LMFDB - Embedded newform 380.2.u.a.321.1

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			321.1
Root			$2.91971 + 1.06269i$ of defining polynomial
Character	$\chi$	$=$	380.321
Dual form			380.2.u.a.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.38017 - 1.99720i) q^{3} +(0.939693 - 0.342020i) q^{5} +(2.42255 + 4.19598i) q^{7} +(1.15545 + 6.55290i) q^{9} +(-0.912094 + 1.57979i) q^{11} +(4.37893 - 3.67435i) q^{13} +(-2.91971 - 1.06269i) q^{15} +(0.843866 - 4.78580i) q^{17} +(3.11816 + 3.04583i) q^{19} +(2.61412 - 14.8254i) q^{21} +(-3.49160 - 1.27084i) q^{23} +(0.766044 - 0.642788i) q^{25} +(5.67662 - 9.83220i) q^{27} +(0.509115 + 2.88733i) q^{29} +(-0.598860 - 1.03726i) q^{31} +(5.32609 - 1.93854i) q^{33} +(3.71156 + 3.11437i) q^{35} +3.79201 q^{37} -17.7610 q^{39} +(6.35728 + 5.33439i) q^{41} +(9.07952 - 3.30467i) q^{43} +(3.32699 + 5.76252i) q^{45} +(0.728153 + 4.12956i) q^{47} +(-8.23747 + 14.2677i) q^{49} +(-11.5667 + 9.70564i) q^{51} +(-1.62200 - 0.590361i) q^{53} +(-0.316767 + 1.79647i) q^{55} +(-1.33861 - 13.4772i) q^{57} +(1.96003 - 11.1159i) q^{59} +(1.03692 + 0.377409i) q^{61} +(-24.6966 + 20.7229i) q^{63} +(2.85814 - 4.95044i) q^{65} +(-0.781955 - 4.43469i) q^{67} +(5.77248 + 9.99823i) q^{69} +(-6.95459 + 2.53126i) q^{71} +(-5.48272 - 4.60055i) q^{73} -3.10709 q^{75} -8.83836 q^{77} +(2.27175 + 1.90623i) q^{79} +(-14.3900 + 5.23754i) q^{81} +(5.31509 + 9.20601i) q^{83} +(-0.843866 - 4.78580i) q^{85} +(4.55479 - 7.88913i) q^{87} +(1.63837 - 1.37475i) q^{89} +(26.0257 + 9.47256i) q^{91} +(-0.646218 + 3.66488i) q^{93} +(3.97185 + 1.79567i) q^{95} +(-1.46425 + 8.30419i) q^{97} +(-11.4061 - 4.15148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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
$3$	−2.38017	−	1.99720i	−1.37419	−	1.15308i	−0.971307	−	0.237830i	$-0.923564\pi$
$3$	−2.38017	−	1.99720i	−1.37419	−	1.15308i	−0.402883	−	0.915252i	$-0.631992\pi$
$4$		0			0
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$		0			0
$7$	2.42255	+	4.19598i	0.915637	+	1.58593i	0.805966	+	0.591962i	$0.201646\pi$
$7$	2.42255	+	4.19598i	0.915637	+	1.58593i	0.109671	+	0.993968i	$0.465020\pi$
$8$		0			0
$9$	1.15545	+	6.55290i	0.385151	+	2.18430i
$10$		0			0
$11$	−0.912094	+	1.57979i	−0.275007	+	0.476326i	−0.970137	−	0.242558i	$-0.922013\pi$
$11$	−0.912094	+	1.57979i	−0.275007	+	0.476326i	0.695130	+	0.718884i	$0.255347\pi$
$12$		0			0
$13$	4.37893	−	3.67435i	1.21450	−	1.01908i	0.215401	−	0.976526i	$-0.430894\pi$
$13$	4.37893	−	3.67435i	1.21450	−	1.01908i	0.999094	−	0.0425570i	$-0.0135504\pi$
$14$		0			0
$15$	−2.91971	−	1.06269i	−0.753865	−	0.274384i
$16$		0			0
$17$	0.843866	−	4.78580i	0.204668	−	1.16073i	−0.693294	−	0.720655i	$-0.743841\pi$
$17$	0.843866	−	4.78580i	0.204668	−	1.16073i	0.897962	−	0.440073i	$-0.145047\pi$
$18$		0			0
$19$	3.11816	+	3.04583i	0.715354	+	0.698762i
$19$	3.11816	+	3.04583i	0.715354	+	0.698762i
$20$		0			0
$21$	2.61412	−	14.8254i	0.570448	−	3.23517i
$22$		0			0
$23$	−3.49160	−	1.27084i	−0.728050	−	0.264988i	−0.0487107	−	0.998813i	$-0.515511\pi$
$23$	−3.49160	−	1.27084i	−0.728050	−	0.264988i	−0.679339	+	0.733824i	$0.737733\pi$
$24$		0			0
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$		0			0
$27$	5.67662	−	9.83220i	1.09247	−	1.89221i
$28$		0			0
$29$	0.509115	+	2.88733i	0.0945402	+	0.536164i	0.994887	+	0.100992i	$0.0322015\pi$
$29$	0.509115	+	2.88733i	0.0945402	+	0.536164i	−0.900347	+	0.435173i	$0.856687\pi$
$30$		0			0
$31$	−0.598860	−	1.03726i	−0.107559	−	0.186297i	0.807222	−	0.590248i	$-0.200970\pi$
$31$	−0.598860	−	1.03726i	−0.107559	−	0.186297i	−0.914781	+	0.403951i	$0.867637\pi$
$32$		0			0
$33$	5.32609	−	1.93854i	0.927154	−	0.337456i
$34$		0			0
$35$	3.71156	+	3.11437i	0.627368	+	0.526424i
$36$		0			0
$37$	3.79201			0.623403			0.311701	−	0.950180i	$-0.399101\pi$
$37$	3.79201			0.623403			0.311701	+	0.950180i	$0.399101\pi$
$38$		0			0
$39$	−17.7610			−2.84403
$40$		0			0
$41$	6.35728	+	5.33439i	0.992841	+	0.833092i	0.985977	−	0.166884i	$-0.0533706\pi$
$41$	6.35728	+	5.33439i	0.992841	+	0.833092i	0.00686419	+	0.999976i	$0.497815\pi$
$42$		0			0
$43$	9.07952	−	3.30467i	1.38461	−	0.503958i	0.461040	−	0.887379i	$-0.347477\pi$
$43$	9.07952	−	3.30467i	1.38461	−	0.503958i	0.923574	+	0.383421i	$0.125254\pi$
$44$		0			0
$45$	3.32699	+	5.76252i	0.495959	+	0.859026i
$46$		0			0
$47$	0.728153	+	4.12956i	0.106212	+	0.602359i	0.990729	+	0.135851i	$0.0433768\pi$
$47$	0.728153	+	4.12956i	0.106212	+	0.602359i	−0.884517	+	0.466508i	$0.845512\pi$
$48$		0			0
$49$	−8.23747	+	14.2677i	−1.17678	+	2.03825i
$50$		0			0
$51$	−11.5667	+	9.70564i	−1.61967	+	1.35906i
$52$		0			0
$53$	−1.62200	−	0.590361i	−0.222799	−	0.0810923i	0.228209	−	0.973612i	$-0.426713\pi$
$53$	−1.62200	−	0.590361i	−0.222799	−	0.0810923i	−0.451008	+	0.892520i	$0.648935\pi$
$54$		0			0
$55$	−0.316767	+	1.79647i	−0.0427128	+	0.242237i
$56$		0			0
$57$	−1.33861	−	13.4772i	−0.177303	−	1.78509i
$58$		0			0
$59$	1.96003	−	11.1159i	0.255174	−	1.44716i	−0.540451	−	0.841376i	$-0.681746\pi$
$59$	1.96003	−	11.1159i	0.255174	−	1.44716i	0.795625	−	0.605789i	$-0.207143\pi$
$60$		0			0
$61$	1.03692	+	0.377409i	0.132764	+	0.0483223i	0.407548	−	0.913184i	$-0.366384\pi$
$61$	1.03692	+	0.377409i	0.132764	+	0.0483223i	−0.274784	+	0.961506i	$0.588606\pi$
$62$		0			0
$63$	−24.6966	+	20.7229i	−3.11149	+	2.61085i
$64$		0			0
$65$	2.85814	−	4.95044i	0.354509	−	0.614027i
$66$		0			0
$67$	−0.781955	−	4.43469i	−0.0955311	−	0.541784i	−0.994583	−	0.103942i	$-0.966854\pi$
$67$	−0.781955	−	4.43469i	−0.0955311	−	0.541784i	0.899052	−	0.437841i	$-0.144257\pi$
$68$		0			0
$69$	5.77248	+	9.99823i	0.694925	+	1.20365i
$70$		0			0
$71$	−6.95459	+	2.53126i	−0.825358	+	0.300406i	−0.719952	−	0.694023i	$-0.755836\pi$
$71$	−6.95459	+	2.53126i	−0.825358	+	0.300406i	−0.105406	+	0.994429i	$0.533614\pi$
$72$		0			0
$73$	−5.48272	−	4.60055i	−0.641704	−	0.538454i	0.262837	−	0.964840i	$-0.415342\pi$
$73$	−5.48272	−	4.60055i	−0.641704	−	0.538454i	−0.904541	+	0.426386i	$0.859786\pi$
$74$		0			0
$75$	−3.10709			−0.358775
$76$		0			0
$77$	−8.83836			−1.00723
$78$		0			0
$79$	2.27175	+	1.90623i	0.255592	+	0.214467i	0.761576	−	0.648076i	$-0.224426\pi$
$79$	2.27175	+	1.90623i	0.255592	+	0.214467i	−0.505984	+	0.862543i	$0.668870\pi$
$80$		0			0
$81$	−14.3900	+	5.23754i	−1.59889	+	0.581949i
$82$		0			0
$83$	5.31509	+	9.20601i	0.583407	+	1.01049i	0.995072	+	0.0991559i	$0.0316142\pi$
$83$	5.31509	+	9.20601i	0.583407	+	1.01049i	−0.411664	+	0.911335i	$0.635052\pi$
$84$		0			0
$85$	−0.843866	−	4.78580i	−0.0915301	−	0.519093i
$86$		0			0
