LMFDB - Embedded newform 380.2.u.a.101.2

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			101.2
Root			$-0.124000 + 0.703239i$ of defining polynomial
Character	$\chi$	$=$	380.101
Dual form			380.2.u.a.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.671023 + 0.244232i) q^{3} +(-0.173648 - 0.984808i) q^{5} +(1.15961 - 2.00851i) q^{7} +(-1.90751 - 1.60059i) q^{9} +O(q^{10})$	\(q+(0.671023 + 0.244232i) q^{3} +(-0.173648 - 0.984808i) q^{5} +(1.15961 - 2.00851i) q^{7} +(-1.90751 - 1.60059i) q^{9} +(-1.57458 - 2.72725i) q^{11} +(5.20266 - 1.89361i) q^{13} +(0.124000 - 0.703239i) q^{15} +(-2.31628 + 1.94359i) q^{17} +(4.24875 + 0.973710i) q^{19} +(1.26867 - 1.06454i) q^{21} +(-0.283534 + 1.60800i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-1.96020 - 3.39516i) q^{27} +(3.91367 + 3.28396i) q^{29} +(1.01198 - 1.75281i) q^{31} +(-0.390495 - 2.21461i) q^{33} +(-2.17936 - 0.793222i) q^{35} -3.94230 q^{37} +3.95359 q^{39} +(6.75417 + 2.45832i) q^{41} +(-0.0418722 - 0.237469i) q^{43} +(-1.24504 + 2.15647i) q^{45} +(-5.49214 - 4.60845i) q^{47} +(0.810595 + 1.40399i) q^{49} +(-2.02896 + 0.738482i) q^{51} +(-0.521860 + 2.95961i) q^{53} +(-2.41239 + 2.02424i) q^{55} +(2.61320 + 1.69106i) q^{57} +(-0.466370 + 0.391331i) q^{59} +(-1.87362 + 10.6258i) q^{61} +(-5.42678 + 1.97519i) q^{63} +(-2.76828 - 4.79480i) q^{65} +(-11.5028 - 9.65202i) q^{67} +(-0.582984 + 1.00976i) q^{69} +(0.791928 + 4.49124i) q^{71} +(13.6128 + 4.95465i) q^{73} -0.714088 q^{75} -7.30359 q^{77} +(-4.11398 - 1.49737i) q^{79} +(0.811064 + 4.59977i) q^{81} +(-2.97839 + 5.15872i) q^{83} +(2.31628 + 1.94359i) q^{85} +(1.82412 + 3.15946i) q^{87} +(8.52005 - 3.10104i) q^{89} +(2.22974 - 12.6455i) q^{91} +(1.10716 - 0.929014i) q^{93} +(0.221130 - 4.35329i) q^{95} +(7.30113 - 6.12637i) q^{97} +(-1.36169 + 7.72250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	0.671023	+	0.244232i	0.387415	+	0.141008i	0.528382	−	0.849007i	$-0.322799\pi$
$3$	0.671023	+	0.244232i	0.387415	+	0.141008i	−0.140967	+	0.990014i	$0.545021\pi$
$4$		0			0
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$		0			0
$7$	1.15961	−	2.00851i	0.438293	−	0.759145i	−0.559265	−	0.828989i	$-0.688917\pi$
$7$	1.15961	−	2.00851i	0.438293	−	0.759145i	0.997558	+	0.0698437i	$0.0222501\pi$
$8$		0			0
$9$	−1.90751	−	1.60059i	−0.635837	−	0.533531i
$10$		0			0
$11$	−1.57458	−	2.72725i	−0.474752	−	0.822295i	0.524829	−	0.851207i	$-0.324129\pi$
$11$	−1.57458	−	2.72725i	−0.474752	−	0.822295i	−0.999582	+	0.0289120i	$0.990796\pi$
$12$		0			0
$13$	5.20266	−	1.89361i	1.44296	−	0.525194i	0.502344	−	0.864668i	$-0.332471\pi$
$13$	5.20266	−	1.89361i	1.44296	−	0.525194i	0.940616	+	0.339474i	$0.110249\pi$
$14$		0			0
$15$	0.124000	−	0.703239i	0.0320167	−	0.181576i
$16$		0			0
$17$	−2.31628	+	1.94359i	−0.561780	+	0.471389i	−0.878907	−	0.476994i	$-0.841726\pi$
$17$	−2.31628	+	1.94359i	−0.561780	+	0.471389i	0.317127	+	0.948383i	$0.397282\pi$
$18$		0			0
$19$	4.24875	+	0.973710i	0.974730	+	0.223384i
$19$	4.24875	+	0.973710i	0.974730	+	0.223384i
$20$		0			0
$21$	1.26867	−	1.06454i	0.276846	−	0.232302i
$22$		0			0
$23$	−0.283534	+	1.60800i	−0.0591210	+	0.335292i	−0.999994	−	0.00346778i	$-0.998896\pi$
$23$	−0.283534	+	1.60800i	−0.0591210	+	0.335292i	0.940873	+	0.338759i	$0.110007\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$		0			0
$27$	−1.96020	−	3.39516i	−0.377240	−	0.653400i
$28$		0			0
$29$	3.91367	+	3.28396i	0.726751	+	0.609817i	0.929244	−	0.369467i	$-0.120460\pi$
$29$	3.91367	+	3.28396i	0.726751	+	0.609817i	−0.202493	+	0.979284i	$0.564904\pi$
$30$		0			0
$31$	1.01198	−	1.75281i	0.181757	−	0.314813i	−0.760722	−	0.649078i	$-0.775155\pi$
$31$	1.01198	−	1.75281i	0.181757	−	0.314813i	0.942479	+	0.334265i	$0.108488\pi$
$32$		0			0
$33$	−0.390495	−	2.21461i	−0.0679764	−	0.385513i
$34$		0			0
$35$	−2.17936	−	0.793222i	−0.368379	−	0.134079i
$36$		0			0
$37$	−3.94230			−0.648110			−0.324055	−	0.946038i	$-0.605046\pi$
$37$	−3.94230			−0.648110			−0.324055	+	0.946038i	$0.605046\pi$
$38$		0			0
$39$	3.95359			0.633081
$40$		0			0
$41$	6.75417	+	2.45832i	1.05482	+	0.383925i	0.810482	−	0.585764i	$-0.199205\pi$
$41$	6.75417	+	2.45832i	1.05482	+	0.383925i	0.244343	+	0.969689i	$0.421428\pi$
$42$		0			0
$43$	−0.0418722	−	0.237469i	−0.00638544	−	0.0362137i	0.981449	−	0.191726i	$-0.0614084\pi$
$43$	−0.0418722	−	0.237469i	−0.00638544	−	0.0362137i	−0.987834	+	0.155512i	$0.950297\pi$
$44$		0			0
$45$	−1.24504	+	2.15647i	−0.185600	+	0.321468i
$46$		0			0
$47$	−5.49214	−	4.60845i	−0.801110	−	0.672211i	0.147358	−	0.989083i	$-0.452923\pi$
$47$	−5.49214	−	4.60845i	−0.801110	−	0.672211i	−0.948468	+	0.316872i	$0.897368\pi$
$48$		0			0
$49$	0.810595	+	1.40399i	0.115799	+	0.200570i
$50$		0			0
$51$	−2.02896	+	0.738482i	−0.284112	+	0.103408i
$52$		0			0
$53$	−0.521860	+	2.95961i	−0.0716829	+	0.406534i	0.927761	+	0.373176i	$0.121731\pi$
$53$	−0.521860	+	2.95961i	−0.0716829	+	0.406534i	−0.999443	+	0.0333580i	$0.989380\pi$
$54$		0			0
$55$	−2.41239	+	2.02424i	−0.325287	+	0.272948i
$56$		0			0
$57$	2.61320	+	1.69106i	0.346127	+	0.223987i
$58$		0			0
$59$	−0.466370	+	0.391331i	−0.0607162	+	0.0509470i	−0.672641	−	0.739969i	$-0.734840\pi$
$59$	−0.466370	+	0.391331i	−0.0607162	+	0.0509470i	0.611925	+	0.790916i	$0.290396\pi$
$60$		0			0
$61$	−1.87362	+	10.6258i	−0.239893	+	1.36050i	0.592167	+	0.805815i	$0.298272\pi$
$61$	−1.87362	+	10.6258i	−0.239893	+	1.36050i	−0.832060	+	0.554685i	$0.812839\pi$
$62$		0			0
$63$	−5.42678	+	1.97519i	−0.683710	+	0.248850i
$64$		0			0
$65$	−2.76828	−	4.79480i	−0.343363	−	0.594722i
$66$		0			0
$67$	−11.5028	−	9.65202i	−1.40529	−	1.17918i	−0.958691	−	0.284450i	$-0.908189\pi$
$67$	−11.5028	−	9.65202i	−1.40529	−	1.17918i	−0.446604	−	0.894732i	$-0.647367\pi$
$68$		0			0
$69$	−0.582984	+	1.00976i	−0.0701830	+	0.121561i
$70$		0			0
$71$	0.791928	+	4.49124i	0.0939845	+	0.533013i	0.995054	+	0.0993375i	$0.0316723\pi$
$71$	0.791928	+	4.49124i	0.0939845	+	0.533013i	−0.901069	+	0.433675i	$0.857217\pi$
$72$		0			0
$73$	13.6128	+	4.95465i	1.59326	+	0.579898i	0.978032	−	0.208454i	$-0.0668433\pi$
$73$	13.6128	+	4.95465i	1.59326	+	0.579898i	0.615224	+	0.788352i	$0.289066\pi$
$74$		0			0
$75$	−0.714088			−0.0824557
$76$		0			0
$77$	−7.30359			−0.832322
$78$		0			0
$79$	−4.11398	−	1.49737i	−0.462859	−	0.168467i	0.100056	−	0.994982i	$-0.468098\pi$
$79$	−4.11398	−	1.49737i	−0.462859	−	0.168467i	−0.562915	+	0.826515i	$0.690320\pi$
$80$		0			0
$81$	0.811064	+	4.59977i	0.0901182	+	0.511086i
$82$		0			0
$83$	−2.97839	+	5.15872i	−0.326920	+	0.566243i	−0.981899	−	0.189405i	$-0.939344\pi$
$83$	−2.97839	+	5.15872i	−0.326920	+	0.566243i	0.654979	+	0.755647i	$0.272678\pi$
