LMFDB - Embedded newform 725.2.l.b.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(226,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("725.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.l (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			401.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	725.401
Dual form			725.2.l.b.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12349 + 1.40881i) q^{2} +(0.0990311 + 0.433884i) q^{3} +(-0.277479 + 1.21572i) q^{4} +(-0.500000 + 0.626980i) q^{6} +(-0.900969 - 3.94740i) q^{7} +(1.22252 - 0.588735i) q^{8} +(2.52446 - 1.21572i) q^{9} +(-2.62349 - 1.26341i) q^{11} -0.554958 q^{12} +(4.67241 + 2.25011i) q^{13} +(4.54892 - 5.70416i) q^{14} +(4.44989 + 2.14295i) q^{16} -1.10992 q^{17} +(4.54892 + 2.19064i) q^{18} +(-0.455927 + 1.99755i) q^{19} +(1.62349 - 0.781831i) q^{21} +(-1.16756 - 5.11543i) q^{22} +(2.57942 - 3.23449i) q^{23} +(0.376510 + 0.472129i) q^{24} +(2.07942 + 9.11052i) q^{26} +(1.60992 + 2.01877i) q^{27} +5.04892 q^{28} +(4.38404 + 3.12733i) q^{29} +(-3.96346 - 4.97002i) q^{31} +(1.37651 + 6.03089i) q^{32} +(0.288364 - 1.26341i) q^{33} +(-1.24698 - 1.56366i) q^{34} +(0.777479 + 3.40636i) q^{36} +(-2.62349 + 1.26341i) q^{37} +(-3.32640 + 1.60191i) q^{38} +(-0.513574 + 2.25011i) q^{39} +0.396125 q^{41} +(2.92543 + 1.40881i) q^{42} +(-3.57942 + 4.48845i) q^{43} +(2.26391 - 2.83885i) q^{44} +7.45473 q^{46} +(-7.02930 - 3.38513i) q^{47} +(-0.489115 + 2.14295i) q^{48} +(-8.46346 + 4.07579i) q^{49} +(-0.109916 - 0.481575i) q^{51} +(-4.03199 + 5.05596i) q^{52} +(2.71648 + 3.40636i) q^{53} +(-1.03534 + 4.53614i) q^{54} +(-3.42543 - 4.29535i) q^{56} -0.911854 q^{57} +(0.519614 + 9.68981i) q^{58} -9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(2.54892 - 11.1675i) q^{62} +(-7.07338 - 8.86973i) q^{63} +(-0.791053 + 0.991949i) q^{64} +(2.10388 - 1.01317i) q^{66} +(0.337282 - 0.162426i) q^{67} +(0.307979 - 1.34934i) q^{68} +(1.65883 + 0.798852i) q^{69} +(10.2763 + 4.94880i) q^{71} +(2.37047 - 2.97247i) q^{72} +(5.57942 - 6.99637i) q^{73} +(-4.72737 - 2.27658i) q^{74} +(-2.30194 - 1.10855i) q^{76} +(-2.62349 + 11.4943i) q^{77} +(-3.74698 + 1.80445i) q^{78} +(0.535344 - 0.257808i) q^{79} +(4.52446 - 5.67349i) q^{81} +(0.445042 + 0.558065i) q^{82} +(-2.09903 + 9.19646i) q^{83} +(0.500000 + 2.19064i) q^{84} -10.3448 q^{86} +(-0.922739 + 2.21187i) q^{87} -3.95108 q^{88} +(0.887395 + 1.11276i) q^{89} +(4.67241 - 20.4712i) q^{91} +(3.21648 + 4.03334i) q^{92} +(1.76391 - 2.21187i) q^{93} +(-3.12833 - 13.7061i) q^{94} +(-2.48039 + 1.19449i) q^{96} +(3.50484 - 15.3557i) q^{97} +(-15.2506 - 7.34432i) q^{98} -8.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 3 q^{6} - q^{7} + 7 q^{8} + 6 q^{9} - 11 q^{11} - 4 q^{12} + 5 q^{13} + 9 q^{14} + 4 q^{16} - 8 q^{17} + 9 q^{18} + q^{19} + 5 q^{21} - 6 q^{22} + 7 q^{23} + 7 q^{24}+ \cdots - 32 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 3 * q^6 - q^7 + 7 * q^8 + 6 * q^9 - 11 * q^11 - 4 * q^12 + 5 * q^13 + 9 * q^14 + 4 * q^16 - 8 * q^17 + 9 * q^18 + q^19 + 5 * q^21 - 6 * q^22 + 7 * q^23 + 7 * q^24 + 4 * q^26 + 11 * q^27 + 12 * q^28 + 6 * q^29 + 5 * q^31 + 13 * q^32 - q^33 + 2 * q^34 + 5 * q^36 - 11 * q^37 - 2 * q^38 + 3 * q^39 + 20 * q^41 + 4 * q^42 - 13 * q^43 + 20 * q^44 - 11 * q^47 - 6 * q^48 - 22 * q^49 - 2 * q^51 + 10 * q^52 - 3 * q^53 + 6 * q^54 - 7 * q^56 + 2 * q^57 + 16 * q^58 - 56 * q^59 + 3 * q^61 - 3 * q^62 - 15 * q^63 + q^64 - 5 * q^66 - 19 * q^67 + 12 * q^68 - 7 * q^69 + 21 * q^71 + 25 * q^73 - 6 * q^74 - 5 * q^76 - 11 * q^77 - 13 * q^78 - 9 * q^79 + 18 * q^81 + 2 * q^82 - 17 * q^83 + 3 * q^84 - 16 * q^86 + 5 * q^87 - 42 * q^88 + 7 * q^89 + 5 * q^91 + 17 * q^93 + 8 * q^94 - 2 * q^96 - q^97 - 19 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	1.12349	+	1.40881i	0.794427	+	0.996180i	0.999847	+	0.0175063i	$0.00557270\pi$
$2$	1.12349	+	1.40881i	0.794427	+	0.996180i	−0.205419	+	0.978674i	$0.565856\pi$
$3$	0.0990311	+	0.433884i	0.0571757	+	0.250503i	0.995437	−	0.0954255i	$-0.0304212\pi$
$3$	0.0990311	+	0.433884i	0.0571757	+	0.250503i	−0.938261	+	0.345928i	$0.887564\pi$
$4$	−0.277479	+	1.21572i	−0.138740	+	0.607858i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.626980i	−0.204124	+	0.255964i
$7$	−0.900969	−	3.94740i	−0.340534	−	1.49198i	−0.797949	−	0.602725i	$-0.794082\pi$
$7$	−0.900969	−	3.94740i	−0.340534	−	1.49198i	0.457415	−	0.889253i	$-0.348775\pi$
$8$	1.22252	−	0.588735i	0.432226	−	0.208149i
$9$	2.52446	−	1.21572i	0.841486	−	0.405238i
$10$		0			0
$11$	−2.62349	−	1.26341i	−0.791012	−	0.380931i	−0.00566249	−	0.999984i	$-0.501802\pi$
$11$	−2.62349	−	1.26341i	−0.791012	−	0.380931i	−0.785349	+	0.619053i	$0.787517\pi$
$12$	−0.554958			−0.160203
$13$	4.67241	+	2.25011i	1.29589	+	0.624069i	0.949425	−	0.313993i	$-0.101667\pi$
$13$	4.67241	+	2.25011i	1.29589	+	0.624069i	0.346467	+	0.938062i	$0.387381\pi$
$14$	4.54892	−	5.70416i	1.21575	−	1.52450i
$15$		0			0
$16$	4.44989	+	2.14295i	1.11247	+	0.535738i
$17$	−1.10992			−0.269194			−0.134597	−	0.990900i	$-0.542974\pi$
$17$	−1.10992			−0.269194			−0.134597	+	0.990900i	$0.542974\pi$
$18$	4.54892	+	2.19064i	1.07219	+	0.516340i
$19$	−0.455927	+	1.99755i	−0.104597	+	0.458269i	0.895321	+	0.445422i	$0.146946\pi$
$19$	−0.455927	+	1.99755i	−0.104597	+	0.458269i	−0.999917	+	0.0128465i	$0.995911\pi$
$20$		0			0
$21$	1.62349	−	0.781831i	0.354275	−	0.170610i
$22$	−1.16756	−	5.11543i	−0.248925	−	1.09061i
$23$	2.57942	−	3.23449i	0.537846	−	0.674437i	−0.436445	−	0.899731i	$-0.643763\pi$
$23$	2.57942	−	3.23449i	0.537846	−	0.674437i	0.974291	+	0.225294i	$0.0723342\pi$
$24$	0.376510	+	0.472129i	0.0768548	+	0.0963729i
$25$		0			0
$26$	2.07942	+	9.11052i	0.407807	+	1.78672i
$27$	1.60992	+	2.01877i	0.309829	+	0.388513i
$28$	5.04892			0.954156
$29$	4.38404	+	3.12733i	0.814096	+	0.580730i
$29$	4.38404	+	3.12733i	0.814096	+	0.580730i
$30$		0			0
$31$	−3.96346	−	4.97002i	−0.711858	−	0.892642i	0.285988	−	0.958233i	$-0.407678\pi$
$31$	−3.96346	−	4.97002i	−0.711858	−	0.892642i	−0.997847	+	0.0655910i	$0.979107\pi$
$32$	1.37651	+	6.03089i	0.243335	+	1.06612i
$33$	0.288364	−	1.26341i	0.0501978	−	0.219931i
$34$	−1.24698	−	1.56366i	−0.213855	−	0.268166i
$35$		0			0
$36$	0.777479	+	3.40636i	0.129580	+	0.567726i
$37$	−2.62349	+	1.26341i	−0.431299	+	0.207703i	−0.636921	−	0.770929i	$-0.719792\pi$
$37$	−2.62349	+	1.26341i	−0.431299	+	0.207703i	0.205622	+	0.978631i	$0.434078\pi$
$38$	−3.32640	+	1.60191i	−0.539613	+	0.259864i
$39$	−0.513574	+	2.25011i	−0.0822376	+	0.360306i
$40$		0			0
$41$	0.396125			0.0618643			0.0309321	−	0.999521i	$-0.490152\pi$
$41$	0.396125			0.0618643			0.0309321	+	0.999521i	$0.490152\pi$
$42$	2.92543	+	1.40881i	0.451403	+	0.217384i
$43$	−3.57942	+	4.48845i	−0.545856	+	0.684482i	−0.975873	−	0.218339i	$-0.929936\pi$
$43$	−3.57942	+	4.48845i	−0.545856	+	0.684482i	0.430017	+	0.902821i	$0.358508\pi$
$44$	2.26391	−	2.83885i	0.341297	−	0.427972i
$45$		0			0
$46$	7.45473			1.09914
$47$	−7.02930	−	3.38513i	−1.02533	−	0.493773i	−0.155870	−	0.987778i	$-0.549818\pi$
$47$	−7.02930	−	3.38513i	−1.02533	−	0.493773i	−0.869459	+	0.494005i	$0.835532\pi$
$48$	−0.489115	+	2.14295i	−0.0705977	+	0.309309i
$49$	−8.46346	+	4.07579i	−1.20907	+	0.582255i
$50$		0			0
$51$	−0.109916	−	0.481575i	−0.0153914	−	0.0674339i
$52$	−4.03199	+	5.05596i	−0.559137	+	0.701135i
$53$	2.71648	+	3.40636i	0.373137	+	0.467899i	0.932577	−	0.360972i	$-0.117555\pi$
$53$	2.71648	+	3.40636i	0.373137	+	0.467899i	−0.559439	+	0.828871i	$0.688984\pi$
$54$	−1.03534	+	4.53614i	−0.140892	+	0.617290i
$55$		0			0
$56$	−3.42543	−	4.29535i	−0.457742	−	0.573990i
$57$	−0.911854			−0.120778
$58$	0.519614	+	9.68981i	0.0682287	+	1.27233i
$59$	−9.10992			−1.18601			−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992			−1.18601			−0.593005	+	0.805199i	$0.702059\pi$
$60$		0			0
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	0.985032	+	0.172374i	$0.0551437\pi$
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	−0.812693	+	0.582693i	$0.801999\pi$
$62$	2.54892	−	11.1675i	0.323713	−	1.41828i
$63$	−7.07338	−	8.86973i	−0.891162	−	1.11748i
$64$	−0.791053	+	0.991949i	−0.0988816	+	0.123994i
$65$		0			0
$66$	2.10388	−	1.01317i	0.258969	−	0.124713i
$67$	0.337282	−	0.162426i	0.0412055	−	0.0198435i	−0.413168	−	0.910655i	$-0.635578\pi$
$67$	0.337282	−	0.162426i	0.0412055	−	0.0198435i	0.454373	+	0.890812i	$0.349863\pi$
$68$	0.307979	−	1.34934i	0.0373479	−	0.163632i
$69$	1.65883	+	0.798852i	0.199700	+	0.0961705i
$70$		0			0
$71$	10.2763	+	4.94880i	1.21957	+	0.587314i	0.929192	−	0.369598i	$-0.120505\pi$
$71$	10.2763	+	4.94880i	1.21957	+	0.587314i	0.290379	+	0.956912i	$0.406219\pi$