$87$	4.55479	−	7.88913i	0.488325	−	0.845804i
$88$		0			0
$89$	1.63837	−	1.37475i	0.173667	−	0.145724i	−0.551811	−	0.833969i	$-0.686063\pi$
$89$	1.63837	−	1.37475i	0.173667	−	0.145724i	0.725478	+	0.688245i	$0.241619\pi$
$90$		0			0
$91$	26.0257	+	9.47256i	2.72823	+	0.992994i
$92$		0			0
$93$	−0.646218	+	3.66488i	−0.0670097	+	0.380031i
$94$		0			0
$95$	3.97185	+	1.79567i	0.407503	+	0.184232i
$96$		0			0
$97$	−1.46425	+	8.30419i	−0.148672	+	0.843162i	0.815673	+	0.578514i	$0.196367\pi$
$97$	−1.46425	+	8.30419i	−0.148672	+	0.843162i	−0.964345	+	0.264649i	$0.914744\pi$
$98$		0			0
$99$	−11.4061	−	4.15148i	−1.14636	−	0.417240i
$100$		0			0
$101$	−2.77564	+	2.32904i	−0.276187	+	0.231748i	−0.770351	−	0.637621i	$-0.779919\pi$
$101$	−2.77564	+	2.32904i	−0.276187	+	0.231748i	0.494164	+	0.869369i	$0.335474\pi$
$102$		0			0
$103$	1.18900	−	2.05941i	0.117155	−	0.202919i	−0.801484	−	0.598016i	$-0.795956\pi$
$103$	1.18900	−	2.05941i	0.117155	−	0.202919i	0.918639	+	0.395097i	$0.129289\pi$
$104$		0			0
$105$	−2.61412	−	14.8254i	−0.255112	−	1.44681i
$106$		0			0
$107$	−8.94605	−	15.4950i	−0.864847	−	1.49796i	−0.867199	−	0.497962i	$-0.834082\pi$
$107$	−8.94605	−	15.4950i	−0.864847	−	1.49796i	0.00235182	−	0.999997i	$-0.499251\pi$
$108$		0			0
$109$	−3.36634	+	1.22525i	−0.322437	+	0.117357i	−0.498167	−	0.867081i	$-0.665993\pi$
$109$	−3.36634	+	1.22525i	−0.322437	+	0.117357i	0.175731	+	0.984438i	$0.443771\pi$
$110$		0			0
$111$	−9.02562	−	7.57339i	−0.856674	−	0.718834i
$112$		0			0
$113$	−9.39037			−0.883371			−0.441686	−	0.897170i	$-0.645619\pi$
$113$	−9.39037			−0.883371			−0.441686	+	0.897170i	$0.645619\pi$
$114$		0			0
$115$	−3.71569			−0.346490
$116$		0			0
$117$	29.1373	+	24.4491i	2.69374	+	2.26032i
$118$		0			0
$119$	22.1254	−	8.05299i	2.02823	−	0.738217i
$120$		0			0
$121$	3.83617	+	6.64444i	0.348743	+	0.604040i
$122$		0			0
$123$	−4.47756	−	25.3935i	−0.403728	−	2.28965i
$124$		0			0
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	−6.76401	+	5.67568i	−0.600209	+	0.503635i	−0.891513	−	0.452996i	$-0.850355\pi$
$127$	−6.76401	+	5.67568i	−0.600209	+	0.503635i	0.291304	+	0.956631i	$0.405911\pi$
$128$		0			0
$129$	−28.2108	−	10.2679i	−2.48383	−	0.904039i
$130$		0			0
$131$	1.47788	−	8.38149i	0.129123	−	0.732294i	−0.849650	−	0.527347i	$-0.823187\pi$
$131$	1.47788	−	8.38149i	0.129123	−	0.732294i	0.978773	−	0.204947i	$-0.0657022\pi$
$132$		0			0
$133$	−5.22635	+	20.4624i	−0.453182	+	1.77431i
$134$		0			0
$135$	1.97147	−	11.1808i	0.169677	−	0.962287i
$136$		0			0
$137$	14.9783	+	5.45166i	1.27968	+	0.465767i	0.890327	−	0.455321i	$-0.150475\pi$
$137$	14.9783	+	5.45166i	1.27968	+	0.465767i	0.389356	+	0.921088i	$0.372698\pi$
$138$		0			0
$139$	−4.15128	+	3.48334i	−0.352107	+	0.295453i	−0.801636	−	0.597813i	$-0.796037\pi$
$139$	−4.15128	+	3.48334i	−0.352107	+	0.295453i	0.449528	+	0.893266i	$0.351592\pi$
$140$		0			0
$141$	6.51442	−	11.2833i	0.548613	−	0.950226i
$142$		0			0
$143$	1.81073	+	10.2692i	0.151421	+	0.858750i
$144$		0			0
$145$	1.46594	+	2.53908i	0.121739	+	0.210859i
$146$		0			0
$147$	48.1020	−	17.5077i	3.96738	−	1.44401i
$148$		0			0
$149$	−13.6788	−	11.4779i	−1.12061	−	0.940306i	−0.121978	−	0.992533i	$-0.538924\pi$
$149$	−13.6788	−	11.4779i	−1.12061	−	0.940306i	−0.998635	+	0.0522265i	$0.983368\pi$
$150$		0			0
$151$	−0.621968			−0.0506150			−0.0253075	−	0.999680i	$-0.508056\pi$
$151$	−0.621968			−0.0506150			−0.0253075	+	0.999680i	$0.508056\pi$
$152$		0			0
$153$	32.3359			2.61420
$154$		0			0
$155$	−0.917507	−	0.769880i	−0.0736960	−	0.0618383i
$156$		0			0
$157$	−13.9123	+	5.06368i	−1.11033	+	0.404125i	−0.831113	−	0.556104i	$-0.812296\pi$
$157$	−13.9123	+	5.06368i	−1.11033	+	0.404125i	−0.279213	+	0.960229i	$0.590073\pi$
$158$		0			0
$159$	2.68157	+	4.64462i	0.212662	+	0.368342i
$160$		0			0
$161$	−3.12616	−	17.7294i	−0.246376	−	1.39727i
$162$		0			0
$163$	−10.1692	+	17.6136i	−0.796516	+	1.37961i	0.125356	+	0.992112i	$0.459993\pi$
$163$	−10.1692	+	17.6136i	−0.796516	+	1.37961i	−0.921872	+	0.387494i	$0.873341\pi$
$164$		0			0
$165$	4.34187	−	3.64326i	0.338014	−	0.283628i
$166$		0			0
$167$	−20.8798	−	7.59961i	−1.61572	−	0.588076i	−0.633164	−	0.774018i	$-0.718244\pi$
$167$	−20.8798	−	7.59961i	−1.61572	−	0.588076i	−0.982561	+	0.185942i	$0.940466\pi$
$168$		0			0
$169$	3.41668	−	19.3769i	0.262821	−	1.49053i
$170$		0			0
$171$	−16.3561	+	23.9523i	−1.25079	+	1.83168i
$172$		0			0
$173$	−1.51218	+	8.57600i	−0.114969	+	0.652021i	0.871797	+	0.489868i	$0.162955\pi$
$173$	−1.51218	+	8.57600i	−0.114969	+	0.652021i	−0.986766	+	0.162153i	$0.948156\pi$
$174$		0			0
$175$	4.55290	+	1.65712i	0.344167	+	0.125266i
$176$		0			0
$177$	−26.8658	+	22.5431i	−2.01936	+	1.69444i
$178$		0			0
$179$	−5.74445	+	9.94968i	−0.429360	+	0.743674i	−0.996817	−	0.0797296i	$-0.974594\pi$
$179$	−5.74445	+	9.94968i	−0.429360	+	0.743674i	0.567456	+	0.823404i	$0.307928\pi$
$180$		0			0
$181$	0.727493	+	4.12582i	0.0540741	+	0.306670i	0.999834	−	0.0181957i	$-0.00579218\pi$
$181$	0.727493	+	4.12582i	0.0540741	+	0.306670i	−0.945760	+	0.324865i	$0.894681\pi$
$182$		0			0
$183$	−1.71429	−	2.96923i	−0.126724	−	0.219492i
$184$		0			0
$185$	3.56332	−	1.29694i	0.261981	−	0.0953532i
$186$		0			0
$187$	6.79089	+	5.69824i	0.496599	+	0.416696i
$188$		0			0
$189$	55.0075			4.00121
$190$		0			0
$191$	17.7153			1.28183			0.640917	−	0.767610i	$-0.278554\pi$
$191$	17.7153			1.28183			0.640917	+	0.767610i	$0.278554\pi$
$192$		0			0
$193$	5.80295	+	4.86926i	0.417706	+	0.350497i	0.827290	−	0.561776i	$-0.189882\pi$
$193$	5.80295	+	4.86926i	0.417706	+	0.350497i	−0.409584	+	0.912272i	$0.634326\pi$
$194$		0			0
$195$	−16.6899	+	6.07461i	−1.19519	+	0.435012i
$196$		0			0
$197$	−8.43937	−	14.6174i	−0.601280	−	1.04145i	−0.992628	−	0.121205i	$-0.961324\pi$
$197$	−8.43937	−	14.6174i	−0.601280	−	1.04145i	0.391347	−	0.920243i	$-0.372009\pi$
$198$		0			0
$199$	−1.21363	−	6.88285i	−0.0860321	−	0.487912i	−0.997129	−	0.0757203i	$-0.975874\pi$
$199$	−1.21363	−	6.88285i	−0.0860321	−	0.487912i	0.911097	−	0.412192i	$-0.135237\pi$
$200$		0			0
$201$	−6.99576	+	12.1170i	−0.493443	+	0.854668i
$202$		0			0
$203$	−10.8818	+	9.13093i	−0.763754	+	0.640866i
$204$		0			0
$205$	7.79836	+	2.83837i	0.544661	+	0.198240i
$206$		0			0
$207$	4.29330	−	24.3485i	0.298405	−	1.69234i
$208$		0			0
$209$	−7.65584	+	2.14796i	−0.529565	+	0.148577i
$210$		0			0
$211$	2.10682	−	11.9484i	0.145040	−	0.822561i	−0.822296	−	0.569060i	$-0.807307\pi$
$211$	2.10682	−	11.9484i	0.145040	−	0.822561i	0.967335	−	0.253500i	$-0.0815818\pi$
$212$		0			0
$213$	21.6085	+	7.86486i	1.48059	+	0.538891i
