LMFDB - Embedded newform 75.2.i.a.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(4,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.i (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.598878015160$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			34.2
Root			$1.08982i$ of defining polynomial
Character	$\chi$	$=$	75.34
Dual form			75.2.i.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.640580 + 0.881682i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(0.741001 - 2.10972i) q^{5} +(-0.336773 + 1.03648i) q^{6} +3.08724i q^{7} +(-2.91489 - 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.640580 + 0.881682i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(0.741001 - 2.10972i) q^{5} +(-0.336773 + 1.03648i) q^{6} +3.08724i q^{7} +(-2.91489 - 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +(1.38543 + 2.00477i) q^{10} +(0.929002 + 0.674959i) q^{11} +(0.477454 + 0.657159i) q^{12} +(-2.39789 - 3.30042i) q^{13} +(-2.72197 - 1.97763i) q^{14} +(0.0527945 - 2.23544i) q^{15} +(1.38794 - 1.00840i) q^{16} +(-4.40109 - 1.43000i) q^{17} +1.08982i q^{18} +(1.84452 - 5.67685i) q^{19} +(1.81584 + 0.0428847i) q^{20} +(0.954011 + 2.93614i) q^{21} +(-1.19020 + 0.386719i) q^{22} +(-1.36700 + 1.88152i) q^{23} -3.06489 q^{24} +(-3.90184 - 3.12661i) q^{25} +4.44596 q^{26} +(0.587785 - 0.809017i) q^{27} +(-2.38501 + 0.774937i) q^{28} +(1.63290 + 5.02554i) q^{29} +(1.93713 + 1.47853i) q^{30} +(-0.182097 + 0.560438i) q^{31} -4.26010i q^{32} +(1.09211 + 0.354847i) q^{33} +(4.08005 - 2.96433i) q^{34} +(6.51322 + 2.28765i) q^{35} +(0.657159 + 0.477454i) q^{36} +(6.70056 + 9.22252i) q^{37} +(3.82361 + 5.26275i) q^{38} +(-3.30042 - 2.39789i) q^{39} +(-4.15806 + 5.44779i) q^{40} +(-7.67919 + 5.57926i) q^{41} +(-3.19987 - 1.03970i) q^{42} +2.42954i q^{43} +(-0.288240 + 0.887112i) q^{44} +(-0.640580 - 2.14235i) q^{45} +(-0.783227 - 2.41052i) q^{46} +(5.75387 - 1.86955i) q^{47} +(1.00840 - 1.38794i) q^{48} -2.53108 q^{49} +(5.25611 - 1.43734i) q^{50} -4.62758 q^{51} +(1.94779 - 2.68091i) q^{52} +(3.08503 - 1.00239i) q^{53} +(0.336773 + 1.03648i) q^{54} +(2.11237 - 1.45979i) q^{55} +(2.92394 - 8.99897i) q^{56} -5.96899i q^{57} +(-5.47693 - 1.77956i) q^{58} +(2.57785 - 1.87292i) q^{59} +(1.74022 - 0.520339i) q^{60} +(-11.1201 - 8.07922i) q^{61} +(-0.377480 - 0.519557i) q^{62} +(1.81464 + 2.49763i) q^{63} +(6.53194 + 4.74573i) q^{64} +(-8.73980 + 2.61327i) q^{65} +(-1.01244 + 0.735584i) q^{66} +(-3.00414 - 0.976103i) q^{67} -3.75895i q^{68} +(-0.718676 + 2.21186i) q^{69} +(-6.18922 + 4.27717i) q^{70} +(1.99795 + 6.14907i) q^{71} +(-2.91489 + 0.947104i) q^{72} +(4.23792 - 5.83300i) q^{73} -12.4236 q^{74} +(-4.67704 - 1.76785i) q^{75} +4.84857 q^{76} +(-2.08376 + 2.86806i) q^{77} +(4.22836 - 1.37388i) q^{78} +(3.81246 + 11.7336i) q^{79} +(-1.09897 - 3.67540i) q^{80} +(0.309017 - 0.951057i) q^{81} -10.3446i q^{82} +(11.7875 + 3.82999i) q^{83} +(-2.02881 + 1.47402i) q^{84} +(-6.27811 + 8.22543i) q^{85} +(-2.14208 - 1.55631i) q^{86} +(3.10596 + 4.27498i) q^{87} +(-2.06868 - 2.84729i) q^{88} +(0.877003 + 0.637180i) q^{89} +(2.29921 + 0.807557i) q^{90} +(10.1892 - 7.40289i) q^{91} +(-1.79668 - 0.583776i) q^{92} +0.589279i q^{93} +(-2.03747 + 6.27068i) q^{94} +(-10.6098 - 8.09797i) q^{95} +(-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} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 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} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 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 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 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 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.640580	+	0.881682i	−0.452958	+	0.623444i	−0.973030	−	0.230679i	$-0.925905\pi$
$2$	−0.640580	+	0.881682i	−0.452958	+	0.623444i	0.520072	+	0.854123i	$0.325905\pi$
$3$	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
$5$	0.741001	−	2.10972i	0.331386	−	0.943495i
$5$	0.741001	−	2.10972i	0.331386	−	0.943495i
$6$	−0.336773	+	1.03648i	−0.137487	+	0.423141i
$7$			3.08724i			1.16687i	0.812160	+	0.583434i	$0.198291\pi$
$7$			3.08724i			1.16687i	−0.812160	+	0.583434i	$0.801709\pi$
$8$	−2.91489	−	0.947104i	−1.03057	−	0.334852i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	1.38543	+	2.00477i	0.438112	+	0.633964i
$11$	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	0.334579	−	0.942368i	$-0.391406\pi$
$13$	−2.39789	−	3.30042i	−0.665056	−	0.915372i	−0.999636	+	0.0269961i	$0.991406\pi$
$14$	−2.72197	−	1.97763i	−0.727477	−	0.528543i
$15$	0.0527945	−	2.23544i	0.0136315	−	0.577189i
$16$	1.38794	−	1.00840i	0.346986	−	0.252100i
$17$	−4.40109	−	1.43000i	−1.06742	−	0.346826i	−0.277938	−	0.960599i	$-0.589651\pi$
$17$	−4.40109	−	1.43000i	−1.06742	−	0.346826i	−0.789482	+	0.613773i	$0.789651\pi$
$18$			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	$-0.140062\pi$
$20$	1.81584	+	0.0428847i	0.406034	+	0.00958930i
$21$	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	−0.927395	−	0.374083i	$-0.877957\pi$
$23$	−1.36700	+	1.88152i	−0.285040	+	0.392324i	0.642355	+	0.766407i	$0.277957\pi$
$24$	−3.06489			−0.625619
$25$	−3.90184	−	3.12661i	−0.780367	−	0.625322i
$26$	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	$0.736769\pi$
$30$	1.93713	+	1.47853i	0.353671	+	0.269941i
$31$	−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
$35$	6.51322	+	2.28765i	1.10094	+	0.386684i
$36$	0.657159	+	0.477454i	0.109527	+	0.0795757i
$37$	6.70056	+	9.22252i	1.10156	+	1.51617i	0.833294	+	0.552830i	$0.186452\pi$
$37$	6.70056	+	9.22252i	1.10156	+	1.51617i	0.268271	+	0.963344i	$0.413548\pi$
$38$	3.82361	+	5.26275i	0.620272	+	0.853731i
$39$	−3.30042	−	2.39789i	−0.528490	−	0.383970i
$40$	−4.15806	+	5.44779i	−0.657446	+	0.861371i
$41$	−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	$0.0593096\pi$
$43$			2.42954i			0.370501i	−0.982691	+	0.185250i	$0.940690\pi$
$44$	−0.288240	+	0.887112i	−0.0434538	+	0.133737i
$45$	−0.640580	−	2.14235i	−0.0954920	−	0.319362i