$72$	2.37047	−	2.97247i	0.279362	−	0.350309i
$73$	5.57942	−	6.99637i	0.653021	−	0.818863i	−0.339542	−	0.940591i	$-0.610272\pi$
$73$	5.57942	−	6.99637i	0.653021	−	0.818863i	0.992563	+	0.121728i	$0.0388436\pi$
$74$	−4.72737	−	2.27658i	−0.549545	−	0.264647i
$75$		0			0
$76$	−2.30194	−	1.10855i	−0.264050	−	0.127160i
$77$	−2.62349	+	11.4943i	−0.298974	+	1.30989i
$78$	−3.74698	+	1.80445i	−0.424262	+	0.204314i
$79$	0.535344	−	0.257808i	0.0602309	−	0.0290057i	−0.403526	−	0.914968i	$-0.632215\pi$
$79$	0.535344	−	0.257808i	0.0602309	−	0.0290057i	0.463757	+	0.885963i	$0.346501\pi$
$80$		0			0
$81$	4.52446	−	5.67349i	0.502718	−	0.630388i
$82$	0.445042	+	0.558065i	0.0491467	+	0.0616280i
$83$	−2.09903	+	9.19646i	−0.230399	+	1.00944i	0.718912	+	0.695101i	$0.244641\pi$
$83$	−2.09903	+	9.19646i	−0.230399	+	1.00944i	−0.949310	+	0.314341i	$0.898217\pi$
$84$	0.500000	+	2.19064i	0.0545545	+	0.239019i
$85$		0			0
$86$	−10.3448			−1.11551
$87$	−0.922739	+	2.21187i	−0.0989280	+	0.237137i
$88$	−3.95108			−0.421187
$89$	0.887395	+	1.11276i	0.0940637	+	0.117952i	0.826636	−	0.562737i	$-0.190252\pi$
$89$	0.887395	+	1.11276i	0.0940637	+	0.117952i	−0.732572	+	0.680689i	$0.761680\pi$
$90$		0			0
$91$	4.67241	−	20.4712i	0.489801	−	2.14596i
$92$	3.21648	+	4.03334i	0.335341	+	0.420505i
$93$	1.76391	−	2.21187i	0.182908	−	0.229360i
$94$	−3.12833	−	13.7061i	−0.322663	−	1.41368i
$95$		0			0
$96$	−2.48039	+	1.19449i	−0.253153	+	0.121912i
$97$	3.50484	−	15.3557i	0.355863	−	1.55914i	−0.407523	−	0.913195i	$-0.633607\pi$
$97$	3.50484	−	15.3557i	0.355863	−	1.55914i	0.763386	−	0.645943i	$-0.223536\pi$
$98$	−15.2506	−	7.34432i	−1.54055	−	0.741888i
$99$	−8.15883			−0.819994
$100$		0			0
$101$	−10.8753	+	13.6372i	−1.08213	+	1.35695i	−0.152570	+	0.988293i	$0.548755\pi$
$101$	−10.8753	+	13.6372i	−1.08213	+	1.35695i	−0.929564	+	0.368661i	$0.879816\pi$
$102$	0.554958	−	0.695895i	0.0549490	−	0.0689039i
$103$	−2.53534	−	1.22096i	−0.249815	−	0.120304i	0.304786	−	0.952421i	$-0.401415\pi$
$103$	−2.53534	−	1.22096i	−0.249815	−	0.120304i	−0.554601	+	0.832116i	$0.687129\pi$
$104$	7.03684			0.690019
$105$		0			0
$106$	−1.74698	+	7.65402i	−0.169682	+	0.743424i
$107$	−6.72132	+	3.23682i	−0.649775	+	0.312915i	−0.729580	−	0.683895i	$-0.760284\pi$
$107$	−6.72132	+	3.23682i	−0.649775	+	0.312915i	0.0798052	+	0.996810i	$0.474570\pi$
$108$	−2.90097	+	1.39703i	−0.279146	+	0.134430i
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	0.989482	−	0.144653i	$-0.0462066\pi$
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	−0.954255	+	0.298993i	$0.903349\pi$
$110$		0			0
$111$	−0.807979	−	1.01317i	−0.0766899	−	0.0961661i
$112$	4.44989	−	19.4962i	0.420475	−	1.84222i
$113$	1.92274	+	8.42407i	0.180876	+	0.792470i	0.981214	+	0.192921i	$0.0617961\pi$
$113$	1.92274	+	8.42407i	0.180876	+	0.792470i	−0.800338	+	0.599549i	$0.795347\pi$
$114$	−1.02446	−	1.28463i	−0.0959493	−	0.120317i
$115$		0			0
$116$	−5.01842	+	4.46198i	−0.465948	+	0.414284i
$117$	14.5308			1.34337
$118$	−10.2349	−	12.8342i	−0.942199	−	1.18148i
$119$	1.00000	+	4.38129i	0.0916698	+	0.401632i
$120$		0			0
$121$	−1.57188	−	1.97108i	−0.142899	−	0.179189i
$122$	−6.79590	+	8.52179i	−0.615272	+	0.771526i
$123$	0.0392287	+	0.171872i	0.00353713	+	0.0154972i
$124$	7.14191	−	3.43936i	0.641362	−	0.308864i
$125$		0			0
$126$	4.54892	−	19.9301i	0.405250	−	1.77552i
$127$	9.43512	+	4.54371i	0.837231	+	0.403189i	0.802822	−	0.596219i	$-0.203331\pi$
$127$	9.43512	+	4.54371i	0.837231	+	0.403189i	0.0344090	+	0.999408i	$0.489045\pi$
$128$	10.0858			0.891463
$129$	−2.30194	−	1.10855i	−0.202674	−	0.0976028i
$130$		0			0
$131$	−0.283520	+	0.355523i	−0.0247712	+	0.0310622i	−0.794063	−	0.607836i	$-0.792038\pi$
$131$	−0.283520	+	0.355523i	−0.0247712	+	0.0310622i	0.769292	+	0.638898i	$0.220609\pi$
$132$	1.45593	+	0.701137i	0.126722	+	0.0610262i
$133$	8.29590			0.719345
$134$	0.607760	+	0.292682i	0.0525025	+	0.0252839i
$135$		0			0
$136$	−1.35690	+	0.653447i	−0.116353	+	0.0560326i
$137$	−11.9291	+	5.74474i	−1.01917	+	0.490806i	−0.867401	−	0.497610i	$-0.834211\pi$
$137$	−11.9291	+	5.74474i	−1.01917	+	0.490806i	−0.151769	+	0.988416i	$0.548497\pi$
$138$	0.738250	+	3.23449i	0.0628440	+	0.275338i
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	−0.850260	−	0.526364i	$-0.823555\pi$
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	0.702367	+	0.711815i	$0.252127\pi$
$140$		0			0
$141$	0.772635	−	3.38513i	0.0650676	−	0.285080i
$142$	4.57338	+	20.0373i	0.383789	+	1.68149i
$143$	−9.41521	−	11.8063i	−0.787339	−	0.987292i
$144$	13.8388			1.15323
$145$		0			0
$146$	16.1250			1.33451
$147$	−2.60656	−	3.26853i	−0.214986	−	0.269584i
$148$	−0.807979	−	3.53999i	−0.0664154	−	0.290985i
$149$	−0.602679	+	2.64051i	−0.0493734	+	0.216319i	−0.993596	−	0.112988i	$-0.963958\pi$
$149$	−0.602679	+	2.64051i	−0.0493734	+	0.216319i	0.944223	+	0.329307i	$0.106815\pi$
$150$		0			0
$151$	−1.51842	+	1.90404i	−0.123567	+	0.154948i	−0.839767	−	0.542947i	$-0.817308\pi$
$151$	−1.51842	+	1.90404i	−0.123567	+	0.154948i	0.716200	+	0.697895i	$0.245880\pi$
$152$	0.618645	+	2.71046i	0.0501788	+	0.219848i
$153$	−2.80194	+	1.34934i	−0.226523	+	0.109088i
$154$	−19.1407	+	9.21768i	−1.54240	+	0.742782i
$155$		0			0
$156$	−2.59299	−	1.24872i	−0.207605	−	0.0999775i
$157$	−17.6775			−1.41082			−0.705411	−	0.708799i	$-0.749238\pi$
$157$	−17.6775			−1.41082			−0.705411	+	0.708799i	$0.749238\pi$
$158$	0.964656	+	0.464554i	0.0767439	+	0.0369579i
$159$	−1.20895	+	1.51597i	−0.0958758	+	0.120224i
$160$		0			0
$161$	−15.0918	−	7.26782i	−1.18940	−	0.572785i
$162$	13.0761			1.02735
$163$	−4.47434	−	2.15473i	−0.350458	−	0.168772i	0.250370	−	0.968150i	$-0.419448\pi$
$163$	−4.47434	−	2.15473i	−0.350458	−	0.168772i	−0.600827	+	0.799379i	$0.705162\pi$
$164$	−0.109916	+	0.481575i	−0.00858302	+	0.0376047i
$165$		0			0
$166$	−15.3143	+	7.37499i	−1.18862	+	0.572410i
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	0.932487	+	0.361203i	$0.117634\pi$
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	−0.683422	+	0.730024i	$0.739509\pi$
$168$	1.52446	−	1.91161i	0.117615	−	0.147484i
$169$	8.66301	+	10.8631i	0.666386	+	0.835621i
$170$		0			0
$171$	1.27748	+	5.59700i	0.0976913	+	0.428013i
$172$	−4.46346	−	5.59700i	−0.340336	−	0.426767i
$173$	−10.5133			−0.799314			−0.399657	−	0.916665i	$-0.630871\pi$
$173$	−10.5133			−0.799314			−0.399657	+	0.916665i	$0.630871\pi$
$174$	−4.15279	+	1.18505i	−0.314822	+	0.0898380i
$175$		0			0
$176$	−8.96681	−	11.2440i	−0.675899	−	0.847550i
$177$	−0.902165	−	3.95264i	−0.0678109	−	0.297099i
$178$	−0.570688	+	2.50035i	−0.0427748	+	0.187409i
$179$	−3.57942	−	4.48845i	−0.267538	−	0.335482i	0.629856	−	0.776712i	$-0.283114\pi$
$179$	−3.57942	−	4.48845i	−0.267538	−	0.335482i	−0.897394	+	0.441230i	$0.854542\pi$
$180$		0			0
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	0.999688	+	0.0249747i	$0.00795053\pi$
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	−0.889852	+	0.456250i	$0.849192\pi$
$182$	34.0894	−	16.4166i	2.52687	−	1.21688i
$183$	−2.42543	+	1.16802i	−0.179293	+	0.0863428i
$184$	1.24914	−	5.47282i	0.0920875	−	0.403462i
$185$		0			0
$186$	5.09783			0.373791
$187$	2.91185	+	1.40227i	0.212936	+	0.102545i
$188$	6.06584	−	7.60633i	0.442397	−	0.554748i
$189$	6.51842	−	8.17384i	0.474145	−	0.594559i
$190$		0			0
$191$	−18.8116			−1.36116			−0.680581	−	0.732673i	$-0.738272\pi$
$191$	−18.8116			−1.36116			−0.680581	+	0.732673i	$0.738272\pi$
$192$	−0.508729	−	0.244991i	−0.0367144	−	0.0176807i
$193$	2.42208	−	10.6118i	0.174345	−	0.763854i	−0.809832	−	0.586662i	$-0.800442\pi$
$193$	2.42208	−	10.6118i	0.174345	−	0.763854i	0.984176	−	0.177192i	$-0.0567013\pi$
$194$	25.5710	−	12.3143i	1.83589	−	0.884118i
$195$		0			0
$196$	−2.60656	−	11.4201i	−0.186183	−	0.815722i
$197$	5.23759	−	6.56773i	0.373163	−	0.467931i	−0.559422	−	0.828883i	$-0.688977\pi$
$197$	5.23759	−	6.56773i	0.373163	−	0.467931i	0.932584	+	0.360952i	$0.117548\pi$
$198$	−9.16637	−	11.4943i	−0.651425	−	0.816861i
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	−0.895476	−	0.445109i	$-0.853165\pi$
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	0.999922	−	0.0124967i	$-0.00397793\pi$
$200$		0			0
$201$	0.103875	+	0.130256i	0.00732681	+	0.00918753i
$202$	−31.4306			−2.21145
$203$	8.39493	−	20.1232i	0.589208	−	1.41237i
$204$	0.615957			0.0431256
$205$		0			0
$206$	−1.12833	−	4.94355i	−0.0786148	−	0.344434i
$207$	2.57942	−	11.3012i	0.179282	−	0.785485i
$208$	15.9698	+	20.0255i	1.10731	+	1.38852i
$209$	3.71983	−	4.66452i	0.257306	−	0.322652i
$210$		0			0
$211$	7.29805	−	3.51456i	0.502419	−	0.241952i	−0.165468	−	0.986215i	$-0.552913\pi$
