LMFDB - Embedded newform 380.2.u.a.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 $ x^18 - 3x^17 + 3x^15 + 36x^14 + 72x^13 - 134x^12 - 741x^11 + 486x^10 + 5700x^9 + 11637x^8 + 13878x^7 + 13978x^6 + 10005x^5 + 5949x^4 + 2649x^3 + 819x^2 + 135x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			321.2
Root			$-0.168248 - 0.0612373i$ of defining polynomial
Character	$\chi$	$=$	380.321
Dual form			380.2.u.a.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.137157 + 0.115088i) q^{3} +(0.939693 - 0.342020i) q^{5} +(-1.55670 - 2.69628i) q^{7} +(-0.515378 - 2.92285i) q^{9} +O(q^{10})$	\(q+(0.137157 + 0.115088i) q^{3} +(0.939693 - 0.342020i) q^{5} +(-1.55670 - 2.69628i) q^{7} +(-0.515378 - 2.92285i) q^{9} +(0.132577 - 0.229630i) q^{11} +(1.46159 - 1.22642i) q^{13} +(0.168248 + 0.0612373i) q^{15} +(0.886403 - 5.02704i) q^{17} +(0.524618 + 4.32721i) q^{19} +(0.0967984 - 0.548971i) q^{21} +(2.59422 + 0.944218i) q^{23} +(0.766044 - 0.642788i) q^{25} +(0.534268 - 0.925379i) q^{27} +(0.236980 + 1.34398i) q^{29} +(-0.337771 - 0.585037i) q^{31} +(0.0446117 - 0.0162373i) q^{33} +(-2.38500 - 2.00125i) q^{35} +6.05525 q^{37} +0.341614 q^{39} +(1.29142 + 1.08363i) q^{41} +(-6.23816 + 2.27050i) q^{43} +(-1.48397 - 2.57031i) q^{45} +(-1.49075 - 8.45444i) q^{47} +(-1.34660 + 2.33239i) q^{49} +(0.700131 - 0.587480i) q^{51} +(-2.22464 - 0.809704i) q^{53} +(0.0460435 - 0.261126i) q^{55} +(-0.426057 + 0.653886i) q^{57} +(-2.24310 + 12.7213i) q^{59} +(3.92356 + 1.42806i) q^{61} +(-7.07853 + 5.93959i) q^{63} +(0.953985 - 1.65235i) q^{65} +(0.447524 + 2.53804i) q^{67} +(0.247147 + 0.428071i) q^{69} +(-6.34605 + 2.30977i) q^{71} +(8.15753 + 6.84498i) q^{73} +0.179046 q^{75} -0.825529 q^{77} +(8.28927 + 6.95552i) q^{79} +(-8.18708 + 2.97985i) q^{81} +(1.66076 + 2.87651i) q^{83} +(-0.886403 - 5.02704i) q^{85} +(-0.122173 + 0.211610i) q^{87} +(-12.5017 + 10.4902i) q^{89} +(-5.58202 - 2.03169i) q^{91} +(0.0210033 - 0.119115i) q^{93} +(1.97297 + 3.88682i) q^{95} +(2.07945 - 11.7931i) q^{97} +(-0.739503 - 0.269157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^9	$ 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.137157	+	0.115088i	0.0791877	+	0.0664464i	0.681522	−	0.731797i	$-0.261318\pi$
$3$	0.137157	+	0.115088i	0.0791877	+	0.0664464i	−0.602335	+	0.798244i	$0.705763\pi$
$4$		0			0
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$		0			0
$7$	−1.55670	−	2.69628i	−0.588376	−	1.01910i	−0.994445	−	0.105254i	$-0.966434\pi$
$7$	−1.55670	−	2.69628i	−0.588376	−	1.01910i	0.406070	−	0.913842i	$-0.366899\pi$
$8$		0			0
$9$	−0.515378	−	2.92285i	−0.171793	−	0.974284i
$10$		0			0
$11$	0.132577	−	0.229630i	0.0399735	−	0.0692361i	−0.845346	−	0.534218i	$-0.820606\pi$
$11$	0.132577	−	0.229630i	0.0399735	−	0.0692361i	0.885320	+	0.464982i	$0.153939\pi$
$12$		0			0
$13$	1.46159	−	1.22642i	0.405372	−	0.340148i	−0.417194	−	0.908818i	$-0.636986\pi$
$13$	1.46159	−	1.22642i	0.405372	−	0.340148i	0.822566	+	0.568670i	$0.192542\pi$
$14$		0			0
$15$	0.168248	+	0.0612373i	0.0434415	+	0.0158114i
$16$		0			0
$17$	0.886403	−	5.02704i	0.214984	−	1.21924i	−0.665949	−	0.745997i	$-0.731973\pi$
$17$	0.886403	−	5.02704i	0.214984	−	1.21924i	0.880934	−	0.473240i	$-0.156916\pi$
$18$		0			0
$19$	0.524618	+	4.32721i	0.120356	+	0.992731i
$19$	0.524618	+	4.32721i	0.120356	+	0.992731i
$20$		0			0
$21$	0.0967984	−	0.548971i	0.0211232	−	0.119795i
$22$		0			0
$23$	2.59422	+	0.944218i	0.540932	+	0.196883i	0.598013	−	0.801486i	$-0.295957\pi$
$23$	2.59422	+	0.944218i	0.540932	+	0.196883i	−0.0570811	+	0.998370i	$0.518179\pi$
$24$		0			0
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$		0			0
$27$	0.534268	−	0.925379i	0.102820	−	0.178089i
$28$		0			0
$29$	0.236980	+	1.34398i	0.0440060	+	0.249570i	0.998873	−	0.0474633i	$-0.0151137\pi$
$29$	0.236980	+	1.34398i	0.0440060	+	0.249570i	−0.954867	+	0.297034i	$0.904003\pi$
$30$		0			0
$31$	−0.337771	−	0.585037i	−0.0606655	−	0.105076i	0.834098	−	0.551617i	$-0.185989\pi$
$31$	−0.337771	−	0.585037i	−0.0606655	−	0.105076i	−0.894763	+	0.446541i	$0.852656\pi$
$32$		0			0
$33$	0.0446117	−	0.0162373i	0.00776590	−	0.00282656i
$34$		0			0
$35$	−2.38500	−	2.00125i	−0.403138	−	0.338273i
$36$		0			0
$37$	6.05525			0.995477			0.497738	−	0.867327i	$-0.334164\pi$
$37$	6.05525			0.995477			0.497738	+	0.867327i	$0.334164\pi$
$38$		0			0
$39$	0.341614			0.0547021
$40$		0			0
$41$	1.29142	+	1.08363i	0.201686	+	0.169235i	0.738037	−	0.674761i	$-0.235753\pi$
$41$	1.29142	+	1.08363i	0.201686	+	0.169235i	−0.536351	+	0.843995i	$0.680198\pi$
$42$		0			0
$43$	−6.23816	+	2.27050i	−0.951310	+	0.346249i	−0.770622	−	0.637292i	$-0.780055\pi$
$43$	−6.23816	+	2.27050i	−0.951310	+	0.346249i	−0.180688	+	0.983541i	$0.557832\pi$
$44$		0			0
$45$	−1.48397	−	2.57031i	−0.221217	−	0.383160i
$46$		0			0
$47$	−1.49075	−	8.45444i	−0.217448	−	1.23321i	−0.876608	−	0.481204i	$-0.840199\pi$
$47$	−1.49075	−	8.45444i	−0.217448	−	1.23321i	0.659161	−	0.752002i	$-0.270912\pi$
$48$		0			0
$49$	−1.34660	+	2.33239i	−0.192372	+	0.333198i
$50$		0			0
$51$	0.700131	−	0.587480i	0.0980380	−	0.0822636i
$52$		0			0
$53$	−2.22464	−	0.809704i	−0.305578	−	0.111221i	0.184680	−	0.982799i	$-0.440875\pi$
$53$	−2.22464	−	0.809704i	−0.305578	−	0.111221i	−0.490258	+	0.871577i	$0.663097\pi$
$54$		0			0
$55$	0.0460435	−	0.261126i	0.00620851	−	0.0352102i
$56$		0			0
$57$	−0.426057	+	0.653886i	−0.0564327	+	0.0866093i
$58$		0			0
$59$	−2.24310	+	12.7213i	−0.292027	+	1.65617i	0.387020	+	0.922071i	$0.373504\pi$
$59$	−2.24310	+	12.7213i	−0.292027	+	1.65617i	−0.679047	+	0.734095i	$0.737607\pi$
$60$		0			0
$61$	3.92356	+	1.42806i	0.502360	+	0.182844i	0.580755	−	0.814078i	$-0.302757\pi$
$61$	3.92356	+	1.42806i	0.502360	+	0.182844i	−0.0783949	+	0.996922i	$0.524980\pi$
$62$		0			0
$63$	−7.07853	+	5.93959i	−0.891811	+	0.748318i
$64$		0			0
$65$	0.953985	−	1.65235i	0.118327	−	0.204949i
$66$		0			0
$67$	0.447524	+	2.53804i	0.0546738	+	0.310070i	0.999865	−	0.0164477i	$-0.00523570\pi$
$67$	0.447524	+	2.53804i	0.0546738	+	0.310070i	−0.945191	+	0.326518i	$0.894125\pi$
$68$		0			0
$69$	0.247147	+	0.428071i	0.0297530	+	0.0515337i
$70$		0			0
$71$	−6.34605	+	2.30977i	−0.753138	+	0.274120i	−0.689926	−	0.723880i	$-0.742357\pi$
$71$	−6.34605	+	2.30977i	−0.753138	+	0.274120i	−0.0632124	+	0.998000i	$0.520135\pi$
$72$		0			0
$73$	8.15753	+	6.84498i	0.954767	+	0.801144i	0.980094	−	0.198535i	$-0.0636183\pi$
$73$	8.15753	+	6.84498i	0.954767	+	0.801144i	−0.0253270	+	0.999679i	$0.508063\pi$
$74$		0			0
$75$	0.179046			0.0206744
$76$		0			0
$77$	−0.825529			−0.0940777
$78$		0			0
$79$	8.28927	+	6.95552i	0.932616	+	0.782557i	0.976285	−	0.216489i	$-0.0694604\pi$
$79$	8.28927	+	6.95552i	0.932616	+	0.782557i	−0.0436696	+	0.999046i	$0.513905\pi$
