LMFDB - Embedded newform 572.2.n.a.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			521.3
Root			$0.695167 + 0.505068i$ of defining polynomial
Character	$\chi$	$=$	572.521
Dual form			572.2.n.a.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.265530 - 0.817217i) q^{3} +(-1.45473 + 1.05692i) q^{5} +(0.157953 + 0.486129i) q^{7} +(1.82971 + 1.32936i) q^{9} +O(q^{10})$	\(q+(0.265530 - 0.817217i) q^{3} +(-1.45473 + 1.05692i) q^{5} +(0.157953 + 0.486129i) q^{7} +(1.82971 + 1.32936i) q^{9} +(-0.205493 + 3.31025i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(0.477461 + 1.46947i) q^{15} +(1.21420 - 0.882166i) q^{17} +(-1.42475 + 4.38494i) q^{19} +0.439214 q^{21} +2.15279 q^{23} +(-0.545937 + 1.68022i) q^{25} +(3.65772 - 2.65749i) q^{27} +(1.97602 + 6.08157i) q^{29} +(7.65739 + 5.56342i) q^{31} +(2.65063 + 1.04690i) q^{33} +(-0.743578 - 0.540241i) q^{35} +(-3.36735 - 10.3636i) q^{37} +(-0.695167 + 0.505068i) q^{39} +(-0.945604 + 2.91027i) q^{41} +5.55119 q^{43} -4.06676 q^{45} +(-2.36656 + 7.28353i) q^{47} +(5.45175 - 3.96093i) q^{49} +(-0.398516 - 1.22650i) q^{51} +(-4.43812 - 3.22448i) q^{53} +(-3.19974 - 5.03270i) q^{55} +(3.20514 + 2.32867i) q^{57} +(0.00952253 + 0.0293073i) q^{59} +(5.28529 - 3.83999i) q^{61} +(-0.357234 + 1.09945i) q^{63} +1.79814 q^{65} -6.32053 q^{67} +(0.571630 - 1.75929i) q^{69} +(-6.64470 + 4.82766i) q^{71} +(-3.55854 - 10.9521i) q^{73} +(1.22814 + 0.892298i) q^{75} +(-1.64167 + 0.422967i) q^{77} +(-10.3998 - 7.55588i) q^{79} +(0.896151 + 2.75807i) q^{81} +(-4.40791 + 3.20253i) q^{83} +(-0.833946 + 2.56662i) q^{85} +5.49466 q^{87} +13.5128 q^{89} +(0.157953 - 0.486129i) q^{91} +(6.57979 - 4.78050i) q^{93} +(-2.56191 - 7.88475i) q^{95} +(10.1099 + 7.34527i) q^{97} +(-4.77652 + 5.78364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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			0
$2$		0			0
$3$	0.265530	−	0.817217i	0.153304	−	0.471821i	−0.844681	−	0.535270i	$-0.820210\pi$
$3$	0.265530	−	0.817217i	0.153304	−	0.471821i	0.997985	+	0.0634489i	$0.0202100\pi$
$4$		0			0
$5$	−1.45473	+	1.05692i	−0.650574	+	0.472669i	−0.863467	−	0.504406i	$-0.831711\pi$
$5$	−1.45473	+	1.05692i	−0.650574	+	0.472669i	0.212893	+	0.977076i	$0.431711\pi$
$6$		0			0
$7$	0.157953	+	0.486129i	0.0597005	+	0.183739i	0.976459	−	0.215702i	$-0.0692040\pi$
$7$	0.157953	+	0.486129i	0.0597005	+	0.183739i	−0.916759	+	0.399442i	$0.869204\pi$
$8$		0			0
$9$	1.82971	+	1.32936i	0.609904	+	0.443121i
$10$		0			0
$11$	−0.205493	+	3.31025i	−0.0619585	+	0.998079i
$11$	−0.205493	+	3.31025i	−0.0619585	+	0.998079i
$12$		0			0
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$		0			0
$15$	0.477461	+	1.46947i	0.123280	+	0.379416i
$16$		0			0
$17$	1.21420	−	0.882166i	0.294486	−	0.213957i	−0.430725	−	0.902483i	$-0.641742\pi$
$17$	1.21420	−	0.882166i	0.294486	−	0.213957i	0.725211	+	0.688527i	$0.241742\pi$
$18$		0			0
$19$	−1.42475	+	4.38494i	−0.326861	+	1.00597i	0.643733	+	0.765251i	$0.277385\pi$
$19$	−1.42475	+	4.38494i	−0.326861	+	1.00597i	−0.970594	+	0.240724i	$0.922615\pi$
$20$		0			0
$21$	0.439214			0.0958444
$22$		0			0
$23$	2.15279			0.448887			0.224444	−	0.974487i	$-0.427944\pi$
$23$	2.15279			0.448887			0.224444	+	0.974487i	$0.427944\pi$
$24$		0			0
$25$	−0.545937	+	1.68022i	−0.109187	+	0.336044i
$26$		0			0
$27$	3.65772	−	2.65749i	0.703929	−	0.511435i
$28$		0			0
$29$	1.97602	+	6.08157i	0.366938	+	1.12932i	0.948759	+	0.316002i	$0.102340\pi$
$29$	1.97602	+	6.08157i	0.366938	+	1.12932i	−0.581821	+	0.813317i	$0.697660\pi$
$30$		0			0
$31$	7.65739	+	5.56342i	1.37531	+	0.999219i	0.997301	+	0.0734165i	$0.0233902\pi$
$31$	7.65739	+	5.56342i	1.37531	+	0.999219i	0.378006	+	0.925803i	$0.376610\pi$
$32$		0			0
$33$	2.65063	+	1.04690i	0.461416	+	0.182243i
$34$		0			0
$35$	−0.743578	−	0.540241i	−0.125688	−	0.0913174i
$36$		0			0
$37$	−3.36735	−	10.3636i	−0.553590	−	1.70377i	−0.699639	−	0.714496i	$-0.746656\pi$
$37$	−3.36735	−	10.3636i	−0.553590	−	1.70377i	0.146050	−	0.989277i	$-0.453344\pi$
$38$		0			0
$39$	−0.695167	+	0.505068i	−0.111316	+	0.0808756i
$40$		0			0
$41$	−0.945604	+	2.91027i	−0.147679	+	0.454508i	−0.997346	−	0.0728116i	$-0.976803\pi$
$41$	−0.945604	+	2.91027i	−0.147679	+	0.454508i	0.849667	+	0.527319i	$0.176803\pi$
$42$		0			0
$43$	5.55119			0.846548			0.423274	−	0.906002i	$-0.360881\pi$
$43$	5.55119			0.846548			0.423274	+	0.906002i	$0.360881\pi$
$44$		0			0
$45$	−4.06676			−0.606238
$46$		0			0
$47$	−2.36656	+	7.28353i	−0.345199	+	1.06241i	0.616279	+	0.787528i	$0.288640\pi$
$47$	−2.36656	+	7.28353i	−0.345199	+	1.06241i	−0.961477	+	0.274884i	$0.911360\pi$
$48$		0			0
$49$	5.45175	−	3.96093i	0.778821	−	0.565847i
$50$		0			0
$51$	−0.398516	−	1.22650i	−0.0558033	−	0.171745i
$52$		0			0
$53$	−4.43812	−	3.22448i	−0.609622	−	0.442916i	0.239659	−	0.970857i	$-0.422964\pi$
$53$	−4.43812	−	3.22448i	−0.609622	−	0.442916i	−0.849281	+	0.527941i	$0.822964\pi$
$54$		0			0
$55$	−3.19974	−	5.03270i	−0.431453	−	0.678610i
$56$		0			0
$57$	3.20514	+	2.32867i	0.424531	+	0.308440i
$58$		0			0
$59$	0.00952253	+	0.0293073i	0.00123973	+	0.00381549i	0.951674	−	0.307109i	$-0.0993615\pi$
$59$	0.00952253	+	0.0293073i	0.00123973	+	0.00381549i	−0.950435	+	0.310924i	$0.899361\pi$
$60$		0			0
$61$	5.28529	−	3.83999i	0.676713	−	0.491661i	−0.195553	−	0.980693i	$-0.562650\pi$
$61$	5.28529	−	3.83999i	0.676713	−	0.491661i	0.872265	+	0.489033i	$0.162650\pi$
$62$		0			0
$63$	−0.357234	+	1.09945i	−0.0450072	+	0.138518i
$64$		0			0
$65$	1.79814			0.223032
$66$		0			0
$67$	−6.32053			−0.772176			−0.386088	−	0.922462i	$-0.626174\pi$
$67$	−6.32053			−0.772176			−0.386088	+	0.922462i	$0.626174\pi$
$68$		0			0
$69$	0.571630	−	1.75929i	0.0688161	−	0.211794i
$70$		0			0
$71$	−6.64470	+	4.82766i	−0.788581	+	0.572938i	−0.907542	−	0.419961i	$-0.862044\pi$
$71$	−6.64470	+	4.82766i	−0.788581	+	0.572938i	0.118961	+	0.992899i	$0.462044\pi$
$72$		0			0
$73$	−3.55854	−	10.9521i	−0.416496	−	1.28184i	−0.910906	−	0.412613i	$-0.864616\pi$
$73$	−3.55854	−	10.9521i	−0.416496	−	1.28184i	0.494411	−	0.869229i	$-0.335384\pi$
$74$		0			0
$75$	1.22814	+	0.892298i	0.141814	+	0.103034i
$76$		0			0
$77$	−1.64167	+	0.422967i	−0.187085	+	0.0482016i
$78$		0			0
$79$	−10.3998	−	7.55588i	−1.17007	−	0.850102i	−0.179049	−	0.983840i	$-0.557302\pi$
$79$	−10.3998	−	7.55588i	−1.17007	−	0.850102i	−0.991017	+	0.133738i	$0.957302\pi$
$80$		0			0
$81$	0.896151	+	2.75807i	0.0995723	+	0.306452i
$82$		0			0
$83$	−4.40791	+	3.20253i	−0.483831	+	0.351524i	−0.802807	−	0.596239i	$-0.796661\pi$
