LMFDB - Embedded newform 825.2.bx.h.724.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
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} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.3
Root			$-1.28932 - 0.418926i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.h.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10527 + 0.359123i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.525387 - 0.381716i) q^{4} +(0.359123 + 1.10527i) q^{6} +(-2.51974 + 3.46813i) q^{7} +(-1.80980 - 2.49097i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(1.10527 + 0.359123i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.525387 - 0.381716i) q^{4} +(0.359123 + 1.10527i) q^{6} +(-2.51974 + 3.46813i) q^{7} +(-1.80980 - 2.49097i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.15911 - 1.00996i) q^{11} -0.649414i q^{12} +(-4.91433 - 1.59676i) q^{13} +(-4.03048 + 2.92831i) q^{14} +(-0.704384 - 2.16787i) q^{16} +(-4.75528 + 1.54508i) q^{17} +(-0.683093 + 0.940197i) q^{18} +(4.53048 - 3.29158i) q^{19} -4.28684 q^{21} +(-3.12896 - 2.25079i) q^{22} +0.219819i q^{23} +(0.951466 - 2.92831i) q^{24} +(-4.85822 - 3.52970i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(2.64768 - 0.860283i) q^{28} +(5.19262 + 3.77266i) q^{29} +(-0.874813 + 2.69240i) q^{31} +3.50898i q^{32} +(-1.03980 - 3.14941i) q^{33} -5.81074 q^{34} +(0.525387 - 0.381716i) q^{36} +(2.30883 - 3.17784i) q^{37} +(6.18947 - 2.01108i) q^{38} +(-1.59676 - 4.91433i) q^{39} +(-4.74165 + 3.44501i) q^{41} +(-4.73811 - 1.53950i) q^{42} +8.90173i q^{43} +(1.27424 + 1.73650i) q^{44} +(-0.0789420 + 0.242959i) q^{46} +(0.139821 + 0.192447i) q^{47} +(1.33982 - 1.84410i) q^{48} +(-3.51569 - 10.8202i) q^{49} +(-4.04508 - 2.93893i) q^{51} +(1.97242 + 2.71480i) q^{52} +(-2.41255 - 0.783885i) q^{53} -1.16215 q^{54} +13.1992 q^{56} +(5.32589 + 1.73049i) q^{57} +(4.38439 + 6.03459i) q^{58} +(-6.36725 - 4.62608i) q^{59} +(-1.50123 - 4.62030i) q^{61} +(-1.93381 + 2.66165i) q^{62} +(-2.51974 - 3.46813i) q^{63} +(-2.66892 + 8.21410i) q^{64} +(-0.0182340 - 3.85436i) q^{66} +12.1280i q^{67} +(3.08815 + 1.00340i) q^{68} +(-0.177837 + 0.129206i) q^{69} +(-3.08459 - 9.49339i) q^{71} +(2.92831 - 0.951466i) q^{72} +(-8.55964 + 11.7813i) q^{73} +(3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(11.4628 - 8.41136i) q^{77} -6.00509i q^{78} +(-2.47274 + 7.61030i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-6.47797 + 2.10482i) q^{82} +(11.9386 - 3.87908i) q^{83} +(2.25225 + 1.63636i) q^{84} +(-3.19682 + 9.83880i) q^{86} +6.41843i q^{87} +(3.20157 + 9.69707i) q^{88} +2.56545 q^{89} +(17.9206 - 13.0201i) q^{91} +(0.0839083 - 0.115490i) q^{92} +(-2.69240 + 0.874813i) q^{93} +(0.0854274 + 0.262919i) q^{94} +(-2.83882 + 2.06253i) q^{96} +(1.91351 + 0.621738i) q^{97} -13.2218i q^{98} +(1.93675 - 2.69240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.10527	+	0.359123i	0.781542	+	0.253938i	0.672499	−	0.740098i	$-0.265221\pi$
$2$	1.10527	+	0.359123i	0.781542	+	0.253938i	0.109044	+	0.994037i	$0.465221\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	−0.525387	−	0.381716i	−0.262693	−	0.190858i
$5$		0			0
$5$		0			0
$6$	0.359123	+	1.10527i	0.146611	+	0.451224i
$7$	−2.51974	+	3.46813i	−0.952373	+	1.31083i	−0.00190785	+	0.999998i	$0.500607\pi$
$7$	−2.51974	+	3.46813i	−0.952373	+	1.31083i	−0.950465	+	0.310831i	$0.899393\pi$
$8$	−1.80980	−	2.49097i	−0.639860	−	0.880691i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−3.15911	−	1.00996i	−0.952508	−	0.304514i
$11$	−3.15911	−	1.00996i	−0.952508	−	0.304514i
$12$		−	0.649414i		−	0.187470i
$13$	−4.91433	−	1.59676i	−1.36299	−	0.442863i	−0.465950	−	0.884811i	$-0.654287\pi$
$13$	−4.91433	−	1.59676i	−1.36299	−	0.442863i	−0.897040	+	0.441948i	$0.854287\pi$
$14$	−4.03048	+	2.92831i	−1.07719	+	0.782624i
$15$		0			0
$16$	−0.704384	−	2.16787i	−0.176096	−	0.541968i
$17$	−4.75528	+	1.54508i	−1.15333	+	0.374738i	−0.822395	−	0.568917i	$-0.807363\pi$
$17$	−4.75528	+	1.54508i	−1.15333	+	0.374738i	−0.330930	+	0.943655i	$0.607363\pi$
$18$	−0.683093	+	0.940197i	−0.161007	+	0.221607i
$19$	4.53048	−	3.29158i	1.03936	−	0.755141i	0.0692013	−	0.997603i	$-0.477955\pi$
$19$	4.53048	−	3.29158i	1.03936	−	0.755141i	0.970161	+	0.242462i	$0.0779549\pi$
$20$		0			0
$21$	−4.28684			−0.935466
$22$	−3.12896	−	2.25079i	−0.667097	−	0.479869i
$23$			0.219819i			0.0458354i	0.999737	+	0.0229177i	$0.00729557\pi$
$23$			0.219819i			0.0458354i	−0.999737	+	0.0229177i	$0.992704\pi$
$24$	0.951466	−	2.92831i	0.194217	−	0.597739i
$25$		0			0
$26$	−4.85822	−	3.52970i	−0.952775	−	0.692232i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	2.64768	−	0.860283i	0.500364	−	0.162578i
$29$	5.19262	+	3.77266i	0.964246	+	0.700566i	0.954133	−	0.299383i	$-0.0967809\pi$
$29$	5.19262	+	3.77266i	0.964246	+	0.700566i	0.0101128	+	0.999949i	$0.496781\pi$
$30$		0			0
$31$	−0.874813	+	2.69240i	−0.157121	+	0.483569i	−0.998370	−	0.0570796i	$-0.981821\pi$
$31$	−0.874813	+	2.69240i	−0.157121	+	0.483569i	0.841249	+	0.540649i	$0.181821\pi$
$32$			3.50898i			0.620306i
$33$	−1.03980	−	3.14941i	−0.181007	−	0.548243i
$34$	−5.81074			−0.996533
$35$		0			0
$36$	0.525387	−	0.381716i	0.0875645	−	0.0636193i
$37$	2.30883	−	3.17784i	0.379570	−	0.522433i	−0.575901	−	0.817520i	$-0.695348\pi$
$37$	2.30883	−	3.17784i	0.379570	−	0.522433i	0.955471	+	0.295087i	$0.0953485\pi$
$38$	6.18947	−	2.01108i	1.00406	−	0.326240i
$39$	−1.59676	−	4.91433i	−0.255687	−	0.786923i
$40$		0			0
$41$	−4.74165	+	3.44501i	−0.740521	+	0.538020i	−0.892874	−	0.450306i	$-0.851315\pi$
$41$	−4.74165	+	3.44501i	−0.740521	+	0.538020i	0.152353	+	0.988326i	$0.451315\pi$
$42$	−4.73811	−	1.53950i	−0.731106	−	0.237551i
$43$			8.90173i			1.35750i	0.734369	+	0.678751i	$0.237478\pi$
$43$			8.90173i			1.35750i	−0.734369	+	0.678751i	$0.762522\pi$
$44$	1.27424	+	1.73650i	0.192099	+	0.261788i
$45$		0			0
$46$	−0.0789420	+	0.242959i	−0.0116394	+	0.0358223i
$47$	0.139821	+	0.192447i	0.0203950	+	0.0280713i	0.819093	−	0.573661i	$-0.194477\pi$
$47$	0.139821	+	0.192447i	0.0203950	+	0.0280713i	−0.798698	+	0.601732i	$0.794477\pi$
$48$	1.33982	−	1.84410i	0.193386	−	0.266173i
$49$	−3.51569	−	10.8202i	−0.502241	−	1.54574i
$50$		0			0
$51$	−4.04508	−	2.93893i	−0.566425	−	0.411532i
$52$	1.97242	+	2.71480i	0.273525	+	0.376475i
$53$	−2.41255	−	0.783885i	−0.331389	−	0.107675i	0.138596	−	0.990349i	$-0.455741\pi$
$53$	−2.41255	−	0.783885i	−0.331389	−	0.107675i	−0.469986	+	0.882674i	$0.655741\pi$
$54$	−1.16215			−0.158148
$55$		0			0
$56$	13.1992			1.76382
$57$	5.32589	+	1.73049i	0.705432	+	0.229209i
$58$	4.38439	+	6.03459i	0.575698	+	0.792381i
$59$	−6.36725	−	4.62608i	−0.828945	−	0.602264i	0.0903156	−	0.995913i	$-0.471212\pi$
$59$	−6.36725	−	4.62608i	−0.828945	−	0.602264i	−0.919261	+	0.393649i	$0.871212\pi$
$60$		0			0
$61$	−1.50123	−	4.62030i	−0.192212	−	0.591569i	−0.999998	−	0.00209225i	$-0.999334\pi$
$61$	−1.50123	−	4.62030i	−0.192212	−	0.591569i	0.807785	−	0.589477i	$-0.200666\pi$
$62$	−1.93381	+	2.66165i	−0.245594	+	0.338031i
$63$	−2.51974	−	3.46813i	−0.317458	−	0.436943i
$64$	−2.66892	+	8.21410i	−0.333615	+	1.02676i
$65$		0			0
$66$	−0.0182340	−	3.85436i	−0.00224445	−	0.474439i
$67$			12.1280i			1.48167i	0.671688	+	0.740834i	$0.265569\pi$
$67$			12.1280i			1.48167i	−0.671688	+	0.740834i	$0.734431\pi$
$68$	3.08815	+	1.00340i	0.374493	+	0.121680i
$69$	−0.177837	+	0.129206i	−0.0214091	+	0.0155546i
$70$		0			0
$71$	−3.08459	−	9.49339i	−0.366073	−	1.12666i	−0.949306	−	0.314353i	$-0.898212\pi$
$71$	−3.08459	−	9.49339i	−0.366073	−	1.12666i	0.583233	−	0.812305i	$-0.301788\pi$
$72$	2.92831	−	0.951466i	0.345105	−	0.112131i
$73$	−8.55964	+	11.7813i	−1.00183	+	1.37890i	−0.0776335	+	0.996982i	$0.524736\pi$
$73$	−8.55964	+	11.7813i	−1.00183	+	1.37890i	−0.924196	+	0.381918i	$0.875264\pi$
$74$	3.69311	−	2.68320i	0.429316	−	0.311916i
$75$		0			0
$76$	−3.63670			−0.417158
$77$	11.4628	−	8.41136i	1.30631	−	0.958564i
$78$		−	6.00509i		−	0.679942i
$79$	−2.47274	+	7.61030i	−0.278205	+	0.856226i	0.710149	+	0.704051i	$0.248628\pi$
