LMFDB - Embedded newform 375.2.g.d.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, 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 $\Q(\zeta_{5})$
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:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.2
Root			$1.08982i$ of defining polynomial
Character	$\chi$	$=$	375.301
Dual form			375.2.g.d.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.881682	+	0.640580i	−0.623444	+	0.452958i	−0.854123	−	0.520072i	$-0.825905\pi$
$2$	−0.881682	+	0.640580i	−0.623444	+	0.452958i	0.230679	+	0.973030i	$0.425905\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.251013	+	0.772537i	−0.125506	+	0.386269i
$5$		0			0
$5$		0			0
$6$	−0.336773	−	1.03648i	−0.137487	−	0.423141i
$7$	−3.08724			−1.16687			−0.583434	−	0.812160i	$-0.698291\pi$
$7$	−3.08724			−1.16687			−0.583434	+	0.812160i	$0.698291\pi$
$8$	−0.947104	−	2.91489i	−0.334852	−	1.03057i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	0.929002	−	0.674959i	0.280105	−	0.203508i	−0.438858	−	0.898556i	$-0.644617\pi$
$11$	0.929002	−	0.674959i	0.280105	−	0.203508i	0.718963	+	0.695048i	$0.244617\pi$
$12$	−0.657159	−	0.477454i	−0.189706	−	0.137829i
$13$	−3.30042	−	2.39789i	−0.915372	−	0.665056i	0.0269961	−	0.999636i	$-0.491406\pi$
$13$	−3.30042	−	2.39789i	−0.915372	−	0.665056i	−0.942368	+	0.334579i	$0.891406\pi$
$14$	2.72197	−	1.97763i	0.727477	−	0.528543i
$15$		0			0
$16$	1.38794	+	1.00840i	0.346986	+	0.252100i
$17$	1.43000	+	4.40109i	0.346826	+	1.06742i	0.960599	+	0.277938i	$0.0896510\pi$
$17$	1.43000	+	4.40109i	0.346826	+	1.06742i	−0.613773	+	0.789482i	$0.710349\pi$
$18$	1.08982			0.256873
$19$	−1.84452	−	5.67685i	−0.423162	−	1.30236i	−0.904744	−	0.425957i	$-0.859938\pi$
$19$	−1.84452	−	5.67685i	−0.423162	−	1.30236i	0.481582	−	0.876401i	$-0.340062\pi$
$20$		0			0
$21$	0.954011	−	2.93614i	0.208182	−	0.640719i
$22$	−0.386719	+	1.19020i	−0.0824488	+	0.253751i
$23$	1.88152	−	1.36700i	0.392324	−	0.285040i	−0.374083	−	0.927395i	$-0.622043\pi$
$23$	1.88152	−	1.36700i	0.392324	−	0.285040i	0.766407	+	0.642355i	$0.222043\pi$
$24$	3.06489			0.625619
$25$		0			0
$26$	4.44596			0.871925
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.774937	−	2.38501i	0.146449	−	0.450725i
$29$	−1.63290	+	5.02554i	−0.303221	+	0.933220i	0.677113	+	0.735879i	$0.263231\pi$
$29$	−1.63290	+	5.02554i	−0.303221	+	0.933220i	−0.980335	+	0.197341i	$0.936769\pi$
$30$		0			0
$31$	−0.182097	−	0.560438i	−0.0327056	−	0.100658i	0.933371	−	0.358913i	$-0.116852\pi$
$31$	−0.182097	−	0.560438i	−0.0327056	−	0.100658i	−0.966077	+	0.258255i	$0.916852\pi$
$32$	4.26010			0.753086
$33$	0.354847	+	1.09211i	0.0617709	+	0.190111i
$34$	−4.08005	−	2.96433i	−0.699723	−	0.508379i
$35$		0			0
$36$	0.657159	−	0.477454i	0.109527	−	0.0795757i
$37$	−9.22252	−	6.70056i	−1.51617	−	1.10156i	−0.963344	−	0.268271i	$-0.913548\pi$
$37$	−9.22252	−	6.70056i	−1.51617	−	1.10156i	−0.552830	−	0.833294i	$-0.686452\pi$
$38$	5.26275	+	3.82361i	0.853731	+	0.620272i
$39$	3.30042	−	2.39789i	0.528490	−	0.383970i
$40$		0			0
$41$	−7.67919	−	5.57926i	−1.19929	−	0.871334i	−0.205073	−	0.978747i	$-0.565743\pi$
$41$	−7.67919	−	5.57926i	−1.19929	−	0.871334i	−0.994215	+	0.107413i	$0.965743\pi$
$42$	1.03970	+	3.19987i	0.160429	+	0.493750i
$43$	2.42954			0.370501			0.185250	−	0.982691i	$-0.440690\pi$
$43$	2.42954			0.370501			0.185250	+	0.982691i	$0.440690\pi$
$44$	0.288240	+	0.887112i	0.0434538	+	0.133737i
$45$		0			0
$46$	−0.783227	+	2.41052i	−0.115481	+	0.355412i
$47$	1.86955	−	5.75387i	0.272701	−	0.839289i	−0.717117	−	0.696953i	$-0.754539\pi$
$47$	1.86955	−	5.75387i	0.272701	−	0.839289i	0.989818	−	0.142336i	$-0.0454613\pi$
$48$	−1.38794	+	1.00840i	−0.200332	+	0.145550i
$49$	2.53108			0.361583
$50$		0			0
$51$	−4.62758			−0.647990
$52$	2.68091	−	1.94779i	0.371775	−	0.270111i
$53$	−1.00239	+	3.08503i	−0.137689	+	0.423762i	−0.995999	−	0.0893696i	$-0.971515\pi$
$53$	−1.00239	+	3.08503i	−0.137689	+	0.423762i	0.858310	+	0.513132i	$0.171515\pi$
$54$	−0.336773	+	1.03648i	−0.0458290	+	0.141047i
$55$		0			0
$56$	2.92394	+	8.99897i	0.390728	+	1.20254i
$57$	5.96899			0.790612
$58$	−1.77956	−	5.47693i	−0.233668	−	0.719157i
$59$	−2.57785	−	1.87292i	−0.335607	−	0.243833i	0.407199	−	0.913340i	$-0.366506\pi$
$59$	−2.57785	−	1.87292i	−0.335607	−	0.243833i	−0.742806	+	0.669507i	$0.766506\pi$
$60$		0			0
$61$	−11.1201	+	8.07922i	−1.42378	+	1.03444i	−0.432650	+	0.901562i	$0.642421\pi$
$61$	−11.1201	+	8.07922i	−1.42378	+	1.03444i	−0.991133	+	0.132876i	$0.957579\pi$
$62$	0.519557	+	0.377480i	0.0659838	+	0.0479400i
$63$	2.49763	+	1.81464i	0.314672	+	0.228623i
$64$	−6.53194	+	4.74573i	−0.816493	+	0.593217i
$65$		0			0
$66$	−1.01244	−	0.735584i	−0.124623	−	0.0905441i
$67$	0.976103	+	3.00414i	0.119250	+	0.367014i	0.992810	−	0.119703i	$-0.0381943\pi$
$67$	0.976103	+	3.00414i	0.119250	+	0.367014i	−0.873560	+	0.486717i	$0.838194\pi$
$68$	−3.75895			−0.455840
$69$	0.718676	+	2.21186i	0.0865184	+	0.266276i
$70$		0			0
$71$	1.99795	−	6.14907i	0.237113	−	0.729760i	−0.759721	−	0.650250i	$-0.774664\pi$
$71$	1.99795	−	6.14907i	0.237113	−	0.729760i	0.996834	−	0.0795103i	$-0.0253357\pi$
$72$	−0.947104	+	2.91489i	−0.111617	+	0.343523i
$73$	−5.83300	+	4.23792i	−0.682701	+	0.496011i	−0.874252	−	0.485472i	$-0.838648\pi$
$73$	−5.83300	+	4.23792i	−0.682701	+	0.496011i	0.191552	+	0.981482i	$0.438648\pi$
$74$	12.4236			1.44421
$75$		0			0
$76$	4.84857			0.556169
$77$	−2.86806	+	2.08376i	−0.326845	+	0.237467i
$78$	−1.37388	+	4.22836i	−0.155561	+	0.478768i
$79$	−3.81246	+	11.7336i	−0.428936	+	1.32013i	0.470239	+	0.882539i	$0.344168\pi$
$79$	−3.81246	+	11.7336i	−0.428936	+	1.32013i	−0.899175	+	0.437590i	$0.855832\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	10.3446			1.14237
$83$	3.82999	+	11.7875i	0.420396	+	1.29384i	0.907335	+	0.420409i	$0.138113\pi$
$83$	3.82999	+	11.7875i	0.420396	+	1.29384i	−0.486939	+	0.873436i	$0.661887\pi$
$84$	2.02881	+	1.47402i	0.221361	+	0.160829i
$85$		0			0
$86$	−2.14208	+	1.55631i	−0.230986	+	0.167821i
$87$	−4.27498	−	3.10596i	−0.458326	−	0.332993i
$88$	−2.84729	−	2.06868i	−0.303522	−	0.220522i
$89$	−0.877003	+	0.637180i	−0.0929621	+	0.0675409i	−0.633295	−	0.773910i	$-0.718298\pi$
$89$	−0.877003	+	0.637180i	−0.0929621	+	0.0675409i	0.540333	+	0.841451i	$0.318298\pi$
$90$		0			0
$91$	10.1892	+	7.40289i	1.06812	+	0.776034i
$92$	0.583776	+	1.79668i	0.0608628	+	0.187317i
$93$	0.589279			0.0611054
$94$	2.03747	+	6.27068i	0.210149	+	0.646772i
$95$		0			0
$96$	−1.31644	+	4.05159i	−0.134359	+	0.413514i
$97$	1.39717	−	4.30003i	0.141861	−	0.436602i	−0.854733	−	0.519067i	$-0.826279\pi$
$97$	1.39717	−	4.30003i	0.141861	−	0.436602i	0.996594	+	0.0824653i	$0.0262794\pi$
$98$	−2.23161	+	1.62136i	−0.225426	+	0.163782i
$99$	−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	$0.606720\pi$
$102$	4.08005	−	2.96433i	0.403985	−	0.293513i
$103$	1.29983	−	4.00047i	0.128076	−	0.394178i	−0.866373	−	0.499398i	$-0.833555\pi$
$103$	1.29983	−	4.00047i	0.128076	−	0.394178i	0.994449	+	0.105220i	$0.0335547\pi$
$104$	−3.86375	+	11.8914i	−0.378872	+	1.16605i
$105$		0			0
$106$	−1.09242	−	3.36213i	−0.106105	−	0.326559i
$107$	−4.01195			−0.387849			−0.193925	−	0.981016i	$-0.562122\pi$
$107$	−4.01195			−0.387849			−0.193925	+	0.981016i	$0.562122\pi$
$108$	0.251013	+	0.772537i	0.0241537	+	0.0743374i
