LMFDB - Embedded newform 819.2.n.d.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.1
Root			$-0.181721 - 0.314749i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.d.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19402 + 2.06810i) q^{2} +(-1.85136 - 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} +(2.60682 - 0.452230i) q^{7} +4.06616 q^{8} -2.34572 q^{10} +0.587802 q^{11} +(2.39227 - 2.69760i) q^{13} +(-2.17733 + 5.93113i) q^{14} +(-1.15235 + 1.99593i) q^{16} +(-3.22710 - 5.58950i) q^{17} -3.82689 q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(4.13001 - 7.15338i) q^{23} +(2.01756 - 3.49452i) q^{25} +(2.72249 + 8.16844i) q^{26} +(-6.27630 - 7.52191i) q^{28} +(-1.98009 - 3.42962i) q^{29} +(1.49436 - 2.58831i) q^{31} +(1.31430 + 2.27644i) q^{32} +15.4129 q^{34} +(1.66501 + 1.99546i) q^{35} +(-0.877941 + 1.52064i) q^{37} +(4.56938 - 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(-1.08823 - 1.88488i) q^{44} +(9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} +(6.59098 - 2.35776i) q^{49} +(4.81802 + 8.34505i) q^{50} +(-13.0792 - 2.67695i) q^{52} +(0.212770 - 0.368529i) q^{53} +(0.288693 + 0.500031i) q^{55} +(10.5997 - 1.83884i) q^{56} +9.45706 q^{58} +(3.00431 + 5.20362i) q^{59} +2.20674 q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(3.46973 + 0.710156i) q^{65} +7.01303 q^{67} +(-11.9491 + 20.6964i) q^{68} +(-6.11486 + 1.06080i) q^{70} +(1.80127 - 3.11988i) q^{71} +(-2.46714 + 4.27321i) q^{73} +(-2.09656 - 3.63134i) q^{74} +(7.08496 + 12.2715i) q^{76} +(1.53229 - 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} -2.26386 q^{80} -8.76812 q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(-7.61885 - 13.1962i) q^{86} +2.39010 q^{88} +(-1.04656 + 1.81269i) q^{89} +(5.01627 - 8.11400i) q^{91} -30.5845 q^{92} +10.3655 q^{94} +(-1.87954 - 3.25546i) q^{95} +(-3.84852 + 6.66584i) q^{97} +(-2.99367 + 16.4460i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29}+ \cdots - 62 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.19402	+	2.06810i	−0.844299	+	1.46237i	0.0419302	+	0.999121i	$0.486649\pi$
$2$	−1.19402	+	2.06810i	−0.844299	+	1.46237i	−0.886229	+	0.463248i	$0.846684\pi$
$3$		0			0
$3$		0			0
$4$	−1.85136	−	3.20665i	−0.925680	−	1.60333i
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	0.954699	−	0.297572i	$-0.0961769\pi$
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	−0.735055	+	0.678008i	$0.762844\pi$
$6$		0			0
$7$	2.60682	−	0.452230i	0.985284	−	0.170927i
$7$	2.60682	−	0.452230i	0.985284	−	0.170927i
$8$	4.06616			1.43761
$9$		0			0
$10$	−2.34572			−0.741782
$11$	0.587802			0.177229			0.0886146	−	0.996066i	$-0.471756\pi$
$11$	0.587802			0.177229			0.0886146	+	0.996066i	$0.471756\pi$
$12$		0			0
$13$	2.39227	−	2.69760i	0.663496	−	0.748179i
$13$	2.39227	−	2.69760i	0.663496	−	0.748179i
$14$	−2.17733	+	5.93113i	−0.581916	+	1.58516i
$15$		0			0
$16$	−1.15235	+	1.99593i	−0.288088	+	0.498983i
$17$	−3.22710	−	5.58950i	−0.782687	−	1.35565i	−0.930371	−	0.366619i	$-0.880515\pi$
$17$	−3.22710	−	5.58950i	−0.782687	−	1.35565i	0.147685	−	0.989035i	$-0.452818\pi$
$18$		0			0
$19$	−3.82689			−0.877950			−0.438975	−	0.898499i	$-0.644658\pi$
$19$	−3.82689			−0.877950			−0.438975	+	0.898499i	$0.644658\pi$
$20$	1.81855	−	3.14983i	0.406641	−	0.704323i
$21$		0			0
$22$	−0.701847	+	1.21563i	−0.149634	+	0.259174i
$23$	4.13001	−	7.15338i	0.861166	−	1.49158i	−0.00963902	−	0.999954i	$-0.503068\pi$
$23$	4.13001	−	7.15338i	0.861166	−	1.49158i	0.870805	−	0.491629i	$-0.163598\pi$
$24$		0			0
$25$	2.01756	−	3.49452i	0.403513	−	0.698904i
$26$	2.72249	+	8.16844i	0.533925	+	1.60196i
$27$		0			0
$28$	−6.27630	−	7.52191i	−1.18611	−	1.42151i
$29$	−1.98009	−	3.42962i	−0.367694	−	0.636864i	0.621511	−	0.783406i	$-0.286519\pi$
$29$	−1.98009	−	3.42962i	−0.367694	−	0.636864i	−0.989205	+	0.146541i	$0.953186\pi$
$30$		0			0
$31$	1.49436	−	2.58831i	0.268395	−	0.464874i	−0.700053	−	0.714091i	$-0.746840\pi$
$31$	1.49436	−	2.58831i	0.268395	−	0.464874i	0.968448	+	0.249218i	$0.0801734\pi$
$32$	1.31430	+	2.27644i	0.232338	+	0.402421i
$33$		0			0
$34$	15.4129			2.64329
$35$	1.66501	+	1.99546i	0.281439	+	0.337294i
$36$		0			0
$37$	−0.877941	+	1.52064i	−0.144333	+	0.249991i	−0.929124	−	0.369769i	$-0.879437\pi$
$37$	−0.877941	+	1.52064i	−0.144333	+	0.249991i	0.784791	+	0.619760i	$0.212770\pi$
$38$	4.56938	−	7.91440i	0.741252	−	1.28389i
$39$		0			0
$40$	1.99705	+	3.45900i	0.315762	+	0.546916i
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	0.973023	−	0.230710i	$-0.0741049\pi$
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	−0.686312	+	0.727307i	$0.740772\pi$
$42$		0			0
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	−0.999880	−	0.0154788i	$-0.995073\pi$
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	0.513345	+	0.858182i	$0.328406\pi$
$44$	−1.08823	−	1.88488i	−0.164058	−	0.284156i
$45$		0			0
$46$	9.86261	+	17.0825i	1.45416	+	2.51868i
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	0.663200	−	0.748442i	$-0.269198\pi$
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	−0.979770	+	0.200127i	$0.935865\pi$
$48$		0			0
$49$	6.59098	−	2.35776i	0.941568	−	0.336823i
$50$	4.81802	+	8.34505i	0.681370	+	1.18017i
$51$		0			0
$52$	−13.0792	−	2.67695i	−1.81376	−	0.371226i
$53$	0.212770	−	0.368529i	0.0292263	−	0.0506214i	−0.851042	−	0.525097i	$-0.824029\pi$
$53$	0.212770	−	0.368529i	0.0292263	−	0.0506214i	0.880269	+	0.474476i	$0.157362\pi$
$54$		0			0
$55$	0.288693	+	0.500031i	0.0389274	+	0.0674242i
$56$	10.5997	−	1.83884i	1.41645	−	0.245725i
$57$		0			0
$58$	9.45706			1.24177
$59$	3.00431	+	5.20362i	0.391128	+	0.677454i	0.992599	−	0.121441i	$-0.0387516\pi$
$59$	3.00431	+	5.20362i	0.391128	+	0.677454i	−0.601470	+	0.798895i	$0.705418\pi$
$60$		0			0
$61$	2.20674			0.282544			0.141272	−	0.989971i	$-0.454881\pi$
$61$	2.20674			0.282544			0.141272	+	0.989971i	$0.454881\pi$
$62$	3.56859	+	6.18097i	0.453211	+	0.784985i
$63$		0			0
$64$	−10.8866			−1.36083
$65$	3.46973	+	0.710156i	0.430367	+	0.0880841i
$66$		0			0
$67$	7.01303			0.856778			0.428389	−	0.903594i	$-0.359081\pi$
$67$	7.01303			0.856778			0.428389	+	0.903594i	$0.359081\pi$
$68$	−11.9491	+	20.6964i	−1.44904	+	2.50980i
$69$		0			0
$70$	−6.11486	+	1.06080i	−0.730866	+	0.126790i
$71$	1.80127	−	3.11988i	0.213771	−	0.370262i	−0.739121	−	0.673573i	$-0.764759\pi$
$71$	1.80127	−	3.11988i	0.213771	−	0.370262i	0.952892	+	0.303311i	$0.0980920\pi$
$72$		0			0
$73$	−2.46714	+	4.27321i	−0.288756	+	0.500141i	−0.973513	−	0.228631i	$-0.926575\pi$
$73$	−2.46714	+	4.27321i	−0.288756	+	0.500141i	0.684757	+	0.728772i	$0.259908\pi$
$74$	−2.09656	−	3.63134i	−0.243720	−	0.422135i
$75$		0			0
$76$	7.08496	+	12.2715i	0.812701	+	1.40764i
$77$	1.53229	−	0.265822i	0.174621	−	0.0302932i
$78$		0			0
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	0.776982	−	0.629522i	$-0.216749\pi$
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	−0.933674	+	0.358125i	$0.883416\pi$
$80$	−2.26386			−0.253108
$81$		0			0
$82$	−8.76812			−0.968277
$83$	2.86819			0.314825			0.157412	−	0.987533i	$-0.449685\pi$
