LMFDB - Embedded newform 405.3.l.i.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.1
Root			$1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	405.28
Dual form			405.3.l.i.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.624069 - 0.167219i) q^{2} +(-3.10260 - 1.79129i) q^{4} +(-4.64741 + 1.84434i) q^{5} +(5.74921 + 1.54050i) q^{7} +(3.46410 + 3.46410i) q^{8} +(3.20871 - 0.373864i) q^{10} +(0.0476751 + 0.0825757i) q^{11} +(-3.30226 + 0.884839i) q^{13} +(-3.33030 - 1.92275i) q^{14} +(5.58258 + 9.66930i) q^{16} +(-14.4086 + 14.4086i) q^{17} -25.7477i q^{19} +(17.7228 + 2.60258i) q^{20} +(-0.0159443 - 0.0595051i) q^{22} +(4.60180 - 1.23305i) q^{23} +(18.1968 - 17.1428i) q^{25} +2.20880 q^{26} +(-15.0780 - 15.0780i) q^{28} +(35.6216 - 20.5661i) q^{29} +(18.5000 - 32.0429i) q^{31} +(-6.93882 - 25.8960i) q^{32} +(11.4014 - 6.58258i) q^{34} +(-29.5601 + 3.44420i) q^{35} +(50.6170 - 50.6170i) q^{37} +(-4.30550 + 16.0684i) q^{38} +(-22.4881 - 9.71010i) q^{40} +(1.13218 - 1.96099i) q^{41} +(9.04235 - 33.7465i) q^{43} -0.341599i q^{44} -3.07803 q^{46} +(-22.3091 - 5.97769i) q^{47} +(-11.7550 - 6.78674i) q^{49} +(-14.2227 + 7.65546i) q^{50} +(11.8306 + 3.17000i) q^{52} +(49.0894 + 49.0894i) q^{53} +(-0.373864 - 0.295834i) q^{55} +(14.5794 + 25.2523i) q^{56} +(-25.6694 + 6.87809i) q^{58} +(-86.6216 - 50.0110i) q^{59} +(27.7477 + 48.0605i) q^{61} +(-16.9035 + 16.9035i) q^{62} -27.3394i q^{64} +(13.7150 - 10.2027i) q^{65} +(13.6638 + 50.9941i) q^{67} +(70.5141 - 18.8942i) q^{68} +(19.0235 + 2.79359i) q^{70} +39.8770 q^{71} +(39.3739 + 39.3739i) q^{73} +(-40.0527 + 23.1244i) q^{74} +(-46.1216 + 79.8849i) q^{76} +(0.146887 + 0.548188i) q^{77} +(-52.0212 + 30.0345i) q^{79} +(-43.7780 - 34.6410i) q^{80} +(-1.03447 + 1.03447i) q^{82} +(28.3267 - 105.717i) q^{83} +(40.3883 - 93.5371i) q^{85} +(-11.2861 + 19.5481i) q^{86} +(-0.120899 + 0.451202i) q^{88} -51.6755i q^{89} -20.3485 q^{91} +(-16.4863 - 4.41749i) q^{92} +(12.9228 + 7.46099i) q^{94} +(47.4876 + 119.660i) q^{95} +(-96.7027 - 25.9114i) q^{97} +(6.20105 + 6.20105i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} + 6 q^{5} + 26 q^{7} + 44 q^{10} - 28 q^{13} + 120 q^{14} + 8 q^{16} + 24 q^{20} + 46 q^{22} + 60 q^{23} + 32 q^{25} + 136 q^{28} + 120 q^{29} + 148 q^{31} - 168 q^{32} + 20 q^{37} - 54 q^{38}+ \cdots - 274 q^{97}+O(q^{100}) $ 8 * q + 6 * q^2 + 6 * q^5 + 26 * q^7 + 44 * q^10 - 28 * q^13 + 120 * q^14 + 8 * q^16 + 24 * q^20 + 46 * q^22 + 60 * q^23 + 32 * q^25 + 136 * q^28 + 120 * q^29 + 148 * q^31 - 168 * q^32 + 20 * q^37 - 54 * q^38 - 48 * q^40 + 2 * q^43 + 232 * q^46 + 6 * q^47 + 42 * q^50 - 112 * q^52 + 52 * q^55 - 66 * q^58 - 528 * q^59 + 112 * q^61 - 84 * q^65 - 76 * q^67 + 156 * q^68 + 396 * q^70 + 260 * q^73 - 852 * q^74 - 204 * q^76 - 318 * q^77 + 340 * q^82 + 582 * q^83 + 194 * q^85 - 72 * q^88 - 896 * q^91 + 228 * q^92 + 342 * q^95 - 274 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.624069	−	0.167219i	−0.312035	−	0.0836094i	0.0994033	−	0.995047i	$-0.468307\pi$
$2$	−0.624069	−	0.167219i	−0.312035	−	0.0836094i	−0.411438	+	0.911438i	$0.634973\pi$
$3$		0			0
$3$		0			0
$4$	−3.10260	−	1.79129i	−0.775650	−	0.447822i
$5$	−4.64741	+	1.84434i	−0.929482	+	0.368869i
$5$	−4.64741	+	1.84434i	−0.929482	+	0.368869i
$6$		0			0
$7$	5.74921	+	1.54050i	0.821315	+	0.220071i	0.644921	−	0.764249i	$-0.276890\pi$
$7$	5.74921	+	1.54050i	0.821315	+	0.220071i	0.176394	+	0.984320i	$0.443557\pi$
$8$	3.46410	+	3.46410i	0.433013	+	0.433013i
$9$		0			0
$10$	3.20871	−	0.373864i	0.320871	−	0.0373864i
$11$	0.0476751	+	0.0825757i	0.00433410	+	0.00750688i	0.868184	−	0.496242i	$-0.165287\pi$
$11$	0.0476751	+	0.0825757i	0.00433410	+	0.00750688i	−0.863850	+	0.503749i	$0.831954\pi$
$12$		0			0
$13$	−3.30226	+	0.884839i	−0.254020	+	0.0680645i	−0.383582	−	0.923507i	$-0.625310\pi$
$13$	−3.30226	+	0.884839i	−0.254020	+	0.0680645i	0.129562	+	0.991571i	$0.458643\pi$
$14$	−3.33030	−	1.92275i	−0.237879	−	0.137339i
$15$		0			0
$16$	5.58258	+	9.66930i	0.348911	+	0.604332i
$17$	−14.4086	+	14.4086i	−0.847565	+	0.847565i	−0.989829	−	0.142264i	$-0.954562\pi$
$17$	−14.4086	+	14.4086i	−0.847565	+	0.847565i	0.142264	+	0.989829i	$0.454562\pi$
$18$		0			0
$19$		−	25.7477i		−	1.35514i	−0.735457	−	0.677572i	$-0.763032\pi$
$19$		−	25.7477i		−	1.35514i	0.735457	−	0.677572i	$-0.236968\pi$
$20$	17.7228	+	2.60258i	0.886140	+	0.130129i
$21$		0			0
$22$	−0.0159443	−	0.0595051i	−0.000724743	−	0.00270478i
$23$	4.60180	−	1.23305i	0.200078	−	0.0536108i	−0.157388	−	0.987537i	$-0.550307\pi$
$23$	4.60180	−	1.23305i	0.200078	−	0.0536108i	0.357466	+	0.933926i	$0.383641\pi$
$24$		0			0
$25$	18.1968	−	17.1428i	0.727872	−	0.685713i
$26$	2.20880			0.0849539
$27$		0			0
$28$	−15.0780	−	15.0780i	−0.538501	−	0.538501i
$29$	35.6216	−	20.5661i	1.22833	−	0.709177i	0.261650	−	0.965163i	$-0.415733\pi$
$29$	35.6216	−	20.5661i	1.22833	−	0.709177i	0.966681	+	0.255986i	$0.0824000\pi$
$30$		0			0
$31$	18.5000	−	32.0429i	0.596774	−	1.03364i	−0.396520	−	0.918026i	$-0.629782\pi$
$31$	18.5000	−	32.0429i	0.596774	−	1.03364i	0.993294	−	0.115617i	$-0.0368845\pi$
$32$	−6.93882	−	25.8960i	−0.216838	−	0.809251i
$33$		0			0
$34$	11.4014	−	6.58258i	0.335334	−	0.193605i
$35$	−29.5601	+	3.44420i	−0.844575	+	0.0984057i
$36$		0			0
$37$	50.6170	−	50.6170i	1.36803	−	1.36803i	0.504781	−	0.863248i	$-0.331573\pi$
$37$	50.6170	−	50.6170i	1.36803	−	1.36803i	0.863248	−	0.504781i	$-0.168427\pi$
$38$	−4.30550	+	16.0684i	−0.113303	+	0.422852i
$39$		0			0
$40$	−22.4881	−	9.71010i	−0.562202	−	0.242753i
$41$	1.13218	−	1.96099i	0.0276140	−	0.0478289i	−0.851888	−	0.523724i	$-0.824542\pi$
$41$	1.13218	−	1.96099i	0.0276140	−	0.0478289i	0.879502	+	0.475895i	$0.157876\pi$
$42$		0			0
$43$	9.04235	−	33.7465i	0.210287	−	0.784803i	−0.777485	−	0.628901i	$-0.783505\pi$
$43$	9.04235	−	33.7465i	0.210287	−	0.784803i	0.987773	−	0.155902i	$-0.0498283\pi$
$44$		−	0.341599i		−	0.00776362i
$45$		0			0
$46$	−3.07803			−0.0669137
$47$	−22.3091	−	5.97769i	−0.474661	−	0.127185i	0.0135547	−	0.999908i	$-0.495685\pi$
$47$	−22.3091	−	5.97769i	−0.474661	−	0.127185i	−0.488215	+	0.872723i	$0.662352\pi$
$48$		0			0
$49$	−11.7550	−	6.78674i	−0.239898	−	0.138505i
$50$	−14.2227	+	7.65546i	−0.284453	+	0.153109i
$51$		0			0
$52$	11.8306	+	3.17000i	0.227512	+	0.0609616i
$53$	49.0894	+	49.0894i	0.926216	+	0.926216i	0.997459	−	0.0712434i	$-0.0226967\pi$
$53$	49.0894	+	49.0894i	0.926216	+	0.926216i	−0.0712434	+	0.997459i	$0.522697\pi$
$54$		0			0
$55$	−0.373864	−	0.295834i	−0.00679752	−	0.00537879i
$56$	14.5794	+	25.2523i	0.260347	+	0.450933i
$57$		0			0
$58$	−25.6694	+	6.87809i	−0.442575	+	0.118588i
$59$	−86.6216	−	50.0110i	−1.46816	−	0.847644i	−0.468799	−	0.883305i	$-0.655313\pi$
$59$	−86.6216	−	50.0110i	−1.46816	−	0.847644i	−0.999364	+	0.0356610i	$0.988646\pi$
$60$		0			0
$61$	27.7477	+	48.0605i	0.454881	+	0.787877i	0.998681	−	0.0513379i	$-0.0163485\pi$
$61$	27.7477	+	48.0605i	0.454881	+	0.787877i	−0.543801	+	0.839214i	$0.683015\pi$
$62$	−16.9035	+	16.9035i	−0.272636	+	0.272636i
$63$		0			0
$64$		−	27.3394i		−	0.427178i
$65$	13.7150	−	10.2027i	0.211000	−	0.156965i
$66$		0			0
$67$	13.6638	+	50.9941i	0.203938	+	0.761107i	0.989771	+	0.142668i	$0.0455680\pi$
$67$	13.6638	+	50.9941i	0.203938	+	0.761107i	−0.785833	+	0.618439i	$0.787765\pi$
$68$	70.5141	−	18.8942i	1.03697	−	0.277856i
$69$		0			0
$70$	19.0235	+	2.79359i	0.271764	+	0.0399084i
$71$	39.8770			0.561647			0.280824	−	0.959759i	$-0.409392\pi$
$71$	39.8770			0.561647			0.280824	+	0.959759i	$0.409392\pi$
$72$		0			0
$73$	39.3739	+	39.3739i	0.539368	+	0.539368i	0.923343	−	0.383975i	$-0.125445\pi$
