LMFDB - Embedded newform 375.2.i.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Root			$-1.08982i$ of defining polynomial
Character	$\chi$	$=$	375.49
Dual form			375.2.i.c.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.640580 - 0.881682i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(-0.336773 + 1.03648i) q^{6} -3.08724i q^{7} +(2.91489 + 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.640580 - 0.881682i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(-0.336773 + 1.03648i) q^{6} -3.08724i q^{7} +(2.91489 + 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.929002 + 0.674959i) q^{11} +(-0.477454 - 0.657159i) q^{12} +(2.39789 + 3.30042i) q^{13} +(-2.72197 - 1.97763i) q^{14} +(1.38794 - 1.00840i) q^{16} +(4.40109 + 1.43000i) q^{17} -1.08982i q^{18} +(1.84452 - 5.67685i) q^{19} +(0.954011 + 2.93614i) q^{21} +(1.19020 - 0.386719i) q^{22} +(1.36700 - 1.88152i) q^{23} -3.06489 q^{24} +4.44596 q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.38501 - 0.774937i) q^{28} +(1.63290 + 5.02554i) q^{29} +(-0.182097 + 0.560438i) q^{31} +4.26010i q^{32} +(-1.09211 - 0.354847i) q^{33} +(4.08005 - 2.96433i) q^{34} +(0.657159 + 0.477454i) q^{36} +(-6.70056 - 9.22252i) q^{37} +(-3.82361 - 5.26275i) q^{38} +(-3.30042 - 2.39789i) q^{39} +(-7.67919 + 5.57926i) q^{41} +(3.19987 + 1.03970i) q^{42} -2.42954i q^{43} +(-0.288240 + 0.887112i) q^{44} +(-0.783227 - 2.41052i) q^{46} +(-5.75387 + 1.86955i) q^{47} +(-1.00840 + 1.38794i) q^{48} -2.53108 q^{49} -4.62758 q^{51} +(-1.94779 + 2.68091i) q^{52} +(-3.08503 + 1.00239i) q^{53} +(0.336773 + 1.03648i) q^{54} +(2.92394 - 8.99897i) q^{56} +5.96899i q^{57} +(5.47693 + 1.77956i) q^{58} +(2.57785 - 1.87292i) q^{59} +(-11.1201 - 8.07922i) q^{61} +(0.377480 + 0.519557i) q^{62} +(-1.81464 - 2.49763i) q^{63} +(6.53194 + 4.74573i) q^{64} +(-1.01244 + 0.735584i) q^{66} +(3.00414 + 0.976103i) q^{67} +3.75895i q^{68} +(-0.718676 + 2.21186i) q^{69} +(1.99795 + 6.14907i) q^{71} +(2.91489 - 0.947104i) q^{72} +(-4.23792 + 5.83300i) q^{73} -12.4236 q^{74} +4.84857 q^{76} +(2.08376 - 2.86806i) q^{77} +(-4.22836 + 1.37388i) q^{78} +(3.81246 + 11.7336i) q^{79} +(0.309017 - 0.951057i) q^{81} +10.3446i q^{82} +(-11.7875 - 3.82999i) q^{83} +(-2.02881 + 1.47402i) q^{84} +(-2.14208 - 1.55631i) q^{86} +(-3.10596 - 4.27498i) q^{87} +(2.06868 + 2.84729i) q^{88} +(0.877003 + 0.637180i) q^{89} +(10.1892 - 7.40289i) q^{91} +(1.79668 + 0.583776i) q^{92} -0.589279i q^{93} +(-2.03747 + 6.27068i) q^{94} +(-1.31644 - 4.05159i) q^{96} +(-4.30003 + 1.39717i) q^{97} +(-1.62136 + 2.23161i) q^{98} +1.14831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	0.640580	−	0.881682i	0.452958	−	0.623444i	−0.520072	−	0.854123i	$-0.674095\pi$
$2$	0.640580	−	0.881682i	0.452958	−	0.623444i	0.973030	+	0.230679i	$0.0740947\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.251013	+	0.772537i	0.125506	+	0.386269i
$5$		0			0
$5$		0			0
$6$	−0.336773	+	1.03648i	−0.137487	+	0.423141i
$7$		−	3.08724i		−	1.16687i	−0.812160	−	0.583434i	$-0.801709\pi$
$7$		−	3.08724i		−	1.16687i	0.812160	−	0.583434i	$-0.198291\pi$
$8$	2.91489	+	0.947104i	1.03057	+	0.334852i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	0.929002	+	0.674959i	0.280105	+	0.203508i	0.718963	−	0.695048i	$-0.244617\pi$
$11$	0.929002	+	0.674959i	0.280105	+	0.203508i	−0.438858	+	0.898556i	$0.644617\pi$
$12$	−0.477454	−	0.657159i	−0.137829	−	0.189706i
$13$	2.39789	+	3.30042i	0.665056	+	0.915372i	0.999636	−	0.0269961i	$-0.00859416\pi$
$13$	2.39789	+	3.30042i	0.665056	+	0.915372i	−0.334579	+	0.942368i	$0.608594\pi$
$14$	−2.72197	−	1.97763i	−0.727477	−	0.528543i
$15$		0			0
$16$	1.38794	−	1.00840i	0.346986	−	0.252100i
$17$	4.40109	+	1.43000i	1.06742	+	0.346826i	0.789482	−	0.613773i	$-0.210349\pi$
$17$	4.40109	+	1.43000i	1.06742	+	0.346826i	0.277938	+	0.960599i	$0.410349\pi$
$18$		−	1.08982i		−	0.256873i
$19$	1.84452	−	5.67685i	0.423162	−	1.30236i	−0.481582	−	0.876401i	$-0.659938\pi$
$19$	1.84452	−	5.67685i	0.423162	−	1.30236i	0.904744	−	0.425957i	$-0.140062\pi$
$20$		0			0
$21$	0.954011	+	2.93614i	0.208182	+	0.640719i
$22$	1.19020	−	0.386719i	0.253751	−	0.0824488i
$23$	1.36700	−	1.88152i	0.285040	−	0.392324i	−0.642355	−	0.766407i	$-0.722043\pi$
$23$	1.36700	−	1.88152i	0.285040	−	0.392324i	0.927395	+	0.374083i	$0.122043\pi$
$24$	−3.06489			−0.625619
$25$		0			0
$26$	4.44596			0.871925
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.38501	−	0.774937i	0.450725	−	0.146449i
$29$	1.63290	+	5.02554i	0.303221	+	0.933220i	0.980335	+	0.197341i	$0.0632306\pi$
$29$	1.63290	+	5.02554i	0.303221	+	0.933220i	−0.677113	+	0.735879i	$0.736769\pi$
$30$		0			0
$31$	−0.182097	+	0.560438i	−0.0327056	+	0.100658i	−0.966077	−	0.258255i	$-0.916852\pi$
$31$	−0.182097	+	0.560438i	−0.0327056	+	0.100658i	0.933371	+	0.358913i	$0.116852\pi$
$32$			4.26010i			0.753086i
$33$	−1.09211	−	0.354847i	−0.190111	−	0.0617709i
$34$	4.08005	−	2.96433i	0.699723	−	0.508379i
$35$		0			0
$36$	0.657159	+	0.477454i	0.109527	+	0.0795757i
$37$	−6.70056	−	9.22252i	−1.10156	−	1.51617i	−0.833294	−	0.552830i	$-0.813548\pi$
$37$	−6.70056	−	9.22252i	−1.10156	−	1.51617i	−0.268271	−	0.963344i	$-0.586452\pi$
$38$	−3.82361	−	5.26275i	−0.620272	−	0.853731i
$39$	−3.30042	−	2.39789i	−0.528490	−	0.383970i
$40$		0			0
$41$	−7.67919	+	5.57926i	−1.19929	+	0.871334i	−0.994215	−	0.107413i	$-0.965743\pi$
$41$	−7.67919	+	5.57926i	−1.19929	+	0.871334i	−0.205073	+	0.978747i	$0.565743\pi$
$42$	3.19987	+	1.03970i	0.493750	+	0.160429i
$43$		−	2.42954i		−	0.370501i	−0.982691	−	0.185250i	$-0.940690\pi$
$43$		−	2.42954i		−	0.370501i	0.982691	−	0.185250i	$-0.0593096\pi$
$44$	−0.288240	+	0.887112i	−0.0434538	+	0.133737i
$45$		0			0
$46$	−0.783227	−	2.41052i	−0.115481	−	0.355412i
$47$	−5.75387	+	1.86955i	−0.839289	+	0.272701i	−0.696953	−	0.717117i	$-0.745461\pi$
$47$	−5.75387	+	1.86955i	−0.839289	+	0.272701i	−0.142336	+	0.989818i	$0.545461\pi$
$48$	−1.00840	+	1.38794i	−0.145550	+	0.200332i
$49$	−2.53108			−0.361583
$50$		0			0
$51$	−4.62758			−0.647990
$52$	−1.94779	+	2.68091i	−0.270111	+	0.371775i
$53$	−3.08503	+	1.00239i	−0.423762	+	0.137689i	−0.513132	−	0.858310i	$-0.671515\pi$
$53$	−3.08503	+	1.00239i	−0.423762	+	0.137689i	0.0893696	+	0.995999i	$0.471515\pi$
$54$	0.336773	+	1.03648i	0.0458290	+	0.141047i
$55$		0			0
$56$	2.92394	−	8.99897i	0.390728	−	1.20254i
$57$			5.96899i			0.790612i
$58$	5.47693	+	1.77956i	0.719157	+	0.233668i
$59$	2.57785	−	1.87292i	0.335607	−	0.243833i	−0.407199	−	0.913340i	$-0.633494\pi$
$59$	2.57785	−	1.87292i	0.335607	−	0.243833i	0.742806	+	0.669507i	$0.233494\pi$
$60$		0			0
$61$	−11.1201	−	8.07922i	−1.42378	−	1.03444i	−0.991133	−	0.132876i	$-0.957579\pi$
$61$	−11.1201	−	8.07922i	−1.42378	−	1.03444i	−0.432650	−	0.901562i	$-0.642421\pi$
$62$	0.377480	+	0.519557i	0.0479400	+	0.0659838i
$63$	−1.81464	−	2.49763i	−0.228623	−	0.314672i
$64$	6.53194	+	4.74573i	0.816493	+	0.593217i
$65$		0			0
$66$	−1.01244	+	0.735584i	−0.124623	+	0.0905441i
$67$	3.00414	+	0.976103i	0.367014	+	0.119250i	0.486717	−	0.873560i	$-0.338194\pi$
$67$	3.00414	+	0.976103i	0.367014	+	0.119250i	−0.119703	+	0.992810i	$0.538194\pi$
$68$			3.75895i			0.455840i
$69$	−0.718676	+	2.21186i	−0.0865184	+	0.266276i
$70$		0			0
$71$	1.99795	+	6.14907i	0.237113	+	0.729760i	0.996834	+	0.0795103i	$0.0253357\pi$
$71$	1.99795	+	6.14907i	0.237113	+	0.729760i	−0.759721	+	0.650250i	$0.774664\pi$
$72$	2.91489	−	0.947104i	0.343523	−	0.111617i
$73$	−4.23792	+	5.83300i	−0.496011	+	0.682701i	−0.981482	−	0.191552i	$-0.938648\pi$
$73$	−4.23792	+	5.83300i	−0.496011	+	0.682701i	0.485472	+	0.874252i	$0.338648\pi$
$74$	−12.4236			−1.44421
$75$		0			0
$76$	4.84857			0.556169
$77$	2.08376	−	2.86806i	0.237467	−	0.326845i
$78$	−4.22836	+	1.37388i	−0.478768	+	0.155561i
$79$	3.81246	+	11.7336i	0.428936	+	1.32013i	0.899175	+	0.437590i	$0.144168\pi$
$79$	3.81246	+	11.7336i	0.428936	+	1.32013i	−0.470239	+	0.882539i	$0.655832\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$			10.3446i			1.14237i