$46$	−0.783227	−	2.41052i	−0.115481	−	0.355412i
$47$	5.75387	−	1.86955i	0.839289	−	0.272701i	0.142336	−	0.989818i	$-0.454539\pi$
$47$	5.75387	−	1.86955i	0.839289	−	0.272701i	0.696953	+	0.717117i	$0.254539\pi$
$48$	1.00840	−	1.38794i	0.145550	−	0.200332i
$49$	−2.53108			−0.361583
$50$	5.25611	−	1.43734i	0.743327	−	0.203270i
$51$	−4.62758			−0.647990
$52$	1.94779	−	2.68091i	0.270111	−	0.371775i
$53$	3.08503	−	1.00239i	0.423762	−	0.137689i	−0.0893696	−	0.995999i	$-0.528485\pi$
$53$	3.08503	−	1.00239i	0.423762	−	0.137689i	0.513132	+	0.858310i	$0.328485\pi$
$54$	0.336773	+	1.03648i	0.0458290	+	0.141047i
$55$	2.11237	−	1.45979i	0.284831	−	0.196838i
$56$	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	$0.233494\pi$
$60$	1.74022	−	0.520339i	0.224661	−	0.0671755i
$61$	−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
$65$	−8.73980	+	2.61327i	−1.08404	+	0.324137i
$66$	−1.01244	+	0.735584i	−0.124623	+	0.0905441i
$67$	−3.00414	−	0.976103i	−0.367014	−	0.119250i	0.119703	−	0.992810i	$-0.461806\pi$
$67$	−3.00414	−	0.976103i	−0.367014	−	0.119250i	−0.486717	+	0.873560i	$0.661806\pi$
$68$		−	3.75895i		−	0.455840i
$69$	−0.718676	+	2.21186i	−0.0865184	+	0.266276i
$70$	−6.18922	+	4.27717i	−0.739753	+	0.511220i
$71$	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	−0.485472	−	0.874252i	$-0.661352\pi$
$73$	4.23792	−	5.83300i	0.496011	−	0.682701i	0.981482	+	0.191552i	$0.0613521\pi$
$74$	−12.4236			−1.44421
$75$	−4.67704	−	1.76785i	−0.540058	−	0.204134i
$76$	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	$0.655832\pi$
$80$	−1.09897	−	3.67540i	−0.122869	−	0.410922i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		−	10.3446i		−	1.14237i
$83$	11.7875	+	3.82999i	1.29384	+	0.420396i	0.873436	−	0.486939i	$-0.161887\pi$
$83$	11.7875	+	3.82999i	1.29384	+	0.420396i	0.420409	+	0.907335i	$0.361887\pi$
$84$	−2.02881	+	1.47402i	−0.221361	+	0.160829i
$85$	−6.27811	+	8.22543i	−0.680957	+	0.892173i
$86$	−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	$0.681702\pi$
$90$	2.29921	+	0.807557i	0.242358	+	0.0851240i
$91$	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
$95$	−10.6098	−	8.09797i	−1.08854	−	0.830834i
$96$	−1.31644	−	4.05159i	−0.134359	−	0.413514i
$97$	4.30003	−	1.39717i	0.436602	−	0.141861i	−0.0824653	−	0.996594i	$-0.526279\pi$
$97$	4.30003	−	1.39717i	0.436602	−	0.141861i	0.519067	+	0.854733i	$0.326279\pi$
$98$	1.62136	−	2.23161i	0.163782	−	0.225426i
$99$	1.14831			0.115409
$100$	1.43601	−	3.79913i	0.143601	−	0.379913i
$101$	−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	−0.499398	−	0.866373i	$-0.666445\pi$
$103$	−4.00047	+	1.29983i	−0.394178	+	0.128076i	0.105220	+	0.994449i	$0.466445\pi$
$104$	3.86375	+	11.8914i	0.378872	+	1.16605i
$105$	6.90136	+	0.162990i	0.673504	+	0.0159062i
$106$	−1.09242	+	3.36213i	−0.106105	+	0.326559i
$107$			4.01195i			0.387849i	0.981016	+	0.193925i	$0.0621218\pi$
$107$			4.01195i			0.387849i	−0.981016	+	0.193925i	$0.937878\pi$
$108$	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	$0.156569\pi$
$110$	−0.0660697	+	2.79755i	−0.00629950	+	0.266736i
$111$	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	0.692496	−	0.721422i	$-0.256511\pi$
$113$	−2.20693	−	3.03758i	−0.207610	−	0.285751i	−0.900106	+	0.435671i	$0.856511\pi$
$114$	5.26275	+	3.82361i	0.492902	+	0.358114i
$115$	2.95653	+	4.27820i	0.275697	+	0.398944i
$116$	−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
$120$	−2.27109	+	6.46606i	−0.207321	+	0.590268i
$121$	−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
$125$	−9.48753	+	5.91496i	−0.848591	+	0.529050i
$126$	−3.36454			−0.299737
$127$	−6.67623	+	9.18904i	−0.592419	+	0.815395i	−0.994988	−	0.0999946i	$-0.968117\pi$
$127$	−6.67623	+	9.18904i	−0.592419	+	0.815395i	0.402569	+	0.915390i	$0.368117\pi$
$128$	−0.265268	+	0.0861909i	−0.0234466	+	0.00761827i
$129$	0.750768	+	2.31063i	0.0661014	+	0.203439i
$130$	3.29446	−	9.37974i	0.288944	−	0.822658i
$131$	−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
$135$	−1.27125	−	1.83954i	−0.109412	−	0.158323i
$136$	11.4743	+	8.33657i	0.983914	+	0.714855i
$137$	−11.4049	−	15.6975i	−0.974387	−	1.34113i	−0.939800	−	0.341726i	$-0.888988\pi$
$137$	−11.4049	−	15.6975i	−0.974387	−	1.34113i	−0.0345870	−	0.999402i	$-0.511012\pi$
$138$	−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	$0.959438\pi$
$140$	−0.132395	+	5.60593i	−0.0111895	+	0.473788i
$141$	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
$145$	11.8125	+	0.278975i	0.980972	+	0.0231676i
$146$	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	$0.502740\pi$
$150$	4.55470	−	2.99122i	0.371890	−	0.244232i
$151$	−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
$155$	1.04743	+	0.799459i	0.0841318	+	0.0642141i
$156$	1.02402	−	3.15160i	0.0819869	−	0.252330i
$157$		−	0.440336i		−	0.0351426i	−0.999846	−	0.0175713i	$-0.994407\pi$
$157$		−	0.440336i		−	0.0351426i	0.999846	−	0.0175713i	$-0.00559341\pi$
$158$	−12.7875	−	4.15490i	−1.01732	−	0.330546i
$159$	2.62429	−	1.90666i	0.208119	−	0.151208i
$160$	−8.98762	−	3.15674i	−0.710533	−	0.249562i
$161$	−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	0.727865	−	0.685720i	$-0.240513\pi$
$163$	−1.90506	−	2.62210i	−0.149216	−	0.205378i	−0.877081	+	0.480342i	$0.840513\pi$
$164$	−6.23776	−	4.53200i	−0.487087	−	0.353889i
$165$	1.55788	−	2.04110i	0.121281	−	0.158899i
$166$	−10.9277	+	7.93941i	−0.848151	+	0.616218i
$167$	15.1793	+	4.93207i	1.17461	+	0.381655i	0.830363	−	0.557223i	$-0.188133\pi$
$167$	15.1793	+	4.93207i	1.17461	+	0.381655i	0.344250	+	0.938878i	$0.388133\pi$
$168$		−	9.46207i		−	0.730015i
$169$	−1.12565	+	3.46438i	−0.0865882	+	0.266491i
$170$	−3.23059	−	10.8043i	−0.247775	−	0.828655i
$171$	−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	−0.796280	−	0.604929i	$-0.793202\pi$
$173$	0.330212	−	0.454497i	0.0251055	−	0.0345548i	0.821385	+	0.570374i	$0.193202\pi$
$174$	−5.75879			−0.436573
$175$	9.65261	−	12.0459i	0.729668	−	0.910586i
$176$	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	$-0.303108\pi$
