.963678	−	0.267067i	$-0.0860546\pi$
$6$		0			0
$7$			0.113492i			0.0428961i	0.999770	+	0.0214480i	$0.00682764\pi$
$7$			0.113492i			0.0428961i	−0.999770	+	0.0214480i	$0.993172\pi$
$8$	−2.10861	−	1.88514i	−0.745507	−	0.666498i
$9$		0			0
$10$	−4.71455	+	2.84036i	−1.49087	+	0.898201i
$11$	3.69189	−	3.69189i	1.11315	−	1.11315i	0.120423	−	0.992723i	$-0.461575\pi$
$11$	3.69189	−	3.69189i	1.11315	−	1.11315i	0.992723	−	0.120423i	$-0.0384251\pi$
$12$		0			0
$13$	−1.53621	−	1.53621i	−0.426068	−	0.426068i	0.461219	−	0.887286i	$-0.347412\pi$
$13$	−1.53621	−	1.53621i	−0.426068	−	0.426068i	−0.887286	+	0.461219i	$0.847412\pi$
$14$	0.0386454	−	0.155780i	0.0103284	−	0.0416341i
$15$		0			0
$16$	2.25239	+	3.30557i	0.563096	+	0.826391i
$17$	−6.62546			−1.60691			−0.803455	−	0.595365i	$-0.797007\pi$
$17$	−6.62546			−1.60691			−0.803455	+	0.595365i	$0.797007\pi$
$18$		0			0
$19$	3.27496	+	3.27496i	0.751327	+	0.751327i	0.974727	−	0.223400i	$-0.0717155\pi$
$19$	3.27496	+	3.27496i	0.751327	+	0.751327i	−0.223400	+	0.974727i	$0.571715\pi$
$20$	7.43841	−	2.29334i	1.66328	−	0.512807i
$21$		0			0
$22$	−6.32464	+	3.81038i	−1.34842	+	0.812377i
$23$			6.20621i			1.29408i	0.762454	+	0.647042i	$0.223994\pi$
$23$			6.20621i			1.29408i	−0.762454	+	0.647042i	$0.776006\pi$
$24$		0			0
$25$		−	10.1473i		−	2.02947i
$26$	1.58552	+	2.63171i	0.310945	+	0.516120i
$27$		0			0
$28$	−0.106090	+	0.200666i	−0.0200491	+	0.0379224i
$29$	−1.51869	−	1.51869i	−0.282014	−	0.282014i	0.551898	−	0.833912i	$-0.313904\pi$
$29$	−1.51869	−	1.51869i	−0.282014	−	0.282014i	−0.833912	+	0.551898i	$0.813904\pi$
$30$		0			0
$31$	−1.10668			−0.198766			−0.0993829	−	0.995049i	$-0.531687\pi$
$31$	−1.10668			−0.198766			−0.0993829	+	0.995049i	$0.531687\pi$
$32$	−1.96606	−	5.30421i	−0.347553	−	0.937660i
$33$		0			0
$34$	9.09416	+	2.25604i	1.55964	+	0.386908i
$35$	0.312334	+	0.312334i	0.0527941	+	0.0527941i
$36$		0			0
$37$	2.61794	−	2.61794i	0.430387	−	0.430387i	−0.458373	−	0.888760i	$-0.651568\pi$
$37$	2.61794	−	2.61794i	0.430387	−	0.430387i	0.888760	+	0.458373i	$0.151568\pi$
$38$	−3.38007	−	5.61040i	−0.548321	−	0.910126i
$39$		0			0
$40$	−10.9909	+	0.614998i	−1.73782	+	0.0972397i
$41$		−	9.18551i		−	1.43453i	−0.696798	−	0.717267i	$-0.745393\pi$
$41$		−	9.18551i		−	1.43453i	0.696798	−	0.717267i	$-0.254607\pi$
$42$		0			0
$43$	3.18841	−	3.18841i	0.486229	−	0.486229i	−0.420885	−	0.907114i	$-0.638281\pi$
$43$	3.18841	−	3.18841i	0.486229	−	0.486229i	0.907114	+	0.420885i	$0.138281\pi$
$44$	9.97873	−	3.07655i	1.50435	−	0.463808i
$45$		0			0
$46$	2.11328	−	8.51869i	0.311587	−	1.25601i
$47$	3.56868			0.520546			0.260273	−	0.965535i	$-0.416187\pi$
$47$	3.56868			0.520546			0.260273	+	0.965535i	$0.416187\pi$
$48$		0			0
$49$	6.98712			0.998160
$50$	−3.45528	+	13.9283i	−0.488651	+	1.96976i
$51$		0			0
$52$	−1.28016	−	4.15219i	−0.177527	−	0.575805i
$53$	−4.08624	+	4.08624i	−0.561289	+	0.561289i	−0.929673	−	0.368385i	$-0.879911\pi$
$53$	−4.08624	+	4.08624i	−0.561289	+	0.561289i	0.368385	+	0.929673i	$0.379911\pi$
$54$		0			0
$55$		−	20.3204i		−	2.74000i
$56$	0.213949	−	0.239311i	0.0285901	−	0.0319793i
$57$		0			0
$58$	1.56744	+	2.60170i	0.205815	+	0.341620i
$59$	−0.942793	+	0.942793i	−0.122741	+	0.122741i	−0.765809	−	0.643068i	$-0.777661\pi$
$59$	−0.942793	+	0.942793i	−0.122741	+	0.122741i	0.643068	+	0.765809i	$0.277661\pi$
$60$		0			0
$61$	−0.437200	−	0.437200i	−0.0559777	−	0.0559777i	0.678564	−	0.734542i	$-0.262603\pi$
$61$	−0.437200	−	0.437200i	−0.0559777	−	0.0559777i	−0.734542	+	0.678564i	$0.762603\pi$
$62$	1.51904	+	0.376837i	0.192918	+	0.0478584i
$63$		0			0
$64$	0.892486	+	7.95006i	0.111561	+	0.993758i
$65$	−8.45538			−1.04876
$66$		0			0
$67$	−3.26764	−	3.26764i	−0.399206	−	0.399206i	0.478747	−	0.877953i	$-0.341091\pi$
$67$	−3.26764	−	3.26764i	−0.399206	−	0.399206i	−0.877953	+	0.478747i	$0.841091\pi$
$68$	−11.7145	−	6.19333i	−1.42059	−	0.751051i
$69$		0			0
$70$	−0.322359	−	0.535066i	−0.0385293	−	0.0639526i
$71$			7.72504i			0.916794i	0.888748	+	0.458397i	$0.151576\pi$
$71$			7.72504i			0.916794i	−0.888748	+	0.458397i	$0.848424\pi$
$72$		0			0
$73$			10.2334i			1.19773i	0.800851	+	0.598863i	$0.204381\pi$
$73$			10.2334i			1.19773i	−0.800851	+	0.598863i	$0.795619\pi$
$74$	−4.48485	+	2.70197i	−0.521353	+	0.314097i
$75$		0			0
$76$	2.72911	+	8.85183i	0.313051	+	1.01537i
$77$	0.419001	+	0.419001i	0.0477496	+	0.0477496i
$78$		0			0
$79$	−1.25408			−0.141095			−0.0705476	−	0.997508i	$-0.522475\pi$
$79$	−1.25408			−0.141095			−0.0705476	+	0.997508i	$0.522475\pi$
$80$	15.2956	+	2.89838i	1.71011	+	0.324049i
$81$		0			0
$82$	−3.12777	+	12.6081i	−0.345404	+	1.39233i
$83$	8.42400	+	8.42400i	0.924655	+	0.924655i	0.997354	−	0.0726993i	$-0.0231613\pi$
$83$	8.42400	+	8.42400i	0.924655	+	0.924655i	−0.0726993	+	0.997354i	$0.523161\pi$
$84$		0			0
$85$	−18.2335	+	18.2335i	−1.97770	+	1.97770i
$86$	−5.46213	+	3.29075i	−0.588997	+	0.354851i
$87$		0			0
$88$	−14.7445	+	0.825028i	−1.57177	+	0.0879483i
$89$			0.361163i			0.0382832i	0.999817	+	0.0191416i	$0.00609333\pi$
$89$			0.361163i			0.0382832i	−0.999817	+	0.0191416i	$0.993907\pi$
$90$		0			0
$91$	0.174348	−	0.174348i	0.0182766	−	0.0182766i
$92$	−5.80142	+	10.9732i	−0.604840	+	1.14404i
$93$		0			0
$94$	−4.89840	−	1.21518i	−0.505232	−	0.125336i
$95$	18.0256			1.84938
$96$		0			0
$97$	13.7287			1.39393			0.696967	−	0.717103i	$-0.254532\pi$
$97$	13.7287			1.39393			0.696967	+	0.717103i	$0.254532\pi$
$98$	−9.59057	−	2.37919i	−0.968794	−	0.240335i
$99$		0			0
$100$	9.48550	−	17.9416i	0.948550	−	1.79416i
$101$	1.77365	−	1.77365i	0.176485	−	0.176485i	−0.613337	−	0.789821i	$-0.710173\pi$
$101$	1.77365	−	1.77365i	0.176485	−	0.176485i	0.789821	+	0.613337i	$0.210173\pi$
$102$		0			0
$103$			1.38364i			0.136334i	0.997674	+	0.0681671i	$0.0217151\pi$
$103$			1.38364i			0.136334i	−0.997674	+	0.0681671i	$0.978285\pi$
$104$	0.343297	+	6.13524i	0.0336631	+	0.601609i
$105$		0			0
$106$	7.00022	−	4.21740i	0.679922	−	0.409630i
$107$	−6.80898	+	6.80898i	−0.658249	+	0.658249i	−0.954966	−	0.296717i	$-0.904108\pi$
$107$	−6.80898	+	6.80898i	−0.658249	+	0.658249i	0.296717	+	0.954966i	$0.404108\pi$
$108$		0			0
$109$	2.42307	+	2.42307i	0.232088	+	0.232088i	0.813564	−	0.581476i	$-0.197524\pi$
$109$	2.42307	+	2.42307i	0.232088	+	0.232088i	−0.581476	+	0.813564i	$0.697524\pi$
$110$	−6.91931	+	27.8919i	−0.659731	+	2.65939i
$111$		0			0
$112$	−0.375156	+	0.255628i	−0.0354489	+	0.0241546i
$113$	10.0794			0.948189			0.474095	−	0.880474i	$-0.342775\pi$
$113$	10.0794			0.948189			0.474095	+	0.880474i	$0.342775\pi$
$114$		0			0
$115$	17.0797	+	17.0797i	1.59269	+	1.59269i
$116$	−1.26557	−	4.10485i	−0.117505	−	0.381125i
$117$		0			0
$118$	1.61512	−	0.973053i	0.148683	−	0.0895768i
$119$		−	0.751939i		−	0.0689301i
$120$		0			0
$121$		−	16.2601i		−	1.47819i