$211$	7.29805	−	3.51456i	0.502419	−	0.241952i	0.667887	+	0.744263i	$0.267199\pi$
$212$	−4.89493	+	2.35727i	−0.336185	+	0.161898i
$213$	−1.12953	+	4.94880i	−0.0773942	+	0.339086i
$214$	−12.1114	−	5.83255i	−0.827919	−	0.398705i
$215$		0			0
$216$	3.15668	+	1.52018i	0.214785	+	0.103435i
$217$	−16.0477	+	20.1232i	−1.08939	+	1.36605i
$218$	−1.85690	+	2.32847i	−0.125765	+	0.157704i
$219$	3.58815	+	1.72796i	0.242464	+	0.116765i
$220$		0			0
$221$	−5.18598	−	2.49744i	−0.348847	−	0.167996i
$222$	0.519614	−	2.27658i	0.0348742	−	0.152794i
$223$	19.7485	−	9.51036i	1.32246	−	0.636861i	0.366512	−	0.930413i	$-0.380552\pi$
$223$	19.7485	−	9.51036i	1.32246	−	0.636861i	0.955943	+	0.293552i	$0.0948374\pi$
$224$	22.5661	−	10.8673i	1.50776	−	0.726101i
$225$		0			0
$226$	−9.70775	+	12.1731i	−0.645750	+	0.809745i
$227$	11.3964	+	14.2907i	0.756407	+	0.948504i	0.999770	−	0.0214309i	$-0.00682218\pi$
$227$	11.3964	+	14.2907i	0.756407	+	0.948504i	−0.243363	+	0.969935i	$0.578251\pi$
$228$	0.253020	−	1.10855i	0.0167567	−	0.0734158i
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	−0.944876	−	0.327427i	$-0.893818\pi$
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	0.709239	−	0.704968i	$-0.249039\pi$
$230$		0			0
$231$	−5.24698			−0.345226
$232$	7.20075	+	1.24218i	0.472752	+	0.0815532i
$233$	−1.95646			−0.128172			−0.0640860	−	0.997944i	$-0.520413\pi$
$233$	−1.95646			−0.128172			−0.0640860	+	0.997944i	$0.520413\pi$
$234$	16.3252	+	20.4712i	1.06721	+	1.33824i
$235$		0			0
$236$	2.52781	−	11.0751i	0.164546	−	0.720925i
$237$	0.164874	+	0.206746i	0.0107097	+	0.0134296i
$238$	−5.04892	+	6.33114i	−0.327273	+	0.410387i
$239$	1.99449	+	8.73844i	0.129013	+	0.565243i	0.997571	+	0.0696554i	$0.0221900\pi$
$239$	1.99449	+	8.73844i	0.129013	+	0.565243i	−0.868558	+	0.495587i	$0.834953\pi$
$240$		0			0
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.910506	−	0.413496i	$-0.864308\pi$
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.244407	+	0.969673i	$0.578593\pi$
$242$	1.01089	−	4.42898i	0.0649822	−	0.284705i
$243$	9.88889	+	4.76224i	0.634372	+	0.305498i
$244$	−7.54288			−0.482883
$245$		0			0
$246$	−0.198062	+	0.248362i	−0.0126280	+	0.0158350i
$247$	−6.62498	+	8.30746i	−0.421537	+	0.528591i
$248$	−7.77144	−	3.74253i	−0.493487	−	0.237651i
$249$	−4.19806			−0.266041
$250$		0			0
$251$	−5.74214	+	25.1579i	−0.362440	+	1.58795i	0.384540	+	0.923108i	$0.374360\pi$
$251$	−5.74214	+	25.1579i	−0.362440	+	1.58795i	−0.746980	+	0.664847i	$0.768497\pi$
$252$	12.7458	−	6.13805i	0.802909	−	0.386661i
$253$	−10.8535	+	5.22679i	−0.682356	+	0.328606i
$254$	4.19902	+	18.3971i	0.263470	+	1.15434i
$255$		0			0
$256$	12.9133	+	16.1928i	0.807084	+	1.01205i
$257$	2.65937	−	11.6514i	0.165887	−	0.726797i	−0.821726	−	0.569883i	$-0.806988\pi$
$257$	2.65937	−	11.6514i	0.165887	−	0.726797i	0.987612	−	0.156914i	$-0.0501545\pi$
$258$	−1.02446	−	4.48845i	−0.0637800	−	0.279438i
$259$	7.35086	+	9.21768i	0.456760	+	0.572759i
$260$		0			0
$261$	14.8693	+	2.56506i	0.920385	+	0.158773i
$262$	−0.819396			−0.0506225
$263$	0.207455	+	0.260141i	0.0127923	+	0.0160410i	0.788186	−	0.615437i	$-0.211020\pi$
$263$	0.207455	+	0.260141i	0.0127923	+	0.0160410i	−0.775394	+	0.631477i	$0.782449\pi$
$264$	−0.391280	−	1.71431i	−0.0240816	−	0.105509i
$265$		0			0
$266$	9.32036	+	11.6874i	0.571468	+	0.716598i
$267$	−0.394928	+	0.495224i	−0.0241692	+	0.0303072i
$268$	0.103875	+	0.455108i	0.00634520	+	0.0278002i
$269$	0.958615	−	0.461645i	0.0584478	−	0.0281470i	−0.404432	−	0.914568i	$-0.632531\pi$
$269$	0.958615	−	0.461645i	0.0584478	−	0.0281470i	0.462879	+	0.886421i	$0.346816\pi$
$270$		0			0
$271$	3.66368	−	16.0516i	0.222553	−	0.975067i	−0.732996	−	0.680233i	$-0.761879\pi$
$271$	3.66368	−	16.0516i	0.222553	−	0.975067i	0.955549	−	0.294834i	$-0.0952642\pi$
$272$	−4.93900	−	2.37850i	−0.299471	−	0.144218i
$273$	9.34481			0.565574
$274$	−21.4955	−	10.3517i	−1.29859	−	0.625367i
$275$		0			0
$276$	−1.43147	+	1.79500i	−0.0861643	+	0.108047i
$277$	5.94116	+	2.86111i	0.356970	+	0.171907i	0.603769	−	0.797159i	$-0.293665\pi$
$277$	5.94116	+	2.86111i	0.356970	+	0.171907i	−0.246800	+	0.969066i	$0.579379\pi$
$278$	−5.03923			−0.302233
$279$	−16.0477	−	7.72818i	−0.960752	−	0.462674i
$280$		0			0
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.641448	−	0.767166i	$-0.278334\pi$
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.999731	−	0.0231840i	$-0.00738037\pi$
$282$	5.63706	−	2.71467i	0.335682	−	0.161656i
$283$	−0.791053	−	3.46583i	−0.0470232	−	0.206022i	0.945959	−	0.324286i	$-0.105124\pi$
$283$	−0.791053	−	3.46583i	−0.0470232	−	0.206022i	−0.992982	+	0.118264i	$0.962267\pi$
$284$	−8.86778	+	11.1198i	−0.526206	+	0.659841i
$285$		0			0
$286$	6.05496	−	26.5285i	0.358037	−	1.56866i
$287$	−0.356896	−	1.56366i	−0.0210669	−	0.0923001i
$288$	10.8068	+	13.5513i	0.636796	+	0.798517i
$289$	−15.7681			−0.927534
$290$		0			0
$291$	7.00969			0.410915
$292$	6.95742	+	8.72433i	0.407152	+	0.510553i
$293$	7.31647	+	32.0556i	0.427433	+	1.87271i	0.485246	+	0.874378i	$0.338730\pi$
$293$	7.31647	+	32.0556i	0.427433	+	1.87271i	−0.0578127	+	0.998327i	$0.518413\pi$
$294$	1.67629	−	7.34432i	0.0977633	−	0.428329i
$295$		0			0
$296$	−2.46346	+	3.08908i	−0.143186	+	0.179549i
$297$	−1.67307	−	7.33020i	−0.0970814	−	0.425342i
$298$	−4.39708	+	2.11752i	−0.254716	+	0.122665i
$299$	19.3300	−	9.30886i	1.11789	−	0.538345i
$300$		0			0
$301$	20.9426	+	10.0854i	1.20711	+	0.581316i
$302$	−4.38835			−0.252521
$303$	−6.99396	−	3.36811i	−0.401792	−	0.193493i
$304$	−6.30947	+	7.91183i	−0.361873	+	0.453774i
$305$		0			0
$306$	−5.04892	−	2.43143i	−0.288627	−	0.138996i
$307$	−14.6703			−0.837275			−0.418638	−	0.908153i	$-0.637492\pi$
$307$	−14.6703			−0.837275			−0.418638	+	0.908153i	$0.637492\pi$
$308$	−13.2458	−	6.37883i	−0.754749	−	0.363468i
$309$	0.278676	−	1.22096i	0.0158533	−	0.0694578i
$310$		0			0
$311$	−16.6918	+	8.03834i	−0.946504	+	0.455812i	−0.842459	−	0.538760i	$-0.818893\pi$
$311$	−16.6918	+	8.03834i	−0.946504	+	0.455812i	−0.104045	+	0.994573i	$0.533179\pi$
$312$	0.696866	+	3.05317i	0.0394523	+	0.172852i
$313$	−14.3354	+	17.9760i	−0.810286	+	1.01607i	0.189132	+	0.981952i	$0.439433\pi$
$313$	−14.3354	+	17.9760i	−0.810286	+	1.01607i	−0.999418	+	0.0341147i	$0.989139\pi$
$314$	−19.8605	−	24.9043i	−1.12080	−	1.40543i
$315$		0			0
$316$	0.164874	+	0.722362i	0.00927491	+	0.0406360i
$317$	−8.76540	−	10.9915i	−0.492314	−	0.617342i	0.472162	−	0.881512i	$-0.343474\pi$
$317$	−8.76540	−	10.9915i	−0.492314	−	0.617342i	−0.964476	+	0.264170i	$0.914902\pi$
$318$	−3.49396			−0.195932
$319$	−7.55041	−	13.7433i	−0.422742	−	0.769479i
$320$		0			0
$321$	−2.07002	−	2.59573i	−0.115537	−	0.144879i
$322$	−6.71648	−	29.4268i	−0.374295	−	1.63989i
$323$	0.506041	−	2.21711i	0.0281569	−	0.123363i
$324$	5.64191	+	7.07473i	0.313439	+	0.393040i
$325$		0			0
$326$	−1.99127	−	8.72433i	−0.110286	−	0.483196i
$327$	−0.662718	+	0.319148i	−0.0366484	+	0.0176489i
$328$	0.484271	−	0.233212i	0.0267394	−	0.0128770i
$329$	−7.02930	+	30.7974i	−0.387538	+	1.69792i
$330$		0			0
$331$	13.9565			0.767116			0.383558	−	0.923517i	$-0.374699\pi$
$331$	13.9565			0.767116			0.383558	+	0.923517i	$0.374699\pi$
$332$	−10.5978	−	5.10365i	−0.581632	−	0.280099i
$333$	−5.08695	+	6.37883i	−0.278763	+	0.349558i
$334$	−16.2506	+	20.3776i	−0.889195	+	1.11501i
$335$		0			0
$336$	8.89977			0.485522
$337$	−12.6114	−	6.07333i	−0.686987	−	0.330836i	0.0576199	−	0.998339i	$-0.481649\pi$
$337$	−12.6114	−	6.07333i	−0.686987	−	0.330836i	−0.744607	+	0.667503i	$0.767363\pi$
$338$	−5.57122	+	24.4091i	−0.303034	+	1.32768i
$339$	−3.46466	+	1.66849i	−0.188174	+	0.0906200i
$340$		0			0
$341$	4.11894	+	18.0463i	0.223053	+	0.977260i
$342$	−6.44989	+	8.08790i	−0.348770	+	0.437344i
$343$	6.04288	+	7.57753i	0.326285	+	0.409148i
$344$	−1.73341	+	7.59455i	−0.0934590	+	0.409471i
$345$		0			0
$346$	−11.8116	−	14.8113i	−0.634997	−	0.796261i
$347$	19.8538			1.06581			0.532905	−	0.846175i	$-0.321100\pi$
$347$	19.8538			1.06581			0.532905	+	0.846175i	$0.321100\pi$
$348$	−2.43296	−	1.73553i	−0.130420	−	0.0930344i
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$		0			0
$351$	2.97972	+	13.0550i	0.159046	+	0.696825i
$352$	4.00820	−	17.5611i	0.213638	−	0.936007i
$353$	2.50335	+	3.13910i	0.133240	+	0.167078i	0.843976	−	0.536382i	$-0.180209\pi$
$353$	2.50335	+	3.13910i	0.133240	+	0.167078i	−0.710736	+	0.703459i	$0.751638\pi$
$354$	4.55496	−	5.71174i	0.242093	−	0.303575i
$355$		0			0
$356$	−1.59903	+	0.770053i	−0.0847485	+	0.0408127i
$357$	−1.80194	+	0.867767i	−0.0953687	+	0.0459271i
$358$	2.30194	−	10.0854i	0.121661	−	0.533032i
