LMFDB - Embedded newform 725.2.r.b.24.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(24,725)]

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([7, 4]))

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

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

chi := DirichletCharacter("725.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.r (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 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:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			24.2
Root			$0.781831 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	725.24
Dual form			725.2.r.b.574.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40881 - 1.12349i) q^{2} +(-0.433884 + 0.0990311i) q^{3} +(0.277479 - 1.21572i) q^{4} +(-0.500000 + 0.626980i) q^{6} +(-3.94740 + 0.900969i) q^{7} +(0.588735 + 1.22252i) q^{8} +(-2.52446 + 1.21572i) q^{9} +O(q^{10})$	\(q+(1.40881 - 1.12349i) q^{2} +(-0.433884 + 0.0990311i) q^{3} +(0.277479 - 1.21572i) q^{4} +(-0.500000 + 0.626980i) q^{6} +(-3.94740 + 0.900969i) q^{7} +(0.588735 + 1.22252i) q^{8} +(-2.52446 + 1.21572i) q^{9} +(-2.62349 - 1.26341i) q^{11} +0.554958i q^{12} +(-2.25011 + 4.67241i) q^{13} +(-4.54892 + 5.70416i) q^{14} +(4.44989 + 2.14295i) q^{16} +1.10992i q^{17} +(-2.19064 + 4.54892i) q^{18} +(0.455927 - 1.99755i) q^{19} +(1.62349 - 0.781831i) q^{21} +(-5.11543 + 1.16756i) q^{22} +(3.23449 + 2.57942i) q^{23} +(-0.376510 - 0.472129i) q^{24} +(2.07942 + 9.11052i) q^{26} +(2.01877 - 1.60992i) q^{27} +5.04892i q^{28} +(-4.38404 - 3.12733i) q^{29} +(-3.96346 - 4.97002i) q^{31} +(6.03089 - 1.37651i) q^{32} +(1.26341 + 0.288364i) q^{33} +(1.24698 + 1.56366i) q^{34} +(0.777479 + 3.40636i) q^{36} +(1.26341 + 2.62349i) q^{37} +(-1.60191 - 3.32640i) q^{38} +(0.513574 - 2.25011i) q^{39} +0.396125 q^{41} +(1.40881 - 2.92543i) q^{42} +(-4.48845 - 3.57942i) q^{43} +(-2.26391 + 2.83885i) q^{44} +7.45473 q^{46} +(-3.38513 + 7.02930i) q^{47} +(-2.14295 - 0.489115i) q^{48} +(8.46346 - 4.07579i) q^{49} +(-0.109916 - 0.481575i) q^{51} +(5.05596 + 4.03199i) q^{52} +(-3.40636 + 2.71648i) q^{53} +(1.03534 - 4.53614i) q^{54} +(-3.42543 - 4.29535i) q^{56} +0.911854i q^{57} +(-9.68981 + 0.519614i) q^{58} +9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(-11.1675 - 2.54892i) q^{62} +(8.86973 - 7.07338i) q^{63} +(0.791053 - 0.991949i) q^{64} +(2.10388 - 1.01317i) q^{66} +(-0.162426 - 0.337282i) q^{67} +(1.34934 + 0.307979i) q^{68} +(-1.65883 - 0.798852i) q^{69} +(10.2763 + 4.94880i) q^{71} +(-2.97247 - 2.37047i) q^{72} +(6.99637 + 5.57942i) q^{73} +(4.72737 + 2.27658i) q^{74} +(-2.30194 - 1.10855i) q^{76} +(11.4943 + 2.62349i) q^{77} +(-1.80445 - 3.74698i) q^{78} +(-0.535344 + 0.257808i) q^{79} +(4.52446 - 5.67349i) q^{81} +(0.558065 - 0.445042i) q^{82} +(-9.19646 - 2.09903i) q^{83} +(-0.500000 - 2.19064i) q^{84} -10.3448 q^{86} +(2.21187 + 0.922739i) q^{87} -3.95108i q^{88} +(-0.887395 - 1.11276i) q^{89} +(4.67241 - 20.4712i) q^{91} +(4.03334 - 3.21648i) q^{92} +(2.21187 + 1.76391i) q^{93} +(3.12833 + 13.7061i) q^{94} +(-2.48039 + 1.19449i) q^{96} +(-15.3557 - 3.50484i) q^{97} +(7.34432 - 15.2506i) q^{98} +8.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9	$ 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9} - 22 q^{11} - 18 q^{14} + 8 q^{16} - 2 q^{19} + 10 q^{21} - 14 q^{24} + 8 q^{26} - 12 q^{29} + 10 q^{31} - 4 q^{34} + 10 q^{36} - 6 q^{39} + 40 q^{41} - 40 q^{44} + 44 q^{49} - 4 q^{51} - 12 q^{54} - 14 q^{56} + 112 q^{59} + 6 q^{61} - 2 q^{64} - 10 q^{66} + 14 q^{69} + 42 q^{71} + 12 q^{74} - 10 q^{76} + 18 q^{79} + 36 q^{81} - 6 q^{84} - 32 q^{86} - 14 q^{89} + 10 q^{91} - 16 q^{94} - 4 q^{96} + 64 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9 - 22 * q^11 - 18 * q^14 + 8 * q^16 - 2 * q^19 + 10 * q^21 - 14 * q^24 + 8 * q^26 - 12 * q^29 + 10 * q^31 - 4 * q^34 + 10 * q^36 - 6 * q^39 + 40 * q^41 - 40 * q^44 + 44 * q^49 - 4 * q^51 - 12 * q^54 - 14 * q^56 + 112 * q^59 + 6 * q^61 - 2 * q^64 - 10 * q^66 + 14 * q^69 + 42 * q^71 + 12 * q^74 - 10 * q^76 + 18 * q^79 + 36 * q^81 - 6 * q^84 - 32 * q^86 - 14 * q^89 + 10 * q^91 - 16 * q^94 - 4 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.40881	−	1.12349i	0.996180	−	0.794427i	0.0175063	−	0.999847i	$-0.494427\pi$
$2$	1.40881	−	1.12349i	0.996180	−	0.794427i	0.978674	+	0.205419i	$0.0658559\pi$
$3$	−0.433884	+	0.0990311i	−0.250503	+	0.0571757i	−0.345928	−	0.938261i	$-0.612436\pi$
$3$	−0.433884	+	0.0990311i	−0.250503	+	0.0571757i	0.0954255	+	0.995437i	$0.469579\pi$
$4$	0.277479	−	1.21572i	0.138740	−	0.607858i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.626980i	−0.204124	+	0.255964i
$7$	−3.94740	+	0.900969i	−1.49198	+	0.340534i	−0.889253	−	0.457415i	$-0.848775\pi$
$7$	−3.94740	+	0.900969i	−1.49198	+	0.340534i	−0.602725	+	0.797949i	$0.705918\pi$
$8$	0.588735	+	1.22252i	0.208149	+	0.432226i
$9$	−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	$0.787517\pi$
$12$			0.554958i			0.160203i
$13$	−2.25011	+	4.67241i	−0.624069	+	1.29589i	0.313993	+	0.949425i	$0.398333\pi$
$13$	−2.25011	+	4.67241i	−0.624069	+	1.29589i	−0.938062	+	0.346467i	$0.887381\pi$
$14$	−4.54892	+	5.70416i	−1.21575	+	1.52450i
$15$		0			0
$16$	4.44989	+	2.14295i	1.11247	+	0.535738i
$17$			1.10992i			0.269194i	0.990900	+	0.134597i	$0.0429740\pi$
$17$			1.10992i			0.269194i	−0.990900	+	0.134597i	$0.957026\pi$
$18$	−2.19064	+	4.54892i	−0.516340	+	1.07219i
$19$	0.455927	−	1.99755i	0.104597	−	0.458269i	−0.895321	−	0.445422i	$-0.853054\pi$
$19$	0.455927	−	1.99755i	0.104597	−	0.458269i	0.999917	−	0.0128465i	$-0.00408927\pi$
$20$		0			0
$21$	1.62349	−	0.781831i	0.354275	−	0.170610i
$22$	−5.11543	+	1.16756i	−1.09061	+	0.248925i
$23$	3.23449	+	2.57942i	0.674437	+	0.537846i	0.899731	−	0.436445i	$-0.143763\pi$
$23$	3.23449	+	2.57942i	0.674437	+	0.537846i	−0.225294	+	0.974291i	$0.572334\pi$
$24$	−0.376510	−	0.472129i	−0.0768548	−	0.0963729i
$25$		0			0
$26$	2.07942	+	9.11052i	0.407807	+	1.78672i
$27$	2.01877	−	1.60992i	0.388513	−	0.309829i
$28$			5.04892i			0.954156i
$29$	−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	$0.979107\pi$
$32$	6.03089	−	1.37651i	1.06612	−	0.243335i
$33$	1.26341	+	0.288364i	0.219931	+	0.0501978i
$34$	1.24698	+	1.56366i	0.213855	+	0.268166i
$35$		0			0
$36$	0.777479	+	3.40636i	0.129580	+	0.567726i
$37$	1.26341	+	2.62349i	0.207703	+	0.431299i	0.978631	−	0.205622i	$-0.0659219\pi$
$37$	1.26341	+	2.62349i	0.207703	+	0.431299i	−0.770929	+	0.636921i	$0.780208\pi$
$38$	−1.60191	−	3.32640i	−0.259864	−	0.539613i
$39$	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	$0.490152\pi$
$42$	1.40881	−	2.92543i	0.217384	−	0.451403i
$43$	−4.48845	−	3.57942i	−0.684482	−	0.545856i	0.218339	−	0.975873i	$-0.429936\pi$
$43$	−4.48845	−	3.57942i	−0.684482	−	0.545856i	−0.902821	+	0.430017i	$0.858508\pi$
$44$	−2.26391	+	2.83885i	−0.341297	+	0.427972i
$45$		0			0
$46$	7.45473			1.09914
$47$	−3.38513	+	7.02930i	−0.493773	+	1.02533i	0.494005	+	0.869459i	$0.335532\pi$
$47$	−3.38513	+	7.02930i	−0.493773	+	1.02533i	−0.987778	+	0.155870i	$0.950182\pi$
$48$	−2.14295	−	0.489115i	−0.309309	−	0.0705977i
$49$	8.46346	−	4.07579i	1.20907	−	0.582255i
$50$		0			0
$51$	−0.109916	−	0.481575i	−0.0153914	−	0.0674339i
$52$	5.05596	+	4.03199i	0.701135	+	0.559137i
$53$	−3.40636	+	2.71648i	−0.467899	+	0.373137i	−0.828871	−	0.559439i	$-0.811016\pi$
$53$	−3.40636	+	2.71648i	−0.467899	+	0.373137i	0.360972	+	0.932577i	$0.382445\pi$
$54$	1.03534	−	4.53614i	0.140892	−	0.617290i
$55$		0			0
$56$	−3.42543	−	4.29535i	−0.457742	−	0.573990i
$57$			0.911854i			0.120778i
$58$	−9.68981	+	0.519614i	−1.27233	+	0.0682287i
$59$	9.10992			1.18601			0.593005	−	0.805199i	$-0.297941\pi$
$59$	9.10992			1.18601			0.593005	+	0.805199i	$0.297941\pi$
$60$		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	$0.801999\pi$
$62$	−11.1675	−	2.54892i	−1.41828	−	0.323713i
$63$	8.86973	−	7.07338i	1.11748	−	0.891162i
$64$	0.791053	−	0.991949i	0.0988816	−	0.123994i
$65$		0			0
$66$	2.10388	−	1.01317i	0.258969	−	0.124713i