$214$		0			0
$215$	7.40169	−	6.21076i	0.504791	−	0.423570i
$216$		0			0
$217$	2.90154	−	5.02561i	0.196969	−	0.341160i
$218$		0			0
$219$	3.86159	+	21.9002i	0.260942	+	1.47988i
$220$		0			0
$221$	−13.8895	−	24.0573i	−0.934309	−	1.61827i
$222$		0			0
$223$	0.405042	−	0.147423i	0.0271236	−	0.00987219i	−0.328423	−	0.944531i	$-0.606517\pi$
$223$	0.405042	−	0.147423i	0.0271236	−	0.00987219i	0.355546	+	0.934659i	$0.384295\pi$
$224$		0			0
$225$	5.09725	+	4.27710i	0.339816	+	0.285140i
$226$		0			0
$227$	−15.9051			−1.05566			−0.527828	−	0.849351i	$-0.676993\pi$
$227$	−15.9051			−1.05566			−0.527828	+	0.849351i	$0.676993\pi$
$228$		0			0
$229$	−11.5868			−0.765676			−0.382838	−	0.923815i	$-0.625053\pi$
$229$	−11.5868			−0.765676			−0.382838	+	0.923815i	$0.625053\pi$
$230$		0			0
$231$	21.0368	+	17.6519i	1.38412	+	1.16141i
$232$		0			0
$233$	1.73793	−	0.632557i	0.113856	−	0.0414402i	−0.284464	−	0.958687i	$-0.591816\pi$
$233$	1.73793	−	0.632557i	0.113856	−	0.0414402i	0.398320	+	0.917247i	$0.369593\pi$
$234$		0			0
$235$	2.09663	+	3.63148i	0.136769	+	0.236891i
$236$		0			0
$237$	−1.60004	−	9.07428i	−0.103934	−	0.589438i
$238$		0			0
$239$	4.35757	−	7.54753i	0.281868	−	0.488209i	−0.689977	−	0.723831i	$-0.742379\pi$
$239$	4.35757	−	7.54753i	0.281868	−	0.488209i	0.971845	+	0.235622i	$0.0757128\pi$
$240$		0			0
$241$	11.4106	−	9.57467i	0.735024	−	0.616758i	−0.196472	−	0.980509i	$-0.562949\pi$
$241$	11.4106	−	9.57467i	0.735024	−	0.616758i	0.931496	+	0.363751i	$0.118504\pi$
$242$		0			0
$243$	12.7054	+	4.62438i	0.815051	+	0.296654i
$244$		0			0
$245$	−2.86084	+	16.2247i	−0.182773	+	1.03655i
$246$		0			0
$247$	24.8456	+	1.88026i	1.58089	+	0.119638i
$248$		0			0
$249$	5.73541	−	32.5271i	0.363467	−	2.06132i
$250$		0			0
$251$	−1.14690	−	0.417438i	−0.0723918	−	0.0263484i	0.305570	−	0.952169i	$-0.401153\pi$
$251$	−1.14690	−	0.417438i	−0.0723918	−	0.0263484i	−0.377962	+	0.925821i	$0.623375\pi$
$252$		0			0
$253$	5.19234	−	4.35689i	0.326439	−	0.273915i
$254$		0			0
$255$	−7.54965	+	13.0764i	−0.472777	+	0.818874i
$256$		0			0
$257$	0.792264	+	4.49315i	0.0494201	+	0.280275i	0.999496	−	0.0317435i	$-0.0101060\pi$
$257$	0.792264	+	4.49315i	0.0494201	+	0.280275i	−0.950076	+	0.312019i	$0.898995\pi$
$258$		0			0
$259$	9.18633	+	15.9112i	0.570811	+	0.988673i
$260$		0			0
$261$	−18.3321	+	6.67235i	−1.13473	+	0.413008i
$262$		0			0
$263$	−4.77092	−	4.00327i	−0.294187	−	0.246852i	0.483733	−	0.875216i	$-0.339281\pi$
$263$	−4.77092	−	4.00327i	−0.294187	−	0.246852i	−0.777920	+	0.628363i	$0.783725\pi$
$264$		0			0
$265$	−1.72610			−0.106034
$266$		0			0
$267$	−6.64524			−0.406682
$268$		0			0
$269$	5.53601	+	4.64527i	0.337537	+	0.283227i	0.795762	−	0.605609i	$-0.207070\pi$
$269$	5.53601	+	4.64527i	0.337537	+	0.283227i	−0.458226	+	0.888836i	$0.651515\pi$
$270$		0			0
$271$	1.18940	−	0.432907i	0.0722511	−	0.0262973i	−0.305642	−	0.952147i	$-0.598871\pi$
$271$	1.18940	−	0.432907i	0.0722511	−	0.0262973i	0.377893	+	0.925849i	$0.376649\pi$
$272$		0			0
$273$	−43.0268	−	74.5246i	−2.60410	−	4.51044i
$274$		0			0
$275$	0.316767	+	1.79647i	0.0191018	+	0.108331i
$276$		0			0
$277$	10.6737	−	18.4875i	0.641323	−	1.11080i	−0.343815	−	0.939038i	$-0.611719\pi$
$277$	10.6737	−	18.4875i	0.641323	−	1.11080i	0.985138	−	0.171767i	$-0.0549475\pi$
$278$		0			0
$279$	6.10508	−	5.12277i	0.365502	−	0.306692i
$280$		0			0
$281$	−23.0219	−	8.37929i	−1.37337	−	0.499867i	−0.453210	−	0.891404i	$-0.649721\pi$
$281$	−23.0219	−	8.37929i	−1.37337	−	0.499867i	−0.920162	+	0.391537i	$0.871943\pi$
$282$		0			0
$283$	4.49853	−	25.5125i	0.267410	−	1.51656i	−0.494673	−	0.869079i	$-0.664712\pi$
$283$	4.49853	−	25.5125i	0.267410	−	1.51656i	0.762083	−	0.647479i	$-0.224177\pi$
$284$		0			0
$285$	−5.86734	−	12.2066i	−0.347551	−	0.723054i
$286$		0			0
$287$	−6.98216	+	39.5978i	−0.412144	+	2.33739i
$288$		0			0
$289$	−6.21702	−	2.26281i	−0.365707	−	0.133107i
$290$		0			0
$291$	20.0703	−	16.8409i	1.17654	−	0.987234i
$292$		0			0
$293$	15.5929	−	27.0077i	0.910947	−	1.57781i	0.0982181	−	0.995165i	$-0.468686\pi$
$293$	15.5929	−	27.0077i	0.910947	−	1.57781i	0.812729	−	0.582642i	$-0.197981\pi$
$294$		0			0
$295$	−1.96003	−	11.1159i	−0.114117	−	0.647192i
$296$		0			0
$297$	10.3552	+	17.9358i	0.600871	+	1.04074i
$298$		0			0
$299$	−19.9590	+	7.26448i	−1.15426	+	0.420116i
$300$		0			0
$301$	35.8619	+	30.0917i	2.06704	+	1.73446i
$302$		0			0
$303$	11.2581			0.646758
$304$		0			0
$305$	1.10347			0.0631845
$306$		0			0
$307$	−21.3108	−	17.8819i	−1.21627	−	1.02057i	−0.999011	−	0.0444593i	$-0.985843\pi$
$307$	−21.3108	−	17.8819i	−1.21627	−	1.02057i	−0.217260	−	0.976114i	$-0.569712\pi$
$308$		0			0
$309$	−6.94305	+	2.52706i	−0.394976	+	0.143760i
$310$		0			0
$311$	3.08016	+	5.33500i	0.174660	+	0.302520i	0.940044	−	0.341054i	$-0.110784\pi$
$311$	3.08016	+	5.33500i	0.174660	+	0.302520i	−0.765384	+	0.643574i	$0.777451\pi$
$312$		0			0
$313$	−0.945877	−	5.36433i	−0.0534641	−	0.303210i	0.946336	−	0.323183i	$-0.104753\pi$
$313$	−0.945877	−	5.36433i	−0.0534641	−	0.303210i	−0.999801	+	0.0199732i	$0.993642\pi$
$314$		0			0
$315$	−16.1196	+	27.9200i	−0.908236	+	1.57311i
$316$		0			0
$317$	−9.31397	+	7.81535i	−0.523125	+	0.438954i	−0.865719	−	0.500530i	$-0.833139\pi$
$317$	−9.31397	+	7.81535i	−0.523125	+	0.438954i	0.342595	+	0.939483i	$0.388694\pi$
$318$		0			0
$319$	−5.02575	−	1.82922i	−0.281388	−	0.102417i
$320$		0			0
$321$	−9.65350	+	54.7477i	−0.538806	+	3.05572i
$322$		0			0
$323$	17.2081	−	12.3526i	0.957482	−	0.687318i
$324$		0			0
$325$	0.992622	−	5.62944i	0.0550607	−	0.312265i
$326$		0			0
$327$	10.4595	+	3.80695i	0.578412	+	0.210525i
$328$		0			0
$329$	−15.5636	+	13.0594i	−0.858046	+	0.719986i
$330$		0			0
$331$	3.30878	−	5.73097i	0.181867	−	0.315003i	−0.760649	−	0.649163i	$-0.775119\pi$
$331$	3.30878	−	5.73097i	0.181867	−	0.315003i	0.942516	+	0.334160i	$0.108453\pi$
$332$		0			0
$333$	4.38149	+	24.8487i	0.240104	+	1.36170i
$334$		0			0
$335$	−2.25155	−	3.89980i	−0.123015	−	0.213069i
$336$		0			0
$337$	−29.9295	+	10.8935i	−1.63037	+	0.593404i	−0.985317	−	0.170737i	$-0.945385\pi$
$337$	−29.9295	+	10.8935i	−1.63037	+	0.593404i	−0.645049	+	0.764142i	$0.723163\pi$
$338$		0			0
$339$	22.3506	+	18.7544i	1.21392	+	1.01860i
$340$		0			0
$341$	2.18487			0.118317
$342$		0			0
$343$	−45.9070			−2.47874
$344$		0			0
$345$	8.84395	+	7.42096i	0.476142	+	0.399531i
$346$		0			0
$347$	−10.4671	+	3.80972i	−0.561904	+	0.204516i	−0.607328	−	0.794452i	$-0.707758\pi$
$347$	−10.4671	+	3.80972i	−0.561904	+	0.204516i	0.0454237	+	0.998968i	$0.485536\pi$
$348$		0			0