$359$	0.672407	+	0.323814i	0.0354883	+	0.0170903i	0.451544	−	0.892249i	$-0.350873\pi$
$359$	0.672407	+	0.323814i	0.0354883	+	0.0170903i	−0.416055	+	0.909339i	$0.636588\pi$
$360$		0			0
$361$	13.3361	+	6.42232i	0.701899	+	0.338017i
$362$	−7.46077	+	9.35551i	−0.392129	+	0.491715i
$363$	0.699554	−	0.877213i	0.0367171	−	0.0460418i
$364$	23.5906	+	11.3606i	1.23648	+	0.595459i
$365$		0			0
$366$	−4.37047	−	2.10471i	−0.228448	−	0.110015i
$367$	−7.57660	+	33.1952i	−0.395495	+	1.73278i	0.249304	+	0.968425i	$0.419798\pi$
$367$	−7.57660	+	33.1952i	−0.395495	+	1.73278i	−0.644799	+	0.764352i	$0.723059\pi$
$368$	18.4095	−	8.86553i	0.959659	−	0.462148i
$369$	1.00000	−	0.481575i	0.0520579	−	0.0250698i
$370$		0			0
$371$	10.9988	−	13.7921i	0.571029	−	0.716048i
$372$	2.19955	+	2.75815i	0.114042	+	0.143004i
$373$	6.23072	−	27.2986i	0.322614	−	1.41347i	−0.510268	−	0.860015i	$-0.670454\pi$
$373$	6.23072	−	27.2986i	0.322614	−	1.41347i	0.832882	−	0.553450i	$-0.186689\pi$
$374$	1.29590	+	5.67770i	0.0670092	+	0.293587i
$375$		0			0
$376$	−10.5864			−0.545953
$377$	13.4472	+	24.4767i	0.692566	+	1.26062i
$378$	18.8388			0.968962
$379$	14.2661	+	17.8891i	0.732798	+	0.918900i	0.998986	−	0.0450211i	$-0.0143355\pi$
$379$	14.2661	+	17.8891i	0.732798	+	0.918900i	−0.266188	+	0.963921i	$0.585764\pi$
$380$		0			0
$381$	−1.03707	+	4.54371i	−0.0531308	+	0.232781i
$382$	−21.1347	−	26.5020i	−1.08134	−	1.35596i
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	−0.933981	−	0.357323i	$-0.883690\pi$
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	0.556194	+	0.831052i	$0.312261\pi$
$384$	0.998804	+	4.37604i	0.0509700	+	0.223314i
$385$		0			0
$386$	17.6712	−	8.51001i	0.899441	−	0.433148i
$387$	−3.57942	+	15.6824i	−0.181952	+	0.797184i
$388$	17.6957	+	8.52179i	0.898362	+	0.432628i
$389$	−10.3913			−0.526862			−0.263431	−	0.964678i	$-0.584854\pi$
$389$	−10.3913			−0.526862			−0.263431	+	0.964678i	$0.584854\pi$
$390$		0			0
$391$	−2.86294	+	3.59001i	−0.144785	+	0.181555i
$392$	−7.94720	+	9.96547i	−0.401394	+	0.503332i
$393$	−0.182333	−	0.0878068i	−0.00919747	−	0.00442927i
$394$	15.1371			0.762594
$395$		0			0
$396$	2.26391	−	9.91882i	0.113766	−	0.498439i
$397$	7.40366	−	3.56541i	0.371579	−	0.178943i	−0.238769	−	0.971076i	$-0.576744\pi$
$397$	7.40366	−	3.56541i	0.371579	−	0.178943i	0.610348	+	0.792133i	$0.291030\pi$
$398$	10.7497	−	5.17677i	0.538832	−	0.259488i
$399$	0.821552	+	3.59945i	0.0411290	+	0.180198i
$400$		0			0
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	0.999996	−	0.00286337i	$-0.000911439\pi$
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	−0.225312	+	0.974287i	$0.572340\pi$
$402$	−0.0668027	+	0.292682i	−0.00333182	+	0.0145976i
$403$	−7.33579	−	32.1402i	−0.365422	−	1.60102i
$404$	−13.5613	−	17.0053i	−0.674700	−	0.846047i
$405$		0			0
$406$	37.7814	−	10.7813i	1.87506	−	0.535069i
$407$	8.47889			0.420283
$408$	−0.417895	−	0.524023i	−0.0206889	−	0.0259430i
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	−0.965958	−	0.258701i	$-0.916706\pi$
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	0.758052	−	0.652194i	$-0.226151\pi$
$410$		0			0
$411$	−3.67390	−	4.60692i	−0.181220	−	0.227243i
$412$	2.18784	−	2.74347i	0.107787	−	0.135161i
$413$	8.20775	+	35.9605i	0.403877	+	1.76950i
$414$	18.8192	−	9.06283i	0.924911	−	0.445414i
$415$		0			0
$416$	−7.13856	+	31.2761i	−0.349996	+	1.53343i
$417$	−1.12133	−	0.540006i	−0.0549120	−	0.0264442i
$418$	10.7506			0.525830
$419$	9.81378	+	4.72607i	0.479435	+	0.230884i	0.657962	−	0.753051i	$-0.271419\pi$
$419$	9.81378	+	4.72607i	0.479435	+	0.230884i	−0.178527	+	0.983935i	$0.557133\pi$
$420$		0			0
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	−0.986383	−	0.164467i	$-0.947410\pi$
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	0.379834	+	0.925055i	$0.375981\pi$
$422$	13.1506	+	6.33301i	0.640163	+	0.308286i
$423$	−21.8605			−1.06290
$424$	5.32640	+	2.56506i	0.258673	+	0.124570i
$425$		0			0
$426$	−8.24094	+	3.96863i	−0.399275	+	0.192281i
$427$	22.0661	−	10.6265i	1.06786	−	0.514252i
$428$	−2.07002	−	9.06937i	−0.100058	−	0.438384i
$429$	4.19016	−	5.25430i	0.202303	−	0.253680i
$430$		0			0
$431$	6.71797	−	29.4334i	0.323593	−	1.41776i	−0.507514	−	0.861643i	$-0.669436\pi$
$431$	6.71797	−	29.4334i	0.323593	−	1.41776i	0.831108	−	0.556112i	$-0.187707\pi$
$432$	2.83781	+	12.4333i	0.136534	+	0.598196i
$433$	12.5891	+	15.7862i	0.604994	+	0.758638i	0.986147	−	0.165874i	$-0.0530444\pi$
$433$	12.5891	+	15.7862i	0.604994	+	0.758638i	−0.381153	+	0.924512i	$0.624473\pi$
$434$	−46.3793			−2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	5.28501	+	6.62720i	0.252816	+	0.317022i
$438$	1.59688	+	6.99637i	0.0763016	+	0.334299i
$439$	2.37316	−	10.3975i	0.113265	−	0.496245i	−0.886193	−	0.463316i	$-0.846659\pi$
$439$	2.37316	−	10.3975i	0.113265	−	0.496245i	0.999458	−	0.0329287i	$-0.0104834\pi$
$440$		0			0
$441$	−16.4107	+	20.5783i	−0.781460	+	0.979920i
$442$	−2.30798	−	10.1119i	−0.109779	−	0.480975i
$443$	−18.3349	+	8.82962i	−0.871117	+	0.419508i	−0.815372	−	0.578937i	$-0.803468\pi$
$443$	−18.3349	+	8.82962i	−0.871117	+	0.419508i	−0.0557448	+	0.998445i	$0.517753\pi$
$444$	1.45593	−	0.701137i	0.0690952	−	0.0332745i
$445$		0			0
$446$	35.5855	+	17.1371i	1.68502	+	0.811464i
$447$	−1.20536			−0.0570115
$448$	4.62833	+	2.22889i	0.218668	+	0.105305i
$449$	12.1102	−	15.1857i	0.571516	−	0.716659i	−0.409124	−	0.912479i	$-0.634166\pi$
$449$	12.1102	−	15.1857i	0.571516	−	0.716659i	0.980640	+	0.195820i	$0.0627369\pi$
$450$		0			0
$451$	−1.03923	−	0.500466i	−0.0489354	−	0.0235660i
$452$	−10.7748			−0.506804
$453$	−0.976501	−	0.470258i	−0.0458800	−	0.0220946i
$454$	−7.32908	+	32.1108i	−0.343971	+	1.50704i
$455$		0			0
$456$	−1.11476	+	0.536840i	−0.0522034	+	0.0251399i
$457$	−2.76391	−	12.1095i	−0.129290	−	0.566457i	−0.997526	−	0.0703045i	$-0.977603\pi$
$457$	−2.76391	−	12.1095i	−0.129290	−	0.566457i	0.868236	−	0.496152i	$-0.165254\pi$
$458$	18.0036	−	22.5759i	0.841255	−	1.05490i
$459$	−1.78687	−	2.24067i	−0.0834041	−	0.104585i
$460$		0			0
$461$	4.88351	+	21.3961i	0.227448	+	0.996514i	0.951712	+	0.306991i	$0.0993223\pi$
$461$	4.88351	+	21.3961i	0.227448	+	0.996514i	−0.724265	+	0.689522i	$0.757821\pi$
$462$	−5.89493	−	7.39201i	−0.274257	−	0.343907i
$463$	33.0073			1.53398			0.766990	−	0.641660i	$-0.221754\pi$
$463$	33.0073			1.53398			0.766990	+	0.641660i	$0.221754\pi$
$464$	12.8068	+	23.3110i	0.594540	+	1.08219i
$465$		0			0
$466$	−2.19806	−	2.75628i	−0.101823	−	0.127682i
$467$	−5.80851	−	25.4487i	−0.268786	−	1.17763i	−0.911427	−	0.411461i	$-0.865019\pi$
$467$	−5.80851	−	25.4487i	−0.268786	−	1.17763i	0.642642	−	0.766167i	$-0.277838\pi$
$468$	−4.03199	+	17.6653i	−0.186379	+	0.816579i
$469$	−0.945042	−	1.18505i	−0.0436380	−	0.0547203i
$470$		0			0
$471$	−1.75063	−	7.67000i	−0.0806647	−	0.353415i
$472$	−11.1371	+	5.36333i	−0.512625	+	0.246867i
$473$	15.0613	−	7.25314i	0.692519	−	0.333500i
$474$	−0.106031	+	0.464554i	−0.00487018	+	0.0213377i
$475$		0			0
$476$	−5.60388			−0.256853
$477$	10.9988	+	5.29674i	0.503601	+	0.242521i
$478$	−10.0700	+	12.6274i	−0.460592	+	0.577564i
$479$	20.6163	−	25.8520i	0.941981	−	1.18121i	−0.0413068	−	0.999147i	$-0.513152\pi$
$479$	20.6163	−	25.8520i	0.941981	−	1.18121i	0.983287	−	0.182060i	$-0.0582765\pi$
$480$		0			0
$481$	−15.1008			−0.688538
$482$	−32.3071	−	15.5583i	−1.47155	−	0.708660i
$483$	1.65883	−	7.26782i	0.0754795	−	0.330697i
$484$	2.83244	−	1.36403i	0.128747	−	0.0620014i
$485$		0			0
$486$	4.40097	+	19.2819i	0.199632	+	0.874645i
$487$	6.33244	−	7.94063i	0.286950	−	0.359824i	−0.617375	−	0.786669i	$-0.711804\pi$
$487$	6.33244	−	7.94063i	0.286950	−	0.359824i	0.904325	+	0.426845i	$0.140375\pi$
$488$	5.11745	+	6.41708i	0.231656	+	0.290487i
$489$	0.491803	−	2.15473i	0.0222401	−	0.0974403i
$490$		0			0
$491$	−12.2714	−	15.3879i	−0.553802	−	0.694446i	0.423596	−	0.905851i	$-0.360768\pi$
$491$	−12.2714	−	15.3879i	−0.553802	−	0.694446i	−0.977399	+	0.211405i	$0.932196\pi$
$492$	−0.219833			−0.00991082
$493$	−4.86592	−	3.47107i	−0.219150	−	0.156329i
$494$	−19.1468			−0.861453
$495$		0			0
$496$	−6.98643	−	30.6095i	−0.313700	−	1.37441i
$497$	10.2763	−	45.0233i	0.460954	−	2.01957i
$498$	−4.71648	−	5.91428i	−0.211351	−	0.265025i
$499$	17.3639	−	21.7736i	0.777315	−	0.974722i	−0.222685	−	0.974890i	$-0.571482\pi$
$499$	17.3639	−	21.7736i	0.777315	−	0.974722i	1.00000		0.000168534i	$5.36461e-5\pi$
$500$		0			0
$501$	−5.79978	+	2.79303i	−0.259115	+	0.124783i
$502$	−41.8940	+	20.1751i	−1.86982	+	0.900459i
$503$	−0.0501138	+	0.219563i	−0.00223446	+	0.00978982i	−0.976033	−	0.217623i	$-0.930170\pi$
