LMFDB - Embedded newform 405.3.l.f.352.2

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:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			352.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	405.352
Dual form			405.3.l.f.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.814313 - 3.03906i) q^{2} +(-5.10867 - 2.94949i) q^{4} +(4.99585 - 0.203583i) q^{5} +(-0.530550 + 1.98004i) q^{7} +(-4.22474 + 4.22474i) q^{8} +O(q^{10})$	\(q+(0.814313 - 3.03906i) q^{2} +(-5.10867 - 2.94949i) q^{4} +(4.99585 - 0.203583i) q^{5} +(-0.530550 + 1.98004i) q^{7} +(-4.22474 + 4.22474i) q^{8} +(3.44949 - 15.3485i) q^{10} +(-1.67423 - 2.89986i) q^{11} +(-3.82478 - 14.2743i) q^{13} +(5.58542 + 3.22474i) q^{14} +(-2.39898 - 4.15515i) q^{16} +(2.65153 + 2.65153i) q^{17} -20.6969i q^{19} +(-26.1226 - 13.6952i) q^{20} +(-10.1762 + 2.72670i) q^{22} +(-6.02093 - 22.4704i) q^{23} +(24.9171 - 2.03414i) q^{25} -46.4949 q^{26} +(8.55051 - 8.55051i) q^{28} +(-0.739215 + 0.426786i) q^{29} +(9.34847 - 16.1920i) q^{31} +(-37.6657 + 10.0925i) q^{32} +(10.2173 - 5.89898i) q^{34} +(-2.24745 + 10.0000i) q^{35} +(38.0454 + 38.0454i) q^{37} +(-62.8992 - 16.8538i) q^{38} +(-20.2461 + 21.9663i) q^{40} +(-14.3485 + 24.8523i) q^{41} +(-30.7286 - 8.23370i) q^{43} +19.7526i q^{44} -73.1918 q^{46} +(-7.22994 + 26.9825i) q^{47} +(38.7962 + 22.3990i) q^{49} +(14.1085 - 77.3810i) q^{50} +(-22.5623 + 84.2036i) q^{52} +(-28.6969 + 28.6969i) q^{53} +(-8.95459 - 14.1464i) q^{55} +(-6.12372 - 10.6066i) q^{56} +(0.695075 + 2.59405i) q^{58} +(96.9378 + 55.9671i) q^{59} +(-47.0454 - 81.4850i) q^{61} +(-41.5959 - 41.5959i) q^{62} +103.495i q^{64} +(-22.0140 - 70.5335i) q^{65} +(74.9934 - 20.0944i) q^{67} +(-5.72512 - 21.3664i) q^{68} +(28.5605 + 14.9733i) q^{70} +68.0000 q^{71} +(-39.7878 + 39.7878i) q^{73} +(146.603 - 84.6413i) q^{74} +(-61.0454 + 105.734i) q^{76} +(6.63010 - 1.77653i) q^{77} +(21.2132 - 12.2474i) q^{79} +(-12.8309 - 20.2702i) q^{80} +(63.8434 + 63.8434i) q^{82} +(-28.8866 - 7.74013i) q^{83} +(13.7865 + 12.7069i) q^{85} +(-50.0454 + 86.6812i) q^{86} +(19.3244 + 5.17795i) q^{88} +94.1816i q^{89} +30.2929 q^{91} +(-35.5173 + 132.553i) q^{92} +(76.1139 + 43.9444i) q^{94} +(-4.21354 - 103.399i) q^{95} +(5.34248 - 19.9384i) q^{97} +(99.6640 - 99.6640i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 8 q - 4 q^{2} - 4 q^{5} - 4 q^{7} - 24 q^{8} + 8 q^{10} + 16 q^{11} + 32 q^{13} + 20 q^{16} + 80 q^{17} - 36 q^{20} - 20 q^{22} + 56 q^{23} - 16 q^{25} - 176 q^{26} + 88 q^{28} + 16 q^{31} - 76 q^{32} + 80 q^{35} + 128 q^{37} - 96 q^{38} - 48 q^{40} - 56 q^{41} + 8 q^{43} - 272 q^{46} + 128 q^{47} + 164 q^{50} + 80 q^{52} - 112 q^{53} - 248 q^{55} + 12 q^{58} - 200 q^{61} - 176 q^{62} - 112 q^{65} + 200 q^{67} - 104 q^{68} + 60 q^{70} + 544 q^{71} + 152 q^{73} - 312 q^{76} + 88 q^{77} - 328 q^{80} + 256 q^{82} - 16 q^{83} - 232 q^{85} - 224 q^{86} - 12 q^{88} - 32 q^{91} + 104 q^{92} + 144 q^{95} + 20 q^{97} + 376 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 - 24 * q^8 + 8 * q^10 + 16 * q^11 + 32 * q^13 + 20 * q^16 + 80 * q^17 - 36 * q^20 - 20 * q^22 + 56 * q^23 - 16 * q^25 - 176 * q^26 + 88 * q^28 + 16 * q^31 - 76 * q^32 + 80 * q^35 + 128 * q^37 - 96 * q^38 - 48 * q^40 - 56 * q^41 + 8 * q^43 - 272 * q^46 + 128 * q^47 + 164 * q^50 + 80 * q^52 - 112 * q^53 - 248 * q^55 + 12 * q^58 - 200 * q^61 - 176 * q^62 - 112 * q^65 + 200 * q^67 - 104 * q^68 + 60 * q^70 + 544 * q^71 + 152 * q^73 - 312 * q^76 + 88 * q^77 - 328 * q^80 + 256 * q^82 - 16 * q^83 - 232 * q^85 - 224 * q^86 - 12 * q^88 - 32 * q^91 + 104 * q^92 + 144 * q^95 + 20 * q^97 + 376 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.814313	−	3.03906i	0.407157	−	1.51953i	−0.392887	−	0.919587i	$-0.628524\pi$
$2$	0.814313	−	3.03906i	0.407157	−	1.51953i	0.800043	−	0.599942i	$-0.204810\pi$
$3$		0			0
$3$		0			0
$4$	−5.10867	−	2.94949i	−1.27717	−	0.737372i
$5$	4.99585	−	0.203583i	0.999171	−	0.0407165i
$5$	4.99585	−	0.203583i	0.999171	−	0.0407165i
$6$		0			0
$7$	−0.530550	+	1.98004i	−0.0757929	+	0.282863i	−0.993412	−	0.114598i	$-0.963442\pi$
$7$	−0.530550	+	1.98004i	−0.0757929	+	0.282863i	0.917619	+	0.397461i	$0.130109\pi$
$8$	−4.22474	+	4.22474i	−0.528093	+	0.528093i
$9$		0			0
$10$	3.44949	−	15.3485i	0.344949	−	1.53485i
$11$	−1.67423	−	2.89986i	−0.152203	−	0.263624i	0.779834	−	0.625986i	$-0.215303\pi$
$11$	−1.67423	−	2.89986i	−0.152203	−	0.263624i	−0.932037	+	0.362363i	$0.881970\pi$
$12$		0			0
$13$	−3.82478	−	14.2743i	−0.294214	−	1.09802i	−0.941840	−	0.336062i	$-0.890905\pi$
$13$	−3.82478	−	14.2743i	−0.294214	−	1.09802i	0.647626	−	0.761958i	$-0.275762\pi$
$14$	5.58542	+	3.22474i	0.398959	+	0.230339i
$15$		0			0
$16$	−2.39898	−	4.15515i	−0.149936	−	0.259697i
$17$	2.65153	+	2.65153i	0.155972	+	0.155972i	0.780779	−	0.624807i	$-0.214822\pi$
$17$	2.65153	+	2.65153i	0.155972	+	0.155972i	−0.624807	+	0.780779i	$0.714822\pi$
$18$		0			0
$19$		−	20.6969i		−	1.08931i	−0.838659	−	0.544656i	$-0.816660\pi$
$19$		−	20.6969i		−	1.08931i	0.838659	−	0.544656i	$-0.183340\pi$
$20$	−26.1226	−	13.6952i	−1.30613	−	0.684759i
$21$		0			0
$22$	−10.1762	+	2.72670i	−0.462554	+	0.123941i
$23$	−6.02093	−	22.4704i	−0.261780	−	0.976975i	−0.964192	−	0.265205i	$-0.914560\pi$
$23$	−6.02093	−	22.4704i	−0.261780	−	0.976975i	0.702413	−	0.711770i	$-0.252106\pi$
$24$		0			0
$25$	24.9171	−	2.03414i	0.996684	−	0.0813655i
$26$	−46.4949			−1.78827
$27$		0			0
$28$	8.55051	−	8.55051i	0.305375	−	0.305375i
$29$	−0.739215	+	0.426786i	−0.0254902	+	0.0147168i	−0.512691	−	0.858573i	$-0.671351\pi$
$29$	−0.739215	+	0.426786i	−0.0254902	+	0.0147168i	0.487201	+	0.873290i	$0.338018\pi$
$30$		0			0
$31$	9.34847	−	16.1920i	0.301564	−	0.522323i	−0.674927	−	0.737885i	$-0.735825\pi$
$31$	9.34847	−	16.1920i	0.301564	−	0.522323i	0.976490	+	0.215561i	$0.0691581\pi$
$32$	−37.6657	+	10.0925i	−1.17705	+	0.315391i
$33$		0			0
$34$	10.2173	−	5.89898i	0.300510	−	0.173499i
$35$	−2.24745	+	10.0000i	−0.0642128	+	0.285714i
$36$		0			0
$37$	38.0454	+	38.0454i	1.02825	+	1.02825i	0.999589	+	0.0286652i	$0.00912566\pi$
$37$	38.0454	+	38.0454i	1.02825	+	1.02825i	0.0286652	+	0.999589i	$0.490874\pi$
$38$	−62.8992	−	16.8538i	−1.65524	−	0.443521i
$39$		0			0
$40$	−20.2461	+	21.9663i	−0.506153	+	0.549157i
$41$	−14.3485	+	24.8523i	−0.349963	+	0.606153i	−0.986242	−	0.165305i	$-0.947139\pi$
$41$	−14.3485	+	24.8523i	−0.349963	+	0.606153i	0.636280	+	0.771458i	$0.280472\pi$
$42$		0			0
$43$	−30.7286	−	8.23370i	−0.714619	−	0.191481i	−0.116849	−	0.993150i	$-0.537279\pi$
$43$	−30.7286	−	8.23370i	−0.714619	−	0.191481i	−0.597769	+	0.801668i	$0.703946\pi$
$44$			19.7526i			0.448922i
$45$		0			0
$46$	−73.1918			−1.59113
$47$	−7.22994	+	26.9825i	−0.153828	+	0.574095i	0.845374	+	0.534174i	$0.179377\pi$
$47$	−7.22994	+	26.9825i	−0.153828	+	0.574095i	−0.999203	+	0.0399212i	$0.987289\pi$
$48$		0			0
$49$	38.7962	+	22.3990i	0.791759	+	0.457122i
$50$	14.1085	−	77.3810i	0.282169	−	1.54762i
$51$		0			0
$52$	−22.5623	+	84.2036i	−0.433890	+	1.61930i
$53$	−28.6969	+	28.6969i	−0.541452	+	0.541452i	−0.923954	−	0.382503i	$-0.875062\pi$
$53$	−28.6969	+	28.6969i	−0.541452	+	0.541452i	0.382503	+	0.923954i	$0.375062\pi$
$54$		0			0
$55$	−8.95459	−	14.1464i	−0.162811	−	0.257208i
$56$	−6.12372	−	10.6066i	−0.109352	−	0.189404i
$57$		0			0
$58$	0.695075	+	2.59405i	0.0119840	+	0.0447251i
$59$	96.9378	+	55.9671i	1.64301	+	0.948595i	0.979754	+	0.200206i	$0.0641612\pi$
$59$	96.9378	+	55.9671i	1.64301	+	0.948595i	0.663261	+	0.748389i	$0.269172\pi$
$60$		0			0
$61$	−47.0454	−	81.4850i	−0.771236	−	1.33582i	−0.936886	−	0.349636i	$-0.886305\pi$
$61$	−47.0454	−	81.4850i	−0.771236	−	1.33582i	0.165650	−	0.986185i	$-0.447028\pi$
$62$	−41.5959	−	41.5959i	−0.670902	−	0.670902i
$63$		0			0
$64$			103.495i			1.61711i
$65$	−22.0140	−	70.5335i	−0.338677	−	1.08513i
$66$		0			0