$83$	−4.40791	+	3.20253i	−0.483831	+	0.351524i	0.318976	+	0.947763i	$0.396661\pi$
$84$		0			0
$85$	−0.833946	+	2.56662i	−0.0904541	+	0.278389i
$86$		0			0
$87$	5.49466			0.589089
$88$		0			0
$89$	13.5128			1.43235			0.716176	−	0.697920i	$-0.245891\pi$
$89$	13.5128			1.43235			0.716176	+	0.697920i	$0.245891\pi$
$90$		0			0
$91$	0.157953	−	0.486129i	0.0165579	−	0.0509601i
$92$		0			0
$93$	6.57979	−	4.78050i	0.682292	−	0.495714i
$94$		0			0
$95$	−2.56191	−	7.88475i	−0.262846	−	0.808958i
$96$		0			0
$97$	10.1099	+	7.34527i	1.02650	+	0.745799i	0.967606	−	0.252465i	$-0.0812411\pi$
$97$	10.1099	+	7.34527i	1.02650	+	0.745799i	0.0588986	+	0.998264i	$0.481241\pi$
$98$		0			0
$99$	−4.77652	+	5.78364i	−0.480059	+	0.581277i
$100$		0			0
$101$	−5.84664	−	4.24783i	−0.581763	−	0.422675i	0.257596	−	0.966253i	$-0.417069\pi$
$101$	−5.84664	−	4.24783i	−0.581763	−	0.422675i	−0.839359	+	0.543577i	$0.817069\pi$
$102$		0			0
$103$	−1.54173	−	4.74497i	−0.151911	−	0.467535i	0.845923	−	0.533304i	$-0.179050\pi$
$103$	−1.54173	−	4.74497i	−0.151911	−	0.467535i	−0.997835	+	0.0657690i	$0.979050\pi$
$104$		0			0
$105$	−0.638936	+	0.464214i	−0.0623538	+	0.0453027i
$106$		0			0
$107$	−5.90306	+	18.1678i	−0.570671	+	1.75634i	0.0797979	+	0.996811i	$0.474572\pi$
$107$	−5.90306	+	18.1678i	−0.570671	+	1.75634i	−0.650469	+	0.759533i	$0.725428\pi$
$108$		0			0
$109$	−15.2828			−1.46383			−0.731915	−	0.681396i	$-0.761373\pi$
$109$	−15.2828			−1.46383			−0.731915	+	0.681396i	$0.761373\pi$
$110$		0			0
$111$	−9.36349			−0.888743
$112$		0			0
$113$	1.43372	−	4.41253i	0.134873	−	0.415096i	−0.860697	−	0.509117i	$-0.829972\pi$
$113$	1.43372	−	4.41253i	0.134873	−	0.415096i	0.995570	+	0.0940209i	$0.0299720\pi$
$114$		0			0
$115$	−3.13172	+	2.27533i	−0.292034	+	0.212175i
$116$		0			0
$117$	−0.698888	−	2.15096i	−0.0646122	−	0.198856i
$118$		0			0
$119$	0.620632	+	0.450915i	0.0568932	+	0.0413354i
$120$		0			0
$121$	−10.9155	−	1.36047i	−0.992322	−	0.123679i
$122$		0			0
$123$	2.12724	+	1.54553i	0.191806	+	0.139356i
$124$		0			0
$125$	−3.75995	−	11.5719i	−0.336300	−	1.03503i
$126$		0			0
$127$	−3.00168	+	2.18085i	−0.266356	+	0.193519i	−0.712945	−	0.701220i	$-0.752639\pi$
$127$	−3.00168	+	2.18085i	−0.266356	+	0.193519i	0.446588	+	0.894740i	$0.352639\pi$
$128$		0			0
$129$	1.47401	−	4.53653i	0.129779	−	0.399419i
$130$		0			0
$131$	6.66043			0.581925			0.290962	−	0.956735i	$-0.406025\pi$
$131$	6.66043			0.581925			0.290962	+	0.956735i	$0.406025\pi$
$132$		0			0
$133$	−2.35669			−0.204351
$134$		0			0
$135$	−2.51223	+	7.73185i	−0.216218	+	0.665452i
$136$		0			0
$137$	17.0037	−	12.3539i	1.45273	−	1.05547i	0.467543	−	0.883970i	$-0.345139\pi$
$137$	17.0037	−	12.3539i	1.45273	−	1.05547i	0.985184	−	0.171498i	$-0.0548607\pi$
$138$		0			0
$139$	−3.29922	−	10.1540i	−0.279836	−	0.861248i	−0.987899	−	0.155098i	$-0.950431\pi$
$139$	−3.29922	−	10.1540i	−0.279836	−	0.861248i	0.708063	−	0.706150i	$-0.249569\pi$
$140$		0			0
$141$	5.32384	+	3.86799i	0.448348	+	0.325744i
$142$		0			0
$143$	2.11197	−	2.55726i	0.176611	−	0.213849i
$144$		0			0
$145$	−9.30230	−	6.75852i	−0.772514	−	0.561265i
$146$		0			0
$147$	−1.78934	−	5.50701i	−0.147582	−	0.454210i
$148$		0			0
$149$	−6.93669	+	5.03980i	−0.568276	+	0.412876i	−0.834478	−	0.551041i	$-0.814231\pi$
$149$	−6.93669	+	5.03980i	−0.568276	+	0.412876i	0.266203	+	0.963917i	$0.414231\pi$
$150$		0			0
$151$	6.90393	−	21.2481i	0.561834	−	1.72915i	−0.115342	−	0.993326i	$-0.536796\pi$
$151$	6.90393	−	21.2481i	0.561834	−	1.72915i	0.677176	−	0.735821i	$-0.263204\pi$
$152$		0			0
$153$	3.39435			0.274417
$154$		0			0
$155$	−17.0195			−1.36704
$156$		0			0
$157$	3.72211	−	11.4555i	0.297057	−	0.914246i	−0.685466	−	0.728104i	$-0.740402\pi$
$157$	3.72211	−	11.4555i	0.297057	−	0.914246i	0.982523	−	0.186142i	$-0.0595984\pi$
$158$		0			0
$159$	−3.81356	+	2.77071i	−0.302435	+	0.219732i
$160$		0			0
$161$	0.340039	+	1.04653i	0.0267988	+	0.0824782i
$162$		0			0
$163$	2.97916	+	2.16449i	0.233346	+	0.169536i	0.698314	−	0.715792i	$-0.253934\pi$
$163$	2.97916	+	2.16449i	0.233346	+	0.169536i	−0.464968	+	0.885328i	$0.653934\pi$
$164$		0			0
$165$	−4.96244	+	1.27855i	−0.386325	+	0.0995349i
$166$		0			0
$167$	4.43338	+	3.22104i	0.343065	+	0.249251i	0.745954	−	0.665998i	$-0.231994\pi$
$167$	4.43338	+	3.22104i	0.343065	+	0.249251i	−0.402889	+	0.915249i	$0.631994\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$		0			0
$171$	−8.43608	+	6.12917i	−0.645123	+	0.468709i
$172$		0			0
$173$	4.36494	−	13.4339i	0.331860	−	1.02136i	−0.636388	−	0.771369i	$-0.719572\pi$
$173$	4.36494	−	13.4339i	0.331860	−	1.02136i	0.968248	−	0.249992i	$-0.0804279\pi$
$174$		0			0
$175$	−0.903036			−0.0682631
$176$		0			0
$177$	0.0264790			0.00199028
$178$		0			0
$179$	−0.517331	+	1.59218i	−0.0386671	+	0.119005i	−0.968527	−	0.248909i	$-0.919928\pi$
$179$	−0.517331	+	1.59218i	−0.0386671	+	0.119005i	0.929860	+	0.367914i	$0.119928\pi$
$180$		0			0
$181$	16.6156	−	12.0719i	1.23503	−	0.897301i	0.237772	−	0.971321i	$-0.423583\pi$
$181$	16.6156	−	12.0719i	1.23503	−	0.897301i	0.997257	+	0.0740206i	$0.0235830\pi$
$182$		0			0
$183$	−1.73470	−	5.33887i	−0.128233	−	0.394661i
$184$		0			0
$185$	15.8521	+	11.5173i	1.16547	+	0.846765i
$186$		0			0
$187$	2.67068	+	4.20058i	0.195300	+	0.307177i
$188$		0			0
$189$	1.86963	+	1.35837i	0.135996	+	0.0988066i
$190$		0			0
$191$	−3.10017	−	9.54136i	−0.224321	−	0.690388i	−0.998360	−	0.0572505i	$-0.981767\pi$
$191$	−3.10017	−	9.54136i	−0.224321	−	0.690388i	0.774039	−	0.633138i	$-0.218233\pi$
$192$		0			0
$193$	−12.4041	+	9.01212i	−0.892868	+	0.648706i	−0.936624	−	0.350336i	$-0.886067\pi$
$193$	−12.4041	+	9.01212i	−0.892868	+	0.648706i	0.0437565	+	0.999042i	$0.486067\pi$
$194$		0			0
$195$	0.477461	−	1.46947i	0.0341917	−	0.105231i
$196$		0			0
$197$	4.86485			0.346606			0.173303	−	0.984869i	$-0.444556\pi$
$197$	4.86485			0.346606			0.173303	+	0.984869i	$0.444556\pi$
$198$		0			0
$199$	9.53526			0.675937			0.337968	−	0.941157i	$-0.390260\pi$
$199$	9.53526			0.675937			0.337968	+	0.941157i	$0.390260\pi$
$200$		0			0
$201$	−1.67829	+	5.16525i	−0.118378	+	0.364329i
$202$		0			0
$203$	−2.64431	+	1.92120i	−0.185594	+	0.134842i
$204$		0			0
$205$	−1.70033	−	5.23307i	−0.118756	−	0.365494i
$206$		0			0
$207$	3.93898	+	2.86184i	0.273778	+	0.198911i
$208$		0			0
$209$	−14.2225	−	5.61737i	−0.983790	−	0.388562i
$210$		0			0
$211$	17.1949	+	12.4928i	1.18375	+	0.860042i	0.992589	−	0.121518i	$-0.0387762\pi$