$84$		0			0
$85$	2.31628	+	1.94359i	0.251236	+	0.210812i
$86$		0			0
$87$	1.82412	+	3.15946i	0.195566	+	0.338730i
$88$		0			0
$89$	8.52005	−	3.10104i	0.903123	−	0.328710i	0.151620	−	0.988439i	$-0.451551\pi$
$89$	8.52005	−	3.10104i	0.903123	−	0.328710i	0.751504	+	0.659729i	$0.229329\pi$
$90$		0			0
$91$	2.22974	−	12.6455i	0.233740	−	1.32560i
$92$		0			0
$93$	1.10716	−	0.929014i	0.114807	−	0.0963342i
$94$		0			0
$95$	0.221130	−	4.35329i	0.0226874	−	0.446638i
$96$		0			0
$97$	7.30113	−	6.12637i	0.741317	−	0.622039i	−0.191874	−	0.981420i	$-0.561457\pi$
$97$	7.30113	−	6.12637i	0.741317	−	0.622039i	0.933191	+	0.359381i	$0.117012\pi$
$98$		0			0
$99$	−1.36169	+	7.72250i	−0.136855	+	0.776141i
$100$		0			0
$101$	−17.8871	+	6.51036i	−1.77983	+	0.647805i	−0.780074	+	0.625687i	$0.784819\pi$
$101$	−17.8871	+	6.51036i	−1.77983	+	0.647805i	−0.999755	+	0.0221177i	$0.992959\pi$
$102$		0			0
$103$	3.18075	+	5.50922i	0.313409	+	0.542840i	0.979098	−	0.203389i	$-0.0651957\pi$
$103$	3.18075	+	5.50922i	0.313409	+	0.542840i	−0.665689	+	0.746229i	$0.731862\pi$
$104$		0			0
$105$	−1.26867	−	1.06454i	−0.123809	−	0.103888i
$106$		0			0
$107$	−8.89168	+	15.4008i	−0.859591	+	1.48886i	0.0127277	+	0.999919i	$0.495949\pi$
$107$	−8.89168	+	15.4008i	−0.859591	+	1.48886i	−0.872319	+	0.488937i	$0.837385\pi$
$108$		0			0
$109$	3.15487	+	17.8922i	0.302182	+	1.71376i	0.636482	+	0.771292i	$0.280389\pi$
$109$	3.15487	+	17.8922i	0.302182	+	1.71376i	−0.334300	+	0.942467i	$0.608500\pi$
$110$		0			0
$111$	−2.64537	−	0.962837i	−0.251088	−	0.0913884i
$112$		0			0
$113$	−7.92400			−0.745427			−0.372714	−	0.927946i	$-0.621573\pi$
$113$	−7.92400			−0.745427			−0.372714	+	0.927946i	$0.621573\pi$
$114$		0			0
$115$	1.63281			0.152260
$116$		0			0
$117$	−12.9550	−	4.71525i	−1.19769	−	0.435925i
$118$		0			0
$119$	1.21773	+	6.90608i	0.111629	+	0.633079i
$120$		0			0
$121$	0.541422	−	0.937770i	0.0492202	−	0.0852518i
$122$		0			0
$123$	3.93180	+	3.29918i	0.354519	+	0.297477i
$124$		0			0
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	−6.28578	+	2.28784i	−0.557773	+	0.203013i	−0.605497	−	0.795848i	$-0.707026\pi$
$127$	−6.28578	+	2.28784i	−0.557773	+	0.203013i	0.0477237	+	0.998861i	$0.484803\pi$
$128$		0			0
$129$	0.0299004	−	0.169574i	0.00263258	−	0.0149301i
$130$		0			0
$131$	8.75979	−	7.35034i	0.765347	−	0.642202i	−0.174166	−	0.984716i	$-0.555723\pi$
$131$	8.75979	−	7.35034i	0.765347	−	0.642202i	0.939513	+	0.342514i	$0.111279\pi$
$132$		0			0
$133$	6.88261	−	7.40453i	0.596798	−	0.642054i
$134$		0			0
$135$	−3.00320	+	2.51998i	−0.258474	+	0.216886i
$136$		0			0
$137$	0.429370	−	2.43508i	0.0366836	−	0.208043i	−0.960957	−	0.276698i	$-0.910760\pi$
$137$	0.429370	−	2.43508i	0.0366836	−	0.208043i	0.997640	+	0.0686553i	$0.0218709\pi$
$138$		0			0
$139$	20.7828	−	7.56434i	1.76278	−	0.641599i	0.762791	−	0.646646i	$-0.223829\pi$
$139$	20.7828	−	7.56434i	1.76278	−	0.641599i	0.999987	+	0.00504701i	$0.00160652\pi$
$140$		0			0
$141$	−2.55982	−	4.43373i	−0.215575	−	0.373388i
$142$		0			0
$143$	−13.3563	−	11.2073i	−1.11691	−	0.937202i
$144$		0			0
$145$	2.55447	−	4.42447i	0.212137	−	0.367432i
$146$		0			0
$147$	0.201028	+	1.14008i	0.0165805	+	0.0940326i
$148$		0			0
$149$	12.9595	+	4.71687i	1.06168	+	0.386421i	0.813061	−	0.582179i	$-0.197800\pi$
$149$	12.9595	+	4.71687i	1.06168	+	0.386421i	0.248623	+	0.968600i	$0.420022\pi$
$150$		0			0
$151$	1.98891			0.161856			0.0809278	−	0.996720i	$-0.474212\pi$
$151$	1.98891			0.161856			0.0809278	+	0.996720i	$0.474212\pi$
$152$		0			0
$153$	7.52922			0.608701
$154$		0			0
$155$	−1.90191	−	0.692237i	−0.152765	−	0.0556018i
$156$		0			0
$157$	−0.00345031	−	0.0195677i	−0.000275365	−	0.00156167i	0.984670	−	0.174429i	$-0.0558079\pi$
$157$	−0.00345031	−	0.0195677i	−0.000275365	−	0.00156167i	−0.984945	+	0.172867i	$0.944697\pi$
$158$		0			0
$159$	−1.07301	+	1.85851i	−0.0850955	+	0.147390i
$160$		0			0
$161$	2.90090	+	2.43414i	0.228623	+	0.191837i
$162$		0			0
$163$	−5.04459	−	8.73749i	−0.395123	−	0.684373i	0.597994	−	0.801501i	$-0.295965\pi$
$163$	−5.04459	−	8.73749i	−0.395123	−	0.684373i	−0.993117	+	0.117128i	$0.962631\pi$
$164$		0			0
$165$	−2.11315	+	0.769125i	−0.164509	+	0.0598763i
$166$		0			0
$167$	2.43270	−	13.7965i	0.188248	−	1.06761i	−0.733462	−	0.679730i	$-0.762097\pi$
$167$	2.43270	−	13.7965i	0.188248	−	1.06761i	0.921711	−	0.387879i	$-0.126792\pi$
$168$		0			0
$169$	13.5234	−	11.3474i	1.04026	−	0.872880i
$170$		0			0
$171$	−6.54603	−	8.65788i	−0.500587	−	0.662085i
$172$		0			0
$173$	−2.91704	+	2.44769i	−0.221779	+	0.186094i	−0.746907	−	0.664929i	$-0.768462\pi$
$173$	−2.91704	+	2.44769i	−0.221779	+	0.186094i	0.525128	+	0.851023i	$0.324017\pi$
$174$		0			0
$175$	−0.402729	+	2.28399i	−0.0304435	+	0.172654i
$176$		0			0
$177$	−0.408521	+	0.148689i	−0.0307063	+	0.0111762i
$178$		0			0
$179$	−5.29756	−	9.17564i	−0.395958	−	0.685819i	0.597265	−	0.802044i	$-0.296254\pi$
$179$	−5.29756	−	9.17564i	−0.395958	−	0.685819i	−0.993223	+	0.116225i	$0.962921\pi$
$180$		0			0
$181$	5.61443	+	4.71107i	0.417317	+	0.350171i	0.827142	−	0.561994i	$-0.189965\pi$
$181$	5.61443	+	4.71107i	0.417317	+	0.350171i	−0.409824	+	0.912165i	$0.634410\pi$
$182$		0			0
$183$	−3.85242	+	6.67259i	−0.284779	+	0.493252i
$184$		0			0
$185$	0.684573	+	3.88241i	0.0503308	+	0.285440i
$186$		0			0
$187$	8.94780	+	3.25673i	0.654328	+	0.238156i
$188$		0			0
$189$	−9.09229			−0.661367
$190$		0			0
$191$	17.9346			1.29770			0.648850	−	0.760917i	$-0.275250\pi$
$191$	17.9346			1.29770			0.648850	+	0.760917i	$0.275250\pi$
$192$		0			0
$193$	4.86560	+	1.77093i	0.350234	+	0.127475i	0.511146	−	0.859494i	$-0.329221\pi$
$193$	4.86560	+	1.77093i	0.350234	+	0.127475i	−0.160912	+	0.986969i	$0.551444\pi$
$194$		0			0
$195$	−0.686533	−	3.89352i	−0.0491637	−	0.278821i
$196$		0			0
$197$	0.651384	−	1.12823i	0.0464092	−	0.0803831i	−0.841888	−	0.539653i	$-0.818556\pi$
$197$	0.651384	−	1.12823i	0.0464092	−	0.0803831i	0.888297	+	0.459270i	$0.151889\pi$
$198$		0			0
$199$	−9.31228	−	7.81393i	−0.660130	−	0.553915i	0.249996	−	0.968247i	$-0.419571\pi$
$199$	−9.31228	−	7.81393i	−0.660130	−	0.553915i	−0.910126	+	0.414332i	$0.864015\pi$
$200$		0			0
$201$	−5.36133	−	9.28609i	−0.378159	−	0.654990i
$202$		0			0
$203$	11.1342	−	4.05252i	0.781469	−	0.284431i
$204$		0			0
$205$	1.24812	−	7.07844i	0.0871725	−	0.494380i
$206$		0			0
$207$	3.11460	−	2.61346i	0.216480	−	0.181648i
$208$		0			0
$209$	−4.03443	−	13.1206i	−0.279068	−	0.907569i
$210$		0			0
$211$	20.4402	−	17.1514i	1.40716	−	1.18075i	0.449352	−	0.893355i	$-0.351655\pi$
$211$	20.4402	−	17.1514i	1.40716	−	1.18075i	0.957812	−	0.287396i	$-0.0927897\pi$
$212$		0			0