$73$	39.3739	+	39.3739i	0.539368	+	0.539368i	−0.383975	+	0.923343i	$0.625445\pi$
$74$	−40.0527	+	23.1244i	−0.541252	+	0.312492i
$75$		0			0
$76$	−46.1216	+	79.8849i	−0.606863	+	1.05112i
$77$	0.146887	+	0.548188i	0.00190762	+	0.00711933i
$78$		0			0
$79$	−52.0212	+	30.0345i	−0.658497	+	0.380183i	−0.791704	−	0.610905i	$-0.790806\pi$
$79$	−52.0212	+	30.0345i	−0.658497	+	0.380183i	0.133207	+	0.991088i	$0.457472\pi$
$80$	−43.7780	−	34.6410i	−0.547225	−	0.433013i
$81$		0			0
$82$	−1.03447	+	1.03447i	−0.0126155	+	0.0126155i
$83$	28.3267	−	105.717i	0.341286	−	1.27370i	−0.555606	−	0.831446i	$-0.687514\pi$
$83$	28.3267	−	105.717i	0.341286	−	1.27370i	0.896892	−	0.442251i	$-0.145820\pi$
$84$		0			0
$85$	40.3883	−	93.5371i	0.475156	−	1.10044i
$86$	−11.2861	+	19.5481i	−0.131234	+	0.227304i
$87$		0			0
$88$	−0.120899	+	0.451202i	−0.00137385	+	0.00512730i
$89$		−	51.6755i		−	0.580623i	−0.956932	−	0.290312i	$-0.906241\pi$
$89$		−	51.6755i		−	0.580623i	0.956932	−	0.290312i	$-0.0937590\pi$
$90$		0			0
$91$	−20.3485			−0.223610
$92$	−16.4863	−	4.41749i	−0.179199	−	0.0480162i
$93$		0			0
$94$	12.9228	+	7.46099i	0.137477	+	0.0793722i
$95$	47.4876	+	119.660i	0.499870	+	1.25958i
$96$		0			0
$97$	−96.7027	−	25.9114i	−0.996935	−	0.267128i	−0.276774	−	0.960935i	$-0.589265\pi$
$97$	−96.7027	−	25.9114i	−0.996935	−	0.267128i	−0.720161	+	0.693807i	$0.755932\pi$
$98$	6.20105	+	6.20105i	0.0632760	+	0.0632760i
$99$		0			0
$100$	−87.1652	+	20.5917i	−0.871652	+	0.205917i
$101$	9.06943	+	15.7087i	0.0897963	+	0.155532i	0.907425	−	0.420214i	$-0.138045\pi$
$101$	9.06943	+	15.7087i	0.0897963	+	0.155532i	−0.817629	+	0.575746i	$0.804712\pi$
$102$		0			0
$103$	61.2331	−	16.4074i	0.594496	−	0.159295i	0.0509890	−	0.998699i	$-0.483763\pi$
$103$	61.2331	−	16.4074i	0.594496	−	0.159295i	0.543507	+	0.839404i	$0.317096\pi$
$104$	−14.5045	−	8.37420i	−0.139467	−	0.0805212i
$105$		0			0
$106$	−22.4265	−	38.8439i	−0.211571	−	0.366452i
$107$	150.617	−	150.617i	1.40764	−	1.40764i	0.635703	−	0.771934i	$-0.280710\pi$
$107$	150.617	−	150.617i	1.40764	−	1.40764i	0.771934	−	0.635703i	$-0.219290\pi$
$108$		0			0
$109$			126.495i			1.16051i	0.814435	+	0.580254i	$0.197047\pi$
$109$			126.495i			1.16051i	−0.814435	+	0.580254i	$0.802953\pi$
$110$	0.183848	+	0.247138i	0.00167134	+	0.00224671i
$111$		0			0
$112$	17.1999	+	64.1908i	0.153570	+	0.573132i
$113$	181.354	−	48.5936i	1.60490	−	0.430032i	0.658383	−	0.752683i	$-0.271241\pi$
$113$	181.354	−	48.5936i	1.60490	−	0.430032i	0.946518	+	0.322652i	$0.104574\pi$
$114$		0			0
$115$	−19.1123	+	14.2178i	−0.166194	+	0.123633i
$116$	−147.359			−1.27034
$117$		0			0
$118$	45.6951	+	45.6951i	0.387246	+	0.387246i
$119$	−105.034	+	60.6417i	−0.882643	+	0.509594i
$120$		0			0
$121$	60.4955	−	104.781i	0.499962	−	0.865960i
$122$	−9.27988	−	34.6330i	−0.0760646	−	0.283877i
$123$		0			0
$124$	−114.796	+	66.2777i	−0.925776	+	0.534497i
$125$	−52.9507	+	113.231i	−0.423605	+	0.905847i
$126$		0			0
$127$	−58.8693	+	58.8693i	−0.463538	+	0.463538i	−0.899813	−	0.436275i	$-0.856297\pi$
$127$	−58.8693	+	58.8693i	−0.463538	+	0.463538i	0.436275	+	0.899813i	$0.356297\pi$
$128$	−32.3269	+	120.646i	−0.252554	+	0.942545i
$129$		0			0
$130$	−10.2652	+	4.07379i	−0.0789631	+	0.0313368i
$131$	−118.153	+	204.647i	−0.901931	+	1.56219i	−0.0769467	+	0.997035i	$0.524517\pi$
$131$	−118.153	+	204.647i	−0.901931	+	1.56219i	−0.824984	+	0.565155i	$0.808816\pi$
$132$		0			0
$133$	39.6643	−	148.029i	0.298228	−	1.11300i
$134$		−	34.1087i		−	0.254543i
$135$		0			0
$136$	−99.8258			−0.734013
$137$	−70.5141	−	18.8942i	−0.514702	−	0.137914i	−0.00788694	−	0.999969i	$-0.502511\pi$
$137$	−70.5141	−	18.8942i	−0.514702	−	0.137914i	−0.506815	+	0.862055i	$0.669177\pi$
$138$		0			0
$139$	138.044	+	79.6996i	0.993121	+	0.573379i	0.906206	−	0.422837i	$-0.138966\pi$
$139$	138.044	+	79.6996i	0.993121	+	0.573379i	0.0869151	+	0.996216i	$0.472299\pi$
$140$	97.8828	+	42.2647i	0.699163	+	0.301891i
$141$		0			0
$142$	−24.8860	−	6.66818i	−0.175253	−	0.0469590i
$143$	−0.230502	−	0.230502i	−0.00161190	−	0.00161190i
$144$		0			0
$145$	−127.617	+	161.278i	−0.880118	+	1.11226i
$146$	−17.9880	−	31.1561i	−0.123205	−	0.213398i
$147$		0			0
$148$	−247.714	+	66.3748i	−1.67374	+	0.448479i
$149$	−72.2341	−	41.7044i	−0.484793	−	0.279895i	0.237619	−	0.971358i	$-0.423633\pi$
$149$	−72.2341	−	41.7044i	−0.484793	−	0.279895i	−0.722412	+	0.691463i	$0.756966\pi$
$150$		0			0
$151$	17.3784	+	30.1003i	0.115089	+	0.199340i	0.917815	−	0.397008i	$-0.129951\pi$
$151$	17.3784	+	30.1003i	0.115089	+	0.199340i	−0.802726	+	0.596347i	$0.796618\pi$
$152$	89.1927	−	89.1927i	0.586794	−	0.586794i
$153$		0			0
$154$		−	0.366669i		−	0.00238097i
$155$	−26.8789	+	183.037i	−0.173412	+	1.18088i
$156$		0			0
$157$	1.72850	+	6.45085i	0.0110096	+	0.0410882i	0.971212	−	0.238216i	$-0.0765627\pi$
$157$	1.72850	+	6.45085i	0.0110096	+	0.0410882i	−0.960203	+	0.279305i	$0.909896\pi$
$158$	37.4872	−	10.0447i	0.237261	−	0.0635738i
$159$		0			0
$160$	80.0087	+	107.552i	0.500054	+	0.672199i
$161$	28.3562			0.176126
$162$		0			0
$163$	171.374	+	171.374i	1.05137	+	1.05137i	0.998607	+	0.0527665i	$0.0168039\pi$
$163$	171.374	+	171.374i	1.05137	+	1.05137i	0.0527665	+	0.998607i	$0.483196\pi$
$164$	−7.02538	+	4.05610i	−0.0428377	+	0.0247323i
$165$		0			0
$166$	−35.3557	+	61.2378i	−0.212986	+	0.368903i
$167$	−19.6402	−	73.2981i	−0.117606	−	0.438911i	0.881863	−	0.471506i	$-0.156289\pi$
$167$	−19.6402	−	73.2981i	−0.117606	−	0.438911i	−0.999469	+	0.0325953i	$0.989623\pi$
$168$		0			0
$169$	−136.236	+	78.6561i	−0.806132	+	0.465420i
$170$	−40.8462	+	51.6199i	−0.240272	+	0.303647i
$171$		0			0
$172$	−88.5045	+	88.5045i	−0.514561	+	0.514561i
$173$	54.1816	−	202.209i	0.313189	−	1.16884i	−0.612476	−	0.790489i	$-0.709826\pi$
$173$	54.1816	−	202.209i	0.313189	−	1.16884i	0.925664	−	0.378346i	$-0.123507\pi$
$174$		0			0
$175$	131.026	−	70.5256i	0.748718	−	0.403003i
$176$	−0.532300	+	0.921970i	−0.00302443	+	0.00523847i
$177$		0			0
$178$	−8.64111	+	32.2491i	−0.0485456	+	0.181175i
$179$		−	140.296i		−	0.783777i	−0.920013	−	0.391889i	$-0.871822\pi$
$179$		−	140.296i		−	0.783777i	0.920013	−	0.391889i	$-0.128178\pi$
$180$		0			0
$181$	114.720			0.633815			0.316907	−	0.948457i	$-0.397356\pi$
$181$	114.720			0.633815			0.316907	+	0.948457i	$0.397356\pi$
$182$	12.6989	+	3.40265i	0.0697740	+	0.0186959i
$183$		0			0
$184$	20.2125	+	11.6697i	0.109851	+	0.0634223i
$185$	−141.883	+	328.593i	−0.766934	+	1.77618i
$186$		0			0
$187$	−1.87673	−	0.502869i	−0.0100360	−	0.00268914i
$188$	58.5083	+	58.5083i	0.311215	+	0.311215i
$189$		0			0
$190$	−9.62614	−	82.6170i	−0.0506639	−	0.434827i
$191$	−128.545	−	222.647i	−0.673012	−	1.16569i	−0.977046	−	0.213030i	$-0.931667\pi$
$191$	−128.545	−	222.647i	−0.673012	−	1.16569i	0.304034	−	0.952661i	$-0.401666\pi$
$192$		0			0
$193$	−120.577	+	32.3085i	−0.624752	+	0.167402i	−0.557287	−	0.830320i	$-0.688158\pi$
$193$	−120.577	+	32.3085i	−0.624752	+	0.167402i	−0.0674648	+	0.997722i	$0.521491\pi$
$194$	56.0163	+	32.3410i	0.288744	+	0.166706i
$195$		0			0
$196$	24.3140	+	42.1131i	0.124051	+	0.214863i
$197$	44.6917	−	44.6917i	0.226862	−	0.226862i	−0.584519	−	0.811380i	$-0.698717\pi$
$197$	44.6917	−	44.6917i	0.226862	−	0.226862i	0.811380	+	0.584519i	$0.198717\pi$
$198$		0			0
$199$		−	297.964i		−	1.49730i	−0.662963	−	0.748652i	$-0.730701\pi$
$199$		−	297.964i		−	1.49730i	0.662963	−	0.748652i	$-0.269299\pi$
$200$	122.420	+	3.65105i	0.612100	+	0.0182553i
$201$		0			0
$202$	−3.03316	−	11.3199i	−0.0150156	−	0.0560391i
$203$	236.478	−	63.3641i	1.16492	−	0.312138i
$204$		0			0
$205$	−1.64495	+	11.2016i	−0.00802415	+	0.0546420i
$206$	−40.9573			−0.198822