$180$	1.49425	−	1.03263i	0.111375	−	0.0769675i
$181$	−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
$185$	24.4221	−	7.30240i	1.79555	−	0.536883i
$186$	−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
$190$	13.9362	−	4.16705i	1.01104	−	0.302310i
$191$	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	$-0.976778\pi$
$193$		−	2.02523i		−	0.145780i	0.997340	−	0.0728898i	$-0.0232221\pi$
$194$	−1.52266	+	4.68626i	−0.109320	+	0.336454i
$195$	−7.50450	+	5.18612i	−0.537408	+	0.371386i
$196$	−0.635333	−	1.95535i	−0.0453809	−	0.139668i
$197$	10.9804	−	3.56774i	0.782319	−	0.254191i	0.109489	−	0.993988i	$-0.465079\pi$
$197$	10.9804	−	3.56774i	0.782319	−	0.254191i	0.672830	+	0.739797i	$0.265079\pi$
$198$	−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	$0.802951\pi$
$200$	8.41218	+	12.8092i	0.594831	+	0.905744i
$201$	−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
$205$	6.08038	+	20.3352i	0.424672	+	1.42027i
$206$	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
$210$	−4.56458	+	5.98040i	−0.314986	+	0.412687i
$211$	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
$215$	5.12564	+	1.80029i	0.349566	+	0.122779i
$216$	−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
$220$	1.65797	+	1.26546i	0.111780	+	0.0853170i
$221$	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	−0.618565	−	0.785734i	$-0.712286\pi$
$223$	4.77652	−	6.57432i	0.319860	−	0.440249i	0.938424	+	0.345485i	$0.112286\pi$
$224$	13.1520			0.878753
$225$	−4.99443	−	0.236039i	−0.332962	−	0.0157359i
$226$	4.09189			0.272188
$227$	−15.0649	+	20.7351i	−0.999895	+	1.37624i	−0.0745050	+	0.997221i	$0.523738\pi$
$227$	−15.0649	+	20.7351i	−0.999895	+	1.37624i	−0.925390	+	0.379017i	$0.876262\pi$
$228$	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	$0.912973\pi$
$230$	−5.66590	−	0.133812i	−0.373599	−	0.00882329i
$231$	−1.09550	+	3.37160i	−0.0720786	+	0.221835i
$232$		−	16.1954i		−	1.06328i
$233$	−2.85305	−	0.927012i	−0.186909	−	0.0607306i	0.214067	−	0.976819i	$-0.431329\pi$
$233$	−2.85305	−	0.927012i	−0.186909	−	0.0607306i	−0.400976	+	0.916088i	$0.631329\pi$
$234$	3.59686	−	2.61327i	0.235134	−	0.170835i
$235$	0.319406	−	13.5244i	0.0208357	−	0.882234i
$236$	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	$0.446031\pi$
$240$	−2.18095	−	3.15591i	−0.140779	−	0.203713i
$241$	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
$245$	−1.87553	+	5.33987i	−0.119823	+	0.341152i
$246$	−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
$250$	0.862406	−	12.1540i	0.0545434	−	0.768686i
$251$	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
$255$	−3.42904	+	9.76289i	−0.214735	+	0.611376i
$256$	−4.89603	+	15.0684i	−0.306002	+	0.941776i
$257$		−	7.06320i		−	0.440590i	−0.975433	−	0.220295i	$-0.929298\pi$
$257$		−	7.06320i		−	0.440590i	0.975433	−	0.220295i	$-0.0707020\pi$
$258$	−2.51816	−	0.818201i	−0.156774	−	0.0509390i
$259$	−28.4722	+	20.6863i	−1.76918	+	1.28538i
$260$	−4.21265	−	6.09586i	−0.261257	−	0.378049i
$261$	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	$-0.983031\pi$
$263$	−12.0118	−	16.5328i	−0.740677	−	1.01945i	0.257903	−	0.966171i	$-0.416969\pi$
$264$	−2.84729	−	2.06868i	−0.175239	−	0.127318i
$265$	0.171255	−	7.25133i	0.0105201	−	0.445446i
$266$	−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	$0.876416\pi$
$270$	2.43623	+	0.0575365i	0.148264	+	0.00350156i
$271$	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
$275$	−1.51448	−	5.53820i	−0.0913265	−	0.333966i
$276$	−1.88914			−0.113713
$277$	11.0121	−	15.1569i	0.661654	−	0.910689i	−0.337880	−	0.941189i	$-0.609710\pi$
$277$	11.0121	−	15.1569i	0.661654	−	0.910689i	0.999535	+	0.0304998i	$0.00970991\pi$
$278$	17.7863	−	5.77912i	1.06675	−	0.346608i
$279$	0.182097	+	0.560438i	0.0109019	+	0.0335525i
$280$	−16.8187	−	12.8369i	−1.00511	−	0.767154i
$281$	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	0.504859	−	0.863202i	$-0.331545\pi$
$283$	6.82865	+	2.21876i	0.405921	+	0.131892i	−0.0989379	+	0.995094i	$0.531545\pi$
$284$	−4.24887	+	3.08699i	−0.252124	+	0.183179i
$285$	−12.5929	−	4.42303i	−0.745939	−	0.261998i
$286$	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
$290$	−7.81279	+	10.2361i	−0.458783	+	0.601087i
$291$	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	$-0.983272\pi$
$293$		−	1.79825i		−	0.105055i	0.998619	−	0.0525276i	$-0.0167277\pi$
$294$	0.852398	−	2.62341i	0.0497129	−	0.153001i
$295$	−2.04114	−	6.82637i	−0.118840	−	0.397447i
$296$	−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
$300$	0.191733	−	4.05694i	0.0110697	−	0.234228i
$301$	−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
$305$	−25.2849	+	17.4736i	−1.44781	+	1.00053i
$306$	1.55844	−	4.79639i	0.0890902	−	0.274191i
$307$			5.98864i			0.341790i	0.985289	+	0.170895i	$0.0546659\pi$
$307$			5.98864i			0.341790i	−0.985289	+	0.170895i	$0.945334\pi$
$308$	−2.73873	−	0.889867i	−0.156054	−	0.0507049i
$309$	−3.40300	+	2.47242i	−0.193590	+	0.140651i
$310$	−1.37583	+	0.411385i	−0.0781421	+	0.0233651i
$311$	−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	0.893898	−	0.448269i	$-0.147959\pi$
$313$	3.38513	+	4.65924i	0.191339	+	0.263356i	−0.702559	+	0.711625i	$0.747959\pi$
$314$	0.388236	+	0.282070i	0.0219094	+	0.0159181i
$315$	6.61395	−	1.97763i	0.372654	−	0.111427i
$316$	−8.10763	+	5.89054i	−0.456090	+	0.331369i
$317$	−11.6486	−	3.78487i	−0.654253	−	0.212580i	−0.0369645	−	0.999317i	$-0.511769\pi$
$317$	−11.6486	−	3.78487i	−0.654253	−	0.212580i	−0.617288	+	0.786737i	$0.711769\pi$
$318$			3.53515i			0.198242i
$319$	−1.87507	+	5.77088i	−0.104984	+	0.323107i
$320$	14.8523	−	10.2640i	0.830271	−	0.573773i
$321$	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
$325$	−0.962929	+	20.3750i	−0.0534137	+	1.13020i
$326$	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
$330$	0.801653	+	2.68104i	0.0441296	+	0.147586i
$331$	−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
$335$	−4.28537	+	5.61459i	−0.234135	+	0.306758i
$336$	4.28492	+	3.11318i	0.233762	+	0.169838i
$337$	−3.25094	−	4.47454i	−0.177090	−	0.243744i	0.711240	−	0.702949i	$-0.248134\pi$