$80$		0			0
$81$	−8.18708	+	2.97985i	−0.909676	+	0.331095i
$82$		0			0
$83$	1.66076	+	2.87651i	0.182292	+	0.315738i	0.942661	−	0.333753i	$-0.108315\pi$
$83$	1.66076	+	2.87651i	0.182292	+	0.315738i	−0.760369	+	0.649491i	$0.774982\pi$
$84$		0			0
$85$	−0.886403	−	5.02704i	−0.0961439	−	0.545259i
$86$		0			0
$87$	−0.122173	+	0.211610i	−0.0130983	+	0.0226870i
$88$		0			0
$89$	−12.5017	+	10.4902i	−1.32518	+	1.11196i	−0.340005	+	0.940424i	$0.610429\pi$
$89$	−12.5017	+	10.4902i	−1.32518	+	1.11196i	−0.985178	+	0.171536i	$0.945127\pi$
$90$		0			0
$91$	−5.58202	−	2.03169i	−0.585154	−	0.212979i
$92$		0			0
$93$	0.0210033	−	0.119115i	0.00217794	−	0.0123517i
$94$		0			0
$95$	1.97297	+	3.88682i	0.202423	+	0.398779i
$96$		0			0
$97$	2.07945	−	11.7931i	0.211136	−	1.19741i	−0.676352	−	0.736579i	$-0.736440\pi$
$97$	2.07945	−	11.7931i	0.211136	−	1.19741i	0.887487	−	0.460832i	$-0.152449\pi$
$98$		0			0
$99$	−0.739503	−	0.269157i	−0.0743228	−	0.0270513i
$100$		0			0
$101$	−3.01399	+	2.52904i	−0.299903	+	0.251649i	−0.780304	−	0.625400i	$-0.784936\pi$
$101$	−3.01399	+	2.52904i	−0.299903	+	0.251649i	0.480401	+	0.877049i	$0.340491\pi$
$102$		0			0
$103$	−4.89662	+	8.48119i	−0.482478	+	0.835677i	−0.999798	−	0.0201156i	$-0.993597\pi$
$103$	−4.89662	+	8.48119i	−0.482478	+	0.835677i	0.517319	+	0.855792i	$0.326930\pi$
$104$		0			0
$105$	−0.0967984	−	0.548971i	−0.00944656	−	0.0535741i
$106$		0			0
$107$	−2.26321	−	3.91999i	−0.218792	−	0.378959i	0.735647	−	0.677365i	$-0.236878\pi$
$107$	−2.26321	−	3.91999i	−0.218792	−	0.378959i	−0.954439	+	0.298406i	$0.903545\pi$
$108$		0			0
$109$	13.9978	−	5.09478i	1.34075	−	0.487991i	0.430698	−	0.902496i	$-0.358267\pi$
$109$	13.9978	−	5.09478i	1.34075	−	0.487991i	0.910047	+	0.414505i	$0.136045\pi$
$110$		0			0
$111$	0.830521	+	0.696890i	0.0788295	+	0.0661458i
$112$		0			0
$113$	7.08578			0.666574			0.333287	−	0.942825i	$-0.391842\pi$
$113$	7.08578			0.666574			0.333287	+	0.942825i	$0.391842\pi$
$114$		0			0
$115$	2.76071			0.257437
$116$		0			0
$117$	−4.33792	−	3.63994i	−0.401040	−	0.336513i
$118$		0			0
$119$	−14.9342	+	5.43559i	−1.36901	+	0.498279i
$120$		0			0
$121$	5.46485	+	9.46539i	0.496804	+	0.860490i
$122$		0			0
$123$	0.0524141	+	0.297255i	0.00472602	+	0.0268026i
$124$		0			0
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	6.06757	−	5.09129i	0.538409	−	0.451779i	−0.332584	−	0.943074i	$-0.607921\pi$
$127$	6.06757	−	5.09129i	0.538409	−	0.451779i	0.870994	+	0.491294i	$0.163476\pi$
$128$		0			0
$129$	−1.11692	−	0.406524i	−0.0983390	−	0.0357925i
$130$		0			0
$131$	0.344789	−	1.95540i	0.0301244	−	0.170844i	−0.966034	−	0.258416i	$-0.916800\pi$
$131$	0.344789	−	1.95540i	0.0301244	−	0.170844i	0.996158	+	0.0875718i	$0.0279107\pi$
$132$		0			0
$133$	10.8507	−	8.15067i	0.940874	−	0.706753i
$134$		0			0
$135$	0.185549	−	1.05230i	0.0159695	−	0.0905678i
$136$		0			0
$137$	−14.6490	−	5.33180i	−1.25155	−	0.455527i	−0.370625	−	0.928783i	$-0.620856\pi$
$137$	−14.6490	−	5.33180i	−1.25155	−	0.455527i	−0.880925	+	0.473256i	$0.843079\pi$
$138$		0			0
$139$	−4.09214	+	3.43371i	−0.347091	+	0.291244i	−0.799621	−	0.600506i	$-0.794966\pi$
$139$	−4.09214	+	3.43371i	−0.347091	+	0.291244i	0.452530	+	0.891749i	$0.350522\pi$
$140$		0			0
$141$	0.768542	−	1.33115i	0.0647229	−	0.112103i
$142$		0			0
$143$	−0.0878497	−	0.498220i	−0.00734636	−	0.0416633i
$144$		0			0
$145$	0.682356	+	1.18187i	0.0566665	+	0.0981493i
$146$		0			0
$147$	−0.453127	+	0.164925i	−0.0373733	+	0.0136028i
$148$		0			0
$149$	4.46146	+	3.74361i	0.365497	+	0.306689i	0.806977	−	0.590582i	$-0.201102\pi$
$149$	4.46146	+	3.74361i	0.365497	+	0.306689i	−0.441480	+	0.897271i	$0.645546\pi$
$150$		0			0
$151$	18.8838			1.53674			0.768371	−	0.640005i	$-0.221068\pi$
$151$	18.8838			1.53674			0.768371	+	0.640005i	$0.221068\pi$
$152$		0			0
$153$	−15.1501			−1.22482
$154$		0			0
$155$	−0.517495	−	0.434230i	−0.0415662	−	0.0348782i
$156$		0			0
$157$	14.2666	−	5.19261i	1.13860	−	0.414415i	0.297190	−	0.954818i	$-0.403951\pi$
$157$	14.2666	−	5.19261i	1.13860	−	0.414415i	0.841406	+	0.540403i	$0.181728\pi$
$158$		0			0
$159$	−0.211938	−	0.367088i	−0.0168078	−	0.0291119i
$160$		0			0
$161$	−1.49254	−	8.46459i	−0.117628	−	0.667103i
$162$		0			0
$163$	−8.16395	+	14.1404i	−0.639450	+	1.10756i	0.346104	+	0.938196i	$0.387504\pi$
$163$	−8.16395	+	14.1404i	−0.639450	+	1.10756i	−0.985554	+	0.169363i	$0.945829\pi$
$164$		0			0
$165$	0.0363678	−	0.0305162i	0.00283123	−	0.00237568i
$166$		0			0
$167$	−6.23503	−	2.26937i	−0.482481	−	0.175609i	0.0893166	−	0.996003i	$-0.471532\pi$
$167$	−6.23503	−	2.26937i	−0.482481	−	0.175609i	−0.571798	+	0.820394i	$0.693754\pi$
$168$		0			0
$169$	−1.62529	+	9.21746i	−0.125022	+	0.709035i
$170$		0			0
$171$	12.3774	−	3.76353i	0.946526	−	0.287804i
$172$		0			0
$173$	4.35064	−	24.6737i	0.330773	−	1.87591i	−0.134761	−	0.990878i	$-0.543027\pi$
$173$	4.35064	−	24.6737i	0.330773	−	1.87591i	0.465534	−	0.885030i	$-0.345862\pi$
$174$		0			0
$175$	−2.92563	−	1.06484i	−0.221157	−	0.0804945i
$176$		0			0
$177$	−1.77173	+	1.48666i	−0.133171	+	0.111744i
$178$		0			0
$179$	11.1911	−	19.3836i	0.836463	−	1.44880i	−0.0563712	−	0.998410i	$-0.517953\pi$
$179$	11.1911	−	19.3836i	0.836463	−	1.44880i	0.892834	−	0.450386i	$-0.148714\pi$
$180$		0			0
$181$	2.58924	+	14.6843i	0.192457	+	1.09148i	0.915994	+	0.401192i	$0.131404\pi$
$181$	2.58924	+	14.6843i	0.192457	+	1.09148i	−0.723537	+	0.690286i	$0.757485\pi$
$182$		0			0
$183$	0.373791	+	0.647425i	0.0276314	+	0.0478590i
$184$		0			0
$185$	5.69007	−	2.07102i	0.418343	−	0.152264i
$186$		0			0
$187$	−1.03684	−	0.870016i	−0.0758216	−	0.0636218i
$188$		0			0
$189$	−3.32677			−0.241987
$190$		0			0
$191$	−6.51501			−0.471409			−0.235705	−	0.971825i	$-0.575740\pi$
$191$	−6.51501			−0.471409			−0.235705	+	0.971825i	$0.575740\pi$
$192$		0			0
$193$	−3.58822	−	3.01087i	−0.258286	−	0.216728i	0.504445	−	0.863444i	$-0.331697\pi$
$193$	−3.58822	−	3.01087i	−0.258286	−	0.216728i	−0.762730	+	0.646717i	$0.776142\pi$
$194$		0			0
$195$	0.321012	−	0.116839i	0.0229882	−	0.00836701i
$196$		0			0
$197$	−0.757915	−	1.31275i	−0.0539992	−	0.0935293i	0.837762	−	0.546035i	$-0.183864\pi$
$197$	−0.757915	−	1.31275i	−0.0539992	−	0.0935293i	−0.891761	+	0.452506i	$0.850530\pi$
$198$		0			0
$199$	−2.33312	−	13.2318i	−0.165390	−	0.937974i	−0.948661	−	0.316294i	$-0.897561\pi$
$199$	−2.33312	−	13.2318i	−0.165390	−	0.937974i	0.783271	−	0.621680i	$-0.213550\pi$
$200$		0			0
$201$	−0.230718	+	0.399615i	−0.0162736	+	0.0281866i
$202$		0			0
$203$	3.25483	−	2.73113i	0.228444	−	0.191688i
$204$		0			0
$205$	1.58416	+	0.576588i	0.110643	+	0.0402706i
$206$		0			0
$207$	1.42281	−	8.06915i	0.0988920	−	0.560844i
$208$		0			0