$79$	−2.47274	+	7.61030i	−0.278205	+	0.856226i	−0.988354	+	0.152174i	$0.951372\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−6.47797	+	2.10482i	−0.715373	+	0.232439i
$83$	11.9386	−	3.87908i	1.31043	−	0.425784i	0.431231	−	0.902242i	$-0.358079\pi$
$83$	11.9386	−	3.87908i	1.31043	−	0.425784i	0.879197	+	0.476458i	$0.158079\pi$
$84$	2.25225	+	1.63636i	0.245741	+	0.178541i
$85$		0			0
$86$	−3.19682	+	9.83880i	−0.344722	+	1.06094i
$87$			6.41843i			0.688128i
$88$	3.20157	+	9.69707i	0.341288	+	1.03371i
$89$	2.56545			0.271937			0.135969	−	0.990713i	$-0.456585\pi$
$89$	2.56545			0.271937			0.135969	+	0.990713i	$0.456585\pi$
$90$		0			0
$91$	17.9206	−	13.0201i	1.87859	−	1.36488i
$92$	0.0839083	−	0.115490i	0.00874805	−	0.0120407i
$93$	−2.69240	+	0.874813i	−0.279189	+	0.0907139i
$94$	0.0854274	+	0.262919i	0.00881116	+	0.0271180i
$95$		0			0
$96$	−2.83882	+	2.06253i	−0.289736	+	0.210506i
$97$	1.91351	+	0.621738i	0.194288	+	0.0631279i	0.404545	−	0.914518i	$-0.367430\pi$
$97$	1.91351	+	0.621738i	0.194288	+	0.0631279i	−0.210257	+	0.977646i	$0.567430\pi$
$98$		−	13.2218i		−	1.33560i
$99$	1.93675	−	2.69240i	0.194650	−	0.270596i
$100$		0			0
$101$	−2.34385	+	7.21362i	−0.233221	+	0.717782i	0.764131	+	0.645061i	$0.223168\pi$
$101$	−2.34385	+	7.21362i	−0.233221	+	0.717782i	−0.997352	+	0.0727205i	$0.976832\pi$
$102$	−3.41546	−	4.70098i	−0.338181	−	0.465467i
$103$	9.91508	−	13.6469i	0.976962	−	1.34467i	0.0385116	−	0.999258i	$-0.487738\pi$
$103$	9.91508	−	13.6469i	0.976962	−	1.34467i	0.938450	−	0.345414i	$-0.112262\pi$
$104$	4.91645	+	15.1313i	0.482098	+	1.48374i
$105$		0			0
$106$	−2.38500	−	1.73281i	−0.231652	−	0.168305i
$107$	−4.56216	−	6.27928i	−0.441041	−	0.607041i	0.529402	−	0.848371i	$-0.322416\pi$
$107$	−4.56216	−	6.27928i	−0.441041	−	0.607041i	−0.970443	+	0.241330i	$0.922416\pi$
$108$	0.617629	+	0.200680i	0.0594314	+	0.0193104i
$109$	−4.45671			−0.426876			−0.213438	−	0.976957i	$-0.568466\pi$
$109$	−4.45671			−0.426876			−0.213438	+	0.976957i	$0.568466\pi$
$110$		0			0
$111$	3.92802			0.372831
$112$	9.29332	+	3.01958i	0.878136	+	0.285324i
$113$	−4.53327	−	6.23952i	−0.426455	−	0.586964i	0.540680	−	0.841228i	$-0.318167\pi$
$113$	−4.53327	−	6.23952i	−0.426455	−	0.586964i	−0.967135	+	0.254264i	$0.918167\pi$
$114$	5.26508	+	3.82530i	0.493120	+	0.358273i
$115$		0			0
$116$	−1.28805	−	3.96421i	−0.119593	−	0.368068i
$117$	3.03722	−	4.18038i	0.280792	−	0.386476i
$118$	−5.37618	−	7.39968i	−0.494918	−	0.681196i
$119$	6.62353	−	20.3851i	0.607178	−	1.86870i
$120$		0			0
$121$	8.95996	+	6.38115i	0.814542	+	0.580105i
$122$		−	5.64579i		−	0.511146i
$123$	−5.57414	−	1.81115i	−0.502603	−	0.163306i
$124$	1.48735	−	1.08062i	0.133568	−	0.0970426i
$125$		0			0
$126$	−1.53950	−	4.73811i	−0.137150	−	0.422104i
$127$	−1.45620	+	0.473149i	−0.129217	+	0.0419852i	−0.372912	−	0.927867i	$-0.621641\pi$
$127$	−1.45620	+	0.473149i	−0.129217	+	0.0419852i	0.243695	+	0.969852i	$0.421641\pi$
$128$	−1.77470	+	2.44266i	−0.156863	+	0.215903i
$129$	−7.20165	+	5.23231i	−0.634070	+	0.460679i
$130$		0			0
$131$	2.66108			0.232500			0.116250	−	0.993220i	$-0.462913\pi$
$131$	2.66108			0.232500			0.116250	+	0.993220i	$0.462913\pi$
$132$	−0.655882	+	2.05157i	−0.0570872	+	0.178566i
$133$			24.0062i			2.08160i
$134$	−4.35544	+	13.4047i	−0.376252	+	1.15799i
$135$		0			0
$136$	12.4549	+	9.04898i	1.06799	+	0.775944i
$137$	−9.75352	+	3.16911i	−0.833300	+	0.270756i	−0.694435	−	0.719556i	$-0.744345\pi$
$137$	−9.75352	+	3.16911i	−0.833300	+	0.270756i	−0.138865	+	0.990311i	$0.544345\pi$
$138$	−0.242959	+	0.0789420i	−0.0206820	+	0.00671999i
$139$	−4.28381	−	3.11237i	−0.363348	−	0.263987i	0.391099	−	0.920348i	$-0.372095\pi$
$139$	−4.28381	−	3.11237i	−0.363348	−	0.263987i	−0.754447	+	0.656361i	$0.772095\pi$
$140$		0			0
$141$	−0.0735083	+	0.226235i	−0.00619051	+	0.0190524i
$142$		−	11.6005i		−	0.973491i
$143$	13.9123	+	10.0076i	1.16340	+	0.836880i
$144$	2.27943			0.189953
$145$		0			0
$146$	−13.6916	+	9.94756i	−1.13313	+	0.823266i
$147$	6.68724	−	9.20420i	0.551554	−	0.759149i
$148$	−2.42606	+	0.788275i	−0.199421	+	0.0647958i
$149$	−1.17068	−	3.60300i	−0.0959062	−	0.295169i	0.891583	−	0.452858i	$-0.149596\pi$
$149$	−1.17068	−	3.60300i	−0.0959062	−	0.295169i	−0.987489	+	0.157689i	$0.949596\pi$
$150$		0			0
$151$	4.78939	−	3.47969i	0.389755	−	0.283173i	−0.375600	−	0.926782i	$-0.622563\pi$
$151$	4.78939	−	3.47969i	0.389755	−	0.283173i	0.765355	+	0.643608i	$0.222563\pi$
$152$	−16.3985	−	5.32819i	−1.33009	−	0.432173i
$153$		−	5.00000i		−	0.404226i
$154$	15.6902	−	5.18024i	1.26435	−	0.417436i
$155$		0			0
$156$	−1.03696	+	3.19144i	−0.0830233	+	0.255519i
$157$	4.36671	+	6.01026i	0.348501	+	0.479671i	0.946900	−	0.321528i	$-0.104196\pi$
$157$	4.36671	+	6.01026i	0.348501	+	0.479671i	−0.598399	+	0.801198i	$0.704196\pi$
$158$	−5.46607	+	7.52340i	−0.434857	+	0.598530i
$159$	−0.783885	−	2.41255i	−0.0621661	−	0.191328i
$160$		0			0
$161$	−0.762360	−	0.553887i	−0.0600824	−	0.0436524i
$162$	−0.683093	−	0.940197i	−0.0536689	−	0.0738688i
$163$	−5.06044	−	1.64424i	−0.396364	−	0.128786i	0.104051	−	0.994572i	$-0.466819\pi$
$163$	−5.06044	−	1.64424i	−0.396364	−	0.128786i	−0.500415	+	0.865785i	$0.666819\pi$
$164$	3.80621			0.297215
$165$		0			0
$166$	14.5884			1.13228
$167$	−1.87490	−	0.609193i	−0.145084	−	0.0471407i	0.235575	−	0.971856i	$-0.424303\pi$
$167$	−1.87490	−	0.609193i	−0.145084	−	0.0471407i	−0.380659	+	0.924716i	$0.624303\pi$
$168$	7.75831	+	10.6784i	0.598567	+	0.823856i
$169$	11.0838	+	8.05285i	0.852599	+	0.619450i
$170$		0			0
$171$	1.73049	+	5.32589i	0.132334	+	0.407281i
$172$	3.39793	−	4.67685i	0.259090	−	0.356607i
$173$	−1.16090	−	1.59784i	−0.0882617	−	0.121482i	0.762603	−	0.646867i	$-0.223921\pi$
$173$	−1.16090	−	1.59784i	−0.0882617	−	0.121482i	−0.850864	+	0.525385i	$0.823921\pi$
$174$	−2.30501	+	7.09409i	−0.174742	+	0.537801i
$175$		0			0
$176$	0.0357642	+	7.55994i	0.00269583	+	0.569852i
$177$		−	7.87035i		−	0.591572i
$178$	2.83551	+	0.921313i	0.212530	+	0.0690553i
$179$	−1.63676	+	1.18918i	−0.122337	+	0.0888832i	−0.647271	−	0.762260i	$-0.724090\pi$
$179$	−1.63676	+	1.18918i	−0.122337	+	0.0888832i	0.524934	+	0.851143i	$0.324090\pi$
$180$		0			0
$181$	6.22299	+	19.1524i	0.462551	+	1.42359i	0.862036	+	0.506846i	$0.169189\pi$
$181$	6.22299	+	19.1524i	0.462551	+	1.42359i	−0.399485	+	0.916740i	$0.630811\pi$
$182$	24.4829	−	7.95498i	1.81479	−	0.589662i
$183$	2.85550	−	3.93026i	0.211085	−	0.290533i
$184$	0.547562	−	0.397827i	0.0403668	−	0.0293282i
$185$		0			0
$186$	−3.28999			−0.241234
$187$	16.5829	−	0.0784497i	1.21266	−	0.00573681i
$188$		−	0.154481i		−	0.0112667i
$189$	1.32471	−	4.07703i	0.0963583	−	0.296560i
$190$		0			0
$191$	−10.2463	−	7.44439i	−0.741398	−	0.538657i	0.151751	−	0.988419i	$-0.451509\pi$
$191$	−10.2463	−	7.44439i	−0.741398	−	0.538657i	−0.893149	+	0.449762i	$0.851509\pi$
$192$	−8.21410	+	2.66892i	−0.592802	+	0.192613i
$193$	−13.2502	+	4.30526i	−0.953773	+	0.309900i	−0.744248	−	0.667904i	$-0.767192\pi$
$193$	−13.2502	+	4.30526i	−0.953773	+	0.309900i	−0.209525	+	0.977803i	$0.567192\pi$
$194$	1.89166	+	1.37437i	0.135813	+	0.0986743i
$195$		0			0
$196$	−2.28314	+	7.02678i	−0.163081	+	0.501913i
$197$			14.6060i			1.04064i	0.853972	+	0.520319i	$0.174187\pi$
$197$			14.6060i			1.04064i	−0.853972	+	0.520319i	$0.825813\pi$
$198$	3.10753	−	2.28029i	0.220842	−	0.162053i
$199$	11.8748			0.841784			0.420892	−	0.907111i	$-0.361717\pi$
$199$	11.8748			0.841784			0.420892	+	0.907111i	$0.361717\pi$
$200$		0			0
$201$	−9.81174	+	7.12864i	−0.692067	+	0.502816i
$202$	−5.18115	+	7.13125i	−0.364545	+	0.501753i
$203$	−26.1681	+	8.50254i	−1.83664	+	0.596762i
$204$	1.00340	+	3.08815i	0.0702520	+	0.216213i
$205$		0			0
$206$	15.8597	−	11.5228i	1.10500	−	0.802830i
$207$	−0.209060	−	0.0679277i	−0.0145307	−	0.00472130i
$208$			11.7784i			0.816683i
$209$	−17.6366	+	5.82288i	−1.21995	+	0.402777i
$210$		0			0
$211$	−6.90710	+	21.2579i	−0.475504	+	1.46345i	0.369772	+	0.929122i	$0.379436\pi$
$211$	−6.90710	+	21.2579i	−0.475504	+	1.46345i	−0.845277	+	0.534329i	$0.820564\pi$