$83$	2.86819			0.314825			0.157412	+	0.987533i	$0.449685\pi$
$84$		0			0
$85$	3.16992	−	5.49045i	0.343826	−	0.595523i
$86$	−7.61885	−	13.1962i	−0.821562	−	1.42299i
$87$		0			0
$88$	2.39010			0.254786
$89$	−1.04656	+	1.81269i	−0.110935	+	0.192145i	−0.916147	−	0.400842i	$-0.868718\pi$
$89$	−1.04656	+	1.81269i	−0.110935	+	0.192145i	0.805213	+	0.592986i	$0.202051\pi$
$90$		0			0
$91$	5.01627	−	8.11400i	0.525848	−	0.850578i
$92$	−30.5845			−3.18866
$93$		0			0
$94$	10.3655			1.06912
$95$	−1.87954	−	3.25546i	−0.192837	−	0.334003i
$96$		0			0
$97$	−3.84852	+	6.66584i	−0.390758	+	0.676813i	−0.992550	−	0.121840i	$-0.961120\pi$
$97$	−3.84852	+	6.66584i	−0.390758	+	0.676813i	0.601791	+	0.798653i	$0.294454\pi$
$98$	−2.99367	+	16.4460i	−0.302406	+	1.66130i
$99$		0			0
$100$	−14.9409			−1.49409
$101$	2.63732			0.262423			0.131212	−	0.991354i	$-0.458113\pi$
$101$	2.63732			0.262423			0.131212	+	0.991354i	$0.458113\pi$
$102$		0			0
$103$	5.43095	+	9.40669i	0.535128	+	0.926868i	0.999157	+	0.0410486i	$0.0130699\pi$
$103$	5.43095	+	9.40669i	0.535128	+	0.926868i	−0.464029	+	0.885820i	$0.653597\pi$
$104$	9.72736	−	10.9689i	0.953846	−	1.07559i
$105$		0			0
$106$	0.508103	+	0.880061i	0.0493514	+	0.0854791i
$107$	−7.99024	+	13.8395i	−0.772446	+	1.33792i	0.163773	+	0.986498i	$0.447634\pi$
$107$	−7.99024	+	13.8395i	−0.772446	+	1.33792i	−0.936219	+	0.351418i	$0.885700\pi$
$108$		0			0
$109$	−4.61738	+	7.99754i	−0.442265	+	0.766026i	−0.997857	−	0.0654294i	$-0.979158\pi$
$109$	−4.61738	+	7.99754i	−0.442265	+	0.766026i	0.555592	+	0.831455i	$0.312492\pi$
$110$	−1.37882			−0.131465
$111$		0			0
$112$	−2.10135	+	5.72416i	−0.198559	+	0.540882i
$113$	5.09012	−	8.81635i	0.478838	−	0.829372i	−0.520867	−	0.853638i	$-0.674391\pi$
$113$	5.09012	−	8.81635i	0.478838	−	0.829372i	0.999706	+	0.0242655i	$0.00772470\pi$
$114$		0			0
$115$	8.11364			0.756601
$116$	−7.33173	+	12.6989i	−0.680734	+	1.17907i
$117$		0			0
$118$	−14.3488			−1.32092
$119$	−10.9402	−	13.1114i	−1.00289	−	1.20192i
$120$		0			0
$121$	−10.6545			−0.968590
$122$	−2.63489	+	4.56376i	−0.238552	+	0.413184i
$123$		0			0
$124$	−11.0664			−0.993792
$125$	8.87502			0.793806
$126$		0			0
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	0.756201	−	0.654340i	$-0.227053\pi$
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	−0.944775	+	0.327719i	$0.893720\pi$
$128$	10.3702	−	17.9617i	0.916606	−	1.58761i
$129$		0			0
$130$	−5.61160	+	6.32781i	−0.492170	+	0.554986i
$131$	−1.08478	−	1.87890i	−0.0947779	−	0.164160i	0.814738	−	0.579829i	$-0.196881\pi$
$131$	−1.08478	−	1.87890i	−0.0947779	−	0.164160i	−0.909516	+	0.415669i	$0.863547\pi$
$132$		0			0
$133$	−9.97601	+	1.73063i	−0.865030	+	0.150065i
$134$	−8.37369	+	14.5037i	−0.723376	+	1.25292i
$135$		0			0
$136$	−13.1219	−	22.7278i	−1.12519	−	1.94889i
$137$	4.18158	+	7.24271i	0.357257	+	0.618787i	0.987501	−	0.157610i	$-0.0503788\pi$
$137$	4.18158	+	7.24271i	0.357257	+	0.618787i	−0.630245	+	0.776396i	$0.717045\pi$
$138$		0			0
$139$	0.288457	−	0.499622i	0.0244666	−	0.0423774i	−0.853533	−	0.521039i	$-0.825545\pi$
$139$	0.288457	−	0.499622i	0.0244666	−	0.0423774i	0.877999	+	0.478662i	$0.158878\pi$
$140$	3.31619	−	9.03343i	0.280269	−	0.763464i
$141$		0			0
$142$	4.30149	+	7.45040i	0.360973	+	0.625224i
$143$	1.40618	−	1.58566i	0.117591	−	0.132599i
$144$		0			0
$145$	1.94500	−	3.36885i	0.161524	−	0.279767i
$146$	−5.89161	−	10.2046i	−0.487593	−	0.844537i
$147$		0			0
$148$	6.50154			0.534423
$149$	−2.80662			−0.229928			−0.114964	−	0.993370i	$-0.536675\pi$
$149$	−2.80662			−0.229928			−0.114964	+	0.993370i	$0.536675\pi$
$150$		0			0
$151$	11.5054	−	19.9280i	0.936300	−	1.62172i	0.164000	−	0.986460i	$-0.447560\pi$
$151$	11.5054	−	19.9280i	0.936300	−	1.62172i	0.772300	−	0.635258i	$-0.219106\pi$
$152$	−15.5608			−1.26215
$153$		0			0
$154$	−1.27984	+	3.48633i	−0.103132	+	0.280937i
$155$	2.93576			0.235806
$156$		0			0
$157$	−11.2880	+	19.5513i	−0.900879	+	1.56037i	−0.0745227	+	0.997219i	$0.523743\pi$
$157$	−11.2880	+	19.5513i	−0.900879	+	1.56037i	−0.826356	+	0.563148i	$0.809590\pi$
$158$	6.65165			0.529177
$159$		0			0
$160$	−1.29101	+	2.23610i	−0.102064	+	0.176779i
$161$	7.53119	−	20.5153i	0.593541	−	1.61683i
$162$		0			0
$163$	8.17714			0.640483			0.320242	−	0.947336i	$-0.396236\pi$
$163$	8.17714			0.640483			0.320242	+	0.947336i	$0.396236\pi$
$164$	6.79761	−	11.7738i	0.530804	−	0.919380i
$165$		0			0
$166$	−3.42467	+	5.93170i	−0.265806	+	0.460389i
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	0.817475	−	0.575964i	$-0.195373\pi$
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	−0.907537	+	0.419972i	$0.862040\pi$
$168$		0			0
$169$	−1.55408	−	12.9068i	−0.119545	−	0.992829i
$170$	7.56988	+	13.1114i	0.580583	+	1.00560i
$171$		0			0
$172$	23.6265			1.80150
$173$	8.13372			0.618396			0.309198	−	0.950998i	$-0.399939\pi$
$173$	8.13372			0.618396			0.309198	+	0.950998i	$0.399939\pi$
$174$		0			0
$175$	3.67909	−	10.0220i	0.278113	−	0.757590i
$176$	−0.677355	+	1.17321i	−0.0510576	+	0.0884343i
$177$		0			0
$178$	−2.49922	−	4.32877i	−0.187324	−	0.324455i
$179$	20.9925			1.56906			0.784528	−	0.620093i	$-0.212905\pi$
$179$	20.9925			1.56906			0.784528	+	0.620093i	$0.212905\pi$
$180$		0			0
$181$	−1.60807			−0.119527			−0.0597635	−	0.998213i	$-0.519035\pi$
$181$	−1.60807			−0.119527			−0.0597635	+	0.998213i	$0.519035\pi$
$182$	10.7910	+	20.0624i	0.799885	+	1.48713i
$183$		0			0
$184$	16.7933	−	29.0868i	1.23802	−	2.14431i
$185$	−1.72477			−0.126807
$186$		0			0
$187$	−1.89690	−	3.28552i	−0.138715	−	0.240261i
$188$	−8.03601	+	13.9188i	−0.586086	+	1.01513i
$189$		0			0
$190$	8.97683			0.651247
$191$	11.5622			0.836614			0.418307	−	0.908306i	$-0.362624\pi$
$191$	11.5622			0.836614			0.418307	+	0.908306i	$0.362624\pi$
$192$		0			0
$193$	23.5788			1.69724			0.848621	−	0.529001i	$-0.177433\pi$
$193$	23.5788			1.69724			0.848621	+	0.529001i	$0.177433\pi$
$194$	−9.19041	−	15.9183i	−0.659833	−	1.14286i
$195$		0			0
$196$	−19.7628	−	16.7699i	−1.41163	−	1.19785i
$197$	−0.735472	−	1.27387i	−0.0524002	−	0.0907598i	0.838636	−	0.544693i	$-0.183354\pi$
$197$	−0.735472	−	1.27387i	−0.0524002	−	0.0907598i	−0.891036	+	0.453933i	$0.850020\pi$
$198$		0			0
$199$	−4.69700	−	8.13543i	−0.332961	−	0.576706i	0.650130	−	0.759823i	$-0.274714\pi$
$199$	−4.69700	−	8.13543i	−0.332961	−	0.576706i	−0.983091	+	0.183117i	$0.941381\pi$
$200$	8.20374	−	14.2093i	0.580092	−	1.00475i
$201$		0			0
$202$	−3.14901	+	5.45425i	−0.221564	+	0.383760i
$203$	−6.71271	−	8.04493i	−0.471140	−	0.564643i
$204$		0			0
$205$	−1.80331	+	3.12343i	−0.125949	+	0.218150i
$206$	−25.9386			−1.80723
$207$		0			0
$208$	2.62749	+	7.88340i	0.182183	+	0.546615i
$209$	−2.24946			−0.155598
$210$		0			0
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	0.977881	−	0.209160i	$-0.0670730\pi$
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	−0.670079	+	0.742290i	$0.733740\pi$
$212$	−1.57566			−0.108217
$213$		0			0
$214$	−19.0810	−	33.0493i	−1.30435	−	2.25920i
$215$	−6.26778			−0.427459
$216$		0			0
$217$	2.72501	−	7.42303i	0.184986	−	0.503908i
$218$	−11.0265	−	19.0984i	−0.746808	−	1.29351i