$122$	0.451233	+	0.748976i	0.0408527	+	0.0678091i
$123$		0			0
$124$	−1.95673	−	1.03450i	−0.175719	−	0.0929008i
$125$	−14.1656	−	14.1656i	−1.26701	−	1.26701i
$126$		0			0
$127$	−20.5524			−1.82373			−0.911864	−	0.410493i	$-0.865357\pi$
$127$	−20.5524			−1.82373			−0.911864	+	0.410493i	$0.865357\pi$
$128$	1.48205	−	11.2162i	0.130996	−	0.991383i
$129$		0			0
$130$	11.6059	+	2.87915i	1.01791	+	0.252518i
$131$	5.33417	+	5.33417i	0.466049	+	0.466049i	0.900632	−	0.434583i	$-0.143104\pi$
$131$	5.33417	+	5.33417i	0.466049	+	0.466049i	−0.434583	+	0.900632i	$0.643104\pi$
$132$		0			0
$133$	−0.371683	+	0.371683i	−0.0322290	+	0.0322290i
$134$	3.37252	+	5.59786i	0.291342	+	0.483581i
$135$		0			0
$136$	13.9705	+	12.4899i	1.19796	+	1.07100i
$137$			12.9748i			1.10851i	0.832345	+	0.554257i	$0.186998\pi$
$137$			12.9748i			1.10851i	−0.832345	+	0.554257i	$0.813002\pi$
$138$		0			0
$139$	−3.85224	+	3.85224i	−0.326743	+	0.326743i	−0.851347	−	0.524604i	$-0.824214\pi$
$139$	−3.85224	+	3.85224i	−0.326743	+	0.326743i	0.524604	+	0.851347i	$0.324214\pi$
$140$	0.260277	+	0.844202i	0.0219974	+	0.0713481i
$141$		0			0
$142$	2.63046	−	10.6035i	0.220744	−	0.889822i
$143$	−11.3430			−0.948551
$144$		0			0
$145$	−8.35898			−0.694175
$146$	3.48458	−	14.0464i	0.288386	−	1.16249i
$147$		0			0
$148$	7.07598	−	2.18160i	0.581642	−	0.179327i
$149$	−11.6686	+	11.6686i	−0.955925	+	0.955925i	−0.999069	−	0.0431435i	$-0.986263\pi$
$149$	−11.6686	+	11.6686i	−0.955925	+	0.955925i	0.0431435	+	0.999069i	$0.486263\pi$
$150$		0			0
$151$			8.86506i			0.721429i	0.932676	+	0.360714i	$0.117467\pi$
$151$			8.86506i			0.721429i	−0.932676	+	0.360714i	$0.882533\pi$
$152$	−0.731857	−	13.0794i	−0.0593615	−	1.06088i
$153$		0			0
$154$	−0.432449	−	0.717798i	−0.0348478	−	0.0578418i
$155$	−3.04562	+	3.04562i	−0.244630	+	0.244630i
$156$		0			0
$157$	3.16022	+	3.16022i	0.252213	+	0.252213i	0.821877	−	0.569664i	$-0.192927\pi$
$157$	3.16022	+	3.16022i	0.252213	+	0.252213i	−0.569664	+	0.821877i	$0.692927\pi$
$158$	1.72136	+	0.427029i	0.136944	+	0.0339726i
$159$		0			0
$160$	−20.0080	−	9.18668i	−1.58177	−	0.726271i
$161$	−0.704357			−0.0555111
$162$		0			0
$163$	12.6421	+	12.6421i	0.990207	+	0.990207i	0.999953	−	0.00974553i	$-0.00310215\pi$
$163$	12.6421	+	12.6421i	0.990207	+	0.990207i	−0.00974553	+	0.999953i	$0.503102\pi$
$164$	8.58640	−	16.2409i	0.670485	−	1.26820i
$165$		0			0
$166$	−8.69439	−	14.4313i	−0.674815	−	1.12009i
$167$		−	20.4420i		−	1.58185i	−0.611912	−	0.790926i	$-0.709599\pi$
$167$		−	20.4420i		−	1.58185i	0.611912	−	0.790926i	$-0.290401\pi$
$168$		0			0
$169$		−	8.28013i		−	0.636933i
$170$	31.2361	−	18.8187i	2.39570	−	1.44333i
$171$		0			0
$172$	8.61790	−	2.65699i	0.657109	−	0.202594i
$173$	−12.7456	−	12.7456i	−0.969033	−	0.969033i	0.0305017	−	0.999535i	$-0.490289\pi$
$173$	−12.7456	−	12.7456i	−0.969033	−	0.969033i	−0.999535	+	0.0305017i	$0.990289\pi$
$174$		0			0
$175$	1.15165			0.0870562
$176$	20.5193	+	3.88822i	1.54670	+	0.293086i
$177$		0			0
$178$	0.122980	−	0.495735i	0.00921774	−	0.0371569i
$179$	6.80898	+	6.80898i	0.508927	+	0.508927i	0.914197	−	0.405270i	$-0.132823\pi$
$179$	6.80898	+	6.80898i	0.508927	+	0.508927i	−0.405270	+	0.914197i	$0.632823\pi$
$180$		0			0
$181$	−15.2537	+	15.2537i	−1.13380	+	1.13380i	−0.144255	+	0.989540i	$0.546079\pi$
$181$	−15.2537	+	15.2537i	−1.13380	+	1.13380i	−0.989540	+	0.144255i	$0.953921\pi$
$182$	−0.298679	+	0.179944i	−0.0221395	+	0.0133383i
$183$		0			0
$184$	11.6996	−	13.0865i	0.862504	−	0.964748i
$185$		−	14.4093i		−	1.05939i
$186$		0			0
$187$	−24.4605	+	24.4605i	−1.78873	+	1.78873i
$188$	6.30981	+	3.33592i	0.460190	+	0.243297i
$189$		0			0
$190$	−24.7420	−	6.13791i	−1.79498	−	0.445291i
$191$	−23.4798			−1.69894			−0.849471	−	0.527635i	$-0.823079\pi$
$191$	−23.4798			−1.69894			−0.849471	+	0.527635i	$0.823079\pi$
$192$		0			0
$193$	17.2922			1.24472			0.622359	−	0.782732i	$-0.286174\pi$
$193$	17.2922			1.24472			0.622359	+	0.782732i	$0.286174\pi$
$194$	−18.8441	−	4.67476i	−1.35293	−	0.335628i
$195$		0			0
$196$	12.3540	+	6.53140i	0.882425	+	0.466528i
$197$	2.24892	−	2.24892i	0.160229	−	0.160229i	−0.622439	−	0.782668i	$-0.713858\pi$
$197$	2.24892	−	2.24892i	0.160229	−	0.160229i	0.782668	+	0.622439i	$0.213858\pi$
$198$		0			0
$199$		−	7.79871i		−	0.552836i	−0.961038	−	0.276418i	$-0.910853\pi$
$199$		−	7.79871i		−	0.552836i	0.961038	−	0.276418i	$-0.0891473\pi$
$200$	−19.1292	+	21.3968i	−1.35264	+	1.51298i
$201$		0			0
$202$	−3.03847	+	1.83058i	−0.213786	+	0.128799i
$203$	0.172360	−	0.172360i	0.0120973	−	0.0120973i
$204$		0			0
$205$	−25.2788	−	25.2788i	−1.76555	−	1.76555i
$206$	0.471145	−	1.89920i	0.0328262	−	0.132323i
$207$		0			0
$208$	1.61790	−	8.53817i	0.112181	−	0.592016i
$209$	24.1816			1.67267
$210$		0			0
$211$	5.34057	+	5.34057i	0.367660	+	0.367660i	0.866623	−	0.498963i	$-0.166286\pi$
$211$	5.34057	+	5.34057i	0.367660	+	0.367660i	−0.498963	+	0.866623i	$0.666286\pi$
$212$	−11.0446	+	3.40518i	−0.758548	+	0.233869i
$213$		0			0
$214$	11.6646	−	7.02752i	0.797375	−	0.480392i
$215$		−	17.5492i		−	1.19685i
$216$		0			0
$217$		−	0.125600i		−	0.00852627i
$218$	−2.50084	−	4.15101i	−0.169379	−	0.281142i
$219$		0			0
$220$	18.9950	−	35.9285i	1.28064	−	2.42230i
$221$	10.1781	+	10.1781i	0.684652	+	0.684652i
$222$		0			0
$223$	−4.29188			−0.287405			−0.143703	−	0.989621i	$-0.545901\pi$
$223$	−4.29188			−0.287405			−0.143703	+	0.989621i	$0.545901\pi$
$224$	0.601987	−	0.223133i	0.0402219	−	0.0149087i
$225$		0			0
$226$	−13.8350	−	3.43214i	−0.920294	−	0.228303i
$227$	4.46745	+	4.46745i	0.296515	+	0.296515i	0.839647	−	0.543132i	$-0.182762\pi$
$227$	4.46745	+	4.46745i	0.296515	+	0.296515i	−0.543132	+	0.839647i	$0.682762\pi$
$228$		0			0
$229$	3.71695	−	3.71695i	0.245623	−	0.245623i	−0.573549	−	0.819172i	$-0.694434\pi$
$229$	3.71695	−	3.71695i	0.245623	−	0.245623i	0.819172	+	0.573549i	$0.194434\pi$
$230$	−17.6279	−	29.2595i	−1.16235	−	1.92931i
$231$		0			0
$232$	0.339383	+	6.06528i	0.0222816	+	0.398205i
$233$			9.52870i			0.624246i	0.950042	+	0.312123i	$0.101040\pi$
$233$			9.52870i			0.624246i	−0.950042	+	0.312123i	$0.898960\pi$
$234$		0			0
$235$	9.82113	−	9.82113i	0.640660	−	0.640660i
$236$	−2.54826	+	0.785655i	−0.165877	+	0.0511418i
$237$		0			0
$238$	−0.256044	+	1.03212i	−0.0165968	+	0.0669022i
$239$	29.2948			1.89492			0.947461	−	0.319872i	$-0.103640\pi$
$239$	29.2948			1.89492			0.947461	+	0.319872i	$0.103640\pi$
$240$		0			0
$241$	−11.3857			−0.733419			−0.366710	−	0.930335i	$-0.619516\pi$
$241$	−11.3857			−0.733419			−0.366710	+	0.930335i	$0.619516\pi$
$242$	−5.53673	+	22.3187i	−0.355915	+	1.43470i
$243$		0			0
$244$	−0.364331	−	1.18170i	−0.0233239	−	0.0756506i
$245$	19.2288	−	19.2288i	1.22848	−	1.22848i
$246$		0			0
$247$		−	10.0620i		−	0.640232i
$248$	2.33356	+	2.08625i	0.148181	+	0.132477i