$213$	−0.565506	+	3.20714i	−0.0387478	+	0.219750i
$214$		0			0
$215$	−0.226590	+	0.0824721i	−0.0154533	+	0.00562455i
$216$		0			0
$217$	−2.34702	−	4.06515i	−0.159326	−	0.275961i
$218$		0			0
$219$	7.92441	+	6.64937i	0.535482	+	0.449323i
$220$		0			0
$221$	−8.37041	+	14.4980i	−0.563055	+	0.975239i
$222$		0			0
$223$	1.94159	+	11.0113i	0.130018	+	0.737372i	0.978200	+	0.207666i	$0.0665866\pi$
$223$	1.94159	+	11.0113i	0.130018	+	0.737372i	−0.848181	+	0.529706i	$0.822302\pi$
$224$		0			0
$225$	2.33991	+	0.851657i	0.155994	+	0.0567771i
$226$		0			0
$227$	0.565133			0.0375092			0.0187546	−	0.999824i	$-0.494030\pi$
$227$	0.565133			0.0375092			0.0187546	+	0.999824i	$0.494030\pi$
$228$		0			0
$229$	−2.02689			−0.133941			−0.0669705	−	0.997755i	$-0.521333\pi$
$229$	−2.02689			−0.133941			−0.0669705	+	0.997755i	$0.521333\pi$
$230$		0			0
$231$	−4.90088	−	1.78377i	−0.322454	−	0.117364i
$232$		0			0
$233$	−5.05833	−	28.6872i	−0.331382	−	1.87936i	−0.460388	−	0.887718i	$-0.652290\pi$
$233$	−5.05833	−	28.6872i	−0.331382	−	1.87936i	0.129006	−	0.991644i	$-0.458821\pi$
$234$		0			0
$235$	−3.58474	+	6.20895i	−0.233842	+	0.405027i
$236$		0			0
$237$	−2.39487	−	2.00954i	−0.155564	−	0.130533i
$238$		0			0
$239$	−4.93291	−	8.54405i	−0.319084	−	0.552669i	0.661214	−	0.750198i	$-0.270042\pi$
$239$	−4.93291	−	8.54405i	−0.319084	−	0.552669i	−0.980297	+	0.197529i	$0.936708\pi$
$240$		0			0
$241$	−4.80460	+	1.74873i	−0.309492	+	0.112646i	−0.492096	−	0.870541i	$-0.663769\pi$
$241$	−4.80460	+	1.74873i	−0.309492	+	0.112646i	0.182605	+	0.983186i	$0.441547\pi$
$242$		0			0
$243$	−2.62148	+	14.8672i	−0.168168	+	0.953728i
$244$		0			0
$245$	1.24190	−	1.04208i	0.0793423	−	0.0665761i
$246$		0			0
$247$	23.9487	−	2.97961i	1.52382	−	0.189588i
$248$		0			0
$249$	−3.25849	+	2.73420i	−0.206498	+	0.173273i
$250$		0			0
$251$	−5.36940	+	30.4514i	−0.338914	+	1.92208i	0.0456071	+	0.998959i	$0.485478\pi$
$251$	−5.36940	+	30.4514i	−0.338914	+	1.92208i	−0.384521	+	0.923116i	$0.625633\pi$
$252$		0			0
$253$	4.83186	−	1.75865i	0.303777	−	0.110566i
$254$		0			0
$255$	1.07959	+	1.86990i	0.0676065	+	0.117098i
$256$		0			0
$257$	10.5875	+	8.88396i	0.660429	+	0.554166i	0.910215	−	0.414135i	$-0.135916\pi$
$257$	10.5875	+	8.88396i	0.660429	+	0.554166i	−0.249786	+	0.968301i	$0.580360\pi$
$258$		0			0
$259$	−4.57154	+	7.91814i	−0.284062	+	0.492009i
$260$		0			0
$261$	−2.20909	−	12.5284i	−0.136739	−	0.775488i
$262$		0			0
$263$	21.5805	+	7.85467i	1.33071	+	0.484340i	0.906875	−	0.421399i	$-0.138461\pi$
$263$	21.5805	+	7.85467i	1.33071	+	0.484340i	0.423837	+	0.905739i	$0.360683\pi$
$264$		0			0
$265$	3.00527			0.184612
$266$		0			0
$267$	6.47452			0.396234
$268$		0			0
$269$	−25.3054	−	9.21042i	−1.54290	−	0.561569i	−0.576161	−	0.817337i	$-0.695450\pi$
$269$	−25.3054	−	9.21042i	−1.54290	−	0.561569i	−0.966738	+	0.255767i	$0.917672\pi$
$270$		0			0
$271$	0.247964	+	1.40628i	0.0150628	+	0.0854251i	0.991412	−	0.130772i	$-0.0417457\pi$
$271$	0.247964	+	1.40628i	0.0150628	+	0.0854251i	−0.976350	+	0.216197i	$0.930635\pi$
$272$		0			0
$273$	4.58463	−	7.94082i	0.277475	−	0.480600i
$274$		0			0
$275$	2.41239	+	2.02424i	0.145473	+	0.122066i
$276$		0			0
$277$	−4.29459	−	7.43844i	−0.258037	−	0.446933i	0.707679	−	0.706534i	$-0.249742\pi$
$277$	−4.29459	−	7.43844i	−0.258037	−	0.446933i	−0.965716	+	0.259601i	$0.916409\pi$
$278$		0			0
$279$	−4.73589	+	1.72372i	−0.283531	+	0.103197i
$280$		0			0
$281$	−0.717482	+	4.06904i	−0.0428014	+	0.242739i	−0.998701	−	0.0509551i	$-0.983773\pi$
$281$	−0.717482	+	4.06904i	−0.0428014	+	0.242739i	0.955900	+	0.293694i	$0.0948846\pi$
$282$		0			0
$283$	−21.6523	+	18.1684i	−1.28710	+	1.08000i	−0.294872	+	0.955537i	$0.595277\pi$
$283$	−21.6523	+	18.1684i	−1.28710	+	1.08000i	−0.992224	+	0.124465i	$0.960279\pi$
$284$		0			0
$285$	1.21160	−	2.86715i	0.0717688	−	0.169835i
$286$		0			0
$287$	12.7698	−	10.7151i	0.753776	−	0.632493i
$288$		0			0
$289$	−1.36441	+	7.73795i	−0.0802594	+	0.455173i
$290$		0			0
$291$	6.39548	−	2.32776i	0.374910	−	0.136456i
$292$		0			0
$293$	−15.5670	−	26.9629i	−0.909436	−	1.57519i	−0.814850	−	0.579672i	$-0.803181\pi$
$293$	−15.5670	−	26.9629i	−0.909436	−	1.57519i	−0.0945860	−	0.995517i	$-0.530153\pi$
$294$		0			0
$295$	0.466370	+	0.391331i	0.0271531	+	0.0227842i
$296$		0			0
$297$	−6.17296	+	10.6919i	−0.358192	+	0.620406i
$298$		0			0
$299$	1.56980	+	8.90280i	0.0907841	+	0.514862i
$300$		0			0
$301$	−0.525514	−	0.191271i	−0.0302901	−	0.0110247i
$302$		0			0
$303$	−13.5927			−0.780878
$304$		0			0
$305$	10.7898			0.617820
$306$		0			0
$307$	7.77449	+	2.82968i	0.443714	+	0.161499i	0.554208	−	0.832378i	$-0.313021\pi$
$307$	7.77449	+	2.82968i	0.443714	+	0.161499i	−0.110494	+	0.993877i	$0.535243\pi$
$308$		0			0
$309$	0.788827	+	4.47366i	0.0448748	+	0.254498i
$310$		0			0
$311$	−6.16019	+	10.6698i	−0.349313	+	0.605027i	−0.986128	−	0.165990i	$-0.946918\pi$
$311$	−6.16019	+	10.6698i	−0.349313	+	0.605027i	0.636815	+	0.771017i	$0.280252\pi$
$312$		0			0
$313$	−0.677188	−	0.568228i	−0.0382769	−	0.0321181i	0.623449	−	0.781864i	$-0.285731\pi$
$313$	−0.677188	−	0.568228i	−0.0382769	−	0.0321181i	−0.661725	+	0.749746i	$0.730176\pi$
$314$		0			0
$315$	2.88753	+	5.00135i	0.162694	+	0.281794i
$316$		0			0
$317$	−11.7423	+	4.27383i	−0.659511	+	0.240042i	−0.650025	−	0.759913i	$-0.725242\pi$
$317$	−11.7423	+	4.27383i	−0.659511	+	0.240042i	−0.00948585	+	0.999955i	$0.503019\pi$
$318$		0			0
$319$	2.79380	−	15.8444i	0.156422	−	0.887116i
$320$		0			0
$321$	−9.72791	+	8.16268i	−0.542959	+	0.455597i
$322$		0			0
$323$	−11.7338	+	6.00244i	−0.652885	+	0.333985i
$324$		0			0
$325$	−4.24125	+	3.55883i	−0.235262	+	0.197408i
$326$		0			0
$327$	−2.25285	+	12.7766i	−0.124583	+	0.706546i
$328$		0			0
$329$	−15.6249	+	5.68699i	−0.861427	+	0.313534i
$330$		0			0
$331$	−3.01501	−	5.22215i	−0.165720	−	0.287035i	0.771191	−	0.636604i	$-0.219661\pi$
$331$	−3.01501	−	5.22215i	−0.165720	−	0.287035i	−0.936911	+	0.349569i	$0.886328\pi$
$332$		0			0
$333$	7.51998	+	6.31001i	0.412092	+	0.345786i
$334$		0			0
$335$	−7.50794	+	13.0041i	−0.410203	+	0.710492i
$336$		0			0
$337$	2.84817	+	16.1528i	0.155150	+	0.879899i	0.958649	+	0.284592i	$0.0918582\pi$
$337$	2.84817	+	16.1528i	0.155150	+	0.879899i	−0.803499	+	0.595306i	$0.797031\pi$
$338$		0			0
$339$	−5.31719	−	1.93530i	−0.288790	−	0.105111i
$340$		0			0
$341$	−6.37377			−0.345159
$342$		0			0
$343$	19.9945			1.07960
$344$		0			0
$345$	1.09565	+	0.398785i	0.0589879	+	0.0214698i
$346$		0			0
$347$	1.88989	+	10.7181i	0.101454	+	0.575377i	0.992577	+	0.121615i	$0.0388073\pi$
$347$	1.88989	+	10.7181i	0.101454	+	0.575377i	−0.891123	+	0.453762i	$0.850082\pi$
$348$		0			0