$67$	−0.162426	−	0.337282i	−0.0198435	−	0.0412055i	0.890812	−	0.454373i	$-0.150137\pi$
$67$	−0.162426	−	0.337282i	−0.0198435	−	0.0412055i	−0.910655	+	0.413168i	$0.864422\pi$
$68$	1.34934	+	0.307979i	0.163632	+	0.0373479i
$69$	−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	$0.406219\pi$
$72$	−2.97247	−	2.37047i	−0.350309	−	0.279362i
$73$	6.99637	+	5.57942i	0.818863	+	0.653021i	0.940591	−	0.339542i	$-0.110272\pi$
$73$	6.99637	+	5.57942i	0.818863	+	0.653021i	−0.121728	+	0.992563i	$0.538844\pi$
$74$	4.72737	+	2.27658i	0.549545	+	0.264647i
$75$		0			0
$76$	−2.30194	−	1.10855i	−0.264050	−	0.127160i
$77$	11.4943	+	2.62349i	1.30989	+	0.298974i
$78$	−1.80445	−	3.74698i	−0.204314	−	0.424262i
$79$	−0.535344	+	0.257808i	−0.0602309	+	0.0290057i	−0.463757	−	0.885963i	$-0.653499\pi$
$79$	−0.535344	+	0.257808i	−0.0602309	+	0.0290057i	0.403526	+	0.914968i	$0.367785\pi$
$80$		0			0
$81$	4.52446	−	5.67349i	0.502718	−	0.630388i
$82$	0.558065	−	0.445042i	0.0616280	−	0.0491467i
$83$	−9.19646	−	2.09903i	−1.00944	−	0.230399i	−0.314341	−	0.949310i	$-0.601783\pi$
$83$	−9.19646	−	2.09903i	−1.00944	−	0.230399i	−0.695101	+	0.718912i	$0.744641\pi$
$84$	−0.500000	−	2.19064i	−0.0545545	−	0.239019i
$85$		0			0
$86$	−10.3448			−1.11551
$87$	2.21187	+	0.922739i	0.237137	+	0.0989280i
$88$		−	3.95108i		−	0.421187i
$89$	−0.887395	−	1.11276i	−0.0940637	−	0.117952i	0.732572	−	0.680689i	$-0.238320\pi$
$89$	−0.887395	−	1.11276i	−0.0940637	−	0.117952i	−0.826636	+	0.562737i	$0.809748\pi$
$90$		0			0
$91$	4.67241	−	20.4712i	0.489801	−	2.14596i
$92$	4.03334	−	3.21648i	0.420505	−	0.335341i
$93$	2.21187	+	1.76391i	0.229360	+	0.182908i
$94$	3.12833	+	13.7061i	0.322663	+	1.41368i
$95$		0			0
$96$	−2.48039	+	1.19449i	−0.253153	+	0.121912i
$97$	−15.3557	−	3.50484i	−1.55914	−	0.355863i	−0.645943	−	0.763386i	$-0.723536\pi$
$97$	−15.3557	−	3.50484i	−1.55914	−	0.355863i	−0.913195	+	0.407523i	$0.866393\pi$
$98$	7.34432	−	15.2506i	0.741888	−	1.54055i
$99$	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	$0.879816\pi$
$102$	−0.695895	−	0.554958i	−0.0689039	−	0.0549490i
$103$	1.22096	−	2.53534i	0.120304	−	0.249815i	−0.832116	−	0.554601i	$-0.812871\pi$
$103$	1.22096	−	2.53534i	0.120304	−	0.249815i	0.952421	+	0.304786i	$0.0985851\pi$
$104$	−7.03684			−0.690019
$105$		0			0
$106$	−1.74698	+	7.65402i	−0.169682	+	0.743424i
$107$	3.23682	+	6.72132i	0.312915	+	0.649775i	0.996810	−	0.0798052i	$-0.0254298\pi$
$107$	3.23682	+	6.72132i	0.312915	+	0.649775i	−0.683895	+	0.729580i	$0.739716\pi$
$108$	−1.39703	−	2.90097i	−0.134430	−	0.279146i
$109$	−0.367781	−	1.61135i	−0.0352270	−	0.154340i	0.954255	−	0.298993i	$-0.0966506\pi$
$109$	−0.367781	−	1.61135i	−0.0352270	−	0.154340i	−0.989482	+	0.144653i	$0.953793\pi$
$110$		0			0
$111$	−0.807979	−	1.01317i	−0.0766899	−	0.0961661i
$112$	−19.4962	−	4.44989i	−1.84222	−	0.420475i
$113$	−8.42407	+	1.92274i	−0.792470	+	0.180876i	−0.599549	−	0.800338i	$-0.704653\pi$
$113$	−8.42407	+	1.92274i	−0.792470	+	0.180876i	−0.192921	+	0.981214i	$0.561796\pi$
$114$	1.02446	+	1.28463i	0.0959493	+	0.120317i
$115$		0			0
$116$	−5.01842	+	4.46198i	−0.465948	+	0.414284i
$117$		−	14.5308i		−	1.34337i
$118$	12.8342	−	10.2349i	1.18148	−	0.942199i
$119$	−1.00000	−	4.38129i	−0.0916698	−	0.401632i
$120$		0			0
$121$	−1.57188	−	1.97108i	−0.142899	−	0.179189i
$122$	8.52179	+	6.79590i	0.771526	+	0.615272i
$123$	−0.171872	+	0.0392287i	−0.0154972	+	0.00353713i
$124$	−7.14191	+	3.43936i	−0.641362	+	0.308864i
$125$		0			0
$126$	4.54892	−	19.9301i	0.405250	−	1.77552i
$127$	4.54371	−	9.43512i	0.403189	−	0.837231i	−0.596219	−	0.802822i	$-0.703331\pi$
$127$	4.54371	−	9.43512i	0.403189	−	0.837231i	0.999408	−	0.0344090i	$-0.0109549\pi$
$128$			10.0858i			0.891463i
$129$	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	$0.220609\pi$
$132$	0.701137	−	1.45593i	0.0610262	−	0.126722i
$133$			8.29590i			0.719345i
$134$	−0.607760	−	0.292682i	−0.0525025	−	0.0252839i
$135$		0			0
$136$	−1.35690	+	0.653447i	−0.116353	+	0.0560326i
$137$	5.74474	+	11.9291i	0.490806	+	1.01917i	0.988416	+	0.151769i	$0.0484969\pi$
$137$	5.74474	+	11.9291i	0.490806	+	1.01917i	−0.497610	+	0.867401i	$0.665789\pi$
$138$	−3.23449	+	0.738250i	−0.275338	+	0.0628440i
$139$	1.74363	−	2.18644i	0.147893	−	0.185451i	−0.702367	−	0.711815i	$-0.747873\pi$
$139$	1.74363	−	2.18644i	0.147893	−	0.185451i	0.850260	+	0.526364i	$0.176445\pi$
$140$		0			0
$141$	0.772635	−	3.38513i	0.0650676	−	0.285080i
$142$	20.0373	−	4.57338i	1.68149	−	0.383789i
$143$	11.8063	−	9.41521i	0.987292	−	0.787339i
$144$	−13.8388			−1.15323
$145$		0			0
$146$	16.1250			1.33451
$147$	−3.26853	+	2.60656i	−0.269584	+	0.214986i
$148$	3.53999	−	0.807979i	0.290985	−	0.0664154i
$149$	0.602679	−	2.64051i	0.0493734	−	0.216319i	−0.944223	−	0.329307i	$-0.893185\pi$
$149$	0.602679	−	2.64051i	0.0493734	−	0.216319i	0.993596	+	0.112988i	$0.0360421\pi$
$150$		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	$0.245880\pi$
$152$	2.71046	−	0.618645i	0.219848	−	0.0501788i
$153$	−1.34934	−	2.80194i	−0.109088	−	0.226523i
$154$	19.1407	−	9.21768i	1.54240	−	0.742782i
$155$		0			0
$156$	−2.59299	−	1.24872i	−0.207605	−	0.0999775i
$157$			17.6775i			1.41082i	0.708799	+	0.705411i	$0.249238\pi$
$157$			17.6775i			1.41082i	−0.708799	+	0.705411i	$0.750762\pi$
$158$	−0.464554	+	0.964656i	−0.0369579	+	0.0767439i
$159$	1.20895	−	1.51597i	0.0958758	−	0.120224i
$160$		0			0
$161$	−15.0918	−	7.26782i	−1.18940	−	0.572785i
$162$		−	13.0761i		−	1.02735i
$163$	2.15473	−	4.47434i	0.168772	−	0.350458i	−0.799379	−	0.600827i	$-0.794838\pi$
$163$	2.15473	−	4.47434i	0.168772	−	0.350458i	0.968150	+	0.250370i	$0.0805522\pi$
$164$	0.109916	−	0.481575i	0.00858302	−	0.0376047i
$165$		0			0
$166$	−15.3143	+	7.37499i	−1.18862	+	0.572410i
$167$	14.1018	−	3.21864i	1.09123	−	0.249066i	0.361203	−	0.932487i	$-0.382366\pi$
$167$	14.1018	−	3.21864i	1.09123	−	0.249066i	0.730024	+	0.683422i	$0.239509\pi$
$168$	1.91161	+	1.52446i	0.147484	+	0.117615i
$169$	−8.66301	−	10.8631i	−0.666386	−	0.835621i
$170$		0			0
$171$	1.27748	+	5.59700i	0.0976913	+	0.428013i
$172$	−5.59700	+	4.46346i	−0.426767	+	0.340336i
$173$		−	10.5133i		−	0.799314i	−0.916665	−	0.399657i	$-0.869129\pi$
$173$		−	10.5133i		−	0.799314i	0.916665	−	0.399657i	$-0.130871\pi$
$174$	4.15279	−	1.18505i	0.314822	−	0.0898380i
$175$		0			0
$176$	−8.96681	−	11.2440i	−0.675899	−	0.847550i
$177$	−3.95264	+	0.902165i	−0.297099	+	0.0678109i
$178$	−2.50035	−	0.570688i	−0.187409	−	0.0427748i
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	0.897394	−	0.441230i	$-0.145458\pi$
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	−0.629856	+	0.776712i	$0.716886\pi$
$180$		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	$0.849192\pi$
$182$	−16.4166	−	34.0894i	−1.21688	−	2.52687i
$183$	−1.16802	−	2.42543i	−0.0863428	−	0.179293i
$184$	−1.24914	+	5.47282i	−0.0920875	+	0.403462i
$185$		0			0
$186$	5.09783			0.373791
$187$	1.40227	−	2.91185i	0.102545	−	0.212936i
$188$	7.60633	+	6.06584i	0.554748	+	0.442397i
$189$	−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	$0.738272\pi$
$192$	−0.244991	+	0.508729i	−0.0176807	+	0.0367144i
$193$	10.6118	+	2.42208i	0.763854	+	0.174345i	0.586662	−	0.809832i	$-0.300442\pi$
$193$	10.6118	+	2.42208i	0.763854	+	0.174345i	0.177192	+	0.984176i	$0.443299\pi$
$194$	−25.5710	+	12.3143i	−1.83589	+	0.884118i
$195$		0			0
$196$	−2.60656	−	11.4201i	−0.186183	−	0.815722i
$197$	−6.56773	−	5.23759i	−0.467931	−	0.373163i	0.360952	−	0.932584i	$-0.382452\pi$
$197$	−6.56773	−	5.23759i	−0.467931	−	0.373163i	−0.828883	+	0.559422i	$0.811023\pi$
$198$	11.4943	−	9.16637i	0.816861	−	0.651425i
$199$	−1.47339	+	6.45532i	−0.104446	+	0.457606i	0.895476	+	0.445109i	$0.146835\pi$
$199$	−1.47339	+	6.45532i	−0.104446	+	0.457606i	−0.999922	+	0.0124967i	$0.996022\pi$
$200$		0			0
$201$	0.103875	+	0.130256i	0.00732681	+	0.00918753i
$202$			31.4306i			2.21145i
$203$	20.1232	+	8.39493i	1.41237	+	0.589208i
$204$	−0.615957			−0.0431256
$205$		0			0