$503$	−0.0501138	+	0.219563i	−0.00223446	+	0.00978982i	0.973798	+	0.227413i	$0.0730267\pi$
$504$	−13.8693	−	6.67909i	−0.617787	−	0.297510i
$505$		0			0
$506$	−19.5574	−	9.41835i	−0.869433	−	0.418697i
$507$	−3.85540	+	4.83452i	−0.171224	+	0.214709i
$508$	−8.14191	+	10.2096i	−0.361239	+	0.452979i
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.864481	−	0.502665i	$-0.167647\pi$
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.145995	+	0.989285i	$0.453362\pi$
$510$		0			0
$511$	−32.6444	−	15.7207i	−1.44410	−	0.695443i
$512$	−3.81604	+	16.7192i	−0.168647	+	0.738890i
$513$	−4.76659	+	2.29547i	−0.210450	+	0.101348i
$514$	19.4025	−	9.34373i	0.855806	−	0.412134i
$515$		0			0
$516$	1.98643	−	2.49090i	0.0874475	−	0.109656i
$517$	14.1645	+	17.7617i	0.622954	+	0.781160i
$518$	−4.72737	+	20.7119i	−0.207709	+	0.910030i
$519$	−1.04115	−	4.56157i	−0.0457013	−	0.200231i
$520$		0			0
$521$	23.5797			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$521$	23.5797			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$522$	13.0918	+	23.8298i	0.573012	+	1.04300i
$523$	−3.96508			−0.173381			−0.0866905	−	0.996235i	$-0.527629\pi$
$523$	−3.96508			−0.173381			−0.0866905	+	0.996235i	$0.527629\pi$
$524$	−0.353543	−	0.443330i	−0.0154446	−	0.0193669i
$525$		0			0
$526$	−0.133415	+	0.584531i	−0.00581719	+	0.0254868i
$527$	4.39911	+	5.51631i	0.191628	+	0.240294i
$528$	3.99061	−	5.00406i	0.173669	−	0.217774i
$529$	1.30947	+	5.73717i	0.0569335	+	0.249442i
$530$		0			0
$531$	−22.9976	+	11.0751i	−0.998011	+	0.480617i
$532$	−2.30194	+	10.0854i	−0.0998017	+	0.437260i
$533$	1.85086	+	0.891325i	0.0801694	+	0.0386076i
$534$	−1.14138			−0.0493921
$535$		0			0
$536$	0.316708	−	0.397139i	0.0136797	−	0.0171538i
$537$	1.59299	−	1.99755i	0.0687426	−	0.0862005i
$538$	1.72737	+	0.831855i	0.0744720	+	0.0358638i
$539$	27.3532			1.17818
$540$		0			0
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	−0.708709	−	0.705501i	$-0.750722\pi$
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	0.944630	−	0.328137i	$-0.106421\pi$
$542$	26.7298	−	12.8724i	1.14814	−	0.552917i
$543$	−2.66272	+	1.28230i	−0.114268	+	0.0550287i
$544$	−1.52781	−	6.69378i	−0.0655044	−	0.286993i
$545$		0			0
$546$	10.4988	+	13.1651i	0.449307	+	0.563414i
$547$	5.52768	−	24.2183i	0.236347	−	1.03550i	−0.707913	−	0.706300i	$-0.750363\pi$
$547$	5.52768	−	24.2183i	0.236347	−	1.03550i	0.944259	−	0.329202i	$-0.106780\pi$
$548$	−3.67390	−	16.0964i	−0.156941	−	0.687604i
$549$	10.5673	+	13.2510i	0.451003	+	0.565540i
$550$		0			0
$551$	−8.24578	+	7.33150i	−0.351282	+	0.312332i
$552$	2.49827			0.106333
$553$	−1.50000	−	1.88094i	−0.0637865	−	0.0799857i
$554$	2.64406	+	11.5844i	0.112335	+	0.492174i
$555$		0			0
$556$	−2.17427	−	2.72645i	−0.0922095	−	0.115627i
$557$	−4.84146	+	6.07100i	−0.205139	+	0.257237i	−0.873749	−	0.486377i	$-0.838318\pi$
$557$	−4.84146	+	6.07100i	−0.205139	+	0.257237i	0.668610	+	0.743613i	$0.266890\pi$
$558$	−7.14191	−	31.2907i	−0.302341	−	1.32464i
$559$	−26.8240	+	12.9178i	−1.13453	+	0.546363i
$560$		0			0
$561$	−0.320060	+	1.40227i	−0.0135129	+	0.0592041i
$562$	49.5734	+	23.8733i	2.09113	+	1.00703i
$563$	−20.8009			−0.876652			−0.438326	−	0.898816i	$-0.644429\pi$
$563$	−20.8009			−0.876652			−0.438326	+	0.898816i	$0.644429\pi$
$564$	3.90097	+	1.87861i	0.164260	+	0.0791036i
$565$		0			0
$566$	3.99396	−	5.00827i	0.167879	−	0.210513i
$567$	−26.4720	−	12.7482i	−1.11172	−	0.535375i
$568$	15.4765			0.649380
$569$	−2.53103	−	1.21888i	−0.106106	−	0.0510981i	0.380078	−	0.924955i	$-0.375897\pi$
$569$	−2.53103	−	1.21888i	−0.106106	−	0.0510981i	−0.486184	+	0.873856i	$0.661612\pi$
$570$		0			0
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	−0.487618	−	0.873057i	$-0.662134\pi$
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	0.378559	+	0.925577i	$0.376420\pi$
$572$	16.9656	−	8.17021i	0.709368	−	0.341614i
$573$	−1.86294	−	8.16206i	−0.0778253	−	0.340975i
$574$	1.80194	−	2.25956i	0.0752114	−	0.0943121i
$575$		0			0
$576$	−0.791053	+	3.46583i	−0.0329605	+	0.144409i
$577$	1.59970	+	7.00872i	0.0665962	+	0.291777i	0.997249	−	0.0741270i	$-0.0236170\pi$
$577$	1.59970	+	7.00872i	0.0665962	+	0.291777i	−0.930653	+	0.365904i	$0.880760\pi$
$578$	−17.7153	−	22.2143i	−0.736859	−	0.923992i
$579$	4.84415			0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$	7.87531	+	9.87533i	0.326442	+	0.409346i
$583$	−2.82304	−	12.3686i	−0.116919	−	0.512254i
$584$	2.70195	−	11.8380i	0.111807	−	0.489860i
$585$		0			0
$586$	−36.9403	+	46.3216i	−1.52599	+	1.91353i
$587$	−6.90635	−	30.2587i	−0.285055	−	1.24891i	−0.891220	−	0.453570i	$-0.850150\pi$
$587$	−6.90635	−	30.2587i	−0.285055	−	1.24891i	0.606165	−	0.795339i	$-0.292707\pi$
$588$	4.69687	−	2.26189i	0.193695	−	0.0932788i
$589$	11.7349	−	5.65123i	0.483528	−	0.232855i
$590$		0			0
$591$	3.36831	+	1.62209i	0.138554	+	0.0667240i
$592$	−14.3817			−0.591082
$593$	32.8560	+	15.8226i	1.34923	+	0.649757i	0.962209	−	0.272312i	$-0.0877884\pi$
$593$	32.8560	+	15.8226i	1.34923	+	0.649757i	0.387025	+	0.922069i	$0.373503\pi$
$594$	8.44720	−	10.5925i	0.346593	−	0.434614i
$595$		0			0
$596$	−3.04288	−	1.46537i	−0.124641	−	0.0600240i
$597$	2.94677			0.120603
$598$	34.8315	+	16.7740i	1.42437	+	0.685939i
$599$	−6.69083	+	29.3144i	−0.273380	+	1.19775i	0.632615	+	0.774466i	$0.281981\pi$
$599$	−6.69083	+	29.3144i	−0.273380	+	1.19775i	−0.905995	+	0.423288i	$0.860876\pi$
$600$		0			0
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.290420	−	0.956899i	$-0.406205\pi$
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.929208	+	0.369558i	$0.120491\pi$
$602$	9.32036	+	40.8351i	0.379869	+	1.66432i
$603$	0.653989	−	0.820077i	0.0266325	−	0.0333961i
$604$	−1.89344	−	2.37429i	−0.0770428	−	0.0966086i
$605$		0			0
$606$	−3.11260	−	13.6372i	−0.126441	−	0.553974i
$607$	9.42729	+	11.8214i	0.382642	+	0.479818i	0.935434	−	0.353502i	$-0.115009\pi$
$607$	9.42729	+	11.8214i	0.382642	+	0.479818i	−0.552792	+	0.833319i	$0.686438\pi$
$608$	−12.6746			−0.514021
$609$	9.56249	+	1.64960i	0.387492	+	0.0668451i
$610$		0			0
$611$	−25.2268	−	31.6334i	−1.02057	−	1.27975i
$612$	−0.862937	−	3.78077i	−0.0348821	−	0.152829i
$613$	0.835658	−	3.66126i	0.0337519	−	0.147877i	−0.955244	−	0.295818i	$-0.904408\pi$
$613$	0.835658	−	3.66126i	0.0337519	−	0.147877i	0.988996	+	0.147942i	$0.0472648\pi$
$614$	−16.4819	−	20.6676i	−0.665154	−	0.834077i
$615$		0			0
$616$	3.55980	+	15.5965i	0.143429	+	0.628401i
$617$	26.8995	−	12.9541i	1.08293	−	0.521514i	0.194681	−	0.980867i	$-0.437633\pi$
$617$	26.8995	−	12.9541i	1.08293	−	0.521514i	0.888254	+	0.459353i	$0.151919\pi$
$618$	2.03319	−	0.979132i	0.0817868	−	0.0393865i
$619$	10.2622	−	44.9615i	0.412472	−	1.80716i	−0.159866	−	0.987139i	$-0.551106\pi$
$619$	10.2622	−	44.9615i	0.412472	−	1.80716i	0.572338	−	0.820018i	$-0.306037\pi$
$620$		0			0
$621$	10.6823			0.428667
$622$	−30.0776	−	14.4846i	−1.20600	−	0.580779i
$623$	3.59299	−	4.50547i	0.143950	−	0.180508i
$624$	−7.10723	+	8.91218i	−0.284517	+	0.356773i
$625$		0			0
$626$	−41.4306			−1.65590
$627$	2.39224	+	1.15204i	0.0955368	+	0.0460081i
$628$	4.90515	−	21.4909i	0.195737	−	0.857579i
$629$	2.91185	−	1.40227i	0.116103	−	0.0559124i
$630$		0			0
$631$	−2.81043	−	12.3133i	−0.111881	−	0.490185i	−0.999558	−	0.0297178i	$-0.990539\pi$
$631$	−2.81043	−	12.3133i	−0.111881	−	0.490185i	0.887677	−	0.460467i	$-0.152318\pi$
$632$	0.502688	−	0.630351i	0.0199959	−	0.0250740i
$633$	2.24764	+	2.81846i	0.0893358	+	0.112024i
$634$	5.63706	−	24.6976i	0.223876	−	0.980867i
$635$		0			0
$636$	−1.50753	−	1.89039i	−0.0597776	−	0.0749587i
$637$	−48.7157			−1.93019
$638$	10.8790	−	26.0776i	0.430702	−	1.03242i
$639$	31.9584			1.26425
$640$		0			0
$641$	−8.67874	−	38.0241i	−0.342790	−	1.50186i	−0.793157	−	0.609017i	$-0.791564\pi$
$641$	−8.67874	−	38.0241i	−0.342790	−	1.50186i	0.450368	−	0.892843i	$-0.351293\pi$
$642$	1.33124	−	5.83255i	0.0525399	−	0.230192i
$643$	−25.7479	−	32.2869i	−1.01540	−	1.27327i	−0.961523	−	0.274723i	$-0.911414\pi$
$643$	−25.7479	−	32.2869i	−1.01540	−	1.27327i	−0.0538762	−	0.998548i	$-0.517158\pi$
$644$	13.0233	−	16.3307i	0.513188	−	0.643518i
$645$		0			0
$646$	3.69202	−	1.77798i	0.145261	−	0.0699538i
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	−0.723306	−	0.690527i	$-0.757378\pi$
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	0.0889021	+	0.996040i	$0.471664\pi$
$648$	2.19106	−	9.59967i	0.0860730	−	0.377111i
$649$	23.8998	+	11.5095i	0.938148	+	0.451788i
$650$		0			0
$651$	−10.3204	−	4.97002i	−0.404487	−	0.194790i
$652$	3.86108	−	4.84164i	0.151211	−	0.189613i
$653$	8.30529	−	10.4145i	0.325011	−	0.407551i	−0.592303	−	0.805715i	$-0.701781\pi$