$67$	74.9934	−	20.0944i	1.11930	−	0.299917i	0.348703	−	0.937233i	$-0.386622\pi$
$67$	74.9934	−	20.0944i	1.11930	−	0.299917i	0.770602	+	0.637317i	$0.219956\pi$
$68$	−5.72512	−	21.3664i	−0.0841930	−	0.314212i
$69$		0			0
$70$	28.5605	+	14.9733i	0.408006	+	0.213904i
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	−39.7878	+	39.7878i	−0.545038	+	0.545038i	−0.925001	−	0.379964i	$-0.875936\pi$
$73$	−39.7878	+	39.7878i	−0.545038	+	0.545038i	0.379964	+	0.925001i	$0.375936\pi$
$74$	146.603	−	84.6413i	1.98112	−	1.14380i
$75$		0			0
$76$	−61.0454	+	105.734i	−0.803229	+	1.39123i
$77$	6.63010	−	1.77653i	0.0861052	−	0.0230718i
$78$		0			0
$79$	21.2132	−	12.2474i	0.268522	−	0.155031i	−0.359694	−	0.933070i	$-0.617119\pi$
$79$	21.2132	−	12.2474i	0.268522	−	0.155031i	0.628216	+	0.778039i	$0.283786\pi$
$80$	−12.8309	−	20.2702i	−0.160386	−	0.253377i
$81$		0			0
$82$	63.8434	+	63.8434i	0.778578	+	0.778578i
$83$	−28.8866	−	7.74013i	−0.348031	−	0.0932546i	0.0805689	−	0.996749i	$-0.474326\pi$
$83$	−28.8866	−	7.74013i	−0.348031	−	0.0932546i	−0.428600	+	0.903494i	$0.640993\pi$
$84$		0			0
$85$	13.7865	+	12.7069i	0.162194	+	0.149492i
$86$	−50.0454	+	86.6812i	−0.581923	+	1.00792i
$87$		0			0
$88$	19.3244	+	5.17795i	0.219595	+	0.0588404i
$89$			94.1816i			1.05822i	0.848553	+	0.529110i	$0.177474\pi$
$89$			94.1816i			1.05822i	−0.848553	+	0.529110i	$0.822526\pi$
$90$		0			0
$91$	30.2929			0.332889
$92$	−35.5173	+	132.553i	−0.386058	+	1.44079i
$93$		0			0
$94$	76.1139	+	43.9444i	0.809722	+	0.467493i
$95$	−4.21354	−	103.399i	−0.0443530	−	1.08841i
$96$		0			0
$97$	5.34248	−	19.9384i	0.0550771	−	0.205550i	−0.932904	−	0.360125i	$-0.882734\pi$
$97$	5.34248	−	19.9384i	0.0550771	−	0.205550i	0.987981	+	0.154575i	$0.0494007\pi$
$98$	99.6640	−	99.6640i	1.01698	−	1.01698i
$99$		0			0
$100$	−133.293	−	63.1010i	−1.33293	−	0.631010i
$101$	86.8105	+	150.360i	0.859509	+	1.48871i	0.872397	+	0.488797i	$0.162564\pi$
$101$	86.8105	+	150.360i	0.859509	+	1.48871i	−0.0128880	+	0.999917i	$0.504102\pi$
$102$		0			0
$103$	−23.7011	−	88.4536i	−0.230108	−	0.858773i	−0.980294	−	0.197546i	$-0.936703\pi$
$103$	−23.7011	−	88.4536i	−0.230108	−	0.858773i	0.750186	−	0.661227i	$-0.229964\pi$
$104$	76.4639	+	44.1464i	0.735229	+	0.424485i
$105$		0			0
$106$	63.8434	+	110.580i	0.602296	+	1.04321i
$107$	4.74235	+	4.74235i	0.0443210	+	0.0443210i	0.728920	−	0.684599i	$-0.240023\pi$
$107$	4.74235	+	4.74235i	0.0443210	+	0.0443210i	−0.684599	+	0.728920i	$0.740023\pi$
$108$		0			0
$109$			39.3031i			0.360579i	0.983614	+	0.180289i	$0.0577034\pi$
$109$			39.3031i			0.360579i	−0.983614	+	0.180289i	$0.942297\pi$
$110$	−50.2837	+	15.6939i	−0.457124	+	0.142672i
$111$		0			0
$112$	9.50015	−	2.54556i	0.0848228	−	0.0227282i
$113$	−5.25564	−	19.6143i	−0.0465101	−	0.173578i	0.938764	−	0.344561i	$-0.111972\pi$
$113$	−5.25564	−	19.6143i	−0.0465101	−	0.173578i	−0.985274	+	0.170983i	$0.945306\pi$
$114$		0			0
$115$	−34.6543	−	111.033i	−0.301342	−	0.965506i
$116$	5.03520			0.0434069
$117$		0			0
$118$	249.025	−	249.025i	2.11038	−	2.11038i
$119$	−6.65691	+	3.84337i	−0.0559404	+	0.0322972i
$120$		0			0
$121$	54.8939	−	95.0790i	0.453668	−	0.785777i
$122$	−285.947	+	76.6194i	−2.34383	+	0.628028i
$123$		0			0
$124$	−95.5164	+	55.1464i	−0.770294	+	0.444729i
$125$	124.068	−	15.2350i	0.992545	−	0.121880i
$126$		0			0
$127$	−114.621	−	114.621i	−0.902527	−	0.902527i	0.0931273	−	0.995654i	$-0.470314\pi$
$127$	−114.621	−	114.621i	−0.902527	−	0.902527i	−0.995654	+	0.0931273i	$0.970314\pi$
$128$	163.864	+	43.9073i	1.28019	+	0.343026i
$129$		0			0
$130$	−232.282	+	9.46556i	−1.78678	+	0.0728120i
$131$	−13.0681	+	22.6346i	−0.0997566	+	0.172783i	−0.911584	−	0.411114i	$-0.865140\pi$
$131$	−13.0681	+	22.6346i	−0.0997566	+	0.172783i	0.811827	+	0.583898i	$0.198473\pi$
$132$		0			0
$133$	40.9808	+	10.9808i	0.308126	+	0.0825621i
$134$		−	244.272i		−	1.82293i
$135$		0			0
$136$	−22.4041			−0.164736
$137$	−5.35536	+	19.9865i	−0.0390902	+	0.145887i	−0.982713	−	0.185137i	$-0.940727\pi$
$137$	−5.35536	+	19.9865i	−0.0390902	+	0.145887i	0.943623	+	0.331023i	$0.107394\pi$
$138$		0			0
$139$	−72.0286	−	41.5857i	−0.518191	−	0.299178i	0.218003	−	0.975948i	$-0.430046\pi$
$139$	−72.0286	−	41.5857i	−0.518191	−	0.299178i	−0.736194	+	0.676770i	$0.763379\pi$
$140$	40.9764	−	44.4578i	0.292688	−	0.317556i
$141$		0			0
$142$	55.3733	−	206.656i	0.389953	−	1.45532i
$143$	−34.9898	+	34.9898i	−0.244684	+	0.244684i
$144$		0			0
$145$	−3.60612	+	2.28265i	−0.0248698	+	0.0157424i
$146$	88.5176	+	153.317i	0.606285	+	1.05012i
$147$		0			0
$148$	−82.1467	−	306.576i	−0.555046	−	2.07146i
$149$	103.184	+	59.5732i	0.692509	+	0.399820i	0.804551	−	0.593883i	$-0.202406\pi$
$149$	103.184	+	59.5732i	0.692509	+	0.399820i	−0.112042	+	0.993703i	$0.535739\pi$
$150$		0			0
$151$	72.4847	+	125.547i	0.480031	+	0.831438i	0.999738	−	0.0229066i	$-0.00729205\pi$
$151$	72.4847	+	125.547i	0.480031	+	0.831438i	−0.519707	+	0.854345i	$0.673959\pi$
$152$	87.4393	+	87.4393i	0.575258	+	0.575258i
$153$		0			0
$154$		−	21.5959i		−	0.140233i
$155$	43.4072	−	82.7962i	0.280046	−	0.534169i
$156$		0			0
$157$	−69.8673	+	18.7209i	−0.445015	+	0.119241i	−0.474366	−	0.880328i	$-0.657323\pi$
$157$	−69.8673	+	18.7209i	−0.445015	+	0.119241i	0.0293510	+	0.999569i	$0.490656\pi$
$158$	−19.9465	−	74.4414i	−0.126244	−	0.471148i
$159$		0			0
$160$	−186.118	+	58.0887i	−1.16324	+	0.363055i
$161$	47.6867			0.296191
$162$		0			0
$163$	189.394	−	189.394i	1.16193	−	1.16193i	0.177872	−	0.984054i	$-0.443079\pi$
$163$	189.394	−	189.394i	1.16193	−	1.16193i	0.984054	−	0.177872i	$-0.0569213\pi$
$164$	146.603	−	84.6413i	0.893921	−	0.516106i
$165$		0			0
$166$	−47.0454	+	81.4850i	−0.283406	+	0.490874i
$167$	132.553	−	35.5173i	0.793728	−	0.212679i	0.160899	−	0.986971i	$-0.448561\pi$
$167$	132.553	−	35.5173i	0.793728	−	0.212679i	0.632828	+	0.774292i	$0.281894\pi$
$168$		0			0
$169$	−42.7675	+	24.6918i	−0.253062	+	0.146106i
$170$	49.8434	−	31.5505i	0.293196	−	0.185591i
$171$		0			0
$172$	132.697	+	132.697i	0.771494	+	0.771494i
$173$	−47.3070	−	12.6759i	−0.273451	−	0.0732709i	0.119488	−	0.992836i	$-0.461875\pi$
$173$	−47.3070	−	12.6759i	−0.273451	−	0.0732709i	−0.392938	+	0.919565i	$0.628541\pi$
$174$		0			0
$175$	−9.19210	+	50.4161i	−0.0525263	+	0.288092i
$176$	−8.03291	+	13.9134i	−0.0456415	+	0.0790534i
$177$		0			0
$178$	286.223	+	76.6933i	1.60800	+	0.430861i
$179$			183.712i			1.02632i	0.858292	+	0.513161i	$0.171526\pi$
$179$			183.712i			1.02632i	−0.858292	+	0.513161i	$0.828474\pi$
$180$		0			0
$181$	−21.7276			−0.120042			−0.0600209	−	0.998197i	$-0.519117\pi$
$181$	−21.7276			−0.120042			−0.0600209	+	0.998197i	$0.519117\pi$
$182$	24.6679	−	92.0617i	0.135538	−	0.505834i
$183$		0			0
$184$	120.369	+	69.4949i	0.654178	+	0.377690i
$185$	197.815	+	182.324i	1.06927	+	0.985535i
$186$		0			0
$187$	3.24978	−	12.1284i	0.0173785	−	0.0648575i
$188$	116.520	−	116.520i	0.619787	−	0.619787i
$189$		0			0
$190$	−317.666	−	71.3939i	−1.67193	−	0.375757i
$191$	−20.0454	−	34.7197i	−0.104950	−	0.181778i	0.808768	−	0.588128i	$-0.200135\pi$
$191$	−20.0454	−	34.7197i	−0.104950	−	0.181778i	−0.913718	+	0.406350i	$0.866802\pi$
$192$		0			0
$193$	28.3909	+	105.956i	0.147103	+	0.548996i	0.999653	+	0.0263498i	$0.00838836\pi$
$193$	28.3909	+	105.956i	0.147103	+	0.548996i	−0.852550	+	0.522646i	$0.824945\pi$
$194$	−56.2435	−	32.4722i	−0.289915	−	0.167382i
$195$		0			0
$196$	−132.131	−	228.858i	−0.674138	−	1.16764i
$197$	67.3031	+	67.3031i	0.341640	+	0.341640i	0.856984	−	0.515344i	$-0.172336\pi$
$197$	67.3031	+	67.3031i	0.341640	+	0.341640i	−0.515344	+	0.856984i	$0.672336\pi$
$198$		0			0
$199$			251.394i			1.26329i	0.775259	+	0.631643i	$0.217619\pi$
$199$			251.394i			1.26329i	−0.775259	+	0.631643i	$0.782381\pi$
$200$	−96.6747	+	113.862i	−0.483374	+	0.569311i
$201$		0			0
$202$	527.644	−	141.382i	2.61210	−	0.699910i
$203$	−0.452863	−	1.69011i	−0.00223085	−	0.00832565i