$209$	1.06321	+	0.453221i	0.0735439	+	0.0313500i
$210$		0			0
$211$	4.56298	−	25.8780i	0.314129	−	1.78151i	−0.262935	−	0.964814i	$-0.584690\pi$
$211$	4.56298	−	25.8780i	0.314129	−	1.78151i	0.577064	−	0.816699i	$-0.304198\pi$
$212$		0			0
$213$	−1.13623	−	0.413556i	−0.0778535	−	0.0283364i
$214$		0			0
$215$	−5.08539	+	4.26715i	−0.346821	+	0.291017i
$216$		0			0
$217$	−1.05161	+	1.82145i	−0.0713882	+	0.123648i
$218$		0			0
$219$	0.331085	+	1.87768i	0.0223726	+	0.126882i
$220$		0			0
$221$	−4.86970	−	8.43458i	−0.327572	−	0.567371i
$222$		0			0
$223$	10.5393	−	3.83599i	0.705764	−	0.256877i	0.0358940	−	0.999356i	$-0.488572\pi$
$223$	10.5393	−	3.83599i	0.705764	−	0.256877i	0.669870	+	0.742479i	$0.266350\pi$
$224$		0			0
$225$	−2.27358	−	1.90776i	−0.151572	−	0.127184i
$226$		0			0
$227$	25.4125			1.68669			0.843345	−	0.537373i	$-0.180583\pi$
$227$	25.4125			1.68669			0.843345	+	0.537373i	$0.180583\pi$
$228$		0			0
$229$	19.4056			1.28236			0.641180	−	0.767391i	$-0.278445\pi$
$229$	19.4056			1.28236			0.641180	+	0.767391i	$0.278445\pi$
$230$		0			0
$231$	−0.113227	−	0.0950089i	−0.00744980	−	0.00625112i
$232$		0			0
$233$	0.417709	−	0.152034i	0.0273650	−	0.00996005i	−0.328301	−	0.944573i	$-0.606476\pi$
$233$	0.417709	−	0.152034i	0.0273650	−	0.00996005i	0.355666	+	0.934613i	$0.384254\pi$
$234$		0			0
$235$	−4.29243	−	7.43471i	−0.280007	−	0.484987i
$236$		0			0
$237$	0.336432	+	1.90800i	0.0218536	+	0.123938i
$238$		0			0
$239$	3.60952	−	6.25187i	0.233480	−	0.404400i	−0.725350	−	0.688381i	$-0.758322\pi$
$239$	3.60952	−	6.25187i	0.233480	−	0.404400i	0.958830	+	0.283981i	$0.0916552\pi$
$240$		0			0
$241$	−16.9786	+	14.2468i	−1.09369	+	0.917715i	−0.996985	−	0.0775979i	$-0.975275\pi$
$241$	−16.9786	+	14.2468i	−1.09369	+	0.917715i	−0.0967055	+	0.995313i	$0.530831\pi$
$242$		0			0
$243$	−4.47815	−	1.62991i	−0.287273	−	0.104559i
$244$		0			0
$245$	−0.467670	+	2.65229i	−0.0298784	+	0.169449i
$246$		0			0
$247$	6.07376	+	5.68121i	0.386464	+	0.361487i
$248$		0			0
$249$	−0.103269	+	0.585668i	−0.00654441	+	0.0371152i
$250$		0			0
$251$	−16.3734	−	5.95944i	−1.03348	−	0.376156i	−0.231076	−	0.972936i	$-0.574224\pi$
$251$	−16.3734	−	5.95944i	−1.03348	−	0.376156i	−0.802405	+	0.596780i	$0.796447\pi$
$252$		0			0
$253$	0.560755	−	0.470529i	0.0352544	−	0.0295819i
$254$		0			0
$255$	0.456978	−	0.791509i	0.0286171	−	0.0495662i
$256$		0			0
$257$	4.85152	+	27.5143i	0.302630	+	1.71630i	0.634458	+	0.772958i	$0.281224\pi$
$257$	4.85152	+	27.5143i	0.302630	+	1.71630i	−0.331828	+	0.943340i	$0.607665\pi$
$258$		0			0
$259$	−9.42618	−	16.3266i	−0.585714	−	1.01449i
$260$		0			0
$261$	3.80612	−	1.38531i	0.235593	−	0.0857487i
$262$		0			0
$263$	6.02485	+	5.05545i	0.371508	+	0.311733i	0.809358	−	0.587316i	$-0.199815\pi$
$263$	6.02485	+	5.05545i	0.371508	+	0.311733i	−0.437850	+	0.899048i	$0.644260\pi$
$264$		0			0
$265$	−2.36742			−0.145429
$266$		0			0
$267$	−2.92201			−0.178824
$268$		0			0
$269$	5.86938	+	4.92499i	0.357862	+	0.300282i	0.803938	−	0.594713i	$-0.202734\pi$
$269$	5.86938	+	4.92499i	0.357862	+	0.300282i	−0.446076	+	0.894995i	$0.647179\pi$
$270$		0			0
$271$	7.47803	−	2.72178i	0.454258	−	0.165336i	−0.104750	−	0.994499i	$-0.533404\pi$
$271$	7.47803	−	2.72178i	0.454258	−	0.165336i	0.559008	+	0.829162i	$0.311182\pi$
$272$		0			0
$273$	−0.531789	−	0.921086i	−0.0321854	−	0.0557467i
$274$		0			0
$275$	−0.0460435	−	0.261126i	−0.00277653	−	0.0157465i
$276$		0			0
$277$	−10.1397	+	17.5624i	−0.609233	+	1.05522i	0.382134	+	0.924107i	$0.375189\pi$
$277$	−10.1397	+	17.5624i	−0.609233	+	1.05522i	−0.991367	+	0.131116i	$0.958144\pi$
$278$		0			0
$279$	−1.53590	+	1.28877i	−0.0919517	+	0.0771566i
$280$		0			0
$281$	−25.1981	−	9.17135i	−1.50319	−	0.547117i	−0.546306	−	0.837585i	$-0.683967\pi$
$281$	−25.1981	−	9.17135i	−1.50319	−	0.547117i	−0.956884	+	0.290469i	$0.906189\pi$
$282$		0			0
$283$	−2.60987	+	14.8013i	−0.155141	+	0.879846i	0.803517	+	0.595282i	$0.202960\pi$
$283$	−2.60987	+	14.8013i	−0.155141	+	0.879846i	−0.958657	+	0.284563i	$0.908151\pi$
$284$		0			0
$285$	−0.176721	+	0.760172i	−0.0104680	+	0.0450287i
$286$		0			0
$287$	0.911418	−	5.16891i	0.0537993	−	0.305111i
$288$		0			0
$289$	−8.51066	−	3.09763i	−0.500627	−	0.182213i
$290$		0			0
$291$	1.64246	−	1.37819i	0.0962830	−	0.0807910i
$292$		0			0
$293$	0.701131	−	1.21439i	0.0409605	−	0.0709457i	−0.844818	−	0.535053i	$-0.820292\pi$
$293$	0.701131	−	1.21439i	0.0409605	−	0.0709457i	0.885779	+	0.464108i	$0.153625\pi$
$294$		0			0
$295$	2.24310	+	12.7213i	0.130598	+	0.740660i
$296$		0			0
$297$	−0.141663	−	0.245368i	−0.00822014	−	0.0142377i
$298$		0			0
$299$	4.94969	−	1.80154i	0.286248	−	0.104186i
$300$		0			0
$301$	15.8328	+	13.2853i	0.912588	+	0.765753i
$302$		0			0
$303$	−0.704454			−0.0404698
$304$		0			0
$305$	4.17537			0.239081
$306$		0			0
$307$	11.5407	+	9.68381i	0.658664	+	0.552684i	0.909686	−	0.415297i	$-0.136322\pi$
$307$	11.5407	+	9.68381i	0.658664	+	0.552684i	−0.251022	+	0.967981i	$0.580767\pi$
$308$		0			0
$309$	−1.64769	+	0.599711i	−0.0937340	+	0.0341164i
$310$		0			0
$311$	8.77503	+	15.1988i	0.497586	+	0.861845i	0.999996	−	0.00278480i	$-0.000886430\pi$
$311$	8.77503	+	15.1988i	0.497586	+	0.861845i	−0.502410	+	0.864630i	$0.667553\pi$
$312$		0			0
$313$	−2.35274	−	13.3430i	−0.132985	−	0.754194i	−0.976242	−	0.216683i	$-0.930476\pi$
$313$	−2.35274	−	13.3430i	−0.132985	−	0.754194i	0.843257	−	0.537510i	$-0.180635\pi$
$314$		0			0
$315$	−4.62018	+	8.00239i	−0.260318	+	0.450884i
$316$		0			0
$317$	−20.4370	+	17.1487i	−1.14786	+	0.963165i	−0.999667	−	0.0257936i	$-0.991789\pi$
$317$	−20.4370	+	17.1487i	−1.14786	+	0.963165i	−0.148189	+	0.988959i	$0.547344\pi$
$318$		0			0
$319$	0.340036	+	0.123763i	0.0190384	+	0.00692940i
$320$		0			0
$321$	0.140731	−	0.798123i	0.00785482	−	0.0445469i
$322$		0			0
$323$	22.2181	+	1.19838i	1.23625	+	0.0666796i
$324$		0			0
$325$	0.331316	−	1.87898i	0.0183781	−	0.104227i
$326$		0			0
$327$	2.50625	+	0.912199i	0.138596	+	0.0504447i
$328$		0			0
$329$	−20.4749	+	17.1804i	−1.12882	+	0.947189i
$330$		0			0
$331$	5.91678	−	10.2482i	0.325215	−	0.563290i	−0.656340	−	0.754465i	$-0.727897\pi$
$331$	5.91678	−	10.2482i	0.325215	−	0.563290i	0.981556	+	0.191175i	$0.0612298\pi$
$332$		0			0
$333$	−3.12074	−	17.6986i	−0.171016	−	0.969878i
$334$		0			0
$335$	1.28859	+	2.23191i	0.0704034	+	0.121942i
$336$		0			0
$337$	−9.66454	+	3.51760i	−0.526461	+	0.191616i	−0.591557	−	0.806263i	$-0.701487\pi$
$337$	−9.66454	+	3.51760i	−0.526461	+	0.191616i	0.0650965	+	0.997879i	$0.479264\pi$
$338$		0			0
$339$	0.971866	+	0.815492i	0.0527845	+	0.0442915i
$340$		0			0
$341$	−0.179123			−0.00970004
$342$		0			0
$343$	−13.4087			−0.724004
$344$		0			0
$345$	0.378651	+	0.317726i	0.0203859	+	0.0171058i
$346$		0			0