$83$	−11.7875	−	3.82999i	−1.29384	−	0.420396i	−0.420409	−	0.907335i	$-0.638113\pi$
$83$	−11.7875	−	3.82999i	−1.29384	−	0.420396i	−0.873436	+	0.486939i	$0.838113\pi$
$84$	−2.02881	+	1.47402i	−0.221361	+	0.160829i
$85$		0			0
$86$	−2.14208	−	1.55631i	−0.230986	−	0.167821i
$87$	−3.10596	−	4.27498i	−0.332993	−	0.458326i
$88$	2.06868	+	2.84729i	0.220522	+	0.303522i
$89$	0.877003	+	0.637180i	0.0929621	+	0.0675409i	0.633295	−	0.773910i	$-0.281702\pi$
$89$	0.877003	+	0.637180i	0.0929621	+	0.0675409i	−0.540333	+	0.841451i	$0.681702\pi$
$90$		0			0
$91$	10.1892	−	7.40289i	1.06812	−	0.776034i
$92$	1.79668	+	0.583776i	0.187317	+	0.0608628i
$93$		−	0.589279i		−	0.0611054i
$94$	−2.03747	+	6.27068i	−0.210149	+	0.646772i
$95$		0			0
$96$	−1.31644	−	4.05159i	−0.134359	−	0.413514i
$97$	−4.30003	+	1.39717i	−0.436602	+	0.141861i	−0.519067	−	0.854733i	$-0.673721\pi$
$97$	−4.30003	+	1.39717i	−0.436602	+	0.141861i	0.0824653	+	0.996594i	$0.473721\pi$
$98$	−1.62136	+	2.23161i	−0.163782	+	0.225426i
$99$	1.14831			0.115409
$100$		0			0
$101$	−6.61332			−0.658050			−0.329025	−	0.944321i	$-0.606720\pi$
$101$	−6.61332			−0.658050			−0.329025	+	0.944321i	$0.606720\pi$
$102$	−2.96433	+	4.08005i	−0.293513	+	0.403985i
$103$	4.00047	−	1.29983i	0.394178	−	0.128076i	−0.105220	−	0.994449i	$-0.533555\pi$
$103$	4.00047	−	1.29983i	0.394178	−	0.128076i	0.499398	+	0.866373i	$0.333555\pi$
$104$	3.86375	+	11.8914i	0.378872	+	1.16605i
$105$		0			0
$106$	−1.09242	+	3.36213i	−0.106105	+	0.326559i
$107$		−	4.01195i		−	0.387849i	−0.981016	−	0.193925i	$-0.937878\pi$
$107$		−	4.01195i		−	0.387849i	0.981016	−	0.193925i	$-0.0621218\pi$
$108$	−0.772537	−	0.251013i	−0.0743374	−	0.0241537i
$109$	7.35691	−	5.34511i	0.704664	−	0.511969i	−0.176784	−	0.984250i	$-0.556569\pi$
$109$	7.35691	−	5.34511i	0.704664	−	0.511969i	0.881448	+	0.472281i	$0.156569\pi$
$110$		0			0
$111$	9.22252	+	6.70056i	0.875363	+	0.635989i
$112$	−3.11318	−	4.28492i	−0.294168	−	0.404887i
$113$	2.20693	+	3.03758i	0.207610	+	0.285751i	0.900106	−	0.435671i	$-0.143489\pi$
$113$	2.20693	+	3.03758i	0.207610	+	0.285751i	−0.692496	+	0.721422i	$0.743489\pi$
$114$	5.26275	+	3.82361i	0.492902	+	0.358114i
$115$		0			0
$116$	−3.47254	+	2.52295i	−0.322417	+	0.234250i
$117$	3.87988	+	1.26065i	0.358695	+	0.116547i
$118$		−	3.47260i		−	0.319678i
$119$	4.41476	−	13.5872i	0.404700	−	1.24554i
$120$		0			0
$121$	−2.99171	−	9.20755i	−0.271974	−	0.837050i
$122$	−14.2466	+	4.62901i	−1.28983	+	0.419091i
$123$	5.57926	−	7.67919i	0.503065	−	0.692409i
$124$	−0.478668			−0.0429856
$125$		0			0
$126$	−3.36454			−0.299737
$127$	6.67623	−	9.18904i	0.592419	−	0.815395i	−0.402569	−	0.915390i	$-0.631883\pi$
$127$	6.67623	−	9.18904i	0.592419	−	0.815395i	0.994988	+	0.0999946i	$0.0318826\pi$
$128$	0.265268	−	0.0861909i	0.0234466	−	0.00761827i
$129$	0.750768	+	2.31063i	0.0661014	+	0.203439i
$130$		0			0
$131$	−0.642289	+	1.97676i	−0.0561170	+	0.172711i	−0.975186	−	0.221385i	$-0.928942\pi$
$131$	−0.642289	+	1.97676i	−0.0561170	+	0.172711i	0.919069	+	0.394096i	$0.128942\pi$
$132$		−	0.932764i		−	0.0811867i
$133$	−17.5258	−	5.69448i	−1.51968	−	0.493774i
$134$	2.78500	−	2.02342i	0.240587	−	0.174797i
$135$		0			0
$136$	11.4743	+	8.33657i	0.983914	+	0.714855i
$137$	11.4049	+	15.6975i	0.974387	+	1.34113i	0.939800	+	0.341726i	$0.111012\pi$
$137$	11.4049	+	15.6975i	0.974387	+	1.34113i	0.0345870	+	0.999402i	$0.488988\pi$
$138$	1.48979	+	2.05051i	0.126819	+	0.174551i
$139$	−13.8830	−	10.0866i	−1.17754	−	0.855531i	−0.185646	−	0.982617i	$-0.559438\pi$
$139$	−13.8830	−	10.0866i	−1.17754	−	0.855531i	−0.991892	+	0.127086i	$0.959438\pi$
$140$		0			0
$141$	4.89454	−	3.55609i	0.412194	−	0.299477i
$142$	6.70137	+	2.17741i	0.562367	+	0.182724i
$143$			4.68458i			0.391744i
$144$	0.530147	−	1.63162i	0.0441789	−	0.135969i
$145$		0			0
$146$	2.42812	+	7.47300i	0.200953	+	0.618470i
$147$	2.40720	−	0.782147i	0.198542	−	0.0645104i
$148$	5.44282	−	7.49140i	0.447397	−	0.615789i
$149$	−0.210127			−0.0172143			−0.00860714	−	0.999963i	$-0.502740\pi$
$149$	−0.210127			−0.0172143			−0.00860714	+	0.999963i	$0.502740\pi$
$150$		0			0
$151$	−4.05924			−0.330336			−0.165168	−	0.986265i	$-0.552817\pi$
$151$	−4.05924			−0.330336			−0.165168	+	0.986265i	$0.552817\pi$
$152$	10.7531	−	14.8004i	0.872194	−	1.20047i
$153$	4.40109	−	1.43000i	0.355807	−	0.115609i
$154$	−1.19390	−	3.67444i	−0.0962070	−	0.296095i
$155$		0			0
$156$	1.02402	−	3.15160i	0.0819869	−	0.252330i
$157$			0.440336i			0.0351426i	0.999846	+	0.0175713i	$0.00559341\pi$
$157$			0.440336i			0.0351426i	−0.999846	+	0.0175713i	$0.994407\pi$
$158$	12.7875	+	4.15490i	1.01732	+	0.330546i
$159$	2.62429	−	1.90666i	0.208119	−	0.151208i
$160$		0			0
$161$	−5.80871	−	4.22027i	−0.457790	−	0.332604i
$162$	−0.640580	−	0.881682i	−0.0503287	−	0.0692715i
$163$	1.90506	+	2.62210i	0.149216	+	0.205378i	0.877081	−	0.480342i	$-0.159487\pi$
$163$	1.90506	+	2.62210i	0.149216	+	0.205378i	−0.727865	+	0.685720i	$0.759487\pi$
$164$	−6.23776	−	4.53200i	−0.487087	−	0.353889i
$165$		0			0
$166$	−10.9277	+	7.93941i	−0.848151	+	0.616218i
$167$	−15.1793	−	4.93207i	−1.17461	−	0.381655i	−0.344250	−	0.938878i	$-0.611867\pi$
$167$	−15.1793	−	4.93207i	−1.17461	−	0.381655i	−0.830363	+	0.557223i	$0.811867\pi$
$168$			9.46207i			0.730015i
$169$	−1.12565	+	3.46438i	−0.0865882	+	0.266491i
$170$		0			0
$171$	−1.84452	−	5.67685i	−0.141054	−	0.434119i
$172$	1.87691	−	0.609844i	0.143113	−	0.0465002i
$173$	−0.330212	+	0.454497i	−0.0251055	+	0.0345548i	−0.821385	−	0.570374i	$-0.806798\pi$
$173$	−0.330212	+	0.454497i	−0.0251055	+	0.0345548i	0.796280	+	0.604929i	$0.206798\pi$
$174$	−5.75879			−0.436573
$175$		0			0
$176$	1.97003			0.148497
$177$	−1.87292	+	2.57785i	−0.140777	+	0.193763i
$178$	1.12358	−	0.365073i	0.0842159	−	0.0273634i
$179$	−4.92532	−	15.1586i	−0.368136	−	1.13301i	−0.947994	−	0.318288i	$-0.896892\pi$
$179$	−4.92532	−	15.1586i	−0.368136	−	1.13301i	0.579858	−	0.814718i	$-0.303108\pi$
$180$		0			0
$181$	−6.64001	+	20.4358i	−0.493548	+	1.51898i	0.325660	+	0.945487i	$0.394414\pi$
$181$	−6.64001	+	20.4358i	−0.493548	+	1.51898i	−0.819208	+	0.573497i	$0.805586\pi$
$182$		−	13.7258i		−	1.01742i
$183$	13.0725	+	4.24750i	0.966344	+	0.313984i
$184$	5.76665	−	4.18972i	0.425123	−	0.308870i
$185$		0			0
$186$	−0.519557	−	0.377480i	−0.0380958	−	0.0276782i
$187$	3.12343	+	4.29903i	0.228408	+	0.314376i
$188$	−2.88859	−	3.97580i	−0.210672	−	0.289965i
$189$	2.49763	+	1.81464i	0.181676	+	0.131995i
$190$		0			0
$191$	14.8810	−	10.8117i	1.07675	−	0.782304i	0.0996355	−	0.995024i	$-0.468232\pi$
$191$	14.8810	−	10.8117i	1.07675	−	0.782304i	0.977113	+	0.212720i	$0.0682323\pi$
$192$	−7.67876	−	2.49498i	−0.554167	−	0.180060i
$193$			2.02523i			0.145780i	0.997340	+	0.0728898i	$0.0232221\pi$
$193$			2.02523i			0.145780i	−0.997340	+	0.0728898i	$0.976778\pi$
$194$	−1.52266	+	4.68626i	−0.109320	+	0.336454i
$195$		0			0
$196$	−0.635333	−	1.95535i	−0.0453809	−	0.139668i
$197$	−10.9804	+	3.56774i	−0.782319	+	0.254191i	−0.672830	−	0.739797i	$-0.734921\pi$
$197$	−10.9804	+	3.56774i	−0.782319	+	0.254191i	−0.109489	+	0.993988i	$0.534921\pi$
$198$	0.735584	−	1.01244i	0.0522757	−	0.0719513i
$199$	−22.9779			−1.62886			−0.814431	−	0.580260i	$-0.802951\pi$
$199$	−22.9779			−1.62886			−0.814431	+	0.580260i	$0.802951\pi$
$200$		0			0
$201$	−3.15873			−0.222800
$202$	−4.23636	+	5.83085i	−0.298069	+	0.410257i
$203$	15.5151	−	5.04115i	1.08894	−	0.353820i
$204$	−1.16158	−	3.57497i	−0.0813268	−	0.250298i
$205$		0			0
$206$	1.41658	−	4.35979i	0.0986978	−	0.303761i
$207$		−	2.32568i		−	0.161646i
$208$	6.65628	+	2.16276i	0.461530	+	0.149960i
$209$	5.54520	−	4.02882i	0.383570	−	0.278680i
$210$		0			0
$211$	5.56717	+	4.04479i	0.383260	+	0.278455i	0.762688	−	0.646767i	$-0.223879\pi$
$211$	5.56717	+	4.04479i	0.383260	+	0.278455i	−0.379428	+	0.925221i	$0.623879\pi$
$212$	−1.54876	−	2.13169i	−0.106370	−	0.146405i
$213$	−3.80033	−	5.23071i	−0.260394	−	0.358402i
$214$	−3.53726	−	2.56997i	−0.241802	−	0.175680i