$349$	9.79484	+	16.9652i	0.524306	+	0.908124i	0.999600	+	0.0282970i	$0.00900841\pi$
$349$	9.79484	+	16.9652i	0.524306	+	0.908124i	−0.475294	+	0.879827i	$0.657658\pi$
$350$		0			0
$351$	−11.2695	−	63.9124i	−0.601520	−	3.41139i
$352$		0			0
$353$	−8.11101	+	14.0487i	−0.431706	+	0.747736i	−0.997020	−	0.0771393i	$-0.975421\pi$
$353$	−8.11101	+	14.0487i	−0.431706	+	0.747736i	0.565315	+	0.824875i	$0.308755\pi$
$354$		0			0
$355$	−5.66943	+	4.75722i	−0.300902	+	0.252487i
$356$		0			0
$357$	−68.7456	−	25.0213i	−3.63840	−	1.32427i
$358$		0			0
$359$	−1.55322	+	8.80876i	−0.0819760	+	0.464909i	0.915992	+	0.401196i	$0.131405\pi$
$359$	−1.55322	+	8.80876i	−0.0819760	+	0.464909i	−0.997968	+	0.0637129i	$0.979706\pi$
$360$		0			0
$361$	0.445808	+	18.9948i	0.0234636	+	0.999725i
$362$		0			0
$363$	4.13953	−	23.4765i	0.217269	−	1.23219i
$364$		0			0
$365$	−6.72556	−	2.44790i	−0.352032	−	0.128129i
$366$		0			0
$367$	−10.3150	+	8.65534i	−0.538441	+	0.451805i	−0.871004	−	0.491276i	$-0.836531\pi$
$367$	−10.3150	+	8.65534i	−0.538441	+	0.451805i	0.332564	+	0.943081i	$0.392086\pi$
$368$		0			0
$369$	−27.6102	+	47.8222i	−1.43733	+	2.48953i
$370$		0			0
$371$	−1.45224	−	8.23607i	−0.0753966	−	0.427595i
$372$		0			0
$373$	1.36277	+	2.36039i	0.0705616	+	0.122216i	0.899148	−	0.437646i	$-0.144188\pi$
$373$	1.36277	+	2.36039i	0.0705616	+	0.122216i	−0.828586	+	0.559862i	$0.810854\pi$
$374$		0			0
$375$	−2.91971	+	1.06269i	−0.150773	+	0.0548769i
$376$		0			0
$377$	12.8385	+	10.7727i	0.661214	+	0.554825i
$378$		0			0
$379$	5.80317			0.298089			0.149044	−	0.988831i	$-0.452380\pi$
$379$	5.80317			0.298089			0.149044	+	0.988831i	$0.452380\pi$
$380$		0			0
$381$	27.4349			1.40553
$382$		0			0
$383$	17.2926	+	14.5102i	0.883612	+	0.741439i	0.966919	−	0.255085i	$-0.0821035\pi$
$383$	17.2926	+	14.5102i	0.883612	+	0.741439i	−0.0833062	+	0.996524i	$0.526548\pi$
$384$		0			0
$385$	−8.30535	+	3.02290i	−0.423280	+	0.154061i
$386$		0			0
$387$	32.1461	+	55.6787i	1.63408	+	2.83031i
$388$		0			0
$389$	1.68123	+	9.53473i	0.0852417	+	0.483430i	0.997304	+	0.0733786i	$0.0233781\pi$
$389$	1.68123	+	9.53473i	0.0852417	+	0.483430i	−0.912062	+	0.410051i	$0.865511\pi$
$390$		0			0
$391$	−9.02844	+	15.6377i	−0.456588	+	0.790833i
$392$		0			0
$393$	−20.2571	+	16.9977i	−1.02184	+	0.857421i
$394$		0			0
$395$	2.78672	+	1.01428i	0.140215	+	0.0510341i
$396$		0			0
$397$	−4.13744	+	23.4646i	−0.207652	+	1.17765i	0.685559	+	0.728017i	$0.259558\pi$
$397$	−4.13744	+	23.4646i	−0.207652	+	1.17765i	−0.893212	+	0.449637i	$0.851553\pi$
$398$		0			0
$399$	53.3070	−	38.2658i	2.66869	−	1.91569i
$400$		0			0
$401$	2.33695	−	13.2535i	0.116702	−	0.661849i	−0.869192	−	0.494475i	$-0.835360\pi$
$401$	2.33695	−	13.2535i	0.116702	−	0.661849i	0.985894	−	0.167373i	$-0.0535286\pi$
$402$		0			0
$403$	−6.43361	−	2.34164i	−0.320481	−	0.116646i
$404$		0			0
$405$	−11.7309	+	9.84336i	−0.582911	+	0.489121i
$406$		0			0
$407$	−3.45867	+	5.99059i	−0.171440	+	0.296943i
$408$		0			0
$409$	0.775482	+	4.39798i	0.0383451	+	0.217466i	0.997959	−	0.0638535i	$-0.0203390\pi$
$409$	0.775482	+	4.39798i	0.0383451	+	0.217466i	−0.959614	+	0.281319i	$0.909228\pi$
$410$		0			0
$411$	−24.7628	−	42.8905i	−1.22146	−	2.11563i
$412$		0			0
$413$	51.3902	−	18.7045i	2.52875	−	0.920389i
$414$		0			0
$415$	8.14320	+	6.83295i	0.399734	+	0.335417i
$416$		0			0
$417$	16.8377			0.824544
$418$		0			0
$419$	−17.4692			−0.853428			−0.426714	−	0.904387i	$-0.640329\pi$
$419$	−17.4692			−0.853428			−0.426714	+	0.904387i	$0.640329\pi$
$420$		0			0
$421$	−29.8887	−	25.0796i	−1.45669	−	1.22231i	−0.927511	−	0.373795i	$-0.878056\pi$
$421$	−29.8887	−	25.0796i	−1.45669	−	1.22231i	−0.529177	−	0.848512i	$-0.677499\pi$
$422$		0			0
$423$	−26.2192	+	9.54302i	−1.27482	+	0.463998i
$424$		0			0
$425$	−2.42982	−	4.20856i	−0.117863	−	0.204145i
$426$		0			0
$427$	0.928395	+	5.26519i	0.0449282	+	0.254800i
$428$		0			0
$429$	16.1997	−	28.0587i	0.782128	−	1.35469i
$430$		0			0
$431$	20.5508	−	17.2442i	0.989899	−	0.830624i	0.00434553	−	0.999991i	$-0.498617\pi$
$431$	20.5508	−	17.2442i	0.989899	−	0.830624i	0.985553	+	0.169367i	$0.0541723\pi$
$432$		0			0
$433$	5.89712	+	2.14638i	0.283398	+	0.103148i	0.479808	−	0.877373i	$-0.340706\pi$
$433$	5.89712	+	2.14638i	0.283398	+	0.103148i	−0.196411	+	0.980522i	$0.562929\pi$
$434$		0			0
$435$	1.58186	−	8.97119i	0.0758445	−	0.430136i
$436$		0			0
$437$	−7.01660	−	14.5975i	−0.335650	−	0.698294i
$438$		0			0
$439$	0.00971623	−	0.0551035i	0.000463731	−	0.00262995i	−0.984575	−	0.174963i	$-0.944019\pi$
$439$	0.00971623	−	0.0551035i	0.000463731	−	0.00262995i	0.985039	+	0.172333i	$0.0551305\pi$
$440$		0			0
$441$	−103.013	−	37.4936i	−4.90537	−	1.78541i
$442$		0			0
$443$	15.3122	−	12.8484i	0.727504	−	0.610448i	−0.201946	−	0.979397i	$-0.564727\pi$
$443$	15.3122	−	12.8484i	0.727504	−	0.610448i	0.929450	+	0.368948i	$0.120282\pi$
$444$		0			0
$445$	1.06937	−	1.85220i	0.0506929	−	0.0878028i
$446$		0			0
$447$	9.63426	+	54.6386i	0.455685	+	2.58432i
$448$		0			0
$449$	−4.25179	−	7.36432i	−0.200654	−	0.347544i	0.748085	−	0.663603i	$-0.230974\pi$
$449$	−4.25179	−	7.36432i	−0.200654	−	0.347544i	−0.948739	+	0.316059i	$0.897640\pi$
$450$		0			0
$451$	−14.2257	+	5.17772i	−0.669861	+	0.243809i
$452$		0			0
$453$	1.48039	+	1.24219i	0.0695546	+	0.0583633i
$454$		0			0
$455$	27.6959			1.29840
$456$		0			0
$457$	1.93292			0.0904182			0.0452091	−	0.998978i	$-0.485605\pi$
$457$	1.93292			0.0904182			0.0452091	+	0.998978i	$0.485605\pi$
$458$		0			0
$459$	−42.2646	−	35.4642i	−1.97274	−	1.65533i
$460$		0			0
$461$	−27.5172	+	10.0154i	−1.28160	+	0.466465i	−0.890962	−	0.454078i	$-0.849969\pi$
$461$	−27.5172	+	10.0154i	−1.28160	+	0.466465i	−0.390641	+	0.920543i	$0.627747\pi$
$462$		0			0
$463$	−10.6298	−	18.4113i	−0.494007	−	0.855645i	0.505969	−	0.862552i	$-0.331135\pi$
$463$	−10.6298	−	18.4113i	−0.494007	−	0.855645i	−0.999976	+	0.00690629i	$0.997802\pi$
$464$		0			0
$465$	0.646218	+	3.66488i	0.0299676	+	0.169955i
$466$		0			0
$467$	17.7562	−	30.7546i	0.821658	−	1.42315i	−0.0827897	−	0.996567i	$-0.526383\pi$
$467$	17.7562	−	30.7546i	0.821658	−	1.42315i	0.904447	−	0.426586i	$-0.140284\pi$
$468$		0			0
$469$	16.7135	−	14.0243i	0.771759	−	0.647583i
$470$		0			0
$471$	43.2268	+	15.7333i	1.99179	+	0.724951i
$472$		0			0
$473$	−3.06067	+	17.3579i	−0.140730	+	0.798119i
$474$		0			0
$475$	4.34647	+	0.328930i	0.199430	+	0.0150924i
$476$		0			0
$477$	1.99443	−	11.3110i	0.0913185	−	0.517893i
$478$		0			0
$479$	34.3531	+	12.5035i	1.56963	+	0.571299i	0.972917	−	0.231154i	$-0.0742501\pi$
$479$	34.3531	+	12.5035i	1.56963	+	0.571299i	0.596715	+	0.802453i	$0.296472\pi$