$109$	−7.35691	−	5.34511i	−0.704664	−	0.511969i	0.176784	−	0.984250i	$-0.443431\pi$
$109$	−7.35691	−	5.34511i	−0.704664	−	0.511969i	−0.881448	+	0.472281i	$0.843431\pi$
$110$		0			0
$111$	9.22252	−	6.70056i	0.875363	−	0.635989i
$112$	−4.28492	−	3.11318i	−0.404887	−	0.294168i
$113$	−3.03758	−	2.20693i	−0.285751	−	0.207610i	0.435671	−	0.900106i	$-0.356511\pi$
$113$	−3.03758	−	2.20693i	−0.285751	−	0.207610i	−0.721422	+	0.692496i	$0.756511\pi$
$114$	−5.26275	+	3.82361i	−0.492902	+	0.358114i
$115$		0			0
$116$	−3.47254	−	2.52295i	−0.322417	−	0.234250i
$117$	1.26065	+	3.87988i	0.116547	+	0.358695i
$118$	3.47260			0.319678
$119$	−4.41476	−	13.5872i	−0.404700	−	1.24554i
$120$		0			0
$121$	−2.99171	+	9.20755i	−0.271974	+	0.837050i
$122$	4.62901	−	14.2466i	0.419091	−	1.28983i
$123$	7.67919	−	5.57926i	0.692409	−	0.503065i
$124$	0.478668			0.0429856
$125$		0			0
$126$	−3.36454			−0.299737
$127$	−9.18904	+	6.67623i	−0.815395	+	0.592419i	−0.915390	−	0.402569i	$-0.868117\pi$
$127$	−9.18904	+	6.67623i	−0.815395	+	0.592419i	0.0999946	+	0.994988i	$0.468117\pi$
$128$	0.0861909	−	0.265268i	0.00761827	−	0.0234466i
$129$	−0.750768	+	2.31063i	−0.0661014	+	0.203439i
$130$		0			0
$131$	−0.642289	−	1.97676i	−0.0561170	−	0.172711i	0.919069	−	0.394096i	$-0.128942\pi$
$131$	−0.642289	−	1.97676i	−0.0561170	−	0.172711i	−0.975186	+	0.221385i	$0.928942\pi$
$132$	−0.932764			−0.0811867
$133$	5.69448	+	17.5258i	0.493774	+	1.51968i
$134$	−2.78500	−	2.02342i	−0.240587	−	0.174797i
$135$		0			0
$136$	11.4743	−	8.33657i	0.983914	−	0.714855i
$137$	15.6975	+	11.4049i	1.34113	+	0.974387i	0.999402	+	0.0345870i	$0.0110116\pi$
$137$	15.6975	+	11.4049i	1.34113	+	0.974387i	0.341726	+	0.939800i	$0.388988\pi$
$138$	−2.05051	−	1.48979i	−0.174551	−	0.126819i
$139$	13.8830	−	10.0866i	1.17754	−	0.855531i	0.185646	−	0.982617i	$-0.440562\pi$
$139$	13.8830	−	10.0866i	1.17754	−	0.855531i	0.991892	+	0.127086i	$0.0405624\pi$
$140$		0			0
$141$	4.89454	+	3.55609i	0.412194	+	0.299477i
$142$	2.17741	+	6.70137i	0.182724	+	0.562367i
$143$	−4.68458			−0.391744
$144$	−0.530147	−	1.63162i	−0.0441789	−	0.135969i
$145$		0			0
$146$	2.42812	−	7.47300i	0.200953	−	0.618470i
$147$	−0.782147	+	2.40720i	−0.0645104	+	0.198542i
$148$	7.49140	−	5.44282i	0.615789	−	0.447397i
$149$	0.210127			0.0172143			0.00860714	−	0.999963i	$-0.497260\pi$
$149$	0.210127			0.0172143			0.00860714	+	0.999963i	$0.497260\pi$
$150$		0			0
$151$	−4.05924			−0.330336			−0.165168	−	0.986265i	$-0.552817\pi$
$151$	−4.05924			−0.330336			−0.165168	+	0.986265i	$0.552817\pi$
$152$	−14.8004	+	10.7531i	−1.20047	+	0.872194i
$153$	1.43000	−	4.40109i	0.115609	−	0.355807i
$154$	1.19390	−	3.67444i	0.0962070	−	0.296095i
$155$		0			0
$156$	1.02402	+	3.15160i	0.0819869	+	0.252330i
$157$	0.440336			0.0351426			0.0175713	−	0.999846i	$-0.494407\pi$
$157$	0.440336			0.0351426			0.0175713	+	0.999846i	$0.494407\pi$
$158$	−4.15490	−	12.7875i	−0.330546	−	1.01732i
$159$	−2.62429	−	1.90666i	−0.208119	−	0.151208i
$160$		0			0
$161$	−5.80871	+	4.22027i	−0.457790	+	0.332604i
$162$	−0.881682	−	0.640580i	−0.0692715	−	0.0503287i
$163$	−2.62210	−	1.90506i	−0.205378	−	0.149216i	0.480342	−	0.877081i	$-0.340513\pi$
$163$	−2.62210	−	1.90506i	−0.205378	−	0.149216i	−0.685720	+	0.727865i	$0.740513\pi$
$164$	6.23776	−	4.53200i	0.487087	−	0.353889i
$165$		0			0
$166$	−10.9277	−	7.93941i	−0.848151	−	0.616218i
$167$	−4.93207	−	15.1793i	−0.381655	−	1.17461i	−0.938878	−	0.344250i	$-0.888133\pi$
$167$	−4.93207	−	15.1793i	−0.381655	−	1.17461i	0.557223	−	0.830363i	$-0.311867\pi$
$168$	−9.46207			−0.730015
$169$	1.12565	+	3.46438i	0.0865882	+	0.266491i
$170$		0			0
$171$	−1.84452	+	5.67685i	−0.141054	+	0.434119i
$172$	−0.609844	+	1.87691i	−0.0465002	+	0.143113i
$173$	−0.454497	+	0.330212i	−0.0345548	+	0.0251055i	−0.604929	−	0.796280i	$-0.706798\pi$
$173$	−0.454497	+	0.330212i	−0.0345548	+	0.0251055i	0.570374	+	0.821385i	$0.306798\pi$
$174$	5.75879			0.436573
$175$		0			0
$176$	1.97003			0.148497
$177$	2.57785	−	1.87292i	0.193763	−	0.140777i
$178$	0.365073	−	1.12358i	0.0273634	−	0.0842159i
$179$	4.92532	−	15.1586i	0.368136	−	1.13301i	−0.579858	−	0.814718i	$-0.696892\pi$
$179$	4.92532	−	15.1586i	0.368136	−	1.13301i	0.947994	−	0.318288i	$-0.103108\pi$
$180$		0			0
$181$	−6.64001	−	20.4358i	−0.493548	−	1.51898i	−0.819208	−	0.573497i	$-0.805586\pi$
$181$	−6.64001	−	20.4358i	−0.493548	−	1.51898i	0.325660	−	0.945487i	$-0.394414\pi$
$182$	−13.7258			−1.01742
$183$	−4.24750	−	13.0725i	−0.313984	−	0.966344i
$184$	−5.76665	−	4.18972i	−0.425123	−	0.308870i
$185$		0			0
$186$	−0.519557	+	0.377480i	−0.0380958	+	0.0276782i
$187$	4.29903	+	3.12343i	0.314376	+	0.228408i
$188$	3.97580	+	2.88859i	0.289965	+	0.210672i
$189$	−2.49763	+	1.81464i	−0.181676	+	0.131995i
$190$		0			0
$191$	14.8810	+	10.8117i	1.07675	+	0.782304i	0.977113	−	0.212720i	$-0.0682323\pi$
$191$	14.8810	+	10.8117i	1.07675	+	0.782304i	0.0996355	+	0.995024i	$0.468232\pi$
$192$	−2.49498	−	7.67876i	−0.180060	−	0.554167i
$193$	−2.02523			−0.145780			−0.0728898	−	0.997340i	$-0.523222\pi$
$193$	−2.02523			−0.145780			−0.0728898	+	0.997340i	$0.523222\pi$
$194$	1.52266	+	4.68626i	0.109320	+	0.336454i
$195$		0			0
$196$	−0.635333	+	1.95535i	−0.0453809	+	0.139668i
$197$	3.56774	−	10.9804i	0.254191	−	0.782319i	−0.739797	−	0.672830i	$-0.765079\pi$
$197$	3.56774	−	10.9804i	0.254191	−	0.782319i	0.993988	−	0.109489i	$-0.0349214\pi$
$198$	1.01244	−	0.735584i	0.0719513	−	0.0522757i
$199$	22.9779			1.62886			0.814431	−	0.580260i	$-0.197049\pi$
$199$	22.9779			1.62886			0.814431	+	0.580260i	$0.197049\pi$
$200$		0			0
$201$	−3.15873			−0.222800
$202$	5.83085	−	4.23636i	0.410257	−	0.298069i
$203$	5.04115	−	15.5151i	0.353820	−	1.08894i
$204$	1.16158	−	3.57497i	0.0813268	−	0.250298i
$205$		0			0
$206$	1.41658	+	4.35979i	0.0986978	+	0.303761i
$207$	−2.32568			−0.161646
$208$	−2.16276	−	6.65628i	−0.149960	−	0.461530i
$209$	−5.54520	−	4.02882i	−0.383570	−	0.278680i
$210$		0			0
$211$	5.56717	−	4.04479i	0.383260	−	0.278455i	−0.379428	−	0.925221i	$-0.623879\pi$
$211$	5.56717	−	4.04479i	0.383260	−	0.278455i	0.762688	+	0.646767i	$0.223879\pi$
$212$	−2.13169	−	1.54876i	−0.146405	−	0.106370i
$213$	5.23071	+	3.80033i	0.358402	+	0.260394i
$214$	3.53726	−	2.56997i	0.241802	−	0.175680i
$215$		0			0
$216$	−2.47955	−	1.80150i	−0.168712	−	0.122576i
$217$	0.562179	+	1.73021i	0.0381632	+	0.117454i
$218$	9.91043			0.671219
$219$	−2.22801	−	6.85710i	−0.150555	−	0.463360i
$220$		0			0
$221$	5.83375	−	17.9544i	0.392420	−	1.20775i
$222$	−3.83910	+	11.8155i	−0.257663	+	0.793006i
$223$	−6.57432	+	4.77652i	−0.440249	+	0.319860i	−0.785734	−	0.618565i	$-0.787714\pi$
$223$	−6.57432	+	4.77652i	−0.440249	+	0.319860i	0.345485	+	0.938424i	$0.387714\pi$
$224$	−13.1520			−0.878753
$225$		0			0
$226$	4.09189			0.272188
$227$	−20.7351	+	15.0649i	−1.37624	+	0.999895i	−0.379017	+	0.925390i	$0.623738\pi$
$227$	−20.7351	+	15.0649i	−1.37624	+	0.999895i	−0.997221	+	0.0745050i	$0.976262\pi$
$228$	−1.49829	+	4.61127i	−0.0992268	+	0.305389i
$229$	0.381062	−	1.17279i	0.0251813	−	0.0775001i	−0.937676	−	0.347510i	$-0.887027\pi$
$229$	0.381062	−	1.17279i	0.0251813	−	0.0775001i	0.962857	+	0.270010i	$0.0870271\pi$
$230$		0			0
$231$	−1.09550	−	3.37160i	−0.0720786	−	0.221835i
$232$	16.1954			1.06328