$653$	8.30529	−	10.4145i	0.325011	−	0.407551i	0.917314	+	0.398164i	$0.130353\pi$
$654$	−1.19418	−	0.575086i	−0.0466960	−	0.0224876i
$655$		0			0
$656$	1.76271	+	0.848876i	0.0688222	+	0.0331430i
$657$	5.57942	−	24.4450i	0.217674	−	0.953691i
$658$	−51.2851	+	24.6976i	−1.99930	+	0.962812i
$659$	−16.9073	+	8.14213i	−0.658615	+	0.317172i	−0.733171	−	0.680045i	$-0.761960\pi$
$659$	−16.9073	+	8.14213i	−0.658615	+	0.317172i	0.0745557	+	0.997217i	$0.476246\pi$
$660$		0			0
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	−0.985331	−	0.170655i	$-0.945412\pi$
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	0.385633	+	0.922652i	$0.373983\pi$
$662$	15.6799	+	19.6620i	0.609418	+	0.764186i
$663$	0.570024	−	2.49744i	0.0221379	−	0.0969924i
$664$	2.84817	+	12.4786i	0.110530	+	0.484265i
$665$		0			0
$666$	−14.7017			−0.569680
$667$	21.4236	−	6.11345i	0.829524	−	0.236714i
$668$	−18.0368			−0.697866
$669$	6.08211	+	7.62672i	0.235148	+	0.294866i
$670$		0			0
$671$	3.91939	−	17.1720i	0.151306	−	0.662916i
$672$	6.94989	+	8.71488i	0.268098	+	0.336184i
$673$	−15.8632	+	19.8919i	−0.611483	+	0.766775i	−0.987118	−	0.159992i	$-0.948853\pi$
$673$	−15.8632	+	19.8919i	−0.611483	+	0.766775i	0.375636	+	0.926767i	$0.377424\pi$
$674$	−5.61260	−	24.5904i	−0.216189	−	0.947188i
$675$		0			0
$676$	−15.6102	+	7.51748i	−0.600393	+	0.289134i
$677$	0.137195	−	0.601090i	0.00527283	−	0.0231018i	−0.972223	−	0.234056i	$-0.924800\pi$
$677$	0.137195	−	0.601090i	0.00527283	−	0.0231018i	0.977496	+	0.210954i	$0.0676572\pi$
$678$	−6.24309	−	3.00652i	−0.239765	−	0.115465i
$679$	−63.7730			−2.44738
$680$		0			0
$681$	−5.07188	+	6.35994i	−0.194355	+	0.243713i
$682$	−20.7962	+	26.0776i	−0.796327	+	0.998563i
$683$	16.2371	+	7.81935i	0.621294	+	0.299199i	0.717924	−	0.696121i	$-0.245092\pi$
$683$	16.2371	+	7.81935i	0.621294	+	0.299199i	−0.0966308	+	0.995320i	$0.530807\pi$
$684$	−7.15883			−0.273725
$685$		0			0
$686$	−3.88620	+	17.0265i	−0.148376	+	0.650077i
$687$	6.42543	−	3.09432i	0.245145	−	0.118056i
$688$	−25.5465	+	12.3026i	−0.973952	+	0.469031i
$689$	5.02781	+	22.0283i	0.191544	+	0.839211i
$690$		0			0
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	0.906385	−	0.422453i	$-0.138831\pi$
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	−0.613551	+	0.789655i	$0.710259\pi$
$692$	2.91723	−	12.7812i	0.110896	−	0.485869i
$693$	7.35086	+	32.2062i	0.279236	+	1.22341i
$694$	22.3056	+	27.9703i	0.846708	+	1.06174i
$695$		0			0
$696$	0.174136	+	3.24730i	0.00660061	+	0.123089i
$697$	−0.439665			−0.0166535
$698$	−30.2446	−	37.9255i	−1.14477	−	1.43550i
$699$	−0.193750	−	0.848876i	−0.00732831	−	0.0321074i
$700$		0			0
$701$	−21.2594	−	26.6584i	−0.802955	−	1.00687i	−0.999651	−	0.0264091i	$-0.991593\pi$
$701$	−21.2594	−	26.6584i	−0.802955	−	1.00687i	0.196696	−	0.980464i	$-0.436979\pi$
$702$	−15.0444	+	18.8650i	−0.567813	+	0.712015i
$703$	−1.32759	−	5.81656i	−0.0500711	−	0.219376i
$704$	3.32855	−	1.60295i	0.125450	−	0.0604133i
$705$		0			0
$706$	−1.60992	+	7.05350i	−0.0605900	+	0.265462i
$707$	63.6299	+	30.6425i	2.39305	+	1.15243i
$708$	5.05562			0.190002
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.446426	−	0.894821i	$-0.647303\pi$
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.977941	+	0.208882i	$0.933018\pi$
$710$		0			0
$711$	1.03803	−	1.30165i	0.0389292	−	0.0488157i
$712$	1.73998	+	0.837930i	0.0652085	+	0.0314028i
$713$	−26.2989			−0.984901
$714$	−3.24698	−	1.56366i	−0.121515	−	0.0585186i
$715$		0			0
$716$	6.44989	−	3.10610i	0.241044	−	0.116080i
$717$	−3.59395	+	1.73076i	−0.134219	+	0.0646362i
$718$	0.299249	+	1.31110i	0.0111679	+	0.0489297i
$719$	−32.5800	+	40.8540i	−1.21503	+	1.52360i	−0.431667	+	0.902033i	$0.642074\pi$
$719$	−32.5800	+	40.8540i	−1.21503	+	1.52360i	−0.783362	+	0.621566i	$0.786497\pi$
$720$		0			0
$721$	−2.53534	+	11.1081i	−0.0944211	+	0.413686i
$722$	5.93512	+	26.0034i	0.220882	+	0.967748i
$723$	−5.52177	−	6.92408i	−0.205357	−	0.257509i
$724$	−8.28083			−0.307755
$725$		0			0
$726$	2.02177			0.0750349
$727$	−18.6953	−	23.4432i	−0.693370	−	0.869459i	0.303138	−	0.952947i	$-0.401966\pi$
$727$	−18.6953	−	23.4432i	−0.693370	−	0.869459i	−0.996509	+	0.0834876i	$0.973394\pi$
$728$	−6.33997	−	27.7772i	−0.234975	−	1.02949i
$729$	3.75733	−	16.4619i	0.139160	−	0.609702i
$730$		0			0
$731$	3.97285	−	4.98180i	0.146941	−	0.184259i
$732$	−0.746980	−	3.27273i	−0.0276092	−	0.120964i
$733$	2.71595	−	1.30793i	0.100316	−	0.0483096i	−0.383053	−	0.923726i	$-0.625127\pi$
$733$	2.71595	−	1.30793i	0.100316	−	0.0483096i	0.483369	+	0.875417i	$0.339413\pi$
$734$	−55.2781	+	26.6205i	−2.04035	+	0.982581i
$735$		0			0
$736$	23.0574	+	11.1039i	0.849907	+	0.409294i
$737$	−1.09006			−0.0401531
$738$	1.80194	+	0.867767i	0.0663302	+	0.0319430i
$739$	−12.9919	+	16.2914i	−0.477916	+	0.599288i	−0.961090	−	0.276237i	$-0.910913\pi$
$739$	−12.9919	+	16.2914i	−0.477916	+	0.599288i	0.483174	+	0.875525i	$0.339484\pi$
$740$		0			0
$741$	−4.26055	−	2.05177i	−0.156515	−	0.0753738i
$742$	31.7875			1.16695
$743$	−27.7189	−	13.3487i	−1.01691	−	0.489718i	−0.150266	−	0.988646i	$-0.548013\pi$
$743$	−27.7189	−	13.3487i	−1.01691	−	0.489718i	−0.866643	+	0.498928i	$0.833727\pi$
$744$	0.854207	−	3.74253i	0.0313168	−	0.137208i
$745$		0			0
$746$	45.4587	−	21.8917i	1.66436	−	0.801514i
$747$	5.88135	+	25.7679i	0.215188	+	0.942798i
$748$	−2.51275	+	3.15088i	−0.0918751	+	0.115208i
$749$	18.8327	+	23.6155i	0.688133	+	0.862892i
$750$		0			0
$751$	0.994492	+	4.35715i	0.0362895	+	0.158995i	0.989826	−	0.142283i	$-0.0454442\pi$
$751$	0.994492	+	4.35715i	0.0362895	+	0.158995i	−0.953537	+	0.301277i	$0.902587\pi$
$752$	−24.0254	−	30.1269i	−0.876117	−	1.09862i
$753$	−11.4843			−0.418510
$754$	−19.3753	+	46.4439i	−0.705607	+	1.69139i
$755$		0			0
$756$	8.12833	+	10.1926i	0.295625	+	0.370702i
$757$	−1.88159	−	8.24379i	−0.0683876	−	0.299626i	0.929155	−	0.369691i	$-0.120536\pi$
$757$	−1.88159	−	8.24379i	−0.0683876	−	0.299626i	−0.997542	+	0.0700652i	$0.977679\pi$
$758$	−9.17456	+	40.1964i	−0.333235	+	1.46000i
$759$	−3.34266	−	4.19156i	−0.121331	−	0.152144i
$760$		0			0
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	−0.971415	−	0.237388i	$-0.923709\pi$
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	0.772216	−	0.635361i	$-0.219149\pi$
$762$	−7.56638	+	3.64377i	−0.274101	+	0.132000i
$763$	6.02930	−	2.90356i	0.218275	−	0.105116i
$764$	5.21983	−	22.8696i	0.188847	−	0.827392i
$765$		0			0
$766$	−21.3676			−0.772045
$767$	−42.5652	−	20.4983i	−1.53694	−	0.740152i
$768$	−5.74698	+	7.20648i	−0.207376	+	0.260042i
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	−0.317418	−	0.948286i	$-0.602816\pi$
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	0.995142	+	0.0984462i	$0.0313872\pi$
$770$		0			0
$771$	5.31873			0.191549
$772$	12.2289	+	5.88911i	0.440126	+	0.211954i
$773$	1.26324	−	5.53462i	0.0454356	−	0.199067i	−0.947116	−	0.320892i	$-0.896018\pi$
$773$	1.26324	−	5.53462i	0.0454356	−	0.199067i	0.992552	+	0.121825i	$0.0388747\pi$
$774$	−26.1151	+	12.5763i	−0.938686	+	0.452048i
$775$		0			0
$776$	−4.75571	−	20.8361i	−0.170720	−	0.747973i
$777$	−3.27144	+	4.10225i	−0.117362	+	0.147168i
$778$	−11.6746	−	14.6394i	−0.418553	−	0.524849i
$779$	−0.180604	+	0.791277i	−0.00647081	+	0.0283504i
$780$		0			0
$781$	−20.7074	−	25.9662i	−0.740968	−	0.929145i
$782$	−8.27413			−0.295882
$783$	0.744587	+	13.8851i	0.0266094	+	0.496213i
$784$	−46.3957			−1.65699
$785$		0			0
$786$	−0.0811457	−	0.355523i	−0.00289437	−	0.0126811i
$787$	−0.803134	+	3.51876i	−0.0286286	+	0.125430i	−0.987223	−	0.159345i	$-0.949062\pi$
$787$	−0.803134	+	3.51876i	−0.0286286	+	0.125430i	0.958594	+	0.284775i	$0.0919190\pi$
$788$	6.53116	+	8.18982i	0.232663	+	0.291750i
$789$	−0.0923264	+	0.115774i	−0.00328691	+	0.00412165i
$790$		0			0
$791$	31.5209	−	15.1797i	1.12075	−	0.539726i
$792$	−9.97434	+	4.80339i	−0.354423	+	0.170681i
$793$	−6.98039	+	30.5831i	−0.247881	+	1.08604i
$794$	13.3409	+	6.42465i	0.473452	+	0.228002i
$795$		0			0
$796$	7.43900	+	3.58243i	0.263668	+	0.126976i
$797$	19.1930	−	24.0672i	0.679850	−	0.852505i	−0.315490	−	0.948929i	$-0.602169\pi$
$797$	19.1930	−	24.0672i	0.679850	−	0.852505i	0.995340	+	0.0964236i	$0.0307403\pi$
$798$	−4.14795	+	5.20136i	−0.146836	+	0.184126i
$799$	7.80194	+	3.75722i	0.276013	+	0.132921i
$800$		0			0
$801$	3.59299	+	1.73029i	0.126952	+	0.0611369i
$802$	−9.97650	+	43.7099i	−0.352282	+	1.54345i
$803$	−23.4768	+	11.3058i	−0.828478	+	0.398974i
$804$	−0.187177	+	0.0901398i	−0.00660123	+	0.00317898i
$805$		0			0
$806$	37.0378	−	46.4439i	1.30460	−	1.63592i
$807$	0.295233	+	0.370210i	0.0103927	+	0.0130320i