$212$	0.968301	+	1.33275i	0.0665032	+	0.0915338i
$213$	5.86724	−	8.07556i	0.402017	−	0.553328i
$214$	−2.78738	−	8.57866i	−0.190541	−	0.586425i
$215$		0			0
$216$	2.49097	+	1.80980i	0.169489	+	0.123141i
$217$	−7.13328	−	9.81811i	−0.484238	−	0.666497i
$218$	−4.92586	−	1.60051i	−0.333621	−	0.108400i
$219$	−14.5625			−0.984044
$220$		0			0
$221$	25.8362			1.73793
$222$	4.34152	+	1.41064i	0.291384	+	0.0946762i
$223$	−11.2610	−	15.4994i	−0.754091	−	1.03792i	−0.997683	−	0.0680388i	$-0.978326\pi$
$223$	−11.2610	−	15.4994i	−0.754091	−	1.03792i	0.243592	−	0.969878i	$-0.421674\pi$
$224$	−12.1696	−	8.84173i	−0.813115	−	0.590763i
$225$		0			0
$226$	−2.76973	−	8.52434i	−0.184239	−	0.567031i
$227$	9.03772	−	12.4394i	0.599855	−	0.825629i	−0.395840	−	0.918319i	$-0.629547\pi$
$227$	9.03772	−	12.4394i	0.599855	−	0.825629i	0.995695	+	0.0926901i	$0.0295466\pi$
$228$	−2.13760	−	2.94215i	−0.141566	−	0.194849i
$229$	−2.75064	+	8.46560i	−0.181767	+	0.559422i	−0.999878	−	0.0156388i	$-0.995022\pi$
$229$	−2.75064	+	8.46560i	−0.181767	+	0.559422i	0.818110	+	0.575061i	$0.195022\pi$
$230$		0			0
$231$	13.5426	+	4.32954i	0.891038	+	0.284863i
$232$		−	19.7624i		−	1.29747i
$233$	−21.7185	−	7.05677i	−1.42283	−	0.462304i	−0.506327	−	0.862342i	$-0.668997\pi$
$233$	−21.7185	−	7.05677i	−1.42283	−	0.462304i	−0.916499	+	0.400037i	$0.868997\pi$
$234$	4.85822	−	3.52970i	0.317592	−	0.230744i
$235$		0			0
$236$	1.57942	+	4.86096i	0.102812	+	0.316422i
$237$	−7.61030	+	2.47274i	−0.494342	+	0.160621i
$238$	14.6416	−	20.1524i	0.949071	−	1.30628i
$239$	13.6405	−	9.91037i	0.882327	−	0.641048i	−0.0515388	−	0.998671i	$-0.516413\pi$
$239$	13.6405	−	9.91037i	0.882327	−	0.641048i	0.933866	+	0.357623i	$0.116413\pi$
$240$		0			0
$241$	−11.9607			−0.770459			−0.385229	−	0.922821i	$-0.625878\pi$
$241$	−11.9607			−0.770459			−0.385229	+	0.922821i	$0.625878\pi$
$242$	7.61154	+	10.2706i	0.489288	+	0.660220i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.974917	+	3.00049i	−0.0624127	+	0.192087i
$245$		0			0
$246$	−5.51049	−	4.00361i	−0.351336	−	0.255261i
$247$	−27.5201	+	8.94184i	−1.75106	+	0.568955i
$248$	8.28992	−	2.69356i	0.526410	−	0.171041i
$249$	10.1556	+	7.37844i	0.643582	+	0.467590i
$250$		0			0
$251$	4.94533	−	15.2201i	0.312146	−	0.960687i	−0.664767	−	0.747051i	$-0.731469\pi$
$251$	4.94533	−	15.2201i	0.312146	−	0.960687i	0.976913	−	0.213637i	$-0.0685308\pi$
$252$			2.78393i			0.175371i
$253$	0.222008	−	0.694432i	0.0139575	−	0.0436586i
$254$	−1.77941			−0.111650
$255$		0			0
$256$	11.1359	−	8.09073i	0.695996	−	0.505671i
$257$	3.21780	−	4.42893i	0.200721	−	0.276269i	−0.696776	−	0.717288i	$-0.745383\pi$
$257$	3.21780	−	4.42893i	0.200721	−	0.276269i	0.897498	+	0.441019i	$0.145383\pi$
$258$	−9.83880	+	3.19682i	−0.612537	+	0.199025i
$259$	5.20348	+	16.0147i	0.323328	+	0.995103i
$260$		0			0
$261$	−5.19262	+	3.77266i	−0.321415	+	0.233522i
$262$	2.94121	+	0.955657i	0.181709	+	0.0590407i
$263$		−	11.9841i		−	0.738971i	−0.929236	−	0.369486i	$-0.879534\pi$
$263$		−	11.9841i		−	0.738971i	0.929236	−	0.369486i	$-0.120466\pi$
$264$	−5.96326	+	8.28992i	−0.367014	+	0.510209i
$265$		0			0
$266$	−8.62119	+	26.5333i	−0.528599	+	1.62686i
$267$	1.50793	+	2.07549i	0.0922841	+	0.127018i
$268$	4.62944	−	6.37188i	0.282788	−	0.389224i
$269$	−4.21700	−	12.9786i	−0.257115	−	0.791318i	−0.993406	−	0.114653i	$-0.963424\pi$
$269$	−4.21700	−	12.9786i	−0.257115	−	0.791318i	0.736291	−	0.676665i	$-0.236576\pi$
$270$		0			0
$271$	−9.57702	−	6.95812i	−0.581763	−	0.422675i	0.257596	−	0.966253i	$-0.417070\pi$
$271$	−9.57702	−	6.95812i	−0.581763	−	0.422675i	−0.839359	+	0.543577i	$0.817070\pi$
$272$	6.69909	+	9.22050i	0.406192	+	0.559075i
$273$	21.0670	+	6.84507i	1.27503	+	0.414283i
$274$	−11.9184			−0.720014
$275$		0			0
$276$	0.142753			0.00859274
$277$	9.76148	+	3.17170i	0.586511	+	0.190569i	0.587215	−	0.809431i	$-0.300224\pi$
$277$	9.76148	+	3.17170i	0.586511	+	0.190569i	−0.000704561		1.00000i	$0.500224\pi$
$278$	−3.61703	−	4.97841i	−0.216935	−	0.298585i
$279$	−2.29029	−	1.66399i	−0.137116	−	0.0996207i
$280$		0			0
$281$	−0.908167	−	2.79505i	−0.0541767	−	0.166739i	0.920307	−	0.391197i	$-0.127939\pi$
$281$	−0.908167	−	2.79505i	−0.0541767	−	0.166739i	−0.974484	+	0.224458i	$0.927939\pi$
$282$	−0.162493	+	0.223652i	−0.00967629	+	0.0133183i
$283$	12.8301	+	17.6592i	0.762673	+	1.04973i	0.996987	+	0.0775682i	$0.0247156\pi$
$283$	12.8301	+	17.6592i	0.762673	+	1.04973i	−0.234314	+	0.972161i	$0.575284\pi$
$284$	−2.00318	+	6.16514i	−0.118867	+	0.365834i
$285$		0			0
$286$	11.7828	+	16.0573i	0.696731	+	0.949490i
$287$		−	25.1252i		−	1.48309i
$288$	−3.33724	−	1.08433i	−0.196649	−	0.0638950i
$289$	6.47214	−	4.70228i	0.380714	−	0.276605i
$290$		0			0
$291$	0.621738	+	1.91351i	0.0364469	+	0.112172i
$292$	8.99424	−	2.92241i	0.526348	−	0.171021i
$293$	14.5574	−	20.0365i	0.850452	−	1.17055i	−0.133311	−	0.991074i	$-0.542561\pi$
$293$	14.5574	−	20.0365i	0.850452	−	1.17055i	0.983763	−	0.179473i	$-0.0574391\pi$
$294$	10.6966	−	7.77156i	0.623840	−	0.453246i
$295$		0			0
$296$	−12.0944			−0.702974
$297$	3.31659	−	0.0156899i	0.192448	−	0.000910423i
$298$		−	4.40269i		−	0.255041i
$299$	0.350999	−	1.08026i	0.0202988	−	0.0624732i
$300$		0			0
$301$	−30.8723	−	22.4301i	−1.77945	−	1.29285i
$302$	6.54319	−	2.12601i	0.376518	−	0.122338i
$303$	−7.21362	+	2.34385i	−0.414411	+	0.134650i
$304$	−10.3269	−	7.50295i	−0.592289	−	0.430323i
$305$		0			0
$306$	1.79562	−	5.52634i	0.102649	−	0.315920i
$307$		−	4.94023i		−	0.281954i	−0.990013	−	0.140977i	$-0.954976\pi$
$307$		−	4.94023i		−	0.281954i	0.990013	−	0.140977i	$-0.0450243\pi$
$308$	−9.23316	+	0.0436798i	−0.526108	+	0.00248889i
$309$	16.8685			0.959618
$310$		0			0
$311$	11.1722	−	8.11707i	0.633517	−	0.460277i	−0.224100	−	0.974566i	$-0.571944\pi$
$311$	11.1722	−	8.11707i	0.633517	−	0.460277i	0.857617	+	0.514289i	$0.171944\pi$
$312$	−9.35164	+	12.8714i	−0.529432	+	0.728701i
$313$	−3.87017	+	1.25750i	−0.218755	+	0.0710779i	−0.416344	−	0.909207i	$-0.636689\pi$
$313$	−3.87017	+	1.25750i	−0.218755	+	0.0710779i	0.197589	+	0.980285i	$0.436689\pi$
$314$	2.66796	+	8.21113i	0.150562	+	0.463381i
$315$		0			0
$316$	4.20412	−	3.05447i	0.236500	−	0.171827i
$317$	24.5562	+	7.97880i	1.37921	+	0.448134i	0.902411	−	0.430876i	$-0.141795\pi$
$317$	24.5562	+	7.97880i	1.37921	+	0.448134i	0.476803	+	0.879010i	$0.341795\pi$
$318$		−	2.94803i		−	0.165317i
$319$	−12.5938	−	17.1626i	−0.705119	−	0.960921i
$320$		0			0
$321$	2.39847	−	7.38173i	0.133870	−	0.412008i
$322$	−0.643698	−	0.885974i	−0.0358719	−	0.0493734i
$323$	−16.4579	+	22.6524i	−0.915743	+	1.26041i
$324$	0.200680	+	0.617629i	0.0111489	+	0.0343127i
$325$		0			0
$326$	−5.00265	−	3.63464i	−0.277071	−	0.201304i
$327$	−2.61959	−	3.60556i	−0.144864	−	0.199388i
$328$	17.1628	+	5.57654i	0.947659	+	0.307913i
$329$	−1.01974			−0.0562203
$330$		0			0
$331$	−3.35008			−0.184137			−0.0920684	−	0.995753i	$-0.529348\pi$
$331$	−3.35008			−0.184137			−0.0920684	+	0.995753i	$0.529348\pi$
$332$	−7.75307	−	2.51913i	−0.425505	−	0.138255i
$333$	2.30883	+	3.17784i	0.126523	+	0.174144i
$334$	−1.85349	−	1.34664i	−0.101419	−	0.0736850i
$335$		0			0
$336$	3.01958	+	9.29332i	0.164732	+	0.506992i
$337$	−16.1052	+	22.1669i	−0.877307	+	1.20751i	0.0998530	+	0.995002i	$0.468163\pi$
$337$	−16.1052	+	22.1669i	−0.877307	+	1.20751i	−0.977160	+	0.212507i	$0.931837\pi$
$338$	9.35859	+	12.8810i	0.509040	+	0.700634i
$339$	2.38328	−	7.33499i	0.129442	−	0.398382i
$340$		0			0
$341$	5.48285	−	7.62206i	0.296913	−	0.412758i
$342$			6.50800i			0.351912i
$343$	17.8452	+	5.79826i	0.963550	+	0.313076i
$344$	22.1739	−	16.1103i	1.19554	−	0.868610i
$345$		0			0
$346$	−0.709284	−	2.18295i	−0.0381313	−	0.117356i
$347$	−15.0519	+	4.89065i	−0.808027	+	0.262544i	−0.683762	−	0.729705i	$-0.739657\pi$
$347$	−15.0519	+	4.89065i	−0.808027	+	0.262544i	−0.124265	+	0.992249i	$0.539657\pi$
$348$	2.45002	−	3.37216i	0.131335	−	0.180767i
$349$	−2.96043	+	2.15088i	−0.158468	+	0.115134i	−0.664194	−	0.747561i	$-0.731225\pi$
$349$	−2.96043	+	2.15088i	−0.158468	+	0.115134i	0.505725	+	0.862695i	$0.331225\pi$