$480$		0			0
$481$	16.6049	−	13.9332i	0.757120	−	0.635299i
$482$		0			0
$483$	−27.9682	+	48.4424i	−1.27260	+	2.20420i
$484$		0			0
$485$	1.46425	+	8.30419i	0.0664883	+	0.377074i
$486$		0			0
$487$	−5.64591	−	9.77901i	−0.255841	−	0.443129i	0.709283	−	0.704924i	$-0.249019\pi$
$487$	−5.64591	−	9.77901i	−0.255841	−	0.443129i	−0.965124	+	0.261795i	$0.915686\pi$
$488$		0			0
$489$	59.3824	−	21.6134i	2.68536	−	0.977392i
$490$		0			0
$491$	26.9477	+	22.6118i	1.21613	+	1.02046i	0.999018	+	0.0443097i	$0.0141088\pi$
$491$	26.9477	+	22.6118i	1.21613	+	1.02046i	0.217114	+	0.976146i	$0.430336\pi$
$492$		0			0
$493$	14.2478			0.641690
$494$		0			0
$495$	−12.1381			−0.545568
$496$		0			0
$497$	−27.4689	−	23.0492i	−1.23215	−	1.03390i
$498$		0			0
$499$	−1.75976	+	0.640499i	−0.0787775	+	0.0286727i	−0.381108	−	0.924530i	$-0.624457\pi$
$499$	−1.75976	+	0.640499i	−0.0787775	+	0.0286727i	0.302331	+	0.953203i	$0.402235\pi$
$500$		0			0
$501$	34.5194	+	59.7893i	1.54221	+	2.67119i
$502$		0			0
$503$	4.67710	+	26.5252i	0.208542	+	1.18270i	0.891768	+	0.452493i	$0.149465\pi$
$503$	4.67710	+	26.5252i	0.208542	+	1.18270i	−0.683226	+	0.730207i	$0.739424\pi$
$504$		0			0
$505$	−1.81167	+	3.13791i	−0.0806184	+	0.139635i
$506$		0			0
$507$	−46.8318	+	39.2966i	−2.07987	+	1.74522i
$508$		0			0
$509$	−21.3143	−	7.75777i	−0.944739	−	0.343857i	−0.176704	−	0.984264i	$-0.556543\pi$
$509$	−21.3143	−	7.75777i	−0.944739	−	0.343857i	−0.768036	+	0.640407i	$0.778766\pi$
$510$		0			0
$511$	6.02164	−	34.1504i	0.266382	−	1.51073i
$512$		0			0
$513$	47.6478	−	13.3683i	2.10370	−	0.590225i
$514$		0			0
$515$	0.412935	−	2.34187i	0.0181961	−	0.103195i
$516$		0			0
$517$	−7.18800	−	2.61622i	−0.316128	−	0.115061i
$518$		0			0
$519$	20.7272	−	17.3922i	0.909823	−	0.763432i
$520$		0			0
$521$	11.3485	−	19.6561i	0.497186	−	0.861151i	−0.502809	−	0.864398i	$-0.667700\pi$
$521$	11.3485	−	19.6561i	0.497186	−	0.861151i	0.999995	+	0.00324627i	$0.00103332\pi$
$522$		0			0
$523$	−4.91928	−	27.8986i	−0.215105	−	1.21992i	−0.880724	−	0.473630i	$-0.842943\pi$
$523$	−4.91928	−	27.8986i	−0.215105	−	1.21992i	0.665619	−	0.746292i	$-0.268168\pi$
$524$		0			0
$525$	−7.52706	−	13.0373i	−0.328508	−	0.568992i
$526$		0			0
$527$	−5.46946	+	1.99072i	−0.238254	+	0.0867172i
$528$		0			0
$529$	−7.04276	−	5.90957i	−0.306207	−	0.256938i
$530$		0			0
$531$	75.1059			3.25932
$532$		0			0
$533$	47.4385			2.05479
$534$		0			0
$535$	−13.7061	−	11.5008i	−0.592568	−	0.497224i
$536$		0			0
$537$	33.5442	−	12.2091i	1.44754	−	0.526861i
$538$		0			0
$539$	−15.0267	−	26.0270i	−0.647246	−	1.12106i
$540$		0			0
$541$	5.93465	+	33.6570i	0.255150	+	1.44703i	0.795686	+	0.605709i	$0.207110\pi$
$541$	5.93465	+	33.6570i	0.255150	+	1.44703i	−0.540536	+	0.841321i	$0.681779\pi$
$542$		0			0
$543$	6.50851	−	11.2731i	0.279307	−	0.483774i
$544$		0			0
$545$	−2.74427	+	2.30271i	−0.117551	+	0.0986373i
$546$		0			0
$547$	−9.80260	−	3.56786i	−0.419129	−	0.152550i	0.123842	−	0.992302i	$-0.460478\pi$
$547$	−9.80260	−	3.56786i	−0.419129	−	0.152550i	−0.542971	+	0.839751i	$0.682701\pi$
$548$		0			0
$549$	−1.27501	+	7.23092i	−0.0544160	+	0.308608i
$550$		0			0
$551$	−7.20683	+	10.5538i	−0.307021	+	0.449609i
$552$		0			0
$553$	−2.49505	+	14.1502i	−0.106100	+	0.601726i
$554$		0			0
$555$	−11.0716	−	4.02972i	−0.469961	−	0.171052i
$556$		0			0
$557$	34.2712	−	28.7569i	1.45212	−	1.21847i	0.521098	−	0.853497i	$-0.325523\pi$
$557$	34.2712	−	28.7569i	1.45212	−	1.21847i	0.931018	−	0.364973i	$-0.118922\pi$
$558$		0			0
$559$	27.6160	−	47.8323i	1.16803	−	2.02309i
$560$		0			0
$561$	−4.78296	−	27.1255i	−0.201937	−	1.14524i
$562$		0			0
$563$	22.6253	+	39.1882i	0.953544	+	1.65159i	0.737666	+	0.675166i	$0.235928\pi$
$563$	22.6253	+	39.1882i	0.953544	+	1.65159i	0.215877	+	0.976420i	$0.430739\pi$
$564$		0			0
$565$	−8.82406	+	3.21169i	−0.371231	+	0.135117i
$566$		0			0
$567$	−56.8371	−	47.6920i	−2.38694	−	2.00288i
$568$		0			0
$569$	−29.3968			−1.23238			−0.616188	−	0.787599i	$-0.711324\pi$
$569$	−29.3968			−1.23238			−0.616188	+	0.787599i	$0.711324\pi$
$570$		0			0
$571$	13.9236			0.582685			0.291342	−	0.956619i	$-0.405898\pi$
$571$	13.9236			0.582685			0.291342	+	0.956619i	$0.405898\pi$
$572$		0			0
$573$	−42.1653	−	35.3809i	−1.76148	−	1.47806i
$574$		0			0
$575$	−3.49160	+	1.27084i	−0.145610	+	0.0529977i
$576$		0			0
$577$	−18.9117	−	32.7560i	−0.787305	−	1.36365i	−0.927613	−	0.373544i	$-0.878143\pi$
$577$	−18.9117	−	32.7560i	−0.787305	−	1.36365i	0.140308	−	0.990108i	$-0.455191\pi$
$578$		0			0
$579$	−4.08713	−	23.1793i	−0.169855	−	0.963298i
$580$		0			0
$581$	−25.7521	+	44.6040i	−1.06838	+	1.85049i
$582$		0			0
$583$	2.41207	−	2.02397i	0.0998977	−	0.0838241i
$584$		0			0
$585$	35.7422	+	13.0091i	1.47776	+	0.537860i
$586$		0			0
$587$	−1.92362	+	10.9094i	−0.0793961	+	0.450278i	0.919030	+	0.394188i	$0.128974\pi$
$587$	−1.92362	+	10.9094i	−0.0793961	+	0.450278i	−0.998426	+	0.0560893i	$0.982137\pi$
$588$		0			0
$589$	1.29197	−	5.05836i	0.0532347	−	0.208426i
$590$		0			0
$591$	−9.10675	+	51.6470i	−0.374602	+	2.12447i
$592$		0			0
$593$	−6.04698	−	2.20092i	−0.248320	−	0.0903810i	0.214862	−	0.976645i	$-0.431070\pi$
$593$	−6.04698	−	2.20092i	−0.248320	−	0.0903810i	−0.463181	+	0.886263i	$0.653292\pi$
$594$		0			0
$595$	18.0368	−	15.1347i	0.739437	−	0.620461i
$596$		0			0
$597$	−10.8578	+	18.8062i	−0.444378	+	0.769686i
$598$		0			0
$599$	2.10667	+	11.9475i	0.0860760	+	0.488161i	0.997119	+	0.0758504i	$0.0241672\pi$
$599$	2.10667	+	11.9475i	0.0860760	+	0.488161i	−0.911043	+	0.412311i	$0.864722\pi$
$600$		0			0
$601$	4.88333	+	8.45817i	0.199195	+	0.345016i	0.948268	−	0.317472i	$-0.102834\pi$
$601$	4.88333	+	8.45817i	0.199195	+	0.345016i	−0.749073	+	0.662488i	$0.769501\pi$
$602$		0			0
$603$	28.1565	−	10.2481i	1.14662	−	0.417337i
$604$		0			0
$605$	5.87735	+	4.93168i	0.238948	+	0.200501i
$606$		0			0
$607$	39.3662			1.59782			0.798912	−	0.601448i	$-0.205409\pi$
$607$	39.3662			1.59782			0.798912	+	0.601448i	$0.205409\pi$
$608$		0			0
$609$	44.1368			1.78851
$610$		0			0
$611$	18.3620	+	15.4076i	0.742847	+	0.623323i
$612$		0			0
$613$	−26.8857	+	9.78559i	−1.08590	+	0.395236i	−0.822101	−	0.569341i	$-0.807198\pi$
$613$	−26.8857	+	9.78559i	−1.08590	+	0.395236i	−0.263801	+	0.964577i	$0.584976\pi$
$614$		0			0
$615$	−12.8926	−	22.3307i	−0.519880	−	0.900459i
$616$		0			0
$617$	1.47446	+	8.36209i	0.0593596	+	0.336645i	0.999996	−	0.00277049i	$-0.000881874\pi$
$617$	1.47446	+	8.36209i	0.0593596	+	0.336645i	−0.940637	+	0.339415i	$0.889771\pi$
$618$		0			0
$619$	−1.44286	+	2.49910i	−0.0579932	+	0.100447i	−0.893564	−	0.448935i	$-0.851804\pi$