$206$	−1.12833	−	4.94355i	−0.0786148	−	0.344434i
$207$	−11.3012	−	2.57942i	−0.785485	−	0.179282i
$208$	−20.0255	+	15.9698i	−1.38852	+	1.10731i
$209$	−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	$0.267199\pi$
$212$	2.35727	+	4.89493i	0.161898	+	0.336185i
$213$	−4.94880	−	1.12953i	−0.339086	−	0.0773942i
$214$	12.1114	+	5.83255i	0.827919	+	0.398705i
$215$		0			0
$216$	3.15668	+	1.52018i	0.214785	+	0.103435i
$217$	20.1232	+	16.0477i	1.36605	+	1.08939i
$218$	−2.32847	−	1.85690i	−0.157704	−	0.125765i
$219$	−3.58815	−	1.72796i	−0.242464	−	0.116765i
$220$		0			0
$221$	−5.18598	−	2.49744i	−0.348847	−	0.167996i
$222$	−2.27658	−	0.519614i	−0.152794	−	0.0348742i
$223$	9.51036	+	19.7485i	0.636861	+	1.32246i	0.930413	+	0.366512i	$0.119448\pi$
$223$	9.51036	+	19.7485i	0.636861	+	1.32246i	−0.293552	+	0.955943i	$0.594837\pi$
$224$	−22.5661	+	10.8673i	−1.50776	+	0.726101i
$225$		0			0
$226$	−9.70775	+	12.1731i	−0.645750	+	0.809745i
$227$	14.2907	−	11.3964i	0.948504	−	0.756407i	−0.0214309	−	0.999770i	$-0.506822\pi$
$227$	14.2907	−	11.3964i	0.948504	−	0.756407i	0.969935	+	0.243363i	$0.0782507\pi$
$228$	1.10855	+	0.253020i	0.0734158	+	0.0167567i
$229$	3.56584	+	15.6230i	0.235638	+	1.03240i	0.944876	+	0.327427i	$0.106182\pi$
$229$	3.56584	+	15.6230i	0.235638	+	1.03240i	−0.709239	+	0.704968i	$0.750961\pi$
$230$		0			0
$231$	−5.24698			−0.345226
$232$	1.24218	−	7.20075i	0.0815532	−	0.472752i
$233$		−	1.95646i		−	0.128172i	−0.997944	−	0.0640860i	$-0.979587\pi$
$233$		−	1.95646i		−	0.128172i	0.997944	−	0.0640860i	$-0.0204132\pi$
$234$	−16.3252	−	20.4712i	−1.06721	−	1.33824i
$235$		0			0
$236$	2.52781	−	11.0751i	0.164546	−	0.720925i
$237$	0.206746	−	0.164874i	0.0134296	−	0.0107097i
$238$	−6.33114	−	5.04892i	−0.410387	−	0.327273i
$239$	−1.99449	−	8.73844i	−0.129013	−	0.565243i	−0.997571	−	0.0696554i	$-0.977810\pi$
$239$	−1.99449	−	8.73844i	−0.129013	−	0.565243i	0.868558	−	0.495587i	$-0.165047\pi$
$240$		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	$0.578593\pi$
$242$	−4.42898	−	1.01089i	−0.284705	−	0.0649822i
$243$	−4.76224	+	9.88889i	−0.305498	+	0.634372i
$244$	7.54288			0.482883
$245$		0			0
$246$	−0.198062	+	0.248362i	−0.0126280	+	0.0158350i
$247$	8.30746	+	6.62498i	0.528591	+	0.421537i
$248$	3.74253	−	7.77144i	0.237651	−	0.493487i
$249$	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	$0.768497\pi$
$252$	−6.13805	−	12.7458i	−0.386661	−	0.802909i
$253$	−5.22679	−	10.8535i	−0.328606	−	0.682356i
$254$	−4.19902	−	18.3971i	−0.263470	−	1.15434i
$255$		0			0
$256$	12.9133	+	16.1928i	0.807084	+	1.01205i
$257$	−11.6514	−	2.65937i	−0.726797	−	0.165887i	−0.156914	−	0.987612i	$-0.550154\pi$
$257$	−11.6514	−	2.65937i	−0.726797	−	0.165887i	−0.569883	+	0.821726i	$0.693012\pi$
$258$	4.48845	−	1.02446i	0.279438	−	0.0637800i
$259$	−7.35086	−	9.21768i	−0.456760	−	0.572759i
$260$		0			0
$261$	14.8693	+	2.56506i	0.920385	+	0.158773i
$262$			0.819396i			0.0506225i
$263$	−0.260141	+	0.207455i	−0.0160410	+	0.0127923i	−0.631477	−	0.775394i	$-0.717551\pi$
$263$	−0.260141	+	0.207455i	−0.0160410	+	0.0127923i	0.615437	+	0.788186i	$0.288980\pi$
$264$	0.391280	+	1.71431i	0.0240816	+	0.105509i
$265$		0			0
$266$	9.32036	+	11.6874i	0.571468	+	0.716598i
$267$	0.495224	+	0.394928i	0.0303072	+	0.0241692i
$268$	−0.455108	+	0.103875i	−0.0278002	+	0.00634520i
$269$	−0.958615	+	0.461645i	−0.0584478	+	0.0281470i	−0.462879	−	0.886421i	$-0.653184\pi$
$269$	−0.958615	+	0.461645i	−0.0584478	+	0.0281470i	0.404432	+	0.914568i	$0.367469\pi$
$270$		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	$-0.0952642\pi$
$272$	−2.37850	+	4.93900i	−0.144218	+	0.299471i
$273$			9.34481i			0.565574i
$274$	21.4955	+	10.3517i	1.29859	+	0.625367i
$275$		0			0
$276$	−1.43147	+	1.79500i	−0.0861643	+	0.108047i
$277$	2.86111	−	5.94116i	0.171907	−	0.356970i	−0.797159	−	0.603769i	$-0.793665\pi$
$277$	2.86111	−	5.94116i	0.171907	−	0.356970i	0.969066	+	0.246800i	$0.0793790\pi$
$278$		−	5.03923i		−	0.302233i
$279$	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	$-0.00738037\pi$
$282$	−2.71467	−	5.63706i	−0.161656	−	0.335682i
$283$	3.46583	−	0.791053i	0.206022	−	0.0470232i	−0.118264	−	0.992982i	$-0.537733\pi$
$283$	3.46583	−	0.791053i	0.206022	−	0.0470232i	0.324286	+	0.945959i	$0.394876\pi$
$284$	8.86778	−	11.1198i	0.526206	−	0.659841i
$285$		0			0
$286$	6.05496	−	26.5285i	0.358037	−	1.56866i
$287$	−1.56366	+	0.356896i	−0.0923001	+	0.0210669i
$288$	−13.5513	+	10.8068i	−0.798517	+	0.636796i
$289$	15.7681			0.927534
$290$		0			0
$291$	7.00969			0.410915
$292$	8.72433	−	6.95742i	0.510553	−	0.407152i
$293$	−32.0556	+	7.31647i	−1.87271	+	0.427433i	−0.998327	−	0.0578127i	$-0.981587\pi$
$293$	−32.0556	+	7.31647i	−1.87271	+	0.427433i	−0.874378	+	0.485246i	$0.838730\pi$
$294$	−1.67629	+	7.34432i	−0.0977633	+	0.428329i
$295$		0			0
$296$	−2.46346	+	3.08908i	−0.143186	+	0.179549i
$297$	−7.33020	+	1.67307i	−0.425342	+	0.0970814i
$298$	−2.11752	−	4.39708i	−0.122665	−	0.254716i
$299$	−19.3300	+	9.30886i	−1.11789	+	0.538345i
$300$		0			0
$301$	20.9426	+	10.0854i	1.20711	+	0.581316i
$302$			4.38835i			0.252521i
$303$	3.36811	−	6.99396i	0.193493	−	0.401792i
$304$	6.30947	−	7.91183i	0.361873	−	0.453774i
$305$		0			0
$306$	−5.04892	−	2.43143i	−0.288627	−	0.138996i
$307$			14.6703i			0.837275i	0.908153	+	0.418638i	$0.137492\pi$
$307$			14.6703i			0.837275i	−0.908153	+	0.418638i	$0.862508\pi$
$308$	6.37883	−	13.2458i	0.363468	−	0.754749i
$309$	−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	$0.533179\pi$
$312$	3.05317	−	0.696866i	0.172852	−	0.0394523i
$313$	−17.9760	−	14.3354i	−1.01607	−	0.810286i	−0.0341147	−	0.999418i	$-0.510861\pi$
$313$	−17.9760	−	14.3354i	−1.01607	−	0.810286i	−0.981952	+	0.189132i	$0.939433\pi$
$314$	19.8605	+	24.9043i	1.12080	+	1.40543i
$315$		0			0
$316$	0.164874	+	0.722362i	0.00927491	+	0.0406360i
$317$	−10.9915	+	8.76540i	−0.617342	+	0.492314i	−0.881512	−	0.472162i	$-0.843474\pi$
$317$	−10.9915	+	8.76540i	−0.617342	+	0.492314i	0.264170	+	0.964476i	$0.414902\pi$
$318$		−	3.49396i		−	0.195932i
$319$	7.55041	+	13.7433i	0.422742	+	0.769479i
$320$		0			0
$321$	−2.07002	−	2.59573i	−0.115537	−	0.144879i
$322$	−29.4268	+	6.71648i	−1.63989	+	0.374295i
$323$	2.21711	+	0.506041i	0.123363	+	0.0281569i
$324$	−5.64191	−	7.07473i	−0.313439	−	0.393040i
$325$		0			0
$326$	−1.99127	−	8.72433i	−0.110286	−	0.483196i
$327$	0.319148	+	0.662718i	0.0176489	+	0.0366484i
$328$	0.233212	+	0.484271i	0.0128770	+	0.0267394i
$329$	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	$0.374699\pi$
$332$	−5.10365	+	10.5978i	−0.280099	+	0.581632i
$333$	−6.37883	−	5.08695i	−0.349558	−	0.278763i
$334$	16.2506	−	20.3776i	0.889195	−	1.11501i
$335$		0			0
$336$	8.89977			0.485522
$337$	−6.07333	+	12.6114i	−0.330836	+	0.686987i	−0.998339	−	0.0576199i	$-0.981649\pi$
$337$	−6.07333	+	12.6114i	−0.330836	+	0.686987i	0.667503	+	0.744607i	$0.267363\pi$
$338$	−24.4091	−	5.57122i	−1.32768	−	0.303034i
$339$	3.46466	−	1.66849i	0.188174	−	0.0906200i
$340$		0			0
$341$	4.11894	+	18.0463i	0.223053	+	0.977260i
$342$	8.08790	+	6.44989i	0.437344	+	0.348770i
$343$	−7.57753	+	6.04288i	−0.409148	+	0.326285i
$344$	1.73341	−	7.59455i	0.0934590	−	0.409471i
$345$		0			0
$346$	−11.8116	−	14.8113i	−0.634997	−	0.796261i
$347$		−	19.8538i		−	1.06581i	−0.846175	−	0.532905i	$-0.821100\pi$
$347$		−	19.8538i		−	1.06581i	0.846175	−	0.532905i	$-0.178900\pi$
$348$	1.73553	−	2.43296i	0.0930344	−	0.130420i
$349$	26.9202			1.44101			0.720503	−	0.693452i	$-0.243911\pi$
$349$	26.9202			1.44101			0.720503	+	0.693452i	$0.243911\pi$
$350$		0			0
$351$	2.97972	+	13.0550i	0.159046	+	0.696825i
$352$	−17.5611	−	4.00820i	−0.936007	−	0.213638i
$353$	−3.13910	+	2.50335i	−0.167078	+	0.133240i	−0.703459	−	0.710736i	$-0.748362\pi$
$353$	−3.13910	+	2.50335i	−0.167078	+	0.133240i	0.536382	+	0.843976i	$0.319791\pi$
$354$	−4.55496	+	5.71174i	−0.242093	+	0.303575i
$355$		0			0
$356$	−1.59903	+	0.770053i	−0.0847485	+	0.0408127i
$357$	0.867767	+	1.80194i	0.0459271	+	0.0953687i
$358$	10.0854	+	2.30194i	0.533032	+	0.121661i