$204$		0			0
$205$	−66.6234	+	127.079i	−0.324992	+	0.619900i
$206$	−288.116			−1.39862
$207$		0			0
$208$	−50.1362	+	50.1362i	−0.241040	+	0.241040i
$209$	−60.0182	+	34.6515i	−0.287168	+	0.165797i
$210$		0			0
$211$	−132.394	+	229.313i	−0.627459	+	1.08679i	0.360601	+	0.932720i	$0.382572\pi$
$211$	−132.394	+	229.313i	−0.627459	+	1.08679i	−0.988060	+	0.154071i	$0.950762\pi$
$212$	231.244	−	61.9618i	1.09078	−	0.292272i
$213$		0			0
$214$	18.2740	−	10.5505i	0.0853926	−	0.0493014i
$215$	−155.192	−	34.8786i	−0.721822	−	0.162226i
$216$		0			0
$217$	27.1010	+	27.1010i	0.124889	+	0.124889i
$218$	119.444	+	32.0050i	0.547910	+	0.146812i
$219$		0			0
$220$	4.02128	+	98.6809i	0.0182785	+	0.448549i
$221$	27.7071	−	47.9902i	0.125372	−	0.217150i
$222$		0			0
$223$	45.6650	+	12.2359i	0.204776	+	0.0548695i	0.359749	−	0.933049i	$-0.382862\pi$
$223$	45.6650	+	12.2359i	0.204776	+	0.0548695i	−0.154973	+	0.987919i	$0.549529\pi$
$224$		−	79.9342i		−	0.356849i
$225$		0			0
$226$	−63.8888			−0.282694
$227$	7.74928	−	28.9207i	0.0341378	−	0.127404i	−0.946754	−	0.321958i	$-0.895659\pi$
$227$	7.74928	−	28.9207i	0.0341378	−	0.127404i	0.980892	+	0.194554i	$0.0623258\pi$
$228$		0			0
$229$	211.135	+	121.899i	0.921988	+	0.532310i	0.884269	−	0.466978i	$-0.154657\pi$
$229$	211.135	+	121.899i	0.921988	+	0.532310i	0.0377192	+	0.999288i	$0.487991\pi$
$230$	−365.656	+	14.9006i	−1.58981	+	0.0647852i
$231$		0			0
$232$	1.31993	−	4.92606i	0.00568936	−	0.0212330i
$233$	−161.712	+	161.712i	−0.694042	+	0.694042i	−0.963119	−	0.269077i	$-0.913281\pi$
$233$	−161.712	+	161.712i	−0.694042	+	0.694042i	0.269077	+	0.963119i	$0.413281\pi$
$234$		0			0
$235$	−30.6265	+	136.272i	−0.130326	+	0.579883i
$236$	−330.149	−	571.834i	−1.39894	−	2.42303i
$237$		0			0
$238$	6.25941	+	23.3604i	0.0263000	+	0.0981531i
$239$	−282.499	−	163.101i	−1.18201	−	0.682431i	−0.225528	−	0.974237i	$-0.572411\pi$
$239$	−282.499	−	163.101i	−1.18201	−	0.682431i	−0.956478	+	0.291806i	$0.905744\pi$
$240$		0			0
$241$	66.7878	+	115.680i	0.277128	+	0.479999i	0.970670	−	0.240417i	$-0.0772842\pi$
$241$	66.7878	+	115.680i	0.277128	+	0.479999i	−0.693542	+	0.720416i	$0.743951\pi$
$242$	−244.250	−	244.250i	−1.00930	−	1.00930i
$243$		0			0
$244$			555.040i			2.27475i
$245$	198.380	+	104.004i	0.809714	+	0.424505i
$246$		0			0
$247$	−295.434	+	79.1612i	−1.19609	+	0.320491i
$248$	28.9123	+	107.902i	0.116582	+	0.435089i
$249$		0			0
$250$	54.7304	−	389.456i	0.218922	−	1.55782i
$251$	404.742			1.61252			0.806260	−	0.591562i	$-0.201488\pi$
$251$	404.742			1.61252			0.806260	+	0.591562i	$0.201488\pi$
$252$		0			0
$253$	−55.0806	+	55.0806i	−0.217710	+	0.217710i
$254$	−441.677	+	255.002i	−1.73889	+	1.00395i
$255$		0			0
$256$	59.8837	−	103.722i	0.233921	−	0.405162i
$257$	−121.900	+	32.6631i	−0.474320	+	0.127094i	−0.488057	−	0.872812i	$-0.662294\pi$
$257$	−121.900	+	32.6631i	−0.474320	+	0.127094i	0.0137364	+	0.999906i	$0.495627\pi$
$258$		0			0
$259$	−95.5164	+	55.1464i	−0.368789	+	0.212921i
$260$	−95.5755	+	425.262i	−0.367598	+	1.63562i
$261$		0			0
$262$	58.1464	+	58.1464i	0.221933	+	0.221933i
$263$	−466.967	−	125.123i	−1.77554	−	0.475754i	−0.785780	−	0.618506i	$-0.787738\pi$
$263$	−466.967	−	125.123i	−1.77554	−	0.475754i	−0.989759	+	0.142751i	$0.954405\pi$
$264$		0			0
$265$	−137.524	+	149.208i	−0.518957	+	0.563049i
$266$	66.7423	−	115.601i	0.250911	−	0.434591i
$267$		0			0
$268$	−442.385	−	118.537i	−1.65069	−	0.442301i
$269$			3.50052i			0.0130131i	0.999979	+	0.00650653i	$0.00207111\pi$
$269$			3.50052i			0.0130131i	−0.999979	+	0.00650653i	$0.997929\pi$
$270$		0			0
$271$	−103.576			−0.382197			−0.191099	−	0.981571i	$-0.561205\pi$
$271$	−103.576			−0.382197			−0.191099	+	0.981571i	$0.561205\pi$
$272$	4.65655	−	17.3785i	0.0171197	−	0.0638915i
$273$		0			0
$274$	56.3791	+	32.5505i	0.205763	+	0.118797i
$275$	−47.6158	−	68.8505i	−0.173148	−	0.250365i
$276$		0			0
$277$	−104.504	+	390.013i	−0.377270	+	1.40799i	0.472730	+	0.881208i	$0.343269\pi$
$277$	−104.504	+	390.013i	−0.377270	+	1.40799i	−0.850000	+	0.526783i	$0.823398\pi$
$278$	−185.035	+	185.035i	−0.665594	+	0.665594i
$279$		0			0
$280$	−32.7526	−	51.7423i	−0.116973	−	0.184794i
$281$	186.348	+	322.765i	0.663162	+	1.14863i	0.979780	+	0.200077i	$0.0641192\pi$
$281$	186.348	+	322.765i	0.663162	+	1.14863i	−0.316618	+	0.948553i	$0.602547\pi$
$282$		0			0
$283$	−28.2542	−	105.446i	−0.0998381	−	0.372601i	0.897870	−	0.440260i	$-0.145114\pi$
$283$	−28.2542	−	105.446i	−0.0998381	−	0.372601i	−0.997709	+	0.0676591i	$0.978447\pi$
$284$	−347.389	−	200.565i	−1.22320	−	0.706216i
$285$		0			0
$286$	77.8434	+	134.829i	0.272180	+	0.471429i
$287$	−41.5959	−	41.5959i	−0.144934	−	0.144934i
$288$		0			0
$289$		−	274.939i		−	0.951345i
$290$	4.00060	+	12.8180i	0.0137952	+	0.0442000i
$291$		0			0
$292$	320.616	−	85.9088i	1.09800	−	0.294208i
$293$	86.5889	+	323.154i	0.295525	+	1.10292i	0.940799	+	0.338964i	$0.110077\pi$
$293$	86.5889	+	323.154i	0.295525	+	1.10292i	−0.645274	+	0.763951i	$0.723257\pi$
$294$		0			0
$295$	495.681	+	259.869i	1.68028	+	0.880910i
$296$	−321.464			−1.08603
$297$		0			0
$298$	265.070	−	265.070i	0.889498	−	0.889498i
$299$	−297.720	+	171.889i	−0.995719	+	0.574879i
$300$		0			0
$301$	32.6061	−	56.4755i	0.108326	−	0.187626i
$302$	440.570	−	118.050i	1.45884	−	0.390896i
$303$		0			0
$304$	−85.9990	+	49.6515i	−0.282891	+	0.163327i
$305$	−251.621	−	397.510i	−0.824987	−	1.30331i
$306$		0			0
$307$	168.969	+	168.969i	0.550389	+	0.550389i	0.926553	−	0.376164i	$-0.122757\pi$
$307$	168.969	+	168.969i	0.550389	+	0.550389i	−0.376164	+	0.926553i	$0.622757\pi$
$308$	−39.1108	−	10.4797i	−0.126983	−	0.0340251i
$309$		0			0
$310$	−216.275	−	199.339i	−0.697662	−	0.643029i
$311$	177.151	−	306.835i	0.569617	−	0.986606i	−0.426986	−	0.904258i	$-0.640425\pi$
$311$	177.151	−	306.835i	0.569617	−	0.986606i	0.996604	−	0.0823482i	$-0.0262420\pi$
$312$		0			0
$313$	−208.146	−	55.7726i	−0.665003	−	0.178187i	−0.0895003	−	0.995987i	$-0.528527\pi$
$313$	−208.146	−	55.7726i	−0.665003	−	0.178187i	−0.575503	+	0.817800i	$0.695194\pi$
$314$			227.576i			0.724763i
$315$		0			0
$316$	−144.495			−0.457262
$317$	156.372	−	583.589i	0.493288	−	1.84097i	−0.0461283	−	0.998936i	$-0.514688\pi$
$317$	156.372	−	583.589i	0.493288	−	1.84097i	0.539416	−	0.842039i	$-0.318645\pi$
$318$		0			0
$319$	2.47524	+	1.42908i	0.00775937	+	0.00447987i
$320$	21.0698	+	517.045i	0.0658430	+	1.61577i
$321$		0			0
$322$	38.8319	−	144.923i	0.120596	−	0.450071i
$323$	54.8786	−	54.8786i	0.169903	−	0.169903i
$324$		0			0
$325$	−124.338	−	347.893i	−0.382579	−	1.07044i
$326$	−421.353	−	729.805i	−1.29249	−	2.23867i
$327$		0			0
$328$	−44.3759	−	165.613i	−0.135292	−	0.504918i
$329$	−49.5906	−	28.6311i	−0.150731	−	0.0870247i
$330$		0			0
$331$	−244.712	−	423.853i	−0.739310	−	1.28052i	−0.952806	−	0.303579i	$-0.901818\pi$
$331$	−244.712	−	423.853i	−0.739310	−	1.28052i	0.213496	−	0.976944i	$-0.431515\pi$
$332$	124.742	+	124.742i	0.375730	+	0.375730i
$333$		0			0
$334$		−	431.757i		−	1.29269i
$335$	370.565	−	115.656i	1.10616	−	0.345242i
$336$		0			0
$337$	−399.141	+	106.950i	−1.18440	+	0.317358i	−0.796669	−	0.604416i	$-0.793406\pi$
$337$	−399.141	+	106.950i	−1.18440	+	0.317358i	−0.387727	+	0.921774i	$0.626740\pi$
$338$	40.2138	+	150.080i	0.118976	+	0.444023i
$339$		0			0
$340$	−32.9517	−	105.578i	−0.0969168	−	0.310524i
$341$	−62.6061			−0.183596
$342$		0			0
$343$	−135.959	+	135.959i	−0.396382	+	0.396382i
$344$	164.606	−	95.0352i	0.478505	−	0.276265i
$345$		0			0
$346$	−77.0454	+	133.447i	−0.222675	+	0.385684i
$347$	437.196	−	117.146i	1.25993	−	0.337598i	0.433767	−	0.901025i	$-0.357184\pi$
$347$	437.196	−	117.146i	1.25993	−	0.337598i	0.826166	+	0.563428i	$0.190518\pi$
$348$		0			0
$349$	497.107	−	287.005i	1.42437	−	0.822363i	0.427705	−	0.903918i	$-0.359322\pi$
$349$	497.107	−	287.005i	1.42437	−	0.822363i	0.996669	+	0.0815556i	$0.0259888\pi$