$233$	−0.927012	−	2.85305i	−0.0607306	−	0.186909i	0.916088	−	0.400976i	$-0.131329\pi$
$233$	−0.927012	−	2.85305i	−0.0607306	−	0.186909i	−0.976819	+	0.214067i	$0.931329\pi$
$234$	−3.59686	−	2.61327i	−0.235134	−	0.170835i
$235$		0			0
$236$	2.09397	−	1.52136i	0.136306	−	0.0990320i
$237$	−9.98116	−	7.25174i	−0.648346	−	0.471051i
$238$	12.5961	+	9.15162i	0.816485	+	0.593211i
$239$	−17.9069	+	13.0101i	−1.15830	+	0.841554i	−0.989562	−	0.144107i	$-0.953969\pi$
$239$	−17.9069	+	13.0101i	−1.15830	+	0.841554i	−0.168738	+	0.985661i	$0.553969\pi$
$240$		0			0
$241$	10.8734	+	7.89999i	0.700418	+	0.508883i	0.880068	−	0.474847i	$-0.157497\pi$
$241$	10.8734	+	7.89999i	0.700418	+	0.508883i	−0.179651	+	0.983730i	$0.557497\pi$
$242$	−3.26043	−	10.0346i	−0.209588	−	0.645046i
$243$	−1.00000			−0.0641500
$244$	−3.45022	−	10.6187i	−0.220877	−	0.679791i
$245$		0			0
$246$	−3.19665	+	9.83827i	−0.203811	+	0.627265i
$247$	−7.52479	+	23.1589i	−0.478791	+	1.47357i
$248$	−1.46115	+	1.06159i	−0.0927829	+	0.0674107i
$249$	−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	$0.296818\pi$
$252$	−2.02881	+	1.47402i	−0.127803	+	0.0928544i
$253$	0.825262	−	2.53990i	0.0518838	−	0.159682i
$254$	3.82516	−	11.7726i	0.240012	−	0.738680i
$255$		0			0
$256$	−4.89603	−	15.0684i	−0.306002	−	0.941776i
$257$	7.06320			0.440590			0.220295	−	0.975433i	$-0.429298\pi$
$257$	7.06320			0.440590			0.220295	+	0.975433i	$0.429298\pi$
$258$	−0.818201	−	2.51816i	−0.0509390	−	0.156774i
$259$	28.4722	+	20.6863i	1.76918	+	1.28538i
$260$		0			0
$261$	4.27498	−	3.10596i	0.264615	−	0.192254i
$262$	1.83257	+	1.33144i	0.113216	+	0.0822566i
$263$	−16.5328	−	12.0118i	−1.01945	−	0.740677i	−0.0532829	−	0.998579i	$-0.516969\pi$
$263$	−16.5328	−	12.0118i	−1.01945	−	0.740677i	−0.966171	+	0.257903i	$0.916969\pi$
$264$	2.84729	−	2.06868i	0.175239	−	0.127318i
$265$		0			0
$266$	−16.2474	−	11.8044i	−0.996192	−	0.723776i
$267$	−0.334985	−	1.03098i	−0.0205008	−	0.0630949i
$268$	−2.56582			−0.156732
$269$	6.54880	+	20.1551i	0.399287	+	1.22888i	0.925572	+	0.378571i	$0.123584\pi$
$269$	6.54880	+	20.1551i	0.399287	+	1.22888i	−0.526285	+	0.850308i	$0.676416\pi$
$270$		0			0
$271$	3.07570	−	9.46603i	0.186835	−	0.575020i	−0.813140	−	0.582069i	$-0.802244\pi$
$271$	3.07570	−	9.46603i	0.186835	−	0.575020i	0.999975	+	0.00704817i	$0.00224352\pi$
$272$	−2.45330	+	7.55047i	−0.148753	+	0.457814i
$273$	−10.1892	+	7.40289i	−0.616679	+	0.448043i
$274$	−21.1460			−1.27747
$275$		0			0
$276$	−1.88914			−0.113713
$277$	15.1569	−	11.0121i	0.910689	−	0.661654i	−0.0304998	−	0.999535i	$-0.509710\pi$
$277$	15.1569	−	11.0121i	0.910689	−	0.661654i	0.941189	+	0.337880i	$0.109710\pi$
$278$	−5.77912	+	17.7863i	−0.346608	+	1.06675i
$279$	−0.182097	+	0.560438i	−0.0109019	+	0.0335525i
$280$		0			0
$281$	8.98981	+	27.6678i	0.536287	+	1.65052i	0.740852	+	0.671668i	$0.234422\pi$
$281$	8.98981	+	27.6678i	0.536287	+	1.65052i	−0.204565	+	0.978853i	$0.565578\pi$
$282$	−6.59339			−0.392630
$283$	2.21876	+	6.82865i	0.131892	+	0.405921i	0.995094	−	0.0989379i	$-0.0315445\pi$
$283$	2.21876	+	6.82865i	0.131892	+	0.405921i	−0.863202	+	0.504859i	$0.831545\pi$
$284$	4.24887	+	3.08699i	0.252124	+	0.183179i
$285$		0			0
$286$	4.13031	−	3.00084i	0.244230	−	0.177444i
$287$	23.7075	+	17.2245i	1.39941	+	1.01673i
$288$	−3.44649	−	2.50402i	−0.203087	−	0.147551i
$289$	−3.57138	+	2.59476i	−0.210081	+	0.152633i
$290$		0			0
$291$	3.65783	+	2.65757i	0.214426	+	0.155789i
$292$	−1.80980	−	5.56998i	−0.105910	−	0.325958i
$293$	−1.79825			−0.105055			−0.0525276	−	0.998619i	$-0.516728\pi$
$293$	−1.79825			−0.105055			−0.0525276	+	0.998619i	$0.516728\pi$
$294$	−0.852398	−	2.62341i	−0.0497129	−	0.153001i
$295$		0			0
$296$	−10.7967	+	33.2287i	−0.627544	+	1.93138i
$297$	0.354847	−	1.09211i	0.0205903	−	0.0633705i
$298$	−0.185265	+	0.134603i	−0.0107321	+	0.00779735i
$299$	−9.48773			−0.548689
$300$		0			0
$301$	−7.50057			−0.432326
$302$	3.57896	−	2.60027i	0.205946	−	0.149629i
$303$	2.04363	−	6.28965i	0.117403	−	0.361331i
$304$	3.16444	−	9.73915i	0.181493	−	0.558579i
$305$		0			0
$306$	1.55844	+	4.79639i	0.0890902	+	0.274191i
$307$	−5.98864			−0.341790			−0.170895	−	0.985289i	$-0.554666\pi$
$307$	−5.98864			−0.341790			−0.170895	+	0.985289i	$0.554666\pi$
$308$	−0.889867	−	2.73873i	−0.0507049	−	0.156054i
$309$	3.40300	+	2.47242i	0.193590	+	0.140651i
$310$		0			0
$311$	−19.3099	+	14.0295i	−1.09497	+	0.795539i	−0.980231	−	0.197857i	$-0.936602\pi$
$311$	−19.3099	+	14.0295i	−1.09497	+	0.795539i	−0.114735	+	0.993396i	$0.536602\pi$
$312$	−10.1154	−	7.34929i	−0.572673	−	0.416072i
$313$	4.65924	+	3.38513i	0.263356	+	0.191339i	0.711625	−	0.702559i	$-0.247959\pi$
$313$	4.65924	+	3.38513i	0.263356	+	0.191339i	−0.448269	+	0.893898i	$0.647959\pi$
$314$	−0.388236	+	0.282070i	−0.0219094	+	0.0159181i
$315$		0			0
$316$	−8.10763	−	5.89054i	−0.456090	−	0.331369i
$317$	3.78487	+	11.6486i	0.212580	+	0.654253i	0.999317	+	0.0369645i	$0.0117688\pi$
$317$	3.78487	+	11.6486i	0.212580	+	0.654253i	−0.786737	+	0.617288i	$0.788231\pi$
$318$	3.53515			0.198242
$319$	1.87507	+	5.77088i	0.104984	+	0.323107i
$320$		0			0
$321$	1.23976	−	3.81559i	0.0691966	−	0.212965i
$322$	2.41801	−	7.44188i	0.134751	−	0.414720i
$323$	22.3466	−	16.2358i	1.24340	−	0.903383i
$324$	−0.812294			−0.0451274
$325$		0			0
$326$	3.53220			0.195631
$327$	7.35691	−	5.34511i	0.406838	−	0.295585i
$328$	−8.98991	+	27.6681i	−0.496385	+	1.52772i
$329$	−5.77175	+	17.7636i	−0.318207	+	0.979340i
$330$		0			0
$331$	−1.86306	−	5.73391i	−0.102403	−	0.315164i	0.886709	−	0.462328i	$-0.152986\pi$
$331$	−1.86306	−	5.73391i	−0.102403	−	0.315164i	−0.989112	+	0.147163i	$0.952986\pi$
$332$	−10.0676			−0.552534
$333$	3.52269	+	10.8417i	0.193042	+	0.594123i
$334$	14.0721	+	10.2240i	0.769991	+	0.559431i
$335$		0			0
$336$	4.28492	−	3.11318i	0.233762	−	0.169838i
$337$	4.47454	+	3.25094i	0.243744	+	0.177090i	0.702949	−	0.711240i	$-0.251866\pi$
$337$	4.47454	+	3.25094i	0.243744	+	0.177090i	−0.459206	+	0.888330i	$0.651866\pi$
$338$	−3.21168	−	2.33342i	−0.174692	−	0.126921i
$339$	3.03758	−	2.20693i	0.164978	−	0.119864i
$340$		0			0
$341$	−0.547441	−	0.397739i	−0.0296456	−	0.0215388i
$342$	−2.01019	−	6.18674i	−0.108699	−	0.334540i
$343$	13.7967			0.744949
$344$	−2.30102	−	7.08182i	−0.124063	−	0.381826i
$345$		0			0
$346$	0.189195	−	0.582283i	0.0101712	−	0.0313038i
$347$	8.01729	−	24.6747i	0.430391	−	1.32461i	−0.467346	−	0.884075i	$-0.654790\pi$
$347$	8.01729	−	24.6747i	0.430391	−	1.32461i	0.897737	−	0.440532i	$-0.145210\pi$
$348$	3.47254	−	2.52295i	0.186148	−	0.135244i
$349$	−19.0025			−1.01718			−0.508591	−	0.861008i	$-0.669833\pi$
$349$	−19.0025			−1.01718			−0.508591	+	0.861008i	$0.669833\pi$
$350$		0			0
$351$	−4.07954			−0.217750
$352$	3.95764	−	2.87539i	0.210943	−	0.153259i
$353$	−2.53126	+	7.79043i	−0.134726	+	0.414642i	−0.995547	−	0.0942642i	$-0.969950\pi$
$353$	−2.53126	+	7.79043i	−0.134726	+	0.414642i	0.860822	+	0.508907i	$0.169950\pi$
$354$	−1.07309	+	3.30263i	−0.0570341	+	0.175533i
$355$		0			0
$356$	−0.272106	−	0.837457i	−0.0144216	−	0.0443852i
$357$	14.2865			0.756120
$358$	5.36771	+	16.5201i	0.283692	+	0.873116i
$359$	21.6701	+	15.7442i	1.14370	+	0.830948i	0.987631	−	0.156797i	$-0.0501170\pi$
$359$	21.6701	+	15.7442i	1.14370	+	0.830948i	0.156071	+	0.987746i	$0.450117\pi$
$360$		0			0