$350$		0			0
$351$	5.16724			0.275807
$352$	3.54393	−	11.0853i	0.188892	−	0.590846i
$353$			27.4937i			1.46334i	0.681658	+	0.731671i	$0.261259\pi$
$353$			27.4937i			1.46334i	−0.681658	+	0.731671i	$0.738741\pi$
$354$	2.82643	−	8.69884i	0.150223	−	0.462338i
$355$		0			0
$356$	−1.34785	−	0.979273i	−0.0714361	−	0.0519014i
$357$	20.3851	−	6.62353i	1.07890	−	0.350555i
$358$	−2.23612	+	0.726559i	−0.118183	+	0.0383998i
$359$	0.387309	+	0.281397i	0.0204414	+	0.0148515i	0.597959	−	0.801527i	$-0.295979\pi$
$359$	0.387309	+	0.281397i	0.0204414	+	0.0148515i	−0.577518	+	0.816378i	$0.695979\pi$
$360$		0			0
$361$	3.81936	−	11.7548i	0.201019	−	0.618673i
$362$			23.4033i			1.23005i
$363$	0.104074	+	10.9995i	0.00546247	+	0.577324i
$364$	−14.3852			−0.753992
$365$		0			0
$366$	4.56754	−	3.31851i	0.238749	−	0.173462i
$367$	−14.9639	+	20.5961i	−0.781111	+	1.07511i	0.214047	+	0.976823i	$0.431335\pi$
$367$	−14.9639	+	20.5961i	−0.781111	+	1.07511i	−0.995158	+	0.0982843i	$0.968665\pi$
$368$	0.476539	−	0.154837i	0.0248413	−	0.00807143i
$369$	−1.81115	−	5.57414i	−0.0942846	−	0.290178i
$370$		0			0
$371$	8.79762	−	6.39184i	0.456750	−	0.331848i
$372$	1.74848	+	0.568116i	0.0906545	+	0.0294554i
$373$			2.75967i			0.142890i	0.997445	+	0.0714451i	$0.0227611\pi$
$373$			2.75967i			0.142890i	−0.997445	+	0.0714451i	$0.977239\pi$
$374$	18.3568	+	5.86861i	0.949205	+	0.303459i
$375$		0			0
$376$	0.226333	−	0.696580i	0.0116722	−	0.0359234i
$377$	−19.4942	−	26.8315i	−1.00400	−	1.38189i
$378$	2.92831	−	4.03048i	0.150616	−	0.207305i
$379$	6.69130	+	20.5937i	0.343709	+	1.05783i	0.962271	+	0.272092i	$0.0877156\pi$
$379$	6.69130	+	20.5937i	0.343709	+	1.05783i	−0.618562	+	0.785736i	$0.712284\pi$
$380$		0			0
$381$	−1.23872	−	0.899983i	−0.0634616	−	0.0461075i
$382$	−8.65148	−	11.9077i	−0.442648	−	0.609253i
$383$	−15.4351	−	5.01518i	−0.788699	−	0.256264i	−0.113149	−	0.993578i	$-0.536094\pi$
$383$	−15.4351	−	5.01518i	−0.788699	−	0.256264i	−0.675550	+	0.737314i	$0.736094\pi$
$384$	−3.01930			−0.154078
$385$		0			0
$386$	−16.1912			−0.824109
$387$	−8.46605	−	2.75079i	−0.430353	−	0.139830i
$388$	−0.768007	−	1.05707i	−0.0389897	−	0.0536647i
$389$	−13.1802	−	9.57598i	−0.668263	−	0.485522i	0.201180	−	0.979554i	$-0.435522\pi$
$389$	−13.1802	−	9.57598i	−0.668263	−	0.485522i	−0.869443	+	0.494033i	$0.835522\pi$
$390$		0			0
$391$	−0.339639	−	1.04530i	−0.0171763	−	0.0528631i
$392$	−20.5901	+	28.3398i	−1.03996	+	1.43138i
$393$	1.56415	+	2.15286i	0.0789007	+	0.108598i
$394$	−5.24537	+	16.1436i	−0.264258	+	0.813302i
$395$		0			0
$396$	−2.04527	+	0.675263i	−0.102779	+	0.0339332i
$397$		−	19.9673i		−	1.00213i	−0.865410	−	0.501064i	$-0.832942\pi$
$397$		−	19.9673i		−	1.00213i	0.865410	−	0.501064i	$-0.167058\pi$
$398$	13.1249	+	4.26453i	0.657890	+	0.213761i
$399$	−19.4214	+	14.1105i	−0.972288	+	0.706408i
$400$		0			0
$401$	−8.44448	−	25.9894i	−0.421697	−	1.29785i	−0.906122	−	0.423017i	$-0.860971\pi$
$401$	−8.44448	−	25.9894i	−0.421697	−	1.29785i	0.484425	−	0.874833i	$-0.339029\pi$
$402$	−13.4047	+	4.35544i	−0.668563	+	0.217229i
$403$	8.59825	−	11.8345i	0.428309	−	0.589517i
$404$	3.98498	−	2.89526i	0.198260	−	0.144044i
$405$		0			0
$406$	−31.9763			−1.58696
$407$	−10.5034	+	7.70731i	−0.520632	+	0.382037i
$408$			15.3950i			0.762168i
$409$	−7.70626	+	23.7174i	−0.381050	+	1.17275i	0.558255	+	0.829669i	$0.311471\pi$
$409$	−7.70626	+	23.7174i	−0.381050	+	1.17275i	−0.939305	+	0.343082i	$0.888529\pi$
$410$		0			0
$411$	−8.29684	−	6.02801i	−0.409253	−	0.297340i
$412$	−10.4185	+	3.38518i	−0.513283	+	0.166776i
$413$	32.0876	−	10.4259i	1.57893	−	0.513025i
$414$	−0.206673	−	0.150157i	−0.0101574	−	0.00737980i
$415$		0			0
$416$	5.60301	−	17.2443i	0.274710	−	0.845471i
$417$		−	5.29507i		−	0.259301i
$418$	−21.5843	+	0.102110i	−1.05572	+	0.00499437i
$419$	−16.8256			−0.821986			−0.410993	−	0.911639i	$-0.634818\pi$
$419$	−16.8256			−0.821986			−0.410993	+	0.911639i	$0.634818\pi$
$420$		0			0
$421$	−19.0933	+	13.8721i	−0.930551	+	0.676085i	−0.946128	−	0.323793i	$-0.895042\pi$
$421$	−19.0933	+	13.8721i	−0.930551	+	0.676085i	0.0155763	+	0.999879i	$0.495042\pi$
$422$	−15.2684	+	21.0151i	−0.743253	+	1.02300i
$423$	−0.226235	+	0.0735083i	−0.0109999	+	0.00357409i
$424$	2.41359	+	7.42826i	0.117214	+	0.360748i
$425$		0			0
$426$	9.38499	−	6.81859i	0.454704	−	0.330362i
$427$	19.8065	+	6.43552i	0.958504	+	0.311437i
$428$			5.04050i			0.243642i
$429$	0.0810736	+	17.1376i	0.00391427	+	0.827411i
$430$		0			0
$431$	−11.6362	+	35.8126i	−0.560497	+	1.72503i	0.120469	+	0.992717i	$0.461560\pi$
$431$	−11.6362	+	35.8126i	−0.560497	+	1.72503i	−0.680966	+	0.732315i	$0.738440\pi$
$432$	1.33982	+	1.84410i	0.0644620	+	0.0887243i
$433$	18.2068	−	25.0594i	0.874961	−	1.20428i	−0.102831	−	0.994699i	$-0.532790\pi$
$433$	18.2068	−	25.0594i	0.874961	−	1.20428i	0.977791	−	0.209581i	$-0.0672100\pi$
$434$	−4.35827	−	13.4134i	−0.209204	−	0.643862i
$435$		0			0
$436$	2.34150	+	1.70120i	0.112137	+	0.0814726i
$437$	0.723552	+	0.995884i	0.0346122	+	0.0476396i
$438$	−16.0955	−	5.22974i	−0.769072	−	0.249887i
$439$	28.2131			1.34654			0.673268	−	0.739399i	$-0.264890\pi$
$439$	28.2131			1.34654			0.673268	+	0.739399i	$0.264890\pi$
$440$		0			0
$441$	11.3770			0.541762
$442$	28.5559	+	9.27837i	1.35827	+	0.441327i
$443$	8.60636	+	11.8456i	0.408900	+	0.562803i	0.962950	−	0.269681i	$-0.0869182\pi$
$443$	8.60636	+	11.8456i	0.408900	+	0.562803i	−0.554050	+	0.832484i	$0.686918\pi$
$444$	−2.06373	−	1.49939i	−0.0979404	−	0.0711578i
$445$		0			0
$446$	−6.88019	−	21.1751i	−0.325787	−	1.00267i
$447$	2.22677	−	3.06489i	0.105323	−	0.144964i
$448$	−21.7626	−	29.9536i	−1.02818	−	1.41517i
$449$	−3.70749	+	11.4105i	−0.174967	+	0.538493i	−0.999632	−	0.0271282i	$-0.991364\pi$
$449$	−3.70749	+	11.4105i	−0.174967	+	0.538493i	0.824665	+	0.565622i	$0.191364\pi$
$450$		0			0
$451$	18.4587	−	6.09429i	0.869187	−	0.286969i
$452$			5.00858i			0.235584i
$453$	5.63026	+	1.82938i	0.264533	+	0.0859519i
$454$	14.4564	−	10.5032i	0.678471	−	0.492938i
$455$		0			0
$456$	−5.32819	−	16.3985i	−0.249515	−	0.767929i
$457$	−9.55211	+	3.10367i	−0.446829	+	0.145183i	−0.523784	−	0.851851i	$-0.675480\pi$
$457$	−9.55211	+	3.10367i	−0.446829	+	0.145183i	0.0769553	+	0.997035i	$0.475480\pi$
$458$	−6.08039	+	8.36893i	−0.284118	+	0.391055i
$459$	4.04508	−	2.93893i	0.188808	−	0.137177i
$460$		0			0
$461$	−13.4491			−0.626386			−0.313193	−	0.949689i	$-0.601399\pi$
$461$	−13.4491			−0.626386			−0.313193	+	0.949689i	$0.601399\pi$
$462$	13.4134	+	9.64876i	0.624046	+	0.448901i
$463$		−	18.7836i		−	0.872946i	−0.899717	−	0.436473i	$-0.856227\pi$
$463$		−	18.7836i		−	0.872946i	0.899717	−	0.436473i	$-0.143773\pi$
$464$	4.52104	−	13.9143i	0.209884	−	0.645957i
$465$		0			0
$466$	−21.4705	−	15.5992i	−0.994602	−	0.722620i
$467$	−25.2515	+	8.20470i	−1.16850	+	0.379668i	−0.828082	−	0.560607i	$-0.810568\pi$
$467$	−25.2515	+	8.20470i	−1.16850	+	0.379668i	−0.340416	+	0.940275i	$0.610568\pi$
$468$	−3.19144	+	1.03696i	−0.147524	+	0.0479335i
$469$	−42.0614	−	30.5594i	−1.94221	−	1.41110i
$470$		0			0
$471$	−2.29571	+	7.06548i	−0.105781	+	0.325560i
$472$			24.2329i			1.11541i
$473$	8.99039	−	28.1216i	0.413379	−	1.29303i
$474$	−9.29944			−0.427137
$475$		0			0
$476$	−11.2613	+	8.18178i	−0.516159	+	0.375011i
$477$	1.49104	−	2.05224i	0.0682699	−	0.0939655i
$478$	18.6354	−	6.05501i	0.852363	−	0.276950i
$479$	−3.33214	−	10.2553i	−0.152249	−	0.468575i	0.845623	−	0.533781i	$-0.179229\pi$
$479$	−3.33214	−	10.2553i	−0.152249	−	0.468575i	−0.997872	+	0.0652062i	$0.979229\pi$
$480$		0			0
$481$	−16.4206	+	11.9303i	−0.748716	+	0.543974i
$482$	−13.2198	−	4.29538i	−0.602146	−	0.195649i
$483$		−	0.942328i		−	0.0428774i
$484$	−2.27166	−	6.77273i	−0.103257	−	0.307851i
$485$		0			0
$486$	0.359123	−	1.10527i	0.0162902	−	0.0501360i
$487$	−4.00338	−	5.51018i	−0.181410	−	0.249690i	0.708621	−	0.705589i	$-0.249318\pi$
$487$	−4.00338	−	5.51018i	−0.181410	−	0.249690i	−0.890031	+	0.455899i	$0.849318\pi$
$488$	−8.79212	+	12.1013i	−0.398001	+	0.547801i