$215$		0			0
$216$	−2.47955	+	1.80150i	−0.168712	+	0.122576i
$217$	1.73021	+	0.562179i	0.117454	+	0.0381632i
$218$		−	9.91043i		−	0.671219i
$219$	2.22801	−	6.85710i	0.150555	−	0.463360i
$220$		0			0
$221$	5.83375	+	17.9544i	0.392420	+	1.20775i
$222$	11.8155	−	3.83910i	0.793006	−	0.257663i
$223$	−4.77652	+	6.57432i	−0.319860	+	0.440249i	−0.938424	−	0.345485i	$-0.887714\pi$
$223$	−4.77652	+	6.57432i	−0.319860	+	0.440249i	0.618565	+	0.785734i	$0.287714\pi$
$224$	13.1520			0.878753
$225$		0			0
$226$	4.09189			0.272188
$227$	15.0649	−	20.7351i	0.999895	−	1.37624i	0.0745050	−	0.997221i	$-0.476262\pi$
$227$	15.0649	−	20.7351i	0.999895	−	1.37624i	0.925390	−	0.379017i	$-0.123738\pi$
$228$	−4.61127	+	1.49829i	−0.305389	+	0.0992268i
$229$	−0.381062	−	1.17279i	−0.0251813	−	0.0775001i	0.937676	−	0.347510i	$-0.112973\pi$
$229$	−0.381062	−	1.17279i	−0.0251813	−	0.0775001i	−0.962857	+	0.270010i	$0.912973\pi$
$230$		0			0
$231$	−1.09550	+	3.37160i	−0.0720786	+	0.221835i
$232$			16.1954i			1.06328i
$233$	2.85305	+	0.927012i	0.186909	+	0.0607306i	0.400976	−	0.916088i	$-0.368671\pi$
$233$	2.85305	+	0.927012i	0.186909	+	0.0607306i	−0.214067	+	0.976819i	$0.568671\pi$
$234$	3.59686	−	2.61327i	0.235134	−	0.170835i
$235$		0			0
$236$	2.09397	+	1.52136i	0.136306	+	0.0990320i
$237$	−7.25174	−	9.98116i	−0.471051	−	0.648346i
$238$	−9.15162	−	12.5961i	−0.593211	−	0.816485i
$239$	17.9069	+	13.0101i	1.15830	+	0.841554i	0.989562	−	0.144107i	$-0.0460309\pi$
$239$	17.9069	+	13.0101i	1.15830	+	0.841554i	0.168738	+	0.985661i	$0.446031\pi$
$240$		0			0
$241$	10.8734	−	7.89999i	0.700418	−	0.508883i	−0.179651	−	0.983730i	$-0.557497\pi$
$241$	10.8734	−	7.89999i	0.700418	−	0.508883i	0.880068	+	0.474847i	$0.157497\pi$
$242$	−10.0346	−	3.26043i	−0.645046	−	0.209588i
$243$			1.00000i			0.0641500i
$244$	3.45022	−	10.6187i	0.220877	−	0.679791i
$245$		0			0
$246$	−3.19665	−	9.83827i	−0.203811	−	0.627265i
$247$	23.1589	−	7.52479i	1.47357	−	0.478791i
$248$	−1.06159	+	1.46115i	−0.0674107	+	0.0927829i
$249$	12.3941			0.785444
$250$		0			0
$251$	18.8799			1.19169			0.595843	−	0.803101i	$-0.296818\pi$
$251$	18.8799			1.19169			0.595843	+	0.803101i	$0.296818\pi$
$252$	1.47402	−	2.02881i	0.0928544	−	0.127803i
$253$	2.53990	−	0.825262i	0.159682	−	0.0518838i
$254$	−3.82516	−	11.7726i	−0.240012	−	0.738680i
$255$		0			0
$256$	−4.89603	+	15.0684i	−0.306002	+	0.941776i
$257$			7.06320i			0.440590i	0.975433	+	0.220295i	$0.0707020\pi$
$257$			7.06320i			0.440590i	−0.975433	+	0.220295i	$0.929298\pi$
$258$	2.51816	+	0.818201i	0.156774	+	0.0509390i
$259$	−28.4722	+	20.6863i	−1.76918	+	1.28538i
$260$		0			0
$261$	4.27498	+	3.10596i	0.264615	+	0.192254i
$262$	1.33144	+	1.83257i	0.0822566	+	0.113216i
$263$	12.0118	+	16.5328i	0.740677	+	1.01945i	0.998579	+	0.0532829i	$0.0169685\pi$
$263$	12.0118	+	16.5328i	0.740677	+	1.01945i	−0.257903	+	0.966171i	$0.583031\pi$
$264$	−2.84729	−	2.06868i	−0.175239	−	0.127318i
$265$		0			0
$266$	−16.2474	+	11.8044i	−0.996192	+	0.723776i
$267$	−1.03098	−	0.334985i	−0.0630949	−	0.0205008i
$268$			2.56582i			0.156732i
$269$	−6.54880	+	20.1551i	−0.399287	+	1.22888i	0.526285	+	0.850308i	$0.323584\pi$
$269$	−6.54880	+	20.1551i	−0.399287	+	1.22888i	−0.925572	+	0.378571i	$0.876416\pi$
$270$		0			0
$271$	3.07570	+	9.46603i	0.186835	+	0.575020i	0.999975	−	0.00704817i	$-0.00224352\pi$
$271$	3.07570	+	9.46603i	0.186835	+	0.575020i	−0.813140	+	0.582069i	$0.802244\pi$
$272$	7.55047	−	2.45330i	0.457814	−	0.148753i
$273$	−7.40289	+	10.1892i	−0.448043	+	0.616679i
$274$	21.1460			1.27747
$275$		0			0
$276$	−1.88914			−0.113713
$277$	−11.0121	+	15.1569i	−0.661654	+	0.910689i	−0.999535	−	0.0304998i	$-0.990290\pi$
$277$	−11.0121	+	15.1569i	−0.661654	+	0.910689i	0.337880	+	0.941189i	$0.390290\pi$
$278$	−17.7863	+	5.77912i	−1.06675	+	0.346608i
$279$	0.182097	+	0.560438i	0.0109019	+	0.0335525i
$280$		0			0
$281$	8.98981	−	27.6678i	0.536287	−	1.65052i	−0.204565	−	0.978853i	$-0.565578\pi$
$281$	8.98981	−	27.6678i	0.536287	−	1.65052i	0.740852	−	0.671668i	$-0.234422\pi$
$282$		−	6.59339i		−	0.392630i
$283$	−6.82865	−	2.21876i	−0.405921	−	0.131892i	0.0989379	−	0.995094i	$-0.468455\pi$
$283$	−6.82865	−	2.21876i	−0.405921	−	0.131892i	−0.504859	+	0.863202i	$0.668455\pi$
$284$	−4.24887	+	3.08699i	−0.252124	+	0.183179i
$285$		0			0
$286$	4.13031	+	3.00084i	0.244230	+	0.177444i
$287$	17.2245	+	23.7075i	1.01673	+	1.39941i
$288$	2.50402	+	3.44649i	0.147551	+	0.203087i
$289$	3.57138	+	2.59476i	0.210081	+	0.152633i
$290$		0			0
$291$	3.65783	−	2.65757i	0.214426	−	0.155789i
$292$	−5.56998	−	1.80980i	−0.325958	−	0.105910i
$293$			1.79825i			0.105055i	0.998619	+	0.0525276i	$0.0167277\pi$
$293$			1.79825i			0.105055i	−0.998619	+	0.0525276i	$0.983272\pi$
$294$	0.852398	−	2.62341i	0.0497129	−	0.153001i
$295$		0			0
$296$	−10.7967	−	33.2287i	−0.627544	−	1.93138i
$297$	−1.09211	+	0.354847i	−0.0633705	+	0.0205903i
$298$	−0.134603	+	0.185265i	−0.00779735	+	0.0107321i
$299$	9.48773			0.548689
$300$		0			0
$301$	−7.50057			−0.432326
$302$	−2.60027	+	3.57896i	−0.149629	+	0.205946i
$303$	6.28965	−	2.04363i	0.361331	−	0.117403i
$304$	−3.16444	−	9.73915i	−0.181493	−	0.558579i
$305$		0			0
$306$	1.55844	−	4.79639i	0.0890902	−	0.274191i
$307$		−	5.98864i		−	0.341790i	−0.985289	−	0.170895i	$-0.945334\pi$
$307$		−	5.98864i		−	0.341790i	0.985289	−	0.170895i	$-0.0546659\pi$
$308$	2.73873	+	0.889867i	0.156054	+	0.0507049i
$309$	−3.40300	+	2.47242i	−0.193590	+	0.140651i
$310$		0			0
$311$	−19.3099	−	14.0295i	−1.09497	−	0.795539i	−0.114735	−	0.993396i	$-0.536602\pi$
$311$	−19.3099	−	14.0295i	−1.09497	−	0.795539i	−0.980231	+	0.197857i	$0.936602\pi$
$312$	−7.34929	−	10.1154i	−0.416072	−	0.572673i
$313$	−3.38513	−	4.65924i	−0.191339	−	0.263356i	0.702559	−	0.711625i	$-0.252041\pi$
$313$	−3.38513	−	4.65924i	−0.191339	−	0.263356i	−0.893898	+	0.448269i	$0.852041\pi$
$314$	0.388236	+	0.282070i	0.0219094	+	0.0159181i
$315$		0			0
$316$	−8.10763	+	5.89054i	−0.456090	+	0.331369i
$317$	11.6486	+	3.78487i	0.654253	+	0.212580i	0.617288	−	0.786737i	$-0.288231\pi$
$317$	11.6486	+	3.78487i	0.654253	+	0.212580i	0.0369645	+	0.999317i	$0.488231\pi$
$318$		−	3.53515i		−	0.198242i
$319$	−1.87507	+	5.77088i	−0.104984	+	0.323107i
$320$		0			0
$321$	1.23976	+	3.81559i	0.0691966	+	0.212965i
$322$	−7.44188	+	2.41801i	−0.414720	+	0.134751i
$323$	16.2358	−	22.3466i	0.903383	−	1.24340i
$324$	0.812294			0.0451274
$325$		0			0
$326$	3.53220			0.195631
$327$	−5.34511	+	7.35691i	−0.295585	+	0.406838i
$328$	−27.6681	+	8.98991i	−1.52772	+	0.496385i
$329$	5.77175	+	17.7636i	0.318207	+	0.979340i
$330$		0			0
$331$	−1.86306	+	5.73391i	−0.102403	+	0.315164i	−0.989112	−	0.147163i	$-0.952986\pi$
$331$	−1.86306	+	5.73391i	−0.102403	+	0.315164i	0.886709	+	0.462328i	$0.152986\pi$
$332$		−	10.0676i		−	0.552534i
$333$	−10.8417	−	3.52269i	−0.594123	−	0.193042i
$334$	−14.0721	+	10.2240i	−0.769991	+	0.559431i
$335$		0			0
$336$	4.28492	+	3.11318i	0.233762	+	0.169838i
$337$	3.25094	+	4.47454i	0.177090	+	0.243744i	0.888330	−	0.459206i	$-0.151866\pi$
$337$	3.25094	+	4.47454i	0.177090	+	0.243744i	−0.711240	+	0.702949i	$0.751866\pi$
$338$	2.33342	+	3.21168i	0.126921	+	0.174692i
$339$	−3.03758	−	2.20693i	−0.164978	−	0.119864i
$340$		0			0
$341$	−0.547441	+	0.397739i	−0.0296456	+	0.0215388i
$342$	−6.18674	−	2.01019i	−0.334540	−	0.108699i
$343$		−	13.7967i		−	0.744949i
$344$	2.30102	−	7.08182i	0.124063	−	0.381826i
$345$		0			0
$346$	0.189195	+	0.582283i	0.0101712	+	0.0313038i
$347$	−24.6747	+	8.01729i	−1.32461	+	0.430391i	−0.884075	−	0.467346i	$-0.845210\pi$
$347$	−24.6747	+	8.01729i	−1.32461	+	0.430391i	−0.440532	+	0.897737i	$0.645210\pi$
$348$	2.52295	−	3.47254i	0.135244	−	0.186148i
$349$	19.0025			1.01718			0.508591	−	0.861008i	$-0.330167\pi$
$349$	19.0025			1.01718			0.508591	+	0.861008i	$0.330167\pi$
$350$		0			0
$351$	−4.07954			−0.217750
$352$	−2.87539	+	3.95764i	−0.153259	+	0.210943i
$353$	−7.79043	+	2.53126i	−0.414642	+	0.134726i	−0.508907	−	0.860822i	$-0.669950\pi$