$211$	17.1949	+	12.4928i	1.18375	+	0.860042i	0.191157	+	0.981560i	$0.438776\pi$
$212$		0			0
$213$	2.18088	+	6.71206i	0.149431	+	0.459903i
$214$		0			0
$215$	−8.07546	+	5.86717i	−0.550742	+	0.400137i
$216$		0			0
$217$	−1.49503	+	4.60123i	−0.101489	+	0.312352i
$218$		0			0
$219$	−9.89512			−0.668650
$220$		0			0
$221$	−1.50083			−0.100957
$222$		0			0
$223$	3.67344	−	11.3057i	0.245992	−	0.757085i	−0.749480	−	0.662027i	$-0.769696\pi$
$223$	3.67344	−	11.3057i	0.245992	−	0.757085i	0.995472	−	0.0950578i	$-0.0303036\pi$
$224$		0			0
$225$	−3.23253	+	2.34857i	−0.215502	+	0.156571i
$226$		0			0
$227$	−2.35614	−	7.25146i	−0.156383	−	0.481296i	0.841916	−	0.539609i	$-0.181428\pi$
$227$	−2.35614	−	7.25146i	−0.156383	−	0.481296i	−0.998298	+	0.0583126i	$0.981428\pi$
$228$		0			0
$229$	1.30037	+	0.944772i	0.0859307	+	0.0624323i	0.629921	−	0.776659i	$-0.283087\pi$
$229$	1.30037	+	0.944772i	0.0859307	+	0.0624323i	−0.543990	+	0.839091i	$0.683087\pi$
$230$		0			0
$231$	−0.0902555	+	1.45391i	−0.00593838	+	0.0956602i
$232$		0			0
$233$	6.99351	+	5.08108i	0.458160	+	0.332873i	0.792809	−	0.609470i	$-0.208618\pi$
$233$	6.99351	+	5.08108i	0.458160	+	0.332873i	−0.334649	+	0.942343i	$0.608618\pi$
$234$		0			0
$235$	−4.25541	−	13.0968i	−0.277593	−	0.854342i
$236$		0			0
$237$	−8.93624	+	6.49256i	−0.580471	+	0.421737i
$238$		0			0
$239$	−6.58777	+	20.2751i	−0.426127	+	1.31149i	0.475783	+	0.879563i	$0.342165\pi$
$239$	−6.58777	+	20.2751i	−0.426127	+	1.31149i	−0.901911	+	0.431923i	$0.857835\pi$
$240$		0			0
$241$	7.94232			0.511610			0.255805	−	0.966728i	$-0.417660\pi$
$241$	7.94232			0.511610			0.255805	+	0.966728i	$0.417660\pi$
$242$		0			0
$243$	16.0555			1.02996
$244$		0			0
$245$	−3.74442	+	11.5241i	−0.239222	+	0.736250i
$246$		0			0
$247$	3.73005	−	2.71004i	0.237338	−	0.172436i
$248$		0			0
$249$	1.44673	+	4.45259i	0.0916830	+	0.282171i
$250$		0			0
$251$	18.3289	+	13.3168i	1.15691	+	0.840546i	0.989385	−	0.145321i	$-0.0464216\pi$
$251$	18.3289	+	13.3168i	1.15691	+	0.840546i	0.167528	+	0.985867i	$0.446422\pi$
$252$		0			0
$253$	−0.442383	+	7.12627i	−0.0278124	+	0.448025i
$254$		0			0
$255$	1.87605	+	1.36303i	0.117483	+	0.0853562i
$256$		0			0
$257$	2.15219	+	6.62376i	0.134250	+	0.413179i	0.995473	−	0.0950490i	$-0.0303008\pi$
$257$	2.15219	+	6.62376i	0.134250	+	0.413179i	−0.861223	+	0.508228i	$0.830301\pi$
$258$		0			0
$259$	4.50618	−	3.27393i	0.280001	−	0.203432i
$260$		0			0
$261$	−4.46907	+	13.7544i	−0.276628	+	0.851374i
$262$		0			0
$263$	15.4413			0.952153			0.476076	−	0.879404i	$-0.342059\pi$
$263$	15.4413			0.952153			0.476076	+	0.879404i	$0.342059\pi$
$264$		0			0
$265$	9.86427			0.605957
$266$		0			0
$267$	3.58805	−	11.0429i	0.219585	−	0.675813i
$268$		0			0
$269$	−9.49261	+	6.89678i	−0.578774	+	0.420504i	−0.838282	−	0.545237i	$-0.816440\pi$
$269$	−9.49261	+	6.89678i	−0.578774	+	0.420504i	0.259508	+	0.965741i	$0.416440\pi$
$270$		0			0
$271$	3.09948	+	9.53922i	0.188280	+	0.579467i	0.999989	−	0.00459500i	$-0.00146264\pi$
$271$	3.09948	+	9.53922i	0.188280	+	0.579467i	−0.811709	+	0.584062i	$0.801463\pi$
$272$		0			0
$273$	−0.355332	−	0.258164i	−0.0215056	−	0.0156248i
$274$		0			0
$275$	−5.44977	−	2.15246i	−0.328633	−	0.129798i
$276$		0			0
$277$	−22.8852	−	16.6270i	−1.37504	−	0.999022i	−0.997325	−	0.0730982i	$-0.976711\pi$
$277$	−22.8852	−	16.6270i	−1.37504	−	0.999022i	−0.377711	−	0.925924i	$-0.623289\pi$
$278$		0			0
$279$	6.61501	+	20.3589i	0.396030	+	1.21886i
$280$		0			0
$281$	9.73411	−	7.07225i	0.580689	−	0.421895i	−0.258284	−	0.966069i	$-0.583157\pi$
$281$	9.73411	−	7.07225i	0.580689	−	0.421895i	0.838972	+	0.544174i	$0.183157\pi$
$282$		0			0
$283$	−2.89193	+	8.90046i	−0.171908	+	0.529077i	−0.999479	−	0.0322836i	$-0.989722\pi$
$283$	−2.89193	+	8.90046i	−0.171908	+	0.529077i	0.827571	+	0.561361i	$0.189722\pi$
$284$		0			0
$285$	−7.12382			−0.421978
$286$		0			0
$287$	−1.56413			−0.0923274
$288$		0			0
$289$	−4.55723	+	14.0257i	−0.268072	+	0.825042i
$290$		0			0
$291$	8.68717	−	6.31160i	0.509251	−	0.369992i
$292$		0			0
$293$	4.03476	+	12.4177i	0.235713	+	0.725451i	0.997026	+	0.0770663i	$0.0245553\pi$
$293$	4.03476	+	12.4177i	0.235713	+	0.725451i	−0.761313	+	0.648385i	$0.775445\pi$
$294$		0			0
$295$	−0.0448282	−	0.0325696i	−0.00261000	−	0.00189627i
$296$		0			0
$297$	8.04533	+	12.6541i	0.466837	+	0.734265i
$298$		0			0
$299$	−1.74164	−	1.26538i	−0.100722	−	0.0731786i
$300$		0			0
$301$	0.876825	+	2.69859i	0.0505394	+	0.155544i
$302$		0			0
$303$	−5.02386	+	3.65005i	−0.288613	+	0.209690i
$304$		0			0
$305$	−3.63009	+	11.1723i	−0.207859	+	0.639723i
$306$		0			0
$307$	6.09130			0.347649			0.173825	−	0.984777i	$-0.444387\pi$
$307$	6.09130			0.347649			0.173825	+	0.984777i	$0.444387\pi$
$308$		0			0
$309$	−4.28705			−0.243881
$310$		0			0
$311$	7.92246	−	24.3828i	0.449241	−	1.38262i	−0.428523	−	0.903531i	$-0.640966\pi$
$311$	7.92246	−	24.3828i	0.449241	−	1.38262i	0.877765	−	0.479092i	$-0.159034\pi$
$312$		0			0
$313$	16.6718	−	12.1128i	0.942347	−	0.684655i	−0.00663721	−	0.999978i	$-0.502113\pi$
$313$	16.6718	−	12.1128i	0.942347	−	0.684655i	0.948985	+	0.315323i	$0.102113\pi$
$314$		0			0
$315$	−0.642357	−	1.97697i	−0.0361927	−	0.111390i
$316$		0			0
$317$	11.0368	+	8.01870i	0.619888	+	0.450375i	0.852882	−	0.522103i	$-0.174852\pi$
$317$	11.0368	+	8.01870i	0.619888	+	0.450375i	−0.232994	+	0.972478i	$0.574852\pi$
$318$		0			0
$319$	−20.5376	+	5.29141i	−1.14988	+	0.296262i
$320$		0			0
$321$	13.2796	+	9.64818i	0.741194	+	0.538509i
$322$		0			0
$323$	2.13831	+	6.58105i	0.118979	+	0.366180i
$324$		0			0
$325$	1.42928	−	1.03843i	0.0792822	−	0.0576019i
$326$		0			0
$327$	−4.05805	+	12.4894i	−0.224411	+	0.690665i
$328$		0			0
$329$	−3.91454			−0.215816
$330$		0			0
$331$	14.8453			0.815969			0.407985	−	0.912989i	$-0.366232\pi$
$331$	14.8453			0.815969			0.407985	+	0.912989i	$0.366232\pi$
$332$		0			0
$333$	7.61577	−	23.4389i	0.417342	−	1.28445i
$334$		0			0
$335$	9.19465	−	6.68030i	0.502357	−	0.364984i
$336$		0			0
$337$	−5.48230	−	16.8728i	−0.298640	−	0.919120i	−0.981974	−	0.189014i	$-0.939471\pi$
$337$	−5.48230	−	16.8728i	−0.298640	−	0.919120i	0.683334	−	0.730106i	$-0.260529\pi$
$338$		0			0
$339$	−3.22530	−	2.34332i	−0.175174	−	0.127272i
$340$		0			0
$341$	−19.9899	+	24.2046i	−1.08251	+	1.31076i
$342$		0			0
$343$	5.68132	+	4.12772i	0.306762	+	0.222876i
$344$		0			0
$345$	1.02787	+	3.16346i	0.0553387	+	0.170315i
$346$		0			0
$347$	−26.9720	+	19.5963i	−1.44793	+	1.05198i	−0.461622	+	0.887077i	$0.652732\pi$