$619$	−1.44286	+	2.49910i	−0.0579932	+	0.100447i	0.835571	+	0.549382i	$0.185137\pi$
$620$		0			0
$621$	−32.3157	+	27.1161i	−1.29678	+	1.08813i
$622$		0			0
$623$	9.73746	+	3.54415i	0.390123	+	0.141993i
$624$		0			0
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$		0			0
$627$	22.5121	+	10.1777i	0.899045	+	0.406459i
$628$		0			0
$629$	3.19995	−	18.1478i	0.127590	−	0.723601i
$630$		0			0
$631$	−18.8983	−	6.87842i	−0.752329	−	0.273826i	−0.0627438	−	0.998030i	$-0.519985\pi$
$631$	−18.8983	−	6.87842i	−0.752329	−	0.273826i	−0.689586	+	0.724204i	$0.742207\pi$
$632$		0			0
$633$	−28.8779	+	24.2314i	−1.14779	+	0.963112i
$634$		0			0
$635$	−4.41489	+	7.64682i	−0.175200	+	0.303455i
$636$		0			0
$637$	16.3534	+	92.7447i	0.647945	+	3.67468i
$638$		0			0
$639$	−24.6228	−	42.6480i	−0.974063	−	1.68713i
$640$		0			0
$641$	10.1310	−	3.68738i	0.400151	−	0.145643i	−0.134103	−	0.990967i	$-0.542815\pi$
$641$	10.1310	−	3.68738i	0.400151	−	0.145643i	0.534253	+	0.845325i	$0.320593\pi$
$642$		0			0
$643$	−19.0031	−	15.9455i	−0.749410	−	0.628830i	0.185937	−	0.982562i	$-0.440468\pi$
$643$	−19.0031	−	15.9455i	−0.749410	−	0.628830i	−0.935347	+	0.353732i	$0.884912\pi$
$644$		0			0
$645$	−30.0214			−1.18209
$646$		0			0
$647$	9.02231			0.354704			0.177352	−	0.984148i	$-0.443247\pi$
$647$	9.02231			0.354704			0.177352	+	0.984148i	$0.443247\pi$
$648$		0			0
$649$	15.7731	+	13.2352i	0.619147	+	0.519526i
$650$		0			0
$651$	−16.9433	+	6.16684i	−0.664059	+	0.241698i
$652$		0			0
$653$	−0.239792	−	0.415332i	−0.00938379	−	0.0162532i	0.861295	−	0.508105i	$-0.169654\pi$
$653$	−0.239792	−	0.415332i	−0.00938379	−	0.0162532i	−0.870679	+	0.491851i	$0.836320\pi$
$654$		0			0
$655$	−1.47788	−	8.38149i	−0.0577457	−	0.327492i
$656$		0			0
$657$	23.8119	−	41.2434i	0.928991	−	1.60906i
$658$		0			0
$659$	−30.2891	+	25.4156i	−1.17989	+	0.990049i	−0.179915	+	0.983682i	$0.557582\pi$
$659$	−30.2891	+	25.4156i	−1.17989	+	0.990049i	−0.999980	+	0.00636726i	$0.997973\pi$
$660$		0			0
$661$	34.9478	+	12.7199i	1.35931	+	0.494749i	0.915841	−	0.401541i	$-0.131525\pi$
$661$	34.9478	+	12.7199i	1.35931	+	0.494749i	0.443470	+	0.896289i	$0.353747\pi$
$662$		0			0
$663$	−14.9879	+	85.0005i	−0.582081	+	3.30115i
$664$		0			0
$665$	2.08738	+	21.0159i	0.0809452	+	0.814960i
$666$		0			0
$667$	1.89171	−	10.7284i	0.0732473	−	0.415406i
$668$		0			0
$669$	−1.25850	−	0.458056i	−0.0486564	−	0.0177095i
$670$		0			0
$671$	−1.54200	+	1.29389i	−0.0595282	+	0.0499501i
$672$		0			0
$673$	1.24483	−	2.15611i	0.0479848	−	0.0831121i	−0.841035	−	0.540980i	$-0.818053\pi$
$673$	1.24483	−	2.15611i	0.0479848	−	0.0831121i	0.889020	+	0.457868i	$0.151387\pi$
$674$		0			0
$675$	−1.97147	−	11.1808i	−0.0758819	−	0.430348i
$676$		0			0
$677$	23.7550	+	41.1449i	0.912980	+	1.58133i	0.809832	+	0.586662i	$0.199558\pi$
$677$	23.7550	+	41.1449i	0.912980	+	1.58133i	0.103149	+	0.994666i	$0.467108\pi$
$678$		0			0
$679$	−38.3914	+	13.9733i	−1.47333	+	0.536247i
$680$		0			0
$681$	37.8567	+	31.7655i	1.45067	+	1.21726i
$682$		0			0
$683$	−34.0911			−1.30446			−0.652229	−	0.758022i	$-0.726166\pi$
$683$	−34.0911			−1.30446			−0.652229	+	0.758022i	$0.726166\pi$
$684$		0			0
$685$	15.9396			0.609020
$686$		0			0
$687$	27.5785	+	23.1411i	1.05218	+	0.882888i
$688$		0			0
$689$	−9.27183	+	3.37467i	−0.353229	+	0.128565i
$690$		0			0
$691$	−18.0270	−	31.2237i	−0.685779	−	1.18780i	−0.973191	−	0.229997i	$-0.926128\pi$
$691$	−18.0270	−	31.2237i	−0.685779	−	1.18780i	0.287412	−	0.957807i	$-0.407205\pi$
$692$		0			0
$693$	−10.2123	−	57.9169i	−0.387933	−	2.20008i
$694$		0			0
$695$	−2.70956	+	4.69309i	−0.102779	+	0.178019i
$696$		0			0
$697$	30.8940	−	25.9232i	1.17020	−	0.981911i
$698$		0			0
$699$	−5.39991	−	1.96541i	−0.204243	−	0.0743385i
$700$		0			0
$701$	−0.00505498	+	0.0286682i	−0.000190924	+	0.00108278i	−0.984903	−	0.173107i	$-0.944619\pi$
$701$	−0.00505498	+	0.0286682i	−0.000190924	+	0.00108278i	0.984712	+	0.174190i	$0.0557305\pi$
$702$		0			0
$703$	11.8241	+	11.5498i	0.445954	+	0.435610i
$704$		0			0
$705$	2.26243	−	12.8309i	0.0852082	−	0.483240i
$706$		0			0
$707$	−16.4967	−	6.00432i	−0.620424	−	0.225816i
$708$		0			0
$709$	−15.5141	+	13.0179i	−0.582643	+	0.488896i	−0.885814	−	0.464041i	$-0.846399\pi$
$709$	−15.5141	+	13.0179i	−0.582643	+	0.488896i	0.303171	+	0.952936i	$0.401955\pi$
$710$		0			0
$711$	−9.86641	+	17.0891i	−0.370019	+	0.640892i
$712$		0			0
$713$	0.772796	+	4.38275i	0.0289414	+	0.164135i
$714$		0			0
$715$	5.21379	+	9.03054i	0.194985	+	0.337723i
$716$		0			0
$717$	−25.4456	+	9.26145i	−0.950285	+	0.345875i
$718$		0			0
$719$	26.5829	+	22.3057i	0.991373	+	0.831861i	0.985766	−	0.168123i	$-0.0537707\pi$
$719$	26.5829	+	22.3057i	0.991373	+	0.831861i	0.00560732	+	0.999984i	$0.498215\pi$
$720$		0			0
$721$	11.5216			0.429088
$722$		0			0
$723$	−46.2817			−1.72124
$724$		0			0
$725$	2.24595	+	1.88457i	0.0834124	+	0.0699913i
$726$		0			0
$727$	5.49635	−	2.00051i	0.203848	−	0.0741947i	−0.238078	−	0.971246i	$-0.576517\pi$
$727$	5.49635	−	2.00051i	0.203848	−	0.0741947i	0.441926	+	0.897051i	$0.354295\pi$
$728$		0			0
$729$	1.96519	+	3.40381i	0.0727849	+	0.126067i
$730$		0			0
$731$	−8.15362	−	46.2415i	−0.301573	−	1.71030i
$732$		0			0
$733$	12.8746	−	22.2995i	0.475534	−	0.823650i	−0.524073	−	0.851673i	$-0.675588\pi$
$733$	12.8746	−	22.2995i	0.475534	−	0.823650i	0.999607	+	0.0280237i	$0.00892138\pi$
$734$		0			0
$735$	39.2131	−	32.9037i	1.44640	−	1.21367i
$736$		0			0
$737$	7.71911	+	2.80953i	0.284337	+	0.103490i
$738$		0			0
$739$	6.21157	−	35.2276i	0.228496	−	1.29587i	−0.627391	−	0.778704i	$-0.715877\pi$
$739$	6.21157	−	35.2276i	0.228496	−	1.29587i	0.855887	−	0.517162i	$-0.173012\pi$
$740$		0			0
$741$	−55.3815	−	54.0970i	−2.03449	−	1.98730i
$742$		0			0
$743$	−1.58183	+	8.97099i	−0.0580316	+	0.329114i	−0.999978	−	0.00664994i	$-0.997883\pi$
$743$	−1.58183	+	8.97099i	−0.0580316	+	0.329114i	0.941946	+	0.335764i	$0.108994\pi$
$744$		0			0
$745$	−16.7796	−	6.10726i	−0.614756	−	0.223753i
$746$		0			0
$747$	−54.1847	+	45.4664i	−1.98251	+	1.66353i
$748$		0			0
$749$	43.3444	−	75.0748i	1.58377	−	2.74317i
$750$		0			0
$751$	−0.364246	−	2.06574i	−0.0132915	−	0.0753799i	0.977441	−	0.211211i	$-0.0677407\pi$
$751$	−0.364246	−	2.06574i	−0.0132915	−	0.0753799i	−0.990732	+	0.135831i	$0.956630\pi$
$752$		0			0
$753$	1.89611	+	3.28416i	0.0690981	+	0.119681i
$754$		0			0
$755$	−0.584458	+	0.212725i	−0.0212706	+	0.00774187i
$756$		0			0
$757$	−24.9150	−	20.9061i	−0.905550	−	0.759847i	0.0657172	−	0.997838i	$-0.479066\pi$
$757$	−24.9150	−	20.9061i	−0.905550	−	0.759847i	−0.971267	+	0.237992i	$0.923511\pi$