$350$	145.732	+	68.9898i	0.416378	+	0.197114i
$351$		0			0
$352$	92.3281	+	92.3281i	0.262296	+	0.262296i
$353$	364.073	+	97.5531i	1.03137	+	0.276354i	0.734532	−	0.678574i	$-0.237402\pi$
$353$	364.073	+	97.5531i	1.03137	+	0.276354i	0.296836	+	0.954928i	$0.404068\pi$
$354$		0			0
$355$	339.718	−	13.8436i	0.956952	−	0.0389961i
$356$	277.788	−	481.143i	0.780303	−	1.35152i
$357$		0			0
$358$	558.311	+	149.599i	1.55953	+	0.417874i
$359$			216.272i			0.602430i	0.953556	+	0.301215i	$0.0973922\pi$
$359$			216.272i			0.602430i	−0.953556	+	0.301215i	$0.902608\pi$
$360$		0			0
$361$	−67.3633			−0.186602
$362$	−17.6930	+	66.0313i	−0.0488758	+	0.182407i
$363$		0			0
$364$	−154.756	−	89.3485i	−0.425154	−	0.245463i
$365$	−190.674	+	206.874i	−0.522394	+	0.566778i
$366$		0			0
$367$	−88.0327	+	328.542i	−0.239871	+	0.895211i	0.736021	+	0.676958i	$0.236702\pi$
$367$	−88.0327	+	328.542i	−0.239871	+	0.895211i	−0.975892	+	0.218252i	$0.929964\pi$
$368$	−78.9240	+	78.9240i	−0.214467	+	0.214467i
$369$		0			0
$370$	715.176	−	452.702i	1.93291	−	1.22352i
$371$	−41.5959	−	72.0462i	−0.112118	−	0.194195i
$372$		0			0
$373$	−120.864	−	451.071i	−0.324032	−	1.20930i	−0.915281	−	0.402816i	$-0.868032\pi$
$373$	−120.864	−	451.071i	−0.324032	−	1.20930i	0.591249	−	0.806489i	$-0.298635\pi$
$374$	−34.2124	−	19.7526i	−0.0914771	−	0.0528143i
$375$		0			0
$376$	−83.4495	−	144.539i	−0.221940	−	0.384412i
$377$	8.91939	+	8.91939i	0.0236589	+	0.0236589i
$378$		0			0
$379$		−	210.000i		−	0.554090i	−0.960857	−	0.277045i	$-0.910645\pi$
$379$		−	210.000i		−	0.554090i	0.960857	−	0.277045i	$-0.0893551\pi$
$380$	−283.448	+	540.658i	−0.745917	+	1.42278i
$381$		0			0
$382$	−121.838	+	32.6465i	−0.318948	+	0.0854620i
$383$	−62.4553	−	233.086i	−0.163069	−	0.608581i	−0.998279	−	0.0586495i	$-0.981321\pi$
$383$	−62.4553	−	233.086i	−0.163069	−	0.608581i	0.835210	−	0.549931i	$-0.185346\pi$
$384$		0			0
$385$	32.7614	−	10.2251i	0.0850944	−	0.0265586i
$386$	345.126			0.894109
$387$		0			0
$388$	−86.1010	+	86.1010i	−0.221910	+	0.221910i
$389$	−474.008	+	273.669i	−1.21853	+	0.703518i	−0.964603	−	0.263705i	$-0.915055\pi$
$389$	−474.008	+	273.669i	−1.21853	+	0.703518i	−0.253926	+	0.967224i	$0.581722\pi$
$390$		0			0
$391$	43.6163	−	75.5457i	0.111551	−	0.193212i
$392$	−258.534	+	69.2739i	−0.659525	+	0.176719i
$393$		0			0
$394$	259.344	−	149.732i	0.658233	−	0.380031i
$395$	103.485	−	65.5051i	0.261987	−	0.165836i
$396$		0			0
$397$	45.2577	+	45.2577i	0.113999	+	0.113999i	0.761805	−	0.647806i	$-0.224313\pi$
$397$	45.2577	+	45.2577i	0.113999	+	0.113999i	−0.647806	+	0.761805i	$0.724313\pi$
$398$	764.001	+	204.713i	1.91960	+	0.514355i
$399$		0			0
$400$	−68.2278	−	98.6546i	−0.170569	−	0.246636i
$401$	−260.151	+	450.595i	−0.648756	+	1.12368i	0.334665	+	0.942337i	$0.391377\pi$
$401$	−260.151	+	450.595i	−0.648756	+	1.12368i	−0.983420	+	0.181340i	$0.941956\pi$
$402$		0			0
$403$	−266.885	−	71.5117i	−0.662246	−	0.177448i
$404$		−	1024.19i		−	2.53511i
$405$		0			0
$406$	−5.50510			−0.0135594
$407$	46.6294	−	174.023i	0.114569	−	0.427576i
$408$		0			0
$409$	−300.606	−	173.555i	−0.734979	−	0.424340i	0.0852621	−	0.996359i	$-0.472827\pi$
$409$	−300.606	−	173.555i	−0.734979	−	0.424340i	−0.820241	+	0.572018i	$0.806161\pi$
$410$	331.950	+	305.955i	0.809633	+	0.746231i
$411$		0			0
$412$	−139.812	+	521.786i	−0.339350	+	1.26647i
$413$	−162.247	+	162.247i	−0.392851	+	0.392851i
$414$		0			0
$415$	−145.889	−	32.7878i	−0.351539	−	0.0790066i
$416$	288.126	+	499.049i	0.692611	+	1.19964i
$417$		0			0
$418$	56.4344	+	210.616i	0.135011	+	0.503866i
$419$	−505.238	−	291.699i	−1.20582	−	0.696180i	−0.243975	−	0.969781i	$-0.578452\pi$
$419$	−505.238	−	291.699i	−1.20582	−	0.696180i	−0.961843	+	0.273602i	$0.911785\pi$
$420$		0			0
$421$	−106.576	−	184.594i	−0.253148	−	0.438466i	0.711243	−	0.702947i	$-0.248133\pi$
$421$	−106.576	−	184.594i	−0.253148	−	0.438466i	−0.964391	+	0.264481i	$0.914799\pi$
$422$	589.085	+	589.085i	1.39594	+	1.39594i
$423$		0			0
$424$		−	242.474i		−	0.571874i
$425$	71.4621	+	60.6749i	0.168146	+	0.142764i
$426$		0			0
$427$	186.304	−	49.9199i	0.436308	−	0.116908i
$428$	−10.2396	−	38.2146i	−0.0239242	−	0.0892864i
$429$		0			0
$430$	−232.373	+	443.235i	−0.540402	+	1.03078i
$431$	−187.364			−0.434720			−0.217360	−	0.976092i	$-0.569745\pi$
$431$	−187.364			−0.434720			−0.217360	+	0.976092i	$0.569745\pi$
$432$		0			0
$433$	154.848	−	154.848i	0.357617	−	0.357617i	−0.505317	−	0.862934i	$-0.668624\pi$
$433$	154.848	−	154.848i	0.357617	−	0.357617i	0.862934	+	0.505317i	$0.168624\pi$
$434$	104.430	−	60.2929i	0.240623	−	0.138924i
$435$		0			0
$436$	115.924	−	200.786i	0.265881	−	0.460519i
$437$	−465.069	+	124.615i	−1.06423	+	0.285160i
$438$		0			0
$439$	−219.043	+	126.464i	−0.498958	+	0.288074i	−0.728283	−	0.685276i	$-0.759681\pi$
$439$	−219.043	+	126.464i	−0.498958	+	0.288074i	0.229325	+	0.973350i	$0.426348\pi$
$440$	97.5959	+	21.9342i	0.221809	+	0.0498504i
$441$		0			0
$442$	−123.283	−	123.283i	−0.278920	−	0.278920i
$443$	−575.275	−	154.144i	−1.29859	−	0.347956i	−0.457673	−	0.889121i	$-0.651317\pi$
$443$	−575.275	−	154.144i	−1.29859	−	0.347956i	−0.840917	+	0.541165i	$0.817984\pi$
$444$		0			0
$445$	19.1737	+	470.518i	0.0430871	+	1.05734i
$446$	74.3712	−	128.815i	0.166752	−	0.288822i
$447$		0			0
$448$	−204.924	−	54.9092i	−0.457420	−	0.122565i
$449$		−	297.909i		−	0.663495i	−0.943368	−	0.331747i	$-0.892362\pi$
$449$		−	297.909i		−	0.663495i	0.943368	−	0.331747i	$-0.107638\pi$
$450$		0			0
$451$	96.0908			0.213062
$452$	−31.0029	+	115.704i	−0.0685905	+	0.255983i
$453$		0			0
$454$	−81.5814	−	47.1010i	−0.179695	−	0.103747i
$455$	151.339	−	6.16710i	0.332612	−	0.0135541i
$456$		0			0
$457$	104.591	−	390.338i	0.228864	−	0.854130i	−0.751956	−	0.659213i	$-0.770890\pi$
$457$	104.591	−	390.338i	0.228864	−	0.854130i	0.980820	−	0.194917i	$-0.0624438\pi$
$458$	542.388	−	542.388i	1.18425	−	1.18425i
$459$		0			0
$460$	−150.454	+	669.444i	−0.327074	+	1.45531i
$461$	263.310	+	456.066i	0.571171	+	0.989298i	0.996446	+	0.0842333i	$0.0268441\pi$
$461$	263.310	+	456.066i	0.571171	+	0.989298i	−0.425275	+	0.905064i	$0.639823\pi$
$462$		0			0
$463$	122.875	+	458.577i	0.265389	+	0.990447i	0.962012	+	0.273009i	$0.0880187\pi$
$463$	122.875	+	458.577i	0.265389	+	0.990447i	−0.696622	+	0.717438i	$0.745315\pi$
$464$	3.54672	+	2.04770i	0.00764380	+	0.00441315i
$465$		0			0
$466$	359.767	+	623.135i	0.772033	+	1.33720i
$467$	−488.742	−	488.742i	−1.04656	−	1.04656i	−0.998862	−	0.0476956i	$-0.984812\pi$
$467$	−488.742	−	488.742i	−1.04656	−	1.04656i	−0.0476956	−	0.998862i	$-0.515188\pi$
$468$		0			0
$469$			159.151i			0.339341i
$470$	389.200	+	204.044i	0.828086	+	0.434137i
$471$		0			0
$472$	−645.984	+	173.091i	−1.36861	+	0.366718i
$473$	27.5703	+	102.894i	0.0582882	+	0.217534i
$474$		0			0
$475$	−42.1004	−	515.708i	−0.0886325	−	1.08570i
$476$	45.3439			0.0952603
$477$		0			0
$478$	−725.716	+	725.716i	−1.51823	+	1.51823i
$479$	160.171	−	92.4745i	0.334385	−	0.193057i	−0.323401	−	0.946262i	$-0.604826\pi$
$479$	160.171	−	92.4745i	0.334385	−	0.193057i	0.657786	+	0.753205i	$0.271493\pi$
$480$		0			0
$481$	397.555	−	688.586i	0.826518	−	1.43157i
$482$	405.944	−	108.772i	0.842207	−	0.225669i
$483$		0			0
$484$	−560.869	+	323.818i	−1.15882	+	0.669045i
$485$	22.6311	−	100.697i	0.0466621	−	0.207623i
$486$		0			0
$487$	−120.682	−	120.682i	−0.247807	−	0.247807i	0.572263	−	0.820070i	$-0.306066\pi$
$487$	−120.682	−	120.682i	−0.247807	−	0.247807i	−0.820070	+	0.572263i	$0.806066\pi$
$488$	543.008	+	145.499i	1.11272	+	0.298153i
$489$		0			0
$490$	477.617	−	518.197i	0.974729	−	1.05754i
$491$	−52.8411	+	91.5234i	−0.107619	+	0.186402i	−0.914805	−	0.403895i	$-0.867656\pi$
$491$	−52.8411	+	91.5234i	−0.107619	+	0.186402i	0.807186	+	0.590297i	$0.200989\pi$
$492$		0			0
$493$	−3.09169	−	0.828415i	−0.00627117	−	0.00168035i