$347$	−26.9720	+	19.5963i	−1.44793	+	1.05198i	−0.986309	+	0.164906i	$0.947268\pi$
$348$		0			0
$349$	0.271348	−	0.835125i	0.0145249	−	0.0447032i	−0.943531	−	0.331283i	$-0.892518\pi$
$349$	0.271348	−	0.835125i	0.0145249	−	0.0447032i	0.958056	+	0.286580i	$0.0925184\pi$
$350$		0			0
$351$	−4.52119			−0.241324
$352$		0			0
$353$	15.2870			0.813647			0.406824	−	0.913507i	$-0.366636\pi$
$353$	15.2870			0.813647			0.406824	+	0.913507i	$0.366636\pi$
$354$		0			0
$355$	4.56377	−	14.0459i	0.242220	−	0.745477i
$356$		0			0
$357$	0.533292	−	0.387460i	0.0282248	−	0.0205065i
$358$		0			0
$359$	−10.0697	−	30.9913i	−0.531458	−	1.63566i	−0.751180	−	0.660097i	$-0.770515\pi$
$359$	−10.0697	−	30.9913i	−0.531458	−	1.63566i	0.219722	−	0.975563i	$-0.429485\pi$
$360$		0			0
$361$	−1.82647	−	1.32701i	−0.0961300	−	0.0698426i
$362$		0			0
$363$	−4.01020	+	8.55913i	−0.210481	+	0.449238i
$364$		0			0
$365$	16.7522	+	12.1712i	0.876849	+	0.637068i
$366$		0			0
$367$	6.13655	+	18.8863i	0.320325	+	0.985859i	0.973507	+	0.228658i	$0.0734338\pi$
$367$	6.13655	+	18.8863i	0.320325	+	0.985859i	−0.653182	+	0.757201i	$0.726566\pi$
$368$		0			0
$369$	−5.59899	+	4.06790i	−0.291472	+	0.211767i
$370$		0			0
$371$	0.866500	−	2.66681i	0.0449864	−	0.138454i
$372$		0			0
$373$	−6.68029			−0.345892			−0.172946	−	0.984931i	$-0.555329\pi$
$373$	−6.68029			−0.345892			−0.172946	+	0.984931i	$0.555329\pi$
$374$		0			0
$375$	−10.4552			−0.539903
$376$		0			0
$377$	1.97602	−	6.08157i	0.101770	−	0.313217i
$378$		0			0
$379$	14.8164	−	10.7647i	0.761066	−	0.552947i	−0.138171	−	0.990408i	$-0.544122\pi$
$379$	14.8164	−	10.7647i	0.761066	−	0.552947i	0.899237	+	0.437462i	$0.144122\pi$
$380$		0			0
$381$	0.985192	+	3.03211i	0.0504729	+	0.155340i
$382$		0			0
$383$	7.14971	+	5.19457i	0.365333	+	0.265430i	0.755273	−	0.655410i	$-0.227504\pi$
$383$	7.14971	+	5.19457i	0.365333	+	0.265430i	−0.389940	+	0.920840i	$0.627504\pi$
$384$		0			0
$385$	1.94113	−	2.35041i	0.0989293	−	0.119788i
$386$		0			0
$387$	10.1571	+	7.37955i	0.516313	+	0.375124i
$388$		0			0
$389$	−6.89023	−	21.2060i	−0.349349	−	1.07518i	−0.959214	−	0.282680i	$-0.908777\pi$
$389$	−6.89023	−	21.2060i	−0.349349	−	1.07518i	0.609866	−	0.792505i	$-0.291223\pi$
$390$		0			0
$391$	2.61391	−	1.89911i	0.132191	−	0.0960424i
$392$		0			0
$393$	1.76854	−	5.44302i	0.0892113	−	0.274564i
$394$		0			0
$395$	23.1148			1.16303
$396$		0			0
$397$	−14.8896			−0.747287			−0.373644	−	0.927572i	$-0.621892\pi$
$397$	−14.8896			−0.747287			−0.373644	+	0.927572i	$0.621892\pi$
$398$		0			0
$399$	−0.625772	+	1.92593i	−0.0313278	+	0.0964170i
$400$		0			0
$401$	9.50209	−	6.90367i	0.474512	−	0.344753i	−0.324685	−	0.945822i	$-0.605258\pi$
$401$	9.50209	−	6.90367i	0.474512	−	0.344753i	0.799197	+	0.601069i	$0.205258\pi$
$402$		0			0
$403$	−2.92486	−	9.00180i	−0.145698	−	0.448412i
$404$		0			0
$405$	−4.21872	−	3.06508i	−0.209630	−	0.152305i
$406$		0			0
$407$	34.9983	−	9.01713i	1.73480	−	0.446963i
$408$		0			0
$409$	−20.6711	−	15.0185i	−1.02212	−	0.742615i	−0.0554055	−	0.998464i	$-0.517645\pi$
$409$	−20.6711	−	15.0185i	−1.02212	−	0.742615i	−0.966717	+	0.255849i	$0.917645\pi$
$410$		0			0
$411$	−5.58085	−	17.1761i	−0.275283	−	0.847234i
$412$		0			0
$413$	−0.0127430	+	0.00925835i	−0.000627043	+	0.000455573i
$414$		0			0
$415$	3.02748	−	9.31762i	0.148613	−	0.457384i
$416$		0			0
$417$	−9.17404			−0.449254
$418$		0			0
$419$	−10.4940			−0.512666			−0.256333	−	0.966589i	$-0.582514\pi$
$419$	−10.4940			−0.512666			−0.256333	+	0.966589i	$0.582514\pi$
$420$		0			0
$421$	−5.94805	+	18.3062i	−0.289890	+	0.892190i	0.695000	+	0.719010i	$0.255404\pi$
$421$	−5.94805	+	18.3062i	−0.289890	+	0.892190i	−0.984890	+	0.173180i	$0.944596\pi$
$422$		0			0
$423$	−14.0126	+	10.1807i	−0.681316	+	0.495005i
$424$		0			0
$425$	0.819358	+	2.52173i	0.0397447	+	0.122322i
$426$		0			0
$427$	2.70156	+	1.96280i	0.130737	+	0.0949864i
$428$		0			0
$429$	−1.52905	−	2.40497i	−0.0738233	−	0.116113i
$430$		0			0
$431$	13.9791	+	10.1564i	0.673349	+	0.489216i	0.871144	−	0.491027i	$-0.163378\pi$
$431$	13.9791	+	10.1564i	0.673349	+	0.489216i	−0.197796	+	0.980243i	$0.563378\pi$
$432$		0			0
$433$	−4.03056	−	12.4048i	−0.193697	−	0.596137i	−0.999989	−	0.00462003i	$-0.998529\pi$
$433$	−4.03056	−	12.4048i	−0.193697	−	0.596137i	0.806293	−	0.591517i	$-0.201471\pi$
$434$		0			0
$435$	−7.99322	+	5.80742i	−0.383246	+	0.278444i
$436$		0			0
$437$	−3.06719	+	9.43985i	−0.146724	+	0.451569i
$438$		0			0
$439$	7.05074			0.336513			0.168257	−	0.985743i	$-0.446186\pi$
$439$	7.05074			0.336513			0.168257	+	0.985743i	$0.446186\pi$
$440$		0			0
$441$	15.2406			0.725745
$442$		0			0
$443$	5.81569	−	17.8988i	0.276312	−	0.850400i	−0.712558	−	0.701614i	$-0.752463\pi$
$443$	5.81569	−	17.8988i	0.276312	−	0.850400i	0.988869	−	0.148786i	$-0.0475367\pi$
$444$		0			0
$445$	−19.6574	+	14.2819i	−0.931850	+	0.677028i
$446$		0			0
$447$	2.27671	+	7.00700i	0.107685	+	0.331420i
$448$		0			0
$449$	7.14363	+	5.19015i	0.337129	+	0.244939i	0.743449	−	0.668792i	$-0.233188\pi$
$449$	7.14363	+	5.19015i	0.337129	+	0.244939i	−0.406321	+	0.913731i	$0.633188\pi$
$450$		0			0
$451$	−9.43941	−	3.72823i	−0.444485	−	0.175555i
$452$		0			0
$453$	−15.5311	−	11.2840i	−0.729716	−	0.530170i
$454$		0			0
$455$	0.284021	+	0.874128i	0.0133151	+	0.0409797i
$456$		0			0
$457$	0.103204	−	0.0749820i	0.00482768	−	0.00350751i	−0.585369	−	0.810767i	$-0.699050\pi$
$457$	0.103204	−	0.0749820i	0.00482768	−	0.00350751i	0.590196	+	0.807260i	$0.299050\pi$
$458$		0			0
$459$	2.09685	−	6.45344i	0.0978725	−	0.301221i
$460$		0			0
$461$	16.7967			0.782302			0.391151	−	0.920327i	$-0.372077\pi$
$461$	16.7967			0.782302			0.391151	+	0.920327i	$0.372077\pi$
$462$		0			0
$463$	19.7964			0.920019			0.460009	−	0.887914i	$-0.347846\pi$
$463$	19.7964			0.920019			0.460009	+	0.887914i	$0.347846\pi$
$464$		0			0
$465$	−4.51919	+	13.9086i	−0.209572	+	0.644997i
$466$		0			0
$467$	−23.1287	+	16.8040i	−1.07027	+	0.777596i	−0.975961	−	0.217947i	$-0.930064\pi$
$467$	−23.1287	+	16.8040i	−1.07027	+	0.777596i	−0.0943089	+	0.995543i	$0.530064\pi$
$468$		0			0
$469$	−0.998346	−	3.07259i	−0.0460993	−	0.141879i
$470$		0			0
$471$	−8.37328	−	6.08354i	−0.385820	−	0.280315i
$472$		0			0
$473$	−1.14073	+	18.3758i	−0.0524509	+	0.844922i
$474$		0			0
$475$	−6.58984	−	4.78780i	−0.302363	−	0.219679i
$476$		0			0
$477$	−3.83397	−	11.7997i	−0.175545	−	0.540273i
$478$		0			0
$479$	−33.5633	+	24.3851i	−1.53354	+	1.11419i	−0.579318	+	0.815102i	$0.696681\pi$