$361$	−13.4530	+	9.77419i	−0.708053	+	0.514431i
$362$	18.9452	+	13.7645i	0.995736	+	0.723444i
$363$	−7.83241	−	5.69058i	−0.411095	−	0.298678i
$364$	−8.27662	+	6.01332i	−0.433813	+	0.315184i
$365$		0			0
$366$	12.1189	+	8.80489i	0.633465	+	0.460239i
$367$	−5.82600	−	17.9306i	−0.304114	−	0.935968i	−0.980006	−	0.198967i	$-0.936241\pi$
$367$	−5.82600	−	17.9306i	−0.304114	−	0.935968i	0.675892	−	0.737001i	$-0.263759\pi$
$368$	3.98992			0.207989
$369$	2.93319	+	9.02743i	0.152696	+	0.469949i
$370$		0			0
$371$	3.09462	−	9.52426i	0.160665	−	0.494475i
$372$	−0.147916	+	0.455240i	−0.00766911	+	0.0236031i
$373$	−14.4391	+	10.4906i	−0.747627	+	0.543183i	−0.895090	−	0.445885i	$-0.852889\pi$
$373$	−14.4391	+	10.4906i	−0.747627	+	0.543183i	0.147464	+	0.989067i	$0.452889\pi$
$374$	−5.79118			−0.299455
$375$		0			0
$376$	−18.5425			−0.956259
$377$	17.4400	−	12.6709i	0.898204	−	0.652583i
$378$	1.03970	−	3.19987i	0.0534764	−	0.164583i
$379$	3.88290	−	11.9503i	0.199451	−	0.613848i	−0.800445	−	0.599407i	$-0.795403\pi$
$379$	3.88290	−	11.9503i	0.199451	−	0.613848i	0.999896	−	0.0144408i	$-0.00459680\pi$
$380$		0			0
$381$	−3.50990	−	10.8024i	−0.179818	−	0.553422i
$382$	−20.0460			−1.02564
$383$	−2.32918	−	7.16849i	−0.119016	−	0.366292i	0.873748	−	0.486379i	$-0.161683\pi$
$383$	−2.32918	−	7.16849i	−0.119016	−	0.366292i	−0.992763	+	0.120087i	$0.961683\pi$
$384$	0.225651	+	0.163945i	0.0115152	+	0.00836628i
$385$		0			0
$386$	1.78561	−	1.29732i	0.0908854	−	0.0660321i
$387$	−1.96554	−	1.42805i	−0.0999138	−	0.0725916i
$388$	2.97123	+	2.15872i	0.150841	+	0.109593i
$389$	11.1103	−	8.07211i	0.563315	−	0.409272i	−0.269356	−	0.963041i	$-0.586811\pi$
$389$	11.1103	−	8.07211i	0.563315	−	0.409272i	0.832671	+	0.553768i	$0.186811\pi$
$390$		0			0
$391$	8.70687	+	6.32591i	0.440325	+	0.319915i
$392$	−2.39719	−	7.37781i	−0.121077	−	0.372636i
$393$	2.07849			0.104846
$394$	3.88819	+	11.9666i	0.195884	+	0.602869i
$395$		0			0
$396$	0.288240	−	0.887112i	0.0144846	−	0.0445790i
$397$	−4.01790	+	12.3658i	−0.201653	+	0.620623i	0.798182	+	0.602417i	$0.205796\pi$
$397$	−4.01790	+	12.3658i	−0.201653	+	0.620623i	−0.999834	+	0.0182061i	$0.994204\pi$
$398$	−20.2592	+	14.7192i	−1.01550	+	0.737807i
$399$	−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	$0.551653\pi$
$402$	2.78500	−	2.02342i	0.138903	−	0.100919i
$403$	−0.742874	+	2.28633i	−0.0370052	+	0.113890i
$404$	1.66003	−	5.10904i	0.0825894	−	0.254184i
$405$		0			0
$406$	5.49395	+	16.9086i	0.272660	+	0.839161i
$407$	−13.0903			−0.648864
$408$	4.38280	+	13.4889i	0.216981	+	0.667798i
$409$	0.899629	+	0.653619i	0.0444838	+	0.0323194i	0.609805	−	0.792552i	$-0.291248\pi$
$409$	0.899629	+	0.653619i	0.0444838	+	0.0323194i	−0.565321	+	0.824871i	$0.691248\pi$
$410$		0			0
$411$	−15.6975	+	11.4049i	−0.774301	+	0.562562i
$412$	2.76424	+	2.00833i	0.136184	+	0.0989435i
$413$	7.95845	+	5.78215i	0.391610	+	0.284521i
$414$	2.05051	−	1.48979i	0.100777	−	0.0732190i
$415$		0			0
$416$	−14.0601	−	10.2153i	−0.689354	−	0.500845i
$417$	5.30282	+	16.3204i	0.259680	+	0.799213i
$418$	7.46989			0.365364
$419$	3.64430	+	11.2160i	0.178036	+	0.547938i	0.999759	−	0.0219489i	$-0.00698712\pi$
$419$	3.64430	+	11.2160i	0.178036	+	0.547938i	−0.821723	+	0.569887i	$0.806987\pi$
$420$		0			0
$421$	−3.12900	+	9.63007i	−0.152498	+	0.469341i	−0.997899	−	0.0647918i	$-0.979362\pi$
$421$	−3.12900	+	9.63007i	−0.152498	+	0.469341i	0.845401	+	0.534133i	$0.179362\pi$
$422$	−2.31747	+	7.13244i	−0.112813	+	0.347202i
$423$	−4.89454	+	3.55609i	−0.237981	+	0.172903i
$424$	9.94189			0.482821
$425$		0			0
$426$	−7.04624			−0.341391
$427$	34.3305	−	24.9425i	1.66137	−	1.20705i
$428$	1.00705	−	3.09938i	0.0486775	−	0.149814i
$429$	1.44761	−	4.45530i	0.0698914	−	0.215104i
$430$		0			0
$431$	−1.75911	−	5.41397i	−0.0847332	−	0.260782i	0.899709	−	0.436490i	$-0.143779\pi$
$431$	−1.75911	−	5.41397i	−0.0847332	−	0.260782i	−0.984442	+	0.175708i	$0.943779\pi$
$432$	1.71559			0.0825415
$433$	−10.2126	−	31.4313i	−0.490788	−	1.51049i	−0.823419	−	0.567434i	$-0.807936\pi$
$433$	−10.2126	−	31.4313i	−0.490788	−	1.51049i	0.332631	−	0.943057i	$-0.392064\pi$
$434$	−1.60400	−	1.16537i	−0.0769945	−	0.0559397i
$435$		0			0
$436$	5.97597	−	4.34180i	0.286197	−	0.207934i
$437$	−11.2308	−	8.15963i	−0.537240	−	0.390328i
$438$	6.35691	+	4.61857i	0.303745	+	0.220684i
$439$	−9.27430	+	6.73818i	−0.442638	+	0.321596i	−0.786682	−	0.617358i	$-0.788203\pi$
$439$	−9.27430	+	6.73818i	−0.442638	+	0.321596i	0.344044	+	0.938954i	$0.388203\pi$
$440$		0			0
$441$	−2.04769	−	1.48773i	−0.0975089	−	0.0708443i
$442$	6.35773	+	19.5671i	0.302406	+	0.930711i
$443$	17.8993			0.850422			0.425211	−	0.905094i	$-0.360200\pi$
$443$	17.8993			0.850422			0.425211	+	0.905094i	$0.360200\pi$
$444$	2.86146	+	8.80667i	0.135799	+	0.417946i
$445$		0			0
$446$	2.73672	−	8.42275i	0.129587	−	0.398829i
$447$	−0.0649328	+	0.199843i	−0.00307122	+	0.00945223i
$448$	20.1657	−	14.6512i	0.952740	−	0.692206i
$449$	−6.82040			−0.321874			−0.160937	−	0.986965i	$-0.551452\pi$
$449$	−6.82040			−0.321874			−0.160937	+	0.986965i	$0.551452\pi$
$450$		0			0
$451$	−10.8998			−0.513249
$452$	2.46740	−	1.79267i	0.116057	−	0.0843203i
$453$	1.25437	−	3.86057i	0.0589356	−	0.181385i
$454$	8.63148	−	26.5650i	0.405096	−	1.24676i
$455$		0			0
$456$	−5.65325	−	17.3989i	−0.264738	−	0.814779i
$457$	2.76381			0.129286			0.0646429	−	0.997908i	$-0.479409\pi$
$457$	2.76381			0.129286			0.0646429	+	0.997908i	$0.479409\pi$
$458$	0.415289	+	1.27813i	0.0194052	+	0.0597230i
$459$	3.74379	+	2.72002i	0.174745	+	0.126960i
$460$		0			0
$461$	7.25254	−	5.26928i	0.337784	−	0.245415i	−0.405942	−	0.913899i	$-0.633057\pi$
$461$	7.25254	−	5.26928i	0.337784	−	0.245415i	0.743726	+	0.668484i	$0.233057\pi$
$462$	3.12566	+	2.27093i	0.145419	+	0.105653i
$463$	−10.6480	−	7.73623i	−0.494855	−	0.359533i	0.312193	−	0.950019i	$-0.398936\pi$
$463$	−10.6480	−	7.73623i	−0.494855	−	0.359533i	−0.807048	+	0.590485i	$0.798936\pi$
$464$	−7.33412	+	5.32855i	−0.340478	+	0.247372i
$465$		0			0
$466$	2.64494	+	1.92166i	0.122524	+	0.0890191i
$467$	−6.73671	−	20.7335i	−0.311738	−	0.959430i	−0.977076	−	0.212889i	$-0.931713\pi$
$467$	−6.73671	−	20.7335i	−0.311738	−	0.959430i	0.665339	−	0.746542i	$-0.268287\pi$
$468$	−3.31379			−0.153180
$469$	−3.01347	−	9.27450i	−0.139149	−	0.428257i
$470$		0			0
$471$	−0.136071	+	0.418784i	−0.00626983	+	0.0192966i
$472$	−3.01785	+	9.28798i	−0.138908	+	0.427514i
$473$	2.25704	−	1.63984i	0.103779	−	0.0753998i
$474$	13.4455			0.617574
$475$		0			0
$476$	11.6048			0.531905
$477$	2.62429	−	1.90666i	0.120158	−	0.0872998i
$478$	7.45417	−	22.9416i	0.340946	−	1.04932i
$479$	13.2102	−	40.6567i	0.603588	−	1.85765i	0.0973673	−	0.995249i	$-0.468958\pi$
$479$	13.2102	−	40.6567i	0.603588	−	1.85765i	0.506221	−	0.862404i	$-0.331042\pi$
$480$		0			0
$481$	14.3710	+	44.2293i	0.655260	+	2.01668i
$482$	−14.6475			−0.667174
$483$	−2.21873	−	6.82854i	−0.100956	−	0.310709i
$484$	−6.36221	−	4.62242i	−0.289192	−	0.210110i
$485$		0			0
$486$	0.881682	−	0.640580i	0.0399939	−	0.0290573i
$487$	−9.18213	−	6.67121i	−0.416082	−	0.302301i	0.359978	−	0.932961i	$-0.382784\pi$
$487$	−9.18213	−	6.67121i	−0.416082	−	0.302301i	−0.776059	+	0.630660i	$0.782784\pi$
$488$	34.0819	+	24.7619i	1.54281	+	1.12092i
$489$	2.62210	−	1.90506i	0.118575	−	0.0861500i