$489$	−1.64424	−	5.06044i	−0.0743549	−	0.228841i
$490$		0			0
$491$	−21.1116	−	15.3385i	−0.952754	−	0.692216i	−0.00129727	−	0.999999i	$-0.500413\pi$
$491$	−21.1116	−	15.3385i	−0.952754	−	0.692216i	−0.951457	+	0.307783i	$0.900413\pi$
$492$	2.23724	+	3.07929i	0.100862	+	0.138825i
$493$	−30.5215	−	9.91703i	−1.37462	−	0.446640i
$494$	−33.6283			−1.51301
$495$		0			0
$496$	6.45297			0.289747
$497$	40.6967	+	13.2231i	1.82549	+	0.593139i
$498$	8.57484	+	11.8022i	0.384248	+	0.528871i
$499$	15.6815	+	11.3933i	0.702000	+	0.510033i	0.880583	−	0.473892i	$-0.157151\pi$
$499$	15.6815	+	11.3933i	0.702000	+	0.510033i	−0.178583	+	0.983925i	$0.557151\pi$
$500$		0			0
$501$	−0.609193	−	1.87490i	−0.0272167	−	0.0837644i
$502$	10.9318	−	15.0464i	0.487911	−	0.671552i
$503$	11.0752	+	15.2437i	0.493819	+	0.679683i	0.981087	−	0.193570i	$-0.0620065\pi$
$503$	11.0752	+	15.2437i	0.493819	+	0.679683i	−0.487268	+	0.873253i	$0.662007\pi$
$504$	−4.07878	+	12.5532i	−0.181684	+	0.559164i
$505$		0			0
$506$	0.494765	−	0.687805i	0.0219950	−	0.0305767i
$507$			13.7003i			0.608453i
$508$	0.945678	+	0.307270i	0.0419577	+	0.0136329i
$509$	−4.16741	+	3.02780i	−0.184717	+	0.134205i	−0.676301	−	0.736625i	$-0.736418\pi$
$509$	−4.16741	+	3.02780i	−0.184717	+	0.134205i	0.491584	+	0.870830i	$0.336418\pi$
$510$		0			0
$511$	−19.2911	−	59.3718i	−0.853387	−	2.62645i
$512$	20.9568	−	6.80928i	0.926168	−	0.300930i
$513$	−3.29158	+	4.53048i	−0.145327	+	0.200025i
$514$	5.14707	−	3.73956i	0.227027	−	0.164945i
$515$		0			0
$516$	5.78091			0.254490
$517$	−0.247346	−	0.749175i	−0.0108783	−	0.0329487i
$518$			19.5692i			0.859820i
$519$	0.610322	−	1.87838i	0.0267902	−	0.0824516i
$520$		0			0
$521$	33.5759	+	24.3944i	1.47099	+	1.06874i	0.980326	+	0.197387i	$0.0632455\pi$
$521$	33.5759	+	24.3944i	1.47099	+	1.06874i	0.490663	+	0.871349i	$0.336754\pi$
$522$	−7.09409	+	2.30501i	−0.310500	+	0.100887i
$523$	−6.58397	+	2.13926i	−0.287897	+	0.0935434i	−0.449405	−	0.893328i	$-0.648364\pi$
$523$	−6.58397	+	2.13926i	−0.287897	+	0.0935434i	0.161508	+	0.986871i	$0.448364\pi$
$524$	−1.39810	−	1.01578i	−0.0610762	−	0.0443745i
$525$		0			0
$526$	4.30377	−	13.2456i	0.187653	−	0.577537i
$527$		−	14.1548i		−	0.616592i
$528$	−6.09510	+	4.47256i	−0.265255	+	0.194643i
$529$	22.9517			0.997899
$530$		0			0
$531$	6.36725	−	4.62608i	0.276315	−	0.200755i
$532$	9.16355	−	12.6125i	0.397290	−	0.546823i
$533$	28.8029	−	9.35863i	1.24759	−	0.405367i
$534$	0.921313	+	2.83551i	0.0398691	+	0.122704i
$535$		0			0
$536$	30.2104	−	21.9492i	1.30489	−	0.948059i
$537$	−1.92413	−	0.625187i	−0.0830322	−	0.0269788i
$538$		−	15.8592i		−	0.683740i
$539$	0.178505	+	37.7329i	0.00768874	+	1.62527i
$540$		0			0
$541$	−8.78173	+	27.0274i	−0.377556	+	1.16200i	0.564182	+	0.825651i	$0.309192\pi$
$541$	−8.78173	+	27.0274i	−0.377556	+	1.16200i	−0.941738	+	0.336348i	$0.890808\pi$
$542$	−8.08635	−	11.1299i	−0.347339	−	0.478071i
$543$	−11.8368	+	16.2920i	−0.507967	+	0.699156i
$544$	−5.42167	−	16.6862i	−0.232452	−	0.715415i
$545$		0			0
$546$	20.8264	+	15.1313i	0.891288	+	0.647559i
$547$	−15.1996	−	20.9205i	−0.649889	−	0.894496i	0.349205	−	0.937046i	$-0.386452\pi$
$547$	−15.1996	−	20.9205i	−0.649889	−	0.894496i	−0.999094	+	0.0425503i	$0.986452\pi$
$548$	6.33407	+	2.05807i	0.270578	+	0.0879162i
$549$	4.85807			0.207337
$550$		0			0
$551$	35.9431			1.53123
$552$	0.643698	+	0.209150i	0.0273976	+	0.00890202i
$553$	−20.1628	−	27.7518i	−0.857411	−	1.18012i
$554$	9.65002	+	7.01115i	0.409990	+	0.297875i
$555$		0			0
$556$	1.06262	+	3.27039i	0.0450649	+	0.138696i
$557$	−4.73996	+	6.52399i	−0.200838	+	0.276430i	−0.897542	−	0.440929i	$-0.854649\pi$
$557$	−4.73996	+	6.52399i	−0.200838	+	0.276430i	0.696704	+	0.717359i	$0.254649\pi$
$558$	−1.93381	−	2.66165i	−0.0818645	−	0.112677i
$559$	14.2140	−	43.7461i	0.601186	−	1.85026i
$560$		0			0
$561$	9.81067	+	13.3698i	0.414207	+	0.564472i
$562$		−	3.41542i		−	0.144071i
$563$	−28.2003	−	9.16284i	−1.18850	−	0.386168i	−0.352983	−	0.935630i	$-0.614833\pi$
$563$	−28.2003	−	9.16284i	−1.18850	−	0.386168i	−0.835519	+	0.549462i	$0.814833\pi$
$564$	0.124978	−	0.0908017i	0.00526252	−	0.00382344i
$565$		0			0
$566$	7.83892	+	24.1257i	0.329494	+	1.01408i
$567$	4.07703	−	1.32471i	0.171219	−	0.0556325i
$568$	−18.0653	+	24.8647i	−0.758002	+	1.04330i
$569$	−34.0618	+	24.7473i	−1.42794	+	1.03746i	−0.437548	+	0.899195i	$0.644153\pi$
$569$	−34.0618	+	24.7473i	−1.42794	+	1.03746i	−0.990395	+	0.138266i	$0.955847\pi$
$570$		0			0
$571$	−26.6823			−1.11662			−0.558311	−	0.829632i	$-0.688550\pi$
$571$	−26.6823			−1.11662			−0.558311	+	0.829632i	$0.688550\pi$
$572$	−3.48924	−	10.5684i	−0.145893	−	0.441887i
$573$		−	12.6652i		−	0.529094i
$574$	9.02304	−	27.7700i	0.376614	−	1.15910i
$575$		0			0
$576$	−6.98733	−	5.07659i	−0.291139	−	0.211525i
$577$	3.14627	−	1.02228i	0.130981	−	0.0425582i	−0.242793	−	0.970078i	$-0.578064\pi$
$577$	3.14627	−	1.02228i	0.130981	−	0.0425582i	0.373774	+	0.927520i	$0.378064\pi$
$578$	8.84214	−	2.87299i	0.367785	−	0.119500i
$579$	−11.2713	−	8.18910i	−0.468420	−	0.340327i
$580$		0			0
$581$	−16.6290	+	51.1788i	−0.689887	+	2.12325i
$582$			2.33822i			0.0969225i
$583$	6.82982	+	4.91296i	0.282862	+	0.203474i
$584$	44.8381			1.85542
$585$		0			0
$586$	23.2854	−	16.9178i	0.961911	−	0.698869i
$587$	−5.01246	+	6.89906i	−0.206886	+	0.284755i	−0.899833	−	0.436234i	$-0.856312\pi$
$587$	−5.01246	+	6.89906i	−0.206886	+	0.284755i	0.692947	+	0.720989i	$0.256312\pi$
$588$	−7.02678	+	2.28314i	−0.289779	+	0.0941550i
$589$	4.89893	+	15.0774i	0.201857	+	0.621252i
$590$		0			0
$591$	−11.8165	+	8.58522i	−0.486068	+	0.353149i
$592$	−8.51544	−	2.76684i	−0.349983	−	0.113716i
$593$			23.4343i			0.962333i	0.876629	+	0.481167i	$0.159787\pi$
$593$			23.4343i			0.962333i	−0.876629	+	0.481167i	$0.840213\pi$
$594$	3.67135	+	1.17372i	0.150637	+	0.0481584i
$595$		0			0
$596$	−0.760259	+	2.33984i	−0.0311414	+	0.0958434i
$597$	6.97985	+	9.60694i	0.285666	+	0.393186i
$598$	0.775895	−	1.06793i	0.0317287	−	0.0436708i
$599$	−5.82017	−	17.9126i	−0.237805	−	0.731890i	−0.996737	−	0.0807194i	$-0.974278\pi$
$599$	−5.82017	−	17.9126i	−0.237805	−	0.731890i	0.758931	−	0.651171i	$-0.225722\pi$
$600$		0			0
$601$	30.4664	+	22.1351i	1.24275	+	0.902911i	0.997778	−	0.0666198i	$-0.0212214\pi$
$601$	30.4664	+	22.1351i	1.24275	+	0.902911i	0.244971	+	0.969530i	$0.421221\pi$
$602$	−26.0670	−	35.8782i	−1.06241	−	1.46229i
$603$	−11.5344	−	3.74775i	−0.469717	−	0.152620i
$604$	−3.84453			−0.156432
$605$		0			0
$606$	−8.81471			−0.358073
$607$	−27.9306	−	9.07520i	−1.13367	−	0.368351i	−0.318699	−	0.947856i	$-0.603246\pi$
$607$	−27.9306	−	9.07520i	−1.13367	−	0.368351i	−0.814969	+	0.579505i	$0.803246\pi$
$608$	11.5501	+	15.8973i	0.468418	+	0.644723i
$609$	−22.2599	−	16.1728i	−0.902019	−	0.655355i
$610$		0			0
$611$	−0.379834	−	1.16901i	−0.0153665	−	0.0472931i
$612$	−1.90858	+	2.62693i	−0.0771498	+	0.106188i
$613$	−7.58894	−	10.4453i	−0.306515	−	0.421881i	0.627776	−	0.778394i	$-0.283965\pi$
$613$	−7.58894	−	10.4453i	−0.306515	−	0.421881i	−0.934290	+	0.356513i	$0.883965\pi$
$614$	1.77415	−	5.46027i	0.0715989	−	0.220359i
$615$		0			0
$616$	−41.6978	−	13.3307i	−1.68005	−	0.537109i
$617$			41.6041i			1.67492i	0.546500	+	0.837459i	$0.315960\pi$
$617$			41.6041i			1.67492i	−0.546500	+	0.837459i	$0.684040\pi$
$618$	18.6443	+	6.05789i	0.749982	+	0.243684i
$619$	3.45545	−	2.51053i	0.138886	−	0.100907i	−0.516173	−	0.856484i	$-0.672644\pi$
$619$	3.45545	−	2.51053i	0.138886	−	0.100907i	0.655059	+	0.755578i	$0.272644\pi$
$620$		0			0
$621$	−0.0679277	−	0.209060i	−0.00272585	−	0.00838929i
$622$	15.2633	−	4.95935i	0.612002	−	0.198852i
$623$	−6.46427	+	8.89731i	−0.258986	+	0.356463i
$624$	−9.52890	+	6.92315i	−0.381461	+	0.277148i
$625$		0			0
$626$	−4.72918			−0.189016
$627$	−15.0774	−	10.8457i	−0.602132	−	0.433137i
$628$		−	4.82455i		−	0.192521i
$629$	−6.06913	+	18.6789i	−0.241992	+	0.744775i
$630$		0			0
$631$	22.2892	+	16.1941i	0.887319	+	0.644675i	0.935178	−	0.354179i	$-0.115240\pi$
$631$	22.2892	+	16.1941i	0.887319	+	0.644675i	−0.0478586	+	0.998854i	$0.515240\pi$