$479$	−33.5633	+	24.3851i	−1.53354	+	1.11419i	−0.954227	+	0.299084i	$0.903319\pi$
$480$		0			0
$481$	−3.36735	+	10.3636i	−0.153538	+	0.472542i
$482$		0			0
$483$	0.945534			0.0430233
$484$		0			0
$485$	−22.4705			−1.02033
$486$		0			0
$487$	6.24176	−	19.2102i	0.282841	−	0.870495i	−0.704196	−	0.710005i	$-0.748693\pi$
$487$	6.24176	−	19.2102i	0.282841	−	0.870495i	0.987037	−	0.160490i	$-0.0513075\pi$
$488$		0			0
$489$	2.55991	−	1.85989i	0.115763	−	0.0841070i
$490$		0			0
$491$	−11.3169	−	34.8299i	−0.510726	−	1.57185i	−0.790927	−	0.611911i	$-0.790401\pi$
$491$	−11.3169	−	34.8299i	−0.510726	−	1.57185i	0.280201	−	0.959941i	$-0.409599\pi$
$492$		0			0
$493$	7.76423	+	5.64104i	0.349683	+	0.254060i
$494$		0			0
$495$	0.835693	−	13.4620i	0.0375616	−	0.605073i
$496$		0			0
$497$	−3.39641	−	2.46764i	−0.152350	−	0.110689i
$498$		0			0
$499$	1.66630	+	5.12834i	0.0745938	+	0.229576i	0.981401	−	0.191970i	$-0.0614876\pi$
$499$	1.66630	+	5.12834i	0.0745938	+	0.229576i	−0.906807	+	0.421546i	$0.861488\pi$
$500$		0			0
$501$	3.80948	−	2.76775i	0.170195	−	0.123654i
$502$		0			0
$503$	3.27982	−	10.0942i	0.146240	−	0.450080i	−0.850929	−	0.525281i	$-0.823960\pi$
$503$	3.27982	−	10.0942i	0.146240	−	0.450080i	0.997168	+	0.0752017i	$0.0239601\pi$
$504$		0			0
$505$	12.9949			0.578265
$506$		0			0
$507$	0.859273			0.0381617
$508$		0			0
$509$	−5.74546	+	17.6827i	−0.254663	+	0.783772i	0.739233	+	0.673450i	$0.235188\pi$
$509$	−5.74546	+	17.6827i	−0.254663	+	0.783772i	−0.993896	+	0.110322i	$0.964812\pi$
$510$		0			0
$511$	4.76203	−	3.45982i	0.210660	−	0.153053i
$512$		0			0
$513$	6.44159	+	19.8252i	0.284403	+	0.875303i
$514$		0			0
$515$	7.25785	+	5.27314i	0.319819	+	0.232362i
$516$		0			0
$517$	−23.6240	−	9.33064i	−1.03898	−	0.410361i
$518$		0			0
$519$	−9.81940	−	7.13421i	−0.431024	−	0.313157i
$520$		0			0
$521$	−10.6181	−	32.6793i	−0.465189	−	1.43170i	−0.858745	−	0.512404i	$-0.828755\pi$
$521$	−10.6181	−	32.6793i	−0.465189	−	1.43170i	0.393556	−	0.919301i	$-0.371245\pi$
$522$		0			0
$523$	21.6604	−	15.7372i	0.947144	−	0.688140i	−0.00298568	−	0.999996i	$-0.500950\pi$
$523$	21.6604	−	15.7372i	0.947144	−	0.688140i	0.950130	+	0.311855i	$0.100950\pi$
$524$		0			0
$525$	−0.239783	+	0.737976i	−0.0104650	+	0.0322079i
$526$		0			0
$527$	14.2054			0.618799
$528$		0			0
$529$	−18.3655			−0.798500
$530$		0			0
$531$	−0.0215366	+	0.0662829i	−0.000934610	+	0.00287643i
$532$		0			0
$533$	2.47562	−	1.79865i	0.107231	−	0.0779080i
$534$		0			0
$535$	−10.6145	−	32.6682i	−0.458907	−	1.41237i
$536$		0			0
$537$	1.16379	+	0.845544i	0.0502213	+	0.0364879i
$538$		0			0
$539$	11.9914	+	18.8606i	0.516505	+	0.812384i
$540$		0			0
$541$	−17.7304	−	12.8819i	−0.762290	−	0.553836i	0.137322	−	0.990526i	$-0.456150\pi$
$541$	−17.7304	−	12.8819i	−0.762290	−	0.553836i	−0.899612	+	0.436691i	$0.856150\pi$
$542$		0			0
$543$	−5.45346	−	16.7840i	−0.234030	−	0.720272i
$544$		0			0
$545$	22.2323	−	16.1527i	0.952329	−	0.691907i
$546$		0			0
$547$	9.73338	−	29.9563i	0.416169	−	1.28084i	−0.495032	−	0.868875i	$-0.664844\pi$
$547$	9.73338	−	29.9563i	0.416169	−	1.28084i	0.911201	−	0.411962i	$-0.135156\pi$
$548$		0			0
$549$	14.7753			0.630595
$550$		0			0
$551$	−29.4827			−1.25600
$552$		0			0
$553$	2.03045	−	6.24910i	0.0863437	−	0.265739i
$554$		0			0
$555$	13.6213	−	9.89647i	0.578193	−	0.420082i
$556$		0			0
$557$	−6.30402	−	19.4018i	−0.267110	−	0.822080i	−0.991200	−	0.132374i	$-0.957740\pi$
$557$	−6.30402	−	19.4018i	−0.267110	−	0.822080i	0.724090	−	0.689706i	$-0.242260\pi$
$558$		0			0
$559$	−4.49100	−	3.26291i	−0.189949	−	0.138006i
$560$		0			0
$561$	4.14193	−	1.06715i	0.174873	−	0.0450551i
$562$		0			0
$563$	−21.3213	−	15.4908i	−0.898586	−	0.652861i	0.0395163	−	0.999219i	$-0.487418\pi$
$563$	−21.3213	−	15.4908i	−0.898586	−	0.652861i	−0.938102	+	0.346358i	$0.887418\pi$
$564$		0			0
$565$	2.57803	+	7.93436i	0.108458	+	0.333801i
$566$		0			0
$567$	−1.19923	+	0.871289i	−0.0503628	+	0.0365907i
$568$		0			0
$569$	−13.4132	+	41.2815i	−0.562309	+	1.73061i	0.113505	+	0.993537i	$0.463792\pi$
$569$	−13.4132	+	41.2815i	−0.562309	+	1.73061i	−0.675814	+	0.737072i	$0.736208\pi$
$570$		0			0
$571$	−19.8144			−0.829206			−0.414603	−	0.910002i	$-0.636079\pi$
$571$	−19.8144			−0.829206			−0.414603	+	0.910002i	$0.636079\pi$
$572$		0			0
$573$	−8.62055			−0.360129
$574$		0			0
$575$	−1.17529	+	3.61716i	−0.0490128	+	0.150846i
$576$		0			0
$577$	−3.65128	+	2.65281i	−0.152005	+	0.110438i	−0.661188	−	0.750220i	$-0.729948\pi$
$577$	−3.65128	+	2.65281i	−0.152005	+	0.110438i	0.509183	+	0.860658i	$0.329948\pi$
$578$		0			0
$579$	4.07119	+	12.5298i	0.169193	+	0.520723i
$580$		0			0
$581$	−2.25308	−	1.63696i	−0.0934737	−	0.0679126i
$582$		0			0
$583$	11.5858	−	14.0287i	0.479837	−	0.581009i
$584$		0			0
$585$	3.29008	+	2.39038i	0.136028	+	0.0988302i
$586$		0			0
$587$	−2.96741	−	9.13276i	−0.122478	−	0.376949i	0.870955	−	0.491363i	$-0.163501\pi$
$587$	−2.96741	−	9.13276i	−0.122478	−	0.376949i	−0.993433	+	0.114414i	$0.963501\pi$
$588$		0			0
$589$	−35.3052	+	25.6507i	−1.45472	+	1.05692i
$590$		0			0
$591$	1.29176	−	3.97564i	0.0531361	−	0.163536i
$592$		0			0
$593$	−38.6794			−1.58837			−0.794186	−	0.607674i	$-0.792103\pi$
$593$	−38.6794			−1.58837			−0.794186	+	0.607674i	$0.792103\pi$
$594$		0			0
$595$	−1.37943			−0.0565512
$596$		0			0
$597$	2.53190	−	7.79238i	0.103624	−	0.318921i
$598$		0			0
$599$	−20.6655	+	15.0144i	−0.844371	+	0.613471i	−0.923588	−	0.383386i	$-0.874758\pi$
$599$	−20.6655	+	15.0144i	−0.844371	+	0.613471i	0.0792174	+	0.996857i	$0.474758\pi$
$600$		0			0
$601$	7.00240	+	21.5512i	0.285634	+	0.879091i	0.986208	+	0.165511i	$0.0529273\pi$
$601$	7.00240	+	21.5512i	0.285634	+	0.879091i	−0.700574	+	0.713580i	$0.747073\pi$
$602$		0			0
$603$	−11.5648	−	8.40229i	−0.470953	−	0.342168i
$604$		0			0
$605$	17.3170	−	9.55776i	0.704038	−	0.388578i
$606$		0			0
$607$	22.7397	+	16.5214i	0.922976	+	0.670582i	0.944263	−	0.329192i	$-0.106776\pi$
$607$	22.7397	+	16.5214i	0.922976	+	0.670582i	−0.0212867	+	0.999773i	$0.506776\pi$
$608$		0			0
$609$	0.867896	+	2.67111i	0.0351689	+	0.108239i
$610$		0			0
$611$	6.19574	−	4.50147i	0.250653	−	0.182110i
$612$		0			0
$613$	−3.88879	+	11.9685i	−0.157067	+	0.483402i	−0.998364	−	0.0571703i	$-0.981792\pi$
$613$	−3.88879	+	11.9685i	−0.157067	+	0.483402i	0.841298	+	0.540572i	$0.181792\pi$
$614$		0			0
$615$	−4.72805			−0.190653
$616$		0			0
$617$	−8.86969			−0.357080			−0.178540	−	0.983933i	$-0.557137\pi$
$617$	−8.86969			−0.357080			−0.178540	+	0.983933i	$0.557137\pi$