$490$		0			0
$491$	−13.4739	−	9.78936i	−0.608068	−	0.441788i	0.240665	−	0.970608i	$-0.422634\pi$
$491$	−13.4739	−	9.78936i	−0.608068	−	0.441788i	−0.848734	+	0.528821i	$0.822634\pi$
$492$	2.38261	+	7.33292i	0.107416	+	0.330594i
$493$	−24.4529			−1.10130
$494$	−8.20067	−	25.2391i	−0.368965	−	1.13556i
$495$		0			0
$496$	0.312405	−	0.961483i	0.0140274	−	0.0431718i
$497$	−6.16817	+	18.9837i	−0.276680	+	0.851534i
$498$	10.9277	−	7.93941i	0.489680	−	0.355773i
$499$	−12.2321			−0.547584			−0.273792	−	0.961789i	$-0.588278\pi$
$499$	−12.2321			−0.547584			−0.273792	+	0.961789i	$0.588278\pi$
$500$		0			0
$501$	15.9605			0.713063
$502$	−16.6460	+	12.0941i	−0.742949	+	0.539784i
$503$	0.404709	−	1.24557i	0.0180451	−	0.0555371i	−0.941629	−	0.336654i	$-0.890705\pi$
$503$	0.404709	−	1.24557i	0.0180451	−	0.0555371i	0.959674	+	0.281117i	$0.0907048\pi$
$504$	2.92394	−	8.99897i	0.130243	−	0.400846i
$505$		0			0
$506$	0.899387	+	2.76803i	0.0399826	+	0.123054i
$507$	−3.64267			−0.161777
$508$	−2.85107	−	8.77469i	−0.126496	−	0.389314i
$509$	−14.3453	−	10.4225i	−0.635844	−	0.461968i	0.222576	−	0.974915i	$-0.428553\pi$
$509$	−14.3453	−	10.4225i	−0.635844	−	0.461968i	−0.858420	+	0.512948i	$0.828553\pi$
$510$		0			0
$511$	18.0079	−	13.0835i	0.796622	−	0.578780i
$512$	14.4206	+	10.4772i	0.637305	+	0.463029i
$513$	−4.82901	−	3.50848i	−0.213206	−	0.154903i
$514$	−6.22750	+	4.52454i	−0.274683	+	0.199569i
$515$		0			0
$516$	−1.59659	−	1.15999i	−0.0702860	−	0.0510658i
$517$	−2.14682	−	6.60723i	−0.0944170	−	0.290586i
$518$	−38.3546			−1.68521
$519$	−0.173602	−	0.534294i	−0.00762030	−	0.0234529i
$520$		0			0
$521$	8.11527	−	24.9762i	0.355536	−	1.09423i	−0.600162	−	0.799879i	$-0.704897\pi$
$521$	8.11527	−	24.9762i	0.355536	−	1.09423i	0.955698	−	0.294349i	$-0.0951030\pi$
$522$	−1.77956	+	5.47693i	−0.0778894	+	0.239719i
$523$	−2.06844	+	1.50281i	−0.0904467	+	0.0657134i	−0.632090	−	0.774895i	$-0.717803\pi$
$523$	−2.06844	+	1.50281i	−0.0904467	+	0.0657134i	0.541643	+	0.840609i	$0.317803\pi$
$524$	1.68834			0.0737557
$525$		0			0
$526$	22.2711			0.971068
$527$	2.20614	−	1.60285i	0.0961008	−	0.0698213i
$528$	−0.608773	+	1.87361i	−0.0264934	+	0.0815384i
$529$	−5.43598	+	16.7302i	−0.236347	+	0.727401i
$530$		0			0
$531$	0.984650	+	3.03044i	0.0427302	+	0.131510i
$532$	−14.9687			−0.648977
$533$	11.9661	+	36.8278i	0.518308	+	1.59519i
$534$	0.955775	+	0.694411i	0.0413604	+	0.0300501i
$535$		0			0
$536$	7.83224	−	5.69046i	0.338301	−	0.245790i
$537$	12.8947	+	9.36852i	0.556446	+	0.404282i
$538$	−18.6849	−	13.5754i	−0.805564	−	0.585277i
$539$	2.35138	−	1.70838i	0.101281	−	0.0735849i
$540$		0			0
$541$	−7.59599	−	5.51881i	−0.326577	−	0.237272i	0.412400	−	0.911003i	$-0.364691\pi$
$541$	−7.59599	−	5.51881i	−0.326577	−	0.237272i	−0.738977	+	0.673731i	$0.764691\pi$
$542$	3.35196	+	10.3163i	0.143979	+	0.443121i
$543$	21.4875			0.922118
$544$	6.09194	+	18.7491i	0.261190	+	0.803860i
$545$		0			0
$546$	4.24150	−	13.0540i	0.181519	−	0.558659i
$547$	−10.7708	+	33.1490i	−0.460524	+	1.41735i	0.404000	+	0.914759i	$0.367619\pi$
$547$	−10.7708	+	33.1490i	−0.460524	+	1.41735i	−0.864525	+	0.502590i	$0.832381\pi$
$548$	−12.7510	+	9.26413i	−0.544695	+	0.395744i
$549$	13.7452			0.586631
$550$		0			0
$551$	31.5411			1.34370
$552$	5.76665	−	4.18972i	0.245445	−	0.178326i
$553$	11.7700	−	36.2244i	0.500512	−	1.54042i
$554$	−6.30942	+	19.4184i	−0.268062	+	0.825009i
$555$		0			0
$556$	4.30745	+	13.2570i	0.182676	+	0.562220i
$557$	−14.1466			−0.599411			−0.299705	−	0.954032i	$-0.596888\pi$
$557$	−14.1466			−0.599411			−0.299705	+	0.954032i	$0.596888\pi$
$558$	−0.198453	−	0.610776i	−0.00840119	−	0.0258562i
$559$	−8.01849	−	5.82577i	−0.339146	−	0.246404i
$560$		0			0
$561$	−4.29903	+	3.12343i	−0.181505	+	0.131871i
$562$	−25.6496	−	18.6355i	−1.08196	−	0.786091i
$563$	−30.8926	−	22.4448i	−1.30197	−	0.945936i	−0.301996	−	0.953309i	$-0.597653\pi$
$563$	−30.8926	−	22.4448i	−1.30197	−	0.945936i	−0.999973	+	0.00737325i	$0.997653\pi$
$564$	−3.97580	+	2.88859i	−0.167411	+	0.121632i
$565$		0			0
$566$	−6.33054	−	4.59941i	−0.266092	−	0.193327i
$567$	−0.954011	−	2.93614i	−0.0400647	−	0.123306i
$568$	−19.8161			−0.831465
$569$	9.15622	+	28.1799i	0.383849	+	1.18136i	0.937312	+	0.348491i	$0.113306\pi$
$569$	9.15622	+	28.1799i	0.383849	+	1.18136i	−0.553463	+	0.832873i	$0.686694\pi$
$570$		0			0
$571$	10.0895	−	31.0524i	0.422234	−	1.29950i	−0.483385	−	0.875408i	$-0.660593\pi$
$571$	10.0895	−	31.0524i	0.422234	−	1.29950i	0.905618	−	0.424093i	$-0.139407\pi$
$572$	1.17589	−	3.61901i	0.0491663	−	0.151318i
$573$	−14.8810	+	10.8117i	−0.621661	+	0.451663i
$574$	−31.9362			−1.33299
$575$		0			0
$576$	8.07392			0.336413
$577$	−18.3188	+	13.3094i	−0.762622	+	0.554077i	−0.899713	−	0.436481i	$-0.856225\pi$
$577$	−18.3188	+	13.3094i	−0.762622	+	0.554077i	0.137091	+	0.990558i	$0.456225\pi$
$578$	1.48667	−	4.57551i	0.0618374	−	0.190316i
$579$	0.625832	−	1.92611i	0.0260087	−	0.0800465i
$580$		0			0
$581$	−11.8241	−	36.3909i	−0.490547	−	1.50975i
$582$	−4.92742			−0.204248
$583$	1.15105	+	3.54257i	0.0476717	+	0.146718i
$584$	17.8775	+	12.9888i	0.739776	+	0.537479i
$585$		0			0
$586$	1.58549	−	1.15193i	0.0654960	−	0.0475856i
$587$	−33.6281	−	24.4323i	−1.38798	−	1.00843i	−0.996083	−	0.0884196i	$-0.971818\pi$
$587$	−33.6281	−	24.4323i	−1.38798	−	1.00843i	−0.391899	−	0.920008i	$-0.628182\pi$
$588$	−1.66332	−	1.20847i	−0.0685943	−	0.0498366i
$589$	−2.84564	+	2.06748i	−0.117252	+	0.0851889i
$590$		0			0
$591$	9.34046	+	6.78624i	0.384215	+	0.279149i
$592$	−6.04350	−	18.6000i	−0.248386	−	0.764454i
$593$	2.09050			0.0858465			0.0429233	−	0.999078i	$-0.486333\pi$
$593$	2.09050			0.0858465			0.0429233	+	0.999078i	$0.486333\pi$
$594$	0.386719	+	1.19020i	0.0158673	+	0.0488345i
$595$		0			0
$596$	−0.0527445	+	0.162331i	−0.00216050	+	0.00664933i
$597$	−7.10057	+	21.8533i	−0.290607	+	0.894397i
$598$	8.36516	−	6.07765i	0.342077	−	0.248533i
$599$	17.9768			0.734511			0.367255	−	0.930120i	$-0.380298\pi$
$599$	17.9768			0.734511			0.367255	+	0.930120i	$0.380298\pi$
$600$		0			0
$601$	−1.11000			−0.0452778			−0.0226389	−	0.999744i	$-0.507207\pi$
$601$	−1.11000			−0.0452778			−0.0226389	+	0.999744i	$0.507207\pi$
$602$	6.61312	−	4.80471i	0.269531	−	0.195826i
$603$	0.976103	−	3.00414i	0.0397500	−	0.122338i
$604$	1.01892	−	3.13591i	0.0414593	−	0.127599i
$605$		0			0
$606$	2.22719	+	6.85458i	0.0904733	+	0.278448i
$607$	−12.2310			−0.496441			−0.248220	−	0.968704i	$-0.579846\pi$
$607$	−12.2310			−0.496441			−0.248220	+	0.968704i	$0.579846\pi$
$608$	−7.85783	−	24.1839i	−0.318677	−	0.980788i
$609$	13.1979	+	9.58884i	0.534806	+	0.388560i
$610$		0			0
$611$	−19.9675	+	14.5072i	−0.807798	+	0.586899i
$612$	3.04106	+	2.20946i	0.122927	+	0.0893120i
$613$	10.4991	+	7.62804i	0.424055	+	0.308094i	0.779267	−	0.626692i	$-0.215591\pi$
$613$	10.4991	+	7.62804i	0.424055	+	0.308094i	−0.355213	+	0.934786i	$0.615591\pi$
$614$	5.28008	−	3.83620i	0.213087	−	0.154817i
$615$		0			0
$616$	8.79028	+	6.38651i	0.354171	+	0.257320i
$617$	6.33241	+	19.4891i	0.254933	+	0.784603i	0.993843	+	0.110799i	$0.0353410\pi$
$617$	6.33241	+	19.4891i	0.254933	+	0.784603i	−0.738910	+	0.673804i	$0.764659\pi$
$618$	−4.58415			−0.184402
$619$	−12.6838	−	39.0367i	−0.509804	−	1.56902i	−0.792541	−	0.609819i	$-0.791242\pi$