$349$	−1.22388	+	2.11982i	−0.0655127	+	0.113471i	−0.896921	−	0.442190i	$-0.854202\pi$
$349$	−1.22388	+	2.11982i	−0.0655127	+	0.113471i	0.831409	+	0.555662i	$0.187535\pi$
$350$		0			0
$351$	−16.6274	−	13.9520i	−0.887504	−	0.744705i
$352$		0			0
$353$	−11.7923	−	20.4248i	−0.627639	−	1.08710i	−0.988024	−	0.154299i	$-0.950688\pi$
$353$	−11.7923	−	20.4248i	−0.627639	−	1.08710i	0.360385	−	0.932804i	$-0.382645\pi$
$354$		0			0
$355$	4.28550	−	1.55979i	0.227450	−	0.0827852i
$356$		0			0
$357$	−0.869564	+	4.93154i	−0.0460222	+	0.261005i
$358$		0			0
$359$	−10.3699	+	8.70141i	−0.547304	+	0.459243i	−0.874027	−	0.485877i	$-0.838500\pi$
$359$	−10.3699	+	8.70141i	−0.547304	+	0.459243i	0.326723	+	0.945120i	$0.394056\pi$
$360$		0			0
$361$	17.1038	+	8.27411i	0.900199	+	0.435479i
$362$		0			0
$363$	0.592340	−	0.497033i	0.0310898	−	0.0260874i
$364$		0			0
$365$	2.51554	−	14.2663i	0.131669	−	0.746735i
$366$		0			0
$367$	−7.01361	+	2.55274i	−0.366107	+	0.133252i	−0.518522	−	0.855065i	$-0.673517\pi$
$367$	−7.01361	+	2.55274i	−0.366107	+	0.133252i	0.152414	+	0.988317i	$0.451295\pi$
$368$		0			0
$369$	−8.94890	−	15.4999i	−0.465861	−	0.806895i
$370$		0			0
$371$	5.33925	+	4.48016i	0.277200	+	0.232599i
$372$		0			0
$373$	−11.4309	+	19.7989i	−0.591869	+	1.02515i	0.402112	+	0.915591i	$0.368276\pi$
$373$	−11.4309	+	19.7989i	−0.591869	+	1.02515i	−0.993981	+	0.109556i	$0.965057\pi$
$374$		0			0
$375$	0.124000	+	0.703239i	0.00640333	+	0.0363151i
$376$		0			0
$377$	26.5801	+	9.67436i	1.36894	+	0.498255i
$378$		0			0
$379$	−21.3110			−1.09467			−0.547337	−	0.836913i	$-0.684358\pi$
$379$	−21.3110			−1.09467			−0.547337	+	0.836913i	$0.684358\pi$
$380$		0			0
$381$	−4.77667			−0.244716
$382$		0			0
$383$	14.8002	+	5.38683i	0.756255	+	0.275254i	0.691235	−	0.722630i	$-0.257067\pi$
$383$	14.8002	+	5.38683i	0.756255	+	0.275254i	0.0650198	+	0.997884i	$0.479289\pi$
$384$		0			0
$385$	1.26826	+	7.19264i	0.0646363	+	0.366571i
$386$		0			0
$387$	−0.300219	+	0.519995i	−0.0152610	+	0.0264328i
$388$		0			0
$389$	14.7732	+	12.3962i	0.749033	+	0.628513i	0.935247	−	0.353996i	$-0.115177\pi$
$389$	14.7732	+	12.3962i	0.749033	+	0.628513i	−0.186214	+	0.982509i	$0.559622\pi$
$390$		0			0
$391$	−2.46855	−	4.27565i	−0.124840	−	0.216229i
$392$		0			0
$393$	7.67321	−	2.79282i	0.387062	−	0.140879i
$394$		0			0
$395$	−0.760233	+	4.31150i	−0.0382515	+	0.216935i
$396$		0			0
$397$	−12.0637	+	10.1227i	−0.605462	+	0.508043i	−0.893196	−	0.449667i	$-0.851543\pi$
$397$	−12.0637	+	10.1227i	−0.605462	+	0.508043i	0.287734	+	0.957710i	$0.407098\pi$
$398$		0			0
$399$	6.42682	−	3.28765i	0.321743	−	0.164588i
$400$		0			0
$401$	12.6661	−	10.6281i	0.632515	−	0.530743i	−0.269194	−	0.963086i	$-0.586757\pi$
$401$	12.6661	−	10.6281i	0.632515	−	0.530743i	0.901709	+	0.432343i	$0.142313\pi$
$402$		0			0
$403$	1.94587	−	11.0356i	0.0969306	−	0.549721i
$404$		0			0
$405$	4.38905	−	1.59748i	0.218094	−	0.0793796i
$406$		0			0
$407$	6.20745	+	10.7516i	0.307692	+	0.532938i
$408$		0			0
$409$	−24.5460	−	20.5965i	−1.21372	−	1.01843i	−0.999129	−	0.0417273i	$-0.986714\pi$
$409$	−24.5460	−	20.5965i	−1.21372	−	1.01843i	−0.214590	−	0.976704i	$-0.568842\pi$
$410$		0			0
$411$	0.882843	−	1.52913i	0.0435474	−	0.0754264i
$412$		0			0
$413$	0.245183	+	1.39050i	0.0120647	+	0.0684221i
$414$		0			0
$415$	5.59754	+	2.03734i	0.274772	+	0.100009i
$416$		0			0
$417$	15.7932			0.773397
$418$		0			0
$419$	−14.3431			−0.700706			−0.350353	−	0.936618i	$-0.613938\pi$
$419$	−14.3431			−0.700706			−0.350353	+	0.936618i	$0.613938\pi$
$420$		0			0
$421$	−26.6417	−	9.69680i	−1.29844	−	0.472593i	−0.401951	−	0.915661i	$-0.631668\pi$
$421$	−26.6417	−	9.69680i	−1.29844	−	0.472593i	−0.896488	+	0.443068i	$0.853890\pi$
$422$		0			0
$423$	3.10006	+	17.5813i	0.150730	+	0.854834i
$424$		0			0
$425$	1.51184	−	2.61859i	0.0733352	−	0.127020i
$426$		0			0
$427$	19.1694	+	16.0851i	0.927674	+	0.778411i
$428$		0			0
$429$	−6.22523	−	10.7824i	−0.300557	−	0.520579i
$430$		0			0
$431$	8.90106	−	3.23972i	0.428749	−	0.156052i	−0.118627	−	0.992939i	$-0.537849\pi$
$431$	8.90106	−	3.23972i	0.428749	−	0.156052i	0.547376	+	0.836887i	$0.315627\pi$
$432$		0			0
$433$	1.88247	−	10.6760i	0.0904658	−	0.513057i	−0.905577	−	0.424182i	$-0.860562\pi$
$433$	1.88247	−	10.6760i	0.0904658	−	0.513057i	0.996043	−	0.0888752i	$-0.0283272\pi$
$434$		0			0
$435$	2.79471	−	2.34504i	0.133996	−	0.112436i
$436$		0			0
$437$	−2.77039	+	6.55592i	−0.132526	+	0.313612i
$438$		0			0
$439$	6.82279	−	5.72500i	0.325634	−	0.273239i	−0.465284	−	0.885161i	$-0.654048\pi$
$439$	6.82279	−	5.72500i	0.325634	−	0.273239i	0.790918	+	0.611922i	$0.209603\pi$
$440$		0			0
$441$	0.700999	−	3.97556i	0.0333809	−	0.189312i
$442$		0			0
$443$	−24.4075	+	8.88360i	−1.15963	+	0.422073i	−0.848967	−	0.528446i	$-0.822775\pi$
$443$	−24.4075	+	8.88360i	−1.15963	+	0.422073i	−0.310668	+	0.950518i	$0.600553\pi$
$444$		0			0
$445$	−4.53342	−	7.85212i	−0.214905	−	0.372226i
$446$		0			0
$447$	7.54411	+	6.33026i	0.356824	+	0.299411i
$448$		0			0
$449$	−0.721317	+	1.24936i	−0.0340410	+	0.0589608i	−0.882544	−	0.470230i	$-0.844171\pi$
$449$	−0.721317	+	1.24936i	−0.0340410	+	0.0589608i	0.848503	+	0.529191i	$0.177504\pi$
$450$		0			0
$451$	−3.93052	−	22.2911i	−0.185081	−	1.04965i
$452$		0			0
$453$	1.33461	+	0.485757i	0.0627053	+	0.0228229i
$454$		0			0
$455$	−12.8405			−0.601973
$456$		0			0
$457$	17.0470			0.797427			0.398713	−	0.917076i	$-0.369457\pi$
$457$	17.0470			0.797427			0.398713	+	0.917076i	$0.369457\pi$
$458$		0			0
$459$	11.1392	+	4.05433i	0.519932	+	0.189240i
$460$		0			0
$461$	5.87148	+	33.2988i	0.273462	+	1.55088i	0.743805	+	0.668396i	$0.233019\pi$
$461$	5.87148	+	33.2988i	0.273462	+	1.55088i	−0.470343	+	0.882484i	$0.655870\pi$
$462$		0			0
$463$	−13.6374	+	23.6208i	−0.633786	+	1.09775i	0.352985	+	0.935629i	$0.385167\pi$
$463$	−13.6374	+	23.6208i	−0.633786	+	1.09775i	−0.986771	+	0.162121i	$0.948167\pi$
$464$		0			0
$465$	−1.10716	−	0.929014i	−0.0513431	−	0.0430820i
$466$		0			0
$467$	−5.46671	−	9.46862i	−0.252969	−	0.438156i	0.711373	−	0.702815i	$-0.248074\pi$
$467$	−5.46671	−	9.46862i	−0.252969	−	0.438156i	−0.964342	+	0.264659i	$0.914740\pi$
$468$		0			0
$469$	−32.7250	+	11.9109i	−1.51110	+	0.549996i
$470$		0			0
$471$	0.00246382	−	0.0139730i	0.000113527	−	0.000643843i
$472$		0			0
$473$	−0.581705	+	0.488108i	−0.0267468	+	0.0224432i
$474$		0			0
$475$	−4.32555	+	0.538170i	−0.198470	+	0.0246929i
$476$		0			0
$477$	5.73258	−	4.81021i	0.262477	−	0.220244i
$478$		0			0
$479$	−1.00848	+	5.71936i	−0.0460785	+	0.261324i	−0.999141	−	0.0414508i	$-0.986802\pi$
$479$	−1.00848	+	5.71936i	−0.0460785	+	0.261324i	0.953062	+	0.302775i	$0.0979131\pi$