$494$			962.302i			1.94798i
$495$		0			0
$496$	−89.7071			−0.180861
$497$	−36.0774	+	134.643i	−0.0725904	+	0.270911i
$498$		0			0
$499$	640.499	+	369.792i	1.28357	+	0.741067i	0.977498	−	0.210943i	$-0.0676535\pi$
$499$	640.499	+	369.792i	1.28357	+	0.741067i	0.306067	+	0.952010i	$0.400987\pi$
$500$	−678.758	−	288.107i	−1.35752	−	0.576215i
$501$		0			0
$502$	329.587	−	1230.04i	0.656548	−	2.45027i
$503$	406.409	−	406.409i	0.807970	−	0.807970i	−0.176357	−	0.984326i	$-0.556431\pi$
$503$	406.409	−	406.409i	0.807970	−	0.807970i	0.984326	+	0.176357i	$0.0564312\pi$
$504$		0			0
$505$	464.303	+	733.504i	0.919412	+	1.45248i
$506$	122.540	+	212.246i	0.242175	+	0.419459i
$507$		0			0
$508$	247.487	+	923.633i	0.487179	+	1.81818i
$509$	168.451	+	97.2554i	0.330945	+	0.191071i	0.656261	−	0.754534i	$-0.272137\pi$
$509$	168.451	+	97.2554i	0.330945	+	0.191071i	−0.325315	+	0.945606i	$0.605470\pi$
$510$		0			0
$511$	−57.6719	−	99.8907i	−0.112861	−	0.195481i
$512$	213.376	+	213.376i	0.416750	+	0.416750i
$513$		0			0
$514$			397.060i			0.772491i
$515$	−136.415	−	437.076i	−0.264883	−	0.848692i
$516$		0			0
$517$	90.3500	−	24.2092i	0.174758	−	0.0468263i
$518$	89.8129	+	335.186i	0.173384	+	0.647078i
$519$		0			0
$520$	390.990	+	204.982i	0.751903	+	0.394197i
$521$	589.605			1.13168			0.565840	−	0.824515i	$-0.308552\pi$
$521$	589.605			1.13168			0.565840	+	0.824515i	$0.308552\pi$
$522$		0			0
$523$	−141.546	+	141.546i	−0.270642	+	0.270642i	−0.829359	−	0.558716i	$-0.811294\pi$
$523$	−141.546	+	141.546i	−0.270642	+	0.270642i	0.558716	+	0.829359i	$0.311294\pi$
$524$	133.521	−	77.0885i	0.254812	−	0.147115i
$525$		0			0
$526$	−760.514	+	1317.25i	−1.44584	+	2.50428i
$527$	67.7214	−	18.1459i	0.128504	−	0.0344324i
$528$		0			0
$529$	−10.5408	+	6.08571i	−0.0199258	+	0.0115042i
$530$	341.464	+	539.444i	0.644272	+	1.01782i
$531$		0			0
$532$	−176.969	−	176.969i	−0.332649	−	0.332649i
$533$	409.628	+	109.759i	0.768532	+	0.205928i
$534$		0			0
$535$	24.6575	+	22.7266i	0.0460888	+	0.0424796i
$536$	−231.934	+	401.722i	−0.432713	+	0.749481i
$537$		0			0
$538$	10.6383	+	2.85052i	0.0197737	+	0.00529836i
$539$		−	150.005i		−	0.278302i
$540$		0			0
$541$	431.303			0.797233			0.398617	−	0.917118i	$-0.369490\pi$
$541$	431.303			0.797233			0.398617	+	0.917118i	$0.369490\pi$
$542$	−84.3429	+	314.772i	−0.155614	+	0.580760i
$543$		0			0
$544$	−126.632	−	73.1112i	−0.232780	−	0.134396i
$545$	8.00142	+	196.352i	0.0146815	+	0.360280i
$546$		0			0
$547$	−163.329	+	609.551i	−0.298590	+	1.11435i	0.639734	+	0.768596i	$0.279044\pi$
$547$	−163.329	+	609.551i	−0.298590	+	1.11435i	−0.938324	+	0.345757i	$0.887622\pi$
$548$	86.3087	−	86.3087i	0.157498	−	0.157498i
$549$		0			0
$550$	−248.015	+	88.6413i	−0.450936	+	0.161166i
$551$	8.83316	+	15.2995i	0.0160311	+	0.0277668i
$552$		0			0
$553$	12.9958	+	48.5009i	0.0235005	+	0.0877050i
$554$	1100.17	+	635.186i	1.98588	+	1.14655i
$555$		0			0
$556$	245.313	+	424.895i	0.441211	+	0.764200i
$557$	−214.091	−	214.091i	−0.384364	−	0.384364i	0.488308	−	0.872672i	$-0.337614\pi$
$557$	−214.091	−	214.091i	−0.384364	−	0.384364i	−0.872672	+	0.488308i	$0.837614\pi$
$558$		0			0
$559$			470.120i			0.841003i
$560$	46.9431	−	14.6513i	0.0838270	−	0.0261630i
$561$		0			0
$562$	1132.65	−	303.492i	2.01539	−	0.540021i
$563$	−245.972	−	917.982i	−0.436896	−	1.63052i	−0.736488	−	0.676451i	$-0.763517\pi$
$563$	−245.972	−	917.982i	−0.436896	−	1.63052i	0.299592	−	0.954067i	$-0.403149\pi$
$564$		0			0
$565$	−30.2495	−	96.9203i	−0.0535390	−	0.171540i
$566$	−343.464			−0.606827
$567$		0			0
$568$	−287.283	+	287.283i	−0.505779	+	0.505779i
$569$	841.916	−	486.081i	1.47964	−	0.854272i	0.479908	−	0.877319i	$-0.340670\pi$
$569$	841.916	−	486.081i	1.47964	−	0.854272i	0.999734	+	0.0230473i	$0.00733683\pi$
$570$		0			0
$571$	462.015	−	800.233i	0.809133	−	1.40146i	−0.104333	−	0.994542i	$-0.533271\pi$
$571$	462.015	−	800.233i	0.809133	−	1.40146i	0.913465	−	0.406917i	$-0.133396\pi$
$572$	281.953	−	75.5491i	0.492925	−	0.132079i
$573$		0			0
$574$	−160.285	+	92.5403i	−0.279241	+	0.161220i
$575$	−195.732	−	547.650i	−0.340404	−	0.952436i
$576$		0			0
$577$	−497.879	−	497.879i	−0.862874	−	0.862874i	0.128797	−	0.991671i	$-0.458889\pi$
$577$	−497.879	−	497.879i	−0.862874	−	0.862874i	−0.991671	+	0.128797i	$0.958889\pi$
$578$	−835.555	−	223.886i	−1.44560	−	0.387346i
$579$		0			0
$580$	25.1551	−	1.02508i	0.0433709	−	0.00176738i
$581$	30.6515	−	53.0900i	0.0527565	−	0.0913770i
$582$		0			0
$583$	131.262	+	35.1717i	0.225150	+	0.0603288i
$584$		−	336.186i		−	0.575661i
$585$		0			0
$586$	1052.59			1.79624
$587$	−107.166	+	399.949i	−0.182566	+	0.681345i	0.812573	+	0.582860i	$0.198066\pi$
$587$	−107.166	+	399.949i	−0.182566	+	0.681345i	−0.995139	+	0.0984849i	$0.968600\pi$
$588$		0			0
$589$	−335.125	−	193.485i	−0.568973	−	0.328497i
$590$	1193.40	−	1294.79i	2.02270	−	2.19456i
$591$		0			0
$592$	66.8144	−	249.355i	0.112862	−	0.421207i
$593$	−451.258	+	451.258i	−0.760974	+	0.760974i	−0.976498	−	0.215524i	$-0.930854\pi$
$593$	−451.258	+	451.258i	−0.760974	+	0.760974i	0.215524	+	0.976498i	$0.430854\pi$
$594$		0			0
$595$	−32.4745	+	20.5561i	−0.0545790	+	0.0345481i
$596$	−351.421	−	608.679i	−0.589633	−	1.02127i
$597$		0			0
$598$	279.943	+	1044.76i	0.468131	+	1.74709i
$599$	28.4560	+	16.4291i	0.0475058	+	0.0274275i	0.523565	−	0.851986i	$-0.324602\pi$
$599$	28.4560	+	16.4291i	0.0475058	+	0.0274275i	−0.476059	+	0.879413i	$0.657935\pi$
$600$		0			0
$601$	92.2418	+	159.768i	0.153481	+	0.265836i	0.932505	−	0.361158i	$-0.117618\pi$
$601$	92.2418	+	159.768i	0.153481	+	0.265836i	−0.779024	+	0.626994i	$0.784285\pi$
$602$	−145.081	−	145.081i	−0.240998	−	0.240998i
$603$		0			0
$604$		−	855.171i		−	1.41585i
$605$	254.885	−	486.176i	0.421298	−	0.803597i
$606$		0			0
$607$	−186.311	+	49.9219i	−0.306938	+	0.0822437i	−0.409000	−	0.912534i	$-0.634122\pi$
$607$	−186.311	+	49.9219i	−0.306938	+	0.0822437i	0.102062	+	0.994778i	$0.467456\pi$
$608$	208.884	+	779.565i	0.343559	+	1.28218i
$609$		0			0
$610$	−1412.95	+	440.993i	−2.31632	+	0.722940i
$611$	412.808			0.675627
$612$		0			0
$613$	−12.7128	+	12.7128i	−0.0207386	+	0.0207386i	−0.717400	−	0.696661i	$-0.754668\pi$
$613$	−12.7128	+	12.7128i	−0.0207386	+	0.0207386i	0.696661	+	0.717400i	$0.254668\pi$
$614$	651.102	−	375.914i	1.06043	−	0.612237i
$615$		0			0
$616$	−20.5051	+	35.5159i	−0.0332875	+	0.0576556i
$617$	−544.705	+	145.953i	−0.882828	+	0.236553i	−0.671627	−	0.740890i	$-0.734404\pi$
$617$	−544.705	+	145.953i	−0.882828	+	0.236553i	−0.211201	+	0.977443i	$0.567737\pi$
$618$		0			0
$619$	709.388	−	409.565i	1.14602	−	0.661656i	0.198108	−	0.980180i	$-0.436520\pi$
$619$	709.388	−	409.565i	1.14602	−	0.661656i	0.947915	+	0.318524i	$0.103187\pi$
$620$	−465.959	+	294.949i	−0.751547	+	0.475724i
$621$		0			0
$622$	−788.232	−	788.232i	−1.26725	−	1.26725i
$623$	−186.483	−	49.9681i	−0.299331	−	0.0802056i
$624$		0			0
$625$	616.725	−	101.370i	0.986759	−	0.162192i
$626$	−338.992	+	587.152i	−0.541521	+	0.937942i
$627$		0			0
$628$	412.146	+	110.434i	0.656283	+	0.175851i
$629$			201.757i			0.320759i
$630$		0			0
$631$	105.485			0.167171			0.0835853	−	0.996501i	$-0.473363\pi$
$631$	105.485			0.167171			0.0835853	+	0.996501i	$0.473363\pi$
$632$	−37.8780	+	141.363i	−0.0599336	+	0.223675i
$633$		0			0
$634$	−1646.23	−	950.448i	−2.59657	−	1.49913i
$635$	−595.964	−	549.294i	−0.938526	−	0.865031i
$636$		0			0
$637$	171.342	−	639.458i	0.268983	−	1.00386i
$638$	6.35867	−	6.35867i	0.00996657	−	0.00996657i
$639$		0			0
$640$	827.580	+	185.994i	1.29309	+	0.290616i
$641$	82.3939	+	142.710i	0.128540	+	0.222637i	0.923111	−	0.384534i	$-0.125638\pi$
$641$	82.3939	+	142.710i	0.128540	+	0.222637i	−0.794571	+	0.607171i	$0.792304\pi$
$642$		0			0
$643$	−279.780	−	1044.15i	−0.435116	−	1.62388i	−0.740788	−	0.671739i	$-0.765548\pi$
$643$	−279.780	−	1044.15i	−0.435116	−	1.62388i	0.305672	−	0.952137i	$-0.401119\pi$