$808$	−5.26659	+	23.0745i	−0.185278	+	0.811757i
$809$	−1.16541	−	5.10598i	−0.0409735	−	0.179517i	0.950300	−	0.311334i	$-0.100776\pi$
$809$	−1.16541	−	5.10598i	−0.0409735	−	0.179517i	−0.991274	+	0.131817i	$0.957919\pi$
$810$		0			0
$811$	41.8646			1.47006			0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646			1.47006			0.735032	+	0.678032i	$0.237167\pi$
$812$	22.1347	+	15.7896i	0.776775	+	0.554107i
$813$	7.32736			0.256982
$814$	9.52595	+	11.9452i	0.333884	+	0.418678i
$815$		0			0
$816$	0.542877	−	2.37850i	0.0190045	−	0.0832641i
$817$	−7.33393	−	9.19646i	−0.256582	−	0.321743i
$818$	21.2289	−	26.6201i	0.742250	−	0.930752i
$819$	−13.0918	−	57.3589i	−0.457464	−	2.00428i
$820$		0			0
$821$	−13.8802	+	6.68433i	−0.484421	+	0.233285i	−0.660121	−	0.751159i	$-0.729495\pi$
$821$	−13.8802	+	6.68433i	−0.484421	+	0.233285i	0.175701	+	0.984444i	$0.443781\pi$
$822$	2.36270	−	10.3517i	0.0824086	−	0.361056i
$823$	−32.1247	−	15.4705i	−1.11980	−	0.539266i	−0.219968	−	0.975507i	$-0.570595\pi$
$823$	−32.1247	−	15.4705i	−1.11980	−	0.539266i	−0.899830	+	0.436241i	$0.856310\pi$
$824$	−3.81833			−0.133018
$825$		0			0
$826$	−41.4403	+	51.9644i	−1.44189	+	1.80807i
$827$	32.4550	−	40.6973i	1.12857	−	1.41518i	0.231760	−	0.972773i	$-0.425552\pi$
$827$	32.4550	−	40.6973i	1.12857	−	1.41518i	0.896812	−	0.442411i	$-0.145877\pi$
$828$	13.0233	+	6.27167i	0.452590	+	0.217956i
$829$	−13.4168			−0.465986			−0.232993	−	0.972478i	$-0.574852\pi$
$829$	−13.4168			−0.465986			−0.232993	+	0.972478i	$0.574852\pi$
$830$		0			0
$831$	−0.653030	+	2.86111i	−0.0226534	+	0.0992508i
$832$	−5.92812	+	2.85483i	−0.205520	+	0.0989734i
$833$	9.39373	−	4.52378i	0.325474	−	0.156740i
$834$	−0.499041	−	2.18644i	−0.0172804	−	0.0757102i
$835$		0			0
$836$	4.63856	+	5.81656i	0.160428	+	0.201170i
$837$	3.65250	−	16.0026i	0.126249	−	0.553132i
$838$	4.36754	+	19.1355i	0.150874	+	0.661024i
$839$	−19.3602	−	24.2769i	−0.668387	−	0.838131i	0.325840	−	0.945425i	$-0.394353\pi$
$839$	−19.3602	−	24.2769i	−0.668387	−	0.838131i	−0.994227	+	0.107294i	$0.965782\pi$
$840$		0			0
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$	−35.9681			−1.23954
$843$	8.47285	+	10.6246i	0.291821	+	0.365931i
$844$	2.24764	+	9.84757i	0.0773671	+	0.338967i
$845$		0			0
$846$	−24.5601	−	30.7974i	−0.844394	−	1.05884i
$847$	−6.36443	+	7.98074i	−0.218684	+	0.274222i
$848$	4.78836	+	20.9792i	0.164433	+	0.720428i
$849$	1.42543	−	0.686450i	0.0489205	−	0.0235589i
$850$		0			0
$851$	−2.68060	+	11.7445i	−0.0918899	+	0.402596i
$852$	−5.70291	−	2.74638i	−0.195378	−	0.0940893i
$853$	−21.3357			−0.730521			−0.365261	−	0.930905i	$-0.619020\pi$
$853$	−21.3357			−0.730521			−0.365261	+	0.930905i	$0.619020\pi$
$854$	39.7618	+	19.1483i	1.36062	+	0.655241i
$855$		0			0
$856$	−6.31133	+	7.91416i	−0.215717	+	0.270500i
$857$	−8.85839	−	4.26597i	−0.302597	−	0.145723i	0.276424	−	0.961036i	$-0.410851\pi$
$857$	−8.85839	−	4.26597i	−0.302597	−	0.145723i	−0.579021	+	0.815313i	$0.696565\pi$
$858$	12.1099			0.413426
$859$	46.6555	+	22.4681i	1.59187	+	0.766602i	0.999244	−	0.0388778i	$-0.0123783\pi$
$859$	46.6555	+	22.4681i	1.59187	+	0.766602i	0.592623	+	0.805480i	$0.298093\pi$
$860$		0			0
$861$	0.643104	−	0.309703i	0.0219169	−	0.0105546i
$862$	49.0136	−	23.6037i	1.66941	−	0.803946i
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	−0.998417	−	0.0562402i	$-0.982089\pi$
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	0.875141	−	0.483868i	$-0.160768\pi$
$864$	−9.95891	+	12.4881i	−0.338809	+	0.424853i
$865$		0			0
$866$	−8.09611	+	35.4714i	−0.275117	+	1.20537i
$867$	−1.56153	−	6.84152i	−0.0530324	−	0.232350i
$868$	−20.0112	−	25.0932i	−0.679224	−	0.851720i
$869$	−1.73019			−0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	1.39828	+	1.75339i	0.0473518	+	0.0593772i
$873$	−9.82036	−	43.0258i	−0.332369	−	1.45620i
$874$	−3.39881	+	14.8912i	−0.114967	+	0.503701i
$875$		0			0
$876$	−3.09634	+	3.88269i	−0.104616	+	0.131184i
$877$	3.29470	+	14.4350i	0.111254	+	0.487436i	0.999601	+	0.0282623i	$0.00899737\pi$
$877$	3.29470	+	14.4350i	0.111254	+	0.487436i	−0.888346	+	0.459174i	$0.848145\pi$
$878$	17.3143	−	8.33813i	0.584330	−	0.281398i
$879$	−13.1838	+	6.34900i	−0.444679	+	0.214146i
$880$		0			0
$881$	16.7920	+	8.08661i	0.565737	+	0.272445i	0.694813	−	0.719190i	$-0.255487\pi$
$881$	16.7920	+	8.08661i	0.565737	+	0.272445i	−0.129076	+	0.991635i	$0.541201\pi$
$882$	−47.4282			−1.59699
$883$	−29.1857	−	14.0551i	−0.982178	−	0.472992i	−0.127325	−	0.991861i	$-0.540639\pi$
$883$	−29.1857	−	14.0551i	−0.982178	−	0.472992i	−0.854854	+	0.518869i	$0.826353\pi$
$884$	4.47517	−	5.61169i	0.150516	−	0.188742i
$885$		0			0
$886$	−33.0383	−	15.9104i	−1.10994	−	0.534521i
$887$	6.16288			0.206929			0.103465	−	0.994633i	$-0.467007\pi$
$887$	6.16288			0.206929			0.103465	+	0.994633i	$0.467007\pi$
$888$	−1.58426	−	0.762940i	−0.0531643	−	0.0256026i
$889$	9.43512	−	41.3379i	0.316444	−	1.38643i
$890$		0			0
$891$	−19.0378	+	9.16812i	−0.637790	+	0.307144i
$892$	6.08211	+	26.6474i	0.203644	+	0.892222i
$893$	9.96681	−	12.4980i	0.333527	−	0.418229i
$894$	−1.35421	−	1.69812i	−0.0452915	−	0.0567937i
$895$		0			0
$896$	−9.08695	−	39.8125i	−0.303574	−	1.33004i
$897$	5.95324	+	7.46513i	0.198773	+	0.249253i
$898$	34.9995			1.16795
$899$	−1.83310	−	34.1838i	−0.0611373	−	1.14009i
$900$		0			0
$901$	−3.01507	−	3.78077i	−0.100446	−	0.125956i
$902$	−0.462500	−	2.02635i	−0.0153996	−	0.0674699i
$903$	−2.30194	+	10.0854i	−0.0766037	+	0.335623i
$904$	7.31013	+	9.16662i	0.243131	+	0.304877i
$905$		0			0
$906$	−0.434584	−	1.90404i	−0.0144381	−	0.0632574i
$907$	39.6284	−	19.0840i	1.31584	−	0.633675i	0.361492	−	0.932375i	$-0.382267\pi$
$907$	39.6284	−	19.0840i	1.31584	−	0.633675i	0.954347	+	0.298700i	$0.0965531\pi$
$908$	−20.5356	+	9.88944i	−0.681499	+	0.328193i
$909$	−10.8753	+	47.6479i	−0.360711	+	1.58038i
$910$		0			0
$911$	−25.6233			−0.848936			−0.424468	−	0.905443i	$-0.639539\pi$
$911$	−25.6233			−0.848936			−0.424468	+	0.905443i	$0.639539\pi$
$912$	−4.05765	−	1.95406i	−0.134362	−	0.0647054i
$913$	17.1256	−	21.4749i	0.566776	−	0.710715i
$914$	13.9547	−	17.4987i	0.461581	−	0.578805i
$915$		0			0
$916$	19.9825			0.660242
$917$	1.65883	+	0.798852i	0.0547795	+	0.0263804i
$918$	1.14914	−	5.03473i	0.0379274	−	0.166171i
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	−0.338828	−	0.940848i	$-0.610030\pi$
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	0.524329	+	0.851516i	$0.324316\pi$
$920$		0			0
$921$	−1.45281	−	6.36518i	−0.0478718	−	0.209740i
$922$	−24.6564	+	30.9182i	−0.812017	+	1.01824i
$923$	36.8796	+	46.2456i	1.21391	+	1.52219i
$924$	1.45593	−	6.37883i	0.0478965	−	0.209848i
$925$		0			0
$926$	37.0834	+	46.5011i	1.21863	+	1.52812i
$927$	−7.88471			−0.258968
$928$	−12.8259	+	30.7445i	−0.421030	+	1.00924i
$929$	−24.5133			−0.804256			−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133			−0.804256			−0.402128	+	0.915583i	$0.631729\pi$
$930$		0			0
$931$	−4.28286	−	18.7644i	−0.140365	−	0.614979i
$932$	0.542877	−	2.37850i	0.0177825	−	0.0779103i
$933$	−5.14071	−	6.44625i	−0.168299	−	0.211041i
$934$	29.3267	−	36.7745i	0.959599	−	1.20330i
$935$		0			0
$936$	17.7642	−	8.55479i	0.580641	−	0.279622i
$937$	−3.68449	+	1.77436i	−0.120367	+	0.0579657i	−0.493098	−	0.869974i	$-0.664136\pi$
$937$	−3.68449	+	1.77436i	−0.120367	+	0.0579657i	0.372731	+	0.927939i	$0.378421\pi$
$938$	0.607760	−	2.66277i	0.0198441	−	0.0869426i
$939$	−9.21917	−	4.43972i	−0.300856	−	0.144885i
$940$		0			0
$941$	−5.55280	−	2.67409i	−0.181016	−	0.0871728i	0.341181	−	0.939998i	$-0.389173\pi$
$941$	−5.55280	−	2.67409i	−0.181016	−	0.0871728i	−0.522197	+	0.852825i	$0.674887\pi$
$942$	8.83877	−	11.0835i	0.287983	−	0.361119i
$943$	1.02177	−	1.28126i	0.0332734	−	0.0417235i
$944$	−40.5381	−	19.5221i	−1.31940	−	0.635391i
$945$		0			0
$946$	27.1395	+	13.0697i	0.882382	+	0.424933i
$947$	−11.0598	+	48.4562i	−0.359395	+	1.57461i	0.395309	+	0.918548i	$0.370638\pi$
$947$	−11.0598	+	48.4562i	−0.359395	+	1.57461i	−0.754704	+	0.656065i	$0.772220\pi$
$948$	−0.297093	+	0.143073i	−0.00964914	+	0.00464678i
$949$	41.8119	−	20.1356i	1.35727	−	0.653628i
$950$		0			0
$951$	3.90097	−	4.89166i	0.126498	−	0.158623i
$952$	3.80194	+	4.76748i	0.123222	+	0.154515i
$953$	3.93541	−	17.2422i	0.127480	−	0.558529i	−0.870335	−	0.492461i	$-0.836098\pi$
$953$	3.93541	−	17.2422i	0.127480	−	0.558529i	0.997815	−	0.0660678i	$-0.0210454\pi$
$954$	4.89493	+	21.4461i	0.158479	+	0.694343i
$955$		0			0
$956$	−11.1769			−0.361486
$957$	5.21528	−	4.63702i	0.168586	−	0.149893i
$958$	59.5827			1.92503
$959$	33.4245	+	41.9130i	1.07933	+	1.35344i
$960$		0			0