$207$		0			0
$208$	−26.9909	−	26.9909i	−0.129764	−	0.129764i
$209$	2.12614	−	1.22753i	0.0101729	−	0.00587333i
$210$		0			0
$211$	67.9864	−	117.756i	0.322210	−	0.558085i	−0.658734	−	0.752376i	$-0.728908\pi$
$211$	67.9864	−	117.756i	0.322210	−	0.558085i	0.980944	+	0.194292i	$0.0622409\pi$
$212$	−64.3716	−	240.238i	−0.303640	−	1.13320i
$213$		0			0
$214$	−119.182	+	68.8095i	−0.556923	+	0.321540i
$215$	20.2167	+	173.511i	0.0940310	+	0.807028i
$216$		0			0
$217$	155.722	−	155.722i	0.717615	−	0.717615i
$218$	21.1524	−	78.9419i	0.0970294	−	0.362119i
$219$		0			0
$220$	0.630026	+	1.58755i	0.00286376	+	0.00721614i
$221$	34.8317	−	60.3303i	0.157610	−	0.272988i
$222$		0			0
$223$	58.5893	−	218.658i	0.262732	−	0.980530i	−0.700892	−	0.713268i	$-0.747214\pi$
$223$	58.5893	−	218.658i	0.262732	−	0.980530i	0.963624	−	0.267262i	$-0.0861190\pi$
$224$		−	159.571i		−	0.712370i
$225$		0			0
$226$	−121.303			−0.536739
$227$	69.1844	+	18.5379i	0.304777	+	0.0816648i	0.407966	−	0.912997i	$-0.366238\pi$
$227$	69.1844	+	18.5379i	0.304777	+	0.0816648i	−0.103189	+	0.994662i	$0.532905\pi$
$228$		0			0
$229$	30.8909	+	17.8348i	0.134895	+	0.0778814i	0.565929	−	0.824454i	$-0.308518\pi$
$229$	30.8909	+	17.8348i	0.134895	+	0.0778814i	−0.431034	+	0.902336i	$0.641851\pi$
$230$	14.3049	−	5.67694i	0.0621950	−	0.0246824i
$231$		0			0
$232$	194.640	+	52.1536i	0.838965	+	0.224800i
$233$	191.102	+	191.102i	0.820180	+	0.820180i	0.986134	−	0.165954i	$-0.0530703\pi$
$233$	191.102	+	191.102i	0.820180	+	0.820180i	−0.165954	+	0.986134i	$0.553070\pi$
$234$		0			0
$235$	114.704	−	13.3648i	0.488103	−	0.0568714i
$236$	179.168	+	310.328i	0.759187	+	1.31495i
$237$		0			0
$238$	75.6892	−	20.2809i	0.318022	−	0.0852137i
$239$	−300.495	−	173.491i	−1.25730	−	0.725904i	−0.284754	−	0.958601i	$-0.591912\pi$
$239$	−300.495	−	173.491i	−1.25730	−	0.725904i	−0.972549	+	0.232696i	$0.925245\pi$
$240$		0			0
$241$	−7.14432	−	12.3743i	−0.0296445	−	0.0513457i	0.850823	−	0.525453i	$-0.176104\pi$
$241$	−7.14432	−	12.3743i	−0.0296445	−	0.0513457i	−0.880467	+	0.474107i	$0.842771\pi$
$242$	−55.2747	+	55.2747i	−0.228408	+	0.228408i
$243$		0			0
$244$		−	198.817i		−	0.814822i
$245$	67.1473	+	9.86054i	0.274071	+	0.0402471i
$246$		0			0
$247$	22.7826	+	85.0258i	0.0922372	+	0.344234i
$248$	175.086	−	46.9141i	0.705991	−	0.189170i
$249$		0			0
$250$	51.9792	−	61.8095i	0.207917	−	0.247238i
$251$	−399.294			−1.59081			−0.795406	−	0.606077i	$-0.792742\pi$
$251$	−399.294			−1.59081			−0.795406	+	0.606077i	$0.792742\pi$
$252$		0			0
$253$	0.321211	+	0.321211i	0.00126961	+	0.00126961i
$254$	46.5826	−	26.8945i	0.183396	−	0.105884i
$255$		0			0
$256$	−14.3303	+	24.8208i	−0.0559777	+	0.0969563i
$257$	−90.4083	−	337.408i	−0.351783	−	1.31287i	−0.884484	−	0.466570i	$-0.845490\pi$
$257$	−90.4083	−	337.408i	−0.351783	−	1.31287i	0.532701	−	0.846303i	$-0.321177\pi$
$258$		0			0
$259$	368.983	−	213.033i	1.42465	−	0.822520i
$260$	−60.8282	+	7.08741i	−0.233955	+	0.0272593i
$261$		0			0
$262$	107.956	−	107.956i	0.412047	−	0.412047i
$263$	−5.67663	+	21.1855i	−0.0215842	+	0.0805532i	−0.975878	−	0.218317i	$-0.929943\pi$
$263$	−5.67663	+	21.1855i	−0.0215842	+	0.0805532i	0.954294	+	0.298871i	$0.0966099\pi$
$264$		0			0
$265$	−318.676	−	137.601i	−1.20255	−	0.519248i
$266$	−49.5065	+	85.7477i	−0.186115	+	0.322360i
$267$		0			0
$268$	48.9517	−	182.690i	0.182656	−	0.681680i
$269$			298.922i			1.11123i	0.831439	+	0.555617i	$0.187518\pi$
$269$			298.922i			1.11123i	−0.831439	+	0.555617i	$0.812482\pi$
$270$		0			0
$271$	−21.0091			−0.0775243			−0.0387622	−	0.999248i	$-0.512341\pi$
$271$	−21.0091			−0.0775243			−0.0387622	+	0.999248i	$0.512341\pi$
$272$	−219.758	−	58.8841i	−0.807935	−	0.216486i
$273$		0			0
$274$	40.8462	+	23.5826i	0.149074	+	0.0860678i
$275$	2.28312	+	0.685327i	0.00830224	+	0.00249210i
$276$		0			0
$277$	−376.011	−	100.752i	−1.35744	−	0.363725i	−0.494565	−	0.869140i	$-0.664673\pi$
$277$	−376.011	−	100.752i	−1.35744	−	0.363725i	−0.862876	+	0.505415i	$0.831339\pi$
$278$	−72.8216	−	72.8216i	−0.261948	−	0.261948i
$279$		0			0
$280$	−114.330	−	90.4682i	−0.408323	−	0.323101i
$281$	81.1601	+	140.573i	0.288826	+	0.500262i	0.973530	−	0.228560i	$-0.0734017\pi$
$281$	81.1601	+	140.573i	0.288826	+	0.500262i	−0.684704	+	0.728822i	$0.740068\pi$
$282$		0			0
$283$	−174.031	+	46.6314i	−0.614949	+	0.164775i	−0.552831	−	0.833294i	$-0.686452\pi$
$283$	−174.031	+	46.6314i	−0.614949	+	0.164775i	−0.0621185	+	0.998069i	$0.519786\pi$
$284$	−123.722	−	71.4311i	−0.435642	−	0.251518i
$285$		0			0
$286$	0.105305	+	0.182393i	0.000368199	+	0.000637739i
$287$	9.53000	−	9.53000i	0.0332056	−	0.0332056i
$288$		0			0
$289$		−	126.216i		−	0.436733i
$290$	106.611	−	79.3084i	0.367622	−	0.273477i
$291$		0			0
$292$	−51.6315	−	192.691i	−0.176820	−	0.659902i
$293$	−264.588	+	70.8962i	−0.903032	+	0.241967i	−0.680318	−	0.732917i	$-0.738158\pi$
$293$	−264.588	+	70.8962i	−0.903032	+	0.241967i	−0.222714	+	0.974884i	$0.571492\pi$
$294$		0			0
$295$	494.803	+	72.6616i	1.67730	+	0.246310i
$296$	350.685			1.18475
$297$		0			0
$298$	38.1053	+	38.1053i	0.127870	+	0.127870i
$299$	−14.1053	+	8.14370i	−0.0471749	+	0.0272365i
$300$		0			0
$301$	103.973	−	180.086i	0.345424	−	0.598292i
$302$	−5.81199	−	21.6907i	−0.0192450	−	0.0718234i
$303$		0			0
$304$	248.963	−	143.739i	0.818956	−	0.472824i
$305$	−217.595	−	172.180i	−0.713426	−	0.564526i
$306$		0			0
$307$	405.347	−	405.347i	1.32035	−	1.32035i	0.406854	−	0.913493i	$-0.366626\pi$
$307$	405.347	−	405.347i	1.32035	−	1.32035i	0.913493	−	0.406854i	$-0.133374\pi$
$308$	0.526232	−	1.96393i	0.00170855	−	0.00637638i
$309$		0			0
$310$	47.3815	−	109.733i	0.152844	−	0.353978i
$311$	87.9893	−	152.402i	0.282924	−	0.490038i	−0.689180	−	0.724590i	$-0.742029\pi$
$311$	87.9893	−	152.402i	0.282924	−	0.490038i	0.972104	+	0.234552i	$0.0753623\pi$
$312$		0			0
$313$	−70.2383	+	262.133i	−0.224404	+	0.837486i	0.758239	+	0.651977i	$0.226060\pi$
$313$	−70.2383	+	262.133i	−0.224404	+	0.837486i	−0.982643	+	0.185509i	$0.940607\pi$
$314$		−	4.31481i		−	0.0137414i
$315$		0			0
$316$	215.202			0.681017
$317$	378.928	+	101.533i	1.19536	+	0.320294i	0.801000	−	0.598664i	$-0.204301\pi$
$317$	378.928	+	101.533i	1.19536	+	0.320294i	0.394355	+	0.918958i	$0.370968\pi$
$318$		0			0
$319$	3.39653	+	1.96099i	0.0106474	+	0.00614729i
$320$	50.4232	+	127.057i	0.157573	+	0.397054i
$321$		0			0
$322$	−17.6962	−	4.74169i	−0.0549572	−	0.0147257i
$323$	370.989	+	370.989i	1.14857	+	1.14857i
$324$		0			0
$325$	−44.9220	+	72.7114i	−0.138221	+	0.223727i
$326$	−78.2922	−	135.606i	−0.240160	−	0.415969i
$327$		0			0
$328$	10.7150	−	2.87108i	0.0326677	−	0.00875330i
$329$	−119.051	−	68.7340i	−0.361856	−	0.208918i
$330$		0			0
$331$	151.622	+	262.616i	0.458071	+	0.793403i	0.998859	−	0.0477564i	$-0.0152071\pi$
$331$	151.622	+	262.616i	0.458071	+	0.793403i	−0.540788	+	0.841159i	$0.681874\pi$
$332$	−277.256	+	277.256i	−0.835108	+	0.835108i
$333$		0			0
$334$			49.0273i			0.146788i
$335$	−157.552	−	211.790i	−0.470305	−	0.632208i
$336$		0			0
$337$	15.6786	+	58.5135i	0.0465242	+	0.173631i	0.985279	−	0.170956i	$-0.0546857\pi$
$337$	15.6786	+	58.5135i	0.0465242	+	0.173631i	−0.938754	+	0.344587i	$0.888019\pi$
$338$	98.1736	−	26.3055i	0.290455	−	0.0778271i
$339$		0			0
$340$	−292.861	+	217.861i	−0.861354	+	0.640769i
$341$	3.52796			0.0103459
$342$		0			0
$343$	−263.354	−	263.354i	−0.767795	−	0.767795i
$344$	148.225	−	85.5777i	0.430887	−	0.248773i
$345$		0			0
$346$	−67.6261	+	117.132i	−0.195451	+	0.338532i
$347$	165.789	+	618.732i	0.477777	+	1.78309i	0.610588	+	0.791948i	$0.290933\pi$
$347$	165.789	+	618.732i	0.477777	+	1.78309i	−0.132811	+	0.991141i	$0.542400\pi$