$758$		0			0
$759$	−21.0602			−0.764436
$760$		0			0
$761$	−12.1184			−0.439293			−0.219646	−	0.975580i	$-0.570490\pi$
$761$	−12.1184			−0.439293			−0.219646	+	0.975580i	$0.570490\pi$
$762$		0			0
$763$	−13.2962	−	11.1569i	−0.481356	−	0.403905i
$764$		0			0
$765$	30.3858	−	11.0595i	1.09860	−	0.399858i
$766$		0			0
$767$	−32.2609	−	55.8775i	−1.16487	−	2.01762i
$768$		0			0
$769$	−1.16096	−	6.58415i	−0.0418654	−	0.237431i	0.956693	−	0.291097i	$-0.0940203\pi$
$769$	−1.16096	−	6.58415i	−0.0418654	−	0.237431i	−0.998559	+	0.0536666i	$0.982909\pi$
$770$		0			0
$771$	7.08799	−	12.2768i	0.255268	−	0.442136i
$772$		0			0
$773$	33.3313	−	27.9683i	1.19884	−	1.00595i	0.199182	−	0.979962i	$-0.436171\pi$
$773$	33.3313	−	27.9683i	1.19884	−	1.00595i	0.999662	−	0.0259878i	$-0.00827309\pi$
$774$		0			0
$775$	−1.12549	−	0.409645i	−0.0404288	−	0.0147149i
$776$		0			0
$777$	9.91278	−	56.2182i	0.355619	−	2.01682i
$778$		0			0
$779$	3.57534	+	35.9967i	0.128100	+	1.28972i
$780$		0			0
$781$	2.34437	−	13.2956i	0.0838881	−	0.475753i
$782$		0			0
$783$	31.2789	+	11.3846i	1.11782	+	0.406852i
$784$		0			0
$785$	−11.3414	+	9.51660i	−0.404793	+	0.339662i
$786$		0			0
$787$	21.3877	−	37.0446i	0.762389	−	1.32050i	−0.179227	−	0.983808i	$-0.557360\pi$
$787$	21.3877	−	37.0446i	0.762389	−	1.32050i	0.941616	−	0.336689i	$-0.109307\pi$
$788$		0			0
$789$	3.36025	+	19.0569i	0.119628	+	0.678444i
$790$		0			0
$791$	−22.7486	−	39.4017i	−0.808847	−	1.40096i
$792$		0			0
$793$	5.92734	−	2.15738i	0.210486	−	0.0766106i
$794$		0			0
$795$	4.10841	+	3.44736i	0.145710	+	0.122265i
$796$		0			0
$797$	−6.62069			−0.234517			−0.117259	−	0.993101i	$-0.537411\pi$
$797$	−6.62069			−0.234517			−0.117259	+	0.993101i	$0.537411\pi$
$798$		0			0
$799$	20.3777			0.720912
$800$		0			0
$801$	10.9017	+	9.14759i	0.385192	+	0.323214i
$802$		0			0
$803$	12.2687	−	4.46543i	0.432952	−	0.157582i
$804$		0			0
$805$	−9.00143	−	15.5909i	−0.317259	−	0.549508i
$806$		0			0
$807$	−3.89912	−	22.1130i	−0.137255	−	0.778415i
$808$		0			0
$809$	11.3622	−	19.6799i	0.399474	−	0.691909i	−0.594187	−	0.804327i	$-0.702526\pi$
$809$	11.3622	−	19.6799i	0.399474	−	0.691909i	0.993661	+	0.112418i	$0.0358596\pi$
$810$		0			0
$811$	−14.0307	+	11.7731i	−0.492683	+	0.413410i	−0.854987	−	0.518650i	$-0.826435\pi$
$811$	−14.0307	+	11.7731i	−0.492683	+	0.413410i	0.362304	+	0.932060i	$0.381990\pi$
$812$		0			0
$813$	−3.69558	−	1.34508i	−0.129610	−	0.0471740i
$814$		0			0
$815$	−3.53174	+	20.0295i	−0.123711	+	0.701602i
$816$		0			0
$817$	38.3768	+	17.3502i	1.34264	+	0.607007i
$818$		0			0
$819$	−32.0013	+	181.488i	−1.11822	+	6.34172i
$820$		0			0
$821$	−13.8655	−	5.04662i	−0.483908	−	0.176128i	0.0885342	−	0.996073i	$-0.471782\pi$
$821$	−13.8655	−	5.04662i	−0.483908	−	0.176128i	−0.572442	+	0.819945i	$0.694004\pi$
$822$		0			0
$823$	−33.8933	+	28.4399i	−1.18145	+	0.991352i	−0.181479	+	0.983395i	$0.558089\pi$
$823$	−33.8933	+	28.4399i	−1.18145	+	0.991352i	−0.999968	+	0.00795749i	$0.997467\pi$
$824$		0			0
$825$	2.83395	−	4.90855i	0.0986656	−	0.170894i
$826$		0			0
$827$	1.05023	+	5.95616i	0.0365201	+	0.207116i	0.997608	−	0.0691275i	$-0.0220215\pi$
$827$	1.05023	+	5.95616i	0.0365201	+	0.207116i	−0.961088	+	0.276243i	$0.910910\pi$
$828$		0			0
$829$	13.7398	+	23.7980i	0.477203	+	0.826540i	0.999659	−	0.0261266i	$-0.00831730\pi$
$829$	13.7398	+	23.7980i	0.477203	+	0.826540i	−0.522456	+	0.852666i	$0.674984\pi$
$830$		0			0
$831$	−62.3284	+	22.6857i	−2.16215	+	0.786957i
$832$		0			0
$833$	61.3312	+	51.4630i	2.12500	+	1.78309i
$834$		0			0
$835$	−22.2198			−0.768947
$836$		0			0
$837$	−13.5980			−0.470016
$838$		0			0
$839$	−4.11775	−	3.45520i	−0.142160	−	0.119287i	0.568934	−	0.822383i	$-0.307356\pi$
$839$	−4.11775	−	3.45520i	−0.142160	−	0.119287i	−0.711095	+	0.703096i	$0.751800\pi$
$840$		0			0
$841$	19.1736	−	6.97862i	0.661158	−	0.240642i
$842$		0			0
$843$	38.0609	+	65.9234i	1.31089	+	2.27052i
$844$		0			0
$845$	−3.41668	−	19.3769i	−0.117537	−	0.666587i
$846$		0			0
$847$	−18.5866	+	32.1929i	−0.638643	+	1.10616i
$848$		0			0
$849$	−61.6606	+	51.7394i	−2.11619	+	1.77569i
$850$		0			0
$851$	−13.2402	−	4.81904i	−0.453868	−	0.165195i
$852$		0			0
$853$	0.694790	−	3.94035i	0.0237892	−	0.134915i	−0.970600	−	0.240698i	$-0.922624\pi$
$853$	0.694790	−	3.94035i	0.0237892	−	0.134915i	0.994389	+	0.105783i	$0.0337348\pi$
$854$		0			0
$855$	−7.17758	+	28.1019i	−0.245468	+	0.961065i
$856$		0			0
$857$	−1.36870	+	7.76229i	−0.0467539	+	0.265155i	−0.999220	−	0.0394901i	$-0.987427\pi$
$857$	−1.36870	+	7.76229i	−0.0467539	+	0.265155i	0.952466	+	0.304645i	$0.0985377\pi$
$858$		0			0
$859$	39.5282	+	14.3871i	1.34869	+	0.490881i	0.912537	−	0.408993i	$-0.134120\pi$
$859$	39.5282	+	14.3871i	1.34869	+	0.490881i	0.436148	+	0.899875i	$0.356342\pi$
$860$		0			0
$861$	95.7033	−	80.3046i	3.26156	−	2.73677i
$862$		0			0
$863$	−7.53653	+	13.0536i	−0.256546	+	0.444351i	−0.965314	−	0.261090i	$-0.915918\pi$
$863$	−7.53653	+	13.0536i	−0.256546	+	0.444351i	0.708768	+	0.705442i	$0.249251\pi$
$864$		0			0
$865$	1.51218	+	8.57600i	0.0514157	+	0.291593i
$866$		0			0
$867$	10.2783	+	17.8025i	0.349068	+	0.604604i
$868$		0			0
$869$	−5.08350	+	1.85024i	−0.172446	+	0.0627652i
$870$		0			0
$871$	−19.7187	−	16.5460i	−0.668144	−	0.560640i
$872$		0			0
$873$	−56.1083			−1.89898
$874$		0			0
$875$	4.84509			0.163794
$876$		0			0
$877$	−31.4458	−	26.3862i	−1.06185	−	0.890998i	−0.0675609	−	0.997715i	$-0.521522\pi$
$877$	−31.4458	−	26.3862i	−1.06185	−	0.890998i	−0.994289	+	0.106717i	$0.965966\pi$
$878$		0			0
$879$	−91.0534	+	33.1407i	−3.07115	+	1.11781i
$880$		0			0
$881$	−14.1872	−	24.5730i	−0.477981	−	0.827887i	0.521701	−	0.853128i	$-0.325298\pi$
$881$	−14.1872	−	24.5730i	−0.477981	−	0.827887i	−0.999681	+	0.0252420i	$0.991964\pi$
$882$		0			0
$883$	2.42919	+	13.7766i	0.0817487	+	0.463620i	0.998011	+	0.0630410i	$0.0200799\pi$
$883$	2.42919	+	13.7766i	0.0817487	+	0.463620i	−0.916262	+	0.400579i	$0.868809\pi$
$884$		0			0
$885$	−17.5354	+	30.3722i	−0.589446	+	1.02095i
$886$		0			0
$887$	10.5658	−	8.86573i	0.354764	−	0.297682i	−0.447936	−	0.894066i	$-0.647841\pi$
$887$	10.5658	−	8.86573i	0.354764	−	0.297682i	0.802700	+	0.596384i	$0.203396\pi$
$888$		0			0
$889$	−40.2011	−	14.6320i	−1.34830	−	0.490742i
$890$		0			0
$891$	4.85083	−	27.5104i	0.162509	−	0.921633i
$892$		0			0
$893$	−10.3075	+	15.0945i	−0.344926	+	0.505117i
$894$		0			0
$895$	−1.99503	+	11.3144i	−0.0666864	+	0.378197i
$896$		0			0
$897$	62.0143	+	22.5714i	2.07060	+	0.753636i
$898$		0			0
$899$	2.69002	−	2.25719i	0.0897171	−	0.0752816i
$900$		0			0