$337$	−3.25094	−	4.47454i	−0.177090	−	0.243744i	−0.888330	+	0.459206i	$0.848134\pi$
$338$	−2.33342	−	3.21168i	−0.126921	−	0.174692i
$339$	−3.03758	−	2.20693i	−0.164978	−	0.119864i
$340$	−7.93033	−	2.78539i	−0.430083	−	0.151059i
$341$	−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
$345$	4.13386	+	3.15519i	0.222559	+	0.169870i
$346$	0.189195	+	0.582283i	0.0101712	+	0.0313038i
$347$	24.6747	−	8.01729i	1.32461	−	0.430391i	0.440532	−	0.897737i	$-0.354790\pi$
$347$	24.6747	−	8.01729i	1.32461	−	0.430391i	0.884075	+	0.467346i	$0.154790\pi$
$348$	−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	$0.330167\pi$
$350$	4.43741	+	16.2269i	0.237190	+	0.867365i
$351$	−4.07954			−0.217750
$352$	2.87539	−	3.95764i	0.153259	−	0.210943i
$353$	7.79043	−	2.53126i	0.414642	−	0.134726i	−0.0942642	−	0.995547i	$-0.530050\pi$
$353$	7.79043	−	2.53126i	0.414642	−	0.134726i	0.508907	+	0.860822i	$0.330050\pi$
$354$	1.07309	+	3.30263i	0.0570341	+	0.175533i
$355$	14.4533	+	0.341344i	0.767101	+	0.0181166i
$356$	−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	$0.549883\pi$
$360$	−0.161810	+	6.85140i	−0.00852811	+	0.361100i
$361$	−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
$365$	−9.16568	−	13.2631i	−0.479754	−	0.694221i
$366$	12.1189	−	8.80489i	0.633465	−	0.460239i
$367$	17.9306	+	5.82600i	0.935968	+	0.304114i	0.737001	−	0.675892i	$-0.236241\pi$
$367$	17.9306	+	5.82600i	0.935968	+	0.304114i	0.198967	+	0.980006i	$0.436241\pi$
$368$			3.98992i			0.207989i
$369$	−2.93319	+	9.02743i	−0.152696	+	0.469949i
$370$	−9.20588	+	26.2103i	−0.478591	+	1.36261i
$371$	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	−0.445885	−	0.895090i	$-0.647111\pi$
$373$	10.4906	−	14.4391i	0.543183	−	0.747627i	0.989067	+	0.147464i	$0.0471109\pi$
$374$	5.79118			0.299455
$375$	−7.19536	+	8.55727i	−0.371567	+	0.441895i
$376$	−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	$-0.204597\pi$
$380$	3.59280	−	10.2291i	0.184307	−	0.524743i
$381$	−3.50990	+	10.8024i	−0.179818	+	0.553422i
$382$			20.0460i			1.02564i
$383$	−7.16849	−	2.32918i	−0.366292	−	0.119016i	0.120087	−	0.992763i	$-0.461683\pi$
$383$	−7.16849	−	2.32918i	−0.366292	−	0.119016i	−0.486379	+	0.873748i	$0.661683\pi$
$384$	−0.225651	+	0.163945i	−0.0115152	+	0.00836628i
$385$	4.50672	+	6.52139i	0.229684	+	0.332361i
$386$	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	$0.813189\pi$
$390$	0.234723	−	9.93871i	0.0118856	−	0.503266i
$391$	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
$395$	27.5796	+	0.651347i	1.38768	+	0.0327728i
$396$	0.288240	+	0.887112i	0.0144846	+	0.0445790i
$397$	−12.3658	+	4.01790i	−0.620623	+	0.201653i	−0.602417	−	0.798182i	$-0.705796\pi$
$397$	−12.3658	+	4.01790i	−0.620623	+	0.201653i	−0.0182061	+	0.999834i	$0.505796\pi$
$398$	14.7192	−	20.2592i	0.737807	−	1.01550i
$399$	18.4277			0.922540
$400$	−8.56840	−	0.404946i	−0.428420	−	0.0202473i
$401$	−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
$405$	−1.77748	−	1.35667i	−0.0883237	−	0.0674136i
$406$	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	$0.308752\pi$
$410$	−21.8241	−	7.66533i	−1.07782	−	0.378564i
$411$	−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
$415$	16.8147	−	22.0303i	0.825403	−	1.08142i
$416$	−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	$0.193013\pi$
$420$	1.60641	+	5.37247i	0.0783849	+	0.262150i
$421$	−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
$425$	12.7013	+	19.3401i	0.616102	+	0.938133i
$426$	−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
$430$	−4.87066	+	3.36596i	−0.234884	+	0.162321i
$431$	−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	−0.567434	−	0.823419i	$-0.692064\pi$
$433$	−31.4313	−	10.2126i	−1.51049	−	0.490788i	−0.943057	+	0.332631i	$0.892064\pi$
$434$	1.60400	−	1.16537i	0.0769945	−	0.0559397i
$435$	11.3205	−	3.38493i	0.542778	−	0.162295i
$436$	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	$0.611797\pi$
$440$	−7.53988	+	2.25448i	−0.359449	+	0.107478i
$441$	−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	$0.139800\pi$
$443$			17.8993i			0.850422i	−0.905094	+	0.425211i	$0.860200\pi$
$444$	−2.86146	+	8.80667i	−0.135799	+	0.417946i
$445$	1.99413	−	1.37808i	0.0945309	−	0.0653272i
$446$	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	$0.448548\pi$
$450$	3.40744	−	4.25230i	0.160628	−	0.200455i
$451$	−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
$455$	−8.06781	−	26.9819i	−0.378225	−	1.26493i
$456$	−5.65325	+	17.3989i	−0.264738	+	0.814779i
$457$		−	2.76381i		−	0.129286i	−0.997908	−	0.0646429i	$-0.979409\pi$
$457$		−	2.76381i		−	0.129286i	0.997908	−	0.0646429i	$-0.0205908\pi$
$458$	1.27813	+	0.415289i	0.0597230	+	0.0194052i
$459$	−3.74379	+	2.72002i	−0.174745	+	0.126960i
$460$	−2.56294	+	3.35791i	−0.119498	+	0.156563i
$461$	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	0.590485	−	0.807048i	$-0.298936\pi$
$463$	−7.73623	−	10.6480i	−0.359533	−	0.494855i	−0.950019	+	0.312193i	$0.898936\pi$
$464$	7.33412	+	5.32855i	0.340478	+	0.247372i
$465$	1.24321	+	0.436656i	0.0576527	+	0.0202495i
$466$	2.64494	−	1.92166i	0.122524	−	0.0890191i
$467$	20.7335	+	6.73671i	0.959430	+	0.311738i	0.746542	−	0.665339i	$-0.231713\pi$
$467$	20.7335	+	6.73671i	0.959430	+	0.311738i	0.212889	+	0.977076i	$0.431713\pi$
$468$		−	3.31379i		−	0.153180i
$469$	3.01347	−	9.27450i	0.139149	−	0.428257i
$470$	11.7196	+	8.94507i	0.540586	+	0.412605i
$471$	−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
$475$	−24.9463	+	16.3830i	−1.14461	+	0.751705i
$476$	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	$-0.531042\pi$
$480$	−9.52322	−	0.224910i	−0.434673	−	0.0102657i
$481$	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
$485$	0.238701	−	10.1072i	0.0108389	−	0.458943i
$486$	0.881682	+	0.640580i	0.0399939	+	0.0290573i
$487$	6.67121	+	9.18213i	0.302301	+	0.416082i	0.932961	−	0.359978i	$-0.117216\pi$
$487$	6.67121	+	9.18213i	0.302301	+	0.416082i	−0.630660	+	0.776059i	$0.717216\pi$
$488$	24.7619	+	34.0819i	1.12092	+	1.54281i