$644$	−243.616	−	140.652i	−0.378285	−	0.218403i
$645$		0			0
$646$	−122.091	−	211.467i	−0.188995	−	0.327349i
$647$	−321.287	−	321.287i	−0.496580	−	0.496580i	0.413792	−	0.910372i	$-0.364204\pi$
$647$	−321.287	−	321.287i	−0.496580	−	0.496580i	−0.910372	+	0.413792i	$0.864204\pi$
$648$		0			0
$649$		−	374.808i		−	0.577516i
$650$	−1158.52	+	94.5771i	−1.78234	+	0.145503i
$651$		0			0
$652$	−1526.17	+	408.935i	−2.34074	+	0.627201i
$653$	62.1595	+	231.982i	0.0951907	+	0.355256i	0.997048	−	0.0767769i	$-0.0244629\pi$
$653$	62.1595	+	231.982i	0.0951907	+	0.355256i	−0.901858	+	0.432033i	$0.857796\pi$
$654$		0			0
$655$	−60.6784	+	115.740i	−0.0926387	+	0.176702i
$656$	137.687			0.209888
$657$		0			0
$658$	−127.394	+	127.394i	−0.193608	+	0.193608i
$659$	−830.313	+	479.381i	−1.25996	+	0.727438i	−0.973066	−	0.230525i	$-0.925956\pi$
$659$	−830.313	+	479.381i	−1.25996	+	0.727438i	−0.286893	+	0.957963i	$0.592622\pi$
$660$		0			0
$661$	−198.196	+	343.286i	−0.299843	+	0.519344i	−0.976100	−	0.217322i	$-0.930268\pi$
$661$	−198.196	+	343.286i	−0.299843	+	0.519344i	0.676257	+	0.736666i	$0.263601\pi$
$662$	−1487.39	+	398.544i	−2.24681	+	0.602030i
$663$		0			0
$664$	154.738	−	89.3383i	0.233040	−	0.134546i
$665$	206.969	+	46.5153i	0.311232	+	0.0699478i
$666$		0			0
$667$	14.0408	+	14.0408i	0.0210507	+	0.0210507i
$668$	−781.925	−	209.516i	−1.17055	−	0.313647i
$669$		0			0
$670$	−49.7296	−	1220.35i	−0.0742233	−	1.82142i
$671$	−157.530	+	272.850i	−0.234769	+	0.406632i
$672$		0			0
$673$	−224.994	−	60.2870i	−0.334315	−	0.0895795i	0.0877564	−	0.996142i	$-0.472030\pi$
$673$	−224.994	−	60.2870i	−0.334315	−	0.0895795i	−0.422072	+	0.906562i	$0.638697\pi$
$674$			1300.10i			1.92894i
$675$		0			0
$676$	291.313			0.430937
$677$	−199.260	+	743.648i	−0.294328	+	1.09845i	0.647422	+	0.762132i	$0.275847\pi$
$677$	−199.260	+	743.648i	−0.294328	+	1.09845i	−0.941750	+	0.336315i	$0.890819\pi$
$678$		0			0
$679$	36.6444	+	21.1566i	0.0539681	+	0.0311585i
$680$	−111.928	+	4.56108i	−0.164599	+	0.00670747i
$681$		0			0
$682$	−50.9810	+	190.264i	−0.0747522	+	0.278979i
$683$	−786.590	+	786.590i	−1.15167	+	1.15167i	−0.165452	+	0.986218i	$0.552908\pi$
$683$	−786.590	+	786.590i	−1.15167	+	1.15167i	−0.986218	+	0.165452i	$0.947092\pi$
$684$		0			0
$685$	−22.6857	+	100.940i	−0.0331178	+	0.147357i
$686$	302.474	+	523.901i	0.440925	+	0.763704i
$687$		0			0
$688$	39.5050	+	147.435i	0.0574200	+	0.214294i
$689$	519.387	+	299.868i	0.753828	+	0.435223i
$690$		0			0
$691$	−178.439	−	309.066i	−0.258233	−	0.447273i	0.707535	−	0.706678i	$-0.249807\pi$
$691$	−178.439	−	309.066i	−0.258233	−	0.447273i	−0.965769	+	0.259405i	$0.916474\pi$
$692$	204.288	+	204.288i	0.295214	+	0.295214i
$693$		0			0
$694$		−	1424.06i		−	2.05196i
$695$	−368.310	−	193.092i	−0.529943	−	0.277831i
$696$		0			0
$697$	−103.942	+	27.8512i	−0.149128	+	0.0399586i
$698$	−467.423	−	1744.45i	−0.669661	−	2.49921i
$699$		0			0
$700$	195.661	−	230.447i	0.279516	−	0.329210i
$701$	−885.680			−1.26345			−0.631726	−	0.775192i	$-0.717653\pi$
$701$	−885.680			−1.26345			−0.631726	+	0.775192i	$0.717653\pi$
$702$		0			0
$703$	787.423	−	787.423i	1.12009	−	1.12009i
$704$	300.121	−	173.275i	0.426308	−	0.246129i
$705$		0			0
$706$	592.939	−	1027.00i	0.839857	−	1.45467i
$707$	−343.776	+	92.1146i	−0.486247	+	0.130289i
$708$		0			0
$709$	−633.107	+	365.524i	−0.892958	+	0.515549i	−0.874909	−	0.484288i	$-0.839079\pi$
$709$	−633.107	+	365.524i	−0.892958	+	0.515549i	−0.0180489	+	0.999837i	$0.505745\pi$
$710$	234.565	−	1043.70i	0.330374	−	1.46999i
$711$		0			0
$712$	−397.893	−	397.893i	−0.558839	−	0.558839i
$713$	−420.128	−	112.573i	−0.589240	−	0.157886i
$714$		0			0
$715$	−167.681	+	181.927i	−0.234518	+	0.254444i
$716$	541.856	−	938.522i	0.756782	−	1.31078i
$717$		0			0
$718$	657.265	+	176.113i	0.915410	+	0.245283i
$719$		−	629.271i		−	0.875204i	−0.899169	−	0.437602i	$-0.855828\pi$
$719$		−	629.271i		−	0.875204i	0.899169	−	0.437602i	$-0.144172\pi$
$720$		0			0
$721$	187.716			0.260356
$722$	−54.8548	+	204.721i	−0.0759762	+	0.283547i
$723$		0			0
$724$	110.999	+	64.0852i	0.153313	+	0.0885155i
$725$	−17.5510	+	12.1379i	−0.0242082	+	0.0167420i
$726$		0			0
$727$	−5.81028	+	21.6843i	−0.00799213	+	0.0298270i	−0.969807	−	0.243875i	$-0.921581\pi$
$727$	−5.81028	+	21.6843i	−0.00799213	+	0.0298270i	0.961815	+	0.273702i	$0.0882481\pi$
$728$	−127.980	+	127.980i	−0.175796	+	0.175796i
$729$		0			0
$730$	473.434	+	747.929i	0.648539	+	1.02456i
$731$	−59.6459	−	103.310i	−0.0815950	−	0.141327i
$732$		0			0
$733$	−143.935	−	537.172i	−0.196364	−	0.732840i	−0.991910	−	0.126947i	$-0.959482\pi$
$733$	−143.935	−	537.172i	−0.196364	−	0.732840i	0.795546	−	0.605894i	$-0.207184\pi$
$734$	926.773	+	535.073i	1.26263	+	0.728982i
$735$		0			0
$736$	453.565	+	785.598i	0.616257	+	1.06739i
$737$	−183.828	−	183.828i	−0.249427	−	0.249427i
$738$		0			0
$739$		−	192.334i		−	0.260262i	−0.991497	−	0.130131i	$-0.958460\pi$
$739$		−	192.334i		−	0.260262i	0.991497	−	0.130131i	$-0.0415398\pi$
$740$	−472.807	−	1514.88i	−0.638928	−	2.04714i
$741$		0			0
$742$	−252.825	+	67.7442i	−0.340734	+	0.0912995i
$743$	16.3619	+	61.0634i	0.0220214	+	0.0821850i	0.976062	−	0.217492i	$-0.0697877\pi$
$743$	16.3619	+	61.0634i	0.0220214	+	0.0821850i	−0.954041	+	0.299677i	$0.903121\pi$
$744$		0			0
$745$	527.619	+	276.613i	0.708214	+	0.371292i
$746$	−1469.25			−1.96951
$747$		0			0
$748$	−52.3745	+	52.3745i	−0.0700194	+	0.0700194i
$749$	−11.9061	+	6.87398i	−0.0158960	+	0.00917755i
$750$		0			0
$751$	−113.893	+	197.269i	−0.151656	+	0.262675i	−0.931836	−	0.362879i	$-0.881794\pi$
$751$	−113.893	+	197.269i	−0.151656	+	0.262675i	0.780181	+	0.625554i	$0.215127\pi$
$752$	129.461	−	34.6889i	0.172155	−	0.0461289i
$753$		0			0
$754$	34.3697	−	19.8434i	0.0455832	−	0.0263175i
$755$	387.682	+	612.459i	0.513486	+	0.811204i
$756$		0			0
$757$	−235.925	−	235.925i	−0.311658	−	0.311658i	0.533894	−	0.845552i	$-0.320728\pi$
$757$	−235.925	−	235.925i	−0.311658	−	0.311658i	−0.845552	+	0.533894i	$0.820728\pi$
$758$	−638.202	−	171.006i	−0.841955	−	0.225601i
$759$		0			0
$760$	454.635	+	419.033i	0.598204	+	0.551359i
$761$	−440.621	+	763.178i	−0.579003	+	1.00286i	0.416592	+	0.909094i	$0.363225\pi$
$761$	−440.621	+	763.178i	−0.579003	+	1.00286i	−0.995594	+	0.0937680i	$0.970109\pi$
$762$		0			0
$763$	−77.8216	−	20.8522i	−0.101994	−	0.0273293i
$764$			236.495i			0.309548i
$765$		0			0
$766$	−759.221			−0.991151
$767$	428.123	−	1597.78i	0.558179	−	2.08315i
$768$		0			0
$769$	1046.51	+	604.201i	1.36087	+	0.785697i	0.989739	−	0.142885i	$-0.0456378\pi$
$769$	1046.51	+	604.201i	1.36087	+	0.785697i	0.371128	+	0.928582i	$0.378971\pi$
$770$	−4.39655	−	107.890i	−0.00570981	−	0.140117i
$771$		0			0
$772$	167.477	−	625.033i	0.216939	−	0.809629i
$773$	815.226	−	815.226i	1.05463	−	1.05463i	0.0562070	−	0.998419i	$-0.482099\pi$
$773$	815.226	−	815.226i	1.05463	−	1.05463i	0.998419	−	0.0562070i	$-0.0179007\pi$
$774$		0			0
$775$	200.000	−	422.474i	0.258065	−	0.545128i
$776$	61.6640	+	106.805i	0.0794640	+	0.137636i
$777$		0			0
$778$	445.704	+	1663.39i	0.572884	+	2.13803i
$779$	514.366	+	296.969i	0.660290	+	0.381219i
$780$		0			0
$781$	−113.848	−	197.190i	−0.145772	−	0.252485i
$782$	−194.070	−	194.070i	−0.248172	−	0.248172i
$783$		0			0
$784$		−	214.939i		−	0.274157i
$785$	−345.236	+	107.751i	−0.439791	+	0.137262i
$786$		0			0
$787$	−1110.59	+	297.582i	−1.41117	+	0.378122i	−0.882343	−	0.470606i	$-0.844035\pi$
$787$	−1110.59	+	297.582i	−1.41117	+	0.378122i	−0.528829	+	0.848728i	$0.677369\pi$
$788$	−145.319	−	542.339i	−0.184415	−	0.688247i
$789$		0			0
$790$	−114.805	−	367.838i	−0.145323	−	0.465617i
$791$	41.6255			0.0526239
$792$		0			0
$793$	−983.201	+	983.201i	−1.23985	+	1.23985i
$794$	174.395	−	100.687i	0.219640	−	0.126809i
$795$		0			0
$796$	741.484	−	1284.29i	0.931512	−	1.61343i