$618$		0			0
$619$	5.16369	−	15.8922i	0.207546	−	0.638762i	−0.792053	−	0.610452i	$-0.790988\pi$
$619$	5.16369	−	15.8922i	0.207546	−	0.638762i	0.999599	−	0.0283092i	$-0.00901231\pi$
$620$		0			0
$621$	7.87430	−	5.72101i	0.315985	−	0.229576i
$622$		0			0
$623$	2.13438	+	6.56895i	0.0855121	+	0.263179i
$624$		0			0
$625$	10.5539	+	7.66788i	0.422157	+	0.306715i
$626$		0			0
$627$	−8.36711	+	10.1313i	−0.334150	+	0.404605i
$628$		0			0
$629$	−13.2311	−	9.61295i	−0.527558	−	0.383293i
$630$		0			0
$631$	3.04262	+	9.36421i	0.121125	+	0.372783i	0.993175	−	0.116633i	$-0.0372100\pi$
$631$	3.04262	+	9.36421i	0.121125	+	0.372783i	−0.872051	+	0.489416i	$0.837210\pi$
$632$		0			0
$633$	14.7751	−	10.7348i	0.587258	−	0.426668i
$634$		0			0
$635$	2.06164	−	6.34508i	0.0818138	−	0.251797i
$636$		0			0
$637$	−6.73873			−0.266998
$638$		0			0
$639$	−18.5756			−0.734840
$640$		0			0
$641$	5.03675	−	15.5015i	0.198940	−	0.612273i	−0.800968	−	0.598707i	$-0.795682\pi$
$641$	5.03675	−	15.5015i	0.198940	−	0.612273i	0.999908	−	0.0135664i	$-0.00431844\pi$
$642$		0			0
$643$	22.1595	−	16.0998i	0.873887	−	0.634916i	−0.0577402	−	0.998332i	$-0.518390\pi$
$643$	22.1595	−	16.0998i	0.873887	−	0.634916i	0.931627	+	0.363416i	$0.118390\pi$
$644$		0			0
$645$	2.65047	+	8.15732i	0.104362	+	0.321194i
$646$		0			0
$647$	−28.3473	−	20.5955i	−1.11445	−	0.809693i	−0.131088	−	0.991371i	$-0.541847\pi$
$647$	−28.3473	−	20.5955i	−1.11445	−	0.809693i	−0.983358	+	0.181678i	$0.941847\pi$
$648$		0			0
$649$	−0.0989715	+	0.0254995i	−0.00388497	+	0.00100094i
$650$		0			0
$651$	3.36323	+	2.44353i	0.131815	+	0.0957696i
$652$		0			0
$653$	−4.45893	−	13.7232i	−0.174491	−	0.537029i	0.825119	−	0.564959i	$-0.191108\pi$
$653$	−4.45893	−	13.7232i	−0.174491	−	0.537029i	−0.999610	+	0.0279307i	$0.991108\pi$
$654$		0			0
$655$	−9.68911	+	7.03955i	−0.378585	+	0.275058i
$656$		0			0
$657$	8.04817	−	24.7697i	0.313989	−	0.966359i
$658$		0			0
$659$	11.1175			0.433078			0.216539	−	0.976274i	$-0.430523\pi$
$659$	11.1175			0.433078			0.216539	+	0.976274i	$0.430523\pi$
$660$		0			0
$661$	34.8001			1.35357			0.676784	−	0.736182i	$-0.263373\pi$
$661$	34.8001			1.35357			0.676784	+	0.736182i	$0.263373\pi$
$662$		0			0
$663$	−0.398516	+	1.22650i	−0.0154771	+	0.0476335i
$664$		0			0
$665$	3.42834	−	2.49083i	0.132945	−	0.0965904i
$666$		0			0
$667$	4.25395	+	13.0923i	0.164714	+	0.506936i
$668$		0			0
$669$	−8.26380	−	6.00400i	−0.319497	−	0.232128i
$670$		0			0
$671$	11.6252	+	18.2848i	0.448788	+	0.705875i
$672$		0			0
$673$	35.5622	+	25.8375i	1.37082	+	0.995961i	0.997672	+	0.0681897i	$0.0217223\pi$
$673$	35.5622	+	25.8375i	1.37082	+	0.995961i	0.373150	+	0.927771i	$0.378278\pi$
$674$		0			0
$675$	2.46829	+	7.59660i	0.0950044	+	0.292393i
$676$		0			0
$677$	17.7700	−	12.9106i	0.682955	−	0.496196i	−0.191382	−	0.981516i	$-0.561297\pi$
$677$	17.7700	−	12.9106i	0.682955	−	0.496196i	0.874337	+	0.485320i	$0.161297\pi$
$678$		0			0
$679$	−1.97386	+	6.07492i	−0.0757498	+	0.233134i
$680$		0			0
$681$	−6.55165			−0.251060
$682$		0			0
$683$	−19.9465			−0.763232			−0.381616	−	0.924321i	$-0.624632\pi$
$683$	−19.9465			−0.763232			−0.381616	+	0.924321i	$0.624632\pi$
$684$		0			0
$685$	−11.6787	+	35.9432i	−0.446219	+	1.37332i
$686$		0			0
$687$	1.11737	−	0.811818i	0.0426304	−	0.0309728i
$688$		0			0
$689$	1.69521	+	5.21732i	0.0645824	+	0.198764i
$690$		0			0
$691$	−11.7996	−	8.57288i	−0.448876	−	0.326128i	0.340276	−	0.940326i	$-0.389480\pi$
$691$	−11.7996	−	8.57288i	−0.448876	−	0.326128i	−0.789152	+	0.614198i	$0.789480\pi$
$692$		0			0
$693$	−3.56606	−	1.40846i	−0.135463	−	0.0535031i
$694$		0			0
$695$	15.5314	+	11.2842i	0.589140	+	0.428035i
$696$		0			0
$697$	1.41919	+	4.36782i	0.0537557	+	0.165443i
$698$		0			0
$699$	6.00933	−	4.36604i	0.227294	−	0.165139i
$700$		0			0
$701$	−10.9963	+	33.8430i	−0.415323	+	1.27823i	0.496639	+	0.867957i	$0.334567\pi$
$701$	−10.9963	+	33.8430i	−0.415323	+	1.27823i	−0.911962	+	0.410275i	$0.865433\pi$
$702$		0			0
$703$	50.2417			1.89490
$704$		0			0
$705$	−11.8329			−0.445652
$706$		0			0
$707$	1.14150	−	3.51318i	0.0429305	−	0.132127i
$708$		0			0
$709$	−23.0380	+	16.7381i	−0.865211	+	0.628613i	−0.929298	−	0.369331i	$-0.879587\pi$
$709$	−23.0380	+	16.7381i	−0.865211	+	0.628613i	0.0640863	+	0.997944i	$0.479587\pi$
$710$		0			0
$711$	−8.98408	−	27.6502i	−0.336929	−	1.03696i
$712$		0			0
$713$	16.4847	+	11.9769i	0.617358	+	0.448537i
$714$		0			0
$715$	−0.369506	+	5.95230i	−0.0138187	+	0.222603i
$716$		0			0
$717$	14.8199	+	10.7673i	0.553459	+	0.402111i
$718$		0			0
$719$	3.09345	+	9.52065i	0.115366	+	0.355060i	0.992023	−	0.126055i	$-0.0402317\pi$
$719$	3.09345	+	9.52065i	0.115366	+	0.355060i	−0.876657	+	0.481116i	$0.840232\pi$
$720$		0			0
$721$	2.06314	−	1.49896i	0.0768354	−	0.0558242i
$722$		0			0
$723$	2.10892	−	6.49060i	0.0784318	−	0.241388i
$724$		0			0
$725$	−11.2972			−0.419566
$726$		0			0
$727$	−1.86100			−0.0690207			−0.0345103	−	0.999404i	$-0.510987\pi$
$727$	−1.86100			−0.0690207			−0.0345103	+	0.999404i	$0.510987\pi$
$728$		0			0
$729$	1.57476	−	4.84661i	0.0583244	−	0.179504i
$730$		0			0
$731$	6.74024	−	4.89707i	0.249297	−	0.181125i
$732$		0			0
$733$	−6.29146	−	19.3631i	−0.232380	−	0.715194i	−0.997458	−	0.0712555i	$-0.977299\pi$
$733$	−6.29146	−	19.3631i	−0.232380	−	0.715194i	0.765078	−	0.643938i	$-0.222701\pi$
$734$		0			0
$735$	8.42347	+	6.12001i	0.310704	+	0.225740i
$736$		0			0
$737$	1.29883	−	20.9226i	0.0478429	−	0.770692i
$738$		0			0
$739$	4.73848	+	3.44270i	0.174308	+	0.126642i	0.671518	−	0.740988i	$-0.265642\pi$
$739$	4.73848	+	3.44270i	0.174308	+	0.126642i	−0.497211	+	0.867630i	$0.665642\pi$
$740$		0			0
$741$	−1.22425	−	3.76786i	−0.0449741	−	0.138416i
$742$		0			0
$743$	32.9360	−	23.9294i	1.20831	−	0.877885i	0.213229	−	0.977002i	$-0.431602\pi$
$743$	32.9360	−	23.9294i	1.20831	−	0.877885i	0.995076	+	0.0991170i	$0.0316018\pi$
$744$		0			0
$745$	4.76432	−	14.6631i	0.174551	−	0.537213i
$746$		0			0
$747$	−12.3225			−0.450858
$748$		0			0
$749$	−9.76428			−0.356779
$750$		0			0
$751$	−8.92854	+	27.4792i	−0.325807	+	1.00273i	0.645268	+	0.763956i	$0.276746\pi$
$751$	−8.92854	+	27.4792i	−0.325807	+	1.00273i	−0.971075	+	0.238774i	$0.923254\pi$
$752$		0			0
$753$	15.7496	−	11.4427i	0.573946	−	0.416996i
$754$		0			0
$755$	12.4142	+	38.2071i	0.451800	+	1.39050i
$756$		0			0
$757$	7.87591	+	5.72219i	0.286255	+	0.207976i	0.721641	−	0.692267i	$-0.243388\pi$
$757$	7.87591	+	5.72219i	0.286255	+	0.207976i	−0.435386	+	0.900244i	$0.643388\pi$