$359$	−0.672407	−	0.323814i	−0.0354883	−	0.0170903i	0.416055	−	0.909339i	$-0.363412\pi$
$359$	−0.672407	−	0.323814i	−0.0354883	−	0.0170903i	−0.451544	+	0.892249i	$0.649127\pi$
$360$		0			0
$361$	13.3361	+	6.42232i	0.701899	+	0.338017i
$362$	9.35551	+	7.46077i	0.491715	+	0.392129i
$363$	0.877213	+	0.699554i	0.0460418	+	0.0367171i
$364$	−23.5906	−	11.3606i	−1.23648	−	0.595459i
$365$		0			0
$366$	−4.37047	−	2.10471i	−0.228448	−	0.110015i
$367$	33.1952	+	7.57660i	1.73278	+	0.395495i	0.968425	−	0.249304i	$-0.0802018\pi$
$367$	33.1952	+	7.57660i	1.73278	+	0.395495i	0.764352	+	0.644799i	$0.223059\pi$
$368$	8.86553	+	18.4095i	0.462148	+	0.959659i
$369$	−1.00000	+	0.481575i	−0.0520579	+	0.0250698i
$370$		0			0
$371$	10.9988	−	13.7921i	0.571029	−	0.716048i
$372$	2.75815	−	2.19955i	0.143004	−	0.114042i
$373$	27.2986	+	6.23072i	1.41347	+	0.322614i	0.860015	−	0.510268i	$-0.170454\pi$
$373$	27.2986	+	6.23072i	1.41347	+	0.322614i	0.553450	+	0.832882i	$0.313311\pi$
$374$	−1.29590	−	5.67770i	−0.0670092	−	0.293587i
$375$		0			0
$376$	−10.5864			−0.545953
$377$	24.4767	−	13.4472i	1.26062	−	0.692566i
$378$			18.8388i			0.968962i
$379$	−14.2661	−	17.8891i	−0.732798	−	0.918900i	0.266188	−	0.963921i	$-0.414236\pi$
$379$	−14.2661	−	17.8891i	−0.732798	−	0.918900i	−0.998986	+	0.0450211i	$0.985664\pi$
$380$		0			0
$381$	−1.03707	+	4.54371i	−0.0531308	+	0.232781i
$382$	−26.5020	+	21.1347i	−1.35596	+	1.08134i
$383$	−9.27108	−	7.39344i	−0.473730	−	0.377787i	0.357323	−	0.933981i	$-0.383690\pi$
$383$	−9.27108	−	7.39344i	−0.473730	−	0.377787i	−0.831052	+	0.556194i	$0.812261\pi$
$384$	−0.998804	−	4.37604i	−0.0509700	−	0.223314i
$385$		0			0
$386$	17.6712	−	8.51001i	0.899441	−	0.433148i
$387$	15.6824	+	3.57942i	0.797184	+	0.181952i
$388$	−8.52179	+	17.6957i	−0.432628	+	0.898362i
$389$	10.3913			0.526862			0.263431	−	0.964678i	$-0.415146\pi$
$389$	10.3913			0.526862			0.263431	+	0.964678i	$0.415146\pi$
$390$		0			0
$391$	−2.86294	+	3.59001i	−0.144785	+	0.181555i
$392$	9.96547	+	7.94720i	0.503332	+	0.401394i
$393$	0.0878068	−	0.182333i	0.00442927	−	0.00919747i
$394$	−15.1371			−0.762594
$395$		0			0
$396$	2.26391	−	9.91882i	0.113766	−	0.498439i
$397$	−3.56541	−	7.40366i	−0.178943	−	0.371579i	0.792133	−	0.610348i	$-0.208970\pi$
$397$	−3.56541	−	7.40366i	−0.178943	−	0.371579i	−0.971076	+	0.238769i	$0.923256\pi$
$398$	5.17677	+	10.7497i	0.259488	+	0.538832i
$399$	−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	$0.572340\pi$
$402$	0.292682	+	0.0668027i	0.0145976	+	0.00333182i
$403$	32.1402	−	7.33579i	1.60102	−	0.365422i
$404$	13.5613	+	17.0053i	0.674700	+	0.846047i
$405$		0			0
$406$	37.7814	−	10.7813i	1.87506	−	0.535069i
$407$		−	8.47889i		−	0.420283i
$408$	0.524023	−	0.417895i	0.0259430	−	0.0206889i
$409$	4.20464	+	18.4217i	0.207906	+	0.910895i	0.965958	+	0.258701i	$0.0832943\pi$
$409$	4.20464	+	18.4217i	0.207906	+	0.910895i	−0.758052	+	0.652194i	$0.773849\pi$
$410$		0			0
$411$	−3.67390	−	4.60692i	−0.181220	−	0.227243i
$412$	−2.74347	−	2.18784i	−0.135161	−	0.107787i
$413$	−35.9605	+	8.20775i	−1.76950	+	0.403877i
$414$	−18.8192	+	9.06283i	−0.924911	+	0.445414i
$415$		0			0
$416$	−7.13856	+	31.2761i	−0.349996	+	1.53343i
$417$	−0.540006	+	1.12133i	−0.0264442	+	0.0549120i
$418$			10.7506i			0.525830i
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	0.178527	−	0.983935i	$-0.442867\pi$
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	−0.657962	+	0.753051i	$0.728581\pi$
$420$		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	$0.375981\pi$
$422$	6.33301	−	13.1506i	0.308286	−	0.640163i
$423$		−	21.8605i		−	1.06290i
$424$	−5.32640	−	2.56506i	−0.258673	−	0.124570i
$425$		0			0
$426$	−8.24094	+	3.96863i	−0.399275	+	0.192281i
$427$	−10.6265	−	22.0661i	−0.514252	−	1.06786i
$428$	9.06937	−	2.07002i	0.438384	−	0.100058i
$429$	−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	$-0.187707\pi$
$432$	12.4333	−	2.83781i	0.598196	−	0.136534i
$433$	−15.7862	+	12.5891i	−0.758638	+	0.604994i	−0.924512	−	0.381153i	$-0.875527\pi$
$433$	−15.7862	+	12.5891i	−0.758638	+	0.604994i	0.165874	+	0.986147i	$0.446956\pi$
$434$	46.3793			2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	6.62720	−	5.28501i	0.317022	−	0.252816i
$438$	−6.99637	+	1.59688i	−0.334299	+	0.0763016i
$439$	−2.37316	+	10.3975i	−0.113265	+	0.496245i	0.886193	+	0.463316i	$0.153341\pi$
$439$	−2.37316	+	10.3975i	−0.113265	+	0.496245i	−0.999458	+	0.0329287i	$0.989517\pi$
$440$		0			0
$441$	−16.4107	+	20.5783i	−0.781460	+	0.979920i
$442$	−10.1119	+	2.30798i	−0.480975	+	0.109779i
$443$	−8.82962	−	18.3349i	−0.419508	−	0.871117i	−0.998445	−	0.0557448i	$-0.982247\pi$
$443$	−8.82962	−	18.3349i	−0.419508	−	0.871117i	0.578937	−	0.815372i	$-0.303468\pi$
$444$	−1.45593	+	0.701137i	−0.0690952	+	0.0332745i
$445$		0			0
$446$	35.5855	+	17.1371i	1.68502	+	0.811464i
$447$			1.20536i			0.0570115i
$448$	−2.22889	+	4.62833i	−0.105305	+	0.218668i
$449$	−12.1102	+	15.1857i	−0.571516	+	0.716659i	−0.980640	−	0.195820i	$-0.937263\pi$
$449$	−12.1102	+	15.1857i	−0.571516	+	0.716659i	0.409124	+	0.912479i	$0.365834\pi$
$450$		0			0
$451$	−1.03923	−	0.500466i	−0.0489354	−	0.0235660i
$452$			10.7748i			0.506804i
$453$	0.470258	−	0.976501i	0.0220946	−	0.0458800i
$454$	7.32908	−	32.1108i	0.343971	−	1.50704i
$455$		0			0
$456$	−1.11476	+	0.536840i	−0.0522034	+	0.0251399i
$457$	−12.1095	+	2.76391i	−0.566457	+	0.129290i	−0.496152	−	0.868236i	$-0.665254\pi$
$457$	−12.1095	+	2.76391i	−0.566457	+	0.129290i	−0.0703045	+	0.997526i	$0.522397\pi$
$458$	22.5759	+	18.0036i	1.05490	+	0.841255i
$459$	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	$0.757821\pi$
$462$	−7.39201	+	5.89493i	−0.343907	+	0.274257i
$463$			33.0073i			1.53398i	0.641660	+	0.766990i	$0.278246\pi$
$463$			33.0073i			1.53398i	−0.641660	+	0.766990i	$0.721754\pi$
$464$	−12.8068	−	23.3110i	−0.594540	−	1.08219i
$465$		0			0
$466$	−2.19806	−	2.75628i	−0.101823	−	0.127682i
$467$	−25.4487	+	5.80851i	−1.17763	+	0.268786i	−0.766167	−	0.642642i	$-0.777838\pi$
$467$	−25.4487	+	5.80851i	−1.17763	+	0.268786i	−0.411461	+	0.911427i	$0.634981\pi$
$468$	−17.6653	−	4.03199i	−0.816579	−	0.186379i
$469$	0.945042	+	1.18505i	0.0436380	+	0.0547203i
$470$		0			0
$471$	−1.75063	−	7.67000i	−0.0806647	−	0.353415i
$472$	5.36333	+	11.1371i	0.246867	+	0.512625i
$473$	7.25314	+	15.0613i	0.333500	+	0.692519i
$474$	0.106031	−	0.464554i	0.00487018	−	0.0213377i
$475$		0			0
$476$	−5.60388			−0.256853
$477$	5.29674	−	10.9988i	0.242521	−	0.503601i
$478$	−12.6274	−	10.0700i	−0.577564	−	0.460592i
$479$	−20.6163	+	25.8520i	−0.941981	+	1.18121i	0.0413068	+	0.999147i	$0.486848\pi$
$479$	−20.6163	+	25.8520i	−0.941981	+	1.18121i	−0.983287	+	0.182060i	$0.941724\pi$
$480$		0			0
$481$	−15.1008			−0.688538
$482$	−15.5583	+	32.3071i	−0.708660	+	1.47155i
$483$	7.26782	+	1.65883i	0.330697	+	0.0754795i
$484$	−2.83244	+	1.36403i	−0.128747	+	0.0620014i
$485$		0			0
$486$	4.40097	+	19.2819i	0.199632	+	0.874645i
$487$	−7.94063	−	6.33244i	−0.359824	−	0.286950i	0.426845	−	0.904325i	$-0.359625\pi$
$487$	−7.94063	−	6.33244i	−0.359824	−	0.286950i	−0.786669	+	0.617375i	$0.788196\pi$
$488$	−6.41708	+	5.11745i	−0.290487	+	0.231656i
$489$	−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	$0.932196\pi$
$492$			0.219833i			0.00991082i
$493$	3.47107	−	4.86592i	0.156329	−	0.219150i
$494$	19.1468			0.861453
$495$		0			0
$496$	−6.98643	−	30.6095i	−0.313700	−	1.37441i
$497$	−45.0233	−	10.2763i	−2.01957	−	0.460954i
$498$	5.91428	−	4.71648i	0.265025	−	0.211351i
$499$	−17.3639	+	21.7736i	−0.777315	+	0.974722i	−1.00000		0.000168534i	$-0.999946\pi$
$499$	−17.3639	+	21.7736i	−0.777315	+	0.974722i	0.222685	+	0.974890i	$0.428518\pi$
$500$		0			0
$501$	−5.79978	+	2.79303i	−0.259115	+	0.124783i
$502$	20.1751	+	41.8940i	0.900459	+	1.86982i
$503$	−0.219563	−	0.0501138i	−0.00978982	−	0.00223446i	0.217623	−	0.976033i	$-0.430170\pi$
$503$	−0.219563	−	0.0501138i	−0.00978982	−	0.00223446i	−0.227413	+	0.973798i	$0.573027\pi$
$504$	13.8693	+	6.67909i	0.617787	+	0.297510i