$347$	−27.3527	+	9.95559i	−1.46837	+	0.534444i	−0.947658	−	0.319287i	$-0.896557\pi$
$347$	−27.3527	+	9.95559i	−1.46837	+	0.534444i	−0.520714	+	0.853731i	$0.674334\pi$
$348$		0			0
$349$	−8.10052	−	14.0305i	−0.433611	−	0.751036i	0.563570	−	0.826068i	$-0.309427\pi$
$349$	−8.10052	−	14.0305i	−0.433611	−	0.751036i	−0.997181	+	0.0750319i	$0.976094\pi$
$350$		0			0
$351$	−0.354022	−	2.00776i	−0.0188963	−	0.107166i
$352$		0			0
$353$	−6.83410	+	11.8370i	−0.363742	+	0.630020i	−0.988573	−	0.150740i	$-0.951834\pi$
$353$	−6.83410	+	11.8370i	−0.363742	+	0.630020i	0.624831	+	0.780760i	$0.285168\pi$
$354$		0			0
$355$	−5.17335	+	4.34096i	−0.274573	+	0.230394i
$356$		0			0
$357$	−2.67390	−	0.973220i	−0.141518	−	0.0515082i
$358$		0			0
$359$	3.32554	−	18.8601i	0.175515	−	0.995396i	−0.762032	−	0.647539i	$-0.775798\pi$
$359$	3.32554	−	18.8601i	0.175515	−	0.995396i	0.937548	−	0.347857i	$-0.113091\pi$
$360$		0			0
$361$	−18.4496	+	4.54027i	−0.971029	+	0.238961i
$362$		0			0
$363$	−0.339815	+	1.92719i	−0.0178357	+	0.101151i
$364$		0			0
$365$	10.0067	+	3.64214i	0.523774	+	0.190638i
$366$		0			0
$367$	−7.94360	+	6.66547i	−0.414652	+	0.347935i	−0.826124	−	0.563488i	$-0.809459\pi$
$367$	−7.94360	+	6.66547i	−0.414652	+	0.347935i	0.411472	+	0.911422i	$0.365015\pi$
$368$		0			0
$369$	2.50172	−	4.33311i	0.130235	−	0.225573i
$370$		0			0
$371$	1.27991	+	7.25872i	0.0664495	+	0.376854i
$372$		0			0
$373$	4.04511	+	7.00634i	0.209448	+	0.362774i	0.951541	−	0.307523i	$-0.0995000\pi$
$373$	4.04511	+	7.00634i	0.209448	+	0.362774i	−0.742093	+	0.670297i	$0.766167\pi$
$374$		0			0
$375$	0.168248	−	0.0612373i	0.00868830	−	0.00316228i
$376$		0			0
$377$	1.99465	+	1.67371i	0.102730	+	0.0862004i
$378$		0			0
$379$	2.89627			0.148771			0.0743857	−	0.997230i	$-0.476300\pi$
$379$	2.89627			0.148771			0.0743857	+	0.997230i	$0.476300\pi$
$380$		0			0
$381$	1.41816			0.0726545
$382$		0			0
$383$	9.28938	+	7.79471i	0.474665	+	0.398291i	0.848493	−	0.529207i	$-0.177510\pi$
$383$	9.28938	+	7.79471i	0.474665	+	0.398291i	−0.373828	+	0.927498i	$0.621955\pi$
$384$		0			0
$385$	−0.775743	+	0.282347i	−0.0395355	+	0.0143898i
$386$		0			0
$387$	9.85136	+	17.0630i	0.500773	+	0.867364i
$388$		0			0
$389$	−5.88197	−	33.3583i	−0.298227	−	1.69133i	−0.653787	−	0.756678i	$-0.726821\pi$
$389$	−5.88197	−	33.3583i	−0.298227	−	1.69133i	0.355560	−	0.934654i	$-0.384290\pi$
$390$		0			0
$391$	7.04615	−	12.2043i	0.356339	−	0.617197i
$392$		0			0
$393$	0.272334	−	0.228515i	0.0137374	−	0.0115271i
$394$		0			0
$395$	10.1683	+	3.70096i	0.511622	+	0.186215i
$396$		0			0
$397$	−5.04822	+	28.6299i	−0.253363	+	1.43689i	0.546878	+	0.837212i	$0.315816\pi$
$397$	−5.04822	+	28.6299i	−0.253363	+	1.43689i	−0.800241	+	0.599679i	$0.795295\pi$
$398$		0			0
$399$	2.42630	+	0.130867i	0.121467	+	0.00655156i
$400$		0			0
$401$	−4.63072	+	26.2621i	−0.231247	+	1.31147i	0.619128	+	0.785290i	$0.287486\pi$
$401$	−4.63072	+	26.2621i	−0.231247	+	1.31147i	−0.850375	+	0.526177i	$0.823625\pi$
$402$		0			0
$403$	−1.21118	−	0.440835i	−0.0603333	−	0.0219595i
$404$		0			0
$405$	−6.67417	+	5.60029i	−0.331642	+	0.278281i
$406$		0			0
$407$	0.802787	−	1.39047i	0.0397927	−	0.0689230i
$408$		0			0
$409$	4.38604	+	24.8745i	0.216876	+	1.22996i	0.877622	+	0.479353i	$0.159129\pi$
$409$	4.38604	+	24.8745i	0.216876	+	1.22996i	−0.660746	+	0.750609i	$0.729760\pi$
$410$		0			0
$411$	−1.39559	−	2.41723i	−0.0688392	−	0.119233i
$412$		0			0
$413$	37.7918	−	13.7551i	1.85962	−	0.676845i
$414$		0			0
$415$	2.54443	+	2.13503i	0.124901	+	0.104804i
$416$		0			0
$417$	−0.956446			−0.0468374
$418$		0			0
$419$	10.8366			0.529401			0.264701	−	0.964331i	$-0.414727\pi$
$419$	10.8366			0.529401			0.264701	+	0.964331i	$0.414727\pi$
$420$		0			0
$421$	22.8967	+	19.2126i	1.11592	+	0.936365i	0.998391	−	0.0567046i	$-0.0180593\pi$
$421$	22.8967	+	19.2126i	1.11592	+	0.936365i	0.117526	+	0.993070i	$0.462504\pi$
$422$		0			0
$423$	−23.9428	+	8.71446i	−1.16414	+	0.423711i
$424$		0			0
$425$	−2.55230	−	4.42071i	−0.123805	−	0.214436i
$426$		0			0
$427$	−2.25735	−	12.8021i	−0.109241	−	0.619535i
$428$		0			0
$429$	0.0452902	−	0.0784450i	0.00218663	−	0.00378736i
$430$		0			0
$431$	1.26927	−	1.06505i	0.0611387	−	0.0513015i	−0.611706	−	0.791085i	$-0.709517\pi$
$431$	1.26927	−	1.06505i	0.0611387	−	0.0513015i	0.672845	+	0.739784i	$0.265072\pi$
$432$		0			0
$433$	−26.2816	−	9.56572i	−1.26301	−	0.459699i	−0.378234	−	0.925710i	$-0.623469\pi$
$433$	−26.2816	−	9.56572i	−1.26301	−	0.459699i	−0.884779	+	0.466011i	$0.845691\pi$
$434$		0			0
$435$	−0.0424302	+	0.240634i	−0.00203437	+	0.0115375i
$436$		0			0
$437$	−2.72486	+	11.7211i	−0.130348	+	0.560696i
$438$		0			0
$439$	2.76255	−	15.6672i	0.131849	−	0.747755i	−0.845153	−	0.534525i	$-0.820490\pi$
$439$	2.76255	−	15.6672i	0.131849	−	0.747755i	0.977002	−	0.213230i	$-0.0683984\pi$
$440$		0			0
$441$	7.51123	+	2.73386i	0.357678	+	0.130184i
$442$		0			0
$443$	−13.5410	+	11.3622i	−0.643350	+	0.539835i	−0.905045	−	0.425316i	$-0.860163\pi$
$443$	−13.5410	+	11.3622i	−0.643350	+	0.539835i	0.261695	+	0.965151i	$0.415719\pi$
$444$		0			0
$445$	−8.15994	+	14.1334i	−0.386818	+	0.669988i
$446$		0			0
$447$	0.181075	+	1.02693i	0.00856454	+	0.0485719i
$448$		0			0
$449$	−19.4043	−	33.6092i	−0.915744	−	1.58611i	−0.805809	−	0.592176i	$-0.798269\pi$
$449$	−19.4043	−	33.6092i	−0.915744	−	1.58611i	−0.109935	−	0.993939i	$-0.535064\pi$
$450$		0			0
$451$	0.420047	−	0.152885i	0.0197792	−	0.00719906i
$452$		0			0
$453$	2.59005	+	2.17331i	0.121691	+	0.102111i
$454$		0			0
$455$	−5.94026			−0.278484
$456$		0			0
$457$	20.7093			0.968738			0.484369	−	0.874864i	$-0.339049\pi$
$457$	20.7093			0.968738			0.484369	+	0.874864i	$0.339049\pi$
$458$		0			0
$459$	−4.17834	−	3.50605i	−0.195028	−	0.163648i
$460$		0			0
$461$	−12.6137	+	4.59101i	−0.587478	+	0.213824i	−0.618620	−	0.785691i	$-0.712308\pi$
$461$	−12.6137	+	4.59101i	−0.587478	+	0.213824i	0.0311419	+	0.999515i	$0.490086\pi$
$462$		0			0
$463$	−19.7557	−	34.2178i	−0.918124	−	1.59024i	−0.802262	−	0.596973i	$-0.796370\pi$
$463$	−19.7557	−	34.2178i	−0.918124	−	1.59024i	−0.115863	−	0.993265i	$-0.536963\pi$
$464$		0			0
$465$	−0.0210033	−	0.119115i	−0.000974003	−	0.00552385i
$466$		0			0
$467$	−1.87193	+	3.24228i	−0.0866228	+	0.150035i	−0.906082	−	0.423103i	$-0.860941\pi$
$467$	−1.87193	+	3.24228i	−0.0866228	+	0.150035i	0.819459	+	0.573138i	$0.194274\pi$
$468$		0			0
$469$	6.14659	−	5.15760i	0.283823	−	0.238156i
$470$		0			0
$471$	2.55437	+	0.929715i	0.117699	+	0.0428390i
$472$		0			0
$473$	−0.305660	+	1.73349i	−0.0140543	+	0.0797058i
$474$		0			0
$475$	3.18336	+	2.97762i	0.146063	+	0.136623i
$476$		0			0
$477$	−1.22011	+	6.91961i	−0.0558652	+	0.316827i
$478$		0			0