$249$		0			0
$250$	14.6203	+	24.2674i	0.924669	+	1.53481i
$251$	7.43944	−	7.43944i	0.469573	−	0.469573i	−0.432203	−	0.901776i	$-0.642264\pi$
$251$	7.43944	−	7.43944i	0.469573	−	0.469573i	0.901776	+	0.432203i	$0.142264\pi$
$252$		0			0
$253$	22.9126	+	22.9126i	1.44050	+	1.44050i
$254$	28.2103	+	6.99831i	1.77007	+	0.439113i
$255$		0			0
$256$	−5.85352	+	14.8908i	−0.365845	+	0.930676i
$257$	−8.73955			−0.545158			−0.272579	−	0.962133i	$-0.587877\pi$
$257$	−8.73955			−0.545158			−0.272579	+	0.962133i	$0.587877\pi$
$258$		0			0
$259$	0.297116	+	0.297116i	0.0184619	+	0.0184619i
$260$	−14.9500	−	7.90390i	−0.927160	−	0.490179i
$261$		0			0
$262$	−5.50538	−	9.13807i	−0.340124	−	0.564552i
$263$			4.90149i			0.302239i	0.988515	+	0.151120i	$0.0482878\pi$
$263$			4.90149i			0.302239i	−0.988515	+	0.151120i	$0.951712\pi$
$264$		0			0
$265$			22.4909i			1.38161i
$266$	0.636737	−	0.383613i	0.0390408	−	0.0235208i
$267$		0			0
$268$	−2.72302	−	8.83205i	−0.166335	−	0.539503i
$269$	18.7476	+	18.7476i	1.14306	+	1.14306i	0.987887	+	0.155173i	$0.0495935\pi$
$269$	18.7476	+	18.7476i	1.14306	+	1.14306i	0.155173	+	0.987887i	$0.450406\pi$
$270$		0			0
$271$	−0.845788			−0.0513779			−0.0256890	−	0.999670i	$-0.508178\pi$
$271$	−0.845788			−0.0513779			−0.0256890	+	0.999670i	$0.508178\pi$
$272$	−14.9231	−	21.9009i	−0.904845	−	1.32794i
$273$		0			0
$274$	4.41808	−	17.8094i	0.266906	−	1.07590i
$275$	−37.4628	−	37.4628i	−2.25909	−	2.25909i
$276$		0			0
$277$	−11.6762	+	11.6762i	−0.701557	+	0.701557i	−0.964745	−	0.263188i	$-0.915226\pi$
$277$	−11.6762	+	11.6762i	−0.701557	+	0.701557i	0.263188	+	0.964745i	$0.415226\pi$
$278$	6.59935	−	3.97589i	0.395803	−	0.238458i
$279$		0			0
$280$	−0.0697975	−	1.24739i	−0.00417120	−	0.0745456i
$281$		−	9.74649i		−	0.581427i	−0.956810	−	0.290713i	$-0.906107\pi$
$281$		−	9.74649i		−	0.581427i	0.956810	−	0.290713i	$-0.0938926\pi$
$282$		0			0
$283$	13.5076	−	13.5076i	0.802943	−	0.802943i	−0.180611	−	0.983555i	$-0.557808\pi$
$283$	13.5076	−	13.5076i	0.802943	−	0.802943i	0.983555	+	0.180611i	$0.0578076\pi$
$284$	−7.22119	+	13.6587i	−0.428499	+	0.810494i
$285$		0			0
$286$	15.5695	+	3.86242i	0.920645	+	0.228390i
$287$	1.04248			0.0615359
$288$		0			0
$289$	26.8967			1.58216
$290$	11.4736	+	2.84633i	0.673753	+	0.167142i
$291$		0			0
$292$	−9.56592	+	18.0937i	−0.559803	+	1.05885i
$293$	−7.02126	+	7.02126i	−0.410186	+	0.410186i	−0.881803	−	0.471617i	$-0.843670\pi$
$293$	−7.02126	+	7.02126i	−0.410186	+	0.410186i	0.471617	+	0.881803i	$0.343670\pi$
$294$		0			0
$295$			5.18919i			0.302126i
$296$	−10.4554	+	0.585033i	−0.607708	+	0.0340044i
$297$		0			0
$298$	19.9896	−	12.0431i	1.15797	−	0.697637i
$299$	9.53403	−	9.53403i	0.551367	−	0.551367i
$300$		0			0
$301$	0.361861	+	0.361861i	0.0208573	+	0.0208573i
$302$	3.01865	−	12.1683i	0.173704	−	0.700204i
$303$		0			0
$304$	−3.44912	+	18.2021i	−0.197821	+	1.04396i
$305$	−2.40638			−0.137789
$306$		0			0
$307$	−20.4265	−	20.4265i	−1.16580	−	1.16580i	−0.983183	−	0.182621i	$-0.941542\pi$
$307$	−20.4265	−	20.4265i	−1.16580	−	1.16580i	−0.182621	−	0.983183i	$-0.558458\pi$
$308$	0.349165	+	1.13251i	0.0198955	+	0.0645307i
$309$		0			0
$310$	5.21751	−	3.14337i	0.296335	−	0.178532i
$311$			24.2311i			1.37402i	0.726649	+	0.687009i	$0.241077\pi$
$311$			24.2311i			1.37402i	−0.726649	+	0.687009i	$0.758923\pi$
$312$		0			0
$313$		−	10.7762i		−	0.609105i	−0.952496	−	0.304552i	$-0.901493\pi$
$313$		−	10.7762i		−	0.609105i	0.952496	−	0.304552i	$-0.0985069\pi$
$314$	−3.26165	−	5.41383i	−0.184066	−	0.305520i
$315$		0			0
$316$	−2.21735	−	1.17229i	−0.124736	−	0.0659463i
$317$	10.6393	+	10.6393i	0.597561	+	0.597561i	0.939663	−	0.342102i	$-0.111139\pi$
$317$	10.6393	+	10.6393i	0.597561	+	0.597561i	−0.342102	+	0.939663i	$0.611139\pi$
$318$		0			0
$319$	−11.2137			−0.627846
$320$	24.3350	+	19.4227i	1.36037	+	1.08576i
$321$		0			0
$322$	0.966806	+	0.239841i	0.0538780	+	0.0133658i
$323$	−21.6981	−	21.6981i	−1.20732	−	1.20732i
$324$		0			0
$325$	−15.5884	+	15.5884i	−0.864690	+	0.864690i
$326$	−13.0479	−	21.6574i	−0.722656	−	1.19950i
$327$		0			0
$328$	−17.3160	+	19.3687i	−0.956115	+	1.06946i
$329$			0.405018i			0.0223294i
$330$		0			0
$331$	−5.59414	+	5.59414i	−0.307482	+	0.307482i	−0.843932	−	0.536450i	$-0.819765\pi$
$331$	−5.59414	+	5.59414i	−0.307482	+	0.307482i	0.536450	+	0.843932i	$0.319765\pi$
$332$	7.01996	+	22.7691i	0.385270	+	1.24962i
$333$		0			0
$334$	−6.96074	+	28.0589i	−0.380875	+	1.53531i
$335$	−17.9853			−0.982642
$336$		0			0
$337$	−19.3807			−1.05573			−0.527867	−	0.849327i	$-0.677008\pi$
$337$	−19.3807			−1.05573			−0.527867	+	0.849327i	$0.677008\pi$
$338$	−2.81948	+	11.3654i	−0.153359	+	0.618194i
$339$		0			0
$340$	−49.2829	+	15.1944i	−2.67274	+	0.824035i
$341$	−4.08574	+	4.08574i	−0.221255	+	0.221255i
$342$		0			0
$343$			1.58743i			0.0857132i
$344$	−12.7337	+	0.712517i	−0.686557	+	0.0384163i
$345$		0			0
$346$	13.1547	+	21.8348i	0.707203	+	1.17385i
$347$	−7.44533	+	7.44533i	−0.399687	+	0.399687i	−0.878122	−	0.478436i	$-0.841204\pi$
$347$	−7.44533	+	7.44533i	−0.399687	+	0.399687i	0.478436	+	0.878122i	$0.341204\pi$
$348$		0			0
$349$	12.7282	+	12.7282i	0.681323	+	0.681323i	0.960298	−	0.278976i	$-0.0899949\pi$
$349$	12.7282	+	12.7282i	0.681323	+	0.681323i	−0.278976	+	0.960298i	$0.589995\pi$
$350$	−1.58076	−	0.392148i	−0.0844950	−	0.0209612i
$351$		0			0
$352$	−26.8410	−	12.3241i	−1.43063	−	0.656875i
$353$	−24.6782			−1.31349			−0.656745	−	0.754113i	$-0.728067\pi$
$353$	−24.6782			−1.31349			−0.656745	+	0.754113i	$0.728067\pi$
$354$		0			0
$355$	21.2596	+	21.2596i	1.12834	+	1.12834i
$356$	−0.337607	+	0.638573i	−0.0178931	+	0.0338443i
$357$		0			0
$358$	−7.02752	−	11.6646i	−0.371416	−	0.616493i
$359$			26.4705i			1.39706i	0.715581	+	0.698530i	$0.246162\pi$
$359$			26.4705i			1.39706i	−0.715581	+	0.698530i	$0.753838\pi$
$360$		0			0
$361$			2.45072i			0.128985i
$362$	26.1313	−	15.7433i	1.37343	−	0.827447i
$363$		0			0
$364$	0.471242	−	0.145289i	0.0246998	−	0.00761521i
$365$	28.1626	+	28.1626i	1.47410	+	1.47410i
$366$		0			0
$367$	−3.67587			−0.191879			−0.0959395	−	0.995387i	$-0.530586\pi$
$367$	−3.67587			−0.191879			−0.0959395	+	0.995387i	$0.530586\pi$
$368$	−20.5150	+	13.9788i	−1.06942	+	0.728694i
$369$		0			0
$370$	−4.90653	+	19.7783i	−0.255078	+	1.02823i
$371$	−0.463757	−	0.463757i	−0.0240771	−	0.0240771i
$372$		0			0
$373$	23.7117	−	23.7117i	1.22774	−	1.22774i	0.262929	−	0.964815i	$-0.415311\pi$
$373$	23.7117	−	23.7117i	1.22774	−	1.22774i	0.964815	−	0.262929i	$-0.0846885\pi$
$374$	41.9037	−	25.2455i	2.16679	−	1.30542i
$375$		0			0
$376$	−7.52497	−	6.72747i	−0.388071	−	0.346943i
$377$			4.66606i			0.240314i
$378$		0			0
$379$	3.57208	−	3.57208i	0.183485	−	0.183485i	−0.609387	−	0.792873i	$-0.708585\pi$