$219$		0			0
$220$	1.06895	−	1.85148i	0.0720686	−	0.124827i
$221$	−22.7983	−	4.66618i	−1.53358	−	0.313881i
$222$		0			0
$223$	−10.9098	−	18.8963i	−0.730574	−	1.26539i	−0.956638	−	0.291279i	$-0.905919\pi$
$223$	−10.9098	−	18.8963i	−0.730574	−	1.26539i	0.226064	−	0.974112i	$-0.427414\pi$
$224$	4.45562	+	5.33989i	0.297704	+	0.356786i
$225$		0			0
$226$	12.1554	+	21.0538i	0.808565	+	1.40048i
$227$	−9.27627	−	16.0670i	−0.615687	−	1.06640i	−0.990263	−	0.139206i	$-0.955545\pi$
$227$	−9.27627	−	16.0670i	−0.615687	−	1.06640i	0.374576	−	0.927196i	$-0.377788\pi$
$228$		0			0
$229$	−9.67525	−	16.7580i	−0.639359	−	1.10740i	−0.985574	−	0.169247i	$-0.945867\pi$
$229$	−9.67525	−	16.7580i	−0.639359	−	1.10740i	0.346215	−	0.938155i	$-0.387467\pi$
$230$	−9.68784	+	16.7798i	−0.638797	+	1.10643i
$231$		0			0
$232$	−8.05137	−	13.9454i	−0.528599	−	0.915560i
$233$	8.08170	+	13.9979i	0.529450	+	0.917034i	0.999410	+	0.0343462i	$0.0109349\pi$
$233$	8.08170	+	13.9979i	0.529450	+	0.917034i	−0.469960	+	0.882688i	$0.655732\pi$
$234$		0			0
$235$	2.13184	−	3.69245i	0.139066	−	0.240869i
$236$	11.1241	−	19.2676i	0.724119	−	1.25421i
$237$		0			0
$238$	40.1785	−	6.97016i	2.60439	−	0.451808i
$239$	−16.1037			−1.04166			−0.520831	−	0.853660i	$-0.674378\pi$
$239$	−16.1037			−1.04166			−0.520831	+	0.853660i	$0.674378\pi$
$240$		0			0
$241$	2.00300	+	3.46930i	0.129025	+	0.223477i	0.923299	−	0.384082i	$-0.125482\pi$
$241$	2.00300	+	3.46930i	0.129025	+	0.223477i	−0.794274	+	0.607559i	$0.792149\pi$
$242$	12.7217	−	22.0346i	0.817779	−	1.41643i
$243$		0			0
$244$	−4.08548	−	7.07625i	−0.261546	−	0.453011i
$245$	5.24279	+	4.44882i	0.334949	+	0.284225i
$246$		0			0
$247$	−9.15497	+	10.3234i	−0.582517	+	0.656864i
$248$	6.07631	−	10.5245i	0.385846	−	0.668305i
$249$		0			0
$250$	−10.5969	+	18.3544i	−0.670209	+	1.16084i
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	−0.810231	−	0.586110i	$-0.800659\pi$
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	0.912702	+	0.408626i	$0.133992\pi$
$252$		0			0
$253$	2.42763	−	4.20477i	0.152624	−	0.264352i
$254$	10.1498			0.636853
$255$		0			0
$256$	13.8778	+	24.0371i	0.867365	+	1.50232i
$257$	−13.4462	+	23.2895i	−0.838751	+	1.45276i	0.0521891	+	0.998637i	$0.483380\pi$
$257$	−13.4462	+	23.2895i	−0.838751	+	1.45276i	−0.890940	+	0.454122i	$0.849953\pi$
$258$		0			0
$259$	−1.60095	+	4.36106i	−0.0994784	+	0.270983i
$260$	−4.14650	−	12.4410i	−0.257155	−	0.771556i
$261$		0			0
$262$	5.18100			0.320084
$263$	3.80706			0.234753			0.117377	−	0.993087i	$-0.462552\pi$
$263$	3.80706			0.234753			0.117377	+	0.993087i	$0.462552\pi$
$264$		0			0
$265$	0.418000			0.0256775
$266$	8.33241	−	22.6978i	0.510893	−	1.39169i
$267$		0			0
$268$	−12.9836	−	22.4883i	−0.793102	−	1.37369i
$269$	−11.9190	−	20.6444i	−0.726716	−	1.25871i	−0.958264	−	0.285886i	$-0.907712\pi$
$269$	−11.9190	−	20.6444i	−0.726716	−	1.25871i	0.231548	−	0.972824i	$-0.425621\pi$
$270$		0			0
$271$	−4.95068	+	8.57482i	−0.300732	+	0.520883i	−0.976302	−	0.216413i	$-0.930564\pi$
$271$	−4.95068	+	8.57482i	−0.300732	+	0.520883i	0.675570	+	0.737296i	$0.263898\pi$
$272$	14.8750			0.901931
$273$		0			0
$274$	−19.9715			−1.20653
$275$	1.18593	−	2.05409i	0.0715142	−	0.123866i
$276$		0			0
$277$	−5.89289	−	10.2068i	−0.354069	−	0.613266i	0.632889	−	0.774243i	$-0.281869\pi$
$277$	−5.89289	−	10.2068i	−0.354069	−	0.613266i	−0.986958	+	0.160977i	$0.948536\pi$
$278$	0.688846	+	1.19312i	0.0413142	+	0.0715584i
$279$		0			0
$280$	6.77022	+	8.11385i	0.404598	+	0.484895i
$281$	−12.9976			−0.775372			−0.387686	−	0.921791i	$-0.626726\pi$
$281$	−12.9976			−0.775372			−0.387686	+	0.921791i	$0.626726\pi$
$282$		0			0
$283$	−16.8050			−0.998952			−0.499476	−	0.866328i	$-0.666474\pi$
$283$	−16.8050			−0.998952			−0.499476	+	0.866328i	$0.666474\pi$
$284$	−13.3392			−0.791534
$285$		0			0
$286$	1.60029	+	4.80143i	0.0946270	+	0.283914i
$287$	6.22369	+	7.45886i	0.367373	+	0.440283i
$288$		0			0
$289$	−12.3283	+	21.3533i	−0.725197	+	1.25608i
$290$	4.64474	+	8.04493i	0.272749	+	0.472414i
$291$		0			0
$292$	18.2702			1.06918
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	−0.995080	−	0.0990757i	$-0.968411\pi$
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	0.583342	+	0.812227i	$0.301745\pi$
$294$		0			0
$295$	−2.95108	+	5.11141i	−0.171818	+	0.297598i
$296$	−3.56985	+	6.18316i	−0.207493	+	0.359389i
$297$		0			0
$298$	3.35116	−	5.80438i	0.194128	−	0.336239i
$299$	−9.41686	−	28.2539i	−0.544591	−	1.63397i
$300$		0			0
$301$	−5.81784	+	15.8480i	−0.335335	+	0.913464i
$302$	27.4754	+	47.5888i	1.58103	+	2.73843i
$303$		0			0
$304$	4.40993	−	7.63822i	0.252927	−	0.438082i
$305$	1.08382	+	1.87723i	0.0620593	+	0.107490i
$306$		0			0
$307$	15.8786			0.906240			0.453120	−	0.891450i	$-0.350311\pi$
$307$	15.8786			0.906240			0.453120	+	0.891450i	$0.350311\pi$
$308$	−3.68922	−	4.42140i	−0.210213	−	0.251932i
$309$		0			0
$310$	−3.50535	+	6.07145i	−0.199091	+	0.344835i
$311$	−14.3017	+	24.7713i	−0.810975	+	1.40465i	0.101208	+	0.994865i	$0.467729\pi$
$311$	−14.3017	+	24.7713i	−0.810975	+	1.40465i	−0.912183	+	0.409784i	$0.865604\pi$
$312$		0			0
$313$	9.28962	+	16.0901i	0.525080	+	0.909465i	0.999573	+	0.0292063i	$0.00929798\pi$
$313$	9.28962	+	16.0901i	0.525080	+	0.909465i	−0.474493	+	0.880259i	$0.657369\pi$
$314$	−26.9561	−	46.6893i	−1.52122	−	2.63483i
$315$		0			0
$316$	−5.15679	+	8.93182i	−0.290092	+	0.502454i
$317$	15.3223	+	26.5389i	0.860584	+	1.49057i	0.871366	+	0.490633i	$0.163234\pi$
$317$	15.3223	+	26.5389i	0.860584	+	1.49057i	−0.0107826	+	0.999942i	$0.503432\pi$
$318$		0			0
$319$	−1.16390	−	2.01594i	−0.0651660	−	0.112871i
$320$	−5.34685	−	9.26102i	−0.298898	−	0.517707i
$321$		0			0
$322$	33.4352	+	40.0709i	1.86327	+	2.23306i
$323$	12.3498	+	21.3904i	0.687160	+	1.19020i
$324$		0			0
$325$	−4.60026	−	13.8024i	−0.255177	−	0.765620i
$326$	−9.76366	+	16.9112i	−0.540759	+	0.936622i
$327$		0			0
$328$	7.46483	+	12.9295i	0.412177	+	0.713911i
$329$	−7.35752	−	8.81772i	−0.405633	−	0.486136i
$330$		0			0
$331$	27.2277			1.49657			0.748284	−	0.663378i	$-0.230878\pi$
$331$	27.2277			1.49657			0.748284	+	0.663378i	$0.230878\pi$
$332$	−5.31005	−	9.19728i	−0.291427	−	0.504766i
$333$		0			0
$334$	5.55867			0.304157
$335$	3.44438	+	5.96584i	0.188187	+	0.325949i
$336$		0			0
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	28.5481	+	12.1969i	1.55281	+	0.663426i
$339$		0			0
$340$	−23.4746			−1.27309
$341$	0.878389	−	1.52141i	0.0475674	−	0.0823892i
$342$		0			0
$343$	16.1152	−	9.12688i	0.870140	−	0.492805i
$344$	−12.9728	+	22.4695i	−0.699445	+	1.21148i
$345$		0			0
$346$	−9.71182	+	16.8214i	−0.522111	+	0.904322i
$347$	3.07253	+	5.32177i	0.164942	+	0.285688i	0.936635	−	0.350308i	$-0.113923\pi$
$347$	3.07253	+	5.32177i	0.164942	+	0.285688i	−0.771693	+	0.635996i	$0.780590\pi$
$348$		0			0
$349$	−6.51563	−	11.2854i	−0.348774	−	0.604094i	0.637258	−	0.770650i	$-0.280068\pi$
$349$	−6.51563	−	11.2854i	−0.348774	−	0.604094i	−0.986032	+	0.166557i	$0.946735\pi$
$350$	16.3336	+	19.5752i	0.873065	+	1.04634i
$351$		0			0
$352$	0.772550	+	1.33810i	0.0411771	+	0.0713208i