$479$	23.0700	+	8.39679i	1.05409	+	0.383659i	0.810207	−	0.586144i	$-0.199355\pi$
$479$	23.0700	+	8.39679i	1.05409	+	0.383659i	0.243888	+	0.969803i	$0.421577\pi$
$480$		0			0
$481$	8.85029	−	7.42628i	0.403539	−	0.338609i
$482$		0			0
$483$	0.769465	−	1.33275i	0.0350119	−	0.0606423i
$484$		0			0
$485$	−2.07945	−	11.7931i	−0.0944228	−	0.535498i
$486$		0			0
$487$	−1.89990	−	3.29072i	−0.0860927	−	0.149117i	0.819764	−	0.572702i	$-0.194105\pi$
$487$	−1.89990	−	3.29072i	−0.0860927	−	0.149117i	−0.905856	+	0.423585i	$0.860771\pi$
$488$		0			0
$489$	−2.74714	+	0.999876i	−0.124230	+	0.0452160i
$490$		0			0
$491$	−13.1947	−	11.0716i	−0.595466	−	0.499656i	0.294518	−	0.955646i	$-0.404841\pi$
$491$	−13.1947	−	11.0716i	−0.595466	−	0.499656i	−0.889985	+	0.455990i	$0.849285\pi$
$492$		0			0
$493$	6.96629			0.313746
$494$		0			0
$495$	−0.786962			−0.0353713
$496$		0			0
$497$	16.1067	+	13.5151i	0.722483	+	0.606235i
$498$		0			0
$499$	6.09378	−	2.21795i	0.272795	−	0.0992892i	−0.202001	−	0.979385i	$-0.564744\pi$
$499$	6.09378	−	2.21795i	0.272795	−	0.0992892i	0.474795	+	0.880096i	$0.342522\pi$
$500$		0			0
$501$	−0.594001	−	1.02884i	−0.0265380	−	0.0459652i
$502$		0			0
$503$	−3.73168	−	21.1634i	−0.166387	−	0.943630i	−0.947622	−	0.319393i	$-0.896521\pi$
$503$	−3.73168	−	21.1634i	−0.166387	−	0.943630i	0.781235	−	0.624237i	$-0.214590\pi$
$504$		0			0
$505$	−1.96724	+	3.40737i	−0.0875412	+	0.151626i
$506$		0			0
$507$	−1.28374	+	1.07719i	−0.0570130	+	0.0478396i
$508$		0			0
$509$	−0.301747	−	0.109827i	−0.0133747	−	0.00486799i	0.335324	−	0.942103i	$-0.391154\pi$
$509$	−0.301747	−	0.109827i	−0.0133747	−	0.00486799i	−0.348699	+	0.937235i	$0.613376\pi$
$510$		0			0
$511$	5.75717	−	32.6505i	0.254682	−	1.44437i
$512$		0			0
$513$	4.28460	+	1.82642i	0.189170	+	0.0806384i
$514$		0			0
$515$	−1.70058	+	9.64446i	−0.0749364	+	0.424986i
$516$		0			0
$517$	−2.13903	−	0.778544i	−0.0940746	−	0.0342403i
$518$		0			0
$519$	3.43638	−	2.88347i	0.150840	−	0.126570i
$520$		0			0
$521$	−2.12082	+	3.67337i	−0.0929148	+	0.160933i	−0.908736	−	0.417370i	$-0.862952\pi$
$521$	−2.12082	+	3.67337i	−0.0929148	+	0.160933i	0.815822	+	0.578304i	$0.196285\pi$
$522$		0			0
$523$	−3.24517	−	18.4043i	−0.141901	−	0.804763i	−0.969803	−	0.243890i	$-0.921577\pi$
$523$	−3.24517	−	18.4043i	−0.141901	−	0.804763i	0.827902	−	0.560874i	$-0.189535\pi$
$524$		0			0
$525$	−0.278720	−	0.482757i	−0.0121643	−	0.0210693i
$526$		0			0
$527$	−3.24040	+	1.17941i	−0.141154	+	0.0513759i
$528$		0			0
$529$	−11.7806	−	9.88510i	−0.512200	−	0.429787i
$530$		0			0
$531$	38.3384			1.66374
$532$		0			0
$533$	3.21651			0.139323
$534$		0			0
$535$	−3.46743	−	2.90952i	−0.149910	−	0.125790i
$536$		0			0
$537$	3.76577	−	1.37063i	0.162505	−	0.0591469i
$538$		0			0
$539$	0.357057	+	0.618442i	0.0153796	+	0.0266382i
$540$		0			0
$541$	−4.08726	−	23.1800i	−0.175725	−	0.996585i	−0.937304	−	0.348513i	$-0.886687\pi$
$541$	−4.08726	−	23.1800i	−0.175725	−	0.996585i	0.761579	−	0.648072i	$-0.224424\pi$
$542$		0			0
$543$	−1.33486	+	2.31205i	−0.0572845	+	0.0992197i
$544$		0			0
$545$	11.4111	−	9.57505i	0.488798	−	0.410150i
$546$		0			0
$547$	−21.1791	−	7.70857i	−0.905554	−	0.329595i	−0.153078	−	0.988214i	$-0.548919\pi$
$547$	−21.1791	−	7.70857i	−0.905554	−	0.329595i	−0.752476	+	0.658619i	$0.771141\pi$
$548$		0			0
$549$	2.15189	−	12.2040i	0.0918405	−	0.520853i
$550$		0			0
$551$	−5.69136	+	1.73054i	−0.242460	+	0.0737233i
$552$		0			0
$553$	5.85014	−	33.1778i	0.248773	−	1.41086i
$554$		0			0
$555$	1.01878	+	0.370807i	0.0432450	+	0.0157399i
$556$		0			0
$557$	−2.22292	+	1.86525i	−0.0941880	+	0.0790331i	−0.688666	−	0.725079i	$-0.741803\pi$
$557$	−2.22292	+	1.86525i	−0.0941880	+	0.0790331i	0.594478	+	0.804112i	$0.297359\pi$
$558$		0			0
$559$	−6.33304	+	10.9691i	−0.267859	+	0.463945i
$560$		0			0
$561$	−0.0420818	−	0.238658i	−0.00177669	−	0.0100761i
$562$		0			0
$563$	20.9940	+	36.3626i	0.884790	+	1.53250i	0.845954	+	0.533255i	$0.179031\pi$
$563$	20.9940	+	36.3626i	0.884790	+	1.53250i	0.0388353	+	0.999246i	$0.487635\pi$
$564$		0			0
$565$	6.65846	−	2.42348i	0.280123	−	0.101957i
$566$		0			0
$567$	20.7793	+	17.4359i	0.872649	+	0.732239i
$568$		0			0
$569$	20.8503			0.874089			0.437044	−	0.899440i	$-0.356025\pi$
$569$	20.8503			0.874089			0.437044	+	0.899440i	$0.356025\pi$
$570$		0			0
$571$	−6.25450			−0.261743			−0.130871	−	0.991399i	$-0.541778\pi$
$571$	−6.25450			−0.261743			−0.130871	+	0.991399i	$0.541778\pi$
$572$		0			0
$573$	−0.893580	−	0.749802i	−0.0373298	−	0.0313234i
$574$		0			0
$575$	2.59422	−	0.944218i	0.108186	−	0.0393766i
$576$		0			0
$577$	7.15843	+	12.3988i	0.298009	+	0.516167i	0.975680	−	0.219198i	$-0.0703441\pi$
$577$	7.15843	+	12.3988i	0.298009	+	0.516167i	−0.677671	+	0.735365i	$0.737011\pi$
$578$		0			0
$579$	−0.145633	−	0.825926i	−0.00605230	−	0.0343243i
$580$		0			0
$581$	5.17058	−	8.95571i	0.214512	−	0.371545i
$582$		0			0
$583$	−0.480869	+	0.403497i	−0.0199156	+	0.0167112i
$584$		0			0
$585$	−5.32124	−	1.93677i	−0.220006	−	0.0800757i
$586$		0			0
$587$	3.44990	−	19.5654i	0.142393	−	0.807550i	−0.827031	−	0.562157i	$-0.809972\pi$
$587$	3.44990	−	19.5654i	0.142393	−	0.807550i	0.969424	−	0.245393i	$-0.0789171\pi$
$588$		0			0
$589$	2.35438	−	1.76853i	0.0970104	−	0.0728709i
$590$		0			0
$591$	0.0471286	−	0.267280i	0.00193861	−	0.0109944i
$592$		0			0
$593$	16.0951	+	5.85814i	0.660947	+	0.240565i	0.650645	−	0.759382i	$-0.274499\pi$
$593$	16.0951	+	5.85814i	0.660947	+	0.240565i	0.0103018	+	0.999947i	$0.496721\pi$
$594$		0			0
$595$	−12.1744	+	10.2156i	−0.499103	+	0.418797i
$596$		0			0
$597$	1.20282	−	2.08334i	0.0492281	−	0.0852656i
$598$		0			0
$599$	−1.40409	−	7.96299i	−0.0573695	−	0.325359i	0.942594	−	0.333942i	$-0.108379\pi$
$599$	−1.40409	−	7.96299i	−0.0573695	−	0.325359i	−0.999963	+	0.00858318i	$0.997268\pi$
$600$		0			0
$601$	−4.79952	−	8.31302i	−0.195777	−	0.339095i	0.751378	−	0.659872i	$-0.229389\pi$
$601$	−4.79952	−	8.31302i	−0.195777	−	0.339095i	−0.947155	+	0.320777i	$0.896056\pi$
$602$		0			0
$603$	7.18766	−	2.61609i	0.292704	−	0.106536i
$604$		0			0
$605$	8.37263	+	7.02547i	0.340396	+	0.285626i
$606$		0			0
$607$	13.5088			0.548307			0.274153	−	0.961686i	$-0.411602\pi$
$607$	13.5088			0.548307			0.274153	+	0.961686i	$0.411602\pi$
$608$		0			0
$609$	0.760745			0.0308269
$610$		0			0
$611$	−12.5475	−	10.5286i	−0.507619	−	0.425943i
$612$		0			0
$613$	20.3672	−	7.41304i	0.822622	−	0.299410i	0.103795	−	0.994599i	$-0.466901\pi$
$613$	20.3672	−	7.41304i	0.822622	−	0.299410i	0.718827	+	0.695189i	$0.244679\pi$
$614$		0			0
$615$	0.150920	+	0.261402i	0.00608570	+	0.0105407i
$616$		0			0
$617$	−2.08734	−	11.8379i	−0.0840330	−	0.476575i	−0.997561	−	0.0697991i	$-0.977764\pi$
$617$	−2.08734	−	11.8379i	−0.0840330	−	0.476575i	0.913528	−	0.406776i	$-0.133347\pi$