$379$	3.57208	−	3.57208i	0.183485	−	0.183485i	0.792873	+	0.609387i	$0.208585\pi$
$380$	31.8711	+	16.8499i	1.63495	+	0.864381i
$381$		0			0
$382$	32.2286	+	7.99515i	1.64896	+	0.409067i
$383$	−20.4413			−1.04450			−0.522251	−	0.852792i	$-0.674908\pi$
$383$	−20.4413			−1.04450			−0.522251	+	0.852792i	$0.674908\pi$
$384$		0			0
$385$	2.30621			0.117535
$386$	−23.7354	−	5.88818i	−1.20810	−	0.299700i
$387$		0			0
$388$	24.2737	+	12.8332i	1.23231	+	0.651509i
$389$	11.1187	−	11.1187i	0.563743	−	0.563743i	−0.366626	−	0.930369i	$-0.619487\pi$
$389$	11.1187	−	11.1187i	0.563743	−	0.563743i	0.930369	+	0.366626i	$0.119487\pi$
$390$		0			0
$391$		−	41.1190i		−	2.07948i
$392$	−14.7331	−	13.1717i	−0.744135	−	0.665272i
$393$		0			0
$394$	−3.85267	+	2.32111i	−0.194095	+	0.116936i
$395$	−3.45127	+	3.45127i	−0.173652	+	0.173652i
$396$		0			0
$397$	−23.4557	−	23.4557i	−1.17721	−	1.17721i	−0.980452	−	0.196757i	$-0.936959\pi$
$397$	−23.4557	−	23.4557i	−1.17721	−	1.17721i	−0.196757	−	0.980452i	$-0.563041\pi$
$398$	−2.65555	+	10.7046i	−0.133111	+	0.536571i
$399$		0			0
$400$	33.5427	−	22.8557i	1.67713	−	1.14279i
$401$	4.06206			0.202850			0.101425	−	0.994843i	$-0.467660\pi$
$401$	4.06206			0.202850			0.101425	+	0.994843i	$0.467660\pi$
$402$		0			0
$403$	1.70009	+	1.70009i	0.0846876	+	0.0846876i
$404$	4.79396	−	1.47803i	0.238509	−	0.0735348i
$405$		0			0
$406$	−0.295273	+	0.177892i	−0.0146542	+	0.00882864i
$407$		−	19.3303i		−	0.958167i
$408$		0			0
$409$		−	7.14483i		−	0.353289i	−0.984275	−	0.176645i	$-0.943476\pi$
$409$		−	7.14483i		−	0.353289i	0.984275	−	0.176645i	$-0.0565243\pi$
$410$	26.0901	+	43.3056i	1.28850	+	2.13871i
$411$		0			0
$412$	−1.29339	+	2.44642i	−0.0637210	+	0.120526i
$413$	−0.107000	−	0.107000i	−0.00526511	−	0.00526511i
$414$		0			0
$415$	46.3662			2.27603
$416$	−5.12809	+	11.1686i	−0.251425	+	0.547588i
$417$		0			0
$418$	−33.1918	−	8.23409i	−1.62346	−	0.402743i
$419$	0.629065	+	0.629065i	0.0307318	+	0.0307318i	0.722306	−	0.691574i	$-0.243082\pi$
$419$	0.629065	+	0.629065i	0.0307318	+	0.0307318i	−0.691574	+	0.722306i	$0.743082\pi$
$420$		0			0
$421$	22.2236	−	22.2236i	1.08311	−	1.08311i	0.0868968	−	0.996217i	$-0.472305\pi$
$421$	22.2236	−	22.2236i	1.08311	−	1.08311i	0.996217	−	0.0868968i	$-0.0276951\pi$
$422$	−5.51198	−	9.14902i	−0.268319	−	0.445368i
$423$		0			0
$424$	16.3194	−	0.913155i	0.792542	−	0.0443467i
$425$			67.2308i			3.26117i
$426$		0			0
$427$	0.0496189	−	0.0496189i	0.00240122	−	0.00240122i
$428$	−18.4039	+	5.67411i	−0.889584	+	0.274268i
$429$		0			0
$430$	−5.97571	+	24.0882i	−0.288174	+	1.16164i
$431$	−25.9792			−1.25137			−0.625686	−	0.780075i	$-0.715181\pi$
$431$	−25.9792			−1.25137			−0.625686	+	0.780075i	$0.715181\pi$
$432$		0			0
$433$	7.22551			0.347236			0.173618	−	0.984813i	$-0.444454\pi$
$433$	7.22551			0.347236			0.173618	+	0.984813i	$0.444454\pi$
$434$	−0.0427681	+	0.172399i	−0.00205294	+	0.00827543i
$435$		0			0
$436$	2.01921	+	6.54927i	0.0967027	+	0.313653i
$437$	−20.3251	+	20.3251i	−0.972281	+	0.972281i
$438$		0			0
$439$			5.04986i			0.241017i	0.992712	+	0.120508i	$0.0384525\pi$
$439$			5.04986i			0.241017i	−0.992712	+	0.120508i	$0.961548\pi$
$440$	−38.3068	+	42.8478i	−1.82620	+	2.04269i
$441$		0			0
$442$	−10.5048	−	17.4363i	−0.499661	−	0.829359i
$443$	14.0015	−	14.0015i	0.665230	−	0.665230i	−0.291378	−	0.956608i	$-0.594114\pi$
$443$	14.0015	−	14.0015i	0.665230	−	0.665230i	0.956608	+	0.291378i	$0.0941137\pi$
$444$		0			0
$445$	0.993931	+	0.993931i	0.0471168	+	0.0471168i
$446$	5.89107	+	1.46143i	0.278950	+	0.0692009i
$447$		0			0
$448$	−0.902271	+	0.101290i	−0.0426283	+	0.00478552i
$449$	21.3288			1.00657			0.503285	−	0.864121i	$-0.332125\pi$
$449$	21.3288			1.00657			0.503285	+	0.864121i	$0.332125\pi$
$450$		0			0
$451$	−33.9118	−	33.9118i	−1.59685	−	1.59685i
$452$	17.8214	+	9.42198i	0.838249	+	0.443172i
$453$		0			0
$454$	−4.61084	−	7.65327i	−0.216397	−	0.359186i
$455$		−	0.959621i		−	0.0449877i
$456$		0			0
$457$		−	18.3129i		−	0.856641i	−0.903627	−	0.428321i	$-0.859105\pi$
$457$		−	18.3129i		−	0.856641i	0.903627	−	0.428321i	$-0.140895\pi$
$458$	−6.36758	+	3.83625i	−0.297537	+	0.179256i
$459$		0			0
$460$	14.2330	+	46.1643i	0.663615	+	2.15242i
$461$	8.03795	+	8.03795i	0.374364	+	0.374364i	0.869064	−	0.494700i	$-0.164722\pi$
$461$	8.03795	+	8.03795i	0.374364	+	0.374364i	−0.494700	+	0.869064i	$0.664722\pi$
$462$		0			0
$463$	−7.12030			−0.330909			−0.165454	−	0.986217i	$-0.552909\pi$
$463$	−7.12030			−0.330909			−0.165454	+	0.986217i	$0.552909\pi$
$464$	1.59946	−	8.44082i	0.0742529	−	0.391855i
$465$		0			0
$466$	3.24463	−	13.0792i	0.150305	−	0.605881i
$467$	23.3189	+	23.3189i	1.07907	+	1.07907i	0.996593	+	0.0824787i	$0.0262836\pi$
$467$	23.3189	+	23.3189i	1.07907	+	1.07907i	0.0824787	+	0.996593i	$0.473716\pi$
$468$		0			0
$469$	0.370852	−	0.370852i	0.0171244	−	0.0171244i
$470$	−16.8248	+	10.1364i	−0.776068	+	0.467555i
$471$		0			0
$472$	3.76528	−	0.210686i	0.173311	−	0.00969763i
$473$		−	23.5425i		−	1.08249i
$474$		0			0
$475$	33.2321	−	33.2321i	1.52479	−	1.52479i
$476$	0.702895	−	1.32951i	0.0322171	−	0.0609378i
$477$		0			0
$478$	−40.2102	−	9.97520i	−1.83917	−	0.456255i
$479$	−20.6631			−0.944121			−0.472061	−	0.881566i	$-0.656490\pi$
$479$	−20.6631			−0.944121			−0.472061	+	0.881566i	$0.656490\pi$
$480$		0			0
$481$	−8.04341			−0.366748
$482$	15.6281	+	3.87697i	0.711842	+	0.176591i
$483$		0			0
$484$	15.1995	−	28.7495i	0.690887	−	1.30679i
$485$	37.7817	−	37.7817i	1.71558	−	1.71558i
$486$		0			0
$487$			11.6477i			0.527806i	0.964549	+	0.263903i	$0.0850099\pi$
$487$			11.6477i			0.527806i	−0.964549	+	0.263903i	$0.914990\pi$
$488$	0.0977014	+	1.74607i	0.00442273	+	0.0790408i
$489$		0			0
$490$	−32.9412	+	19.8459i	−1.48813	+	0.896548i
$491$	−18.6493	+	18.6493i	−0.841630	+	0.841630i	−0.989071	−	0.147441i	$-0.952896\pi$
$491$	−18.6493	+	18.6493i	−0.841630	+	0.841630i	0.147441	+	0.989071i	$0.452896\pi$
$492$		0			0
$493$	10.0620	+	10.0620i	0.453172	+	0.453172i
$494$	−3.42624	+	13.8112i	−0.154154	+	0.621397i
$495$		0			0
$496$	−2.49267	−	3.65821i	−0.111924	−	0.164258i
$497$	−0.876733			−0.0393269
$498$		0			0
$499$	−13.1748	−	13.1748i	−0.589785	−	0.589785i	0.347788	−	0.937573i	$-0.386933\pi$
$499$	−13.1748	−	13.1748i	−0.589785	−	0.589785i	−0.937573	+	0.347788i	$0.886933\pi$
$500$	−11.8046	−	38.2880i	−0.527918	−	1.71229i
$501$		0			0
$502$	−12.7446	+	7.67822i	−0.568821	+	0.342696i
$503$		−	23.6172i		−	1.05304i	−0.850163	−	0.526520i	$-0.823497\pi$
$503$		−	23.6172i		−	1.05304i	0.850163	−	0.526520i	$-0.176503\pi$
$504$		0			0
$505$		−	9.76227i		−	0.434415i
$506$	−23.6480	−	39.2520i	−1.05128	−	1.74497i
$507$		0			0
$508$	−36.3387	−	19.2119i	−1.61227	−	0.852389i
$509$	−20.7412	−	20.7412i	−0.919336	−	0.919336i	0.0776453	−	0.996981i	$-0.475260\pi$