$505$		0			0
$506$	−19.5574	−	9.41835i	−0.869433	−	0.418697i
$507$	4.83452	+	3.85540i	0.214709	+	0.171224i
$508$	−10.2096	−	8.14191i	−0.452979	−	0.361239i
$509$	−22.7974	−	10.9786i	−1.01048	−	0.486620i	−0.145995	−	0.989285i	$-0.546638\pi$
$509$	−22.7974	−	10.9786i	−1.01048	−	0.486620i	−0.864481	+	0.502665i	$0.832353\pi$
$510$		0			0
$511$	−32.6444	−	15.7207i	−1.44410	−	0.695443i
$512$	16.7192	+	3.81604i	0.738890	+	0.168647i
$513$	−2.29547	−	4.76659i	−0.101348	−	0.210450i
$514$	−19.4025	+	9.34373i	−0.855806	+	0.412134i
$515$		0			0
$516$	1.98643	−	2.49090i	0.0874475	−	0.109656i
$517$	17.7617	−	14.1645i	0.781160	−	0.622954i
$518$	−20.7119	−	4.72737i	−0.910030	−	0.207709i
$519$	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	$0.327226\pi$
$522$	23.8298	−	13.0918i	1.04300	−	0.573012i
$523$		−	3.96508i		−	0.173381i	−0.996235	−	0.0866905i	$-0.972371\pi$
$523$		−	3.96508i		−	0.173381i	0.996235	−	0.0866905i	$-0.0276291\pi$
$524$	0.353543	+	0.443330i	0.0154446	+	0.0193669i
$525$		0			0
$526$	−0.133415	+	0.584531i	−0.00581719	+	0.0254868i
$527$	5.51631	−	4.39911i	0.240294	−	0.191628i
$528$	5.00406	+	3.99061i	0.217774	+	0.173669i
$529$	−1.30947	−	5.73717i	−0.0569335	−	0.249442i
$530$		0			0
$531$	−22.9976	+	11.0751i	−0.998011	+	0.480617i
$532$	10.0854	+	2.30194i	0.437260	+	0.0998017i
$533$	−0.891325	+	1.85086i	−0.0386076	+	0.0801694i
$534$	1.14138			0.0493921
$535$		0			0
$536$	0.316708	−	0.397139i	0.0136797	−	0.0171538i
$537$	−1.99755	−	1.59299i	−0.0862005	−	0.0687426i
$538$	−0.831855	+	1.72737i	−0.0358638	+	0.0744720i
$539$	−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	$-0.106421\pi$
$542$	−12.8724	−	26.7298i	−0.552917	−	1.14814i
$543$	−1.28230	−	2.66272i	−0.0550287	−	0.114268i
$544$	1.52781	+	6.69378i	0.0655044	+	0.286993i
$545$		0			0
$546$	10.4988	+	13.1651i	0.449307	+	0.563414i
$547$	−24.2183	−	5.52768i	−1.03550	−	0.236347i	−0.329202	−	0.944259i	$-0.606780\pi$
$547$	−24.2183	−	5.52768i	−1.03550	−	0.236347i	−0.706300	+	0.707913i	$0.749637\pi$
$548$	16.0964	−	3.67390i	0.687604	−	0.156941i
$549$	−10.5673	−	13.2510i	−0.451003	−	0.565540i
$550$		0			0
$551$	−8.24578	+	7.33150i	−0.351282	+	0.312332i
$552$		−	2.49827i		−	0.106333i
$553$	1.88094	−	1.50000i	0.0799857	−	0.0637865i
$554$	−2.64406	−	11.5844i	−0.112335	−	0.492174i
$555$		0			0
$556$	−2.17427	−	2.72645i	−0.0922095	−	0.115627i
$557$	6.07100	+	4.84146i	0.257237	+	0.205139i	0.743613	−	0.668610i	$-0.233110\pi$
$557$	6.07100	+	4.84146i	0.257237	+	0.205139i	−0.486377	+	0.873749i	$0.661682\pi$
$558$	31.2907	−	7.14191i	1.32464	−	0.302341i
$559$	26.8240	−	12.9178i	1.13453	−	0.546363i
$560$		0			0
$561$	−0.320060	+	1.40227i	−0.0135129	+	0.0592041i
$562$	23.8733	−	49.5734i	1.00703	−	2.09113i
$563$		−	20.8009i		−	0.876652i	−0.898816	−	0.438326i	$-0.855571\pi$
$563$		−	20.8009i		−	0.876652i	0.898816	−	0.438326i	$-0.144429\pi$
$564$	−3.90097	−	1.87861i	−0.164260	−	0.0791036i
$565$		0			0
$566$	3.99396	−	5.00827i	0.167879	−	0.210513i
$567$	−12.7482	+	26.4720i	−0.535375	+	1.11172i
$568$			15.4765i			0.649380i
$569$	2.53103	+	1.21888i	0.106106	+	0.0510981i	0.486184	−	0.873856i	$-0.338388\pi$
$569$	2.53103	+	1.21888i	0.106106	+	0.0510981i	−0.380078	+	0.924955i	$0.624103\pi$
$570$		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	$0.376420\pi$
$572$	−8.17021	−	16.9656i	−0.341614	−	0.709368i
$573$	8.16206	−	1.86294i	0.340975	−	0.0778253i
$574$	−1.80194	+	2.25956i	−0.0752114	+	0.0943121i
$575$		0			0
$576$	−0.791053	+	3.46583i	−0.0329605	+	0.144409i
$577$	7.00872	−	1.59970i	0.291777	−	0.0665962i	−0.0741270	−	0.997249i	$-0.523617\pi$
$577$	7.00872	−	1.59970i	0.291777	−	0.0665962i	0.365904	+	0.930653i	$0.380760\pi$
$578$	22.2143	−	17.7153i	0.923992	−	0.736859i
$579$	−4.84415			−0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$	9.87533	−	7.87531i	0.409346	−	0.326442i
$583$	12.3686	−	2.82304i	0.512254	−	0.116919i
$584$	−2.70195	+	11.8380i	−0.111807	+	0.489860i
$585$		0			0
$586$	−36.9403	+	46.3216i	−1.52599	+	1.91353i
$587$	−30.2587	+	6.90635i	−1.24891	+	0.285055i	−0.795339	−	0.606165i	$-0.792707\pi$
$587$	−30.2587	+	6.90635i	−1.24891	+	0.285055i	−0.453570	+	0.891220i	$0.649850\pi$
$588$	2.26189	+	4.69687i	0.0932788	+	0.193695i
$589$	−11.7349	+	5.65123i	−0.483528	+	0.232855i
$590$		0			0
$591$	3.36831	+	1.62209i	0.138554	+	0.0667240i
$592$			14.3817i			0.591082i
$593$	−15.8226	+	32.8560i	−0.649757	+	1.34923i	0.272312	+	0.962209i	$0.412212\pi$
$593$	−15.8226	+	32.8560i	−0.649757	+	1.34923i	−0.922069	+	0.387025i	$0.873503\pi$
$594$	−8.44720	+	10.5925i	−0.346593	+	0.434614i
$595$		0			0
$596$	−3.04288	−	1.46537i	−0.124641	−	0.0600240i
$597$		−	2.94677i		−	0.120603i
$598$	−16.7740	+	34.8315i	−0.685939	+	1.42437i
$599$	6.69083	−	29.3144i	0.273380	−	1.19775i	−0.632615	−	0.774466i	$-0.718019\pi$
$599$	6.69083	−	29.3144i	0.273380	−	1.19775i	0.905995	−	0.423288i	$-0.139124\pi$
$600$		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	$0.120491\pi$
$602$	40.8351	−	9.32036i	1.66432	−	0.379869i
$603$	0.820077	+	0.653989i	0.0333961	+	0.0266325i
$604$	1.89344	+	2.37429i	0.0770428	+	0.0966086i
$605$		0			0
$606$	−3.11260	−	13.6372i	−0.126441	−	0.553974i
$607$	11.8214	−	9.42729i	0.479818	−	0.382642i	−0.353502	−	0.935434i	$-0.615009\pi$
$607$	11.8214	−	9.42729i	0.479818	−	0.382642i	0.833319	+	0.552792i	$0.186438\pi$
$608$		−	12.6746i		−	0.514021i
$609$	−9.56249	−	1.64960i	−0.387492	−	0.0668451i
$610$		0			0
$611$	−25.2268	−	31.6334i	−1.02057	−	1.27975i
$612$	−3.78077	+	0.862937i	−0.152829	+	0.0348821i
$613$	3.66126	+	0.835658i	0.147877	+	0.0337519i	0.295818	−	0.955244i	$-0.404408\pi$
$613$	3.66126	+	0.835658i	0.147877	+	0.0337519i	−0.147942	+	0.988996i	$0.547265\pi$
$614$	16.4819	+	20.6676i	0.665154	+	0.834077i
$615$		0			0
$616$	3.55980	+	15.5965i	0.143429	+	0.628401i
$617$	−12.9541	−	26.8995i	−0.521514	−	1.08293i	−0.980867	−	0.194681i	$-0.937633\pi$
$617$	−12.9541	−	26.8995i	−0.521514	−	1.08293i	0.459353	−	0.888254i	$-0.348081\pi$
$618$	0.979132	+	2.03319i	0.0393865	+	0.0817868i
$619$	−10.2622	+	44.9615i	−0.412472	+	1.80716i	0.159866	+	0.987139i	$0.448894\pi$
$619$	−10.2622	+	44.9615i	−0.412472	+	1.80716i	−0.572338	+	0.820018i	$0.693963\pi$
$620$		0			0
$621$	10.6823			0.428667
$622$	−14.4846	+	30.0776i	−0.580779	+	1.20600i
$623$	4.50547	+	3.59299i	0.180508	+	0.143950i
$624$	7.10723	−	8.91218i	0.284517	−	0.356773i
$625$		0			0
$626$	−41.4306			−1.65590
$627$	1.15204	−	2.39224i	0.0460081	−	0.0955368i
$628$	21.4909	+	4.90515i	0.857579	+	0.195737i
$629$	−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	$-0.152318\pi$
$632$	−0.630351	−	0.502688i	−0.0250740	−	0.0199959i
$633$	−2.81846	+	2.24764i	−0.112024	+	0.0893358i
$634$	−5.63706	+	24.6976i	−0.223876	+	0.980867i
$635$		0			0
$636$	−1.50753	−	1.89039i	−0.0597776	−	0.0749587i
$637$			48.7157i			1.93019i
$638$	26.0776	+	10.8790i	1.03242	+	0.430702i
$639$	−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	$-0.351293\pi$
$642$	−5.83255	−	1.33124i	−0.230192	−	0.0525399i
$643$	32.2869	−	25.7479i	1.27327	−	1.01540i	0.274723	−	0.961523i	$-0.411414\pi$
$643$	32.2869	−	25.7479i	1.27327	−	1.01540i	0.998548	−	0.0538762i	$-0.0171576\pi$
$644$	−13.0233	+	16.3307i	−0.513188	+	0.643518i
$645$		0			0
$646$	3.69202	−	1.77798i	0.145261	−	0.0699538i
$647$	7.77109	+	16.1368i	0.305513	+	0.634404i	0.996040	−	0.0889021i	$-0.0283358\pi$
$647$	7.77109	+	16.1368i	0.305513	+	0.634404i	−0.690527	+	0.723306i	$0.742622\pi$
$648$	9.59967	+	2.19106i	0.377111	+	0.0860730i
$649$	−23.8998	−	11.5095i	−0.938148	−	0.451788i
$650$		0			0
$651$	−10.3204	−	4.97002i	−0.404487	−	0.194790i
$652$	−4.84164	−	3.86108i	−0.189613	−	0.151211i
$653$	10.4145	+	8.30529i	0.407551	+	0.325011i	0.805715	−	0.592303i	$-0.201781\pi$
$653$	10.4145	+	8.30529i	0.407551	+	0.325011i	−0.398164	+	0.917314i	$0.630353\pi$
$654$	1.19418	+	0.575086i	0.0466960	+	0.0224876i
$655$		0			0
$656$	1.76271	+	0.848876i	0.0688222	+	0.0331430i
$657$	−24.4450	−	5.57942i	−0.953691	−	0.217674i
$658$	−24.6976	−	51.2851i	−0.962812	−	1.99930i