$758$		0			0
$759$	5.70624	+	2.25376i	0.207124	+	0.0818064i
$760$		0			0
$761$	−28.5503	−	20.7430i	−1.03495	−	0.751933i	−0.0656538	−	0.997842i	$-0.520913\pi$
$761$	−28.5503	−	20.7430i	−1.03495	−	0.751933i	−0.969293	+	0.245910i	$0.920913\pi$
$762$		0			0
$763$	−2.41397	−	7.42942i	−0.0873914	−	0.268963i
$764$		0			0
$765$	−4.93785	+	3.58756i	−0.178528	+	0.129709i
$766$		0			0
$767$	0.00952253	−	0.0293073i	0.000343839	−	0.00105823i
$768$		0			0
$769$	−1.79250			−0.0646394			−0.0323197	−	0.999478i	$-0.510289\pi$
$769$	−1.79250			−0.0646394			−0.0323197	+	0.999478i	$0.510289\pi$
$770$		0			0
$771$	5.98453			0.215527
$772$		0			0
$773$	−8.38587	+	25.8091i	−0.301619	+	0.928287i	0.679298	+	0.733862i	$0.262284\pi$
$773$	−8.38587	+	25.8091i	−0.301619	+	0.928287i	−0.980917	+	0.194425i	$0.937716\pi$
$774$		0			0
$775$	−13.5282	+	9.82883i	−0.485948	+	0.353062i
$776$		0			0
$777$	−1.47899	−	4.55186i	−0.0530584	−	0.163297i
$778$		0			0
$779$	−11.4141	−	8.29284i	−0.408953	−	0.297122i
$780$		0			0
$781$	−14.6153	−	22.9877i	−0.522978	−	0.822565i
$782$		0			0
$783$	23.3894	+	16.9934i	0.835871	+	0.607296i
$784$		0			0
$785$	6.69287	+	20.5986i	0.238879	+	0.735194i
$786$		0			0
$787$	−21.4553	+	15.5882i	−0.764798	+	0.555658i	−0.900378	−	0.435108i	$-0.856710\pi$
$787$	−21.4553	+	15.5882i	−0.764798	+	0.555658i	0.135580	+	0.990766i	$0.456710\pi$
$788$		0			0
$789$	4.10014	−	12.6189i	0.145969	−	0.449246i
$790$		0			0
$791$	2.37152			0.0843215
$792$		0			0
$793$	−6.53298			−0.231993
$794$		0			0
$795$	2.61926	−	8.06125i	0.0928956	−	0.285903i
$796$		0			0
$797$	−1.39796	+	1.01568i	−0.0495184	+	0.0359772i	−0.612269	−	0.790649i	$-0.709743\pi$
$797$	−1.39796	+	1.01568i	−0.0495184	+	0.0359772i	0.562751	+	0.826627i	$0.309743\pi$
$798$		0			0
$799$	3.55181	+	10.9313i	0.125654	+	0.386723i
$800$		0			0
$801$	24.7245	+	17.9634i	0.873597	+	0.634705i
$802$		0			0
$803$	36.9854	−	9.52909i	1.30518	−	0.336274i
$804$		0			0
$805$	−1.60076	−	1.16302i	−0.0564195	−	0.0409912i
$806$		0			0
$807$	3.11560	+	9.58883i	0.109674	+	0.337543i
$808$		0			0
$809$	−4.92294	+	3.57673i	−0.173081	+	0.125751i	−0.670953	−	0.741500i	$-0.734115\pi$
$809$	−4.92294	+	3.57673i	−0.173081	+	0.125751i	0.497872	+	0.867251i	$0.334115\pi$
$810$		0			0
$811$	−7.77731	+	23.9361i	−0.273098	+	0.840510i	0.716618	+	0.697466i	$0.245689\pi$
$811$	−7.77731	+	23.9361i	−0.273098	+	0.840510i	−0.989716	+	0.143044i	$0.954311\pi$
$812$		0			0
$813$	8.61863			0.302268
$814$		0			0
$815$	−6.62156			−0.231943
$816$		0			0
$817$	−7.90908	+	24.3416i	−0.276704	+	0.851606i
$818$		0			0
$819$	0.935250	−	0.679499i	0.0326803	−	0.0237436i
$820$		0			0
$821$	−4.25795	−	13.1046i	−0.148604	−	0.457355i	0.848853	−	0.528629i	$-0.177294\pi$
$821$	−4.25795	−	13.1046i	−0.148604	−	0.457355i	−0.997457	+	0.0712740i	$0.977294\pi$
$822$		0			0
$823$	11.6546	+	8.46753i	0.406252	+	0.295159i	0.772083	−	0.635522i	$-0.219215\pi$
$823$	11.6546	+	8.46753i	0.406252	+	0.295159i	−0.365831	+	0.930681i	$0.619215\pi$
$824$		0			0
$825$	−3.20611	+	3.88210i	−0.111622	+	0.135157i
$826$		0			0
$827$	−7.51217	−	5.45791i	−0.261224	−	0.189790i	0.449463	−	0.893299i	$-0.351615\pi$
$827$	−7.51217	−	5.45791i	−0.261224	−	0.189790i	−0.710686	+	0.703509i	$0.751615\pi$
$828$		0			0
$829$	0.564591	+	1.73763i	0.0196091	+	0.0603505i	0.960382	−	0.278686i	$-0.0898989\pi$
$829$	0.564591	+	1.73763i	0.0196091	+	0.0603505i	−0.940773	+	0.339037i	$0.889899\pi$
$830$		0			0
$831$	−19.6646	+	14.2872i	−0.682157	+	0.495616i
$832$		0			0
$833$	3.12530	−	9.61869i	0.108285	−	0.333268i
$834$		0			0
$835$	−9.85374			−0.341003
$836$		0			0
$837$	42.7933			1.47915
$838$		0			0
$839$	6.97673	−	21.4722i	0.240864	−	0.741302i	−0.755426	−	0.655234i	$-0.772570\pi$
$839$	6.97673	−	21.4722i	0.240864	−	0.741302i	0.996289	−	0.0860677i	$-0.0274301\pi$
$840$		0			0
$841$	−9.61930	+	6.98883i	−0.331700	+	0.240994i
$842$		0			0
$843$	−3.19486	−	9.83278i	−0.110037	−	0.338659i
$844$		0			0
$845$	−1.45473	−	1.05692i	−0.0500441	−	0.0363592i
$846$		0			0
$847$	−1.06278	−	5.52125i	−0.0365175	−	0.189712i
$848$		0			0
$849$	6.50571	+	4.72668i	0.223276	+	0.162219i
$850$		0			0
$851$	−7.24920	−	22.3107i	−0.248499	−	0.764802i
$852$		0			0
$853$	21.8360	−	15.8648i	0.747650	−	0.543200i	−0.147448	−	0.989070i	$-0.547106\pi$
$853$	21.8360	−	15.8648i	0.747650	−	0.543200i	0.895098	+	0.445870i	$0.147106\pi$
$854$		0			0
$855$	5.79414	−	17.8325i	0.198155	−	0.609860i
$856$		0			0
$857$	47.5087			1.62287			0.811433	−	0.584445i	$-0.198688\pi$
$857$	47.5087			1.62287			0.811433	+	0.584445i	$0.198688\pi$
$858$		0			0
$859$	−3.47729			−0.118644			−0.0593219	−	0.998239i	$-0.518894\pi$
$859$	−3.47729			−0.118644			−0.0593219	+	0.998239i	$0.518894\pi$
$860$		0			0
$861$	−0.415322	+	1.27823i	−0.0141542	+	0.0435620i
$862$		0			0
$863$	−12.5690	+	9.13189i	−0.427853	+	0.310853i	−0.780790	−	0.624794i	$-0.785183\pi$
$863$	−12.5690	+	9.13189i	−0.427853	+	0.310853i	0.352937	+	0.935647i	$0.385183\pi$
$864$		0			0
$865$	7.84878	+	24.1561i	0.266867	+	0.821331i
$866$		0			0
$867$	10.2520	+	7.44850i	0.348175	+	0.252964i
$868$		0			0
$869$	27.1489	−	32.8732i	0.920965	−	1.11515i
$870$		0			0
$871$	5.11342	+	3.71512i	0.173262	+	0.125882i
$872$		0			0
$873$	8.73367	+	26.8795i	0.295590	+	0.909732i
$874$		0			0
$875$	5.03156	−	3.65564i	0.170098	−	0.123583i
$876$		0			0
$877$	−1.31505	+	4.04730i	−0.0444060	+	0.136668i	−0.970801	−	0.239885i	$-0.922890\pi$
$877$	−1.31505	+	4.04730i	−0.0444060	+	0.136668i	0.926395	+	0.376552i	$0.122890\pi$
$878$		0			0
$879$	11.2193			0.378419
$880$		0			0
$881$	38.3267			1.29126			0.645630	−	0.763650i	$-0.276595\pi$
$881$	38.3267			1.29126			0.645630	+	0.763650i	$0.276595\pi$
$882$		0			0
$883$	−10.9591	+	33.7288i	−0.368805	+	1.13506i	0.578760	+	0.815498i	$0.303537\pi$
$883$	−10.9591	+	33.7288i	−0.368805	+	1.13506i	−0.947564	+	0.319566i	$0.896463\pi$
$884$		0			0
$885$	−0.0385197	+	0.0279862i	−0.00129482	+	0.000940745i
$886$		0			0
$887$	10.6932	+	32.9104i	0.359044	+	1.10502i	0.953627	+	0.300990i	$0.0973171\pi$
$887$	10.6932	+	32.9104i	0.359044	+	1.10502i	−0.594583	+	0.804034i	$0.702683\pi$
$888$		0			0
$889$	−1.53430	−	1.11473i	−0.0514587	−	0.0373869i
$890$		0			0
$891$	−9.31406	+	2.39972i	−0.312033	+	0.0803937i
$892$		0			0
$893$	−28.5661	−	20.7545i	−0.955928	−	0.694522i
$894$		0			0
$895$	−0.930234	−	2.86297i	−0.0310943	−	0.0956984i
$896$		0			0
$897$	−1.49655	+	1.08730i	−0.0499682	+	0.0363040i
$898$		0			0
$899$	−18.7031	+	57.5624i	−0.623785	+	1.91981i