$619$	−12.6838	−	39.0367i	−0.509804	−	1.56902i	0.282737	−	0.959198i	$-0.408758\pi$
$620$		0			0
$621$	0.718676	−	2.21186i	0.0288395	−	0.0887588i
$622$	8.03822	−	24.7391i	0.322303	−	0.991948i
$623$	2.70752	−	1.96713i	0.108475	−	0.0788114i
$624$	6.99883			0.280177
$625$		0			0
$626$	−6.27641			−0.250856
$627$	5.54520	−	4.02882i	0.221454	−	0.160896i
$628$	−0.110530	+	0.340176i	−0.00441062	+	0.0135745i
$629$	16.3015	−	50.1709i	0.649984	−	2.00045i
$630$		0			0
$631$	4.35319	+	13.3977i	0.173298	+	0.533356i	0.999552	−	0.0299421i	$-0.00953228\pi$
$631$	4.35319	+	13.3977i	0.173298	+	0.533356i	−0.826254	+	0.563298i	$0.809532\pi$
$632$	37.8128			1.50411
$633$	2.12647	+	6.54460i	0.0845196	+	0.260125i
$634$	−10.7989	−	7.84589i	−0.428881	−	0.311600i
$635$		0			0
$636$	2.13169	−	1.54876i	0.0845271	−	0.0614125i
$637$	−8.35362	−	6.06926i	−0.330983	−	0.240473i
$638$	−5.34992	−	3.88695i	−0.211806	−	0.153886i
$639$	−5.23071	+	3.80033i	−0.206924	+	0.150339i
$640$		0			0
$641$	23.0050	+	16.7141i	0.908644	+	0.660168i	0.940671	−	0.339319i	$-0.110197\pi$
$641$	23.0050	+	16.7141i	0.908644	+	0.660168i	−0.0320278	+	0.999487i	$0.510197\pi$
$642$	1.35111	+	4.15830i	0.0533242	+	0.164115i
$643$	−10.8408			−0.427521			−0.213761	−	0.976886i	$-0.568571\pi$
$643$	−10.8408			−0.427521			−0.213761	+	0.976886i	$0.568571\pi$
$644$	−1.80226	−	5.54678i	−0.0710189	−	0.218574i
$645$		0			0
$646$	−9.30232	+	28.6296i	−0.365995	+	1.12642i
$647$	−10.7040	+	32.9435i	−0.420817	+	1.29514i	0.486126	+	0.873889i	$0.338410\pi$
$647$	−10.7040	+	32.9435i	−0.420817	+	1.29514i	−0.906943	+	0.421253i	$0.861590\pi$
$648$	2.47955	−	1.80150i	0.0974059	−	0.0707695i
$649$	−3.65897			−0.143627
$650$		0			0
$651$	−1.81925			−0.0713020
$652$	2.12991	−	1.54747i	0.0834138	−	0.0606037i
$653$	−1.28398	+	3.95170i	−0.0502462	+	0.154642i	−0.973031	−	0.230673i	$-0.925907\pi$
$653$	−1.28398	+	3.95170i	−0.0502462	+	0.154642i	0.922785	+	0.385315i	$0.125907\pi$
$654$	−3.06249	+	9.42538i	−0.119753	+	0.368561i
$655$		0			0
$656$	−5.03216	−	15.4874i	−0.196473	−	0.604681i
$657$	7.20998			0.281288
$658$	−6.29016	−	19.3591i	−0.245216	−	0.754698i
$659$	3.24759	+	2.35951i	0.126508	+	0.0919135i	0.649240	−	0.760584i	$-0.275087\pi$
$659$	3.24759	+	2.35951i	0.126508	+	0.0919135i	−0.522732	+	0.852497i	$0.675087\pi$
$660$		0			0
$661$	−15.9107	+	11.5598i	−0.618853	+	0.449623i	−0.852521	−	0.522694i	$-0.824927\pi$
$661$	−15.9107	+	11.5598i	−0.618853	+	0.449623i	0.233668	+	0.972316i	$0.424927\pi$
$662$	5.31566	+	3.86205i	0.206599	+	0.150103i
$663$	15.2729	+	11.0964i	0.593152	+	0.430950i
$664$	30.7318	−	22.3279i	1.19262	−	0.866492i
$665$		0			0
$666$	−10.0509	−	7.30240i	−0.389464	−	0.282962i
$667$	3.79760	+	11.6878i	0.147044	+	0.452554i
$668$	12.9646			0.501616
$669$	−2.51117	−	7.72858i	−0.0970873	−	0.298804i
$670$		0			0
$671$	−4.87744	+	15.0112i	−0.188292	+	0.579502i
$672$	4.06418	−	12.5083i	0.156779	−	0.482517i
$673$	33.5308	−	24.3615i	1.29252	−	0.939068i	0.292663	−	0.956215i	$-0.405458\pi$
$673$	33.5308	−	24.3615i	1.29252	−	0.939068i	0.999853	+	0.0171473i	$0.00545843\pi$
$674$	−6.02761			−0.232175
$675$		0			0
$676$	−2.95892			−0.113804
$677$	−14.7109	+	10.6881i	−0.565386	+	0.410777i	−0.833426	−	0.552631i	$-0.813624\pi$
$677$	−14.7109	+	10.6881i	−0.565386	+	0.410777i	0.268040	+	0.963408i	$0.413624\pi$
$678$	−1.26446	+	3.89162i	−0.0485614	+	0.149457i
$679$	−4.31339	+	13.2753i	−0.165533	+	0.509457i
$680$		0			0
$681$	−7.92011	−	24.3756i	−0.303499	−	0.934074i
$682$	0.737453			0.0282385
$683$	8.79224	+	27.0597i	0.336426	+	1.03541i	0.966015	+	0.258484i	$0.0832231\pi$
$683$	8.79224	+	27.0597i	0.336426	+	1.03541i	−0.629590	+	0.776928i	$0.716777\pi$
$684$	−3.92258	−	2.84992i	−0.149983	−	0.108969i
$685$		0			0
$686$	−12.1643	+	8.83786i	−0.464434	+	0.337431i
$687$	0.997634	+	0.724824i	0.0380621	+	0.0276537i
$688$	3.37206	+	2.44994i	0.128558	+	0.0934032i
$689$	10.7059	−	7.77828i	0.407862	−	0.296329i
$690$		0			0
$691$	−19.7541	−	14.3522i	−0.751483	−	0.545984i	0.144803	−	0.989460i	$-0.453745\pi$
$691$	−19.7541	−	14.3522i	−0.751483	−	0.545984i	−0.896286	+	0.443476i	$0.853745\pi$
$692$	−0.141016	−	0.434003i	−0.00536063	−	0.0164983i
$693$	3.54511			0.134668
$694$	8.73740	+	26.8910i	0.331667	+	1.02077i
$695$		0			0
$696$	−5.00465	+	15.4027i	−0.189701	+	0.583840i
$697$	13.5736	−	41.7751i	0.514135	−	1.58235i
$698$	16.7542	−	12.1726i	0.634155	−	0.460741i
$699$	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	$0.656764\pi$
$702$	3.59686	−	2.61327i	0.135755	−	0.0986316i
$703$	−21.0269	+	64.7142i	−0.793045	+	2.44074i
$704$	−2.86501	+	8.81759i	−0.107979	+	0.332325i
$705$		0			0
$706$	−2.75862	−	8.49016i	−0.103822	−	0.319531i
$707$	20.4170			0.767858
$708$	0.799825	+	2.46161i	0.0300593	+	0.0925129i
$709$	−29.5804	−	21.4914i	−1.11091	−	0.807126i	−0.128107	−	0.991760i	$-0.540890\pi$
$709$	−29.5804	−	21.4914i	−1.11091	−	0.807126i	−0.982807	+	0.184634i	$0.940890\pi$
$710$		0			0
$711$	9.98116	−	7.25174i	0.374323	−	0.271961i
$712$	2.68792	+	1.95289i	0.100734	+	0.0731876i
$713$	−1.10874	−	0.805546i	−0.0415226	−	0.0301679i
$714$	−12.5961	+	9.15162i	−0.471398	+	0.342491i
$715$		0			0
$716$	10.4743	+	7.60999i	0.391441	+	0.284399i
$717$	−6.83982	−	21.0508i	−0.255438	−	0.786157i
$718$	−29.1915			−1.08942
$719$	−2.23596	−	6.88157i	−0.0833872	−	0.256639i	0.900667	−	0.434511i	$-0.143079\pi$
$719$	−2.23596	−	6.88157i	−0.0833872	−	0.256639i	−0.984054	+	0.177872i	$0.943079\pi$
$720$		0			0
$721$	−4.01289	+	12.3504i	−0.149448	+	0.459954i
$722$	5.60014	−	17.2355i	0.208416	−	0.641437i
$723$	−10.8734	+	7.89999i	−0.404386	+	0.293804i
$724$	17.4542			0.648679
$725$		0			0
$726$	10.5510			0.391583
$727$	−10.7680	+	7.82337i	−0.399361	+	0.290153i	−0.769281	−	0.638911i	$-0.779385\pi$
$727$	−10.7680	+	7.82337i	−0.399361	+	0.290153i	0.369920	+	0.929064i	$0.379385\pi$
$728$	11.9283	−	36.7117i	0.442094	−	1.36062i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	3.47424	+	10.6926i	0.128499	+	0.395480i
$732$	11.1651			0.412675
$733$	−8.89333	−	27.3709i	−0.328483	−	1.01097i	−0.969844	−	0.243727i	$-0.921630\pi$
$733$	−8.89333	−	27.3709i	−0.328483	−	1.01097i	0.641361	−	0.767239i	$-0.278370\pi$
$734$	16.6226	+	12.0771i	0.613553	+	0.445772i
$735$		0			0
$736$	8.01545	−	5.82357i	0.295454	−	0.214660i
$737$	2.93447	+	2.13202i	0.108093	+	0.0785339i
$738$	−8.36893	−	6.08038i	−0.308065	−	0.223822i
$739$	−32.6202	+	23.7000i	−1.19995	+	0.871818i	−0.994280	−	0.106803i	$-0.965939\pi$
$739$	−32.6202	+	23.7000i	−1.19995	+	0.871818i	−0.205674	+	0.978621i	$0.565939\pi$
$740$		0			0
$741$	−19.7002	−	14.3130i	−0.723704	−	0.525802i
$742$	3.37258	+	10.3797i	0.123811	+	0.381051i
$743$	27.8114			1.02030			0.510151	−	0.860085i	$-0.329589\pi$
$743$	27.8114			1.02030			0.510151	+	0.860085i	$0.329589\pi$
$744$	−0.558109	−	1.71768i	−0.0204613	−	0.0629733i
$745$		0			0
$746$	6.01061	−	18.4988i	0.220064	−	0.677288i
$747$	3.82999	−	11.7875i	0.140132	−	0.431282i
$748$	−3.49207	+	2.53714i	−0.127683	+	0.0927670i
$749$	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	$0.566767\pi$
$752$	8.39703	−	6.10080i	0.306208	−	0.222473i
$753$	−5.83420	+	17.9558i	−0.212610	+	0.654346i
$754$	−7.25980	+	22.3434i	−0.264386	+	0.813698i
$755$		0			0
$756$	−0.774937	−	2.38501i	−0.0281842	−	0.0867420i
$757$	13.7637			0.500251			0.250126	−	0.968213i	$-0.419528\pi$