$348$		0			0
$349$	−123.659	+	71.3947i	−0.354324	+	0.204569i	−0.666588	−	0.745426i	$-0.732246\pi$
$349$	−123.659	+	71.3947i	−0.354324	+	0.204569i	0.312264	+	0.949995i	$0.398913\pi$
$350$	−93.5622	+	22.1029i	−0.267321	+	0.0631511i
$351$		0			0
$352$	1.80757	−	1.80757i	0.00513515	−	0.00513515i
$353$	70.7973	−	264.219i	0.200559	−	0.748496i	−0.790199	−	0.612851i	$-0.790023\pi$
$353$	70.7973	−	264.219i	0.200559	−	0.748496i	0.990758	−	0.135645i	$-0.0433107\pi$
$354$		0			0
$355$	−185.325	+	73.5468i	−0.522041	+	0.207174i
$356$	−92.5656	+	160.328i	−0.260016	+	0.450361i
$357$		0			0
$358$	−23.4601	+	87.5545i	−0.0655311	+	0.244566i
$359$		−	354.888i		−	0.988546i	−0.869307	−	0.494273i	$-0.835434\pi$
$359$		−	354.888i		−	0.988546i	0.869307	−	0.494273i	$-0.164566\pi$
$360$		0			0
$361$	−301.945			−0.836414
$362$	−71.5935	−	19.1834i	−0.197772	−	0.0529929i
$363$		0			0
$364$	63.1332	+	36.4500i	0.173443	+	0.100137i
$365$	−255.605	−	110.367i	−0.700289	−	0.302377i
$366$		0			0
$367$	228.577	+	61.2471i	0.622827	+	0.166886i	0.556413	−	0.830906i	$-0.312177\pi$
$367$	228.577	+	61.2471i	0.622827	+	0.166886i	0.0664143	+	0.997792i	$0.478844\pi$
$368$	37.6126	+	37.6126i	0.102208	+	0.102208i
$369$		0			0
$370$	143.492	−	181.339i	0.387815	−	0.490106i
$371$	206.603	+	357.847i	0.556882	+	0.964548i
$372$		0			0
$373$	227.685	−	61.0080i	0.610415	−	0.163560i	0.0596484	−	0.998219i	$-0.481002\pi$
$373$	227.685	−	61.0080i	0.610415	−	0.163560i	0.550767	+	0.834659i	$0.314335\pi$
$374$	1.08712	+	0.627650i	0.00290674	+	0.00167821i
$375$		0			0
$376$	−56.5735	−	97.9881i	−0.150461	−	0.260607i
$377$	−99.4341	+	99.4341i	−0.263751	+	0.263751i
$378$		0			0
$379$			115.252i			0.304096i	0.988373	+	0.152048i	$0.0485868\pi$
$379$			115.252i			0.304096i	−0.988373	+	0.152048i	$0.951413\pi$
$380$	67.0106	−	456.322i	0.176344	−	1.20085i
$381$		0			0
$382$	42.9904	+	160.442i	0.112540	+	0.420006i
$383$	467.540	−	125.277i	1.22073	−	0.327094i	0.409767	−	0.912190i	$-0.365610\pi$
$383$	467.540	−	125.277i	1.22073	−	0.327094i	0.810964	+	0.585097i	$0.198943\pi$
$384$		0			0
$385$	−1.69369	−	2.27674i	−0.00439919	−	0.00591362i
$386$	80.6510			0.208940
$387$		0			0
$388$	253.615	+	253.615i	0.653647	+	0.653647i
$389$	−289.720	+	167.270i	−0.744783	+	0.430000i	−0.823806	−	0.566872i	$-0.808153\pi$
$389$	−289.720	+	167.270i	−0.744783	+	0.430000i	0.0790230	+	0.996873i	$0.474820\pi$
$390$		0			0
$391$	−48.5390	+	84.0720i	−0.124141	+	0.215018i
$392$	−17.2105	−	64.2304i	−0.0439043	−	0.163853i
$393$		0			0
$394$	−35.3640	+	20.4174i	−0.0897564	+	0.0518209i
$395$	186.370	−	235.527i	0.471823	−	0.596272i
$396$		0			0
$397$	−469.973	+	469.973i	−1.18381	+	1.18381i	−0.205061	+	0.978749i	$0.565739\pi$
$397$	−469.973	+	469.973i	−1.18381	+	1.18381i	−0.978749	+	0.205061i	$0.934261\pi$
$398$	−49.8251	+	185.950i	−0.125189	+	0.467211i
$399$		0			0
$400$	267.344	+	80.2492i	0.668361	+	0.200623i
$401$	94.6393	−	163.920i	0.236008	−	0.408778i	−0.723557	−	0.690265i	$-0.757494\pi$
$401$	94.6393	−	163.920i	0.236008	−	0.408778i	0.959565	+	0.281486i	$0.0908274\pi$
$402$		0			0
$403$	−32.7390	+	122.184i	−0.0812383	+	0.303185i
$404$		−	64.9838i		−	0.160851i
$405$		0			0
$406$	−158.174			−0.389592
$407$	6.59291	+	1.76656i	0.0161988	+	0.00434045i
$408$		0			0
$409$	−370.071	−	213.661i	−0.904819	−	0.522398i	−0.0260585	−	0.999660i	$-0.508296\pi$
$409$	−370.071	−	213.661i	−0.904819	−	0.522398i	−0.878761	+	0.477263i	$0.841629\pi$
$410$	2.89968	−	6.71552i	0.00707240	−	0.0163793i
$411$		0			0
$412$	−219.372	−	58.7806i	−0.532457	−	0.142671i
$413$	−420.964	−	420.964i	−1.01928	−	1.01928i
$414$		0			0
$415$	63.3322	+	543.553i	0.152608	+	1.30977i
$416$	45.8276	+	79.3758i	0.110163	+	0.190807i
$417$		0			0
$418$	−1.53212	+	0.410531i	−0.00366536	+	0.000982131i
$419$	466.301	+	269.219i	1.11289	+	0.642528i	0.939577	−	0.342339i	$-0.111219\pi$
$419$	466.301	+	269.219i	1.11289	+	0.642528i	0.173314	+	0.984867i	$0.444552\pi$
$420$		0			0
$421$	−197.500	−	342.080i	−0.469121	−	0.812542i	0.530256	−	0.847838i	$-0.322096\pi$
$421$	−197.500	−	342.080i	−0.469121	−	0.812542i	−0.999377	+	0.0352961i	$0.988763\pi$
$422$	−62.1192	+	62.1192i	−0.147202	+	0.147202i
$423$		0			0
$424$			340.102i			0.802126i
$425$	−15.1862	+	509.195i	−0.0357322	+	1.19811i
$426$		0			0
$427$	85.4905	+	319.055i	0.200212	+	0.747201i
$428$	−737.104	+	197.506i	−1.72220	+	0.461463i
$429$		0			0
$430$	16.3977	−	111.663i	0.0381342	−	0.259682i
$431$	60.0895			0.139419			0.0697094	−	0.997567i	$-0.477793\pi$
$431$	60.0895			0.139419			0.0697094	+	0.997567i	$0.477793\pi$
$432$		0			0
$433$	−192.514	−	192.514i	−0.444604	−	0.444604i	0.448952	−	0.893556i	$-0.351798\pi$
$433$	−192.514	−	192.514i	−0.444604	−	0.444604i	−0.893556	+	0.448952i	$0.851798\pi$
$434$	−123.221	+	71.1418i	−0.283920	+	0.163921i
$435$		0			0
$436$	226.590	−	392.465i	0.519701	−	0.900149i
$437$	−31.7482	−	118.486i	−0.0726503	−	0.271135i
$438$		0			0
$439$	253.170	−	146.168i	0.576697	−	0.332956i	−0.183123	−	0.983090i	$-0.558621\pi$
$439$	253.170	−	146.168i	0.576697	−	0.332956i	0.759820	+	0.650134i	$0.225287\pi$
$440$	−0.270303	−	2.31990i	−0.000614326	−	0.00527250i
$441$		0			0
$442$	−31.8258	+	31.8258i	−0.0720040	+	0.0720040i
$443$	−97.8721	+	365.264i	−0.220930	+	0.824523i	0.763064	+	0.646323i	$0.223694\pi$
$443$	−97.8721	+	365.264i	−0.220930	+	0.824523i	−0.983994	+	0.178200i	$0.942973\pi$
$444$		0			0
$445$	95.3073	+	240.157i	0.214174	+	0.539679i
$446$	−73.1275	+	126.661i	−0.163963	+	0.283992i
$447$		0			0
$448$	42.1162	−	157.180i	0.0940094	−	0.350848i
$449$			101.349i			0.225721i	0.993611	+	0.112860i	$0.0360013\pi$
$449$			101.349i			0.225721i	−0.993611	+	0.112860i	$0.963999\pi$
$450$		0			0
$451$	0.215906			0.000478728
$452$	−649.714	−	174.090i	−1.43742	−	0.385155i
$453$		0			0
$454$	−40.0760	−	23.1379i	−0.0882731	−	0.0509645i
$455$	94.5677	−	37.5296i	0.207841	−	0.0824826i
$456$		0			0
$457$	−601.725	−	161.232i	−1.31669	−	0.352805i	−0.468950	−	0.883224i	$-0.655368\pi$
$457$	−601.725	−	161.232i	−1.31669	−	0.352805i	−0.847735	+	0.530420i	$0.822034\pi$
$458$	−16.2957	−	16.2957i	−0.0355802	−	0.0355802i
$459$		0			0
$460$	84.7659	−	9.87651i	0.184274	−	0.0214707i
$461$	−291.735	−	505.300i	−0.632831	−	1.09610i	−0.986970	−	0.160903i	$-0.948559\pi$
$461$	−291.735	−	505.300i	−0.632831	−	1.09610i	0.354139	−	0.935193i	$-0.384774\pi$
$462$		0			0
$463$	111.764	−	29.9470i	0.241390	−	0.0646803i	−0.136096	−	0.990696i	$-0.543455\pi$
$463$	111.764	−	29.9470i	0.241390	−	0.0646803i	0.377486	+	0.926015i	$0.376789\pi$
$464$	397.720	+	229.624i	0.857156	+	0.494879i
$465$		0			0
$466$	−87.3049	−	151.217i	−0.187350	−	0.324499i
$467$	145.933	−	145.933i	0.312491	−	0.312491i	−0.533383	−	0.845874i	$-0.679079\pi$
$467$	145.933	−	145.933i	0.312491	−	0.312491i	0.845874	+	0.533383i	$0.179079\pi$
$468$		0			0
$469$			314.225i			0.669989i
$470$	−73.8182	−	10.8402i	−0.157060	−	0.0230642i
$471$		0			0
$472$	−126.823	−	473.309i	−0.268692	−	1.00277i
$473$	3.21774	−	0.862190i	0.00680283	−	0.00182281i
$474$		0			0
$475$	−441.389	−	468.526i	−0.929240	−	0.986371i
$476$	434.507			0.912829
$477$		0			0
$478$	158.519	+	158.519i	0.331630	+	0.331630i
$479$	−325.761	+	188.078i	−0.680086	+	0.392648i	−0.799888	−	0.600150i	$-0.795108\pi$
$479$	−325.761	+	188.078i	−0.680086	+	0.392648i	0.119801	+	0.992798i	$0.461774\pi$
$480$		0			0
$481$	−122.363	+	211.939i	−0.254393	+	0.440621i
$482$	2.38933	+	8.91710i	0.00495711	+	0.0185002i
$483$		0			0
$484$	−375.387	+	216.730i	−0.775592	+	0.447788i
$485$	497.206	−	57.9321i	1.02517	−	0.119448i
$486$		0			0
$487$	−402.693	+	402.693i	−0.826885	+	0.826885i	−0.987085	−	0.160199i	$-0.948786\pi$