$353$	−7.79043	+	2.53126i	−0.414642	+	0.134726i	0.0942642	+	0.995547i	$0.469950\pi$
$354$	1.07309	+	3.30263i	0.0570341	+	0.175533i
$355$		0			0
$356$	−0.272106	+	0.837457i	−0.0144216	+	0.0443852i
$357$			14.2865i			0.756120i
$358$	−16.5201	−	5.36771i	−0.873116	−	0.283692i
$359$	−21.6701	+	15.7442i	−1.14370	+	0.830948i	−0.987631	−	0.156797i	$-0.949883\pi$
$359$	−21.6701	+	15.7442i	−1.14370	+	0.830948i	−0.156071	+	0.987746i	$0.549883\pi$
$360$		0			0
$361$	−13.4530	−	9.77419i	−0.708053	−	0.514431i
$362$	13.7645	+	18.9452i	0.723444	+	0.995736i
$363$	5.69058	+	7.83241i	0.298678	+	0.411095i
$364$	8.27662	+	6.01332i	0.433813	+	0.315184i
$365$		0			0
$366$	12.1189	−	8.80489i	0.633465	−	0.460239i
$367$	−17.9306	−	5.82600i	−0.935968	−	0.304114i	−0.198967	−	0.980006i	$-0.563759\pi$
$367$	−17.9306	−	5.82600i	−0.935968	−	0.304114i	−0.737001	+	0.675892i	$0.763759\pi$
$368$		−	3.98992i		−	0.207989i
$369$	−2.93319	+	9.02743i	−0.152696	+	0.469949i
$370$		0			0
$371$	3.09462	+	9.52426i	0.160665	+	0.494475i
$372$	0.455240	−	0.147916i	0.0236031	−	0.00766911i
$373$	−10.4906	+	14.4391i	−0.543183	+	0.747627i	−0.989067	−	0.147464i	$-0.952889\pi$
$373$	−10.4906	+	14.4391i	−0.543183	+	0.747627i	0.445885	+	0.895090i	$0.352889\pi$
$374$	5.79118			0.299455
$375$		0			0
$376$	−18.5425			−0.956259
$377$	−12.6709	+	17.4400i	−0.652583	+	0.898204i
$378$	3.19987	−	1.03970i	0.164583	−	0.0534764i
$379$	−3.88290	−	11.9503i	−0.199451	−	0.613848i	−0.999896	−	0.0144408i	$-0.995403\pi$
$379$	−3.88290	−	11.9503i	−0.199451	−	0.613848i	0.800445	−	0.599407i	$-0.204597\pi$
$380$		0			0
$381$	−3.50990	+	10.8024i	−0.179818	+	0.553422i
$382$		−	20.0460i		−	1.02564i
$383$	7.16849	+	2.32918i	0.366292	+	0.119016i	0.486379	−	0.873748i	$-0.338317\pi$
$383$	7.16849	+	2.32918i	0.366292	+	0.119016i	−0.120087	+	0.992763i	$0.538317\pi$
$384$	−0.225651	+	0.163945i	−0.0115152	+	0.00836628i
$385$		0			0
$386$	1.78561	+	1.29732i	0.0908854	+	0.0660321i
$387$	−1.42805	−	1.96554i	−0.0725916	−	0.0999138i
$388$	−2.15872	−	2.97123i	−0.109593	−	0.150841i
$389$	−11.1103	−	8.07211i	−0.563315	−	0.409272i	0.269356	−	0.963041i	$-0.413189\pi$
$389$	−11.1103	−	8.07211i	−0.563315	−	0.409272i	−0.832671	+	0.553768i	$0.813189\pi$
$390$		0			0
$391$	8.70687	−	6.32591i	0.440325	−	0.319915i
$392$	−7.37781	−	2.39719i	−0.372636	−	0.121077i
$393$		−	2.07849i		−	0.104846i
$394$	−3.88819	+	11.9666i	−0.195884	+	0.602869i
$395$		0			0
$396$	0.288240	+	0.887112i	0.0144846	+	0.0445790i
$397$	12.3658	−	4.01790i	0.620623	−	0.201653i	0.0182061	−	0.999834i	$-0.494204\pi$
$397$	12.3658	−	4.01790i	0.620623	−	0.201653i	0.602417	+	0.798182i	$0.294204\pi$
$398$	−14.7192	+	20.2592i	−0.737807	+	1.01550i
$399$	18.4277			0.922540
$400$		0			0
$401$	−6.47047			−0.323120			−0.161560	−	0.986863i	$-0.551653\pi$
$401$	−6.47047			−0.323120			−0.161560	+	0.986863i	$0.551653\pi$
$402$	−2.02342	+	2.78500i	−0.100919	+	0.138903i
$403$	−2.28633	+	0.742874i	−0.113890	+	0.0370052i
$404$	−1.66003	−	5.10904i	−0.0825894	−	0.254184i
$405$		0			0
$406$	5.49395	−	16.9086i	0.272660	−	0.839161i
$407$		−	13.0903i		−	0.648864i
$408$	−13.4889	−	4.38280i	−0.667798	−	0.216981i
$409$	−0.899629	+	0.653619i	−0.0444838	+	0.0323194i	−0.609805	−	0.792552i	$-0.708752\pi$
$409$	−0.899629	+	0.653619i	−0.0444838	+	0.0323194i	0.565321	+	0.824871i	$0.308752\pi$
$410$		0			0
$411$	−15.6975	−	11.4049i	−0.774301	−	0.562562i
$412$	2.00833	+	2.76424i	0.0989435	+	0.136184i
$413$	−5.78215	−	7.95845i	−0.284521	−	0.391610i
$414$	−2.05051	−	1.48979i	−0.100777	−	0.0732190i
$415$		0			0
$416$	−14.0601	+	10.2153i	−0.689354	+	0.500845i
$417$	16.3204	+	5.30282i	0.799213	+	0.259680i
$418$		−	7.46989i		−	0.365364i
$419$	−3.64430	+	11.2160i	−0.178036	+	0.547938i	−0.999759	−	0.0219489i	$-0.993013\pi$
$419$	−3.64430	+	11.2160i	−0.178036	+	0.547938i	0.821723	+	0.569887i	$0.193013\pi$
$420$		0			0
$421$	−3.12900	−	9.63007i	−0.152498	−	0.469341i	0.845401	−	0.534133i	$-0.179362\pi$
$421$	−3.12900	−	9.63007i	−0.152498	−	0.469341i	−0.997899	+	0.0647918i	$0.979362\pi$
$422$	7.13244	−	2.31747i	0.347202	−	0.112813i
$423$	−3.55609	+	4.89454i	−0.172903	+	0.237981i
$424$	−9.94189			−0.482821
$425$		0			0
$426$	−7.04624			−0.341391
$427$	−24.9425	+	34.3305i	−1.20705	+	1.66137i
$428$	3.09938	−	1.00705i	0.149814	−	0.0486775i
$429$	−1.44761	−	4.45530i	−0.0698914	−	0.215104i
$430$		0			0
$431$	−1.75911	+	5.41397i	−0.0847332	+	0.260782i	−0.984442	−	0.175708i	$-0.943779\pi$
$431$	−1.75911	+	5.41397i	−0.0847332	+	0.260782i	0.899709	+	0.436490i	$0.143779\pi$
$432$			1.71559i			0.0825415i
$433$	31.4313	+	10.2126i	1.51049	+	0.490788i	0.943057	−	0.332631i	$-0.107936\pi$
$433$	31.4313	+	10.2126i	1.51049	+	0.490788i	0.567434	+	0.823419i	$0.307936\pi$
$434$	1.60400	−	1.16537i	0.0769945	−	0.0559397i
$435$		0			0
$436$	5.97597	+	4.34180i	0.286197	+	0.207934i
$437$	−8.15963	−	11.2308i	−0.390328	−	0.537240i
$438$	−4.61857	−	6.35691i	−0.220684	−	0.303745i
$439$	9.27430	+	6.73818i	0.442638	+	0.321596i	0.786682	−	0.617358i	$-0.211797\pi$
$439$	9.27430	+	6.73818i	0.442638	+	0.321596i	−0.344044	+	0.938954i	$0.611797\pi$
$440$		0			0
$441$	−2.04769	+	1.48773i	−0.0975089	+	0.0708443i
$442$	19.5671	+	6.35773i	0.930711	+	0.302406i
$443$		−	17.8993i		−	0.850422i	−0.905094	−	0.425211i	$-0.860200\pi$
$443$		−	17.8993i		−	0.850422i	0.905094	−	0.425211i	$-0.139800\pi$
$444$	−2.86146	+	8.80667i	−0.135799	+	0.417946i
$445$		0			0
$446$	2.73672	+	8.42275i	0.129587	+	0.398829i
$447$	0.199843	−	0.0649328i	0.00945223	−	0.00307122i
$448$	14.6512	−	20.1657i	0.692206	−	0.952740i
$449$	6.82040			0.321874			0.160937	−	0.986965i	$-0.448548\pi$
$449$	6.82040			0.321874			0.160937	+	0.986965i	$0.448548\pi$
$450$		0			0
$451$	−10.8998			−0.513249
$452$	−1.79267	+	2.46740i	−0.0843203	+	0.116057i
$453$	3.86057	−	1.25437i	0.181385	−	0.0589356i
$454$	−8.63148	−	26.5650i	−0.405096	−	1.24676i
$455$		0			0
$456$	−5.65325	+	17.3989i	−0.264738	+	0.814779i
$457$			2.76381i			0.129286i	0.997908	+	0.0646429i	$0.0205908\pi$
$457$			2.76381i			0.129286i	−0.997908	+	0.0646429i	$0.979409\pi$
$458$	−1.27813	−	0.415289i	−0.0597230	−	0.0194052i
$459$	−3.74379	+	2.72002i	−0.174745	+	0.126960i
$460$		0			0
$461$	7.25254	+	5.26928i	0.337784	+	0.245415i	0.743726	−	0.668484i	$-0.233057\pi$
$461$	7.25254	+	5.26928i	0.337784	+	0.245415i	−0.405942	+	0.913899i	$0.633057\pi$
$462$	2.27093	+	3.12566i	0.105653	+	0.145419i
$463$	7.73623	+	10.6480i	0.359533	+	0.494855i	0.950019	−	0.312193i	$-0.101064\pi$
$463$	7.73623	+	10.6480i	0.359533	+	0.494855i	−0.590485	+	0.807048i	$0.701064\pi$
$464$	7.33412	+	5.32855i	0.340478	+	0.247372i
$465$		0			0
$466$	2.64494	−	1.92166i	0.122524	−	0.0890191i
$467$	−20.7335	−	6.73671i	−0.959430	−	0.311738i	−0.212889	−	0.977076i	$-0.568287\pi$
$467$	−20.7335	−	6.73671i	−0.959430	−	0.311738i	−0.746542	+	0.665339i	$0.768287\pi$
$468$			3.31379i			0.153180i
$469$	3.01347	−	9.27450i	0.139149	−	0.428257i
$470$		0			0
$471$	−0.136071	−	0.418784i	−0.00626983	−	0.0192966i
$472$	9.28798	−	3.01785i	0.427514	−	0.138908i
$473$	1.63984	−	2.25704i	0.0753998	−	0.103779i
$474$	−13.4455			−0.617574
$475$		0			0
$476$	11.6048			0.531905
$477$	−1.90666	+	2.62429i	−0.0872998	+	0.120158i
$478$	22.9416	−	7.45417i	1.04932	−	0.340946i
$479$	−13.2102	−	40.6567i	−0.603588	−	1.85765i	−0.506221	−	0.862404i	$-0.668958\pi$
$479$	−13.2102	−	40.6567i	−0.603588	−	1.85765i	−0.0973673	−	0.995249i	$-0.531042\pi$
$480$		0			0
$481$	14.3710	−	44.2293i	0.655260	−	2.01668i
$482$		−	14.6475i		−	0.667174i
$483$	6.82854	+	2.21873i	0.310709	+	0.100956i
$484$	6.36221	−	4.62242i	0.289192	−	0.210110i
$485$		0			0
$486$	0.881682	+	0.640580i	0.0399939	+	0.0290573i
$487$	−6.67121	−	9.18213i	−0.302301	−	0.416082i	0.630660	−	0.776059i	$-0.282784\pi$
$487$	−6.67121	−	9.18213i	−0.302301	−	0.416082i	−0.932961	+	0.359978i	$0.882784\pi$
$488$	−24.7619	−	34.0819i	−1.12092	−	1.54281i
$489$	−2.62210	−	1.90506i	−0.118575	−	0.0861500i
$490$		0			0