$353$	−31.6665			−1.68544			−0.842718	−	0.538356i	$-0.819046\pi$
$353$	−31.6665			−1.68544			−0.842718	+	0.538356i	$0.819046\pi$
$354$		0			0
$355$	3.53870			0.187814
$356$	7.75021			0.410761
$357$		0			0
$358$	−25.0655	+	43.4147i	−1.32475	+	2.29454i
$359$	9.96610	+	17.2618i	0.525991	+	0.911043i	0.999542	+	0.0302764i	$0.00963874\pi$
$359$	9.96610	+	17.2618i	0.525991	+	0.911043i	−0.473551	+	0.880767i	$0.657028\pi$
$360$		0			0
$361$	−4.35488			−0.229204
$362$	1.92007	−	3.32566i	0.100917	−	0.174793i
$363$		0			0
$364$	−35.3057	−	1.06350i	−1.85052	−	0.0557426i
$365$	−4.84684			−0.253695
$366$		0			0
$367$	19.7190			1.02932			0.514662	−	0.857393i	$-0.327918\pi$
$367$	19.7190			1.02932			0.514662	+	0.857393i	$0.327918\pi$
$368$	9.51844	+	16.4864i	0.496183	+	0.859414i
$369$		0			0
$370$	2.05940	−	3.56699i	0.107063	−	0.185439i
$371$	0.387993	−	1.05691i	0.0201436	−	0.0548719i
$372$		0			0
$373$	17.5469			0.908544			0.454272	−	0.890863i	$-0.349899\pi$
$373$	17.5469			0.908544			0.454272	+	0.890863i	$0.349899\pi$
$374$	9.05972			0.468467
$375$		0			0
$376$	−8.82478	−	15.2850i	−0.455103	−	0.788262i
$377$	−13.9887	−	2.86308i	−0.720452	−	0.147456i
$378$		0			0
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	0.976256	−	0.216620i	$-0.0695034\pi$
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	−0.675727	+	0.737152i	$0.736170\pi$
$380$	−6.95942	+	12.0541i	−0.357010	+	0.618360i
$381$		0			0
$382$	−13.8055	+	23.9119i	−0.706352	+	1.22344i
$383$	21.5288			1.10007			0.550036	−	0.835141i	$-0.314614\pi$
$383$	21.5288			1.10007			0.550036	+	0.835141i	$0.314614\pi$
$384$		0			0
$385$	0.978699	+	1.17293i	0.0498791	+	0.0597783i
$386$	−28.1536	+	48.7634i	−1.43298	+	2.48199i
$387$		0			0
$388$	28.5000			1.44687
$389$	13.2455	−	22.9419i	0.671574	−	1.16320i	−0.305884	−	0.952069i	$-0.598952\pi$
$389$	13.2455	−	22.9419i	0.671574	−	1.16320i	0.977458	−	0.211131i	$-0.0677147\pi$
$390$		0			0
$391$	−53.3118			−2.69609
$392$	26.8000	−	9.58703i	1.35360	−	0.484218i
$393$		0			0
$394$	3.51267			0.176966
$395$	1.36802	−	2.36949i	0.0688327	−	0.119222i
$396$		0			0
$397$	−33.7989			−1.69632			−0.848160	−	0.529740i	$-0.822289\pi$
$397$	−33.7989			−1.69632			−0.848160	+	0.529740i	$0.822289\pi$
$398$	22.4332			1.12447
$399$		0			0
$400$	4.64989	+	8.05384i	0.232494	+	0.402692i
$401$	10.8059	−	18.7164i	0.539623	−	0.934655i	−0.459301	−	0.888281i	$-0.651900\pi$
$401$	10.8059	−	18.7164i	0.539623	−	0.934655i	0.998924	−	0.0463741i	$-0.0147666\pi$
$402$		0			0
$403$	−3.40730	−	10.2231i	−0.169730	−	0.509250i
$404$	−4.88264	−	8.45697i	−0.242920	−	0.420750i
$405$		0			0
$406$	24.6528	−	4.27676i	1.22350	−	0.212252i
$407$	−0.516056	+	0.893835i	−0.0255799	+	0.0443058i
$408$		0			0
$409$	−3.87109	−	6.70492i	−0.191413	−	0.331537i	0.754306	−	0.656523i	$-0.227974\pi$
$409$	−3.87109	−	6.70492i	−0.191413	−	0.331537i	−0.945719	+	0.324986i	$0.894640\pi$
$410$	−4.30637	−	7.45886i	−0.212677	−	0.368367i
$411$		0			0
$412$	20.1093	−	34.8303i	0.990714	−	1.71597i
$413$	10.1849	+	12.2062i	0.501167	+	0.600630i
$414$		0			0
$415$	1.40868	+	2.43991i	0.0691495	+	0.119770i
$416$	9.28509	+	1.90040i	0.455239	+	0.0931746i
$417$		0			0
$418$	2.68589	−	4.65211i	0.131371	−	0.227542i
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	0.749945	−	0.661500i	$-0.230080\pi$
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	−0.947848	+	0.318722i	$0.896746\pi$
$420$		0			0
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	−21.3543			−1.03951
$423$		0			0
$424$	0.865159	−	1.49850i	0.0420158	−	0.0727735i
$425$	−26.0435			−1.26330
$426$		0			0
$427$	5.75257	−	0.997954i	0.278386	−	0.0482944i
$428$	59.1713			2.86015
$429$		0			0
$430$	7.48384	−	12.9624i	0.360903	−	0.625102i
$431$	29.5281			1.42232			0.711159	−	0.703031i	$-0.248171\pi$
$431$	29.5281			1.42232			0.711159	+	0.703031i	$0.248171\pi$
$432$		0			0
$433$	−11.0455	+	19.1314i	−0.530813	+	0.919395i	0.468540	+	0.883442i	$0.344780\pi$
$433$	−11.0455	+	19.1314i	−0.530813	+	0.919395i	−0.999353	+	0.0359531i	$0.988553\pi$
$434$	12.0979	+	14.4988i	0.580716	+	0.695967i
$435$		0			0
$436$	34.1938			1.63758
$437$	−15.8051	+	27.3752i	−0.756060	+	1.30953i
$438$		0			0
$439$	3.17790	−	5.50428i	0.151673	−	0.262705i	−0.780170	−	0.625568i	$-0.784867\pi$
$439$	3.17790	−	5.50428i	0.151673	−	0.262705i	0.931843	+	0.362863i	$0.118201\pi$
$440$	1.17387	+	2.03321i	0.0559622	+	0.0969294i
$441$		0			0
$442$	36.8718	−	41.5777i	1.75381	−	1.97765i
$443$	−6.78135	−	11.7456i	−0.322192	−	0.558052i	0.658748	−	0.752363i	$-0.271086\pi$
$443$	−6.78135	−	11.7456i	−0.322192	−	0.558052i	−0.980940	+	0.194311i	$0.937753\pi$
$444$		0			0
$445$	−2.05602			−0.0974648
$446$	52.1060			2.46729
$447$		0			0
$448$	−28.3794	+	4.92325i	−1.34080	+	0.232602i
$449$	10.9559	−	18.9762i	0.517041	−	0.895541i	−0.482763	−	0.875751i	$-0.660367\pi$
$449$	10.9559	−	18.9762i	0.517041	−	0.895541i	0.999804	−	0.0197900i	$-0.00629977\pi$
$450$		0			0
$451$	1.07911	+	1.86908i	0.0508134	+	0.0880115i
$452$	−37.6946			−1.77300
$453$		0			0
$454$	44.3041			2.07930
$455$	9.36610	+	0.282132i	0.439090	+	0.0132265i
$456$		0			0
$457$	−7.60732	+	13.1763i	−0.355855	+	0.616359i	−0.987264	−	0.159091i	$-0.949144\pi$
$457$	−7.60732	+	13.1763i	−0.355855	+	0.616359i	0.631409	+	0.775450i	$0.282477\pi$
$458$	46.2097			2.15924
$459$		0			0
$460$	−15.0213	−	26.0176i	−0.700371	−	1.21308i
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	−0.990717	−	0.135937i	$-0.956595\pi$
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	0.613084	+	0.790018i	$0.289929\pi$
$462$		0			0
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	9.12705			0.423713
$465$		0			0
$466$	−38.5988			−1.78805
$467$	7.00337	+	12.1302i	0.324078	+	0.561319i	0.981325	−	0.192356i	$-0.0616128\pi$
$467$	7.00337	+	12.1302i	0.324078	+	0.561319i	−0.657248	+	0.753675i	$0.728279\pi$
$468$		0			0
$469$	18.2817	−	3.17150i	0.844169	−	0.146446i
$470$	5.09091	+	8.81772i	0.234826	+	0.406731i
$471$		0			0
$472$	12.2160	+	21.1588i	0.562288	+	0.973912i
$473$	−1.87534	+	3.24818i	−0.0862282	+	0.149352i
$474$		0			0
$475$	−7.72100	+	13.3732i	−0.354264	+	0.613603i
$476$	−21.7895	+	59.3553i	−0.998719	+	2.72055i
$477$		0			0
$478$	19.2281	−	33.3041i	0.879474	−	1.52329i
$479$	30.0243			1.37185			0.685923	−	0.727674i	$-0.259399\pi$
$479$	30.0243			1.37185			0.685923	+	0.727674i	$0.259399\pi$
$480$		0			0
$481$	2.00180	+	6.00611i	0.0912742	+	0.273855i
$482$	−9.56649			−0.435742
$483$		0			0
$484$	19.7253	+	34.1652i	0.896605	+	1.55296i
$485$	−7.56065			−0.343312
$486$		0			0
$487$	14.2452	+	24.6733i	0.645510	+	1.11806i	0.984184	+	0.177152i	$0.0566884\pi$
$487$	14.2452	+	24.6733i	0.645510	+	1.11806i	−0.338674	+	0.940904i	$0.609978\pi$
$488$	8.97297			0.406187
$489$		0			0
$490$	−15.4606	+	5.53064i	−0.698438	+	0.249849i
$491$	−14.2339	−	24.6538i	−0.642365	−	1.11261i	−0.984903	−	0.173105i	$-0.944620\pi$
$491$	−14.2339	−	24.6538i	−0.642365	−	1.11261i	0.342539	−	0.939504i	$-0.388713\pi$
$492$		0			0
$493$	−12.7799	+	22.1354i	−0.575578	+	0.996930i
$494$	−10.4187	−	31.2598i	−0.468759	−	1.40644i
$495$		0			0
$496$	3.44406	+	5.96528i	0.154643	+	0.267849i