$487$	−402.693	+	402.693i	−0.826885	+	0.826885i	0.160199	+	0.987085i	$0.448786\pi$
$488$	−70.3654	+	262.607i	−0.144191	+	0.538130i
$489$		0			0
$490$	−40.2557	−	17.3819i	−0.0821544	−	0.0354734i
$491$	174.608	−	302.429i	0.355616	−	0.615945i	−0.631607	−	0.775289i	$-0.717604\pi$
$491$	174.608	−	302.429i	0.355616	−	0.615945i	0.987223	+	0.159343i	$0.0509377\pi$
$492$		0			0
$493$	−216.928	+	809.587i	−0.440017	+	1.64216i
$494$		−	56.8716i		−	0.115125i
$495$		0			0
$496$	413.111			0.832884
$497$	229.261	+	61.4303i	0.461290	+	0.123602i
$498$		0			0
$499$	462.780	+	267.186i	0.927414	+	0.535443i	0.885993	−	0.463699i	$-0.153478\pi$
$499$	462.780	+	267.186i	0.927414	+	0.535443i	0.0414214	+	0.999142i	$0.486811\pi$
$500$	367.114	−	256.460i	0.734228	−	0.512921i
$501$		0			0
$502$	249.187	+	66.7694i	0.496388	+	0.133007i
$503$	−441.936	−	441.936i	−0.878600	−	0.878600i	0.114790	−	0.993390i	$-0.463381\pi$
$503$	−441.936	−	441.936i	−0.878600	−	0.878600i	−0.993390	+	0.114790i	$0.963381\pi$
$504$		0			0
$505$	−71.1216	−	56.2777i	−0.140835	−	0.111441i
$506$	−0.146745	−	0.254170i	−0.000290011	−	0.000502313i
$507$		0			0
$508$	288.100	−	77.1961i	0.567126	−	0.151961i
$509$	217.149	+	125.371i	0.426619	+	0.246308i	0.697905	−	0.716190i	$-0.254116\pi$
$509$	217.149	+	125.371i	0.426619	+	0.246308i	−0.271286	+	0.962499i	$0.587449\pi$
$510$		0			0
$511$	165.713	+	287.024i	0.324292	+	0.561690i
$512$	366.369	−	366.369i	0.715564	−	0.715564i
$513$		0			0
$514$			225.684i			0.439074i
$515$	−254.314	+	189.187i	−0.493815	+	0.367353i
$516$		0			0
$517$	−0.569974	−	2.12717i	−0.00110246	−	0.00411445i
$518$	−265.894	+	71.2461i	−0.513309	+	0.137541i
$519$		0			0
$520$	82.8534	+	12.1670i	0.159334	+	0.0233980i
$521$	−450.350			−0.864395			−0.432198	−	0.901779i	$-0.642262\pi$
$521$	−450.350			−0.864395			−0.432198	+	0.901779i	$0.642262\pi$
$522$		0			0
$523$	−233.027	−	233.027i	−0.445559	−	0.445559i	0.448316	−	0.893875i	$-0.352024\pi$
$523$	−233.027	−	233.027i	−0.445559	−	0.445559i	−0.893875	+	0.448316i	$0.852024\pi$
$524$	733.163	−	423.292i	1.39917	−	0.807809i
$525$		0			0
$526$	7.08522	−	12.2720i	0.0134700	−	0.0233307i
$527$	195.135	+	728.253i	0.370275	+	1.38188i
$528$		0			0
$529$	−438.471	+	253.152i	−0.828868	+	0.478547i
$530$	175.867	+	139.161i	0.331824	+	0.262568i
$531$		0			0
$532$	−388.225	+	388.225i	−0.729746	+	0.729746i
$533$	−2.00358	+	7.47748i	−0.00375907	+	0.0140290i
$534$		0			0
$535$	−422.190	+	977.769i	−0.789139	+	1.82761i
$536$	−129.316	+	223.982i	−0.241261	+	0.417877i
$537$		0			0
$538$	49.9853	−	186.548i	0.0929096	−	0.346743i
$539$		−	1.29423i		−	0.00240118i
$540$		0			0
$541$	−36.3250			−0.0671442			−0.0335721	−	0.999436i	$-0.510688\pi$
$541$	−36.3250			−0.0671442			−0.0335721	+	0.999436i	$0.510688\pi$
$542$	13.1111	+	3.51312i	0.0241903	+	0.00648176i
$543$		0			0
$544$	473.104	+	273.147i	0.869677	+	0.502108i
$545$	−233.301	−	587.876i	−0.428075	−	1.07867i
$546$		0			0
$547$	478.843	+	128.305i	0.875398	+	0.234562i	0.668420	−	0.743784i	$-0.266971\pi$
$547$	478.843	+	128.305i	0.875398	+	0.234562i	0.206977	+	0.978346i	$0.433637\pi$
$548$	184.932	+	184.932i	0.337468	+	0.337468i
$549$		0			0
$550$	−1.31022	−	0.809471i	−0.00238222	−	0.00147177i
$551$	−529.531	−	917.175i	−0.961037	−	1.66456i
$552$		0			0
$553$	−345.349	+	92.5359i	−0.624501	+	0.167334i
$554$	217.809	+	125.752i	0.393158	+	0.226990i
$555$		0			0
$556$	−285.530	−	494.552i	−0.513543	−	0.889483i
$557$	22.1908	−	22.1908i	0.0398399	−	0.0398399i	−0.686906	−	0.726746i	$-0.741032\pi$
$557$	22.1908	−	22.1908i	0.0398399	−	0.0398399i	0.726746	+	0.686906i	$0.241032\pi$
$558$		0			0
$559$			119.441i			0.213669i
$560$	−198.325	−	266.598i	−0.354151	−	0.476068i
$561$		0			0
$562$	−27.1430	−	101.299i	−0.0482972	−	0.180247i
$563$	−230.270	+	61.7007i	−0.409006	+	0.109593i	−0.457455	−	0.889233i	$-0.651239\pi$
$563$	−230.270	+	61.7007i	−0.409006	+	0.109593i	0.0484491	+	0.998826i	$0.484572\pi$
$564$		0			0
$565$	−753.202	+	560.313i	−1.33310	+	0.991704i
$566$	116.405			0.205662
$567$		0			0
$568$	138.138	+	138.138i	0.243200	+	0.243200i
$569$	500.670	−	289.062i	0.879913	−	0.508018i	0.00928322	−	0.999957i	$-0.497045\pi$
$569$	500.670	−	289.062i	0.879913	−	0.508018i	0.870630	+	0.491939i	$0.163712\pi$
$570$		0			0
$571$	−382.716	+	662.883i	−0.670256	+	1.16092i	0.307576	+	0.951524i	$0.400482\pi$
$571$	−382.716	+	662.883i	−0.670256	+	1.16092i	−0.977832	+	0.209393i	$0.932851\pi$
$572$	0.302260	+	1.12805i	0.000528427	+	0.00197212i
$573$		0			0
$574$	−7.54097	+	4.35378i	−0.0131376	+	0.00758499i
$575$	62.6001	−	101.325i	0.108870	−	0.176218i
$576$		0			0
$577$	176.644	−	176.644i	0.306143	−	0.306143i	−0.537269	−	0.843411i	$-0.680544\pi$
$577$	176.644	−	176.644i	0.306143	−	0.306143i	0.843411	+	0.537269i	$0.180544\pi$
$578$	−21.1057	+	78.7674i	−0.0365150	+	0.136276i
$579$		0			0
$580$	684.840	−	271.781i	1.18076	−	0.468589i
$581$	325.713	−	564.151i	0.560607	−	0.971000i
$582$		0			0
$583$	−1.71325	+	6.39394i	−0.00293868	+	0.0109673i
$584$			272.790i			0.467106i
$585$		0			0
$586$	176.977			0.302008
$587$	527.304	+	141.291i	0.898304	+	0.240700i	0.678288	−	0.734796i	$-0.262722\pi$
$587$	527.304	+	141.291i	0.898304	+	0.240700i	0.220016	+	0.975496i	$0.429389\pi$
$588$		0			0
$589$	−825.033	−	476.333i	−1.40073	−	0.808715i
$590$	−296.641	−	128.086i	−0.502781	−	0.217095i
$591$		0			0
$592$	772.005	+	206.858i	1.30406	+	0.349423i
$593$	−595.579	−	595.579i	−1.00435	−	1.00435i	−0.999990	−	0.00435896i	$-0.998612\pi$
$593$	−595.579	−	595.579i	−1.00435	−	1.00435i	−0.00435896	−	0.999990i	$-0.501388\pi$
$594$		0			0
$595$	376.294	−	475.546i	0.632427	−	0.799237i
$596$	149.409	+	258.784i	0.250686	+	0.434201i
$597$		0			0
$598$	10.1645	−	2.72356i	0.0169974	−	0.00455445i
$599$	384.062	+	221.739i	0.641173	+	0.370181i	0.785066	−	0.619412i	$-0.212629\pi$
$599$	384.062	+	221.739i	0.641173	+	0.370181i	−0.143893	+	0.989593i	$0.545962\pi$
$600$		0			0
$601$	163.594	+	283.354i	0.272204	+	0.471470i	0.969426	−	0.245385i	$-0.0789143\pi$
$601$	163.594	+	283.354i	0.272204	+	0.471470i	−0.697222	+	0.716855i	$0.745581\pi$
$602$	−94.9999	+	94.9999i	−0.157807	+	0.157807i
$603$		0			0
$604$		−	124.519i		−	0.206157i
$605$	−87.8946	+	598.535i	−0.145280	+	0.989315i
$606$		0			0
$607$	−43.0356	−	160.611i	−0.0708988	−	0.264598i	0.921373	−	0.388679i	$-0.127068\pi$
$607$	−43.0356	−	160.611i	−0.0708988	−	0.264598i	−0.992272	+	0.124081i	$0.960402\pi$
$608$	−666.764	+	178.659i	−1.09665	+	0.293847i
$609$		0			0
$610$	107.003	+	143.838i	0.175414	+	0.235801i
$611$	78.9596			0.129230
$612$		0			0
$613$	−60.4318	−	60.4318i	−0.0985837	−	0.0985837i	0.656095	−	0.754678i	$-0.272207\pi$
$613$	−60.4318	−	60.4318i	−0.0985837	−	0.0985837i	−0.754678	+	0.656095i	$0.772207\pi$
$614$	−320.746	+	185.183i	−0.522387	+	0.301600i
$615$		0			0
$616$	−1.39015	+	2.40781i	−0.00225674	+	0.00390878i
$617$	105.071	+	392.130i	0.170293	+	0.635544i	0.997306	+	0.0733596i	$0.0233721\pi$
$617$	105.071	+	392.130i	0.170293	+	0.635544i	−0.827012	+	0.562184i	$0.809961\pi$
$618$		0			0
$619$	391.642	−	226.114i	0.632701	−	0.365290i	−0.149097	−	0.988823i	$-0.547637\pi$
$619$	391.642	−	226.114i	0.632701	−	0.365290i	0.781797	+	0.623533i	$0.214303\pi$
$620$	411.266	−	519.743i	0.663333	−	0.838295i
$621$		0			0
$622$	−80.3958	+	80.3958i	−0.129254	+	0.129254i
$623$	79.6058	−	297.093i	0.127778	−	0.476875i
$624$		0			0
$625$	37.2468	−	623.889i	0.0595949	−	0.998223i
$626$	87.6671	−	151.844i	0.140043	−	0.242562i
$627$		0			0
$628$	6.19248	−	23.1107i	0.00986064	−	0.0368004i
$629$			1458.64i			2.31899i
$630$		0			0
$631$	−195.973			−0.310575			−0.155287	−	0.987869i	$-0.549630\pi$