$618$		0			0
$619$	−4.00380	+	6.93478i	−0.160926	+	0.278732i	−0.935201	−	0.354117i	$-0.884781\pi$
$619$	−4.00380	+	6.93478i	−0.160926	+	0.278732i	0.774275	+	0.632849i	$0.218115\pi$
$620$		0			0
$621$	2.25977	−	1.89617i	0.0906813	−	0.0760907i
$622$		0			0
$623$	47.7459	+	17.3781i	1.91290	+	0.696239i
$624$		0			0
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$		0			0
$627$	0.0936665	+	0.184526i	0.00374068	+	0.00736926i
$628$		0			0
$629$	5.36739	−	30.4400i	0.214012	−	1.21372i
$630$		0			0
$631$	−37.9863	−	13.8259i	−1.51221	−	0.550400i	−0.553023	−	0.833166i	$-0.686526\pi$
$631$	−37.9863	−	13.8259i	−1.51221	−	0.550400i	−0.959189	+	0.282766i	$0.908748\pi$
$632$		0			0
$633$	3.60410	−	3.02420i	0.143250	−	0.120201i
$634$		0			0
$635$	3.96032	−	6.85948i	0.157161	−	0.272210i
$636$		0			0
$637$	0.892301	+	5.06049i	0.0353543	+	0.200504i
$638$		0			0
$639$	10.0217	+	17.3582i	0.396454	+	0.686679i
$640$		0			0
$641$	−32.8766	+	11.9661i	−1.29855	+	0.472632i	−0.896523	−	0.442997i	$-0.853915\pi$
$641$	−32.8766	+	11.9661i	−1.29855	+	0.472632i	−0.402024	+	0.915629i	$0.631693\pi$
$642$		0			0
$643$	−23.8674	−	20.0271i	−0.941237	−	0.789791i	0.0365634	−	0.999331i	$-0.488359\pi$
$643$	−23.8674	−	20.0271i	−0.941237	−	0.789791i	−0.977800	+	0.209540i	$0.932803\pi$
$644$		0			0
$645$	−1.18860			−0.0468010
$646$		0			0
$647$	−22.9037			−0.900437			−0.450218	−	0.892919i	$-0.648654\pi$
$647$	−22.9037			−0.900437			−0.450218	+	0.892919i	$0.648654\pi$
$648$		0			0
$649$	2.62380	+	2.20163i	0.102993	+	0.0864216i
$650$		0			0
$651$	−0.353864	+	0.128796i	−0.0138690	+	0.00504791i
$652$		0			0
$653$	−17.5309	−	30.3644i	−0.686038	−	1.18825i	−0.973110	−	0.230343i	$-0.926015\pi$
$653$	−17.5309	−	30.3644i	−0.686038	−	1.18825i	0.287072	−	0.957909i	$-0.407318\pi$
$654$		0			0
$655$	−0.344789	−	1.95540i	−0.0134720	−	0.0764037i
$656$		0			0
$657$	15.8027	−	27.3710i	0.616521	−	1.06784i
$658$		0			0
$659$	0.178893	−	0.150109i	0.00696869	−	0.00584742i	−0.639297	−	0.768960i	$-0.720774\pi$
$659$	0.178893	−	0.150109i	0.00696869	−	0.00584742i	0.646265	+	0.763113i	$0.276330\pi$
$660$		0			0
$661$	−32.3499	−	11.7744i	−1.25827	−	0.457971i	−0.375079	−	0.926993i	$-0.622385\pi$
$661$	−32.3499	−	11.7744i	−1.25827	−	0.457971i	−0.883187	+	0.469021i	$0.844607\pi$
$662$		0			0
$663$	0.302808	−	1.71731i	0.0117601	−	0.0666948i
$664$		0			0
$665$	7.40862	−	11.3703i	0.287294	−	0.440921i
$666$		0			0
$667$	−0.654232	+	3.71033i	−0.0253320	+	0.143665i
$668$		0			0
$669$	1.88702	+	0.686819i	0.0729564	+	0.0265539i
$670$		0			0
$671$	0.848100	−	0.711640i	0.0327405	−	0.0274726i
$672$		0			0
$673$	−14.0851	+	24.3961i	−0.542941	+	0.940402i	0.455792	+	0.890086i	$0.349356\pi$
$673$	−14.0851	+	24.3961i	−0.542941	+	0.940402i	−0.998733	+	0.0503154i	$0.983977\pi$
$674$		0			0
$675$	−0.185549	−	1.05230i	−0.00714179	−	0.0405031i
$676$		0			0
$677$	−4.48115	−	7.76158i	−0.172225	−	0.298302i	0.766973	−	0.641680i	$-0.221762\pi$
$677$	−4.48115	−	7.76158i	−0.172225	−	0.298302i	−0.939197	+	0.343378i	$0.888429\pi$
$678$		0			0
$679$	−35.0346	+	12.7516i	−1.34450	+	0.489360i
$680$		0			0
$681$	3.48551	+	2.92469i	0.133565	+	0.112074i
$682$		0			0
$683$	−12.5097			−0.478672			−0.239336	−	0.970937i	$-0.576930\pi$
$683$	−12.5097			−0.478672			−0.239336	+	0.970937i	$0.576930\pi$
$684$		0			0
$685$	−15.5892			−0.595631
$686$		0			0
$687$	2.66162	+	2.23336i	0.101547	+	0.0852081i
$688$		0			0
$689$	−4.24455	+	1.54489i	−0.161705	+	0.0588557i
$690$		0			0
$691$	15.2624	+	26.4352i	0.580607	+	1.00564i	0.995407	+	0.0957287i	$0.0305181\pi$
$691$	15.2624	+	26.4352i	0.580607	+	1.00564i	−0.414800	+	0.909912i	$0.636149\pi$
$692$		0			0
$693$	0.425459	+	2.41290i	0.0161619	+	0.0916585i
$694$		0			0
$695$	−2.67095	+	4.62623i	−0.101315	+	0.175483i
$696$		0			0
$697$	6.59218	−	5.53149i	0.249696	−	0.209520i
$698$		0			0
$699$	0.0747890	+	0.0272210i	0.00282878	+	0.00102959i
$700$		0			0
$701$	0.606258	−	3.43826i	0.0228980	−	0.129861i	−0.971216	−	0.238201i	$-0.923442\pi$
$701$	0.606258	−	3.43826i	0.0228980	−	0.129861i	0.994114	+	0.108340i	$0.0345534\pi$
$702$		0			0
$703$	3.17669	+	26.2024i	0.119811	+	0.988241i
$704$		0			0
$705$	0.266912	−	1.51373i	0.0100525	−	0.0570105i
$706$		0			0
$707$	11.5109	+	4.18961i	0.432910	+	0.157566i
$708$		0			0
$709$	10.5028	−	8.81289i	0.394441	−	0.330975i	−0.423899	−	0.905709i	$-0.639339\pi$
$709$	10.5028	−	8.81289i	0.394441	−	0.330975i	0.818340	+	0.574734i	$0.194895\pi$
$710$		0			0
$711$	16.0579	−	27.8130i	0.602217	−	1.04307i
$712$		0			0
$713$	−0.323849	−	1.83664i	−0.0121283	−	0.0687828i
$714$		0			0
$715$	−0.252953	−	0.438128i	−0.00945991	−	0.0163850i
$716$		0			0
$717$	1.21459	−	0.442074i	0.0453597	−	0.0165096i
$718$		0			0
$719$	18.4686	+	15.4970i	0.688763	+	0.577940i	0.918552	−	0.395300i	$-0.129359\pi$
$719$	18.4686	+	15.4970i	0.688763	+	0.577940i	−0.229790	+	0.973240i	$0.573804\pi$
$720$		0			0
$721$	30.4902			1.13551
$722$		0			0
$723$	−3.96838			−0.147586
$724$		0			0
$725$	1.04543	+	0.877219i	0.0388263	+	0.0325791i
$726$		0			0
$727$	−22.7710	+	8.28797i	−0.844531	+	0.307384i	−0.727808	−	0.685781i	$-0.759461\pi$
$727$	−22.7710	+	8.28797i	−0.844531	+	0.307384i	−0.116722	+	0.993165i	$0.537239\pi$
$728$		0			0
$729$	12.6421	+	21.8968i	0.468227	+	0.810994i
$730$		0			0
$731$	5.88439	+	33.3721i	0.217642	+	1.23431i
$732$		0			0
$733$	−25.5971	+	44.3354i	−0.945449	+	1.63757i	−0.190601	+	0.981668i	$0.561044\pi$
$733$	−25.5971	+	44.3354i	−0.945449	+	1.63757i	−0.754849	+	0.655899i	$0.772290\pi$
$734$		0			0
$735$	−0.369392	+	0.309957i	−0.0136252	+	0.0114329i
$736$		0			0
$737$	0.642141	+	0.233720i	0.0236536	+	0.00860920i
$738$		0			0
$739$	1.75933	−	9.97766i	0.0647180	−	0.367034i	−0.935199	−	0.354124i	$-0.884779\pi$
$739$	1.75933	−	9.97766i	0.0647180	−	0.367034i	0.999917	−	0.0129105i	$-0.00410967\pi$
$740$		0			0
$741$	0.179217	+	1.47824i	0.00658370	+	0.0543044i
$742$		0			0
$743$	−4.71509	+	26.7406i	−0.172980	+	0.981017i	0.767470	+	0.641085i	$0.221515\pi$
$743$	−4.71509	+	26.7406i	−0.172980	+	0.981017i	−0.940450	+	0.339932i	$0.889596\pi$
$744$		0			0
$745$	5.47280	+	1.99193i	0.200508	+	0.0729788i
$746$		0			0
$747$	7.55171	−	6.33663i	0.276303	−	0.231845i
$748$		0			0
$749$	−7.04624	+	12.2045i	−0.257464	+	0.445941i
$750$		0			0
$751$	9.11495	+	51.6934i	0.332609	+	1.88632i	0.449669	+	0.893195i	$0.351542\pi$
$751$	9.11495	+	51.6934i	0.332609	+	1.88632i	−0.117060	+	0.993125i	$0.537347\pi$
$752$		0			0
$753$	−1.55987	−	2.70177i	−0.0568448	−	0.0984580i
$754$		0			0
$755$	17.7450	−	6.45864i	0.645805	−	0.235054i
$756$		0			0
$757$	−16.8839	−	14.1673i	−0.613656	−	0.514919i	0.282146	−	0.959371i	$-0.408954\pi$