$632$	23.4322	−	7.61358i	0.932082	−	0.302852i
$633$	−21.2579	+	6.90710i	−0.844924	+	0.274532i
$634$	24.2758	+	17.6374i	0.964116	+	0.700471i
$635$		0			0
$636$	−0.509066	+	1.56674i	−0.0201858	+	0.0621254i
$637$			58.7877i			2.32925i
$638$	−7.75607	−	23.4920i	−0.307066	−	0.930057i
$639$	9.98194			0.394879
$640$		0			0
$641$	−7.41712	+	5.38885i	−0.292958	+	0.212847i	−0.724550	−	0.689222i	$-0.757952\pi$
$641$	−7.41712	+	5.38885i	−0.292958	+	0.212847i	0.431591	+	0.902069i	$0.357952\pi$
$642$	5.30190	−	7.29744i	0.209249	−	0.288007i
$643$	−3.24223	+	1.05346i	−0.127861	+	0.0415446i	−0.372249	−	0.928133i	$-0.621413\pi$
$643$	−3.24223	+	1.05346i	−0.127861	+	0.0415446i	0.244387	+	0.969678i	$0.421413\pi$
$644$	0.189106	+	0.582010i	0.00745184	+	0.0229344i
$645$		0			0
$646$	−26.3254	+	19.1265i	−1.03576	+	0.752523i
$647$	21.2663	+	6.90986i	0.836066	+	0.271654i	0.695598	−	0.718431i	$-0.255139\pi$
$647$	21.2663	+	6.90986i	0.836066	+	0.271654i	0.140468	+	0.990085i	$0.455139\pi$
$648$			3.07901i			0.120955i
$649$	15.4427	+	21.0450i	0.606179	+	0.826087i
$650$		0			0
$651$	3.75019	−	11.5419i	0.146981	−	0.452362i
$652$	2.03106	+	2.79551i	0.0795423	+	0.109481i
$653$	8.69667	−	11.9699i	0.340327	−	0.468420i	−0.604210	−	0.796825i	$-0.706511\pi$
$653$	8.69667	−	11.9699i	0.340327	−	0.468420i	0.944537	+	0.328405i	$0.106511\pi$
$654$	−1.60051	−	4.92586i	−0.0625848	−	0.192616i
$655$		0			0
$656$	10.8083	+	7.85267i	0.421992	+	0.306595i
$657$	−8.55964	−	11.7813i	−0.333943	−	0.459633i
$658$	−1.12709	−	0.366214i	−0.0439385	−	0.0142765i
$659$	47.4724			1.84926			0.924631	−	0.380864i	$-0.124373\pi$
$659$	47.4724			1.84926			0.924631	+	0.380864i	$0.124373\pi$
$660$		0			0
$661$	−21.6525			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$662$	−3.70273	−	1.20309i	−0.143911	−	0.0467594i
$663$	15.1861	+	20.9019i	0.589780	+	0.811763i
$664$	−31.2690	−	22.7183i	−1.21347	−	0.881641i
$665$		0			0
$666$	1.41064	+	4.34152i	0.0546614	+	0.168230i
$667$	−0.829302	+	1.14144i	−0.0321107	+	0.0441966i
$668$	0.752510	+	1.03574i	0.0291155	+	0.0400740i
$669$	5.92024	−	18.2206i	0.228890	−	0.704451i
$670$		0			0
$671$	0.0762228	+	16.1122i	0.00294255	+	0.622005i
$672$		−	15.0424i		−	0.580275i
$673$	36.5133	+	11.8639i	1.40748	+	0.457319i	0.911603	−	0.411072i	$-0.134846\pi$
$673$	36.5133	+	11.8639i	1.40748	+	0.457319i	0.495880	+	0.868391i	$0.334846\pi$
$674$	−25.7612	+	18.7166i	−0.992285	+	0.720937i
$675$		0			0
$676$	−2.74938	−	8.46172i	−0.105745	−	0.325451i
$677$	21.8108	−	7.08677i	0.838259	−	0.272367i	0.141739	−	0.989904i	$-0.454731\pi$
$677$	21.8108	−	7.08677i	0.838259	−	0.272367i	0.696520	+	0.717537i	$0.254731\pi$
$678$	5.26833	−	7.25124i	0.202329	−	0.278482i
$679$	−6.97782	+	5.06969i	−0.267784	+	0.194557i
$680$		0			0
$681$	15.3759			0.589206
$682$	8.79727	−	6.45540i	0.336865	−	0.247190i
$683$		−	25.9084i		−	0.991359i	−0.868505	−	0.495680i	$-0.834919\pi$
$683$		−	25.9084i		−	0.991359i	0.868505	−	0.495680i	$-0.165081\pi$
$684$	1.12380	−	3.45871i	0.0429697	−	0.132247i
$685$		0			0
$686$	17.6414	+	12.8173i	0.673553	+	0.489365i
$687$	−8.46560	+	2.75064i	−0.322983	+	0.104943i
$688$	19.2978	−	6.27024i	0.735722	−	0.239050i
$689$	10.6044	+	7.70454i	0.403995	+	0.293520i
$690$		0			0
$691$	4.57824	−	14.0904i	0.174165	−	0.536023i	−0.825430	−	0.564505i	$-0.809067\pi$
$691$	4.57824	−	14.0904i	0.174165	−	0.536023i	0.999594	+	0.0284814i	$0.00906715\pi$
$692$			1.28262i			0.0487579i
$693$	4.45748	+	13.5010i	0.169325	+	0.512862i
$694$	−18.3927			−0.698177
$695$		0			0
$696$	15.9881	−	11.6161i	0.606029	−	0.440305i
$697$	17.2250	−	23.7082i	0.652445	−	0.898014i
$698$	−4.04450	+	1.31414i	−0.153087	+	0.0497409i
$699$	−7.05677	−	21.7185i	−0.266911	−	0.821469i
$700$		0			0
$701$	−4.45471	+	3.23653i	−0.168252	+	0.122242i	−0.668725	−	0.743510i	$-0.733160\pi$
$701$	−4.45471	+	3.23653i	−0.168252	+	0.122242i	0.500473	+	0.865752i	$0.333160\pi$
$702$	5.71118	+	1.85567i	0.215555	+	0.0700379i
$703$		−	21.9968i		−	0.829626i
$704$	16.7273	−	23.2538i	0.630435	−	0.876409i
$705$		0			0
$706$	−9.87362	+	30.3879i	−0.371599	+	1.14366i
$707$	−19.1119	−	26.3052i	−0.718775	−	0.989309i
$708$	−3.00424	+	4.13498i	−0.112906	+	0.155402i
$709$	5.53161	+	17.0245i	0.207744	+	0.639370i	0.999590	+	0.0286488i	$0.00912044\pi$
$709$	5.53161	+	17.0245i	0.207744	+	0.639370i	−0.791846	+	0.610721i	$0.790880\pi$
$710$		0			0
$711$	−6.47371	−	4.70342i	−0.242783	−	0.176392i
$712$	−4.64294	−	6.39046i	−0.174002	−	0.239493i
$713$	−0.591840	−	0.192300i	−0.0221646	−	0.00720171i
$714$	24.9097			0.932222
$715$		0			0
$716$	1.31386			0.0491012
$717$	16.0353	+	5.21019i	0.598850	+	0.194578i
$718$	0.327024	+	0.450110i	0.0122044	+	0.0167980i
$719$	26.3673	+	19.1570i	0.983334	+	0.714434i	0.958451	−	0.285256i	$-0.0920786\pi$
$719$	26.3673	+	19.1570i	0.983334	+	0.714434i	0.0248831	+	0.999690i	$0.492079\pi$
$720$		0			0
$721$	22.3459	+	68.7735i	0.832204	+	2.56126i
$722$	8.44284	−	11.6206i	0.314210	−	0.432473i
$723$	−7.03035	−	9.67644i	−0.261461	−	0.359871i
$724$	4.04130	−	12.4378i	0.150194	−	0.462248i
$725$		0			0
$726$	−3.83515	+	12.1948i	−0.142336	+	0.452591i
$727$		−	43.0199i		−	1.59552i	−0.602976	−	0.797759i	$-0.706018\pi$
$727$		−	43.0199i		−	1.59552i	0.602976	−	0.797759i	$-0.293982\pi$
$728$	−64.8654	−	21.0760i	−2.40407	−	0.781130i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−13.7539	−	42.3302i	−0.508708	−	1.56564i
$732$	−3.00049	+	0.974917i	−0.110901	+	0.0360340i
$733$	−23.9267	+	32.9323i	−0.883755	+	1.21638i	0.0916123	+	0.995795i	$0.470798\pi$
$733$	−23.9267	+	32.9323i	−0.883755	+	1.21638i	−0.975367	+	0.220589i	$0.929202\pi$
$734$	−23.9357	+	17.3903i	−0.883483	+	0.641888i
$735$		0			0
$736$	−0.771340			−0.0284320
$737$	12.2488	−	38.3136i	0.451189	−	1.41130i
$738$		−	6.81134i		−	0.250729i
$739$	−11.7810	+	36.2581i	−0.433370	+	1.33377i	0.461379	+	0.887203i	$0.347355\pi$
$739$	−11.7810	+	36.2581i	−0.433370	+	1.33377i	−0.894748	+	0.446571i	$0.852645\pi$
$740$		0			0
$741$	−23.4100	−	17.0084i	−0.859989	−	0.624819i
$742$	12.0192	−	3.90527i	0.441238	−	0.143367i
$743$	−17.1553	+	5.57409i	−0.629366	+	0.204493i	−0.606294	−	0.795240i	$-0.707345\pi$
$743$	−17.1553	+	5.57409i	−0.629366	+	0.204493i	−0.0230717	+	0.999734i	$0.507345\pi$
$744$	7.05183	+	5.12345i	0.258532	+	0.187835i
$745$		0			0
$746$	−0.991061	+	3.05017i	−0.0362853	+	0.111675i
$747$			12.5530i			0.459289i
$748$	−8.74240	−	6.28875i	−0.319654	−	0.229940i
$749$	33.2728			1.21576
$750$		0			0
$751$	14.1861	−	10.3068i	0.517657	−	0.376100i	−0.298064	−	0.954546i	$-0.596341\pi$
$751$	14.1861	−	10.3068i	0.517657	−	0.376100i	0.815720	+	0.578446i	$0.196341\pi$
$752$	0.318713	−	0.438670i	0.0116223	−	0.0159967i
$753$	15.2201	−	4.94533i	0.554653	−	0.180218i
$754$	−11.9105	−	36.6568i	−0.433756	−	1.33496i
$755$		0			0
$756$	−2.25225	+	1.63636i	−0.0819136	+	0.0595137i
$757$	−24.6903	−	8.02236i	−0.897383	−	0.291578i	−0.176227	−	0.984350i	$-0.556389\pi$
$757$	−24.6903	−	8.02236i	−0.897383	−	0.291578i	−0.721157	+	0.692772i	$0.756389\pi$
$758$			25.1646i			0.914019i
$759$	0.692300	−	0.228568i	0.0251289	−	0.00829651i
$760$		0			0
$761$	8.65430	−	26.6352i	0.313718	−	0.965525i	−0.662561	−	0.749008i	$-0.730530\pi$
$761$	8.65430	−	26.6352i	0.313718	−	0.965525i	0.976279	−	0.216517i	$-0.0694697\pi$
$762$	−1.04591	−	1.43958i	−0.0378894	−	0.0521503i
$763$	11.2298	−	15.4564i	0.406545	−	0.559561i
$764$	2.54164	+	7.82237i	0.0919534	+	0.283003i
$765$		0			0
$766$	−15.2589	−	11.0862i	−0.551326	−	0.400562i
$767$	23.9040	+	32.9011i	0.863124	+	1.18799i
$768$	13.0911	+	4.25355i	0.472384	+	0.153487i
$769$	−22.9537			−0.827732			−0.413866	−	0.910338i	$-0.635822\pi$
$769$	−22.9537			−0.827732			−0.413866	+	0.910338i	$0.635822\pi$
$770$		0			0
$771$	5.47446			0.197158
$772$	8.60489	+	2.79590i	0.309697	+	0.100627i
$773$	−13.8295	−	19.0347i	−0.497414	−	0.684631i	0.484320	−	0.874891i	$-0.339067\pi$
$773$	−13.8295	−	19.0347i	−0.497414	−	0.684631i	−0.981734	+	0.190259i	$0.939067\pi$
$774$	−8.36938	−	6.08071i	−0.300831	−	0.218567i
$775$		0			0