$631$	−195.973			−0.310575			−0.155287	+	0.987869i	$0.549630\pi$
$632$	−284.249	−	76.1644i	−0.449761	−	0.120513i
$633$		0			0
$634$	−219.499	−	126.728i	−0.346212	−	0.199886i
$635$	165.014	−	382.165i	0.259865	−	0.601835i
$636$		0			0
$637$	44.8232	+	12.0103i	0.0703661	+	0.0188545i
$638$	−1.79175	−	1.79175i	−0.00280839	−	0.00280839i
$639$		0			0
$640$	−72.2758	−	620.312i	−0.112931	−	0.969238i
$641$	130.750	+	226.466i	0.203978	+	0.353300i	0.949807	−	0.312838i	$-0.101280\pi$
$641$	130.750	+	226.466i	0.203978	+	0.353300i	−0.745829	+	0.666138i	$0.767946\pi$
$642$		0			0
$643$	964.305	−	258.385i	1.49970	−	0.401842i	0.586698	−	0.809806i	$-0.300428\pi$
$643$	964.305	−	258.385i	1.49970	−	0.401842i	0.912998	+	0.407963i	$0.133761\pi$
$644$	−87.9780	−	50.7941i	−0.136612	−	0.0788729i
$645$		0			0
$646$	−169.486	−	293.559i	−0.262363	−	0.454426i
$647$	−172.569	+	172.569i	−0.266722	+	0.266722i	−0.827778	−	0.561056i	$-0.810395\pi$
$647$	−172.569	+	172.569i	−0.266722	+	0.266722i	0.561056	+	0.827778i	$0.310395\pi$
$648$		0			0
$649$		−	9.53712i		−	0.0146951i
$650$	40.1931	−	37.8651i	0.0618356	−	0.0582540i
$651$		0			0
$652$	−224.725	−	838.685i	−0.344670	−	1.28633i
$653$	−1068.93	+	286.420i	−1.63696	+	0.438622i	−0.955920	−	0.293626i	$-0.905138\pi$
$653$	−1068.93	+	286.420i	−1.63696	+	0.438622i	−0.681038	+	0.732248i	$0.738471\pi$
$654$		0			0
$655$	171.666	−	1168.99i	0.262085	−	1.78472i
$656$	25.2818			0.0385394
$657$		0			0
$658$	62.8023	+	62.8023i	0.0954442	+	0.0954442i
$659$	−373.508	+	215.645i	−0.566780	+	0.327231i	−0.755862	−	0.654731i	$-0.772782\pi$
$659$	−373.508	+	215.645i	−0.566780	+	0.327231i	0.189082	+	0.981961i	$0.439449\pi$
$660$		0			0
$661$	−252.072	+	436.601i	−0.381349	+	0.660516i	−0.991255	−	0.131958i	$-0.957874\pi$
$661$	−252.072	+	436.601i	−0.381349	+	0.660516i	0.609906	+	0.792473i	$0.291207\pi$
$662$	−50.7080	−	189.245i	−0.0765981	−	0.285868i
$663$		0			0
$664$	464.341	−	268.087i	0.699308	−	0.403746i
$665$	88.6803	+	761.106i	0.133354	+	1.14452i
$666$		0			0
$667$	138.564	−	138.564i	0.207743	−	0.207743i
$668$	−70.3624	+	262.596i	−0.105333	+	0.393108i
$669$		0			0
$670$	62.9082	+	158.517i	0.0938928	+	0.236593i
$671$	−2.64575	+	4.58258i	−0.00394300	+	0.00682947i
$672$		0			0
$673$	96.6593	−	360.737i	0.143624	−	0.536014i	−0.856188	−	0.516664i	$-0.827174\pi$
$673$	96.6593	−	360.737i	0.143624	−	0.536014i	0.999813	−	0.0193499i	$-0.00615965\pi$
$674$		−	39.1382i		−	0.0580686i
$675$		0			0
$676$	563.583			0.833702
$677$	1119.55	+	299.983i	1.65370	+	0.443107i	0.960645	−	0.277779i	$-0.0895984\pi$
$677$	1119.55	+	299.983i	1.65370	+	0.443107i	0.693053	+	0.720886i	$0.256265\pi$
$678$		0			0
$679$	−516.047	−	297.940i	−0.760011	−	0.438793i
$680$	463.931	−	184.113i	0.682251	−	0.270754i
$681$		0			0
$682$	−2.20169	−	0.589941i	−0.00322828	−	0.000865016i
$683$	−390.999	−	390.999i	−0.572473	−	0.572473i	0.360346	−	0.932819i	$-0.382659\pi$
$683$	−390.999	−	390.999i	−0.572473	−	0.572473i	−0.932819	+	0.360346i	$0.882659\pi$
$684$		0			0
$685$	362.555	−	42.2432i	0.529278	−	0.0616689i
$686$	120.313	+	208.389i	0.175384	+	0.303774i
$687$		0			0
$688$	376.785	−	100.959i	0.547653	−	0.146743i
$689$	−205.542	−	118.670i	−0.298320	−	0.172235i
$690$		0			0
$691$	206.234	+	357.208i	0.298457	+	0.516943i	0.975783	−	0.218740i	$-0.0701946\pi$
$691$	206.234	+	357.208i	0.298457	+	0.516943i	−0.677326	+	0.735683i	$0.736861\pi$
$692$	−530.318	+	530.318i	−0.766355	+	0.766355i
$693$		0			0
$694$		−	413.855i		−	0.596332i
$695$	−788.539	−	115.797i	−1.13459	−	0.166614i
$696$		0			0
$697$	11.9420	+	44.5681i	0.0171334	+	0.0639428i
$698$	89.1104	−	23.8771i	0.127665	−	0.0342078i
$699$		0			0
$700$	−532.852	−	15.8918i	−0.761217	−	0.0227025i
$701$	−458.287			−0.653762			−0.326881	−	0.945066i	$-0.605998\pi$
$701$	−458.287			−0.653762			−0.326881	+	0.945066i	$0.605998\pi$
$702$		0			0
$703$	−1303.27	−	1303.27i	−1.85387	−	1.85387i
$704$	2.25757	−	1.30341i	0.00320677	−	0.00185143i
$705$		0			0
$706$	−88.3648	+	153.052i	−0.125163	+	0.216788i
$707$	27.9428	+	104.284i	0.0395231	+	0.147502i
$708$		0			0
$709$	560.267	−	323.470i	0.790221	−	0.456234i	−0.0498194	−	0.998758i	$-0.515865\pi$
$709$	560.267	−	323.470i	0.790221	−	0.456234i	0.840040	+	0.542524i	$0.182531\pi$
$710$	127.954	−	14.9085i	0.180217	−	0.0209980i
$711$		0			0
$712$	179.009	−	179.009i	0.251417	−	0.251417i
$713$	45.6228	−	170.267i	0.0639871	−	0.238803i
$714$		0			0
$715$	1.49636	+	0.646112i	0.00209281	+	0.000903653i
$716$	−251.311	+	435.283i	−0.350993	+	0.607937i
$717$		0			0
$718$	−59.3439	+	221.475i	−0.0826517	+	0.308460i
$719$		−	98.3936i		−	0.136848i	−0.997656	−	0.0684239i	$-0.978203\pi$
$719$		−	98.3936i		−	0.136848i	0.997656	−	0.0684239i	$-0.0217970\pi$
$720$		0			0
$721$	377.317			0.523325
$722$	188.435	+	50.4910i	0.260990	+	0.0699321i
$723$		0			0
$724$	−355.932	−	205.497i	−0.491619	−	0.283836i
$725$	295.637	−	984.893i	0.407775	−	1.35847i
$726$		0			0
$727$	1019.79	+	273.252i	1.40274	+	0.375862i	0.879326	−	0.476220i	$-0.157993\pi$
$727$	1019.79	+	273.252i	1.40274	+	0.375862i	0.523409	+	0.852082i	$0.324660\pi$
$728$	−70.4892	−	70.4892i	−0.0968259	−	0.0968259i
$729$		0			0
$730$	141.060	+	111.619i	0.193233	+	0.152903i
$731$	355.953	+	616.528i	0.486939	+	0.843404i
$732$		0			0
$733$	−111.526	+	29.8832i	−0.152150	+	0.0407684i	−0.334090	−	0.942541i	$-0.608429\pi$
$733$	−111.526	+	29.8832i	−0.152150	+	0.0407684i	0.181940	+	0.983310i	$0.441762\pi$
$734$	−132.406	−	76.4449i	−0.180390	−	0.104148i
$735$		0			0
$736$	−63.8621	−	110.612i	−0.0867692	−	0.150289i
$737$	−3.55945	+	3.55945i	−0.00482965	+	0.00482965i
$738$		0			0
$739$			427.280i			0.578186i	0.957301	+	0.289093i	$0.0933537\pi$
$739$			427.280i			0.578186i	−0.957301	+	0.289093i	$0.906646\pi$
$740$	1028.81	−	765.341i	1.39029	−	1.03424i
$741$		0			0
$742$	−69.0959	−	257.869i	−0.0931212	−	0.347533i
$743$	−330.163	+	88.4669i	−0.444365	+	0.119067i	−0.474061	−	0.880492i	$-0.657213\pi$
$743$	−330.163	+	88.4669i	−0.444365	+	0.119067i	0.0296967	+	0.999559i	$0.490546\pi$
$744$		0			0
$745$	412.618	+	60.5928i	0.553850	+	0.0813326i
$746$	−152.293			−0.204146
$747$		0			0
$748$	4.92197	+	4.92197i	0.00658017	+	0.00658017i
$749$	1097.95	−	633.904i	1.46589	−	0.846334i
$750$		0			0
$751$	521.702	−	903.615i	0.694677	−	1.20322i	−0.275613	−	0.961269i	$-0.588881\pi$
$751$	521.702	−	903.615i	0.694677	−	1.20322i	0.970290	−	0.241947i	$-0.0777859\pi$
$752$	−66.7418	−	249.084i	−0.0887524	−	0.331229i
$753$		0			0
$754$	78.6810	−	45.4265i	0.104352	−	0.0602474i
$755$	−136.280	−	107.837i	−0.180503	−	0.142830i
$756$		0			0
$757$	641.252	−	641.252i	0.847097	−	0.847097i	−0.142673	−	0.989770i	$-0.545570\pi$
$757$	641.252	−	641.252i	0.847097	−	0.847097i	0.989770	+	0.142673i	$0.0455698\pi$
$758$	19.2723	−	71.9254i	0.0254253	−	0.0948884i
$759$		0			0
$760$	−250.013	+	579.017i	−0.328964	+	0.761865i
$761$	307.586	−	532.754i	0.404186	−	0.700071i	−0.590040	−	0.807374i	$-0.700888\pi$
$761$	307.586	−	532.754i	0.404186	−	0.700071i	0.994226	+	0.107303i	$0.0342214\pi$
$762$		0			0
$763$	−194.866	+	727.249i	−0.255394	+	0.953144i
$764$			921.046i			1.20556i
$765$		0			0
$766$	−312.726			−0.408258
$767$	330.299	+	88.5033i	0.430637	+	0.115389i
$768$		0			0
$769$	−217.822	−	125.759i	−0.283253	−	0.163536i	0.351642	−	0.936135i	$-0.385623\pi$
$769$	−217.822	−	125.759i	−0.283253	−	0.163536i	−0.634895	+	0.772598i	$0.718957\pi$
$770$	0.676264	+	1.70406i	0.000878265	+	0.00221307i
$771$		0			0
$772$	431.977	+	115.748i	0.559555	+	0.149932i
$773$	−364.839	−	364.839i	−0.471978	−	0.471978i	0.430576	−	0.902554i	$-0.358310\pi$
$773$	−364.839	−	364.839i	−0.471978	−	0.471978i	−0.902554	+	0.430576i	$0.858310\pi$