$489$	−2.62210	−	1.90506i	−0.118575	−	0.0861500i
$490$	−3.50664	−	5.07424i	−0.158414	−	0.229231i
$491$	−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
$495$	0.850898	−	2.42261i	0.0382450	−	0.108888i
$496$	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	$0.411722\pi$
$500$	−6.95101	−	5.84474i	−0.310859	−	0.261385i
$501$	15.9605			0.713063
$502$	−12.0941	+	16.6460i	−0.539784	+	0.742949i
$503$	−1.24557	+	0.404709i	−0.0555371	+	0.0180451i	−0.336654	−	0.941629i	$-0.609295\pi$
$503$	−1.24557	+	0.404709i	−0.0555371	+	0.0180451i	0.281117	+	0.959674i	$0.409295\pi$
$504$	−2.92394	−	8.99897i	−0.130243	−	0.400846i
$505$	−4.90048	+	13.9523i	−0.218069	+	0.620868i
$506$	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	$0.171447\pi$
$510$	−6.41120	−	9.27723i	−0.283893	−	0.410803i
$511$	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
$515$	−0.222072	+	9.40304i	−0.00978565	+	0.414347i
$516$	−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
$520$	27.9506	+	0.660109i	1.22571	+	0.0289477i
$521$	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	−0.774895	−	0.632090i	$-0.782197\pi$
$523$	1.50281	−	2.06844i	0.0657134	−	0.0904467i	0.840609	+	0.541643i	$0.182197\pi$
$524$	−1.68834			−0.0737557
$525$	5.45778	−	14.4392i	0.238197	−	0.630177i
$526$	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
$530$	6.28367	+	4.79605i	0.272945	+	0.208327i
$531$	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
$535$	8.46408	+	2.97286i	0.365934	+	0.128528i
$536$	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
$540$	1.10202	−	1.44384i	0.0474233	−	0.0621328i
$541$	−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
$545$	−5.82520	−	19.4818i	−0.249524	−	0.834507i
$546$	4.24150	+	13.0540i	0.181519	+	0.558659i
$547$	−33.1490	+	10.7708i	−1.41735	+	0.460524i	−0.914759	−	0.404000i	$-0.867619\pi$
$547$	−33.1490	+	10.7708i	−1.41735	+	0.460524i	−0.502590	+	0.864525i	$0.667619\pi$
$548$	9.26413	−	12.7510i	0.395744	−	0.544695i
$549$	−13.7452			−0.586631
$550$	5.85308	+	2.21237i	0.249576	+	0.0943359i
$551$	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
$555$	20.9702	−	14.4918i	0.890135	−	0.615144i
$556$	4.30745	−	13.2570i	0.182676	−	0.562220i
$557$			14.1466i			0.599411i	0.954032	+	0.299705i	$0.0968884\pi$
$557$			14.1466i			0.599411i	−0.954032	+	0.299705i	$0.903112\pi$
$558$	−0.610776	−	0.198453i	−0.0258562	−	0.00840119i
$559$	8.01849	−	5.82577i	0.339146	−	0.246404i
$560$	11.3468	−	3.39280i	0.479492	−	0.143372i
$561$	−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	$-0.902347\pi$
$563$	−22.4448	−	30.8926i	−0.945936	−	1.30197i	0.00737325	−	0.999973i	$-0.497653\pi$
$564$	3.97580	+	2.88859i	0.167411	+	0.121632i
$565$	−8.04377	+	2.40515i	−0.338404	+	0.101186i
$566$	−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	$0.886694\pi$
$570$	11.9665	−	8.26963i	0.501220	−	0.346377i
$571$	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
$575$	11.2166	−	3.06729i	0.467764	−	0.127915i
$576$	8.07392			0.336413
$577$	−13.3094	+	18.3188i	−0.554077	+	0.762622i	−0.990558	−	0.137091i	$-0.956225\pi$
$577$	−13.3094	+	18.3188i	−0.554077	+	0.762622i	0.436481	+	0.899713i	$0.356225\pi$
$578$	−4.57551	+	1.48667i	−0.190316	+	0.0618374i
$579$	−0.625832	−	1.92611i	−0.0260087	−	0.0800465i
$580$	2.74956	+	9.19559i	0.114169	+	0.381826i
$581$	−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
$585$	−5.53461	+	7.25131i	−0.228828	+	0.299805i
$586$	1.58549	+	1.15193i	0.0654960	+	0.0475856i
$587$	24.4323	+	33.6281i	1.00843	+	1.38798i	0.920008	+	0.391899i	$0.128182\pi$
$587$	24.4323	+	33.6281i	1.00843	+	1.38798i	0.0884196	+	0.996083i	$0.471818\pi$
$588$	−1.20847	−	1.66332i	−0.0498366	−	0.0685943i
$589$	2.84564	+	2.06748i	0.117252	+	0.0851889i
$590$	7.32620	+	2.57320i	0.301615	+	0.105937i
$591$	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	$0.0136671\pi$
$593$			2.09050i			0.0858465i	−0.999078	+	0.0429233i	$0.986333\pi$
$594$	−0.386719	+	1.19020i	−0.0158673	+	0.0488345i
$595$	−25.3939	−	19.3821i	−1.04105	−	0.794587i
$596$	−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	$0.619702\pi$
$600$	11.9587	+	9.58272i	0.488212	+	0.391213i
$601$	−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
$605$	−21.6422	−	0.511124i	−0.879881	−	0.0207802i
$606$	2.22719	−	6.85458i	0.0904733	−	0.278448i
$607$			12.2310i			0.496441i	0.968704	+	0.248220i	$0.0798457\pi$
$607$			12.2310i			0.496441i	−0.968704	+	0.248220i	$0.920154\pi$
$608$	−24.1839	−	7.85783i	−0.980788	−	0.318677i
$609$	−13.1979	+	9.58884i	−0.534806	+	0.388560i
$610$	0.790851	−	33.4865i	0.0320206	−	1.35583i
$611$	−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	0.934786	−	0.355213i	$-0.115591\pi$
$613$	7.62804	+	10.4991i	0.308094	+	0.424055i	−0.626692	+	0.779267i	$0.715591\pi$
$614$	−5.28008	−	3.83620i	−0.213087	−	0.154817i
$615$	12.0667	+	17.4610i	0.486576	+	0.704094i
$616$	8.79028	−	6.38651i	0.354171	−	0.257320i
$617$	−19.4891	−	6.33241i	−0.784603	−	0.254933i	−0.110799	−	0.993843i	$-0.535341\pi$
$617$	−19.4891	−	6.33241i	−0.784603	−	0.254933i	−0.673804	+	0.738910i	$0.735341\pi$
$618$		−	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	$-0.208758\pi$
$620$	−0.354693	+	1.00985i	−0.0142448	+	0.0405567i
$621$	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
$625$	5.44863	+	24.3990i	0.217945	+	0.975961i
$626$	−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
$630$	−2.49313	+	7.09823i	−0.0993286	+	0.282800i
$631$	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
$635$	14.4392	+	20.8941i	0.573002	+	0.829155i
$636$	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
$640$	−0.0147254	+	0.623510i	−0.000582074	+	0.0246464i
$641$	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	$-0.931429\pi$
$643$		−	10.8408i		−	0.427521i	0.976886	−	0.213761i	$-0.0685713\pi$
$644$	1.80226	−	5.54678i	0.0710189	−	0.218574i
$645$	5.43109	+	0.128266i	0.213849	+	0.00505048i
$646$	−9.30232	−	28.6296i	−0.365995	−	1.12642i
$647$	−32.9435	+	10.7040i	−1.29514	+	0.420817i	−0.873889	−	0.486126i	$-0.838410\pi$