$491$	−13.4739	+	9.78936i	−0.608068	+	0.441788i	−0.848734	−	0.528821i	$-0.822634\pi$
$491$	−13.4739	+	9.78936i	−0.608068	+	0.441788i	0.240665	+	0.970608i	$0.422634\pi$
$492$	7.33292	+	2.38261i	0.330594	+	0.107416i
$493$			24.4529i			1.10130i
$494$	8.20067	−	25.2391i	0.368965	−	1.13556i
$495$		0			0
$496$	0.312405	+	0.961483i	0.0140274	+	0.0431718i
$497$	18.9837	−	6.16817i	0.851534	−	0.276680i
$498$	7.93941	−	10.9277i	0.355773	−	0.489680i
$499$	12.2321			0.547584			0.273792	−	0.961789i	$-0.411722\pi$
$499$	12.2321			0.547584			0.273792	+	0.961789i	$0.411722\pi$
$500$		0			0
$501$	15.9605			0.713063
$502$	12.0941	−	16.6460i	0.539784	−	0.742949i
$503$	1.24557	−	0.404709i	0.0555371	−	0.0180451i	−0.281117	−	0.959674i	$-0.590705\pi$
$503$	1.24557	−	0.404709i	0.0555371	−	0.0180451i	0.336654	+	0.941629i	$0.390705\pi$
$504$	−2.92394	−	8.99897i	−0.130243	−	0.400846i
$505$		0			0
$506$	0.899387	−	2.76803i	0.0399826	−	0.123054i
$507$		−	3.64267i		−	0.161777i
$508$	8.77469	+	2.85107i	0.389314	+	0.126496i
$509$	14.3453	−	10.4225i	0.635844	−	0.461968i	−0.222576	−	0.974915i	$-0.571447\pi$
$509$	14.3453	−	10.4225i	0.635844	−	0.461968i	0.858420	+	0.512948i	$0.171447\pi$
$510$		0			0
$511$	18.0079	+	13.0835i	0.796622	+	0.578780i
$512$	10.4772	+	14.4206i	0.463029	+	0.637305i
$513$	3.50848	+	4.82901i	0.154903	+	0.213206i
$514$	6.22750	+	4.52454i	0.274683	+	0.199569i
$515$		0			0
$516$	−1.59659	+	1.15999i	−0.0702860	+	0.0510658i
$517$	−6.60723	−	2.14682i	−0.290586	−	0.0944170i
$518$			38.3546i			1.68521i
$519$	0.173602	−	0.534294i	0.00762030	−	0.0234529i
$520$		0			0
$521$	8.11527	+	24.9762i	0.355536	+	1.09423i	0.955698	+	0.294349i	$0.0951030\pi$
$521$	8.11527	+	24.9762i	0.355536	+	1.09423i	−0.600162	+	0.799879i	$0.704897\pi$
$522$	5.47693	−	1.77956i	0.239719	−	0.0778894i
$523$	−1.50281	+	2.06844i	−0.0657134	+	0.0904467i	−0.840609	−	0.541643i	$-0.817803\pi$
$523$	−1.50281	+	2.06844i	−0.0657134	+	0.0904467i	0.774895	+	0.632090i	$0.217803\pi$
$524$	−1.68834			−0.0737557
$525$		0			0
$526$	22.2711			0.971068
$527$	−1.60285	+	2.20614i	−0.0698213	+	0.0961008i
$528$	−1.87361	+	0.608773i	−0.0815384	+	0.0264934i
$529$	5.43598	+	16.7302i	0.236347	+	0.727401i
$530$		0			0
$531$	0.984650	−	3.03044i	0.0427302	−	0.131510i
$532$		−	14.9687i		−	0.648977i
$533$	−36.8278	−	11.9661i	−1.59519	−	0.518308i
$534$	−0.955775	+	0.694411i	−0.0413604	+	0.0300501i
$535$		0			0
$536$	7.83224	+	5.69046i	0.338301	+	0.245790i
$537$	9.36852	+	12.8947i	0.404282	+	0.556446i
$538$	13.5754	+	18.6849i	0.585277	+	0.805564i
$539$	−2.35138	−	1.70838i	−0.101281	−	0.0735849i
$540$		0			0
$541$	−7.59599	+	5.51881i	−0.326577	+	0.237272i	−0.738977	−	0.673731i	$-0.764691\pi$
$541$	−7.59599	+	5.51881i	−0.326577	+	0.237272i	0.412400	+	0.911003i	$0.364691\pi$
$542$	10.3163	+	3.35196i	0.443121	+	0.143979i
$543$		−	21.4875i		−	0.922118i
$544$	−6.09194	+	18.7491i	−0.261190	+	0.803860i
$545$		0			0
$546$	4.24150	+	13.0540i	0.181519	+	0.558659i
$547$	33.1490	−	10.7708i	1.41735	−	0.460524i	0.502590	−	0.864525i	$-0.332381\pi$
$547$	33.1490	−	10.7708i	1.41735	−	0.460524i	0.914759	+	0.404000i	$0.132381\pi$
$548$	−9.26413	+	12.7510i	−0.395744	+	0.544695i
$549$	−13.7452			−0.586631
$550$		0			0
$551$	31.5411			1.34370
$552$	−4.18972	+	5.76665i	−0.178326	+	0.245445i
$553$	36.2244	−	11.7700i	1.54042	−	0.500512i
$554$	6.30942	+	19.4184i	0.268062	+	0.825009i
$555$		0			0
$556$	4.30745	−	13.2570i	0.182676	−	0.562220i
$557$		−	14.1466i		−	0.599411i	−0.954032	−	0.299705i	$-0.903112\pi$
$557$		−	14.1466i		−	0.599411i	0.954032	−	0.299705i	$-0.0968884\pi$
$558$	0.610776	+	0.198453i	0.0258562	+	0.00840119i
$559$	8.01849	−	5.82577i	0.339146	−	0.246404i
$560$		0			0
$561$	−4.29903	−	3.12343i	−0.181505	−	0.131871i
$562$	−18.6355	−	25.6496i	−0.786091	−	1.08196i
$563$	22.4448	+	30.8926i	0.945936	+	1.30197i	0.953309	+	0.301996i	$0.0976530\pi$
$563$	22.4448	+	30.8926i	0.945936	+	1.30197i	−0.00737325	+	0.999973i	$0.502347\pi$
$564$	3.97580	+	2.88859i	0.167411	+	0.121632i
$565$		0			0
$566$	−6.33054	+	4.59941i	−0.266092	+	0.193327i
$567$	−2.93614	−	0.954011i	−0.123306	−	0.0400647i
$568$			19.8161i			0.831465i
$569$	−9.15622	+	28.1799i	−0.383849	+	1.18136i	0.553463	+	0.832873i	$0.313306\pi$
$569$	−9.15622	+	28.1799i	−0.383849	+	1.18136i	−0.937312	+	0.348491i	$0.886694\pi$
$570$		0			0
$571$	10.0895	+	31.0524i	0.422234	+	1.29950i	0.905618	+	0.424093i	$0.139407\pi$
$571$	10.0895	+	31.0524i	0.422234	+	1.29950i	−0.483385	+	0.875408i	$0.660593\pi$
$572$	−3.61901	+	1.17589i	−0.151318	+	0.0491663i
$573$	−10.8117	+	14.8810i	−0.451663	+	0.621661i
$574$	31.9362			1.33299
$575$		0			0
$576$	8.07392			0.336413
$577$	13.3094	−	18.3188i	0.554077	−	0.762622i	−0.436481	−	0.899713i	$-0.643775\pi$
$577$	13.3094	−	18.3188i	0.554077	−	0.762622i	0.990558	+	0.137091i	$0.0437754\pi$
$578$	4.57551	−	1.48667i	0.190316	−	0.0618374i
$579$	−0.625832	−	1.92611i	−0.0260087	−	0.0800465i
$580$		0			0
$581$	−11.8241	+	36.3909i	−0.490547	+	1.50975i
$582$		−	4.92742i		−	0.204248i
$583$	−3.54257	−	1.15105i	−0.146718	−	0.0476717i
$584$	−17.8775	+	12.9888i	−0.739776	+	0.537479i
$585$		0			0
$586$	1.58549	+	1.15193i	0.0654960	+	0.0475856i
$587$	−24.4323	−	33.6281i	−1.00843	−	1.38798i	−0.920008	−	0.391899i	$-0.871818\pi$
$587$	−24.4323	−	33.6281i	−1.00843	−	1.38798i	−0.0884196	−	0.996083i	$-0.528182\pi$
$588$	1.20847	+	1.66332i	0.0498366	+	0.0685943i
$589$	2.84564	+	2.06748i	0.117252	+	0.0851889i
$590$		0			0
$591$	9.34046	−	6.78624i	0.384215	−	0.279149i
$592$	−18.6000	−	6.04350i	−0.764454	−	0.248386i
$593$		−	2.09050i		−	0.0858465i	−0.999078	−	0.0429233i	$-0.986333\pi$
$593$		−	2.09050i		−	0.0858465i	0.999078	−	0.0429233i	$-0.0136671\pi$
$594$	−0.386719	+	1.19020i	−0.0158673	+	0.0488345i
$595$		0			0
$596$	−0.0527445	−	0.162331i	−0.00216050	−	0.00664933i
$597$	21.8533	−	7.10057i	0.894397	−	0.290607i
$598$	6.07765	−	8.36516i	0.248533	−	0.342077i
$599$	−17.9768			−0.734511			−0.367255	−	0.930120i	$-0.619702\pi$
$599$	−17.9768			−0.734511			−0.367255	+	0.930120i	$0.619702\pi$
$600$		0			0
$601$	−1.11000			−0.0452778			−0.0226389	−	0.999744i	$-0.507207\pi$
$601$	−1.11000			−0.0452778			−0.0226389	+	0.999744i	$0.507207\pi$
$602$	−4.80471	+	6.61312i	−0.195826	+	0.269531i
$603$	3.00414	−	0.976103i	0.122338	−	0.0397500i
$604$	−1.01892	−	3.13591i	−0.0414593	−	0.127599i
$605$		0			0
$606$	2.22719	−	6.85458i	0.0904733	−	0.278448i
$607$		−	12.2310i		−	0.496441i	−0.968704	−	0.248220i	$-0.920154\pi$
$607$		−	12.2310i		−	0.496441i	0.968704	−	0.248220i	$-0.0798457\pi$
$608$	24.1839	+	7.85783i	0.980788	+	0.318677i
$609$	−13.1979	+	9.58884i	−0.534806	+	0.388560i
$610$		0			0
$611$	−19.9675	−	14.5072i	−0.807798	−	0.586899i
$612$	2.20946	+	3.04106i	0.0893120	+	0.122927i
$613$	−7.62804	−	10.4991i	−0.308094	−	0.424055i	0.626692	−	0.779267i	$-0.284409\pi$
$613$	−7.62804	−	10.4991i	−0.308094	−	0.424055i	−0.934786	+	0.355213i	$0.884409\pi$
$614$	−5.28008	−	3.83620i	−0.213087	−	0.154817i
$615$		0			0
$616$	8.79028	−	6.38651i	0.354171	−	0.257320i
$617$	19.4891	+	6.33241i	0.784603	+	0.254933i	0.673804	−	0.738910i	$-0.264659\pi$
$617$	19.4891	+	6.33241i	0.784603	+	0.254933i	0.110799	+	0.993843i	$0.464659\pi$
$618$			4.58415i			0.184402i
$619$	12.6838	−	39.0367i	0.509804	−	1.56902i	−0.282737	−	0.959198i	$-0.591242\pi$
$619$	12.6838	−	39.0367i	0.509804	−	1.56902i	0.792541	−	0.609819i	$-0.208758\pi$
$620$		0			0
$621$	0.718676	+	2.21186i	0.0288395	+	0.0887588i
$622$	−24.7391	+	8.03822i	−0.991948	+	0.322303i
$623$	1.96713	−	2.70752i	0.0788114	−	0.108475i
$624$	−6.99883			−0.280177
$625$		0			0
$626$	−6.27641			−0.250856
$627$	−4.02882	+	5.54520i	−0.160896	+	0.221454i
$628$	−0.340176	+	0.110530i	−0.0135745	+	0.00441062i
$629$	−16.3015	−	50.1709i	−0.649984	−	2.00045i
$630$		0			0
$631$	4.35319	−	13.3977i	0.173298	−	0.533356i	−0.826254	−	0.563298i	$-0.809532\pi$
$631$	4.35319	−	13.3977i	0.173298	−	0.533356i	0.999552	+	0.0299421i	$0.00953228\pi$
$632$			37.8128i			1.50411i
$633$	−6.54460	−	2.12647i	−0.260125	−	0.0845196i