$774$		0			0
$775$	−212.666	−	900.221i	−0.274408	−	1.16158i
$776$	−245.228	−	424.748i	−0.316016	−	0.547355i
$777$		0			0
$778$	208.776	−	55.9414i	0.268350	−	0.0719042i
$779$	−50.4909	−	29.1509i	−0.0648150	−	0.0374210i
$780$		0			0
$781$	1.90114	+	3.29287i	0.00243424	+	0.00421622i
$782$	44.3501	−	44.3501i	0.0567137	−	0.0567137i
$783$		0			0
$784$		−	151.550i		−	0.193304i
$785$	−19.9306	−	26.7918i	−0.0253893	−	0.0341297i
$786$		0			0
$787$	243.371	+	908.273i	0.309239	+	1.15410i	0.929235	+	0.369490i	$0.120468\pi$
$787$	243.371	+	908.273i	0.309239	+	1.15410i	−0.619996	+	0.784605i	$0.712866\pi$
$788$	−218.716	+	58.6049i	−0.277559	+	0.0743717i
$789$		0			0
$790$	−155.692	+	115.821i	−0.197079	+	0.146609i
$791$	1117.50			1.41277
$792$		0			0
$793$	−134.156	−	134.156i	−0.169175	−	0.169175i
$794$	371.884	−	214.707i	0.468367	−	0.270412i
$795$		0			0
$796$	−533.739	+	924.462i	−0.670526	+	1.16138i
$797$	301.039	+	1123.49i	0.377716	+	1.40965i	0.849336	+	0.527852i	$0.177003\pi$
$797$	301.039	+	1123.49i	0.377716	+	1.40965i	−0.471621	+	0.881802i	$0.656331\pi$
$798$		0			0
$799$	407.573	−	235.312i	0.510103	−	0.294508i
$800$	−570.195	−	352.274i	−0.712744	−	0.440342i
$801$		0			0
$802$	−86.4720	+	86.4720i	−0.107820	+	0.107820i
$803$	−1.37417	+	5.12848i	−0.00171130	+	0.00638665i
$804$		0			0
$805$	−131.783	+	52.2986i	−0.163705	+	0.0649672i
$806$	40.8628	−	70.7765i	0.0506983	−	0.0878120i
$807$		0			0
$808$	−22.9992	+	85.8340i	−0.0284643	+	0.106230i
$809$			753.586i			0.931504i	0.884915	+	0.465752i	$0.154216\pi$
$809$			753.586i			0.931504i	−0.884915	+	0.465752i	$0.845784\pi$
$810$		0			0
$811$	568.270			0.700703			0.350352	−	0.936618i	$-0.386062\pi$
$811$	568.270			0.700703			0.350352	+	0.936618i	$0.386062\pi$
$812$	−847.200	−	227.007i	−1.04335	−	0.279565i
$813$		0			0
$814$	−3.81903	−	2.20492i	−0.00469168	−	0.00270874i
$815$	−1112.52	−	480.372i	−1.36505	−	0.589414i
$816$		0			0
$817$	−868.896	−	232.820i	−1.06352	−	0.284969i
$818$	195.222	+	195.222i	0.238657	+	0.238657i
$819$		0			0
$820$	25.1689	−	31.8076i	0.0306938	−	0.0387897i
$821$	−298.755	−	517.458i	−0.363891	−	0.630278i	0.624706	−	0.780860i	$-0.285219\pi$
$821$	−298.755	−	517.458i	−0.363891	−	0.630278i	−0.988598	+	0.150582i	$0.951885\pi$
$822$		0			0
$823$	90.1649	−	24.1596i	0.109556	−	0.0293555i	−0.203624	−	0.979049i	$-0.565272\pi$
$823$	90.1649	−	24.1596i	0.109556	−	0.0293555i	0.313181	+	0.949694i	$0.398605\pi$
$824$	268.955	+	155.281i	0.326401	+	0.188448i
$825$		0			0
$826$	192.317	+	333.104i	0.232830	+	0.403273i
$827$	−7.50861	+	7.50861i	−0.00907934	+	0.00907934i	−0.711632	−	0.702553i	$-0.752044\pi$
$827$	−7.50861	+	7.50861i	−0.00907934	+	0.00907934i	0.702553	+	0.711632i	$0.252044\pi$
$828$		0			0
$829$		−	161.036i		−	0.194254i	−0.995272	−	0.0971269i	$-0.969035\pi$
$829$		−	161.036i		−	0.194254i	0.995272	−	0.0971269i	$-0.0309653\pi$
$830$	51.3687	−	349.805i	0.0618900	−	0.421452i
$831$		0			0
$832$	24.1910	+	90.2819i	0.0290757	+	0.108512i
$833$	267.160	−	71.5854i	0.320721	−	0.0859369i
$834$		0			0
$835$	226.463	+	304.423i	0.271213	+	0.364578i
$836$	−8.79541			−0.0105208
$837$		0			0
$838$	−245.986	−	245.986i	−0.293539	−	0.293539i
$839$	−80.9864	+	46.7575i	−0.0965272	+	0.0557300i	−0.547487	−	0.836814i	$-0.684415\pi$
$839$	−80.9864	+	46.7575i	−0.0965272	+	0.0557300i	0.450959	+	0.892545i	$0.351082\pi$
$840$		0			0
$841$	425.432	−	736.870i	0.505864	−	0.876183i
$842$	66.0514	+	246.507i	0.0784459	+	0.292764i
$843$		0			0
$844$	−421.869	+	243.566i	−0.499845	+	0.288586i
$845$	488.077	−	616.813i	0.577606	−	0.729957i
$846$		0			0
$847$	509.216	−	509.216i	0.601199	−	0.601199i
$848$	−200.615	+	748.706i	−0.236575	+	0.882908i
$849$		0			0
$850$	94.6242	−	315.233i	0.111323	−	0.370863i
$851$	170.516	−	295.343i	0.200372	−	0.347054i
$852$		0			0
$853$	−40.7138	+	151.946i	−0.0477301	+	0.178131i	−0.985676	−	0.168651i	$-0.946059\pi$
$853$	−40.7138	+	151.946i	−0.0477301	+	0.178131i	0.937946	+	0.346782i	$0.112726\pi$
$854$		−	213.408i		−	0.249892i
$855$		0			0
$856$	1043.51			1.21905
$857$	−100.177	−	26.8424i	−0.116893	−	0.0313214i	0.199898	−	0.979817i	$-0.435939\pi$
$857$	−100.177	−	26.8424i	−0.116893	−	0.0313214i	−0.316791	+	0.948495i	$0.602605\pi$
$858$		0			0
$859$	−431.090	−	248.890i	−0.501851	−	0.289744i	0.227626	−	0.973749i	$-0.426904\pi$
$859$	−431.090	−	248.890i	−0.501851	−	0.289744i	−0.729478	+	0.684004i	$0.760237\pi$
$860$	248.084	−	574.549i	0.288470	−	0.668081i
$861$		0			0
$862$	−37.5000	−	10.0481i	−0.0435035	−	0.0116567i
$863$	597.165	+	597.165i	0.691965	+	0.691965i	0.962664	−	0.270699i	$-0.0872549\pi$
$863$	597.165	+	597.165i	0.691965	+	0.691965i	−0.270699	+	0.962664i	$0.587255\pi$
$864$		0			0
$865$	121.138	+	1039.67i	0.140044	+	1.20194i
$866$	87.9499	+	152.334i	0.101559	+	0.175905i
$867$		0			0
$868$	−762.088	+	204.201i	−0.877982	+	0.235254i
$869$	−4.96023	−	2.86379i	−0.00570798	−	0.00329550i
$870$		0			0
$871$	−90.2432	−	156.306i	−0.103609	−	0.179456i
$872$	−438.193	+	438.193i	−0.502515	+	0.502515i
$873$		0			0
$874$			79.2523i			0.0906777i
$875$	−478.856	+	569.417i	−0.547264	+	0.650763i
$876$		0			0
$877$	−230.613	−	860.660i	−0.262957	−	0.981368i	−0.963489	−	0.267748i	$-0.913721\pi$
$877$	−230.613	−	860.660i	−0.262957	−	0.981368i	0.700532	−	0.713621i	$-0.252946\pi$
$878$	−182.438	+	48.8840i	−0.207788	+	0.0556765i
$879$		0			0
$880$	0.773384	−	5.26651i	0.000878846	−	0.00598468i
$881$	1619.10			1.83780			0.918902	−	0.394487i	$-0.129078\pi$
$881$	1619.10			1.83780			0.918902	+	0.394487i	$0.129078\pi$
$882$		0			0
$883$	881.301	+	881.301i	0.998076	+	0.998076i	0.999998	−	0.00192213i	$-0.000611833\pi$
$883$	881.301	+	881.301i	0.998076	+	0.998076i	−0.00192213	+	0.999998i	$0.500612\pi$
$884$	−216.138	+	124.787i	−0.244500	+	0.141162i
$885$		0			0
$886$	122.158	−	211.584i	0.137876	−	0.238808i
$887$	94.6674	+	353.303i	0.106728	+	0.398313i	0.998535	−	0.0541016i	$-0.0172295\pi$
$887$	94.6674	+	353.303i	0.106728	+	0.398313i	−0.891808	+	0.452414i	$0.850563\pi$
$888$		0			0
$889$	−429.140	+	247.764i	−0.482722	+	0.278700i
$890$	−19.3196	−	165.812i	−0.0217074	−	0.186305i
$891$		0			0
$892$	−573.459	+	573.459i	−0.642891	+	0.642891i
$893$	−153.912	+	574.407i	−0.172354	+	0.643233i
$894$		0			0
$895$	258.754	+	652.013i	0.289111	+	0.728506i
$896$	−371.709	+	643.818i	−0.414853	+	0.718547i
$897$		0			0
$898$	16.9474	−	63.2485i	0.0188724	−	0.0704327i
$899$		−	1521.89i		−	1.69287i
$900$		0			0
$901$	−1414.62			−1.57006
$902$	−0.134740	−	0.0361036i	−0.000149380	−	4.00262e-5i
$903$		0			0
$904$	796.561	+	459.895i	0.881152	+	0.508733i
$905$	−533.153	+	211.584i	−0.589119	+	0.233794i
$906$		0			0
$907$	103.567	+	27.7508i	0.114187	+	0.0305963i	0.315460	−	0.948939i	$-0.397841\pi$
$907$	103.567	+	27.7508i	0.114187	+	0.0305963i	−0.201273	+	0.979535i	$0.564508\pi$
$908$	−181.445	−	181.445i	−0.199829	−	0.199829i
$909$		0			0
$910$	−65.2924	+	7.60756i	−0.0717499	+	0.00835995i
$911$	−422.343	−	731.520i	−0.463604	−	0.802985i	0.535533	−	0.844514i	$-0.320111\pi$
$911$	−422.343	−	731.520i	−0.463604	−	0.802985i	−0.999137	+	0.0415286i	$0.986777\pi$
$912$		0			0
$913$	10.0801	−	2.70096i	0.0110407	−	0.00295834i
$914$	348.557	+	201.240i	0.381354	+	0.220175i
$915$		0			0
$916$	−63.8947	−	110.669i	−0.0697540	−	0.120818i
$917$	−994.544	+	994.544i	−1.08456	+	1.08456i
$918$		0			0
$919$			298.720i			0.325049i	0.986704	+	0.162525i	$0.0519637\pi$
$919$			298.720i			0.325049i	−0.986704	+	0.162525i	$0.948036\pi$
$920$	−115.459	−	16.9550i	−0.125499	−	0.0184294i
$921$		0			0
$922$	97.5673	+	364.126i	0.105821	+	0.394931i
$923$	−131.684	+	35.2847i	−0.142670	+	0.0382283i
$924$		0			0
$925$	53.3487	−	1788.79i	0.0576743	−	1.93382i