$797$	425.130	−	113.913i	0.533413	−	0.142928i	0.0179491	−	0.999839i	$-0.494286\pi$
$797$	425.130	−	113.913i	0.533413	−	0.142928i	0.515464	+	0.856911i	$0.327620\pi$
$798$		0			0
$799$	−90.7153	+	52.3745i	−0.113536	+	0.0655501i
$800$	−917.991	+	328.093i	−1.14749	+	0.410116i
$801$		0			0
$802$	1157.54	+	1157.54i	1.44332	+	1.44332i
$803$	181.993	+	48.7649i	0.226641	+	0.0607283i
$804$		0			0
$805$	238.236	−	9.70819i	0.295945	−	0.0120599i
$806$	−434.656	+	752.846i	−0.539276	+	0.934053i
$807$		0			0
$808$	−1001.99	−	268.481i	−1.24008	−	0.332279i
$809$			150.000i			0.185414i	0.995693	+	0.0927070i	$0.0295520\pi$
$809$			150.000i			0.185414i	−0.995693	+	0.0927070i	$0.970448\pi$
$810$		0			0
$811$	−132.847			−0.163806			−0.0819032	−	0.996640i	$-0.526100\pi$
$811$	−132.847			−0.163806			−0.0819032	+	0.996640i	$0.526100\pi$
$812$	−2.67143	+	9.96990i	−0.00328993	+	0.0122782i
$813$		0			0
$814$	−490.896	−	283.419i	−0.603066	−	0.348180i
$815$	907.627	−	984.741i	1.11365	−	1.20827i
$816$		0			0
$817$	−170.412	+	635.988i	−0.208583	+	0.778443i
$818$	−772.232	+	772.232i	−0.944048	+	0.944048i
$819$		0			0
$820$	715.176	−	452.702i	0.872166	−	0.552075i
$821$	254.947	+	441.581i	0.310532	+	0.537857i	0.978478	−	0.206353i	$-0.0661595\pi$
$821$	254.947	+	441.581i	0.310532	+	0.537857i	−0.667946	+	0.744210i	$0.732826\pi$
$822$		0			0
$823$	109.943	+	410.312i	0.133588	+	0.498556i	1.00000		0.000773801i	$-0.000246309\pi$
$823$	109.943	+	410.312i	0.133588	+	0.498556i	−0.866412	+	0.499330i	$0.833580\pi$
$824$	473.825	+	273.563i	0.575030	+	0.331994i
$825$		0			0
$826$	360.959	+	625.200i	0.436997	+	0.756900i
$827$	1030.76	+	1030.76i	1.24638	+	1.24638i	0.957307	+	0.289073i	$0.0933469\pi$
$827$	1030.76	+	1030.76i	1.24638	+	1.24638i	0.289073	+	0.957307i	$0.406653\pi$
$828$		0			0
$829$			37.4235i			0.0451429i	0.999745	+	0.0225714i	$0.00718533\pi$
$829$			37.4235i			0.0451429i	−0.999745	+	0.0225714i	$0.992815\pi$
$830$	−218.443	+	416.665i	−0.263184	+	0.502006i
$831$		0			0
$832$	1477.31	−	395.845i	1.77562	−	0.475775i
$833$	43.4777	+	162.261i	0.0521941	+	0.194791i
$834$		0			0
$835$	654.982	−	204.425i	0.784410	−	0.244820i
$836$	408.817			0.489016
$837$		0			0
$838$	−1297.91	+	1297.91i	−1.54882	+	1.54882i
$839$	997.984	−	576.186i	1.18949	−	0.686754i	0.231301	−	0.972882i	$-0.425702\pi$
$839$	997.984	−	576.186i	1.18949	−	0.686754i	0.958191	+	0.286129i	$0.0923685\pi$
$840$		0			0
$841$	−420.136	+	727.696i	−0.499567	+	0.865275i
$842$	−647.778	+	173.572i	−0.769333	+	0.206142i
$843$		0			0
$844$	1352.71	−	780.989i	1.60274	−	0.925342i
$845$	−208.633	+	132.064i	−0.246903	+	0.156288i
$846$		0			0
$847$	159.136	+	159.136i	0.187882	+	0.187882i
$848$	188.084	+	50.3968i	0.221797	+	0.0594302i
$849$		0			0
$850$	242.587	−	167.769i	0.285397	−	0.197375i
$851$	625.828	−	1083.97i	0.735403	−	1.27375i
$852$		0			0
$853$	−948.800	−	254.230i	−1.11231	−	0.298042i	−0.344542	−	0.938771i	$-0.611966\pi$
$853$	−948.800	−	254.230i	−1.11231	−	0.298042i	−0.767768	+	0.640728i	$0.778632\pi$
$854$		−	606.838i		−	0.710583i
$855$		0			0
$856$	−40.0704			−0.0468112
$857$	−152.697	+	569.873i	−0.178176	+	0.664963i	0.817813	+	0.575485i	$0.195187\pi$
$857$	−152.697	+	569.873i	−0.178176	+	0.664963i	−0.995989	+	0.0894780i	$0.971480\pi$
$858$		0			0
$859$	−421.639	−	243.434i	−0.490849	−	0.283392i	0.234077	−	0.972218i	$-0.424793\pi$
$859$	−421.639	−	243.434i	−0.490849	−	0.283392i	−0.724927	+	0.688826i	$0.758126\pi$
$860$	689.949	+	635.920i	0.802267	+	0.739442i
$861$		0			0
$862$	−152.573	+	569.411i	−0.176999	+	0.660570i
$863$	411.319	−	411.319i	0.476615	−	0.476615i	−0.427432	−	0.904047i	$-0.640582\pi$
$863$	411.319	−	411.319i	0.476615	−	0.476615i	0.904047	+	0.427432i	$0.140582\pi$
$864$		0			0
$865$	−238.919	−	53.6959i	−0.276207	−	0.0620762i
$866$	−344.497	−	596.687i	−0.397803	−	0.689015i
$867$		0			0
$868$	−58.5159	−	218.384i	−0.0674146	−	0.251595i
$869$	−71.0318	−	41.0102i	−0.0817397	−	0.0471924i
$870$		0			0
$871$	−573.666	−	993.619i	−0.658630	−	1.14078i
$872$	−166.045	−	166.045i	−0.190419	−	0.190419i
$873$		0			0
$874$			1514.85i			1.73323i
$875$	−35.6585	+	253.743i	−0.0407526	+	0.289992i
$876$		0			0
$877$	−454.259	+	121.718i	−0.517969	+	0.138789i	−0.508327	−	0.861164i	$-0.669736\pi$
$877$	−454.259	+	121.718i	−0.517969	+	0.138789i	−0.00964182	+	0.999954i	$0.503069\pi$
$878$	205.963	+	768.665i	0.234582	+	0.875472i
$879$		0			0
$880$	−37.2987	+	71.1447i	−0.0423849	+	0.0808463i
$881$	−533.151			−0.605166			−0.302583	−	0.953123i	$-0.597849\pi$
$881$	−533.151			−0.605166			−0.302583	+	0.953123i	$0.597849\pi$
$882$		0			0
$883$	−745.939	+	745.939i	−0.844778	+	0.844778i	−0.989476	−	0.144698i	$-0.953779\pi$
$883$	−745.939	+	745.939i	−0.844778	+	0.844778i	0.144698	+	0.989476i	$0.453779\pi$
$884$	−283.093	+	163.444i	−0.320241	+	0.184891i
$885$		0			0
$886$	−936.908	+	1622.77i	−1.05746	+	1.83157i
$887$	−527.568	+	141.361i	−0.594778	+	0.159370i	−0.543636	−	0.839321i	$-0.682953\pi$
$887$	−527.568	+	141.361i	−0.594778	+	0.159370i	−0.0511420	+	0.998691i	$0.516286\pi$
$888$		0			0
$889$	287.766	−	166.142i	0.323696	−	0.186886i
$890$	1445.54	+	324.879i	1.62421	+	0.365032i
$891$		0			0
$892$	−197.197	−	197.197i	−0.221073	−	0.221073i
$893$	558.455	+	149.638i	0.625369	+	0.167567i
$894$		0			0
$895$	37.4005	+	917.797i	0.0417883	+	1.02547i
$896$	−173.876	+	301.163i	−0.194058	+	0.336119i
$897$		0			0
$898$	−905.363	−	242.591i	−1.00820	−	0.270146i
$899$			15.9592i			0.0177521i
$900$		0			0
$901$	−152.182			−0.168903
$902$	78.2480	−	292.026i	0.0867495	−	0.323753i
$903$		0			0
$904$	105.069	+	60.6617i	0.116227	+	0.0671037i
$905$	−108.548	+	4.42335i	−0.119942	+	0.00488768i
$906$		0			0
$907$	−346.751	+	1294.09i	−0.382306	+	1.42678i	0.460065	+	0.887885i	$0.347826\pi$
$907$	−346.751	+	1294.09i	−0.382306	+	1.42678i	−0.842371	+	0.538899i	$0.818841\pi$
$908$	−124.890	+	124.890i	−0.137544	+	0.137544i
$909$		0			0
$910$	104.495	−	464.949i	0.114830	−	0.510933i
$911$	−574.681	−	995.377i	−0.630824	−	1.09262i	−0.987383	−	0.158347i	$-0.949383\pi$
$911$	−574.681	−	995.377i	−0.630824	−	1.09262i	0.356559	−	0.934273i	$-0.383950\pi$
$912$		0			0
$913$	25.9176	+	96.7258i	0.0283873	+	0.105943i
$914$	−1101.09	−	635.714i	−1.20469	−	0.695530i
$915$		0			0
$916$	−719.080	−	1245.48i	−0.785021	−	1.35970i
$917$	−37.8842	−	37.8842i	−0.0413132	−	0.0413132i
$918$		0			0
$919$			412.577i			0.448941i	0.974481	+	0.224470i	$0.0720652\pi$
$919$			412.577i			0.448941i	−0.974481	+	0.224470i	$0.927935\pi$
$920$	615.492	+	322.681i	0.669013	+	0.350741i
$921$		0			0
$922$	1600.43	−	428.833i	1.73582	−	0.465112i
$923$	−260.085	−	970.650i	−0.281782	−	1.05163i
$924$		0			0
$925$	1025.37	+	870.592i	1.10851	+	0.941180i
$926$	1493.70			1.61307
$927$		0			0
$928$	23.5357	−	23.5357i	0.0253618	−	0.0253618i
$929$	131.382	−	75.8536i	0.141423	−	0.0816508i	−0.427619	−	0.903959i	$-0.640647\pi$
$929$	131.382	−	75.8536i	0.141423	−	0.0816508i	0.569042	+	0.822308i	$0.307314\pi$
$930$		0			0
$931$	463.590	−	802.962i	0.497949	−	0.862473i
$932$	1303.10	−	349.164i	1.39817	−	0.374640i
$933$		0			0
$934$	−1883.31	+	1087.33i	−2.01639	+	1.16416i
$935$	13.7663	−	61.2531i	0.0147233	−	0.0655113i
$936$		0			0
$937$	662.090	+	662.090i	0.706606	+	0.706606i	0.965820	−	0.259214i	$-0.0834635\pi$
$937$	662.090	+	662.090i	0.706606	+	0.706606i	−0.259214	+	0.965820i	$0.583463\pi$
$938$	483.669	+	129.599i	0.515639	+	0.138165i
$939$		0			0
$940$	558.395	−	605.838i	0.594037	−	0.644508i
$941$	−766.885	+	1328.28i	−0.814969	+	1.41157i	0.0943819	+	0.995536i	$0.469913\pi$
$941$	−766.885	+	1328.28i	−0.814969	+	1.41157i	−0.909350	+	0.416031i	$0.863421\pi$
$942$		0			0
$943$	644.832	+	172.782i	0.683809	+	0.183226i
$944$		−	537.056i		−	0.568915i
$945$		0			0
$946$	335.151			0.354282
$947$	−429.417	+	1602.61i	−0.453450	+	1.69230i	0.239155	+	0.970982i	$0.423130\pi$
$947$	−429.417	+	1602.61i	−0.453450	+	1.69230i	−0.692605	+	0.721317i	$0.743537\pi$