$480$		0			0
$481$	−20.5105	+	7.46519i	−0.935196	+	0.340384i
$482$		0			0
$483$	1.35207	+	2.34186i	0.0615214	+	0.106558i
$484$		0			0
$485$	−7.30113	−	6.12637i	−0.331527	−	0.278184i
$486$		0			0
$487$	16.3401	−	28.3019i	0.740442	−	1.28248i	−0.211853	−	0.977302i	$-0.567950\pi$
$487$	16.3401	−	28.3019i	0.740442	−	1.28248i	0.952294	−	0.305181i	$-0.0987170\pi$
$488$		0			0
$489$	−1.25106	−	7.09511i	−0.0565748	−	0.320852i
$490$		0			0
$491$	34.3475	+	12.5015i	1.55008	+	0.564184i	0.968437	−	0.249259i	$-0.0801872\pi$
$491$	34.3475	+	12.5015i	1.55008	+	0.564184i	0.581645	+	0.813443i	$0.302409\pi$
$492$		0			0
$493$	−15.4478			−0.695735
$494$		0			0
$495$	7.84164			0.352455
$496$		0			0
$497$	9.93903	+	3.61751i	0.445827	+	0.162268i
$498$		0			0
$499$	−2.22383	−	12.6120i	−0.0995523	−	0.564589i	−0.993257	−	0.115934i	$-0.963014\pi$
$499$	−2.22383	−	12.6120i	−0.0995523	−	0.564589i	0.893705	−	0.448656i	$-0.148097\pi$
$500$		0			0
$501$	5.00196	−	8.66365i	0.223471	−	0.387063i
$502$		0			0
$503$	−29.7181	−	24.9364i	−1.32506	−	1.11186i	−0.985204	−	0.171383i	$-0.945176\pi$
$503$	−29.7181	−	24.9364i	−1.32506	−	1.11186i	−0.339858	−	0.940477i	$-0.610379\pi$
$504$		0			0
$505$	9.51751	+	16.4848i	0.423524	+	0.733564i
$506$		0			0
$507$	11.8459	−	4.31155i	0.526095	−	0.191483i
$508$		0			0
$509$	1.35459	−	7.68223i	0.0600409	−	0.340509i	−0.939959	−	0.341288i	$-0.889137\pi$
$509$	1.35459	−	7.68223i	0.0600409	−	0.340509i	1.00000		0.000778981i	$0.000247957\pi$
$510$		0			0
$511$	25.7370	−	21.5959i	1.13854	−	0.955348i
$512$		0			0
$513$	−5.02249	−	16.3339i	−0.221748	−	0.721158i
$514$		0			0
$515$	4.87319	−	4.08910i	0.214739	−	0.180187i
$516$		0			0
$517$	−3.92059	+	22.2348i	−0.172427	+	0.977884i
$518$		0			0
$519$	−2.55521	+	0.930020i	−0.112161	+	0.0408233i
$520$		0			0
$521$	−11.8725	−	20.5638i	−0.520145	−	0.900918i	−0.999726	−	0.0234202i	$-0.992544\pi$
$521$	−11.8725	−	20.5638i	−0.520145	−	0.900918i	0.479580	−	0.877498i	$-0.340789\pi$
$522$		0			0
$523$	−32.0810	−	26.9192i	−1.40280	−	1.17709i	−0.959838	−	0.280554i	$-0.909482\pi$
$523$	−32.0810	−	26.9192i	−1.40280	−	1.17709i	−0.442966	−	0.896538i	$-0.646074\pi$
$524$		0			0
$525$	−0.828065	+	1.43425i	−0.0361397	+	0.0625959i
$526$		0			0
$527$	1.06270	+	6.02686i	0.0462919	+	0.262534i
$528$		0			0
$529$	19.1077	+	6.95462i	0.830767	+	0.302375i
$530$		0			0
$531$	1.51597			0.0657874
$532$		0			0
$533$	39.7948			1.72370
$534$		0			0
$535$	16.7109	+	6.08227i	0.722475	+	0.262959i
$536$		0			0
$537$	−1.31379	−	7.45090i	−0.0566944	−	0.321530i
$538$		0			0
$539$	2.55269	−	4.42138i	0.109952	−	0.190442i
$540$		0			0
$541$	4.29180	+	3.60124i	0.184519	+	0.154830i	0.730368	−	0.683054i	$-0.239349\pi$
$541$	4.29180	+	3.60124i	0.184519	+	0.154830i	−0.545849	+	0.837883i	$0.683793\pi$
$542$		0			0
$543$	2.61682	+	4.53246i	0.112298	+	0.194507i
$544$		0			0
$545$	17.0725	−	6.21388i	0.731306	−	0.266174i
$546$		0			0
$547$	7.13453	−	40.4619i	0.305050	−	1.73003i	−0.318218	−	0.948018i	$-0.603084\pi$
$547$	7.13453	−	40.4619i	0.305050	−	1.73003i	0.623268	−	0.782008i	$-0.285805\pi$
$548$		0			0
$549$	20.5816	−	17.2700i	0.878401	−	0.737066i
$550$		0			0
$551$	13.4306	+	17.7635i	0.572163	+	0.756752i
$552$		0			0
$553$	−7.77811	+	6.52661i	−0.330759	+	0.277539i
$554$		0			0
$555$	−0.488845	+	2.77238i	−0.0207503	+	0.117681i
$556$		0			0
$557$	1.84636	−	0.672021i	0.0782329	−	0.0284744i	−0.302607	−	0.953115i	$-0.597857\pi$
$557$	1.84636	−	0.672021i	0.0782329	−	0.0284744i	0.380840	+	0.924641i	$0.375635\pi$
$558$		0			0
$559$	−0.667521	−	1.15618i	−0.0282331	−	0.0489012i
$560$		0			0
$561$	5.20878	+	4.37068i	0.219915	+	0.184530i
$562$		0			0
$563$	8.21286	−	14.2251i	0.346131	−	0.599516i	−0.639428	−	0.768851i	$-0.720829\pi$
$563$	8.21286	−	14.2251i	0.346131	−	0.599516i	0.985559	+	0.169335i	$0.0541620\pi$
$564$		0			0
$565$	1.37599	+	7.80362i	0.0578883	+	0.328301i
$566$		0			0
$567$	10.1792	+	3.70493i	0.427486	+	0.155592i
$568$		0			0
$569$	−14.9560			−0.626989			−0.313494	−	0.949590i	$-0.601500\pi$
$569$	−14.9560			−0.626989			−0.313494	+	0.949590i	$0.601500\pi$
$570$		0			0
$571$	−41.0971			−1.71986			−0.859930	−	0.510412i	$-0.829493\pi$
$571$	−41.0971			−1.71986			−0.859930	+	0.510412i	$0.829493\pi$
$572$		0			0
$573$	12.0345	+	4.38020i	0.502749	+	0.182986i
$574$		0			0
$575$	−0.283534	−	1.60800i	−0.0118242	−	0.0670583i
$576$		0			0
$577$	−0.00404408	+	0.00700455i	−0.000168357	+	0.000291603i	−0.866110	−	0.499854i	$-0.833387\pi$
$577$	−0.00404408	+	0.00700455i	−0.000168357	+	0.000291603i	0.865941	+	0.500146i	$0.166720\pi$
$578$		0			0
$579$	2.83241	+	2.37668i	0.117711	+	0.0987712i
$580$		0			0
$581$	6.90755	+	11.9642i	0.286574	+	0.496360i
$582$		0			0
$583$	8.89330	−	3.23690i	0.368323	−	0.134059i
$584$		0			0
$585$	−2.39400	+	13.5770i	−0.0989795	+	0.561341i
$586$		0			0
$587$	19.7483	−	16.5708i	0.815100	−	0.683950i	−0.136719	−	0.990610i	$-0.543656\pi$
$587$	19.7483	−	16.5708i	0.815100	−	0.683950i	0.951819	+	0.306660i	$0.0992114\pi$
$588$		0			0
$589$	6.00639	−	6.46186i	0.247489	−	0.266256i
$590$		0			0
$591$	0.712644	−	0.597979i	0.0293143	−	0.0245976i
$592$		0			0
$593$	7.66557	−	43.4736i	0.314787	−	1.78525i	−0.258623	−	0.965978i	$-0.583269\pi$
$593$	7.66557	−	43.4736i	0.314787	−	1.78525i	0.573410	−	0.819268i	$-0.305620\pi$
$594$		0			0
$595$	6.58970	−	2.39845i	0.270151	−	0.0983271i
$596$		0			0
$597$	−4.34034	−	7.51769i	−0.177638	−	0.307678i
$598$		0			0
$599$	16.8792	+	14.1633i	0.689665	+	0.578698i	0.918813	−	0.394694i	$-0.129149\pi$
$599$	16.8792	+	14.1633i	0.689665	+	0.578698i	−0.229148	+	0.973392i	$0.573594\pi$
$600$		0			0
$601$	−14.7335	+	25.5192i	−0.600993	+	1.04095i	0.391678	+	0.920102i	$0.371895\pi$
$601$	−14.7335	+	25.5192i	−0.600993	+	1.04095i	−0.992671	+	0.120848i	$0.961439\pi$
$602$		0			0
$603$	6.49283	+	36.8227i	0.264409	+	1.49954i
$604$		0			0
$605$	−1.01754	−	0.370354i	−0.0413689	−	0.0150570i
$606$		0			0
$607$	−48.9118			−1.98527			−0.992635	−	0.121143i	$-0.961344\pi$
$607$	−48.9118			−1.98527			−0.992635	+	0.121143i	$0.961344\pi$
$608$		0			0
$609$	8.46107			0.342860
$610$		0			0
$611$	−37.3004	−	13.5762i	−1.50901	−	0.549235i
$612$		0			0
$613$	1.42748	+	8.09563i	0.0576553	+	0.326979i	0.999970	−	0.00774885i	$-0.00246656\pi$
$613$	1.42748	+	8.09563i	0.0576553	+	0.326979i	−0.942315	+	0.334728i	$0.891355\pi$
$614$		0			0
$615$	2.56630	−	4.44497i	0.103483	−	0.179238i
$616$		0			0
$617$	23.2296	+	19.4920i	0.935190	+	0.784718i	0.976742	−	0.214419i	$-0.0687857\pi$
$617$	23.2296	+	19.4920i	0.935190	+	0.784718i	−0.0415517	+	0.999136i	$0.513230\pi$
$618$		0			0
$619$	2.79735	+	4.84515i	0.112435	+	0.194743i	0.916751	−	0.399458i	$-0.130802\pi$