$509$	−20.7412	−	20.7412i	−0.919336	−	0.919336i	−0.996981	+	0.0776453i	$0.975260\pi$
$510$		0			0
$511$	−1.16141			−0.0513778
$512$	13.1051	−	18.4461i	0.579168	−	0.815208i
$513$		0			0
$514$	11.9960	+	2.97592i	0.529120	+	0.131262i
$515$	3.80782	+	3.80782i	0.167793	+	0.167793i
$516$		0			0
$517$	13.1752	−	13.1752i	0.579444	−	0.579444i
$518$	−0.306653	−	0.508996i	−0.0134735	−	0.0223640i
$519$		0			0
$520$	17.8291	+	15.9396i	0.781859	+	0.698997i
$521$		−	6.36883i		−	0.279024i	−0.990220	−	0.139512i	$-0.955447\pi$
$521$		−	6.36883i		−	0.279024i	0.990220	−	0.139512i	$-0.0445533\pi$
$522$		0			0
$523$	−13.6343	+	13.6343i	−0.596186	+	0.596186i	−0.939295	−	0.343109i	$-0.888520\pi$
$523$	−13.6343	+	13.6343i	−0.596186	+	0.596186i	0.343109	+	0.939295i	$0.388520\pi$
$524$	4.44511	+	14.4176i	0.194186	+	0.629837i
$525$		0			0
$526$	1.66901	−	6.72783i	0.0727724	−	0.293347i
$527$	7.33227			0.319399
$528$		0			0
$529$	−15.5170			−0.674653
$530$	7.65841	−	30.8712i	0.332660	−	1.34096i
$531$		0			0
$532$	−1.00461	+	0.309734i	−0.0435556	+	0.0134287i
$533$	−14.1109	+	14.1109i	−0.611209	+	0.611209i
$534$		0			0
$535$			37.4770i			1.62027i
$536$	0.730222	+	13.0502i	0.0315408	+	0.563681i
$537$		0			0
$538$	−19.3493	−	32.1168i	−0.834208	−	1.38466i
$539$	25.7957	−	25.7957i	1.11110	−	1.11110i
$540$		0			0
$541$	−18.7486	−	18.7486i	−0.806067	−	0.806067i	0.177969	−	0.984036i	$-0.443047\pi$
$541$	−18.7486	−	18.7486i	−0.806067	−	0.806067i	−0.984036	+	0.177969i	$0.943047\pi$
$542$	1.16093	+	0.288000i	0.0498664	+	0.0123707i
$543$		0			0
$544$	13.0260	+	35.1428i	0.558487	+	1.50674i
$545$	13.3367			0.571283
$546$		0			0
$547$	15.4922	+	15.4922i	0.662398	+	0.662398i	0.955945	−	0.293547i	$-0.0948356\pi$
$547$	15.4922	+	15.4922i	0.662398	+	0.662398i	−0.293547	+	0.955945i	$0.594836\pi$
$548$	−12.1286	+	22.9409i	−0.518107	+	0.979985i
$549$		0			0
$550$	38.6653	+	64.1783i	1.64869	+	2.73657i
$551$		−	9.94732i		−	0.423770i
$552$		0			0
$553$		−	0.142329i		−	0.00605243i
$554$	20.0028	−	12.0510i	0.849836	−	0.511998i
$555$		0			0
$556$	−10.4122	+	3.21018i	−0.441574	+	0.136142i
$557$	15.5155	+	15.5155i	0.657415	+	0.657415i	0.954768	−	0.297353i	$-0.0961038\pi$
$557$	15.5155	+	15.5155i	0.657415	+	0.657415i	−0.297353	+	0.954768i	$0.596104\pi$
$558$		0			0
$559$	−9.79614			−0.414332
$560$	−0.328944	+	1.73594i	−0.0139004	+	0.0733568i
$561$		0			0
$562$	−3.31879	+	13.3781i	−0.139995	+	0.564321i
$563$	−19.8096	−	19.8096i	−0.834873	−	0.834873i	0.153306	−	0.988179i	$-0.451008\pi$
$563$	−19.8096	−	19.8096i	−0.834873	−	0.834873i	−0.988179	+	0.153306i	$0.951008\pi$
$564$		0			0
$565$	27.7388	−	27.7388i	1.16698	−	1.16698i
$566$	−23.1401	+	13.9411i	−0.972652	+	0.585990i
$567$		0			0
$568$	14.5628	−	16.2891i	0.611041	−	0.683476i
$569$			7.58727i			0.318075i	0.987273	+	0.159037i	$0.0508390\pi$
$569$			7.58727i			0.318075i	−0.987273	+	0.159037i	$0.949161\pi$
$570$		0			0
$571$	−11.1860	+	11.1860i	−0.468119	+	0.468119i	−0.901305	−	0.433186i	$-0.857389\pi$
$571$	−11.1860	+	11.1860i	−0.468119	+	0.468119i	0.433186	+	0.901305i	$0.357389\pi$
$572$	−20.0556	−	10.6032i	−0.838568	−	0.443342i
$573$		0			0
$574$	−1.43092	−	0.354978i	−0.0597255	−	0.0148165i
$575$	62.9765			2.62630
$576$		0			0
$577$	−2.17810			−0.0906755			−0.0453378	−	0.998972i	$-0.514436\pi$
$577$	−2.17810			−0.0906755			−0.0453378	+	0.998972i	$0.514436\pi$
$578$	−36.9187	−	9.15864i	−1.53561	−	0.380949i
$579$		0			0
$580$	−14.7795	−	7.81378i	−0.613687	−	0.324449i
$581$	−0.956060	+	0.956060i	−0.0396640	+	0.0396640i
$582$		0			0
$583$			30.1719i			1.24959i
$584$	19.2914	−	21.5782i	0.798282	−	0.892913i
$585$		0			0
$586$	12.0283	−	7.24662i	0.496883	−	0.299355i
$587$	10.8317	−	10.8317i	0.447072	−	0.447072i	−0.447308	−	0.894380i	$-0.647617\pi$
$587$	10.8317	−	10.8317i	0.447072	−	0.447072i	0.894380	+	0.447308i	$0.147617\pi$
$588$		0			0
$589$	−3.62434	−	3.62434i	−0.149338	−	0.149338i
$590$	1.76698	−	7.12272i	0.0727453	−	0.293238i
$591$		0			0
$592$	14.5504	+	2.75716i	0.598017	+	0.113319i
$593$	24.9038			1.02268			0.511338	−	0.859379i	$-0.329150\pi$
$593$	24.9038			1.02268			0.511338	+	0.859379i	$0.329150\pi$
$594$		0			0
$595$	−2.06936	−	2.06936i	−0.0848354	−	0.0848354i
$596$	−31.5387	+	9.72373i	−1.29188	+	0.398299i
$597$		0			0
$598$	−16.3329	+	9.84004i	−0.667903	+	0.402389i
$599$			7.33156i			0.299559i	0.988719	+	0.149780i	$0.0478564\pi$
$599$			7.33156i			0.299559i	−0.988719	+	0.149780i	$0.952144\pi$
$600$		0			0
$601$			17.1141i			0.698098i	0.937105	+	0.349049i	$0.113495\pi$
$601$			17.1141i			0.698098i	−0.937105	+	0.349049i	$0.886505\pi$
$602$	−0.373475	−	0.619910i	−0.0152217	−	0.0252657i
$603$		0			0
$604$	−8.28685	+	15.6744i	−0.337187	+	0.637780i
$605$	−44.7482	−	44.7482i	−1.81927	−	1.81927i
$606$		0			0
$607$	37.4078			1.51833			0.759167	−	0.650895i	$-0.225606\pi$
$607$	37.4078			1.51833			0.759167	+	0.650895i	$0.225606\pi$
$608$	10.9323	−	23.8098i	0.443363	−	0.965616i
$609$		0			0
$610$	3.30301	+	0.819398i	0.133735	+	0.0331765i
$611$	−5.48224	−	5.48224i	−0.221788	−	0.221788i
$612$		0			0
$613$	16.0391	−	16.0391i	0.647813	−	0.647813i	−0.304651	−	0.952464i	$-0.598540\pi$
$613$	16.0391	−	16.0391i	0.647813	−	0.647813i	0.952464	+	0.304651i	$0.0985398\pi$
$614$	21.0822	+	34.9931i	0.850807	+	1.41221i
$615$		0			0
$616$	−0.0936344	−	1.67339i	−0.00377264	−	0.0674226i
$617$		−	31.3570i		−	1.26238i	−0.775626	−	0.631192i	$-0.782566\pi$
$617$		−	31.3570i		−	1.26238i	0.775626	−	0.631192i	$-0.217434\pi$
$618$		0			0
$619$	0.124018	−	0.124018i	0.00498470	−	0.00498470i	−0.704610	−	0.709595i	$-0.748878\pi$
$619$	0.124018	−	0.124018i	0.00498470	−	0.00498470i	0.709595	+	0.704610i	$0.248878\pi$
$620$	−8.23195	+	2.53800i	−0.330603	+	0.101928i
$621$		0			0
$622$	8.25095	−	33.2598i	0.330833	−	1.33359i
$623$	−0.0409892			−0.00164220
$624$		0			0
$625$	−27.2318			−1.08927
$626$	−3.66940	+	14.7914i	−0.146659	+	0.591185i
$627$		0			0
$628$	2.63350	+	8.54170i	0.105088	+	0.340851i
$629$	−17.3451	+	17.3451i	−0.691593	+	0.691593i
$630$		0			0
$631$			29.6408i			1.17998i	0.807410	+	0.589990i	$0.200868\pi$
$631$			29.6408i			1.17998i	−0.807410	+	0.589990i	$0.799132\pi$
$632$	2.64437	+	2.36412i	0.105187	+	0.0940397i
$633$		0			0
$634$	−10.9808	−	18.2263i	−0.436101	−	0.723860i
$635$	−56.5607	+	56.5607i	−2.24454	+	2.24454i
$636$		0			0
$637$	−10.7337	−	10.7337i	−0.425284	−	0.425284i
$638$	15.3920	+	3.81839i	0.609375	+	0.151171i
$639$		0			0
$640$	−26.7887	−	34.9460i	−1.05892	−	1.38136i
$641$	−3.79784			−0.150006			−0.0750029	−	0.997183i	$-0.523897\pi$
$641$	−3.79784			−0.150006			−0.0750029	+	0.997183i	$0.523897\pi$
$642$		0			0
$643$	−15.6762	−	15.6762i	−0.618207	−	0.618207i	0.326864	−	0.945071i	$-0.394008\pi$
$643$	−15.6762	−	15.6762i	−0.618207	−	0.618207i	−0.945071	+	0.326864i	$0.894008\pi$
$644$	−1.24538	−	0.658417i	−0.0490747	−	0.0259452i