$497$	3.28467	−	8.94755i	0.147337	−	0.401353i
$498$		0			0
$499$	13.1164	+	22.7183i	0.587172	+	1.01701i	0.994601	+	0.103775i	$0.0330921\pi$
$499$	13.1164	+	22.7183i	0.587172	+	1.01701i	−0.407429	+	0.913237i	$0.633575\pi$
$500$	−16.4309	−	28.4591i	−0.734811	−	1.27273i
$501$		0			0
$502$	3.87684	+	6.71488i	0.173032	+	0.299700i
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	−0.755112	−	0.655595i	$-0.772418\pi$
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	0.945318	+	0.326149i	$0.105751\pi$
$504$		0			0
$505$	1.29529	+	2.24352i	0.0576398	+	0.0998351i
$506$	5.79726	+	10.0412i	0.257720	+	0.446384i
$507$		0			0
$508$	−7.86876	+	13.6291i	−0.349120	+	0.604693i
$509$	−6.51298	+	11.2808i	−0.288683	+	0.500014i	−0.973496	−	0.228706i	$-0.926551\pi$
$509$	−6.51298	+	11.2808i	−0.288683	+	0.500014i	0.684813	+	0.728719i	$0.259884\pi$
$510$		0			0
$511$	−4.49890	+	12.2552i	−0.199020	+	0.542137i
$512$	−24.8008			−1.09605
$513$		0			0
$514$	−32.1100	−	55.6162i	−1.41631	−	2.45312i
$515$	−5.33472	+	9.24000i	−0.235076	+	0.407163i
$516$		0			0
$517$	−1.27571	−	2.20959i	−0.0561055	−	0.0971775i
$518$	−7.10753	−	8.51811i	−0.312287	−	0.374264i
$519$		0			0
$520$	14.1085	+	2.88761i	0.618698	+	0.126630i
$521$	2.23285	−	3.86741i	0.0978230	−	0.169434i	−0.812960	−	0.582319i	$-0.802145\pi$
$521$	2.23285	−	3.86741i	0.0978230	−	0.169434i	0.910783	+	0.412885i	$0.135479\pi$
$522$		0			0
$523$	1.45406	−	2.51850i	0.0635815	−	0.110126i	−0.832482	−	0.554051i	$-0.813081\pi$
$523$	1.45406	−	2.51850i	0.0635815	−	0.110126i	0.896064	+	0.443925i	$0.146414\pi$
$524$	−4.01665	+	6.95704i	−0.175468	+	0.303920i
$525$		0			0
$526$	−4.54570	+	7.87339i	−0.198202	+	0.343296i
$527$	−19.2898			−0.840277
$528$		0			0
$529$	−22.6139	−	39.1684i	−0.983213	−	1.70297i
$530$	−0.499100	+	0.864466i	−0.0216795	+	0.0375500i
$531$		0			0
$532$	24.0187	+	28.7855i	1.04134	+	1.24801i
$533$	12.9696	+	2.65451i	0.561775	+	0.114980i
$534$		0			0
$535$	−15.6973			−0.678654
$536$	28.5161			1.23171
$537$		0			0
$538$	56.9262			2.45426
$539$	3.87419	−	1.38590i	0.166873	−	0.0596948i
$540$		0			0
$541$	9.23193	+	15.9902i	0.396912	+	0.687471i	0.993343	−	0.115193i	$-0.0367486\pi$
$541$	9.23193	+	15.9902i	0.396912	+	0.687471i	−0.596431	+	0.802664i	$0.703415\pi$
$542$	−11.8224	−	20.4770i	−0.507815	−	0.879562i
$543$		0			0
$544$	8.48277	−	14.6926i	0.363696	−	0.629940i
$545$	−9.07112			−0.388564
$546$		0			0
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	15.4832	−	26.8177i	0.661411	−	1.14560i
$549$		0			0
$550$	2.83204	+	4.90524i	0.120759	+	0.209160i
$551$	7.57760	+	13.1248i	0.322817	+	0.559135i
$552$		0			0
$553$	−4.72140	−	5.65842i	−0.200774	−	0.240621i
$554$	28.1449			1.19576
$555$		0			0
$556$	−2.13615			−0.0905930
$557$	−0.0531413			−0.00225167			−0.00112583	−	0.999999i	$-0.500358\pi$
$557$	−0.0531413			−0.00225167			−0.00112583	+	0.999999i	$0.500358\pi$
$558$		0			0
$559$	7.27451	+	21.8261i	0.307679	+	0.923146i
$560$	−5.90148	+	1.02379i	−0.249383	+	0.0432629i
$561$		0			0
$562$	15.5194	−	26.8804i	0.654646	−	1.13388i
$563$	3.99253	+	6.91527i	0.168265	+	0.291444i	0.937810	−	0.347149i	$-0.112850\pi$
$563$	3.99253	+	6.91527i	0.168265	+	0.291444i	−0.769545	+	0.638593i	$0.779517\pi$
$564$		0			0
$565$	9.99985			0.420697
$566$	20.0655	−	34.7544i	0.843414	−	1.46084i
$567$		0			0
$568$	7.32424	−	12.6860i	0.307318	−	0.532291i
$569$	−13.3621	+	23.1438i	−0.560167	+	0.970237i	0.437315	+	0.899308i	$0.355930\pi$
$569$	−13.3621	+	23.1438i	−0.560167	+	0.970237i	−0.997481	+	0.0709285i	$0.977404\pi$
$570$		0			0
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	−0.971958	−	0.235153i	$-0.924441\pi$
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	0.689627	+	0.724164i	$0.257774\pi$
$572$	−7.68799	−	1.57352i	−0.321451	−	0.0657920i
$573$		0			0
$574$	−22.8569	+	3.96520i	−0.954028	+	0.165504i
$575$	−16.6651	−	28.8648i	−0.694982	−	1.20374i
$576$		0			0
$577$	−6.00662	+	10.4038i	−0.250059	+	0.433115i	−0.963542	−	0.267558i	$-0.913783\pi$
$577$	−6.00662	+	10.4038i	−0.250059	+	0.433115i	0.713483	+	0.700673i	$0.247117\pi$
$578$	−29.4406	−	50.9925i	−1.22457	−	2.12101i
$579$		0			0
$580$	−14.4036			−0.598078
$581$	7.47684	−	1.29708i	0.310192	−	0.0538119i
$582$		0			0
$583$	0.125067	−	0.216622i	0.00517974	−	0.00897158i
$584$	−10.0318	+	17.3756i	−0.415118	+	0.719005i
$585$		0			0
$586$	−16.8305	−	29.1512i	−0.695260	−	1.20422i
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	0.953307	−	0.302002i	$-0.0976548\pi$
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	−0.738195	+	0.674588i	$0.764321\pi$
$588$		0			0
$589$	−5.71876	+	9.90518i	−0.235637	+	0.408136i
$590$	−7.04728	−	12.2062i	−0.290132	−	0.502523i
$591$		0			0
$592$	−2.02339	−	3.50462i	−0.0831610	−	0.144039i
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	0.539998	−	0.841666i	$-0.318425\pi$
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	−0.998903	+	0.0468194i	$0.985091\pi$
$594$		0			0
$595$	5.78044	−	15.7461i	0.236975	−	0.645528i
$596$	5.19607	+	8.99986i	0.212839	+	0.368649i
$597$		0			0
$598$	69.6759	+	14.2607i	2.84926	+	0.583163i
$599$	0.579463	−	1.00366i	0.0236762	−	0.0410084i	−0.853945	−	0.520364i	$-0.825796\pi$
$599$	0.579463	−	1.00366i	0.0236762	−	0.0410084i	0.877621	+	0.479356i	$0.159130\pi$
$600$		0			0
$601$	−21.0907	−	36.5301i	−0.860306	−	1.49009i	−0.871633	−	0.490158i	$-0.836939\pi$
$601$	−21.0907	−	36.5301i	−0.860306	−	1.49009i	0.0113271	−	0.999936i	$-0.496394\pi$
$602$	−25.8287	−	30.9547i	−1.05270	−	1.26162i
$603$		0			0
$604$	−85.2029			−3.46686
$605$	−5.23284	−	9.06355i	−0.212745	−	0.368486i
$606$		0			0
$607$	−18.1569			−0.736965			−0.368482	−	0.929635i	$-0.620123\pi$
$607$	−18.1569			−0.736965			−0.368482	+	0.929635i	$0.620123\pi$
$608$	−5.02970	−	8.71169i	−0.203981	−	0.353306i
$609$		0			0
$610$	−5.17640			−0.209586
$611$	−15.3324	−	3.13811i	−0.620282	−	0.126954i
$612$		0			0
$613$	−0.902645			−0.0364575			−0.0182288	−	0.999834i	$-0.505803\pi$
$613$	−0.902645			−0.0364575			−0.0182288	+	0.999834i	$0.505803\pi$
$614$	−18.9594	+	32.8386i	−0.765137	+	1.32526i
$615$		0			0
$616$	6.23055	−	1.08087i	0.251036	−	0.0435497i
$617$	−13.0218	+	22.5544i	−0.524238	+	0.908008i	0.475363	+	0.879790i	$0.342317\pi$
$617$	−13.0218	+	22.5544i	−0.524238	+	0.908008i	−0.999602	+	0.0282180i	$0.991017\pi$
$618$		0			0
$619$	−13.4171	+	23.2390i	−0.539277	+	0.934056i	0.459666	+	0.888092i	$0.347969\pi$
$619$	−13.4171	+	23.2390i	−0.539277	+	0.934056i	−0.998943	+	0.0459638i	$0.985364\pi$
$620$	−5.43515	−	9.41396i	−0.218281	−	0.378074i
$621$		0			0
$622$	−34.1530	−	59.1547i	−1.36941	−	2.37189i
$623$	−1.90843	+	5.19863i	−0.0764596	+	0.208279i
$624$		0			0
$625$	−5.72894	−	9.92281i	−0.229158	−	0.396912i
$626$	−44.3679			−1.77330
$627$		0			0
$628$	83.5925			3.33570
$629$	11.3328			0.451869
$630$		0			0
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	−0.309135	−	0.951018i	$-0.600039\pi$
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	0.978173	−	0.207791i	$-0.0666273\pi$
$632$	−5.66296	−	9.80853i	−0.225260	−	0.390162i
$633$		0			0
$634$	−73.1802			−2.90636