$619$	2.79735	+	4.84515i	0.112435	+	0.194743i	−0.804317	+	0.594201i	$0.797468\pi$
$620$		0			0
$621$	6.01521	−	2.18936i	0.241382	−	0.0878560i
$622$		0			0
$623$	3.65149	−	20.7086i	0.146294	−	0.829673i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$		0			0
$627$	0.497270	−	9.78954i	0.0198590	−	0.390957i
$628$		0			0
$629$	9.13146	−	7.66220i	0.364095	−	0.305512i
$630$		0			0
$631$	0.0628199	−	0.356269i	0.00250082	−	0.0141829i	−0.983532	−	0.180735i	$-0.942152\pi$
$631$	0.0628199	−	0.356269i	0.00250082	−	0.0141829i	0.986033	+	0.166552i	$0.0532634\pi$
$632$		0			0
$633$	17.9048	−	6.51681i	0.711652	−	0.259020i
$634$		0			0
$635$	3.34460	+	5.79301i	0.132726	+	0.229889i
$636$		0			0
$637$	6.87587	+	5.76954i	0.272432	+	0.228598i
$638$		0			0
$639$	5.67804	−	9.83465i	0.224620	−	0.389053i
$640$		0			0
$641$	−6.77181	−	38.4048i	−0.267470	−	1.51690i	−0.761907	−	0.647686i	$-0.775737\pi$
$641$	−6.77181	−	38.4048i	−0.267470	−	1.51690i	0.494437	−	0.869214i	$-0.335374\pi$
$642$		0			0
$643$	−1.65858	−	0.603673i	−0.0654079	−	0.0238065i	0.309109	−	0.951027i	$-0.399969\pi$
$643$	−1.65858	−	0.603673i	−0.0654079	−	0.0238065i	−0.374517	+	0.927220i	$0.622191\pi$
$644$		0			0
$645$	−0.172189			−0.00677995
$646$		0			0
$647$	−31.8882			−1.25366			−0.626828	−	0.779158i	$-0.715647\pi$
$647$	−31.8882			−1.25366			−0.626828	+	0.779158i	$0.715647\pi$
$648$		0			0
$649$	1.80159	+	0.655725i	0.0707186	+	0.0257395i
$650$		0			0
$651$	−0.582060	−	3.30103i	−0.0228127	−	0.129377i
$652$		0			0
$653$	10.2106	−	17.6853i	0.399573	−	0.692081i	−0.594100	−	0.804391i	$-0.702492\pi$
$653$	10.2106	−	17.6853i	0.399573	−	0.692081i	0.993673	+	0.112310i	$0.0358250\pi$
$654$		0			0
$655$	−8.75979	−	7.35034i	−0.342273	−	0.287201i
$656$		0			0
$657$	−18.0362	−	31.2396i	−0.703658	−	1.21877i
$658$		0			0
$659$	24.1407	−	8.78649i	0.940387	−	0.342273i	0.174068	−	0.984734i	$-0.444309\pi$
$659$	24.1407	−	8.78649i	0.940387	−	0.342273i	0.766319	+	0.642461i	$0.222086\pi$
$660$		0			0
$661$	−0.441437	+	2.50351i	−0.0171699	+	0.0973753i	−0.992188	−	0.124748i	$-0.960188\pi$
$661$	−0.441437	+	2.50351i	−0.0171699	+	0.0973753i	0.975019	+	0.222123i	$0.0712988\pi$
$662$		0			0
$663$	−9.15761	+	7.68415i	−0.355652	+	0.298428i
$664$		0			0
$665$	−8.48719	−	5.49227i	−0.329119	−	0.212981i
$666$		0			0
$667$	−6.39028	+	5.36208i	−0.247433	+	0.207621i
$668$		0			0
$669$	−1.38647	+	7.86304i	−0.0536039	+	0.304003i
$670$		0			0
$671$	31.9295	−	11.6214i	1.23262	−	0.448638i
$672$		0			0
$673$	1.09447	+	1.89568i	0.0421888	+	0.0730731i	0.886349	−	0.463018i	$-0.153234\pi$
$673$	1.09447	+	1.89568i	0.0421888	+	0.0730731i	−0.844160	+	0.536091i	$0.819900\pi$
$674$		0			0
$675$	3.00320	+	2.51998i	0.115593	+	0.0969942i
$676$		0			0
$677$	17.8893	−	30.9853i	0.687544	−	1.19086i	−0.285087	−	0.958502i	$-0.592022\pi$
$677$	17.8893	−	30.9853i	0.687544	−	1.19086i	0.972630	−	0.232359i	$-0.0746443\pi$
$678$		0			0
$679$	−3.83839	−	21.7686i	−0.147304	−	0.835402i
$680$		0			0
$681$	0.379217	+	0.138024i	0.0145316	+	0.00528909i
$682$		0			0
$683$	−22.0944			−0.845420			−0.422710	−	0.906265i	$-0.638921\pi$
$683$	−22.0944			−0.845420			−0.422710	+	0.906265i	$0.638921\pi$
$684$		0			0
$685$	−2.47265			−0.0944749
$686$		0			0
$687$	−1.36009	−	0.495033i	−0.0518907	−	0.0188867i
$688$		0			0
$689$	2.88931	+	16.3861i	0.110074	+	0.624260i
$690$		0			0
$691$	−20.2387	+	35.0544i	−0.769916	+	1.33353i	0.167693	+	0.985839i	$0.446368\pi$
$691$	−20.2387	+	35.0544i	−0.769916	+	1.33353i	−0.937608	+	0.347694i	$0.886965\pi$
$692$		0			0
$693$	13.9317	+	11.6901i	0.529221	+	0.444069i
$694$		0			0
$695$	−11.0583	−	19.1536i	−0.419466	−	0.726536i
$696$		0			0
$697$	−20.4225	+	7.43318i	−0.773557	+	0.281552i
$698$		0			0
$699$	3.61209	−	20.4852i	0.136622	−	0.774821i
$700$		0			0
$701$	13.2392	−	11.1090i	0.500037	−	0.419581i	−0.357570	−	0.933886i	$-0.616395\pi$
$701$	13.2392	−	11.1090i	0.500037	−	0.419581i	0.857607	+	0.514305i	$0.171950\pi$
$702$		0			0
$703$	−16.7498	−	3.83866i	−0.631732	−	0.144778i
$704$		0			0
$705$	−3.92187	+	3.29084i	−0.147706	+	0.123940i
$706$		0			0
$707$	−7.66596	+	43.4758i	−0.288308	+	1.63508i
$708$		0			0
$709$	−15.2703	+	5.55795i	−0.573490	+	0.208733i	−0.612452	−	0.790507i	$-0.709817\pi$
$709$	−15.2703	+	5.55795i	−0.573490	+	0.208733i	0.0389627	+	0.999241i	$0.487595\pi$
$710$		0			0
$711$	5.45080	+	9.44105i	0.204421	+	0.354067i
$712$		0			0
$713$	2.53158	+	2.12425i	0.0948086	+	0.0795538i
$714$		0			0
$715$	−8.71773	+	15.0996i	−0.326025	+	0.564691i
$716$		0			0
$717$	−1.22336	−	6.93803i	−0.0456873	−	0.259106i
$718$		0			0
$719$	−38.8579	−	14.1431i	−1.44915	−	0.527449i	−0.506800	−	0.862064i	$-0.669172\pi$
$719$	−38.8579	−	14.1431i	−1.44915	−	0.527449i	−0.942355	+	0.334615i	$0.891394\pi$
$720$		0			0
$721$	14.7538			0.549459
$722$		0			0
$723$	−3.65109			−0.135786
$724$		0			0
$725$	−4.80083	−	1.74736i	−0.178298	−	0.0648953i
$726$		0			0
$727$	5.68484	+	32.2403i	0.210839	+	1.19573i	0.887983	+	0.459877i	$0.152107\pi$
$727$	5.68484	+	32.2403i	0.210839	+	1.19573i	−0.677143	+	0.735851i	$0.736782\pi$
$728$		0			0
$729$	1.61598	−	2.79896i	0.0598511	−	0.103665i
$730$		0			0
$731$	0.558529	+	0.468662i	0.0206579	+	0.0173341i
$732$		0			0
$733$	21.5832	+	37.3832i	0.797194	+	1.38078i	0.921437	+	0.388528i	$0.127016\pi$
$733$	21.5832	+	37.3832i	0.797194	+	1.38078i	−0.124243	+	0.992252i	$0.539650\pi$
$734$		0			0
$735$	1.08786	−	0.395947i	0.0401262	−	0.0146047i
$736$		0			0
$737$	−8.21135	+	46.5689i	−0.302469	+	1.71539i
$738$		0			0
$739$	−19.8020	+	16.6158i	−0.728427	+	0.611223i	−0.929702	−	0.368312i	$-0.879936\pi$
$739$	−19.8020	+	16.6158i	−0.728427	+	0.611223i	0.201275	+	0.979535i	$0.435491\pi$
$740$		0			0
$741$	16.7978	+	3.84965i	0.617083	+	0.141420i
$742$		0			0
$743$	−10.6605	+	8.94520i	−0.391095	+	0.328167i	−0.817039	−	0.576582i	$-0.804386\pi$
$743$	−10.6605	+	8.94520i	−0.391095	+	0.328167i	0.425945	+	0.904749i	$0.359942\pi$
$744$		0			0
$745$	2.39482	−	13.5817i	0.0877394	−	0.497595i
$746$		0			0
$747$	13.9383	−	5.07313i	0.509976	−	0.185616i
$748$		0			0
$749$	20.6218	+	35.7180i	0.753505	+	1.30511i
$750$		0			0
$751$	−9.12380	−	7.65578i	−0.332932	−	0.279363i	0.460961	−	0.887420i	$-0.347505\pi$
$751$	−9.12380	−	7.65578i	−0.332932	−	0.279363i	−0.793893	+	0.608057i	$0.791949\pi$
$752$		0			0
$753$	−11.0402	+	19.1222i	−0.402328	+	0.696852i
$754$		0			0
$755$	−0.345371	−	1.95870i	−0.0125694	−	0.0712843i
$756$		0			0
$757$	−34.8317	−	12.6777i	−1.26598	−	0.460778i	−0.380208	−	0.924901i	$-0.624147\pi$
$757$	−34.8317	−	12.6777i	−1.26598	−	0.460778i	−0.885771	+	0.464123i	$0.846370\pi$
$758$		0			0
$759$	3.67181			0.133278
$760$		0			0