$647$	−32.9435	+	10.7040i	−1.29514	+	0.420817i	−0.421253	+	0.906943i	$0.638410\pi$
$648$	−1.80150	+	2.47955i	−0.0707695	+	0.0974059i
$649$	3.65897			0.143627
$650$	−17.3474	−	13.9008i	−0.680422	−	0.545234i
$651$	−1.81925			−0.0713020
$652$	1.54747	−	2.12991i	0.0606037	−	0.0834138i
$653$	3.95170	−	1.28398i	0.154642	−	0.0502462i	−0.230673	−	0.973031i	$-0.574093\pi$
$653$	3.95170	−	1.28398i	0.154642	−	0.0502462i	0.385315	+	0.922785i	$0.374093\pi$
$654$	3.06249	+	9.42538i	0.119753	+	0.368561i
$655$	3.69448	+	2.81983i	0.144355	+	0.110180i
$656$	−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	$0.324913\pi$
$660$	1.96787	+	0.691179i	0.0765993	+	0.0269041i
$661$	−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
$665$	25.0004	−	32.7549i	0.969474	−	1.27018i
$666$	−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
$670$	−2.20516	−	7.37493i	−0.0851929	−	0.284918i
$671$	−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	$0.494542\pi$
$673$	−24.3615	+	33.5308i	−0.939068	+	1.29252i	−0.956215	+	0.292663i	$0.905458\pi$
$674$	6.02761			0.232175
$675$	−4.82292	+	1.31888i	−0.185634	+	0.0507636i
$676$	−2.95892			−0.113804
$677$	−10.6881	+	14.7109i	−0.410777	+	0.565386i	−0.963408	−	0.268040i	$-0.913624\pi$
$677$	−10.6881	+	14.7109i	−0.410777	+	0.565386i	0.552631	+	0.833426i	$0.313624\pi$
$678$	3.89162	−	1.26446i	0.149457	−	0.0485614i
$679$	4.31339	+	13.2753i	0.165533	+	0.509457i
$680$	26.0903	−	18.0302i	1.00052	−	0.691425i
$681$	−7.92011	+	24.3756i	−0.303499	+	0.934074i
$682$		−	0.737453i		−	0.0282385i
$683$	27.0597	+	8.79224i	1.03541	+	0.336426i	0.776928	−	0.629590i	$-0.216777\pi$
$683$	27.0597	+	8.79224i	1.03541	+	0.336426i	0.258484	+	0.966015i	$0.416777\pi$
$684$	3.92258	−	2.84992i	0.149983	−	0.108969i
$685$	−41.5684	+	12.4293i	−1.58825	+	0.474899i
$686$	−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
$690$	−5.42994	+	1.62360i	−0.206714	+	0.0618093i
$691$	−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
$695$	−31.5671	+	21.8150i	−1.19741	+	0.827490i
$696$	−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
$700$	11.7288	+	4.43332i	0.443309	+	0.167564i
$701$	−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
$705$	−3.87550	−	12.9612i	−0.145960	−	0.488146i
$706$	−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	$0.0591101\pi$
$710$	−9.55944	+	12.5246i	−0.358760	+	0.470038i
$711$	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
$715$	−9.88314	−	3.47128i	−0.369609	−	0.129818i
$716$	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	$0.0569212\pi$
$720$	−3.04943	−	2.32750i	−0.113646	−	0.0867407i
$721$	−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
$725$	9.34161	−	24.7143i	0.346939	−	0.917865i
$726$	10.5510			0.391583
$727$	−7.82337	+	10.7680i	−0.290153	+	0.399361i	−0.929064	−	0.369920i	$-0.879385\pi$
$727$	−7.82337	+	10.7680i	−0.290153	+	0.399361i	0.638911	+	0.769281i	$0.279385\pi$
$728$	−36.7117	+	11.9283i	−1.36062	+	0.442094i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	17.5652	+	0.414837i	0.650116	+	0.0153538i
$731$	3.47424	−	10.6926i	0.128499	−	0.395480i
$732$		−	11.1651i		−	0.412675i
$733$	−27.3709	−	8.89333i	−1.01097	−	0.328483i	−0.243727	−	0.969844i	$-0.578370\pi$
$733$	−27.3709	−	8.89333i	−1.01097	−	0.328483i	−0.767239	+	0.641361i	$0.778370\pi$
$734$	−16.6226	+	12.0771i	−0.613553	+	0.445772i
$735$	−0.133627	+	5.65809i	−0.00492891	+	0.208702i
$736$	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	$0.434061\pi$
$740$	11.7716	+	17.0340i	0.432733	+	0.626181i
$741$	−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	$0.170411\pi$
$743$			27.8114i			1.02030i	−0.860085	+	0.510151i	$0.829589\pi$
$744$	0.558109	−	1.71768i	0.0204613	−	0.0629733i
$745$	−0.155704	+	0.443309i	−0.00570457	+	0.0162416i
$746$	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
$750$	−2.93559	−	11.8256i	−0.107193	−	0.431811i
$751$	−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
$755$	−3.00790	+	8.56386i	−0.109469	+	0.311671i
$756$	−0.774937	+	2.38501i	−0.0281842	+	0.0867420i
$757$		−	13.7637i		−	0.500251i	−0.968213	−	0.250126i	$-0.919528\pi$
$757$		−	13.7637i		−	0.500251i	0.968213	−	0.250126i	$-0.0804719\pi$
$758$	13.0237	+	4.23166i	0.473042	+	0.153701i
$759$	−2.16056	+	1.56974i	−0.0784235	+	0.0569780i
$760$	23.2566	+	33.6532i	0.843607	+	1.22073i
$761$	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
$765$	−0.244311	+	10.3447i	−0.00883308	+	0.374013i
$766$	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	$0.0860058\pi$
$770$	−8.63671	−	0.203973i	−0.311245	−	0.00735069i
$771$	−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	−0.452377	−	0.891827i	$-0.649424\pi$
$773$	14.8910	−	20.4957i	0.535592	−	0.737180i	0.987970	+	0.154647i	$0.0494240\pi$
$774$	−2.64776			−0.0951716
$775$	2.46278	−	1.61739i	0.0884658	−	0.0580983i
$776$	−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
$780$	−5.89019	−	4.49572i	−0.210903	−	0.160973i
$781$	−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
$785$	−0.928985	−	0.326289i	−0.0331569	−	0.0116458i
$786$	−1.83257	−	1.33144i	−0.0653656	−	0.0474909i
$787$	−22.7167	−	31.2669i	−0.809763	−	1.11454i	−0.991360	−	0.131170i	$-0.958127\pi$
$787$	−22.7167	−	31.2669i	−0.809763	−	1.11454i	0.181597	−	0.983373i	$-0.441873\pi$
$788$	5.51242	+	7.58719i	0.196372	+	0.270283i
$789$	−16.5328	−	12.0118i	−0.588582	−	0.427630i
$790$	−18.2412	+	23.8992i	−0.648992	+	0.850295i
$791$	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
$795$	−2.07791	−	6.94934i	−0.0736959	−	0.246468i
$796$	−5.76775	−	17.7513i	−0.204432	−	0.629178i
$797$	49.5519	−	16.1004i	1.75522	−	0.570306i	0.758533	−	0.651635i	$-0.225917\pi$
$797$	49.5519	−	16.1004i	1.75522	−	0.570306i	0.996687	+	0.0813294i	$0.0259166\pi$
$798$	−11.8044	+	16.2474i	−0.417872	+	0.575152i
$799$	−27.9968			−0.990454
$800$	−13.3197	+	16.6222i	−0.470921	+	0.587684i
$801$	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
$805$	−13.2078	+	9.12752i	−0.465515	+	0.321703i
$806$	−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	$0.111222\pi$