$757$	−16.8839	−	14.1673i	−0.613656	−	0.514919i	−0.895802	+	0.444453i	$0.853398\pi$
$758$		0			0
$759$	0.131064			0.00475732
$760$		0			0
$761$	19.8303			0.718849			0.359424	−	0.933174i	$-0.382973\pi$
$761$	19.8303			0.718849			0.359424	+	0.933174i	$0.382973\pi$
$762$		0			0
$763$	−35.5272	−	29.8109i	−1.28617	−	1.07923i
$764$		0			0
$765$	−14.2365	+	5.18165i	−0.514721	+	0.187343i
$766$		0			0
$767$	12.3231	+	21.3442i	0.444962	+	0.770696i
$768$		0			0
$769$	5.49699	+	31.1750i	0.198226	+	1.12420i	0.907749	+	0.419515i	$0.137800\pi$
$769$	5.49699	+	31.1750i	0.198226	+	1.12420i	−0.709522	+	0.704683i	$0.751089\pi$
$770$		0			0
$771$	−2.50116	+	4.33214i	−0.0900772	+	0.156018i
$772$		0			0
$773$	30.5314	−	25.6189i	1.09814	−	0.921448i	0.100841	−	0.994903i	$-0.467847\pi$
$773$	30.5314	−	25.6189i	1.09814	−	0.921448i	0.997299	+	0.0734542i	$0.0234023\pi$
$774$		0			0
$775$	−0.634802	−	0.231049i	−0.0228028	−	0.00829952i
$776$		0			0
$777$	0.586139	−	3.32416i	0.0210276	−	0.119254i
$778$		0			0
$779$	−4.01160	+	6.15674i	−0.143730	+	0.220588i
$780$		0			0
$781$	−0.310947	+	1.76347i	−0.0111266	+	0.0631019i
$782$		0			0
$783$	1.37030	+	0.498748i	0.0489705	+	0.0178238i
$784$		0			0
$785$	11.6302	−	9.75891i	0.415100	−	0.348310i
$786$		0			0
$787$	6.60318	−	11.4370i	0.235378	−	0.407687i	−0.724005	−	0.689795i	$-0.757701\pi$
$787$	6.60318	−	11.4370i	0.235378	−	0.407687i	0.959382	+	0.282109i	$0.0910339\pi$
$788$		0			0
$789$	0.244527	+	1.38678i	0.00870540	+	0.0493708i
$790$		0			0
$791$	−11.0304	−	19.1052i	−0.392196	−	0.679304i
$792$		0			0
$793$	7.48604	−	2.72469i	0.265837	−	0.0967567i
$794$		0			0
$795$	−0.324708	−	0.272462i	−0.0115162	−	0.00966325i
$796$		0			0
$797$	−32.4888			−1.15081			−0.575406	−	0.817868i	$-0.695156\pi$
$797$	−32.4888			−1.15081			−0.575406	+	0.817868i	$0.695156\pi$
$798$		0			0
$799$	−43.8222			−1.55032
$800$		0			0
$801$	37.1045	+	31.1343i	1.31102	+	1.10008i
$802$		0			0
$803$	2.65332	−	0.965728i	0.0936335	−	0.0340798i
$804$		0			0
$805$	−4.29758	−	7.44363i	−0.151470	−	0.262354i
$806$		0			0
$807$	0.238217	+	1.35100i	0.00838563	+	0.0475573i
$808$		0			0
$809$	−6.77182	+	11.7291i	−0.238085	+	0.412375i	−0.960165	−	0.279435i	$-0.909853\pi$
$809$	−6.77182	+	11.7291i	−0.238085	+	0.412375i	0.722080	+	0.691810i	$0.243186\pi$
$810$		0			0
$811$	−22.6195	+	18.9800i	−0.794277	+	0.666478i	−0.946800	−	0.321822i	$-0.895705\pi$
$811$	−22.6195	+	18.9800i	−0.794277	+	0.666478i	0.152523	+	0.988300i	$0.451260\pi$
$812$		0			0
$813$	1.33891	+	0.487324i	0.0469577	+	0.0170912i
$814$		0			0
$815$	−2.83531	+	16.0798i	−0.0993166	+	0.563252i
$816$		0			0
$817$	−13.0976	−	25.8027i	−0.458227	−	0.902722i
$818$		0			0
$819$	−3.06148	+	17.3625i	−0.106977	+	0.606695i
$820$		0			0
$821$	1.88644	+	0.686609i	0.0658373	+	0.0239628i	0.374729	−	0.927134i	$-0.377736\pi$
$821$	1.88644	+	0.686609i	0.0658373	+	0.0239628i	−0.308892	+	0.951097i	$0.599958\pi$
$822$		0			0
$823$	−40.4933	+	33.9779i	−1.41151	+	1.18439i	−0.455796	+	0.890084i	$0.650645\pi$
$823$	−40.4933	+	33.9779i	−1.41151	+	1.18439i	−0.955710	+	0.294310i	$0.904910\pi$
$824$		0			0
$825$	0.0237374	−	0.0411144i	0.000826430	−	0.00143142i
$826$		0			0
$827$	−6.84268	−	38.8068i	−0.237943	−	1.34944i	−0.836326	−	0.548233i	$-0.815301\pi$
$827$	−6.84268	−	38.8068i	−0.237943	−	1.34944i	0.598383	−	0.801210i	$-0.295810\pi$
$828$		0			0
$829$	21.4777	+	37.2005i	0.745953	+	1.29203i	0.949748	+	0.313015i	$0.101339\pi$
$829$	21.4777	+	37.2005i	0.745953	+	1.29203i	−0.203795	+	0.979014i	$0.565328\pi$
$830$		0			0
$831$	−3.41196	+	1.24185i	−0.118359	+	0.0430793i
$832$		0			0
$833$	10.5314	+	8.83686i	0.364890	+	0.306179i
$834$		0			0
$835$	−6.63518			−0.229620
$836$		0			0
$837$	−0.721841			−0.0249505
$838$		0			0
$839$	−17.3758	−	14.5800i	−0.599878	−	0.503357i	0.291529	−	0.956562i	$-0.405836\pi$
$839$	−17.3758	−	14.5800i	−0.599878	−	0.503357i	−0.891406	+	0.453205i	$0.850281\pi$
$840$		0			0
$841$	25.5010	−	9.28159i	0.879344	−	0.320055i
$842$		0			0
$843$	−2.40058	−	4.15792i	−0.0826803	−	0.143206i
$844$		0			0
$845$	1.62529	+	9.21746i	0.0559115	+	0.317090i
$846$		0			0
$847$	17.0142	−	29.4695i	0.584615	−	1.01258i
$848$		0			0
$849$	−2.06142	+	1.72974i	−0.0707478	+	0.0593644i
$850$		0			0
$851$	15.7086	+	5.71748i	0.538485	+	0.195993i
$852$		0			0
$853$	−7.86981	+	44.6319i	−0.269457	+	1.52817i	0.486578	+	0.873637i	$0.338245\pi$
$853$	−7.86981	+	44.6319i	−0.269457	+	1.52817i	−0.756035	+	0.654531i	$0.772866\pi$
$854$		0			0
$855$	10.3438	−	7.76989i	0.353750	−	0.265725i
$856$		0			0
$857$	0.588997	−	3.34037i	0.0201198	−	0.114105i	−0.973094	−	0.230409i	$-0.925994\pi$
$857$	0.588997	−	3.34037i	0.0201198	−	0.114105i	0.993214	+	0.116304i	$0.0371047\pi$
$858$		0			0
$859$	−35.3562	−	12.8686i	−1.20634	−	0.439071i	−0.340906	−	0.940098i	$-0.610734\pi$
$859$	−35.3562	−	12.8686i	−1.20634	−	0.439071i	−0.865432	+	0.501027i	$0.832956\pi$
$860$		0			0
$861$	0.719889	−	0.604059i	0.0245338	−	0.0205863i
$862$		0			0
$863$	−0.284329	+	0.492472i	−0.00967867	+	0.0167639i	−0.870824	−	0.491595i	$-0.836414\pi$
$863$	−0.284329	+	0.492472i	−0.00967867	+	0.0167639i	0.861146	+	0.508359i	$0.169748\pi$
$864$		0			0
$865$	−4.35064	−	24.6737i	−0.147926	−	0.838932i
$866$		0			0
$867$	−0.810797	−	1.40434i	−0.0275361	−	0.0476939i
$868$		0			0
$869$	2.69617	−	0.981324i	0.0914611	−	0.0332891i
$870$		0			0
$871$	3.76679	+	3.16072i	0.127633	+	0.107097i
$872$		0			0
$873$	−35.5413			−1.20289
$874$		0			0
$875$	−3.11339			−0.105252
$876$		0			0
$877$	−15.1873	−	12.7436i	−0.512837	−	0.430322i	0.349289	−	0.937015i	$-0.386423\pi$
$877$	−15.1873	−	12.7436i	−0.512837	−	0.430322i	−0.862126	+	0.506694i	$0.830868\pi$
$878$		0			0
$879$	0.235928	−	0.0858708i	0.00795765	−	0.00289635i
$880$		0			0
$881$	5.55299	+	9.61806i	0.187085	+	0.324041i	0.944277	−	0.329151i	$-0.106763\pi$
$881$	5.55299	+	9.61806i	0.187085	+	0.324041i	−0.757192	+	0.653192i	$0.773429\pi$
$882$		0			0
$883$	−0.187741	−	1.06473i	−0.00631800	−	0.0358311i	0.981486	−	0.191535i	$-0.0613466\pi$
$883$	−0.187741	−	1.06473i	−0.00631800	−	0.0358311i	−0.987804	+	0.155704i	$0.950235\pi$
$884$		0			0
$885$	−1.15641	+	2.00297i	−0.0388724	+	0.0673290i
$886$		0			0
$887$	−30.8852	+	25.9158i	−1.03702	+	0.870166i	−0.991670	−	0.128805i	$-0.958886\pi$
$887$	−30.8852	+	25.9158i	−1.03702	+	0.870166i	−0.0453535	+	0.998971i	$0.514441\pi$
$888$		0			0
$889$	−23.1729	−	8.43424i	−0.777194	−	0.282875i
$890$		0			0
$891$	−0.401155	+	2.27506i	−0.0134392	+	0.0762174i
$892$		0			0
$893$	35.8021	−	10.8861i	1.19807	−	0.364290i
$894$		0			0
$895$	3.88663	−	22.0422i	0.129916	−	0.736789i
$896$		0			0
$897$	0.886222	+	0.322558i	0.0295901	+	0.0107699i
$898$		0			0
$899$	0.706231	−	0.592599i	0.0235541	−	0.0197643i
$900$		0			0
$901$	−6.04235	+	10.4657i	−0.201300	+	0.348662i