$761$	0.464156			0.0168257			0.00841283	−	0.999965i	$-0.497322\pi$
$761$	0.464156			0.0168257			0.00841283	+	0.999965i	$0.497322\pi$
$762$		0			0
$763$	39.5950	+	14.4114i	1.43344	+	0.521728i
$764$		0			0
$765$	−1.30744	−	7.41483i	−0.0472704	−	0.268084i
$766$		0			0
$767$	−1.68534	+	2.91909i	−0.0608540	+	0.105402i
$768$		0			0
$769$	3.80822	+	3.19548i	0.137328	+	0.115232i	0.708864	−	0.705345i	$-0.249208\pi$
$769$	3.80822	+	3.19548i	0.137328	+	0.115232i	−0.571536	+	0.820577i	$0.693652\pi$
$770$		0			0
$771$	4.93470	+	8.54715i	0.177719	+	0.307818i
$772$		0			0
$773$	−35.9253	+	13.0757i	−1.29214	+	0.470302i	−0.894430	−	0.447208i	$-0.852418\pi$
$773$	−35.9253	+	13.0757i	−1.29214	+	0.470302i	−0.397713	+	0.917510i	$0.630196\pi$
$774$		0			0
$775$	−0.351458	+	1.99322i	−0.0126247	+	0.0715985i
$776$		0			0
$777$	−5.00147	+	4.19673i	−0.179427	+	0.150557i
$778$		0			0
$779$	26.3031	+	17.0214i	0.942407	+	0.609855i
$780$		0			0
$781$	11.0018	−	9.23159i	0.393674	−	0.330332i
$782$		0			0
$783$	3.47801	−	19.7248i	0.124294	−	0.704906i
$784$		0			0
$785$	−0.0186713	+	0.00679578i	−0.000666406	+	0.000242552i
$786$		0			0
$787$	−11.9870	−	20.7621i	−0.427291	−	0.740090i	0.569340	−	0.822102i	$-0.307199\pi$
$787$	−11.9870	−	20.7621i	−0.427291	−	0.740090i	−0.996631	+	0.0820119i	$0.973865\pi$
$788$		0			0
$789$	12.5627	+	10.5413i	0.447243	+	0.375281i
$790$		0			0
$791$	−9.18878	+	15.9154i	−0.326715	+	0.565887i
$792$		0			0
$793$	10.3734	+	58.8306i	0.368371	+	2.08914i
$794$		0			0
$795$	2.01660	+	0.733984i	0.0715216	+	0.0260317i
$796$		0			0
$797$	29.1600			1.03290			0.516450	−	0.856317i	$-0.327253\pi$
$797$	29.1600			1.03290			0.516450	+	0.856317i	$0.327253\pi$
$798$		0			0
$799$	21.6782			0.766921
$800$		0			0
$801$	−21.2156	−	7.72184i	−0.749616	−	0.272838i
$802$		0			0
$803$	−7.92182	−	44.9269i	−0.279555	−	1.58544i
$804$		0			0
$805$	1.89343	−	3.27951i	0.0667345	−	0.115588i
$806$		0			0
$807$	−14.7310	−	12.3608i	−0.518557	−	0.435121i
$808$		0			0
$809$	−8.25448	−	14.2972i	−0.290212	−	0.502662i	0.683648	−	0.729812i	$-0.260393\pi$
$809$	−8.25448	−	14.2972i	−0.290212	−	0.502662i	−0.973860	+	0.227150i	$0.927059\pi$
$810$		0			0
$811$	17.6902	−	6.43870i	0.621186	−	0.226093i	−0.0122045	−	0.999926i	$-0.503885\pi$
$811$	17.6902	−	6.43870i	0.621186	−	0.226093i	0.633391	+	0.773832i	$0.281663\pi$
$812$		0			0
$813$	−0.177068	+	1.00420i	−0.00621005	+	0.0352190i
$814$		0			0
$815$	−7.72876	+	6.48520i	−0.270727	+	0.227167i
$816$		0			0
$817$	0.0533214	−	1.04972i	0.00186548	−	0.0367250i
$818$		0			0
$819$	−24.4935	+	20.5525i	−0.855871	+	0.718161i
$820$		0			0
$821$	−9.24920	+	52.4548i	−0.322799	+	1.83068i	0.201911	+	0.979404i	$0.435285\pi$
$821$	−9.24920	+	52.4548i	−0.322799	+	1.83068i	−0.524710	+	0.851281i	$0.675826\pi$
$822$		0			0
$823$	17.1418	−	6.23909i	0.597524	−	0.217481i	−0.0255114	−	0.999675i	$-0.508121\pi$
$823$	17.1418	−	6.23909i	0.597524	−	0.217481i	0.623036	+	0.782194i	$0.285899\pi$
$824$		0			0
$825$	1.12439	+	1.94749i	0.0391461	+	0.0678030i
$826$		0			0
$827$	−3.53939	−	2.96990i	−0.123077	−	0.103274i	0.579172	−	0.815205i	$-0.303376\pi$
$827$	−3.53939	−	2.96990i	−0.123077	−	0.103274i	−0.702249	+	0.711932i	$0.747820\pi$
$828$		0			0
$829$	−16.1562	+	27.9833i	−0.561128	+	0.971901i	0.436271	+	0.899815i	$0.356299\pi$
$829$	−16.1562	+	27.9833i	−0.561128	+	0.971901i	−0.997398	+	0.0720861i	$0.977034\pi$
$830$		0			0
$831$	−1.06506	−	6.04024i	−0.0369465	−	0.209534i
$832$		0			0
$833$	−4.60635	−	1.67657i	−0.159600	−	0.0580898i
$834$		0			0
$835$	−14.0094			−0.484815
$836$		0			0
$837$	−7.93475			−0.274265
$838$		0			0
$839$	27.8440	+	10.1344i	0.961280	+	0.349877i	0.774535	−	0.632531i	$-0.217984\pi$
$839$	27.8440	+	10.1344i	0.961280	+	0.349877i	0.186745	+	0.982408i	$0.440206\pi$
$840$		0			0
$841$	−0.503361	−	2.85470i	−0.0173573	−	0.0984379i
$842$		0			0
$843$	−1.47524	+	2.55519i	−0.0508099	+	0.0880053i
$844$		0			0
$845$	−13.5234	−	11.3474i	−0.465218	−	0.390364i
$846$		0			0
$847$	−1.25568	−	2.17490i	−0.0431457	−	0.0747305i
$848$		0			0
$849$	−18.9665	+	6.90325i	−0.650929	+	0.236919i
$850$		0			0
$851$	1.11778	−	6.33922i	0.0383169	−	0.217306i
$852$		0			0
$853$	−23.6305	+	19.8283i	−0.809092	+	0.678909i	−0.950391	−	0.311058i	$-0.899317\pi$
$853$	−23.6305	+	19.8283i	−0.809092	+	0.678909i	0.141299	+	0.989967i	$0.454872\pi$
$854$		0			0
$855$	−7.38964	+	7.95000i	−0.252720	+	0.271884i
$856$		0			0
$857$	−10.0351	+	8.42045i	−0.342792	+	0.287637i	−0.797888	−	0.602805i	$-0.794049\pi$
$857$	−10.0351	+	8.42045i	−0.342792	+	0.287637i	0.455096	+	0.890443i	$0.349605\pi$
$858$		0			0
$859$	−0.180797	+	1.02535i	−0.00616873	+	0.0349846i	−0.987737	−	0.156128i	$-0.950099\pi$
$859$	−0.180797	+	1.02535i	−0.00616873	+	0.0349846i	0.981568	+	0.191113i	$0.0612097\pi$
$860$		0			0
$861$	11.1858	−	4.07130i	0.381211	−	0.138749i
$862$		0			0
$863$	−7.00427	−	12.1318i	−0.238428	−	0.412970i	0.721835	−	0.692065i	$-0.243299\pi$
$863$	−7.00427	−	12.1318i	−0.238428	−	0.412970i	−0.960263	+	0.279095i	$0.909966\pi$
$864$		0			0
$865$	2.91704	+	2.44769i	0.0991825	+	0.0832240i
$866$		0			0
$867$	−2.80541	+	4.85911i	−0.0952766	+	0.165024i
$868$		0			0
$869$	2.39409	+	13.5776i	0.0812140	+	0.460587i
$870$		0			0
$871$	−78.1226	−	28.4343i	−2.64708	−	0.963459i
$872$		0			0
$873$	−23.7328			−0.803234
$874$		0			0
$875$	2.31923			0.0784042
$876$		0			0
$877$	−46.8125	−	17.0383i	−1.58074	−	0.575344i	−0.605379	−	0.795937i	$-0.706978\pi$
$877$	−46.8125	−	17.0383i	−1.58074	−	0.575344i	−0.975366	+	0.220593i	$0.929201\pi$
$878$		0			0
$879$	−3.86062	−	21.8947i	−0.130216	−	0.738490i
$880$		0			0
$881$	1.53504	−	2.65877i	0.0517168	−	0.0895761i	−0.839008	−	0.544119i	$-0.816864\pi$
$881$	1.53504	−	2.65877i	0.0517168	−	0.0895761i	0.890725	+	0.454543i	$0.150197\pi$
$882$		0			0
$883$	15.5594	+	13.0559i	0.523616	+	0.439366i	0.865890	−	0.500234i	$-0.166753\pi$
$883$	15.5594	+	13.0559i	0.523616	+	0.439366i	−0.342274	+	0.939600i	$0.611197\pi$
$884$		0			0
$885$	0.217369	+	0.376495i	0.00730679	+	0.0126557i
$886$		0			0
$887$	−4.46339	+	1.62454i	−0.149866	+	0.0545468i	−0.415864	−	0.909427i	$-0.636521\pi$
$887$	−4.46339	+	1.62454i	−0.149866	+	0.0545468i	0.265998	+	0.963974i	$0.414299\pi$
$888$		0			0
$889$	−2.69393	+	15.2781i	−0.0903516	+	0.512410i
$890$		0			0
$891$	11.2676	−	9.45466i	0.377480	−	0.316743i
$892$		0			0
$893$	−18.8474	−	24.9279i	−0.630705	−	0.834181i
$894$		0			0
$895$	−8.11633	+	6.81041i	−0.271299	+	0.227647i
$896$		0			0
$897$	−1.12098	+	6.35738i	−0.0374284	+	0.212267i
$898$		0			0
$899$	9.71672	−	3.53660i	0.324071	−	0.117952i
$900$		0			0
$901$	−4.54350	−	7.86957i	−0.151366	−	0.262173i
$902$		0			0