$757$	13.7637			0.500251			0.250126	+	0.968213i	$0.419528\pi$
$758$	4.23166	+	13.0237i	0.153701	+	0.473042i
$759$	2.16056	+	1.56974i	0.0784235	+	0.0569780i
$760$		0			0
$761$	11.9257	−	8.66451i	0.432305	−	0.314088i	−0.350265	−	0.936651i	$-0.613908\pi$
$761$	11.9257	−	8.66451i	0.432305	−	0.314088i	0.782570	+	0.622562i	$0.213908\pi$
$762$	10.0144	+	7.27588i	0.362783	+	0.263577i
$763$	22.7126	+	16.5017i	0.822251	+	0.597400i
$764$	−12.0877	+	8.78224i	−0.437318	+	0.317730i
$765$		0			0
$766$	6.64559	+	4.82830i	0.240115	+	0.174454i
$767$	4.01692	+	12.3628i	0.145043	+	0.446395i
$768$	15.8439			0.571717
$769$	−0.753239	−	2.31823i	−0.0271625	−	0.0835976i	0.936556	−	0.350517i	$-0.113994\pi$
$769$	−0.753239	−	2.31823i	−0.0271625	−	0.0835976i	−0.963719	+	0.266920i	$0.913994\pi$
$770$		0			0
$771$	−2.18265	+	6.71750i	−0.0786061	+	0.241925i
$772$	0.508359	−	1.56457i	0.0182963	−	0.0563101i
$773$	−20.4957	+	14.8910i	−0.737180	+	0.535592i	−0.891827	−	0.452377i	$-0.850576\pi$
$773$	−20.4957	+	14.8910i	−0.737180	+	0.535592i	0.154647	+	0.987970i	$0.450576\pi$
$774$	2.64776			0.0951716
$775$		0			0
$776$	−13.8574			−0.497450
$777$	−28.4722	+	20.6863i	−1.02143	+	0.742115i
$778$	−4.62493	+	14.2341i	−0.165812	+	0.510317i
$779$	−17.5082	+	53.8846i	−0.627296	+	1.93062i
$780$		0			0
$781$	−2.29427	−	7.06103i	−0.0820953	−	0.252664i
$782$	−11.7289			−0.419426
$783$	1.63290	+	5.02554i	0.0583550	+	0.179598i
$784$	3.51299	+	2.55234i	0.125464	+	0.0911550i
$785$		0			0
$786$	−1.83257	+	1.33144i	−0.0653656	+	0.0474909i
$787$	31.2669	+	22.7167i	1.11454	+	0.809763i	0.983373	−	0.181597i	$-0.0581266\pi$
$787$	31.2669	+	22.7167i	1.11454	+	0.809763i	0.131170	+	0.991360i	$0.458127\pi$
$788$	7.58719	+	5.51242i	0.270283	+	0.196372i
$789$	16.5328	−	12.0118i	0.588582	−	0.427630i
$790$		0			0
$791$	9.37774	+	6.81333i	0.333434	+	0.242254i
$792$	1.08757	+	3.34719i	0.0386450	+	0.118937i
$793$	56.0741			1.99125
$794$	−4.37879	−	13.4765i	−0.155397	−	0.478264i
$795$		0			0
$796$	−5.76775	+	17.7513i	−0.204432	+	0.629178i
$797$	16.1004	−	49.5519i	0.570306	−	1.75522i	−0.0813294	−	0.996687i	$-0.525917\pi$
$797$	16.1004	−	49.5519i	0.570306	−	1.75522i	0.651635	−	0.758533i	$-0.274083\pi$
$798$	16.2474	−	11.8044i	0.575152	−	0.417872i
$799$	27.9968			0.990454
$800$		0			0
$801$	1.08404			0.0383025
$802$	5.70490	−	4.14485i	0.201447	−	0.146360i
$803$	−2.55844	+	7.87407i	−0.0902854	+	0.277870i
$804$	0.792882	−	2.44024i	0.0279628	−	0.0860606i
$805$		0			0
$806$	−0.809598	−	2.49169i	−0.0285169	−	0.0877659i
$807$	−21.1923			−0.746006
$808$	6.26350	+	19.2771i	0.220349	+	0.678166i
$809$	−25.7217	−	18.6879i	−0.904328	−	0.657033i	0.0352461	−	0.999379i	$-0.488778\pi$
$809$	−25.7217	−	18.6879i	−0.904328	−	0.657033i	−0.939574	+	0.342346i	$0.888778\pi$
$810$		0			0
$811$	25.1777	−	18.2927i	0.884108	−	0.642342i	−0.0502268	−	0.998738i	$-0.515994\pi$
$811$	25.1777	−	18.2927i	0.884108	−	0.642342i	0.934335	+	0.356395i	$0.115994\pi$
$812$	10.7206	+	7.78896i	0.376219	+	0.273339i
$813$	8.05229	+	5.85033i	0.282406	+	0.205180i
$814$	11.5415	−	8.38541i	0.404530	−	0.293908i
$815$		0			0
$816$	−6.42281	−	4.66645i	−0.224843	−	0.163358i
$817$	−4.48133	−	13.7921i	−0.156782	−	0.482525i
$818$	−1.21188			−0.0423725
$819$	−3.89193	−	11.9781i	−0.135995	−	0.418550i
$820$		0			0
$821$	−14.5319	+	44.7247i	−0.507168	+	1.56090i	0.289927	+	0.957049i	$0.406369\pi$
$821$	−14.5319	+	44.7247i	−0.507168	+	1.56090i	−0.797095	+	0.603854i	$0.793631\pi$
$822$	6.53446	−	20.1110i	0.227916	−	0.701452i
$823$	−22.9296	+	16.6593i	−0.799276	+	0.580708i	−0.910702	−	0.413065i	$-0.864458\pi$
$823$	−22.9296	+	16.6593i	−0.799276	+	0.580708i	0.111426	+	0.993773i	$0.464458\pi$
$824$	−12.8920			−0.449113
$825$		0			0
$826$	−10.7208			−0.373023
$827$	11.4622	−	8.32775i	0.398579	−	0.289584i	−0.370383	−	0.928879i	$-0.620774\pi$
$827$	11.4622	−	8.32775i	0.398579	−	0.289584i	0.768962	+	0.639295i	$0.220774\pi$
$828$	0.583776	−	1.79668i	0.0202876	−	0.0624389i
$829$	0.468647	−	1.44235i	0.0162768	−	0.0500948i	−0.942588	−	0.333957i	$-0.891616\pi$
$829$	0.468647	−	1.44235i	0.0162768	−	0.0500948i	0.958865	+	0.283862i	$0.0916159\pi$
$830$		0			0
$831$	5.78942	+	17.8180i	0.200833	+	0.618099i
$832$	32.9379			1.14192
$833$	3.61944	+	11.1395i	0.125406	+	0.385961i
$834$	−15.1299	−	10.9925i	−0.523906	−	0.380640i
$835$		0			0
$836$	4.50433	−	3.27259i	0.155786	−	0.113185i
$837$	−0.476737	−	0.346370i	−0.0164784	−	0.0119723i
$838$	−10.3979	−	7.55449i	−0.359188	−	0.260965i
$839$	−8.48811	+	6.16697i	−0.293042	+	0.212908i	−0.724586	−	0.689184i	$-0.757969\pi$
$839$	−8.48811	+	6.16697i	−0.293042	+	0.212908i	0.431544	+	0.902092i	$0.357969\pi$
$840$		0			0
$841$	0.871777	+	0.633383i	0.0300613	+	0.0218408i
$842$	−3.41004	−	10.4950i	−0.117518	−	0.361683i
$843$	−29.0916			−1.00197
$844$	1.72732	+	5.31614i	0.0594568	+	0.182989i
$845$		0			0
$846$	2.03747	−	6.27068i	0.0700496	−	0.215591i
$847$	9.23615	−	28.4259i	0.317358	−	0.976727i
$848$	−4.50221	+	3.27104i	−0.154606	+	0.112328i
$849$	−7.18007			−0.246419
$850$		0			0
$851$	−26.5120			−0.908820
$852$	−4.24887	+	3.08699i	−0.145564	+	0.105758i
$853$	4.59110	−	14.1300i	0.157196	−	0.483801i	−0.841180	−	0.540755i	$-0.818139\pi$
$853$	4.59110	−	14.1300i	0.157196	−	0.483801i	0.998377	+	0.0569538i	$0.0181388\pi$
$854$	−14.2909	+	43.9828i	−0.489024	+	1.50506i
$855$		0			0
$856$	3.79973	+	11.6944i	0.129872	+	0.399705i
$857$	26.4088			0.902109			0.451054	−	0.892496i	$-0.351048\pi$
$857$	26.4088			0.902109			0.451054	+	0.892496i	$0.351048\pi$
$858$	1.57764	+	4.85547i	0.0538597	+	0.165763i
$859$	7.38643	+	5.36656i	0.252022	+	0.183105i	0.706622	−	0.707591i	$-0.250218\pi$
$859$	7.38643	+	5.36656i	0.252022	+	0.183105i	−0.454601	+	0.890695i	$0.650218\pi$
$860$		0			0
$861$	−23.7075	+	17.2245i	−0.807951	+	0.587011i
$862$	5.01906	+	3.64656i	0.170950	+	0.124202i
$863$	10.0962	+	7.33532i	0.343679	+	0.249697i	0.746212	−	0.665708i	$-0.231870\pi$
$863$	10.0962	+	7.33532i	0.343679	+	0.249697i	−0.402534	+	0.915405i	$0.631870\pi$
$864$	3.44649	−	2.50402i	0.117252	−	0.0851886i
$865$		0			0
$866$	29.1386	+	21.1704i	0.990168	+	0.719399i
$867$	−1.36415	−	4.19841i	−0.0463288	−	0.142585i
$868$	−1.47776			−0.0501586
$869$	4.37789	+	13.4738i	0.148510	+	0.457066i
$870$		0			0
$871$	3.98205	−	12.2555i	0.134927	−	0.415262i
$872$	−8.61262	+	26.5069i	−0.291660	+	0.897638i
$873$	−3.65783	+	2.65757i	−0.123799	+	0.0899450i
$874$	15.1289			0.511741
$875$		0			0
$876$	5.85662			0.197877
$877$	−33.0177	+	23.9888i	−1.11493	+	0.810043i	−0.983433	−	0.181273i	$-0.941978\pi$
$877$	−33.0177	+	23.9888i	−1.11493	+	0.810043i	−0.131496	+	0.991317i	$0.541978\pi$
$878$	3.86065	−	11.8819i	0.130291	−	0.400993i
$879$	0.555691	−	1.71024i	0.0187430	−	0.0576850i
$880$		0			0
$881$	−1.12544	−	3.46374i	−0.0379170	−	0.116696i	0.930306	−	0.366783i	$-0.119541\pi$
$881$	−1.12544	−	3.46374i	−0.0379170	−	0.116696i	−0.968223	+	0.250087i	$0.919541\pi$
$882$	2.75842			0.0928808
$883$	0.102858	+	0.316564i	0.00346144	+	0.0106532i	0.952772	−	0.303686i	$-0.0982172\pi$
$883$	0.102858	+	0.316564i	0.00346144	+	0.0106532i	−0.949311	+	0.314339i	$0.898217\pi$
$884$	12.4061	+	9.01357i	0.417263	+	0.303159i
$885$		0			0
$886$	−15.7815	+	11.4659i	−0.530190	+	0.385206i
$887$	0.924496	+	0.671685i	0.0310415	+	0.0225530i	0.603198	−	0.797592i	$-0.293893\pi$