$635$	2.08747	−	3.61561i	0.0828388	−	0.143481i
$636$		0			0
$637$	9.40711	−	23.4202i	0.372723	−	0.927942i
$638$	5.55889			0.220078
$639$		0			0
$640$	20.3729			0.805310
$641$	10.5921	+	18.3460i	0.418361	+	0.724622i	0.995775	−	0.0918294i	$-0.0292714\pi$
$641$	10.5921	+	18.3460i	0.418361	+	0.724622i	−0.577414	+	0.816452i	$0.695938\pi$
$642$		0			0
$643$	−0.330770	+	0.572910i	−0.0130443	+	0.0225933i	−0.872474	−	0.488661i	$-0.837486\pi$
$643$	−0.330770	+	0.572910i	−0.0130443	+	0.0225933i	0.859430	+	0.511254i	$0.170819\pi$
$644$	−79.7282	+	13.8312i	−3.14173	+	0.545027i
$645$		0			0
$646$	−58.9834			−2.32067
$647$	40.0323			1.57383			0.786916	−	0.617060i	$-0.211676\pi$
$647$	40.0323			1.57383			0.786916	+	0.617060i	$0.211676\pi$
$648$		0			0
$649$	1.76594	+	3.05870i	0.0693193	+	0.120065i
$650$	34.0376	+	6.96654i	1.33506	+	0.273250i
$651$		0			0
$652$	−15.1388	−	26.2212i	−0.592883	−	1.02690i
$653$	6.35602	−	11.0089i	0.248730	−	0.430813i	−0.714444	−	0.699693i	$-0.753320\pi$
$653$	6.35602	−	11.0089i	0.248730	−	0.430813i	0.963174	+	0.268880i	$0.0866534\pi$
$654$		0			0
$655$	1.06556	−	1.84560i	0.0416349	−	0.0721138i
$656$	−8.46215			−0.330391
$657$		0			0
$658$	27.0209	−	4.68759i	1.05339	−	0.182741i
$659$	−7.09522	+	12.2893i	−0.276391	+	0.478723i	−0.970485	−	0.241161i	$-0.922472\pi$
$659$	−7.09522	+	12.2893i	−0.276391	+	0.478723i	0.694094	+	0.719884i	$0.255805\pi$
$660$		0			0
$661$	50.1780			1.95170			0.975848	−	0.218449i	$-0.0700996\pi$
$661$	50.1780			1.95170			0.975848	+	0.218449i	$0.0700996\pi$
$662$	−32.5104	+	56.3096i	−1.26355	+	2.18853i
$663$		0			0
$664$	11.6625			0.452594
$665$	−6.37183	−	7.63640i	−0.247089	−	0.296127i
$666$		0			0
$667$	−32.7112			−1.26658
$668$	−4.30944	+	7.46417i	−0.166737	+	0.288797i
$669$		0			0
$670$	−16.4506			−0.635542
$671$	1.29713			0.0500751
$672$		0			0
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	0.883522	−	0.468389i	$-0.155166\pi$
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	−0.847398	+	0.530958i	$0.821832\pi$
$674$	14.7056	−	25.4708i	0.566438	−	0.981100i
$675$		0			0
$676$	−38.5104	+	28.8785i	−1.48117	+	1.11071i
$677$	−1.00439	−	1.73966i	−0.0386020	−	0.0668607i	0.846079	−	0.533058i	$-0.178957\pi$
$677$	−1.00439	−	1.73966i	−0.0386020	−	0.0668607i	−0.884681	+	0.466197i	$0.845624\pi$
$678$		0			0
$679$	−7.01790	+	19.1170i	−0.269322	+	0.733644i
$680$	12.8894	−	22.3251i	0.494286	−	0.856128i
$681$		0			0
$682$	2.09762	+	3.63319i	0.0803222	+	0.139122i
$683$	−7.05061	−	12.2120i	−0.269784	−	0.467280i	0.699022	−	0.715100i	$-0.253619\pi$
$683$	−7.05061	−	12.2120i	−0.269784	−	0.467280i	−0.968806	+	0.247820i	$0.920286\pi$
$684$		0			0
$685$	−4.10748	+	7.11437i	−0.156939	+	0.271826i
$686$	−0.366563	+	44.2255i	−0.0139955	+	1.68854i
$687$		0			0
$688$	−7.35298	−	12.7357i	−0.280330	−	0.485546i
$689$	−0.485139	−	1.45559i	−0.0184823	−	0.0554536i
$690$		0			0
$691$	17.8460	−	30.9102i	0.678895	−	1.17588i	−0.296419	−	0.955058i	$-0.595793\pi$
$691$	17.8460	−	30.9102i	0.678895	−	1.17588i	0.975314	−	0.220822i	$-0.0708741\pi$
$692$	−15.0585	−	26.0820i	−0.572437	−	0.991489i
$693$		0			0
$694$	−14.6746			−0.557041
$695$	0.566691			0.0214958
$696$		0			0
$697$	11.8489	−	20.5229i	0.448809	−	0.777360i
$698$	31.1191			1.17788
$699$		0			0
$700$	−38.9483	+	6.75674i	−1.47211	+	0.255381i
$701$	6.15865			0.232609			0.116305	−	0.993214i	$-0.462895\pi$
$701$	6.15865			0.232609			0.116305	+	0.993214i	$0.462895\pi$
$702$		0			0
$703$	3.35979	−	5.81932i	0.126717	−	0.219480i
$704$	−6.39918			−0.241178
$705$		0			0
$706$	37.8103	−	65.4894i	1.42301	−	2.46473i
$707$	6.87501	−	1.19268i	0.258561	−	0.0448552i
$708$		0			0
$709$	34.0371			1.27829			0.639144	−	0.769087i	$-0.279289\pi$
$709$	34.0371			1.27829			0.639144	+	0.769087i	$0.279289\pi$
$710$	−4.22527	+	7.31838i	−0.158571	+	0.274654i
$711$		0			0
$712$	−4.25547	+	7.37069i	−0.159480	+	0.276228i
$713$	−12.3434	−	21.3794i	−0.462265	−	0.800667i
$714$		0			0
$715$	2.03952	+	0.417432i	0.0762736	+	0.0156111i
$716$	−38.8648	−	67.3158i	−1.45244	−	2.51571i
$717$		0			0
$718$	−47.5989			−1.77637
$719$	22.9648			0.856444			0.428222	−	0.903674i	$-0.359140\pi$
$719$	22.9648			0.856444			0.428222	+	0.903674i	$0.359140\pi$
$720$		0			0
$721$	18.4115	+	22.0655i	0.685679	+	0.821761i
$722$	5.19981	−	9.00633i	0.193517	−	0.335181i
$723$		0			0
$724$	2.97712	+	5.15653i	0.110644	+	0.191641i
$725$	−15.9798			−0.593476
$726$		0			0
$727$	1.06558			0.0395203			0.0197601	−	0.999805i	$-0.493710\pi$
$727$	1.06558			0.0395203			0.0197601	+	0.999805i	$0.493710\pi$
$728$	20.3970	−	32.9928i	0.755963	−	1.22280i
$729$		0			0
$730$	5.78721	−	10.0237i	0.214194	−	0.370996i
$731$	41.1833			1.52322
$732$		0			0
$733$	13.1689	+	22.8092i	0.486404	+	0.842476i	0.999878	−	0.0156289i	$-0.00497504\pi$
$733$	13.1689	+	22.8092i	0.486404	+	0.842476i	−0.513474	+	0.858105i	$0.671642\pi$
$734$	−23.5448	+	40.7809i	−0.869056	+	1.50525i
$735$		0			0
$736$	21.7123			0.800326
$737$	4.12228			0.151846
$738$		0			0
$739$	34.2149			1.25862			0.629308	−	0.777156i	$-0.283338\pi$
$739$	34.2149			1.25862			0.629308	+	0.777156i	$0.283338\pi$
$740$	3.19317	+	5.53073i	0.117383	+	0.203314i
$741$		0			0
$742$	1.72252	+	2.06438i	0.0632358	+	0.0757857i
$743$	11.2391	+	19.4667i	0.412322	+	0.714163i	0.995143	−	0.0984379i	$-0.0313846\pi$
$743$	11.2391	+	19.4667i	0.412322	+	0.714163i	−0.582821	+	0.812600i	$0.698051\pi$
$744$		0			0
$745$	−1.37845	−	2.38754i	−0.0505023	−	0.0874726i
$746$	−20.9513	+	36.2888i	−0.767083	+	1.32863i
$747$		0			0
$748$	−7.02368	+	12.1654i	−0.256811	+	0.444810i
$749$	−14.5705	+	39.6905i	−0.532393	+	1.45026i
$750$		0			0
$751$	21.2712	−	36.8428i	0.776197	−	1.34441i	−0.157923	−	0.987451i	$-0.550480\pi$
$751$	21.2712	−	36.8428i	0.776197	−	1.34441i	0.934119	−	0.356961i	$-0.116187\pi$
$752$	10.0038			0.364801
$753$		0			0
$754$	22.6239	−	25.5114i	0.823912	−	0.929069i
$755$	22.6031			0.822612
$756$		0			0
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	0.949886	−	0.312596i	$-0.101199\pi$
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	−0.745659	+	0.666327i	$0.767865\pi$
$758$	−27.9433			−1.01495
$759$		0			0
$760$	−7.64252	−	13.2372i	−0.277223	−	0.480165i
$761$	−12.8084			−0.464306			−0.232153	−	0.972679i	$-0.574577\pi$
$761$	−12.8084			−0.464306			−0.232153	+	0.972679i	$0.574577\pi$
$762$		0			0
$763$	−8.41994	+	22.9362i	−0.304822	+	0.830347i
$764$	−21.4059	−	37.0760i	−0.774437	−	1.34136i
$765$		0			0
$766$	−25.7058	+	44.5238i	−0.928789	+	1.60871i
$767$	21.2244	+	4.34404i	0.766369	+	0.156854i
$768$		0			0
$769$	25.6759	+	44.4719i	0.925895	+	1.60370i	0.790115	+	0.612958i	$0.210021\pi$
$769$	25.6759	+	44.4719i	0.925895	+	1.60370i	0.135780	+	0.990739i	$0.456646\pi$
$770$	−3.59433	+	0.623543i	−0.129531	+	0.0224709i
$771$		0			0
$772$	−43.6529	−	75.6091i	−1.57110	−	2.72123i
$773$	10.0023	+	17.3245i	0.359759	+	0.623120i	0.987920	−	0.154963i	$-0.0495257\pi$
$773$	10.0023	+	17.3245i	0.359759	+	0.623120i	−0.628162	+	0.778083i	$0.716192\pi$
$774$		0			0
$775$	−6.02993	−	10.4441i	−0.216602	−	0.375165i
$776$	−15.6487	+	27.1044i	−0.561756	+	0.972990i
$777$		0			0