$948$		0			0
$949$	720.120	+	415.762i	0.758820	+	0.438105i
$950$	−1601.55	−	292.002i	−1.68584	−	0.307371i
$951$		0			0
$952$	11.8865	−	44.3610i	0.0124858	−	0.0465977i
$953$	145.501	−	145.501i	0.152676	−	0.152676i	−0.626636	−	0.779312i	$-0.715569\pi$
$953$	145.501	−	145.501i	0.152676	−	0.152676i	0.779312	+	0.626636i	$0.215569\pi$
$954$		0			0
$955$	−107.212	−	169.373i	−0.112264	−	0.177354i
$956$	962.130	+	1666.46i	1.00641	+	1.74316i
$957$		0			0
$958$	−150.606	−	562.071i	−0.157209	−	0.586713i
$959$	−36.7327	−	21.2077i	−0.0383032	−	0.0221143i
$960$		0			0
$961$	305.712	+	529.509i	0.318119	+	0.550998i
$962$	−1768.92	−	1768.92i	−1.83879	−	1.83879i
$963$		0			0
$964$		−	787.959i		−	0.817385i
$965$	163.407	+	523.562i	0.169334	+	0.542551i
$966$		0			0
$967$	−1573.24	+	421.548i	−1.62693	+	0.435934i	−0.953026	−	0.302888i	$-0.902049\pi$
$967$	−1573.24	+	421.548i	−1.62693	+	0.435934i	−0.673901	+	0.738822i	$0.735382\pi$
$968$	169.772	+	633.597i	0.175384	+	0.654542i
$969$		0			0
$970$	−287.595	−	150.776i	−0.296490	−	0.155439i
$971$	−72.4383			−0.0746017			−0.0373009	−	0.999304i	$-0.511876\pi$
$971$	−72.4383			−0.0746017			−0.0373009	+	0.999304i	$0.511876\pi$
$972$		0			0
$973$	120.556	−	120.556i	0.123901	−	0.123901i
$974$	−465.033	+	268.487i	−0.477447	+	0.275654i
$975$		0			0
$976$	−225.722	+	390.962i	−0.231272	+	0.400576i
$977$	964.876	−	258.538i	0.987591	−	0.264624i	0.271352	−	0.962480i	$-0.412529\pi$
$977$	964.876	−	258.538i	0.987591	−	0.264624i	0.716238	+	0.697856i	$0.245862\pi$
$978$		0			0
$979$	273.113	−	157.682i	0.278972	−	0.161065i
$980$	−706.699	−	1116.44i	−0.721122	−	1.13923i
$981$		0			0
$982$	235.116	+	235.116i	0.239425	+	0.239425i
$983$	−183.953	−	49.2900i	−0.187134	−	0.0501424i	0.164035	−	0.986455i	$-0.447549\pi$
$983$	−183.953	−	49.2900i	−0.187134	−	0.0501424i	−0.351169	+	0.936312i	$0.614216\pi$
$984$		0			0
$985$	349.938	+	322.535i	0.355267	+	0.327446i
$986$	−5.03520	+	8.72123i	−0.00510670	+	0.00884506i
$987$		0			0
$988$	1742.76	+	466.970i	1.76392	+	0.472642i
$989$			740.059i			0.748290i
$990$		0			0
$991$	−1131.94			−1.14222			−0.571109	−	0.820874i	$-0.693487\pi$
$991$	−1131.94			−1.14222			−0.571109	+	0.820874i	$0.693487\pi$
$992$	−188.699	+	704.233i	−0.190221	+	0.709913i
$993$		0			0
$994$	379.809	+	219.283i	0.382101	+	0.220606i
$995$	51.1794	+	1255.93i	0.0514366	+	1.26224i
$996$		0			0
$997$	−408.216	+	1523.48i	−0.409444	+	1.52807i	0.386265	+	0.922388i	$0.373765\pi$
$997$	−408.216	+	1523.48i	−0.409444	+	1.52807i	−0.795709	+	0.605679i	$0.792902\pi$
$998$	1645.39	−	1645.39i	1.64868	−	1.64868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.f.352.2		8
3.2	odd	2		405.3.l.h.352.1		8
5.3	odd	4	inner	405.3.l.f.28.1		8
9.2	odd	6		405.3.l.h.217.2		8
9.4	even	3		45.3.g.b.37.2		4
9.5	odd	6		15.3.f.a.7.1	✓	4
9.7	even	3	inner	405.3.l.f.217.1		8
15.8	even	4		405.3.l.h.28.2		8
36.23	even	6		240.3.bg.a.97.1		4
36.31	odd	6		720.3.bh.k.577.1		4
45.4	even	6		225.3.g.a.82.1		4
45.13	odd	12		45.3.g.b.28.2		4
45.14	odd	6		75.3.f.c.7.2		4
45.22	odd	12		225.3.g.a.118.1		4
45.23	even	12		15.3.f.a.13.1	yes	4
45.32	even	12		75.3.f.c.43.2		4
45.38	even	12		405.3.l.h.298.1		8
45.43	odd	12	inner	405.3.l.f.298.2		8
72.5	odd	6		960.3.bg.i.577.1		4
72.59	even	6		960.3.bg.h.577.2		4
180.23	odd	12		240.3.bg.a.193.1		4
180.59	even	6		1200.3.bg.k.1057.2		4
180.103	even	12		720.3.bh.k.433.1		4
180.167	odd	12		1200.3.bg.k.193.2		4
360.203	odd	12		960.3.bg.h.193.2		4
360.293	even	12		960.3.bg.i.193.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	9.5	odd	6
15.3.f.a.13.1	yes	4	45.23	even	12
45.3.g.b.28.2		4	45.13	odd	12
45.3.g.b.37.2		4	9.4	even	3
75.3.f.c.7.2		4	45.14	odd	6
75.3.f.c.43.2		4	45.32	even	12
225.3.g.a.82.1		4	45.4	even	6
225.3.g.a.118.1		4	45.22	odd	12
240.3.bg.a.97.1		4	36.23	even	6
240.3.bg.a.193.1		4	180.23	odd	12
405.3.l.f.28.1		8	5.3	odd	4	inner
405.3.l.f.217.1		8	9.7	even	3	inner
405.3.l.f.298.2		8	45.43	odd	12	inner
405.3.l.f.352.2		8	1.1	even	1	trivial
405.3.l.h.28.2		8	15.8	even	4
405.3.l.h.217.2		8	9.2	odd	6
405.3.l.h.298.1		8	45.38	even	12
405.3.l.h.352.1		8	3.2	odd	2
720.3.bh.k.433.1		4	180.103	even	12
720.3.bh.k.577.1		4	36.31	odd	6
960.3.bg.h.193.2		4	360.203	odd	12
960.3.bg.h.577.2		4	72.59	even	6
960.3.bg.i.193.1		4	360.293	even	12
960.3.bg.i.577.1		4	72.5	odd	6
1200.3.bg.k.193.2		4	180.167	odd	12
1200.3.bg.k.1057.2		4	180.59	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.814313 - 3.03906i) q^{2} +(-5.10867 - 2.94949i) q^{4} +(4.99585 - 0.203583i) q^{5} +(-0.530550 + 1.98004i) q^{7} +(-4.22474 + 4.22474i) q^{8} +O(q^{10})\)	\(q+(0.814313 - 3.03906i) q^{2} +(-5.10867 - 2.94949i) q^{4} +(4.99585 - 0.203583i) q^{5} +(-0.530550 + 1.98004i) q^{7} +(-4.22474 + 4.22474i) q^{8} +(3.44949 - 15.3485i) q^{10} +(-1.67423 - 2.89986i) q^{11} +(-3.82478 - 14.2743i) q^{13} +(5.58542 + 3.22474i) q^{14} +(-2.39898 - 4.15515i) q^{16} +(2.65153 + 2.65153i) q^{17} -20.6969i q^{19} +(-26.1226 - 13.6952i) q^{20} +(-10.1762 + 2.72670i) q^{22} +(-6.02093 - 22.4704i) q^{23} +(24.9171 - 2.03414i) q^{25} -46.4949 q^{26} +(8.55051 - 8.55051i) q^{28} +(-0.739215 + 0.426786i) q^{29} +(9.34847 - 16.1920i) q^{31} +(-37.6657 + 10.0925i) q^{32} +(10.2173 - 5.89898i) q^{34} +(-2.24745 + 10.0000i) q^{35} +(38.0454 + 38.0454i) q^{37} +(-62.8992 - 16.8538i) q^{38} +(-20.2461 + 21.9663i) q^{40} +(-14.3485 + 24.8523i) q^{41} +(-30.7286 - 8.23370i) q^{43} +19.7526i q^{44} -73.1918 q^{46} +(-7.22994 + 26.9825i) q^{47} +(38.7962 + 22.3990i) q^{49} +(14.1085 - 77.3810i) q^{50} +(-22.5623 + 84.2036i) q^{52} +(-28.6969 + 28.6969i) q^{53} +(-8.95459 - 14.1464i) q^{55} +(-6.12372 - 10.6066i) q^{56} +(0.695075 + 2.59405i) q^{58} +(96.9378 + 55.9671i) q^{59} +(-47.0454 - 81.4850i) q^{61} +(-41.5959 - 41.5959i) q^{62} +103.495i q^{64} +(-22.0140 - 70.5335i) q^{65} +(74.9934 - 20.0944i) q^{67} +(-5.72512 - 21.3664i) q^{68} +(28.5605 + 14.9733i) q^{70} +68.0000 q^{71} +(-39.7878 + 39.7878i) q^{73} +(146.603 - 84.6413i) q^{74} +(-61.0454 + 105.734i) q^{76} +(6.63010 - 1.77653i) q^{77} +(21.2132 - 12.2474i) q^{79} +(-12.8309 - 20.2702i) q^{80} +(63.8434 + 63.8434i) q^{82} +(-28.8866 - 7.74013i) q^{83} +(13.7865 + 12.7069i) q^{85} +(-50.0454 + 86.6812i) q^{86} +(19.3244 + 5.17795i) q^{88} +94.1816i q^{89} +30.2929 q^{91} +(-35.5173 + 132.553i) q^{92} +(76.1139 + 43.9444i) q^{94} +(-4.21354 - 103.399i) q^{95} +(5.34248 - 19.9384i) q^{97} +(99.6640 - 99.6640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 8 q - 4 q^{2} - 4 q^{5} - 4 q^{7} - 24 q^{8} + 8 q^{10} + 16 q^{11} + 32 q^{13} + 20 q^{16} + 80 q^{17} - 36 q^{20} - 20 q^{22} + 56 q^{23} - 16 q^{25} - 176 q^{26} + 88 q^{28} + 16 q^{31} - 76 q^{32} + 80 q^{35} + 128 q^{37} - 96 q^{38} - 48 q^{40} - 56 q^{41} + 8 q^{43} - 272 q^{46} + 128 q^{47} + 164 q^{50} + 80 q^{52} - 112 q^{53} - 248 q^{55} + 12 q^{58} - 200 q^{61} - 176 q^{62} - 112 q^{65} + 200 q^{67} - 104 q^{68} + 60 q^{70} + 544 q^{71} + 152 q^{73} - 312 q^{76} + 88 q^{77} - 328 q^{80} + 256 q^{82} - 16 q^{83} - 232 q^{85} - 224 q^{86} - 12 q^{88} - 32 q^{91} + 104 q^{92} + 144 q^{95} + 20 q^{97} + 376 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 - 24 * q^8 + 8 * q^10 + 16 * q^11 + 32 * q^13 + 20 * q^16 + 80 * q^17 - 36 * q^20 - 20 * q^22 + 56 * q^23 - 16 * q^25 - 176 * q^26 + 88 * q^28 + 16 * q^31 - 76 * q^32 + 80 * q^35 + 128 * q^37 - 96 * q^38 - 48 * q^40 - 56 * q^41 + 8 * q^43 - 272 * q^46 + 128 * q^47 + 164 * q^50 + 80 * q^52 - 112 * q^53 - 248 * q^55 + 12 * q^58 - 200 * q^61 - 176 * q^62 - 112 * q^65 + 200 * q^67 - 104 * q^68 + 60 * q^70 + 544 * q^71 + 152 * q^73 - 312 * q^76 + 88 * q^77 - 328 * q^80 + 256 * q^82 - 16 * q^83 - 232 * q^85 - 224 * q^86 - 12 * q^88 - 32 * q^91 + 104 * q^92 + 144 * q^95 + 20 * q^97 + 376 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more