$659$	16.9073	−	8.14213i	0.658615	−	0.317172i	−0.0745557	−	0.997217i	$-0.523754\pi$
$659$	16.9073	−	8.14213i	0.658615	−	0.317172i	0.733171	+	0.680045i	$0.238040\pi$
$660$		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	$0.373983\pi$
$662$	19.6620	−	15.6799i	0.764186	−	0.609418i
$663$	2.49744	+	0.570024i	0.0969924	+	0.0221379i
$664$	−2.84817	−	12.4786i	−0.110530	−	0.484265i
$665$		0			0
$666$	−14.7017			−0.569680
$667$	−6.11345	−	21.4236i	−0.236714	−	0.829524i
$668$		−	18.0368i		−	0.697866i
$669$	−6.08211	−	7.62672i	−0.235148	−	0.294866i
$670$		0			0
$671$	3.91939	−	17.1720i	0.151306	−	0.662916i
$672$	8.71488	−	6.94989i	0.336184	−	0.268098i
$673$	−19.8919	−	15.8632i	−0.766775	−	0.611483i	0.159992	−	0.987118i	$-0.448853\pi$
$673$	−19.8919	−	15.8632i	−0.766775	−	0.611483i	−0.926767	+	0.375636i	$0.877424\pi$
$674$	5.61260	+	24.5904i	0.216189	+	0.947188i
$675$		0			0
$676$	−15.6102	+	7.51748i	−0.600393	+	0.289134i
$677$	−0.601090	−	0.137195i	−0.0231018	−	0.00527283i	0.210954	−	0.977496i	$-0.432343\pi$
$677$	−0.601090	−	0.137195i	−0.0231018	−	0.00527283i	−0.234056	+	0.972223i	$0.575200\pi$
$678$	3.00652	−	6.24309i	0.115465	−	0.239765i
$679$	63.7730			2.44738
$680$		0			0
$681$	−5.07188	+	6.35994i	−0.194355	+	0.243713i
$682$	26.0776	+	20.7962i	0.998563	+	0.796327i
$683$	−7.81935	+	16.2371i	−0.299199	+	0.621294i	−0.995320	−	0.0966308i	$-0.969193\pi$
$683$	−7.81935	+	16.2371i	−0.299199	+	0.621294i	0.696121	+	0.717924i	$0.254908\pi$
$684$	7.15883			0.273725
$685$		0			0
$686$	−3.88620	+	17.0265i	−0.148376	+	0.650077i
$687$	−3.09432	−	6.42543i	−0.118056	−	0.245145i
$688$	−12.3026	−	25.5465i	−0.469031	−	0.973952i
$689$	−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	$0.710259\pi$
$692$	−12.7812	−	2.91723i	−0.485869	−	0.110896i
$693$	−32.2062	+	7.35086i	−1.22341	+	0.279236i
$694$	−22.3056	−	27.9703i	−0.846708	−	1.06174i
$695$		0			0
$696$	0.174136	+	3.24730i	0.00660061	+	0.123089i
$697$			0.439665i			0.0166535i
$698$	37.9255	−	30.2446i	1.43550	−	1.14477i
$699$	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	$-0.436979\pi$
$702$	18.8650	+	15.0444i	0.712015	+	0.567813i
$703$	5.81656	−	1.32759i	0.219376	−	0.0500711i
$704$	−3.32855	+	1.60295i	−0.125450	+	0.0604133i
$705$		0			0
$706$	−1.60992	+	7.05350i	−0.0605900	+	0.265462i
$707$	30.6425	−	63.6299i	1.15243	−	2.39305i
$708$			5.05562i			0.190002i
$709$	37.9267	+	18.2645i	1.42437	+	0.685939i	0.977941	−	0.208882i	$-0.0669825\pi$
$709$	37.9267	+	18.2645i	1.42437	+	0.685939i	0.446426	+	0.894821i	$0.352697\pi$
$710$		0			0
$711$	1.03803	−	1.30165i	0.0389292	−	0.0488157i
$712$	0.837930	−	1.73998i	0.0314028	−	0.0652085i
$713$		−	26.2989i		−	0.984901i
$714$	3.24698	+	1.56366i	0.121515	+	0.0585186i
$715$		0			0
$716$	6.44989	−	3.10610i	0.241044	−	0.116080i
$717$	1.73076	+	3.59395i	0.0646362	+	0.134219i
$718$	−1.31110	+	0.299249i	−0.0489297	+	0.0111679i
$719$	32.5800	−	40.8540i	1.21503	−	1.52360i	0.431667	−	0.902033i	$-0.357926\pi$
$719$	32.5800	−	40.8540i	1.21503	−	1.52360i	0.783362	−	0.621566i	$-0.213503\pi$
$720$		0			0
$721$	−2.53534	+	11.1081i	−0.0944211	+	0.413686i
$722$	26.0034	−	5.93512i	0.967748	−	0.220882i
$723$	6.92408	−	5.52177i	0.257509	−	0.205357i
$724$	8.28083			0.307755
$725$		0			0
$726$	2.02177			0.0750349
$727$	−23.4432	+	18.6953i	−0.869459	+	0.693370i	−0.952947	−	0.303138i	$-0.901966\pi$
$727$	−23.4432	+	18.6953i	−0.869459	+	0.693370i	0.0834876	+	0.996509i	$0.473394\pi$
$728$	27.7772	−	6.33997i	1.02949	−	0.234975i
$729$	−3.75733	+	16.4619i	−0.139160	+	0.609702i
$730$		0			0
$731$	3.97285	−	4.98180i	0.146941	−	0.184259i
$732$	−3.27273	+	0.746980i	−0.120964	+	0.0276092i
$733$	1.30793	+	2.71595i	0.0483096	+	0.100316i	0.923726	−	0.383053i	$-0.125127\pi$
$733$	1.30793	+	2.71595i	0.0483096	+	0.100316i	−0.875417	+	0.483369i	$0.839413\pi$
$734$	55.2781	−	26.6205i	2.04035	−	0.982581i
$735$		0			0
$736$	23.0574	+	11.1039i	0.849907	+	0.409294i
$737$			1.09006i			0.0401531i
$738$	−0.867767	+	1.80194i	−0.0319430	+	0.0663302i
$739$	12.9919	−	16.2914i	0.477916	−	0.599288i	−0.483174	−	0.875525i	$-0.660516\pi$
$739$	12.9919	−	16.2914i	0.477916	−	0.599288i	0.961090	+	0.276237i	$0.0890874\pi$
$740$		0			0
$741$	−4.26055	−	2.05177i	−0.156515	−	0.0753738i
$742$		−	31.7875i		−	1.16695i
$743$	13.3487	−	27.7189i	0.489718	−	1.01691i	−0.498928	−	0.866643i	$-0.666273\pi$
$743$	13.3487	−	27.7189i	0.489718	−	1.01691i	0.988646	−	0.150266i	$-0.0480129\pi$
$744$	−0.854207	+	3.74253i	−0.0313168	+	0.137208i
$745$		0			0
$746$	45.4587	−	21.8917i	1.66436	−	0.801514i
$747$	25.7679	−	5.88135i	0.942798	−	0.215188i
$748$	−3.15088	−	2.51275i	−0.115208	−	0.0918751i
$749$	−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	$0.902587\pi$
$752$	−30.1269	+	24.0254i	−1.09862	+	0.876117i
$753$		−	11.4843i		−	0.418510i
$754$	19.3753	−	46.4439i	0.705607	−	1.69139i
$755$		0			0
$756$	8.12833	+	10.1926i	0.295625	+	0.370702i
$757$	−8.24379	+	1.88159i	−0.299626	+	0.0683876i	−0.369691	−	0.929155i	$-0.620536\pi$
$757$	−8.24379	+	1.88159i	−0.299626	+	0.0683876i	0.0700652	+	0.997542i	$0.477679\pi$
$758$	−40.1964	−	9.17456i	−1.46000	−	0.333235i
$759$	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	$-0.219149\pi$
$762$	3.64377	+	7.56638i	0.132000	+	0.274101i
$763$	2.90356	+	6.02930i	0.105116	+	0.218275i
$764$	−5.21983	+	22.8696i	−0.188847	+	0.827392i
$765$		0			0
$766$	−21.3676			−0.772045
$767$	−20.4983	+	42.5652i	−0.740152	+	1.53694i
$768$	−7.20648	−	5.74698i	−0.260042	−	0.207376i
$769$	−18.7939	+	23.5668i	−0.677724	+	0.849839i	−0.995142	−	0.0984462i	$-0.968613\pi$
$769$	−18.7939	+	23.5668i	−0.677724	+	0.849839i	0.317418	+	0.948286i	$0.397184\pi$
$770$		0			0
$771$	5.31873			0.191549
$772$	5.88911	−	12.2289i	0.211954	−	0.440126i
$773$	5.53462	+	1.26324i	0.199067	+	0.0454356i	0.320892	−	0.947116i	$-0.396018\pi$
$773$	5.53462	+	1.26324i	0.199067	+	0.0454356i	−0.121825	+	0.992552i	$0.538875\pi$
$774$	26.1151	−	12.5763i	0.938686	−	0.452048i
$775$		0			0
$776$	−4.75571	−	20.8361i	−0.170720	−	0.747973i
$777$	4.10225	+	3.27144i	0.147168	+	0.117362i
$778$	14.6394	−	11.6746i	0.524849	−	0.418553i
$779$	0.180604	−	0.791277i	0.00647081	−	0.0283504i
$780$		0			0
$781$	−20.7074	−	25.9662i	−0.740968	−	0.929145i
$782$			8.27413i			0.295882i
$783$	−13.8851	+	0.744587i	−0.496213	+	0.0266094i
$784$	46.3957			1.65699
$785$		0			0
$786$	−0.0811457	−	0.355523i	−0.00289437	−	0.0126811i
$787$	3.51876	+	0.803134i	0.125430	+	0.0286286i	0.284775	−	0.958594i	$-0.408081\pi$
$787$	3.51876	+	0.803134i	0.125430	+	0.0286286i	−0.159345	+	0.987223i	$0.550938\pi$
$788$	−8.18982	+	6.53116i	−0.291750	+	0.232663i
$789$	0.0923264	−	0.115774i	0.00328691	−	0.00412165i
$790$		0			0
$791$	31.5209	−	15.1797i	1.12075	−	0.539726i
$792$	4.80339	+	9.97434i	0.170681	+	0.354423i
$793$	−30.5831	−	6.98039i	−1.08604	−	0.247881i
$794$	−13.3409	−	6.42465i	−0.473452	−	0.228002i
$795$		0			0
$796$	7.43900	+	3.58243i	0.263668	+	0.126976i
$797$	−24.0672	−	19.1930i	−0.852505	−	0.679850i	0.0964236	−	0.995340i	$-0.469260\pi$
$797$	−24.0672	−	19.1930i	−0.852505	−	0.679850i	−0.948929	+	0.315490i	$0.897831\pi$
$798$	−5.20136	−	4.14795i	−0.184126	−	0.146836i
$799$	−7.80194	−	3.75722i	−0.276013	−	0.132921i
$800$		0			0
$801$	3.59299	+	1.73029i	0.126952	+	0.0611369i
$802$	43.7099	+	9.97650i	1.54345	+	0.352282i
$803$	−11.3058	−	23.4768i	−0.398974	−	0.828478i
$804$	0.187177	−	0.0901398i	0.00660123	−	0.00317898i
$805$		0			0
$806$	37.0378	−	46.4439i	1.30460	−	1.63592i
$807$	0.370210	−	0.295233i	0.0130320	−	0.0103927i
$808$	−23.0745	−	5.26659i	−0.811757	−	0.185278i
$809$	1.16541	+	5.10598i	0.0409735	+	0.179517i	0.991274	−	0.131817i	$-0.0420813\pi$
$809$	1.16541	+	5.10598i	0.0409735	+	0.179517i	−0.950300	+	0.311334i	$0.899224\pi$
$810$		0			0
$811$	41.8646			1.47006			0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646			1.47006			0.735032	+	0.678032i	$0.237167\pi$
$812$	15.7896	−	22.1347i	0.554107	−	0.776775i
$813$			7.32736i			0.256982i
$814$	−9.52595	−	11.9452i	−0.333884	−	0.418678i