$645$		0			0
$646$	22.3946	+	37.1715i	0.881102	+	1.46249i
$647$		−	45.6841i		−	1.79603i	−0.439968	−	0.898014i	$-0.645010\pi$
$647$		−	45.6841i		−	1.79603i	0.439968	−	0.898014i	$-0.354990\pi$
$648$		0			0
$649$			6.96137i			0.273258i
$650$	26.7048	−	16.0888i	1.04745	−	0.631053i
$651$		0			0
$652$	10.5350	+	34.1701i	0.412583	+	1.33821i
$653$	10.4717	+	10.4717i	0.409791	+	0.409791i	0.881666	−	0.471875i	$-0.156423\pi$
$653$	10.4717	+	10.4717i	0.409791	+	0.409791i	−0.471875	+	0.881666i	$0.656423\pi$
$654$		0			0
$655$	29.3596			1.14717
$656$	30.3633	−	20.6893i	1.18549	−	0.807781i
$657$		0			0
$658$	0.137913	−	0.555931i	0.00537642	−	0.0216725i
$659$	7.63723	+	7.63723i	0.297504	+	0.297504i	0.840036	−	0.542531i	$-0.182534\pi$
$659$	7.63723	+	7.63723i	0.297504	+	0.297504i	−0.542531	+	0.840036i	$0.682534\pi$
$660$		0			0
$661$	−11.6936	+	11.6936i	−0.454827	+	0.454827i	−0.896953	−	0.442126i	$-0.854224\pi$
$661$	−11.6936	+	11.6936i	−0.454827	+	0.454827i	0.442126	+	0.896953i	$0.354224\pi$
$662$	9.58343	−	5.77369i	0.372471	−	0.224401i
$663$		0			0
$664$	−1.88252	−	33.6434i	−0.0730558	−	1.30562i
$665$			2.04576i			0.0793313i
$666$		0			0
$667$	9.42533	−	9.42533i	0.364950	−	0.364950i
$668$	19.1087	−	36.1436i	0.739339	−	1.39844i
$669$		0			0
$670$	24.6868	+	6.12420i	0.953733	+	0.236598i
$671$	−3.22819			−0.124623
$672$		0			0
$673$	−15.6249			−0.602295			−0.301147	−	0.953578i	$-0.597370\pi$
$673$	−15.6249			−0.602295			−0.301147	+	0.953578i	$0.597370\pi$
$674$	26.6021	+	6.59935i	1.02468	+	0.254198i
$675$		0			0
$676$	7.74007	−	14.6401i	0.297695	−	0.563082i
$677$	−5.51701	+	5.51701i	−0.212036	+	0.212036i	−0.805132	−	0.593096i	$-0.797905\pi$
$677$	−5.51701	+	5.51701i	−0.212036	+	0.212036i	0.593096	+	0.805132i	$0.297905\pi$
$678$		0			0
$679$			1.55810i			0.0597943i
$680$	72.8200	−	4.07464i	2.79252	−	0.156255i
$681$		0			0
$682$	6.99936	−	4.21688i	0.268019	−	0.161473i
$683$	−7.87115	+	7.87115i	−0.301181	+	0.301181i	−0.841476	−	0.540295i	$-0.818313\pi$
$683$	−7.87115	+	7.87115i	−0.301181	+	0.301181i	0.540295	+	0.841476i	$0.318313\pi$
$684$		0			0
$685$	35.7071	+	35.7071i	1.36430	+	1.36430i
$686$	0.540538	−	2.17892i	0.0206378	−	0.0831915i
$687$		0			0
$688$	17.7210	+	3.35797i	0.675609	+	0.128022i
$689$	12.5546			0.478294
$690$		0			0
$691$	−30.3567	−	30.3567i	−1.15482	−	1.15482i	−0.985573	−	0.169251i	$-0.945865\pi$
$691$	−30.3567	−	30.3567i	−1.15482	−	1.15482i	−0.169251	−	0.985573i	$-0.554135\pi$
$692$	−10.6213	−	34.4499i	−0.403761	−	1.30959i
$693$		0			0
$694$	12.7547	−	7.68430i	0.484163	−	0.291692i
$695$			21.2030i			0.804275i
$696$		0			0
$697$			60.8582i			2.30517i
$698$	−13.1367	−	21.8048i	−0.497231	−	0.825326i
$699$		0			0
$700$	2.03623	+	1.07653i	0.0769622	+	0.0406890i
$701$	−27.7023	−	27.7023i	−1.04630	−	1.04630i	−0.998875	−	0.0474268i	$-0.984898\pi$
$701$	−27.7023	−	27.7023i	−1.04630	−	1.04630i	−0.0474268	−	0.998875i	$-0.515102\pi$
$702$		0			0
$703$	17.1473			0.646723
$704$	32.6457	+	26.0558i	1.23038	+	0.982014i
$705$		0			0
$706$	33.8735	+	8.40321i	1.27485	+	0.316259i
$707$	0.201296	+	0.201296i	0.00757050	+	0.00757050i
$708$		0			0
$709$	−9.75588	+	9.75588i	−0.366390	+	0.366390i	−0.866159	−	0.499769i	$-0.833418\pi$
$709$	−9.75588	+	9.75588i	−0.366390	+	0.366390i	0.499769	+	0.866159i	$0.333418\pi$
$710$	−21.9419	−	36.4201i	−0.823465	−	1.36682i
$711$		0			0
$712$	0.680843	−	0.761552i	0.0255157	−	0.0285404i
$713$		−	6.86829i		−	0.257220i
$714$		0			0
$715$	−31.2163	+	31.2163i	−1.16742	+	1.16742i
$716$	5.67411	+	18.4039i	0.212051	+	0.687784i
$717$		0			0
$718$	9.01350	−	36.3336i	0.336381	−	1.35596i
$719$	−7.31237			−0.272705			−0.136353	−	0.990660i	$-0.543538\pi$
$719$	−7.31237			−0.272705			−0.136353	+	0.990660i	$0.543538\pi$
$720$		0			0
$721$	−0.157033			−0.00584820
$722$	0.834498	−	3.36388i	0.0310568	−	0.125191i
$723$		0			0
$724$	−41.2288	+	12.7113i	−1.53226	+	0.472412i
$725$	−15.4107	+	15.4107i	−0.572339	+	0.572339i
$726$		0			0
$727$		−	52.6529i		−	1.95279i	−0.215999	−	0.976394i	$-0.569301\pi$
$727$		−	52.6529i		−	1.95279i	0.215999	−	0.976394i	$-0.430699\pi$
$728$	−0.696302	+	0.0389616i	−0.0258067	+	0.00144401i
$729$		0			0
$730$	−29.0665	−	48.2458i	−1.07580	−	1.78566i
$731$	−21.1247	+	21.1247i	−0.781326	+	0.781326i
$732$		0			0
$733$	15.1486	+	15.1486i	0.559526	+	0.559526i	0.929172	−	0.369647i	$-0.120521\pi$
$733$	15.1486	+	15.1486i	0.559526	+	0.559526i	−0.369647	+	0.929172i	$0.620521\pi$
$734$	5.04553	+	1.25168i	0.186234	+	0.0462002i
$735$		0			0
$736$	32.9190	−	12.2018i	1.21341	−	0.449763i
$737$	−24.1275			−0.888749
$738$		0			0
$739$	10.0140	+	10.0140i	0.368373	+	0.368373i	0.866883	−	0.498511i	$-0.166120\pi$
$739$	10.0140	+	10.0140i	0.368373	+	0.368373i	−0.498511	+	0.866883i	$0.666120\pi$
$740$	13.4695	−	25.4772i	0.495148	−	0.936559i
$741$		0			0
$742$	0.478642	+	0.794471i	0.0175715	+	0.0291660i
$743$		−	8.29320i		−	0.304248i	−0.988361	−	0.152124i	$-0.951389\pi$
$743$		−	8.29320i		−	0.304248i	0.988361	−	0.152124i	$-0.0486113\pi$
$744$		0			0
$745$			64.2244i			2.35300i
$746$	−40.6209	+	24.4727i	−1.48724	+	0.896011i
$747$		0			0
$748$	−66.1137	+	20.3836i	−2.41736	+	0.745297i
$749$	−0.772767	−	0.772767i	−0.0282363	−	0.0282363i
$750$		0			0
$751$	−48.0073			−1.75181			−0.875906	−	0.482483i	$-0.839735\pi$
$751$	−48.0073			−1.75181			−0.875906	+	0.482483i	$0.839735\pi$
$752$	8.03805	+	11.7965i	0.293118	+	0.430175i
$753$		0			0
$754$	1.58885	−	6.40467i	0.0578623	−	0.233244i
$755$	24.3969	+	24.3969i	0.887895	+	0.887895i
$756$		0			0
$757$	4.50348	−	4.50348i	0.163682	−	0.163682i	−0.620514	−	0.784196i	$-0.713076\pi$
$757$	4.50348	−	4.50348i	0.163682	−	0.163682i	0.784196	+	0.620514i	$0.213076\pi$
$758$	−6.11939	+	3.68673i	−0.222266	+	0.133908i
$759$		0			0
$760$	−38.0089	−	33.9808i	−1.37873	−	1.23261i
$761$		−	46.9072i		−	1.70038i	−0.526474	−	0.850192i	$-0.676486\pi$
$761$		−	46.9072i		−	1.70038i	0.526474	−	0.850192i	$-0.323514\pi$
$762$		0			0
$763$	−0.275000	+	0.275000i	−0.00995567	+	0.00995567i
$764$	−41.5148	−	21.9484i	−1.50195	−	0.794066i
$765$		0			0
$766$	28.0579	+	6.96050i	1.01377	+	0.251493i
$767$	2.89665			0.104592
$768$		0			0
$769$	−44.4316			−1.60225			−0.801123	−	0.598500i	$-0.795764\pi$
$769$	−44.4316			−1.60225			−0.801123	+	0.598500i	$0.795764\pi$
$770$	−3.16552	−	0.785289i	−0.114077	−	0.0282998i
$771$		0			0
$772$	30.5744	+	16.1643i	1.10040	+	0.581767i
$773$	0.710086	−	0.710086i	0.0255400	−	0.0255400i	−0.694221	−	0.719761i	$-0.744251\pi$
$773$	0.710086	−	0.710086i	0.0255400	−	0.0255400i	0.719761	+	0.694221i	$0.244251\pi$
$774$		0			0
$775$			11.2299i			0.403389i
$776$	−28.9484	−	25.8805i	−1.03919	−	0.929055i
$777$		0			0
$778$	−19.0477	+	11.4756i	−0.682895	+	0.411421i
$779$	30.0822	−	30.0822i	1.07781	−	1.07781i
$780$		0			0
$781$	28.5200	+	28.5200i	1.02053	+	1.02053i