$810$	2.33477	−	0.698116i	0.0820356	−	0.0245293i
$811$	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
$815$	−6.94354	+	2.07618i	−0.243222	+	0.0727253i
$816$	−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
$820$	−14.1834	+	9.80171i	−0.495307	+	0.342290i
$821$	−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	−0.413065	−	0.910702i	$-0.635542\pi$
$823$	16.6593	−	22.9296i	0.580708	−	0.799276i	0.993773	+	0.111426i	$0.0355418\pi$
$824$	12.8920			0.449113
$825$	−3.15175	−	4.79915i	−0.109730	−	0.167085i
$826$	−10.7208			−0.373023
$827$	8.32775	−	11.4622i	0.289584	−	0.398579i	−0.639295	−	0.768962i	$-0.720774\pi$
$827$	8.32775	−	11.4622i	0.289584	−	0.398579i	0.928879	+	0.370383i	$0.120774\pi$
$828$	−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	$0.908384\pi$
$830$	8.65252	+	28.9374i	0.300333	+	1.00443i
$831$	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
$835$	21.6532	−	28.3695i	0.749339	−	0.981766i
$836$	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	$0.642031\pi$
$840$	−19.9623	−	7.01140i	−0.688765	−	0.241916i
$841$	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
$845$	6.47477	+	4.94191i	0.222739	+	0.170007i
$846$	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
$850$	−25.1880	−	1.19040i	−0.863941	−	0.0408302i
$851$	−26.5120			−0.908820
$852$	−3.08699	+	4.24887i	−0.105758	+	0.145564i
$853$	−14.1300	+	4.59110i	−0.483801	+	0.157196i	−0.540755	−	0.841180i	$-0.681861\pi$
$853$	−14.1300	+	4.59110i	−0.483801	+	0.157196i	0.0569538	+	0.998377i	$0.481861\pi$
$854$	14.2909	+	43.9828i	0.489024	+	1.50506i
$855$	−13.3433	−	0.315130i	−0.456333	−	0.0107772i
$856$	3.79973	−	11.6944i	0.129872	−	0.399705i
$857$		−	26.4088i		−	0.902109i	−0.892496	−	0.451054i	$-0.851048\pi$
$857$		−	26.4088i		−	0.902109i	0.892496	−	0.451054i	$-0.148952\pi$
$858$	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	$0.349782\pi$
$860$	−0.104190	+	4.41164i	−0.00355284	+	0.150436i
$861$	−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	0.915405	−	0.402534i	$-0.131870\pi$
$863$	7.33532	+	10.0962i	0.249697	+	0.343679i	−0.665708	+	0.746212i	$0.731870\pi$
$864$	−3.44649	−	2.50402i	−0.117252	−	0.0851886i
$865$	−0.714175	−	1.03344i	−0.0242827	−	0.0351379i
$866$	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
$870$	−4.26727	+	12.1494i	−0.144674	+	0.411904i
$871$	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
$875$	−18.2609	−	29.2903i	−0.617332	−	0.990194i
$876$	5.85662			0.197877
$877$	−23.9888	+	33.0177i	−0.810043	+	1.11493i	0.181273	+	0.983433i	$0.441978\pi$
$877$	−23.9888	+	33.0177i	−0.810043	+	1.11493i	−0.991317	+	0.131496i	$0.958022\pi$
$878$	−11.8819	+	3.86065i	−0.400993	+	0.130291i
$879$	−0.555691	−	1.71024i	−0.0187430	−	0.0576850i
$880$	1.45979	−	4.15621i	0.0492097	−	0.140106i
$881$	−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	0.314339	−	0.949311i	$-0.398217\pi$
$883$	0.316564	+	0.102858i	0.0106532	+	0.00346144i	−0.303686	+	0.952772i	$0.598217\pi$
$884$	−12.4061	+	9.01357i	−0.417263	+	0.303159i
$885$	−4.05070	−	5.86152i	−0.136163	−	0.197033i
$886$	−15.7815	−	11.4659i	−0.530190	−	0.385206i
$887$	−0.671685	−	0.924496i	−0.0225530	−	0.0310415i	0.797592	−	0.603198i	$-0.206107\pi$
$887$	−0.671685	−	0.924496i	−0.0225530	−	0.0310415i	−0.820145	+	0.572156i	$0.806107\pi$
$888$	−20.5365	−	28.2660i	−0.689159	−	0.948546i
$889$	−28.3688	−	20.6111i	−0.951459	−	0.691276i
$890$	−0.0623716	+	2.64096i	−0.00209070	+	0.0885252i
$891$	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
$895$	−35.6300	−	0.841475i	−1.19098	−	0.0281274i
$896$	−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
$900$	−1.07131	−	3.91763i	−0.0357105	−	0.130588i
$901$	−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
$905$	38.1936	+	29.1515i	1.26960	+	0.969030i
$906$	1.36704	−	4.20732i	0.0454169	−	0.139779i
$907$			18.4202i			0.611632i	0.952091	+	0.305816i	$0.0989293\pi$
$907$			18.4202i			0.611632i	−0.952091	+	0.305816i	$0.901071\pi$
$908$	−19.8001	−	6.43345i	−0.657090	−	0.213502i
$909$	−5.35029	+	3.88721i	−0.177458	+	0.128931i
$910$	28.9576	+	10.1708i	0.959933	+	0.337159i
$911$	−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
$915$	−18.6477	+	24.4318i	−0.616475	+	0.807691i
$916$	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	$0.157209\pi$
$920$	−4.56603	−	15.2706i	−0.150538	−	0.503457i
$921$	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
$925$	2.69076	−	56.9348i	0.0884717	−	1.87200i
$926$	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	$0.571236\pi$
$930$	−1.18137	+	0.816407i	−0.0387386	+	0.0267710i
$931$	−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
$935$	−11.3842	+	3.40397i	−0.372303	+	0.111322i
$936$	10.1154	+	7.34929i	0.330633	+	0.240219i
$937$	−0.000771322	−	0.00106163i	−2.51980e−5	−	3.46821e-5i	0.809004	−	0.587803i	$-0.200007\pi$
$937$	−0.000771322	−	0.00106163i	−2.51980e−5	−	3.46821e-5i	−0.809030	+	0.587768i	$0.800007\pi$
$938$	6.24680	+	8.59798i	0.203965	+	0.280734i
$939$	4.65924	+	3.38513i	0.152048	+	0.110470i
$940$	10.5283	−	3.14804i	0.343394	−	0.102678i
$941$	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
$945$	5.67912	−	3.92466i	0.184742	−	0.127669i
$946$	−0.939548	−	2.89163i	−0.0305473	−	0.0940151i
$947$	−32.2661	+	10.4839i	−1.04851	+	0.340681i	−0.782083	−	0.623174i	$-0.785843\pi$
$947$	−32.2661	+	10.4839i	−1.04851	+	0.340681i	−0.266426	+	0.963855i	$0.585843\pi$
$948$	−5.89054	+	8.10763i	−0.191316	+	0.263324i
$949$	−29.4134			−0.954800
$950$	1.53546	−	32.4893i	0.0498169	−	1.05409i
$951$	−12.2481			−0.397172
$952$	−25.7370	+	35.4240i	−0.834142	+	1.14810i
$953$	7.89670	−	2.56579i	0.255799	−	0.0831142i	−0.178310	−	0.983974i	$-0.557063\pi$
$953$	7.89670	−	2.56579i	0.255799	−	0.0831142i	0.434109	+	0.900860i	$0.357063\pi$
$954$	1.09242	+	3.36213i	0.0353685	+	0.108853i
$955$	−11.7827	−	39.4061i	−0.381281	−	1.27515i
$956$	−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
$960$	10.9537	−	14.3512i	0.353528	−	0.463184i
$961$	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