$815$		0			0
$816$	0.542877	−	2.37850i	0.0190045	−	0.0832641i
$817$	−9.19646	+	7.33393i	−0.321743	+	0.256582i
$818$	26.6201	+	21.2289i	0.930752	+	0.742250i
$819$	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	$0.443781\pi$
$822$	−10.3517	−	2.36270i	−0.361056	−	0.0824086i
$823$	15.4705	−	32.1247i	0.539266	−	1.11980i	−0.436241	−	0.899830i	$-0.643690\pi$
$823$	15.4705	−	32.1247i	0.539266	−	1.11980i	0.975507	−	0.219968i	$-0.0705954\pi$
$824$	3.81833			0.133018
$825$		0			0
$826$	−41.4403	+	51.9644i	−1.44189	+	1.80807i
$827$	−40.6973	−	32.4550i	−1.41518	−	1.12857i	−0.972773	−	0.231760i	$-0.925552\pi$
$827$	−40.6973	−	32.4550i	−1.41518	−	1.12857i	−0.442411	−	0.896812i	$-0.645877\pi$
$828$	−6.27167	+	13.0233i	−0.217956	+	0.452590i
$829$	13.4168			0.465986			0.232993	−	0.972478i	$-0.425148\pi$
$829$	13.4168			0.465986			0.232993	+	0.972478i	$0.425148\pi$
$830$		0			0
$831$	−0.653030	+	2.86111i	−0.0226534	+	0.0992508i
$832$	2.85483	+	5.92812i	0.0989734	+	0.205520i
$833$	4.52378	+	9.39373i	0.156740	+	0.325474i
$834$	0.499041	+	2.18644i	0.0172804	+	0.0757102i
$835$		0			0
$836$	4.63856	+	5.81656i	0.160428	+	0.201170i
$837$	−16.0026	−	3.65250i	−0.553132	−	0.126249i
$838$	−19.1355	+	4.36754i	−0.661024	+	0.150874i
$839$	19.3602	+	24.2769i	0.668387	+	0.838131i	0.994227	−	0.107294i	$-0.0342185\pi$
$839$	19.3602	+	24.2769i	0.668387	+	0.838131i	−0.325840	+	0.945425i	$0.605647\pi$
$840$		0			0
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$			35.9681i			1.23954i
$843$	−10.6246	+	8.47285i	−0.365931	+	0.291821i
$844$	−2.24764	−	9.84757i	−0.0773671	−	0.338967i
$845$		0			0
$846$	−24.5601	−	30.7974i	−0.844394	−	1.05884i
$847$	7.98074	+	6.36443i	0.274222	+	0.218684i
$848$	−20.9792	+	4.78836i	−0.720428	+	0.164433i
$849$	−1.42543	+	0.686450i	−0.0489205	+	0.0235589i
$850$		0			0
$851$	−2.68060	+	11.7445i	−0.0918899	+	0.402596i
$852$	−2.74638	+	5.70291i	−0.0940893	+	0.195378i
$853$		−	21.3357i		−	0.730521i	−0.930905	−	0.365261i	$-0.880980\pi$
$853$		−	21.3357i		−	0.730521i	0.930905	−	0.365261i	$-0.119020\pi$
$854$	−39.7618	−	19.1483i	−1.36062	−	0.655241i
$855$		0			0
$856$	−6.31133	+	7.91416i	−0.215717	+	0.270500i
$857$	−4.26597	+	8.85839i	−0.145723	+	0.302597i	−0.961036	−	0.276424i	$-0.910851\pi$
$857$	−4.26597	+	8.85839i	−0.145723	+	0.302597i	0.815313	+	0.579021i	$0.196565\pi$
$858$			12.1099i			0.413426i
$859$	−46.6555	−	22.4681i	−1.59187	−	0.766602i	−0.592623	−	0.805480i	$-0.701907\pi$
$859$	−46.6555	−	22.4681i	−1.59187	−	0.766602i	−0.999244	+	0.0388778i	$0.987622\pi$
$860$		0			0
$861$	0.643104	−	0.309703i	0.0219169	−	0.0105546i
$862$	−23.6037	−	49.0136i	−0.803946	−	1.66941i
$863$	15.8667	−	3.62147i	0.540108	−	0.123276i	0.0562402	−	0.998417i	$-0.482089\pi$
$863$	15.8667	−	3.62147i	0.540108	−	0.123276i	0.483868	+	0.875141i	$0.339232\pi$
$864$	9.95891	−	12.4881i	0.338809	−	0.424853i
$865$		0			0
$866$	−8.09611	+	35.4714i	−0.275117	+	1.20537i
$867$	−6.84152	+	1.56153i	−0.232350	+	0.0530324i
$868$	25.0932	−	20.0112i	0.851720	−	0.679224i
$869$	1.73019			0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	1.75339	−	1.39828i	0.0593772	−	0.0473518i
$873$	43.0258	−	9.82036i	1.45620	−	0.332369i
$874$	3.39881	−	14.8912i	0.114967	−	0.503701i
$875$		0			0
$876$	−3.09634	+	3.88269i	−0.104616	+	0.131184i
$877$	14.4350	−	3.29470i	0.487436	−	0.111254i	0.0282623	−	0.999601i	$-0.491003\pi$
$877$	14.4350	−	3.29470i	0.487436	−	0.111254i	0.459174	+	0.888346i	$0.348145\pi$
$878$	8.33813	+	17.3143i	0.281398	+	0.584330i
$879$	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	$0.541201\pi$
$882$			47.4282i			1.59699i
$883$	14.0551	−	29.1857i	0.472992	−	0.982178i	−0.518869	−	0.854854i	$-0.673647\pi$
$883$	14.0551	−	29.1857i	0.472992	−	0.982178i	0.991861	−	0.127325i	$-0.0406390\pi$
$884$	−4.47517	+	5.61169i	−0.150516	+	0.188742i
$885$		0			0
$886$	−33.0383	−	15.9104i	−1.10994	−	0.534521i
$887$		−	6.16288i		−	0.206929i	−0.994633	−	0.103465i	$-0.967007\pi$
$887$		−	6.16288i		−	0.206929i	0.994633	−	0.103465i	$-0.0329929\pi$
$888$	0.762940	−	1.58426i	0.0256026	−	0.0531643i
$889$	−9.43512	+	41.3379i	−0.316444	+	1.38643i
$890$		0			0
$891$	−19.0378	+	9.16812i	−0.637790	+	0.307144i
$892$	26.6474	−	6.08211i	0.892222	−	0.203644i
$893$	12.4980	+	9.96681i	0.418229	+	0.333527i
$894$	1.35421	+	1.69812i	0.0452915	+	0.0567937i
$895$		0			0
$896$	−9.08695	−	39.8125i	−0.303574	−	1.33004i
$897$	7.46513	−	5.95324i	0.249253	−	0.198773i
$898$			34.9995i			1.16795i
$899$	1.83310	+	34.1838i	0.0611373	+	1.14009i
$900$		0			0
$901$	−3.01507	−	3.78077i	−0.100446	−	0.125956i
$902$	−2.02635	+	0.462500i	−0.0674699	+	0.0153996i
$903$	−10.0854	−	2.30194i	−0.335623	−	0.0766037i
$904$	−7.31013	−	9.16662i	−0.243131	−	0.304877i
$905$		0			0
$906$	−0.434584	−	1.90404i	−0.0144381	−	0.0632574i
$907$	−19.0840	−	39.6284i	−0.633675	−	1.31584i	−0.932375	−	0.361492i	$-0.882267\pi$
$907$	−19.0840	−	39.6284i	−0.633675	−	1.31584i	0.298700	−	0.954347i	$-0.403447\pi$
$908$	−9.88944	−	20.5356i	−0.328193	−	0.681499i
$909$	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	$0.639539\pi$
$912$	−1.95406	+	4.05765i	−0.0647054	+	0.134362i
$913$	21.4749	+	17.1256i	0.710715	+	0.566776i
$914$	−13.9547	+	17.4987i	−0.461581	+	0.578805i
$915$		0			0
$916$	19.9825			0.660242
$917$	0.798852	−	1.65883i	0.0263804	−	0.0547795i
$918$	5.03473	+	1.14914i	0.166171	+	0.0379274i
$919$	−5.62349	+	2.70813i	−0.185502	+	0.0893330i	−0.524329	−	0.851516i	$-0.675684\pi$
$919$	−5.62349	+	2.70813i	−0.185502	+	0.0893330i	0.338828	+	0.940848i	$0.389970\pi$
$920$		0			0
$921$	−1.45281	−	6.36518i	−0.0478718	−	0.209740i
$922$	30.9182	+	24.6564i	1.01824	+	0.812017i
$923$	−46.2456	+	36.8796i	−1.52219	+	1.21391i
$924$	−1.45593	+	6.37883i	−0.0478965	+	0.209848i
$925$		0			0
$926$	37.0834	+	46.5011i	1.21863	+	1.52812i
$927$			7.88471i			0.258968i
$928$	−30.7445	−	12.8259i	−1.00924	−	0.421030i
$929$	24.5133			0.804256			0.402128	−	0.915583i	$-0.368271\pi$
$929$	24.5133			0.804256			0.402128	+	0.915583i	$0.368271\pi$
$930$		0			0
$931$	−4.28286	−	18.7644i	−0.140365	−	0.614979i
$932$	−2.37850	−	0.542877i	−0.0779103	−	0.0177825i
$933$	6.44625	−	5.14071i	0.211041	−	0.168299i
$934$	−29.3267	+	36.7745i	−0.959599	+	1.20330i
$935$		0			0
$936$	17.7642	−	8.55479i	0.580641	−	0.279622i
$937$	1.77436	+	3.68449i	0.0579657	+	0.120367i	0.927939	−	0.372731i	$-0.121579\pi$
$937$	1.77436	+	3.68449i	0.0579657	+	0.120367i	−0.869974	+	0.493098i	$0.835864\pi$
$938$	2.66277	+	0.607760i	0.0869426	+	0.0198441i
$939$	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	$0.674887\pi$
$942$	−11.0835	−	8.83877i	−0.361119	−	0.287983i
$943$	1.28126	+	1.02177i	0.0417235	+	0.0332734i
$944$	40.5381	+	19.5221i	1.31940	+	0.635391i
$945$		0			0
$946$	27.1395	+	13.0697i	0.882382	+	0.424933i
$947$	48.4562	+	11.0598i	1.57461	+	0.359395i	0.918548	−	0.395309i	$-0.129362\pi$
$947$	48.4562	+	11.0598i	1.57461	+	0.359395i	0.656065	+	0.754704i	$0.272220\pi$
$948$	−0.143073	−	0.297093i	−0.00464678	−	0.00964914i
$949$	−41.8119	+	20.1356i	−1.35727	+	0.653628i
$950$		0			0
$951$	3.90097	−	4.89166i	0.126498	−	0.158623i
$952$	4.76748	−	3.80194i	0.154515	−	0.123222i
$953$	17.2422	+	3.93541i	0.558529	+	0.127480i	0.492461	−	0.870335i	$-0.336098\pi$
$953$	17.2422	+	3.93541i	0.558529	+	0.127480i	0.0660678	+	0.997815i	$0.478955\pi$
$954$	−4.89493	−	21.4461i	−0.158479	−	0.694343i
$955$		0			0
$956$	−11.1769			−0.361486
$957$	−4.63702	−	5.21528i	−0.149893	−	0.168586i
$958$			59.5827i			1.92503i
$959$	−33.4245	−	41.9130i	−1.07933	−	1.35344i
$960$		0			0
$961$	−2.09395	+	9.17419i	−0.0675468	+	0.295942i
$962$	−21.2742	+	16.9656i	−0.685908	+	0.546993i
$963$	−16.3424	−	13.0327i	−0.526628	−	0.419971i
$964$	5.52177	+	24.1925i	0.177844	+	0.779187i
$965$		0			0
$966$	12.1027	−	5.82834i	0.389397	−	0.187524i
$967$	12.5701	+	2.86904i	0.404226	+	0.0922620i	0.419800	−	0.907617i	$-0.362100\pi$
$967$	12.5701	+	2.86904i	0.404226	+	0.0922620i	−0.0155736	+	0.999879i	$0.504957\pi$
$968$	1.48426	−	3.08211i	0.0477060	−	0.0990626i