$782$	−14.0015	+	56.4402i	−0.500692	+	2.01830i
$783$		0			0
$784$	15.7377	+	23.0964i	0.562060	+	0.824871i
$785$	17.3940			0.620820
$786$		0			0
$787$	−18.6891	−	18.6891i	−0.666195	−	0.666195i	0.290638	−	0.956833i	$-0.406132\pi$
$787$	−18.6891	−	18.6891i	−0.666195	−	0.666195i	−0.956833	+	0.290638i	$0.906132\pi$
$788$	6.07857	−	1.87409i	0.216540	−	0.0667617i
$789$		0			0
$790$	5.91244	−	3.56205i	0.210355	−	0.126732i
$791$			1.14393i			0.0406736i
$792$		0			0
$793$			1.34326i			0.0477006i
$794$	24.2086	+	40.1825i	0.859130	+	1.42602i
$795$		0			0
$796$	7.29005	−	13.7889i	0.258389	−	0.488735i
$797$	−6.84618	−	6.84618i	−0.242504	−	0.242504i	0.575381	−	0.817885i	$-0.304854\pi$
$797$	−6.84618	−	6.84618i	−0.242504	−	0.242504i	−0.817885	+	0.575381i	$0.804854\pi$
$798$		0			0
$799$	−23.6442			−0.836471
$800$	−53.8236	+	19.9503i	−1.90295	+	0.705349i
$801$		0			0
$802$	−5.57562	−	1.38318i	−0.196882	−	0.0488417i
$803$	37.7805	+	37.7805i	1.33324	+	1.33324i
$804$		0			0
$805$	−1.93841	+	1.93841i	−0.0683200	+	0.0683200i
$806$	−1.75466	−	2.91246i	−0.0618053	−	0.102587i
$807$		0			0
$808$	−7.08351	+	0.396358i	−0.249197	+	0.0139438i
$809$			4.40889i			0.155008i	0.996992	+	0.0775042i	$0.0246951\pi$
$809$			4.40889i			0.155008i	−0.996992	+	0.0775042i	$0.975305\pi$
$810$		0			0
$811$	25.7763	−	25.7763i	0.905130	−	0.905130i	−0.0907446	−	0.995874i	$-0.528925\pi$
$811$	25.7763	−	25.7763i	0.905130	−	0.905130i	0.995874	+	0.0907446i	$0.0289247\pi$
$812$	0.465869	−	0.143632i	0.0163488	−	0.00504051i
$813$		0			0
$814$	−6.58218	+	26.5329i	−0.230705	+	0.929978i
$815$	69.5830			2.43739
$816$		0			0
$817$	20.8839			0.730634
$818$	−2.43290	+	9.80705i	−0.0850642	+	0.342896i
$819$		0			0
$820$	−21.0655	−	68.3255i	−0.735639	−	2.38603i
$821$	8.25620	−	8.25620i	0.288143	−	0.288143i	−0.548202	−	0.836346i	$-0.684688\pi$
$821$	8.25620	−	8.25620i	0.288143	−	0.288143i	0.836346	+	0.548202i	$0.184688\pi$
$822$		0			0
$823$			44.7718i			1.56065i	0.625377	+	0.780323i	$0.284945\pi$
$823$			44.7718i			1.56065i	−0.625377	+	0.780323i	$0.715055\pi$
$824$	2.60836	−	2.91756i	0.0908664	−	0.101638i
$825$		0			0
$826$	0.110434	+	0.183303i	0.00384249	+	0.00637794i
$827$	27.3174	−	27.3174i	0.949918	−	0.949918i	−0.0488865	−	0.998804i	$-0.515567\pi$
$827$	27.3174	−	27.3174i	0.949918	−	0.949918i	0.998804	+	0.0488865i	$0.0155673\pi$
$828$		0			0
$829$	−5.69917	−	5.69917i	−0.197940	−	0.197940i	0.601176	−	0.799117i	$-0.294699\pi$
$829$	−5.69917	−	5.69917i	−0.197940	−	0.197940i	−0.799117	+	0.601176i	$0.794699\pi$
$830$	−63.6426	−	15.7882i	−2.20907	−	0.548017i
$831$		0			0
$832$	10.8419	−	13.5840i	0.375875	−	0.470940i
$833$	−46.2929			−1.60395
$834$		0			0
$835$	−56.2571	−	56.2571i	−1.94686	−	1.94686i
$836$	42.7555	+	22.6044i	1.47873	+	0.781788i
$837$		0			0
$838$	−0.649256	−	1.07766i	−0.0224282	−	0.0372273i
$839$		−	30.7493i		−	1.06158i	−0.847502	−	0.530792i	$-0.821894\pi$
$839$		−	30.7493i		−	1.06158i	0.847502	−	0.530792i	$-0.178106\pi$
$840$		0			0
$841$		−	24.3871i		−	0.840936i
$842$	−38.0717	+	22.9369i	−1.31204	+	0.790459i
$843$		0			0
$844$	4.45044	+	14.4349i	0.153190	+	0.496870i
$845$	−22.7872	−	22.7872i	−0.783902	−	0.783902i
$846$		0			0
$847$	1.84539			0.0634084
$848$	−22.7111	−	4.30355i	−0.779904	−	0.147785i
$849$		0			0
$850$	22.8928	−	92.2815i	0.785218	−	3.16523i
$851$	16.2475	+	16.2475i	0.556957	+	0.556957i
$852$		0			0
$853$	−15.4479	+	15.4479i	−0.528926	+	0.528926i	−0.920252	−	0.391326i	$-0.872016\pi$
$853$	−15.4479	+	15.4479i	−0.528926	+	0.528926i	0.391326	+	0.920252i	$0.372016\pi$
$854$	−0.0850030	+	0.0512115i	−0.00290874	+	0.00175242i
$855$		0			0
$856$	27.1934	−	1.52161i	0.929450	−	0.0520074i
$857$		−	22.1434i		−	0.756404i	−0.925723	−	0.378202i	$-0.876543\pi$
$857$		−	22.1434i		−	0.756404i	0.925723	−	0.378202i	$-0.123457\pi$
$858$		0			0
$859$	37.5869	−	37.5869i	1.28245	−	1.28245i	0.343177	−	0.939271i	$-0.388497\pi$
$859$	37.5869	−	37.5869i	1.28245	−	1.28245i	0.939271	−	0.343177i	$-0.111503\pi$
$860$	16.4046	−	31.0289i	0.559392	−	1.05808i
$861$		0			0
$862$	35.6592	+	8.84620i	1.21456	+	0.301303i
$863$	−11.4549			−0.389928			−0.194964	−	0.980810i	$-0.562459\pi$
$863$	−11.4549			−0.389928			−0.194964	+	0.980810i	$0.562459\pi$
$864$		0			0
$865$	−70.1528			−2.38527
$866$	−9.91779	−	2.46037i	−0.337020	−	0.0836067i
$867$		0			0
$868$	0.117408	−	0.222074i	0.00398508	−	0.00753767i
$869$	−4.62993	+	4.62993i	−0.157060	+	0.157060i
$870$		0			0
$871$			10.0396i			0.340178i
$872$	−0.541485	−	9.67715i	−0.0183370	−	0.327710i
$873$		0			0
$874$	34.8193	−	20.9774i	1.17778	−	0.709573i
$875$	1.60769	−	1.60769i	0.0543499	−	0.0543499i
$876$		0			0
$877$	−7.30722	−	7.30722i	−0.246747	−	0.246747i	0.572887	−	0.819634i	$-0.305823\pi$
$877$	−7.30722	−	7.30722i	−0.246747	−	0.246747i	−0.819634	+	0.572887i	$0.805823\pi$
$878$	1.71954	−	6.93148i	0.0580315	−	0.233926i
$879$		0			0
$880$	67.1703	−	45.7693i	2.26431	−	1.54288i
$881$	35.5970			1.19929			0.599647	−	0.800265i	$-0.295308\pi$
$881$	35.5970			1.19929			0.599647	+	0.800265i	$0.295308\pi$
$882$		0			0
$883$	30.4914	+	30.4914i	1.02612	+	1.02612i	0.999650	+	0.0264692i	$0.00842639\pi$
$883$	30.4914	+	30.4914i	1.02612	+	1.02612i	0.0264692	+	0.999650i	$0.491574\pi$
$884$	8.48168	+	27.5102i	0.285270	+	0.925267i
$885$		0			0
$886$	−23.9862	+	14.4509i	−0.805832	+	0.485487i
$887$			29.8064i			1.00080i	0.865794	+	0.500400i	$0.166814\pi$
$887$			29.8064i			1.00080i	−0.865794	+	0.500400i	$0.833186\pi$
$888$		0			0
$889$		−	2.33254i		−	0.0782307i
$890$	−1.02583	−	1.70272i	−0.0343860	−	0.0570754i
$891$		0			0
$892$	−7.58849	−	4.01195i	−0.254081	−	0.134330i
$893$	11.6873	+	11.6873i	0.391100	+	0.391100i
$894$		0			0
$895$	37.4770			1.25272
$896$	1.27295	+	0.168201i	0.0425264	+	0.00561922i
$897$		0			0
$898$	−29.2761	−	7.26271i	−0.976957	−	0.242360i
$899$	1.68071	+	1.68071i	0.0560548	+	0.0560548i
$900$		0			0
$901$	27.0732	−	27.0732i	0.901941	−	0.901941i
$902$	35.0003	+	58.0950i	1.16538	+	1.93435i
$903$		0			0
$904$	−21.2535	−	19.0011i	−0.706881	−	0.631966i
$905$			83.9571i			2.79083i
$906$		0			0
$907$	−7.57821	+	7.57821i	−0.251630	+	0.251630i	−0.821639	−	0.570008i	$-0.806940\pi$
$907$	−7.57821	+	7.57821i	−0.251630	+	0.251630i	0.570008	+	0.821639i	$0.306940\pi$
$908$	3.72285	+	12.0750i	0.123547	+	0.400722i
$909$		0			0
$910$	−0.326762	+	1.31718i	−0.0108320	+	0.0436642i
$911$	−29.7497			−0.985653			−0.492826	−	0.870128i	$-0.664036\pi$
$911$	−29.7497			−0.985653			−0.492826	+	0.870128i	$0.664036\pi$
$912$		0			0
$913$	62.2009			2.05855
$914$	−6.23575	+	25.1364i	−0.206260	+	0.831439i
$915$		0			0
$916$	10.0465	−	3.09744i	0.331945	−	0.102342i
$917$	−0.605388	+	0.605388i	−0.0199917	+	0.0199917i
$918$		0			0
$919$			45.0236i			1.48519i	0.669739	+	0.742596i	$0.266406\pi$