$776$	−1.91434	−	5.89172i	−0.0687207	−	0.211500i
$777$	−9.89761	+	13.6229i	−0.355075	+	0.488718i
$778$	−11.1287	−	15.3173i	−0.398983	−	0.549153i
$779$	−10.1424	+	31.2151i	−0.363389	+	1.11840i
$780$		0			0
$781$	0.156616	+	33.1060i	0.00560416	+	1.18463i
$782$		−	1.27731i		−	0.0456765i
$783$	−6.10429	−	1.98341i	−0.218150	−	0.0708811i
$784$	−20.9804	+	15.2431i	−0.749298	+	0.544397i
$785$		0			0
$786$	0.955657	+	2.94121i	0.0340872	+	0.104910i
$787$	24.0356	−	7.80964i	0.856777	−	0.278384i	0.152495	−	0.988304i	$-0.451269\pi$
$787$	24.0356	−	7.80964i	0.856777	−	0.278384i	0.704282	+	0.709921i	$0.251269\pi$
$788$	5.57536	−	7.67383i	0.198614	−	0.273369i
$789$	9.69534	−	7.04408i	0.345163	−	0.250776i
$790$		0			0
$791$	33.0621			1.17555
$792$	−10.2118	+	0.0483095i	−0.362861	+	0.00171660i
$793$			25.1028i			0.891427i
$794$	7.17071	−	22.0692i	0.254479	−	0.783205i
$795$		0			0
$796$	−6.23888	−	4.53281i	−0.221131	−	0.160661i
$797$	−8.23277	+	2.67499i	−0.291620	+	0.0947530i	−0.451173	−	0.892436i	$-0.648994\pi$
$797$	−8.23277	+	2.67499i	−0.291620	+	0.0947530i	0.159554	+	0.987189i	$0.448994\pi$
$798$	−26.5333	+	8.62119i	−0.939268	+	0.305187i
$799$	−0.962236	−	0.699105i	−0.0340414	−	0.0247326i
$800$		0			0
$801$	−0.792768	+	2.43989i	−0.0280111	+	0.0862092i
$802$		−	31.7579i		−	1.12141i
$803$	38.9395	−	28.5736i	1.37415	−	1.00834i
$804$	7.87607			0.277768
$805$		0			0
$806$	13.7534	−	9.99243i	0.484443	−	0.351968i
$807$	8.02120	−	11.0402i	0.282360	−	0.388635i
$808$	22.2108	−	7.21672i	0.781373	−	0.253883i
$809$	3.15582	+	9.71261i	0.110953	+	0.341477i	0.991081	−	0.133258i	$-0.0425438\pi$
$809$	3.15582	+	9.71261i	0.110953	+	0.341477i	−0.880129	+	0.474735i	$0.842544\pi$
$810$		0			0
$811$	38.5273	−	27.9917i	1.35288	−	0.982923i	0.354015	−	0.935240i	$-0.384816\pi$
$811$	38.5273	−	27.9917i	1.35288	−	0.982923i	0.998862	−	0.0476835i	$-0.0151839\pi$
$812$	16.9940	+	5.52167i	0.596371	+	0.193773i
$813$		−	11.8379i		−	0.415172i
$814$	−14.3769	+	4.74664i	−0.503910	+	0.166370i
$815$		0			0
$816$	−3.52192	+	10.8394i	−0.123292	+	0.379453i
$817$	29.3008	+	40.3291i	1.02510	+	1.41094i
$818$	−17.0350	+	23.4466i	−0.595613	+	0.819792i
$819$	6.84507	+	21.0670i	0.239186	+	0.736139i
$820$		0			0
$821$	38.4767	+	27.9550i	1.34285	+	0.975635i	0.999334	+	0.0364868i	$0.0116167\pi$
$821$	38.4767	+	27.9550i	1.34285	+	0.975635i	0.343512	+	0.939148i	$0.388383\pi$
$822$	−7.00543	−	9.64215i	−0.244343	−	0.336309i
$823$	23.5253	+	7.64384i	0.820041	+	0.266448i	0.688845	−	0.724909i	$-0.258118\pi$
$823$	23.5253	+	7.64384i	0.820041	+	0.266448i	0.131196	+	0.991356i	$0.458118\pi$
$824$	−51.9384			−1.80936
$825$		0			0
$826$	39.2096			1.36428
$827$	−1.48523	−	0.482580i	−0.0516465	−	0.0167810i	0.283080	−	0.959096i	$-0.408644\pi$
$827$	−1.48523	−	0.482580i	−0.0516465	−	0.0167810i	−0.334726	+	0.942315i	$0.608644\pi$
$828$	0.0839083	+	0.115490i	0.00291602	+	0.00401355i
$829$	34.1365	+	24.8016i	1.18561	+	0.861396i	0.992793	−	0.119839i	$-0.0382377\pi$
$829$	34.1365	+	24.8016i	1.18561	+	0.861396i	0.192817	+	0.981235i	$0.438238\pi$
$830$		0			0
$831$	3.17170	+	9.76148i	0.110025	+	0.338622i
$832$	26.2320	−	36.1052i	0.909430	−	1.25172i
$833$	33.4362	+	46.0210i	1.15850	+	1.59453i
$834$	1.90158	−	5.85247i	0.0658465	−	0.202655i
$835$		0			0
$836$	11.4887	+	3.67292i	0.397346	+	0.127031i
$837$		−	2.83095i		−	0.0978521i
$838$	−18.5968	−	6.04247i	−0.642416	−	0.208734i
$839$	−5.09236	+	3.69982i	−0.175808	+	0.127732i	−0.672209	−	0.740361i	$-0.734654\pi$
$839$	−5.09236	+	3.69982i	−0.175808	+	0.127732i	0.496401	+	0.868093i	$0.334654\pi$
$840$		0			0
$841$	3.76886	+	11.5994i	0.129961	+	0.399978i
$842$	−26.0850	+	8.47554i	−0.898949	+	0.292086i
$843$	1.72744	−	2.37761i	0.0594961	−	0.0818893i
$844$	11.7434	−	8.53205i	0.404223	−	0.293685i
$845$		0			0
$846$	−0.276449			−0.00950451
$847$	−44.7074	+	14.9954i	−1.53617	+	0.515249i
$848$			5.78225i			0.198563i
$849$	−6.74521	+	20.7596i	−0.231495	+	0.712468i
$850$		0			0
$851$	0.698548	+	0.507525i	0.0239459	+	0.0173977i
$852$	−6.16514	+	2.00318i	−0.211214	+	0.0686276i
$853$	−6.91532	+	2.24692i	−0.236776	+	0.0769332i	−0.425002	−	0.905193i	$-0.639726\pi$
$853$	−6.91532	+	2.24692i	−0.236776	+	0.0769332i	0.188225	+	0.982126i	$0.439726\pi$
$854$	19.5803	+	14.2259i	0.670025	+	0.486802i
$855$		0			0
$856$	−7.38491	+	22.7284i	−0.252411	+	0.776841i
$857$			39.8590i			1.36156i	0.732489	+	0.680779i	$0.238359\pi$
$857$			39.8590i			1.36156i	−0.732489	+	0.680779i	$0.761641\pi$
$858$	−6.06490	+	18.9707i	−0.207052	+	0.647650i
$859$	−13.5278			−0.461564			−0.230782	−	0.973006i	$-0.574128\pi$
$859$	−13.5278			−0.461564			−0.230782	+	0.973006i	$0.574128\pi$
$860$		0			0
$861$	20.3267	−	14.7682i	0.692732	−	0.503299i
$862$	−25.7223	+	35.4037i	−0.876104	+	1.20585i
$863$	47.8493	−	15.5472i	1.62881	−	0.529232i	0.654812	−	0.755792i	$-0.272748\pi$
$863$	47.8493	−	15.5472i	1.62881	−	0.529232i	0.973997	+	0.226560i	$0.0727479\pi$
$864$	−1.08433	−	3.33724i	−0.0368898	−	0.113535i
$865$		0			0
$866$	29.1228	−	21.1589i	0.989632	−	0.719010i
$867$	7.60845	+	2.47214i	0.258397	+	0.0839581i
$868$			7.88119i			0.267505i
$869$	15.4977	−	21.5444i	0.525725	−	0.730844i
$870$		0			0
$871$	19.3655	−	59.6009i	0.656175	−	2.01950i
$872$	8.06574	+	11.1015i	0.273140	+	0.375946i
$873$	−1.18262	+	1.62773i	−0.0400255	+	0.0550903i
$874$	0.442073	+	1.36056i	0.0149534	+	0.0460217i
$875$		0			0
$876$	7.65096	+	5.55875i	0.258502	+	0.187813i
$877$	0.709667	+	0.976773i	0.0239638	+	0.0329833i	0.820831	−	0.571171i	$-0.193511\pi$
$877$	0.709667	+	0.976773i	0.0239638	+	0.0329833i	−0.796867	+	0.604155i	$0.793511\pi$
$878$	31.1830	+	10.1320i	1.05237	+	0.341937i
$879$	24.7665			0.835354
$880$		0			0
$881$	1.91816			0.0646245			0.0323123	−	0.999478i	$-0.489713\pi$
$881$	1.91816			0.0646245			0.0323123	+	0.999478i	$0.489713\pi$
$882$	12.5746	+	4.08575i	0.423410	+	0.137574i
$883$	34.1439	+	46.9950i	1.14903	+	1.58151i	0.745446	+	0.666566i	$0.232237\pi$
$883$	34.1439	+	46.9950i	1.14903	+	1.58151i	0.403587	+	0.914941i	$0.367763\pi$
$884$	−13.5740	−	9.86208i	−0.456543	−	0.331698i
$885$		0			0
$886$	5.25828	+	16.1833i	0.176656	+	0.543690i
$887$	17.7762	−	24.4668i	0.596866	−	0.821516i	−0.398551	−	0.917146i	$-0.630487\pi$
$887$	17.7762	−	24.4668i	0.596866	−	0.821516i	0.995417	+	0.0956306i	$0.0304868\pi$
$888$	−7.10892	−	9.78459i	−0.238560	−	0.328349i
$889$	2.02832	−	6.24251i	0.0680275	−	0.209367i
$890$		0			0
$891$	1.96213	+	2.67395i	0.0657340	+	0.0895808i
$892$			12.4417i			0.416578i
$893$	1.26691	+	0.411644i	0.0423956	+	0.0137752i
$894$	3.56185	−	2.58784i	0.119126	−	0.0865503i
$895$		0			0
$896$	−3.99968	−	12.3098i	−0.133620	−	0.411240i
$897$	1.08026	−	0.350999i	0.0360689	−	0.0117195i
$898$	−8.19553	+	11.2802i	−0.273488	+	0.376425i
$899$	−14.7001	+	10.6802i	−0.490275	+	0.356206i
$900$		0			0
$901$	12.6835			0.422550
$902$	22.5904	−	0.106870i	0.752179	−	0.00355837i
$903$		−	38.1603i		−	1.26990i
$904$	−7.33815	+	22.5845i	−0.244063	+	0.751149i
$905$		0			0
$906$	5.56597	+	4.04391i	0.184917	+	0.134350i
$907$	30.4023	−	9.87830i	1.00949	−	0.328004i	0.242839	−	0.970066i	$-0.421921\pi$
$907$	30.4023	−	9.87830i	1.00949	−	0.328004i	0.766652	+	0.642063i	$0.221921\pi$
$908$	−9.49660	+	3.08563i	−0.315156	+	0.102400i
$909$	−6.13627	−	4.45826i	−0.203527	−	0.147871i
$910$		0			0
$911$	−16.0211	+	49.3079i	−0.530803	+	1.63364i	0.221745	+	0.975105i	$0.428825\pi$
$911$	−16.0211	+	49.3079i	−0.530803	+	1.63364i	−0.752547	+	0.658538i	$0.771175\pi$
$912$		−	12.7648i		−	0.422684i
$913$	−41.6330	+	0.196955i	−1.37785	+	0.00651826i
$914$	−11.6722			−0.386083
$915$		0			0
$916$	4.67660	−	3.39775i	0.154519	−	0.112265i
$917$	−6.70525	+	9.22898i	−0.221427	+	0.304768i
$918$	5.52634	−	1.79562i	0.182396	−	0.0592642i
$919$	10.5710	+	32.5341i	0.348704	+	1.07320i	0.959571	+	0.281468i	$0.0908212\pi$
$919$	10.5710	+	32.5341i	0.348704	+	1.07320i	−0.610866	+	0.791734i	$0.709179\pi$
$920$		0			0
$921$	3.99673	−	2.90379i	0.131697	−	0.0956832i
$922$	−14.8648	−	4.82988i	−0.489547	−	0.159064i
$923$			51.5790i			1.69774i