$969$	−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	$0.189553\pi$
$972$	10.7006	+	8.53348i	0.343223	+	0.273712i
$973$	−4.91288	+	10.2017i	−0.157500	+	0.327052i
$974$	−18.3013			−0.586411
$975$		0			0
$976$	−6.64795	+	29.1266i	−0.212796	+	0.932319i
$977$	−7.13394	−	14.8138i	−0.228235	−	0.473935i	0.755130	−	0.655575i	$-0.227574\pi$
$977$	−7.13394	−	14.8138i	−0.228235	−	0.473935i	−0.983365	+	0.181640i	$0.941859\pi$
$978$	1.72796	+	3.58815i	0.0552541	+	0.114736i
$979$	0.922207	+	4.04045i	0.0294739	+	0.129133i
$980$		0			0
$981$	2.88740	+	3.62068i	0.0921874	+	0.115599i
$982$	−34.5763	−	7.89181i	−1.10337	−	0.251838i
$983$	−25.8349	+	5.89666i	−0.824007	+	0.188074i	−0.613678	−	0.789557i	$-0.710311\pi$
$983$	−25.8349	+	5.89666i	−0.824007	+	0.188074i	−0.210329	+	0.977631i	$0.567453\pi$
$984$	−0.149145	−	0.187022i	−0.00475457	−	0.00596204i
$985$		0			0
$986$	−0.576728	−	10.7549i	−0.0183668	−	0.342505i
$987$			14.0586i			0.447490i
$988$	10.3592	−	8.26122i	0.329571	−	0.262824i
$989$	−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	$0.563912\pi$
$992$	−30.7445	−	24.5179i	−0.976137	−	0.778444i
$993$	−6.05548	+	1.38212i	−0.192165	+	0.0438604i
$994$	−74.9747	+	36.1059i	−2.37805	+	1.14521i
$995$		0			0
$996$	1.16487	−	5.10365i	0.0369105	−	0.161715i
$997$	−10.1769	+	21.1325i	−0.322305	+	0.669273i	−0.997671	−	0.0682093i	$-0.978271\pi$
$997$	−10.1769	+	21.1325i	−0.322305	+	0.669273i	0.675366	+	0.737483i	$0.263986\pi$
$998$			50.1831i			1.58852i
$999$	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.r.b.24.2		12
5.2	odd	4		725.2.l.b.401.1		6
5.3	odd	4		29.2.d.a.24.1	yes	6
5.4	even	2	inner	725.2.r.b.24.1		12
15.8	even	4		261.2.k.a.82.1		6
20.3	even	4		464.2.u.f.401.1		6
29.23	even	7	inner	725.2.r.b.574.1		12
145.3	even	28		841.2.e.b.651.2		12
145.8	even	28		841.2.b.c.840.1		6
145.13	odd	28		841.2.d.c.605.1		6
145.18	even	28		841.2.e.c.236.2		12
145.23	odd	28		29.2.d.a.23.1	✓	6
145.28	odd	4		841.2.d.d.778.1		6
145.33	odd	28		841.2.d.c.645.1		6
145.38	odd	28		841.2.a.f.1.3		3
145.43	even	28		841.2.e.d.267.2		12
145.48	even	28		841.2.e.c.196.2		12
145.52	odd	28		725.2.l.b.226.1		6
145.53	odd	28		841.2.d.e.571.1		6
145.63	odd	28		841.2.d.a.571.1		6
145.68	even	28		841.2.e.c.196.1		12
145.73	even	28		841.2.e.d.267.1		12
145.78	odd	28		841.2.a.e.1.1		3
145.83	odd	28		841.2.d.b.645.1		6
145.93	odd	28		841.2.d.d.574.1		6
145.98	even	28		841.2.e.c.236.1		12
145.103	odd	28		841.2.d.b.605.1		6
145.108	even	28		841.2.b.c.840.6		6
145.113	even	28		841.2.e.b.651.1		12
145.118	even	28		841.2.e.b.270.1		12
145.123	odd	28		841.2.d.e.190.1		6
145.128	even	4		841.2.e.d.63.2		12
145.133	even	4		841.2.e.d.63.1		12
145.138	odd	28		841.2.d.a.190.1		6
145.139	even	14	inner	725.2.r.b.574.2		12
145.143	even	28		841.2.e.b.270.2		12
435.23	even	28		261.2.k.a.226.1		6
435.38	even	28		7569.2.a.p.1.1		3
435.368	even	28		7569.2.a.r.1.3		3
580.23	even	28		464.2.u.f.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	145.23	odd	28
29.2.d.a.24.1	yes	6	5.3	odd	4
261.2.k.a.82.1		6	15.8	even	4
261.2.k.a.226.1		6	435.23	even	28
464.2.u.f.81.1		6	580.23	even	28
464.2.u.f.401.1		6	20.3	even	4
725.2.l.b.226.1		6	145.52	odd	28
725.2.l.b.401.1		6	5.2	odd	4
725.2.r.b.24.1		12	5.4	even	2	inner
725.2.r.b.24.2		12	1.1	even	1	trivial
725.2.r.b.574.1		12	29.23	even	7	inner
725.2.r.b.574.2		12	145.139	even	14	inner
841.2.a.e.1.1		3	145.78	odd	28
841.2.a.f.1.3		3	145.38	odd	28
841.2.b.c.840.1		6	145.8	even	28
841.2.b.c.840.6		6	145.108	even	28
841.2.d.a.190.1		6	145.138	odd	28
841.2.d.a.571.1		6	145.63	odd	28
841.2.d.b.605.1		6	145.103	odd	28
841.2.d.b.645.1		6	145.83	odd	28
841.2.d.c.605.1		6	145.13	odd	28
841.2.d.c.645.1		6	145.33	odd	28
841.2.d.d.574.1		6	145.93	odd	28
841.2.d.d.778.1		6	145.28	odd	4
841.2.d.e.190.1		6	145.123	odd	28
841.2.d.e.571.1		6	145.53	odd	28
841.2.e.b.270.1		12	145.118	even	28
841.2.e.b.270.2		12	145.143	even	28
841.2.e.b.651.1		12	145.113	even	28
841.2.e.b.651.2		12	145.3	even	28
841.2.e.c.196.1		12	145.68	even	28
841.2.e.c.196.2		12	145.48	even	28
841.2.e.c.236.1		12	145.98	even	28
841.2.e.c.236.2		12	145.18	even	28
841.2.e.d.63.1		12	145.133	even	4
841.2.e.d.63.2		12	145.128	even	4
841.2.e.d.267.1		12	145.73	even	28
841.2.e.d.267.2		12	145.43	even	28
7569.2.a.p.1.1		3	435.38	even	28
7569.2.a.r.1.3		3	435.368	even	28

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.r (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40881 - 1.12349i) q^{2} +(-0.433884 + 0.0990311i) q^{3} +(0.277479 - 1.21572i) q^{4} +(-0.500000 + 0.626980i) q^{6} +(-3.94740 + 0.900969i) q^{7} +(0.588735 + 1.22252i) q^{8} +(-2.52446 + 1.21572i) q^{9} +O(q^{10})\)	\(q+(1.40881 - 1.12349i) q^{2} +(-0.433884 + 0.0990311i) q^{3} +(0.277479 - 1.21572i) q^{4} +(-0.500000 + 0.626980i) q^{6} +(-3.94740 + 0.900969i) q^{7} +(0.588735 + 1.22252i) q^{8} +(-2.52446 + 1.21572i) q^{9} +(-2.62349 - 1.26341i) q^{11} +0.554958i q^{12} +(-2.25011 + 4.67241i) q^{13} +(-4.54892 + 5.70416i) q^{14} +(4.44989 + 2.14295i) q^{16} +1.10992i q^{17} +(-2.19064 + 4.54892i) q^{18} +(0.455927 - 1.99755i) q^{19} +(1.62349 - 0.781831i) q^{21} +(-5.11543 + 1.16756i) q^{22} +(3.23449 + 2.57942i) q^{23} +(-0.376510 - 0.472129i) q^{24} +(2.07942 + 9.11052i) q^{26} +(2.01877 - 1.60992i) q^{27} +5.04892i q^{28} +(-4.38404 - 3.12733i) q^{29} +(-3.96346 - 4.97002i) q^{31} +(6.03089 - 1.37651i) q^{32} +(1.26341 + 0.288364i) q^{33} +(1.24698 + 1.56366i) q^{34} +(0.777479 + 3.40636i) q^{36} +(1.26341 + 2.62349i) q^{37} +(-1.60191 - 3.32640i) q^{38} +(0.513574 - 2.25011i) q^{39} +0.396125 q^{41} +(1.40881 - 2.92543i) q^{42} +(-4.48845 - 3.57942i) q^{43} +(-2.26391 + 2.83885i) q^{44} +7.45473 q^{46} +(-3.38513 + 7.02930i) q^{47} +(-2.14295 - 0.489115i) q^{48} +(8.46346 - 4.07579i) q^{49} +(-0.109916 - 0.481575i) q^{51} +(5.05596 + 4.03199i) q^{52} +(-3.40636 + 2.71648i) q^{53} +(1.03534 - 4.53614i) q^{54} +(-3.42543 - 4.29535i) q^{56} +0.911854i q^{57} +(-9.68981 + 0.519614i) q^{58} +9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(-11.1675 - 2.54892i) q^{62} +(8.86973 - 7.07338i) q^{63} +(0.791053 - 0.991949i) q^{64} +(2.10388 - 1.01317i) q^{66} +(-0.162426 - 0.337282i) q^{67} +(1.34934 + 0.307979i) q^{68} +(-1.65883 - 0.798852i) q^{69} +(10.2763 + 4.94880i) q^{71} +(-2.97247 - 2.37047i) q^{72} +(6.99637 + 5.57942i) q^{73} +(4.72737 + 2.27658i) q^{74} +(-2.30194 - 1.10855i) q^{76} +(11.4943 + 2.62349i) q^{77} +(-1.80445 - 3.74698i) q^{78} +(-0.535344 + 0.257808i) q^{79} +(4.52446 - 5.67349i) q^{81} +(0.558065 - 0.445042i) q^{82} +(-9.19646 - 2.09903i) q^{83} +(-0.500000 - 2.19064i) q^{84} -10.3448 q^{86} +(2.21187 + 0.922739i) q^{87} -3.95108i q^{88} +(-0.887395 - 1.11276i) q^{89} +(4.67241 - 20.4712i) q^{91} +(4.03334 - 3.21648i) q^{92} +(2.21187 + 1.76391i) q^{93} +(3.12833 + 13.7061i) q^{94} +(-2.48039 + 1.19449i) q^{96} +(-15.3557 - 3.50484i) q^{97} +(7.34432 - 15.2506i) q^{98} +8.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9	\( 12 q + 4 q^{4} - 6 q^{6} - 12 q^{9} - 22 q^{11} - 18 q^{14} + 8 q^{16} - 2 q^{19} + 10 q^{21} - 14 q^{24} + 8 q^{26} - 12 q^{29} + 10 q^{31} - 4 q^{34} + 10 q^{36} - 6 q^{39} + 40 q^{41} - 40 q^{44} + 44 q^{49} - 4 q^{51} - 12 q^{54} - 14 q^{56} + 112 q^{59} + 6 q^{61} - 2 q^{64} - 10 q^{66} + 14 q^{69} + 42 q^{71} + 12 q^{74} - 10 q^{76} + 18 q^{79} + 36 q^{81} - 6 q^{84} - 32 q^{86} - 14 q^{89} + 10 q^{91} - 16 q^{94} - 4 q^{96} + 64 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 - 6 * q^6 - 12 * q^9 - 22 * q^11 - 18 * q^14 + 8 * q^16 - 2 * q^19 + 10 * q^21 - 14 * q^24 + 8 * q^26 - 12 * q^29 + 10 * q^31 - 4 * q^34 + 10 * q^36 - 6 * q^39 + 40 * q^41 - 40 * q^44 + 44 * q^49 - 4 * q^51 - 12 * q^54 - 14 * q^56 + 112 * q^59 + 6 * q^61 - 2 * q^64 - 10 * q^66 + 14 * q^69 + 42 * q^71 + 12 * q^74 - 10 * q^76 + 18 * q^79 + 36 * q^81 - 6 * q^84 - 32 * q^86 - 14 * q^89 + 10 * q^91 - 16 * q^94 - 4 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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