$961$	−2.09395	+	9.17419i	−0.0675468	+	0.295942i
$962$	−16.9656	−	21.2742i	−0.546993	−	0.685908i
$963$	−13.0327	+	16.3424i	−0.419971	+	0.526628i
$964$	−5.52177	−	24.1925i	−0.177844	−	0.779187i
$965$		0			0
$966$	12.1027	−	5.82834i	0.389397	−	0.187524i
$967$	−2.86904	+	12.5701i	−0.0922620	+	0.404226i	−0.999879	−	0.0155736i	$-0.995043\pi$
$967$	−2.86904	+	12.5701i	−0.0922620	+	0.404226i	0.907617	+	0.419800i	$0.137900\pi$
$968$	−3.08211	−	1.48426i	−0.0990626	−	0.0477060i
$969$	1.01208			0.0325127
$970$		0			0
$971$	3.01610	−	3.78207i	0.0967912	−	0.121372i	−0.731077	−	0.682295i	$-0.760982\pi$
$971$	3.01610	−	3.78207i	0.0967912	−	0.121372i	0.827868	+	0.560923i	$0.189553\pi$
$972$	−8.53348	+	10.7006i	−0.273712	+	0.343223i
$973$	10.2017	+	4.91288i	0.327052	+	0.157500i
$974$	18.3013			0.586411
$975$		0			0
$976$	−6.64795	+	29.1266i	−0.212796	+	0.932319i
$977$	14.8138	−	7.13394i	0.473935	−	0.228235i	−0.181640	−	0.983365i	$-0.558141\pi$
$977$	14.8138	−	7.13394i	0.473935	−	0.228235i	0.655575	+	0.755130i	$0.272426\pi$
$978$	3.58815	−	1.72796i	0.114736	−	0.0552541i
$979$	−0.922207	−	4.04045i	−0.0294739	−	0.129133i
$980$		0			0
$981$	2.88740	+	3.62068i	0.0921874	+	0.115599i
$982$	7.89181	−	34.5763i	0.251838	−	1.10337i
$983$	5.89666	+	25.8349i	0.188074	+	0.824007i	0.977631	+	0.210329i	$0.0674535\pi$
$983$	5.89666	+	25.8349i	0.188074	+	0.824007i	−0.789557	+	0.613678i	$0.789689\pi$
$984$	0.149145	+	0.187022i	0.00475457	+	0.00596204i
$985$		0			0
$986$	−0.576728	−	10.7549i	−0.0183668	−	0.342505i
$987$	−14.0586			−0.447490
$988$	−8.26122	−	10.3592i	−0.262824	−	0.329571i
$989$	5.28501	+	23.1551i	0.168054	+	0.736291i
$990$		0			0
$991$	25.1930	+	31.5910i	0.800281	+	1.00352i	0.999721	+	0.0236111i	$0.00751634\pi$
$991$	25.1930	+	31.5910i	0.800281	+	1.00352i	−0.199440	+	0.979910i	$0.563912\pi$
$992$	24.5179	−	30.7445i	0.778444	−	0.976137i
$993$	1.38212	+	6.05548i	0.0438604	+	0.192165i
$994$	74.9747	−	36.1059i	2.37805	−	1.14521i
$995$		0			0
$996$	1.16487	−	5.10365i	0.0369105	−	0.161715i
$997$	−21.1325	−	10.1769i	−0.669273	−	0.322305i	0.0682093	−	0.997671i	$-0.478271\pi$
$997$	−21.1325	−	10.1769i	−0.669273	−	0.322305i	−0.737483	+	0.675366i	$0.763986\pi$
$998$	50.1831			1.58852
$999$	−6.77413	−	3.26225i	−0.214324	−	0.103213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.l.b.401.1		6
5.2	odd	4		725.2.r.b.24.1		12
5.3	odd	4		725.2.r.b.24.2		12
5.4	even	2		29.2.d.a.24.1	yes	6
15.14	odd	2		261.2.k.a.82.1		6
20.19	odd	2		464.2.u.f.401.1		6
29.23	even	7	inner	725.2.l.b.226.1		6
145.4	even	14		841.2.d.c.645.1		6
145.9	even	14		841.2.a.f.1.3		3
145.14	odd	28		841.2.e.d.267.2		12
145.19	odd	28		841.2.e.c.196.2		12
145.23	odd	28		725.2.r.b.574.1		12
145.24	even	14		841.2.d.e.571.1		6
145.34	even	14		841.2.d.a.571.1		6
145.39	odd	28		841.2.e.c.196.1		12
145.44	odd	28		841.2.e.d.267.1		12
145.49	even	14		841.2.a.e.1.1		3
145.52	odd	28		725.2.r.b.574.2		12
145.54	even	14		841.2.d.b.645.1		6
145.64	even	14		841.2.d.d.574.1		6
145.69	odd	28		841.2.e.c.236.1		12
145.74	even	14		841.2.d.b.605.1		6
145.79	odd	28		841.2.b.c.840.6		6
145.84	odd	28		841.2.e.b.651.1		12
145.89	odd	28		841.2.e.b.270.1		12
145.94	even	14		841.2.d.e.190.1		6
145.99	odd	4		841.2.e.d.63.2		12
145.104	odd	4		841.2.e.d.63.1		12
145.109	even	14		841.2.d.a.190.1		6
145.114	odd	28		841.2.e.b.270.2		12
145.119	odd	28		841.2.e.b.651.2		12
145.124	odd	28		841.2.b.c.840.1		6
145.129	even	14		841.2.d.c.605.1		6
145.134	odd	28		841.2.e.c.236.2		12
145.139	even	14		29.2.d.a.23.1	✓	6
145.144	even	2		841.2.d.d.778.1		6
435.194	odd	14		7569.2.a.r.1.3		3
435.284	odd	14		261.2.k.a.226.1		6
435.299	odd	14		7569.2.a.p.1.1		3
580.139	odd	14		464.2.u.f.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	145.139	even	14
29.2.d.a.24.1	yes	6	5.4	even	2
261.2.k.a.82.1		6	15.14	odd	2
261.2.k.a.226.1		6	435.284	odd	14
464.2.u.f.81.1		6	580.139	odd	14
464.2.u.f.401.1		6	20.19	odd	2
725.2.l.b.226.1		6	29.23	even	7	inner
725.2.l.b.401.1		6	1.1	even	1	trivial
725.2.r.b.24.1		12	5.2	odd	4
725.2.r.b.24.2		12	5.3	odd	4
725.2.r.b.574.1		12	145.23	odd	28
725.2.r.b.574.2		12	145.52	odd	28
841.2.a.e.1.1		3	145.49	even	14
841.2.a.f.1.3		3	145.9	even	14
841.2.b.c.840.1		6	145.124	odd	28
841.2.b.c.840.6		6	145.79	odd	28
841.2.d.a.190.1		6	145.109	even	14
841.2.d.a.571.1		6	145.34	even	14
841.2.d.b.605.1		6	145.74	even	14
841.2.d.b.645.1		6	145.54	even	14
841.2.d.c.605.1		6	145.129	even	14
841.2.d.c.645.1		6	145.4	even	14
841.2.d.d.574.1		6	145.64	even	14
841.2.d.d.778.1		6	145.144	even	2
841.2.d.e.190.1		6	145.94	even	14
841.2.d.e.571.1		6	145.24	even	14
841.2.e.b.270.1		12	145.89	odd	28
841.2.e.b.270.2		12	145.114	odd	28
841.2.e.b.651.1		12	145.84	odd	28
841.2.e.b.651.2		12	145.119	odd	28
841.2.e.c.196.1		12	145.39	odd	28
841.2.e.c.196.2		12	145.19	odd	28
841.2.e.c.236.1		12	145.69	odd	28
841.2.e.c.236.2		12	145.134	odd	28
841.2.e.d.63.1		12	145.104	odd	4
841.2.e.d.63.2		12	145.99	odd	4
841.2.e.d.267.1		12	145.44	odd	28
841.2.e.d.267.2		12	145.14	odd	28
7569.2.a.p.1.1		3	435.299	odd	14
7569.2.a.r.1.3		3	435.194	odd	14

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.l (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12349 + 1.40881i) q^{2} +(0.0990311 + 0.433884i) q^{3} +(-0.277479 + 1.21572i) q^{4} +(-0.500000 + 0.626980i) q^{6} +(-0.900969 - 3.94740i) q^{7} +(1.22252 - 0.588735i) q^{8} +(2.52446 - 1.21572i) q^{9} +(-2.62349 - 1.26341i) q^{11} -0.554958 q^{12} +(4.67241 + 2.25011i) q^{13} +(4.54892 - 5.70416i) q^{14} +(4.44989 + 2.14295i) q^{16} -1.10992 q^{17} +(4.54892 + 2.19064i) q^{18} +(-0.455927 + 1.99755i) q^{19} +(1.62349 - 0.781831i) q^{21} +(-1.16756 - 5.11543i) q^{22} +(2.57942 - 3.23449i) q^{23} +(0.376510 + 0.472129i) q^{24} +(2.07942 + 9.11052i) q^{26} +(1.60992 + 2.01877i) q^{27} +5.04892 q^{28} +(4.38404 + 3.12733i) q^{29} +(-3.96346 - 4.97002i) q^{31} +(1.37651 + 6.03089i) q^{32} +(0.288364 - 1.26341i) q^{33} +(-1.24698 - 1.56366i) q^{34} +(0.777479 + 3.40636i) q^{36} +(-2.62349 + 1.26341i) q^{37} +(-3.32640 + 1.60191i) q^{38} +(-0.513574 + 2.25011i) q^{39} +0.396125 q^{41} +(2.92543 + 1.40881i) q^{42} +(-3.57942 + 4.48845i) q^{43} +(2.26391 - 2.83885i) q^{44} +7.45473 q^{46} +(-7.02930 - 3.38513i) q^{47} +(-0.489115 + 2.14295i) q^{48} +(-8.46346 + 4.07579i) q^{49} +(-0.109916 - 0.481575i) q^{51} +(-4.03199 + 5.05596i) q^{52} +(2.71648 + 3.40636i) q^{53} +(-1.03534 + 4.53614i) q^{54} +(-3.42543 - 4.29535i) q^{56} -0.911854 q^{57} +(0.519614 + 9.68981i) q^{58} -9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(2.54892 - 11.1675i) q^{62} +(-7.07338 - 8.86973i) q^{63} +(-0.791053 + 0.991949i) q^{64} +(2.10388 - 1.01317i) q^{66} +(0.337282 - 0.162426i) q^{67} +(0.307979 - 1.34934i) q^{68} +(1.65883 + 0.798852i) q^{69} +(10.2763 + 4.94880i) q^{71} +(2.37047 - 2.97247i) q^{72} +(5.57942 - 6.99637i) q^{73} +(-4.72737 - 2.27658i) q^{74} +(-2.30194 - 1.10855i) q^{76} +(-2.62349 + 11.4943i) q^{77} +(-3.74698 + 1.80445i) q^{78} +(0.535344 - 0.257808i) q^{79} +(4.52446 - 5.67349i) q^{81} +(0.445042 + 0.558065i) q^{82} +(-2.09903 + 9.19646i) q^{83} +(0.500000 + 2.19064i) q^{84} -10.3448 q^{86} +(-0.922739 + 2.21187i) q^{87} -3.95108 q^{88} +(0.887395 + 1.11276i) q^{89} +(4.67241 - 20.4712i) q^{91} +(3.21648 + 4.03334i) q^{92} +(1.76391 - 2.21187i) q^{93} +(-3.12833 - 13.7061i) q^{94} +(-2.48039 + 1.19449i) q^{96} +(3.50484 - 15.3557i) q^{97} +(-15.2506 - 7.34432i) q^{98} -8.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 3 q^{6} - q^{7} + 7 q^{8} + 6 q^{9} - 11 q^{11} - 4 q^{12} + 5 q^{13} + 9 q^{14} + 4 q^{16} - 8 q^{17} + 9 q^{18} + q^{19} + 5 q^{21} - 6 q^{22} + 7 q^{23} + 7 q^{24}+ \cdots - 32 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 3 * q^6 - q^7 + 7 * q^8 + 6 * q^9 - 11 * q^11 - 4 * q^12 + 5 * q^13 + 9 * q^14 + 4 * q^16 - 8 * q^17 + 9 * q^18 + q^19 + 5 * q^21 - 6 * q^22 + 7 * q^23 + 7 * q^24 + 4 * q^26 + 11 * q^27 + 12 * q^28 + 6 * q^29 + 5 * q^31 + 13 * q^32 - q^33 + 2 * q^34 + 5 * q^36 - 11 * q^37 - 2 * q^38 + 3 * q^39 + 20 * q^41 + 4 * q^42 - 13 * q^43 + 20 * q^44 - 11 * q^47 - 6 * q^48 - 22 * q^49 - 2 * q^51 + 10 * q^52 - 3 * q^53 + 6 * q^54 - 7 * q^56 + 2 * q^57 + 16 * q^58 - 56 * q^59 + 3 * q^61 - 3 * q^62 - 15 * q^63 + q^64 - 5 * q^66 - 19 * q^67 + 12 * q^68 - 7 * q^69 + 21 * q^71 + 25 * q^73 - 6 * q^74 - 5 * q^76 - 11 * q^77 - 13 * q^78 - 9 * q^79 + 18 * q^81 + 2 * q^82 - 17 * q^83 + 3 * q^84 - 16 * q^86 + 5 * q^87 - 42 * q^88 + 7 * q^89 + 5 * q^91 + 17 * q^93 + 8 * q^94 - 2 * q^96 - q^97 - 19 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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