$887$	0.924496	+	0.671685i	0.0310415	+	0.0225530i	−0.572156	+	0.820145i	$0.693893\pi$
$888$	−28.2660	−	20.5365i	−0.948546	−	0.689159i
$889$	28.3688	−	20.6111i	0.951459	−	0.691276i
$890$		0			0
$891$	0.929002	+	0.674959i	0.0311227	+	0.0226120i
$892$	−2.03980	−	6.27787i	−0.0682977	−	0.210199i
$893$	−36.1123			−1.20845
$894$	−0.0707650	−	0.217792i	−0.00236674	−	0.00728407i
$895$		0			0
$896$	−0.266092	+	0.818948i	−0.00888953	+	0.0273591i
$897$	2.93187	−	9.02336i	0.0978923	−	0.301281i
$898$	6.01342	−	4.36901i	0.200671	−	0.145796i
$899$	3.11385			0.103853
$900$		0			0
$901$	−15.0109			−0.500086
$902$	9.61012	−	6.98216i	0.319982	−	0.232481i
$903$	2.31780	−	7.13347i	0.0771317	−	0.237387i
$904$	−3.55604	+	10.9444i	−0.118272	+	0.364004i
$905$		0			0
$906$	1.36704	+	4.20732i	0.0454169	+	0.139779i
$907$	−18.4202			−0.611632			−0.305816	−	0.952091i	$-0.598929\pi$
$907$	−18.4202			−0.611632			−0.305816	+	0.952091i	$0.598929\pi$
$908$	−6.43345	−	19.8001i	−0.213502	−	0.657090i
$909$	5.35029	+	3.88721i	0.177458	+	0.128931i
$910$		0			0
$911$	−14.7651	+	10.7274i	−0.489188	+	0.355416i	−0.804872	−	0.593449i	$-0.797766\pi$
$911$	−14.7651	+	10.7274i	−0.489188	+	0.355416i	0.315684	+	0.948864i	$0.397766\pi$
$912$	8.28462	+	6.01913i	0.274331	+	0.199313i
$913$	11.5141	+	8.36551i	0.381062	+	0.276858i
$914$	−2.43681	+	1.77044i	−0.0806024	+	0.0585611i
$915$		0			0
$916$	0.810372	+	0.588770i	0.0267754	+	0.0194535i
$917$	1.98290	+	6.10275i	0.0654812	+	0.201531i
$918$	−5.04322			−0.166451
$919$	3.34919	+	10.3078i	0.110480	+	0.340022i	0.990977	−	0.134029i	$-0.0427914\pi$
$919$	3.34919	+	10.3078i	0.110480	+	0.340022i	−0.880498	+	0.474050i	$0.842791\pi$
$920$		0			0
$921$	1.85059	−	5.69554i	0.0609791	−	0.187674i
$922$	−3.01904	+	9.29166i	−0.0994269	+	0.306005i
$923$	−21.3389	+	15.5036i	−0.702378	+	0.510308i
$924$	2.87967			0.0947342
$925$		0			0
$926$	14.3438			0.471368
$927$	−3.40300	+	2.47242i	−0.111769	+	0.0812051i
$928$	−6.95631	+	21.4093i	−0.228352	+	0.702795i
$929$	−16.1768	+	49.7870i	−0.530743	+	1.63346i	0.221930	+	0.975063i	$0.428764\pi$
$929$	−16.1768	+	49.7870i	−0.530743	+	1.63346i	−0.752673	+	0.658395i	$0.771236\pi$
$930$		0			0
$931$	−4.66862	−	14.3685i	−0.153008	−	0.470910i
$932$	2.43678			0.0798193
$933$	−7.37574	−	22.7002i	−0.241471	−	0.743171i
$934$	19.2211	+	13.9649i	0.628933	+	0.456947i
$935$		0			0
$936$	10.1154	−	7.34929i	0.330633	−	0.240219i
$937$	0.00106163		0.000771322i	3.46821e−5		2.51980e-5i	0.587803	−	0.809004i	$-0.299993\pi$
$937$	0.00106163		0.000771322i	3.46821e−5		2.51980e-5i	−0.587768	+	0.809030i	$0.699993\pi$
$938$	8.59798	+	6.24680i	0.280734	+	0.203965i
$939$	−4.65924	+	3.38513i	−0.152048	+	0.110470i
$940$		0			0
$941$	17.5737	+	12.7680i	0.572885	+	0.416225i	0.836152	−	0.548498i	$-0.184800\pi$
$941$	17.5737	+	12.7680i	0.572885	+	0.416225i	−0.263267	+	0.964723i	$0.584800\pi$
$942$	−0.148293	−	0.456399i	−0.00483165	−	0.0148703i
$943$	−22.0754			−0.718874
$944$	−1.68926	−	5.19900i	−0.0549807	−	0.169213i
$945$		0			0
$946$	−0.939548	+	2.89163i	−0.0305473	+	0.0940151i
$947$	−10.4839	+	32.2661i	−0.340681	+	1.04851i	0.623174	+	0.782083i	$0.285843\pi$
$947$	−10.4839	+	32.2661i	−0.340681	+	1.04851i	−0.963855	+	0.266426i	$0.914157\pi$
$948$	8.10763	−	5.89054i	0.263324	−	0.191316i
$949$	29.4134			0.954800
$950$		0			0
$951$	−12.2481			−0.397172
$952$	−35.4240	+	25.7370i	−1.14810	+	0.834142i
$953$	−2.56579	+	7.89670i	−0.0831142	+	0.255799i	−0.983974	−	0.178310i	$-0.942937\pi$
$953$	−2.56579	+	7.89670i	−0.0831142	+	0.255799i	0.900860	+	0.434109i	$0.142937\pi$
$954$	−1.09242	+	3.36213i	−0.0353685	+	0.108853i
$955$		0			0
$956$	−5.55594	−	17.0994i	−0.179692	−	0.553035i
$957$	−6.06786			−0.196146
$958$	14.3967	+	44.3085i	0.465136	+	1.43154i
$959$	−48.4620	−	35.2097i	−1.56492	−	1.13698i
$960$		0			0
$961$	24.7986	−	18.0172i	0.799955	−	0.581201i
$962$	−41.0030	−	29.7904i	−1.32199	−	0.960482i
$963$	3.24573	+	2.35816i	0.104592	+	0.0759907i
$964$	−8.83240	+	6.41711i	−0.284472	+	0.206681i
$965$		0			0
$966$	6.33044	+	4.59933i	0.203679	+	0.147981i
$967$	8.58804	+	26.4313i	0.276173	+	0.849972i	0.988907	+	0.148538i	$0.0474567\pi$
$967$	8.58804	+	26.4313i	0.276173	+	0.849972i	−0.712734	+	0.701434i	$0.752543\pi$
$968$	29.6724			0.953707
$969$	8.53565	+	26.2700i	0.274205	+	0.843915i
$970$		0			0
$971$	−9.59377	+	29.5266i	−0.307879	+	0.947554i	0.670708	+	0.741721i	$0.265990\pi$
$971$	−9.59377	+	29.5266i	−0.307879	+	0.947554i	−0.978587	+	0.205833i	$0.934010\pi$
$972$	0.251013	−	0.772537i	0.00805123	−	0.0247791i
$973$	−42.8601	+	31.1397i	−1.37403	+	0.998292i
$974$	12.3692			0.396333
$975$		0			0
$976$	−23.5811			−0.754814
$977$	−35.9137	+	26.0928i	−1.14898	+	0.834783i	−0.988345	−	0.152231i	$-0.951354\pi$
$977$	−35.9137	+	26.0928i	−1.14898	+	0.834783i	−0.160635	+	0.987014i	$0.551354\pi$
$978$	−1.09151	+	3.35932i	−0.0349027	+	0.107419i
$979$	−0.384667	+	1.18388i	−0.0122940	+	0.0378370i
$980$		0			0
$981$	2.81009	+	8.64857i	0.0897193	+	0.276127i
$982$	18.1506			0.579208
$983$	−13.5305	−	41.6427i	−0.431557	−	1.32820i	−0.896574	−	0.442894i	$-0.853952\pi$
$983$	−13.5305	−	41.6427i	−0.431557	−	1.32820i	0.465017	−	0.885302i	$-0.346048\pi$
$984$	−23.5359	−	17.0998i	−0.750297	−	0.545123i
$985$		0			0
$986$	21.5597	−	15.6640i	0.686600	−	0.498844i
$987$	−15.1106	−	10.9785i	−0.480977	−	0.349450i
$988$	−16.0023	−	11.6264i	−0.509102	−	0.369884i
$989$	4.57121	−	3.32118i	0.145356	−	0.105607i
$990$		0			0
$991$	−27.8586	−	20.2404i	−0.884957	−	0.642959i	0.0496015	−	0.998769i	$-0.484205\pi$
$991$	−27.8586	−	20.2404i	−0.884957	−	0.642959i	−0.934558	+	0.355810i	$0.884205\pi$
$992$	−0.775752	−	2.38752i	−0.0246302	−	0.0758039i
$993$	6.02899			0.191324
$994$	−6.72219	−	20.6888i	−0.213215	−	0.656208i
$995$		0			0
$996$	3.11107	−	9.57490i	0.0985781	−	0.303392i
$997$	5.99154	−	18.4401i	0.189754	−	0.584002i	−0.810244	−	0.586093i	$-0.800665\pi$
$997$	5.99154	−	18.4401i	0.189754	−	0.584002i	0.999998	+	0.00209042i	$0.000665403\pi$
$998$	10.7848	−	7.83564i	0.341388	−	0.248033i
$999$	−11.3997			−0.360670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.d.301.2		16
5.2	odd	4		75.2.i.a.64.2	yes	16
5.3	odd	4		375.2.i.c.199.3		16
5.4	even	2		375.2.g.e.301.3		16
15.2	even	4		225.2.m.b.64.3		16
25.3	odd	20		1875.2.b.h.1249.6		16
25.4	even	10		1875.2.a.m.1.4		8
25.9	even	10		375.2.g.e.76.3		16
25.12	odd	20		375.2.i.c.49.3		16
25.13	odd	20		75.2.i.a.34.2	✓	16
25.16	even	5	inner	375.2.g.d.76.2		16
25.21	even	5		1875.2.a.p.1.5		8
25.22	odd	20		1875.2.b.h.1249.11		16
75.29	odd	10		5625.2.a.bd.1.5		8
75.38	even	20		225.2.m.b.109.3		16
75.71	odd	10		5625.2.a.t.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.2	✓	16	25.13	odd	20
75.2.i.a.64.2	yes	16	5.2	odd	4
225.2.m.b.64.3		16	15.2	even	4
225.2.m.b.109.3		16	75.38	even	20
375.2.g.d.76.2		16	25.16	even	5	inner
375.2.g.d.301.2		16	1.1	even	1	trivial
375.2.g.e.76.3		16	25.9	even	10
375.2.g.e.301.3		16	5.4	even	2
375.2.i.c.49.3		16	25.12	odd	20
375.2.i.c.199.3		16	5.3	odd	4
1875.2.a.m.1.4		8	25.4	even	10
1875.2.a.p.1.5		8	25.21	even	5
1875.2.b.h.1249.6		16	25.3	odd	20
1875.2.b.h.1249.11		16	25.22	odd	20
5625.2.a.t.1.4		8	75.71	odd	10
5625.2.a.bd.1.5		8	75.29	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

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