$900$		0			0
$901$	−8.23328			−0.274290
$902$		0			0
$903$	2.43816			0.0811369
$904$		0			0
$905$	−11.4121	+	35.1228i	−0.379350	+	1.16752i
$906$		0			0
$907$	1.09662	−	0.796740i	0.0364126	−	0.0264553i	−0.569430	−	0.822040i	$-0.692836\pi$
$907$	1.09662	−	0.796740i	0.0364126	−	0.0264553i	0.605843	+	0.795584i	$0.292836\pi$
$908$		0			0
$909$	−5.05076	−	15.5446i	−0.167523	−	0.515583i
$910$		0			0
$911$	−21.5276	−	15.6407i	−0.713243	−	0.518201i	0.170976	−	0.985275i	$-0.445308\pi$
$911$	−21.5276	−	15.6407i	−0.713243	−	0.518201i	−0.884218	+	0.467074i	$0.845308\pi$
$912$		0			0
$913$	−9.69539	−	15.2494i	−0.320871	−	0.504681i
$914$		0			0
$915$	8.16628	+	5.93315i	0.269969	+	0.196144i
$916$		0			0
$917$	1.05203	+	3.23783i	0.0347412	+	0.106922i
$918$		0			0
$919$	11.2327	−	8.16106i	0.370534	−	0.269209i	−0.386899	−	0.922122i	$-0.626454\pi$
$919$	11.2327	−	8.16106i	0.370534	−	0.269209i	0.757432	+	0.652914i	$0.226454\pi$
$920$		0			0
$921$	1.61742	−	4.97792i	0.0532959	−	0.164028i
$922$		0			0
$923$	8.21331			0.270344
$924$		0			0
$925$	19.2516			0.632988
$926$		0			0
$927$	3.48686	−	10.7314i	0.114523	−	0.352467i
$928$		0			0
$929$	−19.0505	+	13.8410i	−0.625026	+	0.454108i	−0.854673	−	0.519166i	$-0.826243\pi$
$929$	−19.0505	+	13.8410i	−0.625026	+	0.454108i	0.229647	+	0.973274i	$0.426243\pi$
$930$		0			0
$931$	9.60103	+	29.5489i	0.314661	+	0.968427i
$932$		0			0
$933$	−17.8224	−	12.9487i	−0.583480	−	0.423923i
$934$		0			0
$935$	−8.32479	−	3.28799i	−0.272250	−	0.107529i
$936$		0			0
$937$	−2.29050	−	1.66415i	−0.0748274	−	0.0543653i	0.549743	−	0.835334i	$-0.314726\pi$
$937$	−2.29050	−	1.66415i	−0.0748274	−	0.0543653i	−0.624570	+	0.780969i	$0.714726\pi$
$938$		0			0
$939$	−5.47191	−	16.8408i	−0.178569	−	0.549579i
$940$		0			0
$941$	43.3644	−	31.5061i	1.41364	−	1.02707i	0.420859	−	0.907126i	$-0.361729\pi$
$941$	43.3644	−	31.5061i	1.41364	−	1.02707i	0.992781	−	0.119943i	$-0.0382713\pi$
$942$		0			0
$943$	−2.03568	+	6.26519i	−0.0662910	+	0.204023i
$944$		0			0
$945$	−4.15549			−0.135178
$946$		0			0
$947$	33.3680			1.08431			0.542157	−	0.840277i	$-0.317608\pi$
$947$	33.3680			1.08431			0.542157	+	0.840277i	$0.317608\pi$
$948$		0			0
$949$	−3.55854	+	10.9521i	−0.115515	+	0.355519i
$950$		0			0
$951$	9.48362	−	6.89025i	0.307527	−	0.223432i
$952$		0			0
$953$	12.1805	+	37.4877i	0.394565	+	1.21435i	0.929300	+	0.369326i	$0.120411\pi$
$953$	12.1805	+	37.4877i	0.394565	+	1.21435i	−0.534735	+	0.845020i	$0.679589\pi$
$954$		0			0
$955$	14.5944	+	10.6034i	0.472263	+	0.343119i
$956$		0			0
$957$	−1.12911	+	18.1887i	−0.0364991	+	0.587957i
$958$		0			0
$959$	8.69139	+	6.31467i	0.280660	+	0.203911i
$960$		0			0
$961$	18.1045	+	55.7198i	0.584015	+	1.79741i
$962$		0			0
$963$	−34.9525	+	25.3945i	−1.12633	+	0.818325i
$964$		0			0
$965$	8.51950	−	26.2203i	0.274253	−	0.844062i
$966$		0			0
$967$	−48.8844			−1.57202			−0.786008	−	0.618216i	$-0.787856\pi$
$967$	−48.8844			−1.57202			−0.786008	+	0.618216i	$0.787856\pi$
$968$		0			0
$969$	5.94594			0.191011
$970$		0			0
$971$	4.28746	−	13.1955i	0.137591	−	0.423462i	−0.858393	−	0.512993i	$-0.828537\pi$
$971$	4.28746	−	13.1955i	0.137591	−	0.423462i	0.995984	+	0.0895306i	$0.0285367\pi$
$972$		0			0
$973$	4.41501	−	3.20769i	0.141539	−	0.102834i
$974$		0			0
$975$	−0.469109	−	1.44377i	−0.0150235	−	0.0462376i
$976$		0			0
$977$	−39.2862	−	28.5431i	−1.25688	−	0.913174i	−0.258276	−	0.966071i	$-0.583155\pi$
$977$	−39.2862	−	28.5431i	−1.25688	−	0.913174i	−0.998600	+	0.0528970i	$0.983155\pi$
$978$		0			0
$979$	−2.77678	+	44.7307i	−0.0887464	+	1.42960i
$980$		0			0
$981$	−27.9632	−	20.3164i	−0.892796	−	0.648654i
$982$		0			0
$983$	4.56025	+	14.0350i	0.145449	+	0.447647i	0.997069	−	0.0765141i	$-0.0243790\pi$
$983$	4.56025	+	14.0350i	0.145449	+	0.447647i	−0.851619	+	0.524161i	$0.824379\pi$
$984$		0			0
$985$	−7.07703	+	5.14177i	−0.225493	+	0.163830i
$986$		0			0
$987$	−1.03943	+	3.19903i	−0.0330854	+	0.101826i
$988$		0			0
$989$	11.9505			0.380004
$990$		0			0
$991$	−11.2165			−0.356303			−0.178151	−	0.984003i	$-0.557012\pi$
$991$	−11.2165			−0.356303			−0.178151	+	0.984003i	$0.557012\pi$
$992$		0			0
$993$	3.94186	−	12.1318i	0.125091	−	0.384991i
$994$		0			0
$995$	−13.8712	+	10.0780i	−0.439747	+	0.319495i
$996$		0			0
$997$	15.8073	+	48.6498i	0.500621	+	1.54075i	0.808010	+	0.589169i	$0.200545\pi$
$997$	15.8073	+	48.6498i	0.500621	+	1.54075i	−0.307389	+	0.951584i	$0.599455\pi$
$998$		0			0
$999$	−39.8582	−	28.9587i	−1.26106	−	0.916211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.521.3	yes	20
11.3	even	5	inner	572.2.n.a.157.3	✓	20
11.5	even	5		6292.2.a.w.1.6		10
11.6	odd	10		6292.2.a.x.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.157.3	✓	20	11.3	even	5	inner
572.2.n.a.521.3	yes	20	1.1	even	1	trivial
6292.2.a.w.1.6		10	11.5	even	5
6292.2.a.x.1.6		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.265530 - 0.817217i) q^{3} +(-1.45473 + 1.05692i) q^{5} +(0.157953 + 0.486129i) q^{7} +(1.82971 + 1.32936i) q^{9} +O(q^{10})\)	\(q+(0.265530 - 0.817217i) q^{3} +(-1.45473 + 1.05692i) q^{5} +(0.157953 + 0.486129i) q^{7} +(1.82971 + 1.32936i) q^{9} +(-0.205493 + 3.31025i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(0.477461 + 1.46947i) q^{15} +(1.21420 - 0.882166i) q^{17} +(-1.42475 + 4.38494i) q^{19} +0.439214 q^{21} +2.15279 q^{23} +(-0.545937 + 1.68022i) q^{25} +(3.65772 - 2.65749i) q^{27} +(1.97602 + 6.08157i) q^{29} +(7.65739 + 5.56342i) q^{31} +(2.65063 + 1.04690i) q^{33} +(-0.743578 - 0.540241i) q^{35} +(-3.36735 - 10.3636i) q^{37} +(-0.695167 + 0.505068i) q^{39} +(-0.945604 + 2.91027i) q^{41} +5.55119 q^{43} -4.06676 q^{45} +(-2.36656 + 7.28353i) q^{47} +(5.45175 - 3.96093i) q^{49} +(-0.398516 - 1.22650i) q^{51} +(-4.43812 - 3.22448i) q^{53} +(-3.19974 - 5.03270i) q^{55} +(3.20514 + 2.32867i) q^{57} +(0.00952253 + 0.0293073i) q^{59} +(5.28529 - 3.83999i) q^{61} +(-0.357234 + 1.09945i) q^{63} +1.79814 q^{65} -6.32053 q^{67} +(0.571630 - 1.75929i) q^{69} +(-6.64470 + 4.82766i) q^{71} +(-3.55854 - 10.9521i) q^{73} +(1.22814 + 0.892298i) q^{75} +(-1.64167 + 0.422967i) q^{77} +(-10.3998 - 7.55588i) q^{79} +(0.896151 + 2.75807i) q^{81} +(-4.40791 + 3.20253i) q^{83} +(-0.833946 + 2.56662i) q^{85} +5.49466 q^{87} +13.5128 q^{89} +(0.157953 - 0.486129i) q^{91} +(6.57979 - 4.78050i) q^{93} +(-2.56191 - 7.88475i) q^{95} +(10.1099 + 7.34527i) q^{97} +(-4.77652 + 5.78364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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