$902$		0			0
$903$	0.642597	+	3.64435i	0.0213843	+	0.121276i
$904$		0			0
$905$	7.45543	+	12.9132i	0.247827	+	0.429249i
$906$		0			0
$907$	−26.4706	+	9.63451i	−0.878942	+	0.319909i	−0.741783	−	0.670640i	$-0.766019\pi$
$907$	−26.4706	+	9.63451i	−0.878942	+	0.319909i	−0.137159	+	0.990549i	$0.543797\pi$
$908$		0			0
$909$	8.94535	+	7.50604i	0.296699	+	0.248960i
$910$		0			0
$911$	−31.0632			−1.02917			−0.514585	−	0.857439i	$-0.672054\pi$
$911$	−31.0632			−1.02917			−0.514585	+	0.857439i	$0.672054\pi$
$912$		0			0
$913$	0.880713			0.0291473
$914$		0			0
$915$	0.572681	+	0.480537i	0.0189323	+	0.0158860i
$916$		0			0
$917$	−5.80902	+	2.11431i	−0.191831	+	0.0698207i
$918$		0			0
$919$	11.4742	+	19.8738i	0.378498	+	0.655578i	0.990844	−	0.135012i	$-0.0431074\pi$
$919$	11.4742	+	19.8738i	0.378498	+	0.655578i	−0.612346	+	0.790590i	$0.709774\pi$
$920$		0			0
$921$	0.468396	+	2.65641i	0.0154342	+	0.0875316i
$922$		0			0
$923$	−6.44258	+	11.1589i	−0.212060	+	0.367299i
$924$		0			0
$925$	4.63859	−	3.89224i	0.152516	−	0.127976i
$926$		0			0
$927$	27.3129	+	9.94108i	0.897073	+	0.326508i
$928$		0			0
$929$	−8.73363	+	49.5309i	−0.286541	+	1.62505i	0.413187	+	0.910646i	$0.364415\pi$
$929$	−8.73363	+	49.5309i	−0.286541	+	1.62505i	−0.699728	+	0.714409i	$0.746696\pi$
$930$		0			0
$931$	−10.7992	−	4.60343i	−0.353929	−	0.150871i
$932$		0			0
$933$	−0.545649	+	3.09453i	−0.0178637	+	0.101310i
$934$		0			0
$935$	−1.27188	−	0.462926i	−0.0415948	−	0.0151393i
$936$		0			0
$937$	42.5008	−	35.6624i	1.38844	−	1.16504i	0.422473	−	0.906375i	$-0.361162\pi$
$937$	42.5008	−	35.6624i	1.38844	−	1.16504i	0.965967	−	0.258665i	$-0.0832824\pi$
$938$		0			0
$939$	1.21294	−	2.10087i	0.0395827	−	0.0685592i
$940$		0			0
$941$	0.338051	+	1.91718i	0.0110201	+	0.0624983i	0.989822	−	0.142312i	$-0.0454535\pi$
$941$	0.338051	+	1.91718i	0.0110201	+	0.0624983i	−0.978802	+	0.204810i	$0.934342\pi$
$942$		0			0
$943$	2.32704	+	4.03056i	0.0757789	+	0.131253i
$944$		0			0
$945$	−3.12614	+	1.13782i	−0.101693	+	0.0370134i
$946$		0			0
$947$	15.9097	+	13.3498i	0.516996	+	0.433811i	0.863583	−	0.504207i	$-0.168215\pi$
$947$	15.9097	+	13.3498i	0.516996	+	0.433811i	−0.346587	+	0.938018i	$0.612659\pi$
$948$		0			0
$949$	20.3178			0.659543
$950$		0			0
$951$	−4.77669			−0.154895
$952$		0			0
$953$	3.36299	+	2.82189i	0.108938	+	0.0914099i	0.695630	−	0.718401i	$-0.255125\pi$
$953$	3.36299	+	2.82189i	0.108938	+	0.0914099i	−0.586692	+	0.809810i	$0.699570\pi$
$954$		0			0
$955$	−6.12210	+	2.22826i	−0.198107	+	0.0721049i
$956$		0			0
$957$	0.0323947	+	0.0561092i	0.00104717	+	0.00181375i
$958$		0			0
$959$	8.42804	+	47.7978i	0.272156	+	1.54347i
$960$		0			0
$961$	15.2718	−	26.4516i	0.492639	−	0.853276i
$962$		0			0
$963$	−10.2911	+	8.63529i	−0.331627	+	0.278268i
$964$		0			0
$965$	−4.40160	−	1.60205i	−0.141693	−	0.0515719i
$966$		0			0
$967$	7.52574	−	42.6806i	0.242012	−	1.37252i	−0.585320	−	0.810802i	$-0.699031\pi$
$967$	7.52574	−	42.6806i	0.242012	−	1.37252i	0.827332	−	0.561714i	$-0.189858\pi$
$968$		0			0
$969$	2.90945	+	2.72141i	0.0934651	+	0.0874244i
$970$		0			0
$971$	−7.02451	+	39.8380i	−0.225427	+	1.27846i	0.636439	+	0.771327i	$0.280407\pi$
$971$	−7.02451	+	39.8380i	−0.225427	+	1.27846i	−0.861867	+	0.507135i	$0.830705\pi$
$972$		0			0
$973$	15.6284	+	5.68829i	0.501025	+	0.182358i
$974$		0			0
$975$	0.261692	−	0.219585i	0.00838084	−	0.00703236i
$976$		0			0
$977$	27.7522	−	48.0682i	0.887870	−	1.53784i	0.0454823	−	0.998965i	$-0.485518\pi$
$977$	27.7522	−	48.0682i	0.887870	−	1.53784i	0.842388	−	0.538871i	$-0.181149\pi$
$978$		0			0
$979$	0.751425	+	4.26154i	0.0240156	+	0.136199i
$980$		0			0
$981$	−22.1054	−	38.2877i	−0.705772	−	1.22243i
$982$		0			0
$983$	44.1913	−	16.0843i	1.40948	−	0.513010i	0.478505	−	0.878085i	$-0.341179\pi$
$983$	44.1913	−	16.0843i	1.40948	−	0.513010i	0.930978	+	0.365075i	$0.118957\pi$
$984$		0			0
$985$	−1.16119	−	0.974356i	−0.0369987	−	0.0310456i
$986$		0			0
$987$	−4.78554			−0.152326
$988$		0			0
$989$	−18.3270			−0.582764
$990$		0			0
$991$	−29.9240	−	25.1092i	−0.950567	−	0.797620i	0.0288263	−	0.999584i	$-0.490823\pi$
$991$	−29.9240	−	25.1092i	−0.950567	−	0.797620i	−0.979393	+	0.201964i	$0.935267\pi$
$992$		0			0
$993$	1.99097	−	0.724655i	0.0631816	−	0.0229962i
$994$		0			0
$995$	−6.71794	−	11.6358i	−0.212973	−	0.368880i
$996$		0			0
$997$	8.99787	+	51.0294i	0.284965	+	1.61612i	0.705409	+	0.708800i	$0.250763\pi$
$997$	8.99787	+	51.0294i	0.284965	+	1.61612i	−0.420444	+	0.907318i	$0.638126\pi$
$998$		0			0
$999$	3.23513	−	5.60340i	0.102355	−	0.177284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.321.2	yes	18
19.3	odd	18		7220.2.a.x.1.4		9
19.9	even	9	inner	380.2.u.a.161.2	✓	18
19.16	even	9		7220.2.a.v.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.161.2	✓	18	19.9	even	9	inner
380.2.u.a.321.2	yes	18	1.1	even	1	trivial
7220.2.a.v.1.6		9	19.16	even	9
7220.2.a.x.1.4		9	19.3	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.137157 + 0.115088i) q^{3} +(0.939693 - 0.342020i) q^{5} +(-1.55670 - 2.69628i) q^{7} +(-0.515378 - 2.92285i) q^{9} +O(q^{10})\)	\(q+(0.137157 + 0.115088i) q^{3} +(0.939693 - 0.342020i) q^{5} +(-1.55670 - 2.69628i) q^{7} +(-0.515378 - 2.92285i) q^{9} +(0.132577 - 0.229630i) q^{11} +(1.46159 - 1.22642i) q^{13} +(0.168248 + 0.0612373i) q^{15} +(0.886403 - 5.02704i) q^{17} +(0.524618 + 4.32721i) q^{19} +(0.0967984 - 0.548971i) q^{21} +(2.59422 + 0.944218i) q^{23} +(0.766044 - 0.642788i) q^{25} +(0.534268 - 0.925379i) q^{27} +(0.236980 + 1.34398i) q^{29} +(-0.337771 - 0.585037i) q^{31} +(0.0446117 - 0.0162373i) q^{33} +(-2.38500 - 2.00125i) q^{35} +6.05525 q^{37} +0.341614 q^{39} +(1.29142 + 1.08363i) q^{41} +(-6.23816 + 2.27050i) q^{43} +(-1.48397 - 2.57031i) q^{45} +(-1.49075 - 8.45444i) q^{47} +(-1.34660 + 2.33239i) q^{49} +(0.700131 - 0.587480i) q^{51} +(-2.22464 - 0.809704i) q^{53} +(0.0460435 - 0.261126i) q^{55} +(-0.426057 + 0.653886i) q^{57} +(-2.24310 + 12.7213i) q^{59} +(3.92356 + 1.42806i) q^{61} +(-7.07853 + 5.93959i) q^{63} +(0.953985 - 1.65235i) q^{65} +(0.447524 + 2.53804i) q^{67} +(0.247147 + 0.428071i) q^{69} +(-6.34605 + 2.30977i) q^{71} +(8.15753 + 6.84498i) q^{73} +0.179046 q^{75} -0.825529 q^{77} +(8.28927 + 6.95552i) q^{79} +(-8.18708 + 2.97985i) q^{81} +(1.66076 + 2.87651i) q^{83} +(-0.886403 - 5.02704i) q^{85} +(-0.122173 + 0.211610i) q^{87} +(-12.5017 + 10.4902i) q^{89} +(-5.58202 - 2.03169i) q^{91} +(0.0210033 - 0.119115i) q^{93} +(1.97297 + 3.88682i) q^{95} +(2.07945 - 11.7931i) q^{97} +(-0.739503 - 0.269157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^9	\( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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