$778$	31.6308	+	54.7861i	1.13402	+	1.96418i
$779$	−7.02558	−	12.1687i	−0.251717	−	0.435987i
$780$		0			0
$781$	1.05879	−	1.83388i	0.0378864	−	0.0656212i
$782$	63.6552	−	110.254i	2.27631	−	3.94268i
$783$		0			0
$784$	−2.88920	+	15.8721i	−0.103186	+	0.566861i
$785$	−22.1759			−0.791492
$786$		0			0
$787$	−14.6596	−	25.3911i	−0.522558	−	0.905096i	−0.999656	−	0.0262462i	$-0.991645\pi$
$787$	−14.6596	−	25.3911i	−0.522558	−	0.905096i	0.477098	−	0.878850i	$-0.341689\pi$
$788$	−2.72325	+	4.71680i	−0.0970117	+	0.168029i
$789$		0			0
$790$	3.26689	+	5.65842i	0.116231	+	0.201318i
$791$	9.28199	−	25.2845i	0.330030	−	0.899013i
$792$		0			0
$793$	5.27912	−	5.95291i	0.187467	−	0.211394i
$794$	40.3566	−	69.8996i	1.43220	−	2.48064i
$795$		0			0
$796$	−17.3917	+	30.1232i	−0.616431	+	1.06769i
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	−0.837258	−	0.546809i	$-0.815842\pi$
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	0.892179	+	0.451682i	$0.149176\pi$
$798$		0			0
$799$	−14.0075	+	24.2618i	−0.495551	+	0.858319i
$800$	10.6068			0.375005
$801$		0			0
$802$	25.8050	+	44.6956i	0.911206	+	1.57826i
$803$	−1.45019	+	2.51180i	−0.0511761	+	0.0886395i
$804$		0			0
$805$	21.1508	−	3.66923i	0.745467	−	0.129323i
$806$	25.2108	+	5.15995i	0.888013	+	0.181751i
$807$		0			0
$808$	10.7238			0.377261
$809$	−7.99003			−0.280914			−0.140457	−	0.990087i	$-0.544857\pi$
$809$	−7.99003			−0.280914			−0.140457	+	0.990087i	$0.544857\pi$
$810$		0			0
$811$	−48.2554			−1.69448			−0.847239	−	0.531213i	$-0.821737\pi$
$811$	−48.2554			−1.69448			−0.847239	+	0.531213i	$0.821737\pi$
$812$	−13.3696	+	36.4194i	−0.469182	+	1.27807i
$813$		0			0
$814$	−1.23236	−	2.13451i	−0.0431942	−	0.0748146i
$815$	4.01612	+	6.95612i	0.140679	+	0.243662i
$816$		0			0
$817$	12.2094	−	21.1473i	0.427153	−	0.739851i
$818$	18.4886			0.646439
$819$		0			0
$820$	13.3543			0.466353
$821$	−13.7760	+	23.8607i	−0.480785	+	0.832743i	−0.999757	−	0.0220477i	$-0.992981\pi$
$821$	−13.7760	+	23.8607i	−0.480785	+	0.832743i	0.518972	+	0.854791i	$0.326315\pi$
$822$		0			0
$823$	−10.2137	−	17.6907i	−0.356028	−	0.616659i	0.631265	−	0.775567i	$-0.282536\pi$
$823$	−10.2137	−	17.6907i	−0.356028	−	0.616659i	−0.987293	+	0.158908i	$0.949203\pi$
$824$	22.0831	+	38.2491i	0.769303	+	1.33247i
$825$		0			0
$826$	−37.4047	+	6.48896i	−1.30148	+	0.225780i
$827$	27.7142			0.963719			0.481859	−	0.876249i	$-0.339962\pi$
$827$	27.7142			0.963719			0.481859	+	0.876249i	$0.339962\pi$
$828$		0			0
$829$	9.25664			0.321496			0.160748	−	0.986995i	$-0.448609\pi$
$829$	9.25664			0.321496			0.160748	+	0.986995i	$0.448609\pi$
$830$	−6.72797			−0.233531
$831$		0			0
$832$	−26.0437	+	29.3677i	−0.902904	+	1.01814i
$833$	−34.4484	−	29.2315i	−1.19357	−	1.01281i
$834$		0			0
$835$	1.14323	−	1.98014i	0.0395632	−	0.0685255i
$836$	4.16456	+	7.21323i	0.144034	+	0.249475i
$837$		0			0
$838$	19.3477			0.668357
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	0.475287	+	0.879831i	$0.342344\pi$
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	−0.999599	+	0.0283045i	$0.990989\pi$
$840$		0			0
$841$	6.65848	−	11.5328i	0.229603	−	0.397683i
$842$	38.3428	−	66.4116i	1.32138	−	2.28869i
$843$		0			0
$844$	16.5552	−	28.6745i	0.569854	−	0.987016i
$845$	10.2163	−	7.66106i	0.351450	−	0.263548i
$846$		0			0
$847$	−27.7743	+	4.81827i	−0.954336	+	0.165558i
$848$	0.490373	+	0.849350i	0.0168395	+	0.0291668i
$849$		0			0
$850$	31.0964	−	53.8606i	1.06660	−	1.84740i
$851$	7.25180	+	12.5605i	0.248589	+	0.430568i
$852$		0			0
$853$	−5.30773			−0.181733			−0.0908666	−	0.995863i	$-0.528964\pi$
$853$	−5.30773			−0.181733			−0.0908666	+	0.995863i	$0.528964\pi$
$854$	−4.80481	+	13.0885i	−0.164417	+	0.447878i
$855$		0			0
$856$	−32.4896	+	56.2737i	−1.11047	+	1.92340i
$857$	−8.31857	+	14.4082i	−0.284157	+	0.492175i	−0.972404	−	0.233302i	$-0.925047\pi$
$857$	−8.31857	+	14.4082i	−0.284157	+	0.492175i	0.688247	+	0.725476i	$0.258380\pi$
$858$		0			0
$859$	5.29426	+	9.16993i	0.180638	+	0.312874i	0.942098	−	0.335338i	$-0.108850\pi$
$859$	5.29426	+	9.16993i	0.180638	+	0.312874i	−0.761460	+	0.648212i	$0.775517\pi$
$860$	11.6039	+	20.0986i	0.395690	+	0.685356i
$861$		0			0
$862$	−35.2571	+	61.0671i	−1.20086	+	2.07995i
$863$	−28.0316	−	48.5522i	−0.954207	−	1.65273i	−0.736173	−	0.676793i	$-0.763369\pi$
$863$	−28.0316	−	48.5522i	−0.954207	−	1.65273i	−0.218033	−	0.975941i	$-0.569964\pi$
$864$		0			0
$865$	3.99480	+	6.91919i	0.135827	+	0.235260i
$866$	−26.3771	−	45.6864i	−0.896329	−	1.55249i
$867$		0			0
$868$	−28.8481	+	5.00455i	−0.979167	+	0.169866i
$869$	−0.818634	−	1.41792i	−0.0277703	−	0.0480995i
$870$		0			0
$871$	16.7771	−	18.9183i	0.568469	−	0.641024i
$872$	−18.7750	+	32.5193i	−0.635803	+	1.10124i
$873$		0			0
$874$	−37.7432	−	65.3731i	−1.27668	−	2.21128i
$875$	23.1355	−	4.01355i	0.782124	−	0.135683i
$876$		0			0
$877$	−3.66051			−0.123607			−0.0618033	−	0.998088i	$-0.519685\pi$
$877$	−3.66051			−0.123607			−0.0618033	+	0.998088i	$0.519685\pi$
$878$	7.58894	+	13.1444i	0.256114	+	0.443603i
$879$		0			0
$880$	−1.33071			−0.0448581
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	0.939233	−	0.343281i	$-0.111538\pi$
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	−0.766906	+	0.641759i	$0.778205\pi$
$882$		0			0
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$	27.2451	+	81.7451i	0.916353	+	2.74938i
$885$		0			0
$886$	32.3882			1.08810
$887$	−7.11039	+	12.3155i	−0.238743	+	0.413516i	−0.960354	−	0.278784i	$-0.910069\pi$
$887$	−7.11039	+	12.3155i	−0.238743	+	0.413516i	0.721611	+	0.692299i	$0.243402\pi$
$888$		0			0
$889$	−7.20440	−	8.63420i	−0.241628	−	0.289582i
$890$	2.45493	−	4.25206i	0.0822894	−	0.142529i
$891$		0			0
$892$	−40.3960	+	69.9678i	−1.35256	+	2.34270i
$893$	8.30550	+	14.3855i	0.277933	+	0.481394i
$894$		0			0
$895$	10.3103	+	17.8579i	0.344635	+	0.596924i
$896$	18.9104	−	51.5127i	0.631753	−	1.72092i
$897$		0			0
$898$	26.1631	+	45.3158i	0.873074	+	1.51221i
$899$	−11.8359			−0.394749
$900$		0			0
$901$	−2.74652			−0.0915000
$902$	−5.15392			−0.171607
$903$		0			0
$904$	20.6973	−	35.8487i	0.688381	−	1.19231i
$905$	−0.789789	−	1.36795i	−0.0262535	−	0.0454723i
$906$		0			0
$907$	43.4253			1.44191			0.720956	−	0.692981i	$-0.243703\pi$
$907$	43.4253			1.44191			0.720956	+	0.692981i	$0.243703\pi$
$908$	−34.3474	+	59.4915i	−1.13986	+	1.97429i
$909$		0			0
$910$	−11.7668	+	19.0332i	−0.390065	+	0.630944i
$911$	−24.8617			−0.823706			−0.411853	−	0.911250i	$-0.635118\pi$
$911$	−24.8617			−0.823706			−0.411853	+	0.911250i	$0.635118\pi$
$912$		0			0
$913$	1.68593			0.0557961
$914$	−18.1666	−	31.4654i	−0.600896	−	1.04078i
$915$		0			0
$916$	−35.8248	+	62.0503i	−1.18368	+	2.05020i
$917$	−3.67752	−	4.40737i	−0.121443	−	0.145544i
$918$		0			0
$919$	−1.66327			−0.0548664			−0.0274332	−	0.999624i	$-0.508733\pi$
$919$	−1.66327			−0.0548664			−0.0274332	+	0.999624i	$0.508733\pi$
$920$	32.9914			1.08769
$921$		0			0
$922$	−19.3625	−	33.5369i	−0.637671	−	1.10448i
$923$	−4.10708	−	12.3227i	−0.135186	−	0.405607i
$924$		0			0
$925$	3.54260	+	6.13597i	0.116480	+	0.201749i
$926$	1.72857	−	2.99397i	0.0568044	−	0.0983880i