$926$	−74.7559			−0.0807299
$927$		0			0
$928$	−779.753	−	779.753i	−0.840251	−	0.840251i
$929$	−959.561	+	554.003i	−1.03290	+	0.596343i	−0.917813	−	0.397012i	$-0.870047\pi$
$929$	−959.561	+	554.003i	−1.03290	+	0.596343i	−0.115084	+	0.993356i	$0.536714\pi$
$930$		0			0
$931$	−174.743	+	302.664i	−0.187694	+	0.325096i
$932$	−250.594	−	935.231i	−0.268878	−	1.00347i
$933$		0			0
$934$	−115.475	+	66.6697i	−0.123635	+	0.0713808i
$935$	9.64940	−	1.12430i	0.0103202	−	0.00120246i
$936$		0			0
$937$	−895.973	+	895.973i	−0.956214	+	0.956214i	−0.999081	−	0.0428666i	$-0.986351\pi$
$937$	−895.973	+	895.973i	−0.956214	+	0.956214i	0.0428666	+	0.999081i	$0.486351\pi$
$938$	52.5443	−	196.098i	0.0560174	−	0.209060i
$939$		0			0
$940$	−379.821	−	164.003i	−0.404065	−	0.174471i
$941$	647.160	−	1120.91i	0.687737	−	1.19119i	−0.284832	−	0.958578i	$-0.591938\pi$
$941$	647.160	−	1120.91i	0.687737	−	1.19119i	0.972568	−	0.232617i	$-0.0747290\pi$
$942$		0			0
$943$	2.79205	−	10.4201i	0.00296082	−	0.0110499i
$944$		−	1116.76i		−	1.18301i
$945$		0			0
$946$	−2.15226			−0.00227512
$947$	−214.593	−	57.4999i	−0.226602	−	0.0607179i	0.143731	−	0.989617i	$-0.454090\pi$
$947$	−214.593	−	57.4999i	−0.226602	−	0.0607179i	−0.370334	+	0.928899i	$0.620757\pi$
$948$		0			0
$949$	−164.862	−	95.1833i	−0.173722	−	0.100299i
$950$	197.111	+	366.201i	0.207485	+	0.385475i
$951$		0			0
$952$	−573.919	−	153.781i	−0.602856	−	0.161535i
$953$	342.541	+	342.541i	0.359435	+	0.359435i	0.863605	−	0.504170i	$-0.168201\pi$
$953$	342.541	+	342.541i	0.359435	+	0.359435i	−0.504170	+	0.863605i	$0.668201\pi$
$954$		0			0
$955$	1008.04	+	797.650i	1.05554	+	0.835235i
$956$	621.545	+	1076.55i	0.650152	+	1.12610i
$957$		0			0
$958$	234.748	−	62.9005i	0.245039	−	0.0656581i
$959$	−376.294	−	217.253i	−0.392382	−	0.226542i
$960$		0			0
$961$	−204.000	−	353.338i	−0.212279	−	0.367678i
$962$	111.803	−	111.803i	0.116219	−	0.116219i
$963$		0			0
$964$			51.1901i			0.0531018i
$965$	500.783	−	372.536i	0.518946	−	0.386048i
$966$		0			0
$967$	303.679	+	1133.35i	0.314043	+	1.17202i	0.924877	+	0.380266i	$0.124167\pi$
$967$	303.679	+	1133.35i	0.314043	+	1.17202i	−0.610834	+	0.791758i	$0.709166\pi$
$968$	572.535	−	153.410i	0.591462	−	0.158482i
$969$		0			0
$970$	−319.978	−	46.9886i	−0.329875	−	0.0484419i
$971$	−1454.35			−1.49779			−0.748894	−	0.662690i	$-0.769415\pi$
$971$	−1454.35			−1.49779			−0.748894	+	0.662690i	$0.769415\pi$
$972$		0			0
$973$	670.866	+	670.866i	0.689482	+	0.689482i
$974$	318.646	−	183.970i	0.327152	−	0.188881i
$975$		0			0
$976$	−309.808	+	536.602i	−0.317426	+	0.549798i
$977$	−6.20014	−	23.1393i	−0.00634610	−	0.0236840i	0.962680	−	0.270642i	$-0.0872358\pi$
$977$	−6.20014	−	23.1393i	−0.00634610	−	0.0236840i	−0.969026	+	0.246958i	$0.920569\pi$
$978$		0			0
$979$	4.26714	−	2.46363i	0.00435867	−	0.00251648i
$980$	−190.668	−	150.873i	−0.194559	−	0.153952i
$981$		0			0
$982$	−159.539	+	159.539i	−0.162463	+	0.162463i
$983$	−108.551	+	405.117i	−0.110428	+	0.412123i	−0.998904	−	0.0467995i	$-0.985098\pi$
$983$	−108.551	+	405.117i	−0.110428	+	0.412123i	0.888476	+	0.458923i	$0.151764\pi$
$984$		0			0
$985$	−125.274	+	290.128i	−0.127182	+	0.294546i
$986$	270.756	−	468.964i	0.274601	−	0.475622i
$987$		0			0
$988$	81.6203	−	304.611i	0.0826117	−	0.308311i
$989$		−	166.444i		−	0.168296i
$990$		0			0
$991$	−632.405			−0.638148			−0.319074	−	0.947730i	$-0.603372\pi$
$991$	−632.405			−0.638148			−0.319074	+	0.947730i	$0.603372\pi$
$992$	−958.153	−	256.736i	−0.965880	−	0.258807i
$993$		0			0
$994$	−132.802	−	76.6735i	−0.133604	−	0.0771363i
$995$	549.547	+	1384.76i	0.552309	+	1.39172i
$996$		0			0
$997$	−842.872	−	225.847i	−0.845409	−	0.226527i	−0.189984	−	0.981787i	$-0.560844\pi$
$997$	−842.872	−	225.847i	−0.845409	−	0.226527i	−0.655425	+	0.755261i	$0.727510\pi$
$998$	−244.128	−	244.128i	−0.244617	−	0.244617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.i.28.1		8
3.2	odd	2		405.3.l.e.28.2		8
5.2	odd	4		405.3.l.e.352.2		8
9.2	odd	6	inner	405.3.l.i.298.1		8
9.4	even	3		405.3.g.d.163.3	yes	8
9.5	odd	6		405.3.g.d.163.2	yes	8
9.7	even	3		405.3.l.e.298.2		8
15.2	even	4	inner	405.3.l.i.352.1		8
45.2	even	12		405.3.l.e.217.2		8
45.7	odd	12	inner	405.3.l.i.217.1		8
45.22	odd	12		405.3.g.d.82.3	yes	8
45.32	even	12		405.3.g.d.82.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.d.82.2	✓	8	45.32	even	12
405.3.g.d.82.3	yes	8	45.22	odd	12
405.3.g.d.163.2	yes	8	9.5	odd	6
405.3.g.d.163.3	yes	8	9.4	even	3
405.3.l.e.28.2		8	3.2	odd	2
405.3.l.e.217.2		8	45.2	even	12
405.3.l.e.298.2		8	9.7	even	3
405.3.l.e.352.2		8	5.2	odd	4
405.3.l.i.28.1		8	1.1	even	1	trivial
405.3.l.i.217.1		8	45.7	odd	12	inner
405.3.l.i.298.1		8	9.2	odd	6	inner
405.3.l.i.352.1		8	15.2	even	4	inner

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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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.624069 - 0.167219i) q^{2} +(-3.10260 - 1.79129i) q^{4} +(-4.64741 + 1.84434i) q^{5} +(5.74921 + 1.54050i) q^{7} +(3.46410 + 3.46410i) q^{8} +(3.20871 - 0.373864i) q^{10} +(0.0476751 + 0.0825757i) q^{11} +(-3.30226 + 0.884839i) q^{13} +(-3.33030 - 1.92275i) q^{14} +(5.58258 + 9.66930i) q^{16} +(-14.4086 + 14.4086i) q^{17} -25.7477i q^{19} +(17.7228 + 2.60258i) q^{20} +(-0.0159443 - 0.0595051i) q^{22} +(4.60180 - 1.23305i) q^{23} +(18.1968 - 17.1428i) q^{25} +2.20880 q^{26} +(-15.0780 - 15.0780i) q^{28} +(35.6216 - 20.5661i) q^{29} +(18.5000 - 32.0429i) q^{31} +(-6.93882 - 25.8960i) q^{32} +(11.4014 - 6.58258i) q^{34} +(-29.5601 + 3.44420i) q^{35} +(50.6170 - 50.6170i) q^{37} +(-4.30550 + 16.0684i) q^{38} +(-22.4881 - 9.71010i) q^{40} +(1.13218 - 1.96099i) q^{41} +(9.04235 - 33.7465i) q^{43} -0.341599i q^{44} -3.07803 q^{46} +(-22.3091 - 5.97769i) q^{47} +(-11.7550 - 6.78674i) q^{49} +(-14.2227 + 7.65546i) q^{50} +(11.8306 + 3.17000i) q^{52} +(49.0894 + 49.0894i) q^{53} +(-0.373864 - 0.295834i) q^{55} +(14.5794 + 25.2523i) q^{56} +(-25.6694 + 6.87809i) q^{58} +(-86.6216 - 50.0110i) q^{59} +(27.7477 + 48.0605i) q^{61} +(-16.9035 + 16.9035i) q^{62} -27.3394i q^{64} +(13.7150 - 10.2027i) q^{65} +(13.6638 + 50.9941i) q^{67} +(70.5141 - 18.8942i) q^{68} +(19.0235 + 2.79359i) q^{70} +39.8770 q^{71} +(39.3739 + 39.3739i) q^{73} +(-40.0527 + 23.1244i) q^{74} +(-46.1216 + 79.8849i) q^{76} +(0.146887 + 0.548188i) q^{77} +(-52.0212 + 30.0345i) q^{79} +(-43.7780 - 34.6410i) q^{80} +(-1.03447 + 1.03447i) q^{82} +(28.3267 - 105.717i) q^{83} +(40.3883 - 93.5371i) q^{85} +(-11.2861 + 19.5481i) q^{86} +(-0.120899 + 0.451202i) q^{88} -51.6755i q^{89} -20.3485 q^{91} +(-16.4863 - 4.41749i) q^{92} +(12.9228 + 7.46099i) q^{94} +(47.4876 + 119.660i) q^{95} +(-96.7027 - 25.9114i) q^{97} +(6.20105 + 6.20105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} + 6 q^{5} + 26 q^{7} + 44 q^{10} - 28 q^{13} + 120 q^{14} + 8 q^{16} + 24 q^{20} + 46 q^{22} + 60 q^{23} + 32 q^{25} + 136 q^{28} + 120 q^{29} + 148 q^{31} - 168 q^{32} + 20 q^{37} - 54 q^{38}+ \cdots - 274 q^{97}+O(q^{100}) \) 8 * q + 6 * q^2 + 6 * q^5 + 26 * q^7 + 44 * q^10 - 28 * q^13 + 120 * q^14 + 8 * q^16 + 24 * q^20 + 46 * q^22 + 60 * q^23 + 32 * q^25 + 136 * q^28 + 120 * q^29 + 148 * q^31 - 168 * q^32 + 20 * q^37 - 54 * q^38 - 48 * q^40 + 2 * q^43 + 232 * q^46 + 6 * q^47 + 42 * q^50 - 112 * q^52 + 52 * q^55 - 66 * q^58 - 528 * q^59 + 112 * q^61 - 84 * q^65 - 76 * q^67 + 156 * q^68 + 396 * q^70 + 260 * q^73 - 852 * q^74 - 204 * q^76 - 318 * q^77 + 340 * q^82 + 582 * q^83 + 194 * q^85 - 72 * q^88 - 896 * q^91 + 228 * q^92 + 342 * q^95 - 274 * q^97

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