$965$	−4.27268	−	1.50070i	−0.137542	−	0.0483093i
$966$	6.33044	−	4.59933i	0.203679	−	0.147981i
$967$	−26.4313	−	8.58804i	−0.849972	−	0.276173i	−0.148538	−	0.988907i	$-0.547457\pi$
$967$	−26.4313	−	8.58804i	−0.849972	−	0.276173i	−0.701434	+	0.712734i	$0.747457\pi$
$968$			29.6724i			0.953707i
$969$	−8.53565	+	26.2700i	−0.274205	+	0.843915i
$970$	8.75840	+	6.68490i	0.281215	+	0.214639i
$971$	−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
$975$	5.38041	+	19.6753i	0.172311	+	0.630114i
$976$	−23.5811			−0.754814
$977$	−26.0928	+	35.9137i	−0.834783	+	1.14898i	0.152231	+	0.988345i	$0.451354\pi$
$977$	−26.0928	+	35.9137i	−0.834783	+	1.14898i	−0.987014	+	0.160635i	$0.948646\pi$
$978$	3.35932	−	1.09151i	0.107419	−	0.0349027i
$979$	0.384667	+	1.18388i	0.0122940	+	0.0378370i
$980$	−4.59603	−	0.108544i	−0.146815	−	0.00346733i
$981$	2.81009	−	8.64857i	0.0897193	−	0.276127i
$982$		−	18.1506i		−	0.579208i
$983$	−41.6427	−	13.5305i	−1.32820	−	0.431557i	−0.442894	−	0.896574i	$-0.646048\pi$
$983$	−41.6427	−	13.5305i	−1.32820	−	0.431557i	−0.885302	+	0.465017i	$0.846048\pi$
$984$	23.5359	−	17.0998i	0.750297	−	0.545123i
$985$	0.609536	−	25.8092i	0.0194214	−	0.822349i
$986$	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
$990$	1.59091	+	2.30210i	0.0505623	+	0.0731655i
$991$	−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
$995$	−17.0267	+	48.4770i	−0.539782	+	1.53682i
$996$	3.11107	+	9.57490i	0.0985781	+	0.303392i
$997$	18.4401	−	5.99154i	0.584002	−	0.189754i	−0.00209042	−	0.999998i	$-0.500665\pi$
$997$	18.4401	−	5.99154i	0.584002	−	0.189754i	0.586093	+	0.810244i	$0.300665\pi$
$998$	−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	75.2.i.a.34.2	✓	16
3.2	odd	2		225.2.m.b.109.3		16
5.2	odd	4		375.2.g.d.76.2		16
5.3	odd	4		375.2.g.e.76.3		16
5.4	even	2		375.2.i.c.49.3		16
25.2	odd	20		375.2.g.d.301.2		16
25.6	even	5		1875.2.b.h.1249.6		16
25.8	odd	20		1875.2.a.m.1.4		8
25.11	even	5		375.2.i.c.199.3		16
25.14	even	10	inner	75.2.i.a.64.2	yes	16
25.17	odd	20		1875.2.a.p.1.5		8
25.19	even	10		1875.2.b.h.1249.11		16
25.23	odd	20		375.2.g.e.301.3		16
75.8	even	20		5625.2.a.bd.1.5		8
75.14	odd	10		225.2.m.b.64.3		16
75.17	even	20		5625.2.a.t.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.2	✓	16	1.1	even	1	trivial
75.2.i.a.64.2	yes	16	25.14	even	10	inner
225.2.m.b.64.3		16	75.14	odd	10
225.2.m.b.109.3		16	3.2	odd	2
375.2.g.d.76.2		16	5.2	odd	4
375.2.g.d.301.2		16	25.2	odd	20
375.2.g.e.76.3		16	5.3	odd	4
375.2.g.e.301.3		16	25.23	odd	20
375.2.i.c.49.3		16	5.4	even	2
375.2.i.c.199.3		16	25.11	even	5
1875.2.a.m.1.4		8	25.8	odd	20
1875.2.a.p.1.5		8	25.17	odd	20
1875.2.b.h.1249.6		16	25.6	even	5
1875.2.b.h.1249.11		16	25.19	even	10
5625.2.a.t.1.4		8	75.17	even	20
5625.2.a.bd.1.5		8	75.8	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.640580 + 0.881682i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(0.741001 - 2.10972i) q^{5} +(-0.336773 + 1.03648i) q^{6} +3.08724i q^{7} +(-2.91489 - 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.640580 + 0.881682i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.251013 + 0.772537i) q^{4} +(0.741001 - 2.10972i) q^{5} +(-0.336773 + 1.03648i) q^{6} +3.08724i q^{7} +(-2.91489 - 0.947104i) q^{8} +(0.809017 - 0.587785i) q^{9} +(1.38543 + 2.00477i) q^{10} +(0.929002 + 0.674959i) q^{11} +(0.477454 + 0.657159i) q^{12} +(-2.39789 - 3.30042i) q^{13} +(-2.72197 - 1.97763i) q^{14} +(0.0527945 - 2.23544i) q^{15} +(1.38794 - 1.00840i) q^{16} +(-4.40109 - 1.43000i) q^{17} +1.08982i q^{18} +(1.84452 - 5.67685i) q^{19} +(1.81584 + 0.0428847i) q^{20} +(0.954011 + 2.93614i) q^{21} +(-1.19020 + 0.386719i) q^{22} +(-1.36700 + 1.88152i) q^{23} -3.06489 q^{24} +(-3.90184 - 3.12661i) q^{25} +4.44596 q^{26} +(0.587785 - 0.809017i) q^{27} +(-2.38501 + 0.774937i) q^{28} +(1.63290 + 5.02554i) q^{29} +(1.93713 + 1.47853i) q^{30} +(-0.182097 + 0.560438i) q^{31} -4.26010i q^{32} +(1.09211 + 0.354847i) q^{33} +(4.08005 - 2.96433i) q^{34} +(6.51322 + 2.28765i) q^{35} +(0.657159 + 0.477454i) q^{36} +(6.70056 + 9.22252i) q^{37} +(3.82361 + 5.26275i) q^{38} +(-3.30042 - 2.39789i) q^{39} +(-4.15806 + 5.44779i) q^{40} +(-7.67919 + 5.57926i) q^{41} +(-3.19987 - 1.03970i) q^{42} +2.42954i q^{43} +(-0.288240 + 0.887112i) q^{44} +(-0.640580 - 2.14235i) q^{45} +(-0.783227 - 2.41052i) q^{46} +(5.75387 - 1.86955i) q^{47} +(1.00840 - 1.38794i) q^{48} -2.53108 q^{49} +(5.25611 - 1.43734i) q^{50} -4.62758 q^{51} +(1.94779 - 2.68091i) q^{52} +(3.08503 - 1.00239i) q^{53} +(0.336773 + 1.03648i) q^{54} +(2.11237 - 1.45979i) q^{55} +(2.92394 - 8.99897i) q^{56} -5.96899i q^{57} +(-5.47693 - 1.77956i) q^{58} +(2.57785 - 1.87292i) q^{59} +(1.74022 - 0.520339i) q^{60} +(-11.1201 - 8.07922i) q^{61} +(-0.377480 - 0.519557i) q^{62} +(1.81464 + 2.49763i) q^{63} +(6.53194 + 4.74573i) q^{64} +(-8.73980 + 2.61327i) q^{65} +(-1.01244 + 0.735584i) q^{66} +(-3.00414 - 0.976103i) q^{67} -3.75895i q^{68} +(-0.718676 + 2.21186i) q^{69} +(-6.18922 + 4.27717i) q^{70} +(1.99795 + 6.14907i) q^{71} +(-2.91489 + 0.947104i) q^{72} +(4.23792 - 5.83300i) q^{73} -12.4236 q^{74} +(-4.67704 - 1.76785i) q^{75} +4.84857 q^{76} +(-2.08376 + 2.86806i) q^{77} +(4.22836 - 1.37388i) q^{78} +(3.81246 + 11.7336i) q^{79} +(-1.09897 - 3.67540i) q^{80} +(0.309017 - 0.951057i) q^{81} -10.3446i q^{82} +(11.7875 + 3.82999i) q^{83} +(-2.02881 + 1.47402i) q^{84} +(-6.27811 + 8.22543i) q^{85} +(-2.14208 - 1.55631i) q^{86} +(3.10596 + 4.27498i) q^{87} +(-2.06868 - 2.84729i) q^{88} +(0.877003 + 0.637180i) q^{89} +(2.29921 + 0.807557i) q^{90} +(10.1892 - 7.40289i) q^{91} +(-1.79668 - 0.583776i) q^{92} +0.589279i q^{93} +(-2.03747 + 6.27068i) q^{94} +(-10.6098 - 8.09797i) q^{95} +(-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	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) \) 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 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 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 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more