$634$	10.7989	−	7.84589i	0.428881	−	0.311600i
$635$		0			0
$636$	2.13169	+	1.54876i	0.0845271	+	0.0614125i
$637$	−6.06926	−	8.35362i	−0.240473	−	0.330983i
$638$	3.88695	+	5.34992i	0.153886	+	0.211806i
$639$	5.23071	+	3.80033i	0.206924	+	0.150339i
$640$		0			0
$641$	23.0050	−	16.7141i	0.908644	−	0.660168i	−0.0320278	−	0.999487i	$-0.510197\pi$
$641$	23.0050	−	16.7141i	0.908644	−	0.660168i	0.940671	+	0.339319i	$0.110197\pi$
$642$	4.15830	+	1.35111i	0.164115	+	0.0533242i
$643$			10.8408i			0.427521i	0.976886	+	0.213761i	$0.0685713\pi$
$643$			10.8408i			0.427521i	−0.976886	+	0.213761i	$0.931429\pi$
$644$	1.80226	−	5.54678i	0.0710189	−	0.218574i
$645$		0			0
$646$	−9.30232	−	28.6296i	−0.365995	−	1.12642i
$647$	32.9435	−	10.7040i	1.29514	−	0.420817i	0.421253	−	0.906943i	$-0.361590\pi$
$647$	32.9435	−	10.7040i	1.29514	−	0.420817i	0.873889	+	0.486126i	$0.161590\pi$
$648$	1.80150	−	2.47955i	0.0707695	−	0.0974059i
$649$	3.65897			0.143627
$650$		0			0
$651$	−1.81925			−0.0713020
$652$	−1.54747	+	2.12991i	−0.0606037	+	0.0834138i
$653$	−3.95170	+	1.28398i	−0.154642	+	0.0502462i	−0.385315	−	0.922785i	$-0.625907\pi$
$653$	−3.95170	+	1.28398i	−0.154642	+	0.0502462i	0.230673	+	0.973031i	$0.425907\pi$
$654$	3.06249	+	9.42538i	0.119753	+	0.368561i
$655$		0			0
$656$	−5.03216	+	15.4874i	−0.196473	+	0.604681i
$657$			7.20998i			0.281288i
$658$	19.3591	+	6.29016i	0.754698	+	0.245216i
$659$	−3.24759	+	2.35951i	−0.126508	+	0.0919135i	−0.649240	−	0.760584i	$-0.724913\pi$
$659$	−3.24759	+	2.35951i	−0.126508	+	0.0919135i	0.522732	+	0.852497i	$0.324913\pi$
$660$		0			0
$661$	−15.9107	−	11.5598i	−0.618853	−	0.449623i	0.233668	−	0.972316i	$-0.424927\pi$
$661$	−15.9107	−	11.5598i	−0.618853	−	0.449623i	−0.852521	+	0.522694i	$0.824927\pi$
$662$	3.86205	+	5.31566i	0.150103	+	0.206599i
$663$	−11.0964	−	15.2729i	−0.430950	−	0.593152i
$664$	−30.7318	−	22.3279i	−1.19262	−	0.866492i
$665$		0			0
$666$	−10.0509	+	7.30240i	−0.389464	+	0.282962i
$667$	11.6878	+	3.79760i	0.452554	+	0.147044i
$668$		−	12.9646i		−	0.501616i
$669$	2.51117	−	7.72858i	0.0970873	−	0.298804i
$670$		0			0
$671$	−4.87744	−	15.0112i	−0.188292	−	0.579502i
$672$	−12.5083	+	4.06418i	−0.482517	+	0.156779i
$673$	24.3615	−	33.5308i	0.939068	−	1.29252i	−0.0171473	−	0.999853i	$-0.505458\pi$
$673$	24.3615	−	33.5308i	0.939068	−	1.29252i	0.956215	−	0.292663i	$-0.0945416\pi$
$674$	6.02761			0.232175
$675$		0			0
$676$	−2.95892			−0.113804
$677$	10.6881	−	14.7109i	0.410777	−	0.565386i	−0.552631	−	0.833426i	$-0.686376\pi$
$677$	10.6881	−	14.7109i	0.410777	−	0.565386i	0.963408	+	0.268040i	$0.0863760\pi$
$678$	−3.89162	+	1.26446i	−0.149457	+	0.0485614i
$679$	4.31339	+	13.2753i	0.165533	+	0.509457i
$680$		0			0
$681$	−7.92011	+	24.3756i	−0.303499	+	0.934074i
$682$			0.737453i			0.0282385i
$683$	−27.0597	−	8.79224i	−1.03541	−	0.336426i	−0.258484	−	0.966015i	$-0.583223\pi$
$683$	−27.0597	−	8.79224i	−1.03541	−	0.336426i	−0.776928	+	0.629590i	$0.783223\pi$
$684$	3.92258	−	2.84992i	0.149983	−	0.108969i
$685$		0			0
$686$	−12.1643	−	8.83786i	−0.464434	−	0.337431i
$687$	0.724824	+	0.997634i	0.0276537	+	0.0380621i
$688$	−2.44994	−	3.37206i	−0.0934032	−	0.128558i
$689$	−10.7059	−	7.77828i	−0.407862	−	0.296329i
$690$		0			0
$691$	−19.7541	+	14.3522i	−0.751483	+	0.545984i	−0.896286	−	0.443476i	$-0.853745\pi$
$691$	−19.7541	+	14.3522i	−0.751483	+	0.545984i	0.144803	+	0.989460i	$0.453745\pi$
$692$	−0.434003	−	0.141016i	−0.0164983	−	0.00536063i
$693$		−	3.54511i		−	0.134668i
$694$	−8.73740	+	26.8910i	−0.331667	+	1.02077i
$695$		0			0
$696$	−5.00465	−	15.4027i	−0.189701	−	0.583840i
$697$	−41.7751	+	13.5736i	−1.58235	+	0.514135i
$698$	12.1726	−	16.7542i	0.460741	−	0.634155i
$699$	−2.99987			−0.113466
$700$		0			0
$701$	−25.0371			−0.945638			−0.472819	−	0.881159i	$-0.656764\pi$
$701$	−25.0371			−0.945638			−0.472819	+	0.881159i	$0.656764\pi$
$702$	−2.61327	+	3.59686i	−0.0986316	+	0.135755i
$703$	−64.7142	+	21.0269i	−2.44074	+	0.793045i
$704$	2.86501	+	8.81759i	0.107979	+	0.332325i
$705$		0			0
$706$	−2.75862	+	8.49016i	−0.103822	+	0.319531i
$707$			20.4170i			0.767858i
$708$	−2.46161	−	0.799825i	−0.0925129	−	0.0300593i
$709$	29.5804	−	21.4914i	1.11091	−	0.807126i	0.128107	−	0.991760i	$-0.459110\pi$
$709$	29.5804	−	21.4914i	1.11091	−	0.807126i	0.982807	+	0.184634i	$0.0591101\pi$
$710$		0			0
$711$	9.98116	+	7.25174i	0.374323	+	0.271961i
$712$	1.95289	+	2.68792i	0.0731876	+	0.100734i
$713$	0.805546	+	1.10874i	0.0301679	+	0.0415226i
$714$	12.5961	+	9.15162i	0.471398	+	0.342491i
$715$		0			0
$716$	10.4743	−	7.60999i	0.391441	−	0.284399i
$717$	−21.0508	−	6.83982i	−0.786157	−	0.255438i
$718$			29.1915i			1.08942i
$719$	2.23596	−	6.88157i	0.0833872	−	0.256639i	−0.900667	−	0.434511i	$-0.856921\pi$
$719$	2.23596	−	6.88157i	0.0833872	−	0.256639i	0.984054	+	0.177872i	$0.0569212\pi$
$720$		0			0
$721$	−4.01289	−	12.3504i	−0.149448	−	0.459954i
$722$	−17.2355	+	5.60014i	−0.641437	+	0.208416i
$723$	−7.89999	+	10.8734i	−0.293804	+	0.404386i
$724$	−17.4542			−0.648679
$725$		0			0
$726$	10.5510			0.391583
$727$	7.82337	−	10.7680i	0.290153	−	0.399361i	−0.638911	−	0.769281i	$-0.720615\pi$
$727$	7.82337	−	10.7680i	0.290153	−	0.399361i	0.929064	+	0.369920i	$0.120615\pi$
$728$	36.7117	−	11.9283i	1.36062	−	0.442094i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	3.47424	−	10.6926i	0.128499	−	0.395480i
$732$			11.1651i			0.412675i
$733$	27.3709	+	8.89333i	1.01097	+	0.328483i	0.767239	−	0.641361i	$-0.221630\pi$
$733$	27.3709	+	8.89333i	1.01097	+	0.328483i	0.243727	+	0.969844i	$0.421630\pi$
$734$	−16.6226	+	12.0771i	−0.613553	+	0.445772i
$735$		0			0
$736$	8.01545	+	5.82357i	0.295454	+	0.214660i
$737$	2.13202	+	2.93447i	0.0785339	+	0.108093i
$738$	6.08038	+	8.36893i	0.223822	+	0.308065i
$739$	32.6202	+	23.7000i	1.19995	+	0.871818i	0.994280	−	0.106803i	$-0.0340614\pi$
$739$	32.6202	+	23.7000i	1.19995	+	0.871818i	0.205674	+	0.978621i	$0.434061\pi$
$740$		0			0
$741$	−19.7002	+	14.3130i	−0.723704	+	0.525802i
$742$	10.3797	+	3.37258i	0.381051	+	0.123811i
$743$		−	27.8114i		−	1.02030i	−0.860085	−	0.510151i	$-0.829589\pi$
$743$		−	27.8114i		−	1.02030i	0.860085	−	0.510151i	$-0.170411\pi$
$744$	0.558109	−	1.71768i	0.0204613	−	0.0629733i
$745$		0			0
$746$	6.01061	+	18.4988i	0.220064	+	0.677288i
$747$	−11.7875	+	3.82999i	−0.431282	+	0.140132i
$748$	−2.53714	+	3.49207i	−0.0927670	+	0.127683i
$749$	−12.3859			−0.452569
$750$		0			0
$751$	−11.4124			−0.416443			−0.208221	−	0.978082i	$-0.566767\pi$
$751$	−11.4124			−0.416443			−0.208221	+	0.978082i	$0.566767\pi$
$752$	−6.10080	+	8.39703i	−0.222473	+	0.306208i
$753$	−17.9558	+	5.83420i	−0.654346	+	0.212610i
$754$	7.25980	+	22.3434i	0.264386	+	0.813698i
$755$		0			0
$756$	−0.774937	+	2.38501i	−0.0281842	+	0.0867420i
$757$			13.7637i			0.500251i	0.968213	+	0.250126i	$0.0804719\pi$
$757$			13.7637i			0.500251i	−0.968213	+	0.250126i	$0.919528\pi$
$758$	−13.0237	−	4.23166i	−0.473042	−	0.153701i
$759$	−2.16056	+	1.56974i	−0.0784235	+	0.0569780i
$760$		0			0
$761$	11.9257	+	8.66451i	0.432305	+	0.314088i	0.782570	−	0.622562i	$-0.213908\pi$
$761$	11.9257	+	8.66451i	0.432305	+	0.314088i	−0.350265	+	0.936651i	$0.613908\pi$
$762$	7.27588	+	10.0144i	0.263577	+	0.362783i
$763$	−16.5017	−	22.7126i	−0.597400	−	0.822251i
$764$	12.0877	+	8.78224i	0.437318	+	0.317730i
$765$		0			0
$766$	6.64559	−	4.82830i	0.240115	−	0.174454i
$767$	12.3628	+	4.01692i	0.446395	+	0.145043i
$768$		−	15.8439i		−	0.571717i
$769$	0.753239	−	2.31823i	0.0271625	−	0.0835976i	−0.936556	−	0.350517i	$-0.886006\pi$
$769$	0.753239	−	2.31823i	0.0271625	−	0.0835976i	0.963719	+	0.266920i	$0.0860058\pi$
$770$		0			0
$771$	−2.18265	−	6.71750i	−0.0786061	−	0.241925i
$772$	−1.56457	+	0.508359i	−0.0563101	+	0.0182963i
$773$	−14.8910	+	20.4957i	−0.535592	+	0.737180i	−0.987970	−	0.154647i	$-0.950576\pi$
$773$	−14.8910	+	20.4957i	−0.535592	+	0.737180i	0.452377	+	0.891827i	$0.350576\pi$
$774$	−2.64776			−0.0951716
$775$		0			0
$776$	−13.8574			−0.497450