$903$	−0.305917	−	0.256695i	−0.0101803	−	0.00854227i
$904$		0			0
$905$	3.66456	−	6.34721i	0.121814	−	0.210988i
$906$		0			0
$907$	−4.59549	−	26.0623i	−0.152591	−	0.865385i	−0.960955	−	0.276703i	$-0.910758\pi$
$907$	−4.59549	−	26.0623i	−0.152591	−	0.865385i	0.808365	−	0.588682i	$-0.200353\pi$
$908$		0			0
$909$	44.5402	+	16.2113i	1.47731	+	0.537695i
$910$		0			0
$911$	44.1499			1.46275			0.731375	−	0.681975i	$-0.238879\pi$
$911$	44.1499			1.46275			0.731375	+	0.681975i	$0.238879\pi$
$912$		0			0
$913$	18.7588			0.620825
$914$		0			0
$915$	7.24018	+	2.63521i	0.239353	+	0.0871174i
$916$		0			0
$917$	−4.60525	−	26.1177i	−0.152079	−	0.862481i
$918$		0			0
$919$	−15.0032	+	25.9864i	−0.494912	+	0.857212i	−0.999983	−	0.00586572i	$-0.998133\pi$
$919$	−15.0032	+	25.9864i	−0.494912	+	0.857212i	0.505071	+	0.863078i	$0.331466\pi$
$920$		0			0
$921$	4.52576	+	3.79756i	0.149129	+	0.125134i
$922$		0			0
$923$	12.6248	+	21.8668i	0.415551	+	0.719755i
$924$		0			0
$925$	3.70455	−	1.34835i	0.121805	−	0.0443333i
$926$		0			0
$927$	2.75070	−	15.6000i	0.0903448	−	0.512371i
$928$		0			0
$929$	−34.7617	+	29.1685i	−1.14049	+	0.956988i	−0.999455	−	0.0330164i	$-0.989489\pi$
$929$	−34.7617	+	29.1685i	−1.14049	+	0.956988i	−0.141039	+	0.990004i	$0.545044\pi$
$930$		0			0
$931$	2.07694	+	6.75450i	0.0680688	+	0.221370i
$932$		0			0
$933$	−6.73953	+	5.65514i	−0.220642	+	0.185141i
$934$		0			0
$935$	1.65349	−	9.37739i	0.0540748	−	0.306673i
$936$		0			0
$937$	−11.7430	+	4.27412i	−0.383628	+	0.139629i	−0.526633	−	0.850093i	$-0.676546\pi$
$937$	−11.7430	+	4.27412i	−0.383628	+	0.139629i	0.143005	+	0.989722i	$0.454324\pi$
$938$		0			0
$939$	−0.315629	−	0.546685i	−0.0103002	−	0.0178404i
$940$		0			0
$941$	32.3348	+	27.1321i	1.05409	+	0.884483i	0.993517	−	0.113681i	$-0.0362643\pi$
$941$	32.3348	+	27.1321i	1.05409	+	0.884483i	0.0605681	+	0.998164i	$0.480709\pi$
$942$		0			0
$943$	−5.86802	+	10.1637i	−0.191089	+	0.330976i
$944$		0			0
$945$	1.57886	+	8.95416i	0.0513603	+	0.291279i
$946$		0			0
$947$	−21.2492	−	7.73406i	−0.690505	−	0.251323i	−0.0271535	−	0.999631i	$-0.508644\pi$
$947$	−21.2492	−	7.73406i	−0.690505	−	0.251323i	−0.663351	+	0.748308i	$0.730867\pi$
$948$		0			0
$949$	80.2050			2.60356
$950$		0			0
$951$	−8.92313			−0.289352
$952$		0			0
$953$	26.6745	+	9.70873i	0.864072	+	0.314497i	0.735764	−	0.677238i	$-0.236823\pi$
$953$	26.6745	+	9.70873i	0.864072	+	0.314497i	0.128308	+	0.991734i	$0.459045\pi$
$954$		0			0
$955$	−3.11430	−	17.6621i	−0.100777	−	0.571532i
$956$		0			0
$957$	5.74442	−	9.94962i	0.185691	−	0.321626i
$958$		0			0
$959$	−4.39298	−	3.68615i	−0.141857	−	0.119032i
$960$		0			0
$961$	13.4518	+	23.2992i	0.433928	+	0.751586i
$962$		0			0
$963$	41.6115	−	15.1453i	1.34091	−	0.488051i
$964$		0			0
$965$	0.899127	−	5.09920i	0.0289439	−	0.164149i
$966$		0			0
$967$	3.37327	−	2.83051i	0.108477	−	0.0910230i	−0.586936	−	0.809633i	$-0.699666\pi$
$967$	3.37327	−	2.83051i	0.108477	−	0.0910230i	0.695413	+	0.718610i	$0.255222\pi$
$968$		0			0
$969$	−9.33963	+	1.16200i	−0.300032	+	0.0373290i
$970$		0			0
$971$	4.85458	−	4.07348i	0.155791	−	0.130724i	−0.561560	−	0.827436i	$-0.689799\pi$
$971$	4.85458	−	4.07348i	0.155791	−	0.130724i	0.717351	+	0.696712i	$0.245354\pi$
$972$		0			0
$973$	8.90702	−	50.5142i	0.285546	−	1.61941i
$974$		0			0
$975$	−3.71516	+	1.35221i	−0.118980	+	0.0433053i
$976$		0			0
$977$	24.9390	+	43.1956i	0.797869	+	1.38195i	0.921001	+	0.389560i	$0.127373\pi$
$977$	24.9390	+	43.1956i	0.797869	+	1.38195i	−0.123132	+	0.992390i	$0.539294\pi$
$978$		0			0
$979$	−21.8728	−	18.3534i	−0.699057	−	0.586578i
$980$		0			0
$981$	22.6201	−	39.1792i	0.722204	−	1.25089i
$982$		0			0
$983$	5.90145	+	33.4688i	0.188227	+	1.06749i	0.921739	+	0.387812i	$0.126769\pi$
$983$	5.90145	+	33.4688i	0.188227	+	1.06749i	−0.733512	+	0.679677i	$0.762120\pi$
$984$		0			0
$985$	−1.22420	−	0.445573i	−0.0390063	−	0.0141971i
$986$		0			0
$987$	−11.8736			−0.377940
$988$		0			0
$989$	0.393723			0.0125196
$990$		0			0
$991$	−34.0508	−	12.3935i	−1.08166	−	0.393692i	−0.261135	−	0.965302i	$-0.584097\pi$
$991$	−34.0508	−	12.3935i	−1.08166	−	0.393692i	−0.820525	+	0.571610i	$0.806319\pi$
$992$		0			0
$993$	−0.747723	−	4.24055i	−0.0237283	−	0.134570i
$994$		0			0
$995$	−6.07816	+	10.5277i	−0.192691	+	0.333750i
$996$		0			0
$997$	−40.4963	−	33.9805i	−1.28253	−	1.07617i	−0.992890	−	0.119037i	$-0.962019\pi$
$997$	−40.4963	−	33.9805i	−1.28253	−	1.07617i	−0.289642	−	0.957135i	$-0.593536\pi$
$998$		0			0
$999$	7.72769	+	13.3847i	0.244493	+	0.423475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.101.2	✓	18
19.4	even	9		7220.2.a.v.1.4		9
19.15	odd	18		7220.2.a.x.1.6		9
19.16	even	9	inner	380.2.u.a.301.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.101.2	✓	18	1.1	even	1	trivial
380.2.u.a.301.2	yes	18	19.16	even	9	inner
7220.2.a.v.1.4		9	19.4	even	9
7220.2.a.x.1.6		9	19.15	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)

\(f(q)\)	\(=\)	\(q+(0.671023 + 0.244232i) q^{3} +(-0.173648 - 0.984808i) q^{5} +(1.15961 - 2.00851i) q^{7} +(-1.90751 - 1.60059i) q^{9} +O(q^{10})\)	\(q+(0.671023 + 0.244232i) q^{3} +(-0.173648 - 0.984808i) q^{5} +(1.15961 - 2.00851i) q^{7} +(-1.90751 - 1.60059i) q^{9} +(-1.57458 - 2.72725i) q^{11} +(5.20266 - 1.89361i) q^{13} +(0.124000 - 0.703239i) q^{15} +(-2.31628 + 1.94359i) q^{17} +(4.24875 + 0.973710i) q^{19} +(1.26867 - 1.06454i) q^{21} +(-0.283534 + 1.60800i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-1.96020 - 3.39516i) q^{27} +(3.91367 + 3.28396i) q^{29} +(1.01198 - 1.75281i) q^{31} +(-0.390495 - 2.21461i) q^{33} +(-2.17936 - 0.793222i) q^{35} -3.94230 q^{37} +3.95359 q^{39} +(6.75417 + 2.45832i) q^{41} +(-0.0418722 - 0.237469i) q^{43} +(-1.24504 + 2.15647i) q^{45} +(-5.49214 - 4.60845i) q^{47} +(0.810595 + 1.40399i) q^{49} +(-2.02896 + 0.738482i) q^{51} +(-0.521860 + 2.95961i) q^{53} +(-2.41239 + 2.02424i) q^{55} +(2.61320 + 1.69106i) q^{57} +(-0.466370 + 0.391331i) q^{59} +(-1.87362 + 10.6258i) q^{61} +(-5.42678 + 1.97519i) q^{63} +(-2.76828 - 4.79480i) q^{65} +(-11.5028 - 9.65202i) q^{67} +(-0.582984 + 1.00976i) q^{69} +(0.791928 + 4.49124i) q^{71} +(13.6128 + 4.95465i) q^{73} -0.714088 q^{75} -7.30359 q^{77} +(-4.11398 - 1.49737i) q^{79} +(0.811064 + 4.59977i) q^{81} +(-2.97839 + 5.15872i) q^{83} +(2.31628 + 1.94359i) q^{85} +(1.82412 + 3.15946i) q^{87} +(8.52005 - 3.10104i) q^{89} +(2.22974 - 12.6455i) q^{91} +(1.10716 - 0.929014i) q^{93} +(0.221130 - 4.35329i) q^{95} +(7.30113 - 6.12637i) q^{97} +(-1.36169 + 7.72250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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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