$901$	−4.19411	+	7.26440i	−0.139726	+	0.242012i
$902$		0			0
$903$	−25.2582	−	143.246i	−0.840541	−	4.76694i
$904$		0			0
$905$	2.09473	+	3.62818i	0.0696312	+	0.120605i
$906$		0			0
$907$	−11.2383	+	4.09042i	−0.373163	+	0.135820i	−0.521792	−	0.853073i	$-0.674736\pi$
$907$	−11.2383	+	4.09042i	−0.373163	+	0.135820i	0.148629	+	0.988893i	$0.452514\pi$
$908$		0			0
$909$	−18.4691	−	15.4974i	−0.612581	−	0.514017i
$910$		0			0
$911$	−24.4191			−0.809040			−0.404520	−	0.914529i	$-0.632561\pi$
$911$	−24.4191			−0.809040			−0.404520	+	0.914529i	$0.632561\pi$
$912$		0			0
$913$	−19.3915			−0.641764
$914$		0			0
$915$	−2.62644	−	2.20385i	−0.0868275	−	0.0728569i
$916$		0			0
$917$	38.7488	−	14.1034i	1.27960	−	0.465735i
$918$		0			0
$919$	−0.543238	−	0.940916i	−0.0179198	−	0.0310380i	0.856926	−	0.515439i	$-0.172371\pi$
$919$	−0.543238	−	0.940916i	−0.0179198	−	0.0310380i	−0.874846	+	0.484401i	$0.839038\pi$
$920$		0			0
$921$	15.0096	+	85.1237i	0.494583	+	2.80492i
$922$		0			0
$923$	−21.1529	+	36.6379i	−0.696255	+	1.20595i
$924$		0			0
$925$	2.90485	−	2.43746i	0.0955109	−	0.0801431i
$926$		0			0
$927$	14.8689	+	5.41184i	0.488359	+	0.177748i
$928$		0			0
$929$	−4.32315	+	24.5178i	−0.141838	+	0.804403i	0.828014	+	0.560708i	$0.189471\pi$
$929$	−4.32315	+	24.5178i	−0.141838	+	0.804403i	−0.969852	+	0.243695i	$0.921640\pi$
$930$		0			0
$931$	−69.1428	+	19.3990i	−2.26606	+	0.635778i
$932$		0			0
$933$	3.32374	−	18.8499i	0.108814	−	0.617117i
$934$		0			0
$935$	8.33026	+	3.03197i	0.272429	+	0.0991560i
$936$		0			0
$937$	20.8371	−	17.4844i	0.680717	−	0.571189i	−0.235499	−	0.971875i	$-0.575672\pi$
$937$	20.8371	−	17.4844i	0.680717	−	0.571189i	0.916216	+	0.400685i	$0.131228\pi$
$938$		0			0
$939$	−8.46228	+	14.6571i	−0.276156	+	0.478316i
$940$		0			0
$941$	6.03637	+	34.2340i	0.196780	+	1.11600i	0.909861	+	0.414913i	$0.136188\pi$
$941$	6.03637	+	34.2340i	0.196780	+	1.11600i	−0.713081	+	0.701082i	$0.752701\pi$
$942$		0			0
$943$	−15.4180	−	26.7047i	−0.502078	−	0.869624i
$944$		0			0
$945$	51.6902	−	18.8137i	1.68148	−	0.612009i
$946$		0			0
$947$	−31.3296	−	26.2886i	−1.01807	−	0.854265i	−0.0286896	−	0.999588i	$-0.509133\pi$
$947$	−31.3296	−	26.2886i	−1.01807	−	0.854265i	−0.989384	+	0.145323i	$0.953578\pi$
$948$		0			0
$949$	−40.9125			−1.32808
$950$		0			0
$951$	37.7776			1.22502
$952$		0			0
$953$	29.8279	+	25.0286i	0.966222	+	0.810756i	0.981954	−	0.189120i	$-0.0605635\pi$
$953$	29.8279	+	25.0286i	0.966222	+	0.810756i	−0.0157324	+	0.999876i	$0.505008\pi$
$954$		0			0
$955$	16.6469	−	6.05899i	0.538682	−	0.196064i
$956$		0			0
$957$	8.30880	+	14.3913i	0.268585	+	0.465203i
$958$		0			0
$959$	13.4106	+	76.0555i	0.433052	+	2.45596i
$960$		0			0
$961$	14.7827	−	25.6044i	0.476862	−	0.825950i
$962$		0			0
$963$	91.2004	−	76.5263i	2.93889	−	2.46602i
$964$		0			0
$965$	7.11838	+	2.59088i	0.229149	+	0.0834033i
$966$		0			0
$967$	10.4689	−	59.3720i	0.336657	−	1.90927i	−0.0735693	−	0.997290i	$-0.523439\pi$
$967$	10.4689	−	59.3720i	0.336657	−	1.90927i	0.410226	−	0.911984i	$-0.365450\pi$
$968$		0			0
$969$	−65.6286	−	4.96661i	−2.10830	−	0.159551i
$970$		0			0
$971$	5.29729	−	30.0424i	0.169998	−	0.964108i	−0.773762	−	0.633476i	$-0.781627\pi$
$971$	5.29729	−	30.0424i	0.169998	−	0.964108i	0.943760	−	0.330631i	$-0.107262\pi$
$972$		0			0
$973$	−24.6727	−	8.98012i	−0.790970	−	0.287890i
$974$		0			0
$975$	−13.6057	+	11.4165i	−0.435731	+	0.365622i
$976$		0			0
$977$	−29.8653	+	51.7283i	−0.955477	+	1.65493i	−0.222204	+	0.975000i	$0.571325\pi$
$977$	−29.8653	+	51.7283i	−0.955477	+	1.65493i	−0.733273	+	0.679935i	$0.762008\pi$
$978$		0			0
$979$	0.677481	+	3.84219i	0.0216524	+	0.122797i
$980$		0			0
$981$	−11.9186	−	20.6436i	−0.380530	−	0.659098i
$982$		0			0
$983$	−10.5510	+	3.84027i	−0.336526	+	0.122485i	−0.504755	−	0.863262i	$-0.668417\pi$
$983$	−10.5510	+	3.84027i	−0.336526	+	0.122485i	0.168229	+	0.985748i	$0.446195\pi$
$984$		0			0
$985$	−12.9299	−	10.8494i	−0.411980	−	0.345692i
$986$		0			0
$987$	63.1260			2.00932
$988$		0			0
$989$	−35.9018			−1.14161
$990$		0			0
$991$	27.5934	+	23.1536i	0.876534	+	0.735499i	0.965463	−	0.260539i	$-0.0839001\pi$
$991$	27.5934	+	23.1536i	0.876534	+	0.735499i	−0.0889294	+	0.996038i	$0.528345\pi$
$992$		0			0
$993$	−19.3213	+	7.03238i	−0.613143	+	0.223166i
$994$		0			0
$995$	−3.49451	−	6.05268i	−0.110784	−	0.191883i
$996$		0			0
$997$	6.52357	+	36.9970i	0.206604	+	1.17171i	0.894896	+	0.446274i	$0.147249\pi$
$997$	6.52357	+	36.9970i	0.206604	+	1.17171i	−0.688293	+	0.725433i	$0.741640\pi$
$998$		0			0
$999$	21.5258	−	37.2838i	0.681047	−	1.17961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.321.1	yes	18
19.3	odd	18		7220.2.a.x.1.9		9
19.9	even	9	inner	380.2.u.a.161.1	✓	18
19.16	even	9		7220.2.a.v.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.161.1	✓	18	19.9	even	9	inner
380.2.u.a.321.1	yes	18	1.1	even	1	trivial
7220.2.a.v.1.1		9	19.16	even	9
7220.2.a.x.1.9		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)

\(f(q)\)	\(=\)	\(q+(-2.38017 - 1.99720i) q^{3} +(0.939693 - 0.342020i) q^{5} +(2.42255 + 4.19598i) q^{7} +(1.15545 + 6.55290i) q^{9} +(-0.912094 + 1.57979i) q^{11} +(4.37893 - 3.67435i) q^{13} +(-2.91971 - 1.06269i) q^{15} +(0.843866 - 4.78580i) q^{17} +(3.11816 + 3.04583i) q^{19} +(2.61412 - 14.8254i) q^{21} +(-3.49160 - 1.27084i) q^{23} +(0.766044 - 0.642788i) q^{25} +(5.67662 - 9.83220i) q^{27} +(0.509115 + 2.88733i) q^{29} +(-0.598860 - 1.03726i) q^{31} +(5.32609 - 1.93854i) q^{33} +(3.71156 + 3.11437i) q^{35} +3.79201 q^{37} -17.7610 q^{39} +(6.35728 + 5.33439i) q^{41} +(9.07952 - 3.30467i) q^{43} +(3.32699 + 5.76252i) q^{45} +(0.728153 + 4.12956i) q^{47} +(-8.23747 + 14.2677i) q^{49} +(-11.5667 + 9.70564i) q^{51} +(-1.62200 - 0.590361i) q^{53} +(-0.316767 + 1.79647i) q^{55} +(-1.33861 - 13.4772i) q^{57} +(1.96003 - 11.1159i) q^{59} +(1.03692 + 0.377409i) q^{61} +(-24.6966 + 20.7229i) q^{63} +(2.85814 - 4.95044i) q^{65} +(-0.781955 - 4.43469i) q^{67} +(5.77248 + 9.99823i) q^{69} +(-6.95459 + 2.53126i) q^{71} +(-5.48272 - 4.60055i) q^{73} -3.10709 q^{75} -8.83836 q^{77} +(2.27175 + 1.90623i) q^{79} +(-14.3900 + 5.23754i) q^{81} +(5.31509 + 9.20601i) q^{83} +(-0.843866 - 4.78580i) q^{85} +(4.55479 - 7.88913i) q^{87} +(1.63837 - 1.37475i) q^{89} +(26.0257 + 9.47256i) q^{91} +(-0.646218 + 3.66488i) q^{93} +(3.97185 + 1.79567i) q^{95} +(-1.46425 + 8.30419i) q^{97} +(-11.4061 - 4.15148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47}+ \cdots - 21 q^{99}+O(q^{100}) \) 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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