$919$			45.0236i			1.48519i	−0.669739	+	0.742596i	$0.733594\pi$
$920$	−3.81680	−	68.2120i	−0.125836	−	2.24888i
$921$		0			0
$922$	−8.29594	−	13.7700i	−0.273212	−	0.453489i
$923$	11.8673	−	11.8673i	0.390616	−	0.390616i
$924$		0			0
$925$	−26.5651	−	26.5651i	−0.873457	−	0.873457i
$926$	9.77338	+	2.42454i	0.321173	+	0.0796754i
$927$		0			0
$928$	−5.06962	+	11.0413i	−0.166418	+	0.362449i
$929$	−35.6267			−1.16888			−0.584438	−	0.811438i	$-0.698685\pi$
$929$	−35.6267			−1.16888			−0.584438	+	0.811438i	$0.698685\pi$
$930$		0			0
$931$	22.8825	+	22.8825i	0.749945	+	0.749945i
$932$	−8.90721	+	16.8477i	−0.291765	+	0.551866i
$933$		0			0
$934$	−24.0674	−	39.9481i	−0.787509	−	1.30714i
$935$			134.632i			4.40293i
$936$		0			0
$937$		−	2.73661i		−	0.0894012i	−0.999000	−	0.0447006i	$-0.985767\pi$
$937$		−	2.73661i		−	0.0894012i	0.999000	−	0.0447006i	$-0.0142334\pi$
$938$	−0.635314	+	0.382755i	−0.0207437	+	0.0124974i
$939$		0			0
$940$	26.5453	−	8.18421i	0.865813	−	0.266940i
$941$	−0.695790	−	0.695790i	−0.0226821	−	0.0226821i	0.695675	−	0.718357i	$-0.255105\pi$
$941$	−0.695790	−	0.695790i	−0.0226821	−	0.0226821i	−0.718357	+	0.695675i	$0.755105\pi$
$942$		0			0
$943$	57.0072			1.85641
$944$	−5.23999	−	0.992930i	−0.170547	−	0.0323171i
$945$		0			0
$946$	−8.01650	+	32.3147i	−0.260639	+	1.05064i
$947$	−2.34125	−	2.34125i	−0.0760803	−	0.0760803i	0.668043	−	0.744123i	$-0.267132\pi$
$947$	−2.34125	−	2.34125i	−0.0760803	−	0.0760803i	−0.744123	+	0.668043i	$0.767132\pi$
$948$		0			0
$949$	15.7206	−	15.7206i	0.510312	−	0.510312i
$950$	−56.9306	+	34.2988i	−1.84707	+	1.11280i
$951$		0			0
$952$	−1.41751	+	1.58555i	−0.0459418	+	0.0513879i
$953$		−	21.5675i		−	0.698640i	−0.937004	−	0.349320i	$-0.886413\pi$
$953$		−	21.5675i		−	0.698640i	0.937004	−	0.349320i	$-0.113587\pi$
$954$		0			0
$955$	−64.6172	+	64.6172i	−2.09096	+	2.09096i
$956$	51.7962	+	27.3841i	1.67521	+	0.885664i
$957$		0			0
$958$	28.3623	+	7.03602i	0.916345	+	0.227323i
$959$	−1.47254			−0.0475509
$960$		0			0
$961$	−29.7753			−0.960492
$962$	11.0404	+	2.73887i	0.355958	+	0.0883047i
$963$		0			0
$964$	−20.1312	−	10.6431i	−0.648381	−	0.342792i
$965$	47.5886	−	47.5886i	1.53193	−	1.53193i
$966$		0			0
$967$			48.8993i			1.57250i	0.617911	+	0.786248i	$0.287979\pi$
$967$			48.8993i			1.57250i	−0.617911	+	0.786248i	$0.712021\pi$
$968$	−30.6525	+	34.2861i	−0.985209	+	1.10200i
$969$		0			0
$970$	−64.7245	+	38.9944i	−2.07818	+	1.25203i
$971$	−34.8864	+	34.8864i	−1.11956	+	1.11956i	−0.127751	+	0.991806i	$0.540776\pi$
$971$	−34.8864	+	34.8864i	−1.11956	+	1.11956i	−0.991806	+	0.127751i	$0.959224\pi$
$972$		0			0
$973$	−0.437200	−	0.437200i	−0.0140160	−	0.0140160i
$974$	3.96616	−	15.9877i	0.127084	−	0.512278i
$975$		0			0
$976$	0.460450	−	2.42994i	0.0147387	−	0.0777804i
$977$	−46.9456			−1.50192			−0.750962	−	0.660346i	$-0.770410\pi$
$977$	−46.9456			−1.50192			−0.750962	+	0.660346i	$0.770410\pi$
$978$		0			0
$979$	1.33337	+	1.33337i	0.0426148	+	0.0426148i
$980$	51.9731	−	16.0239i	1.66022	−	0.511863i
$981$		0			0
$982$	31.9484	−	19.2479i	1.01952	−	0.614224i
$983$			42.9885i			1.37112i	0.728016	+	0.685560i	$0.240443\pi$
$983$			42.9885i			1.37112i	−0.728016	+	0.685560i	$0.759557\pi$
$984$		0			0
$985$		−	12.3782i		−	0.394403i
$986$	−10.3850	−	17.2375i	−0.330726	−	0.548953i
$987$		0			0
$988$	9.40576	−	17.7907i	0.299237	−	0.565999i
$989$	19.7880	+	19.7880i	0.629221	+	0.629221i
$990$		0			0
$991$	−59.3620			−1.88570			−0.942848	−	0.333224i	$-0.891863\pi$
$991$	−59.3620			−1.88570			−0.942848	+	0.333224i	$0.891863\pi$
$992$	2.17580	+	5.87006i	0.0690817	+	0.186375i
$993$		0			0
$994$	1.20341	+	0.298537i	0.0381699	+	0.00946903i
$995$	−21.4623	−	21.4623i	−0.680400	−	0.680400i
$996$		0			0
$997$	−10.9879	+	10.9879i	−0.347990	+	0.347990i	−0.859360	−	0.511370i	$-0.829138\pi$
$997$	−10.9879	+	10.9879i	−0.347990	+	0.347990i	0.511370	+	0.859360i	$0.329138\pi$
$998$	13.5977	+	22.5700i	0.430426	+	0.714440i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.c.109.2	✓	24
3.2	odd	2	inner	432.2.k.c.109.11	yes	24
4.3	odd	2		1728.2.k.c.1297.12		24
12.11	even	2		1728.2.k.c.1297.1		24
16.5	even	4	inner	432.2.k.c.325.2	yes	24
16.11	odd	4		1728.2.k.c.433.12		24
48.5	odd	4	inner	432.2.k.c.325.11	yes	24
48.11	even	4		1728.2.k.c.433.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.c.109.2	✓	24	1.1	even	1	trivial
432.2.k.c.109.11	yes	24	3.2	odd	2	inner
432.2.k.c.325.2	yes	24	16.5	even	4	inner
432.2.k.c.325.11	yes	24	48.5	odd	4	inner
1728.2.k.c.433.1		24	48.11	even	4
1728.2.k.c.433.12		24	16.11	odd	4
1728.2.k.c.1297.1		24	12.11	even	2
1728.2.k.c.1297.12		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37261 - 0.340511i) q^{2} +(1.76810 + 0.934777i) q^{4} +(2.75203 - 2.75203i) q^{5} +0.113492i q^{7} +(-2.10861 - 1.88514i) q^{8} +O(q^{10})\)	\(q+(-1.37261 - 0.340511i) q^{2} +(1.76810 + 0.934777i) q^{4} +(2.75203 - 2.75203i) q^{5} +0.113492i q^{7} +(-2.10861 - 1.88514i) q^{8} +(-4.71455 + 2.84036i) q^{10} +(3.69189 - 3.69189i) q^{11} +(-1.53621 - 1.53621i) q^{13} +(0.0386454 - 0.155780i) q^{14} +(2.25239 + 3.30557i) q^{16} -6.62546 q^{17} +(3.27496 + 3.27496i) q^{19} +(7.43841 - 2.29334i) q^{20} +(-6.32464 + 3.81038i) q^{22} +6.20621i q^{23} -10.1473i q^{25} +(1.58552 + 2.63171i) q^{26} +(-0.106090 + 0.200666i) q^{28} +(-1.51869 - 1.51869i) q^{29} -1.10668 q^{31} +(-1.96606 - 5.30421i) q^{32} +(9.09416 + 2.25604i) q^{34} +(0.312334 + 0.312334i) q^{35} +(2.61794 - 2.61794i) q^{37} +(-3.38007 - 5.61040i) q^{38} +(-10.9909 + 0.614998i) q^{40} -9.18551i q^{41} +(3.18841 - 3.18841i) q^{43} +(9.97873 - 3.07655i) q^{44} +(2.11328 - 8.51869i) q^{46} +3.56868 q^{47} +6.98712 q^{49} +(-3.45528 + 13.9283i) q^{50} +(-1.28016 - 4.15219i) q^{52} +(-4.08624 + 4.08624i) q^{53} -20.3204i q^{55} +(0.213949 - 0.239311i) q^{56} +(1.56744 + 2.60170i) q^{58} +(-0.942793 + 0.942793i) q^{59} +(-0.437200 - 0.437200i) q^{61} +(1.51904 + 0.376837i) q^{62} +(0.892486 + 7.95006i) q^{64} -8.45538 q^{65} +(-3.26764 - 3.26764i) q^{67} +(-11.7145 - 6.19333i) q^{68} +(-0.322359 - 0.535066i) q^{70} +7.72504i q^{71} +10.2334i q^{73} +(-4.48485 + 2.70197i) q^{74} +(2.72911 + 8.85183i) q^{76} +(0.419001 + 0.419001i) q^{77} -1.25408 q^{79} +(15.2956 + 2.89838i) q^{80} +(-3.12777 + 12.6081i) q^{82} +(8.42400 + 8.42400i) q^{83} +(-18.2335 + 18.2335i) q^{85} +(-5.46213 + 3.29075i) q^{86} +(-14.7445 + 0.825028i) q^{88} +0.361163i q^{89} +(0.174348 - 0.174348i) q^{91} +(-5.80142 + 10.9732i) q^{92} +(-4.89840 - 1.21518i) q^{94} +18.0256 q^{95} +13.7287 q^{97} +(-9.59057 - 2.37919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{4}+O(q^{10}) \) 24 * q + 16 * q^4	\( 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) \) 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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