$777$	20.6863	−	28.4722i	0.742115	−	1.02143i
$778$	−14.2341	+	4.62493i	−0.510317	+	0.165812i
$779$	17.5082	+	53.8846i	0.627296	+	1.93062i
$780$		0			0
$781$	−2.29427	+	7.06103i	−0.0820953	+	0.252664i
$782$		−	11.7289i		−	0.419426i
$783$	−5.02554	−	1.63290i	−0.179598	−	0.0583550i
$784$	−3.51299	+	2.55234i	−0.125464	+	0.0911550i
$785$		0			0
$786$	−1.83257	−	1.33144i	−0.0653656	−	0.0474909i
$787$	22.7167	+	31.2669i	0.809763	+	1.11454i	0.991360	+	0.131170i	$0.0418734\pi$
$787$	22.7167	+	31.2669i	0.809763	+	1.11454i	−0.181597	+	0.983373i	$0.558127\pi$
$788$	−5.51242	−	7.58719i	−0.196372	−	0.270283i
$789$	−16.5328	−	12.0118i	−0.588582	−	0.427630i
$790$		0			0
$791$	9.37774	−	6.81333i	0.333434	−	0.242254i
$792$	3.34719	+	1.08757i	0.118937	+	0.0386450i
$793$		−	56.0741i		−	1.99125i
$794$	4.37879	−	13.4765i	0.155397	−	0.478264i
$795$		0			0
$796$	−5.76775	−	17.7513i	−0.204432	−	0.629178i
$797$	−49.5519	+	16.1004i	−1.75522	+	0.570306i	−0.996687	−	0.0813294i	$-0.974083\pi$
$797$	−49.5519	+	16.1004i	−1.75522	+	0.570306i	−0.758533	+	0.651635i	$0.774083\pi$
$798$	11.8044	−	16.2474i	0.417872	−	0.575152i
$799$	−27.9968			−0.990454
$800$		0			0
$801$	1.08404			0.0383025
$802$	−4.14485	+	5.70490i	−0.146360	+	0.201447i
$803$	−7.87407	+	2.55844i	−0.277870	+	0.0902854i
$804$	−0.792882	−	2.44024i	−0.0279628	−	0.0860606i
$805$		0			0
$806$	−0.809598	+	2.49169i	−0.0285169	+	0.0877659i
$807$		−	21.1923i		−	0.746006i
$808$	−19.2771	−	6.26350i	−0.678166	−	0.220349i
$809$	25.7217	−	18.6879i	0.904328	−	0.657033i	−0.0352461	−	0.999379i	$-0.511222\pi$
$809$	25.7217	−	18.6879i	0.904328	−	0.657033i	0.939574	+	0.342346i	$0.111222\pi$
$810$		0			0
$811$	25.1777	+	18.2927i	0.884108	+	0.642342i	0.934335	−	0.356395i	$-0.115994\pi$
$811$	25.1777	+	18.2927i	0.884108	+	0.642342i	−0.0502268	+	0.998738i	$0.515994\pi$
$812$	7.78896	+	10.7206i	0.273339	+	0.376219i
$813$	−5.85033	−	8.05229i	−0.205180	−	0.282406i
$814$	−11.5415	−	8.38541i	−0.404530	−	0.293908i
$815$		0			0
$816$	−6.42281	+	4.66645i	−0.224843	+	0.163358i
$817$	−13.7921	−	4.48133i	−0.482525	−	0.156782i
$818$			1.21188i			0.0423725i
$819$	3.89193	−	11.9781i	0.135995	−	0.418550i
$820$		0			0
$821$	−14.5319	−	44.7247i	−0.507168	−	1.56090i	−0.797095	−	0.603854i	$-0.793631\pi$
$821$	−14.5319	−	44.7247i	−0.507168	−	1.56090i	0.289927	−	0.957049i	$-0.406369\pi$
$822$	−20.1110	+	6.53446i	−0.701452	+	0.227916i
$823$	−16.6593	+	22.9296i	−0.580708	+	0.799276i	−0.993773	−	0.111426i	$-0.964458\pi$
$823$	−16.6593	+	22.9296i	−0.580708	+	0.799276i	0.413065	+	0.910702i	$0.364458\pi$
$824$	12.8920			0.449113
$825$		0			0
$826$	−10.7208			−0.373023
$827$	−8.32775	+	11.4622i	−0.289584	+	0.398579i	−0.928879	−	0.370383i	$-0.879226\pi$
$827$	−8.32775	+	11.4622i	−0.289584	+	0.398579i	0.639295	+	0.768962i	$0.279226\pi$
$828$	1.79668	−	0.583776i	0.0624389	−	0.0202876i
$829$	−0.468647	−	1.44235i	−0.0162768	−	0.0500948i	0.942588	−	0.333957i	$-0.108384\pi$
$829$	−0.468647	−	1.44235i	−0.0162768	−	0.0500948i	−0.958865	+	0.283862i	$0.908384\pi$
$830$		0			0
$831$	5.78942	−	17.8180i	0.200833	−	0.618099i
$832$			32.9379i			1.14192i
$833$	−11.1395	−	3.61944i	−0.385961	−	0.125406i
$834$	15.1299	−	10.9925i	0.523906	−	0.380640i
$835$		0			0
$836$	4.50433	+	3.27259i	0.155786	+	0.113185i
$837$	−0.346370	−	0.476737i	−0.0119723	−	0.0164784i
$838$	7.55449	+	10.3979i	0.260965	+	0.359188i
$839$	8.48811	+	6.16697i	0.293042	+	0.212908i	0.724586	−	0.689184i	$-0.242031\pi$
$839$	8.48811	+	6.16697i	0.293042	+	0.212908i	−0.431544	+	0.902092i	$0.642031\pi$
$840$		0			0
$841$	0.871777	−	0.633383i	0.0300613	−	0.0218408i
$842$	−10.4950	−	3.41004i	−0.361683	−	0.117518i
$843$			29.0916i			1.00197i
$844$	−1.72732	+	5.31614i	−0.0594568	+	0.182989i
$845$		0			0
$846$	2.03747	+	6.27068i	0.0700496	+	0.215591i
$847$	−28.4259	+	9.23615i	−0.976727	+	0.317358i
$848$	−3.27104	+	4.50221i	−0.112328	+	0.154606i
$849$	7.18007			0.246419
$850$		0			0
$851$	−26.5120			−0.908820
$852$	3.08699	−	4.24887i	0.105758	−	0.145564i
$853$	14.1300	−	4.59110i	0.483801	−	0.157196i	−0.0569538	−	0.998377i	$-0.518139\pi$
$853$	14.1300	−	4.59110i	0.483801	−	0.157196i	0.540755	+	0.841180i	$0.318139\pi$
$854$	14.2909	+	43.9828i	0.489024	+	1.50506i
$855$		0			0
$856$	3.79973	−	11.6944i	0.129872	−	0.399705i
$857$			26.4088i			0.902109i	0.892496	+	0.451054i	$0.148952\pi$
$857$			26.4088i			0.902109i	−0.892496	+	0.451054i	$0.851048\pi$
$858$	−4.85547	−	1.57764i	−0.165763	−	0.0538597i
$859$	−7.38643	+	5.36656i	−0.252022	+	0.183105i	−0.706622	−	0.707591i	$-0.749782\pi$
$859$	−7.38643	+	5.36656i	−0.252022	+	0.183105i	0.454601	+	0.890695i	$0.349782\pi$
$860$		0			0
$861$	−23.7075	−	17.2245i	−0.807951	−	0.587011i
$862$	3.64656	+	5.01906i	0.124202	+	0.170950i
$863$	−7.33532	−	10.0962i	−0.249697	−	0.343679i	0.665708	−	0.746212i	$-0.268130\pi$
$863$	−7.33532	−	10.0962i	−0.249697	−	0.343679i	−0.915405	+	0.402534i	$0.868130\pi$
$864$	−3.44649	−	2.50402i	−0.117252	−	0.0851886i
$865$		0			0
$866$	29.1386	−	21.1704i	0.990168	−	0.719399i
$867$	−4.19841	−	1.36415i	−0.142585	−	0.0463288i
$868$			1.47776i			0.0501586i
$869$	−4.37789	+	13.4738i	−0.148510	+	0.457066i
$870$		0			0
$871$	3.98205	+	12.2555i	0.134927	+	0.415262i
$872$	26.5069	−	8.61262i	0.897638	−	0.291660i
$873$	−2.65757	+	3.65783i	−0.0899450	+	0.123799i
$874$	−15.1289			−0.511741
$875$		0			0
$876$	5.85662			0.197877
$877$	23.9888	−	33.0177i	0.810043	−	1.11493i	−0.181273	−	0.983433i	$-0.558022\pi$
$877$	23.9888	−	33.0177i	0.810043	−	1.11493i	0.991317	−	0.131496i	$-0.0419781\pi$
$878$	11.8819	−	3.86065i	0.400993	−	0.130291i
$879$	−0.555691	−	1.71024i	−0.0187430	−	0.0576850i
$880$		0			0
$881$	−1.12544	+	3.46374i	−0.0379170	+	0.116696i	−0.968223	−	0.250087i	$-0.919541\pi$
$881$	−1.12544	+	3.46374i	−0.0379170	+	0.116696i	0.930306	+	0.366783i	$0.119541\pi$
$882$			2.75842i			0.0928808i
$883$	−0.316564	−	0.102858i	−0.0106532	−	0.00346144i	0.303686	−	0.952772i	$-0.401783\pi$
$883$	−0.316564	−	0.102858i	−0.0106532	−	0.00346144i	−0.314339	+	0.949311i	$0.601783\pi$
$884$	−12.4061	+	9.01357i	−0.417263	+	0.303159i
$885$		0			0
$886$	−15.7815	−	11.4659i	−0.530190	−	0.385206i
$887$	0.671685	+	0.924496i	0.0225530	+	0.0310415i	0.820145	−	0.572156i	$-0.193893\pi$
$887$	0.671685	+	0.924496i	0.0225530	+	0.0310415i	−0.797592	+	0.603198i	$0.793893\pi$
$888$	20.5365	+	28.2660i	0.689159	+	0.948546i
$889$	−28.3688	−	20.6111i	−0.951459	−	0.691276i
$890$		0			0
$891$	0.929002	−	0.674959i	0.0311227	−	0.0226120i
$892$	−6.27787	−	2.03980i	−0.210199	−	0.0682977i
$893$			36.1123i			1.20845i
$894$	0.0707650	−	0.217792i	0.00236674	−	0.00728407i
$895$		0			0
$896$	−0.266092	−	0.818948i	−0.00888953	−	0.0273591i
$897$	−9.02336	+	2.93187i	−0.301281	+	0.0978923i
$898$	4.36901	−	6.01342i	0.145796	−	0.200671i
$899$	−3.11385			−0.103853
$900$		0			0
$901$	−15.0109			−0.500086
$902$	−6.98216	+	9.61012i	−0.232481	+	0.319982i
$903$	7.13347	−	2.31780i	0.237387	−	0.0771317i
$904$	3.55604	+	10.9444i	0.118272	+	0.364004i
$905$		0			0
$906$	1.36704	−	4.20732i	0.0454169	−	0.139779i
$907$		−	18.4202i		−	0.611632i	−0.952091	−	0.305816i	$-0.901071\pi$
$907$		−	18.4202i		−	0.611632i	0.952091	−	0.305816i	$-0.0989293\pi$
$908$	19.8001	+	6.43345i	0.657090	+	0.213502i
$909$	−5.35029	+	3.88721i	−0.177458	+	0.128931i
$910$		0			0
$911$	−14.7651	−	10.7274i	−0.489188	−	0.355416i	0.315684	−	0.948864i	$-0.397766\pi$
$911$	−14.7651	−	10.7274i	−0.489188	−	0.355416i	−0.804872	+	0.593449i	$0.797766\pi$
$912$	6.01913	+	8.28462i	0.199313	+	0.274331i
$913$	−8.36551	−	11.5141i	−0.276858	−	0.381062i
$914$	2.43681	+	1.77044i	0.0806024	+	0.0585611i
$915$		0			0
$916$	0.810372	−	0.588770i	0.0267754	−	0.0194535i
$917$	6.10275	+	1.98290i	0.201531	+	0.0654812i
$918$			5.04322i			0.166451i
$919$	−3.34919	+	10.3078i	−0.110480	+	0.340022i	−0.990977	−	0.134029i	$-0.957209\pi$
$919$	−3.34919	+	10.3078i	−0.110480	+	0.340022i	0.880498	+	0.474050i	$0.157209\pi$
$920$		0			0
$921$	1.85059	+	5.69554i	0.0609791	+	0.187674i