$924$	−5.46245	−	7.44411i	−0.179702	−	0.244893i
$925$		0			0
$926$	6.74561	−	20.7609i	0.221675	−	0.682244i
$927$	9.91508	+	13.6469i	0.325654	+	0.448224i
$928$	−13.2382	+	18.2208i	−0.434565	+	0.598127i
$929$	−5.66990	−	17.4502i	−0.186023	−	0.572521i	0.813941	−	0.580947i	$-0.197318\pi$
$929$	−5.66990	−	17.4502i	−0.186023	−	0.572521i	−0.999964	+	0.00842624i	$0.997318\pi$
$930$		0			0
$931$	−51.5433	−	37.4484i	−1.68926	−	1.22732i
$932$	8.71693	+	11.9978i	0.285533	+	0.393002i
$933$	13.1337	+	4.26740i	0.429978	+	0.139708i
$934$	−30.8561			−1.00964
$935$		0			0
$936$	−15.9100			−0.520033
$937$	3.21852	+	1.04576i	0.105144	+	0.0341635i	0.361117	−	0.932521i	$-0.382396\pi$
$937$	3.21852	+	1.04576i	0.105144	+	0.0341635i	−0.255972	+	0.966684i	$0.582396\pi$
$938$	−35.5145	−	48.8815i	−1.15959	−	1.59604i
$939$	−3.29217	−	2.39190i	−0.107436	−	0.0780567i
$940$		0			0
$941$	−10.8465	−	33.3822i	−0.353587	−	1.08823i	−0.956824	−	0.290668i	$-0.906123\pi$
$941$	−10.8465	−	33.3822i	−0.353587	−	1.08823i	0.603237	−	0.797562i	$-0.293877\pi$
$942$	−5.07476	+	6.98480i	−0.165344	+	0.227577i
$943$	−0.757278	−	1.04230i	−0.0246604	−	0.0339421i
$944$	−5.54375	+	17.0619i	−0.180434	+	0.555318i
$945$		0			0
$946$	20.0359	−	27.8532i	0.651423	−	0.905585i
$947$		−	39.0512i		−	1.26899i	−0.772925	−	0.634497i	$-0.781207\pi$
$947$		−	39.0512i		−	1.26899i	0.772925	−	0.634497i	$-0.218793\pi$
$948$	4.94223	+	1.60583i	0.160516	+	0.0521549i
$949$	60.8769	−	44.2297i	1.97615	−	1.43576i
$950$		0			0
$951$	7.97880	+	24.5562i	0.258730	+	0.796290i
$952$	−62.7660	+	20.3939i	−2.03426	+	0.660971i
$953$	−14.5055	+	19.9652i	−0.469881	+	0.646735i	−0.976521	−	0.215422i	$-0.930887\pi$
$953$	−14.5055	+	19.9652i	−0.469881	+	0.646735i	0.506640	+	0.862158i	$0.330887\pi$
$954$	2.38500	−	1.73281i	0.0772173	−	0.0561017i
$955$		0			0
$956$	−10.9495			−0.354131
$957$	6.48236	−	20.2765i	0.209545	−	0.655448i
$958$		−	12.5315i		−	0.404873i
$959$	13.5855	−	41.8118i	0.438698	−	1.35017i
$960$		0			0
$961$	18.5958	+	13.5107i	0.599865	+	0.435827i
$962$	−22.4336	+	7.28913i	−0.723290	+	0.235011i
$963$	7.38173	−	2.39847i	0.237873	−	0.0772896i
$964$	6.28401	+	4.56560i	0.202394	+	0.147048i
$965$		0			0
$966$	0.338412	−	1.04153i	0.0108882	−	0.0335105i
$967$			1.20724i			0.0388222i	0.999812	+	0.0194111i	$0.00617914\pi$
$967$			1.20724i			0.0388222i	−0.999812	+	0.0194111i	$0.993821\pi$
$968$	−0.320445	−	33.8676i	−0.0102995	−	1.08855i
$969$	−27.9999			−0.899486
$970$		0			0
$971$	−40.7599	+	29.6138i	−1.30805	+	0.950353i	−0.999999	−	0.00101751i	$-0.999676\pi$
$971$	−40.7599	+	29.6138i	−1.30805	+	0.950353i	−0.308049	+	0.951370i	$0.599676\pi$
$972$	−0.381716	+	0.525387i	−0.0122435	+	0.0168518i
$973$	21.5882	−	7.01442i	0.692085	−	0.224872i
$974$	−2.44597	−	7.52793i	−0.0783740	−	0.241210i
$975$		0			0
$976$	−8.95877	+	6.50893i	−0.286763	+	0.208346i
$977$	−5.59535	−	1.81804i	−0.179011	−	0.0581642i	0.218140	−	0.975917i	$-0.430001\pi$
$977$	−5.59535	−	1.81804i	−0.179011	−	0.0581642i	−0.397151	+	0.917753i	$0.630001\pi$
$978$		−	6.18362i		−	0.197730i
$979$	−8.10454	−	2.59100i	−0.259022	−	0.0828088i
$980$		0			0
$981$	1.37720	−	4.23858i	0.0439706	−	0.135328i
$982$	−17.8256	−	24.5348i	−0.568837	−	0.782937i
$983$	−21.4482	+	29.5210i	−0.684093	+	0.941573i	−0.999974	−	0.00722580i	$-0.997700\pi$
$983$	−21.4482	+	29.5210i	−0.684093	+	0.941573i	0.315881	+	0.948799i	$0.397700\pi$
$984$	5.57654	+	17.1628i	0.177774	+	0.547131i
$985$		0			0
$986$	−30.1730	−	21.9219i	−0.960903	−	0.698137i
$987$	−0.599391	−	0.824990i	−0.0190788	−	0.0262597i
$988$	17.8720	+	5.80695i	0.568583	+	0.184744i
$989$	−1.95677			−0.0622216
$990$		0			0
$991$	−36.8404			−1.17027			−0.585137	−	0.810934i	$-0.698959\pi$
$991$	−36.8404			−1.17027			−0.585137	+	0.810934i	$0.698959\pi$
$992$	−9.44757	−	3.06970i	−0.299961	−	0.0974631i
$993$	−1.96913	−	2.71027i	−0.0624883	−	0.0860078i
$994$	40.2320	+	29.2302i	1.27608	+	0.927127i
$995$		0			0
$996$	−2.51913	−	7.75307i	−0.0798216	−	0.245666i
$997$	20.4957	−	28.2099i	0.649105	−	0.893417i	−0.349955	−	0.936767i	$-0.613803\pi$
$997$	20.4957	−	28.2099i	0.649105	−	0.893417i	0.999060	+	0.0433498i	$0.0138030\pi$
$998$	13.2406	+	18.2242i	0.419125	+	0.576877i
$999$	−1.21383	+	3.73577i	−0.0384037	+	0.118195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.h.724.3		16
5.2	odd	4		825.2.n.k.526.2		8
5.3	odd	4		165.2.m.a.31.1	yes	8
5.4	even	2	inner	825.2.bx.h.724.2		16
11.5	even	5	inner	825.2.bx.h.49.2		16
15.8	even	4		495.2.n.d.361.2		8
55.7	even	20		9075.2.a.dj.1.2		4
55.18	even	20		1815.2.a.o.1.3		4
55.27	odd	20		825.2.n.k.676.2		8
55.37	odd	20		9075.2.a.cl.1.3		4
55.38	odd	20		165.2.m.a.16.1	✓	8
55.48	odd	20		1815.2.a.x.1.2		4
55.49	even	10	inner	825.2.bx.h.49.3		16
165.38	even	20		495.2.n.d.181.2		8
165.128	odd	20		5445.2.a.bv.1.2		4
165.158	even	20		5445.2.a.be.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.1	✓	8	55.38	odd	20
165.2.m.a.31.1	yes	8	5.3	odd	4
495.2.n.d.181.2		8	165.38	even	20
495.2.n.d.361.2		8	15.8	even	4
825.2.n.k.526.2		8	5.2	odd	4
825.2.n.k.676.2		8	55.27	odd	20
825.2.bx.h.49.2		16	11.5	even	5	inner
825.2.bx.h.49.3		16	55.49	even	10	inner
825.2.bx.h.724.2		16	5.4	even	2	inner
825.2.bx.h.724.3		16	1.1	even	1	trivial
1815.2.a.o.1.3		4	55.18	even	20
1815.2.a.x.1.2		4	55.48	odd	20
5445.2.a.be.1.3		4	165.158	even	20
5445.2.a.bv.1.2		4	165.128	odd	20
9075.2.a.cl.1.3		4	55.37	odd	20
9075.2.a.dj.1.2		4	55.7	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10527 + 0.359123i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.525387 - 0.381716i) q^{4} +(0.359123 + 1.10527i) q^{6} +(-2.51974 + 3.46813i) q^{7} +(-1.80980 - 2.49097i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(1.10527 + 0.359123i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.525387 - 0.381716i) q^{4} +(0.359123 + 1.10527i) q^{6} +(-2.51974 + 3.46813i) q^{7} +(-1.80980 - 2.49097i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.15911 - 1.00996i) q^{11} -0.649414i q^{12} +(-4.91433 - 1.59676i) q^{13} +(-4.03048 + 2.92831i) q^{14} +(-0.704384 - 2.16787i) q^{16} +(-4.75528 + 1.54508i) q^{17} +(-0.683093 + 0.940197i) q^{18} +(4.53048 - 3.29158i) q^{19} -4.28684 q^{21} +(-3.12896 - 2.25079i) q^{22} +0.219819i q^{23} +(0.951466 - 2.92831i) q^{24} +(-4.85822 - 3.52970i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(2.64768 - 0.860283i) q^{28} +(5.19262 + 3.77266i) q^{29} +(-0.874813 + 2.69240i) q^{31} +3.50898i q^{32} +(-1.03980 - 3.14941i) q^{33} -5.81074 q^{34} +(0.525387 - 0.381716i) q^{36} +(2.30883 - 3.17784i) q^{37} +(6.18947 - 2.01108i) q^{38} +(-1.59676 - 4.91433i) q^{39} +(-4.74165 + 3.44501i) q^{41} +(-4.73811 - 1.53950i) q^{42} +8.90173i q^{43} +(1.27424 + 1.73650i) q^{44} +(-0.0789420 + 0.242959i) q^{46} +(0.139821 + 0.192447i) q^{47} +(1.33982 - 1.84410i) q^{48} +(-3.51569 - 10.8202i) q^{49} +(-4.04508 - 2.93893i) q^{51} +(1.97242 + 2.71480i) q^{52} +(-2.41255 - 0.783885i) q^{53} -1.16215 q^{54} +13.1992 q^{56} +(5.32589 + 1.73049i) q^{57} +(4.38439 + 6.03459i) q^{58} +(-6.36725 - 4.62608i) q^{59} +(-1.50123 - 4.62030i) q^{61} +(-1.93381 + 2.66165i) q^{62} +(-2.51974 - 3.46813i) q^{63} +(-2.66892 + 8.21410i) q^{64} +(-0.0182340 - 3.85436i) q^{66} +12.1280i q^{67} +(3.08815 + 1.00340i) q^{68} +(-0.177837 + 0.129206i) q^{69} +(-3.08459 - 9.49339i) q^{71} +(2.92831 - 0.951466i) q^{72} +(-8.55964 + 11.7813i) q^{73} +(3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(11.4628 - 8.41136i) q^{77} -6.00509i q^{78} +(-2.47274 + 7.61030i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-6.47797 + 2.10482i) q^{82} +(11.9386 - 3.87908i) q^{83} +(2.25225 + 1.63636i) q^{84} +(-3.19682 + 9.83880i) q^{86} +6.41843i q^{87} +(3.20157 + 9.69707i) q^{88} +2.56545 q^{89} +(17.9206 - 13.0201i) q^{91} +(0.0839083 - 0.115490i) q^{92} +(-2.69240 + 0.874813i) q^{93} +(0.0854274 + 0.262919i) q^{94} +(-2.83882 + 2.06253i) q^{96} +(1.91351 + 0.621738i) q^{97} -13.2218i q^{98} +(1.93675 - 2.69240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

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