$927$		0			0
$928$	5.20488	−	9.01512i	0.170859	−	0.295936i
$929$	−9.49521			−0.311528			−0.155764	−	0.987794i	$-0.549784\pi$
$929$	−9.49521			−0.311528			−0.155764	+	0.987794i	$0.549784\pi$
$930$		0			0
$931$	−25.2230	+	9.02289i	−0.826649	+	0.295713i
$932$	29.9243	−	51.8304i	0.980202	−	1.69776i
$933$		0			0
$934$	−33.4486			−1.09447
$935$	1.86328	−	3.22730i	0.0609359	−	0.105544i
$936$		0			0
$937$	−6.41678			−0.209627			−0.104813	−	0.994492i	$-0.533425\pi$
$937$	−6.41678			−0.209627			−0.104813	+	0.994492i	$0.533425\pi$
$938$	−15.2697	+	41.5952i	−0.498573	+	1.35813i
$939$		0			0
$940$	−15.7872			−0.514922
$941$	−25.7593	+	44.6164i	−0.839730	+	1.45445i	0.0503911	+	0.998730i	$0.483953\pi$
$941$	−25.7593	+	44.6164i	−0.839730	+	1.45445i	−0.890121	+	0.455725i	$0.849380\pi$
$942$		0			0
$943$	30.3282			0.987621
$944$	−13.8481			−0.450717
$945$		0			0
$946$	−4.47838	−	7.75678i	−0.145605	−	0.252195i
$947$	−4.20109	+	7.27651i	−0.136517	+	0.236455i	−0.926176	−	0.377091i	$-0.876924\pi$
$947$	−4.20109	+	7.27651i	−0.136517	+	0.236455i	0.789659	+	0.613546i	$0.210258\pi$
$948$		0			0
$949$	5.62534	+	16.8780i	0.182606	+	0.547883i
$950$	−18.4380	−	31.9356i	−0.598209	−	1.03613i
$951$		0			0
$952$	−44.4846	−	53.3131i	−1.44175	−	1.72789i
$953$	−18.0455	+	31.2558i	−0.584552	+	1.01247i	0.410379	+	0.911915i	$0.365396\pi$
$953$	−18.0455	+	31.2558i	−0.584552	+	1.01247i	−0.994931	+	0.100559i	$0.967937\pi$
$954$		0			0
$955$	5.67867	+	9.83575i	0.183758	+	0.318277i
$956$	29.8138	+	51.6390i	0.964246	+	1.67012i
$957$		0			0
$958$	−35.8496	+	62.0933i	−1.15825	+	2.00614i
$959$	14.1760	+	16.9894i	0.457766	+	0.548616i
$960$		0			0
$961$	11.0338	+	19.1111i	0.355928	+	0.616486i
$962$	−14.8114	−	3.03148i	−0.477540	−	0.0977390i
$963$		0			0
$964$	7.41656	−	12.8459i	0.238871	−	0.413737i
$965$	11.5805	+	20.0580i	0.372790	+	0.645691i
$966$		0			0
$967$	3.18338			0.102371			0.0511853	−	0.998689i	$-0.483700\pi$
$967$	3.18338			0.102371			0.0511853	+	0.998689i	$0.483700\pi$
$968$	−43.3229			−1.39245
$969$		0			0
$970$	9.02756	−	15.6362i	0.289857	−	0.502048i
$971$	−37.7476			−1.21138			−0.605690	−	0.795701i	$-0.707103\pi$
$971$	−37.7476			−1.21138			−0.605690	+	0.795701i	$0.707103\pi$
$972$		0			0
$973$	0.526010	−	1.43287i	0.0168631	−	0.0459358i
$974$	−68.0359			−2.18001
$975$		0			0
$976$	−2.54294	+	4.40451i	−0.0813977	+	0.140985i
$977$	21.3076			0.681692			0.340846	−	0.940119i	$-0.389287\pi$
$977$	21.3076			0.681692			0.340846	+	0.940119i	$0.389287\pi$
$978$		0			0
$979$	−0.615168	+	1.06550i	−0.0196609	+	0.0340536i
$980$	4.55951	−	25.0482i	0.145648	−	0.800134i
$981$		0			0
$982$	67.9819			2.16939
$983$	−11.0158	+	19.0799i	−0.351350	+	0.608556i	−0.986486	−	0.163844i	$-0.947611\pi$
$983$	−11.0158	+	19.0799i	−0.351350	+	0.608556i	0.635136	+	0.772400i	$0.280944\pi$
$984$		0			0
$985$	0.722439	−	1.25130i	0.0230188	−	0.0398698i
$986$	−30.5189	−	52.8603i	−0.971919	−	1.68341i
$987$		0			0
$988$	50.0528	+	10.2444i	1.59239	+	0.325918i
$989$	26.3529	+	45.6446i	0.837975	+	1.45141i
$990$		0			0
$991$	−22.0259			−0.699676			−0.349838	−	0.936810i	$-0.613763\pi$
$991$	−22.0259			−0.699676			−0.349838	+	0.936810i	$0.613763\pi$
$992$	7.85617			0.249434
$993$		0			0
$994$	14.5825	+	17.4766i	0.462528	+	0.554323i
$995$	4.61376	−	7.99127i	0.146266	−	0.253340i
$996$		0			0
$997$	−5.04102	−	8.73130i	−0.159651	−	0.276523i	0.775092	−	0.631848i	$-0.217703\pi$
$997$	−5.04102	−	8.73130i	−0.159651	−	0.276523i	−0.934743	+	0.355325i	$0.884370\pi$
$998$	−62.6450			−1.98299
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.d.172.1		12
3.2	odd	2		91.2.g.b.81.6	yes	12
7.2	even	3		819.2.s.d.289.6		12
13.9	even	3		819.2.s.d.802.6		12
21.2	odd	6		91.2.h.b.16.1	yes	12
21.5	even	6		637.2.h.l.471.1		12
21.11	odd	6		637.2.f.k.393.6		12
21.17	even	6		637.2.f.j.393.6		12
21.20	even	2		637.2.g.l.263.6		12
39.23	odd	6		1183.2.e.g.508.1		12
39.29	odd	6		1183.2.e.h.508.6		12
39.35	odd	6		91.2.h.b.74.1	yes	12
91.9	even	3	inner	819.2.n.d.100.1		12
273.23	odd	6		1183.2.e.g.170.1		12
273.74	odd	6		637.2.f.k.295.6		12
273.101	even	6		8281.2.a.cf.1.6		6
273.107	odd	6		1183.2.e.h.170.6		12
273.152	even	6		637.2.g.l.373.6		12
273.179	odd	6		8281.2.a.ce.1.6		6
273.185	even	6		8281.2.a.ca.1.1		6
273.191	odd	6		91.2.g.b.9.6	✓	12
273.230	even	6		637.2.h.l.165.1		12
273.263	odd	6		8281.2.a.bz.1.1		6
273.269	even	6		637.2.f.j.295.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	273.191	odd	6
91.2.g.b.81.6	yes	12	3.2	odd	2
91.2.h.b.16.1	yes	12	21.2	odd	6
91.2.h.b.74.1	yes	12	39.35	odd	6
637.2.f.j.295.6		12	273.269	even	6
637.2.f.j.393.6		12	21.17	even	6
637.2.f.k.295.6		12	273.74	odd	6
637.2.f.k.393.6		12	21.11	odd	6
637.2.g.l.263.6		12	21.20	even	2
637.2.g.l.373.6		12	273.152	even	6
637.2.h.l.165.1		12	273.230	even	6
637.2.h.l.471.1		12	21.5	even	6
819.2.n.d.100.1		12	91.9	even	3	inner
819.2.n.d.172.1		12	1.1	even	1	trivial
819.2.s.d.289.6		12	7.2	even	3
819.2.s.d.802.6		12	13.9	even	3
1183.2.e.g.170.1		12	273.23	odd	6
1183.2.e.g.508.1		12	39.23	odd	6
1183.2.e.h.170.6		12	273.107	odd	6
1183.2.e.h.508.6		12	39.29	odd	6
8281.2.a.bz.1.1		6	273.263	odd	6
8281.2.a.ca.1.1		6	273.185	even	6
8281.2.a.ce.1.6		6	273.179	odd	6
8281.2.a.cf.1.6		6	273.101	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19402 + 2.06810i) q^{2} +(-1.85136 - 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} +(2.60682 - 0.452230i) q^{7} +4.06616 q^{8} -2.34572 q^{10} +0.587802 q^{11} +(2.39227 - 2.69760i) q^{13} +(-2.17733 + 5.93113i) q^{14} +(-1.15235 + 1.99593i) q^{16} +(-3.22710 - 5.58950i) q^{17} -3.82689 q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(4.13001 - 7.15338i) q^{23} +(2.01756 - 3.49452i) q^{25} +(2.72249 + 8.16844i) q^{26} +(-6.27630 - 7.52191i) q^{28} +(-1.98009 - 3.42962i) q^{29} +(1.49436 - 2.58831i) q^{31} +(1.31430 + 2.27644i) q^{32} +15.4129 q^{34} +(1.66501 + 1.99546i) q^{35} +(-0.877941 + 1.52064i) q^{37} +(4.56938 - 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(-1.08823 - 1.88488i) q^{44} +(9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} +(6.59098 - 2.35776i) q^{49} +(4.81802 + 8.34505i) q^{50} +(-13.0792 - 2.67695i) q^{52} +(0.212770 - 0.368529i) q^{53} +(0.288693 + 0.500031i) q^{55} +(10.5997 - 1.83884i) q^{56} +9.45706 q^{58} +(3.00431 + 5.20362i) q^{59} +2.20674 q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(3.46973 + 0.710156i) q^{65} +7.01303 q^{67} +(-11.9491 + 20.6964i) q^{68} +(-6.11486 + 1.06080i) q^{70} +(1.80127 - 3.11988i) q^{71} +(-2.46714 + 4.27321i) q^{73} +(-2.09656 - 3.63134i) q^{74} +(7.08496 + 12.2715i) q^{76} +(1.53229 - 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} -2.26386 q^{80} -8.76812 q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(-7.61885 - 13.1962i) q^{86} +2.39010 q^{88} +(-1.04656 + 1.81269i) q^{89} +(5.01627 - 8.11400i) q^{91} -30.5845 q^{92} +10.3655 q^{94} +(-1.87954 - 3.25546i) q^{95} +(-3.84852 + 6.66584i) q^{97} +(-2.99367 + 16.4460i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29}+ \cdots - 62 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more