$922$	9.29166	−	3.01904i	0.306005	−	0.0994269i
$923$	−15.5036	+	21.3389i	−0.510308	+	0.702378i
$924$	−2.87967			−0.0947342
$925$		0			0
$926$	14.3438			0.471368
$927$	2.47242	−	3.40300i	0.0812051	−	0.111769i
$928$	−21.4093	+	6.95631i	−0.702795	+	0.228352i
$929$	16.1768	+	49.7870i	0.530743	+	1.63346i	0.752673	+	0.658395i	$0.228764\pi$
$929$	16.1768	+	49.7870i	0.530743	+	1.63346i	−0.221930	+	0.975063i	$0.571236\pi$
$930$		0			0
$931$	−4.66862	+	14.3685i	−0.153008	+	0.470910i
$932$			2.43678i			0.0798193i
$933$	22.7002	+	7.37574i	0.743171	+	0.241471i
$934$	−19.2211	+	13.9649i	−0.628933	+	0.456947i
$935$		0			0
$936$	10.1154	+	7.34929i	0.330633	+	0.240219i
$937$	0.000771322		0.00106163i	2.51980e−5		3.46821e-5i	0.809030	−	0.587768i	$-0.199993\pi$
$937$	0.000771322		0.00106163i	2.51980e−5		3.46821e-5i	−0.809004	+	0.587803i	$0.799993\pi$
$938$	−6.24680	−	8.59798i	−0.203965	−	0.280734i
$939$	4.65924	+	3.38513i	0.152048	+	0.110470i
$940$		0			0
$941$	17.5737	−	12.7680i	0.572885	−	0.416225i	−0.263267	−	0.964723i	$-0.584800\pi$
$941$	17.5737	−	12.7680i	0.572885	−	0.416225i	0.836152	+	0.548498i	$0.184800\pi$
$942$	−0.456399	−	0.148293i	−0.0148703	−	0.00483165i
$943$			22.0754i			0.718874i
$944$	1.68926	−	5.19900i	0.0549807	−	0.169213i
$945$		0			0
$946$	−0.939548	−	2.89163i	−0.0305473	−	0.0940151i
$947$	32.2661	−	10.4839i	1.04851	−	0.340681i	0.266426	−	0.963855i	$-0.414157\pi$
$947$	32.2661	−	10.4839i	1.04851	−	0.340681i	0.782083	+	0.623174i	$0.214157\pi$
$948$	5.89054	−	8.10763i	0.191316	−	0.263324i
$949$	−29.4134			−0.954800
$950$		0			0
$951$	−12.2481			−0.397172
$952$	25.7370	−	35.4240i	0.834142	−	1.14810i
$953$	−7.89670	+	2.56579i	−0.255799	+	0.0831142i	−0.434109	−	0.900860i	$-0.642937\pi$
$953$	−7.89670	+	2.56579i	−0.255799	+	0.0831142i	0.178310	+	0.983974i	$0.442937\pi$
$954$	1.09242	+	3.36213i	0.0353685	+	0.108853i
$955$		0			0
$956$	−5.55594	+	17.0994i	−0.179692	+	0.553035i
$957$		−	6.06786i		−	0.196146i
$958$	−44.3085	−	14.3967i	−1.43154	−	0.465136i
$959$	48.4620	−	35.2097i	1.56492	−	1.13698i
$960$		0			0
$961$	24.7986	+	18.0172i	0.799955	+	0.581201i
$962$	−29.7904	−	41.0030i	−0.960482	−	1.32199i
$963$	−2.35816	−	3.24573i	−0.0759907	−	0.104592i
$964$	8.83240	+	6.41711i	0.284472	+	0.206681i
$965$		0			0
$966$	6.33044	−	4.59933i	0.203679	−	0.147981i
$967$	26.4313	+	8.58804i	0.849972	+	0.276173i	0.701434	−	0.712734i	$-0.252543\pi$
$967$	26.4313	+	8.58804i	0.849972	+	0.276173i	0.148538	+	0.988907i	$0.452543\pi$
$968$		−	29.6724i		−	0.953707i
$969$	−8.53565	+	26.2700i	−0.274205	+	0.843915i
$970$		0			0
$971$	−9.59377	−	29.5266i	−0.307879	−	0.947554i	−0.978587	−	0.205833i	$-0.934010\pi$
$971$	−9.59377	−	29.5266i	−0.307879	−	0.947554i	0.670708	−	0.741721i	$-0.265990\pi$
$972$	−0.772537	+	0.251013i	−0.0247791	+	0.00805123i
$973$	−31.1397	+	42.8601i	−0.998292	+	1.37403i
$974$	−12.3692			−0.396333
$975$		0			0
$976$	−23.5811			−0.754814
$977$	26.0928	−	35.9137i	0.834783	−	1.14898i	−0.152231	−	0.988345i	$-0.548646\pi$
$977$	26.0928	−	35.9137i	0.834783	−	1.14898i	0.987014	−	0.160635i	$-0.0513543\pi$
$978$	−3.35932	+	1.09151i	−0.107419	+	0.0349027i
$979$	0.384667	+	1.18388i	0.0122940	+	0.0378370i
$980$		0			0
$981$	2.81009	−	8.64857i	0.0897193	−	0.276127i
$982$			18.1506i			0.579208i
$983$	41.6427	+	13.5305i	1.32820	+	0.431557i	0.885302	−	0.465017i	$-0.153952\pi$
$983$	41.6427	+	13.5305i	1.32820	+	0.431557i	0.442894	+	0.896574i	$0.353952\pi$
$984$	23.5359	−	17.0998i	0.750297	−	0.545123i
$985$		0			0
$986$	21.5597	+	15.6640i	0.686600	+	0.498844i
$987$	−10.9785	−	15.1106i	−0.349450	−	0.480977i
$988$	11.6264	+	16.0023i	0.369884	+	0.509102i
$989$	−4.57121	−	3.32118i	−0.145356	−	0.105607i
$990$		0			0
$991$	−27.8586	+	20.2404i	−0.884957	+	0.642959i	−0.934558	−	0.355810i	$-0.884205\pi$
$991$	−27.8586	+	20.2404i	−0.884957	+	0.642959i	0.0496015	+	0.998769i	$0.484205\pi$
$992$	−2.38752	−	0.775752i	−0.0758039	−	0.0246302i
$993$		−	6.02899i		−	0.191324i
$994$	6.72219	−	20.6888i	0.213215	−	0.656208i
$995$		0			0
$996$	3.11107	+	9.57490i	0.0985781	+	0.303392i
$997$	−18.4401	+	5.99154i	−0.584002	+	0.189754i	−0.586093	−	0.810244i	$-0.699335\pi$
$997$	−18.4401	+	5.99154i	−0.584002	+	0.189754i	0.00209042	+	0.999998i	$0.499335\pi$
$998$	7.83564	−	10.7848i	0.248033	−	0.341388i
$999$	11.3997			0.360670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.c.49.3		16
5.2	odd	4		375.2.g.e.76.3		16
5.3	odd	4		375.2.g.d.76.2		16
5.4	even	2		75.2.i.a.34.2	✓	16
15.14	odd	2		225.2.m.b.109.3		16
25.2	odd	20		375.2.g.e.301.3		16
25.6	even	5		1875.2.b.h.1249.11		16
25.8	odd	20		1875.2.a.p.1.5		8
25.11	even	5		75.2.i.a.64.2	yes	16
25.14	even	10	inner	375.2.i.c.199.3		16
25.17	odd	20		1875.2.a.m.1.4		8
25.19	even	10		1875.2.b.h.1249.6		16
25.23	odd	20		375.2.g.d.301.2		16
75.8	even	20		5625.2.a.t.1.4		8
75.11	odd	10		225.2.m.b.64.3		16
75.17	even	20		5625.2.a.bd.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.2	✓	16	5.4	even	2
75.2.i.a.64.2	yes	16	25.11	even	5
225.2.m.b.64.3		16	75.11	odd	10
225.2.m.b.109.3		16	15.14	odd	2
375.2.g.d.76.2		16	5.3	odd	4
375.2.g.d.301.2		16	25.23	odd	20
375.2.g.e.76.3		16	5.2	odd	4
375.2.g.e.301.3		16	25.2	odd	20
375.2.i.c.49.3		16	1.1	even	1	trivial
375.2.i.c.199.3		16	25.14	even	10	inner
1875.2.a.m.1.4		8	25.17	odd	20
1875.2.a.p.1.5		8	25.8	odd	20
1875.2.b.h.1249.6		16	25.19	even	10
1875.2.b.h.1249.11		16	25.6	even	5
5625.2.a.t.1.4		8	75.8	even	20
5625.2.a.bd.1.5		8	75.17	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.640580 - 0.881682i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(-0.336773 + 1.03648i) q^{6} -3.08724i q^{7} +(2.91489 + 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.640580 - 0.881682i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(-0.336773 + 1.03648i) q^{6} -3.08724i q^{7} +(2.91489 + 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.929002 + 0.674959i) q^{11} +(-0.477454 - 0.657159i) q^{12} +(2.39789 + 3.30042i) q^{13} +(-2.72197 - 1.97763i) q^{14} +(1.38794 - 1.00840i) q^{16} +(4.40109 + 1.43000i) q^{17} -1.08982i q^{18} +(1.84452 - 5.67685i) q^{19} +(0.954011 + 2.93614i) q^{21} +(1.19020 - 0.386719i) q^{22} +(1.36700 - 1.88152i) q^{23} -3.06489 q^{24} +4.44596 q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.38501 - 0.774937i) q^{28} +(1.63290 + 5.02554i) q^{29} +(-0.182097 + 0.560438i) q^{31} +4.26010i q^{32} +(-1.09211 - 0.354847i) q^{33} +(4.08005 - 2.96433i) q^{34} +(0.657159 + 0.477454i) q^{36} +(-6.70056 - 9.22252i) q^{37} +(-3.82361 - 5.26275i) q^{38} +(-3.30042 - 2.39789i) q^{39} +(-7.67919 + 5.57926i) q^{41} +(3.19987 + 1.03970i) q^{42} -2.42954i q^{43} +(-0.288240 + 0.887112i) q^{44} +(-0.783227 - 2.41052i) q^{46} +(-5.75387 + 1.86955i) q^{47} +(-1.00840 + 1.38794i) q^{48} -2.53108 q^{49} -4.62758 q^{51} +(-1.94779 + 2.68091i) q^{52} +(-3.08503 + 1.00239i) q^{53} +(0.336773 + 1.03648i) q^{54} +(2.92394 - 8.99897i) q^{56} +5.96899i q^{57} +(5.47693 + 1.77956i) q^{58} +(2.57785 - 1.87292i) q^{59} +(-11.1201 - 8.07922i) q^{61} +(0.377480 + 0.519557i) q^{62} +(-1.81464 - 2.49763i) q^{63} +(6.53194 + 4.74573i) q^{64} +(-1.01244 + 0.735584i) q^{66} +(3.00414 + 0.976103i) q^{67} +3.75895i q^{68} +(-0.718676 + 2.21186i) q^{69} +(1.99795 + 6.14907i) q^{71} +(2.91489 - 0.947104i) q^{72} +(-4.23792 + 5.83300i) q^{73} -12.4236 q^{74} +4.84857 q^{76} +(2.08376 - 2.86806i) q^{77} +(-4.22836 + 1.37388i) q^{78} +(3.81246 + 11.7336i) q^{79} +(0.309017 - 0.951057i) q^{81} +10.3446i q^{82} +(-11.7875 - 3.82999i) q^{83} +(-2.02881 + 1.47402i) q^{84} +(-2.14208 - 1.55631i) q^{86} +(-3.10596 - 4.27498i) q^{87} +(2.06868 + 2.84729i) q^{88} +(0.877003 + 0.637180i) q^{89} +(10.1892 - 7.40289i) q^{91} +(1.79668 + 0.583776i) q^{92} -0.589279i q^{93} +(-2.03747 + 6.27068i) q^{94} +(-1.31644 - 4.05159i) q^{96} +(-4.30003 + 1.39717i) q^{97} +(-1.62136 + 2.23161i) q^{98} +1.14831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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